17. What is the probability that the student will play football and baseball? (a) 28 /33 (b) 35 /66 (c) 4 /33 (d) 8 /11

The number of copies sold (x) to date is 463043

The given parameters are:

Copies sold = 42,600

Proportion sold = 9.2% of the number of copies sold to date.

The number of copies sold (x) to date is calculated as:

Copies sold = Proportion * number of copies sold to date

Substitute the known values in the above equation

9.2% * x = 42,600

Divide both sides by 9.2%

x = 463043

Hence, the number of copies sold (x) to date is 463043

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The limit does not exist. There are infinitely many infinite discontinuities at [tex]x=n\pi[/tex], where [tex]n\in\Bbb N[/tex]. The function oscillates wildly between negative and positive infinity.

Answer:

The function h(x) is decreasing on the interval (3, ∞).

Step-by-step explanation:

Please take a look at the attached image.

You will see a graph of the given function h(x) = -2[tex]\sqrt{x-3}[/tex]. The function is decreasing.

The function starts at 3 and starts to go towards negative infinity on the x-axis. Therefore the function is decreasing on the interval (3, ∞).

Answer:

x ≤ −8

Step-by-step explanation:

Let's solve your inequality step-by-step.

3 - 3x/4 ≥ 9

Step 1: Simplify both sides of the inequality.

-3/4x + 3 ≥ 9

Step 2: Subtract 3 from both sides.

-3/4x + 3 - 3 ≥ 9 − 3

-3/4x ≥ 6

Step 3: Multiply both sides by 4/(-3).

(4/-3) * (-3/4x) ≥ (4/-3) * (6)

x ≤ −8

Answer:

x ≤ −8

Answer:

421/6 degrees

Step-by-step explanation:

The acute angles of a right triangle are complementary, so

[tex]10x+6+2x+7=90 \\ \\ 12x+13=90 \\ \\ 12x=77 \\ \\ x=\frac{77}{12}[/tex]

So, the acute angles measures 421/6 degrees and 119/6 degrees, and thus the larger angle is 421/6 degrees.

The single payment six months from now is required to settle the debt will be $4042.

The interest rate monthly will be 8/1200.

The number of time period given is 6 months.

Therefore, the future value will be:

= 2000(1 - 8/1200)^6

= 2081.35

The present value will be:

= 2000(1 - 8/1200)^3

= 1960.53

Therefore, the single payment will be:

= 2081.35 + 1960.53

= 4042

In conclusion, the correct amount is $4042.

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The statement that a linear equation is an equation whose graph is a straight line is True.

A  linear equation can be defined as an algebraic equation with each term having an exponent and the graphing of the equation results in a straight line.

From the definition, it can be deduced that the statement is True.

Thus, the statement that a linear equation is an equation whose graph is a straight line is True.

The complete question is:

True or false

A linear equation is an equation whose graph is a straight line.

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Answer:

yes

Step-by-step explanation:

f the exterior angle of a polygon is given, then the formula to find the interior angle is Interior Angle of a polygon = 180° – Exterior angle of a polygon Method 3: If we know the sum of all the interior angles of a regular polygon, we can obtain the interior angle by dividing the sum by the number of sides

In the case above, the value of the overhead rate for the second quarter is $17,640.

Note that:

In the case above, for one to be able to calculate the predetermined overhead rate, a person need to divide the value of the  estimated overhead costs which is $52,500 by that of the estimated direct labor hours .

Predetermined overhead rate=Estimated overhead costs/ estimated direct labor hours

Predetermined overhead rate=$52,500/  12,500

Predetermined overhead rate=$4.20/DLH overhead rate

Hence:  $52,500/ 12,500 =   $4.20/DLH overhead rate.

Since the Overhead that was applied at standard hours was said to be allowed, then:

= $4.2 x 2,400 x 1.75

= $17,640.

Therefore, In the case above, the value of the overhead rate for the second quarter is $17,640.

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The number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.

Given that there are 60 students out of which 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities.

Let A, B, and W denote the sets of students apply to Addis Ababa Uni (A), Bahir Dar Uni (B), or Wachemo Uni (W). Let U denote the universal set of all students in the class.

We're given the cardinalities of several sets:

total number of students n(U)=60, A applicants is n(A)=30, B applicants n(B)=25, W applicants n(W)=24, A and B applicants n(A∩B)=11, A and W applicants n(A∩W)=6, B and W applicants n(B∩W)=9 non-applicants n(U\(A∪B∪W))=4

The last cardinality tells us n(A∪B∪W),60-4=56 students applied anywhere at all.

