Answer: 3/8
Step-by-step explanation:
Firstly, let's look at the possible outcome when 3 coins are tossed.
If two coins are first tossed, the possible outcome will be,
{HH, HT, TH, TT}
if one more coin is tossed together with the two to make it 3coins, the possible outcome will be gotten by matching the H and T of the third coin with the set of sample space above to give us,
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
This gives a total sample space of 8.
Outcomes that has at least two consecutive heads in the sequence are {HHH, HHT, THH} which is the possible outcome i.e 3
Probability that the outcome has at least two consecutive heads in the sequence will be;
Possible outcome/total outcome
= 3/8
Jody, a statistics major, grows tomatoes in her spare time. She measures the diameters of each tomato. Assume the Normal model is appropriate. One tomato was in the 50th percentile. What was its z-score?
Answer:
Zscore = 0.5
Step-by-step explanation:
If we assume a normal distribution, we mean that the diameters of each tomato follow a normal distribution. This is N~ (0,1).
By that, we mean that the mean (μ) = 0 and variance ([tex]\sigma^{2}[/tex]) = 1. Thus, since we are told that one tomato was in the 50th percentile. This implies the median. And is 0.5. And if the distribution is normal, the mean and median and mode should be equal.
Thus:
==> Z score = [tex]\frac{x-\mu}{\sigma}[/tex] = [tex]\frac{0.5 - \mu}{\sigma} = \frac{0.5-0}{1} = 0.5[/tex]
(Geometry Question) A sledding run is 300 yards long with a vertical drop of 27.6 yards. Find the angle of depression of the run.
Please show all work on how you got your answer
Answer:
5.28°
Step-by-step explanation:
Draw the triangle formed by the sledding run. The hypotenuse is 300. The height is 27.6. The angle of depression is opposite of the height.
Using sine:
sin θ = 27.6 / 300
sin θ = 0.092
θ = 5.28°
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:
[tex]m\angle H = 44.4\°[/tex].
Step-by-step explanation:
Given:
In Right Angle Triangle GIH
∠ I = 90°
GI = 7 ....Side opposite to angle H
GH = 10 .... Hypotenuse
To Find:
m∠H = ?
Solution:
In Right Angle Triangle ABC ,Sine Identity,
[tex]sin \ H = \frac{Oppsite\ side\ to\ \angle H}{Hypotenuse}[/tex]
Substituting the values we get;
[tex]sin\ H = \frac{7}{10} = 0.7[/tex]
Now taking [tex]sin^{-1}[/tex] we get;
[tex]\angle H = sin^{-1}\ 0.7 = 44.427[/tex]
rounding to nearest tenth we get.
[tex]m\angle H = 44.4\°[/tex].
Hence [tex]m\angle H = 44.4\°[/tex].
Select one of the factors of the quadratic expression.
x2 + 5x - 14
A)
(x + 14)
B)
(x + 2)
C)
(x + 7)
D)
(x - 3)
Answer:
The answer to your question is letter C (x + 7)
Step-by-step explanation:
Expression
x² + 5x - 14
Factor the expression
- Find two number that multiplied give -14 and that added give 5
- Find the prime factors of -14
-14 2
- 7 7
-1
-From the prime factors, we notice that these numbers are + 7 and -2
- x² + 7x - 2x - 14
- Factor the expression
(x + 7)(x - 2)
A group of students formed a circle during a game.The circumference of the circle was about 43.96 feet,and the diameter of the circle was 14 feet.Which expression best represents the value of x?
Answer:
A group of students formed a circle during a game.The circumference of the circle was about 43.96 feet,and the diameter of the circle was 14 feet.Which expression best represents the value of π?
The expression which represents the value of π is option C from the attachment that is π = 43.96/14
Step-by-step explanation:
Given:
Circumference of the circle = 43.96 feet
Diameter f the circle = 14 feet
So,
We know that :
Circumference of the circle = [tex]2(\pi )r[/tex] or [tex](\pi)d[/tex]
Re-arranging the formula:
⇒ [tex](\pi)d = Circumference\ (C)[/tex]
⇒ [tex](\pi )d =C[/tex]
⇒ [tex]\frac{\pi\times d}{d}=\frac{C}{d}[/tex]
⇒ [tex]\pi =\frac{C}{d}[/tex]
Plugging the numeric values:
⇒ [tex]\pi =\frac{43.96}{14}[/tex]
So the expression for π is 43.96/ 14,and option C is the correct choice.
The required expression for value of x is [tex]\frac{43.96}{14}[/tex].
Given that,
The circumference of the circle was about 43.96 feet,
And the diameter of the circle was 14 feet
We have to determine,
Which expression best represents the value of x.
According to the question,
Circumference of the circle = 43.96 feet
Diameter f the circle = 14 feet
Then,
Circumference of the circle = [tex]\pi \times d[/tex]
Let, [tex]\pi = x[/tex]
Circumference of the circle [tex]= x d[/tex]
Circumference of the circle = 43.96 feet
Therefore,
[tex]= 43.96 = x\times 14\\\\= x = \frac{43.96}{14} \\\\[/tex]
Hence, The required expression for value of x is [tex]\frac{43.96}{14}[/tex].
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Jeanine owes $1,200 on a credit card. The cars charges 16% interest, compounded continuously. Write a formula that describes how much you knew on her card after t years, assuming she makes no payments and does not incur any additional charges.
The letter e is used for continuous compound, it is raised by the interest rate times the amount of time.
The formula would be 1200e^0.16t
The answer is C
Use the figure below to enter the sides of triangle according to size from largest to smallest. The shortest side is side NA MA MN
WILL GIVE BRAINLIEST TO 1ST CORRECT ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
MA
Step-by-step explanation:
Antonio is having a pizza party for his birthday. He ordered 5 large pizzas, which have a total of 40 slices. He invited 8 people to his party. If he plans to divide the pizza up equally among him and his friends, how many slices will each person get
Answer: the number of slices that each person will get is 4 4/9
Step-by-step explanation:
Antonio ordered 5 large pizzas, which have a total of 40 slices.
He invited 8 people to his party. If he plans to divide the pizza up equally among him and his friends, it means that the pizza would be divided among 9 people(Antonio and 8 friends = 9 people).
The number of slices that each of them will get would be
40/9 = 4 4/9 slices
When equal amounts are invested in each of three accounts paying 7%, 9%, and 12.5%, one years combined interest income is $1,225.5. How much is invested in each account?
Answer:
$4300.
Step-by-step explanation:
Let x represent amount of money invested in each account.
We have been given that equal amounts are invested in each of three accounts paying 7%, 9%, and 12.5%, one years combined interest income is $1,225.5.
We will use simple interest formula to solve our given problem.
[tex]I=Prt[/tex], where,
I = Amount of interest after t years,
P = Principal amount,
r = Annual interest rate.
Since principal for each amount is equal and time is equal to 1 year, so we can represent our given information in an equation as:
[tex]1225.5=x(0.07+0.09+0.125)(1)[/tex]
[tex]1225.5=x(0.285)[/tex]
[tex]x=\frac{1225.5}{0.285}[/tex]
[tex]x=4300[/tex]
Therefore, an amount of $4300 is invested in each account.
Final answer:
The amount invested in each of the three accounts with different interest rates, which together yield a total interest income of $1,225.5, is $4,300 in each account.
Explanation:
To solve for the amount invested in each account, we need to set up an equation that represents the total interest income from the accounts.
Letting x represent the amount invested in each account, we can say that the interest from the first account at 7% is 0.07x, the second account at 9% is 0.09x, and the third account at 12.5% is 0.125x. The total interest income is the sum of these individual interests, which equals $1,225.5. Hence, the equation to solve is:
0.07x + 0.09x + 0.125x = 1,225.5
Combining like terms gives:
0.285x = 1,225.5
Dividing both sides by 0.285 gives us:
x = 1,225.5 / 0.285
x = 4,300
Therefore, the amount invested in each account is $4,300.
Use the formula for computing future value using compound interest to determine the value of an account at the end of 6 years if a principal amount of $6,000 is deposited in an account at an annual interest rate of 6% and the interest is compounded quarterly.
Answer: the value of the account at the end of 6 years is is $8577
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 6000
r = 6% = 6/100 = 0.06
n = 4 because it was compounded 4 times in a year.
t = 6 years
Therefore,.
A = 6000(1+0.06/4)^4 × 6
A = 6000(1+0.015)^24
A = 6000(1.015)^24
A = $8577
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠R.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠R = °
The measure of the angle R is [tex]m \angle R=69.4[/tex]
Explanation:
It is given that the lengths of the triangle are PQ = 8 and QR = 3
To find the angle of R using the opposite and adjacent side, we shall use the tangent formula.
[tex]\tan \theta=\frac{o p p}{a d j}[/tex]
where opp = 8 and adj = 3
Thus, substituting these values in the formula, we get,
[tex]\tan \theta=\frac{8}{3}[/tex]
Multiplying both sides by [tex]tan^{-1}[/tex], we get,
[tex]\theta=tan^{-1} (\frac{8}{3})[/tex]
Dividing, we get,
[tex]\theta=69.44[/tex]
Rounding off to the nearest tenth, we have,
[tex]\theta=69.4[/tex]
Thus, the measure of the angle R is [tex]m \angle R=69.4[/tex]
Find the exact value of tan A in simplest radical form.
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle,
AB represents the hypotenuse of the right angle triangle.
With m∠A as the reference angle,
AC represents the adjacent side of the right angle triangle.
BC represents the opposite side of the right angle triangle.
To determine tan m∠A, we would apply the tangent trigonometric ratio.
Tan θ = opposite side/adjacent side. Therefore,
Tan A = √32/2 = (√16 × √2)/2
Tan A = (4√2)/2
Tan A = 2√2
The value of tan A is in the simplest radical form [tex]2\sqrt{2}[/tex].
We have to determineThe exact value of tanA in the simplest radical form.
According to the question,The value of tan A is determined by using the formula;
The tangent is equal to the length of the side opposite the angle divided by the length of the adjacent side.[tex]\rm TanA = \dfrac{Perendicular}{Base}\\\\[/tex]
Where Perpendicular = [tex]\sqrt{32}[/tex] and Base = 2
Substitute all the values in the formula;
[tex]\rm TanA = \dfrac{Perendicular}{Base}\\\\TanA = \dfrac{\sqrt{32}}{2}\\\\TanA = \dfrac{4}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}\\\\TanA = 2\sqrt{2}[/tex]
Hence, The value of tan A is [tex]2\sqrt{2}[/tex].
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Given 10 < x + 12 Choose the solution set.
{x| x∈R, x > 2}
{x| x∈R, x < -2}
{x| x∈R, x > -2}
{x| x∈R, x < 2}
{x| x∈R, x > -4}
Answer:
{x| x∈R, x > -2}
Step-by-step explanation:
You solve the inequality just like you would solve an equality.
Everything that has the x on the left side, everything without x on the right side.
Be careful that when you multiply by -1, the inequality signal changes(for example, lesser than becomes higher than
So
[tex]10 < x + 12[/tex]
[tex]-x < 12 - 10[/tex]
[tex]-x < 2[/tex]
Multiplying by -1
[tex]x > -2[/tex]
So the correct answer is:
{x| x∈R, x > -2}
{x| x∈R, x > -2}
Step-by-step explanation:
You solve the inequality just like you would solve an equality.
Everything that has the x on the left side, everything without x on the right side.
Be careful that when you multiply by -1, the inequality signal changes(for example, lesser than becomes higher than
So
Multiplying by -1
So the correct answer is:
{x| x∈R, x > -2}
You use math in day-to-day routines when grocery shopping, going to the bank or mall, and while cooking. How do you imagine you will use math in your healthcare career?
Answer:
Use math in healthcare career: In healthcare career one must translate medication orders into the right doses and number of pills to administer.
Step-by-step explanation:
Consider the provided information.
Math in healthcare career play significant role one should must know the units of the measurement for temperature, blood pressure, pulse rate, breathing rate etc.
In healthcare career one must translate medication orders into the right doses and number of pills to administer.
