Evaluate the following expressions by substituting s = 10 and t = 2.
3t2s.
1. 110
2. 120
3. 100
4. 130

The probability that exactly 9 buyers would prefer green is 0.1408

We will use the Binomial probability formula to find the answer

The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ-ˣ

We have

n, the number of trial = 12

x, the sample we aim to try = 9

p, the probability of success = 0.6

Substitute these values into the formula

[tex]P(9)= ^{12}C_{9} (0.6)^{9} (1-0.6)^{12-9}[/tex]

P(9) = 0.1408 (rounded to four decimal places)

Hence, The probability that exactly 9 buyers would prefer green is 0.1408

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1.9

Step-by-step explanation:

A = kB/C -----------(1)

A=12

B = 3

C= 2

substitute A, B and C into equation (1).

12 = K × 3/2

12 = 3k/2

12×2 = 3k

3K = 24

dividing bothsides by 3

3K/3 = 24/3

K = 8

substitute K = 8 into equation (1)

A = 8B /C --------------(2)

Equation (2) is the equation connecting

A,B and C.

Finding B when A = 10 and C = 1.5

10 = 8B / 1.5

10× 1.5 = 8B

15 = 8B

Dividing bothsides by 8 :

B = 15/8

B = 1.875

B = 1. 9 ( approximately)

Answer:

[tex](x+8)^2=y;\ x\ge -8[/tex]

Step-by-step explanation:

So the inverse is when the x and y are swapped

Original equation:

[tex]y=\sqrt{x}-8[/tex]

Swap x and y:

[tex]x=\sqrt{y}-8[/tex]

add 8 to both equations:

[tex]x+8=\sqrt{y}[/tex]

Square both sides

[tex](x+8)^2=y[/tex]

Now while this looks like a normal quadratic, it has to have the range restriction the original function had, but as it's domain restriction. So the range of the original function was y >= -8, because the smallest value you could input is 0, and the square root of that is 0, then subtract 8 and you get -8. So the domain is x >= -8

Using it's concept, the desired probability is given as follows:

P(decaf or sugar) = 0.41.

A probability is given by the number of desired outcomes divided by the number of total outcomes. A probability can also be represented as a proportion.

From the table, we have that:

Hence:

P(decaf or sugar) = 0.22 + 0.19 = 0.41.

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The percentage of cars that are black when 80 cars of 300 cars are black is 26.67 or 26 2/3 %.

The percentage is similar to the fractional representation of quantities, where the quantity is shown as a part of the whole, but here the whole is fixed to be 100.

To derive a percentage in fractional form, we divide it by 100.

To derive a fractional form in percentage, we multiply it by 100.

In the question, we are given that 80 cars of 300 cars are black.

We are asked the percentage of cars that are black.

The fraction representing black cars of whole cars can be shown as 80/300 = 4/15.

To convert this into a percentage, we multiply it by 100.

Thus, the percentage of cars that are black = 4/15 * 100% = 80/3% = 26 2/3% = 26.67%.

Thus, the percentage of cars that are black when 80 cars of 300 cars are black is 26.67 or 26 2/3 %.

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The statement that best describes a relationship between angles in the figure is option d: m SRU = m QPS  x 2.

In Geometry, an angle is known to be any figure is is created  by two rays or lines that  is said to have a common endpoint known as  an angle.

Note that:

From the diagram, angle QPS   is right angle and angle SRU is an angle on a straight line.

Therefore:

= QPS  x 2

= 90 x 2

= 180 degrees

Angle SRU = 180 degrees

Therefore, The statement that best describes a relationship between angles in the figure is option d: m SRU = m QPS  x 2.

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Answer:

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

→ Evaluate n as 1, 2, 3 and 4 in 5n

5, 10, 15 and 20

→ Find the sum of these numbers

5 + 10 + 15 + 20 = 50

Answer:

x ≥ 21.5/19

Step-by-step explanation:

-1.5(4x + 1) ≥ 45 - 25(x + 1)

-6x - 1.5 ≥ 45 - 25x - 25

-6x + 25x ≥ 45 - 25 + 1.5

19x ≥ 21.5

x ≥ 21.5/19

(a) The lateral surface area of the prism is 720 sq units and the total surface area is 752 sq units.

(b) The lateral surface area of the cone is 136π sq units and the total surface area is 200π sq units.

