This Venn diagram shows sports played by 10 students

Let event A - The student plays basketball.
Let event B - The student plays soccer.
What is P(AB)?

Answer:

  64

Step-by-step explanation:

The value of a+b+c is the value of the expression when x=1:

  (3+5)^2 = 8^2 = 64

The answer is:

The correct option is:

A. 10 in.

To calculate the length of the rectangle using its perimeter and one of its sides (width), we need to remember the formula to calculate the perimeter of a rectangle.

[tex]Perimeter_{rectangle}=2width+2length[/tex]

Now, we are given the following information:

[tex]Perimeter=34in\\Width=7in[/tex]

Then, substituting and calculating, we have:

[tex]Perimeter_{rectangle}=2width+2length[/tex]

[tex]34in=2*7in+2length[/tex]

[tex]34in-14in=2length\\\\2length=20in\\\\length=\frac{20in}{2}=10in[/tex]

Hence, we have that the length of the rectangle is equal to 10 inches.

So, the correct option is:

A. 10 in.

Have a nice day!

Answer:

The correct answer is option A.  10 in

Step-by-step explanation:

Points to remember

Perimeter of rectangle = 2(Length + width)

It is given that, Perimeter = 34 inches

Width = 7 inches

To find the length of rectangle

Perimeter = 2(Length + width)

34 = 2(Length + 7)

17 = Length + 7

Length = 17 - 7 = 10 inches

Therefore the length of rectangle = 10 inches

The correct answer is option A.  10 in

Answer:

x2+3

Step-by-step explanation:

The selected value is 3 units up from g (x), the correct option is C.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

g(x) = x2 + 3.

f(x) = g(x+2)

Now,

Using these rules, we can fill in the blanks as follows:

The function g(x)+3. The function f(x) = g(x+2),

The function /(x) is shifted horizontally

Select a Value

2 units left from g (x).

The function /(x)is shifted vertically

Select a Value

3 units up from g (x).

Therefore, the answer of the function will be 3 units up from g (x).

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a tangential line to a circle is one that "touches" the circle but doesn't go inside, and keeps on going, in this case that'd be CD.

The correct answer would be:  segment CD

The probability of rolling either a 3 or a 5 on a six-sided die is 1/3, or about 0.3333, as there are two favorable outcomes (3 or 5) and six possible outcomes in total.

The question asks to find the probability of rolling either a 3 or a 5 when a fair six-sided die is rolled. The sample space for a six-sided die is {1, 2, 3, 4, 5, 6}. To calculate the probability of rolling either a 3 or a 5, we need to count the favorable outcomes, which are 2 (rolling a 3 and rolling a 5), and divide this by the total number of possible outcomes, which is 6.

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability (rolling a 3 or 5) = 2 / 6 = 1 / 3.

Therefore, the probability of rolling either a 3 or a 5 on a six-sided die is 1/3, or approximately 0.3333.

Answer:

• g(1) = 25

• g(n) = g(n-1) -49

Step-by-step explanation:

You can get a clue by filling in n=2 in the explicit formula:

g(2) = 25 -49(2-1) = 25 -49 = g(1) -49

The explicit formula is of the form for an arithmetic sequence:

g(n) = g(1) +d(n-1) . . . . where g(1) is the first term and d is the common difference

Of course, this translates to the recursive formula ...

• g(1) = g(1)

• g(n) = g(n-1) +d

Here you have g(1) = 25, and d = -49. Filling these into the recursive form, you get ...

• g(1) = 25

• g(n) = g(n-1) -49

Answer:

• g(1) = 25

• g(n) = g(n-1) -49

Step-by-step explanation:

You can get a clue by filling in n=2 in the explicit formula:

g(2) = 25 -49(2-1) = 25 -49 = g(1) -49

The explicit formula is of the form for an arithmetic sequence:

g(n) = g(1) +d(n-1) . . . . where g(1) is the first term and d is the common difference

Of course, this translates to the recursive formula ...

• g(1) = g(1)

• g(n) = g(n-1) +d

Here you have g(1) = 25, and d = -49. Filling these into the recursive form, you get ...

• g(1) = 25

• g(n) = g(n-1) -49

Answer:

  $58.75

Step-by-step explanation:

The monthly interest rate is 8.4%/12 = 0.7%, so the first month's interest is ...

  $95,000×0.007 = $665

The amount of the first payment that goes to note reduction is the part that does not go for paying interest. That difference is ...

  $723.75 - 665.00 = $58.75

Answer:$58.75

Step-by-step explanation:

Answer:

  y = 2.5(x +4)(x -1.5) = 2.5x^2 +6.25x -15

Step-by-step explanation:

Each given zero corresponds to a factor that is zero at that point. Those factors are (x +4) and (x -1.5).

The y-intercept tells us the scale factor, the multiplier that is needed to make the function value be -15 at x=0.

  y = a(x +4)(x -1.5) = a(0 +4)(0-1.5) = -6a

  -15 = -6a

  -15/-6 = a = 2.5

So, the quadratic is ...

  y = 2.5(x +4)(x -1.5) = 2.5x^2 +6.25x -15

___

"The equation" can be written in many different forms. The simplest, given the information here, is the factored form (also called "intercept form"). We have also shown "standard form" (US version). The "standard form" (UK version) is also known as vertex form:

  y = 2.5(x +1.25)^2 -18.90625

Answer:

it is 27 because of my cacculations

Step-by-step explanation:

you would fist subtract your numbers and thne get rid of the 5

Answer:

27

Hope It Helps

The volume of the solid generated by revolving the plane region about the y-axis is approximately 35,929.77 cubic units.

Here,

To use the shell method to find the volume of the solid generated by revolving the plane region bounded by the curves [tex]y = x^{(5/2)}, y = 32[/tex],

and x = 0 about the y-axis, we need to integrate the circumference of cylindrical shells along the y-axis.

The volume V can be expressed as the integral of the circumference of the cylindrical shells from y = 0 to y = 32:

V = ∫[0 to 32] 2π * x * h(y) dy

where h(y) represents the height (or thickness) of each shell, and x is the distance from the y-axis to the curve [tex]y = x^{(5/2)[/tex].

To find h(y), we need to express x in terms of y by rearranging the equation [tex]y = x^{(5/2)[/tex]:

[tex]x = y^{(2/5)[/tex]

Now, we can express the volume integral:

V = ∫[0 to 32] 2π * [tex]y^{(2/5)[/tex] * (32 - y) dy

Now, we'll evaluate the integral:

V = 2π ∫[0 to 32] ([tex]32y^{(2/5)} - y^{(7/5)[/tex]) dy

Integrate each term separately:

[tex]V = 2\pi [(32 * (5/7) * y^{(7/5)}) - (5/12) * y^{(12/5)}] | [0 to 32]\\V = 2\pi [(32 * (5/7) * (32)^{(7/5)}) - (5/12) * (32)^{(12/5)}] - [0][/tex]

Now, evaluate the expression:

[tex]V = 2\pi [(32 * (5/7) * 2^7) - (5/12) * 2^{12}][/tex]

V = 2π [(32 * 1280/7) - (5/12) * 4096]

V = 2π [81920/7 - 341.33]

V ≈ 2π * 81920/7 - 2π * 341.33

V ≈ 36608π - 678.13

The volume of the solid generated by revolving the plane region about the y-axis is approximately 35,929.77 cubic units.

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Final answer:

The shell method is used to evaluate the volume of a solid created by revolving a region around the y-axis using a vertical shell element, integrating from x=0 to the x value corresponding to y=32.

Explanation:

To use the shell method to find the volume of the solid generated by revolving the given plane region about the y-axis, we consider a vertical element or 'shell' at a certain x-value with thickness dx. Given the equations [tex]x^{5/2}[/tex], y = 32, and x = 0, these will be the bounds for our region.

The volume of each infinitesimal shell with radius x and height [tex](32 - x^{5/2})[/tex], when revolved around the y-axis, is [tex]2πx(32 -x^{5/2})dx[/tex]. To find the total volume, we integrate this expression from x=0 to where y is 32, which corresponds to the x value where [tex]x^{5/2} = 32[/tex].

