Find the midpoint of A and B where A has coordinates (2, 3)
and B has coordinates (8,9).
y
10
9
8
7
6
5
4
3
2
1
X
O
1 2 3 4 5 6 7 8 9 10

Answer:

29+8x

Step-by-step explanation:

5+8(3+x)

5+24+8x - Open parentheses

29+8x - Add like terms

Answer:

2x+5= g(−1)=12

Step-by-step explanation:

Simplify is simple

Answer:

V=201.06

Step-by-step explanation:

V=πr2h

3=π·42·12

3≈201.06193

Answer:

B

Step-by-step explanation:

Add $125.62 and $532.50 and then subtract 40 from the total

The amount that he will be depositing into his savings account is,  $618.12

We know that;

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Roger wants to make a deposit into his savings account. He is depositing 2 checks, one for $125.62 and the other for $532.50. He would like to receive $40.00 in cash after the deposit.

Hence, The amount that he will be depositing into his savings account is,

⇒ $125.62 + $532.50 - $40

⇒ $658.12 - $40

⇒ $618.12

Thus, The amount that he will be depositing into his savings account is,  $618.12

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Combining the two equations gives us

We add 0.5x to both sides and get

and subtracting 1 from both sides gives

And finally, dividing both sides by 2.5 gives

Putting this value of x into y = 2x + 1 gives

Hence our solution is

The requried equation of the diagonals for which WXYZ will be rhombus is y = -x + 12 and y = x + 12.

A rhombus is a parallelogram with all sides of equal length. This means that the diagonals of a rhombus bisect each other at right angles.

Let's first find the length of the diagonals of rhombus WXYZ using the distance formula:

WY = \(\sqrt{[(9-1)^2 + (11-3)^2]]}\) = 8√2

Since the diagonals of a rhombus bisect each other at right angles, we can use the midpoint formula to find the midpoint M of the diagonal WY:

Midpoint M = ((1+9)/2, (3+11)/2) = (5, 7)

The slope of the line passing through W and Y is:

slope WY = (11-3)/(9-1) = 8/8 = 1

Therefore, the slope of the line perpendicular to WY is -1/1 = -1.

Using the point-slope form with point M and slope -1, we get:

y - 7 = -1(x - 5)

y = -x + 12

So, the equation of the line passing through M with a slope perpendicular to the line passing through W and Y is y = x + 12 equation for XZ will be the same but the slope will be +1 so the equation is y = x + 1.

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Answer:

The critical value is 6.26.

Step-by-step explanation:

It is provided that there are 5 independent variables involved in a multiple regression model and the sample consist of 10 data points.

The critical value of F to test the significance of the model is:

\(\text{Critical Value}=F_{\alpha, (k, n-k-1)}\)

Here,

k = number of independent variables

n = number of observations.

Then the critical value is:

\(\text{Critical Value}=F_{\alpha, (k, n-k-1)}\)

                      \(=F_{\alpha, (5, 10-5-1)}\\=F_{0.05,(5, 4)}\\=6.2561\\\approx 6.26\)

*Use a F-table.

Thus, the critical value is 6.26.

both x-axis in the graph is before 5 or -5

SLOPE-INTERCEPT: y=3x-2

The coterminal angle of 31π/6 is angle of 210 degrees.

To find a coterminal angle, we can add or subtract a full revolution (2π) or any multiple of it.

Let's calculate the coterminal angle:

31π/6 = (30π/6) + (π/6) = 5π + π/6

To simplify the angle, we can express it in terms of a common denominator:

5π + π/6 -2π

3π+ π/6

19π/6

570 degrees.

The other coterminal angle is 210 degrees which lies in the third quadrant.

Therefore, the coterminal angle of 31π/6 is  210 degrees.

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Answer:

3.72kg

$29.76

See explanation below

Step-by-step explanation:

The question is incomplete as we are not told what we are to determine. Consider the following question

Question:

Tomas has two boxes to be shipped. One box weighs 3 kilograms. The other box weighs 720 grams.

a) What is the total weight of the boxes in kilogram?

b) If the shipping cost $8 per kilogram, what is the total cost of shipping.

Solution:

This is a question on measuring mass.

a) Total weight of the two boxes = weight of 1st box + weight of 2nd box

1st box = 3kg

2nd box = 720g

1000 g is equal to 1 kg

720g = (720/1000)kg = 0.72 kg

2nd box = 0.72 kg

Total weight of the two boxes = 3kg + 0.72kg

Total weight of the two boxes = 3.72kg

b) cost of shipping per kg = $8

cost of shipping for 3.72 kg = 8 × 3.72

Total cost of shipping for both boxes = $29.76

Answer: from my calculations its 3.72

which is also 3720 grams

I believe that the answer B,D,and E

Answer:

A, D, and E (I think)

Step-by-step explanation:

I'm pretty sure those would be the right answers, sorry that this isn't much of an explanation lol

Answer:

95°

Step-by-step explanation:

120° = 25° + y ( exterior angle of a triangle is equal to the sum of two opposite interior angles)

y = 120° - 25°

y = 95°

Hope it will help :)❤

Answer:

1. y = 2x - 5

2. y = (-1/3)x

3. y = -4

4. y = (-3/4)x + 7

5. x = 6

6. y = -3x - 8

Step-by-step explanation:

1.

Point 1: (0, -5) Point 2: (-1, -7)

            (x₁, y₁)                (x₂, y₂)

        y₂ - y₁        -7 - (-5)     -7 + 5       -2

m = ------------ = ----------- = ---------- = ------ = 2

        x₂ - x₁         -1 - 0           -1           -1

y - y₁ = m (x - x₁)

y - (-5) = 2(x - 0)

y + 5 = 2x - 0

   -5           -5

y = 2x - 5

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

2.

Point 1: (0, 0) Point 2: (3, -1)

            (x₁, y₁)             (x₂, y₂)

        y₂ - y₁        -1 - 0            -1

m = ------------ = ----------- = ----------

        x₂ - x₁         3 - 0            3

y - y₁ = m (x - x₁)

y - (0) = (-1/3)(x - 0)

y - 0 = (-1/3)x - 0

   -0                -0

y = (-1/3)x

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

3.

Point 1: (0, -4) Point 2: (-5, -4)

            (x₁, y₁)                (x₂, y₂)

        y₂ - y₁        -4 - (-4)   -4 + 4         0

m = ------------ = ----------- = ---------- = ------ = 0

        x₂ - x₁         -5 - 0          -5          -5

y = -4

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

4.

Point 1: (0, 7) Point 2: (4, 4)

            (x₁, y₁)             (x₂, y₂)

        y₂ - y₁        4 - 7            -3

m = ------------ = ----------- = ----------

        x₂ - x₁         4 - 0            4

y - y₁ = m (x - x₁)

y - 7 = (-3/4)(x - 0)

y - 7 = (-3/4)x - 0

   +7               +7

y = (-3/4)x + 7

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

5.

Point 1: (6, 0) Point 2: (6, 3)

            (x₁, y₁)              (x₂, y₂)

        y₂ - y₁        3 - 0             3

m = ------------ = ----------- = ---------- = undefined

        x₂ - x₁         6 - 6           0

x = 6

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

6.

Point 1: (0, -8) Point 2: (-4, 4)

            (x₁, y₁)                (x₂, y₂)

        y₂ - y₁        4 - (-8)      4 + 8       12

m = ------------ = ----------- = ---------- = ------ = -3

        x₂ - x₁         -4 - 0          -4         -4

y - y₁ = m (x - x₁)

y - (-8) = -3(x - 0)

y + 8 = -3x - 0

   -8           -8

y = -3x - 8

I hope this helps!

Answer:

jkh and ihk

Step-by-step explanation:

Answer:

<JHK and IHK

Step-by-step explanation:

Answer:

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

If the system of linear equations has infinitely many solutions, it means the two lines overlap.

In other words, each point of one of the lines also belongs to the second line.

Choices a, b, c  give us one or no solutions and therefore not the answer.

Choice d is reflecting the infinitely many solutions and hence is the correct one.

The equation which represents the cost of renting the house, y, depends on the number of nights x is y = 229x + 89.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

As per the given,

Per night cost =  $229 per night

Fixed cost (cleaning fee) = $89

Total cost = Fixed cost + per night cost × number of nights.

The total cost y for x number of nights will be,

y = 229 + 89x

y = 89x + 229

Hence "The equation which represents the cost of renting the house, y, depends on the number of nights x is y = 229x + 89".

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Answer:

I think the answer is C Angle-Angle-Side im not sure if im accurate but i hope it helps

Step-by-step explanation:

Answer:

40%.

Step-by-step explanation:

There are 6 / 15 apples out of the bowl.

6/15 = 2/5 = 0.4

So, 40% of the fruit in the bowl are apples.

Hope this helps!

Answer:

D . 0.4

Step-by-step explanation:

let the height be the y coordinate

let the width be the x coordinate

first point :

width/x : 0.5

height/y : 0.8

according to the formula given:

height = constant/width :

so:

0.8 = constant/0.5

constant = 0.4

next point:

x : 0.8

y : 0.5

0.5 = constant/0.8

constant = 0.4

for all of the points, the constant is 0.4

Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

To determine the range of the number of RVs that need to be sold each month for the company to make a profit, we need to consider the profit function and find the values of x that result in a positive profit.

The profit function is given by P(x) = -50x + 20,000x - 1,500,000.

To make a profit, the value of P(x) must be greater than zero (P(x) > 0). We can set up the inequality:

-50x + 20,000x - 1,500,000 > 0.

Combining like terms, we have:

19,950x - 1,500,000 > 0.

Now, let's solve this inequality for x:

19,950x > 1,500,000.

Dividing both sides by 19,950, we get:

x > 1,500,000 / 19,950.

Simplifying the right side, we have:

x > 75.

The range of the number of RVs that need to be sold each month for the company to make a profit is x > 75.

Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

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using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

About 27 years.

Step-by-step explanation:

Byron deposits $13,500 in an account that earns 2.6% interest compounded monthly, and we want to determine how many years it will take for Byron's money to double.

Recall that compound interest is given by the formula:

\(\displaystyle A = P\left( 1 + \frac{r}{n}\right)^{nt}\)

Since our initial deposit is $13,500 at a rate of 2.6% compounded monthly, P = 13500, r = 0.026, and n = 12:

\(\displaystyle \begin{aligned} A &= (13500)\left( 1 + \frac{(0.026)}{(12)}\right)^{(12)t} \\ \\ &=13500\left(\frac{6013}{6000}\right)^{12t} \end{aligned}\)

For his deposit to double, A must equal $27,000. Hence:

\(\displaystyle (27000) &=13500\left(\frac{6013}{6000}\right)^{12t}\)

Solve for t:

\(\displaystyle \begin{aligned} 27000 &= 13500 \left(\frac{6013}{6000}\right)^{12t} \\ \\ \left(\frac{6013}{6000}\right)^{12t} &= 2 \\ \\ \ln\left(\frac{6013}{6000}\right)^{12t} &= \ln (2)\\ \\ 12t \ln \frac{6013}{6000} &= \ln 2 \\ \\ t &= \frac{\ln 2}{12\ln \dfrac{6013}{6000}} = 26.6883... \approx 27\end{aligned}\)

In conclusion, it will take Byron about 27 years for his deposit to double.

Answer:

a) 0.5768 = 57.68% probability that the shop sells at least 3 in a week.

b) 0.988 = 98.8% probability that the shop sells at most 7 in a week.

c) 0.0104 = 1.04% probability that the shop sells more than 20 in a month.

Step-by-step explanation:

For questions a and b, the Poisson distribution is used, while for question c, the normal approximation is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}\)

In which

x is the number of successes

e = 2.71828 is the Euler number

\(\lambda\) is the mean in the given interval.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Poisson distribution can be approximated to the normal with \(\mu = \lambda, \sigma = \sqrt{\lambda}\), if \(\lambda>10\).

Poisson variable with the mean 3

This means that \(\lambda= 3\).

(a) At least 3 in a week.

This is \(P(X \geq 3)\). So

\(P(X \geq 3) = 1 - P(X < 3)\)

In which:

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)\)

Then

\(P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498\)

\(P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494\)

\(P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240\)

So

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0498 + 0.1494 + 0.2240 = 0.4232\)

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 1 - 0.4232 = 0.5768\)

0.5768 = 57.68% probability that the shop sells at least 3 in a week.

(b) At most 7 in a week.

This is:

\(P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)\)

In which

\(P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498\)

\(P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494\)

\(P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240\)

\(P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240\)

\(P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680\)

\(P(X = 5) = \frac{e^{-3}*3^{5}}{(5)!} = 0.1008\)

\(P(X = 6) = \frac{e^{-3}*3^{6}}{(6)!} = 0.0504\)

\(P(X = 7) = \frac{e^{-3}*3^{7}}{(7)!} = 0.0216\)

Then

\(P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 + 0.1008 + 0.0504 + 0.0216 = 0.988\)

0.988 = 98.8% probability that the shop sells at most 7 in a week.

(c) More than 20 in a month (4 weeks).

4 weeks, so:

\(\mu = \lambda = 4(3) = 12\)

\(\sigma = \sqrt{\lambda} = \sqrt{12}\)

The probability, using continuity correction, is P(X > 20 + 0.5) = P(X > 20.5), which is 1 subtracted by the p-value of Z when X = 20.5.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{20 - 12}{\sqrt{12}}\)

\(Z = 2.31\)

\(Z = 2.31\) has a p-value of 0.9896.

1 - 0.9896 = 0.0104

0.0104 = 1.04% probability that the shop sells more than 20 in a month.

The probability of the selling the video recorders for considered cases are:

Let X ~ Pois(λ)

Then we have:

E(X) = λ = Var(X)

Since standard deviation is square root (positive) of variance,

Thus,

Standard deviation of X = \(\sqrt{\lambda}\)

Its probability function is given by

f(k; λ) = Pr(X = k) = \(\dfrac{\lambda^{k}e^{-\lambda}}{k!}\)

For this case, let we have:

X = the number of weekly demand of video recorder for the considered shop.

Then, by the given data, we have:

X ~ Pois(λ=3)

Evaluating each event's probability:

Case 1: At least 3 in a week.

\(P(X > 3) = 1- P(X \leq 2) = \sum_{i=0}^{2}P(X=i) = \sum_{i=0}^{2} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 3) = 1 - e^{-3} \times \left( 1 + 3 + 9/2\right) \approx 1 - 0.4232 = 0.5768\)

Case 2: At most 7 in a week.

\(P(X \leq 7) = \sum_{i=0}^{7}P(X=i) = \sum_{i=0}^{7} \dfrac{3^ie^{-3}}{i!}\\\\P(X \leq 7) = e^{-3} \times \left( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120 + 729/720 + 2187/5040\right)\\\\P(X \leq 7) \approx 0.9881\)

Case 3: More than 20 in a month(4 weeks)

That means more than 5 in a week on average.

\(P(X > 5) = 1- P(X \leq 5) =\sum_{i=0}^{5}P(X=i) = \sum_{i=0}^{5} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 5) = 1- e^{-3}( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120)\\\\P(X > 5) \approx 1 - 0.9161 \\ P(X > 5) \approx 0.0839\)

Thus, the probability of the selling the video recorders for considered cases are:

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x = 65

Step-by-step explanation:

cos theta = 25/x

cos theta = x/169

25/x = x/169

x² = 169 x 25

x = 65

The missing length x = 65, using the Pythagoras Theorem.

According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

In the question, we are asked to find the value of x.

In the right triangle ABC, by Pythagoras' Theorem,

AC² + BC² = AB²,

or, x² + BC² = (144 + 25)²,

or, BC² = 169² - x² ... (i).

In the right triangle ACD, by Pythagoras Theorem,

AD² + DC² = AC²,

or, 25² + DC² = x²,

or, DC² = x² - 25² ... (ii).

In the right triangle BCD, by Pythagoras Theorem,

BD² + DC² = BC²,

or, 144² + x² - 25² = 169² - x² {Substituting BC² = 169² - x² from (i) and DC² = x² - 25² from (ii)},

or, x² + x² = 169² + 25² - 144² {Rearranging},

or, 2x² = 28561 + 625 - 20736,

or, 2x² = 8450,

or, x² = 4225,

or, x = √4225 = 65.

Thus, the missing length x = 65, using the Pythagoras Theorem.

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Answer:

K = 4 ; N = 106

Step-by-step explanation:

Given the following :

Source of VARIATION - SS - df - - MS - - - - - F

Between groups - 1,959.79 - 3 - - 653.26 - 21.16*

Error - - - - - - - - 3,148.61 - - - - 102 - - 30.86

Total - - - - - - - - - - - 5,108.41 - 105

The degree of freedom between group (treatment) (DFT) is obtained using the formula ;

K - 1, where k = number of groups observed

DFT = K - 1 ; From the ANOVA table, DFT = 3

3 = K - 1

3 + 1 = K

K = 4

To obtain sample size (N) :

Degree of freedom of Error (DFE) is the difference between the sample size and the number of groups observed.

DFE = N - K ; From. The table DFE = 102 ; K = 4

102 = N - 4

102 + 4 = N

N = 106

Answer:

0.77

Step-by-step explanation:

From the information given:

The breakdown time (a)= 3 hours

The breakdown rate (λ) = 1/a = 1/3

Average flow time in the system (W) = 2.305 hours

For the entire system;

The average down machines L = Wλ

= 2.305 × (1/3)

= 0.77

Answer:

The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.

Answer:

(-4,-2)

Step-by-step explanation:

Answer: 2000

Step-by-step explanation: First, let's focus on the number 484. Let's always ask ourselves this: "Is this number (484 in our case) greater than 500?"

I say 500 because that's the number that we start to round up to the nearest thousandth. So, 484 is less than 500, telling us to round down.

So, therefore 2484 rounded to the nearest thousand is 2000. I hope this helped.