Please help me with question 25. And please include an explanation.

Step-by-step explanation:

2pi/3 is the same thing as 2pi/3 * 180/pi = 120 degrees

From your choices, we know that it is either c or d.

sin(120) is in the 2nd quadrant, so the x is negative and the y is positive. Remember that sin corresponds to the y value, so it is positive. Therefore option (d) is not true.

The cost for 5 t-shirts, including Sales tax, is $53.

The cost of 5 t-shirts with a price of $10 each and a sales tax of 6%, we need to multiply the total price of the t-shirts by the sales tax rate and add it to the original price.

The original price of one t-shirt is $10. Therefore, the total price of 5 t-shirts is:

$10 * 5 = $50

To calculate the sales tax, we need to multiply the total price by the sales tax rate of 6%:

$50 * 6% = $50 * 0.06 = $3

Adding the sales tax to the total price:

$50 + $3 = $53

Therefore, the cost for 5 t-shirts, including sales tax, is $53.

The correct answer is: $53.

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The area of the sector is approximately 36.0 ft²

To find the area of the sector formed by a central angle of 260° in a circle with a radius of 4 ft, you can use the formula:

Area of sector = (θ/360°) * π * r²

where θ is the central angle in degrees, π is the value of pi, and r is the radius.

Plugging in the values:

θ = 260°

r = 4 ft

π = 3.14

Area of sector = (260/360) * 3.14 * 4²

Area of sector = (0.7222) * 3.14 * 16 = 36.3 square feet

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627 x 26 equals 16,302 when solved using the standard algorithm.

The steps below can be used to solve the multiplication issue 627 x 26 using the conventional algorithm:

627 and 26 should be written one above the other, with the larger number appearing above and the smaller number beneath.

Start by adding each digit of the top number to the ones digit of the bottom number (six). Write the answers below the line after multiplying 6 by 7 and then by 2.

1254 -- a 6 x 7 partial product

1254 -- a half 6 x 2 product

Repeat the process by moving the bottom number one position to the left after that. Multiply 2 by 7 and then by 2, and then write the results one space to the left of the line below the line.

1254 x 627

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Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for [tex]S_{n}[/tex] , that is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (a₁ + [tex]a_{n}[/tex] )

with a₁ = 5 and [tex]a_{n}[/tex] = a₂₇ = 83 , then

S₂₇ = [tex]\frac{27}{2}[/tex] (5 + 83) = 13.5 × 88 = 1188

The surface integral in terms of ρ and θ ∫∫S.((6y - 5)e^(x^2))

To evaluate ∬s.curl F•nds using Stokes' Theorem, we first need to find the curl of the vector field F and then compute the surface integral over the given surface S.

Given vector field F = (6yz)i + (5x)j + (yz(e^(x^2)))k, let's find its curl:

∇ × F = ∂/∂x (yz(e^(x^2))) - ∂/∂y (5x) + ∂/∂z (6yz)

Taking the partial derivatives, we get:

∇ × F = (0 - 0) i + (0 - 0) j + (6y - 5)e^(x^2)

Now, let's parametrize the surface S, which is the portion of the paraboloid z = (1/4)x^2 + y^2 for 0 ≤ z ≤ 4. We can use cylindrical coordinates for this parametrization:

r(θ, ρ) = ρcos(θ)i + ρsin(θ)j + ((1/4)(ρcos(θ))^2 + (ρsin(θ))^2)k

where 0 ≤ θ ≤ 2π and 0 ≤ ρ ≤ 2.

Next, we need to find the normal vector n to the surface S. Since S is oriented upward, the normal vector points in the positive z-direction. We can normalize this vector to have unit length:

n = (∂r/∂θ) × (∂r/∂ρ)

Calculating the partial derivatives and taking the cross product, we have:

∂r/∂θ = -ρsin(θ)i + ρcos(θ)j

∂r/∂ρ = cos(θ)i + sin(θ)j + (1/2)(ρcos(θ))k

∂r/∂θ × ∂r/∂ρ = (-ρsin(θ)i + ρcos(θ)j) × (cos(θ)i + sin(θ)j + (1/2)(ρcos(θ))k)

Expanding the cross product, we get:

∂r/∂θ × ∂r/∂ρ = (ρcos(θ)(1/2)(ρcos(θ)) - (1/2)(ρcos(θ))(-ρsin(θ)))i

+ ((1/2)(ρcos(θ))sin(θ) - ρsin(θ)(1/2)(ρcos(θ)))j

+ (-ρsin(θ)cos(θ) + ρsin(θ)cos(θ))k

Simplifying further:

∂r/∂θ × ∂r/∂ρ = ρ^2cos(θ)i + ρ^2sin(θ)j

Now, we can calculate the surface integral using Stokes' Theorem:

∬s.curl F•nds = ∮c.F•dr

= ∫∫S.((∇ × F)•n) dS

Substituting the values we obtained earlier:

∫∫S.((∇ × F)•n) dS = ∫∫S.((6y - 5)e^(x^2))•(ρ^2cos(θ)i + ρ^2sin(θ)j) dS

We can now rewrite the surface integral in terms of ρ and θ:

∫∫S.((6y - 5)e^(x^2))

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Given statement solution is :-The ingredients available in the warehouse, a maximum of 15 "Special" cakes and 10 "Supreme" cakes can be made.

To determine how many cakes they can make of each specialty, we need to review the amount of ingredients available in the warehouse and then calculate how many cakes can be made with that amount.

Amount of ingredients in the warehouse:

Sugar: 10 kilos

Eggs: 120

For the "Special" cake:

It requires half a kilo of sugar per cake.

It requires 8 eggs per cake.

Sale price: $200 per cake.

To calculate how many "Special" cakes can be made, we divide the amount of sugar and eggs available in the store by the ingredients required per cake:

"Special" cakes that can be made:

Available sugar / Sugar required per cake = 10 kilos / 0.5 kilos = 20 cakes

Eggs Available / Eggs Required per Cake = 120 Eggs / 8 Eggs = 15 Cakes

Therefore, with the ingredients available in the store, a maximum of 15 "Special" cakes can be made.

For the "Supreme" cake:

It requires a kilo of sugar per cake.

It requires 8 eggs per cake.

Sale price: $270 per cake.

To calculate how many "Supreme" cakes can be made, we again divide the amount of sugar and eggs available in the store by the ingredients required per cake:

"Supreme" cakes that can be made:

Available sugar / Sugar required per cake = 10 kilos / 1 kilo = 10 cakes

Eggs Available / Eggs Required per Cake = 120 Eggs / 8 Eggs = 15 Cakes

Thus, with the ingredients available in the warehouse, a maximum of 10 "Supreme" cakes can be made.

In short, with the ingredients available in the warehouse, a maximum of 15 "Special" cakes and 10 "Supreme" cakes can be made.

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The polynomial with the given zeros is [tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i.[/tex]

To find the factors corresponding to the given zeros, we can use the fact that if a number is a zero of a polynomial, then (x - zero) is a factor of the polynomial.

Given zeros: 5, -3/4, 2i

For the zero 5, the corresponding factor is (x - 5).

For the zero -3/4, the corresponding factor is (x + 3/4).

For the zero 2i, the corresponding factor is (x - 2i).

To find the complete polynomial, we can multiply these factors together:

[tex](x - 5)(x + 3/4)(x - 2i)[/tex]

To simplify the polynomial, we can multiply the factors using the distributive property:

[tex](x^2 - 5x + (3/4)x - 15/4)(x - 2i)[/tex]

Combining like terms:

[tex](x^2 - (17/4)x - 15/4)(x - 2i)[/tex]

Expanding further:

[tex]x^3 - (17/4)x^2 - (15/4)x - 2ix^2 + (34/4)ix + (30/4)i[/tex]

Simplifying and combining like terms, we have the final polynomial:

[tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i[/tex]

Therefore , the polynomial with the given zeros is [tex]x^3 - (25/4)x^2 + (19/4)ix + (30/4)i.[/tex]

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Answer:

An ordinary annuity has payments made at the end of each period, while an annuity due has payments made at the beginning of each period.

Now, let's calculate the future value of the annuity due, given that the future value of the ordinary annuity is $100,000 and the interest rate is 5 per cent.

Step 1: Determine the future value factor of the ordinary annuity.

Future Value of Ordinary Annuity (FVOA) = $100,000

Interest Rate (r) = 5% = 0.05

Number of Periods (n) = 5 years

Step 2: Use the FVOA formula to find the annuity payment (PMT).

FVOA = PMT * [(1 + r)ⁿ - 1] / r

$100,000 = PMT * [(1 + 0.05)⁵ - 1] / 0.05

PMT = $18,039.37 (approx.)

Step 3: Calculate the future value of the annuity due (FVAD).

FVAD = PMT * [(1 + r)ⁿ - 1] / r * (1 + r)

FVAD = $18,039.37 * [(1 + 0.05)⁵ - 1] / 0.05 * (1 + 0.05)

FVAD = $105,000 (approx.)

Step-by-step explanation:

Answer: Consider me the brainiest. The answer is... Decimal form =4.083

Exact form= 49/12

The mixed number form=4 1/12

How do we solve fractions step by step?

Conversion a mixed number 2  1/3 to a improper fraction: 2 1/3 = 2  1/3 = 2 3 + 1/3 = 6 + 1/3 = 7/3

To find a new numerator

A;   Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3

b) Add the answer from the previous step 6 to the numerator 1. The new numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one-third are seven-thirds.

Conversion a mixed number 1  3/4 to a improper fraction: 1 3/4 = 1  3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4

To find a new numerator:

a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4

b) Add the answer from the previous step 4 to the numerator 3. The new numerator is 4 + 3 = 7

c) Write a previous answer (new numerator 7) over the denominator 4. One and three quarters are seven quarters.

Add: 7/3 + 7/4 = 7 · 4/3 · 4 + 7 · 3/4 · 3 = 28/12 + 21/12 = 28 + 21/12 = 49/12 It

is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions.  The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12.  It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by cancelling.  In other words - seven thirds plus seven quarters is forty-nine twelfths.

The larger number is 35.Let's assume the two numbers are represented by the variables "x" and "y," where "x" is the smaller number.

Equation 1: x + y = 59 (The sum of the two numbers is 59)

Equation 2: x - y = 11 (The difference between the two numbers is 11, with the smaller number being y)

According to the given information, the sum of the two numbers is 59, which can be expressed as:

x + y = 59

The difference between the two numbers is 11, with "x" being the smaller number. This can be expressed as:

y - x = 11

We can now solve these two equations simultaneously to find the values of "x" and "y."

Rearranging the first equation to solve for "y" gives us:

y = 59 - x

Substituting this value of "y" into the second equation:

(59 - x) - x = 11

Simplifying the equation:

59 - 2x = 11

Subtracting 59 from both sides:

-2x = 11 - 59

-2x = -48

Dividing both sides by -2:

x = -48 / -2

x = 24

Therefore, the smaller number is 24. To find the larger number, we substitute the value of "x" into the first equation:

24 + y = 59

y = 59 - 24

y = 35.

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1) The area of a circle circumscribed about a square is 307.7 cm².

2.a.) The angle ACB is 39 degrees.°.

2b.) The value of x is 5.42.

We shall find the radius to determine the area of a circle.

First,  find the side length of the square:

Since the perimeter of the square = 56 cm, then, each side of the square is 56 cm / 4 = 14 cm.

Next, find the diagonal of the square, using the Pythagorean theorem:

Diagonal = the diameter of the circumscribed circle.

Diagonal² = side length² + side length²

= 14 cm² + 14 cm²

= 196 cm² + 196 cm²

= 392 cm²

Take the square root of both sides:

Diagonal = √392 cm ≈ 19.80 cm (rounded to two decimal places)

Then, the radius of the circle which is half the diagonal:

Radius = Diagonal / 2 ≈ 19.80 cm / 2 ≈ 9.90 cm (rounded to two decimal places)

Finally, compute the area of the circle using the formula:

Area = π * Radius²

Area = 3.14 * (9.90 cm)²

Area ≈ 307.7 cm² (rounded to two decimal places)

Therefore, the area of the circle that is circumscribed about a square with a perimeter of 56 cm is 307.7 cm².

2. a) We use the property of angles in a circle to solve for angle ACB: an angle inscribed in a circle is half the measure of its intercepted arc.

Given that arc AB has a measure of 78°, we can find angle ACB as follows:

Angle ACB = 1/2 * arc AB

= 1/2 * 78°

= 39°

Therefore, the angle ACB is 39 degrees.

2b.) To solve for the value of x, we use the information that the angle ADB =  (3x - 12)⁴.

Given that angle ADB is (3x - 12)⁴, we can equate it to the measure of the intercepted arc AB, which is 78°:

(3x - 12)⁴ = 78

Solve the equation for x, by taking the fourth root of both sides:

∛∛((3x - 12)⁴) = ∛∛78

Simplify,

3x - 12 = ∛(78)

Isolate x by adding 12 to both sides:

3x - 12 + 12 = ∛(78) + 12

3x = ∛(78) + 12

Finally, divide both sides by 3:

x = (∛(78) + 12) / 3

x = (4.27 +12) / 3

x = 5.42

So, x is 5.42

Therefore,

1) The area of the circle is 154 cm².

2a.) Angle ACB is equal to 102°.

2b.) The value of x is 5.42

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Answer:

Volume = 7.912

Step-by-step explanation:

V = πr²h

V = 3.14 × 3/4 × 3/4 × 6 3/4 ( π = 22/7 or 3.14 )

V = 3.14 × 9/16 ×18/4

V = 3.14 × 0.56 × 4.5

V = 7.912

This has to do with proprotions.

RV is 12

AE/AC = BF/BD

BD/AC = BF/AE

DF/CE = BD/AC

In mathematics, proportions express the relationship between two ratios.

They compare two equivalent fractions or ratios and state that they are equal, allowing us to solve for unknown values in a proportional relationship.

To solve the equation (24/32) = (RV/16), we can cross-multiply and solve for RV.

Cross-multiplying gives us

24 * 16 = 32 * RV

Simplifying further

384 = 32 * RV

To isolate RV, divide both sides of the equation by 32

384 / 32 = RV

Simplifying the division

12 = RV

Therefore, the value of RV in the equation (24/32) = (RV/16) is 12.

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Answer:

[tex]x \leq -4[/tex]

There will be a filled-in hole at -4.

Step-by-step explanation:

We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)

[tex]-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4[/tex]

The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.

For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.

In another example, [tex]x \leq -4[/tex], -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.

A filled-in hole means the number is included in the inequality, while an empty one means it isn't.

In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.

Answer:

$393,120

Step-by-step explanation:

To find the decrease in the house's value in dollars, we need to calculate 9% of the initial value:

Decrease in value = (Initial value) * (Percentage decrease) = $432,000 * 9%

Converting the percentage to a decimal:

Decrease in value = $432,000 * 0.09 = $38,880

The house's value decreased by $38,880.

Now, to find the current value of the house, we need to subtract the decrease in value from the initial value:

Current value = Initial value - Decrease in value = $432,000 - $38,880 = $393,120

The current value of the house is $393,120.

Hope this helps!

P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q

T T T T T F F F F F T    T

F T T F F T T T T T F    F

P F T F F T T T T T F     F

-P T T F F T T T T T F     F

-Q T T T T F T F F F T     T

-P V -Q T T F F T T T T T F

-P -> Q T T F F T T T T T F

-P -> -Q T T F F T T T T T F

P <-> Q T T T T F T T T T F

Here is a more detailed explanation of how I filled out the table:

P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.

P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.

-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.

-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.

-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.

-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.

-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.

P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.

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Answer:

26 units

Step-by-step explanation:

Step 1: Determine the y-intercepts of the lines:

The first line y = -5x has a y-intercept of 0 (when x = 0).

The second line y = -5x + 26 has a y-intercept of 26 (when x = 0).

Step 2: Calculate the difference in the y-intercepts:

Difference = |0 - 26| = 26 units

Therefore, the distance between the pair of parallel lines y = -5x and y = -5x + 26 is 26 units.

Trevor’s total investment is $2850.30.(Option-c)

Trevor buys 80 shares of Upton Group and 70 shares of TJH Small-Cap. The offer price for Upton Group is $18.96 and the offer price for TJH Small-Cap is $19.05. Therefore, Trevor's total investment is:

80 shares * $18.96 + 70 shares * $19.05 = $1516.80 + $1333.50 = $2850.30

The offer price is the price at which a mutual fund is sold to investors. It is calculated by adding the net asset value (NAV) of the fund to the sales charge. The NAV is the value of the fund's assets minus its liabilities. The sales charge is a fee that is paid to the fund's distributor.

Trevor's total investment of $2,850.30 is the sum of the offer prices of the two funds he purchased. The offer price of Upton Group is $18.96 per share, and the offer price of TJH Small-Cap is $19.05 per share. Trevor purchased 80 shares of Upton Group and 70 shares of TJH Small-Cap, so his total investment is 80 shares * $18.96 + 70 shares * $19.05 = $1516.80 + $1333.50 = $2850.30.(Option-c)

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