Yana is making new cushion covers for a chair. There are three sizes of
cushions on the chair. What is the surface area of the seat back cushion?
26 in
14 in
5 in
5 in
Net for Seat Back
26 in
26 in
5 in
seat back
18 in
14 in arm rest
18 in
18 in
seat bottom
5 in
5 in
26 in
21 in
26 in

Answer:

Step-by-step explanation:

4x^2-8x-5=0

The discriminant is the number under the √. In this case it's 144

Answer:

\(\Delta=144\)

Step-by-step explanation:

For a quadratic in standard form, the discriminant is given by:

\(\Delta=b^2-4ac\)

We have the equation:

\(4x^2-8x-5=0\)

Hence, our a=4; b=-8; and c=-5.

Substituting into our formula, we acquire:

\(\Delta=(-8)^2-4(4)(-5)\)

Evaluate:

\(\Delta=64+80\)

Add:

\(\Delta=144\)

Therefore, our discriminant is 144.

Notes:

Since our discriminant is a positive value, this tells us that our quadratic has two real roots.

We can conclude that only some of the ratios in Table A are greater than the ratios in Table B. (option-c)

To compare the ratios of squares to circles in the tables, we must divide the value in the Squares column by the value in the Circles column for each row in the table.

For Table A, the ratios of squares to circles are:

5/3 = 1.67

10/6 = 1.67

For Table B, the ratios of squares to circles are:

10/3 = 3.33

20/9 = 2.22

Comparing the ratios in Table A to the ratios in Table B, we see that the first two ratios are equal (1.67) and the last two ratios are different (3.33 in Table B is greater than 1.67 in Table A, and 2.22 in Table B is less than 1.67 in Table A).

Specifically, the ratio in the second row of Table B is greater than both ratios in Table A, but the ratios in the first row of each table are equal.(option-c)

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Answer:

ans - 25.77°

Step-by-step explanation:

tan a = 14/29

a = tan ^ -1 14/29

a = 25.77°

Answer:

25.77

Step-by-step explanation:

It's logically impossible for this angle to be .008.

Alternatively (the harder way), use trigonometric ratios to solve this problem.

Since you know the adjacent and opposite angle, you need to use tangent ratio.

tan = a/o

Use \(tan^-1\)

 \(tan^-1(14/29)\)

a = 25.76932762, ~25.77

Answer:

y=-1/3x+3

Step-by-step explanation:

Answer:

12, 15, 18

Step-by-step explanation:

4x+5x+6x=45

15x=45

x=3

4x=12, 5x=15, 6x= 18

Answer: radius is is 12.

Step-by-step explanation:

Explanation: A circle with equation of the form x2+y2=r2 will have radius r=√144=12 .

Sorry, I'm not sure on the bottom part

We know,

The general equation for circle is –

\( { \boxed{\bf{\rm \red {(x \: - \: a)² \: + \: (y \: - \: b)² \: = \: r²}}}} \)

\( \bf (a, \: b) \: = \: center \: coordinates \)

\( \bf r \: = \: radius \)

\( \bf a \: = \: 0 \: , \: b \: = \: 0 \: , \: r \: = \sqrt{144} \: = \: 12 \)

\( \bf Center \: coordinates \: = \: (0, \: 0) \) [Answer]

\( \bf Radius \: = \: 12 \) [Answer]

__________________________________________________

NOTE – Refer the above attachment.

__________________________________________________

There is evidence, at the 0.1 significance level, to suggest that the 2x4s used for prefabricated homes are either too long or too short.

To determine if the 2x4s used for prefabricated homes are either too long or too short, we can perform a hypothesis test using the given information.

The null hypothesis (H₀) assumes that the mean length of the 2x4s is equal to the desired length of 13 feet, while the alternative hypothesis (H₁) suggests that the mean length deviates from 13 feet.

We are given a sample of 84 2x4s with an average length of 12.95 feet, and the population standard deviation is known to be 0.15 feet.

To conduct the hypothesis test, we can use the Z-test since the sample size is relatively large and the population standard deviation is known.

The test statistic, Z, can be calculated using the formula:

Z = (x- μ) / (σ / √n)

Where X is the sample mean, μ is the hypothesized population mean (13 feet), σ is the population standard deviation, and n is the sample size.

Substituting the given values:

Z = (12.95 - 13) / (0.15 / √84)

Calculating the numerator:

Z = (-0.05) / (0.15 / √84)

Simplifying the denominator:

Z = (-0.05) / (0.15 / 9.165)

Further simplification:

Z = -0.05 / 0.016368

Calculating Z:

Z ≈ -3.05

The calculated Z value of -3.05 corresponds to a p-value that is extremely small. Since the p-value is less than the significance level of 0.1, we can reject the null hypothesis.

Therefore, there is evidence, at the 0.1 significance level, to suggest that the 2x4s used for prefabricated homes are either too long or too short.

