The graph of y =ex is transformed as shown in the graph below. Which equation represents the transformed function?

Answer: \(\dfrac15\)

Step-by-step explanation:

Given : A cloth bag contains 6 cards numbered 1 through 6. Two cards are drawn without replacement.

Favorable outcome: sum of the numbers on the two drawn cards is 7

Since 1+6 = 7 , 2+5=7, 4+3 = 7

So, sum of 7 can be obtained as (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)

Probability of getting (first 1, second 6) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 2, second 5) = (\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 3, second 4) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 4, second 3) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 5, second 2) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 6, second 1) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Required probability =\(6\times\dfrac{1}{30}=\dfrac15\)

Hence, the required probability = \(\dfrac15\)

Answer:

49

Step-by-step explanation:

Answer:

The answer is 49 :)

Step-by-step explanation:

The expensive a car that you can afford is $42666.42.

What is interest rates?

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).

Given that you can deposit $325 each month. The interest rates is 4.25%.

Future Value of an Ordinary Annuity

\(S = R[\frac{(1+i)^n-1}{i}]\)

where

S is the future value;

R is the periodic payment;

i is the interest rate per period;

n is the number of periods.

The value of R is $325, i = 0.0425/12 = 0.00354

n = (12 × 9) =108

The future value is

\(S = 325[\frac{(1+0.00354)^{108}-1}{0.00354}]\)

S = 42666.42

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Answer:

C. 360-85=12h

Step-by-step explanation:

360=85+12h

360-85=12h

Answer:

Step-by-step explanation:

Slope of the line:

\(m = \frac{y-y1}{x-x1} \\\)

Given:

slope = -3/4

point (x1,y1) = (2, -1)

Substitute and solve

\(m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0\)

1/2 is the y-intercept

(0,1/2)

Since we have 2 points already, we can then graph the line.

(2, -1) and (0, 1/2)

In terms of measures of spread, Group B has a wider IQR than Group A

The comparative dot plots show the points scored in a game by two groups, Group A and Group B. Both groups have a similar spread, with most of the dots clustered around the middle of the distribution. However, there are some differences in the tails of the distribution that affect the measures of spread.

For Group A, the lowest score is 41, and the highest score is 50. The interquartile range (IQR), which is the range containing 50% of the scores, is approximately from 45 to 48. The range, which is the difference between the highest and lowest scores, is 9.

For Group B, the lowest score is 41, and the highest score is 50. The interquartile range (IQR) is approximately from 43 to 49. The range is also 9.

This indicates that Group B has a more variable distribution of scores within the middle 50% of the distribution, indicating a more variable distribution of scores within the middle.

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Answer:

---------------------------

There are two triangular faces with base of 16 cm and height of 15 cm and three rectangular faces.

Find the sum of areas of all five faces:

Answer:

he fraction 8/12 simplified is equal to 2/3.

Step-by-step explanation:

The solution to this problem can be found by first figuring out the greatest common denominator between.

The given conclusion "(x + 2)² = (x² + 2)" is false.

The two set representation methods are -

Given is the set A{1, 2, 3}.

(x + 2)² should be equal to (x² + 2) for all x ∈ A.

We can write -

(1 + 2)² = 1² + 2

9 ≠ 3

Therefore, the given conclusion "(x + 2)² = (x² + 2)" is false.

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{Question in english -

For all x in A: {1, 2, 3}, (x + 2)² is equal to (x² + 2). True or false?}

Answer:

- \(\frac{9}{10}\) > - \(\frac{10}{10}\)

Step-by-step explanation:

Which number is closer to 0, meaning that number is bigger.

-9/10 = -0.9

-10/10 = -1

We see -0.9 is closer to 0, meaning it is bigger.

So,  - \(\frac{9}{10}\) > - \(\frac{10}{10}\)

Answer:

9.5 seconds pass before the object reaches the ground.

Step-by-step explanation:

Height of the ball:

The height of the ball after t seconds is given by the following equation:

\(h(t) = -16t^2 + 1444\)

Find how many seconds pass before the object reaches the ground.

This is t for which h(t) = 0. So

\(h(t) = -16t^2 + 1444\)

\(-16t^2 + 1444 = 0\)

\(16t^2 = 1444\)

\(t^2 = \frac{1444}{16}\)

\(t^2 = 90.25\)

\(t = \pm \sqrt{90.25}\)

Since it is time, we only take the positive value.

