given the equation 4x + 3y = 18. find the value of y when x = −3

Neither of the equation represent the a line that passes through (0, 5) and (4, 15)

The equation of a line can be represented in slope intercept form and point slope form as follows:

slope intercept form:

y = mx + b

where

Therefore,

m = 15 - 5 / 4 - 0

m = 10 / 4

m = 5 / 2

let's find y-intercept using (0, 5)

y = 5 / 2 x + b

5 = 5 / 2(0) + b

b = 5

Hence,

y = 5 / 2 x + 5

Let's find the equation in point slope form:

(0, 5)

y - y₁ = m(x - x₁)

y - 15 = 5 / 2(x - 4)

Therefore, neither of the equation represent the line.

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Answer:

a.) each line segment represents a length of 1/8

b.) N = 3/8

c.) -3/8

Step-by-step explanation:

a.) In order to find the interval / length of each line segment, simply count how many line segments there are until you reach one whole integer. Basically, start on one number and count how many sections until the next number.

So for this example, let's start counting from the number 0. From 0 to the next number, 1, there are a total of 8 sections from 0 to 1, so they're each split up into 1/8s.

b.) Count each line as 1/8 from 0 to N to get what N represents. So from 0 to N, there are 3 lines/portions, so N is 3/8 because 1/8 + 1/8 + 1/8 = 3/8

c.) Just put a negative sign in front of N to get the opposite

Answer:

10 ft

Step-by-step explanation:

Use theorem pythagoras

Length = x

\( {x}^{2} = 8 {}^{2} + {6}^{2} \\ x = - 10 \\ x = 10\)

the answer is 10 because length can't be in negative number

Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer:

There are 23 students

-- 9 students play neither sport

-- therefore, 23 - 9  =  14 students play at least one of the two sports; some play both sports.

Inclusive or:  the probability will be:  14 / 23 that a student chosen at random will play at least one of the two sports.

Exclusive or: we need to first find how many students play both sports.

Since 14 persons play sports and since 7 play basketball and 12 play baseball, this requires 7 + 12 = 19 students.

Subtracting  19 - 14 = 5 give the number of students who play both sports.

If we eliminate these 5 persons as well as the 9 who play neither sport, we have to eliminate 5 + 9  =  14 persons.

This gives 23 - 14 = 9 persons who play only one of the two sports.

The probability will be:  9/23 play a sport, but only one sport.

Step-by-step explanation:

The probability that a student does not play an instrument given that they play a sport is 6/7 or approximately 0.857.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

To find the probability that a student does not play an instrument given that they play a sport, we need to use conditional probability.

Let A be the event that a student plays a sport and B be the event that a student plays an instrument.

We want to find P(not B | A), which is the probability that a student does not play an instrument given that they play a sport.

We know that,

P(A) = 7/23, P(B) = 9/23, and P(A and B) = 3/23.

Using the formula for conditional probability, we have:

P(not B | A) = P(A and not B) / P(A)

We can find P(A and not B) by using the fact that,

P(A and B) = P(B) - P(A and not B).

P(A and not B)

= P(B) - P(A and B)

= 9/23 - 3/23

= 6/23

Substituting into the formula, we get:

P(not B | A) = (6/23) / (7/23) = 6/7

Therefore,

The probability that a student does not play an instrument given that they play a sport is 6/7 or approximately 0.857.

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Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

The probability that the couple will have 3 normal girls is approximately 0.422

Since both parents are normal, they both have to be heterozygous carriers for the recessive allele that causes albinism. We can represent the normal allele with the letter N and the albino allele with the letter n. Then, we can write the genotypes of the parents as Nn x Nn.

The daughter is albino, so her genotype must be nn. The son is normal, so his genotype must be Nn.

We want to find the probability that the couple will have 3 normal girls. We can use the multiplication rule of probability to find this probability:

P(3 normal girls) = P(normal girl) x P(normal girl) x P(normal girl)

The probability of having a normal girl is 3/4 since there are three possible genotypes that result in a normal phenotype (NN, Nn, Nn) out of a total of four possible genotypes. The probability of having a normal boy is also 3/4, for the same reason.

Therefore, the probability of having 3 normal children (in this case, girls) is:

P(3 normal girls) = (3/4) x (3/4) x (3/4) = 27/64 ≈ 0.422

So, the probability that the couple will have 3 normal girls is approximately 0.422, or about 42.2%.

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Answer: 84

Step-by-step explanation:

4 x 21 is 84 a fraction can be simplified and be a whole number so if 84 divided by 4 it will be 21 if you want to write it as a fraction it will be 21/1 which is equal to 21

Did it help? :)

Answer:

Option B.  house B; monthly payment of $1,550.89 is the correct answer.

Step-by-step explanation:

In order to calculate the highest payment Pete can afford we have to subtract his expenses from his housing budget.

Given

Total housing budget = $2250

Monthly costs = $215.75

Utilities = $143.50

Taxes = $273

First all expenses can be added together to subtract from the housing budget.

So

\(Monthly\ costs = Insurance\ +\ Utilities\ +\ taxes\\ = \$215.75 + \$143.50 + \$273\\= \$632.25\)

Now the total monthly cost will be subtracted from housing budget.

\(Amount\ for\ monthly\ payment = Housing\ budget - Monthly\ Expenses\\=\$2250\ -\ \$632.25\\=\$1617.75\)

Hence, he saves $1617.75 for monthly payment.

Looking at the options, C and D will be ruled out as both the quantities are greater than 1617.75

Option A and B both are smaller than 1617.75 but as $1,550.89>$1,327.18, Option B is the highest monthly payment Pete can afford.

Hence,

Option B.  house B; monthly payment of $1,550.89 is the correct answer.

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

the 8 is basically x sooooo

f (8) = 8+11

f(x) = 19

Answer:

D. 91%

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Less than 15 minutes.

Event B: Less than 10 minutes.

We are given the following probability distribution:

\(f(T = t) = \frac{3}{5}(\frac{5}{t})^4, t \geq 5\)

Simplifying:

\(f(T = t) = \frac{3*5^4}{5t^4} = \frac{375}{t^4}\)

Probability of arriving in less than 15 minutes:

Integral of the distribution from 5 to 15. So

\(P(A) = \int_{5}^{15} = \frac{375}{t^4}\)

Integral of \(\frac{1}{t^4} = t^{-4}\) is \(\frac{t^{-3}}{-3} = -\frac{1}{3t^3}\)

Then

\(\int \frac{375}{t^4} dt = -\frac{125}{t^3}\)

Applying the limits, by the Fundamental Theorem of Calculus:

At \(t = 15\), \(f(15) = -\frac{125}{15^3} = -\frac{1}{27}\)

At \(t = 5\), \(f(5) = -\frac{125}{5^3} = -1\)

Then

\(P(A) = -\frac{1}{27} + 1 = -\frac{1}{27} + \frac{27}{27} = \frac{26}{27}\)

Probability of arriving in less than 15 minutes and less than 10 minutes.

The intersection of these events is less than 10 minutes, so:

\(P(B) = \int_{5}^{10} = \frac{375}{t^4}\)

We already have the integral, so just apply the limits:

At \(t = 10\), \(f(10) = -\frac{125}{10^3} = -\frac{1}{8}\)

At \(t = 5\), \(f(5) = -\frac{125}{5^3} = -1\)

Then

\(P(A \cap B) = -\frac{1}{8} + 1 = -\frac{1}{8} + \frac{8}{8} = \frac{7}{8}\)

If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{8}}{\frac{26}{27}} = 0.9087\)

Thus 90.87%, approximately 91%, and the correct answer is given by option D.

Answer:

6

Step-by-step explanation:

use the pythagorean theorem

a² + b² = c²

8² + b² = 10²

b² = 100-64

b= (square root of) 36

b=6

Answer:

87

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

The answer is (-4,9)

Step-by-step explanation:

The other ones are not near the line (-8,-10) does not even fit on the screenshot. (-4,9) Is the only one that is on the line.

Answer:

20:

3 5/12 or 41/12

21:

-9 5/8 or -77/8

Answer:

100 inches

Step-by-step explanation:

Well, 500 feet is 6,000 inches. So, to find out how far does the worm travel in 1 hour (60 minutes) we would have to divide: 6,000 ÷ 60 minutes (1 hour) = 100. So, the worm can travel 100 inches in 1 minute

(sorry if wrong!)

Answer: y=8x-7 just took the quiz hope that helps

The other equation could be y = 8x - 7

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

to determine the other equation:

The first equation is given as:

y = 8x + 7

For the system of equation to have no solution, then the equations in the system would have different constant values.

Take for instance:

y = 8x + b

Where:

b is a constant not equal to 7

From the options, we have:

y = 8x - 7

Notice that -7 and 7 are not the same

Hence, the other equation could be y = 8x - 7

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Answer:

Step-by-step explanation:

20 * ((2*20)-6)

20*34

680

Solution :

Zoe's ball pool is a cylinder with height 20 cm and diameter 90 cm.

Height = 20 cm

Diameter = 90 cm

Calculate :

(a) The Radius of the pool.

Answer :

We are given with Diameter of pool 90 cm.

We know that,

Radius = Diameter/2

Radius = 90/2 = 45 cm.

(b) The circumference of the pool .

Answer :

Circumference = 2 πr

\(2 \times \dfrac{22}{7} \times 45 \\ \\ \dfrac{ 44 \times 45}{7} \\ \\ \frac{1980}{7} \\ \\ 282.8 \: cm\)

(c) The area of the base of the pool.

Answer :

Area of base = πr²

\( \dfrac{22}{7} \times {(45)}^{2} \\ \\ \frac{22}{7} \times 2025 \\ \\ 22 \times 289.28 \\ \\ 578.56 \: {cm}^{2} \\ \)

(d) The volume of the pool

Answer :

Volume of cylinder = πr²h

\( \dfrac{22}{7} \times {(45)}^{2} \times 20 \\ \\ \dfrac{22}{7} \times 2025 \times 2 \\ \\ \dfrac{22}{7} \times 4050 \\ \\ \frac{89100}{7} \\ \\ 12728.57 \: {cm}^{3} \)

The constant of proportionality is equal to 3/10.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 3/10 = 6/20 = 9/30

Constant of proportionality, k = 3/10.

Therefore, the required linear equation is given by;

y = kx

y = 3/10(x)

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Step-by-step explanation:

One possible equivalent equation to the given formula is:

uppercase B = 3 uppercase V ÷ h

To see why this equation is equivalent, we can isolate uppercase B in the original formula by multiplying both sides by 3/h:

3/h * uppercase V = 3/h * (one-third uppercase B h)

Simplifying the right-hand side:

3/h * (one-third uppercase B h) = uppercase B

Substituting back in the original formula gives:

uppercase B = 3/h * uppercase V

Answer:

The answer is (2a²b)(6ab)=12a³b².

The explicit formula of the geometric sequence is given as follows:

\(a_n = 100(4)^{n-1}\)

The recursive formula of the geometric sequence is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio (q). In other words, a geometric sequence is a sequence where each term is a fixed multiple of the previous term.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

For the recursive formula, we just take the first term and each consecutive term is the previous term multiplied by the common ratio.

There are 100 views in day one, hence the first term is given as follows:

\(a_1 = 100\)

The number of viewers is multiplied by 4 each day, hence the common ratio is given as follows:

q = 4.

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To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.

To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.

We know that there are 51 coins in total, so we can write the equation: d + q = 51.

We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for d: d = 51 - q.

Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.

Simplify and solve for q: 510 - 10q + 25q = 1020.

Combine like terms: 15q = 510.

Divide both sides by 15: q = 34.

Now substitute this value back into the first equation to solve for d: d + 34 = 51.

Subtract 34 from both sides: d = 17.

Therefore, you have 17 dimes and 34 quarters.

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