Planning for his retirement, mr Lloyd opened a saving

Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

Based on the information, it can be inferred that this salesperson must make sales equivalent to $28,000 to obtain an equal profit with both options.

To find the amount of money that we must sell to have the same profit with both options we must carry out the following mathematical procedure.

1. We must calculate how much you would earn with option A in a week.

$28 * 40 = $1,120

2. We must make a rule of three to find a value of which 4% is equal to 1,120

Based on the above, the salesperson must sell $28,000 to make the same profit on both options in one week.

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The volume of the right prism include the following: 8,640 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Next, we would determine the area of the triangle at the base of the right prism as follows:

Base area = 1/2 × ( 36 × 12)

Base area = 1/2 × 432

Base area = 216 in².

Now, we can calculate the the volume of this right prism:

Volume = base area × height

Volume = 216 × 40

Volume = 8,640 in³.

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In the provided figure, the value of angle JKM is 118.3°.

In Euclidean geometry, an angle is the figure produced by two rays, called the sides of the angle, sharing a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are termed dihedral angles. An angle is formed by joining two rays (half-lines) that have a shared terminal. The latter is referred to as the angle's vertex, while the rays are referred to as the angle's sides, legs, and arms.

Here,

x+70+y=180

x+y=110

x=110-y

x+2x-5=180

3x=185

x=185/3

3(110-y)=185

330-3y=185

145=3y

y=145/3

2x-5=2(185/3)-5

∠JKM=118.3°

The value of angle ∠JKM is 118.3° in the given figure.

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To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.

Therefore, we have:

P(z ≥ c) = 0.55

P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45

Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.

So, c = -0.126.

Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.

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obviously yes..........

Answer: C

Step-by-step explanation:

First off we can eliminate A and D because the lines are solid, this can only apply if our inequality equations are less than or equal to..., OR greater than or equal to...

Now we can pick any point on the graphs that the lines do not cross, lets do (0,0)

plug it in the inequalities equations

1. x + y < -2

0 + 0 < -2; this is false

2.  y - x < 3

0 - 0 < 3; this is true

this means the shading does not shade (0,0) since 1 was false which so the answer is C since B has (0,0) shaded

Answer:

Step-by-step explanation:

f(g(x)) = 6x^3 + 4 dollars/hour

Answer: f(x) and g(x) both represent y of the equations

Step-by-step explanation: f(x) and  g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.

The rotor failure distribution is modeled as a Weibull distribution with parameters β=2 and η=5.6 years. The mean time to failure (MTTF) of the rotor can be calculated using the formula μT = ηΓ(1+1/β),

The mean time to failure (MTTF) of the rotor can be obtained by substituting the given values of β=2 and η=5.6 years into the formula μT = ηΓ(1+1/β), where Γ(x) represents the gamma function.

To calculate the probability of a failure occurring during the first year, we can utilize the CDF of the Weibull distribution with the given parameters. By evaluating the CDF at 1 year, we can determine the probability of failure within that time frame.

If the first year passes without a failure, we can apply Bayes' rule to calculate the conditional probability of observing a failure in the second year. Bayes' rule allows us to update the probability based on the new information and the prior probability.

By performing these calculations, we can determine the MTTF of the rotor, the probability of failure during the first year, and the probability of observing a failure in the second year given that the first year passed without failure.

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Confidence interval refers to a statistical measure that helps quantify the amount of uncertainty present in a sample's estimate of a population parameter.

This measure expresses the degree of confidence in the estimated interval that can be calculated from a given set of data. In this scenario, the task is to build a 95% confidence interval for the regression line's slope. The regression analysis output has already been given. According to the output given, the estimated regression model is:y = 25,000 + 9,000 x, where x represents the number of miles the car has been driven and y represents the car's selling price.

The formula to calculate the 95% confidence interval for the slope is:Slope ± t · SE, where Slope is the point estimate for the slope, t represents the critical t-value for a given level of confidence and degrees of freedom, and SE represents the standard error of the estimate. The value of t can be calculated using the degrees of freedom and a t-table. Here, the number of pairs in the sample size is 20, and the model uses two parameters.

Therefore, the degrees of freedom would be 20 - 2 = 18.The critical t-value for a 95% confidence interval and 18 degrees of freedom is 2.101. Using the formula given above, we can calculate the 95% confidence interval for the slope as follows:Slope ± t · SE= 9000 ± (2.101)(700) ≈ 9000 ± 1,467.7 = [7,532.3, 10,467.7]Therefore, the 95% confidence interval for the slope is [7,532.3, 10,467.7]. This means that we are 95% confident that the true value of the slope for this model falls within the interval [7,532.3, 10,467.7].

It implies that the price of the car increases by $7,532.3 to $10,467.7 for each mile driven by the car. In conclusion, a 95% confidence interval has been calculated for the regression line's slope, which indicates that the actual slope of the model lies between the range [7,532.3, 10,467.7].

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We need to know about circumference of a circle to solve the problem. The number of revolutions that the car wheel makes to travel 1 mile is 672.

The circumference of the circle is the perimeter of the circle. In the given question we know that the diameter of the car wheel is 30 inches, and we need to find out the number of revolutions it will take for the car to travel 1 mile. We need to find the circumeference of the circle from there we will know how much distance it covers in one revolution, so we can find out after that the number of revolutions it will take to cover 1 mile.

radius= 30/2 = 15 inches

circumference= 2\(\pi\)r = 2x \(\pi\)x 15=94.25 sq inches

1 mile = 63360 inches

revolutions = 63360/94.25= 672

Therefore the number of revolutions the car will make to travel 1 mile is 672.

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The triangle formed by a complex number and its complex conjugate with the origin is an isosceles right triangle.

When a complex number and its complex conjugate are plotted in the complex plane, the two points are reflected about the real axis. Thus, the triangle formed by these points and the origin is an isosceles triangle with the real axis as its axis of symmetry.

Since the complex conjugate has the same magnitude as the original complex number, the two sides of the isosceles triangle have equal length. Therefore, the angle opposite the base (i.e., the origin) is a right angle, since it is the angle between the real axis and the imaginary axis.

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Answer:

99 1/2

Step-by-step explanation:

Answer:

5 / 8

Step-by-step explanation:

Total possible outcomes = (1, 2, 3, 4, 5, 6, 7, 8)

Odd outcomes = (1, 3, 5, 7)

Outcomes > 7 = 8

Required outcomes = (1, 3, 5, 7, 8)

Number of required outcomes = 5

P(pointer stops on odd or number > 7) = required outcome / Total possible outcomes

P(pointer stops on odd or number > 7) :

= 5 / 8

Answer:

23

Step-by-step explanation:

thgric7cuf j u gif dude jfcrcifcru u fug tu

0.8458 rounded to the nearest tenth is 0.8 given cos is 0.696706709347

Answer:

c

Step-by-step explanation:

i just had that question

The common difference is 8.

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

here, we have,

We have given sequence:

8,16,24,32..

We have to find the common difference in the sequence.

The given sequence is:

8,16,24,32..

16-8=8

24-16 = 8

32-24 = 8

So, the common difference is 8.

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Answer:

\(v = u + at \\ u = 6 \\ a = 10 \\ t = 2 \\ then \\ v = 6 + 10 \times 2 \\ = 6 + 20 = 26 \\ thank \: you\)

The predicted GPA of the student who sleeps for 2.5 hours per day is 2.27; option D.

The GPA of a student refers to the grade point average of the student which is the average of the student's grade points in his or her courses.

The predicted GPA of the student who sleeps for 2.5 hours per day is obtained from the scatter plot given below:

The equation for the least squares regression line is y = 0.375x + 1.33

x = 2.5

y = 0.375 * 2.5 + 1.33

y = 2.27

In conclusion,  the predicted GPA for the student is obtained from the scatter plot.

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Answer:

2.27

Step-by-step explanation:

Got it right on the test.

Step-by-step explanation:

77 ft

Answer:

 101.5 ft^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) h where b1 and b2 are the lengths of the bases and h is the height

A = 1/2 ( 11+18) * 7

   = 1/2 (29) *7

     101.5 ft^2

The expression representing height of kite from ground is Height = sin 50° × 40.

The kite, person holding the string and ground from where height is to be measured will form right angled triangle. We can use the sine function to find the height of kite from the ground. Writing the trigonometric relation -

sin theta = perpendicular ÷ hypotenuse

Keep the values in mentioned trigonometric relation to find the expression -

sin 50 = height ÷ 40

Height = sin 50° × 40

Finding the height using formed equation -

Height = 0.77 × 40

Performing multiplication

Height = 30.64 meters

Therefore, the expression to find the height of kite from ground is Height = sin 50° × 40.

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Answer:

\(P(Cheese) = 0.30\)

Step-by-step explanation:

Given

\(Cheese = 36\)

\(Pepperoni = 64\)

\(Veggie = 20\)

Required

\(P(Cheese)\)

This is calculated as:

\(P(Cheese) = \frac{Cheese}{Total}\)

\(P(Cheese) = \frac{36}{36+64+20}\)

\(P(Cheese) = \frac{36}{120}\\\)

\(P(Cheese) = 0.30\)

Using proportions, it is found that the possible amounts that he will spend on candy are represented by the inequality \(c \leq 54\).

A proportion is a fraction of a total amount.

In this problem, each pound of candy costs $6, and he will buy at most 9 pounds, hence the maximum amount he will spend is given by:

M = $6 x 9 = $54.

Hence, the possible amounts that he will spend on candy are represented by the inequality \(c \leq 54\).

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Answer:

9.16515138991

Step-by-step explanation:

a^2 + b^2 = c^2

7^2 + 5^2 = c^2

49 + 25 = 84

√84 = 9.16515138991

Answer: 7.21

Step-by-step explanation:

Some default named "MathWiz0001" deleted my answer. The "Reason":

"Uh oh! It looks like there are some mistakes in your answer. Please double-check your work and repost your answer. The second time's a charm!"

I even double checked it with calculators. So Ima put it here so it's actually here:

Just square root everything to get the answer,

 \(\sqrt{4^2+6^2} = \sqrt{c^2}\)

\(\sqrt{16+36} = \sqrt{c}\)

\(\sqrt{52} = \sqrt{c}\)

The length is 7.21. That is just what it is. :D

(it's the Pythagorean Theorem ofc they're gonna be grouped like that)

Answer: x=2

Step-by-step explanation:

\(6x=12\)

\(\frac{6}{6}x=\frac{12}{6}\)

\(x=2\)

Kyle's speed in feet per minute. That has to be what it is; if it's not, I am sorry. I hope this is the correct answer. Good luck.

Answer:

2(n+7)=4

Step-by-step explanation:

n is the number

The value of p in the given equation is -1.

Given is an equation p-3 = -4, we need to find the value of p,

So,

p-3 = -4

p = -4+3

p = -1

Hence, the value of p in the given equation is -1.

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