The first three terms of a geometric sequence are as follows.
-7, 14, -28
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
-7, 14, -28, 00

Answer:

third one

Step-by-step explanation:

the third one should be the answer

step 4 came out becoz of taking the common factor(x+1) and combining x2 and (-16)

Step 5 came out becoz of the theory of (a^2-b^2) = (a+b)(a-b)

ps 16 here is equal to 4^2

Answer:

True

Step-by-step explanation:

expression

3x+5

equation

3x+5 =0

To show that the vector field F(x, y, z) = (-2y, -2x, 7z) is a gradient vector field, we need to find a scalar function V(x, y, z) such that its gradient, ∇V, is equal to F. We can determine the function V by integrating the components of F with respect to their respective variables.

Let's find the function V(x, y, z) by integrating the components of F(x, y, z) = (-2y, -2x, 7z) with respect to their variables.
∫-2y dx = -2xy + g(y, z)
∫-2x dy = -2xy + h(x, z)
∫7z dz = 7/2 z^2 + k(x, y)
We can see that -2xy is a common term in the first two integrals. Similarly, we observe that there are no common terms between the first and third integrals, as well as the second and third integrals. Therefore, we can assume that g(y, z) = h(x, z) = 0, since they will cancel out in the subsequent calculations.
Now, we can rewrite the integrals:
∫-2y dx = -2xy + C1(y, z)
∫-2x dy = -2xy + C2(x, z)
∫7z dz = 7/2 z^2 + C3(x, y)
By comparing these integrals with the components of the gradient vector, we can conclude that ∇V = (-2y, -2x, 7z), where V(x, y, z) = -xy + 7/2 z^2 + C.
To determine the constant C, we use the condition V(0, 0, 0) = 0:
V(0, 0, 0) = -(0)(0) + 7/2 (0)^2 + C = 0
C = 0
Therefore, the function V(x, y, z) that satisfies V(0, 0, 0) = 0 is V(x, y, z) = -xy + 7/2 z^2. Thus, the vector field F(x, y, z) = (-2y, -2x, 7z) is indeed a gradient vector field F = ∇V.

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Answer:

13212

Step-by-step explanation:

An angle is fefined as the point where two lines meet. The measure of the segment FB is 21 units.

This theorem equates their relative lengths  of the triangle to the relative lengths of the other two sides of the triangle.

From the given figure, the line CF bisects the angle DFB, this shows that the line segment DF is equal to FB.

Given the following

DF = 4x + 9

FB = 6x + 3

Equate

DF = FB

4x + 9 = 6x + 3

4x - 6x = 3 - 9

-2x = -6

x = 3

Determine the length of FB

FB = 6x + 3

FB = 6(3) + 3

FB = 21 units

Hence the length of FB from the given figure is 21units.

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The one-sample z-statistic for evaluating the hypothesis that unvaccinated people get COVID-19 is not 0.03 is -85.7. This statistic tested the hypothesis that unvaccinated people do not get COVID-19 at 0.03%.

In order to compute the one-sample z-statistic, we must first do a comparison between the observed proportion of COVID-19 instances in the placebo group and the expected proportion of 0.03. (p - p0) / [(p0(1-p0)) / n is the formula for the one-sample z-statistic. In this formula, p represents the actual proportion, p0 represents the predicted proportion, and n represents the sample size.

The observed proportion of COVID-19 instances among those who received the placebo is 162/18325 less than 0.0088. According to the received wisdom, the proportion that should be anticipated is 0.03. The total number of people sampled is 18325. After entering these numbers into the formula, we receive the following results:

z = (0.0088 - 0.03) / √[(0.03(1-0.03)) / 18325] ≈ (-0.0212) / √[(0.0291) / 18325] ≈ -85.7

As a result, the value of the z-statistic for just one sample is about -85.7. This demonstrates that the observed proportion of COVID-19 cases in the unvaccinated population is significantly different from the expected proportion of COVID-19 cases in that population.

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Answer:

Solution

20x+8

Step-by-step explanation:

hope this helps you

Answer: 28

Step-by-step explanation:

First you do 9-5                {10+[5*4]-2}

Then you multiply that by 5 {10+20-2}

After that you add 10 +20     {30-2}

Then you Subtract 30-2

Chance is a term used to represent the percentage of time a specific result is expected to occur when the same basic procedure is repeated over and over again, where each repetition is independent.

Chance is a term that is used to describe the probability that a certain outcome will occur given a set of fundamental instructions repeated again with each repetition being independent.

Ultimately, this means the number of times a result of an event occurs when repeated over a number of times is chance.

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The function g(x) is g(x) = 6(1/3)^-x

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

f(x) = 6(one-third) Superscript x

Rewrite as

f(x) = 6(1/3)^x

The transformation rule is given as

Reflection across the y-axis

This is represented as

g(x) = f(-x)

So, we have

g(x) = 6(1/3)^-x

Hence, the function is g(x) = 6(1/3)^-x

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Answer:

x + y + 90 = 180

x = 67

y = 23

Step-by-step explanation:

x + y + 90 = 180

x + 2 = 3y

x + y = 90

x - 3y = -2

      x  +  y = 90

(+)  -x + 3y =  2

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

            4y = 92

y = 23

x + y = 90

x + 23 = 90

x = 67

Step-by-step explanation:

Let's call the shorter base of the trapezoid "b1", the longer base "b2", and the height "h". We can use the formula for the surface area of a right prism to set up an equation:

Surface area of prism = 2(base area) + (lateral area) = 1280

The base area is the area of the trapezoid, which is given by:

(base area) = (1/2)(b1 + b2)h

The lateral area is the area of the four rectangular faces of the prism, which are all congruent. Each face has an area equal to the product of the height and the length of one of the legs of the trapezoid, so the lateral area is:

(lateral area) = 4hl

where l is the length of one of the legs of the trapezoid.

Substituting these expressions into the formula for the surface area of the prism, we get:

2[(1/2)(b1 + b2)h] + 4hl = 1280

Simplifying and rearranging, we get:

h(b1 + b2) + 2hl = 1280

We also know that the sum of the lengths of the legs of the trapezoid is 52 feet, which means:

l1 + l2 = 52

But we can express l1 and l2 in terms of b1 and b2 using the formula for the area of a trapezoid:

(base area) = (1/2)(b1 + b2)h = (1/2)(l1 + l2)h

Simplifying, we get:

b1 + b2 = (l1 + l2)h

Substituting this into the previous equation, we get:

h[(l1 + l2)h] + 2hl = 1280

Simplifying, we get:

h^2(l1 + l2) + 2hl = 1280

Substituting l1 + l2 = 52, we get:

h^2(52) + 2hl = 1280

This is a quadratic equation in h. We can solve it using the quadratic formula:

h = [-2l ± sqrt(4l^2 + 4h^2(52)(1280 - 2hl))] / 2(52)

Simplifying and factoring out a 2, we get:

h = [-l ± sqrt(l^2 + h^2(1280 - 2hl))] / 52

We have two possible solutions for h, but one of them is negative, which doesn't make sense in the context of the problem. So we can discard the negative solution and focus on the positive one:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

We don't know the exact value of h yet, but we can use this equation to set up a system of equations that we can solve for h. Specifically, we can use the fact that the legs of the trapezoid add up to 52 feet to solve for l in terms of b1 and b2:

l = 52 - (b1 + b2)

Substituting this into the equation for h, we get:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

h = [-52 + (b1 + b2) + sqrt((52 - (b1 + b2))^2 + h^2(1280 - 2h(b1 + b

Answer:

f(n) = 2 * 4^n

Step-by-step explanation:

The initial population = a male and a female = 2

The population quadruple every year, this means, a multiplication by 4 every year.

Hence, we have :

f(n) = (Initial population * multiple^years)

f(n) = 2 * 4^n

Organizing the survey results in a two-way table with the marginal frequencies is as follows:

                                                              Number of        Marginal

                                                           Respondents   Frequencies

Have Played a Musical Instrument            118                56.5%

Have Participated in a Sport                      57                 27.3%

Have not Played or Participated                34                 16.3%

Total                                                          209

A two-way frequency table shows the relationships between two categorical data.

