Draw a model to show a 26-pack of candy bars divided equally among 7 people. How
many candy bars will each person have?

(2) The first five terms of the sequence are, -3, -1, 1, 3, 5.

(3) The explicit rule is,  \(a_n = 5 + (n-1)(-2)\).

The recursive rule is, \(a_n = a_n_-_1 + (-2)\).

(5) The fourth term of the sequence is, -28.

What is recursive rule and explicit rule?

The value of any term in a series can be determined using an explicit formula for the sequence. The integers are divided into the natural numbers, which are 1, 2, 3, 4, etc.

If you know the value of the (n-1)th term in a sequence, you may use a recursive formula to find the value of the nth term in the sequence.

(2) Let, \(a_n = 2n - 5\)

So,

\(a_1 = 2(1) - 5 = -3\\a_2 = 2(2) - 5 = -1\\a_3 = 2(3) - 5 = 1\\a_4 = 2(4) - 5 = 3\\a_5 = 2(5) - 5 = 5\)

The first five terms of the sequence are, -3, -1, 1, 3, 5.

(3) The given sequence is 5, 3, 1, -1, 1, ...

The explicit rule is: \(a_n=a_1+(n-1)d\)

where,

\(a_n\) = nth term

\(a_1\)= First term

n = number of terms

d = common difference.

Here, \(a_1\) = 5 and d = -2

So, Explicit rule: \(a_n = 5 + (n-1)(-2)\)

Recursive rule is: \(a_n=a_n_-_1+ d\)

Here, d = -2

So, Recursive rule: \(a_n = a_n_-_1 + (-2)\)

(5) Let \(a_n = 3a_n_-_1 + 2\)

Here \(a_1= -2\)

We have to find the fourth term of the sequence.

\(a_2 = 3a_1 + 2= 3(-2)+2=-6+2=-4\\a_3 = 3a_2+2=3(-4)+2=-12+2=-10\\a_4 = 3a_3+2=3(-10)+2=-30+2=-28\)

Hence, the fourth term of the sequence is -28.

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Answer:

f(3)=-10

Step-by-step explanation:

f(3)=-4(3)+2=-12+2=-10

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer:

x = 4, -2

Step-by-step explanation:

x^2-2x=8

Move the constant term to the right side of the equation.

x^2 - 2x = 8

Take half of the coefficient of x and square it.

(-2/2)^2 = 1

Add the square to both sides of the equation.

x^2 - 2x + 1 = 8 + 1

Factor the perfect square trinomial.

(x - 1)^2 = 9

Take the square root of both sides of the equation.

x-1=\(\sqrt{9}\)
x-1=±3

Isolate x to find the solutions.

Taking positive

x=3+1=4

x=4

Taking negative

x=-3+1

x=-2

The solutions are:

x = 4, -2

Answer:

\(x = -2,\;\;x=4\)

Step-by-step explanation:

To solve the quadratic equation x² - 2x = 8 by factoring, subtract 8 from both sides of the equation so that it is in the form ax² + bx + c = 0:

\(x^2-2x-8=8-8\)

\(x^2-2x-8=0\)

Find two numbers whose product is equal to the product of the coefficient of the x²-term and the constant term, and whose sum is equal to the coefficient of the x-term.

The two numbers whose product is -8 and sum is -2 are -4 and 2.

Rewrite the coefficient of the middle term as the sum of these two numbers:

\(x^2-4x+2x-8=0\)

Factor the first two terms and the last two terms separately:

\(x(x-4)+2(x-4)=0\)

Factor out the common term (x - 4):

\((x+2)(x-4)=0\)

Apply the zero-product property:

\(x+2=0 \implies x=-2\)

\(x-4=0 \implies x=4\)

Therefore, the solutions to the given quadratic equation are:

\(\boxed{x = -2,\;\;x=4}\)

Answer:

D.