We want to find n(A∩B∩W), the number of students that applied to each of the three universities.

By the inclusion/exclusion principle,

n(A∪B∪W)=n(A)+n(B)+n(W)-n(A∩B)-n(A∩W)-n(B∩W)+n(A∩B∩W)

56=30+25+24-11-6-9+n(A∩B∩W)

n(A∩B∩W)=3

Now, we will find the number of students that applied for at least two of the universities.

n(A∩B)=n(A∩B∩W)+n(A∩B∩W')

11=3+n(A∩B∩W')

8=n(A∩B∩W')

Similarly, we will find

n(A∩B'∩W)=3

n(A'∩B∩W)=6

n(A∩B'∩W')=16

n(A'∩B∩W')=8

n(A'∩B'∩W)=12

then the total number of students applied for at least two students is

n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B∩W)=20

Now, we will find the number of students that applied for atmost two universities, we get

n(A∩B∩W')+n(A∩B'∩W)+n(A'∩B∩W)+n(A∩B'∩W')+n(A'∩B∩W')+n(A'∩B'∩W)=53

now, we will find the number of students that applied for Addis Ababa but not Bahir Dar University is

n(A∩B')=n(A)-n(B)

n(A∩B')=30-25

n(A∩B')=5

hence, the total students is 60 and the number of students that applied for all universities is 3, the number of students that applied for at least two of the universities is 20, the number of students that applied for at most two of the universities is 53, and the number of students that applied for Addis Ababa but not Bahir Dar University is 5.

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The length of the semi-major axis of the ellipse is 7.

What is the semi-major axis of an ellipse?

The semi-major axis of an ellipse is the half of the longest diameter passing through its vertex and focus.

The general equation of an ellipse is :

⇒ x²/a²+y²/b²=1, where a is the semi-major axis and b, is the semi-minor axis

x²/49+y²/36=1

x²/(7²)+y²/(6²)=1

x²/a²+y²/b²=1

a=7

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Answer 1:

1.23456789 × (10-6) = 4.93827156

Answer 2:

(1.23456789 × 10) - 6 = 6.3456789

Answer 3:

1.23456789 × [tex]10^{-6}[/tex] = 0.000000123456789

Hope this helped! :)

Answer:

f(g(x)) = f(2x - 3) = 3(2x - 3) + 5 = 6x - 9 + 5 = 6x - 4

f(g(2)) = f(2*2 - 3) = f(4 - 3) = f(1) = 3*1 + 5 = 3 + 5 = 8

The composite function values:

f(g(x)) = 6x- 4

f(g(2)) = 8.

Any function that is created by combining two or more other functions is referred to as a composite function. To put it another way, given two functions, f, and g, the composite function of f and g, denoted as f(g(x)), is a new function that applies g to the input x before applying f to the output of g. (x).

To find the value of fg(x), we need to compute g(x) first and then substitute it into f(x).

g(x) = 2x - 3

Substitute g(x) into f(x):

f(g(x)) = 3(2x - 3) + 5

f(g(x)) = 6x - 4

Therefore, fg(x) = 6x - 4.

To find the value of fg(2), substitute 2 into fg(x):

fg(2) = 6(2) - 4

fg(2) = 8

Therefore, fg(2) = 8.

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The slope of a line that is parallel to y=5x+3 is 5x.

Two lines must have the same slope to be parallel to each other.

It will take 6 weeks for the number of infected people to reach 1200

The function is given as:

y equals 15 times 2 to the power of t

Rewrite the function properly as follows

y = 15 * 2^t

When the population is 1200, the equation becomes

15 * 2^t = 1200

Divide both sides by 15

2^t = 80

Take the logarithm of both sides

t * log(2) = log(80)

Divide both sides by log(2)

t = 6.3

Approximate

t = 6

Hence, it will take 6 weeks for the number of infected people to reach 1200

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Applying the Pythagorean theorem, the length of the radius is: 35.3 units.

According to the Pythagorean theorem, the sum of the squares of the shorter sides of a right triangle equals the square of the longest side. For example, if a and b are two smaller legs of a right triangle, and c is the longest leg (hypotenuse) of the right triangle, then the Pythagorean theorem states that:

a² + b² = c².

