When he was 40 Keefer began investing $150 per month in various securities for his retirement savings. His investments averaged a 4.5% annual rate of return until he retired at age 70. What was the value of Keefer's retirement savings when he retired? Assume monthly compounding of interest.

Answer:

a is correct

Step-by-step explanation:

Answer:

[tex]a=7[/tex]

Step-by-step explanation:

we have

[tex]7(a-10)=13-2(2a+3)[/tex]

Solve for a

[tex]7a-70=13-4a-6[/tex]

Group terms that contain the same variable and move the constants to the other side

[tex]7a+4a=13-6+70[/tex]

Combine like terms

[tex]11a=77[/tex]

Divide by [tex]11[/tex] both sides

[tex]a=7[/tex]

Answer:

a - 21 inches

Step-by-step explanation:

Following the formula [tex]Area = l*w[/tex], we can find the length of the rectangle by plugging in values into the formula, then solving for [tex]l[/tex].

[tex]357=l*17[/tex]

[tex]\frac{357}{17} =\frac{l*17}{17} \\\\21=l\\l=21[/tex]

Answer:You would earn .05 x $500 or $25 over that time period.

Step-by-step explanation:

Answer:

Line MN is the answer

Step-by-step explanation:

Answer: 35.0%

Step-by-step explanation:

Answer:

The answer 5.23

Step-by-step explanation:

Answer:

She worked [tex]6\frac{7}{8}[/tex]  hours in evening.

Step-by-step explanation:

Suppose, x be the hours waitress worked in evening,

Given,

She works 1.75 hours less in the afternoon than in the evening.

Thus, the number of hours she worked in afternoon = x - 1.75,

According to the question,

[tex]x-1.75 = 5\frac{1}{8}[/tex]

[tex]x-\frac{175}{100}=\frac{41}{8}[/tex]

[tex]x-\frac{7}{4}=\frac{41}{8}[/tex]

[tex]x=\frac{41}{8}+\frac{7}{4}[/tex]

[tex]x=\frac{41+14}{8}[/tex]

[tex]x=\frac{55}{8}=6\frac{7}{8}[/tex]

Therefore, she worked [tex]6\frac{7}{8}[/tex] hours in evening.

The dimensions of the box are: length=3 feet, width=15 feet, and height=3 feet.

This is a classic problem of volume where we need to consider the volume formula of a box, which is length × width × height. The question states that the box has a volume of 135 cubic feet, with the length being the same as the height, and the width being 5 times the length.

To find the dimensions of the box, we can set up the equation: length × 5 ×length × length = 135. Simplifying, we get that the length is the cube root of 135/5, which equals to 3. Thus, the dimensions of the box are: length=3 feet, width=15 feet, and height=3 feet.

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About 3 nails is correct on grad point

Periodic data is useful for analyzing trends over time, helping to forecast future events, and measure frequencies of occurrences. It is applicable in various fields including business, environmental science, and health for planning strategies and understanding patterns.

Periodic data is useful when we are interested in analyzing and understanding trends over regular intervals of time. It helps us to observe patterns and forecast future occurrences based on historical information. For example, in business, we may look at quarterly sales figures to identify seasonal effects on sales and plan inventory accordingly. In environmental science, climate data recorded over decades can be critical for studying changes in weather patterns and predicting future climate events. In health, collecting epidemiological data periodically can enable public health officials to track the spread of diseases and the effectiveness of interventions.

Frequency, relative frequency, and cumulative relative frequency are measures that can describe how often certain events occur within periodic data. These measures help answer questions like 'How many students study five hours or more for an exam?' or 'What percent of families own two pets?' They are crucial for understanding the distribution of data and for making informed decisions based on that data.

Answer:

Option A  is correct.

Step-by-step explanation:

Given:

AG = 6 ft ⇒ Radius of the circle , r = 6 ft

⇒ GB = AG = 6 ft

To find: Area of shaded Segment.

Area of Shaded Segment  = Area of Sector AGBA - Area of Δ AGB

Sector AGBA forming 90° angle at center. [tex]\implies\,\theta=90^{\circ}[/tex]

Area of Sector = [tex]\frac{\theta}{360}\times\pi r^2[/tex]

Area of Sector AGBA = [tex]\frac{90}{360}\times3.14\times6^2[/tex]

                                   = [tex]\frac{1}{4}\times3.14\times36[/tex]

                                   = [tex]28.26\:ft^2[/tex]

ΔAGB is a right angled triangle.

So, Area of ΔAGB = [tex]\frac{1}{2}\times AG\times GB[/tex]

                              = [tex]\frac{1}{2}\times6\times6[/tex]

                              = [tex]6\times3[/tex]

                              = [tex]18\:ft^2[/tex]

Area of Shaded Segment  = 28.26 - 18 = 10.26 ≈ 10.3 ft²

Therefore, Option A  is correct.

All options involve descriptive statistics, but option B is a classic example as it involves computation of a median, an important tool in descriptive statistics.

Descriptive statistics is used to describe, show or summarize data in a meaningful way. All the options given indicate the use of descriptive statistics because they all describe a given population or set of data using numerical measures. However, the most classical use of descriptive statistics is found in option B: 'A recent survey of the cost of new homes in the United States shows that the median price of a new home is up $15,000 since last year.' This situation involves the computation of a median, a common measure in descriptive statistics, to summarize property price data.

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Answer:

6 truck containers can hold 144 cases

Step-by-step explanation:

A truck container holds 24 cases and we have to find number of cases would 6 truck container will hold.

We will solve this question by unitary method.

∵ One truck container holds cases = 24

∴ 6 truck containers will hold cases = 24×6 = 144

Therefore 144 cases is the answer.

Answer:

270

Step-by-step explanation:

Just multiply.

5*6*9=270

Answer: There would be 270 leaves of a tree diagram.

Step-by-step explanation:

Since we have given that

Number of salads = 5

Number of entrees = 6

Number of desserts = 9

If we draw a tree diagram, we need to find the number of leaves there would be :

So, the number of leaves there would be is given by

[tex]5\times 6\times 9\\\\=270[/tex]

Hence, there would be 270 leaves of a tree diagram.

Answer:
10) 35
14) x = 1/2
18) 10 cm

Explanation:
For question 10, we can set up a proportional equation, cross-multiply and solve for the missing number:

[tex]\frac{x}{14} = \frac{5}{2}[/tex]

2x = 14(5)
2x = 70
2x / 2 = 70 / 2
x = 35

The missing number is 35

For question 14, we isolate variables on one side of the equation and constants on the other by performing whatever operations are necessary and then solve for the variable:
14x + 2 = 9
14x + 2 - 2 = 9 - 2
14x + 0 = 7
14x = 7
14x / 14 = 7 / 14
x = 7 / 14
x = 1/2

x = [tex]\frac{1}{2}[/tex]

For question 18, there are 10 millimeters (mm) in 1 centimeter (cm) so we can use this relationship so set up a conversion factor and cross-multiply to find the missing value like we did in question 10:
[tex]\frac{10}{1} = \frac{100}{x}[/tex]

10x = 100(1)
10x = 100
10x / 10 = 100 / 10
x = 10

There are 10 cm in 100 mm.