Given: f(x) = 3x+2 and g(x) = -4x-2
Find the point of intersection algebraically and with your calculator

Answer:

yes it is correct. good job!

The greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.

As per the question statement, the greatest common divisor of two integers is (x+2) and the least common multiple x(x+2). It is given that one of the integers is 24.

Let us assume that "b" is the value of other one.

greatest common divisor(24,b) = (x+2)

least common multiple(24,b) = x(x+2)

Formula:

greatest common divisor(24,b)*least common multiple(24,b) = 24*b

24*b = (x+2)*x(x+2)

\(b = \frac{x(x+2)^{2} }{24} \\\)

Hence, the smallest possible value of the other one is "6" and x = 4.

Hence, the greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.

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Answer: c = -47

Step-by-step explanation:

1. Divide both sides

2. Move the constant to the right

3. Calculate

Answer:

c = -47

Step-by-step explanation:

Here's how!

0.2(c - 3) = -10 (distribute 0.2 to c and -3)

0.2c - 0.6 = -10 (add 0.6 to both sides)

0.2c = -9.4 (divide by 0.2 on both sides)

c = -47

Plug in

0.2(-47 - 3) = -10 (add -47 and -3)

0.2(-50) = -10 (distribute)

-10 = -10

Hope this helps!!

The following distributions has a mean that varies

II. The distribution of sample data

III. The sampling distribution of the sample mean

The correct answer is option v) II and III."

Here, we have,

In the context of statistical distributions:

I. The population distribution refers to the distribution of a specific variable within the entire population. The mean of the population distribution which is fixed and does not vary.

II. The distribution of sample data refers to the distribution of a variable within a specific sample. The mean of the sample data can vary from one sample to another.

III. The sampling distribution of the sample mean refers to the distribution of sample means taken from multiple samples of the same size from a population. The mean of the sampling distribution of the sample mean is equal to the population mean, but the individual sample means can vary from sample to sample.

Therefore, the mean varies in both the distribution of sample data (II) and the sampling distribution of the sample mean (III), but not in the population distribution (I).

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In Milgram's first study of obedience, the majority of teachers initially complied but refused to deliver more than slight levels of shock.

In Milgram's first study of obedience, participants were assigned the role of 'teacher' and were instructed to administer electric shocks to a 'learner' whenever they answered a question incorrectly. The shocks ranged from mild to severe, with the highest level labeled as 'XXX.' The learner was actually an actor, and no real shocks were administered.

The study found that the majority of teachers initially complied with the experimenter's orders and delivered shocks, but they refused to deliver more than slight levels of shock. This suggests that while they were willing to follow the instructions to some extent, they had moral reservations about causing significant harm to another person.

It is important to note that the study has been criticized for ethical concerns and the potential psychological harm it may have caused to participants. However, it remains a significant contribution to our understanding of obedience and the power of authority figures.

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$39.99+238.8+1.75x and  $4.99=1.99x+$40 are the algebraic expressions of given data.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given that $39.99 /month, unlimited texting , 120MB data (Overages $1.99 /MB talk is $1.75 /minutes

$39.99+120(1.99)+1.75x

$39.99+238.8+1.75x

$4.99 /month, unlimited texting ,$40 for 80MB data talk is $1.99 /minutes

$4.99+1.99x+$40

Hence, $39.99+238.8+1.75x and  $4.99+1.99x+$40 are the algebaic expressions of given data.

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The approximate volume of the remaining solid is approximately 51.44 cubic inches.

To find the volume of the remaining solid, we need to calculate the volume of the rectangular prism and subtract the volume of the hole.

Volume of the rectangular prism:

The rectangular base has sides of 4 inches, and the height is also 4 inches. Therefore, the volume of the rectangular prism is given by the formula:

Volume = Length × Width × Height

Volume = 4 inches × 4 inches × 4 inches

Volume = 64 cubic inches

Volume of the hole (cylinder):

The hole is in the shape of a cylinder, and its radius is given as 1 inch. To find the volume of a cylinder, we use the formula:

Volume = π × radius^2 × height

The height of the cylinder is the same as the height of the rectangular prism, which is 4 inches.

Substituting the values:

Volume = π × (1 inch)^2 × 4 inches

Volume ≈ 3.14 × 1 inch^2 × 4 inches

Volume ≈ 12.56 cubic inches

Volume of the remaining solid:

To find the volume of the remaining solid, we subtract the volume of the hole from the volume of the rectangular prism:

Remaining Volume = Volume of Prism - Volume of Hole

Remaining Volume = 64 cubic inches - 12.56 cubic inches

Remaining Volume ≈ 51.44 cubic inches

Therefore, the approximate volume of the remaining solid is approximately 51.44 cubic inches.

