Factor -4 out of -8+20 expression

If the two cyclists are 82 miles apart after 2 hours, The rate of each cyclist is: The slower cyclist's speed is 17 mph and the faster cyclist's speed is 24 mph.

Let x mph = speed of the slower cyclist = (x +7) mph

Let 2x miles represent the slower cyclist has traveled

2(x + 7) = 2x + 14 miles

Hence,

2x + (2x + 14) = 82

4x = 68

Divide both side by 4x

x = 68/4

x= 17 mph (slower)

So,

(x +7) mph

= 17 + 7

= 24 mph (fastest)

Therefore the speed is 17 mph and 24 mph.

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The percentage discount of 40% from the regular price of shoes and  the $73.5 Gwen saves indicates that the regular price of each pair of shoe she buys is $61.25

A percentage is the expression of a proportion based on a scale of 100. A percentage can be described as a fraction that has 100 as the denominator.

The percentage discount = 40%

The amount Gwen saves = $73.50

The number of shoes she buys = 3

The discount on each shoe = $73.5 ÷ 3 = $24.5

Let x represent the regular price of each shoe, from the information in the question, we have;

40% of x = $24.5

40% × x = $24.5

The regular selling price is therefore the ratio of $24.5 and 40% as follows;

The regular selling price = $24.5 ÷ 40% = $61.25

Each pair of shoe regularly costs $61.25

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The probability that the hat was blue or was from Manufacturer B is 0.8677.

The P[tex](red)^{c}[/tex] is 0.6985.

The P(manufacturer B and Red) is 0.1640.

The P(Manufacturer B or Red) is 0.8456.

Probability is used to determine the odds that a random event would happen. The odds that the random event happens range from 0 to 1.

The probability that the hat was blue or was from Manufacturer B = (number of blue hats / total number of hats) + (number of hats from manufacturer B / total number of hats)

The probability that the hat was blue or was from Manufacturer B = (44 / 136) + (74 / 136) = 118/136 = 0.8677

The P[tex](red)^{c}[/tex] = complement of red = hats that are not red = (number of black hats + number of blue hats) / total number of hats

The P[tex](red)^{c}[/tex] = (51 + 44) / 136

The P[tex](red)^{c}[/tex] = 95 / 136

The P[tex](red)^{c}[/tex] = 0.6985

The P(manufacturer B and Red) = (number of hats produced by manufacturer B / total number of hats) x (number of red hats / total number of hats)

(74 / 136) x (41 / 136) = 0.1640

The P(Manufacturer B or Red) =  (number of hats produced by manufacturer B / total number of hats) + (number of red hats / total number of hats)

(74 / 136) + (41 / 136) = 115 / 136 = 0.8456

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Answer:

175760000

Step-by-step explanation:

There are 10 possibilities for each number and 26 possibilities for each letter.

Using the multiplication principle, the answer is [tex](10)(26^3)(10^3)=175760000[/tex]

The simplified exponential expression (z^9z^(-3))^(-2) is given as follows:

1 over z raised to the twelfth power.

The expression for this problem is given as follows:

(z^9z^(-3))^(-2)

The parenthesis takes precedence, hence the first term to be simplified is:

z^9z^(-3)

We have the multiplication of two terms with the same base and different exponents, hence the base z is kept and the addition of the exponents 9 and -3 is of:

9 - 3 = 6.

Hence the simplified part is of:

z^6

Then the expression is:

(z^6)^(-2).

Now we have the power of power rule, in which the base z is kept and then the exponents 6 and -2 are multiplied, as follows:

6 x (-2) = -12.

Then the simplified expression is:

z^(-12).

A negative exponent means that the number can be written into the denominator with a positive exponent, hence:

1/(z^12) = 1 over z raised to the twelfth power.

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The third number so that the three numbers form a right triangle,

1)40

2)84

Therefore, we can form a right triangle with 9,41,40 and 13,85,84

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

1) By applying Pythagorean theorem,

a²+b²=c²

x²+9²=41²

x²=41²-9²

x²=1681-81

x²=1600

x=√1600

x=40

Therefore, the third number is 40

2) x²+13²=85²

x²=85²-13²

x²=7225-169

x²=7056

x=√7056

x=84

Therefore, the third number is 84

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The fraction formed in the lowest form is [tex]\frac{3}{20}[/tex]

What are fractions?

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.

A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.

In the given question, we have:

6 persons for 40 dresses;

So, here

The numerator is 6;

and,

The denominator is 40;

So, The fraction that will be formed is: [tex]\frac{6}{40}[/tex]

In order to simplify to the simplest form, we have to divide it by the common divisor of 6 and 40.

So,

The fraction formed in the lowest form is [tex]\frac{3}{20}[/tex]

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According to the concept of inequality, the interval notation is 0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85 based on these range the second and third car seats are suitable.

Inequality:

Inequality refers the non equal relation of the sets.

Given,

A family is comparing different car seats. One car seat is designed for a child up to and including 25 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 25 lb and 85 lb, inclusive. Model those ranges with compound inequalities.

Here we need to find in which car seats are appropriate for a 35-lb child

In this question, they provided that, there are three car seats are designed as follows:

First, on is the car seat made for children upto 30lb.

Second one is the seat for children between 15lbs and 40lbs and

And the third one is the seat designed for a child between 30 lb and 85 lb

Here we know that, the seat designed for a child upto and including 30 lb would not be suitable for 35 lb child. Because 35lb is more than the 30 lb.

So, now, the seat designed for a child between 30 lb and 85 lb, 30lbs and 85lbs would be suitable as the child is within these weight ranges that is 35lb.

Therefore, the interval notation is written as,

=> 0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;

So, the  second and third car seats are suitable.

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Using the initial amount of the radioactive substance, in 1 gram 913.28 hours remaining.

In the given question;

The half- life of the radioactive substance is

[tex]t_{1/2}[/tex]=14days

For changing this into hours we have to multiply 24 in 14 because in 1 day have 24 hours.

[tex]t_{1/2}[/tex]=14*24

[tex]t_{1/2}[/tex]=336 hours

Initial amount of the radioactive substance is:

N(0)=6.58g

Now here we use the radioactive substance formula

[tex]N(t)=N(0)(\frac{1}{2})^{t/t_{1/2}}[/tex]

Where; N(t)= the radioactive substance after t hours

N(0)= Initial amount of the radio active substances

[tex]t_{1/2}[/tex] = Half lie

t=time (in hours)

Now put the value in formula

N(t)=6.58[tex](\frac{1}{2})^{t/336}[/tex]

N(t)=6.58[tex](0.5)^{t/336}[/tex]

By the question we know

N(t)=1

1=6.58[tex](0.5)^{t/336}[/tex]

Divide by 6.58 on both side, we get

1/6.58=[tex](0.5)^{t/336}[/tex]

[tex](0.5)^{t/336}[/tex]=1/6.58

Now taking the log on both side:

log [[tex](0.5)^{t/336}[/tex]]=log [1/6.58]

t/336 log[0.5]=log[1/6.58]

The formula of log used here, is as follows: Log(m^b)=blog(m)

Multiply by 336 on both side,we get

t*log[0.5]=336 log[1/6.58]

t=(336 log[1/6.58])/ log[0.5]

t=913.28hours

Hence, In 1 gram 913.28 hours remaining.

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Answer:

y = -14x + 61

Step-by-step explanation:

You need the slope and the y-intercept to write the equation.  They give us the slope.  We will use the point given (4,5) to find the y intercept.  A point is given in the form (x,y)

slope (m) = -14

y = 5   Given from the point (4,5)

x = 4  Given from the point (4,5)

y = mx + b  Plug in what we know

5 = -14(4) + b

5 = -56 + b  Add 56 to both sides of the equation

61 = b

y = -14x + 61

Answer:

Q1: 13 :)

Q2: 9 :)

Q3: 5 :)

Q4: 1 :)

Step-by-step explanation:

For functions, we must replace the x with the value given in the table and solve from there! :D

Question 1:

y = -2(-2) + 9

y = 4 + 9

y = 13

Question 2:

y = -2(0) + 9

y = 0 + 9

y = 9

Question 3:

y = -2(2) + 9

y = -4 + 9

y = 5

Question 4:

y = -2(4) + 9

y = -8 + 9

y = 1

Have an amazing day!!

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Answer:

80/44 = 1.81

The unit rate is $1.81

Answer:

1.875 years or 1.9 if rounded to nearest tenth

Step-by-step explanation:

8% simple interest of $800 is $64. you know that 1% will be $8 per year and that 2 years of 8% simple interest will be $128. If you subtract 8 from 128, it is $120. So it will take him 1.875 years or [tex]1\frac{7}{8}[/tex]

For an atom to be considered as such it needs to be composed of subtatomic particle (neutrons, electrons, protons), an molecule includes two or more atoms, an element has defined properties and a compound includes two or more element.

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The length of the line segment is 18 units. option B is the correct answer.

We know that

The distance(D) between two points (x₁ , y₁) and (x₂, y₂) is

D = √( y₂ - y₁)² + (x₂ - x₁)²

From the question, we have

Two endpoints of the line segment are (-10, 9) and (5, -1).

D = √( y₂ - y₁)² + (x₂ - x₁)²

D = √(-1 - 9)² + (5 - (-10))²

D = √100 + 225

D = √325

D = 18 units (approx.)

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

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Answer: 18 units

Step-by-step explanation: I got it right on the quiz

Answer:

[tex] \huge{ \boxed{y = - 52x - 49}}[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is given by

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

where

m is the slope

c is the y intercept

From the question

m = -52

In order to find c we substitute the points (−1,3) into the equation and find c

We have

[tex]3 = ( - 52)( - 1) + c \\ 3 = 52 + c \\ c = 3- 52 \\ c = -49[/tex]

We have m and c now so we substitute it into the main equation

We have the final answer as

[tex] \bold{y = - 52x - 49}[/tex]

Hope this helps you

The value of  (tan20° + tan40°)/(1 - tan20°tan40°) is √3.

tan(A + B) = (tanA + tanB)/(1 - tanA.tanB).

Given, tan 20 degrees + tan 40 degrees/1-tan 20 degrees tan 40 degrees

which is,

= (tan20° + tan40°)/(1 - tan20°tan40°).

= tan(20 + 40)°.

= tan60°.

= √3.

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Answer: option a

Step-by-step explanation:

Based on the z-score value, Latisha earned a higher IQ score.

In order to determine the person who earned a higher IQ score, we would have to calculate the z-score for the two IQ tests that Felix and Latisha took.

Mathematically, the z-score of a given sample score can be calculated by using this formula:

Z-score = (x - μ)/σ

Where:

For Felix, we have the following:

Z-score = (130 - 105)/10

Z-score = 25/10

Z-score = 2.5.

For Latisha, we have the following:

Z-score = (120 - 95)/5

Z-score = 25/5

Z-score = 5.0.

Therefore, Latisha had the higher score because she has a higher z-score than Felix.

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Answer:

BELOW

Step-by-step explanation:

The equation ( you need to commit to memory) is:

FV = PV ( 1+i)^n      FV = future value    PV = present value(270)

                                     i = decimal interest per PERIOD = .15

                                       n = # of periods = 3  (it is an ANNUAL Period)

FV = 270 ( 1 + .15)^3 = 410.63 dollars

Answer:

$410.64

Step-by-step explanation:

start with the compound interest formula

plug in p=270 , r=0.15 (divide 15 by 100 to get 0.15), n=1, and t=3

divide 0.15 by 1 to get 0.15

multiply the exponents 1 and 3 to get 3

add 1 and 0.15 to the 3 th power to get 1.520875

multiply 270 and 1.520875 to get 410.63625

so if you invest $270 at an interest rate 15%, which is compounded 1 times a year for 3 years, the return is about $410.64 (which is rounded to the nearest cent)

Then you'll have $410.64 in 3 years.

The equivalent expression to the given expression 3x - 4 - (5x + 7) with fewer terms is  - 2x - 11.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given expression,

3x - 4 - (5x + 7)

Open the bracket

3x - 4 - (5x + 7) = 3x - 4 - 5x - 7

Take likely terms together

3x - 4 - (5x + 7) = 3x - 5x - 4 - 7

Solving to get.

3x - 4 - (5x + 7) = - 2x - 11

Hence "The equivalent expression to the given expression 3x - 4 - (5x + 7) with fewer terms is  - 2x - 11".

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Answer:

  2 points: b, d

Step-by-step explanation:

Given the graph of a cubic function, you want to know the number of relative extreme points.

A point is a relative extreme if the points on either side of it are both less than or both greater than the extreme point. A relative extreme is a peak point or valley point on a graph, a point where the slope is zero, and changes sign from one side of the point to the other.

The relative extremes on the given graph are labeled 'b' and 'd'. There are two relative extremes.

__

Additional comment

Point 'b' is a relative minimum, where the slope changes from decreasing to increasing, and adjacent points are more positive. Point 'd' is a relative maximum, where the slope changes from increasing to decreasing, and adjacent points are more negative.

An "absolute extreme" is a relative extreme such that no points anywhere on the graph are more extreme.

The number of relative extremes a polynomial graph may have is 1 less than the degree of the polynomial. This can help you determine the degree from the number of extremes, or the number of extremes from the degree.

Step-by-step explanation:

from the first line s

y - 7 = 9/10 × (x - 4)

we only need the slope, which is 9/10.

the -7 did not disturb this. only if y had a factor different to 1, we would have to re-simplify the equation to get the slope.

remember, a slope expresses the ratio (y change / x change).

a perpendicular slope note turns the y/x ratio upside-down and flips the sign.

so, 9/10 turns into -10/9, which is the slope of the new line t.

we can use the point-slope form to incorporate the given point and get the y-intercept for the final slope-intercept equation :

y - 6 = -10/9 × (x - -6) = -10/9 × (x + 6) =

= -10/9 × x - 60/9 = -10/9 × x - 20/3

y = -10/9 × x - 20/3 + 6 = -10/9 × x - 20/3 + 18/3 =

= -10/9 × x - 2/3

the line t is

y = -10/9 × x - 2/3

The equation of a line that is perpendicular to -9x = 15 - 3y is y = -1/3(x) + c.

Given:

-9x = 15 - 3y

3y = 15+9x

divide by 3 on both sides

3y/3 = 15/3 + 9x/3

y = 3x + 5

m = 3

Perpendicular slope m1 = -1/m

= -1/3

substitute m value in y = m1x +c

y = -1/3(x) + c.

Therefore the equation of a line that is perpendicular to -9x = 15 - 3y is y = -1/3(x) + c.

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Answer:

16

Step-by-step explanation:

multiply sides

The value of x using the F.O.I.L method can be determined by the expression: [tex]54x^2-129x-23[/tex]

What is FOIL Method?

FOIL is a mnemonic for the standard method of multiplying two binomials, hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product:

First (“first” terms of each binomial are multiplied together)

Outer (“outside” terms are multiplied—that is, the first term of the first binomial and the second term of the second)

Inner (“inside” terms are multiplied—the second term of the first binomial and the first term of the second)

Last (“last” terms of each binomial are multiplied)

In the question, It is given:

(6x + 1)°

(9x - 23)°

Now Apply the F.O.I.L Method, to find the value of x;

⇒(6x + 1) (9x-23)  

Remove parenthesis and multiply;

⇒6x×9x+6x×(-23)+1×9x+1×(-23)  

⇒6x x 9x+6 x 23x + 1 x 9x + 1 x 23

Now, we have to simplify the terms,

⇒6x x 9x + 6 x 23x + 1 x 9x + 1 x 23

So after simplification, we get:

[tex]54x^2-129x-23[/tex]

Hence,

The value of x can be determined by the expression: [tex]54x^2-129x-23[/tex]

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Answer:

SS: $3,602.20

M: $842.45

Step-by-step explanation:

58100 x 0.062 = 3,602.2

58100 x 0.0145 = 842.45

Answer:

$1742.12

Step-by-step explanation:

I'm assuming it would be compounded annually so,

A = 1300(1 + 0.05)^6

A = 1742.12