The ratio of boys to girls in a group is 2:1. If there are 22 more boys than girls, work out how many people there are in total

Answer:

The FCI for tennis league is $ 58.32 and FCI for basketball league is $65.30

Step-by-step explanation:

We have been given the following data:

The FCIs for an independent tennis league and an independent basketball league totaled $123.62

Let the FCI for tennis league be "x" and the FCI for basketball league be "y". Since, the total for both leagues is $ 123.62, this means the sum of x and y must be $ 123.62. Using this we can set up our first equation as:

x + y = 123.62                              Equation 1

The basketball FCI was $ 6.98 more than that of tennis FCI. This means y would be more than x by 6.98. Using this we can set up our second equation as:

y = x + 6.98                                 Equation 2

Substituting the value of y from Equation 2 to Equation 1, gives us:

x + x + 6.98 = 123.62

2x + 6.98 = 123.62

2x = 123.62 - 6.98

2x = 116.64

x = 116.64/2

x = 58.32

Using the value of x in Equation 2 gives us:

y = x + 6.98 = 58.32 + 6.98 = 65.3

Therefore, the FCI for tennis league is $ 58.32 and FCI for basketball league is $65.30

In order to solve using substitution, we'll need to first isolate one variable in one equation. I will be using 7x - 2y = 3 and solving for y to begin.

7x - 2y = 3

-2y = -7x + 3

2y = 7x - 3

y = 3.5x - 1.5

Next, we'll plug in our value of y (found above) into the equation 3x + 4y = 11 and solve for x.

3x + 4(3.5x - 1.5) = 11

3x + 14x - 6 = 11

17x = 17

x = 1

Finally, we'll plug our value of x in to the first equation (7x - 2y = 3) and solve for y.

7(1) - 2y = 3

7 - 2y = 3

-2y = -4

y = 2

The solution to these equations is (1, 2).

Hope this helps! :)

Answer:

Number of hits of Paulo favorite baseball player is 26.

Step-by-step explanation:

Given:

Average of favorite baseball player = 0.47272727

Number of bats = 55

We need to find the number of hits.

Solution:

Let the number of hits be 'x'.

Now we know that.

Batting average can be calculated by dividing Number of hits from number of bats.

framing in equation form we get;

[tex]\frac{x}{55}=0.47272727[/tex]

Multiplying both side by 55 we get;

[tex]\frac{x}{55}\times 55=0.47272727\times 55\\\\x=26[/tex]

Hence Number of hits of Paulo favorite baseball player is 26.

Using the formula Number of hits = Batting average * Number of bats, Paul's favorite baseball player had approximately 26 hits from 55 bats, given a batting average of 0.4727272.

To calculate the number of hits of the baseball player, if we know their batting average, we can use the formula:

Number of hits = Batting average * Number of bats

In this case, the batting average is 0.4727272. The number of bats is 55. By substituting these values into the formula, we get:

Number of hits = 0.4727272 * 55 = 26

So, the baseball player had 26 hits. Please note that in practical situation, number of hits should be a whole number, so we might round the result to the closest whole number.

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There are 45 oranges and 90 apples in the beginning.

Step-by-step explanation:

Let the no. of orange be 'b'

Let the no. of apples be 'a'

Given that,

2b = a

3(b-15) = a

3b - 45 = a

3b - 45 = 2b

3b - 2b = 45

b = 45

2b = a

2(45) = a

a = 90

There are 45 oranges and 90 apples in the beginning.

Answer:

4 as a trapezoid, a rectangle, and two squares

Step-by-step explanation:

The diagram below is a composite figure .To determine it area the composite figure can be decomposed into various shapes.

The shapes it can be decomposed are a trapezoid , a rectangle and 2 squares.

The top side of the composite figure forms a trapezoid . A trapezoid is a quadrilateral with one pair of parallel sides. It is also known as trapezium.

The shape below the trapezoid can be cut into a rectangle .A rectangle is a quadrilateral with opposite sides equal in length and are also parallel.

The two shapes formed below the rectangle are squares. Squares are quadrilaterals with all sides equal in length and opposite sides are parallel.  

Answer:

D

Step-by-step explanation:

Answer:

6x+12

Step-by-step explanation:

Final answer:

The experimental probability that the next student will be a boy with brown eyes cannot be determined without specific observational data. You would need the number of boys with brown eyes and the total number of students Theo observed to calculate it.

Explanation:

To find the experimental probability that the next student Theo sees will be a boy with brown eyes based on his observations, we need to count the number of boys with brown eyes that were observed and then divide by the total number of students observed. However, the data provided does not include specific information on the number of boys with brown eyes seen by Theo. To calculate the experimental probability, you would need that information, as it is defined by the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.

For example, if Theo observed 10 boys and 4 of them had brown eyes, and the total number of students observed was 30, then the experimental probability of the next student being a boy with brown eyes would be 4 out of 30, or 4/30. To express this as a percentage, divide 4 by 30 and then multiply by 100 to get 13.33%.

The y values are y₁ = 0.04, y₂ = 0.2, y₃ = 1, y₄ = 5

A graphing calculator is an electronic device capable of performing various mathematical calculations and plotting graphs of various functions. It is commonly used in education and engineering for tasks such as solving equations, graphing functions, and statistical analysis. Graphing calculators typically have a screen for displaying graphs, a keypad for entering equations and commands, and various built-in functions and tools.

Desmos is a free online graphing calculator that allows users to plot graphs, create animations, and perform various mathematical calculations. It has an easy-to-use interface and supports a wide range of mathematical functions and operations.

Given y = 0.2 ([tex]5^{x}[/tex]) and [tex]x_{1}[/tex] = -1, x₂ = 0, x₃ = 1, x₄ = 2

Putting x values x₁, x₂, x₃, x₄ in the equation of y we get y₁ = 0.04, y₂ = 0.2, y₃ = 1, y₄ = 5 are the corresponding y values

Hence the y values are y₁ = 0.04, y₂ = 0.2, y₃ = 1, y₄ = 5

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Answer:

Large - 24

Small - 15

Step-by-step explanation:

The graph clearly shows that the ball has a height of 35 feet at t = 0.947 s and 2.178 s.

A rugby player kicks a rugby ball 2 feet above the ground at a 50-foot-per-second starting vertical velocity. After t seconds, the height h of the rugby ball is given by:

h = -16t² + 50t +2 ......(1)

Here,

h is the height in feet, and t is the time in seconds

We must determine the time when the ball's height reaches 35 feet. (1) will be transformed into

h = -16t² + 50t +2 - 35

h = -16t² + 50t - 33.

Using the Desmos calculator, we can plot the graph of the preceding equation. The linked graph depicts the period when the rugby ball's height is 35 feet.

The graph clearly shows that the ball has a height of 35 feet at t = 0.947 s and 2.178 s.

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Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = $5

For the alternative hypothesis,

µ < $5

number of samples taken = 10

Sample mean, x = (4 + 3 + 2 + 3 + 1 + 7 + 2 + 1 + 1 + 2)/10 = 2.6

To determine sample standard deviation, s

s = √(summation(x - mean)/n

n = 12

Summation(x - mean) = (4 - 2.6)^2 + (3 - 2.6)^2 + (2 - 2.6)^2 + (3 - 2.6)^2 + (1 - 2.6)^2 + (7 - 2.6)^2 + (2 - 2.6)^2 + (1 - 2.6)^2 + (1 - 2.6)^2 + (2 - 2.6)^2 = 30.4

s = √30.4/10 = 1.74

Since the number of samples is 10 and no population standard deviation is given, the distribution is a student's t.

Since n = 10,

Degrees of freedom, df = n - 1 = 10 - 1 = 9

t = (x - µ)/(s/√n)

Where

x = sample mean = 2.6

µ = population mean = 5

s = samples standard deviation = 1.74

t = (2.6 - 5)/(1.74/√10) = - 4.36

We would determine the p value at alpha = 0.05. using the t test calculator. It becomes

p = 0.000912

In this scenario, a hypothesis test is conducted with the null hypothesis positing that the stock's price growth rate is $5 per week. The calculated p-value ends up being less than the significance level (0.05), leading to the rejection of the null hypothesis. Therefore, there is statistical evidence to support the investor's belief that the stock's growth rate is less than $5 per week.

