1. The rectangle shown is dilated by a scale factor of 3. (a) Calculate the length of each side of the dilated image. (b) Draw the new image and label it .

The vocabulary for a is called the apothem

The area of the regular polygon is [tex]2419.68 cm^2.[/tex]

a = 7√3 cm

s = 14 cm

The perimeter of the polygon is:

P = ns

where n is the number of sides of the polygon. We can find n using the formula:

[tex]n = 360 / (180 - (360 / 2n))[/tex]

where n is the number of sides. Substituting the given value for s, we get:

[tex]n = 360 / (180 - (360 / 2*7)) = 14[/tex]

Therefore, the polygon has 14 sides.

a = [tex]\sqrt{31.820 cm)^2 - (14 cm/2)^2}[/tex])

= 24.615 cm

A = (1/2) * apothem * perimeter

[tex](\frac{1}{2} ) * 24.615 cm * 196 cm \\=\\ 2419.68 cm^2[/tex]

Therefore, the area of the regular polygon is [tex]2419.68 cm^2.[/tex][tex]2419.68 cm^2.[/tex]

In summary,

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Answer:

a) The population is the 1,500 employees, while the sample is the 60 female and 80 male employees selected using proportional allocation.

b) The scope of data collection is a sample survey, as only a subset of the population is being studied.

c) The variable of interest is the average monthly income of the employees.

d) The possible sources of data collection could include surveys or interviews of the selected employees, or obtaining salary data from the human resources department of the company.

e) The type of statistics used would be inferential statistics, specifically confidence interval estimation and hypothesis testing, to make inferences about the population based on the sample data.

Answer:

Step-by-step explanation:

The sampling distribution of the sample mean for samples of size n is approximately normal with mean μ and standard deviation σ/sqrt(n), where μ is the mean of the population, σ is the standard deviation of the population, and sqrt(n) is the square root of the sample size.

In this case, the population mean is μ = 112 and the population standard deviation is σ = 22. We are interested in the sampling distribution of the sample mean for samples of size n = 16.

The mean of the sampling distribution of the sample mean is the same as the population mean, which is μ = 112.

The standard deviation of the sampling distribution of the sample mean is σ/sqrt(n) = 22/sqrt(16) = 5.5.

Therefore, the sampling distribution of the sample mean for samples of size 16 is approximately normal with mean 112 and standard deviation 5.5.

Answer:

P = $1341.53

Step-by-step explanation:

A(t) = amount in t years

P = Principal (original investment)

r = annual interest rate (in decimal form)

n = number of times that interest is compounded each year

A(t) = P(1 + r/n)nt

Substitute in the given values:  2000 = P(1 + 0.04/12)12(10)

2000 = P(1.490832682)

P = $1341.53

1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.

In statistics, the unitary approach is a way towards resolving proportional problems. It entails first determining the value of a single unit of either a statistic, and then applying that knowledge to determine the value of any other required number of units. Consider the scenario where we are aware that 5 bananas cost $2.50. We can employ the unitary technique to calculate the price of seven apples as follows: Determine the price of a single apple: 2.50 ÷ 5 = 0.50 .Divide the price of one banana by the quantity you want of apples. 0.50 × 7 = 3.50 .It follows that 7 bananas would cost $3.50. Additionally, this technique can be applied to more challenging issues requiring numerous ratios and proportions.

given

Divide the total number of feet of coastline by the state's population to get the amount of coastline per person in Oregon:

Total shoreline / Population equals coastline per person.

coastline divided by population (3,800,000) equals 6,000,000 feet.

1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.

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Answer:

C

Step-by-step explanation:

0 is base like for example negatives are below and positives are above and zero is the thing right in between so sea level would be 0!

Correct answer is 0.

Sea level si always the parameter to use when indicating the elevation of any place on earth. If you happen to be located at the same altitude than the sea, then you are at level 0 altitude in any unit of measure.

Answer:

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

Step-by-step explanation:

The given figure which is a quadratic is the shape of a parabola

The general vertex form equation of a parabola is
[tex]y = a(x - h)^2 + k[/tex]

where,
( h, k ) is the vertex and a is a constant

Looking at the figure we see the vertex is at [tex](1, 3)[/tex]

So the equation of the parabola is

[tex]y = a(x - 1)^2 + 3[/tex]

To compute the constant [tex]a[/tex] take a point (x, y) through which the parabola passes, plug in these x, y values into the above equation and solve

The parabola passes through point   [tex](3, -5)[/tex]

Plugging

[tex]x = 3, y = -5[/tex]

gives
[tex]- 5 = a(3-1)^2 + 3\\\\-5 = a\cdot 2^2 + 3\\\\-5 = 4a + 3\\\\-5-3=4a\\\\-8 = 4a\\\\a = -8/4 = -2\\\\[/tex]

Therefore the equation of the given quadratic(parabola) is

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

Answer:

x = 7.9 (nearest tenth)

y = 24.6° (nearest tenth)

Step-by-step explanation:

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

As we have been given the lengths of both legs of the right triangle, we can use Pythagoras Theorem to find the length of the hypotenuse, x:

[tex]\begin{aligned}3.2^2+7^2&=x^2\\10.24+49&=x^2\\59.24&=x^2\\x^2&=59.24\\x&=\sqrt{59.24}\\x&=7.6967525...\\x&=7.9\; \sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, x = 7.9.

[tex]\hrulefill[/tex]

The tangent ratio is a trigonometric ratio that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]

As we have been given the lengths of the sides that are opposite and adjacent angle y, we can use the tangent trigonometric ratio to find the measure of angle y:

[tex]\begin{aligned}\tan(y)&=\dfrac{3.2}{7}\\y&=\tan^{-1}\left(\dfrac{3.2}{7}\right)\\y&=\vphantom{\dfrac12}24.5671713...^{\circ}\\y&=24.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, y = 24.6°.

To find the mean time it takes for Diane and her friends to complete the obstacle course, we added up the time taken by each person and divided by the total number of people. The mean time is 13.0 minutes.

Add up the time taken by each person

Diane: 12

Friend 1: 14

Friend 2: 10

Friend 3: 16

Total time = 12 + 14 + 10 + 16 = 52 minutes

Count the total number of people:

Diane and three friends, so the total number of people = 4

Divide the total time by the total number of people to find the mean time

Mean time = Total time / Total number of people

Mean time = 52 / 4

Mean time = 13.0 minutes

Therefore, the mean time it takes for Diane and her three friends to complete the obstacle course is 13.0 minutes.

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--The given question is incomplete, the complete question is given

" Diane is a camp counselor she designs a new obstacle course in testicles with three friends. The plot data shows the time it takes them to complete the obstacle course. What is the mean of time

the plot data for the time taken by each person in minutes is as follows

Diane: 12

Friend 1: 14

Friend 2: 10

Friend 3: 16 "--

the equation for the curve C as n approaches infinity     is           y = x This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).

what is diagonal line ?

A diagonal line is a straight line that runs obliquely (at an angle) between two opposite corners of a geometric shape, such as a rectangle or a square. It is called "diagonal" because it connects two non-adjacent vertices of the shape, forming a diagonal across the interior of the shape.

In the given question,

As n increases, the process described in the question creates a set of line segments that connect the equally spaced points on the x-axis to the equally spaced points on the y-axis. The resulting curve is a piecewise linear function that converges to a continuous curve as n approaches infinity.

To derive an equation for this curve, we can start by considering the line segment connecting the first mark on the x-axis to the last mark on the y-axis. Let's call this point (0, 1) and the nth mark on the x-axis (1, 0). The slope of the line connecting these two points is given by:

m = (0 - 1) / (1 - nth mark) = (1 - nth mark)^(-1)

where the nth mark on the x-axis is given by:

nth mark = 1 - (1/n)

Substituting this expression for nth mark into the equation for m, we get:

m = (n/(n-1))

The y-intercept of the line is given by:

b = 1 - m = 1 - (n/(n-1)) = 1/(n-1)

Therefore, the equation for the line segment connecting the first mark on the x-axis to the last mark on the y-axis is:

y = (n/(n-1))x + 1/(n-1)

Similarly, the equation for the line segment connecting the second mark on the x-axis to the second last on the y-axis is:

y = (n/(n-2))x + 1/(n-2)

Continuing this process for all n line segments, we get:

y = (n/(n-k))x + 1/(n-k)

where k = 1, 2, ..., n.

To get the equation for the curve C, we need to take the limit as n approaches infinity. As n goes to infinity, the value of k becomes insignificant compared to n, and we can approximate the equation for the curve as:

y = x

Therefore, the equation for the curve C as n approaches infinity is:

y = x

This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).

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Answer:31.42

Step-by-step explanation:

C=2πr=2·π·5≈31.41593

Answer:

34

Step-by-step explanation:

This is sequnce has an easy pattern with adding 1 to the difference every time and goes +4, +5, +6 , so the next should be +7

Answer: think it’s a5=34

Step-by-step explanation:

In a case whereby Michelle has 3 kg of strawberries that she divided equally into small bags with 1/5 kg in each bag  the number of bags of strawberries she make is 15bags of strawberries.

We should note that 1kg = 1000g

3kg = 1000g

Since each of the bag is  1/5 kg = 1000/5 g = 200g

The needed bag will now be =3000/200= 15

Therefore, we can see that she made 15bags of strawberries the conversion were made so that it can be calculated easily since ythe kg are very small.

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The correct statement which is true about all perfect cubes is,

⇒ A perfect cube represents 3 times the area of a face of the cube.

We have to given that;

The model shown below is a perfect cube with a volume of 27 cubic units.

Now, We can formulate;

⇒ V = 27 cubic units.

⇒ V = 3 × 9 cubic units.

⇒ V = 3 × 3² cubic units.

Thus, The correct statement which is true about all perfect cubes is,

⇒ A perfect cube represents 3 times the area of a face of the cube.

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Answer:

symbols V

The symbols V L and D are not written to the left of a symbol that has greater value

The probability that the population percentage would differ from the sample proportion of flops in a sample of 407 released films by less than 3% is roughly 0.8354, rounded to four decimal places.

For the trials we are looking at, the probability of receiving a success in a binomial distribution must stay constant. Since there are only two possible outcomes when tossing a coin, for instance, the probability of flipping a coin is 12 or 0.5 for each experiment we conduct.

To determine the likelihood that the sample proportion of flops is within 3% of the population proportion, we need to know the chance that |p - 0.09| 0.03.

We can suppose that the sample proportion's distribution is

approximately normal with mean μ = 0.09 and standard deviation σ = √((0.09)(0.91)/407)

≈ 0.017.

We may calculate the z-scores for the top and lower boundaries of the interval using the conventional normal distribution:

z1 = (0.06 - 0.09) / 0.017 ≈ -1.76

z2 = (0.12 - 0.09) / 0.017 ≈ 1.76

The probability between these two z-scores is represented by the region beneath the standard normal curve:

P(-1.76 < Z < 1.76)

= 0.9177 - 0.0823

= 0.8354

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The number of acres pollinated by the bees in 18 beehives is 48 acres.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

x: number of beehives.

y: number of acres.

From the table, the constant is obtained as follows:

3k = 8

k = 8/3

Hence the equation is of:

y = 8x/3.

The number of acres that will be pollinated by 18 beehives is then given as follows:

y = 8(18)/3

y = 48 acres.

Therefore, the number of acres pollinated by the bees in 18 beehives is 48 acres.

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The probability of choosing a red marble is 6/17.

The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes.

To calculate this probability, we can use the formula:

P(red marble) = number of red marbles / total number of marbles

In this case, we substitute the numbers we know:

P(red marble) = 6 / 17

So the probability of choosing a red marble is 6/17 or approximately 0.35.

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Observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.

A histogram is a graph that displays the values of a numeric variable's distribution as a collection of bars.

The height of a bar represents the frequency of data points with values falling within the relevant bin; each bar typically spans a range of numerical values known as a bin or class.

Similar to a bar chart, a histogram is produced with bars of varying widths.

In a histogram, the frequency is revealed by the bar's area rather than its height.

We plot the frequency density rather than frequency on the y-axis. To figure this out, divide a group's frequency by its width.

So, the x-axis of the given histogram represents the mass of the pumpkins.

The y-axis of the histogram represents the number of pumpkins.

Then, the pumpkins with greater mass than 6 kilograms:

= 8 + 6 + 2

= 16

Therefore, observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.

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4w+6.

The perimeter is just the summation of the length of all sides of a shape. In the case of a circle, the perimeters is its circumference length. So for this case, all we need to do is add up all the sides in a single expression that will represent the perimeter.

So perimeter for this triangle should be:

Side 1 + Side 2 + Side 3.

Where:

Side 1= w+4;

Side 2= 2w+2;

Side 3= w.

Then, perimeter is:

(w+4)+(2w+2)+(w)

Adding up all the like terms:

(w+2w+w)+(4+2)

(4w)+(6)

4w+6.

