What is the standard form equivalent to -2(x - 6)2 + 20 ​

The solution set of the inequality is:

m > 12

Here we want to solve the inequality:

5m > 60

To find the solution set of the inequality, we need to isolate the variable, m, in one of the sides of it.

To do so, divide both sides by 5, we will get:

5m/5 > 60/5

m > 12

So any value of m that is larger than 12 is a solution.

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Answer:

9r/1 is the correct answer that satisfies the given conditions or if you wanna express your answer in the form of just 9r would be your answer

Step-by-step explanation:

(27r)1/3

9r/1 (9 times 3 is 27)

The simplified Expression of  (27\(r)^{1/3\) is 3\(r^{1/3\).

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as \(3^4\), where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.

Given:

We have to simplify (27\(r)^{1/3\)

Now, prime factorizing 27 = 3 x 3 x 3

(27\(r)^{1/3\)

= (3 x 3 x 3 x \(r)^{1/3\)

= (3³ \(r)^{1/3\)

= \(r^{1/3\) \((3^3)^{1/3\)

= 3\(r^{1/3\)

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Answer:

#3

Step-by-step explanation:

hope it helps you ♡♡

Answer:

790

Step-by-step explanation:

7098uuilu4645

The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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Answer: 3

Step-by-step explanation:

Since the numbers that we are using are in the forms of tens, we can draw a simplified number line like

For the first problem, we are adding -30 to -20. This means that we will jump 3 times to the left since we are dealing with negative numbers. The jump is 3 times because each jump represents 10. Hence, this is described as

For the second part, we are adding +30 to -20. Since we are adding up a positive number to a negative number, we will jump 3 times to the right. This can be represented in the number line as

ANSWER and EXPLANATION

We have letter W on the graph.

The cordinates of its vertices are:

(0, 4), (1, 0), (2, 2), (3, 0), (4, 4)

Now, on a cartesian plane, (x - y plane), we have 4 quadrants. The letter is on the first quadrant.

Because it rotates 180 degrees around the origin, it means that it mmoves by 2 quadrants:

So, it moves from quadrant 1 to quadrant 4.

The new cordinates become:

(0, -4), (-1, 0), (-2, -2), (-3, 0), (-4, -4)

Then it is translated 4 units up, so we add 4 units to each of the y values (Remember that cordinates are written as (x, y)):

(0, 0), (-1, 4), (-2, 2), (-3, 4), (-4, 0)

Now, plot those:

a) It forms the letter M.

b) For one shape to be congruent to another, it means that they have the same size. So, yes, the M is congruent to the W.

X varies directly as y , that x = 9 when y = 3,the value of x when y = 12 by  the constant of Variation , value of x is 36.

X  varies directly as y, it means that there is a constant ratio between x and y. We can express this relationship using the formula:

x = ky

where k is the constant of variation.

To find the value of k, we can use the given information that x = 9 when y = 3. Substituting these values into the formula, we have:

9 = k * 3

Solving for k, we divide both sides of the equation by 3:

k = 9/3

k = 3

Now that we have the value of k, we can find x when y = 12 by substituting it into the formula:

x = 3 * 12

x = 36

Therefore, when y = 12, the corresponding value of x is 36.

if x varies directly as y and we are given that x = 9 when y = 3, we can find the value of x when y = 12 by determining the constant of variation (k) and using the formula x = ky. In this case, the constant of variation is 3, so when y = 12, x equals 36.

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Answer:

Step-by-step explanation:

I added a screenshot of the graph hope it helps

Answer:

a

\(0.0028  < p_1 - p_2  < 0.0288\)

b

The  interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack  and the non-Vioxx users (the placebo group  ) who suffered from heart attack  lie within the interval

The  use of Vioxx drug should be stopped

Step-by-step explanation:

From the question we are told that

   The sample size for Vioxx users is  \(n_1 = 3025\)

   The second sample size for placebo is  \(n_2 =  2875\)

   The number of Vioxx users that suffered heart attack is  \(k  = 334\)

     The number of non-Vioxx users that suffered heart attack is  \(g  = 272\)

    Generally the  sample proportion for Vioxx users is mathematically represented as

      \(\r p_1 =  \frac{k}{n_1}\)

=>   \(\r p_1 =  \frac{334}{3025}\)

=>   \(\r p_1 =  0.11041 \)

    Generally the  sample proportion for placebo users is mathematically represented as

       \(\r p_2 =  \frac{g}{n_2}\)

=>   \(\r p_2 =  \frac{272}{2875}\)

=>   \(\r p_2 =  0.09461 \)  

Generally the confidence level is 90% , then the level of significance is  \(\alpha =  (100-90)\%\)

=>   \(\alpha =  0.10\)

Generally the critical value of  \(\frac{\alpha }{2}\) from the normal distribution table  is  

     \(Z_{\frac{\alpha }{2} } =  1.645\)

Generally the standard error is mathematically represented as

      \(SE =  \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }\)

=>  \(SE =  \sqrt{\frac{0.11041 (1- 0.11041)}{3025} + \frac{0.09461 (1-0.09461)}{2875} }\)

=>  \(SE = 0.0079\)

Generally the margin of error is mathematically represented as

    \( E=  Z_{\frac{\alpha }{2} } *  SE\)

=>  \( E=  1.645  *  0.0079\)  

=>  \( E=  0.013\)  

Generally the 90%  confidence interval is mathematically represented as

     \(0.11041 - 0.09461- 0.013 < p_1 - p_2  < 0.11041 - 0.09461+ 0.013 \)

=>       \(0.0028  < p_1 - p_2  < 0.0288\)

The  interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack  and the non-Vioxx users (the placebo group  )  lie within the interval

Looking at the interval we see that proportion of Vioxx users who suffered is  more compared to  non-Vioxx users (the placebo group  )[i.e the both limit of the interval is  positive ] hence the  use of Vioxx drug should be stopped

Answer:  initial cost 26956.00 USD

value after 6 years approx= 21100.00 USD

Step-by-step explanation:

The initial cost is the price of new car , it means t ( time)=0

Substitute t by 0 in our equation and get the initial car's value

v(0)= 26956*0.96^0=26956.00 USD

The value after 6 years:  substitute t by 6

v(6)=26956*0.96^6=21100.00 USD

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Answer:

32760

Step-by-step explanation:

15!/(15-4)!=32760

Since order matters in the group of four officers we are choosing, we have to use permutations. This scenario is (15P4) because we have 15 people for 4 spots. Apply the formula for permutations.

The different ways are 32760 possible.

The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.

We are given club of fifteen people. we need to pick a president, treasurer, and secretary from the fifteen.

This scenario is (15P4) because, we have 15 people for 4 spots.

= 15!/(15-4)!

=32760

Since the order matters in the group of four officers we are choosing, thus we have to use permutations.

The different ways are 32760 possible.

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Answer:

approximately 254.5

btw area of circle= pi multiplied by radius

Step-by-step explanation: I got you bro

Answer: Circle area = π * r² = π * 81 [inch²] ≈ 254.47 [in²]

but because it asks for nearest tenth

254.5 in²

this is your real answer

This is the final static variable for all instances.

That makes the behaviour much more obvious. Modern IDEs will usually suggest changing the second listing into the third.

There is no reason to have an inline declaration initializing the value like the following, as each instance will have its own NUMBER but always with the same value. This is the same than to have only one final static variable for all instances.

The static keyword means the value is the same for every instance of the class. The final keyword means once the variable is assigned a value it can never be changed. The combination of static final in Java is how to create a constant value.

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Answer: the first answer

Step-by-step explanation: sorry i know it would’ve been better if i typed it but i’m running out of charge so it would be you first answer. this is because domain shows the minimum and maximum values x can be and range is the same but for y. the second and third functions aren’t in any format that i’ve learned before and it’s closest to interval notation which can be written as [min,max] with parentheses if it doesn’t touch those values. but yeah i hope this helped and i’m sorry if it is incorrect. good luck!

Answer:0.79 that is your answer

Solving some linear equations for the angles of the quadrilateral we can see that x = 19 and y = 30.

We know that AB is a line of symmetry, then the angles in the left side are equal to the ones in the right side, this means that we can write the linear equation:

5x - 24 = 2x + 33

Solving this for x:

5x - 2x = 33 + 24

3x = 57

x = 57/3 = 19

Now, any two angles that share a side should add up to 180°, then we also can write:

2x + 33 + x + 3y = 180

Replacing x there we can get:

2*19 + 33 + 19 + 3y = 180

90 + 3y = 180

3y = 180 - 90

3y = 90

y = 90/3 = 30

So x = 19 and y = 30.

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Answer:

f(4)=-2

Step-by-step explanation:

Plug in 4 into the equation. f(4)= 2(4)-10 then simplify the equation. Multiply 2 by 4, then subtract 10.

Answer:

V=6240 in^3

Step-by-step explanation:

I am not sure what the base is but here is my guess:

V=13Ah

V=13(48)(10)

V=6240 in^3

The photos are similar because the enlarged photo is 1.5 times the size of the original photo.

What is meant by similarity transformations?

Similarity transformations turn items in space into similar objects. If two items have the same shape or have the same shape as their mirror images, they are said to be similar. More specifically, by uniformly scaling (enlarging or decreasing), maybe with additional translation, rotation, and reflection, one can be created from the other. This indicates that one object may be properly aligned with the other object by rescaling, moving, and reflecting it. When two things are comparable to one another, one is consistent with the outcome of a specific uniform scaling of the other.

Here the initial dimension of the photo is  5" by 7" and after enlarging it has dimensions 7.5" by 10.5".

The scale factor is = 7.5/5 = 10.5/7 = 1.5

Since the scale factor is constant for all sides, the pictures before and after enlargement are similar.

Therefore the photos are similar because the enlarged photo is 1.5 times the size of the original photo.

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The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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9514 1404 393

Answer:

  168 square feet

Step-by-step explanation:

The model has shading in groups of 10 where possible. This makes it relatively easy to find the partial products and add them up.

  (10 +4)(10 +2) = 10·10 + 4·10 +10·2 + 4·2

  = 100 +40 +20 +8

  = 168 . . . . square feet

7(4x) = 28x

Hope this helps :)

Answer: 7(4x) > 4 x 7 = 28x

Answer: 28x