Graph the logarithmic function f(x) = log₂(x - 1) +2.

Check the picture below.

\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=8\\ h=12\\ A=66 \end{cases}\implies 66=\cfrac{12(8+b)}{2} \\\\\\ 66=6(8+b)\implies \cfrac{66}{6}=8+b\implies 11=8+b\implies 3=b\)

1. The first write-up is missing an equal sign before the 16 in the first line. The second line should be x² + 6x - 16 = 0 (instead of x² + 6x _ 16 = 0). The last line has an error in the second solution, where it says x = -8_ instead of x = -8.

2. In the second write-up, the equation should be 12 - 2x = x + 10 (instead of 12 _ 2x = x + 10). The sign error also carried over to the next line, where it should be x² - 3x - 10 (instead of x2 _ 3x _ 10). The correct solutions are x = 5 and x = -2 (instead of 5 and _2).

3. In the third write-up, there is a calculation error in the expansion of (7+2y)(y² + Sy - 6). The correct answer is 2y³ + 17y² - 23y - 42 (instead of 2y³ + l7y2 + 23y - 42).

4. In the fourth write-up, there is an incomplete sentence that is cut off.

5. In the fifth write-up, the inequality should be Va > a for all a > 1 (instead of Va < a for all a > 1). The last line is missing an explanation of how Va+3 is less than (a+3) in order to justify the inequality (Va+ 3)² < (a+3)².

The write-ups that provided are about different topics in mathematics, including algebra, calculus, and number theory.

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Yes, 90 degrees (clockwise) and -270 degrees (counterclockwise) are coterminal angles.

Two angles are coterminal if they share the same terminal side when drawn in standard position. In other words, coterminal angles differ by an integer multiple of 360 degrees.

To see if 90 degrees and -270 degrees are coterminal, we can add 360 degrees to the smaller angle (-270 degrees) and see if we get the other angle:

-270 + 360 = 90

Since we obtain 90 degrees after adding 360 degrees to -270 degrees, these two angles are coterminal. They share the same terminal side in standard position, even though their rotations have different directions (clockwise and counterclockwise).

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The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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Answer:

2.8 goals

Step-by-step explanation:

35 * 0.08 = 0.35*8

0.35*8=2.8

The expected number of goals scored on the goaltender would be 2.8.

The expected number of goals scored by the goaltender can be calculated using the formula:

Expected goals = Total shots * Probability of a goal

Therefore, for a goaltender with a save percentage of 0.920 (which means the probability of a goal is 0.08), and facing 35 shots:

The expected number of goals scored on this goaltender in a game where she faced 35 shots would be 2.8 goals.

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He borrowed $24,000.

The vertex of the graph of f(x) = |x - 5| - 6 is (5, -6). It lies in the fourth quadrant.

Therefore the answer is (5, -6).

The graph f(x) = |x - 5| - 6 is symmetrical about the axis  x = 5.

A vertex of a graph is a node of a graph. For a graph of the form f(x) = a|x - h| + k, the vertex is (h, k). So in this case where f(x) = |x - 5| - 6, a = 1, h = 5 and k = -6. Therefore the vertex of the given graph f(x) is

(5, -6)

--The question is incomplete, answering to the question --

"What is the vertex of the graph of f(x) = |x - 5| - 6?"

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Answer:

92.7?????

Step-by-step explanation:

The probability that exactly 3 out of the first 11 customers buy a magazine is 2.23%

The proportion of customers that buy a magazine = 8.4%

If 3 out of the first 11 customers buy a magazine, then this proportion is given as; 3/11 or 27.27%

Therefore, the probability that 3 out of the first 11 customers will buy a magazine is calculated as follows;

probability = 8.4% × 27.27%

probability = (8.4/100) × (27.27/100)

probability = 0.084 × 0.2727

probability = 0.0223

Converting it into percentage as follows;

probability = 0.0223 × 100

probability = 2.23%

Therefore, the probability that 3 out of the first 11 customers buy a magazine is calculated to be 2.23%.

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Answer:

C

Step-by-step explanation:

(180- 80+65 = 35) sum of the angle in a triangle.

to get the exterior angle

180 - 35 = 145 (sum of angle on a straight line is 180)

...C. 145° on Ap3x.....

The statements that best describes the relationship between the mean and median of the distribution of ages in the histogram is the option (C)

(C) The mean is most likely less than the median because the distribution is skewed to the left

A histogram graphically represents the distribution of data, which consists of rectangles, representing the range of values, divided into intervals which is represented as the width of each rectangle, and the number of values within each interval, represented as the height of the rectangle.

Please find attached the possible histogram in the question, created with MS Excel

The histogram indicates that the distribution of the ages is skewed to the left, based on the tail consisting of four smaller rectangles to the left and  two smaller rectangles to the right of the modal frequency interval of 35 to 40. The left skewed histogram indicates that there are a higher frequency of the older age groups.

The mean of a left skewed histogram is usually less than the median.

The correct option is therefore, option (C)

The options in the question are;

(A) The mean and median are equivalent because the histogram has a symmetric distribution

(B) The mean is less than the median because the distribution is skewed to the right

(C) The mean is less than the median because the distribution is skewed to the left

(D) The median is likely less than the mean because the distribution is skewed to the right

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To find the absolute maximum and minimum of a function, determine the critical points and evaluate the function at those points and the endpoints of the interval.

To find the absolute maximum and minimum of a function, you need to follow these steps:

1. Determine the critical points of the function by finding where its derivative equals zero or is undefined. These points can be potential candidates for the maximum or minimum values.

2. Evaluate the function at the critical points and at the endpoints of the interval you are considering. The highest value among these points will be the absolute maximum, while the lowest value will be the absolute minimum.

Let's illustrate this with an example:

Consider the function f(x) = x^2 - 4x + 5 on the interval [0, 5].

1. To find the critical points, we need to find where the derivative is equal to zero or undefined. Taking the derivative of f(x),

we get f'(x) = 2x - 4.

Setting this equal to zero gives us 2x - 4 = 0, which implies x = 2. So, x = 2 is the only critical point.

2. Now, we evaluate the function at the critical point and the endpoints of the interval:
f(0) = 0^2 - 4(0) + 5 = 5
f(2) = 2^2 - 4(2) + 5 = 1
f(5) = 5^2 - 4(5) + 5 = -5

From these evaluations, we see that f(0) = 5 is the absolute maximum and f(5) = -5 is the absolute minimum.

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If the car's speed is 65 kilometres per hour, then the bus' speed may be 75 kilometres per hour.

How to find the distance travelled by an object?

The distance travelled by an object in a specified direction is velocity×time.

if the car's speed is 65 kilometres per hour then in 2 hours it will travel a distance of 65×2 kilometres.

65×2=130 kilometres

if the bus' speed is 75 kilometres per hour then in 2 hours it will travel a distance of 75×2 kilometres.

75×2=150 kilometres

So, after 2 hours the distance between the two vehicles will be 130+150= 280 kilometres

which is less than 350 kilometres.

Hence, it is possible that if the car's speed is 65 kilometres per hour then the bus' speed is 75 kilometres per hour.

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Answer:

30 ft

Step-by-step explanation:

We can use the given information to set up a ratio...

\(\frac{Mark's\ height}{Mark's\ shadow}=\frac{Tree's\ height}{Tree's\ shadow}\)

\(\frac{6\ ft}{4\ ft}=\frac{x}{20\ ft}\)

We can solve this ratio using cross multiplication (multiply the numerator of the first fraction by the denominator of the second and the numerator of the second fraction by the denominator of the first):

120 = 4x

Divide both sides by 4

x=30 ft

Step-by-step explanation:

The slope of tghe line (m) = (y₂ - y₁) ÷ (x₂ - x₁)

                                          =  (- 6 -0) ÷ ( 0 - 7)

                                          =    ⁶/₇

We can now use the point-slope form to write the equation for this line:

y - y₁ = m(x - x₁) where (x₁ , y₁) = (7 , 0)

              y =  ⁶/₇ ( x  -  7 )

The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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Answer: Distributive property

Step-by-step explanation:

Answer:

mean= 12

median= 10

mode= 10

Step-by-step explanation:

mean: add up all values, then divide by how many values you have(84/7=12)

median: when sorted, value in middle(See pic)

mode: value that appears most

Answer:

m = 12

Step-by-step explanation:

\(-\frac{m}{3} =-4\\\)

→ Multiply both sides by 3

\({-m} =-12\\\)

→ Multiply both sides by -1

m = 12

Answer:

  small table

Step-by-step explanation:

You want to know where a person would get the most pie if 12 pies are shared by 4 people at the large table; 10 pies are shared by 4 people at the medium table; and 8 pies are shared by 3 people at the small table.

The amount of pie per person is found by dividing the number of pies by the number of people.

  pie/person = (12 pies)/(5 persons) = 2.40 pies/person

  pie/person = (10 pies)/(4 persons) = 2.50 pies/person

  pie/person = (8 pies)/(3 persons) ≈ 2.67 pies/person

  2.40 < 2.50 < 2.67

A person at the small table would get the most pie.

The correct description for the polar function, r = 6sin(θ) is: D. Circle symmetric on the line theta = 0, with a radius of 6.

In Mathematics, the relationship between the polar coordinates (r, θ) and rectangular coordinates (x, y) is given by these polar functions:

On the horizontal plane:

x = rcosθ

On the vertical plane:

y = rsinθ

Where:

In conclusion, the correct description for the polar function, r = 6sin(θ) is circle symmetric on the line with an angle (θ) equal to zero (0) and a radius of 6.

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solving steps:

2( 9 - 7r ) + 8r

2(9) - 2(7r) + 8r

18 - 14r + 8r

18 - 6r

Answer:

18 - 6r

Step-by-step explanation:

2(9 - 7r) + 8r

Expand the brackets:

⇒ 2 · 9 - 2 · 7r + 8r

⇒ 18 - 14r + 8r

Combine like terms:

⇒ 18 - 6r

Answer:

In Amanda Bean’s Amazing Dream, Cindy Neuschwander makes a convincing case to children about why they should learn to multiply. The story helps children see what multiplication is, how it relates to the world around them, and how learning to multiply can help them.

Answer:

A) s and t.

Step-by-step explanation:

just trust me. Plus lines s and t are the only pair of lines that don't touch each other and can go on forever not touching each other.

Answer:

x = 10

y= 12

Step-by-step explanation:

We know that TSV = 90 degrees

5x+4x = 90

9x = 90

Divide by 9

9x/9 = 90/9

x = 10

We know that RSU = 180

10y+10 +5x= 180

10y + 10 + 5(10) = 180

10y + 10 +50 = 180

10y +60 = 180

Subtract 60 from each side

10y = 120

Divide by 10

y = 12

Answer: D) the significance level of the test

=======================================================

Explanation:

The significance level of the test, also known as "alpha", is the probability of making a type 1 error. A type 1 error is where you reject the null hypothesis but it was true all along.

The null hypothesis is where we test a certain probability distribution (eg: normal distribution). Specifically we gather a sample of values and compute the test statistic. If the probability of getting that test statistic or more extreme is smaller than alpha, then we reject the null. This probability value is known as the p-value.

If you lower the alpha value, then that will make it more likely you do not reject the null. Consider an example where alpha = 0.10 to start with. If you get a p-value of 0.02, then you would reject the null. The same would apply for alpha = 0.05; however, with alpha = 0.01, the p-value is no longer smaller than alpha. At this point we do not reject the null. Your textbook may use the phrasing "fail to reject the null".

Going in the opposite direction, increasing the alpha value will make it more likely to reject the null. Each time you adjust the alpha value, keep the p-value to some fixed number (between 0 and 1).

The height of the equilateral triangle is 3√3 cm.

Hypothesis testing is a statistical method that is used to make decisions about a population based on a sample of data.

It involves testing a null hypothesis (H0) against an alternative hypothesis (Ha) using statistical techniques.

We have,

To minimize the probability of incorrectly rejecting the null hypothesis in a hypothesis test with a fixed sample size of 40, the statistician can adjust the significance level of the test.

The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is actually true.

By choosing a smaller significance level, the statistician can decrease the probability of making a Type I error (rejecting the null hypothesis when it is actually true).

However, decreasing the significance level also increases the probability of making a Type II error (failing to reject the null hypothesis when it is actually false).

Therefore,

The choice of significance level involves a trade-off between the two types of errors and should be based on the specific context of the problem and the consequences of each type of error.

Now,

The height of an equilateral triangle can be found using the formula:

height = (side length / 2) x √3

The side length = 6 cm

So,

height = (6 / 2) x √3

           = 3√3 cm

Therefore,

The height of the equilateral triangle is 3√3 cm.

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Answer:

800

Step-by-step explanation:

Answer:

2/45 or 0.04

Step-by-step explanation:

Answer:

2/45

Step-by-step explanation:

find LCM of 9 & 10 which is 90

√ (10*4 - 9*4)/90 = (40-36)/90

√ 4/90 and simplify to 2/45