4/7
of a square is painted green.5/6 of the remainder is painted red. If the green
part is 36 cm² more than the red. find the area of the square.

Answer: Yes

Step-by-step explanation:

Because if you keep going it will reach 86, since it's added by 4, so 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86.

The two operations that are needed to write the expression that represents "five less than the quotient of a number and three" are Division and subtraction.

What is the quotient?

A result is obtained by dividing two amounts.

The quotient is the result of a division.

The term "less than" represents subtraction.

So, the two operations that are needed to write the expression that represents "five less than the quotient of a number and three" are Division and subtraction.

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Answer: y=2x+8

Step-by-step explanation:

you take the reverse of the slope being 2 including the negative.

Given polynomial with descending degrees of x would be,

x^4z^4 + x^3 - x^2z + z^3

In this question we have been given a polynomial x^3 + z^3 - x^2z + x^4z^4

We need to write given polynomial by descending degrees of x.

The highest degree of x in above polynomial is 4

x^3 + z^3 - x^2z + x^4z^4

then the second term would be x with degree 3.

x^3 + z^3 - x^2z + x^4z^4

the third term would be x with degree 2

x^3 + z^3 - x^2z + x^4z^4

and the last term is the term x with degree 0:

x^3 + z^3 - x^2z + x^4z^4

Therefore, given polynomial with descending degrees of x would be, x^4z^4 + x^3 - x^2z + z^3

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Trignometric equation can be used to answer this:

acc to our question-

5. cos(75)= 2-√3

6. tan(22/7)= 1+√2

7. sin 3π/6= √2-√√2/2

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Answer:

Rector, Pine, Taylor

Step-by-step explanation:

The opposite side of each angle's lengths depend on how large the angle is. The larger the angle is, the longer the side. Because the angle opposite to Rector is the greatest, then it is the longest. Thus, then follows Pine and Taylor. Hope this helps!

1. An algebraic expression that represents each purchase is as follows:

2. Supposing that x has the same value in both expressions written above, the two algebraic expressions are not equivalent because the slope of expression A is greater than the slope of expression B.

3. The cost of a soccer ball in relation to the cost of a baseball cannot be represented by the algebraic expression 4 + 5x because it is given that the cost of a soccer ball is $15, and no number can substitute the x variable to equate the two.

An algebraic expression is a combination of terms (variables and constants) using the mathematical operations of addition, subtraction, multiplication, division, etc.

a) 15x + 4(6) = 15x + 24

b) 4(6) + 5x = 24 + 5x or 5x + 24

c) Cost of a soccer ball = $15

Cost of a baseball = $6

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Soccer balls = $15 each

Baseballs=$6 each

Sweat socks =$5 per pair

Step-by-step explanation:

first put 4 3/4 into a improper fraction ---> 19/4

you get 19/4 because  4 is equal to 16/3 plus the 3/4

then you will do keep, flip change so it becomes multiplication

so instead of 1/3 divided by 19/4 it will be 1/3 x 4/19 then

multiply it out to get 19/12

Answer:

x=1 y=3

Step-by-step explanation:

By looking at the equations, you can use substitution

Set the equation equal to y

y=-5x+8

y=-2x+5

Then put equation together

-5x+8=-2x+5

Move numbers over

3x=3

x=1

Put x back into equation

5+y=8

2+y=5

y=3

a) Length of Fence = 50 meters

b) Weight of Grass Seeds = 20 kg

c) Area of Carriageway = 516 sq. meters

d) Time taken by the Striping Car = 7.6 minutes

What is a Circle?

A circular plane figure with a circumference made up of points equidistant from a given point (the center).

Solution:

a) To calculate the length of fence we need to find the circumference of the inner circle

Circumference of Circle = 2*22/7 *Radius

Circumference of Circle = 2 * 22/7 * (16)/2

Circumference of Circle = 50.24

So, the length of fence is 50 meters approx

b) To calculate the the total weight of grass we need to first find the area of the inner circle

Area of Circle = 22/7 * (Radius)^2

Area of Circle = 22/7 * (16)^2

Area of Circle = 22/7 * 256

Area of Circle = 803.84 meter sq.

For 1 meter sq. = 25 grms of grass seeeds are required

So, for 804 meters = 25*804 = 20100 grams

20100 grams = 20.1 kg = 20 kg (approx)

c) The are of Inner Carriageway will be calculated by substracting the area of inner circle from outer circle

Area of Outer Circle = 3.14 * (16+4.5)^2

Area of Outer Circle = 1320 sq. meters (approx)

Area of Inner Circle = 804 sq. meters (approx) #we have calculated it above

Area of Carriageway = 1320 - 804 = 516 sq. meters (approx)

d) Speed of Stripping Car = 25 cm/sec

Circumference of the part to be stripped = 2*3.14*(16+2.25)

Circumference = 115 meters approx. = 11500 cm

Time = Distance / Speed

Time = 11500/25 = 460 seconds

460 seconds in minutes = 7.6  minutes

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Answer:

3.3 miles with a bar notation on decimal 3

Step-by-step explanation:

convert 2/3 to decimal (2 divided by 3)

multiply 5 by decimal of 2/3

add bar notation on repeating decimal

Answer:

1000

Step-by-step explanation:

n x 5 = 5000

n = 5000/5

n = 1000

The solution of the equation given as 1/3a² + a=0 is a = 3

From the question, we have the following equation that can be used in our computation:

1/3a^2+a=0

Rewrite the equation properly

So, we have

1/3a² + a=0

Multiply through the above equation by 3

So, we have the following equation

3 * (1/3a² + a) =0 * 3

Evaluate the products

So, the equation becomes

a² + 3a = 0

Next, we divide through the equation by the variable a

This gives

a + 3 = 0

Subtract 3 from both sides of the equation

i.e. Add -3 to both sides of the equation

a = -3

The above equation cannot be solved further.

So, we leave it like that and stop solving

Hence, the solution to the equation is a = -3

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Answer:

he read 9 chapters

Step-by-step explanation:

4:30 pm to 6:00 pm is 1:30 hours, which is 90 minutes

90/10=9

Answer:

B) 7,720,360 sq. km

Step-by-step explanation:

8,508,238 - 787,878 = 7,720,360 sq. km

Hope this helped :)

The answers to the worksheet are in the included picture! :p

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This is just an example on how to simplify fractions: Write the simplified form of the fraction 12/24.

The given fraction is 12/24.

Step 1: Let us write the factors of 12 and 24.

Factors of 12 are: 1, 2, 3, 4, 6, 12

Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

Step 2: Let us identify the common factors of 12 and 24.

Common factors are: 1, 2, 3, 4, 6, 12

Step 3: Keep dividing the numerator and denominator by the common factors.

(12 ÷ 2)/(24 ÷ 2) = 6/12

And

(6 ÷ 2)/(12 ÷ 2) = 3/6

Now divide by 3,

(3 ÷ 3)/(6 ÷ 3) = 1/2

Thus, 1/2 is the simplified fraction of 12/24.

-------------------------------------------------------

Have a great day and God bless! :D

The ending balance after 3 years is $1508.34

What is compound interest?

The interest that is paid on both the initial principal and the accumulated past interest is known as compound interest.

The compound amount and compound interest are calculated by:

  Compound amount,   [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

  Compound interest, [tex]I = A - P[/tex]

where, P is the principal amount

           r is the rate of interest(in decimal)

           n is the number of  times the interest is compounded annually

           t is the time.

Given, Principal amount, P = $1400

           rate of interest, r = 2.5% = 0.025

           n = 2 (compounded semi-annually)

           t = 3 years

Then, the compound amount is calculated by:

                 [tex]A=1400(1+\frac{0.025}{2} )^{2*3}\\[/tex]

          or,       [tex]A=1400(1+0.0125 )^{6}\\[/tex]

          or,       [tex]A=1400(1.0125 )^{6}\\[/tex]

          or,       [tex]A=1508.34[/tex]

Therefore, the ending balance is $1508.34

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Answer:

B

Step-by-step explanation:

if x = 0 ; y = 3

if x = -7 ; y = 0

A 0 + 7(3) = 21

0 + 21 = 21

21 = 21 (ok)

3(-7) + 0 = 21

-21 = 21 (false)

B

0 + 21 = 21

21 = 21 (ok)

(-3)(-7) + 0 = 21

21 = 21 (ok)

The initial population of the bacterial population at time t = 0, can be found to be 1,406.25.

The size of the bacterial population after 3 hours is 720,000.

The doubling period of the bacterial population is said to be 20 minutes. The number of doubling periods in 120 minutes is:

= 120 / 20

= 6 doubling periods

The initial population is:

= Population at 120 minutes / 2 ^ number of doubling periods

= 90,000 / 2⁶

= 1,406.25

The bacterial population at 3 hours is:

= Bacterial population at t = 0 x 2 ^ number of doubling periods in 3 hours

= 1,406.25 x 2 ^ (180 minutes in 3 hours / 20)

= 1,406.25 x 2⁹

= 720,000

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The average speed for the given situation is 56 mph.

Given that, Abby 3 hours to drive from Ashdown to Bridgeton at an average speed of 60 mph.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Now, distance = Speed × Time

= 60 × 3

= 180 miles

She then drives 30 miles from Bridgeton to Carton at an average speed of 40 mph.

Now, Time = 30/40

= 0.75 hours

Total time =3+0.75=3.75 and total distance =180+30=210

Then average speed = 210/3.75

= 56 mph

Therefore, the average speed for the given situation is 56 mph.

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Answer:

3.2 pages per minute

Step-by-step explanation:

Unit Rate: 64 / 20 = 3.2 pages per minute

A unit rate is just a measure of either how fast you can do one of something, or how fast you can do something in one unit of time :)

Answer:

Step-by-step explanation

64 pages ÷ 20 =

20 minutes ÷ 20 =

3.2 pages

1 minute

so she read 3.2 pages per minute

The probability that more than one-fourth of them will have low levels of literacy as described above is 0.3043.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given: A study conducted by the Institute of Education Sciences from 1992 to 2003 found that about 22% of adult Americans had low levels of literacy and were “not able to locate information in text,” could not “make low-level inferences using printed materials” and were unable to “integrate easily identifiable pieces of information.”

A simple random sample of 50 adult Americans is collected.

n(p) = 50(0.22)

n(1 - p) = 50(1 - 0.22)

The CLT would hold here.

n = 50

p = 0.22

p cap = 0.25

The test statistic, z = (p cap - p) / (√p (1 - p) / n)

z = (0.25 - 0.22)/(√0.22(1-0.22)/50)

z = 0.51

The p-value is 0.3043.

Hence, The probability that more than one-fourth of them will have low levels of literacy as described above is 0.3043.

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The equations that represent the proportional relationships between the variables are as follows:

     Problem                   Variables to use          Equation

1. Tyler swimming         Time / Distance          D = 1.25t

2. Factory production   Total quantity, Q,         Q = 3s + 8p

                                      and Sparkling / Plain

3. Paint mixture            Blue / White Paints  6q = 1.5b + 5w

An equation models a mathematical statement in which two or more expressions (involving numbers, variables, and operands combined) are equated using the equation symbol (=).

Speed = 5 m/4s

= 1.25 m/s (5/4)

Swimming equation: D = 1.25t

Where D = distance and t = time spent.

Given the speed and time, we can find the swimming distance covered by Tyler.

Bottles of sparkling water = 3

Bottles of plain water = 8

Ratio = 3:8

Production equation, Q = 3s + 8p

Where Q = total quantity, s = sparkling water, and p = plain water

Blue paint = 1 ½ quarts

White paint = 5 quarts

Ratio = 1.5:5

Production equation, 6q = 1.5b + 5w

Where 6q = 6 quarts, b = blue paint, and w = white paint

Thus, using the equations, we can use the known variables to find the unknown variables.

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Answer:

5x=325+160

Step-by-step explanation:

this was very easy but i guess with so many words it could confuse people

The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x

Given,

The points which the line passes through = (6, 4)

Slope = 2/3

We have to find the equation of line;

Linear equation;

Y = mx + b is one way to represent a linear equation.

Here,

x is 6 and y is 4

Slope, m is 2/3

Then,

Substitute the values in y = mx + b

Here,

y = mx + b

4 = 2/3 (6) + b

4 = 12/3 + b

4 = 4 + b

b = 4 -4

b = 0

Then,

The equation of line is, y = 2/3x + 0

That is,

The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x

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The solution of 5√3 × 3√12 = 30√3.

Square root of a number is defined as the number in which the multiplication by itself gives the original number. That is the square root of 9 would be = 3 in which when multiplied by itself gives the original number being 9.

Other examples include √ 4 = 2, √ 25 = 5, √100 = 10.

To simplify the give expression;

5√3 × 3√12= 5√3 × 3√4×3

= 5√3 × 3×2√3

= 5√3 × 6 √3

= 30√3.

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By using linear pair, we have found that the value of x is 3.

Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

Given that  Angle QGP = 80°, Angle ROP = 3 + 59x and Angle ROG= 32x + 4. Find x.

Therefore, we can see that Angle ROG and Angle QGP lie in a straight line.

Thus, by linear pair

Angle ROG + Angle QGP = 180

80° + 32x + 4 = 180

32x = 100 - 4

x = 96/32

x = 3

Hence, the value of x is 3.

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The probability that the proportion of no-shows in a sample of 789 ticketed passengers would differ from the population proportion by less than 3% is 0.9968

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = p = 9% = 0.09

sample size, n = 789

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.09(1 - 0.09)) / 789}

= √{(0.09 * 0.91) / 789}

= 0.0102

The probability

differ from the population proportion by less than 3%

|X - 0.09| < 0.03

X < 0.12 OR X > 0.06

0.06 < X < 0.12

P(z < 0.12) - P(z < 0.06 )

z score for z < 0.06

z = (0.06 - 0.09) / 0.0102

= -2.9412

p value for z < -2.9412 = 0.0016

z score for z < 0.12

z = (0.12 - 0.09) / 0.0102

=  2.9412

p value for z < 2.9412 = 0.9984

The probability required = 0.9984 - 0.0016 = 0.9968

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