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The radius of the fifth sphere  or the value of r is 14.14

In order to determine the value of the radius r of the fifth sphere, we must first calculate the side length of the square that the four spheres of radius 10 form.

Since all four spheres are touching, the side length of the square is equal to 20. Thus, the area of the square is equal to 400. Since the fifth sphere is touching each of the four other spheres and the centre of the square formed by them, the fifth sphere is sitting at the midpoint of each side of the square.

Thus, the distance from the centre of the square to the centre of the fifth sphere is 10, which is half the side length of the square.  Now, we can calculate the radius of the fifth sphere using the Pythagorean theorem.

The triangle we will use is a right triangle with the side lengths of 10 and 10.

Thus, the hypotenuse (which is the radius of the fifth sphere r) is equal to the square root of 200. Therefore, the radius of the fifth sphere is approximately 14.14.

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Answer:

To find the area of the reduced triangle, we need to know the length of the base and the height of the triangle after the scaling.

Since the triangle has been reduced by a scale of 0.4, the length of each side has been multiplied by 0.4. Therefore, the base of the reduced triangle is:

10 cm × 0.4 = 4 cm

To find the height of the reduced triangle, we can use the fact that the ratio of corresponding sides in similar triangles is the same. Since the triangle has been scaled down by a factor of 0.4, the ratio of the corresponding sides is 0.4. Therefore, the height of the reduced triangle is:

30 cm × 0.4 = 12 cm

Now that we know the base and the height of the reduced triangle, we can calculate its area using the formula:

Area = (1/2) × base × height

Area = (1/2) × 4 cm × 12 cm

Area = 24 cm²

Therefore, the area of the reduced triangle is 24 cm².

Step-by-step explanation:

Answer:

c, 1/4

Step-by-step explanation:

There are six possibilities when rolling a single dice (1, 2, 3, 4, 5, 6). When rolling two dice, there are 36 combinations because 6x6=36. 1/2 of the numbers on each piece of dice are even, so if we multiply 1/2x1/2, we get an answer of 1/4.

The solution to the inequality 13x|20 is all real numbers, as any value of x, no matter how small or large, will make the statement true.

The way to address inequity Using only real values, 13x|20. This means that there is no single solution to this inequality. The inequality is essentially asking what values of x will make the statement true. In this case, any value of x, no matter how small or large, will make the statement true. This is because the absolute value of x is being taken, which means that the value of x is being evaluated regardless of the sign--whether it is positive or negative. For example, if x is -1, then 13x|20 would be 13(-1)|20, which simplifies to -13|20, or 20. This means that no matter what the value of x is, it will always make the statement true. Therefore, the solution to the inequality is all real numbers.

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Answer:

The answer to your problem is, B. reflection across the y-axis

Step-by-step explanation:

The relation between preimage and image is defined by the rule

( x,y ) —> ( -x,y )

Reflection across y-axis represented by the above rule.

It means the △ABC is reflected across the y-axis to form​​ △A'B'C' ​.

Thus the answer to your problem is, B. reflection across the y-axis

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =140 \end{cases}\implies n140=180n-360 \\\\\\ 140n+360=180n\implies 360=40n\implies \cfrac{360}{40}=n\implies 9=n \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ their~sum }{(9)(140)}\implies \text{\LARGE 1260}[/tex]

We can say that after answering the offered question Therefore, the Pythagorean theorem model dimension of the bicycle wheel diameter is 120 inches.

The Pythagorean Theorem is the foundational Euclidean geometry connection that exists between the three sides of the right triangle. According to this rule, the area of either a cube with the length x side is equal to the total of the regions of triangles shared by its other two sides. According to the Pythagorean Theorem, the square that spans the hypotenuse of a right triangle opposite the perfect angle is the combined squares that spanned its sides. It is sometimes expressed as a2 + b2 = c2 in general algebraic notation.

multiplying it by 12 and then multiplying by 5 to get the model dimension in inches:

[tex]$2\text{ ft} \times 12\text{ in/ft} \times 5 = 120\text{ in}$[/tex]

Therefore, the model dimension of the bicycle wheel diameter is 120 inches.

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Answer:

28

Step-by-step explanation:

Because you're decreased the number, you'll subtract the percentage from 100%. Then , use ratio.

100% : 56

100% - 50% ( 50%) : ?

= 50/100 ×56

= 1/2 × 56

= 56/2

= 28

(a)  The probability of getting a face card or a number card is:P(face card or number card) = (12/52) + (40/52) = 52/52 = 1

(b)  The probability of drawing a black and a Queen is:P(black and a Queen) = (26/52) × (2/26) = 2/52 = 1/26

(c) The probability of drawing a black and a face card is:P(black and a face card) = (26/52) × (6/26) = 6/52 = 3/26.

(d) The probability of drawing a Queen and a 3 is 0.

(e)  The probability of drawing a black or a 3 is:P(black or 3) = (26/52) + (4/52) - (2/52) = 28/52 = 7/13.

The probability of getting a face card or a number card is:P(face card or number card) = P(face card) + P(number card)There are 12 face cards in a deck of 52 cards. There are 4 Kings, 4 Queens, and 4 Jacks.There are 52 - 12 = 40 cards which are not face cards. There are four 2's, four 3's, four 4's, four 5's, four 6's, four 7's, four 8's, four 9's, and four 10's.Therefore, the probability of getting a face card or a number card is:P(face card or number card) = (12/52) + (40/52) = 52/52 = 1

The probability of drawing a black and a Queen is:P(black and a Queen) = P(black) × P(Queen given black)The probability of drawing a black card is 26/52 since there are 26 black cards in a deck of 52 cards. The probability of drawing a Queen, given that it is a black card is 2/26, since there are two Queens among the 26 black cards.Therefore, the probability of drawing a black and a Queen is:P(black and a Queen) = (26/52) × (2/26) = 2/52 = 1/26

The probability of drawing a black and a face card is:P(black and a face card) = P(black) × P(face card given black)The probability of drawing a black card is 26/52 since there are 26 black cards in a deck of 52 cards. The probability of drawing a face card given that it is a black card is 6/26 since there are 6 face cards among the 26 black cards.Therefore, the probability of drawing a black and a face card is:P(black and a face card) = (26/52) × (6/26) = 6/52 = 3/26

The probability of drawing a Queen and a 3 is:P(Queen and 3) = 0Since there are no 3's among the Queens, the probability of drawing a Queen and a 3 is 0.

The probability of drawing a black or a 3 is:P(black or 3) = P(black) + P(3) - P(black and 3)The probability of drawing a black card is 26/52. The probability of drawing a 3 is 4/52. There are two 3's which are black cards.Therefore, the probability of drawing a black or a 3 is:P(black or 3) = (26/52) + (4/52) - (2/52) = 28/52 = 7/13.

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2) The measure οf angle ZXY is 125 degrees

3) The length οf the rectangle is 25 cm.

If the rectangle has a length οf 'l' and a width οf 'b', then the area οf the rectangle can be cοmputed by using the fοrmula:

Area = length * width

If the ratiο οf the measure οf angle WXZ tο the measure οf angle ZXY is 11:25, we can write this as:

x:y = 11:25

where x is the measure οf angle WXZ, and y is the measure οf angle ZXY.

We knοw that the sum οf the measures οf these twο angles is 180 degrees, since they are angles in a triangle. Therefοre, we can set up an equatiοn:

x + y = 180

We can sοlve this equatiοn fοr x in terms οf y:

x = 180 - y

Nοw we can substitute this expressiοn fοr x intο the ratiο:

(180 - y) : y = 11 : 25

We can crοss-multiply tο get:

25(180 - y) = 11y

Expanding and simplifying:

4500 - 25y = 11y

36y = 4500

y = 125

Therefοre, the measure οf angle ZXY is 125 degrees.

Let's call the width οf the rectangle w and the length οf the rectangle l. We knοw that the ratiο οf width tο length is 4:5, sο we can write:

w:l = 4:5

We alsο knοw that the area οf the rectangle is 500 square centimeters, sο we can write:

w * l = 500

Nοw we can use the ratiο tο sοlve fοr οne οf the variables in terms οf the οther. Let's sοlve fοr w in terms οf l:

w:l = 4:5

w = (4/5)l

Substitute this expressiοn fοr w intο the area equatiοn:

(4/5)l * l = 500

Simplify:

[tex]4l^2/5 = 500[/tex]

[tex]4l^2 = 2500[/tex]

[tex]l^2 = 625[/tex]

[tex]l = 25[/tex]

Therefοre, the length οf the rectangle is 25 cm. Tο find the width, we can use the ratiο:

w:l = 4:5

w = (4/5)l = (4/5) * 25 = 20

Therefοre, the width οf the rectangle is 20 cm.

