Jason wants to find more information about the heights of players on his school's soccer team and his school's basketball team. Jason surveys 29 members of the soccer team and 16 members of the basketball team. The results of his study are shown in the dot plots below .

Answer:

To find the value of "c" for which the number "a" (-5 in this case) is a solution of the equation, we can substitute "a" into the equation and solve for "c".

Given equation: 4x + 1 + 7c = 8c - 3x + 6

Substituting x with "a": 4(-5) + 1 + 7c = 8c - 3(-5) + 6

Simplifying the equation: -20 + 1 + 7c = 8c + 15 + 6

Combining like terms: -19 + 7c = 8c + 21

Moving all "c" terms to one side: 7c - 8c = 21 + 19

Simplifying: -c = 40

Dividing both sides by -1 to isolate "c": -c/-1 = 40/-1

Flipping the sign when dividing by a negative number: c = -40

So, the value of "c" for which the number "a" (-5) is a solution of the equation is c = -40.

Answer:

[tex]c=-40[/tex]

Step-by-step explanation:

Since a is a Solution to the Equation , then it satisfies the Equation

Substitute by [tex]x=a=-5[/tex] into the Equation [tex]4x+1+7c=8c-3x+6[/tex]

Then [tex]4(-5)+1+7c=8c-3(-5)+6[/tex]

Then [tex]-20+1+7c=8c+15+6[/tex]

By adding like-terms

Then [tex]-19+7c=8c+21[/tex]

Then [tex]8c-7c=-19-21[/tex]

Then [tex]c=-40[/tex]

Answer:

As the number of sides of the bases of a prism increases, the shape of the prism becomes more complex and closer in form to a cylinder. For example, a prism with two identical polygonal bases, such as a rectangular prism or a triangular prism, will have a more blocky or pyramidal shape. However, as the number of sides of the base increases, the shape of the prism becomes more cylindrical and less pyramidal in appearance. This is because the more sides a polygon has, the more closely it approximates a circle, and the cross-section of the prism becomes more circular in shape.

When the number of sides of the base of a prism increases, the prism becomes more like a cylinder.

Answer: cos∅= [tex]\frac{\sqrt{7} }{4}[/tex]

Step-by-step explanation:

All numbers are positive because it is first quadrant.  Draw a line out.

sin = opp/hypotenuse.  the opposite line of the angle (y) =3

and hypotenuse=4

use pythagorean theorem to find x

4²=3²+x²

[tex]x=\sqrt{7}[/tex]

now use cos=adjacent/hypotenuse

cos∅= [tex]\frac{\sqrt{7} }{4}[/tex]

The formula and the differences are shown below

The formula to calculate weighted average is:

weighted average = (w1x1 + w2x2 + ... + wnxn) / (w1 + w2 + ... + wn)

Where x1, x2, ..., xn are the values being averaged, and w1, w2, ..., wn are their corresponding weights.

The weighted average gives more importance or weight to certain values than others.

The weights can represent the relative importance, significance, or contribution of each value to the final average.

The main difference between ROR and weighted return is that ROR measures the return of a single investment, while weighted return measures the return of a portfolio or investment that is composed of multiple assets with different weights.

Weighted return takes into account the relative importance of each asset or security in the portfolio, while ROR does not consider the impact of other investments.

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Answer:

it would be 3 or 2

Step-by-step explanation:

Where the conditions above are given with regard to the above triangle, the ratio AD:DB is 1:1.

Since D is the midpoint of AB, we have:

AD = DB

Let M and N be the midpoints of OA and OB, respectively. Then we have:

AM = MO = x/2

BN = NO = y/2

Also, from the given information, we have:

OD = 3/7x + 4/7y

Since D is the midpoint of AB, we have:

AD + DB = AB

Substituting AD = DB, we get:

2AD = AB

Therefore:

AD = AB/2

We can express AB in terms of x and y using the law of cosines:

AB^2 = OA^2 + OB^2 - 2(OA)(OB)cos(BOA)

Since M and N are midpoints, we have:

OM = OA/2 and ON = OB/2

Therefore, using the law of cosines, we have:

MN^2 = OM^2 + ON^2 - 2(OM)(ON)cos(MON)

Substituting OM = OA/2 and ON = OB/2, we get:

MN^2 = OA^2/4 + OB^2/4 - (OA)(OB)/2 cos(BOA)

But MN = OD, so we can also express this as:

OD^2 = (3/7x + 4/7y)^2 = OA^2/4 + OB^2/4 - (OA)(OB)/2 cos(BOA)

Substituting OD^2 = (3/7x + 4/7y)^2 and simplifying, we get:

9x^2 + 16y^2 = 49(OA^2 + OB^2) - 42(OA)(OB) cos(BOA)

Substituting AB^2 = OA^2 + OB^2 - 2(OA)(OB) cos(BOA) and simplifying, we get:

9x^2 + 16y^2 = 49AB^2

Substituting AD = AB/2, we get:

9x^2 + 16y^2 = 49(2AD)^2

Simplifying, we get:

x^2 + 4y^2 = 28AD^2

We want to find the ratio AD:DB, which is the same as the ratio AD:(AB - AD). Substituting AB = 2AD, we get:

AD:(AB - AD) = AD:AD = 1:1

Therefore, the ratio AD:DB is 1:1.

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Answer:

C. y = 3/2x + 4

Step-by-step explanation:

C. y = 3/2x + 4

Every six months, you will receive $21.50 back from your bond.

The 4.3% coupon is the annual interest rate, which is paid semi-annually (twice a year).

To find the amount earned every 6 months, we need to divide the annual interest rate by 2:

(4.3% / 2) = 2.15%

Next, we need to calculate the dollar amount earned every 6 months. To do this, we need to find 2.15% of the bond's face value:

2.15% of $1000 = $21.50

Therefore, you will earn $21.50 off your bond every 6 months.

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Answer:

24.6 degrees.

Step-by-step explanation:

To find the degree measure of the radians in a right triangle with hypotenuse = 7 and opposite = 3, we need to use trigonometric ratios. Since the opposite and hypotenuse are given, we can use the sine ratio.

sin(θ) = opposite/hypotenuse

sin(θ) = 3/7

Now we need to find the angle measure θ. We need to use the inverse sine or arcsine function to do this.

θ = sin^-1(3/7)

θ ≈ 0.429 radians

To find the degree measure, we must convert radians to degrees by multiplying by 180/π.

θ ≈ 0.429 x 180/π

θ ≈ 24.6 degrees

Therefore, the degree measure of the radians in the given triangle is approximately 24.6 degrees.

The description that correctly represents g(x) is g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0 (third option).

Looking at the graph, we can see that:

Thus, the correct piecewise function that represents g(x) is:

g(x) = {-2 if x ≤ -1

{ (x-1)^2 if -1 < x ≤ 0

{ -x+1 if x > 0

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Approximately 1.18 hours the concentration is highest.

The given function is c(t)=100t/t² +85.

When the concentration is highest, the function becomes

100t/t² +85 =0

100/t +85=0

100+85t=0

85t=100

t=100/85

t=1.18 hours

Therefore, approximately 1.18 hours the concentration is highest.

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The area of the rectangular picture frame with twenty inches in length, and a width of fifteen inches is 180inches.

Given length of the rectangular picture frame = 20inches

Given width of the rectangular picture frame = 15inches

The formula for finding the area of a rectangular frame is the multiplication of both length and width = Length x Width

So, the area of the given rectangular picture frame = 20 x 15 = 180 inches

From the above explanation, we can conclude that the area of the given rectangular frame with length of 20 inches and the width of 15 inches is 180 inches.

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the cost of day old donuts after the discount is $4.95.

         A discount is a decrease in the cost of a good or service. Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price.

       Discounts are offers or rebates made to customers on the marked-down prices of goods. We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Let's examine the connections between these concepts.

       The formula to calculate the discount is:

Discount = List Price - Selling Price

Discount (%) = (Discount/List Price) × 100

the discount is 40% ⇒0.4

customer buys 3 donuts.

price of 1 donut = $2.75

total cost for 3 donuts= $2.75 x 3 = $8.25

discount for 1 donut= [tex]\frac{0.4}{100}* 2.75[/tex]=$1.1

so, for 3 donuts discount = $1.1 x 3 = $3.3

therefore the final price to be paid by customer is

                    =$8.25-$3.3

                    =$4.95

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The scatter plots that do not show a linear relationship are B and C

The distribution of points on a scatter plot's graph can show a linear relationship between two variables. A linear relationship exists between two variables when there is a consistent change in one variable for every change in the other.

The horizontal axis and the vertical axis of a scatter plot each indicate a separate variable. Each data point is plotted on the graph based on its values for the two variables. If the variables are related to one another linearly, the points will often fall in a straight line.

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Option 2 is the correct answer, that is, the equation of the given circle is (x+3)² + (y - 6)² = 4 with center at (-3,6) and radius 2.

The distance formula is a mathematical formula used to determine the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem as:

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

where  (x₁, y₁) and (x₂, y₂) are the x and y coordinates of the said two points. This formula works for any two points in a two-dimensional space with a Cartesian coordinate system.

