A research group surveyed 250 students. The students were asked how often they go to the movies and whether they prefer comedies or dramas

Answer:

$54288

Step-by-step explanation:

87•48•9=37584÷27=1392•39=54288

Using integrals, we have that:

a) The mean is of 1205 and the standard deviation is of 2.87.

b) P(1200 < X < 1202) = 0.2.

The distribution is given by:

f(x) = 0.1, 1200 < x < 1210.

The integral of this function will be used to find the probabilities.

The mean of the distribution is given by:

[tex]\mu = \int_{1200}^{1210} xf(x) dx[/tex]

Hence:

[tex]\mu = \int_{1200}^{1210} 0.1x dx [/tex]

[tex]\mu = 0.05x^2|_{x = 1200}^{x = 1210}[/tex]

Hence the mean is:

0.05(1210² - 1200²) = 1205.

The variance of the distribution is given by:

[tex]\sigma^2 = \int_{1200}^{1210} (x - \mu)^2 f(x) dx[/tex]

Hence:

[tex]\sigma^2 = \int_{1200}^{1210} 0.1(x - 1205)^2 dx[/tex]

[tex]\sigma^2 = 0.033(x - 1205)^3|_{x = 1200}^{x = 1210}[/tex]

[tex]\sigma^2 = 0.033(1210 - 1205)^3 - 0.033(1200 - 1205)^3[/tex]

[tex]\sigma^2 = 8.25[/tex]

The standard deviation is the square root of the variance, hence:

[tex]\sigma = \sqrt{8.25} = 2.87[/tex]

For item b, the probability is given by:

[tex]P(1196 < X < 1202) = \int_{1200}^{1202} 0.1 dx[/tex]

P(1196 < X < 1202) = 0.1x, from x = 1200 to x = 1202.

Applying the Fundamental Theorem of Calculus:

0.1(1202) - 0.1(1200) = 0.2.

The lower bound is of 1200 because the distribution is not defined for values less than 1200.

Hence:

P(1200 < X < 1202) = 0.2.

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Answer:

908 - 394 = 514

Step-by-step explanation:

It's 514 because you took out the 394 from 908. That's why you got 514.

You subtracted the number 394 from 908.

That's why you got 514.

I hope you get it.

Answer:

Step-by-step explanation:

36

6*6

3*2*6

3*2*3*2

Answer:

[tex] \sf \: h = \frac{v}{lw} [/tex]

Step-by-step explanation:

Let's solve for h.

v=lwh

Step 1: Flip the equation.

hlw=v

Step 2: Divide both sides by lw.

hlw/lw = v/lw

h=v/lw

Answer:

11x - 12

Step-by-step explanation:

First, group like terms (numbers with a coefficient (x) together)

12x - 3x + 2x -10 -2

Next, use BODMAS (brackets, of, division, multiplication, addition, subtraction) to know the order to solve.

Addition is before subtraction so we do: -3x + 2x which is -x

12x - x - 10 -2

12x - x = 11x and -10 -2 ÷ -12 so final answer is:

11x -12

Hope I didn't overexplain :)

Hence , the instantaneous rate of change of f(x) = e^(2x)e^(7x) at x = -1 will be 9e⁻⁹ .

We have given a function f(x) = e²ˣ e⁷ˣ.

You can realize the fast rate of modification of a perform at a degree by finding the by-product of that perform and plugging within the x-value of the purpose.

On simplifying , we can write f(x) as e⁹ˣ

Differentiating f(x) with respect to x , we get

     f'(x) =  d/dx (e⁹ˣ)

     f'(x) = e⁹ˣ × 9

Putting x = - 1 in f'(x) , we get

     f'(-1) = 9e⁹⁽⁻¹⁾

            = 9e⁻⁹

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Answer:

6/7

Find a number that goes into both numbers ie 2 which goes in 6 and 7 times respectively

He wouldn’t be able to meet the specifications as the heigh is greater than the maximum height.

Maximum width of the wall hanging can be 3.75 feet and maximum height can be 6.5 feet.

After completing the work it was found that the width measures 3 3/5 feet and height was 3 3/4 tall.

If the height and width after completing the work is less than or equal to the maximum height and width then he will be able to meet the specifications .

Width

3 3/4

= (12+3)/4

= 15/4

= 3.75

Height

6 3/4

= (24+3)/4

= 27/4

= 6.75

He wouldn’t be able to meet the specifications as the heigh is greater than the maximum height .

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Answer:

D

Step-by-step explanation:

Irrational numbers are those which cannot be expressed by the ratio of two integers.

A is rational because it is a recurring decimal. Recurring decimals can be represented by the ratio of two integers (this one can be represented by the fraction -2752/333, which is a ratio of two integers).

B is a fraction with two integers, therefore it is rational. -5/9 is a ratio of two integers.

C can be represented by 1747/100.

D is an infinite decimal but isn't recurring like A, meaning it cannot be represented by the ratio of two integers, and is therefore it is irrational, unless you are shown further digits of the decimal which prove it to be recurring, which is not the case here.

The equations that are equivalent to the given equation are m - 4 = -7m - 8, -7m - 8 = m - 4 and -8 - 7m = m - 4

The equation is given as

-2m - 5m - 8 = 3 + (-7) + m

Remove the bracket

So, we have

-2m - 5m - 8 = 3 - 7 + m

Evaluate the like terms

So, we have

-7m - 8 = - 4 + m

The above expression can be written as follows

m - 4 = -7m - 8

-7m - 8 = m - 4

-8 - 7m = m - 4

Hence, the equations that are equivalent to the given equation are m - 4 = -7m - 8, -7m - 8 = m - 4 and -8 - 7m = m - 4

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The slope of the graph is 20 and the y-intercept is -1050.

The slope of a linear graph is defined as the gradient of the graph .It is also defined by trigonometric properties as the tangent of the angle formed by the line with the positive y-axis.

The y-intercept is the point of intersection of the graph and the y-axis.

The general equation of a straight line in the cartesian plane is given by

y = m x + c where 'm' represents the slope and 'c' represents the y-intercept.

It is given that the one time editing cost is 1050 dollars.

Variable cost of printing each book = 15 dollars

Each book is sold at = 35 dollars

∴profit per book sold = 35 - 15 = 20 dollars

Let Gary sells x number of books . Profit from selling x books = 20 x

Let us consider the net profit of Gary after selling x books be represented by y.

∴ y = profit from x books - establishment cost

or, y = 20 x -1050

Now comparing the above equation with the general equation of a straight line( y = mx + c ) we  can infer that:

slope(m) = 20

y-intercept (c) = -1050

Therefore the slope of the graph is 20 and the y-intercept is -1050.

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Using linear functions, we have that:

The table for Carrier A is missing and has two points (3,500) and (6,650).

A linear function is modeled by:

y = mx + b

In which:

For Carrier B, the function is:

yB(x) = 55x + 300.

For Carrier A, when in 3 months, the price increases by $150, hence the slope is:

m = 150/3 = 50.

Hence:

yA = 50x + b.

When x = 3, y = 500, hence we use it to find b as follows.

500 = 50(3) + b

b = 350.

Then:

yA = 50x + 350.

Due to the lower intercept, we have that:

Carrier B has the lower initial fee.

They will have the same amount when:

yA = yB.

Hence:

50x + 350 = 55x + 300

5x = 50

x = 10 months.

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Answer: [tex]x^{2} (5x-9)[/tex]

Step-by-step explanation:

[tex]3x^3 - x^2 + 2(x^3 - 4x^2)[/tex]

[tex]= 3x^3 - x^2 +2x^3 - 8x^2[/tex]

[tex]=5x^3 -9x^2[/tex]

[tex]=x^2 (5x-9)[/tex]

The answer to it would be 32.

Answer:

32

32 is the answer hope this helps

After evaluation we get the values as a = 8 + -0.4285714286b

Given, the expression is (7a ₊ 10)/(3b ₊ 6) = 72

Simplifying

(7a ₊ 10) ₊ (3b ₊ 6) = 72

Reorder the terms:

(10 ₊ 7a) ₊ (3b ₊ 6) = 72

Remove parenthesis around (10 ₊ 7a)

10 ₊ 7a ₊ (3b ₊ 6) = 72

Reorder the terms:

10 + 7a + (6 + 3b) = 72

Remove parenthesis around (6 + 3b)

10 + 7a + 6 + 3b = 72

Reorder the terms:

10 + 6 + 7a + 3b = 72

Combine like terms: 10 + 6 = 16

16 + 7a + 3b = 72

Solving

16 + 7a + 3b = 72

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-16' to each side of the equation.

16 + 7a + -16 + 3b = 72 + -16

Reorder the terms:

16 + -16 + 7a + 3b = 72 + -16

Combine like terms: 16 + -16 = 0

0 + 7a + 3b = 72 + -16

7a + 3b = 72 + -16

Combine like terms: 72 + -16 = 56

7a + 3b = 56

Add '-3b' to each side of the equation.

7a + 3b + -3b = 56 + -3b

Combine like terms: 3b + -3b = 0

7a + 0 = 56 + -3b

7a = 56 + -3b

Divide each side by '7'.

a = 8 + -0.4285714286b

Simplifying

a = 8 + -0.4285714286b

hence we get the solution of the equation.

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Steve can store 96 more photos on the memory card.

Total space in the memory card is = 1000 mega bytes.

Sapec required to store 1 photo = 2.4 mega bytes.

Now, we are given that:

Steve has already saved 320 photos in that memory card.

so, the space required by 320 photos will be calculated by using multiplication.

Space filled = 320 × 2.4 = 768 mega bytes.

Space left in the memory card = 1000 mega bytes - 768 mega bytes = 232 mega bytes.

Photos that can be stored in the space left = 232 / 2.4 = 96.67

which will be = 96

Therefore, Steve can store 96 more photos on the memory card.

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Answer:

180.

Step-by-step explanation:

9/5 = 1.8 and 10^5/10^3 = 10^2
so tis 1.8 x 10^2 which is 180

pls give branliest

Answer: 180

Step-by-step explanation:

(9 x 10^5) / (5 x 10^3)=

(9 x 10^(2+3)) / (5 x 10^3)=

(9 x 10^2 x 10^3) / (5 x 10^3)=

(9 x 10^2)/5=        ==> Divide each side by 10^3

900/5=180

The amount of bricks that Jack would need to complete the wall is 180.

The first step is to determine the total amount of bricks he would need to build the wall. In order to determine this value, ratio analysis would be used.

Total bricks needed = (area of wall x number of blocks already used) / (area of wall already built)

Area of wall = 8 x 1.5 = 12

Area of wall already built = 5 x 1.5 = 7.5

Total bricks needed = (12 x 300) / 7.5 = 400 bricks

Number of bricks needed to complete the wall = 400 - 300 = 180 bricks

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Answer: 70

Step-by-step explanation:

Looking at line p, we can form an equation to find the missing angle that would make the line equal to 180* (all straight lines, unless stated otherwise, should be assumed they are a 180* angle). We can use the equation below:

[tex]180 = 80 + 30 + x\\x = 180 - (80 + 30)\\x= 70[/tex]

If lines n and m are parallel, the angles should be equal when looking at an intersecting line.

Hope this helps!

Answer:

Step-by-step explanation:

2x - 8 = -30

2x = 8 - 30

2x = -22

x = -11

check

2 * (-11) - 8 = -30

-22 - 8 = -30

-30 = -30

the answer is good

Yes, a statement with the word 'per' is always a unit rate;

When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the rate's denominator is 1, we refer to the rate as a unit rate. In actuality, the amount included in each unit or per unit is referred to as the unit rate. Let's use some instances to help us grasp this:

Unit rate is 20 miles per hour, or 40 miles in two hours.

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Larry Mitchell invested $7600 at 3% rate of interest and $11400 at 2% rate of interest.

In the field of finance, interest is the payment of a sum over and above the principal amount owed by a lender or depositor to a borrower or deposit-taking financial institution at a set rate.

Rate of an interest in defined as the amount that a lender charges a borrower in interest as a percentage of the principal.

Larry invested part of his $19000 at 3% and the rest at 2%

Let he invested $'x' at 3% interest .

Therefore amount invested at 2%=$(19000-x)

Interest earned annually at 3% on $x = [tex]\frac{3}{100} \times x =0.03x[/tex] .

Interest earned annually at 2% on $(19000-x)=[tex]\frac{2}{100} \times(19000-x)[/tex]

=[tex]380-0.02x[/tex]

Now the combined interest for both the investment is $560 .

Therefore we can form a linear equation to solve for x:

0.03x+380-0.02x=560

or, 0.01x=180

or, x=18000

Therefore Larry invested $18000 at 3% interest.

Money invested at 2%=$(19000-18000)=$1000

Hence Larry invested $18000 at 3% rate of interest and $1000 at 2% rate of interest.

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Answer:

Step-by-step explanation:

at first we must find x  according to y :

[tex]y=\frac{8-x}{8}[/tex]   8y= 8-x  ,  x = 8-8y

now we  change the place of x and y

y = 8 - 8x

Answer:90

Step-by-step explanation:

you add 30 + 60 gives you 90 degrees

Answer:

-2≤x<3

Step-by-step explanation:

that's the answer

Answer:

A

Step-by-step explanation:

Each hash mark between "School" and "Declan's house" is one-eighth of a mile.  Starting at "School" count 5 hash marks to the left to get where Harper lives.

Answer:

So first you do 47 -20=27, So x=27

The answer 27 is X =

The range of the function on the graph containing all the real numbers greater than or equal to –3 . So the correct option is (d)

The collection of all a function's outputs constitutes its range.

The elements of the co-domain that are mapped are known as the images, while the elements of the domain are known as pre-images.

The set of all images of the domain's elements in this case serves as the function's range, as does the set of all of its outputs.

We have to find the function on the graph.

From the given graph, we can see from the graph that the function's maximum y value is -3 and that the graph keeps going up.

Therefore, the range includes all real values that are greater than or equal to -3.

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