Algebra, help please ASAP

If a distribution of scores is shown in a bar graph, it suggests that the scores were measured on an ordinal scale of measurement.

An ordinal scale is a type of measurement scale that categorizes and orders variables or data points based on their relative ranking or position. In this case, the bar graph represents the frequencies or counts of different categories or ranges of scores, indicating an ordered arrangement of the data. However, the bar graph alone does not provide information about the exact numerical differences between the scores or their precise magnitudes.

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Answer:

93.2° (nearest tenth)

Step-by-step explanation:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

From inspection of the given triangle:

Substitute the values into the sine rule to find the measure of angle C:

\(\implies \dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

\(\implies \dfrac{\sin 38^{\circ}}{9}=\dfrac{\sin C}{11}\)

\(\implies \sin C=\dfrac{11\sin 38^{\circ}}{9}\)

\(\implies C=\sin ^{-1} \left(\dfrac{11\sin 38^{\circ}}{9}\right)\)

\(\implies C=48.80523914...^{\circ}\)

Interior angles of a triangle sum to 180°.

\(\implies A+B+C=180^{\circ}\)

\(\implies A+38^{\circ}+48.80523914...^{\circ}=180^{\circ}\)

\(\implies A=93.19476086...^{\circ}\)

Therefore, the size of angle A is 93.2° (nearest tenth).

The convergence set of the given power series is the set of all values of x in the interval (-|x-7|, |x-7|).

In order to determine the convergence set of the given power series, we can use the ratio test.

The ratio test states that if the limit as n goes to infinity of the absolute value of aₙ₊₁ / aₙ is less than 1, then the series converges for all x in the interval (-R, R) where R is the reciprocal of the limit.

The given power series is:

sigma n = 1 to infinity (17/ (n² + 5n))×(x - 7)ⁿ

We can apply the ratio test as follows:

aₙ₊₁ / aₙ = |(17/(n+1)² + 5(n+1))×(x - 7)⁽ⁿ⁺¹⁾ | / |(17/ (n² + 5n))×(x - 7)ⁿ|

aₙ₊₁ / aₙ = |(17/(n+1)² + 5(n+1))/(n² + 5n) × |(x - 7)|⁽ⁿ⁺¹⁾ | / |(x - 7)|ⁿ

As we can see the limit as n goes to infinity of the absolute value of

aₙ₊₁ / aₙ = |(x - 7)|

Let R = |x - 7|, therefore, the series converges for all x in the interval (-R, R)

So the series converges for all values of x in the interval (-|x-7|, |x-7|).

--The given question is incomplete, answering to the question below--

"Determine the convergence set of the given power series.

sigma n = 1 to infinity ( 17/ (n² + 5n))×(x - 7)ⁿ"

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Answer:

Set your calculator to degree mode.

Draw a line from point O to a vertex of this octagon to form a right triangle.

tan(67.5°) = 17/x, so x = 17/tan(67.5°)

Area = (1/2)(34/tan(67.5°))(8)(17) = 957.7

\(\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=na^2\cdot \tan\left( \frac{180}{n} \right) ~~ \begin{cases} n=sides\\ a=apothem\\[-0.5em] \hrulefill\\ n=8\\ a=17 \end{cases}\implies A=(8)(17)^2\tan\left( \frac{180}{8} \right) \\\\\\ A=2312\tan(22.5^o)\implies A\approx 957.7\)

Make sure your calculator is in Degree mode.

The different programs (in terms of order) that can be arranged is 120 different ways

Since we are dealing with arrangements, this is a permutation problem.

If there are three bands and two comics performing at a show, the total band will be 5 bands

The number of different programs that can be arranged will be 5!

5! = 5 * 4 * 3 * 2

5! = 60 * 2

5! = 120 ways

Hence the different programs (in terms of order) that can be arranged is 120 different ways

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Answer:

The change in the angle of elevation is approximately 63.435°

Step-by-step explanation:

The given parameters are;

The speed of the tightrope walker = 3 ft./sec

The altitude at which the tightrope walker is moving = 100 ft.

The horizontal distance of the tightrope walker from the searchlight = 200 feet

The final angle of elevation, θ, is given by the trigonometric ratio as follows;

\(tan\angle \theta = \dfrac{Opposite \ leg \ length}{Adjacent\ leg \ length} = \dfrac{Elevation \ of \, the \ tightrope}{Horizontal \ distance \ to \ the \ tight rope \ walker}\)

\(tan\angle \theta = \dfrac{Elevation \ of \, the \ tightrope}{Horizontal \ distance \ to \ the \ tight rope \ walker} = \dfrac{100}{200} = \dfrac{1}{2}\)

\(\theta = tan^{-1} \left (\dfrac{1}{2} \right ) \approx 26.565 ^ {\circ}\)

Whereby the tightrope walker was initially vertically overhead the search light, the initial angle of elevation = 90°

The change in the angle of elevation = The initial angle of elevation - The final angle of elevation

Substituting the values gives

The change in the angle of elevation = 90° - 26.565 ≈ 63.435°

Change in the angle of elevation = 63.4°

The original position of the tightrope Walker is vertical

That is, the initial angle of elevation, θ = 90 degrees

Horizontal distance of the Walker = 200 feet

The altitude of the Walker = 100 feet

The final angle of elevation of the tightrope Walker is calculated as follows

\(tan \theta \: = \frac{opposite}{adjacent} \)

\(tan \: \theta \: = \frac{100}{200} \)

\(tan \: \theta \: = 0.5\)

\(\theta \: = {tan}^{ - 1} 0.5\)

\(\theta = {26.6}^{0} \)

Change in the angle of elevation = Final angle of elevation - Initial angle of elevation

Change in the angle of elevation = 90 - 26.6

Change in the angle of elevation = 63.4°

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Answer:

=69

=69+66

=135

-unequal

-dependent

the expressions that are equivalent to 1 3/5 - 1/4 are:27/20

Given expression: 1 3/5 - 1/4

We can convert the mixed fraction to an improper fraction, so that we can subtract easily.1 3/5 = (5 × 1) + 3 / 5 = 8/5

Thus, the expression becomes: 8/5 - 1/4

To subtract two fractions, we need to find the LCM (Least Common Multiple) of the denominators.

LCM of 5 and 4 is 20.So, we convert the above fractions into like fractions having 20 as their denominator.

8/5 - 1/4 can be written as:

(8 × 4) / (5 × 4) - (1 × 5) / (4 × 5)= 32/20 - 5/20= 27/20

Therefore, the expression 1 3/5 - 1/4 is equivalent to the fraction 27/20, when expressed in its simplest form.

So, the expressions that are equivalent to 1 3/5 - 1/4 are:27/20

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Given:

The function is given

Required:

Find the amplitude and graph the function.

Explanation:

compare the equation with the equation

Where a = amplitude

period =

Phase shift =

Vertical shife = d

Compare the given equation with the standard equation we get

a = 2, b = 1,

d = 2

Period

Phase shift

Vertical shift d = 2

The hypothesis for the given scenario can be written as follows:

Null hypothesis

H_0: μ = 7.2

Alternative hypothesis

H_1: μ ≠ 7.2

Here, μ = Population mean

The mean pressure produced by the valve is not 7.2 lbs/square inch.

The given level of significance (α) = 0.05

The given population variance is known to be 1.

Need to determine if there is sufficient evidence to show that the valve does not perform to the given specifications if the valve was designed to produce a mean pressure of 7.2 lbs/square inch. That is, whether to reject or accept the null hypothesis with the given level of significance (α) = 0.05.

The sample mean pressure of 190 engines tested was 7.3 lbs/square inch. Mean pressure (μ) = 7.3 lbs/square inch, σ² = Variance = 1, n = Number of observations = 190

Significance level (α) = 0.05

Test Statistic: Z = (x - μ) / (σ / √n)

where x = Sample mean

The formula for the test statistic can be written as:

Z = (7.3 - 7.2) / (1 / √190)Z = 4.3588 (approx.)The calculated value of Z = 4.3588 is greater than the Z critical value at 0.05 level of significance.

Hence, there is sufficient evidence to reject the null hypothesis H_0. Therefore, we can conclude that the valve does not perform to the given specifications. The mean pressure produced by the valve is not 7.2 lbs/square inch.

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The ratio of the number of children to the number of adults in this group is 19:2 or 19/2.

Let the number of children in the group be x, and the number of adults be y.

Since the admission fee is $4 for children and $6 for adults, we can write two equations as follows:

x + y = 21 - - - - - - - - (1)4x + 6y = 900 - - - - - - - - (2)

Solving these equations, we get:x = 9y

Substituting this value in the equation (1), we get:

9y + y = 2110y = 21y = 2.1So, the number of adults in the group is y = 2.1, and the number of children is x = 9y = 9(2.1) = 18.9 (rounded off to 19).

Therefore, the ratio of the number of children to the number of adults in this group is 19:2 or 19/2.

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The cost function for each of the given scenarios are as follows:

1) Cost function for chain-saw rental firm = $25 + $5h

2) Cost function for trailer hauling service = $95 + $8m

1.)

Cost function for chain-saw rental firm = $25 + $5h

Where, h is the number of hours the chainsaw is rented

Variables used in this scenario are:

Cost = C ($), Renting time = h (hours),

Charge per hour = c ($)

2.)

Cost function for trailer hauling service = $95 + $8m

Where, m is the number of miles the trailer has traveled.

Variables used in this scenario are:

Cost = C ($),

Distance traveled = m (miles),

Charge per mile = c ($)

Therefore the two cost functions are:

1) Cost function for chain-saw rental firm = $25 + $5h

2) Cost function for trailer hauling service = $95 + $8m

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Answer:

80°

Step-by-step explanation:

20°+80°+missing angle=180°

missing angle=180°-100°=80°

To write the characteristic equation for matrix a, we first need to find the determinant of the matrix (a-λI), where λ is the eigenvalue and I is the identity matrix. The characteristic equation is then obtained by setting the determinant equal to zero.

Once we have the characteristic equation, we can solve it to find the eigenvalues of a. Each eigenvalue corresponds to a specific solution of the equation. The eigenvalues may be repeated, in which case we refer to their multiplicity.

For example, if the characteristic equation of a is (λ-3)(λ-2)(λ+1) = 0, then the eigenvalues of a are λ1=3, λ2=2, and λ3=-1. The multiplicity of λ1 is 1, the multiplicity of λ2 is also 1, and the multiplicity of λ3 is 1.

The multiplicity of an eigenvalue corresponds to the number of times it appears as a solution to the characteristic equation. If an eigenvalue has a multiplicity of 1, it corresponds to a single eigenvector. If an eigenvalue has a multiplicity greater than 1, it corresponds to multiple linearly independent eigenvectors. The concept of eigenvalues and eigenvectors is fundamental in linear algebra and is used in many applications in engineering, physics, and computer science.
To write the characteristic equation for a matrix A and find its eigenvalues, follow these steps:

1. Set up the equation: det(A - λI) = 0, where λ represents the eigenvalue and I is the identity matrix of the same size as A.
2. Calculate the determinant of (A - λI).
3. Solve the resulting polynomial equation for λ to find the eigenvalues.
4. Determine each eigenvalue's multiplicity by counting the number of times it appears as a root of the polynomial equation.

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The probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

What is a binomial distribution?

The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.

Formula to calculate the binomial distribution

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ

Here, we know that

Solar-heat installations successfully reduce the utility bill 60% of the time.

We have to calculate the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill.

We have 60% = 0.6 = p and n = 10.

We have a binomial distribution: X : (10, 0.6).

We use the binomial distribution formula to calculate the probability

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ, we get

P(x ≥ 9) = 1 - P(x < 9)

P(x ≥ 9) = 1 - P(x ≤ 8)

P(x ≥ 9) = 1 - ∑⁸₀ P(x = x)

P(X ≥ 9) = 1 - ∑⁸₀¹⁰Cₓ × (0.6)ˣ × (1-0.6)¹⁰⁻ˣ

P(X ≥ 9) = 1 -( 0.00011 + 0.00157 + 0.01062 + 0.04247 + 0.11148 + 0.20066 + 0.25082 + 0.21499 + 0.12093)

P(X ≥ 9) = 1 -0.95365

P(X ≥ 9) = 0.04635

Hence, the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

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Answer:

Step-by-step explanation:

We know that:

Solution:

[Simplifying]

[Final Answer]

Hence, the total number of minutes she practiced over the course of the three days is 7m minutes.

Answer:

B or 4/3 i think

Step-by-step explanation:

hope this helps :3

sorry if im wrong

Answer:

You save $6.31.

Step-by-step explanation:

For this we need to find the unit price. To do that we take the cost/unit(in this case gallon

For the one gallon can we'll do 9.92/1 =9.92.

The unit price for the one gallon is $9.92 per gallon.

For the 5 gallon we'll do 43.29/5 = 8.66

The unit price for the five gallon is $8.66.

So we'll subtract 5•(9.92)-5•(8.66) =49.6-43.29= $6.31.

You save $6.31.

Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!

Answer:

She saw the letter K, and other letters Are X and Y

Step-by-step explanation:

The points of intersection are (1/2, 2) and (1, 1), which corresponds to option A. To find the points of intersection of the given line and ellipse, we need to solve the system of equations:

1) 2x + y = 3
2) 4x^2 + y^2 = 5

From equation (1), we can express y as y = 3 - 2x, and substitute this into equation (2):

4x^2 + (3 - 2x)^2 = 5
4x^2 + (9 - 12x + 4x^2) = 5
8x^2 - 12x + 4 = 0

Now, we can solve for x:

Divide by 4:
2x^2 - 3x + 1 = 0

Factor:
(2x - 1)(x - 1) = 0

Solutions for x:
x = 1/2 and x = 1

Now, we find the corresponding y-values:

For x = 1/2:
y = 3 - 2(1/2) = 2

For x = 1:
y = 3 - 2(1) = 1

Thus, the points of intersection are (1/2, 2) and (1, 1), which corresponds to option A.

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Answer:

question 1: answer is 4

question 2: answer is 1

Step-by-step explanation:

The correct  solution to the initial value problem is

5y + (3/4)cos(2y) = t + 21 + (3/4)cos(8)

Starting with the initial value problem:

5(dy/dt) - 1 = 3cos(2y),   y(-1) = 4

We can rearrange the equation:

5(dy/dt) = 3cos(2y) + 1

Next, we integrate both sides with respect to t:

∫5(dy/dt) dt = ∫(3cos(2y) + 1) dt

5∫dy = 3∫cos(2y) dt + ∫dt

5y = (3/2)∫cos(2y) dt + t + C

Now, let's integrate the right side of the equation:

5y = (3/2)∫(1/2)sin(2y) d(2y) + t + C

5y = (3/4)(-cos(2y)) + t + C

To determine the constant of integration, we use the initial condition y(-1) = 4:

5(4) = (3/4)(-cos(2(4))) + (-1) + C

20 = (3/4)(-cos(8)) - 1 + C

20 = (-3/4)cos(8) - 1 + C

C = 20 + (3/4)cos(8) + 1

C = 21 + (3/4)cos(8)

Now, substitute the value of C back into the equation:

5y = (3/4)(-cos(2y)) + t + 21 + (3/4)cos(8)

Rearranging the equation to isolate y:

5y + (3/4)cos(2y) = t + 21 + (3/4)cos(8)

This is the correct final solution to the initial value problem.

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Answer:

\(5 \sqrt{3} - 20 \sqrt{2} \)

Step-by-step explanation:

\(simpify \\ \sqrt{75} - 4 \sqrt{8} - 3 \sqrt{32} \\ from \: the \: above \: get \: two \: numbers \: \\ such \: that \: when \: multiplied \: gives \\ \: the \: numbers \: inside \: the \: root \\ and \: one \: of \: the \: numers \: should \\ be \: a \: perfect \: square. \\ \sqrt{25 \times 3} - 4 \sqrt{4 \times 2} - 3\sqrt{16 \times 2} \\ 5 \sqrt{3} - 4 \times 2 \sqrt{2} -3 \times 4\sqrt{2} \\ 5 \sqrt{3} - 8 \sqrt{2} - 12\sqrt{2} \\ 5 \sqrt{3} - 20 \sqrt{2} \)

Answer:

\(the \: third \: answer \: is \: correct\)

Answer:

x^2+y^2=16

Step-by-step explanation:

i think so

Answer: you didn’t even say please

explanation: why don’t you ask your mother you make me sad

Answer:

The answer is "Linear function".

Step-by-step explanation:

Linear features would be those that have a linear graph. Its following location identified to a linear function, that is \(\bold{f(x) = a+bx}\).

This function had a variable one of reliant to its variable, which is "x", and it's distinct and the response variable is reliant.

please find the attachment of the graph.