Gloria took our a 30-year mortgage for $70,000 at 7.5%. How much will she pay over 30 years?

The second stem-and-leaf combination of 8-5 indicates that the cost of chocolate bars is 85 cents. Similarly, the third stem-and-leaf combination of 8-5 indicates that the cost of chocolate bars is 85 cents. The fourth stem-and-leaf combination of 8-7 indicates that the cost of chocolate bars is 87 cents. The last stem-and-leaf combination of 8-9 indicates that the cost of chocolate bars is 89 cents.

Chocolate bars are on sale for the prices shown in the given stem-and-leaf plot. Cost of a Chocolate Bar (in cents) at Several Different Stores.

Stem Leaf

7 7

8 5 5 7 8 9

9 3 3 3

10 0 5

There are four stores at which the cost of chocolate bars is displayed. Their costs are indicated in cents, and they are categorized in the given stem-and-leaf plot. In a stem-and-leaf plot, the digits in the stem section correspond to the tens place of the data.

The digits in the leaf section correspond to the units place of the data.

To interpret the data, look for patterns in the leaves associated with each stem.

For example, the first stem-and-leaf combination of 7-7 indicates that the cost of chocolate bars is 77 cents.

The second stem-and-leaf combination of 8-5 indicates that the cost of chocolate bars is 85 cents.

Similarly, the third stem-and-leaf combination of 8-5 indicates that the cost of chocolate bars is 85 cents.

The fourth stem-and-leaf combination of 8-7 indicates that the cost of chocolate bars is 87 cents.

The last stem-and-leaf combination of 8-9 indicates that the cost of chocolate bars is 89 cents.

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The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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ToTo evaluate cos 120° using the reference angle theorem, we first draw the angle and then find the alpha angle which is  α = 60°.

To evaluate cos 120° using the reference angle theorem, we follow the four steps. First, we draw the angle of 120° in the coordinate plane. Next, we find the reference angle, which is the acute angle formed between the terminal side of the angle and the x-axis.

The reference angle is denoted as α. In this case, the reference angle for 120° is 60°, as it is the acute angle formed when we subtract 120° from a full rotation (360°). By using the reference angle theorem, we can determine that cos 120° is equal to cos 60°. Therefore, the alpha angle in this case would be α = 60°.

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We will see that the linear equations are:

Parallel line: x = -9

Perpendicular line: y = 3

Here we have the vertical line:

x = -2

A parallel line to this one will also be vertical, of the form:

x = a

And a perpendicular line to this one will be horizontal, of the form:

y = b

We want the parallel line to pass through (-9, 3)

So our line x = a needs to pass through that point, then:

x = -9

Is the parallel line.

And if the perpendicular line y = b needs to pass through that point, then:

y = 3

Is the perpendicular line.

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Answer:

2916 and 6724 respectively

Step-by-step explanation:

the steps on how to evaluate 54^2 and 82^2 using the formula for squaring a binomial are:

1. Write the binomial as a sum of two terms.

\(54^2 = (50 + 4)^2\)

\(82^2 = (80 + 2)^2\)

2. Square each term in the sum.

\(54^2 = (50)^2 + 2(50)(4) + (4)^2\\82^2 = (80)^2 + 2(80)(2) + (2)^2\)

3. Add the products of the terms.

\(54^2 = 2500 + 400 + 16 = 2916\\82^2 = 6400 + 320 + 4 = 6724\)

Therefore, the values  \(54^2 \:and \:82^2\)are 2916 and 6724, respectively.

Answer:

54² = 2916

82² = 6724

Step-by-step explanation:

A binomial refers to a polynomial expression consisting of two terms connected by an operator such as addition or subtraction. It is often represented in the form (a + b), where "a" and "b" are variables or constants.

The formula for squaring a binomial is:

\(\boxed{(a + b)^2 = a^2 + 2ab + b^2}\)

To evaluate 54² we can rewrite 54 as (50 + 4).

Therefore, a = 50 and b = 4.

Applying the formula:

\(\begin{aligned}(50+4)^2&=50^2+2(50)(4)+4^2\\&=2500+100(4)+16\\&=2500+400+16\\&=2900+16\\&=2916\end{aligned}\)

Therefore, 54² is equal to 2916.

To evaluate 82² we can rewrite 82 as (80 + 2).

Therefore, a = 80 and b = 2.

Applying the formula:

\(\begin{aligned}(80+2)^2&=80^2+2(80)(2)+2^2\\&=6400+160(2)+4\\&=6400+320+4\\&=6720+4\\&=6724\end{aligned}\)

Therefore, 82² is equal to 6724.

Answer:

3 minutes per table

Step-by-step explanation:

15 minutes = 5 tables

to get how much it will be per table, divided both sides by 5

since 5 / x = 1 and x would be 5

15 / 5 minutes = 5 / 5 tables

3 minutes = 1 table

The area of the shaded face of the cylinder is 1,520 mm².

We can see that the shaded area of the cylinder is circular in shape.

This means that we can find the area of the shaded area by finding the area of the circle.

The radius of the circle is given as 22 mm.

The formula for finding the area of a circle is given as:

Area = πr²

= 3.14 × 22 × 22

= 1,519.76

≈ 1520 mm²

Therefore, we have found the area of the shaded face of the cylinder to be 1,520 mm².

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Disclaimer: The question was incomplete, the complete question is attached below.

Answer:

8 bags but 8.4 to be exact but its still 8 bags

Step-by-step explanation:

5 1/4 div 5/8= 21/4 div 5/8=21/4 times 8/5= 42/5=8.4 bags

The solution to the equation 2 csc x = 3 csc θ − csc θ sin θ in the range 0 ≤ θ < 2π is:

θ = 7π/6

We can start by manipulating the given equation to express cscθ in terms of cscx:

2 csc x = 3 csc θ − csc θ sin θ

2/cscθ = 3 - sinθ

cscθ/2 = 1/(3 - sinθ)

cscθ = 2/(3 - sinθ)

Now we can use the identity sin²θ + cos²θ = 1 and substitute for cscθ in terms of sinθ:

1/cosθ = 2/(3 - sinθ)

cosθ = (3 - sinθ)/2

Next, we can use the identity sin²θ + cos²θ = 1 to solve for sinθ:

sin²θ + cos²θ = 1

sin²θ + [(3 - sinθ)/2]² = 1

Multiplying both sides by 4, we get:

4sin²θ + (3 - sinθ)² = 4

Expanding and simplifying, we get:

8sin²θ - 6sinθ - 8 = 0

Dividing both sides by 2, we get:

4sin²θ - 3sinθ - 4 = 0

Using the quadratic formula with a = 4, b = -3, and c = -4, we get:

sinθ = [3 ± √(3² - 4(4)(-4))]/(2(4))

sinθ = [3 ± √49]/8

sinθ = (3 ± 7)/8

Since 0 ≤ θ < 2π, we only need to consider the solution sinθ = (3 - 7)/8

= -1/2 corresponds to an angle of 7π/6 in the third quadrant.

To find cosθ, we can use the identity sin²θ + cos²θ = 1:

cosθ = ±√(1 - sin²θ)

Since we are in the third quadrant, we want the value of cosθ to be negative, so we take the negative square root:

cosθ = -√(1 - (-1/2)²)

cosθ = -√(3/4)

cosθ = -√3/2

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Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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Answer:

x = 16

Step-by-step explanation:

71 - 15 = 56

56 ÷ 14 = 4

\(\sqrt{16}\) = 4

Check work:

\(\sqrt{16}\) = 4

14 x 4 = 56

56 + 15 = 71

Answer:

254.34

Step-by-step explanation:

3.14 x 9^2

or

3.14(9 x 9)

hope this helps

have a good day

Answer:

53721.23

Step-by-step explanation:

V=πr^2h

v = 3.14(30)^2(19)

v = 53721.23

Answer:

a cylinder can hold a liquid of  53,721 cm³

Step-by-step explanation:

volume  of a cylinder = π r² h

vol = π * (60/2)² * 19

vol = 53,721 cm³

Answer:

3125 bacteria.

Step-by-step explanation:

We can write an exponential function to represent the situation.

We know that the current population is 100,000.

The population doubles each day.

The standard exponential function is given by:

\(P(t)=a(r)^t\)

Since our current population is 100,000, a = 100000.

Since our rate is doubling, r = 2.

So:

\(P(t)=100000(2)^t\)

We want to find the population five days ago.

So, we can say that t = -5. The negative represent the number of days that has passed.

Therefore:

\(\displaystyle P(-5)=100000(2)^{-5} = 100000 \Big( \frac{1}{32}\Big) = 3125 \text{ bacteria}\)

However, we dealing within this context, we really can't have negative days. Although it works in this case, it can cause some confusion. So, let's write a function based on the original population.

We know that the bacterial population had been doubling for 5 days. Let A represent the initial population. So, our function is:

\(P(t)=A(2)^t\)

After 5 days, we reach the 100,000 population. So, when t = 5, P(t) = 100000:

\(100000=A(2)^5\)

And solving for A, we acquire:

\(\displaystyle A=\frac{100000}{2^5}=3125\)

So, our function in terms of the original day is:

\(P (t) = 3125 (2)^t\)

So, it becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.

Answer:

We can express the question in a exponential function

The current population is 100,000.

The population doubles each day.

The exponential function is given by: P(t)=a(r)^t

The current population is 100,000, a = 100000.

The rate is doubling, r = 2.

P(t)=100000(2)^t

As we know that the bacterial population had been doubling for 5 days. Let A represent the initial population. So, the function is:

P(t)=A(2)^t

After 5 days, the population reaches 100,000. So, when t = 5, P(t) = 100000:

100000=A(2)⁵

Now solving for A, we get

A=(100000)/(2⁵)=3125

So, the function in terms of the original day is:

P (t) = 3125 (2)^t

Hence, the initial population is 3125 bacteria.

1. Indian

2.South

3.Africa

4.stormyy

Answer:

y = 5x+18

Step-by-step explanation:

y - 3 = 5(x + 3)

Distribute

y -3 = 5x+15

Add 3 to each side

y - 3+3 = 5x + 15 +3

y = 5x+18

This is slope intercept form (y = mx+b) where m is the slope and b is the y intercept

Thus, the expression [1 - 4sin²a] written in the product of its values is:

(1 + 2sina)(1 - 2sina).

We can solve mathematical equations thanks to algebra's inherent characteristics. Take note that both addition and multiplication adhere to these characteristics.

This Order of Operations is a set of rules that enables mathematicians to solve issues uniformly. In this order:

using the algebraic formula:

(a² - b²) = (a + b)(a - b)

Given expression:

= 1 - 4sin²a

This can be written as:

= 1² - (2sina)²

Now, using identity:

= (1 + 2sina)(1 - 2sina)

Thus, the expression [1 - 4sin²a] written in the product of its values is:

(1 + 2sina)(1 - 2sina).

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Complete question-

Express the given as the product of both values.

1 - 4sin²a

The sum of the squares of the lengths of the medians of a triangle is equal to three-fourths the sum of the squares of the lengths of the sides of the triangle, based on the expression: 3(a^2 + b^2 + c^2)^2 - 6a^2b^2 - 6a^2c^2 - 6b^2c^2

To prove the statement using Stewart's Formula, consider a triangle ABC with sides of lengths a, b, and c. Let D, E, and F be the midpoints of sides BC, AC, and AB, respectively. The medians AD, BE, and CF intersect at a point called the centroid.

Using Stewart's Formula, we have:

m_a^2 * b * c + m_b^2 * a * c + m_c^2 * a * b = 4(a^2 + b^2 + c^2) * d^2 + 4 * d^2 * m^2

Since the centroid divides the medians in a 2:1 ratio, we have d = (2/3) * m, where m is the length of the median. Substituting this value into the equation, we get:

m_a^2 * b * c + m_b^2 * a * c + m_c^2 * a * b = 4(a^2 + b^2 + c^2) * (4/9) * m^2 + 4 * (4/9) * m^2 * m^2

m_a^2 * b * c + m_b^2 * a * c + m_c^2 * a * b = (16/9) * (a^2 + b^2 + c^2) * m^2 + (16/9) * m^4

m_a^2 = (2b^2 + 2c^2 - a^2) / 4

m_b^2 = (2a^2 + 2c^2 - b^2) / 4

m_c^2 = (2a^2 + 2b^2 - c^2) / 4

[(2b^2 + 2c^2 - a^2) / 4] * b * c + [(2a^2 + 2c^2 - b^2) / 4] * a * c + [(2a^2 + 2b^2 - c^2) / 4] * a * b = (16/9) * (a^2 + b^2 + c^2) * m^2 + (16/9) * m^4

a^4 + b^4 + c^4 + 2a^2b^2 + 2a^2c^2 + 2b^2c^2 - a^2b^2 - a^2c^2 - b^2c^2 = (16/9) * (a^2 + b^2 + c^2) * m^2 + (16/9) * m^4

3(a^4 + b^4 + c^4 + 2a^2b^2 + 2a^2c^2 + 2b^2c^2 - a^2b^2 - a^2c^2 - b^2c^2)

3(a^4 + b^4 + c^4 + a^2b^2 + a^2c^2 + b^2c^2)

Now, recall the identity (a^2 + b^2 + c^2)^2 = a^4 + b^4 + c^4 + 2a^2b^2 + 2a^2c^2 + 2b^2c^2.

3[(a^2 + b^2 + c^2)^2 - 2a^2b^2 - 2a^2c^2 - 2b^2c^2]

Simplifying further, we obtain:

3(a^2 + b^2 + c^2)^2 - 6a^2b^2 - 6a^2c^2 - 6b^2c^2

Therefore, the sum of the squares of the lengths of the medians of a triangle is equal to three-fourths the sum of the squares of the lengths of the sides of the triangle, based on the expression:

3(a^2 + b^2 + c^2)^2 - 6a^2b^2 - 6a^2c^2 - 6b^2c^2

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Answer:

x>8

Step-by-step explanation:

Hope that helps you!!

Answer:

u = 32°

Step-by-step explanation:

Since p║q then angle u and angle y are corresponding angles meaning the equal each other.

Answer:

∠u = 32°

Step-by-step explanation:

∠u = ∠y = 32°  because they are corresponding congruent mangles

Answer: 2nd one

Step-by-step explanation:

Answer:

Step-by-step explanation:

To apply the intermediate value theorem, we need to show that the function f(x) = x^2 + 3x + 2 is continuous on the closed interval [0, 5].

Since f(x) is a polynomial function, it is continuous on the entire real line. Therefore, it is also continuous on the closed interval [0, 5].

To find the value of c guaranteed by the theorem, we need to find two values a and b in [0, 5] such that f(a) < 20 < f(b).

We have:

f(0) = 2

f(5) = 60

Since f(x) is an increasing function on [0, 5], we can conclude that for any value of x between 0 and 5, f(x) will lie between f(0) and f(5).

Therefore, there exists a value c in [0, 5] such that f(c) = 20.

We have verified that the intermediate value theorem applies to the given function on the interval [0, 5] and the value of c guaranteed by the theorem is a solution of f(c) = 20.

Answer:

Step-by-step explanation:

2 quarts = 8 cups.

$0.3 per cup

(0.3 x 8 = $2.40)

On solving the provided question we can say that As a result, because the Pythagorean theorem is not met, the presented numbers do not represent the sides of a right triangle.

The Pythagorean Theorem is the fundamental Euclidean geometry relationship between the three sides of a right triangle. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. According to the Pythagorean Theorem, the square that spans the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span its sides. It is sometimes expressed as a2 + b2 = c2 in general algebraic notation.

The supplied figures reflect the lengths of the three sides of a right triangle, with the hypotenuse (the side opposite the right angle) being 5.47722557505, and the other two sides being 2.2360679775 and 5.

The sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse, according to the Pythagorean theorem. In this situation, we can write:

2.2360679775² + 5² = 5.47722557505²

When we simplify and solve for one of the variables, we get:

5² = 5.47722557505² - 2.2360679775²

25 = 24.9999999999971

As a result, because the Pythagorean theorem is not met, the presented numbers do not represent the sides of a right triangle. We could round the data to approach the sides of a right triangle, but it would not get accurate solutions.

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To calculate the surface aarea, we will use the formula;

T.S.A = 1/2 (pl) + B

where;

p= perimeter of the base

l= slant height

B= area of the base

From the diagram

l= 10 yard

P= 4(16) = 64 yard

B= 16 x 16= 256 yards

Substitute the value into the formula;

T.S.A = 1/2 (64)(10) + 256

=320 + 256

=576 inches²

Answer:

75%

Step-by-step explanation:

Answer:

First there are 4 terms. I think/believe that there are 3 factors in the first term. And the answer to the last question is 16 or term 3.

Step-by-step explanation:

I hope this helps, plz mark me as brainlyest anyways I hope you get a good score on your test!!

Answer:

a. There are 4 terms in the expression

b. There are 3 factors in the first term.

c. The constant is 16.

8ab + 3b + 16 - 4a

A term is any signed number, a variable, or a constant  multiplied by a

variable or variables.

Therefore, the terms are 8ab,  3b,  16, and -4a. The terms are 4 in numbers.

The first term is 8ab .The first term has the factors 8 , a and b. This means the first term have 3 factors.

The term that is a constant is 16

Step-by-step explanation:

The Maclaurin polynomials of orders n=0, 1, 2, 3, and 4 for the function 5/(1+x) are P0(x) = 5, P1(x) = 5 - 5x, P2(x) = 5 - 5x + 5x^2, P3(x) = 5 - 5x + 5x^2 - 5x^3, and P4(x) = 5 - 5x + 5x^2 - 5x^3 + 5x^4, respectively.

The Maclaurin polynomials are a way to approximate a function using a polynomial expansion centered at x = 0. The Maclaurin polynomial of order n for a function f(x) is given by Pn(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ... + (f^n(0)/n!)x^n, where f'(0), f''(0), f'''(0), ..., f^n(0) are the derivatives of f(x) evaluated at x = 0.

In this case, the given function is f(x) = 5/(1+x). To find the Maclaurin polynomials of orders n=0, 1, 2, 3, and 4, we evaluate the function and its derivatives at x = 0 and substitute them into the general formula for the Maclaurin polynomials.

For n=0, P0(x) = 5, as f(0) = 5.

For n=1, P1(x) = 5 - 5x, as f(0) = 5 and f'(0) = -5.

For n=2, P2(x) = 5 - 5x + 5x^2, as f(0) = 5, f'(0) = -5, and f''(0) = 10.

For n=3, P3(x) = 5 - 5x + 5x^2 - 5x^3, as f(0) = 5, f'(0) = -5, f''(0) = 10, and f'''(0) = -30.

For n=4, P4(x) = 5 - 5x + 5x^2 - 5x^3 + 5x^4, as f(0) = 5, f'(0) = -5, f''(0) = 10, f'''(0) = -30, and f^4(0) = 120.

These Maclaurin polynomials provide polynomial approximations of the given function 5/(1+x) for different orders. The higher the order (n), the more terms are included in the polynomial expansion, resulting in a more accurate approximation of the original function around x = 0.

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