What is the exact volume of this cone?

196π in³

392/3π in³

196/3π in³

392π in³

The equations of line that are perpendicular to each other are:

A: y = (1/6)x + 6; y = -6x + 4

The general formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

Now, for two equations to be perpendicular, it means that their slope must be negative reciprocals of each other. Thus:

Looking at the equations, we can say the only ones that have slopes that are negative reciprocals of each other is option A.

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Measure of angle  ∠R = 55° , Measure of ∠S = x+10 =55+10 = 65°, Measure of ∠T = x+5= 55 + 5 =60°

Recall that a triangle is a three-sided polygon that consists of three edges and three vertices.

Since we have given that RST is a triangle,

Angle S is 10° greater than angle R and

angle T us 5° less than Angle S

Let the measure of ∠R be 'x'.

Let the measure of ∠S be 'x+10'

Let the measure of ∠T be 'x+10-5'='x+5'

As we know that "Sum of all angles in triangle is 180°.

So, it becomes,

∠R + ∠S + ∠T =180°

x + x + 10 + x + 5 = 180

3x +15 = 180

3x = 180-15

3x = 165

x = 165/3

x =55

So, Measure of ∠R = 55°

Measure of ∠S = x+10 =55+10 = 65°

Measure of ∠T = x+5= 55 + 5 =60°

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Answer:

y = 1/28(x²)

Step-by-step explanation:

Not totally sure about this, but here's what I think is the answer:

focus (0,7)

directrix y = -7

Always a good idea to plot the point (0,7) and the line y = -7 so you can visualize what the parabola looks like.

From the graph, you can see that p = 7  (halfway between the focus and the directrix).

The vertex of this parabola is (0,0), which are your (h, k) values.  You can see that from the graph.  The parabola opens UP.

4p(y-k) = (x-h)²  →  4p(y-0) = (x-0)²

4py = x²

y = x²/4p = x²/4(7) = x²/28

y = 1/28(x²)

sorry if this isn't the right answer, but I tried  (I'm not a paid expert, just a fellow student trying to learn math)!

Answer:

1.2974634e+14

Step-by-step explanation:

ye

After five years of investing $100 at a 3% annual interest rate compounded twice, the total amount is $116.18.

What is principle?

The whole sum borrowed (or invested), exclusive of interest and dividends.

What is compound interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

The formula for the amount A accumulated after investing a principle P for t years at an annual interest rate r compounded k times per year is:

A = P * [tex](1 + r/k)^{(k*t)}[/tex]

Substituting the given values into this formula, we have:

A = $100 *[tex](1 + 0.03/2)^(2*5)[/tex]

A = $100 * [tex](1 + 0.015)^{10}[/tex]

A = $100 * 1.161834...

A = $116.18 (rounded to the nearest cent)

Therefore, the amount accumulated after investing a principle of $100 for 5 years at an interest rate of 3% compounded twice a year is $116.18.

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Answer:

The answer is 2√10

Step-by-step explanation:

Hyp²=opp²+adj²

let hyp be x

x²=6²+2²

x²=36+4

x²=40

square root both sides

√x²=√40

x=2√10

Let's denote the speed of the boat in still water as "b", and let's denote the distance between the two points as "d" (in this case, d = 24 miles).

When the boat is traveling upstream against the current, its effective speed is b - 2 mph (since the current is working against the boat). When the boat is traveling downstream with the current, its effective speed is b + 2 mph (since the current is helping the boat).

We know that the boat travels a total distance of 24 miles upstream and then 24 miles downstream, for a total distance of 48 miles. We also know that the total time it takes for the boat to make this round trip is 5 hours. So we can set up the following equation:

24/(b-2) + 24/(b+2) = 5

Multiplying both sides by (b-2)(b+2), we get:

24(b+2) + 24(b-2) = 5(b-2)(b+2)

Simplifying and rearranging, we get:

10b^2 - 96b - 208 = 0

We can solve this quadratic equation using the quadratic formula:

b = (-(-96) ± sqrt((-96)^2 - 4(10)(-208))) / (2(10))

b = (96 ± sqrt(96^2 + 8320)) / 20

b = (96 ± sqrt(9024)) / 20

b = (96 ± 96) / 20

So the possible values of b are b = 9.6 or b = -0.8. We can discard the negative value since it doesn't make sense as a speed, so we have:

b = 9.6 mph

Therefore, the speed of the boat in still water is 9.6 miles per hour

Therefore, it will take 173 months to pay off the loan, or approximately 14 years and 5 months.

A percentage is a way of expressing a number as a fraction of 100. The symbol for a percentage is "%". For example, 50% is the same as 50/100 or 0.5 as a decimal. Percentages are often used to express a portion or share of a whole. For instance, if you scored 90% on a test, it means you got 90 out of 100 possible points. In finance, percentages are commonly used to express interest rates, returns on investments, or changes in stock prices.

First, we need to convert the monthly interest rate from a percentage to a decimal by dividing by 100.

0.25% / 100 = 0.0025

Now we can plug in the values into the formula:

N= (-log⁡ (1-0.0025*70000/250))/ (log⁡ (1+0.0025))

Simplifying the equation in the parentheses:

N= (-log⁡ (1-175))/ (log⁡ (1.0025))

N= (-log⁡ (0.9964))/ (0.002499)

N= 172.9

Rounding up to the nearest whole number since we can't make partial payments:

N= 173

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We can see that the choice falls within the range of (A) less than 1 hour. Therefore, the answer is (A), Kristen spends less than 1 hour .

Finding the value of a single unit using the unitary technique allows us to determine the value of the necessary number of units based on this value.

To find out approximately how much time Kristen spent gardening each day, we can divide the total time she spent gardening by the number of days she gardened.

Total time = 4 hours

Number of days = 7

So, Kristen spent approximately 4/7 = 0.57 hours or about 34 minutes each day gardening.

Since the answer choices are in ranges, we can see that this falls within the range of (A) less than 1 hour. Therefore, the answer is (A).

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The minimum value of Jeri Dammers' total deductions is $200.68.

Based on the given information, we can calculate the total deductions for Jeri Dammers as follows:

Social Security: Jeri pays 6% of the first S$90,000 of her gross pay towards Social Security. As her gross pay is only $735.00, her Social Security deduction will be:

Medicare: Jeri pays 1.45% of all her income towards Medicare. As her gross pay is $735.00, her Medicare deduction will be:

Federal Income Tax: To calculate the federal income tax, we need to refer to the tax tables provided by the IRS. As the gross pay is only $735.00, Jeri's federal income tax deduction will be very minimal or possibly none.

State Tax: Jeri pays 2% of her gross pay towards state tax. As her gross pay is $735.00, her state tax deduction will be:

Local Tax: Jeri pays 1.5% of her gross pay towards local tax. As her gross pay is $735.00, her local tax deduction will be:

Medical: Jeri has a deduction of $32.00 towards medical expenses.

Union Dues and Others: No information is given about Jeri's union dues or other deductions.

Therefore, the total deductions for Jeri Dammers will be:

We cannot calculate the exact value of Total Deductions without information about Union Dues and Others.

However, the minimum value of Total Deductions would be:

= $44.10 + $10.65 + $88.20 + $14.70 + $11.03 + $32.00

= $200.68

Therefore, the minimum value of Jeri Dammers' total deductions is $200.68.

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See full text below

Find the total deduction The person pays Social Security 6 percent of the first S90,000. Medicare is 1.45 percent of all income Use the tax tables for federal tax The state tax is 2 percent of gross pay and the local tax is 1.5 percent of gross pay. (Remember to add the Medical; Union Dues, and Others for total deduction: FIT Federal Income Tax, FICA Social Security) .4. Jeri Dammers is married and claims 3 allowances.

Dept

Employee

Check Number -3205

Gross Pay -$735.00

Net Pay

44B Jeri Dammers

Tax Deductions

Other Deductions

FIT

FICA

Medicare

State

Local

Medical -32.00

Union

Dues

Others

Answer:

To find the height of the building, we can use the following formula:

height = y(d-x)/x

Substituting the given values, we get:

height = 6(6-3)/3

height = 6(3)/3

height = 6 meters

Therefore, the height of the building is 6 meters.

Answer:

It is irrational, because the product of an irrational number and a rational number is irrational.

Step-by-step explanation:

sqrt 27 is  irrational =5.19615.......

3 is rational

  subtracting 3 from the irrational number just creates a smalller irrational number    ....then multiplying by 9 just creates a larger irrational number

For the given data the general trend is neither continuously rising nor falling. thus, the correct answer is option a: The median age of a man at the time of his first marriage is, on the average, constant.

We can compute the rates of change by deducting the current year's median age from the prior year's median age. A result of zero denotes no change, a result of zero denotes no decline, and a result of one denotes an increase.

[tex]\text{Rate of Change} = Median\; Age (current \;year) - Median \;Age (previous \;year)[/tex]

[tex]1910-1920: 24.6 - 25.1 = -0.5\\1920-1930: 24.3 - 24.6 = -0.3\\1930-1940: 24.3 - 24.3 = 0\\1940-1950: 22.8 - 24.3 = -1.5\\1950-1960: 22.8 - 22.8 = 0\\1960-1970: 23.2 - 22.8 = 0.4\\1970-1980: 24.7 - 23.2 = 1.5\\1980-1990: 26.1 - 24.7 = 1.4\\1990-2000: 26.8 - 26.1 = 0.7\\[/tex]

The rates of change, as we can see, alternate between positive and negative values, but the general trend is neither continuously rising nor falling. Several times, the rate of change is zero, showing that, generally speaking, the median age of a man at the time of his first marriage is holding steady through time.

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Answer:

x = 8

Step-by-step explanation:

1/4 (8x + 12) = 19

Distribution property

1/4 x 8= 2

1/4 x 12= 3

2x + 3 = 19

19 - 3= 16

2x= 16

16/2 = 8

X= 8

Therefore, the answer is (A) 7x-9 when it is given that function F(x) = 4x - 8 and g(x) = -3x + 1.

In mathematics, a function is a relationship between two sets of values, where each input (or domain element) is associated with a unique output (or range element). In other words, a function is a rule or a process that takes an input (or inputs) and produces a corresponding output. Functions can be expressed using various mathematical notations, such as algebraic formulas, graphs, tables, or even verbal descriptions. They are widely used in many fields of mathematics, science, engineering, economics, and computer science, to model and solve problems that involve relationships between variables or quantities.

Here,

To find (f - g)(x), we need to subtract g(x) from f(x), so we get:

(f - g)(x) = f(x) - g(x)

Substituting the given functions, we get:

(f - g)(x) = (4x - 8) - (-3x + 1)

Simplifying the expression by distributing the negative sign, we get:

(f - g)(x) = 4x - 8 + 3x - 1

Combining like terms, we get:

(f - g)(x) = 7x - 9

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With the given compound interest, Total amount paid is $5,593.20 and you paid $1,379.40 more for the loan due to your bad credit score.

What is Compound interest?

Compound interest is the interest calculated on the initial principal as well as on the accumulated interest from previous periods. In other words, it is the interest earned not only on the principal amount but also on the interest previously earned.

Now,

To find the monthly payment, we can use the loan payment formula:

P = (Pv*r)/(1-(1+r)⁻ⁿ)

where P is the monthly payment, Pv is the present value of the loan, r is the monthly interest rate, and n is the total number of payments.

For your loan with a 15% APR, the monthly interest rate is 15%/12 = 1.25%.

For a 5-year loan with monthly payments, the total number of payments is 5 x 12 = 60.

So, plugging in the values, we get:

P = (5000*0.0125)/(1-(1+0.0125)⁻⁶⁰)) = $116.21

Your total amount paid over 5 years is:

Total amount paid = P x n = $116.21 x 60 = $6,972.60

For your friend's loan with a 5% APR, the monthly interest rate is 5%/12 = 0.42%.

Using the same formula as above, we get:

P = (5000*0.0042)/(1-(1+0.0042)⁻⁶⁰) = $93.22

Your friend's total amount paid over 5 years is:

Total amount paid = P x n = $93.22 x 60 = $5,593.20

The difference in the total amount paid is:

$6,972.60 - $5,593.20 = $1,379.40

Therefore, you paid $1,379.40 more for the loan due to your bad credit score.

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There are 43,680 different ways to choose a President, Vice President, Treasurer, and Secretary from 16 students.

An arrangement of items in a particular order is referred to as a permutation. Permutations are frequently used in mathematics to count the number of possible configurations of a set of items. P(n,r) stands for the quantity of permutations of n items taken r at a time and is equal to n! / (n - r)!, where n! (also known as "n factorial") is the sum of all positive numbers from 1 to n.

Given that, the number of students = 16 and the positions are 4.

Thus, after every selection we have:

16 * 15 * 14 * 13 = 43,680

Hence, there are 43,680 different ways to choose a President, Vice President, Treasurer, and Secretary from 16 students.

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1. The ratio for sin x in the trigonometry will be 12/13.

The ratio for cos x in the trigonometry will be 5/13.

The ratio for tan x in the trigonometry will be 12/5

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used extensively in various fields, including physics, engineering, and astronomy.

The three primary functions in trigonometry are sine, cosine, and tangent. These functions relate the ratios of the sides of a right triangle to its angles.

The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Trigonometry also involves inverse functions, such as the arcsine, arccosine, and arctangent. These functions are used to find the angle whose sine, cosine, or tangent is a given value.

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Step-by-step explanation:

Vertex at  -4,3 would result in vertex form of parabola  

g(x) = (x+4)^2 + 3

a. There are twelve unique pentominos possible in all.

b. In total, only 6 pentominos have the refection symmetry.

What is a pentomino?

A pentomino is an order 5 polyomino, or a plane polygon formed of 5 identical squares joined edge to edge. This is just linked with a certain arrangement of squares.

a. There are twelve unique pentominos possible in all which on reflection and rotation can create multiple more pentominos.

b. In total, 6 pentominos have refection symmetry which means that now the total pentominos are 18 of which 6 have reflection symmetry.

Hence, the required solution has been obtained.

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Since the calculated F-value of 0.555 is less than the critical value of 4.025, we fail to reject the null hypothesis.

A null hypothesis is a statement that establishes the equality of two expressions and frequently includes variables, constants, and mathematical operations.

The equal sign (=) is used to denote the space between the two sides, which are referred to as the left-hand side (LHS) and the right-hand side (RHS).

To test the given hypothesis, we will use the F-test for two variances.

The null and alternative hypotheses are:

H0: σ1² = σ2² (no difference in population variances)

Ha: σ1² > σ2² (population variance of first group is greater than that of second group)

The test statistic is calculated as:

F = s1² / s2²

Where s1² and s2² are the sample variances of the two groups.

The degrees of freedom for the F-distribution are df1 = n1 - 1 and df2 = n2 - 1.

Using the given sample information, we have:

n1 = 10, n2 = 11

s1² = 562, s2² = 1013

Therefore, the test statistic is:

F = s1² / s2² = 562 / 1013 = 0.555

The degrees of freedom are df1 = 9 and df2 = 10.

Using a significance level of α = 0.01 and the F-distribution tables or a calculator, the critical value for the right-tailed test with df1 = 9 and df2 = 10 is 4.025.

Since the calculated F-value of 0.555 is less than the critical value of 4.025, we fail to reject the null hypothesis. There is not enough evidence to conclude that the population variance of the first group is greater than that of the second group at a significance level of α = 0.01.

We can conclude that there is not enough evidence to support the claim that σ1² > σ2².

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Examining the curve the information obtained are

vertex (3, 13)

axis of symmetry: x = 13

y intercept: (0, 5)

maximum

Domain (-∞, ∞)

Range (-∞, 12]

A parabolic curve, also known as a parabola, is a symmetrical U-shaped curve. It is defined by a mathematical equation of the form

y = ax^2 + bx + c,

where a, b, and c are constants, and x and y are the coordinates of points on the curve.

The graph of a parabolic curve is smooth and continuous, with no sharp corners or discontinuities.

The vertex is at the peak of the curve and the coordinates is (3, 13) where the axis of symmetry is where the curve is divided into two equal parts. This is represented by the equation x = 3

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So according to the given figure ∠mah is right angle(90°), The value of x is 17, ∠mat is 38° and ∠tah is equal to 52°.

(A) ∠mah is right angle(90°) [GIVEN IN THE FIGURE]

(B) (2x+4)+(3x+1) = 90

5x+5 = 90

x= 17

(C) 2x+4 = 2×17 + 4 = 38°

(D) 3X + 1 = 3 × 17 + 1 = 52°

A graph is a visual representation or diagram that displays facts or values in an organised manner in mathematics. The points on a graph are typically used to depict the relationships between two or more things.

A graph in discrete mathematics is made up of vertices, which are groups of points, and edges, which are the connections between those vertices. There are numerous different types of graphs besides linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs.

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Answer:

We can use the formula for simple interest to solve this problem:

I = Prt

where I is the amount of interest earned, P is the principal (the initial amount invested), r is the annual interest rate (as a decimal), and t is the time (in years).

In this problem, we know that P = $6,000, r = 0.08, and I = $1,680. We want to find t, the time required to earn $1,680 in interest.

Substituting these values into the formula, we get:

$1,680 = $6,000 x 0.08 x t

Simplifying and solving for t, we get:

t = $1,680 / ($6,000 x 0.08) = 3.5 years

Therefore, it will take 3.5 years for $6,000 invested at 8% interest to earn $1,680 in interest.

Answer:

Step-by-step explanation:

The distance formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

x1 is a,

x2 is 0,

y1 is 0 and

y2 is b. Fitting those into the formula where they belong:

[tex]d=\sqrt{(0-a)^2+(b-0)^2}[/tex] and

[tex]d=\sqrt{(-a)^2+(b)^2}[/tex]

Since a negative squared is a positive, then

[tex]d=\sqrt{a^2+b^2}[/tex]

which is the second choice down.

Using equations, we can find that the number of pop tarts that Taylor has with him, p = 13.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others.

Let the cost of one granola bar = x.

Let the cost of one pop tart = y.

Now, assume Taylor had money, m.

So, as per the question:

90x = m

⇒ x = m/90

78y = m

⇒ y = m/78

75x + py = m

Substituting the values of x and y:

⇒ 75 × m/90 + p × m/78 = m

⇒ 75m/90 + pm/78 = m

⇒ (5850m + 90pm) / 7020 = m

⇒ 5850m + 90pm = 7020m

⇒ 90pm = 7020m - 5850m

⇒ 90pm = 1170m

⇒ p = 1170m/90m

⇒ p = 13.

Therefore, the number of pop tarts, p = 13.

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Answer:

[tex]1. \: \: - 2 {a}^{2} [/tex]

[tex]2. \: \: 4ab[/tex]

[tex]3. \: \: - 2[/tex]

Step-by-step explanation:

-2a(a+b-5) +3(-5a+2b) +b(6a-b-8)

[tex] - 2 {a}^{2} - 2ab + 10a - 15a + 6b + 6ab + {b}^{2} - 8b[/tex]

collecting like terms

[tex] -2 {a }^{2} + {b}^{2} - 2ab + 6ab + 10a - 15a + 6b - 8b[/tex]

[tex] = - 2 {a}^{2} + {b }^{2} + 4ab - 5a - 2b[/tex]

Answer:

The probability of picking a yellow envelope is 2/7

Step-by-step explanation:

red envelope =2

blue " " =1

green " "=2

yellow " " =2

Total envelope =2+1+2+2=7

Probability thay at least one envelope will be yellow

P=number of yellow envelope/Total envelope

P=2/7