Find the first six terms of each sequence. a n =2ⁿ - 1

The polygons that are regular are:

Triangle, Parallelogram, and Square.

Options A, B, and C are the correct answer.

It is a polygon having six faces.

The volume of a cube is side³.

We have,

A regular polygon is a polygon where all the sides are equal and the interior angles are equal.

Now,

Figure 1 is a triangle.

Figure 2 is a parallelogram.

Figure 3 is a square.

Figure 4 does not have the same side and the same interior angles.

Thus,
Figure 4 is not a regular polygon.

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Answer:

A and C

Step-by-step explanation:

Took the test :/

The integral, after converting to spherical coordinates, evaluates to 10√2\((√2 - 1)^7\).

To convert the integral to spherical coordinates, we need to express the integrand and the volume element in terms of spherical coordinates. In spherical coordinates, we have three variables: r (radius), θ (polar angle), and φ (azimuthal angle).

The integral is given by:

∫∫∫ 12\(V^4\) – \(x^{2}\)\(V^8\) – \(x^{2}\) – \(y^2\) dVx dy dz,

To express this in spherical coordinates, we use the following transformations:

x = r sinθ cosφ,

y = r sinθ sinφ,

z = r cosθ,

The Jacobian determinant of the coordinate transformation is \(r^2\) sinθ. The volume element dVx dy dz becomes \(r^2\) sinθ dr dθ dφ.

Substituting the transformed variables and the volume element into the integral, we have:

∫∫∫ 12\(r^4V^4\) – \(r^2\) \(sin^2θV^8\) – \(r^2\) (\(sin^2θ + sin^2φ\))\(r^2\) sinθ dr dθ dφ.

Simplifying the integrand and evaluating the integral over the appropriate ranges of r, θ, and φ, we find that the integral evaluates to 10√2\((√2 - 1)^7\).

Therefore, the answer to the problem is option C: 10(\(V^2\)-1)\(^7\).

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The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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To calculate the area of the enclosed region, we need to find the area between the curves y = 11x² and y = x² + 4. This can be done by integrating the difference between the two functions over their common interval of intersection.

By setting the two equations equal to each other and solving, we find the points of intersection as x = -2 and x = 1. Integrating the difference between the curves from x = -2 to x = 1 gives us the area of the enclosed region. The calculated area is 35 square units.

To find the area of the enclosed region, we need to determine the points of intersection between the curves y = 11x² and y = x² + 4. By setting these two equations equal to each other, we can solve for x:

11x² = x² + 4

10x² = 4

x² = 4/10

x = ±√(4/10)

x = ±√(2/5)

Since we are interested in the region enclosed by the curves, we consider the interval from x = -2 to x = 1 (as the curves intersect within this range).

To calculate the area of the enclosed region, we integrate the difference between the two functions over this interval:

Area = ∫(11x² - (x² + 4)) dx from -2 to 1

= ∫(10x² - 4) dx from -2 to 1

= [10/3 * x³ - 4x] evaluated from -2 to 1

= (10/3 * 1³ - 4 * 1) - (10/3 * (-2)³ - 4 * (-2))

= (10/3 - 4) - (10/3 * (-8) - 4 * (-2))

= (10/3 - 4) - (-80/3 + 8)

= (10/3 - 12/3) + (80/3 - 8)

= -2/3 + 80/3

= 78/3

= 26

Hence, the area of the enclosed region is 26 square units.

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12 + 34 = 46

x = 46

Answer:

Step-by-step explanation:

take 55 degree as reference angle

using tan rule

tan 55=opposite/adjacent

1.42=37/x

x=37/1.42

x=26.05

Answer: x

≤

−

4

or

x

≥

8

Step-by-step explanation:

Answer:

c = 7.45

Step-by-step explanation:

its easy and im smart that's why i got it

Responsible financial plan will take into consideration both short term and long term goals.

Given,

A financial plan is to be made.

A financial plan protects you from life's surprises. A Personal financial plan reduces doubt or uncertainty about your decisions and make adjustments to help overcome obstacles that could alter your lifestyle.

Now,

To make a better financial plan one should consider his/her short term as well long term goals.

Short term goals:

Short term goals include the goals that are needed to be achieved in the time frame 2-4 years.

For example,

One has to buy a car in the coming 3 years than this type of goals are considered short term and financial plan is to be made according to the price of car that is to be paid after 3 years while buying a car.

Long term goals:

Long term goals include the goals that are needed to be achieved in the time frame 10-12 years.

For example,

Retirement can be considered as long term plan for which one has to save a big amount of corpus so that after retirement his/her expenses will be well taken care off.

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Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.

Given: The total amount Jerome earned this weekend is $252.50.

           He earned every weekend = $80.

            He earned 15% of the cost of meals as tips by serving them.

To find: The cost of meals served by Jerome in this weekend.

The total amount, $252.50,  is the sum of the tips amount Jerome earned from serving meals and sum of the amount Jerome earned every weekend. To solve this, we must first translate the conditions of the problem, into an algebraic expression with a variable referring to the unknown quantity. This expression is then converted to an equation to find the value of the unknown quantity.

Let x be the cost of meals that Jerome served this weekend.

The equation for the problem statement becomes

\(\$80 + \frac{15}{100} x = \$252.50\\\\\)

Keeping only the x term on the left side of the equation and constant terms on the right side we get

\(\frac{15}{100} x = \$252.50 - \$80\\\\\frac{15}{100} x = \$172.50\\\\\\\)

Multiply both the sides of the equation by 100

\(\frac{15}{100} x \times 100 = \$172.50 \times 100\\\\15x = \$17250\)

Divide both sides of the equation by 15

\(\frac{15x}{15} = \frac{\$17250}{15}\\\\x = \$1150\)

Algebra is a field of mathematics in which letters are substituted for numbers, and an algebraic equation depicts a scale in which what is done on one side of the scale is likewise done on the other side of the scale, with the numbers acting as constants.

An equation is a mathematical statement that two expressions are equal. If it is an algebraic equation, two algebraic expressions has to have the same value  on either side of the equal sign.

A meaningful collection of numbers, variables, and signs (positive or negative) of operations that must make mathematical and logical sense is referred to as an algebraic expression.

Expressions contain any number of algebraic terms. They use signs of operation like addition, subtraction, multiplication, and division and also do not contain an equality sign (=).

Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.

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Speed is given by Distance/ Time taken

The Velocity is 7.27m/s in the direction of the runner

Answer:

A.7

Step-by-step explanation:

You first have to add 8 and -15

Then, find the absolute value

So, the answer is 7

Answer:

1/5 + 3/5 = 45 = 0.8

Step-by-step explanation:

Spelled result in words is four fifths.

True. Paired samples t-tests are used to compare the means of two related groups, such as a group of individuals tested before and after an intervention or treatment (pretest and post-test).

matched examples When comparing the means of two related groups, t-tests are a type of hypothesis test that pairs up each subject in one group with a subject in the other. The same group of people is assessed twice in a pretest-posttest design—once before and once after an intervention or treatment.
Paired samples t-tests do look at one group of individuals tested twice, such as with a pretest and post-test. This type of t-test is used to compare the means of the two related samples and analyze the difference between the two testing instances.

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Answer:

1/2

Step-by-step explanation:

There are three odd and three even numbers on the die which would make 3/6 and simplified it is 1/2.

Answer:

it would be a 50% chance or 1/2 of rolling an odd nummber

Step-by-step explanation:

Answer:

No, he won't have enough money to make the purchase.

The sales tax is 2.9352

The total amount for the purchase is 51.8552

So, $50 is not enough to make the purchase.

Step-by-step explanation:

I used a calculator.

Answer:

Step-by-step explanation:

Lines with different slopes intersect at some point. That point is the solution of the system represented by those lines.

Vertical and horizontal lines have different slopes and therefore will intersect and this will result in one solution.

Correct choice is C

Answer:

\(\large \boxed{\sf \ \ \ p=-11 \ \ \ }\)

Step-by-step explanation:

Hello,

\(\alpha \text{ and } \beta \text{ are the roots of the following equation}\)

   \(2x^2+6x-7=p\)

It means that

   \(2\alpha^2+6\alpha-7=p \\\\2\beta ^2+6\beta -7=p \\\\\)

And we know that

\(\alpha= 2\cdot \beta\)

So we got two equations

   \(2(2\beta)^2+6\cdot 2 \cdot \beta -7=p \\\\<=>8\beta^2+12\beta -7=p\\\\ and \ 2\beta ^2+6\beta -7=p \ So \\\\\\8\beta^2+12\beta -7 = 2\beta ^2+6\beta -7\\\\<=>6\beta^2+6\beta =0\\\\<=>\beta(\beta+1)=0\\\\<=> \beta =0 \ or \ \beta=-1\)

For \(\beta =0, \ \ \alpha =0, \ \ p = -7\)

For \(\beta =-1, \ \ \alpha =-2, \ \ p= 2-6-7=-11, \ p=2*4-12-7=-11\)

I assume that we are after two different roots so the solution for p is p=-11

b) \(\alpha +2 =-2+2=0 \ and \ \beta+2=-1+2=1\)

So a quadratic equation with the expected roots  is

\(x(x-1)=x^2-x\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

14 \(u^2\)

Step-by-step explanation:

The attached image shows the diagram of the triangle drawn on the Cartesian plane.

We can see that it has the following measures:

base: \(b=7u\)

height: \(h=4u\)

the area of a triangle is given by the formula:

\(A=\frac{b*h}{2}\)

substituting the values:

\(A=\frac{(7u)(4u)}{2}\\ \\A=\frac{28u^2}{2} \\\\A=14u^2\)

the area, in square units, of the triangle is 14

Answer:

Step-by-step explanation:

110+z=180  180-110=70  z=70

y=110  x=70

Answer:

0

Step-by-step explanation:

The slope is the difference in y values / difference in x values of the points.

For (-9, 5), and (-17, 5) slope is zero because the y-coordinates are the same.

m= (5-5)/ (-17- -9) = 0/ 8 = 0

The line has the slope 0 so is a horizontal line

Answer:

\(\sqrt{16}\sqrt{11}\)

Step-by-step explanation:

\(\sqrt{176}\implies \sqrt{16\cdot 11}\implies \sqrt{4^2\cdot 11}\implies 4\sqrt{11}\)

The probability of selecting 4 defective calculators is 0.0009.

The probability of selecting 4 defective calculators out of a group containing 47 defective and 29 non-defective calculators can be calculated using the formula for a combination. The formula is n!/r!(n-r)! where n is the total number of items and r is the number of items being selected. In this case, n is 76 (47 defective + 29 non-defective) and r is 4. Therefore, the probability of selecting 4 defective calculators is 0.0009. To round this answer to four decimal places, the answer is 0.0009.

To calculate this answer, the first step is to calculate the total number of combinations that can be made using 4 items out of 76 items. This is calculated using the formula n!/r!(n-r)!. The numerator, n!, is equal to 76! which is equal to 5.43e+102. The denominator, r!(n-r)!, is equal to 4!(76-4)! which is equal to 5.90e+09. By dividing the numerator by the denominator, the probability of selecting 4 defective calculators is 0.0009. To round this answer to four decimal places, the answer is 0.0009.

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Let \(X(s)\) and \(Y(s)\) denote the Laplace transforms of \(x(t)\) and \(y(t)\).

Taking the Laplace transform of both sides of both equations, we have

\(\dfrac{dx}{dt} + 3x + \dfrac{dy}{dt} = 1 \implies \left(sX(s) - x(0)\right) + 3X(s) + \left(sY(s) - y(0)\right) = \dfrac1s \\\\ \implies (s+3) X(s) + s Y(s) = \dfrac1s\)

\(\dfrac{dx}{dt} - x + \dfrac{dy}{dt} = e^t \implies \left(sX(s) - x(0)\right) - X(s) + \left(sY(s) - y(0)\right) = \dfrac1{s-1} \\\\ \implies (s-1) X(s) + s Y(s) = \dfrac1{s-1}\)

Eliminating \(Y(s)\), we get

\(\left((s+3) X(s) + s Y(s)\right) - \left((s-1) X(s) + s Y(s)\right) = \dfrac1s - \dfrac1{s-1} \\\\ \implies X(s) = \dfrac14 \left(\dfrac1s - \dfrac1{s-1}\right)\)

Take the inverse transform of both sides to solve for \(x(t)\).

\(\boxed{x(t) = \dfrac14 (1 - e^t)}\)

Solve for \(Y(s)\).

\((s - 1) X(s) + s Y(s) = \dfrac1{s-1} \implies -\dfrac1{4s} + s Y(s) = \dfrac1{s-1} \\\\ \implies s Y(s) = \dfrac1{s-1} + \dfrac1{4s} \\\\ \implies Y(s) = \dfrac1{s(s-1)} + \dfrac1{4s^2} \\\\ \implies Y(s) = \dfrac1{s-1} - \dfrac1s + \dfrac1{4s^2}\)

Taking the inverse transform of both sides, we get

\(\boxed{y(t) = e^t - 1 + \dfrac14 t}\)

Answer:

E=20, F=50, G=110

Step-by-step explanation:

E=2/18*180=20

F=5/18*180=50

G=180-20-50

  =110

it A

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

C and A

Step-by-step explanation:

The required GCF is 8.

The greatest common factor is that greatest number from the factors which divides the number completely.

For example take numbers 12 and 16.

The factors of 12 are 2×2×3.

And the factors of 16 are 2×2×2×2.

We can clearly see that the common factors are 2×2 which gives 4. So, 4 is the greatest common factor which divides both 12 and 16.

Here it is given to find the greatest common factor of 16 and 40.

Factors of 16 = 2×2×2×2

Factors of 40 = 2×2×2×5

We can see clearly the common factors are 2×2×2 which gives 8.

So, 8 is the greatest common factor.

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