7. In multiplying 0.125 x 0.08, Dina knew the rule that says she should multiply 125 x 8 and then move the decimal point 5 places. When she did it on the calculator, she saw it was 0.01. She was confused. How would you help her?

The wooden artifact was made approximately 3,183 years ago. The amount of carbon-14 present in an artifact can be used to determine how long ago the organism that the artifact came from died.

The half-life of carbon-14 is 5730 years, which means that every 5730 years, half of the carbon-14 in a sample will decay. Let's call the amount of carbon-14 in the living tree sample 100%. Since the artifact contains 35% of that amount, we can write:

0.35 x 100% = 100% x (1/2)^(t/5730)

where t is the number of years since the artifact was made.

Simplifying this equation, we get the following:

0.35 = 0.5^(t/5730)

Taking the logarithm of both sides, we get:

log(0.35) = (t/5730) x log(0.5)

Solving for t, we get:

t = (5730 x log(0.35)) / log(0.5)

Using a calculator, we get:

t ≈ 3,183 years

Therefore, the wooden artifact was made approximately 3,183 years ago.

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You should deposit approximately $340.84 monthly to reach $293,000 in 28 years at a 4.4% annual interest rate compounded monthly.

To calculate the monthly deposit required for an investment plan paying 4.4% interest compounded monthly to reach $293,000 in 28 years, we use the future value of an annuity formula:

FV = P * (((1 + r)^n - 1) / r)

Here, FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of payments. First, convert the annual interest rate (4.4%) to a monthly rate by dividing by 12, which gives 0.0367 (4.4%/12) or 0.00367 as a decimal. The number of payments (n) is 28 years * 12 months/year = 336.

We want to find P, so rearrange the formula:

P = FV / (((1 + r)^n - 1) / r)

Substitute the values:

P = $293,000 / (((1 + 0.00367)^336 - 1) / 0.00367)

P ≈ $340.84

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Answer:

A rectangular prism would be best to model a suitcase

Step-by-step explanation:

Hope that helps!

Answer:

Rectangular Prism

Step-by-step explanation:

If you look at a suitcase, it resembles a rectangular prism quite well.

Defining a confidence interval would be important for testing the validity of data in a dataset where the sample size is relatively small or there is a significant variation within the data. This is crucial when trying to estimate population parameters and determine the level of certainty or reliability in the findings.

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. When dealing with a dataset, it is important to understand the characteristics and limitations of the data. If the sample size is small, the estimates obtained from that sample may not accurately reflect the true population parameter. A larger sample size generally provides more reliable estimates. Additionally, if there is significant variation within the data, it can lead to a wider range of possible values for the population parameter.

To determine the confidence interval, several factors need to be considered. Firstly, the desired level of confidence must be chosen. Common choices are 95% or 99%. A 95% confidence level means that if the same study were repeated 100 times, we would expect the true population parameter to fall within the calculated confidence interval in 95 of those studies. Secondly, the standard deviation or variance of the sample must be calculated. This measure of variability helps quantify the spread of the data points around the mean.

With these considerations in mind, the confidence interval can be calculated using a statistical formula. The most commonly used formula is based on the t-distribution when the sample size is small, and the z-distribution when the sample size is large. The formula incorporates the sample mean, the sample standard deviation, the level of confidence, and the sample size. The resulting interval provides a range of values within which the true population parameter is likely to fall.

By defining a confidence interval, we can assess the validity of the data by determining the precision of the estimates. A narrow confidence interval indicates a higher level of certainty in the estimated parameter, whereas a wider interval suggests more uncertainty. Therefore, defining a confidence interval is important for testing the validity of data, particularly in datasets with a small sample size or significant variation, as it allows us to evaluate the reliability of the findings and draw conclusions about the population based on the sample data.

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The researcher is trying to reduce the cause of within-group variance related to individual differences or heterogeneity within the sample.

In statistics, within-group variance, also known as within-group variation or error variance, refers to the variability of data within a specific group or sample. It represents the differences among individuals within the same group or sample.

There are several causes of within-group variance, such as individual differences, measurement error, and uncontrolled extraneous variables.

In this scenario, the researcher is trying to limit who the findings will generalize to, which means that she wants to control or reduce the effect of individual differences or heterogeneity within the sample.

By limiting the sample to a specific population or subgroup, the researcher can reduce the within-group variance related to individual differences and increase the likelihood of finding significant results.

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Answer:

11.35 g/mL

Step-by-step explanation:

D = m/v

D = 567.5 g ÷ 50.0 mL (I assume its measured in mL)

D = 11.35 g/mL

Answer:

11.35

Step-by-step explanation:

Step-by-step explanation:

let's just write it down in mathematical notation :

length = 2×width - 1

the perimeter is the way all around an object.

so, for a rectangle that is

2×length + 2×width

for our rectangle here

2×length + 2×width = 70

now we use the original identity of length via width and get

2×(2×width - 1) + 2×width = 70

4×width - 2 + 2×width = 70

6×width - 2 = 70

6×width = 72

width = 12

FYI

length = 2×width - 1 = 2×12 - 1 = 24 - 1 = 23

Since it is a right triangle, we can apply the trigonometric function:

Sin a = opposite side / hypotenuse

Where:

a= angle = x

Opposite side = 5

Hypotenuse= 13

Replacing:

Sin x = 5/13

Solve for x

x = arc sin (5/13)

x= 22.6 = 23 ° (rounded)

Answer : A. 23°

The experimental design which is used in the study is Completely randomized design.

Completely Randomized design may be defined as a technique in which all the solutions are assigned at random so that each questions receive all the possible solutions. According to the question we know that the sample size is 100 volunteers who are suffering from chronic pain. Now, out of the 100 volunteers, 50 males and 50 females are chosen. Further out of the 50 males, 25 males are randomly assigned to the treatment group while the other 25 males are assigned to a control group. Since, the treatments are randomly assigned completely, each of the volunteers have an equal chance of receiving the treatments.

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Answer:

Answer:

Diagonal=11.3m

Area of square (A) =1/2*d^2

=1/2*(11.3)^2

=63.845m^2

We know,

Area of square A= l^2

63.845=l^2

L=

\( \sqrt{63.845 } \)

L=7.99m

Now,

Perimeter of square =4l

=4*7.99

=31.96m

Answer:

The maker of a cell phone screen protector would like to estimate the proportion of customers who file a warranty claim. To do so, they select a random sample of 200 customers and determine that the 96% confidence interval for the true proportion of customers who file a warranty claim to be 0.15 to 0.28.

Step-by-step explanation:

Answer:

52

you take 5 ÷ it by 7 the ×it by 595

A ratio is an ordered pair of numbers a and b written as a/b where b is not equal to zero.

if the number of women in the social club is 595 then the number of men in the social club is 425.

A ratio is an ordered pair of numbers a and b written  as:

a / b where b does not equal 0.

A proportion is an equation in which two ratios are equal to each other.

We have,

The ratio of men to women:

= 5:7

= 5/7

Let,

The number of men = 5x

The number of women = 7x

Now,

If the number of women = 595

We have,

7x = 595

Multiplying both sides by 5/7 we get,

5/7 x (7x) = 5/7 x 595

5x = 5/7 x 595

5x = 5 x 85

5x = 425

This means if there are 435 men in the social club if the number of women is 595.

Thus if the number of women in the social club is 595 then the number of men in the social club is 425.

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Answer:

You can answer this very easily by using modern calculaters.

Thanks!

Answer:

He is wrong since reflecting the image across the x-axis means reflecting it on the axis that is horizontal and reflecting it over the y-axis means reflecting it on the y-axis which is verticle.

Answer:No, it would not be the same if you reflect it from the X axis.

Step-by-step explanation:

because the the shape is not "on" the X axis. When you reflect the shape across the X axis, then you will not really get a shape. It's easier if you imagine you put a mirror on the x axis and looked at it. Malik would have to shift the whole shape down so that the current points (3,1) and (-3,1) would change to (3,0) and (-3,0) Also shifting down the other two points too. Reflecting it is like if you had the shape in paper and you folded it in half. If it matches perfectly, then you know that you have a match and that it is reflecting. If it doesn't fold perfectly, then it doesn't reflect. So if you folded the shape from the X axis, you wouldn't get a perfect match so he is wrong. Does it help?

The measurement of the two shorter sides in Monica's wrapping paper is 17 inches.

We can use proportions to solve this problem. Since Francisco's piece of paper is similar to Monica's piece of paper, the ratios of the corresponding sides will be equal. Specifically, we have:

17 / x = 34 / y

where x is the length of one of Francisco's shorter sides, and y is the length of one of Monica's shorter sides.

To solve for y, we can cross-multiply and simplify:

17y = 34x

y = 2x

So the length of one of Monica's shorter sides is half the length of one of her longer sides, or:

y = 1/2 * 34 = 17

Therefore, the measurement of the two shorter sides in Monica's wrapping paper is 17 inches. Answer: a. inches.

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The total cost of the guitar including sales tax is $85.31

A sales tax is a tax levied on the sale of certain goods and services and paid to the government. In general, rules compel the seller to collect tax money from the buyer at the time of purchase.

The tax is added on the sale price and it is not apart of the profit.

Cost of the guitar = $131.25

Sales tax = 6.5%

Total cost of guitar = 6.5% of 131.25 = 0.65 × 131.25 = $85.31

A use tax is a levy on services or goods that a client pays directly to a governing body. Food, education, and medications are usually exempt from sales and use tax under state law.

Hence the total cost of the guitar is $85.31

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She uses 1/2 quart of yellow paint for every 9/2 quarts of blue paint. Then, she uses 1/2 quart of yellow paint for every 1/2 + 9/2 = 10/2 = 5 quart of paint.

We can use the next proportion:

Solving for x:

She uses 1/10 quart of yellow paint for every quart of paint

To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Answer:

x = 8

y = 8

Step-by-step explanation:

y = 8

2x - 3y = -8

We substitute 8 in for y and solve for x

2x - 3(8) = -8

2x - 24 = -8

2x = 16

x = 8

Let's Check the answer.

2(8) - 3(8) = -8

16 - 24 = -8

-8 = -8

So, x = 8 and y = 8 is the correct answer.

Answer:

x = 8 and y = 8.

Step-by-step explanation:

To solve the system of linear equations using the elimination method, we'll eliminate the variable "y" by substituting the given value of y into the second equation. Let's start:

Given equations:

y = 8

2x - 3y = -8

Substitute y = 8 into equation 2:

2x - 3(8) = -8

2x - 24 = -8

Next, we'll solve this equation for x:

2x - 24 = -8

2x = -8 + 24

2x = 16

x = 16/2

x = 8

Now that we have the value of x, we can substitute it back into equation 1 to find the value of y:

y = 8

So, y = 8

Therefore, the solution to the given system of equations is x = 8 and y = 8.

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer: b is the answer

Step-by-step explanation:

The line goes up 1 over 3

Answer:

slope is rise over run. so the slope would be 1/3.

Answer:

3 is the slope and -1 is the y intercept

Step-by-step explanation:

y= -1+3x

Using the slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = 3x-1

3 is the slope and -1 is the y intercept

Answer: 3

Step-by-step explanation:

1: Convert to Slope-Intercept Form

y=3x-1

2: When y=mx+b, m= slope, thus, the slope is 3.

The mean of the population is 46 and standard deviation of the population is 4.

The mean of the sampling distribution of the sample mean will always be the same as the mean of the original non-normal distribution. In other words, the sample mean is equal to the population mean. Based on the information provided, the population mean is 46 minutes same as the mean of sample.

The standard deviation of the sampling distribution of means is equal to the standard deviation of the population divided by the square root of the sample size. Hence, standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the same size. Standard deviation 0.4 minutes and sample size is 100, hence standard deviation = 0.4/√100 = 0.4/10 = 4.

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Answer

the answer is x = 9 root 3

The temperature in Celsius (C) increased by 273.15 to get the temperature in Kelvin (K). The equation with the subject Celsius (C) is C=K-273.15, Option A correct.

Given that,

The temperature in Celsius (C) increased by 273.15 to get the temperature in Kelvin (K).

The formula K = C + 273.15 can be used to simulate this.

We have to find the equation with the subject C.

K=C+273.15

Taking the C to left hand side and K to right hand side.

-C=273.15-K

Multiplying -1 on both sides

-1(-C)=-1(273.15-K)

C=K-273.15

Therefore, The equation with the subject Celsius (C) is C=K-273.15, Option A correct.

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The total surface area of the pyramid is  335 square centimeters

The formula for determining the total surface area of a pyramid is expressed as;

TSI = 1/2(PI) + B

Given that;

Now, let's determine the base perimeter

Perimeter = 2( l + w)

Substitute the values

Perimeter = 2 ( 8 + 12)

Perimeter = 40 centimeters

The base area is given as;

Base area =  8(12)

Base area = 96 square centimeters

Substitute the values, we have;

Total surface area = 1/ 2 (40)(12) + 96

Total surface area = 240 + 96

Total surface area = 335 square centimeters

Hence, the value is 335 square centimeters

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