4. Two numbers are shown on the number line?
A. ㅠ
9/3
Which value is NOT located between these two
numbers on the number line?
B. 9
2π
C. 픔
D.
이름 이
쯩

Answer:

Variance is a measure of variability which describes the average degree of spread in the data about the mean.

Step-by-step explanation:

Answer: 50 1/3

Step-by-step explanation: (30 X 5 +4) divided by 3 = 50 1/3

The volume of the cylinder is 29.78 inches cube.

The volume of the cone is  9.93 inches cube.

The figure above is a sphere, cylinder and a cone. The volume of the figure can be represented as follows:

volume of a sphere = 4 / 3πr³

where

20 = 4 / 3 × π × r³

cross multiply

4r³π = 60

r³π = 15

r = ∛15 / π

r = ∛4.78

r = 1.68 inches

volume of a cylinder = πr²h

where

volume of a cone = 1 / 3 πr²h

where

Therefore, let's find the volume of the cylinder and cone with the following information.

Hence,

volume of the cylinder = π × (r)² × 2r

volume of the cylinder = 2(1.68)³π

volume of the cylinder = 29.78 inches cube

Therefore,

volume of the cone = 1 / 3 πr²h

volume of the cone = 1 / 3 × 3.14 × r² × 2r

volume of the cone = 1 / 3 × 3.14 × 2(1.68)³

volume of the cone = 29.77744896 / 3

volume of the cone = 9.93 inches cube

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The probability that a pack of 16 baseballs would have an average weight of more than 147 grams, given our assumptions, is approximately 1 - 0.0082 = 0.9918, or 99.18%.

What is probability?

Probability is a way to gauge how likely or unlikely something is to happen. It measures the degree of ambiguity surrounding the result of a single event or a series of related occurrences. Typically, probability is stated as a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certain or guaranteed event.

To determine the probability that a pack of 16 baseballs would have an average weight of more than 147 grams, we need information about the distribution of baseball weights. Without specific information about the distribution, it is challenging to provide an exact probability.

However, assuming the weights of baseballs follow a normal distribution with a known mean and standard deviation, we can provide a general guideline for calculating the probability using the Central Limit Theorem.

Let's assume the mean weight of a baseball is μ grams, and the standard deviation is σ grams. Since we don't have the exact values, we'll need to make some assumptions. Let's say the mean weight of a baseball is 150 grams, and the standard deviation is 5 grams.

The average weight of the 16 baseballs follows a normal distribution with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ/[tex]\sqrt[1]{n}[/tex]).

In this case, the mean is 150 grams, and the standard deviation is 5 grams divided by the square root of 16 (since we have 16 baseballs). The square root of 16 is 4.

The standard deviation of the average weight is 5 grams / 4 = 1.25 grams.

Now, we want to calculate the probability that the average weight is more than 147 grams. To do this, we can convert it into a standard normal distribution by subtracting the mean (150 grams) and dividing by the standard deviation (1.25 grams).

The z-score for 147 grams is (147 - 150) / 1.25 = -2.4.

Using a standard normal distribution table or calculator, we can find the probability associated with a z-score of -2.4. Let's assume it is P(Z < -2.4) = 0.0082.

However, since we are interested in the probability that the average weight is more than 147 grams, we need to consider the area to the right of the z-score (-2.4). This is equal to 1 - P(Z < -2.4).

Therefore, the probability that a pack of 16 baseballs would have an average weight of more than 147 grams, given our assumptions, is approximately 1 - 0.0082 = 0.9918, or 99.18%.

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Answer:

  4

Step-by-step explanation:

You want to know the leaf unit corresponding to data value 0.014 when values are rounded to thousandths.

The leaf unit for data values in a stem-and-leaf plot is the least-significant digit of the data value, when all data values are expressed to the same precision.

The least significant digit of 0.014 is 4. The leaf unit is 4.

<95141404393>

Answer:

Here are the correct answers:

B. gram

C. milligram

The approximate probability that "x" will be within 0.5 of population mean is (c) 0.3026.

We use "Central-limit-theorem" to find probability that "x" will be within 0.5 of population mean. According to the central limit theorem, the distribution of sample means approaches a "Normal-Distribution" with mean μ and standard deviation σ/√(n), where μ = population mean, σ = population standard deviation, and n = sample size,

In this case, we have, sample-size of (n) = 49, population mean (μ) = 43, and population "standard-deviation" of (σ) = 9.

