Z-scores measure an observation's standing relative to the ____ of the given data set.

Answer:

B and C

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

Verify each statement.

A) 2⁻³ raised to the third power equals 1.

B) 2⁻³ is less than 1.

C) 2⁻³ is greater than 3⁻².

D) 2⁻³ multiplied by -1 equals 2³.

E) 2⁻³ is equal to -8.​

The probability of getting exactly 7 heads when a fair coin is tossed 9 times is 0.164 to the nearest thousandth.

To calculate the probability of getting exactly 7 heads when a fair coin is tossed 9 times, we can use the binomial probability formula below:

P(X = k) = [tex]^nC_k * p^k * (1 - p)^{n - k}[/tex]

where;

p is the probability of success on a single trial = 0.5

n is the number of trials = 9

k is the number of desired successes = 7

Substituting:

P(X = 7) = ⁹C⁷ * (0.5)⁷ * (1 - 0.5)²

P(X = 7) ≈ 0.164

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The Cumulative Distribution Function (CDF) can be used to find the probability of a continuous random variable that is uniformly distributed between 3 and 8.

The formula for the CDF is F(x) = (x-a)/(b-a) where a is the lower bound of the distribution and b is the upper bound of the distribution. In this case, a = 3 and b = 8. Therefore, the CDF equation is F(x) = (x-3)/(8-3). The Cumulative Distribution Function (CDF) can be used to find the probability of a continuous random variable that is uniformly distributed between 3 and 8.As an example, let's find the probability of x being less than or equal to 5. The CDF equation would be F(5) = (5-3)/(8-3) = 2/5. Therefore, the probability of x being less than or equal to 5 is 2/5.

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The proportional relationship that best represent the machine labeling y cans in x minutes is given as follows:

y = 400x.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

A machine can label 4,000 cans in 10 minutes, hence the constant is given as follows:

k = 4000/10

k = 400.

Hence the proportional relationship that best represent the machine labeling y cans in x minutes is given as follows:

y = 400x.

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3268760 different samples of size 10 people are possible to be selected.

15818400 different license plates are possible.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

The combination formula aids in determining the number of possible combinations that may be created by selecting a portion of a bigger collection of objects.

We need the number of possible combinations of choosing 10 people out of 25 (any order). The 25 binomial coefficient, (10) gives the number. Possible number of combinations are:

²⁵C₁₀ =  25! / (25-10)!(10!)

²⁵C₁₀ = 3268760

We want 3 letters and 3 digits but the first digit can't be zero. There are 26 alphabets and 10 digits. Since repetition is allowed we can use any of the 26 alphabets in place of all 3 letters.

This gives us 26 x 26 x 26 = 26³ ways to choose the first three letters.

For digits, since the first digit can't be 0, we can choose the rest 9 digits. For the next two digits, we can choose any one digit from 10. This gives us 9 x 10 x 10 ways to choose digits.

Finally, by law of multiplication, the total number of ways of choosing license plates is :

number of license plates = 26³ × 9 × 100

= 15818400

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3268760 different samples of size 10 people are possible to be selected.

15818400 different license plates are possible.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

The combination formula aids in determining the number of possible combinations that may be created by selecting a portion of a bigger collection of objects.

We need the number of possible combinations of choosing 10 people out of 25 (any order). The 25 binomial coefficient, (10) gives the number. Possible number of combinations are:

²⁵C₁₀ =  25! / (25-10)!(10!)

²⁵C₁₀ = 3268760

We want 3 letters and 3 digits but the first digit can't be zero. There are 26 alphabets and 10 digits. Since repetition is allowed we can use any of the 26 alphabets in place of all 3 letters.

This gives us 26 x 26 x 26 = 26³ ways to choose the first three letters.

For digits, since the first digit can't be 0, we can choose the rest 9 digits. For the next two digits, we can choose any one digit from 10. This gives us 9 x 10 x 10 ways to choose digits.

Finally, by law of multiplication, the total number of ways of choosing license plates is :

number of license plates = 26³ × 9 × 100

= 15818400

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The area of triangle FGH is given as follows:

15.05 units².

The area of a triangle is given by half the multiplication of the base length by the height.

The base length is given by the distance between points F and G, hence:

b = sqrt((-2 - (-4))² + (6 - 1)²)

b = 5.385.