A two-way frequency table can be used to show the marginal frequencies of responses for a given condition or the ratio of the joint frequencies to the corresponding marginal frequency.

The total number of students surveyed = 397

The total number of respondents = 209 (118 + 57 + 34)

The number of students who have played a musical instrument = 118

The number of students who have participated in a sport = 57

The number of students who have not played a musical instrument or participated in a sport = 34

                                                              Number of        Marginal

                                                           Respondents   Frequencies

Have Played a Musical Instrument            118                56.5% (118/209)

Have Participated in a Sport                      57                 27.3% (57/209)

Have not Played or Participated                34                 16.3% (34/209)

Total                                                          209

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Answer:

\(y = 2x - 5 - - - eqn \: (i) \\ 5x - 2y = 19 - - - eqn \: (ii) \\ substitute \: for \: y \: in \: eqn \: (ii) \: from \: eqn \: (i) \\ 5x - 2(2x - 5) = 19 \\ 5x - 4x + 10 = 19 \\ x + 10 = 19 \\ x = 19 - 10 \\ x = 9 \\ from \: eqn \: (i) \\ y = 2x - 5 \\ y = (2 \times 9) - 5 \\ y = 18 - 5 \\ y = 13\)

Answer:

A rational number is a number such as -3/7 that can be expressed as the quotient or fraction a/b of two integers, a numerator q and a non-zero denominator b. Every integer is a rational number: for example, 10 = 10/1.

No.

\(5 \frac{1}{3} \)

So we can turn from 5 1/3 to 16/3

Note that 16/3 makes infinity decimal but if the infinity decimal can be turnt into a fraction, it will be classified as rational number.

Answer:

0.34

Step-by-step explanation:

To solve the problem, we can use the equations for the axial deformation of a bar under axial load:

ε = δ/L

σ = Eε

where ε is the strain, δ is the displacement, L is the length of the bar, σ is the stress, and E is the modulus of elasticity.

(a) To find the displacements at points B and C, we can use the equation:

δ = PL/AE

where P is the axial load, L is the length of the bar, A is the cross-sectional area, and E is the modulus of elasticity.

For point B, the axial load is 5000 lb and the cross-sectional area is 1 sq in. The length of the bar is 10 in (15 in - 5 in). The modulus of elasticity is 30x10^6 psi. Therefore, the displacement at point B is:

δB = (5000 lb x 10 in) / (1 sq in x 30x10^6 psi) = 0.0167 in

For point C, the axial load is 2000 lb and the cross-sectional area is 0.25 sq in. The length of the bar is 12 in (15 in - 3 in). The modulus of elasticity is 30x10^6 psi. Therefore, the displacement at point C is:

δC = (2000 lb x 12 in) / (0.25 sq in x 30x10^6 psi) = 0.008 in

(b) To find the axial load in each shaft, we can use the equation:

P = σA

where P is the axial load, σ is the stress, and A is the cross-sectional area.

For shaft AB, the stress is:

σAB = δB/LAB x E = 0.0167 in / 10 in x 30x10^6 psi = 50 psi

The cross-sectional area is 1 sq in. Therefore, the axial load in shaft AB is:

PAB = σAB x AAB = 50 psi x 1 sq in = 50 lb

For shaft BC, the stress is:

σBC = (δC - δB)/LBC x E = (0.008 in - 0.0167 in) / 3 in x 30x10^6 psi = -25 psi

The cross-sectional area is 0.196 sq in (π(0.375 in)^2 / 4). Therefore, the axial load in shaft BC is:

PBC = σBC x ABC = -25 psi x 0.196 sq in = -4.9 lb

The negative sign indicates that the load is compressive.

For shaft CD, the stress is:

σCD = -δC/LCD x E = -0.008 in / 3 in x 30x10^6 psi = -80 psi

The cross-sectional area is 0.049 sq in (π(0.25 in)^2 / 4). Therefore, the axial load in shaft CD is:

PCD = σCD x ACD = -80 psi x 0.049 sq in = -3.92 lb

The negative sign indicates that the load is compressive.

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The solution for x in the inequality expression is x < -8

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

-4x+5>37

Subtract 5 from both sides of the inequality

So, we have

-4x + 5 - 5 >37 - 5

Evaluate the like terms

This gives

-4x > 32

Divide both sides by -4

x < -8

Hence, the solution is x < -8

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We must invest  396.90, at an interest rate of 8.

Hobby is the fee you pay to borrow cash or the cost you price to lend money. interest is most customarily contemplated as an annual percent of the amount of a mortgage. This percent is called the interest price on the loan. for example, a bank will pay you interest when you deposit your money in a savings account.

The forms of interest consist of simple hobby, accumulated hobby, and compounding hobby. while money is borrowed, generally via the way of a loan, the borrower is required to pay the interest agreed upon by the two events.

There has been a energetic hobby inside the elections inside the final  weeks. She'd appreciated him in the beginning, but soon lost interest. Synonyms: significance, issue, importance, moment extra Synonyms of interest. countable noun.

value = Amount*(1+i)n

                     = 500*(1+.08)3

                         = 500*0.7938

                  Present value = 396.90

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To calculate the amount of glass needed to cover the office with a parallelogram-shaped glass façade, we need to know the measurements of the structure. Specifically, we need to know the length of the base and the height of the parallelogram.

Once we have those measurements, we can use the formula for the area of a parallelogram, which is:
Area = base x height

In this case, the area of the parallelogram will give us the amount of glass needed to cover the façade.
For example, if the base of the parallelogram is 10 meters and the height is 5 meters, the area of the parallelogram is:
Area = 10 meters x 5 meters = 50 square meters

Therefore, we would need 50 square meters of glass to cover the parallelogram-shaped façade of the office.

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Answer: -17/12 or -1 5/12 or 1 5/12

Step-by-step explanation:

convert both equations into improper fractions

− 55/12 - (-19/6)

-55/12+19/6

find the common factor of the denominators

-55/12 + 38/12

-17/12

-1 5/12

500 miles = 248 + 62(m/h)• Time

then Time T is = ( 500 - 248)/ 62 = 4.1 hours

Answer:

300

Step-by-step explanation:

5:6

300:360

You do 360/6=60

Then you do 60*5=300

Hope this helps!!

Answer:

300

Step-by-step explanation:

6 times X = 360

360/6 = 60

60 times 5 = 300

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Answer:

x = 7

y = 2

Step-by-step explanation:

In the above question, we are given 2 equations which are simultaneous. To solve this equation, we have to find the values of x and y

x + 3y = 13 ........ Equation 1

x - y = 5...........Equation 2

From Equation 2,

x = 5 + y

Substitute 5 + y for x in Equation 1

x + 3y = 13 ........ Equation 1

5 + y + 3y = 13

5 + 4y = 13

4y = 13 - 5

4y = 8

y = 8/4

y = 2

Since y = 2, substitute , 2 for y in Equation 2

x - y = 5...........Equation 2

x - 2 = 5

x = 5 + 2

x = 7

Therefore, x = 7 and y = 2

Answer:

12 x 9 = 108

Step-by-step explanation:

Just multiply the 2 given lengths when finding AREA of a rectangle.

Answer:

D.108

Step-by-step explanation:

Answer:

1,000,000

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

Hi,

4 + 2x - x = -3x - 4

4 + x = -3x - 4

x = -3x - 8

4x = -8

x = -2

Hope this helps :)

Answer:

161° and 19°

Step-by-step explanation:

supplementary angles =180

(142+x)+(x)=180

142+2x=180

2x=180-142

2x=38

x=19

142+19=161

Answer:

196, 245, 294

Step-by-step explanation:

sum the parts of the ratio, 4 + 6 + 6 = 15 parts

Divide the total by 15 to find the value of one part of the ratio

735 ÷ 15 = 49 ← value of 1 part of the ratio, thus

4 parts = 4 × 49 = 196

5 parts = 5 × 49 = 245

6 parts = 6 × 49 = 294

Answer:

5x⁴

Step-by-step explanation:

10x⁸÷2x⁴=

5x⁴