Whats your favorite dog breed...?

(a) The probability that at most 8 involve a single vehicle = 0.057

(b) The probability that exactly 8 involve a single vehicle = 0.035

(c) The probability that exactly 10 involve multiple vehicles = 0.117

(d) The probability that between 5 and 8, involve a single

vehicle = 0.056

(e) The probability that at least 5 involve a single vehicle = 1

(f) The probability exactly 8 involve a single vehicle and the other 12 involve multiple vehicles = 0.035

Probability is defined as the ratio of favorable outcomes to all other possible outcomes of an event. For an experiment with 'n' number of outcomes, the symbol x can be used to indicate the number of excellent outcomes. The probability formula is as follows:

x/n, where Probability is Favorable Outcomes/Total Results (Event).

Now, P = 0.6

n = 20

x ≅ Binomial (20; 0.6)

P(x) = (nx) Px q n-x

Now, at most 8 involve a single vehicle is:

P (x ≤ 8) = 0.057

Again, exactly 8 involve a single vehicle is:

P (x =8) = 0.035

Now exactly 10 involve multiple vehicles is:

P (x = 10) = 0.117

Similarly, between 5 and 8, involve a single vehicle is:

P (5 ≤ x ≤ 8) = 0.056

The probability of at least 5 involve a single vehicle is:

P (x ≥ 5) = 1

The probability that 8 involve a single vehicle and the other 12 in multiple vehicles is:

P (x = 8) = 0.035

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Answer:

0.25

Step-by-step explanation:

The cost per ounce of candy can be calculated by dividing the total cost of the box by the number of ounces in the box. Since 1 pound equals 16 ounces, the cost per ounce is $4.00 / 16 ounces = $0.25 per ounce.

So the cost per ounce of candy is $0.25.

Answer: 16/1 16x4 = 64/4

The value of the equation f ( x ) is

f ( x ) = x³ + x² - 8x - 12

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = ( x + 2 )²( x -3 )   be equation (1)

Now , on simplifying the equation , we get

f ( x ) = ( x + 2 )²( x -3 )

f ( x ) = ( x² + 4x + 4 ) ( x - 3 )

Now , multiplying each term with ( x - 3 ) , we get

f ( x ) = ( x - 3 ) x² + ( x - 3 ) 4x + ( x - 3 ) 4

f ( x ) = x³ - 3x² + 4x² - 12x + 4x - 12

On simplifying the equation ,we get

f ( x ) = x³ + x² - 8x - 12

Now , the value of the equation f ( x ) = x³ + x² - 8x - 12

On graphing the equation , we get

The graph of the equation f ( x ) = x³ + x² - 8x - 12 is shown below

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x is 146 degrees

This is because angle y and angle x are supplementary, which means their measures add up to 180 degrees

180 - 34 = 146

Answer: x = 146°

Step-by-step explanation:

Given that y = 35°, Using linear pair

x+y = 180

x+35=180(Substitute value of y)
x=180-35(Transposition Method)

x=145°

First, we will start by converting 607,200 feet to miles

1 mile= 5280 foot

607, 200 feet can be changed to mile by dividing it by 5280

That is;

607,200 feet to mile = 607, 200 / 5280 = 115 miles

Hence; speed

= distance over t/

= 115 /1

=115 miles per hour

Answer:

\(d = 0.112* 10^3\)

Step-by-step explanation:

Given

\(h = 8.4 * 10^3\)

\(d = \sqrt{\frac{3h}{2}}\)

Required

Find d

We have:

\(d = \sqrt{\frac{3h}{2}}\)

Substitute: \(h = 8.4 * 10^3\)

\(d = \sqrt{\frac{3*8.4 * 10^3}{2}}\)

\(d = \sqrt{\frac{25.2 * 10^3}{2}}\)

\(d = \sqrt{12.6 * 10^3}\)

Express as:

\(d = \sqrt{1.26 *10* 10^3}\)

\(d = \sqrt{1.26 *10^4}\)

Split

\(d = \sqrt{1.26} *\sqrt{10^4}\)

\(d = 1.122* 10^2\)

To write in form of: \(a * 10^b\)

The value of a must be: \(0 \le a \le 1\)

So, we have:

\(d = 0.1122* 10 * 10^2\)

\(d = 0.1122* 10^3\)

Approximate

\(d = 0.112* 10^3\)

Answer:

16 cups a day

Step-by-step explanation:

The solution to the system of equations is x = -3 and y = -4.

To solve the system of equations:

Equation 1: 2x - y = -10

Equation 2: 3x + 2y = -1

We can use the method of substitution or elimination to find the values of x and y.

Let's use the method of elimination:

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(2x - y) = 2(-10)

4x - 2y = -20

Now, we can eliminate y by adding Equation 2 and the modified Equation 1:

(3x + 2y) + (4x - 2y) = -1 + (-20)

7x = -21

x = -3

Substitute the value of x into Equation 1 to solve for y:

2(-3) - y = -10

-6 - y = -10

y = -10 + 6

y = -4

Therefore, the solution to the system of equations is x = -3 and y = -4.