Answer:

1:8

Step-by-step explanation:

The original volume of the box can be calculated by multiplying the length, height, and width:

V = l x h x w = 40 x 8 x 20 = 6,400 cubic inches

If each of the dimensions is reduced by half, the new dimensions become:

Length = 20 inches

Height = 4 inches

Width = 10 inches

The volume of the new box can be calculated as follows:

V_new = l x h x w = 20 x 4 x 10 = 800 cubic inches

The ratio of the volume of the new box to the volume of the original box is:

V_new / V = 800 / 6,400 = 1/8

Therefore, the ratio of the volume of the new box to the volume of the original box is 1:8.

Answer:

I think it's 1 : 8

Step-by-step explanation:

if you don't understand, you can ask me

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The solution to the inputs of the given function are:

a) f(0) = 13

b) f(2) = -1

c) f(-2) = 27

d) f(1) + f(-1) = 26

The set of input values of a function is referred to as the domain of the function. Then, the set of output values of the function is referred to as the range of the function. Thus, if we possess a set of ordered pairs, we can find the domain by listing all of the input values, which are the x-coordinates.

We are given the function:

f(x) = (-x)³ - x² - x + 13

a) f(0) = (-0)³ - (0)² - 0 + 13

f(0) = 13

b) f(2) = (-2)³ - (2)² - 2 + 13

f(2) = -1

c) f(-2) = (2)³ - (-2)² + 2 + 13

f(-2) = 27

d) f(1) = (-1)³ - (1)² - 1 + 13

f(1) = 10

f(-1) = (1)³ - (-1)² + 1 + 13

f(-1) = 16

f(1) + f(-1) = 10 + 16 = 26

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Answer:

they are correct

Step-by-step explanation:

Answer:  The value of the test statistic to 2 d.p is z= 1.65

Step-by-step explanation:

P cap= 0.72

n= 170

P= 0.66

q= 1- p

q= 1- 0.66

q= 0.34

Z=( p cap - p)/√(p*q)/n

Z= (0.72- 0.66)/√(0.66*0.34)/170

Z= 0.06/0.036332

Z= 1.65

Answesar:

Step-by-step explanation:

SA = 10(5)² = 250cm²

Volume² = 2 (5)³ = 250cm³

They are not equal.

Surface area is in square cm and volume is in cm³.

The missing part of the attached proof:

a) definition of angle congruence

b) ∠CPA ≅ ∠CPB

c) CP ≅ CP

The complete paragraph proof would be,

Because CP is perpendicular bisector of AB, CP is perpendicular to AB and point P is the midpoint of AB.

By definition of midpoint,

AP = BP

and by the definition of perpendicuar lines,

m∠CPA = m∠CPB = 90°

Then by definition of segment congruence,

AP ≅ BP

and by definition of angle congruence,

∠CPA ≅ ∠CPB

By the reflexive property of segment congruene,

CP ≅ CP

So, ΔCPA ≅ ΔCPB         ........by SAS congruence theorem

and CA ≅ CB because corresponding parts of congruent triangles are congruent.

So, CA = CB by the definition of segment congruence.

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Answer:

<2  = 30°

Step-by-step explanation:

Let angle 1 = x

Let angle 2 = y

x + y = 95

x = 35 + y  Substitute 35 + y for x in x + y = 95

x + y = 95

35 + y + y = 95  Subtract 35 from both sides

y + y = 60    Combine like terms

2y = 60  Divide both sides by 2

y = 30

Helping in the name of Jesus.

After 5 years, there will be $4,528.73 in Charlie's account if no withdrawals are made.

Compound interest means addition of interest to the principal sum of a loan or deposit. To get the amount, we will use the formula [tex]A=P(1+r/n)^{nt}[/tex] to get sum of money in the account.

Data:

P = 4,200, r = 1.51%, m = 4, t = 5

Plugging the values, we get:

[tex]A = 4200(1+0.0151/4)^{4*5}\\A = 4200* {1.003775}^{20}\\A = 4200*(1.07826994224)\\A = $4528.73375741\\A = $4528.73.[/tex]

Complete question "A bank offers an investment account with an annual interest rate of 1.51% compounded quarterly. Charlie invests 4200 into the account for 5 years. Answer the questions below. Assuming no withdrawals are made, how much money is in Greg's account after 5 years?"

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