Let g(x) = -x² + 4. What is the value of g at x = -3 and x = 1 ?
A. g(−3) = −5, g(1) = 3
B. g(-3) = 13, g(1) = 3
C. g(-3) = -5, g(1)=5
D. g(-3) = 13, g(1) = 5

The probability that Colleen selected a bottle of water and then a bottle of lemonade without replacement is 35/138

Probability is the measure of that how likely is an event can occur.

Probability of an event = Favorable outcomes of the event / total outcomes

Multiplication rule of probability states that probability of two events happening at the same time = (probability of one event )*(probability of another event )

Given that A cooler contains 14 bottles of water and 10 bottles of lemonade. Colleen randomly selects 2 bottles from the cooler

Total bottle = 14 +10 = 24

Let E be the event that Colleen selects a bottle of water first

Probability of E = 14/24

Let F be an event that Colleen selects bottle of lemonade when at the same time a bottle of lemonade is already taken out  

Probability of F = 10/23

Therefore , The probability that Colleen selected a bottle of water and then a bottle of lemonade without replacement is

= Probability of E * Probability of F = (14/24)*(10/23) =35/138.

Also, Learn more about probability from:

https://brainly.com/question/16644299

#SPJ1

Answer: (3/2,-6)

Step-by-step explanation:

Answer:

Formula for midpoint is given as [(x1+x2)÷2, (y1+y2)÷2] where x and y are the coordinates of the points.

Midpoint = [(8+(-5))÷2, (-3+(-9))÷2]

= (3/2, -12÷2)

= (3/2, -6)

Slant height of the conical frustum, l = 5 units.

Total surface area of the conical frustum, a = 329.87 square units.

Volume of the conical frustum, v = 1394.87 cubic units.

Given,

Radii of bases of a conical frustum,

r₁= 9

r₂ = 12

Height = 4

We have to find the total surface area of the frustum and volume of the frustum.

Formula for total surface area, a = [tex]\pi l(r_{1} +r_{2}[/tex][tex])[/tex]

Volume of the frustum, v = [tex]\frac{1}{3} \pi h(r_{1} ^{2} +r_{2} ^{2} +(r_{1} r_{2} )} )[/tex]

Here l is the slant height.

Slant height, l = [tex]\sqrt{(r_{1} -r_{2} )^{2} +h^{2} }[/tex]

First we have to find the slant height.

l = [tex]\sqrt{(r_{1} -r_{2} )^{2} +h^{2} }[/tex]

l = [tex]\sqrt{(9-12)^{2}+4^{2} }[/tex]

l = [tex]\sqrt{(-3)^{2} +16}[/tex]

l = [tex]\sqrt{9+16}[/tex]

l = [tex]\sqrt{25}[/tex]

Slant height, l = 5 units

Now,

Total surface area, a = [tex]\pi l(r_{1} +r_{2}[/tex][tex])[/tex]

a = [tex]\pi[/tex] × 5 × ( 9 + 12)

a = [tex]\pi[/tex] × 5 × 21

a = 329.87 square units.

Then,

Volume of the frustum, v = [tex]\frac{1}{3} \pi h(r_{1} ^{2} +r_{2} ^{2} +(r_{1} r_{2} )} )[/tex]

v = [tex]\frac{1}{3}[/tex] × π × 4 × (9² + 12² + ( 9×12))

v = [tex]\frac{1}{3}[/tex] × π × 4 × (81 + 144 + 108)

v = [tex]\frac{1}{3}[/tex] × π × 4 × 333

v = 1394.87 cubic units.

Learn more about conical frustum here: https://brainly.com/question/22562165

#SPJ1

Answer:

A. 0

Step-by-step explanation:

Slope tells you steepness or flatness of your line.

If you know two points on a line find slope by subtracting the y's and put that on top of a fraction. And subtract the x's and put that on the bottom of the fraction.

Subtract y's: 3 - 3

Put it on top: 0/...

Subtract x's: 5 - -4

same as 5+4

Put that on the bottom: 0/9

slope, usually called m, is 0/9, which is 0.

Notice if you graph these two points its a hOrizOntal line. HOrizOntal lines have zerO slope.

Answer:

I believe it's 25% .............