The coordinates of the midpoint of segment FG are given as follows:

The distance between the midpoint and vertex H is the height, given as follows:

h = sqrt((-3 - 2)² + (3.5 - 6)²)

h = 5.59.

Hence the area of the triangle is given as follows:

A = 0.5 x 5.385 x 5.59

A = 15.05 units².

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Answer:

where represents the time two hours later than the current time. represents the time one hour later than current time. Henceforth, the time at present is 9 pm.

Step-by-step explanation:

The (A) mean is the least acceptable metric of central tendency for data collection with outliers.

There are various mean types in mathematics, particularly in statistics.

Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.

In mathematics, the mean is the average of a set of data, which is calculated by adding all the numbers together and then dividing the result by the total number of numbers.

For instance, the mean for the collection of values 8, 9, 5, 6, and 7 is 7, since 8 + 9 + 5 + 6 + 7 = 35, and 35/5 = 7.

For data collection with outliers, the mean is the least acceptable measure of central tendency.

Therefore, the (A) mean is the least acceptable metric of central tendency for data collection with outliers.

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Answer:

15

Step-by-step explanation:

5*3 = 15

Bistro’s food cost percent is 35.83%

Food cost percentage is calculated by taking the cost of goods sold and dividing that by the revenue or sales generated from that finished dish.

Food cost percent is calculated using the following formula:

Total Food Cost Percentage = (Total Cost of Goods Sold / Total Revenue) x 100

From the parameters in the question,

Total Food Cost Percentage = 67,000/187,000 x 100

Total Food Cost Percentage = 6,700,000/187000

Total Food Cost Percentage = 35.73%

Hence, the Bistro’s food cost percent is 35.83%

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Answer:

see the attachment photo!

Answer:

3/4 servings

Step-by-step explanation:

Each serving = 1/2

There are 3/8 cookies.

How many times 1/2 "fits" into 3/8 = how many servings.

3/8 / 1/2

= 3/8 * 2

= 3/4 servings

The required chance that the digits can form the number 510 is 6/1000, or approximately 0.006, or 0.6%.

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.

The chance that the digits drawn can form the number 510 is given by the probability of drawing the digits 5, 1, and 0 in that order or in some rearrangement of the order.

There are 3! = 6 ways to arrange the digits 5, 1, and 0, and there are 10^3 = 1000 total possible outcomes when the random number generator is run three times.

So, the chance that the digits can form the number 510 is 6/1000, or approximately 0.006, or 0.6%.

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Answer:

The equation 3x^2 - bx = 0 can be factored into two linear factors as follows:

x (3x - b) = 0

So either x = 0 or 3x - b = 0, which gives x = b/3.

Therefore, the solutions to the equation 3x^2 - bx = 0 are x = 0 or x = b/3.

Answer:

see below

Step-by-step explanation:

170*70=11900

after one year 170*80 = 13600
gain on paper = 13600-11900 = 1700

80/70 = 1.14 so 14% if you had paid out of pocket

but then you bought on margin meaning you only used

15% of your money = 11900* 15% = 1785

but your gain was 1700, so your return = 1700/1785 = 95%

45% of your money = 11900* 45% = 5355

but your gain was 1700, so your return = 1700/5355 = 32%

85% of your money = 11900* 85% = 10115

but your gain was 1700, so your return = 1700/10115 = 17%

Answer:

$16,050.00

Step-by-step explanation:

10[(40 x 30) + (9 x 45)]  

In one week, he works 40 hours (8 x 5) for $30 and 9 hours of overtime each week (one extra hour 5 days during a week week plus 4 hours on Sat.)

10(1200 +405)

10(1605)

$16,050.00

To calculate the carpenter's earnings, separate the regular work hours from the overtime hours. Compute earnings for both from their respective rates and add them together. Multiply by the number of days worked and finally, by the total number of weeks.

In order to calculate the earnings of a carpenter during a 10-week period, we must consider how many hours were worked at regular and overtime rates. During the weekdays, the carpenter worked 9 hours per day. The first 8 hours were paid at the regular rate, and the remaining 1 hour was considered overtime. On Saturdays, the carpenter worked 4 hours at the regular rate as it didn't supersede the 8-hour workday.

