Answer: option C is the correct answer
Step-by-step explanation:
Let x represent the cost of one night at the hotel.
Let y represent the cost of renting the car for one day.
Connor went to New York for vacation. He spent 3 nights at a hotel and rented a car for 4 days. If Connor paid $675, it means that
3x + 4y = 675 - - - - - - - - - - - 1
Jillian stayed at the same hotel, but spent 4 nights and rented a car for 5 days from the same company. If Jillian paid $875, It means that
4x + 5y = 875 - - - - - - - - - - - -2
Multiplying equation 1 by 4 and equation 2 by 3, it becomes
12x + 16y = 2700
12x + 15y = 2625
Subtracting, it becomes
y = 75
Substituting y = 75 into equation 1, it becomes
3x + 4 × 75 = 675
3x + 300 = 675
3x = 675 - 300 = 375
x = 375/3 = $125
At a basketball game a vendor sold a combined total of 146 sodas and hotdogs the number of sodas was 36 more than the number of hotdogs sold find the number sodas I have a basketball game a vendor sold a combined total of 146 sodas and hotdogs the number of Sotos was 36 more than the number of hotdogs sold find the number Sotos sold and the number of hotdogs sold
Answer:
hot dogs sold=110
sodas sold=36
Step-by-step explanation:
146-36=110
110+36=146
Answer:91 Sodas and 55 hot dogs were sold.
Step-by-step explanation:
Let x represent the number of Sodas that were sold at the basketball game.
Let y represent the number of hot dogs that were sold at the basketball game.
At the basketball game a vendor sold a combined total of 146 sodas and hotdogs. This means that
x + y = 146 - - - - - - - - - - - - - - -1
The number of Sodas was 36 more than the number of hotdogs sold. This means that
x = y + 36
Substituting x = y + 36 into equation 1, it becomes
y + 36 + y = 146
2y + 36 = 146
2y = 146 - 36 = 110
y = 110/2 = 55
x = y + 36 = 55 + 36
x = 91
Jose is training for a half -marathon .Each week he runs x miles per day for 5 days .For 3 days of the week he runs at a speed of 8 minutes per mile .For 2 days he runs 7-minute miles. Write an expression to represent the amount of time,in minutes,that jose runs in 4 weeks
Answer:
152x miles
Step-by-step explanation:
Jose runs x miles per day each week for 5 days.
For 3 days of the week he runs at a speed of 8 minutes per mile. So we have
3*8*x = 24x
For 2 days he runs 7 minutes per miles. We have
2*7*x = 14x
in one week, he runs 24x + 14x = 38x
In 4 weeks, he runs
4*38x = 152x miles
URGENT PLZ HELP. DUE TOMORROW
Answer:
9 x⁵y⁵
Step-by-step explanation:
for a rectangle
area = length x width, (rearranging)
width = area / length
given area = 45x⁸y⁹ and length = 5x³y⁴
width = 45x⁸y⁹ / 5x³y⁴
= (45/5) ( x⁸y⁹ / x³y⁴)
= 9 ( x⁸y⁹ / x³y⁴)
= 9 ( x⁸⁻³y⁹⁻⁴ )
= 9 ( x⁵y⁵ )
= 9 x⁵y⁵
A 2956 kg car starts from rest at the top of a driveway of length 6 m that is sloped at 35◦ with the horizontal. An average frictional force of 3080 N impedes the motion. Find the speed of the car at the bottom of the driveway. The acceleration of gravity is 9.8 m/s 2 . Answer in units of m/s.
Answer:
7.41 m/s
Step-by-step explanation:
Force of a car inclined at an angle
F=mg Sin Θ where; m = 2956 kg , g = 9.8m/s² , Θ = 35⁰
F = 2956 x 9.8 x Sin 35 = 16615.82 N
Net force due to friction = 16615.82 - 3080 = 13535.82 N
To calculate acceleration; F= Ma
13535.82 = 2956 x a
a = 4.58 m/s²
From equation of motion
[tex]V^{2} = V_{o} ^{2} + 2aS[/tex]
V² = 0 + (2 x 4.58 x 6)
V = [tex]\sqrt{54.95}[/tex]
V = 7.41 m/s
Use the definition of a derivative to find f’(x).
f(x) = 9/x
Please show the steps. I cannot find a way to solve it in the way that is shown by the examples given around online e.t.c.