We start by stating the null and alternative hypotheses. The null hypothesis (H0) is that the mean growth rate of the stock is $5 per week - as initially believed. The alternative hypothesis (Ha), which the investor believes, is that the mean growth rate is less than $5 per week.

To test these hypotheses, we first calculate the sample mean and standard deviation. The given observations for the ten weeks are: $4, $3, $2, $3, $1, $7, $2, $1, $1, $2. The mean of these values is $2.6. The standard deviation is approximately $1.72.

Next, we calculate the Z score, which is (sample mean - population mean) / (standard deviation / square root of the sample size). We therefore have (2.6 - 5) / (1.72 / √10) = -4.41.

Using a Z-score table or software, we then find the p-value associated with this Z-score. The result is a p-value significantly less than 0.05, which is our alpha (significance level). Therefore, we reject the null hypothesis. This implies that with a 5% significance level, there is enough statistical evidence suggesting that the stock's price growth rate is less than $5 per week.

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Answer:

The equation of the line is y = 3 x - 5.

Step-by-step explanation:

The slope intercept form of the equation of a straight line is:

[tex]y=mx + b[/tex]

Here,

m = slope

b = intercept.

The two points are:

A = (2, 1)

B = (3, 4)

Use two-point form method to determine the equation of straight line.

[tex](y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})[/tex]

 [tex](y-1)=\frac{4-1}{3-2}\ (x-2)[/tex]

    [tex]y-1=3(x-2)\\y-1=3x-6[/tex]

          [tex]y=3x-5[/tex]

Thus, the equation of the line is y = 3 x - 5.

The equation of the line in slope-intercept form is y = 3x - 5.

To find the equation of the line containing the points (2, 1) and (3, 4) in slope-intercept form (y = mx + b), you first need to determine the slope (m) and then use one of the points to solve for the y-intercept (b).

The slope (m) can be found using the formula:

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

Let's plug in the coordinates of the two points:

Point 1: (x1, y1) = (2, 1)

Point 2: (x2, y2) = (3, 4)

Now, calculate the slope (m):

m = (4 - 1) / (3 - 2)

m = 3 / 1

m = 3

Now that you have the slope (m), you can use one of the points, for example, (2, 1), and the slope to find the y-intercept (b). You can use the point-slope form of the equation:

y - y1 = m(x - x1)

Using the point (2, 1):

y - 1 = 3(x - 2)

Now, distribute the 3 on the right side:

y - 1 = 3x - 6

Next, add 1 to both sides to isolate y:

y = 3x - 6 + 1

Simplify:

y = 3x - 5

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Answer:

3

Step-by-step explanation:

YS = DI = 6

A = YS * AI = 24

height = A/b = 24 / 8 = 3

Answer:

Step-by-step explanation:

Step 1:we should turn the “facts” into logical expressions.

Step 2:Assign variables

Our variables are: b (for butler), c (for cook), g (for gardener), h (for handyman)

Step 3 . Let the value of true indicate that the person is telling the truth. For example, b = T means the butler is telling the truth. Then we can translate the statements as follows:

Check attachment

Step 4

We know all of these must hold. So we really want to know when (b→c)∧¬(c∧g)∧¬(¬g∧¬h)∧(h → ¬c) is true.

Step 5

Behold, another truth table task! If you work out the truth table, you see that this statement is only true when:

Check attachment

Step 6

Therefore we can say the butler and cook are definitely lying, but we can not determine if the gardener or handyman are lying. However, there are four variables in this problem. Instead, we can do this with some straight reasoning. Notice that:

If the butler is telling the truth, then by (a) the cook is telling the truth.

If the cook is telling the truth, then by (b) the gardener is lying.

If the gardener is lying, then by (c) the handyman is telling the truth.

If the handyman is telling the truth, they by (d) the cook is lying.

This leads to a contradiction (the cook can not be both telling the truth and lying)! Therefore the butler and cook must be lying. What about the gardener and the handyman? We don’t have enough information to figure out if they are lying. Since the cook is lying, we can’t use (b) to come to any conclusions about the gardener. Even if we are able to conclude that the gardener is telling the truth, we can’t use (c) to come to any conclusions about the handyman.

Answer: a

first you solve the top one find it for x

solve the bottom one  combine the numbers

Answer:

-200,700

Step-by-step explanation:

(-1676+-108)/2 = -892 x 225 = -200,700

225 = number of terms -108 + 1676 / 7

Answer: You are not comparing two things, and you're asking a question that can only be answered one way.

Step-by-step explanation: Statistical questions are comparing two things, or one alone. Therefore, Asking someone what grade are they in is not statistical  because of how it is one student being compared, not anyone else.

Answer:

D=142

Step-by-step explanation:

Answer:

14 degrees?

Step-by-step explanation:

The complete question is:

Elizabeth has a lot of jewelry. She has four times as many earrings as watches but half the number of necklaces as earrings. Elizabeth has the same number of necklaces as bracelets. If Elizabeth has 117 pieces of jewelry, has many earrings does she have?

Answer:

Elizabeth has 52 pieces of earrings.

Step-by-step explanation:

- Let the number of Elizabeth's watches = p

- Earrings = 4p (Because she has 4 times as many earrings as watches)

- necklaces = (1/2)4p = 2p (half the number of necklaces as earrings)

=> necklaces = 2p

- bracelets = 2p (same number of necklaces as bracelets.)

Since the total number of pieces of jewelry = 117, the addition of all the jewelry will be 117

That is, watches + earrings + necklaces + bracelets = 117

p + 4p + 2p + 2p = 117

9p = 117

p = 117/9 = 13

Therefore,

p = 13 (watches)

4p = 4×13 = 52 (earrings)

2p = 2×13 = 26 (necklaces)

and 26 bracelets.

Elizabeth has 52 pieces of earrings.

The expected value of Eva flipping a coin is $0.5. If she flips a fair coin, she can expect to gain half a dollar on average with each flip over a long period of time.

The question asks to find the expected value of a coin flip for Eva's case. The expected value is a statistical concept used to predict the outcome of a random event, calculated by multiplying each possible outcome by their respective probability, and then adding these values together.

In Eva's case, a coin has 2 outcomes, heads or tails, and both have an equal chance of occurring i.e., 0.5 probability each in a fair coin flip. If Eva gets heads, she wins $4; if tails, she loses $3. So, we need to calculate the expected gain or loss for each flip.

Her expected value of a coin flip would be calculated as follows:

So, in the long term, Eva's expected value per flip of the coin is $0.5. This implies that on average, Eva can expect to gain $0.5 for each coin flip over the long haul.

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The student asked about the expected value in a coin flip game. Eva's expected value per coin flip is $0.50, calculated by multiplying the probability of each outcome by its respective win or loss and summing these products.

The student has asked about the expected value of a game involving a coin flip. Expected value is a concept from probability theory used to determine the average outcome of a random event over a long period of time. In the described scenario, to calculate the expected value, Eva must consider the amount she wins or loses on a head or tail and the probability of each event.

The formula for expected value (EV) is EV = (probability of heads × winnings on heads) + (probability of tails × loss on tails). Since a fair coin has an equal chance for heads and tails, the probability for each is 0.5. Thus, the expected value for Eva's game is calculated as follows:

EV = (0.5 × $4) + (0.5 × -$3) = ($2) + (-$1.5) = $0.5.

So the expected value for a single flip of the coin in Eva's game is $0.50. This means that on average, Eva will earn 50 cents per flip over a large number of flips.

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Answer:$253

Step-by-step explanation: A=220(1+(0.05*3))=253

Answer:

2 gallons of orange juice

Step-by-step explanation:

Final answer:

The Nelson family drank a total of 11/12 of a gallon of orange juice.

Explanation:

To find the total amount of orange juice the Nelson family drank, we need to add the amount they drank on Saturday morning and Sunday morning. They drank 1/4 of a gallon on Saturday and 2/3 of a gallon on Sunday. To add these fractions, we need to find a common denominator. The least common denominator (LCD) for 4 and 3 is 12.

Converting 1/4 to twelfth, we get 3/12. Converting 2/3 to twelfths, we get 8/12. Now we can add 3/12 + 8/12 to get a total of 11/12. Therefore, the Nelson family drank 11/12 of a gallon in total.

Answer:

A

Step-by-step explanation:

Those two lines are the same. If you divide the second equation by 2, you will end up with the first equation. A system of linear equations cannot have two of the same line.

Answer:

D

Step-by-step explanation:

You have to find a slope but when you apply the slope to the intercept the intercept can not be equal to the neaver mind i suck at explaining.

Answer:

you would multiple length base and height together and since they're all 6 centimeters you would multiply 6 by 6 by 6 and you get216 cubic centimeters

Hope this helps!

Step-by-step explanation:

The volume of a cube with a side length of 6 cm is 216 cm³. Since we know that volume of a cube is obtained by multiplying its side length three times.

The volume of  a cube is given as:

Volume = [tex]s^3[/tex]

Where 's' is the length of its side

Since all the side lengths of a cube are the same, the volume of a cube can be found by multiplying the edge length three times.

Given that the length of the side of a cube is s=6 cm

Then, the volume of the cube is:

Volume = s³

             = 6³

             = 6 × 6 × 6

             = 216 cm³

Therefore, the volume of the cube is 216 cubic centimeters.

So, option D is correct.

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There are 6 different paving stones with a different-size base that have a volume of 360 cubic inches.

To find the different paving stones with a volume of 360 cubic inches, we need to consider the possible combinations of length and width for each stone.

Given that each stone has a volume of 30 cubic inches and a height of 3 inches, we can calculate the area of the base by dividing the volume by the height. So, the area of the base is [tex]\( \frac{360}{3} = 120 \)[/tex] square inches.

Since no stone can have a length or width of 1 or 2 inches, we need to find all the possible combinations of length and width that result in an area of 120 square inches, excluding 1 and 2 inches.

One approach to finding these combinations is to factorize 120:

[tex]\[ 120 = 2 \times 2 \times 2 \times 3 \times 5 \][/tex]

Then, we can use these factors to form different pairs of length and width. However, we must remember that the length and width cannot be 1 or 2 inches. So, the possible lengths and widths could be:

[tex]\[ \text{Length} \times \text{Width} \]\[ 3 \times 40 \]\[ 4 \times 30 \]\[ 5 \times 24 \]\[ 6 \times 20 \]\[ 8 \times 15 \]\[ 10 \times 12 \][/tex]

These are all the combinations that result in a base area of 120 square inches. So, there are 6 different paving stones with a different-size base that have a volume of 360 cubic inches.

Answer: the first number is 11 38/41

The second number is 10 4/41

Step-by-step explanation:

Let x represent the first number.

Let y represent the second number.

4 times one number plus 3 times the other is 78. It means that

4x + 3y = 78- - - - - - - - - -1

3 times the first number minus 8 times the other is -45. It means that

3x - 8y = - 45- - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 3 and equation 2 by 4. It becomes

12x + 9y = 234

12x - 32y = - 180

Subtracting, it becomes

41y = 414

y = 414/41

y = 10 4/41

Substituting y = 414/41 into equation 1, it becomes

4x + 3 × 414/41 = 78

4x + 1242/41 = 78

4x = 78 - 1242/41

4x = 1956/41

x = 1956/41 × 1/4

x = 1956/164

x = 11 38/41

Answer:

step1:add 3y to both sides

step2:add 4 to both sides

step3:multiply both sides by(1/5)

14/15

Step-by-step explanation:

The steps to solve the equation -3y + 2/3 = 2y - 4 are accurate and lead to the conclusion of y = 14/15.

In examining the steps for solving the equation

-3y + 2/3 = 2y - 4

, we can conclude they are correctly performed.

In summary, the steps are correctly structured and the solution to the equation is y = 14/15.

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Answer:

x = 3- 3y/2

Step-by-step explanation:

Answer:

x= 3/2 (3 over 2)

Step-by-step explanation:

2x + 3y= 6

(2x + 3) + (- 3) = 6+ (- 3)

2x + 3 - 3 + 6 - 3

2x = 3

2x/2 = 3/2

x = 3/2