Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 26, adjacent side A C is 24, opposite C B is 10. For the triangle above, find sin A. a. 36° c. 0.9323 b. 50° d. 0.385

Answer:

32

Step-by-step explanation:

A = l*w

55 = 5*w

55 /5 = 5w/5

11 = w

The perimeter is

P =2(l+w)

P = 2(5+11)

  =2(16)

  = 32

Answer:

32Units

Step-by-step explanation:

We know Area of rectangle=LENGTH×BREADTH

Here, breadth and Area given

55=5×L

L=11(value of length=11)

Perimeter=2(L+B)

32=2(5+11).

Answer:

A-> a(n)=a+(n-1)d

B-> Yes, I do agree

Step-by-step explanation:

A=   a+(n-1)d

where a=the first term

           n=the term's location

           d= the difference between two adjacent terms

B= I agree

a3=12+2d=4.........equation 1

          2d=-8

             d=-4

a10=12+9d=-24.....equation 2

            9d=-36

              d=-4

Hence, to find the next term of the sequence, add -4 to  the previous term.

{I hope this answers your question}

The arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

In mathematics, an expression or mathematical expression is a combination of terms both variables and constants. For example -

2x + 4y + 5z

4y + 2x

Given are the expressions as given in the questions.

{a} -

5 - 9 = - 4

{b} -

8 - 8 = 0

{c} -

- 1 + 12 = 11

{d} -

- 12 + 12 = 0

{e} -

- 2 + 4 + 3

5

{f} -

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

Therefore, the arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

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{Complete question -

Calculate the following:

a) 5-9

b) 8-8

c) -1 + 12

d) -12 + 12

e) -2 +4+3

f) -4-3+2-1}

Answer:

HL, SAS, ans SSS

Step-by-step explanation:

ASA and AAS cannot be used because we can only confirm one angle of each triangle.

Congruent shapes have equal corresponding sides and angles.

The congruence theorems that can be used to prove \(\triangle ABR \cong \triangle ACR\) are HL, SAS, and SSS

\(\triangle ABR \cong \triangle ACR\) means that, the triangles are congruent.

From the attached figure, we have the following congruent sides and angle:

The above highlights mean that the following theorems can be used to prove that the triangles are congruent:

HL, SAS, and SSS

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Answer:

A

Step-by-step explanation:

Given :

2x + 4y = 14  ---------- eq 1

4x + y = 20 ---------- eq 2

if you multiply eq 2 by -4 on both sides, you get

-4 (4x + y = 20) = -4 (20)

-16x -4y = -80 --------- eq3

we can see that eq. 1 and eq 2 together forms the system of equations presented in option A, Hence A is equvalent to the orginal system of equations given in the question.

The system of equations which is equivalent to the \(2x + 4y = 14\),\(4x + y = 20\)  is given in option \((A)\) i.e. \(2x + 4y = 14\) and \(-16x - 4y = -80\).

System of equations comprises of two or more equations and seeks common solutions to the equations.

We have,

\(2x + 4y = 14\)   \(........(i)\)

  \(4x + y = 20\)    \(........(ii)\)

Now,

To check that which option suits best for system of equation,

Lets multiply equation \((ii)\) by \((-4)\),

  \((-4) (4x + y) = (-4)*(20)\)

\(-16x-4y=-80\),

So, this above obtained equation is in option  \((A)\).

Hence, we can say that the system of equations which is equivalent to the \(2x + 4y = 14\) ,\(4x + y = 20\) is given in option \((A)\) i.e. \(2x + 4y = 14\) and \(-16x - 4y = -80\).

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Step 1: The average price is $4.17.

Step 2: To calculate the average price, we need to find the sum of all the prices and divide it by the total number of items. In this case, the student purchased groceries at the prices of $1.01, $3.46, $5.84, and $7.38.

Summing up these prices, we get $1.01 + $3.46 + $5.84 + $7.38 = $17.69.

Since there are four prices, we divide the sum by 4 to find the average price: $17.69 / 4 = $4.4225.

Rounding this to the nearest cent, the average price is $4.42.

Step 3: The average price of the groceries purchased by the student is $4.17. This is calculated by summing up the individual prices and dividing the sum by the total number of items. The average price is commonly used as a measure to understand the typical or representative value of a set of prices.

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Answer:

would come out as a very weird answer

Step-by-step explanation:

(4/5)^7(5/4)^7

The 99% confidence interval estimating the proportion of all Ford Fusion drivers who are women is (0.40685, 0.67007). The closest option to this interval is option 2) (0.40385, 0.67307).

The answer is option 1) (0.41689, 0.66003). To design a new advertising campaign, Ford Motor Company conducted a sample survey of 91 Fusion owners and found that 49 of them were women. To estimate the proportion of all drivers who are women, a confidence interval is calculated. The formula for calculating the confidence interval is:

sample proportion ± z*(standard error)

where z is the critical value for the desired confidence level and the standard error is calculated as:

sqrt((sample proportion*(1 - sample proportion))/sample size)

For a 99% confidence interval, the critical value is 2.576. Plugging in the values from the sample, we get:

sample proportion = 49/91 = 0.5385
sample size = 91

Using the formula above, we can calculate the standard error as:

sqrt((0.5385*(1 - 0.5385))/91) = 0.0625

Finally, we can plug in the values into the confidence interval formula:

0.5385 ± 2.576*0.0625

which gives us the interval (0.41689, 0.66003). Therefore, option 1) is the correct answer.

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When the balloon is on the ground, it is at point 0. It starts to go up at 5 f/m for a time of 4 minutes. So we will multiply 5 by 4 to get 20. At this point, the balloon is 20 feet off the ground. However, we now know that the balloon descends at 2 f/m at a time of 7 minutes. So we must multiply 2 by 7 to get 14. So we know it was at 20, and then it went down by 14.

20 - 14 = 6 feet

This means that the balloon is now 6 feet above the ground.

I hope I've helped! :)

The mean, standard deviation, of the average number of moths in 30 traps is approximately 0.5 ± 0.018 and is approximately 0.5 respectively. The probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.

The mean of the average number of moths in 30 traps can be calculated as the mean of a sample of 30 trap counts, where the mean of each sample follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30) (using the standard error of the mean formula). Therefore, the mean of the average number of moths in 30 traps is:

mean = 0.5 ± 0.1/sqrt(30) = 0.5 ± 0.018

So the mean of the average number of moths in 30 traps is approximately 0.5 ± 0.018.

The standard deviation of the average number of moths in 30 traps can also be calculated using the standard error of the mean formula:

standard deviation = standard error of the mean * sqrt(sample size)

standard deviation = 0.5/sqrt(30) * sqrt(30) = 0.5

So the standard deviation of the average number of moths in 30 traps is approximately 0.5.

Using the central limit theorem, we can assume that the sample mean of the 30 traps follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30). We want to find the probability that the average number of moths in 30 traps is greater than 0.4.

To do this, we can standardize the sample mean using the formula:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

z = (0.4 - 0.5) / (0.5/sqrt(30)) = -1.8257

Using a standard normal distribution table or calculator, we can find the probability that Z is greater than -1.8257, which is approximately 0.965. Therefore, the probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.

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Answer:

The new value of the list after changing 71° to 93° would be:

58, 61, 93, 77, 91, 100, 105, 102, 95, 82, 66, 57

The measure that changes the most would be the median. Without the change, the median was 86.5°, which was the average of the 7th and 8th values in the list (100 + 77) / 2. However, after changing 71° to 93°, the median becomes 91°, which is the average of the 6th and 7th values in the list (91 + 91) / 2.

Therefore, the median has changed by 4.5° (from 86.5° to 91°).

Joe need to purchase fence to go around his garden area = 24  feet²

What does a math area mean?