For example, If a doctor recommends a 100 gram of a drug every 6 hours and the hospital has 50 milligram pills, then you need to give two pills every 6 hours. Because 50 milligram times 2 is 100 milligram.
Math is vital in a healthcare career for tasks such as dosage calculations, interpreting vital signs, and handling medical billing. Proper math skills ensure accuracy and safety. Mastery in math will enhance your ability to provide effective patient care.
You asked how you will use math in your healthcare career. Math is essential in healthcare for various day-to-day operations. Here are some specific examples:
Dosage Calculations: Nurses and pharmacists use arithmetic to calculate the correct dosages of medication for patients based on their weight and age. For instance, if a patient requires a dosage of 5 mg per kg of body weight and they weigh 70 kg, the total dosage would be 350 mg.Vital Signs: Medical professionals regularly monitor a patient's vital signs, such as heart rate, blood pressure, and respiratory rate. Understanding how to interpret these numbers often requires basic math skills to identify any abnormal trends and take appropriate actions.Medical Billing: Healthcare administrators use basic math when handling billing and insurance claims. Ensuring that the proper amounts are billed and received involves addition, subtraction, and sometimes percentages.Statistical Analysis: Research in healthcare often involves statistical analysis to determine the effectiveness of treatments. This requires knowledge of algebra and sometimes calculus to analyze data correctly.In conclusion, math is a vital skill in the healthcare field. Its applications range from dosage calculations to interpreting vital signs, and even handling billing. Mastery of math in your healthcare career will enable you to provide safe and effective patient care.
The following equation has denominators that contain variables. For this equation write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. Keeping the restrictions in mind, solve the equation.
2/x=4/5x+2
x=
Answer:
X = 3/5
Step-by-step explanation:
2/x=4/5x+2
Find the LCM of the denominator 5x and 1
2/x =4/5x + 2/1
2/x = (4 + 10x)/5x
Cross multiply the equation
2× 5x = (4+ 10x) × x
10x = 4x + 10x^2
Collect like term of the mixed number
10x - 4x = 10x^2
6x = 10x^2
Divide both side by 2x
6x/2x = {10x^2 } / 2x
3 = 5x
Divide both side by the coefficient of x
3/5 = 5x/5
X = 3/5
What is the angle measure 52∘48′51′′ equivalent to in decimal degrees? Enter your answer, rounded to the nearest thousandth of a degree, in the box.
Answer:
52.814 degrees
Step-by-step explanation:
we know that
[tex]1^o=60'\\1'=60''[/tex]
we have
[tex]52^o48'51''[/tex]
[tex]52^o48'51''=52^o+48'+51''[/tex]
Convert 51'' to minutes
[tex]51''=\frac{51}{60}= 0.85'[/tex]
[tex]52^o48'51''=52^o+48'+0.85'=52^o+48.85'[/tex]
Convert 48.85' to degrees
[tex]48.85'=\frac{48.85}{60}= 0.814^o[/tex]
[tex]52^o+48.85'=52^o+0.814^o=52.814^0[/tex]
Final answer:
The angle measure 52°48'51'' is equivalent to 52.814 degrees in decimal form when you convert the minutes and seconds to a decimal and add them to the degree part.
Explanation:
The angle measure 52°48'51'' equivalent to in decimal degrees is calculated by converting minutes and seconds to a decimal form. One degree equals 60 minutes, and one minute equals 60 seconds. To convert, divide the number of minutes by 60 and the number of seconds by 3600, then add those amounts to the degrees to get the decimal degree.
Starting with the minutes: 48 minutes / 60 = 0.8 degrees.
Now converting the seconds: 51 seconds / 3600 = approx. 0.014167 degrees.
So, adding these together: 52 + 0.8 + 0.014167 = 52.814167 degrees, which rounded to the nearest thousandth of a degree is 52.814.
Use two points on the like to find the equation of the line in standard form
Answer:
y=1/3x-1
Step-by-step explanation:
A(0,-1)=(x1,y1) x1=0,y1=-1
B(3,0)=(x2,y2) x2=3, y2=0
m=(y2-y1)/(x2-x1)
m=(0-(-1))/(3-0)
m=1/3
y-y1=m(x-x1)
y-(-1)=1/3(x-0)
y+1=1/3*x
y=1/3*x-1
last question and im not sure how to solve it?? pls help
Height of the rock wall is 52.2 ft.
Step-by-step explanation:
These two triangles are similar, so using the similarity ratio, we can write as,
Δ HTV ~ Δ JSV
Now we can write the ratio as,
HT/TV = JS/SV
5.8/4 = x/36
Rearranging the equation to get x as,
x = 36 × 5.8 /4
= 52.2 ft
A small business averages $5,500 per month in online revenue, plus another $300 per salesperson per month. Which graph shows all solutions for the number of salespeople who need to be working for the business to generate at least $7,300 in monthly revenue?
Answer:
Step-by-step explanation:
7,300 = 5,500 + 300x
7,300 - 5,500 = 300x
1,800 = 300x
x = 6
Answer:
greater than or equal to 6
Step-by-step explanation:
i just took the plato test
Let P(x) and Q(x) be predicates and suppose D is the domain of x. For the statement forms in each pair, determine whether (a) they have the same truth value for every choice of P(x), Q(x), and D, or (b) there is a choice of P(x), Q(x), and D for which they have opposite truth values.
∃x∈D,(P(x)∧Q(x))
(∃x∈D,P(x))∧(∃x∈D,Q(x))
Answer / Step-by-step explanation:
Given the statement:
∃x∈D,(P(x)∧Q(x)) and (∃x∈D,P(x))∧(∃x∈D,Q(x)) ,
Then,
(a), The variable used in a ∃ statement does not matter, thus, we can change the appearance of one of the variable used in the ∃ statement.
That is:
(∃x∈D,P(x))∧(∃x∈D,Q(x)) = (∃x∈D,P(x))∧(∃y∈D,Q(y))
Where
(∃x∈D,P(x))∧(∃x∈D,Q(x)) = (∃x∈D,P(x))∧(∃y∈D,Q(y)) implies that P(x) is true for some element x in D and Q(y) is true for some element y in D. However, x and y are not necessary the same element and thus, we cannot be sure that
P(x) ∧ Q(x) or P(y) ∧ Q(y) is true.
Moreover, if P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D, while x ≠ y,
Then, P(x) ∧ Q(x) is false and P(y) ∧ Q(y) is also false. Moreover, there is no other known element (z) such that P(z) ∧ Q(z) is true and thus the statement
∃x∈D,(P(x)∧Q(x)) is false while the statement (∃x∈D,P(x))∧(∃x∈D,Q(x)) is true.
(b)
If the statement P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D, while x ≠ y, then Then, P(x) ∧ Q(x) is false and P(y) ∧ Q(y) is also false. Moreover, there is no other known element (z) such that P(z) ∧ Q(z) is true and thus the statement
∃x∈D,(P(x)∧Q(x)) is false while the statement (∃x∈D,P(x))∧(∃x∈D,Q(x)) is true.
So in summary, we can say for:
(a) the statement does not contain the same truth value.
(b) The statement depicts there is such a choice in the first place.
In this exercise we have to use the knowledge of sets to identify which of the statements is true and false, thus we can state that:
A) the statement does not contain the same truth value.
B) The statement depicts there is such a choice in the first place.
Then, the first statement says that:
A)The variable used in a ∃ statement does not matter, thus, we can change the appearance of one of the variable used in the ∃ statement. That is:
[tex](\exists \ x \in D,P(x)) \wedge ( \exists \ x\in D,Q(x)) = (\exists \ x \in D,P(x)) \wedge (\exists \ y \in D,Q(y))[/tex]
Where the equation above implies that P(x) is true for some element x in D and Q(y) is true for some element y in D.
However, x and y are not necessary the same element and thus, we cannot be sure that is true.
If P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D. Then, [tex]P(x) \wedge Q(x)[/tex] is false and [tex]P(y) \wedge Q(y)[/tex] is also false.
B) If the statement P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D. Then, [tex]P(x) \wedge Q(x) \ or \ P(y) \wedge Q(y)[/tex] is also false.
