Jim can swim 3/8 mile in 1/4 hr. What is Jim's unit rate?

The number of possibilities for 8 of 37 servers to fail is 38608020

From the question, we have

Total number of servers, n = 37

Numbers to servers that fail, r = 8

The number of ways for 8 serves to fail is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 37 and r = 8

Substitute the known values in the above equation

Total = ³⁷C₈

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 37!/29!8!

Evaluate

Total = 38608020

Hence, the number of ways is 38608020

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Answer: 4. helping the victim rest as comfortably as possible

Step-by-step explanation:

When a person goes into shock, it is as a result of insufficient blood flowing through to the tissues due to an external event. As a result, the person might begin cold, weak and thirsty as more blood is needed in certain places.

The first aid treatment for this is to get the person as comfortable as possible so that they enter a resting mode where less blood is needed. You can also elevate their legs IF you know this will not cause more harm.

The hypothesis, at the 0.05 significance level,

H₀ : the observed distribution of X may be fitted by the geometric distribution

Hₐ : the observed distribution of X may not be fitted by the geometric distribution

we conclude p-Value > α so, cannot reject null hypothesis. The observed distribution of X may be fitted by the geometric distribution g(x ; 1 / 2), x=1,2,3

A coin is thrown until a head occurs and the number X of tosses recorded.

The probability that head occur on toss ,p = 0.5

Consider the null and alternative hypothesis,

H₀ : the observed distribution of X may be fitted by the geometric distribution

Hₐ : the observed distribution of X may not be fitted by the geometric distribution

The chi square test statistic here as:

χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ

where Oᵢ--> observed value

Eᵢ --> expected value

and the expected frequencies for each X here E(x) = P(X = x) = 256×g(x)

The probability mass function of geometric distribution with parameter 1/2 is g(x) = (1/2)(1 - 1/2)⁽ˣ⁻¹⁾

where x = 0, 1,2 ,3,......

Observed values are f :136 60 34 12 9 1 3 1

Using the data,we calculate the expected values

E₁ = P( x = 1) = 256×g(1) = 256×(1/2)(1/2)⁰

= 128

E₂ = P( x =2) = 256×g(2) = 256×(1/2)(1/2)¹

= 64

E₃ = P( x = 3) = 256×g(3) = 256×(1/2)(1/2)² = 32

E₄ = P( x = 4) = 256×g(4) = 256×(1/2)(1/2)³

= 16

E₅ = P( x = 5) = 256×g(5) = 256×(1/2)(1/2)⁴

= 8

E₆ = P( x = 6) = 256×g(6) = 256×(1/2)(1/2)⁵

= 4

E₇ = P( x = 7) = 256×g(7) = 256×(1/2)(1/2)⁶

= 2

E₈ = P( x = 8) = 256×g(8) = 256×(1/2)(1/2)⁷

= 1

Hence, χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ

= (136 - 128)²/128 + (60 - 64)²/64 + (34 - 32)²/32 + (12-16)²/16 +(9 - 8)²/8 + (1 - 4 )²/4 + (3 - 2)²/2 +(1 - 1)²/1

= 0.5 + 0.25 + 0.125 + 1 + 0.125 + 2.25 + 0.5 =4.75

Significance level is α =0.05

Using the χ² table, the p- value for χ² is 0.6290 .. Now P value > 0.05 , therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we have sufficient evidence here that the frequencies given are fitted by the geometric (p = 0.5) distribution.

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Answer:

Step-by-step explanation:

I think it will be

Answer:

B

Step-by-step explanation:

As said in B, use the vertical line test. For any vertical line, does it hit the graph in two points? No. Therefore, the answer is B.

This particular function is f(x)=x^2.

Hope that helped,

-sirswagger21

Answer:

Yes is passes the vertical line test

Step-by-step explanation:

This parabola is a function. it has a one to one correspondence and passes the vertical line test

The percent cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage.

Let the cost price of rice is R and cost price of sugar is S.

Case 1 :  total cost of 5 kg rice and 6 kg sugar is Rs. 940.

5R + 6S = 940 ...(1)

Case 2 : rate of rice increased by 20% and the rate of sugar decreased by 10%.

The new cost price of rice = R + 20% of R = 1.2R

The new cost price of sugar = S - 10% of S = 0.9S

So, the total cost of 4 kg rice and 3 kg sugar will be Rs. 627.

Thus,

4 × 1.2R + 3 × 0.9S = 4.8R + 2.7S = 627 ..(2)

From equations (1) and (2) we have,

(5R + 6S)/(4.8R + 2.7R) = 940/627

R/S = 8/9

Hence, if the price of rice is 8 then the price of sugar is 9.

It is clear that the price of sugar is more than that of rice.

The percent cost by which cost of rice is less than sugar is:

(9 - 8)/ 9 (100) = 11 1/9%.

Hence, the cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

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The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

its c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I think it's d because the end of the table is on 12 so its less and more than 12.

Given statement solution is :- It takes approximately 1.122 seconds for the ball to reach its maximum height.

To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the parabolic function given by the equation h(t) = \(-4.9t^2 + 11t + 7.\)

The vertex of a parabola in the form y = \(ax^2 + bx\) + c is given by the formula t = -b / (2a).

Comparing the equation h(t) = \(-4.9t^2 + 11t + 7\) to the standard form, we have:

a = -4.9

b = 11

Using the formula for the vertex, we can calculate the time it takes to reach the maximum height:

t = -11 / (2 * -4.9)

t = -11 / -9.8

t ≈ 1.122

Therefore, it takes approximately 1.122 seconds for the ball to reach its maximum height.

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Answer:

\(\Huge \boxed{\boxed{ x = 1}}\)

Step-by-step explanation:

Isolate the variable on one side of the equation before trying to solve it. It means that you should only have constants (numbers) on the other side of the equal sign and the variable alone on the one side.

To do this, you can add, subtract, multiply, divide, or use any other operation to both sides of the equation as long as you do the same thing on both sides.

Your final step depends on the equation and how you've simplified it. In general, you want to figure out how you arrived at the final equation by working backwards from it. You'll isolate the variable in the last action you took.

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

Step1: Subtract \(\bold{2x}\) from both sides

Step 2: Subtract 3 from both sides

Step 3: Divide both sides of the equation by 6

So the solution to the equation \(\bold{8x + 3 = 2x + 9}\) is \(\bold{x = 1}\).

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1) The decimal 0.31313131...as a fraction is; 310/990

2) The decimal 0.02020202 as a fraction is; 200/9990

3) The difference of the two numbers as a repeating decimal is; 0.29292929

We are given the decimals as;

0.31313131...

0.02020202...

1) The decimal 0.31313131... is repeating decimal.

If we write it as;

x = 0.31313131...

Multiply both sides by 10 to get;

10x = 3.131313  --- (1)

Multiply both sides of initial equation by 1000 to get;

1000x = 313.131313   ----(2)

Subtract eq 1 from eq 2 to get;

990x = 310

x = 310/990

2) The decimal 0.02020202 is a repeating decimal.

If we write it as;

x = 0.02020202...

Multiply both sides by 100 to get;

10x = 2.020202  --- (1)

Multiply both sides of initial equation by 10000 to get;

10000x = 202.0202 02  ----(2)

Subtract eq 1 from eq 2 to get;

9990x = 200

x = 200/9990

3) The difference of the two numbers as a repeating decimal is;

0.31313131 - 0.02020202 = 0.29292929

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Answer:

0.75 .......................

Answer:

pretty sure its all real numbers

Step-by-step explanation:

the arrows imply it continues onward without a defined endpoint.

domain is the grouping of x-values represented.

The greater solution of x is x = -12 + 2√3 ÷ 3, and the lesser solution is x = -12 ± 2√3 ÷ 3.

Apart from integration, differentiation is one of the two key ideas in calculus. A technique for determining a function's derivative is differentiation. Mathematicians use a process called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time. Finding an antiderivative is the opposite of differentiation.

The given function \(f(x) = \frac{x}{x + 4}\).

The differentiation of the function is:

\(f'(x) = \frac{g(x)f'(x) - f(x)g'(x)}{g(x)^2} \\\\f'(x) = \frac{(x+4)(1) - x(1)}{(x+1)^2}\\\\f'(x) = \frac{x + 4 - x}{(x+4)^2} \\\\f'(x) = \frac{4}{(x+4)^2}\)

The value of f'(x) = 3:

Thus,

3 = 4/ (x + 4)^2

3(x + 4)^2 = 4

3(x² + 8x + 16) = 4

3x² + 24x + 48 - 4 = 0

3x² + 24x + 44= 0

Use the quadratic formula to find the roots of the equation:

x = -12 ± 2√3 ÷ 3

Hence, the greater solution of x is x = -12 + 2√3 ÷ 3, and the lesser solution is x = -12 ± 2√3 ÷ 3.

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Answer:

\(P(R\ and\ B) = 0.0256\)

Step-by-step explanation:

Given

\(Red = 22\)

\(Yellow = 38\)

\(Green = 20\)

\(Purple = 28\)

\(Blue = 26\)

\(Orange = 16\)

Required

Determine the probability of red then blue jelly? i.e. P(R and B)

From the question, we understand that the red jelly bean was not replaced. This means that the number of jelly beans reduced by 1 after the picking of the red jelly bean

So, we have:

\(P(R\ and\ B) = P(R)\ and\ P(B)\)

This is then solved further as:

\(P(R\ and\ B) = P(R)\ *\ P(B)\)

\(P(R\ and\ B) = \frac{n(R)}{Total}\ *\frac{n(B)}{Total - 1}\)

The probability has a denominator of Total - 1 because the number of jelly beans reduced by 1 after the picking of the red jelly bean

The equation becomes:

\(P(R\ and\ B) = \frac{22}{150}\ *\frac{26}{150- 1}\)

\(P(R\ and\ B) = \frac{22}{150}\ *\frac{26}{149}\)

\(P(R\ and\ B) = \frac{22*26}{150*149}\)

\(P(R\ and\ B) = \frac{572}{22350}\)

\(P(R\ and\ B) = 0.02559284116\)

\(P(R\ and\ B) = 0.0256\)

The solution of the given problem of Test statistic comes out to be Using a table or calculator with 98 degrees of freedom, we find the value to be approximately 0.06.

The test statistic for anything akin to a Z-test has been the Z-statistic, which shows the ordinary normal neutral hypothesis is correct. Suppose you perform a 2 different X y test with a 0.05 threshold of significance and, based on your data, you obtain a 2.5 R t (also referred as a Z-value). 0.0124 is the value for the this Z-value.

Here,

: un - ud <= 0 (the mean GPA of night students is less than or equal to the mean GPA of day students)

H: un - ud > 0 (the mean GPA of night students is greater than the mean GPA of day students)

We will use a significance level of 0.05.

The test statistic is calculated as:

t = (xn - xd - 0) / √(s²/n + s²/n)

where xn and xd are the sample means, s and s are the sample standard deviations, and n is the sample size.

Plugging in the values from the problem, we get:

t = (2.91 - 2.87 - 0) / √0.08²/50 + 0.06²/50) = 1.57

The degrees of freedom for the t-distribution is

f = n₁ + n₂ - 2 = 50 + 50 - 2 = 98 (assuming equal variances).

Using a table or calculator with 98 degrees of freedom, we find the

value to be approximately 0.06.

Since the value (0.06) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to support the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.05 significance level.

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In a case whereby a boat travels with velocity vector (25, 25√3) the directional bearing of the boat is ON 30° E.

The given velocity vector are; 25 and  25√3)

horizontal  components =25

vertical components =25√3

Then the angle

Tan(θ) = {vertical component / horizontal component }

= 25√3 / 25

= √3 / 1

= √3

Tangent √3= 60 degrees, Then the directional bearing of angle 60 degrees is 30° E

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The amount of money earned by Elisa in 22 years is obtained by summing the geometric series as $1366857.15.

In a geometric sequence, the ratio of two consecutive terms are always equal.

The general expression for the nth term is given as aₙ = a₁ × rⁿ⁻¹ .

The sum of n terms for this sequence is given as Sₙ = (rⁿ - 1)/(r - 1)

The earning for first year is $31500.

For, the next year it is 31500(1 + 6/100) = 1.06 × 31500

For another year, 1.06² × 31500

It implies that it is a geometric sequence with a₁ = 31500 and r = 1.06.

Now, the sum of first 22 terms is given by the following expression,

S₂₂ = a₁(r²²- 1)/(r - 1)

Plug a₁ = 31500 and r = 1.06 as,

⇒ 31500(1.06²²- 1)/(1.06 - 1)

⇒ 1366857.15

Hence, the money earned by Eliza in 22 years is obtained as $1366857.15.

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Answer:

C and D

Step-by-step explanation:

\(\cos(2x)\\=\cos(x+x)\\=\cos(x)\cos(x)-\sin(x)\sin(x)\\=\cos^2(x)-\sin^2(x)\\=\cos^2(x)-(1-\cos^2(x))\\=2\cos^2(x)-1 \,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option D}\\=2(1-\sin^2(x))-1\\=2-2\sin^2(x)-1\\=1-2\sin^2(x)\,\,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option C}\)

Answer:

48

Step-by-step explanation:

You are doubling 2 dimensions, so you just multiply the volume by 2 each time. Since you are doing it twice, you multiply the volume by 4. 12*4=48. You could also brute force it and just do 24*36*12/216(the volume of the 6 inch cube).

Given that, a box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side.

We need to find that how many cubes it holds if the length and width of the base are doubled,

We know that,

Volume of a rectangular prism = length × width × height

Volume of the new rectangular prism, = 2length × 2width × height

= 4(length × width × height)

= 4(12·12·18)

= 4×2592

= 10,368

Volume of the cube = side³

= 6³ = 216

The number of cube that the new rectangular prism can hold = Volume of the rectangular prism / Volume of the cube

= 10,368 / 216

= 48

Hence, the new rectangular prism, can hold 48 cubes.

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Answer:

three

Step-by-step explanation:

stem. is the tens place and the leaf is the. ones place

so you want to find 68 so you look in the stem column and look for six

in the row there are 6 numbers which mean:

60, 61, 67, 68, 68, 68

as you can see there is three 68 there for the answer ths 3

Answer:

1

Step-by-step explanation:

The probability of drawing a vowel, replacing it, and then drawing a Z is 5/676.

The alphabet consists of 26 letters, and 5 of them are vowels (A, E, I, O, U). Hence, 5/26 of the time, a vowel will be drawn in the initial draw.

The likelihood of drawing a Z on the second draw is also 1/26, due to the fact that the card is changed after the first draw.

We can multiply the probabilities to determine the likelihood that both of these occurrences will occur:

P(Draw a Z after a vowel is drawn) = P(Draw a vowel) P(Draw a Z after the vowel is replaced) = (5/26) (1/26) = 5/676

As a result, the likelihood of drawing a Z after substituting a vowel is 5/676.

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Answer:

Round both numbers to 1 significant figure.

400+400=800

800 is the answer.

Answer: 48

Step-by-step explanation:

V = b x h

V = 8 x 6

V = 48

Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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See the attached graph.

Answer:

x = 3

Step-by-step explanation:

\( {5}^{2x} \ast {5}^{3} = {5}^{9} \\ {5}^{2x + 3} = {5}^{9} \\ 2x + 3 = 9 \\ (bases \: are \: equal \: so \: exponents \: will \: also \: \\ be \: equal) \\ 2x = 9 - 3 \\ 2x = 6 \\ x = \frac{6}{2} \\ \huge \red { \boxed{x = 3}}\)

The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is