Lois is planning to retire from her job. She has been working there for 27 years. If she retires this year, her monthly pension will be calculated with a flat benefit formula using the flat amount of $52 for each year of
service. She was informed that if she works another 4 years that the flat amount would increase to $60 for each year of service. How much more would her pension be if she waited the 4 years?

The antiderivative of the function is t³/3 i + ln |cos(t)| j.

option C.

The antiderivative of the function is calculated as follows;

r = t²i + tan(t)j

tan(t) = sin(t)/cos(t)

Substituting sin(t)/cos(t) for tan(t) in the given function;

r = t²i + (sin(t)/cos(t))j

The antiderivative of sin(t)/cos(t) with respect to t is calculated as;

u = cos(t)

du = -sin(t)dt

∫ (sin(t)/cos(t)) dt = -∫ du/u

= -ln |u| + C

= -ln |cos(t)| + C

The antiderivative of t² is calculated as;

∫ t² dt = t³/3 + C

Add the two equations, to obtain the antiderivative;

∫ r dt = t³/3 i + ln |cos(t)| j

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Rounding to the nearest hundredth, the diameter of the sphere is approximately 4.26 cm.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The surface area of a sphere is expressed as:

S =  4πr²

Where S is the surface area and r is the radius of the sphere.

Given that surface area of 18.2π cm²

We can solve for the radius as follows:

S =  4πr²

r = √( S / 4π )

r = √( 18.2π / 4π )

r = 2.13 cm

The diameter of the sphere is twice the radius, so:

d = 2r

d = 2( 2.13cm )

d = 4.26 cm

Therefore, the diameter of the sphere is 4.26 cm.

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The values of the arc length and angles are:

HE = 62

HD = 118

DG = 62

EG = 118

∠DEG + ∠HGE = 62

We have,

The central angle is equal to the intercepted arc length.

So,

62° = HE

And,

∠A = HD

∠A + 62 = 180

∠A = 180 - 62

∠A = 118

HD = 118

And,

DG = ∠M (say)

∠A + 118 = 180

∠M = 180 - 118

∠M = 62

DG = 62

And,

∠A is opposite to ∠N (say)

So,

∠A = ∠N = 118

∠A = EG

EG = 118

And,

From the definition of the exterior angle.

∠DEG + ∠HGE = 62 ______(1)

Also,

The sum of the three angles in AEG = 180

∠EAG + ∠DEG + ∠HGE = 180

∠EAG = 180 - 62 = 118

So,

∠DEG + ∠HGE = 180 - 118

∠DEG + ∠HGE = 62 _______(2)

Thus,

HE = 62

HD = 118

DG = 62

EG = 118

∠DEG + ∠HGE = 62

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The distribution of the numbers of siblings is best described as skewed to the right so, the median will be a more appropriate measure of the center than the mean

If data is positively skewed - which means that the tail of the distribution leans towards higher values - the median will often be a superior indicator for ascertaining the center than the mean.

This advantage can be attributed to the fact that the median outright ignores extreme values, unlike the median which may become influenced by them and thus pulled towards the extremes of the overall set. Since it is simply the middle value obtained upon sorting the data, its sensitivity to conspicuous outliers is more limited.

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Answer:

[tex]12 \times 10 \times h = 3600[/tex]

[tex]120h = 3600[/tex]

[tex]h = 30[/tex]

The height is 30 millimeters.

The explicit rule for the situation whereby a new car that costs $30,000 depreciates at an average rate of 14% per year, giving the depreciated value of the car after n years, is given by B. an = 30,000 × 0.86^n-1.

The depreciated value of an asset in any year can be determined using the exponential decay function or equation.

An exponential decay equation shows the value of an asset given a constant rate of periodic decrease.

The cost of the new car = $30,000

The average depreciation rate per year = 14%

Depreciation factor = 86% or 0.86 (1 - 14%)

Let the number of years after the purchase = n

Let the depreciated value after n years = an

an = 30,000 × 0.86^n-1.

Thus, the correct explicit rule is Option B.

