Ethan and David are brothers. If Ethan is 3 years older than David, and the sum of their ages is 17, how old is David?

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.

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:

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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By answering the above question, we may state that Graphical equation depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph

When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.

Mathematicians use graphs to visually express or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph

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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

Answer:

Step-by-step explanation:

To find the hiker's elevation above sea level upon reaching High Point Vista, we need to add up the elevation gain from the start of the trail to High Point Vista. We can use the table to do this:

Elevation gain from start to Old Cabin: -32.78 ft (negative because the hiker loses elevation)

Elevation gain from Old Cabin to Ruby Falls: 8634 ft

Elevation gain from Ruby Falls to Thunder Gorge: -14725 ft (negative because the hiker loses elevation)

Elevation gain from Thunder Gorge to High Point Vista: 346.47 ft

To find the hiker's elevation above sea level at High Point Vista, we add up these elevation gains:

179 ft (start) - 32.78 ft + 8634 ft - 14725 ft + 346.47 ft = -5668.31 ft

The negative value means that the hiker is below sea level at High Point Vista, which is not possible. Therefore, there must be an error in the elevation gain listed for one of the points of interest. It's possible that the elevation gain for Ruby Falls is incorrect, as it seems unlikely that the hiker would gain more than 8000 ft in elevation between Old Cabin and Ruby Falls. Without more information, it's difficult to say for sure where the error lies.

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 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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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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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 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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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: 126 Spelling Words

Answer:

Step-by-step explanation:

On the first day, Ms. Dubacek gave 6 new spelling words.

On each subsequent day, she gave an additional 3 new spelling words.

Therefore, on the second day of school, she gave a total of 6 + 3 = 9 new spelling words.

On the third day of school, she gave a total of 6 + 3 + 3 = 12 new spelling words.

We can see a pattern emerging here: on each day, she gives 6 more words than the previous day.

So on the 21st day of school, she will have given a total of:

6 + (9 + 12 + 15 + ... + 60)

To find the sum of this arithmetic series, we can use the formula:

S = n/2 * (a + l)

where:

S = the sum of the series

n = the number of terms in the series

a = the first term in the series

l = the last term in the series

In this case, we have:

n = 19 (since we're counting from the second day of school to the 21st day)

a = 9 (since that was the total number of spelling words given on the second day)

l = 60 (since that will be the total number of spelling words given on the 21st day)

So, plugging in these values, we get:

S = 19/2 * (9 + 60) = 19/2 * 69 = 655.5

Therefore, by the end of the 21st day of school, Ms. Dubacek will have given her students a total of 6 + 655.5 = 661.5 new spelling words (rounded to the nearest whole number, this is 662).

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.

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?

Answer:

Step-by-step explanation:

FG = FE, ∴ ΔFGE is isosceles.

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

So ∠G = 63°

The trigonometric ratios gives the values required.

The three main trigonometric ratios that we need are the sine the cosine and the tangent.

1) The hypotenuse is;

c^2 = 5^2 + 12^2

c = √5^2 + 12^2

c = 13

Then;

sin x + cos x

= 5/13 + 12/13

= 17/13

2) The adjacent is;

13^2 = x^2 + 5^2

x^2 = 13^2 - 5^2

x = √13^2 - 5^2

x = √ 169 - 25

x = 12

Cos p = 12/13

3) The adjacent is;

13^2 = x^2 + 12^2

x^2 = 169 - 144

x = 5

2sinx + 1/2Cos x

2(12/13) + 1/2 (5/13)

144/13 + 5/26

=293/26

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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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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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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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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:

Answer:

Step-by-step explanation: OK so is A'B'C'D' a translation, rotation, or reflection of ABCD? OK so A'B'C'D' is a rotation i believe because like you i'm on the same thing. Is A"B"C"D" a translation, rotation, or reflection of A'B'C'D'? OK so A"B"C"D" is a reflection i believe i'm not really sure on that one. Suppose the measure of angle B is 89°. Which other angle must be 89°? OK so angle A, angle C, and angle B. But I really don't get what you trying to ask? Hope I kind of helped, like i said im in 8th grade and it is kind of hard for me too.

Answer:6cm

Step-by-step explanation:You can use the formulas  or  to solve for diameter using volume. I will use the first forumla for this problem.

Substitute 113 for "V"

Multiply in the parenthesis

Divide by pi (3.14)

678 ÷ 3.14 = 215.923567

Apply the exponent

d = 5.99907...

d = 6 cm

Answer:

the final price of Ray's laptop is 89.1% of the original price.

Step-by-step explanation:

To find the composite function that can be used to calculate the final price of Ray's laptop, we need to find the composition of the two functions given:

f(c) = 1.08c (function for calculating the price of the laptop with tax)

c(p) = 0.75p (function for calculating the sale price of the laptop)

We can find the composite function f(c(p)) by substituting c(p) into the formula for f(c):

f(c(p)) = 1.08c(p)

Substituting c(p) with 0.75p, we get:

f(c(p)) = 1.08(0.75p)

Simplifying, we get:

f(c(p)) = 0.81p

Therefore, the composite function that can be used to calculate the final price of Ray's laptop is f(c(p)) = 0.81p.

This means that to find the final price of the laptop, we need to take the original price, multiply it by 0.75 to get the sale price, and then multiply the sale price by 1.08 to add the sales tax. In other words, the final price is:

final price = f(c(p)) = 0.81p = 1.08(0.75p)

final price = 0.81p + 0.081p

final price = 0.891p

Therefore, the final price of Ray's laptop is 89.1% of the original price.

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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Answer:25% of the number is 30

Step-by-step explanation:

Let's call the number we're looking for "x". We can use the information given in the problem to set up two equations:

10% of x is 12:

0.1x = 12

35% of x is 42:

0.35x = 42

Now we can solve for x:

0.1x = 12

x = 120

0.35x = 42

x = 120

We get the same value for x from both equations, which confirms that our solution is correct. Now that we know x = 120, we can find 25% of that number:

25% of 120 = 0.25 x 120 = 30

Therefore, 25% of the number is 30.

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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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:

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

Step-by-step explanation:

Answer:

20B

Step-by-step explanation:

Answer:

20B

Step-by-step explanation: