The spinner will be spun two times.

What is the probability that both spins result in the same color?

Step 1: Find a common denominator.

The denominators are 3y, 4, and 8. The least common multiple (LCM) of these is 24y.

Step 2: Adjust each term to have a denominator of 24y.

To do this, we multiply the numerator and denominator of each term by the appropriate factor:

For the term 8/3y, multiply numerator and denominator by 8: (8/3y) * (8/8) = 64/24y.

For the term 5y/4, multiply numerator and denominator by 6y: (5y/4) * (6y/6y) = 30y^2/24y.

For the term 5/8, multiply numerator and denominator by 3: (5/8) * (3/3) = 15/24y.

Step 3: Combine the terms.

Now that all terms have a common denominator of 24y, we can add them together:

(64/24y) + (30y^2/24y) - (15/24y)

Step 4: Combine the numerators.

Add the numerators of the fractions:

(64 + 30y^2 - 15) / 24y

Step 5: Simplify the numerator.

Combine like terms in the numerator:

(49 + 30y^2) / 24y

Thus, the simplified expression is (49 + 30y^2) / 24y, considering all permissible values of y.

Answer:

The number line has a closed circle at -2 and a closed circle at -6.

Step-by-step explanation:

|x+4| = 2

x + 4 = 2  or  x + 4 = -2

x = -2  or  x = -6

The number line has a closed circle at -2 and a closed circle at -6.

Answer:

1890ml<10litres

1.72m=172cm

Step-by-step explanation:

10 x 1000 = 10000 ml which is greater than 1890 ml.

1.72 x 100 = 172 cm

a)The concentration will be 0.5 mg/L at approximately 1.18 hours.

c) [0, ∝) is a reasonable domain for this function.

d) The patient must receive the next intravenous dose of the drug between 0.75 and 1.35 hours after the initial dose.

e) The concentrations of the two drugs cannot be compared

A. To find when the concentration will be 0.5 mg/L, we can set the function equal to 0.5 and solve for t:

20t c(t)-20 2 +4 = 0.5

20t c(t)-20 2 = 3.5

20t c(t) = 2

3.5c(t) = 1.175

So the concentration will be 0.5 mg/L at approximately 1.18 hours.

B. Using the given formula, we can complete the table as follows:

| t    | c(t)         |

0    | 4            |

2    | 2.86        |

4    | 2.14         |

6    | 1.62         |

8    | 1.23         |

10   | 0.95         |

12   | 0.74         |

14   | 0.57         |

16   | 0.44         |

18   | 0.34         |

20   | 0.27        

C. Because time cannot be negative and the function has no imaginary values, the domain of the function is all non-negative real numbers.

As a result, [0,] is a reasonable domain for this function.

D. To maintain a concentration above 1 mg/L and below 8 mg/L, we need to solve the inequality:

1 < 20t

c(t)-20 2 +4 < 8

Simplifying this inequality, we get:

0.75 < t < 1.35

To maintain the desired concentration, the patient must receive the next intravenous dose of the drug between 0.75 and 1.35 hours after the initial dose.

E. Without additional information, we cannot compare the concentrations of the two drugs.

The information provided only allows us to analyze the intravenous drug concentration

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a) The required down payment = $4,700

b) The amount of the auto loan is = $42,300

c)  The monthly payment is $864.97

Given data ,

Maria plans to purchase a new work truck. The dealer requires a 10% down payment on the $47,000 vehicle

Maria will finance the rest of the cost with a fixed-rate amortized auto loan at 8.5% annual interest with monthly payments over 5 years

(a)

The required down payment is 10% of $47,000, which is:

Down payment = 0.1 x $47,000 = $4,700

(b)

The amount of the auto loan is the total cost of the truck minus the down payment, which is:

Auto loan = $47,000 - $4,700 = $42,300

(c)

To find the monthly payment, we can use the formula for a fixed-rate amortized loan:

PMT = r(PV) / [1 - (1 + r)^(-n)]

where PMT is the monthly payment, r is the monthly interest rate (which is the annual interest rate divided by 12), PV is the present value of the loan (which is the auto loan amount), and n is the total number of payments (which is the number of years multiplied by 12).

Substituting the given values, we get:

r = 0.085 / 12 = 0.00708333 (monthly interest rate)

PV = $42,300

n = 5 x 12 = 60 (total number of payments)

PMT = 0.00708333($42,300) / [1 - (1 + 0.00708333)^(-60)] = $864.97

Hence , the monthly payment is $864.97

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The measure of the angle ∠S is 95°

Let's call angle Q as x. Then we can express the other angles in terms of x as follows:

Angle R = x + 25 (since angle R is 25° more than angle Q)

Angle S = x + 65 (since angle S is 65° more than angle Q)

We know that the sum of the angles in a triangle is always 180°, so we can write:

x + (x + 25) + (x + 65) = 180

Simplifying this equation, we get:

3x + 90 = 180

Subtracting 90 from both sides, we get:

3x = 90

Dividing both sides by 3, we get:

x = 30

Therefore, angle S is:

x + 65 = 30 + 65 = 95 degrees

So the measure of angle S is 95 degrees.

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Angle 1 and angle 2 are corresponding angles since they are in the same relative position. Corresponding angles are congruent. So, to solve, we will need to set the given expressions equal to each other and then solve for the value of x algebraically.

80 - 2x = 93 - 3x

80 + x = 93

x = 13

Answer: x = 13

Hope this helps!

Answer:

x = 10

Step-by-step explanation:

m<1 = m<2

(80-2x) = (90-3x)

80 - 2x = 90 - 3x

80 = 90 - x

-10 = -x, x = 10

Answer:

The large prism is 5 inches taller than the small prism

Step-by-step explanation:

We know that the formula for volume of a rectangular prism is

V = lwh, where

Step 1:  We're given the volume, length, and width for both rectangular prisms, but not the height.  We can find the height of each rectangular prism by rewriting the volume formula in terms of h (i.e., isolate h), which gives us:

V / (lw) = h

Step 2:  To find the height of the small prism, we plug in 100 for V, 5 for l, and 4 for w in the volume formula (in terms of h) and simplify:

100 / (5 * 4) = h

100 / 20 = h

5 inches = height

Optional Confirmation of Step 2:

We can check that our height is correct by plugging in 5 for h in the regular volume formula, with 100 for V, 5 for l, and 4 for w;

100 = 5 * 4 * 5

100 = 20 * 5

100 = 100

Step 3:  To find the height of the large prism, we plug in 200 for V, 5 for l, and 4 for w in the volume formula (in terms of h) and simplify:

200 / (5 * 4) = h

200 / 20 = h

10 inches = height

Optional Confirmation of Step 3:

We can check that our height is correct by plugging in 5 for h in the regular volume formula, with 200 for V, 5 for l, and 4 for w;

200 = 5 * 4 * 10

200 = 20 * 10

200 = 200

Step 5:  

10 - 5 = 5 inches taller

The result to the equation is x = 7.

To find the results of the equation √( 2x- 5) 4 = 1, we can break it step by step

Abate 4 from both sides of the equation

√( 2x- 5) = 1- 4

√( 2x- 5) = -3

Square both sides of the equation to exclude the square root

√( 2x- 5))² = (- 3)²

2x- 5 = 9

Add 5 to both sides of the equation

2x = 9 + 5

2x = 14

Divide both sides of the equation by 2

x = 14/2

x = 7

Thus, the result to the equation is x = 7.

Checking the extraneous result

Substituting x = 7 back into the original equation

√(2(7)-5)+4=1

√(14-5)+4=1

√9+4=1

3+4=1

7 = 1

This equation isn't true, which means that x = 7 is an extraneous result.

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The estimated proportion of adults in the country who have donated blood in the past two years is approximately 0.1803 or 18.03%. the 95% confidence interval for the proportion of adults in the country who have donated blood in the past two years is approximately 0.1589 to 0.2017.

(a) Estimate the proportion of adults in the country who have donated blood in the past two years.

To estimate the proportion of adults who have donated blood, we divide the number of adults who have donated blood by the total number of adults surveyed.

Number of adults who have donated blood = 414

Total number of adults surveyed = 2290

Proportion of adults who have donated blood = Number of adults who have donated blood / Total number of adults surveyed

Proportion of adults who have donated blood = 414 / 2290

Proportion of adults who have donated blood ≈ 0.1803 (rounded to four decimal places)

Therefore, the estimated proportion of adults in the country who have donated blood in the past two years is approximately 0.1803 or 18.03% (rounded to two decimal places).

(b) Construct a 95% confidence interval for the proportion of adults in the country who have donated blood in the past two years.

To construct a confidence interval, we can use the formula for a proportion with a confidence level of 95%:

Confidence interval = Sample proportion ± Margin of error

Sample proportion = Proportion of adults who have donated blood = 0.1803 (from part a)

Margin of error = Z * √[(Sample proportion * (1 - Sample proportion)) / Sample size]

Z represents the critical value for a 95% confidence level. Since the sample size is large (n > 30), we can use the standard normal distribution and take Z = 1.96.

Sample size = Total number of adults surveyed = 2290

Margin of error = 1.96 * √[(0.1803 * (1 - 0.1803)) / 2290]

Calculating the margin of error:

Margin of error ≈ 1.96 * √[(0.1803 * 0.8197) / 2290]

Margin of error ≈ 0.0214 (rounded to four decimal places)

Confidence interval = 0.1803 ± 0.0214

Lower bound = 0.1803 - 0.0214 ≈ 0.1589 (rounded to four decimal places)

Upper bound = 0.1803 + 0.0214 ≈ 0.2017 (rounded to four decimal places)

Therefore, the 95% confidence interval for the proportion of adults in the country who have donated blood in the past two years is approximately 0.1589 to 0.2017 (or 15.89% to 20.17%, rounded to two decimal places).

(c) Interpret the confidence interval in the context of the problem.

The confidence interval provides a range of values within which we can be 95% confident that the true proportion of adults in the country who have donated blood lies. Based on the survey data, the estimated proportion is 18.03% (from part a). The 95% confidence interval for this proportion is approximately 15.89% to 20.17%.

This means that we are 95% confident that the true proportion of adults in the country who have donated blood in the past two years falls within this range. In other words, if we were to repeat the survey multiple times and construct confidence intervals, approximately 95% of those intervals would contain the true proportion.

Therefore, based on this survey, we can conclude that the proportion of adults who have donated blood in the past two years in the country is likely to be between 15.89% and 20.17%, with a confidence level of 95%.

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The correct option is the first one, we need to round down to the nearest whole so we will get:

f(1.4) = 1

Here we have the step function:

f(/x) = [x]

This function rounds down to the nearest whole any input we give (like you can see on the graph).

Then we have:

f(0) = 0

f(0.5) = 0

f(0.7) = 0

f(1.2) = 1

f(1.3) = 1

f(5.2) = 5

And so on.

With that in mind, if we evaluate in 1.4, then we round down to the nearest whole which is 1, then:

f(1.4) = 1

The correct option is the first one.

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Answer:

The average cost is 4400

Step-by-step explanation:

c=800+40x

where x=number of items

c=800+4x;when x=90

c=800+40(90)

c=800+3600

c=4400

Answer:

4400

Step-by-step explanation:

Answer:

-7

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

To find the value of t, we can use the formula for the slope of a line:

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

Given that the slope of the line is 0, we have:

0 = (-7 - t) / (5 - 3)

To solve for t, we can cross-multiply:

0 * (5 - 3) = -7 - t

0 = -7 - t

To isolate t, we can add 7 to both sides:

7 = -t

Dividing both sides by -1, we get:

t = -7

Therefore, the value of t is -7.

Answer:

  A. If you moved the students from the top 25% in Class 1 into Class 2, the Class 2 median would increase.

Step-by-step explanation:

You want to know the effect of changing or combining class data, given the box plots show two classes with the same median.

We can consider the choices:

The medians of the two classes are the same. The maximum value of Class 1 is in the third quartile of Class 2, so the top 25% of Class 1 would be added to the data values currently in the 3rd quartile of Class 2.

In general, one might expect that adding data values above the median will raise the median. Whether this is actually true depends on the details of the distribution and the number of data points added.

It is probably true that the Class 2 median would increase.

The students who did no homework in Class 1 are the reason for the whisker extending to 0. Removing those from the data set will increase the minimum, likely increasing the value of Q1. This will cause the IQR to be reduced, not increased.

The range of the combined data sets will be the difference of the largest maximum (70) and the smallest minimum (0). The combined range will be 70, not 105.

Combining two data sets with the same median will result in a set of data with the same median. The median will not change, as half the combined data will be above it, and half the combined data will be below it.

Choice A is the only one that makes sense.

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Answer:

The answer is y>-x+3

Step-by-step explanation:

slope=rise/run

(0,3),(3,0)

m=y2-y1/x2-x1

m=0-3/3-0

m=-3/3

m= -1

y=mx+b

y= -x+b

3=-(0)+b

b=3

y>-x+3

The proportion that shows the relationship is h/4 = 8/h

The values of a, h and b are a = 16√3, b = 16√6 and h = 4√2

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

The similar triangles

Using the right triangle/altitude similarity theorem, we have

h/4 = 8/h

Calculating the values of a, h and b

In (a), we have

h/4 = 8/h

This means that

h² = 32

So, we have

h = 4√2

For the value of (a), we have

a² = h² + 4²

So, we have

a² = 32 + 4²

a² = 48

Evaluate

a = 16√3

Next, we have

b² = 32 + 8²

b² = 96

So, we have

b = 16√6

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The mean absolute deviation for the data-set in the table is given as follows:

1.52 million.

The mean of a data-set is given by the sum of all observations divided by the cardinality of the data-set, which is the number of observations in the data-set.

Hence the mean for the data-set in this problem is given as follows:

(1.5 + 3.8 + 1.3 + 1.6 + 2.9 + 1.4 + 0.9 + 2.3 + 8.4 + 1.3)/10 = 2.54.

The deviations are given as follows:

Hence the mean absolute deviation is given as the sum of the deviations divided by the number of observations, hence:

(1.04 + 1.26 + 1.24 + 1.06 + 0.46 + 1.14 + 1.64 + 0.24 + 5.86 + 1.24)/10 = 1.52 million.

The table is given by the image presented at the end of the answer.

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75 chairs expected to be understaffed.

Given : number of common problems found during one such spot check. manufacturer makes 1500 beanbag chairs per day.

To Find : how many of those chairs would they expect to be understaffed?

Common Problems   Frequency

Open seam                  4

Cuts in upholstery       14

Understaffed                15

None                             267

Total                              300

Probability of understaffed  = Understaffed   / Total

= 15/300

= 1/20

manufacturer makes 1500 beanbag chairs per day,

Number of chairs expected to be understaffed = (1/20) x 1500 = 75

Hence 75 chairs expected to be understaffed.

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If you start at (0,0) and increase 2 units in the x-direction on both lines, Line B goes up 2 units in the y-direction, while Line A only goes up 1 unit in the y-direction.

Put another way, if you started at the origin and were walking up either line (pretend their two hills), your elevation on Line B increases more quickly because it's a steeper hill.

So Line B has a great rate of change.  The rise compared to the run is greater.

Answer:

A, the line is shorter, therefore the result is faster. Hence - change for the greater!

But not necessarily when I’m terms of God Almighty. Change can take longer and God uses it for His glory all the meanwhile He’s teaching, loving and correcting people. That’s Gods endless unconditional love!

John 3:16!!

Step-by-step explanation:

The correct equation is:

39 × 3 = 30 × 3 + 9 × 3

This equation shows that multiplying 39 by 3 is equal to the sum of multiplying 30 by 3 and multiplying 9 by 3.

Therefore, the answer is:

39 × 3 = 30 × 3 + 9 × 3

The area of the figure is 225 ft²

From the figure shown, we have that it is made up of a triangle and a rectangle.

Now, the formula for calculating the area of a triangle is expressed as;

A = 1/2bh

Such that;

Substitute the values

Area = 1/2 × 10 × 15

Multiply the values

Area = 75 ft²

Area of the rectangle is;

Area = length × width

Area = 10(15)

Area = 150 ft²

Total area = 225 ft²

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To match a given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form is y = (3/4)x - 5.

The formula y = mx + b,

where "m" stands for the slope and "b" for the y-intercept, is used to match a given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form.
1. If m = 2 and b = 3, the slope-intercept form of the equation would be y = 2x + 3

2. With m = -1/2 and b = 4, the slope-intercept form of the equation would be: y = (-1/2)x + 4.

3. If m = 0 and b = 2, then the slope-intercept form of the equation is: y = 0x + 2 (or just y = 2).

4. With m = 3/4 and b = -5, the slope-intercept form of the equation is: y = (3/4)x - 5.
Therefore, The equation of the line in slope-intercept form is y = (3/4)x - 5, which may be used to match a given slope (m) and y-intercept (b) with it.

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The theoretical probability of exactly 4 students from your school being selected as contestants out of 10 possible contestant spots is approximately 0.009.

Assuming that each member of the audience has an equal chance of being selected as a contestant, the total number of possible ways to select 10 contestants from the audience is:

[tex]150 $ choose 10 = 150! / (10! \times (150 - 10)!) = 2,535,316,699,000[/tex]

To calculate the probability of exactly 4 students from your school being selected as contestants, we need to count the number of ways this can happen and divide it by the total number of possible outcomes.

There are 30 students from your school and 120 students from other schools in the audience.

We need to choose 4 students from your school and 6 students from other schools for the contestant spots.

The number of ways to do this is:

[tex]30 $ choose 4 \times 120 $ choose 6 = (30! / (4! \times 26!)) \times (120! / (6! \times 114!)) = 23,400,140,040,000[/tex]

Therefore, the probability of exactly 4 students from your school being selected as contestants is:

P(4 students selected) = (number of ways to select 4 students from your school and 6 students from other schools) / (total number of ways to select 10 contestants from the audience)

P(4 students selected) = 23,400,140,040,000 / 2,535,316,699,000.

P(4 students selected) ≈ 0.00923 (rounded to 3 decimal places).

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Answer:

[tex]\sqrt[2]{(m)^1}[/tex]

Step-by-step explanation:

denominator = the root number ___

numerator = to the power of ___

Answer:

(-1, 3 1/4) and (3, 12 3/4)

Step-by-step explanation:

These are the only two pairs that will work for the graph.

The measurement is the same for Charles and Jermod are lower quartile and upper quartile. Therefore, options C and D are the correct answer.

From the given dot plot.

The number of minutes Charles spent on homework.

15, 15, 20, 20, 25, 30, 30, 30, 30, 30, 45, 50, 55, 60, 60.

Here, lower quartile = 20

Upper quartile = 50

Median = 30

Range = 60-15

= 45

The number of minutes Jermod spent on homework.

15, 15, 15, 20, 20, 30, 35, 45, 45, 45, 50, 50, 55, 55.

Here, lower quartile = 20

Upper quartile = 50

Median = 45

Range = 55-15

= 40

Therefore, options C and D are the correct answer.

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The expression simplifies to |2x| = -2x, when x<0 by definition of absolute value

If x<0, then the expression |2x| simplifies to -2x.

The absolute value of a number is the distance of the number from zero on the number line.

Since x is negative in this case, 2x will be negative as well.

Taking the absolute value of -2x will give us the opposite of -2x, which is 2x.

However, since we know that x<0, this means that -2x will always be a positive number.

Hence, the expression simplifies to |2x| = -2x, when x<0.

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Complete question

Simplify the expression |2x|  when x is less than 0, x<0

The probability that the respondent has a pet given that the respondent has had a pet is  32/85  or 0.38

We are given the following results below;

Let event B = respondent has a pet now

Now, Probability that the respondent has had a pet = P(A) = 0.88

Probability that the respondent has a pet now and has had a pet =   0.32

So, Probability that the respondent has a pet given that the respondent has had a pet is given by = P(B/A)

This conditional probability is solved as ;

    P(B/A)  =  32/85

                =   0.3764705882

                ≈ 0.38

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Answer:

The value of y is -5, so the ordered pair is (9, -5).

Step-by-step explanation:

To determine the value of y for the ordered pair (9, y) on the line AC, we first need to find the equation of the line AC.

To find the slope of the line AC, substitute the points A and C into the slope formula:

[tex]\textsf{Slope}\;(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y_C-y_A}{x_C-x_A}=\dfrac{-3-1}{4-(-6)}=\dfrac{-4}{10}=-\dfrac{2}{5}[/tex]

To determine the equation of line AC, substitute the found slope and one of the points into the point-slope formula:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\\\y-1&=-\dfrac{2}{5}(x-(-6)\\\\y-1&=-\dfrac{2}{5}x-\dfrac{12}{5}\\\\y&=-\dfrac{2}{5}x-\dfrac{7}{5} \end{aligned}[/tex]

Now we have found the equation of the line AC, to determine the value of y for the ordered pair (9, y), substitute x = 9 into the equation:

[tex]\begin{aligned}y&=-\dfrac{2}{5}(9)-\dfrac{7}{5}\\\\&=-\dfrac{18}{5}-\dfrac{7}{5}\\\\&=\dfrac{-18-7}{5}\\\\&=\dfrac{-25}{5}\\\\&=-5\end{aligned}[/tex]

Therefore, the value of y for the ordered pair is y = -5.

So the ordered pair is (9, -5).

The description of the difference between the graph of g(x) and f(x), based on the equation relating the functions is the option C.

A function is a definition or rule that maps an input on to an output.

The possible function, obtained from a similar function on the internet can be presented as follows;

f(x) = 2ˣ

g(x) = 2·f(x) = 2·(2ˣ)

Therefore;

The graph of g(x) can be obtained from the graph of f(x), by a transformation of vertical stretch by factor of 2 and the correct option therefore is option C.

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