Area of garden  = 576

he need to purchase fence to go around his garden    = √576

                                                                                         = 24 feet²

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Answer:

Step-by-step explanation:

Refer to the definition of a function. I'll just give you a layman's definition to be concise.

For something to be a function, there needs to be exactly 1 output for every input. You cannot have a case where you input 1 value, and get 2 or more values as an output.

In math we call all the possible input values the domain, and we call all the possible output values the range.

Let's take a look at each situation on your worksheet.

1. Is a function. This is because only one arrow stems from each input value. There are cases where the different input values give the same output, sure, but each input returns 1 discrete thing, not an array of things.

(Think of it this way, if i had a machine that could answer any question I had with yes, no or maybe. I wouldn't want the machine to give me "yes and maybe" or "yes and no" as the result when I ask it a question. That doesn't make sense and I would think the machine is broken. What could happen, is that I ask the machine different questions, and for those different questions, it gave me the same answer, like "yes" and "yes" respectively. in that case, it would be acceptable, because it isn't contradicting itself for any individual question.)

2. Not a function. There are 2 different output values for b.

(Refer back to my machine analogy. The "machine" in this question is contradicting itself. I gave the machine one input, and the machine is telling me, "it's this and actually it's this other thing too")

3. Is a function for the same reasons as 1.

4. Isn't a function.

(It's basically telling you, the machine reads -6 as -4, but it also reads -6 as 0, and also 2. And it also tells you the machine reads -4 as -3, but it also reads it as 8. Again, the machine should only read 1 input in 1 way and not contradict itself. )

The required answer is :

a. The third side of the reflective sticker cannot be 12 cm long.

b. It is not possible to form a triangle with side lengths of 6 cm, 8 cm, and 2 cm.

According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side.

In this case, the sum of the two given sides (6 cm + 8 cm = 14 cm) is less than the length of the third side (12 cm).

Therefore, it is not possible to form a triangle with side lengths 6 cm, 8 cm, and 12 cm.

(b) The third side of the reflective sticker cannot be 2 cm long.

Applying the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side.

The sum of the two given sides (6 cm + 8 cm = 14 cm) is greater than the length of the third side (2 cm).

Hence, it is not possible to form a triangle with side lengths 6 cm, 8 cm, and 2 cm.

Therefore, a. The third side of the reflective sticker cannot be 12 cm long.

b. It is not possible to form a triangle with side lengths of 6 cm, 8 cm, and 2 cm.

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The total multiplier is calculated by summing the coefficients of the distributed lag model. The coefficients represent the weight of each lag, and the sum of the weights represents the total effect of the independent variable on the dependent variable.

A finite distributed lag model is a model in which the effect of an independent variable on a dependent variable is spread out over a period of time. The model is represented by the following equation:

y_t = α + β_1 x_t + β_2 x_{t-1} + ... + β_x x_{t-x} + u_t

where:

y_t is the dependent variable at time t

x_t is the independent variable at time t

α is the constant term

β_1, β_2, ..., β_x are the coefficients of the distributed lag model

u_t is the error term

The total multiplier is calculated by summing the coefficients of the distributed lag model. The coefficients represent the weight of each lag, and the sum of the weights represents the total effect of the independent variable on the dependent variable.

For example, if the distributed lag model has 3 lags and the coefficients are 0.5, 0.3, and 0.2, then the total multiplier would be 1.0. This means that a unit change in the independent variable would lead to a 1 unit change in the dependent variable, with 0.5 of the effect occurring immediately, 0.3 of the effect occurring in the next period, and 0.2 of the effect occurring in the second period.

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Answer:

240 :)

Step-by-step explanation:

easy all u have to do is just add all the sides together but the empty sides with no number u have to try to figure out how much meters that is.

they're both 36 because they're the same size as the meters on the other side.

so its going to be

60+36+36+36+36+36

hope this helps

good luck!

Answer:

x=55.5

Step-by-step explanation:

2x=111

Isolate x by dividing both sides by 111

x=55.5

The average duration of a customer's stay in the restaurant is approximately 27 seconds.

To find the average time a customer spends in the restaurant, we divide the total time spent by the total number of customers. Given that the outlet processes 2000 customers in 15 hours and there are 50 customers in the restaurant on average, we can calculate the average time as follows:

Total time spent = 15 hours

Total number of customers = 2000

Average time per customer = Total time spent / Total number of customers

= 15 hours / 2000

= 0.0075 hours or 27 seconds.

Therefore, a customer typically spends around 27 seconds in the restaurant.

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Answer:

40cm

Step-by-step explanation:

A box is normally in the shape of a cube

formula of volume of a cube;

We want to find the height(tallness)

Volume=LengthxWidthxHeight

10000=25x10xHeight

10000=250H. (divide both side by 250 to remain with H only)

10000/250=250H/250

40cm=Height

\(a(t+z)=45z+67\implies at+az=45z+67\implies az=45z+67-at \\\\\\ az-45z=67-at\implies \stackrel{common~factoring}{z(a-45)}=67-at\implies z=\cfrac{67-at}{a-45}\)

Vertex: The vertex of the parabola is (-0.75, 4.125).

Axis of Symmetry: The axis of symmetry is x = -0.75.

Maximum or Minimum Value: The parabola opens upward, so it has a minimum value. The minimum value is 4.125.

Range: The range of the parabola is y ≥ 4.125.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c. In this case, a = 2, b = -6, and c = 3.

Using the formula, we substitute the values into x = -(-6) / (2 * 2) = 6 / 4 = 1.5 / 2 = -0.75. This gives us the x-coordinate of the vertex.

To find the y-coordinate of the vertex, we substitute the x-coordinate into the equation. y = 2(-0.75)² - 6(-0.75) + 3 = 2(0.5625) + 4.5 + 3 = 1.125 + 4.5 + 3 = 4.125. Therefore, the vertex is (-0.75, 4.125).

The axis of symmetry is given by the x-coordinate of the vertex, which is x = -0.75.

Since the coefficient of x² is positive, the parabola opens upward, indicating a minimum value. The minimum value is the y-coordinate of the vertex, which is 4.125.

Finally, the range of the parabola is determined by the minimum value. Since the parabola opens upward and has a minimum value of 4.125, the range is y ≥ 4.125, indicating that the y-values of the parabola are greater than or equal to 4.125.

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The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

An official list of the players who will take part in the event when the game starts is known as a starting lineup in sports. The players who are in the starting lineup are frequently referred to as starters, while the rest are known as bench players or replacements.

Case 1: Bob starts (and Yogi doesn't). In this case, the coach must choose 4 more players from the 10 remaining players (remember that Yogi won't play, so there are only 10 players left to select from). Thus there are 10C4 lineups that the coach can choose.

⇒ ¹⁰C₄ = 10!/4!(10-4)! = 10!/4!6!

⇒ ¹⁰C₄ = (10*8*9*7)/(4*3*2*1)

⇒ ¹⁰C₄ = 210

Case 2: Yogi starts (and Bob doesn't). As in Case 1, the coach must choose 4 more players from the 10 remaining players. So there are 10C4 lineups in this case.

⇒ ¹⁰C₄ = 210

Case 3: Neither Bob nor Yogi starts. In this case, the coach must choose all 5 players in the lineup from the 10 remaining players. Hence there are 10C5 lineups in this case.

⇒ ¹⁰C₅ = 10!/5!(10-5)! = 10!/5!5!

⇒ ¹⁰C₅ = (10*8*9*7*6)/(5*4*3*2*1)

⇒ ¹⁰C₅ = 252

To get the total number of starting lineups, we add the number of lineups in each of the cases:

Case 1 + Case 2 + Case 3

= 210 + 210 + 252 = 672

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

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Answer:

Look below

Step-by-step explanation:

The digit three is in the thousands place in the number 63,297, so it represents 3,000. The digit three is in the hundreds place in the number 60,325, so it represents 300.

Answer:

1.7 or 1 7/10

Step-by-step explanation:

Answer:

\( \frac{17}{16} = 1 \frac{1}{16} \)

Step-by-step explanation:

\(4 \frac{1}{4} \div 2 \frac{1}{2} \\ \frac{17}{4} \div 2 \times \frac{1}{2} \\ \frac{17}{4} \times \frac{1}{2} \times \frac{1}{2} \\ \)

\( \boxed{Answer:{\boxed{\green{= \frac{17}{16} = 1 \frac{1}{16} }}}}\)

The integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

To evaluate the integral of du/sqrt(a^2 - u^2), we can use a trigonometric substitution. Let's substitute u = asin(theta), where theta is a new variable. Differentiating u with respect to theta gives du = acos(theta)*d(theta).

Now, let's substitute these expressions back into the integral:

∫(du/sqrt(a^2 - u^2)) = ∫((acos(theta)d(theta))/sqrt(a^2 - a^2sin^2(theta)))

Simplifying the expression under the square root:

= ∫((acos(theta)d(theta))/sqrt(a^2(1 - sin^2(theta))))

= ∫((a*cos(theta)d(theta))/(acos(theta)))

= ∫d(theta)

= theta + C

Since we made the substitution u = asin(theta), we need to express the result in terms of u. Using the relationship u = asin(theta), we can find theta = arcsin(u/a). Therefore, the integral becomes:

∫(du/sqrt(a^2 - u^2)) = theta + C = arcsin(u/a) + C

Hence, the integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

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The problem where the professor states that the average age of students in the university is 21 years is an example of statistical inference.

Statistical inference is the process of using data from a sample to make inferences or conclusions about a population. It allows us to draw conclusions about a larger group of individuals or objects based on information from a smaller sample. It is a fundamental part of statistical analysis and is used in many fields, including research, business, and government.

Statistical inference includes two main types: estimation and hypothesis testing.

Estimation: This involves using sample data to make estimates about population parameters. For example, using the sample mean to estimate the population mean or the sample proportion to estimate the population proportion.

Hypothesis testing: This involves using sample data to test a claim or hypothesis about a population parameter. For example, testing the claim that a coin is fair, based on the proportion of heads in a sample of coin flips.

The goal of statistical inference is to use the information from a sample to make informed decisions or predictions about a population. It allows us to draw general conclusions from a specific set of data, and it is an essential tool for making sense of data in many fields.

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If  bag contains 26 letters and 10 numerals, the probability of drawing 2 numerals is 1/14.

To calculate the probability of Robin drawing 2 numerals, you need to consider the total number of cards and the number of numerals. There are 26 letters and 10 numerals, making a total of 36 cards in the bag.

For the first draw, there are 10 numerals out of 36 cards, so the probability is 10/36. After drawing one numeral, there are now 9 numerals and 35 cards remaining. The probability of drawing a second numeral is 9/35.

To find the overall probability of drawing 2 numerals, multiply the individual probabilities: (10/36) * (9/35) = 90/1260.

Simplifying the fraction, the probability of drawing 2 numerals is 1/14.

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Solution:

As we know that f(x) = y

∴ y = f-1(x) ----------> (1)

Given f(x) = 4x

y = 4x

To find the inverse of the f(x), put y for all values of x and x for all values of y.

x = 4y

Divide both sides by 4.

x/4 = y

Using eq (1).

y = 1/ 4x or x / 4

Which represents the inverse of the function f(x) = 4x?

h(x) = x + 4, h(x) = x – 4, h(x) = 3/4 x, h(x) = 1/4 x

Summary:

The equation which represents the inverse of the function f(x) = 4x is h(x) = 1/4 x.