The ratio of 7th grade students to 8th grade students in a soccer league is 7:13, if there are 100 students in all ,how many are in 7th grade ?

well, one focus point at (9 , 0) and another at (-9 , 0) will mean the major axis runs over the x-axis, with a center at the origin, so the "c" distance will be 9 units, and since the major axis is 36 units, that means its "a" component or namely its half is half of 36 or 18 units, so

[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} a=18\\ h=0\\ k=0 \end{cases}\implies \cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ b^2}=1\qquad \textit{we also know that }C=9[/tex]

[tex]9=\sqrt{18^2 - b^2}\implies 9^2=18^2-b^2\implies 9^2+b^2=18^2\implies b^2=18^2-9^2 \\\\\\ b^2=243\hspace{5em}\cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ 243}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{324}+\cfrac{y^2}{243}=1 \end{array}}[/tex]

Check the picture below.

The major criteria to be considered when going for a bank to have a new savings account registered with them are as follows:

As an entrepreneur, finding a good bank to open a savings account with might be much tedious to do. However, I have live to understand that banks with low interest rate are a better catch if I am considering a good saving lifestyles. I cannot stand a banking system that charges me unnecessarily all the time all in the name of fee or the other, which results to reducing my money in their system.

That being said, discovering a bank which has welcoming and helping customer service is also an important factor to be considered when choosing to right banking system.

In conclusion, it can be deduced that a bank with which does not deduct one's money anyhow all in the name of interest is worth having a savings account with.

Complete question:

What are the conditions to be considered in choosing the best bank for a new savings account?

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The point estimate of the population mean  is 22 and margin of error for the confidence interval is 3.

1. Point estimate

Point estimate = Upper bound+ Lower bound/2

Point estimate = (25+19) /2

Point estimate = 44/2

Point estimate = 22

2. Margin error

Margin error = Upper bound  - Lower bound/2

Margin error = ( 25-19) /2

Margin error = 6 /2

Margin error = 3

Therefore the point estimate is 22.

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Answer:3.55 , 71/20

Step-by-step explanation:

The time required for for the balance to reach $4635 is 5 years.

The formula for simple interest can be expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

First convert the interest rate from percent to decimal

Interest rate = 0.6%

Interest rate = 0.6/100

Interest rate = 0.006

Plug the given values into the above formula and solve for time t.

A = P( 1 + rt )

t = ( 4635/4500 - 1) / 0.006

t = ( 1.03 - 1) / 0.006

t = ( 0.03) / 0.006

t = 5 years.

Therefore, the required time is 5 years.

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If from a population of 50 bank accounts, we want to take a random sample of four accounts in order to learn about the population. The number of  different random samples of four accounts that are possible is 230,300.

Given data:

Number of population of bank account = 50

Random sample = 4 accounts

Now let find the different random samples of four account that are possible

Different random sample = 50! / (50 -4)! × 4!

Different random sample = 50! / 46! × 4!

Different random sample = 230,300

Therefore the different random samples is 230,300.

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The measure of the intercepted arc, [tex]\widehat{XY}[/tex], formed by the secants ZW and ZV is 30°

A secant line is a straight-line which has two points of intersection with a circle.

From a similar question on the internet, the figure consists of an outside angle of 41° formed by two secants and two intercepted consisting of [tex]\widehat{XY}[/tex]and [tex]\widehat{VW}[/tex] which measures 112°

The outside angles of a circle theorem states that the outside angle formed by two secants or two tangent or a combination of a secant and a tangent is the difference of the measure of the difference of the angles of the intercepted arcs divided by two.

Mathematically;

[tex]m\angle z = \dfrac{\widehat{VW} - \widehat{XY}}{2}[/tex]

Where;

The outside angle formed by the secant ZW and ZV, m∠z = 41°

[tex]\widehat{VW}[/tex] = 112°

Which gives;

[tex]41^{\circ}= \dfrac{112^{\circ}- \widehat{XY}}{2}[/tex]

2 × 41° = 112° - [tex]\widehat{XY}[/tex]

82° = 112° - [tex]\widehat{XY}[/tex]

[tex]\widehat{XY}[/tex] = 112° - 82° = 30°

[tex]\widehat{XY}[/tex] = 30°

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The required domain of the function shown is (-∞, ∞) and the range is (-3, ∞).

Range, it is the set of values that come out to an outcome for certain mathematical operations.

Here,
A graph of the function is shown,
and the graph of the function is defined from -∞ to ∞, so the domain of the function is (-∞, ∞).
Also, the function has a value of the y-axis from -3 to ∞, and the range of the function is (-3, ∞).

Thus, the required domain of the function shown is (-∞, ∞) and the range is (-3, ∞).

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Answer:

x= 68  z= 180  y=38

Step-by-step explanation:

Using the greatest common factor, the number of light bulbs in each box is 24.

The greatest common factor (GCF) is the number that can divide two or more numbers without a remainder.

The GCF is a divisor that divides dividends evenly, leaving only quotients without remainders.

For instance, the greatest common factor of 120, 168, and even 288 is 24.

Using this GCF implies that 24 can divide 120, 168, and 288 without leaving any remainders.

                                            Company A      Company B        Total

Total orders for light bulbs         120                     168             288

Greatest common factor of          24                      24               24

Number of boxes delivered           5                        7                12

Thus, with the greatest common factor as 24 light bulbs in each box, Company A will be supplied 5 boxes, while Company B will be supplied with 7 boxes.

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A)  the domain is:

D: [0, 6]

The range is:

B)  

"The slope is __1/2__ So, the water amount in the rain barrel changes at a rate of __1/2__ inch per day."

"The Y-intercept is __2__ So, the amount of water in the rain barrel before the rain began was __2__ inches."

And the graph can be seen at the end.

Here we have the linear equation:

d(t) = (1/2)*t + 2

This refers to the amount of water in a barrel for six rainy days, where t is the number of days.

So the domain goes between t = 0 and t = 6.

The range will go between:

d(0) = (1/2)*0 + 2 = 2

d(6) = (1/2)*6 + 2 = 3 + 2 = 5

So the domain is:

D: [0, 6]

The range is:

T: [2, 5]

b) The complete sentences are:

"The slope is __1/2__ So, the water amount in the rain barrel changes at a rate of __1/2__ inch per day."

"The Y-intercept is __2__ So, the amount of water in the rain barrel before the rain began was __2__ inches."

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The number of Hamilton Circuits with 8 vertices are 5040.

Given that, a complete, weighted graph with 8 vertices.

A Hamiltonian circuit is a circuit that visits every vertex once with no repeats. Being a circuit, it must start and end at the same vertex. A Hamiltonian path also visits every vertex once with no repeats, but does not have to start and end at the same vertex.

For N vertices in a complete graph, there will be (n−1)!=(n−1)(n−2)(n−3)…3⋅2⋅1 routes. Half of these are duplicates in reverse order, so there are (n−1)!/2 unique circuits.

A complete graph with 8 vertices would have = 5040 possible Hamiltonian circuits. Half of the circuits are duplicates of other circuits but in reverse order, leaving 2520 unique routes.

Therefore, the number of Hamilton Circuits with 8 vertices are 5040.

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The value g(7) of the function g(x) = 7  / 8 x  - 1 / 2 is 45 / 8.

A function relates each element of a set with exactly one element of another set (possibly the same set).

In a simpler term, a function relates an input to an output.

Therefore, let's find the value of g(7) for the function below:

g(x) = 7  / 8 x  - 1 / 2

Hence,

g(7) = 7 / 8 (7)  - 1 / 2

g(7) = 49 / 8  - 1 / 2

g(7) =  49 - 4 / 8

Therefore,

g(7) = 45 / 8

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If lliot and Jack share some money in the ratio . 8:5 Elliot got £21 more than Jack. The amount that Elliot received is £56.

Given data;

Sharing ratio 8:5

Amount Elliot got = 21

In order to determine  the amount that Elliot received we need to formulate and equation and then use the formulated equation to find the amount received.

Equation

21 × 8 ÷ (8-5)

Hence,

£21 × 8 ÷ (8-5)

£168 ÷ 3

=  £56

Therefore Elliot received £56.

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The required area of the flour in the square yard is A =n[ L×W ] where L and W are the length and width of the tiles respectively.

Given that,
A rectangular floor is long and wide. Pablo wants to carpet the floor with carpet titles sold by the square yard.

Surface area is defined as the area of the surface that is uncovered.

here,
Let for a tile the length be L and the width be W,
Assume that the number of tiles required is N,
The area of the N tiles is equal to the area of the rectangular floor,
Area of the floor = N [area of the tile]
Area of the floor (A = N [L× W]

Thus, the required area of the flour in the square yard is A =n[ L×W ] where L and W are the length and width of the tiles respectively.

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The total possible outcome when a coin is flipped and a die is rolled is 12

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total possible outcomes.

For example if a coin is flipped, a coin only has two faces, this means that it will have 2 Total possible outcome. When a die is rolled, a die has 6 faces which means that it will Total outcome of 6. When both a coin is flipped and a die is rolled the total possible outcome is 6×2 = 12 outcomes.

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Answer:

[tex]\frac{9}{100}[/tex]

Step-by-step explanation:

According to the map, North America makes up [tex]\frac{16}{100}[/tex] of the world's land surface area, while Europe makes up [tex]\frac{7}{100}[/tex]. Since both fractions already have a common denominator ( [tex]\frac{n}{100}[/tex] ), we can simply subtract the two to find how much greater the fractional part of North America is than the fractional part of Europe:

[tex]\frac{16}{100}-\frac{7}{100}=\frac{9}{100}[/tex]

The equation used to find the length of each afternoon practice is given as follows:

4(h + 3) = 20.

The variables in this problem are defined as follows:

During the summer, the team practices 4 days per week, for a total of 20 hours each week, hence the equation is of:

4(x + h) = 20.

The number of hours practiced during the morning is of:

x = 3.

Hence the equation to solve for h is given as follows:

4(3 + h) = 20

Applying the commutative property:

4(h + 3) = 20.

Hence the second option is correct.

The problem is given by the image shown at the end of the answer.

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Valentina is trying to decide whether to join her school's swim team. During the summer, the team practices 4 days per week. Each of those days, they practice for 3 hours in the morning and practice again in the afternoon. They practice for a total of 20 hours each week.

Which equation can you use to find h, the length of each afternoon practice in hours?

Summer swim practice is 4 days per week. Each day has 3 hours of morning practice and h hours of afternoon practice. So, the number of hours of practice each day is h+3. Weekly practice is a total of 20 hours. This equation represents the situation.

4 (h+3)

=

20

days of practice per week

hours of practice each day

total hours of practice each week

The equation 4(h+3)=20 can be used to find the length of each afternoon practice in hours. Solve the equation for h.

4(h+3)

= 20

h+3

= 5 Divide both sides by 4

h

= 2 Subtract 3 from both sides

Each afternoon practice is 2 hours.

Solving for X the value is = 45, 6

acc to our question-

90/x=90/x+15+1/2

(15-x)90 - 90x/15x-x^2 = 5

x= 45 or 6

hence, for X the value is = 45, 6

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The number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.

According to the question,

We have the following information:

Cost of 1 pound of grapes = $3.75

Cost of 1 pound of apples = $4

Total cost made by selling = $251.75

And the weight of the apples and grapes sold = 64

Now, let's take the weight of grapes to be x pounds and the weight of apples to be y pounds.

So, we have:

x+y = 64

x = 64-y ....(1)

3.75x+4y = 251.75

Putting the value of x in this equation:

3.75(64-y)+4y = 251.75

3.75*64-3.75y+4y = 251.75

240+0.25y = 251.75

0.25y = 251.75-240

0.25y = 11.75

y = 11.75/0.25

y = 47 pounds

Now, putting this value of y in equation 1:

x = 64-y

x = 64-47

x = 17 pounds

Hence, the number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.

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Answer:

a = 7

Step-by-step explanation:

Substitute x for 2 and f(x) for 14

14 = -2(2³) + a(2²) + 2

14 = -16 + 4a + 2

14 = -14 + 4a

14 + 14 = 4a

28 = 4a

4a = 28

Divide both sides by 4

4a/4 = 28/4

a = 7

Alternative:

Since from the question, you're already told that f(2) = 14, you just have to find the number that can be multiplied by 2 with a resultant of 14; that number is 7. To confirm, substitute a for 7 in the equation.

Answer: 17:4

Step-by-step explanation:

21 washing machines

4 broken

21 - 4 = 17

17:4

The total distance of the triathlon is 12000 m.

Two or more expressions with an equal sign are defined as an equation.

Let the total distance of the triathlon be x.

Tasneem swims 1/4of the total route, therefore, she swims for a distance of S = (1/4)x.

Now the remaining route is,

x - (1/4)x

=3/4x

After swimming, she cycles 3/5 of the remaining route, therefore, she cycles for a distance of C = (3/5)×(3/4)x,

C = (9/20)x

Now, she runs for the rest of the route, therefore, she runs for a distance of R = x - (1/4)x-(9/20)x

Or, R = (20x - 5x - 9x)/20

R = (6x)/20

Given that Tasneem runs 3600 m, therefore, substitute R = 3600 into the above equation,

3600 = (6x)/20

(3600×20)/6 = x

12000 = x

Therefore, the total distance of the triathlon is 12000 m.

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Answer:44/52

Step-by-step explanation:There are four aces in a deck of 52 cards, so the probability of not drawing an ace is 44/52 =

The number of pounds of 29% alloy and 51% alloy required to make the third alloy containing 50% aluminum is 45.82 pounds and 2.18 pounds respectively.

Let

x + y = 48

29x + 51y = 50*48

x + y = 48

29x + 51y = 2400

Solve simultaneously

From (1)

x = 48 - y

Substitute into (2)

29x + 51y = 2400

29(48 - y) + 51y = 2400

1392 - 29y + 51y = 2400

- 29y + 51y = 2400 - 1392

22y = 1008

y = 1008/22

y = 45.82 pounds

Substitute y = 45.82 pounds into (1)

x + y = 48

x + 45.82 = 48

x = 48 - 45.82

x = 2.18 pounds

So therefore, the number of pounds of 29% alloy and 51% alloy is 45.82 pounds and 2.18 pounds respectively.

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The potential outliers, given the normal annual precipitation in the different U.S. cities are E. 59.4; 65.3.

Outliers in a data distribution are values or data points that are far from the other points in the data. These can be statistically significant when they distort measures of central tendency such as mean.

In this case, the potential outliers in the normal annual precipitation 59.4 and 65.3 because they are far from the highest annual precipitation (before them) of 47.2 inches. 9.2 inches is quite low but it is close to 12.3 inches and 13.6 inches and so is not an outlier.

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(7,0); (7,−5) ;(7,3); (7,10);. (7,y)

Step-by-step explanation:

Answer:

The equation x = 7 forms a vertical line which we refer to as undefined. So any points with a x value of 7 will pass through the line.

Step-by-step explanation:

For example, points like (7, 0) (7, 1) (7, 2) are all points that the line x = 7 passes through.

A point is made up of 2 values. An x-value and and a y-value. You simply plug in 7 for the x and any value for y.

Points that are on the line x = 7 include:

(7, 0)

(7, 1)

(7, 2)

(7, 4)

(7, 5)

(7, 6)

The rate of spray at both times is 40 gallons/hour and it is the same.

What is the rate of change?

How quickly something changes over time is referred to as its rate of change, or ROC. Thus, it is the acceleration or deceleration of changes (i.e., the rate) rather than the magnitude of individual changes.

We have,

spray 20 gallons of water in 1/2 hour.

30 gallons and 3/4 hours (it's not 347 hours).

We simply calculate the rate for one hour:

1/2 hour = 20 gallons

3/4 hours = 30 gallons

Then for 1 hour,

1 hour = 20 * 2 = 40 gallons

1 hour = 30 * 4/3 = 40 gallons

Hence, the rate of spray at both times is 40 gallons/hour and it is the same.

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Answer:

x = - 10

Step-by-step explanation:

2(x + 3) = x - 4

==> distribute the 2

2x + 6 = x - 4

==> subtract 6 from both sides

2x = x - 10

==> subtract x from both sides

x = - 10