How to solve this mathematical question

Students taking both honors courses and prefer basketball to football is 450.

Total number of students at a high school = 6000

Number of students who has taken honors courses = 1500

Number of students who prefer watching basketball to football = 1800

Let event of taking honors courses be A

and event of preferring watching basketball be B

P(A) = 1500 / 6000 = 0.25

P(B) = 1800 / 6000 = 0.3

If both the event of taking honors courses and preferring watching basketball is independent then

By using property of independent events ,

P(A∩B) = P(A) . P(B)

= (0.25)(0.3) = 0.075

Number of students taking both honors courses and prefer basketball to football = 0.075 × 6000

= 450 Students

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Answer: B^5

Step-by-step explanation: truss

Answer:

a=5

a=2x-5

Step-by-step explanation:

hope it helps

have a nice day!

or night

Answer:

Step-by-step explanation:

The volume of the given rectangular box is given by 225 cubic inches.

We know that the volume of the rectangular box with length L and width W and height H is given by,

V = LWH

So given the length of rectangular box is = 12 1/2 inches = 25/2 inches

The width of rectangular box is = 4 1/2 inches = 9/2 inches

The height of box is = 4 inches

So the volume of the rectangular box = (25/2)*(9/2)*4 = 25*9 = 225 cubic inches.

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The relationship between the mean and median of the collected data is that the mean will be smaller than the median.

Since the SAT Math scores for these students will be mostly high scores, the distribution will be skewed to the left. Thus, the few low scores (outliers) will make the mean smaller than the median.

Outliers that do not change the mean have an impact just on the mean. As a result, the mean is frequently lower than that of the median when the distribution of data is skewed to the left. The mean is frequently higher than the median when the distribution is tilted toward the right. We anticipate that the mean and median in symmetrical distribution will be about identical in value. This is a crucial link between the connection here between mean and median as well as the distribution's form. Nevertheless, it isn't applicable to all sets of data. Collections of data sets are where exceptions happen much more frequently.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

the highest exponent is 2, so, we expect to get 2 factors in x (as the multiplication of x×x = x²).

3 is a prime number, and the only factors to get 3 are 3 and 1

3 = 3×1

so, we expect to get factors that look like

(3x + a)(x + b)

when we do the multiplication, we get

3x² + 3bx + ax + ab = 3x² +(3b + a)x + ab

now we compare this to our original expression

3x² +(3b + a)x + ab = 3x² - 13x + 12

3b + a = -13

ab = 12

so, we know a and b must both be negative

(-×- = +, - - - = -).

the negative factors of 12 are

-12 × -1

-6 × -2

-4 × -3

which one of these pairs can make

3b + a = -13

be true ?

3×-12 + -1 = -37 no

3×-1 + -12 = -15 no

3×-6 + -2 = -20 no

3×-2 + -6 = -12 no

3×-4 + -3 = -15 no

3×-3 + -4 = -13 yes

so, our factors are

(3x - 4)(x - 3)

The parallel line has an equation of y = 2x + 3

The equation is given as

2y = 4x + 14

Make y the subject

2y = 4x + 14

Divide through by 2

y = 2x + 7

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = 2

This means that the slope of 2y = 4x + 14 is 2

The slopes of parallel lines are equal

This means that the slope of the other line is 2

i.e. m = 2

Recall that:

The equation of a line can be represented as

y = mx + c

Where

slope = m

So, we have

y = 2x + c

Assume any value for c

This gives

y = 2x + 3

Hence, the equation of the parallel line is y = 2x + 3

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Using front end estimation, the solutions to the given problems are;

1) 25.72

2) 137.521

3) 17.1

Front-end estimation is defined as a particular way of rounding numbers to estimate sums and differences.

The procedure for using front- end estimation, is to add or subtract only the numbers in the greatest place value. Thereafter, we add the decimals rounded to the nearest tenth.

1) 32.47 - 6.75

First of all, let's deal with the whole numbers part;

32 - 6 = 26

Next is to deal with the decimal part to get;

0.47 is approximately 0.5 while 0.75 is approximately 0.8. Thus;

0.5 - 0.8 = - 0.3

Thus, we have;

26 + (-0.3) = 25.70

Therefore, our given solution can be written as; 25.72

2) 118.234 + 19.287

First of all, let's deal with the whole numbers part;

118 + 19 = 137

Next is to deal with the decimal part to get;

0.234 is approximately 0.2 while 0.287 is approximately 0.3. Thus;

0.2 + 0.3 =0.5

Thus, we have;

137 + 0.5 = 137.5

Therefore, our given solution can be written as; 137.521

C)  17.9 - 0.8

First of all, let's deal with the whole numbers part;

17 - 0 = 17

Next is to deal with the decimal part to get;

0.9 - 0.8 = 0.1

Thus, we have;

17 + 0.1 = 17.1

Therefore, our given solution can be written as; 17.1

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The average apple weight's 95% confidence interval is (119.14, 125.86).

