Make a two column proof to solve 1\2 (4x-6) =15

Answer:

127

Step-by-step explanation:

so h(g(-5)) means that solve the function in a specific way. This means that solve for function h but the x is the answer to function g when x is -5. So first what u do is solve for g. Plug -5 in so u get -5-3 which is -8. Then u plug in -8 to function h. U have 2(-8)^2-1. Then u solve the square which is 64. Then u multiply that by 2 to get 128. Then u minus one to get ure final answer of 127. Hope this helps :D

The formula for K in terms of F is \(K = \frac{5}{9} (F-32) + 273\)

The given expression:

\(F = \frac{9}{5} (K-273) + 32\)

To find the formula for K

The formula for K is obtained by making K the subject of the formula as shown below:

\(F = \frac{9}{5} (K-273) + 32\)

subtract 32 from LHS.

\(F-32 = \frac{9}{5} (K-273)\)

multiply 5 with LHS

\(5(F-32) = 9(K-273)\)

Take numerator 9 to LHS

\(\frac{5}{9}(F-32) = K-273\)

take -273 from RHS to LHS

\(\frac{5}{9}(F-32) + 273 = K\)

Thus the formula for K in terms of F is \(K = \frac{5}{9} (F-32) + 273\)

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Answer:

Step-by-step explanation: is (2 b)

Answer:

32

Step-by-step explanation:

8*4=32

For f (t) = teat for t ≥ 0, the Laplace transform of f (t) is 1 / (s+a)^2.

The Laplace transform of f(t) is defined as:

Lf(t) = ∫[0,∞) f(t) e^(-st) dt

Substituting f(t) into the above equation, we get:

Lf(t) = ∫[0,∞) t e^(-at) e^(-st) dt

We can simplify this by factoring out e^(-at) from the integral, giving:

Lf(t) = ∫[0,∞) t e^(-(a+s)t) dt

We can now integrate by parts, using u = t and dv = e^(-(a+s)t) dt:

Lf(t) = [-t e^(-(a+s)t) / (a+s)] [0,∞) + ∫[0,∞) e^(-(a+s)t) dt/(a+s)

The first term evaluates to 0, since t e^(-(a+s)t) approaches 0 as t approaches infinity. The second term simplifies to:

Lf(t) = [1 / (a+s)] ∫[0,∞) e^(-(a+s)t) dt

This integral is a standard Laplace transform, so we can substitute in its value from the Laplace transform table:

Lf(t) = [1 / (a+s)] * [1 / (a+s)]

Lf(t) = 1 / (s+a)^2

Therefore, the Laplace transform of f(t) is 1 / (s+a)^2.

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Answer:

2

Step-by-step explanation:

We want to find the value of p/2 - 5 when p = 14.

Simply put 14 in the place of p and solve:

14/2 - 5

7 - 5 = 2

The value of 2.

A fraction is a smaller part of a whole number.

A whole number is defined as the number that is natural and it includes numbers such as 0, 1,2,3,4,5,6,7,8,9, 10. This means that is doesn't contain numbers that has decimal points or fractions such as. 1.5 or 1½ respectively.

A fraction is defined as the part of a whole value such as 1/4 which is 25% of 1. This means that it is the smaller part of a whole number.

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Answer:

Z=23

Step-by-step explanation:

Multiply both sides of the equation by 15, the least common multiple of 3,5.

Use the distributive property to multiply 5 by 2z−1.

Use the distributive property to multiply −3 by 3z+1.

Combine 10z and −9z to get z.

Subtract 3 from −5 to get −8.

Add 8 to both sides.

Add 15 and 8 to get 23.

The correct answer is option D. No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is approximately normal.Researchers investigated whether there is a difference between two headache medications, R and S.

Researchers measured the mean times required to obtain relief from a headache for patients taking one of the medications. From a random sample of 75 people with chronic headaches, 38 were randomly assigned to medication R and the remaining 37 were assigned to medication S. The time, in minutes, until each person experienced relief from a headache was recorded. The sample mean times were calculated for each medication.To construct a confidence interval, we require that some conditions are satisfied. The assumptions that should be met for inference with a confidence interval for the difference in population means are as follows:The data is independent;The data in each group should be roughly normally distributed;Both groups have the same variance, and each group should have a large enough sample size so that the central limit theorem (CLT) holds. The CLT holds for the difference in the sample means since both samples are taken from a population that is normally distributed. We can also assume that the sample size is large enough to use the t-distribution since each sample has more than 30 observations. As a result, all of the conditions have been met. As a result, we may employ a t-distribution to make inferences about the population difference between the two headache medications.

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The regression equation is y = 0.9x+ 7.5

given that

xi:  2   6    9    13    20

Yi : 7   18   9    26   23  

from the given data we have:

∑x = 2+6+9+13+20 = 50

∑y = 7+18+9+26+23 = 83

Also, we need to calculate:

∑xy = 2 × 7+ 6 × 18+ 9× 9+ 13 × 26+ 20×23 = 1001

∑\(x^{2}\) = \(2^{2}\) + \(6^{2}\) + \(9^{2}\) + \(13^{2}\) + \(20^{2}\) = 690

∑\(y^{2}\)= \(7^{2}\) +  \(18^{2}\) + \(9^{2}\) + \(26^{2}\) + \(23^{2}\) = 1659

the slope b is calculated:

b = ∑xy - ∑x × ∑y/n ÷ ∑\(x^{2}\) - (∑x)^2 /n

now we need to substitute above values in the equation:

b = 1001 - 50×83 /5 ÷ 690 - (50)^2/5

b= 0.9

the y-intercept (a) is :

a = y - bx

where

y = ∑y/n = 83/5 = 16.6

x = ∑x/n = 50/5 = 10

now substitute these values

a = 16.5 - 0.9 × 10

a = 7.5

the regression equation:

y = bx + a

now ,

y = 0.9x+ 7.5

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Answer:

mary should be 29 while her daughter 6.

Product means the number that you get to by multiplying two or more other numbers together. so when u multiply 29 and 6 u get 174.

Answer:

Mary is 29 and her daughter is 6

Step-by-step explanation:

when Mary was 23, her daughter was 0

                  so the product is           23 × 0 = 0

when Mary was 24, her daughter was 1

                                                          23 × 1 = 1

when Mary was 25, her daughter was 2

                                                          25 × 2 = 50

·

·

·

when Mary was 29, her daughter was 6

                                                          29 × 6 = 174

∴ Mary is 29 and her daughter is 6

(im sure there is a way easier method to find this ;-; but this is how i did it)

Answer:

N = 2

Step-by-step explanation:

−7+6n−9=−4

−7+6n+−9=−4

(6n)+(−7+−9)=−4(Combine Like Terms)

6n+−16=−4

6n−16=−4

Step 2: Add 16 to both sides.

6n−16+16=−4+16

6n=12

Step 3: Divide both sides by 6.

6n

6

=

12

6

n=2

<3

Answer:

n = 2

Step-by-step explanation:

First combine like terms on the left of the equals sign, and get 6n - 16 =  -4. Now add 16 to both sides. You should have 6n = 12. Now divide 6 from both sides and get n = 2

Answer:

i think it is the most difficult one

Answer:

11 I think I'm not sure though

Step-by-step explanation:

We know that in a parallelogram

\(\\ \:\:\:\:\sf {:}\dashrightarrow 5in,10in,10in,5in\)

\(\boxed{\sf Perimeter=Sum\:of\:all\:sides}\)

\(\\ \:\:\:\:\sf {:}\dashrightarrow Perimeter_{(Parallelogram)}=5+5+10+10\)

\(\\ \:\:\:\:\sf {:}\dashrightarrow Perimeter_{(Parallelogram)}=10+20\)

\(\\ \:\:\:\:\sf {:}\dashrightarrow {\underline{\boxed{\bf Perimeter_{(Parallelogram)}=30inches}}}\)

Answer:

sinxcosh + cosxsinh

Step-by-step explanation:

The expansion for sin(x + h) is

sin(x + h)

= sinxcosh + cosxsinh

Answer:

Step-by-step explanation:

-8+x-4+9x = -8-4+x+9x

= -12+10x

PLEASE MARK BRAINLIEST.

Answer:

Add three zeros to the end.

Step-by-step explanation:

When you add three zeros, the result is equivalent to when multiplying by 1000. For example, 20 times 1000 is 20,000.

Hi! I believe your answer is 3 zeros. For example, 7 × 1,000 = 7,000 (add 3 zeros). I hope this helps you! Good luck and have a great day/night. ❤️✨

In goverment  , a geographic information system (gis) is used to make the best use of personnel and equipment while dealing with a tight budget and maintaining crime statistics.

A good example of geographic segmentation is a clothing retailer that offers different products based on the weather and season in which their online customers live. Customers in New York need very different clothing during the winter months than customers in Los Angeles.

Geographic Sentence Example.Geographic isolation somewhat encourages state-owned industry I've been Living in the same geographical area all her life, she is exposed to only a small part of the biosphere. They laid a solid foundation with the publication of Charles Tissot's Geographical Comparisons (1884).

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Answer:

-4a² + 7a + 4

Step-by-step explanation:

Subtract -4 + 3a² from 7a - a².

(7a - a²) - (-4 + 3a²) =

= 7a - a² + 4 - 3a²

= -4a² + 7a + 4

Two or more figures are said to be similar when they have common properties. The value of MP is 18 units.

More than one figure are said to be similar if they have some relatable common properties, either considering their length of sides or measure of their internal angles. But similarity is not the same as congruence.

In the given question, it can be deduced that ΔMNP is similar to ΔQRP. Thus, relating the corresponding sides of the two triangles we have;

\(\frac{12}{30}\) = \(\frac{5x-2}{11x+1}\)

cross multiply to have

30(5x-2) = 12(11x+1)

150x - 60 = 132x + 12

collect like terms

150x - 132x = 12 + 60

18x = 72

x = 4

So that,

MP = 5x - 2

      = 5(4) - 2

      = 20 -2

MP = 18 units

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Answer:

Step-by-step explanation:

Let the numbers be x and y

The statement

difference of two numbers is 166 is written as

x - y = 166.......... Equation 1

The sum of the same two numbers is 234 is written as

x + y = 234 ............. Equation 2

Solve the equations simultaneously

Add both equations 1 and 2

That's

x + x + y - y = 166 + 234

2x = 400

Divide both sides by 2

Substitute the value into the first equation

That's

100 + y = 234

y = 100 - 234

Hope this helps you

The sample proportion (360 out of 1200) can be used to estimate the population proportion, and statistical tests such as a one-sample proportion test or a Z-test can be applied to evaluate the hypotheses and determine the significance of the results.

The null and alternative hypotheses that should be used in this scenario are as follows:

Null Hypothesis (H₀): The proportion of families interested in the program is still 20% or less.

Alternative Hypothesis (H₁): The proportion of families interested in the program has increased, i.e., it is greater than 20%.

Symbolically, we can represent the hypotheses as:

H₀: p ≤ 0.20 (proportion is 20% or less)

H₁: p > 0.20 (proportion is greater than 20%)

In this case, "p" represents the population proportion of families in New Jersey interested in the renewable energy program.

To determine if there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis, a hypothesis test can be conducted using appropriate statistical methods.

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Step-by-step explanation:

42=2b-14 where b=price of the blouse

42+14=2b

56=2b

b=56/2

b=$28 is the price of the blouse

Answer: 42-14=28$

Step-by-step explanation:

Answer:

it is linear and proportional

Step-by-step explanation:

Answer:

46 boxes of nails

Step-by-step explanation:

She has $187 to spend, the maximum.

187/4 = 46.75

Since she cannot buy 0.75 of a box of nails, she can only buy 46. So she is left with an extra $3 and buys 46 boxes of nails.

Hope this helps, and please mark me the brainliest! :D

(a) The projection of u onto v is -1/2i + j + 3/2k.

(b) The vector component of u orthogonal to v is (5/2)i - 2j - (5/2)k.

(a) Finding the projection of u onto v:

First, calculate the dot product of u and v:

u · v = (2)(-1) + (-1)(2) + (-1)(3) = -2 - 2 - 3 = -7

Next, calculate the magnitude of v:

\(|v| = √((-1)^2 + 2^2 + 3^2) = √(1 + 4 + 9) = √14\)

Now, substitute the values into the projection formula:

proj_v(u) = (-7 / 14) * (-i + 2j + 3k)

Simplifying, we get:

proj_v(u) = (1/2)(-i + 2j + 3k) = -1/2i + j + 3/2k

Therefore, the projection of u onto v is -1/2i + j + 3/2k.

