Twelve education students, in groups of four, are taking part in a student-teacher program. Mark cannot be in the first group because he will be arriving late. How many ways can the instructor choose the first group of four education students?.

The congruence postulate or theorem that is stated is the: C. AAS congruence theorem.

Triangles that are referred to as congruent triangles are triangles that have corresponding congruent sides and corresponding congruent angles.

According to the angle-angle-side congruence theorem (AAS) two triangles are congruent if two angles and a non-included side of one triangle are congruent to two corresponding angles and a non-included side of the other are congruent to each other.

For example, in triangles GUM and RED given in the image attached below, we have the following:

∠G ≅ ∠R [a pair of congruent angles]

∠M ≅ ∠D [a pair of congruent angles]

GU ≅ RD [a pair of non-included congruent side]

Thus, both triangles are congruent by the AAS, which is the congruence theorem that is stated above.

The answer is: C. AAS.

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Answer:

aas

Step-by-step explanation:

Answer: (8,0) and (0,-4)

Step-by-step explanation:

The x-intercept of an equation is when the equation touches the x-axis which is also where y = 0

So the x coordinate of the x-intercept is -2x + 0 = -16 as y = 0

x = 8 so the x-intercept is (8,0)

The y-intercept of an equation is when the equation touches the y-axis which is also where x = 0

So the y coordinate of the y-intercept is 0 + 4y = -16 as x = 0

y = -4 so the y intercept is (0,-4)

Answer:

13.5

Step-by-step explanation:

213.21/15.8 --->  ((213.21)100)/((15.8)100)

21321/1580 = 13 R 781.

781/1580 = 0.49~~~

We only need to be concerned about the tenth and hundredth place digits.

The decimal tells us that it rounds up from 4, so it's 5.

Thus, the answers 13+0.5, which is 13.5

Answer:

Kelvin can get 6 free sweets

The equation 35 = 15-24y represent the growth rate.

According to the statement

we have given that the

A weeping willow that is 15 feet in height grows to a maximum height of 35 feet in y years at a constant rate of 24 inches per year.

And we have to describe all conditions in the equation.

So,

firstly the given height of weeping pillow before growing is 15 feet.

It means the maximum real height it grows is to subtract from the maximum given height it grows.

it means we have to find the growth rate.

real height he grows is = 35-15 = 20 feet

And it grows at the 24 inches per year so, it means it become

24 y

By combining these we get the equations is

35 = 15-24y.

So, The equation 35 = 15-24y represent the growth rate.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

A weeping willow that is 15 feet in height grows to a maximum height of

35 feet in y years at a constant rate of 24 inches per year. Which of the following equations best describes this situation?

A. 37 = 15-24y

B. 35 = 15-24y

C. 35 = 15-22y

D. 39 = 15-27y

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Answer: 35= 15+2y

Step-by-step explanation:

I am taking the Khan Academy Lesson.

Answer:

6.5%

Step-by-step explanation:

I = prt

5616 = 7200 × r × 12

r = 5616/(7200 × 12)

r = 0.065

r = 6.5%

Answer:

16, 32, and 64

Step-by-step explanation:

We can see that this is an exponential function, since y multiplies by 2 every time x increases by 1. So the values of y are basically just powers of 2, because the equation of the table is y=2^x.

Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

First let us revise the rounding rules before getting down to the process of rounding :

[tex]\sf{763.9 \ to \ the \ nearest \ whole \ number :}\\\hfill\stackrel{\small\text{add 1 }}{3^{+1}}.\\\hfill\stackrel{\small\text{drop it}}{9}}[/tex]

[tex]\sf{763.9\approx764}[/tex]

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

The inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.

In the question, we are asked to find the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3.

The domain for the given function is x ≥ -3.

Thus, its range is x ≤ - 1/2.

To find the inverse, we equate f(x) = y, to get:

(-1/2)√(x + 3) = y,

or, √(x + 3) = -2y.

