Express as a fraction or a mixed number: [tex]33\frac{1}{3}[/tex]%

Answer:

Step-by-step explanation:

the amount of mark up = 23% of 80

= [tex]\frac{23*80}{100}[/tex]

= 23 * 0.8 = $18.4

a. She pays $100 for 5 sheets

b. 25+15x dollars for x sheets

c. 8 sheets

Step-by-step explanation:

Given

Sitting cost = $25

Per sheet picture cost = $15

Let p be the number of sheets of pictures

Then the cost can be written as a function of p

[tex]c(p) = 25+15p[/tex]

Now,

a. How much does she pay for 5 sheets of pictures?!

Putting p = 5 in the function

[tex]c(5) = 25 + 15(5)\\= 25+75\\=100[/tex]

She will pay $100 for 5 sheets of pictures

b. How much does she pay for "x" sheets?

Putting x in place of p

[tex]c(x) = 25+15x[/tex]

c. How many sheets can she buy for $145?

We know the cost now, we have to find p so,

[tex]145 = 25+15p\\145-25 = 25+15p-25\\120 = 15p[/tex]

Dividing both sides by 15

[tex]\frac{15p}{15} = \frac{120}{15}\\p = 8[/tex]

Hence,

She can buy 8 sheets for $145

Keywords: Linear equation, Algebraic functions

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Answer:

9.

Step-by-step explanation:

It's given that A = 16. It shows that B = A-7, so that would mean B is 16-7, which is 9.

Final answer:

The quotient when 4x^3 + 2x + 7 is divided by x + 3 is 4x^2 - 10x + 32 with a remainder of -89.

Explanation:

To find the quotient when 4x^3 + 2x + 7 is divided by x + 3, we can use long division. Divide the first term, 4x^3, by x which gives 4x^2. Multiply x + 3 by 4x^2 to get 4x^3 + 12x^2. Subtract this from the original expression to get -10x^2 + 2x + 7. Then, divide -10x^2 by x which gives -10x. Multiply x + 3 by -10x to get -10x^2 - 30x. Subtract this from the previous result to get 32x + 7. Finally, divide 32x by x which gives 32. Multiply x + 3 by 32 to get 32x + 96. Subtract this from the previous result to get -89. Therefore, the quotient when 4x^3 + 2x + 7 is divided by x + 3 is 4x^2 - 10x + 32 with a remainder of -89.

Final answer:

C paid Rs. 127,050 for the car.

Explanation:

To find out what C paid for the car, we need to consider the gains made by A and B. A bought the car for Rs.100,000 and spent Rs. 10,000 on repairs. This means A's total cost is Rs. 110,000. A then sells the car to B at a gain of 10%, which means B buys the car for 110% of Rs. 110,000, or Rs. 121,000.

Now, B sells the car to C at a gain of 5%. To find out what C paid, we need to calculate 105% of Rs. 121,000, which gives us Rs. 127,050. Therefore, C paid Rs. 127,050 for the car.

Time taken by stone in air is 7 seconds and time taken by stone in water is 5 seconds

Solution:

Let "x" represents the time taken by stone in the air

Given that the stone's entire fall took 12 seconds

Thus, the total time taken by it in both air and water = 12 seconds

time taken by stone in the air = x

time taken by stone in water = 12 - x

In the air, it had an average speed of 16 m/s

average speed in air = 16 m/s

We know that,

distance = speed x time

distance covered by it in air = [tex]16 \times x = 16x[/tex]

distance covered in air = 16x

It had an average speed of 3 m/s before hitting the seabed

average speed in water = 3 m/s

distance covered by it in water = [tex]3 \times (12 - x) = 36 - 3x[/tex]

distance covered in water = 36 - 3x

Then,

Total distance covered = distance covered in air + distance covered in water

Total distance covered = 16x + 36 - 3x = 13x + 36

But, the total distance covered by it = 127 meters ( Given )

Therefore,

13x + 36 = 127

13x = 127 - 36

13x = 91

x = 7

Hence, the time taken by stone in air = x seconds = 7 seconds,

And, the time taken by it in water = 12 - x = 12 - 7 = 5 seconds

There were 45 markers originally in each box.

Step-by-step explanation:

Given,

Boxes ordered = 3 large boxes

Markers given to one teacher = 15

Markers given to 3 teachers = 15*3 = 45 markers

Remaining markers = 90

Let,

x be the original number of markers in 3 boxes.

Total markers - markers given to teachers = markers left

[tex]x-45=90\\x=90+45\\x=135[/tex]

There were 135 markers in 3 boxes.

3 boxes = 135 markers

1 box = [tex]\frac{135}{3}=45\ markers[/tex]

There were 45 markers originally in each box.

Keywords: multiplication, addition

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Answer: H-7

Step-by-step explanation: I got it right on test!  have a great day! :)

Solve for x in this equation.

x+(-9)=-36

x-9=-36

x=-27

answer: -27

Answer:

Step-by-step explanation:

Answer:

-32

Step-by-step explanation:

Divide both sides by 3/4 to solve for x.

－24/1*4/3 = -96/3

－96/3=－32

Answer:

Y = 5x + 2 . . . . . . . . . . (1)

3x = -y + 10 . . . . . . . . (2)

3x = -(5x + 2) + 10

3x = -5x - 2 + 10

3x + 5x = -2 + 10

8x = 8

x = 1

y = 5(1) + 2 = 5 + 2 = 7

Solution is (1, 7)

Step-by-step explanation:

The Solution is (1,7) is the solution to the system of equations:

y=5x+2, 3x=-y + 10

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

We need to find the solution of the system of following equations.

y= 5x + 2        eq(1)

3x = -y +10      eq(2)

We will solve the equations using Substitution method to find the values of x and y

we put value of y from eq (1) into eq (2), The eq(2) will be:

3x = - (5x + 2) + 10

3x = -5x -2 +10

3x+5x = -2+10

8x = 8

x= 1

Now, putting value of z in eq(1) to find value of y

y = 5x +2

y = 5(1) + 2

y = 5+2

y = 7

So, Solution is (1,7).

Hence, The Solution is (1,7) is the solution to the system of equations:

y=5x+2, 3x=-y + 10

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Answer:

V ≈ 63.4

Step-by-step explanation:

The arc length of the segment becomes the circumference of the cone's base.  Therefore, we can find the radius of the cone:

s = C

(90/360) 2π (10) = 2π r

r = 2.5

The radius of the segment is the slant length of the cone.  So we can use Pythagorean theorem to find the cone's height.

l² = r² + h²

10² = 2.5² + h²

h = √93.75

The volume of the cone is:

V = π/3 r² h

V = π/3 (2.5)² √93.75

V ≈ 63.4

Answer:

x = -5 + 5i, -5 - 5i

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

A difference of 2 squares factors in general as

a² - b² = (a - b)(a + b)

(x - 1)² - 25 ← is a difference of squares

with a = x - 1 and b = 5, thus

(x - 1)² - 25

=(x - 1 - 5)(x - 1 + 5) = (x - 6)(x + 4), then

(x - 6)(x + 4) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 4 = 0 ⇒ x = - 4

Solutions are x = - 4, x = 6

Answer:

6*(3/4) is 75% of 6.

Step-by-step explanation:

3/4 =0.75

Consider this:

6*1 =6, so 1=100%.

6*1/2 =6*0.5=3, so 1/2=50%.

You can then see that 6*0.75=4.5 is 75% of 6.

Answer: 14ft > 4 1/2 yd

Step-by-step explanation:

Answer:

Step-by-step explanation:

P = Q - 7.......Q is the quantity of baskets....and he makes 15 baskets....so sub in 15 for Q and solve for P, the price

P = 15 - 7

P = 8 <====

Answer:

D.$8

Step-by-step explanation:

Firstly, you replace Q with 15. Then you solve the equation.

P=15-7

P=8

Answer:

The ordered pair is not a solution of the system of inequalities

Step-by-step explanation:

we know that

If a ordered pair is a solution of a system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

we have the system

[tex]x+5y < 16[/tex] ----> inequality A

[tex]x< 8[/tex] ----> inequality B

substitute the value of x and the value of y of the ordered pair in each inequality

ordered pair (6,2)

Verify inequality A

For x=6, y=2

[tex]6+5(2) < 16[/tex]

[tex]16 < 16[/tex] ----> is not true

so

The ordered pair not satisfy the inequality A

therefore

The ordered pair is not a solution of the system of inequalities

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

By definition, if two lines are perpendicular then the product of their slopes is -1.

We have the following equation of the line:

[tex]y = 2x-5[/tex]

Then [tex]m_ {1} = 2[/tex]

We find [tex]m_ {2}:[/tex]

[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {2}\\m_ {2} = - \frac {1} {2}[/tex]

Thus, the perpendicular line will be of the form:

[tex]y = - \frac {1} {2} x + b[/tex]

We substitute the given point and find "b":

[tex]-2 = - \frac {1} {2} (8) + b[/tex]

[tex]-2 = -4 + b\\-2 + 4 = b\\b = 2[/tex]

Finally, the equation is of the form:

[tex]y = - \frac {1} {2} x + 2[/tex]

ANswer:

[tex]y = - \frac {1} {2} x + 2[/tex]

Answer:

Triangle ABC is dilated is dilated with a scale factor of ⅓ with the center of dilation at the point (3,4) resulting in triangle DEC

Step-by-step explanation:

From triangle ABC,

|AC|=3 units

From triangle DEC,

|EC|= 1 unit

Since the two triangles are similar, we can find the scale factor using the ratio of the image length over the corresponding object length.

[tex]scale \: factor = \frac{ |EC| }{ |AC| } [/tex]

Let us substitute the values to get:

[tex]scale \: factor = \frac{1}{3 } [/tex]

When we trace through AD and EB, they will meet at C. Hence C(3,4) is the center of dilation.

Answer:

641

Step-by-step explanation:

24,358 ÷ 38=641

Hope this helps!!

24,358 / 38 = 641

Use long division to find the answer :)

Hope this helps!

Answer:

D and E

Step-by-step explanation:

Using the rule of radicals

[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

Given

[tex]3^{\frac{4}{7} }[/tex]

= ([tex]\sqrt[7]{3}[/tex])^4 → D or

= [tex]\sqrt[7]{3^{4} }[/tex] = [tex]\sqrt[7]{81}[/tex] → E

Solve: 4(6x - 10) = 8x + 40

A 0

B.5/2

c. 23

D. 5​

Option D

The solution to given equation is x = 5

Given that we have to solve the given equation

4(6x - 10) = 8x + 40

Let us solve the above expression and find value of "x"

Multiplying 4 with terms inside bracket in L.H.S we get,

24x - 40 = 8x + 40

Move the variables to one side and constant terms to other side

24x - 8x = 40 + 40

Combine the like terms,

16x = 80

[tex]x = \frac{80}{16} = 5[/tex]

Thus solution to given equation is x = 5

Answer:

x=5, y=22. (5, 22).

Step-by-step explanation:

y-x=17

y=4x+2

----------

4x+2-x=17

3x+2=17

3x=17-2

3x=15

x=15/3

x=5

y-5=17

y=17+5

y=22

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y-x=17&(1)\\y=4x+2&(2)\end{array}\right\\\\\\\text{substitute (2) to (1):}\\\\(4x+2)-x=17\qquad\text{combine like terms}\\\\(4x-x)+2=17\qquad\text{subtract 2 from both isdes}\\\\3x+2-2=17-2\\\\3x=15\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=\dfrac{15}{3}\\\\x=5[/tex]

[tex]\text{Put the value of x to (2):}\\\\y=4(5)+2\\\\y=20+2\\\\y=22[/tex]

Answer:

Step-by-step explanation:

Use the formula

[tex]A(t)=P(1+\frac{r}{n})^{(n)(t)}[/tex]

where A(t) is the amount after all the compounding is done, P is the initial investment, r is the interest rate as a decimal, n is the number of times the investment is compounded each year, and t is time in years.  For us,

P = 6050

r = .046

n = 4

t = 6

A(t) = ?

Filling in our given info:

[tex]A(t)=6050(1+\frac{.046}{4})^{(4)(6)}[/tex]

which simplifies to

[tex]A(t)=6050(1+.0115)^{24}[/tex]

which simplifies a bit more to

[tex]A(t)=6050(1.0115)^{24}[/tex] and

A(t) = 6050(1.31577397) so

A(t) = $7960.43

which is choice C

Final answer:

The balance after 6 years is $6810.53 that is option A is correct.

Explanation:

To find the balance after 6 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt).

Given that the initial principal (P) is $6050, the interest rate (r) is 4.6% (or 0.046 in decimal form), and it is compounded quarterly (n=4 times per year), we can plug in the values and solve for A.

A = $6050(1 + 0.046/4)^(4*6) = $6810.53

Therefore, the balance after 6 years is $6810.53, which corresponds to answer choice A.

The equation that relates y, the amount of yellow paint in liters, and b, the amount of blue paint in liters, needed to make the Green Goober's special green paint is y + b = 888

Solution:

Given that the Green Goober mixes 333 liters of yellow paint with 555 liters of blue paint to make 888 liters of special green paint for his costume.

Let "y" be the amount of yellow paint in liters needed to make the Green Goober's special green paint

Let "b" be the amount of blue paint in liters needed to make the Green Goober's special green paint

The required equation is:

amount of yellow paint in liters +  amount of blue paint in liters = Green Goober's special green paint

y + b = 888

Where y = 333 liters and b = 555 liters ( from given information)

Thus the equation is found

Answer:

y=3/5b

Step-by-step explanation:

Answer:

The answer should be C. 1 1/4

Step-by-step explanation:

Eliminate A and B because none of them work

Eliminate E because we are using 1/4s

Eliminate D because we aren't using decimals

You can also think of a clock with adding 1/4s: 0.75 + 1/4= 1

1 + 1/4 = 1 1/4

(you can divide 1/2 into 2 one fourths)

The answer is 1 1/4 option C.

What is the sum of 1/2 and 0.75?

Simply add these two terms i.e:

1/2 + 0.75

Write 0.75 as a 75/100 and take lcm and lcm is 100.

1/2 + 75/100

On solving we get,

= ( 50 + 75 )/100

= 125/100

= 5/4

= 1 1/4

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Step-by-step explanation:

You must write formulas regarding the volume and surface area of ​​the given solids.

[tex]\bold{\#1\ Rectangular\ prism:}\\\\V=lwh\\SA=2lw+2lh+2wh=2(lw+lh+wh)\\\\\bold{\#2\ Cylinder:}\\\\V=\pi r^2h\\SA=2\pi r^2+2\pi rh=2\pir(r+h)\\\\\bold{\#3\ Sphere:}\\\\V=\dfrac{4}{3}\pi r^3\\SA=4\pi r^2[/tex]

[tex]\bold{\#4\ Cone:}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\text{we need calculate the length of a slant length}\ l\\\text{use the Pythagorean theorem:}\\\\l^2=r^2+h^2\to l=\sqrt{r^2+h^2}\\\\SA=\pi r^2+\pi rl=\pi r^2+\pi r\sqrt{r^2+h^2}=\pi r(r+\sqrt{r^2+h^2})\\\\\bold{\#5\ Rectangular\ Pyramid:}\\\\V=\dfrac{1}{3}lwh\\\\[/tex]

[tex]\\\text{we need to calculate the height of two different side walls}\ h_1\ \text{and}\ h_2\\\text{use the Pythagorean theorem:}\\\\h_1^2=\left(\dfrac{l}{2}\right)^2+h^2\to h_1=\sqrt{\left(\dfrac{l}{2}\right)^2+h^2}=\sqrt{\dfrac{l^2}{4}+h^2}=\sqrt{\dfrac{l^2}{4}+\dfrac{4h^2}{4}}\\\\h_1=\sqrt{\dfrac{l^2+4h^2}{4}}=\dfrac{\sqrt{l^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{l^2+4h^2}}{2}[/tex]

[tex]\\\\h_2^2=\left(\dfrac{w}{2}\right)^2+h^2\to h_2=\sqrt{\left(\dfrac{w}{2}\right)^2+h^2}=\sqrt{\dfrac{w^2}{4}+h^2}=\sqrt{\dfrac{w^2}{4}+\dfrac{4h^2}{4}}\\\\h_2=\sqrt{\dfrac{w^2+4h^2}{4}}=\dfrac{\sqrt{w^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{w^2+4h^2}}{2}[/tex]

[tex]SA=lw+2\cdot\dfrac{lh_1}{2}+2\cdot\dfrac{wh_2}{2}\\\\SA=lw+2\!\!\!\!\diagup\cdot\dfrac{l\cdot\frac{\sqrt{l^2+4h^2}}{2}}{2\!\!\!\!\diagup}+2\!\!\!\!\diagup\cdot\dfrac{w\cdot\frac{\sqrt{w^2+4h^2}}{2}}{2\!\!\!\!\diagup}\\\\SA=lw+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw}{2}+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw+l\sqrt{l^2+4h^2}+w\sqrt{w^2+4h^2}}{2}[/tex]

The solution to the given equation (-20+5) (58-65) is 105. This is calculated by first simplifying the expressions within the brackets and then multiplying the resulting numbers.

The student's question relates to the calculations and simplifying of expressions in mathematics. This type of operation can be found in basic algebra, and its mastery is an essential part of succeeding in mathematics.

To solve the equation given, which is (-20+5) (58-65), we'll need to separate it into two steps. First, simplify the expressions in the brackets. Therefore, -20+5 equals -15 and 58-65 equals -7. Now, substitute these values back into the equation getting -15 * -7. Multiplying these two values will give a product of 105. That is the final answer. The provided list of numbers following the initial problem statement seems to be irrelevant to this specific calculation.

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Final answer:

The new balance in the checkbook register is $114.04.

Explanation:

To find the new balance in a checkbook register after a deposit and a check are processed, you need to add the deposit to the current balance and then subtract the amount of the check.

Initially, the checkbook register has a balance of $158.

A deposit of $35 is made, and a check for $78.96 is written.

Calculating the new balance involves the following steps:

After completing these steps, the new balance in the register would be $193 - $78.96 = $114.04.

Balancing your checkbook regularly is essential to manage your money efficiently and to avoid fees associated with overdrafts or insufficient funds.