Step-by-step explanation:

6a² = surface area for cube

6(5)² = 150

2\(\pi\)(r)(h)+2\(\pi\)r²  = surface area cylinder

2\(\pi\)(2)(3)+2\(\pi\)(4) = 20pi

150 + 20pi = 212.8318531

The annual equivalent cost (AEC) for the pickup truck is $4,308. We found the equivalent uniform annual cost (EUAC) first.

To calculate the AEC, we need to first find the equivalent uniform annual cost (EUAC) which includes both the initial cost and the present value of the maintenance and operation costs.

Find the present value of maintenance costs over five years using the gradient formula:

where A = $135, i = 12%, g = 0, n = 5

PV maintenance = $501.21

Find the present value of operating costs over five years using the present value formula:

where C = $0.2/mile * 344 miles/month * 12 months/year = $827.52/year, i = 12%, n = 5

PV operation = $3,322.08

Find the EUAC using the formula:

where A/P = [(1+i)^n * i] / [(1+i)^n - 1]

Finally, convert the EUAC to AEC by adding the present value of the salvage value and multiplying by the interest rate:

where PV salvage = $3,580 / \((1+i)^5\)

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The Probability that an incoming lot contain 36% of imperfect cloths will be acceptable is 0.00957

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1,

Given that Cappelli Inc. designs and manufactures women's apparel using material from various mills.

Their acceptance sampling plan states that 10 two inch squares of the incoming material must be carefully checked. If 3 or less squares reveal imperfections, the lot is accepted

Here no of defects in the 10 checked is Binomial because each trial is independent and there are only two outcomes.

X = no of defects is Bin (10, 0.36)

The probability  that an incoming lot from Blufton Mills that contains 36 percent imperfect cloth will be accepted

P (X ≤ 3) = 0.00957.

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Answer:

a six sided dice roling a seven

Step-by-step explanation:

Answer:

1.1 apeex

Step-by-step explanation:

Answer:

Step-by-step explanation:

The milepost number of the rest area is 7 miles away from milepost 58, so it can be represented by the equation:

m = 58 + 7

This equation states that the milepost number of the rest area is equal to 58 plus 7, or 65. Therefore, the rest area can be located at milepost 65.

Answer:

attached below

Step-by-step explanation:

loops have permutations , steps to  show that the given set of permutations is a stationary distribution is attached below

We can represent the sum of the three consecutive integers as:

Then, we need to solve the equation for n, then:

Then, the largest of the integers is n + 2 or 58 +2 = 60.

The reason is that the other integers are 58, 58 + 1 = 59, that is, 58 and 59.

We can check that:

58 + 59 + 60 = 177.

Answer:

No

Step-by-step explanation

The square root of 10 is irrational because it isn't a fraction

A statement that describes the median of a triangle include the following: A. a segment drawn from a vertex to the midpoint of the opposite side.

In Mathematics and Geometry, a triangle is a two-dimensional geometric shape that comprises three sides, three vertices and three angles only.

In Mathematics and Geometry, the median of a triangle can be defined as a line segment with end points that is typically drawn from a vertex to the midpoint of the opposite side of the triangle.

In this context, we can logically deduce that a line segment with end points at the vertex and the midpoint of the triangle's opposite side simply refers to the median of a triangle.

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04) The complementary angles are the angles whose sum is 90° thus { 26°,54°,48°,29°,22°} will be the corresponding angles.05)The supplementary angles are the angles whose sum is 180° thus {54°,48°,12°,135°,91°} will be the corresponding angles.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

If m∠A + m∠B = 90° then A and B will be the complimentary angle.

The complementary of 64° = 90° - 64° = 26°

The complementary angle of 36° = 90° - 36° = 54°

The complementary angle of 42°= 90° - 42° = 48°

The complementary angle of 51°= 90° - 51° = 29°

The complementary angle of 68°= 90° - 68° = 22°

If m∠A + m∠B = 180° then A and B will be the supplementary angle.

The supplementary of   = 180° - 126°  = 54°

The supplementary of   = 180° -  132° = 48°

The supplementary of   = 180° - 178°  = 12°

The supplementary of   = 180° -   45° = 135°

The supplementary of   = 180° -  89°  = 91°

Hence " { 26°,54°,48°,29°,22°} will be the corresponding complementary angle and {54°,48°,12°,135°,91°} will be the corresponding supplementary angles".

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Given

To Determine: The system of equations

From the first statement

From the second statement

Hence, the system of equations representing the given information are

The correct option is OPTION D

Answer:

2e14

Step-by-step explanation:

Just use the calculator and that is what i got

Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

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Question:

Are the lines in the diagram perpendicular, parallel, skew, or none of these?

Answer:

l and m:

none of these

l and n:

skew

m and n:

perpendicular

Answer:

l and m:

✔ none of these

l and n:

✔ skew

m and n:

✔ perpendicular

I guess it sort of depends on whether you are folding the rectangle in half "long-ways" or "short-ways", however, if the rectangle is folded "long-ways", then the length of the new long side would be 5.5, with the shorter end being 4.25, or just 4.2.

Hope this helps!

Answer: 1000000

Step-by-step explanation:

Answer:

answer 1000000

have a nice day

Answer:

31906.hope it helps you.

Step-by-step explanation:

742*73=31906

Based on the given data, the probability that exactly 2 insects will survive is 0.1402 rounded to four decimal places.

The probability mass function for the binomial distribution is given by:

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

where X is the random variable representing the number of successes (surviving insects), k is the specific number of successes we're interested in (k=2 in this case), n is the total number of trials (n=11), p is the probability of success (p=0.3), and (n choose k) is the binomial coefficient, which is the number of ways to choose k objects from a set of n objects.

Plugging in the values, we get:

P(X=2) = (11 choose 2) * 0.3² * 0.7²

= (55) * 0.09 * 0.02825

= 0.1402

Therefore, the probability that exactly 2 insects will survive is 0.1402 (rounded to four decimal places).

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Answer:

384 ounces

Step-by-step explanation:

1 pound = 16 ounces

8 pounds = 128 ounces

1 bag = 8 pounds

1 bag = 128 ounces

3 bags = 24 pounds

3 bags = 384 ounces

Answer:

384 ounces

Step-by-step explanation:

There are 16 ounces per pound, so if you multiply that by 8 you get 128, and then you multiply that by 3 to get the total ounces which is 384

Based on the observed in the picture, you can notice that:

Knowing that:

You can substitute values into the equation and then solve for "x". You get that its value is:

Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).

Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).

Answer:

33 \(\frac{99}{100}\)

Step-by-step explanation:

hope this helps :)

Answer:99/100

Step-by-step explanation:

Answer:

Step-by-step explanation:

y  =2/3x  +  1/3

slope 2/3

y-intercept:   (0  ,1/  3)

Answer:

Step-by-step explanation:

- 2x + 3y = -1​ is the equation of a line

Pick any values for x then find y or for y and then find x;

if you have two points you can draw a line trough those two points.

For example,

pick x= -1 then find y

- 2*(-1) + 3y = -1​

         2+ 3y = -1

              3y = -1-2

                y= -3/3

                y= -1

First point has the coordinates (-1, -1)

pick y = 1 then find x

- 2x + 3*1  = -1​

      -2x +3 = -1

           -2x = -1-3

            -2x = -4

                x= -4/-2

                x= 2

Second point has the coordinate (2, 1)

Draw a line trough the points (-1, -1) and (2,1) to sketch the graph of -2x+3y = -1

Answer:

sorry if im wrong but im pretty sure -5/3

Step-by-step explanation:

Answer:

2/1

Step-by-step explanation:

A calculator showed me that this was the answer. I would give you the link but I would probably get deleted. I already got warned so yeah.

Hope this helps!

Answer:

2w=c 2 times each week so 2 times how many weeks