A recipe requires 31 cup of milk for each 41 cup of water. How
many cups of water are needed for each cup of milk?​

Answer:

option 1 both statements are true

Step-by-step explanation:

Prove by PMI -- Principle of Mathematical  Induction

1) n³ + 2n

n= 1 , 1³ +2*1 = 1+2 = 3 = 3*1   ---->divisible by 3

n = 2 ; 2³ + 2*2 = 8+4 = 12  = 3*4  ----> is divisible by 3

Assume that It is valid for n = k ;  

[tex]k^{3}+2k[/tex] = 3*m -----(I) , for all m ∈ N

We have to prove for n =k +1 , the statement is true.

n = k+1, [tex](k+1)^{3}+2(k +1) =k^{3}+3k^{2}+3k +1 +2k +2[/tex]

                                           = k³ + 3k² + 3k + 3 + 2k

                                           =  k³ +  2k + 3k² + 3k + 3

                                           = 3m + 3 (k² + k + 1)

                                          = 3(3 + [k² + k + 1] ) is divisible by 3

Therefore, this statement is true

2) [tex]5^{2n}-1\\[/tex]

[tex]n=1 ; 5^{2}-1 = 25 -1 = 24 divisible by 24\\\\n = 2 ; 5^{2*2}-1 = 5^{4}-1 = 625 - 1 = 624 divisible by 24[/tex]

This statement is also true

Answer:

  13.636

Step-by-step explanation:

The area can be found using Heron's formula:

  A = √(s(s-a)(s-b)(s-c))

where s=(a+b+c)/2.

For the given triangle, ...

  a=9, b=4, c=12, s=(9+4+12)/2 = 12.5

  A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636

The area of the triangle is about 13.636 square units.

Answer:

24 units\

Step-by-step explanation:

Answer:

0.8413

Step-by-step explanation:

p = 0.10

σ = √(pq/n) = 0.01

z = (x − μ) / σ

z = (0.11 − 0.10) / 0.01

z = 1

P(Z < 1) = 0.8413

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

We have,

We can use the normal approximation to the binomial distribution to find the probability that the proportion of books checked out in a sample of 899 books would be less than 11%.

First, we need to calculate the mean and standard deviation of the binomial distribution:

Mean:

np = 899 × 0.1 = 89.9

Standard deviation:

√(np(1-p)) = √(899 × 0.1 × 0.9) = 9.427

Next, we need to standardize the sample proportion of 11% using the formula:

z = (x - μ) / σ

where x is the sample proportion, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Substituting the values we have, we get:

z = (0.11 - 0.1) / 0.9427 = 0.1059

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 0.1059 is 0.5425.

Therefore,

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

Rounded to four decimal places, the answer is 0.5425.

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Answer:

39°

Step-by-step explanation:

==>Given:

Shadow length = 20ft

Flag height = 16ft

==>Required:

Angle of elevation of sun (θ)

==>Solution:

To calculate the angle of elevation of the sun, recall the trigonometry formula SOHCAHTOA.

We are given adjacent side = 20ft, and opposite side = 16ft

Therefore, we would use TOA, which is:

tan θ = Opposite/Adjacent

tan θ = 16/20

tan θ = 0.8

θ = 38.6598083 ≈ 39°

Angle of elevation of the sun = 39°

Answer:

2/3

Step-by-step explanation:

divide by a fraction = multiply by reciprocal

1/4 * 8/3

2/3

Answer:

⅔

Step-by-step explanation:

= ¼ ÷ ⅜

= ¼ × ⁸/3

= ⅔

Have a great day !

Answer:

Step-by-step explanation:

When you have several evaluations to do, it is often convenient to put the formula into a graphing calculator or spreadsheet.

__

If you must evaluate a polynomial by hand, it is often easier if the expression is written in "Horner form":

  g(x) = (-2x +3)x -5

Then we have ...

  g(-2) = (-2(-2) +3)(-2) -5 = 7(-2) -5 = -19

  g(0) = (-2(0) +3)(0) -5 = -5

  g(3) = (-2(3) +3)(3) -5 = (-3)(3) -5 = -14

Answer:

Yes

Step-by-step explanation:

b is as in 1b so. . .

2 + 1 = 3

We can plug in b or as "b"

2b + b = 3b

So yes in whatever case 2b + b's value  will always equal 3b's value

Answer:

yes

Step-by-step explanation:

because you can use any number to put for B and they will have the same value as an example we will use 3 for b so 2b = 6 + b = 9 and 3b = 9

The function is f(x)= 2x+1/x+3.

A work domain is a set of all possible inputs for a job. For example, the domain f (x) = x² is all real numbers, and the domain g (x) = 1 / x is all real numbers except x = 0. And we can define the special functions of its most limited domains.

The function domain f (x) is a set of all values ​​defined by the function, and the scope of the function is a set of all values ​​taken by f. (In grammar school, you probably call the domain a set of substitutes and a set of solutions.

