in a standardized exam the mean score is 400 with a standard deviation of 50. if a random sample of 25 students is selected , what is the standard deviation of the sampling distribution of the sample mean ?

The four fundamental subspaces of a matrix are the row space, column space, null space, and left null space.(a) A basis for the row space of A is {{1,2,3}, {2,3,4}}. The row rank of A is 2.(b) A basis for the column space of A is {{1,2}, {2,3}, {3,4}}.

(c) A basis for the null space of A is {{-1,1,0}, {1,-2,1}, {0,1,-1}}. The nullity of A is 3.

(d) A basis for the null space of At is {{1,-1,0}, {-1,1,1}, {0,-1,-1}}. The nullity of At is 3.The four fundamental subspaces of a matrix are the row space, column space, null space, and left null space. The row space is the set of all linear combinations of the rows of the matrix, and its dimension is the row rank. The column space is the set of all linear combinations of the columns of the matrix, and its dimension is the column rank. The null space is the set of all vectors that are solutions to the system of equations Ax = 0, and its dimension is the nullity. The left null space is the set of all vectors that are solutions to the system of equations A^T x = 0, and its dimension is the nullity.

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Any p-value less than 0.05 is a cause to reject the null hypothesis.

What is Null Hypothesis?

The statement "The null hypothesis is a claim about population parameter that is assumed to be false until it is declared false" is false. The null hypothesis is denoted by H0 assumes that the claim you are trying to prove did not happen. It is a claim about a population parameter that is assumed to be true until it is declared false.

Explanation:
In this case, 0.015 is the only option for p-value that would lead to a rejection of the null hypothesis (if the level of significance for the test is 0.05).

Any p-value less than 0.05 is a cause to reject the null hypothesis.

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Answer:

(-4,-7)

Step-by-step explanation:

Multiply both sides of the first equation by-5 or 2 (I'll use 5) and both sides of the second equation by - 2 or 3 (I'll use -2).

3x - 2y = 2

5(3x-2y)= 5(2)

-15x - 10y = 10

2x - 5y = 27

-2(2x - 5y) = -2(27)

-4x + 10y = -54

Now you see that the absolute values of the y-values of the 2 equations match up . They are still the same equations but scaled up.

-15x + 10y = 10

-4x - 10y = -54

Add to eliminate y.

-11x = 44

Divide both sides by -11.

[tex]\frac{-11x}{-11} = \frac{44}{-11}[/tex]

x = -4

Plug back in to either equation to solve. I'll use the first equation.

3x - 2y = 2

x = - 4

3(-4) - 2y = 2

-12 - 2y = 2

Add 12 on both sides.

-12 + 12 - 2y = 2 + 12

- 2y = 14

Divide -2y on both sides.

[tex]\frac{-2y}{-2} = \frac{14}{-2}[/tex]

y = -7

(-4,-7)

Answer:

34

Step-by-step explanation:

First you arrange the data in an ascending order and the median is the middle value. if the number of values is an even number, then the median will be the average of the two middle numbers. In this case, the median is 34.

The solution is

a) The area of the sign is 3950 cm²

b) The total number of cans of paint is 3 cans of paint

What is the Area of a Rectangle?

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the total area of the sign be = S

Now , the area of the triangle be = T

Let the area of the rectangle be = R

The height of the triangle = 50 cm

The base of the triangle = 50 cm

So , the area of the triangle = ( 1 / 2 ) Height x Base

Area of Triangle T = ( 1/2 ) x 50 x 50

Area of Triangle T = 1250 cm²

Length of the rectangle = 90 cm

Width of the rectangle = 30 cm

Now , the area of rectangle R = Length x Width

Area of the rectangle R = 90 x 30

Area of the rectangle R = 2700 cm²

And , the area of the sign = Area of the rectangle R + Area of Triangle T

Substituting the values in the equation , we get

Area of the sign = 2700 cm² + 1250 cm²

Area of the sign = 3950 cm²

b)

Each can of paint covers = 1m²

So , Each can of paint covers = 10000 cm²

The number of signs = 6 signs

So , the total area of 6 signs = 6 x Area of the sign

The total area of 6 signs = 6 x 3950

The total area of 6 signs = 23700 cm²

And , the number of cans of paint for 6 signs = The total area of 6 signs / Area covered by each can

Substituting the values in the equation , we get

The number of cans of paint for 6 signs = 23700 / 10000

The number of cans of paint for 6 signs = 2.37 cans

The number of cans of paint for 6 signs ≈ 3 cans

Hence ,

a) The area of the sign is 3950 cm²

b) The total number of cans of paint is 3 cans of paint

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Answer:

y=10x+10

Step-by-step explanation:

Remember, y=mx+b, where m is the slope and b is the y-intercept.

In this case, the slope, or m, is 10 and the y-intercept, or b, is 10. We then substitute m=10 and b=10 in and get the equation y=10x+10.

Standard error of the mean is 1.375 and margin of error of the mean is 2.694.

Based on the provided information, mean µ = 67.8 and standard deviation σ = 11.5. The sample size n = 70

The standard error (SE) of a statistic refers to the standard deviation of its sampling distribution or an estimate of that standard deviation.

Standard error (SE) is given by:

SE = σ/√n = 11.5/√70 = 1.375

The margin of error (MOE) refers to a statistic demonstrating the amount of random sampling error in the results of a survey.

Margin of error (MOE) is the standard error multiplied by a Z value that correspondence to a confidence percentage. Assuming a 95% confidence the Z value is 1.96. Hence,

MOE = z * σ/√n = 1.96 x 1.374 = 2.694

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Answer:

31%

Step-by-step explanation:

total number of candy bars in the beginning =  28

number of milkyway bars in the beginning = 9

probability = 9/28 x 100 = 32% (rounded)

number of candy bars after = 27

number of milkway bars after = 8

probablity = 8/27 x 100 = 30 (rounded)

total probablity = (30+32)/200 x 100 = 31

Answer:

Step-by-step explanation: Here is your answer 97



The point is located (d) outside the target in relation to the target

From the question, we have the following parameters that can be used in our computation:

This means that we substitute (-1,-6) for x and y in the circle equation = (x + 5)² + (y + 5)² = 16.

So, we have the following representation

(x + 5)² + (y + 5)² = 16.

Substitute the known values in the above equation, so, we have the following representation

(-1 + 5)² + (-6 + 5)² = 16.

Evaluate the sum

(4)² + (-1)² = 16.

Evaluate the exponent

16 + 1 = 16.

Evaluate the sum

17 = 16

17 is greater than 16

Hence, the point is not in the target

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The dimensions of the rectangular( length and width) are 14m and 15m.

Here we have to find the dimension of the length and width.

Data given:

Fencing = 58m

Area = 210 m²

Let us assume the length be x

By this, we get the width as:

width = 58 - 2x / 2

         = 29-x

As the area is 210 m²

The formula to find the area of the rectangular is:

Area = length ×width

210 = x ( 29 -x)

x² - 29 x + 210 = 0

Formula to find the value of x from the quadratic equation:

x = -b ±[tex]\sqrt{b^{2} - 4ac }[/tex]

For the general equation ax² + bx + c =0

As the equation is:

x² - 29x + 210 = 0

a = -1

b = -29

c = -210

So,

x = 29 ±[tex]\sqrt{(29)^{2} - 4(-1)(-210) }[/tex] / 2(-1)

  = 29± 1/-2

  = 14, 15

29 - x = 15, 14 (for the value of x = 14 and 15 respectively)

Therefore the dimensions are 14m and 15m.

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The limit of a constant times a function is equal to the constant times the limit of the function. lim x →a(c f(x)) = c lim x →a f(x).

limit of a function

The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input.

the right-hand limit of a function is the value of the function approaches when the variable approaches its limit from the right. The left-hand limit of a function is the value of the function approaches when the variable approaches its limit from the left.

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The value of the expression 7/ 9 × 5 2/ 5 is 4 1/5

A fraction can be described as the part of a whole element, number or expression.

There are several types of fractions which includes;

From the information given, we have that;

7/ 9 × 5 2/ 5

Convert the mixed fraction to improper fraction

7/ 9 × 27/ 5

Now, reduce to simpler terms

7/ 1 × 3/ 5

Multiply the values

21/ 5

4 1/5

Hence, the value is 4 1/5

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Let X be a random variable representing the time until the first sale of a book. Then X has a Poisson distribution with rate a*p per hour.

Let X be a random variable representing the time until the first sale of a book. This random variable is the sum of the times that customers take to arrive and purchase a book. Since customers arrive at a bookstore according to a Poisson process with rate a per hour, the time until the first customer arrives has an exponential distribution with rate a per hour. Moreover, each customer buys a book with probability p, independently of everything else. Thus, the time until the first sale of a book is the sum of the time until the first customer arrives and the time until the first successful purchase. This sum of two independent exponential random variables is a Poisson random variable with rate a*p per hour. Therefore, the distribution of the time until the first sale of a book is a Poisson distribution with rate a*p per hour.

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Option-B is correct that is exponential growth. The new Malthusians fear that a lack of food will result from the population's exponential growth.

Given that,

The new Malthusians worry that ______ of the population will lead to a scarcity of food.

We have to fill the blank.

We know that,

A pattern of data that exhibits larger increases over time, forming the curve of an exponential function, is said to exhibit exponential growth.

The formula for the exponential growth is

V=S×(1+R[tex])^{T}[/tex]

The starting value, S, of an initial starting point subject to exponential growth can be multiplied by the sum of one plus the interest rate, R, raised to the power of T, or the number of periods that have passed, to get the current value, V.

Therefore, Option-B is correct that is exponential growth. The new Malthusians fear that a lack of food will result from the population's exponential growth.

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The inequality formed is x + 6 > 20 and Julie will sell more than 14 items after the first Week

A relationship between two expressions or values that is not equal to one another is referred to as "inequality" in mathematics.

According to the given information

Let x be the more items that Julie will sell after First week

Number of items soled in First week = 6

So

The inequality formed will be

x + 6 > 20

Solving the inequality is

x > 20 - 6

x > 14

So

The inequality formed is x + 6 > 20 and Julie will sell more than 14 items after the first Week

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Answer:

To find the equation of the line through the two given points, we can use the slope-intercept form of the equation of a line, which is $y = mx + b$, where $m$ is the slope of the line and $b$ is the $y$-intercept (the point where the line crosses the $y$-axis).

We can find the slope of the line by using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the two given points. In this case, the slope is

$$m = \frac{(-3) - 5}{3 - (-6)} = \frac{-8}{9} = -\frac{4}{3}.$$

To find the $y$-intercept, we can plug the coordinates of one of the points and the slope into the equation of a line, so we have $y = -\frac{4}{3} x + b$. If we plug in the coordinates of the first point, we get

$$5 = -\frac{4}{3} (-6) + b \Rightarrow b = -\frac{4}{3} (-6) + 5 = \frac{28}{3}.$$

Therefore, the equation of the line through the two given points is

$$y = -\frac{4}{3} x + \frac{28}{3} = -\frac{4}{3} x + \frac{28}{3}.$$

Answer:

Step-by-step explanation:

(-6,5)     (3,-3)

The equation of the line:    

 [tex]\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

x₁=-6      x₂=3     y₁=5     y₂=-3

Hence,

[tex]\displaystyle\\\frac{x-(-6)}{3-(-6)} =\frac{y-5}{-3-5} \\\\\frac{x+6}{3+6}=\frac{y-5}{-8} \\\\\frac{x+6}{9} =\frac{y-5}{-8} \\\\[/tex]

Multiply both parts of the equation by -72:

[tex]-8(x+6)=9(y-5)\\\\-8x-48=9y-45\\\\-8x-48+45=9y-45+45\\\\-8x-3=9y\\\\[/tex]

Divide both parts of the equation by 9:

[tex]\displaystyle\\-\frac{8}{9} x-\frac{1}{3} =y\\\\Thus,\ y=-\frac{8}{9}x-\frac{1}{3}[/tex]

Using the divergence theorem we can compute that the outward flux of the vector field is 16π .

The outward flux of F over the solid cylinder and z = 0 is

∫∫F·ds  = ∫∫∫ DivF dv

F = 2xy² i   +  2x²y j + 2xy k

Div F  =  D/dx (2xy²)  +   D/dy (2x²y )

Div F  =  2y²  +  2x²

In cylindrical coordinates   dV = rdrdθdz and as z = 0 the region is a surface ds = r·dr·dθ

Using the parametric form of the surface equation

x = rcosθ        y =  r sinθ      and z = z

Div F  = 2r² sin²θ  + 2r²cos²θ

∫∫∫ DivF dv  =  ∫∫ [2r²sin²θ  + 2r²cos²θ] × rdrdθ

∫∫ 2r² [sin²θ  + cos²θ] × rdrdθdz   ⇒  ∫∫ 2r³ drdθ

Integration limits

0 < r < 2          0 < θ < 2π

2∫₀² r³ ∫dθ

(2/4) × (2)⁴ × 2π

The divergence theorem, commonly known as Gauss' theorem or Ostrogradsky's theorem, is a theorem that connects the flow of a vector field across a closed surface to the field's divergence in the volume enclosed.

In more detail, the divergence theorem states that the surface integral of a vector field across a closed surface, sometimes referred to as the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface.

Therefore the flux is 16π .

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The linear function in slope intercept form is y = -3x + 6

A linear function is a function represented by a straight line.

Slope intercept form of a linear function is y = mx + c where

To write the linear function in slope intercept form, we need to know its slope, which is given by

m = (y₂ - y₁)/x₂ - x₁) where

Substituting the values of the variables into the equation, we have

m = (y₂ - y₁)/x₂ - x₁)

m = (-6 - 0)/4 - 2)

m = -6/2

m = -3

Next we find the equation of the linear function in slope-point form which is

m = (y - y₁)/x - x₁) where

Substituting the the values of the variables into the equation, we have

m = (y - y₁)/x - x₁)

-3 = (y - 0)/x - 2)

-3 = y/(x - 2)

-3(x - 2) = y

-3x + 6 = y

y = -3x + 6 which is the slope-intercept form

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The linear function relating the variables C and S is given as follows:

C(S) = 5000 + 200S.

The graph of the linear function is given by the image at the end of the answer.

The linear function in this problem is defined in the slope-intercept as follows:

y = mx + b.

In which the coefficients of the function are defined as follows:

In the context of this problem, the variables are given as follows:

It will cost $5000 to rent trucks, hence the intercept is of:

b = 5000.

It will cost an additional $200 for each ton of sugar transported, hence the slope is of:

m = 200.

Then the equation is defined as follows:

C(S) = 5000 + 200S.

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The standard deviation for the binomial distribution is 3.39

The standard deviation for the binomial distribution is given by,

σ = [tex]\sqrt{n * P(1-P}[/tex]

where n = Number of trials

P = probability of success of an individual trail

If n = 48 and P = 0.6

σ = [tex]\sqrt{48 *0.6(1-0.6})[/tex]

= [tex]\sqrt{48*0.24}[/tex]

=[tex]\sqrt{11.52}[/tex]

=3.39

Therefore, the standard deviation for the binomial distribution will be 3.36.

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Emma and Ryan both have 125/32 pizzas.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given, Emma has [tex]3\frac{1}{8}[/tex]  slices of pizza.

Simplifying to improper fraction;

Emma has 25/8 slices of pizza.

And Ryan has 1/4 x The amount of pizza Emma has, slices of pizza.

That means, Ryan has 1/4 x (25/8) slices of pizza.

Applying multiplication of fraction.

That is, 25/32 slices of pizza.

To find the total amount of pizza;

add the number of pizza,

25/8 + 25/32

To add the number:

First, we take LCM,

25/8 + 25/32

= (100+ 25) / 32

= 125/32

Therefore, they both have 125/32 pizzas.

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The steps of the perpendicular bisector construction in order from 1 to 4 are;

1) Open the compass

2) Draw arcs above and below the segment to be bisected

3) Draw arcs from the other endpoint of the segment to be bisected

4) Join the intersection of the arcs with a line

A perpendicular bisector is a line, that is perpendicular to another line, and which divides the other line into two congruent segments.

The steps of a perpendicular bisector construction includes;

1) Opening the compass to a radius that is more than half the length of the segment to be bisected

2) With the radius of the compass opening in step 1, place the compass at one endpoint of the segment to be bisected and draw arcs above and below the the segment to be bisected

3) With the same radius of the compass from step 1, place the compass at the other endpoint and draw arcs above and below the segment to be bisected to intersect the arcs drawn in step 2

4) With a straightedge, draw a straight line joining the point of intersection of the arcs in step 3. The line is the perpendicular bisector of the segment.

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p = 9

see explanation in image

using law of sines

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Length of p to the nearest 10th of an inch is 8.9 inches.

Sines law of a triangle defines that the ratio of the side lengths of a triangle to the sine of the opposite angles to the side lengths are equal.

a / sin A = b / sin B = c / sin C

where a, b and c are the sides opposite to A, B and C respectively.

Given is a triangle ΔPQR.

Given, ∠Q = 37° and ∠R = 12°.

Sum of the interior angles of a triangle is 180°.

∠P = 180° - (37° + 12°)

     = 131°

Using the sine law,

p / sin P = q / sin Q

p / sin (131°) = 7.1 / sin (37°)

p = (7.1 / sin (37°)) × (sin (131°))

  = 8.9 inches

Hence the length of p is 8.9 inches.

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Answer:

24 divided by 6 equals 4

Step-by-step explanation:

Answer: I think is 4

Step-by-step explanation:

Answer:

To divide polynomials, we need to use polynomial long division. First, we divide the first term of the dividend by the first term of the divisor to get the first term of the quotient, which we write above the division bar. In this case, the first term of the dividend is 2x² and the first term of the divisor is x, so the first term of the quotient is 2x. We then multiply the divisor by the quotient and subtract it from the dividend to get the remainder.

Here's how the long division would look:

2x² + 15x + 20
===
x + 5

2x

_______

 15x - 10x

 15x + 20 - 10x - 20

 ___________

    5x - 20

After we perform the polynomial long division, we get the quotient 2x + 5 and the remainder -20. Therefore, the final result of the division is:

(2x² + 15x + 20) ÷ (x + 5) = 2x + 5 + (-20)/(x + 5)

Note that the remainder -20 is written as a fraction with the divisor x + 5 in the denominator. This is the correct way to write the remainder because it tells us that the remainder has a degree that is one less than the degree of the divisor. In this case, the degree of the divisor is 1, so the degree of the remainder is 0.

fff is a random variable in a game of luck

A random variable is a formula that gives each result in a sample space a numerical value.

There are two types of random variables: discrete and continuous. If a random variable only takes specified values inside an interval, it is said to be discrete. It is continuous if not.

We typically use capital letters, such X and Y, to designate the random variables

A random variable must be measured in order to be able to assign probabilities to a set of potential values. It is evident that the outcomes depend on a number of unpredictable physical elements.

According to the question,

In a game of luck, a turn consists of a player rolling 777 six-sided dice and counting how many of the dice show a 555. Let fff be the number of dice showing a 555 in a turn.

Here, fff is a Random variable.

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y=10x+235 is the equation of the least squares regression line.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We need to find the equation of the least squares regression line.

The value of the slope of the regression line can be find by using any two points from the table.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

(58, 335) and (70, 450)

Slope of line = 450-335/70-58

=115/12

=10

The equation of line is y=10x+b

335=10(10)+b

335=100+b

335-100=b

235=b

Hence, the equation of the least squares regression line is y=10x+235.

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