\(t = 9.5\)

9.5 seconds pass before the object reaches the ground.

Answer:

Step-by-step explanation:

Price:

Equations:

Multiply the first equation by 5 and the second equation by 2 and subtract to eliminate x:

Use the first equation to find x:

Iced tea costs $4.50 per gallon

Lemonade costs $4.75 per gallon

The reflection of the point (–4, 6) across both axes is (b) (4, -6)

From the question, we have the following parameters that can be used in our computation:

Point = (-4, 6)

The rule of reflections across both axes is

(x, y) = (-x, -y)

Using the above as a guide, we have the following:

Image = (4, -6)

Hence, the reflection of the point (–4, 6) across both axes is (b) (4, -6)

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Step-by-step explanation:

There are a total of 4 numbers to pick.

P(9) means is the probability of you picking the number 9.

Since you are only picking one number, the probability will be 1/4 or 0.25

Answer

volume = 416 cubic ft

Explanation:

Parameters of the top prism

Lenght = 4 ft

Height = 16 ft

width = 4 ft

Parameters of the bottom prism

Length = 4 ft

width = 10 ft

Height = 4 ft

The final amount momentum of the t-shirt is 17.5 kg⋅m/s, which is the sum of the initial momentum of the t-shirt (2 kg⋅m/s) and the change in momentum (15.5 kg⋅m/s) due to the force applied.

The final amount momentum of the t-shirt is 17.5 kg⋅m/s, which is calculated by summing the initial momentum of the t-shirt (2 kg⋅m/s) and the change in momentum (15.5 kg⋅m/s) due to the force applied. Momentum is a vector quantity which is equal to the product of the mass and velocity of an object. In this case, the t-shirt has a mass of 4 kg and a velocity of 4 m/s. The force of 15 N applied to the t-shirt for 3 seconds causes the t-shirt to accelerate, increasing its velocity from 4 m/s to 8 m/s. This increase in velocity results in an increase in the momentum of the t-shirt from 2 kg⋅m/s to 17.5 kg⋅m/s. Thus, by calculating the change in momentum due to the applied force, we can determine the final momentum of the t-shirt.

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Use reduction of order. Given a solution \(y_1(x) = x^2\), look for a second solution of the form \(y_2(x) = y_1(x)v(x)\).

Compute the first two derivatives of \(y_2(x)\):

\(y_2 = x^2v \\\\ {y_2}' = x^2v' + 2xv \\\\ {y_2}'' = x^2v''+4xv' + 2v\)

Substitute them into the ODE:

\(x^4 (x^2v'' + 4xv' + 2v) + x^3 (x^2v' + 2xv) - 4x^2 (x^2v) = 1 \\\\ x^6v'' + 5x^5v' = 1\)

Now substitute \(w(x) = v'(x)\) and you end up with a linear ODE:

\(x^6w'+5x^5w=1\)

Multiply through both sides by \(\frac1x\) (if you're familiar with the integrating factor method, this is it):

\(x^5w'+5x^4w = \dfrac1x\)

Bear in mind that in order to do this, we require \(x\neq0\). Just to avoid having to deal with absolute values later, let's further assume \(x>0\).

Notice that the left side is the derivative of a product,

\(\left(x^5w\right)' = \dfrac1x\)

Integrate both sides with respect to \(x\) :

\(x^5w = \displaystyle \int\frac{\mathrm dx}x \\\\ x^5w = \ln(x) + C_1\)

Solve for \(w(x)\) :

\(w = \dfrac{\ln(x)+C_1}{x^5}\)

Solve for \(v(x)\) by integrating both sides:

\(v = \displaystyle \int \frac{\ln(x)+C_1}{x^5} \,\mathrm dx\)

Integrate by parts:

\(\displaystyle f = \ln(x) + C_1 \implies \mathrm df = \frac{\mathrm dx}x \\\\ \mathrm dg = \frac{\mathrm dx}{x^5} \implies g = -\frac1{4x^4} \\\\ \implies v = -\frac{\ln(x)+C_1}{4x^4} + \frac14 \int \frac{\mathrm dx}{x^5} \\\\ v = -\frac{\ln(x)+C_1}{4x^4} - \frac1{16x^4} + C_2 \\\\ v = -\frac{4\ln(x)+C_1}{16x^4}+C_2\)

Solve for \(y_2(x)\) :

\(\displaystyle \frac{y_2}{x^2} = -\frac{4\ln(x)+C_1}{16x^4}+C_2 \\\\ y_2 = -\frac{4\ln(x)+C_1}{16x^2} + C_2x^2\)

But since \(y_1(x)=x^2\) is already accounted for, the second solution is just

\(\displaystyle y_2 = -\frac{4\ln(x)+C_1}{16x^2}\)

Still, the general solution would be

\(\displaystyle \boxed{y(x) = -\frac{4\ln(x)+C_1}{16x^2} + C_2x^2}\)

Answer:

SAS

Step-by-step explanation:

edg

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

Answer:

28. B

29. D

30. A

Step-by-step explanation:

28.

