Laura and Kirk are comparing how much they have been running. Laura has already
run 36 miles and Kirk has run 64. Laura begins running 21 miles per week and Kirk runs 17 miles
per week. How many additional weeks, w, will it take for their total distance run to be equal?

The value of 8x ÷ (16+8) ÷ 32 is x/96

The four basic arithmetic operations in Maths, for all real numbers, are:

Addition (Finding the Sum; ‘+’)

Subtraction (Finding the difference; ‘-’)

Multiplication (Finding the product; ‘×’ )

Division (Finding the quotient; ‘÷’)

Discussing about division or quotient

The division is usually denoted by ‘÷‘ and is the inverse of multiplication. It constitutes two terms dividend and divisor.

To simplify

8x÷(16+8)÷32= 8x×1/24×1/32

= x/96

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3x - 2 (2.3x + 2.5)  = -1.6x-5 are equivalent expressions while 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3 are not equivalent expressions

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s)

Given: 3x - 2 (2.3x + 2.5) = -1.6x -5 and 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3

For 3x - 2 (2.3x + 2.5):

First, clear the parenthesis by using -2 to multiply what's in the parenthesis. Then add/subtract like terms:    

3x - 2 (2.3x + 2.5) =  3x-4.6x- 5 = -1.6x-5          

For 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3:

First, clear the parenthesis by using -3 to multiply what's in the parenthesis. Then add/subtract like terms:  

5 - 3 (-1.6x - 2.1) = 5 + 4.8x + 6.3  = 4.8x + 11.3

Since 3x - 2 (2.3x + 2.5) is equal to  -1.6x-5 and  5 - 3 (-1.6x - 2.1) is not equal to 4.8x - 1.3.

Therefore, 3x - 2 (2.3x + 2.5)  = -1.6x-5 are equivalent expressions and 5 - 3 (-1.6x - 2.1) = 4.8x - 1.3 are not equivalent expressions

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The composite function ( f. g(x)) is x² + 4x + 3

A function can be described mathematically as a rule, law or equation that explains, shows and elaborates the relationship between to variables.

The variables are known as;

From the information given, we have the functions as;

To determine the composite function ( f. g(x)), we have to substitute the value of g(x) as a function in the function f(x) as the variable 'x', we get;

( f. g(x)) = (x + 2)² - 1

Now, let's expand the square

( f. g(x)) = (x + 2) ( x+ 2) - 1

Expand the bracket

( f. g(x)) = x² + 2x + 2x + 4 - 1

Now, let's collect like terms, we get

( f. g(x)) = x² + 4x + 3

Thus, the function is x² + 4x + 3

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The complete question:

Find ( f. g(x)) if f(x)=x^2-1, g(x)=x+2

Answer:

Step-by-step explanation:

3x + 3x equals 11x

The two numbers with sum is 10 and difference of their squares is 10  are 5.5 and 4.5.

What is square of numbers?

A square number, sometimes known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another integer by itself. For instance, 9 is a square number since it equals 3^2 and is represented by the symbol 3 x 3.

Suppose x and y are the two numbers with sum is 10 and difference of their squares is 10.

As sum of two numbers is 10.

So, x + y = 10            ..(1)

As difference of their squares is 10.

So,  x^2 - y^2 = 10             ..(1)

From equation (1), x = 10 - y

Plug value of x in equation (2)

          (10 - y)^2 - y^2 = 10

100 - 20y + y^2 - y^2 = 10

                  100 - 20y = 10

                           20y = 100 + 10

                             2y = 110

                               y = 5.5

Plug y = 5.5 in equation (1)

x + 5.5 = 10

        x = 10 - 5.5

        x = 4.5

Therefore, The two numbers with sum is 10 and difference of their squares is 10  are 5.5 and 4.5.

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Answer:

graphs 2 and 4 are functions

Step-by-step explanation:

To know if a graph represents a function, draw multiple vertical (straight up and down) lines through the graph. If any of the vertical lines crosses the graph 2 or more times, it is NOT a function.

The vertical asymptote of a given function is x = -2 and x = -3.

What is the vertical asymptote of a function?

A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. It appears at the x-value that is outside the domain of the function, therefore the graph can never cross it.

To find the vertical asymptotes, set the denominator equal to zero and solve for x.

For the given function,

                           [tex]F(x) = \frac{1}{7(x+2)(x+3)}[/tex]

To find the vertical asymptote, equate the denominator to zero.

                            7(x + 2)(x + 3) = 0

                              (x + 2)(x + 3) = 0

                  x + 2 = 0           (or)         x + 3 = 0

                  x = -2                (or)         x = -3

Hence, The vertical asymptote of the given function is x = -2 and x = -3.

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Upon graphing of the function rule h = 8 - 0.4j, we see that the graph is continuous.

We are given the function as; h = 8 - 0.4j

Let h represent the height in inches on the y-axis and let j represent the amount of juice in ounces on the x-axis.

We are told that the height of the juice in a 20-oz bottle depends on the amount of juice. This means that j is an independent variable and h is dependent variable.

The function  represents the height of juice after drinking j ounces of juice. Therefore as the juice is being drank, the height of the juice in bottle will change continuously. Therefore, the graph of our given function will be continuous because we can drink fractions of an ounce juice.

The equation of a line in slope-intercept form is given as;

y = mx + b

where;

m is Slope of line

b is y-intercept

If we rewrite our function slope-intercept form of equation, we will get;

h = -0.4j + 8

Thus;

Slope = -0.3

y-intercept = 8.

The graph is as plotted in the attached file

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The statement that proves the claim about the angle is incorrect is that;

c) Incorrect because arctan(-3/4) = -36.87

The 6 main trigonometric ratios of a right angle triangle are;

Sine θ = length of the opposite leg / length of the hypotenuse

Cosine θ = length of the adjacent leg / length of the hypotenuse

Tangent θ = sine θ/cosine θ = opposite leg / adjacent leg.

cosecant θ = 1 / sine θ = hypotenuse / opposite leg

secant θ = 1 / cosine θ = hypotenuse / adjacent leg

cotangent θ= 1 tangent θ = adjacent leg / opposite leg.

Now, we are told that the angle formed is 53.13°. Since the options are either arctan or arccos, we will use them to verify the angles;

cos 53.13° = 0.6

tan 53.13° = 1.33

They are both positive and it means both x and y values are positive since we are told that it involves the positive x-axis.

Thus, y/x cannot be negative or -3/4 as given.

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Answer:

The answer is a D. a circle

The base shape of the cylinder can only be a circle.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A cylinder is a three-dimensional shape that has two congruent parallel circular bases connected by a curved surface.

The shape of the base determines the shape of the cylinder. If the base is circular, then the cylinder is called a circular cylinder.

A non-square rectangle and a square are not circular, and thus cannot be the base shape of a cylinder.

Hence, the base shape of the cylinder can only be a circle.

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With the help of unitary method it can be found out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.

It is given to us that -

Tomás first chose a tray with oranges whose label says 1,350 gram

We have to find out more grams of oranges that he should buy if he wants to reach 5 kilogram.

We know that

1 kilogram = 1000 grams

=> 1000 grams = 1 kilogram ----- (1)

By unitary method, we can find out the number of kilograms equivalent to 1350 grams of oranges.

From equation (1), we have

1000 grams = 1 kilogram

=> 1350 grams = (1/1000) * 1350

=> 1350 grams = 1.35 kilograms ----- (2)

Now, from equation (2), we can see that Tomás first chose 1,350 grams of oranges which is equal to 1.35 kilograms of oranges.

This implies that the more kilograms of oranges that Tomás has to buy to reach 5 kilograms is given by -

(5 - 1.35) kilograms

= 3.65 kilograms

From equation (1), we have

1 kilogram = 1000 grams

=> 3.65 kilograms = 3.65 * 1000 grams

=> 3.65 kilograms = 3650 grams.

Thus, by solving through unitary method we find out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.

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The acceleration when the car comes to a full stop is 20.76 meters per square second.

