Wade Boggs played professional baseball for three different teams in 18 years. The table shows his total of number hits for each team Red Sox 2,098 , Yankees 702, Devil Rays 210. Suppose he made the same numbers of hits each of the 18 years. If t= total number of hits and a = number of hits per year, which two equations can be used to determine the number of hits he made each year ?

If the car's speed is 65 kilometres per hour, then the bus' speed may be 75 kilometres per hour.

How to find the distance travelled by an object?

The distance travelled by an object in a specified direction is velocity×time.

if the car's speed is 65 kilometres per hour then in 2 hours it will travel a distance of 65×2 kilometres.

65×2=130 kilometres

if the bus' speed is 75 kilometres per hour then in 2 hours it will travel a distance of 75×2 kilometres.

75×2=150 kilometres

So, after 2 hours the distance between the two vehicles will be 130+150= 280 kilometres

which is less than 350 kilometres.

Hence, it is possible that if the car's speed is 65 kilometres per hour then the bus' speed is 75 kilometres per hour.

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50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.

The ratio of sparkling water to grape juice is,

1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) =  2 : 1

The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is

2/3 · 75quarts = 50 quarts

Then the grape juice content is,

1/3 · 75 quarts = 25 quarts

Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

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Answer:19/12 or 1 7/12

Step-by-step explanation:

51/12 - 32/12=19/12

1 7/12

Answer:

1 7/12

Step-by-step explanation:

4 3/12 - 2 8/12

First, subtract the integers:

2 3/12 - 8/12

Since 3/12 cannot subtract 8/12, we can take 1 from the 2 and turn it to 12/12 to add to our 3/12:

1 15/12 - 8/12

Simplify:

1 7/12

Answer:

23

Step-by-step explanation:

Taking an algebraic approach

let the number be n, then (n - 17) is 17 subtracted from the number, and -2(n - 17) = - 12 ( divide both sides by - 2 )n - 17 = 6 ( add 17 to both sides ) which is n=23

The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.

What is linear equation?

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.

Given, the equation y = 2x -4

Which is linear function and have y a dependent variable and x be the independent variable,

because value of y depends upon the value of x.

Hence, a is the correct answer.

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Answer: A

Step-by-step explanation: Trust me

The equation of the line in slope-intercept form is: y = 5/2x.

If the value of the slope of the line is represented by m, and y-intercept of the line is b, therefore, the equation of the line in slope-intercept form can be written as: y = mx + b.

The slope of the line (m) = rise/run = 5/2

m = 5/2

The line intercepts the y-axis at 0. The y-intercept therefore is b = 0.

To write the equation of the line, substitute m = 5/2 and b = 0 into y = mx + b:

y = 5/2x + 0

y = 5/2x

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The average rate of change in median age per year from 1950 to 1990 is 0.085 years of age per year.

The median is the mid-value in a set of data. to find it we first arrange the data set from smallest to largest, then pick the middle value which divides the data set in half.

From the given table,

The median age at the time of the first marriage in 1950 = 22.8 years,

While the median age in 1990 = 26.1 years,

Hence, the average rate of change in median age per year from 1950 to 1990

= (22.8-26.1)/(1950-1990)

= (-3.3)/(-40)

= 0.0825 years of age per year.

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Answer: 11 14/15

Step-by-step explanation:

The single trigonometric function form of the expression is 2sin(3π/8) cos(3π/8).

Trigonometric function:

In math, trigonometric functions are the periodic functions which denote the relationship between angle and sides of a right-angled triangle.

Given,

Here we need to write the given expression as a single trigonometric function. 2 sine (start fraction 3 pi over 8 end fraction) cosine (start fraction 3 pi over 8 end fraction)

Here we have the expression,

2 sine (start fraction 3 pi over 8 end fraction) cosine (start fraction 3 pi over 8 end fraction)

Now, we have to convert this into the form of trigonometric function,

For that we have to rewrite the given expression based on the arithmetic operators, then we get the resulting function as,

=> 2sin(3π/8) cos(3π/8).

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Answer:C

Step-by-step explanation:

did it on edge

Reject H0 if the test statistic is less than  -1.321  or greater than  1.321  .

What is a hypothesis simple definition?

A tested assertion regarding the relationship between two or more variables .

                  a theory put out to explain an observed occurrence is referred to as a hypothesis (plural: hypotheses) in a scientific context.      

Reject H0 if the test statistic is less than  -1.321  or greater than  1.321  .

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The equivalent expression of (6x² - 9x) - (2x -3) is 6x² - 11x + 3

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, equivalent expressions are expressions that have similar value or worth but do not look the same.

To find equivalent expression we can simplify the expression.

Therefore,

(6x² - 9x) - (2x -3)

open the brackets

6x² - 9x - 2x + 3

combine like terms

Therefore,

(6x² - 9x) - (2x -3) = 6x² - 11x + 3

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Answer:

y=2x+3

Step-by-step explanation:

The slope formula is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].

[tex]\frac{5-3}{1-0}[/tex]

[tex]\frac{2}{1}[/tex]

So the slope is 2.

Then you choose any coordinate, in my case (1,5).

To find the y-intercept look at where the line crosses the y-axis. The line crosses at 3.

The number of sides in the polygon that has 1,260° as the sum of the interior angles, found using the formula for the sum of the interior angles in the polygon, S = 180·(n - 2) is 9 sides

A polygon is a figure consisting of a specified number of straight sides such that they form a closed loop. The number of sides in a polygon are three or more.

The formula for the sum of the interior angles of a polygon, S, can be be used to find the number of sides in the polygon as follows;

S = 180·(n - 2)

Where;

n = The number of sides the polygon has

The sum of the interior angles in the specified polygon = 1,260°

The number of sides in the polygon can be found by equating the formula for S to 1,260° as follows;

When S = 1.260°, we get;

1,260 = 180·(n - 2)

Which indicates;

n - 2 = 1,260 ÷ 180 = 7

Therefore; n - 2 + 2 = 7 + 2 = 9

n = 9

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The domain of the function is{x | −4 < x < 6}.

A function's domain is the set of all potential inputs.

For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

What is range?

The statistical difference between the highest and lowest values for a given data collection is called the range.

For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. It is possible to think of the range as the distance between the highest and lowest observation as a result.

the domain of the function is{x | −4 < x < 6} because

there is no restriction on x domain and range both are the set of real numbers.

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Using PEMDAS to solve the mathematical expression, the result is -637.947

The mathematical operation refers to calculating a value using operands and a math operator. The symbol of the math operator has predefined rules to be applied to the given operands or numbers.

In this kind of problem, we need to use the PEDMAS rule which is

Parenthesis, Exponents, Division, Multiplication, Addition and Subtraction.

The order in which this must be prioritized is from parenthesis and the least is subtraction.

Applying PEMDAS to this mathematical operation, we would have

19.42 - 34.89(19.3) + 10.23 + 5.78

Using a calculator which follows this rule, we would have;

19.42 - 34.89(19.3) + 10.23 + 5.78 = -637.947

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Answer:

16.(a)  24

16.(b)  See attachment.

Step-by-step explanation:

Cumulative frequency means ‘running total’. A cumulative frequency diagram plots this running total so you can estimate the median and the quartiles easily.

According to the given cumulative frequency graph, the number of necklaces that have a mass 21 g or less is 16.

Therefore, an estimate of the number of necklaces with a mass of 21 g or greater is:

[tex]\implies 40-16=24[/tex]

To draw a box plot to represent the data, estimate the median and quartiles from the graph.  

Calculate the position of the median and quartiles, then go to the position on the vertical scale of the graph and read off the value from the horizontal axis.  (See attached annotated graph).

[tex]\sf Median \; position=\dfrac{40}{2}=20[/tex]

So the median = 22

[tex]\sf Q_1 \; position = \dfrac{1}{4} \times 40=10[/tex]

So Q₁ = 18

[tex]\sf Q_3 \; position = \dfrac{3}{4} \times 40=30[/tex]

So Q₃ = 24

Draw the box plot with the calculated median and quartiles, and the given lowest and highest values.  (See second attachment).

X=pi/2 only in the interval 0 to 4 . We have the maximum value of f(x) = sinx = 1

What is  function interval ?

If the value of the function f (x) grows with an increase in the value of x, the function interval is said to be positive.

                         The function interval, on the other hand, is said to be negative if the value of the function f (x) decreases as the value of x increases.

First of all to apply the extreme value theorem function must be countions at the interval 0 to 4.

F(x)=(x^2-16)/(x^2+x-20) is countinious int the given interval .

Now we find

F'(x)= d(F(x))/dx=1/(x+5)^2 so here we don't have in critical point therefore this choice is incorrect

Similarly if we take

F(x)= sinx

F'(x) = cosx

For critical point ,

Cosx =0

X=pi/2 only in the interval 0 to 4

And this point we have the maximum value of f(x) = sinx = 1

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The largest possible area of rectangle with base on the x-axis and upper vertices on the curve [tex]y = 8 -x^{2}[/tex] is [tex]\frac{64\sqrt{6} }{9}[/tex].

It is given to us that -

The rectangle has the base on x-axis

The rectangle has its upper vertices on the curve [tex]y = 8 -x^{2}[/tex] ----- (1)

We have to find out the largest possible area for the rectangle with given specifications.

We know that the area of a rectangle can be represented as -

[tex]A = xy[/tex] ---- (2)

where,

[tex]x =[/tex] length of the base of the rectangle

[tex]y =[/tex] vertices of the curve = width of the rectangle

Since it is given to us that the rectangle has it base on the x-axis, therefore the length of the base of the rectangle = [tex]2x[/tex] ---- (3)

Substituting equations (1) and (3) in equation (2), we have

[tex]A = xy\\= > A = (2x)(8-x^{2}) \\= > A = 16x-2x^{3}[/tex]----- (4)

For the largest possible area, we know that -

[tex]\frac{dA}{dx}=0[/tex] ---- (5)

Substituting equation (4) in equation (5), we have

[tex]\frac{dA}{dx}=0\\= > \frac{d}{dx}(16x-2x^{3}) =0\\ = > \frac{d}{dx}(16x)-\frac{d}{dx}(2x^{3} )=0\\= > 16-6x^{2} =0\\= > 6x^{2} =16\\= > x^{2} =\frac{16}{6} \\= > x=\frac{4}{\sqrt{6} }[/tex]------ (6)

To find out the largest possible area, we have to put the value of x from equation (6) in the area of the rectangle in equation (4). So, we have

[tex]A = 16x-2x^{3}\\= > A = (16*\frac{4}{\sqrt{6} }) -[2(\frac{4}{\sqrt{6} } )^{3} ]\\= > A = \frac{16*4}{\sqrt{6} } -\frac{2*4*4*4}{\sqrt{6}*\sqrt{6}*\sqrt{6} } \\= > A = \frac{64\sqrt{6} }{9}[/tex]

Therefore, the largest possible area of rectangle with base on the x-axis and upper vertices on the curve [tex]y = 8 -x^{2}[/tex] is [tex]\frac{64\sqrt{6} }{9}[/tex].

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The total revenue function if the revenue from 115 devices $2116 is 200 when R'(x)=4x(x²+25000[tex])^{2/3}[/tex].

Given that,

The following function calculates the marginal revenue (in thousands of dollars) from the sale of a portable gaming system.

R'(x)=4x(x²+25000[tex])^{2/3}[/tex]

We have to find the total revenue function if the revenue from 115 devices $2116.

We know that,

R'(x)=4x(x²+25000[tex])^{2/3}[/tex]

Integrating on both sides

R(x)= [tex]\int {4x(x^{2} +25000)^{2/3} } \, dx[/tex]

Let x²+25000=t

=> 2xdx=dt

=> 4xdx=2dt

We get,

R(x)= [tex]\int {2t^{-2/3} } \, dt[/tex]

R(x)= [tex]6t^{1/3}[/tex]+C

By Substitution then

R(x)= 6(x²+25000[tex])^{1/3}[/tex]+C

We get

Given R(115)=$2,116 or 2.116 (in thousands of dollars) and x=115 units

Then total revenue function(in thousands of dollars)

2.116= 6(115²+25000[tex])^{1/3}[/tex]+C

C=200

Therefore, The total revenue function if the revenue from 115 devices $2116 is 200.

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The rational equation with the desired asymptotes and intercepts is given by: f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].

Vertical asymptotes are x values that are outside the domain and, in a fraction, are the denominator zeroes.

As long as this value differs from infinity, the horizontal asymptote is the value of f(x) as x approaches infinity.

The vertical asymptotes are related to the denominator roots, so:

f(x) = a / ( x + 5)( x + 2 )

f(x) = a / ( x² + 7x + 10 )

The x-intercepts are related to the function's numerator, so:

f(x) = [a( x + 1 )( x - 6) ] / [x² + 7x  + 10 ]

The y-intercept is to find a, hence, when x = 0, y = 5, thus:

4 = a(-6)/ 10

a = (-40/6)

a = -20 / 3

The equation will be written as,

f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].

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The best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.

In the given question,

The best fitting line is one where the intercept of the regression equation:

As we know that;

The slope of the line of best fit is the coefficient in a simple regression with a single independent variable. The slope is a mixture of the two coefficients in this example and in any regression with two independent variables. The y-intercept of the line of best fit is constant C.

So, the best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.

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The initial value of the function obtained from the table of values for the linear function is; 7

A linear function is a function that when plotted, produces a straight line on the coordinate plane.

The initial value of a function is the value of the function, when the input value is 0.

The initial value indicates the point where the graph intersects the y-axis, which is the y-intercept. It the point the graph enters quadrant I, where the x and y-values are positive.

From the initial value, and to the right of the x-axis, the input variable (x) is positive, such that the values of the function for natural value input, such as time can be found, and the initial value then represents the start of the measurement of the output values of the function.

The data in the table indicates that when the input variable x = 0, the output variable, y = 7

Therefore:

Which indicates that at the initial point of the positive value inputs of the function, the output is 7

Question details are:

Please find the table of the linear function, which is to be examined, presented as follows:

[tex]\begin{array}{|c|c|}In put (x) & Out put (y)\\-3 &14 \\0 & 7 \\3 & 0 \\6 & -7 \\\end{vmatrix}[/tex]

The initial value of the function that the above table represents is required.

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The volume of this cone is 83.7 cubic meters and the given height 5m then diameter 3.99 m.

What is Volume?

Volume is a measurement of three-dimensional space that is occupied. Numerous imperial or US customary units, as well as SI-derived units (such the cubic meter and liter), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch).

Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.

Given that ;

volume of cone = [tex]\pi r^{2} \frac{h}{3}[/tex]

volume of cone = 83.7 [tex]m^3[/tex]

height = 5m

to find diameter :
[tex]d = \sqrt{\frac{3\times V}{\pi \times h} }[/tex]

[tex]d=\sqrt{\frac{3\times 83.7}{3.14\times 5} }[/tex]

[tex]d = \sqrt{\frac{251.1}{15.7} }[/tex]

[tex]d = \sqrt{15.993}[/tex]

d = 3.99 m

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The solution to the equation represented by One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x is (b) x = negative 4

The statement in the question is given as

One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x

Mathematically, this statement can be represented as

1/4x - 1/8 = 7/8 + 1/2x

Multiply through the equation by 8

So, we have:

2x - 1 = 7 + 4x

Collect the like terms

4x - 2x = -1 - 7

Evaluate the like terms

2x = -8

Divide both sides by 2

x = -4

Hence, the solution is -4

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The composition of the function are as follows:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10

What is a Composite Function?
If we are given two functions, we can compose one function into the other to produce a third function. The steps needed to complete this operation are the same as those needed to solve any function for any given value. These are referred to as composite functions.

We have,

i] f(x) = 8x  and
g(x) = (2x+8)

(g ∘ g) (x) = g[g(x)]
Substitute x with (2x+8) in the function g(x) = (2x+8).
= 2((2x+8))+8
= 4x + 16

(f ∘ g) (x) = f [g (x)]
Substitute x with (2x+8) in the function f(x) =  8x.
(f ∘ g) (x) = 8(2x+8)  
= 16x + 64

ii]  f(x) = 6x + 2 and g(x) = x -5
f [g(7)] = 6(x-5) + 2  
= 6x - 28

g [f(3)] = (6x + 2 ) - 5
= -30x - 10

Hence, the composition of the function is:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10

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to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{4 +3}{3 +1} \implies {\Large \begin{array}{llll} \cfrac{7 }{ 4 } \end{array}}[/tex]

Answer:

75÷50

Step-by-step explanation:

1.5 or 3÷2 is the correct answer

Probability of people less than 19 year old = 0.5343

Probability of people greater than 10 year old = 0.8116

What is probability?

Mathematical descriptions of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the probability of an event, with 0 roughly denoting impossibility and 1 denoting certainty.

People under age 10 = 253

People between the age of 10-18 = 466

People between the age of 19-30 = 174

People above the age of 30 = 450

Total no. of people = 1343

a) people less than 19 years old = 253+466 = 719

probability of people<19 year old = P(age<19) = 719/1343 = 0.5354

b) people of age greater than 10 = 466+174+450 = 1090

probability of people >10 year old = P(age>10) = 1090/1343 = 0.8116

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Answer:

P = 16w - 4

Step-by-step explanation:

P = (5w-2 + 3w)2

P = (8w-2)2

P = 16w - 4

The three statements about his solution that are true include the following:

1. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

2. He did not multiply the numerator and denominator by the correct number to equal 1,500.

5. He should have multiplied the numerator and denominator by 75, not 30,  because 20 × 75 = 1,500.

Based on the information provided, a mathematical expression which models the number of songs of each genre on Josiah's MP3 player to be 300 songs:

10/20 = x/1500

Multiplying the mathematical expression by 75, we have the following:

75 × (10/20) = x/1,500

750/1500 = x/1500

1,500x = (750 × 1,500)

x = (750 × 1,500)/1,500

x = 750.

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