Manny and Ada pool their money from a fundraiser. Manny raised 7 dollars less than twice what Ada raised.
Manny made $45 more than Ada. If the amount that Ada raised is represented by a then which of the following equations correctly models the information given?
(1) 2a-7-a=45
(2) 7-2a + a = 45
(3) 2a -7+ a = 45
(4) 2a-7+45=a

Answer:

x -2x and the y is -2y

Step-by-step explanation:

Answer:

Horizontal: y=-8

Vertical: x=-3

Step-by-step explanation:

Answer:

x = - 3 and y = - 8

Step-by-step explanation:

the equation of a vertical line parallel to the y- axis is

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (- 3, - 8 ) with x- coordinate - 3 , then

x = - 3 ← equation of vertical line

the equation of a horizontal line parallel to the x- axis is

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (- 3, - 8 ) with y- coordinate - 8 , then

y = - 8 ← equation of horizontal line

If a math test is worth 100 points and has 30 problems and  each problem is worth either 3 or 4 points, then there are 10 4 point problems

Total number of questions = 30

Number of 3 point questions = x

Number of 4 point questions = y

The first equation will be

x + y = 30

x = 30-y

Total score of the test = 100 points

Then the second equation will be

3x + 4y = 100

Here we have to use the substitution method, substitute the value of x in the equation

3(30-y) + 4y = 100

90 - 3y +4y = 100

y = 100 - 90

y  = 10

Hence, if a math test is worth 100 points and has 30 problems and  each problem is worth either 3 or 4 points, then there are 10 4 point problems

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Answer:

4

Step-by-step explanation:

1

From the given statements the valid statement is, If I buy cookies, then I bake a cake.

What is valid statement?

Valid: An argument is only considered to be valid if all of the premises must be true in order for the conclusion to be true. It is also impossible for all of the premises to be true while the conclusion is false.

Consider, the given statements

If I bake a cake, then I won't buy cookies.

If I don't buy cookies, then I don't need milk.

Since an argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true.

Here, the premises are true, so the valid argument is,  If I buy cookies, then I bake a cake.

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The slope of the points (15,-6) and (-4,11) is  0.895.

The slope of a line is the ratio of the amount that y increases as x increases some amount.

To calculate the slope of the two points given, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the slope of the points is 0.895.

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If a simple random sample of 31 observations was taken from a large population. The sample mean equals 5 then the five is a point estimate

Total number of population = 31 observations

Sample mean of the population = 5

Sample mean is the average value of the sample that is selected from a large population of data.

The point estimate is defined as the single value estimate of the parameter. Point estimate is usually use when we have to choose single value from a larger population, that should be the best estimate to represents the parameter.

Here the sample mean of population is 5

Therefore, five is a point estimate

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Answer:

$980

Step-by-step explanation:

33 1/3%           x

------------ = -------------                  Cross multiply

100%         $2,940

33 1/3 x 2,940 = 100x               Multiply

98000 = 100x                           Divide 100 to both sides

980 = x

The measure of the angle is 39°.

Complementary angles are angles whose sum is equivalent to 90°. On the other hand, supplementary angles are angles whose sum is equivalent to 180°.

Let x be the measure of the angle.

90° - x = complement angle of x

180° - x = supplement angle of x

If the measure of its supplement is 39 more than twice the measure of its complement, then

180° - x = 39 + 2(90° - x)

Simplify and solve for x.

180° - x = 39 + 2(90° - x)

180° - x = 39 + 180° - 2x

x = 39°

Hence, the measure of the angle is 39°.

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Answer:

Below

Step-by-step explanation:

m = slope

Use two points on the graph to find  m

    m = ( x1-x2)/(y1-y2)  = ( 1- -1) / ( -4 - -2) =  2 / -2 = -1

Perpindicular slope is   - 1/m   =   -1 / (-1) = 1

Answer:

d = 4

Step-by-step explanation:

Because the slope formula is:

y2-y1 / x2-x1 = m

10-d / 10+6 = 3/8

Cross multiply 10+6 and 3/8

10-d = 16(3/8)

10-d = 6

10-6=d

4=d

Answer:

Step-by-step explanation: (a)

(c)Maximum number of hours Lia can work at the restaurant and still meet her earnings goal = 15 hours

(d)Maximum Earning = $160

Step-by-step explanation:

Let r be the number of hours worked at the restaurant.

Let y be the number of hours of yard work,

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour.

Since she does yard work,

Lia’s parents allow her to work a maximum of 15 hours per week overall.

Lia’s goal is to earn at least $120 per week.

The restaurant, r pays $8 per hour

Yard work, y pays $12 per hour.

Therefore:

The system of inequalities that represent this problem is therefore:

(b)The graph of the inequality is attached below

(c)When the graph is plotted, the vertices of the feasible region are:

(5,10)

(5, 6.7)

(15,0)

Where the first term is for the number of hours worked in the restaurant.

The maximum value of r possible is 15 from the three points.

Therefore, she can work at the restaurant for 15 hours and still meet her earning goal.

(d)Maximum Amount Lia can earn in 1 Week

At (5,10), Earning=(5X8)+(10X12)=40+120=$160

At (5, 6.7), Earning=(5X8)+(6.7X12)=40+80.4=$120.4

At (15,0) Earning=(15X8)+(0X12)=$120

Since she has to work at least 5 hours at the restaurant, the maximum amount possible is $160.

6 is the answer.

Explanation- You have to plug in, multiply, and divide using p1q1=p2q2 formula

The parabola has a vertex at (-3, -2), has a p-value of 3 and it opens up.

Mathematically, the vertex form of a parabola is represented by this mathematical expression:

y = a(x - h)² + k

Where:

h and k represents the vertex of the equation.

In Mathematics, the focus for either a right or left parabola is modeled by this mathematical expression (h + p, k) while its directrix is modeled by this mathematical expression x = h - p;

h + p = 0   ⇒ h = -p

h - p = -6

Solving the set of linear equations simultaneously, we have:

-p - p = -6

-2p = -6

p = 6/2

p = 3

For the value of h, we have:

h = -3.

Additionally, the vertex form of this parabola is given by:

y = a(x - h)² + k

y = a(x - 3)² - 2

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Complete Question:

A parabola can be drawn given a focus of (0, −2) and a directrix of x = −6. What can be said about the parabola?

The parabola has a vertex at ( , ), has a p-value of

and it

-opens up

-opens down

-opens right

-opens left

Segment BC  is congruent to segment EF,

Angle BAC  is congruent to angle EDF,

Angle CBA is congruent to angle DEF.

Given:

Triangle ABC is congruent to triangle DEF.

if two triangles are congruent:

congruent sides are:

AB ↔ DE ,BC↔EF, CA ↔ FD

congruent angles are:

<A ↔ <D , <B ↔ <E, <C ↔ <F.

Therefore Segment BC  is congruent to segment EF, Angle BAC  is congruent to angle EDF, Angle CBA is congruent to angle DEF are correct.

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Answer:

x is equal to 2

Step-by-step explanation:

simplify the equation

distribute the 0.3

0.3*4-0.3x=x-1.4

1.2-0.3x=x-1.4

get x by itself on one side

1.2+1.4=x+0.3x

simplify

2.6=1.3x

2=x

In order to solve for the variable in the equation 2 (4 x 3) 4 = 3 x minus (2 x 4), giovanni first applies the distributive property.

The equation is a result is 8x+6+4 = 3x-2x-4.

Given that the distributive property is to multiplying by the numbers outside of the parentheses into the inside of the parentheses

So we now that,

2×4x=8x

2×3=6

8x+6+4

Then do the same thing on the other side also so that Which we gets is equal to the below

3x-2x-4

so the equation we get is

8x+6+4 = 3x-2x-4

Hence the answer is, we get the equation is a result is 8x+6+4 = 3x-2x-4

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On average, Logan drinks (2)/(3) of a 6-ounce glass of water in 1(4)/(5) hours. How much water does he drink, in glasses per hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.

