The stem and leaf plot shows the number of laps around a track
that several teams walked as part of a fund-raiser for the library.
The teams that walked more than 50 laps raised an extra $100 for
the library.

What fraction of the teams raised this extra money?

The value of n(A) is 35 if n(B) = 35, n(A nB) = 15, and n(A U B) = 55.

A set is a collection of well defined objects.

We can use the formula: n(A U B) = n(A) + n(B) - n(A nB)

Substituting the given values, we get:

55 = n(A) + 35 - 15

Simplifying, we get:

55 = n(A) + 20

Subtracting 20 from both sides, we get:

n(A) = 35

Therefore, the value of n(A) is 35.

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Answer:
Black

Step-by-step explanation:

1/2 is half the bag of marbles so it's 50% likely to pick black.

The probability that the arrow will land on an even number is 1/2.

Option D) 1/2 is the correct answer.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

the probability that the arrow will land on an even number:

Given that;

Total number of Integers on the spinner = 8

Total number f even integers on the spinner = 4

Probability that the arrow will land on an even number = ?

The probability that the arrow will land on an even number will be;

P = Total number f even integers on the spinner / Total number of Integers on the spinner

P = 4 / 8

P = 1/2

Therefore the probability that the arrow will land on an even number is 1/2.

Option D) 1/2 is the correct answer.

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Answer:

Question 19: The person who traveled the farthest lives 12 miles from the restaurant, which is the same distance as Kellan.

Question 20: Kellan would have left his house at 8:10 AM in order to arrive at Andrea's house at 8:30 AM and then walk to the restaurant with Andrea at a rate of 2.5 miles per hour, arriving at the restaurant at 8:50 AM, five minutes early. So the answer is 810.

Answer50.5

ffffffffffffffff

The area of the picture frame is 72 cm². Thus, option C is correct.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm²), square metres (m²) or square kilometres (km²).

Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The area of the picture frame will be given by:

Area = (area of picture and frame)-(area of pictures)

area of picture and frame is given by:

A1=Length × width

A1 = 10 × 12

= 120cm²

area of the picture will be:

A2=8 × 6 = 48 cm²

thus the area of the frame will be:

A = A1 - A2

A = 120 - 48

A = 72cm²

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Complete question:

Select the correct answer.

Aaron made a picture frame with the dimensions shown in the figure. What is the area of the picture frame?

A bigger outer rectangle has sides of 12 cm and 10 cm, and an inner rectangle has sides of 8 cm and 6 cm.

A. 120 square centimeters

B. 88 square centimeters

C. 72 square centimeters

D. 64 square centimeters

Chelsea has $13,385 in her savings account after 7 years.

A savings account is an effective way to store your money in a secure location where it can earn interest.

After 5 years, the amount in Chelsea's savings account will be:

a = 1000(1.03)^5 = 1000(1.159274) = 1159.27

Let's say that Chelsea sells her car for x dollars. She adds that to her savings account, so the new amount in her account is:

1159.27 + x

After two more years (i.e., 7 years after initially starting the savings account), the amount in her savings account will be:

a = (1159.27 + x)(1.03)^2 = (1159.27 + x)(1.0609) = 1232.56 + 1.0609x

To find the value of x, we need to know the current value of the car. Once we have that, we can substitute it into the equation above to find the final amount in Chelsea's savings account.

For example, let's say that Chelsea sold her car for $5000. Then, the final amount in her savings account would be:

a = 1232.56 + 1.0609(5000) = 13384.91

Therefore, to the nearest dollar, Chelsea has $13,385 in her savings account after 7 years.

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The dogs were fed, 7/8 of them. 98 dogs in the shelter received food. 112 dogs are total in the shelter.

Human habitations come in a wide variety. Huts made of mud, branches, and leaves are possible. People may reside in large apartment complexes made of steel, cement, and glass or in houses made of wood, masonry, or stone. They might make use of portable structures like tents, houseboats, trailers, or even rvs (RVs). There are three types of shelter: temporary, semi-permanent, and permanent. One of the fundamental necessities for survival is shelter.

