4. Five times the sum of 3 times a number and -5

(a) The probability of ending up with two hits is approximately 0.1406.

(b) The probability of ending up with no hits is approximately 0.4219.

(c) The probability of ending up with exactly three hits is approximately 0.0156.

(d) The probability of ending up with at most one hit is approximately 0.8438.

To solve the given problem, we need to use the concept of binomial probability since each at-bat is independent and has the same probability of a hit. We'll use the batting average of 0.250 to calculate the probabilities.

The probability of a hit is given by the batting average, which is 0.250.

(a) To find the probability that she ends up with two hits:

Using the binomial probability formula, the probability of getting exactly two hits in three at-bats can be calculated as follows:

P(X = 2) = (3 choose 2) * \((0.250)^2 * (1 - 0.250)^(^3^ -^ 2^)\)

Calculating the values:

P(X = 2) = (3 choose 2) * \((0.250)^2 * (0.750)^1\)

P(X = 2) = 3 * 0.0625 * 0.750

P(X = 2) ≈ 0.1406

Therefore, the probability that she ends up with two hits is approximately 0.1406.

(b) To find the probability that she ends up with no hits:

Using the same binomial probability formula, the probability of getting no hits in three at-bats can be calculated as follows:

P(X = 0) = (3 choose 0) *\((0.250)^0 * (1 - 0.250)^(^3^ -^ 0^)\)

Calculating the values:

P(X = 0) = (3 choose 0) *\((0.250)^0 * (0.750)^3\)

P(X = 0) = 1 * 1 * 0.4219

P(X = 0) ≈ 0.4219

Therefore, the probability that she ends up with no hits is approximately 0.4219.

(c) To find the probability that she ends up with exactly three hits:

Using the same binomial probability formula, the probability of getting three hits in three at-bats can be calculated as follows:

P(X = 3) = (3 choose 3) \(* (0.250)^3 * (1 - 0.250)^(^3^ -^ 3^)\)

Calculating the values:

P(X = 3) = (3 choose 3) *\((0.250)^3 * (0.750)^0\)

P(X = 3) = 1 * 0.0156 * 1

P(X = 3) ≈ 0.0156

Therefore, the probability that she ends up with exactly three hits is approximately 0.0156.

(d) To find the probability that she ends up with at most one hit:

We can find this probability by calculating the sum of the probabilities of getting 0 hits and 1 hit.

P(X ≤ 1) = P(X = 0) + P(X = 1)

Substituting the calculated values:

P(X ≤ 1) ≈ 0.4219 + P(X = 1)

To calculate P(X = 1), we can use the binomial probability formula as before:

P(X = 1) = (3 choose 1) * \((0.250)^1 * (0.750)^(^3^-^1^)\)

Calculating the values:

P(X = 1) = (3 choose 1) * \((0.250)^1 * (0.750)^2\)

P(X = 1) = 3 * 0.250 * 0.5625

P(X = 1) ≈ 0.4219

Substituting back into the equation:

P(X ≤ 1)

≈ 0.4219 + 0.4219

P(X ≤ 1) ≈ 0.8438

Therefore, the probability that she ends up with at most one hit is approximately 0.8438.

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For given right triangles the value of a = 6√2 and b = 5/√3

In this question we have been given two right triangles.

In the first right triangle, we need to find the value of b.

Consider the tangent of angle 30°

tan(30°) = b/5

1/√3 = b/5

b = 5 × (1/√3)

b = 5/√3

In the second right triangle, we need to find the value of a.

This right triangle is isosceles right triangle.

So, the sides of right triangle are: a, 6, and 6

Using Pythagoras theorem,

a = √(6² + 6²)

a = √[2×(6²)]

a = 6√2

Therefore, for given right triangles the value of a = 6√2 and b = 5/√3

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Step-by-step explanation:

The angle is 13.134 degree

I Hope this is right and help for you

good night :)

The amplitude of the function y = 3 - 4 sin(3x) is 4.

To find the amplitude of the function y = 3 - 4 sin(3x), we look at the coefficient of the sine function, which in this case is -4.

The amplitude of a sinusoidal function determines the maximum displacement from the midline.

In general, the amplitude represents the "height" or "magnitude" of the oscillation.

For the function y = 3 - 4 sin(3x), the amplitude is equal to the absolute value of the coefficient in front of the sine function, which in this case is |-4| = 4.

This means that the graph of the function oscillates vertically between a maximum value of 3 + 4 = 7 and a minimum value of 3 - 4 = -1, with a total vertical distance of 4 units.

It's important to note that the amplitude is always positive, as it represents the magnitude of the oscillation and is independent of any vertical shifts or translations of the function.

Understanding the amplitude helps in visualizing the range of the function's values and how it varies over the given domain.

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Answer is on the attachment...

☆...Hope this helps...☆

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Beckett spent $88 in total his estimate of $80 is wrong.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Beckett went to two different stores at the mall. He purchased a $36 hat at the first store and a $52 pair of shoes at the second. Beckett estimates that he spent a little less than $80 in total.

