If the third and fourth term of an arithmetic sequence are -1 and -4, what are the first and second terms?

(a) To compute the experimental probability of rolling a 1 or 6 from Latoya's results, we need to determine the number of times a 1 or 6 was rolled and divide it by the total number of rolls Latoya made.

Let's assume that Latoya rolled the dice 100 times and obtained 20 1's and 10 6's. The total number of successful outcomes (rolling a 1 or 6) is 20 + 10 = 30.

Therefore, the experimental probability of rolling a 1 or 6 is 30/100 = 0.3 or 30%.

(b) Assuming the cube is fair, the theoretical probability of rolling a 1 or 6 can be determined by considering the favorable outcomes (rolling a 1 or 6) divided by the total possible outcomes (rolling any number from 1 to 6).

Since there are two favorable outcomes (1 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6), the theoretical probability is 2/6 = 1/3 or approximately 0.3333.

(c) The correct statement is B. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is due to the law of large numbers, which states that as more trials are conducted, the experimental probability tends to converge towards the theoretical probability. However, it is not necessary for them to be exactly equal. Random variations can cause some discrepancy, but with a larger number of rolls, the experimental probability should approach the theoretical probability more closely.

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Answer:

9.8

Step-by-step explanation:

Answer:

9.9

Step-by-step explanation:

Answer:

The answer to this question should be D. 0.67

Hope this helped.

Raspberries must be more expensive than both strawberries and blueberries. Thus, the statement is true. Hence, option A is correct.

The statement "Raspberries cost more than strawberries and blueberries" is true based on the given information. The first two statements indicate that blueberries are more expensive than strawberries and less expensive than raspberries.

So the only logical conclusion is that raspberries must be more expensive than both strawberries and blueberries. Therefore, the answer is option A true.

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The complete question is -

Blueberries cost more than strawberries. Blueberries cost less than raspberries. Raspberries cost more than strawberries and blueberries. If the first two statements are true, the third statement is A. true B. false C. uncertain.

Answer:

hola como estas soy de guatemala

It would take them approximately 6.24 hours (or 6 hours and 14 minutes) to complete the order if they work together.

To solve this problem, we can use the formula:

Time = Work ÷ Rate

Time is the time it takes to complete the job, Work is the amount of work to be done, and Rate is the rate of work.

Let's assume that the amount of work to be done is 1 (it doesn't matter what unit we use as long as we are consistent).

Then, Maria's rate of work is 1/12 (she can do 1 job in 12 hours) and the new clerk's rate of work is 1/13 (he can do 1 job in 13 hours).

If they work together, their combined rate of work is the sum of their individual rates:

Rate = Maria's rate + New clerk's rate

Rate = 1/12 + 1/13

Rate = (13 + 12) / (12 x 13)

Rate = 25 / 156

So, their combined rate of work is 25/156 jobs per hour.

Now, we can use the formula to find the time it takes for them to complete the job together:

Time = Work ÷ Rate

Time = 1 ÷ (25/156)

Time = 156/25

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Centroid, orthocenter, circumcenter, and incenter are the four locations that commonly concur.

A segment whose ends are the triangle's vertex and the middle of the other side is called a median of a triangle. A triangle's three medians are parallel to one another. The centroid, also known as the point of concurrency, is always located inside the triangle.

The incenter of a triangle is the location where the three angle bisectors meet. The only point that can be inscribed into the triangle is the center of the circle, which is thus equally distant from each of the triangle's three sides.

Draw the medians BE, CF, and their intersection at point G in the triangle ABC. Create a line from points A through G that crosses BC at point D. We must demonstrate that AD is a median and that medians are contemporaneous at G since AD bisects BC (the centroid)

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If f(x) = g(x)

Then :

(x-4)/(x²+1) = (x² - 4) / (x²+ 1)

We can simplify on both sides by x² + 1 :

x - 4 = x² - 4

x = x²

x - x² = 0

x(1-x) = 0

So either x = 0, or x = 1

S = {0,1}

Good Luck

Answer:

Step-by-step explanation:

( x , y )

( 0 , - 4 )

( 1 , - 1.5 )

\(y_{1}\) = - 4

\(y_{2}\) = - 1.5

Answer:

The sample required is  \(n = 135\)

Step-by-step explanation:

From the question we are told that

     The  standard deviation is  \(\sigma = 9\)

      The margin of error is \(E = 2\)

Given that the confidence level is  99%  then the level of  significance is mathematically evaluated as

         \(\alpha = 100-99\)

        \(\alpha = 1 \%\)

        \(\alpha = 0.01\)

Next we will obtain the critical value  \(\frac{\alpha }{2}\) from the normal distribution table(reference  math dot armstrong dot edu) , the value is  

             \(Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 2.58\)

The  sample size is mathematically represented as

          \(n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2\)

substituting values

           \(n = [ \frac{ 2.58 * 9 }{2} ]^2\)

            \(n = 135\)

Answer: No, the answer is 29, this is false.

Step-by-step explanation: 63-x=34

subtract 63 from both sides

34-63= -29

-x=-29

divide both sides by the negative and you get 29

plug in 29 for x, 63-29=34

Answer:

$108

Step-by-step explanation:

Let n be the cost of a keychain, then the cost of a T-Shirt would be 4n. We can use this to set up an equation...

4n+n=135

Combine like terms

5n=135

Divide both sides by 5

n=27

Now we need to find how much she made from selling T-Shirts...

4n=4(27)=$108

Maurice has a pot that is 3/4 full of chicken stock. He then pours 2/3 of the stock into an identical pot to make soup. Therefore, how full is Mario's soup pot after he pours in the stock? So, the correct answer is  1/2.

Maurice's soup pot has 1/4 of the chicken stock remaining after pouring 2/3 of the stock into another identical pot. That means Mario's soup pot is filled with 2/3 of the initial amount of the chicken stock or 2/3 x 3/4 = 6/12 Or 1/2 is equivalent in fractions to 6/12. The soup pot is half full, so that's your answer. Hence, the answer is 1/2.

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The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:

Write the dividend and divisor in polynomial long division format:

_________________________

x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...

Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).

Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).

Subtract the result obtained in step 3 from the original dividend:

x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...

Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.

Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.

-3x^(2n-2) + 0x^(2n-3) + ... = -80

Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.

This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:

2n-2 = 0

2n = 2

n = 1

Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

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The equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is 16 = 2 1/2 + 2 1/4b (option b)

To start with, we know that the farmer picks 16 quarts of berries. Out of those, 2 1/2 quarts cannot be used, which means the farmer has 16 - 2 1/2 quarts of berries that can be used to make jam.

Now, the recipe requires 2 1/4 quarts of berries to make one batch of jam. Let's represent the number of batches of jam the farmer can make with the remaining berries as "b".

Therefore, the equation we need to find will relate the amount of remaining berries to the number of batches of jam the farmer can make is written as,

=> 16 = 2 1/2 + 2 1/4b

Hence the correct option is (b).

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Step-by-step explanation:

The graphs are not give but the graph looks like the above picture.

The roots of the given equation are rational for all values of p.

A second-degree algebraic equation known as a quadratic equation is used in mathematics (having one or more variables raised to the second power). It appears that ancient Egyptian mathematicians were not familiar with solving quadratic equations, despite evidence of this in old Babylonian cuneiform documents from the period of Hammurabi. They have played a significant role in the physics of accelerated motion, such as free fall in a vacuum, since Galileo's time. ax² + bx + c = 0 is a general quadratic equation in one variable, where a, b, and c are arbitrary constants (or parameters) and a is not equal to 0.

As per the given data:

The given quadratic equation is:

(p+1)x² + 2px + 3x = -2

Simplifying the equation:

(p + 1)x² + (2p + 3)x + 2 = 0

Now for roots to be rational:

b² - 4ac should be a perfect square.

(2p + 3)² - 4(p + 1)(2)

4p² + 12p + 9 - 8p - 8

4p² + 4p + 1

(p + 1/2)²

For all value of p, b² - 4ac is a perfect square.

Hence, the roots of the given equation are rational for all values of p.

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Answer:

Length = 4 cm

Breadth = 3 cm

Step-by-step explanation:

Its Simple, We use The Pythagoreas theorem,

We know that the Hypotenuse of a triangle squared is equal to the sum of the legs square,

So  A^2 + B^2 = C^2

substitute the values,

    3^2 + B^2 = 5^2

     9 + B^2 = 25.

Subtract 9 from both sides

    B^2 = 25 - 9

    B^2 = 16

     B = sqrt[16] = 4

I am assuming that you are not asking for an actual construction of a rectangle on paper, but if you are, just ask

Answer: As we know that the formula of outlier is

IQR = Q3 - Q1

= 52 - 32

= 20

52 + 1.5(20) = 82...

so anything above 82 is an outlier

now

32 - 1.5(20) = 2.

..anything below 2 is an outlier

so...the 83 is outlier

so correct option is D

hope it helps

Step-by-step explanation:

Answer:

juice wrld

Step-by-step explanation:

fast

Answer:

yuh

Step-by-step explanation:

The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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Answer:

Surface area = 528 cm²

Step-by-step explanation:

The net of the prism is composed of 2 equal triangles and 3 rectangles (only 2 are of the same dimensions)

Area of the 2 triangles:

Area of the 2 triangles = 2(½*bh)

= 2(½*6*8)

= 6*8

= 48 cm²

Area of the 2 equal rectangles:

Area = 2(L*W)

L = 20

W = 9

Area of the 2 equal rectangles = 2(20*9)

= 360 cm²

Area of the 3rd rectangle:

Area = L*W

L = 20

W = 6

Area = 20*6 = 120 cm²

✔️Surface area of prism = 48 + 360 + 120 = 528 cm²

Answer:

  total deposits: $35,100

Step-by-step explanation:

You have the value of an annuity earning 5% with payments of $65 a month for 45 years as $131,718.42. You want to know the total value of payments.

12 payments per year of $65 for 45 years will have a total value of ...

  12·65·45 = 35100

Total deposits will be $35,100.

The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

Given that

f(x) = 2x^2 - 2

g(x) = 4x/(x - 1)

So, we have

f(10) = 2(10)^2 - 2 = 198

g(-6) = 4(-6)/(-6 - 1) = 24/7

Here, we have

h(x) = (7x - 4)/5x

Where

1 < x < 5

So, we have

h(1) = (7(1) - 4)/5(1) = 3/5

h(5) = (7(5) - 4)/5(5) = 31/25

So the range is 3/5 < h(x) < 31/25

Here, we have

P(x) = (5x - 1)/(3 - x)

So, we have

x = (5y - 1)/(3 - y)

This gives

3x - xy = 5y - 1

So, we have

y(5 + x) = -1 - 3x

This gives

y = -(1 + 3x)/(5 + x)

So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

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Answer:

63

Step-by-step explanation:

Answer:

42,43,44

Step-by-step explanation:

yeah-ya...... right?

Answer:

Step-by-step explanation:

The three consecutive integers are:

x, x+1 and x+2.

So,

(x+2)*3 > 2x+1.

(x+2)*3 is equal to 3x + 6

so 3x+6-47 = 2x+1

If something +6, then -47, it is the same as -41.

3x-41 = 2x+1

Which is the same as:

3x = 2x+42

So x is 42.

The integers therefore are

42, 43 and 44.

To test this, 44x3 is 132.

42+43=85

132 - 85 is 47.

\(a \: = \: square \: area \: + \: triangle \: area \: + \: rectangle \: area \: \\ \)

\(a \: = (3 \times 3) + ( \frac{1}{2} \times 3 \times 11) + (3 \times 11) \\ \)

\(a = 9 + \frac{33}{2} + 33 \\ \)

\(a = 9 + 16.5 + 33\)

\(a = 25.5 + 33\)

\(a = 58.5 \: \: {ft}^{2} \)

What happens to frogs who double park?

They get toad

haha get it?

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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Project's cost at time 0 is $46,272.84

What is profitability index?

Profitability index is the present value of future cash flows divided by the project cost at time 0.

The present value of each future cash flow can be determined using the present value formula of a single cash flow as  below;

PV=FV/(1+r)^N

FV=future cash inflows in years 1-4

r=discount rate=8.5%

N=the year of cash flows, 1 for year 1 , 2 for year 2, 3 for year 3 and 4 for year 4.

PV of future cash flows=$12,150/(1+8.5%)^1+$12,600/(1+8.5%)^2+$15,700/(1+8.5%)^3+$10,200/(1+8.5%)^4

PV of future cash flow=$41,553.01

Profitability index=PV of future cash flows/Project cost

Profitability index= .898

Project cost=unknown(assume it is X)

.898=$41,553.01 /X

X=$41,553.01/ .898

X=project's cost=$46,272.84

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