When we find the total number of dogs in the shelter, we obtain:

Let , Total number of dogs = y.

Dogs were fed , [tex]\frac{7}{8}[/tex] of y =98

⇒y×[tex]\frac{7}{8}[/tex]= 98

⇒y =98× [tex]\frac{8}{7}[/tex]

⇒y = 14×8= 112.

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Answer:

Step-by-step explanation:

We need to show that the path given by r(t) = (e^t sin t, e^(-t) cos t, e) intersects the sphere 2y^2 + 2z^2 = 4 once, traveling from outside the sphere to inside as t goes from -∞ to +∞.

The equation of the sphere is 2y^2 + 2z^2 = 4. To find the intersection points of the path and the sphere, we need to substitute the components of r(t) into the equation of the sphere:

2y^2 + 2z^2 = 4

2(e^(-t) cos t)^2 + 2e^2 = 4

2e^(-2t) cos^2(t) + 2e^2 = 4

e^(-2t) cos^2(t) + e^2 = 2

Multiplying both sides by e^(2t), we get:

cos^2(t) + e^(4t) = 2e^(2t)

We can rewrite this equation as:

e^(4t) - 2e^(2t)cos^2(t) + cos^2(t) - 1 = 0

This is a quadratic equation in e^(2t) with solutions:

e^(2t) = cos^2(t) ± sqrt(cos^4(t) - 4(cos^2(t) - 1))

We want to show that there is only one intersection point, which means we want to show that the discriminant of the quadratic is negative, i.e.:

cos^4(t) - 4(cos^2(t) - 1) < 0

Expanding the left-hand side, we get:

cos^4(t) - 4cos^2(t) + 4 < 0

Simplifying, we get:

(cos^2(t) - 2)^2 < 0

Since the square of a real number is always non-negative, this inequality has no real solutions. Therefore, the discriminant of the quadratic is negative, and there is only one intersection point.

To show that the path travels from outside the sphere to inside as t goes from -∞ to +∞, we can observe that as t goes from -∞ to +∞, the first component of r(t) goes from -∞ to +∞, while the second and third components oscillate between 0 and +∞. This means that the path starts outside the sphere (at the point (0, +∞, +∞)) and ends inside the sphere (at the point (+∞, 1, 1)). Therefore, the path must intersect the sphere once, traveling from outside to inside.

For given piecewise function, g(x)= |x-4|/x-4 when x approaches 4 the left-hand limit will be 0 i.e. B.

What exactly is a piecewise function?

A piecewise function is one that has multiple definitions in different x intervals. A piecewise function's graph is divided into parts that correspond to each of its definitions. A very excellent example of a piecewise function is the absolute value function. Let us investigate why it is thus named. We know that an absolute value function is defined as f(x) = |x|.

f(x)=(x if x≥0 ,

     -x if x<0

This piecewise function should be interpreted as

When x is higher than or equal to 0, f(x) equals x.

When x is less than zero, f(x) equals -x.

Now,

when x will approach 0

given function will give value

g(x)=4-4/4-4

=0/0

=0

Hence,

       for   g(x)= |x-4|/x-4 when x approaches 4 the left-hand limit will be 0.

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For given piecewise function, g(x)= |x-4|/x-4 when x approaches 4 the left-hand limit will be 0 i.e. B.

What exactly is a piecewise function?

A piecewise function is one that has multiple definitions in different x intervals. A piecewise function's graph is divided into parts that correspond to each of its definitions. A very excellent example of a piecewise function is the absolute value function. Let us investigate why it is thus named. We know that an absolute value function is defined as f(x) = |x|.

f(x)=(x if x≥0 ,

    -x if x<0

This piecewise function should be interpreted as

When x is higher than or equal to 0, f(x) equals x.

When x is less than zero, f(x) equals -x.

Now,

when x will approach 0

given function will give value

g(x)=4-4/4-4

=0/0

=0

Hence,

      for  g(x)= |x-4|/x-4 when x approaches 4 the left-hand limit will be 0.

