Find the common difference of the arithmetic sequence 13, 18, 23, ...

Answer:

/////////

Step-by-step explanation:

Answer:

12 weekly payments

Step-by-step explanation:

Here, we want to get the number of weeks in which he made payment for the ring

We start by subtracting the deposit,

That would be;

225-75 = 150

Now, we proceed to divide what ie left by the weekly payment to get the number of weeks

That would be;

150/12.5 = 12

Answer:

12 weekly payments

Step-by-step explanation:

Here, we want to get the number of weeks in which he made payment for the ring

We start by subtracting the deposit,

That would be;

225-75 = 150

Now, we proceed to divide what ie left by the weekly payment to get the number of weeks

That would be;

150/12.5 = 12

Step-by-step explanation:

Answer:

300 units

Step-by-step explanation:

You did the steps correctly, but you forgot that it does not go by 1s, but goes by 5s. Check your grid!

(I messed up on this too! ^^)

Hope this helps!

x represents the cost of each bottle of juice. Given that he bought a pack containing 6 bottles of juice, the cost of the 6 pack juice bottles would be $6x

Given that the total cost of a bag of popcorn which costs $2.11 and a 6-pack of juice bottles is $11.41, it means that

2.11 + 6x = 11.41

6x = 11.41 - 2.11

6x = 9.3

x = 9.3/6

x = 1.55

The cost of each bottle of juice is $1.55

Since η² ≈ 0.33 and not 0.50, the statement "If an analysis of variance produces SS between = 20 and SS within = 40, then η² = 0.50" is false.

ANOVA, or Analysis of Variance, is a statistical method used to compare the means of two or more groups to determine if there are any statistically significant differences between them. It is commonly used in experimental and observational studies to analyze the variance between group means and within-group variability.

ANOVA tests the null hypothesis that the means of the groups are equal, against the alternative hypothesis that at least one of the group means is different. It calculates the F-statistic, which compares the between-group variability to the within-group variability. If the F-statistic is large enough and exceeds a critical value, it indicates that there is evidence to reject the null hypothesis and conclude that there are significant differences between the group means.

We can determine if η² = 0.50 is true or false by calculating the effect size η² using the provided SS between and SS within values.
η² = SS_between / (SS_between + SS_within)
η² = 20 / (20 + 40)
η² = 20 / 60
η² = 1/3 ≈ 0.33
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True, the eta-squared value is indeed 0.50, indicating that 50% of the total variance is accounted for by the between-group variation.

The formula to calculate eta squared (η2) is:
η2 = SSbetween / (SSbetween + SSwithin)
If SSbetween = 20 and SSwithin = 40, then:
η2 = 20 / (20 + 40) = 0.5
Therefore, η2 = 0.50, which means that 50% of the total variance in the dependent variable can be attributed to the independent variable (or factor) being analyze. The statement "If an analysis of variance produces SS between = 20 and SS within = 40, then η 2 = 0.50" is true. To determine η 2 (eta-squared), you'll need to calculate the proportion of total variance explained by the between-group variation. This can be done using the formula η 2 = SS between / (SS between + SS within). In this case, η 2 = 20 / (20 + 40) = 20 / 60 = 0.50. Therefore, the eta-squared value is indeed 0.50, indicating that 50% of the total variance is accounted for by the between-group variation.

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Answer:

4^8

Step-by-step explanation:

If you are multiplying two bases that are the same with different exponents, the exponents get added and the base stays the same:

\(x^a*x^b=x^{a+b}\\\\4^3*4^5=4^{3+5}\\\\4^3*4^5=4^8\)

Therefore, 4^3 * 4^5 = 4^8

Answer: x-int: (-4, 0), y-int: (0, 1/2)

Step-by-step explanation:

x-int: when y = 0

-x + 8*0 = 4

-x = 4

x = -4

(-4, 0)

y-int: when x = 0

0 + 8y = 4

8y = 4

y = 1/2

(0, 1/2)

Answer:

D

Step-by-step explanation:

x/(-6)+y/(-7)=1

7x+6y=-42

7x+6y+42=0

y=(-7/6)x-7

Answer: B.)  Point S is the correct answer

Step-by-step explanation:

On the Edge quiz point S also known as the vertex of the angle is the correct answer. I got it correct! Trust me!  Hope this helps! :)

The endpoint of a ray in the diagram is: B. point S.

A ray can be defined as a line that starts at one end and extends in the other direction without an end. The endpoint of the ray is that point where the ray starts from.

Thus, in the image given, all the rays or lines starts from point S, so, the endpoint of a ray is: B. point S.

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Answer:

\(x=8,\\y\approx 6.9\)

Step-by-step explanation:

The side lengths of all 30-60-90 triangles are in ratio \(x:x\sqrt{3}:2x}\), where \(2x\) is the hypotenuse of the triangle and \(x\) is the side opposite to the 30 degree angle.

In the given diagram, the side labelled 4 is opposite to the 30 degree angle. Since \(x\) is labelled as the hypotenuse of the triangle, \(x\) must be \(4\cdot 2=\boxed{8}\).

Variable \(y\) must then represent \(x\sqrt{3}\) for \(x=4\), yielding \(y=4\sqrt{3}\approx \boxed{6.9}\)

Answer:

\(f^{-1}(f(58))=58\)

\(f(f(5))=11\)

Step-by-step explanation:

We are given that the table which shows some inputs and outputs of the invertible function f with domain all real numbers.

We are given that

x         f(x)

5         9

3         -2

1          -5

18          -1

0           1

9           11

We have to find

\(f^{-1}(f(58))\) \(f(f(5))\)

We know that

\(f^{-1}(f(x))=x\)

Using the property

\(f^{-1}(f(58))=58\)

\(f(5)=9\)

\(f(f(5))=f(9)\)

\(f(f(5))=11\)

The dimensions of the package of maximum volume that can be sent are approximately 7.8 inches in radius and 21.3 inches in height.

Let's assume that the package has a height 'h' and a radius 'r'. The perimeter of the cross-section of a cylinder is the circumference of the circle plus the height multiplied by two, which can be written as:

Perimeter = 2πr + 2h

Given that the maximum combined length and circumference is 114 inches, we can write:

2πr + 2h + 2r = 114

Simplifying this equation, we get:

πr + h = 57 - r ----(1)

The volume of the cylinder is given by:

\(V = πr^2h\)

Now, we can use equation (1) to eliminate 'h' from the volume equation:

\(V = πr^2(57 - r - πr)\)

Expanding and simplifying this equation, we get:

\(V = πr^3 - π^2r^3/3 + 57πr^2 - 57π^2r\)

To find the dimensions of the package that maximize the volume, we need to find the value of 'r' that maximizes the volume. We can do this by taking the derivative of the volume equation with respect to 'r' and setting it equal to zero:

\(dV/dr = 3πr^2 - π^2r^2 + 114πr - 57π^2 = 0\)

Solving for 'r', we get:

r ≈ 7.8 inches

Substituting this value of 'r' back into equation (1), we can find the value of 'h':

h ≈ 21.3 inches

Therefore, the dimensions of the package of maximum volume that can be sent are approximately 7.8 inches in radius and 21.3 inches in height.

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Answer:

V = 378y³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Geometry

Volume of a Rectangular Prism: V = lwh

Step-by-step explanation:

Step 1: Define

Identify variables

l = 9y

w = 7y

h = 6y

Step 2: Find Volume

___________________________________

\(\quad\quad\quad\quad \boxed{\tt{v = lwh}}\)

\(\quad\quad\quad\quad\tt{length (l)= 9y}\)

\(\quad\quad\quad\quad\tt{width(w)= 7y}\)

\(\quad\quad\quad\quad\tt{height(h)= 6y}\)

\(\quad\quad\quad\quad\tt{v = lwh}\)

\(\quad\quad\quad\quad\tt{v = (9y)(7y)(6y)}\)

\(\quad\quad\quad\quad\tt{v = (9y)(42 {y}^{2}) }\)

\(\quad\quad\quad\quad \underline{\tt{v = 378 {y}^{3} }}\)

\(\quad\quad\quad\quad \underline { \boxed{\tt{ \color{magenta}v = 378 {y}^{3} }}}\)

___________________________________

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✍︎ C.Rose❀

a) An equation to show the relationship between the number of gallons of gasoline and the distance driven is r = 25 mpg.

b) The total distance to be traveled using 6.3 gallons is 157.5 miles.

c) If the car is driven 14,000 miles in one year, the gallons of gasoline used would be 560 gallons.

d) If the gasoline costs $4.10 per gallons, the total cost of purchasing gasoline for the year is $2,296.

e) The miles per gallon is 25 mpg.

f) The gasoline cost per mile is $0.164.

Miles per gallon (MPG) shows the distance traveled by a vehicle, measured in miles, per gallon of gasoline.

The mpg is used to assess a vehicle's fuel efficiency.

a) The volume of the car's gas tank = 17 gallons

The distance on a single tank of gas = 425 miles

Let r = the rate of gasoline consumption per mile

An equation to show the relationship between the number of gallons of gasoline and the distance driven = 425/17 = 25 mpg

b) The number of gallons of gas in the tank = 6.3 gallons

The total distance to be traveled using 6.3 gallons = 157.5 miles (6.3 x 25)

c) If the car is driven 14,000 miles in one year, the gallons of gasoline used would be = 560 gallons (14,000/25).

d) The cost of gasoline per gallon = $4.10

The total cost of purchasing gasoline for the year = $2,296 ($4.10 x 560)

e) The miles per gallon = 25 mpg (14,000/560).

f) The gasoline cost per mile = $0.164 (560 x $4.10)/14,000

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Answer:

Step-by-step explanation o:

Answer:

8

Step-by-step explanation:

131211109876543210-1-2-3-4-5

A verbal statement could be: The quotient of h and eight

There is a 34% chance that the randomly purchased item from the manufacturer will last longer than 8 years.

The question is asking for the probability that a randomly purchased item from a manufacturer will last longer than 8 years. To answer this question, we must use the normal distribution formula and find the area under the curve between 8 and infinity.

The formula for the normal distribution is as follows:

\(1/(\sigma\sqrt{2\pi}) e^{-((x-\mu)^2)2\sigma^2}\)

Where μ is the mean and σ is the standard deviation.

In this problem, μ = 6.5 years and σ = 0.8 years.

Using the formula, the probability of the randomly purchased item lasting longer than 8 years is 0.34.

To calculate the probability, we use the z-score formula, which is \((x-\mu)/\sigma\). Plugging in 8-6.5/0.8 gives us a z-score of 1.875.

Using the z-table, we can find the area under the curve, which is 0.34. This means that the probability of the randomly purchased item lasting longer than 8 years is 0.34.

Therefore, the answer to the question is that there is a 34% chance that the randomly purchased item from the manufacturer will last longer than 8 years.

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Answer

When simplified, the answer is

Explanation

[2/x² - 5x + 6] - [5/x - 2​]

To solve this, we need to first factorize x² - 5x + 6

x² - 5x + 6

= x² - 3x - 2x + 6

= x (x - 3) - 2 (x - 3)

= (x - 3) (x - 2)

So, we can rewrite the question, and then take an LCM

We will then take the LCM

Hope this Helps!!!

Answer:

12

Step-by-step explanation:

21-9

12

Answer:

The answer is 12

Step-by-step explanation:

|21| = just 21

|-9| = positive 9

so take that into this:

21 - 9 = 12

Answer:

This correlation simply means that, in every twin whether identical or fraternal twins, there is a relation between their IQ scores and when they are raised together.

Regarding to the test carried out, it showed that, when an identical twin is raised together, their IQ score tends to be higher in direct comparison with a fraternal twin that was raised together. That is, if the fraternal twin IQ is 100, then, the identical twin IQ is going to be above 100 (probably around 120)

Step-by-step explanation:

According to Descartes' Rule of Signs, the polynomial P(x) = x² + x² + x² + x + 14 can have at most 2 positive real zeros and 0 negative real zeros. The total number of real zeros can be either 0, 2, or any even number.

Descartes' Rule of Signs provides a way to determine the number of positive and negative real zeros a polynomial can have by examining the signs of its coefficients. For the polynomial P(x) = x² + x² + x² + x + 14, we can rewrite it as P(x) = 3x² + x + 14.

First, we count the sign changes in the coefficients of P(x). There is one sign change from positive to negative (3x² to x) indicating one negative real zero.

Next, we consider the polynomial P(-x) = 3(-x)² + (-x) + 14 = 3x² - x + 14. Counting the sign changes again, we find no sign changes from positive to negative. Therefore, there are no positive real zeros.

Based on Descartes' Rule of Signs, we conclude that P(x) can have at most 2 positive real zeros and 0 negative real zeros. The total number of real zeros can be 0, 2, or any even number, as there can be complex conjugate pairs of zeros for the remaining possibilities.

In summary, the polynomial P(x) = x² + x² + x² + x + 14 can have at most 2 positive real zeros and 0 negative real zeros. The total number of real zeros can be 0, 2, or any even number.

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Answer:

The range for this function is the set (-5)

Answer:

Step-by-step explanation:

factors of 8

Answer:

F- of a 8* i think

Step-by-step explanation:

Answer:

12 hours

Step-by-step explanation:

Let's say that the trainee can do the job in $x$ hours.

Since the trainer is three times faster than the trainee, the trainer can do the same job in $x/3$ hours.

Working together, the trainer and trainee can complete the job in 3 hours, so we can set up the equation:

$$\frac{1}{x}+\frac{1}{x/3}= \frac{1}{3}$$

To solve for $x$, we can first simplify the left-hand side:

$$\frac{1}{x}+\frac{3}{x}= \frac{1}{3}$$

Combining like terms, we get:

$$\frac{4}{x}= \frac{1}{3}$$

Multiplying both sides by $x$, we get:

$$x=\frac{4}{1/3}=12$$

Therefore, the trainee can complete the job in 12 hours.

A regular polygon with angles that all measure 162 degrees has 20 sides.

Let's first consider a formula to find the measure of an interior angle of a regular polygon. We can use the formula:

Interior angle = (n-2) x 180 / n,

where n is the number of sides of the polygon.

If all angles of the polygon measure 162 degrees, then we can set up an equation:

(n-2) x 180 / n = 162

Multiplying both sides by n, we get:

(n-2) x 180 = 162n

Expanding the left side, we get:

180n - 360 = 162n

Subtracting 162n from both sides, we get:

18n - 360 = 0

Adding 360 to both sides, we get:

18n = 360

Dividing both sides by 18, we get:

n = 20

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Answer:

  (a)  $810.45

Step-by-step explanation:

You want the value of an investment of $300 earning 5% interest compounded quarterly for 20 years.

The compound interest formula tells you the value is ...

  A = P(1 +r/n)^(nt)

where P = 300, r = 0.05, n = 4, t = 20.

Using the given parameters in the given equation, you find the account value to be ...

  A = $300(1 +0.05/4)^(4·20) ≈ $810.45

__

Additional comment

The "rule of 72" tells you the account value will approximately double in a number of years equal to 72 divided by the interest rate percentage: 72/5 = 14.4 years. After 20 years, it will be worth more than that doubled amount, $600. This only leaves one reasonable answer choice.

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