Prove that ST^2=TU*TV

The correct answer is (a) a = 0, b = two-thirds, c = 3.

This can be seen by comparing the given equation, y = two-thirds x squared + 3, to the general form of a quadratic equation, y = ax^2 + bx + c.

In the given equation, the coefficient of x^2 is two-thirds, so a = two-thirds. The coefficient of x is 0, so b = 0. And the constant term is 3, so c = 3.

Therefore, the correct answer is (a) a = 0, b = two-thirds, c = 3.

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Answer:

Based on the information, the probability of rolling a number less than a 3 (that is, a 1 or a 2) is 56/200 = 7/25 = 28%.

A government structure that is authoritarian or dictatorial in nature would be threatened by debate over public policy.

In such a system, the government exercises complete control over decision-making and any opposition or dissent is not tolerated.

Open debate and discussion over public policy would challenge the authority of the government and its ability to maintain control over the population.

Democracies, on the other hand, thrive on healthy debate and discussion over public policy, as it allows for diverse perspectives and ideas to be heard and considered.

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The quadratic equation in the given graph is:

y = -3(x - 1)^2 + 4

How to write the quadratic.

Look at the vertex, is it at (1, 4), then we can write the general quadratic equation in the vertex form (with a leading coefficient a) as follows:

y = a(x - 1)^2 + 4

Now the function passes through (0, 1) then we can replace these values in the equation above to get.

1 = a(0 - 1)^2 + 4

1 = a + 4

1 - 4 = a

-3  =a

The quadratic equation is:

y = -3(x - 1)^2 + 4

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The statement "The least expensive animal to feed may not be the favorite animal for a pet" explains why Katie asked the wrong question.

What is graphs?

Graphs are used by mathematicians to logically express or chart facts and values visually. A graph point typically depicts the relationship between several things.

While the cost of feeding an animal may be an important consideration for some people when choosing a pet, it is not necessarily the only or even the most important factor. Many people choose pets based on factors such as their personality, behavior, and the amount of attention and care they require.

Therefore, the animal that is least expensive to feed may not necessarily be the animal that people consider to be their favorite pet.

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The area of the parallelogram is[tex]39\sqrt(15)[/tex] square units.

In the preceding diagram, we must determine the height of the parallelogram in order to determine its area. The length of the perpendicular line segment drawn from vertex A to side BC determines the parallelogram's height. We'll refer to this line segment as AD. Since AD is perpendicular to BC, we can calculate its length using the Pythagorean theorem:

[tex]AD^2 = AC^2 - CD^2[/tex]

[tex]AD^2 = 12^2 - 3^2[/tex]

[tex]AD^2 = 135[/tex]

[tex]AD = \sqrt(135) = 3\sqrt(15)[/tex]

Now that we know the height of the parallelogram, we can use the formula for the area of a parallelogram:

Area = base x height

The base of the parallelogram is the length of side AB, which is 13 units. Therefore, the area of the parallelogram is:

[tex]Area = 13 \times 3\sqrt(15)[/tex]

[tex]Area = 39\sqrt(15) square units[/tex]

Therefore, the area of the parallelogram is [tex]39\sqrt(15)[/tex] square units.

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The margin of error for the 95% confidence interval used to estimate the population proportion is 0.0680. So, the correct answer is option d.

Calculate the sample proportion:

The formula (p) = x/n, where x is the sample size (163) and n is the number of successes (96), yields the sample proportion.

Therefore, the sample proportion is 96/163 = 0.5896.

Calculate the standard error:

The formula SE(p) yields the sample proportion's standard error = √[p(1-p)/n], where n is the sample size, and p is the sample proportion.

Consequently, the sample proportion's standard error is as follows:

SE(p) = √[0.5896(1-0.5896)/163] = 0.037

Calculate the margin of error:

The margin of error is given by the formula ME = z × SE(p), where SE(p) is the standard error of the sample proportion and z is the z-score corresponding to the desired level of confidence.

The z-score for a 95% confidence interval is 1.96.

As a result, the error margin is:

ME = 1.96 × 0.037 = 0.0680

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The equation line which is parallel to y = - (1/8)x - 8 and passes through (8, 5) will be y = -(1/8)x + 6.

Given that:

Equation, y = - (1/8)x - 8

The slope of the parallel lines is equal. Then the equation of the parallel line is given as,

y = -(1/8)x + c

The equation passes through (8, 5), then we have

5 = -(1/8) * 8 + c

5 = - 1 + c

c = 6

The equation of the parallel line will be y = -(1/8)x + 6.

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The zeros of the function f(x) are:

For a function y = f(x), the zeros are the values of x such that:

f(x)= 0

Here we have:

f(x)= (4x-3) (2x-1)

The zeros are the values such that any of the coefficients are zero, then we have:

4x - 3 = 0

x = 3/4

And:

2x - 1 = 0

x = 1/2

These are the zeros.

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The range of this data set include the following: D. 6.

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph (dot plot) shown in the image attached above, we can reasonably and logically deduce the following range:

Range = {18, 19, 20, 21, 22, 24} = 6.

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Answer:

concurrent lines

Step-by-step explanation:

If there are more than 2 lines (or in this case, 3 lines) that meet at a singular and same point, then they are called concurrent lines.

Answer:

[tex]m = \frac{14 - 7}{2 - 0} = \frac{7}{2} [/tex]

[tex]14 = \frac{7}{2} (2) + b[/tex]

[tex]14 = 7 + b[/tex]

[tex]b = 7[/tex]

[tex]y = \frac{7}{2} x + 7[/tex]

the overall gain is positive, we can conclude that the stockholder made a profit of $190.10. Therefore, the correct answer is: "The overall gain is $190.10."

How to solve the question?

To calculate the overall gain or loss, we need to first find the total cost of buying the shares and the total revenue from selling them.

For the 40 shares of Zycodec purchased at its lowest price of 29.39, the total cost would be:

40 shares x $29.39/share = $1,175.60

For the 95 shares of Unix purchased at its highest price of 16.12, the total cost would be:

95 shares x $16.12/share = $1,531.40

The total cost of purchasing both stocks would be:

$1,175.60 + $1,531.40 = $2,707

Now, we need to find the total revenue from selling the shares. The closing price of Zycodec is 34.95, so the revenue from selling 40 shares would be:

40 shares x $34.95/share = $1,398

The closing price of Unix is 15.78, so the revenue from selling 95 shares would be:

95 shares x $15.78/share = $1,499.10

The total revenue from selling both stocks would be:

$1,398 + $1,499.10 = $2,897.10

The overall gain or loss would be the difference between the total revenue and total cost:

Overall gain/loss = total revenue - total cost

Overall gain/loss = $2,897.10 - $2,707

Overall gain/loss = $190.10

Since the overall gain is positive, we can conclude that the stockholder made a profit of $190.10. Therefore, the correct answer is: "The overall gain is $190.10."

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The correct answer is D. Trapezoid EFGH is congruent to Trapezoid ABCD after undergoing transformation D.

Let's first define the transformations:

A. Translation down, followed by rotation of 90°, followed by dilation by a scale factor of 3.

B. Rotation of 45°, followed by a reflection, followed by a translation left.

C. Dilation by a scale factor of 12, followed by a translation up, followed by a reflection.

D. Reflection, followed by a dilation of a scale factor of 1, followed by a rotation of 180°.

To determine if Trapezoid EFGH is congruent to, an enlargement of, or a reduction of Trapezoid ABCD, we need to analyze the effects of each transformation on the trapezoid.

A. Translation down, followed by rotation of 90°, followed by dilation by a scale factor of 3.

This transformation involves moving the trapezoid down, rotating it 90 degrees clockwise, and then increasing its size by a scale factor of 3. This transformation does not preserve angles or side lengths, so Trapezoid EFGH is not congruent to Trapezoid ABCD.

B. Rotation of 45°, followed by a reflection, followed by a translation left.

This transformation involves rotating the trapezoid 45 degrees clockwise, reflecting it across a line of reflection, and then moving it left. This transformation does not preserve angles or side lengths, so Trapezoid EFGH is not congruent to Trapezoid ABCD.

C. Dilation by a scale factor of 12, followed by a translation up, followed by a reflection.

This transformation involves increasing the size of the trapezoid by a scale factor of 12, moving it up, and then reflecting it across a line of reflection. This transformation does not preserve angles or side lengths, so Trapezoid EFGH is not congruent to Trapezoid ABCD.

D. Reflection, followed by a dilation of a scale factor of 1, followed by a rotation of 180°.

This transformation involves reflecting the trapezoid across a line of reflection, then increasing its size by a scale factor of 1 (i.e., not changing its size), and then rotating it 180 degrees. This transformation preserves angles and side lengths, so Trapezoid EFGH is congruent to Trapezoid ABCD.

Therefore, the correct answer is D. Trapezoid EFGH is congruent to Trapezoid ABCD after undergoing transformation D.

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The first option, "one half," corresponds to the scale factor of 0.5.

Scale factor = Dimensions of the new shape Dimensions of the original shape is the fundamental formula used to calculate it. The formula is expressed as Scale factor = Larger image dimensions Smaller figure dimensions in the event that the original figure is enlarged.

We can contrast the side lengths of triangles D and D′ to determine the scaling factor.

Let's contrast the side lengths for the two triangles.

Triangle D has sides that are 4.2 in length, and triangle D′ has sides that are 2.1 in length.

Scale factor = (Side length of triangle D′) / (Side length of triangle D)

Scale factor = 2.1 / 4.2

Scale factor = 0.5

The first option, "one half," corresponds to the scale factor of 0.5.

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Answer:

y = -5x + 14 is the correct equation.

The value of the variables are x = -2 and y = 4

From the information given, we have that the simultaneous equations are;

4x-5y=-28

-9x-2y=10

Make 'x' the subject from equation 1

4x = -28 + 5y

x = -28 + 5y/4

Now, substitute the value in equation 2, we get;

-9(-28 + 5y/4) - 2y = 10

expand the bracket

252 - 45y/4 - 2y = 10

find the lowest common multiple

252 - 45y - 8y/4 = 10

cross multiply

252 - 45y -8y = 40

collect the like terms

-53y = -212

Make y the subject

y = 4

substitute the value

x = -28 + 5y/4

x = -28 + 20/4

x = -8/4

x = -2

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The probability that Cherish, Taffy, Haunter, and Maverick are chosen is 1/126

The total number of ways to choose 4 dogs out of 9 is given by the combination formula:

9Cr4 [this reads "nine combination four"]

9Cr4 = 9! / (4! 5!)

        = 126

This means there are 126 possible outcomes, each equally likely.

The number of ways to choose Cherish, Taffy, Haunter, and Maverick out of the 9 dogs is:

5Cr0 * 4Cr4 = 1

This means there is only 1 favourable outcome.

Therefore, the probability of choosing Cherish, Taffy, Haunter, and Maverick is:

1/126

So the answer is 1/126.

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Let the speed in still water be [tex]x[/tex] miles per hour.

The speed upstream will be slower than the speed downstream.

Speed upstream [tex]= x-4[/tex] miles per hour and speed downstream will be [tex]x+4[/tex] miles per hour.

[tex]\text{Time Taken}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]

The time taken for the trip upstream and the trip downstream are the same:

[tex]\text{time}_{\text{up}}=\dfrac{3}{x-4}[/tex]

[tex]\text{time}_{\text{down}}=\dfrac{11}{x+4}[/tex]

[tex]\dfrac{11}{x+4} =\dfrac{3}{x-4} \ \ \ \ \ \ \ \leftarrow \ \text{cross multiply}[/tex]

[tex]11(x-4)=3(x+4)[/tex]

[tex]11x-44=3x+12[/tex]

[tex]11x-3x=12+44[/tex]

[tex]8x=56[/tex]

[tex]\bold{x=7}[/tex] miles per hour

Answer:

3/8x8/3 = 1    

ur welcome I hoped I helped u answering ur question!!

Answer: 1

Step-by-step explanation:

3/8 * 8/3 just simplifies to 1 because the numerator and denominator will be equal meaning it equals 1.

None of the descriptive alternatives are correct.

What is the null hypothesis?

In statistical hypothesis testing, null and alternate hypotheses are utilized. The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

Here, we have

Given:  if obtained from an experiment, would lead to rejecting the null hypothesis if a = .01.

for 1st choice ; p-value =fdist(5,3,18)= 0.0107

for 2nd choice : p-value =fdist(4.08,3,8)=0.0496

for 3rd choice : p-value =fdist(150,1,1)=0.052

since none of the choices have p value less than 0.01; none of these would lead to a rejected null hypothesis.

Hence, none of the descriptive alternatives are correct.

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First, we need to calculate the total amount of time the machine runs each day:

Starting time: 09:30

Ending time: 16:10

We can convert the starting time and ending time to minutes:

09:30 = 9 x 60 + 30 = 570 minutes

16:10 = 16 x 60 + 10 = 970 minutes

The total running time of the machine is:

970 - 570 = 400 minutes

Since the machine produces a bolt every 8 seconds, we need to convert the running time from minutes to seconds:

400 x 60 = 24,000 seconds

Finally, we can calculate the number of bolts produced by dividing the total running time by the time it takes to produce one bolt:

24,000 / 8 = 3,000

Therefore, the machine produces 3,000 bolts each day.

The average size of the 15 diameters is 25.00mm. Using the concept of percentages, the mass of copper, lead, and tin in the bronze bearing are 140 kg, 40 kg, and 20 kg, respectively.

To find the average size of the 15 diameters, we need to calculate the sum of all the dimensions and then divide by 15 (the total number of diameters).

The sum of the dimensions can be calculated as follows:

(5 x 24.99mm) + (6 x 25.01mm) + (4 x 25.00mm)

= 375.01mm

Now, we can calculate the average size by dividing the sum by 15:

Average size = 375.01mm / 15

= 25.00mm (rounded to 2 decimal places)

Therefore, the average size of the 15 diameters is 25.00mm.

b.

To find the mass of each metal, we need to determine how much of each metal is present in the bronze bearing. This can be done using the concept of percentage

Let's start by finding the mass of copper in the bearing:

Mass of copper = 70% of 200 kg = 0.7 x 200 kg = 140 kg

Next, let's find the mass of lead in the bearing:

Mass of lead = 20% of 200 kg = 0.2 x 200 kg = 40 kg

Finally, let's find the mass of tin in the bearing:

Mass of tin = 10% of 200 kg = 0.1 x 200 kg = 20 kg

Therefore, the mass of copper, lead, and tin in the bronze bearing are 140 kg, 40 kg, and 20 kg, respectively.

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The probability for the possibility on a failing the exam is  1/3 , shown on the scale.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Any collection of results constitutes an event. Events are represented by capital letters, such as A and B. For instance, if the experiment involves flipping a single fair coin, event A might only receive one head. P(A) represents the probability of an event A.

Given that-

probability = number of favourable outcome / total outcome

number of favourable outcome = 1

number of total outcome = 3

probability = 1/3

Thus, the probability for the possibility on a  failing exam is 1/3 , shown on the scale.

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Complementary angles are two angles whose sum is equal to 90 degrees. In other words, if you add the measures of two complementary angles, you get 90 degrees. Complementary angles are often referred to as "complements" for short. For example, if one angle is 30 degrees, its complement would be 60 degrees.

Supplementary angles, on the other hand, are two angles whose sum is equal to 180 degrees. In other words, if you add the measures of two supplementary angles, you get 180 degrees. Supplementary angles are often referred to as "supplements" for short. For example, if one angle is 120 degrees, its supplement would be 60 degrees.

since the now has a value of ten so the p is equalled to 59

Answer:

15%

Step-by-step explanation:

0.15 x 100 = 15%

The centerline is 612, the upper control limit is 710.4, and the lower control limit is 513.6.

To find the centerline, upper control limit, and lower control limit for this data, we need to calculate the average and standard deviation of the values.

Given data:

601, 625, 619, 626, 619, 619, 650, 670, 656, 629, 633, 618, 652, 639, 667

Calculate the average (mean):

Sum = 9180

Number of values = 15

Average = Sum / Number of values = 9180 / 15 = 612

Calculate the standard deviation (SD):

Squared differences from mean:

961, 169, 49, 196, 49, 49, 1444, 3364, 1936, 289, 441, 36, 1600, 729, 3025

Sum of squared differences = 15078

Variance = Sum of squared differences / (Number of values - 1) = 15078 / 14 = 1077

SD = sqrt(Variance) = sqrt(1077) ≈ 32.8

Calculate control limits:

Centerline (CL) = Average = 612

Upper Control Limit (UCL) = CL + 3 * SD = 612 + 3 * 32.8 ≈ 710.4

Lower Control Limit (LCL) = CL - 3 * SD = 612 - 3 * 32.8 ≈ 513.6

The centerline is 612, the upper control limit is 710.4, and the lower control limit is 513.6.

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