For the following image, find x :

x =

Answer:

Let’s start by defining the variables:

Let A be the area of the preimage.

Let k be the scale factor.

If the scale factor is k, then the area of the preimage is multiplied by k² to calculate the area of the new image. Therefore, we have:

Area of new image = k²A

We are given that:

k = 1/5

Therefore, we have:

k² = (1/5)² = 1/25

The area of the preimage is not given. Therefore, we cannot calculate the area of the new image

Let's start by calculating the store's revenue at the current price of $50 per pair of swimming flippers:

Revenue = Price x Quantity Sold = $50 x 92 = $4,600 per day

Now, let's see how changes in the price affect the quantity sold. According to the problem, for each $3 increase in price, 3 fewer sales are made. This means that the demand function is:

Quantity Sold = 92 - 3/3 (Price - $50) = 92 - (Price - $50)

where Price is measured in dollars.

To calculate the store's profit, we need to subtract the cost of producing each pair of swimming flippers from the revenue:

Profit = (Price - Cost) x Quantity Sold

We don't have information about the cost of producing each pair of swimming flippers, so let's assume that it is a constant of $20 per pair. This means that the profit function is:

Profit = (Price - $20) x (92 - (Price - $50)) = (Price - $20) x (-Price + $142)

Expanding the brackets and simplifying, we get:

Profit = -$Price^2 + $122Price - $2840

To find the price that maximizes profit, we need to take the derivative of the profit function with respect to price, and set it equal to zero:

dProfit/dPrice = -$2Price + $122 = 0

Solving for Price, we get:

Price = $61

So, the store should charge $61 per pair of swimming flippers to maximize profit. To verify that this is indeed the maximum, we can take the second derivative of the profit function with respect to price:

d^2Profit/dPrice^2 = -$2

Since this is negative, we know that the profit function is concave down, which means that the critical point we found is indeed a maximum.

Answer:

5.625 inches

Step-by-step explanation:

We Know

A 6-inch candle burns down in 8 hours.

6 / 8 = 0.75 inches burn down per hour

So, we know 0.75 inches burn down per hour

How far has it burned after 7 1/2 hours?

We take

0.75 x 7.5 = 5.625 inches

So, it burned 5.625 inches after 7 1/2 hours.

The units of measurement for prpblck are percentage points, while the units for income are typically a currency, like dollars or euros.

To find the average value of prpblck and income in the sample, you need to sum the values for each variable and then divide by the total number of observations. The average is also known as the mean. The standard deviation is a measure of dispersion that indicates how much the values vary from the mean. To calculate the standard deviation, you will need to find the difference between each value and the mean, square those differences, find the average of those squared differences, and then take the square root of that average.

The units of measurement for prpblck and income depend on the context and data source. Typically, prpblck is expressed as a proportion or percentage, representing the proportion of the population that is black. In this case, the unit of measurement for prpblck would be percentage points. On the other hand, income is usually measured in a currency, such as dollars or euros, and it can be presented as an individual's income or a household's income.

To summarize, to find the average values and standard deviations of prpblck and income in the sample, follow these steps:

1. Calculate the mean by summing the values and dividing by the number of observations.

2. Calculate the standard deviation by finding the square root of the average of the squared differences between each value and the mean.

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AK = AL ≈ 28.77,  KL < 57.54. In summary, the values of AK = AL ≈ 28.77 and  KL < 57.54 .

A closed triangle is a polygon with three sides and three angles in two dimensions.

We know that the radius of the circle, OA, is 25. Since OA is a radius of the circle and bisects triangle ΔKAL, we can conclude that AK = AL.

Let's call AK = AL = x.

Now we use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle K.

We know that angle L is 25 degrees, and since angle KAL is 100 degrees, angle K must be:

K = 180 - L - KAL

K = 180 - 25 - 100

K = 55 degrees

Now, we can use the law of sines to find x, which is the length of both AK and AL:

sin(K) / x = sin(L) / OA

sin(55) / x = sin(25) / 25

x = sin(55) * 25 / sin(25)

x ≈ 28.77

Therefore, AK = AL ≈ 28.77.

