Margin of error: 0.04; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 60%
A) 577 B) 1441 C) 996 D) 519

Answer:

$800

Step-by-step explanation:

5% × 6000 = $350

14640 - 6000 = $8640

7.5% × 6000 = $450

8640 - 6000 = $2640

350 + 450 = $800

Answer:

Figure B

Step-by-step explanation:

A translation moves a certain amount of spaces, but will never turn nor will it rotate.

To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

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Answer:

A square pyramid has 5 faces: 1 square base and 4 triangular faces.

The area of the base is:

A = s^2

where s is the length of the base edge.

In this case, s = 1 m, so:

A = 1^2 = 1 m^2

The area of each triangular face is:

A = 1/2 * b * h

where b is the base of the triangle (which is equal to the length of one side of the square base) and h is the height of the triangle (which is given as 1 m).

In this case, b = 1 m and h = 1 m, so:

A = 1/2 * 1 * 1 = 0.5 m^2

The total surface area of the pyramid is the sum of the area of the base and the area of the four triangular faces:

SA = A_base + 4 * A_triangles

SA = 1 + 4(0.5)

SA = 1 + 2

SA = 3 m^2

Therefore, the surface area of the pyramid is 3 square meters.

Answer:

Step-by-step explanation:

Answer:

The remainder is 88

Step-by-step explanation:

The Remainder of a Division

We have to find the remainder when we divide 849,400 by 216.

It could be found by doing the long division, but we'll do it with a calculator.

Entering the division in the calculator we get:

849,400/216=3,932.4074...

We take the whole part of the quotient (3,932) and multiply it by the divisor:

3,932*216=849,312

The remainder is obtained by subtracting 849,400-849,312=88

The remainder is 88

So the formula to find the volume of a cone is,

\(V = \pi r^{2} \frac{h}{3}\)

Given,

To Find : The Volume of the cone

Applying the values we get,

\(V = 3.14X(3)^{2} X \frac{11}{3}\)

\(V = 28.26X\frac{11}{3}\)

\(V = 103.62in^{3}\)

Hence , the volume of the cone is 103.62in³

After answering the presented question, we can conclude that probability Therefore, the probability of 30 or more seconds between vehicle arrivals is approximately 0.0498.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

Sketch of exponential probability distribution with mean of 12 seconds:

   |                            

   |                            

   |              .            

   |             . .            

   |             . .            

   |             . .            

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . . .        

   |             . . . .        

   |             . . . .        

   |             . . . . .      

   |             . . . . .      

   |_____________. . . . . . .

        0       12             X

The X-axis represents the time between vehicle arrivals, and the Y-axis represents the probability density. The peak of the distribution is at 12 seconds, which is the mean.

b. Probability of the arrival time between vehicles being 12 seconds or less:

Since the mean of the exponential distribution is 12 seconds, we can use the cumulative distribution function (CDF) to find the probability of the arrival time being 12 seconds or less:

\(P(X < = 12) = 1 - e^(-12/12) = 1 - e^(-1) ≈ 0.6321\)

Therefore, the probability of the arrival time between vehicles being 12 seconds or less is approximately 0.6321.

c. Probability of the arrival time between vehicles being 6 seconds or less:

\(P(X < = 6) = 1 - e^(-6/12) = 1 - e^(-0.5) ≈ 0.3935\)

Therefore, the probability of the arrival time between vehicles being 6 seconds or less is approximately 0.3935.

d. Probability of 30 or more seconds between vehicle arrivals:

\(P(X > = 30) = e^(-30/12) ≈ 0.0498\)

Therefore, the probability of 30 or more seconds between vehicle arrivals is approximately 0.0498.

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Answer:

A.  The probability of event B​ occurring, given that event A has occurred

Step-by-step explanation:

Conditional probability

A probability is conditional if is depends on what has already happened.

The probability that event B happens, given that event A has already happened is "B given A" or P(B | A)

Therefore, P(B | A) means "The probability of event B​ occurring, given that event A has occurred"

Additional information:

P(A | B) means "A given B", i.e. the probability of event A​ occurring, given that event B has occurred

P(A ∩ B) means the probability of event A and event B both happening.

Answer:

1 , 2 , 17 or 34

Step-by-step explanation:

34 can divide by these numbers and still be a whole number

hope this helps...

Answer: The result would be - 2x^2 + 3xy + 8y^2.

Step-by-step explanation:

(-x^2 + 9xy) - (x^2 + 6xy - 8y^2)

The objective of this question is to remove the brackets.

The first pair of brackets could simply be removed since it won't need changing (because it's positive, without symbols in front). As for the second one, we must remove the brackets in some way, which is to make basically every term in that bracket the negative of the 'original' ones.

