In gym class, a student can do 40 sit-ups in 60 seconds and 100 sit-ups in 150 seconds.

Graph the proportional relationship.

graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 60
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 30
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 50
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30
Question 6 (Essay Worth 4 points)

Take into account that the median of a data set is given by the element of the set that is at the center of the ordered list of elements. If there is no possible to determine a central element in the list, then, you take two elements of the center and calculate the average value in between such elements.

Then, first order the elements, as follow:

1 , 2 , 3 , 4 , 4 , 5 , 7 , 8 , 9 , 12​

THe number of elements is 10, then, you conisder the two elements at the center of the list, that is, the 5th and 6th elements:

1 , 2 , 3 , 4 , 4 , 5 , 7 , 8 , 9 , 12​

and calculate the average in between these numbers:

median = (4 + 5)2 = 9/2 = 4.5

Hence, the median of the given data set id 4.5

The length of the lines GH and CH are 16 units and 12 units.

So, the measure of lines GH and CH:

We know that AC ⊥ GH hence cuts GH in two equal lines.

But,

We can observe that △GCH is an isosceles triangle.

Therefore, the length of the lines GH and CH is 16 units and 12 units.

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ANSWER

EXPLANATION

The parent function is y = |x|. The vertex of this function is at the origin.

When we add/subtract a constant from the variable, x, we have a horizontal translation, so the answer must be one of the first two options.

Since the constant is being subtracted from the variable, the translation is to the right. Hence, the graph of the function is the one with the vertex at (1, 0).

the sum of all the angles in a rectangle is 360°

ANSWER

Quadrant II

EXPLANATION

There are four (4) quadrants on the coordinate plane:

Let us now plot the point:

Therefore, the point (-1, 9) lies on quadrant II.

The slope is 6 and the y-intercept is 9

The given equation is:

y = 6x + 9

The general form of the equation of a line is

y = mx + c

where m is the slope and c is the y-intercept.

Comparing these equations, we see that

m = 6 and c = 9

Therefore, the slope is 6 and the y-intercept is 9

Answer

Number of possible outcomes for everything = 240 ways

Explanation

The number of possible outcomes can be calculated by taking each of these two groups.

First group contains 2 elements

Number of possible ways to pick the elements = 2! = 2 × 1 = 2 ways

Second group contains 5 elements

Number of possible ways to pick the elements = 5! = 5 × 4 × 3 × 2 × 1 = 120 ways

Number of possible outcomes for everything = 2! × 5! = 2 × 120 = 240 ways

Hope this Helps!!!

Answer 3/4 = m + 1/4 is 2/4

3/4 = m + 1/4

m = 3/4 - 1/4

m = (3 - 1)/4

m = [tex]\frac{2}{4}[/tex]

__________________

Class: Elementary School

Lesson: Fractions

[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]

Answer:

3/4

Step-by-step explanation:

To find the slope (gradient) of the line = change in y / change in x

[tex]slope=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\(x_{1} ,y_{1} ) = (-2,6)\\(x_{2} ,y_{2} ) = (-6,3)[/tex]

insert those coordinates in the equation:

[tex]slope=\frac{3-6}{-6-(-2)} =\frac{-3}{-4} =\frac{3}{4}[/tex]

Solution

Step 1:

Write the compounded interest continuously formula.

Step 2:

Given data

P = $6000

r = 6% = 0.06

t = 10 years

Step 3:

Substitute in the formula

Final answer

A = $10933 ( nearest whole number)

Answer:

x = 1.44

Step-by-step explanation:

Multiply both sides by 4 to get rid of the denominator on the LHS(Left hand Side) of the equation and you get x

(x/4) x 4 = 1.8/5 x 4

x = 1.44

Answer

63

Explanation

Given the product 9 * 7/8

We are to find the number of one eighths that are in the product

Finding the product;

= 9 * 7/8

= (9*7)/8

= 63/8

= 63 * 1/8

= 63 * one-eighth

This shows that there are 63 one eighth in the product

Answer:

13 and 389

Explanation:

Let the two positive integers be x and y

If a positive integer is 38 more than 27 times another, then;

x = 27y+ 38 ...1

If their product is 5057, then;

xy = 5057 .....2

Substitute equation 1 into 2

(27y + 38)y = 5057

Expand the bracket

27y^2 + 38y = 5057

27y^2 + 38y - 5057 = 0

Factorize

27y^2 -351y + 389y - 5057 = 0

27y(y-13) + 389(y-13) =0

(27y+389)(y−13) = 0

27y + 389 = 0 and y - 13 = 0

27y = -389 and y = 13

Since y is a positive integer, hence y = 13

Substiute y = 13 into equation 1;

x = 27y+ 38 ...1

x = 27(13)+ 38

x = 351 + 38

x= 389

Hencethe two positive integers are 13 and 389

Algebraic expressions are compound by algebraic terms that are compound by a signed number or coefficient, one or more variables and one or more exponents.

In the given expression:

There are 2 terms which are 5c^2 and 7d, its coefficients are 5 and 7 respectively and there is not any constant, which are independent terms.

From the given graph, it is seen that f(x) is not defined for x<-4. The function g(x) is not defined for x>2

But the function p(x) represents a straight line which is defined for all real x.

Hence, the function p(x) has all real numbers as its domain.

Thus, the correct option is (D)

1) We can fill in the gaps, this way since we can write the following when we translate into mathematical language:

Note that we could do it in two steps. Subtracting and then multiplying and dividing

Let's factor the trinomial step by step:

1. Multiply and divide the whole trinomial by the leading coefficient. For the middle term, leave it expressed:

2. We'll factor just like a regular x^2+bx+c trinomial:

• Open two sets of parenthesis and put the square root of the first term on each one

• Put the sign of the second term of the trinomial in the first set of parenthesis, and the result of multiplying the sign of the second term by the sign of the third term on the second set:

• Find two numbers whose product is 36 and whose sum is 20

• Fill both sets with such numbers, in ascending order:

3. Simplify one of the terms with the denominator:

Therefore, the factorization of our trinomial is:

The required third degree expression is 1/7 (x³ + 2x² - 5x - 6)

Given,

Find a third degree expression f(x) that has zeros -3, -2, 1 and the equation y = f(x)  passes through (4, 10). ,

If the roots/zeroes of a nth  order expression are given as r₁, r₂, r₃....rₙ, the expression is given by f(x) = c(x - r₁) (x - r₂) (x - r₃)....(x - rₙ)

      Since we know the three roots of the third degree expression, the function is;

f(x) = c(x - (-3)) (x - (-2)) (x - 1)

= c(x + 3) (x + 2)  (x - 1)

= c (x³ + 2x² - 5x - 6)

Also y = f(x),  passes through(4, 10) , so

10 = c(4³ + 2 x 4² - 5 x 4 - 6)

10 = c(64 + 32 - 20 - 6)

10 = 70c

c = 10/70 = 1/7

∴Required expression is 1/7 (x³ + 2x² - 5x - 6)

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hello

to know what type of sequence they are, we need to test either for common difference of common ratio

first sequence

(98.3, 94.1, 89.9)

first term = 98.3

in this case there's a common difference here

we can find that by subtracting the second term from the first term or the third term from the second term

first sequence is an arithmetic progression

second sequence

(1, 0, -1, 0)

first term = 1

common difference or common ratio does not exist here

third sequence

(1.75, 3.5, 7, 14)

first term = 1.75

in this case, there's no common difference but rather common ratio

common ratio (r) can be found by dividing the second term by the first term or the third term by the second term

the common ratio here is 2 and this is a geometric progression

fourth sequence

(-12, -10.8, -9.8, -8.4)

first term = -12

in this sequence, there's no common difference or common ratio

fifth sequence

(-1, 1, -1, 1)

the fifth sequence is neither a geometric or artimethic progression because there no common difference or ratio

To get the equation of the line graph, first, we have to find its slope. The slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:

From the picture, the line passes through the points (0,0) and (10, 1), then its slope is:

The slope-intercept form of a line is:

y = mx + b

where m is the slope and b is the y-intercept.

From the graph, the line intersects the y-axis at y = 0, this means that b = into

the equation. Therefore, the equation is:

y = 1/10x

where x is distance (in inches) and y is time (in minutes).

To find how long it takes the snail to crawl 86 inches, we have to replace x = 86 into te equation as follows:

The snail takes 8.6 minutes to crawl 86 inches

A parabola with focus (a, b ) and directrix y = c has the equation

In our case, (a, b) = (2, 7) and c = -1; therefore, the above becomes

which is our answer!

Given the data set:

5, 4, 3, 5, 4, 2, 4, 1, 5, 4, 6, 1, 4, 5, 2, 3

Using the given data set, let's answer the following questions:

• (a). Construct a frequency distribution table.

Let's first arrange the terms in ascending order:

1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6

Here, we can have the following:

1 ==> Occurs twice

2 ==> Occurs twice

3 ==> Occurs twice

4 ==> Occurs 5 times

5 ==> Occurs 4 times

6 ==> Occurs once.

Therefore, for the frequency distribution table, we are to use the number of times each data occur (this is the frequency).

We have the table below:

• Part b.

Let's sketch a histogram of the frequency distribution.

• We have the histogram of the frequency distribution below:

Solution

- We are given the two functions below:

- We are asked to find u(w(-3)).

- In order to find u(w(-3)), we need to first find u(w(x)) and then we can substitute x = -3.

- Since we have been given u(x), then, it means that we can find u(w) as follows:

- But we have an expression for w in terms of x. This means that we can say:

- Now that we have an expression for u(w(x)), we can proceed to find u(w(-3)) as follows:

Final Answer

The answer is

Answer

The simplified fraction is 2 1/2

Step-by-step explanation:

ANSWER:

2nd option: 4/25

STEP-BY-STEP EXPLANATION:

To find the expected value of the distribution, we multiply each outcome by its probability and the sum of this would be the expected value, like so:

Therefore, the correct answer is the 2nd option: 4/25

We have two points C(0, 0) and D (0, 12).

P is on the line segment and 3/4 of the distance from C to D.

Answer:

Explanation:

If a varies jointly with b, we write the equation

a = kb

If a varies inversely with b, we write the equation

a = k/b

So, if u varies jointly with p and d and inversely with w, the equation is

Given:

A deck of 52 playing cards is given.

Required:

Probability of selecting a number card, a red card and an ace.

Answer:

There are 40 number cards.

Therefore, probability of selecting a number card=

There are 26 red cards.

Therefore, probability of selecting a red card=

The probability of selecting an ace =

Final Answer:

The Probabilities of selecting a number card, a red card and an ace are,

respectively.

Given

The number of fence post is 12.

The dimension of each fence post is 8ft tall and 1ft diameter.

To find: How much paint is needed to paint all the surfaces of the 12 fenceposts.

Explanation:

It is given that,

The number of fence post is 12.

The dimension of each fence post is 8ft tall and 1ft diameter.

Therefore,

The fencepost is cylindrical in shape.

Then, the total surface area of the cylinder is,

That implies,

Hence, the required quantity of paint is 320ft^2.