Find the x-intercept of the function: f(x) = 6^x - 2. Round answer to the nearest hundredth, if necessary.

Answer:

A) 100%; B) 0.517; C) 0.858

Step-by-step explanation:

For part A,

We find the sum of the probabilities:

45.2+16.4+6.5+6.3+4.2+3.7+2.1+15.6 = 100

Since they sum to 100%, this is a probability distribution.

For part B,

We add together the probabilities for the US and Canada:  

45.2+6.5 = 51.7% = 51.7/100 = 0.517

For part C,

We first add together the probabilities for Italy, the UK and France:

6.3+4.2+3.7 = 14.2%

Next we subtract this from 100%:

100-14.2 = 85.8% = 85.8/100 = 0.858

Final answer:

The table gives a probability distribution. The probability that a U.S. user obtained music from the United States or Canada is 51.7%. The probability that a U.S. user does not obtain music from Italy, the U.K., or France is 85.8%.

Explanation:

To verify that the table gives a probability distribution, we need to show that the sum of the percentages is equal to 100%. Summing the percentages from the table, we get:

45.2 + 16.4 + 6.5 + 6.3 + 4.2 + 3.7 + 2.1 + 15.6 = 100%

This confirms that the table does give a probability distribution for the experiment.

To find the probability that a U.S. user obtained music from either the United States or Canada, we add the percentages for these two countries:

45.2 + 6.5 = 51.7%

Therefore, the probability is 0.517 or 51.7%.

To find the probability that a U.S. user does not obtain music from Italy, the United Kingdom (U.K.), or France, we subtract the percentages for these three countries from 100%:

100% - (6.3 + 4.2 + 3.7) = 100% - 14.2% = 85.8%

Therefore, the probability is 0.858 or 85.8%.

Answer:

Option D.75°

Step-by-step explanation:

we know that

The sum of the interior angles of a regular dodecagon is equal to

[tex]S=(n-2)*180[/tex]

where

n is the number of sides

In this problem

n=12 sides

substitute

[tex]S=(12-2)*180[/tex]

[tex]S=1,800\°[/tex]

Find the measure of each interior angle

Divide the sum of the interior angles by the number of sides

[tex]1,800\°/12=150\°[/tex]

The measure of the angle formed by the radius and the side of a regular dodecagon is half the measure of the interior angle

therefore

[tex]150\°/2=75\°[/tex]

[tex]y = \frac{4}{x + 6} + 2 \\ [/tex]

found by:

as value of x approaches -6 from left, value of y appoaches negative infinity

as value of x approaches -6 from the right, value of y approaches infinity

(undefined solution)

therefore, the value of x = 0 is translated to x = - 6

if x = -6,

(x + 6) = 0

(x + 6) is the value of x in the equation

[tex]y = \frac{4}{x + 6} + c[/tex]

as x increases, the value of 4/x approaches 0

in the graph, it approaches 2 instead

meaning 2 units is added to the value of y,

therefore c = 2.

Answer:

[tex]y=\frac{4}{x+6} +2[/tex]

Step-by-step explanation:

Answer:

A. 1 12

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is B because if you subtract the correct way then you should get 17

Answer:  B

Step-by-step explanation:

If the shapes are similar, the correspondent sides are in proportion:

[tex]AB\div DE = BC \div EF[/tex]

Let's plug the values and solve for x:

[tex]5x \div 5 = 4 \div x \iff \dfrac{5x}{5}=\dfrac{4}{x}\iff x = \dfrac{4}{x}[/tex]

Multiply both sides by x to get

[tex]x^2=4 \iff x=\pm2[/tex]

The only feasible solution, though, is [tex]x=2[/tex], because it wouldn't make sense to have negative lengths.

The value of x in the similar polygons in the given diagram is: B. x = 2.

Similar polygons have the same shape but different size, thus, the length of their corresponding sides are proportional together and have equal ratio.

In essence, we will have the following ratio:

5x/5 = 4/x

(x)(5x) = (4)(5)

5x² = 20

5x²/5 = 20/5

x² = 4

x = √4

x = 2 (option B)

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Answer:

the answer is:

d. 5

Answer:

d

Step-by-step explanation:

You reason this out by saying

4^x = 4^5

Since the bases are the same, the answer is x = 5

Answer:

(4, 2.4)

Step-by-step explanation:

(2x+5y=20)3

-

6x-5y=12

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

then....

6x+15y=60

-

6x-5y=12

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

0 + 20y = 48

y=2.4

plug in 2.4 into one of the equations and you get that x= 4

I have attached a hand drawn graph with the correct equation.Brainliest would be greatly appreciated!

Answer:

Part a) The translation between each position is 2 units to the left and 3 units down

Part b) The location of position 4 is (-3,-4)

Step-by-step explanation:

we know that

step 1

Position 1 is located at (3,5) and then go to position 2 at (1,2)

so

The rule of the translation Position 1 to Position 2 is

(x,y)-----> (x-2,y-3)

that means-----> The translation is 2 units to the left and 3 units down

step 2

Position 2 is located at (1,2) and then go to position 3 at (-1,-1)

so

The rule of the translation Position 2 to Position 3 is

(x,y)-----> (x-2,y-3)

that means-----> The translation is 2 units to the left and 3 units down

step 3

Find the location of the 4th position

Applying the rule of the translation to position 3 at (-1,-1)

(x,y)-----> (x-2,y-3)

(-1,-1)-----> (-1-2,-1-3) -------> (-3,-4)

The position 4 is (-3,-4)

Answer:

D.

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Answer:

The correct option is 3.

Step-by-step explanation:

The parent function is

[tex]f(x)=|x|[/tex]

The horizontal stretch and compression is defined as

[tex]g(x)=|bx|[/tex]

If 0<b<1, then it is horizontal stretch and if b>1, then it is horizontal compression.

Graph 1 passing thought the point (1,-1).

[tex]-1=|b(1)|[/tex]

This statement is false for any value of b, because the value of modulus can not be negative.

Graph 2 passing thought the point (1,2).

[tex]2=|b(1)|[/tex]

[tex]2=b[/tex]

Since b>1, therefore this graph represent the horizontal compression.

Graph 3 passing thought the point (2,1).

[tex]1=|b(2)|[/tex]

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

Since 0<b<1, therefore this graph represent the horizontal stretch.

Thus, the correct option is 3.

Answer:

$1444

Step-by-step explanation:

7% of 9200 = 644

644 + 800 = 1444

:)

he earned 8,301.56 last month

Answer:

H0:  µ = 85.1

Ha:  µ ≠ 85.1

Step-by-step explanation:

She wants to see if the number of days is different.  It could be higher or lower, so the alternate hypothesis uses the "not equal to" sign. If she wanted to see if it rained more on the farm, her alternate hypothesis would be

Ha:  µ > 85.1

If she wanted to see if it rained less, then she would use the alternate hypothesis of Ha: µ < 85.1  

The solution for the null hypothesis is given below,

H0:  µ = 85.1

Ha:  µ ≠ 85.1

When there are two possibilities then we calculate the null hypothesis if the hypothesis is true hypothesis is accepted if it is To conduct a hypothesis test for the above situation. We define the null hypothesis and the alternative hypothesis.

She is checking to see if the number of days has changed. The alternative hypothesis utilizes the "not equal to" marker since it might be either higher or lower. Her alternate hypothesis, if she wanted to determine whether it rained more frequently on the farm, is

Ha:  µ > 85.1

If she wanted to see if it rained less, then she would use the alternate hypothesis of Ha: µ < 85.1.

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Answer:

v^(20/21).

Step-by-step explanation:

v^2/3 x v^2/7

= v^(2/3 + 2/7)

= v^( 14/21 + 6/21)

= v^(20/21).

Answer:

39.473%

Step-by-step explanation:

It is actually fairly simple to get the answer to this. What you can do to find any percentage, is to take the amount done, or whatever it is in the scenario, and divide it by the total. It is like turning it into a fraction, which you can do as well. Turn this into a fraction, and then convert it. 15/38, 15 divided by 38 = 39.473.

Hope this helped ^-^

To find the percentage you have done, divide the number you did by the total number you have to do:

15 / 38 = 0.3947

Multiply that by 100 to get the percentage:

0.3947 x 100 = 39.47% ( Round as needed).

Answer:

a. 21 327 hot dogs/run

b. 70 runs/yr

c. 4 da/run

Step-by-step explanation:

Data:

Production rate (p)           = 5000/da

Usage rate (u)                  =    260/da

Setup cost (S)                   = $66

Annual carrying cost (H) = $0.45/hot dog

Production days (d)         = 294 da

Calculations:

a. Optimal run size

(i) Annual demand (D) = pd = (5000 hot dogs/1 day) × (294 days/1 yr)

= 1 470 000 hot dogs/yr

(ii) Economic run size

[tex]Q_{0}= \sqrt{\frac{2DS }{ h}\times\frac{ p}{p-u }}[/tex]

[tex]= \sqrt{\frac{2\times1470000\times66 }{ 0.45}\times\frac{ 5000}{5000-260 }}[/tex]

[tex]= \sqrt{431200000\times\frac{ 5000}{4740 }}[/tex]

[tex]= \sqrt{454852321}[/tex]

= 21 327 hot dogs/run

b. Number of runs per year

Runs = D/Q₀ = (1 470 000 hot dogs/1yr) × (1 run/21 327 hotdogs)

= 70 runs/yr

c. Length of a run

Length = Q₀/p = (21 327 hot dogs/1 run) × (1 da/5000 hot dogs)

= 4 da/run

To find the optimal run size, use the EOQ formula and calculate the square root. Divide the annual demand by the optimal run size to find the number of runs per year. Finally, calculate the length of a run by dividing the days in a year by the number of runs per year.

The optimal run size can be found using the Economic Order Quantity (EOQ) formula. EOQ = sqrt((2DS)/(H)) where D is the annual demand, S is the setup cost per order, and H is the holding cost per unit per year.

Using the given values:

D = 260 per day * 294 days = 76,440

S = $66

H = $0.45

EOQ = sqrt((2 * 76,440 * 66) / (0.45)) ≈ 6868

The optimal run size is approximately 6868 hot dogs.

The number of runs per year can be calculated by dividing the annual demand by the optimal run size:

Number of runs = 76,440 / 6868 ≈ 11.15

Since the factory operates 294 days a year, the number of runs per year is approximately 11.

The length of a run can be calculated by dividing the days in a year by the number of runs per year:

Length of a run = 294 / 11 ≈ 26.73

The length of a run is approximately 27 days.

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Answer:

B.) -2x^2-3

Step-by-step explanation:

You only need to look at the values of the offered answers for x=1 in order to determine the correct one.

A.) for x = 1, 2·1+3 = 5

B.) for x = 1, -2·1-3 = -5 . . . . matches the graph

C.) for x = 1, -1/2·1-3 = -3 1/2

D.) for x = 1, 1/2·1-3 = -2 1/2

___

Comparing the values at x=1 to the values at x=0, you find that f(1)-f(0) = 1, while g(1)-g(0) = -2. This tells you the multiplier is -2, so matches choice B.

The fact that the vertex of g(x) is 3 units below that of f(x) tells you that -3 has been added to the product -2x^2.

_____

Comment on vertical scale factor

Since 1^2 = 1, it is often convenient to look at a point that is 1 unit away from the vertex of the function. The function value relative to the vertex value at that point will tell you the vertical scale factor.

For example, we know that the coefficient of x^2 is 1 in f(x), and we see on the graph that f(1) is 1 unit above the vertex at (0, 0). The value of g(1) is -5, which is 2 units below the vertex of g(x) at (0, -3). So, the vertical scale factor is -5-(-3) = -2.

Answer:

18.6 units

Step-by-step explanation:

A rectangle is a four sided shape with 4 perpendicular angles. It has two pairs of parallel sides which are equal in distance: width and length. A diagonal can be drawn between opposite corners that splits the triangle into two equal right triangles. The distance of this diagonal is found using the Pythagorean Theorem a² + b² = c². In the rectangle a = 11 and b = 15. Substitute these values and simplify using a square root operation.

11² + 15² = c²

121 + 225 = c²

346 = c²

√346 = c

18.6= c

Final answer:

To simplify the expression, factorize the numerator and then cancel out any common terms with the denominator, resulting in the expression 1 / 3 + 2 / (3x).

Explanation:

To simplify the given expression 2x2 - 10x - 28 over 6x × (6x - 7), we need to factorize the numerator and see if any terms cancel out with the denominator. The factored form of the numerator is (2x + 4)(x - 7). The denominator can be written as 6x(6x - 7).

When we place the numerator over the denominator, we see that (x - 7) cancels out, simplifying our expression to (2x + 4) / 6x. This can further be simplified to 1 / 3 + 2 / (3x) by dividing both terms in the numerator by 6x

Answer:

Option B. [tex]5.5[/tex]

Step-by-step explanation:

we know that

Applying the law of cosines

Let

c------> the missing side length

[tex]c^{2}=9^{2}+6^{2} -2(9)(6)cos(37)[/tex]

[tex]c^{2}=30.747[/tex]

[tex]c=5.5[/tex]

Answer:

y = -2x+4

y = (3/2)x -3

The point of intersection is (2, 0), or x=2 and y=0.

Step-by-step explanation:

The downward-sloping line drops 2 grid squares for each 1 it goes to the right, so its slope is -2. It intersects the y-axis at +4. In slope-intercept form, its equation is ...

y = slope · x + (y-intercept)

y = -2x + 4

Similarly, the upward-sloping line rises 3 grid squares for each 2 it goes to the right, so its slope is 3/2. It intersects the y-axis at -3. Its equation is ...

y = (3/2)x -3

The two lines intersect at the point where x=2 and y=0, so the coordinates are (2, 0). These are the values of x and y that satisfy both equations, so are the solution to the system.

The total televisions sold over the weekend equals 177.

The cost of parking equals 50 cents for the first hour plus 25 cents for the additional 7 hours. Cost = .5 +7 x .25 = $2.25

In order to see if Tom is staying on his diet you need to add the total calories of the food that he is planning on eating for dinner. The total is 1,344 calories, so if he ate all of it he would not be staying on his diet.

The left sum would be f0+f1+f2+f3

The right sum would be f1+f2+f3+f4

The trapezoidal rule value is:

(f0+f1)/2 + (f1+f2)/2+(f2+f3)/2 +(f3+f4)/2

This would put the trapezoidal rule in the middle , which makes the answer:

Lower sum < Trapezoidal rule Value < Upper sum

Answer:

Step-by-step explanation:

Given function f(x) is positive, increasing and concave up on the closed interval [a, b],

it means f(x1) < f(x2) if x1 < x2

So Lower sum < Upper sum

As Trapezoidal is average of f(x1) and f(x2) = [f(x1) + f(x2)] / 2

it is average of the Lower and Upper sum.

The answer is Lower sum < Trapezoidal rule Value < Upper sum

Answer: 56 large cars and 86 small cars.

Step-by-step explanation:

Let's call:

[tex]l[/tex]: the number of large cars.

[tex]s[/tex]: the number of small cars.

Then, you can set up the following system of equations:

[tex]\left \{ {{l+s=142} \atop {5.50l+4.0s=652.50}} \right.[/tex]

You can use the Elimination Method:

- Multiply the first equation by -4.0

- Add both equations.

- Solve for l.

[tex]\left \{ {{-4.0l-4.0s=-568} \atop {5.50l+4.0s=652.50}} \right.\\--------\\1.5l=84.5[/tex]

[tex]l[/tex]≈[tex]56[/tex]

Substitute [tex]l=56[/tex] into one of the original equations and solve for s:

[tex]56+s=142\\s=142-56\\s=86[/tex]

Answer: Choice B

Step-by-step explanation: The correct answer is 10, because 10 is the largest number that can you can divide both of these numbers by evenly.

Answer:

The answer is the first answer

P = 8 + 4√13 cm

A = 36 cm²

Step-by-step explanation:

* Lets study the figure

- Its a kite with two diagonals

- The shortest one is 12 cm

- The longest one is 26 ⇒ axis of symmetry of the kite

- the shortest diagonal divides the longest into two parts

- The smallest part is 8 cm and the largest one is 18 cm

* To find the area reserved for the logo divide

 the hexagonal piece into two congruent trapezium

- The length of the two parallel bases are 4 cm and 8 cm and

  its height is 3 cm

- The length of non-parallel bases can calculated by Pythagoras rule

∵ The lengths of the two perpendicular sides are 2 cm and 3 cm

- 3 cm is the height of the trapezium

- 2 cm its the difference between the 2 parallel bases ÷ 2

  (8 - 4)/2 = 4/2 = 2 cm

∴ The length of the non-parallel base = √(2² + 3²) = √13

* Now we can find the area of the space reserved for the logo

- The area of the trapezium = (1/2)(b1 + b2) × h

∴ The area = (1/2)(4 + 8) × 3 = (1/2)(12)(3) = 18 cm²

∵ The space reserved for the logo are 2 trapezium

∴ The area reserved for the logo = 2 × 18 = 36 cm²

* The area of the reserved space for the logo = 36 cm²

* The perimeter of the reserved space for the logo is the

  perimeter of the hexagon

∵ The lengths of the sides of the hexagon are:

   4 cm , 4 cm , √13 cm , √13 cm , √13 cm , √13 cm

∴ The perimeter = 2(4) + 4(√13) = 8 + 4√13 cm

* The perimeter of the reserved space for the logo = 8 + 4√13 cm

Answer:

  see the attachment

Step-by-step explanation:

There are 16 ounces in 1 pound, so 96 ounces is 6 pounds. You solve this problem by making up the difference between the given amount and 6 pounds—basically, you subtract it from 6.

  6 - 3 1/2 = 2 1/2 . . . . for example

The answer is y = 6.43

Answer:

y = 6.43

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan47° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{6}[/tex]

Multiply both sides by 6

6 × tan47° = y

⇒ y = 6.43 ( to 2 dec. places )

Answer:

The amount of money A pays is [tex]\$51[/tex]

Step-by-step explanation:

Let

x-----> amount of money A pays

y-----> amount of money B pays

we know that

[tex]x+y=85[/tex] ------> equation A

[tex]\frac{x}{y}=\frac{3}{2}[/tex]

so

[tex]y=\frac{2}{3}x[/tex] ------> equation B

substitute equation B in equation A and solve for x

[tex]x+(\frac{2}{3}x)=85[/tex]

[tex]\frac{5}{3}x=85[/tex]

[tex]x=85*3/5=\$51[/tex]