Find A using the formula A = Pert given the following values of P, r, and t. Round to the nearest hundredth. See Example.

EXAMPLE

Investing. If $25,000 accumulates interest at an annual rate of 8%, compounded continuously, find the balance in the account in 50 years.

Strategy We will substitute 25,000 for P, 0.08 for r, and 50 for t in the formula A = Pert and calculate the value of A.

Why The words compounded continuously indicate that we should use the base-e exponential growth/decay formula.

The amount that store earns is $120. By writing the equation for the given payment of the computer by Rudo, we get the required value.

It is given that, Rudo buys a computer for $920. This is 115% of what the store paid for the same computer.

So, consider the amount paid by the store for the same computer as 'x'.

Then, from the given information we can write that,

$920 = 115% of x

⇒ 920 = 0.15x

⇒ x = 920/0.15 = 800

So, the amount paid by the store for the same computer is $800

Thus, the amount earned by the store on the sale is $920 - $800 = $120.

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To solve the given quadratic equation,  [tex]\frac{81}{4}[/tex] must be added to complete the square

What is quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A two degree equation is known as quadratic equation.

[tex]x^2+9x+7=0\\x^2+9x = -7\\x^2+2\times x \times \frac{9}{2} + (\frac{9}{2})^2 = -7 + (\frac{9}{2})^2\\x^2+2\times x \times \frac{9}{2} + \frac{81}{4}= -7 + \frac{81}{4}\\(x+ \frac{9}{2})^2 = \frac{53}{4}[/tex]

So, [tex]\frac{81}{4}[/tex] must be added to complete the square for solving the given quadratic equation

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Answer:

[tex]y=\dfrac{\boxed{1}}{\boxed{2}}\:x+\boxed{4}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Therefore, the slope of the given line  y = -2x + 5  is -2.

If two lines are perpendicular to each other, their slopes are negative reciprocals.  

Therefore, the slope of a perpendicular line ¹/₂.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and point (-4, 2) into the point-slope formula:

[tex]\implies y-2=\dfrac{1}{2}(x-(-4))[/tex]

Rearrange to slope-intercept form:

[tex]\implies y-2=\dfrac{1}{2}(x+4)[/tex]

[tex]\implies y-2=\dfrac{1}{2}x+2[/tex]

[tex]\implies y=\dfrac{1}{2}x+4[/tex]

Answer:

  57.8

Step-by-step explanation:

You have quadrilateral JKLM similar to quadrilateral NOPQ with given sides JK = 9, LM = 13.7, NO = 38, and you want the measure of PQ.

Corresponding sides in similar figures are proportional in length:

  PQ/LM = NO/JK

  PQ/13.7 = 38/9

  PQ = 13.7(38/9) = 2603/45 ≈ 57.8

The measure of PQ is approximately 57.8 units.

Answer:

multiply

(x square + 5) ( x square +2x - 3)

Answer: 42 is a 19.231% decrease of 52.

gg against the jags yesterday

The coordinates of the y-intercept is (0, 10)

The coordinate of the x-intercept is (5 / 2, 0)

Cynthia is participating in the Spartan Super, a 10-mile obstacle course.  She completes 4 miles of the obstacle course every hour.

Cynthia’s distance from this finish line, y, after x hours is represented by the function 4x + y = 10.

Therefore, the y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x = 0.

The x-intercept is where a line crosses the x-axis. The x-intercept is the value of x when y = 0.

Linear function in slope intercept form is as follows:

y = mx + b

where

Hence,

4x + y = 10

y = -4x + 10

Hence, y-intercept is 10.

y = -4x + 10

Let's find x-intercept

0 = -4x + 10

-10 = -4x

x = 10 / 4

x = 5 / 2

x-intercept is 5 / 2.

Hence the coordinate of the y-intercept is (0, 10) and the x-intercept is (5 / 2, 0)

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Meiosis causes the cell to divide instead of makeing new cells.

Cells are the fundamental building blocks of all life. Trillions of cells make up the human body. They support the body's structure, absorb nutrients from food, convert those nutrients into energy, and perform specialized functions.

Meiosis is a type of cell division that occurs in sexually reproducing organisms and results in a reduction in the number of chromosomes in gametes; he sex cells, or egg and sperm. Body or somatic cells in humans are diploid, with two sets of chromosomes one from each parent.

It should be noted that meiosis is a type of cell division of germ cells that produces gametes such as sperm or egg cells in sexually reproducing organisms. It consists of two rounds of division that result in four cells with only one copy of each chromosome.

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The wave function that satisfies wave equation is D(x,t) = A cos(kx + ωt) that is option C is correct.

This wave function satisfies the wave equation because it can be rewritten as:

D(x,t) = A cos(kx) cos(ωt) - A sin(kx) sin(ωt)

And the left-hand side of the wave equation is simply the sum of the second derivatives of the two cosine and sine functions with respect to x, while the right-hand side is the product of the second derivative of the cosine function with respect to t and the second derivative of the sine function with respect to t.

For the transverse velocity of a particle at point x, the function is given by:

v(x,t) = -Aω sin(kx) cos(ωt) - Ak cos(kx) sin(ωt)

And for the transverse acceleration, the function is given by:

a(x,t) = -Aω^2 cos(kx) cos(ωt) + Ak^2 sin(kx) sin(ωt)

These functions can be derived by taking the first and second derivatives of the wave function with respect to time.

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(A) 4x² - 3x + 7 and (B) y² + √2 are polynomials with one variable and the rest are not.

A polynomial is a mathematical equation made up of coefficients and indeterminates that exclusively uses the operations of addition, subtraction, multiplication, or powers of positive numbers of the variables.

x² - 4x + 7 is an illustration of a quadratic with a solitary indeterminate x.

(A) 4x² - 3x + 7:

'x' is the only variable in the provided polynomial.

As a result, the polynomial 4x² - 3x + 7 has one variable.

(B) y² + √2:

'Y' is the only variable in the provided polynomial.

y² + √2 is a polynomial in one variable as a result.

(C) 3√t + t√2:

Since the power of the variable in the first term is 1/2, which is not a whole integer, 3√t + t√2 is not a polynomial.

(D) y + (2/y):

Because the power of the variable in the second term is -1, which is not a whole number, y + 2y⁻¹ is not a polynomial.

(E) x¹⁰ + y³ + t⁵⁰

Due to the fact that x, y, and t are all three variables, x¹⁰ + y³ + t⁵⁰ is not a polynomial in one variable.

Therefore, (A) 4x² - 3x + 7 and (B) y² + √2 are polynomials with one variable and the rest are not.

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The inverse function of f(x) = 4x + 12 is [tex]f^{-1}(x) = \frac{x}{4}-3[/tex] .

Option (A) is correct.

What is the inverse of a function?

The inverse of a function is a new function that "undoes" the original function. If f(x) is a function that takes in an input x and produces an output y, then the inverse function denoted as [tex]f^{-1}(x)[/tex], takes in an input y and produces an output x.

The inverse function of f(x) = 4x + 12 is denoted as [tex]f^{-1}(x)[/tex]. To find the inverse function, we can follow these steps:

Replace f(x) with y.

Interchange x and y.

Solve for y.

Following these steps, we get:

y = 4x + 12

x = 4y + 12

x - 12 = 4y

y = (x - 12)/4

Hence, the inverse function of f(x) = 4x + 12 is [tex]f^{-1}(x) = \frac{(x - 12)}{4}[/tex] = (x/4) - 3

Option (A) is correct.

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Answer: 122.5

Step-by-step explanation:

Laurel must increase her net income to $10,000 in order to keep her housing costs at 25%.

To determine how much Laurel must increase her net income in order to keep her housing costs at 25%, we need to know the following information:

The amount of Laurel's new mortgage, which is $2500

The percentage of Laurel's net income that she wants to use for housing costs, which is 25%

To find the amount of net income that Laurel needs to maintain a housing cost of 25%, we can use the following formula:

Net income = Mortgage / (Housing cost percentage)

Substituting the values from the problem, we get:

Net income = $2500 / (25/100)

Net income = $2500 / 0.25

Net income = $10,000

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Laurel must increase her net income to $10,000 to keep her housing costs at 25%.

The amount of Laurel's new mortgage is $2500

The percentage of Laurel's net income that she wants to use for housing costs, which is 25%

To find the amount of net income that Laurel needs to maintain a housing cost of 25%, we can use the following formula:

Net income = Mortgage / (Housing cost percentage)

Substituting the values from the problem, we get:

Net income = $2500 / (25/100)

Net income = $2500 / 0.25

Net income = $10,000

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The equation of the given circle is

[tex](x - 3)^2 + (y + 7)^2 = 25[/tex]

What is a circle?

Circle is a two dimensional round figure in which every point on the figure maintains a fixed distance from a point known as the center of the circle.

The fixed distance is called the radius of the circle.

Diameter of circle = 10 units

Radius of the circle = [tex]\frac{10}{2}[/tex] = 5 units

Coordinates of center = (3, -7)

Equation of circle = [tex](x - 3)^2 + (y - (-7))^2 = 5^2[/tex]

                                 [tex](x - 3)^2 + (y + 7)^2 = 25[/tex]

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Answer:

Step-by-step explanation:

6-(-2^3)+-2

The equation to represent the given situation is [tex]500(2)^x=16000[/tex] after 5 hours. Therefore, option B is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a bacteria has an initial population of 500 and is doubling every hour.

Let x be the number of hour bacteria population to reach 16,000

The bacteria reaches a population of 16,000 bacteria.

So, the equation is [tex]500(2)^x=16000[/tex]

⇒ [tex]2^x[/tex]=16000/500

⇒ [tex]2^x[/tex]=160/5

⇒ [tex]2^x=2^5[/tex]

⇒ x=5

Therefore, after 5 hours the bacteria population reaches 16,000.

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The integral is ∫ x sec x tan x dx. We can solve it using integration by parts xln|sec(x) + tan(x)| - x + C

We have u = x, dv = sec(x)tan(x)dx, du = dx, and v = ln|sec(x) + tan(x)|.

The integral is then

Integrating the second part we get:

xln|sec(x) + tan(x)| - x + C

The integral is ∫ x sec x tan x dx. We can solve it using integration by parts. We let u = x and dv = sec(x)tan(x)dx. Then, du = dx and v = ln|sec(x) + tan(x)|. So, the integral becomes xln|sec(x) + tan(x)| - ∫ ln|sec(x) + tan(x)| dx. We can integrate the second part to get xln|sec(x) + tan(x)| - x + C.

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This probability means that in a very long series of hands of poker, about 8.8% of the time we will get 4 of a kind.

The results of a chance process are unpredictable, yet they follow a predictable distribution over a large number of repeats. The frequency of a particular occurrence happening across many repeats approaches a single number, according to the law of large numbers. The likelihood of a chance result is determined by its long-term relative frequency. The probability given in the question is 88/1000, which means that we should anticipate 88 poker hands with a four-of-a-kind for every 100 hands with a pair.

The probability stated in the question for different Texas hold'em poker games has this meaning. Because it is also possible that 87 or 89 of 1000 such hands will have four of a kind, this probability does not guarantee that exactly 88 of those hands will contain four of a kind. There are frequently more than 88 fours of a kind, though this isn't always the case.

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Balloon's altitude = 43.7ft as

change in altitude/500 = tan 5°  

change in altitude = .0875*500

                              =43.7ft

Answer:

3 years

Step-by-step explanation:

Lawson's tree starts at 14 inches and grows 3 inches every year, so we can represent that as 3x+14

Ezra's tree starts at 8 inches and grows 5 inches every year, so we can represent that as 5x+8

x=years

So, now that we have an equation for each tree, we will now set them as equal

5x+8=3x+14

Subtract 8 from each side

5x=3x+6

Subtract 3x from each side

2x=6

Divide each side by 2

x=3

It will take 3 years for the trees to reach the same height.

Each right triangle has a missing value of 1.9096 where = angle, O = opposing side, A = adjacent side, and H = hypotenuse.

A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangle triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.

given,

1.9096 is what's lacking.

SOH CAH TOA's identification would appear to be:

The opposite or hypotenuse of sin

Sinθ = O/H

the following being spoken

H = 11 \sin θ = 0.1736

To replace having, use:

0.1736 = O/11

O = 11 * 0.1736

O = 1.9096

the missing value is 1.9096.

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A discrete random variable has either a finite or a countable number of values.

Discrete random variables are defined as variables that can only take on a finite number of values. If any random variable takes a countable number of all the possible values, it is referred to be a discrete random variable. For instance, while flipping a coin, the random variable X will take the values 0, 1, and 2 depending on the number of heads.

If the value of any variable, such as X, is uncertain, that variable is said to be a random variable. It may also be defined as a function that is crucial in giving values to the results of any random experiment. Depending on the sort of numeric values they include, random variables can be either discrete or continuous.

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Answer:

y = 5

Step-by-step explanation:

The equation 5x − 2y = 30 tells us that if we take 5 times x and subtract 2 times y, the answer will be 30.  If we know either x or y, we can solve for the other.

We are given that x=8.  Use the 8 for x in the equation:

5x − 2y=30  

5*(8) − 2y=30

40 − 2y=30

-2y = -10

y = 5

Answer: 11 ft.

Step-by-step explanation:

Start by listing the variables that you have.

-Total Area=1,848; lot a 33ft wide, 42ft long; lot b xft wide, 42ft long.

- so, our equation looks like 1,848=(33x42)+(42x)

-multiply 33x42=1,386

-subtract 1,386 from both sides to get 462.

-equation should look like 462=42x

-divide by 42 to 11

Answer:

The value of the discriminant is 17.

Step-by-step explanation:

⭐What is the discriminant?

Thus, we have to substitute the values a, b, and c from the quadratic equation we are given into the discriminant formula.

Let's identify what a, b, and c are.

[tex]y = ax^2 + bx + c[/tex]

[tex]y = \sqrt{2}x^2 -5x + \sqrt{2}[/tex]

a = [tex]\sqrt{2}[/tex]

b = -5

c = [tex]\sqrt{2}[/tex]

Now, substitute these values into the discriminant formula.

[tex]b^2 - 4ac =[/tex]

[tex](-5)^2 - 4(\sqrt{2}*\sqrt{2}) =[/tex]

[tex]25 -4(2) =[/tex]

[tex]25-8 =[/tex]

= 17

∴ The value of the discriminant is 17.

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On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -

1 - A

2 - C

3 - B

4 - D

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Answer:

To find the sum of the two fractions, we first need to express them in a common denominator. Since the denominators of the two fractions are different, we will need to find the least common multiple (LCM) of the two denominators.

The LCM of 4 and 5 is 20, so we can express the two fractions in terms of 20 as follows:

-3 1/4 = -3 5/20

-4 2/5 = -4 8/20

Now that the two fractions have a common denominator, we can add them by adding the numerators and keeping the denominator the same:

(-3 5/20) + (-4 8/20) = (-3 + -4) 13/20 = -7 13/20

Therefore, the sum of the two fractions is -7 13/20.

The sum of −3 1/4 + (−4 2/5) is 7.65

Mixed fractions are type of a fraction which includes a whole number and a fraction.

So, any improper fraction can be written as a mixed fraction. Quotient will be the whole number and in the fractional part, numerator is the remainder and denominator will be the divisor.

[−(3 1/4)] + [−(4 2/5)] = [-(13/4)] + [-(22/5)]

When cross multiplying, we will get

-(13/4 + 22/5) = -(65 + 88)/20 = -153/20 = 7.65

Hence, the sum of −3 1/4 + (−4 2/5) is 7.65.

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Answer: 1 decameter

Step-by-step explanation:

Answer:

1 decameter

Step-by-step explanation:

1 decameter is 10 meters or 1000 centimeters

Answer:

a. w = -18 x = -10 y = -2 z = 10

b. x and z are opposites because they are the opposite value of each other.

c. the integers w, x, y are less than zero because they are negative integers.

Step-by-step explanation:

a. because they are counting by twos it has to be the even numbers for both sides of the number line

b. because they are the same number just one is negative while the other isn't making them opposites.

c. because every number besides ten are negative making them below the value of zero.

Answer:

3.444 repeating on

Step-by-step explanation: