Question 1-1
Barrett earns $15 per hour cutting grass and $10 per hour tutoring reading. In one month, Barrett needs to save at least $400 for a
new lawnmower but does not want to work more than 35 hours.
Part A: Let z represent the hours cutting grass and y represent the hours tutoring. Given z 20 and y ≥ 0, select all the inequalities
that represent the situation.

Answer:

[tex]a^{12} b^{4}[/tex]

Step-by-step explanation:

To simplify we will have to use the negative exponent rule and the power rule along with some algebra.

Negative Exponent Rule

[tex]a^{-b} =\frac{1}{a^b}[/tex]

Power Rule

[tex](a^b)^{c} =a^{bc}[/tex]

Given

[tex](a^{-4}b^{-1}c )^{2} (a^2bc)^{2}[/tex]

Rewrite [tex]a^{-4}[/tex] using negative exponent rule.

[tex](\frac{1}{a^{4}}* b^{-1}c )^{2} (a^2bc)^{2}[/tex]

Rewrite [tex]b^{-1}[/tex] using negative exponent rule.

[tex](\frac{1}{a^{4}}* \frac{1}{b}*c )^{2} (a^2bc)^{2}[/tex]

Simplify

[tex](\frac{c}{a^4b} )^{2} (a^2bc)^{2}[/tex]

Rewrite the base as its reciprocal.

[tex](\frac{a^4b}{c} )^{2} (a^2bc)^{2}[/tex]

Apply the power rule.

[tex]\frac{a^8b^2}{c^2} *(a^2bc)^{2}[/tex]

Apply the power rule.

[tex]\frac{a^8b^2}{c^2} *a^4b^2c^2[/tex]

Cancel the common factor of [tex]c^2[/tex].

[tex]a^8b^2 a^4b^2[/tex]

Apply the power rule.

[tex]a^{12} b^{4}[/tex]

Answer:

[tex]a^{12}\:b^{4}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(a^{-4}\:b^{-1}\:c\right)^{-2}\left(a^2\:b\:c\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies a^{(-4 \times -2)}\:b^{(-1 \times -2)}\:c^{-2}\:a^{(2 \times 2)}\:b^2\:c^2[/tex]

Simplify:

[tex]\implies a^{8}\:b^{2}\:c^{-2}\:a^{4}\:b^2\:c^2[/tex]

Collect like terms:

[tex]\implies a^{8}a^{4}\:b^{2}b^2\:c^{-2}c^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies a^{(8+4)}\:b^{(2+2)}\:c^{(-2+2)}[/tex]

Simplify:

[tex]\implies a^{12}\:b^{4}\:c^{0}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]

[tex]\implies a^{12}\:b^{4}(1)[/tex]

[tex]\implies a^{12}\:b^{4}[/tex]

You can get 3/8 from 13/8 by subtraction. The solution is 10 / 8

In order to get 3/8 from 13/8 we would have to carry out a subtraction of fractions.

That is we would have: 13/8 - 3/8

take the lcm of the denominator

[tex]\frac{13 - 3}{8}[/tex]

= 10 / 8

Hence when we take 3 / 8 from 13 / 8, the solution that we would have would be from subtraction. This is 10 / 8

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The population change for each period is given as follows:

Hence the average annual change for the period between 1970 and 1995 is given as follows:

7,932,000 people a year.

The population change over a period is given by the subtraction of the population at the end of the period by the population at the beginning of the period.

The population data for each year is given by the table on the image presented at the end of the answer.

Hence the changes are obtained as follows:

The change between 1970 and 1995 is of:

5.691 - 3.708 = 1.983 billion.

This period is composed by 25 years, hence the average annual change is of:

1.983/25 = 0.07932 billion people a year = 7,932,000 people a year.

The chart is given by the image presented at the end of the answer.

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The amount (present value) of a semi-annual coupon paid for a 3% bond with a face value of 80,000 which matures after 15 years is $80,000.

The price of a bond is its present value.

The present value can be determined as the discounted cash inflows.

In this situation, we can determine the present value of the bond using an online finance calculator as follows:

N (# of periods) = 30 (15 years x 2)

I/Y (Interest per year) = 3%

PMT (Periodic Payment) = $1,200

FV (Future Value) = $80,000

Results:

Present Value (PV) = $80,000.00

Sum of all periodic payments = $36,000.00

Total Interest = $36,000.00

Thus, the amount of the bond is $80,000.

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The solutions to the equation 4(x² − 5) − 1 = 3 are ±√6

From the question, we have the following parameters that can be used in our computation:

4(x 2−5)−1=3

Express properly

This gives

4(x² − 5) − 1 = 3

Subtract -1 from both sides of the equation

So, we have the following representation

4(x² − 5) = 4

Divide both sides by 4

This gives

x² − 5 = 1

Subtract -5 from both sides of the equation

So, we have the following representation

x² = 6

Take the square root of both sides

x = ±√6

Hence, the solution is ±√6

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Step-by-step explanation:

Let’s see … one division every 20 minutes? That would be like <grinding noise> three binary doublings per hour, right? Now for the tough part … three doublings per hour, for eight straight hours? <more grinding noises> … Is that even mathematically possible? After much thinking, I decide that the total number of binary doublings has to be in the neighborhood of no less than eight times three!

Would you believe that 224=16777216 ? While mathematically true, it is not the answer to the posted question… Since we started at 0 minutes, there are only 23 buddings inside eight hours … so the answer has to be 223=8388608 , right?

Wrong again, this time forgetting all about the newlybud bacteria generations, that all go on budding side by side of their ancestors …

Now that you’ve caught on to the basic idea, I leave it to you to figure out the real answer! Keep in mind that after 20 minutes, you have two budding bacteria to reckon with, for 440 minutes … after 40 minutes another two (for 420 minutes), and so on, down the line.

Hint: the answer still is not 16777216 …

Answer:

after 1 division,there is 3 cell

after 2 divisions,there is 9 cell.

after 3 divisions,there is 27 cell

The above data takes the form of Geometric sequence.

3,9,27......,last term

here,Common ratio(r)=9/3=27/9=3

and,first term(a)=3

Let, n be the no.of divisions.

then, n=8 hrs/20 min=480 min/20min=24

Now,from the G.S,

last term=ar^n-1

=3×3^24-1

=9²³

Hence,9²³ organisms will there be after 8 hours

It can be written as 8.86293812×10²¹ as well

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Answer:

there is not enough info but i think it would be (5,11)

Step-by-step explanation:

divide

Answer:

[tex]y=\dfrac{11}{4}x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Choose two (x, y) points from the given table:

Substitute them into the slope formula:

[tex]\implies \dfrac{22-11}{8-4}=\dfrac{11}{4}[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute point (4, 11) and the found slope into the point-slope formula and rearrange to slope-intercept form:

[tex]\implies y-11=\dfrac{11}{4}(x-4)[/tex]

[tex]\implies y-11=\dfrac{11}{4}x-11[/tex]

[tex]\implies y=\dfrac{11}{4}x[/tex]

Answer:

3.5 miles per hours

Step-by-step explanation:

7/2 =3.5

Answer:

a₁₂₀ = 64.5 , S₁₂₀ = 4170

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 5 and d = 0.5 , then

a₁₂₀ = 5 + (119 × 0.5) = 5 + 59.5 = 64.5

---------------------------------------------------------

the sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ] , then

S₁₂₀ = [tex]\frac{120}{2}[/tex] [ (2 × 5) + (119 × 0.5) ]

      = 60(10 + 59.5)

      = 60 × 69.5

      = 4170

Answer:

11.1 and 38.9

Step-by-step explanation:

16x + 18 (1-x) = 16.89

2x = 1.11

x = 0.222

0.222 x 50 = 11.1

50-11.1 = 38.9

Answer:

x ≥ 10

Step-by-step explanation:

Total Points = 50 + 3.5x
Total Points ≥ 85
50 + 3.5x ≥ 85
3.5x ≥ 35

then divide both sides by 3.5

x ≥ 10

Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.

Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.

The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.

Now we have [tex]x1[/tex]=2    [tex]x2[/tex]=-11

then quadratic function will be

(x+2) (x+11)

[tex]x^2+2x+11x+22[/tex]

[tex]x^2+13x +22[/tex]

this is our required quadratic equation.

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Complete question is: Write a quadratic function f whose zeros are 2 and -13.

Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.

Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.

The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.

Now we have x¹ = 2    x² = -11

then quadratic function will be

(x+2) (x+11)

x² + 2x + 11x + 22

x² + 13x + 22

This is our required quadratic equation.

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The complete question is-

Write a quadratic function f whose zeros are 2 and -13.

The center of the circle is (-10,4) and the radius is 10.

The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The equation of the circle is,

( x - h )² + ( y - k )² = r²

(x+10)² + (y−4)² = 100

(x+10)² + (y−4)² = 10²

Compare the equations and find the center and radius,

Center = ( h,k) = ( -10,4)

Radius = r = 10

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According to the given conditions in the question, the movie did finish at 8:15pm exactly.

The average movie length of movies in hollywood is  around 120 -130 mins per movie. However this fact can vary as per the genre and type of the film.

The movie business, usually referred to as the film industry, has a big influence on the economy. For those involved in the industry, such as performers, directors, camera operators, sound technicians, special effects designers, and theater owners, the creation and distribution of films can result in jobs and financial gain.

The local economy can benefit from the tourists that movies can bring to an area where a movie is being made or is located. The money made by persons employed in the film business is likely to be spent on other goods and services, stimulating extra economic activity. As a result, the film industry may also have a "multiplier impact" on the economy.

So according to the question, the movie itself started at 6:15 pm, and it lasted for 105 mins , also adding the time for commercials of 9 mins and 6 mins , which ultimately added 15 more mins, the total screen time would be ,

105 + 15 = 120 mins

Which is equal to 2 hrs, so the movie finished at 8:15 pm.

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Using place value along with division facts in a division equation, helps in dividing larger numbers easily. Place value counters and tape diagrams are often used to represent division using place value.

What is division?

With the arithmetic operation of division, we can divide a collection of items into equal pieces. Typically, it is represented by the symbol "÷".

The bigger amount that is divided into equal halves is called the dividend.

The number of groups that divide the payout is known as the divisor. Following division, the result is the quotient.

The value of a digit in a number is determined by its place in the number, or place value.

Divide larger numbers simply by applying place value and division facts in a division equation. Place value division is frequently shown using tape diagrams and place value counters.

Example - 4 ÷ 2 = 2

In the first equation, the digits are 4 and 2. We can write it as 4 ones ÷ 2 ones = 2 ones (using the division fact).

Example - 40 ÷ 20 = 2

For the second equation, the digits are the same, but a zero has been added after 4, and the quotient thus has one zero at the end. So, we can write it as 4 tens ÷ 2 ones = 2 tens (using place value and the division fact).

Example - 400 ÷ 200 = 2

Similarly, for the third division equation, the same digits are present, but the number of zeros has increased. We are dividing 4 hundreds ÷ 2 ones = 2 hundreds (using place value and the division fact).

Therefore, place value blocks help in division for making it simpler.

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Therefore , As a result, h = 2 is the answer to the equation in the given question.

An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra is the fundamental foundation of mathematics.

Here,

The formula is as follows: 6x + 18 = h(3x + 9)

To ensure that the expression has an unlimited number of answers, h's value must be determined.

Take the expression now and continue solving it.

=> 6x + 18 = h(3x + 9)

=>3hx + 9h= 6x +8

The expression will have an endless number of solutions if the coefficients of the left-hand side and the right-hand side are equal.

Therefore, 3h = 6 and h = 2

As a result, h = 2 is the answer to the equation in the given question.

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The next decimal number should be changed to hexadecimal. Your final response may contain up to six fractional digits. In decimal 386210, subscript 10 to F16.

F16 is 001000011000.1111. 218. F716 is 001000011000.111101112. 710 = (h0)16 = 716 is how the hexadecimal number is represented. It is necessary to add a 1 to the left and modify the number for both to 0. In base-2, the numeral 15 is represented as 1111, and the number 16 is represented as 10000. The greatest value in base-16 is the letter F, in a similar vein. such that 10 is the new value.

Binary 10 equals 1010, thus. Dividing 10 by 2 successively until the quotient equals 0 will yield the decimal to binary equivalent. By writing the remainder in each division step from bottom to top, it is possible to determine the binary equivalent.Base-16 is the definition given to hexadecimal. There are many powers of 16 in each place value in the number. The hexadecimal numbers are: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. 10 through 15 are represented, accordingly, by the letters A through F.

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Answer:

i dont understand this question but i think maybe 21

Step-by-step explanation:

30-9 =21

Answer:

21

Step-by-step explanation:

Answer:

5-3=2m

3x2=6m^2

Step-by-step explanation:

I can’t explain

LETTER B I DON’T KNOW THE ANSWER

Answer:

1 circle

Step-by-step explanation:

Angle bisectors will meet at one specific point. Radius taken from centre to one side of triangle is the radius of the incircle. There can be no other configuration to form an incircle so only one incircle can be inscribed in a triangle.

Answers:  

Explanation:

The angles TSO and QRP are marked with the same double angle arc markers. This signifies they are congruent or the same measure. For example, they both could be 30 degrees each.

The naming "angle TSO" is the same as saying "angle OST". The order of the letters does not matter as long as point S is in the middle. Similarly, saying "angle QRP" is the same as "angle PRQ".

The total number of times social media browsers have been showed your content.

A general, but simplified earned media value formula is: EMV = impressions x cost per 1000 impressions x adjustable variable. The adjustable variable can be anything you are looking to track like engagement or impressions.

Simplifying

22 = 2(x + 8)

Reorder the terms:

22 = 2(8 + x)

22 = (8 * 2 + x * 2)

22 = (16 + 2x)

Solving

22 = 16 + 2x

Solving for variable ‘x’.

Move all terms containing x to the left, all other terms to the right.

Add ‘-2x’ to each side of the equation.

22 + -2x = 16 + 2x + -2x

Combine like terms: 2x + -2x = 0

22 + -2x = 16 + 0

22 + -2x = 16

Add ‘-22’ to each side of the equation.

22 + -22 + -2x = 16 + -22

Combine like terms: 22 + -22 = 0

0 + -2x = 16 + -22

-2x = 16 + -22

Combine like terms: 16 + -22 = -6

-2x = -6

Divide each side by ‘-2’.

X = 3

Simplifying

X = 3

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Answer: To compare the level of support for the new after-school club between teachers and students, we can calculate the percentage of individuals in each group that responded "yes" to the proposal.

For teachers: 13 out of 20 is equivalent to 13/20 = 0.65 or 65%

For students: 37 out of 50 is equivalent to 37/50 = 0.74 or 74%

Based on the percentage of individuals in each group that responded "yes," we can see that students are more in favor of the new after-school club than teachers. 74% of students responded "yes" to the proposal, while only 65% of teachers responded "yes."

It's worth mentioning that it's important to keep in mind that this comparison is based on the sample size of teachers and students that responded to the survey and not the whole population, also if the sample size isn't representative of the population and not randomly selected it can't be generalized.

Step-by-step explanation:

Answer:

9.6 hours

Step-by-step explanation:

12×8 would equal the amount of hours it takes to complete the job in 12 days so you simply divide that number by 10 which will give you 9.6h

Answer:

6.67 hour per day

Step-by-step explanation:

If

=8 hours a day = 12 days

then

= ? = 10 days

= 10/12 × 8hours per

= 6.67 hours per day.

The expression in the simplest form is -90p - 102

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

We are given an expression as 9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)

Then Rewrite in simplest terms:

9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)

2 [ 9(-6p-4)+3(3p-5) ]

Solve the like terms;

2 [-54p - 36 + 9p - 15]

2 [-54p + 9p - 15 -  36]

2 x ( -45p - 51)

-90p - 102

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Answer: 27 boys

Step-by-step explanation:

There is a rule in math, what you do to one side, you do to the other.

So in this case the ration is 3:5

                                             ?:45

As you can see, they multiplied 5 by 9 to get 45, remember the rule, so we do the same.

3 times 9 is 27, so 27 boys

the simplest form of the given expression is 3n+2.

What is polynomials?

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

-n + (-4) - (-4n) + 6

= -n + (-4) + 4n + 6

= 3n -4 +6

= 3n+2

Hence the simplest form of the given expression is 3n+2.

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If we use 2 liters of OJ, you will need to change the recipe and use:

We know that a recipe calls for 6 liters of OJ, 3 liters of grape juice and 9.5 liters of ice cream.

If instead we use 2 liters of OJ, then the ratio of the recipe that we use is given by the quotient below:

2L/6L = 1/3

So we will just use 1/3 of each of the amounts that the recipe calls, we will se:

(1/3)*3 liters of grape juice = 1 liter of grape juice.

(1/3)*9.5 liters of water = 3.2 liters of water.

These are the amounts that you need to use.

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On solving the provided question we can say that from data provided by the graph, we have a straight line, which means that the coordinates are equal. so the equation will be x = y = > x-y = 0

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle.

from data provided by the graphs,

we have a straight line,

which means that the coordinates are equal.

so the equation will be x = y

x-y = 0

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