Moreover, there is no other known element (z) such that is true and thus the statement.
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A 4-foot tall child walks directly away from a 12-foot tall lamppost at 2 mph. How quickly is the length of her shadow increasing when she is 6 feet away from the lamppost (rounded to the nearest tenth of a foot per second)
Answer:
The length of the shadow is increasing with the rate of 1.5 feet per sec
Step-by-step explanation:
Let AB and CD represents the height of the lamppost and child respectively ( shown below )
Also, let E be a point represents the position of child.
In triangles ABE and CDE,
[tex]\angle ABE\cong \angle CDE[/tex] ( right angles )
[tex]\angle AEB\cong \angle CED[/tex] ( common angles )
By AA similarity postulate,
[tex]\triangle ABE\sim \triangle CDE[/tex]
∵ Corresponding sides of similar triangles are in same proportion,
[tex]\implies \frac{AB}{CD}=\frac{BE}{DE}[/tex]
We have, AB = 12 ft, CD = 4 ft, BE = BD + DE = 6 + DE,
[tex]\implies \frac{12}{4}=\frac{6+DE}{DE}[/tex]
[tex]12DE = 24 + 4DE[/tex]
[tex]8DE = 24[/tex]
[tex]DE=3[/tex]
Now, the speed of walking = 2 mph = [tex]\frac{2\times 5280}{3600}\approx 2.933\text{ ft per sec}[/tex]
Note: 1 mile = 5280 ft, 1 hour = 3600 sec
Thus, the time taken by child to reach at E
[tex]= \frac{\text{Walked distance}}{\text{Walking speed}}[/tex]
[tex]=\frac{6}{2.933}[/tex]
= 2.045 hours
Hence, the change rate in the length of shadow
[tex]= \frac{\text{Length of shadow}}{\text{Time taken}}[/tex]
[tex]=\frac{3}{2.045}[/tex]
= 1.5 ft per sec.
When Akiko measured a rose, its height was 5.8 in. After 10 weeks, the height was 1 1/3 times the original height. What was the height of the rose after 10 weeks?
The solution is in the attachment
The height of the rose after 10 weeks was approximately 7.714 inches. This is calculated by multiplying the original height of the rose (5.8 inches) by 1 1/3 (converted to a decimal as 1.33).
Explanation:The subject of this question is Mathematics, and it involves performing multiplication to find the height of the rose after 10 weeks. Given that the height of the rose was 5.8 inches originally, and after 10 weeks, the height was 1 1/3 times the original height, we can calculate the new height as follows:
Convert 1 1/3 to a decimal. 1 1/3 equals 1.33 when converted to a decimal.Multiply the original height of the rose (5.8 inches) by 1.33 to get the new height after 10 weeks.So, 5.8 inches * 1.33 = 7.714 inches.
Therefore, the height of the rose after 10 weeks was approximately 7.714 inches.
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Consider the triangle graphed below. Classify it by its angles.
Answer:
The answer to your question is right
Step-by-step explanation:
Acute is a triangle in which three internal angles are acute (less than 90°). The other angles measure 90°, so this option is incorrect.
Obtuse is a triangle that has one angle greater than 90°. This option is incorrect because of the angles of this triangle measure 30, 60, 90.
Equiangular is a triangle in which angles measures the same. This option is wrong because the angles have different values.
A Right triangle is a triangle that has an angle that measures 90°. This option is right.
A rectangle initially has width 7 meters and length 10 meters and is expanding so that the area increases at a rate of 8 square meters per hour. If the width increases by 40 centimeters per hour how quickly does the length increase initially
Final answer:
The length of the rectangle increases at a rate of 4/7 meters per hour (approximately 0.57 m/h) initially when the area is increasing at 8 square meters per hour and the width at 0.4 meters per hour.
Explanation:
To find how quickly the length of the rectangle increases, given that the area increases at a rate of 8 square meters per hour and the width increases by 40 centimeters (0.4 meters) per hour, we can use the area formula for a rectangle (Area = length × width). The rate of change of the area with respect to time (ΔA/Δt) can be related to the rates of change of the length and width with respect to time (ΔL/Δt and ΔW/Δt respectively) by the product rule for differentiation if we consider length and width as functions of time.