So, standard-deviation of sample mean distribution is:

standard deviation = σ/√(n) = 9/√(49) = 1.2857,

To find the probability that x will be within 0.5 of the population mean, we need to standardize the interval using the standard deviation of the sample mean distribution,

z = (x - μ)/(σ/√n) = (43 + 0.5 - 43)/(1.2857) = 0.3892,

The probability that "x" will be within 0.5 of the population mean is the area under the standard normal distribution curve between z = -0.3892 and z = 0.3892.

P(-0.3892 < Z < 0.3892) = P(Z < 0.3892) - P(Z < -0.3892)

= 0.6513 - 0.3487

= 0.3026

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Suppose that a random sample of size 49 is to be selected from a population with mean 43 and standard-deviation 9. What is the approximate probability that "x" will be within 0.5 of the population mean?

(a) 0.5026

(b) 0.6974

(c) 0.3026

(d) 0.6053

Check the picture below.

Answer: 5

Step-by-step explanation:

You could multiply every number but that would take too much time

Instead you have to logic through the problem

Numbers in multiplication follow cyclical sets. i.e. the ones place in the multiples of 3 goes 3,6,9,2,5,8,1,4,7,0,3 forever. (That is why 3 is a "mod 10" number there are 10 possible 1s place values)

The helpful number here is 5

5 is mod 2 because any multiple ends in a 5 or a 0. Given that you are doing all of the odd numbers, five times any odd number will end in a 5, and any odd number ending in 5 times another odd number will also end in 5 so the ones place for all odd numbers multiplied from 1 to 2023 is 5.

When multiplying all the odd numbers from 1 to 2023, inclusive, the last digit of the product will be 5. This is based on the pattern observed in the last digits of the products of odd numbers.

In mathematics, specifically in number theory, we often make use of patterns to solve problems. When you're asked to find the last digit of the product when you multiply all the odd numbers from 1 to 2023, inclusive, it is helpful to look for a pattern in the last digits of the products of odd numbers.

Let's start small. The first five odd numbers are 1, 3, 5, 7, and 9. The product of these numbers is 945, and the last digit, or unit digit, is 5. Let's add another odd number to the product, 11. The product becomes 10395, and again, the unit's digit is 5. As you can see, the pattern is that no matter how many odd numbers you multiply together, the unit's digit (or the last digit) of the product is always 5.

Therefore, when you multiply all the odd numbers from 1 to 2023, inclusive, the last digit of the product will be 5.

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Juan made a 10% down payment of $198 on a $1,980 tool set, leaving a remaining balance of $1,782. He will make 16 monthly payments of $116 to cover the remaining balance.

Juan purchased a tool set for $1,980 using an installment plan.
1. Down payment: Juan made a 10% down payment on the $1,980 tool set. To calculate this, multiply the total cost by the down payment percentage:
  $1,980 * 0.10 = $198
2. Remaining balance: Subtract the down payment from the total cost to find the remaining balance:
  $1,980 - $198 = $1,782
3. Monthly payments: Juan agreed to pay $116 per month to cover the remaining balance. To determine the number of months needed to pay off the balance, divide the remaining balance by the monthly payment:
  $1,782 / $116 ≈ 15.36
Since Juan can't make partial payments, he will need to make 16 monthly payments to fully pay off the balance.
4. In conclusion, Juan made a 10% down payment of $198 on a $1,980 tool set, leaving a remaining balance of $1,782. He will make 16 monthly payments of $116 to cover the remaining balance.

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The area of the carpet is 108 sq. ft.

To find the area of the carpet, we first need to multiply the length and width of the carpet. Therefore, 9 ft. x 12 ft. = 108 sq. ft.

The Smiths need to buy a 108 sq. ft. carpet to center it in their 15 ft. by 20 ft. room.

The area of the carpet is 108 sq. ft.


To find the area of the carpet, you need to multiply its length by its width. In this case, the dimensions of the carpet are 9 ft. by 12 ft.

Area = length × width
Area = 9 ft × 12 ft


The area of the 9 ft. by 12 ft. carpet that the Smiths want to buy and center in their 15 ft. by 20 ft. room is 108 sq. ft.

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The answer could be that Mr. Jacobs's histogram will have 4 bars.

The test scores are listed below;

79, 82, 65, 61, 94, 97, 84, 77, 89, 91, 90, 83, 99, 71, 68, 77, 87 and, 85

We have that the range of the data is from 61 to 99. To create the bars for the histogram, we need to divide this range into intervals.

In that case, the intervals would be:

60-69

70-79

80-89

90-99

thus, the histogram would have 4 bars.

Therefore,  Mr. Jacobs's histogram will have 4 bars.

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Answer: that would be 4

Step-by-step explanation:  there would be 3 numbers in the 60-69 range, 4 numbers that fall into the 70-79 range, 6 numbers that fall into the 80-89 range, and 5 numbers that fall into the 90-99 range.  The interval with more data than any other is the 80-89 range, therefore, making it the mode interval. i hope this helps

Answer:

4 days

Step-by-step explanation:

first, figure out how many cars are produced in a day. since there are 7 days in a week, and 1400 cars are produced in a week, divide 1400 by 7. 1400/7 equals 200. so, if 200 cars produced each day, then:

200x= 800 (x = days)

200x/200 = 800/200

So, 4 days.

The proportion of students that choose nachos is given as follows:

0.3333.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The proportion of students choosing nachos is the probability that a single student choose nachos.

Out of 33 students, 11 choose nachos, hence the proportion is given as follows:

11/33 = 1/3 = 0.3333.

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We need to look at the coefficients of the x and y terms in the equation. The lengths of the transverse and conjugate axes are 10 and 14, respectively.

The standard form of the equation for a hyperbola with a horizontal transverse axis is (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k) is the center of the hyperbola. In this case, the equation given is already in standard form with (h,k) = (0,0).

Comparing the given equation to the standard form, we see that a^2 = 25 and b^2 = 49. Therefore, a = 5 and b = 7.

The transverse axis is the longer axis and is parallel to the x-axis, so its length is 2a = 10. The conjugate axis is the shorter axis and is perpendicular to the transverse axis, so its length is 2b = 14.

Therefore, the lengths of the transverse and conjugate axes are 10 and 14, respectively.

The equation of the hyperbola you provided is x^2/25 - y^2/49 = 1. In this equation, we can identify the terms a^2 and b^2:

a^2 = 25
b^2 = 49

To find the lengths of the transverse and conjugate axes, we need to first find the values of a and b:

a = √25 = 5
b = √49 = 7

The length of the transverse axis is 2a, and the length of the conjugate axis is 2b. Therefore:

Length of transverse axis = 2a = 2(5) = 10
Length of conjugate axis = 2b = 2(7) = 14

So, the lengths of the transverse and conjugate axes are 10 and 14, respectively.

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Step-by-step explanation:

This is a bowl shaped parabola with axis of symmetry  x = 0

From - inf to 0 it is DEcreasing

from 0 to + inf it is INcreasing

Answer:

The RN should set up the infusion pump to deliver 125 mL/hour.

To calculate the infusion rate, we can use the following formula:

Infusion rate = Volume / Time

In this case, the volume is 1000 mL and the time is 8 hours. Plugging these values into the formula, we get the following:

Infusion rate = 1000 mL / 8 hours

Infusion rate = 125 mL/hour

Therefore, the RN should set up the infusion pump to deliver 125 mL/hour.

It is important to note that this is just the calculated rate. The actual rate may vary slightly depending on the type of infusion pump and the settings that are used.

Step-by-step explanation:

The length of the tangent x is 11.2 units.

Given is circle with radius 8.4 units and a tangent with x units, we need to find the length of the tangent,

Since we know that the tangents are perpendicular to the circle, so to find the length,

Using Pythagoras theorem,

Hypotenuse is 5.6+8.4 = 14 units,

So,

14² = 8.4² + x²

x = √196 - 70.56

x = 11.2

Hence the length of the tangent x is 11.2 units.

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Answer:

=62/63

=[tex]\frac{62}{63}[/tex]

Step-by-step explanation:

Convert everything to a denominator 63

=[tex]=\frac{3*9}{63} +-\frac{2*7}{63} +\frac{7*7}{63}[/tex]

=[tex]\frac{27}{63} +\frac{-14}{63} +\frac{49}{63}\\[/tex]

Add up the numerators

= [tex]\frac{62}{63}[/tex]

After 20 years, the investment compounded periodically will be worth $ 3, 238. 47 more than the investment compounded annually.

First, find the value of the investment when it is compounded periodically, 12 times a year.

The formula is:

= Amount invested x ( 1 + rate ) ^ number of periods

= 9, 000 x ( 1 + 9 % / 12 ) ^ ¹² ˣ ²⁰

= $ 53, 678. 16

If compounded annually, the value would be :

= 9, 000 x ( 1 + 9 % ) ²⁰

= $ 50, 439. 69

The difference is :

= 53, 678. 16 - 50, 439. 69

= $ 3, 238. 47

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Possible committees contain at least one member of each class is 5235.

Number of freshman = 3

Number of sophomores = 4

Number of juniors = 4

Number of seniors = 5

Total = 3 + 4+ 4 + 5 = 16

Number of committees of five members of the council would contain at least one member of each class is given by = total - Number of possibility without freshmen - Number of possibility without sophomores - Number of possibility without juniors - Number of possibility without seniors

= [tex](\left \116 \atop 5\right. ) - (\left \413 \atop 5\right. ) -(\left \112 \atop 5\right. )-(\left \112 \atop 5\right. )-(\left \111 \atop 5\right. )[/tex]

= 8568 - 1287 - 792 - 792 - 462

= 5235

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Answer:

48%

Step-by-step explanation:

Let x equal the percent

25x = 12

25x/25 = 12/25

x =0.48

0.48 = 48%

The 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).

To calculate the 95.44% confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

First, let's determine the critical value. Since the confidence level is 95.44%, we need to find the z-score that corresponds to a tail probability of (1 - 0.9544)/2 = 0.0228. Looking up this value in the standard normal distribution table or using a statistical calculator, we find that the z-score is approximately 2.17.

Next, we need to determine the standard deviation of the population. Since we don't have that information, we'll use the sample standard deviation as an estimate. Let's assume the sample standard deviation is 5 minutes.

Now we can calculate the confidence interval:

Confidence Interval = 22.3 ± (2.17) * (5 / sqrt(20))

Calculating the expression inside the parentheses:

= 22.3 ± (2.17) * (5 / sqrt(20))

= 22.3 ± 2.17 * (5 / 4.472)

= 22.3 ± 2.17 * 1.118

Calculating the confidence interval:

Lower Limit = 22.3 - (2.17 * 1.118)

Upper Limit = 22.3 + (2.17 * 1.118)

Lower Limit = 22.3 - 2.42706 ≈ 19.87294

Upper Limit = 22.3 + 2.42706 ≈ 24.72706

Therefore, the 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).

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The equation of the parabola that opens up or down, with a vertex at (0, 5) and passing through (-6, 4), is y = (-1/36)x^2 + 5

To find the equation of a parabola that opens up or down given the vertex and a point, we can use the standard form of the equation:

y = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola. In this case, the vertex is (0, 5), so we have h = 0 and k = 5.

Now, we can substitute the given point (-6, 4) into the equation to determine the value of a:

4 = a(-6 - 0)^2 + 5

4 = 36a + 5

36a = -1

a = -1/36

Substituting the value of a back into the equation, we have:

y = (-1/36)(x - 0)^2 + 5

y = (-1/36)x^2 + 5

Therefore, the equation of the parabola that opens up or down, with a vertex at (0, 5) and passing through (-6, 4), is y = (-1/36)x^2 + 5.

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The value of x and y are 10 and 10√3

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Here the hypotenuse is 20 and the opposite to angle 30 is x and the adjacent is y

Therefore;

sin30 = x/20

1/2 = x/20

2x = 20

x = 20/2 = 10

cos 30 = y/20

√3/2 = y/20

2y = 20√3

y = 20√3/2

y = 10√3

therefore the value of x and y are 10 and 10√3

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The dimensions that minimize the length of fencing needed are approximately 28.28 feet by 28.28 feet, creating a square-shaped playground.

To minimize the length of fencing needed for the enclosure, we need to find the dimensions that maximize the area of the playground. Since one side of the playground is already bordered by the school building, we can focus on the remaining three sides.

Let's assume the length of the playground parallel to the school building is L, and the width perpendicular to the school building is W. The area of the playground can be expressed as A = L * W.

Given that the total area of the enclosure is 800 square feet, we have the constraint L * W = 800.

To minimize the length of fencing needed, we want to maximize the area A. This occurs when the length and width are as close as possible to each other. In other words, we want to find the dimensions that form a square shape.

In a square, the length and width are equal, so we can solve the constraint equation L * L = 800.

Taking the square root of both sides, we find L = √800 ≈ 28.28 feet.

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The distance between two opposite corners of the intersection is, 15 meters.

We have to given that;

Hillsdale Street and Salem Avenue intersect.

And,  Hillsdale Street is 12 meters wide and Salem Avenue is 9 meters wide,

Since, WE know that;

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Now, Let us assume that,  distance between two opposite corners of the intersection is, x

Hence, We can formulate for the given condition,

⇒ Hypotenuse² = Base² + Opposite²

⇒ x² = 12² + 9²

⇒ x² = 144 + 81

⇒ x² = 225

Taking square root on both side,

⇒ x = √225

⇒ x = 15

Therefore, We get;

The distance of two opposite corners of the intersection is,

⇒ 15 meters.

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Answer:

y= 32

Step-by-step explanation:

Answer:

The answer for y is 32

Step-by-step explanation:

-3=-11+√2y

-3+11=√2y

8=√2y

square both sides

8²=√2y²

64=2y

divide both sides by 2

2y/2=64/2

y=32