Help me with this plsss

Help Me With This Plsss

Answers

Answer 1

1.

a. 8 x 7 x 1/2 = 56 x 1/2 = 28

b. 24 x 14 x 1/2 = 336 x 1/2 = 168

c. 5 x 12 x 1/2 = 60 x 1/2 = 30

d. 4 x 4.8 x 1/2 = 19.2 x 1/2 = 9.6

2.

two triangles: 2(4 x 8 x 1/2) = 4 x 8 = 32

rectangle: 15 x 8 = 120

total area: 32 + 120 = 152


Related Questions

If you left $25.00 on your table for a $21.50 meal, what was the percent of the tip?
A.15.0%
B.14.0%
C.18.4
D.16.3

Answers

Answer:

I THINK it would be B.

Step-by-step explanation:

I’m very sorry if I’m wrong.

Answer:

16.3%

Step-by-step explanation:

21.5 times 0.163= 3.5

A train travels along a horizontal line according to the function s(t) = –13 + 3t2 – 4t – 4 where t is measured in hours and s is measured in miles. What is the velocity of the train after 4 hours?

Answers

The velocity of the train after 4 hours is 20 miles per hour.

To find the velocity of the train after 4 hours, we need to differentiate the given function s(t) with respect to t.

Velocity is the derivative of position with respect to time.

That is,v(t) = ds(t)/dtTo differentiate s(t) = –13 + 3t² – 4t – 4, we differentiate each term separately.v(t) = d/dt(-13) + d/dt(3t²) - d/dt(4t) - d/dt(4)v(t) = 0 + 6t - 4

The velocity of the train after 4 hours is given by substituting t = 4 in the above equation.v(4) = 6(4) - 4 = 20

The velocity of the train after 4 hours is 20 miles per hour.To sum up, the velocity of the train after 4 hours is 20 miles per hour.

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In the figure shown, what is the measure of the indicated angle?

Answers

Answer:

60 degrees

Step-by-step explanation:

Each triangle needs to add up to 180 total degrees.  70+50=120,

180

-

120

___

60

Answer; 120

Why? because all triangles equal 180, so 70+50= 120 and 180-120= 60, all straight lines are 180 and 180-60= 120

A particular high school claims that its students have unusually high math SAT scores. A random sample of 50 students from this school was selected, and the mean math SAT score was 544. Is the high school justified in its claim? Explain since it within the range of a usual event, namely within of the mean of the because the score) sample means (Round to two decimal places as needed)

Answers

The school is not justified to make this claim because of the reasons defined.

The following is a statement that might be made about the high school to justify its claim No, because the z-score of Z = 1.06 is not uncommon because it does not fall within the range of a typical event, namely within 2 standard deviations of the sample mean.

It has been given to us that:

μ = 511

σ = 119

Sample size (n) = 55

and

s = 119 / √55

= 16.046

As we all know,

Only when z > 2 then, the high school's allegation is valid and warranted.

To locate,

Z's value is

So,

Z = ( X - μ )/σ

by applying the Central Limit Theorem to the values,

z = ( 528 - 511 ) / 16.046

= 1.06

Since, z < 2, as a result, the allegation is unjustified.

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Correct question:

The average math SAT score is 511 with a standard deviation of 119. A particular high school claims that its students have unusually high math SAT scores. A random sample of 55 students from this school was​ selected, and the mean math SAT score was 528. Is the high school justified in its​ claim? Explain. ▼ No Yes ​, because the​ z-score ​( nothing​) is ▼ unusual not unusual since it ▼ does not lie lies within the range of a usual​ event, namely within ▼ 1 standard deviation 2 standard deviations 3 standard deviations of the mean of the sample means. ​(Round to two decimal places as​ needed.)

here are the options



∠2and∠4



∠1and∠5



∠3and∠6

Answers

Answer:

∠1and∠5

Step-by-step explanation:

Hello There!

