In the relationship below, the color of the circle changes according to the
height of the rectangle. Which expression below is the best choice to
describe this relationship in function notation?
A. H (c)
B. R (h)
C. C (h)

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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Answer:

y = 15x

Step-by-step explanation:

If A is:

y = 30x

Then the gradient is 30, a higher gradient would be steeper or more vertical;

A lower gradient would be more shallow or more horizontal;

A is steeper than B, therefore the gradient of B must be lower;

If the two options are 15 and 60, the answer will be 15 since it is the one that is less than 30

If the data were graphed with x on the horizontal axis and y on the vertical axis, this would be the approximate slope of the line between points C and D.

E. 0.17

The approximate slope between points C and D can be calculated by taking the difference in the y-values (9-15) and dividing it by the difference in the x-values (4-2). This yields a slope of -0.17.

The approximate slope between points C and D can be determined by first calculating the change in y-values (9-15) and the change in x-values (4-2). Then, the change in y-values is divided by the change in x-values to calculate the slope. In this case, the slope is -0.17. This means that for every unit of increase in x-values, the corresponding y-values decrease by 0.17. If the data were graphed with x on the horizontal axis and y on the vertical axis, this would be the approximate slope of the line between points C and D.

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Answer:

-17/32

this is the answer I got

The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

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Answer:

D. is correct.

\(2 * 1 = 2\)

\(4 * 1=4\)

\(4 + 2 = 6\)

________________________________________________________

The product of answer choice D.(6) is not equal to the product of \(\frac{2}{3}\) × 4, because \(\frac{2}{3}\) × 4 is actually \(2\frac{2}{3}\)

________________________________________________________

We learned how to find whole numbers through an expression with fractions.

Questions related to the topic? Ask me in the comments box.

Answer:

The median is going to be 7

Answer:

There are two, the first one is 4 and the second is 132

Step-by-step explanation:

36 divided by 3 is 12, so 48 divided by 12 would give us the answer 4. In the last one, you multiply 11 by 12 instead.

Step-by-step explanation:

the second one is 132 uuwwuu

Answer:

Step-by-step explanation:

You want the coordinates of the vertices of QRST after it has been translated right 2 units, then reflected across the y-axis. The original coordinates are Q(1, 5), R(3, -1), S(0, 0), T(-2, 3).

The problem statement is written as a composition of the transformations Ry and T(2,0). A composition of functions is generally executed right to left, meaning the translation will be done first, then the reflection.

The numbers in the translation vector are added to the coordinates:

  (x, y) ⇒ (x+2, y+0)

Reflection over the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

Then the composition of transformations is ...

  (x, y) ⇒ (-(x+2), y)

  Q(1, 5) ⇒ Q'(-3, 5)

  R(3, -1) ⇒ R'(-5, -1)

  S(0, 0) ⇒ S'(-2, 0)

  T(-2, 3) ⇒ T'(0, 3)

Answer:

Unlabeled side length = 15.00 units

Step-by-step explanation:

Because this is a right triangle, we can find the unlabeled side length using the Pythagorean theorem, which is

a^2 + b^2 = c^2, where

In the triangle, we're given that the legs are 12 and 9 units and the unlabeled side is the hypotenuse, which we must find:

Step 1:  Plug in 12 for a and 9 for b and simplify:

12^2 + 9^2 = c^2

144 + 81 = c^2

225 = c^2

Step 2:  Take the square root of both sides to solve for c, the hypotenuse (aka the unlabeled side):

± √225 = √(c)^2

± 15 = c

15.00 units = c

Although taking the square root of a number produced both a positive and negative answer since squaring both a positive and negative answer gives us a positive answer (e..g, 15 * 15 = 225 and -15 * -15 = 225), you can't have a negative measure.  Therefore, c, the unlabeled side length = 15.00 units.

The actual consumer spending at a price of $27 per unit is $268.26.

Substitute the given price into the supply equation to get the corresponding quantity supplied:

p = q + 10

27 = q + 10

q = 17

Substitute q = 17 into the demand equation to get the corresponding price:

4q² + p² = 1405

4(17)² + p² = 1405

p² = 1405 - 1156

p² = 249

p = 15.78

The actual consumer spending can be calculated by multiplying the quantity demanded by the price:

Actual consumer spending = quantity demanded x price per unit

= 17 x 15.78

= $268.26

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The demand and supply equations for a certain product are given by space 4 q squared plus p squared equals 1405 and p equals q plus 10 where p is in dollars per unit and q is in units. For a price of $27 per unit, determine the actual consumer spending.

