Express the expression as a single logarithm and simplify. if necessary, round your answer to the nearest thousandth. log2 51.2 − log2 1.6

Out of the students surveyed, 90 played a musical instrument.

To find the total number of students who played a musical instrument, we need to look at the table provided and sum up the number of boys and girls who played an instrument.

From the table, we can see the following:
- Boys who played an instrument: 42
- Girls who played an instrument: 48

To find the total number of students who played a musical instrument, simply add the number of boys and girls together:

Total students who played an instrument = (Number of boys who played an instrument) + (Number of girls who played an instrument)

Total students who played an instrument = 42 (boys) + 48 (girls)

Total students who played an instrument = 90

So, of the students surveyed, 90 played a musical instrument.

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The volume of water a cone with a diameter of 6 inches and a height of 21 inches can hold is 198 cubic inches. So, the correct answer is B) 198 cubic inches.

To find the volume of water a cone with a diameter of 6 inches and a height of 21 inches can hold, we will use the formula for the volume of a cone: V = (1/3)πr²h.

Given a diameter of 6 inches, the radius (r) is 3 inches. The height (h) is 21 inches, and we will use 3.14 as an approximation for π.

V = (1/3) * 3.14 * (3²) * 21
V = (1/3) * 3.14 * 9 * 21
V = 3.14 * 3 * 21
V = 197.82 cubic inches

Rounding to the nearest whole number, the volume of water the cone can hold is approximately 198 cubic inches. Therefore, the answer is B) 198 cubic inches.

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The value of angle Y in the pentagon is 139°.

The sum of the interior angles of a polygon can be found using the formula:

sum of  interior angles = (n - 2) * 180

where n is the number of sides of the polygon

A polygon with 5 sides is called pentagon. Thus, n = 5.

sum of  interior angles = (5 - 2)*180 = 540°

Thus,

∠U + ∠W + ∠X + ∠Y  + ∠Z = 540°

90 + 108 + 121 + ∠Y + 82 = 540

401 + ∠Y = 540

∠Y = 540 - 401

∠Y = 139°

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a) We can reject the null hypothesis and cthat theronclude is significant evidence that the probability of Kerrich's coin coming up heads is not 0.5. b) we get a confidence interval of 0.495 to 0.517.

a) To test the hypothesis that the probability of Kerrich's coin coming up heads is not 0.5, we can use a one-sample proportion test at the 5% level of significance. The null hypothesis is that the true proportion of heads is 0.5, and the alternative hypothesis is that it is not equal to 0.5.

The test statistic can be calculated as (5067-0.510000)/(sqrt(100000.5*0.5)) which simplifies to 5.401. The corresponding P-value can be found using a standard normal distribution table or a calculator to be approximately 3.3x10^-8, which is much smaller than 0.05. Therefore, we can reject the null hypothesis .

b) To construct a 95% confidence interval for the true proportion of heads, we can use the formula p ± z*sqrt((p(1-p))/n), where p is the sample proportion, z is the z-score corresponding to a 95% confidence level (which is 1.96), and n is the sample size. Substituting the values, we get a confidence interval of 0.495 to 0.517, which means that we can be 95% confident that the true proportion of heads falls within this range.

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Answer:16 + (1/2) × 8 = 16 + 4 = 20 unit2

Step-by-step explanation:

The monthly payment on the car is approximately $640.62. The correct option is A

The formula for the monthly payment on a continuously compounded loan can be expressed as:

P = (r * A) / (1 - (1 + r)^(-n))

Where

Plugging in the given values, we get:

P = (0.046 * 35000) / (1 - (1 + 0.046/12)^(-6*12))

P ≈ $640.62

Therefore, the monthly payment on the car is approximately $640.62.

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The function that represents the total cost (y) of buying x shirt online of $3.50 each and shipping charges of $9.50 is 3.50x + 9.50 = y

Cost of each shirt = $3.50

The fee for shipping the shirts is = $9.50

Total number of shirts bought by shirt online = x

The total cost of buying x shirts is represented by y

The total cost will be the sum of each cost of the shirt and shipping charges

y = 3.50x + 9.50

Hence, the function that represents the total cost y of buying x shirt online of $3.50 each and shipping charges of $9.50 is 3.50x + 9.50 = y

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The question is incomplete complete question is :

The teacher could buy the shirt online at 3.50 each she would also pay a fee of 9.50 for shipping the shirts. Write a function that can be used to find y the total cost in dollars of buying x shirts online.

The expression that is equivalent to 3x – (2x + 4) + 5 is x+1 ( optionB)

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.

For example , 2a+6a is equivalent to 2a( 1+3) and they will surely have the same value when a value is replaced with a

3x – (2x + 4) + 5 = 3x-2x-4+5

= x-4+5

= x +1

therefore the equivalent of 3x – (2x + 4) + 5 is x+1

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a. The Taylors may want to avail themselves of the help of a professional investment advisor.

b. They may prefer to find a reputable planner with appropriate credentials and experience

c,.  The Taylors should track their expenses more closely because overspending without replacement income can be disastrous

Because successfully managing a large investment portfolio takes a great deal of time and​ knowledge, the Taylors may want to avail themselves of the help of a professional investment advisor.

2) They may prefer to find a reputable planner with appropriate credentials and experience. It will be important for them to shop around to find someone with whom they feel comfortable. A​ fee-only planner might be the best​ choice, especially if their current investments are doing well and the Taylors are not interested in making big changes that would generate​ sales, and​ commissions, for the planner

e) Whether or not Tim and Jill continue to work with a financial planner depends on their financial​ knowledge, time and commitment. Given their​ successful, independent, management of their financial situation to​ date, they may want to develop their own plan and have it reviewed by a planner as confirmation that they are on the right track.

f) The Taylors should track their expenses more closely because overspending without replacement income can be disastrous. In the event of an unexpectedly bad financial situation or a long downturn in the​ economy, they would not have the time or resources to rectify their misfortune and achieve their goals.

Their big five expenses are likely to be the same as the average U.S. household​ - taxes,​ food, housing, medical care and transportation. Most retirement benefits will be​ taxable, as will other investment earnings. Depending on the age of the house or​ appliances, repairs or replacements may be necessary.

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The student could model the chance of it raining on each day by

The experimental probability of having rain on both days expressed as a percentage is 20%.

The experimental probability of having rain on both days can be determined using the probability formula given below as follows:

The number of trials with rain on both days = 2 (Saturday and Sunday)

The total number of trials = 10

Experimental probability = 2 / 10

Experimental probability = 0.2 or 20%

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The different possible exams for the 6 essay questions from which only 4 appear is equal to 15.

n is the total number of items in the set = 6 essay questions

r is the number of items we want to choose = 4 questions

Using combinations,

which is a way of counting the number of ways to choose a certain number of items from a larger set without regard to order.

Choose 4 out of the 6 essay questions, without regard to the order in which they appear on the exam.

Use the formula for combinations,

C(n, r) = n! / (r! × (n - r)!)

Plugging in the values, we get,

⇒C(6, 4) = 6! / (4! × (6 - 4)!)

⇒C(6, 4) = 6! / (4! ×2!)

⇒C(6, 4) = (6 × 5 × 4 × 3) / (4 × 3 × 2 × 1)

⇒C(6, 4) = 15

Therefore, there are 15 different exams possible, each consisting of 4 out of the 6 essay questions provided by the professor.

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The absolute maximum value of the function on the interval (-5, 11) is 670, which occurs at x = -5, and the absolute minimum value is approximately 400.847, which occurs at x ≈ 1.154.

To find the absolute maximum and minimum values of the function f(x) = -2x^3 + 8x + 400 on the interval (-5, 11), we need to consider the critical points and the endpoints of the interval.

First, we find the derivative of the function:

f'(x) = -6x^2 + 8

Setting f'(x) = 0 to find the critical points, we get:

-6x^2 + 8 = 0

x^2 = 4/3

x = ±√(4/3)

Since only √(4/3) is within the interval (-5, 11), this is the only critical point we need to consider.

Next, we evaluate the function at the endpoints of the interval:

f(-5) = -2(-5)^3 + 8(-5) + 400 = 670

f(11) = -2(11)^3 + 8(11) + 400 = -1666

Finally, we evaluate the function at the critical point:

f(√(4/3)) = -2(√(4/3))^3 + 8(√(4/3)) + 400 ≈ 400.847

Therefore, the absolute maximum value of the function on the interval (-5, 11) is 670, which occurs at x = -5, and the absolute minimum value is approximately 400.847, which occurs at x ≈ 1.154.

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The downhill side of the crane base should be raised by approximately 4.53 inches to level the crane on a 2.5° slope.

We can use trigonometry here. Let x be the length (in inches) that the downhill side of the base should be raised. The slope of the ground is given to be 2.5°,

tan(2.5°) ≈ 0.0436

Now, using the equation,

x / 12 = 9tan(2.5°)

Here, we converted the base's width from feet to inches (by dividing by 12) and calculated the crane's required vertical displacement (inches) using the angle's tangent. When we simplify this equation, we obtain,

x = 9tan(2.5°)12

x ≈ 4.53 inches

Therefore, the downhill side of the base should be raised by about 4.53 inches to level the crane.

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Complete question - A crane is being set up on a slope of 2.5 degrees. If the base of the crane is 9.0 ft​ wide, how many inches should the downhill side of the base be raised in order to level the​ crane?

we cannot determine whether the triangles are congruent or similar based on the given information .

Neither student is correct.

To determine whether two triangles are congruent or similar, we need to compare all three pairs of corresponding angles and all three pairs of corresponding sides.

In this case, we are given two pairs of corresponding angles: angle A in triangle ABC is congruent to angle Z in triangle XYZ, and angle B in triangle ABC is congruent to angle Y in triangle XYZ. However, we do not know the measure of angle C in triangle ABC or angle X in triangle XYZ, so we cannot compare the third pair of corresponding angles.

Furthermore, we are not given any information about the lengths of the sides of the two triangles, so we cannot compare the corresponding sides.

Therefore, we cannot determine whether the triangles are congruent or similar based on the given information.

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The critical point is x = -1/2, the function has a local minimum at x = 1 and an absolute maximum at x = 4, and the absolute minimum is at x = -1/2.

a. The critical point is x = -1/2.

To find the critical point(s), we need to find where the derivative of the function is equal to zero or undefined. In this case, we have:

f(x) = -4x - x^2 + 2

f'(x) = -4 - 2x

Setting f'(x) equal to zero, we get:

-4 - 2x = 0

-2x = 4

x = -2/2

x = -1

However, we need to check if this value is in the given interval (1-4, 4). Since -1 is not in the interval, it is not a critical point.

Next, we check the endpoints of the interval.

When x = 1, f(x) = -4 - 1^2 + 2 = -3.

When x = 4, f(x) = -4 - 4^2 + 2 = -22.

So the function has a local minimum at x = 1, and an absolute maximum at x = 4, and no local maximum.

b. The local maximum is at x = 4, and the local minimum is at x = 1.

We can use the First Derivative Test to locate the local maximum and minimum points. If the derivative changes sign from positive to negative at a point, then it is a local maximum. If the derivative changes sign from negative to positive at a point, then it is a local minimum.

In this case, we have f'(x) = -4 - 2x. It is negative for x < -2 and positive for x > -2. Therefore, the function is decreasing for x < -2 and increasing for x > -2. Since the interval is (1-4, 4), the critical points are -2 and 4.

For x = 4, we have f'(4) = -4 - 2(4) = -12, which is negative, so x = 4 is a local maximum.

For x = 1, we have f'(1) = -4 - 2(1) = -6, which is negative, so x = 1 is a local minimum.

Therefore, the local maximum is at x = 4, and the local minimum is at x = 1.

c. The absolute maximum is at x = 4, and the absolute minimum is at x = -1/2.

To find the absolute maximum and minimum, we need to evaluate the function at the critical points and endpoints of the interval, and choose the largest and smallest values, respectively.

We have already found that the local maximum is at x = 4, and the local minimum is at x = 1. We also found that x = -1/2 is a critical point, but it is not in the given interval, so we can ignore it.

Evaluating the function at the endpoints of the interval, we get:

f(1) = -3

f(4) = -22

Therefore, the absolute maximum is at x = 4, and the absolute minimum is at x = 1/2.

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Answer:

3a - 2b - c + 16 = 23

Step-by-step explanation:

so we want to write an equetion which containe a, b and c so we have given

4a - 2b = 10 and a + c = 3

so we are going to differentiate 10 to 7 + 3 it will be

4a - 2b = 10

4a - 2b = 7 + 3 ...then we insert a + c in place of 3 b/c they are equal

4a - 2b = 7 + a + c .... we take to the left side of the equal sighn

4a - a - 2b - c = 7

3a - 2b - c = 7

thrn if we want to write the equetion =23 we add 16 both side 3a - 2b - c + 16 = 23 .

The conjecture "X, Y, Z and W are noncolinear" is always true when given that line segments XY and ZW intersect at point A. So option D is the correct answer.

When line segments XY and ZW intersect at point A, it means that X, Y, Z, and W do not all lie on the same line. Since they do not all lie on the same line, they are considered non-collinear.

So the correct answer is option D. X, Y, Z and W are noncolinear. ​

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Martin expects to wait longer than Selena. This can be Mathematically represented as: t > s

To determine who expects to wait longer, we need to compare the values on the number lines for Selena and Martin. Let's say Selena expects to wait for t minutes, and Martin expects to wait for s minutes. Looking at the number lines, we can see that Selena's expected wait time is closer to 10 minutes, while Martin's expected wait time is closer to 5 minutes. Therefore, we can say that Martin expects to wait longer than Selena.

Mathematically, we can represent this as:

t > s

This means that Selena's expected wait time is greater than Martin's expected wait time. Therefore, Martin expects to wait longer than Selena.

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The equation of the straight line connecting these points in the form of y = mx + c is given as y = (1/2)x + 1.

The line in the slope-intercept equation is given as,

y = mx + c

where:

m = the slope of the line

c = the y-intercept

The slope m of the line connecting two points (x1, y1) and (x2, y2) is given by the formula

= (y₂ - y₁) / (x₂ - x₁)

Substituting the coordinates values of P and Q into this formula, we get

[tex]m = (3 - 0) / (4 - (-2))[/tex]

= 3/6

= 1/2

Therefore, the value of the m is 1/2

We can find the value of c by substituting the m and x values in the equation. using the point P and  Substituting x and y values in the equation we get

x = - 2

y = 0  

[tex]0 = (1/2) × (-2) + c[/tex]

c = 1

Therefore, the value of c is 1.

By substuting the m and c values in the standard slope-intercept formula we get y = (1/2)x + 1.

Therefore, the equation of the line connecting points P and Q is y = (1/2)x + 1.

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The value of x in the equation is -32.8.

To solve for X in the equation X - (-1.8) = -31, we need to follow some basic algebraic steps.

The first step is to simplify the equation by adding the two negatives, which would result in X + 1.8 = -31. The next step would be to isolate X by subtracting 1.8 from both sides of the equation.

This will give us X = -32.8.
The value of X in this equation is -32.8.
It's essential to keep in mind the basic rules of algebra when solving such equations.

By following the rules and taking it step by step, we can solve any equation, regardless of how complex it may seem.
In conclusion,

X - (-1.8) = -31 is a straight forward equation that can be solved using basic algebraic steps.

The value of X is -32.8.
The given equation is X - (-1.8) = -31.
When you see a subtraction of a negative number, you can rewrite it as addition of the positive number. So, X - (-1.8) becomes X + 1.8. The equation now is:
X + 1.8 = -31
To find the value of X, subtract 1.8 from both sides of the equation:
X + 1.8 - 1.8 = -31 - 1.8

We can simplify by adding the values of the two negative numbers on the left side of the equation:

X + 1.8 = -31

Next, we can isolate the variable x by subtracting 1.8 from both sides of the equation:

X = -31 - 1.8

Simplifying further, we get:

X = -32.8
This simplifies to: X = -32.8
So, the value of X is -32.8 in the equation X - (-1.8) = -31.

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Answer:148

Step-by-step explanation:

Assuming he only bought milk, fish and chicken.
220+132=352
500-352=148

Answer:

8x - 16 = 40

8x = 56

x = 7

Hope this helps! :D

If the area of rectangle abcd is 16in² and the area of the rectangle a’b’c’d’ is 64in², the scale factor used to dilate the rectangle was 2.

When a rectangle is dilated, its dimensions are multiplied by a common factor known as the scale factor. The scale factor is the ratio of the corresponding sides of the original rectangle and the dilated rectangle.

Let the scale factor be represented by k. The area of the original rectangle is 16 in², so we can write:

length x width = 16

Let L and W represent the length and width of the original rectangle, respectively. Therefore, we have:

LW = 16

After dilation, the area of the new rectangle is 64 in². The length and width of the new rectangle are kL and kW, respectively. Therefore, we can write:

(kL)(kW) = 64

Simplifying the above equation, we get:

k²LW = 64

Substituting the value of LW from the first equation, we get:

k²(16) = 64

Solving for k, we get:

k = √4 = 2

This means that the length and width of the new rectangle are twice the length and width of the original rectangle.

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The probability that a randomly chosen student is a male who enjoys reading P(male and enjoys reading) ≈ 0.261

To calculate the probability that a randomly chosen student is a male who enjoys reading, you need the number of males who enjoy reading divided by the total number of students.

The probability that a randomly chosen student is a male who enjoys reading can be found by dividing the number of males who enjoy reading by the total number of students.

From the table, we see that there are 30 males who enjoy reading and a total of 115 students. Therefore, the probability is:

P(male and enjoys reading) = 30/115

Rounding to the nearest thousandth, we get:

Therefore, The probability that a randomly chosen student is a male who enjoys reading P(male and enjoys reading) ≈ 0.261

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The equation 15√2 = x√2 can be solved, the value of x that satisfies the equation is 15.

To solve the equation 15√2 = x√2, you can divide both sides by √2 since the square root of 2 is a common factor on both sides of the equation. This gives:

15√2 / √2 = x√2 / √2

On the left side of the equation, the √2 and the denominator cancel out, leaving:

15

On the right side of the equation, the √2 and the denominator also cancel out, leaving:

x

So the solution to the equation is:

x = 15

Therefore, the value of x that satisfies the equation is 15.

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The probability of drawing either a two or a ten is (4+4)/52, which simplifies to 2/13.
The probability of drawing either a two or a club is (3+13)/52, which simplifies to 4/13.

For the first question: In a standard deck of 52 cards, there are four 2s and four 10s. The probability of drawing either a two or a ten is the number of successful outcomes (drawing a 2 or a 10) divided by the total number of possible outcomes (52 cards). So, the probability is (4+4)/52 = 8/52. This can be reduced to the fraction 2/13.

For the second question: There are four 2s and thirteen clubs in a standard deck of 52 cards. Since one of the 2s is a club, there are three additional 2s that are not clubs. The probability of drawing either a two or a club is the number of successful outcomes (3 additional 2s + 13 clubs) divided by the total number of possible outcomes (52 cards). So, the probability is (3+13)/52 = 16/52. This can be reduced to the fraction 4/13.

Therefore,
1) Probability of drawing either a two or a ten: 2/13
2) Probability of drawing either a two or a club: 4/13

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One way to model this situation is by using a probability distribution, such as the binomial distribution. The binomial distribution models the probability of a certain number of successes (in this case, rain) in a fixed number of trials (in this case, school days during springtime).

Let's say we want to simulate whether it will be raining when school is dismissed on a particular day during springtime. We can define a success as rain and a failure as no rain. Then, the probability of success (rain) is 0.4, and the probability of failure (no rain) is 0.6.

To simulate whether it will be raining on a particular day, we can use a random number generator to generate a value between 0 and 1. If the value is less than or equal to 0.4, we can consider it a success (rain) and if it's greater than 0.4, we can consider it a failure (no rain).

We can repeat this process for a large number of trials (school days during springtime) to simulate the probability of rain over a given period of time. By keeping track of the number of successes (rainy days) and failures (non-rainy days), we can estimate the probability of rain during springtime when school is dismissed.

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bro idrk but I think

Answer:  The correct option is

(A) {-1, -5}.

Step-by-step explanation:  We are given to find the zeroes of the quadratic function graphed in the figure shown.

We know that

the zeroes of a quadratic function f(x) are the value of x for which f(x) is equal to zero.

That is, the points on the graph where the curve crosses the X-axis.

From the graph, we note that the curve of the function crosses the X-axis at the points x = 1 and x = -5.

Therefore, the zeroes of the given function are x = -1 an x = -5.

Thus, option (A) is CORRECT.

the slope of   [tex]6.5[/tex] in this equation indicates that for each additional year of age, the median height of boys increases by approximately 6.5 cm. Thus, option D is correct.

The statement that best interprets the slope in the context of the problem is "The slope is 6.5, this means that each year boys grow approximately  [tex]6.5[/tex]  cm."

The slope of a linear equation represents the rate of change, or the amount by which the dependent variable (in this case, median height) changes for each unit increase in the independent variable (in this case, age).

Therefore, the slope of  [tex]6.5[/tex] in this equation indicates that for each additional year of age, the median height of boys increases by approximately [tex]6.5[/tex] cm.

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