Simplify. Express your answer using positive exponents.​

Answer:

X = 25, Angles are 65 degrees

Step-by-step explanation:

3x-10 = x+40

2x=50

x=25

Complete Question

Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 42% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 12%. There is only a 52% chance that she will find a tutor at such short notice

a What is the probability that Christine fails the course

b Christine ends up failing the course. What is the probability that she had found a tutor? (Round your answer to 4 decimal places.) Probability

Answer:

a

   [tex]P(F) =   0.264[/tex]

b

[tex]P(T | F ) = 0.23636 [/tex]

Step-by-step explanation:

From the question we are told that

The probability that Christine will fail the course if she does not have a tutor is [tex]P(F| T') = 0.42[/tex]

The probability that Christine will fail the course if she has a tutor is [tex]P(F| T) = 0.12[/tex]

The probability that she will find a tutor is [tex]P(T) = 0.52[/tex]

Generally the probability that she will not find a tutor is

[tex]P(T') = 1 - 0.52[/tex]

=> [tex]P(T') = 0.48[/tex]

Generally the probability of failing the course is

[tex]P(F) = P(F \ n \ T) + P(F \ n \ T')[/tex]

=> [tex]P(F) = P(F| T) * P(T) + P(A | T') * P(T')[/tex]

=> [tex]P(F) = 0.12 * 0.52 + 0.42* 0.48[/tex]

=> [tex]P(F) = 0.264[/tex]

Generally if Christine ends up failing the course the probability that she had found a tutor? (Round your answer to 4 decimal places.) Probability is mathematically represented as

[tex]P(T | F ) = \frac{ P(F | T) * P(T)}{ P(F)}[/tex]

=> [tex]P(T | F ) = \frac{ 0.12 * 0.52}{ 0.264}[/tex]

=> [tex]P(T | F ) = 0.23636 [/tex]

Answer:

c, alternate interior angles theorem

Step-by-step explanation:

if 1 is equal to 3, and 3 is equal to 2 by alternate interior angles theorem, then that should also apply to angle 1.

Answer:

The answer is 3,166.7

Step-by-step explanation:

2,000*9.5 = 19,000

19,000/6 = 3,166.6666

Answer: $98,835.

Step-by-step explanation:

Given: Annual profit at a chain of stores is normally distributed with a mean ([tex]\mu[/tex]) of $61,000 and a standard  deviation([tex]\sigma[/tex]) of $23,000.

Let [tex]x[/tex] denoted the profit.

Let [tex]x_0[/tex] be the minimum profit required to have a party.

The stores in the top 5% (i.e. 0.05) of annual profit were rewarded with a celebration.

i.e. [tex]P(x>x_0)=0.05[/tex]

[tex]\Rightarrow\ P(\dfrac{x-\mu}{\sigma}>\dfrac{x_0-61000}{23000})=0.05\\\\\Rightarrow\ P(z>\dfrac{x_0-61000}{23000})=0.05\ \ \ [z=\dfrac{x-\mu}{\sigma}]\\\\\Rightarrow\ \dfrac{x_0-61000}{23000}=1.645\ \ [\text{critical z-value for p-value 0.05=1.645}]\\\\\Rightarrow\ x_0-61000 =1.645\times 23000\\\\\Rightarrow\ x_0-61000 =37835\\\\\Rightarrow\ x_0=37835+61000\\\\\Rightarrow\ x_0=98835[/tex]

Hence, the annual profit required to have a party was $98,835.

Answer:

3 - x ≥ 9

Step-by-step explanation:

At least in inequality means greater than or equal to (≥)

Difference in mathematics means subtraction

The difference between a number x and 3

3 - x

is at least nine

3 - x ≥ 9

The inequality for the sentence is

3 - x ≥ 9

Answer:

B

Step-by-step explanation:

Answer:

a. m<C = 50 deg

b. m<G = 125 deg

c. m<K = 75 deg

Step-by-step explanation:

a.

Look at the two lines marked parallel with 2 marks each.

Angle C and angle 50 deg are alternate interior angles of 2 parallel lines cut by a transversal That makes angle C congruent to the 50-deg angle.

Answer: m<C = 50 deg

b.

Angle G is vertical to thh 125-deg angle. Vertical angles are congruent, so m<G = 125 deg

Answer: m<G = 125 deg

c.

Look at the two lines marked parallel with one mark each.

Angles e and c are corresponding angles, so they are congruent.

m<E = m<C = 50 deg

The 125 deg angle and angle F are a linear pair, so their measures add up to 180.

f + 125 = 180

m<F = 55 deg

Angles E, F and K are the interior angles of a triangle, so their measures add up to 180 deg.

e + f + k = 180

50 + 55 + k = 180

k = 75

m<K = 75 deg

Answer:

-7.5 US$

Step-by-step explanation:

that's how i got it =)

Answer: The answer is B

Step-by-step explanation:

Answer:

Here you go

Step-by-step explanation:

The first term is,  9e2  its coefficient is  9 .

The middle term is,  +30e  its coefficient is  30 .

The last term, "the constant", is  +25

Step-1 : Multiply the coefficient of the first term by the constant   9 • 25 = 225

Step-2 : Find two factors of  225  whose sum equals the coefficient of the middle term, which is   30 .

     15    +    15    =    30    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  15  and  15

                    9e2 + 15e + 15e + 25

Step-4 : Add up the first 2 terms, pulling out like factors :

                   3e • (3e+5)

             Add up the last 2 terms, pulling out common factors :

                   5 • (3e+5)

Step-5 : Add up the four terms of step 4 :

                   (3e+5)  •  (3e+5)

            Which is the desired factorization

Answer:

0.0008228 to standard form =

8.228 x 10^-4

Answer:

the square root of 2(x^3 * x^2)

Step-by-step explanation:

twice means 2 and product means either division or multiplication (multiplication in this scenario because twice means multiply).  cubed means to the third power

Answer:

first option

Step-by-step explanation:

the area of a rectangle is

base*height

[tex]Purple=(3)\times(a)\\\\=3a\\\\\\Green=(\frac{1}{2})\times(3)\\\\=\frac{3}{2}\\\\\\Red=1\times a\\\\=a\\\\\\Yellow=\frac{1}{2}\times 1\\\\=\frac{1}{2}[/tex]

so the sum is

[tex]\Sigma A=3a+a+\frac{3}{2}+\frac{1}{2}[/tex]

which is the first option

The expression for the area of the poster is written as the sum of the areas of each colored section is 3a + a + 3 1/2 + 1/2

Area of a rectangle = length × width

Purple color:

Area = length × width

= 3 × a

= 3a

Red color:

Area = length × width

= 1 × a

= a

Green color:

Area = length × width

= 3 × 1/2

= 3 1/2

Yellow color:

Area = length × width

= 1 × 1/2

= 1/2

Sum of the areas = purple + red + green + yellow

= 3a + a + 3 1/2 + 1/2

Therefore, expression for the area of the poster is written as the sum of the areas of each colored section is 3a + a + 3 1/2 + 1/2

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Answer:

$14.25

Step-by-step explanation:

12 x 0.45 = 5.4

8.40-5.40=3

3 is the flat fee

3+(0.45 x 25) = 14.25

Answer:

$14.25

Step-by-step explanation:

8.40 = .45(12) + b

8.40 = 5.4 + b

b = 3

b = .45(25) + 3

b = 11.25 + 3

b = 14.25

Answer:

= 6.2g+9

Step-by-step explanation:

Answer:

[tex](1)\; G(x)=2(x-14)^2+6[/tex]

Step-by-step explanation:

Assuming, right and up are positive directions.

The given parent function, [tex]f(x)=x^2[/tex]

Let [tex]f_1(x)[/tex] be the function when the parent function is stretched by a scale factor of 2.

So, [tex]f_1(x)=2f(x)[/tex]

[tex]\Rightarrow f_1(x)=2x^2[/tex]

Let [tex]f_2(x)[/tex] be the function when [tex]f_1(x)[/tex] is translated [tex]14[/tex] units right.

So, [tex]f_2(x)=f_1(x-14)[/tex]

[tex]\Rightarrow f_2(x)=2(x-14)^2[/tex]

Again, let [tex]f_3(x)[/tex] be the function when [tex]f_2(x)[/tex] is translated 4 units up.

So, [tex]f_3(x)=f_2(x)+6[/tex]

[tex]\Rightarrow f_3(x)=2(x-14)^2+6[/tex]

So, the resulting function, [tex]f_3(x)=G(x)=2(x-14)^2+6[/tex].

Hence, option (1) is correct.

Answer:

1. 10d + 5n = 85

2. look at graph  or graph coordinates (0, 17) and (8.5, 0) and make a line through them

3. 17 nickels since its only nickels, on the graph you see where the line hits the y-axis which is 17.

4. 8.5 dimes since its only dimes, on the graph you see where the line meets the x-axis which is 8.5

Step-by-step explanation:

y-axis is nickels

x-axis is dimes

Answer:

1) Find the measure of each angle.

The measure of each angle = 63° and 27°

2) Which equation below accurately translates the sentence and could be used to find the measure of each angle?

a) 2x + 9 = 90 - x

Step-by-step explanation:

1) Find the measure of each angle.

Two Angles are Complementary when they add up to 90 degrees (a Right Angle)

Mathematically this is represented as:

x° + y° = 90°

From the above question, we are told that:

The measure of an angle is 9 more than twice its complement.

Let the complement of an angle be represented by x

And its measure of an angle be represented by y

Hence,

y = 2× x+ 9

y =(2x + 9)°

x° + y° = 90°

Substitute 2y + 9 for x

x + 2x + 9 = 90

Collect like terms

x + 2x = 90 - 9

3x = 81

Divide both sides by 3

3x/3 = 81/3

x = 27°

We find y(measure of the angle)

x + y = 90

27 + y = 90

y = 90 - 27

y = 63°

Therefore, the measure of each angle is given as:

Measure of an angle = 63°

Complement of an angle = 27°

2) Which equation below accurately translates the sentence and could be used to find the measure of each angle?

a)2x + 9 = 90 - x

b) x + 9 = 2(x - 90)

c) x = 9 + 2(90 - x)

d) 2x = (x - 90) + 9

Option a) is the correct option

Answer:

DA FA WERE ARE THE QUESTIONS?????????

Step-by-step explanation:

Step-by-step explanation:

First, we need to add all the checks and money he has.

295.50

 10.00

   6.25

+________

  3   6  1  . 7 5

Total- $361.75

Now, we have to subtract 5 from this.

361.75

   5.00

-______

3 5 6 . 7 5

The total deposit is $356.75

Answer:

$306.75 is the right answer i just took the test.

Step-by-step explanation:

x = 3, y² = -5x -12, x² + y² =81. are all not functions. the others are functions.

Step-by-step explanation:

I just did it

A function assigns the values. The correct options are C and E.

A function assigns the value of each element of one set to the other specific element of another set.

An equation is said to be a function if for each different value of x(input) it should give a different output. Therefore, for different inputs of x, the value of the output y should be different and unique. Also, the values if the equation produces the same output for two values of x it also said to be a function.

A.)

x = 3, since for every value of x the value is 3, which is not possible. Hence, this is not a function.

B.)

x² + y² = 81

For the given equation if the value of x is given as 0, the value of y will be,

x² + y² = 81

0² + y² = 81

y² = 81

y = ±√81

y = -9, 9

Hence, this can not be a function.

C.) y = -x + 11

For the given equation if the value of x is kept anything the value of y will be different. Thus, this is a function.

D.)

y² = -5x - 12

For the given equation if the value of x is given as less than -2.4, there will be two values of y. Thus, the given equation is not a function.

E.)

y = 2x² - 6x + 4

The given function will return will the same value of y for 2 different values of x. Hence, this is a function.

F.)

y = -7

Since the given equation can only have the value of y as 7. Therefore, it is not a function.

Hence, the equations that are a function are y = -x + 11 and  y = 2x² - 6x + 4.

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#SPJ2

A part of the question is missing which is;

What is the minimum duration for which an apartment remained empty for the company to update the kitchen appliances? Round to the nearest whole number.

Answer:

133 days

Step-by-step explanation:

We are given;

Population mean; μ = 85 days Population standard deviation; σ = 29 days

significance level; α = 5% = 0.05

Critical value of z at significance level of 0.05 = 1.645

Now, formula for z-score is;

z = (x - μ)/σ

Where x is the minimum duration for which an apartment remained empty for the company to update the kitchen appliances.

1.645 = (x - 85)/29

(1.645 × 29) = x - 85

47.705 = x - 85

x = 85 + 47.705

x = 132.705

x ≈ 133 days

Answer: 37 days

Step-by-step explanation:

Answer:

its 1,456,000

Step-by-step explanation:

first you multiply 200 times 5280 and add 4000 if thats right uon

Answer:

The speed increases (45—>47—>49) then decreases (48—>47) over time.

Step-by-step explanation:

HOPE THIS HELPED ✨

Answer: The speed increases (45—>47—>49) then decreases (48—>47) over time.

Answer:

-12

Step-by-step explanation:

Substitute x for 3

6(3-5)

Simplify in the parenthesis

6(-2)

multiply

-12

Answer:

b 5.75%

Step-by-step explanation: