Rewrite the given formula relating the area of a square to the length of its diagonal to solve for d. The 2nd screenshot is the formula sorry for the poor sc

Answer:

the variance of X is 0.126.

Step-by-step explanation:

The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:

P(X = k) = (nCk)(N-nCk) / (NCk)

where C denotes the combination function.

(a) Expectation of X:

E(X) = np = nK/N = (4/20) * 4 = 0.8

Therefore, the expected number of white balls drawn is 0.8.

(b) Variance of X:

Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126

Therefore, the variance of X is 0.126.

Answer:

The expected number of white balls drawn is 0.4 and the variance of X is 0.24.

Step-by-step explanation:

The probability that a sample of size n = 158 is randomly selected with a mean greater than 242.4 is 0.751.

z = (x - μ) / (σ/√n)

where x is the sample mean.

Substituting the values, we get:

z = (242.4 - 246) / (89.7/√158) ≈ -0.670

We want to find the probability of obtaining a sample mean greater than 242.4, which is equivalent to finding the probability of obtaining a standardized sample mean greater than z = -0.670. We can use a standard normal distribution table or calculator to find this probability.

P(z > -0.670) ≈ 0.751

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Note that the limit of the expression as x approaches infinity is 1/2.

start by multiplying both the numerator and denominator by the conjugate  expression

√ (x ² - 9x + 1) + x,

this will eliminates the root in the numerator

lim x->∞ [(√(x ² - 9x + 1) - x)  * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)

Expanding the numerator

lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)

Simplifying further:

lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)

we can see that the 1/x ² term approaches zero, and the expression simplifies to

lim x->∞ [(1 - 0)]  / (√(1 - 0) + 1)

= 1/2

So it is correct to state that the limit of the expression as x approaches infinity is 1/2.

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If the total distance available is 92.75 yards, and there is a sign 5 yards before the starting line, the actual distance available for the race is:

92.75 - 5 = 87.75 yards

Since there are 5 sections of the race, each section covers:

87.75 / 5 = 17.55 yards

Therefore, each section of the race is 17.55 yards long.

The unknown angles in the circle are as follows:

a. m∠AEB = 73°

b. arc angle VW = 155°

a.

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore,

m∠AEB = 1 / 2 (99 + 47)

m∠AEB = 146 / 2

m∠AEB = 73 degrees

b.

If two secants intersect outside a circle , then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs .

Therefore,'

arc angle VW = x

55 = 1 / 2 (x - 45)

55 = 0.5x  - 22.5

0.5x = 55 + 22.5

0.5x = 77.5

divide both sides by 0.5

x = 77.5 / 0.5

x = 155 degrees

Therefore,

arc angle VW = 155 degrees

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Answer:

To answer these, we can use the standard normal distribution & z-scores. A z-score represents the number of standard deviations a value is from the mean. The formula to calculate a z-score is: z = (x - μ) / σ, where x is the value, μ is the mean and σ is the standard deviation.

A) To find the proportion of pregnancies that last more than 278 days, we first calculate the z-score for 278 days: z = (278 - 272) / 12 = 0.5. Using a standard normal distribution table, we find that the proportion of values above a z-score of 0.5 is approximately 0.3085. So, about 30.85% of pregnancies last more than 278 days.

B) To find the proportion of pregnancies that last between 257 and 275 days, we first calculate the z-scores for both values: z1 = (257 - 272) / 12 = -1.25 and z2 = (275 - 272) / 12 = 0.25. Using a standard normal distribution table, we find that the proportion of values between z-scores of -1.25 and 0.25 is approximately 0.3944. So, about 39.44% of pregnancies last between 257 and 275 days.

C) To find the probability that a randomly selected pregnancy lasts no more than 266 days, we first calculate the z-score for 266 days: z = (266 - 272) / 12 = -0.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -0.5 is approximately 0.3085. So, there is about a 30.85% chance that a randomly selected pregnancy lasts no more than 266 days.

D) To determine if very preterm babies are unusual, we first calculate the z-score for 242 days: z = (242 - 272) / 12 = -2.5. Using a standard normal distribution table, we find that the proportion of values below a z-score of -2.5 is approximately 0.0062. Since this value is less than 0.05, we can conclude that very preterm babies are unusual.

Answer:

Step-by-step explanation:

6x² - 10x + 21x - 35 = 6x² + 11x - 35

6x² - 6x² + 11x - 11x - 35 + 35 = 0

0 = 0

The equation is an identity. Its solution set is {all real numbers}.

Answer:

√75 =8.66.

Step-by-step explanation:

The square root of 75 is an irrational number where the numbers after the decimal point go up to infinity. √75 = 8.660.√75 cannot be written in the form of p/q, hence it is an irrational number. irrational with never-ending digits.

Let's see how to find the square root of 75 by the long division method.

Step 1: Express 75 as 75.000000. We take the number in pairs from the right. Take 75 as the dividend.

Step 2: Now find a quotient which is the same as the divisor. Multiply quotient and the divisor and subtract the result from 75.

Step 3: Now double the quotient obtained in step 2. Here is 2 × 8 = 16. 160 becomes the new divisor.

Step 4: Apply decimal after quotient '8' and bring down two zeros. We have 1100 as the dividend now.

Step 5: We need to choose a number that while adding to 160 and multiplying the sum with the same number we get a number less than 1100. 160+ 6 = 166 and 166 × 6 = 996. Subtract 996 from 1100. We get 104

Step 6: Bring down two zeros again and place it after 104, so that it becomes 10400 which is the new dividend. Now multiply the number in the quotient by 2. Here it is 86. We get 172. Have it as 1720. Now find a number at the unit's place of 1720 multiplied by itself gives 10400 or less. We find that  1726  × 6 = = 10356. Find the remainder.

Step 7 : Repeat the process until we get the remainder equal to zero. The square root of 75 up to two places is obtained by the long division method. Thus √75 = 8.66

Answer:

Step-by-step explanation:

An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

Answer:

301.4 in^3

Step-by-step explanation:

Divide 12 by 2 to get the radius

12/2=6

Square 6 and multiply by 3.14 according to the area of a circle formula πr^2.

6^2=36 36*3.14=113.04

We now have the area of the base.

Multiply it by the height and divide by three to follow the formula for the volume of a cone, 1/3bh.

113.04*8=904.32. 904.32/3= 301.44, or 301.4 after rounding.

The rectangular block of wax can make approximately 2 candles.

To calculate the number of candles, we use the formula

V of wax = l x w x h = 10 cm x 9 cm x 20 cm = 1800 cubic cm

V of candle = l x w x h = 9 cm x 9 cm x 12 cm = 972 cubic cm

1800 / 972 = 1.85

The above answer is based on the full question below;

you are melting a rectangular block of wax to make candles. how many candles of the given shape can be made using a block that measures 10 cm by 9cm by 20 cm.

The height of the candle is 12cm and the base width is 9cm

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Some of the common order of operation mistakes that students make when evaluating expressions are the use of basic mathematical operations.

You should know that an error or fault results from defective judgment, deficient knowledge, or carelessness.

A combination of numbers, letters, and relational operators containing at least one operation is deemed a mathematical expression. Additionally, it must also include variables and/or numbers, excluding an equal sign.

Some prevalent errors include using both a positive and a negative sign, using two negative signs, and misusing brackets.

By being unable to comprehend the problems accurately, learners often commit significant errors while assessing formulations, which underscores the importance of employing fundamental mathematical operations.

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Answer:

Step-by-step explanation:

[tex]\left \{ {{x+y=0} \atop {-3x+4y=14}} \right.[/tex] ⇔ [tex]\left \{ {{y=-x} \atop {y=\frac{3}{4} x+ \frac{7}{2} }} \right.[/tex]

Using the tangent ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6  units.

The tangent ratio is part of the trigonometry ratios that is applied when solving a right triangle, and it is expressed as:

tan ∅ = length of the opposite side / length of the adjacent side.

We are given the following information from the image above:

Reference angle (∅) = 43 degrees

length of the opposite side = x

length of the adjacent side = 2.8

Plug in the values:

tan 43 = x/2.8

2.8 * tan 43 = x

x = 2.6 [to the nearest tenth]

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Answer:

52 is the  least common dominator

Answer:

52/65

Step-by-step explanation:

The same fraction we can express in many different forms. If the numerator and denominator ratio is the same, the fractions represent the same rational number.

The least common denominator of a set of fractions is the least number that is a multiple of all the denominators: their least common multiple

The method of calculating the LCD is the same as the calculation least common multiple of fractions denominators.

The simple method for common computing denominators (not least at all) is to multiply all denominators.

Answer:

x^2(x+5)-6(x+5)!!!!!!!!

Answer:

Let's start by using algebra to solve for the original amount that Alex paid for his shares.

Let X be the original amount that Alex paid for his shares.

We know that his shares dropped in value by 35%, so after the drop, he had 65% of his original investment left:

0.65X = $72,800

Solving for X:

X = $72,800 / 0.65

X = $112,000

Therefore, Alex paid $112,000 for his shares to begin with.

Answer:

3

Step-by-step explanation:

3 * 3 = 6

1/2 * 6 = 3 not 4.5

Because, when we multiply with 1/2, we are actually dividing the number by 2, and 6/2 = 3.

The 3 x 3 part turns into 9

So we have 1/2 x 9 or 9/2

Use long division to find that 9/2 gives a quotient of 4 and remainder 1

Imagine you had 9 cookies and 2 friends. Each friend would get 4 cookies each, eating 4*2 = 8 cookies overall. Then there's 9-8 = 1 cookie as the remainder.

The "remainder 1" then leads to 1/2 = 0.5

quotient = 4

remainder = 1 ---> decimal portion = 1/2 = 0.5

So that's how we get to 4+0.5 = 4.5

You can use a calculator to see that 9/2 = 4.5

Carson can line up his textbooks on his bookshelf in 24 different ways

What is Permutation?

Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.

What is Combination?

The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.

According to the given information:

Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:

n! / (n - r)!

where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).

On substituting the values in the formula,

4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24

Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.

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The measure of ∠ADC is equal to 180 degrees.

The measure of ∠ABC is equal to 90 degrees.

In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.

In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.

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The standard deviation for the given distribution is 8.739 using either the direct method or the shortcut method.

Standard deviation is defined as a measure of how spread out numbers are. It is also referred to as the square root of the Variance, and then the Variance is the average of the squared differences from the Mean.

To calculate the standard deviation for the given distribution, we will utilize either the direct method or the shortcut method.

Direct method:

Calculate the mean wage (F) for the distribution:

Mean = (20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10

Mean = 34

Calculate the differences between each wage and the mean wage:

20 - 34 = -14

22 - 34 = -12

27 - 34 = -7

30 - 34 = -4

31 - 34 = -3

32 - 34 = -2

35 - 34 = 1

45 - 34 = 11

40 - 34 = 6

48 - 34 = 14

Square each of the differences:

(-14)² = 196

(-12)² = 144

(-7)² = 49

(-4)² = 16

(-3)² = 9

(-2)² = 4

1² = 1

11² = 121

6² = 36

14² = 196

Add up the squared differences: 196 + 144 + 49 + 16 + 9 + 4 + 1 + 121 + 36 + 196 = 756

Divide the sum of the squared differences by the number of workers: 756/10 = 75.6

Take the square root of the result to get the standard deviation:

√75.6 = 8.739

Shortcut method:

The mean wage (F) for the distribution:

(20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10 = 34

The sum of the squares of the differences between each wage and the mean wage:

(20 - 34)² + (22 - 34)² + (27 - 34)² + (30 - 34)² + (31 - 34)² + (32 - 34)² + (35 - 34)² + (45 - 34)² + (40 - 34)² + (48 - 34)² = 756

Divide the sum by the number of workers: 756/10 = 75.6

Take the square root of the result to get the standard deviation:

Standard deviation = √75.6 = 8.739

Therefore,

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Complete question is:

Calculate standard deviation for the following

distribution by direct and shortcut method.

Assume mean as 32.

Serial No. of Workers

1

2

3

4

5

6

7

8

9

10

Wage (F)

20

22

27

30

31

32

35

45

40

48

a) The measure of 9π/5 radians in degrees is approximately 324 degrees.

b) The measure of -π/3 radians in degrees is approximately -60 degrees.

To convert the given angle measures from radians to degrees, we can use the formula:

angle in degrees = (angle in radians) × (180/π)

a) To convert 9π/5 radians to degrees, we can substitute the given value in the above formula as:

angle in degrees = (9π/5) × (180/π) ≈ 324 degrees (rounded to two decimal places)

b) To convert -π/3 radians to degrees, we can substitute the given value in the above formula as:

angle in degrees = (-π/3) × (180/π) ≈ -60 degrees (rounded to two decimal places)

In general, we can convert an angle measure from radians to degrees by multiplying it by 180/π. Since π is an irrational number, the conversion factor 180/π is an irrational number as well. Therefore, when we round the result to two decimal places, we are actually approximating the true value of the angle measure.

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The discussion for both cases is shown below.

Part a:

H0: there is no association between climate change and certainty.

H1: there is no association between climate change and certainty.

It seems that the null hypothesis (H0) and the alternative hypothesis (H1) are identical, which doesn't make sense. Typically, the null hypothesis states that there is no association or effect, while the alternative hypothesis states that there is an association or effect.

The statement also mentions that the p-value is a non-zero number, but it doesn't provide the actual value. The p-value is used to determine the statistical significance of the association and should be compared to a predetermined significance level (e.g., 0.05) to make a decision.

Part 2:

H0: there is no association between sleeping and the income class.

H1: there is a association between the income class and sleeping.

Similarly, the null hypothesis (H0) and the alternative hypothesis (H1) are stated incorrectly. The null hypothesis should state no association or effect, while the alternative hypothesis should state that there is an association or effect.

Again, the statement mentions a non-zero p-value but doesn't provide the actual value. The p-value needs to be compared to a significance level to determine the statistical significance of the association.

In both cases, it is important to provide the actual p-value and compare it to the significance level to make a proper conclusion about the association between the variables.

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The curved surface area of the cone is 148 cm².

Given that we need to find the curved surface area of the cone with height of 8 cm and radius of 5 cm,

The curved surface area gives the area of the face of an object.

The CSA of a cone = π × radius × slant height.

Slant height = √r²+h²

= √64+25

= 9.43 cm.

Now the csa = 3.14 × 5 × 9.43

= 148

Hence the curved surface area of the cone is 148 cm².

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The values of missing variables are given by:

x = 51°, y = 105°, z = 90°.

We know that the sum of external and internal angles is 180°.

So from the given figure we can see that y° is the external angle and the corresponding internal angle is 75°.

So, 75° + y° = 180°

y° = 180° - 75° = 105°

And also external angle is right angle that is 90° and the corresponding internal angle is z°.

So, z° + 90° = 180°

z° = 180° - 90° = 90°

This is a pentagon and the sum of all internal angles = (5 - 2)180° = 3*180° = 540°

According to the given figure the sum of all internal angles of the pentagon is = (180° - 36°) + z° + (180° - x°) + (180° - 78°) + 75° = 144° + 90° + 180° - x + 102° + 75° = 591° - x.

So, 591° - x = 540°

x = 591° - 540° = 51°

Hence the value of missing variables are: x = 51°, y = 105°, z = 90°.

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Since the containers were not given in the question, In a case whereby Ruth has a cylindrical cup that is filled with water where the cup has a diameter of 2 inches and a height of 6 inches,  the  volume of cylinder cup is 18.85inch^3.

Note that ; the container were not given in the question, so  we will just need to calculate the volume of the cylindrical cup to know how much water it can hold .

The volume of a cylinder can be caluculated using te exppresion  π r² h

Then from the question the  diameter = 2 inches radius = 2/2 = 1 inches

height =6 inches

π r² h

=π  * 1^2 * 6

=18.85inch^3

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The probability of choosing a ball numbered 29 is among the 28 balls numbered 1 through 28 is 0

From the question, we are to calculate the probability of choosing a ball numbered 29

From the formula for probability

P(A) = Number of favorable outcomes to A / Total number of possible outcomes

From the given information,

"A lottery game contains 28 balls numbered 1 through 28"

This means there are only 28 balls and they are numbered from 1, 2, 3, up until 28.

Now,

We are to determine the probability of choosing a ball numbered 29. Since there is no ball numbered 29,

Number of favorable outcomes = 0

Total number of possible outcomes = 28

Thus,

Probability of choosing a ball numbered 29 = 0/28

Probability of choosing a ball numbered 29 = 0

Hence,

Probability of choosing a ball numbered 29 is 0

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