In a sample, 76 people or 38% of the people in the sample said that the mayor should be prosecuted for misconduct. How many people were in the sample

Answer:

y = 3 4 x − 25 4

Explanation:

We could use calculus but first as with all Mathematical problems one should step back and think about what the question is asking you, and in this case we can easily answer the question using knowledge of the equation, in this case:

x 2 + y 2 = 25

represents a circle of centre ( a , b ) = ( 0 , 0 ) and radius r = 5

First verify that ( 3 , − 4 ) actually lies on the circle;

Subs x = 3 oito the circle equation:

⇒ 3 2 + y 2 = 25 = y 2 = 16 ⇒ y = ± 4 So ( 3 , − 4 )

So does indeed lie on the circle. A straight line passing between that point and the centre of the circle ( 0 , 0 ) will be perpendicular to the tangent. So the gradient of the normal is given by:

m N = Δ y Δ x = − 4 − 0 3 − 0 = − 4 3 Then as the normal is perpendicular to the tangent the product of their gradients is − 1 , so then: m T = 3/4

So using the point/slope form y − y 1 = m ( x − x 1 ) the equation we seek is;

y − ( − 4 ) = 3/4 ( x − 3 )

∴ y + 4 = 3/4 x − 9/4

∴ y = 3/4 x − 25/4

We can confirm this solution is correct graphically:

If x 2 + y 2 = 25 then differentiating wrt x implicitly gives us:

2 x + 2 y d y d x = 0

∴ d y d x = − x/y

When x = 3 and y = − 4 ⇒ d y d x = − 3 − 4 = 3 4 , which is what we obtained.

Hoped I helped

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Answer:

Area of parallelogram = 25.2 m²

Step-by-step explanation:

Given:

Base = 6 m

Height = 4.2 m

Find:

Area of parallelogram

Computation:

Area of parallelogram = Base × Height

Area of parallelogram = 6 × 4.2

Area of parallelogram = 25.2 m²

Answer:

8

Step-by-step explanation:

1/2(6+18)-2^2

=1/2(24)-4

=12-4

=8

Answer:

Step-by-step explanation:

if the fraction is (4/9)*7 then the answer =28/9

if the fraction is 4/(9*7) then the answer is 4/63

Answer:

6

Step-by-step explanation

The only f(0) answer in table is 6

Answer:

6

Step-by-step explanation:

f(0) = 6.  That is, when the input (x) is 0, the output (y) is 6.

Answer:

1.29 for 1 pack

Step-by-step explanation:

5.16/4=1.29

Answer:

36 cans for $3.32

Step-by-step explanation:

36 cans = $3.32

1 can =$ 0.092

9 cans = $0.91

1 can = $0.01

0.09 and 0.1 the cheaper is 0.09 dollars so 36 cans for $3.32 is better

Answer:

hi i have the same question and im super confused, what was your answer for that question?

Step-by-step explanation:

Answer:

5 calories

Step-by-step explanation:

Greetings from Brasil...

The point (-2; -4) is in the blue area, so it is the solution to the equation;

The point (-1; -5) is in the blue area, so it is the solution to the equation;

The point (0; -3) is in the blue area, so it is the solution to the equation;

The point (2; -1) is exactly on the function line. As this line is dashed, it does not include its values, so this point is not a solution (no point on the dashed line is a solution)

Answer:

1.375

Step-by-step explanation:

I recommend using a calculator. Divide 3/8. Add 1 back.

The decimal value of 1(3/8) is 1.375.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

1(3/8)

This can be written as,

11/8

Now,

11/8 = 1.375

Thus,

The decimal value of 1(3/8( is 1.375.

Learn more about fractions here:

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Answer:

128

Step-by-step explanation:

32 x 4 = 128

o

32 + 32 + 32 + 32 = 128

(a) For each value of X we have:

[tex]X=0\quad\Rightarrow\quad Y=4\\\\X=1\quad\Rightarrow\quad Y=-23\\\\X=2\quad\Rightarrow\quad Y=-32\\\\X=3\quad\Rightarrow\quad Y=-23\\\\X=4\quad\Rightarrow\quad Y=4\\\\X=5\quad\Rightarrow\quad Y=49[/tex]

so the range of Y = {-32, -23, 4, 49}

(b)

[tex]P\{Y=4\}=P\{X=0\}+P\{X=4\}=0.00032+0.4096=\boxed{0.40992}[/tex]

(c)

Y cannot equal 0, so

[tex]P\{Y=0\}=0[/tex]

Answer:

OD. 13/12 or 1 1/12

Step-by-step explanation:

[tex] \frac{1}{6} + \frac{2}{3} + \frac{1}{4} \\ lcm = 12 \\ = \frac{2 + 8 + 3}{12} \\ [/tex]

[tex] = \frac{13}{12 } \\ 13 \div 12 = 1r1 \\ = 1 \frac{1}{12} [/tex]

(a) Recall that

[tex]\dfrac{\mathrm d[\sin^{-1}x]}{\mathrm dx}=\dfrac1{\sqrt{1-x^2}}[/tex]

[tex]\dfrac{\mathrm d[\ln x]}{\mathrm dx}=\dfrac1x[/tex]

[tex]\dfrac{\mathrm d[\sqrt x]}{\mathrm dx}=\dfrac1{2\sqrt x}[/tex]

Then by the chain rule,

[tex]y=\sin^{-1}(\sqrt x)+\ln(\sqrt x)[/tex]

[tex]\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm d[\sin^{-1}(\sqrt x)+\ln(\sqrt x)]}{\mathrm dx}[/tex]

[tex]=\dfrac1{\sqrt{1-(\sqrt x)^2}}\dfrac{\mathrm d[\sqrt x]}{\mathrm dx}+\dfrac1{\sqrt x}\dfrac{\mathrm d[\sqrt x]}{\mathrm dx}[/tex]

[tex]=\dfrac1{2\sqrt x\sqrt{1-x}}+\dfrac1{2(\sqrt x)^2}[/tex]

[tex]=\dfrac1{2\sqrt{x-x^2}}+\dfrac1{2x}[/tex]

[tex]=\boxed{\dfrac{x+\sqrt{x-x^2}}{2x\sqrt{x-x^2}}}[/tex]

(b) I'll assume [tex]\log x[/tex] refers to the logarithm of base [tex]e[/tex]. Recall that

[tex]\dfrac{\mathrm d[e^x]}{\mathrm dx}=e^x[/tex]

[tex]2^x=e^{\log2\,x}\implies\dfrac{\mathrm d[2^x]}{\mathrm dx}=e^{\log2\,x}\dfrac{\mathrm d[\log2\,x]}{\mathrm dx}=\log2\cdot2^x[/tex]

Then using the chain rule and implicit differentiation, we get

[tex]e^y=2^x\log x-e^{2x}[/tex]

[tex]\implies e^y\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm d[2^x]}{\mathrm dx}\log x+2^x\dfrac{\mathrm d[\log x]}{\mathrm dx}-e^{2x}\dfrac{\mathrm d[2x]}{\mathrm dx}[/tex]

[tex]e^y\dfrac{\mathrm dy}{\mathrm dx}=\log2\cdot2^x\log x+\dfrac{2^x}x-2e^{2x}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\log2\cdot2^x\log x+\frac{2^x}x-2e^{2x}}{e^y}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\log2\cdot2^x\log x+\frac{2^x}x-2e^{2x}}{2^x\log x-e^{2x}}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\boxed{\dfrac{\log2\cdot2^xx\log x+2^x-2xe^{2x}}{x(2^x\log x-e^{2x})}}[/tex]

If instead [tex]\log x=\log_{10}x[/tex] denotes the base 10 logarithm, you need only make the following adjustment:

[tex]\log x=\dfrac{\ln x}{\ln 10}\implies\dfrac{\mathrm d[\log_{10}x]}{\mathrm dx}=\dfrac1{\ln10\,x}[/tex]

where [tex]\ln x[/tex] is logarithm of base [tex]e[/tex].

Answer:

  real, rational

Step-by-step explanation:

Without knowing what the average number of students is, we know the number must be a real number, and must be rational. (An average of integers is always the ratio of two integers.) It may or may not be a natural number, whole number, or integer.

Answer: The word phrase for this expression is the last option, "The sum of the quotient of d and 5 and 2." d is being divided by 5, so we would use "quotient of d and 5" for that part, and then we would add the "sum" because d/5 is being added to 2.

Answer:

see below

Step-by-step explanation:

First, she should subtract 6 from both sides of the inequality. This makes it so that the x terms are on one side and the non-x terms are on the other side so she can then solve for x by multiplying the entire inequality by 2.

Answer: [tex](-\infty, \infty)[/tex]

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

Explanation:

Draw out a number line. Plot 0 and -4 on the number line.

Shade to the left of x = 0, and have a filled in circle at the endpoint. This is the graph of [tex]x \le 0[/tex]

Then graph [tex]x \ge -4[/tex] by plotting a filled in circle at -4, and shading to the right.

Note how the two graphs overlap to cover the entire real number line

So if we have [tex]x \le 0 \ \text{ or } \ x \ge -4[/tex] then we're basically saying x is any real number. To write this in interval notation, we write [tex](-\infty, \infty)[/tex]

This is the interval from negative infinity to positive infinity (or just infinity). We exclude each endpoint because we can't actually reach infinity itself. Infinity is not a number. Infinity is a concept.

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

Side note: if you change the "or" to "and", then the solution to [tex]x \le 0 \ \text{ and } \ x \ge -4[/tex] would be [tex][-4, 0][/tex] to indicate the interval from x = -4 to x = 0, including both endpoints. This is the region where the two graphs overlap.

Answer:

Step-by-step explanation:

We are to prove the cofunction Identity using the Addition and Subtraction Formulas. [tex]tan(\pi/2 - u) = cot (u)[/tex]

From trigonometry identity, [tex]tan x = sinx/cosx[/tex], starting from right hand side of the equation, the expression above will become;

[tex]tan(\pi/2 - u) = \dfrac{sin(\frac{\pi}{2}-u )}{cos(\frac{\pi}{2}-u) }........ \ 1 \\\\from\ quadrant;\\\\sin(\frac{\pi}{2}-u) = cos (u) \ and \ cos(\frac{\pi}{2}-u) = sin(u)[/tex]

Substituting this trigonometry identities into equation 1 we will have;

[tex]tan(\pi/2 - u) = \dfrac{cos(u)}{sin(u)}[/tex]

Since cot(u) = 1/tan(u) = cos(u)/sin(u), hence;

[tex]tan(\pi/2 - u) = \dfrac{cos(u)}{sin(u)} = cot(u)\\\\tan(\pi/2 - u) = cot (u)\ Proved![/tex]

Answer:

B.

Step-by-step explanation:

96x90x120x1= 1,036,800

Answer:

Hey there!

The wealthy person can have 96x90x120 different outfits, and that is 1036800 combinations.

Let me know if this helps :)

Question:

Based on a survey, assume that 28% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly selected, exactly three of them are comfortable with delivery by drones.

Identify the values of n, x, p, and q.

Answer:

[tex]n = 5[/tex]

[tex]x = 3[/tex]

[tex]p = 0.28[/tex]

[tex]q = 0.72[/tex]

Step-by-step explanation:

Given

Proportion of customers that prefer drone = 28%

Selected customers= 5

Customers expected to prefer drone = 3

Required

Determine the value of n, x, p and q

In probability; n represents the selected sample;

So;

[tex]n = 5[/tex]

The expected number of people to prefer drone is represented by x;

So;

[tex]x = 3[/tex]

In probability, opposite probabilities add up to 1

i.e.

[tex]p + q = 1[/tex]

Where p is the given probability;

[tex]p = 28\%[/tex]

Convert to decimal

[tex]p = 0.28[/tex]

Substitute 0,28 for p in the above equation

[tex]p + q = 1[/tex] becomes

[tex]0.28 + q = 1[/tex]

Make q the subject of formula

[tex]q = 1 - 0.28[/tex]

[tex]q = 0.72[/tex]

Answer & Step-by-step explanation:

Working from the inner circle out:

Natural Numbers: 1,2,3,4

These are the numbers you would use to count

Whole Numbers: 0,1,2,3

The natural numbers and zero

Integers: -3,-2,-1,0,1,2,3

The natural numbers, their opposites, and zero

Rational Numbers: [tex]-\frac{1}{2}, 0.22222222....,1,2,\frac{2}{3} ,\frac{5}{4} ,6.1[/tex]

-are all numbers that you can write as a quotient of integers [tex]\frac{a}{b}, b\neq 0[/tex]

-include terminating decimals. For example,  [tex]\frac{1}{8}=0.125[/tex]

-include repeating decimals. For example, [tex]\frac{1}{3}=0.333333...[/tex]

In the rectangle:

Irrational Numbers: [tex]\sqrt{2} ,\pi[/tex]

-have decimal representations that neither terminate nor repeat. For example, [tex]\sqrt{2} =1.414213...[/tex]

-cannot be written as quotients of integers

Answer:

x=60

Step-by-step explanation:

1/6x=10

multiply both sides by 6 to get x

x=60

Answer:

x=60

Step-by-step explanation:

In order to solve for x, we must isolate x on one side of the equation.

The equation given is:

[tex]\frac{1}{6}x=10[/tex]

1/6 and x are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 1/6

[tex]\frac{1}{6}x/\frac{1}{6}=10/\frac{1}{6}[/tex]

When dividing by a fraction, you can multiply by the reciprocal of the fraction instead.

To find the reciprocal, flip the numerator and denominator.

1/6 ⇒ flip top number and bottom number ⇒ 6/1=6

Replace the division by 1/6 with multiplication by 6.

[tex]\frac{1}{6}x * 6=10*6[/tex]

[tex]x= 10 *6[/tex]

[tex]x=60[/tex]

The solution to this equation is x=60

To find the area of the arena, you will need to find the areas of the rectangular spaces and the 2 semicircles. Because the formulas are given, I will just substitute in the values and show the work for finding the areas.

To find the perimeter, you will look at the distances of lines that take you around the space. Because two of these spaces are half circles, you will need to find the circumference of the full circle.

Also, the answers need to be given in meters, so all units given in centimeters will be divided by 100 to convert them to meters.

Perimeter:

C= 3.14 x 20 m

C = 62.8 meters

62.8 + 8 + 25 + 8 + 5 + 8 + 10 + 8 + 40= 174.8 meters for the Perimeter

Area:

A = 25 x 8

A = 200 square meters

A = 10 x 8

A = 80 square meters

A = 20 x 40

A = 800 square meters

A = 3.14 x 10^2

A = 314 square meters

Total Area: 314 + 800 + 80 + 200= 1394 square meters

Answer:

the average is

add 22 8 times and add 13 4 times

8×22=176

4×13=52

52+176=228

The average price you paid for each movie will be $19.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean.

It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

You bought 8 DVDs for $22 each and 4 DVDs for $13 each.

Then the total number of the DVDs will be

Total DVDs = 8 + 4 = 12

The total amount of dollars spent will be

Total amount = 22 x 8 + 13 x 4

Total amount = $228

Then the average price you paid for each movie will be

Average = $228 / 12

Average = $19

The average price you paid for each movie will be $19.

More about the mean link is given below.

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Answer:

$65.04

Step-by-step explanation:

Given:

Total amount left by the customer on table = $80

It contains cost of the food + 15% tip + 8% sales tax.

Sales tax and tip are calculated from the cost of food.

To find:

Cost of the food = ?

Solution:

Let the cost of food = $[tex]x[/tex]

As per given question statement:

Tip = 15% of [tex]x[/tex]

Sales Tax = 8% of [tex]x[/tex]

Money left on table = Cost of food + Tip + Sales tax

$80 = [tex]x[/tex] + 15% of [tex]x[/tex] + 8% of [tex]x[/tex]

Now, let us solve the equation:

[tex]\$80 = x + 15\%\ of\ x + 8\%\ of\ x\\\Rightarrow 80 = x + \dfrac{15}{100} \times x + \dfrac{8}{100} \times x\\\Rightarrow 80 = \dfrac{100x + 15\times x + 8\times x}{100}\\\Rightarrow 80 = \dfrac{123x}{100}\\\Rightarrow 80 \times 100= 123x\\\Rightarrow x = \dfrac{8000}{123}\\\Rightarrow \bold{x = \$65.04}[/tex]

Therefore, the cost of food, rounded off to nearest cent is $65.04.

Answer:

Step-by-step explanation:

The cost of the food as x, the tips as 0.15, and the tax as 0.08x. Then setting up and solving the equation x+0.15x+0.08x=80.

 A. Draw a second line using a straightedge so that it intersects the first.

Step-by-step explanation:

trust me i took the test and got it right

Answer:

Draw a second line using a straightedge so that it intersects the first.

Answer above is correct, just took the test.

Step-by-step explanation:

Answer: ∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA =  5/3

Step-by-step explanation:

Given that;

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy)

Green's Theorem is given as;

∫c (P(x,y)dx + Q(x,y)dy) = ∫∫ₐ { (-β/βy) P(x,y) + (β/βy) Q(x,y) } dA

Now our P(x,y) = 3y + 7e^(√x) and our Q(x,y) = 8x + 5 cos (y²)

Since we know this, therefore; we substitute

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ { (-β/βy) (3y + 7e^(√x))  + (β/βy) (8x + 5 cos (y²)) } dA

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ ( 8-3) dA

∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy)  = ∫∫ₐ 5dA

from the question, our region is defined by a lower bound: y = x² and an upper bound of y = √x

going from x = 0 to x = 1

Now calculating ∫∫ₐ 5dA  by means of the description of the region, we say;

∫∫ₐ 5dA  = 5¹∫₀   ₓ²∫^(√x) dydx

∫∫ₐ 5dA =  5¹∫₀ (y)∧(y-√x) ∨(y-x²)  dx

∫∫ₐ 5dA = 5¹∫₀ (√x-x²) dx

∫∫ₐ 5dA = 5 [ ((x^(3/2))/(3/2)) - x³/3]¹₀     NOW since ∫[f(x)]ⁿ dx = ([f(x)]ⁿ⁺¹ / n+1) + C

then

∫∫ₐ 5dA = 5 [ ((1^(3/2))/(3/2)) - 1³ / 3) - ((0^(3/2))/(3/2)) - 0³ / 3) ]

∫∫ₐ 5dA = 5 [ ((1^(3/2))/(3/2)) - 1³ / 3)

∫∫ₐ 5dA = 5/3

Therefore ∫c ((3y + 7e^(√x) dx + (8x + 5 cos (y²)) dy) = ∫∫ₐ 5dA =  5/3

In this exercise we have to use green's theorem to calculate the values ​​of the curve through the integers, so we will find that:

[tex]\int\limits \int\limits_a{5} \, dA = 5/3[/tex]

First, the integral given in this exercise corresponds to:  

[tex]\int\limits_C {((3y+7e{\sqrt{x}} dx) + (8x+5cos(y^2)) } \, dy[/tex]

Green's Theorem is given as;

[tex]\int\limits_C {(P(x,y)dx + Q(x,y)dy)} \, = \int\limits \int\limits_a { (-\beta/ \beta_y) P(x,y) + (\beta/ \beta_y) Q(x,y) } dA \,[/tex]

Now our:

[tex]P(x,y) = 3y + 7e^{(\sqrt{x} )} \\ Q(x,y) = 8x + 5 cos (y^2)[/tex]

Since we know this, therefore; we substitute:

[tex]\int\limits_C {((3y + 7e^{(\sqrt{x} )} dx + (8x + 5 cos (y^2)) dy)} = \int\limits \int\limits_a {(-\beta / \beta_y) (3y + 7e^{(\sqrt{x} )} + (\beta / \beta_y) (8x + 5 cos (y^2))} \, dA\\\int\limits_C {((3y + 7e^{(\sqrt{x} )}dx + (8x + 5 cos (y^2)) dy} = \int\limits \int\limits_a {( 8-3) dA}\\\int\limits_C {((3y + 7e^{(\sqrt{x} )}dx + (8x + 5 cos (y^2)) dy} = \int\limits \int\limits_a {5 dA}\\[/tex]

From the question, our region is defined by:

Now calculating  by means of the description of the region, we say;

[tex]\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 \int\limits^{\sqrt{x} }_{x^2} {x^2} \, dydx\\\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 {y^{\sqrt{x} } \, dx \\\int\limits \int\limits_a {5} \, dA = 5 \int\limits^1_0 {{\sqrt{x} -x^2} \, dx\\\int\limits \int\limits_a {5} \, dA = 5 [ ((x^{3/2})/(3/2)) - x^3/3][/tex]  

Knowing the formula:

[tex]\int\limits {[f(x)]^n} \, dx = ([f(x)]^{n+1} / n+1) + C[/tex]

Applying the values ​​in the presented formula we find that:

[tex]\int\limits \int\limits_a{5} \, dA = 5/3[/tex]

See more about Green's Theorem at brainly.com/question/15062695

Answer: (0,0)

Step-by-step explanation:

When x is 0  then input 0 into the equation for x and solve for y.

y = -3(0)

y = 0

So x is 0 and y will also be zero so we will have the ordered pair (0,0)

Answer:

The ordered pair is (0,0)

Step-by-step explanation:

y=-3x

Let x = 0

y = -3*0

y = 0

The ordered pair is (0,0)

Subtract starting population from current one:

6.34 - 1.9 = 4.44

The population increased by 4.44 million.