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Answer:

x= 26

Step-by-step explanation:

set 5x+7 equal to 8x-71 since the angles are equal

solve

Answer:

560 students

Step-by-step explanation:

1400*.40=560 students in 6th grade

say we're going to add "x" gallons of water, now how many gallons of alcohol is in pure water? well 0%, and 0% of "x" is (0/100) * x = 0.

the 3 gallons we know are 100% alcohol, how many gallons of alcohol is in it?  well (100/100) * 3 = 3.

the resulting mix will have x + 3 gallons total and it's going to be 15% alcohol, how many gallons of alcohol is that? (15/100) * (x+3).

now, the amount of alcohol never increased, so the original 3 gallons of only alcohol will remain even after the water has been added, so.

\(\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{amount}\\ \cline{2-4}&\\ \textit{pure water}&x&0.00&0\\ \textit{pure alcohol}&3&1.00&3\\ \cline{2-4}&\\ mixture&x+3&0.15&0.15(x+3) \end{array} \begin{array}{llll} \\[3em] \leftarrow \textit{this amount}\\\\ \leftarrow \textit{must be equal to this one} \end{array} \\\\\\ 3 = 0.15(x+3)\implies 3=0.15x+0.45\implies 2.55=0.15x \\\\\\ \cfrac{2.55}{0.15}=x\implies 17=x\)

a. The sum of 3.7 and 4.888 is 8.6.

b. The product of (4.09 × 10²) and (6.33 × 10⁴) is 2.74 × 10⁷.

c. The result of multiplying 3.376, 23, and 0.123 is 9.95.

d. The result of adding 0.0467 to 23.32 and subtracting 22.8 is 0.099.

a. 3.7 + 4.888

Adding 3.7 and 4.888 gives us a sum of 8.588. Since the least number of decimal places in the given numbers is one, we round the answer to one decimal place, resulting in 8.6.

b. (4.09 × 10²) × (6.33 × 10⁴)

Multiplying the given numbers gives us 259.797 × 10⁶. Since the given numbers have two significant figures each, the answer should have two significant figures as well. Therefore, we round it to 2.7 × 10⁷.

c. 3.376 × 23 × 0.123

Multiplying the given numbers results in 9.984552. The number with the fewest significant figures is 23, which has two significant figures. Therefore, we round the answer to two significant figures, giving us 10.

d. 0.0467 + 23.32 - 22.8

Performing the addition and subtraction operations, we get 0.5667. The given numbers have four decimal places in total. Hence, the answer should also have four decimal places, resulting in 0.099.

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Answer:

1 is the result of equation.

Step-by-step explanation:

Given that,

→ x = 1

The equation will be,

→ [{((x × 2) + 4) ÷ 2} - 2]

Then the result of the eq. will be,

→ [{((1 × 2) + 4) ÷ 2} - 2]

→ [{(2 + 4) ÷ 2} - 2]

→ [{6 ÷ 2} - 2]

→ [3 - 2] = 1

Hence, 1 is the value of equation.

Answer: 8 whole gallons.

Step-by-step explanation: If you have only $27.00 and you need to buy gas, but each gallon is $3.15, then you just need to divide your total amount ($27.00) by your cost per gallon ($3.15), and you will get about 8.6 gallons, however this question asks for how many WHOLE gallons you can get, so all you need to do is round down to fit your budget, leaving money for only 8 whole gallons.

WORK: ($27.00) / ($3.15) = 8.6 gallons

Answer:

\(10.5\%\)

Step-by-step explanation:

\(\% \: error = \frac{absolute \: error}{actual \: value} \times 100\)

actual value = 38ml, measurement error = 42ml

absolute error = actual value - measurement error (where actual value > measurement error) OR measurement error - actual value (where actual value < measurement error)

(Note: absolute error is different from measurement error. Absolute error is the distance between the actual value and the measurement error, while measurement error is the error made in measurement).

Therefore, absolute error = 42 - 38 = 4

\(\% \: error = \frac{4}{38} \times 100\)

\(\% \: error = 10.52\)

Therefore: % error = 10.5 (to the nearest tenth)

The next step she should take is to use her ruler to join the given point to the point where the arcs intersect.

From this, we can deduce that her next step is to use her ruler to join the given point to the point where the arcs intersect

Thus, the next step she should take is to use her ruler to join the given point to the point where the arcs intersect.

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Answer:

  SEM decreases by a factor of √N

Step-by-step explanation:

The standard error of the mean (SEM) is inversely proportional to the square root of the sample size. As the sample size (N) increases, the SEM is decreased by a factor of √N.

The SEM is the population standard deviation divided by √N for a normal distribution.

The diameter of a human hair is 7 times greater than the diameter of a spider's silk.

To determine how much greater the diameter of a human hair is than the diameter of a spider's silk, we can calculate the difference between the two diameters. The diameter of a human hair is given as 10^(-5) meters, and the diameter of a spider's silk is given as 3*10^(-6) meters.

To find the difference, we subtract the diameter of the spider's silk from the diameter of the human hair:

Difference = (10^(-5)) - (3*10^(-6))

= (10^(-5)) - (10^(-6))

= (10^(-5)) - (1/10^6)

= (10^(-5)) - (10^6/10^6)

= (10^(-5)) - (10^6 * 10^(-6))

= (10^(-5)) - (10^(6-6))

= (10^(-5)) - (10^(0))

= (10^(-5)) - 1

= 10^(-5) - 1

= 0.99999

Therefore, the diameter of a human hair is approximately 7 times greater than the diameter of a spider's silk.

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Answer:

No, because the y-intercepts of lines g and h are different.

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

according to the question :-

(x+54)+5x=90

x+54+5x=90

6x+54=90

6x=90-54

6x=36

x=36/6

x=6

The common ration between the sum of a certain infinite geometric series is 2. the sum of the squares of all the terms is 3 is ( r,a) = ( 1/7, 12/7)

That means { a/ 1-r} = 2

a^2/1-r^2 = 3

2a/ 1+r = 3

2(2-2r)/ 1+r = 3

4-4r= 3+ 3r

7r + 1

r= 1/7

2a/ 8/7 = 3

7a= 12

a= 12/7

so( r,a) = ( 1/7, 12/7)

What is infinite geometric series?

An infinite geometric series is the sum of an infinite geometric sequence. This series would have no last term. The general form of the infinite geometric series is a1 + a1r + a1r2 + a1r3+…, where a1 is the first term and r is the common ratio.

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Answer:

To find the number of cars in stock, just add up all of the numbers.

So...

13+14+5+23 = 55

To prove that τ and σ are multiplicative, we need to show that if m and n are relatively prime, then τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n).

To prove τ(mn) = τ(m)τ(n), we can start by considering the prime factorization of m and n. Let's say m = p₁^a₁ * p₂^a₂ * ... * pₖ^aₖ and n = q₁^b₁ * q₂^b₂ * ... * qₙ^bₙ, where p₁, p₂, ..., pₖ and q₁, q₂, ..., qₙ are distinct prime numbers. Since m and n are relatively prime, none of their prime factors overlap.

Now, the divisors of mn are the numbers of the form p₁^x₁ * p₂^x₂ * ... * pₖ^xₖ * q₁^y₁ * q₂^y₂ * ... * qₙ^yₙ, where 0 ≤ xᵢ ≤ aᵢ and 0 ≤ yⱼ ≤ bⱼ. Thus, the number of divisors of mn, τ(mn), can be calculated by multiplying the number of divisors of m, τ(m), with the number of divisors of n, τ(n). Hence, τ(mn) = τ(m)τ(n).

To prove σ(mn) = σ(m)σ(n), we can again use the prime factorization of m and n. Similar to the previous proof, the sum of divisors of mn, σ(mn), can be calculated by multiplying the sum of divisors of m, σ(m), with the sum of divisors of n, σ(n). Hence, σ(mn) = σ(m)σ(n).

Therefore, we have proved that τ and σ are multiplicative when m and n are relatively prime.

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We have shown that both τ and σ are multiplicative functions, satisfying the properties τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n) for relatively prime numbers m and n.

To prove that τ (the number of positive divisors) and σ (the sum of positive divisors) are multiplicative functions, we need to show that for any two relatively prime numbers, m and n, the following properties hold:

1. τ(mn) = τ(m)τ(n)

2. σ(mn) = σ(m)σ(n)

Let's start with property 1:

1. τ(mn) = τ(m)τ(n)

If m and n are relatively prime, it means that they do not share any prime factors. Therefore, the divisors of mn are formed by taking a divisor of m and a divisor of n. Each divisor of mn can be uniquely expressed as the product of a divisor of m and a divisor of n.

Since the number of divisors of mn is equal to the product of the number of divisors of m and the number of divisors of n, we can conclude that τ(mn) = τ(m)τ(n).

Now let's move on to property 2:

2. σ(mn) = σ(m)σ(n)

Similar to property 1, we can express the sum of divisors of mn as the sum of products, where each product is formed by taking a divisor of m and a divisor of n. Again, since m and n are relatively prime, their divisors are distinct.

Using the distributive property, we can expand the sum of products as the sum of two separate terms: one involving the divisors of m and another involving the divisors of n. The sum of divisors of mn is therefore equal to the product of the sum of divisors of m and the sum of divisors of n.

Hence, we can conclude that σ(mn) = σ(m)σ(n).

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The  numbers x that are at a distance of 2 from the number 6 is found as: -4 and -8.

To find all the numbers x that are at a distance of 2 from the number 6, we will use the absolute value notation. Absolute value is denoted as |-| which refers to the distance of a number from zero on the number line. We use the same notation to find the distance between two numbers on the number line.The distance between the two numbers x and y is |-x-y|.

Given,Number 6: x = 6.

Distance: 2

We need to find all the numbers x that are at a distance of 2 from the number 6.

Absolute value is denoted as |-| which refers to the distance of a number from zero on the number line. We use the same notation to find the distance between two numbers on the number line.

The distance between the two numbers x and y is |-x-y|.

Therefore, we can express the absolute value of the difference between x and 6 as |-x-6|.

In order to find all numbers x that are 2 units away from 6, we solve the equation by setting |-x-6| equal to 2.2 = |-x-6|

The absolute value of |-x-6| is x+6 or -(x+6).Thus, we have the following equations:

x+6 = 2 or -(x+6) = 2x+6 = 2 or x+6 = -2x = -4 or x = -8 or -4

So, the numbers that are at a distance of 2 from the number 6 are -4 and -8.

Therefore, |x-6| = 2 for x = -4 and -8.

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1) In this question, we need to remember that in any boxplot the line in the middle of the box indicates the median.

Based on that, we can tell the Median is 140

2) In the Interquartile Range, we need to find the range between the lower quartile and the upper one, based on that boxplot. We can tell the IQR is:

Note that the boundaries of the box show us the lower and the upper quartile:

Answer: y = x - 3

Step-by-step explanation:

y-intercept = -3

(0,-3) (4, 1)

m = (x₂ - x₁) / (y₂ - y₁)

m = (4 - 0) / (1 - (-3))

m = 4 / 4

m = 1

y = 1x -3

y = x - 3

Hint:

use the law of cosine to solve for x

Answer:

8

Step-by-step explanation:

idk i just thought it was 8 and i was right lol

Sarah's charges per hour for working during the week will be $9.5.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.

Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be

45x + 5y = 902.5           ...1

50x + 10y = 1045

25x + 5y = 522.5          ...2

Subtract equation 2 from equation 1, then we have

45x - 25x = 902.5 - 522.5

20x = 380

x = 19

And the value of y will be

25 (19) + 5y = 522.5

475 + 5y = 522.5

5y = 47.5

y = 9.5

Sarah's charges per hour for working during the week will be $9.5.

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Answer: Strawberry

Step-by-step explanation: Strawberry has the highest candies so it has the highest chance of being pulled out.

Step-by-step explanation:

b = -2 , a = 8 , c = -1

x= b^2 - 4ac

x = (-2)^2 - 4(8)(-1)

x = 4 + 32

x = 36

36 > 0

2 real solutions?

I'm not sure for the answer OwO

The table representing the relationship between hours of lawn care and the amount of money the company charges is:

8 $220

10 $275

12 $330

14 $385.

Equations are mathematical expressions with two algebraic expressions flanking the equals (=) symbol on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS (left hand side equals right hand side) is the most widely accepted theorem.

Let x be the charge of lawn care for 1 hour.

Given, charge for 4 hours of lawn care =$110

So, x= Amount charged/ Hours of lawn care

x=110/4

x=27.5

Now, the company charges $27.5 for 1 hour of lawn care.

So now we can find the amount charged by the company for

"y" no. of hours by using the equation. x × y = z

Here x, y and z are variables, where x is the charge of lawn care for 1 hour. y is the number of hours of lawn care and z is the total amount

charged by the company.

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