A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 33% of the residents of the city have heard the ad and recognize the company's product. The radio station conducts a random phone survey of 332 people. The survey shows that 70 people have heard the ad and recognize the company's product. For this test, the radio station uses a 5% significance level and will reject the null hypothesis (will renew the contract) for any * * sample proportion that is greater than p. What is the value of p in the test (assume 20.05 = 1.645)?

Answer:

3

Step-by-step explanation:

step1 Isolate the square root on the left hand side

    Original equation

    √2x-5-4 = -x

    Isolate

    √2x-5 = 4-x

step2 eliminate the radical on the left hand side

    Raise both sides to the second power

    (√2x-5)2 = (4-x)2

    After squaring

    2x-5 = x2-8x+16

step3 Solve the quadratic equation

    Rearranged equation

    x2  - 10x  + 21 = 0

    This equation has two rational roots:

      {x1, x2}={7, 3}

step4 Check that the first solution is correct

    Original equation, root isolated

    √2x-5 = 4-x

    Plug in 7 for  x  

     √2•(7)-5 = 4-(7)

     Simplify

     √9 = -3

     Solution does not check

     3 ≠ -3

step5 Check that the second solution is correct

    Original equation, root isolated

    √2x-5 = 4-x

    Plug in 3 for  x  

     √2•(3)-5 = 4-(3)

     Simplify

     √1 = 1

     Solution checks !!

    Solution is:

     x = 3

Answer:

-3

Step-by-step explanation: i got it right on my test

No, Lydia's assertion that δSTU is a right triangle is not correct.

A right triangle is a triangle in which one of the angles measures 90 degrees (a right angle). To determine if δSTU is a right triangle, we need to examine the angles formed by the given coordinates.

Using the coordinates:

s (-3, 0)

t (0, -3)

u (3, -3)

We can calculate the slopes of the lines formed by connecting these points to see if any of them are perpendicular (indicating a right angle).

The slope of the line connecting points s and t is:

m(st) = (y₂ - y₁) / (x₂ - x₁) = (-3 - 0) / (0 - (-3)) = -3/3 = -1

The slope of the line connecting points s and u is:

m(su) = (y₂ - y₁) / (x₂ - x₁) = (-3 - 0) / (3 - (-3)) = -3/6 = -1/2

The slope of the line connecting points t and u is:

m(tu) = (y₂ - y₁) / (x₂ - x₁) = (-3 - (-3)) / (3 - 0) = 0/3 = 0

None of the slopes calculated are perpendicular to each other, meaning none of the angles formed by the given coordinates are 90 degrees. Therefore, δSTU is not a right triangle.

In summary, Lydia's assertion that δSTU is a right triangle is incorrect because the angles formed by the given coordinates do not include a 90-degree angle.

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Answer:

-2/9  

Step-by-step explanation:

The mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

Given data values are 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and 2. We need to calculate the mean, median, and mode of this sample.So, let's first arrange the data values in ascending order:2, 50, 52, 53, 55, 56, 57, 61, 69, 70, 73

Mean:The mean is the sum of all the data values divided by the total number of data values. So, we can use the following formula to calculate the mean:

Mean = (sum of all the data values) / (total number of data values)Sum of all the data values = 55 + 56 + 70 + 61 + 53 + 57 + 50 + 73 + 52 + 69 + 2 = 598Total number of data values = 11

Therefore,Mean = (sum of all the data values) / (total number of data values) = 598 / 11 = 54.36 (rounded to two decimal places)Therefore, the mean of the given data values is 54.36.

Median:The median is the middle value of a sorted data set. Since the data set has 11 data values, the median is the average of the 6th and 7th values (counting from smallest to largest).

Therefore, the median is :Median = (55 + 56) / 2 = 55.5Therefore, the median of the given data values is 55.5.

Mode:The mode is the data value that appears most frequently in the data set. In this case, there is no data value that appears more than once. So, there is no mode.

Therefore, the mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

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True. A pie chart is a segmented circle that represents different categories and their relative sizes based on a numerical variable.

A pie chart is a circular statistical graphic divided into sectors, or "slices," which correspond to different categories or groups. The size of each sector is proportional to the value it represents within the given numerical variable. The chart is named after its resemblance to a sliced pie, with each slice representing a portion or percentage of the whole. Pie charts are commonly used to display data with discrete categories, such as survey results, market shares, or budget allocations. The length of each sector's arc is determined by the magnitude of the data it represents, allowing for easy visual comparison between categories. The whole pie represents 100% or the total of the variable being measured. By examining the relative sizes of the sectors, one can quickly understand the distribution and proportions of the categories being represented. Therefore, it is accurate to say that a pie chart is a segmented circle that portrays the categories and their relative sizes based on a numerical variable.

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The Mean of a standard normal distribution is always equal to 0. This statement is true.

The standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one. The density curve of a standard normal distribution is bell-shaped and symmetric. Its total area under the curve is equal to 1.00.A normal distribution with a mean (µ) of zero and a standard deviation (σ) of one is called a standard normal distribution. Any normal distribution can be converted into a standard normal distribution by using a process known as standardization. Z-score formula is used to find the probability and value associated with any normal distribution.What is a normal distribution?A normal distribution is a statistical term that describes a symmetrical, bell-shaped probability distribution that has a particular mathematical formula. It's used to explain and assess natural phenomena such as height, blood pressure, and intelligence quotient (IQ).A normal distribution is a probability distribution with a bell-shaped curve that is symmetrical. The mean (µ) is the center of the curve, while the standard deviation (σ) determines its width. Most of the values in a standard normal distribution are concentrated within three standard deviations of the mean, as seen in the figure. The standard normal distribution is one of the most often utilized continuous probability distributions in statistical theory.

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The total distance Raven is driving is 300 mi. The distance she has left to drive is 210 mil.

Percentage is the fraction out of an amount that is usually expressed as a number out of hundred. It is a measure of frequency.

Total distance = 90 mi / 30%

=90 / 0.3 = 300 mi

Distance he has left = 300 - 90 = 210 mi

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Answer:

Josh earned $151

Step-by-step explanation:

Answer:

Step-by-step explanation:

The quotient of the polynomials is 6x^2 - 2x + 5 with a remainder of -50.

To find the quotient of the polynomials  ÷ (2x + 5), you can use polynomial long division as follows:

       6x^2 - 2x + 5

 -----------------------

2x + 5 | 12x^3 + 26x^2 + 25

- (12x^3 + 30x^2)

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

-4x^2 + 25

- (-4x^2 - 10x)

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

35x + 25

- (35x + 75)

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

-50

Therefore, the quotient of the polynomials is 6x^2 - 2x + 5 with a remainder of -50.

Watermelon can be divided into a maximum of 56 pieces using ten cuts.

A watermelon splits into two parts when you make a cut through it. Anywhere that a subsequent cut crosses an earlier cut, a new piece is formed. As a result, there are more pieces after each cut.

We need to take into account how the cuts cross to find the maximum number of pieces. Two pieces are produced by the first cut, two more are produced by the second cut intersecting those two pieces, and so on.

Figured out using a formula.

The formula given below is to calculate the greatest number of fragments from n cuts.

N=(n²+n+2)/2

In the formula, change n = 10 to represent ten cuts as follows

N=(10²+10+2)/2

N = (100+10+2)/2

N=112/2 N=56

A watermelon may only be divided into a maximum of 56 pieces with ten cuts.

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Using translation concepts, it is found that the coordinates of the image of the origin under the same translation are given by:

3. (-2,1).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A translation maps A(1,2) onto A'(-1,3), hence the rule is given by:

(x,y) -> (x - 2, y + 1).

Then the image of the origin (0,0) is given by:

(0,0) -> (0 - 2, 0 + 1) = (-2,1)

Which means that option 3 is correct.

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\(90 \sqrt{72} \)

which is equal to 763.6753236815

Answer:

C

Step-by-step explanation:

b=360-2(65)=360-130=230

Answer:

230

Step-by-step explanation:

b= 360-2(65)

=360-130

=230

Answer:57

Step-by-step explanation: Because I don’t know

The maximum number of miles Julie can drive the car is 272 miles.

Let's check how:

Julie's budget for renting a car is $200.

number of days she'll rent a car is 3.

car rental per day is $44 + $0.25 per mile.

so to know maximum no. of miles she can drive

we'll first subtract the 3 days rent from Julie's budget = $200 - ( 3 x $44 )

= $200 - $132

= $132

Now, the left money is $68.

so, we will divide $68 by $0.25 to know how much miles she can drive.

= $68 ÷ $0.25

= 272 miles

Hence, the maximum number of miles Julie can drive the car for 3 days is 272 miles.

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Answer:

Step-by-step explanation:

Answer:

Answer: B'(-5,2)

Step-by-step explanation:

Rotations

When rotating a point B(x,y) 90 degrees counterclockwise about the origin it maps to an image point B'(-y,x).

The image shows a figure formed by points ABCD. The coordinates of B are B(2,5).

This point will be rotated 90 degrees counterclockwise about the origin, thus the coordinates of the image point B' are B'(-5,2).

Answer: B'(-5,2)

Answer:

y=16x

Step-by-step explanation:

24=1 1/2x=3/2x

x=24*(2/3)=16

y= total money earned; x=number of hours worked

There was an increase in sales by 20% x Number of units sold x original price.

There was an increase in sales by 20% x Number of units sold x original price.

Due to the 30% drop in prices of mobile sets in the shop, there was an increase in sales by 20%.

The effect on the mobile shop is that there was a decrease in revenue but an increase in the number of units sold.

If there is a 30% drop in the prices of mobile sets, then the new price would be 70% of the original price.

This is calculated by the formula;

New price = 100% - 30%

= 70%

Thus, the new price of the mobile set is 70% of the original price.

Now, if there is a 20% increase in sales due to this price drop, this means that the number of units sold has increased by 20%.

So, the revenue from selling mobile sets can be calculated as:

Revenue = Number of units sold x Price of each unit

Since the price has decreased by 30%, the revenue from each unit sold would also decrease.

The new revenue from selling each unit can be calculated as:

New Revenue = 70% of the original price = 0.7 x original price

So, the total revenue from all units sold would be:

Number of units sold x New revenue from each unit

This can be further expressed as:Number of units sold x (0.7 x original price) = 0.7 x (Number of units sold x original price)

Thus, the revenue has decreased by 30% x Number of units sold x original price.

Now, since the number of units sold has increased by 20%, the net effect on the mobile shop would be:

Net effect = Decrease in revenue + Increase in units sold

= 30% x Number of units sold x original price + 20% x Number of units sold x original price

= 50% x Number of units sold x original price

Therefore, due to the drop of 30% in prices of mobile sets, there was a decrease in revenue by 50% x Number of units sold x original price.

However, there was an increase in sales by 20% x Number of units sold x original price.

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Step-by-step explanation:

1. =9-(-2)

=9-(-2)=11

2. =-6-3

. =-6-3=-9

3. =-4-(-2)

. =-4-(-2)= -2

5. =4-(-8)

. =4-(-8)=12

5. =-5-9

. =-5-9=-14

6. =5-(-3)

. =5-(-3)=8

if specifically they do not want the directions don't include the signs of the outputs because distance cannot be negative!!!!

Answer:

a) X + X + 1 = 11

Step-by-step explanation:

Em matemática, a soma de consecutivos é expressa matematicamente como:

X + (X + 1) + (X + 2) + (X + 3) .............

Na pergunta acima, somos solicitados a encontrar a expressão algébrica que indica que a soma de DOIS inteiros consecutivos é igual a 11

Portanto, esta expressão algébrica é dada como:

X + (X + 1) = 11

X + X + 1 = 11

Portanto, a opção a) X + X + 1 = 11 é a opção correta

The simplified sum of the expression ∑+1=−1 (2 − 1) is 2.

The given expression is the sum of (2 - 1) from i = -1 to n, where n = 1. Therefore, the expression can be simplified as follows:

∑+1=−1 (2 − 1) = (2 - 1) + (2 - 1) = 1 + 1 = 2

In this case, the value of n is 1, which means that the summation will only be performed for i = -1. The expression inside the summation is (2 - 1), which equals 1. Thus, the summation is equal to 1.