(b) To find the vector component of u orthogonal to v, we can subtract the projection of u onto v from u:

comp_v(u) = u - proj_v(u)

Substituting the values, we get:

comp_v(u) = (2i - j - k) - (-1/2i + j + 3/2k)

Simplifying, we get:

comp_v(u) = 2i - j - k + 1/2i - j - 3/2k

         = (2 + 1/2)i + (-1 - 1)j + (-1 - 3/2)k

         = (5/2)i - 2j - 5/2k

Therefore, the vector component of u orthogonal to v is (5/2)i - 2j - (5/2)k.

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The interest rates implied by the given combinations are: a. 4.39%. b. 5.19%. c. 0%. a.  The value of the 3.6% perpetuity is approximately £64.29. b. The value of the 2.1% perpetuity is approximately £37.50. a. The investment would be worth approximately $1,073,741.82 today. b. Approximately $3,839.28 was invested in 1901.

To find the interest rate implied by the given combinations of present and future values, we can use the formula for the interest rate:

Interest Rate = ((Future Value / Present Value)^(1 / Years)) - 1

a. Present Value = $340

  Years = 12

  Future Value = $611

Interest Rate = (($611 / $\(340)^(1 / 12)) - 1\)

Interest Rate ≈ 0.0439 or 4.39%

b. Present Value = $153

  Years = 5

  Future Value = $225

Interest Rate = (($225 /\($153)^(1 / 5)) - 1\)

Interest Rate ≈ 0.0519 or 5.19%

c. Present Value = $240

  Years = 8

  Future Value = $240

Interest Rate = (($240 / $\(240)^(1 / 8)) - 1\)

Interest Rate = 0 or 0%

Therefore, the interest rates implied by the given combinations are:

a. 4.39%

b. 5.19%

c. 0%

Regarding the perpetuities:

a. The value of a 3.6% perpetuity if the long-term interest rate is 5.6% can be calculated using the formula:

Value = Cash Flow / Interest Rate

Value = £3.6 / 0.056

Value ≈ £64.29

Therefore, the value of the 3.6% perpetuity is approximately £64.29.

b. The value of a 2.1% perpetuity can be calculated in the same way:

Value = £2.1 / 0.056

Value ≈ £37.50

Therefore, the value of the 2.1% perpetuity is approximately £37.50.

Regarding the stock market investment:

a. To calculate the value of a $1,000 investment in 1901 with a compound growth rate of 5% until 2019, we can use the formula:

Value = Present Value * (1 + Growth Rate)^Years

Value = $1,000 * (1 + 0.05)^(2019 - 1901)

Value ≈ $1,073,741.82

Therefore, the investment would be worth approximately $1,073,741.82 today.

b. To calculate the initial investment if it has grown to $1 million, we rearrange the formula:

Present Value = Future Value / (1 + Growth Rate)^Years

Present Value = $1,000,000 / \((1 + 0.05)^(2019 - 1901)\)

Present Value ≈ $3,839.28

Therefore, approximately $3,839.28 was invested in 1901.

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Thus here, the height of the tallest person is more extreme as per the z-score.

What is the z-score?

Formula for z-score: \(\frac{X-\mu }{\sigma }\)

Z-score for the tallest person = {258-176.07}/{7.32}

                                                    = 11.1926.

Similarly, Z-score for the shortest person = -7.0587.

The more the absolute value, the more extreme the value.

Thus here, the height of the tallest person is more extreme as per the z-score.

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Answer:

1) 20 % decrease

2)21% decrease

3)8% increase

4)39.9% increase

5)23 % increase

6) 43.3 decrease

Step-by-step explanation:

Regarding the graphs of the functions \(h(x) = x^2 - 4\) and \(g(x) = (x - 4)^2,\) the following statements are true:

The vertex of the graph of h(x) is located at (0, -4), while the vertex of the graph of g(x) is located at (4, 0).

The vertex represents the minimum or maximum point of the parabola.

The graph of h(x) opens upwards, indicating a positive coefficient for the \(x^2\)  term, while the graph of g(x) also opens upwards due to the positive coefficient of the squared term \((x - 4)^2.\)

The graph of h(x) intersects the x-axis at x = -2 and x = 2, indicating the solutions to the equation \(x^2 - 4 = 0.\)

On the other hand, the graph of g(x) intersects the x-axis at x = 4, representing the solution to the equation \((x - 4)^2 = 0.\)

It's important to note that the graph of h(x) is a standard quadratic function, while the graph of g(x) is a quadratic function with a horizontal shift of 4 units to the right.

The differences in their vertex, x-intercepts, and shape indicate these variations between the two functions.

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