The image shown below shows an example of what corresponding angles look like

Properties of corresponding angles

Must be on the same side of the transversalMust be congruent

angles 2 and 4 are on the same side of the transversal however they are supplementary angles not congruent

angles 2 and 4 are an example of adjacent angles therefore this is not the answer

angles 1 and 5 are on the same side of the transversal and they are most definitely congruent

This might be our answer but lets check the last answer just to be sure

Angles 3 and 6 are congruent but they are not on the same side of the transversal

angles 3 and 6 are an example of alternate interior angles therefore this is not the correct answer

So we can conclude that angles 1 and 5 are corresponding angles

At a certain university, the average cost of books was $330 per
student last semester and the population standard deviation was $75. This
semester a sample of 50 students revealed an average cost of books of $365 per
student. The Dean of Students believes that the costs are greater this semester.
What is the test value for this hypothesis?

Answers

The test value for this hypothesis is 3.0.

What is the test value for the hypothesis that the average cost of books is greater this semester at a certain university?

The test value for this hypothesis can be calculated using the formula for a one-sample t-test:

test value = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Population mean (last semester) = $330Sample mean (this semester) = $365Sample size = 50Population standard deviation = $75

Calculating the test value:

test value = ($365 - $330) / ($75 / sqrt(50))

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What is the slope of the line connecting the pair of points (0,7) (4,12)

Answers

Answer: 5/4

Step-by-step explanation: That should be right because I have big brain. Mark brainlist please :)

The product of three consecutive non-zero integers is taken. Which statement must be true?

Select one:

O A. The third consecutive integer must be even,

B. The product must be odd,

C. Two of the three integers must be even.

D. The product must be even.

E. Two of the three integers must be odd.

©

Answers

Answer:

d

Step-by-step explanation:

integer is a whole number

imagine the sum of the first set of 3 integers = 4 + 5 + 6

product = 4 x 5 x 6 = 120

imagine the sum of the 2nd set of 3 integers = 6 + 7 + 8 = 21

6 x 7 x 8 = 3364

Let p be a real number with 0 < p < 1, and n an integer which is greater than or equal to one. Recall that a binomial random variable X is one for which Prob(X = k): = (*) p* (1 k (1 − p)n-k for k = 0,1, n, and Prob(X x) for any x other than one of these n+1 = possible values.
a. In the case n 3 and p = 3/4, compute E(X) and Var(X).
b. Using (a) as a model case, compute E(X) and Var(X) for any value of p and n. (Hint: Write the formula from the binomial theorem and use differentiation.)
c. What is the value of p such that Var(X) is the smallest?
d. For any t > 0, compute E(etx). (Hint: Use the binomial theorem.)

Answers

The expected value E(X) of a binomial random variable X can be calculated as n * p, and the variance Var(X) can be calculated as n * p * (1 - p). These formulas can be generalized for any values of p and n, and the value of p that minimizes the variance can be found by setting the derivative of Var(X) with respect to p equal to zero.

a. In part (a), we are given specific values for n (3) and p (3/4). The expected value E(X) of a binomial random variable X can be calculated as n * p, which gives us:

3 * 3/4

= 2.25.

The variance Var(X) can be calculated as n * p * (1 - p), which gives us:

3 * 3/4 * (1 - 3/4)

= 0.5625.

b. In part (b), we generalize the calculation of E(X) and Var(X) for any value of p and n. Using the binomial theorem, we can expand (p + (1 - p))ⁿ and differentiate it to find the coefficients for E(X) and Var(X).

c. To find the value of p that minimizes the variance Var(X), we can take the derivative of Var(X) with respect to p binomial, set it equal to zero, and solve for p. This will give us the value of p that minimizes the variance.

d. For any t > 0, we can calculate E(e^(tx)) using the binomial theorem by substituting e^t for p in the expansion of (p + (1 - p))ⁿ. This will give us the expected value of the exponential of tx.

Therefore, the expected value E(X) of a binomial random variable X can be calculated as n * p, and the variance Var(X) can be calculated as n * p * (1 - p). These formulas can be generalized for any values of p and n, and the value of p that minimizes the variance can be found by setting the derivative of Var(X) with respect to p equal to zero.