The total spending will be calculated as,

Total = 52 + 36

Total = $88

The estimated spending is $80. Therefore, Beckett spent $88 in total his estimate of $80 is wrong.

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The two given triangles are congruent because of SAS.

In geometry, two figures or objects are congruent if their shapes and sizes match, or if one is the mirror image of the other.  Both of the bread slices have the same shape and size when stacked on top of the other. Congruent refers to having the same precise size and shape. Having the same size and shape makes two shapes congruent. The mirror image of one shape is the same as the other if the two shapes are congruent.

The given triangles are RTP and STP

P is the midpoint of RS and TP is the altitude of triangle RTS.

In the triangles RTP and STP

TP = TP (common)

∠RPT = ∠ SPT (90°)

RP = SP (median divides the side equally)

So, both triangles are congruent using SAS property.

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Answer: Seven trillion i think

Step-by-step explanation:

Answer:It should be 49.365

Step-by-step explanation:

Answer:

the answer is 49.365

Step-by-step explanation:

because if you line the decimals up and just add normal

hope this helped

Answer:

It is not clear what you mean by "pre-image" in this context. However, based on the given information, we can say that the second triangle is a dilation of the first triangle.

A dilation is a transformation that changes the size of an object, but not its shape. In this case, the second triangle has the same shape as the first triangle, but its sides are scaled up by a factor of 8/3, which is greater than 1. Therefore, the second triangle is an enlargement (or a magnification) of the first triangle.

Answer: Your welcome!

Step-by-step explanation:

The transformation of the triangle is a reduction. This is because the side of the triangle that was 3 cm has been reduced to 8 cm, while the other two sides have stayed the same. This reduction has resulted in the triangle being smaller than the original triangle.

Answer:

I believe it is E. 95.

Hope this helps! Sorry if it doesn't!

Answer:

85

Step-by-step explanation:

180°-50°-35° = 95

180°-95° = 85°

sorry if I got it wrong

Answer:

C = 10 π cm

Step-by-step explanation:

Diameter is 2 x radius = 2*5.4 = 10.8 cm

radius r = 5 cm

diameter d = 10 cm

circumference C = 31.4 cm

area A = 78.5 cm2

In Terms of Pi π

circumference C = 10 π cm

area A = 25 π cm²

Formulas: Circle Formulas in terms of Pi π, radius r, and diameter d

Radius and Diameter:

r = d/2

d = 2r

Area of a circle:

A = πr2 = πd2/4

Circumference of a circle:

C = 2πr = πd

Answer:

c

Step-by-step explanation:

got it right on my test

The building's depression angle relative to the plane is found as  24.49°.

According to an aerial photographer who specializes in taking pictures of real estate properties.

The ideal shot should be taken at a height of around 406 feet and a distance of 891 feet from the structure.

Height h = 406 ft

Distance d =891 ft

The building's depression angle relative to the plane:

tan Ф = Height / Distance

tan Ф = 406 / 891

tan Ф = 0.455

Ф = 24.49°

Thus, the building's depression angle relative to the plane is found as  24.49°.

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Answer:

5 / 37

Step-by-step explanation:

Solution:-

- An archer stall game was played to receive a prize to pierce an arrow through a polka dot balloon.

- There are three types of balloons clustered together. The distribution of each balloon is given as such:

                 Type                        Number

                 Solid                             15

                 Striped                          17

                 Polka Dot                      5

- The probability of an arrow piercing through a polka dot balloon can be determined from the basic definition of probability of an event.

- Define event ( A ) : The number of Polka dots balloon popped

- Then, the probability of event ( A ) would be defined as:

    p ( A ) =  [ Number of polka dots balloons available ] / [ Total balloons ]

- We have 5 polka dots balloons among the cluster. The cluster comprises of balloons of all types with their specific distribution as expressed above. Hence:

                  p ( A ) = [ 5 ] / [ 15 + 17 + 5 ]

                  p ( A ) = [ 5 ] / [ 37 ]

- The probabbility that an arrow pops a polka dot balloon is 5 / 37.

Note: If we are given more than 1 arrow or multiple tries, then we must remember that the probability of event ( A ) changes after every popped balloon ( irrespective of type ). Hence, the probability of popping polka dot balloon is dependent event over number of trials. Except if you miss an arrow and none of the balloons is popped, only then the p ( A ) remains same for the next trial.

The rational numbers from the given numbers are -5/7, -6/7, 1/7, 2/7,3/7.

According to the statement

we have to find that the rational numbers.

So, For this purpose, we know that the

Rational number, a number that can be represented as the quotient p/q of two integers such that q ≠ 0.

From the given information:

The given numbers are between -1/2 and 4/7

Then to find the numbers then

Rational numbers = (-1/2 +4/7) /2

Rational numbers = (-1 +2/7)

Rational numbers = -5/7.

And then the number becomes -6/7, 2/7,3/7.

Now, The rational numbers from the given numbers are -5/7, -6/7, 1/7, 2/7,3/7.

So, The rational numbers from the given numbers are -5/7, -6/7, 1/7, 2/7,3/7.

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A relationship that has a zero slope include the following: A. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2.

In Mathematics, the slope of a linear relationship can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following slope and data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (2 - 2)/(-1 - (-3))

Slope, m = 0/2

Slope, m = 0.

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Answer:

IT IS C!!! ITS RIGHTTTTTTT

Answer:

∠ GHE = 40°

Step-by-step explanation:

∠ IHE and ∠ GHE are adjacent angles and are supplementary, then

∠ GHE + ∠ IHE = 180°

∠ GHE + 140° = 180° ( subtract 140° from both sides )

∠ GHE = 40°

The crying manchild can choose the 5 lollypops in 32 different ways.

The doctor allows a crying manchild to pick 5 lollypops from a bin that has an unlimited number of cherry, grape, lemon, and orange lollies. All pops of a particular color are essentially identical. To find out how many different ways the crybaby can choose these lollipops, we need to use the concept of combinations.

There are four types of lollies: cherry, grape, lemon, and orange. We can choose these types of lollies in 4C1 ways (which is equivalent to 4). For each type of lolly, the manchild can either choose that lolly or not. Therefore, we have two choices for each type of lolly.

Using the multiplication principle, we can multiply the number of choices for each lolly to get the total number of ways the manchild can choose the lollipops.

Thus, the total number of ways the manchild can choose the lollipops is:4 x 2 x 2 x 2 x 2 = 32 ways.

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Answer:

The answer above is wrong!! dont get fooled

Step-by-step explanation:

the answer is C. Length of a bead necklace compared with the number of identical

beads !!!

A                  p                          e                        x !!!!

The angles and length of the right triangle are as follows:

WX = 10√141 units

m∠X  = 30°

m∠V = 60°

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right angle triangle is 180 degrees.

Trigonometric ratios can be used to find the side and angles of the right triangle as follows;

Therefore,

Using Pythagoras's theorem,

WX² = (20√47)² - (10√47)²

WX² = 400(47) - 100(47)

WX² = 18800 - 4700

WX = √14100

WX = 10√141

Let's find the angles

sin m∠X  = opposite / hypotenuse

sin m∠X  = 10√47 / 20√47

sin m∠X  = 1 / 2

m∠X  = sin⁻¹ 0.5

m∠X  = 30 degrees

Therefore,

m∠V = 180 - 90 - 30

m∠V = 60 degrees

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The Annual Percentage Yield (APY) in this situation is approximately 2.454%.

To find the Annual Percentage Yield (APY) in this situation, use the formula:

\(APY = (1 + r/n)^n - 1\)

where:

- r is the annual interest rate (APR) expressed as a decimal,

- n is the number of compounding periods per year.

In this case, the APR is 2.42% or 0.0242 (expressed as a decimal), and the interest is compounded monthly, so there are 12 compounding periods per year (n = 12).

Substituting these values into the formula,

\(APY = (1 + 0.0242/12)^{12} - 1\)

Calculating this expression:

\(APY = (1 + 0.002017)^{12} - 1\)

  \(= (1.002017)^{12} - 1\)

   ≈ 0.02454 or 2.454%

Therefore, the Annual Percentage Yield (APY) in this situation is approximately 2.454%.

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Answer:

m <B = 41°

Step-by-step explanation:

Fact: complementary angles measures add to 90 degrees

Given: m < A = 2x-19,  and m <B = x+7

Find: m <B = ?

Find x

2x-19 + x+7 = 90

2x+x = 90 +19-7

3x = 102

x = 34

Find m <B

m <B = x+7

m <B = 34+7

m <B = 41

Answer:

\(Halfway = 4.5\)

Step-by-step explanation:

Given

4 and 5

Required

Determine the halfway

This is calculated as:

\(Halfway = \frac{1}{2}(4 + 5)\)

\(Halfway = \frac{1}{2}(9)\)

Remove bracket

\(Halfway = \frac{1}{2} * 9\)

\(Halfway = 4.5\)

Answer: 4 1/2

Step-by-step explanation:

This is because

This is found through trial and error.

This is for problem 1 only. Problems 2 through 6 will follow a similar structure.

Answer:

1, 10

Step-by-step explanation:

The differential equation to describe the situation is:
dP/dt = 0.000508 * P * (1 - P/732)

We can write a logistic differential equation to describe the rate of change of students who heard the rumor. The equation is:

dP/dt = k * P * (1 - P/M)

where dP/dt is the rate of change in the number of students who heard the rumor, k is a constant, P is the number of students who have heard the rumor at a given time, and M is the maximum capacity of the school (732 students).

At 12 PM, P = 227 and dP/dt = 24 students per hour. We can plug these values into the equation:

24 = k * 227 * (1 - 227/732)

Now, solve for k:

k ≈ 0.000508

So, the differential equation to describe the situation is:

dP/dt = 0.000508 * P * (1 - P/732)

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