Answer:

40%

Step-by-step explanation:

The cash price = $4,250

If Steve rents the computer for $595 for 10 months he would have to spend $595 x 10 = $5,950

The difference in money = 5950 - 4250 =$1700

As a percentage of the cash price this would be
1700/4250 x 100 =  40%

Answer:
Rent option is  40% more than the cash price 40%

We can verify this by noting that if there is an increase of r% in the price of an item then
Increased price = Old price + Increase

= Old price + Old price x r/100

In this case, Old price = 4250
r = 40%, r/100 = 0.04

New price = 4250 + 4250 x 0.04  = 4250(1 + 0.04) = 4250(1.04) = 5950 which tallies with given figures

The correct answer for the given expression is 5.

Given,

evaluate the expression 4ˣ + 1

By putting x= 1,

we get 4¹ + 1

= 4+ 1

= 5

So, the the answer for the question, evaluate  4ˣ + 1 is 5.

"See a similar question here-

https://brainly.com/question/723406 "

#SPJ4

Answer:

Step-by-step explanation:

The most appropriate choice for modulus function is given by-

values of [tex]x[/tex] = [tex]\frac{48}{29}[/tex] and [tex]\frac{50}{27}[/tex]

What is modulus function?

Modulus function returns the absolute value of a function.

[tex]|x| = \left \{ {{x, x \geq 0} \atop {-x, x < 0}} \right.[/tex]

Here,

For [tex]14 - 8x \geq 0[/tex]

[tex]7(14-8x) = 2x + 2\\98 - 56x = 2x + 2\\56x + 2x =98 -2\\58 x = 96\\x = \frac{96}{58}\\ \\x = \frac{48}{29}[/tex]

For [tex]14 - 8x < 0[/tex],

[tex]7(8x - 14) = 2x + 2\\56x - 98 = 2x + 2\\56x - 2x =98 +2\\54 x = 100\\x = \frac{100}{54}\\ \\x = \frac{50}{27}[/tex]

So,  [tex]x = \frac{48}{29}[/tex] and [tex]x =\frac{50}{27}[/tex]

To learn more about Modulus function, refer to the link

https://brainly.com/question/1301718

#SPJ9

Triangle ABC is rotated 85° around the point D to create A'B'C'.

Rotation is a transformation in which a figure is turned around a point . This point is fixed and is called the center of rotation.

From the given diagram we can see that the triangle is rotated about the fixed point D with an angle of 85° such that A' is new location of A and B' and C' are new locations of B and C respectively.

Also, Learn more about rotation of triangles from here:

https://brainly.com/question/27949069

#SPJ1

Answer:

B, 15 pencils

Step-by-step explanation:

Our equation: (5 x 42)/14

42 x 5 = 210

210/14= 15

If two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, The speed (in mi/h) of the faster cyclist is: 5 mph and 10 mph.

Let r represent the speed of one

Let 2r represent thee speed of the other

Total distance traveled by both the sisters = 30 miles

Time ×rate = Distance

Hence,

2(2r+r) = 30

2(3r)=30

6r=30

r=30/6

r=5 mph

Speed=5 mph and (5 mph×2)

Speed=5 mph and 10 mph

Therefore If two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, The speed (in mi/h) of the faster cyclist is: 5 mph and 10 mph.

Learn more about speed here:https://brainly.com/question/13943409

#SPJ1

The expression to illustrate the information when Toby's seventh grade class is going on a field trip to a history museum will be 0.2 (10x + 30y).

It should be noted that there are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each and the history museum gave the class 20% off as part of a group promotion.

Therefore, it should be noted that the expression to illustrate this will be:

= 20% × (10 × x) + (20 × y)

= 0.2 (10x + 30y)

Therefore, the expression to illustrate the information when Toby's seventh grade class is going on a field trip to a history museum will be 0.2 (10x + 30y).

Learn more about expressions on:

brainly.com/question/25968875

#SPJ1

Toby's seventh grade class is going on a field trip to a history museum. There are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each. The history museum gave the class 20% off as part of a group promotion. What expression will illustrate this?

The magnitude of the Pennsylvania earthquake is 4.

An exponent is a logarithm. You may convert any exponential expression to logarithmic form. As an illustration, if 8 = 23, the base is 2, the exponent is 3, and the outcome is 8. This may be represented as 3 = log2 8 in logarithmic notation.

The equation y=logb(x+h)+k shifts the logarithmic function, y=logbx, by k units vertically and h units horizontally.

Using the formula,

log I₁ / I₂ = M₁ - M₂

M₁ = 7.7,     I₁ / I₂ = 4900

log 4900 = 7.7 - M₂

log 4900 ≈ 3.69

On calculating,

M₂ ≈ 4

The magnitude of the Pennsylvania earthquake is 4.

To learn more about logarithmic function from given link

https://brainly.com/question/13473114

#SPJ4

Answer: E. The 20 plants in the two groups

Step-by-step explanation: experimental units are individuals on which the experiment is being performed. In this case the pepper plants are being used to test the effectiveness of the new fertilizer.

  Solving the problem by multiplying and simplifying we have as a result 16x¹⁵

Simplification is a process of reducing terms to expressions, which do not generate changes or values.

  Multiplication is also known as product, and it is a mathematical operation of a successive sum, this operation consists of adding a number a certain number of times:

a x b the number "a" will be added "b" times.

  The algebraic expression that we must simplify to its minimum expression is:

4√16 x⁸ . 4√x¹⁴

4×4x⁸ × 4x¹⁴/²  

16x⁸× 4x⁷  ; multiply power of equal base

16x⁸⁺⁷

16x¹⁵

Lear more about simplification in:

https://brainly.com/question/28595186

#SPJ4

The expression to represent the total amount of juice left in the jar is: (.25 + .30+  .75) -.20 and  the property used in each step is addition and extraction of Liquid from the mixture.

Expression:

(AJ+GP+PJ)-M

Where:

Apple juice=AJ

Grape juice=GP

Pineapple juice=PJ

Mixture=M

Hence,

(.25 + .30+  .75) -.20

b. Simplifying the expression

(.25 + .30+  .75) -.20

=1.3-.20

=1.10

Therefore the expression to represent the total amount of juice left in the jar is: (.25 + .30+  .75) -.20 and  the property used in each step is addition and extraction of Liquid from the mixture.

Learn more about expression here:https://brainly.com/question/723406

#SPJ1

Answer:

Smaller

Step-by-step explanation:

When you multiply something by 1/3, basically what you are doing is multiplying that thing by one and dividing it by 3.

To put it in a better perspective, let's say you have something that is 5 inches long and you multiply it by a scale factor of 1/3. The equation would be: (5*1)/3.

*Please mark brainliest answer

The required zeros of the polynomial f(x) are 1 and ±√-1.

What are zeros of the polynomial?

All the possible values of x that will make the polynomial zero are called the zeros of the polynomial, p(x). Zeros of a polynomial can either be negative or positive.

Solving for the zeros of a polynomial

y = x³ - x² + x - 1

Let, f(x) = 0

x³ - x² + x - 1 = 0

Using heat and trial method, we get,

x =1 as one of the zero of the polynomial

It implies that (x-1) is the root of polynomial

Thus, dividing x³ - x² + x - 1 by x - 1, we get

x² + 1, which is then equated to 0 to obtain the zeros of the given polynomial

i.e. x² + 1 = 0

x = 1, ±√-1

Hence, the required zeros of the polynomial y are 1 and ±√-1.

To learn more about the zeros of the polynomial, visit the link:

https://brainly.com/question/28560646

#SPJ4

Answer:

-9.2 or -9 1/5

Step-by-step explanation:

Hope it helps!

Answer:

m = -40

Step-by-step explanation:

Solve for m by simplifying both sides of the equation, then isolating the variable.

The estimate for the side length of the square = the width of the rectangle (w) = √44.

Area of Rectangle = (length)(width)

Given the parameters below:

If this rectangle is divided to form two squares with equal areas, then the side length of each square would be equal to the length of the original rectangle = w.

(2w)(w) = 88

2w² = 88

w² = 88/2

w² = 44

√w² = √44

w = √44

Thus, an estimate of the side length of the square = the width of the rectangle (w) = √44.

Learn more about area of rectangle on:

https://brainly.com/question/25292087

#SPJ1

The variance of the data sets is 77.7

Variance is the average of the squared differences from the Mean.

Therefore, to find the variance we have to find the mean, Then for each number: subtract the Mean and square the result.

Then work out the average of those squared differences.

Hence,

mean = 4 + 16 + 21 + 32 + 11 + 12 / 6 = 96 / 6 = 16

Therefore, lets find the difference and square it.

(4 - 16)² + (16 - 16)² + (21 - 16)² + (32 - 16)² + (11 - 16)²+ (12 - 16)²

144 + 0 + 25 + 256 + 25 + 16 = 466

Therefore,

variance = 466 / 6

variance = 77.6666666667

variance = 77.7

learn more on variance here: https://brainly.com/question/11105955

#SPJ1

The function which f(2) = 3 is the function with the equation f(x) = x + 1

The function value is given as

f(2) = 3

The above means that the value of the function is 3 when x = 2

i.e., f(x) = 3 when x = 2 or we substitute 2 for x in f(x)

Next, we test the above function in the list of given options

So, we have

f(x) = x^2 + 1

Substitute 2 for x in f(x)

f(2) = 2^2 + 1

Evaluate the exponent in the above equation

So, we have

f(2) = 4 + 1

Evaluate the sum in the above equation

So, we have

f(2) = 5

f(x) = 2x + 1

Substitute 2 for x in f(x)

f(2) = 2 x 2 + 1

Evaluate the product in the above equation

So, we have

f(2) = 4 + 1

Evaluate the sum in the above equation

So, we have

f(2) = 5

f(x) = x + 1

Substitute 2 for x in f(x)

f(2) = 1 x 2 + 1

Evaluate the product in the above equation

So, we have

f(2) = 2 + 1

Evaluate the sum in the above equation

So, we have

f(2) = 3

Hence, the function which f(2) = 3 is the function with the equation f(x) = x + 1

Read more about functions at

https://brainly.com/question/1415456

#SPJ1

Possible question

Identify each function for which f (2) = 3

f(x) = x^2 + 1

f(x) = 2x + 1

f(x) = x + 1

f(x) = 2x^3 + 1

The absolute value of the given modulus function are -1 and 7.

The given modulus function is;

|4x - 12| = 16

Removing modulus sign will provide two values;

4x - 12 = ±16

Solve for positive value of modulus function;

4x - 12 = 16

Add 12 on both side;

4x - 12 + 12 = 16 + 12

4x = 28

Dive both side by 4.

x = 7

Now, solve for negative value of modulus function.

4x - 12 = -16

Add 12 on both side;

4x - 12 + 12 = -16 + 12

4x = -4

Divide both side by 4;

x = -1

Thus, the two value of the given modulus function are -1 and 7.

To know more about the modulus function, here

https://brainly.com/question/27880466

#SPJ9

The height of building is 0.2 miles.

The given points form a right angled triangle. Top of the building to base of building is the perpendicular, base of building to the angle of elevation is base and angle of elevation to top of the building is hypotenuse. So, considering this, tan of angle of elevation related the two sides of triangle as follows -

tan theta = perpendicular ÷ base

tan 6° = perpendicular ÷ 2

Perpendicular = 2 × tan 6°

Keep the value of tan 6°

Perpendicular = 2 × 0.1

Performing multiplication

Perpendicular = 0.2 miles

Hence, the height of the building is 0.2 miles.

Learn more about calculations on angle of elevation -

https://brainly.com/question/88158

#SPJ4

Answer:

Step-by-step explanation:(2x+5)(2x+9)

      use foil method           ([tex]4x^{2}[/tex]+18x+10x+45)

                                            [tex]4x^{2}[/tex]+28x+45

The value of the composite function (h⁰ g)(x) calculated by  function operation is  2x+28 .

A function is described as the relationship between a set's domain and range and its elements. f, g, or h are frequently used to denote functions.

Each element of an algebraic function, denoted by the formula y=g(x), is connected to a single value of x.

(h ∘ g)(x) can also be expressed as h[g(x)] , which signifies that the value of x=g(x) will be replaced in the function h, is referred to as a composite function.

A composite function is produced by combining two existing functions to produce a third, distinct function.

In h of g of x, the output of one function becomes the input of another.

Given functions are:

f(x)=4 x and g(x)=1/2x+7

Therefore (f ∘ g)(x)=f[g(x)]

=f(1/2x+7)

=4×(1/2x+7)

=2x+28

Therefore the value of the function operation  (f⁰ g)(x) is  2x+28

To learn more about function operations on Composite functions visit:

brainly.com/question/20379727

#SPJ4

Answer:

n=-3

Step-by-step explanation:

2-2n=3n+17

-2n=3n+15

-5n=15

n=-3

Answer:

-1

Step-by-step explanation:

i just inserted it into an online graphing calculator called desmos.