To find KL, we can use the fact that AK = AL = x and OA = 25 to find OK and OL:

OK = OA - AK

OK = 25 - 28.77

OK ≈ -3.77

OL = OA - AL

OL = 25 - 28.77

OL ≈ -3.77

Since OK and OL are both negative, we know that O must be located inside triangle ΔKAL. Therefore, we can use the triangle inequality to find KL:

KL < AK + AL

KL < 2x

KL < 2(28.77)

KL < 57.54

Therefore, KL < 57.54.

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One way to approach this problem is to use the formula:

total cost = cost of parts + cost of labor

We can plug in the given values:

719.75 = 116 + cost of labor x 5.25

Simplifying:

603.75 = cost of labor x 5.25

To solve for the cost of labor per hour (cc), we can divide both sides by 5.25:

cc = 603.75 / 5.25

Simplifying:

cc ≈ 114.76

Therefore, the equation that could be used to determine the cost of labor per hour is:

cc = (total cost - cost of parts) / hours of labor

or:

cc = (719.75 - 116) / 5.25

Answer:

  47/60

Step-by-step explanation:

You want to know the probability of a randomly selected student is on the honor roll or varsity team when 176 of 240 students are on the honor roll, 48 are on the varsity team, and 36 are on both.

The probability of A or B is ...

  P(A+B) = P(A) +P(B) - P(A·B)

The probability of interest is ...

  P(honor roll + varsity) = P(honor roll) + P(varsity) - P(honor roll & varsity)

  P(honor roll + varsity) = 176/240 +48/240 -36/240 = (176 +48 -36)/240

  = 188/240 = 47/60

The probability of interest is 47/60.

[tex]\blue{\huge {\mathrm{PROBABILITY}}}[/tex]

[tex]\\[/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]

[tex]{===========================================}[/tex]

[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}[/tex]

We can use the inclusion-exclusion principle to find the number of students who are on the honor roll or are members of the varsity team.

This principle states that:

where:

Using this principle, we can find that:

[tex]\begin{aligned}\sf |Honors\cup Varsity|& =\sf |Honors| + |Varsity| − |Honors\cap Varsity|\\& =\sf 176 + 48 - 36\\& =\sf\red{188}\end{aligned}[/tex]

Therefore, there are 188 students who are on the honor roll or are members of the varsity team.

The probability that a randomly selected student is on the honor roll or is a member of the varsity team is then:

[tex]\begin{aligned}\sf P(Honors\cup Varsity)& =\sf \dfrac{|Honors\cup Varsity|}{|Total|} \\ &=\sf \dfrac{188}{240} \\&=\boxed{\bold{\: \dfrac{47}{60}\:}}\end{aligned}[/tex]

Therefore, the probability that a randomly selected student is on the honor roll or is a member of the varsity team is [tex]\boxed{\bold{\:\dfrac{47}{60}\:}}[/tex]

[tex]{===========================================}[/tex]

[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\qquad\qquad\qquad\tt 04/02/2023[/tex]

The distance from Gladville to Columbus is 144 miles.

The scale of map B is (3.4 cm) / (6.8 cm) = 1/2 that of map A.

Then the distance (d) between the cities is:

= (1.8 cm)/d = (1/2)·(1 cm) / (40 mi)

Multiplying by d·80 mi, we get

 144 mi·cm = d cm

Dividing by cm, we have ...

 144 mi = d

The distance from Gladville to Columbus is 144 miles.

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The correct hypothesis for a one-sample z-test for a population proportion p for germination is p <0.9

A hypothesis is an informed estimate about the solution to a scientific issue that is supported by sound reasoning. It is the expected result of the trial, though it is not evidence in an experiment. Depending on the information collected, it might be supported or might not be allowed at all.

The material provided indicates that the following is the appropriate theories for a one-sample z-test for a population proportion where H0 is p = 0.9 and H1 <0.9. Thus, at the null hypothesis, it is tested if the germination rate is actually of 90%, that is H = 0.9 and at the alternative hypothesis, it is tested if the germination rate is of less than 90%, that is H1 <0.9.

Complete Question:

The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?.

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Answer:

Undefined at x = 2 and x = -2

Step-by-step explanation:

(5x²+x+11)/(x²-4)

Function becomes undefined when the denominator goes to zero.

x² - 4 = 0

x = 2, -2

Answer:

In Real numbers: none (defined for all real numbers)

In Complex numbers: not defined for [tex]x = 2i, -2i[/tex]

Step-by-step explanation:

Fraction becomes undefined when the denominator = 0

[tex]x^2 + 4 = 0[/tex]

Has no real solutions

The fraction is defined for all real values of x

[tex]x^2 + 4 = 0[/tex]

[tex]x^2 = -4[/tex]

[tex]x = 2i, -2i[/tex]

The fraction is not defined for [tex]x = \dfrac{+}{-2i}[/tex] (in Complex Numbers)

The simplified expression for expression √0.2 × √25y² will be √5|y| and for 1/16x² if x is greater than or equal to 0 simplified expressions will be (1/4)x.

a) Simplifying the expression √0.2 × √25y² using the properties of square roots, we get:

= √0.2 × √25y²

= √(0.2 × 25 × y²)

= √(5y²)

= √5 × √y²

= √5 × |y|

Since y<0, we need to take the absolute value of y to ensure that the result is positive. Therefore, the simplified expression is √5|y|.

b) Simplifying the expression √(1/16 x²), we get:

= √(1/16 x²)

= (1/4) √(x²)

= (1/4) |x|

Since x≥0, we do not need to take the absolute value of x. Therefore, the simplified expression is (1/4)x.

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Answer:

16.7%

Step-by-step explanation:

The regular price for a lubrication job is $6.50. With the promotion, customers can purchase 6 coupons for $32.50.

To find the percentage discount offered, we need to compare the regular price with the discounted price.

The regular price for 6 lubrication jobs would be:

$6.50 x 6 = $39

With the coupon book, the customer pays $32.50 for 6 lubrication jobs.

The amount of discount is:

$39 - $32.50 = $6.50

Therefore, the percentage discount offered is:

($6.50 / $39) x 100% = 16.7%

So the station is offering a discount of 16.7% to customers who purchase the 6-coupon lube book.

We can estimate that around 205,313 cases of measles would have been reported in the U.S. in 1987 if the number of cases reported from 1960 to 1996 decreased linearly.

To estimate the number of measles cases reported in 1987 if the number of cases reported from 1960 to 1996 decreased linearly, we need to use a linear regression model. Linear regression is a statistical method that allows us to estimate the relationship between two variables by fitting a straight line to a set of data points.

In this case, we can use the number of reported measles cases as the dependent variable (y) and the year as the independent variable (x). We can then fit a linear regression line to the data from 1960 to 1996 and use this line to estimate the number of cases in 1987.

Assuming a linear relationship between the number of cases and the year, we can calculate the slope of the regression line as follows:

slope = (500 - 450,000) / (1996 - 1960) = -10,125

This means that the number of reported measles cases decreased by 10,125 per year, on average, between 1960 and 1996.

Using this slope and the known values for 1960 and 1996, we can estimate the number of cases in 1987 as follows:

y = mx + b

where y is the number of cases, m is the slope, x is the year (1987), and b is the y-intercept of the regression line.

We can solve for b as follows:

b = y - mx

where y is the number of cases in 1996, m is the slope, and x is the year (1996).

Substituting in the values, we get:

b = 500 - (-10,125) * 1996 = 20,503,500

Therefore, the equation of the regression line is:

y = -10,125x + 20,503,500

Substituting x = 1987, we get:

y = -10,125 * 1987 + 20,503,500 = 205,313

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The expression that represents the total change in the amount of snow on the ground over the two days is -3 + (-8) = -11

The problem asks for the total change in the amount of snow on the ground over two days after a blizzard. The problem states that the snow melted by 3 inches one day and 8 inches the next day. The expression that represents the total change can be found by adding the two changes together. However, since the snow is melting, we need to use negative values to represent the change. Therefore, we can write the expression as:

-3 + (-8)

Simplifying this expression, we get:

-3 - 8 = -11

Therefore, the total change in the amount of snow on the ground over the two days is -11 inches.

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[tex]\textit{area of a sector of a circle}\\\\ A=\theta\cdot \cfrac{ r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{7\pi }{4}\\[1em] r=6 \end{cases}\implies A=\cfrac{7\pi }{4}\cdot \cfrac{6^2}{2} \\\\\\ A=\cfrac{63\pi }{2}\implies A\approx 98.96~in^2[/tex]

All functions have an inverse function, and for a function to have an inverse. The inverse of  [tex]f(x) = 3\sqrt(4x + 7) is f^-1(x) = (x^3 - 189)/108[/tex]

The inverse function, often known as the "inverse mapping," is a function that "undoes" another function's operation. If a function f(x) translates an input x to an output y, the inverse function f(-1)(y) transfers the result y back to the input x.

To find the inverse of the function f(x) = 3√(4x + 7), we need to solve for x in terms of y.

Step 1: Replace f(x) with y

[tex]y = 3√(4x + 7)[/tex]

Step 2: Cube both sides to eliminate the cube root

[tex]y^3 = 27(4x + 7)[/tex]

Step 3: Simplify and solve for x

[tex]y^3 = 108x + 189[/tex]

[tex]x = (y^3 - 189)/108[/tex]

Step 4: Replace x with [tex]f^-1(x)[/tex]

[tex]f^-1(x) = (x^3 - 189)/108[/tex]

Therefore, the inverse of   [tex]f(x) = 3√(4x + 7) is f^-1(x) = (x^3 - 189)/108[/tex] .

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The  procedure permute-without-identity does what Professor Kelp intends.

As per the given question,

Professor Kelp wants to write a procedure that produces any permutation randomly except the identity permutation in which every element ends up where it started.

He has proposed the procedure permute-without-identity. We need to check whether this procedure does what Professor Kelp intends or not.

Procedure permute-without-identity:

Generate a permutation π ∈ Sn−1 uniformly at random. (Note that the identity permutation is not in Sn−1.)

Return the permutation obtained by shuffling the elements of π using a uniformly random shuffle.

Randomly shuffle the list using the Fisher-Yates shuffle, which creates a uniformly random permutation of the list.

Professor Kelp's procedure permute-without-identity chooses a permutation at random from the set of all permutations except the identity permutation.

So, there are n! - 1 possible choices of π.

Then, the elements of π are shuffled randomly using a uniformly random shuffle.

The identity permutation is excluded from π as it is not included in Sn-1.

Since the identity permutation is not included in Sn-1, it cannot be chosen by the procedure permute-without-identity.

Hence, the procedure does what Professor Kelp intends.

This procedure achieves the desired outcome by avoiding the case where all elements end up where they started.

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The discount is 75% off the original price of $185.

To find the amount of the discount, we can multiply the original price by 0.75:

$185 x 0.75 = $138.75

Therefore, the dress has been discounted by $138.75.

To find the sales price, we can subtract the discount from the original price:

$185 - $138.75 = $46.25

Therefore, the sale price of the dress is $46.25.

Of the 180 students in a college course, of the 4 1 students earned an a for the course, of the students 3 earned a b for the course, and the rest of the students earned a c for the course. So, 136 students earned a C for the course.

To find the number of students who earned a C in the course, we'll follow these steps:

1. Determine the total number of students in the course.
2. Find out how many students earned an A and how many earned a B.
3. Subtract the number of A and B students from the total to find the number of C students.

We are given that there are 180 students in the course. It is also mentioned that 41 students earned an A and 3 students earned a B.

Now let's perform the calculations:

Step 1: We know that the total number of students is 180.

Step 2: We need to find the combined number of A and B students. We are given that 41 students earned an A, and 3 students earned a B. So, to find the total number of A and B students, we simply add these two numbers:

41 (A students) + 3 (B students) = 44 (A and B students)

Step 3: To find the number of C students, we subtract the total number of A and B students (44) from the total number of students (180):

180 (total students) - 44 (A and B students) = 136 (C students)

So, 136 students earned a C for the course.

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Answer:

6x^3-5x^2+9x+10

Step-by-step explanation:

Use the distributive property and multiply like terms.

However, depending on the project, other units of time, such as minutes or sprints, may also be used.

When estimating a task, the values that are likely to be used include 2 hours, 2 days, and 2 weeks. These values are commonly used in project management for estimating the time required to complete a task.

An estimation is an approximate calculation of the time, effort, or resources required to complete a particular task or project.

It is a critical aspect of project planning, and a good estimate can help ensure that the project is completed on time and within budget. The most common time values used when estimating a task are hours, days, and weeks.

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Answer: The pattern grows by adding the consecutive counting numbers starting from 1.

For example:

Step 1: 1 square

Step 2: 1 + 2 = 3 squares

Step 3: 1 + 2 + 3 = 6 squares

Step 4: 1 + 2 + 3 + 4 = 10 squares

So at each step, the number of squares increases by adding the next consecutive counting number.

Step-by-step explanation:

The spinner has 8 equal-sized sections, each labeled 1, 2, 3, or 4 and correct options are:

a. The spinner landing on 1 - 1 (Likely)

b. The spinner landing on an even number - 2 and 4 (Equally likely to occur or not occur)

c. The spinner landing on the number 8 - Impossible (0)

d. The spinner landing on a number - 1, 2, 3, and 4 (Equally likely to occur or not occur)

e. The spinner landing on the left side of the circle - Unlikely (2)

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.

Here,

a. The spinner landing on 1 - There is only one section labeled 1 on the spinner, out of a total of 8 sections. Therefore, the probability of the spinner landing on 1 is 1/8. On the probability scale provided, this probability would be located closer to "Likely" than to "Equally Likely to Occur or Not Occur", but not as close to "Certain".

b. The spinner landing on an even number - There are 4 sections labeled with even numbers (2 and 4), out of a total of 8 sections. Therefore, the probability of the spinner landing on an even number is 4/8 or 1/2. On the probability scale provided, this probability would be located exactly halfway between "Equally Likely to Occur or Not Occur" and "Certain".

c. The spinner landing on the number 8 - There is no section labeled 8 on the spinner, so this event is impossible. On the probability scale provided, this probability would be located at the very bottom of the scale, labeled "Impossible".

d. The spinner landing on a number - Every section of the spinner is labeled with a number, so this event is certain to occur. On the probability scale provided, this probability would be located at the very top of the scale, labeled "Certain".

e. The spinner landing on the left side of the circle - There are 2 sections labeled with numbers that are on the left side of the circle (1 and 2), out of a total of 8 sections. Therefore, the probability of the spinner landing on the left side of the circle is 2/8 or 1/4. On the probability scale provided, this probability would be located closer to "Unlikely" than to "Equally Likely to Occur or Not Occur", but not as close to "Impossible".

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Answer:10

Step-by-step explanation: one side of a triangle must be greater than the differnce and less than the sum of the lengths of the other two sides

Answer: 5.83095

explanation:

The statement, "Events which occur in extremes of normal-curve have a very small-probability of occurrence" is True because the normal distribution is a bell-shaped curve that is symmetrical around mean.