Answer:
f'(x) = [tex]-\frac{9}{x^2}[/tex]
Step-by-step explanation:
i) f(x) = 9 / x
ii) f'(x) = [tex]$\lim_{h\to 0} \frac{f(x+h) - f(x)}{h} $ \hspace{0.2cm}[/tex]
[tex]= $\lim_{h\to 0} \frac{\frac{9}{x+h} - \frac{9}{x} }{h} = \hspace{0.1cm} $\lim_{h\to 0} \frac{9x - 9(x+h)}{hx(x+h)} $ \hspace{0.1cm} = \hspace{0.1cm}$\lim_{h\to 0} \frac{-9h}{hx(x+h)} = $\lim_{h\to 0} \frac{-h}{x(x+h)} = \frac{-9}{x^2}$[/tex]
In reference to the diagram below, Juan claims that the area of circle B is twice the area of circle A since it's radius is twice as big.
Circle A radius = 2
Circle B radius = 4
Explain why Juan is mistaken in his conclusion about the area of circle B. In writing your response, be sure to explain what happens to the radius when it is squared. Explain the steps in finding the area of a circle.
Answer:
circle b
Step-by-step explanation:
Answer:
Step-by-step explanation:
amosc: marcos62280 ( ;
A candy jar contains 200 pieces of candy Each of which is either red white or blue there are 50 red pieces and 40 white pieces if B represents the number of blue pieces in the jar by the equation you can use to find the value of B South equation label your answer
Answer:
200-50-40=B
B =110 blue pieces
Step-by-step explanation:
What is the range of g(x) = 3|x − 1| − 1? A. (-∞, 1] B. [-1, ∞) C. [1, ∞) D. (-∞, ∞)
Answer:
B. [-1, ∞).
Step-by-step explanation:
g(x) = 3|x − 1| − 1
When x = 1 g(x) = 3(0) - 1 = -1.
As all negative vales of x will give positive values of |x - 1| then g(x) = -1 is its minimum value. The graph will be shaped like a letter V with the vertex at (1,-1).
Therefore the range is [-1, ∞).
The range of g(x)=3|x-1|-1 is [-1,∞) i.e. option B is correct.
What is range?The set of all the outputs of a function is known as the range of the function .
According to the given question
we have,
A function, g(x) = 3|x-1| - 1
Lets, find the value of g(x) for the different values of "x"
when,
x=0 ⇒ g(0) = -1
x=1 ⇒ g(1) = -1
x=2 ⇒g(2) = 2
Similarly, we can check for the negative values of x.
So, for all the negative values of x we will gives only positive values for g(x) and only at x=0, g(x) = -1 , which is its minimum value .
⇒ The range of given function g(x) is {-1,∞).
Hence , option B is correct.
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Point P is located at (2, 2) and point T is located at (7, 17).
What are the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio?
Use the section formula and show values for: m: n, Point 1, Point 2, and ALL work to find coordinates of
partitioning point.
Answer:
The coordinates of the point that partitions the directed line segment PT in a 3:2 ratio will be (5, 11).
Step-by-step explanation:
Given the points
P(2, 2) and T(7, 17)What are the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio?
Let D be the Divided point of the directed line segment PT.
