How can you eliminate the y-terms in this system?​

Answer:

830.53 in²

Step-by-step explanation:

Find the area of the full circle and divide it by 2:Use the circle area formula, A = r²Plug in 3.14 as pi, and plug in the radius:A = r²A = 3.14(23²)A = 1661.06Divide this by 2:1661.06 / 2= 830.53So, the area of one semicircle is 830.53 in²

Answer: The area of one semicircle is approximately 830.53 square inches.

Step-by-step explanation:

The area of a circle is given by the formula:

A = πr²

where A is the area of the circle and r is its radius.

The radius of the circle cut out of the piece of wood is about 23 inches. Therefore, its area is:

A = πr²

A = π(23)²

A = π(529)

A ≈ 1661.06 square inches

The carpenter cuts the circle into two semicircles. Therefore, the area of one semicircle is:

A/2 ≈ 830.53 square inches

Therefore, the area of one semicircle is approximately 830.53 square inches.

I hope this helps! Let me know if you have any other questions.

Answer:7

Step-by-step explanation:

Using the Law of Cosines, the angle between the lines PX and PY is found to be approximately 101.5°. Subtracting this angle from the bearing of Y from P (125°) and the bearing of X from P (35°) gives a bearing of approximately 54.5° from X to Y.

We can use the Law of Cosines to find the angle between the lines PX and PY, and then add this angle to the bearing of X from P to find the bearing of Y from X.

Let A be the angle between the lines PX and PY, and let C be the distance between X and Y. Then we have

C² = PX² + PY² - 2(PX)(PY)cos(A)

Substituting the given values, we get

950² = 420² + PY² - 2(420)(PY)cos(A)

Solving for cos(A), we get

cos(A) = (PY^2 - 950^2 - 420^2) / (-2)(420)(950)

cos(A) = -0.186

Since A is an acute angle, we can take the inverse cosine to find its measure

A = cos⁻¹ (-0.186)

A ≈ 101.5°

The bearing of X from P is 35°, so the bearing of Y from X is

125° - 35° - A ≈ 54.5°

Therefore, the bearing of Y from X is approximately 54.5 degrees to the nearest minute.

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--The given question is incomplete, the complete question is given

" The bearings from a point P of two landmarks X and Y are 35° and 125° and their distances from P are 420 m and 950 m respectively. Find the bearing of Y from X (to the nearest minute)."--

we can say that the pattern for how the numerator and denominator change in the fractions model is that they are multiplied or divided by the same non-zero integer.

Let's consider the fraction 2/ 3.

If we multiply both the numerator & the denominator by 2, we get 4 /6.

Also  multiplying both by 3, we will  get 6 /9

In general,  if we multiply the numerator and the denominator by the same non-zero integer, we get an equivalent fraction.

On the other hand, if we divide both the numerator and   the denominator by the same non-zero integer,

we also get an equivalent fraction. For example    if we divide 6/9 by 3, we get 2/3 again.

Hence , the above conclusion is correct.

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Full Question:

Fraction 2/ 3.

What pattern can you use to describe how the numerator and denominator change in the fraction models above?

The graph of y=4[tex](2)^{x}[/tex]-3 is the same as the graph of y=4[tex](2)^{x}[/tex] shifted downwards by 3 units.

The function y=4[tex](2)^{x}[/tex] is an exponential function with base 2 and vertical intercept at (0, 4).

To translate this function to the graph of y=4[tex](2)^{x}[/tex]-3, we need to shift the graph downwards by 3 units. This can be achieved by subtracting 3 from the original function as follows:

y = 4[tex](2)^{x}[/tex] - 3

Now, the vertical intercept of the new function y=4[tex](2)^{x}[/tex]-3 is at (0, 1), which is 3 units below the intercept of the original function.

Notice how the entire graph has shifted down by 3 units, while maintaining the same shape as the original exponential function y=4[tex](2)^{x}[/tex].

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Answer: x = 0

Step-by-step explanation:

simplify the expression

−5−3(6x−8)=−5x+19

−5−18+24=−5+19

19−18x=−5x+19

−18+19=−5+19

−5−3(6x−8)=−5x+19

−18x+19=−5x+19

−5−3(6x−8)=−5x+19

−18x+19=−5x+19

−18+19−19=−5+19−19

−18x=−5x+19 − 19

−18x+19−19=−5x+19 − 19

−18x=−5x

−18x+5x=−5x+5x

x=−5x+5x−13

x−13=−5+5

−13x=0

−13x/−13 = 0/-13

x= 0/−13

x= 0

The given Mayan number which is : :|| :|| in decimal (base 10) is 42.

The Mayan number system is a base-20 system that uses three symbols: a dot (.), a horizontal bar (|), and a shell-like symbol (:). The symbol for zero is a shell-like symbol (:).

To convert the given Mayan number to decimal (base 10), we need to understand the positional value of each symbol. Each position in the number represents a power of 20, with the rightmost position being 20⁰, the next position to the left being 20¹, and so on.

The Mayan number given, : :|| :||, can be broken down as follows:

The leftmost position has no symbol, which represents a value of 0.

The second position from the left has two shell-like symbols (:), which represents a value of 2x20¹ = 40.

The third position from the left has two horizontal bars (||), which represents a value of 2x20⁰ = 2.

The given Mayan number in decimal (base 10) is 40 + 2 = 42.

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Complete question is:

Convert the following Mayan number to decimal (base 10).

: :|| :||

The evaluated probability that 2 will find an excuse is 12.8%, under the condition that 35% of those failed will evaluate an excuse to avoid jury duty.

According to the data I found, about 23% of those evaluated to find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty.
In the event 10 people are called for jury duty, then the evaluated probability that 2 will find an excuse can be found out using the binomial probability distribution formula.
The formula is:
[tex]P(X=k) = C(n,k) * p{^k }* (1-p)^{(n-k)}[/tex]

Here,
P(X=k) = successes  probability of k in n trials
C(n,k) =  combinations of number in n things taken k at a time
p=  success probability of any one trial
n = trial number
For the given case
k = 2
n = 10
p = 0.23
Staging these values into the formula
[tex]P(X=2) = C(10,2) * 0.23^{2}* (1-0.23)^{(10-2)}[/tex]
       = 45 × 0.0529 × 0.5225
       = 0.128

Hence, the probability that exactly 2 out of 10 people will evaluate an excuse to avoid jury duty is 0.128 or approximately 12.8%.
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Using the future value,

Steven's grandmother needed to deposit $55,469.56 into the trust account.

We have,

We can use the formula for the future value of a present sum:

FV = PV(1 + r)^n

where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years.

In this case, we have:

FV = $100,000

PV = unknown

r = 4% = 0.04

n = 15 years (18 - 3 = 15)

Substituting these values into the formula, we get:

$100,000 = PV(1 + 0.04)^15

Solving for PV, we get:

PV = $55,469.56

Thus,

Steven's grandmother needed to deposit $55,469.56 into the trust account.

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Answer:

  d = (20/7)t

Step-by-step explanation:

You want the distance traveled as a function of travel time if Jack's speed going up was 2 mph and going down was 5 mph.

The relation between time, speed, and distance is ...

  t = d/s

If the total distance is d, the total travel time up and back is ...

  t = t1 +t2

  t = (d/2)/(2) +(d/2)/5 = d(1/4 +1/10) = 0.35d

Solving for distance, we have ...

  d = t/0.35

  d = (20/7)t . . . . miles, where t is in hours

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The test statistic is z₀ = 2.65 and the P-value is 0.004. The null hypothesis is rejected at the 5% level of significance, and we conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8.

To test the hypothesis using the P-value approach, we can follow these steps:

Check whether the sample size is large enough for the normal approximation to the binomial distribution. The requirements are satisfied if np₀ >= 10 and n(1-p₀) >= 10,

where p₀ is the hypothesized proportion under the null hypothesis. In this case, p₀ = 0.8, n = 125, so np₀ = 100 and n(1-p₀) = 25, both of which are greater than 10.

Set up the null and alternative hypotheses.

The null hypothesis is H₀: p = 0.8 (the true proportion is 0.8).

The alternative hypothesis is H₁: p > 0.8 (the true proportion is greater than 0.8).

Calculate the test statistic.

Under the null hypothesis, the test statistic follows a standard normal distribution.

The test statistic is calculated as:

z₀ = (x - np₀) / sqrt(np₀(1-p₀))

where x is the number of successes in the sample.

Plugging in the values, we get:

z₀ = (105 - 1250.8) / √(1250.8 x 0.2)

z₀ = 2.65

Calculate the P-value.

The P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample, assuming the null hypothesis is true.

Since this is a right-tailed test (H₁: p > 0.8), we calculate the area to the right of the test statistic.

Using a standard normal table or calculator, we find that the area to the right of z₀= 2.65 is 0.004.

Therefore, the P-value is 0.004.

Make a decision and interpret the results.

Using a significance level of α = 0.05, we compare the P-value to α.

Since the P-value (0.004) is less than α (0.05), we reject the null hypothesis.

We conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8 at a 5% level of significance.

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The value of number of years that the money was invested rounded to two decimal places is​, 2.5 years

We have to given that;

An amount of R1965,00 is invested in an account paying 11,50% interest per year, compounded semi-annually at the time of withdrawal the amount of interest earned is R633,75

Hence, We get;

Interest = P ( (1 + r/2)ⁿ - 1965)

R633.75 = 1965 (1 + 11.5%/2)ⁿ - 1965

1965 × 1.0575ⁿ - 1965 = 633.75

1965 × 1.0575ⁿ = 2598.75

1.0575ⁿ = 1.3225

n = log₁.₀₅₇₅ (1.3225)

n = 5

Hence, Number of years is, 5/2 = 2.5

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It is very likely that a vacuum will last between 5.5 and 7.5 years.

This is because we can use the properties of the normal distribution to calculate that about 68% of the vacuum cleaners will fall within one standard deviation of the mean, which in this case is between 6.5 - 0.5 = 6 and

6.5 + 0.5 = 7

About 95% of the vacuum cleaners will fall within two standard deviations of the mean, which in this case is between 6 - 0.5 = 5.5 and 6.5 + 0.5 = 7

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The per cent of fruit juice in the mixture is 28%. The correct option is B.

To determine the percent of fruit juice in the mixture, we need to calculate the total amount of fruit juice in the 6 L of Brand A juice and the 9 L of Brand B juice, and then divide it by the total volume of the mixture.

The amount of fruit juice in 6 L of Brand A juice is:

0.52 x 6 L = 3.12 L

The amount of fruit juice in 9 L of Brand B juice is:

0.12 x 9 L = 1.08 L

The total amount of fruit juice in the mixture is:

3.12 L + 1.08 L = 4.20 L

The total volume of the mixture is:

6 L + 9 L = 15 L

So, the per cent of fruit juice in the mixture is:

(4.20 L / 15 L) x 100% = 28%

Therefore, the correct answer is (B) 28%.

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Answer:

Step-by-step explanation:

No, the corresponding angles are not congruent.,

They have to be EXACTLY the same.

Lol i am learning this to.

The sum of the interior angle of the regular hexagon is S = 720°

Given data ,

Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

where n is the number of sides

θ = angle in degrees

when n = 6 for a hexagon , we get

nθ = 180 ( 6 - 2 )

nθ = 180 x 4

nθ = 720°

Hence , the sum of interior angles of a hexagon is 720°

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The Common factor:

a) 2x+6 = 2(x+3)

b) 9x² - 12x = 3x(3x - 4)

Expand and simplify:

a) [tex](x+3)(x+5) = x^2 + 5x + 3x + 15 = x^2 + 8x + 15[/tex]

b) [tex](x-6)(x+7) = x^2 + 7x - 6x - 42 = x^2 + x - 42[/tex]

Common factor:

a) 2x+6 = 2(x+3)

b) 9x² - 12x = 3x(3x - 4)

Factorization is the process of expressing a number or equation in terms of its factors, which are integers or individual terms that when combined together generate the original number or expression. This is an essential concept in algebra and number theory.

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The median is 81.5.

The median of the lower half of the data is 67.

The median of the upper half of the data is 92.

Given a data set,

82, 62, 95, 81, 89, 51, 72, 56, 97, 98, 79, 85

Median of a data set is the middle element when the data are arranged in a order.

Arranging in ascending order,

51, 56, 62, 72, 79, 81, 82, 85, 89, 95, 97, 98

There are even number of data sets.

So, Median = Average of the middle two elements.

Median = (81 + 82) / 2 = 81.5

Lower half of the data set is,

51, 56, 62, 72, 79, 81

Median = (62 + 72) / 2 = 67

Upper half of the data set is,

82, 85, 89, 95, 97, 98

Median = (89 + 95) / 2 = 92

Hence the median is 81.5, lower half median is 67 and upper half median is 92.

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Answer: 6

Step-by-step explanation:

The value of the expression 4/12 + 2/3 is 1 1/12

A fraction is a part of a whole. A fraction consist of the upper part( numerator ) and the lower part ( denominator). Examples of fractions are; simple fraction , complex fraction, mixed fraction, improper fraction.

In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Solving 4/12 + 1/3

= (9+4)/12

= 13/12

= 1 1/12

therefore the value of 4 twelfth + 2 third is 1 1/12

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When the number of milligrams reaches 11, the drug is to be injected again. We need approximately 6.7 hours between injections.

The given function is D(h)=30[tex]e^{-0.35h[/tex], which gives the number of milligrams D(h) of the drug in the patient's bloodstream h hours after it is injected.

When the drug is injected again, the number of milligrams in the bloodstream will be 11. Therefore, we need to find the value of h that satisfies the equation:

11 = 30[tex]e^{-0.35h[/tex]

To solve for h, we can first divide both sides by 30:

11/30 = [tex]e^{-0.35h[/tex]

Next, we take the natural logarithm of both sides:

ln(11/30) = ln([tex]e^{-0.35h[/tex])

Using the property of logarithms that ln(eˣ) = x, we can simplify the right side:

ln(11/30) = -0.35h

Finally, we can solve for h by dividing both sides by -0.35 and multiplying by -1:

h = (-1/0.35)ln(11/30)

Using a calculator, we get:

h ≈ 6.7

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The value of a third-degree polynomial function with real coefficients and the given zeros are,

⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i

We have to given that;

Zeroes of the polynomial are,

⇒ 7, i

Now, The value of a third-degree polynomial function with real coefficients and the given zeros are,

⇒ P (x) = (x - 7)² (x - i)

⇒ P (x) = (x² + 49 - 14x) (x - i)

⇒ P (x) = (x³ - ix² + 49x - 49i - 14x² + 14ix)

⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i

Thus, The value of a third-degree polynomial function with real coefficients and the given zeros are,

⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i

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The Area of Triangle is 10 square unit.

We have,

base = 4 unit

Height = 5 unit

So, Area of Triangle

= 1/2 x base x height

= 1/2 x 4 x 5

= 2 x 5

= 10 square unit

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The bond price at 12% maturity is $435.42, at 10% maturity is $500.00, at 8% maturity is $607.28, and at 6% maturity is $748.65. The balance at the end of 28 months is approximately $41,097,019.67.

To determine the price of the bond at different yield to maturity rates, we need to use the bond pricing formula

Bond price = (Coupon payment / (1 + YTM)¹) + (Coupon payment / (1 + YTM)²) + ... + (Coupon payment + Face value) / (1 + YTM)ⁿ

Where Coupon payment = Annual coupon rate x Face value

YTM = Yield to maturity

n = Number of years to maturity x Number of coupon payments per year

Using $1,000 as the face value and an annual coupon rate of 10%, we have

At 12% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.12)¹) + ($100 / (1 + 0.12)²) + ... + ($100 + $1,000) / (1 + 0.12)⁴⁰

Bond price = $435.42

At 10% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.10)¹) + ($100 / (1 + 0.10)²) + ... + ($100 + $1,000) / (1 + 0.10)⁴⁰

Bond price = $500.00

At 8% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.08)¹) + ($100 / (1 + 0.08)²) + ... + ($100 + $1,000) / (1 + 0.08)⁴⁰

Bond price = $607.28

At 6% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.06)¹) + ($100 / (1 + 0.06)²) + ... + ($100 + $1,000) / (1 + 0.06)⁴⁰

Bond price = $748.65

To calculate the monthly payment and balance of the loan from the bank, we can use the formula for the monthly payment of an amortizing loan

P = (r × A) / (1 - (1 + r)⁻ⁿ)

where P is the monthly payment, r is the monthly interest rate (which is the annual interest rate divided by 12), A is the loan amount, and n is the total number of months in the loan.

First, we need to calculate the values of r, A, and n

r = 0.08 / 12 = 0.00667 (monthly interest rate)

A = $50,000,000 (loan amount)

n = 5 years × 12 months/year = 60 months (total number of months in the loan)

Now, we can plug these values into the formula to calculate the monthly payment

P = (0.00667 × $50,000,000) / (1 - (1 + 0.00667)⁻⁶⁰)

P ≈ $1,029,299.29

Therefore, the monthly payment on the loan is approximately $1,029,299.29.

To find the balance at the end of 28 months, we can use the formula for the remaining balance of an amortizing loan

B = (P * (1 - (1 + r)⁻ⁿ')) / r

where B is the remaining balance, r is the monthly interest rate, P is the monthly payment, and n' is the number of months remaining in the loan (which is equal to the total number of months minus the number of months already paid).

After 28 months, the number of months remaining in the loan is

n' = 60 - 28 = 32

We can now plug the values of P, r, and n' into the formula to find the balance

B = ($1,029,299.29 × (1 - (1 + 0.00667)⁻³²)) / 0.00667

B ≈ $41,097,019.67

Therefore, the balance at the end of 28 months is approximately $41,097,019.67.

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Answer:

[tex] 36 < 47 < 49[/tex]

[tex] \sqrt{36} < \sqrt{47} < \sqrt{49} [/tex]

[tex]6 < \sqrt{47} < 7[/tex]

√47 is approximately 6.9

a) The confidence level of 99% means that we are 99% sure that the interval contains the true population proportion.

b) The 99% confidence interval for the population proportion is given as follows: (0.3145, 0.4055). It means that we are 99% sure that the true population proportion is between 0.3145 and 0.4055.

c) The 95% confidence interval would be narrower, as it would have a lower critical value, thus the margin of error would also be lower.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The parameters for this problem are given as follows:

[tex]\pi = 0.36, n = 739[/tex]

The lower bound of the interval is given as follows:

0.36 - 2.575 x sqrt(0.36 x 0.64/739) = 0.3145.

The upper bound of the interval is given as follows:

0.36 + 2.575 x sqrt(0.36 x 0.64/739) = 0.4055.

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The perimeter of the composite figure that is given above would be = 96.6m.

To calculate the perimeter of the given shape, it has to be divided into two.

First shape is a rectangle. Therefore the perimeter of a rectangle is calculated with the formula = 2(l+w)

Where ;

length = 16m

width = 11m

perimeter = 2(16+11)

= 2×27

= 54m

The second shape:

Perimeter of triangle = l+w+h

where;

length = 18-11 = 7m

width = 16m

height = 19.5m

perimeter = 7+16+19.5 = 42.5m

Therefore, the perimeter of the shape = 54+42.5 = 96.6m

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The number of residents Town A used to have is 1400, and the number of residents Town B used to have is 3600, as shown by the simple equation below.

Let x be the number of residents Town A used to have. The number of residents in Town B is:

5000 - x

We know that Town A had 12% whites and Town B had 10% whites. After the merge, the percentage of whites is 10.56%. With that in mind:

12%x+10%(5000-x) = 10.56%(5000)

0,12x + 500 - 0,1x = 528

0.02x = 28

x = 1400

Therefore, the number of residents Town A used to have is 1400. Now, the number of residents town B used to have is:

5000 - 1400 = 3600

With that in mind, we can conclude our answer is correct.

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