Given the following parameters of the right triangle:

Triangle ABC is a right triangle with angle ACB as the right angle according to the tangent theorem since segment BC is tangent to Circle A

Segment AB = 58 (hypotenuse of the right triangle)

Segment BC = 46 (small leg of the right triangle)

Radius = AC (small leg of the right triangle)

Using the Pythagorean theorem, we have:

AC = √(AB² - BC²)

AC = √(58² - 46²)

AC = 35.3 units (to the nearest tenth).

Therefore, by using the Pythagorean theorem, the length of the radius of the circle, which is segment AC, to the nearest tenth is: 35.5 units.

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The interquartile range of 48, 26, 31, 50, 38, 40, 42, 34, 44, 36, is: D. 10.

The interquartile range of a data distribution is determined as: upper quartile (Q3) - lower quartile (Q1).

The upper quartile of a data distribution is the center of the second half of a data distribution while the lower quartile is the center of the first half of a data distribution.

Given the data, 48, 26, 31, 50, 38, 40, 42, 34, 44, 36:

Order the data set as, 26, 31, 34, 36, 38, 40, 42, 44, 48, 50

The first half of the data is: 26, 31, 34, 36, 38.

The center is 34.

Lower quartile (Q1) = 34.

The second half of the data is: 40, 42, 44, 48, 50. The center is 44.

Upper quartile (Q3) = 44.

Interquartile range = 44 - 34

Interquartile range = 10

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Answer:

Step-by-step explanation:

y-4=0(x+8)

y-4=0

y=4

Answer:

i

Step-by-step explanation:

y-4=0(x+8)

y-4=0

y=4

The perimeter of the bigger octagon that is similar to the smaller one is: 238 units.

An octagon can be described as a polygon that has 8 sides and 8 angles.

What are Similar Octagons?

Octagons are referred to as similar to each other if they have the same angle measure but corresponding sides that are proportional to each other. That is, they have the same shape but different sizes.

How to Find the Perimeter of Similar Polygons?

Given the two octagons in the diagram are similar, and:

Perimeter of the smaller octagon = 34 units

A side of the smaller octagon = 4 units

Perimeter of the bigger octagon = ?

A corresponding side of the bigger octagon = 28 units

Therefore:

Perimeter of the smaller octagon/Perimeter of the bigger octagon = side of the smaller octagon/corresponding side of the bigger octagon

Plug in the values

34/Perimeter of the bigger octagon = 4/28

Perimeter of the bigger octagon = (28 × 34)/4

Perimeter of the bigger octagon = 238 units.

In summary, the perimeter of the bigger octagon is: 238 units.

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The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

By analytical geometry we know that foci are along the major axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the standard form of the equation of the ellipse is of the following form:

(x - h)² / a² + (y - k)² / b² = 1, where a > b     (1)

Where:

Now, we proceed to find the vertex and the lengths of the semiaxes:

a = 10 units.

b = 8 units.

Vertex

V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)

V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)

V(x, y) = (1.5, 1) + (- 4.5, 1)

V(x, y) = (- 3, 2)

The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

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Mean = 402.5.

Variance = 77,556.3

Standard deviation = 278.5

See attachment for the complete table.

The mean of a data is the sum of all data values divided by the number of data values we have in the data set.

Variance is calculated by finding the sum of the squares of the deviations from the mean, find the average, then find the average.

The standard deviation = the square root of variance.

The mean of the data given would be: 402.5.

402.5 is subtracted from each of the data points to get the deviations which are squared.

It is the sum of the deviations that gives us 310,225.2.

To find the variance, divide 310,225.2 by the number of data values which is 4.

Variance = 310,225.2/4

Variance = 77,556.3

Standard deviation = √77,556.3

Standard deviation = 278.5

The complete table containing the missing values is given in the image attached below.

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The required number is 7. The expression formed with the given information is x - 21 = 2(-x).

An expression is the combination of variables, constants, and coefficients.

If two expressions are related by an equal in between them, then that is said to be an equation.

From the given data,

Consider the required number = x

The number is decreased by 21 i.e., x - 21

Twice the opposite of the number = 2(-x)

So, on equating,

x - 21 = 2(-x)

On simplifying,

⇒ x - 21 = -2x

⇒ x + 2x = 21

⇒ 3x = 21

∴ x = 7

Thus, the required number is 7.

