f(x) = 2x + 3 and g(x) = 24 – X.

Solve the equation f(x) = g(14).

20% of all people surveyed chose blue and 20% of the teachers surveyed chose green. Then the correct options are A and D.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Students and teachers at a school were asked if they preferred blue, green, red, or yellow.

The table shows the results of the survey.

[tex]\begin{matrix}&\rm Blue &\rm Green &\rm Red &\rm Yellow &\rm Total \\\\\rm Students &5 &10 &20 &15 &50 \\\\\rm Teachers &15 &10 &5 &20 &50\\\\\rm Total &20 &20 &25 &35 &100\end{matrix}[/tex]

A. The probability of the people who chose blue will be

[tex]\rm P = \dfrac{20}{100} = 0.2 \ or \ 20\%[/tex]

B. The probability of the student who chose red will be

[tex]\rm P = \dfrac{20}{50} = 0.4 \ or \ 40\%[/tex]

C. The probability of the student who chose blue will be

[tex]\rm P = \dfrac{5}{50} = 0.1 \ or \ 10\%[/tex]

D. The probability of the teachers who chose green will be

[tex]\rm P = \dfrac{10}{50} = 0.2 \ or \ 20\%[/tex]

E. The probability of the teachers who chose red will be

[tex]\rm P = \dfrac{5}{50} = 0.1 \ or \ 10\%[/tex]

F. The probability of the teachers who chose yellow will be

[tex]\rm P = \dfrac{20}{50} = 0.4 \ or \ 40\%[/tex]

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you could solve this problem one of two ways-

1)

100/4 25/2 12.5

100, equals the entire pizza. 4, is the number of people. 25, is the amount they all get. They you divide by 2 since it is only a half pizza.

-or-

2)

100/2 50 50/4 12.5

100, equals the entire pizza. Divide that by 2 since it half a pizza. 100/2 equals 50. Then, since there is 4 friends you divide 50 by 4. Which equals 12.5.

In conclusion, the final answer is 12.5% of the pizza each.

Hope this helps!!

Answer:

350 divided by 70

Step-by-step explanation:

350 by 5= 70  350 by 70 = 5

Hope this helps

Answer:

70

Step-by-step explanation:

Answer:

7x^3 -24x^2 +6x +37

Step-by-step explanation:

Step 1:

Expand (2x-3)^3

(2x)^3 - 3(2x)^2 * 3+3 * 2x * 3^2 -3

(8x^3 -36x^2 +54x -27)

Step 2:

Expand (x-4)^3

x^3 -3x^2 *4 +3x *4^2 -4^3

(x^3 -12x^2 +48x -64)

Step 3: Subtract and add like terms

(8x^3 -36x^2 +54x -27) - (x^3 -12x^2 +48x -64)

7x^3 -24x^2 +6x +37

Ans: 7x^3 -24x^2 +6x +37

Answer:

[tex]\dfrac12 < p < 5[/tex]

Step-by-step explanation:

To solve this, we need to use the discriminant.

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

If the given equation has 2 real roots, then we need to use:

[tex]b^2-4ac > 0[/tex]

Given equation:  [tex]8x^2-4x+1-p=0[/tex]

[tex]\implies a=8, \quad b=-4, \quad c=(1-p)[/tex]

Substituting these values into [tex]b^2-4ac > 0[/tex] and solve for p:

[tex]\implies (-4)^2-4(8)(1-p) > 0[/tex]

[tex]\implies 16-32(1-p) > 0[/tex]

[tex]\implies 16-32+32p > 0[/tex]

[tex]\implies -16+32p > 0[/tex]

[tex]\implies 32p > 16[/tex]

[tex]\implies p > \dfrac{16}{32}[/tex]

[tex]\implies p > \dfrac12[/tex]

For the roots to be less than 1, first find the value of p when the root is 1.

If the root is 1, then [tex](x-1)[/tex] will be a factor, so [tex]f(1)=0[/tex]

Substitute [tex]x=1[/tex] into the given equation and solve for p:

[tex]\implies 8(1)^2-4(1)+1-p=0[/tex]

[tex]\implies 5-p=0[/tex]

[tex]\implies p=5[/tex]

Therefore, the values of p for which the given equation has two different real roots less than 1 are:

[tex]\dfrac12 < p < 5[/tex]

Answer:

Tama po

Yan

Step-by-step explanation:

Enjoy po

Godbless

Answer:

38

Step-by-step explanation:

|-7|×|5|+18÷|-6|

First take the absolute value of each number, which means take the positive value

7×5+18÷6

Multiply and divide from left to right

35 + 3

Then add

38

Length x width x price
8x2 = 16

16x$3 = $48

the total cost is $48

Answer:

Step-by-step explanation:

Given

Combination Formula

Number of possible ways

The area of the region is 0.193 square units for the region bounded by the curves and find the area of the region.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

To find the area of the bounded region by the curves(refer to attached picture):

[tex]\rm A= \int\limits^2_1 {(\frac{1}{x}-\frac{1}{x^2}) } \, dx[/tex]

After solving:

A = 0.193 square units

Thus, the area of the region is 0.193 square units for the region bounded by the curves and find the area of the region.

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The volume of the conical mountain, to the nearest whole number, is approximately 143 cubic kilometers.

Volume of a cone = 1/3πr²h, where h os the height, r is the radius.

Given the following dimensions of the conical mountain:

Volume of the mountain = 1/3πr²h = 1/3π(6²)(3.8)

Volume of the mountain ≈ 143 km³

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Answer:

4r ^2 +9r + 12

Step-by-step explanation:

Hope this helps! :)

If it's a regular nonagon, each exterior angle has measure 360°/9 = 40°, so the supplementary interior angles each have measure 180° - 40° = 140°.

We can split up the nonagon into 9 congruent isosceles triangles whose longer side coincides with the radius of the circle. (The language in the question is a bit ambiguous; I think it's clearler to say the nonagon is itself circumscribed by the circle, so that each of its vertices lie on the circle. See attached image - not mine, but it's in public domain.)

As the image suggests, each triangle will have interior angles measuring 70°, 70°, and 40°.

We can use trigonometry to find the side length of the nonagon, i.e. the length of the shortest side of each triangle - I'll call it x. For example, using the law of cosines,

x² = 4² + 4² - 2 • 4 • 4 cos(40°)   ⇒   x = 4√2 √(1 - cos(40°))

Then the perimeter of the nonagon is

9x = 36√2 √(1 - cos(40°)) in ≈ 24.623 in

The area of a triangle is 1/2 the product of its base and height. The base will be b = x, but to get the height we cut the isosceles triangle in half to produce a right triangle. We use trig again to determine its height h:

tan(70°) = h/(b/2)   ⇒   h = 1/2 x tan(70°)

so each triangle contributes an area of

a = 1/2 bh = 1/4 x² tan(70°) ≈ 5.142 in²

and so the area of the nonagon is

9a = 9x²/8 tan(70°) ≈ 46.281 in²

Answer:

The area of figure is 29.

Step-by-step explanation:

By counting the square box.

Answer:

28.5 square units

Step-by-step explanation:

Spit it into a triangle and a rectangle.

The Triangle is

(3 * 3) / 2

= 9 / 2

= 4.5

The Rectangle is

3 * 8

=24

The total is 4.5 + 24 = 28.5

Answer:

Step-by step Explanation:

∴ Exponent rule: Any number that has an exponent as 0, the result is 1.

Thus, the result is 1.

Answer: 28 yards

You just have to multiple the 7 by the 4. :)

Answer:

D

Step-by-step explanation:

All you have to do is put it in desmos, hope this helped :)))

The graph of the equation is f ( x ) = x⁴ - x³ - 3x² + 3

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the equation of the graph be represented as A

Now , the value of A is

f ( x ) = x⁴ - x³ - 3x² + 3

There are no asymptotes for the function

And , the graph of the function is plotted below

Hence , the equation is f ( x ) = x⁴ - x³ - 3x² + 3

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Answer:

The answer is 50.

Step-by-step explanation:

Set up a proportion: [tex]\frac{41}{y} =\frac{82}{100}[/tex]
Step 2- Multiply 41 by 100 to get 4100
Step 3. Divide 4100 by 82 to get 50.
Hope this helps! :)

Answer:

(Chairs):C=29−8t/3

(Tables):T=87/8−3c/8

Step-by-step explanation:

For C: Move all terms that don't contain c to the right side and solve.

For T: Move all terms that don't contain t to the right side and solve.

(Do the same thing with the other numbers as well)

(CHeck your work for each one)

Answer:

4,569,760 different passwords

Step-by-step explanation:

[tex]26 \times 26 \times 26 \times 26 \times 10 = 4569760[/tex]

Digits can be repeated means repeatation is allowed

So

Total ways

Answer: D

Step-by-step explanation:

Answer:

D. 95 ≤ u ≤ 155

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Yes the one you clicked on is the right answer.

Answer:

E. 4/6 = 18/x

Step-by-step explanation:

4 hour using 6 logs

18 hours using x logs

Answer:

6√2

Step-by-step explanation:

Given,

θ = 45

Opposite side = 6

To find : - Hypotenuse

Formula : -

sin θ = Opposite side / Hypotenuse

[ The value of sin 45 = 1 / √2 ]

sin 45 = 6 / Hypotenuse

1 / √2 = 6 / Hypotenuse

Cross multiply,

Hypotenuse = 6√2

Answer:

6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

a 45-45-right triangle always has the same relationship between the legs and hypotenuse.

leg:leg:hypotenuse

x:x:x[tex]\sqrt{2}[/tex]

The function f(x) = |x| shift horizontally to the right by 5 units with a stretch of 3 units. The resulting function will be f(x) = 3|x - 5|

Transformation is a technique used to change the position of an object on an x-plane.

The parent function of the shown graph is f(x) = |x|

The attached graph shows that the function f(x) = |x| shift horizontally to the right by 5 units with a stretch of 3 units. The resulting function will be f(x) = 3|x - 5|

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Answer:

ALL RED = 19/5000

Two Red = 3831/10000

No red marbles = 16/26

Step-by-step explanation:

1. Find the total number of marbles

7+10+9= 26

2. There are 10 red marbles so the probability that the first marble is red 10/26

3. When the second marble there are 25 marbles so the probability that it is red is 9/25

4. Third Marble probability

8/24

5. Fourth Marble probablity

7/23

6. Fifth marble probability

6/22

7. Now to find that ALL the marbles are red you multiply all the fractions above

10/26 * 9/25 * 8/24 * 7/23 * 6/22 = 0.0038

8. Convert to fraction form

19/5000

9. Two marbles are red

5!/(3!*2!) * 10/26 * 9/25 * 16/24 * 15/23 * 14/22 = 0.3831

10. Convert to fraction

3831/10000