Given the triangle with angle a being 53° angle C being 58° what is angle B

The regression equation for the given sample observations is Y = 12.071 - 1.087X.

By analyzing the given sample observations, we can determine the regression equation that represents the relationship between the variables X and Y.

The regression equation is derived through statistical analysis and allows us to estimate the value of Y based on the given values of X. In this case, the regression equation is Y = 12.071 - 1.087X.

This equation indicates that for every unit increase in X, the value of Y decreases by 1.087 units.

To determine the regression equation, statistical techniques such as linear regression are applied to find the best-fitting line that represents the relationship between the variables.

The coefficients in the equation, 12.071 and -1.087, represent the intercept and slope of the line, respectively.

They provide insights into the relationship and can be used to make predictions or analyze the impact of changes in X on the value of Y.

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Hydraulic engineers in the US use the acre-foot as a unit of water 9. A thunderstorm dumped 2.9 inches of rain in 30 minutes, resulting in a total volume of 4046.86 cubic feet of water. The volume of rainwater is calculated as 36 km² × 2.9 in × (1 ft/12 in) = 2.35 km³, which equals 325,851 US gallons. The total volume of water that fell on the town is 218,241 acre-feet.

Hydraulic engineers in the United States often use, as a units of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre (where 1 acre =43560ft ) of land to a depth of 1ft. A severe thunderstorm dumped 2.9in. of rain in 30 min on a town of area 36 km2.

Given:

Area of town = 36 km²

Depth of rain = 2.9 inches

Time taken for rain = 30 minutes

We know, 1 acre = 43,560 ft².

∴ 36 km² = 36 × 10³ × 10³ m² = 36 × 10⁶ m²

1 acre = 43,560 ft² = 43,560/10.764 = 4046.86 m²

1 ft = 12 in

Therefore, 1 acre-ft of water = 4046.86 ft² × 1 ft = 4046.86 cubic feet of water= 4046.86/43560 = 0.092903 acre-ft of water

The volume of rainwater, V = area × depth

= 36 km² × 2.9 in × (1 ft/12 in)

= 2.35 km³Since 1 km³ = 264,172,052.3581 US gallons

1 acre-ft of water = 325,851 gallons2.35 km³ = 2.35 × 10⁹ acre-ft

Therefore, the volume of water that fell on the town is 2.35 × 10⁹ × 0.092903 = 218,241 acre-feet.

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The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:

∂ψ/∂x = 2y

∂ψ/∂y = 2x

∂φ/∂x = 2x

∂φ/∂y = -2y

From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.

To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:

V = ∇φ x ∇ψ

Taking the curl of V:

∇ x V = ∇ x (∇φ x ∇ψ)

Using vector calculus identities and simplifying the expression, we find:

∇ x V = 0

Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.

Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

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The statistic that is resistant to outliers is the 0.75 quantile.Outliers are extreme values that significantly deviate from the majority of the data.

A statistic is considered resistant if it is not heavily influenced by the presence of outliers and provides a robust measure of central tendency or relationship.

(a) Sample standard deviation is not resistant to outliers because it takes into account the deviation of each data point from the mean. Outliers can have a large impact on the standard deviation, pulling the value away from the typical spread of the data.

(b) Sample correlation measures the strength and direction of the linear relationship between two variables. It is not resistant to outliers because outliers can disproportionately affect the correlation coefficient, leading to misleading results.

(c) The 0.75 quantile, also known as the third quartile, is resistant to outliers. It represents the value below which 75% of the data falls. It is less affected by extreme values as it focuses on the data in the upper quartile, providing a more robust measure of the data's central tendency.

(d) Least squares estimates for regression models, such as the slope and intercept, are not resistant to outliers. Outliers can have a substantial impact on the estimated coefficients, altering the relationship between the variables and affecting the accuracy of predictions.

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Answer:

The answer is B. 24.5

Step-by-step explanation:

2÷49

first divide 2 ÷4 = 2 then, 2 ÷ 9 = 4, 9 - 8 = 1 then add a zero and then, divide 2 ÷ 10 = 5

24.5

Answer:

-20 Absalute value=20

14 Absalute value=14

20+14=34

Step-by-step explanation:

Answer:   $1450

The profit that is gained from the production and selling of the jeans is given to be calculated through the the equation,

                         P = 20x - 50

For 75 jeans, we just have to substitute 75 to the x's of the equation. This then becomes,

                       P = 20(75) - 50 = 1450

Thus, the company will make a profit of $1450 by production of 75 jeans. 

Step-by-step explanation:

The company will make a profit of $1450 by the production of 75 jeans.

The profit that is gained from the production and selling of the jeans is modeled by the equation;

P = 20x - 50

If 75 jeans are produced, substitute 75 to represent the value of x in the equation.

P = 20(75) - 50 = 1450

Hence, the company will make a profit of $1450 by the production of 75 jeans.

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The volume of space that was not used= Volume of each box × number of boxes not packed into the truck= 6ft³ × 6 2/3= 40ft³.

In order to determine the amount of space that was not used in the pick up truck, we have to calculate the maximum number of boxes that can fit into the truck.

The pick up truck has a length of 8ft, width of 10ft and height of 2ft. Therefore, the volume of the pick up truck can be calculated as follows;

Volume of the pick up truck= length × width × height= 8ft × 10ft × 2ft = 160ft³

On the other hand, the dimensions of each box are length of 2ft, width of 2ft and height of 1.5ft. Therefore, the volume of each box can be calculated as follows;Volume of each box= length × width × height= 2ft × 2ft × 1.5ft = 6ft³.

Hence, the total number of boxes that can fit into the pick up truck can be calculated by dividing the volume of the truck by the volume of each box.

This is as follows;

Total number of boxes that can fit into the pick up truck= Volume of the truck ÷ Volume of each box= 160ft³ ÷ 6ft³ = 26.67.

From the calculation above, we can see that a total of 26 boxes and 2/3 of a box can be loaded into the pick up truck with a cover. Since we have packed 20 boxes, it implies that the remaining number of boxes that was not packed into the pick up truck is;

Number of boxes that was not packed into the truck = 26 2/3 - 20 = 6 2/3 boxesWe can then determine the volume of space that was not used by multiplying the volume of each box by the number of boxes not packed into the truck.

Hence;Volume of space that was not used= Volume of each box × number of boxes not packed into the truck= 6ft³ × 6 2/3= 40ft³.Therefore, the amount of space that was not used is 40ft³.

The amount of space that was not used in the pick up truck with a cover is 40ft³.

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Probability that first two babies born are boys is 0.23

Number of Mothers to be received ultrasound = 14

Number of mother giving birth to girl = 7

Number of mother giving birth to boy = 14 - 7 = 7

P(giving birth to girl) = P(G) = 7 / 14 = 0.5

P(giving birth to boy) = P(B) = 7 / 14 = 0.5

Probability that the first two babies that are born happen to be boys =

favorable outcome / total outcome

here, favorable outcome = ⁷C₂

Total outcome = ¹⁴C₂

Required probability = ⁷C₂ / ¹⁴C₂

= (7×6 / 2×1) / (14×13 / 2×1)

= 7×6/14×13

= 42 / 182

=0.23

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the y intercept is 0 because it's the number with the x and you have to divide everything by the 2 w/ the y to get it by itself and the 2's cancel out just leaving x !!

The test statistic for a Z-test is the Z-statistic, which has the standard normal distribution under the null hypothesis

A test statistic shows how closely your data’s distribution fits the distribution anticipated by the statistical test’s null hypothesis. The frequency with which each observation happens is defined by the distribution of data, which may be represented by its central tendency and variance around that central tendency.

Z= (x – y)/(x2/n1 + y2/n2) is the formula for calculating the test statistic when comparing two population means. To compute the statistic, we must first compute the sample means (x and y) and standard deviations (x and y) for each sample independently. In statistics, there are many different types of tests, such as the t-test, Z-test, chi-square test, anova test, binomial test, one sample median test, and so on. If parametric tests are applied,

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Answer:

its c!

Step-by-step explanation:

The matching rational numbers and their equivalent decimal expansions are:

7/9 = 0.777777...

7/15 = 0.466666...

7/10 = 0.7

7/8 = 0.875

What is a rational number?

A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In other words, a rational number is a number that can be written as a fraction with a finite or repeating decimal expansion.

Matching the given rational numbers to their decimal expansions:

7/9 = 0.777777... (repeating decimal)

7/15 = 0.466666... (repeating decimal)

7/10 = 0.7 (terminating decimal)

7/8 = 0.875 (terminating decimal)

Therefore, the matching rational numbers and their equivalent decimal expansions are:

7/9 = 0.777777...

7/15 = 0.466666...

7/10 = 0.7

7/8 = 0.875

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Answer:

x=4

Step-by-step explanation:

Answer:

9 times x = 9x

9 times -2 = -18

So, 9x-18 = 18

Now, we are looking for x, so we have to get rid of anything else, either added or taken away from it.

So we are going to add 18 to both sides, to get rid of the -18, and add 18 to the other side of the equals sign.

Therefore 9x = 36.

We are not done yet because we need x on its own, not 9x, so we are going to divide 36 by 9 to find out what x equals.

36 divided by 9 = 4

x = 4

Step-by-step explanation:

The inverse of the log is exponential.

An exponential function is a mathematical function with the formula f (x) = ax, where x is a variable and an is a constant that serves as the function's basis and must be greater than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

STEP 1: Replace the function notation f(x) by y

f(x) -> y

STEP 2: Switch the roles of x and y.

x -> y

y -> x

STEP 3: Isolate the log expression on one side (left or right) of the equation.

STEP 4: Convert or transform the log equation into its equivalent exponential equation.

Notice that the subscript b in the log form becomes the base with an exponent N in exponential form.

The variable M stays in the same place.

STEP 5: Solve the exponential equation for y to get the inverse. Then replace y by \(f^{-1}(x)\) is the inverse notation to write the final answer.

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The goal of a hypothesis test is to determine if the data can refuse an assumption a parameter or a population.

Statistical hypothesis test: A statistical hypothesis test is a technique for determining whether the available data are sufficient to support a specific hypothesis. We can make probabilistic claims about population parameters through hypothesis testing.

The purpose of a hypothesis test is to ascertain whether the data can refute a parameter or population assumption.

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The solution of the following options is angle between the gradient and directional derivative is equal to zero and the gradient's highest value, the directional derivative is maximized..

A directional derivative shows the rate at which a function changes in any particular direction. The directional derivative may be calculated using a formula that uses the gradient. A function of more than one variable's gradient shows the direction of greatest change.

We may determine the instantaneous rate of z change in any direction at a place using the directional derivative. These instantaneous rates of change may be used to construct planes and lines that are perpendicular to a surface at a particular location, which is the subject of the next section.

Part A:

When the angle between the gradient and directional derivative is equal to zero and the gradient's highest value, the directional derivative is maximized.

Part B:

When the angle between the directional derivative and gradient is 180 degrees, the minimal value will be reached.

Part C:

When the gradient and directional derivative are 90 degrees apart, the result will be zero.

Part D:

At an angle of 60 degrees between the gradient and the directional derivative, its maximum value will be half its maximum value.

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The exact probability that the absolute value of the difference between the sample sum of the labels and -581.4 exceeds 31.54 is approximately 0.1128 or 11.28%.

To find the exact probability, we will use the properties of the normal distribution.

Let X be the random variable representing the sum of the labels on the tickets. We know that the mean of X (μ) is -581.4 and the standard deviation of X (σ) is √(17) × 4.5.

We want to find the probability that the absolute value of the difference between X and -581.4 exceeds 31.54. In other words, we want to find P(|X - (-581.4)| > 31.54).

Convert the inequality into a standard normal distribution form.

The standard normal distribution has a mean of 0 and a standard deviation of 1. To convert X to a standard normal random variable Z, we use the formula:

Z = (X - μ) / σ

In our case:

Z = (X - (-581.4)) / (√(17) * 4.5)

Calculate the Z-score.

Z = (31.54) / (√(17) * 4.5) ≈ 1.591

Find the probability using a standard normal distribution table or a calculator.

P(Z > 1.591) ≈ 0.0564 (rounded to four decimal places)

Account for both tails of the distribution.

Since we are interested in the absolute difference, we need to consider both tails of the normal distribution. Therefore, the total probability of the absolute difference exceeding 31.54 is:

P(|X - (-581.4)| > 31.54) = 2 P(Z > 1.591) ≈ 2 × 0.0564 ≈ 0.1128

So, the exact probability that the absolute value of the difference between the sample sum of the labels and -581.4 exceeds 31.54 is approximately 0.1128 or 11.28%.

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The resulting cross-section of a cylinder intersected by a plane parallel to the bases is a circle.

When a plane passes through a cylinder parallel to the bases, it creates a cross-section that is congruent to the bases of the cylinder. Since the bases of a cylinder are circles, the resulting cross-section is also a circle. The circle formed will have the same diameter as the bases of the cylinder and will be parallel to them. This is because the plane slices through the cylinder at a constant distance from the bases, resulting in a circular shape that is perpendicular to the axis of the cylinder. This characteristic holds true for any position of the plane parallel to the bases, resulting in circular cross-sections.

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Answer:

21

Step-by-step explanation:

84% of 25 is 21

The maximum score is 100%, 100÷25= 4, meaning each question was 4 points or 4% of the total grade 84÷4=21 .

Answer:

21 questions were correctly answered

Step-by-step explanation:

If one scores an 84% on a quiz, that means that as an expression out of 100, a person has gotten 84 correct. To find how much the 84% equates to, one must convert the percent to a decimal. This means that one must divide the 84 by 100. After doing so, multiply the result by the number of questions on the quiz. The value attained will be the number of questions answered correctly.

Convert percent to decimal:

84% / 100 = 0.84

Multiply by the number of questions to find the amount answered correctly:

25 * 0.84 = 21

Hypothesis testing is an important statistical tool that helps us make informed decisions based on data and evidence.

The hypothesis statement h: µ = 25 is an example of a null hypothesis. A null hypothesis is a statement that suggests there is no significant difference between two variables or that any difference is due to chance. It is often denoted as H0 and is used to compare against an alternative hypothesis, which suggests that there is a significant difference between two variables. In this case, the null hypothesis is that the population mean µ is equal to 25, and there is no significant difference between the sample mean and the population mean. If the null hypothesis is rejected, it means that there is enough evidence to suggest that the alternative hypothesis is true. However, if the null hypothesis cannot be rejected, it does not necessarily mean that it is true. It only suggests that there is not enough evidence to support the alternative hypothesis.

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The total amount reported in the cash flows from investing activities section of the statement of cash flows would be a gain of $12,000.

The cash flows from investing activities section of the statement of cash flows captures the cash transactions related to the purchase or sale of long-term assets, such as property, plant, and equipment. When an office equipment is sold for cash, the cash received from the sale is recorded as an inflow in the investing activities section.

In this scenario, a gain of $12,000 is incurred from the sale of office equipment with a book value of $110,000. The gain represents the excess of the cash received from the sale over the book value of the equipment. Since the gain is considered a positive cash flow, it would be included as an inflow in the cash flows from investing activities section.

Therefore, the total amount reported in the cash flows from investing activities section would be the gain of $12,000, indicating a positive cash inflow resulting from the sale of the office equipment.

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Answer:

Step-by-step explanation:

n17 = ?

n  = 17

d = 6

a1 =12

a17 = a1 +(n - 1)d

a17 = 12 + (17 - 1)*6

a17 = 12 + 16*6

a17 = 12 + 96

a17 = 108

Answer:

3.00c≥24.00

Step-by-step explanation:

57.00-33.00≤3.00c

Answer:

102.14

Step-by-step explanation:

Answer:

The answer to your question is 102.14

Step-by-step explanation:

#Nova

Have a good day sir or, madam

The total number of miles for the four trips is 25 miles.

Given that;

Linda traveled for one hour each day for four days at a speed that made her cover one mile in an even number of minutes. After the first day, she started to lose speed, and it took her 5 minutes longer to complete a mile than the day before. Her journey distance was also an integer amount of miles throughout the four days.

We know that,

Distance is a product of speed and time. We need to find the distance here with the use of the given conditions, time is 1 hour.

Speed = Distance / Time

Hence, speed is 1 mile per x minutes because we want to distance by multiplying the time and speed together yielding 60 min * 1 mile / x mins.

Minutes cancel out, so now we have 60/x as our distance for the first day.

The distance for the given case;

⇒ \(\frac{60}{x},\frac{60}{x+5},\frac{60}{x+10},\frac{60}{x+15}\)

It is given that x = 5;

⇒ \(\frac{60}{5},\frac{60}{10},\frac{60}{15},\frac{60}{20}\)

= 12 + 6 + 4 + 3

= 25

The total number of miles for the four trips is 25 miles.

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The linear equation for both Uber and Lyft  will be Y = 0.75x + 3 and

Y = 0.5x + 5 .

A linear equation is an algebraic equation of the form y = mx+b. Involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Here we have,

Uber charge $3 fix on every trip and additional charges on per mile $0.75

So, linear equation be

Y = 0.75x + 3 where, x = no. of mile covered

Similarly, lyft charge $5 fix and $0.5 as an additional

So, linear equation be

Y = 0.5x + 5 where, x = no. of mile covered

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Answer:

it should be y= -4x + 10

Step-by-step explanation:

hope this helps.

the y-coordinate must be 7 in order for the point to lie on the line.

A line in the xy-plane passes through the origin and has a slope of 1/7. Point B (1, 7) lies on the line, as the slope of the line is calculated by the equation y = mx + b, where m is the slope of the line, and b is the y-intercept. Since the line passes through the origin, the y-intercept is 0. This can be expressed as y = (1/7)x + 0

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