The chart shows the number of students who participate
in various sports.
Sport
Number of
Students
Students can only play one sport at a time. What is the
ratio of students who cheer to students who participate
in a sport?
Step 1: Decide what comparison is being represented
You know the comparison is part-to-whole because the
question is asking you to compare some students to
the total number of students who participate in sports.
Flag Football
35
Tennis
27
The ratio of students who cheer to those who
participate in a sport is
to 164.
Dance
43
Basketball
33
Cheer
26​

Step-by-step explanation:

4x2 + x3

Rearrange

x3 + 4x2

x2 (x + 4)

Answer:

line AB is congruent to line CB . proof: given

line AE is congruent to line CD . proof: definition of a rectangle

angle EAB is congruent to angle BCD . proof: definition of a rectangle

triangle ABE is congruent to CBD . proof: SAS

line BE is congruent to line BD . proof: CPCTC

Step-by-step explanation:

Sorry if I'm wrong on this, but I hope you understand the general idea!

Answer:

Step-by-step explanation:

a. The explanatory variables in this case is the mothers BMI on which the child's BMI is determined.

The response variable is the child's BMI which is also the outcome variable that exists if a child has an obese parent.

Other lurking variables may include the diets and exercise plan of either of these two variables.

b. No, this study cannot be used to conclude that maternal obesity causes obesity in daughters if the lurking variables are not dealt with.

Answer: First side is 40.5 meters. Second side is 121.5 meters. The third side is 159.

Step-by-step explanation:

x + 3x + 4x -3 = 321

8x - 3 =321

      +3     +3

8x = 324

x = 40.5

Second Side:   3(40.5) = 121.5

Third side:  4(40.5) - 3  = 159

Check: 159 + 121.5 + 40.5 =  321    

Answer:

Expectation number of books a customer will​ purchase  =  1.3

Step-by-step explanation:

x     :​ 0      1              2

p(x) :0.2​,  0.3​, and 0.5​

Expectation

E(X) = ∑x P(x)

      = 0 X 0.2 +1 X 0.3+ 2 X 0.5

     = 1.3

Expectation  E(X) =  1.3

Expectation number of books a customer will​ purchase  =  1.3

Step-by-step explanation:

The surface area of a square pyramid is the area of the square base plus the area of the 4 lateral faces:

A = b² + 4 (½ bl)

A = b² + 2 bl

where b is the width of the base,

and l is the slant height.

Answe The surface area of a square pyramid is the area of the square base plus the area of the 4 lateral faces:

A = b² + 4 (½ bl)

A = b² + 2 bl

where b is the width of the base,

and l is the slant height.:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Health issues are a concern of managers, especially as they evaluate the cost of medical insurance. A recent survey of 150 executives at Elvers Industries, a large insurance and financial firm located in the Southwest, reported the number of pounds by which the executives were overweight. Compute the mean and the standard deviation.

Pounds Overweight Frequency

0 up to 6 14

6 up to 12 42

12 up to 18 58

18 up to 24. 28

24 up to 30. 8

Solution:

This is grouped data. We would determine the midpoint or class mark, x of each class by taking their averages.

The table would become

Class. x f fx

0 up to 6 (0+6)/2 = 3 14 42

6 up to 12 (6+12)/2 = 9 42 378

12 up to 18 (12+18)/2 = 15 58 870

18 up to 24 (18+24)/2= 21 28 588

24 up to 30 (24+30)/2 = 27 8 216

Summation f = 14 + 42 + 58 + 28 + 8 = 150

Summation fx = 42 + 378 + 870 + 588 + 216 = 2094

Mean = Summation fx/Summation f

Mean, m = 2094/150 = 13.96

Standard deviation = √summation of f(x - m)²)/(n - 1)

We would create another column on the table

f x x - m f(x - m)²

14 3 - 10.96 1681.7024

42 9 - 4.96 1033.2672

58 15 1.04 62.7328

28 21 7.04 1387.7248

8 27 12.04 1159.6928

Total = 5325.12

Standard deviation = √5325.12/150 - 1)

Standard deviation = 5.98

The question is incomplete. Here is the complete question.

The number of students, S, serviced by the school system in the town of Emor, t years from 2000 can be modeled by the function S(t) = 10000.[tex](1.1)^{t}[/tex]. The number of classrooms, C, in the town of Emor, t years from 2000 can be modeled by the function C(t) = 450 + 40t. Let D be the average number of students per classroom in Emor's school system t years from 2000.

Write a formula for D(t) in terms of S(t) and C(t).

Write a formula in terms of t.

Answer: D(t) = S(t) / C(t)

D(t) = [tex]\frac{10000.(1.1^{t} )}{450+40t}[/tex]

Step-by-step explanation: First, it is asked to write D(t), which is the average number of students per classroom in terms of students, S(t) and classroom, C(t).

Average is the total number of students divided by the total number of classrooms. Therefore:

D(t) = [tex]\frac{S(t)}{C(t)}[/tex]

Second, to write in term of t, which is time in years, for the average number of students per classroom:

D(t) = [tex]\frac{10000.(1.1)^{t} }{450+40t}[/tex]

In this formula it is clear that the average number of students per classroom is dependent of the growth factor of students each year represented by [tex]1.1^{t}[/tex] and the "growth factor" of classroom each year, represented by 40t.

Answer:

Circle O is similar to Circle X because they have the same radius

Answer:

Ok, i will answer in English.

The first step is to know that when we have a linear equation like:

y = a*x + b

any line with a slope equal to -1/a will be perpendicular to our line.

So first let's write our equation in the standard form:

4x + 6y - 6 = 0

6y = -4x + 6

y = (-2/3)*x + 1

then the slope is (-2/3)

then the slope of the perpendicular line will be:

-(1/(-2/3)) = 3/2

So the only thing any line with the equation:

y = (3/2)*x + c

where c can be any real number, is perpendicular to 4x+6y-6=0

Corrected Question

The function is: [tex]R(x)=80+7.440\sqrt{x} , 0\leq x\leq 15000[/tex]

Answer:

(a)$48.02

(b)$656,299.92

Step-by-step explanation:

(a) We are to determine the change in monthly revenue if the monthly expenditure, x is raised from its current level of 6000 to 6001.

[tex]R(x)=80+7.440\sqrt{x}\\R'(x)=\dfrac{d}{dx} (80+7.440\cdot x^{1/2})\\=7.440 \times \frac{1}{2} \times x^{\frac{1}{2}-1}\\=3.72\times x^{-\frac{1}{2}}\\\\R'(x)=\dfrac{3.72}{\sqrt{x} }[/tex]

Therefore, the expected change in monthly revenue

[tex]R'(6000)=\dfrac{3.72}{\sqrt{6000} }=$0.04802 (thousands)[/tex]

=$48.02

(b)When the amount spent on advertising is $6000

[tex]Revenue, R(6000)=80+7.440\sqrt{6000}\\=\$656.29992$ (in thousands)\\=\$656,299.92[/tex]

Answer:

[tex] f(x) = x^2 -8x -20[/tex]

We know that one factor is (x-10). We know that we need to find two values that added we got -8 and multiplied we got -20. So then we can set the following options:

[tex] a(10) = -20[/tex]

[tex] a-10= -8[/tex]

And solving for a we got:

[tex] a = -8+10=-2[/tex]

And we got:

[tex] a = -2[/tex]

So then the other factor would [tex] x +2[/tex]

Step-by-step explanation:

For this case we have the following expression:

[tex] f(x) = x^2 -8x -20[/tex]

We know that one factor is (x-10). We know that we need to find two values that added we got -8 and multiplied we got -20. So then we can set the following options:

[tex] a(10) = -20[/tex]

[tex] a-10= -8[/tex]

And solving for a we got:

[tex] a = -8+10=-2[/tex]

And we got:

[tex] a = -2[/tex]

So then the other factor would [tex] x +2[/tex]

Answer:

Step-by-step explanation:

Answer:

She liked the smell and was turned on slightly.

Step-by-step explanation:

Some people get aroused when smelling a fart. The teacher was most likely trying to get into your pants.

Answer:

G1 : 0.3(2000) = 600

G2: 0.2(2000) = 400

G3: 0.15(2000) = 300

G4: 2000/15=150

Answer:

D

Step-by-step explanation:

f(x ) = [tex]x^{2} - 1\\[/tex]

inverse ----> f(x) = y = x

x = [tex]y^{2}[/tex] - 1

[tex]y^{2} = x + 1[/tex]

y = ± [tex]\sqrt{x + 1}[/tex]

Answer:

f^-1(y) =[ In(x-2) + 1] /3

Step-by-step explanation:

The inverse of this expression is to find x

Now taking In of both sides we have

y=2^3x-1

In y = In2^3x-1

In y = (3x- 1)In 2

(Iny / In2) + 1= 3x

x =[ (Iny / In2) + 1] /3

Therefore the inverse of y is

f^-1(y) =[ (Inx / In2) + 1] /3

f^-1(y) =[ In(x-2) + 1] /3

The equation of the inverse of the provided equation, which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.

The inverse of an equation is the reverse of the original equation. The equation and the inverse of it has symmetry in each other.

To find the inverse of equation, we have to interchange the variable of equation to each other.

The given equation is,

[tex]y=2^{3x-1}[/tex]

Taking log both side of the equation,

[tex]\ln y = \ln 2^{3x-1}[/tex]

Use the log of power and simplify the equation further, as,

[tex]\ln y = \ln 2^{3x-1}\\\ln y = (3x-1)\ln 2\\\dfrac{\ln y}{\ln 2} = (3x-1)\\\ln (y-2)= (3x-1)\\\ln (y-2)+1= 3x\\x=\dfrac{\ln (y-2)+1}{3}[/tex]

Interchange the place of x and y,

[tex]y=\dfrac{\ln (x-2)+1}{3}[/tex]

This is the required inverse equation.

Thus, the equation of the inverse of the provided equation which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.

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Answer:

x = 40

Step-by-step explanation:

Given 2 secants to a circle from an external point, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is

8(8 + x) = 12(12 + 20) ← distribute parenthesis on both sides

64 + 8x = 12 × 32 = 384 ( subtract 64 from both sides )

8x = 320 ( divide both sides by 8 )

x = 40

Answer:

h = 76

Step-by-step explanation:

2 + h - 48 = 30

h + 2 - 48 = 30

h - 46 = 30

h - 46 + 46 = 30 + 46

h = 76

Answer:

2+h-48=30

2-48+h=30

-46+h=30

h=30+46

∴h=76

Answer:

2x+1

Step-by-step explanation:

that's a hard question

we know that g(x)= x-3

so f(g(x))= f(x-3)

we put it in the equation :

f(x-3)= 2(x-3) +7 = 2x-6+7 = 2x +1

Answer:

  900

Step-by-step explanation:

We can write the proportion as ...

  calories/crackers = 60/12 = y/180

Multiplying by 180, we have ...

  180(5) = y = 900

There are 900 calories in 180 crackers.

Answer:

84

Step-by-step explanation:

This is in the form

ax^2 + bx +c

3x^2 +12x +5

a =3  b = 12  c =5

The discriminant is

b^2 - 4ac

12^2 - 4 * 3 *5

144 - 60

84

Answer:

Step-by-step explanation:

y = -3x + 3

-2x + 2y = 6

-2x + 2(-3x + 3) = 6

-2x - 6x + 6 = 6

-8x + 6 = 6

-8x = 0

x = 0

y = -3(0) + 3

y = 0+ 3

y = 3

(0, 3)

Null hypothesis (H0): The reaction time for the dominant hand is not faster than the non-dominant hand.

Alternative hypothesis (Ha): The reaction time for the dominant hand is faster than the non-dominant hand.

The null and alternative hypotheses for testing if the reaction time is faster for the dominant hand can be formulated as follows:

Null hypothesis (H0): The reaction time for the dominant hand is not faster than the non-dominant hand.

Alternative hypothesis (Ha): The reaction time for the dominant hand is faster than the non-dominant hand.

To test these hypotheses, we can perform a paired t-test because the same subjects are tested with both hands. The paired t-test compares the means of the paired observations and determines if there is a statistically significant difference between them.

Using a 5% level of significance (α = 0.05), we can calculate the test statistic and compare it to the critical value from the t-distribution with (n-1) degrees of freedom, where n is the number of subjects.

If the calculated test statistic falls in the critical region (i.e., the p-value is less than 0.05), we reject the null hypothesis and conclude that there is evidence to suggest that the reaction time for the dominant hand is indeed faster.

If the calculated test statistic does not fall in the critical region (i.e., the p-value is greater than or equal to 0.05), we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest a difference in reaction times between the dominant and non-dominant hand.

