Which pair of angles are congruent?
A. 4 and 5
B. 1 and 7
D. 6 and 8
C. 2 and 5

The conditions required for the normal approximation to the binomial are met. The test statistic is -2.26. The critical value is z = ±1.28. There is sufficient evidence to reject the null hypothesis.

The normal approximation to the binomial can be used if the conditions are met. In this case, the conditions are met since both np^ and n(1 - p^) are greater than 10, where n is the sample size and p^ is the sample proportion. Therefore, the normal approximation can be used.

To calculate the test statistic, we need to find the z-score. The formula for the z-score is (p^ - p) / sqrt(p(1 - p) / n), where p is the hypothesized proportion under the null hypothesis. Substituting the given values, we have (0.775 - 0.85) / sqrt(0.85(1 - 0.85) / 120) ≈ -2.26.

To determine the critical value(s) for the hypothesis test, we need to find the z-score corresponding to the significance level α. Since α = 0.2, the critical value is z = ±1.28.

Based on the test statistic of -2.26, we can see that it falls in the rejection region beyond the critical value of -1.28. Therefore, we reject the null hypothesis.

In summary, the test statistic is approximately -2.26, the critical value is ±1.28, and we reject the null hypothesis at the given level of significance.

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The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

(( C )) ----¢ Yes & others ----¢ No

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Each banana Split costs $6 and each hot fudge sundae costs $2.

Let b be the cost of one banana split and h be the cost of one hot fudge sundae. We can set up a system of two equations with two variables based on the given information:

6b + 5h = 46    (equation 1)

2b + 5h = 22    (equation 2)

We can solve for one variable in terms of the other in one of the equations and substitute that expression into the other equation to solve for the remaining variable. For example, we can solve equation 2 for b in terms of h:

2b + 5h = 22

2b = 22 - 5h

b = (22 - 5h)/2

We can substitute this expression for b into equation 1 and solve for h:

6b + 5h = 46

6[(22 - 5h)/2] + 5h = 46

66 - 15h + 5h = 46

-10h = -20

h = 2

Now that we know the cost of one hot fudge sundae is $2, we can substitute this value into either equation to solve for the cost of one banana split:

6b + 5(2) = 46

6b + 10 = 46

6b = 36

b = 6

Therefore, each banana split costs $6 and each hot fudge sundae costs $2.

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Answer: Solve the system of equations using substitution.

3x + 2y = 5

x = 2y + 7

(3, −2)

(5, −5)

(7, 0)

(11, 2)

Step-by-step explanation:

Answer:

Calculator

Step-by-step explanation:

Fraction: 163/900

Decimal: 0.1811111

Answer:

13.56

+5.78

_____

19.34

54

-19.34

_____

25.66

checking:

25.66

+19.34

______

Step-by-step explanation:

Answer:

1/15

Step-by-step explanation:

10 blocks altogether

P(Y,G) = 3/10 x 2/9

Answer:1/15

Step-by-step explanation:

The formula for the surface area of the box, in terms of the length of one side of the square base (s), is A = s^2 + 4s^2 = 5s^2.

The derivative of the surface area function with respect to s, denoted as dA/ds, gives us the rate of change of the surface area with respect to the length of one side of the base.

1. The surface area of the box consists of the area of the square base and the four equal sides. The area of the square base is s^2, and each side has a length of s. Therefore, the total surface area is given by A = s^2 + 4s^2 = 5s^2.

2. To find the derivative of the surface area function, we differentiate 5s^2 with respect to s using the power rule of differentiation. The power rule states that if we have a function f(x) = cx^n, then the derivative is f'(x) = cnx^(n-1).

  Applying the power rule, we have dA/ds = d(5s^2)/ds = 10s.

3. The derivative, dA/ds = 10s, represents the rate of change of the surface area with respect to the length of one side of the square base. This means that for every unit increase in s, the surface area increases by 10s units.

  The derivative does not provide information about minimizing the amount of material used. To find the dimensions of the box that minimize the amount of material used, we need to set up an optimization problem and solve for the critical points. This involves setting the derivative equal to zero and finding the values of s that satisfy this equation. However, since the problem statement does not provide a specific volume constraint or objective function, we cannot proceed with the optimization process.

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Option-A is correct that is Hₐ: p₁-p₂<0 is the alternative theories best fits this claim.

Given that,

According to a scientist, the percentage of women in the national academy of sciences is lower than the percentage of women in the general population. Let p₁ stand for the percentage of women in the National Academy of Sciences and p₂ for the overall percentage of women.

We have to find what is the alternative theories best fits this claim.

We know that,

p₁ represent the proportion of women in the National Academy of Sciences.

p₂ represent the proportion of women in the nationwide.

The alternative hypothesis is ,

Hₐ: p₁-p₂<0

Therefore, Option-A is correct that is Hₐ: p₁-p₂<0 is the alternative theories best fits this claim.

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Answer: 8

Step-by-step explanation:

7.69 to the nearest whole number is 8

Answer:

there is not enough information

Step-by-step explanation:

For k1Θ¹ + k2Θ² to be an unbiased estimator of θ, the condition that must be imposed on the constants k1 and k2 is that k1 + k2 = 1.

Let Θ¹ and Θ² be two unbiased estimators of the same parameter θ. Then, we have E(Θ¹) = θ and E(Θ²) = θ. Now, let k1Θ¹ + k2Θ² be a linear combination of these two estimators, where k1 and k2 are constants.

To show that this estimator is unbiased, we need to find its expected value and verify whether it equals θ.

So, E(k1Θ¹ + k2Θ²) = k1E(Θ¹) + k2E(Θ²)

= k1θ + k2θ

= (k1 + k2)θ

For this estimator to be unbiased, we need (k1 + k2)θ to equal θ. Therefore, we must have k1 + k2 = 1.

Therefore, to ensure that k1Θ¹ + k2Θ² is an unbiased estimator of θ, we need to impose the condition that k1 + k2 = 1.

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Answer:

X=-4

Step-by-step explanation:

5x-10x=22-2

-5x=20

x=-4

Answer:

please write in the comments ,the total minutes she spent in the gym , then only we can solve the answer , without total minutes we cannot solve this question

Answer:

13 minutes lifting weights.

Step-by-step explanation:

Diana spent a total of 25 minutes and spent 12 more minutes running than she did lifting weights. So if you subtract 25 from 12 you get 13.

Answer: 16: orders per day

Step-by-step explanation:

This is a fraction equal to

48 orders ÷ 3 days

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 3

48 orders ÷ 3

3 days ÷ 3

=

16 orders

1 day

=

16 orders

day

= 16 orders per day

Answer: 4x+6/x^2

Step-by-step explanation:

Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

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The proportion of infants with birth weights under 95 ounces is approximately 0.1587 or 15.87%.

We are given a normal distribution with mean µ = 110 and standard deviation σ = 15. We want to find the proportion of infants with birth weights under 95 ounces, i.e., P(X < 95).

To solve this, we need to find the z-score for 95 ounces, which is given by:

z = (X - µ) / σ = (95 - 110) / 15 = -1

Using a standard normal distribution table, we can find the probability of a z-score being less than -1. This is the same as the probability of an infant having a birth weight less than 95 ounces.

From the standard normal distribution table, the probability of a z-score being less than -1 is 0.1587.

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Answer:

Step-by-step explanation:

b

When 94.7 g of neon gas undergoes isothermal contraction, there will be a decrease in entropy.

To explain why, we can start by recalling that entropy is a measure of the number of ways in which energy can be distributed among the particles of a system. When a gas undergoes isothermal contraction, its volume decreases while its temperature remains constant. This means that the particles in the gas are now more confined and have fewer ways in which they can move around. As a result, the energy of the particles becomes more constrained, which leads to a decrease in entropy.

To calculate the exact change in entropy, we would need to know more about the specifics of the contraction (such as the pressure and volume before and after). However, we can say with confidence that the change in entropy will be negative because the gas is becoming more ordered and its energy is becoming more constrained. Therefore, the change in entropy when 94.7 g of neon gas undergoes isothermal contraction will be negative.

Therefore, When 94.7 g of neon gas undergoes isothermal contraction, there will be a decrease in entropy.

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Katherine will make a profit of $100.

To calculate the profit, we need to calculate the total revenue and the total cost. The total cost includes the cost of growing flowers, and the total revenue includes the amount from selling the flowers as well as the money made from piano lessons.The total cost is given by the sum of the cost of planting seeds and growing flowers.

Cost of planting seeds = $50

Total hours spent in planting seeds = 5

Cost of growing flowers = 0 (because the problem doesn’t state how much it costs to grow flowers)

Total Cost = Cost of planting seeds = $50

The total revenue is given by the sum of the money earned from selling the flowers and the money earned from giving piano lessons.

Money earned from selling flowers = $150

Money earned from piano lessons = 0 (because it is not mentioned in the problem)

Total Revenue = Money earned from selling flowers = $150

Total profit is given by the difference between total revenue and total cost.

Profit = Total Revenue - Total Cost = $150 - $50 = $100

Therefore, A profit of $100 is made by Katherine.

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a. The motion is in the positive direction for t < 5 and t > 7, and it is in the negative direction for 5 < t < 7.

b. The displacement over the interval [0,8] is 200 units.

c. The distance traveled over the interval [0,8] is 428 units.

a. To determine when the motion is in the positive direction and when it is in the negative direction, we need to examine the sign of the velocity function v(t).

The given velocity function is \(v(t) = 3t^2 - 36t + 105\).

To find when the motion is in the positive direction, we need to find the values of t for which v(t) > 0.

Solving the inequality \(3t^2 - 36t + 105 > 0\):

First, we find the roots of the quadratic equation \(3t^2 - 36t + 105 = 0\) by factoring or using the quadratic formula:

\(3t^2 - 36t + 105 = (t - 5)(3t - 21) = 0\)

The roots are t = 5 and t = 7.

We now test the intervals between these roots and outside them:

For t < 5: Plug in a test value, such as t = 0: \(v(0) = 3(0)^2 - 36(0) + 105 = 105\). Since it's positive, the motion is in the positive direction for t < 5.

For 5 < t < 7: Plug in a test value, such as t = 6: \(v(6) = 3(6)^2 - 36(6) + 105 = -81\). Since it's negative, the motion is in the negative direction for 5 < t < 7.

For t > 7: Plug in a test value, such as t = 8: \(v(8) = 3(8)^2 - 36(8) + 105 = 57\). Since it's positive, the motion is in the positive direction for t > 7.

Therefore, the motion is in the positive direction for t < 5 and t > 7, and it is in the negative direction for 5 < t < 7.

b. To find the displacement over the given interval [0,8], we need to find the change in position by evaluating the definite integral of the velocity function v(t) from t = 0 to t = 8.

Displacement = ∫[0 to 8] v(t) dt

Plugging in the given velocity function:

Displacement = ∫[0 to 8] \((3t^2 - 36t + 105)\) dt

Evaluating the integral:

Displacement = \([t^3 - 18t^2 + 105t]\) from 0 to 8

Displacement = \((8^3 - 18(8)^2 + 105(8)) - (0^3 - 18(0)^2 + 105(0))\)

Displacement = (512 - 18(64) + 840) - (0 - 0 + 0)

Displacement = 512 - 1152 + 840

Displacement = 200

Therefore, the displacement over the interval [0,8] is 200 units.

c. To find the distance traveled over the given interval [0,8], we need to consider the total distance covered, regardless of the direction of motion. This can be obtained by integrating the absolute value of the velocity function |v(t)| over the interval [0,8].

