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If in the circle centered at "A", we have NA ≅ PA, MO⊥NA, and RO⊥PA, then the measure of the the segment PO is (d) 3.5 ft.

From the figure, we observe the triangles OAN and OAP are "right-triangles" where one "common-side" is OA and the two "congruent-sides" NA ≅ PA (given), it follows that they are congruent.

⇒ OP ≅ ON;

We know that, the perpendicular drawn from circle's center on chord divides it in two "congruent-segments",

So, We have;

PO ≅ RP, and NO ≅ MN;

​Which means that, PO = RO/2 and ON = MO/2 = 7/2;

Since, OP ≅ ON, we get:

⇒ PO = 7/2 = 3.5,

Therefore, the correct option is (d).

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9514 1404 393

Answer:

  (a) All three pyramids have the same volume

Step-by-step explanation:

The triangular base has an area of ...

  B = 1/2bh . . . . where b is the base of the triangle and h is its height.

The volume of the pyramid is ...

  V = 1/3BH . . . . where B is the area of the base, and H is the height of the pyramid.

Combining these equations gives ...

   V = 1/3(1/2bh)H = 1/6bhH

__

Pyramid 1 volume

  V1 = 1/6(12 m)(2 m)(10 m) = 40 m³

Pyramid 2 volume

  V2 = 1/6(6 m)(4 m)(10 m) = 40 m³

Pyramid 3 volume

  V3 = 1/6(12 m)(4 m)(5 m) = 40 m³

All three pyramids have the same volume.

Answer:

See attached image

Step-by-step explanation:

This is how I did it

I made point A as (0,0)

Point B is 12 units right and 4 units up from A. So B is(12,4)

Point C is 8 units right and 8 units down from A so it is at (8, -8)

When dilated by 1/4 with point A as center of dilation, B coordinates are reduced by 1/4 so the image B' coordinates are (12/4, 4/4) = (3,1)

C coordinates are reduced by 1/4 so C' coordinates of image are (8/4, -8/4) = (2, -2)

The A' coordinates are unchanged at A'(0,0)

So the image is A'B'C' as shown in the blue triangle

I do not know what that other triangle is for, it plays no role in the dilation

I also realize you may have been given some other strategy for solving but this is the way I did it

I hope that works for you.

Answer:

5

Step-by-step explanation:

1 ÷ 1/5= 1 x 5/1 =5

I hope im right!!

The required solution for the solution of the inequalities has been shown.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
For each system of linear inequalities,

The inequalities that show the region above both lines is,

Option B
y > 5 + x

y > 7 + x

The inequalities that show a region below the lines is,
Option A
y < 8 + 2x
y < 3 + 2x

The inequalities that show the region between the line,

Option D

6 - x < y
y > 9 - x

The inequalities  that represent no solution is
Option C

y > 12 - 3x
10 - 3x > y

Thus, the requried solution is mentioned above.

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Answer:

To solve the equation 3+2(4+2x)+1=20-2(2-x), we can follow these steps:Simplify the terms inside the parentheses on both sides of the equation:

3 + 8 + 4x + 1 = 20 - 4 + 2xCombine like terms on both sides of the equation:

12 + 4x = 16 + 2xSubtract 2x from both sides of the equation:

2x = 4Divide both sides of the equation by 2:

x = 2Therefore, the solution to the equation 3+2(4+2x)+1=20-2(2-x) is x = 2.

Step-by-step explanation:

Answer:

x =2

Step-by-step explanation:

3+2(4+2x)+1=20-2(2-×)

3 + 8 + 4x + 1 = 20 - 4 - 2(-x)

12 + 4x = 16 + 2x

4x - 2x = 16 - 12

2x = 4

x = 2

Answer:

864 ft3

Step-by-step explanation:

length = 12 ft

width = 8 ft

depth = 9 ft

Volume = ? = length * width * depth

Answer:

5

Step-by-step explanation:

No, it is not necessarily true that both ABT and ATB are defined for matrices A and B of size m × n.

In order for the matrix product ABT to be defined, the number of columns in A (which is n) must be equal to the number of columns in BT (which is also n). This means that the number of rows in B (which is m) must be equal to the number of rows in A (which is also m). So, if A and B are both square matrices of size n × n, then ABT is defined

On the other hand, in order for the matrix product ATB to be defined, the number of columns in AT (which is m) must be equal to the number of columns in B (which is also n). This means that the number of rows in A (which is m) must be equal to the number of rows in B (which is also m). So, if A and B are both square matrices of size m × m, then ATB is defined.

However, if A and B are not square matrices, then it is possible that only one of ABT or ATB is defined, or neither of them are defined. In general, the product of two matrices is only defined if the number of columns in the first matrix is equal to the number of rows in the second matrix.

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Answer:

They started the morning shift with 80 cups of coffee

3 hours into the shift the chef made 40 more cups of coffee

45 minutes into the shift 60 cups of coffee were sold

Explanation:

The graph says that:

1. They started the shift with 80 cups of coffee in stock (point A)

2. 25 minutes later, they had 60 cups of coffee (point B)

3. at 45 minutes, they had 20 cups of coffee (point C)

4. at 2 hours they had 0 cups of coffee. (point D)

5. After 3 hours they had 40 cups of coffee (point E)

6. At the end of the morning they had 10 cups of coffee. (point F)

Therefore, the true statement are:

They started the morning shift with 80 cups of coffee because that is the information showed by point A.

3 hours into the shift the chef made 40 more cups of coffee because at point D there was no cups of coffee, then at point E which is 3 hours into the shift there were 40 cups of coffee.

45 minutes into the shift 60 cups of coffee were sold because they started with 80 cups and 45 minutes later they had 20 cups. It means that they sell 80 - 20 = 60 cups of coffee.

So, the answers are:

They started the morning shift with 80 cups of coffee

3 hours into the shift the chef made 40 more cups of coffee

45 minutes into the shift 60 cups of coffee were sold

The percent increase in the cost of the uniform from last year to this year is 25%.

To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.

The difference between this year's price and last year's price is:

$65 - $52 = $13

The original price (last year's price) is $52.

So the percent increase in the cost of the uniform is:

percent increase = (difference / original price) x 100

percent increase = ($13 / $52) x 100

percent increase = 0.25 x 100

percent increase = 25%

Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.

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Answer:

6.4

Step-by-step explanation:

when rounding a number, the decimal points go from tenth, hundredth, and thousandth.

In this case, the number in the tenths place is 4.

Because the number next to 4, which is 2, is less than 5, it cannot raise the number of the number in the tenths place, so the 4 stays the same and the other two numbers after it are eliminated

This gives you 6.4 as your final answer.

I hope this helps you!

Answer:

Yes. The two parallelograms are similar.

Step-by-step explanation:

Similarity:

     Two parallelograms are said to be similar when the corresponding sides are in the same ratio.

  \(\sf \dfrac{WX}{AB}= \dfrac{3}{2}\\\\\dfrac{XY}{BC}=\dfrac{9}{6} = \dfrac{9 \div 3}{6 \div 3}\\\\\)

        \(\sf = \dfrac{3}{2}\)

           \(\bf \dfrac{WX}{AB}=\dfrac{XY}{BC}=\dfrac{3}{2}\)

Therefore, two parallelograms are similar.

  Among the given options (A, B, C, D), the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

In a population regression model, we are interested in modeling the relationship between a dependent variable (Y) and one or more independent variables (X1, X2, etc.). The model equation consists of the regression coefficients (β0, β1, β2, etc.) that represent the effect of each independent variable on the dependent variable, and the error term (e) that captures the unexplained variation in the data.
Among the given options, only option D includes all the necessary components of a population regression model with two independent variables (k = 2). It includes the dependent variable Y, the regression coefficients β0, β1, and β2 for the independent variables X1 and X2, respectively, and the error term e.
Options A, B, and C are incorrect because they either omit the error term or have an incomplete equation. The error term is crucial in accounting for the unobserved factors and random variation in the relationship between the variables.
Therefore, the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

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Answer:

0,25

Step-by-step explanation:

Answer:

0.25 or 1/4

Step-by-step explanation:

Answer: No solution

Step-by-step explanation:

2m+4p=22

6m+12p=66

First, to choose one variable to simplified, I choose to find 1st equations in m form.

2m+4p=22

      2m=22-4p            [Subtract 4p from both side]

         m=22/2 - 4/2p  [Divide 2 on both side to find m]

         m= 11 - 2p

6m+12p=66          

6(11-2p)+12p=66          [Plug in the 11-2p in to m,according to the 1st equation]

66-12p+12p=66

The -12p has cancel with 12p, so it means that there is no solution

Answer:

can yhu see the answer i put?

Step-by-step explanation:

Answer: The answer is (yes)

Step-by-step explanation:I got it correct.

An equation that can be used to determine the number of hours, h, that Moira needs to read to finish the book is h + 178 = 214.

In order to write an equation that model this situation, we would assign a variable to the number of hours that is needed to read to finish the book and the total number of hours respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that she read for 178 hours yesterday as follows;

h + 178 = T

Substituting the given parameters into the algebraic equation, we have the following;

h + 178 = 214

Solving for h, we have the following;

h = 214 - 178

h = 36 hours.

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x = 5 and x = 3. We'll take into account the midpoint equation to get point B's coordinates. The x-coordinate of a midway (x, y) will be equal to the sum of the x-coordinates of the source and destination nodes.  It may be expressed mathematically as x1 + x2 / 2x.

Provide the coordinates for point B. (x,y)

B:(5,4) and C: (11,-2)

A = 2 units.

AB2 = 4

thus using the distance formula

\((5 - x)2 + (4 - Y)2 = 4\)

\(25 + x2 - 10x + 16 + y2 - 8y = 4\)

\(x2 + y2 - 10x - 8y = -37\)

x2 + y2 = 10x + 8y -37 I

moreover, AC2 equals 100

thus using the distance formula

\(( 11 - x)2 + ( 2 + y)2 = 100\)

\(121 + x2 - 22x + 4 + y2 + 4y = 100\)

\(x2 + y2 - 22x + 4y = - 25\)

\(x2 + y2 = 22x - 4y - 25 .(ii) (ii)\)

using I and (ii)

\(22x - 4y - 25 = 10x + 8y - 37\)

\(12x - 12y + 12 = 0\)

\(x - y = -1\)

x = y - 1....(iii) (iii)

When we add (iii) to I we obtain

\(( y -1)2 + y2 = 10(y - 1) + 8y - 37\)

\(2y2 -2y + 1 = 10y - 10 + 8y - 37\)

\(2y2 - 20y + 48 = 0\)

\(y2 - 10y + 24 = 0\)

\((y - 6)(y - 4)=0y = 6 and y = 4\)

therefore, x = 5 and x = 3.

The position of A is therefore either (5, 6) or (3,4)

If B is the origin, what are its coordinates?

The origin's coordinates are (0, 0). As a result, the values of a and b are both 0.

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Answer:

1) 4x(3x²+2)

2) 2a(9a+1)

3) 5b³(5b+6)

4) (x-2)(5x²-3)

5) (a-5)(9a²-7)

6) (x²-3)(5y-2)

Step-by-step explanation:

Hey, if you need any more in depth explanation comment down below.

The height of a man with a z-score of 0 is 69 inches.

The average height of adult men = 69.0 inches, Standard deviation of adult men = 2.8 inches to find the Z-score the following formula is used:

z = (x- μ)/σ where z is the z-score, x is the value to be standardized, μ is mean and σ is the standard deviation.

To find the height of a man with a z-score of Standardized value(z) = 0

z = (x - μ)/σ

0 = (x - 69)/2.8

x = 69 + 0 (2.8)

x = 69 inches.

Therefore, the height of a man with a z-score of 0 is 69 inches.

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Answer:

Yes, the probability distribution for the number of years of experience can be modelled by a binomial probability distribution

Step-by-step explanation:

We are told that on a recent sample, the paper claims that 45% of all employees believe their company president possesses low ethical standards.

This means the chance of success is p = 45% = 0.45

Now, 20 of the company's employees are randomly and independently sampled. This means that for any amount of success within this sample number can be represented by;

P(X = x) = C(n, x) × p^(x) × (1 - p)^(n - x)

Where;

x is the number of possible successes

n is the number of trials

p is the chance or probability of success

C(n, x) is the number of possible combinations that could occur

This formula represents the binomial probability distribution formula.

So yes, the probability distribution for the number of years of experience can be modelled by a binomial probability distribution

Answer: SSS Postulate

Step-by-step explanation:

Since DF is congruent to FD, there are three congruent sides.

Answer: Triangle FGH is an equilateral with values of x as 9.

Step-by-step explanation: The triangle given is an equilateral because all the given side are equal.  The value of x is 9.

Answer:

x = 9

Step-by-step explanation:

if x = 2 then

If x = 22.25 then

if x = 180 then

If x = 9 then

Answer:

56°

Step-by-step explanation:

angles on a straight line add up to 180°

so we are already given that the other angle which lies on the same straight line with angle X is 124 ° .which means that we should subtract 124° from 180°

Answer:

The expression 2(100 − x) expands to 200 − 2x.

Step-by-step explanation:

2(100) − 2(x).

Multiply within each term:

200 − 2x.

Answer:

2(100 − x)

Distribute the 2:

2(100) − 2(x).

Multiply within each term:

200 − 2x.

The expression 2(100 − x) expands to 200 − 2x.

Step-by-step explanation:

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Therefore, Drug C has a stronger impact on cell survival compared to Drug A, making it the drug with the greatest effect.

To draw a representation of the survival curve and identify the drug that has the greatest effect on cell survival, we can use a graph where the x-axis represents the drug concentration in μg/ml, and the y-axis represents the percentage of cell survival.

Since Drug B has no IC90 value, it means that it does not reach a concentration that causes a 90% reduction in cell survival. Therefore, we can assume that Drug B has no significant effect on cell survival and can omit it from the survival curve.

For Drug A and Drug C, we have IC90 values of 5 and 3 μg/ml, respectively. This means that when the drug concentration reaches these values, there is a 90% reduction in cell survival.

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