given that f(x)= 7x-1 and g(x) = 7-x^2, calculate

Answer:

The sum of the series is 260.

------------------------

Each term of given series is expressed as:

This is an arithmetic progression with 13 terms and the first and last terms are:

Use the sum of the first terms of AP formula:

Answer:

The sum of the series is 260.

Step-by-step explanation:

[tex]\displaystyle \sum^{13}_{n=1}(3n-1)[/tex]

The given sigma notation means:

As (3n - 1) is linear, the series is arithmetic.

The first term (n = 1) is:

The second term (n = 2) is:

The third term (n = 3) is:

… and the last term (n = 13) is:

Therefore, we need to find 2 + 5 + 8 + ... + 38.

Since we know that the first term, a, is 2, the last term, l, is 38, and the common difference, d, is 3, we can use the sum of the first n terms formula to calculate the sum of the series of the first 13 terms.

[tex]\begin{aligned}\text{Using:} \quad S_{n}&=\dfrac{1}{2}n(a+l)\\\\\implies S_{13}&=\dfrac{1}{2}(13)(2+38)\\\\&=\dfrac{1}{2}(13)(40)\\\\ &=\dfrac{520}{2}\\\\&=260\end{aligned}[/tex]

Therefore, the sum of the series is 260.

Answer:

Step-by-step explanation:

S+8=D

S+D equals 94.

94/2= 45+2=47

47-8=39

Sydney is 39

Answer:

43

Step-by-step explanation:

94-8= 86

86/2= 43

43+8= 51

a:43

prove it :

51+43= 94

The total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 51 square units.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Divide the figure is into two rectangles and a triangle.

The points B, C, E, and F form a rectangle with base BC and height 7 units.

The points A, D, and G form a rectangle with base AG and height 5 units. The points C, D, and E form a triangle with base CE and height 4 units.

The length of BC is 4 - 4 = 0, so the area of the rectangle with base BC is 0.

The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.

Therefore, the total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6)  is 45 + 6 = 51 square units.

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A beginning employee will produce 3 items per day

An experienced employee will produce 17 items per day

Beginning employee

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

[tex]P\left(d\right)=3\ +\ 15\left(1-e^{-0.2d}\right)[/tex]

Next, we plot the graph (see attachment)

A beginner employee is represented as d = 0

From the graph, we have

P(0) = 3

An experienced employee

Using the graph as a guide, we have

The maximum number of production approximates to 17

This represents the number of items per day for an experienced employee

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The graph that represents the function f(x) = sqrt(x - 1) is given by the following option:

C. Graph Y.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

For this problem, the function is defined as f(x) = sqrt(x - 1), meaning that the parent square root function was moved one unit right, and thus the correct graph is given by graph Y.

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The simplified expression of  K-7 ft-X-8 ft-K-20 ft is -35ft-X

An expression is combination of variables, numbers and operators.

The given expression is K-7 ft-X-8 ft-K-20 ft

We need to simplify the given expression.

Add the like terms

-7 ft-X-8 ft-20 ft

-27ft-X-8 ft

-35ft-X

Hence, -35ft-X is the simplified expression of  K-7 ft-X-8 ft-K-20 ft

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Answer:

the last one

Step-by-step explanation:

first you have to distribute the 5 to all the variables.

when you do that you get

x---9x5=45

y---1x5=5

z---4x5=20

hope it helped

please mark brainliest

Answer:

Step-by-step explanation:

6x4=24

another way of writing it is using addition

add 4, six times

so

4+4+4+4+4+4

6 boxes each has four cakes

The required modulus is 41 .

A real and imaginary number combo with the formula a + bi , where

a and b are real numbers, and

i is the "unit imaginary number" √(−1)

a and b may also have zero values.

We are aware that complex numbers are made up of both actual and fictitious numbers.

The imaginary part, y, is multiplied by I the square root of -1, and the real part, x.

Modulus of x+iy = [tex]\sqrt{x^2 +y^2}[/tex]

Here, 9 and 40 are substituted for x and y.

i.e. 9+40i

We square the coefficients, add them, and then find the square root to obtain the modulus.

|9+40i| =[tex]\sqrt{9^2 +40^2} =\sqrt{81+1600} =\sqrt{1681}[/tex][tex]=41[/tex]

By long division method we find that

|9+40i| =41

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Answer:

[tex]x = -64\\\\y = -63\\\\z = -57[/tex]

Step-by-step explanation:

Diagonally opposite angles of a parallelogram are equal

Therefore

-y - 3 = 60

Add 3 to both sides; -3 terms on left side cancel out

- y = 60 + 3

- y = 63

Multiply both sides by -1

-1(-y) = -1(63)

y = - 63

Another property of a parallelogram is that the angles formed on either end by a side must equal 180°.

Rephrased,

The consecutive or adjacent angles are supplementary which means they add up to 180°

We see that -2z + 6 and 60° are adjacent angles
So

- 2z + 6 + 60 = 180

-2z + 66 = 180

-2z = 180 - 66

-2z = 114

z = 114/-2

z = -57

Similarly

-2x - 8 + 60 = 180

-2x + 52 = 180

-2x = 180 - 52

-2x = 128

x = 128/-2

x = -64

Answer:

Length = 26 feet; Width = 8 feet

Step-by-step explanation:

Let:

x = Length of rectangle

y = Width of rectangle

4 times the width = 4y

∴ 6 less than 4 times the width = 4y - 6

Perimeter of a rectangle = 2 × [Length + Width]
                                     68 = 2 × [(4y - 6) + y]

Expand the brackets or parenthesis by applying the Distributive Law and bring the like terms together:

                                    68 = 2 × [4y - 6 + y]
                                    68 = 2 × [5y - 6]

                                    68 = 10y - 12

                             68 + 12 = 10y

Isolate y by making it the subject of the equation:

                                  80 = 10y

                                    y = [tex]\frac{80}{10}[/tex]

                            y = Width of rectangle: 8 feet

Substitute y into the equation to calculate x:

       x = 4(8) - 6

         x = Length of rectangle = [tex](32 - 6)[/tex] feet

                                               x = 26 feet

The amount of money which would be in the account after 14 years is; $18,123.77.

The number of years it'd take for the money to double is; 13.86 years.

Since the given model of the account is;

A (t) = 9000e^0.05t

After 14 years, it follows that; t = 14.

Therefore;

A (14) = 9000e^0.05(14)

A (14) = 9000 × 2.013752707

A (14) = $18,123.77.

Also, the doubling time implies that; A (t) = 18,000

Therefore, 18000 = 9000e^0.05t

2 = e^0.05t

0.05t = ln (2)

t = ln (2) / 0.05

t = 13.86 years.

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The number of ways to arrange all the letters if the arrangement must end in a vowel is; 25,200.

The number of arrangement using only five letters is; 6720.

Since there are 5 options for the last letter, and there a 7 letters left to make an arrangement of 7.

Hence, The number of ways can you arrange all of the letters if the arrangement must end in a vowel is; 5 × 7!

= 5 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 25,200.

b). The number of arrangements if one can only use five letters is; ⁸P₅

= 6720.

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The perimeter of the triangle is 3x + 42.This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42.

The perimeter of a triangle is the sum of the lengths of its three sides. In this problem, the lengths of the three sides of the triangle are given as x + 15, 2x + 15, and x + 12, where x cannot equal zero. To calculate the perimeter of the triangle, we need  to add these three lengths together. This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42. Therefore, the perimeter of the triangle is 3x + 42.

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Answer: OD. 13

Step-by-step explanation:

Answer: If the ratio of first-class, second-class, and third-class passengers who survived the shipwreck is 101:59:89, then for every 101 first-class passengers who survived, there were 59 second-class and 89 third-class passengers who survived.

If the total number of first-class passengers was 202, then there were 202 * 59/101 = 118 second-class passengers who survived, and 202 * 89/101 = 180 third-class passengers who survived.

Therefore, the total number of passengers who survived the shipwreck is 202 + 118 + 180 = 500 passengers.

Step-by-step explanation:

Answer:

2/35

Step-by-step explanation:

[tex](-\frac{1}{5})(-\frac{2}{7}) = \frac{2}{35}[/tex]

The length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.

What is length?

The length of something measured from end to end or along its longest side, or the length of a specific section of something.

Convert the width from inches to feet:

Since there are 12 inches in a foot, the width in feet is:

9 / 12 = 0.75 ft

Calculate the length needed:

We know that the area of the gasket material is 19 sq ft, and the width is 0.75 ft. Let L be the length needed in feet. Then we have:

Area = Width x Length

19 sq ft = 0.75 ft x L

Solving for L, we get:

L = 19 sq ft / 0.75 ft

L = 25.33 ft (rounded to two decimal places)

Therefore, the length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.

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It can  be estimated that there are 395 penguins in the area.

Proportion is a mathematical comparison between two numbers.  According to proportion, two sets of specified numbers are said to be directly proportional to each other if they increase or decrease in the same ratio. Symbols of proportions include "::" and "=".

We approach this problem by doing a simple proportion.We can presume that the same proportion of penguins were tagged during mating season if the biologists discovered 11 tagged individuals out of 82 penguins.

The proportion should therefore be [tex]x:53=82:11[/tex]  where x represents the total number of penguins. By solving this proportion, we may determine what x is worth:

[tex]11x=53*82\\\\11x=4346\\\\x=395.0909[/tex]

Since there is no such thing as half a penguin, we can round off the answer to the nearest unit.

395 penguins are in the area according to our estimation.

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Answer:

x <-1.5

or

x <9.6

Step-by-step explanation:

12x + 7 < - 11

12x < -11 - 7

12x < - 18

12x/12 < -18/12

x = -1.5

OR.

5x - 8 > 40

5x > 40 + 8

5x > 48

5x/5 > 48/5

x > 9.6.

The margin of error for the confidence interval for a population is 0.71 ± 0.1.

The degree of error in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced likelihood of relying on a survey's or poll's findings, meaning that there will be less confidence in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.

The margin of error is given as:

MOE = U - L / 2

MOE = 0.81 - 0.61 / 2

MOE = 0.2 / 2

MOE = 0.1

The interval is:

Interval = P ± 0.1

Interval = (0.61 + 0.1) ± 0.1

Interval = 0.71 ± 0.1

Hence, the margin of error for the confidence interval for a population is 0.71 ± 0.1.

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Answer:

D

Step-by-step explanation:

using the rules of logarithms

• log a - log b = log ([tex]\frac{a}{b}[/tex] )

• log [tex]x^{n}[/tex] = nlog x

then

[tex]log_{4}[/tex] [tex]\frac{7}{x^3}[/tex]

= [tex]log_{4}[/tex] 7 - [tex]log_{4}[/tex] x³

= [tex]log_{4}[/tex] 7 - 3[tex]log_{4}[/tex] x

The rate at which its unemployment changes  is, 54.6 %

Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.

So formula for the rate is,

m = change in one quantity/change in another quantity = Δy/Δx

Given that,

The initial number of unemployed workers was 3.4 million and the final number was 5.5 million.

The change in the number of unemployed workers is:

5.5 million - 3.4 million = 2.1 million

To find the initial number of employed workers, we need to subtract the initial number of unemployed workers from the total population:

76 million - 3.4 million = 72.6 million

Now, we can calculate the initial unemployment rate as:

3.4 million / 72.6 million = 0.0469 or 4.69%

Similarly, the final unemployment rate is:

5.5 million / 76 million = 0.0724 or 7.24%

The change in the unemployment rate is:

(0.0724 - 0.0469) / 0.0469 ≈ 0.546 or 54.6%

Therefore, the unemployment rate increased by about 54.6%, which is closest to answer choice A. It increased by about 27%.

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The magnitude of the sum of these two vectors is 2.9486m

In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles.

The parameters that will help us to find the magnitude are

/OB/ = 3.14m

/OA/ = 2.71 m

Let /AB/= x

Sum of the angles is (-60+30)⁰ = 30⁰

Using cosine rule

x²= 3.14² +2.71² - 2*3.14*2.71 *cos30⁰

x² = 9.8596+7.3441 -8.5094

x²= 17.2037 -8.5094

x²= 8.6943

x = √8.6943

x = 2.9486

Therefore, the magnitude of the sum

of these two vectors is 2.9486m or 2.9m approximately

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The procedure for angle measurement by the protractor is mentioned below:

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

To measure an angle using a protractor, follow these steps:

1. Place the protractor on the angle you want to measure, with the base of the protractor aligned with one side of the angle.

2. Make sure the protractor is centered and level, with the zero-degree mark on the protractor aligned with the vertex (corner) of the angle.

3. Read the measurement of the angle from the protractor, where the second side of the angle intersects with the protractor scale. The measurement is usually given in degrees.

If the angle is larger than 180 degrees, you may need to use a full-circle protractor or measure the angle in two parts and add the measurements together.

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Answer:

3 lunch specials are possible.

Answer:

Step-by-step explanation:

There are several ways to approach this problem, but one common method is to use the complementary counting principle, which states that the number of favorable outcomes can be obtained by subtracting the number of unfavorable outcomes from the total number of outcomes. In this case, the favorable outcome is that the sample contains at least one defective phone, and the unfavorable outcome is that the sample contains no defective phones.

The number of possible samples of 4 phones out of 15 can be calculated as the number of combinations of 4 items from a set of 15, which can be written as:

C(15, 4) = 15! / (4! * (15 - 4)!) = 1365

The number of samples containing no defective phones can be calculated as the number of combinations of 4 phones out of the remaining 12 non-defective phones, which can be written as:

C(12, 4) = 12! / (4! * (12 - 4)!) = 495

So, the number of samples containing at least one defective phone can be calculated as:

1365 - 495 = 870

Therefore, out of the 1365 possible samples of 4 phones, 870 of them contain at least one defective phone.

A.) f(x-2)+f(2x)

To find this expression, we can substitute the definition of f(x) into the expression and simplify:

f(x-2)+f(2x) = [10(x-2)-4] + [10(2x)-4]

= 10x - 20 - 4 + 20x - 4

= 30x - 28

Therefore, f(x-2)+f(2x) = 30x - 28.

Given f(x) = 10x - 4, we need to find f(2a) - f(a).

f(2a) = 10(2a) - 4 = 20a - 4

f(a) = 10a - 4

Therefore,

f(2a) - f(a) = (20a - 4) - (10a - 4)

= 10a

Answer: f(2a) - f(a) = 10a. This means that the difference between the function evaluated at 2a and a is simply 10 times a.

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After 1 day, each woman would have made 8 scarves.

The expression that represents the number of scarves that Greta can make each day is:

Number of scarves she can make = number of scarves already made + (number of scarves she can make per day x number of days)

= 7 + d

The expression that represents the number of scarves that Evelyn can make each day is:

Number of days x number of scarves she can make per day

d x 8 = 8d

When both of them make the same number of scarves, the two expressions above would be equal.

7 + d = 8d

7 = 8d - d

7 = 7d

d = 7/7

d = 1 day

Number of scarves that would be made in 1 day = 8 x 1 = 8 scarves

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