The half of the moon facing the sun is always lit, but the different phases we view from Earth happen because:

the Earth moves to different positions around the Sun

we only see parts of the lit side as the moon goes around the Earth

only part of the light gets reflected to Earth

the spinning of the moon lets us see different amounts of light

Answer:

The cost of orange juice is $3 per jug

Step-by-step explanation:

A unit rate is a rate where the second quantity is one unit.

Answer:

10) 5

11) Scalene

Step-by-step explanation:

10) A regular hexagon has equal sides, so one side is just 30/6, which is 5 feet.

11) A scalene triangle has no two sides that are the same length, where an isosceles triangle has two sides the same, and an equilateral triangle has all sides the same length.  

The annual rate of interest paid by the credit union is 5%.

What is compound interest?

⇒ Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

What is the annual interest rate?

⇒ The annual interest rate refers to the rate that is applied over a period of one year. Interest rates can be applied over different periods, such as monthly, quarterly, or bi-annually. However, in most cases, interest rates are annualized.

We know that the compound interest is given as:

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Calculation:

We have

P = $5,000

And the interest earned is $810

A=$5,000+$810=$5810

let the annual rate of interest is %

r = x/100

n = 3

\(A=P(1+r)^{n}\)

\(5810=5000(1+\frac{x}{100}) ^{3}\)

\(\frac{5810}{5000} =(1+\frac{x}{100}) ^{3}\)

\(1.162=(1+\frac{x}{100}) ^{3}\)

\((1+\frac{x}{100})=1.05\)

\(\frac{x}{100}=0.05\)

x=5%

So, the annual interest rate paid by the credit union is 5%

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Answer:

75:50

Step-by-step explanation:

15 x 5 = 75

10 x 5 = 50

Answer:

10 2/3

Step-by-step explanation:

16 x 2/3

32/3 or 10 2/3

Aubree need the amount of cheese  for 16 pizzas would be 10.6 pounds

A proportion is a fraction of a total amount, and the measures are related using a rule of three. The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The given parameters are;

Pizza = 16

Proportion of cheese = 2/3

The amount of cheese is the proportion of cheese needed for the flower can be calculated as;

Cheese = Proportion x Pizza

So, we have:

Cheese = 2/3 x 16

Evaluate the product;

Cheese = 32/3

Cheese = 10.6

Hence, 10.6 pounds of cheese is needed for 16 pizzas.

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Answer:

D

Step-by-step explanation:

i multiplied the first equation by 60 to eliminate the fractions: 30x - 45y = 11

i multiplied the second equation by 30 to eliminate the fractions: 12x + 5y = 9

I graphed them and (2/3, 1/5) is the intersection of both lines

Original line: y = -5/6x - 1

A line that is parallel to the original will have the same slope. To find the new y-intercept, we'll take the original line, plug in the given point, and solve for b.

y = -5/6x + b

-2 = -5/6(5) + b

-2 = -25/6 + b

b = 13/6

Parallel Line: y = -5/6x + 13/6

A line that is perpendicular to the original will have the opposite reciprocal slope. To find the new y-intercept, we'll take our perpendicular slope, plug in the given point, and solve for b.

y = 6/5x + b

-2 = 6/5(5) + b

-2 = 6 + b

b = -8

Perpendicular Line: y = 6/5x - 8

Hope this helps!! :)

The volume of the given rectangular prism is 27.6 cubic cm.

Length of the prism = 4⅗ cm

Width of the prism = 3 cm

Height of the prism = 2 cm

Volume of the rectangular prism = length × width × height

= 4⅗ × 3 × 2

= 23/5 × 6

= 138/5

= 27.6 cm³

In conclusion, the rectangular prism has the volume 27.6 cm³

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The average weight of a random sample of 50 NFL players is 244.4 pounds.

An equation shows the relationship between two or more numbers and variables.

For a samples size (n) in normally distributed population, the sample mean is normally distributed, with mean μX=μ and standard deviation σX=σ/√n.

Hence for a sample of 50 NFL players with an average weight of 244.4 pounds:

Mean = mean = 244.4 pounds

The average weight is 244.4 pounds.

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The equality that does not hold for every x in {F} is x^2 = x + 1.  In a field, all elements have additive inverses, so the equation -1 * x = -x holds for every x.

That means that multiplying any element by -1 gives its additive inverse. Additionally, the property of additive inverses implies that x + (-x) = 0, as adding an element and its additive inverse yields the additive identity element, which is typically denoted as 0.

However, the equation x^2 = x + 1 does not hold for every element x in a field. This equation represents a quadratic equation, and not all elements in a field satisfy this equation. The existence of solutions to this equation depends on the properties of the specific field and the characteristics of the field's elements. Therefore, x^2 = x + 1 is not universally true for every x in {F}.

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Answer:

D = 0

Step-by-step explanation:

Given

x-intercept = -3

Required

What does the discriminant represent?

The discriminant of a quadratic function can take any 3 values; these are as follows;

Which translates to

The question says that x-intercept = -3 is the only value;

This means that: x = -3 or x = -3

Analyzing the roots

This means they satisfy condition number 3;

Hence, D = 0

Researchers must carefully consider their choice of words to avoid bias and ensure a more accurate representation of the responses. 

a. The wordings of the questions contain the word "destroyed" and "80 acres per minute," which could cause the respondent to exaggerate the severity of the issue. Therefore, they may respond with strong negative reactions.

b. The question contains the phrase "vanishing tropical forests," which could cause the respondent to exaggerate the severity of the issue. Therefore, they may respond with strong negative reactions.

c. The question is loaded with the phrase "man-made extinction of animal and plant species," hence, the respondents could lean more towards the idea of the need to prevent it. The question is likely to elicit responses directed toward prevention and preservation.

d. The question contains the phrase "changes in the earth’s atmosphere," which suggests a link between the destruction of tropical forests and changes in the earth’s atmosphere. The question is likely to elicit responses that lean towards agreeing with the statement made in the question. 

Therefore, researchers must carefully consider their choice of words to avoid bias and ensure a more accurate representation of the responses. 

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The value of cv1, the lower critical value, is approximately 54.19.

To find the critical value (cv1) for a two-tailed hypothesis test at a 10% significance level, we need to divide the significance level (α) by 2.

Since α = 0.10, we divide it by 2 to get 0.10/2 = 0.05.

Next, we need to find the z-score associated with the cumulative probability of 0.05.

Using a standard normal distribution table or a calculator, we can find that the z-score for a cumulative probability of 0.05 is approximately -1.645.

Now, we can calculate the critical value by multiplying the z-score by the standard deviation (27) and adding it to the population mean (100).

cv1 = 100 + (-1.645 * 27)
cv1 ≈ 54.19 (rounded to two decimal places)

Therefore, the value of cv1, the lower critical value, is approximately 54.19.

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The supply of styluses is falling at a rate of 0.0144p² styluses per week.

To determine the exact rate of change in supply, we need to look at the equation provided: 500p²x² = 1996. We can rearrange this equation to solve for x, which represents the supply of styluses:

x² = (1996/500p²)

x = √(1996/500p²)

Now, we can differentiate this equation with respect to time to find the rate of change in supply:

dx/dt = (-1/2)(1996/500p²)(-1000p²/1996)*dp/dt

Simplifying this equation, we get:

dx/dt = (6/25)p²dp/dt

Using the information provided in each situation, we can plug in the appropriate values to find the rate of change in supply:

In the first situation, where the price is rising at 12 cents per week, dp/dt = 0.12. Plugging this into the equation above, we get:

dx/dt = (6/25)(p²)(0.12) = 0.0288p²

This means that the supply of styluses is rising at a rate of 0.0288p² styluses per week.

In the second situation, where the price is falling at 6 cents per week, dp/dt = -0.06. Plugging this into the equation above, we get:

dx/dt = (6/25)(p²)(-0.06) = -0.0144p²

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Answer:

your new balance is -47$

Step-by-step explanation: it is now -47 $ because 35 + 12 is 47.

The expected value of the square of the distance of the knight after 2016 moves is approximately 462.05.

The expected value of the square of the distance of the knight from the origin after n moves can be calculated using the following formula:

E(d²) = (1/8) * (2 * (E(d²) - 1) + 5)

where d is the distance from the origin, and E(d²) is the expected value of d².

Using this formula, the expected value of the square of the distance after 2016 moves can be calculated iteratively.

Starting with an initial estimate of E(d²), we can use the formula to calculate a better estimate in each iteration. This process can be repeated until the estimate converges to a value within a desired accuracy.

Using this approach, the expected value of the square of the distance after 2016 moves can be approximated to be 462.05.

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Answer:

a

Step-by-step explanation:

1/3 is one third and times by 30

Answer:

(3 2/3 x 1 1/2) = 5.5

Step-by-step explanation:

Result:

5.8333333 = 58333333/10000000 = 5.8333333

Spelled result in words is five point eight three three three three three three.

The calculator makes basic and advanced operations with decimals, real numbers and integers. It also shows detailed step-by-step information about calculation procedure. Solve problems with two, three or more decimals in one expression. Add, subtract and multiply decimals step-by-step. This calculator uses addition, subtraction, multiplication or division for calculations on positive or negative decimal numbers, integers, real numbers and whole numbers. This online decimals calculator will help you understand how to add, subtract, multiply or divide decimals.The calculator follows well-known rules for order of operations. The most common mnemonics for remembering this order of operations are:

PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction

BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.

GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.

Be careful, always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.

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The variable x as the subject of the formula is x = (y + b)/a

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

y = ax - b

The above equation is a linear equation

To make the variable x the subject of the formula, we start by adding the variable b to both sides of the equation

Using the above as a guide, we have the following:

y + b = ax - b + b

Evaluate the like terms

This gives

y + b = ax

Next, we divide both sides of the equation by a

This gives

x = (y + b)/a

Hence, the solution is x = (y + b)/a

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Answer:

12 hours

Step-by-step explanation:

We are given the function [ F(t) = 1084 - 65t ]

t represents the time so we are going to solve for f(t).

Substitute and solve

304 = 1084 - 65t

~Subtract 1084 to both sides

-780 = -65t

~Divide -65 to both sides

12 = t

Best of Luck!

Hello!

Five times x increased by three times y is  5x + 3y

The number of inches the height of the plant increase is (b) 4 inches

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

At week 3 and 4, we have

Heights = 8 inches and 12 inches

Calculate the difference between these heights

So, we have

Difference = 12 inches - 8 inches

Evaluate

Difference = 4 inches

Hence, the height increase is (b) 4 inches

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Answer:

Step-by-step explanation:

let y be 2x

90 + 66 + 24 + X + 2x = 360° (angles at a point)

180° + 3x = 360°

3x = 360° - 180°

3x = 180°

divide both sides by 3

3x/3 = 180/3

X = 60

2x = 2(60) = 120°

therefore X = 60°

Y = 120°

90° + 66° + 24° + 60° + 120° = 360°

Answer:

x = +2

y = +.5

Step-by-step explanation:

Above is how they increase in each column

We know that the linear model:

To determine the cost for a given mileage we just need to plug the later in the equation; in this case we know that m=16, then we have:

Therefore, it cost $34.20 to travel sixteen miles.

The feature NOT associated with the function h(x) is that the domain of h(x) is [0.).

The function h(x) is defined as (x - 5)² - log₁ x + 6.

Let's analyze each given option to determine which one is NOT a key feature of h(x).

Option 1 states that the domain of h(x) is [0, ∞).

However, the function h(x) contains a logarithm term, which is only defined for positive values of x.

Therefore, the domain of h(x) is actually (0, ∞).

This option is not a key feature of h(x).

Option 2 states that the x-intercept of h(x) is (5, 0).

To find the x-intercept, we set h(x) = 0 and solve for x. In this case, we have (x - 5)² - log₁ x + 6 = 0.

However, since the logarithm term is always positive, it can never equal zero.

Therefore, the function h(x) does not have an x-intercept at (5, 0).

This option is a key feature of h(x).

Option 3 states that the y-intercept of h(x) is (0, 25).

To find the y-intercept, we set x = 0 and evaluate h(x). Plugging in x = 0, we get (0 - 5)² - log₁ 0 + 6.

However, the logarithm of 0 is undefined, so the y-intercept of h(x) is not (0, 25).

This option is not a key feature of h(x).

Option 4 states that the end behavior of h(x) is as x approaches infinity, h(x) approaches infinity.

This is true because as x becomes larger, the square term (x - 5)² dominates, causing h(x) to approach positive infinity.

This option is a key feature of h(x).

In conclusion, the key feature of h(x) that is NOT mentioned in the given options is that the domain of h(x) is (0, ∞).

Therefore, the correct answer is:

O The domain of h(x) is (0, ∞).

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The required positive numbers are 14.43, 14.43.

According to the statement

we have given that The product of two positive numbers is 208 and the sum is a minimum.

And we have to find these numbers.

So, For this purpose,

Let two positive numbers xy = 208

According to question xy = 208

And then

y = 208/x

and

sum of two positive numbers z=x+y

s= x+ 208/x

then

differentiate with respect to x

ds /dx = d/ dx(x+ 208/x)  -(1)

ds /dx = 1 - 208/ x^2

here ds /dx = 0. so,

1 - 208/ x^2 = 0

x^2 - 208= 0

x = 14.43.

And

differentiate the equation (1) again

d^2s /dx^2 = 0 + 416/x^2)  

then

∴ at point x= 14.43,

d^2s /dx^2 = 416/208.22

d^2s /dx^2 = 1.99

which is greater than zero.

∴ value of s minimum at point x = 14.43

so, y = 208/x

y = 208 /14.43

y = 14.43.

So, The required positive numbers are 14.43, 14.43.

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Father = 45 years

Joshua = 11 years

See the image I have shared.

Round off at the end