SECTION FORMULA
The point (x, y) which partitions the line segment of the points (x₁, y₁) and
(x₂, y₂) in a ratio [tex]m:n[/tex] will be:
[tex]\left(\frac{m\:x_2+n\:x_1}{m+n},\:\frac{m\:y_2+n\:y_1}{m+n}\right)[/tex]
Here,
x₁ = 2 y₁ = 2 x₂ = 7y₂ = 17[tex]m=3,\:n=2[/tex]Substituting the values in the above formula
[tex]D\left(x\right)=\left(\frac{3\times \:7\:+\:2\times 2}{3+2},\:\frac{3\times 17\:+\:2\times 2}{3+2}\right)[/tex]
[tex]D\left(x\right)=\left(\frac{21\:+\:4}{5},\:\frac{51\:+\:4}{5}\right)[/tex]
[tex]D\left(x\right)=\left(\frac{25}{5},\:\frac{55}{5}\right)[/tex]
As
[tex]\frac{25}{5}=5,\:\frac{55}{5}=11[/tex]
So
[tex]$D(x)=(5, 11)[/tex]
Therefore, the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio will be (5, 11).
In a recent poll,only 8% of the people surveyed were againt a new bill making it mandatory to recycle. How many of he 75 people surveyed were against the bill?
Answer:
There were 6 people against the bill.
Step-by-step explanation:
Given:
In a recent poll,only 8% of the people surveyed were against a new bill making it mandatory to recycle.
Now, to find of the 75 people surveyed were against the bill.
Total number of people = 75.
Percent of the people surveyed were against the bill = 8%.
Now, to get the number of people who were against the bill:
8% of 75
[tex]=\frac{8}{100}\times 75[/tex]
[tex]=0.08\times 75[/tex]
[tex]=6.[/tex]
Therefore, there were 6 people against the bill.
An experimenter conducted a two-tailed hypothesis test on a set of data and obtained a p-value of 0.44. If the experimenter had conducted a one-tailed test on the same set of data, which of the following is true about the possible p-value(s) that the experimenter could have obtained? A) The only possible p-value is 0.44. B) The only possible p-value is 0.88. C) The possible p-values are 0.22 and 0.78. D) The possible p-values are 0.22 and 0.88.
Answer:
Correct option is (C).
The possible value of the p-value for a one-tailed test are 0.22 and 0.78.
Step-by-step explanation:
The p-value is the probability of acquiring a result as extreme as the observed result, assuming the null hypothesis statement is true.
The p value of a test is:
Left-tailed test: [tex]P(TS<ts)[/tex]
Right-tailed test: [tex]P(TS>ts) = 1- P(TS<ts)[/tex].
Here,
TS = Test statistic
ts = computed value of the test statistic.
The two-tailed p-value is: [tex]2P(TS<ts)[/tex] or [tex]2P(TS>ts)[/tex].
The p-value of the two tailed test is, 0.44.
Compute the p-value for one-tailed test a follows:
For a left-tailed test:[tex]2P(TS<ts)=0.44\\P(TS<ts)=\frac{0.44}{2}\\ =0.22[/tex]
For a right-tailed test:[tex]P(TS>ts) = 1- P(TS<ts)\\=1-0.22\\=0.78[/tex]
Thus, the possible value of the p-value for a one-tailed test are 0.22 and 0.78.
The correct option is (C).
Given a p-value of 0.44 from a two-tailed test, the equivalent one-tailed test would yield a p-value of 0.22. Out of the provided choices, option C is closest to the correct interpretation.
Explanation:The question presented is about the computation of the p-value in a one-tailed test, given the p-value from a two-tailed test. A p-value essentially indicates the probability that you would obtain the observed data, or data more extreme if the null hypothesis is true. In this instance, the experimenter has a p-value of 0.44 from a two-tailed test.
When converting this to a one-tailed test, the p-value would effectively be halved. Therefore, if they conducted a one-tailed test on the same data, the p-value would be 0.22 (i.e., 0.44/2) in the direction specified by the alternative hypothesis. Thus, between the provided options, none are perfectly correct, but option C) 'The possible p-values are 0.22 and 0.78.' is closest to the correct interpretation, with the accurate p-value being 0.22 rather than 0.78.
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N To be able to afford the house of their dreams, Dave and Leslie must clear $128,000 from the sale of their first house. If they must pay $780 in closing costs and 6% of the selling price for the sales commission, then what is the minimum selling price for which they will get $128,000?