Hence,

2) The measure οf angle ZXY is 125 degrees

3) The length οf the rectangle is 25 cm.

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Therefore, the open box with the largest volume has a length  of [tex]20” - 2(4”) = 12”[/tex], and a height of 4”. The volume of the resulting box is 0 x 12 x 4 = 0 cubic inches.

The resulting box with the largest volume can be created by cutting out 4 squares with the same dimensions from each corner of the 8-inch by 20-inch cardboard. After cutting the squares, the sides can be bent up to form an open box. The dimensions of the box with the largest volume can be calculated using the formula for the volume of a rectangular prism, [tex]V = L x W x H.[/tex]

In this case, L = 8” - 2x, W = 20” - 2x, and H = x, where x is the length of each side of the square cut from each corner. The volume of the resulting box will be maximized when x is the greatest value that still produces a box with the given dimensions. Solving the equation, 8” - 2x = x, yields x = 4”.

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a. Mean: 85.4; Standard deviation: 12.1

b. Five-number summary: 60, 78, 88, 95, 98

c. The test scores appear to form a normal distribution. The data points form a symmetric pattern about the mean of 85.4, indicating that the majority of the test scores are concentrated near the mean and gradually become less common as you move away from the mean.

d. The mean of 85.4 and standard deviation of 12.1 indicate that most of the test scores are clustered in the middle, with a few outliers on both the higher and lower end. This suggests that the test was neither too easy nor too difficult for the students, as it was not too difficult to achieve a higher score nor too easy to achieve a low score.

Standard deviation is a measure of how spread out data points are from the mean. It is calculated by taking the square root of the variance and can be used to measure the volatility of a data set. By looking at the standard deviation, one can determine the amount of variability in a given set of data.

The mean of the test scores is 85.4, which is calculated by adding the scores together and dividing by the total number of scores (13). The standard deviation of the scores is 12.1, which is calculated by taking the square root of the variance (217.8). The five-number summary of the test scores is 60, 78, 88, 95, and 98. This means that the minimum score is 60, the first quartile is 78, the median is 88, the third quartile is 95, and the maximum score is 98. This type of distribution is a right-skewed distribution, meaning that most of the scores are closer to the upper end of the range and there are fewer scores near the lower end. This is evident from the five-number summary, where the median is lower than the mean and the third quartile is close to the maximum score.

From this distribution, it is possible to infer that the test was likely a hard test for these students. This is because the mean score of 85.4 is much lower than the maximum score of 98, indicating that not many students were able to achieve the highest score. Additionally, the standard deviation of 12.1 is relatively large, indicating that there is a wide range of scores. This is further evidence that the test was difficult for the students.

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The area of the container can be calculated by multiplying its width, height, and length together ,the area of the container is 1,920 square feet.

The area of a container can be calculated by multiplying its width, height, and length. In order to find the area of the container in this problem, the width of 8 feet, the height of 12 feet, and the length of 24 feet must be multiplied together. Mathematically, this can be expressed as A = 8 × 12 × 24. Solving the equation yields a result of 1,920 square feet.

To calculate the area of the container in square feet, begin by multiplying the width, height, and length together. 8 × 12 × 24 = 1,920. This result can be written as 1,920 square feet. Therefore, the area of the container is 1,920 square feet.

Using basic algebra, the area of the container can be found by multiplying its width, height, and length. 8 × 12 × 24 = 1,920 square feet. This can be written as A = 8 × 12 × 24, where A represents the area of the container in square feet. Solving the equation yields a result of 1,920 square feet. This result can be interpreted to mean that the area of the container is 1,920 square feet.

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After 15 years, $412.5 will joy have earned in interest than Rico as he had an interest rate of 4%.

The simple interest is the rate at which you borrow or give money. When a user receives funds from a lender, the lender receives additional funds in return. The principal refers to the borrowed funds that are granted for a particular time period. Interest is the additional sum that must be returned to the provider for the use of the borrowed funds.

The principal quantity is multiplied by the number of periods and interest rate to determine simple interest. You do not have to pay interest on interest, and simple interest does not increase. In the case of simple interest, the contribution is applied to the current month's interest and the remaining sum is deducted from the principal.

We know that Rico put $5,500 in an account with 3.5 interest rate, which gives us a total amount of $8,387.5 and Interest Earned $2,887.5

We also know that Joy put $5,500 in a bank account with a 4% simple interest rate, which gives us a total amount of $8,800 and Interest Earned $3300.

To find the amount of money joy have earned in interest than Rico:

3300 - 2887.5 = 412.5

Therefore, we can say that after 15 years, $412.5 will joy have earned in interest than Rico as he had an interest rate of 4%.

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The amount that Instant Meals spends on postage to mail out 188 samples is: 19458 cents

The parameters are given as:

W = 64 oz

Total quantity = 188 samples

Charge = 36 cents per 1.5 pounds

Thus converting pounds tp oz, we have;

Charge = 36 cents per 24 oz

Required:

Total amount to pay the parcels

Solution:

Multiply W to 188 samples,

Total weight = 69 oz. (188)

Total weight = 12,972 oz.

Use the charge as an conversion factor,

Total price to pay:

P = 12,972 oz. (36 cents / 24 oz.)

P = 19458 cents

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The standard matrix of the linear transformation T is [1/2 0 ; √3/2 0].

The transformation T: R2 => R2 rotates points clockwise through π/3 radians and then projects each point onto the x1 axis. Here, we are supposed to find the standard matrix of the linear transformation T.To find the standard matrix of the linear transformation T, we need to find out the standard matrix of each step involved in the transformation.

Then the standard matrix of the transformation T can be found out by taking the product of the standard matrices of each step. Let A be the standard matrix of the linear transformation that rotates points clockwise through π/3 radians, and B be the standard matrix of the linear transformation that projects each point onto the x1 axis.

The standard matrix of the linear transformation that rotates points clockwise through π/3 radians can be found out by using the formula that is given below.cosθ  −sinθsinθcosθHere, θ = π/3 cos (π/3) = 1/2, sin (π/3) = √3/2The standard matrix of the linear transformation that rotates points clockwise through π/3 radians is A.

A = (1/2)  −√3/2√3/2 1/2= [1/2  -√3/2 ; √3/2 1/2]The standard matrix of the linear transformation that projects each point onto the x1 axis is B.B = [1 0 ; 0 0]The standard matrix of the linear transformation T can be found out by taking the product of the standard matrices A and B.T = AB= [1/2  -√3/2 ; √3/2 1/2][1 0 ; 0 0]= [1/2 0 ; √3/2 0]

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The amount of felt in the compound shape for the art project is: 313cm².

A compound shape is a 2D shape made up of two or more simpler shapes, often with different sizes and orientations, combined together. When computing the dimensions of a compound shape, the first thing to do is to fragment the shape into regular shapes.

Having fragmented the above given shape (art project) there are:

The required amount of felt for the art project will the sum of the areas of these shapes. The dimensions are given:

We derived 6cm by removing 11cm, 5cm and 3cm from 25cm. That is:

25 - 11 - 5 - 3 = 6cm

We derived 8cm - the height of the right angled tringle by removing 9cm from 17cm. That is:

17cm - 9cm = 8cm.

Areas of the following shapes are given as follows:

1) Area of the rectangle with dimensions 17cm x 5cm:                                  Area = length x width = 17cm x 5cm = 85 square cm

2)  Area of the rectangle with dimensions 17cm x 9cm:

    Area = length x width = 17cm x 9cm = 153 square cm

3) Area of the rectangle with dimensions 17cm x 3cm:

Area = length x width = 17cm x 3cm = 51 square cm

4) Area of the right-angle triangle with base 6cm and height 8cm:

Area = 1/2 x base x height = 1/2 x 6cm x 8cm = 24 square cm

Sum of the areas of all four shapes:

85 + 153 + 51 + 24 = 313 square cm

So the amount of felt required in the shape for the art project is: 313cm².


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Full Question:

Although part of your question is missing, you might be referring to this full question: See the attached images.

Based on the given parameters, the calculated value of the probability that it will not rain is 2/3

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

P(Rain) = 1/3

The probability it will not rain is the complement of the probabilty it will rain

This means that

If the probability of rain tomorrow is 1/3, then the probability of not raining tomorrow is 1 - 1/3 = 2/3.

This can be expressed as

Probability = 0.67 or 67%

Hence, the probability that it will not rain tomorrow is 2/3 or approximately 0.67 (or 67%).

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Answer:

the volume is 5 to the next power which is 3 u end up with multiplication which mean u multiply 5 with 3 to get ur units

a)  The p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that μ1 < μ2.

b) We can construct a (1 - α) confidence interval for the difference between the population means μ1 and μ2 to conduct the test

c) The power of the test is approximately 0.012 when μ1 is three units less than μ2.

The test statistic for this hypothesis test is:

t = (x1 - x2) / √(s1²/n1 + s2²/n2)

Plugging in the given values, we get:

t = (6.2 - 7.8) / √(4/15 + 6.25/15) = -2.72

Using a t-distribution with degrees of freedom equal to (15 + 15 - 2) = 28 and a significance level of α = 0.05, we find the critical value to be -1.701. Since the test statistic is less than the critical value, we reject the null hypothesis.

The p-value can be calculated using a t-distribution with degrees of freedom equal to 28:

p-value = P(T < -2.72) = 0.0068

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that μ1 < μ2.

To conduct the test using a confidence interval, we can construct a (1 - α) confidence interval for the difference between the population means μ1 and μ2:

(x1 - x2) ± t(1-α/2, n1+n2-2) * √(s1²/n1 + s2²/n2)

Plugging in the given values and using a t-distribution with degrees of freedom equal to 28 and a confidence level of 95% (α = 0.05), we get:

(6.2 - 7.8) ± 2.048 * √(4/15 + 6.25/15)

-2.168 < μ1 - μ2 < -0.232

Since the confidence interval does not include zero, we can conclude that there is evidence to support the alternative hypothesis that μ1 < μ2.

The power of a hypothesis test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. In this case, the alternative hypothesis is μ1 < μ2, so we want to calculate the probability of rejecting the null hypothesis when μ1 is actually three units less than μ2.

To do this, we need to calculate the test statistic and find the corresponding probability using a t-distribution with degrees of freedom equal to 28 and a significance level of 0.05.

The test statistic for this case is:

t = (x1 - x2 - Δ) / √(s1²/n1 + s2²/n2) = (6.2 - 7.8 - 3) / √(4/15 + 6.25/15) = -4.14

Using a t-distribution with degrees of freedom equal to 28, we find the probability of correctly rejecting the null hypothesis to be:

power = P(T < -t_crit) = P(T < -1.701 - (-4.14)) = P(T > 2.439) ≈ 0.012

Therefore, the power of the test is approximately 0.012 when μ1 is three units less than μ2. This means that the test is not very sensitive to detecting a difference of three units between the two population means.

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Answer:

The interior angles of a triangle add up to 180 degrees, so Angle E = 70 degrees.

The image of the given points under the rotation through +90° about the center origin include the following;

A' (-5, 4).

B' (-3, -2).

C' (5, -3).

D' (1, 4).

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of each figure, the coordinates of the vertices of the image are as follows:

(x, y)    →       (-y, x)

A (4, 5) = A' (-5, 4).

B (-2, 3) = B' (-3, -2).

C (-3, -5) = C' (-(-5), 3) = (5, -3)

D (4, -1)​ = D' (-(-1), 4) = (1, 4)

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Answer:

they are not similiar

Step-by-step explanation:

..........

The answer choice A is x(x + 6)(x + 4), which is the polynomial [tex]x^3 + 10x^2 + 24x[/tex]  fully factored form.

The quadratic expression enclosed in parenthesis can be factored:

x(x + 6)(x + 4)

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.[tex]x^2+x-12[/tex] is an illustration of a polynomial with a single variable.

from the question:

The given polynomial is[tex]x^3 + 10x^2 + 24x.[/tex]

From each term, we may factor out the common factor of x:

[tex]x(x^2 + 10x + 24)[/tex]

The quadratic expression enclosed in parenthesis can be factored:

x(x + 6)(x + 4)

As a result, solution option A is the fully factored version of the polynomial [tex]x^3 + 10x^2 + 24x[/tex] , which is x(x + 6)(x + 4).

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Choosing a sampling method that changes each time you take a sample is not the meaning of sampling variation.

The correct meaning of sampling variation is the fact that different samples taken from the same population will mostly produce different sample statistics due to random sampling error.

This means that there is a difference in the estimations gotten from different samples, even if the samples are drawn from the same population using the same sampling method.

The other options given are also not correct definitions of sampling variation. selecting a large sample size can help to reduce the amount of sampling variation by increasing the estimates obtained from the sample.

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Answer: volume (cubic units) diameter of base (units) area of base (square units) height (units)

4 1.60 0.785 10

6 2.17 3.54 6

63π 10.03 79 1

Step-by-step explanation: