which statements is true of the function f(x)= x2 + 6x3 - 4 + 2x5?

A. the function is positive for all values of x
B. the end behavior of the graph f(x) is similar to that of g(x) = -x
C.the graph has exactly one x-intercept
D. the function is increasing for all real numbers

The current age of Jenny is 6 years.

Let the current age of Phil be = x years

So the current age of Bill is = 2x years

The current age of Jenny is = 2x-2 years

Sum of their ages is = x+2x+2x-2 = 5x-2 years

Now the age of their dad is = 2(5x-2) = 10x-4 years

Now after nine years,

Age of Phil = x+9

Age of Bill = 2x+9

Age of Jenny = 2x-2+9 = 2x+7

Sum of their ages = x+9+2x+9+2x+7 = 5x+25

New age of their father = 10x-4+9 = 10x+5

According to question, the required linear equation to solve the question is,

5x+25 = 10x+5

5x = 20

x = 4

Hence the Jenny's current age = 2*4-2 = 8-2 = 6 years

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The probability of the randomly selected bank being a) guilty of fraud is 0.1 and b) guilty of fraud, it is given it is a private bank is 0.15

Here

let A be the event of the Bank being a fraud

Let B be the event of the bank being private

Here we see that 100 banks have been sampled.

a)

Probability = no. of favorable outcomes/total no. of outcomes

Here we see that under the row of Bank Fraud and Yes section there are

6 + 4

= 10 banks.

Hence,

n(A) = 10

n = 100

Therefore,

P(A) = 10/100

= 0.1

b)

The conditional Probability

P(X|Y) = P(X ∩ Y) / P(Y)

Here,

we need to find the bank is a fraud given that it is a private bank. Hence we need to find,

P(A|B)

= P(A ∩ B) / P(B)

Here we see that the private banks that are fraud are given to be 6.

Hence,

n(A ∩ B) = 6

Therefore,

P(A ∩ B) = 6/100

n(B) = 6 + 34 = 40

P(B) = 40/100

Hence P(A|B) = (6/100) / (40/100

= 6/40

= 3/20

= 0.15

Complete Question

(Information attached as an image)

if an audit company picks a bank at random for audit what is the probability that a bank

(a) is guilty of fraud?

(b) is guilty of fraud given it is a private bank?

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24 meters per second = 53.6865 miles per hour

53.6865 to 1 d.p = 53.7

Answer: 53.7

Since each input is mapped to only one output, the best description of the ordered pairs is given by:

B. both a relation and a function.

When does a relation represents a function?

A relation represents a function if each value of the input is mapped to only one value of the output.

For a point in the format (x, y), we have that:

=> x is the input.

=> y is the output.

=> The meaning is that the input x is mapped to the output y.

For this problem, the points are given as follows:

(-2, -1), (1, -4), (5, -8), (9, -12)

Each input is mapped to only one input, that is, there are no repeated values of x, hence the best description of the ordered pairs is given by:

B. both a relation and a function.

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Answer:

x = 52°

y = 25°

z = 90°

Step-by-step explanation:

        We know there are 180 degrees in a triangle. The box represents 90 degrees.

90° + x + 38° = 180°

x + 128° = 180°

x = 52°

        Next, we know that a straight line is equal to 180 degrees. Again, the box represents 90 degrees.

90° + z = 180°

z = 90°

        Lastly, we will use the same process for angle x, but for angle y.

y + z + 65° = 180°

y + 90° + 65° = 180°

y + 155° = 180°

y = 25°

The concurrency statement for the given triangles is that (D) △RGB ≅ △DCS  under ASA condition.

So, the congruence statement of the given 2 triangles is as follows:

△RGB ≅ △DCS

Hence, △RGB ≅ △DCS  under ASA condition.

Therefore, the concurrency statement for the given triangles is that (D) △RGB ≅ △DCS  under ASA condition.

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BC is the common side of both the triangles.

Answer:

BC

Step-by-step explanation:

Common side in both triangles is BC

    Sides of ΔABC,

                   AB ;  BC  and AC

   Sides of ΔDCB,

                  DC, BC and DB

Answer:

x =11

Step-by-step explanation:

report this so that girl in the comments can give you an answer

Answer: -50

Step-by-step explanation:

The time taken to reach the maximum height is 1.25 seconds and the maximum height is 32 feet

The function is given that

h(t) =  + 40t + 7

Where h is the height

t is the time taken

We know

[tex]-16t^2[/tex] + bx + c = 0

Compare the equations

a = -16

b = 40

c = 7

Compare both the equation

Time taken to reach maximum height = - b/2a

= - 40/2(-16)

= - 40/-32

= 5/4

= 1.25 seconds

Time taken to reach maximum height is t = 1.25 seconds

Substitute the value of t in the function to find the maximum height

h(1.25) = -16× + 40(1.25) + 7

= -25 + 50 + 7

= 32 feet

Hence, the time taken to reach the maximum height is 1.25 seconds and the maximum height is 32 feet

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The Sum of 40 terms of the Arithmetic Sequence is 3,420..

Arithmetic Series is defined as a sum of the terms of arithmetic progression or sequence.

An Arithmetic progression is a sequence of terms in which the difference between two consecutive terms is a constant number.

We have following information about series

sum of 12 terms of an arithmetic series (S₁₂) = 186

the 20th term of arithmetic sequence = 83

i.e., a₂₀ = 83

As we know that nth term of arithmetic progression is aₙ= a + (n-1)d

where , a---> first term of sequence

n ----> nth term

d -----> constant difference between two consecutive terms

put n= 20 in above formula we get,

83 = a + (20-1 )d = a+ 19d ----(1)

Now , Using the sum of n arithmetic terms formula, Sₙ = n/2 ( 2a + (n-1)d)

so, for n = 12

186 = 12/2 ( 2a + 11d ) => 2a + 11d = 31 ---(2)

Solving equations (1) and (2) we get,

27d = 135 => d = 5

putting the value of d in equation (1)

83 = a + 19×5 => a = 83 - 95 = -12

thus sequence is like as -12, -7 , -2 , ------

Sum of first 40 terms of arithmetic sequence (S₄₀) = 40/2 ( 2× (-12) + 39d ) = 20 ( -24 + 39×5)

= 20( 171) = 3,420

So, required result is 3,420..

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Answer:

Step-by-step explanation:

Answer:  [tex]y=\frac{3}{4} x[/tex]

Step-by-step explanation:

        We will create a point-slope equation to solve.

        First, we need to find the slope.

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}= \frac{6--3}{8--4} =\frac{9}{12} =\frac{3}{4}[/tex]

        Next, we will create our point-slope equation.

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

[tex]\displaystyle y--3=\frac{3}{4} (x--4)[/tex]

 [tex]\displaystyle y+3=\frac{3}{4} (x+4)[/tex]

 [tex]\displaystyle y=\frac{3}{4} x+3 -3[/tex]

 [tex]\displaystyle y=\frac{3}{4} x[/tex]

Answer:

Value of x is 1440

Step-by-step explanation:

According to the question,

720 ÷ 50 gives same answer as x ÷ 100

[tex] \therefore[/tex]

[tex] \rm \implies \dfrac{720}{50} = \dfrac{x}{100} \\ \\ \rm \implies x = \frac{720}{50} \times 100 \\ \\ \rm \implies x = 720 \times 2 \\ \\ \rm \implies x = 1440[/tex]

The length of backyard in drawing is 37 inch when 74 feet long in real life and scale of drawing is 1 inch: 2 feet.

A proportion is a form of ratio in which the denominator also contains the numerator. For example, the fraction of male deaths would be deaths to men divided by deaths to males + deaths to females (i.e. the total population). A population proportion is a percentage of the population that possesses a specific feature. Assume you have 1,000 persons in your population, with 237 of them having blue eyes. Blue eyes account for 237 of every 1,000 persons, or 237/1000.

Here,

as the given scale is 1 inch: 2 feet.

actual length of backyard=74 feet

length of backyard in drawing is x inch,

1/2=x/74

2x=74

x=37 inch

The length of the backyard in the drawing is 37 inches, although it is 74 feet long in real life, and the scale of the drawing is 1 inch: 2 feet.

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The volume of the sphere is 7241.142 m[tex]m^{3}[/tex].

Given:

A sphere has a diameter of 24 mm.

Radius r = diameter/2

= 24/2

r = 12 mm.

volume of sphere = 4/3π[tex]r^{3}[/tex]

= 4/3 * 22/7 * [tex]12^{3}[/tex]

= 88*[tex]12^{3}[/tex]/21

= 88*1728/21

= 152064/21

= 7241.142 m[tex]m^{3}[/tex].

Therefore the volume of the sphere is 7241.142 m[tex]m^{3}[/tex].

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The formula that plots the radius against the area of such water puddle here on floor; A = πr².

For the given question,

Let the area of the water puddle on the floor be 'A'.

Let the radius of the water puddle be 'r'.

Then, using the area of the circle,

The function for the area of the water puddle be,

A = πr²

Thus, the formula that plots the radius against the area of such water puddle here on floor; A = πr².

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The area of the tile in square centimeters is 929cm2

The area in square centimeters is calculated as follows

First, let convert the tile measures 12 inches on each side into centimeters

1 inch = 2.54 centimeters

= 12 x 2.54
= 30.48 centimeters

Next is to find the area of the tile in square centimeters
The area of square = (side) x (side) square units
= 30.48 centimeters x 30.48 centimeters

= 929.0304

= 929 square centimeters (rounded)

So, the area of the tile in square centimeters is 929 square centimeters

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Answer:

The area of the tile in square centimeters is 929cm2

Step-by-step explanation:

I took the exam and got it right

Answer:

volume = 3 ml

Step-by-step explanation:

the reading on the left without the nugget is 17 ml

the reading on the right with the nugget is 20 ml

volume of nugget = 20 - 17 = 3 ml

The corresponding measure of each angle is 80, 80, 80, 100 and 100 degrees

Given: m<7=100 degrees

To find <6, <8, <2, <5 and <11

In the <7 is vertically opposite <5. Since vertically opposite angles are equal.

Thus, <5 =  <7 =   100 degrees

Also,  <5 and <6 are angles on a straight, and the sum of angles on a straight line is 180 degrees. Thus:

<5 + <6 = 180

100 + <6 = 180

<6 = 180 -100 = 80 degrees

Also, <6  and <8 are vertically opposite.

Thus, <8 = <6 = 80 degrees

<2 and <6 are corresponding angles, and corresponding angles are equal. Thus, <2 = <6 = 80 degrees

Likewise, <11 and <7 are corresponding angles

Thus, <11 = <7 = 100 degrees

Therefore, the measure of angle <6, <8, <2, <5 and <11 are 80, 80, 80, 100 and 100 degrees respectively

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The required values are x=0 and x=2/3.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

f(x) = -3x² + 2x - 1

Substitute f(x) = -1

-1 = -3x² + 2x - 1

-3x² + 2x - 1+1=0

-3x² + 2x = 0

x( -3x+2)=0

=> x=0,

 -3x+2 = 0

-3x=-2

x=2/3

The required values are x=0 and x=2/3.

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Answer:

-1/3

Step-by-step explanation:

m = y2-y1/x2-x1                     formula for slope

m = 7-9/8-2                          Plug in the numbers

m = -2/6                                Subtract 7-9 and 8-2

m = -1/3                                 Simplify

Answer:

horizontal line: y = 12

vertical line: x = -3

Step-by-step explanation:

The horizontal line has 12 as the y-coordinate for all its points.

y = 12

The vertical line has -3 as the x-coordinate for all its points.

x = -3

Answer:

x = -3

y = 12

Step-by-step explanation:

For a point (x, y):

A horizontal line is represented by the equation y = a where (0, a) is the y-intercept of the line.

A vertical line is represented by the equation x = a where (a, 0) is the x-intercept of the line.

Therefore, for the given point (-3, 12):

From the given figure, m∠AEB = (3x + 54)° and m∠DEC = (7x -30)°, then the measure of angle AEB is equal to 117°.

As given in the question,

For the given figure,

Two lines AC and BD intersect each other at point E.

Measure of angles in the form of x is given as :

m∠AEB = (3x + 54)°

m∠DEC = (7x -30)°

∠AEB and  ∠DEC are vertically opposite angles.

⇒m∠AEB = m∠DEC

⇒ (3x + 54)°= (7x -30)°

⇒ 7x - 3x = ( 54 + 30 )°

⇒ 4x = 84°

⇒ x = 21°

Hence,

m∠AEB = (3x + 54)°

⇒m∠AEB = (3(21) + 54)°

⇒m∠AEB = 117°

Therefore, from the given figure m∠AEB = (3x + 54)° and

m∠DEC = (7x -30)°, then the measure of angle AEB is equal to 117°.

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Answer:

Common side: UV

Step-by-step explanation:

Answer: C. 100,000 gallons

Step-by-step explanation:

10,000 gallons a minute.

10 minutes.

10,000 x 10 = 100,000.

Gallons:  10,000     20,000     30,000     40,000     50,000     60,000    

Minutes:       1               2               3                4               5                6              

... 70,000     80,000     90,000     100,000

...      7                8                9              10

Answer:

plsssssssssssssssssssssssssssssssssss

D( x ) function and also a rule for the set of points (5, 10), (6, 12), and (-2, -4). Both the statment is true.

Given that,
Among the options which statment best represents the expression D(x) = 2x is to be determined.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
D(x) = 2x

As from the observation D(x) is a function of the independent variable x.
Also,
At x = 5, 6, -2
D(x) = 10, 12, -4
So it is also a rule for the set of points (5, 10), (6, 12), and (-2, -4).

Thus, the D( x ) function and also a rule for the set of points (5, 10), (6, 12), and (-2, -4). Both the statment is true.

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By studying the change of the y-intercept, we can see that the shift is of one unit upwards.

We know that the original y-intercept of the line is y = -1, then the line is of the form:

y = a*x - 1

Where a is the slope.

Now we apply a vertical shift of N units, this is written as:

y = a*x - 1 + N

And we know that the new y-intercept is 0, so:

y = a*0 - 1 + N = 0

y = -1 + N = 0

-1 + N = 0

N = 1

The shift is of 1 unit up.

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Answer:

The value of x=35 and the co-ordinates at the top of the chair lift are (35,20).

What are co-ordinates?

Step-by-step explanation:

Given:

    20 = 1/2x + 5/2

20 * 2 = x + 5

     40 = x + 5

        x = 35

Therefore, the co-ordinates of the chair at the top of the chair lift are (35,20)

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