So, on weekdays, he earned: 8 hours * $30 + 1 hour * $45. On Saturdays, his earnings were 4 hours * $30. To find the weekly earnings we add weekday and Saturday earnings, then multiply by 5 (for weekdays) and add 1 Saturday, then multiply the total earnings by 10 weeks. Using these computations, we are able to find the total amount earned by the carpenter.

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Answer:

[tex]240\pi cm^{2}[/tex]

Step-by-step explanation:

Lateral area of a cylinder is the curved surface area, (which connects the top with the base)

Curved Surface Area= [tex]2\pi rh[/tex]

where  r = radius of base

           h =  height of cylinder

Substituting the provided values:

Lateral area of cylinder = [tex]2\pi (6 cm)(20 cm)[/tex]

                                        = [tex]240\pi cm^{2}[/tex]

The measure of it's opposite angle is 135

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

The base angles equals 45

Using the above as a guide, we have the following:

Base angle + Opposite angle = 180

Substitute the known values in the above equation, so, we have the following representation

45 + Opposite angle = 180

Evaluate the like terms

Opposite angle = 135

Hence, the angle is 135 degrees

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There are 45697600 number of different license plates can be manufactured for this state.

The combination is a mathematical technique that is the number of ways to arrange the n number of collections where the order of selection does not matter.

ⁿCₐ= n!/(n-a)!a!

Here given in the question is,

On the license plate, there are 4 letters and 2 numbers.

Since, There are 26 alphabets in English from A to Z for which at position 1, there are 26 possibilities of alphabets at every position by,

²⁶C₁ = 26!/(26-1)!1!

       = 26!/25!1!

       = 26!/25!

        = 26

So, for 4 different positions of letters,

Then, The number of ways is,

⇒ 26×26×26×26 = 26⁴= 456976

And, There are 10 numbers in math for which at position 1, there are 10 possibilities of numbers at every position by,

¹⁰C₁ = 10!/(10-1)!1!

       = 10!/9!1!

       = 10!/9!

        = 10

So, for 2 different positions of numbers, the number of ways is,

= 10×10 = 10²= 100

Thus, The total number of ways the license can be manufactured = 456976 × 100= 45697600

Therefore, 45697600 different license plates can be manufactured for this state.

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Answer:

x(y/2 + z)

Step-by-step explanation:

There are two triangles here.

The small triangle which is bound by dotted lines has base = y and height = x

The height of the larger triangle is 2x and its base is y + z

Area of larger triangle = 1/2 ·  2x · (y + z)
= x(y + z) = xy + xz

Area of smaller triangle = 1/2 · x · y = xy/2

Shaded region area = Area of larger triangle - area of smaller triangle

= xy + xz - xy/2

= xy/2 + xz

= x(y/2 + z)

The change in electric potential is approximately 135.19 volts if you move from coordinate (-8.03, -4.24) to coordinate (7.02, 2.60)

What is a coordinate point?

Coordinates are a pair of numbers that are used to determine the position of a point or a shape in a 2-dimensional plane. We define the position of a point on a 2D plane using two numbers, called the x-coordinate and the y-coordinate.

The change in electric potential (ΔV) can be calculated using the equation:

ΔV = -∫ E dl

where E is the electric field and dl is an infinitesimal displacement along the path. We need to find the path integral of the electric field between the two coordinates.

Since the electric field is in the x-y plane, we can use the two-dimensional version of the equation:

ΔV = -∫ E * dx - ∫ E * dy

where dx and dy are the changes in x and y, respectively.

We can calculate the change in x and y as follows:

dx = 7.02 m - (-8.03 m) = 7.02 m + 8.03 m = 15.05 m

dy = 2.60 m - (-4.24 m) = 2.60 m + 4.24 m = 6.84 m

Next, we'll use the electric field equation to find the components of the electric field in the x and y directions:

Ex = -3.67 N/C

Ey = -4.359 N/C

Finally, we can use these values to calculate the change in electric potential:

ΔV = -∫ E * dx - ∫ E * dy = -Ex * dx - Ey * dy = -(-3.67 N/C) * (15.05 m) - (-4.359 N/C) * (6.84 m)

Converting from joules to volts:

ΔV = ΔV / (1.602 * 10^-19 C)

ΔV = (3.67 N/C * 15.05 m + 4.359 N/C * 6.84 m) / (1.602 * 10^-19 C) = 135.19 Volts

Hence, the change in electric potential is approximately 135.19 volts.