Initially, the area A is 10m × 7m = 70m². When the area is increasing at 8m²/h and the width is increasing at 0.4m/h, we can write the relation as follows:
ΔA/Δt = ΔL/Δt × W + L × ΔW/Δt
Substituting the given values and solving for the rate of change of the length (ΔL/Δt):
8 = ΔL/Δt × 7 + 10 × 0.4
8 = 7ΔL/Δt + 4
7ΔL/Δt = 4
ΔL/Δt = 4/7 m/h
Therefore, the length increases at a rate of 4/7 meters per hour (approximately 0.57 m/h) initially.
Which expression is equivalent to RootIndex 4 StartRoot x Superscript 10 Baseline EndRoot? x squared (RootIndex 4 StartRoot x squared EndRoot) x2.2 x cubed (RootIndex 4 StartRoot x EndRoot) x5
Answer:
The option x squared ( root index 4 start root x squared end root) is correct
Therefore the equivalent expression to the given expression is [tex]x^2\sqrt[4]{x^2}[/tex]
Step-by-step explanation:
Given expression is [tex]\sqrt[4]{x^{10}}[/tex]
To find the equivalent expression to the given expression :
[tex]\sqrt[4]{x^{10}}[/tex]
[tex]=\sqrt[4]{x^{8+2}}[/tex]
[tex]=\sqrt[4]{x^8.x^2}[/tex] ( using the property [tex]a^m.a^n=a^{m+n}[/tex] )
[tex]=\sqrt[4]{x^{2\times 4}.x^2}[/tex]
[tex]=\sqrt[4]{(x^2)^4x^2}[/tex] ( using the peoperty [tex]a^{mn}=(a^m)^n[/tex] )
[tex]=\sqrt[4]{(x^2)^4}\times \sqrt[4]{x^2}[/tex] ( using the property [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex] )
[tex]=x^2\sqrt[4]{x^2}[/tex]
Therefore [tex]\sqrt[4]{x^{10}}=x^2\sqrt[4]{x^2}[/tex]
Therefore the equivalent expression to the given expression is [tex]x^2\sqrt[4]{x^2}[/tex]
The option "x squared (RootIndex 4 StartRoot x squared EndRoot)" is correct
That is [tex]x^2\sqrt[4]{x^2}[/tex] is correct
Answer:
the correct answer is A
Step-by-step explanation:
hope this helped
Worth 50 points and I will mark brainliest.
Use the linear combination method to solve the system of equations. Justify each step of your solution. Please explain the steps you used so I could learn.
-3x-7y= -28
2x+3y=7
Answer:
x= -13 , y=11
Step-by-step explanation:
Using elimination method, make the x variable equal to eliminate the variable
-3x - y = -28
2x+ 3y=7
2(-3x-y =28)
3(2x+3y=7)
-6x - 2y =56
6x +9y=21
Apply addition
7y = 77
y=77/7 = 11
Use the value of y=11 in
2x+ 3y=7
2x +3(11) =7
2x +33 =7
2x=7-33
2x= -26
x= -26/2 = -13
Learn More
Solving simultaneous equations :https://brainly.com/question/12318095
Keywords ; linear combination method,equations, justify,steps
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Martha has 8 cubic feet ofputting soil in the three flowerpots she wants to put the same amount of soil in each pot how many cubic feet of soil she put in each flower pot
Answer:
[tex]2\frac{2}{3}\text{ ft}^3\approx 2.67\text{ ft}^3[/tex]
Step-by-step explanation:
We have been given that Martha has 8 cubic feet of putting soil in the 3 flowerpots. She wants to put the same amount of soil in each pot.
To find the amount of soil in each pot, we need to divide total soil (8 cubic feet) by number of pots (3) as shown below:
[tex]\text{Amount of soil in each pot}=\frac{8\text{ ft}^3}{3}[/tex]
[tex]\text{Amount of soil in each pot}=2\frac{2}{3}\text{ ft}^3[/tex]
[tex]\text{Amount of soil in each pot}=2.6666\text{ ft}^3[/tex]
[tex]\text{Amount of soil in each pot}\approx 2.67\text{ ft}^3[/tex]
Therefore, Martha needs to put approximately 2.67 cubic feet of soil in each flower pot.
To determine the amount of soil Martha puts in each flowerpot, divide the total cubic feet of soil (8) by the number of flowerpots (3), which results in approximately 2.67 cubic feet of soil per pot.
Explanation:The question pertains to the division of cubic feet of soil into equal amounts across three flowerpots. To find out how many cubic feet of soil Martha should put in each flower pot, we simply divide the total amount of soil by the number of flowerpots. In this case, Martha has 8 cubic feet of soil to distribute evenly into 3 pots.
The calculation would be as follows:
Determine the total volume of soil available: 8 cubic feet.Count the number of flowerpots: 3.Divide the total volume of soil by the number of pots to get the amount of soil per pot: 8 cubic feet ÷ 3 pots = 2.67 cubic feet per pot.Therefore, Martha can put approximately 2.67 cubic feet of soil in each flower pot.
In this year’s
7
th
7th
grade class, there are 4 boys for every 5 girls. How many girls are in the class if there are 20 boys in the class?
Answer:
The answer to your question is 25 girls
Step-by-step explanation:
Data
4 boys for every 5 girls
20 boys ? number of girls
To solve this problem use proportions
Number of boys : Number of girls :: New number of boys : New number of
girls
Substitution
4 : 5 :: 20 : x
Solve for x
x = (5 x 20) / 4
Simplification
x = 100 / 4
Result
x = 25
There are 25 girls
The manufacturer of a CD player has found that the revenue R (in dollars) is Upper R (p )equals negative 5 p squared plus 1 comma 550 p comma when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar? A. $961 comma 000
Answer:
The maximum revenue is $1,20,125 that occurs when the unit price is $155.
Step-by-step explanation:
The revenue function is given as:
[tex]R(p) = -5p^2 + 1550p[/tex]
where p is unit price in dollars.
First, we differentiate R(p) with respect to p, to get,
[tex]\dfrac{d(R(p))}{dp} = \dfrac{d(-5p^2 + 1550p)}{dp} = -10p + 1550[/tex]
Equating the first derivative to zero, we get,
[tex]\dfrac{d(R(p))}{dp} = 0\\\\-10p + 1550 = 0\\\\p = \dfrac{-1550}{-10} = 155[/tex]
Again differentiation R(p), with respect to p, we get,
[tex]\dfrac{d^2(R(p))}{dp^2} = -10[/tex]
At p = 155
[tex]\dfrac{d^2(R(p))}{dp^2} < 0[/tex]
Thus by double derivative test, maxima occurs at p = 155 for R(p).
Thus, maximum revenue occurs when p = $155.
Maximum revenue
[tex]R(155) = -5(155)^2 + 1550(155) = 120125[/tex]
Thus, maximum revenue is $120125 that occurs when the unit price is $155.
Alex has a truck. 42% of the miles he drove last month were for work. If Alex drove 588 miles for work, how many miles did he drive last month all together? A) 1,200 B) 1,400 C) 1,600 D) 1,800
Answer:
He drive 1,400 miles last month all together.
So, option B) 1,400 is the correct answer.
Step-by-step explanation:
Given:
Alex has a truck. 42% of the miles he drove last month were for work.
If Alex drove 588 miles for work.
Now, to find miles he drive last month all together.
Let the miles he drive last month all together be [tex]x.[/tex]
42% of the miles he drove last month were for work.
Alex drove 588 miles for work.
Now, to get the miles he drive last month all together we put an equation:
[tex]42\%\ of\ x=588[/tex]
[tex]\frac{42}{100} \times x=588[/tex]
[tex]0.42\times x=588[/tex]
[tex]0.42x=588[/tex]
Dividing both sides by 588 we get:
[tex]x=1400\ miles.[/tex]
Therefore, he drive 1,400 miles last month all together.
So, option B) 1,400 is the correct answer.
Answer:
The answer is 1,400
Step-by-step explanation: If you do 1,400x42%=588 So the answer is 1400!!!!!