Express the following expression as a function of an acute angle less than 45°:
cot (-859°)

Monica should report the mode, because the mode of a data set is always the value that appears the greatest number of times. Option C is correct.

Answer:

20B

Step-by-step explanation:

Answer:

20B

Step-by-step explanation:

The farmer's market originally had 400 peaches on hand.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and radicals.

Let's use x to represent the original number of peaches the farmer's market had on hand.

We know that the farmer's market sold 35% of its produce, which means it sold 0.35x peaches. The remaining number of peaches can be calculated by subtracting the number of peaches sold from the original number of peaches:

remaining peaches = x - 0.35x

We also know that there are 260 peaches remaining, so we can set up an equation:

260 = x - 0.35x

Simplifying this equation, we can combine like terms:

260 = 0.65x

To solve for x, we need to isolate the variable by dividing both sides by 0.65:

x = 260 / 0.65

x = 400

Therefore, the farmer's market originally had 400 peaches on hand.

To explain how we used equivalent ratios, we used the fact that the farmer's market sold 35% of its produce. This can be represented as a ratio of 35/100 or 0.35. We then used this ratio to find the number of peaches sold, which is 0.35x. We also used the fact that the remaining peaches are the original peaches minus the peaches sold, or x - 0.35x. Finally, we set up an equation using the remaining peaches and solved for x to find the original number of peaches.

Hence, the farmer's market originally had 400 peaches on hand.

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The height of the pole is 336 feet.

The 24 foot shrub has a 6 foot shadow . The height of the pole that has an 84 foot shadow is as follows:

Hence. let's use proportion to find the height of the pole.

Therefore,

let

h = height of the pole

Hence,

24  /h = 6 / 84

cross multiply

6h = 84 × 24

6h = 2016

divide both sides by 6

h = 2016 / 6

h = 336 ft

Therefore,

height of the pole = 336 ft

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Answer:-(-1,026/3

Step-by-step explanation:

The table that shows a proportional relationship is Table A.

A proportional relationship is a type of relationship between two variables in which the ratio of their values remains constant. In other words, as one variable increases or decreases, the other variable also increases or decreases in proportion to it.

In table A, we see that :

= 150 / 3

= 50

= 200 / 4

= 50

= 250 / 5

= 50

Every single value of y, gives the same value of x so this means that the table shows a proportional relationship.

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The area of the triangle LKJ is 150 square meters

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

The figure

The area of a shape is the measurement of the size of the region enclosed by the shape in a two-dimensional plane.

It is the amount of space inside the shape, usually measured in square units, such as square meters or square feet.

From the figurr, we have

KM^2 = LM * MJ

Substitute the known values in the above equation, so, we have the following representation

12^2 = LM * 16

So, we have

LM = 9

Next, we have

Area = 1/2 * LM * KM

So, we have

Area = 1/2 * 12 * (9 + 16)

Evaluate

Area = 150

Hence, the value of the area is 150

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Answer:

10 weeks

Step-by-step explanation:

40 books= ? weeks

4 books.  = 1 week

so do 40/4 and get 10

Answer:

10 weeks

Step-by-step explanation:

The equations that have the same value of x as the given equation are:

18x - 9 = 72

3(6x - 3) = 72

x = 4.5

The correct options are the third, fourth, and fifth options

From the question, we are to determine the equations that have the same value of x as the given equation

To solve the given equation, we can begin by simplifying it:

3/5 (30 x - 15) = 72

Multiplying both sides by 5/3, we get:

30 x - 15 = 120

Adding 15 to both sides, we get:

30 x = 135

Dividing both sides by 30, we get:

x = 4.5

Now, to check which equations have the same value of x as the above result, we can substitute x = 4.5 in each option and see which ones result in a true statement.

Substituting x = 4.5, we get:

18(4.5) - 15 = 72

81 - 15 = 72

This is not a true statement, so this option is not correct.

Substituting x = 4.5, we get:

50(4.5) - 25 = 72

225 - 25 = 72

This is not a true statement, so this option is not correct.

Substituting x = 4.5, we get:

18(4.5) - 9 = 72

81 - 9 = 72

This is a true statement, so this option is correct.

Substituting x = 4.5, we get:

3(6(4.5) - 3) = 72

3(24) = 72

This is a true statement, so this option is correct.

4.5 = 4.5

This is a true statement, so this option is correct.

Hence, the equations are:

18x - 9 = 72

3(6x - 3) = 72

x = 4.5

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The number of possible outcomes is 10.

To find the number of possible outcomes find the number of outcomes when the coin is flipped and the number of outcomes when the spinner is spinning.

Multiply the number of outcomes from the coin by the number of outcomes from the spinner.  

Here we have

Enola is designing a new board game,

She flips a coin and spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday    

No of possible outcomes when a coin is flipped = 2 [Head and Tail]  

No of possible outcomes when she spins a spinner = 5

[ i.e Monday, Tuesday, Wednesday, Thursday, Friday ]  

Hence, No of out comes = 2 × 5 = 10

Therefore,

The number of possible outcomes is 10.

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Answer:

Step-by-step explanation:

FG = FE, ∴ ΔFGE is isosceles.

∴∠G = ∠E (Base angle in isosceles triangle are equal)

So ∠G = 63°

Answer:

200 x 7 = 1,400 x = 7 because there are 7 days in a week

Step-by-step explanation:

The solution is, in PRYZ square, the value of m∠YKZ = 90.

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

here, we have,

Remember that

In a Square

All sides are equal

Diagonals bisect each other perpendicularly

so

Find out KY

In the right triangle RYK

Applying the Pythagorean Theorem

RY^2=RK^2+KY^2

substitute given values

13^2=5^2+KY^2

KY^2=13^2-5^2

KY^2=144

KY=12

Find out PK

Remember that

Diagonals bisect each other perpendicularly

that means

PK=KY=12

Remember that

Diagonals bisect each other perpendicularly

so, that means

m∠YKZ = 90

Hence, The solution is, in PRYZ square, the value of m∠YKZ = 90.

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Answer:

Step-by-step explanation:

To use elimination method, we need to eliminate one of the variables (x or y) by adding or subtracting the two equations. To do this, the coefficients of one of the variables in the two equations should be the same or opposite.

Looking at the two equations:

Equation #1: 2x + 18y = -9

Equation #2: 4x + 18y = -27

We can see that the coefficients of y are already the same in both equations. So, we can eliminate y by subtracting Equation #1 from Equation #2.

However, to do this we need to make sure that the coefficients of x in the two equations are opposites, i.e., one is positive and one is negative.

Therefore, the first step we could take to solve this system using elimination is to multiply Equation #1 by -2 to get:

-4x - 36y = 18

Now the coefficients of x in the two equations are opposites, so we can subtract Equation #1 from Equation #2 to eliminate y and solve for x.

So, the correct answer is:

Multiply equation #1 by -2.

Of the first 100 vehicles, there are nine convertible green cars.

The sequence of green cars:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99

The sequence of convertible cars:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100.

Convertible and Green cars (in the very first 100 cars):

12, 24, 36, 48, 60, 72, 84, and 96.

Thus, of the first 100 vehicles of auto assembly line, there are nine convertible green cars.

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The complete question is-

On an automobile assembly line, every third car is green. Every fourth car is a convertible. How many cars out of the first 100 will be green convertibles?

The right response is B. It is the graph of f(x) scaled down by 11 units.

For any given value of x, the output of f(x) is subtracted by 11 to get the function g(x) = f(x) - 11.

The result is the same as the input for the function f(x) = x. Thus, if we take 11 out of the result, we get:

g(x) = f(x) - 11 = x - 11

In other words, the graph of g(x) is the graph of f(x), 11 units lower.

Thus, assertion B is the correct one. It is the graph of f(x) scaled down by 11 units.

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The algebraic expressions for the given questions are found as:

1) g/4 + 15.

2) 6 - y + 3

3) d * 8

What are algebraic expressions?

A mathematical expression made up of variables, constant algebraic numbers, and algebraic operations are known as an algebraic expression. Everything with a variable value is anything whose value changes over time. Variables in expressions are often represented by letters of the alphabet. Finding the simplified term of the given expression is the goal of simplifying the algebraic expression. We must first understand how to join like terms, factor a number, and the order of operations before we can factorise or simplify the expression. When like terms are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.

1) The quotient of g and 4 is given by g/4.

Now, this is added to 15.

So the algebraic expression is g/4 + 15.

2) The difference between y and 3 is y - 3.

Now from 6, this difference is subtracted.

So the expression becomes,

6 - (y-3) = 6 - y + 3

3) The product of two numbers is found by multiplying the numbers.

  So the expression is :

      d * 8

Therefore the algebraic expressions for the given questions are found according to the given statements.

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Answer: 1.24

Step-by-step explanation:

40% abundance in decimals = 0.4

0.4 multiplied by 3.1 = 1.24

Answer:

EPIC: They Troy Saga Full Speed

Step-by-step explanation:

Six hundred men, six hundred men under my command

With only one goal in mind

Make it back alive to our homeland

Six hundred men, six hundred miles of open sea

But the problem's not the distance

It's what lies in between

And Ithaca's waiting Ithaca's waiting

My kingdom is waiting The kingdom is waiting

Penelope's waiting for me

So full speed ahead, full speed ahead

Each input value has exactly one corresponding output value, which satisfies the definition of a function.

A function is a relation between two sets of values where each input value (independent variable) corresponds to exactly one output value (dependent variable). In this case, the input values are the values of "x" column, and the output values are the values of "y" column.

Looking at the given table, for each unique value of "x", there is a unique corresponding value of "y".

For example, when "x" is 25, "y" is 5; when "x" is -25, "y" is -5; when "x" is 36, "y" is 6; and when "x" is -36, "y" is -6.

Therefore, each input value has exactly one corresponding output value, which satisfies the definition of a function.

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Statements B, C, and D are not true. Diego would travel a greater distance from D to B than from C to D. He would also create different angles at ΔBDA and ΔBDC, and the distance traveled from A to B would not be the same as from B to C.

According to the given figure, Diego attempts to walk in a sequence of lines to create ΔABD and ΔCDB. He can traverse each side only once and cannot jump from point to point. We need to determine which of the following statements are not true:

A) The distance Diego travels from A to B is the same as the distance traveled from C to D. This statement is not true because the distance from A to B is the sum of the lengths of AB and BD, whereas the distance from C to D is the sum of the lengths of CD and BD, and BD is being counted twice.

B) The distance Diego travels from D to B is the same as the distance traveled from C to D. We cannot determine the truth of this statement without more information about the lengths of the sides.

C) The distance Diego travels from A to B is the same as the distance traveled from B to C. This statement is not true because the distance from A to B is the sum of the lengths of AB and BD, whereas the distance from B to C is the sum of the lengths of BC and BD, and BD is being counted twice.

D) The angle Diego creates at ΔBDA has the same measure as the angle he creates at ΔBDC. This statement is not true because the angles at ΔBDA and ΔBDC are vertical angles, which are congruent, but not necessarily equal to each other.

E) The angle Diego creates at ΔDAB has the same measure as the angle he creates at ΔBCD. We cannot determine the truth of this statement without more information about the angles.

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11)  (A) a t-interval for a difference between means for independent samples.

12) the appropriate t-statistic is (C) 1.98.

13) option (c)

The central limit theorem is a principle in probability theory that states that the distribution of sample means will eventually approximate a normal distribution as the sample size becomes larger.

11) The type of study being conducted by Ron is a completely randomized design, where he randomly assigns the two types of golf balls (new and current) to two separate groups and then compares the mean driving distances between the two groups.

The appropriate t-interval for inference is (A) a t-interval for a difference between means for independent samples.

12) To test the hypothesis of whether there is a significant difference in mean driving distance between the new golf balls and the old golf balls, we need to calculate the appropriate t-statistic.

The formula for the t-statistic for a difference between means for independent samples is:

[tex]t = (x_1 - x_2) / [s1^2/n1 + s_2^2/n_2]^{0.5}[/tex]

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes for the two groups.

Using the given data, we have:

x1 = 203.5 yards, x2 = 197.4 yards

s1 = 5.6 yards, s2 = 10.3 yards

n1 = n2 = 30

Substituting these values into the formula, we get:

[tex]t = (203.5 - 197.4) / [(5.6)^2/30 + 10.3^2/30]^{0.5} = 1.98[/tex]

Therefore, the appropriate t-statistic is (C) 1.98.

13) The correct statement about the study being conducted by Ron is (C) The central limit theorem tells us that the sampling distribution of driving distance for each of the individual samples of balls will be approximately normal.

Hence, The answers to the question:
11)  (A) a t-interval for a difference between means for independent samples.

12) the appropriate t-statistic is (C) 1.98.

13) option (c)

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Answer: c

Step-by-step explanation:

Since the denominator of the expression (1 + 0.1t) cannot be zero, the domain of the model is between t = 0 and t = -10.

In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).

(b) We must assess the model at t = 0 in order to determine the starting number of elk in the herd:

P = (10 + 3.3t)/(1 + 0.1t)

P = (10 + 3.3(0))/(1 + 0.1(0))

P = 10/1

P = 10

(c) We can easily enter the relevant values of t into the model to determine the populations of elk after 25, 59, and 113 years, then round the results to the nearest integer.

When t = 25:

P = (10 + 3.3t)/(1 + 0.1t)

P = (10 + 3.3(25))/(1 + 0.1(25))

P ≈ 47

When t = 59:

P = (10 + 3.3t)/(1 + 0.1t)

P = (10 + 3.3(59))/(1 + 0.1(59))

P ≈ 189

When t = 113:

P = (10 + 3.3t)/(1 + 0.1t)

P = (10 + 3.3(113))/(1 + 0.1(113))

P ≈ 458

(d) We can use the expression's limit as t approaches infinity to determine the expected population limit:

lim P as t → ∞ = lim (10 + 3.3t)/(1 + 0.1t) as t → ∞

Using L'Hopital's rule, we can find that the limit is equal to:

lim P as t → ∞ = lim 3.3/0.1 as t → ∞

lim P as t → ∞ = 33

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Answer:

17m−5n)(17n−5m) when u expand it your answer would be −85m 2+314mn−85n 2

Step-by-step explanation:

If your parents are buying a house for $187,500. their realized income be before each month is $5250.

Loan amount = $187,500 - (187,500 * 20%)

Loan amount = $ 150,000

Monthly rate = 4.65% / 12 = 0.3875%

Interest rate for the first month is:

Interest rate = $ 150,000 * 0.3875% = $ 581.25.

Loan repayment =$ 1,575 - $ 581.25 = $ 993.75.

Amount  parents owe = $ 150,000 - $ 993.75 = $149,006.25

Second  month Loan = $ 1,575 - ($149,006.25 * 0.3875%) = $ 997.60

Second month ending amount owe = ( $149,006.25 - $997.60)

Second month ending amount owe =  $ 148,008.65

A monthly loan payment that is not more than 30% of monthly income will be used to find the realized income.

Realized income = $ 1,575/30% = $ 5,250

Therefore the realized income is $5250

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The mass of each bun is 50g.

Two or more expressions with an Equal sign is called as Equation.

Given that the total mass of 2 loaves of bread and 5 buns is 650g.

The 2 loaves of bread weigh 400 g.