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Answer:

a) You will reach 9 meters above the pool.

b) The length of time you are in the air is 2 seconds.

c) The height of the diving board is 7 meters.

Step-by-step explanation:

Given quadratic equation:

[tex]m(d)=-4d^2 + 5.5d + 7[/tex]

To determine how far above the pool you reach on your dive, find the y-value of the vertex of the given quadratic equation.

The formula for the x-value of the vertex is -b/2a for a quadratic equation in the form y=ax²+bx+c.  Therefore, the x-value of the vertex for the given equation is:

[tex]\implies -\dfrac{5.5}{2(-4)}=0.6875[/tex]

To find the y-value of the vertex, substitute d = 0.6875 into the given equation:

[tex]\begin{aligned}m(0.6875)&=-4(0.6875)^2+5.5(0.6875)+7\\&=-1.890625+3.78125+7\\&=1.890625+7\\&=8.890625\\&=9\; \sf m\;(nearest\;meter)\end{aligned}[/tex]

Therefore, you will reach 9 meters above the pool (rounded to the nearest meter).

You will hit the water when your height is zero. Therefore, to find the length of time you are in the air, set the given quadratic equation to zero and solve for d using the quadratic formula.

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

[tex]\implies d=\dfrac{-5.5 \pm \sqrt{5.5^2-4(-4)(7)}}{2(-4)}[/tex]

[tex]\implies d=\dfrac{-5.5 \pm \sqrt{142.25}}{-8}[/tex]

[tex]\implies d=\dfrac{-5.5 \pm \sqrt{142.25}}{-8}[/tex]

[tex]\implies d=-0.803357..., \;2.178357...[/tex]

As time is positive we can discount the negative solution. Therefore, the length of time you are in the air is 2 seconds (rounded to the nearest second).

The height of the diving board is the y-intercept of the graph of the equation. The y-intercept is the value of y when x = 0. Therefore, to find the height of the diving board, substitute d = 0 into the equation.

[tex]\begin{aligned}\implies d(0)&=-4(0)^2+5.5(0)+7\\&=0+0+7\\&=7\end{aligned}[/tex]

Therefore, the height of the diving board is 7 meters.

Answer:

14 in^2

Step-by-step explanation:

4+3=7 in. Area of the triangle is BH/2=7*4/2=14 in^2.

Substitute the expression for y in the second equation into the first equation and solve for x:

4x + 3(-1/3x + 6) = 36

4x - x + 18 = 36

3x = 18

x = 6

Now substitute x = 6 into the second equation to solve for y:

y = (-1/3)(6) + 6

y = 4

Therefore, the solution to the system of equations is the ordered pair (6, 4).

The value of x in the line segment is - 7 / 3.

A line segment is a section of a line bounded by two points or connecting two points. The value of x if U is between T and V can be found as follows:

TU = 7x + 35

UV = 4(x + 7)

TU ≅ UV

Therefore, let's find x as follows:

7x + 35 = 4(x + 7)

7x + 35 = 4x + 28

7x - 4x = 28 - 35

3x = - 7

x = -7  /3

Therefore,

x = - 7 / 3

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The annual percentage yield for money invested at the rates are:

To solve for the APY in the first question:

APY = [tex](1+ r/n)^n^-^1[/tex]

r= interest rate

n= number of times interest is compounded per year

We put in the values

APY = [tex]( 1 + 0.0441/12)^1^2^-^1[/tex]

APY = 4.5%

To solve for the second one

4.42% compounded quarterly

plug in the values into the formula

[tex](1 + 0.0442)/4^4^-^1[/tex]

APR = 4.49%

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Answer:

x= 45°

Step-by-step explanation:

They are angle on a straight line

85+2x+5 = 180

2x+ 90 = 180

2x = 180-90

2x = 90

dividing both sides of the equation by 2

x = 45

Answer:

  9.  9x -4y = -36

  10.  geometric; terms have a common ratio of 1/2. Never 0 or negative; 1/2 times a positive number is a positive number.

Step-by-step explanation:

You want the equation of the line with x-intercept (-4, 0) and y-intercept (0, 9), and you want to know if the sequence 40, 20, 10, 5, ... is arithmetic.

It is helpful to know a few different forms of the equation for a line. One of them is "intercept form," x/a +y/b = 1, where 'a' and 'b' are the x- and y-intercepts, respectively.

For intercepts (-4, 0) and (0, 9), the equation in this form is ...

  x/(-4) +y/9 = 1

Multiplying by -36 puts it in standard form:

  9x -4y = -36

(a) First differences of the sequence 40, 20, 10, 5 are ...

  -20, -10, -5 . . . . . not constant

Since the first differences are not constant this is not an arithmetic sequence.

Ratios of successive terms are ...

  20/40 = 10/20 = 5/10 = 1/2 . . . . . . constant

A sequence of terms with a common ratio is a geometric sequence. This sequence has a common ratio, so is geometric.

(b) The common ratio is 1/2, a positive number. The given terms of the sequence are positive numbers. Each successive term is 1/2 the previous term, so all terms will be positive—never 0 or negative. (The product of two positive numbers is always positive.)

Mila's monthly mortgage payment would be approximately $4,658.99.

In finance, interest refers to the cost of borrowing money or the return earned on an investment. It is usually expressed as a percentage of the amount borrowed or invested and is typically calculated on an annual basis.

For borrowing money, interest is the cost that the borrower has to pay to the lender for the privilege of using their funds. The lender earns interest on the loan as compensation for lending their money to the borrower. The interest rate on a loan is determined by a variety of factors, including the borrower's creditworthiness, the term of the loan, and prevailing market conditions.

For investments, interest is the return earned by an investor on their principal amount. For example, when someone deposits money in a savings account, they earn interest on that money. The interest rate on savings accounts and other investments is typically determined by the prevailing market conditions and the financial institution offering the investment.

Interest can be calculated in different ways, including simple interest and compound interest. Simple interest is calculated on the original principal amount, while compound interest is calculated on the principal amount plus any accumulated interest. The frequency at which interest is compounded, such as monthly or annually, can have a significant impact on the total amount of interest earned or paid.

Overall, interest plays a critical role in finance and can have a significant impact on the cost of borrowing money or the return earned on an investment.

To calculate Mila's monthly mortgage payment, we can use the formula for a fixed-rate mortgage:

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

where:

M = monthly mortgage payment

P = loan amount

r = monthly interest rate

n = number of payments (total number of years * 12)

Plugging in the given values, we get:

M = 730000 * (0.00325 * (1 + 0.00325)^(2012)) / ((1 + 0.00325)^(2012) - 1)

Simplifying this expression using a calculator, we get:

M ≈ $4,658.99

Therefore, Mila's monthly mortgage payment would be approximately $4,658.99.

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Answer:

13/24

Step-by-step explanation:

13/11+13= 13/24

The probability that a randomly selected person is male given the person is left handed is 13/200.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Here, total number of outcomes = 200

Number of favorable outcomes = 13

Now probability of an event = 13/200

Therefore, the probability that a randomly selected person is male given the person is left handed is 13/200.

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Answer:

The answer is A my friend! Good luck on your test Mr Rush.

The area between -

C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square

units.

A function is a relation between a dependent and a independent variable. Mathematically we can write the function as -

y = f(x)

Given is that a factory selling cell phones has a marginal cost function C(x) = 0.01x² - 3x + 229, where {x} represents the number of cellphones, and a marginal revenue function given by R(x) = 429 - 2x.

We can write the area between -

C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 as -

Area = ∫C(x) dx  +  ∫{C(x) - R(x)} dx

We can write the area with limits as -

Area =

∫(0.01x² - 3x + 229) dx             {limits from 229 to 429}

+

∫(0.01x² - 3x + 229 - 429 + 2x) dx       {limits from 429 to 629}

Area = 71548.7 + 420548.7

Area = 492097.4 square units

Therefore, the area between -

C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square

units.