The Events which occur in extremes of normal curve have a very small probability of occurring because normal-distribution is a bell-shaped curve that is symmetrical around mean, with most values falling close to mean and fewer values occurring further away from mean.

So, as one moves further from the mean, the probability of occurrence decreases exponentially.

So, events that occur in the tails (extremes) of the normal curve have a very small probability of occurring.

Therefore, the statement is True.

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This is the slope-intercept form of the equation of the line. To convert it to the standard form, we need to rearrange it so that the x and y terms are on the same side of the equation: [tex](\frac{13}{4} )x + y = -7[/tex]

To find the standard form of the line that passes through the given points [tex](-4, 6)[/tex] and [tex](0, -7)[/tex], we need to first find the slope of the line using the slope formula:

[tex]\text{slope} = \dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]

where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the coordinates of the two points.

Using the given points, we get:

[tex]\text{slope}=\dfrac{(-7-6)}{(0-(-4))}[/tex]

[tex]\text{slope}=-\dfrac{13}{4}[/tex]

Now that we have the slope of the line, we can use the point-slope form of the equation of a line:

[tex]y - y_1= m(x - x_1)[/tex]

where m is the slope and [tex](x_1, y_1)[/tex] is one of the points on the line. Using the point [tex](-4, 6)[/tex], we get:

[tex]y - 6 = \huge \text(-\dfrac{13}{4}\huge \text )(x - (-4))[/tex]

[tex]y - 6 = \huge \text(-\dfrac{13}{4}\huge \text )x-13[/tex]

[tex]y = \huge \text(-\dfrac{13}{4}\huge \text )x-7[/tex]

This is the slope-intercept form of the equation of the line. To convert it to the standard form, we need to rearrange it so that the x and y terms are on the same side of the equation:

[tex]\huge \text(-\dfrac{13}{4}\huge \text )x+y=-7[/tex]

This is the standard form of the equation of the line that passes through the given points.

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Answer:

Using division the answer to the equation is 10 2/3 but the correct answer to the question would most likely be he needs to refill his tank after 10 days.

Step-by-step explanation:

19 5/9 ÷ 1 5/6 = 10 2/3

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ s=\pi \end{cases}\implies \pi =\cfrac{\theta \pi (4)}{180}\implies \cfrac{180}{4\pi }\cdot \pi =\theta\implies 45=\theta[/tex]

To calculate the probability that the sample mean for a sample of size 45 will be less than 34.5, we can use the Central Limit Theorem (CLT).

The CLT states that, given a large enough sample size, the distribution of the sample means will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Step 1: Identify the population mean (μ) and population standard deviation (σ) from the given information. Since it is not provided in the student question, I will assume that you have already calculated these values.
Step 2: Calculate the standard deviation of the sample mean (σ_sample_mean). This can be done using the formula:
σ_sample_mean = σ / √n
where n is the sample size (45 in this case).
Step 3: Convert the sample mean (34.5) into a z-score using the formula:
z = (x - μ) / σ_sample_mean
where x is the sample mean and μ is the population mean.
Step 4: Use the standard normal distribution table (also known as the z-table) or a calculator to find the probability associated with the calculated z-score. This probability represents the chance that the sample mean will be less than 34.5.
Step 5: Round the probability to the nearest percent.
Following these steps will give you the probability that the sample mean for a sample of size 45 will be less than 34.5, based on the information provided in the question.

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Answer:

The cosine curve is a type of periodic curve that is commonly used in mathematics and physics. It is defined by the equation y=cos(x). The cosine curve is a smooth wave-like curve that has the same shape as the sine wave, but shifted by a quarter of a period. The cosine curve is used to describe cyclical phenomena, such as sound waves and light waves. In addition, it is used in trigonometry and calculus to solve complex problems.