2. Gwen uses 3 teaspoons of sweetener for every 5 cups of iced tea. How many teaspoons of sweetener should she
add to 30 cups of iced tea if she wants the same flavor?
A. 9
B. 18
C. 28
D. 50

Answer:

$170.80

Step-by-step explanation:

Since it's $4.88 per yard, you could times that by 35, because she bought 35 yards of fencing.

Equation:

4.88(35)

   or

4.88x   x=35

I hope this helped! <3

The time taken by Vijay's family to drive on the second day is 5.5 hours.

What is Distance?

Distance is the total movement of an object without any regard to direction.

Given that;

Vijay's family house is 544 miles from the resort.

Vijay's family plan to stop and spend the night at a hotel after 3 hours of driving.

Average speed = 64 miles per hour.

Now, For 3 hours of driving at an average speed of 64 miles per hour, the distance covered is,

⇒ d = 64 x 3 = 192 miles

And, Remaining distance for the second day is,

⇒ 544 - 192 = 352 miles

Hence, Time taken for distance 352 miles second day is,

T = 352 / 64 = 5.5 hours

So, The time taken by Vijay's family to drive on the second day is 5.5 hours.

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9x+3y=18 and 5x+2y=10.75

where x is price of 1 cookie and

y is price of 1 brownie.

steps for writing  Systems of Linear Equations from Word Problems:

Savannah and Serenity were goes to the bakery for purchasing some cookies and brownies .

We have to write a system of linear equations for the given condition .

Let the cost of 1 cookie be  $x and

cost of 1 brownie be  $y

Savannah bought 9 cookies and 3 brownies at  $18

so, linear equation for this situation is

9x+3y=18

Serenity bought 5 cookies and2 brownies at  $10.75

so, linear equation for this situation is

5x+2y=10.75

Hence, System of equations for the given situation is

9x+3y=18 and

5x+2y=10.75

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In Compound inequality the value of the x is 1/14 < x and 2/3≤ x.

According to the statement

We have to find that the value of the compound inequality.

So, For this purpose, we know that the

A compound inequality consists of two inequalities that are joined together by the word "and" or the word "or".

From the given information:

The equations are:

1/2x -4< 3 and 7≤ 3x +5

Now solve these equations then

1/2x -4< 3

1/2x < 3+4

1/2x < 7

1 < 14x

The value becomes 1/14 < x.

And then take second equation:

7≤ 3x +5

7-5 ≤ 3x

2≤ 3x

The value becomes 2/3≤ x.

So, In Compound inequality the value of the x is 1/14 < x and 2/3≤ x.

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The amount invested at each rate is $30,000 at 4%, and $2000 at 6%.

Given that;

Larry Mitchell invested part of his $32,000 advance at 4% annual simple interest and the rest at 6% annual simple interest.

If his total yearly interest from both accounts was $1,340.

To find;

The amount invested at each rate.

Let x is the amount at 4%, therefore the amount at 6% is 32000 - x.

The total interest is:

0.04x + 0.06(32000 - x) = 1320

0.04x - 0.06x + 1920 = 1320

0.02x = 1920 - 1320

0.02x = 600

x = 600/0.02

x = 30,000

The amount at 6% is:

$32,000 - $30,000 = $2000

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Given Expression

[tex]9v^2-1=-77[/tex]

Step-By-Step Process.

________________

1. Add 1 to both sides of the equation.

[tex]9v^2-1+1=-77+1[/tex]

________________

2. Simplify.

[tex]9v^2=-76[/tex]

________________

3. Divide both sides by 9.

[tex]\frac{9v^2}{9} =\frac{-76}{9}[/tex]

________________

4. Simplify.

[tex]v^2=-\frac{76}{9}[/tex]

For [tex]x^2=f(a)[/tex] the solutions are [tex]x=\sqrt{f(a),} - \sqrt{f(a)} \\[/tex].

[tex]v=\sqrt{-\frac{76}{9} }, v=-\sqrt{-\frac{76}{9} }[/tex]

_________________

[tex]\sqrt{-\frac{76}{9}}=\frac{2\sqrt{19} }{3}i[/tex]

[tex]-\sqrt{-\frac{76}{9} } =-\frac{2\sqrt{19} }{3}i[/tex]

_________________

Solution:

[tex]v=\frac{2\sqrt{19} }{3}i,v=-\frac{2\sqrt{19} }{3}i[/tex]

Hope this helps!

Answer:

Done: $9.75 an hour

Amy: $10 an hour

Amy makes more than Done per hour

Step-by-step explanation:

[tex]Done:\\97.50/ 10 = 9.75\\Amy:\\120/12=10\\[/tex]

f(x)=-4x+1

h(x)=19-3x

Using the concept of function we can solve the question

A function can be defined as an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

f(-6) can be found out by substituting x=-6 in f(x)

  f(-6)=-4×(-6)+1

 f(-6)=24+1

 f(-6)=25

The question h(8)-f(-7) can be solved by first finding value of 8 in h(x)

h(8)=19-(3×8)

h(8)=19-24

h(8)=5

Now lets find f(-7)

f(-7)=-4×(-7)+1

f(-7)=28+1

f(-7)=29

Now we can find h(8)-f(-7) by substituting the values of h(8) and f(-7), which was found earlier

h(8)-f(-7)=5-29

h(8)-f(-7)=-24

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The correct question is " f(x)=-4x+1,h(x)=19-3x then find f(-6) and h(8)-f(-7)."

Answer: £261

Step-by-step explanation: Subtracting 429 from 690 will give you 261 which is the remaining amount needed to purchase the computer.

The total cost of the service in the light cell phone company is $24.05.

According to the statement,We have to find that the cost of the cellphone service.

So, For this purpose, we know that the

A cost function is a mathematical formula used to used to chart how production expenses will change at different output levels.

From the given information:

Each bill includes a $19.95 service fee for 500 minutes plus a $3.95 communication tax and 15 cents for each minute over 500 minutes.

Then

Total cost become of 500 minutes = service fee + communication tax + Cost per minute

Then

Total cost become of 500 minutes = $19.95 + $3.95 + 15 cents

We know that the 0.15 dollars in 15 cents.

Then

Total cost become of 500 minutes = $19.95 + $3.95 + $0.15

Total cost become of 500 minutes =  24.05.

So, The total cost of the service in the light cell phone company is $24.05.

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Answer:

25 and 6

Step-by-step explanation:

According to the solving the explicit rule:

y = 52000 - 58000 * x

The explicit formula for an arithmetic sequence is a = a + (n - 1)d, and each term of the sequence may be computed without knowing the previous terms of the sequence. In general, the explicit formula is the nth term of an arithmetic, geometric, or harmonic sequence.

An implicit function is a function containing numerous variables, one of which is a function of the other set of variables. An explicit function is one in which the dependent variable may be clearly stated in terms of the independent variable.

Initial = 52000

Rate = 58000 each year

Determine the equation of the graph:

The equation can be used:

Amount = initial - rate * years

We used minus (-) because, the amount reduces as the student pays.

So,

y = amount

x = years

we have:

y = initial  - rate * x

putting the values we get:

y = 52000 - 58000 * x

According to the solving the explicit rule:

y = 52000 - 58000 * x

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The circles whose shaded area is equivalent to 2/6 of the total area are:

a. The circle which is labeled 1/3 shaded.

b. The circle which is labeled 4/12 shaded.

Given, a circle is 2/6 shaded.

Six equal halves of a circle are separated, two of which are darkened. The circle is marked as shaded by two-sixths.

= 2/6

which means that the fraction can be simplified furthermore.

= 1/3

which means for every 3 parts, one part is shaded.

Therefore, we need to find the circle which has the shaded area equivalent to 2/6 of the total area, that is for every 3 parts of the parts, there should be one part shaded.

a. A circle is divided into 3 equal parts with 1 parts shaded

The circle is labeled 1 third shaded.

= 1/3 which is equivalent to the area of the circle 2/6.

b. A circle is divided into 5 equal parts with 2 parts shaded.

The circle is labeled 2 fifths shaded.

= 2/5 which is not equivalent to 2/6.

c. A circle is divided into 10 equal parts with 4 parts shaded.

The circle is labeled 4 tenths shaded.

= 4/10

= 2/5 which is again not equivalent to 2/6.

d. A circle is divided into 12 equal parts with 4 parts shaded.

The circle is labeled 4 twelfths shaded.

= 4/12

after simplifying it furthermore, we get:

= 1/3 which is equivalent to the area of the circle 2/6.

hence we get the desired results.

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The value of g(-4) is (-18)

A function is defined as a relation between a set of inputs having one output each. A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given function:

g(x)=5x+2

So, the value of g(-4)

g(-4) = 5(-4) +2

g(-4) = -20+2

g(-4) = -18

Hence, the value of g(-4) is -18.

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Answer:

The slope intercept of a line is given by y=mx+c, where:

m=slope, c=y-intercept.

Thus the slope-intercept form of our equation will be:

-6+2y≤42

adding 6 in both sides we get:

-6+6+2y≤42+6

2y≤6

dividing both sides by 2 we get:

(2y)/2≤6/2

y≤3

the answer is y≤3

Step-by-step explanation:

Answer:

6 3/8

Step-by-step explanation:

2 6/8 + 3 5/8

= (2 + 3) + ( 6/8 + 5/8)

= 5 + (6 + 5)/8

= 5 + 11/8

= 5 + 1 3/8

= 6 3/8

Answer:

14 us cups

Step-by-step explanation:

Answer: 450

Step-by-step explanation:

x is the original price.

40 percent times x = 180

or [tex]\frac{40}{100}[/tex] times x= 180

multiplying both sides by 100 and dividing by 40

x=180 times [tex]\frac{100}{40}[/tex]

now just do 180 times 100 divided by 40

which gives you 450

The expression is equivalent to 16.8 - 18.6 is 16.8 + (-18.6)

The expression is given as

16.8 - 18.6

The additive inverse property states that:

a - b = a + (-b)

Using the above as a guide, we have the following expression that is equivalent

16.8 - 18.6 = 16.8 + (-18.6)

Hence, the expression is equivalent to 16.8 - 18.6 is 16.8 + (-18.6)

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If my disposable income from a part-time job in 2019 was $17,000, and I repaid a loan of $560 at 15 percent interest, borrowed in 2018 from my income of 2019, then I will have $ available for spending in 2019.

As per the question statement, my disposable income from a part-time job in 2019 was $17,000, and I repaid a loan of $560 at 15 percent interest, borrowed in 2018 from it.

We are required to calculate the amount I will be left with, to spend in 2019.

To solve this question, first, let us calculate the amount we had to pay to close our loan of 2018, along with it's 1 year's interest.

Since the loan was repaid in a year, hence, it does not matter if the interest was simple or compound as the magnitude of simple and compound interest on the same principle and at same rate of interest for a year is equal.
Let us proceed with the consideration that the interest was compounded annually at the rate of 15% per annum.

As per the basic formula of Compound Interest,

[tex]A=[P*(1+\frac{R}{100})^n][/tex]

Where, A = Final Amount i.e., (Principle + Interest).

P = Principle on which Interest in compounded

R = Rate of Compound Interest per annum

n = Time period of interest .

Here, (P = $560), (R = 15%) and (n = 1).

Therefore, total amount to be repaid to close the loan in 2019

[tex]=[560*(1+\frac{15}{100})^1]\\\\=[560*(1+\frac{3}{20})]\\=[560*(\frac{20+3}{20})]\\ =(560*\frac{23}{20})\\ =(28*23)\\=644[/tex]

Hence, my left-over balance after paying $644 from my disposable income of $17,000 which I earned from a part time job in 2019, will be $(17000 - 644) = $16356.

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The sales tax to the nearest dollars is $89 whereas it is $88.87 to the nearest cents.

The cents is normally expressed to 2 decimal places, in other words, the sales in cents in this case is to express the sales tax amount to 2 figures after the decimal which is $88.87 since the 2 before 7 is insignificant and cannot be rounded to 1 because it is less than 5.

In dollars, the sales tax is $89 because the 8 after the decimal when rounded to 1 and added to 8 gives 9.

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Full question: Kosanga lives in San Mateo. He bought an item for $844.29 and when the clerk calculated the sales tax it came out to exactly $88.87287. Round the sales tax to the nearest:(a) dollars(b) cents

The sales tax when rounded to the nearest dollars is $89 whereas it is $88.87 to the nearest cents.

The cents is normally expressed to 2 decimal places, in other words, the sales in cents in this case is to express the sales tax amount to 2 figures after the decimal which is $88.87 since the 2 before 7 is insignificant and cannot be rounded to 1 because it is less than 5.

In dollars, the sales tax is $89 because the 8 after the decimal when rounded to 1 and added to 8 gives 9.

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Full question:

Kosanga lives in San Mateo. He bought an item for $844.29 and when the clerk calculated the sales tax it came out to exactly $88.87287. Round the sales tax to the nearest:

(a) dollars

(b) cents

The minute hand moves a full circle in 60 minutes (1 hour); so 360 degrees.

10 minutes is 1/6 of an hour so the hour hand has also moved 1/6 of the distance between the 3 and the 4, which adds 5° (1/6 of 30°). The total measure of the angle, therefore, is 35°.

Since a clock is a circle and circles have 360 degrees, and there are 60 seconds in one minute, the answer can be derived by using the equation:

360°/60 minutes = 6° per minute

Edited to replace 60 seconds with 60 minutes in the formula.

Therefore,

Answer is 60 minutes the hand make 1/6 of a rotation.

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The number of sets of spoons Enola should buy is given by this inequality: ss ≥ 42.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

Based on the information provided, the total number of sets of spoons after ss sets are purchased is given by:

T(ss) = 263 + 12ss

The number of sets of spoons needed by the restaurant is given by this inequality:

T(ss) ≥ 767

Substituting the value of T(ss) into the inequality above, we have;

263 + 12ss ≥ 767

12ss ≥ 767 - 263

12ss ≥ 504

ss ≥ 504/12

ss ≥ 42

In conclusion, the number of sets of spoons Enola should buy is 42.

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The conclusion of the conditional statement is that; D) The angles are congruent.

Vertical angles are also called opposite angles and they are formed when two lines meet each other at a point.

Now, we are given the conditional statement "If two angles are vertical angles, then they are congruent."

Now, we can say that the conditional statement is always true according to the definition of vertical angles. Thus, we can say that the conclusion of the conditional is that The angles are congruent.

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Answer:

There is no mode for this distribution.

Step-by-step explanation:

The mode is the value that appears most frequently in a data set.  If there are no repeating numbers in a given list, there is no mode existing for that particular list.

a) The total dollar interest payments for the six months using the short-term financing interest rates is $377.73.

b.1) The total dollar interest payments for the six months using the long-term financing interest rate is $442.00.

b.2) If long-term financing at 12 percent had been utilized throughout the six months, the total-dollar interest payments would be larger than with the short-term financing plan by $64.27.

Month     Amount     Interest Rate         Interest       Long-Term

                              Annual   Month       Amount    Rate   Amount

January   $9,700     6%          0.50%     $48.50      1%     $97.00

February $3,700      7%          0.58%       21.46       1%       37.00

March     $4,700     10%          0.83%       39.01       1%       47.00

April       $9,700      13%          1.08%      104.76       1%      97.00

May      $10,700      12%          1.00%      107.00       1%    107.00

June      $5,700      12%          1.00%       57.00       1%      57.00

Total interest amount =                       $377.73            $442.00

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Carmen's Beauty Salon has estimated monthly financial requirements for the next six months as follows:

Month     Amount     Interest Rate

January   $9,700               6%

February $3,700                7%

March     $4,700               10%

April       $9,700                13%

May      $10,700                12%

June      $5,700                12%

a) Compute total dollar interest payments for the six months.

b.1) Compute the total dollar interest payments if the long-term financing at 12% had been used throughout the six months.