Here we have the velocity function:

v(t) = -3t^2 + 18t + 9

To find the acceleration we need to differentiate with respect to the variable t, so we will get the acceleration:

a(t) = 2*(-3)*t + 1*18

a(t) = - 6*t + 18

Now, the car will come to a stop when the velocity is equal to zero, so we need to solve:

-3t^2 + 18t + 9 = 0

Dividing all by -3 we get:

(-3t^2 + 18t + 9)/-3 = 0

t^2 - 6t - 3 = 0

The solutions are:

[tex]t = \frac{6 \pm \sqrt{(-6)^2 - 4*1*-3} }{2*1} \\\\t = \frac{6 \pm 6.92}{2}[/tex]

We only care for the positive solution:

t = (6 + 6.92)/2 = 6.46

The acceleration at that time is:

a(6.46) =  - 6*6.46 + 18 = -20.76

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Answer:

Raymond

Step-by-step explanation:

1 ) Eve and Patty swam fewer laps than Maureen so...

Eve and Patty < Maureen

2 ) Patty swam more laps than Eve...

Patty > Eve

3 ) Maureen swam fewer laps than Raymond...

Maureen < Raymond

4 ) We can eliminate Eve and Patty since they swam fewer laps than Maureen. The ones who are left are...

Maureen and Raymond

5 ) We know that Maureen swam fewer laps than Raymond so we can eliminate Maureen.

Raymond

6 ) This mean that the one who swam the most laps is...

Raymond

Hope this helps! :)

The price of the lumber per square foot is $115.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that the cost of the lumber yard plywood per square meter is $1240.

The cost of the lumber plywood per square foot is calculated as,

Cost = $1240 per square meter

The square meter is equal to 1 m = 3.28 ft. The cost will be calculated as,

Cost = $1240 / m²

Cost = $1240 / (3.28)² ft²

Cost = $115 per square feet

Therefore, the price of the lumber per square foot is $115.

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Answer:

Step-by-step explanation:

Solve as below

a) a² + ab with a = 6.6, b = 3.4;

b) x² - xu at x = 0.5, y = 2.5;

c) -5a² - 5ah at a = 4, h = -3;

Answer:

Step-by-step explanation:

a) a² + ab = ?

→ (6.6)² + (6.6 × 3.4)

→ 43.56 + 22.44

→ 66

So, the answer is 66.

b) x² - xu = ?

→ (0.5)² - (0.5 × 2.5)

→ 0.25 - 1.25

→ -1

So, the answer is -1.

c) -5a² - 5ah = ?

→ -5(4)² - 5(4 × -3)

→ (-5 × 16) - (5 × -12)

→ -80 + 60

→ -20

So, the answer is -20.

Answer: 4.014e+9 square inches

The possible pair of null and alternative hypotheses for this experiment is   "The null hypothesis is that the flu infection rate has no impact on the number of students absent from school.

The alternative hypothesis is that as the flu infection rate increases, the number of students absent from school also increases."

Hypotheses

Hypotheses refers the testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

Given,

A group of elementary school students designed a study to find a possible relationship between the number of students absent from school and the overall rate of flu infections in their town.

Here we need to find the correct pairing of possible null and alternative hypotheses for this experiment.

Here the given situation is relationship between  the number of students absent from school and the overall rate of flu infections in their town.

So, the null hypotheses of this relation is flu infection rate has no impact on the number of students absent from school

And the alternative hypotheses of the relation is defines that the flu infection rate increases, the number of students absent from school also increases.

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Answer:

Step-by-step explanation:

The null hypothesis is that the flu infection rate has no impact on the number of students absent from school.

The alternative hypothesis is that as the flu infection rate increases, the number of students absent from school also increases.

A value for x is therefore represented by the first number in an ordered pair, and a value for y is represented by the second.The x- and y-coordinates are the names given to these values.

The Method of Elimination

To ensure that the two equations have the same leading coefficient, multiply each equation by a reasonable number in step one.

Step 2: Reverse the first equation and subtract the second one.

Step 3: Find y using this new equation.

Step 4: Change Equation 1 or Equation 2 above to y = 2 and then solve for x.

multiply the equation y = x - 6 by -6.

You will then get the equation: 6y = -6x + 36

The two equations will be:

6y = -6x + 36

y = 6x - 19

And you can see that if you add them, you will be able to eliminate x. answer is -6.

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Answer:

R = 19 yr old; T = 7 yr old

Step-by-step explanation:

From the information given, we can create a system of equations to find both Richard and Teo's ages, letting R represent Richard's age and T represent Teo's age.

Thus we have:

[tex]R +T=26\\2T+5=R\\\\2T+5+T=26\\3T+5=26\\3T=21\\T=7\\\\R+7=26\\R=19[/tex]

When you plug in the numbers, you find that twice Teo's age is 14 as 7*2 = 14.  5 more than 14 is 19 as 14 + 5 = 19.

When a six sided dice through with the coin all the possible outcomes  are as follows

H-1 H-2 H-3 H-4 H-5 H-6

T-1 T-2 T-3 T-4 T-5 T-6

Probability that she gets an outcome of tails and 2 = 1 / 12

Isabelle flips a fair coin and rells a fair six-sided dice.

Coin has two face H or T

Dice has six face hat is 1, 2, 3, 4, 5, 6  

When a six sided dice through with the coin all the possible outcomes  are as follows

H-1 H-2 H-3 H-4 H-5 H-6

T-1 T-2 T-3 T-4 T-5 T-6

So there are total 12 outcomes possible when a six sided dice through with the coin.

Probability that she gets an outcome of tails and 2 = event occur / total number of events = 1 / 12

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Answer: 7.9766443e+22 all added and multiplied correctly

Answer:

I think B. 3.85 units

Step-by-step explanation:

The probability of rolling a 3 first time and a number greater than 4 thre second time is 1/18

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain. An example of a certain event is tomorrow being Friday if today is Thursday. This is definitely going to happen.

The possible outcomes of a fair die are : 1, 2, 3, 4, 5, 6. which is 6 in all

the required outcome for obtaining a 3 = 3 which is 1 outcome

the required outcome for obtaining a number greater than 4 : 5, 6. which is 2 outcomes.

probability of getting 3 first time = 1/6

probability of getting a number greater than 4 = 2/6 ( lowest term = 1/3)

Probability of rolling a 3 first time and a number greater than 4 second time is  = 1/6 x 1/3 = 1/18

In conclusion, probability of obtaining a 3 and a number greater than 4 is 1/18.

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The expression that is equivalent to (f × g²) + 5 - (g² × f) is 5

The expression whose equivalence is to be determined is given as

(f × g²) + 5 - (g² × f)

To start with, we need to remove the brackets in the expression

So, we have the following representation

(f × g²) + 5 - (g² × f) = f × g² + 5 - g² × f

Evaluate the products

This gives

(f × g²) + 5 - (g² × f) = fg² + 5 - fg²

Next, we collect the like terms

So, we have

(f × g²) + 5 - (g² × f) = fg²  - fg² + 5

Lastly, we evaluate the like terms

So, we have

(f × g²) + 5 - (g² × f) = 5

The above expression cannot  be further simplified

Hence, the equivalent expression is 5

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Answer:

[tex]y-8=4(x+3)[/tex]

Step-by-step explanation:

The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].

By using the formula of average speed, it can be inferred that

My average speed is 14 miles per hour

What is average speed?

Speed of an object is the distance covered by the object per unit time

Average speed is calculated by dividing the total distance covered by the total time taken

Length of one block = 560 feet = [tex]\frac{560}{5280}[/tex] miles

Number of blocks = 33

Total distance = [tex]\frac{560}{5280} \times 33\\[/tex]

                        = [tex]\frac{7}{2}[/tex] miles

Total time = 15 minutes = [tex]\frac{15}{60}[/tex] hours = [tex]\frac{1}{4}[/tex] hours

Average speed = [tex]\frac{\frac{7}{2}}{\frac{1}{4}}[/tex] = [tex]\frac{7}{2} \times 4[/tex] = 14 miles per hour

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