Squaring both sides, we get:

x + 3 = (-2y)²,

or, x + 3 = 4y²,

or, x = 4y² - 3.

Thus, the inverse of the function f(x) = (-1/2)√(x + 3), is, f⁻¹(x) = 4x² - 3.

The inverse will have the domain equal to the range of the original function, that is, x ≤ - 1/2.

Thus, the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.

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The provided question is incomplete. The complete question is:

"Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Find the inverse of the given function.

f(x) = (-1/2)√(x + 3), x ≥ -3

f⁻¹(x) =   x² -   , for x ≤    ."

Answer:

Graph X

Step-by-step explanation:

First, convert the equation into slope-intercept form. The first step is the bring the x to the right side by subtracting 8x from both sides: -y=-8x-4. Now multiply both sides by -1: y=8x+4. Now, if you know about the slope-intercept form, you'll know that 4 is the y-intercept and that [tex]\frac{8}{1}[/tex] is the slope. 8 is the rise and 1 is the run, so the answer is graph X.

The prove that BOC = 90° + A/2. is given below:

Note that, bisectors of angles B and C and that of a triangle ABC is one that pass across each other at the point O.

Hence: one need to to prove that ∠BOC = 90° + A/2

Since:

BO is said to be the bisector of angle B e.g. ∠OBC = (∠1)

CO is said to be the bisector of angle C e.g.  ∠OCB = (∠2)

Looking at the triangle BOC, to interpret  by the use of angle sum property, then:

∠OBC + ∠BOC + ∠OCB = 180°

∠1 + ∠BOC + ∠2 = 180° ---- ( equation 1)

Looking at triangle ABC and by the use of angle sum property, So;

∠A + ∠B + ∠C = 180°

∠A + 2(∠1) + 2(∠2) = 180°

Then we divide by 2 on the two sides, and it will be:

∠A/2 + ∠1 + ∠2 = 180°/2

∠A/2 + ∠1 + ∠2 = 90°

∠1 + ∠2 = 90° - ∠A/2 ---(equation 2)

Then one need to Substitute (2) in (1), So:

∠BOC + 90° - ∠A/2 = 180°

∠BOC - ∠A/2 = 180° - 90°

∠BOC - ∠A/2 = 90°

Hence , ∠BOC = 90° + ∠A/2

Therefore, from the above, we care able to prove that BOC = 90° + A/2.

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t is vertical to s because they share a point and are directly across from each other. vertical angles are congruent. therefore s=113 degrees

t and p are corresponding angles, which means they are congruent. this means p is also 113 degrees.

s and o are corresponding angles, so o is also 113 degrees.

t and u are supplementary. they share a straight line, so they add up to 180. you can find u by subtracting 113 from 180. 180-113= 67, so u is 67 degrees.

u and r are vertical angles, so r is 67 degrees.

r and m are corresponding, as well as u and q. therefore m and q both equal 67 degrees.

hope this helped :)

Answer:

  (c)  40.5 square units

Step-by-step explanation:

Assuming the kite is oriented so its diagonals are parallel to the sides of the square, each diagonal is 9 units long. The area of the kite is given by an appropriate formula.

A kite is a parallelogram with two pairs of adjacent congruent sides. Its diagonals meet at right angles. One diagonal bisects the other.

The formula for the area of a kite is ...

   A = 1/2(d1)(d2) . . . . . where d1 and d2 are the lengths of the diagonals

In this problem, the inscribed kite has congruent diagonals, both of length 9 units.

The area of the kite is ...

  A = 1/2(9)(9) = 81/2 = 40.5 . . . . square units

Answer:

93.32 %

Step-by-step explanation:

33.2   is    1.2   away from 32     this is  1.2 / .8 = 1.5 standard deviations ABOVE the mean     z -score = + 1.5

from z-score table this corresponds to .9332     this is  93.32 %

The probability that a randomly selected passenger car gets more than 33.2 mpg is 0.14.

The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.

Let the random variable X represent the miles-per-gallon rating of passenger cars. Compute the probability that a randomly selected passenger car gets more than 33.2 mpg as follows:

The probability will be calculated as below;-

[tex]P(x > 33.2) = p(\dfrac{x-\mu}{\sigma} > \dfrac{33.2 - 32}{0.8})[/tex]

P( x > 33.2) = 1 - P ( z < 1 )

P( x > 33.2) = 1 - 0.86

P( x > 33.2) = 0.14

Thus, the probability that a randomly selected passenger car gets more than 33.2 mpg is 0.14.

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The time it will take Lucas to paint the house using rate is 3 hours

They both paint the same house.

Lucas and Jacob can paint a house in 1 hour working together.

Jacob works alone, he can paint the house in 1.5 hours.

Therefore, the time it will take Lucas to paint the house using rate is as follows:

let

x = time it will take Lucas to paint the house

1 / 1 = 1 / x + 1 / 1.5

1  = 1.5 + x / 1.5x

cross multiply

1.5x = 1.5 + x

1.5x  - x = 1.5

0.5x = 1.5

divide both sides by 0.5

x = 1.5 / 0.5

x = 3

Therefore, the time it will take Lucas to pain the house is 3 hours.

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Answer:

[tex]\frac{133}{66}[/tex]

Step-by-step explanation:

we require 2 equations with the repeating digits placed after the decimal point.

let x = 2.01515... ( multiply both sides by 10 and 1000 )

10x = 20.1515.... (1)

1000x = 2015.1515... (2)

subtract (1) from (2) thus eliminating the repeating digits

990x = 1995 ( divide both sides by 990 )

x = [tex]\frac{1995}{990}[/tex] = [tex]\frac{133}{66}[/tex] ← in simplest form

The sum of the complex number in standard form is 8 + 3i

Complex numbers are square roots of negative numbers. The square root of -1 for example is equal to "i" as shown;

√-1 = i

The complex number is written as x + iy. Given the expression

(9 + 6i) − (1 + 3i)

Expand to have:

9 + 6i − 1 - 3i

Collect the like terms

9-1 + 6i - 3i

Group into real and imaginary parts

(9-1) + (6i-3i)

8 + 3i

Hence the sum of the complex number in standard form is 8 + 3i

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The list of the possible outcomes for spinning the spinner with four sectors A, B, C, D, and flipping a fair coin goes as follows,

AH, BH, CH, DH, AT, BT, CT, DT

The possible outcomes for spinning a spinner (assuming that the spinner has four sectors, A, B, C, D) are: A, B, C, D  (4 outcomes)

Now, the possible outcomes for flipping a fair coin are: Tales (T) and Heads (H) (2 outcomes)

For each possible outcome of the spinner, there can be two possible outcomes associated, because of the flipping of the fair coin. Hence, the total possible outcomes for spinning the spinner with four sectors A, B, C, D, and flipping a fair coin are 4 × 2, i.e. 8 outcomes.

These possible outcomes are AH, BH, CH, DH, AT, BT, CT, DT.

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Answer:2x+y=8

3x-2y=5

Step-by-step explanation:multiply 1 st equation by 2

4x+2y=16

3x-2y=5

7x=21

x=21/7

x=3

2×3+y=8

6+y=8

y=8-6

y=2

The value of k if (x+1) is a factor of f(x) is -4

The polynomial function is given as:

f(x)=x^3-kx^2+x+6

(x+1) is a factor of f(x)

So, we start by setting x + 1 to 0

x + 1 = 0

Solve for x

x = -1

Substitute x = -1 in f(x)=x^3-kx^2+x+6 and set the equation to 0

(-1)^3-k(-1)^2+(-1)+6 = 0

Evaluate the exponents

-1 - k - 1 + 6 = 0

Evaluate the like terms

k + 4 = 0

Solve for k

k = -4

Hence, the value of k if (x+1) is a factor of f(x) is -4

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The surface area of the baseball is 176.6 cm² b.

