The measures of the angles of a triangle are shown in the figure below. Find the
measure of the smallest angle.
90°
(4x-7)°
(3x-15)°

Answer:

P(B) = 0.20

Step-by-step explanation:

If A and B are events with P(A)=0.5, P(A OR B)=0.54, and P(A AND B)=0.16, find P(B).

Provide your answer below:

We are given two events A and B and the formula for the probability of two events is given as:

P ( A ∪ B) = P(A ) + P( B ) - P( A∩ B)

Where:

P(A)=0.5

P ( A ∪ B) = P(A OR B)=0.54

P( A∩ B) = P(A AND B)=0.16

P(B) = ??

Hence, we have:

0.54 = 0.5 + P(B) - 0.16

Making P(B) subject of the formula

P(B) = 0.54 - 0.5 + 0.16

P(B) = 0.20

Answer: SE = √. pA(1 - pA). nA. +. pB(1 - pB). nB. = √. 0.08(0.92). 200. +. 0.344(0.656). 200. = 0.039. (b) The sample sizes of 200 are large enough

Step-by-step explanation:

Answer:

line symmetry & rotational symmetry

Step-by-step explanation:

The measure of <1 is 31°.

Two angles are said to be vertical angles when they are formed by two straight lines intersecting at a point. This produces a series of angles of which some are vertical, thus they have equal measure.

In the information given in the question, it was given that <1 and <2 are vertical angles. This implies that they have equal measure, such that;

<2 = 31° (given)

So that;

<1 = <2 = 31°

Thus,

<1 = 31°

Therefore, it can be concluded that the measure of <1 is 31°.

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Part A: You can decompose Figure ABCDE into two triangles and two rectangles. The two triangles are triangle ABC and triangle AED. The two rectangles are rectangle BCD and rectangle AEB.

Part B: The length of Side AB is 4 units and the length of Side AE is 5 units.

Part C: To find the area of Figure ABCDE, we can simply add the areas of the two triangles and two rectangles. The area of triangle ABC is 3 units2, the area of triangle AED is 6 units2, the area of rectangle BCD is 10 units2, and the area of rectangle AEB is 3 units2. Thus, the area of Figure ABCDE is 3 + 6 + 10 + 3 = 22 units2.

Answer:

yes

Step-by-step explanation:

because x=3 in both scenarios

Answer:

The factorial of 11! is exactly 39916800

The number of trailing 0s in 11! is 2

The number of digits in 11 factorial is 8.

The factorial of 11 is calculated as below:

11! = 11 • 10 • 9 • 8 • 7 ... 3 • 2 • 1

Step-by-step explanation:

Answer:

10 root 2

Step-by-step explanation:

root 200 = root 2 × root 100 = 10 root 2

Answer:

m∠D = (180 - 62) / 2 = 59°

Step-by-step explanation:

Also m∠C = 59°

The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

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Answer:

y = x + 15

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = - x - 2. Its slope is -1. A line perpendicular to this will have a slope of 1.

Plug this value (1) into your standard point-slope equation of y = mx + b.

y = 1x + b or y = x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-5, 10). Plug in the x and y values into the x and y of the standard equation.

10 = (-5) + b

Simplify.

10 = -5 + b

Now, add 5 to both sides to isolate b.

15 = b

Plug this into your standard equation.

y = x + 15

This equation is perpendicular to your given equation (y = -x - 2) and contains point (-5, 10)

Hope this helps!

During halftime of a basketball game, a slingshot launches T-shirts at the crowd.

What is the maximum height?

Generally, To find the time it takes the T-shirt to reach its maximum height, we need to find the time when the height of the T-shirt stops increasing and starts decreasing. At this point, the velocity of the T-shirt will be 0, since it is not moving up or down.

The velocity of the T-shirt at any time t can be found by taking the derivative of the equation for height:

v(t) = dh/dt = -32t + 72

Setting the velocity to 0 and solving for t, we get:

0 = -32t + 72 32t = 72 t = 72/32 t = 9/4

So it takes the T-shirt 9/4 seconds, or approximately 2.25 seconds, to reach its maximum height.

To find the maximum height, we plug this value back into the equation for height:

h(t) = -16(9/4)^2 + 72(9/4) + 4 h(t) = -81 + 162 + 4 h(t) = 77

The maximum height of the T-shirt is 77 feet.

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Answer:

88.4505 kilograms

Step-by-step explanation:

Answer:

\(f(3) = \frac{-26}{9}\)

\(f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}\)

Step-by-step explanation:

Given

\(f(x) = \frac{1}{x^2} - 3\)

Required

Find f(3) and f(2 + h)

Solving f(3)

Substitute 3 for x in \(f(x) = \frac{1}{x^2} - 3\)

\(f(3) = \frac{1}{3^2} - 3\)

\(f(3) = \frac{1}{9} - 3\)

Take LCM

\(f(3) = \frac{1 - 27}{9}\)

\(f(3) = \frac{-26}{9}\)

Solving f(2 + h)

Substitute 2 + h for x in \(f(x) = \frac{1}{x^2} - 3\)

\(f(2 + h) = \frac{1}{(2 + h)^2} - 3\)

\(f(2 + h) = \frac{1}{(2 + h)(2 + h)} - 3\)

\(f(2 + h) = \frac{1}{4 + 2h + 2h + h^2} - 3\)

\(f(2 + h) = \frac{1}{4 + 4h + h^2} - 3\)

Take LCM

\(f(2 + h) = \frac{1- 3(4 + 4h + h^2)}{4 + 4h + h^2}\)

\(f(2 + h) = \frac{1- 12 - 12h - 12^2}{4 + 4h + h^2}\)

\(f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}\)

The number of times that the band played an encore at 7 out of the next 14 shows.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The band should do an encore at a rate of 2 out of every 4 gigs, or 2/4 = 1/2 shows, according to the available statistics.

We may use the following percentage to determine how many of the following 14 performances will likely have an encore:

1/2 = x/14

14 = 2x

x = 7

Therefore, we can expect the band to play an encore at 7 out of the next 14 shows.

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On the fifth day there were 4 tοmatοes left tο be sοld. Jοann had 71 tοmatοes tο begin with.

Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 indicates that the event is impοssible, and 1 indicates that the event is certain tο οccur.

Let's wοrk backwards frοm the last day and figure οut hοw many tοmatοes Jοann had οn the fοurth day.

On the fifth day, there were 4 tοmatοes left tο be sοld, which means she sοld half οf what was left οn the fοurth day. Sο she must have started with 8 tοmatοes οn the fοurth day (since half οf 8 is 4).

On the fοurth day, she sοld half οf what was left, which means she had 16 tοmatοes befοre she sοld any.

On the third day, she sοld 12 tοmatοes, which means she had 28 tοmatοes befοre she sοld any.

On the secοnd day, she sοld half οf what was left, which means she had 56 tοmatοes befοre she sοld any.

Finally, οn the first day, she sοld 15 tοmatοes.

Therefοre, Jοann had 71 tοmatοes tο begin with.

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Answer:

  5/10

Step-by-step explanation:

An equivalent fraction will have the numerator and denominator multiplied by the same value.

The denominator of 2 must be multiplied by 5 to get a denominator of 10. Then the equivalent fraction is ...

  \(\dfrac{1}{2}=\dfrac{1}{2}\cdot\dfrac{5}{5}=\dfrac{1\cdot5}{2\cdot5}=\boxed{\dfrac{5}{10}}\)

Answer:

Area of the given regular pentagon is 61.5 cm².

Step-by-step explanation:

Area of a regular polygon is given by,

Area = \(\frac{1}{2}aP\)

Here, a = Apothem of the polygon

P = Perimeter of the polygon

Apothem of the regular pentagon given as 4.1 cm.

Side of the pentagon = 6 cm

Perimeter of the pentagon = 5(6)

                                             = 30 cm

Substituting these values in the formula,

Area = \(\frac{1}{2}(4.1)(30)\)

        = 61.5 cm²

Therefore, area of the given regular pentagon is 61.5 cm².

Answer:

C. 4218.75

Step-by-step explanation:

1. We can see that A, C, and D are given to us. (A=3, C=2, and D=5)

2. You input the values of A, C, and D into the equation.

      --> \(log_b\frac{(3)^3 (5)^4}{(2)^2}\)

3. Simplify.

      --> \(log_b\frac{(27)(625)}{4}\)

         = \(log_b\frac{16,875}{4}\)

         = \(log_b 4,218.75\)

Answer:

IG=28.9 ft

Step-by-step explanation:

we know that

In the right triangle GHI

----> by CAH )adjacent side divided by the hypotenuse)

substitute the given values

solve for IG

see the attached figure to better understand the problem

Answer:

H=38.2466≈38.2

Step-by-step explanation:

Answer:

3/4 there are 4 lines indicating the numbers and it is on the 3rd.

The equation of the line is y = 4 and the y-coordinate of every point along this line is 4.

The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the y-axis, also known as the y -intercept.

Given that, we need to find an equation of a line passing through given points,

Considering two points, (-3, 4) and (1, 4)

We know that, the equation of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by,

(y-y₁) = (y₂ - y₁ / x₂ - x₁)(x-x₁)

Here, (x₁, y₁) and (x₂, y₂) = (-3, 4) and (1, 4)

Therefore, the equation =

y-4 = 4-4 / 1+3(x+3)

y-4 = 0

y = 4

Since, the slope is zero and y-intercept is 4 that mean, the line given is parallel to x-axis,

Hence, all the y coordinates will be 4.

Hence, the equation of the line is y = 4 and the y-coordinate of every point along this line is 4.

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Answer:

The answer is 30 scoops.

Step-by-step explanation:

6/(1/5) is also equal to 6x5. If we do this problem 6x5 we get 30.

Answer:

30 scoops

Step-by-step explanation:

Step 1:

6 ÷ 1/5

Step 2:

6/1 ÷ 1/5

Step 3:

6/1 × 5/1

Answer:

30

Hope This Helps :)

Answer:

  k = 110

Step-by-step explanation:

You want the integer multiple of pi that is the area of 300° of a donut with inner radius 8 cm and outer radius of 14 cm.

The area of a circle is given by the formula ...

  A = πr²

Then the area of the outer circle is ...

  A = π(14 cm)² = 196π cm²

The area of the inner circle is ...

  A = π(8 cm)² = 64π cm²

The area of the whole donut is the difference of these areas:

  whole donut area = (196 -64)π cm² = 132π cm²

The shaded area of the figure represents 300° of the 360° full donut. The area is proportional to the central angle, so the shaded area is ...

  shaded area = (300°/360°)×whole donut area

  shaded area = 5/6 × 132π cm² = 110π cm²

Comparing this to the expression kπ cm², we see that ...

  k = 110

The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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