To answer this we need to know the equation of a circle.

Let (a,b) be the center of a circle with radius r, then the equation of the circle can be written as:

(x - a)² + (y - b)² = r²

We see that from the given graph center of the circle is the point (-3,6) and radius will be 2.

We can now substitute these information in the circle equation,

(x - -3)² + (y - 6)² = 2²

(x+3)² + (y - 6)² = 4

That is the equation of the given circle is (x+3)² + (y - 6)² = 4.

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The resale value of the car after 3 years is $9,984.

Since the resale value decreases by 20%. Thus, the resale value of the car will be 80% of its original value.

After the first year, the resale value of the car will be 80% of its original value:

Resale value after 1 year = 80/100 * $19,500 = $15,600

After the second year, the resale value of the car will be 80% of its value after the first year:

Resale value after 2 years = 80/100 * $15,600 = $12,480

After the third year, the resale value of the car will be 80% of its value after the second year:

Resale value after 3 years = 80/100 * $12,480 = $9,984

Therefore, the resale value of the car after 3 years will be $9,984.

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On solving the question, we can say that Therefore, none of the answers to the question's assertions are true.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

Let's use "x" to symbolise box A's weight. Then, we could type:

Given that box B weighs 5 kg more than box A, its weight is "x + 5".

Given that box C weighs 3 kg more than box B, its weight is calculated as "x + 5 + 3" = "x + 8".

We can write: Since we are aware that the combined weight of the three boxes is 51 kg:

[tex]x + (x + 5) + (x + 8) = 51\\3x + 13 = 51\\3x = 38\\x = 12.67\\[/tex]

Therefore, box A weights around 12.67 kg. The weights of boxes B and C may also be ascertained using the equations we discovered earlier:

17.67 kg (x + 5) is the estimated weight of Box B.

The approximate weight of Box C is 25.67 kg (x + 8).

Therefore, none of the answers to the question's assertions are true.

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The correct answer is not listed among the options. The correct answer is E. 1/x.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find f'(x), we need to differentiate the function f(x) with respect to x. Since we are given k(x) = 3x, we can use the chain rule to differentiate f(x) = ln(k(x)) = ln(3x) as follows:

f'(x) = d/dx [ln(3x)]

= 1/(3x) * d/dx [3x] (applying the chain rule)

= 1/(3x) * 3

= 1/x

Therefore, the correct answer is not listed among the options. The correct answer is E. 1/x.

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Answer:

Using the FOIL method to multiply (x + 80)(x - 20), we get:

(x + 80)(x - 20) = x^2 - 20x + 80x - 1600

Simplifying the expression, we get:

(x + 80)(x - 20) = x^2 + 60x - 1600

Therefore, the answer is x^2 + 60x - 1600.

Answer:

If the value of y is directly proportional to the value of x, we can use the formula for direct variation to find the value of x when y = 30. The formula for direct variation is:

y = kx

where k is the constant of proportionality.

To find the value of k, we can use the values given in the problem:

y = kx

12 = k(8)

Solving for k, we get:

k = 12/8 = 3/2

Now that we know k, we can use the formula for direct variation to find the value of x when y = 30:

y = kx

30 = (3/2)x

Solving for x, we get:

x = (30)/(3/2) = 20

Therefore, when y = 30, x = 20

The expression that is equivalent to 6x2y + 2xy^5 include:

2(3x²y + xy^5).

2xy(3x + y⁴)

xy(6x + 2y⁴)

An expression can refer to a variety of things depending on the context in which it is used.

In mathematics and computer programming, an expression typically refers to a combination of numbers, variables, operators, and/or functions that are evaluated to produce a value. For example, "2 + 3" is an expression that evaluates to "5"

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The difference between 6 5/6 and 5 1/2 is 4/3 .

To subtract these mixed numbers, we need to first convert them into improper fractions:

6 5/6 = (6 x 6 + 5)/6 = 41/6

5 1/2 = (5 x 2 + 1)/2 = 11/2

Now we can subtract:

41/6 - 11/2

To deduct divisions with various denominators, we really want to track down a shared factor. 6 is the smallest common multiple of 6 and 2 in this instance. Therefore, we can use denominator 6 to convert 11/2 into an equivalent fraction:

11/2 = (11 x 3)/(2 x 3) = 33/6

Now we can subtract the fractions with the same denominator:

41/6 - 33/6 = 8/6

Working on the portion by partitioning both the numerator and denominator by their most prominent normal component, we get:

8/6 = 4/3

As a result, in mixed numbers, the difference between 6 5/6 and 5 1/2 is 4/3, or 1 1/3..

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The complete question is:

What is the rule for the sequence

5/6, 1 1/2, 2 1/6, 2 5/6.....

Answer:

If (x-1) is a factor of the polynomial f(x) = 4x² - 4x² - x - K, then we know that (x-1) divides evenly into the polynomial, which means that the polynomial can be written as:

f(x) = (x-1)(ax + b)

where a and b are constants that we need to determine. We can use the distributive property to expand this expression and equate it with the original polynomial:

f(x) = (x-1)(ax + b) = 4x² - 4x - K

Expanding the left side of the equation, we get:

ax² + bx - ax - b = ax² - (a-b)x - b = 4x² - 4x - K

Now we can equate the coefficients of the like terms on both sides of the equation.

The coefficient of x^2 on the left side is a, and on the right side it is 4. Therefore, we have:

a = 4

The coefficient of x on the left side is b - a, and on the right side it is -4. Therefore, we have:

b - a = -4

Substituting a=4, we get:

b - 4 = -4

Solving for b, we get:

b = 0

So the polynomial can be written as:

f(x) = (x-1)(4x + 0) = 4x² - 4x

Therefore, K = 0.

To find the roots of the equation, we need to set f(x) = 0 and solve for x:

4x² - 4x = 0

Factor out 4x:

4x(x - 1) = 0

So the roots of the equation are x = 0 and x = 1.

hi

4/7  =   8

7/7 =  ?  

so ?  =  7/7 * 8  /4/7 =   8/4/7 =  8 *7/4 = 4*2*7 /4 =   2*7 = 14

so whole thing  is  14

let's check :    14 * 4/7 =   56/7 = 8

Match initial data. answer is correct.

Answer:

s^2+2s-8

Step-by-step explanation:

(s-2)(s+4)

=s^2+4s-2s-8

simplified= s^2+2s-8

Answer:

s^2+2s-8

Step-by-step explanation:

(s-2)(s+4)

=s^2+4s-2s-8

simplified= s^2+2s-8

Answer:

B

Step-by-step explanation:

All of the lines of best fit are close to the points in the scatter plot except B.

The line of best fit in B does not even touch any of the points in the scatter plot, so it is not a good example of a line of best fit.

Therefore, you are three times more likely to be on time than be late if you take Route C to school.

Relative frequency is a statistical term that refers to the proportion or percentage of times an event or a particular value occurs within a larger set of data. It is calculated by dividing the number of times the event or value occurs by the total number of observations in the data set.

Here,

To determine how many times more likely you are to be on time than late if you take Route C, we need to compare the heights of the green and red bars for Route C. From the graph, we can see that the green bar (representing on-time arrivals) is approximately three times taller than the red bar (representing late arrivals) for Route C.

To calculate how many times more likely you are to be on time than late if you take Route C, we need to find the ratio of the heights of the green and red bars:

Ratio = height of green bar / height of red bar

Looking at the segmented bar graph, we can see that the height of the green bar for Route C is approximately 0.45, and the height of the red bar is approximately 0.15.

Ratio = 0.45 / 0.15

= 3

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Answer:

Step-by-step explanation:

b

Answer:

47 + 9f [tex]\leq[/tex] 120

Step-by-step explanation:

B is the correct answer.

The line plot representing the values on the number line can be presented as follows;

[tex]{}[/tex]         ×

[tex]{}[/tex]         ×                             ×

[tex]{}[/tex]         ×      ×                     ×      ×

<-|------|------|------|------|------|------|------|------|->

 [tex]{}[/tex]0     1/8    1/4          1/2   5/8  3/4           1

A line plot is a graph displaying data as points above a number, which indicates the frequency of the data.

The values in the fraction can be expressed as follows;

5/8, 5/8, 1/4, 1/8, 1/8, 3/4, 1/8

The values that are repeated can be excluded to get;

Values to be represented are; 5/8, 1/4, 1/8, 3/4

The above fractions can be expressed as fractions with a denominator of 8 as follows;

5/8, 1/4, 1/8, 3/4 = 5/8, 2/8, 1/8, 6/8

The fractions can be arranged in increasing order as follows;

5/8, 2/8, 1/8, 6/8; 1/8, 2/8, 5/8, 6/8

The fractions 1/8, 2/8, 5/8, 6/8, can therefore, be entered into the number line as follows;

<-|------|------|------|------|------|------|------|------|->

 0[tex]{}[/tex]    1/8   2/8          1/2    5/8  6/8           1

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