Dan and Paul went shopping at a department store

Dan spent $4 more than Paul spent

Dan spent $24 at the store

Which equation could be used to calculate p, the amount Paul spent?


A. P-4=24

B. 4p=24

C. 4+24=p

D. 4+p=24

The interest amount (simple interest ) on the loan amount $5315 at 5% from 10th aug to 23rd dec. of same year is $105.50

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

For this case, we're specified that:

Converting this time in terms of year, we get:

Aug has 31 days, Sept has 30 days, Oct. has 31 days, Nov has 30 days.

From 10th aug, till its last, there went 22 days.

Whole sept and oct and nov. was spent (30+31+30 = 91 days)

And then there were 22 days of december(23rd day not covered assumingly)

So, total days = 22+22+91 = 145 days.

Assuming averagely 365.25 days in an year, we get the average time for which the interest will be calculated as:

[tex]\dfrac{145}{365.25} \approx 0.397 \: \rm years[/tex]

Thus, we get: the amount of interest as:

[tex]I = \dfrac{P \times R \times T}{100}\\\\I \approx \dfrac{5315 \times 5\times 0.397}{100} \approx 105.50 \: \rm dollars[/tex]

Thus, the interest amount (simple interest ) on the loan amount $5315 at 5% from 10th aug to 23rd dec. of same year is $105.50

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The options that are prime polynomials are,

15x^2  +10x -9x+7, 8x^3+20x^2+3x+12 and 11x^4+4x^2-6x^2-16

A polynomial with integer coefficients that cannot be factored into polynomials of lower degree, also with integer coefficients, is called an irreducible or prime polynomial.

To determine all options in order to check that the polynomials are prime or not:

1). 15x^2  +10x -9x+7

5x(3x + 2) - (9x - 7)

Therefore,  this polynomial can not be factored into lower degree polynomial. Therefore, it is a prime polynomial.

2). 20x^2-12x+30x-18

4x(5x - 3)+6(5x-3)

(4x + 6)(5x - 3)

Therefore,  this polynomial is converted into a lower degree polynomial. Therefore, it is not a prime polynomial.

3). 6x^3+14x^2-12x-28

2x^2(3x+7)-4(3x+7)

(2x^2-4)(3x+7)

Therefore,  this polynomial is converted into a lower degree polynomial. Therefore, it is not a prime polynomial.

4). 8x^3+20x^2+3x+12

4x^2(2x+5)+(3x+20)

Therefore, this polynomial can not be factored into lower degree polynomial. Therefore, it is a prime polynomial.

5). 11x^4+4x^2-6x^2-16

x^2(11x^2+4)-2(3x^2+8)

So, this polynomial can not be factored into lower degree polynomial. Therefore, it is a prime polynomial.

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Answer:

they sold 1,397,262,266 less seeds this season but made 1,397,262,266 last season

Step-by-step explanation:

2,995,748,111 - 1,598,485,845 = 1,397,262,266

Answer:

Any number that can be written as a ratio (or fraction) of two integers

Step-by-step explanation:

Answer:

A rational number is a number that can be written as a fraction of two integers.

This makes the last option A number that can be written as a fraction correct

The ground speed (G) is given as

.[tex]G=\sqrt{(600\dfrac{\sqrt{3}}{2}+20)^2+(300+40\dfrac{\sqrt{3}}{2}})^2}[/tex]

The correct potion is B.

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

An airplane is flying in the direction of 30 degrees South of West at 600 mph. A wind is blowing in the direction of 60 degrees North of East at 40 mph.

It means the airplane is flying in the opposite direction of the wind.

The component of an airplane will be

[tex]x=-600sin30\\\\x=\dfrac{-600}{2}=-300\\\\y=-600cos30\\\\y=\dfrac{-600 \sqrt{3}}{2}}[/tex]

The component of wind will be

[tex]x=40cos60\\\\x=\dfrac{40}{2}=20\\\\y=40sin45\\\\y=\dfrac{40\sqrt{3}}{2}}[/tex]

Then the ground speed will be

.[tex]G=\sqrt{(600\dfrac{\sqrt{3}}{2}+20)^2+(300+40\dfrac{\sqrt{3}}{2}})^2}[/tex]

Then the correct potion is B.

More about the vector link is given below.

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Answer:

C and B

Step-by-step explanation:

C and B

Answer:

8

Step-by-step explanation:

Just move the modellus

x-5=3

x=5+3

x=8

Answer:

D

Step-by-step explanation:

I think it is sorry if I'm wrong

The factors of the expression are [tex]\rm(3 - 7x^2)(x - 3)[/tex]

First group the first two terms and the last two terms together respectively.

The factors of the expression are given by;

[tex]\rm= -7x^3 + 21x^2 + 3x - 9\\\\=-7x^2(x - 3) + 3(x - 3)\\\\=(3 - 7x^2)(x - 3)[/tex]

Hence, the factors of the expression are [tex]\rm \rm(3 - 7x^2)(x - 3)[/tex].

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Dilating the triangle ABC would create a triangle with a different side length from triangle ABC

From the diagram, we have the coordinates to be:

A = (2,-5)

B = (2,4)

C = (-4,3)

The dilation rule is given as:

(x,y) => (1.5x, 1.5y)

So, we have:

A' = (3,-7.5)

B' = (3,6)

C' = (-6,4.5)

See attachment for the image of the dilation

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Question

An isosceles right triangle has legs that are 10 centimeters long. To the nearest tenth of a centimeter, what is the length of the hypotenuse?​

Answer:

14.1 cm

Step-by-step explanation:

is a right triangle and we use the Pythagorean theorem

√(10² + 10²) =

√(100 + 100) =

√200 =

14.1

The total annual FICA tax for an annual salary of $165,000 would be 12622.50. So, option d is correct.

Income tax is a tax applied on individuals or entities concerning income or profit earned by them.

The categories are 6.2% as social security tax 1.45% as Medicare tax 0.9% as Medicare surtax for employees earning more than $200,000

Medicare Tax

6.2% x 165000

= 10230

Social Security Tax

= 1.45% x 165000

= 2392.5

Since 10230+2392.5 = 12622.50

Social security is taxed at 6.5 percent and medicare is taxed at 1.45 percent. it will always be that number unless the government changes it.

The categories are 6.2% as social security tax 1.45% as Medicare tax 0.9% as Medicare surtax for employees earning more than $200,000

As the income of the employee is less than $200000, so there will be no medical surtax.  

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Answer:

a. 901.41

(I just took the test)

Answer: 81/16

Step-by-step explanation:

When you have a negative exponent, it is equivelant to taking the reciprocal of the exponential and making the exponent positive:

[tex](2/3)^-^4=\frac{1}{(2/3)^4}[/tex]

Distribute the exponent to the base. We are able to do this because the base is composed of a single term. If it were composed of addition and subtraction, you cannot distribute the exponent:

[tex]\frac{1}{(2/3)^4}=\frac{1}{(2^4/3^4)}=\frac{1}{(16/81)}[/tex]

Dividng by a fraction is equivalent to multiplying by the reciprocal:

[tex]\frac{1}{(16/81)}=1\frac{81}{(16)}=\frac{81}{16}[/tex]

Answer:

14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2

Step-by-step explanation:

(7x^2)(2x^3+5)(x^2-4x-9)

(14x^5+35x^2)(x^2-4x-9)

14x^7 -56x^6 - 126x^5 + 35x^4 -140x^3 - 315x^2

I don't see a correct answer option.

The one written as:

O 14x7-56x8-126x5+35x4-140X3-315x2

comes the closest, but it is not exact.  I get 56x^6, not 56x^8.

Answer:

45 people

Step-by-step explanation:

1) Add all of the origanal visitors (376)

2) Find the ratio (28/376) = 0.0744

3) Either 28/376 * 600 OR 0.0744 * 600 (I would recomend the fraction for more accurate answers, but because it says to round to the nearest whole number either will work, but you should still use fraction)

4) 44.6908

5) Round to 45 people

Answer:

600 visitors expected. Add 28 visitors for buying more than one costume and you get 628 visitors. I think you are complicating it.

Step-by-step explanation:

Answer:

The answer is

→ Option D.) 40

Step-by-step explanation:

32 ÷ 4 + 4 x 8

= 32 ÷ 4 = 8

= 8 + 4 x 8

= 8 + 32

= 40

Therefore, Option D.) 40 is your answer.

Hope this helped! :^)

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- ✨7272033Alt✨

Submitted on 4/19/2022 at 7:25 PM

(To avoid plagarism, by users whom decide to copy.)

Answer:

Step-by-step explanation: 36 see attachment

The surface area of the larger sphere with a volume of 64π cm³ comes to be 16π∛36 cm³.

The volume of the larger sphere = 64π cm³

Suppose the radius of the larger sphere is r

So, 4/3*π*r³ =64π

r³=48

r=2∛6

The surface area of a sphere is 4πr² where r is the radius.

So, the surface area of the larger sphere = 4π(2∛6)²

The surface area of the larger sphere = 16π∛36

Hence, The surface area of the larger sphere with a volume of 64π cm³ is 16π∛36 cm³.

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Answer:

no

Step-by-step explanation:

Answer:

2x+3

or

2N + 3

The angles are in correct order greatest to least is 330°, 5π/3, 7π/6, 2π/3, π/2.

A reference angle means the measure of the smallest, positive, acute angle that is formed by the terminal side of the angle. Therefore, positive reference angles possess terminal sides in the first quadrant.

Lets convert all the values into degrees

330° = 330°

π/2 = 180/2 = 90°

5π/3 = 300°

7π/6 = 210°

2π/3 = 120°

Arrange them from greatest to lowest.

330°, 300°, 210°, 120°, 90°

or

330°, 5π/3, 7π/6, 2π/3, π/2

Hence, the angles are in correct order greatest to least is 330°, 5π/3, 7π/6, 2π/3, π/2.

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Answer:

d

Step-by-step explanation:

thats what the guy above me said

Answer: C

Step-by-step explanation:

[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]

════════════════════

Lily's basketball team won 4/5 of their games. Lily scored points 2/3 of the games her team won. In waht fraction of her team's winning games did Lily score points?

Answer: =D.[tex] \frac{5}{6}[/tex]

Solution:

[tex]\frac{ 2 }{ 3 } \div \frac{ 4 }{ 5 } =[/tex]

[tex]\frac{2}{3}\times \left(\frac{5}{4}\right) [/tex]

[tex]\frac{2\times 5}{3\times 4} [/tex]

[tex]\frac{10}{12} [/tex]

=[tex] \frac{5}{6}[/tex]

I reduced the fraction [tex] \frac{10}{12}[/tex] into the Lowest terms by doing extracting and cancelling out the [tex]2[/tex]

=[tex] \frac{5}{6}[/tex]

So the answer is letter D.[tex] \frac{5}{6}[/tex]

════════════════════

Explanation:

#Carry on learning

Answer:

the answer is (-5/35) or (-1/7)

Step-by-step explanation:

yea i think that explains it pretty nicely

Answer:

[tex]y=-\frac{1}{5}x+4[/tex]

Step-by-step explanation:

Step-by-step explanation:

8) 52

9) (135/2) or 67.5

10)(32/5) or 6.4

Answer:

Solve for 's' using inverse operations;

4s + 3 = 9

Get rid of constants first.

By doing this, we subtract 3 from both sides because the inverse operation of addition is subtraction.

-3           -3

4s = 6

Isolate 's' by dividing 4 from both sides because the inverse operation of multiplication is division.

÷ 4 ÷ 4

s = 6/4 which equals 1.5 therefore the value of 's' to make this equation true is 1.5.

Answer:

Hope the picture will help you....

Answer:

C. 14 units

Step-by-step explanation:

Perimeter is the distance around the outside of the shape. Add up all the sides. See image.