erica solved the equation -5x - 25 = 78; her work is shown below. Identify the error and were it was made
-5x - 25 = 78
Step 1:-5x - 25 -25 = 78 - 25
Step 2: -5x = 53
Step 3:-5x/-5 = 53/-5
step 4: x = -53/-5

a step 1: She should have added 25 to each side
b step 1: She should have divided both sides by -5.
c step 3: She should have divided both sides by -5.
d step 3: She should have multiplied both sides by -5.

Answer:

-180√3

Step-by-step explanation:

3√10 x - 6√30

= 3x-6 x -√10 x √30

= -18 x√300

= -18 x 10√3

= -180√3

The annual profits of the company Eve works for will increase by 25% every year. The annual profits in 3 years will be approximately $709,555.52.

The annual profits of the company Eve works for will increase by 25% every year. If the company makes $363,200 this year, we can calculate the annual profits in 3 years by applying the 25% growth rate.

To find the annual profits in 3 years, we need to multiply the current year's profits by \((1 + \text{growth rate})^{\text {number of years}\).

In this case, the growth rate is 25% or 0.25, and the number of years is 3.

So, the calculation would be:

Annual profits in 3 years = $363,200 * (1 + 0.25)³

To simplify the calculation, let's break it down step by step:

Step 1: Calculate the growth rate by adding 1 to the percentage growth rate: 1 + 0.25 = 1.25

Step 2: Raise the growth rate to the power of the number of years: 1.25³ ≈ 1.9531

Step 3: Multiply the current year's profits by the result of step 2: $363,200 * 1.9531 ≈ $709,555.52

Therefore, the annual profits in 3 years will be approximately $709,555.52.

Please note that rounding the answer to the nearest cent gives $709,555.52.

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Answer:

slope:-11/5

y-intercept : (0, 3/5)

Step-by-step explanation:

Answer:

  -4.697 in/s

Step-by-step explanation:

You want to know the rate of change of radius of a cone 11 inches high with a radius of 5 inches and a volume that is decreasing at the rate of 541 cubic inches per second.

The volume of a cone is given by ...

  V = π/3r²h

The rate of change is found by implicit differentiation:

  V' = (π/3)((2rr')h +r²h')

Here, the height is constant, so h' = 0. Solving for r', we find ...

  r' = 3V'/(2πrh)

Using the given values of V', r, and h, we find the rate of change of radius to be ...

  r' = 3(-541 in³/s)/(2π(5 in)(11 in)) = -1623/(110π) in/s ≈ -4.69652 in/s

The radius is decreasing at about -4.697 inches per second.

__

Additional comment

The initial radius of the cone is irrelevant to the problem, since we want to know the rate of change at a specific different radius. Whether the cone is inverted or not is also irrelevant to its volume.

Answer:

29

Step-by-step explanation:

Answer:

Step-by-step explanation:

The correct answer is:

the initial height of the plant

The y-intercept represents the point where the graph intersects the y-axis. In the context of a relationship between plant growth and time, the y-intercept would represent the initial height of the plant, which is the height of the plant at the start of the experiment, before any growth has occurred.

Right triangles ABC and DEF are drawn to measure the slope of the line is:

a) run = 2 rise = 3 slope = 3/2

b) run = 6 rise = 9 slope = 9/6 = 3/2

c) Yes, they are similar because the 2 triangles are similar.

Two triangles are similar if they meet one of the following criteria. : Two pairs of corresponding angles are equal.

What is Right triangles?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4

\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5

\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls. The calculation results in approximately 0.369, or 36.9%.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

[P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

[P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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Answer:

s = 1/2

Step-by-step explanation:

Solve for s:

4 s^2 - 4 s + 1 = 0

Divide both sides by 4:

s^2 - s + 1/4 = 0

Write the left hand side as a square:

(s - 1/2)^2 = 0

Take the square root of both sides:

s - 1/2 = 0

Add 1/2 to both sides:

Answer: s = 1/2

Answer:

s = \(\frac{1}{2}\)

Step-by-step explanation:

To find the zero set the quadratic equal to zero, that is

4s² - 4s + 1 = 0 ← in standard form

(2s - 1)(2s- 1) = 0 ← in factored form

(2s - 1)² = 0 ← perfect square, thus

2s - 1 = 0 ⇒ 2s = 1 ⇒ s = \(\frac{1}{2}\) ← is the zero

Answer:

f(4)>g(4)

Step-by-step explanation:

f(x)=3x^5 ,  f(4)= 3072

g(x)=11*4^x when x=4 then g(4)=2816

The time period of a pendulum depends only on the length, so they have the same period.

What is time period of a simple pendulum?

The time period of a simple pendulum is equal to the time it takes to complete one oscillation.

T = 2π√l/g

where l is length of the string of the pendulum.

According to the given question:

Jim and Gina are swinging on adjacent, equal length swings.

Jim weights about twice as much as Gina.

Swing set can be considered as simple pendulum.

The period of a pendulum depends only on the length, so they have the same period (meaning it takes them the same time to swing back and forth).

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The ordered pair lie on the inverse of the function is (62,−3).

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -(x - 1)³ - 2

The inverse of f(x).

y = -(x - 1)³ - 2

interchange x and y and solve for y.

x = -(y - 1)3 - 2

(y - 1)³ = -2 - x

(y - 1)³ = -(2 + x)

Cuberoot on both sides.

y - 1 = ∛-(2 + x)

y = ∛-(2 + x) + 1

Now,

Substitute in the inverse of g(x).

(62, -3) = (x, y)

(−4, 123) = (x, y)

(3, 1) = (x, y)

(3,−6) = (x, y)

So,

y = ∛-(2 + x) + 1

y = ∛-(2 + 62) + 1

∛-1 = -1

y = -1∛64 + 1

y = -1 x 4 + 1

y = -4 + 1

y = -3

So,

(62, -3) ______(1)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 - 4) + 1

∛-1 = -1

y = ∛(-2 + 4) + 1

y = ∛2 + 1

y =  1.26 + 1

y = 2.26

So,

(-4, 2.26) _______(2)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) _______(3)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) ______(4)

Thus,

From (1), (2), (3), (4) we see that,

(62, -3) is the solution to the inverse of g(x).

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A person tosses a coin 15 times. In how many ways can he get 3 heads? The answer is 455 ways.

To find the answer, we can use the formula for combinations, which is:
C(n, k) = n! / (k! * (n-k)!)
Where n is the total number of tosses, and k is the number of heads we want to get.
In this case, n = 15 and k = 3, so we can plug these values into the formula:
C(15, 3) = 15! / (3! * (15-3)!)
C(15, 3) = 15! / (3! * 12!)
C(15, 3) = (15 * 14 * 13 * 12!)/ (3! * 12!)
C(15, 3) = 455
So there are 455 ways to get 3 heads when tossing a coin 15 times.

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Given Expression: cos^-1(xos(4π/3))(i) We know that cos (2π - θ) = cos θ, so that cos(4π/3) = cos(2π/3).∴ cos^-1[xos(4π/3)] = cos^-1[cos(2π/3)] = 2π/3Thus the value of (i) is 2π/3.(ii) Now, we know that cos (θ) = cos (-θ) .Thus cos^-1(cos(3π/4)) = cos^-1(cos(-π/4)) = π/4.

Thus the value of (ii) is π/4.(iii) We know that cos (θ + 2nπ) = cos θ and cos (θ - 2nπ) = cos θ, where n is any integer. Thus cos(5π/3) = cos(5π/3 - 2π) = cos(-π/3).∴ cos^-1[cos(5π/3)] = cos^-1[cos(-π/3)] = π/3.Thus the value of (iii) is π/3.(iv) We know that cos π = -1.So cos^-1(cos π) = cos^-1(-1) = π.

Thus the value of (iv) is π.Hence the answer is,cos^-1(xos(4π/3)) = 2π/3cos^-1(cos(3π/4)) = π/4cos^-1(cos(5π/3)) = π/3cos^-1(cos(π)) = π.

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The 2 inches on the model represent 2 feet in real life.

Fortunately, the math is not too difficult. A single unit on the map corresponds to 12 actual units. In other words, there are 12 inches in reality for every inch on the map. And one foot is equal to 12 inches!

In essence, you are multiplying the size of the map by 12.

Let's imagine you have 2 inches instead of 1 inch. We multiply 2 x 12 to get 24 since the real world is only the map size times 12. Now that we have divided this into feet and inches, we have 2 feet. Alternatively, we can just realize that multiplication by 12 effectively multiplies something by two to get two times one foot!

We thus have 2 feet.

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Answer:

12.55

Step-by-step explanation:

20-7.45=12.55 explanation

Answer:0.41

Step-by-step explanation:

If the homeowner also had to pay late fees in the amount of $35 four different times, the total cost of the dryer is $809.48. So, correct option is A.

To calculate the total cost of the dryer, we need to add the initial cost of the dryer, the monthly payments, the credit card fees, and the late fees.

The total cost of the dryer can be calculated as follows:

Cost of dryer = $698.27

Total credit card charges = 12 x $1.25 = $15

Total late fees = 4 x $35 = $140

Total cost of the dryer = Cost of dryer + Total credit card charges + Total late fees

= $698.27 + $15 + $140

= $809.27

Therefore, the total cost of the dryer is $809.48, which is the closest option to the calculated answer.

So, correct option is A.

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The points B, C, H, I lie on a single circle, then O lies on this circle too.

For given question,

We have been given I, O, H be the incenter, circumcenter, and orthocenter of an acute triangle ABC, respectively

In an acute ΔABC, O is circumcenter. Thus, by applying the inscribed angle theorem to the circle, we have:

∠BOA = 2∠BAC.               ..................(1)

Assuming H is orthocenter; Thus, the angle formed by angles BAC and BC at H are supplementary angles:

∠BAC + BHC = 180°.

BHC = 180° - ∠BAC.           ...................(2)

Assuming I is incenter; Thus, the angle formed by BIC is given by:

∠BIC = 90° + ∠A/2.            ...................(3)

Since points B, C, H, I lie on a single circle and the angles formed in the same side of an arc of a circle are equal, we have:

BIC = BHC                           ...................(4)

Substituting the parameters into equation (4), we have;

⇒ 180° - ∠BAC = 90° + ∠A/2

⇒ ∠BAC + ∠BAC/2 - 3∠BAC/2 = 180° - 90°

⇒ ∠BAC = 90° × 2/3

⇒ ∠BAC = 60°.

From equation (1), we have:

⇒ ∠BOA = 2∠BAC.

⇒ ∠BOA = 2 × 60

⇒ ∠BOA = 120°.

Hence, this proves that since points B, C, H, I lie on a single circle, then O lies on this circle too.

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Answer:

a. x^2 + 5x + 6 --> the entire figure

b. Length: x+3. Width: x+2

c. A=(x+3)(x+2)

Step-by-step explanation:

b.  x^2+5x+6=

x^2+2x+3x+6=

x(x+2)+3(x+2)=(x+2)(x+3)

Answer:

uuuu

Step-by-step explanation:

Answer:

1. A heterotroph

2. An autotrophs

3. Genus

4. An habitat

5.The binomial nomenclature system combines two names into one to give all species unique scientific names.

6. Carolus Linnaeus

7. Living organisms residing in a habitat are called biotic components.

8. Photosynthesis

Answer:7/10

Step-by-step explanation:

Answer:

\( \frac{7}{9} \)

Explanation:

First, you have to write a number in the numerator, that is after the comma (in this case it's 7)

And then, in the denominator, you have to write a number that is made of nines only (the number of nines you have to write is the number of decimal numbers, in this case it's 1 nine)

Answer:

F. 113

Step-by-step explanation:

Answer:

e < 6         n > 4           w > 2

Step-by-step explanation:

e/2 < 3

e < 6

n - 1 > 3

n > 4

5 < 3 + w

w > 2

Answer:

ASA - Angle Side Angle, it creates two separate triangles that face each other in which makes it identified as an Angle Side Angle.

(Picture Placed Below)

Step-by-step explanation:

Answer:

6.2

Step-by-step explanation:

ahmm recommend answer lang

Answer:

6.8

Step-by-step explanation:

hope this helped! :)

Answer:

the answer is new

Step-by-step explanation:

I just took the test

If having a warranty on a car is important a person should buy a car that is new.

Warranty can be defined as a form of  assurance given to a buyer by the seller to repair the product that the buyer in case of damages occur within  the stipulated warranty time.

Most new product often comes with a warranty and this warranty help to give the buyer an assurance that the product bought will either be repair or change in a situation were the product has issues after being bought from the seller or manufacturer.

Inconclusion if having a warranty on a car is important a person should buy a car that is new.

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The simplification of the given rational expression when x is not equal to 2 or negative 3 is determined as (x + 1)/(x + 3).

The simplification of the given expression when x is not equal to 2 or negative 3 is determined as follows;

\($=\frac{(x+1)(x-2)}{(x-2)(x+3)}$\)

cancel "\($\mathrm{x}$-2\)" since it is common to numerator and denominator

\($$=\frac{(x+1)}{(x+3)}$$\)

Thus, the simplification of the given rational expression when \($\mathrm{x}$\)is not equal to 2 or negative 3 is determined as \($(x+1) /(x+3)$\).

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