Applications of linear equations

One number is 7 more than another number. If the smaller number is doubled and added to 3 times the larger number, the sum is 86. Find the two numbers.

Smaller number=
Larger number=
(Type the integers or decimals.)

In golf, players use the concept of angles to evaluate their club head position and the angle of attack on the ball. By understanding the principles of geometric angles, golfers can adjust their swing and improve the accuracy and distance of their shots.

In basketball, players use the concept of spatial awareness to evaluate their positioning on the court. By understanding geometric concepts such as lines, angles and planes, they can improve their ability to move without the ball and find open spaces on the court.

In soccer, players use the concept of geometric shapes to evaluate their positioning on the field. By understanding the principles of triangles and circles, soccer players can improve their ability to move and pass the ball effectively, as well as to anticipate the movements of the opposing team.

Overall, the concepts of geometry, such as angles, spatial awareness, and geometric shapes, are essential for athletes in many sports to evaluate their positions and postures and improve their performance.

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Penalty time = 2 months of interest = 2 x (7/100 x 18,000) = $2520.00

This serves as a deterrent to encourage individuals to leave their money in the CD until the maturity date.

Penalty = 2 months of interest = 2 x (Interest rate/100 x Value of CD)

= 2 x (7/100 x 18,000)

= $2520.00

A certificate of deposit (CD) is a financial product offered by banks and credit unions that allows an individual to deposit a certain amount of money for a fixed period of time, usually a few months to a few years. Most CDs will pay a higher rate of interest than a traditional savings account, but they come with certain restrictions. One of these restrictions is that if you withdraw funds from the CD before it reaches maturity, you will be charged a penalty time. This penalty usually involves two months of interest. Therefore, the amount of the penalty for early withdrawal on a CD with a value of $18,000 and paying 7 percent interest would be 2 x (7/100 x 18,000) = $2520.00. This serves as a deterrent to encourage individuals to leave their money in the CD until the maturity date.

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Based on the table which shows the pricing for four different types of gasoline, a type that cost the least per gallon is: C. type C.

In order to determine the gasoline that costs least per gallon, we would determine the unit rate for the cost per gallon by using the following mathematical expression;

Unit rate = Cost of gasoline/number of gallons

Substituting the given parameters into the unit rate formula, we have the following;

Unit rate = $20.20/10

Unit rate = $2.02 per gallon.

For type B, we have the following unit rate:

Unit rate = $26.04/12

Unit rate = $2.17 per gallon.

For type C, we have the following unit rate:

Unit rate = $28.24 / 24

Unit rate = $2.01 per gallon.

For type D, we have the following unit rate:

Unit rate = $30.45 / 25

Unit rate = $2.03 per gallon.

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Answer:

see below

Step-by-step explanation:

116+16=132 =120% * x

x=110

profit =132-110 =22

He made $12 by selling the bicycle helmet to Jin!

Let x be the original cost of the bicycle.

The cost of the helmet is $16, so the original cost of the bicycle and helmet is x + $16 algebraically.

Jin pays a total of $116 + $16 = $132 for the bicycle and helmet, which is 120% of what Stefan spent originally, so x + $16 = 1.2 * (x + $16)

Expanding the right-hand side gives x + $16 = 1.2x + 1.2 * $16.

Solving for x, we find that x = $104.

So, Stefan originally spent $104 for the bicycle and $16 for the helmet, for a total of $104 + $16 = $120.

Stefan sells the bicycle and helmet to Jin for $116 + $16 = $132, so he makes a profit of $132 - $120 = $12.

The required decimal value of fraction 2/5 is 0.4, and a fraction of decimal value is 0.55 is 11/20.

Fraction is defined as the number of compositions that constitutes the Whole.

Here,
Given expression,
Fraction = 2 / 5
decimal value = 0.4

Given expression,
decimal value = 0.55
fraction value = 0.55 = 55/100
fraction = 11/20

Thus, the required decimal value of fraction 2/5 is 0.4, and a fraction of decimal value is 0.55 is 11/20.

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f(x)=5x−3f(x)=5x-3 g(x)=x2−3g(x)=x2-3

Set up the composite result function. g(f(x))g(f(x))Evaluate g(5x−3)g(5x-3) by substituting in the value of f(5x−3)=(5x−3)2−3g(5x-3)=(5x-3)2-3

Simplify each term: g(5x−3)=25x2−30x+9−3g(5x-3)=25x2-30x+9-3 Subtract 33 from g(5x−3)=25x2−30x+6

To find the value of the function g(x) = 5x - 3 at x = -2, substitute -2 for x. This gives g(-2) = -13.

The function given is g(x) = 5x - 3. To find the value of this function when x = -2, you substitute -2 for x in the equation. This yields:

g(-2) = 5(-2) - 3

Which simplifies to:

g(-2) = -10 - 3

So, g(-2) = -13.

In summary, you substituted -2 for x in the function g(x)=5x−3 and then performed the arithmetic operations to find that g(−2) equals -13.

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The slope of the line perpendicular to the line whose equation is 15x - 12y = 216 is m{p} =  -0.8.

What is the general equation of a straight line?

straight line equation: The general equation of a straight line is -

y = mx + c.

where,

{m}: slope of the line.

{c} : y-intercept

To find the slope of a line perpendicular to the line whose equation is 15x - 12y = 216, we need to find the negative reciprocal of the original line's slope.

To find the original line's slope, we can use the equation of the line in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

To convert the equation of the line from standard form to slope-intercept form, we can add 12y to both sides to get 12y = -15x + 216.

Then divide both sides by 12 to get y = -(15/12)x + 18.

So the slope of the original line is -(15/12).

The slope of a line perpendicular to the original line is the negative reciprocal of the original line's slope.

So the slope of the line perpendicular to 15x - 12y = 216 is -12/15 or -0.8

The slope of the line perpendicular to the given line is -

m =  -12/15 =  -0.8

Therefore, the slope of the line perpendicular to the line whose equation is 15x - 12y = 216 is m{p} =  -0.8.

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The sum of all the integers from -√14 to √84 is 39.

To find the sum of the integers that are between √14 to √84, you first need to find √14 and √84.

The value is √14 is :

= √14

= 3. 74

The value of  √84 is :

=  √84

= 9.17

Integers are whole numbers and the whole numbers between these figures are:

4, 5, 6, 7, 8, 9

The sum of these integers is:

= 4 + 5 + 6 + 7+ 8 + 9

= 39

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Answer:

Step-by-step explanation:

By the way you've worded this, I'm guessing that you're looking for how much money Chris made at the end of the year.

When we're dealing with annual income, we must always consider how much was already present in savings before actually performing any operation, because that will give us the final answer.

Since Chris started with $5200, we do [tex](0.07)($5200) = $364[/tex] to find that Chris made $364 by the end of the year.

Lastly, to find his total income at the end of the year, we add [tex]5200 + 364 =[/tex] $5,564 at the end of the year.

The probabilities are given as follows:

The 31% share value is not wrong, as at most one household is not an unlikely outcome, as the probability is higher than 5%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter values for this problem are given as follows:

n = 12, p = 0.31.

The probability of none is given as follows:

P(X = 0) = (0.69)^12 = 0.0116.

The probability of at least one is given as follows:

P(X >= 1) = 1 - 0.0116 = 0.9884.

The probability of at most one is given as follows:

P(X <= 1) = P(X = 0) + P(X = 1)

In which:

P(X = 1) = 12 x 0.31 x 0.69^11

P(X = 1) = 0.0628.

Hence:

P(X <= 1) = P(X = 0) + P(X = 1)

P(X <= 1) = 0.0116 + 0.0628

P(X <= 1) = 0.0744.

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An expression that narrates this sentence using function notation and mathematical symbol: C(B) ≥ A

According to the question,

The cost of the large pizza is at least A dollars B days into the promotion.

The statement that a pizza is at least A dollars B days into the promotion means that the cost of a large pizza B days into the promotion and denoted C(B) and it is greater than or equal to A dollars. Thus, an expression that reports this sentence using function notation and mathematical symbols is simply :

                 C(B) ≥ A

So, the expression is C(B) ≥ A .

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The volume of water which the tank holds when it is full is 136830 cm³.

The amount of space a three-dimensional solid shape takes up is referred to as its volume. Though difficult to visualise in any shape, it can be compared to others. In comparison to an eraser placed inside of it, a compass box has a larger volume. The area of any two-dimensional shape can be calculated by splitting it into equal squares. When calculating the volume of solid shapes, equal cubical units will also be divided.

If the both have diameter of 46 cm then the height of hemisphere is

46/2 = 23 cm = radius

Height of the cylinder = 90 - 23

                                     = 67

Volume of hemisphere + Volume of cylinder =  volume of water

volume of water = (2/3)πr³ + πr²h

volume of water = (2/3)π(23)³ + π(23)²×67

                            = 136830 cm³

                            = 136.83 l

Thus, the volume of water which the tank holds when it is full is 136830 cm³.

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Step-by-step explanation:

it'll be undefined and 2 for the surface area

c From the graph, it appears that around 50% of seniors had used alcohol in 2015.

d.This gives us: A=-0.8(25)+63=50%. So, both the line graph and the formula estimate that around 50% of seniors had used alcohol in 2015.

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Answer:

[tex]\huge\boxed{\sf 25x\² + 30x + 9}[/tex]

Step-by-step explanation:

= (5x + 3)²

= (5x + 3)(5x + 3)

= 5x(5x + 3) + 3(5x + 3)

= 25x² + 15x + 15x + 9

[tex]\rule[225]{225}{2}[/tex]

The relative frequency of A, B and C BE 0.5, 0.20 and 0.29.

The proportion between a given event's frequency and all events' frequencies in a statistical experiment.

The ratio of the total number of occurrences occurring in a particular scenario to the frequency of an event can be used to determine relative frequency. Relative frequency is defined as Subgroup frequency divided by Total frequency.

Due to the possibility of interpreting the heights of relative frequency histograms as probabilities, they are significant. These probability histograms offer a graphical representation of a probability distribution that may be used to estimate the probability that specific outcomes will materialize within a given population.

The relative frequency is the ratio of the frequency to the total frequency corresponding to each entry.

The total samples be 60 + 25 + 35 = 10

Also, the frequency corresponding to A is: 60

Corresponding to B is: 25

and corresponding to C is: 35

Hence, the Frequency table is as follows:

Data               Frequency

A                          60  

B                           25

C                           35

The relative frequency table is given by:

Data               Relative Frequency          

A                      60/120 = 0.5

B                       25/120 = 0.20

C                       35/120 = 0.29

Therefore, the relative frequency of A, B and C BE 0.5, 0.20 and 0.29.

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The equation for the growth of the number of bacteria is x(t) = 10000t - 550t² + 110000

The growth rate of the number of bacteria is given as:

V = 10000 - 100mt,

Such that

t = time in hours,

m = 11.

To find the equation for the growth of the number of bacteria x(t), we can integrate this formula with respect to t.

Using the initial condition x(0) = 10000*m, we have

x(t) = ∫V dt + C

Substitute the known values in the above equation, so, we have the following representation

x(t) = ∫(10000 - 100mt) dt + C

Integrate

x(t) = 10000t - 50mt² + C

Recall that x(0) = 10000*m.

So, we have

10000m = 10000 * 0 - 50 * m * 0² + c

Evaluate

c = 10000m

c = 10000 * 11

c = 110000

So, the equation is

x(t) = 10000t - 50mt² + 110000

Since m = 11, we have

x(t) = 10000t - 550t² + 110000

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The price of first 3 video games is $57.3 and the other 2 videos games is $34.2 in the given arithmetic problem.

The study and use of numbers, mathematical relationships between numbers, and mathematical observations are all covered by the branch of mathematics known as arithmetic.

The core ideas in number theory, measurement, and computation are typically referred to as "arithmetic" (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots). It hasn't always meant the same thing, though, in the mathematical community.

Susan bought total 5 games

Lets the higher price be x

and lower be y

3x + 2y = $91.50

and

x - y = $2

x = 2 + y

Putting the value of x in first formula

3(2 + y) + 2y = 91.50

6 + 3y + 2y = 91.50

3y + 2y = 91.50 - 6

5y = 85.5

y = 85.5/5

y = 17.1

2y = 34.2

Putting the value of y in x

x = 2 + (17.1)

x = 19.1

3x = 57.3

Thus, the price of first 3 video games is $57.3 and the other 2 videos games is $34.2.

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The two different quantities to measure which school has higher academic performance are :

• Graduation rate / Budget per student

• SAT average / Budget per student

To specify a number that represents academic achievement. We compare the budget per pupil for each school to a related metric or parameter that measures the academic performance of the students in each school.

The following variables could be used to gauge academic achievement:

• Each school's graduation rate.

• Each school's average SAT score.

Therefore, Graduation rate / Budget per student and SAT average / Budget per student are appropriate in this case.

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(a) The sample mean of the 49 fly balls is 250 feet.

(b) The standard error of the 49 fly balls is 50/sqrt(49) = 7.14 feet

(c) P(x bar < 240) = P(Z < (240-250)/7.14) = P(Z < -1.40) = 0.0822

(ii) The sketch of the distribution of the average of the 49 fly balls is a normal curve with a mean of 250 feet and a standard deviation of 7.14 feet. The probability of getting a sample mean of less than 240 feet is 0.0822.

(iii) This is usual, as the probability of getting a sample mean of less than 240 feet is 0.0822, which is within the range of expected probabilities for a normal distribution.

(d) P(X< 240) = P(Z < (240-250)/50) = P(Z < -2) = 0.0228

(e) The 80th percentile of the distribution of the average of the 49 fly balls is equal to the mean plus (1.28 * standard deviation), which is equal to 250 + (1.28 * 7.14) = 266.6 feet.

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The area of the trapezoid is 278.63 square units.

An open, flat object with four straight sides and one set of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.

Given:

KFLM is a trapezoid.

Side KF = 10 units

KL = 26 units

The angle measure of KFM = 48°.

So, in ΔFPK,

Sin48° = FP / KF

Sin48° = FP / 10

FP= Sin48° x 10

FP = 0.7431 x 10

FP  = 7.431

Now, the area of the trapezoid,

= 1/2 x sum of the parallel sides x distance between parallel sides,

= 1/2 (26 + 49) (7.431)

= 278.63 square units

Therefore, the area is 278.63 square units.

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$656.25 is the difference between the investor paying for the share and the investor selling the share.

The mathematical expression combines 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 denote the logical syntax's operation order and other properties.

Given that At the beginning of 2017, the share was worth $1050.

From the beginning of 2015 to the beginning of 2017 the value of the share halved each year.

In 2017 it is 1050.

In 2016, it is 2100

In 2015, it is 4200

Beginning of 2017 to the beginning of 2019, the value of the share increased by 1.5 times each year.

In 2017, 1050×1.5=1575

In 2018, 1575×1.5=2362.5

In 2019, 2362.5×1.5=3543.75

The investor paid for the share 4200 and the investor sold 3543.75.

Difference =4200-3543.75

=656.25

Hence, $656.25 is the difference between the investor who paid for the share and the investor who sold the share.

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Therefore, the explicit formula for f(n) is: f(n) = 10 * [tex]3^{(n - 1)}[/tex]

f(1)=10

An explicit formula for f(n), the number of members the creators have a goal of getting n weeks after the website is made available, can be determined by using the information provided that the number of members is tripled every week.

So, we can start with the initial number of members (10) and multiply it by 3 for each week.

Therefore, the explicit formula for f(n) is:

f(n) = 10 * [tex]3^{(n - 1)}[/tex]

A recursive formula for f(n) can be determined by using the information that the number of members is tripled every week, and the initial number of members is 10.

So, we can start with the initial number of members (f(1)=10) and use the previous value of f(n-1) to calculate the current value of f(n).

Therefore, the recursive formula for f(n) is:

f(n) = 3f(n-1) + 10

for n>1

f(1)=10

In this way, we can calculate the number of members for any week using the explicit formula or the recursive formula.

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The flavors that have chocolate as one of the ingredients will be 10 and the flavors that don't have chocolate as one of the ingredients will be 30.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

In this case, the bakery makes 40 different flavors of muffins. 25% of the flavors have chocolate as one of the ingredients

The flavors that have chocolate as one of the ingredients will be:

= 25% × 40

= 10

The flavors that don't have chocolate as one of the ingredients will be:

= 40 - 10

= 30

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The cost of the guitar string is given by the equation b = $ 1.30

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the cost of one guitar pick be = c

Let the cost of one guitar string be = b

And , Patrick bought 25 guitar picks and 25 guitar strings for = $ 40

Substituting the values in the equation , we get

25c + 25b = 40   be equation (1)

Now , cost of one guitar string = 1 + c

b = 1 + c   be equation (2)

Substituting the value of b in equation (1) , we get

25c + 25 ( 1 + c ) = 40

On simplifying the equation , we get

25c + 25 + 25c = 40

Subtracting 25 on both sides of the equation , we get

50c = 15

Divide by 50 on both sides of the equation , we get

c = $ 0.30

So , the cost of one guitar string = $ 1 + $ 0.30 = $ 1.30

Hence , the cost of one guitar string is $ 1.30

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The equation for the cross section exists x = z , -z.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

When two expressions in a variable (or variables) have the same value, the condition is said to be an equation. The equation's solution, or root, is the value of the variable for which the equation holds true. Even if the RHS and LHS are switched, an equation still holds true.

In the question it is given that

Equation of curve => x² = 49y² + z²

(a) Write an equation for the cross section at z = -7

Putting z = -7 in the equation,

⇒ x² = 49y² + (-7)²

⇒ x² - 49y² = 49

(b) Write an equation for the cross section at z = 0

Putting z=0

⇒ x² - 49y² = 0

(c) Write an equation for the cross section at z = 7

Putting z = 7 ,

⇒  x² - 49y² = 49

(d) Write an equation for the cross section at y = -7

Putting y = -7 in equation this time,

⇒  x² = 49( -7)² + z²

⇒ x² - z² = 2401

(e) Write an equation for the cross section at y = 0

Putting y = 0,

⇒ x² = z²

⇒ x = z , -z

Therefore, the equation for the cross section exists x = z , -z.

The compete question is:

Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) x2 = 49y2 + z2 = (Write an equation for the cross section at z = -7 using x and y.) (Write an equation for the cross section at z = 0 using x and y.) (Write an equation for the cross section at z = 7 using x and y.) (Write an equation for the cross section at y = -7 using x and z.) IIIIIIII (Write an equation for the cross section at y = 0 using x and z.) (Write an equation for the cross section at y = 7 using x and z.) (Write an equation for the cross section at x = -7 using y and z.) (Write an equation for the cross section at x = 7 using y and z.)

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Answer:

A gain of $5,000.

Step-by-step explanation:

The function y = 1/4(x - 4)² + 2, after a translation right 3 units and down 4 units, is given as follows:

y = 1/4(x - 7)² - 2.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The parent function for this problem is given as follows:

y = 1/4(x - 4)² + 2

The changes with each translation are given as follows:

Hence the function is defined as follows:

y = 1/4(x - 3 - 4)² + 2 - 4

y = 1/4(x - 7)² - 2.

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Answer:

8,00000

Step-by-step explanation:

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