A theater has 19 rows of seats there are 22 seats on the first row 26 seats in the second row and 30 seats in the third row and so on how many seats are in the last row of the auditorium?

Answer:

\(6\sqrt{5}-4\sqrt{15}\)

Step-by-step explanation:

\(\sqrt{5} \times (6 - 4\sqrt{3} )\)

\(\sqrt{5}\times 6-\sqrt{5}\times4\sqrt{3}\)

\(6\sqrt{5}-4\sqrt{5}\sqrt{3}\)

\(6\sqrt{5}-4\sqrt{5 \times 3}\)

\(6\sqrt{5}-4\sqrt{15}\)

Answer:

6\(\sqrt{5}\) - 4 \(\sqrt{15}\)

Step-by-step explanation:

1. Multiply each term in the parentheses by \(\sqrt{5}\)

2. calculate the product

3. solution :)

Vectors, a = (-3, -2, 10) and b = (-7, 5, -2).(A) Scalar Projection:The scalar projection of b onto a is given as follows Where |b| is the magnitude of b, θ is the angle between the vectors a and b.

Based on the above formula, the magnitude of vector b, |b| can be calculated as:

|b| = √((-7)² + 5² + (-2)²) = √74

The angle between the vectors a and b, θ can be calculated as:cos(θ) = a.b/|a||b|where, Now,cos(θ) = 41/(√113 × √74) = 0.684The scalar projection of b onto a can be calculated by multiplying |b| by cos(θ).Hence,Scalar projection = S = |b| cos(θ) = √74 × 0.684 ≈ 6.47 (rounded off to two decimal places)(B) Component decomposition:

Let the parallel component of b be represented as bₐ and the orthogonal component of b be represented as b⊥.Thus Therefore,Parallel component Orthogonal Component

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An amount 'a' divided by 3 can be expressed as a/3. For instance, if the number 30 is divided by 3, the result will be 10.

The mathematical statement a divided by 3 can be expressed as an algebra as follows: a/3. Often in algebra, words, and letters are used for mathematical expressions.

To resolve an equation of this nature, you simply have to insert the figure represented by 'a' and then divide it by 3 to arrive at your answer. For instance, if the number is 30, we could divide it by 3 to arrive at the answer 10.

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The missing terms in the blanks  and number of terms  are determined below.

The missing terms in the blanks for the pattern and number of terms  can be determined as follows:

1. 32, 30, 28, 26, 32__________________________, 0

The difference is 2. Thus, subtract 2 till you reach 0. That is:

32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0

Number of terms: 16

2. 75, 70, 65, 60, 55, 50, ____________________, 0

The difference is 5. Thus, subtract 5 till you reach 0. That is:

75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 0

Number of terms: 15

3. 30, 27, 24, 21, ___________________________, 0

The difference is 3. Thus, subtract 3 till you reach 0. That is:

30, 27, 24, 21, 18, 15, 12, 9, 6, 3, 0

Number of terms: 10

4. 81, 72, 63, ______________________________, 0

The difference is 9. Thus, subtract 9 till you reach 0. That is:

81, 72, 63, 54, 45, 36, 27, 18, 9, 0

Number of terms: 9

5. 48, 44, 40, 36, __________________________, 0

The difference is 4. Thus, subtract 4 till you reach 0. That is:

48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0

Number of terms: 12

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the probability that in a randomly selected office hour, the number of student arrivals is 7 is approximately 0.0857 or 8.57%.

To find the probability that the number of student arrivals is 7, we need to determine the probability of a specific count of arrivals in a Poisson distribution.

The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space, given the average rate of occurrence.

In this case, the average rate of student arrivals in an office hour is given as 1.9 students.

The probability mass function of the Poisson distribution is given by the formula:

P(x; λ) = (e^(-λ) * λ^x) / x!

Where:

P(x; λ) represents the probability of x events occurring,

λ is the average rate of occurrence,

e is the base of the natural logarithm (approximately 2.71828), and

x! represents the factorial of x.

Plugging in the values, we have:

P(7; 1.9) = (e^(-1.9) * 1.9^7) / 7!

Using a calculator or software, we can calculate this probability:

P(7; 1.9) ≈ 0.0857

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Answer:

x=50

Step-by-step explanation:

+1x=50

divide both sides by 1

x=50

Answer:

x = 50

Step-by-step explanation:

If you divide anything by one, it will remain the same.

To isolate the x variable, you need to divide both sides by 1.

