Tell which number is prime: 19, 28, 49, 63.

Answer:

1-287

2- x^4 + 2

3 -6

4 16

Step-by-step explanation:

Answer:

1) is 95   G(6) = 3(6) ^2 - 2(6) - 1

2) is F(x²) = x⁴ + 2

3)is -4      f(-1)=-1^2+3(-1)-2

4) is 16    F(3) = (3) 2 + 3(3) - 2

Step-by-step explanation:

2) F(x) = x 2 + 2

F(x2) =        F(x^2) = (x^2)^ 2 + 2x^4+2

=    f(x^2)=x^4+2

The number of votes received by winner is: 1168

Let the number of vote that is received by winning candidate be: a

and the number of votes received by other candidate be: b

It is given that:

Two candidates running for the same office received a total of 1,926 votes.    

i.e.

         [tex]a+b=1926--------------(1)[/tex]

and

The winning candidate had 410 more votes than the other candidate.

This means that:

          [tex]a-b=410--------------(2)[/tex]

Now on solving the equation by the method of elimination .

i.e.  on adding both the equation we have:

[tex]2a=1926+410\\\\i.e.\\\\2a=2336\\\\i.e.\\\\a=1168[/tex]

Now on putting the value of a in equation (1) we get:

[tex]1168+b=1926\\\\i.e.\\\\b=1926-1168\\\\i.e.\\\\b=758[/tex]

         Hence, the answer is:  1168

Final answer:

The number of hours when the cost of renting a jet ski from two different companies is the same is 5 hours, when rounded to the nearest whole number.

Explanation:

To find the number of hours where the cost to rent a jet ski from two different companies is the same, we can set up two equations to represent the cost from each company and solve for the number of hours.

For the first company, the cost C is given by C = 26 + 1h, where h represents the number of hours.

For the second company, the cost C is given by C = 14.75 + 3.25h.

To find when the costs are the same, we set the two equations equal to each other:

26 + 1h = 14.75 + 3.25h

Now we solve for h:

Subtract 1h from both sides: 26 = 14.75 + 2.25h

Subtract 14.75 from both sides: 11.25 = 2.25h

Divide both sides by 2.25: h = 11.25 / 2.25

Calculate h: h = 5 hours

Therefore, the number of hours at which the costs are the same, when rounded to the nearest whole number, is 5 hours.

Scientific notations are the way through which a very small or a very large number can be written in shorthand. The area of Greenland in scientific notation is 8.4×10⁵ square miles.

Scientific notations are the way through which a very small or a very large number can be written in shorthand. In scientific notations when a number between 1 and 10s is multiplied by a power of 10.

For example, 6,500,000,000,000 can be written as 6.5e+12.

The given area of Greenland is 840,000 square miles. Therefore, the area of Greenland in scientific notation can be written as,

Area of Greenland = 840,000 square miles

                               = 8.4 × 10⁵ square miles

Hence, the area of Greenland in scientific notation is 8.4×10⁵ square miles.

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Median will be 18, Range will be 15 to 21, 25th percentile will be 15 to 17, 75th percentile 15 to 20, and Inter-quartile Range will be 17 to 20.

Solid lines on either outside of the rectangle represent the minimum and maximum interquartile range.

Based on the box-and-whisker plot shown below.

1) Median will be 18.

2) Range will be 15 to 21.

3) 25th percentile will be 15 to 17.

4) 75th percentile 15 to 20.

5) Inter-quartile Range will be 17 to 20.

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The insurance company is obligated to pay $99,000 for the claim of the stolen family heirloom ring.

Rowena's basic homeowners' insurance policy has a coverage limit of $150,000 with a $1,000 deductible. The deductible is the amount that Rowena must pay out of pocket before the insurance company pays for a claim.

When the family heirloom ring worth $100,000 is stolen, the insurance company will cover the value of the ring up to the policy limit minus the deductible.

Since the value of the ring is within the policy limit, the calculation for the amount the insurance company is obligated to pay is as follows:

Value of the ring = $100,000

Deductible = $1,000

Amount covered by insurance = Value of the ring - Deductible

Amount covered by insurance = $100,000 - $1,000

Amount covered by insurance = $99,000

Final answer:

The equation for the plane that is perpendicular to the vector v = (1, 1, 1) and passes through the point (1, 0, 0) is x + y + z = 1.

Explanation:

To find an equation for the plane that is perpendicular to the vector v = (1, 1, 1) and passes through the point (1, 0, 0), we need to use the normal vector v as the coefficient of the variables in the plane equation.

Step 1: The vector v is perpendicular to the plane, so its components are the coefficients of x, y, and z in the plane equation. Since v has components (1, 1, 1), the plane equation can be written as x - y - z = D, where D is a constant.

Step 2: The plane passes through the point (1, 0, 0). Substituting these coordinates into the plane equation allows us to find D.

Substituting, we get 1(1) + 1(0) + 1(0) = D. Hence, D = 1. Therefore, the equation of the plane is x + y + z = 1.

Step-by-step explanation:

The length of the textbook, l = 48.28 cm

The breadth of the textbook, b = 24.83 cm

The shape of the textbook is a rectangle. The perimeter is equal to the sum of all sides. Mathematically, it is given by :

[tex]p=2(l+b)[/tex]

[tex]p=2\times (48.28+24.83)[/tex]

p = 146.22 cm

So, the perimeter of the textbook is 146.22 cm. There are 5 significant figures in this number since non zero digits are always significant. Hence, this is the required solution.

Final answer:

Sally and Steve will take approximately 3.21 hours to paint a room together. This is calculated by adding their individual rates of painting and then finding the reciprocal of their combined rate.

Explanation:

To determine how long it would take Sally and Steve to paint a room together, we need to calculate their combined work rate. Sally's rate of painting is 1 room per 5 hours, while Steve's rate is 1 room per 9 hours. Their combined rate is the sum of their individual rates. This can be expressed as:

Combined rate = Sally's rate + Steve's rate = (1 room / 5 hours) + (1 room / 9 hours)

The least common multiple (LCM) of 5 and 9 is 45, so to add these rates together, we convert them into a common denominator:

Combined rate = (9 rooms / 45 hours) + (5 rooms / 45 hours) = (9+5) rooms / 45 hours = 14 rooms / 45 hours

To find out how long it takes them to paint one room together, we take the reciprocal of their combined rate:

Time to paint one room = 1 / (Combined rate) = 45 hours / 14 rooms

Therefore, rounding to two decimal places, Sally and Steve would take approximately 3.21 hours to paint the room together.

The revenue function for Gymnast Clothing is R(x) = 110x. The profit function is P(x) = 110x - (3000 + 10x + 0.2x^2). To determine the profit maximizing quantity, we need to find the value of x that makes P(x) greater than zero.

To find the revenue function for Gymnast Clothing, we need to multiply the number of hockey jerseys sold (x) by the selling price per jersey ($110). Therefore, the revenue function is R(x) = 110x.

To find the profit function, we subtract the cost function C(x) from the revenue function R(x). Therefore, the profit function is P(x) = R(x) - C(x). Substituting the given cost function, we have P(x) = 110x - (3000 + 10x + 0.2x^2).

To determine how many jerseys Gymnast Clothing should manufacture to make a profit, we need to find the value of x that makes P(x) greater than zero. We can solve this mathematically or graphically. In this case, it is more efficient to solve it graphically by plotting the profit function and finding the quantity that corresponds to a positive profit.

From the diagram, we are given that triangle ABC and triangle ADC shares the same side AC, so it means both triangles have one congruent side.

 We are also given that angle BAC and angle DAC are equal.

If we want to prove the triangles congruent using Angle-Angle-Side congruent postulate, we need to see one angle in each triangle that is congruent. We will need the information either: ACB = ACD or ABC = ADC

Correct answer: fourth option

Answer:

Caroline expect to earn is $63 .

Step-by-step explanation:

As given

Caroline works in Shelley’s store.

She earns $36 for a 4-hour shift.

Thus

[tex]Caroline\ earns\ for\ one\ hour\ shift = \frac{Total\ hour\ of\ earning}{Number\ of\ hour}[/tex]

[tex]Caroline\ earns\ for\ one\ hour\ shift = \frac{36}{4}[/tex]

Caroline earns for one hour shift = $ 9

As given

If  Caroline works for 7 hours .

Thus

Caroline earns from work = Caroline earns for one hour shift × Number of hour .

                                          = 9 × 7

                                          = $ 63

Therefore the  Caroline expect to earn is $63 .

Final answer:

To find the perimeter of the catalog page, we add the length and width and multiply by 2, resulting in 6.2 meters. For the area, we multiply the length by the width, resulting in 2.28 square meters.

Explanation:

The question asks for the perimeter and area of a page from a fashion catalog with dimensions of 1.2 meters by 1.9 meters. To calculate the perimeter of a rectangle, the formula is 2(length + width), and to calculate the area, the formula is length × width.

For the perimeter:
2(1.2m + 1.9m) = 2(3.1m) = 6.2 meters.

For the area:
1.2m × 1.9m = 2.28 square meters.

The triangle with the given side lengths are scalene triangles.

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees

An isosceles triangle has two sides of equal length. A scalene triangle has sides lengths of different sizes. A right angled triangle have side length in which the sum of the square of the two sides is equal to the square of the third side.

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Answer:

I agree as well, the answer is 24/25. =)

Step-by-step explanation:

it would become 11 - 18 which would equal -7

never and never

 2 negatives multiplied by each other = a positive number

 lets look at the first one:

 let a = -2

 you then have -2*(1/-2) = -2 * (-.5) = 1 ( positive 1 )

2nd eq, multiply a negative by a negative:

a = -3, b=-4, -3*-4 = 12 ( positive 12)

 both equations give positive numbers for answers