Did I get the first question correct? Question 1:

The side length c of the triangle is equal to:

c^2=a^2+b^2 −2ab cosC

where a and b are the other two side lengths of the triangle, and C is the angle opposite side c.

To solve for c, we can plug in the values of a, b, and C into the formula and solve for c. For example, if a=3, b=4, and C=60 then we would plug in these values into the formula and solve for c as follows:
c^2=3^2+4^2 −2⋅3⋅4cos60
c^2=25
c= square root 25 =5
Therefore, the side length c of the triangle is equal to 5.

Answer:I need part A to answer

Step-by-step explanation:

The proportion of cans that are scrapped is approximately 0.0241.

We know that the fill volume of cans follows a normal distribution with a mean of 367 ml and a standard deviation of 3 ml. Let's define X as the fill volume of a single can. Then we can write:

X ~ N(367, 3)

We want to find the proportion of cans that are scrapped, i.e., the proportion of cans with a fill volume less than 358 ml or greater than 373 ml. Let's call this proportion p:

p = P(X < 358 or X > 373)

To solve this problem, we can use the standard normal distribution and the z-score formula:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution. We can standardize the values 358 and 373 using this formula:

z1 = (358 - 367) / 3 = -3

z2 = (373 - 367) / 3 = 2

Now we can find the probabilities of the two events separately using the standard normal distribution table or a calculator:

P(X < 358) = P(z < -3) ≈ 0.0013

P(X > 373) = P(z > 2) ≈ 0.0228

The probability of either event happening is the sum of the probabilities:

P(X < 358 or X > 373) = P(X < 358) + P(X > 373) ≈ 0.0241

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An equation that could represent P(x) include the following: A. P(x) = (x + 1)(x - 2)²

In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Also, the graph has a zero of multiplicity 2 at x = 2 and zero of multiplicity 1 at x = -1;

x = 2 ⇒ x - 2 = 0.

(x - 2)²

x = -1 ⇒ x + 1 = 0.

(x + 1)

In this context, an equation that represent the polynomial function is given by:

p(x) = a(x - 2)²(x + 1)

By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, 4), we have;

4 = a(0 - 2)²(0 + 1)

4 = a4

a = 4/4.

a = 1

Therefore, the required polynomial function is given by:

p(x) = (x - 2)²(x + 1)

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Answer:

1:4

Step-by-step explanation:

30% of (B - A) = 18% of (A + B)

0.3(B - A) = 0.18(A + B) (converting percentages to decimals)

0.3B - 0.3A = 0.18A + 0.18B (distributing on both sides)

0.3B - 0.18B = 0.18A + 0.3A (grouping like terms)

0.12B = 0.48A

Simplifying further gives:

B/A = 0.48/0.12 = 4/1

Therefore, the ratio of A:B is 1:4.

Let's start by simplifying the given equation:

30% of (B-A) = 18% of (A+B)

0.3(B-A) = 0.18(A+B)

0.3B - 0.3A = 0.18A + 0.18B

0.12B = 0.48A

B = 4A

Now we know that B is 4 times A.

To find the ratio A:B, we can express B in terms of A:

B = 4A

A:B = A/4A = 1/4

Therefore, the ratio A:B is 1:4.

Answer:

A: (2x + 7)(5x + 9) = 10x^2 + 53x + 63

B: second-degree (quadratic) polynomial

C: The product of two polynomials is a polynomial.

Part A: we simply need to multiply this out using the distributive property:

Area = 2x5x + 2x9 + 75x + 79

= 10x² + 18x + 35x + 63

= 10x² + 53x + 63 (4 points)

Part B:A polynomial of degree 2 is called a quadratic polynomial. So, the classification of this polynomial is "quadratic". (3 points)

Part C:In the case of the set of polynomials, the closure property for multiplication says that multiplying any two polynomials results in another polynomial. This is demonstrated in Part A where we multiplied two polynomials - (2x + 7) and (5x + 9) - and the result was another polynomial - 10x² + 53x + 63. This shows that the set of polynomials is closed under multiplication. (3 points)

Part A:

The area of a rectangle is given by the product of its length and width. Therefore, for a rectangle with sides measuring (2x + 7) units and (5x + 9) units, the area can be represented as:

Area = (2x + 7)(5x + 9)

Now, we simply need to multiply this out using the distributive property:

Area = 2x5x + 2x9 + 75x + 79

= 10x² + 18x + 35x + 63

= 10x² + 53x + 63 (4 points)

Part B:

The degree of a polynomial is the highest power of x in the polynomial. Here, the highest power of x is 2 (in the term 10x²), so the degree of this polynomial is 2.

A polynomial of degree 2 is called a quadratic polynomial. So, the classification of this polynomial is "quadratic". (3 points)

Part C:

The closure property of an operation (like addition, multiplication, etc.) on a set says that applying the operation to any elements in the set always results in an element that is also in the set.

In the case of the set of polynomials, the closure property for multiplication says that multiplying any two polynomials results in another polynomial. This is demonstrated in Part A where we multiplied two polynomials - (2x + 7) and (5x + 9) - and the result was another polynomial - 10x² + 53x + 63. This shows that the set of polynomials is closed under multiplication. (3 points)

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Answer:

[tex]\frac{11}{24}[/tex] yards

Step-by-step explanation:

[tex]\frac{1}{8}[/tex] + [tex]\frac{1}{3}[/tex]  we need a common denominator which is 24

[tex]\frac{1}{8}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{3}{24}[/tex]

[tex]\frac{1}{3}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{8}{24}[/tex]

[tex]\frac{3}{24}[/tex] + [tex]\frac{8}{24}[/tex] = [tex]\frac{11}{24}[/tex] yards

Helping in the name of Jesus.

Joelle gave a total of 300 yards of ribbon in all

Let's assume that the total amount of ribbon Joelle has is "x" yards.

We know that 24 yards of ribbon is 8% of her total amount of ribbon. So we can write an equation:

0.08x = 24

To solve for x, we divide both sides of the equation by 0.08:

x = 24 ÷ 0.08

x = 300

Therefore, Joelle has a total of 300 yards of ribbon.

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Answer:

Step-by-step explanation: the answer is 300 just divide and you’ll get the answer that simple

Answer:

Answer is obstacle by giving up yours

The distance you live from the library, would be 6. 4 miles.

Assigning the distance between your house and where you can find books as x miles, we could approximate that initially you cycled 0.75x miles before retracing your route back a third of what had already been travelled; converting to 0.25x mile. Thus, at this stage, you will have covered an accumulated distance of 0.5x - taking into account earlier computations.

Realizing that borrowing such book would be unnecessary, you rode back to the library from whence you started- making it 3.2 miles. As you have advanced some length by travelling a cumulative distance of 0.5x from your private residence on previous trial, only another 0.5x miles stands between you and the target place after spinning around anew.

The equation is:

0. 5 x = 3. 2

x = 3. 2 / 0. 5

x = 6. 4 miles

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Answer:

Area of the shape is 244.98cm² is B

Step-by-step explanation:

Area of shape=Area of semi circle+Area of trapezoid

A=1/2 πr² + 1/2(a+b)h

A=1/2×3.142×7² + 1/2(14+18)10.5

A=1/2×3.142×49 + 1/2×32×10.5

A=76.98+168

A=76.98+168

A=244.98cm²

The percent of the raisins that Victoria she keep for herself is 70%

Based on the information, a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100.

Since Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother. The percent of the raisins she keep for herself will be:

= (1 - 3/10) × 100

= 70%

Therefore, the percent of the raisins that Victoria she keep for herself is J 70%

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Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother.

About what percent of the raisins did she keep for herself?

F 30%

G 33%

H 66%

J 70%

The residual plot shows that the regression equation is a good model of the data because it shows a random scatter of points around a horizontal line at zero, with no pattern or trend

A residual plot is a scatter plot of the residuals against the predictor variable(s) or the fitted values. It is used to verify whether the regression equation fits the data well.

In the event that the residual plot shows a random scatter of points around a horizontal line at zero, with no pattern or trend, it shows that the regression equation is a good model of the data.

On the other hand, supposing the residual plot shows a pattern or trend, such as a curve, a U-shape, or a funnel shape, it shows that the regression equation is a bad model of the data.

Therefore, from the graph given, the residual plot shows that the regression equation is a good model of the data.

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a) If the minimum payment is 15% on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,291.99.

b)  If the minimum payment is $75 on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,293.99.

The credit card balance refers to the difference between the beginning balance, payments, and interests.

a) Current balance on a credit card = $1,500

Interest rate = 15.99%

Minimum payment = 15%

= $225 ($1,500 x 15%)

Interest = $16.99 ($1,500 - $225 x 15.99% x 1/12)

Ending Balance = $1,291.99 ($1,500 +$16.99 - $225)

b) Current balance on a credit card = $1,500

Interest rate = 15.99%

Minimum payment = $75

Interest = $18.99 ($1,500 - $75 x 15.99% x 1/12)

Ending Balance = $1,293.99 ($1,500 +$18.99 - $225)

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The solution to the simultaneous equations is x = 2 and y = -4. To obtain these values,  18 = 7x - y  is rearranged to y = 7x - 18, and then substituted into 3x + y = 2  to obtain the value of x and y.

Rearranging equation (1) to make y the subject

18 = 7x - y

Add y to both sides

18 + y = 7x

Subtract 18 from both sides

y = 7x - 18

Using the answer to part a) to solve the simultaneous equations

Substitute the expression for y from equation (1) into equation (2)

3x + (7x - 18) = 2

Simplify

10x - 18 = 2

Add 18 to both sides

10x = 20

Divide both sides by 10

x = 2

Substitute x = 2 into equation (1) to find y

18 = 7(2) - y

18 = 14 - y

Subtract 14 from both sides

4 = -y

Multiply both sides by -1

-4 = y

Therefore, the solution to the simultaneous equations is x = 2 and y = -4.

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According to given information, the arc length of a partial circle is 14.67 units.

A partial circle is a portion of a circle, usually defined by an angle that is less than 360 degrees.

To find the arc length of a partial circle, we need to know the measure of the central angle, θ, in radians.

Let's say that the central angle of the partial circle is 2π/3 radians, which corresponds to an angle of 120 degrees.

Then, the arc length, denoted by L, can be calculated using the formula:

L = rθ

where r is the radius of the circle.

Plugging in the values we have, we get:

L = 7(2π/3)

L = (14/3)π

Using 3.14 for π, we get:

L ≈ 14.67 units (rounded to two decimal places)

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Answer:

a discount rate of 5%

Step-by-step explanation:

The formula to calculate the present value of a perpetuity is:

PV = PMT / r

Where PV is the present value, PMT is the constant payment, and r is the discount rate.

In this case, the PMT is $25,000 and the PV is -$500,000 (negative because it represents a cash outflow). So we can rearrange the formula to solve for r:

r = PMT / PV

r = $25,000 / -$500,000

r = -0.05 or -5%

Therefore, at a discount rate of 5%, the policy would be a fair deal.

To calculate this in Excel, you can use the following formula in a cell:

=r(-25000/500000)

This will give you a result of -0.05, or -5%, which represents the fair discount rate.

Hope this helps!

The 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.

A confidence interval is a range of values that is calculated from a sample of data. It provides a level of certainty, usually expressed as a percentage, that a population parameter lies within this range. It is used to estimate a population parameter, such as a mean, a proportion, or a difference between two means.

The 95.44% confidence interval for the mean score, μ, of all students taking the test can be calculated using the formula:
Confidence Interval = overbar(x) ± (1.96 x (σ/√n))
where overbar(x) is the mean score on the aptitude test, σ is the standard deviation of the population (15 in this case), and n is the sample size (5 in this case).
Plugging in the given values, we get:
Confidence Interval = 73 ± (1.96 x (15/√5))
= 73 ± (1.96 x 3)
= 73 ± 5.88
Therefore, the 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.

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Answer:

-78, -5/6, -0.2001, 20%

Step-by-step explanation:

The first step is to convert all of the numbers into the same form. In this case, it is easiest to use decimal form.

-5/6 = -0.8333...

-0.2001

20% = 0.2

-78

-78 is the smallest by far

-0.8333... is the next smallest

-0.2 is next

and 0.2 is the largest

Start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl. Then move 11 yards to the right to represent Karl throwing the disc to Alice the result shows that.

To represent Jenna throwing the disc to Karl, we need to move 18 yards to the right on the number line. This is because Jenna threw the disc directly to Karl, so the distance between them is 18 yards. Therefore, we can start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl.

To represent Karl throwing the disc to Alice, we need to move 11 yards to the right from Karl's position on the number line. This is because Karl threw the disc 11 yards in the same direction as Jenna threw it to him.

So, we can start at Karl's position on the number line (which is 18 yards to the right of 0) and move 11 yards to the right to represent Karl throwing the disc to Alice.

Overall, to represent the entire throwing sequence from Jenna to Karl and then to Alice, we can start at 0 on the number line and move 18 + 11 = 29 yards to the right.

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If f(x)= √(x−1) and g(x)=12x+5, then the value of (f∘g)(2) is 2√7.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find the value of (f∘g)(2), we first need to evaluate g(2), and then use the result as the input for f.

So,

g(2) = 12(2) + 5 = 24 + 5 = 29

Now, we use the value g(2) = 29 as the input for f:

f(g(2)) = f(29)

Since f(x) = √(x-1), we have:

f(29) = √(29-1) = √28 = 2√7

Therefore, the value of (f∘g)(2) is 2√7.

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Answer: 92.5

Step-by-step explanation:

Answer:

w = 92.5

Step-by-step explanation:

You cannot use Law of Sine in this case.

Use Law of Cosine.

They gave you 2 side length and one angle.

plug in your values into the equation and solve for w.

Let just use u, v, & w: Let u be 25 and v be 84.

[tex]w^2 = u^2 + v^2 - 2*u*v*cos(W)[/tex]

[tex]w^2 = 25^2 + 84^2 - 2*25*84*cos(102)[/tex]°

[tex]w^2=625+7056-4200*cos(102)[/tex]

[tex]w^2=7681-4200*(-0.2079116908)[/tex]

[tex]w^2=7681+873.2291014[/tex]

[tex]w^2=8554.229101[/tex]

[tex]w=\sqrt{8554.229101}= 92.48907558[/tex]

a. The proportion of students have scores less than 380 is 11.51%.

b. The proportion of students have scores greater than 639 is 8.23%.

1. Using the z-score formula:

We can calculate that score of 380 corresponds to a z-score of -1.2 since z = (x - μ) / σ.

Using a standard normal distribution table, we find that:

2. Similarly, a score of 639 corresponds to a z-score of 1.39.

Using a standard normal distribution table, we find that:

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Answer:

Step-by-step explanation:

B. 40.63

Answer:

Step-by-step explanation:

B. 40.63

Answer:

[tex]\$1342.64[/tex]

Step-by-step explanation:

We can represent the value [tex]A[/tex] of a quantity [tex]P[/tex] compounded continuously for [tex]t[/tex] years at [tex]r[/tex] rate of interest as:

[tex]A = P\cdot e^{rt}[/tex]

This formula uses the mathematical constant [tex]e[/tex] (approx. 2.72), which is the theoretical limit for continuous compounding.

Plugging the given values into the formula:

[tex]A = \$900 \cdot e^{(0.04 \, \cdot \, 10)}[/tex]

We can now solve for [tex]A[/tex].

↓ simplifying [tex]e[/tex]'s exponent

[tex]A = \$900 \cdot e^{0.4}[/tex]

↓ plugging into a calculator

[tex]A \approx \$1342.64222788[/tex]

↓ rounding to the nearest cent

[tex]\boxed{A \approx \$1342.64}[/tex]

Answer:

  x° = 36°

Step-by-step explanation:

You want to find the angle between a secant and a tangent to a circle, where the intercepted arcs are 126° and 54°.

The angle at D, labeled x°, is half the difference of the intercepted arcs:

  x° = (126° -54°)/2 = 72°/2

  x° = 36°

__

Additional comment

The same relationship applies for the angle between two secants.

This is easy to prove by considering triangle ADE. Angle DAE is half of arc CE. The exterior angle to the triangle at E is half of arc AE. That exterior angle is equal to the sum of the remote interior angles at D and A:

  AE/2 = x° + CE/2   ⇒   x° = (AE -CE)/2

Answer:

the answer os 53

Step-by-step explanation:

Using the Pythagorean's theorem we can see that the length of the ramp is 6.32ft

We know that the ramp is a right triangle whose legs are 2 ft and 6 ft. Remember that by Pythagorean's theorem we know that the square of the hypotenuse is equal to the sum of the squares of the legs.

Then the length of the ramp L will be:

L² = (2ft)² + (6ft)²

L = √((2ft)² + (6ft)²)

L = 6.32ft

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Answer:

We can use the vector addition property to find the coordinates of the points M, N, and I.

Let

[tex]\bold{ A = (x_1, y_1), B = (x_2, y_2), C = (x_3, y_3), and\: D = (\frac{x_2+x_3}{2}, \frac{y_2+y_3}{2})}[/tex]

To find M, we use the fact that MA + MB = 0. Therefore, we have:

MA = -MB

A - M = -(B - M)

A - M = -B + M

2M = A + B

M =[tex]\frac{A + B}{2}[/tex]

So, the coordinates of point M are

[tex]\bold{(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})}[/tex]

To find N, we use the fact that 3NA + NC = 0. Therefore, we have:

3NA = -NC

3A - N = -(C - N)

3A - N = -C + N

4N = 3A + C

N =[tex]\frac{ 3A + C}{4}[/tex]

So, the coordinates of point N are [tex]\bold{(\frac{3x_1+x_3}{4},\frac{ 3y_1+y_3}{4})}[/tex]

To find I, we use the fact that IM + 2IN = 0. Therefore, we have:

IM = -2IN

M - I = -2(N - I)

M - I = -2N + 2I

3I = M + 2N

I = [tex] \frac{(M + 2N)}{3} [/tex]

Substituting the values of M and N that we found earlier, we get:

I = (A + B + 2(3A + C)/4)/3

Simplifying this expression, we get:

I = [tex]\frac{(7A + 2B + 2C)}{12}[/tex]

So, the coordinates of a point I are[tex]\bold{(\frac{7x_1+2x_2+2x_3}{12}, \frac{7y_1+2y_2+2y_3}{12}).}[/tex]