Yes, the situation represents the function, with x as independent variable and y as dependent variable of y=2x.6 stacks of points then domain is 6 and codomain is 12.

A relation is a function if it has only One y-value for each x-value.

Given,

We arrange coins in stacks so that each stack has twice as many coins as the previous stack.

If the first stack has 2 coins

Yes the situation represent a function,

y=2x

y represents the number of coins in stack 2. and x represent the number of coins in first stack.

Here x is independent variable and y is dependent variable.

We have 6 stack coins then it has 12 coins in second stack.

6 is the domain and 12 is the codomain of the function.

Hence the situation represents the function, with x as independent variable and y as dependent variable of y=2x.6 stacks of points then domain is 6 and codomain is 12.

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The number 2755 flights were scheduled.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Recently many airlines have had to cancel flights in a single day.

Republic airlines had to cancel 416 flights representing 15.1% of the airlines' scheduled flights.

The number of flights scheduled,

= 416 x 100/ 15.1

= 41600/15.1

= 2754.96

≈ 2755

Therefore, 2755 flights were scheduled.

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Answer:

22 1/2

Step-by-step explanation:

There are 12 lowercase words of length 8 in which each distinct letter appears exactly twice.

To form a lowercase word of length 8 in which each distinct letter appears exactly twice, we can choose 4 distinct letters from the English alphabet and then arrange them in pairs in the word. The number of ways to choose 4 distinct letters from 26 is:

C(26, 4) = 26! / (4! * 22!) = 14,950

Once we have chosen 4 distinct letters, we can arrange them in pairs in the word in the following way:

Therefore, the total number of such words is:

4 * 3 * 1 = 12

Thus, there are 12 lowercase words of length 8 in which each distinct letter appears exactly twice. Here are all the possible words:

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Answer: (4.01, -3.05)

Step-by-step explanation:

Use the midpoint formula (x1+x2/2,y1+y2/2)

-3.1 + -4.92 /2 =4.01

-2.8 + -3.3 /2 = -3.05

(4.01, -3.05)

Answer: the standard form of the equation of the line is -3x + 2y = -4.

Step-by-step explanation:

The slope-intercept form of the equation of a line is given by: y = mx + b, where m is the slope of the line and b is the y-intercept.

In this case, the slope is 3/2 and the y-intercept is -2. So we can write the equation in slope-intercept form as:

y = (3/2)x - 2

To convert this equation to standard form, we want to write it in the form Ax + By = C, where A, B, and C are constants. To do this, we can start by multiplying both sides of the equation by 2 to get rid of the fraction:

2y = 3x - 4

Next, we can rearrange the terms to get all the variables on one side and the constants on the other:

-3x + 2y = -4

So the standard form of the equation of the line is -3x + 2y = -4

Hence, the value of the expression \(t+4+3-2.2t\) is \(-2.1875\).

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

The equation is \(t+4+3-2.2t\)

So,

\(t+4+3-2.2t=0\\\\3.2t+7=0\\\\3.2t=-7\\\\t=\frac{-7}{3.2}\\\\t=-2.1875\)

Hence, the value of the expression \(t+4+3-2.2t\) is \(-2.1875\).

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Answer:

Step-by-step explanation:

Answer:

X ≥ 3   (D)

Step-by-step explanation:

I got it right on Khan Academy :)

Two workers finished a job in 7.5 days.

How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

let t = time required by one worker to complete the job alone

then

(t+8) = time required by the other worker (shirker)

let the completed job = 1

A typical shared work equation

7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1

multiply by t(t+8), cancel the denominators, and you have

7.5(t+8) + 7.5t = t(t+8)

7.5t + 60 + 7.5t = t^2 + 8t

15t + 60 = t^2 + 8t

form a quadratic equation on the right

0 = t^2 + 8t - 15t - 60

t^2 - 7t - 60 = 0

Factor easily to

(t-12) (t+5) = 0

the positive solution is all we want here

t = 12 days, the first guy working alone

then

the shirker would struggle thru the job in 20 days.

Answer:7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days. Hope this helps! jul15

Step-by-step explanation:

Answer:

B. 11/7

Step-by-step explanation:

Use rise over run, (y2 - y1) / (x2 - x1)

Plug in the points:

(y2 - y1) / (x2 - x1)

(-4 - 7) / (-5 - 2)

-11 / -7

= 11/7

Answer:

a) 0.0465 = 4.65% probability that in one upperclassman House at MIT, enough students are vaccinated to achieve herd immunity.

b) \(1.02 \times 10^{-16}\) probability that herd immunity is achieved in all 12 Houses.

c) We needed that \(np \geq 10, n(1-p) \geq 10\), which was achieved.

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution, normal probability distribution and the central limit theorem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

For a proportion p in a sample of size n, as long as \(np \geq 10, n(1-p) \geq 10\) the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

a) Suppose that 94% of undergraduate students in the United States report having received two doses of the MMR vaccine. What is the probability that in one upperclassman House at MIT, enough students are vaccinated to achieve herd immunity? There are approximately 400 students in any house.

We have that \(p = 0.94, n = 400\). So

\(np = 400*0.94 = 376 \geq 10\)

\(n(1-p) = 400*0.06 = 24 \geq 10\)

The standard deviation is:

\(s = \sqrt{\frac{0.94*0.06}{400}} = 0.0119\)

The probability is 1 subtracted by the pvalue of Z when X = 0.96. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.96 - 0.94}{0.0119}\)

\(Z = 1.68\)

\(Z = 1.68\) has a pvalue of 0.9535

1 - 0.9535 = 0.0465 = 4.65% probability that in one upperclassman House at MIT, enough students are vaccinated to achieve herd immunity.

b) Calculate the probability that herd immunity is achieved in all 12 Houses.

Now, we use the binomial distribution. This is \(P(X = 12)\) when \(n = 12\) with \(p = 0.0465\). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 12) = C_{12,12}.(0.0465)^{12}.(0.9535)^{0} = 1.02 \times 10^{-16}\)

\(1.02 \times 10^{-16}\) probability that herd immunity is achieved in all 12 Houses.

c) Discuss the validity of the assumptions required to make the calculation in part i.

We needed that \(np \geq 10, n(1-p) \geq 10\), which was achieved.

The number of watts will be 4700 watts to the nearest 100 watt.

It should be noted that 1 watt equals to 3.41 Btu per hour.

In this case, the air conditioner is rated at 16000 BTU per hour.

Therefore, the number of watt will be:

= 16000/3.41.

= 4692

= 4700 watts to the nearest 100 watt.

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Answer:

10

Step-by-step explanation:

using HYPOTHENUS theorem

8^2 + 6^2 = x^2

64 + 36= 100

√100=10

Answer:

10

Step-by-step explanation:

pythagros theorem

8 time 8 is 64

and

6 time 6 is 36

add them up we have

100

square root of 100 is 10

so the answer is 10

ur. welcome

Step-by-step explanation:

\(( \: n - 1) \times (n + 1) \times \: ( {n }^{ 2 - 2)} \)

Please find attached photograph for your answer.

Hope it helps.

Do comment if you have any query.

The value of the car after 3 years is $79, 000

To determine the value, we have to use the formula;

Value = Initial value × (1 - Depreciation rate)ⁿ

Substitute the values given, we get;

Remaining value after 3 years = $100,000 × (1 - 0.10)³

Expand the bracket, we get;

Value after 3 years = $100,000 × (0.90)³

Find the cube value and substitute, we have;

Value after 3 years = $100,000 × 0.729

Multiply the values, we have;

Value after 3 years = $72,900

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Given:

Price of car = $32,000

Sales tax = 8%

To find:

The price of car including sales tax.

Solution:

We have,

Price of car = $32,000

Salas tax = 8%

Amount of sales tax = 8% of price of car

\(\text{ Sales Tax}=\dfrac{8}{100}\times 32000\)

\(\text{Sales Tax}=2560\)

Now,

Total price of car including tax = Price of car + Sales tax

\(\text{Total price of car including tax}=32000+2560\)

\(\text{Total price of car including tax}=34560\)

Therefore, the price of car including tax is $34560.