Add 7 x 10−6 and 2.1 x 10−5.

Use the data to create a stemplot.

Twenty-four workers were surveyed about how long it takes them to travel to work each day. The data below are given in minutes.

20 35 42 52 65 20 60 49 24 37 23 24

22 20 41 25 28 27 50 47 58 30 32 48

The data in a stem-and-leaf plot:

3/0257

2/0002344578

4/12789

5/028

6/05

Another presentation that is similar to a histogram is a stemplot. In statistics, a stemplot is a tool for presenting quantitative data in a graphical format, similar to a histogram, namely to assist in visualizing the shape of the data distribution which is often used in exploratory analysis. Stemplots were introduced by Arthur Bowley in the early 1900's. However, its general use only began in 1980 after John Tukey's published Exploratory Data Analysis in 1977.

Stem-and-leaf plots provide more information about true values than histograms. As in a histogram, the length of each bar corresponds to the number of events that fall into a given interval. On Histograms. we can only see the frequency value of the data but we don't know what the actual number value is. In contrast to the histogram, in SLP besides we can know the frequency value, we can also know what the actual data value is. This is done by dividing the observed values into two components, stem and leaf.

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Answer:

12 constant terms and 12 variable terms

Step-by-step explanation:

Answer:

8m

Step-by-step explanation:

a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c) . A 90% confidence interval would be wider than the 95% interval

To verify the Central Limit Theorem (CLT) conditions, we need to check the following:

1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.

2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.

3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.

Therefore, the Central Limit Theorem conditions are met.

b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:

CI = p ± z * √(p(1-p)/n)

where:

- p is the sample proportion (82% or 0.82 in decimal form).

- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

- n is the sample size (800).

Calculating the confidence interval:

CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)

CI = 0.82 ± 1.96 * √(0.82*0.18/800)

CI = 0.82 ± 1.96 * √(0.1476/800)

CI = 0.82 ± 1.96 * √0.0001845

CI ≈ 0.82 ± 1.96 * 0.01358

CI ≈ 0.82 ± 0.0266

The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.

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Answer: I'm not exactly sure what your asking, but throughout two days Marcus borrowed $13.45 and then made $45.32. If he immediately paid his owed money back then he would have a current amount of 31.87 in his possession. That is unless he had interest on that owed money for one day

Step-by-step explanation:

$45.32-$13.45 = $31.87

In this, question the equation is missing that's why in the solution we define the equation and its complete solution:

Let the given equation:

\(\bold{\hat{h}=17.6+3.8x_1-2.3x_2+7.6x_3+2.7x_4}\)

\(\bold{b1 = 3.8}\) units expect changes in the y for each 1 unit change in \(\bold{x_1}\)

\(\bold{b2 = -2.3 }\) units expect changes in the y for each 1 unit change in  \(\bold{x_2}\)

\(\bold{b3 = 7.6 }\) units expect changes in the y for each 1 unit change in \(\bold{x_3}\)

\(\bold{b4 = 2.7}\) units expect changes in the y for each 1 unit change in \(\bold{x_4}\)

Calculating the estimated value of the y when:

\(\to \bold{x_1 = 10}\\\\ \to \bold{x_2 = 5}\\\\\to \bold{x_3 = 1}\\\\\to \bold{x_4 = 2}\\\\\)

Put the value into the above-given equation:

\(\to \bold{17.6 + 3.8(10) - 2.3(5) + 7.6(1) + 2.7(2)} \\\\\to \bold{17.6 + 38 - 11.5 + 7.6 + 5.4} \\\\\to \bold{17.6 + 38 - 11.5 + 7.6 + 5.4} \\\\\to \bold{68.6-11.5}\\\\\to \bold{57.1}\)

So, the final answer is "57.1".  

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Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:

Yes

Step-by-step explanation:

if it's a less than or equal to it goes from the left to the right and has a full dot

Answer:

Step-by-step explanation:

when a line is perpendicular to a given line, it uses the opposite reciprocal of the slope (basically flip the top and bottom numbers of the slope fraction and then change its sign from negative to positive or vice versa)

the slope of the given line is 1/4

the opposite would be -1/4

the reciprocal would be -4/1 or just -4

so the slope of this new line is -4

what we know so far is

y = -4x + b

since it has to go through point P (9, -2)

we’ll substitute 9 for x and -2 for y to find b

-2 = -4(9) + b

-2 = -36 + b

34 = b

so the final equation is

y = 4x + 34

The real court is 9 by 18 meters in length and width.

