Five times the difference of a number and 5.

Answer:

Step-by-step explanation:

The monthly compound interest formula.

Future Value = monthly deposit x (1 + r) - 1/r

r = .07/12 = .00583

n = total number of time for compound = 35 years x 12 months/1 year = 420 months

PMT = monthly deposit = $200

Future Value = $200 x (1 + .00583)⁴²⁰ - 1/.00583

Future Value = $394,001.64 in 35 years

Total money you put into the account.

$200 x 420 months = $84,000

Total interest earned.

$394,001.64 - $84,000 = $310,001.64

He has 5hrs  to drive and 275 miles to drive to cover to arrive at the university.

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

here, we have,

His college is 330 miles away.

After an hour of driving, he still has 275 miles to go.

If the roads are clear, he'll be able to keep up that pace for the whole drive.

If he drives 55 miles in 1 hr

he would drive 330 miles in

=6hrs.

his total travel time is 6 hr

He has 5hrs  to drive and 275 miles to drive.

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Answer:

Step-by-step explanation:original quantity = $30

New quantity = $39

increase amount = 39-30 = 9

Percent change:

30 x = 9

x = 9/30

x = 0.3

0.3x 100 = 30%

Since the quantity grows, it's a percent increase.

Answer:

πr2

Step-by-step explanation:

The formula of a circle/finding its area is pi(r)^2

Answer: The formula for the area of a circle is π r squared

The solution of the system of equations -6x -12= (1/2)x -4 include the following: D. x = -4 and x = -2.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-axis, which is given by  x = -4 and x = -2.

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The temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M.

What is the temperature?

Temperature is a physical property of matter that measures the degree of hotness or coldness of an object. It is a scalar quantity that is expressed in units such as Celsius, Fahrenheit, or Kelvin.

The statement "f(4) < f(5)" means that the outside temperature 4 hours after 3 A.M. is less than the temperature 5 hours after 3 A.M. In other words, the temperature is rising over time and the value of f(t) increases as t increases. So, the temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M."f(4) < f(5)" means that the outside temperature 4 hours after 3 A.M. is less than the temperature 5 hours after 3 A.M. In other words, the temperature is rising over time and the value of f(t) increases as t increases. So, the temperature at 4 hours after 3 A.M. is lower than the temperature at 5 hours after 3 A.M.

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Se requiere agregar un volumen adicional de 24 yardas cúbicas para obtener una concentración de grava de 85 %.

Este problema es un caso de aplicación de promedios ponderados, en donde se mezcla un volumen de un porcentaje menor de grava con otro volumen de un porcentaje mayor de grava para obtener una mezcla con un porcentaje deseado. Esta situación queda descrita en la siguiente ecuación:

(6 yd³) · 65 + x · 90 = (6 yd³ + x) · 85

Donde x es el volumen del cargamento de grava al 90 %, en yardas cúbicas. A continuación, procedemos a determinar el volumen requerido:

390 + 90 · x = 510 + 85 · x

5 · x = 120

x = 24 yd³

No aparecen problemas verificados en español sobre promedios ponderados. Se ha agregado un problema en inglés por defecto.

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The value of y'(2) is 135/16.

The correct option is A.

Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.

Given:

y = (x - 1/x)³

Differentiating the function with respect to x,

y' = 3x² +3/x⁴ - 3 - 3/x²

y'(2) = 12 + 3/16 - 3 -3/4

y'(2) = 135/16

Therefore, the value is 135/16.

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The total number of shaded squares will be equal to the product of 4 x 2/3.

A. For the problem 4 x 2/3, you can draw a model using rectangular arrays or area models. Draw four columns, each representing one of the four groups, and two rows to represent the two-thirds. Shade in two-thirds of the first column, then repeat for the next three columns. The total number of shaded squares will be equal to the product of 4 x 2/3.

B. For the problem 3 x 2/5, you can also draw a model using rectangular arrays or area models. Draw three columns, each representing one of the three groups, and two rows to represent the two-fifths. Shade in two-fifths of the first column, then repeat for the next two columns. The total number of shaded squares will be equal to the product of 3 x 2/5.

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The graph of y = 4x + 5 that models this situation is added as an attachment

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

Already eaten = 5 mini hot dogs

Rate = 4 hot dogs per minute

So, the equation is

y = 4x + 5

A linear equation is represented as

y = mx + c

Where

slope = m = 4

y-intercept = c = 5

See attachment for the graph

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The given function

g(x)  = [x² - 3x -10][x²+ 2x² -5x +4  ]

is continuous at  x = -1,

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  [x² - 3x -10][x²+ 2x² -5x +4  ]

To check whether it is continuous at x = -2

First taking LHL,

[tex]\lim_{h \to \00}[/tex]  [(-1-h)² - 3(-1-h) -10][(-1-h)²+ 2(-1-h)² -5(-1-h) +4  ]

[tex]\lim_{h \to \00}[/tex]  [(-1-0)² - 3(-1-0) -10][(-1-0)²+ 2(-1-0)² -5(-1-0) +4  ]

⇒   -6 x 12

⇒     -72

Now, taking RHL

[tex]\lim_{h \to \00}[/tex]  [(-1+h)² - 3(-1+h) -10][(-1+h)²+ 2(-1+h)² -5(-1+h) +4  ]

[tex]\lim_{h \to \00}[/tex]  [(-1+0)² - 3(-1+0) -10][(-1+0)²+ 2(-1+0)² -5(-1+0) +4  ]

⇒   -6 x 12

⇒     -72

The value at x = -1

F(-1)  =  [(-1)² - 3(-1) -10][(-1)²+ 2(-1)² -5(-1) +4  ]

⇒ -6 x 12

⇒   -72

RHL = LHL =  F(-1)

Hence Proved,  the function is continuous at x = -1

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Any sequence of five spins that consists only of numbers 1 and 2 would be an outcome of Event A.

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

Event A = the spinner lands on numbers all less than 3

An outcome of Event A would be a sequence of five spins on the spinner that result in numbers all less than 3,

For example: 1, 2, 1, 2, 1.

See that each number in the above sequence is less than 3

Hence, the event A represents outcomes less than 3

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Answer:

527.52 ft²

Step-by-step explanation:

The surface area of a cylinder is:

[tex]\displaystyle{2\pi r^2 + 2\pi r h}[/tex]

where r is radius and h is height.

From the attachment, we know that the radius (r) is 7 ft and the height is 5 ft. Therefore:

[tex]\displaystyle{\text{Surface Area} = 2 \cdot 3.14 \cdot (7)^2 + 2\cdot 3.14 \cdot 7 \cdot 5}\\\\\displaystyle{\text{Surface Area} = 6.28 \cdot 49 + 6.28 \cdot 35}\\\\\displaystyle{\text{Surface Area} = 307.72 + 219.80}\\\\\displaystyle{\text{Surface Area} = 527.52 \ \: \text{ft}^2}[/tex]

Therefore, the surface area of the cylinder is 527.52 ft²

the 25 brick masons complete the same job in 120 hours.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

It took 10 brick masons 300 hours to brick a new home.

1 brick mason will take 300*10 =3000 hours

So 25 brick masons will take 3000/25 = 120 hours.

Hence the 25 brick masons complete the same job in 120 hours.

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1) X2 + 6x + 3 = 0. is resolved using the discriminant technique, and the value of s for the second equation, 52 + 2s - 6 = 0, is 9.5.

The statistic is said to be in its simplest form is divided into its smallest equivalent fraction. What to do to find the most basic form. Look for common factors in the denominator and numerators. Confirm a fractional integer to verify if it qualifies as a prime number. A statement having two equal sides and an equaled sign in the middle is called an equation in mathematics. The general form of any equation contains the diplomas of all the variables in descending order. The conventional form of an equation is an x + b = 0. The general form of a linear function with two variables is an x + b y + c = 0. (or something similar). An identification holds true no matter what value is given to the variables.

given

equation 1 ) X2 +6x +3=0

by discriminant method

x =(6+√48)/2

=3+2√ 3

= 6.464.

equation 2) 5^2 + 2s - 6 = 0

= 25 + 2s - 6 = 0

= 19 = - 2s

s = 9.5

1) X2 + 6x + 3 = 0. is resolved using the discriminant technique, and the value of s for the second equation, 52 + 2s - 6 = 0, is 9.5.

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The length of the UW of the triangle is 18. The correct option is D.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. 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.

The length UW will b calculated as:-

First, in ΔTWU apply the Pythagorean theorem,

TU² = UW² + 12²

TU² = UW² + 144

In ΔTWV apply the Pythagorean theorem,

VT² = 12² + 8²

VT² = 208

Apply Pythagorean theorem in ΔVTU,

( 8 + UW)² = VT² + TU²

Substitute the value of TU² in the above equation,

( 8 + UW)² = 208 + UW² + 144

UW² + 16UW + 64 = UW² + 208 + 144

16UW = 288

UW = 288 / 16 = 18

Therefore, the length of UW is 18.

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Step-by-step explanation:

Since we're solving for L, it has to equal L.

Which means C & D are the only options.

Only problem is... we don't have the original formula. Not sure if it was part of #1 or...

Answer:

-10 and -7

Step-by-step explanation:

Notice that (-10) + (-7) = -17, and (-10)(-7) = 70, so these are the integers.

Answer:

-7 & -10

Step-by-step explanation:

-7 + -10 = -17

-7 x -10 = +70

Answer:

i hope this help

Step-by-step explanation:

If each question is worth 4 points, then 100 questions would be worth 400 points.

If Chee got 10 questions wrong, she would have answered 100-10 = 90 questions correctly.

Her score would be 90 x 4 = 360 points out of 400 points.

As a percentage, her score would be 360/400 x 100 = 90%.

If Chee got x questions wrong, her score would be (100-x) x 4 points.

Kevin's solution is incorrect because he used wrong formula.

Correct area of triangle = 20 square inches.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height,

i.e. A = 1/2 × b × h

Given,

Height of triangle h = 8 inches

Base of the triangle b = 5 inches

Formula for area of triangle A = 1/2(b h)

A = 1/2 (8 × 5)

A = 40/2

A = 20 square inches.

Area by given formula for area of the triangle A = b h

A = 8 × 5

A = 40

Since actual area of the triangle is 20 square inch, Kevin found the area with wrong formula.

Actual area of triangle is 20 square inches.

Hence, Kevin's solution is incorrect, as the formula used is wrong.

20 square inches is correct area of the triangle.

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Applying the angle bisector theorem, the lengths are:

A. KL = 2.4, LW = 3.6

The Angle Bisector Theorem states that in a triangle, the ratio of the length of a side to the length of another side is equal to the ratio of the length of the angle bisector of one of the angles to the angle bisector of the corresponding angle.

In other words, if two angles of a triangle have angle bisectors of lengths x and y, then x/y = a/b where a and b are the lengths of the sides of the triangle corresponding to the bisected angles.

Based on the angle bisector theorem, we have:

(6 - x)/(x) = 4/6

Cross multiply:

4x = 6(6 - x)

4x = 36 - 6x

4x + 6x = 36

10x = 36

x = 36/10

x = 3.6

LW = x = 3.6

KL = 6 - x = 6 - 3.6 = 2.4

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Peeta worked 9.41 hours on Sunday. The equation 5.5h + 90.2 = 142.2 can be used to determine the number of hours Peeta worked given his earnings.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let h be the number of hours that Peeta worked on Sunday. We know that he earned $5.50 per hour and $90.20 in tips. So, his total earnings can be represented as:

5.5h + 90.2 = 142.2

Solving for h:

5.5h = 142.2 - 90.2
5.5h = 52

h = 52 / 5.5
h = 9.41 hours

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Answer: The temperature of an oven can be modeled by a linear equation. In this case, the initial temperature of the oven is 75° and it will increase at a rate of 25° per minute after being turned on.

The equation to model the temperature of the oven t minutes after being turned on is:

Temp = 75 + 25t

Where Temp is the temperature of the oven in degrees and t is the number of minutes after being turned on.

For example, if we want to find the temperature of the oven 17 minutes after being turned on, we can substitute t = 17 into the equation:

Temp = 75 + 25 * 17 = 75 + 425 = 500°

So, the temperature of the oven 17 minutes after being turned on is 500°.

In general, the temperature of the oven t minutes after being turned on can be found by substituting the value of t into the equation:

Temp = 75 + 25t.

Step-by-step explanation:

The temperature of an oven can be modeled by a linear equation. In this case, the initial temperature of the oven will be;  75° and it will increase at a rate of 25° per minute after being turned on.

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation to model the temperature of the oven t minutes is:

Temp = 75 + 25t

Where, Temp is the temperature of the oven in degrees and t is the number of minutes after being turned on.

For example, if we need to find the temperature of the oven 17 minutes after being turned on, we can substitute t = 17 into the equation:

Temp = 75 + 25 * 17 = 75 + 425

Temp = 500°

Thus, the temperature of the oven 17 minutes after being turned on is 500°.

In general, the temperature of the oven t minutes after being turned on can be find by substituting the value of t into the equation:

Temp = 75 + 25t.

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Answer:

the answer is 20

Step-by-step explanation:

.........

Answer:

20

Step-by-step explanation:

Do it one step at a time using the correct order of operations.

11 - 12 ÷ 4 + 3(6 - 2) =

= 11 - 3 + 3 × 4

= 8 + 12

= 20

The relationship between x and y is y = (1/2)x. When x is 2, then the value of 'y' is 1.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

If x and y are in direct proportion. Then the equation is given as,

y ∝ = x

y = kx

At x = 12 and y = 6, then the value of 'k' is given as,

6 = 12k

k = 1/2

Then the equation is given as,

y = (1/2)x

If the value of the variable 'x' is 2. Then the value of y is given as,

y = (1/2) 2

y = 1

The relationship between x and y is y = (1/2)x. When x is 2, then the value of 'y' is 1.

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Note that the angle labeled ∠PQR is given as 70°

First, note that the Lengths of tangents drawn from external points to a circle are equal in length. This means that:

Length of PT = Lenght of TR

This makes Δ TPR and Isosceles Triangle.

This also makes ∠P = ∠R..............................1

Thus:

∠P + ∠R + ∠T = 180°

Given expression 1 above,

we can say:

x + x + 38° = 180°

Thatis 2x = 180 - 40

2x = 140°

x = 140/2

x = 70°

Note that Line TP is parallel to Line QR and Line PQ is a transversal line. Thus, ∠P and ∠Q are co-interior angles. This means that:

∠P + ∠Q = 180°

Recall that:

70 + 40 + ∠Q = 180°
∠Q = 180 -70 -40

∠Q = 70°

Thus: ∠ PQR = 70°

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Full Question:

See attached image.

Answer:

a) $40.05

b) $161.99

c) C(x) = 6.45 + 0.93x, if x ≤ 20

C(x) = 6.45 + 0.84x, if x > 20 and x ≤ 50

C(x) = 6.45 + 0.77x if x > 50

The money left from last month's earnings is $1660.35.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

The process of subtraction can also be termed as finding difference.

In order to find the money left, we have to find the difference of earnings and expense.

Earnings = $4,283.30

Expense for bills = $4,283.30 × (3/5) = $2569.98

Expense for shirts = $19.99 × 2 = $39.98

Expense for sunglasses = $12.99

Total expense = $2569.98 + $39.98 + $12.99 = $2622.95

Money left = $4,283.30 - $2622.95 = $1660.35

Hence $1660.35 amount of money is left.

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The complete question is :

Selena earned $4,283.30 last month she used 3/5 of her earnings to pay her bills with the remaining money she bought two shirts $19.99 each and a pair of sunglasses for $12.99 how much money does Selena have left from last month's earnings?

[tex]x=-2\hspace{5em}y=2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x^2 - y^3}{x^3 + y^2}\implies \cfrac{(-2)^2 - (2)^3}{(-2)^3 + (2)^2}\implies \cfrac{(-2)(-2)~~ - ~~(2)(2)(2)}{(-2)(-2)(-2)~~ + ~~(2)(2)} \\\\\\ \cfrac{(+4)~~ - ~~(+8)}{(-8)~~ + ~~(+4)}\implies \cfrac{4-8}{-8 + 4}\implies \cfrac{-4}{-4}\implies \text{\LARGE 1}[/tex]

for the sake of clarity, is better to parenthesize all, since plugging in the value for the variable, only includes the variable, no any exponents or signs in front.

that said, let's recall that minus * minus = plus, and that plus * plus = plus, however minus * plus = minus.

so you can think of it this way, if you have a negative value multiplied an "even times", it'll positivize, if you multiply it an "odd times", it'll go back to negative, so is not like it remains negative, it changed a few times and in the end negativized back.