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Compute the Laplace transform of the function f on (0,0) defined by f(t) = { i Se4 0 3 Give your answer as a function in the variable s for s > 0. L(f)(s) =___

Answers

The Laplace transform of the function f on (0,0) defined by f(t) = i Se^4t is L(f)(s) = i S / (2s-4).

Given function is f(t) = i Se^4t

Here, Laplace transform of the function f is given by:

L(f)(s) = ∫[0,∞) e^(-st) f(t) dt

On substituting the given function in the above equation, we get:

L(f)(s) = ∫[0,∞) e^(-st) i Se^(4t) dt

L(f)(s) = i S ∫[0,∞) e^(t(4-s)) dt

We know that the Laplace transform of e^(at) is 1/(s-a).

Therefore, Laplace transform of e^(t(4-s)) = 1/(s - (4-s)) = 1/(2s - 4).

Therefore,L(f)(s) = i S * ∫[0,∞) e^(t(4-s)) dt

L(f)(s) = i S * 1/(2s-4) * [-e^(-(4-s)t)]_0^∞

L(f)(s) = i S * 1/(2s-4) * [0 - (-1)] (since the exponentials evaluated at ∞ is zero)

L(f)(s) = i S * 1/(2s-4) * 1

L(f)(s) = i S / (2s-4)

Therefore, the Laplace transform of the function f on (0,0) defined by f(t) = i Se^4t is  L(f)(s) = i S / (2s-4).

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What is the slope of a line perpendicular to the line y=2/3 x + 3 ( just find the slope)

Answers

the slope would be 3/2

Slove the system of the linear equations by either sus substitution or elimination 8x-12y=20 4x-4y=-4

Answers

Answer:

x = -8 and y = -7

Step-by-step explanation:

I will solve your system by substitution.

(You can also solve this system by elimination.)

8x−12y=20;4x−4y=−4

Step: Solve8x−12y=20for x:

8x−12y+12y=20+12y(Add 12y to both sides)

8x=12y+20

8x

8

=

12y+20

8

(Divide both sides by 8)

x=

3

2

y+

5

2

Step: Substitute

3

2

y+

5

2

forxin4x−4y=−4:

4x−4y=−4

4(

3

2

y+

5

2

)−4y=−4

2y+10=−4(Simplify both sides of the equation)

2y+10+−10=−4+−10(Add -10 to both sides)

2y=−14

2y

2

=

−14

2

(Divide both sides by 2)

y=−7

Step: Substitute−7foryinx=

3

2

y+

5

2

:

x=

3

2

y+

5

2

x=

3

2

(−7)+

5

2

x=−8(Simplify both sides of the equation)

The first one is 2x - 3y - 5 = 0
The second one is x - y + 1 = 0

The slope intercept form of these would be

The first one is y = 2/3x -5/3
The second one is y = x + 1

Phil has 5 times as many toy race cars as Richard has. Phil has 425 toy race cars. How many race cars does Richard have? *

Answers

Answer:

85

Step-by-step explanation:

425 divided by 8= 85

Answer:

He as 85 race cars.

Step-by-step explanation:

Just divide 425 by 5 and you have your answer.

Joe earns a monthly salary of 250 plus a commission on his total sales. Last month his total sales were $7,289 and he earned a total of $1,275. What is his commission rate?

Answers

Answer: Joe earns a monthly salary of 250 plus a commission on his total sales. Last month his total sales were $7,289 and he earned a total of $1,275. What is his commission rate?

Step-by-step explanation:  

250 + $7,289 + $1,275 = 8814

−8x 4y>3 6x−7y<−5 is (2,3) a solution of the system?

Answers

The ordered pair (2,3) is not a solution of the system

How to determine if (2,3) a solution of the system?

From the question, we have the following parameters that can be used in our computation:

−8x + 4y > 3

6x - 7y < −5

The solution is given as

(2, 3)

Next, we test this value on the system

So, we have

−8(2) + 4(3) > 3

-4 > 3 --- false

This means that (2,3) is not a solution of the system

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Write 3^4 in expanded form. (3^4 means 3 raised to the fourth power.)

A: 3x3
B :3x3x3
C: 3x3x3x3
D: 3x3x3x3x3

Answers

Answer:

c because 3.3.3.3 is 3 to the 4th power expanded

Danny has a scale drawing of his house. If
3 inches (in) on the scale drawing equals
7 feet on the real house, what is the actual
height of the house?
5.4 in

Answers

Answer:

151.2

Step-by-step explanation:

7x12=84

84/3=28

28x5.4=151.2

Pls help this is sooOOOOOOO annoying!!
(07.06)Number line with closed circle on 9 and shading to the left.

Which of the following inequalities best represents the graph above?

a > 9
a < 9
a ≤ 9
a ≥ 9

Answers

Answer:

a ≤ 9

Step-by-step explanation:

Closed circle means ≤ or ≥

Shading to the left means left direction < or ≤

The inequality sign that has both is: ≤

a ≤ 9

Answer:

The answer is C

Step-by-step explanation:

I took the test and I got it right

What is the volume of the cylinder above?

A. 168 units^3
B. 96 units^3
C. 84 units^3
D. 112 units^3

Answers

The volume of the oblique cylinder is calculated as: B. 96π units³.

What is the Volume of a Cylinder?

Volume = πr²h, where h is the height and r is the radius of the given cylinder.

Given the following:

Radius = 4 unitsHeight = 6 units

Volume = πr²h = π(4²)(6)

Volume = 96π units³ (option B)

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A group of 5 friends sold lemonade. If they sold each cup for $0.50 on Friday and for $0.45 on each other day of the week, how much money did each friend make if they split the money evenly?

Day Number of cups

Monday 15
Tuesday 8
Wednesday 5
Thursday 11
Friday 23

Answers

Answer:

69

Step-by-step explanation:

Answer:

Step-by-step explanation:

62.00

Consider the system of equations shown below 2x₁ + 3x₂ + 3x3 = 20 3x₁ +5x₂ + 2x3 = 9 -x₁ + 3x₂ + 5x3 = 4. What is the coefficient matrix for this system of equations?

Answers

The coefficient matrix is a square matrix with dimensions equal to the number of variables in the system of equations.

The coefficient matrix is a matrix of the coefficients of the variables in a system of linear equations.

Now, we arrange these coefficients in a matrix format by placing them row-wise. This gives us the coefficient matrix:

[tex]2x + 3y + 3x3 = 20[/tex]

[tex]3x + 5y + 2x3 = 9[/tex]

[tex]-x + 3y + 5x3 = 4[/tex]

Each row of the coefficient matrix corresponds to an equation in the system, and each column represents the coefficients of a specific variable (x₁, x₂, x₃).

In summary, the coefficient matrix for the given system of equations is:

[tex]| 2 3 3 |[/tex]

[tex]| 3 5 2 |[/tex]

[tex]|-1 3 5 |[/tex]

This matrix provides a compact representation of the coefficients in the system, which can be further used for various operations and calculations.

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The elephants at the Putnam Zoo are fed 9 1/2 barrels of corn each day. The buffalo are fed 1/2 as much corn as the elephants. How many barrels of corn are the buffalo fed each day?

Answers

The elephants at the Putnam Zoo are fed 9 1/2 barrels of corn each day. The buffalo are fed 1/2 as much corn as the elephants.
*7/20

Answer:

7/20

Step-by-step explanation:

Consider the curve defined by 2x2+3y2−4xy=36 .
(a) Show that ⅆyⅆx=2y−2x3y−2x .
(b) Find the slope of the line tangent to the curve at each point on the curve where x=6
(c) Find the positive value of x at which the curve has a vertical tangent line. Show the work that leads to your answer.

Answers

(a) `dy/dx = (2y - 2x)/(3y - 2x)`.

(b) The slope of the tangent line at points where x = 6 is 0.

