Which of the following equations has infinitely many solutions? How do you know?
a) 3x - 7 = 7 - 3x
b) 2x + 8 = 8
c) 4x - 10 = -10 + 4x
d) 5x - 10 = 4x - 10

The negative slope of the linear equation indicates that the number of violent crimes has decreased over the years. The intercept of the line at (0, 1,773,900) represents the number of violent crimes in 1993.

The scatter plot shows a negative linear relationship between the number of violent crimes and the years since 1993. As the number of years increases, the number of violent crimes decreases. The linear equation that best models this relationship is y = -31,256x + 1,773,900. This means that for every one-year increase since 1993, the number of violent crimes decreases by 31,256.

The y-intercept of 1,773,900 represents the number of violent crimes in 1993, the starting year of the data set. The slope of -31,256 indicates that the decrease in violent crimes over time is quite significant.

It is important to note that while the linear equation provides a good model for this data set, it does not necessarily mean that it can accurately predict the number of violent crimes in future years. Other factors not accounted for in the data set may influence the number of violent crimes in the future.

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The mean of the test is 7.

We can do the two equations as

a. A score of 48 falls one standard deviation below the mean, 48 = xm - d. First equation.

b. A score of 34 falls three standard deviation below the mean, 34 = xm - 3d

Subtract eq 1 from eq 2

48 = xm- d

34 = xm - 3d

14 = 0 + 2d

d= 7

That is the mean.

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Answer:

Step-by-step explanation:

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where,

\( \underline{\rm \star{ \green{ \: A : x_1 = 2 , x_2 = 5 \: }}}\)

\( \underline{\rm{ \star{ \color{green} \: B : y_1 = -53 , y_2 = -69 \: }}}\)

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or

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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

a) We fail to reject the null hypothesis at the 5% level of significance. Therefore, the population mean is 8.75

b) We fail to reject the null hypothesis at the 5% level of significance. Therefore, the population mean is 8.75.

The claim about the population mean under the one-tailed alternative hypothesis and two-tailed alternative hypothesis are tested by the z-test statistic. The critical value approach is used to identify the true statement under the null and the alternative hypothesis at the 5% level of significance.

Sample size , n = 20

Sample mean, x(bar) = 9.5

Population standard deviation, σ = 3.5

a) Null hypothesis: \(H_0:\)μ = 8.75

Alternative hypothesis: \(H_a\) μ \(\neq\) 8.75 Two tailed

Level of significance, α = 0.05

Excel function for the critical value:

=NORMINV(0.05/2,0,1)

\(Z_0_._0_5_/_2\) = ± 1.96

The Z-test statistic is defined as:

Z = x(bar) - μ /  σ / \(\sqrt{n}\)

Z = 9.5 - 8.75 / 3.5/\(\sqrt{20}\)

Z = 0.958

The test statistic value is less than the critical value at the 5% level of significance. We fail to reject the null hypothesis at the 5% level of significance. Therefore, the population mean is 8.75.

b)  Null hypothesis: \(H_0:\)μ = 8.75

Alternative hypothesis: \(H_a\) μ \(>\) 8.75 Right tailed

Level of significance, α = 0.05

Excel function for the critical value:

=NORMINV(0.05,0,1)

\(Z_0_._0_5_/_2\)  = + 1.645

The Z-test statistic is defined as:

Z = x(bar) - μ /  σ / \(\sqrt{n}\)

Z = 9.5 - 8.75 / 3.5/\(\sqrt{20}\)

The test statistic value is less than the critical value at the 5% level of significance. We fail to reject the null hypothesis at the 5% level of significance. Therefore, the population mean is 8.75.

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Answer:

3/4

Step-by-step explanation:

1 1/2 can be expressed as an improper fraction 3/2

hence

1 1/2 ÷ 2

= 3/2 ÷ 2

= 3/2 x 1/2

= 3/4

A rhombus with MK = 24 m, JL = 20, ∠MJL = 50°. So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

We need the information about the measurements or a description of the missing measures in the rhombus. We can make it MK = 24 m, JL = 20, ∠MJL = 50° for example. Since it's a rhombus, all sides are equal in length. Therefore, NK = MK = 24 m, JM = JL = 20 m, and ML = NL.

To find ML (or NL), we can use the Law of Cosines on the triangle MJL. In this case,

ML² = JM² + JL² - 2(JM)(JL)cos(∠MJL):

ML² = 20² + 20² - 2(20)(20)cos(50°)

ML² = 400 + 400 - 800cos(50°)

ML² ≈ 617.4

Taking the square root of both sides, we get ML ≈ √617.4 ≈ 24.8 m.

So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

The complete question is The quadrilateral below is a rhombus. Given MK = 24 m, JL = 20, ∠MJL = 50°. Find NK, NL, ML, and JM. Any decimal answers should be rounded to the nearest tenth.

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The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​:

(a) P(3) = 0.2636

(b) P(x≥4) = 0.1814

(c) P(x<8) = 0.9997

(a) To find the probability that exactly three out of twelve U.S. adults favor the use of unmanned drones by police agencies, we can use the binomial probability formula:

P(3) = (12 choose 3) * (0.38)^3 * (1-0.38)^(12-3) = 0.2636

where (12 choose 3) = 12! / (3! * 9!) represents the number of ways to choose 3 out of 12 adults.

(b) To find the probability that at least four out of twelve U.S. adults favor the use of unmanned drones by police agencies, we can use the complement rule and subtract the probability of having three or fewer adults who favor the use of drones from 1:

P(x≥4) = 1 - P(x≤3) = 1 - [(12 choose 0) * (0.38)^0 * (1-0.38)^(12-0) + (12 choose 1) * (0.38)^1 * (1-0.38)^(12-1) + (12 choose 2) * (0.38)^2 * (1-0.38)^(12-2) + (12 choose 3) * (0.38)^3 * (1-0.38)^(12-3)] = 0.1814

(c) To find the probability that less than eight out of twelve U.S. adults favor the use of unmanned drones by police agencies, we can sum up the probabilities of having zero to seven adults who favor the use of drones:

P(x<8) = P(x=0) + P(x=1) + ... + P(x=7) = (12 choose 0) * (0.38)^0 * (1-0.38)^(12-0) + (12 choose 1) * (0.38)^1 * (1-0.38)^(12-1) + ... + (12 choose 7) * (0.38)^7 * (1-0.38)^(12-7) = 0.9997

Note that the probability of having eight or more adults who favor the use of drones is negligible.

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A. They are congruent

Hope this helps! :)

Answer:

$33,734

87x355+2849

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

Knowing that a cube has 6 faces which all are equal.

Thus, Multiply the area of one face by the number of faces to get the total surface area of the cube.

Since, it given that one face is 5 cm

Then, we also must know the formula for area of a cube

Which is:

\(Area=6a^2\)

Thus,

\(Area=6a^2\)

\(Area=6(5)^2\)

\(Area=6(25)\)

\(Area=150\)

Kavinsky

In a coordinate system, a vector is oriented at an angle this statement is false.

In a coordinate system, vectors are typically represented by their components along the coordinate axis . These components determine the direction and magnitude of the vector. The orientation of a vector is determined by the angles it makes with the coordinate axis or by the direction cosines or direction angles that specify its direction in space.

The direction of a vector can be represented using angles, such as the azimuthal angle (horizontal angle) and inclination angle (vertical angle) in spherical coordinates or the angles of inclination from the positive x-axis and positive z-axis in cylindrical coordinates.

Therefore, it is incorrect to say that a vector is oriented at an angle in a coordinate system. The orientation of a vector is defined by its components or direction angles relative to the coordinate axis.

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True. In a coordinate system, a vector can be oriented at any angle with respect to the reference axis.

In a coordinate system, a vector can be oriented at any angle with respect to the reference axis. The angle at which a vector is oriented is measured with respect to a reference axis, usually the positive x-axis. This angle is typically measured in degrees or radians.

The orientation of a vector can be described using trigonometric functions such as sine, cosine, and tangent. These functions relate the angle of orientation to the coordinates of the vector in the coordinate system. For example, the x-coordinate of a vector can be determined using the cosine function, while the y-coordinate can be determined using the sine function.

The orientation of a vector can also be represented using direction angles. In two-dimensional space, the orientation of a vector can be described using a single angle. In three-dimensional space, the orientation of a vector can be described using direction angles, which are the angles between the vector and each of the coordinate axes.

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Answer:

$372

Step-by-step explanation:

12 × 10 = 120

1 foot = $3.10

120 feet = ?

120 feet × $3.10

= $372

$372÷ 1 foot = $372

The value of x from the solution =4
The value of y from the solution =7

Equation 1: 2x + y = 15
Equation 2: y + 5 = 3x

Let's solve for y in Equation 1:

y = 15 - 2x

Now, substitute this expression for y in Equation 2:

(15 - 2x) + 5 = 3x

Simplify and solve for x:

15 - 2x + 5 = 3x
20 = 5x
x = 4

Now that we have the value of x, substitute it back into the expression for y:

y = 15 - 2(4)
y = 15 - 8
y = 7

So, the solution for the system of equations is x = 4 and y = 7.

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The probability is 0.9772. The average age of professors at a certain university is normally distributed with an average of 45.0 years and a standard deviation of 6.0 years.

If 16 professors are chosen at random for a committee, find the probability that the average age of those professors is greater than 42.0 years. We are required to find the probability that the average age of the 16 professors is greater than 42 years. Let us consider the mean of sample means as mu_x = 45 years. The standard error of the mean can be calculated as;  standard error = standard deviation/sqrt(n)`where n = sample size.

Standard error = 6.0/sqrt(16) = 1.5. Therefore, z-score is calculated as; z-score = (sample mean - population mean)/standard error = (42-45)/1.5 = -2. Now, the probability of Z being less than -2 can be found from the z-table as P(Z < -2) = 0.0228. So, the probability that the average age of those professors is greater than 42 years is 1- P(Z < -2) = 1- 0.0228 = 0.9772.

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Answer:

It is false

Step-by-step explanation:

Answer:

There is no product but the equation is false

Step-by-step explanation:

If you meant 3.242 x 2.12 it is = 6.87304

To find the coordinates of the centroid for the region bounded by the curves y=16x, y=9/x, y=0, and x=10, we need to calculate the x-coordinate and y-coordinate of the centroid separately. First, let's find the x-coordinate of the centroid.

We can use the formula: x-bar = (1/A) ∫[a,b] xf(x) dx, where A is the area of the region. The intersection points of the curves y=16x and y=9/x can be found by setting the equations equal to each other: 16x=9/x.

Solving this equation, we get x=±√(9/16)=±3/4. Since the region is bounded by x=10, we take the positive value x=3/4. To find the area A, we integrate the difference between the curves: A=∫[3/4,10] (16x-9/x) dx. Evaluating this integral, we find A=400-9ln(10).

Now we can calculate the x-coordinate of the centroid: x-bar=(1/A) ∫[3/4,10] x(16x-9/x) dx. Simplifying the integral and evaluating it, we get x-bar=(8160-36ln(10))/(400-9ln(10)). Next, let's find the y-coordinate of the centroid.

Since the region is symmetric about the x-axis, the y-coordinate of the centroid will be y-bar=0. Therefore, the exact coordinates of the centroid for the given region are: (x-bar, y-bar)=((8160-36ln(10))/(400-9ln(10)), 0).

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The four integers are 8, 8, 1, and 10, and their sum is 27.So  the value of a+b+c+d= 8+8+1+10 = 27.
Let's start by expanding the left side of the equation given:

(9-a)(9-b)(9-c)(9-d) = 9
(9-a)(9-b)(9-c) = (d-9)

Notice that the left side of the equation is always positive since a, b, c, and d are positive integers. Therefore, d must be greater than 9. Let's set d = 10 and see if we can find values for a, b, and c that satisfy the equation:

(9-a)(9-b)(9-c) = 1

The only way for the product of three factors to equal 1 is if one of the factors is equal to 1 and the other two are equal to 8. Without loss of generality, let's assume a = 8, b = 8, and c = 1:

(9-8)(9-8)(9-1)(9-10) = 1

Therefore, the four integers are 8, 8, 1, and 10, and their sum is 27.

So the value of a+b+c+d= 8+8+1+10 = 27.

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There are 14 questions out of which the student decided to answer 7 true and 7 false.-total sequences = 17297280

From the question, we have

There are 14 questions out of which the student decided to answer 7 true and 7 false.

Total sequences = P(14,7)

= 14!/7!

= 17297280

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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The maximum earning is v(r,b)

Let v(r,b) be the expected value of the game for the player, assuming optimal play, if the remaining deck has r red cards and b black cards.

Then v(r,b) satisfies the recursion

and

The stopping rule is simple: Stop when v(r,b)=0.

To explain the recursion . . .

If r,b>0, and the player elects to play a card, then:

Thus, if r,b>0, electing to play a card yields the value f(r,b).

But the player always has the option to quit, hence, if r,b>0, we get v(r,b)=max(0,f(r,b)).

Implementing the recursion in Maple, the value of the game is

v(26,26)=41984711742427/15997372030584

v(26,26)  ≈2.624475549

and the optimal stopping strategy is as follows . . .

So, The maximum earning is v(r,b)

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Answer:

Step-by-step explanation:

1/2x - y = 8

1/2x = 8 + y

2(1/2x = 8 + y)

x = 16 + 2y

Answer:

J= 45

Step-by-step explanation:

You have to multiply 5 by 9 to get what J is.

To determine which proposal(s) to select, we need to compare the present worth or net present value (NPV) of each proposal. The NPV represents the difference between the present value of cash inflows and outflows for each proposal.

For independent proposals at MARR = 15.5% per year:

Calculate the NPV for each proposal using the cash inflows and outflows and discounting them to present value using the MARR of 15.5%.

Select the proposal(s) with a positive NPV. Positive NPV indicates that the project's expected cash inflows exceed the initial investment and the MARR.

For mutually exclusive proposals at MARR = 10% per year:

Calculate the NPV for each proposal using the cash inflows and outflows and discounting them to present value using the MARR of 10%.

Select the proposal with the highest positive NPV. The proposal with the highest positive NPV indicates the project that generates the highest expected return or value relative to the MARR.

For mutually exclusive proposals at MARR = 14% per year:

Calculate the NPV for each proposal using the cash inflows and outflows and discounting them to present value using the MARR of 14%.

Select the proposal with the highest positive NPV. The proposal with the highest positive NPV indicates the project that generates the highest expected return or value relative to the MARR.

It's important to note that the specific details of the proposals, including cash inflows, outflows, and timing, are needed to calculate the NPV accurately. Without this information, it is not possible to provide a definitive answer.

The simplify of given equation 11k/ (55k^2+ 22k) is 1/(5k+2).

Given,

\(\frac{11x}{55^{2}+22k }\)  We have to simplify in rational expression

The common factor is 11. So, we have to pick the common factor from the equation.

= \(\frac{11x}{55^{2}+22k }\)

= \(\frac{1}{5x + 2}\)

Therefore the simplification of given equation is 1/(5k+2).

Reasonable expressions resemble fractions with variable denominators (and often numerators too). An example of a rational expression is x 2 x + 3 dfracx2x+3 x+3x2 start fraction, x, squared, divided by, x, plus, 3, end fraction.

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The chart element that gives a realistic, three-dimensional look is D. plot area.

In a chart, the plot area is the area where the actual chart data is plotted. It is the main part of the chart where the lines, bars, or other data markers are displayed. To give a chart a realistic, three-dimensional look, shading and depth are applied to the plot area. This creates the illusion of depth and makes the chart appear more visually appealing and easier to read. The axis, chart area, and legend do not typically have a three-dimensional appearance, as they are typically two-dimensional elements that provide information about the chart data rather than displaying the data itself.

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Answer:

b = 70

b = a = 70

b = c = 70

Step-by-step explanation:

snice b and 70 are opposite the top; they are equal.

b and a are alternate internal they are again equal so a is 70.

and finally a is equal with c because they are opposite at the top.

I hope I helped you! :)))

Answer:

28

Step-by-step explanation:

7.2 is rounded down to 7, 7.3 is rounded down to 7, 6.9 is rounded up to 7, and 6.8 is rounded up to 7. Then you can add 7+7+7+7 to get an estimation of 28.