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Answer:

second option

Step-by-step explanation:

the volume of a cone is calculated as

[tex]\frac{1}{3}[/tex] πr²h

the volume of a sphere is calculated as

[tex]\frac{4}{3}[/tex] πr³

then the volume of a hemisphere is

[tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex] πr³ = [tex]\frac{2}{3}[/tex] πr³

then the volume (V) of the composite solid is

V = [tex]\frac{1}{3}[/tex] πr²h + [tex]\frac{2}{3}[/tex] πr³

The IQR of the data set is 4.

First, let's arrange the data set in order from smallest to largest:

1, 2, 3, 5, 6, 6, 6, 7, 9

Next, let's find the median (Q2) of the data set. Since there are an odd number of values in the data set, the median is the middle value:

Q2 = 6

Now, let's find the median (Q1) of the lower half of the data set. This includes the values from the minimum (1) up to (but not including) the median (6). There are four values in this lower half, so the median is the average of the two middle values:

Q1 = (2 + 3) / 2 = 2.5

Finally, let's find the median (Q3) of the upper half of the data set. This includes the values from the median (6) up to (and including) the maximum (9). There are also four values in this upper half, so the median is the average of the two middle values:

Q3 = (7 + 6) / 2 = 6.5

Now that we have Q1, Q2, and Q3, we can calculate the IQR as:

IQR = Q3 - Q1

IQR = 6.5 - 2.5

IQR = 4

Therefore, the IQR of the given data set is 5.5.

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Answer:

X can be any number greater than -2 and less than or equal to 1/4.

Step-by-step explanation:

To solve for x in the inequality 3x + 1 ≤ 2 - x < 18 + 7x, we will first isolate the variable x on one side of the inequality.

3x + 1 ≤ 2 - x

Adding x to both sides, we get:

4x + 1 ≤ 2

Subtracting 1 from both sides, we get:

4x ≤ 1

Dividing both sides by 4, we get:

x ≤ 1/4

Next, we solve the second inequality:

2 - x < 18 + 7x

Adding x to both sides, we get:

2 < 18 + 8x

Subtracting 18 from both sides, we get:

-16 < 8x

Dividing both sides by 8, we get:

-2 < x

Therefore, the solution to the inequality 3x + 1 ≤ 2 - x < 18 + 7x is:

-2 < x ≤ 1/4

This means that x can be any number greater than -2 and less than or equal to 1/4.

The relationships between the figures is a dilation of 3.5 from the small triangle to the big triangle

From the question, we have the following parameters that can be used in our computation:

The two triangles

From the figure, we can see that

These mean that the triangles are related by dilation

The constant of dilation is then calculated as

k = (7, 7)/(2, 2)

Evaluate

k = 3.5

Hence, the scale factor is 3.5

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Answer:

V = π(19.1^2)(11.8) = 13,523.8 cubic mm

V = 3.14(1.91^2)(11.8) = 13,516.9 cubic mm

The average reading time for the entire book club each day is 55 minutes

From the question, we have the following parameters that can be used in our computation:

The weighted average of the numbers is calculated as

Average = Product of numbers and weights/Sum of weights

So, we have

Average = (10 * 65 + 5 * 35)/15

Evaluate

Average = 55

Hence, the weighted average is 55

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1A) This sampling technique employed is known as a systematic random sample.

1B) The demographic examined in the study is the total production run of 15,600 LED monitors. The representativeness of the sample within such population is relied upon if every 120th monitor selected is an unbiased, irregular choice from the larger collective.

For question 2, the sampling method utilized here is called a convenience sample. Kenya only enquires the middle school pupils in her 7th grade science course, which cannot be characterized as a representative or randomly chosen group of all middle school learners.

The sample may not accurately reflect the population because it merely involves students in her lesson, and not necessarily those enrolled at her school or district.

