Marcus plots the point (4, 7) in Quadrant I on the coordinate plane. Nicole then plots the point (4, –3) in Quadrant IV of the same graph. Explain what the line that goes through those two points would look like, and evaluate the slope.

Answer:

x² + 4x + 3

Step-by-step explanation:

Dividing by (x - 5) then use h = 5 as divisor

5 | 1    - 1    - 17    - 15

    ↓     5     20     15

   -------------------------------

     1     4      3       0 ← remainder = 0

quotient = x² + 4x + 3

\(x^{2} +4x+3\) is the quotient when \(x^{3} - x^{2} -17x-15\) is solved using synthetic division.

Synthetic division is a simplified method for dividing a polynomial by another polynomial of the first degree by writing down only the coefficients of the several powers of the variable and changing the sign of the constant term in the divisor so as to replace the usual subtractions by additions.

Synthetic division of the given question-

5    |     1        -1        -17        -15

                     5         20        15

---------------------------------------------

           1         4         3           |0|          

Remainder = 0

Quotient = \(x^{2} + 4x+3\)

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Answer:

the velocity of the man is 5 m/s.

Step-by-step explanation:

The kinetic energy of a moving object is given by the equation:

K.E. = 0.5 * m * v^2

where

K.E. is the kinetic energy

m is the mass of the object

v is the velocity of the object

In this problem, we are given that the man has a mass of 60 kg and a kinetic energy of 750 J.

So,

750 J = 0.5 * 60 kg * v^2

Solving for v:

v^2 = (2 * 750 J) / 60 kg

v^2 = 25 J/kg

v = sqrt(25 J/kg)

v = 5 m/s

Therefore, the velocity of the man is 5 m/s.

Answer: $‭3,076.88‬

Step-by-step explanation:

Rachel earns $384.61 per week that she works and she worked for 8 weeks.

Her total earnings are therefore:

= Weekly pay * Number of weeks

= 384.61 * 8

= $‭3,076.88‬

The nonzero vector orthogonal to the plane through the points P, Q, and R is [-8/13, -8/13, -12/13].

To find a nonzero vector orthogonal to the plane through the points P, Q, and R, we can use the cross product of two vectors that lie in the plane.

Let's find the vectors PQ and PR, which can be found by subtracting the coordinates of P from the coordinates of Q and R:

PQ = Q - P = (-2, 1, 3) - (1, 0, 1) = (-3, 1, 2)

PR = R - P = (4, 2, 5) - (1, 0, 1) = (3, 2, 4)

Next, we'll take the cross product of these two vectors to find a vector orthogonal to the plane:

n = PQ x PR =

[(1)(4) - (2)(2), (2)(-3) - (3)(1), (3)(3) - (2)(-2)]

= [-8, -8, -12]

This vector is orthogonal to the plane through the points P, Q, and R. To make it a nonzero vector, we can scale it to have magnitude 1:

n = [-8, -8, -12] / sqrt((-8)^2 + (-8)^2 + (-12)^2) = [-8/13, -8/13, -12/13]

So, the nonzero vector orthogonal to the plane through the points P, Q, and R is [-8/13, -8/13, -12/13].

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Answer:

13/40.

Step-by-step explanation:

We add the probability in this case.

So it is 1/5 + 1/8

=  8/40 + 5/40

= 13/40.

Lateral area of cylinder is,

⇒ A = 80π cm²

We have to given that;

A figure for a cylinder is shown.

Since, We know that;

Lateral area of cylinder is,

A = 2πrh

Here, We have;

Radius of cylinder = 16 /2 cm

Radius of cylinder = 8 cm

And, Height of cylinder = 5 cm

Hence, Substitute given values, we get;

⇒ A = 2πrh

⇒ A = 2π × 8 × 5

⇒ A = 80π cm²

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Answer:

y=(x-5)^2 - 6

Step-by-step explanation:

Subtracting the 5 to the x moves the parabola 5 units to the right. Putting the -6 at the end moves the parabola down 6 units.

Answer:

\(y=\left(x-5\right)^{2}-6\)

Step-by-step explanation:

I graphed the original parabola and the new parabola on the graph below. I moved the original parabola down 6 and right 5.

Answer:

let r ,v be the radius and volume of sphere.

dv/dt=64πft³/min

r=2ft

Dr/dt=?

Step-by-step explanation:

we have

volume of sphere=4/3πr²

v=4/3πr²

differentiating both side with respect to t we get

dv/dt=4πdr²/dr×dr/dt=4π×2r×dr/dt=8/3×πr×dr/dt

substituting the given value we get

dv/dt=8/3×πr×dr/DT

64π×3/(8π×2)=dr/dt

Dr/dt=12ft/min

The balloon's radius is increasing at a rate of12 ft/min

The balloon's radius increasing at the instant the radius is 2 ft will be 10106.47 ft³ per minute.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

A spherical balloon is inflating with helium at a rate of 64π ft/min.

dr/dt = 64π ft/min

Then the balloon's radius increasing at the instant the radius is 2 ft will be

V = (4/3)πr³

Differentiate with respect to time. Then we have

\(\rm V' = \dfrac{dV}{dt} \\\\ V' = \dfrac{4}{3}\cdot \pi 3r^2 \cdot \dfrac{dr}{dt}\)

Simplify the equation, then we have

V' = 4πr² × 64π

V' = 4π × (2)² × 64π

V' = 10106.47 ft³ per minute

The balloon's radius increasing at the instant the radius is 2 ft will be 10106.47 ft³ per minute.

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Answer:

10/5 - 4

Step-by-step explanation:

you have to write down what you understand from the sentence.

First, you read it carefully since it says quotient then you will have to put that first and then subtraction. Normally you would put subtraction in front because the sentence is in that order. But since your dealing with division then the subtraction part would go afer.

10/5 - 4

Answer: uhh i think both are correct since the order of operation states that you must do division over subtraction first, it doesn't matter which position 4 is in, but you must do the division first.

A. In the alternate universe, the p subshell would have 5 orbitals.

B. In the alternate universe, the d subshell would have 10 orbitals.

In the alternate universe where the possible values of mℓ range from -l-1 to l+1, the number of orbitals in each subshell can be determined.

A. For the p subshell, the value of l is 1. Therefore, the range of mℓ would be -1, 0, and 1. Including the additional values of -2 and 2 from the alternate universe, the total number of orbitals in the p subshell would be 5 (mℓ = -2, -1, 0, 1, 2).

B. For the d subshell, the value of l is 2. In the conventional universe, the range of mℓ would be -2, -1, 0, 1, and 2, resulting in 5 orbitals. However, in the alternate universe, the range would extend to -3 and 3. Including these additional values, the total number of orbitals in the d subshell would be 10 (mℓ = -3, -2, -1, 0, 1, 2, 3).

Therefore, in the alternate universe, the p subshell would have 5 orbitals, and the d subshell would have 10 orbitals.

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Answer:

\(y = {(x + 3)}^{2} - 14\)

Step-by-step explanation:

The original equation

\( f(x) = {x }^{2} + 6x - 5\)

vertex form

\(y = a {(x - h)}^{2} + k \\ where \: (h. \: k) \: is \: the \: vertex\)

solve for the x coordinate of the vertex, h

\(x = h = - \frac{b}{2a} = - \frac{6}{2(1)} = - \frac{6}{2} = - 3 \\ x = h = - 3\)

substitute -3 back into the original equation to solve for y

\(y = { (- 3)}^{2} + 6( - 3) - 5 \\ y = 9 - 18 - 5 \\ y = 4 - 18 \\ y = k = - 14 \)

substitute h and k values into the vertex form

a = 1 So we can omit it

\(y = {(x - ( - 3)}^{2} - 14 \\ y = {(x + 3)}^{2} - 14\)

Answer:

\(\frac{1}{6}\) = .167

\(\frac{2}{6}\) = .333

\(\frac{3}{6}\) = .5

\(\frac{4}{6}\) = .667

\(\frac{5}{6}\) =.833

Step-by-step explanation:

Hope this helps !

Answer:

167

Step-by-step explanation:

By BODMAS rule,

13 + 14 x 11

= 13 + ( 14 x 11 )

= 13 + 154

= 167

Note : -

B - Brackets

O - Of

D - Division

M - Multiplication

A - Addition

S - Subtraction

Therefore, the correct answer is c) 3, as there are three F ratios calculated in a 2x2 factorial design.

In a two-way analysis of variance (ANOVA) known as a 2x2

factorial design, there are three F ratios or F statistic values calculated. This design involves two independent variables, each with two levels or categories.

The three F ratios represent the main effects of each independent variable and the interaction between the two variables.The main effects F ratios determine whether there are significant differences between the levels of each independent variable individually, ignoring the other independent variable.

There will be two main effects F ratios, one for each independent variable.The interaction F ratio examines whether there is a significant interaction between the two independent variables. It determines whether the effect of one independent variable differs across the levels of the other independent variable.

This F ratio assesses the joint influence of both independent variables.

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The final quotient is the concatenation of the quotients obtained in each step: 2, 1. The remainder is 4

To divide 466 by 22, we can perform long division as follows:

First, we divide the leftmost digit of the dividend (4) by the divisor (22). Since 4 is less than 22, we bring down the next digit (6) to form a new dividend of 46.

Next, we divide 46 by 22. The quotient is 2 (22 times 2), and the remainder is 2. We write the remainder next to the new dividend.

We then bring down the next digit (6) to form a new dividend of 26.

We divide 26 by 22. The quotient is 1 (22 times 1), and the remainder is 4.

Since there are no more digits to bring down, we have completed the division. The final quotient is the concatenation of the quotients obtained in each step: 2, 1. The remainder is 4

Therefore, 466 divided by 22 equals 21 with a remainder of 4.

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Divide. Give the quotient and remainder 466-:22

Answer:

$1.25

Step-by-step explanation:

Given:

The student council sold 140 sodas for $175.00 at the fall festival.

To Find:

What is the cost per soda?

Note:

To find cost per soda you have to divide Cost by number of Sodas

Solve:

$175.00/140 = 1.25

Hence, the cost per soda is $1.25

~Learn with Lenvy~

The value of (-1678 / 345) + 64 will be -60.86.

In this situation, it's important to use PEDMAS. This implies that the parentheses will be solved first.

The value of (-1678 / 345) +64 is illustrated thus:

= (-1678 / 345) + 64

= -4.86 + 64

= -60.86

In this case, the concept was to solve the numbers in the parentheses before addition

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Therefore, the probability mass function of N is:

\(P(N=3) = p*(1-p)\\P(N=4) = p*p*(1-p) + (1-p)*(1-p)*p\\P(N=5) = p*p*p*(1-p) + (1-p)*(1-p)*(1-p)*p + 2*p*(1-p)*p*(1-p)\\P(N=6) = p*p*p*p*(1-p) + (1-p)*(1-p)*(1-p)*(1-p) + 3*p*p*(1-p)*(1-p) + \    \ \ \  2*p*(1-p)*p*p*(1-p) + 2*p*p*(1-p)*p*(1-p) \\\)

And so on, for larger values of N.

To find the probability mass function of N, we need to consider the two cases mentioned in the question.

Case 1: A sequence of events followed by an odd.
For this case, the probability of rolling an even number on the first roll is p. The probability of rolling the same even number on the second roll is also p. The probability of rolling an odd number on the third roll is (1-p) because the even numbers have been exhausted. So, the probability of this specific sequence of rolls occurring is p*p*(1-p).

Case 2: A sequence of odds followed by an even.
For this case, the probability of rolling an odd number on the first roll is 1-p. The probability of rolling the same odd number on the second roll is also 1-p. The probability of rolling an even number on the third roll is p because the odd numbers have been exhausted. So, the probability of this specific sequence of rolls occurring is (1-p)*(1-p)*p.

We can then find N's overall probability mass function by adding the probabilities of all possible sequences that lead to observing both an even and an odd number.

The smallest value in support of N must be 3, since it takes at least 3 rolls to observe both an even and an odd number.

Therefore, the probability mass function of N is:

\(P(N=3) = p*(1-p)\\P(N=4) = p*p*(1-p) + (1-p)*(1-p)*p\\P(N=5) = p*p*p*(1-p) + (1-p)*(1-p)*(1-p)*p + 2*p*(1-p)*p*(1-p)\\P(N=6) = p*p*p*p*(1-p) + (1-p)*(1-p)*(1-p)*(1-p) + 3*p*p*(1-p)*(1-p) + \    \ \ \  2*p*(1-p)*p*p*(1-p) + 2*p*p*(1-p)*p*(1-p) \\\)

And so on, for larger values of N.

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Answer: 52

There are 52 weeks in a year, because 365 ÷ 7 is 52.

It is a whole number, so you do not need to do the next following steps according to your question.

So, the answer is 52.

The number of weeks is 52 in a year 52 is not a whole number and the remainder is 1.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that are +, -, ×, and ÷.

It is given that:

There are 365 days in a non-leap year. There are 7 days per week.

Let x be the number of weeks x:

x = 365/7

x = 52.14

52 is not the whole number.

The remainder is 1

Thus, the number of weeks is 52 in a year and 52 is not a whole number and the remainder is 1.

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0.167 or 0.17 rounded to the nearest hundredth.

How do you round off decimal to the nearest hundredth?

When rounding to the nearest hundredth, you want to look at the third decimal place, the one to the right of the hundredth place. If the value in the third decimal place is less than 5, you truncate everything to the right of the hundredth place, leaving the number unchanged.

If the value in the third decimal place is greater than or equal to 5, you add one to the number in the hundredth place.

The total area of the rectangle is 15*5 = 75 square feet.

The area of the triangle inside the rectangle is (1/2)25 = 12.5 square feet.

The shaded region is the area of the triangle, so the probability that a randomly chosen point lies inside the shaded region is

12.5/75 = 0.167 or 0.17 rounded to the nearest hundredth.

Hence, 0.167 or 0.17 is rounded to the nearest hundredth.

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Answer:

.96/12= .08 cents

Step-by-step explanation:

Use a calculator

Answer:

32

Step-by-step explanation:

There are 80 biscuits inside the tin.

Also, they said that those biscuits are in the ratio

Short bread    :      Choc - chip

          2          :        3

Altogether there are 5 shares ( 2 + 3)

And now you can divide 80 by 5 to find how many biscuits contain per a share.

80 ÷ 5 = 16

In the question, they asked us to to find the number of short biscuits inside the tin.

Let us find that.

There are 2 shares for short bread biscuits.

So,

Number of short biscuits ⇒ 2 × 16

                                         ⇒ 32

Hope this helps you :-)

Answer:

Assuming 64y - 24z = 0, y= 3z/8 and z = 8y/3

Step-by-step explanation:

plugged it into a calculator.

Step-by-step explanation:

3,13] has a span of 10

with 4 rectangles, each has width 2.5

So the distance is 2.5(f(5.5)+f(8)+f(10.5)+f(13))

You don't give the table, so if the given data points are unevenly spaced, that will have to be changed some.

Therefore , the solution of the given problem of probability comes out to be 3 flights will depart on time is roughly 0.311, the likelihood that at most 4 flights will depart on time is roughly 0.672,

Finding the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as parameter estimation. Any number between range 0 but rather 1, where 1 is usually used to symbolise certainty and 0 is typically used to represent possibility, may be utilized to represent chance. A probability diagram shows the chance that a specific event will occur. .

Here,

=> P(X = k)  = (n choose k) * p * k * (1-p) (n-k)

where p is the chance of success and (1-p) is the probability of failure, (n choose k) is the binomial coefficient, and P(X = k) is the probability of k successes in n trials.

The likelihood that precisely 3 planes will depart on time is:

P(X = 3)

=> (6 choose 3) * 0.60 * 0.40 * 0.311

The likelihood that up to 4 planes depart on time is:

=> P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

         = > (6 choose 0) * 0.60^0 * 0.40^6 + (6 choose 1) * 0.60^1 * 0.40^5 + (6 choose 2) * 0.60^2 * 0.40^4 + (6 choose 3) * 0.60^3 * 0.40^3 + (6 choose 4) * 0.60^4 * 0.40^2

         ≈> 0.672

The likelihood that at least three planes will depart on time is:

P(X >= 3) = 1 - P(X < 3)

         = 1 - P(X = 0) - P(X = 1) - P(X = 2)

         = 1 - (6 choose 0) * 0.60^0 * 0.40^6 - (6 choose 1) * 0.60^1 * 0.40^5 - (6 choose 2) * 0.60^2 * 0.40^4

         ≈ 0.695

=> P(X>=3) = 1 - P(X3) = 1 - P(X0) - P(X = 1) - P(X = 2)

=>  1 - (6 choose 0) (6 choose 0) * 0.60^0 * 0.40^6 - (6 choose 1) (6 choose 1) * 0.60 * 0.40 * 6 (select 2) * 0.60 * 0.40 * 4

≈> 0.695

Therefore, the likelihood that precisely 3 flights will depart on time is roughly 0.311, the likelihood that at most 4 flights will depart on time is roughly 0.672, and the likelihood that at least 3 flights will depart on time is roughly 0.695.

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Bisect means that the angles are split equally.

RTV would be half of RTS

RTV = 1/2(RTS)

16x-6 = 1/2(26x+18)

Simplify:

16x - 6 = 13x +9

Subtract 13x from both sides:

3x - 6 = 9

Add 6 to both sides:

3x = 15

Divide both sides by 3:

x = 5

Now you have x, replace x in the equation for RTV:

RTV = 16x -6 = 16(5) -6 = 80 - 6 = 74

RTV = 74 degrees.

The quotient of the expression is 4x+1.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined

Given:

The expression is

\((4x^{2} - 7x - 2) / (x-2)\)

By long division method the following steps are :

Divide the tens column dividend by the divisor. Then Multiply the divisor by the quotient in the tens place column ,Subtract the product from the divisor then at last Bring down the dividend in the ones column and repeat.

We have to find the quotient of the expression.

According to given question we have

\((4x^{2} - 7x - 2) / (x-2)\\\\=(x-2)(4x+1)/(x-2)\\\\=4x+1\)

Therefore, the quotient of the expression is 4x+1.

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Answer:

Step-by-step explanation:

The bank paid for somthing for David. Now Davids Bank Account is in the negitve of $52. Now he owes the bank money.

if you take how much money david had

and subtact it with 95 it will equal up to $-52

________________________________________________________

The x-intercept is 12 and the y-intercept is 48 for the equation y = 48 - 4x.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that four-inch pieces are repeatedly cut from a 48-inch string. The length of the string after x cuts is given by y=48 - 4x.

The x-intercept will be calculated as,

y = 48 - 4x

0 = 48 - 4x

4x = 48

x = 12

The y-intercept will be calculated as,

y = 48 - 4x

y = 48 - 0

y = 48

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