the second drop down box is (does not equal) or equals

Answer:

-27

Step-by-step explanation:

8(-3)-3

-24-3

-27

hope this helps

Answer:

− 27

Step-by-step explanation:

Use the given functions to set up and simplify  f ( − 3 ) .

(a) h(t) is quadratic, so we can complete the square to write

h(t) = 100 + 40 t - 5 t²

h(t) = 100 - 5 (t² - 8 t)

h(t) = 100 - 5 (t² - 8 t + 16 - 16)

h(t) = 100 + 80 - 5 (t² - 8 t + 16)

h(t) = 180 - 5 (t - 4)²

The squared quantity is always non-negative, which means h(t) has a maximum value of 180 m.

(b) First, find when the projectile hits the ground, which happens when h(t) = 0:

0 = 180 - 5 (t - 4)²

180 = 5 (t - 4)²

36 = (t - 4)²

± 6 = t - 4

t = -2   OR   t = 10

Omit the negative solution. The velocity of the ball at t = 10 s is equal to the derivative at the point, h' (10).

\(h'(10)=\displaystyle\lim_{t\to10}\frac{h(t)-h(10)}{t-10}\)

\(h'(10)=\displaystyle\lim_{t\to10}\frac{(180-5(t-4)^2)-80}{t-10}\)

\(h'(10)=\displaystyle\lim_{t\to10}\frac{100+40t-5t^2}{t-10}\)

\(h'(10)=\displaystyle-5\lim_{t\to10}\frac{(t+2)(t-10)}{t-10}\)

\(h'(10)=\displaystyle-5\lim_{t\to10}(t+2)=-60\)

So the projectile has a downward velocity of 60 m/s at the moment it touches the ground.

Hello!

Find the maximum height by finding the maximum of the function, where the derivative switches from positive to negative. Find the derivative of the equation:

h(t) = 100 +40t -5t²

Power rule:

h'(t) = 40 - 10t

Set the equation equal to 0:

0 = 40 - 10t

-40 = -10t

t = 4

Test values on both sides of 4 to ensure that there is a maximum at this x value:

40 - 10(3) = 10

40 - 10(5) = -10

Therefore, the derivative switches from positive to negative. There is a maximum at t = 4. Find the height by plugging in this value for time into the original equation:

h(4) = 100 + 40(4) - 5(4)²

h(4) = 100 + 160 - 80

h(4) = 180 meters

Find the velocity when it hits the ground. Begin by finding the time necessary for the object to hit the ground:

0 = 100 + 40t - 5t²

Rearrange and factor:

0 = -5t² + 40t + 100

0 = (5t + 10)(-t + 10)

Set each factor equal to 0:

5t + 10 = 0

t = -2

-t + 10 = 0

t = 10

Therefore, the object takes 10 seconds to reach the ground. Plug this into the derivative of the equation (solved for earlier), which is the velocity:

h'(t) = 40 - 10t

h'(10) = 40 - 10(10)

h'(1) = -60 m/s. This is the *downward* velocity when the object hits the ground.

Answer:

a) 62.625 lb

b) 8.35

Step-by-step explanation:

a)

Use a proportion.

4 gal is to 33.4 lb as 7.5 gal is to x lb.

4/33.4 = 7.5/x

4x = 33.4 * 7.5

4x = 250.5

x = 62.625

Answer: 62.625 lb

b)

33.4/4 = 8.35

1) Cost of 7.5 gallons of water = 62.63 lb

2) The constant of variation = 8.35 lb

We have to given that,

1) Cost of 4 gallons = 33.4 lb

2) And, Cost of 4 gallon of water = 33.4 lb

Hence, We can simplify it as,

1) Since, Cost of 4 gallons = 33.4 lb

Hence, Cost of 7.5 gallons = 7.5 × 33.4 / 4 lb

                                         = 62.63 lb

2) Since, Cost of 4 gallon of water = 33.4 lb

Hence,  the constant of variation = 33.4 / 4

                                                   = 8.35

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Answer:

A

Step-by-step explanation:

Took the test

The probability that 2 or fewer in the sample will favor the project is  4.368 × 10⁻⁶ and Also The data seem to indicate that the percent favoring the increase in fees is less than 70%

According to the question,

It is given that according to the student's government

The probability that number of students in favor of increment in fees : p = 0.70

The probability that number of students against the increment : q = 0.30

Sample Size : n = 12

Number of students follows Binomial distribution

(a) We have to find the probability that 2 or fewer in the sample will favor the project

P( x ≤ 2) = P(0) + P(1) + P(2)

As we know ,

P(x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾

=> P( x ≤ 2) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰

=>  P( x ≤ 2) = 1×(0.30)¹² + 12×(0.70)(0.30)¹¹  + 12×11/2 × (0.70)²(0.30)¹⁰

=> P( x ≤ 2) = (0.30)¹⁰ [ 0.09 + 0.21 + 0.48]

=>  P( x ≤ 2) = 5.9×10⁻⁶[0.78]

=>  P( x ≤ 2) = 4.368 × 10⁻⁶

Which is very close to zero

(b) The data doesn't support the student government claim.

The data seem to indicate that the percent favoring the increase in fees is less than 70%.

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Answer:

The cutoff value for the top 5% of all IQs is 131.255.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 100, \sigma = 19\)

What is the cutoff value for the top 5% of all IQs

This is the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.645 = \frac{X - 100}{19}\)

\(X - 100 = 19*1.645\)

\(X = 131.255\)

The cutoff value for the top 5% of all IQs is 131.255.

The answer in exponent form is 147x^29.

A scientific notation is a method of expressing very large numbers in the form of exponent.

In the given question, we have;

(7x^9)^2*3x^11

applying the law of indices,

(7x^9)^2*3x^11 = (7^2)*x^(9*2)*3x^11

                        = 49x^18*3x^11

                        = (49*3)*x^(18+11)

                        = 147x^29

Thus, the expression can be simplified as: 147x^29.

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Answer:

Step-by-step explanation:

With reference < H

perpendicular (p) = 12

base (b) = 5

so now

tangent of < H

= p / b

= 12 / 5

hope it helps :)

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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Step 1: Write the dividend and divisor:

\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 2: Divide the first term of the dividend by the first term of the divisor:

\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)

Step 3: Multiply the divisor (x - 4) by the result (x^2):

\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)

Step 4: Subtract the result from the original dividend:

\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)

Step 5: Bring down the next term from the dividend:

\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 6: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)

\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)

\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)

Step 7: Bring down the next term from the dividend:

\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)

Step 8: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)

\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)

\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)

Step 9: There are no more terms to bring down, so the division is complete.

Step 10: Write the final result:

The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.

Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:

\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)

y = 1/4x + 1 is parallel to line a

-4x + y = -8 is neither parallel nor perpendicular to line a

4x + y = -3 is perpendicular to line a

From the question, we are to determine how the given equations compare to line a.

From the given information,

Line a is -x + 4y = 32

First, we will determine the slope of line a

To do this, we will compare the equation to the slope-intercept form of a line

The slope-intercept form of a line is

y = mx + b
Where m is the slope

and b is the y-intercept

Writing -x + 4y = 32 in the slope-intercept form

-x + 4y = 32

4y = x + 32

Divide through by

y = 1/4 x + 8

By comparison, the slope of line a is 1/4

NOTE: If two lines are parallel, their slopes will be equal

and

If two lines are perpendicular, their slopes will be the negative reciprocal of each other

Now, we will determine the slopes of each of the lines

For y = 1/4x + 1

By comparing with the slope-intercept form of a line, y = mx + b

The slope of the line is 1/4

Thus, the line is parallel to line a

For -4x+y=-8

Rewrite in the slope-intercept form of a line

-4x + y = -8

y = 4x - 8

By comparing with the slope-intercept form of a line, y = mx + b

The slope of the line is 4

4 is not equal to 1/4 and 4 is not the negative reciprocal of 1/4.

Thus, the line is neither parallel nor perpendicular to line a.

For 4x+y=-3

Rewrite in the slope-intercept form of a line

4x + y = -3

y = -4x - 3

By comparing with the slope-intercept of a line, y = mx + b

The slope of the line is -4

-4 is the negative reciprocal of 1/4.

Thus, the line is perpendicular to line a.

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Answer:

Meters Per Minute (12 meters per minute)

Step-by-step explanation:

480/40 = 12

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Given the graph of f(x) and the function:

You need to remember that, by definition, the Axis of Symmetry of a parabola passes through its vertex, and divides the parabola into two equal parts.

• You can identify in the graph that the vertex of the parabola is its maximum point:

Therefore, you can draw the vertical lines that pass through the vertex:

Notice that the x-coordinate of each point on the line is always the x-coordinate of the vertex of the parabola. Therefore, the equation for that line is:

• In order to find the Axis of Symmetry of g(x), you need to rewrite it in this form:

By definition:

Therefore, you can expand the function:

Now you can find the Axis of Symmetry using this formula:

In this case:

Then, you get:

Hence, the answer is: Option B.

Find slope of both

#1

\(\\ \tt\hookrightarrow m=\dfrac{4-2}{22-11}=\dfrac{2}{11}=1.8\)

#2

\(\\ \tt\hookrightarrow m=\dfrac{1-0}{5-0}=\dfrac{1}{5}=0.2\)

Option C is correct

YES, Standardized score necessarily a z-score.

Z-scores, usually referred to as standardized scores, are data values or scores that have been assigned a common standard. This benchmark has a zero mean and a one standard deviation. Contrary to popular belief, z-scores are not always evenly distributed.

By reducing a score's variance by the standard deviation in a data set, the z-score, also known as the standard score, may be used to standardize scores on the same scale. A standard score is the end outcome. It counts how many standard deviations a particular data point deviates from the mean. Z-scores can be either positive or negative.

According to the given question;

YES, Standardized score necessarily a z-score.

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To calculate the mean, median, and mode, we first need to know what each of these terms represents. The mean, also known as the average, is the sum of all the values divided by the total number of values. To find the mean, add up all of the values and divide by the number of values. The median is the middle value in a set of data when it is arranged in order from least to greatest. The mode is the value that occurs most frequently in a set of data. Here's an example to illustrate these concepts:

Let's say we have a set of data consisting of the following values: 2, 5, 5, 7, 8, 10, 12. To find the mean, we add up all of the values and divide by the number of values. In this case, the sum of the values is 49 (2+5+5+7+8+10+12) and there are 7 values, so we divide 49 by 7 to get the mean, which is approximately 7. To find the median, we first need to arrange the data in order from least to greatest: 2, 5, 5, 7, 8, 10, 12. The middle value is 7, so that is the median. To find the mode, we look for the value that occurs most frequently. In this case, 5 occurs twice, which is more than any other value, so the mode is 5.
In conclusion, the mean, median, and mode are all measures of central tendency that can be used to describe a set of data. The mean is the average value, the median is the middle value, and the mode is the value that occurs most frequently. When calculating these measures, it is important to carefully consider the data and choose the appropriate method for finding each value.

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Answer:

5.9+z=−9

Step 1: Simplify both sides of the equation.

z+5.9=−9

Step 2: Subtract 5.9 from both sides.

z+5.9−5.9=−9−5.9

z=−14.9

Answer:

z=−14.9

Step-by-step explanation:

I hope this can help!!!

Answer: 4

Step-by-step explanation:

Given

\(F(x)=2x+4\)

\(R(x)=x\)

We need to find \(R(F(x))\) at \(x=0\)

\(R(F(x))=[2x+4]\)

\(R(F(x))=2x+4\)

\(R(F(0))=2\times 1+4=4\)

\(R(F(0))=4\)

Answer:

B

Step-by-step explanation:

ok wait, how do you want us to answer them

Answer:

−24x−38y

Hope this helps!! (:

Answer:

False

Step-by-step explanation:

1 + 2 (-4) = -7

1 - 8 = -7

-7 = -7

-4 (-4) = -1

16 = -1

Answer:

907.46 mm2

Step-by-step explanation:

Area of circle = (¶d^2)/4

d = 34 mm

Therefore

Area A = (3.14 x 34^2)/4

= 907.46 mm2

\(907.43 \: {yrds}^{2} \)

Step-by-step explanation:

The formula to find the area of a circle is:

\(\pi {r}^{2} \)

since pi is 3.14 then, and the radius is half of the diameter, then:

\(diameter = 34 \\ radius = \frac{34}{2} \\ radius = 17\)

Therefore;

\(area = \pi {r}^{2} \\ area = (3.14) {(17)}^{2} \\ = 3.14 \times 289 \\ = 907.46 {yrds}^{2} \)

Answer:

21.75

Step-by-step explanation:

Alternative forms 87

21 3

4 4

24 2.25

Calculate the first two terms

21.75

Answer:

Step-by-step explanation:

If you round it to the nearest whole number, then 17.526  becomes 18 because if the first digit after the decimal(in this case,5) is 5 or greater you round to the next whole number.

If you round it to the nearest tenth, it would result in 17.5, because if the second digit after the decimal (in this case, 2) is 5 or greater you round to the next tenth of decimal.

Hope this helps!

Answer:

Step-by-step explanation:

It can be rounded down to 17.5 if rounding to 1 decimal place. If you are rounding to the nearest whole number, you would round to 18.

Hope this helps :)

The 36th derivative of f(x) = cos(2x) is \(2^{17}\)* cos(2x).

To find the 36th derivative of the function f(x) = cos(2x), we can apply the chain rule repeatedly. The chain rule states that if we have a composite function y = f(g(x)), then its derivative is given by dy/dx = f'(g(x)) * g'(x).

Let's start by finding the first few derivatives of f(x) = cos(2x):

f'(x) = -2sin(2x)

f''(x) = -4cos(2x)

f'''(x) = 8sin(2x)

f''''(x) = 16cos(2x)

We observe a pattern where the derivatives of cos(2x) alternate between sin(2x) and cos(2x), with the signs changing accordingly.

Based on this pattern, we can see that the 36th derivative will be:

f^(36)(x) =\((-1)^{17} * 2^{17} *\) cos(2x)

Simplifying this expression, we have:

f^(36)(x) = \(2^{17} * cos(2x)\)

Therefore, the 36th derivative of f(x) = cos(2x) is\(2^{17\) * cos(2x).

It's important to note that in this case, the number 36 is even, and since the derivatives of cos(2x) follow a repeating pattern every 4 derivatives, the sign (-1) raised to the power of 17 accounts for the change in sign in the 36th derivative.

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Answer:

B ). IF = IT

Step-by-step explanation:

IG is perpendicular to FT, means that the line IG divides the line FT into two equal parts without remainder.

Line IG does not only divide line FT, it also bisect the arc FT into two equally parts also.

It also divide the segment of the circle FIT into two equal parts.

So to the correct answer to the question, IF = IT

Answer: 480 mL, 600 mL

Step-by-step explanation:

Given

The concentration of the first acid is 75%

The concentration of the second acid is 30%

The final mixture has a concentration of 50%

The final volume is 1080 mL

Suppose x and y be the volume of the first and second acid

\(\therefore x+y=1080\quad \ldots(i)\\0.75x+0.3y=0.5\times 1080\quad \ldots(ii)\)

Solving the above equations we get

\(x=480,y=600\)

So, the quantity of the first acid is 480 mL and 600 mL for the second mixture.