Answer: Let the Number of hours Enzo sleeps on average per day while School is in session be Y
Y = SS/115% = SS/1.15
Step-by-step explanation:
Given in the question:
- While on vacation, Enzo sleeps 115% as much as he sleeps when school is in session.
- Enzo sleeps SS hours per day during vacation
Mathematically, SS = 115% of Y
SS = 115% × Y
115% × Y = SS
Y = SS/115%
But 115% = 115/100 = 1.15
Therefore,
Y = SS/1.15
Solved!
Significance tests A test of H0: p = 0.65 against Ha: p < 0.65 has test statistic z = −1.78. (a) What conclusion would you draw at the 5% significance level? At the 1% level? (b) If the alternative hypothesis were Ha: p ≠ 0.65, what conclusion would you draw at the 5% significance level? At the 1% level?
Answer:
(a) At 5% significance level, reject H0
At 1% significance level, reject H0
(b) At 5% significance level, fail to reject H0
At 1% significance level, fail to reject H0
Step-by-step explanation:
(a) The test is a one tailed test
At 5% significance level, the critical value is 1.645
Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 1.645
At 1% significance level, the critical value is 2.326
Conclusion: Reject H0 because the test statistic -1.78 is less than the critical value 2.326
(b) The test is a two tailed test
At 5% significance level, the critical value is 1.96. The region of no rejection of H0 lies between -1.96 and 1.96
Conclusion: Fail to reject H0 because the test statistic -1.78 falls within -1.96 and 1.96
At 1% significance level, the critical value is 2.576. The region of no rejection of H0 lies between -2.576 and 2.576
Conclusion: Fail to reject H0 because the test statistic falls within -2.576 and 2.576
The conclusion that can be made from an hypothesis test depends on
the significance level and p-value.
Response:
(a) The conclusion at 5% is there is statistical evidence to suggest that p < 0.65
At 1% level; fail to reject H₀: p = 0.65, there is statistical evidence to suggest that p = 0.65
(b) With Hₐ ≠ 0.65, the conclusion at the 5% significance level is that there is sufficient statistical evidence that p = 0.65
At the 1% level, fail to reject H₀: p = 0.65,
Which is the method to draw conclusion from an hypothesis test?The null hypothesis, H₀: p = 0.65
The alternative hypothesis, Hₐ: p < 0.65
The z-score is z = -1.78, which gives;
The p-value = 0.0375
(a) The significance level is 5%
Which gives, α = 0.05
Given that the p-value is less than the significant level, we have that
there is sufficient evidence against the null hypothesis, given that the
probability that the null hypothesis is correct is less than the significant
level of 5%.
Therefore, reject H₀, p = 0.65
There is sufficient statistical evidence to suggest that the the p is less than 0.65, (p < 0.65)However, at 1% significant level, α = 0.01, and the p-value, p = 0.0375 is
larger than the significance level.
Therefore, we fail to reject the null hypothesis and there is sufficient statistical evidence to suggest that p = 0.65(b) Hₐ: p ≠ 0.65
We have;
[tex]\alpha = \dfrac{5 \%}{2} = 2.5 \% = \mathbf{0.025}[/tex]
Which gives;
The p-value (0.0375) is larger than the significant level, therefore, we
fail to reject the null hypothesis.
There is sufficient statistical evidence to suggest that p = 0.65At the 1% level of significance, we have;
[tex]\alpha = \dfrac{1 \%}{2} = 0.5 \% = 0.005[/tex]
Which gives;
The p-value at z = -1.78 (p = 0.0375) is larger than the significant level
Therefore;
There is sufficient evidence to suggest that p = 0.65Learn more about hypothesis testing here:
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Jacob bought 13 packs of gum to add to the 5 pieces he already had. He then shared all of his pieces of gum with six friends. If Jacob and his six friends each revived 27 pieces of gum, how many were in each pack
Answer:
14 gums.
Step-by-step explanation:
Given: Jacob bought 13 pack of gum
He already had 5 piece of gum.
He shared gum with six of his friends.
Each one of them received 27 pieces of gum.
Lets assume the number of gums in each pack be "x".
Total number of gum= [tex]number\ of\ gum\ in\ each\ pack\times number\ of\ pack + 5[/tex]
Also gum has been shared among jacob and his 6 friends, which is 7 person.
∴ Share of each person= [tex]\frac{Total\ number\ of\ gums}{number\ of\ person}[/tex]
Now, forming equation to find number of gums in each pack.
⇒ [tex]\frac{13\times x+5}{7} = 27[/tex]
Multiplying both side by 7
⇒ [tex]13x+5= 189[/tex]
Subtracting both side by 5
⇒ [tex]13x= 189-5[/tex]
⇒[tex]13x= 184[/tex]
Dividing both side by 13
⇒ [tex]x= \frac{184}{13}[/tex]
∴[tex]x= 14.15 \approx 14\ gum[/tex]
Hence, each pack have 14 gums.
Assume that the weight of two year old babies have distribution that is approximately normal with a mean of 29 pounds and a standard deviation of 3 pounds. what weight of two year old baby corresponds to 10th percentile?
Answer:
25.15 ponds is the weight of two year old baby corresponds to 10th percentile.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 29 pounds
Standard Deviation, σ = 3 pounds
We are given that the distribution of weight of two year old babies is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.10
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 29}{3})=0.10[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z < -1.282) = 0.10[/tex]
[tex]\displaystyle\dfrac{x - 29}{3} = -1.282\\x = 25.154 \approx 25.15[/tex]
Thus, 25.15 ponds is the weight of two year old baby corresponds to 10th percentile.
Statistics can be referred to as numerical facts. In a broader sense, statistics is the field of study dealing with the collection, analysis, presentation and interpretation of data. a. True b. False
Answer:
True
Step-by-step explanation:
Statistics is indeed a procedure consists of collection, presentation, analysis and presentation of the data. Statistics is widely used in every field of life. For example we want to assess the performance of students. For this purpose we choose a sample of students and ask about their grading. This is the procedure of collection of data. Then this data can be presented in tabular form or graphical form and this stage is known as presentation of the data. Then we evaluate their average and this procedure is known as analysis of data. Then according to average we make statement about performance of students and this stage is interpretation of the data.
PLEASE HELP PLEASE PLEASE DUE TONIGHT AAA
Answer:
Measurement of all angle= [tex]76.79\º+102.66\º+15.35\º+265.16\º= 360\º[/tex]
Step-by-step explanation:
Given angles are [tex]x\º, (\frac{5x}{9} +60)\º, (\frac{x}{5} )\º, (4x-142)\º[/tex]
The given is a quardilateral.
We know the sum of all angles of quardilaterals is 360º
∴ [tex]x\º+ (\frac{5x}{9} +60)\º+ (\frac{x}{5} )\º+(4x-142)\º= 360\º[/tex]
Now, solving the equation to find value of x.
⇒ [tex]x\º+ (\frac{5x}{9} +60)\º+ (\frac{x}{5} )\º+(4x-142)\º= 360\º[/tex]
Opening parenthesis.
⇒ [tex]x\º+ \frac{5x}{9} +60\º+ \frac{x}{5} \º+4x-142\º= 360\º[/tex]
⇒ [tex]5x\º+ \frac{5x}{9} + \frac{x}{5} \º-82\º= 360\º[/tex]
Adding both side by 82
⇒ [tex]5x+ \frac{5x}{9} + \frac{x}{5} = 442[/tex]
Taking LCD 45
⇒ [tex]\frac{45\times 5x+ 5\times 5x+9x}{45} = 442[/tex]
Multiplying both side by 45
⇒ [tex]225x+25x+9x= 19890[/tex]
⇒[tex]259x= 19890[/tex]
Dividing both side by 259
⇒[tex]x= \frac{19890}{259}[/tex]
∴[tex]x= 76.79\º[/tex]
Next subtituting the value of x to find measurement of other interior angle.
[tex]x\º, (\frac{5x}{9} +60)\º, (\frac{x}{5} )\º, (4x-142)\º[/tex]
2. [tex](\frac{5x}{9} +60)\º[/tex]
= [tex]\frac{5\times 76.79}{9} +60= 42.66+ 60[/tex]
= [tex]102.66\º[/tex]
3. [tex](\frac{x}{5} )\º[/tex]
= [tex](\frac{76.79}{5} )\º= 15.35\º[/tex]
4. [tex](4x-142)\º[/tex]
= [tex]4\times 76.79- 42= 307.16-42[/tex]
= [tex]265.16\º[/tex]
The rate of transmission in a telegraph cable is observed to be proportional to x2ln(1/x) where x is the ratio of the radius of the core to the thickness of the insulation (0
Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
[tex]f'(x) = k*((x^2)'*ln(1/x) + x^2*(ln(1/x)')) = k*(2x\,ln(1/x)+x^2*(\frac{1}{1/x}*(-\frac{1}{x^2})))\\= k * (2x \, ln(1/x)-x)[/tex]
We need to equalize f' to 0
k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp1/x = e^(1/2)x = 1/e^(1/2) = 1/√e ≅ 0.607Thus, the value of x that gives the maximum transmission is 1/√e.
