Determine the 10th term of the sequence –17, -13,-9, ...
A. 19
B. -53
C. 36
D. 53

Step-by-step explanation:

Let's call the shorter base of the trapezoid "b1", the longer base "b2", and the height "h". We can use the formula for the surface area of a right prism to set up an equation:

Surface area of prism = 2(base area) + (lateral area) = 1280

The base area is the area of the trapezoid, which is given by:

(base area) = (1/2)(b1 + b2)h

The lateral area is the area of the four rectangular faces of the prism, which are all congruent. Each face has an area equal to the product of the height and the length of one of the legs of the trapezoid, so the lateral area is:

(lateral area) = 4hl

where l is the length of one of the legs of the trapezoid.

Substituting these expressions into the formula for the surface area of the prism, we get:

2[(1/2)(b1 + b2)h] + 4hl = 1280

Simplifying and rearranging, we get:

h(b1 + b2) + 2hl = 1280

We also know that the sum of the lengths of the legs of the trapezoid is 52 feet, which means:

l1 + l2 = 52

But we can express l1 and l2 in terms of b1 and b2 using the formula for the area of a trapezoid:

(base area) = (1/2)(b1 + b2)h = (1/2)(l1 + l2)h

Simplifying, we get:

b1 + b2 = (l1 + l2)h

Substituting this into the previous equation, we get:

h[(l1 + l2)h] + 2hl = 1280

Simplifying, we get:

h^2(l1 + l2) + 2hl = 1280

Substituting l1 + l2 = 52, we get:

h^2(52) + 2hl = 1280

This is a quadratic equation in h. We can solve it using the quadratic formula:

h = [-2l ± sqrt(4l^2 + 4h^2(52)(1280 - 2hl))] / 2(52)

Simplifying and factoring out a 2, we get:

h = [-l ± sqrt(l^2 + h^2(1280 - 2hl))] / 52

We have two possible solutions for h, but one of them is negative, which doesn't make sense in the context of the problem. So we can discard the negative solution and focus on the positive one:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

We don't know the exact value of h yet, but we can use this equation to set up a system of equations that we can solve for h. Specifically, we can use the fact that the legs of the trapezoid add up to 52 feet to solve for l in terms of b1 and b2:

l = 52 - (b1 + b2)

Substituting this into the equation for h, we get:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

h = [-52 + (b1 + b2) + sqrt((52 - (b1 + b2))^2 + h^2(1280 - 2h(b1 + b

Answer:

x = 10

y = 4

Hope this helps :)

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Answer:

x= 1.62500

Step-by-step explanation:

Step 1- Distribute into the parenthesis.

(12)4x-(12)5= 18

Step 2- Multiply to simplify.

48x-60= 18

Step 3- Add 60 to both sides.

48x-60= 18

     +60 +60

48x= 78

Step 4- Divide both sides by 48.

48x= 78

48    48

x= 1.62500

Hope this helps!

Answer:

We conclude that Neither A nor B represents the function.

Hence, the correct option is:

Step-by-step explanation:

A function relates an input to an output.

For example, a certain animal grows 30 cm each year. Thus, the height of the animal is associated with its age using the function

h (age) = age × 30

Therefore, if the age of the animal is 3 years, the height is:

h(3) = 3 × 10 = 90 cm

Set A

A = {(1, −5), (8, −5), (8, 7), (2, 9)}

Please check that there are duplicated inputs.

i.e. x = 8 is appeared twice.

Thus, set A does not represent the function because the function has repeated inputs or x-values. In other words, each input is not related to exactly one output.

Therefore, the set A of ordered pairs does not represent a function.

Set B

B = {(7, −4), (7, −2), (6, −3), (−9, 5)}

Please check that there are duplicated inputs.

i.e. x = 7 is appeared twice.

Thus, the set B does not represent the function because the function has repeated inputs or x-values. In other words, each input is not related to exactly one output.

Therefore, the set B of ordered pairs also does not represent a function.

Conclusion:

We conclude that Neither A nor B represents the function.

Hence, the correct option is:

The  Ivan ran a total distance of 550 meters and the Ivan's displacement was 150 meters to the east.

1. To calculate the distance, we need to add up all the distances Ivan ran, regardless of the direction.

Total distance = 300 m + 200 m + 50 m = 550 m

2. To calculate the displacement, we need to find the net change in Ivan's position, which takes into account both distance and direction.

We can start by drawing a diagram to represent Ivan's motion:

      <--- 300 m --->  <--- 200 m ---> <--- 50 m --->

              East              West             East

                (+)               (-)              (+)

Here, the arrows represent the direction of Ivan's motion, and the symbols (+) and (-) represent the direction of his displacement.

To find the displacement, we can add up the individual displacements:

Displacement = +300 m - 200 m + 50 m = +150 m

The positive sign indicates that Ivan ended up 150 meters east of his starting position.

So Ivan's displacement was 150 meters to the east.

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Answer:

Her results changed because the power increased due to the fact that she reduced variability in her data as a result of using a sample that had lesser variability.

Step-by-step explanation:

She is trying to find if there is difference between people who consumed 1 versus 2 beverages.

Now initially she surveyed 40 people between ages 18 to 38 years and of huge weights and found out there was no difference. However, she decided to run the survey again on only women aged 18 to 22 years with normal body weight.

Since she used a lesser sample size and surveyed only women, it means there will be lesser variability in the result as the sample is smaller and streamlined to only women.

Thus, her result changed because the power increased due to the fact that she reduced variability in her data as a result of using a sample that had lesser variability.

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Answer:

1,10

Step-by-step explanation:

The initial point of the vector is P(2,−4) and the terminal point of the vector is Q(3,6).

Subtract the coordinates of the initial point from the coordinates of the terminal point.

PQ−⇀−=<xQ−xP,yQ−yP>

Substitute the coordinates of the given points.

PQ−⇀−=<3−2,6−(−4)>

Simplify.

PQ−⇀−=<1,10>

Therefore, the component form of vector PQ−⇀− is <1,10>.

The component form of the vector is A =  i + 10j , PQ = < 1 , 10 >

The i,j notation can be used to describe a vector. In Cartesian coordinates, the unit vectors along the axis are represented by the letters I and j, respectively.

A unit vector is a vector of length 1. It is possible to express any two-dimensional vector in the manner ai + bj.

To find the vector in component form given the initial and terminal points, simply subtract the initial point from the terminal point.

Given data ,

Let the component form be represented as A

Let the first point be represented as P

Now , the coordinates of the initial point = P ( 2 , -4 )

The coordinates of the terminal point is = Q ( 3 , 6 )

And , the vector in component form given the initial and terminal points, simply subtract the initial point from the terminal point.

So , on simplifying , we get

A = PQ = ( 3 - 2 ) i + ( 6 - ( - 4 ) ) j

PQ = i + 10j

PQ = < 1 , 10 >

Therefore , the value of A is  i + 10j

Hence , the component form is PQ = < 1 , 10 >

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Answer:

F(t)=6t+15t^2−16/3 t^3 + C

Step-by-step explanation:

hope this helps

Answer:

x= 104

Step-by-step explanation:

Angle in a triangle is 180

35+41+x=180

76+x=180

x=180-76

x=104

Answer:

The 95% confidence interval for the population proportion of all persons who do not have any health insurance is (0.148, 0.192).

Here is the calculation:

Sample size = 800

Number of persons who do not have any health insurance = 120

Sample proportion = 120 / 800 = 0.15

Confidence level = 95%

Z-critical value for 95% confidence level = 1.96

Confidence interval = (sample proportion - Z-critical value * standard error of the sample proportion, sample proportion + Z-critical value * standard error of the sample proportion)

Standard error of the sample proportion = sqrt(sample proportion * (1 - sample proportion) / sample size)

Standard error of the sample proportion = sqrt(0.15 * (1 - 0.15) / 800) = 0.0128

Confidence interval = (0.15 - 1.96 * 0.0128, 0.15 + 1.96 * 0.0128)

Confidence interval = (0.148, 0.192)

Step-by-step explanation:

Answer:

answer is 3.75 step-by-step explanation:

750÷2= 375 ..3.75

Answer:

u-7 = ?

13u-9=4

13u=13

u=1

1-7=-6

answer is -6

Step-by-step explanation:

(a) To plot the point (6, 1/3, 1/6), we first convert to Cartesian coordinates as follows:

x = r sinφ cosθ = 6(1/3)cos(1/6π) ≈ 2.991

y = r sinφ sinθ = 6(1/3)sin(1/6π) ≈ 0.499 z = r cosφ = 6 cos(1/3π) ≈ 5.196

Therefore, the rectangular coordinates of the point (6, 1/3, 1/6) are approximately (2.991, 0.499, 5.196).

(b) To plot the point (3, 7/2, 37/4), we first convert to Cartesian coordinates as follows:

x = r sinφ cosθ = 3(1/2)cos(37/8π) ≈ -1.149

y = r sinφ sinθ = 3(1/2)sin(37/8π) ≈ -1.172 z = r cosφ = 3 cos(7/4π) ≈ -1.097

The rectangular coordinates of the point (3, 7/2, 37/4) are approximately (-1.149, -1.172, -1.097).

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Answer:

The undefined terms needed to define parallel lines are 'lines' and 'points. ' In geometry, there are three undefined terms: points, lines

Step-by-step explanation:

The matrix exponential eAt can be expressed as:

eAt = (5/4)*e^(3t/2) * [1 3/5; 2/5 1]

Sketching the phase plane, we can see that it represents a spiral source. The solution X(t) satisfying X(0) = [-2] can be found by substituting

t=0 and X(0) = [-2] in the general solution as follows:

X(t) = e^(3t/2) * [1 3/5; 2/5 1] * [-2]X(t) = [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)]

Hence, the solution X(t) satisfying

X(0) = [-2] is X(t) = [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)].

Given system of differential equation is

X'

= AX, where [2 - A

= 3 2

We need to find the general solution, sketch the phase plane and determine its type.The general solution is given by: X(t)

= eAt X(0)

Where eAt is the matrix exponential. Since A is a 2x2 matrix, we can find eAt by using the formula:

eAt

= (I + tA + (t^2/2!)A^2 + (t^3/3!)A^3 + ....)

The matrix exponential eAt can be expressed as:

eAt

= (5/4)*e^(3t/2) * [1 3/5; 2/5 1]

Sketching the phase plane, we can see that it represents a spiral source. The solution

X(t) satisfying X(0)

= [-2]

can be found by substituting t

=0 and X(0)

= [-2] in the general solution as follows:

X(t)

= e^(3t/2) * [1 3/5; 2/5 1] * [-2]X(t)

= [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)]

Hence, the solution X(t) satisfying

X(0)

= [-2] is X(t)

= [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)].

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Answer:

Each friend will get 1/9 of the pizza (I think).

Step-by-step explanation:

I believe you would divide 1/3 by 3, or in other words, multiply 1/3 * 1/3:

1/3 * 1/3 = 1/9

Have a nice day!! It would be TOTALLY RAD if I could get brainliest!!!

While allowing subjects to choose their preferred TV show might seem intuitively appealing, random assignment is generally preferred in experimental designs to reduce confounding and provide more reliable results.

Allowing subjects to choose the type of TV show they want to watch could potentially introduce biases and confounding factors into the study. If participants have the freedom to select the content they prefer, they may be more likely to choose shows that align with their pre-existing attitudes and preferences. This could introduce systematic differences between the groups and make it difficult to isolate the effects of violence and sex in the content on memory recall.

By randomly assigning subjects to different types of TV shows, the researchers can create comparable groups that are balanced in terms of individual characteristics and preferences. This random assignment helps to reduce confounding variables and allows for a more accurate evaluation of the impact of violence and sex on memory recall

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First Question:

Follow PEMDAS

Parentheses, Exponents, Multiplication or Division, Addition or Subtraction

3 ÷ \(\frac{1}{4}\) × (12 + 2³)

= 3 ÷ \(\frac{1}{4}\) × (12 + 8)

= 3 ÷ \(\frac{1}{4}\) × (20)

= 3 × 4 × 20

= 12 × 20

= 240

Second Question:

change the mixed number into an improper fraction:

\(3\frac{2}{3}\) = \(\frac{11}{3}\)

= \(\frac{11}{3}\) ÷ \(\frac{3}{4}\)

= \(\frac{11}{3}\) × \(\frac{4}{3}\)

= \(\frac{44}{3}\)

rounded to WHOLE number: 14 containers

Part 1: Kate should buy 100 coats to maximize profits.Part 2: The probability that the coats sell out is 0.25 (25%), and the probability that they do not sell out is 0.75 (75%).

To maximize profits, Kate should consider the scenario where she sells all the coats without any left over at the end of the season.

Since the sales are uniformly distributed between 100 and 400, buying 100 coats ensures that she meets the minimum expected sales of 100. Purchasing more than 100 coats would increase costs without a guarantee of higher sales, potentially leading to excess inventory and lower profits.

Given that the sales are uniformly distributed between 100 and 400 coats, Kate's purchase of 100 coats covers the minimum expected sales.

The probability of selling out can be calculated by finding the proportion of the range covered by the desired sales (100 out of 300). Therefore, the probability of selling out is 100/300 = 0.25 or 25%. The probability of not selling out is the complement, which is 1 - 0.25 = 0.75 or 75%.

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The general solution of the differential equation is:

y = Ax^-5 + Bx^-5ln(x)

where A and B are constants determined by the initial or boundary conditions.

To solve the differential equation x^2y'' + 11xy' + 25y = 0, we can assume the solution to be of the form y = x^r, where r is a constant.

Then, we have:

y' = rx^(r-1)

y'' = r(r-1)x^(r-2)

Substituting these into the differential equation, we get:

x^2y'' + 11xy' + 25y = x^2r(r-1)x^(r-2) + 11xrx^(r-1) + 25x^r = 0

Dividing both sides by x^2, we have:

r(r-1) + 11r + 25 = 0

Simplifying, we get:

r^2 + 10r + 25 = (r+5)^2 = 0

Therefore, r = -5.

Thus, the general solution of the differential equation is:

y = Ax^-5 + Bx^-5ln(x)

where A and B are constants determined by the initial or boundary conditions.

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There are \(2^n-1\) different partitions of a set containing n elements into precisely two subsets.

imagine we have a set S containing n elements. We can choose to include each element in the first subset or the second subset, giving us a total of \(2^n\) possible combinations of subsets. However, we don't want to include the empty set or the entire set as one of our subsets, so we subtract those two possibilities from the total. This gives us \(2^n-2\) possible partitions. But each partition has a corresponding partition in which the two subsets are swapped (i.e. if A and B are two subsets in one partition, then the partition consisting of S-A and S-B is the corresponding partition), so we divide by 2 to get the final answer of \(2^n-1.\) Therefore, there are \(2^n-1\) different partitions of a set containing n elements into precisely two subsets.

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The equation of a circle with center (a, b) and radius r is:

(x - a)^2 + (y - b)^2 = r^2

(x, y) represents any point on the circle

A circle is described as a shape consisting of all points in a plane that are at a given distance from a given point, the center.

The properties of the circle are as follows:

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Answer:

13.8 cm^2

Step-by-step explanation:

Area of a triangle = 1/2 base * height

                              = 1/2 * 6.9 * 4 = 13.8 cm^2

The components of the vector with initial point (7,−6) and a terminal point at (6,−3) are:

The components of a vector are the vectors that makes up the resultant as described in the problem to have starting point (7,−6) and terminal point (6,−3).

This can be gotten by plotting these points and getting the coordinates of the points that makes the initial point and the terminal point the hypotenuse of the triangle

From the graph, the coordinates are:

component 1: (6, -6) to (3, -6)

component 2: (7, -6) to (6, -6)

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Answer: Hi the answer would be 32 Degrees

Step-by-step explanation:

Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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