Unit 4 Lesson 10 MODIFIED Inequalities:

You are working a summer job as a retail salesperson at Macy’s. You earn $230 per week plus a commission of 8% of your sales. This week, you need to earn $510. You will write and solve an INEQUALITY to determine how to meet your goal.

1): Give the decimal form of 8%. __________________________

2): If you make $945 in sales, how much will you make from your 8% commission?

Show your work and circle your solution.


3): Create an expression representing how much you will make in one week if you sell

x amount of sales.


4): Create an inequality using the expression in problem 3 to find how much you need

to sell at a MINIMUM to make your goal.

Answer:

Options A and D.

Step-by-step explanation:

To check the identities we have to check each option given.

A. tan(x - π) = tanx

We take left hand side (L.H.S.) of the equation.

tan(π - x) = tanx [ since we know tan(π ± x) = tanx ]

So L.H.S. = R.H.S.

It's an identity.

B. sin(x + y) + sin(x - y) = 2cosx siny

We take L.H.S. first

sin(x + y) + sin(x - y)

= sinx coxy + siny cosx + sinx cosy - cosx siny

= 2sinx cosy ≠ R.H.S.

Option B is not an identity.

C. cos(x + y) - cos(x - y) = 2cosx cosy

We take L.H.S. of the equation.

cos(x + y) - cos(x - y) = cosx cosy - sinx siny - (cosx cosy + sinx siny)

= -2sinx siny ≠ R.H.S.

Therefore, option C is not an identity.

D. cos(x + y) + cos(x - y) = 2cosx cosy

We take L.H.S. of the equation.

cos(x + y) + cos(x - y) = cosx cosy - sinx siny + cosx cosy + sinx siny

                                  = 2cosx cosy = R.H.S.

Therefore, option D is an identity.

Options A and D are the identities.

Answer:

24

Step-by-step explanation:

⇒The question is on probability, to be specific its about counting principal

⇒You need to understand the counting rule where we multiply events together to get the total number of outcomes .

⇒In general  if we have an event t and another event s the total outcome for the events is given by t×s

⇒In this question  you multiply the number of ways we can make the different sandwiches

Given

meat=3 choices

cheese=2 choices

bread=4 choices

Outcomes= 3×2×4=24

The  total number of sandwiches that can be made = 24

There are 24 different sandwiches that can be made with 3 choices of meat, 2 choices of cheese, and 4 choices of bread.

The subject of this question is related to combinatorics, a topic in mathematics. The question asks, 'How many different sandwiches with one meat, one cheese, and one type of bread can be made if there are 3 choices of meat, 2 choices of cheese, and 4 choices of bread?'.

To find the answer, you would use the fundamental principle of counting which states that if there are n ways to do one thing and m ways to do another thing, then there are n * m total ways to perform both actions. In this case, we multiply the number of options together:

Hence, the total number of different sandwiches that can be made is given by 3 (choices of meat) * 2 (choices of cheese) * 4 (choices of bread), which equals 24 different sandwiches.

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Answer:

$107.50

Step-by-step explanation:

$3.50 = 1 STUDENT

$5.00 = 1 ADULT

TWENTY FIVE STUDENTS = $3.50 × 25 = $87.50

FOUR ADULTS (ONE TEACHER AND THREE PARENTS) = $5.00 × 4 = $20.00

TOTAL COST = $87.50 + $20.00 = $107.50

Answer:

2 1/2 months by the 3rd month

Step-by-step explanation:

Answer:

Kylee will receive the table in 24 months.

Step-by-step explanation:

Layaway is a type of purchasing method where the buyer places a deposit on an item to secure it or lay it aside. The buyer will pick up the item later when he pays the full balance.

This system allows the buyer to make smaller payments on the item until the full amount has been paid off.

So, if Kylee put the kitchen table on layaway, and agrees to pay $48 a month starting next month for 24 months. She will get the table in 24 months after completing her payment.

Answer:

x = ±11

Step-by-step explanation:

x^2 = 121

Take the square root of each side

sqrt(x^2) = sqrt(121)

x = ±11

Answer:

interest earned= 1853.98

the future value of an annuity= 2453.98

Step-by-step explanation:

Given Data:

Interest rate= 9%

time,t = 16 years

Semi-Annual payment, P= 600

n= 2 as Semi-Annual

At the end of 16 years, final investment A= ?

As per the interest formula for compounded interest

A= P(1+r/n)^nt

Putting the values in above equation

= 600(1+0.09/2)^32

= 2453.98

Interest earned = A-P

                          = 2453.98-600

                          = 1853.98 !

Answer:

A. Monday

Step-by-step explanation:

The solution to this problem can be found by creating a table

If Day 1 was Monday, then

Mon    Tues      Wed      Thur    Fri      Sat      Sun

1              2           3             4        5        6          7

8             9           10           11        12       13        14

...............

We can see that the multiples of 7 are falling on Sundays so we will divide 36 by 7 to get the closest multiple of 7 to 36.

The closest multiple of 7 near 36 is 35 so Day 35th will fall on Sunday and Day 36 will be on Monday

Hence, Option A is the correct answer..

Answer:

A. Monday

Step-by-step explanation:

The solution to this problem can be found by creating a table

If Day 1 was Monday, then

Mon    Tues      Wed      Thur    Fri      Sat      Sun

1              2           3             4        5        6          7

8             9           10           11        12       13        14

...............

We can see that the multiples of 7 are falling on Sundays so we will divide 36 by 7 to get the closest multiple of 7 to 36.

The closest multiple of 7 near 36 is 35 so Day 35th will fall on Sunday and Day 36 will be on Monday

Hence, Option A is the correct answer..

Answer:

Step-by-step explanation: (5,-2)

Answer:

(5,-2)

Step-by-step explanation:

Answer:

(5, - 9)

Step-by-step explanation:

Given

f(x) = (x - 8)(x - 2) ← in factored form

Find the zeros by equating f(x) to zero, that is

(x - 8)(x - 2) = 0

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x - 2 = 0 ⇒ x = 2

The vertex lies on the axis of symmetry which is located at the midpoint of the zeros, hence

[tex]x_{vertex}[/tex] = [tex]\frac{8+2}{2}[/tex] = 5

Substitute x = 5 into f(x) for corresponding y- coordinate

f(5) = (5 - 8)(5 - 2) = (- 3)(3) = - 9

vertex = (5, - 9)

Answer: (5,-9)

Step-by-step explanation:

Make the multiplication indicated:

[tex]f(x) = x^2-2x-8x+16[/tex]

Add the like terms:

[tex]f(x) = x^2-10x+16[/tex]

Now find the x-coordinate of the vertex with this formula:

[tex]x=\frac{-b}{2a}[/tex]

In this case:

[tex]b=-10\\a=1[/tex]

Then:

[tex]x=\frac{-(-10)}{2(1)}=5[/tex]

Rewrite the expression with [tex]f(x)=y[/tex]

[tex]y = x^2-10x+16[/tex]

Now substitute [tex]x=5[/tex] into the function to find the y-coordinate of the vertex:

[tex]y = (5)^2-10(5)+16[/tex]

[tex]y =-9[/tex]

Therefore, the vertex is:

(5,-9)

Answer:

Part 1) The center is the point [tex](20,0.05)[/tex]

Part 2) The radius is equal to [tex]r=9\ units[/tex]

Step-by-step explanation:

we know that

The equation of the circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

(h,k) is the center of the circle

r is the radius of the circle

In this problem we have

[tex](x-20)^{2}+(y-0.05)^{2}=81[/tex]

[tex](x-20)^{2}+(y-0.05)^{2}=9^{2}[/tex]

so

[tex](h,k)=(20,0.05)[/tex]

[tex]r=9\ units[/tex]

Answer:   $65 dollars to johnson plumbing

Step-by-step explanation:

she would owe johnson plumbing 40 for the check plus the returned check fee of 25

$40 + $25 = $65 to johnson plumbing

plus whatever her bank charged ( i did not see that amount listed)

Final answer:

Sarah Saver must have enough money to cover the original $40 check, the $25 fee from Johnson Plumbing, and any additional bank charges. The expression representing the total amount needed is $40 + $25 + B, where B represents the bank's charges.

Explanation:

The student is asking about the total amount Sarah Saver must have to balance her debts after writing a $40 check that was returned with additional charges and a $25 fee for the returned check from the company. To find the total amount Sarah owes, you need to sum the amount of the check and the additional fees charged by her bank and Johnson Plumbing.

Add the original check amount: $40.

Add the fee charged by Johnson Plumbing for the returned check: $25.

Add any additional charges by her bank (the question doesn't specify an amount, so let's denote this amount as B).

The total amount Sarah needs to settle her debts will be $40 + $25 + B.

Therefore, without knowing the specific bank charges, we cannot provide a numerical answer, but the expression $40 + $25 + B represents the total amount Sarah needs to cover her debts, with B being the additional bank charges.

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=9\\ h=13 \end{cases}\implies V=\cfrac{\pi (9)^2(13)}{3} \\\\\\ V=351\pi \implies V\approx 1102.70[/tex]

"Something" is a variable. A variable is a number that we do not know. The variable will be x.

5,652 is the total; the total is 12 plus x.

5652 = 12 + x

Subtract 12 from each side

5652 - 12 = 12 + x - 12

5640 = x

change it around

x = 5640.

5640 is your answer

Answer:0.16091954023

Step-by-step explanation:

Answer: Based on the calculator it’s...

0.16091954023

Step-by-step explanation:

Answer:

Step-by-step explanation:

Final answer:

The probability that a given event does not occur in any of the trials when an experiment is repeated n times is calculated using the formula (1 - P(A))^n, where P(A) is the probability of the event occurring in a single trial.

Explanation:

The question is about finding the probability that a given event does not occur in any of the trials when an experiment is repeated n times. Let's denote the probability of the event occurring as P(A) and the probability of the event not occurring as P(~A). The probability that an event does not occur in a single trial is 1 - P(A). Therefore, if the experiment is repeated n times independently, the probability that the event does not occur in any of these trials is given by (1 - P(A))^n. This formula arises from the principle that for independent events, the probability of both events A and B occurring is the product of their individual probabilities, P(A) and P(B). Since each trial is independent, and we are looking for the event not happening across all n trials, we multiply the probability of it not happening in one trial by itself n times.

Answer:

Divide by 6

Step-by-step explanation:

The reverse or inverse of multiply by 6 is divide by 6.

Answer:

You would need to sell 100 of each

Step-by-step explanation:

$5 times 100 people equals $500.

$10 times 100 people equals $1,000.

$1,000+$500=1,500

I hope this helped!

Answer:

100 each

Step-by-step explanation:

All you must do to find out how much is with held from his paycheck is

solve this

x amount of dollars

÷                                     = 4.63%

$895

To solve, multiply $895 by 0.0463 (the equivalent of 4.63%)

You get:  $41 . 43

That is how much is withheld from Wes' check

The amount of tax withheld from his paychecks is $41.43

Percentage is defined as a given part or amount in every hundred

Income tax rate given in the question = 4.63%

Weekly income given in the question = $895

Tax deducted = (4.63 / 100) * 895 = $41.43

Hence, $41.43 will be deducted from his paychecks every week.

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Answer:

The answers are on the image shown.

remember that all the angles of a triangle add up to 180

Step-by-step explanation:

hope this helps

Answer:

The measure of angle B is 54°. The measure of angle A is 51°. The measure of angle AFE is 47°.

Step-by-step explanation:

According to exterior angle theorem: It a triangle

Exterior angle = Sum of opposite interior angles

In triangle BED,

[tex]\angle AEF=\angle B+\angle D[/tex]

[tex]82=\angle B+28[/tex]

[tex]82-28=\angle B[/tex]

[tex]54=\angle B[/tex]

The measure of angle B is 54°.

In triangle ABC,

[tex]\angle ACD=\angle A+\angle B[/tex]

[tex]105=\angle A+54[/tex]

[tex]105-54=\angle A[/tex]

[tex]51=\angle A[/tex]

The measure of angle A is 51°.

In triangle AEF,

Using angle sum property,

[tex]\angle A+\angle E+\angle AFE=180[/tex]

[tex]51+82+\angle AFE=180[/tex]

[tex]133+\angle AFE=180[/tex]

[tex]\angle AFE=180-133[/tex]

[tex]\angle AFE=47[/tex]

Therefore the measure of angle AFE is 47°.

Answer:  75%

Step-by-step explanation:

32 dollars times 75% = 24

32 - 24 = $8

The Discount is of amount $32.

The discount is equivalent to the difference between the purchase price and the par value. A discount is a decrease or deduction in a product's cost price.

Discount = Original price – Sale price.

We have,

Original price: $32

Sale price: $8

So, Discount Price = Original price - Sale price

                               = 32 - 8

                               = $24

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Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x----> the time in months

y ----> the total inventory of the warehouse

we know that

The linear equation that represent this situation is equal to

[tex]y=3,000x+6,000[/tex]

using a graphing tool

see the attached figure

Answer: Guessing this is off the test.

The graph with

6

12

18

21

30 should be correct.

Step-by-step explanation:

Answer:

The inequality x3 − 14x2 + 48x − 1,680 ≤ 0 can be used to find pool’s length.

⇒The water level in the pool cannot exceed 14 feet.

Step-by-step explanation:

The question is on inequalities

Given;

Length= x ft

depth= x-6  ft

Width= x-8 ft

volume ≤ 1680 ft³

Forming the inequality to find length x of the pool

Volume= base area × depth

base area × depth ≤ volume

x(x-8) × (x-6) = 1680

(x²-8x )(x-6) = 1680

x(x²-8x) -6 (x²-8x)=1680

x³-8x²-6x²+48x=1680

x³-14x²+48x=1680

x³-14x²+48x-1680 ≤ 0

⇒The water level in the pool cannot exceed 14 feet...why?

taking the value of x at maximum to be 17 according to the graph, then maximum depth will be;

d=x-6 = 17-6=11 ft

⇒11 ft is less than 14ft

Answer:

0.028

Step-by-step explanation:

0.08 Is Bigger Than 0.028

Answer:

Domain = All non-negative numbers; Range = All real numbers greater than or equal to 49; (1, 50)

Step-by-step explanation:

Answer:

Domain = all real number greater than or equal to 49

Range=all non- negative numbers

point=(50,1)

Step-by-step explanation:

The graph of q(x)=x-49

domain is the collection of numbers which assign for x in the function q(x)=x-49

therefore domain is the collection pf real number which is greater than or equal to 49 .

Range is the collection of numbers whic is obtained after aasignig value of x in the function q(x)=x-49

hence, range is the collection of non negative numbers which is obtained after putting the value of x in the given function  q(x)=x-49

when we put x=50 in q(x)=x-49 then we obtain 1

hence, the poin is (50,1) on the given graph.

4/3 I hope this helps

Answer:

[tex]\boxed{\text{101 fl oz}}[/tex]

Step-by-step explanation:

Step 1. Convert litres to millilitres

[tex]\text{V} = \text{3 L}  \times \dfrac{\text{1000 mL}}{\text{1 L}} = \text{3000 mL}[/tex]

Step 2.Convert millilitres to fluid ounces

[tex]\text{v} = \text{3000 mL} \times \dfrac{\text{1 fl oz}}{\text{29.6 mL}} = \boxed{\textbf{101 fl oz}}[/tex]

Distribute sum groups

a(2a^2 - 5a - 2) - 2(2a^2 - 5a - 2)

Expand

2a^3 - 5a^2 - 2a - (4a^2 - 10a - 4)

Simplify brackets

2a^3 - 5a^2 - 2a - 4a^2 + 10a + 4

Collect like terms

2a^3 + (-5a^2 - 4a^2) + (- 2a + 10a) + 4

Simplify

= 2a^3 - 9a^2 + 8a + 4

Answer:

14 inches long

Step-by-step explanation:

Answer:

14 inches long

Step-by-step explanation:

119 square inches long

Answer:

119

Step-by-step explanation:

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