+1x/1 = 50/1

x = 50

Answer:

-17.6,-13.8,-9.4,-3.6,-3.2,13.8

From number line the closer a decimal number is to zero the greater it is

The first chi-square statistic of 3.86 is not statistically significant at an alpha level of .01 because it is smaller than the critical value of 6.63. However, the second chi-square statistic of 67.81 is statistically significant at an alpha level of .05 because it is greater than the critical value of 3.84.

In statistical hypothesis testing, the chi-square statistic is used to determine if there is a significant association between categorical variables. To assess the statistical significance of the results, we compare the chi-square statistic to the critical value obtained from the chi-square distribution at a specific alpha level. The alpha level represents the probability of rejecting the null hypothesis when it is true.

For the first case, where the chi-square statistic is 3.86 and the critical value is 6.63 with an alpha level of .01, we find that the chi-square statistic is smaller than the critical value. In this scenario, we fail to reject the null hypothesis and conclude that the results are not statistically significant at the specified alpha level. This means that there is insufficient evidence to suggest a significant association between the categorical variables.

In the second case, where the chi-square statistic is 67.81 and the critical value is 3.84 with an alpha level of .05, we observe that the chi-square statistic is greater than the critical value. In this situation, we reject the null hypothesis and conclude that the results are statistically significant at the specified alpha level. This indicates strong evidence to support the presence of a significant association between the categorical variables.

Finally, the first chi-square statistic of 3.86 is not statistically significant at an alpha level of .01, while the second chi-square statistic of 67.81 is statistically significant at an alpha level of .05. The decision to reject or fail to reject the null hypothesis is based on comparing the chi-square statistic to the critical value obtained from the chi-square distribution at a specific alpha level.

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Answer:

option D; 20/3 OR 6 2/3

Step-by-step explanation:

CONVERT THE HOURS INTO MINUTES;

3/4 × 60 = 45 mins

1hour = 60 mins

45 mins = 5 miles

60 mins = ??

cross multiply;

60 by 5 ÷ 45 to get 20/3.

A cube root function that is translated to the right 3 units, up 4 units, and stretched vertically by a factor of 2.

-> c. f(x) = 2∛(x-3) + 4

A cube root function that is translated to the left 4 units, up 3 units, and stretched vertically by a factor of 2.

-> b. f(z) = 2∛(z+4) + 3

A cube root function that is translated to the right 4 units, up 3 units, and stretched vertically by a factor of -2.

-> d. f(x) = -2∛(x-4) + 3

A cube root function that is translated to the left 3 units, up 4 units, and stretched vertically by a factor of -2.

-> a. f(x) = -2∛(x+3) + 4

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Answer:

Step-by-step explanation:

i dont know im 11

Answer:

its a i belive

Step-by-step explanation:

they deleted it for some reason

Answer:

d over 5 or d divided by five

or an unknown number over or divided by 5

Step-by-step explanation:

7−(2−5(4−7)+6)+7

=7−(2−(5)(−3)+6)+7

=7−(2−(−15)+6)+7

=7−(17+6)+7

=7−23+7

=−16+7

=−9

Thus, the answer is -9

Answer:

the answer is the second to the left :D

Step-by-step explanation:

each number is divided then you solve\

The third scatter plot is correct.

A scatter plot is a set of points plotted on a horizontal and vertical axes. Scatter plots are important in statistics because they can show the extent of correlation, if any, between the values of observed quantities or phenomena (called variables).

According to the given table for bulldogs and condors.

To get the scatter plot we can make coordinates using x-axis as Bulldogs and y-axis as condors.

The coordinates will be

(5, 3), (6,2) , (3, 4), (2, 5), (7, 4), (6, 5), (3, 9), (6, 7), (5, 4) (6, 3).

So, these coordinates are well represented by third scatter plot.

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Answer:

5cd=157qr

1cd=157/55qr

or

qr=55/157cd

Step-by-step explanation:

1qr=30nc

55/157×cd=30nc

55/157×1/30×cd=1nc

1nc=0.011670cd

rs2870=0.01167×2870cd=33.49cd

₹2870 is equal to 33.49 CD.

Given that, 55 Canadian Dollars=157 Qatari Riyal and 1 Qatari Riyal=30NC.

We need to find how much the Canadian Dollar is equal to ₹2870.

The Canadian dollar is the currency of Canada. It is abbreviated with the dollar sign $, or sometimes CA$, Can$ or C$ to distinguish it from other dollar-denominated currencies. It is divided into 100 cents.

Converting the Canadian Dollar to rupees use 1 NC=0.011670 CD.

1 QR=30 NC

55/157 CD=30 NC

55/157×1/30×CD=1 NC

1 NC=0.011670CD

₹2870=0.01167×2870 CD=33.49 CD

Therefore, ₹2870 is equal to 33.49 CD.

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Answer: 100:3

Step-by-step explanation:

Answer:

the ratio of first-year college basketball players to high school seniors playing basketball is 3:100.

Step-by-step explanation:

The problem states that for every 75,000 high school seniors playing basketball, about 2,250 play college basketball as first-year students. To write the ratio of first-year college basketball players to high school seniors playing basketball, we need to compare the two quantities.

The ratio is a way of expressing the relationship between two numbers as a fraction or a pair of numbers separated by a colon (:). In this case, we want to express the ratio of the number of first-year college basketball players to the number of high school seniors playing basketball.

To write the ratio, we start by putting the number of first-year college basketball players (2,250) in the numerator of a fraction. We put the number of high school seniors playing basketball (75,000) in the denominator of the same fraction.

So the ratio can be expressed as:

2,250/75,000

To simplify this fraction, we can divide both the numerator and denominator by a common factor. In this case, both 2,250 and 75,000 are divisible by 750. Dividing both numbers by 750 gives:

2,250/75,000 = 3/100

Answer:

This algebraic problem can be solved by setting up a system of equations. For example, let x be the number of pounds of 3-inch nails that Toni buys, and y be the number of pounds of 2-inch nails that Toni buys. We know that x + y = 5 (since Toni believes a total of 5 pounds of pins) and that 0.99x + 1.39y = 6.15 (since that is the total cost of the nails). We can solve for one of the variables using one equation and then substitute that value into the other equation.

Solving for x in the first equation: x + y = 5

x = 5 - y

Substituting this into the second equation: 0.99(5 - y) + 1.39y = 6.15

4.95 - 0.99y + 1.39y = 6.15

4.95 = 0.4y + 6.15

-1.2 = 0.4y

y = -3

Since the number of pounds of nails cannot be harmful, we know that this solution is not possible. We can check by plugging in y = 3 (possible) into the first equation and seeing that x + 3 = 5, so x = 2.

Hence, Toni bought 2 lb of 3-inch nails and 3 lb of 2-inch nails.

Step-by-step explanation:

Answer:

okay check this ans

Step-by-step explanation:

HOPE YOU FOUND THIS HELPFUL...

PLZ MARK BRAINLIEST IF YOU DID

The answer is \($0.8-0.5625$\)

given data

Probability density function. \($f(x)=0.025 x+0.15$\)

where \($2 < x < 6$\)

Now

Probability that measurement is b/w 3 and 4

Find,\($P(3 < x < 4)$\)

\($=\int_{3}^{4} f(x) d x$\)

\($\int_{3}^{4}(0.025 x+0.15)$\)

\($=\left(\frac{0.025 x^{2}}{2}+0.15 x\right)_{3}^{4}$\)

\($=0.8-0.5625$\)

What is probability density function?

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If the discount rate is 4%,the present value of the savings account is $5,448.50.

From the question above, :Savings amount = $7,942

Discount rate = 4%

Time period = 9 years

We need to calculate the present value of the savings account.To calculate the present value, we will use the formula,PV = FV / (1 + r)n

Where,PV = Present value of savings account

FV = Future value of savings account

r = discount rate, and

n = Time period

In this problem,PV = ?

FV = $7,942

r = 4%

n = 9 years

Substitute the values in the formula,

PV = 7,942 / (1 + 0.04)9

PV = $5,448.50

Therefore, the present value of the savings account is $5,448.50.

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Answer:

4

Step-by-step explanation:

2-1=1

?-2=2

7-?=3

11-7=4

16-11=5

22-16=6

? must be 2+2= 4 since its true in both cases

hope this helped!

Answer: John Graunt

Step-by-step explanation:

John Graunt is referred to as the Columbus of statistics because his book made a fundamental contribution by attempting to demonstrate the quantitative characteristics of birth and death data.

He's regarded as the founder of demography which is the statistical study of the population of human beings.

Answer: 20

Step-by-step explanation:

3+2 = 5 yards

5 divided by 1/4 = 5 x 4 = 20 bookmarks

The equation of the line through the points (0, 9) and (3, 0) is y = -3x + 9.

To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is one of the points on the line and m is the slope of the line.

First, we calculate the slope (m) using the formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points. Substituting the values (0, 9) and (3, 0), we get m = (0 - 9)/(3 - 0) = -9/3 = -3.