The rate of transmission in a telegraph cable is given by the equation: rate of transmission = x^2 ln(1/x), where x is the ratio of the radius of the core to the thickness of the insulation.
Explanation:The rate of transmission in a telegraph cable is given by the equation: rate of transmission = x2 ln(1/x), where x is the ratio of the radius of the core to the thickness of the insulation.
This equation shows that the rate of transmission is directly proportional to the square of x and logarithmically inversely proportional to x.
For example, if x is 0.5, the rate of transmission is (0.5)2 ln(1/0.5) = 0.25 ln(2).
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please help with a, b, and c. thank you!:)
Answer:
The answer to your question is below
Step-by-step explanation:
a) The intervals in which the graph is decreasing are the right section of the first parabola, the left section of the second parabola and also the right section of the third parabola.
(9, 11) U (14.5, 17) U (21, 27)
b) There are only two intervals in which the graph is increasing
(1, 9) U (17, 21)
c) During the time the graph is increasing, Andre is getting away from his origin.
Which two-dimensional cross sections are squares?
Select all that apply.
a cross-section that is perpendicular to the base of a cube
a cross-section that is parallel to the base of a triangular pyramid
a cross-section that is parallel to the base of a cylinder
a cross section through the center of a sphere
a cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same
Answer:
A cross-section that is perpendicular to the base of a cube.
A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.
Step-by-step explanation:
We have to select from options that the two-dimensional cross section are squares.
The correct options are :
A cross-section that is perpendicular to the base of a cube.
A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.
In both the cases the length and the width of the section are equal. (Answer)
Among the given options, only the cross-section that is perpendicular to the base of a cube is guaranteed to be a square. The other options will generally result in different shapes, such as triangles or circles.
Explanation:The question asks which two-dimensional cross sections are squares. To find the answer, we must consider the shape of the object and the orientation of the cross section.
A cross-section that is perpendicular to the base of a cube. If we cut a cube with a plane perpendicular to one of its faces, the cross section is the same shape as the face, which is a square.A cross-section that is parallel to the base of a triangular pyramid would not be a square because the base itself is a triangle.A cross-section that is parallel to the base of a cylinder would be a circle, as it would be cut along the cylinder's circular base.A cross section through the center of a sphere would also result in a circle, assuming the cut goes through the sphere's diameter.A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same, also known as a right circular cylinder, would only result in a square if the cylinder is cut along a plane that is at 45 degrees to the base, which is not the typical perpendicular cut, so typically it would not be a square.At first glance, only the cross-section perpendicular to the base of a cube is a square. However, depending on specific conditions not typically met by the listed shapes, other cross-sections can appear square-shaped. Therefore, generally, the answer is a cross-section that is perpendicular to the base of a cube will be square.
Does the graph represent a function? Why or Why Not
Answer:
not a function - it does not pass the vertical line test.
Step-by-step explanation:
In 1995, Orlando, Florida was about 175,000. At that same time , the population was growing at a rate of about 2000 per years, write an equation in slope - intercept form to find orlando's population for any year
Answer:
Y=2000x+175,000
Step-by-step explanation:
y=mx+b so your M will be your 2000 and your x is gonna be years, and your b is gonna be 175,000
Help asap, thank you! :) 2 questions, multiplying monomials.
Answer:
Correct answer choices are [tex]27x^{2}[/tex] and [tex]657 cm^{2}[/tex]
Step-by-step explanation:
We are able to arrive at these answers through basic equation used to calculate area of an triangle and monomial laws
Write some code that uses a loop to read such a sequence of non-negative integers, terminated by a negative number. When the code exits the loop it should print the number of consecutive duplicates encountered. In the above case, that value would be 3.
To solve the programming task, you would create a loop to read integers, use a counter to track consecutive duplicates and print the count after a negative number is entered to end the input.
The student's question involves writing a piece of code that reads a sequence of non-negative integers, ends the input with a negative integer, and reports the number of consecutive duplicate values entered before the negative integer is encountered. This is a programming task that typically involves a loop and a counter.
To address this question, you would write a loop that continues to accept input until a negative number is entered. Inside the loop, you would use a counter to keep track of the number of consecutive duplicates. Here is a pseudocode example:
Initialize the previous Value to None (or some value that won't occur in the sequence).
Initialize the count Of Duplicates to 0.
Start a loop that reads integers until a negative number is encountered.
Inside the loop, compare the current number to the previous Value.
If they are the same, increment the count Of Duplicates by 1.
Set the previous Value to the current number before the next iteration.
Outside the loop, print count Of Duplicates.
The counter pattern is a fundamental concept in programming that is used to tally occurrences within iteration structures like loops.
Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment, and they have an average credit score. How much is the principal balance after applying their first month’s payment of $925.67?
Answer:
$88812.33
Step-by-step explanation:
Principal = $89,000
But there's a sales tax of 4.2%
Tax = (4.2 / 100) * 89000 = $3738
Total cost of the mobile house = $89000 + $3738 = $92,738
However, they made a down payment of $3000
Balance after down payment = $92,738 - $3000 = $89,738
They've also paid the first monthly payment of $925.67
Balance after first monthly payment =
$89,738 - $925.67 = $88,812.33
The principal balance after applying there first monthly payment is $88,812.33
The principal balance, after applying the first month's payment of $925.67 to an initial loan of $89,738 for a mobile home, is $88,812.33.
Explanation:To calculate the principal balance after the first month’s payment, start by adding the initial price of the mobile home and the sales tax. The sales tax is 4.2% (or 0.042) of $89,000, which comes out to $3,738. Then, subtract the down payment from the sum to get the initial loan amount. So, $89,000 + $3,738 - $3,000 equals $89,738. After applying the first month’s payment of $925.67, subtract that amount from the initial loan, leaving a principal balance of $88,812.33.
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The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?A. 21/55
B. 28/55
C. 34/55
D. 5/8
E. 139/220
Answer: B. [tex]\dfrac{28}{55}[/tex] .
Step-by-step explanation:
Given : Number of blue disks =4
Number of green disks = 8
Total disks = 12
Total number of combinations of drawing any 3 disks from 12 = [tex]^{12}C_3[/tex]
Number of combinations of drawing 1 blue and 2 green disks = [tex]^{4}C_1\times^{8}C_2[/tex]
Now , the probability that 1 of the disks selected is blue, and 2 of the disks selected are green will be :
[tex]\dfrac{^{4}C_1\times^{8}C_2}{^{12}C_3}\\\\=\dfrac{4\times\dfrac{8!}{2!6!}}{\dfrac{12!}{3!9!}}\\\\=\dfrac{4\times28}{220}\\\\=\dfrac{28}{55}[/tex]
Hence, the correct answer is B. [tex]\dfrac{28}{55}[/tex] .
A furniture salesperson earns 4.5% commission on every piece of furniture sold. The salesperson sells a sofa for $1000 and a chair for $200. What commission does the salesperson earn?
Answer: the salesperson earns $54 as commission.
Step-by-step explanation:
A furniture salesperson earns 4.5% commission on every piece of furniture sold. The salesperson sells a sofa for $1000. This means that the commission that he earned from the sale of the sofa is
4.5/100 × 1000 = 0.045 × 1000 = $45
The salesperson also sold a chair for $200. This means that the commission that he earned from the sale of the chair is
4.5/100 × 200 = 0.045 × 200 = $9
The total commission that the salesperson earns is
45 + 9 = $54
Home Away, a nongovernmental not-for-profit organization, provides food and shelter to victims of natural disasters. Home Away received a $15,000 gift with the stipulation that the funds be used to buy beds. In which net asset class should Home Away report the contribution?
Answer:
Home away should record the contribution to a Net assets with donor restriction
Step-by-step explanation
A Net asset with donor restriction is the part of net assets of a not- for - profit making organisation that is subject to donor-imposed restrictions.
The stipulation that the fund of $15,000 should be used to buy beds automatically makes it to be classified as a Net assets with donor restriction item.
Two different suppliers, A and B, provide a manufacturer with the same part. All supplies of this part are kept in a large bin. in the past, 5% of the parts supplied by A and 9% of the parts supplied by B have been defective. A supplies four times as many parts as B. Suppose you reach into the bin and select a part, and find it is nondetective. What is the probability that it was supplied by A
Answer:
The probability of selecting a non-defective part provided by supplier A is 0.807.
Step-by-step explanation:
Let A = a part is supplied by supplier A, B = a part is supplied by supplier B and D = a part is defective.
Given:
P (D|A) = 0.05, P(D|B) = 0.09
A supplies four times as many parts as B, i.e. n (A) = 4 and n (B) = 1.
Then the probability of event A and B is:
[tex]P(A)=\frac{n(A)}{n(A)+N(B)}= \frac{4}{4+1}=0.80\\P(B)\frac{n(B)}{n(A)+N(B)}= \frac{1}{4+1}=0.20[/tex]
Compute the probability of selecting a defective product:
[tex]P(D)=P(D|A)P(A)+P(D|B)P(B)\\=(0.05\times0.80)+(0.09\times0.20)\\=0.058[/tex]
The probability of selecting a non-defective part provided by supplier A is:
[tex]P(A|D')=\frac{P(D'|A)P(A)}{P(D')} = \frac{(1-P(D|A))P(A)}{1-P(D)}\\=\frac{(1-0.05)\times0.80}{(1-0.058)}\\ =0.80679\\\approx0.807[/tex]
Thus, the probability of selecting a non-defective part provided by supplier A is 0.807.
The required probability of selecting a non-defective part provided by supplier A is 0.807.
Let,
A part is supplied by supplier A,
B part is supplied by supplier B,
And D = a part is defective.
Given:
P ([tex]\frac{D}{A}[/tex]) =5% = 0.05,
P([tex]\frac{D}{B}[/tex]) = 9% = 0.09
A supplies four times as many parts as B, .
Then, n (A) = 4 and n (B) = 1.
The probability of event A and B is:
Probability of event P(A) = [tex]\frac{n (A)}{n (A) + n(B)}[/tex] = [tex]\frac{4}{4+1}[/tex]
P(A) = [tex]\frac{4}{5}[/tex]
And Probability of Event P(B) = [tex]\frac{n (B )}{n (A) + n(B)} = \frac{1}{4+1}[/tex]
P(B) = [tex]\frac{1}{5}[/tex]
Then , the probability of selecting a defective product:
P(D) = [tex]P(\frac{D}{A}) P(A) + P(\frac{D}{B}) P(B)[/tex]
P(D) = 0.50×0.80 + 0.09×0.20
P(D) = 0.058
The probability of selecting a non-defective part provided by supplier A is
[tex]P(\frac{A}{D'} )= \frac{P(D'(A)) . P(A)}{P(D')} \\\\[/tex]
= [tex]\frac{1- P(D(A)). P(A)}{1-P(A)} \\\\\frac{(1-0.05) . 0.80}{1- 0.05} \\\\[/tex]
= 0.807
Hence, the probability of selecting a non-defective part provided by supplier A is 0.807.
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Julia earns $6 an hour babysitting and earns $5 an hour walking dogs. She earned $43 after working a total of 8 hours at her two jobs. Complete the system of equations below to represent the situation. Let b= the number of hours that Julia babysits and d= the number of hours she walks dogs. _+_=8 _+_=43
Answer: the equations are
b + d = 8
6x + 5y = 43
Step-by-step explanation:
Let b represent the number of hours that Julia babysits.
Let d represent the number of hours she walks dogs.
Julia worked for a total of 8 hours babysitting and walking the dogs.. This means that
b + d = 8
Julia earns $6 an hour babysitting and earns $5 an hour walking dogs. She earned a total of $43 after working a total of 8 hours at her two jobs. This means that
6x + 5y = 43
A Ferris wheel is 50 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. How many minutes of the ride are spent higher than 40 meters above the ground?
To calculate the time spent above 40 meters on a Ferris wheel, we analyze the wheel's structure and use trigonometry to find the proportional time of the ride corresponding to the arc above the 40-meter mark.
Explanation:Calculating Time Spent Above 40 meters on a Ferris Wheel
To determine how many minutes of the ride on the Ferris wheel are spent higher than 40 meters above the ground, we need first to understand the wheel's structure and motion. Given that the Ferris wheel has a diameter of 50 meters and is boarded from a platform 4 meters above the ground, we can calculate the highest and lowest points riders will reach during the ride. The highest point of the wheel will be 50 meters (the radius) plus 4 meters (the platform height), totaling 54 meters. The lowest point will be 4 meters (platform height) above the ground since the diameter is equal to twice the radius and the wheel's lowest point touches the platform level.
Because riders want to be above 40 meters, we're interested in the segment of the ride where they are between 40 meters and the maximum of 54 meters above the ground. This range covers a portion of the wheel's circumference. If the wheel's highest point is at 12 o'clock and the loading platform is at 6 o'clock, then the 40-meter height will be somewhere between 6 o'clock and 12 o'clock.
Using the fact that the Ferris wheel completes one revolution in 4 minutes, we can find the time spent over 40 meters by calculating the angle θ that corresponds to the arc between 40 meters and 54 meters above the ground. The 40-meter height will fall at the point where the vertical distance from the top of the wheel equals the wheel's radius minus 40 meters. Using this, we can use trigonometry to find θ, and then convert this angle to a proportion of the full revolution time to determine the time spent on this segment of the ride.
I have some geometric sequence questions, will give 5 points for every answer and will give Brainliest!