The length of something is its width or size measured across its entire surface. Or, to put it another way, it is the larger of a geometric shape's higher two or three dimensions.

This statement implies that the court's original dimensions have been reduced by 22.5 for every 1 centimeter in the size of the current drawing, which is 40 cm by 80 cm. To get the original dimension, we will multiply the required dimension by each 22.5 cm as shown. Original length for a 40-cm length = 40 * 22.5 originally 900 cm long 100 cm equals one meter in metres. Multiply 900cm by x to get 9m: 100x = 900*1x = 900/100x Therefore, 900cm = 9m For the 80-cm width: Original width is equal to 80 * 22.5, or 1800 cm. 100 cm equals one meter in metres. multiplying 1800cm by x yields 100x, 1800*1, 1800/100x, and 18m. So 1800cm = 9m. As a result, the real court is 9 meters long and 18 meters wide.

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Rounding to the nearest whole number. The correct option is D) 216 m²; 244 m².

Since the prism has a rectangular base, we know that its lateral faces are all rectangles with heights equal to the height of the prism. Let's first find the lateral area of the prism using the formula:

Lateral Area = Perimeter of Base * Height

The perimeter of the base is the sum of the lengths of all four sides of the rectangle. Since there are two bases, we will add their perimeters together. The length and width of each base are 12 m and 7 m, respectively, so:

Perimeter of Base = 2 * (Length + Width) = 2 * (12 + 7) = 38 m

The height of the prism is given as 10 m, so:

Lateral Area = 38 * 10 = 380 m²

Next, we need to find the surface area of the prism. This consists of the lateral area we just found, plus the areas of the two bases. Each base has an area of 12 * 7 = 84 m², so:

Surface Area = 2 * Base Area + Lateral Area = 2 * 84 + 380 = 548 m²

Rounding to the nearest whole number, we get:

Lateral Area ≈ 380 m²

Surface Area ≈ 548 m²

Therefore, the answer is option D) 216 m²; 244 m².

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Answer:

The answer to the expression is 16.

Step-by-step explanation:

So, when c = -7, first plug in -7 to every c variable in the expression.

\((-7)^{2} + 4(-7) -5\\\)

Now simplify:

49 - 28 - 5

16

When c = -7, the expression evaluates to 16.

3a. An equation in slope-point for this line is y + 2 = 1/2(x - 0).

3b. The equation in slope-intercept form is y = 1/2(x) - 2.

4a. An equation in slope-point form to represent this function is y - 3875 = -1/695(x - 19375).

4b. The cost of operating a car that has been driven 31250 km is $3892.086.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Part 3.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 + 2)/(4 - 0)

Slope (m) = 1/2

At data point (0, -2) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 1/2(x - 0)

y = 1/2(x) - 2

Part 4a.

Based on the information provided about Jay's business, we would determine the slope of the line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3900 - 3875)/(2000 - 19375)

Slope (m) = 25/-17375

Slope (m) = -1/695

At data point (19375, 3875) and a slope of -1/695, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3875 = -1/695(x - 19375)

Part 4b.

For the cost when x = 31250 km, we have:

y - 3875 = -1/695(31250 - 19375)

y = 17.086 + 3875

y = $3892.086.

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The daily percentage rate (DPR) for the given Annual Percentage Rate (APR) on credit card is 17.8% is equal to 0.048%.

Given the Annual Percentage Rate (APR) on credit card is 17.8%.

Now, we need to find the daily percentage rate (DPR) for the given yearly percentage on credit card.

To find your current annual percentage rate, look at your monthly statements. To determine the daily percentage rate (DPR), divide the annual percentage rate (APR) by 365 (the number of days in a year).

So, given APR = 17.8%

Now, daily percentage rate will be:

⇒ Daily percentage rate = Annual Percentage Rate ÷ 365

⇒ DPR = APR / 365

⇒ DPR = 17.8% ÷ 365

⇒ DPR = 0.048%

Therefore, daily percentage rate (DPR) is equal to 0.048%.