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The null and alternate hypothesis tests are:

H₀: μd = μnd

H₁: μd < μnd

Given data:

The hypotheses for testing if the reaction time is faster for the dominant hand can be stated as follows:

Null Hypothesis (H₀): The reaction time is the same for the dominant and non-dominant hand.

Alternative Hypothesis (H₁): The reaction time is faster for the dominant hand.

Mathematically, these can be represented as:

H₀: μd = μnd

H₁: μd < μnd

Where:

μd is the population mean reaction time for the dominant hand.

μnd is the population mean reaction time for the non-dominant hand.

To test these hypotheses, a statistical test such as a paired t-test can be used. The test will compare the means of the paired observations (reaction times for the dominant and non-dominant hand) and determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

The significance level of 5% (0.05) indicates that if the p-value obtained from the test is less than 0.05, we would reject the null hypothesis and conclude that there is evidence to support the claim that the reaction time is faster for the dominant hand.

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Answer:

On the first account, she invests $300, earning 0.02*300 = $6.

On the second acount, she invests 800 - 300 = $500, earning $25.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

In this question:

Two acounts, one with 2% interest(I = 0.02) and the other with 5% interest(I = 0.05).

Each account has two earnings, that i will call [tex]E_{1}[/tex] and [tex]E_{2}[/tex]

Two investments adding up to 800. I will call the first investment P and the second is 800 - P.

Time is not given, but for simplicity, i will use 1 year.

First investment:

I at 2%. The earnings are [tex]E_{1}[/tex].

[tex]E_{1} = 0.02P[/tex]

Second Investment:

Earnings [tex]E_{2}[/tex], at 5%. So

[tex]E_{2} = 0.05(800 - P)[/tex]

The earnings add to 31, so [tex]E_{1} + E_{2} = 31[/tex], then

[tex]E_{2} = 31 - E_{1}[/tex]

So

[tex]31 - E_{1} = 0.05(800 - P)[/tex]

[tex]31 - 0.02P = 0.05(800 - P)[/tex]

[tex]31 - 0.02P = 40 - 0.05P[/tex]

[tex]0.03P = 9[/tex]

[tex]P = \frac{9}{0.03}[/tex]

[tex]P = 300[/tex]

So:

On the first account, she invests $300, earning 0.02*300 = $6.

On the second acount, she invests 800 - 300 = $500, earning $25.

Answer:60

Step-by-step explanation:

⅟₂ of 30=15

¼ of 60=15

The required value is 60.

The size, number, or amount of one thing or group as compared to the size, number, or amount of another is considered as proportion.

Given that, 1/2 of 30 = 1/4 of ??

So, 1/2 of 30 = 15

a/b = c/d

ad = bc

Let the unknown value be x,

Therefore,

30 / 2 = x / 4

2x = 120

x = 60

Hence, the value of unknown element is 60.

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Answer:

85 + 35=120

Step-by-step explanation:

85 + 35= 120

85 - 35= 50

the difference is fifty

Answer: I dont have one for sure but I can explain why this is true.

Step by Step:

sin(x+y)−sin(x−y)=sinxcosy+sinycosx−(sinxcosy−sinycosx)

=sinxcosy+sinycosx−sinxcosy+sinycosx

=sinxcosy+sinycosx−sinxcosy+sinycosx

=sinycosx+sinycosx

=2sinycosx

henceforth proved.

The work done by the man against gravity in climbing to the top is 16740 lb-ft

The work done against gravity relies on the height of the object and the weight at which the object is changing.

From the given information:

Taking the vertical y-axis when y = 0, then:

w(0) = 20 lb

w(90) = 20 - 8 = 12 lb

Provided that the paint leaks steadily, the function of y i.e. w(y) can be expressed as a linear function in the form:

w(y) = a + by ---- (1)

Thus;

From equation (1)

w(y) = 20 - 4y/45

The total weight becomes;

w = w(y) + the man's weight

w = 20 - 4y/45 + 170

w = 190 - 4y/45

Therefore, the work done against gravity is computed as:

W = ∫ w dy

where;

[tex]\mathbf{W = \int ^{90}_{0}( 190 - \dfrac{4y}{45} )\ dy }[/tex]

W = 16740 lb-ft

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Answer:

33.0220147 % reduction

Step-by-step explanation:

Take the original price and subtract the new price

14.99-10.04 = 4.95

Divide by the original price

4.95/14.99 =.330220147

Change to percent form

33.0220147 %