Next, we choose one of the points, let's say (0, 9), and substitute its coordinates into the point-slope form: y - 9 = -3(x - 0).

Simplifying the equation, we get y - 9 = -3x, or rearranging it, y = -3x + 9.

Therefore, the equation of the line passing through the points (0, 9) and (3, 0) is y = -3x + 9.

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Answer: I think the answer is B

Step-by-step explanation:

8(x-4) = 8(1-4) = 8-32

2(4x-16) =2(4*1-16) = 8-32

8(x-4) = 8(2-4) = 16-32

2(4x-16) = 2(4*2-16) = 16-32

Answer:

B. Infinitely many solutions.

Step-by-step explanation:

8(x - 4) = 2(4x - 16)

^--This is the original equation.

If we replace x with 1...

we have the same equation, but we add an extra set of brackets. (You'll see why in a second)

8(1 - 4) = 2{4(1) - 16}

1 - 4 = -3

We start by subtracting 4 from 1. When using positive numbers, we can't do this, however. This gets us to -3. leave it in the parenthesis though!

8(-3) = 2{4(1) - 16}

4(1) = 4

Now, the reason we made an extra set of brackets is because 4x is asking you to multiply 4 by x. but as a number, you have to make an extra set of parenthesis to show that. 4 x 1 = 4 so it stays as a 4.

8(-3) = 2(4 - 16)

^-- Now, we are given this new equation. We'll move away from 8(-3) for just a second, to finish the other parenthesis. But still don't remove the parenthesis for 8(-3)!

4 - 16 = -12

We know that 4-16 would also not be possible with positive numbers, but for this equation, as said before.. you're using negative numbers. so 4 - 16 = 12

8(-3) = 2(-12)

^-- And again, we have a new equation. 8(-3) = 2(-12). Don't remove the parenthesis, as I have said before.

8(-3) = -24

Again, the equation shows with parenthesis, it wants us to multiply. Now we take 8, and multiply it by -3. This is a bit tricky, as it is with negative numbers. But in the end, you should have -24.

-24 = 2(-12)

^--The equation becomes -24 = 2(-12). We'll have to multiply again, so keep the parenthesis.

2(-12) = -24

2(-12) Is also asking you to multiply, so now we do the same as before, which again, is a bit tricky because we are using negative numbers. You should end up with -24 though.

-24 = -24

^--Now, you have -24 = -24. This is true since both are the same number.

8(x - 4) = 2(4x - 16)

^-- Here's our wonderful equation again! Let's replace X with a 2 this time!

If you don't understand, read the tips from above to understand what I'm doing in the following equations!

8(2 - 4) = 2{4(2) - 16}

2 - 4 = -2

8(-2) = 2{4(2)-16}

4(2) = 8

8(-2) = 2(8 - 16)

8 - 16 = -8

8(-2) = 2(-8)

8(-2) = -16

-16 = 2(-8)

2(-8) = -16

-16 = -16

And again, we get the same two numbers!

Hope I helped! <3

The equation X^2 + Y^2 + Z^2 = 4 represents a sphere in Cartesian coordinates. In spherical coordinates, this equation can be expressed as ρ^2 = 4, where ρ is the radial distance from the origin.

The equation X^2 + Y^2 + Z^2 = 4 represents a sphere with a radius of 2 units in Cartesian coordinates. To express this equation in spherical coordinates, we need to convert the Cartesian variables (X, Y, Z) into spherical variables (ρ, θ, φ).

In spherical coordinates, ρ represents the radial distance from the origin, θ represents the azimuthal angle (measured from the positive x-axis), and φ represents the polar angle (measured from the positive z-axis).

To rewrite the equation X^2 + Y^2 + Z^2 = 4 in spherical coordinates, we replace X with ρ sin(φ) cos(θ), Y with ρ sin(φ) sin(θ), and Z with ρ cos(φ). Substituting these values, we obtain (ρ sin(φ) cos(θ))^2 + (ρ sin(φ) sin(θ))^2 + (ρ cos(φ))^2 = 4.

Simplifying this equation, we have ρ^2 sin^2(φ) (cos^2(θ) + sin^2(θ)) + ρ^2 cos^2(φ) = 4. Since cos^2(θ) + sin^2(θ) = 1, we can further simplify the equation to ρ^2 sin^2(φ) + ρ^2 cos^2(φ) = 4.

Finally, recognizing that sin^2(φ) + cos^2(φ) = 1, we arrive at the equation ρ^2 = 4, which represents a sphere with a radius of 2 units in spherical coordinates.

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