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Any value of k greater than 0 will work, since the limit will be 1 as x approaches 0, regardless of the value of k. Other values of k can also work.

The limit in question is 3*_4limX-0 ekx+1. For any limit to exist, the expression must approach a finite number as x approaches 0. In this case, that number is 1. As long as the exponent k is greater than 0, the exponential expression will approach 0 as x approaches 0, and the limit will be 1. Therefore, any value of k greater than 0 will work. It is worth noting, however, that other values of k can also work. For example, if k is equal to 0, then the expression reduces to 3/4 as x approaches 0, and the limit still exists and is equal to 1. Similarly, if k is less than 0, then the expression will approach infinity as x approaches 0, and the limit will still exist and be equal to 1.

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Answer expressed in terms of pi: [tex]V=2304 \pi (m^{3})\\[/tex].

Answer rounded to the nearest whole number: [tex]V=7238(m^{3})[/tex].

Given figure: Sphere.

Given dimension: diameter (d)= 24m.

We're trying to calculate the volume of a sphere, here's the formula for that:

[tex]V=\frac{4}{3} \pi r^{3}[/tex]

There's something worth paying a bit extra ttention in this problem, and that is the fact that we were not given a value of radius (r) to use in the formula. Instead, we were given the diameter (d), which happens to be double of the radius, by definition. Hence, to find the radius we do the following:

[tex]d=2r\\\\ r=\frac{d}{2} =\frac{24m}{2} =12m[/tex]

Use the data in the volume formula:

[tex]V=\frac{4}{3} \pi (12m)^{3}[/tex]

[tex]V= \pi(\frac{4}{3} (12m)^{3})\\ \\V= \pi(2304m^{3} )\\ \\V=2304 \pi (m^{3})\\[/tex]

We were asked to express our answer in terms of pi. Therefore, let's isolate pi from the calculations for now:

[tex]V= \pi(\frac{4}{3} (12m)^{3})\\ \\V= \pi(2304m^{3} )\\ \\V=2304 \pi (m^{3})\\[/tex]

Answer expressed in terms of pi: [tex]V=2304 \pi (m^{3})\\[/tex].

The problem also asks to round to the nearest whole number. So, let's go ahead and calculate an approximate value and round it to the nearest whole number:

[tex]V=7238.229474 (m^{3})[/tex]

Since the first number after the dot (.) isn't 5 or greater, we may leave the whole part of the number as it is and delete the remaining decimal numbers.

Answer rounded to the nearest whole number: [tex]V=7238(m^{3})[/tex].

There are 2518 sets of five marbles that include either the lavender one or exactly one yellow one, but not both.

To solve this problem, we need to find the number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both colors. Here's one way to approach the problem:

Number of sets of five marbles that include the lavender one: There is only one lavender marble, so we can choose any 4 other marbles to go with it.

There are a total of 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 7 x 6 x 5 x 4 = 840 possible sets of five marbles that include the lavender one.

Number of sets of five marbles that include exactly one yellow one: There are two yellow marbles,

So there are 2 possible choices for the yellow marble. For each choice, we can choose any 4 other marbles to go with it.

As before, there are 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 2 x (7 x 6 x 5 x 4) = 1680 possible sets of five marbles that include exactly one yellow one.

Number of sets of five marbles that include both the lavender one and exactly one yellow one:

We need to subtract these sets from the total number of sets that include either the lavender one or exactly one yellow one.

We have already found that there are 840 sets of five marbles that include the lavender one, and 1680 that include exactly one yellow one.

To find the number of sets that include both, we can choose any one yellow marble and the lavender one.

There are 2 choices for the yellow marble and 1 choice for the lavender one,

So there are 2 x 1 = 2 possible sets of five marbles that include both the lavender one and exactly one yellow one.

Number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both:

Finally, we need to subtract the number of sets that include both the lavender one and exactly one yellow one from the total number of sets that include either the lavender one or exactly one yellow one.

The total number of sets that include either the lavender one or exactly one yellow one is 840 + 1680 = 2520. The number of sets that include both is 2,

So the number of sets that include either the lavender one or exactly one yellow one, but not both, is 2520 - 2 = 2518.

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Therefore , the solution of the given problem of test statistics comes out to be the p-value is 0.00052.

The Z-statistic, which demonstrates that the ordinary normal balanced hypothesis is true, has been used as the statistic for anything resembling a Z-test. Let's say you run two separate X-y tests with a 0.05 level of significance, and the results show that you got a 2.5 R t. (also referred as a Z-value). The p-value for this Z-value is 0.0124.

Here,

(a) State the null hypothesis [tex]H_{0}[/tex] and the alternative hypothesis H1.

The null hypothesis (H0) is that the population mean sodium level for healthy adults is equal to the textbook value of 141 Eq per liter of blood.

[tex]H_{0}[/tex]     : μ = 141

The alternative hypothesis (H1) is that the population mean sodium level for healthy adults differs from the textbook value.

H1: μ ≠ 141

(b) Determine the type of test statistic to use.

Since the sample size is greater than 30 and the population standard deviation is known, we can use a z-test to test the hypothesis.

(c) Find the value of the test statistic. (Round to three or more decimal places.)

The test statistic is calculated as:

z = (x'- μ) / (σ / √n)

Where x' is the sample mean, μ is the population mean under the null hypothesis, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

z = (149 - 141) / (13 / √21) = 3.464

Therefore, the value of the test statistic is 3.464.

(d) Find the p-value. (Round to three or more decimal places.)

Since this is a two-tailed test, we need to find the area under the normal curve beyond 3.464 in both directions. Using a standard normal table or calculator, we find that the area beyond 3.464 is 0.00026 in one direction. So, the p-value is:

p-value = 2 * 0.00026 = 0.00052

Therefore, the p-value is 0.00052.

(e) Can we conclude that the population mean adult sodium level differs from that given in the textbook?

Since the p-value (0.00052) is less than the level of significance (0.01), we can reject the null hypothesis and conclude that the population mean adult sodium level differs from that given in the textbook at the 0.01 level of significance.

Answer: Yes, we can conclude that the population mean adult sodium level

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The fraction of the jug filled is given by the equation A = 5/8 of the jug

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction of the jug filled be represented as A

Now , the equation will be

The amount of paint poured initially = ( 2/3 ) gallons

The amount of jug filled initially = ( 1/4 ) of the jug

Now ,

The amount of jug filled for 1 gallon = ( 1/4 ) / ( 2/3 ) of the jug

On simplifying the equation , we get

The amount of jug filled for 1 gallon = ( 3/8 ) of the jug

And , an additional 1 gallon of paint is added

So , the new amount of paint = [ ( 2/3 ) + 1 ] = ( 5/3 ) gallons

And , the amount of jug filled for ( 5/3 ) gallons = ( 5/3 ) x amount of jug filled for 1 gallon

Substituting the values in the equation , we get

The amount of jug filled for ( 5/3 ) gallons A = ( 5/3 ) x ( 3/8 )

On simplifying the equation , we get

The amount of jug filled for ( 5/3 ) gallons A = ( 5/8 ) of the jug

The amount of jug filled for ( 5/3 ) gallons A = 0.625 of the jug = 62.5 %

Hence , the fraction is ( 5/8 ) of the jug

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Based on their contribution ratios, the amount each will get from the winnings is as follows:

A ratio shows the relative size of a variable, quantity, or value when compared to another.

Ratios are fractional values expressed as decimals, percentages, or fractions.

The cost of a ticket = R60

Contributions by:

Hanna = R15

Sarah = R21

Mthunzi = R24

Ratio = 5: 7: 8

Sum of ratios = 20 (5 + 7 + 8)

Hanna = R1,000 (5/20 x R4,000)

Sarah = R1,400 (7/20 x R4,000)

Mthunzi = R1,600 (8/20 x R4,000)

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The expression with exactly two terms for the amount of money the club

will make for selling 'f' frames is 7f- 36.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression.

Given:

Price of frame= $13

Material cost = $6

Renting both cost = $36

For selling 'f' frames the amount of money the club make

= (13f - 6f) - 36

= (13-6)f- 36

= 7f- 36

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