8. the z-table gives the area under the standard normal curve to the left of z. what does the t-table give?

The Answer of the given question based on the triangle is angle ∠α ≈ 56.4° degrees , angle ∠β ≈ 33.6° degrees , side C ≈ 14.4° units.

In a right triangle, the hypotenuse is the longest side and it is opposite the right angle. It is the side that is directly opposite the right angle and is always opposite the largest angle of the triangle. The hypotenuse is also the side that connects the two legs of the right triangle. The length of hypotenuse can be found using Pythagorean theorem.

From the problem statement, we know that angle ∠gamma = 90° degrees, which means that BC is the hypotenuse of the right triangle. We also know that side A = 12 and side B = 8.

Using Pythagorean Theorem, we can find length of  hypotenuse by:

c² = a² + b²

c² = 12² + 8²

c² = 144 + 64

c² = 208

c = √(208)

c ≈ 14.4

So the length of BC is approximately 14.4 units.

To find the altitude CA, we can use the formula for the area of a right triangle:

area = (1/2) * base * height

Since angle gamma = 90° degrees, the altitude CA is equal to the length of side A:

CA = A = 12 units.

Now we can use the trigonometric ratios to find the acute angles∠α and :

sin(α) = opposite/hypotenuse = CA/c

sin(α) = 12/14.4

α ≈ 56.4° degrees

Since α and gamma are complementary angles (they add up to 90° degrees), we can find β using the following formula:

β = 90 - α

β ≈ 33.6° degrees

Therefore, the unknown values for the given right triangle are:

angle ∠α ≈ 56.4° degrees

angle ∠β ≈ 33.6° degrees

side C ≈ 14.4° units.

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The system of equation with the same solution with 2x + 2y = 16 3x  - y = 4 is 2x + 2y = 16, 6x - 2y = 8. Therefore, the answer is 2.

System of equation can be solved using different method such as elimination method, substitution method and graphical method.  Therefore, let's solve the system of equation as follows;

2x + 2y = 16

3x  - y = 4

multiply equation(ii) by 2

2x + 2y = 16

6x - 2y = 8

add the equations

8x = 24

x = 24  / 8

x = 3

y = 3x - 4

y = 3(3) - 4

y = 9 - 4

y = 5

Therefore,

2x + 2y = 16

6x - 2y = 8

add the equation

8x = 24

x = 24  / 8

x = 3

Therefore,

2(3) + 2y = 16

6 + 2y = 16

2y = 16 - 6

2y = 10

y = 5

Therefore, the equation with the same solution is 2x + 2y = 16

6x - 2y = 8.

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Answer:

The ring-shaped region has an inner radius of 10m and a width of 3m. To find the area of the shaded region, we need to subtract the area of the inner circle from the area of the outer circle. The area of a circle is given by A = πr^2, where r is the radius. Therefore, the area of the outer circle is A1 = π(10+3)^2 = 169π m^2 and the area of the inner circle is A2 = π(10)^2 = 100π m^2. Subtracting these two areas gives us: A1 - A2 = (169π - 100π) m^2 = 69π m^2. Therefore, the area of the shaded region is approximately 216.27 m^2 (69π ≈ 216.27) .

The population density of the people living in the given square area would be = 159.20 persons pre square miles.

Population density can be defined as the amount of people that can be found in a unit area of a land.

Population density is found by dividing the total population by the total land area.

The total population of the region = 32,000 people

The total land area = 201 miles².

Therefore the population desity = 32,000/201 = 159.20 persons pre square miles.

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The margin of error of the 98.4% confidence interval for snapdragons  is 3.71.

The midpoint of the range is calculated by adding the upper and lower bounds and then dividing by two. So, the sample mean is `(20.91 + 38.43) / 2 = 29.67`.

The margin of error is calculated by multiplying the critical value of z* (1.96 for a 98.4% confidence level) by the standard error of the mean. The formula for calculating the margin of error is:

`Margin of error z*(standard deviation/√n`).

The formula is `range/4 = 1.96 * standard deviation/√n`.Now, solve for the standard deviation:

`standard deviation = (range/4) * √n / 1.96`

Substituting the values: `(38.43 - 20.91)/4 = 1.96 * standard deviation/√n`

Simplifying the equation: `4.26 = (1.96*standard deviation)/√n`

Squaring both sides: `4.26^2 = 3.8416 = (1.96^2 * standard deviation^2)/n`

Substituting the value of the standard deviation: `3.8416 = (1.96^2 * ((38.43 - 20.91)/4)^2) / n`

Solving for n: `n = ((1.96^2 * ((38.43 - 20.91)/4)^2) / 3.8416) = 31.54`

Now that we know the sample size, we can calculate the standard error of the mean:

`standard error = standard deviation/√n = ((38.43 - 20.91)/4)/√31.54 = 1.89`.

The margin of error is `1.96 * 1.89 = 3.71`.

The 98.4% confidence interval for snapdragons grown in compost is (20.91, 38.43). The margin of error of this confidence interval is 3.71.

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Step-by-step explanation:

2(x+10y)+2(7x^2-x+9y)

= 2x+20y+14x^2-2x+18y

= (14x^2+38y) units^2

The confidence interval for variance is (0.29,0.58)

A family of continuous probability distributions is known as the chi-square (X2) distribution. They are frequently employed in hypothesis tests, such as the chi-square test of independence and the goodness of fit test.

The parameter k, which stands for the degrees of freedom, determines the shape of a chi-square distribution.

The distribution of real-world observations rarely has a chi-square shape. Chi-square distributions are primarily used for testing hypotheses rather than for modeling actual distributions.

Since we have given that the sample size n= 54,

variance = 0.44

we need to find a 98% confidence interval to estimate the variance.

So, we will use Chi-square distribution,

For this, we will find

df=n-1 = 54-1 = 53,

the interval would be,

[tex]\frac{(n-1)s^2}{X^2_{\alpha/2}} < \sigma^2 < \frac{(n-1)s^2}{X^2_{1-\alpha/2}}\\\\\alpha=1-0.98=0.02\\\\\alpha/2=0.02/2=0.01\\X^2_{0.01,53}=79.84\\Similarly\\\\1-\alpha/2=0.99\\\\X_{1-\alpha/2}^2,df=X^2_{0.99,53}=40.308\\\\So,\\\frac{53*0.44}{79.84} < \sigma^2 < \frac{53*0.44}{40.308}\\\\0.29 < \sigma^2 < 0.58[/tex]

Hence the confidence interval is (0.29,0.58)

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Answer:

A=61

B=57

C=61

Step-by-step explanation:

The sun of the three angles must give us 180 degrees. so the sum of these three angles is giving us 179 wrong degrees.

The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

To calculate this probability, we need to consider the following components:

1. The total number of customers purchasing cooking and BobVilla books: This is the denominator of our equation, and it represents the total number of customers who purchased the two books.

2. The number of customers purchasing the biography book: This is the numerator of our equation, and it represents the number of customers who purchased the biography book.

3. The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books: This is the fraction of customers who purchased the biography book over the total number of customers who purchased the two books.

To calculate the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books, we need to divide the numerator (the number of customers purchasing the biography book) by the denominator (the total number of customers purchasing the two books).

This probability can be expressed as a decimal, which is 0.08. This value can also be rounded to two decimal places, which is 0.08.

In conclusion, the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

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Answer:

(-2,-3)  

Step-by-step explanation:

3x+y=-9                      

-3x    -3x

y=-3x-9

5x-3(-3x-9)=-1

14x+ 27= -1

-27      -27

14x= -28

/14    /14

x=-2

plug in x    

3(-2)+y=-9  

    -6+y=-9

     +6    +6

          y=-3

Answer: 540 cm²

Step-by-step explanation:To find the area of the dilated rectangle, we need to first find the dimensions of the new rectangle after it has been dilated by a factor of 3.

The length of the new rectangle will be 3 times the original length, which is:

10 cm x 3 = 30 cm

The width of the new rectangle will also be 3 times the original width, which is:

6 cm x 3 = 18 cm

Therefore, the area of the dilated rectangle will be:

30 cm x 18 cm = 540 cm²

The sum of all positive integers k that satisfy the property is 1800.

To find the sum of all positive integers k that satisfy the property of the least common multiple of k and 720 being 3600, we need to use the concept of prime factorization and LCM. What is LCM?The least common multiple (LCM) of a set of numbers is the smallest number that is a multiple of all the given numbers. It is calculated by taking the common prime factors of the numbers and multiplying them by their highest powers.

Now mentioned in the question that  the LCM of k and 720 is 3600. Let's write 720 and 3600 in prime factorization form. 720 = 2⁴ × 3² × 5¹, 3600 = 2³ × 3² × 5²Let LCM of k and 720 be L. So, L = 2⁴ × 3² × 5²Let k = 2ᵃ × 3ᵇ × 5ᶜ. So, LCM of k and 720 = 2ⁿ × 3ᵐ × 5ᴬ, where, n = max (4, a) , m = max (2, b) , A = max (2, c)Given, LCM of k and 720 = 3600.So, 2ⁿ × 3ᵐ × 5ᴬ = 2⁴ × 3² × 5².

As we know, n = max (4, a) , m = max (2, b) , A = max (2, c)Thus, n = 4, m = 2, A = 2. Since, n = max (4, a) , a = 4 is the only possible solution And, m = max (2, b) , b = 2 is the only possible solution, And, A = max (2, c) , c = 2 is the only possible solution.So, the possible value of k is k = 2⁴ × 3² × 5²i.e. k = 1800. Sum of all possible values of k is 1800.Therefore, the sum of all positive integers k that satisfy the property is 1800.

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The score located at -3sx (standard deviation) from the mean in a normal distribution is 75. This is because in a normal distribution, the mean is the center and -3sx is three standard deviations away from the mean. Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

To further explain, a normal distribution is a probability distribution characterized by a symmetrical bell-shaped graph, and it's determined by the mean and standard deviation of the dataset. In this case, the mean is 120 and the standard deviation is 15. Therefore, the data would have an average score of 120 and an average range of 30 (15 plus and minus from the mean). If the score is located at -3sx, it would be three standard deviations away from the mean and the score would be 75.

Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

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A scientist can use bootstrap analysis to estimate the strength of evidence that a particular node in a phylogeny exists.

Bootstrap analysis is a statistical method used to determine the reliability and robustness of phylogenetic trees' topologies. In bootstrap analysis, a series of random resampling with replacement is used to assess how well the observed data fit the phylogenetic hypothesis.

Bootstrap values range from 0 to 100 and reflect the proportion of times that a particular node or branch occurs in the bootstrap replicate trees. Bootstrap values greater than 70% are usually considered strong evidence that a particular node or branch exists in the phylogenetic tree.

Bootstrap analysis is an important tool for understanding the reliability of phylogenetic trees and the evolutionary relationships among organisms.

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Optiοn A : Side AD is οppοsite tο the angle ACD in the given triangle ADC.

Every triangle has 3 sides and thus 3 angles. Each side οf a triangle has 2 angles οf it fοrmed at the 2 endings οf the side and οne angle is the οne present οppοsite tο the side.

Thus, fοr each side, 2 angles are tοuched and 1 angle at the οppοsite is called the οppοsite angle tο that side.

Here, the triangle is ADC.

The 3 angles οf the triangle are : ADC, ACD, and CAD

Fοr side AD,

The twο angles A ( CAD ) and D( ADC ) are cοnnected with the side AD and are adjacent tο it.

The third angle C ( CAD ) is nοn-adjacent tο side AD and is οppοsite tο it. Hence, Optiοn D is cοrrect.

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The total number of listings possible for the 14 teams in the local little league is 11,664. This is because there are 14 teams, so the number of possible listings is equal to 14! (14 factorial). 14! is equal to 1x2x3x4x5x6x7x8x9x10x11x12x13x14, which equals 11,664.

To further explain, 14! is the number of ways to arrange 14 items. This is because the first item can be arranged in 14 ways, the second item in 13 ways, the third in 12, and so on. This means that the total number of possible arrangements is 14x13x12x11x10x9x8x7x6x5x4x3x2x1, which equals 11,664.

Therefore, the total number of listings possible for the 14 teams in the local little league is 11,664.

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The probabilities of different events related to the type B' blood in four randomly selected people from the United States are 0.000207, 0.0600,  0.400. The events in parts (a) and (b) are considered unusual.

The probability that a person in the united states has type b* blood is 12%. four unrelated people in the united states are selected at random of different scenarios are calculated.

The probability that all four have type B' blood is 0.000207, The probability that none of the four have type B' blood is 0.0600, The probability that at least one of the four has type B' blood is 0.400, The events in parts (a) and (b) can be considered unusual because their probabilities are less than or equal to 0.05.

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_____The given question is incomplete, the complete question is given below:

The probability that a person in the United States has type B' blood is 12 % Four unrelated people in the United States are selected at random Complete parts (a) through (d) The probability that all four have type B' blood is 000207 (Round to six decimal places as needed) (b) Find the probability that none of the four have type B' blood The probability that none of the four have type B' blood is 0600 (Round to three decimal places as needed) (c) Find the probability that at least one of the four has type B' blood The probability that at least one of the four has type B' blood is 400 (Round to three decimal places as needed) (d) Which of the events can be considered unusual? Explain Select all that apply OA The event in part (a) is unusual because its probability is less than or equal to 0.05 OB. The event in part (c) is unusual because its probability is less than or equal to 0.05 O C. None of these events are r uual O D. The event in part (b) is unusual because its probability is less than or equal to 0.05 Click to select your answer and then click Check Answer

8 is the maximum number of tablets the pharmacist will tell them they should take of this product per day.

According to FDA guidelines, the maximum daily dosage of acetaminophen for healthy adults should not exceed 4,000 milligrams. This equates to a maximum of eight 500 mg tablets per day. It's essential to remember that the recommended dosage may differ based on individual factors such as age, weight, and medical conditions. Therefore, it's crucial to consult with a healthcare provider or licensed pharmacist before taking any medication. Always follow the recommended dosage and avoid exceeding the daily limit to prevent potential health risks associated with acetaminophen overdose.

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An operations manager has carefully examined the 1500 parts produced in his factory and classified them into 30 families with geometric similarities using codes that contain design attributes. This is an example of: group technology.

Group technology is a manufacturing philosophy that seeks to improve efficiency and productivity by grouping similar parts together and standardizing their production processes.

By grouping similar parts together, manufacturing processes can be standardized and streamlined, reducing the time and cost associated with producing each part. This approach is particularly effective in high-volume manufacturing operations where a large number of parts are produced repeatedly.

In this case, the operations manager has identified 30 families of parts with geometric similarities and used codes that contain design attributes to classify them. By doing so, the manager has created a basis for grouping similar parts together and standardizing their production processes. This can lead to a more efficient and cost-effective manufacturing operation.

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There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.

When a dataset is sorted from lowest to highest, the median, a measure of central tendency, reflects the midpoint value of the dataset. The values are first presented from lowest to greatest in order to get the median of a set of data. The median is the middle value when there are an odd number of values. Use the following data set as an example: 5, 7, 24, 3, 6, 4, 4, 30, 19. We first organise the data in order before calculating the median: 3, 4, 4, 5, 6, 7, 19, 24, 30

The dataset contains 9 values, which is strange. The middle value, which is six, is therefore the median.

given

We must first arrange the numbers in ascending order in order to determine the median of the group:

3, 4, 4, 5, 6, 7, 19, 24, 30

The median will be the middle number as there are nine numbers in this collection.

There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.

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The width of the dumpster that minimizes its surface area is approximately 1.71 yards, and the length is approximately 3.42 yards.

The length of the rectangular dumpster is equal to two times its width, or 2x, if x is its width. The dumpster's height is not specified, however it is not necessary for this issue.

We need to determine the dumpster's size to reduce the amount of surface area it has. The following sources provide the rectangular dumpster's surface area:

A = lw + lh + lw

where w stands for width, l for length, and h for height.

Given that the container must hold [tex]20 yd3[/tex] of waste, we can use the formula for the volume of a rectangular solid to create the following sentence:

[tex]V = lwh = (2x) (x)\\h = 2x^2 h = 20\\h = 10/x^2[/tex]

Inputting this expression for h into the surface area A formula yields the following results:

[tex]A = 2lw + 2lh + 2wh = 2(x)(2x) + 2(x)(10/x) + 2(2x)(10/x) = 4(x)(2x) + 40(x)[/tex]

We can take the derivative of A with respect to x, set it equal to zero, and solve for x to determine the dimensions that minimise A:

[tex]dA/dx = 8x - 40/x^2 = 0\\8x = 40/x^2\\x^3 = 5\\x = (5)^(1/3)\\[/tex]

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Answer:

13,161.5

Step-by-step explanation:

5x3= 15 then go over and carry the one then do 5x9= 45+1= 46 then go over to 3 and carry the four and 5x3= 15+4= 19 put 9 down and carry the one then 5x3= 10+1= 11 after x the 0 the repeat what you did and add up the final numbers so 239.5x 55= 13161.5

Answer: We can solve the given inequality as follows:

|2x + 2| > 4

There are two cases to consider, depending on whether the expression inside the absolute value is positive or negative:

Case 1: 2x + 2 > 4

2x > 2

x > 1

Case 2: 2x + 2 < -4

2x < -6

x < -3

Therefore, the solution to the inequality is x < -3 or x > 1.

To graph the solution, we can plot the two critical points x = -3 and x = 1 on a number line, and shade the regions to the left of -3 and to the right of 1. This gives us the following graph:

<==================o-----------------o===================>

    x < -3       x > 1

The open circles indicate that the points -3 and 1 are not included in the solution, since the inequality is strict (|2x + 2| > 4).

Step-by-step explanation:

Solving a linear equation we can see that the answer is 40 months.

We know that company A only charges $70 per month, so the cost in dollars after x months is given by the linear equation:

A(x) = 70*x

For company B you need to pay $50 per month plus the $500 phone, so here the cost is:

B(x) =500 + 50*x

We want to find for what value of x we have B(x) = A(x), then we needto solve:

70x = 500 + 50x

70x - 50x = 500

20x = 500

x = 500/20

x = 40

After 40 months the cost will be the same one than in company A.

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[tex] \: [/tex]

[tex] \: [/tex]

put the value of y = 2 in equation

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

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hope it helps ⸙

I think it equals 18 tens

Answer:

3 x 60 x 30 = 5400

Step-by-step explanation:

Answer:

First, we need to calculate the daily interest rate on the credit card. We can do this by dividing the annual percentage rate (APR) by the number of days in a year:

Daily interest rate = APR / 365

Daily interest rate = 0.2445 / 365

Daily interest rate = 0.00067 or 0.067%

Next, we can calculate the interest that will accrue over the course of one month, which is approximately 30 days:

Interest = Balance * Daily interest rate * Number of days

Interest = $1,359 * 0.00067 * 30

Interest = $27.42

Adding the interest to the outstanding balance, we get:

Balance after one month = $1,359 + $27.42

Balance after one month = $1,386.42

Therefore, the balance on the credit card after one month will be approximately $1,386.42.

a) Mean time between counts is 0.3333 minutes.

b) Standard deviation of time between counts is 0.5774 minutes.

a. Mean time between counts: The mean time between counts can be computed as the inverse of the Poisson rate parameter (λ): Mean time between counts = 1/λ.

The average of 3 counts per minute is the same as the rate parameter λ in a Poisson process. Thus, the mean time between counts is: Mean time between counts = 1/λ = 1/3 = 0.3333 minutes (20 seconds approximately).

b. Standard deviation of the time between counts: The standard deviation of a Poisson process is equal to the square root of the mean.

Therefore, the standard deviation of the time between counts can be calculated as follows: Standard deviation of time between counts = sqrt(mean) = sqrt(1/λ) = sqrt(1/3) = 0.5774 minutes (approximately 35 seconds).

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According to Pythagorean Theorem, The length of the horizontal portion of the support, x, is 3.87 feet.

The length of the horizontal portion of the support, x, can be determined by using the Pythagorean Theorem. The Pythagorean Theorem states that a2 + b2 = c2, where a and b are the sides of a right triangle and c is the hypotenuse.

In this case, a = 7 feet, b = x, and c = 8 feet. We can use the Pythagorean Theorem to solve for x: 72 + x2 = 82, or 49 + x2 = 64. This can be solved for x to get x2 = 15 and x = √15 ≈ 3.87 feet.

Therefore, the length of the horizontal portion of the support, x, is 3.87 feet.

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