The solution to -2(1 - 4x) = 3x + 8 is

To solve the equation for "x" we first need to simplify it.

The answer for this equation is either -3 or 3.

Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

The statement that shows equivalent measurements is "52 meters = 520 decimeters." Option C.

To determine the equivalent measurements, we need to understand the relationship between different metric units.

In the metric system, each unit is related to others by factors of 10, where prefixes indicate the magnitude. For example, "deci-" represents one-tenth (1/10), "centi-" represents one-hundredth (1/100), and "kilo-" represents one thousand (1,000).

Let's analyze each statement:

5.2 meters = 0.52 centimeters: This statement is incorrect. One meter is equal to 100 centimeters, so 5.2 meters would be equal to 520 centimeters, not 0.52 centimeters.

5.2 meters = 52 decameters: This statement is incorrect. "Deca-" represents ten, so 52 decameters would be equal to 520 meters, not 5.2 meters.

52 meters = 520 decimeters: This statement is correct. "Deci-" represents one-tenth, so 520 decimeters is equal to 52 meters.

5.2 meters = 5,200 kilometers: This statement is incorrect. "Kilo-" represents one thousand, so 5.2 kilometers would be equal to 5,200 meters, not 5.2 meters.

Based on the analysis, the statement "52 meters = 520 decimeters" shows equivalent measurements. So Option C is correct.

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Note the correct and the complete question is

Select the statement that shows equivalent measurements.

A.) 5.2 meters = 0.52 centimeters

B.) 5.2 meters = 52 decameters

C.) 52 meters = 520 decimeters

D.) 5.2 meters = 5,200 kilometers

The probability that it will not be orange is 0.9

What is probability?

Probability is the branch of mathematics concerning numerical descriptions of how probably an event is to do, or how likely it's that a proposition is true.

given:

There are:

5 pink marbles

9 green marbles,

13 blue marbles, and

3 orange marbles.

There is a total of 30 marbles in the jar.

Step 1. Take 1 marble from the jar.

Step 2. Probability that it is orange, = P(orange) = ( 3/30 ) = ( 1/10 ) = 0.10 = 10%

Step 3. Probability that the chosen marble is not orange, = ( 1 - Probability that the chosen marble IS orange) = ( 1 - 0.1 ) = 0.9 = 90%.

hence , the probability that it will not be orange is 0.9

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Answer:

Slope intercept form: y=mx+b; where m is the slope and B is the y intercept

For 2 lines to be parallel they must have the same slope. Thus, the slope of the new line is going to be 1.

To find the y intercept plug in the slope and the x, y into the equation y=mx+b:

y=mx+b

y=1x+b

2=1(2)+b

2=2+b

0=b

b=0

Now that we have your slope and y intercept we can make the equation:

y=1x+0

y=x

Step-by-step explanation:

Answer:

7/9

Step-by-step explanation:

To add fractions, you have to have like denominators. First find the LCM (Least Common Multiple) of both denominators. That is 9. The second fraction already has a denominator of 9, so leave it as is. The first fraction doesn't so what will happen is you will be converting it into a fraction with a denominator of 9. Multiply the denominator by 3 to get 9. Then multiply the top by 3 because whatever you do to the bottom you do the top. You will then get 3/9. 3/9+4/9 is equal to 7/9 because you just add the numerators, but keep the denominators the same.

Step-by-step explanation:

Let the number is n.

The product of n and 10 is:

The periodic signal x(t) can be found by using the complex exponential Fourier series coefficients D0, D1, D-1, D2, and D-2 = -1 + ejπt + e-jπt + (-0.5j)ej2πt + (0.5j)e-j2πt

The Fourier series of a periodic signal is given by:
x(t) = ∑n=-∞∞ Dnejnω0t
Where Dn are the Fourier series coefficients, ω0 is the fundamental frequency, and j is the imaginary unit.

Given that the fundamental period T0 = 2, the fundamental frequency can be found as:
ω0 = 2π/T0 = 2π/2 = π

Substitute the given Fourier series coefficients and the fundamental frequency into the Fourier series equation to find the periodic signal x(t):

x(t) = D0ej0ω0t + D1ej1ω0t + D-1ej(-1)ω0t + D2ej2ω0t + D-2ej(-2)ω0t
x(t) = -1ej0πt + 1ejπt + 1ej(-π)t + (-0.5j)ej2πt + (0.5j)ej(-2)πt
x(t) = -1 + ejπt + e-jπt + (-0.5j)ej2πt + (0.5j)e-j2πt

Therefore, the periodic signal x(t) is:
x(t) = -1 + ejπt + e-jπt + (-0.5j)ej2πt + (0.5j)e-j2πt

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Answer:

y=-4/3x+1 is the equation of the line perpendicular to 3/4x+5 and goes through the point 3,-3

Step-by-step explanation:

Note that the co-efficient before x is the slope, which i will call m, and a perpendicular line has a slope of -1/m.

-1/m=-4/3

so

y=-4/3x+z,

plug in 3 for x, and -3 for y to get z=1

y=-4/3x+1 is the equation

A bivariate probability distribution is a statistical distribution that describes the joint probability of two random variables. It provides the probability of each combination of values for the two variables. In simple words, it's a way to model the joint probability of two variables and the relationship between them.

A bivariate probability distribution is represented by a probability density function (pdf) or a probability mass function (pmf) depending on whether the variables are continuous or discrete. The function gives the probability of a given pair of values of the two variables. Bivariate probability distributions are useful in understanding the relationship between two variables and can be used to make predictions or draw inferences. It can be visualized using a scatter plot, a contour plot or a 3D plot. It can also be used to calculate the covariance and correlation between the two variables.

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Complete question:

Describe Bivariate Probability Distribution.

The resulting control chart will help identify any points that fall outside the control limits, indicating potential anomalies or special causes of variation in the idle time ratio.

To construct the control chart for the idle time ratio based on three standard deviations, we need to follow several steps:

Step 1: Calculate the average idle time ratio.

To calculate the idle time ratio, we divide the idle time (in minutes) by the total effective working time (in minutes). In this case, the total effective working time per day is 8 hours or 480 minutes. Calculate the idle time ratio for each day using the formula:

Idle Time Ratio = Idle Time / Total Effective Working Time

Day 1: 40 / 480 = 0.083

Day 2: 35 / 480 = 0.073

...

Day 25: 28 / 480 = 0.058

Step 2: Calculate the average idle time ratio.

Sum up all the idle time ratios and divide by the number of days to find the average idle time ratio:

Average Idle Time Ratio = (Sum of Idle Time Ratios) / (Number of Days)

Step 3: Calculate the standard deviation.

Calculate the standard deviation of the idle time ratio using the formula:

Standard Deviation = sqrt((Sum of (Idle Time Ratio - Average Idle Time Ratio)^2) / (Number of Days))

Step 4: Calculate the control limits.

The upper control limit (UCL) is the average idle time ratio plus three times the standard deviation, and the lower control limit (LCL) is the average idle time ratio minus three times the standard deviation.

UCL = Average Idle Time Ratio + 3 * Standard Deviation

LCL = Average Idle Time Ratio - 3 * Standard Deviation

Step 5: Plot the control chart.

Plot the idle time ratio data on a graph, along with the UCL and LCL calculated in Step 4. Each data point represents the idle time ratio for a specific day.

The resulting control chart will help identify any points that fall outside the control limits, indicating potential anomalies or special causes of variation in the idle time ratio.

Note: Since the calculations involve a large number of values and the table provided is not suitable for easy calculation, I recommend using a spreadsheet or statistical software to perform the calculations and create the control chart.

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Answer:

y = 5

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Because the slope is 0 and the y-intercept is 5, our equation will be

y = 5

If we take a sample of 50 students from your school and measure their height , then (c) The mean of the sample data. will be a Random Variable .

A Random Variable is a defined as a variable whose value depends on the outcome of a random event.

Option (c) : the random event is the selection of 50 students from the school to measure their height. The mean height of this sample of 50 students is a random variable because it can vary depending on the specific students who are selected.

Option (a) : The true mean height of all students from your school is a population parameter and is a fixed value, so it cannot be called as a random variable.

Option (b) : The mean of the sampling distribution of mean heights for samples of size 50 is a population parameter as well, and it represents the average of all possible sample means of size 50 taken from the population. So,  it is a fixed value and not a random variable.

Therefore , The mean of the sample data will be a random variable .

The given question is incomplete , the complete question is

Suppose you take a sample of 50 students from your school and measure their height.  Which one of the following is a random variable?

(a) The true mean height of all students from your school.

(b) The mean of the sampling distribution of mean heights for samples of size 50.

(c) The mean of the sample data.

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The rectangular coordinates of the point with the polar coordinates (-5, 5π/3) are (-5/2, 5√3/2).

To find the rectangular coordinates, follow these steps:

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Answer:

5.8

Step-by-step explanation:

Since AE ≅FD and AC ≅BD are already given, we need to prove that Angle ADF and Angle CAE are also congruent.

Since we know that AE is parallel to FD and AD is also a straight segment that intersects both AE and FD, this will serve as our transversal segment. In this case, we have Angle ADF and Angle CAE as alternate interior angles. By definition, alternate interior angles are congruent. Hence, ∠ADF and ∠CAE are congruent with the reason that they are alternate interior angles.

From this, we can say that ΔAEC≅ ΔDFB is congruent by SAS Triangle Congruence Theorem stating that if two sides and an included angle are congruent to both triangles, then the two triangles are congruent.

The equation of the tangent line to the curve e^y sin(x) - x - xy = π at (π, 0) is y = -x, the slope of the tangent line at a point is equal to the derivative of the function at that point. The derivative of the function e^y sin(x) - x - xy = π is e^y sin(x) - 1 - y.

To find the equation of the tangent line, we need to calculate the slope of the curve at the given point (π, 0). We can do this by taking the derivative of the curve with respect to x and evaluating it at x = π. Taking the derivative, we get dy/dx = cos(x)e^y - 1 - y - x(dy/dx). Substituting x = π and y = 0,

we have dy/dx = cos(π)e^0 - 1 - 0 - π(dy/dx). Simplifying further, we find dy/dx = -1 - π(dy/dx). Rearranging the equation, we get dy/dx + π(dy/dx) = -1. Factoring out dy/dx, we have (1 + π)dy/dx = -1. Solving for dy/dx, we find dy/dx = -1 / (1 + π).

Now that we have the slope of the tangent line, we can use the point-slope form of a linear equation to find the equation of the line.

Using the point (π, 0) and the slope -1 / (1 + π), we can write the equation as y - 0 = (-1 / (1 + π))(x - π). Simplifying, we have y = (-1 / (1 + π))(x - π), which is the equation of the tangent line in slope-intercept form.

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Answer:

x = \(\frac{54}{91}\)

Step-by-step explanation:

Let x = the scale factor

91 x = 54  Divide both sides by 91

\(\frac{91x}{91}\) = \(\frac{54}{91}\)

x = \(\frac{54}{91}\)

Helping in the name of Jesus.

Answer:

2.5%

Step-by-step explanation:

x=distance   y=time

x has been increased by 17%

100%+17% = 117%

y has been increased by 20%

100%+20%=120%

Now let's make the percentages into decimals. 117%=1.17 120%=1.2

To find the average speed you do the distance traveled divided by the time taken.

Average speed = 2.5%

Answer:

Sierra is trying to find out how tall the flagpole is outside of the courthouse in her hometown. She is

standing 20 feet from the base of the flagpole and the angle from her eyes to the top of the flagpole

is 80°. Her eyes are 4.5 feet from the ground. What is the height of the flagpole? Round to the

nearest tenth and show your work.

its 5.0

Lets find out,

• The slope parallel to 9x+3y=6:-

\(m = - 3\)

• Substituting,

\(m = - 3 \\ x = 5 \: \: \: into \\ y = 3\)

So,

\(y = mx + b\)

\( = > 3 = - 3 \times 5 + b\)

\( = > 3 = - 15 + b\)

\( = > 3 + 15 = b\)

\( = > 18 = b\)

• Substitute,

\(m = - 3 \\ b = 18\)

Use,

\(y = mx + b\)

\( = > y = - 3x + 18\)

• Now rewrite y= -3x+18 in slope intercept form,

(Please check the image attached for it)

Answer:

You divide 360 by 5 which is 72 & Then muiltiply that by 2.
Your answer would be 144 tho.

The house would have slid 910 yards in 15 days.

A geometric progression is a sequence in which successive terms differ by a common ratio.

It is a sequence in which the ratio of two consecutive terms is a constant.

Analysis:

first term, a= 1

second term, ar = 2

third term, ar^2= 4

common ratio = ar/a = 2/1 = 2

Sum of the G.P where n = 15

sum of G.p = a(\(\frac{r^{n} - 1}{r-1}\))

= 1(\(2^{15}\) - 1)/2 - 1 = 32768 - 1 = 32768 inches

converting the inches to yard, where 1 yard = 36 inches

so 32768/36 = 910 yards

In conclusion, the house would slide 910 yards in  15 days.

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The shorter leg of the right triangle measures 3 units, while the larger lag measures 11 units.

Here we know that we have a right triangle, and we know that:The hypotenuse measures √130 units.

The perimeter measures 14 + √130 units.

If we define:

x = shorter leg.

y = larger leg.

Then, using the Pythagorean theorem, we can write:x^2 + y^2 = √130^2 = 130

And for the perimeter equation we know that:

perimeter = x + y + √130 = 14 + √130

We can simplify this equation to:x + y = 14Then we have the system of equations:

x^2 + y^2 = 130

x + y = 14

Isolating one variable in the second equation we get.

x = 14 - y

Replacing that in the other equation we get:

(14 - y)^2 + y^2 = 130

Now we can solve this for y.

196 - 28y + y^2 + y^2 = 130

2y^2 - 28y + 196 - 130 = 0

2y^2 - 28y + 66 = 0

y^2 - 14y + 33 = 0

Using Bhaskara's formula we can get:

y = (14 ± √( 14^2 - 4*1*33))/2*1y = (14 ± 8)/2

Now, remember that y is the larger leg of the triangle, then:y = (14 + 8)/2 = 11For the value of x we use:

x = 14 - y = 14 - 11 = 3x = 3the shorter leg of the right triangle measures 3 units, while the larger lag measures 11 units.

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Answer:

$218.6625

Step-by-step explanation:

In general, they're not similar.

In any triangle with side lengths a, b, and c, we have the aptly-named triangle inequality that says the largest side is no larger than the sum of the smaller sides. In other words, if a and b are both smaller than c, then

a + b ≥ c

Suppose x < 12. Then BC corresponds to either YZ or XY.

• If BC corresponds to YZ, then the triangles are similar if and only if

BC/YZ = AB/XY = AC/XZ

x/2 = 9/3 = 12/4 = 3   ⇒   x = 6

• If BC corresponds to XY, then triangle similarity means

BC/XY = AB/YZ = AC/XZ

x/3 = 9/2 = 12/4

but this fails because 9/2 ≠ 12/4 = 3.

Suppose x > 12. Then BC corresponds to XZ, and

x/4 = 12/3 = 9/2

but this also fails because 12/3 = 4 ≠ 9/2.

(We ignore the case of x = 12 because that would make ∆ABC isosceles, and ∆XYZ certainly is not.)

So ∆ABC and ∆XYZ are similar only if x = 6. Under this condition, similarity would follow from the SSS similarity theorem.