Find the missing length

Answer:

x = 70

Step-by-step explanation:

The total sum of all of the angles in a parallelogram is equal to 360 degrees. Opposite angles are also congreuent meaning that angle ADC and angle ABC are equal. Adding the sum of the two angles gives you 220. Subtract 220 form 360 and you get 140 which is equal to the sum of angles BCD and BAD. Angles BCD and BAD and the sam so dividing 140 by 2 would give you the angle measure of x.

The first four nonzero terms of the Maclaurin series for the function g(x) are:

1 - x + 1/2 x^2 - 1/6 x^3

So the correct answer is option (c).

To find the Maclaurin series for the given function g(x) = (1 + x)e^(-x), we can use the formula for the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ...

First, we find the first few derivatives of g(x):

g(x) = (1 + x)e^(-x)

g'(x) = -xe^(-x) + e^(-x)

g''(x) = xe^(-x) - 2e^(-x)

g'''(x) = -xe^(-x) + 3e^(-x)

Evaluating these derivatives at x = 0, we get:

g(0) = 1

g'(0) = 0

g''(0) = -2

g'''(0) = 3

Using the Maclaurin series formula and substituting in these values, we get:

g(x) = 1 + 0x - 2/2! x^2 + 3/3! x^3 + ...

Simplifying this expression, we get:

g(x) = 1 - x + 1/2 x^2 - 1/6 x^3 + ...

Therefore, the first four nonzero terms of the Maclaurin series for the function g(x) are:

1 - x + 1/2 x^2 - 1/6 x^3

So the correct answer is option (c).

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Answer:

A=2(2x+1)(3x+4

Step-by-step explanation:

Answer:

(12÷s)·60

Step-by-step explanation:

The hours it takes is 12/s so you multiply 60 to get the minutes. Next time, I would reccomend asking for help from the teacher or doing homework help, instead of putting all the RSM questions online. Thank you and have a good day :)

Answer:

12/s

Step-by-step explanation:

The rate of flow in cups per year is  3645 cups per year.

To convert the rate of flow from quarts per day to cups per year, we first need to convert quarts to cups and days to years.

1 quart is equal to 4 cups,

So 5 quarts is equal to 5 x 4 = 20 cups.

1 year is equal to 365 days, so

2 days is equal to 2/365 = 1/182.5 years.

So the rate of flow in cups per year is 20 cups / (1/182.5 years) = 3645 cups per year.

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Answer: 13/12

Step-by-step explanation:

Reduce the fraction 3/9 to the lowest terms by extracting and canceling out 3.

The least common multiple of 4 and 3 is 12. Convert 3/4 and 1/3 to fractions with denominator 12.

Since 9/12 and 4/12 have the same denominator, add them by adding their numerators.

Add 9 and 4 to get 13.

Hi there!

h(x) = 5x + 11

To find h(7) - 3, we can substitute 7 for x and subtract 3:

h(7) = 5(7) + 11 - 3

Simplify:

h(7) = 35 + 11 - 3

h(7) = 43

h(x) = 5x + 11

h(7) = 5 · 7 + 11 = 35 + 11 = 46

h(7) - 3 = 46 - 3 = 43 ← the end answer

The orthogonal projection of v onto the subspace of R^3 spanned by u1 and u2 is given by:

proj_v = ((v * u1)/(u1 * u1)) * u1 + ((v * u2)/(u2 * u2)) * u2

where "*" denotes the dot product.

Using the given values, we have:

v = [5, -1, 79]

u1 = [-6, -6, -1]

u2 = [-4, -12, 0]

proj_v = (([5, -1, 79] * [-6, -6, -1])/([-6, -6, -1] * [-6, -6, -1])) * [-6, -6, -1] + (([5, -1, 79] * [-4, -12, 0])/([-4, -12, 0] * [-4, -12, 0])) * [-4, -12, 0]

After calculating the dot products and simplifying the equation, we get:

proj_v = [-5, -5, 0]

Therefore, the orthogonal projection of v onto the subspace spanned by u1 and u2 is [-5, -5, 0].

To find the orthogonal projection of a vector onto a subspace, we need to first find a basis for the subspace. In this case, the subspace is spanned by u1 and u2. Then, we can use the formula for projecting a vector onto a subspace, which involves taking the dot product of the vector and each basis vector, dividing by the dot product of the basis vector with itself, and multiplying by the basis vector.

The resulting vector is the projection of the original vector onto the subspace. In this case, we plug in the given values for v, u1, and u2 into the formula and simplify to obtain the orthogonal projection of v onto the subspace spanned by u1 and u2, which is [-5, -5, 0].