Using the substitution [tex]x^{5/2}[/tex] to solve for dx, we get the integral in terms of y, which simplifies the computation. Finally, we evaluate the definite integral to find the volume of the solid of revolution.

Answer:

  See the attachment

Step-by-step explanation:

The point of the dashed line y=x in the problem statement graph is that the inverse function is a reflection of the function across that line. (y and x are interchanged) The graph of selection C has the appropriate pair of curves.

There’s really no work to it tho unless you want to put the division. I did the first 5 since you only needed 5 of them. ( the r^# is the exponent numbers I don’t know how to make them look like exponents in my notes) Hope this helps <3

Find the ratio of the bases: 15 in / 5 in = 3

The triangle on the right side is 3 times larger.

X = 8 * 3

x = 24 inches.

Answer:

Find the attached

Step-by-step explanation:

We have been given the following expression;

(x-2)=5(x+1)

We are required to determine the graph of the solution set. To do this we formulate the following set of equations;

y = x - 2

y = 5(x+1)

We then graph these two equations on the same cartesian plane. The solution will be the point where these two graphs intersect.

Find the attachment below;

Answer:

{-1.75}

Step-by-step explanation:

The given equation is

[tex]x-2=5(x+1)[/tex]

Let as assume f(x) be left hand side and g(x) be the right hand side.

[tex]f(x)=x-2[/tex]

[tex]g(x)=5(x+1)[/tex]

The solution set of given equation is the intersection point of f(x) and g(x).

Table of values are:

For f(x)                    For g(x)

x      f(x)                  x          g(x)

0      -2                   0           5

2       0                    -1          0

Plot these corresponding ordered pairs on a coordinate plan and connect them by straight lines

From the below graph it is clear that the intersection point of f(x) and g(x) is (-1.75,-3.75).

Therefore, the solution set of given equation is {-1.75}.

Answer:

The answer is (-5,2)

Step-by-step explanation:

So we have 2 equations and we need to solve them by substitution.

1) y = 4x + 22

2) 4x – 6y = –32

Since we already have y isolated in equation #1, we'll use that value in equation #2:

4x - 6(4x + 22) = -32

4x - 24x - 132 = -32

-20x = 100

x = -5

Then we put that value of x in the first equation:

y = 4 (-5) + 22 = -20 + 22 = 2

The answer is then (-5,2)

Answer:

(-5, 2)

Step-by-step explanation:

We have the equations:

[tex]y=4x+22[/tex] and [tex]4x-6y=-32[/tex]

Using the substitution method, with y = 4x + 22 and replace it in the equation 4x - 6y = -32

4x - 6(4x + 22) = -32

4x -24x -132 = -32

-20x = -32 + 132

x = 100/-20= -5

Substituting the value of x in the first equations of the systems to clear x.

y = 4x + 22

y = 4(-5) + 22

y= -20 + 22 = 2

Answer:

The numbers are 14 and 25

Step-by-step explanation:

Let one of the numbers be x. The second number we are told is 3 less than twice x. The second number will thus be;

2x - 3

The sum of the numbers is thus;

x + (2x - 3) = 3x - 3

But the sum of the numbers is said to be 39, therefore;

3x - 3 = 39

3x = 42

x = 14

The second number is thus;

2(14) - 3 = 28 - 3 = 25

The set of equations representing the word problem is ( x + y = 39 ) and ( x = 2y - 3 )

The correct answer is option

a).( x + y = 39 ) and ( x = 2y - 3 )

To solve this problem, let's first understand the given information.

Let's denote x as the number of one type of fruit (let's say apples) and y as the number of another type of fruit (let's say oranges). The problem states two conditions:

1. The total number of fruits is 39.

2. The number of apples (x) is either three less than twice the number of oranges (y) or it's the same as three more than twice the number of oranges.

Let's represent these conditions mathematically:

1. x + y = 39   (Equation 1)

2. x = 2y - 3   or   x = 2y + 3   (Equation 2)

Now, let's compare these equations with the options provided:

a) ( x + y = 39 ) and ( x = 2y - 3 )

b) ( x - y = 39 ) and ( x = 2y - 3 )

c) ( x + y = 39 ) and ( x = 3y - 2 )

d) ( x - y = 39 ) and ( x = 3y - 2 )

Comparing Equation 1 with the options, we see that options a) and c) match.