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Answer: x = 25, y=15, z = 58

Step-by-step explanation:

The steps that Patel could he use to solve the quadratic equation include:

8(x² + 2x) = –3

8(x² + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.

The equation given is:

8x² + 16x + 3 = 0

8(x² + 2x) = -3

Completing squares in the brackets and balancing the equation:

8(x² + 2x + 1) = -3 + 8

Factoring the perfect square will give 8(x + 1)² = 5.

This is illustrated in the options picked for the step.

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Answer:

1. y = 2x + 7

Step-by-step explanation:

The equation of a linear function is y = mx + b. The "x" has to be a first-degree polynomial (no exponents).

Answer:

y=3x^2

Step-by-step explanation:

edge

Answer:

he's right

Step-by-step explanation:

Answer:

it'd be $1.06 rounded to the nearest thousendth or $1.06400

Step-by-step explanation:

13.30*8/100=Your Answer

Answer:

For question 6 :

> Vertical stretch by 4 ( Multiply y co-ordinates by a)

> Horizontal compress by 2 ( Multiply x co-ordinates by 1/a)

For question 7 :

> Horizontal compress by 3 (Multiply x co-ordinates by 1/a)

> Graph moved down 4.

I hope this is what you looking for.

Answer:

6.  Stretched horizontally by a factor of 1/2 and stretched vertically by a factor of 4.

7.  Stretched horizontally by a factor of 1/3 and translated 4 units down.

Step-by-step explanation:

Transformations

\(\textsf{For $a > 0$}\)

\(f(x+a) \implies f(x) \: \textsf{translated $a$ units left}\)

\(f(x-a) \implies f(x) \: \textsf{translated $a$ units right}\)

\(f(x)+a \implies f(x) \: \textsf{translated $a$ units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated $a$ units down}\)

\(a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}\)

\(f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}\)

\(-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}\)

\(f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}\)

Parent function:

\(f(x)=\sqrt{x}\)

Stretched horizontally by a factor of 1/2:

Multiply the x-variable by 2:

\(\implies f(2x)=\sqrt{2x}\)

Stretched vertically by a factor of 4:

Multiply the function by 4:

\(\implies4f(2x)=4\sqrt{2x}\)

Parent function:

\(f(x)=\lfloor x \rfloor\)

Stretched horizontally by a factor of 1/3:

Multiply the x-variable by 3:

\(\implies f(3x)=\lfloor 3x \rfloor\)

Translated 4 units down:

Subtract 4 from the function:

\(\implies f(3x)-4=\lfloor 3x \rfloor-4\)

There is a typo here. We cannot evaluate the given expression if there is no b and z to replace with the given values. Get it?

When factorized, the quadratic expression would then take the form of B. (x - 4)(x ² + 25)

x³ - 4x + 25x² - 100

First, we can factor out an x from the first two terms, and then group the last two terms:

x(x² - 4) + 25(x² - 4)

Now we can factor out the common factor of (x² - 4):

(x² - 4)(x + 25)

The factored form of the given quadratic expression is:

(x² - 4)(x + 25)

Now let's factor (x² - 4), which is a difference of squares:

(x - 2)(x + 2)(x + 25)

(x - 4)(x² + 25)

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After considering the given data we come to the conclusion that the area to the left of z is 0.982, which is Option D. And the standard deviation of the given data is 87.6, which is Option C.


In order to  calculate the area to the left of z=2.09 we have to  apply the z-table:
1. Search for the row that starts with "2.0" in the leftmost column of the z-table.
2. Then for the column that starts with "0.09" in the top row of the z-table.
3. Here the value at the intersection of this row and column is 0.9821.
4. Finally round this value to three decimal places to get 0.982.
Hence , the area to the left of z=2.09 is 0.982.

Now for the second part of the question
Applying the given data set {10, 26, 84, 48, 250, 56}, we can evaluate the standard deviation as follows:

1. Evaluate the mean:
mean = (10 + 26 + 84 + 48 + 250 + 56) / 6 = 74
2. Applying subtraction of the mean from each data point:
{10 - 74, 26 - 74, 84 - 74, 48 - 74, 250 - 74, 56 - 74}
= {-64, -48, 10, -26, 176, -18}
3. Applying square of the result of step 2:
{(-64)², (-48)², (10)², (-26)², (176)², (-18)²}
= {4096, 2304, 100, 676, 30976, 324}
4. Exercising summation of the result of step 3:
4096 + 2304 + 100 + 676 + 30976 + 324
= 38176
5. Applying division of the result of step 4 by the number of data points (n):
standard deviation = √(38176 / (6 -1))
= √7625.2)
≈ 87.6.
Therefore, the answer is  87.6
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Using the data points given, the equation is \(\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1\).

What is an ellipse?

An ellipse is a locus of a point that moves in such a way that its perpendicular distance from a fixed straight line (directrix) and its distance from a set point (focus) remain constant. which is smaller than unity, i.e. eccentricity(e).

We are given that the center of the ellipse is at (4,-2), and a vertex is at (9,-2).

