The mean of the standard normal distribution is 1 and the standard deviation is 0. Group of answer choices False True

If x is in the nullspace of A, then Ax = 0. Consider the augmented matrix

\(\left[\begin{array}{ccc|c}1&-1&2&0\\0&1&-3&0\end{array}\right]\)

Add row 2 to row 1 to get this into reduced-row echelon form:

\(\left[\begin{array}{ccc|c}1&0&-1&0\\0&1&-3&0\end{array}\right]\)

Then x = [x₁, x₂, x₃]ᵀ such that

x₁ - x₃ = 0

x₂ - 3 x₃ = 0

If you let x₃ = 1, you end up with x₁ = 1 and x₂ = 3, so x = [1, 3, 1]ᵀ.

More generally, if you let x₃ = y, then any vector of the form [y, 3y, y]ᵀ would belong to the nullspace.

Check that this is orthogonal to the rows of A :

[1, -1, 2] • [1, 3, 1]ᵀ = 1•1 + (-1)•3 + 2•1 = 1 - 3 + 2 = 0

[0, 1, -3] • [1, 3, 1]ᵀ = 0•1 + 1•3 + (-3)•1 = 0 + 3 - 3 = 0

The equation of the line in slope-intercept form is

y=mx+b

In this problem we have

m=-1/3

point (-9,4)

substitute in the equation above and solve for b

4=-(1/3)(-9)+b

4=3+b

b=1

therefore

the equation of the line is

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

Answer: 39 ft2

Step-by-step explanation:

The area of the trapezoid is 39 square feet.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) × (base1 + base2) × height

Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:

Area = (1/2) × (16 + 10) × 3

Area = (1/2) × 26 × 3

Area = (1/2) × 78

Area = 39 ft^2

Therefore, the area of the trapezoid is 39 square feet.

for such more question on trapezoid

https://brainly.com/question/22351006

#SPJ8

Answer:

B) y = 7x

Step-by-step explanation:

Start with:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Substitute in two points from the graph.

(Let's use (8,56) & (16,112)

\(m=\frac{112-56}{16-8}\)

Combine like terms.

\(m=\frac{56}{8}\)

Simplify.

\(m=7x\)

Answer:

y = 7x

Step-by-step explanation:

We need to find the slope

We have two points (0,0) and (8,56)

m = (y2-y1)/(x2-x1)

   = (56-0)/( 8-0)

  = 56/8

  = 7

The proportional relationship is

y= kx where k is the slope

y = 7x

Answer: $22.50

Step-by-step explanation:

20% = 0.2

$22.50 x 0.2 = $4.50

$22.50 - $4.50 = $18.00

Therefore, the answer is 22.50. I hope this helps !

The original price of the hat after 20% discount is $22.5.

Discount is defined as the financial amount by which the original cost of an entity is reduced.

Original price after {x}% discount is -

P{O} = P{O} - {x}% of P{O}

P{O} = P{O} - xP{O}/100

Given is that a store is offering a 20 percent discount on all items. The price of the hat after the discount is 18 dollars.

Price after discount → $18

Let the original price of the hat be → {x}.

We can write -

18 = x - {20% of x}

\($18 = x -\frac{20x}{100}\)

\($18 = x -\frac{x}{5}\)

\($\frac{4x}{5} = 18\)

4x = 90

x = 22.5

Therefore, the original price of the hat after 20% discount is $22.5.

To solve more questions on discount prices, visit the link below

https://brainly.com/question/13887247

#SPJ2

Answer:

1

Step-by-step explanation:

Hello, please consider the following.

First, we develop and move everything to the left side, then we solve the equation, using the discriminant.

Finally, we get the expression of the two solutions and we can conclude.

\((x+1)(x+2)=(x+3)\\\\<=> x^2+3x+2-x-3=0\\\\<=>x^2+2x-1=0\\\\\Delta=b^2-4ac=4+4=8\\\\x_1=\dfrac{-2-\sqrt{8}}{2}=\dfrac{-2-2\sqrt{2}}{2}=-1-\sqrt{2}\\\\x_2=\dfrac{-2+\sqrt{8}}{2}=-1+\sqrt{2}\)

So, m=-1 and n = 2

m+n = -1 + 2 = 1

Thank you

The value of m + n is 1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 is an equation.

We have,

(x + 1)(x + 2) = x + 3

x² + 2x + x + 2 = x + 3

x² + 3x + 2 - x - 3 = 0

x² + 2x - 1 = 0

This is in the form of ax² + bx + c = 0

a = 1, b = 2, and c = -1

Now,

Using the determinant.

x = -b ± √(b² - 4ac) / 2a

x = -2 ± √(4 + 4) / 2

x = (-2 ± 2√2) / 2

x = (-1 ± √2)

x = -1 + √2

x = -1 - √2

Now,

The solutions can be written in the form of (m + √n) and (m - √n).

This means,

m + √n = -1 + √2

m - √n = -1 - √2

m = -1 and n = 2

Now,

m + n

= -1 + 2

= 1

Thus,

m + n is 1.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

Answer:

48 Inches

Step-by-step explanation:

The diagonal of the TV = 60 Inches

Height of the Screen =36 Inches

We are to determine the actual width of the screen.

This TV across the diagonal forms a right triangle in which the diagonal is the hypotenuse.

We therefore use the Pythagorean Theorem to solve for the width of the screen.

Pythagorean Theorem: \(Hypotenuse^2=Opposite^2+Adjacent^2\)

Let w be the width of the television

\(60^2=36^2+w^2\\w^2=60^2-36^2\\w^2=2304\\w=\sqrt{2304}\\ $Width of the television, w=48 inches\)

Answer:

  I, B

Step-by-step explanation:

You want the surface area of the triangular prism and the composite cuboid+pyramid figures shown.

The surface area is the area of the two bases plus the lateral area of the rectangular faces.

  SA = bh +PH

  SA = (8 ft)(6 ft) +(8 ft +6 ft +10 ft)(12 ft) = 48 ft² +(24 ft)(12 ft) = 336 ft²

The surface area of the prism is 336 square feet. (choice I)

The surface area of this figure is the sum of the areas of the square base, the lateral area of the cuboid, and the later area of the triangular faces.

  SA = s² +4sh +2sH

  SA = (10 in)² +4(10 in)(5.6 in) + 2(10 in)(11 in)

  SA = 100 in² +224 in² +220 in² = 544 in²

The area of the pyramid figure is 544 square inches. (choice B)

<95141404393>

The true expression about the account is D.) It is the sum of the initial amount and the additional amount after d days.

The answer is D because it represents the sum of the initial amount and the additional amount after d days. The initial amount is $10 and Owen adds $0.50 to the account each day for a number of days, represented by d.

By subtracting 1 from d, the expression ensures that on the first day (when d=1), only the initial $10 is counted. On each subsequent day, the additional amount of $0.50 is added to the total. Therefore, the expression 10+0.5(d−1) gives the amount of money in Owen's account after d days.

Read more about expression

brainly.com/question/1859113

#SPJ1

Answer:

Equation of given line: y = (3/2)x - 3

a) 2y = 3x - 6

-3x + 2y = -6

3x - 2y = 6

6x - 4y = 12

b) y = (3/2)x + 2

c) m = (3 - 2)/(4 - 2) = 1/2

2 = (1/2)(2) + b

2 = 1 + b, so b = 1

y = (1/2)x + 1

The probability that the mean weight of the sample of 25 cartons is greater than 7.19 ounces is given as follows:

0.0571 = 5.71%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 7, \sigma = 0.6, n = 25, s = \frac{0.6}{\sqrt{25}} = 0.12\)

The probability that the mean weight is greater than 7.19 ounces is one subtracted by the p-value of Z when X = 7.19, considering the standard error s, hence:

Z = (7.19 - 7)/0.12

Z = 1.58

Z = 1.58 has a p-value of 0.9429.

Hence:

1 - 0.9429 = 0.0571 = 5.71%.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

The inequality that can be used to solve the possible values of the number is 11 + 3/4x < 112 where the number x is x < 134 2/3

sum of 11 and three-fourths of a number is less than 112.

Let

The unknown number = x

11 + 3/4x < 112

Subtract 11 from both sides

3/4x < 112 - 11

3/4x < 101

divide both sides by 3/4

x < 101 ÷ 3/4

multiply by the reciprocal of 3/4

x < 101 × 4/3

x < 404/3

x < 134 2/3

Therefore, the inequality which represents the situation is 11 + 3/4x < 112.

Read more on inequality:

https://brainly.com/question/25275758

#SPJ1

Answer:

B) 6

Step-by-step explanation:

Let the number be x

Product of 6 and square of number plue 15 : (6x²) + 15

Coefficient of x² = 6

i. Costco is more effective at collecting its accounts receivable faster.

ii. The trend in the accounts receivable turnover ratio and the number of days sales in accounts receivable for both companies is that they are both decreasing.

iii. Costco is more effective at collecting its accounts receivable faster than Sam's Club.

Accounts Receivable Turnover: Year ended in 2022: 10.2 times; Year ended in 2021: 10.1 times.

Number of Days Sales in Accounts Receivable: 2022: 38.6 days; 2021: 39.1 days.

Sam's Club

Accounts Receivable Turnover: Year ended in 2022: 8.6 times; Year ended in 2021: 8.5 times.

Number of Days Sales in Accounts Receivable: 2022: 45.2 days; 2021: 46.2 days.

This could be due to a number of factors, such as the economic environment, changes in customer payment habits, or changes in the way that the companies are managing their receivables.

This could be due to a number of factors, such as the companies' different business models, customer bases, or payment terms.

So, Costco is more effective at collecting its accounts receivable faster.

The trend in the accounts receivable turnover ratio and the number of days sales in accounts receivable for both companies is that they are both decreasing. Costco is more effective at collecting its accounts receivable faster than Sam's Club.

