A teacher runs each morning before school. Last week, he ran a total of 5 3/4 miles. This week, he ran 4/5 of the total number of miles he ran last week. What is the total number of miles that the teacher ran last week and this week?

Answer:  7 4/10 + 2/10 = 38/5 = 7 3/5 = 7.6

Answer Overall : 38/5

Step-by-step explanation:  Conversion a mixed number 7 4/10 to a improper fraction: 7 4/10 = 7 4/10 = 7 · 10 + 4/10= 70 + 4/10= 74/10

To find a new numerator:

a) Multiply the whole number 7 by the denominator 10. Whole number 7 equally 7 * 10/10 = 70/10

b) Add the answer from previous step 70 to the numerator 4. New numerator is 70 + 4 = 74

c) Write a previous answer (new numerator 74) over the denominator 10.

Seven and four tenths is seventy-four tenths

Add: 74/10 + 2/10 = 74 + 2/10 = 76/10 = 2 · 38/2 · 5 = 38/5

The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 38/5.

In other words - seventy-four tenths plus two tenths is thirty-eight fifths.

First convert the mixed number to a fraction by multiplying 7 by 10 and adding 4

add them together but DONT add the denominators

These numbers can be simplified by 2 so the final answer is:

By solving the given fraction equation we get the answer is 1.

What is an exponent?

Exponent is the process of expressing large numbers in terms of powers. In other words, the exponent describes how many times a number has been multiplied by itself.

According to the zero exponent rule, any base with a zero exponent is equal to one. For instance, [tex]x^{0} = 1[/tex].

We have,

[tex]= \frac{1.25\\ * \\ 10^{-3}}{1.25 \\ * \\ 10^{-3}}[/tex]

[tex]= \frac{1.25\\ * \\ 10^{-3}}{1.25 \\} * 10^{3}[/tex]

Using the multiplication rule of fraction [tex]a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]

[tex]= \frac{1.25 \ * \ 10^{-3} \ * \ 10^{3}}{1.25 \\}[/tex]

= [tex]= 10^{-3} * 10^{3}[/tex]

By applying the exponent rule [tex]\:a^b\cdot \:a^c=a^{b+c}[/tex] we get,

Add or subtract the numbers = 3 + 3 = 0

[tex]= 10^{0}[/tex]

By applying the rule [tex]a^{0} = 1[/tex], [tex]a \neq e^{0}[/tex]

= 1

Hence, by solving the above fraction equation we get the answer is 1.

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Answer:

10^3 = 1000

Step-by-step explanation:

10 * 10 * 10 = 1000

Answer:

1000

Step-by-step explanation:

it is ten to the third power so 10*10*10  and then you get the answer of:

1000

I hope this helped!

Answer:$190

Step-by-step explanation:

for an expression is $80+$65+$50=190 per dog to adopt a from the animal shelter.

Answer:

Step-by-step explanation:

9.65+0.4=10.05

16.058-1.2=14.858

According to the histogram, the percentage of participants aged 40 to 59, who attended the restaurant's food festival, is 35%.

A histogram approximately represents a distribution of grouped data with numerical values.

A histogram uses rectangular bars to show the frequency of data items in successive numerical intervals of equal sizes.

Age Group (year)  Number of People

0 to 19                            20

20 to 39                         40

40 to 59                         60

60 to 79                         50

Total                             170

Percentage of ages 40 to 59  =  60/170 x 100 = 35.29%

Thus, using the histogram, we can assure the restaurant manager that 35% of the festival participants are between 40 and 59 years old.

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Answer:

the length of WZ is 10

Step-by-step explanation:

Answer:

There is only one solution

Step-by-step explanation:

4x - 7 = 2x + 15

+7        +7

4x = 2x + 22

-2x   -2x

2x = 22

divide by 2 into both sides

x = 11

Since there is only one answer, there is only ONE solution.

Fraction of her career has she been at her current job is 1/3 or 0.333.

Given:

Mr.Marx has been in the journalism industry for 24 years.

She has worked at her current job 8 of those years.

Fraction = number of year in current job/number of years in journalism industry.

= 8 years/24 years

= 8/24

= 1/3 ≈ 0.333.

Therefore fraction of her career has she been at her current job is 1/3 or 0.333.

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The balance in Lee's account at the end of 6 years is $384,830.53.

The first step is to determine the future value of the initial amount deposited in the savings account.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

Balance at the end of 3 years: $17,000 x (1.045)^(3 x2) = $22,138.42

The total value of the account after $42,000 is deposited is:

$42,000 + $22,138.42 = $64,138.42

The future value of $64,138.42 at the end of 6 years is:

Balance at the end of 6 years: $64,138.42 x (1.045)^(3 x2) = $384,830.53

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Answer:

8.25

Step-by-step explanation:

Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

WE have been given an expression as 43πr³ represents the volume of a sphere, with radius r.

Terms can be added or subtracted to make a polynomial. They are composed of variables and constants all in multiplication.

So we know that if there is one term, then the polynomial will be called monomial.

Therefore, this expression is a monomial which have inly one term as 43πr³ .

Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.

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The surface area of the largest sphere that could fit into the rectangular box of dimensions 12 in x 14 in x 18 in is 324π inches²

The surface area of sphere = 324π inches²

What is a Sphere?

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

The Surface Area of a Sphere = 4πr²

The Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

Given data ,

Let the surface area of the Sphere be = S

Let the dimensions of the rectangular box be L x W x H

12 inches x 14 inches x 18 inches

Now , for the surface area of the sphere to have the largest surface area , the radius should be maximum

From the rectangular box , we can see that the height of the rectangle is best suited as the diameter of the sphere

So , Height of the Box = Diameter of the Sphere

And , Radius of the sphere = Height of the Box / 2

                                             = 18 / 2

Radius of the sphere = 9 inches

Now ,

Surface Area of a Sphere = 4πr²

r = 9 inches

Substituting the values in the equation , we get

Surface Area of a Sphere S = 4 x π x ( 9 )²

                                              = 4 x π x 81

                                              = 324π inches²

Therefore , the value of S is 324π inches²

Hence , The surface area of sphere = 324π inches²

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Answer:

Left graph.

Domain: all real numbers.

Range: y ≤ 4

Middle graph.

Domain: all real numbers

Range: y ≥ 3

Right graph.

Domain: x ≥ -2

Range: y ≥ -3

Answer:

1.  Domain:  (-∞, ∞)     Range:  (-∞, 4]

2.  Domain:  (-∞, ∞)     Range:  [3, ∞)

3.  Domain:  [-2, ∞)     Range:  [-3, ∞)

Step-by-step explanation:

Definitions

Note:  Assume that each square on the given graphs is 1 unit.

As there are arrows at both endpoints of the curve, the domain of the function is unrestricted.

The curve has a maximum point at (2, 4) and continues indefinitely towards negative infinity at both endpoints.

Therefore, the range of the function is restricted.

As there are arrows at both endpoints of the function, the domain is unrestricted.

The function has a minimum point at y = 3.

When x > -2, the line continues indefinitely at y = 3.

When x < -2, the line continues indefinitely towards infinity.

Therefore, the range of the function is restricted.

The domain of the function is restricted since there is a closed circle at one endpoint: (-2, -3).  When x > -2, the line continues indefinitely towards infinity.

The function has a minimum point at (-2, -3). As x continues towards infinity, so does y.

Therefore, the range of the function is restricted.

The equation have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p

Given: 2.3p – 10.1 = 6.5p – 4 – 0.01p.

Using this given property, let's write the equation

We can subtract like terms (6.5p– 0.01p = 6.49p) to get:

2.3p – 10.1 = 6.5p – 0.01p – 4

2.3p – 10.1 = 6.49p – 4

Also, we can multiply both sides of the algebraic equation by 100:

(2.3p – 10.1) x 100 = (6.5p – 4 – 0.01p) x 100

230p – 1010 = 650p – 400 – p

Therefore, the equations have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p. The 2nd and 3rd options are the answers

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The number of miles (m) between the two cities as represented in the equation given 2[(4m * 3.5) / 400] = 171.5 is 2450 miles

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

In the equation given;

2[(4m * 3.5) / 400] = 171.5

Using changing the subject of formula to find the miles travelled;

2[(4m * 3.5) / 400] = 171.5

28m / 400 = 171.5

28m = 400 * 171.5

28m = 68600

m = 68600 / 28

m = 2450

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Answer: y=5 is the asymptote answer

The number of adult tickets were sold is 130 tickets.

Given,

In the question:

Total tickets were sold for the school play is 390 tickets.

The number of student tickets sold was two times number of adult tickets sold.

To find the how many adult tickets were sold?

Now, According to the question:

Based on the given conditions:

Let the number of adult tickets be x.

Formulate the condition:

x × (1 + 2) = 390

x × 3 = 390

Simplify

x = 390/3

x = 130

Hence, The number of adult tickets were sold is 130 tickets.

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The required equation  can be used to determine the pounds of laundry the customer brought in is A. 0.61x + 28.00 = 41.42

An equation is a mathematical expression that shows the relationship between two variables.

To find the given equation,

Let x be the number of pounds of clothes washed and folded at the laundromat.

Given that the laundromat will wash and fold clothes at $0.61 per pound for those customers with a laundry service, the total amount paid for the number of poundsof clothes is P = rate × number of pounds = $0.61 × x = 0.61x

Also, the laundromat has a wash-and-fold service for a monthly fee of $28.00.

So, the total amount paid is T = P + $28.00 = $0.61x + $28.00

Now, since one customer paid $41.42 in total for the month, since this is the total amount paid, then T = $41.42

So, $0.61x + $28.00 = $41.42

So, the required equation is A. 0.61x + 28.00 = 41.42

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A triangle is said to be right angle if one of the angles is 90 degrees, the value of the side x for the given right angle triangle is 50.51.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° .

The given right-angle triangle has the following sides,

AC = Base

BC = Perpendicular

AB = Hyp.

By tan function,

Since,tanθ = Perp/Base

tan29° = 28/x

x = 50.51

Hence, "A triangle is said to be right angle if one of the angles is 90 degrees, the value of the side x for the given right angle triangle is 50.51".

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Answer:

m∠1 = 26°

Step-by-step explanation:

Interior angles of a triangle sum to 180°, not 360°.

Therefore, the correct calculations to find the measure of angle 1 are:

[tex]\boxed{\begin{aligned}115^{\circ}+39^{\circ}+m \angle 1 &=180^{\circ}\\\\154^{\circ}+m \angle1 & = 180^{\circ}\\\\m \angle1 & = 26^{\circ}\end{aligned}}[/tex]

Answer:

Step 1:subtract 5 from both sides

step 2: divide both sides by two

final answer: c= p-5/2

Answer:

Step 1: Subtract 5 from both sides.

Step 2: Divide 2 from both sides.

Final answer: C= p-5 / 2

Step-by-step explanation:

The independent variable x is the hour of work.

The dependent variable y is the total money Ethan earn per visit.

The y-intercept is 25.

The slope is 22.

Ethan charges a one time fee of 25 dollars. For each visit Ethan earns 22 dollars for each hour of work.

Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges 25 plus 22 per hour of work.

A linear equation that expresses the total amount of money Ethan earns per visit is y = 25 + 22x.

Using slope intercept equation,

y = mx + b

where

y = 25 + 22x

The independent variable x is the hour of work.

The dependent variable y is the total money Ethan earn per visit.  

The y-intercept is the value of y when x = 0. Therefore, the y-intercept is 25.

The slope is the change in the dependent variable with respect to the change in the independent variable. The slope is 22.

Ethan charges a one time fee of 25 dollars. For each visit Ethan earns 22 dollars for each hour of work.

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The equation of the line is : y = -1x + 3

What is Equation of line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

Given,

3x + 3y = 2

3y = -3x + 2

y = -x + 2/3

Comparing it with

y = mx + c

we get,

m = -1

Now, let the equation of line be

y = mx + c

where, m = -1

Now we have to check for point (0,0) that it satisfies

0 = -1(0) + c

c = 0

So, the equation of line will be y = -1x

Now, let y = mx + c be the equation of line of point (-3, 6) should satisfy]

6 = -1(-3) + c

6 = 3 + c

c = 6 - 3

c = 3

So the equation of line is y = -1x + 3

Hence, The equation of the line is  y = -1x + 3

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When you add polynomials of different degrees, it is not adding up the degrees, in special cases this may end up with smaller degree polynomials.

When you multiply polynomials of different degrees, it adds up the degrees, and the final polynomial is off the higher degree.

The answers:

Jada is planning a kayak trip. She finds an expression for the time, T(s), in hours it takes her to paddle 10 kilometers upstream in terms of s, the speed of the current in kilometers per hour. Jada gets if she allows s to take on any value between 0 and 7.5.

The domain of the function that represents Jada's trip is the set of input value the function can take

The appropriate domain is all real numbers except

x = 5.5

by looking at the graph, we can see that:

The x-value starts at negative infinity, and ends near 5.5

The x-value then continues near 5.5, and ends at positive infinity

This means that the input of the graph cannot be 5.5

Hence, an appropriate domain would be: x # 5.5

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[tex]log_{4}(2) + log_{4}(3)+ log_{4}(5+2x)[/tex] is the completely expanded logarithmic expression .

Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to  base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8.

The most common types of logarithms are  the base 10 common logarithm, the base 2 binary logarithm, and  the base  e ≈ 2.71828 natural logarithm.

the product rule for logarithms is

[tex]log_{b}(MN) = log_{b}(M) + log_{b}(N)[/tex]  for b > 0

now ,

[tex]log_{4}(6(5 + 2x)) \\\\log_{4}(6) + log_{4}(5 + 2x)\\ \\ log_{4}(2.3) + log_{4}(5 + 2x) \\\\ log_{4}(2) + log_{4}(3)+ log_{4}(5 +2x)[/tex]

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Zach's investment is $100,000.

A ratio shows us the number of times a number contains another number.

Given that Zach, Kolby, and Peyton are investing a total of $350,000 to open a coffee shop. And their investments are in the ratio 1:2:0.5, respectively.
Therefore, Zach, Kolby, and Peyton's investment can be written as  1x, 2x, and 0.5x, respectively.

Now, the total sum of the investment of the three can be written as,

Zach's investment + Kolby's investment + Peyton's investment = $350,000

1x + 2x + 0.5x = $350,000

3.5x = $350,000

x = $350,000 / 3.5

x = 100,000

Further, Zach's investment can be written as,

Zach's investment = 1x = 1($100,000) = $100,000

Hence, Zach's investment is $100,000.

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