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Answer:

3

Step-by-step explanation:

The cardinality of a set a measure of the number of elements in a set.

A set is a group of objects that have a well defined relationship between them.

In the given set,  A={1,4,9}​

 The set of A has 3 elements which are 1, 4 and 9

So, the cardinality of this set is 3.

However, I can still give you some general steps to solve a math problem in 200 words.

Step 1: Read the problem thoroughly and understand what it's asking you to find. This may involve identifying the given information and what you need to find. Also, identify any constraints on the problem, like time or cost.

Step 2: Plan how to solve the problem. Think about what mathematical operations or formulas you can use to find the answer. Make a list of the steps you need to take to solve the problem. Also, determine the units for your answer.

Step 3: Solve the problem. Use the mathematical operations or formulas you've identified in step 2 to find the answer. Show all of your work, including any calculations, so that you can easily check your work later.

Step 4: Check your answer. Make sure that your answer makes sense and that it satisfies any constraints given in the problem. Also, check that your units are correct. If your answer doesn't make sense, go back and review your work to see if you made an error.

Step 5: Reflect on what you've learned. Think about what you did well and what you could improve upon in future problem-solving situations. This will help you become a more effective problem solver in the future.

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Using central angle theorem,

The measure of the arc BC = 110°.

An angle with its vertex in the middle of the circle it creates with its two radii is said to be central.

Here in the question,

As per the central angle theorem:

(2x -30) ° + x° = 180°

⇒ 2x - 30 + x = 180

⇒ 3x - 30 = 180

Adding 30 on both sides:

⇒ 3x = 180 + 30

⇒ 3x = 210

Dividing both sides by 3.

⇒ x = 70°

Now BC = 2x-30

= 2 × 70 -30

= 140 - 30

= 110°

Therefore, the measure of BC = 110°.

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Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)

Calculating this expression:

A ≈ 5000\((1.00583)^{(24)\)

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

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Number of Std errors away from 0.12 one need to go = 1.227

Standard deviation (or σ) is a measure of how far the data are from the mean. A low standard deviation means that the data are clustered around the mean, and a high standard deviation means that the data are more scattered. Standard deviation shows how the data are distributed. This is a measure of how far each observation is from the mean.

The variance is the mean squared deviation from the mean and the standard deviation is the square root of that number. Both measures reflect the variability of the distribution, but in different units. The standard deviation is expressed in the same units as the original value (minutes, meters, etc.).

A. for 89%  ; critical z value = 1.227

                                     89% = 0.89

Critical z value = 0.89 × 0.14

                         = 1.227

Therefore number of Std errors away from 0.12 one need to go = 1.227

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The correct answer is U - II = I + III + IV.

In order to solve problems based on these sets, we can use a Venn diagram to depict the logical relationship between sets and their components. Although other closed figures like squares may be used, a Venn diagram commonly uses intersecting and non-intersecting circles to indicate the relationship between sets.

c represent the compliment of the particular state.

U is the union set

∩ represent intersection between the neighbouring sets

Therefore,

Bc = U - B = I + II

Bc∩A = Area common in Bc and A = II

(Bc∩A)c = Area in U but not in (Bc∩A) = U - II = I + III + IV

So, answer is d.

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The total amount Frank pays back to the bank = $210642.72

Assuming the given interest rate- that is the simple interest rate.

so the future value A for the simple interest rate is given by,

A = P(1 + rt)

here, P = $56022

r = 0.04

t = 69

Substitute these values in above formula.

A = 56022 (1 + 0.04 * 69)

A = 56022 * 3.76

A = $210642.72

Therefore, the total amount Frank pays back to the bank = $210642.72

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In rectangle the length of QR is y - 64.

What is rectangle ?

A rectangle is a four-sided flat shape where all four angles are right angles (90 degrees). It has two pairs of parallel sides of equal length, making it a special case of a parallelogram. The opposite sides of a rectangle are congruent, meaning they have the same length, and the diagonals bisect each other. The length of a rectangle is usually denoted by "l" and its width by "w". The perimeter of a rectangle is the sum of the lengths of all four sides, and the area is found by multiplying the length and width together.

According to the question:
Since PQRS is a rectangle, PQ = RS = y, and QR = SP - PQ.

Substituting the given values, we have:

QR = SP - PQ

QR = (2y - 64) - (y)

QR = y - 64

So the length of QR is y - 64.

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Answer:

--------------------------

Convert this to vertex form by completing the square.

Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:

Answer:

\((x-3)^2-11\)

Step-by-step explanation:

Given quadratic expression:

\(x^2-6x-2\)

To write the given expression in the form (x + a)² + b, complete the square.

Add and subtract the square of half the coefficient of the term in x:

\(\implies x^2-6x+\left(\dfrac{-6}{2}\right)^2-2-\left(\dfrac{-6}{2}\right)^2\)

Simplify:

\(\implies x^2-6x+\left(-3\right)^2-2-\left(-3\right)^2\)

\(\implies x^2-6x+9-2-9\)

The first three terms x² - 6x + 9 form a perfect square trinomial.

A perfect square trinomial can be written as the square of a binomial.

Factor the perfect square trinomial:

\(\implies(x-3)^2-2-9\)

Simplify:

\(\implies(x-3)^2-11\)

Therefore, the given expression written in the form (x + a)² + b is:

\(\boxed{(x-3)^2-11}\)

Answer:

X     Y    

0     -1

2     -0.5

4     0

6     0.5

8     1

Step-by-step explanation:

I hope i got that right

The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units

For two triangles to be similar, the corresponding sides of the triangles must be in proportion

Having said  that

The side AC corresponds to the side AC in the other triangle

The length BC is calculated as

BC/9 = 25/15

Express as products

So, we have

BC = 9 * 25/15

Evaluate the products

BC = 15

Hence, the length of BC is 15 units

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Part (a)

Why not? Because we can locate the tallest building without having to gather a sample and computing any statistical values based on the sample data. Note how we have one single building and we're focused on just that building only. We aren't asking anything about a population of buildings. Statistics is the science of trying to measure a population in some way, often through the use of a sample statistic. For example, if we asked "what is the average building height in Chicago, Illinois?", then we would be asking a statistical question. Ideally, we would measure every single building in the city. Of course, that's very time consuming and impractical. So the next best thing is to randomly select a sample of buildings and try to estimate the average height like that.

Once again, we're only focused on one single building and not several. So we don't do the operations of gathering a sample and we aren't doing any statistics here. We're simply measuring the building, or looking up the building height in some records database.

=============================================================

Part (b)

The population is the set of teenagers. This could be narrowed to just the teens in one specific town, county, or regional area. It doesn't make much sense to extend the population out too far because teens too far away would likely not visit this particular mall in question. Let's say the population is every teen in a certain county. We have a lot of people in this population, so we'll have to gather a sample. Doing a census is too time consuming and expensive. This process of gathering a sample points to this question being a statistical one. We don't know which store is the most popular, but we can get a fairly good idea through the sampling process. It won't be a 100% guarantee that we got the right one considering that again the sample isn't the exact population, but we should get close if we did the sampling right.

Note how the variable in question is a qualitative one. The store names are the categories or names that the teens select in the survey. This data type is nominal and not ordinal, since stores do not have an inherent rank (other than alphabetical but that's not of much importance). Also note that the responses for this random variable are, more or less, random in nature. We simply don't know how the teens will respond assuming we go into this completely blind. It's a good idea to do so to avoid bias. This random nature helps add evidence we have a statistical question here. The random variable value is not set in stone like the tallest building is. Keep in mind that the question for part (a) is asked to refer to a very specific narrow window of time. The same can be said for part (b) as well. Be sure to carefully set up the question and avoid any ambiguity.

To summarize, to answer such a question given to us we would need to gather a sample and compute sample statistics. This is why we have a statistical question here.

Answer:

90

Step-by-step explanation:

For the polynomial 9x² - 49, the values of a and b include the following:

a = 3x

b = 7

In Mathematics, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:

a² - b² = (a + b)(a - b).

Where:

a and b are numerical values (numbers or numerals).

Based on the information provided, we have the following polynomial function:

9x² - 49

By using the sum-product pattern, we have the following:

9x² + 21x - 21x - 49

By writing the common factor from the two pairs, we have the following:

(9x² + 21x) + (-21x - 49)

3x(3x + 7) - 7(3x + 7)

By rewriting in factored form, we have the following:

9x² - 49 = (3x - 7)(3x + 7)

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