the speeds of cars on a highway are normally distributed and have a mean of 68 mph with a standard deviation of 6 mph. if you are asked to find the probability that a sample of 25 cars has a mean speed that is less than 70 mph, which distribution would you use?

Two independent solution for the differential equation is,

\(x_{1}(t) = 1\)

\(x_{2}(t) = 1/t-1\)

Given,

Spring mass system is free oscillating free of damping .

Mass = 1

Time varying spring constant k(t) = t-1

For the arrangements of differential equation using newtons law ,

mx'' = -k(s+x) + mg

mx'' = -ks -kx +mg

∴ mg = kx

mx'' = ks -kx + kx

mx'' = -kx

Substitute m = 1 and k = t-1

x'' = -kx

x'' + (t - 1)x = 0

d²x /dt² + (t-1)x = 0  for t> 0

Function \(x^{r}\) is the solution of differential equation at (0, ∞) .

\(r(r-1)x^{r-2} + \frac{1}{x} rx^{r-1} - \frac{1}{x^{2} } x^{r}\) = 0  ∀ x > 0

r = 1 or r = -1

Thus the two independent solution for the differential equation is,

\(x_{1}(t) = 1\)

\(x_{2}(t) = 1/t-1\)

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Answer:

729 ways

Step-by-step explanation:

Given

Number of questions = 6

Choices = 3

Required

Number of ways of answering the questions

For each of the 6 questions;

There are 3 possible ways of selecting an answer;

The possible ways for the 6 questions is:

\(Possible\ Ways = 3 * 3 * 3 * 3 * 3 * 3\)

\(Possible\ Ways = 729\)

Hence, there are 729 ways of answering the question

Answer:

4

Step-by-step explanation:

3*4 is 12 and if you divide 12 by 3(the divisor) you will get 4

The dividend of the given divisor and quotient is 36.

The dividend is the number that is being divided in a division problem. In this case, we can use the formula:

Dividend = divisor × quotient

Here is the step-by-step explanation:

Therefore, if the divisor is 3 and the quotient is 12, the dividend is 36.

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Answer:

x=20-y

y=20-x

Step-by-step explanation:

divide by 2 on both sides: x+y=20

to find x, subtract y:

x=20-y

to find y, subtract x:

y=20-x

nothing else can be done unless you know either y or x.

The area of the region under the parabola y = 5x - x^2, where 1 ≤ x ≤ 4, is 14.33 square units.

To find the area under the parabola, we need to integrate the equation y = 5x - x^2 with respect to x over the given interval [1, 4]. The integral represents the area between the curve and the x-axis.

Integrating y = 5x - x^2 gives us the antiderivative F(x) = (5/2)x^2 - (1/3)x^3 + C, where C is the constant of integration. To find the definite integral over the interval [1, 4], we evaluate F(4) - F(1).

F(4) = (5/2)(4)^2 - (1/3)(4)^3 + C = 40 - (64/3) + C

F(1) = (5/2)(1)^2 - (1/3)(1)^3 + C = 5 - (1/3) + C

Substituting these values into the definite integral expression, we have:

Area = F(4) - F(1) = (40 - (64/3) + C) - (5 - (1/3) + C)

= 14.33

The area of the region under the parabola y = 5x - x^2, where 1 ≤ x ≤ 4, is approximately 14.33 square units.

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Answer:

p = 3

Step-by-step explanation:

Given

4(2 + px) = 12x

If the coefficient of the x- term is the same on both sides of the equation, it will have no solution.

Distributing gives

8 + 4px = 12x ( equate the coefficients of the x- term )

4p = 12 ( divide both sides by 4 )

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

4(2 + px) = 12x

8 + 4px = 12x

If the coefficient of the x-term is the same on both sides of the equation, it will have no solution.

4p = 12

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

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Answer:

I know the answer .    

Step-by-step explanation:

The overall sample for the survey consists of 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors, totaling 155 students.

To create an overall sample for the survey, the administrators selected a certain number of students from each class level. They randomly sampled 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors. By combining these individual samples from each class, the administrators obtained an overall sample size of 50 + 40 + 35 + 30 = 155 students. This overall sample represents a portion of the student population from each class level and allows for a representation of students from different academic years in the survey.

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Answer:

838 inches²

Step-by-step explanation:

Finding the area of the countertop including the hole

⇒ Area of countertop including hole: LB

⇒ Area of countertop including hole: (24)(48)

⇒ Area of countertop including hole: 1152 inches²

Finding the area of the hole (sink)

⇒ Area of hole: πr²

⇒ Area of hole: (π)(D/2)²

⇒ Area of hole: (π)(20/2)²

⇒ Area of hole: (π)(10)²

⇒ Area of hole: (π) x 100

⇒ Area of hole: 3.14 x 100 = 314 inches²

Finding the area excluding the hole

1152 - 314 = Area of countertop (excluding the hole)

838 inches² = Area of countertop (excluding the hole)

Answer:

YA if you said it first ya you are supposed to get brainlies ONLY if the question says will give brainliest if your right

Step-by-step explanation:

The constant of variation given that  r varies directly with p and inversely with the product of s and t is one-half

r ∝ p ∝ 1/st

r ∝ p / st

r = Kp / st

Cross multiply

r × st = Kp

Divide both side by p

K = rst / p => constant of variation

K = rst / p

K = (18 × 1/6 × 2) / 12

K = 6 / 12

K = 1 / 2 = one-half

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Answer:

a) Non car si le fils a 10 ans la mère a 30 ans et le père 33 or 10+30+33=73

b) Oui car si le fils a 12 ans la mère a 36 ans et le père 39 et 12+36+39=87

Step-by-step explanation:

The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

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5/8 is greater then 7/12.

Step-by-step explanation:

Find the least common denominator or LCM of the two denominators:

LCM of 8 and 12 is 24

For the 1st fraction, since 8 × 3 = 24,

5/8=5x3/8x3=15/24

Likewise, for the 2nd fraction, since 12 × 2 = 24,

7/12= 7x2/12x2=14/24

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

15/24>14/24 or 5/8>7/12

Answer:

k=42

Step-by-step explanation:

Answer:

k = 42

Step-by-step explanation:

That's a right angle, indicated by the square. A right angle is 90 degrees.

To find \((k+1)\), we need to subtract 47 from 90. 90 - 47 = 43.

To find k, we subtract 1 on both sides. k = 42.

Answer:

I dont know

Step-by-step explanation:

I was looking for the same answer to this question☠

The jack,s new payment per hour it will take t = 1 hour for Jack and his crew to lay the remaining (40 - x) = 25 yards of pavement.

To find out how long it will take Jack and his crew to finish laying the remaining pavement, we need to know how many yards are left after Sanjay and his crew finished.

If Sanjay and his crew laid 40 yards of new pavement, that means there are (40 - x) yards left to be laid, where x is the number of yards that Jack and his crew have already laid.

Assuming that Jack and his crew work at a constant rate of 15 yards per hour, we can use the formula:

time = distance / rate

where distance is the remaining number of yards to be laid and rate is the number of yards that Jack and his crew can lay per hour.

Substituting the values we have:

time = (40 - x) / 15

We want to find the time it will take for Jack and his crew to finish the remaining pavement, so we need to solve for x:

40 - x = 15t

where t is the time it will take for Jack and his crew to finish laying the remaining pavement.

Solving for x:

x = 40 - 15t

Substituting this value of x into the equation we derived earlier:

(40 - x) / 15 = t

Substituting x = 40 - 15t:

(40 - (40 - 15t)) / 15 = t

Simplifying:

15t / 15 = t

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1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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Answer:

9 gallons per minute

Step-by-step explanation:

441 divided by 49 is 9, so here's a way we can check it

49 = minutes

9 = estimated gallons

441 = goal we have to reach

49 x 9 = 441

Thus, meaning that every minute the pool fills with 9 gallons per minute

Answer:

the range is 8

Step-by-step explanation:

the range is the highest value number minus the lowest value number. You can find that by the whiskers of the box plot which are 10 and 2. 10 minus 2 is 8.

Please mark as brainliest

Answer:

8 is the answer

Step-by-step explanation:

Answer:

8

Thank you!!!

He probably won't get too suspicious if you get 100% on three quizzes when you regularly get A's in that class.  A ninety-something percent jump to a 100 is less than a 10-point increase.  

That being said, it's still best to learn the math so that you don't become dependent on using Brainly for every question.  Maybe only use it when you're having a lot of trouble with a particular problem or concept; but some of the explanations on here are actually really helpful in teaching things.

Answer:

Step-by-step explanation:

428÷107

Use the 1 st

 digit 4 from dividend 428

107)1

107)428

​

​ Since 4 is less than 107, use the next digit 2 from dividend 428 and add 0 to the quotient

107)02

107)428

​

​Use the 2nd

 digit 2 from dividend 428

107)03

107)428

​

​

Since 42 is less than 107, use the next digit 8 from dividend 428 and add 0 to the quotient

107)004

107)428

​

Use the 3rd

 digit 8 from dividend 428

107)005

107)428

​

​ Find closest multiple of 107 to 428. We see that 4×107=428 is the nearest. Now subtract 428 from 428 to get reminder 0. Add 4 to quotient.

107)0046

107)428

​

 107)428

​

 107)9990

​

 Since 0 is less than 107, stop the division. The reminder is 0. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.

Quotient: 4

Reminder: 0

With the measurements mentioned, 142 boxes may fit into the truck.

Volume is the quantity of space in a 3D object in arithmetic. A fish tank, for example, is 3 feet long, 1 foot wide, and 2 feet tall. To calculate the volume, multiply the length by the breadth by the height, which is 3x1x2, which is six. Volume is defined as the space occupied by an item inside the confines of three-dimensional space. It is also known as the object's capacity.

Here,

interior dimensions of truck,

=168 in x 96 in x 77 in

dimensions of storage boxes,

=24 in x 13 in x 28 in

=168 x 96  x 77/24 x 13 x 28

=142.12

142 boxes can fit into the truck with given dimensions.

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Answer:

C. y = ⁶/5x + ⁷/2

Step-by-step explanation:

First, find the slope of line AB that goes through A(3, 1) and B(-3, 6):

\( slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 1}{-3 - 3} = \frac{5}{-6} \).

Slope of line AB = -⅚.

The slope of the line that is a perpendicular bisector of line AB will be a negative reciprocal of the slope of line AB.

Thus:

Negative reciprocal of -⅚ = ⁶/5. (Reciprocal of ⅚, also the sign will change from positive to negative).

Next is to find the y-intercept, b, of the line.

To do this, you need to find the midpoint where the two lines intersect:

Therefore,

Midpoint (M) of AB, for A(3, 1) and B(-3, 6) is given as:

\( M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) \)

Let \( A(3, 1) = (x_1, y_1) \)

\( B(-3, 6) = (x_2, y_2) \)

Thus:

\( M(\frac{3 +(-3)}{2}, \frac{1 + 6}{2}) \)

\( M(\frac{0}{2}, \frac{7}{2}) \)

\( M(0, \frac{7}{2}) \)

Substitute x = 0, y = ⁷/2, and m = ⁶/5 into y = mx + b and find the value of b.

⁷/2 = ⁶/5(0) + b

⁷/2 = b

b = ⁷/2

The slope (m) and the y-intercept, b, of the line we are looking for are ⁶/5 and ⁷/2, respectively.

Therefore, substitute m = ⁶/5 and b = ⁷/2 into y = mx + b.

y = ⁶/5x + ⁷/2

The equation that is the perpendicular bisector of the line AB is y = ⁶/5x + ⁷/2.

The values are as follows: (a) -0.52, (b) 0.68, (c) 0.7764, (d) the value of the PDF at 0.8 using the given parameters, and (e) 0.3300.

(a) The value at which the cumulative distribution function (CDF) of a standard normal distribution (N(0,1)) takes on the value of 0.3 is approximately -0.52.

(b) The value at which the CDF of a standard normal distribution (N(0,1)) takes on the value of 0.75 is approximately 0.68.

(c) The value of the CDF of a normal distribution N(-2,5) at 0.8 can be calculated by standardizing the value using the formula Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation. After standardizing, we find that Z ≈ 0.76. Using a standard normal distribution table or calculator, we can determine that the CDF value at Z = 0.76 is approximately 0.7764.

(d) The value of the probability density function (PDF) of a normal distribution N(-2,5) at 0.8 can be calculated using the formula f(x) = (1 / (σ * √(2π\(^(-(x -\) μ)))) * e² / (2σ²)), where x is the given value, μ is the mean, σ is the standard deviation, and e is Euler's number (approximately 2.71828). Plugging in the values, we can compute the PDF at x = 0.8.

(e) The value of the CDF of a normal distribution N(-2,5) at -1.2 can be calculated in a similar manner as in part (c). After standardizing the value, we find that Z ≈ -0.44. Using a standard normal distribution table or calculator, we can determine that the CDF value at Z = -0.44 is approximately 0.3300.

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Answer: m=2 or m=6 works with it

Answer:

Acute Scalene Triangle

Step-by-step explanation:

This depends on the classification type. Because we are given both the angle measure and information on the sides, I am combining the angle and side classification.

1. In terms of angles, it's acute. All the angles are less than 90, so it makes it acute.

2. In terms of sides, it's scalene because it has no equal sides.

Answer:

first question : I think it's corresponding angle

second question : is lines AD and GH ,b/c skew means two lines that are not parallel and don't intersect

Step-by-step explanation:

HOPE THIS HELPS

a0 is the regression term that describes the constant or intercept in the linear regression equation.

In a simple linear regression model, the equation takes the form of y = a0 + a1x + e1, where y is the dependent variable (or response variable), x is the independent variable (or predictor variable), a0 is the intercept or constant term, a1 is the coefficient of the independent variable, and e1 is the error term.

The intercept term, a0, represents the value of the dependent variable when the independent variable is zero. For example, in a linear regression model that predicts salary based on years of experience, the intercept would represent the starting salary for someone with zero years of experience. The intercept is an important component of the regression equation because it allows us to make predictions for values of x that are outside the range of our observed data.

The coefficient, a1, represents the change in the dependent variable for each one-unit increase in the independent variable. In the salary example, the coefficient would represent the average increase in salary for each additional year of experience.

Both the intercept and coefficient are estimated from the data using methods such as least squares regression. Once these values are estimated, we can use them to make predictions for new values of x.

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