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Answer:

6.21

Step-by-step explanation:

tha ratio 2.97/2.2 has to be the same as x/4.6.

so the new lenght, x, is 4.6×(2.97/2.2)

[tex]\stackrel{ \textit{ratio of (L)ength to (w)idth of old phone} }{\stackrel{L}{2.2}~~ : ~~\stackrel{w}{4.6}\qquad \implies \qquad \cfrac{L}{w}~~ = ~~\cfrac{2.2}{4.6}} \\\\\\ \stackrel{\textit{Length of new phone}}{2.97}\qquad \stackrel{\textit{keeping the same ratio}}{\cfrac{2.97}{w}~~ = ~~\cfrac{2.2}{4.6}} \\\\\\ (2.97)(4.6)=2.2w\implies \cfrac{(2.97)(4.6)}{2.2}=w\implies \stackrel{ new~width }{6.21=w}[/tex]

the variance will be 0.6217.

What is frequency distribution?

The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.

A small data analysis class has six computer science majors among the fourteen total students.

Three people are chosen at random to form a group.

here this is hypergeometric distribution with parameter n=sample size =3 ; N =population size =14

and k=computer sience major =6

a) E(X) =nk/N =3*6/14 =18/14 =9/7 =1.2857

b)|varaince =σ²=(nk/N)*(1-k/N)*(N-n)/(N-1)) =(3*6/14)(1-6/14)*(14-3)/(14-1)= 0.6217

Hence, the variance will be 0.6217.

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Answer:

D) -53.23

Step-by-step explanation:

Use PEMDAS to evaluate the expression

We do parentheses first.

[tex]|65.45-42.45|-76.23[/tex]

Evaluate what's inside of the absolute value bracket.

[tex]|23|-76.23[/tex]

Simplify

[tex]23+-76.23[/tex]

Evaluate

-53.23

2.183 miles is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two buildings.

Distances between two things or places can sometimes be measured qualitatively and sometimes quantitatively. A physical length or an estimate based on other criteria might be referred to as distance in physics or everyday language. The entire movement of an item, independent of direction, is called distance. No matter where an item starts or ends, distance may be described as the amount of ground it has covered.

Given that,

If the White House is located at (−8,−6) and the Pentagon is located at (−1,10).

Then, distance = √(-8-(-1))² + (-6 -10)² × 0.125

= 2.183 miles

Thus, 2.183 miles is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two buildings.

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The value for the [tex]\lim_{x \to 3^{+}}[/tex]f(x) = 3.

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.

Given:

We have given the graph, from the graph we can se a red dot.

So, the [tex]\lim_{x \to 3^{+}}[/tex]f(x) = 3

Also, limit is defined as a value that a function approaches the output for the given input values.

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Answer:

PART A:

The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.

Here is Matt's equation:

y = 40x + 50

The y-intercept of this equation is 50, while the slope is 40.

Here is Kylie's equation:

y = 50x

The slope of this equation is 50, and the y-intercept is 0. | /

    |          /

    |        /

    |      /

    |    /

-----|------------------

    | /         \

    |/            \

    /-------------\

0 1 2 3 4 5 6 x-axis

The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.

PART B:

When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:

(Matt's distance) y=40x+50

Kylie's distance is given by y = 50(x – 20).

Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.

We can set the two equations equal to one another to determine how many solutions this system has:

40x + 50 = 50(x - 20) (x - 20)

40x + 50 = 50x - 1000\s100 = 10x

x = 10

This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

PART A:

The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.

Here is Matt's equation:

y = 40x + 50

The y-intercept of this equation is 50, while the slope is 40.

Here is Kylie's equation:

y = 50x

The slope of this equation is 50, and the y-intercept is 0. | /

   |          /

   |        /

   |      /

   |    /

-----|------------------

   | /         \

   |/            \

   /-------------\

0 1 2 3 4 5 6 x-axis

The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.

PART B:

When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:

(Matt's distance) y=40x+50

Kylie's distance is given by y = 50(x – 20).

Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.

We can set the two equations equal to one another to determine how many solutions this system has:

40x + 50 = 50(x - 20) (x - 20)

40x + 50 = 50x - 1000\s100 = 10x

x = 10

This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

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