If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. TRUE or FALSE​

Using linear functions, it is found that:

A linear function is modeled by:

\(y = mx + b\)

In which:

Jose:

Gavin:

The day they will both be on the same page is x for which:

\(J = G\)

Hence:

\(17x + 10 = 14x + 37\)

\(3x = 27\)

\(x = \frac{27}{3}\)

\(x = 9\)

They will be on the same page on the 9th day.

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We have the following configuration for this problem:

where y is the distance, in feet, Corey stepped back.

Then, we have:

And:

Now, using the first into the second equation, we obtain:

Therefore, Corey stepped back approximately 59.71 feet.

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

The volume common to two spheres is \(V=\frac{27 \pi r^3}{32}\)

Step-by-step explanation:

Let r be the radius of each sphere

We are given that distance between their centers is \(\frac{r}{2}\)

Let \((\frac{-r}{4},0)\) be the center of sphere 1 and \((\frac{r}{4},0)\)be the center of sphere 2 .

Using the disk points

a=0 and b =\(\frac{3r}{4}\)

\((x+(\frac{r}{4}))^2+y^2=r^2\\V=2 \int_{0}^{\frac{3r}{4}} \pi y^2 dx\\V=2 \int_{0}^{\frac{3r}{4}} \pi [r^2-(x+(\frac{r}{4}))^2]dx\\V=\frac{27 \pi r^3}{32}\)

Hence the volume common to two spheres is \(V=\frac{27 \pi r^3}{32}\)

In attached diagram, we can see 2 circumferences with radius r, and separated centers by r/2.

The solution is:

V = (11/12)×π×r³

Let´s call circumferences  1 and 2, by symmetry, rotating area A will produce a volume V₁ identical a V₂, Obtained by rotating area B ( both around x-axis), then the whole volume V will be:

V = 2× V₁

V₁ = ∫π×y²×dx         (1)

Now

( x - r/2)²  +  y² = r²       the equation of circumference 1

y² = r² - ( x - r/2)²

Plugging this value in equation (1)

V₁ = ∫π×[  r² - ( x - r/2)²]×dx        with integrations limits    0 ≤ x ≤ r/2

V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx

V₁ = π× [  r²×x - x³/3 + (r/2)²×x - (1/2) ×r×x²]    evaluate between 0 and r/2

V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) ×r×x²]

V₁ =  π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ -  (1/2) ×r×(r/2)²]

V₁ =  π× [ (5/8)×r³ - r³/24 - r³/8]

V₁ =  π× (11/24)×r³

Then

V = 2× V₁

V = 2×π×11/24)×r³

V = (11/12)×π×r³

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Answer:

x = 30°

Step-by-step explanation:

the first triangle is equilateral.

An equilateral triangle has also congruent angles whose measure is 60°

The vertex of the under triangle is the supplementary of the angle of the equilateral triangle

180 - 60 = 120°

the triangle is isosceles because the two oblique sides are congruent

An isosceles triangle has two congruent base angles

120 + 2x = 180

2x = 180 - 120

2x = 60

2 / 2 x = 60/2

x = 30°

Answer:

x = 30

y = 5

Step-by-step explanation:

The triangle to the left has all congruent angles.

Since the sum of the measures of the angles of a triangle is 180°, and all angles are congruent, then each angle measures 180°/3 = 60°.

An equiangular triangle (all angles are congruent) is also an equilateral triangle (all sides are congruent.

Since one side of the left triangle measures 40, then all sides of the left triangle measure 40.

Now let's look at the triangle on the right side. One side measures 40. The left side also measures 40 since we know from the triangle at left. Opposite angles of congruent sides are congruent. The bottom right angle of the triangle to the right also measures x°. The upper angle is the supplement of 60°, so it measures 120°.

x + x + 120 = 180

2x = 60

x = 30

The upper left small triangle is equilateral.

8y = 40

y = 5

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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(a) The percentage of boxes that weigh less than 15.4 ounces is approximately 84.13%.

(b) Approximately 15.87% of boxes weigh more than 15.4 ounces.

(c) The percentage of boxes that weigh less than 14 ounces is approximately 0.62%.

(d) Approximately 83.51% of boxes weigh between 14 and 15.4 ounces.

The percentage of boxes that weigh less than 15.4 ounces, we need to calculate the z-score for this value:

z = (15.4 - 15) / 0.4 = 1

A standard normal distribution table or a calculator with a normal distribution function, we can find that the percentage of boxes that weigh less than 15.4 ounces is approximately 84.13%.

The percentage of boxes that weigh more than 15.4 ounces, we can subtract the percentage from part (a) from 100%:

100% - 84.13% = 15.87%

Approximately 15.87% of boxes weigh more than 15.4 ounces.

The percentage of boxes that weigh less than 14 ounces, we need to calculate the z-score for this value:

z = (14 - 15) / 0.4 = -2.5

A standard normal distribution table or a calculator with a normal distribution function, we can find that the percentage of boxes that weigh less than 14 ounces is approximately 0.62%.

The percentage of boxes that weigh between 14 and 15.4 ounces, we need to calculate the area under the curve between these two values.

The z-scores for these values and subtracting the area to the left of the lower z-score from the area to the left of the higher z-score:

z1 = (14 - 15) / 0.4

= -2.5

z2 = (15.4 - 15) / 0.4

= 1

A standard normal distribution table or a calculator with a normal distribution function, we can find that the area to the left of z1 is approximately 0.62% (as found in part (c)) and the area to the left of z2 is approximately 84.13% (as found in part (a)).

The area between these two z-scores is:

84.13% - 0.62% = 83.51%

Approximately 83.51% of boxes weigh between 14 and 15.4 ounces.

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Answer:

Can I get a brainliest- and also that so nice!!✨

Answer:

0.54 as a fraction is 54/100

4.18 as a mixed number is 4 18/100

0.51 as a fraction is 51/100

it would be really cool if you could mark me as brainliest :)

Step-by-step explanation:

Answer:

The copy machine can print 80 pages in 1 minute.

Step-by-step explanation:

160 ÷ 2 = 80

The zeros of g(x) = (x + 2)(x − 1)(x − 2) are x = -2, 1 and 2

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

The 5 functions of g(x)

To determine the key features of the function g(x), we make use of the first

g(x) = (x + 2)(x − 1)(x − 2)

So, we have

Zeros

This is when the function equals 0

(x + 2)(x − 1)(x − 2) = 0

Evaluate

x = -2, 1 and 2

The y-intercept

This is when the value of x in the function equals 0

g(0) = (0 + 2)(0 − 1)(0 − 2)

Evaluate

g(0) = 4

End behaviour

This is the behavior of the graph of the function as it approaches the ends of the x-axis

So, we have

\(\mathrm{as}\:x\to \:+\infty \:,\:g\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:g\left(x\right)\to \:-\infty \:\)

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Answer: in the third draw 33.33% people eliminated.

Step-by-step explanation:

Answer:

9 OR 1

Step-by-step explanation:

Let the number be x

x² - 10x = -9

x² - 10x + 9=0

a=1

b=-10

c=9

Solve using the quadratic formula

x =9 or 1

Step 1: Write the dividend and divisor:

\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 2: Divide the first term of the dividend by the first term of the divisor:

\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)

Step 3: Multiply the divisor (x - 4) by the result (x^2):

\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)

Step 4: Subtract the result from the original dividend:

\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)

Step 5: Bring down the next term from the dividend:

\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 6: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)

\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)

\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)

Step 7: Bring down the next term from the dividend:

\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)

Step 8: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)

\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)

\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)

Step 9: There are no more terms to bring down, so the division is complete.

Step 10: Write the final result:

The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.

Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:

\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)

The solution is, the product is 9.25* 10^83.2.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

2.5\times 10^22.5×10^2 and 3.7 \times 10^53.7×10^5

=2.5* 10^22.5×10^2 × 3.7 * 10^53.7×10^5

=9.25* 10^24.5*10^58.7

=9.25* 10^83.2

Hence, The solution is, the product is 9.25* 10^83.2.

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Answer:

  x = 5.5

Step-by-step explanation:

Multiply both sides of the equation by 24 (the least common denominator). This gives ...

  2(x +2) = 3(5)

  2x +4 = 15

Subtracting 4 gives you ...

  2x = 11

  x = 11/2 . . . divide by 2

  x = 5.5 . . . . . . . . write as decimal

Hello!

3x + 4 = 1

3x + 4 - 4 = 1 - 4

3x = -3

3x/3 = -3/3

x = -1

The solution of the equation 3x + 4 = 1 is -1.

The answer is:

C) x = -1

Work/explanation:

To solve this equation, I subtract 4 from each side:

\(\sf{3x+4=1}\)

Subtract :

\(\sf{3x=-3}\)

Divide each side by 3:

\(\sf{x=-1}\)

Hence, C is correct.

Answer: the present age of son is 15 years, and the present age of father is 45 years.

Step-by-step explanation:

Let the age of son be 'x' and that of his father be 'y'.

So according to the question, the 1st equation that can be formed will be:

y = 3(x) ->(1)

[as father's age is 3 times the age of son]

Now after 5 years:

Age of son = (x+5)

Age of father = (y+5)

So according to the question, the 2nd equation that can be formed will be:

(y+5) = 2.5×(x+5) ->(2)

[as father is now two and half times old as his son]

Substituting the value of equation (1) in (2), we get:

(3x+5) = 2.5×(x+5)

=> 3x + 5 = 2.5x + 12.5

=> 3x - 2.5x = 12.5 - 5

=> 0.5x = 7.5

=> x = 7.5/0.5 = 15

Thus, the present age of son is 15 years.

Note : we can calculate the age of father by putting the value of x in equation (1) or (2):

y = 3(x) = 3 × 15 = 45 (putting x in equation 1)

Thus, the present age of father is 45 years.

Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.

To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.

Let's examine the chart and count the number of times each sum occurs:

Sum: 2, Occurrences: 1

Sum: 3, Occurrences: 2

Sum: 4, Occurrences: 3

Sum: 5, Occurrences: 4

Sum: 6, Occurrences: 5

Sum: 7, Occurrences: 6

Sum: 8, Occurrences: 5

Sum: 9, Occurrences: 4

Sum: 10, Occurrences: 3

Sum: 11, Occurrences: 2

Sum: 12, Occurrences: 1

Now, let's calculate the probabilities of each sum occurring.

Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:

Probability of sum 2 = 1/36

Probability of sum 3 = 2/36

Probability of sum 4 = 3/36

Probability of sum 5 = 4/36

Probability of sum 6 = 5/36

Probability of sum 7 = 6/36

Probability of sum 8 = 5/36

Probability of sum 9 = 4/36

Probability of sum 10 = 3/36

Probability of sum 11 = 2/36

Probability of sum 12 = 1/36

To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.

For example, to find the expected number of times the sum is 7:

Expected occurrences of sum 7 = (6/36) \(\times\) 180 = 30

Similarly, we can calculate the expected occurrences for all other sums.

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Answer:

11

Step-by-step explanation:

\(61 {}^{2} - {60 }^{2} = 121\)

\( \sqrt{121} = 11\)

The amount of gas that is left in the tank if there is only 1 / 8 of the tank is 1.5 gallons

The car tank can accommodate 12 gallons of gas .

Her fuel gauge says that there is 1 / 8 of the tank left in the car tank.

Therefore, the amount of gas that is left in the tank is calculated as follows:

amount left in the tank = 1 / 8 × 12

amount left in the tank = 12 / 8

amount left in the tank = 6 / 4

amount left in the tank = 3 / 2

amount left in the tank = 1.5 gallons

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The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

The monthly payments during the term of the loan will be $1,043.

Step-by-step explanation:

Given that Curtis is buying a home, and it's mortgage loan is 360,000 at 4.3 percent interest for 30 years, making 12 payments a year one per month, to determine her monthly payment the following calculation has to be done:

360,000 x 0.043 = 15,480

15,480 + 360,000 = 375,480

375,480 / (12 x 30) = X

375,480 / 360 = X

1.043 = X

Thus, the monthly payments during the term of the loan will be $ 1,043.

You would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four years.

To calculate the monthly savings required to reach a savings goal of $3,000.00 over four years with a 10% annual interest rate,  we can use the PMT (Payment) function.

The PMT function helps us determine the fixed payment amount needed to achieve a specific future value within a given time frame.

Let's break down the given information:

Present Value (PV): $0.00 (initial account balance)

Future Value (FV): $3,000.00 (savings goal)

Interest Rate (rate): 10% per year (annual interest rate)

Number of Periods (nper): 4 years (48 months)

Using the PMT function, we need to plug in the values and solve for the monthly payment (savings amount).

The formula for the PMT function is:

PMT(rate, nper, pv, [fv], [type])

Where:

rate = Interest rate per period

nper = Total number of periods

pv = Present value (initial account balance)

fv = Future value (savings goal)

type = (Optional) Indicates whether the payment is made at the beginning (1) or end (0) of the period.

We'll assume 0 for monthly savings.

Let's calculate the monthly savings using the PMT function:

PMT(10%/12, 4*12, 0, -3000, 0)

Here, we divide the annual interest rate by 12 to get the monthly interest rate (10%/12), multiply the number of years by 12 to get the total number of months (4*12), set the initial account balance (pv) as $0, set the future value (fv) as -$3,000 (negative because it's an outgoing payment), and assume the savings are made at the end of each month (type = 0).

Using a financial calculator or spreadsheet software, the monthly savings required to reach the goal of $3,000.00 over four years with a 10% annual interest rate is approximately $56.62.

Therefore, you would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four year.

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Question : you want to reach $3,000.00 in savings over four years. Your account will earn 10% interest per yea Initially your account has a zero balance. How much must you save each month to achieve this goal? Use the PMT() function. Look it up in the e-book if you do not know how to use it. TIP: This is monthly so do not forget to adjust the interest rate and number of payment.

Ciana should purchase the skirt at the store across town because the total economic cost will be lowest.

Ciana makes $30 per hour at her work, and her purchase decision includes the opportunity cost of lost wages:

Total economic cost:

Local store = $114 + [1/4 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $144

Across town = $86 + [1/2 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $131

Neighboring city = $60 + [1 hour x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $135

Ciana should buy a skirt at the store across town. Because it has the lowest total economic cost ($131).

Opportunity cost is the lost benefit or additional cost of choosing one activity or investment over another. Economic costs include both accounting costs and opportunity costs.  

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Answer:

-5p+99

Step-by-step explanation:

Original Equation;

3(p - 29) - 4(2p - 39 -5)

★First Step: Multiply the number 3 by p and -29 which is in the first term so it's going to be;

3 multiplied by p and 3 multiplied by -29

3p - 87

★Second step: Add the -39 and -5 which is going to give you -44 because - + - is = -

-44

★Third step: Multiply -4 by 2p and -44 so it's going to be;

-4×2p=-8p and -4×-44=176 we have positive 176 because - × - = +

★Fourth Step: Remove brackets

So it's going to be;

3p - 87 -8p +176

★Then you combine like terms

3p - 8p - 87 +176

-5p + 99

3(p-29)-4(2p-39-5)

3p-87-4(2p-44)

3p-87-8p+176

3p-8p-87+176

-5p+99

f ' (0) exists if the limit,

\(\displaystyle \lim_{h\to0}\frac{f(0+h)-f(0)}h\)

exists, and f ' (0) has the value of this limit.

In order for this limit to exist, both limits from either side of h = 0 must exist.

Suppose h < 0. Then 0 + h is also negative, so by definition of f(x) we have

f (0 + h) = ((0 + h) + 1)² = h ² + 2h + 1

Then in the limit, if h is approaching 0, it must be from below or from the left:

\(\displaystyle \lim_{h\to0^-}\frac{f(0+h)-f(0)}{h} = \lim_{h\to0^-}\frac{(h^2+2h+1)-1}{h} = \lim_{h\to0^-}(h+2) = 2\)

Now suppose h > 0, so that 0 + h is positive and h approaches 0 from above or from the right. Then

f (0 + h) = 2 (0 + h) + 1 = 2h + 1

and

\(\displaystyle \lim_{h\to0^+}\frac{f(0+h)-f(0)}h = \lim_{h\to0^+}\frac{(2h+1)-1}{h} = \lim_{h\to0^+}2 = 2\)

Both one-sided limits match, so f ' (0) = 2.

All u have to do is use the Traingle Inequality theorem, which states that the sum of two sides lenghts of a triangle is always greater than the third side. if this is true for all three combinations of added side lengths then you will have a triangle

Hope this helps :>

Answer:

3, 5, 7

Step-by-step explanation:

given 3 sides, for a triangle to be formed, then the sum of any 2 sides must be greater than the third side.

4 , 4 , 8

4 + 4 = 8 , not greater than 8, so does not form a triangle

1 , 2 , 3

1 + 2 = 3 , not greater than 3, so does not form a triangle

3 , 9 , 14

3 + 9 = 12 < 14 , so does not form a triangle

3 , 5 , 7

3 + 5 = 8 > 7

3 + 7 = 10 > 5

5 + 7 = 12 > 3

condition is satisfied , so will form a triangle