Distance = ∫[0 to 8] |v(t)| dt

Plugging in the given velocity function:

Distance = ∫[0 to 8] \(|3t^2 - 36t + 105|\) dt

Since the velocity function is continuous over the interval, we can break it into subintervals where the sign changes:

Distance = ∫[0 to 5] \((3t^2 - 36t + 105)\) dt + ∫[5 to 7] \((36t - 3t^2 + 105)\) dt + ∫[7 to 8] \((3t^2 - 36t + 105)\) dt

Evaluating the integrals:

For the first interval [0 to 5]:

Distance = ∫[0 to 5] \((3t^2 - 36t + 105)\) dt

Distance = \([t^3 - 18t^2 + 105t]\) from 0 to 5

Distance = \((5^3 - 18(5)^2 + 105(5)) - (0^3 - 18(0)^2 + 105(0))\)

Distance = (125 - 18(25) + 525) - (0 - 0 + 0)

Distance = 125 - 450 + 525

Distance = 200

For the second interval [5 to 7]:

Distance = ∫[5 to 7] \((36t - 3t^2 + 105)\) dt

Distance = [\((18t^2 - t^3 + 105t)\)] from 5 to 7

Distance = \((18(7)^2 - (7)^3 + 105(7)) - (18(5)^2 - (5)^3 + 105(5))\)

Distance = (882 - 343 + 735) - (450 - 125 + 525)

Distance = 1274 - 1050

Distance = 224

For the third interval [7 to 8]:

Distance = ∫[7 to 8] \((3t^2 - 36t + 105)\) dt

Distance = [\((t^3 - 18t^2 + 105t)\)] from 7 to 8

Distance = \((8^3 - 18(8)^2 + 105(8)) - (7^3 - 18(7)^2 + 105(7))\)

Distance = (512 - 18(64) + 840) - (343 - 18(49) + 105(7))

Distance = 512 - 1152 + 840 - 343 + 882 - 735

Distance = 4

Therefore, the distance traveled over the interval [0,8] is 200 + 224 + 4 = 428 units.

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Answer:

Oppositeleg

adjacenleg

Answer:

option 1

Step-by-step explanation:

Just remember this to get the trigonometric ratio in a right triangle :

    Old Henry And His Old Aunt

O for opposite

H for hypotenuse

A for Adjacent

Sin = O/ H

Cos = A /H

Tan = O /A

Answer:

Step-by-step explanation:

It is an arithmetic sequence with common difference = -6

32nd term = 311 - 31(6) = 125

If his beard  was 8 millimeter long and each passing week it grew 2 additional millimeters, the graph that represents the relationship between the length of his beard in millimeter and time in week has been plotted

The initial length of the beard = 8 millimeter

The length of beard grow in each week = 2 millimeter

Consider the number of week as x

Therefore the linear relationship will be

The length of the beard y = 2x + 8

Plot the graph using the equation

Hence, If his beard  was 8 millimeter long and each passing week it grew 2 additional millimeters, the graph that represents the relationship between the length of his beard in millimeter and time in week has been plotted

The complete question is

Rip van Winkle fell asleep for a very long time. When he fell asleep, his beard was 8 millimeters long, and each passing week it grew 2additional millimeters.

Graph the relationship between the length of Rip van Winkle's beard (in millimeters) and time (in weeks).

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A: In a frequency table, each category listed in one column has a characteristic about it in the second column. The table described in the given statement has this property.

B: The set of states is clearly defined and each state has a clearly defined capitol.

A frequency table is a tabular representation of data that shows the number of times each category or value occurs. In a frequency table, one column represents the categories or values, and the other column represents their corresponding frequencies.

A: The statement makes sense. In a frequency table, each category listed in one column has a characteristic about it in the second column. The table described in the given statement has this property.

B: The statement makes sense. The set of states is clearly defined and each state has a clearly defined capitol.

C: The statement does not make sense. In a frequency table, each category must have a frequency greater than 1. Because each state has exactly one capitol, each category in the table described in the given statement would have frequency 1.

D: The statement does not make sense. In a frequency table, one of the columns lists the frequency of each category, which is the number of data values in the category. The table described in the given statement does not have this column.

The correct answer is:

A: In a frequency table, each category listed in one column has a characteristic about it in the second column. The table described in the given statement has this property.

B: The set of states is clearly defined and each state has a clearly defined capitol.

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Answer: Thomas spent .15 less

Step-by-step explanation:

Dan: 2.50/2=1.25

Thomas: 3.30/3=1.1

1.25-1.1=.15

Answer:

C

Step-by-step explanation:

Each cone they bought was 1.10 each and 1.25 each

1.10<1.25

1.25-1.10=0.15