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Answer:

B

Step-by-step explanation:

i got it right! :)

Answer:

60%

Step-by-step explanation:

Total Cards = 5

Even Numbers = 3

P(even) = 3/5

In %age:

=> 60%

Answer:

60%

Step-by-step explanation:

The numbers that are even from the list are 2, 4, and 6.

3 numbers are even out of 5 total numbers.

3/5 = 0.6

P(even) = 60%

Answer:

0.9 (9/10)

Step-by-step explanation:

(see picture)

Step-by-step explanation:

The difference between. Each numbers is 5 so, it's answer is 22 and 27

Answer:

1. Red red blue blue

2. Red blue red blue

Step-by-step explanation:

A 50 percent chance

Answer:

D.y-4=f(x+3)

Step-by-step explanation:

The correct translation would be y-4 because the y-coordinate moves down 4 units and f(x+3) because the x-coordinate would move 3 spaces to the right.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

The equation of the translation image of the function is  y - 4 = f(x + 3).

which is the correct answer would be an option (D).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit,  add 1 to the function

If shift down by 4 units, subtract 4 from the function

To determine the graph of y (x) is translated as 3 units right and 4 units down.

The x-coordinate will increase by 3 if we move it to the right.

If we shift it downward, it will become negative and read as y - 4.

So y - 4 = f(x + 3)

Therefore, the equation of the translation image of the function is  y - 4 = f(x + 3).

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Answer:

y = Vx - 5

Step-by-step explanation:

shift down is -5

y = Vx - 5 is the function whose graph is the graph of y= Vx, but is translated 5 units downward.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The function y = Vx represents the square root function, which is a graph of a half of a parabola opening upwards and passing through the point (0, 0).

To translate this function 5 units downward, we need to subtract 5 from the function. Therefore, the function we need is:

y = Vx - 5

This is the square root function shifted downward by 5 units.

The graph of this function will be the same as the graph of y = Vx, but shifted 5 units downward.

Hence, y = Vx - 5 is the function whose graph is the graph of y= Vx, but is translated 5 units downward.

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Answer:

(C)[tex]6t^2+5[/tex]

Step-by-step explanation:

Given the distance, d(t) of a particle moving in a straight line at any time t is:

[tex]d(t) = 2t^3 + 5t - 2, $ where t is given in seconds and d is measured in meters.[/tex]

To find an expression for the instantaneous velocity v(t) of the particle at any given point in time, we take the derivative of d(t).

[tex]v(t)=\dfrac{d}{dt}\\\\v(t) =\dfrac{d}{dt}(2t^3 + 5t - 2) =3(2)t^{3-1}+5t^{1-1}\\\\v(t)=6t^2+5[/tex]

The correct option is C.

Answer:

6t2+5

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

√12 can be rewritten as √2²·3 = 2√3

√75 can be rewritten as √5²·3 = 5√3

2/5 * 5 = 2

so

2√3 - 2/5 * 5√3 = 2√3 - 2√3 = 0

Answer:

0

Step-by-step explanation:

Answer:

Step-by-step explanation: 4

Answer:

see below

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

  = 4/3 pi ( 7)^3

  = 1372/3 pi in^3

Using 3.14 for pi

V =1436.0266666 in^3

Using the pi button

1436.75504 in^3

Answer:

30 ways

Step-by-step explanation:

Given the following :

Number of boys in school (n1) = 5

Number of girls in school (n2) = 3

Total number of team members to be selected = 4

Number of boys required in team(r1) = 2

Number of girls required in team(r2) = 2

How many different teams made up of two girls and two boys could be chosen?

= (2 boys from 5) * (2 girls from 3)

Using combination :

5C2 * 3C2

Recall :

nCr = n! ÷ (n-r)! r!

5C2 = 5! ÷ (5-2)! 2!

5C2 = 5! ÷ 3!2!

5C2 = (5*4) / 2 * 1 = 10ways

3C2 = 3! ÷ (3-2)! 2!

3C2 = 3! ÷ 1!2!

3C2 = (3) /  1 = 3ways

3C2 = 3/1 = 3ways

10 * 3 = 30 ways

Answer:

Width is 15, length is 35.We can check our answer by multiplying the length by 2 and the width by two in order for the perimeter to be equal to 200.15 times 2 is 30 and 35 times two equals 70.70+30=100 so our solution satisfies our problem.

Step-by-step explanation:

Let the width be x.Then the length should be x+20.The farmer can’t use more than 100 ft of fencing and by mentioning enclosing a rectangle area for a pigpen, we can tell that 100 is the perimeter.So 2(x+20) + 2(x)=100.2x+ 40 + 2x=100.4x+40=100.4x=60.X is 15 which is the width so then the length is 35.

Answer: 30 folders - 15 folders which she keeps = 15 folders; 15 folders / 3 friends = 5 folders per firend.

Step-by-step explanation:

Answer:

x= (30 -15)/3

Step-by-step explanation:

If we call x the number each friend gets, then the equation is:

Solving this we get:

Each friend gets 5 folders

Answer:

The answer is explained below

Step-by-step explanation:

What use are statistics if there is no engineer to use them? In other words, a statistician corrects, improves, reinforces, and supports an engineer in building / designing / developing a new product and / or improving an existing product.

The statistician provides a special kind of vision through which I see the same problem in a completely different vision. So you can see the strengths, weaknesses of my product and the promise of improvements that can be made.

Each class of statistics is essential for a student to see and understand a problem in a whole new way where it is much easier to understand information.

Answer:

B. y = 3x + 4

Step-by-step explanation:

Step 1: Find slope-intercept form of 1st equation

2y = 6x + 4

2y/2 = 6x/2 + 4/2

y = 3x + 2

A parallel line has the same slope but different y-intercept:

y = -3x + 3 (No, different slope)

y = 3x + 4 (Yes, same slope, different y-int)

y = x + 3 (No, different slope)

y = -2x - 3 (No, different slope)

y = 1/2x + 3 (No, different slope)

Answer:

1/2

Step-by-step explanation:

The non-even numbers are 1, 3, and 5 on the dice.

3 numbers out of 6.

3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

Total sides of 6-sided die = 6

Numbers not even = 3

Probability of not getting an even = 3/6

=> 1/2

Answer:

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

here is where stephen makes the mistake, he uses the 4 in the rooth and the 3 in the power.

so the expression actually is:

∛(16)/e

Answer:

Step-by-step explanation:

We assume you want the integral ...

  [tex]\displaystyle\int_4^{14}{\sqrt{\ln{x}}}\,dx[/tex]

The width of each interval is 1/6 of the difference between the limits, so is ...

  interval width = (14 -4)/6 = 10/6 = 5/3

Then the point p[n] at the left end of each interval is ...

  p[n] = 4 +(5/3)n

__

Trapezoidal Rule

The area of a trapezoid is the product of its average base length multiplied by the width of the trapezoid. Here, the "bases" are the function values at each end of the interval. The integral according to the trapezoidal rule can be figured as ...

  [tex]\dfrac{5}{3}\sum\limits_{n=0}^{5}\left(\dfrac{f(p[n])+f(p[n+1])}{2}\right)[/tex]

  integral ≈ 14.559027

If you're doing this on a spreadsheet, you can avoid evaluating the function twice at the same point by using a weighted sum. Weights are 1, 2, 2, ..., 2, 1.

__

Midpoint Rule

This rule uses the area of the rectangle whose height is the function value at the midpoint of the interval.

  [tex]\dfrac{5}{3}\sum\limits_{n=0}^{5}{f(p[n+\frac{1}{2}])}[/tex]

  integral ≈ 14.587831

__

Simpson's Rule

This rule gives the result of approximating the function over each double-interval by a parabola. It is like the trapezoidal rule in that the sum is a weighted sum of function values. However, the weights are different. Again, multiple evaluations of the function can be avoided by using a weighted sum in a spreadsheet. Weights for 6 intervals are 1, 4, 2, 4, 2, 4, 1. The sum of areas is ...

  [tex]\dfrac{10}{3}\sum\limits_{n=0}^{2}{\left(\dfrac{f(p[2n])+4f(p[2n+1])+f(p[2n+2])}{6}\right)}[/tex]

  integral ≈ 14.577542

Answer:

P-value =0.062

At a signficance level of 0.05, there is not enough evidence to support the claim that the unemployment rate is less than 5%.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the unemployment rate is less than 5%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]

The significance level is 0.05.

The sample has a size n=1500.

The sample proportion is p=0.041.

[tex]p=X/n=61/1500=0.041[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1500}}\\\\\\ \sigma_p=\sqrt{0.000032}=0.0056[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.041-0.05+0.5/1500}{0.0056}=\dfrac{-0.0087}{0.0056}=-1.5401[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-1.5401)=0.062[/tex]

As the P-value (0.062) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the unemployment rate is less than 5%.

Answer:

solution,

[tex] \frac{ac}{ef} = \frac{cb}{fd} \\ or \: \: \frac{12}{y} = \frac{15}{5} \\ or \: 15 \times y = 12 \times 5( \: cross \: multiplication) \\ or \: 15y = 60 \\ or \: y = \frac{60}{15} \\ y = 4[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

The value of y is 4

Step-by-step explanation:

What is similarity ?

In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given,

ΔACB~ΔEFD

The proportional sides are equal.

[tex]\frac{AC}{EF}=\frac{CB}{FD}=\frac{AB}{DE} \\\frac{12}{y}=\frac{15}{5} \\y=12*\frac{5}{15}\\\\ y=4[/tex]

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Answer:

Step-by-step explanation:

Product of 5 and a number:  5n

Six more than that would be 5n + 6

Finally, "six more than the product of 5 and a number, decreased by one" would be

5n + 6 - 1, or 5n + 5

Answer: A) 6 + 5n - 1

Step-by-step explanation: edge. 2022