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Answer: look at the images for the answer and the solution

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

here it is I hope it helps

Step-by-step explanation:

verified

Answer:

Statement,                                                        Reason

Given segment RV = segment TU,                 Given  

m∠R = m∠T,                                                      Given

Segment RS ≅ segment ST,                            Base angles theorem

ΔRSV ≅ ΔTSU,                                                 SAS rule of congruency

Segment SV ≅ segment SU,                          CPCTC

VU ≅ UV,                                                          Reflexive property

RU = RV + VU, TV = TU + UV,                          Addition of segments

RV + VU ≅ TU + UV,                                         Addition property of equality

RU ≅ TV,                                                           Transitive property of addition

ΔRSU ≅ ΔTSV,                                                  SSS rule of congruency

Step-by-step explanation:

Where:

SAS- Side Angle Side

CPCTC -Congruent Parts of Congruent Triangles are Congruent

SSS -Side Side Side

¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

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Seashells glued on 1 photo frame = k

So, seashells glued on 5 photo frame

= Seashells glued on 1 photo frame × 5

= k × 5

= 5k

So, Erynn used 5k seashells.

Answer:

11.35 g/mL

Step-by-step explanation:

D = m/v

D = 567.5 g ÷ 50.0 mL (I assume its measured in mL)

D = 11.35 g/mL

Answer:

11.35

Step-by-step explanation:

Answer:

12 L = 12000 mL

Step-by-step explanation:

We want to complete the following sentence:

12L = _____ mL

In other words, we want to convert 12 L to mL.

To do that, we can do something similar to that of dimensional analysis, which is common in chemistry, where we will convert one label to another by using conversion factors, which are written as fractions.

Recall that 1 L = 1000 mL, so the conversion factor is \(\frac{1L }{1000mL}\).

When doing dimensional analysis, we want to cancel out common labels.

This means that we want to cancel out the L label to get mL.

So, we will put L on the bottom.

Our new conversion factor is: \(\frac{1000mL }{1L}\)

Now, we multiply this by 12L.

\(12L * \frac{1000mL }{1L}\)

This simplifies to 12000 mL

So, 12L = 12000 mL

Answer:

8 and -16

Step-by-step explanation:

Let’s take the square root of both sides.

We get  |a+b|=12

 then replace 4 with “a”,

→  |4+b|=12

Now there are two possibilities for “b”.

→  4+b=12

or  4+b=−12

→ We get b = 8 from the first one and we get -16 from the second one,

So the answers are 8 and -16 .

The rule for the nth term of the geometric sequence is: \(an = 6 * 4^{(n-1)\)

The rule for the nth term of a geometric sequence can be found using the third and fifth terms of the sequence. In this case, the rule is a = 24 and r = 4.

To find the rule for the nth term of a geometric sequence, we use the formula:

an = a1 *\(r^{(n-1)\)

where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

Given that the third term is 96 and the fifth term is 1,536, we can write two equations:

a * r²  = 96

a *\(r^4\)= 1536

Dividing the second equation by the first equation, we get:

r² = 16

Taking the square root of both sides, we get:

r = 4 (since r cannot be negative in a geometric sequence)

Substituting r = 4 into either of the two equations, we get:

a * 16 = 96

a = 6

Therefore, the rule for the nth term of the geometric sequence is:

\(an = 6 * 4^{(n-1)\)

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Answer: Directly proportional relationships they always pass through the origin (0,0). There are other linear relationships that dont pass through the origin.

Answer:

15%

Step-by-step explanation:

You add up all the frequencies and divide by 9 (the amount 6 was rolled).

It adds up to 60. Divide 9 by 60 and you have 15%.

Answer:

I would go with line n

Step-by-step explanation:

If a 0.10 significance level is used in place of a 0.05 significance level, the power of the test will generally increase. As we are increasing the probability of rejecting the null hypothesis.

The significance level (alpha) of a hypothesis test determines the probability of making a Type I error, which is the probability of rejecting the null hypothesis when it is actually true. The power of a test, on the other hand, is the probability of correctly rejecting the null hypothesis when it is actually false (i.e., the probability of detecting a true effect).

By using a higher significance level (0.10 instead of 0.05), we are increasing the probability of rejecting the null hypothesis, which means we are more likely to detect a true effect. This results in an increase in the power of the test. However, it's worth noting that using a higher significance level also increases the risk of making a Type I error, which means we have to be careful when interpreting the results of the test.

In summary, increasing the significance level generally increases the power of the test, but it also increases the risk of making a Type I error

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Answer:

Step-by-step explanation:

Given two congruent, isosceles triangles are joined, as shown, to form a parallelogram, the largest angle of the parallelogram is 116 degrees. Write two equations. Write them find the value of a and the value of b.

We know that the sum of all the internal angles is 360 degree. So the equation will be

4 a + 2b = 360

According to the question the largest internal angle of the parallelogram is 116 degree.                So a + b = 116

Now we have the two equations as  

4a + 2b = 360

a + b = 116

Multiply the second equation by 4 we get

4a + 2b = 360

4a + 4b = 464

    Or – 2b = - 104

   Or b = 52

Now a + b = 116

Or a + 52 = 116

Or a = 116 – 52

Or a = 64

Therefore the values of  a and b are 64 and 52 degrees

hope that help mark me brinilylist

Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.

1. -x² + x - x² + 1

Combine like terms: -x² + x - x² + 1 = -2x² + x + 1

This polynomial has degree 2 because the highest power of the variable is 2.

2. x² + x + 2x³ - x

Rearrange terms: 2x³ + x² + x - x = 2x³ + x²

This polynomial has degree 3 because the highest power of the variable is 3.

3. 4x + x + x - 2

Combine like terms: 4x + x + x - 2 = 6x - 2

This polynomial has degree 1 because the highest power of the variable is 1.

4. 3x² + 4 - 3x² - 1

Combine like terms: 3x² - 3x² + 4 - 1 = 3

This polynomial has degree 0 because there is no variable term.

Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.

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Answer:

f(x) = x-2

for inverse function just flip the numerator and denominator

since there isn’t a ’known’ denominator, the denominator is always 1 (since anything divided by 1 is itself)

so it’ll be

1 / (x-2)

The Taylor series formula in summation notation f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n } where f^n(a) denotes the nth derivative of f(t) evaluated at t = a.

Since the functions f(t) and g(t) have not been given in the question, I cannot provide a specific answer to this question. However, I can provide a general approach to finding the power series expansion of a function about a point.

To find the power series expansion of a function f(t) about a point t = a, we can use the Taylor series formula:

f(t) = f(a) + f'(a)(t-a) + (1/2!)f''(a)(t-a)^2 + (1/3!)f'''(a)(t-a)^3 + ...

where f'(a), f''(a), f'''(a), ... are the first, second, third, and higher-order derivatives of f(t) evaluated at t = a.

To find the first four nonzero terms of the power series expansion, we can calculate the values of f(a), f'(a), f''(a), and f'''(a) at t = a, substitute them into the Taylor series formula, and simplify the resulting expression. The first four nonzero terms will be the constant term, the linear term, the quadratic term, and the cubic term.

To find the general term of the power series expansion, we can write the Taylor series formula in summation notation:

f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n }

where f^n(a) denotes the nth derivative of f(t) evaluated at t = a. The general term of the power series expansion is given by the expression in the curly braces. We can use this expression to find any term in the series by plugging in the appropriate values of n and f^n(a).

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No, the given table does not represent a valid discrete probability distribution. A valid discrete probability distribution must satisfy two conditions:

The probabilities assigned to each outcome should be between 0 and 1 (inclusive): In the given table, the probabilities range from 0.06 to 0.51. These values fall within the valid range of 0 to 1, satisfying the condition.

The sum of all probabilities should be equal to 1: To check this, we add up the probabilities given in the table: 0.11 + 0.06 + 0.25 + 0.41 + 0.51 = 1.34. The sum of the probabilities exceeds 1, violating the condition.

Since the sum of the probabilities is greater than 1, the given table does not satisfy the second condition for a valid probability distribution. The probabilities assigned to the outcomes are not properly normalized to ensure that the total probability is 1.

In order to represent a valid discrete probability distribution, the probabilities assigned to each outcome should be scaled down by dividing each probability by the sum of all probabilities. This normalization process ensures that the total probability across all outcomes adds up to 1.

Therefore, the correct answer is "No," as the given table does not represent a valid discrete probability distribution due to the violation of the sum of probabilities being equal to 1.

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Answer:

how is it possible this is impossible

Answer:

3990/(1.14)=3500

Step-by-step explanation:

When Alonzo splits 3/4 pounds of candy among 4 people the unit rate in pounds per person is 3/16 pounds per person

The ratio of two measures, with one as the second of the item, is known as unit rate.

For the problem where Alonzo have to split 3/4 pounds of candy, the  unit rate is solved by division.

In this case, Alonzo will divide each the 3/4 pounds by 4 to get a value of which is the unit rate

The unit rate of candy in pounds per person

= 3/4 pounds / 4 persons

= 3/16 pounds per person

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Answer:

x = 63° , y = 83°

Step-by-step explanation:

In a trapezium

each lower base angle is supplementary to the upper base angle on the same side , then

x + 117° = 180° ( subtract 117° from both sides )

x = 63°

the sum of the 3 angles in the outer triangle = 180° , that is

x + y + 34° = 180° ( substitute x = 63° )

63° + y + 34° = 180°

97° + y = 180° ( subtract 97° from both sides )

y = 83°