What is the approximate volume of a half sphere with a diameter of 8 cm?

The input value for the expression is 1 and the remainder is -15.

The Remainder Theorem begins with an unnamed polynomial p(x), where "p(x)" simply means "some polynomial p with variable x". The Theorem then discusses dividing that polynomial by some linear factor x a, where an is simply a number.

Given polynomial is 5x⁴⁵ - 3x¹⁷ +2x⁴ - 19 and is divided by x + 1. Find the value of the polynomial at 1 and then calculate the remainder by synthetic solution.

F(x) = 5x⁴⁵ - 3x¹⁷ +2x⁴ - 19

F(1) = 5 - 3 + 2 - 19

F(1) = -19 + 4

F(1) = -15

The remainder will be calculated by synthetic calculation,

1 __5 ___-3___2_____-19

 |

 | ______5___ 2______4          

      5         2      4          -15

The remainder of the given expression is -15.

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Answer:

[tex]x=1[/tex]

Step-by-step explanation:

[tex]2^{2x}-2^2 2^x-12=0 \\ \\ (2^x)^2-4(2^x)-12=0[/tex]

Factoring the quadratic in [tex]2^x[/tex],

[tex](2^x+6)(2^x-2)=0 \\ \\ 2^x=-6,2 \\ \\ 2^x=2 \implies x=1 \\ \\ 2^x=-6 \implies x \notin \mathbb{R} \\ \\ \therefore x=\log_{2} (6)[/tex]

We need to use Right Angled Triangle Properties.

PR≈15 and QR≈12 is the length of the sides.

What is a Right Angled Triangle?

According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of its angles is a right angle (90o). Triangle PQR is a right triangle in the illustration, and its components are its base, height, and hypotenuse. Here, QR is the base, PQ is the height, and PR is the hypotenuse. The essential side of a right triangle is its hypotenuse, which is also its largest side and sits across from the triangle's right angle.

In a right triangle we have: (Hypotenuse)2 = (Base)2 + (Altitude)2

Area of a right triangle = (1/2 × base × height) square units.

PR is the Hypotenuse of the Triangle.

PQ=9

Angle ∡PQR=37° and Angle ∡RPQ=53°

So Sin(theta)=opposite side/Hypotenuse

⇒Sin(37°)=9/Hypotenuse

⇒Hypotenuse=9/0.6018

⇒Hypotenuse=14.955

PR⇒14.955

We know that (Hypotenuse)2 = (Base)2 + (Altitude)2

⇒(14.955)2=(9)2+(QR)2

QR=11.9438

PR≈15 and QR≈12

We need to use Right Angled Triangle Properties.

PR≈15 and QR≈12 is the length of the sides.

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Final conclusion would be that the difference between the means of the two samples is not statistically significant.

What is Null Hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

It is not possible to test the claim that the two samples come from populations with the same mean without more information about the samples themselves. In order to test this claim, you need to have the sample data, the sample sizes, and the standard deviations of the samples. You can then use a t-test for independent samples to determine whether the difference between the means of the two samples is statistically significant.

The t-test is a statistical test that is used to compare the means of two samples. The test statistic for the t-test is the difference between the means of the two samples divided by the standard error of the difference. The degree of freedom for the t-test is the sum of the sample sizes minus 2. The significance level, alpha, is the probability of making a type I error, which is the probability of rejecting the null hypothesis when it is true. The rejection region for the t-test is the set of values of the test statistic for which the null hypothesis is rejected.

If the test statistic does not fall in the rejection region, you cannot reject the null hypothesis, and you must conclude that the difference between the means of the two samples is not statistically significant.

Final conclusion would be that the difference between the means of the two samples is not statistically significant.

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The equation that matches the graph is 7x-30y=-275

We should know that an equation is a mathematical expression in which two sides are equal.

The equation of a line is the equation formed with the slope of the straight line

The slope of the of the is determined taking the points

[tex]M=\frac{Y_{2}-Y_{1} }{X_{2}-X_{1} }[/tex]

Slope=(7-1)÷(35-5)

m=1/5

The equation of the line is

1/5 = (y-1)÷(x-35)

Cross multiplying the equation

7x-245=30y-30

Rearrange,

7x-30y=-30-245

7x-30y=-275

In conclusion the equation to match the graph is 7x-30y=-275

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The journal entry is given in answer part b

A discount coupon is defined as a certificate that entitles the customer to avail of a reduction in the invoice price if the terms mentioned on it are met. It is a technique applied by the sellers to expand sales.

Given that, Clarks Inc., a shoe retailer, sells boots in different styles. In early November, the company starts selling “SunBoots” to customers for $70 per pair. When a customer purchases a pair of SunBoots, Clarks also gives the customer a 30% discount coupon for any additional future purchases made in the next 30 days. Customers can’t obtain the discount coupon otherwise. Clarks anticipates that approximately 20% of customers will utilize the coupon, and that on average those customers will purchase additional goods that normally sell for $100.

a) Two performance obligations are associated with contract. The first one is related to the sun boots, and the other one is associated with discount coupon provided. The discount coupon would be considered a separate obligation because it gives a certain right to the customers that they would not have received if the sale was not made to them.

b) Journal entry =

Account title and explanation            Debit ($)                    Credit ($)

Cash (1000×$70)                                    $70000                  

Sales Revenue ($70,000-$6000)                                           $64000

Deferred Revenue                                                                    $6000

Now,

Computation of the deferred revenue:

Deferred revenue = pairs sold × Average purchase price × Discount × Redemption of coupon

= 1000 × 100 × 30% × 20%

= $6000

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∠U is congruent ∠S because all right angles are congruent.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence. When two sides and their included angle in one triangle are equal to two sides and their included angle in another, two triangles are said to be congruent. This concept of congruence appears to be based on the idea of a "rigid body," which may be moved without affecting the internal relationships between its components.

Given

∠U ≅ ∠S

All right angles are congruent.

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Answer:

Step-by-step explanation: 9 multiplied by .95 = $8.55 before tax

Alex's speed in the first half of the time is 12 miles per hour

Information from the problem include:

For the first half of the time, Alex biked a 48-mile trail in 4 hours.

he biked twice as fast as he did the second half of the time.

Average speed is calculated using the ratio of distance to time spent

this is represented by the formula

= distance / time

The speed for the first half is  solved as below

= 48 mile / 4 hours

= 12 mile / hours

= 12 mph

speed for the first half is 12 mph

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Answer: 1.0017805194 ounces

Step-by-step explanation:

To change 28.4 g to oz divide the mass in grams by 28.349523125. The 28.4 grams to ounces formula is [oz] = [28.4] / 28.349523125. Thus, we get (all results rounded to 2 decimals):

28.4 g to oz = about 1 oz

28.4 g to ounces =  about 1 ounces

28.4 grams to ounces = about  1 oz

Twenty-eight point four grams to ounces equal 1 international avoirdupois ounces, the unit used to measure grocery products (mass) in retail stores in the United States for example.

The expression that represents the volume of the prism is

2 × 3 × 9 units³. That is option C.

Prism is defined as the type of polyhedron that has two polygonal faces lying in parallel planes and with the other faces parallelograms.

A prism can be of a regular shape or of an irregular shape. The volume of a regular shapes prism can be calculated using the formula stated below

volume of a prism = l × b × h

Length (l) = 9 units

Breath = 2 units

Height (h) = 3 units.

Therefore, the volume of the given prism can be calculated as 2 × 3 × 9 units³.

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The expected number of students that pick soda is 80

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

Ice cream = 40

Soda = 20

popsicle = 10

This means that the proportion of soda is

Soda = 20/(40 + 20 + 10)

Evaluate the sum

Soda = 20/70

So, we have

Soda = 2/7

For a group of 280 students, we have

Soda = 2/7 *280

Evaluate

Soda = 80

Hence, the number of students is 80

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Answer:

C

Step-by-step explanation:

Multiply z times itself. Then multiply z times that first answer, to get z^3.

There's a formula for cubing a binomial but even if you don't remember it (like me) you can still find z^3.

But remember that i^2 = -1

This is related to sqrt(-1)= i, a definition for the imaginary number.

On the graph, go left or right for the real part and up or down for the imaginary part.

see image.

Applying the definition of congruent triangles, the values of x and y are:

x = 2; y = 6

Length of CR = 8 units.

If two triangles are congruent to each other, based on the CPCTC, all their corresponding angles, and their corresponding sides will be equal to each other.

Given that triangles NEW and CAR are congruent to each other, therefore:

NE = CA

NW = CR

EW = AR

Given the following measures:

NE = 11

EW = 12

AR = 4y - 12

CA = 4x + 3

NW = x + y

Therefore:

NE = CA

11 = 4x + 3

Solve for x:

11 - 3 = 4x

8 = 4x

8/4 = x

x = 2

EW = AR

12 = 4y - 12

12 + 12 = 4y

24 = 4y

24/4 = y

y = 6

NW = CR = x + y

Plug in the values of x and y:

CR = 2 + 6

CR = 8 units.

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The number or visits that Jim must make to make Plan A the cheaper option is more than 5 visits

An equation is the statement that illustrates the variables given. Jim has to choose between two gym membership plans.

For Plan A: $50 monthly membership fee and $10 per visit. This will be:

50 + 10v

Plan B: $25 one time membership fee and $15 per visit. This will be:

= 25 + 15v

Let v = number of visit

This will be illustrated as:

50 + 10v = 25 + 15v

Collect like terms

15v - 10v = 50 - 25

5v = 25

Divide

v = 25 / 5

v = 5

There will be more than 5 visits for a cheaper option.

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Radius = TW

Diameter = TX

Chord = UV

The length of TX is 6 units.

A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as πr².

We have,

From the figure:

Diameter = TX

Radius = TW or WX or WY

Chord = UV

WY = 3 units

TX = TW + WX = 3 + 3 = 6 units.

Thus,

TX is 6 units.

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Answer:

no melissa isn't correct she has made 3 mistakes

Step-by-step explanation:

The formula to find the arc length of a circle = θ/360 ×2××r

The formula to find the area of a sector= θ/360××r²

The only thing missing is "θ"

The arc length is given to be 15cm so basically θ/360×2×3.14×12 = 15

θ= 360×15 ÷ 2×3.14×12 = 5400÷ 75.36= 71.65

now that we found "θ" we just continue with the formula to find the area of a sector (θ/360×r²)

=71.65×3.14×12²= 90cm

(it's a bit complicated but i hope this helped i tried to simplify it as much as i could)

The Venn diagram has been drawn and the product of LCM and GCF are the same as 24 x 36.

A Venn diagram is a pictorial representation of data represented in a circle.

The intersection parts of the circle represent the commonality of both sets.

As per the given, 24 and 36

The factors of 24 are as 2³ × 3

The factors of 36 are as 2² × 3²

The common factors 2² × 3

The LCM of 24 and 36 is 72 and the GCF is 12.

LCM x GCF = 24 x 12

72 x 12 = 24 x 12

864 = 864

Hence "After drawing a Venn diagram, it was discovered that the LCM and GCF product equals 24 x 36.".

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Answer: a=3 and b=1

Step-by-step explanation:

Let p(x)=x 2 +ax+2b

If x+2 is a factor of p(x)

Then by factor theorem

p(−2)=0

⇒(−2)

2

+a(−2)+2b=0

⇒4−2a+2b=0

⇒a−b=2   ---(i)

Also given that a+b=4    ---(ii)

Adiing (i) and (ii) we get

2a=6

⇒a=3

putting a=3 in (i) we get

a−b=2

⇒3−b=2

⇒b=1

Therefore we get a=3 and b=1

Answer:

The area of the circle is 113.04 square feet.

Step-by-step explanation:

A = 3.14 × (6)² ft

A = 3.14 × 36 ft

A = 113.04 square feet.

Thus, The area of the circle is 113.04 square feet.

Answer:

28.274 square feet

Step-by-step explanation:

Multiply the radius by pi

Answer:

the price of one gallon of milk has increased by 25%.

Step-by-step explanation:

The price of one gallon of milk has increased from $3.24 to $4.05, which is an increase of $4.05 - $3.24 = $0.81. To find the percentage increase, we can divide the amount of the increase by the original price and multiply by 100%. This gives us:

(0.81 / 3.24) * 100% = 25%

Therefore, the price of one gallon of milk has increased by 25%.

The solution is 25 %

The percentage increase in the price of one gallon of milk is given by the equation P = 25 %

What is Percentage Error?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage error is the difference between the measured value and the true value , as a percentage of the true value

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Given data ,

Let the original price of the milk be A = $ 3.24

Let the increased price of the milk be B = $ 4.05

Let the percentage increase in the price be = P

Now , the equation will be

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Substituting the values in the equation , we get

Percentage increase P = [ ( 4.05 - 3.24 ) / 3.24 ] x 100

On simplifying the equation , we get

Percentage increase P = ( 0.81 / 3.24 ) x 100

Percentage increase P = 0.25 x 100

Percentage increase P = 25 %

Therefore , the value of P is 25 %

Hence , the percentage increase is 25 %

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In the aforementioned scenario, the choice you must include in your response is to find a common denominator.

One can refer to a fraction as being in its lowest term or in its simple form when the numerator and denominator are known to have no common factors besides 1. In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in daily speech.

The common denominator will be between 10 and 20, and there is a common numerator as well. The common denominator will be 20 because both can divide it and 10 is less than 20.

Finding a common denominator is the solution you should choose in the scenario mentioned above.

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The remainder term Rn is equal to (-2) raised to the power of n multiplied by e raised to the power of -2c, divided by n+1 factorial, multiplied by (x-2) raised to the power of n, for some c between x and 2.

The remainder term Rn in the nth order Taylor polynomial centered at a for the given function f(x)=e^-2x, a=2 is equal to (-2) raised to the power of n multiplied by e raised to the power of -2c, divided by n+1 factorial, multiplied by (x-2) raised to the power of n, for some c between x and 2. This remainder term represents the difference between the approximate value of the function given by the Taylor polynomial and the actual value of the function. By taking the limit as n approaches infinity, the remainder term can be used to determine the exact value of the function. The remainder term is an important concept in calculus as it is used to determine the accuracy of a given approximation.

For n=5, R5(x) = (-2)^5 e^-2c/(5+1)! (x-2)^5 for some c between x and 2.

Substituting n=5, x=7 and c=4, we have:

R5(7) = (-2)^5 e^-8/(6)! (7-2)^5

R5(7) = (-2)^5 e^-8/(720) (25)

R5(7) = (-2)^5 e^-8/18000

R5(7) = (-2)^5 e^-8/18000

R5(7) = -1.388888888 x 10^-9

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Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor.

To determine the total increase recorded in the Work in Process account related to direct labor, we need to first calculate the total standard cost of direct labor for the period and then compare it to the actual cost of direct labor.

According to the standard cost card, each unit of the product requires 2 hours of direct labor at a rate of $16.00 per hour.

This means that the total standard cost of direct labor for the period is 2 * $16.00 * 7,800 = $248,000.

Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor. Therefore, the total increase recorded in the Work in Process account related to direct labor would be $0.

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Answer:

  see below for the chart

  64 pages in 1 hour

Step-by-step explanation:

You want to fill in the chart showing the analysis of the problem statement saying HP can read 16 pages in 1/4 hour. The problem statement is requesting the number of pages he can read in 1 hour.

See below for a filled-in chart.

Analysis of the bottom line tells you that the right column is 4 times the middle column.

  1 = 4 × 1/4

  ?? = 4 × 16 = 64

Harry Potter can read 64 pages in one hour.

a) The value of x is 42.6 when k =16/3 is directly proportional to y.

b) The value of x is -56 when k is -7  is directly proportional to y.

What kind of variation is one where x and y are directly proportional?

x varies directly as y

x α y

x = ky

a) x=6 ; y = 32

x = ky

6 = k(32)

k = 16/3

if y = 8

then,

x = (16/3) * 8

= 128/3

x = 42.6

Hence, the value of x is 42.6 when k =16/3 is directly proportional to y.

b) x= 14 and y = -2

x = ky

14 = k(-2)

k = -7

if y = 8

then,

x = ky

x= (-7) 8

x = -56

Hence, the value of x is -56 when k is -7  is directly proportional to y.

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Answer: 2x+1

                  x

Step-by-step explanation:

Answer:

My sister is

18

years old.

Step-by-step explanation:

s = m + 8        Eq. 1

s + m = 28      Eq. 2

s = my sister age

m = my age

Replacing Eq. 1 in Eq. 2:

(m+8) + m = 28

2m + 8 = 28

2m = 28 - 8

2m = 20

m = 20/2

m = 10

From Eq. 1:

s = m + 8

s = 10 + 8

s = 18

Check:

from Eq. 2:

s + m = 28

18 + 10 = 28

Answer:

[tex]\frac{x}{x+2}+\frac1x=1\\\rightarrow \frac{x^2+(x+2)}{(x^2+2x}=1\\\rightarrowx^2+x+2=x^2+2x\\\rightarrowx+2=2x\\\rightarrow x=\boxed2[/tex]

Only one solution, which is two. The answer should be C. You could obviously see that if there is no squaring then there will be no extraneous solutions.