Check:

7 - 21 = -14 and 2(-7) = -14.

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The cost of hiring a car for 2 days in 2013 is Rs. 316.8

The cost for hiring a car for 2 days in 2018 was Rs. 264 which was 20% more than in 2013.

Therefore,

cost of hiring for 2018 = Rs. 264

Therefore,

let

cost of hiring in 2013 = 20%(264) + 264

cost of hiring in 2013 = 20 / 100 × 264 + 264

cost of hiring in 2013 = 1 / 5 × 264 + 264

cost of hiring in 2013 = 264 / 5 + 264

cost of hiring in 2013 = 52.8 + 264

cost of hiring in 2013 = 316.8

Therefore, the cost of hiring a car for 2 days in 2013 is Rs. 316.8.

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Using the normal distribution, the indicated probability is given as follows:

P(7 ≤ x ≤ 11) = 0.6247.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 8, \sigma = 2[/tex]

P(7 ≤ x ≤ 11) is the p-value of Z when X = 11 subtracted by the p-value of Z when X = 7, hence:

X = 11:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (11 - 8)/2

Z = 1.5

Z = 1.5 has a p-value of 0.9332.

X = 7:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (7- 8)/2

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

0.9332 - 0.3085 = 0.6247.

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Answer:

[tex]y=\frac{-3}{4}x-3[/tex]

Step-by-step explanation:

This is a linear graph so the equation will be in the format of y=mx+b.

b, the y-intercept, will be -3, as that is where the line crosses the y-axis.

m, the slope, is [tex]\frac{-3}{4}[/tex], calculated from the change in y over the change in x from points (-4,0) to (0,-3).

Now substitute the values in our equation:

[tex]y=\frac{-3}{4}x-3[/tex]

Answer:

y= -3/4+[-3]

Step-by-step explanation:

Answer: [tex]\Large\boxed{3.52~;~66.88}[/tex]

Step-by-step explanation:

Given information

One number is 19 times the other

The smaller number is less than 5

Sum = 70.4

Set variables

Let x be the smaller number

Let 19x be the larger number

Set equation according to the given information

Smaller number + Larger number = Sum

x + 19x = 70.4

Simplify by addition

20x = 70.4

Divide 20 on both sides

20x / 20 = 70.4 / 20

[tex]\Large\boxed{x=3.52}[/tex]

Substitute values into the variables to find the larger number

Larger number = 19x

                         = 19 (3.52)

                         [tex]\Large\boxed{=66.88}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

smaller number 3.52

greater number 66.88

Step-by-step explanation:

Let x and y be two numbers ,where x < 5 and x ≤ y.

x + y = 70.4

y = 19x

By replacing y by 19x in the first equation we get :

x + 19x = 70.4

Then

20x = 70.4

Then

x = 70.4÷20

  = 3.52

y = 19x

Then

y = 19 × 3.52  (just replace x by 3.52)

  = 66.88

The amount of money which you must invest today is equal to $68,517.85.

Mathematically, the present value of an investment can be calculated by using this formula:

Present Value, PV = FV/(1 + r)^t

Given the following data:

Time, t = 9 years.

Future value, FA = $190,000.

Interest rate, r = 12% = 0.12.

Substituting the given parameters into the formula, we have;

PV = 190,000/(1 + 0.12)^9

PV = 190,000/(1.12)^9

PV = 190,000/2.7730

PV = $68,517.85.

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Answer:

3

Step-by-step explanation:

6.01 has 3 sig fig

I think that's how I do it

The measure of angle 1 (m ∠1) is 28° and the measure of angle 2 (m ∠2) is 62°

From the question, we are to determine the measure of angle 1 and the measure of angle 2

The given diagram is a kite and the diagonals intersect at right angles

Thus,

m ∠2 + 28° + 90° = 180°

m ∠2 = 180° - 28° - 90°

m ∠2 = 62°

Hence, the measure of angle 2 is 62°

For the measure of angle 1

Consider ΔADB

ΔADB is an isosceles triangle

Thus,

In the triangle, m ∠D = m ∠B

Then, we can write that

m ∠1 + 62° + 90° = 180°

m ∠1 = 180° - 62° - 90°

m ∠1 = 28°

∴ The measure of angle 1 is 28°

Hence, the measure of angle 1 (m ∠1) is 28° and the measure of angle 2 (m ∠2) is 62°

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