A senator wants to know what her constituents think of a proposed health bill. Her staff reports that 222 letters have been received on the subject, of which 200 opposed the bill. Define both the population and the sample in this scenario.

The equation of the new function, if we vertically compress the absolute value parent function, f(x) = |x| by a factor of 3: y = 1/x |x|

In this question we have been given an absolute value function f(x) = |x|

We need to find the equation of the function, if we vertically compress the absolute value parent function, f(x) = |x| by a factor of 3.

We know in function transformtaion there are two types of dilations.

1) Horizontal Dilation: a function y = f(x) into the form y = f(kx)

2) Vertical Dilation: a function y = f(x) into the form y = k f(x)

In both the cases, if k > 1, then the graph stretches and if 0 < k < 1, then the graph shrinks.

Since we vertically compress the absolute value parent function f(x) = |x| by a factor of 3, a scaling factor k must be 0 < k < 1

So, k = 1/3

And the required function wuld be, y = 1/3 * f(x)

y = 1/3 |x|

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The absolute value parent function is f(x)= x. When we vertically compress the absolute value parent function f(x)= x by a factor of 3, the new equation is f(x)=⅓x.

The vertical compression by a factor of 3 means that the original graph will be compressed to a vertically scaled-down version of the original graph. This means that the graph will be shorter by a factor of 3.

To calculate the new equation, we must first determine the value of the constant “a”. The equation of the original absolute value parent function is f(x)=x. When we vertically compress the absolute value parent function f(x)=x by a factor of 3, the new equation is f(x)=ax. The value of “a” is equal to ⅓. Therefore, the new equation of the absolute value parent function f(x)=x when it is vertically compressed by a factor of 3 is f(x)=⅓x.

The graph of the new equation is shown below. The graph is shorter than the original absolute value parent function by a factor of 3.

From the graph, we can also see that the new equation has a minimum value of -1/3, a maximum value of 1/3, and the graph is symmetrical along the y-axis.

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The fraction of a small bag of chips does Sonia eat altogether if Sonia finds a 3/4- full bag of chips, she eats the rest of the chips in the bag, is 7 / 8.

Only verbal descriptions of a portion of the whole were used to write fractions in ancient Rome. The numerator and denominator of fractions is first written in India with one number above the other but without a line. The line used to divide the numerator and the denominator were only added by Arabs.

Given:

Sonia finds a 3/4- full bag of chips, she eats the rest of the chips in the bag,

Calculate the fraction as shown below,

The Fraction of small bag of chips does Sonia eat altogether = total chips eat

The Fraction = 3/4 = 6/8

The Fraction = 6/8 + 1/8 = 7/8

Thus, the fraction is 7 / 8.

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The complete question is:

Sonia finds a 3/4- full bag of chips . she eats the rest of the chips in the bag. Then she opens another small bag of chips. Sonia eats 1/8 of those chips. what fraction of a small bag of chips does Sonia eat altogether?

Answer:

B. 105

Step-by-step explanation:

right!!

Answer:

  E.  26.25°

Step-by-step explanation:

Given a diagram showing an angle at crossed chords of 2x, you want the value of x/2.

The measure of an inscribed angle is half the measure of the arc it subtends. This means the triangle interior angle at upper left has half the measure of the 40° arc it subtends: 20°.

The sum of angles in the triangle is 180°. The third angle is a vertical angle to the one marked 2x, so has that same measure. Then the relation is ...

  2x +20° +55° = 180°

  2x = 105° . . . . . . . . . . . . . subtract 75°

  x/2 = 26.25° . . . . . . . . . divide by 4

__

Additional comment

You can apply a "reasonableness" test to the answer choices. Any angle where lines cross cannot have a measure more than 180°. If that angle is 2x, then x/2 cannot be more than 180°/4 = 45°. Only one answer choice is less than 45°.

The midpoint M of the line segment PQ is 14 units

From the question, we have the following parameters that can be used in our computation:

A line segment PQ

The midpoint M

Using the above as a guide, we have the following:

P = 5

Q = 23

The midpoint M can be calculated using any of the following formulas

M = (Q - P)/2 + P or M = (P + Q)/2

Substitute the known values in the above equation, so, we have the following representation

M = (23 - 5)/2 + 5 or M = (23 + 5)/2

Evaluate the equations

M = 14

Hence, the value of M is 14 units

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Answer:

3453.5

Step-by-step explanation:

(a(1) + a(2) + a(3) + a(4) + a(5) ) ÷ 5 = 790.6

a(5) = (790.6 × 5) - (80.2+91.6+123+204.7) = 3953 - 499.5 = 3453.5

The probability that the point will also be inside the circle will be 0.7854.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A square has a circle inside it. If a square's the inside point is chosen at random.

The length of the edge of the square and the diameter of the circle will be congruent. Then the probability that the point will also be inside the circle will be given as,

P = [(π/4)a²] / [a²]

P = π/4

P = 0.7854

The probability that the point will also be inside the circle will be 0.7854.

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Answer:

c

Step-by-step explanation:

Answer:

y=5x-15

Step-by-step explanation:

Slope intercept form:y=mx+b

m=slope=5

y=0

x=3

b=y intercept

Plug it in

0=5(3)+b

Subtract 15 from both sides

-15=b

y=5x-15

Hope this helps :)

The variable x as the subject of the formula is x = (y + b)/a

From the question, we have the following parameters that can be used in our computation:

y = ax - b

The above equation is a linear equation

To make the variable x the subject of the formula, we start by adding the variable b to both sides of the equation

Using the above as a guide, we have the following:

y + b = ax - b + b

Evaluate the like terms

This gives

y + b = ax

Next, we divide both sides of the equation by a

This gives

x = (y + b)/a

Hence, the solution is x = (y + b)/a

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Answer:

less than a mile is the answer

The measure of the length of side v is 228.8 inches

From the question, we have the following parameters that can be used in our computation:

A triangle

The readings from the triangle are given as

Angle U = 82 degrees

Angle W = 79 degrees

Side w = 690 inches

Start by calculating the measure of angle V using the following equation

Angle V = 180 - Angle U - Angle W

Substitute the known values in the above equation, so, we have the following representation

Angle V = 180 - 82 - 79

Evaluate the difference

Angle V = 19

The length of V is then calculated by making use of the following sine law

v/sin(V) = w/sin(W)

Substitute the known values in the above equation, so, we have the following representation

v/sin(19) = 690/ sin(79)

This gives

v =/sin(19) * 690/ sin(79)

Evaluate the expression

v = 228.8

Hence, the length is 228.8 inches

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Answer:

6.5

Step-by-step explanation:

y = 6.5x

The number of comparisons required for an array of length 512 is

1+log2(512)=1+9=10.

Binary search:

Searching is an operation done to find the required element (or key) among a group of elements (an array).

Binary search or logarithmic search is a type of searching algorithm that can be used on a sorted array.

In this algorithm, we always check the middle number and compare the key with it. If the key equals the middle number, we're done. If the key is greater than the middle number, we know the key (if it's in the array at all) must be in the right half of the array. Conversely, if the key is less than the middle number, we know the key (if it's in the array at all) must be in the left half of the array. In other words, at every step of the search, we cut the array we're searching through in half. Of course, this only works because the array we started with is sorted.

In a binary search, at every step we compare the key with the middlemost value. If the key is greater than the middlemost value, we discard the left half of the data. If the key is less than the middlemost value, we discard the right half of the data. This process is repeated until we find the element we are looking for.

If we start with an array of length 2=21

, the worst-case scenario is we have to compare the key with both elements: 2 comparisons.

If we start with an array of length

4=22, the worst-case scenario is the key is not the middlemost element, we reduce our search to a 2-element array, and then we're in the worst-case scenario of the previous case: 1+2=3 comparisons.

If we start with an array of length

8=23

, the worst-case scenario is the key is not the middlemost element, we reduce our search to a 4-element array, and then we're in the worst-case scenario of the previous case: 1+3=4 comparisons.

Do you see a pattern? If we start with an array of length

2k, the worst-case scenario is we make 1+k

comparisons. Since 512=2log2(512)=29

The number of comparisons required for an array of length 512 is

1+log2(512)=1+9=10.

In general, the number of comparisons required for an array of length

n is 1+log2(n)

. We usually just round this to

log2(n). Remember that

log2(n)

is basically the number of times n can be cut in half until we get down to 1 or less, so this makes sense.

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The Formula to calculate the area of the equilateral triangle with side length as "x" units is [tex]\frac{\sqrt{3} }{4} x^{2}[/tex] square units .

What is an Equilateral Triangle ?

An equilateral triangle is defined as a type of triangle in which all the sides and all the angles are equal in measure .

The measure of each angle of equilateral triangle is 60° .

The area of the equilateral triangle can be calculated by the formula :

Area = [tex]\frac{\sqrt{3} }{4} x^{2}[/tex]  , where x is = the side of the equilateral triangle .

For Example : if the side length of equilateral triangle is 2 units ,

then its area will be = [tex]\frac{\sqrt{3} }{4} \times 2^{2}= \frac{\sqrt{3} }{4} \times 4 =\sqrt{3}[/tex] square units .

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The following logarithm expressions are,

(a) [tex]ln e^{-11}[/tex] = -11

(b) [tex]e^{ln5}[/tex] = 5

(c) [tex]e^{ln\sqrt{2} }[/tex] = 1.414

(d) [tex]ln^{\frac{1}{e^{4} } }[/tex] = -4

It is important to remember the following logarithm properties in order to solve the exercise:

[tex]ln(a) + ln(b) = ln(ab)[/tex]

[tex]ln(a) -ln(b) = ln(\frac{a}{b} )[/tex]

[tex]ln(a^{m})= m ln(a)[/tex]

[tex]ln(e)=1[/tex]

Given data,

(a) \ln e ^ { -11 }

[tex]ln e^{-11}[/tex] = [tex]ln_{e} ^{e^{-11} }[/tex]

[tex]ln e^{-11}[/tex] = -11

(b) e ^ {\ln 5 }

[tex]e^{ln5}[/tex] = 5

(c) e ^ {\ln \sqrt { 2 } }

[tex]e^{ln\sqrt{2} }[/tex] = [tex]\sqrt{2}[/tex]

[tex]e^{ln\sqrt{2} }[/tex] = 1.414

(d) \ln ( 1/e^ { 4} )

[tex]ln^{\frac{1}{e^{4} } }[/tex] = [tex]elne^{-4}[/tex]

[tex]ln^{\frac{1}{e^{4} } }[/tex] = -4

Therefore,

The following logarithm expressions are,

(a) [tex]ln e^{-11}[/tex] = -11

(b) [tex]e^{ln5}[/tex] = 5

(c) [tex]e^{ln\sqrt{2} }[/tex] = 1.414

(d) [tex]ln^{\frac{1}{e^{4} } }[/tex] = -4

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y = (4/5)x - 1 is the equation of the line in slope-intercept form

The equation of a line in slope-intercept form is y = mx + c.

Where m is the slope and c is the y-intercept (0, y)

slope = (y2-y1)/(x2-x1)

where (x1, y1) and (x2, y2) are the coordinates of two points that lie on the line

From the graph:

c = -1

x1 = 0, y1 = -1 and x2 = 5, y2 = 3

slope (m) = (3-(-1)) / (5-0) = 4/5

substitute m = 4/5 and c = -1 into y = mx + c:

y = (4/5)x - 1

Thus, the equation of the line in slope-intercept form is y = (4/5)x - 1

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Answer:

range of r is between -1 and 1.

Step-by-step explanation:

(-1)^2 = 1, 0^2 = 0 and 1^2 = 1

Answer:

Answer Below

Step-by-step explanation:

The key difference between line and line segment is, a line is extended in both directions infinitely but a line segment has two endpoints.

Answer:

(12,-5) and (13,-6) m = (6/-1) = -6

(13,3) and (14,3) m = 0

(3,-20) and (5,8) m = (8- -20)/(5-3) = 28/2 = 14

(1,2) and (3,8) m = (8-2)/(3-1) = 6/2 = 3

(-1,1) and (15,1) m = 0

(1,5) and (6,15) m = (15-5)/(6-1) = 10/5 = 2

(2,-12) and (10,12) m = (12--12)/(10-2) = 24/8 = 3

(1,8) and (3,0) m = (0-8)/(3-1) = -8/2 = -4

(0,0) and (-4,-8) m = (-8-0)/(-4-0) = -8/-4 = 2

(5,3) and (12,10) m = (10-3)/(12-5) = 7/7 = 1

Note that the slope of a line can be found by using the formula m = (y2 - y1)/(x2 - x1)

Step-by-step explanation:

1. (12,-5) and (13,-6) m= -1

2. (13,3) and (14,3) m= 0

3. (3,-20) and (5,8) m= 14

4. (1,2) and (3,8) m= 3

5. (-1,1) and (15,1) m= 0

6. (1,5) and (6,15) m= 2

7. (2,-12) and (10,12) m= 3

8. (1,8) and (3,0) m= -4

9. (0,0) and (-4,-8) m= 2

10 (5,3) and (12,10) m= 1

Sine, cosine, and tangent are the three letters in the acronym SOH CAH TOA. It is a mnemonic tool for remembering the three primary trigonometric ratios' definitions: tangent, cosine, and sine.

The following are the meanings of the acronym SOH CAH TOA: Cosine is the ratio of the adjacent side to the hypotenuse, tangent is the ratio of the opposite side to the adjacent side, and sine is the ratio of the side opposite the angle to the hypotenuse.

To help remember the definitions of the trigonometric ratios, SOH CAH TOA is a useful tool. It can be used to solve trigonometric equations, determine right triangle side lengths, and calculate triangle angles. It can also be used to calculate the sine, cosine, and tangent of any right triangle's angles.

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Answer: h+8

Step-by-step explanation:

It’s simple h MORE than 8

Answer: h+8

Step-by-step explanation:

Answer:

12 (c)

Step-by-step explanation:

13.5 / 1.125

A- 37% of 142 is 52.54

B- 137% of 142 is 194.54

To calculate Percent of Number we use,

P% of Number = X

⇒P/100 x Number=X

where P is the percent to be calculated

and X is the required percentage of that number

A-37% of 142=  37/100 x 142

=0.37 x 142

=52.54

B- 137% of 142= 137/100 x 142

=1.37 x 142

194.54

∴ 37% and 137% of 142 are 52.54 and 194.54 respectively.

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(C) False. The chi-square distribution is skewed to the right.

'What is chi square?'

The chi-square test, a statistical method, is used to compare actual results with forecasts. This test's objective is to determine whether a disparity between observed and anticipated data is due to chance or a correlation between the variables under study. Thus, using a chi-square test is a fantastic alternative for better understanding and interpreting the relationship between our two category variables.

To perform a chi-square test to determine the statistical significance of the connection between s2q10 and s1truan, choose Analyze, Descriptive Statistics, and then Crosstabs.

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Answer:

23,2.3,0.23,0.023

Step-by-step explanation:

*23÷10^0=23/1=23

*23÷10^1=23/10=2.3

*23÷10^2=23/100=0.23

*23÷10^3=23/1000=0.023

I hope it helps you..

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Answer:

23

23.23

0.23

0.023

Answer:

D

Step-by-step explanation:

It is D

Distance of a fallen object is 25 feet.

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.

Given:

The formula for the speed of a falling object is v= √64d,

where v is the speed of the object in feet per second and d is the distance the object has fallen, in feet.

And also given that v = 200 feet per second.

Substituting the value to the formula,

200 = √64d

d = 200 / √64

d = 200 / 8

d = 25 feet.

Therefore, 25 feet are the distance.

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The equation that would model this situation is 2a + 3p = 24

From the question, we have the following parameters that can be used in our computation:

Also, from the question, we have

These parameters above mean that:

2 * a + 3 * p = 24

Evaluate

2a + 3p = 24

Hence, the equation is 2a + 3p = 24

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Answer:

Step-by-step explanation:

They're congruent triangles, so 1 = 40