2 5/8 yd × 5/6 yd =

= 21/8 × 5/6 yd²

= 105/48 yd²

= 35/16 yd²

= 2 3/16 yd²

Answer: B

29.

2641 becomes 6241.

In 6241, the 6 is in the thousands place.

6 × 1000 = 6000

Answer: D

30.

90 + 7 × (7 - 1) =

Use the correct order of operations.

= 90 + 7 × 6

= 90 + 42

= 132

Answer: A

a. To create a pie chart to show the total medal winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games:

Obtain the data for the medal winnings of the Top 10 NOCs

Calculate the total medal winnings for each NOC (i.e., the sum of gold, silver, and bronze medals)

Create a pie chart in Excel or any other software by selecting the data and choosing the pie chart option

Add a title and labels to the chart to show the NOCs and their corresponding medal winnings

b. The interpretation of the pie chart produced in Question 8a) depends on the shape and distribution of the chart. Two probable justifications for the behavior of the data are:

Dominance of certain NOCs: The pie chart may show that certain NOCs have a significantly higher share of medal winnings compared to others. This may be due to the dominance of these NOCs in specific sports or events, or due to their superior training and preparation.

Balanced distribution of medals: The pie chart may show a relatively balanced distribution of medal winnings among the Top 10 NOCs. This may indicate a high level of competitiveness and equal opportunities for success among the NOCs.

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Answer:

50.24 feet^2

Step-by-step explanation:

let radius of the basketball court be r feet.

circumference = 2 x 3.14 x r

25.12 = 6.28r

r = 4

therefore, area = 3.14 x 4^2 = 50.24feet^2

Topic: Mensuration (Properties of circles)

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Answer:

area is 50.24 feet^2

Step-by-step explanation:

Circumference of the logo=25.12

2πr=25.12

r=25.12/(2×3.14)

r=25.12/6.28

r=4feet

So area of logo=πr^2

=3.14×4×4

=3.14×16

=50.24feet^2

So the area is 50.24 feet^2

Answer:

<

Step-by-step explanation:

Inequality symbols:

<     less than

>     greater than

=     equal to

≤     less than or equal to

≥     greater than or equal to

In this case, it is known that -4 is less than 5, or:

-4 < 5.

~

Answer:

>

Step-by-step explanation:

because 5 is bigger than -4

Answer:

$42.00

Step-by-step explanation:

We can represent the given information as a ratio:

% of original price : price

                          5% : $2.00

Then, we can multiply both sides of this ratio by 20 (or 100% / 5%) to get 100% of the original price, which IS the original price.

5%      :  $2.00

↓ × 20   ↓ × 20

100%  :  $40.00

Now that we know the original price, we can add $2.00 to get the new price.

$40.00 + $2.00 = $42.00

Part A

For Todd's class, we have this given info:

Compute the z score for x = 74.6

z = (x-mu)/sigma

z = (74.6 - 70.6)/(11.9)

z = 0.34 approximately

Side note: Convention usually has z scores rounded to two decimal places. If your teacher instructs otherwise, then go with those instructions of course.

======================================================

Part B

For Garret's English class, we have:

Compute the z score for x = 68.8

z = (x-mu)/sigma

z = (68.8 - 63.7)/(8.6)

z = 0.59 approximately

======================================================

Part C

Garret has the higher z score, which means that Garret did relatively better to his classmates compared to Todd's performance (in relation to his classmates). The z score is the distance, in units of standard deviation, the score is from the mean. Positive z values are above the mean, while negative z values are below the mean.

Answer:

150

Step-by-step explanation:

Hello !

68/17 = 4

=> yes for 68

84/17 = 4.941...

=> no for 84

357/17 = 21

=> yes for 357

1001/17 = 58.882...

=> no for 1001