Mr. Black bought 2 magazines for $9.95 each and 1 book for $14.95. If the sales tax is 6%, what is the total cost of Mr. Black's purchases?

Answer:

58 and 42.

Step-by-step explanation:

Let the 2 numbers be x and 100-x.

Also let x be the largest number, so

x ≥ 100 - x + 16     ( 'At least 16' means equal to 16 or greater than 16).

Add in x to both sides:

x + x  ≥ 100 + 16

2x ≥ 116

x ≥ 58.

But since the sum of the 2 numbers is 100,  x must be 58 and the other number is 42.

Answer:

Therefore,

The Dimensions are,

[tex]Length = 34\ cm\\\\Width = 9\ cm[/tex]

Step-by-step explanation:

Given:

Perimeter of a rectangle,

Perimeter = 86 cm

let "x" be the width of rectangle,

Width = x

then according to the given condition,

length will be given as,

[tex]Length = 3x+7[/tex]

To Find:

Length =?

Width =?

Solution:

Perimeter of rectangle is given by,

[tex]\textrm{Perimeter of Rectangle}=2(Length+Width)[/tex]

Substituting the values we get

[tex]86=2(3x+7+x)\\\\86=2(4x+7).........Equation\\\\86=8x+14\\\\8x=86-14=72\\\\x=\dfrac{72}{8}=9\ cm[/tex]

Substituting "x" in Length we get

[tex]Length = 3\times 9 +7=34[/tex]

Also Area Of Rectangle is given by

[tex]\textrm{Areaof Rectangle}=(Length\times Width)=34\times 9=306\ cm^{2}[/tex]

Therefore,

The Dimensions are,

[tex]Length = 34\ cm\\\\Width = 9\ cm[/tex]

Final answer:

The dimensions of the rectangle with an area of 306 cm squared and a perimeter of 86 cm, where the length is 7 more than three times the width, are 9 cm by 34 cm.

Explanation:

To solve for the dimensions of the rectangle with an area of 306 cm squared and a perimeter of 86 cm, where the length (L) is 7 more than three times the width (W), we will set up a system of equations. First, express the given relationships:

Perimeter (P) = 2W + 2L = 86 cm

Area (A) = W * L = 306 cm squared

L = 3W + 7

Next, substitute the expression for L into the perimeter equation:

2W + 2(3W + 7) = 86

2W + 6W + 14 = 86

8W + 14 = 86

8W = 72

W = 9 cm

Now, plug the value of W back into the equation for L:

L = 3(9) + 7 = 34 cm

Thus, the dimensions of the rectangle are 9 cm by 34 cm.

Answer:

x = 4

Step-by-step explanation:

from the given expression, factorise to have;

x (x - 4) = 0

Thus, X = 0 or x - 4 = 0

x - 4 = 0

x = 4

Thus, x = 0 or x = 4

Therefore the positive solution to the quadratic function is 4.

Answer:

The milligrams of vitamin C in a serving of orange juice is 96 and the milligrams of vitamin C in a serving of pineapple juice is 25

Step-by-step explanation:

Let

x ----> the milligrams of vitamin C in a serving of orange juice

y ----> the milligrams of vitamin C in a serving of pineapple juice

we know that

Servings of two juices contain a total of 121 mg of vitamin C

so

[tex]x+y=121[/tex] -----> equation A

A one-cup serving of orange juice contains 4 mg less than four times the amount of vitamin C as a one cup serving of pineapple juice

so

[tex]x=4y-4[/tex] ----> equation B

substitute equation B in equation A

[tex]4y-4+y=121[/tex]

solve for y

[tex]5y=121+4\\5y=125\\y=25\ mg[/tex]

Find the value of x

[tex]x=4(25)-4=96\ mg[/tex]

therefore

The milligrams of vitamin C in a serving of orange juice is 96 and the milligrams of vitamin C in a serving of pineapple juice is 25

Answer:

24.708

Step-by-step explanation:

Answer:

x-3

Step-by-step explanation:

5x²-15x

in order to get the equivalent of the equation, simplify to the lowest term.

To simplify to the lowest term, divide through by the common factor in the equation which is 5x

5x²÷5x - 15x÷5x

=x-3

Step-by-step explanation:

We have,

[tex]\dfrac{37}{74}[/tex]

To find, the reciprocals of the fraction [tex]\dfrac{37}{74}[/tex] = ?

∴ [tex]\dfrac{37}{74}[/tex]

Dividing numerator and denominator by 37, we get

= [tex]\dfrac{1}{2}[/tex]

= [tex]\dfrac{37}{74}[/tex] or, [tex]\dfrac{1}{2}[/tex]

We know that,

The reciprocals of the fraction [tex]\dfrac{x}{y} =\dfrac{y}{x}[/tex]

The reciprocals of the fraction [tex]\dfrac{37}{74}[/tex] = [tex]\dfrac{74}{37}[/tex] or [tex]\dfrac{2}{1}[/tex]

= [tex]\dfrac{74}{37}[/tex] or 2

Thus, the reciprocals of the fraction [tex]\dfrac{37}{74}[/tex] =  [tex]\dfrac{74}{37}[/tex] or 2.

Answer: 3 inches

Step-by-step explanation:    

1/60 = x/15,

x = 1/4

1/4 foot = 3 inches.

Answer:

Step-by-step explanation:

student teacher ratio of 5:2....added = 7

so students make up 5/7 of the total people and teachers make up 2/7 of the total people.

Last year.....56 people

students : 5/7 * 56 = 280/7 = 40 students

teachers : 2/7 * 56 = 112/7 = 16 teachers

this year....70 total people

students : 5/7 * 70 = 350/7 = 50 students

teachers : 2/7 * 70 = 140/7 = 20 teachers

Final answer:

To find the number of students and teachers based on their ratio and total count, we applied the ratio of 5:2 to the total counts of 56 and 70 for the last year and this year, respectively. This calculation revealed there were 40 students and 16 teachers last year, and 50 students and 20 teachers this year.

Explanation:

The student has asked about finding the number of students and teachers at a preschool in two different years based on a given student-to-teacher ratio and the total count of students and teachers for those years.

Step-by-Step Solution:

First, understand the ratio of students to teachers is 5:2. This means for every 5 students, there are 2 teachers.

To solve for last year, we have a total of 56 individuals (students and teachers). Let's represent students as 5x and teachers as 2x, given their ratio. Therefore, 5x + 2x = 56, solving this gives us x = 8. This means there were 40 students (5*8) and 16 teachers (2*8) last year.

For this year, we have a total of 70 individuals. Using the same method, 5x + 2x = 70, we find that x = 10. This means there are 50 students (5*10) and 20 teachers (2*10) this year.

By understanding and applying the concept of ratios, we were able to find the number of students and teachers for both years.

The answer is W, just took the test.

Answer:

-6b+21

Step-by-step explanation:

a) Probability of both being males is 27%

b) Probability of both being females is 23%

c) Probability of having exactly one male and one female is 50%

Step-by-step explanation:

a)

The probability that the birth is a male can be written as

[tex]p(m) = 0.52[/tex] (which corresponds to 52%)

While the probability that the birth is a female can be written as

[tex]p(f) = 0.48[/tex] (which corresponds to 48%)

Here we want to calculate the probability that over  2 births, both are male. Since the two births are two independent events (the probability of the 2nd to be a male  does not depend on the fact that the 1st one is a male), then the probability of both being males is given by the product of the individual probabilities:

[tex]p(mm)=p(m)\cdot p(m)[/tex]

And substituting, we find

[tex]p(mm)=0.52\cdot 0.52 = 0.27[/tex]

So, 27%.

b)

In this case, we want to find the probability that both children are female, so the probability

[tex]p(ff)[/tex]

As in the previous case, the probability of the 2nd child to be a female is independent from whether the 1st one is a male or a female: therefore, we can apply the rule for independent events, and this means that the probability that both children are females is the product of the individual probability of a child being a female:

[tex]p(ff)=p(f)\cdot p(f)[/tex]

And substituting

[tex]p(f)=0.48[/tex]

We find:

[tex]p(ff)=0.48\cdot 0.48=0.23[/tex]

Which means 23%.

c)

In this case, we want to find the probability they have exactly one male and exactly one female child. This is given by the sum of two probabilities:

- The probability that 1st child is a male and 2nd child is a female, namely [tex]p(mf)[/tex]

- The probability that 1st child is a female and 2nd child is a male, namely [tex]p(fm)[/tex]

So, this probability is

[tex]p(mf Ufm)=p(mf)+p(fm)[/tex]

We have:

[tex]p(mf)=p(m)\cdot p(f)=0.52\cdot 0.48=0.25[/tex]

[tex]p(fm)=p(f)\cdot p(m)=0.48\cdot 0.52=0.25[/tex]

Therefore, this probability is

[tex]p(mfUfm)=0.25+0.25=0.50[/tex]

So, 50%.

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Angle measures are ∠M = 90° and ∠L = 24°

Step-by-step explanation:

Tangents create right angles at the point of contact with a circle.

So ∠M = 90°

⇒ ∠L = 180° - (∠M + ∠N) = 180° - (90° + 66°)

         = 180° - 156° = 24°

Answer:

m= 90 degrees and L= 24 degrees

Step-by-step explanation:

How many cups in a batch of batter??

Answer:

16 corn muffins made.

Step-by-step explanation:

Since there is 8 cups of cornmeal, and corn muffins need 1/2 cornmeal per batch. We need to divide.

Equation: 8 divided by 1/2 = M

Then in order to divide fractions. We have to use the kcf.(Keep, change, flip)

8 is 8,(Keep) division turns into multiplication(change) and then 1/2 is 2/1 (flip).

Then multiply 8 x 2.(Since 2/1 is 2)

Your answer is 16!

Answer:

[tex]\large \boxed{\$70.02}[/tex]

Step-by-step explanation:

The compound interest formula is

[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]

Data:

P = 300

r = 2.12 % = 0.0212

t = 10 yr

n = 1 calculation per year

1. Accrued amount:  

A = 300(1+ 0.0212)¹⁰

  = 300 × 1.0212¹⁰

  = 300 × 1.233 41

  = 370.02

2. Interest

I = A - P = 370.02 - 300.00 = 70.02

[tex]\text{The interest is $\large \boxed{\mathbf{\$70.02}}$}[/tex]

Final answer:

Using the compound interest formula, investing $300 at an annual interest rate of 2.12% compounded annually for 10 years will result in approximately $70.37 in interest, totaling $370.37.

Explanation:

A bank offers 2.12% interest compounded annually for investing money in a savings account, and you open an account with $300. How much money in interest will you earn if you leave it for 10 years?

To calculate the amount of money you will have after 10 years, including interest, you can use the formula for compound interest: [tex]A = P(1 + r/n)^{(nt)[/tex], where:

Plugging these values into the formula gives us: [tex]A = $300(1 + 0.0212/1)^{(1*10)[/tex] = [tex]$300(1 + 0.0212)^{10[/tex] = [tex]$300(1.0212)^{10.[/tex]

Calculating this, we get A = $300(1.234567), which equals approximately $370.37. Therefore, the total interest earned over 10 years is approximately $70.37.

Answer:

6 13 15 18 22

Step-by-step explanation:

absolute value just makes it positive unless it is a negative absolute value-|n|

Answer:

The surface area of the triangular prism is [tex]145.3[/tex]  [tex]ft^2[/tex]

Step-by-step explanation:

Step 1:  Finding the two area of two triangles

Area of the triangle  =  [tex]\frac{1}{2} (base \times height})[/tex]

Area of the triangle  = [tex]\frac{1}{2} (9.8\times 5.33})[/tex]

Area of the triangle  = 26.117

Area of 2 triangles  =  [tex]52.234[/tex]

Step 2: Finding the area of the side rectangles

Area of the rectangle  = [tex]length \times breadth[/tex]

Area of the rectangle  1 = [tex]6.2 \times 3.8[/tex]  = 23.56 [tex]ft^2[/tex]

Area of the rectangle  2  = [tex]8.5 \times 3.8[/tex] = 32.3 [tex]ft^2[/tex]

Area of the rectangle  3  = [tex]9.8 \times 3.8[/tex] = 37.24 [tex]ft^2[/tex]

Step 3: surface area of the triangular prism.

Surface area of the triangular prism =  52.234 + 23.56 + 32.3 + 37.24

Surface area of the triangular prism = 145.334 [tex]ft^2[/tex]

Answer:

B. 145.3 ft2

Step-by-step explanations:

Answer:

147.27 degrees.

Step-by-step explanation:

All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the angles, we know that the sum of all the angles is 1620 degrees (from above)... And there are eleven angles... So, the measure of the interior angle of a regular 11-gon is about 147.27 degrees.

The solution is, the measure of the interior angle of a regular 11-gon is about 147.27 degrees.

A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.

here, we have,

we know that,

All sides are the same length (congruent) and all interior angles are the same size (congruent).

To find the measure of the angles, we know that the sum of all the angles is 1620 degrees (from above)...

And there are eleven angles...

So, the measure of the interior angle of a regular 11-gon is about 147.27 degrees.

Hence, The solution is, the measure of the interior angle of a regular 11-gon is about 147.27 degrees.

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In these kinds of problems, take 15 and 3/4 (Manny's distance) and multiply it by the factor 5/6. (15 3/4 = 15.75)

(15.75) * (5/6) = 13.125 = 13 1/8

This should get you 13 and 1/8 miles for Zander's distance.

Answer:

61.375

Step-by-step explanation:

Given : [tex]\frac{491}{8}[/tex]

The fraction is not dividing by a common number in numerator and denominator to simplify, So dividing the numerator directly by 8.

Gives   [tex]\frac{491}{8}= 61.375[/tex]

So, 61.375 is the answer of the above problem.

Answer:

width = 1.8 in

length =   3.6 in

height =[tex]8-3w =8-3(1.8)= 2.6 in[/tex]

Step-by-step explanation:

A designer is making a rectangular prism box with maximum volume, with the sum of its length, width, and height 8 in

Let l , w and h are the length , width and height

[tex]l +w+h=8\\l=2w[/tex]

Plug it in the first equation

[tex]2w+w+h=8\\3w+h=8\\h=8-3w[/tex]

volume the box is length times width times height

[tex]volume = (2w)(w)(8-3w)\\16w^2-6w^3[/tex]

To get maximum volume we take derivatived

[tex]v'=32w-18w^2[/tex]

set the derivative =0 and solve for w

[tex]0=32w-18w^2\\0=-2w(9w-16)\\w=0 , w= \frac{16}{9}[/tex]

width = 1.8 in

length = 2w= 3.6 in

height =[tex]8-3w =8-3(1.8)= 2.6 in[/tex]

Step-by-step explanation:

As the distance from the equator to the north pole is almost 10,000 km.

As we know that

As the planet Earth is outspread or widest at its Equator and the distance around the Earth at the Equator - its circumference - is [tex]24,901\:miles[/tex].

[tex]24,901\:miles\:=\:40,075\:kilometers[/tex]

So, the distance around the Earth at the Equator - its circumference - is [tex]40,075\:kilometers[/tex].

Also, at the equator, [tex]1^{0}[/tex] ( [tex]1\:degree[/tex] ) of longitude and latitude both cover about [tex]111[/tex] km, or just under [tex]70[/tex] miles.

Keywords: equator, longitude, north pole

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4r + 5 = 3 is not an algebraic expression because expressions are basically equations but WITHOUT answers. In this equation, 3 is shown as the answer, which makes it an equation, not an expression.

Hope this helps! Please correct me if I'm wrong! :D

4r + 5 = 3 is not an algebraic expression because it contains an equals sign making it an equation rather than an algebraic expression. Algebraic expressions are mathematical phrases lacking an equals sign.

The equation 4r + 5 = 3 is not an algebraic expression because it is, in fact, an equation. The distinction between these two lies in the presence of the equals sign (=).

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operators (like +, -, ×, ÷), but it does not have an equals sign. For example, 4r + 5 is an algebraic expression. However, when there is an equals sign present, as is the case in 4r + 5 = 3, the resulting mathematical phrase is an equation, which is a statement that two algebraic expressions are equal.

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Answer:

The answer for this problem is

C) y = -x + 6

Step-by-step explanation:

I know this because I just did the test

Answer:

The Graph below have the same shape.Equation of the red graph

Step-by-step explanation:

The graph is shifted up 1 unit. That's equivalent to adding 1 to all points:

In other words:

G(x) = F(x) + 1

Plugging in F(x) = 3 - x^4:

G(x) = 3 - x^4 + 1

G(x) = 4 - x^4

Answer:

A. G(x) = 4 - x^4

98 small cups of lemonade and 57 large cups of lemonade were sold by Harold.

Step-by-step explanation:

Given,

Cost of small cup of lemonade = $1.25

Cost of large cup of lemonade = $2.50

Total cups sold = 155

Total worth of cups = $265

Let,

x be the number of small cups sold

y be the number of large cups sold

According to given statement;

x+y=155      Eqn 1

1.25x+2.50y=265   Eqn 2

Multiplying Eqn 1 by 1.25

[tex]1.25(x+y=155)\\1.25x+1.25y=193.75\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](1.25x+2.50y)-(1.25x+1.25y)=265-193.75\\1.25x+2.50y-1.25x-1.25y=71.25\\1.25y=71.25[/tex]

Dividing both sides by 1.25

[tex]\frac{1.25y}{1.25}=\frac{71.25}{1.25}\\y=57[/tex]

Putting y=57 in Eqn 1

[tex]x+57=155\\x=155-57\\x=98[/tex]

98 small cups of lemonade and 57 large cups of lemonade were sold by Harold.

Keywords: linear equation, elimination method

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Answer:

52.1

Step-by-step explanation:

The given expression is 36 - [-49 + 32.9]

First we have to simplify the numbers which are in parenthesis.

= 36 -(-16.1)

Here -(-16.1) = + 16.1          

So, we get

= 36 + 16.1

= 52.1

The answer is 52.1

The amount of mark-up is $4.25

Step-by-step explanation:

To find the mark-up cost of each  dog collar, increase $1.19 by 356 %

Lets take that 100% = $1.19

So the 356% =?

Perform cross-product as;

(356*1.19)/100 = $4.25

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Keywords : Dog collars, manufacturer, mark-up, cost , amount

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Answer:

4.25

Step-by-step explanation:

I did the quiz