Which is a cubic function?

f(x) = 3x + 1
f(x) = 3x2 + x + 2
f(x) = 5x3 + 2x + 1
f(x) = x3 + x4 + 5

The probability that out of 52 card the selected 3 cards are not a face card is 0.183.

There are 12 face cards in a deck of 52 cards.

The probability of selecting 3 cards which should not be a face card is ,

=30c3 / 52c3

= 4060 / 22,100

= 0.183

Combination is a means to choose items from a collection without worrying about their order. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

It is easy to count the number of combinations in smaller cases, but the likelihood of a set of combinations is also higher in cases with many groups of components or sets. As a result, a formula has been developed to determine the number of items that could be chosen, i.e., nCr .

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Answer:

A single number that estimates the value of an unknown parameter is called a point estimate.

Step-by-step explanation:

Don't see the point (haha) of elaborating

The soda left in the bottle is 0.4 liters in a 2-liter bottle.

Let’s understand this with the concept of Ratio.

How does ratio work?

When two objects are related using numbers or amounts, the relationship is known as a ratio.

Initially, we are given that the bottle is 2 liters. From that, Sergio poured ⅘ of the soda.

So, the soda left is the initial quantity- the final quantity

= 2(initial quantity) - ⅘*2(final quantity)

=2 - 1.6= 0.4 liter

So finally, the soda left in the 2-liter bottle is 0.4 liter.

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(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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The graph of all the functions then we get the correct function is \(log_3(x)\)

We have given the graph of the logarithm function.

The logarithm is the inverse function of exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b must be raised, to produce that number x.

So we can draw the graph of all the functions then we get the correct function is \(log_3(x)\)

Therefore option b is correct.

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Examples of random variables are option A: the weight of a bag of a dozen apples, and option C: the number of dots uppermost of rolling a pair of dice.

Because they can only have a finite number of values, discrete random variables include things like the weight of a bag of twelve apples and the number of dots that appear on top of a pair of dice.

Examples of continuous random variables are the length of an airline flight and the quantity of drive-through clients at a bank on a particular day since they might have any value within a specified range.

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Correct question:

Choose the random variables from this set that are discrete. select all that apply. multiple select question.

the weight of a bag of a dozen apples.

the travel time of an airline flight.

the number of dots uppermost of rolling a pair of dice.

number of drive-thru customers to the bank on a given day.

Answer:

slope = \(\frac{6}{5}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{6}{5}\) x - 4 ← is in slope- intercept form

with slope m = \(\frac{6}{5}\)

Answer:

6/5

Step-by-step explanation:

this equation is already in the slope intercept form, meaning the slope (gradient)is the coefficient of x( the number before x). in this case it's 6/5.

I hope this helps

Answer:

The graph is attached and the horozontal asymptote is 1

Step-by-step explanation:

When you graph the function this is the graph you get. You can see that the top line gets close but does not touch the 1. For that reason 1 is the horizontal asymptote.

Answer:

46 degrees

Step-by-step explanation:

Angles 4 and 6 are consecutive interior angles which means that they are supplementary. Angle 6 is equal to 180-134, so angle 6 is 46 degrees.

Add the file first cause there is none

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

Answer: -5

If f(t) = t^2 - 2t - 5, then f(0) = 0^2 - 2(0) - 5. That simplifies to be f(0) = -5

Answer: \(y-2=3(x-4)\\y=3x-12+2\\-3x+y=-10\\3x-y=10\)

Step-by-step explanation:

I showed the steps to find the equation. In case you need to know, I used point-slope form, which involves using the formula y-y1=m(x-x1), in which you use a point like (4,2) and the slope, which we know is 3x since it's parallel to the original line. Simplifying and bringing it to standard form such as Ax+By=C. Ax has to be positive, which is why -3x went to positive, and y and -10 switched signs.

The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

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Answer:

A= C + 12%C = 1.12C

S=.C -2%C = .98C

A,C and S are the speeds of Alex, Cameron and Sam

400 meter race

how far is Sam from the finish line when Alex crosses the finish line?

distance = speed times time

400 = AT where T=Alex' finish time

400=1.12T

400=CU where U = Cameron's finish time

400=SV where V = Sam's finish time

T<U<V

Alex' finish time is less than Cameron's finish time is less than Sam's finish time

if Cameron runs at 20 meters per second, finishing in 20 seconds

then Sam is about 50 meters from the finish line when Alex finishes

sorry if i´m too late, hope this helps!

Answer:

she spent approximately 7.3 months abroad in total

Step-by-step explanation:

1.3+3.2+2.6= 7.3

Answer:

105, C

Step-by-step explanation:

16x + 1 + 40 = 27x - 3

This is because 180 - (27x - 3) = the missing angle in the triangle shown

16x + 1 + 40 = 27x - 3

1+ 40 = 41

16x + 41 = 27x - 3

        +3            +3

16x + 44 = 27x

-16x           -16x

44 = 11x

44/11 = x

x = 4

27x - 3 is equal to 27(4) - 3 = 108 - 3 = 105

Ans = 105

The two other roots of p(x) are 8 - 4√31 and 8 + 4√31. The smaller root is 8 - 4√31 and the larger root is 8 + 4√31. We can calculate it in the following manner.

We know that the sum of the roots of a polynomial with real coefficients is equal to the negative of the coefficient of the second-to-last term divided by the coefficient of the leading term.

Therefore, the sum of the roots of p(x) is:

1 + 7 + r1 + r2 = -(-24)/1 = 24

where r1 and r2 are the two other roots of the polynomial. We can rewrite this equation as:

r1 + r2 = 16

We also know that the product of the roots of a polynomial is equal to the constant term divided by the coefficient of the leading term. Therefore, the product of the roots of p(x) is:

1 x 7 x r1 x r2 = 7/1 = 7

We can rewrite this equation as:

r1 x r2 = 7/7 = 1

Now, we can use this information to write a quadratic factor of p(x) that has r1 and r2 as its roots. We know that:

(x - r1)(x - r2) = x^2 - (r1 + r2)x + r1r2

Substituting in the values we know, we get:

(x - r1)(x - r2) = x^2 - 16x + 1

Therefore, we have:

p(x) = (x^2 - 16x + 1)(x^2 - 16x + 238)

The roots of the second quadratic factor can be found using the quadratic formula:

x = (16 ± √(16^2 - 4(1)(238))) / 2

x = 8 ± √(496)

The smaller root is 8 - √(496), which can be simplified to:

8 - √(496) = 8 - 4√31

The larger root is 8 + √(496), which can be simplified to:

8 + √(496) = 8 + 4√31

Therefore, the two other roots of p(x) are 8 - 4√31 and 8 + 4√31. The smaller root is 8 - 4√31 and the larger root is 8 + 4√31.

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Answer:

198.975 (198.98 rounded)

Step-by-step explanation:

189.50x1.05=198.98

Answer:

Group A, because seven children have a forearm length longer than 10 inches

Step-by-step explanation:

Create the dot plots based on the given information (please see attached images).

Group A = blue dots

Group B = red dots

From inspection of the attached dot plots, we can see that Group A appears to have the longer average forearm length.  This is because 7 children have a forearm length of longer than 10 inches.

To calculate the average forearm length, sum all data values and divide by the total number of data values.

\(\textsf{Average of Group A}=\dfrac{ 3 \times 10 + 4 \times 11 + 3 \times 12}{10}=11\)

\(\textsf{Average of Group B}=\dfrac{ 3 \times 9 + 5\times 10+ 2\times 11}{10}=9.9\)

Thus proving that Group A has the longer average former length.

According to given text data

Average of both groups

A:-

B:-

Group A has bigger average

Answer:

4x + 8x = 180

12x = 180

divide by 12 on both sides:

X = 15

4 x 15 = 60 degrees

8 x 15 = 120 degrees

Answer:

Hello! answer: x = 15

Step-by-step explanation:

Since this is a supplementary angle it will equal a total of 180 15 × 4 = 60 15 × 8 = 120 you add these up and... 60 + 120 = 180 therefore x = 15 and

4x = 60 and 8x = 120 HOPE THAT HELPS!

Answer:

d

Step-by-step explanation:

i think i helped. have a nice day

Answer:

< COD and <DOE

Step-by-step explanation:

A linear pair is when two angle measures add up to 180 degrees, in other words, form a straight line.

If one looks at the picture, <COD and <DOE form line CE, therefore, they are a linear pair; they form a line.

Answer:

x=-3

Step-by-step explanation:

-4(-x+3)+8=2+6x

<=> 4x-12+8-2-6x=0

<=> -2x-6=0

<=> x=-3

Answer:

-3.5

Step-by-step explanation:

\(-4(-x+3)+8=2+6x \\ \\ 4x-12+7=2+6x \\ \\ 4x-5=2+6x \\ \\ -5=2+2x \\ \\ -7=2x \\ \\ x=-3.5\)

Answer:

Step-by-step explanation:

42)1.50/6=0.25

43)3/2=1.5

44)1x2=2

Answer:

42.) $0.25 per banana.

43.) 1.5 cakes per hour.

44.) 2 pounds of food per hour.

Step-by-step explanation:

42.)

\(\frac{Cost}{Amount}=\frac{1.50}{6}=0.25\)

43.)

\(\frac{Amount}{Time}=\frac{3}{2}=1.5\)

44.)

\(\frac{Amount}{Time}=\frac{1}{0.5}=2\)

Answer:

y + 1 = 2(x + 3)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)  

Step-by-step explanation:

Step 1: Define

Slope m = 2

Point (-3, -1)

Step 2: Write Function

Substitute variables into general form.

y + 1 = 2(x + 3)

Answer:

p=45-2.5f

Step-by-step explanation:

5f+2p=90

We have to isolate p in one side

5f+2p=90

-5f. -5f

2p=90-5f

/2. /2. /2

p=45-2.5f

Hopes this helps please mark brainliest

To simplify by distribution you multiply the term outside the parenthesis by the terms inside the parenthesis:

The conclusion that is appropriate at a 5% level of significance is this:C. There are statistically significant differences in the mean time to recurrence of depression symptoms for patients in the three treatment groups. this suggests that there is a treatment effect.

The correct conclusion is that the result obtained from the analysis is statistically significant, so the null hypothesis can be rejected. This also means that there are 1 in 20 chances of obtaining an error.

So, for a study checking the relationship between the mean time to recurrence of depression symptoms, the 5% level of significance would demonstrate a relationship.

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