What is the area, in square units, of the parallelogram shown?

Answer:

222

Step-by-step explanation:

If you have applied for two jobs a and b and the probability that you get an offer for the job a is 0.25 and the probability of being offered job b is 0.20, then the probability that you will be offered both jobs is 0.05.

Probability is that branch of mathematics that deals with the numerical description of the possibility of an event to occur. The probability of any event is a number between 0 and 1 where 0 represents the impossibility of the event to occur while 1 represents certainty of that event to occur.

As the probability of the job a and job b are independent of each other, the probability that both jobs will be offered can be determined by using the formula;

P(A∩B) = P(A) × P(B)

Here, P(A∩B) represents the probability of both the events happening together

As P(A) = 0.25

P(B) = 0.20

P(A∩B) = 0.25 × 0.20

P(A∩B) = 0.05

Hence, the probability that both jobs will be offered is calculated to be 0.05.

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The solution of the equation √5 x + 1 - 2√x = 1 is [tex]\frac{4}{5}[/tex].

An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

Consider the equation,

√5 x + 1 - 2√x = 1

Subtracting 1 from each side of the equation.

√5 x + 1 - 2√x - 1 = 1 - 1

√5 x - 2√x = 0

√5 x = 2√x

Dividing each side of the equation by √x.

( √5 x/√x ) = ( 2√x / √x )

√(5x) = 2

Squaring each side of the equation.

[ √(5x) ]² = (2)²

5x = 4

Dividing by 5 from each side of the equation.

( 5x/5 ) = ( 4/5)

x = 4/5

Now checking the extraneous solution:

[tex]\sqrt{5}x + 1 -2\sqrt{x} =1\\\sqrt{5}(\frac{4}{5} ) + 1 - 2(\sqrt{\frac{4}{5} } ) = 1\\ \frac{4}{\sqrt{5} } + 1 - \frac{4}{\sqrt{5} } = 1\\ 1 = 1[/tex]

The solution for the equation is 4/5.

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Answer: .8 or 4/5

Step-by-step explanation:

You can do this a couple ways.

1) what you started is right, you can change your fraction into a decimal and divide.

2/5 = .4

.32/.4 = .8

2) you can change .32 into 32/100 and divide by 2/5

32/100 divided by 2/5

When you divide fractions, you flip the divisor and multiply

32/100 x 5/2

Multiply across

160/200

Simplify

4/5

The function that models the inverse variation is y = -56/x.

So,

Then,

Since x · y = C then we obtain:

Therefore, the function that models the inverse variation is y = -56/x.

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Answer:

82

Step-by-step explanation:

if g(3)= substitute a as 3 = (3)^3 +5(3)^2= 27+45= 72

if f(3)= substitute a as 3= 2(3) +4=10

join them up since it said there to add  g(3) +f(3)

72 +10= 82

Answer:

Hey!  the breadth is 12 m and the length is 12+6=18 m

Mark me as brain?

Step-by-step explanation:

let the breadth be X metre

so the length will be 6+ x metre

perimeter is equal to 60 m

2(6+x+x)=60

2 (6+2x)=60

12+4x=60

4x=60-12=48

x=48/4=12

so

Answer:

Step-by-step explanation:

Try the code AEAA. Let me know if its right or not.

Answer:

CHGD

Step-by-step explanation:

You should actually solve each of these puzzles to get the right code
1. To evaluate f(-2)

We have f(x) = x³ - 2x

Substitute -2 for x

==> (-2)³ - (2 x-2)
-2³ = -8
2 x -2 = -4

==> f(-2) = -8 - (-4)
==> f(-2) = -8 + 4      (two negatives make a positive
==> f(-2) = -4            Letter C

2. Evaluate g(-10)
[tex]g(x) = \dfrac{3x}{2}[/tex]

[tex]g(-10) = \dfrac{3 \times -10}{2} \\= \dfrac{-30}{2} \\\\= \boldsymbol{-15}[/tex]        Letter H

3. Evaluate h(-1)
h(x) = 2x² + x
h(1) = 2 x (-1)² - 1

= 2 x 1 - 1

= 1            Letter G

4. Evaluate f(3)
f(x) = x³ -2x
f(3) = 3³ - 2 x 3

= 27 - 6

= 21              Letter D

So the correct code is CHGD

You got everything right except the third :)

Answer:

Step-by-step explanation:

The simplified expression of 6 -√25 + √4 is 3

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

6 -√25 + √4

Evaluate the exponents

So, we have

6 -√25 + √4 = 6 - 5 + 2

Evaluate the difference

So, we have

6 -√25 + √4 = 1 + 2

Evaluate the sum

So, we have

6 -√25 + √4 = 3

Hence, the simplified expression of 6 -√25 + √4 is 3

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Answer:

Step-by-step explanation:

6-√√25= 0.25

-2-√15/2= A, -2.94

x=5+√-49/6= C, 5/6+7/6i

Based on the fact that no less than a third of the juniors went to prom and there were 37 juniors, the minimum amount of juniors at the school was 111 juniors

The school paper reported that out of the total juniors in school, no less than a third juniors went to prom.

We also know that 37 juniors went to prom. Assuming that 37 juniors represents a third of the juniors, the minimum amount of juniors at the school can be found as:

= Number of juniors who went to prom / Proportion of juniors who went to prom

Solving for the minimum amount of juniors at the school gives:

= 37 / 1/3

= 37 x 3/1

= 111 juniors

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Answer:

23

Step-by-step explanation:

x=3  PEMDAS says that exponents go first so 3x3=9  then 2x9=18+5=23

Answer:

f(-3) = -26

Step-by-step explanation:

f(n)=7n-5; f(-3)

f(-3) = 7(-3) - 5

f(-3) = -21 - 5

f(-3) = -26

I hope this helps!

The value of the expression ∛ - 7. ∛ 49 after multiplying it and simplifying it, we get the result as - 7.

We are given the expression:

∛ - 7. ∛ 49

We need to multiply and simplify it.

We will first multiply the expression:

= ∛ - 7 × 49

Solving it, we get that:

= ∛ - 343

Now this can also be written as:

= ∛ (- 7 )³

Now, simplifying the cube root to get the value of the expression:

= - 7

Therefore, we get that, the value of the expression ∛ - 7. ∛ 49 after multiplying it and simplifying it, we get the result as - 7.

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Solution of exponential equation is , x =  [tex]800. 7^4[/tex]

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as  [tex]a^x[/tex] .

where, a = the base of function

           x = main expression

Mathematically, if  [tex]log_aN = x[/tex] is an logarithmic function then, this can be converted to exponential function as  [tex]a^x = N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

Some important formulas of exponential :

According to given statement,

[tex]7^{-4} x = 800[/tex]

=> [tex]\frac{1}{7^4} x = 800[/tex]

=> [tex]x = 800 . 7^4[/tex]

Thus solution for this equation is x =  [tex]800. 7^4[/tex]

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The complete question is :

What is the solution of each exponential equation? Check your answer.

a. 7⁻⁴x=800

b. 5.2³x=400

Answer:

i THINK im not sure but i think its C please let me know if im wrong

Step-by-step explanation:

Answer:

(y - y1) = m(x - x1)

Step-by-step explanation:

(y - y1) = m(x - x1)

Answer:Solution

Result will not divisible by 3

5

3

×2−8=250−8=242

If we divide 242 by 3 it will leave reminder 2.

Step-by-step explanation:

The equation is given by A = n³ - 8 , where n is a number

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number be represented as n

A = 8 is subtracted from the cube of a number

Substituting the values in the equation , we get

A = n³ - 8   be equation (1)

Now , when 8 is subtracted from twice the cube of 5 , the result is not divisible by 3

So , A = 2 x 5³ - 8

A = 242 which is not divisible by 3

Hence, the equation is A = n³ - 8

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It will take the painter more than 40 hours to paint all 20 rooms in stately wayne manor .

Time taken for the first 3 rooms =9hrs

Learning curve rate = 85%

Time taken for the next 20 rooms =?

Time taken for 1 room = 9hrs / 3 rooms = 3 hrs

If it takes 3 hrs to paint 1 room

Therefore, it will take x hrs to paint 20 rooms would take;

Hence, 20 rooms multiplied 3 hrs = 60 hours

It may take 60 hours to complete painting the 20 rooms.

At a learning curve rate of 85%, 15% will be the progress rate

Therefore, it will take additional 15% of 60 hours to paint the 20 room.

60+9(15% of 60) =69 hours

The painter would take more than 40 hours to paint the 20 rooms given his efficiency and learning curve rate.  The answer is derived by relating the data provided in the question to the desired answer.

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Expand using which formula? If it is using Sum/Difference Formulas, the expanded solution would be:

Solution:

[tex]z^3-17z^2+78z-54[/tex]

Hope this helps!

The correct statements among given statements are statement C and E.

What is a rational number ?

If p & q are any two numbers where q is not equal to 0, then the fraction in form p/q is called as rational number.

A number is given which is √22.

√22 = 4.69041576

Let's check which of the statements are correct.

A.

√22 is not rational number as the number has non - terminating decimal value which is 4.69041576 and it doesn't lies between 10 and 12. So , this option is not correct.

B.

This option is also not correct as the value of √22 nearly equals 4.69 is and not greater than 4.691.

C.

The value of √22 is 4.69041576.

If we round off to the nearest hundredth , 9 is at the hundredth place , so the value will be 4.69. This is a correct option.

D.

√22 is not a rational number as the number has non - terminating decimal value which is 4.69041576 but it lies between 4 and 5. So , this option is not correct.

E.

The value of √22 is 4.69041576. We can observe that the decimal number doesn't repeat. So , this is a correct option.

F.

As we know √22 is not a rational number we can't represent it as fraction. This option is not correct.

Therefore , the correct statements among given statements are statement C and E.

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Answer:

n = (W - Z)/a

Step-by-step explanation:

W = an + Z

Rearrange the equation so that the subject is alone, in the format Ax = B

W = an + Z

W - Z = an + Z - Z

W - Z = an

Isolate the subject by dividing or multiple so that the equation is in the format x = C

W - Z = an

(W - Z)/a = an/a

(W - Z)/a = n

The answers will be :

a. The equation of perpendicular bisector of QR is y = [tex]\frac{-5}{3}[/tex] x + 3.

b. The slope of median of triangle passing through point R is 1/4.

c. The slope of the altitude of the triangle that passes through point R doesn't exists.

What is slope of a line segment ?

Slope is the ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.

It is given that the vertices of a triangle are P(-6,1), Q(-2,-5) and R(8,1).

a.

The midpoint (M) of QR will be equal to

( [tex]\frac{-2 + 8}{2} , \frac{-5 + 1}{2}[/tex] )

or

M = (-3 , 2)

Now , slope of line QR will be ;

[tex]m_{QR}[/tex] = [tex]\frac{1+5}{8+2}[/tex]

[tex]m_{QR}[/tex] = 6 / 10

We know that :

m × [tex]m_{QR}[/tex] = -1

m = -10 / 6

or

m = -5 / 3

Equation of line will be given as :

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

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

b.

The midpoint of PQ will be :

= ([tex]\frac{-6 - 2}{2} , \frac{1 - 5}{2}[/tex])

= ( -4 , -2)

The slope of median of triangle that passes through point R will be ;

m = [tex]\frac{-2 - 1}{-4-8}[/tex]

m = -3 / -12

m = 1/4

or

m = 0.25

c.

Slope of altitude of triangle that passes through point Q will be :

m = [tex]\frac{1 - 1}{-6-8}[/tex]

m = 0 / -14

m = 0

The slope in this case doesn't exist.

Therefore the answers will be :

a. The equation of perpendicular bisector of QR is y = [tex]\frac{-5}{3}[/tex] x + 3.

b. The slope of median of triangle passing through point R is 1/4.

c. The slope of the altitude of the triangle that passes through point R doesn't exists.

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The equation that can be used to determine the value of x is 7x + 18 = 65

Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines

The figure that completes the question is added as an attachment

The given parameter is the angles in the figure

From the figure, we have the following angles:

Angle 1 = 23

Angle 2 = 7x - 5

Angle 3 = 67

The relationship between the above angles is

Angle 1 + Angle 2 = Angle 3

This is so because the angles 1 and 2 are adjacent angles and they add up to angle 3

Substitute the known values in the above equation

So, we have

23 + 7x - 5 = 65

Collect the like terms in the above equation

So, we have

23 - 5 + 7x  = 65

Evaluate the like terms in the above equation

So, we have

18 + 7x  = 65

Rewrite the above equation as

7x + 18 = 65

Hence, the equation that can be used to determine the value of x is 7x + 18 = 65

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