4a. Find the 120th term of the sequence: a1 = 5, d = 0.5 (3 marks) b. Find the sum of the first 120 terms of that sequence. (3 marks)

Answer:

I believe its C. If not then it is A. :D

Step-by-step explanation:

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Answer:

324

Step-by-step explanation:

if you do 36 times 9 you get 324

The equation that justifies  ten to the one third power equals the cube root of ten is ten to the one third power all raised to the third power equals ten to the one third times three power equals ten. Option B

we are to find [tex]10^{\frac{1}{3} } = \sqrt[3]{10}[/tex]

The justification has to be done with the use of the properties of powers as well as roots.

[tex]a^\frac{m}{n} = \sqrt[n]{a^m}[/tex]

then we would have:

[tex]\sqrt[3]{10} = \sqrt[3]{10^1} =10^\frac{1}{3}[/tex]

then we would have

[tex](10^\frac{1}{3} )^3\\\\= 10^\frac{3}{3}[/tex]

= 10

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The trigonometric ratios for the angle x in the triangle are given as follows:

The three trigonometric ratios are defined as follows:

In the right triangle in this problem, we have that d represents the hypotenuse, while the sides relative to angle x are given as follows:

These sides are used along with the definitions of each ratio to give the three trigonometric ratios of angle x.

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Answer:

The result of the integral is [tex]\frac{\pi}{4}(-\cos{16} + \frac{9})[/tex]

Step-by-step explanation:

Polar coordinates:

In polar coordinates, we have that:

[tex]x^2 + y^2 = r^2[/tex]

And

[tex]\int \int_{dA} f(x,y) da = \int \int f(r) r dr d\theta[/tex]

In this question:

[tex]\int \int_{dA} \sin{(x^2+y^2)} dA = \int \int_{dR} = \sin{r^2}r dr d\theta[/tex]

Region in the first quadrant between the circles with center the origin and radii 3 and 4

First quadrant means that [tex]\theta[/tex] ranges between [tex]0[/tex] and [tex]\frac{\pi}{2}[/tex]

Between these circles means that r ranges between 3 and 4. So

[tex]\int \int_{dR} = \sin{r^2}r dr d\theta = \int_{0}^{\frac{\pi}{2}} \int_{3}^{4} \sin{r^2} r dr d\theta[/tex]

Applying the inner integral:

[tex]\int_{3}^{4} \sin{r^2} r dr[/tex]

Using substitution, with [tex]u = r^2, du = 2rdr, dr = \frac{du}{2r}[/tex], and considering that the integral of the sine is minus cosine, we have:

[tex]-\frac{\cos{r^2}}{2}|_{3}{4} = \frac{1}{2}(-\cos{16} + \frac{9})[/tex]

Applying the outer integral:

[tex] \int_{0}^{\frac{\pi}{2}} \frac{1}{2}(-\cos{16} + \frac{9}) d\theta[/tex]

Has no factors of [tex]\theta[/tex], so the result is the constant multiplied by [tex]\theta[/tex], and then we apply the fundamental theorem.

[tex]\frac{\theta}{2}(-\cos{16} + \frac{9}) = \frac{\pi}{4}(-\cos{16} + \frac{9})[/tex]

The result of the integral is [tex]\frac{\pi}{4}(-\cos{16} + \frac{9})[/tex]

Answer:

You started correctly....

Step-by-step explanation:

d = c/n      Multiply both sides by 'n'

dn = c        now divide both sides of the equation by 'd'

n = c/d       Done.

Answer:

C

Step-by-step explanation:

The correct statement about the interpretation of the interval is

We are 95% confident that the mean number of hours worked per week for employed adults in the sample is between 41.18 hours and 42.63 hours.

Option D is the correct answer.

A confidence interval is a range of values that is likely to contain the true value of an unknown parameter, such as a population means or proportion, based on a sample of data from that population.

It is a statistical measure of the degree of uncertainty or precision associated with a statistical estimate.

We have,

We are 95% confident that the mean number of hours worked per week for employed adults in the sample is between 41.18 hours and 42.63 hours.

This is the correct interpretation of the 95% confidence interval given for the mean number of hours worked per week for all employed adults, based on the data collected from the random sample of 1,501 employed adults.

It means that if we were to take many random samples of 1,501 employed adults from the population and calculate the mean number of hours worked per week for each sample, we can be 95% confident that the true population mean lies between 41.18 hours and 42.63 hours.

Thus,

The correct statement about the interpretation of the interval is

We are 95% confident that the mean number of hours worked per week for employed adults in the sample is between 41.18 hours and 42.63 hours.

