Question 2(Multiple Choice Worth 4 points)
(01.04 LC)
Given the linear functions f(x) = x -2 and g(x)=-3x + 4, determine (f- g)(x).
(f-g)(x) = -3x - 8
(f-g)(x)=-3x²-8
(f-g)(x) = -3x² + 10x - 8
(f-g)(x) = -3x² - 2x - 8

Starting from the same point when bike riding, two individuals are riding. Tom and Juanita goes on biking in opposite directions to each other. Tom rides at speed of 30 mph and Juanita rides at speed of 30 mph in one hour. This will both be added together. And later will be add both speed in third hour that gives us the final value. The answer of this will be seventy two miles.

[tex]30+30[/tex] in one hour

[tex]30+30[/tex] in second hour

[tex]30+30[/tex] in the third hour

[tex]\boxed{\bold{= 270 \ miles}}[/tex]

Ana will hit the water 3 seconds after diving.

We need to solve for when her height is 0. We can set h(x) = 0 and solve for x:

-5(x+1)(x-3) = 0

This expression equals zero when either (x+1) = 0 or (x-3) = 0. Solving for these values gives:

x+1 = 0 or x-3 = 0

x = -1 or x = 3

The negative value for x doesn't make sense in this context since it represents a time before Ana even jumped off the board, so we can ignore it.

Therefore, Ana will hit the water 3 seconds after diving.

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the value of c is 11.165 lbs. This was calculated using the z-score formula, assuming a normal distribution with a mean weight of 10 lbs and a standard deviation of 0.5 lbs. This ensures that 99% of all parcels are at least 1 lb under the surcharge weight.

To find the value of c, we need to use the standard normal distribution and the z-score formula. Since we know that 99% of all parcels are at least 1 lb under the surcharge weight, we can use the z-score associated with the 99th percentile, which is 2.33 (from a z-score table).

The formula for the z-score is:

z = (x - μ) / σ

where x is the weight of the parcel, μ is the mean weight, and σ is the standard deviation.

In this case, we want to find the weight of the parcel that is at the 99th percentile, which is 1 lb under the surcharge weight. Let's call this weight x. We know that the surcharge weight is c, so the weight of the parcel that is 1 lb under the surcharge weight is (c - 1).

Using the z-score formula and substituting the values we know, we get:

2.33 = ((c - 1) - μ) / σ

We want to solve for c, so we need to rearrange the equation:

c - 1 = 2.33σ + μ
c = 2.33σ + μ + 1

We don't know the values of μ and σ, but we can use the fact that the distribution is normal to estimate them. We can assume that the distribution is centered at the mean weight of all parcels, and that the standard deviation is equal to the average difference between the weight of each parcel and the mean weight.

Let's say that the mean weight is 10 lbs, and the standard deviation is 0.5 lbs. Then, we can plug these values into the equation for c:

c = 2.33(0.5) + 10 + 1
c = 11.165

So, the value of c that ensures that 99% of all parcels are at least 1 lb under the surcharge weight is approximately 11.165 lbs.

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The value of the unknown number -12.

Given that: twice a certain number is added to 10 and the result is minus 14.

Let's assume that the number we are trying to find is "x".

We can represent the statement twice this number (2x) is added to 10, and the result is -14 in an algebraic equation.

2x + 10 = -14

We can solve for x by isolating it on one side of the equation. We can start by subtracting 10 from both sides of the equation:

2x + 10 - 10  = -14 - 10

2x = -14 - 10

Simplifying the right side of the equation, we get:

2x = -24

Finally, we can solve for x by dividing both sides of the equation by 2:

2x/2 = -24/2

x = -12

Therefore, the number we are looking for is -12.

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hi

10/9 - 11/3 =  10/9 - 33/9 =  -23/9

Answer:

-23/9

Step-by-step explanation:

You would need to find a common denominator which would be 9.

The next step would be to combine the top 10-11 (times)3 over 9

Then you multiply -11 by 3 tp get 10 -33 /9

The last and final step would be tp subract 33 from 10 to get 33 -10

Which will led you to your final awnser which is -23/9

The cost to paint the room with two coats of paint is $48, using paint that costs $8 per gallon and covers 300 square feet per gallon.

To determine how much it costs to paint the room if the paint costs $8 a gallon and each gallon covers 300 square feet of wall, we first need to determine how many gallons of paint we need. From problem #18, we know that the room has a total wall area of 800 square feet, and we need to apply two coats of paint.

The total wall area that needs to be covered by paint is:

800 square feet x 2 coats = 1600 square feet

To determine how many gallons of paint we need, we divide the total square footage by the coverage of one gallon of paint:

1600 square feet ÷ 300 square feet/gallon = 5.33 gallons (rounded up to the nearest gallon)

Therefore, we need 6 gallons of paint to complete the job (since we can't purchase a fractional amount of a gallon).

The cost of the paint can now be calculated by multiplying the number of gallons of paint by the cost per gallon

6 gallons x $8/gallon = $48

So it would cost $48 to paint the room.

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Jow will need to pay a commision of $7.50. The total amount charged by the broker will be $17.50

Joes current portfolio is worth $50,000

A purchase price one share =  $15

He wants to purchase 50 shares of a company's stock

Using unitary method the cost of 50 shares would be,

C = 50 × 15

C = $750

Since his portfolio is less than $100000 the amount chanrged by the broker would be equal to the 1% commision plus fees per trade.

First we find the commision.

1 percent of $750

= 1/100 × 750

= $7.5

And the fees per trade = $10

So, the total amount charged by the broker = $10 + $7.5

                                                                     = $17.5

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Find the complete question below.

The equations to represent each girl's shoppins spree is 3x + y = 38.0 and 4x + 3y = 71.50. Price of one shirt costs $8.50 and price of one pair of shorts costs $12.50.

Let x be the price of one shirt, and y be the price of one pair of shorts. Then, we can write the following system of equations

For Jazmin

3x + y = 38.0

For Justine

4x + 3y = 71.50

To solve for the price of one pair of shorts using elimination method, we need to eliminate one of the variables. We can do this by multiplying the first equation by 3 and the second equation by -1, and then adding them together

9x + 3y = 114.0

-4x - 3y = -71.50

5x = 42.50

x = 8.50

So, one shirt costs $8.50.

To find the price of one pair of shorts, we can substitute the value of x into either of the original equations and solve for y. Using the first equation

3(8.50) + y = 38.0

25.50 + y = 38.0

y = 12.50

Therefore, one pair of shorts costs $12.50.

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Answer:

[tex]percentage = \frac{56}{145} \times 100[/tex]

56/145×100

0.386...×100

38.6%

Answer: is option (3) -4x²-6.

Step-by-step explanation: First, we need to add the two given polynomials:

4x^2 - x + 1 + (-6x^2 + x - 4) = -2x^2 - 3

Now, we need to multiply this sum by 2:

2(-2x^2 - 3) = -4x^2 - 6

Therefore, the polynomial that is twice the sum of 4x^2-x+1 and -6x^2+x-4

The quotient of the expression 5x^2/7÷10x^3/21 is 3/(2x)

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

5x^2/7÷10x^3/21

Assume that no denominator has a value of 0, we have

5x^2/7÷10x^3/21 = 5x^2/7 ÷ 10x^3/(7 * 3)

Express as products

So, we have the following representation

5x^2/7÷10x^3/21 = 5x^2/7 * (7 * 3)/10x^3

When the factors are evaluated, we have

5x^2/7÷10x^3/21 = 5 * 3/10x

So, we have

5x^2/7÷10x^3/21 = 15/10x

This gives

5x^2/7÷10x^3/21 = 3/(2x)

Hence, the solution is 3/(2x)

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Machelle can get a grade of D or higher on her exam.

In mathematics, an inequality is a mathematical statement that describes a relationship between two quantities that are not necessarily equal. An inequality can express that one quantity is less than, less than or equal to, greater than, greater than or equal to, or not equal to another quantity.

Inequalities can be represented using various symbols. For example, the symbol < represents "less than," the symbol > represents "greater than," the symbol ≤ represents "less than or equal to," and the symbol ≥ represents "greater than or equal to." The symbol ≠ represents "not equal to."

Inequalities are also used in algebra to solve equations and to represent the solution set of an equation. In this context, an inequality can represent all the possible values of a variable that satisfy the equation. For example, the inequality x > 5 represents all the values of x that make the expression x - 5 positive.

We can write an inequality to represent the number of points, m, obtained by Machelle on her exam:

m > 100 - 27

Simplifying this expression, we get:

m > 73

This means that Machelle must have scored more than 73 points on her exam. Based on the table, we can see that a score of more than 73 points corresponds to a grade of at least a D. Therefore, Machelle can get a grade of D or higher on her exam.

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The complete question is:

The correlation coefficient is a statistical measure that indicates the strength and direction of the relationship between two variables.

Correlation coefficient is denoted by the symbol "r" and ranges from -1 to 1.

A correlation coefficient of 1 indicates a perfect positive correlation, where as one variable increases, the other variable also increases at the same rate.

A correlation coefficient of -1 indicates a perfect negative correlation, where as one variable increases, the other variable decreases at the same rate.

A correlation coefficient of 0 indicates no correlation between the two variables.

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Answer:

a

Step-by-step explanation:

Answer:

The answer is B) -35.16 grams per half-life cycle

Answer:

Banks are eligible to charge service fees to cover the costs of providing and maintaining various banking services such as account maintenance, ATM access, online banking, and customer support. These fees help banks to generate revenue and continue to offer their services to customers. The specific fees and their amounts can vary depending on the bank and the type of account or service being used.

Answer:

19.25

Step-by-step explanation:

You add up all three sides which would be 10+3.25+6 to get the awnser 19.25

Answer:

240m

Step-by-step explanation:

You need to find the area of each surface.

FORMULAS

A= L × W

A= 1/2(L × W)

SIDES

Base = 12×6 = 72

Top of triangle = 6×13 = 78

Side of triangle = 5×6 = 30

Triangular side 1 = 1/2(5×12) = 30

Triangular side 2 = 1/2(5×12) 30

Now you need to add all of the surface areas together.

72+78+30+30+30 = 240

Therefore, the surface area of the triangular prism is 240m.

IM SO SORRY IF THIS DOESN'T MAKE ANY SENSE!

If 1/4 of this amount is blue paint, and the rest is white paint, Area used 5.4 pints of white paint to paint her bedroom walls.

Given that Area used a total of 7.2 pints of blue and white paint to paint her bedroom walls. And 1/4 of the amount is blue paint, then the remaining 3/4 of the amount must be white paint.

To find the amount of white paint used, we can use the following formula:

Amount of white paint = Total amount of paint - Amount of blue paint

Since we know that the total amount of paint used is 7.2 pints and 1/4 of that amount is blue paint, we can calculate the amount of blue paint as:

Amount of blue paint = (1/4) x 7.2 = 1.8 pints

Now we can substitute these values in the formula to find the amount of white paint used:

Amount of white paint = 7.2 - 1.8 = 5.4 pints

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The volume and total surface area of each shape combined is calculated below.

For cone-hemisphere shape

Volume = volume of cone + volume of hemisphere

Volume = 1/3πr²h + 2/3πr³

where r = 9/2 = 4.5 m

h = √(13² - 4.5²)      (Pythagoras)

h = 12.20 m

Volume = 1/3πr²h + 2/3πr³

Volume = (1/3 * 3.14 * 4.5² * 12.2) + (2/3 * 3.14 * 4.5³)

Volume = 449.33 m³

Surface area = curved surface area of cone + curved surface area of hemisphere

Surface area = πrl + 2πr², where l = 13 m

Surface area = (3.14 * 4.5 * 13) + (2 * 3.14 * 4.5²)

Surface area = 310.86 cm²

For hemisphere-cylinder shape

Volume = volume of hemisphere + volume of cylinder

Volume =  2/3πr³ + πr²h

where r = 22/2 = 11 ft

height of cylinder (h) = 45 - 11 = 34 ft

Volume =  (2/3 * 3.14 * 11³) + (3.14 * 11² * 34)

Volume =  15704.19 ft³

Surface area = curved surface area of hemisphere + curved surface area of  cylinder + curved surface area circular base of cylinder

Surface area =  2πr² + πr² + 2πrh

Surface area =  3πr² + 2πrh

Surface area =  (3 * 3.14 * 11²) + (2 * 3.14 * 11 * 34)

Surface area = 3488.54 ft²

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The correct option is the fourth one, the slope and y-intercept are different.

Here we have the linear equation:

3x - 5y = 4

We know that it is dilated by a scale factor of 5/3, so let's find the dilation.

We can rewrite the linear equation as:

-5y = 4 - 3x

y =  (3/5)x - 4/5

Now let's apply the dilation:

y = (5/3)*[ (3/5)x - 4/5]

y = x - 4/3

Then we can see that the slope and the y-intercept are different, the correct option is 4.

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The perimeter of the triangle is 23.623 units.

What is perimeter of triangle?

Finding the distance around a triangle entails determining its perimeter. The distance formula can be used to calculate the side lengths if you don't already know all of them. The simplest way to find a triangle's perimeter is to add up all of its sides' lengths.

The distance between two points (x1,y1) and (x2,y2) can be determined using the following formula: √(x₂-x₁)² + (y₂ - y₁)²

Let the given vertices are (-7, -2), (-2, -5) , and (2, 3).

Distance formula for two points is = √(x₂-x₁)² + (y₂ - y₁)²

Using the formula,

AB = √((-2)-(-7))² +((-5)-(-2))²

= √(-2+7)² + (-5+2)²

= √5² + (-3)²

= √25 + 9

= √31

Similarly, BC = √(2 - (-2))² + (3-(-5))²

= √(2+2)² + (3+5)²

= √4² + 8²

= √16+64

= √80

CA = √((-7)-2)² + (-2 + 3)²

= √(-9²) + 1

= √81+1

=√82

Perimeter of triangle = AB + BC + CA

= √31 +√81 +√82

= 5.5677 + 9 + 9.0553

= 23.623

Therefore, the perimeter of the triangle is 23.623 units.

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The result of 9 divided by 7/3 is 12 3/7.

When dividing by a fraction, it's the same as multiplying by its reciprocal. Therefore, to divide 9 by 7/3, we can multiply 9 by 3/7. This gives us (9 x 3) / 7 = 27/7.

However, this fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 3.

Thus, 27/7 can be simplified to 9 and 6/7, or 12 and 3/7 when expressed as a mixed number. Therefore, the answer to 9 divided by 7/3 is 12 and 3/7.

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Answer: [tex]6.75\pi[/tex] inches^2

Step-by-step explanation:

If the diameter is 18 inches, the radius must be 18/2 = 9 inches.

Thus, we can calculate the area using the area of a circle = [tex]\pi r^{2}[/tex].

Plugging in the values, we get the area = [tex]81\pi[/tex] inches^2.

Since 30 degrees is 1/12 of 360 degrees, a 30-degree sector would be equal to 1/12 the area of the circle.

Therefore, we divide [tex]81\pi[/tex]/12 to get the area of the sector = [tex]6.75\pi[/tex] inches^2.

Answer: To find the coordinates of F' and G', we need to reflect points F and G across the line y = 5, since point D is located on this line.

For point F, the y-coordinate changes from 11 to -1, since the distance between the line y = 5 and point F is 6 units (2 times the distance between D and the line). Therefore, the coordinates of F' are (3,-1).

For point G, the y-coordinate changes from 8 to 2, since the distance between the line y = 5 and point G is 3 units (1.5 times the distance between D and the line). Therefore, the coordinates of G' are (2,2).

Thus, the coordinates of F' are (3,-1) and the coordinates of G' are (2,2).

Answer: 100 times

Step-by-step explanation:

The cube is numbered 1 to 6. That is, 1, 2, 3, 4, 5, 6. That means there are 6 possible outcomes for each toss. But there are 2 outcomes we want, 5 and 6 (greater than 4).

So, for each toss, there is a probability of 2/6 = 1/3 that this will occur.

With 300 tosses, we can say that this will probably happen 300 times. This means that it will happen

1/3 * 300 times = 100 times.

Therefore, we can predict we will get a 5 or 6 about 100 times.

Parallel cross sections of a sphere look like circles with the same radius as the sphere, while perpendicular cross sections look like points. Cross sections taken at other angles will be ellipses.

A sphere is a three-dimensional geometric shape that is perfectly round in shape, like a ball. It is defined as the set of all points in three-dimensional space that are at a constant distance (the radius) from a given point called the center.

If we take a cross section of a sphere, the resulting shape will depend on the angle at which the section is taken relative to the center of the sphere.

If we take a plane that is parallel to the base of the sphere, the cross section will be a circle with the same radius as the sphere. This is because the intersection of the plane with the sphere will be a circle, and since the plane is parallel to the base of the sphere, the circle will have the same radius as the sphere.

On the other hand, if we take a plane that is perpendicular to the base of the sphere, the cross section will be a point. This is because the plane will intersect the sphere at only one point, which is the point at which the plane is perpendicular to the sphere.

If we take a plane that is neither parallel nor perpendicular to the base of the sphere, the resulting cross section will be an ellipse. The size and shape of the ellipse will depend on the angle at which the plane intersects the sphere.

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I'm confused what's being asked here...but if you're looking for someone to check it then:

The line of best fit is drawn correctly; there are about the same amount of dots on the top and bottom of the line.

And the correlation is positive

Answer:

c > 7

Step-by-step explanation:

Now we have to,

→ Find the required value of c.

The equation is,

→ 2(3c + 15) + 4c > 100

Then the value of c will be,

→ 2(3c + 15) + 4c > 100

Applying Distributive property:

→ 2(3c) + 2(15) + 4c > 100

→ 6c + 30 + 4c > 100

Combining the like terms:

→ 10c + 30 > 100

→ 10c > 100 - 30

→ 10c > 70

Dividing the value 70 with 10:

→ c > 70 ÷ 10

→ [ c > 7 ]

Hence, the answer is c > 7.

Hello !

Answer:

[tex]\boxed{\sf c > 7 \ \ \ ||\ \ \ \sf (7,+\infty)}[/tex]

Step-by-step explanation:

We are looking for the values of c that satisfy the following inequality :

[tex]\sf 2(3c + 15) + 4c > 100[/tex]

Let's expand the left side of the inequality.

[tex]\sf 2\times 3c +2\times 15+4c > 100\\6c+30+4c > 100[/tex]

Now we will combine like terms :

[tex]\sf 10c+30 > 100[/tex]

Let's substract 30 from both sides of the inequality.

[tex]\sf 10c+30-30 > 100-30\\10c > 70[/tex]

Finally, let's divide both sides by 10.

10>0 so the inequality remains the same.

[tex]\sf\frac{10c}{10} > \frac{70}{10} \\\boxed{\sf c > 7}[/tex]

Have a nice day ;)