Find the missing side length BM. Round your answer to the nearest tenth.

Answer:

The weight of peanuts in the mixture   = 8  kg

The weight of corns in the given mixture = 4 kg

Step-by-step explanation:

Let us assume the weight of peanuts in the mixture   = x kg

The weight if corns in the given mixture = y kg

Total weight = (x + y) kg

The combined mixture weight = 12 kg

⇒ x  + y = 12  ..... (1)

Cost of per kg if mixture  = $ 40

So, the cost of (x + y) kg mixture  = (x+y) 40 = 40(x+ y)   ..... (2)

The cost of 1 kg of peanuts =  $ 42

So cost of x kg of peanuts  = 42 (x)  = 42 x

The cost of 1 kg of corns  = $ 36

So cost of y kg of corns  = 36 (y)  = 36 y

So, the total cost of x kg peanuts  + y kg corns =  42 x +  36 y  .... (3)

From (1) and (2), we get:

40(x+ y)  = 42 x +  36 y

x +  y = 12 ⇒ y = 12 -x

Put this in  40(x+ y)  = 42 x +  36 y

We get:

40(x+ 12 -x)  = 42 x +  36 (12 -x)

480 = 42 x + 432 - 36 x

or, 480 - 432 = 6 x

or, x  = 8

⇒ y = 12 -x = 12 - 8 = 4

⇒  y = 4

Hence, the weight of peanuts in the mixture   = 8  kg

The weight of corns in the given mixture = 4 kg

Final answer:

The weight of peanuts in the mixture is 8  kg and the weight of corns in the given mixture = 4 kg

Explanation:

A mixture of peanuts and corn sells for P40 per kilo.

Let us assume the weight of peanuts in the mixture   = x kg

The weight of corn in the given mixture = y kg

Total weight = (x + y) kg

The combined mixture weight = 12 kg

= x  + y = 12  ..... (1)

Cost of per kg if mixture  = $ 40

So, the cost of (x + y) kg mixture  = (x+y) 40 = 40(x+ y)   ..... (2)

The cost of 1 kg of peanuts =  $ 42

So cost of x kg of peanuts  = 42 (x)  = 42 x

The cost of 1 kg of corn = $ 36

So cost of y kg of corn  = 36 (y)  = 36 y

So, the total cost of x kg peanuts  + y kg corns =  42 x +  36 y  .... (3)

From (1) and (2):

40(x+ y)  = 42 x +  36 y

x +  y = 12 ⇒ y = 12 -x

Put this in  40(x+ y)  = 42 x +  36 y

We get:

40(x+ 12 -x)  = 42 x +  36 (12 -x)

480 = 42 x + 432 - 36 x

or, 480 - 432 = 6 x

or, x  = 8

= y = 12 -x = 12 - 8 = 4

= y = 4

To find the central angle of an arc with a length of 8/5 in a circle with a circumference of 12, we set up a proportion with the full circle's 360 degrees and solve for the angle, resulting in a central angle of 48 degrees.

You want to find the central angle of an arc in degrees for a circle with a circumference of 12 units and an arc length of 8/5 units. Since the circumference of a circle is 2π times the radius (2πr) and corresponds to a full circle or 360 degrees, the angle for the entire circle is 360°. The arc length of 8/5 is a fraction of the total circumference, so to find the corresponding angle in degrees, set up the proportion:

(arc length) / (circumference) = (angle of arc) / (360 degrees)

Plug in the known values and solve for the angle of the arc:

(8/5) / 12 = (angle) / 360

Cross-multiply to solve for the angle:

360 * (8/5) = 12 * (angle)

angle = (360 * 8) / (5 * 12)

angle = 48 degrees

Therefore, the central angle of the arc is 48 degrees.

Answer:

240π  

Step-by-step explanation:

Turbine blade that was 24 inches long is the radius of the circle the bug travels.

So the Circumference is = 2rπ = 2*24*π = 48π

The bug held on for 5 rotations. so the distance that the bug travels = 5*48π  = 240π  

Answer:

25 and 21 hours respectively

Step-by-step explanation:

Let the number of hours worked by each welder be x and y respectively.

They worked a total of 46 hours. This means :

x + y = 46 hours.......(I)

Now, given their hourly charges, since we have the total amount of money realized, we can make an equation out of it. This means:

34x + 39y = 1669........(ii)

We then solve both simultaneously. From I, x = 46 -y

We can substitute this into ii

34(46 -y) + 39y = 1669

1564 -34y + 39y = 1669

5y = 1669 - 1564

5y = 105

y = 105/5 = 21

x = 46 - y

x = 46 - 21 = 25 hours

The numbers of hours worked by the welders are 25 and 21 respectively

Final answer:

To determine the hours worked by each welder, we set up two equations based on their hourly rates and solve them. A system of equations is used to find that each welder worked 23 hours, each earning $782, summing to the total earnings of $1669.

Explanation:

To solve the problem of how many hours each welder worked, we need to set up two equations based on the given information. Let's designate x as the number of hours the first welder worked, and y as the number of hours the second welder worked. The first welder's rate is $34 per hour, and the second welder's rate is $39 per hour. We know that x + y = 46 because together they worked a total of 46 hours. We also have the total earnings equation, which is 34x + 39y = $1669.

We can now solve these equations using substitution or elimination. For instance, if we solve the first equation for x, we get x = 46 - y. Substituting this into the second equation gives us 34(46 - y) + 39y = $1669. After distributing and combining like terms, we can find the value for y, and then substitute back to find x.

After solving, we would find that the first welder worked 23 hours and the second welder worked 23 hours as well. Each welder earned $782, which adds up to the total earnings of $1669.

Option D: 13 units is the distance between the two points

Explanation:

Given that the points are [tex](-5,-2)[/tex] and [tex](8,-3)[/tex]

We need to find the distance between the two points.

The distance between the two points can be determined using the distance formula,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Let us substitute the points [tex](-5,-2)[/tex] and [tex](8,-3)[/tex] in the above formula, we get,

[tex]d=\sqrt{(8-(-5))^2+(-3-(-2))^2}[/tex]

Simplifying the terms within the bracket, we have,

[tex]d=\sqrt{(8+5)^2+(-3+2)^2}[/tex]

Adding the terms within the bracket, we get,

[tex]d=\sqrt{(13)^2+(-1)^2}[/tex]

Squaring the terms, we have,

[tex]d=\sqrt{169+1}[/tex]

Adding, we get,

[tex]d=\sqrt{170}[/tex]

Simplifying, we have,

[tex]d=13.04[/tex]

Rounding off to the nearest tenth, we get,

[tex]d=13.0 \ units[/tex]

Hence, the distance between the two points is 13 units.

Therefore, Option D is the correct answer.

To determine the distance between two points, we apply the distance formula, substituting the x and y coordinates for each point into the equation. After simplifying, the resulting square root of 170 corresponds to a distance of 13.0 units when rounded to the nearest tenth. Thus, the distance between the given points is 13.0 units.

Let's apply the distance formula to the two points given: (-5, -2) and (8, -3). The distance formula, d = √[(x2 - x1)2 + (y2 - y1)2], allows us to calculate the distance between two points in a Cartesian coordinate system.

First identify the x and y coordinates for each point. For the point (-5, -2), x1= -5 and y1= -2. For the point (8, -3), x2= 8 and y2= -3.

Step 1: Substitute these values into the distance formula.

d = √[(8 - (-5))2 + ((-3) - (-2))2]

Step 2: Simplify inside the square root, which involves removing the brackets and calculating the squares of the differences of the coordinates.

d=√[(13)2 + (-1)2 ] = √[169 + 1] = √170

The final distance d is the square root of 170. Rounded to the nearest tenth, this equals 13.0 units.

Therefore, the distance between point (-5, -2) and point (8, -3) is 13.0 units.

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Answer: the computer towers will be worth $10521 after 8 years

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

A represents the value of the computer towers after t years.

t represents the number of years.

P represents the initial value of the computer towers.

r represents rate of decay.

From the information given,

P = $30900

r = 12.6% = 12.6/100 = 0.126

Therefore, the function that models the value of the computer towers after (t)years from now is

A = 30900(1 - 0.126)^t

A = 30900(0.874)^t

Therefore, when t = 8 years, then

A = 30900(0.874)^8

A = $10521

Answer:

These should be the question: a) What is the average seek time = 149.995 ms, b) average rotational latency = 4.16667ms , c) transfer time for a sector = 13.88us, and d) total average time to satisfy a request = 153.1805ms.

Step-by-step explanation:

A) average seek time.

Number of tracks transversed = 299.99ms

Seek time to access  the track = 0ms

= (0+299.99)/2 ==> 149.995ms

B) average rotational latency.

Rotation speed = 7,200rpm

rotation time = 60 / 7,200 = 0.008333s/rev

Rotational latency = 0.008333/2 = 0.004166sec

= 4.16667ms

C) Transfer time for a sector

at 7200rpm, a rev = 60 / 7200 = 0.00833s :    8.33ms

transfer time one sector = 8.333/600 ms

                                         = 0.01388ms  => 13.88us

D) average time to satisfy request

149 + 4.16667 + 0.013888

153.1805ms

Japanese earthquake is 1996 times intense than the Pennsylvania earthquake.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

An earthquake measuring 6.4 on the Richter scale struck Japan in July 2007.

and, a minor earthquake measuring 3.1 on the Richter scale was felt in parts of Pennsylvania.

Mow,  Mj= log Ij/S and Mp = log Ip/ S

Where S is the standard earthquake intensity.

Then,

6.4 = log Ij/S and 3.1  = log Ip/ S

S x [tex]10^{6.4[/tex] = Ij  and S x [tex]10^{3.1[/tex] = Ip

So, ratio of the intensities

Ij : Ip= [tex]10^{6.4[/tex] /  [tex]10^{3.1[/tex]

      = [tex]10^{3.3[/tex]

      = 1996

Hence, Japanese earthquake is 1996 times intense than the Pennsylvania earthquake.

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Answer:

160 Chairs

Step-by-step explanation:

Convert 6 hrs to seconds, this gives you 21600 seconds. Convert 2 min and 15 sec to seconds, and this gives you 135 seconds per chair. Divide 21600 by 135. This gives you 160 Chairs produced in 6 hours.

Answer:

Step-by-step explanation:

You can use the cosine rule to solve this problem:

cos(∠KLJ) = (KL² + JL² - KJ²)/(2*JL*KL) = 21463/21960 = 0.97737

∠KLJ = cos⁻¹(0.97737) = 12.2°

Answer:

Step-by-step explanation:

We would apply the law of Cosines which is expressed as

a² = b² + c² - 2abCosA

Where a,b and c are the length of each side of the triangle and A is the angle corresponding to a. Likening the expression to the given triangle, it becomes

JL² = JK² + KL² - 2(JK × KL)CosK

122² = 39² + 90² - 2(39 × 90)CosK

14884 = 1521 + 8100 - 2(3510)CosK

14884 = 9621 - 7020CosK

7020CosK = 9621 - 14884

7020CosK = - 5263

CosK = - 5263/7020

CosK = - 0.7497

K = Cos^- 1(- 0.7497)

K = 138.6° to the nearest tenth

Option B: 5 is the value of f(3)

Explanation:

The equation of the piecewise function is given by

[tex]f(x)=\left\{\begin{aligned}-x^{2}, & x<-2 \\3, &-2 \leq x<0 \\x+2, & x \geq 0\end{aligned}\right.[/tex]

We need to find the value of [tex]f(3)[/tex]

The value of the function f can be determined when [tex]x=3[/tex] by identifying in which interval does the value of [tex]x=3[/tex] lie in the piecewise function.

Thus, [tex]x=3[/tex] lies in the interval [tex]x\geq 0[/tex] , the function f is given by

[tex]f(x)=x+2[/tex]

Substituting [tex]x=3[/tex] in the function [tex]f(x)=x+2[/tex], we get,

[tex]f(3)=3+2[/tex]

[tex]f(3)=5[/tex]

Thus, the value of [tex]f(3)[/tex] is 5.

Therefore, Option B is the correct answer.

Answer:

23

Step-by-step explanation:

if you have $16.10, he could buy 23 bluebarry muffins. Because if yo do

16.10 / 0.70 you woould get 23, and if you put that in the equasion you would

get this, P=$0.70(23) .  23 * 0.70 = 16.1

Answer:

  7

Step-by-step explanation:

5 × 7 = 35

35 cans of cola can be grouped into 7 groups of 5 cans. For each of those 7 groups, James needs to buy one orange soda.

James should buy 7 orange sodas.

The table represents an exponential function, and the function formula is: [tex]\[ y = 3 \cdot 2^x \][/tex]

To determine whether the table represents a linear or an exponential function, we need to examine the rate of change in the `y` values as `x` increases.

For a linear function, the rate of change (the difference between one `y` value and the next) is constant.

For an exponential function, the rate of change is multiplicative – the `y` value is multiplied by a constant factor as `x` increases by a regular increment.

Looking at the provided table:

- When `x` increases by 1 (from 0 to 1, from 1 to 2, etc.), the `y` values are:

 - At `x=0`, `y=3`

 - At `x=1`, `y=6`

 - At `x=2`, `y=12`

 - At `x=3`, `y=24`

 - At `x=4`, `y=48`

 - At `x=5`, `y=96`

 - At `x=6`, `y=192`

 - At `x=7`, `y=384`

Each time `x` increases by 1, `y` is doubled. This is a characteristic of an exponential function.

The pattern suggests that `y` is being multiplied by 2 as `x` increases by 1. Therefore, we can express the function as:

[tex]\[ y = ab^x \][/tex]

where `a` is the initial value of `y` when `x` is 0 (which is 3 in this case), and `b` is the factor by which `y` is multiplied each time `x` increases by 1 (which is 2 in this case).

So the exponential function that fits the table is:

[tex]\[ y = 3 \cdot 2^x \][/tex]

Thus the table represents an exponential function, and the function formula is:

[tex]\[ y = 3 \cdot 2^x \][/tex]

Answer:

1215

Step-by-step explanation:

Using the Binomial theorem

With coefficients obtained from Pascal's triangle for n = 6, that is

1  6  15  20  15  6  1

and the term 3x decreasing from [tex](3x)^{6}[/tex] to [tex](3x)^{0}[/tex]

and the term - y increasing from ([tex](-y)^{0}[/tex] to [tex](- y)^{6}[/tex]

Thus

[tex](3x-y)^{6}[/tex]

= 1 × [tex](3x)^{6}[/tex] [tex](-y)^{0}[/tex] + 6 × [tex](3x)^{5}[/tex] [tex](-y)^{1}[/tex] + 15 × [tex](3x)^{4}[/tex] [tex](-y)^{2}[/tex] + .........

The term required is

15 × [tex](3x)^{4}[/tex] [tex](-y)^{2}[/tex]

= 15 × 81[tex]x^{4}[/tex] y²

with coefficient 15 × 81 = 1215

that is 1215[tex]x^{4}[/tex]y²

Answer:

14 rows.

Step-by-step explanation:

We have been given that Jess  is planting rows of squash. To plant a row of squash Jess needs 6/7 square feet. There are 12 square feet in Jess's backyard.

To find number of rows that Jess can plant, we will divide total area of backyard by area needed to plant each row as:

[tex]\text{Number of rows that Jess can plant}=12\div\frac{6}{7}[/tex]

[tex]\text{Number of rows that Jess can plant}=\frac{12}{1}\div\frac{6}{7}[/tex]

Convert into multiplication problem by flipping the 2nd fraction:

[tex]\text{Number of rows that Jess can plant}=\frac{12}{1}\times \frac{7}{6}[/tex]

[tex]\text{Number of rows that Jess can plant}=\frac{2}{1}\times \frac{7}{1}[/tex]

[tex]\text{Number of rows that Jess can plant}=14[/tex]

Therefore, Jess can plant 14 rows of squash in her backyard.

Answer:

The Chef planner should prepare 320 cups of soups

Step-by-step explanation:

Number of guests expected to come = 800

2 out of every 5 guest will order for soup appetizer

Hence using equivalent ratios

2:5 = X :800

X = (800 × 2) ÷ 5 = 320

Hence the Chef planner should prepare 320 cups of soups

Asuming the added image is part of the complete question...

Answer:

C) rectangle C

Step-by-step explanation:

Observing the image we can see that when the rectangle C is reflected across the x-axis and then moved up 2 units, it will land exactly where the rectangle E is.

I hope you find this information useful and interesting! Good luck!

Answer:

C) Triangle C.

Step-by-step explanation:

The triangle C satisfies all the conditions described in the statement.

Answer:

the answer is going to be B

Step-by-step explanation:

if you you plug in the number witch is 3 for your x and -9 for y and solve it you notice that the statement is true for instance

-9+ 9 = -2/3(3 - 3)

0=-6/3+6/3

0=-2+2

0=0

if you subtract a negative with a positive its zero.

in the multiplication negative times negative turn positive

The point and slope of the equation y + 9 = -2/3(x - 3) are (3, -9), -2/3 respectively.

The equation y + 9 =-2/3(x - 3) is given in point-slope form. The point-slope form of a line's equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line. To find the point and the slope from the given equation, consider that x1 and y1 will have opposite signs to those in the equation because they get subtracted in the formula. Therefore, the point on the line is (3, -9), and the slope, m, which is the coefficient of x in the equation, is -2/3.

Answer:

0.81

Step-by-step explanation:

0.45 + 0.59 - 0.23

= 0.81

The probability that a randomly selected American either enjoys cooking or shopping or both is 0.81

The probability of the union of two events (A or B) is the sum of their individual probabilities minus the probability of their intersection (A and B).

i.e.

P(A or B) = P(A) + P(B) - P(A and B)

In this case, A represents the event of enjoying cooking, and B represents the event of enjoying shopping.

So, we have

P(A) = 45% = 0.45

P(B) = 59% = 0.59

P(A and B) = 23% = 0.23

By substitution, we have

P(A or B) = 0.45 + 0.59 - 0.23 = 0.81

Hence, the probability that a randomly selected American either enjoys cooking or shopping or both is 0.81 or 81%.

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Answer:

int i = 0; while (i < 4) { readData(); i = i + 1; }

Step-by-step explanation:

the above method is proper way to call the method readData four times because it will start from zero and will call readData until i=3, if i=4 it will stop calling readData.

double k = 0.0; while (k != 4) { readData(); k = k + 1; }

This is not the proper way to call readData four times because it will call readData only if k!=4 otherwise condition k!=4 will not be true and readData will not be called.

int i = 0; while (i <= 4) { readData(); i = i + 1; }

This is not the proper way to call readData four times because condition i<=4 will call readData five times starting from zero to 4.

int i = 0; while (i < 4) { readData(); }

This is not the proper way to call readData four times because it will call readData only one time i.e. value of is not incremented.

The proper way to call the 'readData()' method four times is by using a 'while' loop with a counter that starts at 0 and continues until it is less than 4, incrementing by 1 in each iteration.

The correct way to call the method readData() four times using a while loop is:

This loop initializes a counter variable i to 0, then enters a while loop that continues to iterate as long as i is less than 4. Inside the loop, the method readData() is called, and after each call, the counter i is incremented by 1. The loop will execute a total of four times before the condition i < 4 becomes false, thereby stopping the loop.

Answer:

40°

Step-by-step explanation:

Alternate angles

Angles BAC and ACD are equal

Answer:

a) 9(t - u)

Step-by-step explanation:

x = 10t + u

y = 10u + t

x - y = 10t + u - 10u - t

= 9t - 9u

= 9(t - u)

The required answer for the question is a) 9(t − u)

In mathematics , a set of simultaneous equations, also known as system of equations or an equation system, is a finite set of equations for which common solution are sought.

The given expression of x is given by,

x = 10t + u

If y be the 2-digit number formed by reversing the digits of x

then, the expression for y can be written,

y = 10u + t

Subtracting x with y we obtain,

x - y = 10t + u - 10u - t

Solving them we get

x - y = 9t - 9u

which can be written as,

x - y = 9(t - u)

Hence, the required expressions is equivalent to x − y =  9(t − u)

So the correct answer is a) 9(t − u)

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Answer:

log 2 ( 128 ) = x So C.

Step-by-step explanation:

Answer:

There is no significant improvement in the scores because of inserting easy questions at 1% significance level

Step-by-step explanation:

given that Montarello and Martins (2005) found that fifth grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of µ= 100 and a standard deviation of σ = 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions and gives the modified test to a sample of n = 36 students.

Set up hypotheses as

[tex]H_0: \bar x= 100\\H_a: \bar x >100[/tex]

(right tailed test at 1% level)

Mean difference = 104-100  =4

Std error of mean = [tex]\frac{\sigma}{\sqrt{n} } \\=3[/tex]

Since population std deviation is known and also sample size >30 we can use z statistic

Z statistic= mean diff/std error = 1.333

p value = 0.091266

since p >0.01, we accept null hypothesis.

There is no significant improvement in the scores because of inserting easy questions at 1% significance level

Final answer:

Using a one-tailed test with α = .01 and the provided test scores' information, the calculated z-value was 1.33, which did not surpass the critical value of 2.33. Therefore, it was concluded that there is insufficient evidence to support that inserting easy questions improves performance on the mathematics achievement test.

Explanation:

To determine if inserting easy questions into a standardized mathematics achievement test improves student performance, we conduct a hypothesis test using the given information: the test has a normal distribution of scores with mean µ = 100 and standard deviation σ = 18. A sample of n = 36 students took the modified test, scoring an average of M = 104. We use a one-tailed test with α = .01.

Step 1: Formulate the Hypotheses

Null Hypothesis (H0): µ = 100; the modifications do not affect test scores.

Alternative Hypothesis (H1): µ > 100; the modifications improve test scores.

Step 2: Calculate the Test Statistic

Use the formula for the z-score: z = (M - µ) / (σ/√n)

Substituting values: z = (104 - 100) / (18/√36) = 4 / 3 = 1.33

Step 3: Determine the Critical Value

For α = .01 in a one-tailed test, the critical z-value is approximately 2.33.

Step 4: Make a Decision

Since the calculated z-value of 1.33 is less than the critical value of 2.33, we do not reject the null hypothesis. Therefore, there is not sufficient evidence at the .01 level of significance to conclude that inserting easy questions improves student performance on the math achievement test.

Answer:

Yes.

Step-by-step explanation:

A prime number is a number that is ony divisible by itself and 1.

2 is only divisible by 2(=1) and 1 (=2)

Answer:

YES

Step-by-step explanation:

PRIME NUMBERS A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. ... The number 1 is neither prime nor composite.

Answer:

50

Step-by-step explanation:

7+7=14

14/7=2

2+7=9..

Answer:

50

Step-by-step explanation:

not enough information

Answer:

Thus, the pmf of the number of granite specimens selected for analysis is [tex]P(X=x)={20\choose x}0.50^{x}(1-0.50)^{20-x}[/tex].

Step-by-step explanation:

The experiment consists of collecting rocks.

The sample consisted of, 10 specimens of basaltic rock and 10 specimens of granite.

The total sample is of size, n = 20.

Let the random variable X be defined as the number of granite specimen selected.

The probability of selecting a granite specimen is:

[tex]P(Granite)=p=\frac{10}{20}=0.50[/tex]

A randomly selected rock can either be basaltic or granite, independently.

The success is defined as the selection of granite rock.

The random variable X follows a Binomial distribution with parameter n = 20 and p = 0.50.

The probability mass function of X is:

[tex]P(X=x)={20\choose x}0.50^{x}(1-0.50)^{20-x}[/tex]

Answer:

0.6517

Step-by-step explanation:

Given that in a certain game of chance, your chances of winning are 0.3.

We know that each game is independent of the other and hence probability of winning any game = 0.3 (constant)

Also there are only two outcomes

Let X be the number of games you win when you play 4 times

Then X is binomial with p = 0.3 and n =4

Required probability

= Probability that you win at most once

= [tex]P(X\leq 1)\\=P(X=0)+P(X=1)[/tex]

We have as per binomial theorem

P(X=r) = [tex]nCr p^r (1-p)^{n-r}[/tex]

Using the above the required prob

= 0.6517

Final answer:

To calculate the probability of winning at most once over four games with a win probability of 0.3, we calculate the binomial probabilities for winning 0 times and 1 time then add them, resulting in a total probability of approximately 0.6517.

Explanation:

The question involves calculating the probability of winning at most once in a game of chance played four times, where the chances of winning each game are 0.3. We use the binomial probability formula P(x) = C(n, x) * pˣ * q⁽ⁿ⁻ˣ⁾, where C(n, x) is the number of combinations, p is the probability of winning, q is the probability of losing (1-p), and n is the total number of games. In this case, n=4, p=0.3, and q=0.7. We need to find the probability of winning 0 times (P(0)) and 1 time (P(1)) and then add these probabilities together.

Adding these probabilities gives the probability of winning at most once as P(0) + P(1) = 0.2401 + 0.4116 = 0.6517. Therefore, the probability of winning at most once in four games is approximately 0.6517.

Answer:

  64 ft

Step-by-step explanation:

The equation can be factored as ...

  s = -16t(t -4)

This is the equation of a downward-opening parabola with t-intercepts of 0 and 4. The maximum height is at the vertex, halfway between those values, at t=2. At that time, the height is ...

  s = -16(2)(2-4) = 64 . . . . feet

The maximum height is 64 feet and it occurs at 2 seconds.

A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables. There are different types of polynomials such as linear, quadratic, cubic, etc.

A quadratic equation is of degree two and it has only two solution.

Given that  s= -16t²+64t

The maximum height is at ds/dt = 0

Hence:

ds/dt = -32t + 64

-32t + 64 = 0

32t = 64

t = 2 seconds

The maximum height is at 2 seconds, hence:

Maximum height = -16(2)² + 64(2) = 64 feet

The maximum height is 64 feet and it occurs at 2 seconds.

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