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The calculated value of the prime fractorization of the number 130 is 2 * 3 * 5

From the question, we have the following parameters that can be used in our computation:

Number = 130

When the above number is expanded, we have

Number = 2 * 5 * 13

The above product of numbers cannot be further simplified

This means that 2 * 5 * 13 is the prime fractorization of the number 130

Hence, the prime fractorization of the number 130 is 2 * 3 * 5

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We would expect the spinners to land on the same number approximately 2 times in 10 spins.

Based on the given probabilities, we know that the probability of the red spinner and blue spinner landing on the same number is 21%, and the probability of them landing on different numbers is 79%. We can use this information to calculate the expected number of times the spinners would land on the same number in 10 spins.

If we assume that the probability of the spinners landing on the same number is constant across all 10 spins, then we can model the number of times they land on the same number as a binomial distribution with n=10 (number of trials) and p=0.21 (probability of success).

Using the formula for expected value of a binomial distribution, we can calculate the expected number of times the spinners would land on the same number in 10 spins as:

E(X) = np = 100.21 = 2.1

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Complete question is:

The outcome of spinning 2 spinners 100 times is shown as.

Events                                            Actual outcomes                  Probability

P(red spinner = blue spinner)                  21                                            21%

P(not red spinner = blue spinner)          79                                            79%

How many times would you expect these spinners to land on the same number in 10 spins?

The testable question can be Which sprouts faster, a moist lima bean or a dry lima bean?

We have,

June laces a lima bean inside a damp paper towel, then places it in a baggie.

June takes another lima bean and places it in a dry paper towel and puts it in a baggie.

The Experiment is related to moisture because one damp and one dry towel is used.

So, the testable question can be

Which sprouts faster, a moist lima bean or a dry lima bean?

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Answer:

26,225.3 = 3.14(12^2)h + (2/3)(3.14)(12^3)

26,225.3 = 452.16h + 3,617.28

452.16h = 22608.02

h = 50 feet

26,225.3 = π(12^2)h + (2/3)π(12^3)

26,225.3 = 144πh + 1,152π

144πh = 26,225.3 - 1,152π

h = (26,225.3 - 1,152π)/(144π)

h = 49.97 feet = 50 feet

Answer:

The graph appears to be a cosine function that has been shifted π units to the left and vertically reflected.

Option (d) represents this transformation:

f(x) = -4 cos(x + π)

Therefore, the answer is (d).

Step-by-step explanation:

The range of the given linear function; f(t) = 2t + 1 given its domain (1, 2, 3, 5) is; (3, 5, 7, 11).

It follows from the task content that the range of the given function is to be determined given its domain as defined by the set; (1, 2, 3, 5).

Therefore;

At t = 1; f(1) = 2(1) + 1 = 3.

At t = 2; f(2) = 2(2) + 1 = 5.

At t = 2; f(3) = 2(3) + 1 = 7.

At t = 5; f(5) = 2(5) + 1 = 11.

Ultimately, the range of the given function as required is given by the set; (3, 5, 7, 11).

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The value of variable θ would be,

⇒  θ = 5π/3 and θ = 4π/3

We have to given that;

Expression is,

⇒ - 10sin θ - 8 = 5√3 - 8

Now, We can simplify as;

⇒ - 10sin θ - 8 = 5√3 - 8

⇒ - 10sin θ = 5√3

⇒ sin θ = - 5√3/10

⇒ sin θ = - √3/2

We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).

However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.

Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.

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The polar coordinate (3, 45°) lies in the same location on the polar plane as (-3, Ø), where -360° < Ø < 0. Then, the value of Ø is 45°.

The polar coordinates (r, θ) represent a point on the polar plane, where r is the radial distance from the origin (in this case, 3 units) and θ is the angle measured counterclockwise from the positive x-axis (in this case, 45°).

According to the given statement, the polar coordinate (-3, Ø) lies in the same location on the polar plane as (3, 45°). This means that these two points represent the same location, and their radial distances and angles must be equivalent.

Comparing the radial distances;

|r| = 3 (for (3, 45°))

|-r| = 3 (for (-3, Ø))

Since |-r| = |r|, we can conclude that r = -r, which implies r = 0, as r cannot be negative in polar coordinates.

