Can someone please help

If 2 angles are formed on a line, then they make a supplementary / linear pair of angles, i.e, both the angles form 180°.

Here,

Angle A = 80°

Angle B = x°

So,

Angle A + Angle B = 180°

80° + x° = 180°

x° = 180° - 80°

x° = 100°

=》 Angle B = 100°

_____

Hope it helps ⚜

To bring the average up to 90%, you would need to get a score of 96% in 7 consecutive tests.

The first four tests have an average of 84% and the student is looking to achieve a 90% average by scoring 96% on the remaining tests. Let the number of remaining tests be x.

Then, we can set up the equation as:(84*4 + 96x)/ (4 + x) = 90

Simplifying this equation, we get:336 + 96x = 360 + 90x

Solving for x, we get:x = 6

This means there are 6 remaining tests.

To find out how many consecutive 96% scores are needed to bring the average up to 90%, we can set up the equation as:(84*4 + 96*6)/ 10 = 90

This simplifies to:744/10 = 90

Multiplying both sides by 10, we get:744 = 900

To find the number of consecutive 96% scores, we can use the following equation: (84*4 + 96x)/ (4 + x) = 90, where x is the number of consecutive tests.

Substituting the values, we get:(84*4 + 96x)/ (4 + x) = 90

Solving for x, we get:x = 7

Hence, the number of consecutive 96% scores required to bring the average up to 90% is 7.

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The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Answer:

it will be worth 880 dollars in 8 years, it will be worth nothing in 14 years

Step-by-step explanation:

Answer:

447 ft

Step-by-step explanation:

Add 417 and 30 together. That will give you the total direct distance between the two. 417+30=447

Answer:

x = 4

Step-by-step explanation:

5x + 2 and 4x + 6 are alternate angles and are congruent, thus

5x + 2 = 4x + 6 ( subtract 4x from both sides )

x + 2 = 6 ( subtract 2 from both sides )

x = 4

The angle between the vectors can be found using the dot product. The formula is θ= |A| =√(x12 + y12 + z12) The angle between the vectors -2i + 3j + k and i + 2j - 4k is approximately 137.8 degrees.

v1 • v2 = (-2i + 3j + k) • (i + 2j - 4k)

= -2 - 6 + 1 = -7

|v1| = \(\sqrt{((-2)^2 + 3^2 + 1^2)}\)

=\(\sqrt{(4 + 9 + 1)}\)

=\(\sqrt{14}\)

|v2| = \(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)

= \(\sqrt{(1 + 4 + 16) }\)

= (\(\sqrt{21}\)

θ= |A| (-7/\(\sqrt{14}\)\(\sqrt{21}\))

=  |A| (-7/21*14)

=  |A|(-7/294)

= 137.8 degrees

The angle between two vectors can be found using the dot product formula. This formula isθ= |A| =√(x12 + y12 + z12). In the case of the vectors -2i + 3j + k and i + 2j - 4k, this formula can be used to find the angle between them. The dot product of the two vectors is -2 - 6 + 1 = -7. The magnitude of the first vector, |v1|, can be found using the Pythagorean theorem, which is

\(\sqrt{((-2)^2 + 3^2 + 1^2)}\)

= \(\sqrt{(4 + 9 + 1)}\)

= \(\sqrt{14}\).

The magnitude of the second vector, |v2|, can be found using the Pythagorean theorem, which is

\(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)

= \(\sqrt{(1 + 4 + 16)}\)

= \(\sqrt{21}\)

Once the dot product and magnitudes are known, the angle between the two vectors can be found using the formula .Therefore, the angle between the two vectors is approximately 137.8 degrees.

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The age of Layla who youngest of four siblings is 18 years old

The age of 4 sibling are in consecutive even integers

Age of 1st sibling = x

Age of 2nd sibling = x + 2

Age of 3rd sibling = x + 4

Age of 4th sibling = x + 6

Sum of the sibling age = 84

x + x + 2 + x + 4 + x + 6 =84

4x + 12 = 84

4x = 84 -12

4x = 72

x = 18

Layla is youngest  sibling hence her age will be 18 years

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The question is incorrect the correct question is :

Layla is the youngest of four siblings whose ages are consecutive even integers. If the sum of their ages is 84, find Layla's age

The given integral is ₁∫₀^(π/2) sin²(x)dx.

The trapezoidal rule is given by:(b - a) [(f(a) + f(b))/2]And, the Gauss-Quadrature formula for n = 2 is: ∫ᵇₐ f(x) dx = (b - a) [ w₁ f( [ (b - a)/2 ] gp₁ + (b + a)/2 ) + w₂ f( [ (b - a)/2 ] gp₂ + (b + a)/2 ) ]

Here, a = 0, b = π/2, gp₁ = -0.5773, gp₂ = 0.5773, w₁ = w₂ = 1.

(i) Trapezoidal Rule: The trapezoidal rule with one interval is given by:(b - a) [(f(a) + f(b))/2] = π/4 [sin²(0) + sin²(π/2)] = 0.7854

(ii) Gauss-Quadrature: Using the Gauss-Quadrature formula with n = 2, we get:∫ᵇₐ f(x) dx = (b - a) [ w₁ f( [ (b - a)/2 ] gp₁ + (b + a)/2 ) + w₂ f( [ (b - a)/2 ] gp₂ + (b + a)/2 ) ]= π/2 [ sin²( [ (π/2)/2 ] (-0.5773) + π/4 ) + sin²( [ (π/2)/2 ] (0.5773) + π/4 ) ]= 0.7853Comparing the above two methods, the trapezoidal rule and Gauss-Quadrature method are nearly the same and are close to the exact value.

Exact value = (π/2)/2 - sin(π)/4 = 0.7854Conclusion:Thus, it can be concluded that the given integral using the trapezoidal rule (using only one interval) and Gauss- Quadrature (n=2) is approximately equal to 0.7854.

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Answer:

The set of factors of 20 is {1, 2, 4, 5, 10, 20} and the set of factors of 16 is {1, 2, 4, 8, 16}. {1, 2, 4, 5, 10, 20} ∩ {1, 2, 4, 8, 16} = {1, 2, 4} which has greatest value 4. So, GCF(20, 16) = 4.

Step-by-step explanation:

Answer:

The factors of 20 is 1, 2, 4, 5, 10, 20

The factors of 16 is 1, 2, 4, 8, 16

Step-by-step explanation:

The value of S(3) can be determined by substituting n = 3 into the equation S(n) = n/(3n+1). By doing so, we obtain S(3) = 3/(3*3+1) = 3/10.

To verify the equation S(n) = n/(3n+1), we need to evaluate S(3).

In the given equation, S(n) represents the sum of a series of fractions. The general term of the series is 1/[(3n-2)(3n+1)].

To find S(3), we substitute n = 3 into the equation:

S(3) = 1/[(33-2)(33+1)] + 1/[(34-2)(34+1)] + 1/[(35-2)(35+1)]

Simplifying the denominators:

S(3) = 1/(710) + 1/(1013) + 1/(13*16)

Finding the common denominator:

S(3) = [(1013)(1316) + (710)(1316) + (710)(1013)] / [(710)(1013)(13*16)]

Calculating the numerator:

S(3) = (130208) + (70208) + (70130) / (71010131316)

Simplifying the numerator:

S(3) = 27040 + 14560 + 9100 / (710101313*16)

Adding the numerator:

S(3) = 50600 / (710101313*16)

Calculating the denominator:

S(3) = 50600 / 2872800

Reducing the fraction:

S(3) = 3/10

Therefore, S(3) = 3/10, confirming the equation S(n) = n/(3n+1) for n = 3.

the process of verifying the equation by substituting the given value into the series and simplifying the expression.

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The given series is divergent.

We can determine the convergence or divergence of the given series using the nth term test. According to this test, if the nth term of a series does not approach zero as n approaches infinity, then the series is divergent.

Here, the nth term of the series is given by 9e^(n+3)/(n(n+1)). We can simplify this expression by using the fact that e^(n+3) = e^3 * e^n. Therefore, we have:

9e^(n+3)/(n(n+1)) = 9e^3 * (e^n / n(n+1))

As n approaches infinity, the term e^n grows faster than n(n+1). Therefore, the expression e^n / n(n+1) does not approach zero, and the nth term of the series does not approach zero either. Thus, by the nth term test, the series is divergent.

Therefore, the given series is divergent.

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The new estimator θ^3 is also an unbiased estimator with an expectation equal to θ.

(a) The values of E(θ^1) and E(θ^2) are unknown without further information. Being unbiased estimators means that, on average, they provide estimates that are equal to the true population parameter θ. Therefore, we have:

E(θ^1) = θ

E(θ^2) = θ

(b) To find the expectation E(θ^3), we can use the linearity property of expectations:

E(θ^3) = E(aθ^1 + (1 - a)θ^2)

Since θ^1 and θ^2 are unbiased estimators, their expectations are equal to θ:

E(θ^3) = E(aθ^1 + (1 - a)θ^2) = aE(θ^1) + (1 - a)E(θ^2)

Using the values from part (a), we have:

E(θ^3) = aθ + (1 - a)θ = θ(a + 1 - a) = θ

Therefore, the new estimator θ^3 is also an unbiased estimator with an expectation equal to θ.

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=============================================================

Explanation:

Focus on point F only. Ignore the other points.

Point F is at (-5, -5).

The x coordinate of this point is x = -5

The horizontal distance from x = -5 to the reflection line x = -1 is 4 units. We move 4 units to the right going from x = -5 to x = -1. Move another 4 units to the right to land on x = 3

Point F = (-5, -5) reflects over x = -1 to land on point G = (3, -5) as shown in the diagram below.

Then going from point G to H has us move upward 4 units up to land on the purple line y = -1, then another 4 units up to finally arrive at point H = (3,3). This is also the location of F'.

Answer:

18/100 or 9/50

Step-by-step explanation:

0.18 = 0.18/1

times 100 then 18/100

divided by 2 then 9/50

The inequalities that have symbols that will be reversed when the variable is isolated are option C, D, and E: –4.5c > 9, –215 ≤ –52d, and e – 13 ≥ 11.

When solving an inequality, if you ever multiply or divide both sides by a negative number, you must reverse the inequality sign. For example,

if you have an inequality like -3x > 6, you will divide both sides by -3 to get x < -2. The inequality sign is reversed because you divided by a negative number.

Here, in the question, when both sides of an inequality are multiplied or divided by a negative number, the sign of inequality is reversed.

For example, if we multiply or divide –4.5c > 9 by –1, we get 4.5c < –9 which has a reversed symbol. Similarly, if we multiply or divide –215 ≤ –52de – 13 ≥ 11 by –1, we get 215 ≥ 52de + 13 ≤ –11 which also has a reversed symbol.

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Complete question is:

Select all the inequalities that have symbols that will be reversed when the variable is isolated.

–10.5 < 3a

b6 ≤ 7

–4.5c > 9

–215 ≤ –52d

e – 13 ≥ 11

Answer:

\(area = {a}^{2} \\ = {20}^{2} \\ = 400 {cm}^{2} \\ thank \: you\)

Answer:

\(\huge\boxed{\sf A = 400\ cm\²}\)

Step-by-step explanation:

Side length of square = L = 20 cm

Formula:

Area of the square (A) = L² = L × L

Solution:

A = 20 cm × 20 cm

A = 400 cm²

\(\rule[225]{225}{2}\)

Hope this helped!

The sample size will now have to be is 3200.

Given:

the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum allowable error (e) must be reduced to just 0.025. if the original calculation led to a sample size of 1000.

n = p(1-p)(z/E)^2

800 = 0.5(1-0.5)(z/0.05)^2

800 = 0.5*0.5* z^2/0.0025

800 = 0.25 * z^2/0.0025

800 = 25/100*10000*z^2/25

800 = 1*100*z^2

800/100 = z^2

8 = z^2

z = \(\sqrt{8}\)

z = 2.8284

n = p(1-p)(z/E)^2

= 0.25(2.8284/0.025)^2

= 0.25*(113.136)^2

= 0.25*12799.754496

= 3199.938 ≈ 3200

Therefore the sample size will now have to be is 3200.

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If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.

When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.

This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.

The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.

In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.

It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.

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Answer:

GIVE ME BRAINLIEST

Step-by-step explanation:

Answer:

\(\huge\boxed{\text{1.}}\)

She did the ratio of GIRLS to BOYS, while the question asked for the ratio of BOYS to GIRLS. Therefore she swapped her proportion and data can get mixed up when you swap them. It's always important to keep the proportion in the same way that it was asked.

\(\huge\boxed{2.}\)

\(\text{15 to 13}\)

\(\text{15:13}\)

\(\frac{15}{13}\)

Step-by-step explanation:

We have 13 girls and 15 boys in the class. Therefore we can represent this as \(\frac{g}{b} = \frac{13}{15}\), where g is the number of girls and b is the number of boys. Now let's look at what the question is asking.

"She wrote the ratio of boys to girls in 3 ways."

Note: boys to girls. Our original proportion is currently at girls to boys. Therefore these proportions are swapped. We can see that she messed this up.

Therefore, we need to swap the values.

So 13 to 15 becomes 15 to 13

13:15: becomes 15:13

\(\frac{13}{15}\) becomes \(\frac{15}{13}\).

Hope this helped!

The total earnings of the bus driver in a year is $28500.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

The bus driver works 2000 hours each year and makes $14 per hour.

If the bus driver gets $50 for each new recruit he hired.

Let y be his total earnings and x be the number of new drivers he recruits.

Then his total earnings can be represented by the function:

y = 14 × 2000 + 50 × x

If the bus driver recruits x = 7 new drivers.

y = 28000 + 50 × 7

y = 28000 + 350

y = $28350

The total earnings of the bus driver are $2850.

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Answer:

Step-by-step explanation:

You want a sequence of transformations that will place trapezoid ABCD on top of trapezoid TSCU.

The two trapezoids have opposite orientations: ABCD is clockwise, TSCU is counterclockwise. This means at least one reflection is involved in the transformation.

Corresponding line segments are not parallel to each other, so the transformation must involve a rotation.

It can be convenient to perform the reflection over a line that includes point C (the invariant point). Similarly, the center of rotation will be invariant, so C is also a good choice for that. We can move ABCD to the desired location by ...

__

Additional comment

Quadrilateral TCSU is not a trapezoid, and cannot be obtained by transforming ABCD. We assume a typographical error is involved, so we have given transformations from ABCD to TSCU.

The mapping can be done by one transformation—reflection over the angle bisector of angle DCU.

There are many possible transformation sequences. We have described on of them. The transformations we have described can be done in either order, where the reflection is over the rotated line CD'.

<95141404393>

Answer:

Step-by-step explanation:

reflect over line CD

Answer:

60 +24 = 84

Step-by-step explanation:jjjjjhjhjhj

6 x 4 +5 x 12

Answer:

9(10+5)

Step-by-step explanation:

because 10+5 is fifteen so then when you as them together you get the same expression as before

Answer:

9(10+5)

Step-by-step explanation:

because 10+5=15 and it's 9(15)