(c) The lateral surface area of the cylinder is 242π sq units and the total surface area is 484π sq units.

L.S.A = Ph

where;

h² = 17² - 8²

h² = 225

h = 15

L.S.A = (3 x 16) x 15 = 720 sq units

T.S.A = PH + 2B

T.S.A = 720 + 2(16) = 752 sq units

L.S.A = πrt

where;

r² = 17² - 15²

r² = 64

r = 8

L.S.A = π(8)(17) = 136π sq units

T.S.A = πrt + πr²

T.S.A = 136π sq units + π(8)²

T.S.A = 200π sq units

L.S.A = 2πrh

where;

L.S.A = 2π(11 x 11) = 242π sq units

T.S.A = 2πrh + 2πr² = 2πr(r + h)

T.S.A = 2π(11)(11 + 11)

T.S.A = 484π sq units.

Thus, the lateral surface area of the prism is 720 sq units and the total surface area is 752 sq units.

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Answer: Draw a line through (0,5) and (1,2)

The graph is shown below.

=====================================================

Reason:

The equation y = -3x+5 is in the form y = mx+b

m = -3 = slope

b = 5 = y intercept

The y intercept is where the graph crosses the y axis. In this case, it's at (0,5). This is one point needed.

Another point can be found by going down 3 and to the right 1 to arrive at (1,2). The motion "down 3, right 1" is from the slope of -3/1.

Therefore, this line goes through (0,5) and (1,2)

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

Another approach:

Plug in x = 0 to get...

y = -3x+5

y = -3(0) + 5

y = 5

The input x = 0 leads to the output y = 5

This tells us the point (x,y) = (0,5) is on the line.

Repeat for x = 1

y = -3x+5

y = -3(1)+5

y = 2

So (1,2) is another point on the line.

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

Check out the graph below.

Step-by-step explanation:

[tex]y=-3x+5.\\[/tex]

x | 0 | 1 |

y | 5 | 2 |

By the definition of a rectangle, JML and KLM are right angles.

From the information given, JKLM is a rectangle based on the definition as the opposite sides are equal.

Also, JML and KLM will be 90° since they're right angles. The opposite sides of a rectangle are congruent and equal.

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Answer:

5

Step-by-step explanation:

→ Let x = √20 + √20 .....

x

→ Square both sides

x² = 20 + √20 +√20 + √20

→ Replace √20 +√20 + √20 with x

x² = 20 + x

→ Move everything to the left hand side

x² - 20 - x = 0

→ Factorise

( x + 4 ) ( x - 5 )

→ Solve

x = -4 , 5

→ Discard negative result

x = 5

Note that

[tex]\left(\sqrt{x+a} + b\right)^2 = \left(\sqrt{x+a}\right)^2 + 2b \sqrt{x+a} + b^2 = x + 2b \sqrt{x+a} + a+b^2[/tex]

Taking square roots on both sides, we have

[tex]\sqrt{x+a} + b = \sqrt{x + 2b \sqrt{x+a} + a+b^2}[/tex]

Now suppose [tex]a+b^2=0[/tex] and [tex]2b=1[/tex]. Then [tex]b=\frac12[/tex] and [tex]a=-\frac14[/tex], so we can simply write

[tex]\sqrt{x-\dfrac14} + \dfrac12 = \sqrt{x + \sqrt{x - \dfrac14}}[/tex]

This means

[tex]\sqrt{x-\dfrac14} = -\dfrac12 + \sqrt{x + \sqrt{x - \dfrac14}}[/tex]

and substituting this into the root expression on the right gives

[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x + \sqrt{x - \dfrac14}}}[/tex]

and again,

[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac14}}}[/tex]

and again,

[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac14}}}}[/tex]

and so on. After infinitely many iterations, the right side will converge to an infinitely nested root,

[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{\cdots}}}}}[/tex]

We get the target expression when [tex]x=\frac{41}2[/tex], since [tex]\frac{41}2-\frac12=\frac{40}2=20[/tex], which indicates the infinitely nested root converges to

[tex]\sqrt{20+\sqrt{20+\sqrt{20+\sqrt{\cdots}}}} = \sqrt{\dfrac{41}2 - \dfrac14} + \dfrac12 \\\\ ~~~~~~~~ = \sqrt{\dfrac{81}4} + \dfrac12 \\\\ ~~~~~~~~ = \dfrac92 + \dfrac12 = \dfrac{10}2 = \boxed{5}[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{81} -2\\=3-2 \\=1[/tex]

Answer:

6 quarts

Step-by-step explanation:

2 pints = 1 quart

4 cups = 1 quart

• 5 pints of orange juice

5 pints = 5/2 =>2.5 quarts

• 6 cups of grape juice

6 cups = 6/4 => 1.5 quarts

• 8 cups of apple juice

8 cups = 2 quarts

2.5 + 1.5 + 2 = 6 quarts

Step-by-step explanation:

f(x) = y = -1/2 × sqrt(x + 3), x >= -3

-2y = sqrt(x + 3)

4y² = x + 3

x = 4y² - 3

and now we need to rename x to y and y to x to make it a "normal" function :

y = 4x² - 3

since in the original function x >= -3, this gave us y <=0.

and therefore (remember the x of the inverse function actually stands for the y of the original function) the limit for the inverse function is x <= 0.

so, again, the full answer is

f^-1(x) = 4x² - 3, x <= 0

Answer:

Using the slope-intercept form, the slope is 34 . All lines that are parallel to y=3x4+2 y = 3 x 4 + 2 have the same slope of 34 .

Step-by-step explanation:

3/4

The slope of a line describes the steepness of a line, as well as the direction.

Slope-Intercept Form

To answer the question, we first need to find the slope of the original line. This line is represented in the slope-intercept form, which is y=mx+b.

So, using this information we can say that the slope is 3/4.

Parallel Lines

Parallel lines are 2 lines that will never intersect. You can tell if 2 lines are parallel by their slopes. All parallel lines have equal slopes.

This means that the slope of a line parallel to y = 3/4x + 2 must be 3/4 as well.

The angle pairs that we can observe from the figure are

Straight angle pairs, often referred to as linear pairs, are formed when two lines cross, creating two side-by-side angles that sum to 180 degrees. The requirement that the two angles in a straight angle or linear pair be adjacent is crucial. The two angles cannot form a linear pair if they are not side-by-side (share the same side) (even if they add to 180 degrees). Check out the depiction of straight angle/linear pairings in the picture below.

The angle pairs that we can observe from the figure are

As we can see in the following figure that supplementary angles are called angle pairs.

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Answer: 360

Step-by-step explanation:

The area of the bottom square is 100.

The area of each of the four triangular faces is 65.

Adding these together, we get 65(4) + 100 = 360.

The triangle ∆ABC inscribed in sphere P is given by the first graphic.

One figure is said to be inscribed in another figure when the vertices of the inscribed figure rests on the perimeter of the circumscribing figure.

The relationship between the figures in the given diagram are;

1st graphic : All points of the triangle ∆ABC are located on the surface of the sphere, P

Therefore;

2nd graphic: Point C of the triangle ∆ABC is located outside sphere P.

Therefore;

The 2nd graphic does not depicts ∆ABC inscribed in sphere P

3rd graphic: Point A of the triangle ∆ABC in the 3rd graphic is located outside sphere P.

Therefore;

The 3rd graphic does not depicts ∆ABC inscribed in sphere P

4th graphic: Point B of triangle ∆ABC in the 4th graphic is located outside sphere P.

Therefore;

The 4th graphic does not depicts ∆ABC inscribed in sphere P

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-0.22 as  a repeating fraction is -22/99

The decimal is given as:

-0.22

Express as fraction

-22/100

Subtract 1 from the denominator to rewrite it as a repeating number

-22/99

Hence, -0.22 as  a repeating fraction is -22/99

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Answer:

The given lines are perpendicular.

Step-by-step explanation:

In the question, two lines are given as line 1 passes through (0,5) and (3,3). Whereas, line 2 passes through (1,-5) and (3,-2).

It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.

To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{1}=\frac{3-5}{3-0} \\&m_{1}=\frac{-2}{3} \\&m_{1}=-\frac{2}{3}\end{aligned}$$[/tex]

Step 2 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{2}=\frac{-2-(-5)}{3-1} \\&m_{2}=\frac{3}{2} \\&m_{2}=\frac{3}{2}\end{aligned}$$[/tex]

And

[tex]$$\begin{aligned}&m_{1} m_{2}=-\frac{2}{3}\left(\frac{3}{2}\right) \\&m_{1} m_{2}=-1\end{aligned}$$[/tex]

Since, both slopes are reciprocals .

Therefore. the lines are perpendicular.

Answer:

108

Step-by-step explanation:

First evaluate both the squares separately, because combining the two within the sqrt symbol would result in a large number(harder to deal with).

sqrt81 = 9 (because 9*9=81)

sqrt144 = 12 (because 12*12=144)

Then multiply.

9*12 = 108

The percent of time the photographer spent negotiating with the bison greater than the time he spent taking pictures is 500%

Percentage of time negotiating greater than taking pictures = (difference in time) / time to take pictures × 100

= (30 - 5) / 5 × 100

= 25/5 × 100

= 5 × 100

= 500%

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The  trigonometry angle range -π ≤ α ≤ π in radians means angle α is

To answer the question, we need to know what a trigonometric angle range is

A trigonometric angle range is the range of values which the trigonometric angle can have

Since we need to find the meaning of the  trigonometry angle range -π ≤ α ≤π.

We know that

Since α is in the range -π ≤ α ≤ π = -180° ≤ α ≤ 180°, this implies that the angle α is

So, the  trigonometry angle range -π ≤ α ≤ π in radians means that angle α is

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The probability that the randomly selected student is female or Physics major is 0.625.

Given Information

Total number of students = 40

Number of Physics major out of the total students, P = 15

Number of females in the class, F = 16

Number of females that are Physics major, (P∩F) = 6

We have to find the probability P(P∪F).

Calculating the Probability

Probability of Physics major students, P(P) = 15/40

= 0.375

Probability of female students, P(F) = 16/40

= 0.4

Probability of female students who are Physics major, P(P∩F) = 6/40

= 0.15

Since, we know that,

P(P∪F) = P(P) + P(F) - P(P∩F)

∴ P(P∪F) = 0.375 + 0.4 - 0.15

P(P∪F) = 0.625

Thus, the probability that the randomly selected student will be a Physics major or a female is 0.625

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Answer:

no matter what he has to pay $52

Step-by-step explanation:

because it is annually.

The linear equation is represented by the second table as  y= -2 .5 x-15 and the solution to the system of equations is  (-6, 0).

First, take two point from the table and as such it will be:

P (-4, -5) and Q(-2, -10)

So the two point is used to create a straight line and as such it will be:

y - y₁ = y₂ - y₁/ x₂ - x₁ (x₁-x )

y -(-5) = [tex]\frac{-10-(-5)}{-2-(-4)}[/tex]  (x -(-4))

y + 5 = [tex]\frac{-5}{2}[/tex]  x +4

y + 5 =  [tex]\frac{-5}{2}[/tex]  x - 10

y =  [tex]\frac{-5}{2}[/tex]  x - 15

y= -2 .5 x-15

The linear equation is represented by the second table as  y= -2 .5 x-15 and the solution to the system of equations is  (-6, 0)

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Answer:

1st one option A to lazy to right out location

2nd one -6,0

Step-by-step explanation:

Answer:

Step-by-step explanation:

So in this case you need to use the Pythagorean Theorem which states that: [tex]a^2+b^2=c^2[/tex] where c is the value of the hypotenuse, and a and b are the other two sides (the order in which you put them doesn't matter). So in this case I'll say a=8.4 (I could've also input it as b, doesn't matter) and c=10.5 (here it does matter, c is hypotenuse, it's not the other sides...)

So given this information we have the equation:

[tex](8.4 cm)^2 + b^2 = (10.5 cm)^2\\[/tex]

Square known values:

[tex]70.56 cm^2 + b^2 = 110.25 cm^2[/tex]

subtract 70.56 cm^2 from both sides

[tex]b^2 =39.69 cm^2[/tex]

Take the square root of both sides

[tex]b=6.3 cm[/tex]

x=6.3 cm

Problem 3: a = 9 cm, c=20 cm

Input known values

[tex](9 cm)^2 + b^2 = (20 cm)^2[/tex]

Square known values

[tex]81 cm^2 + b^2 = 400 cm^2[/tex]

Subtract 81 cm^2 from both sides

[tex]b^2 = 319cm^2[/tex]

take the square root of both sides

[tex]b\approx 17.86 cm[/tex]

so the side x is approximately 17.86 cm