We need to find the mass of each bun.

2 loaves of bread + 5 buns = 650g

2 loaves of bread = 400g

5 buns = 650g - 400g

=250g

1 bun = 250/ 5

= 50g

The mass of each bun is 50g.

Hence, the mass of each bun is 50g.

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Complete question

The total mass of 2 loaves of bread and 5 buns is 650 g. The 2 loaves of bread weigh 400 g. What is the mass of each bun?

Answer:

Below

Step-by-step explanation:

1  8/10  = 18/10

18 / 10   pound  *  $ 4.10 / pound  =  (18 * 4.1) / 10 =  73.8 /10 = $ 7.38

( see how the unit 'pound' cancels out and you are left with  $  ???)

In flowchart, If the dice do not show the same number, add 0 points to the player's score.

A flowchart quick answer is what it sounds like.

A flowchart is a diagram that shows a procedure, a system, or a computer algorithm. It is a diagrammatic representation of a particular problem's solution, but more significantly, it breaks out the crucial actions that must be taken in order to solve the problem.

1.Roll three dice

2.Compare numbers on the dice

3.If two dice show the same number, add 10 points to the player's score

4.If three dice show the same number, add 25 points to the player's score

5.If the dice do not show the same number, add 0 points to the player's score.

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Therefore, the probability that at least one of the dice shows the number 2, given that the sum of the dice is 4, is 1 - (1/5) = 4/5, or 0.8, which is the probability that at least one of the two dice is a 2.

It is founded on the likelihood that something will occur. The rationale for probability is the central tenet of theoretical probability. For instance, there is a 12% chance that a coin will land on its head when flipped.

There are five possible ways to obtain a sum of 4 with two 6-sided dice: {(1,3),(2,2),(3,1),(2,1),(1,2)}.

Out of these five possible outcomes, there is only one outcome where neither of the dice show a 2, which is {(1,3)}.

Therefore, the probability that at least one of the dice shows the number 2, given that the sum of the dice is 4, is 1 - (1/5) = 4/5, or 0.8, which is the probability that at least one of the two dice is a 2.

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The probability that at least one of a pair of fair 6-sided dice shows the number 2, given that the sum of the dice is 4 is 1/3.

The measure of the likelihood or chance of an event occurring is known as Probability. It is a quantitative measure that ranges from 0 (indicating an impossible event) to 1 (indicating a certain event).

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes in a given situation or experiment. Probability theory is a branch of mathematics that deals with the study of random events, and it is widely used in many fields such as statistics, physics, economics, finance, and more.

If the sum of the dice is 4, then the possible pairs are (1, 3), (2, 2), and (3, 1). Out of these three pairs, only one has at least one die showing the number 2, which is (2, 2).

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Answer:

[tex]416 \;in^2[/tex]

Step-by-step explanation:

The surface area of the rectangular prism

[tex]S = 2(lw + lh + wh)[/tex]

where

l = length = 12 in

w = width = 10 in

h = height = 4 in

Therefore

[tex]S = 2(12\cdot 10 \;+ \; 12\cdot 4 \;+\;10 \cdot 4)\\\\= 2(120 + 48 + 40)\\\\= 2 (208)\\\\= 416 \: in^2[/tex]

The time at which Neo reaches the work destination is A = 8 : 15 AM

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the time at which Neo reaches the work destination be A

Now , the time at which Neo leaves home = 6 : 45 AM

And , the distance between Neo and work = 45 miles

where the speed of Neo is S = 30 miles per hour

So , the distance traveled by Neo in 1 hour = 30 miles

The distance traveled by Neo in 1.5 hours = 45 miles

Therefore , the time required by Neo to reach office is 1.5 hours

And , the time at which Neo reaches the work destination A = 6 : 45 AM + 1.5 hours

On simplifying the equation , we get

The time at which Neo reaches the work destination A = 8 : 15 AM

Hence , the equation is A = 8 : 15 AM

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