For such more questions on accounts

https://brainly.com/question/1859113

#SPJ8

The line parallel to the x-axis passing through the points (5,5) and (-5,5) has a slope of 0, indicating a horizontal line with a constant y-coordinate value of 5.

To determine the slope of the line that represents this relationship, we can use the formula for slope, which is given by:

slope = (change in y-coordinates) / (change in x-coordinates)

In this case, we are given two points on the line: (5,5) and (-5,5).

The change in y-coordinates is 5 - 5 = 0, as the y-coordinate remains constant.

The change in x-coordinates is -5 - 5 = -10.

Substituting these values into the slope formula, we get:

slope = 0 / -10 = 0

Therefore, the slope of the line that represents this relationship is 0.

A slope of 0 indicates that the line is parallel to the x-axis. This means that the line has a constant y-coordinate value for all x-coordinate values. In this case, the line passes through the point (5,5) and (-5,5), and it remains at y = 5 for all x-values.

Visually, a line with a slope of 0 would be a horizontal line on the coordinate plane. It does not have an upward or downward slope but remains parallel to the x-axis.

It's important to note that the slope of 0 indicates a relationship where the dependent variable (y) does not change with respect to the independent variable (x). In this case, no matter the value of x, the corresponding y-value remains constant at 5.

For more such information on: slope

https://brainly.com/question/16949303

#SPJ8

If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.

A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :

g(x) = {-(1/2)x + 1,    for x<-2

       = {-(x+1)²,        for -2≤x≤1

      =  {4                 for x>1

We have to find the value of g(-5) ,g (-2), and g(-1),

For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,

⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,

For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function

"-(x+1)²" will be used,

⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,

For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,

⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,

Learn more about Function here

https://brainly.com/question/17602515

#SPJ1

The skier's distance to the east of the center of the ski trail is

x = 1.25cosθ

The skier's distance to the north of the center of the ski trail is

y = 1.25sinθ

When radius 'r' and the angle θ are given, the coordinates (x,y) as shown

x = east direction

y = north direction

In this case we get,

x = r cosθ

y = r sinθ

Given r = 1.25 km

We get,

x = 1.25 cosθ in east direction

y = 1.25 sinθ in north direction

To know more about Trigonometry, refer to:

http://brainly.com/question/25618616

#SPJ4

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

For more questions on equilateral triangle:

https://brainly.com/question/17264112

#SPJ8

Answer:

Step-by-step explanation:

0,0,1,3,6,10,13,16,19

Answer:

Plane B

Step-by-step explanation:

Plane A: 2800/5 = 560 m/h

Plane B: 3885/7 = 555 m/h

Answer: 18 minutes: 27 minutes

Here the steps see attachment

The student's GPA is of 2.33.

Grade Point Average (GPA) is the measure used to summaries your academic achievement at Griffith.

Given:

A worth 4​ points,

B worth 3​ points,

C worth 2​ points,

D worth 1 point

The GPA is

= 3(3) + 1(3) + 2(4) + 2(2)/9+3+4+2

=9+3+8+4/18

=2.33

Hence, The student's GPA is of 2.33.

Learn more about GPA here:

https://brainly.com/question/11952783

#SPJ1

Answer:

1. 51°

2. 40°

3. 65°

4. 60°

Step-by-step explanation:

The sum of the angles in a triangle is 180°. We can use the angles given to find the missing angle.

1. 51°

42+87+x=180

129+x=180

x=51

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

2. 40°

110+30+x=180

140+x=180

x=40

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

3. 65°

20+95+x=180

115+x=180

x=65

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

4. 60°

60+60+x=180

120+x=180

x=60

Answer:

5

Step-by-step explanation:

The cube root of 125

What number times itself times itself is 125

s*s*s = 125

s = 5

5*5*5 = 125

Answer:

The sample mean year is 1261 A.D.

The standard standard deviation is of 46 A.D.

Step-by-step explanation:

Sample mean:

Sum of all values divided by the number of values. So

\(x = \frac{1271+1187+1194+1250+1268+1316+1275+1317+1275}{9} = 1261.4\)

Rounding to the nearest whole number, the sample mean year is 1261 A.D.

Sample standard deviation:

Square root of the sum of the difference squared between each value and the mean, divided by one less than the sample size. So

\(s = \sqrt{\frac{(1271-1261.4)^2+(1187-1261.4)^2+(1194-1261.4)^2+(1250-1261.4)^2+(1268-1261.4)^2+(1316-1261.4)^2+(1275-1261.4)^2+(1317-1261.4)^2+(1275-1261.4)^2}{8}} = 45.8\)

Rounding to the nearest whole number, the standard standard deviation year is of 46 A.D.

Answer:

51/3 miles in 1 hour

Step-by-step explanation:

First step let us multiply f(x) by -5

The general form of the linear equation is f(x) = mx + b, where

m is the slope

b is the y-intercept

Since h(x) = 35 x - 45, then

m = 35

b = -45

So:

The slope = 35

y-intercept = -45