We know that the distance from the center to a vertex is a, where a is the length of the semi-major axis.

Therefore, we have -

a = 9 - 4 = 5

Since the point (4,3) is on the ellipse, we can use the distance formula to find the length of the semi-minor axis -

c = distance from (4,-2) to (4,3)

c = \(\sqrt{((4-4)^2 + (3-(-2))^2}\)

c = 5

Now, we can use the equation of an ellipse -

\(\frac{\Big(\frac{(x - h)^2}{a^2}+ (y - k)^2\Big)}{b^2} = 1\)

where (h,k) is the center of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.

Plugging in the values we have found, we get -

\(\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1\)

Therefore, the equation for the ellipse is \(\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1\).

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ANSWER

EXPLANATION

Given equation

To find the slope and intercepts of the equation, follow the steps below

Step 1: Write the general form of the slope-intercept equation

Where

m is the slope of the line

b is the y-intercept o the y-axis

Step 2: Find the slope intercept of the equation

Neither of the equation represent the a line that passes through (0, 5) and (4, 15)

The equation of a line can be represented in slope intercept form and point slope form as follows:

slope intercept form:

y = mx + b

where

Therefore,

m = 15 - 5 / 4 - 0

m = 10 / 4

m = 5 / 2

let's find y-intercept using (0, 5)

y = 5 / 2 x + b

5 = 5 / 2(0) + b

b = 5

Hence,

y = 5 / 2 x + 5

Let's find the equation in point slope form:

(0, 5)

y - y₁ = m(x - x₁)

y - 15 = 5 / 2(x - 4)

Therefore, neither of the equation represent the line.

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Answer:

The answer is M = (C-5)/4

Scale factor for the dimensions of the gymnasium on the blue print will be represented by the expression,

Scale factor = \(\frac{\text{Dimension of the blueprint}}{\text{Dimension of the original}}\)

Length of the gymnasium = \(96\) feet

Length of the gymnasium on the blueprint = \(5.5\) inches

Therefore, scale factor for the blueprint = \(\frac{5.5}{96}\)

                                                                  = \(0.0573\)

If the width of the gymnasium = \(75\) feet

For the width on the blueprint,

\(0.0573=\frac{\text{Width on the blueprint}}{75}\)

Width on the blueprint = \(4.29\)

                                      ≈ \(4.3\) inches

Therefore, width of the gymnasium on the blueprint will be \(4.3\) inches.

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The percentage of buyers is approximately 68.26% of buyers of new houses paid between \($149,000\) and \($151,000\) .

We are given that the prices of the new homes are normally distributed with a mean of \($150,000\) and a standard deviation of $1000.

Using the 68-95-99.7 rule, we know that: approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the data falls within two standard deviations of the mean, approximately 99.7% of the data falls within three standard deviations of the mean.

In order to determine the proportion of customers who spent between $149,000 and , we must first determine the z-scores for these values:

z1 = (149,000 - 150,000) / 1000 = -1 z2 = (151,000 - 150,000) / 1000 = 1

Now, we can determine the proportion of data that falls between z1 and z2 using the z-table or a calculator. The region to the left of z1 is 0.1587, and the area to the left of z2 is 0.8413, according to the z-table. Thus, the region bounded by z1 and z2 is:

0.8413 - 0.1587 = 0.6826

We can get the percentage of consumers who spent between by multiplying this by 100% is  \($149,000\)  and \($151,000\):

0.6826 x 100% = 68.26%

Therefore, the standard deviation of customers who paid between is \($149,000\) and \($151,000\)  for this model of new homes.

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The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Explanation

The formula for the Amount based on compound interest is given as:

Since the principal is compounded annually, therefore n =1. Also, P = principal = $7000, ratte = r = 8%, t= time

Hence when t = 1 year

Answer A: $7560

When t = 2 years

Answer B: $8164.8

According to the information, the vertex at the top left of the parallelogram is (4, 8.25). Thus, the other two vertices of the parallelogram are (2, 5), (9, 5), (7, 8), and (4, 8.25).

To find the vertex of the parallelogram we can use the point-slope form of a line: y - y1 = m(x - x1), where,

For the side sloping up from left to right, we can use the point (2, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:

Simplifying, we get:

To find the point where this line intersects the top side of the parallelogram, we can use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (2, 5) is 5 units away from the intersection point in the x-direction, so we can add 5 to the x-coordinate to find the intersection point. Plugging in x = 7 into the equation above, we get:

Therefore, the vertex at the top right of the parallelogram is (7, 8).

For the side sloping down from left to right, we can use the point (9, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:

Simplifying, we get:

To find the point where this line intersects the top side of the parallelogram, we can again use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (9, 5) is 5 units away from the intersection point in the x-direction, so we can subtract 5 from the x-coordinate to find the intersection point. Plugging in x = 4 into the equation above, we get:

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Answer:

40 + 5 = 45

45 ÷ 9 = 5

Therefore, he will have 5 boxes of rocks.

Answer:

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Step-by-step explanation:

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