Which two expressions are equivalent​

Answer:

81

Step-by-step explanation:

The percent change from the first value to the second will be 18%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The first number is 50 and the second number is 41. Then the percentage change is calculated as,

P = [(50 - 41) / 50] x 100

P = (9 / 50) x 100

P = 9 x 2

P = 18%

The percent change from the first value to the second will be 18%.

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An equation that could be the equation of this parabola include the following: C. x = 1/12(y²).

In Mathematics, the standard equation of the directrix lines for any parabola that opens to the right is represented by this mathematical expression:

x = a(y - k)² + h.

Where:

By critically observing the graph which models the equation of this parabola, we can logically deduce that the vertex is at point (0, 0) and as such, we have the following:

h = 0

k = 0

a = positive.

x = a(y - k)² + h.

x = a(y - 0)² + 0.

x = ay²

Therefore, a possible equation is x = 1/12(y²).

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Given:

Two cards are drawn from a standard deck of 52 cards without replacement.

To find:

The probability that both cards selected for black.

Solution:

We know that,

Total number of cards = 52

Total number of red cards = 26

Total number of black cards = 26

\(\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\)

Probability of selecting first black card is

\(\text{Probability}=\dfrac{26}{52}\)

\(\text{Probability}=\dfrac{1}{2}\)

Number of remaining total cards = 52-1 = 51

Number of remaining black cards = 26-1 = 25

Probability of selecting second black card is

\(\text{Probability}=\dfrac{25}{51}\)

So, the probability that both cards selected for black is

\(\text{Probability}=\dfrac{1}{2}\times \dfrac{25}{51}\)

\(\text{Probability}=\dfrac{25}{102}\)

Therefore, the required probability is \(\dfrac{25}{102}\).

hope this helps :)

............

The given expression is:

To find the derivative, use the product rule:

Substitute, U, V, dU/dx, and dV/dx into the product rule given above:

Step-by-step explanation:

tan0=opp/adj

where opposite =3,adjacent =x,=70

tan 70=3/x

2.7474=3/x

2.7474x=3

divide both sides by 2.7474

x=3/2.7474

x=1.0919

x=1.10 to 1 d.p

Answer:

Step-by-step explanation:

Use the figure to complete the transformations.

1. Reflect the triangle across the y-axis.

2. Reflect the image across the x-axis.

The final image is the same as what single transformation?

a translation 2 units to the left and 2 units down

a reflection across the y-axis

a 180° rotation about the origin

a clockwise rotation 90° about the origin

The graph of the linear inequality y ≥ 2x - 5 is attached below with it's shaded part included.

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

In the given problem, the inequality presented is;

y ≥ 2x - 5

To graph this, we would use a graphing calculator to find the boundary lines and plane.

In the graph below, the x and y intercept is at (2.5, -5) and the shaded part is on the left side of the graph.

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Answer:

(no solutions exist)

Step-by-step explanation:

f(x)=-8+4 has no roots

Answer

The equation of the line given is

y = (4x/3) - 8

Explanation

The general form of the equation in point-slope form is

y - y₁ = m (x - x₁)

where

y = y-coordinate of a point on the line.

y₁ = This refers to the y-coordinate of a given point on the line

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

x₁ = x-coordinate of the given point on the line

So, we just need to pick a point on the graph and calculate the slope of the line to write the equation of this line.

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

For this question,

(x₁, y₁) and (x₂, y₂) are (6, 0) and (3, -4)

So, picking the point (x₁, y₁) to be (6, 0)

Recall

y - y₁ = m (x - x₁)

m = slope = (4/3)

Point = (x₁, y₁) = (6, 0)

x₁ = 6

y₁ = 0

y - y₁ = m (x - x₁)

y - 0 = (4/3) (x - 6)

y = (4x/3) - 8

Hope this Helps!!!

Answer: 2 would be on the 3rd number on the number line, 1 would be before that, and negative one is 1 below 0 means it would be the one in between -2 and 0. Have a nice day ;)

The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.

Now when no letters are repeated:

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.

So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes

if letters can be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.

So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes

if adjacent letters cannot be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.

So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes

Hence the total number of codes as calculated by permutation and combination is 1280.

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To calculate the interest charged on a credit card account, we need to consider the average daily balance and the annual percentage rate (APR). Let's break down the calculations step by step for the given scenario.

1. April 1: Starting balance of $552.

2. April 10: Made a $119 purchase. The balance is now $552 + $119 = $671.

3. April 24: Made a $25 gift card purchase. The balance is now $671 + $25 = $696.

4. April 29: Made a $150 payment. The balance is reduced to $696 - $150 = $546.

Now, let's calculate the average daily balance for the billing cycle in April. The billing cycle can vary depending on the number of days in the month. Assuming April has 30 days, we calculate the average daily balance as follows:

Average Daily Balance = (Total balance for the month) / (Number of days in the month)

Total balance = Starting balance + Purchases - Payments = $552 + $119 + $25 - $150 = $546.

Number of days = 30 (April has 30 days).

Average Daily Balance = $546 / 30 = $18.20.

Now, we can calculate the interest charged for the billing cycle. The APR is 26.49%, which needs to be converted to a daily rate by dividing it by the number of days in a year (365):

Daily Interest Rate = (APR / 365) = (26.49% / 365) = 0.0725%.

Interest Charged = (Average Daily Balance) * (Daily Interest Rate) * (Number of days in the billing cycle)

Interest Charged = $18.20 * (0.000725) * 30 = $0.3969.

Therefore, the interest charged on the credit card account for the April billing cycle is approximately $0.40.

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Bruce and Felicia would have a unique solution to the given equation. The value of x that satisfies the equation is 15.

To determine if the equation 6x + 2 = 5x + 17 has a unique solution, we need to check if the variable x has a consistent value that satisfies the equation.

By simplifying the equation, we can see that the equation becomes:

6x - 5x = 17 - 2

Simplifying further, we have:

x = 15

Since the variable x has a specific value, in this case, x = 15, the equation does have a unique solution. When x is substituted with 15 in the equation, both sides are equal.

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Answer:

y = 6x + 8

Step-by-step explanation:

The interest paid for the loan is $1748

Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,

We need to find the interest paid for the same.

So,

Simple Interest = principal × time × rate / 100

= 28654 × 1 × 6.1 / 100

= 28654 × 0.061

= 1747.894

= 1748

Hence the interest paid for the loan is $1748

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Answer:

False; false; true

Step-by-step explanation:

Answer:

100mph

Step-by-step explanation:

Based on the information given about the combination, the number of different parts of fruits that can be selected from the bowl will be 6.

Since the bowl contains an apple, a plum, a pear, and a banana, the different pairs of fruit that can be selected from the bowl will be 4C2.

We can solve this further which will be:

= 4C2

= 4! /2! (4 - 2)!

= 4! / 2!2!

= (4 × 3 × 2)/ 2 × 2

= 24/4

= 6

Therefore, 6 different pairs of fruit can be selected.

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The range is the best measure of variability for this data, and its value is 4.

The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).

The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:

Range = Maximum value - Minimum value = 4 - 0 = 4

Therefore, the range is the best measure of variability for this data, and its value is 4.

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Answer:

Slope = (1/2)

Step-by-step explanation:

Rearrange the equation into the y = mx + b format.

-x + 2y = 5

2y = x + 5

y = (1/2)x + (5/2)

m represents slope, which is (1/2) in this question.

The actual base of the building is 1890 square feet.

A rectangle is a two-dimensional figure with length and width.

The area of a rectangle is Length x width.

We have,

1 inch = 15 feet

Rectangular base:

Length = 4.2 in

Width = 2 in

So,

4.2 in = 4.2 x 15 feet = 63 feet

2 in = 2 x 15 = 30 feet

Now,

The actual base of the building.

= 63 x 30

= 1890 square feet

Thus,

1890 square feet.

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The inequalities representing the graph are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

First, we have to determine the two lines.

Line₁.

(0, 2) and (1, - 1).

m = (- 1 - 2)/(1 - 0).

m = - 3.

- 1 = - 3(1) + b.

b = 2.

y = - 3x + 2.

Line₂.

(0, - 2) and (3, 0).

m = (0 + 2)/(3 - 0).

m = 2/3.

0 = (2/3)(3) + b.

b = - 1.

y = (2/3)x - 1.

So, The two inequalities are y ≥ - 3x + 2 and y ≥ (2/3)x - 1.

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John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. $75 = $15p + A

What is the total of the cost?

Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.

Let the number of people on John's family plan be represented by p.

According to the problem, the family plan cost is $68, and there is an additional cost of $15 for each person on the plan. Therefore, the total cost C of the plan with p people is:

C = $68 + $15p

We know that John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. Therefore, we can write:

$143 = C + A

where A represents any additional charges.

Substituting C into this equation, we get:

$143 = ($68 + $15p) + A

Simplifying, we can write:

$75 = $15p + A

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Answer:

\(\displaystyle m=\frac{4}{3}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (3, 7)

Point (6, 11)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

Step-by-step explanation:

(11 - 7)/(6 - 3) = 4/3