The following response has been constructed in a straightforward, step-by-step approach.

Measure: 1 ounce

2/3×6 =4 glass

Considering that a person consumes four glasses every hour.

he Drinks x glasses after one hour.

Reason: Since 21/5x=4,

21x=5×4

Glass 21x=20x=20/21

Answer: So, consume 20/21 glasses in an hour.

The response is a correct fraction.

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The  equation of the regression line is  [tex]\bar{y}[/tex]=9.1006+(-0.2157)x and the point prediction of ammonium concentration for 25ml/h is  [tex]\bar{y}[/tex]=3.7081

A regression line is an approximation of the line that describes the true, but unknown, linear connection between two variables. The regression line equation is used to predict (or estimate) the value of the response variable from a given value of the explanatory variable.

In statistical modeling, regression analysis is a collection of statistical techniques for estimating the associations between a dependent variable and one or more independent variables.

a) [tex]\bar{y}[/tex]=β₀+β₁x

Where,

β₁=[tex]S_{xy}[/tex]/[tex]S_{xx}[/tex] -------(1)

Where,

[tex]S_{xy}[/tex]= -341.959231

[tex]S_{xx}[/tex]1585.230769

By substituting these values in equation 1 we get,

β₁= -0.2157

β₀= [tex]\bar{y}[/tex]-β₁x

Where,

[tex]\bar{y}[/tex]=∑[tex]y_{i}[/tex]/n

∑[tex]y_{i}[/tex]=52.8

n=13

Then,

[tex]\bar{y}[/tex]=4.0615

[tex]\bar{x}[/tex]=∑[tex]x_{i}[/tex]/n

∑[tex]x_{i}[/tex]=303.7

n=13

[tex]\bar{x}[/tex]=23.3615

β₀=4.0615-(-0.2157)(23.3615)

=9.1006

Therefore, β₀=9.1006

The regression equation is  [tex]\bar{y}[/tex]=9.1006+(-0.2157)x

If x=25,

[tex]\bar{y}[/tex]=9.1006+(-0.2157)(25)

[tex]\bar{y}[/tex]=3.7081

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40 percentage of 75 is 30 and 2/5 of 75 is 30. So, Priya calculated in a correct way.

Given,

To find 40% of 75, Priya calculates 2/5 of 75

We have to find the value of 40% of 75.

Percentage;

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The sign "%" is used to denote it.

Now,

Lets find;

40% of 75

40/100 × 75 = 40/4 × 3 = 10 × 3 = 30

That is,

40% of 75 is 30.

Now,

2/5 of 75

2/5 × 75 = 2 × 15 = 30

That is,

2/5 of 75 is also 30

Therefore,

40 percentage of 75 is 30 and 2/5 of 75 is 30. So, Priya calculated in a correct way

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8) A system of two equations that could be used to find out the price of package A and package B are;

C = 150 + 55h

C = 210 + 40h

9) The number of nights  Kareem would need to stay in a hotel to pay the same amount for either vacation package is; 4 nights

We are told that Kareem is going to Florida and the cost for two different vacation packages is;

Package A

Roundtrip Airfare Cost = $150

Hotel Cost (per night) = $55

Package B;

Roundtrip Airfare Cost = $210

Hotel Cost (per night) = $40

A) Now, if  h represents Hotel Cost and C represents Cost of package, then we have;

For package A;

C = 150 + 55h   ------(1)

For package B;

C = 210 + 40h    ------(2)

9) The number of nights  Kareem would need to stay in a hotel to pay the same amount for either vacation package is;

150 + 55h = 210 + 40h

210 - 150 = 55h - 40h

60 = 15h

h = 60/15

h = 4

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Answer:

$91.92

Step-by-step explanation:

1/2 lb of shrimp is 11.49 how much for 4lb?

1/2 pounds = 0.5 pounds

4lb/0.5lb = 8

11.49 * 8 = $91.92

The equation of the straight line having gradient -7/6 with the point on the line as (3,-1) is y [tex]=[/tex] (-7/6)x [tex]+[/tex] 5/2  .

In the question ,

it is given that

the gradient (slope) of the required line is -7/6 ,

and the coordinate of point on the line is (3 , -1) .

We know that the equation of the line passing through the points (x₁ , y₁) with gradient(m) is given by the formula

(y - y₁) = m(x - x₁)

So , the equation of the straight line will be written as

(y -(-1)) = (-7/6)(x - 3)

y + 1 = (-7/6)(x - 3)

y + 1 = (-7/6)x + 7/2

y = (-7/6)x + 7/2 -1

y = (-7/6)x + 7/2 - 2/2

y = (-7/6)x + 5/2

Therefore , the equation of the straight line is y [tex]=[/tex] (-7/6)x + 5/2 .

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(a) The function "f" is increasing for the x-values of [(-∞) < x ≤ 0] and            [2 < x < ∞], while "f" is decreasing for the x-values of [0 < x ≤ 2].

(b) The function f(x) is greater than 0 at [(-1) < x < ∞], excluding the point  (x = 2)

(c) The function f(x) is less than 0 when [x < (-1)]

In the reference attachment attached along with the question statement, we are provided with a graph of a certain function "f",

And as per the question statement, we are required to determine the x-values for the following:

(a) for which "f" is increasing or decreasing,

(b) [f(x) > 0]

(c) [f(x) < 0]

From the graph, it is very clear that, the slope is rising from [(-∞) < x ≤ 0] and [2 < x < ∞], while, declining from [0 < x ≤ 2] of the x-axis. Therefore,

(a) The function "f" is increasing for the x-values of [(-∞) < x ≤ 0] and            [2 < x < ∞], while "f" is decreasing for the x-values of [0 < x ≤ 2].

(b) The function f(x) is greater than 0 at [(-1) < x < ∞], excluding the point  (x = 2)

(c) The function f(x) is less than 0 when [x < (-1)]

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Answer:

3.54

Step-by-step explanation:

Answer:

249.40

Step-by-step explanation:

How to calculate amount of work?

According to this question, Jaida worked 21 ½ hours last week and earned $11.60 per hour of work.

If Jaida earned $11.60 per hour, this means that Jaida earned 21.5 × 11.6 = $249.4.

Therefore, If Jaida worked 21½ hours last week and earned $11.60 per hour of work. The amount of money Jaida earned last week is $249.4.

The value of  [tex]n ^ {mn}[/tex] = [tex]5^{10}[/tex]  or 9765625.

An index is a number that is raised to power. It is written as a small number to the right and above the base number. Other names for the index are exponent or power.

The index of a number says how many times to use the number in multiplication.

[tex]m^n[/tex]=32

m and n are positive integers.

32 = 2 x 2 x 2 x 2 x 2

32 = [tex]2^5[/tex]

hence, m = 2 and n = 5.

Now, Let's find the value of [tex](n ^ m)^n[/tex].

[tex](n ^ m)^n = n^{m*n}[/tex]

          = [tex]5^{2*5}[/tex]

          = [tex]5^{10}[/tex]     or

          = 9765625

Hence, the value of  [tex]n ^ {mn}[/tex] = [tex]5^{10}[/tex]  or 9765625.

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Answer:

12

Step-by-step explanation:

1) Substitute x into the equation

To substitute you would need to multiply the number before it by 2 (in other questions it would be the value told that is x)

2) Put the numbers you have worked out into the equation

-6 + 1.5 + 5 - 4.5 + 16

3) Work out the final equation

Hope this helps, have a great day!

Answer:

33.333...% over the base 100% (100% is representing the $5.40)

Step-by-step explanation:

she gets $7.20 from selling the 18 chocolate bars

7.20 divided by 5.40 is 1.3333...

the 1 in 1.3333... represents the base 5.40 and the 0.3333... represents the profit