To find the surface area of the baseball:

  r=3.75

[tex]A=4\pi r^{2}[/tex]

[tex]A=4*\pi *3.75^{2}[/tex]

A=176.6 cm² b.

The surface area of the baseball is 176.6 cm² b.

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The sum of an arithmetic progression with first term of 2 and the common difference of 35 is 2340

Series are defined as the sum of sequence. The formula for calculating the nth term of an arithmetic sequence is expressed as:

S = n/2[2a+(n-1)d]

where;

n is the number of terms

d is the common difference

a is the first term

Given the following parameters from the question

a -2

d = 35

n = 12

Substitute

S = 12/2[2(2)+(12-1)(35)]

S = 6(4+11(35))

S = 6(5+385)
S = 6(390)

S = 2340

Hence the sum of an arithmetic progression with first term of 2 and the common difference of 35 is 2340

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The correct option of this expression is (B) 2(x-3)(x-4)

What is expression?

Given, expression is ;  2x²-14x+24 = 0

Now take common 2 from  this expression  both side.

        2(  x² - 7x + 12) = 0

          2(x² - (4 +3)x + 12) = 0

        2 (  x² - 4x - 3x + 12) = 0

        2 ( x( x - 4 ) -3 ( x - 4 )) = 0

        2  ( x - 3 ) ( x - 4 ) = 0

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The complete question is -

Select the correct answer. Which expression is equivalent to the given expression? 2x²-14x+24

A.(2x-12)(x-2)

B.2(x-3)(x-4)

C.2(x-8)(x+3)

D.2(x-5)(x-2)

Answer:

24 / 7

Step-by-step explanation:

y - 4(2y - 5) = -4

y - 8y + 20 = -4

-7y = -24

7y = 24

y = 24/7,

y = 3 and 3/7

or

y = 3.428571 all recurring

(they are all the same value in different forms I would just write 24/7)

The answer is Figure A.

Given: "If it is an triangle, then it has three vertices.

To find which diagram represents the given statement.

From the first diagram

Triangles have three vertices because they are formed by the intersection of three triangles.

using the second diagram

Three vertices make up the triangle's intersection zone.

Therefore, we cannot infer from the second diagram that a triangle has three vertices.

As a result, figure A represents the stated assertion.

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The factor of [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex] exists [tex]$\left(a^{2}+3\right)(b+2)$$[/tex].

Let the given factor be [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex]

To factor this we use the grouping method

We group the first two terms and last two terms then we factor out the greatest common factor (GCF) from each group.

[tex]$\left(a^{2} b+2 a^{2}\right)+(3 b+6)$$[/tex]

Take out GCF from each group

[tex]$a^{2}(b+2)+3(b+2)$$[/tex]

Now factor out b+2, we get

[tex]$\left(a^{2}+3\right)(b+2)$$[/tex]

The factor of [tex]$a^{2} b+2 a^{2}+3 b+6$[/tex] exists [tex]$\left(a^{2}+3\right)(b+2)$$[/tex].

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The probability that the hypothesis test will result in a type ii error, β is 0.20.

In this question,

A type II error is one of two types of statistical errors that can result from a hypothesis test (the other being a type I error). A type II error will occur if the statistical test is not powerful enough. And it occurs when one rejects the alternative hypothesis (fails to reject the null hypothesis) when the alternative hypothesis is true.

The probability of a type II error is denoted by *beta*, β.

Power of a test = 0.80

The relation between power of a test and type II error is given as,

Power = 1 - type II error

⇒ Type II error, β = 1 - 0.80

⇒ Type II error, β = 0.20

Hence we can conclude that the probability that the hypothesis test will result in a type ii error, β is 0.20.

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Answer:  18 cows

Step-by-step explanation: C = how many cows can graze on 720 acres of land. 40(C) = 720. 720/40 = 18 C = 18.

Answer:

40x = 720

x = 18

Step-by-step explanation:

x = number of cows