According to one manufacturer, an apple weighs 120 grams on average with a 12-gram standard variation. According to statistics generated from a sample of 49 apples randomly selected from a shipment, the average weight per apple was 122. 5 grams.

Let, 

n = 49

x = 122.5 

σ = 12

To figure up and analyze a 95% confidence interval for the average apple weight; 

The formula for a 95% confidence interval is

(x ± 1.96*σ√n) 

(122.5 ± 1.96*12/√49)

(119.14, 125.86)

Consequently, a 95% confidence interval for the average apple weight is (119.14, 125.86).

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Train B is traveling faster because it traveled 100 meters in four seconds.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

We have to determine which train is moving faster based on the image.

We can tell by looking at the train speeds.

As per the formula,

distance/time = speed

Train A travels 12.5 metres in one second = 12.5/1 = 12.5 metres per second

Train B travels 100 meters in four seconds, hence its speed is 100/4 = 25 meters per second.

This is because it traveled 100 meters in four seconds, whereas train A covered 12.5 meters in one second.

Hence, train B is traveling faster.

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The question seems to be incomplete the correct question has been in attached file

Answer: 7 comic books would be left after putting them into groups of 8.

Step-by-step explanation: There will be 326 groups of comic books. 326 x 8 = 2,608 which means that there will be 7 comic books left after putting them all into groups of 8.

x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.

According to the question,

The two numbers are positive and the sum of the two numbers is 16 and the sum of the squares of the two numbers is the minimum.

Now to solve the question we will consider,

x and y are the two numbers, such that x > 0 and y > 0

Sum of the numbers : x + y = 16

Sum of squares of the numbers: S = x²+ y²

x + y = 16 y = (16 - x)

Assume, S = x² + y²

S = x² + (16 - x)²

Now we will differentiate with respect to x

dS/dx = 2x+ 2(16-x)(-1)

2x-2(16-x)=0

2x-32+2x=0

4x-32=0

4x=32

x=32/4

x=8

As x > 0, x = 8

d²S/dx² = d/dx [2x+ 2(16-x)(-1)]

d²S/dx² = d/dx (2x) - 2 d/dx (16-x)

d²S/dx² = 2 - 2[0-1]

d²S/dx² = 4

Now when x=8

d²S/dx²  = 4 ≥0

Therefore, the function S = sum of the squares of the two numbers is minimum at x = 8.

y = 16-8 = 8

Therefore, x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.

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The maximum or minimum value of the function y = -2x² + 32x - 12 is (8, 116) and the range of the function y = -2x² + 32x - 12 lies in the interval

(−∞ ,116).

Given, the function is y = -2x2 + 32x - 12

According to the question we have to extract the maximum or minimum value of the function.

The maximum or minimum of a function which is a quadractic function occurs at the point x = -b/2a.

If a is negative, then the maximum value of the function is f(-b/2a).

If a is positive, then the minimum value of the function is f(-b/2a).

According to this, we can derive the general equation as

fmax(x) =ax²+bx+c occurs at x = -b/2a.

From the given equation, comparing we get

a = -2, b = 32, c = -12

Substitute the value of a and b in in the general equation and we get

x = -32/2(-2)

x = -32/-4

x = 8

Put x = 8 in the given general equation,

y = -2(8)² + 32(8) - 12

y = -2(64) + 256 - 12

y = -128 + 256 - 12

y = 256 - 140

y = 116

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Answer:

c=40n+10

Step-by-step explanation:

They charge 40$ per night from which we get 40n

The extra 10$ is from the bathing fee

The rest of the information they give us isn't useful in this case because they didn't ask us the cost per hour

The slope of the line that passes through (9, 1) and (-8, 2) is -1/17

If we have a linear equation or a segment that passes through two points (x₁, y₁) and (x₂, y₂), then the slope is given by the formula:

slope = (y₂ - y₁)/(x₂ - x₁)

In this case, we know that the two points are (9, 1) and (-8, 2), using the above formula we can find the slope to be:

slope = (2 - 1)/(-8 - 9)

slope = 1/-17 = -1/17

That is the slope of the line or segment that passes through the given points.

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Answer:14

Step-by-step explanation:All you have to do is Divide 378 by 27 to get x

Hope This Helps!

Answer:

3√10 units

Step-by-step explanation:

[tex] \sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \sqrt{10} = 5 \sqrt{10} [/tex]

[tex]3x + 2x = 5 \sqrt{10} [/tex]

[tex]5x = 5 \sqrt{10} [/tex]

[tex]x = \sqrt{10} [/tex]

So the length of the longer piece is 3√10 units.

Given f(x)=2−∣x−5∣

Domain of f(x) is defined for all real values of x.

Since, ∣x−5∣≥0⟹−∣x−5∣≤0

⟹2−∣x−5∣≤2⟹f(x)≤2

Hence, range of f(x) is (−∞,2].

Answer:

Step-by-step explanation:

Which one adds up to 14 is the question?  There are dots on the dice which correspond to numbers. The dots are saying that they are numbers. And if you get to 14 with the dices, you pick it.

Answer:

y=6

Step-by-step explanation:

4(y-4)=8

4×y-16=8

4×y=8+16

4×y=24

y=6

4(6-4)=8

4×2=8

Answer:

Step-by-step explanation:

Answer:

b= c + t (the amount bought)

Step-by-step explanation:

Answer:

-5/3 or -1.67

Step-by-step explanation:

Answer:

-5/3

Step-by-step explanation:

Oh it's you again, I am just gonna copy paste my format from your previous question.

Use the slope formula: s=(y2-y1)/(x2-x1)

It doesn't matter the order.

Let's say -6 is x2 and 8 is y2; 3 is x1 and -7 is y1

Plug in the equation: s=[(8)-(-7)]/[(-6)-(3)]

Simplify and solve: s=[8+7]/[-9]

                               s = -15/9

                               s = -5/3

To calculate the p-value, we have to follow the following steps:

To calculate the p-value, we need

p = sample proportion

p' = assumed population proportion in the null hypothesis

n = sample size

Example

Given, n =40, σ = 32.17 and X = 105.37. calculate p-value.

σₓ = σ/ √n

σₓ = 32.17 / √40

    = 5.0865

Now, by applying the test static formula, we get

t = (105.37 – 120) / 5.0865

t = -2.8762

Using the table, we find the value of P(t>-2.8762)

From the table, we get

P (t<-2.8762) = P(t>2.8762) = 0.003

If P(t>-2.8762) = 1- 0.003 = 0.997

P- value = 0.997 > 0.05

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Answer:

9:40

Step-by-step explanation:

Distance = rate x time

Let t = time

40 = 60t  Divide both sides by 60

[tex]\frac{40}{60}[/tex] = t  An hour would be 60 minutes so the number of minutes out of the total would be 40.

Translation 1 unit up is the transformation which accomplish the graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

Figure C is the result of a transformation on Figure B

We need to find which transformation is used for this.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

and  A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis

Horizontally translating a graph is equivalent to shifting the base graph left or right in the direction of the x-axis.

The graph is just shifted slightly to right.

Figure B undergoes a translation of translation 1 unit up.

Hence translation 1 unit up is the transformation which accomplish the graph.

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Answer:$26

Step-by-step explanation:

52+22=74

100-74=26

The range of the given relation is (-6, -3, 0, 3, 6).

Range:

Basically the set contains 2 elements in it, in which set contains all the second elements, on the other hand, is known as the range of the relation.

Given,

Here we have the relation (-5,6), (-3,3), (-1,0), (1,-3) and (3,-6)

Here we need to find the range of the relation.

According to the definition of the relation,

Range refers the y values of the coordinates,

So, based on this the value of the given coordinates are extracted as,

(-5, 6) => 6

(-3, 3) => 3

(-1, 0) => 0

(1, -3) => -3

(3, -6) => -6

Now we have arrange the range values from the smallest to largest,

Therefore, the range of the relation is (-6, -3, 0, 3, 6).

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By first subtraction b and then dividing by m, the solution of the linear equation for x is:

(y - b)/m = x

Here we have a linear equation that defines the variable y in terms of the variable x:

y = m*x + b

Where m and b are real numbers.

Now we want to find x in terms of the variable y, this means that we need to isolate the variable x.

if first we subtract b in both sides, we get:

y - b = m*x + b - b

y - b = m*x

If now we divide both sides by m, we get:

(y - b)/m = m*x/m

(y - b)/m = x

This is the linear equation solved for x.

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Answer:If you’re using imagine math it will be the the third one

Step-by-step explanation: