John and Sam have a lawn mowing service. At one home, John can mow the lawn by himself in 2 hours, but it takes Sam 2.5 hours. How many hours twill it take them to mow the same lawn
together? Give the answer correct to one decimal place.

Here is a table that shows the frequency and the relative frequency distributions:

Class  Frequency    Relative frequency

A           57                      0.475

B           26                     0.217

C           37                      0.308

Total      120                         1

Frequency measures the number of times a response is observed in a dataset. For example, the frequency of A is 57. Relative frequency measures how often a value appears relative to the sum of the total values. The sum of relative frequency is equal to 1.

Relative frequency = frequency / total frequency

A = 57 / 120 = 0.475

B =26 / 120 = 0.217

C = 37 / 120 = 0.308

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The meaning of the 0.4m in this equation is the additional cost of hiring the delivery truck for m number of miles.

Given equation:

C = 0.4m + 68

Where

m = number of miles

C = total cost of hiring the delivery truck

68 = Fixed cost of hiring the delivery truck

0.48 = Additional cost per mile of hiring the delivery truck

For instance,

If the truck is hired for 10 miles

C = 0.4m + 68

= 0.4(10) + 68

= 4 + 68

C = $72

Therefore, the meaning of the 0.4m in this equation is the additional cost of hiring the delivery truck for m number of miles.

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Part a: Expression for length; l = 2w + 3.

Part b: Perimeter equation; P = 2(l + 10).

Part c: Length of rectangle = 29 feet.

The given conditions are-

Let 'l' be the length of the rectangle.

Let 'w' be the width of the rectangle.

Part a: expression for the length of a rectangle in the terms of w.

Length is three feet more than twice its width.

l = 2w + 3

Thus, the expression of l in terms of w is: l = 2w + 3.

Part b: Perimeter equation.

The width is given as 10 feet.

The formulae of perimeter if rectangle is;

P = 2(l + w)

Put the value;

P = 2(l + w)

P = 2(l + 10)

Thus, the equation for perimeter is P = 2(l + 10)

Part c: Length of rectangle.

perimeter of rectangle = 78 units.

P = 2(l + w)

w = 10 feet.

78 = 2(l + 10)

l + 10 = 39

l = 29

Thus, the length of the rectangle is found as 29 feet.

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Answer:

30

Step-by-step explanation:

Divide

[tex]\frac{12}{6}\\\\\bold{Long\:division}\\6 \times 2 = 12\\= 2[/tex]

[tex]\mathrm{2\:remainder\:0}[/tex]

Simplify the rest of the expression

[tex]= 30 - 0\\= 30[/tex]

Hope this helps!

Based on the scores given in the table, the mean of the scores can be found to be 78

The mean of the scores can be found by adding all the scores together and then dividing the sum by the number of scores in the table.

The sum of the scores is:

= 56+ 82 + 90 + 83 + 79 + 59 + 71 + 66 + 53 + 94 + 78 + 80 + 67 + 65 + 86 + 76 + 83 + 92 + 69 + 69 + 91 + 68 + 78 + 87 + 87 + 81 + 87 + 76 + 96 + 83

= 2,332

The mean is:

= 2,332 / 30

= 77.73

= 78

Question is:

What is the mean of the scores?

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Five 10-oz water bottles will have a lower unit price. The correct option is B.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that there are two conditions for water bottles Five 10-oz bottles for $2.30 and Seven 12-oz bottles for $4.20. The water bottle having the lower price will be:-

Five 10-oz bottles = $2.30

One 10- oz bottle = 2.30 / 5 = $0.46

Seven 12-oz bottles = $4.20

One 12-oz bottles = $4.20 / 7 = $0.6

Therefore, five 10-oz water bottles will have a lower unit price. The correct option is B.

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According to the solving his unused inventory will have = x - [tex]\frac{468}{5}[/tex]

A mixed fraction is defined by its quotient as well as remainder. 2/3, for example, is a mixed fraction in which 2 is the quotient and 1 is the remainder. A mixed fraction is thus the product of a whole number as well as a proper fraction.

If the only common factor of a fraction's numerator and the denominator is 1, the fraction is considered to be in its simplest form. For example,89, because 1 is the sole common factor in this fraction of 8 and 9. We simplify fractions simply because it is usually easier to work with or compute fractions when they are in their simplest form.

Every day, a farmer sells on average of 15 3/5 bushels of maize.

Converting  mixed fraction to proper fraction;

[tex]15\frac{3}{5}[/tex] this can be written as [tex]\frac{78}{5}[/tex]

Assume he has a total of x bushels.

As a result, he will sell in 6 days.

= 6 x [tex]\frac{78}{5}[/tex]

= [tex]\frac{468}{5}[/tex]

So,

According to the solving his unused inventory will have = x - [tex]\frac{468}{5}[/tex]

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I understand that the question you are looking for is:

A farmer sells an average of 15 3/5 bushels of corn each day. What integer represents the change in bushels of corn in his inventory after 6 days.

Since no equation of the line, or graph is provided in the question statement, considering the line to be [3x +4y = 12], the y-intercept of the line is 3.

As per question statement, we are supposed to determine the y-intercept of the line on the graph, but no equation of the line, or graph is provided. Hence, we considered the equation of a random line, say,

[3x +4y = 12] and then, determine it's y-intercept.

To solve this question, we can use two methods:

One method is by converting the given equation into the format of the standard equation of a line, and then comparing it to the standard equation to determine the y-intercept, i.e.,

The standard equation of line is (y = mx + c), where, "m" is the slope of the line, and "c" is the y-intercept. Converting [3x +4y = 12] to the form of the standard equation, we get,

[tex]3x+4y=12\\or,4y=-3x+12\\or,y=\frac{-3x+12}{4}\\ or,[y=(\frac{-3}{4})x+3]...(i)[/tex]

Now comparing (i) to the standard equation of line, we can identify that

(c = 3), i.e., y-intercept of the line [3x +4y = 12] is 3.

Another way we can determine the y-intercept of a line is by, substituting (x = 0) and then solving the equation for "y".

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Answer:

Step-by-step explanation:

-3√(4)(10)  - √(16)(10)

-3(2)√(10) - 4√(10)

-6√(10) - 4√(10)

-10√(10)

Based on the fact that Shannon has created 4 levels for her game after 8 weeks, the equation for the relationship between x and y is y = 2x

y is used to denote the number of weeks it takes to program the number of levels which is 8 weeks.

x is the number of levels that Shannon would have made for the game which is 4 levels.

The relationship between y and x is:

= y / x

= 8 weeks / 4 levels

= 2 weeks per level

The relationship can then be shown as:

y = 2x

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Answer:

c= 1    w =1.25    

Step-by-step explanation:

10w +6c = 26-   2w +6c= 16      Subtration =  8w = 10  =     10/8   = 1.25  = w =1.25 12(1.25)+ 6c = 16  = 2.5 + 6c = 8.5     Subtration = 6c = 8.5 -2.5 =  6c = 6  = c= 6/6 = 1  c= 1

Tanya will then have 286 cookies after baking 12 more batches.

A linear equation's slope-intercept form is y = mx + b. The variables in the equation are x as well as y. The integers m and b represent the the line's slope (m) and the value of y when x is 0 respectively (b). Because (0,y) is the point when the line crosses the y-axis, the value of y when x is 0 is known as the y-intercept.

A linear equation with one variable is one with only one variable. It has the formula Ax + B = 0, where A and B can be any two real numbers as well as x is an unknown variable with a single solution. 9x + 78 = 18, for example, is a one-variable linear equation.

y = 70 + 18(x)

x = 12 batches.

substituting the value in the equation:

y = 70 + 18(x)

y = 70 + 18(12)

   = 70 + 216

y  = 286.

Tanya will then have 286 cookies after baking 12 more batches.

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Answer:

Step-by-step explanation:

(0.1)²=0.01

(0.2)²=0.04

(0.3)²=0.09

(0.4)²=0.16

(0.5)²=0.25

(0.6)²=0.36

(0.7)²=0.49

(0.8)²=0.64

√0.5 or √0.50 is between √0.49 and √0.64

or

0.7 and 0.8

(0.01)²=0.0001

(0.02)²=0.0004

(0.03)²=0.0009

(0.04)²=0.0016

(0.05)²=0.0025

so √0.002 or √0.0020 is between √0.0016 and √0.0025

or between 0.04 and 0.05

A truth table is a breakdown of a logic function by listing all possible values the function can attain.

This tool generates truth tables for propositional logic formulas. You can enter logical operators in several different formats. For example, the propositional formula p ∧ q → ¬r could be written as p /\ q -> ~r, as p and q => not r, or as p && q -> !r. The connectives ⊤ and ⊥ can be entered as T and F.

P Q (Q ∧ P)

F F F

F T F

T F F

T T T

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[tex]6000 + \frac{14 \\ }{100} \times 6000 = 6840 \times 6 = 41040[/tex]

The photograph is 6 inches wide and 15 inches long.

Answer:

13

Step-by-step explanation:

According to the Pythagorean principle

[tex]c^{2} = a^{2} +b^{2}[/tex]

[tex]c^{2} = (5^{2} ) + (12^{2} ) = 25 +144= 169\\c= \sqrt{169 } = 13[/tex]

Answer:

2/3

Step-by-step explanation:

To find this, we need to find out how many numbers are greater than 2 but no more than 6. This set includes 3, 4, 5, 6; there are 4 numbers that qualify for this. This means that out of all 6 numbers, 4 numbers are in the probability, so our answer would be 4/6 = 2/3

Answer:

2/3

Step-by-step explanation:

The probability of a die getting 3,4,5,6 over a 1 or 2 is 4 chances out of the 6 chances in a die, or 2/3.

It should be noted that the information regarding the transformation illustrates that Elena is wrong.

A point, line, or geometric figure can be transformed in a way that affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

It should be noted that the first step makes the figures be the same by size but the second step, reflection over line AE doesn't map them together.

In this case, the correct line of reflection would be a vertical line through point D.

Therefore, it should be noted that the information regarding the transformation illustrates that Elena is wrong.

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Elena gives the following sequence of transformations to show that the two figures are similar by

transforming ABCD into EFGD.

1. Dilate using center D and scale factor 2.

2. Reflect using the line AE.

All the roots of equation x⁴ +2x³ -x² -2x +10 are: (1 + i), (1 - i), -2i, 2i

In the given question, we have to find out all the roots or solutions for the equation x⁴ +2x³ -x² -2x +10. One of the roots given for this equation is 1+i

According to the 'Complex Conjugate' pairs, if an equation has a complex number as a root then its conjugate will also be a root of the equation.

So, we get z = 1 + i as a root then z* = 1 - i which is the conjugate of z, and z* will also be a root of the equation.

Also, the product of two roots will also be a root of the equation. So,

we know that, x = 1 + i, x = 1 - i, we get their product:

(x -(1 + i))*(x - (1 - i))   => by solving we get => x² -2x +2 = 0

     => x² -2x +1 = 1  => x² -x -x +1 = 1 (by middle term split)

     => x(x-1) -1(x-1) = 1  => we get (x - 1) as a factor

So, (x - 1) = 1  => x = 2

    => x = -2i, we get x = -2i

Again, by Complex conjugate pairs if x = -2i is a factor then it's conjugate x = 2i is also a factor.

Hence, the roots of the equation are: (1 + i), (1 - i), -2i, 2i

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It should be noted that two perfect squares so that the square root will fall between consecutive numbers of 0.4 and 0.5 include 0.2025 and 0.2209.

It should be noted that based on the information, we want to find two perfect squares so that the square root will fall between consecutive numbers of 0.4 and 0.5.

In this case, it should be noted that 0.45 × 0.45 = 0.2025. It should be noted also that 0.47 × 0.47 = 0.2209.

As a result, 0.2025 and 0.2209 are two perfect squares such that the square root will lie between consecutive numbers of 0.4 and 0.5.

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Answer:

rational numbers

Step-by-step explanation:

An adult's weight can be a non-integer, but is likely of the form of a decimal.

This matches best with the set of rational numbers (of which we take the positive ones).

Answer:

=The numbers which donot have factors and can be only divided by themselves are know as prime numbers.Eg: 2,3,5,7

= A number that can be represented as the quotient p/q of two integers such that q ≠ 0 are known as rational numbers. Eg 4/8,5,-10

=An irrational number is a number that cannot be expressed as a fraction for any integers.Eg -0.25,3.5

Answer:

f(1) = 11

Step-by-step explanation:

ƒ(x) = 3x + 8 for x = 1.

f(1) = 3(1) + 8

f(1) = 3+ 8

f(1) = 11

I hope this helps!

Answer: offf

Step-by-step explanation:off

Answer:12.35 = t

Step-by-step explanation:

95 + t + 3.5 = 110.85

where t  = tax

12.35 = t