The negative of x^2 = - x^2

The negative of + 6xy = - 6xy

The negative of - 8y^2 = + 8y^2

Combine them with the first two terms and it'll be like below.

= - x^2 + 9xy - x^2 - 6xy + 8y^2

Then, rearrange and sum all like terms together.

There are 2 sets of like terms:

First set: (- x^2 and- x^2)

Second set: ( + 9xy and - 6xy)

So, it becomes...

= - x^2 - x^2 + 9xy - 6xy + 8y^2

= - 2x^2 + 3xy + 8y^2

The answer is A.

An indefinite integral is a function that, when differentiated, equals the original function. It is denoted by ∫f(x)dx, where f(x) is the function to be integrated. An indefinite integral always has an arbitrary constant of integration, which is denoted by C. This is because the derivative of any constant is zero, so the derivative of ∫f(x)dx+C is still equal to f(x).

A definite integral is the limit of a Riemann sum as the number of terms tends to infinity. It is denoted by ∫

a

b

​

f(x)dx, where a and b are the limits of integration. A definite integral does not have an arbitrary constant of integration, because the limits of integration specify a unique value for the integral.

In other words, an indefinite integral is a family of functions that share the same derivative, while a definite integral is a single number.

Answer:

13

Step-by-step explanation:

Use sin = opposite/hypotenuse

Setup an equation. I'm going to use x to represent the hypotenuse.

\(sin44=\frac{9}{x}\)

Now move the x to the other side by multiplying. We want to solve for x.

\(x(sin44)=(\frac{9}{x})x\)

The x cancels on the right side. Now divide both sides by sin44. To get  by itself on the left.

\(\frac{x(sin44)}{sin44} = \frac{9}{sin44}\)

\(x = \frac{9}{sin44}\)

Use your scientific calculator, make sure it is on degrees, and divide 9 by sin44.

\(x = 12.9560088566\)

Round to the nearest whole number

\(x = 13\)

Answer:

Step-by-step explanation:

100 more than 365 is equal to 65more then

we can solve with an equation

100 + 365 = 65 + x

100 + 365 - 65 = x

465 - 65 = x

400 = x

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

check

100 + 365 = 65 + 400

465 = 465

the answer is good

Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Answer-29 bronze, 46 gold,and 29 silver.

The first thing to do is take 104 and subtract the 17 medal difference between them all. This is 87. Next we divided 87 into three, which gives us 29. Now we have 29 medals for silver, bronze, and gold. However we must add 17 to the gold medals that we took away earlier. 29+17 is 46. To make sure this is correct we can add 29+29+46. This equals 104, which our original answer, so this was correct.

In 2012 the United States earned 29 bronze medals, 46 gold medals, and 29 silver medals.

HOPE THIS HELPS!! GOOD LUCK!!! <3

Answer:

\( \sqrt{170} \)

Answer:

Line n bisects segment XY

The length of segment XY = 6

Step-by-step explanation:

Line n is the segment bisector of segment XY

A bisector is to divide into two equal parts, so;

5x + 8 = 9x + 12

4x = -4

x = -1

Total segment = 5x + 8 + 9x + 12

plug in -1 for x;

-5 + 8 + -9 + 12

XY = 3 + 3

XY = 6

Answer:

the answer i came up with for the first question the answer is C

for the second question, i go 11.4

Step-by-step explanation:

how i got 11.4 add all like valuables

12+8=20

9x+5x=14x

then divide to get x alone to get 11.4

Answer:

ans is A

area = l*b

area=(5/6)*(4/6)=20/36=5/9

Answer:

i hope this helpes

Step-by-step explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer:

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}

The correct answer is option b. When the homoskedasticity assumption is violated, The beta parameter estimates are biased while the rest of the OLS assumptions are correct.

When the homoskedasticity assumption is violated, the ordinary least squares (OLS) estimator is still consistent but no longer efficient. This means that the estimates of the regression coefficients (beta parameters) are still unbiased, but they have higher variances and covariances.

In other words, the OLS estimator is no longer the best linear unbiased estimator (BLUE) and it may be biased when the errors are heteroscedastic. Therefore, option b is correct.

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Answer: 77

Step-by-step explanation:

Answer:

(a) The event that represents success here is the percentage of adults who do not work at all while on summer vacation.

(b) X is a binomial random variable.

(c) The value of p for this binomial experiment is 0.30 or 30%.

(d) P(X = 3) = 0.2541.

(e) The probability that 2 or fewer of the 8 adults do not work during summer vacation is 0.5518.

Step-by-step explanation:

We are given that in a school it is found that 30% of adults do not work at all while on summer vacation. In a random sample of 8 adults, let X represent the number who do not work during summer vacation.

Let X = the number of adults who do not work during summer vacation

(a) The event that represents success here is the percentage of adults who do not work at all while on summer vacation.

(b) The conditions required for any variable to be considered as a random variable is given by;

So, in our question; all these conditions are satisfied which means X is a binomial random variable.

(c) The value of p for this binomial experiment is 0.30 or 30%.

(d) The above situation can be represented through binomial distribution;

\(P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......\)

where, n = number of trials (samples) taken = 8 adults

            r = number of success = exactly three

            p = probability of success which in our question is % of adults who

                  do not work at all while on summer vacation, i.e; p = 0.25

SO, X ~ Binom(n = 8, p = 0.30)

Now, the probability that exactly 3 adults do not work at all while on summer vacation is given by = P(X = 3)

          P(X = 3) =  \(\binom{8}{3}\times 0.30^{3} \times (1-0.30)^{8-3}\)

                        =  \(56 \times 0.30^{3} \times 0.70^{5}\)

                        =  0.2541

(e) The probability that 2 or fewer of the 8 adults do not work during summer vacation is given by = P(X \(\leq\) 2)

      P(X \(\leq\) 2) = P(X = 0) + P(X = 1) + P(X = 2)

= \(\binom{8}{0}\times 0.30^{0} \times (1-0.30)^{8-0}+\binom{8}{1}\times 0.30^{1} \times (1-0.30)^{8-1}+\binom{8}{2}\times 0.30^{2} \times (1-0.30)^{8-2}\)

= \(1 \times 0.30^{0} \times 0.70^{8}+8 \times 0.30^{1} \times 0.70^{7}+28\times 0.30^{2} \times 0.70^{6}\)

= 0.5518

By using trigonometry, the missing sides are

Example 1: x = 16.7

Example 2: x = 3.2

Example 3: x = 23.5

Example 4: x = 9.3

From the question we are to determine the value of the missing sides in the given triangles

We can determine the value of the missing sides by using SOH CAH TOA

Example 1

Angle = 42°

Opposite side = x

Hypotenuse = 25

Thus,

sin (42°) = x / 25

x = 25 × sin (42°)

x = 16.7

Example 2

Angle = 75°

Opposite side = 12

Adjacent side = x

Thus,

tan (75°) = 12 / x

x = 12 / tan (75°)

x = 3.2

Example 3

Angle = 36°

Hypotenuse side = x

Adjacent side = 19

Thus,

cos (36°) = 19 / x

x = 19 / cos (36°)

x = 23.5

Example 4

Angle = 53°

Opposite side = x

Adjacent side = 7

Thus,

tan (53°) = x / 7

x = 7 × tan (53°)

x = 9.3

Hence,

The missing sides are 16.7, 3.2, 23.5 and 9.3

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let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said

\(\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill\)

\(\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}\)

243 = the pages read on Saturday

243 - 53 = 190 = the pages read on Sunday

190 + 243 =  433 = total pages read

Answer = 433

The answer to the equation −0.22x + x − 0.33x is 0.11x.

The answer is 0.11x. To solve this, we can start by rearranging the terms of the equation. The equation can be written as:

−0.22x + x − 0.33x = −0.22 + 0.33x

We then subtract x from both sides of the equation, resulting in:

−0.22x − x = −0.22 + 0.33x − x

We then combine like terms on the left side of the equation, resulting in:

−1.22x = −0.55

Finally, we divide both sides of the equation by -1.22 to solve for x, resulting in:

x = 0.11

Therefore, the answer is 0.11x.

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Complete question

What is the value of -0.22+−0.33−0.22x+x−0.33x?

Expansion of x(3.25y - 4.86) is 3.25xy - 4.86x and expansion of

x(-1.75y + 5y - 3.86) + x is 3.25xy - 2.86x. The expressions are not equivalent as the coefficient of x is different in the expanded form.

What are equivalent expressions?

In expanded form, the expression combines all its like terms.

Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other.

According to the given question:

The given expressions are

1. x (3.25y - 4.86)

2. x (-1.75y + 5y - 3.86) + x

Expanding each expression

1. x (3.25y - 4.86)

= 3.25*x*y - 4.86*x

= 3.25xy - 4.86x

2. x (-1.75y + 5y - 3.86) + x

= -1.75*x*y + 5*x*y - 3.86*x + x

= 3.25xy - 2.86x

Clearly coefficient of x variable is different after expansion of expressions. Therefore, the expressions are not equivalent.

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