Adding 1 to the result of the summation gives:

∑+1=−1 (2 − 1) + 1 = 1 + 1 = 2

Therefore, the simplified sum of the expression ∑+1=−1 (2 − 1) is 2.

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Answer:

In the beginning there were 20 bacterias in the petri dish.

When data are positively skewed, the mean will usually be:d) greater than the median.

The median is the value in the middle of the value series which is arranged using data in order from the smallest to the largest, for example in a series of 3, 4, 7 the median is 4.

The median is the value that can divide the data into two equal parts. With a note, that the data must be sorted first from the smallest to the largest.

In addition, the median can also be used to determine the average of a data set, but it cannot be equated with the mean.

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Naya's gross annual income is approximately $46,416.67.

To determine Naya's gross annual income, we need to reverse engineer the tax calculation based on the given information.

Let's denote Naya's gross annual income as G. We know that Naya's net annual income, after income tax, is 36,560. We also know that Naya pays income tax at the same rates and has the same annual tax credits as Emma.

Emma pays income tax on her taxable income at a rate of 20% on the first 35,300 and 40% on the balance. She has annual tax credits of 1,650.

Based on this information, we can set up the following equation:

G - (0.2 * 35,300) - (0.4 * (G - 35,300)) = 36,560 - 1,650

Let's solve this equation step by step:

G - 7,060 - 0.4G + 14,120 = 34,910

Combining like terms, we have:

0.6G + 7,060 = 34,910

Subtracting 7,060 from both sides:

0.6G = 27,850

Dividing both sides by 0.6:

G = 27,850 / 0.6

G ≈ 46,416.67

Therefore, Naya's gross annual income is approximately $46,416.67.

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Answer:

Read Below

Step-by-step explanation:

The 56 = 7 x 8 are consecutive number 5, 6, 7, 8. So, 7x8 equals 56. (This only works for two facts - 1, 2, 3, 4 is 12 = 3x4 and 5, 6, 7, 8 is 56 = 7x8)

The situation for 7 x -8 = -56 is the multiplication of a number with its negative consecutive where the number is 7.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

7 x - 8 =- -56

This can be described as a situation:

Multiplication of a number with its negative consecutive where the number is 7.

Number = M

Negative consecutive = -(M + 1)

So,

M x -(M + 1)

M = 7

So,

7 x -(8)

= -56

Thus,

The situation is the multiplication of a number with its negative consecutive where the number is 7.

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New current if the voltage is increased to 4 volts. = 0.1 A or 100 mA

What is a current simple definition?

amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit.

=> I  ∝  V

=> I  = V/R    

R is a constant

and R  is resistance

When 3 volts are applied to a circuit, 75 milliamperes of current flow through the circuit.

=> 75 x 10⁻³  = 3 /R

=> R = 3 x 10³/75

=> R =  10³/25

=> R = 40

I  = V/R    

V = 4

R = 40

=> I  = 4/40

=> I  = 1/10

=> I = 0.1 A

or 100 mA

new current if the voltage is increased to 4 volts. = 0.1 A or 100 mA

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1. True. This statement is true because it is possible for a function to have a negative value, positive derivative, and negative second derivative over all x values.

2. True. This is because the derivative of a function is the rate of change of the function.

1. This kind of function has an example in f(x) = x^3 - 3x^2. This function has a first derivative off'(x) = 3x^2 - 6x that is positive for all x values, a second derivative of f''(x) = 6x - 6 that is negative for all x values, and is negative for all x values.

2. The rate of change of the function is always non-zero if the derivative is non zero for all x, and the value of the function at any two locations will not be the same.

Hence, if f '(x) exists and is nonzero for every x, then f(10) ≠ f(0). Consider the function f(x) = x2 as an illustration of this. This function's derivative with respect to x is given by the expression f '(x) = 2x, which is non zero for every x.

As a result, f(10) = 102 = 100 and f(0) = 0, which are clearly not equal.

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The total number of seeds that Josiah would plant would be = nR×S

To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.

Let each row be represented as = nR

Where n represents the number of rows planted by him.

Let the seed be represented as = S

The total number of seeds he planted = nR×S

Therefore, the total number of seeds that was planted Josiah would be = nR×S.

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3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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