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Answer:

12mm

Step-by-step explanation:

circumference (distance around) is equal to πd.

here, if π is 3, we do 3 x the diameter, which is 4. 3 x 4 = 12mm

Answer:

C

Step-by-step explanation:

20 - 13 = 7

Answer:

C)

Step-by-step explanation:

7 + 13 = 20

The answer is C

Answer:

n

Step-by-step explanation:

[tex]\Bigg[\bigg[ [1/n]^{-1}\bigg]^{-1} \Bigg] ^{-1}[/tex]

=[tex]\bigg[ [1/n]^{-1}\bigg]^{(-1) (-1)}[/tex]

=[tex]\bigg[ [1/n]^{-1}\bigg]^{1}[/tex]

=[tex] [1/n]^{-1\times 1}[/tex]

=[tex] [1/n]^{-1}[/tex]

=[tex] [1/n^{-1}][/tex]

= n

Hope it helps you in your learning process

Answer:

x = 26

Step-by-step explanation:

180=(4x+10)+(x+40)

180 = 4x + x +10 + 40

180 - 50 = 5x

130 = 5x

130 / 5 = x

26 = x

Answer:

Vertex: (-1,-4)

Axis of Symmetry: x=-1

Step-by-step explanation:

The vertex is the minimum of the parabola, or (h,k), which is located at (-1,-4)

The axis of symmetry is a vertical line that marks the halfway point of the parabola, which is equal to x=h. Therefore, the axis of symmetry is x=-1

Answer:

I'd say A or D but I have a feeling it's A

The truth value of "If 3 + 4 = 12, then 3 + 2 = 6", is true.

Truth value is defined as whether the given proposition is either true or false, not both.

Here the proposition is of the form if p, then q.

Here p is the statement 3 + 4 = 12 and q is the statement 3 + 2 = 6.

Here, both of the propositions are false.

The truth value of 'if p, then q' is false only when p is true and q is false. In all other cases the truth value is true.

Here, since both of the statements are false, the truth value is true.

Hence the truth value of the given proposition is true.

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Answer: 40 cm

Step-by-step explanation:

The wooden frame needed = perimeter of the drawing
The length of the picture: 96 :8 = 12cm
The perimeter: (12 + 8) x 2 = 40 cm

Answer: y = -150x + 1800

Step-by-step explanation:

1. Find the linear slope of the line between two points.

(Change in Y)/(Change in X)

2. Write out an equation in point slope form.

(y-y1) = m(x-x1)

y-1800 = -150(x-0)

3. Simplify the equation and turn it into slope-intercept form.

y = -150x + 1800

Answer:

The function is neither even nor odd.

Step-by-step explanation:

A function is odd if:

f(x) = - (f-x)

A function is even if:

f(x) = f(-x)

A function is neither odd nor even if neither of the above two equalities are true, that is to say:

f(x) != f(-x) and f(x) != -f(-x)

Which is our case. (because substituting (-x) in place of (x) will not give us either of the equations. So the function is neither odd, nor even.

Answer:

It is.... 9! i got it right on edgunity 2022! sorry plase exscuse my spelling! Step-by-step explanation:

By analyzing the inequality and solving, the range of values of x for which the inequality is true is x € (-4/3, 4)

Domain is the input to the function.

Range is the output of the function.

First, we'll consider the case where |2x+1|-x-3<0.

|2x+1|-x-3<0

|2x+1|<x+3

Now we need to take the absolute value of 2x+1, we have two cases to consider:

Case 1:

2x + 1 > 0

2x + 1 < x + 3

2x - x < 3 + 1

x < 4

Case 2:

2x + 1 < 0

-2x - 1 < x + 3

-2x - 1 -x - 3 < 0

-3x - 4 < 0

x > -4/3

Now we must find the intersection between the two cases:

x € (-4/3, 4)

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The complete statement about the product of the polynomials is that:

The product of f(x) and g(x) is always a polynomial because the coefficients are real numbers and the exponents are whole numbers. Real numbers and whole numbers are closed under addition

From the question, we have the following parameters that can be used in our computation:

Polynomials f(x) and g(x)

When these polynomials are multiplied;

We get another polynomial

This is because, when you multiply two polynomials you get a sum of monomials.

A sum of monomials is always a polynomial

The sum of monomials stated above implies that the whole exponents and the real coefficients are closed under addition

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Answer:

(a)

[tex]List = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),\\(4,1),(4,2),(4,3).(4,4)\}[/tex]

(b) Sampling Distribution (Table)

[tex]\begin{array}{cccccccc}{\bar x} & {1} & {1.5} & {2} & {2.5} & {3} & {3.5} & {4} & {Pr}& {\frac{1}{16}} & {\frac{1}{8}} & {\frac{3}{16}} & {\frac{1}{4}} & {\frac{3}{16}} & {\frac{1}{8}} & {\frac{1}{16}} \ \end{array}[/tex]

(b) Sampling Distribution (Histogram)

See attachment

Step-by-step explanation:

Given

[tex]Set = \{1,2,3,4\}[/tex]

[tex]n =4[/tex]

Solving (a): A list of sample size 2

We have:

[tex]n =4[/tex]

[tex]r = 2[/tex] --- the sample size

First, we calculate the number of list using permutation (orders matter)

[tex]n(List) = n^r[/tex]

So, we have:

[tex]n(List) = 4^2[/tex]

[tex]n(List) = 16[/tex]

And the list is:

[tex]List = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),\\(4,1),(4,2),(4,3).(4,4)\}[/tex]

Solving (b): Sample distribution  of sample means of (a)

First, calculate the mean of each set using:

[tex]Mean = \frac{Sum}{2}[/tex]

So, we have:

[tex](1,1) \to \frac{1+1}{2} \to 1[/tex]       [tex](1,2) \to \frac{1+2}{2} \to 1.5[/tex]    [tex](1,3) \to \frac{1+3}{2} \to 2[/tex]    [tex](1,4) \to \frac{1+4}{2} \to 2.5[/tex]

[tex](2,1) \to \frac{2+1}{2} \to 1.5[/tex]    [tex](2,2) \to \frac{2+2}{2} \to 2[/tex]     [tex](2,3) \to \frac{2+3}{2} \to 2.5[/tex]    [tex](2,4) \to \frac{2+4}{2} \to 3[/tex]

[tex](3,1) \to \frac{3+1}{2} \to 2[/tex]       [tex](3,2) \to \frac{3+2}{2} \to 2.5[/tex]    [tex](3,3) \to \frac{3+3}{2} \to 3[/tex]    [tex](3,4) \to \frac{3+4}{2} \to 3.5[/tex]

[tex](4,1) \to \frac{4+1}{2} \to 2.5[/tex]    [tex](4,2) \to \frac{4+2}{2} \to 3[/tex]    [tex](4,3) \to \frac{4+3}{2} \to 3.5[/tex]    [tex](4,4) \to \frac{4+4}{2} \to 4[/tex]

Write out the sample means (sorted)

[tex]\bar x =\{1,1.5,1.5,2,2,2,2.5,2.5,2.5,2.5,3,3,3,3.5,3.5,4\}[/tex]

Construct a frequency table

[tex]\begin{array}{cc}{\bar x} & {f} & {1} & {1} & {1.5} & {2} & {2} & {3} & {2.5} & {4} & {3} & {3} & {3.5} &{2} & {4} & {1} & Total & 16\ \end{array}[/tex]

Construct the sampling distribution where the probability is calculated using: [tex]\frac{f}{Total}[/tex]

So, we have:

[tex]\begin{array}{cccccccc}{\bar x} & {1} & {1.5} & {2} & {2.5} & {3} & {3.5} & {4} & {Pr}& {\frac{1}{16}} & {\frac{1}{8}} & {\frac{3}{16}} & {\frac{1}{4}} & {\frac{3}{16}} & {\frac{1}{8}} & {\frac{1}{16}} \ \end{array}[/tex]

Answer:

B

Step-by-step explanation:

They basically give the answer.

Answer:

I am a bit confused. You stated that "Sabrina is going to make 1, batches of cookies" and you also wrote "for one batch of cookies, Sabrina needs 2 cups of flour." Hence, your answer should be 2 cups like you previously stated. However, I think that the question is wrong.

Step-by-step explanation:

The solution to the equations is

Addition : 2.49 + 6.7 = 9.19  ;  6.7 + 2.49 = 9.19

Subtraction : 9.19 - 6.7 = 2.49  ;  9.19 - 2.49 = 6.7

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the three decimals be represented as set x = { 2.49 , 6.7 , 9.19 }

Now , the addition facts are given by equations ,

2.49 + 6.7 = 9.19  be equation (1)

6.7 + 2.49 = 9.19   be equation (2)

And , the subtraction facts are given by the equations ,

9.19 - 6.7 = 2.49  be equation (3)

9.19 - 2.49 = 6.7  be equation (4)

Hence , the equations are solved

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Answer:

Step-by-step explanation:

The first equation:

The second equation:

Convert to slope-intercept form:

The graph is attached

Intersection point is (9, 7)

He doesn't need a truck. He can buy an aeroplane.

Answer:

Jorgen would still have enough money for the truck.

Step-by-step explanation:

Seeing as - (or negative) 0000000000000... isn't a real number and you put a comma after the 123456789, Jorgen would actually have enough for the truck. If you actually wanted the truck to be worth 123456789000000000... Jorgen would need to save up more than 9 octovigintillion to reach his goal of getting the truck, and that is one expensive truck.