What is the slope of the line that passes through these two points (8, 4) and (5, 3)?

Answers

Answer 1

Answer:

the answer is 3/1

Step-by-step explanation:

u do 8-5/4-3 which is 3/1


Related Questions

need asap pleaseeeeeeee

Answers

28
28 • 28 • 28 = 21,952
it’s 28 to the third power (aka “f^3”)

Answer:

c) f = 28

Step-by-step explanation:

Given problem,

→ f³ = 21952

Now the value of f will be,

→ f³ = 21952

→ f = ³√21952

→ [ f = 28 ]

Let's check the following,

→ 28³

→ (28 × 28) × 28

→ 784 × 28 = 21952

Hence, option (c) is correct.

At a butcher​ shop, karl bought 2 7/20 lb of beef and some pork. he left with 14 14/25 lb of meat. Express the number of pounds of pork he bought using a decimal.

Answers

The number of pounds of pork he bought in decimal is 12.21 lb

Decimal:

A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

For example 12.34 is a decimal.

Given,

At a butcher​ shop, karl bought 2 7/20 lb of beef and some pork. he left with 14 14/25 lb of meat.

Here we need to find the number of pounds of pork he bought using a decimal.

First, we have to convert the given fractions into decimal then we get,

Amount of beef = 2 7/20

Which is equal to,

=> 2 + 7/20

=> 2 + 0.35 = 2.35 lb

Similarly,  total amount of meat = 14 14/25

=> 14 + 14/25

=> 14 + 0.56 = 14.56

Therefore, the amount of pork is,

=> total amount of meat - the amount of beef

=> 14.56 - 2.35

=> 12.21.

Therefore, the the number pounds of pork in decimal is 12.21 lb.

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Determine the rule for translating ABC to A'B'C'

Answers

Correct answer is A, the rule for translating ABC to A'B'C' is left 2, up 9.

What does translating a triangle mean?

An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction. are frequently called slides. You can use notation or words to express a translation, such as "moved up 3 and over 5 to the left."

A translation in geometry is a type of transformation that shifts a geometric figure in a certain direction without altering its size or orientation. The figures are congruent before and after the transformation since it is a type of stiff transformation.

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A local builder estimated that each year 57 homes are built in the surrounding area. In 2002 there was 43,800 homes. Find the number of homes in 2011.

Answers

Answer:

The number of homes in 2011 is 44,313

Explanation:

Given that 57 homes are built each year, in 2002, there were 43,800 homes, then the next years have the number of homes as follows:

2003: 43,800 + 57

2004: 43,800 + 57 + 57

2005: 43,800 + 57 + 57 + 57

This goes on until 43,800 + 57n

where n is the number of years after 2002.

2011 is 9 years after 2002, so the number of homes will be:

43,800 + 57(9)

= 43,800 + 513

= 44,313

X - 11 = -44 solve one step equation.

Answers

Answer: x = -33

Explanation:

Given the following question:

x - 11 = -44

Step 1: collect the like terms

x = -44 + 11

x = -33

Therefore, x = -33

Translate this phrase into an algebraic expression. Seven more than the product of 17 and Julie's savings Use the variable j to represent Julie's savings.

Answers

17j+7 is the algebraic expression for Seven more than the product of 17 and Julie's savings.

What is Expression?

Expression is a combination of variables, operators and numbers.

The given phrase is

"Seven more than the product of 17 and Julie's savings"

and j is variable to represent Julie's savings.

In the phrase we have Seven more than, it means we are adding 7 to something.

According to problem we are adding 7 to "product of 17 and Julie's savings"

Product means multiplying a number with another factor. Here the factor is julies saving j.

17j+7 is the translated algebraic expression.

Hence 17j+7 is the translation of  Seven more than the product of 17 and Julie's savings.

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If what is the length of DF? ​

Answers

Answer:

DF = 13

Step-by-step explanation:

Congruent triangles:

        In ΔABC & ΔDEF,

                     ∠A = ∠D

                     ∠C = ∠F

                      CB = FE

            ΔABC ≅ ΔDEF   {Angle Angle Side congruency}

              DF = AC = 13

That is easy it’s just 13

Thu has the same amount of money automatically deposited into a new savings account each week. After 2 weeks, she has $14. After 5 weeks, she has $35. The unit rate is measured in dollars per week. What is the constant of proportionality?

Answers

For the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.

As given in the question,

For the saving account,

Amount deposited is directly proportional to the number of weeks

Let y be the amount deposited and x be the number of weeks

y ∝ x

y = kx

'k' is the constant of proportionality

As per data unit rate is measured in dollars per week

For y = $14 then x = 2 weeks

14 = 2k

⇒ k = $7

For y = $35 then x = 5weeks

35 =5k

⇒ k = $7

Therefore, for the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.

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The midpoint of GH is M(3, 6). One endpoint is H(6, 5). Find the coordinates of the other endpoint G.

Answers

The coordinates of the endpoint G is (0, 7).

The midpoint of the coordinate is the centre point which can be calculated by finding the average. So, the relation representing the endpoints and midpoint is as follows -

Midpoint (x, y) = ([tex] x_{1}[/tex] + [tex] x_{2}[/tex]/2), ([tex] y_{1}[/tex] + [tex] y_{2}[/tex]/2)

Keep the value in mentioned formula to find the endpoint G, represented as [tex] x_{1}[/tex] and [tex] y_{1}[/tex].

(3, 6) = ([tex] x_{1}[/tex] + 6/2) ([tex] y_{1}[/tex] + 5/2)

Relating the x and y values -

x value :

3 = [tex] x_{1}[/tex] + 6/2

[tex] x_{1}[/tex] + 6 = 3×2

[tex] x_{1}[/tex] + 6 = 6

[tex] x_{1}[/tex] = 6 - 6

[tex] x_{1}[/tex] = 0

y value :

6 = [tex] y_{1}[/tex] + 5/2

[tex] y_{1}[/tex] + 5 = 6×2

[tex] y_{1}[/tex] + 5 = 12

[tex] y_{1}[/tex] = 12 - 5

[tex] y_{1}[/tex] = 7

Thus, the coordinates of point G from the line GH is (0, 7).

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Water is drained at constant rate of 2 gallons per minute from a fish tank containing 28 gallons of water which equation represent the number of gallons of water remaining in the tank y based on the number of minutes t since water started draining from the fish tank where 0<_t_<14?

Answers

The equation represent the number of gallons of water remaining in the tank is y = 28 - 2t

What is an equation?

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The water remaining is illustrated as y.

The time taken is t.

The appropriate equation will be:

y = 28 - (2 × t)

y = 28 - 2t

This illustrates the water remaining in the tank.

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Write an equation is point slope form of a line given that the slope is 2/3 and that the line goes through the point (5,-2)

Answers

Answer:

[tex](y+2)=\frac{2}{3} (x-5)[/tex]

Step-by-step explanation:

Point slope form is shown below:

[tex](y-y_1)=m(x-x_1)[/tex]

We are given the slope m = 2/3 and the point x1 = 5, y1 = -2

Simply plug in these numbers into the above equation.

[tex](y--2)=\frac{2}{3} (x-5)[/tex]

Simplify:

[tex](y+2)=\frac{2}{3} (x-5)[/tex]

Amy got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 19 cents per yard. If after that purchase there was $16.77 left on the card, how many yards of ribbon did Amy buy? pls answer this!

Answers

Answer:

price for one ribbon =19 cents

she got $20

20- 16.77 the rest from the money = 3.23

so she spends 3.23 from buying the ribbon

how much ribbon does she buy

3.23 ÷ 0.19= 17 ribbons

A scale drawing of a field is shown below.8 in.10 in.6 in.The drawing uses a scale of 1 in. = 14 ft. What is the area of the actual field?

Answers

We can multiply each side by 14ft yo find the value on feet and late calculate the area

[tex]\begin{gathered} 8\times14=112ft \\ 10\times14=140ft \\ 6\times14=84ft \end{gathered}[/tex]

tha area formula is

[tex]A=\frac{b\times h}{2}[/tex]

where b=84ft and h=112ft

[tex]\begin{gathered} A=\frac{84\times112}{2} \\ A=4704 \end{gathered}[/tex]

the area is 4,704ft2

A pedestrian is walking at a speed of 3 km/hr. Express the distance in kilometers, d, as a function of time in hours, t.
The question format : d(t) =

Answers

Answer:   d(t) = 3t

This is because

distance = rate*time

Rate is another term for speed.

Which of the following shows the values of −0.5, −2.8, 1.9, 0.9, and −1.7 plotted on a number line?

A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.9, negative 2, negative 0.6, 0.9, and 1.7 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5, 0.9, and 1.9 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 3, negative 1.9, negative 0.7, 0.8, and 1.9 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.9, negative 2, negative 0.6, 0.9, and 1.9 are plotted.

Answers

The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7,negative 0.5,0.9 and 1.9 are plotted."

Here the values are

-0.5,-2.8,1.9,0.9 and -1.7

The number line a graphical representation that a line on which numbers are marked at intervals, used to represents the simple numerical operations.
Here there are three negative numbers -0.5,-2.8 and -1.7

The positive numbers are 1.9 and 0.9

The statement "A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5,0.9 and 1.9 are plotted" is suited of all the given conditions

Hence, The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5, 0.9, and 1.9 are plotted."

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Simplify the expression,

Assume all variables are positive.

Answers

Answer:

x²[tex]\sqrt{5}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

given

5[tex]\sqrt{20x^4}[/tex] - 3[tex]\sqrt{45x^4}[/tex]

simplify the 20 and 45 inside the radicals

[tex]\sqrt{20}[/tex] = [tex]\sqrt{4(5)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{5}[/tex]

[tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex]

Then

= 5(2[tex]\sqrt{5}[/tex] x² ) - 3(3[tex]\sqrt{5}[/tex] x² )

= 10[tex]\sqrt{5}[/tex] x² - 9[tex]\sqrt{5}[/tex] x²

= x²[tex]\sqrt{5}[/tex]

C = dn or C = 2rn

(What is the radius of a circle with a circumference of 25cm?)

Answers

Hello!

Let's take this problem step by-step:

What is the formula for the circumference of a circle:

 [tex]\text{Circumference} = 2\pi *\text{radius}[/tex]

Since the circumference is 25 cm

  [tex]25 = 2\pi *\text{radius}\\\\\text{radius} = \dfrac{25}{2\pi }[/tex]

Answer: [tex]\text{radius} = \dfrac{25}{2\pi }[/tex]

Hope that helps!

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Solve the equation for x. −0.24x − 16.4 = 1.48 x = −62.2 x = 62.2 x = −74.5 x = 74.5
hurry pls​

Answers

The solution of the given linear equation is x = -9.53

How to solve the equation for x?

Here we have the linear equation:

-0.24*x - 16.4 = 1.48*x

To solve this, first we need to move all the terms with x to the left and the terms without x to the right.

-0.24*x - 1.48*x = 16.4

(-0.24 - 1.48)*x = 16.4

-1.72*x = 16.4

Now we can divide both sides by -1.72 to get:

x = 16.4/-1.72 = -9.53

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Answer: c) (is it c?)

Step-by-step explanation: c) x= - 74.5

0.24x+16.4=-1.48 step 1- subtract: -1.48- 16.4

0.24x= -17.88    (divide)

x= −74.5

there

i hope this helps!!

Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) Q(x) + R(x).
P(x) = 3x³-4x²-3x, D(x) = 3x - 4
P(x) =

Answers

The value of  Q(x) =   x² - 1  

R(x) = 4

What is Long Division?

Long division is a common division procedure in mathematics that may be easily performed manually and is appropriate for dividing multi-digit Hindu-Arabic numbers. It simplifies a division problem into several shorter stages.

By long Division method:

                        x² - 1            

                     _______________________________

         (3x - 4) | 3x³ - 4x² - 3x

                       3x³ - 4x²

                       _________________

                            0 - 0   - 3x      

                                       - 3x + 4  

                                ___________________

                                          0  + 4

                                                   

Q(x) =   x² - 1  

R(x) = 4

Hence, (3x³-4x²-3x) = (3x - 4)(x² - 1  ) + 4

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Select the pair that could be a reasonable approximation for the diameter and
circumference of a circle.
5 meters and 22 meters
19 inches and 60 inches
33 centimeters and 80 centimeters
Explain your reasoning.
Your answer

Answers

We know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.

What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.

So, let 'D' be the diameter and 'C' be the circumference.

Calculate C as:

C = πD (π = 3.14)

(A) D = 5 m and C = 22 m

C = πD C = 3.14 × 5C = 15.7 m

So, C = 15.7 m does not approximate 22 m.

(B) D = 19 in and C = 60 in

C = πD C = 3.14 × 19C = 59.66 in

So, C = 59.66 approximates 60 in.

(C) D = 33 cm and D = 80 cm

C = πD C = 3.14 × 33C = 103.62cm

So, C = 103.62cm does not approximate 80cm.

Therefore, we know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.

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The correct question is given below:
Select all the pairs that could be reasonable approximations for the diameter and circumference of a circle. * 1 point A. 5 meters and 22 meters. B. 19 inches and 60 inches. C. 33 centimeters and 80 centimeters.

What is the slope of the line that passes through the points (-8, -1)(−8,−1) and (-8, -11)(−8,−11)? Write your answer in simplest form.

Answers

Answer:

Undefined slope

Step-by-step explanation:

Slope , m is equal to rise/run    Or   ( y1-y2) / ( x1 -x2)

              This line is a vertical line at x = -8    And thus has undefined slope

              (Because you cannot divide by zero)

Answer:

Undefined

Step-by-step explanation:

Hey! Let's help you with your question here! I am unsure if the points are correct cause you've written each one down twice. If it does change, I will change my answer accordingly.

We're looking for a slope of the line that passes through 2 points I see! Alright, so as you would recall, most equations of a linear line are described in the form of slope-intercept form. And that being this:

[tex]y=mx+b[/tex]

When we're finding for slope of the line, we're essentially just look for m. But how can we find m with only just 2 points? Well, we can! Using a formula that helps us find the slope using exactly 2 points! And that is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now, all we have to do is plug in the values as such and solve:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-11-(-1)}{-8-(-8)}[/tex]

From here, we come to a problem. If we were to solve this equation to find the slope, we will get an undefined value mainly because the denominator will equal 0 and we can't have it equal 0. So therefore, it is undefined.

The graph of f(x) is shown.
For what values of x does f(x) = 0?
A) −1, 1, 2
B) −2, −1, 1
C) −3, −1, 1
D) −1, 1, 3

Answers

Answer:

C

Step-by-step explanation:

f(x) =0

when the curve intersects the x axis

goodluck :)

Fill in the blanks to express the quantities given in ratio language. Ratios must be
expressed in simplest form.
Number of Animals in the Pet Store:

Animal Count
16 cats
8 dogs


For every __ cats in the pet store, there are __dogs.

Answers

for every 2 cats in the pet store, there are 1 dogs

I need help with this

Answers

Answer:

113.85

Step-by-step explanation:

230*55% because 100%-45%=55% is 126.5

Then 126.5*90% because 100%-10%=90% which is 113.85

Question 4(Multiple Choice Worth 1 points)
(03.01 MC)

Simplify square root of three times square root of twenty one.

square root of twenty four
square root of sixty three
three square root of seven
nine square root of seven

Answers

The Simplification of square root of three times square root of twenty one is; C: three square root of seven

How to use law of Exponents?

The Laws of Exponents are;

When multiplying like bases, ensure that the base is kept the same while we add the exponents. When raising a base with a particular power to another specific power, ensure that the base is kept the same and multiply the exponents. When dividing like bases, ensure that the base is kept the same and subtract the denominator exponent from the numerator exponent.

We have the expression;

√3 * √21

= √3 * √3 * √7

= (√3 * √3) * √7

= 3√7

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Evaluate g(18), when g(x)=−8x+14

Answers

Answer:

-130

Step-by-step explanation:

g(18)= -8(18)+14

=-144+14

=-130

Determine the range of the following graph:

Answers

Answer:

The range is the allowed values of y.

Set notation: { y | -9 [tex]\leq[/tex] y [tex]\leq[/tex] 0, y ∈ R}

Interval notation: [-9,0]

Hope that helps

​the long division method to find the result when 12x^{3}+5x^{2}-27x+1312x
3
+5x
2
−27x+13 is divided by 3x-13x−1. If there is a remainder, express the result in the form q(x)+\frac{r(x)}{b(x)}q(x)+
b(x)
r(x)

(hope it makes sense)

Answers

The solution of the polynomial division 12x³ + 5x² - 27x + 13 is divided by 3x - 1 is; 4x² + 3x - 8 + (5/(3x - 1))

How to carry out Polynomial Long Division?

We want to use long division method to solve the polynomial division when 12x³ + 5x² - 27x + 13 is divided by 3x - 1.

             4x² + 3x - 8

          -------------------------

3x - 1  | 12x³ + 5x² - 27x + 13

         -  12x³ - 4x²        

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

                     9x² - 27x  

                 -   9x² - 3x

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

                            -24x + 13

                        -    -2x + 8

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

                                      5

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

Expressing the solution of the polynomial division in the given quotient and remainder form gives us;   4x² + 3x - 8 + (5/(3x - 1))

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Find the value of x.
(5x − 17)°

13
132
12
48

Answers

Answer:

its 12

Step-by-step explanation:

What are the The values of X and why that satisfy this equation (x+yi)+(4+9i)=9-4i

Answers

The values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13  .

In the question ,

the equation is given as

(x+yi)+(4+9i)=9-4i

to find the value of x and y , we solve LHS and RHS of the equation separately

So LHS =

(x+yi)+(4+9i)

x+yi+4+9i

Adding the real and imaginary terms , we get

(x+4)+(y+9)i which is equal to RHS that is 9-4i

So , on comparing , we get

x+4 = 9    and      y+9 = -4

x= 9-4      and      y = -4-9

x = 5       and       y = -13

Therefore , the values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .

The given question is incomplete , the complete question is

What are the The values of X and Y that satisfy this equation (x+yi)+(4+9i)=9-4i  ?

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Two exponential functions, f(x) and g(x), are graphed on the same coordinate plane. Graph of f of x equals 2 to the x power going through points 0 comma 1 and 1 comma 2 and graph of g of x equals 2 to the x power plus 4 going through points 0 comma 5 and 1 comma 6. What effect does adding 4 to the parent function have on the transformed function? a Adding 4 to the parent function shifts the function down four units. b Adding 4 to the parent function shifts the function up four units. c Adding 4 to the parent function shifts the function right four units. d Adding 4 to the parent function shifts the function left four units. Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Of all the most important substances imported intoWestern Europe from the East after 1480, these threeitems had the least impact on both population growth andlife-expectancy (compared to the one item on the list thatdid):MedicineCinnamonSteelSalt Please help me with this. Show the solution as well. Thank you Evaluate the expression |2x 5| for x = 3 and for x = 3. How do they puppy in pet store?(GIVING BRAINLIEST) A 4 1/2 bag of raisians must be divided equally into 1/4 bag portions This paragraph is mostly aboutA: The Appalachian MountainsB: Europeans moving to AmericaC. Westward movement in AmericaD. The heights of mountain ranges Question 16The underlined phrase is a poor choice. Choose the best word or phrase to replace it:Although high school often seems like a social club, in college it is all about studying hard and doing one's work.Group of answer choicesA. the objective isB. the way to go isC. the most important things isD. it isQuestion 17The underlined word in this sentence is dull and vague. Choose the best word to take its place. HINT: although many of the choices are grammatically correct, only one is the most precise and descriptive wording possible.The model wore a bright dress with a blue sash.Group of answer choicesA. dazzling white... midnight blueB. very light-colored.... very blueC. brilliant.... blueD. bright... really dark blueQuestion 18The underlined word in this sentence is dull and vague. Choose the best word to take its place. HINT: although many of the choices are grammatically correct, only one is the most precise and descriptive wording possible.Although I have never met Shakina, she seems interesting.Group of answer choicesA. really niceB. like super "cool"C. an alright sort of personD. like a personable individualQuestion 19Turn the following short simple sentences into a more effective single sentnence.Healthcare professionals are a brave group of people. They have high-stress jobs. They must be ready anytime for emergencies. [HINT: think simple sentences and relationships between ideas.]Group of answer choicesA. Healthcare professionals are a brave group of people who must be ready anytime for emergencies. They have high-stress jobs.B. Healthcare professionals are a brave group of people, have high-stress jobs, must be ready at any time for emergencies.C. Healthcare professionals they are a brave group of people and they have high-stress jobs and they must be ready at any time for emergencies.D. Healthcare professionals are a brave group of people who have high-stress jobs because they must be ready at any time for emergencies.Question 20Correct the following sentence.Although things are difficult in today's economic climate, a person willing to work hard, who has determination, wants to make something of himself, can be successful. [HINT: think parallelism]Group of answer choicesA. Although things are difficult in today's economic climate, a person willing to work hard, a person who has determination, wants to make something of themselves, can be successful.B. Although things are difficult in today's economy, a person willing to do work hard, determination, and wants to make something, being successful.C. Although things are difficult in today's economic climate, a person willing to work hard, who has determination, wants to make something of himself, can will be successful.D. Although today's economic climate makes achieving one's dreams more elusive than in past years, a person who is willing to work hard, who possesses determination, and who wants to make something of him or herself can still be successful.Question 21A simple sentence requires three things to be a complete sentence; they are a ______________, a ________________, and a ________________ _________________.Question 22A compound sentence is a sentence with two or more _________________________ clauses.Question 23A complex sentence is a sentence which has one or more ______________________ clauses and one ________________________ clause. Select three adjectives dont select any articles with a , an , the for the interview Katie you like to wear a professional white blouse and a pair of gray with pinstripes The team's engagement score was 5.20 this month. the score has been improving at a rate of 8% per month. what was the score 3 months ago? 1.60 3.95 4.13 4.78 5.12