Need help with question 15

given,

f(x)=(1/2)x-3

g(x)=2x+6

Now,

f(4)=(1/2)×4-3

=2-3=-1

g(4)=2×4+6=14

Then,

f(g(4))=f(14)=(1/2)×14-3=7-3=4

g(f(4))=g(-1)=2×(-1)+6=-2+6=4

Answer:

see explanation

Step-by-step explanation:

To evaluate f(g(4)) substitute x = 4 into g(x) and then substitute the value obtained into f(x)

g(4) = (2 × 4) + 6 = 8 + 6 = 14, then

f(14) = (0.5 × 14) - 3 = 7 - 3 = 4

Hence f(g(4)) = 4

--------------------------------------------------------

To evaluate g(f(4)) substitute x = 4 into f(x) and then substitute the value obtained into g(x)

f(4) = (0.5 × 4) - 3 = 2 - 3 = - 1, then

g(- 1) = (2 × - 1) + 6 = - 2 + 6 = 4

Hence g(f(4)) = 4

Answer:

16

Step-by-step explanation:

128 stamps and 8 pages have the same amount to add up to 128

So 128 ÷ 8 I'll make it easier

8÷8=1

40÷8=5

80÷8=10

(128÷8)

10+5+1 = 16

There are 16 stamps per page.

Answer:

16 stamps.

Step-by-step explanation:

128 stamps divided by 8 stamps per page is 16 stamps.

Answer:

original price= $150, sale price= $105

Step-by-step explanation:

since it is on sale for 70% of original price, there is 30% off discount.

$45 is 30% of original price (original price is 100%)

1% of original price

= $45 ÷ 30

= $1.50

original price

= $1.50 × 100

=$150

sale price (70% of original price)

= $1.50 × 70

= $105

Final answer:

The original price of the jacket was $150, and after a discount of $45, the sale price is $105.

Explanation:

To find the original price of the jacket when the discount saves $45 and the sale is 70% of the original price, we can set up an equation where the original price is represented by 'P'.

70% of the original price is the same as 0.70P. If this amount is $45 less than the original price, we can express this as:

Original price - Discount = Sale price

P - 0.70P = P(1 - 0.70)

0.30P = $45

To find P, we divide both sides by 0.30:

P = $45 / 0.30

P = $150

Therefore, the original price of the jacket was $150. To calculate the sale price, we subtract the discount of $45 from the original price:

Sale price = Original price - Discount

Sale price = $150 - $45

Sale price = $105

So, the jacket is on sale for $105.

Answer:

Step-by-step explanation:

In general, graphs that go from lower left to upper right have a positive slope (think of it as going up the stairs...positive), and graphs that go from upper left to lower right have a negative slope (think of it as going down the stairs...negative).  I don't see graphs here but use this general idea and you'll be fine.  Of course, this applies to graphs of lines of the form y = mx + b.

Answer:

Part 1) [tex]\angle\ C=50.3\°[/tex]

Part 2) [tex]\angle\ B=67.4\°[/tex]

Part 3) [tex]\angle\ A=62.3\°[/tex]

Step-by-step explanation:

step 1

Find the measure of angle C

Applying the law of cosines

[tex]c^{2} =a^{2} +b^{2} -2(a)(b)cos(C)[/tex]

substitute the given values and solve for cos(C)

[tex]20^{2} =23^{2} +24^{2} -2(23)(24)cos(C)[/tex]

[tex]2(23)(24)cos(C)=23^{2} +24^{2} -20^{2}[/tex]

[tex]1,104cos(C)=705[/tex]

[tex]cos(C)=705/1,104[/tex]

[tex]C=arccos(705/1,104)=50.3\°[/tex]

step 2

Find the measure of angle B

Applying the law of cosines

[tex]b^{2} =c^{2} +a^{2} -2(c)(a)cos(B)[/tex]

substitute the given values and solve for cos(B)

[tex]24^{2} =20^{2} +23^{2} -2(20)(23)cos(B)[/tex]

[tex]2(20)(23)cos(B)=20^{2} +23^{2} -24^{2}[/tex]

[tex]920cos(B)=353[/tex]

[tex]cos(B)=353/920[/tex]

[tex]B=arccos(353/920)=67.4\°[/tex]

step 3

Find the measure of angle A

Remember that the sum of the internal angles of triangle must be equal to 180 degrees

[tex]\angle\ A+\angle\ B+\angle\ C=180\°[/tex]

substitute the given values and solve for ∠A

[tex]\angle\ A+67.4\°+50.3\°=180\°[/tex]

[tex]\angle\ A=180\°-117.7\°[/tex]

[tex]\angle\ A=62.3\°[/tex]

Answer:

The height of the can is [tex]h=9\ in[/tex]

Step-by-step explanation:

we know that

The surface area of the cylinder (can of peas) is equl to

[tex]SA=2\pi r^{2}+2\pi rh[/tex]

we have

[tex]SA=180.64\ in^{2}[/tex]

[tex]r=5/2=2.5\ in[/tex] ----> the radius is half the diameter

assume

[tex]\pi=3.14[/tex]

substitute and solve for h

[tex]180.64=2(3.14)(2.5)^{2}+2(3.14)(2.5)h[/tex]

[tex]180.64=39.25+15.70h[/tex]

[tex]h=[180.64-39.25]/15.70[/tex]

[tex]h=9\ in[/tex]

The height of the can of peas is equal to 33.628 inches.

Given the following data:

[tex]Radius = \frac{5}{2} = 2.5\;centimeters.[/tex]

To calculate the height of the can of peas:

Note: A can of peas is cylindrical in nature.

Mathematically, the surface area (SA) of a cylinder is given by this formula:

[tex] SA = 2\pi rh + 2\pi r^2[/tex]

Where:

Making h the subject of formula, we have:

[tex]h= \frac{SA-2\pi r^2 }{2\pi r} [/tex]

Substituting the given parameters into the formula, we have;

[tex]h= \frac{180.64-(2\times 2.5^2) }{2\times 2.5} \\ \\ h= \frac{180.64-(2\times 6.25) }{5} [/tex]

Height, h = 33.628 inches.

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Okay the scale for this equation is each inch equals 30 miles. SO to get how many miles 4.5 inches equals to, we have to multiply 30 by 4.5, and the answer we get is 135.

I hope this helps!

Answer:

the first one is .6826%

Answer:

Step-by-step explanation:

Given that the graph shows the normal distribution of the length of similar components produced by a company with a mean of 5 centimeters and a standard deviation of 0.02 centimeters.

A component is chosen at random, the probability that the length of this component is between 4.98 centimeters and 5.02

=P(|z|<1) (since 1 std dev on either side of the mean)

=2(0.3418)

=0.6826

=68.26%

The probability that the length of this component is between 5.02 centimeters and 5.04 centimeters is

=P(1<z<2) (since between 1 and 2 std dev from the mean)

=0.475-0.3418

=0.3332

=33.32%

Answer:

x = 240

Step-by-step explanation:

The measure of the 2 arcs must sum to 360°, hence

x = 360° - 120° = 240°

The inside dimensions of the living room, taking into account the thickness of the walls, are 12' 1 3/4" x 21' 1 3/4".

To solve this problem, we should subtract the thickness of the walls from the outside dimensions of the living room, as the inside dimensions will be the total length and width minus the thickness of the two opposing walls on each side. The thickness of two walls on one side totals 10 1/4" (since the wall thickness is 5 1/8" per wall) and this total should be subtracted from each outside dimension.

When converting 10 1/4" to feet, the total thickness is approximately 0.852'. Therefore, subtracting this from each dimension gives us:

13' - 0.852' = 12' 1.8" = 12' 1 3/4"

22' - 0.852' = 21' 1.8" = 21' 1 3/4"

Therefore, the correct answer to the question is (A) 12' 1 3/4" x 21' 1 3/4".

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Answer:

The first choice is the one you want

Step-by-step explanation:

Solve the inequalities one at a time:

[tex]\frac{2}{3}x>8[/tex]

Multiply both sides by 3:

2x > 24 and

x > 12

For the next one:

[tex]\frac{2}{3}x <4[/tex]

Again, multiply both sides by 3:

2x < 12 and

x < 6

So the solution set is {x I x > 12 or x < 6}

Answer:

The second choice down is the one you want

Step-by-step explanation:

There's a couple of things to know about parabolas in this form before you can write the equation from information given.  The first is that if the parabola opens upward or downward it is y = x^2 or y = -x^2.  If it opens to the right or to the left it is a x = y^2 or x = -y^2 parabola.  We can tell how it opens from the location of the focus and what type of directrix it has.  First, a parabola wraps itself around the focus, and the way in which it wraps itself is dependent upon the equation of the directrix.  A "y = " directrix means that the parabola opens up or down (again, it wil wrap itself around the focus) and an "x =" directrix means that the parabola opens to the right or to the left.  Ok.  Now.  Our directrix is a "y =" equation, so the parabola opens either up or down.  If we plot the focus and then draw in the directrix, we see that the focus is above the directrix, so the parabola opens upwards.  

Because of this, the standard form for our parabola is:

[tex](x-h)^2=4p(y-k)[/tex]

where h and k are the coordinates of the vertex and p is the distance between the vertex and the focus, or the vertex and the directrix.  This distance is the same for both.  That means that the vertex lies directly in between the focus and the directrix.  Since our focus is (-5, -1) and the directrix is y = -3, then the vertex lies at a y-coordinate of -1, and will lie on the same x coordinate as does the focus.  So that means our vertex is at (-5, -2).  From this point we see that there is unit that separates it from both the focus and the directrix.  That is our "p" value.  Filling in our equation:

[tex](x+5)^2=4(1)(y+2)[/tex]

which of course simplifies to

[tex](x+5)^2=4(y+2)[/tex]

And there you go!

Answer:

(x+5)2=4(y+2)

Step-by-step explanation:

Ethan's car used 6 gallons of gasoline for his 180 miles trip, which at a cost of $4 per gallon, results in a total gasoline cost of $24.

To calculate the total cost of gasoline for Ethan's trip, you need to understand how many gallons were used and then multiply that figure by the cost per gallon. As Ethan's car can travel 30 miles per gallon, and Ethan drove 180 miles in total, Ethan's car used 6 gallons of gasoline (180 miles ÷ 30 miles/gallon). Given that gasoline costs $4 per gallon including tax, Ethan therefore spent a total of $24 on gasoline for his trip (6 gallons x $4/gallon).

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The cost per gallon is $24.

To calculate the total cost of the gasoline, we need to divide the distance driven by the car by the car's gas mileage to find the number of gallons used.

Then, we can multiply the number of gallons used by the cost per gallon to find the total cost. In this case,

Ethan drove 180 miles and his car can travel 30 miles per gallon, so he used 180/30 = 6 gallons of gasoline.

The cost per gallon is $4, so the total cost is 6 * $4 = $24.

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Answer:

The correct answer would be choice number 1

Answer: 171 green marbles

Step-by-step explanation: There are 7 total marbles so 100/7 equals 14.28

Then there is a 2 out of 7 total tries so  14.28 * 2 equals 28.57% chance to get a green marble.

600 * 0.2857 = 171.41 marbles but you cant get half a marble so 171 green marbles.

Final answer:

A baker would need to use 7 scoops of flour with a 1 1⁄2 cup measuring scoop to have at least 4 3⁄4 cups of flour.

Explanation:

The question at hand requires us to determine how many scoops of flour a baker would need to use to obtain at least 4 3⁄4 cups of flour with a scoop that holds 1 1⁄2 cups. To solve this, we will divide the total amount of flour needed by the capacity of the scoop:

Therefore, the baker must use 7 scoops to have at least 4 3⁄4 cups of flour.

Answer:

A. (-5, 0) and (-2, 0)

Step-by-step explanation:

Assuming you mean x^2 + 7x + 10. Simply graph using Desmos and locate where the graph crosses the x-axis! :)

Final answer:

The correct option is (A) (–5, 0) and (–2, 0). The x-intercepts of the quadratic equation y = x^2 + 7x + 10 are (-5, 0) and (-2, 0), after factoring the equation as (x + 5)(x + 2) = 0.

Explanation:

The question is asking for the x-intercepts of the quadratic equation y = x^2 + 7x + 10. To find the x-intercepts, we need to set y to 0 and solve for x.

This gives us the equation 0 = x^2 + 7x + 10. Factoring the quadratic equation, we get (x + 5)(x + 2) = 0, which means that the solutions are x = -5 and x = -2. Therefore, the x-intercepts of the graph are (-5, 0) and (-2, 0).

To find the sum of the x-coordinates of all possible positive integer solutions to the equation 1/x + 1/y = 1/7, we can rearrange the equation and use Simon's Favorite Factoring Trick to solve for x.

To find the sum of the x-coordinates of all possible positive integer solutions to the equation 1/x + 1/y = 1/7, we can rearrange the equation to 7x + 7y = xy. Simplifying further, we have xy - 7x - 7y = 0. Applying Simon's Favorite Factoring Trick, we add 49 to both sides of the equation: xy - 7x - 7y + 49 = 49. Factoring the left side gives us (x - 7)(y - 7) = 49. Since we are looking for positive integer solutions, we can set x - 7 and y - 7 to be divisors of 49 and solve for x.

The divisors of 49 are 1, 7, and 49. Setting x - 7 = 1, we get x = 8. Setting x - 7 = 7, we get x = 14. And setting x - 7 = 49, we get x = 56. So the sum of the x-coordinates is 8 + 14 + 56 = 78.

Answer:  Second option.

Step-by-step explanation:

Let be "e" the number of easy puzzles Tina solved and "h"  the number of hard puzzles Tina solved.

Set up a system of equations:

[tex]\left \{ {{e+h=50} \atop {30e+60h=1,950 }} \right.[/tex]

You can use the Eliminationn Method to solve this system of equations:

Therefore, through this proccedure, you get:

[tex]\left \{ {-30e-30h=-1,500} \atop {30e+60h=1,950 }} \right.\\.........................\\30h=450\\\\h=\frac{450}{30} \\\\h=15[/tex]

Tina solved 15 hard puzzles.

Let's assume Tina solved x easy puzzles and y hard puzzles.

Since a player earns 30 points for solving an easy puzzle and 60 points for solving a hard puzzle, the total points Tina earned can be expressed as:

30x + 60y = 1950 (equation 1)

The second piece of information given is that Tina solved a total of 50 puzzles. So, the total number of puzzles can be expressed as:

x + y = 50 (equation 2)

To solve this system of equations, we can use the substitution method. Solve equation 2 for x:

x = 50 - y

Substitute this expression for x in equation 1:

30(50 - y) + 60y = 1950

1500 - 30y + 60y = 1950

30y = 450

y = 15

Therefore, Tina solved 15 hard puzzles.

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Answer:

1/2

Step-by-step explanation:

see the picture.

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1, then

cosx = [tex]\sqrt{1-sin^2x}[/tex]

note that ([tex]\frac{\sqrt{3} }{2}[/tex] )² = [tex]\frac{3}{4}[/tex]

cosΘ = [tex]\sqrt{1-\frac{3}{4} }[/tex] = [tex]\sqrt{\frac{1}{4} }[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

Option B is correct.

Step-by-step explanation:

CPI stands for Consumer Price index and is used to find the inflation.

The formula used to find CPI is

CPI = (Price of baskets of goods in one year/ Price of baskets of goods in base year) * 100

Here the base year is the starting year, in our case it is 1983 and price of can of paint is $16.35

So, CPI in 2000

Using the above formula and putting the values

CPI in 2000 = (28.94 / 16.35) * 100

CPI in 2000 = 177

CPI in 2005

Using the above formula and putting the values

CPI in 2005 = (32.54 / 16.35) * 100

CPI in 2005 = 199

Difference in CPI between 2000 and 2005 = CPI in 2005  - CPI in 2000

Difference in CPI between 2000 and 2005 = 199 - 177

Difference in CPI between 2000 and 2005 = 22

So, Option B is correct.

Answer:

22

Step-by-step explanation:

Answer:

x³ + 5x² + 16x - 3

Step-by-step explanation:

(f+g)(x) is just another way of writing f(x) + g(x).

f(x) + g(x)

8x² + 16x + 6 + x³ - 3x² - 9

x³ + 5x² + 16x - 3

This is actually quite comical as I just had a DBA concerning equations of circles so, I'm pretty sure I'm qualified to help you.

Equation of a Circle: (x-h)²+(y-k)²=r² where (h, k) is the center and r is the radius.

So, all we need to do is plug in your info:

(x+3)²+(y+2)²=5²

And, there goes your answer.

The Equation of Circle with center (-3, -2) and radius 5 is (x+3)²+(y+2)²=25.

A circle is a round 2-dimensional shape. It is a closed shape with a distance from center to circumference termed as radius 'r' and distance from one point on the circumference to another point passing through center termed as diameter 'd'.

Here,

Equation of a Circle:

                               (x-h)²+(y-k)²=r²

where (h, k) is the center and r is the radius.

So, all we need to put the value of h, k and r in equation of circle:

                                (x+3)²+(y+2)²=5²

                                 (x+3)²+(y+2)²=25

Thus, the Equation of Circle with center (-3, -2) and radius 5 is (x+3)²+(y+2)²=25.

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Answer:

0.75-0.5=0.25

Step-by-step explanation:

Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is 0.25 or 1/4.

Answer:

C

Step-by-step explanation:

The range is the difference between the largest and smallest values in the data set.

largest = 1 [tex]\frac{3}{4}[/tex] and smallest = [tex]\frac{1}{2}[/tex]

range = 1 [tex]\frac{3}{4}[/tex] - [tex]\frac{1}{2}[/tex] = 1 [tex]\frac{1}{4}[/tex] → C

ANSWER

There are 210 different permutations

EXPLANATION

The word 'ALFALFA' has 7 letters.

The letter 'A' repeats three times.

The letter 'F' repeats two times.

The letter 'L' also repeats two times.

The number of different permutation is

[tex] \frac{7!}{3!2!2!} = 210[/tex]

There are 210 different permutations.

Answer: There are 210 distinct permutations of the letter of that word.

Step-by-step explanation:

Since we have given that

ALFALFA

Here, 3 A,

2 F,

2 L

Number of letters in that word = 7

So, Number of distinct permutations of the letters of the word "ALFALFA":

[tex]\dfrac{7!}{3!\times 2!\times 2!}\\\\=210[/tex]

Hence, there are 210 distinct permutations of the letter of that word.

Answer:

answer to the first question in the image attached above

Step-by-step explanation:

Hope it's helps

Answer:

A:(-2,-3)

B:(-4.009,1.018) And (-2,-3)

C:x≈0,1.61878812

Step-by-step explanation:

I found the equations

g(x)=e^x+1

p(x)=5/2x+2

f(x)=-2x-7

plugged it in on a graph found the answer to find g(x) all you need to do is know the parent function y=e^2(exponential) and I found where the lines intersect for part A and B and or p(x)=g(x) I did e^x+1=(5/2)x+2

Answer:

The line x = 8 is our vertical asymptote

The limit of [tex]\frac{1}{x-8}[/tex] as x approaches 8 from the left is negative infinity; -∞

Step-by-step explanation:

We have been given the following function;

[tex]\frac{1}{x-8}[/tex]

Considering that the function is rational, it will defined everywhere on the real line except where the expression in the denominator will be 0;

That is the function will not be defined where;

x - 8 = 0

solving for x yields;

x = 8

The function will be approaching the vertical line x = 8 asymptotically, meaning that the function will never touch or cross this line. We can therefore say that,

The line x = 8 is our vertical asymptote for the given function

The limit of [tex]\frac{1}{x-8}[/tex] as x approaches 8 from the left;

[tex]\lim_{x \to8^{-} }\frac{1}{x-8}[/tex]

For x approaching 8 from the left, [tex]x<8[/tex] which implies that [tex]x-8<0[/tex]

The denominator will be a negative quantity approaching 0 from the left, that is -∞.

Thus;

[tex]\lim_{x \to8^{-} }\frac{1}{x-8}[/tex] = -∞

Find the graph attached.

Answer:

it goe towards negative infinity

Step-by-step explanation:

1/6-8=-1/2

1/7-8=-1

1-7.999-8=-10000

therefore you can assume that it is going to a negative infinity direction

Answer:

14 ft³

Step-by-step explanation:

First, find the volume of a single cube: V = s³, where s = side length

V = s³; s = 1/5

V = (1/5)³

V = 0.008 ft³

**Note: (1/5)³ is equal to 1/125 as a fraction. I put it down in decimal form because it's easier for me to work with decimals.**

Now, to find the volume of the prism (which is completely filled with cubes), multiply the volume of one cube by the total number of cubes: 1750.

(1750)(0.008)

14 ft³

The volume of the prism is 14 ft³.

Hope this helps!

radius=diameter/2

therefore r=3÷2 ie 1.5m

area=pi (r^2)m^2

=1.5^2 pi m^2

2.25 pi m^2 is required area