In 3-way light bulbs, the highest wattage
is the sum of the two lower ones. If the
lowest is 60 watts, and the highest is
150 watts, what is the middle wattage?

The correct sample space for the gumballs in her bag is;

A: Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape

The sample space of an experiment is defined as the set of all the possible outcomes. For example, when we toss a coin, the sample space is; {head, tail}.

Now, the parameters for the bag filled with gumballs are;

1 watermelon.

2 lemon-lime.

3 grape gumballs.

Therefore the sample space is the different types of gumballs there and it is; {Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape}

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The measure of HG is 12

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is called a rectangle.

The opposite sides of a parallelogram are equal. This means that 3y = y+8

3y = y+8

3y-y = 8

2y = 8

divide both sides by 2

y = 8/2

y = 4

if y = 4 and HG is y+8

therefore

the measure of HG = 4+8

= 12

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Answer:

28

Step-by-step explanation:

The constant variation, a, is equal to the product of x and y when they are both known. In this case, when x = 7 and y = 4, the constant variation is 4 * 7 = 28. So, the equation for the inverse variation is y = 28 / x.

Answer:

12 feet

Step-by-step explanation:

this is a rectangle! because DC = 16 feet, you know that AB is also equal to 16 feet

therefore, DA + CB = 24

because ABCD is a rectangle, you know that DA = CB and you can use substitution to say that CB + CB = 24

2CB = 24

CB = 12

The percent of people satisfied with the survey is 55%

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, in a survey of 1,600 people who owned a certain type of​ car, 880 said they would buy that type of car again, we need to find what percent of the people surveyed were satisfied with the​ car,

The percent of people satisfied with the survey = 880 / 1600 × 100

= 55%

Hence, the percent of people satisfied with the survey is 55%

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The expression for the number of pencils she has left will be 100 - 2 × 22 - 2 × 19. Then the correct option is C. And yes, she has enough pencils.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Ms. Florinda is a kindergarten educator. She purchases 100 pencils and needs to give 2 pencils to every one of her understudies. She has 2 classes, a class with 22 understudies and a class with 19 understudies.

Then the expression is given as,

⇒ 100 - 2 × (22 + 19)

⇒ 100 - 2 × 22 - 2 × 19

⇒ 100 - 44 - 38

⇒ 18

The expression for the number of pencils she has left will be 100 - 2 × 22 - 2 × 19. Then the correct option is C. And yes, she has enough pencils.

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Note that in question 28 above:

X = 56° (Alternative Angles)

Y = 124° (Angles in a straight line)

Z = 81° (Sum of angles in an irregular parallelogram).

in Question 29,
x = 126° (Co-interior angles and Bisector theorem).

Question 28: Note that the sum of angles in an irregular parallelogram always equal 360°. Since X and 56° are alternate angles and are therefore congruent, and Y and 56° are on the same line and therefore sum up to 180°, resulting in Y being equal to 124°, then we have three interior angles of an irregular parallelogram:

∠X = 56°

∠Y = 124°; and

∠99° (As given), which is co-interior with ∠Z

Thus whether by the Co-interior principle where two co-interior angels sum up to 180° or by sum of angles in an irregular parallelogram, we will still obtain a result where:

∠Z = 81°. That is

360° = 56 + 124 + 99 + ∠Z

∠Z = 360 - (56 + 124 + 99)
∠Z = 81°

OR

Using the Co-Interior angles theorem, we can state that:

∠Z = 180 - 99
∠Z = 81°

Question 29:
Recall that an angle bisector of a triangle's angle divides the opposing side into two portions that are proportionate to the triangle's other two sides, according to the angle bisector theorem.

Thus, we can state that 27° is half of the angle whose Co-interior is x.

Thus ∠x = 180 - (27*2)

∠x = 180 -54
∠x = 126°


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Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3  transformed .

Mathematics includes the study of numbers, various variable, the natural reality, architecture, and both actual and hypothetical locations. A function is a visual representation of the relationship between the number of inputs and the corresponding outputs for each. Simply explained, a function range is a collection of inputs that, whenever combined, result in a different output by each input. Every function is assigned a city, county, or scope, sometimes known as a realm. The letter f is frequently used to denote functions (x).

Here,

Given :

=>  f(x) = log x

=> g(x) = log (x) - 3

So , it is transformed as logx = f(x)

it is transformed as :

=> g(x) = f(x) - 3

Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3  transformed .

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The car can travel 528 miles on a one full tank gas that averages 44 miles per gallon.

In mathematics, the central value of a set of data is expressed as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data.

Given that, Juanita has a hybrid car that averages 44 miles per gallon.

Her car has a 12-gallon tank.

So, the car travels:

(12) (44) = 528 miles.

Hence, the car can travel 528 miles on a one full tank gas.

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Answer: 4 and 1

Step-by-step explanation:

the expression 4x² + x + 3.
the coefficients are 4 and 1
so the answer is 4 and 1
because 4 is the quadratic coefficient and 1 is the primary term coefficent

Answer:

3 terms

4 and 1 coefficients

Step-by-step explanation:

Answer:

Dina =z gerbils

Jacki =4z

W = 4z

Independent:z

Dependeny:w

Step-by-step explanation:

I think it's right

Answer:

A. 1436.03 ft³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(7 ft)³

V = 1436.03 ft³

The slope intercept form of the equation is given as y = 0.75x + 1.75

The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope (m) is the cost per taco, which is $0.75. The y-intercept (b) is the cost of the drink, which is $1.75.

So, the equation that represents the total cost (y) for x number of tacos and a drink is:

y = 0.75x + 1.75

This equation states that for every taco ordered (x), the cost will increase by $0.75, and the minimum cost will always be $1.75 for the drink.

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On solving the provided question, we can say that all the factors of 30 on the hundred chart are = 1,2,3,5,6,10,15,30 and mistake he made was he didn't mark = 2,6,10,30

In mathematics, the integer m serves as the divisor (also known as factor n) of an integer n, which may be multiplied by the integers to get n. We may also state that n in this situation is a multiple of m. A number without a residue that divides another number is said to be a factor. In other words, if you multiply two integers to create a product, the numbers you multiply are factors of the product since the result is divisible by the numbers you multiply. Factors can be found using either division or multiplication.

all the factors of 30 on the hundred chart are = 1,2,3,5,6,10,15,30

mistake he made was he didn't mark = 2,6,10,30

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Answer:

Below

Step-by-step explanation:

He wants to DIVIDE the 3/4 gallon into 5 bux

 so divide 3/4 by 5

3/4  /  5 = (3/4) / (5/1) = 3/4 * 1/5 = (3*1) / ( 5*4) = 3/20 gallon per bux

The amount of paint that Ralph store in each container is 3/20 gallon.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Total amount of paint that Ralph has = 3/4 gallon

He wants to store all of the paint equally among 5 containers.

If the paint is stored in 5 containers,

Amount of paint in each container = 3/4 ÷ 5

                                                         = 3/4 × 1/5

                                                         = 3/20

Hence 3/20 gallon of paint is stored in each container.

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y=4 is the minimum y-value after which the exponential function will always be greater than the linear function.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

From the graph we can see that in the interval [0,1] the value of y is less than 1.

In the interval [1,2] the value of y value is 2 to 4.

In the interval [2,infinity) the graph is going up, and the value of y is greater than or equal to 4.

Therefore, the graph going up after y=4 above the line.

Therefore, the minimum y-value is 4 after which the exponential function will always be greater than the linear function.

Hence, y=4 is the minimum y-value after which the exponential function will always be greater than the linear function.

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The median wage of workers in the firm is given as follows:

Rs 2.37 per hour.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

From the data-set in this problem, the median is obtained as follows:

Hence the median class is:

Rs 2.25 to Rs 2.49 per hour.

The median is the middle value of the class, hence:

(2.25 + 2.49)/2 = Rs 2.37 per hour.

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The dimensions for a square that has a perimeter of 14 units and area or 49 units² will be 7 units by 7 units.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

In this situation, the square has a perimeter of 14 units and area or 49 units². The dimensions will be 7 units by 7 units.

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Answer:

He is incorrect

Step-by-step explanation:

7n = 49

Isolate variable "n" by dividing both sides by 7:

n = 7

Since doing this step makes n to equal 7, [Ben is incorrect to say that n = 6]

There are 50 hundredths in the fraction 5/10.

In Mathematics, a place value can be defined as a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:

From the information provided about the numerical value, we have:

5/10 = 0.5.

Note: 1 hundredth is equal to 1/100 = 0.01.

Therefore, by dividing 0.5 by 0.01 we have:

Number of hundredths = 0.5/0.01 = 50.

In conclusion, 5 tenths or 5/10 is equivalent to 50 hundredths.

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The shortest distance  from A to B in the figure is length AB, So Option A is correct

The smallest (straight line) distance between a body's beginning position and its final location—represented by an arrow pointing from starting position to final position—is referred to as a body's displacement as it moves from one position to another. Being a vector quantity, it.

Given that,

A quadrilateral figure ABCD

and it has one diagonal BD

Shortest distance from A to B  =?

Possible paths, For A to B

1. Directly A to B

Distance = AB

2. A to D then D to B

Distance =  AD + DB

3.   A to D then D to C and then C to A

Distance =  AD + DC + CA

It can be seen that distance covered is lesser in case 1 in compare to case 2 & 3

Hence, the shortest distance is  AB

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Answer:

d. x = 7

Step-by-step explanation:

To find the value of x, you can cross multiply the fractions to get 32 * x = 8 * 28, then simplify:

32x = 224

x = 7.

Answer:

Thus, the equation of line for point (-1, 2)  is y = x + 3.

Step-by-step explanation:

Answer:

The equation of the line is y = x + 3.

Step-by-step explanation:

A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.

y = mx + b

y = 1 * -1 + b

y = -1 + b

b = y + 1

b = 2 + 1

b = 3

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 7x^2-6 \qquad \begin{cases} x_1=4\\ x_2=b \end{cases}\implies \cfrac{f(b)-f(4)}{b - 4} \\\\\\ \cfrac{(7b^2-6)~~ - ~~(7(4)^2-6)}{b-4}\implies \cfrac{7b^2-6~~ - ~~(112-6)}{b-4} \implies \cfrac{7b^2-112}{b-4}[/tex]

[tex]\cfrac{7(b^2-16)}{b-4}\implies \cfrac{7(b^2-4^2)}{b-4}\implies \cfrac{7~~\begin{matrix} (b-4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(b+4)}{~~\begin{matrix} b-4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \boxed{7(b+4)}[/tex]

This expression gives the average rate of change of the function over the interval [4, b].

The average rate of change of a function on an interval is equal to the rise (change in the y-value) divided by the run (change in the x-value) over that interval.

For f(x) = 7x² - 6 on the interval [4, b], the average rate of change can be found by calculating the slope of the secant line connecting the points (4, f(4)) and (b, f(b)).

Therefore, the average rate of change of f(x) = 7x² - 6 on the interval [4, b] is:

(7b² - 6 - (7(4)² - 6)) / (b - 4) = (7b² - 28) / (b - 4)

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Solving the provided question, we can say that Using quadratic formula, x = 19 or x = 3; Sum of the 2 numbers = 3 + 19 = 22

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

Let x represent a number that is twice as far away from 5 than 17.

|x - 5| = 2|x - 17|

(x - 5)² = 4(x - 17)²

[tex]x^2 + 25 - 10x = 4(x^2 + 49 - 14x)\\x^2 + 25 - 10x = 4x^2 + 196 - 56x\\3x^2 - 46x + 171 = 0\\[/tex]

Using quadratic formula,

x = 19 or x = 3

Sum of the 2 numbers = 3 + 19 = 22

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The area of the rectangular closet is given by the equation A = 64 feet²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular closet be represented as A

Now , the equation will be

The area of 1 carpet square = 1 foot²

The number of rows = 4 rows

The number of carpet square in each row = 16 carpet squares

So , the total number of carpet squares in 4 rows = number of rows x number of carpet square in each row

Substituting the values in the equation , we get

The total number of carpet squares in 4 rows = 16 x 4 = 64 carpet squares

So , the area of 64 carpet squares = 64 x area of 1 carpet square

Substituting the values in the equation , we get

The area of the rectangular closet A = 64 feet²

Hence , the area of the rectangular floor is 64 feet²

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Lisa's remaining of her monthly income is $490. Her net worth is $142.980. Her saving ratio is 17%, liquidity ratio is 23% and Debt-to-asset ratio is 63%.

Based on the given data, we can construct Lisa's personal cash flow statement and personal balance sheet as:

Personal Cash Flow Statement

Cash Inflow:

Cash Outflow:

Debts:

Living expenses:

Total cash = $490

Personal Balance Sheet

Assets:

Total Assets = $383,140

Liabiities:

Total Liabilties = $240,160

Net worth = $142,980

Saving ratio can be calculated by assuming that the amount of Lisa's cash on bank is her saving. Then:

saving ratio = saving : net income

Saving ratio = cash in bank : net income

Saving ratio = $600 : $3,600

Saving ratio = 17%

Liquidity ratio is calculated by comparing Lisa's current assets with her net worth. Hence:
Liquidity ratio = Current assets : Net worth

Liquidity ratio = (Cash in bank + Car + Clothing owned + Furniture) : Net worth

Liquidity ratio = ($600 + $18,000 + $540 + $14,000) : $142,980

Liquidity ratio = 23%

Debt-to-asset ratio = Total Liabilities  : Total Assets

Debt-to-asset ratio = $383,140 : $240,160

Debt-to-asset ratio = 63%

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Answer: false

Step-by-step explanation: