Total score:
of 15 points
(Score for Question 1: of 5 points)
1. The diagram shown is two intersecting lines. The measure of 22 is 29
2
(a) What is the measure of 24? How do you know? Explain your answer in complete sentences.
(b) Suppose the measure of 3 can be represented by (3x - 8)*. What equation can be written to solve for the value of x?
(c) What is the value of x? Show all work.
Answer:
•(Score for Question 2: _ of 5 points)
2. Draw a right triangle with side lengths of 6, 8, and 10 units. For full credit, be sure to include appropriate labels and symbols where necessary. © Stride, Inc. All rights reserved. No reproduction without written consent of Stride, Inc.
Answer:
•Score for Question 3:
_ of 5 points)
3. At a park, a statue has a ring-shaped brick path around it. The outer edge of the brick path is a circle with a radius of 13 m. The inner edge of the brick path is a circle with a radius of 8 m.
Brick path
13 m
8 m
Statue
(a) Write and simplify an expression for the exact area of the brick path. Show all work.
(b) Find the approximate area of the brick path. Use 3.14 to approximate r. Show all work.

Step-by-step explanation:

2x - 17 = - 53

2x = - 53 + 17

2x = - 36

x = - 36/2

x = - 18

Answer:

x = -18

Step-by-step explanation:

2x - 17 =  -53

    +17 = + 17            Add 17 to both sides

2x       =   -36            

  x = -36 ÷ 2           Divide by 2

   x = -18

Based on the image attached, the solution for GE  is approximately 22.72.

To  be able to solve the equation √129 + √129 = GE, one need to simplify the  expression and then isolate GE.

Step 1: One can add the square roots:

Note that the equation:

√129 + √129 = GE.

Step 2:  Do put together the square root terms:

2√129 = GE.

Step 3:  Then Divide by 2:

√129 = GE/2.

Step 4: The Square both sides:

129 = (GE²)/4.

Step 5: So, Multiply by 4:

516 = GE².

Lastly, Take the square root:

√516 = √(GE²)

√516 = GE

GE = 22.72. approx.

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See text below



Step 26

Solve the equation for GE:

√129+√129 = GE

GE=2/129

Show steps

True, One drawback to job sharing is that employees may become competitive with one another, which could cause communication difficulties.

The advantage of job sharing is which of the following?

Maintain the degree of accountability and strategic weight of a full-time post. Take advantage of part-time employment's flexibility.

                             Skills and knowledge exchange between job sharers. While modifying the organization's structure of their hours, they maintain a certain level of seniority.

What potential drawbacks might there be to job sharing?

Equity issues in performance: Occasionally, one job-sharing partner fails to control their share of the task. When this occurs, managers could find it challenging to determine which partner is at fault.

                               The weak partner may also need to be fired, which could result in decreased production and difficulty finding replacements.

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Answer:

There will be 66 bacteria in 8 hours.

Step-by-step explanation:

The number of bacteria after t hours is given by the following formula.

\(P(t) = P(0)(1-r)^{t}\)

In which P(0) is the initual number of bacteria and r is the decay rate.

Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication.

This means that \(P(0) = 750000, P(48) = 250\)

We use this to find r. So

\(P(t) = P(0)(1-r)^{t}\)

\(250 = 750000(1-r)^{48}\)

\((1-r)^{48} = \frac{250}{750000}\)

\(\sqrt[48]{(1-r)^{48}} = \sqrt[48]{\frac{250}{750000}}\)

\(1-r = 0.84637\)

So

\(P(t) = 750000(0.84637)^{t}\)

How many bacteria will there be in 8 hours?

8 hours from now, in this context, is 8 + 48 = 56 hours. So this is P(56).

\(P(56) = 750000(0.84637)^{56} = 65.83\)

Rounding to the nearest number

There will be 66 bacteria in 8 hours.

Answer:

197,488

Step-by-step explanation:

This problem requires two main steps. First, we must find the unknown rate, k. Then, we use that value of k to help us find the unknown number of bacteria.

Identify the variables in the formula.

AA0ktA=250=750,000=?=48hours=A0ekt

Substitute the values in the formula.

250=750,000ek⋅48

Solve for k. Divide each side by 750,000.

13,000=e48k

Take the natural log of each side.

ln13,000=lne48k

Use the power property.

ln13,000=48klne

Simplify.

ln13,000=48k

Divide each side by 48.

ln13,00048=k

Approximate the answer.

k≈−0.167

We use this rate of growth to predict the number of bacteria there will be in 8 hours.

AA0ktA=?=750,000=ln13,00048=8hours=A0ekt

Substitute in the values.

A=750,000eln13,00048⋅8

Evaluate.

A≈197,488.16

At this rate of decay, researchers can expect 197,488 bacteria.

Answer:

The signs will be + and -

Step-by-step explanation:

Required

The signs in the parenthesis of difference of two squares

Let the expression be:

\((x^2 - a^2)\)

Expand

\(x^2 - a^2 = x^2 -ax + ax - a^2\)

Factorize

\(x^2 - a^2 = x(x -a) + a(x - a)\)

Factor out x - a

\(x^2 - a^2 = (x +a)(x - a)\)

See that the sign in front of a is + and - in the parentheses

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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Answer:

(2.5,-0.5)

Step-by-step explanation:

3x-y=8

x+y=2

4x=10

x=2.5

x+y=2

2.5+y=2

y=-0.5

ANS: (2.5,-0.5)

Answer: 5.6 kilograms.

Step-by-step explanation:

We know that 1,000 paperclips have a mass of 1 kilogram.

Therefore, one paperclip has a mass of 1/1000 kilograms, or 0.001 kilograms.

To find out how many kilograms 5,600 paperclips have, we can multiply the mass of one paperclip (0.001 kilograms) by the number of paperclips:

0.001 kilograms/paperclip * 5,600 paperclips = 5.6 kilograms

Therefore, 5,600 paperclips have a mass of 5.6 kilograms.

To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Answer:

8

Step-by-step explanation:

well because since you have to add u add 3+b

Answer:

This would be adding like terms togeather. So c3 plus c2 equals c5. So b2+c5 is your awnser.

Step-by-step explanation:

Answer:

Let's solve your equation step-by-step.

p=(0.5)(2.718282)−5

Step 1: Simplify both sides of the equation.

p=(0.5)(2.718282)−5

p=1.359141+−5

p=(1.359141+−5)(Combine Like Terms)

p=−3.640859

p=−3.640859

Answer:

p=−3.640859

Step-by-step explanation:

Answer:

y= 2x + 11

Step-by-step explanation: Hopefully that helps ;)

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad N(\stackrel{x_2}{5}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PN=\sqrt{(~~5 - 1~~)^2 + (~~-8 - (-1)~~)^2} \implies PN=\sqrt{(5 -1)^2 + (-8 +1)^2} \\\\\\ PN=\sqrt{( 4 )^2 + ( -7 )^2} \implies PN=\sqrt{ 16 + 49 } \implies PN=\sqrt{ 65 }\implies PN\approx 8.06\)

Answer:

fourth option

Step-by-step explanation:

∠ FTC = ∠ MTL ( vertical angles )

Since FC and ML are parallel, then

∠ FCT = ∠ TML (corresponding angles )

Thus

Δ TCF ~ Δ TML by the AA postulate

Answer:

\(\large \boxed{\mathrm{similar, \ AA \ similarity}, \ \Delta TML}\)

Step-by-step explanation:

The two triangles are similar.

We can prove by angle-angle similarity, in \(\mathrm{AA}\) similarity, there are two pairs of congruent corresponding angles in two triangles, this proves the two triangles are similar.

\(\angle U\) and \(\angle M\) are a pair of congruent corresponding angles.

\(\angle V\) and \(\angle L\) are a pair of congruent corresponding angles.

Therefore,

\(\Delta TUV \sim \Delta TML\)

Answer:

a)  P (COO)  = 0,135

b) P ( SISI) = 0,00015

Step-by-step explanation:

a) the probability of an ion channel in open position is 50 %   0,5

   the probability of an ion channel in close position is 50 %   0,5

probability for the following sequence of states COO

to be closed   0,5    (C)

from (C) to pass to open  0,3  (O)

and to stay O  is 0,9

Then the probability of the sequence of states COO is

P (COO)  = 0,5 * 0,3 * 0,9  

P (COO)  = 0,135

b) If people are either infected or susceptible, then

Probability of an individual infected is  0,5

Probability of an individual susceptible  is 0,5

to pass from susceptible to infected is 0,05

to pass from infected to susceptible is 0,12

then

P ( SISI) = 0,5 * 0,05*0,12*0,05

P ( SISI) = 0,00015

probability for the following sequence of states COO

Answer:

122 degrees

Step-by-step explanation:

The two intersecting lines are parallel for this problem, which means that the angle next to angle3 is the same degree measure as the one that is 58 degrees.

Also, remember that two angles next to each other on a straight line are supplementary, meaning that they add to 180 degrees.

When keeping these two things in mind, you can solve like this:

180 = angle3 + 58

180 - 58 = angle3

angle3 = 122

122 degrees

Answer:

46 inches

Step-by-step explanation:

Area of Rectangle: A = LW

                           1012 = 22L

Divide both sides by 22:  1012/22 = 22L/22

                                          46 = L

Answer: 2cm represents 200km

3cm represents 300km

Step-by-step explanation:

I do not see the question

\(\large\texttt{Answer\::}\)

pls refer to the explanation !

\(\large\texttt{Calculations\::}\)

\(\textsf{Area of a circle : $A=\pi r^2$}\)

We're asked to use 3.14 for pi , so we'll do just that .

We have the diameter , so we divide it by 2 to find the radius (remember , the radius is 1/2 of the diameter).

Plug in :

A=3.14*(7)²

A=3.14*49

Multiply :

A=153.86 inches²

\(\footnotesize\texttt{hope\:helpful~}\)

Answer:

Step-by-step explanation:

Given:

Use the area of the circle formula.

AREA OF THE CIRCLE FORMULA:

\(\Longrightarrow: \sf{A=\pi r^2}\)

\(\Longrightarrow: \sf{\pi =3.14}\)

\(\Longrightarrow: \sf{r=\dfrac{14}{2}=7}\)

\(\Longrightarrow: \sf{3.14*7^2}\)

Use the order of operations.

PEMDAS stands for:

BODMAS stands for:

\(\sf{3.14*7^2}\)

First, solve exponents.

\(\Longrightarrow: \sf{7^2=7*7=49}\)

\(\Longrightarrow: \sf{3.14*49}\)

Then, multiply.

\(\sf{3.14*49=\boxed{\sf{153.86}}\)

Solutions:

\(\Longrightarrow: \boxed{\sf{153.86\ in^2}}\)

I hope this helps, let me know if you have any questions.

Answer:

You should use AAS for this problem

Step-by-step explanation:

Maybe Brainliest Please

Answer:

Step-by-step explanation:

sin² x + cos² x = 1

\(\frac{1}{cosx}\) = sec x

( \(\frac{1}{cosx}\) )² = sec² x

Answer:

There’s two options for each. Look below.

Step-by-step explanation:

Savings: there is no risk of losing any money put into this account

              interest income is the only way to earn money in this type

‘investment: this account may generate income from a variety of sourses.

                  If no deposits or withdrawals are made, money held in this acct..

Answer:

Hi good job

Step-by-step explanation:

Answer:

B. Since Ax-b is consistent, its solution set is obtained by translating the solution set of Ax=0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax= 0 is a single vector, and that happens if and only if Ax 0 has only the trivial solution.

Step-by-step explanation:

the answer to the question is answer B. and here is the explanation below

let us imagine that the equation ax = b has a solution

now our goal will be to show that the solution of ax =b when ax = 0 has only trivial solution.

ax = 0 is homogenous

if this equation was consistent for b, we define

ax = b to be a set of vector that has the form

w = m + gh(h is a subscript)

gh is a solution of ax = 0

from what we have above, ax=b is in the form ofw= m+gh

with

m = solution of ax=b

gh = soulution of ax=0

ax = 0 has only trivial solution

gh = 0

with gh = 0

ax=b is w=m

so ax = b is unique.

(1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

Given are the polynomials,

1) x² - 2 x - 8

Factors = (x+2)(x-4)

2) x² + 2 x - 8

Factors = (x-2)(x+4)

3) x²-2x-4 = There will be no integral root.

4) x²+2x-4 = There will be no integral root.

Hence the (1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

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The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.

The correct answer is D.

The function f(x) has some specific characteristics as shown in the graph.

The graph of f(x) has five intercepts, as can be seen from the graph.

The intercepts of f(x) can be determined by observing where the graph of f(x) crosses the x-axis.

The function f(x) intercepts the x-axis at five different points: -6 only, -2, -1, 1, and 3 only.

At these points, f(x) = 0.
Furthermore, the graph of f(x) is increasing from -∞ to -6, then decreasing from -6 to -2.

The graph of f(x) then increases from -2 to -1, decreases from -1 to 1, increases from 1 to 3, and finally decreases from 3 to +∞.

Hence, we can deduce that the graph of f(x) has a local maximum point at x = -6, a local minimum point at x = -2, and another local minimum point at x = 3.
We can also conclude that f(x) is an odd function, meaning that f(-x) = -f(x).

This can be deduced from the symmetry of the graph about the origin.

Finally, we can see from the graph that the function f(x) is continuous everywhere except at x = -2 and x = 3.

At these points, f(x) is not defined.
The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.

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Answer: 25

Step-by-step explanation:

Multiplication and Division always come before Addition and Subtraction unless they are in brackets, which has top priority. In this case, the order would be ( ) [ ] ÷ +

( ) :

3 x 6 = 30 + 5 = 35

[ ] :

35 + 1 = 36

÷ :

36 ÷ 2 = 18

+ :

7 + 18 = 25

Answer: 25

Answer:

  17 bars

Step-by-step explanation:

Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.

The error in a rounded number is assumed to be as much as half of the least significant digit of the number.

Peter's load limit may actually be as low as ...

  1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100

Peter's bar weight might be as high as ...

  60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10

If Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...

  (1150 kg) / (65 kg/bar) ≈ 17.7 bars

The greatest number of bars Peter can load safely is 17.

Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).

Probability is a measure of the likelihood or chance that a particular event or outcome will occur. It is expressed as a value between 0 and 1, where 0 represents an event that is impossible to occur, and 1 represents an event that is certain to occur.

To solve this problem, we can use the formula for the standard deviation of the sample mean:

Standard deviation of sample mean = standard deviation / √(sample size)

Plugging in the given values:

Standard deviation of sample mean = 7 / √(31)

Next, we can calculate the z-score, which is the number of standard deviations the sample mean is below the population mean:

z-score = (sample mean - population mean) / standard deviation of sample mean

Plugging in the given values:

z-score = (141.5 - 145) / (7 / √(31))

Using a calculator, we find that the z-score is approximately -2.22.

Finally, we can use a standard normal distribution table or a calculator to find the probability that a z-score is less than -2.22.

Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).

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