Comparing Equation 2 with the options, we see that options a) and b) match.

Therefore, the correct system of equations is option a):

(x + y = 39) and (x = 2y - 3).

1. The first equation represents the total number of fruits, which should be 39. We add the number of apples (x) and oranges (y) to get 39.

2. The second equation represents the relationship between the number of apples and oranges. The number of apples is three less than twice the number of oranges. So, we set up the equation x = 2y - 3.

Thus, the correct answer is option a)( x + y = 39 ) and ( x = 2y - 3 )

Complete question

One number is 3 less than twice another. If their sum is 39, find the numbers?

Which of the following systems of equations represents the word problem?

a) ( x + y = 39 ) and ( x = 2y - 3 )

b) ( x - y = 39 ) and ( x = 2y - 3 )

c) ( x + y = 39 ) and ( x = 3y - 2 )

d) ( x - y = 39 ) and ( x = 3y - 2 )

Answer:

-9⃣ = t

Step-by-step explanation:

You know that 6 - ? = -12, so just simply deduct six from both sides, leaving you with -18 = 2t; -9⃣ = t.

Answer:

No, it is not a square

Step-by-step explanation:

If one wall is 19", that would mean the wall perpendicular to this wall is also 19" (in fact all of the walls would be 19"!) If this was a square, then the diagonal we draw at 20.62" would serve as the hypotenuse of a right triangle.  One wall would serve as a leg, and another wall as another leg.  If this is a square, then the Pythagorean's Theorem would be satisfied when we plug in the 2 wall measures for a and b, and the diagonal for c:

[tex]19^2+19^2=20.62^2[/tex]

We need to see if this is a true statement.  If the left side equals the right side, then the 2 legs of the right triangle are the same length, and the room, then is a square.

361 + 361 = 425.1844

Is this true?  Does 722 = 425.1844?  Definitely not.  That means that the room is not a square.

Answer:

2 outcomes

Step-by-step explanation:

Let's list count all the possible outcomes:

(1,3) (1,4) (1,5) (1,6)

(2,3) (2,4) (2,5) (2,6)

(3,3) (3,4) (3,5) (3,6)

As expected, there are 12 (3x4) possible outcomes.

How many outcomes do not show an even number (so showing 1 or 3) on the first spinner and show a 6 on the second spinner?

There are two cases where 6 is on the second spinner and NOT an even number on the first spinner: (1,6) and (3,6)

Answer:

36

Step-by-step explanation:

⇒The question is on third quartile

⇒To find the third quartile we calculate the median of the upper half of the data

Arrange the data in an increasing order

20, 21, 24, 25, 28, 29, 35, 37, 42

Locate the median, the center value

20, 21, 24, 25, 28, 29, 35, 37, 42

The values 20, 21, 24, 25 ------------lower half used in finding first quartile Q1

The value 28 is the median

The vlaues 29, 35, 37, 42...............upper half used in finding 3rd quartile Q3

Finding third quartile Q3= median of the upper half

upper half= 29,35,37,42

median =( 35+37)/2 = 36

Answer:

Your answer should be A

Step-by-step explanation:

For this case we have the following functions:

[tex]f (x) = - 7x-9\\g (x) = 6x ^ 3-23x[/tex]

We must find [tex]f (9)[/tex] and [tex]g (-9):[/tex]

Substituting we have:

[tex]f (9) = - 7 (9) -9\\f (9) = - 63-9\\f (9) = - 72[/tex]

On the other hand:

[tex]g (-9) = 6 (-9) ^ 3-23 (-9)\\g (-9) = 6 (-729) -23 (-9)\\g (-9) = - 4374 + 207\\g (-9) = - 4167[/tex]

Answer:

Option C

Answer:

252 candies

Step-by-step explanation:

Let A = 8x

Let B = 5x

Let C = 10x

10x = 8x + 24         Subtract 8x from both sides

10x - 8x = 24          Do the subtraction

2x = 24                   Divide by 2

2x/2 = 24/2            Do the division

x = 12

So Adrian has 8*12 = 96 candies.

Ben has 5 * 12 =         60 candies

Charlie has 10*12 =    120 candies

Total                      =  276 candies

The total number of sweets shared by Adrian, Ben, and Charlie is 276,

To solve how many sweets were shared by Adrian, Ben, and Charlie, with the given ratio of 8:5:10 and knowing Charlie got 24 more sweets than Adrian, we can set up a ratio problem. Let the ratio part be 'x', so Adrian has 8x sweets, Ben has 5x sweets, and Charlie has 10x sweets. As Charlie got 24 more sweets than Adrian, we can write the equation 10x = 8x + 24. Solving this equation for 'x' gives us x = 12. Thus, Adrian has 96 sweets (8 x 12), Ben has 60 sweets (5 x 12), and Charlie has 120 sweets (10 x 12). Adding these together gives us a total of 276 sweets.

Answer:

  AB = (2 +2√3)r

Step-by-step explanation:

Let X be the point of tangency of circle O3 and AB. Then length XO3 is r. The triangle BXO3 is a 30°-60°-90° right triangle. You know this because BO3 bisects the 60° angle at B of the equilateral triangle ABC.

A 30°-60°-90° triangle has side lengths in the ratios 1 : √3 : 2. That means side XB of triangle BXO3 has length r√3. The distance from A to the point of tangency of AB with circle O1 has the same measure.

Of course the distance between those points of tangency is the same measure as the distance between centers O3 and O1: 2r. So, the total length of AB is ...

  AB = r√3 + 2r + r√3

  AB = (2 +2√3)r

4/5 is equivalent to the percentage 80%.

Answer:

The correct answer is given by,

The fraction 4/5 is equivalent to 80%

Step-by-step explanation:

Points to remember

To convert fraction into percentage we have to multiply fraction with 100

x/y ⇒ 100x/y%

To find the equivalent percentage

Here fraction is 4/5

4/5 is equivalent to (4/5) * 100 = 400/5 = 80%

Therefore the correct answer is,

The fraction 4/5 is equivalent to 80%

Answer:

  (n -13)/(n -7)

Step-by-step explanation:

Simplify the fraction on the left, then add the two fractions.

[tex]\displaystyle\frac{n^2-10n+24}{n^2-13n+42}-\frac{9}{n-7}=\frac{(n-6)(n-4)}{(n-6)(n-7)}-\frac{9}{n-7}\\\\=\frac{n-4}{n-7}-\frac{9}{n-7}\\\\=\frac{n-4-9}{n-7}\\\\=\frac{n-13}{n-7}[/tex]

_____

Comment on the graph

The vertical asymptote tells you the simplified form has one zero in the denominator at x=7. That is, the denominator is x-7.

The x-intercept at 13 tells you that x-13 is a factor of the numerator.

The horizontal asymptote at y=1 tells you there is no vertical scaling, so the simplest form is ...

  (n -13)/(n -7)

The hole at x=6 is a result of the factor (x-6) that is cancelled from the first fraction in the original expression. At that value of x, the fraction is undefined. So, the above solution should come with the restriction x ≠ 6.

namely, how many go-around or revolutions does a tire have to make for those 165 meters.

[tex]\bf \textit{circuference of a circle}\\\\ C=\pi d~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ d=1.7 \end{cases}\implies C=1.7\pi \impliedby \textit{one revolution} \\\\\\ \textit{how many times does }1.7\pi \textit{ go into 165?}\qquad \stackrel{\pi =3.14}{\cfrac{165}{1.7\pi }\qquad \implies \qquad 30.9}[/tex]

The number of times the tire will have to turn in travelling the length of the street is 30.9 times.

To determine the number of times the tire will have to turn in travelling the length of the street, we will first calculate the circumference of the tire.  

Since the tire is circular, the circumference of the tire can be calculated from the formula for calculating the circumference of a circle.

The circumference of a circle is given by

C = πd

Where C is the circumference and d is the diameter

From the question d = 1.7m and π = 3.14

∴ C = 3.14 × 1.7

C = 5.338 m

Therefore, the circumference of the tire is 5.338 m

Now, for the number of times the tire will have to turn in travelling the length of the street, we will divide the length of the street by the circumference of the tire.

Number of times the tire will have to turn = Length of the street ÷ Circumference of the tire

Number of times the tire will have to turn = 165 m ÷ 5.338 m

Number of times the tire will have to turn = 30.91045 times

Number of times the tire will have to turn ≅ 30.9 times

Hence,  the number of times the tire will have to turn in travelling the length of the street is 30.9 times

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Answer: -4 1/2 , -1/2 , 1/4 , 2/3 , 2 1/3

Step-by-step explanation:

For this case we have the following numbers:

[tex]\frac {2} {3} = 0.6667[/tex]

[tex]-4 \frac {1} {2} = \frac {-8 + 1} {2} = \frac {-7} {2} = - 3.5[/tex]

[tex]\frac {1} {4} = 0.25[/tex]

[tex]- \frac {1} {2} = - 0.5\\2 \frac {1} {3} = \frac {3 * 2 + 1} {3} = \frac {7} {3} = 2.3333[/tex]

If we order from least to greatest we have:

[tex]-3.5; -0.5; 0.25; 0.6667; 2.3333[/tex]

Answer:

[tex]-4 \frac {1} {2}; -\frac {1} {2}; \frac {1} {4}; \frac {2} {3}; 2 \frac {1} {3}[/tex]

Answer:

  $953.4 billion

Step-by-step explanation:

Each year, exports are (1-0.027) = 0.973 of what they were the year before. After 3 years, the export value is multiplied by 0.973^3. So, in 2013, the value of exports would be ...

  ($1035 billion)(0.973^3) ≈ $953.4 billion

Answer:

[tex]N= 4543[/tex] Labrador retrievers

Step-by-step explanation:

We know that the mean [tex]\mu[/tex] is:

[tex]\mu = 62.5[/tex]

and the standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=2.5[/tex]

The probability that a randomly selected Labrador retriever weighs less than 65 pounds is:

[tex]P(X<65)[/tex]

We calculate the Z-score for X =65

[tex]Z = \frac{X-\mu}{\sigma}\\\\Z =\frac{65-62.5}{65}=1[/tex]

So

[tex]P(X<65) = P(Z<1)[/tex]

Looking in the table for the standard normal distribution we have to:

[tex]P(Z<1) =0.8413[/tex].

Finally the amount N of Labrador retrievers that weigh less than 65 pounds is:

[tex]N = P(X<65) *5400[/tex]

[tex]N = 0.8413*5400[/tex]

[tex]N= 4543[/tex] Labrador retrievers

Answer:

If what you are doing here is trying to get the value of x then:

Those two lines passing through the circle are secants.

Now, a formula I was taught in class is:

(outside)(whole) = (outside)(whole)

**1 SEGMENT'S VALUES PER SIDE** **DO NOT MIX**

"Outside" represents the value of the segment which is found outside of the circle.

The "whole" would be the outside segment plus the inside segment.

Thus, the formula would be:

(4)(9+4) = (x)(x + 12)

Next, you would simplify by adding, multiplying, and doing the distributive property:

(4)(13) = (x)(x + 12)

52 = x² + 12x

In this case, you would have to use the quadratic formula, while at other times, you could simply move around the terms and get the square root of a number.

Set the equation to zero:

x² + 12x - 52 = 0

Next plug-in the values

(-b (+ or -)√b² - 4 (a)(c) )/ (2)(a)

(-(12) (+ or - )√12² - 4(1)(-52)) / (2)(1)

(-12 (+ or -) √144 + 208) / 2

(-12 (+ or -) √352) / 2

Now, the square root of 352 would be approximate, since 352 is not a perfect square.

352 is approximately 18.7616630393 or, when rounded to the nearest hundredth, 18.76.

So.....

(-12 (+ or -) 18.76) / 2

Solve for both the + and the -

(-12 + 18.76) /2 = (approximately) 3.38 = x

(-12 - 18.76)/2 = (approximately) -15.38 = x

Therefore, x would be equal to 3.