Comparing the angles;

θ = 45° (for (3, 45°))

θ = Ø (for (-3, Ø))

Since the angles are equivalent, we can equate them:

45° = Ø

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Answer:

k = 8.4; j = 13.1

Step-by-step explanation:

We can find the measures of j and k using trigonometric ratios, namely the tangent ratio and the cosine ratio

If we allow 40 to be our reference angle...

Because we're not given the measure of either j or k, we have to use 10 each time

Steps to find j:

[tex]cos(40)=\frac{10}{j}\\ \\j*cos(40)=10\\\\j=\frac{10}{cos(40)}\\ \\j=13.05407289\\\\j=13.1[/tex]

Steps to find k:

[tex]tan(40)=\frac{k}{10}\\ \\10*tan(40)=k\\\\8.390996312=k\\\\8.4=k[/tex]

4 things can be selected from a total of 9 without replacement in 126 times without replacement.

Combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of selection does not matter.

How to determine this

To calculate the combination without replacement

nCr = n!/r!(n-r)!

9C4= 9!/4!(9-4)!

= 9!/4!(5!)

= 9*8*7*6*5*4*3*2*1/4*3*2*1*5*4*3*2*1

= 362880/24*120

= 362880/2880

= 126

Therefore, it can be combined in 126 times

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The given statement, "Signed numbers are also called directed numbers" is true.

Signed numbers are numbers that can be positive, negative, or zero, and they are sometimes referred to as directed numbers because they have a direction or orientation on the number line. Positive numbers are usually associated with movements to the right on the number line, while negative numbers are associated with movements to the left.

Therefore, the given statement, "Signed numbers are also called directed numbers" is true.

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In this example of heart attack, it would be appropriate to calculate Conditional row percentages. Therefore, the correct option is option A.

When the blood supply for the heart is significantly impeded or blocked, a heart attack happens. The accumulation of fat, cholesterol, and other chemicals in the heart's (coronary) arteries is typically what causes the obstruction. Plaques are the name given to the fatty, cholesterol-containing deposits.

Atherosclerosis is the name for the phenomenon of plaque accumulation. A plaque may occasionally burst and generate a clot that restricts blood flow. A portion for the heart muscle can be harmed or destroyed by a shortage of blood flow. In this example, it would be appropriate to calculate Conditional row percentages.

Therefore, the correct option is option A.

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Your question is incomplete but most probably your full question was,

The quantity of pasta is served to Olivia is 60 in³.

Olivia's mother packed her lunch in a lunch box which is in the shape of rectangular prism, with dimension = length= 5 in, width= 4 in, height= 3 in,

We need to find the quantity of the lunched packed in the box,

So, we will find the volume of the box = length × width × height

= 5 × 4 × 3

= 60 in³

Hence the quantity of pasta is served to Olivia is 60 in³.

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The length of the intercepted arc is 4π unit.

We have,

Angle = 2π/3 = 2(180)/ 3 = 120 degree

r = 6 unit

So, length of Arc

= θ /360 x 2πr

= 120/360 2 π(6)

= 1/3 (12)π

= 4π unit

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The fraction 4/3 we get by using the  numbers 3 and 4 to make a fraction that is greater than 1 and a fraction less than 1

To make a fraction greater than 1 using the numbers 3 and 4, we can divide 3 by 4 and add 1.

3/4 + 1 = 7/4

The resulting fraction, 7/4, is greater than 1 because the numerator (7) is greater than the denominator (4).

We can also see this by writing 7/4 as a mixed number:

7/4 =[tex]1\frac{3}{4}[/tex]

The whole number part of the mixed number is 1, which means the fraction is greater than 1.

To make a fraction less than 1 using the same numbers, we can divide 4 by 3. This gives us:

4/3

The resulting fraction, 4/3, is less than 1 because the numerator (4) is smaller than the denominator (3).

We can also see this by writing 4/3 as a mixed number:

4/3 =[tex]1\frac{1}{3}[/tex]

The whole number part of the mixed number is 1, which means the fraction is less than 1.

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