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Answer:

64.5

Step-by-step explanation:

You understand the question, and already have the numbers in order, you're almost there!

So you need to find the median first so you can divide the data set into the upper and lower halves. The median, as you probably know, is the center of the data. What I do for this is list all the numbers out in order, like you've already done, and start crossing them out, one at a time, alternating the sides. I'll show you what I mean. (I'm using underline because there's no strikethrough.)

52, 54, 55, 55, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, 65, 68, 70, 72

52, 54, 55, 55, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, 65, 68, 70, 72

52, 54, 55, 55, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, 65, 68, 70, 72

52, 54, 55, 55, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, 65, 68, 70, 72

52, 54, 55, 55, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, 65, 68, 70, 72

...and so on, until you have:

52, 54, 55, 55, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, 65, 68, 70, 72

Because there's an even number of numbers, the median is the mean of the middle two numbers. Luckily, though, the two numbers in the middle are the same:61. Mean is calculated by adding the terms and dividing by the number of terms. In this case:

(61+61)/2

=61

(You didn't really have to do this mean step, but I'll explain later.)The median is 61. Another way you could have done this is by just counting the number of terms (20) and finding the middle one. Again, since there's no middle one, you'd have to find the mean.

Since you're looking for the third quartile and not the median, you didn't exactly have to do that step. I just wanted to explain how to calculate the median, since you'll have to do it in the next step. All we had to do here was divide the data set into the halves, so we used that visual demonstration by underlining the numbers one at a time. We didn't have to find the mean, we could have split the set down the middle instead.

52, 54, 55, 55, 57, 58, 59, 59, 61, 61, | 61, 62, 63, 63, 64, 65, 65, 68, 70, 72

                                                             ^median/half-way point

We could have also divided the number of terms (20) by 2 (because halves, 2 parts) to get 10 and used the upper 10 values of the set, but I don't know, the crossing out method helps me. Anyway, now we have to look at just the upper 10 values:

61, 62, 63, 63, 64, 65, 65, 68, 70, 72

And you repeat the process! (I'm not going to show the underlining though lol)

There are 10 terms, so the median is between the 5th and the 6th. (10/2=5)

61, 62, 63, 63, 64, 65, 65, 68, 70, 72

This is what I was talking about, there are an even number of values in the upper half of the data set as well, so we have to find the mean of the middle 2: 64 and 65.

 (64+65)/2

=129/2

=64.5

That's your final answer. Hope I could help you!

Answer:

64.5

Step-by-step explanation:

i just answered and got it right

A higher R-squared value indicates a better fit of the regression model to the data.

R-squared is a statistical measure that is commonly used to evaluate the goodness of fit of a regression model.

To understand how R-squared works, let's first review the concept of regression. Regression analysis is a statistical technique used to explore the relationship between two or more variables.

In a simple linear regression, we have a dependent variable (Y) and an independent variable (X), and we are trying to find a line of best fit that can predict the value of Y based on X.

Now, let's assume that we have a set of data points for Y and X. We can use regression analysis to find the line of best fit that minimizes the distance between the predicted values and the actual values of Y. The sum of the squared errors between the predicted and actual values of Y is called the regression sum of squares (SSR).

SSR is an important component in calculating R-squared. To find R-squared, we divide SSR by the total sum of squares (SST), which is the sum of the squared differences between the actual values of Y and the mean of Y. The resulting value of R-squared ranges from 0 to 1, with higher values indicating a better fit of the regression model to the data.

In mathematical terms, R-squared can be expressed as:

R-squared = SSR / SST

Therefore, to find the value of R-squared, we first need to calculate SSR using the formula within it. Once we have SSR and SST, we can divide SSR by SST to obtain the value of R-squared.

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The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

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Answer:

The inequality to represent the situation is \(20x\geq 3000\) and the team must sell at least \(15\) "Jaguar Cards".

Step-by-step explanation:

Given: The ADMHS football team is trying to raise money to buy new equipment so the players are selling "Jaguar Cards" for \(\$20\) each.

If the football team needs to raise at least \(\$3,000\) for equipment.

To find: The inequality to represent the situation and the least number of "Jaguar Cards" the team must sell.

Solution:

Let the ADMHS football team sold \(x\) "Jaguar Cards" for \(\$20\) each.

Now, the football team needs to raise at least \(\$3,000\) for equipment.

So, the inequality to represent the situation is \(20x\geq 3000\).

Now, on solving we get,

\(20x\geq 3000\)

\(\implies x\geq \frac{300}{20}\)

\(\implies x\geq 15\)

Hence, the inequality to represent the situation is \(20x\geq 3000\) and the team must sell at least \(15\) "Jaguar Cards".

The inequality to represent the situation should be 20x≥30,000 and the number of jaguar cards should be 15.

Since

Here we assume Jaguar cards be x for $20 each to raise at least $3,000 for equipment

20x≥30,000

x≥15

Based on this, the above represent the inequality function.

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Answer:

is finding the square root

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number.

When a number is squared, it is multiplied by itself. For example, squaring the number 4 gives 4^2 = 16.

The inverse operation undoes the effect of squaring and returns you to the original number. In this case, finding the square root of a number is the inverse operation of squaring.

The square root of a number "x" is a value that, when squared, gives the original number. It is denoted by the symbol √x.

For example, if you have the number 25 and you want to find its square root, you calculate:

√25 = 5

5 is the square root of 25 because when you square 5 (5^2), you get 25.

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number. The concept of square root and squaring are inverse operations that are used in various mathematical calculations and problem-solving.

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a) The price of fuel A is decreasing by a rate of 12% per month.

b) The greater percentage change over the previous month was of Fuel A.

A decreasing exponential function is modeled as follows:

y = a(1 - r)^x.

In which the parameters are given as follows:

The function for fuel A is given as follows:

f(x) = 2.27(0.88)^x.

As 0.88 < 1, the function is decreasing, and the percentage is obtained as follows:

1 - r = 0.88

r = 1 - 0.88

r = 0.12 = 12%.

The rate for fuel B is given as follows:

3.04/3.17 = 0.96 (approximately).

Hence the change is of 4%, meaning that fuel A has the greater percentage change.

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Answer:

it's 13

Step-by-step explanation:

if f(13)= 3-2x and g (13) + 1 + x+5

Answer: 25.00$

Step-by-step explanation:50.00 take away 50% from it you have 25$

Answer:

$25

Step-by-step explanation:

It would be 25 because half of 50 is 25.

Answer:

99/250

Step-by-step explanation:

85 + 66 + 99 = 250. Now that you have the total it's at simple as figuring out the fraction for Wednesday. Rosalia gave out 99 flyers out of 250 total flyers. So now just convert that to fraction form, which would be 99/250.

#####

So you would do 37 + 12 = 49

and they 49 - 35 = 14 so

you would do 14 / 49 = ##### = ratio form

and you get ##### :)

Answer:

sin = 12 / 37

Step-by-step explanation:

Using trig functions, sin A = opp side / hypotenuse

sin = 12 / 37

The solution of the given conditions are;

a. Smallest possible value of 100 draws = 100

b. Largest possible value of 100 draws = 600

c. Average of the box = 3.6

d. The expected value of the sum = 360

e. Standard Error = 0.189

Given tickets: 5, 1, 2, 4, 3, and 6.

Value of n = 100

Question a :

Smallest possible value of 100 draws = 100 * (Least of the ticket values)

                                                              = 100 * 1

                                                              = 100

Question b :

Largest possible value of 100 draws = 100 * (Highest of the ticket values)

                                                             = 100 * 6

                                                             = 600

Question c :

Average of the box = (5+1+2+4+3+6) / 6

                                = 22/6

                                = 3.6

Question d :

The expected value of the sum = 100 * the Average of the box

                                                     = 100 * 3.6

                                                     = 360

Question e :

Given, SD = 1.89

Standard Error =?

Standard Error = SD/\(\sqrt{n}\)

SE = 1.89/√100

    = 1.89 / 10

    = 0.189

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2.64 is greater than 1.9

Answer:

D

Step-by-step explanation:

For a quadratic equation ax² +bx +c= 0, the quadratic formula is as below:

\(\boxed{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }\)

x² -12x +7= 0

\(x = \frac{ - ( - 12)± \sqrt{( - 12) {}^{2} - 4(1)(7) } }{2(1)} \)

\(x = \frac{12± \sqrt{144 - 28} }{2} \)

\(x = \frac{12± \sqrt{116} }{2} \)

\(x = \frac{12± \sqrt{4(29)} }{2} \)

\(x = \frac{12±( \sqrt{4})( \sqrt{29} )}{2} \)

\(x = \frac{12±2 \sqrt{29} }{2} \)

\(x = 6± \sqrt{29} \)

\(∴x = 6 + \sqrt{29} \: \: \: or \: \: \:x = 6 - \sqrt{29}\)

A function f from A to B is called one-to-one (or 1-1) if whenever f (a) = f (b) then a = b. No element of B is the image of more than one element in A.

a. To prove that if f ◦ g is onto, then f must also be onto, we assume f ◦ g is onto. This means that for every c ∈ C, there exists an a ∈ A such that (f ◦ g)(a) = f(g(a)) = c. Since g(a) ∈ B, we can say that for every c ∈ C, there exists a b = g(a) ∈ B such that f(b) = c. Hence, f is onto.

b. To prove that if f ◦ g is one-to-one, then g must also be one-to-one, we assume f ◦ g is one-to-one. This means that for any a1, a2 ∈ A, if g(a1) ≠ g(a2), then (f ◦ g)(a1) = f(g(a1)) ≠ f(g(a2)) = (f ◦ g)(a2). If g(a1) = g(a2), then we can conclude that a1 = a2 to maintain the one-to-one property of f ◦ g. Therefore, g must also be one-to-one.

c. If f ◦ g is a bijection, it means that it is both onto and one-to-one. From part a, we know that f must be onto. Now, to prove that g is onto if and only if f is one-to-one, we can use the contrapositive. If g is not onto, then there exists a b ∈ B that is not in the range of g. In that case, f(g(a)) cannot be one-to-one because there are multiple values of a that map to the same b. Similarly, if f is not one-to-one, then there exist b1, b2 ∈ B such that f(b1) = f(b2) but b1 ≠ b2. In this case, g(a) can't be one-to-one because there are multiple values of a that map to the same b. Therefore, g is onto if and only if f is one-to-one.

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Answer:

10 and 8

Step-by-step explanation:

must be in the ratio 5:4, 5 x 4 =20, so if you multiply by 2 the ratio is 10:8 (same thing). The least common multiple of 10 and 8 is 40 because you can do 10 x 4 = 40 and 8 x 5 = 40.

Answer:

Sebastian is going to choose design elements that include color, pattern, font, and image for the design of a sweatshirt for his dance team. There are 10 colors, 14 patterns, 12 fonts, and 9 images for him to choose from. (He will choose only one of each.)

How many different sweatshirt designs are possible?

Step-by-step explanation:

It's 4320

Answer:

a) 7(x + 2)

b) 9(x - 3)

c) 5(2y - 5)

d) 4(2n + 7)

e) -3(x + 9)

f) -6(x - 5)

Step-by-step explanation:

Factor both numbers and then find the greatest factor that both numbers hav e in common.

a)

7x + 14

7: 1, 7

14: 1, 2, 7, 14

The greatest common factor here is 7. Now, you can factor that out by dividing both numbers by 7 and then multiplying the whole thing by 7 to keep the value equal.

\(7x+14\\\frac{7}{7}x+\frac{14}{7}\\x+2\\\\7x+14=7(x+2)\)

b)

9x - 27

9: 1, 3, 9

27: 1 3, 9, 27

The greatest common factor here is 9.

\(9x-27\\x-3\\9(x-3)\)

c)

10y - 25

10: 1, 2, 5, 10

25: 1, 5, 25

The GCF here is 5.

\(10y-25\\2y-5\\5(2y-5)\)

d)

8n + 28

8: 1, 2, 4, 8

28: 1, 2, 4, 7, 14, 28

The GCF here is 4.

\(8n+28\\2n+7\\4(2n+7)\)

e)

-3x - 27

3: 1, 3

27: 1, 3, 9, 27

The GCF here is 3, but both -3 and -27 also have a common factor of -1. Multiply that with the 3, and you get -3.

\(-3x-27\\x+9\\-3(x+9)\)

f)

-6x + 30

6: 1, 2, 3, 6

30: 1, 2, 3, 5, 6, 10, 15, 30

The GCF here is 6.

\(-6x+30\\-x+5\\6(-x+5)\)

You could also factor out a -6 instead. It doesn't really matter, but I think it looks nicer like this:

\(-6(x-5)\)

Answer:

The answer is A

Step-by-step explanation:

This shows a mirroring effect over the vertical y axis.

Choices B and C are a translation (aka shifting)

Choice D is a reflection but over the horizontal x axis.

Answer:

x = 4

Step-by-step explanation:

2/3x + 1/6 = 4/3x

Easiest way to solve is by multiplying the entire equation by 6x.

6x (2/3x + 1/6 = 4/3x)

4 + x = 8

subtract 4 rom both sides

x=4

The area of a square is given by the formula A = s^2, where s is the length of a side of the square. If the area of the square is 100 sq meters, then:

s^2 = 100

Taking the square root of both sides, we get:

s = 10

Therefore, the length of a side of the square is 10 meters. Since all four sides of a square are equal, the perimeter of the square is:

4s = 4(10) = 40 meters

Answer:

  b)  -3

Step-by-step explanation:

You want the value of 'a' when the quadratic y = –3x² – 15x – 11 is written in the form y = a(x – h)² + k.

The leading coefficient in either form is the coefficient of x². It is the same in both forms: -3.