A water truck is filling a swimming pool. The equation that represents this relationship is y = 18.25x where y is the number of gallons of water in the pool and x is the
number of minutes the truck has been filling the pool.
Select True or False for each statement.
The unit rate for this relationship is 1 gallon per 18.25 minutes.
O True
O False
This is a proportional relationship because the graph of the equation is a straight line through the origin.
O True
O False
o o o o
The water in the swimming pool increases by about 33 gallons every 10 minutes.
O True
o o o o o
O False
A table of related x- and y-values for this relationship would show equivalent ratios.
O True
O False
The point (12,219) could be a point on this graph.
O True
O False

The linear function is given as follows:

\(y = \sqrt{x} + 4\)

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The y-intercept is of 4, hence the parameter b is given as follows:

b = 4.

The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:

m = tan(60º)

\(m = \sqrt{3}\)

Thus the function is given as follows:

\(y = \sqrt{x} + 4\)

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Answer:

(x-2)(x-2) or (x+2)(x+2)

Step-by-step explanation:

since you are squaring it, technically the terms are negative, but the product will be positive. when you multiply two negative factors, you get a positive answer. so either both can be negative or both can be positive.

When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

It seems like you want to find the sum of 38 to 115:

\( \displaystyle \large{38 + 39 + 40 + 41 + ... + 114 + 115}\)

If we notice, this is arithmetic series or the sum of arithmetic sequences.

To find the sum of the sequences, there are three types of formulas but I will demonstrate only one and the best for this problem.

\( \displaystyle \large{S_n = \frac{n(a_1+a_n) }{2} }\)

This formula only applies to the sequences that have the common difference = 1.

Given that a1 = first term of sequence/series, n = number of terms and a_n = last term

We know the first term which is 38 and the last term is 115. The problem here is the number of sequences.

To find the n, you can use the following formula.

\( \displaystyle \large{n = (a_n - a_1) + 1}\)

Substitute an = 115 and a1 = 38 in the formula of finding n.

\( \displaystyle \large{n = (115 - 38) + 1} \\ \displaystyle \large{n = (77) + 1} \\ \displaystyle \large{n = 78}\)

Therefore the number of sequences is 78.

Then we substitute an = 115, a1 = 38 and n = 78 in the sum formula.

\( \displaystyle \large{S_{78} = \frac{78(38+115) }{2} } \\ \displaystyle \large{S_{78} = \frac{39(38+115) }{1} } \\ \displaystyle \large{S_{78} = 39(153) } \\ \displaystyle \large \boxed{S_{78} = 5967}\)

Hence, the sum is 5967.

The answer would be 10 I believe.

AB=8.7 cm. Work out the length of BC. ... 1. Adi. Diagram NOT accurately drawn. POR is a triangle. Angle Q = 90° ... Give your answer correct to 1 decimal place. ton o. Ady ... Ad. POR is a right-angled triangle. PR = 12 cm. OR = 4.5 cm. Angle PRO = 90°. ... AB= 7 cm. BC = 12 cm. Angle BAD= 65°. Calculate the length of AC.

Answer:

60 contain 6 tens

then

60+10

contain

7 tens

the

correct answer

is

7 tens

Answer:

6 tens + 1 ten = 7 tens

Step-by-step explanation:

6 tens = 60

1 ten = 10

7 tens = 70

Answer:

40 students

Step-by-step explanation:

and all the frequencies

there should one student per tally mark because the tally is measuring grades

Hope that helped!!! k

Answer:

\(\Huge \boxed{40}\)

Step-by-step explanation:

Adding all the frequencies in the frequency distribution gives the total number of students.

\(6+10+8+9+7=40\)

The number of students in class VIII whose marks obtained in an examination are 40.

Answer:

$9000

Step-by-step explanation:

36000:4=$9000

Answer:

Equation: y = 2x

Graph: see attachment

Step-by-step explanation:

Pieces of paper = x

Number of Valentines = y

The equation is a proportional equation and can be represented as y = kx

k is the constant of proportionality

k = y/x

Using (2, 4),

k = 4/2 = 2

To find the equation, substitute k = 2 into y = kx

Thus:

y = 2x

The graph has been plotted and attached below.

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

Answer:

look below

Step-by-step explanation:

To determine the upper-tail critical value of the test statistic for a chi-square test for independence in a contingency table, you can use a table of critical values for the chi-square distribution or you can use a statistical software package or calculator to compute the critical value.

In each of the following circumstances:

a. a=0.05, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.05.

b. a=0.01, r=5, c=6: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.

c. a=0.01, r=5, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.

d. a=0.01, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.01.

e. α=0.01, r=6, c=5: The critical value would be the upper-tail critical value of the chi-square distribution with 6 degrees of freedom and an alpha level of 0.01.

It's important to note that the critical value is dependent on the degrees of freedom and the alpha level, so you will need to use the appropriate values for these parameters in order to determine the correct critical value.

The value of lesser integer will come out to be 6.

Let the required lesser integer be x and its even consecutive integer would become x+2 .

A number is said to be consecutive if it follows a order after other number either an even number or an odd number.

Following equations will be in order;

\(7(x+2)-x = 50\)

Solving the above equation we get

\(7x+14-x = 50\)

\(6x+14=50\)

\(6x= 50-14= 36\)

\(x = 6\)

And,

\(x+2 = 8\)

Hence, the value of lesser integer will come out to be 6.

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7 is not included and hence it is depicted on the number line using an open dot. Hence, solution to the inequality is option B.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The given inequality is:

x + 8 > 15

Subtracting 8 on both sides of the equation:

x + 8 - 8 > 15 - 8

x > 7

Here, 7 is not included and hence it is depicted using an open dot.

Hence, option B is the correct answer.

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The rational function in the simplest form of (f/g)(x)  is x / 5x - 2.

Composite functions are when the output of one function is used as the input of another. A typical example of a composite function is (f/g)(x).

Therefore, let's solve the rational function in the simplest form.

Hence,

f(x) = -x

g(x) = -5x + 2

(f/g)(x) = f(x) / g(x)

Therefore,

(f/g)(x) = - x / -5x + 2

Hence,

(f/g)(x) = - x / - (5x - 2)

Finally,

(f/g)(x) = x / 5x - 2

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Answer:

Step-by-step explanation:

To find the new coordinate of a point after it has been scaled by a factor of 1/2, you can multiply the x- and y-coordinates of the point by 1/2.

For example, to find the new coordinate of point K', you can multiply the x-coordinate of K' (-8) by 1/2 to get the new x-coordinate, and multiply the y-coordinate of K' (8) by 1/2 to get the new y-coordinate. This gives you the new coordinate of K' as (-4,4).

You can use the same method to find the new coordinates of points L' and M'. The new coordinate of L' is (4,4) and the new coordinate of M' is (-2,4).

I hope this helps! Let me know if you have any questions.

The result of the addition operation of 1204.2 + 4.72613 is approximately 1208.93.

An addition operation involves two addends added together to result in a number called the sum.

The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.

Mathematical operations combine numbers, variables, and values with mathematical operands to solve mathematical questions.

1204.2 + 4.72613

= 1208.92613

= 1208.93

Thus, the addition of 1204 and 4.72613 yields a total of 1208.93 approximately.

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By algebra properties and trigonometric formulas, the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b².

In this problem we must prove that the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b², this can be done both by algebra properties and trigonometric formulas. First, write the given expression:

(a · cos A + b · sin A)² + (a · sin A - b · cos A)²

Second, expand the expression by algebra properties:

a² · cos² A + 2 · a · b · cos A · sin A + b² · sin² A + a² · sin² A - 2 · a · b · cos A · sin A + b² · cos² A

(a² + b²) · cos² A + (2 · a · b - 2 · a · b) · cos A · sin A + (a² + b²) · sin² A

(a² + b²) · (cos² A + sin² A)

Third, use the fundamental trigonometric formula:

a² + b²

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The sum of expected marks is given as follows:

9375.

Each question has four choices, hence the probability of choosing the correct choice is given as follows:

p = 1/4 = 0.25.

Then the expected number of correct answers is given as follows:

E(X) = 0.25 x 150

E(X) = 37.5.

Then the expected grade for a single student is given as follows:

37.5 - 0.25(150 - 37.5) = 9.375.

The expected sum for the 1000 students is then given as follows:

1000 x 9.375 = 9375.

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Answer:

Ben's garden has 1 rose.

Ben's garden have 4 tulips and 1 rose (equals to 5)

Ina's garden has 5 roses.

Ina's garden has 2 tulips and roses together.

There are 6 tulips altogether in both gardens.

There are 6 roses altogether in both gardens.

Step-by-step explanation:

Answer:

1) P(1,0)Q(-2,3)R(-3,3)S(3,2)

2) (3,4)

3) (0,-4)

4) (1,2)

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

10(4)-3(4)^2

10(4)-3(16)

40-3(16)

40-48

-8

Please mark Brainliest :)

Answer: -8

Step-by-step explanation:

10x - 3x^2

10 x 4 - 3 x 4^2

40 - 3 x 16

40 - 48

-8

Answer:

I hope D option is write

I hope you help

Answer:

c

Step-by-step explanation:

it is 4×+5 which is easy as u tines it by fixing the sum into parts and its eisier

Answer:

x = -34/3, y = 1/3, and z = -35/3

Step-by-step explanation:

2х+5y-3z-=14   let's call this equation 1.

x-2y=-12   let's call this equation 2.

-x+Зу-2z =13  let's call this equation 3.

USING EQUATION 1 AND EQUATION 3.

2х+5y-3z-=14   (EQUATION 1)

-x+Зу-2z =13  (EQUATION 3)

LET'S GET RID OF z, BY MAKING THE COEFFICIENT OF z IN THE TWO EQUATION THE SAME. WE WILL MULTIPLY EQUATION 1 BY 2 AND EQUATION 3 BY 3.

2х+5y-3z-=14   (EQUATION 1) * 2

-x+Зу-2z =13  (EQUATION 3) * 3

4х+10y-6z-=28   let's call this equation 4.

-3x+9у-6z =39  let's call this equation 5.

TO GET RID OF z, WE WILL HAVE TO SUBTRACT EQUATION 5 FROM EQUATION 4 PLEASE TAKE NOTE OF THE SIGNS (-) (+).

4х+10y-6z-=28   (EQUATION 4)

- (-3x+9у-6z =39) (EQUATION 5)

(4x - 3x) + ((+10y) - (+9y)) + ((-6z) - (-6z)) = (28 - 39)

x + y + 0 = -11

x + y = -11  let's call this equation 6.

USING EQUATION 2 AND EQUATION 6, LET'S FIND x AND y.

x-2y=-12  (EQUATION 2)

x + y = -11  (EQUATION 6)

x has the same coefficient in both equations, which is 1. Let's get rid of x so we can find the value of y.

We will subtract equation 6 from equation 2. Take note of the signs.

x-2y=-12  (EQUATION 2)

- (x + y = -11)  (EQUATION 6)

(x - x) + ((-2y) - (+y)) = ((-12) - (-11))

0 + -3y = -1

-3y = -1

Divide both sides by -3.

-3y/-3 = -1/-3

y = 1/3

LET'S SUBSTITUTE THE VALUE OF y INTO EQUATION 2 TO GET THE VALUE OF x.

x-2y=-12  (EQUATION 2)

x-2(1/3)=-12  

x -2/3 = -12

Add 2/3 to both sides.

x -2/3 + (2/3) = -12 + (2/3)

x + 0 = -34/3

x = -34/3

LET'S SUBSTITUTE THE VALUES OF x and y INTO EQUATION 1 TO GET THE VALUE OF z.

2х+5y-3z-=14   (EQUATION 1)

2(-34/3)+5(1/3)-3z-=14  

-68/3 + 5/3 - 3z = 14

-21 - 3z = 14

Add 21 to both sides.

-21 + (21) - 3z = 14 + (21)

0 - 3z = 35

-3z = 35

Divide both sides by -3.

-3z/-3 = 35/-3

z = -35/3 or  

Therefore, x = -34/3, y = 1/3, and z = -35/3

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