1. List the first four terms of a geometric sequence with t5 = 24 and t6 = 3
2. List the first four terms of a geometric sequence with t1 = 4 and tn = -3tn-1
3. Find the three geometric means between 1/2 and 8
Thank you so much!!
Answer:
Step-by-step explanation:
1) since the sixth term is 3 and the fifth term 24, the common ratio would be 3/24 = 1/8
The formula for finding the nth term of a geometric sequence is
Tn = ar^(n - 1)
If t6 = 3,r = 1/8, then
3 = a × 1/8^(6 - 1) = a × (1/8)^5
a = 3/(0.125)^5 = 98304
The first term is 98304.
Second term is 98304 × 1/8 = 12288
Third term is 12288 × 1/8 = 1536
Third term is 1536 × 1/8 = 192
2) t1 = 4
t2 = - 3t(2- 1) = - 3t1 = - 3 × 4 = - 12
t3 = - 3t(3- 1) = - 3t2 = - 3 × - 12 = 36
t4 = - 3t(4- 1) = - 3t3 = - 3 × 36 = - 108
3) let the numbers be t2,t3 and t4
The sequence becomes
1/2, t2,t3, t4,8
The formula for finding the nth term of a geometric sequence is
Tn = ar^(n - 1)
8 = 1/2 × r^(5 - 1)
8 = 1/2 × r^4
16 = r^4
2^4 = r^4
r = 2
t2 = 1/2 × 2 = 1
t3 = 1 × 2 = 2
t4 = 2 × 2 = 4
If circumstances are less than desirable or if something seems suspicious or amiss, approach the vehicle form the right-hand or passenger side, especially when:________
Answer:
Only one person is in the stopped vehicle
Step-by-step explanation:
A tower that is 106 feet tall casts a shadow 141 feet long. Find the angle of elevation of the sun to the nearest degree.
Final answer:
To determine the angle of elevation of the sun, calculate the inverse tangent (arctan) of the height of the tower (106 feet) divided by the length of its shadow (141 feet). The angle of elevation is approximately 37 degrees to the nearest degree.
Explanation:
To find the angle of elevation of the sun given that a 106 feet tall tower casts a shadow of 141 feet long, we can use trigonometry. Specifically, the tangent of the angle, which is the ratio of the opposite side (the height of the tower) to the adjacent side (the length of the shadow).
We use the formula:
tangent of angle = opposite / adjacent
Tan(angle) = 106 / 141
Now we need to calculate the inverse tangent (arctan) of this ratio to find the angle in degrees:
Angle = arctan(106/141)
After performing this calculation with a calculator or using a trigonometric table, we find that the angle to the nearest degree is approximately 37 degrees.
4 Erin and Devon are playing a game. Erin has 42 points. If Devon had 14 more points, he'd have double the points Erin has. How many points does Devon have?
Final answer:
The question is a mathematical problem where we find that Devon has 70 points after setting up and solving an algebraic equation based on the conditions given.
Explanation:
The student's question revolves around a Mathematical problem concerning the points scored by two players, Erin and Devon, in a game. Erin has 42 points, and the question provides a condition that if Devon had 14 more points, he would have double the points Erin has. This scenario can be translated into an algebraic equation to solve for the number of points Devon currently has.
Let's denote the current number of points Devon has as D. According to the problem, if Devon had 14 more points, his total would be D + 14. We are also told that this hypothetical total would be double the points Erin has, which is 42. Therefore, we can write the equation as:
D + 14 = 2 × 42
By solving this equation, we can find out how many points Devon has:
D + 14 = 84 (since 2 × 42 equals 84)D = 84 - 14D = 70Devon currently has 70 points.
Erin has 42 points. Devon has 70 points. If he had 14 more, he'd have double Erin's points.
let's break it down step by step:
Given:
- Erin has 42 points.
- If Devon had 14 more points, he'd have double the points Erin has.
Let's denote Devon's points as [tex]\( D \).[/tex]
According to the given information, if Devon had 14 more points, he'd have double the points Erin has. So, mathematically, we can represent Devon's points as [tex]\( 2 \times 42 \)[/tex] when we add those 14 points.
So, we can write the equation:
[tex]\[ D + 14 = 2 \times 42 \][/tex]
Now, let's solve for [tex]\( D \):[/tex]
[tex]\[ D + 14 = 84 \][/tex]
Subtract 14 from both sides of the equation:
[tex]\[ D = 84 - 14 \]\[ D = 70 \][/tex]
So, Devon currently has 70 points.
Sixty-seven biscuits are to be fed to 10 pets; each pet is either a cat or a dog. Each dog is to get seven biscuits, and each cat is to get six. How many dogs are there?
Answer:
There are 7 dogs.
Step-by-step explanation:
7 (dogs) x 7 (biscuits) = 49
3 (cats) x 6 (biscuits) = 18
49 + 18 = 67
hello loves!! I've been stuck on this question for like 2 hours lol! i need some help, ill give 100 points :)
Answer:
61.12 units²
Step-by-step explanation:
(½ × pi × r²) + (½ × b × h)
½ [(3.14 × 4²) + (8 ×9)]
½(122.24)
61.12 units²
Answer:
61.13 units squared
Step-by-step explanation:
This figure is composed of a semicircle and a triangle. Let's find these areas separately:
1) SEMICIRCLE:
The area of a semicircle is: [tex]A=\frac{\pi r^2}{2}[/tex] , where r is the radius (which is the distance from the center to a point on the circle). In this case, the radius of the circle is 4. So, we have:
[tex]A=\frac{\pi *4^2}{2} =\frac{16\pi }{2} =8\pi[/tex] ≈ 25.13 units squared
2) TRIANGLE:
The area of a triangle is: [tex]A=\frac{bh}{2}[/tex] , where b is the base and h is the height. Here, the base is 8 (b = 8) and the height is 9 (h = 9). So, we have:
[tex]A=\frac{8*9}{2} =\frac{72}{2} =36[/tex] units squared
Finally, we add these two areas together:
25.13 + 36 = 61.13 units squared.
Hope this helps!
At a college, the cost of tuition increased by 10%. Let b represent the former cost of tuition. Use the expression b+0.10b for the new cost of tuition.
Question is Incomplete,Complete question is given below;
At a college, the cost of tuition increased by 10%. Let b be the former cost of tuition. Use the expression b + 0.10b for the new cost of tuition.
a) Write an equivalent expression by combining like terms.
b) What does your equivalent expression tell you about how to find the new cost of tuition?
Answer:
a. The equivalent expression is [tex]1.1b[/tex].
b. The new cost of tuition is 1.1 times the former cost of tuition.
Step-by-step explanation:
Given:
Former cost of tuition = [tex]b[/tex]
the cost of tuition increased by 10%.
New cost of tuition = [tex]b+0.10b[/tex]
Solving for part a.
we need to find the equivalent expression by combining the like terms we get;
Now Combining the like terms we get;
new cost of tuition = [tex]b(1+0.1) = 1.1b[/tex]
Hence The equivalent expression is [tex]1.1b[/tex].
Solving for part b.
we need to to say about equivalent expression about how to find the new cost of tuition.
Solution:
new cost of tuition = [tex]1.1b[/tex]
So we can say that.
The new cost of tuition is 1.1 times the former cost of tuition.
Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h = 0.01, 0.001, and 0.0001.) HINT [See Example 4.] (Round your answers to five decimal places.) f(x) = 3 x ; a = 7
Step-by-step explanation:
average rate of change of function is given by :
[tex]f= (f(a+h)-f(a))/h[/tex]
where
[tex]f(x)=3x[/tex]
and a= 7
so inserting values is formula for h=1
[tex]f=(f(7+1)-f(7))/1[/tex]
[tex]f= f(8)-f(7)= 3(8)-3(7)=24-21=3[/tex]
now for h= 0.1
[tex]f=(f(7+0.1)-f(7))/0.1=(f(7.1)-f(7))/0.1=(3(7.1)-3(7))/0.1[/tex]
[tex]f=3[/tex]
similarly average rate of change of given function is same for all given step sizes.
Final answer:
The question involved calculating the average rate of change of the function f(x) = 3x over various intervals, showing that the rate of change is constant and equals 3 for all given values of h.
Explanation:
The question asks to calculate the average rate of change of the function f(x) = 3x over the intervals [a, a + h] for values of h = 1, 0.1, 0.01, 0.001, and 0.0001, where a = 7.
The average rate of change is calculated using the formula [tex]\frac{f(a+h) - f(a)}{h}[/tex]
For each value of h, we substitute a and h into the function and use the formula to find the average rate of change.
For h = 1, the average rate of change is 3.
For h = 0.1, the average rate of change is also 3.
For h = 0.01, the average rate of change remains 3.
For h = 0.001, the average rate is again 3.
Similarly, for h = 0.0001, the average rate of change is 3.
Using technology for values of h smaller than 0.1 is recommended due to the precision required in calculations. However, for this particular function, the rate of change is constant across these intervals, simplifying the process.
Each chef at "Sushi Emperor" prepares 151515 regular rolls and 202020 vegetarian rolls daily. On Tuesday, each customer ate 222 regular rolls and 333 vegetarian rolls. By the end of the day, 444 regular rolls and 111 vegetarian roll remained uneaten.
Each chef at "sushi emperor" prepares 15 regular rolls and 20 vegetarian rolls daily. On tuesday, each customer ate 2 regular rolls & 3 vegetarian rolls. by the end of the day, 4 regular rolls & 1 vegetarian roll remained uneating. how many chefs were on tuesday ? and how many customers were they ?
Answer:There were 2 chefs and 13 customers on tuesday
Solution:Let x be the number of chefs at Sushi Emperor and y be the number of customers on Tuesday.
From given,
Each chef prepares 15 regular rolls and 20 vegetarian rolls daily
If each chef prepares 15 regular rolls, then x chefs prepare 15x regular rolls
If each customer ate 2 regular rolls, then y customers ate 2y regular rolls
By the end of the day, 4 regular roll remained un eating
Therefore,
15x - 2y = 4 --------- eqn 1
If each chef prepares 20 vegetarian rolls, then x chefs prepare 20x vegetarian rolls
If each customer ate 3 vegetarian rolls, then y customers ate 3y vegetarian rolls
By the end of the day, 1 vegetarian roll remained uneating
Therefore,
20x - 3y = 1 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 3
45x - 6y = 12 ------- eqn 3
Multiply eqn 2 by 2
40x - 6y = 2 ------- eqn 4
Subtract eqn 4 from eqn 3
45x - 6y = 12
40x - 6y = 2
( - ) --------------
5x = 10
x = 2
Substitute x = 2 in eqn 1
20(2) - 3y = 1
40 - 3y = 1
3y = 39
y = 13
Thus there were 2 chefs and 13 customers
Which is the graph of f (x) = 4 (1/2) Superscript x?
Answer:
Option (2) is correct graph.
Step-by-step explanation:
Given:
The function to graph is given as:
[tex]f(x)=4(\frac{1}{2})^x[/tex]
Now, the above function is an exponential function of the form [tex]f(x)=ka^x[/tex]
Where, 'k' and 'a' are constants.
The range of an exponential function is always greater than 0.
The domain is all real numbers.
Now, for graphing it, we need to find some points on it and its end behaviour.
Now, for x = 0, the function value is given as:
[tex]f(0)=4(\frac{1}{2})^0=4[/tex]
So, (0, 4) is a point on the graph.
Now, for x = 1, the function value is given as:
[tex]f(1)=4(\frac{1}{2})^1=4\times\frac{1}{2}=2[/tex]
So, (1, 2) is another point on the graph.
Now, for x = 2, the function value is given as:
[tex]f(2)=4(\frac{1}{2})^2=4\times\frac{1}{4}=1[/tex]
So, (2, 1) is another point on the graph.
Now, as 'x' tends to ∞, the function value tends to:
[tex]f(x\to\infty)=4\cdot\frac{1}{2}^{\infty}=\frac{4}{\infty}=0[/tex]
So, as
[tex]x\to\infty,f(x)\to0\\\\x\to-\infty,f(x)\to\infty[/tex]
Now, from among all the options, only option (2) fulfills all the conditions given above.
So, option (2) is correct graph.
Answer:
option 2
Step-by-step explanation:
Consider the reaction 2x2y2+z2⇌2x2y2z which has a rate law of rate= k[x2y2][z2] select a possible mechanism for the reaction.
The question is about identifying a reaction mechanism based on the provided rate law, which is derived from the reactant concentrations. A likely mechanism is a single-step process where the reactants come together to form the product, mirroring the rate law's implication that reactant concentration directly influences the reaction rate.
Explanation:The student is asking about the mechanism of a reaction and its rate law. In chemistry, the rate law expresses the relationship among the reaction rate, the reaction mechanism, and the concentrations of the reactants.
The provided rate law is rate = k[x2y2][z2], which suggests that the reaction is first order with respect to both x2y2 and z2. A plausible mechanism for this reaction would involve a single step where one molecule of each reactant comes together to form the product, 2x2y2z.
In a single-step mechanism, the rate law is derived directly from the stoichiometry of the reactants in the balanced chemical equation. Since the rate law matches the stoichiometry of the reactants, it is likely that this could represent an elementary reaction, given that the stoichiometry and the rate law coincide.
The direct relationship implied by the rate law between the concentration of the reactants and the reaction rate can be explained by the likelihood of reactant particles colliding and reacting being greater with increased concentrations, a concept fundamental in kinetics.