While you could use the associative property on all the following expressions, select two of the following expressions that using the associative property to write an equivalent expression that would help you calculate the value of the expression using mental math.
Group of answer choices

The unknown side AC will be equal to 2.33.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that a right triangle ABC. Angle ACB is a right angle. Angle ABC is twenty-five degrees. The side AC is unknown. Side BC is five units.

The unknown side will be calculated as:-

tan(25) = P / B

tan(25) = AC / BC

AC = BC x tan(25)

AC = 5 x tan(25)

AC = 2.33

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the fourth one. I know it is correct, you may look it up on the desmos graphing calculator if you have suspicion it is not.

Differentiating the expression [tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex] with respect to x will be [tex]16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]

We are given with

[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]

Here we will be using the chain rule. According to the chain rule, we will first have to solve the parentheses as a variable. Then we will have to solve the expression within the parenthesis

First, we will differentiate [tex](4x-7)^4[/tex] keeping [tex](7x+8)^5[/tex] constant. Here we will first assume [tex](4x-7)[/tex] as one variable and differentiate using the formula d/dx[x^n] then we will differentiate 4x - 7 to get just 4. They would be multiplied by one another

Hence we get

[tex]4 X4(4x-7)^3(7x+8)^5[/tex]

[tex]16(4x-7)^3(7x+8)^5[/tex]

Now, we will keep [tex](4x-7)^4[/tex] constant and differentiate [tex](7x+8)^5[/tex] and adding it up we get

[tex]16(4x-7)^3(7x+8)^5 + 5X7(4x-7)^4(7x+8)^4[/tex]

[tex]= 16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]

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Complete Question

[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]

Answer:

(x^2 - 7)(4x - 3)

Step-by-step explanation:

first, we split the expression by grouping the first two terms in parentheses and the last two terms in parentheses. this gives us:

[tex](4x^{3}-3x^{2})(-28x+21)[/tex]

next, we factor out the GCF of each group. this gives us:

[tex]x^{2}(4x-3)-7(4x-3)[/tex]

finally, all you have to do is take each factored-out term and put them together into a group/expression. the leftover expression from both groups is the same value, so you get:

[tex](x^{2}-7)(4x-3)[/tex]

hope this helped, good luck!

Answer:

The total number of planes landing at O’Hare Airport categorized by type.

Answer:

Step-by-step explanation:

[tex]-63y^2+27y[/tex]

[tex]-63yy+27y[/tex]

[tex]-9\cdot \:7yy+9\cdot \:3y[/tex]

[tex]9y\left(-7y+3\right)[/tex]

it would take 29.5 hours the second airplane to overtake the first.

speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.

Given, Two airplanes leave Philadelphia for Rochester. The first airplane to leave travels at an average speed of 590 kilometers per hour. The second airplane, which leaves 3 hours later, travels at an average speed of 650 kilometers per hour.

So, in 3 hours first airplane will reach at;

Distance = speed *time

Distance = 590 * 3

Distance travels by first airplane in 3 hours will be = 1770 km

Since, Relative speed of given two planes = 650 - 590

Relative speed of given two planes = 60 km/hour

To reach 1770 km it would take  = 1770/60 hours

Thus,

To reach 1770 km it would take  = 29.5 hours

therefore, it would take 29.5 hours the second airplane to overtake the first.

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(a) The average rate of change over the interval [2, 5] is given by (f(5) - f(2)) / (5 - 2), which is equal to (24 - 16) / (5 - 2) = 8 / 3 = 2.67.

(b) The average rate of change over the interval [3.8, 4] is given by (f(4) - f(3.8)) / (4 - 3.8), which is equal to (19 - 19.6) / (4 - 3.8) = -0.6 / 0.2 = -3.

The average rate of change over a given interval [a, b] is a measure of how much the value of a function changes on average as the input changes over that interval. It is calculated as the difference between the value of the function at the endpoints of the interval divided by the difference of the corresponding inputs.

Formally, the average rate of change over the interval [a, b] is given by:

f_avg = (f(b) - f(a)) / (b - a)

where f is the function being evaluated and f_avg represents the average rate of change.

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Answer:

m∠ABD = 111

Step-by-step explanation:

69 + x = 180

x = 111

Answer:

< ABD  = 111 °

Step-by-step explanation:

< ABD and < DBE form a straight line which is 180 degrees

< ABD + < DBE = 180

< ABD + 69= 180

< ABD  = 180 -69

< ABD  = 111

Probability of less than 50 % democrats for the example based on sample proportion is equal to 0.1562.

Sample size 'n' = 100

Registered voters  'p' = 55%

                                    = 0.55

σ = √ p( 1- p )/ n

  = √0.55( 0.45)/ 100

  = 0.04975

Mean 'μ' = 55%

               = 0.55

Probability of getting less than 50% democrats in a sample size of 100 voters

X = 0.5

Z = ( X - μ ) / σ

  = ( 0.5 - 0.55) / 0.4975

 = -1. 005

 = -1.01

p-value pf -1.01 is equal to 0.156248

Therefore, the probability of getting 50% democrats for the given sample size id equal to 0.1562. The given example represents sample proportion.

The above question is incomplete , the complete question is :

In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of getting less than 50% Democrats in a random sample of size 100?

Is this an example of a sample proportion OR a sample mean?

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The cost of one muffin after taxes is $2.56. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

For all the real numbers, there are four basic mathematical operations which are:

1. Addition(‘+’) wherein the sum of the numbers is obtained.

2. Subtraction(‘-’) wherein the difference of the numbers is obtained.

3. Multiplication(‘×’) wherein the product of the numbers is obtained.

4. Division(‘÷’) wherein the quotient of the numbers is obtained.

Let cost of one muffin after taxes be 'x'

We are given that there were six friends and each person ordered a small cup of coffee and a muffin.

The total for the order, including taxes, was $38.10

Also, the cost of a small coffee is $3.79 after taxes.

So, we get

⇒ 6(3.79 + x) = 38.10

⇒ 22.74 + 6x = 38.10

⇒ 6x = 15.36

⇒ x = $2.56

Hence, the cost of one muffin after taxes is $2.56.

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The depiction of 35% as a fraction is 7/ 20, and option D is the correct answer.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given that the chance of getting hit by the ball is 35%.

35 % = 35/100

Simplifying the fraction:

35/100 = 7/ 20

Hence, depiction of 35% as a fraction is 7/ 20, and option D is the correct answer.

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Answer:

20,45 kg,

Step-by-step explanation:

45  Lb * (1 kg / 2,2 Lb) + (12 Austrália * (1 kg / 35 ,2 Austrália)) = 20,45 kg

Um resposta é 20,45 kg.

The type of sampling used in this example is Convenience sampling.

Convenience sampling is a type of non-probability sampling in which the sample is selected based on the ease of access or availability of the subjects. The sample is selected based on the researcher's convenience, and it does not use a random selection process.

In this case, the reporter chose to interview people in his own apartment building because it was convenient for him and he had easy access to them.

The other options you listed are:

a) Cluster sampling, which is a form of probability sampling in which the sample is selected by first dividing the population into smaller groups or clusters, and then selecting a random sample of those clusters.

b) Voluntary response sampling, which is a type of non-probability sampling where individuals choose to participate in the study.

c) Systematic sampling, which is a form of probability sampling in which the sample is selected by choosing a random starting point and then selecting every nth subject from the population.

d) Attempted census, which is when the researcher tries to include all members of a population in the sample.

Therefore, The type of sampling used in this example is Convenience sampling.

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The triangles abc and cda are congruent by sss congruence criteria.

The full form of CPCT is Corresponding parts of Congruent triangles. After proving triangles congruent, the remaining dimension can be predicted without actually measuring the sides and angles of a triangle. Different rules of congruency are as follows. SSS (Side-Side-Side)

SSS (Side-Side-Side) :-If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

so, sides

AB=CD

BC=DA

AC=CA

Hence by SSS (Side-Side-Side) the triangles are congruent.

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The required value of exponential function for the given values of x are 1.43, 1 , 0.7.

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread. ​

We have,

f(x) = [tex](0.7)^{x}[/tex]

So, at x = -1

f(x) = (0.7)^-1

f(x) = 1.43

At x = 0

f(x) = (0.7)^0

f(x) = 1

At x = 1

f(x) = (0.7)^1

f(x) = (0.7)

Thus, required value of function are 1.43, 1, 0.7

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The number of​ 18-inch wreaths is 7, and

the number of 22-inch wreaths is 18.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given the cost of an 18-inch wreath = $15

cost of a 22-inch wreath = $30

let the number of 18-inch wreaths be x and the number of  22-inch wreaths is y,

the total cost of both wreaths = $645

cost of x 18-inch wreaths = $15x

cost of y  22-inch wreaths = $30y

equation is,

$15x + $30y = $654

and the number of​ 22-inch wreaths sold was four more than twice the number of​ 18-inch wreaths,

y = 4 + 2x

substitute the value of y in the equation

15x + 30y = 645

15x + 30(4 + 2x) = 645

15x + 60x = 645 - 120

75x = 525

x = 525/75

x = 7

and y = 4 + 2x

y = 4 + 2*7

y = 18

Hence store sells 18  22-inch wreaths and 7  18-inch wreaths.

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The amount Jacob has to pay in a month where he used x GB over the limit is  y=25+20x.

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

Given that, Jacob has a smart phone data plan that costs $25 per month that includes 5 GB of data, but will charge an extra $20 per GB over the included amount.

Amount Jacob has to pay in a month where he used 4 GB over the limit is

25+4×20

= $105

Amount Jacob has to pay in a month where he used x GB over the limit is

y=25+20x

Where, y is total amount of money

Hence, the amount Jacob has to pay in a month where he used x GB over the limit is  y=25+20x.

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Answer:

Step-by-step explanation:

I don’t know just 5 point

divide the lateral height in half, Height squared lateral height squared is subtracted from height squared, the answer from step three, and find its square root. The radius of the cone is the outcome.

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Therefore , the solution of the given problem of volume comes out to be 9,003.75π cubic cm.

The following are the conical Frustum formulas in terms of r and h: V = (1/3) * * h * (r12 + r22 + (r1 + r2)) is the formula for a conical frustum's volume. The base's radius is the same as the cylinder's radius. The cylinder's height is equal to the length of the altitude, which is a segment running perpendicular to the planes of each of its bases.

Here,

Given :

=> 15 cm is the AB

=> radius = 49/2 = 24.5 cm

The radius of base is 24.5 cm

and

the volume of frustrum:

=> π(24.5)(24.5)(15)

=> 9,003.75π cubic cm

Therefore , the solution of the given problem of volume comes out to be

9,003.75π cubic cm.

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Answer:

Answer in attached photo.

Step-by-step explanation:

Solution in attached photo, do take note the standard form of an equation is:

y = mx + c,

where m is the gradient and c is the y-intercept.

Answer: (x– 8)2= 4(1)(y+ 3); vertex: (8, –3); opens upward

Answer: The height of the ball (in meters) after t seconds is given by the equation h = 2 + 5t - 5t^2. We can use this equation to find the values of t for which the ball's height is 3 meters.

We need to find the values of t that make h = 3, so we can substitute 3 for h in the equation:

3 = 2 + 5t - 5t^2

Then we can solve for t by moving all the terms to one side of the equation and factoring it:

-5t^2 + 5t - 1 = 0

And we can use the quadratic formula to find the solutions of this equation:

t = (5 +/- sqrt(5^2 - 4*(-1)(-1)))/ 2(-1)

t = (5 +/- sqrt(25 + 4))/ -2

t = (5 +/- sqrt(29))/ -2

The solutions of this equation are t = (5 +/- sqrt(29))/ -2

Since the time, t, is a real value the square root of 29 should be positive.

The values of t for which the ball's height is 3 meters are not real values, so there's no time when the ball's height is 3 meters.

Step-by-step explanation:

Kathy’s and Mark's investments worth will be $1248000 and $312000.

From the information, Kathy and Mark Smith believe investing in their retirement is critical. Kathy began investing 20% of each paycheck in a retirement account when she was 20 years old. She has saved four times more than Mark who began saving when he was 35.

Let Mark = x

Kathy = 4 × x = 4x

The equation to represent this will be:

4x + x = 1560000

5x = 1560000

Divide

x = 1560000 / 5

x = 312000

Mark contributed $312000

Kathy contributed

= 312000 × 4

= 1248000

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After the raise, Tyler's brother will make $14 x 1.05 = $14.70 per hour.

Answer:

14 x 1.05 = 14.70

Step-by-step explanation:

Answer: Anything that has the same two numbers

Step-by-step explanation:

You don't have a picture, so I'm basing this off of what I know. A number over another number that is the same is equivalent to one.

Answer:

Yes, one gallon is enough

Step-by-step explanation:

16ft x 12ft = 192ft

If one gallon covers 250 square feet then she will have enough for another 58ft remaining

The required  initial and final amounts of water contained in the pool are 46 ans 26 gallons of water.

A graph is made up of vertices, or points, and edges, or lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and uncorrected graphs, and simple graphs, there are many other forms of graphs.

As graph says

The initial amount of water contained in the pool is

at t = 0

= 46 gallons of water

And at t = 5, is final amount of water in pool

= 26 gallon of water

Thus, there are 46 ans 26 gallons of water.

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Answer:

1.478 x 10^2 AU

Step-by-step explanation:

To convert this distance to astronomical units (AU), we can use the fact that 1 AU is approximately equal to 93 million miles.

So, 13.8 billion miles is approximately:

13.8 billion miles / 93 million miles/AU = 147.8 AU

In scientific notation, this distance would be written as: 1.478 x 10^2 AU

Smallest = 16, median=22, largest value of data=26 , interquartile range=Q3-Q1=23-19=4.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

We have the data 19 22 22 26 23 24 21 16 16, and we have to calculate smallest, Q1, median ...

First rearrange the data 16,16,19,21,22,22,23,24,26

So, Smallest = 16

Median of the data = middle number of data=22

Q1=middle of smallest and median=19

Q3=23

largest value of data=26

range= 19-26

interquartile range=Q3-Q1=23-19=4

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Based on the information, we can infer that of the 250 adults surveyed, 190 wanted the park to be expanded and 60 did not want the park to be expanded.

To complete the table we must take into account the available information. In this case, they are only referring to the adults who wanted the park to be expanded:

According to the above, if we add these two values we would have a group of 190 adults who want the park to be expanded. So the number of adults who do not want the park to be expanded would be 60.

Finally, if there are 60 people who do not want the park to be expanded, we can infer that there may be 30 who are parents and 30 who are not parents.

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