Question 3(Multiple Choice Worth 1 points)
(02.04 MC)
In triangle DEF, if mZD = (2x)°, mZE = (2x - 4)º, and mZF = (x + 9)°, what is the value of x?
A)35
B)37
C)44
D)71

Answer:

  (d)  Jamar's ending account balance is higher than Beth's ending balance.

Step-by-step explanation:

You want to know the best description of the relationship between final balances of two ordinary annuities:

The attached calculator display shows the ending balance for Jamar's annuity and for Beth's annuity. We assume the final balance is the balance after the final payment. That is, Beth's balance will be known 15 years before Jamar's balance is known.

Jamar's balance: $274,083.57

Beth's balance: $167,247.33

The best description is ...

Jamar's ending account balance is higher than Beth's ending balance.

__

Additional comment

Jamar makes twice as many payments of half the amount each, so his total contribution is the same as Beth's. His early payments are earning interest for twice as long as Beth's, so his account earns more interest.

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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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 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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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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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

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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Answer:

1000

Step-by-step explanation:

n x 5 = 5000

n = 5000/5

n = 1000

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

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)

Answer:

5x=325+160

Step-by-step explanation:

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

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

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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4500 is the Cost price.

What do you mean by price at cost?

SP = 5625

Profit = 25%

CP = ?

 CP =    5625/125 * 100

       = 45 * 100

       = 4500

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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:

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

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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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!

Answer:

B) 7,720,360 sq. km

Step-by-step explanation:

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

Hope this helped :)

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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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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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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Answer: y=2x+8

Step-by-step explanation:

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

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: 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.

Step-by-step explanation:

=6a^3+7a^2-5a^3-9a^2-a

=a^3-2a^2-a this is the final answer.