Answer:
the selling price of the house is estimated as $137,000
Step-by-step explanation:
Given data:
clear amount is $128,000
closing cost is $780
sales commission rate is 6%
let S be the selling price of house
from the information given in the question we have following relation
[tex]128,000 \leq S - 0.06S - 780[/tex]
[tex]128,000 \leq 0.94S - 780[/tex]
adding 780 on both side, we get
[tex]128,000 - 780 \leq 0.94S[/tex]
divide the both side by 0.94, we get
[tex]137,000 \leq S[/tex]
therefor the selling price of the house is estimated as $137,000
What is the slope of the line passing through the points (−1, −7) and (−9, −2) ?
[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{-9}-\underset{x_1}{(-1)}}}\implies \cfrac{-2+7}{-9+1}\implies -\cfrac{5}{8}[/tex]
Answer:
The answer to your question is m = [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
Data
A (-1, -7)
B (-9, -2)
Formula
slope = m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Use the slope formula to find the answer. Just substitute the values and simplify them.
Substitution
x1 = -1
x2 = -9
y1 = -7
y2 = -2
m = [tex]\frac{-2 + 7}{-9 + 1}[/tex]
Simplification
m =- [tex]\frac{5}{8}[/tex]
Result
m =- [tex]\frac{5}{8}[/tex]
Find the vehicle's acceleration when its final velocity is measured as 45 m/s, the initial initial velocity was 0.0 m/s and the time elapsed was 8.5 seconds.
Answer:
Acceleration (a) [tex]=5.29\ m\./s^2[/tex]
Step-by-step explanation:
Given that
final velocity (v) [tex]=45\ m/s[/tex]
Initial velocity (u) [tex]=0\ m/s[/tex]
Time (t) [tex]=8.5\ seconds[/tex]
Then
[tex]v=u+at\ ...................................... (1)[/tex]
Where [tex]a[/tex] is acceleration.
put the value in equation [tex](1)[/tex]
[tex]45=0+a\times8.5\\a\times8.5=45[/tex]
dividing [tex]8.5[/tex] both sides
[tex]\frac{a\times8.5}{8.5}=\frac{45}{8.5}\\\\a=\frac{45}{8.5}\\\\a=\frac{450}{85}\\\\a=5.29\ m/s^2[/tex]
NEED HELP ASAP Need someone to explain how to do this
Answer:
Oh cool! The answer is 90 since a and c or parallel, b cuts through them perpendicularly, forming a right angle.
Step-by-step explanation:
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠H.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠H = °
Answer:
Step-by-step explanation:
Triangle GHI is a right angle triangle.
From the given right angle triangle,
GH represents the hypotenuse of the right angle triangle.
With m∠H as the reference angle,
HI represents the adjacent side of the right angle triangle.
GI represents the opposite side of the right angle triangle.
To determine m∠H, we would apply
the Sine trigonometric ratio.
Sin θ = adjacent side/hypotenuse. Therefore,
Sin m∠H = 7/10 = 0.7
m∠H = Sin^-1(0.7)
m∠H = 44.4° to the nearest tenth.
Answer: gayness
Step-by-step explanation:
Please assist me in 6-30
Answer:
Yes to both.
Step-by-step explanation:
It is true that
[tex]\dfrac{x}{y}=1 \iff x=y[/tex]
In fact, if you know that x/y=1, just multiply both sides by y to get x=y. On the other hand, if you know that x=y (and they are not zero), you can divide both sides by y to get x/y=1.
Since the two expressions are equivalent, you can always use Phil's or Don's expression, at will.
please help me I really need help
Answer:
both are done
look at picture
1. 13/36
2. 3/16
-------100 POINTS------
Complete the proof of the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse's length equals the sum of the squares of the other two sides' lengths. This can be proven via the areas of squares with sides corresponding to the triangle's sides, demonstrating that a²+b²=c².
Explanation:The Pythagorean theorem is a fundamental principle in geometry, named after the Greek mathematician Pythagoras. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a²+b²=c².
To prove this, we can begin with a right-angled triangle with sides a, b, and hypotenuse c. If we square the length of c (i.e., c²), this is equivalent to the area of a square with side length c. Similarly, a² and b² represent the areas of squares with side lengths a and b, respectively.
If we add together the areas of the two smaller squares (a²+b²), this equals the area of the larger square (c²). This proves the Pythagorean theorem. For instance, consider a right triangle with sides of lengths 3, 4, and 5. The squares would have areas 9 and 16, which add up to 25 - the area of the square on the hypotenuse.
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The Pythagorean Theorem states that a² + b² = c². A step-by-step proof involves constructing a square with the right-angled triangle and equating the areas. This logical deduction confirms the theorem's correctness.
The Pythagorean Theorem is one of the fundamental results in Geometry, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c². Here is a step-by-step proof:
Construct a right-angled triangle with legs a and b and hypotenuse c.Construct a square with side a + b. Within this square, place four identical right-angled triangles, each having sides a, b, and c.The four triangles will leave a smaller square in the middle with side c.The area of the larger square is (a + b)², which can be expanded as a² + 2ab + b².The area of the larger square is also the sum of the areas of the four triangles and the smaller square in the center, which is 4 (1/2ab) + c² simplifying to 2ab + c².Setting the two expressions for the area of the larger square equal gives: a² + 2ab + b² = 2ab + c².By subtracting 2ab from both sides, we get the Pythagorean Theorem: a² + b² = c².Thus, we have proven that the theorem holds true using logical deductions.
You go shopping and buy 3 new shirts and 2 pairs of pants for $29.75. Your friend buys 4 shirts and 3 pairs of pants for 42.00. How much did one shirt cost?
Answer:
$5.25
Step-by-step explanation:
The two purchases can be described by the equations ...
3s +2p = 29.75
4s +3p = 42.00
If you multiply the first equation by 3 and subtract 2 times the second equation, the cost of a shirt pops out.
3(3s +2p) -2(4s +3p) = 3(29.75) -2(42.00)
9s +6p -8s -6p = 89.25 -84.00 . . . . . . . eliminate parentheses
s = 5.25 . . . . . . . . . . collect terms
One shirt costs $5.25.
A force of 6 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching it from its natural length to 11 in. beyond its natural length?
Answer:
Work done is 1.02J
Step-by-step explanation:
Work (W) done in stretching a spring = 1/2Fe
F (force) = 6 lb = 6×4.4482N = 26.6892N
e (extension) = 11in - 8in = 3in = 3×0.0254m = 0.0762m
W = 1/2 × 26.6892 × 0.0762 = 1.02J
Stephanie is saving money to buy a new computer. So far she has saved $200. Write an inequality to show how much she needs to save each month for the next year so she has at least $1200 to spend on the computer,then solve the inequality.
Answer:
Step-by-step explanation:
Let x represent the amount that she needs to save each month for the next year.
Stephanie is saving money to buy a new computer. So far she has saved $200. This means that the total amount that she would have saved in y months is
200 + xy
Since there are 12 months in a year,
an inequality to show how much she needs to save each month for the next year so she has at least $1200 to spend on the computer is
200 + 12x ≥ 1200
12x ≥ 1200 - 200
12x ≥ 1000
x ≥ 1000/12
x ≥ 83.33
Chris pays a fee if her balance falls below $10 on the statement data. Prior to the statement date, her balance was -$3.46. Then Chris made a deposit, d, in ample time, so she did not have to pay a fee. Write and solve an inequality to represent this situation. P
Answer:
The solution of the inequality required for the situation is d ≥ $13.46.
Step-by-step explanation:
i) the minimum deposit is $10.
ii) the balance before the statement is $-3.46
iii) a deposit d is made so that the fee did not have to be made
iv) therefore d + (-3.46) ≥ 10
d - 3.46 ≥ 10
therefore d ≥ 10 + 3.46
therefore d ≥ $13.46
Chris would have to deposit at least $13.46 into her account in order to avoid being charged a fee. This amount is determined by setting up and solving the inequality -3.46 + d ≥ 10, which represents her account balance.
Explanation:In this situation, Chris is trying to avoid a fee by maintaining a balance of at least $10 in her account. Prior to making a deposit, her account balance is -$3.46. Thus, we need to find out the minimal deposit, d, that she needs to make in order to bring her balance up to $10. To do this, we can set up the following inequality:
-3.46 + d ≥ 10
To solve the inequality for d, we simply add 3.46 to both sides of the inequality:
d ≥ 13.46
Therefore, Chris must make a deposit of at least $13.46 to avoid incurring the fee.
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Which of the following statements would be correct to use when proving that limx→4(3x−4)=8?
a. Given 0<∣∣x−4∣∣<ϵ, then ∣∣(3x−4)−8∣∣<ϵ3.
b. Given 0<∣∣x−4∣∣<ϵ3, then ∣∣(3x−4)−8∣∣<ϵ.
c. Given 0<∣∣x−8∣∣<ϵ, then ∣∣(3x−4)−4∣∣<ϵ3.
d. Given 0<∣∣x−8∣∣<ϵ3, then ∣∣(3x−4)−4∣∣<ϵ.
e. Given 0<∣∣x−4∣∣<3ϵ, then ∣∣(3x−4)−8∣∣<ϵ.
f. Given 0<∣∣x−4∣∣<3ϵ, then ∣∣(3x−4)−8∣∣<ϵ3.
Answer:
Option c
Step-by-step explanation:
given that limit x tending to 4 of the function (3x-4) is 8
This implies for all values of x such that for epsilon >0 arbitrary small ,
[tex]||x-4||<\epsilon[/tex], we get
|f(x)-8|<3epsilon
this is equivalent to the option c.
Proof:
Consider
[tex]||x-4||<\epsilon\\3||x-4||<3\epsilon\\||3x-12||<3\epsilon\\||3x-4|-8| <3\epsilon[/tex]
Hence it follows that option C is right.
The correct statement to use when proving that limx→4(3x−4)=8 is option b: Given 0 < | x - 4 | < epsilon/3, then | (3x - 4) - 8 | < epsilon. This uses the formal definition of limit and abides the epsilon-delta parameters definition to provide the correct proof.
Explanation:To verify the given limit, we need to utilize the formal definition of a limit. This formal definition gives us a systematic method to prove a limit based on epsilon-delta parameters. The purpose is to show that as x gets closer and closer to 4 (with| x - 4 | being smaller than an arbitrary positive delta), the expression (3x-4) increasingly approaches 8 (with |(3x - 4) - 8| getting within an epsilon range).
The correct choice is: b. Given 0 < | x - 4 | < epsilon/3, then | (3x - 4) - 8 | < epsilon. In this case, 'epsilon/3' in | x - 4 | < 'epsilon/3' is the delta in the epsilon-delta definition of limit. Essentially, it captures the notion that for every epsilon > 0, there exists a delta > 0 such that 0 < | x - 4 | < delta implies | (3x - 4) - 8 | < epsilon, thereby proving the limit.
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Jerome is painting a rectangular toolbox that is 20 inches by 10 inches by 8 inches. A tube of paint covers 300 square inches. What is the surface area of the toolbox?
Answer:
880 in³
Step-by-step explanation:
L = 20, W = 10, H = 8
2(h × W) + 2(h × L) + 2(W × L)
= 2(8*10) + 2(8*20) + 2(10*20)
= 2(80) + 2(160) + 2(200)
= 160 + 320 + 400
= 880 in³
Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected . Find the probability of selecting a black card and selecting a red card. The probability of selecting a black card and then selecting a red card is
(A) Probability of the black card is 1 /2.
(B) Probability of a red card is 26/51.
(C) Probability of selecting a black card and then selecting a red card is 13/51.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total number of cards in the deck = 52
Total number of black cards = 26
Total number of red cards = 26
Probability of selecting a black card = 26 / 52 = 1 / 2
Now, the total number of card become after selecting 1 black card = 51
Probability of selecting a red card = 26 / 51
Now,
The probability of selecting a black card and then selecting a red card is,
= 1 / 2 * 26 / 51
= 13 / 51
Thus, (A) the Probability of a black card is 1 /2.
(B) Probability of a red card is 26/51.
(C) Probability of selecting a black card and then selecting a red card is 13/51.
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The probability of selecting a black card first and then a red card is [tex]\(\frac{13}{51}\).[/tex]
To find the probability of selecting a black card and then selecting a red card from a standard deck of 52 playing cards without replacement, we need to follow these steps:
1. Calculate the probability of selecting a black card first:
- There are 26 black cards in a standard deck (13 spades and 13 clubs).
- The probability of selecting a black card first is:
[tex]\[ P(\text{Black card first}) = \frac{26}{52} = \frac{1}{2} \][/tex]
2. Calculate the probability of selecting a red card second, given that the first card was black:
- After drawing the first black card, there are 51 cards left in the deck.
- There are still 26 red cards in the deck (since the black card was not replaced).
- The probability of selecting a red card given that the first card was black is:
[tex]\[ P(\text{Red card second} \mid \text{Black card first}) = \frac{26}{51} \][/tex]
3. Calculate the combined probability of both events occurring:
- The probability of both events happening (selecting a black card first and then a red card) is the product of the individual probabilities:
[tex]\[ P(\text{Black card first and Red card second}) = P(\text{Black card first}) \times P(\text{Red card second} \mid \text{Black card first}) \][/tex]
Substituting the values we found:
[tex]\[ P(\text{Black card first and Red card second}) = \left(\frac{1}{2}\right) \times \left(\frac{26}{51}\right) = \frac{26}{102} = \frac{13}{51} \][/tex]
Therefore, the probability of selecting a black card first and then a red card is [tex]\(\frac{13}{51}\).[/tex]
A random sample of the actual weight of 5-lb bags of mulch produces a mean of 4.963 lb and a standard deviation of 0.067 lb. If n=50, which of the following will give a 95% confidence interval for the mean weight (in pounds) of the mulch produced by this company?
A) 4.963±0.016.
B) 4.963±0.019.
C) 4.963±0.067.
D) 4.963±0.009.
E) None of the above.
Answer: B) 4.963±0.019.
Step-by-step explanation:
Confidence interval for population mean ( when population standard deviation is not given) is given by :-
[tex]\overline{x}\pm t^*\dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = Sample mean
n= Sample size
s= sample standard deviation
t* = critical t-value.
As per given:
n= 50
Degree of freedom = n-1 =49
[tex]\overline{x}= 4.963\ lb[/tex]
s= 0.067 lb
For df = 49 and significance level of 0.05 , the critical two-tailed t-value ( from t-distribution table) is 2.010.
Now , substitute all values in the formula , we get
[tex]4.963\pm (2.010)\dfrac{0.067}{\sqrt{50}}\\\\ 4.963\pm (2.010)(0.0094752)\\\\ 4.963\pm0.019045152\approx4.963\pm0.019[/tex]
Hence, a 95% confidence interval for the mean weight (in pounds) of the mulch produced by this company is [tex]4.963\pm0.019[/tex].
Thus , the correct answer is B) 4.963±0.019.
Answer:
the correct answer is B) 4.963±0.019.
Step-by-step explanation:
A pre-paid cell phone company charges $18.5 as a monthly access fee and $0.11 per minute of calling time. Express the monthly cost C as a function of x, the number of minutes use. What will the monthly cost be if you make 329 minutes of calls this month? $
Answer:
c=54.69
Step-by-step explanation:
so this is a two step problem
c=18.5+0.11x
we created the function
now we plug in 329 into x and solve to get the c
c=54.69
The monthly cost for pre-paid cell phone usage can be expressed as a function, C = 18.5 + 0.11x where x is the number of calling minutes. The monthly cost for making 329 minutes of calls would be $54.69.
Explanation:The pre-paid cell phone company charges a fixed monthly access fee and an additional cost per minute of calling time. Here, the monthly access fee is $18.5 and the cost per minute is $0.11. We are asked to express the monthly cost C as a function of x, the number of minutes used.
Therefore, we can write the function as C = 18.5 + 0.11x where, C represents the monthly cost and x represents the number of minutes used.
Now, if you make 329 minutes of calls this month, you can use this function to calculate the total cost. Substituting x = 329 into the function gives: C = 18.5 + 0.11 * 329 = $54.69.
Therefore, the monthly cost for making 329 minutes of calls would be $54.69.
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Carmen has money in her bank account. Each week she withdraws the same amount of money from her account. Write an equation that relates b, her account balance after w weeks. 1week=$825 2weeks=$750 3weeks=$675 4weeks=$600
Step-by-step explanation:
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If Alex and Brandon work together they will clean the school in 15 hours. Working alone, Brandon can finish the same job in 20 hours. How long will it take Alex to do the job by himself? PLEASE HELP ME PRETTY PLEASE
Answer:
It takes 60 hours for Alex to complete the job alone.
Step-by-step explanation:
Given:
Number of hours Brandon alone can finish job =20 hours
Let the number of hours required by Alex alone to complete the job be 'x' hrs.
We need to find the number of hours required by Alex alone to complete the job.
Solution:
Now we can say that;
Rate at which Alex can complete the job alone = [tex]\frac1x[/tex] job/hour
Rate at which Brandon can complete the job alone = [tex]\frac{1}{20}[/tex] job /hour
Also Given:
Number of hours required for both to complete the job = 15
So rate of both complete the job = [tex]\frac{1}{15}[/tex] job/hour
Now we can say that;
rate of both complete the job is equal to sum of Rate at which Alex can complete the job alone and Rate at which Brandon can complete the job alone.
framing in equation form we get;
[tex]\frac1x+\frac{1}{20}=\frac{1}{15}[/tex]
Now taking LCM for making the denominators same we get;
[tex]\frac{20}{20x}+\frac{x}{20x}=\frac{1}{15}[/tex]
Now denominators are common so we will solve the numerators.
[tex]\frac{20+x}{20x}=\frac{1}{15}[/tex]
Now Using cross multiplication we get;
[tex]15(20+x)=20x[/tex]
Applying Distributive property we get;
[tex]15\times20+15\times x =20x\\\\300+15x=20x[/tex]
Combining like terms we get;
[tex]300=20x-15x\\\\300=5x[/tex]
Now Dividing both side by 5 we get;
[tex]\frac{300}{5}=\frac{5x}{5}\\\\x=60\ hrs[/tex]
Hence It takes 60 hours for Alex to complete the job alone.
To find how long it will take Alex to complete the job by himself, we first establish the individual work rates of Alex and Brandon. We know the combined work rate (1/15 jobs per hour) and Brandon's work rate (1/20 jobs per hour). Alex's work rate is thus 1/15 - 1/20 = 1/60 jobs per hour, which means it will take him 60 hours to do the job alone.
Explanation:This question requires knowledge of work rate calculations in Mathematics. The scenario involves two workers, Alex and Brandon, who can complete a cleaning task together in 15 hours. It's also given that Brandon can do the job alone in 20 hours, and we need to calculate how long it would take for Alex to complete the job by himself.
First, let's define their rates of work. If Brandon can complete the job in 20 hours, his work rate is 1 job per 20 hours, or 1/20 jobs per hour. Similarly, if Alex and Brandon together can complete the job in 15 hours, their combined work rate is 1 job per 15 hours, or 1/15 jobs per hour.
To find Alex's work rate, we subtract Brandon's work rate from the combined work rate. Thus, Alex's work rate is 1/15 - 1/20 = 1/60 jobs per hour. This means it would take Alex 60 hours to complete the job on his own.
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