(c) the curve has a vertical tangent line when x = (3/2)y.

(a) To show that `dy/dx = (2y - 2x)/(3y - 2x)`, we need to find the derivative of `y` with respect to `x`. We can do this by implicitly differentiating the given equation.

Differentiating both sides of the equation with respect to `x`, we get:

4x(dx/dx) + 6y(dy/dx) - 4[(dx/dx)y + x(dy/dx)] = 0

Simplifying the equation, we have:

4x + 6y(dy/dx) - 4xy - 4xy - 4x(dy/dx) = 0

Rearranging the terms and combining like terms, we get:

(6y - 4x)(dy/dx) = 8x - 8xy

Dividing both sides by (6y - 4x), we obtain:

dy/dx = (8x - 8xy)/(6y - 4x)

Simplifying further, we have:

dy/dx = (2x(4 - 4y))/(2(3y - 2x))

Canceling out the common factors, we get:

dy/dx = (2y - 2x)/(3y - 2x)

Therefore, `dy/dx = (2y - 2x)/(3y - 2x)`.

(b) To find the slope of the tangent line at the points where x = 6, substitute x = 6 into the expression we found for `dy/dx` in part (a):

dy/dx = (2(6) - 2(6))/(3y - 2(6))

      = 0/(3y - 12)

      = 0

The slope of the tangent line at points where x = 6 is 0.

(c) To find the value of x at which the curve has a vertical tangent line, we need to find the point(s) where the slope `dy/dx` is undefined. In other words, we need to find the values of x where the denominator of `dy/dx` becomes zero.

Setting the denominator equal to zero and solving for x:

3y - 2x = 0

2x = 3y

x = (3/2)y

So, the curve has a vertical tangent line when x = (3/2)y.

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Martin recorded the low temperatures at his house for one week. The temperatures are shown below.
-7, -3, 4, 1, 2, 8, 7
Approximately what was the average low temperature for the week?
Α. 7
B. "1
C. 1
D "8

Answers

It would be 1. You add all the temperatures. Get the sum and divide it by the amount of temperatures.

Let X and Y be two continuous random variables with joint probability density function Calculate the positive constant b. Show the result with at least two decimal places. 5 -bcx cb - bzycb f(x,y) = 0 otherwise

Answers

The positive constant b is 0. This is obtained by setting the coefficient of the xy^2 term to zero in the equation derived from equating the integral of the joint probability density function to 1.

To compute the positive constant b, we need to calculate the integral of the joint probability density function (pdf) over the entire probability space and set it equal to 1 since it represents a valid probability density.

∫∫ f(x, y) dx dy = 1

Since the joint pdf is defined as:

f(x, y) = 5 - bcx * cb - bzycb

And it is zero otherwise, we can set up the integral as follows:

∫∫ (5 - bcx * cb - bzycb) dx dy = 1

To solve this integral, we need to determine the limits of integration. Since the joint pdf is not specified outside of the equation, we assume it is defined for all real values of x and y.

∫∫ (5 - bcx * cb - bzycb) dx dy = ∫∫ 5 - bcx * cb - bzycb dx dy

Integrating with respect to x first:

∫ (5x - bcx^2/2 * cb - bzy * cb) ∣∣ dy = 1

Now integrating with respect to y:

(5xy - bcxy^2/2 * cb - bzy^2/2 * cb) ∣∣ dy = 1

Since this equation holds for all real values of x and y, we can ignore the limits of integration.

Next, we can solve for b by equating the integral to 1 and simplifying:

(5xy - bcxy^2/2 * cb - bzy^2/2 * cb) = 1

Simplifying further:

5xy - bcxy^2/2 - bzy^2/2 = 1

Now, we can compare the coefficients of the terms on both sides of the equation:

- bc/2 = 0 (since there is no xy^2 term on the right-hand side)

Solving for b:

bc = 0

Since we are looking for a positive constant b, we can conclude that b = 0.

Therefore, the positive constant b is 0.

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Need Help which one is it???

Answers

Answer:

the blue one but not sure

Answer:

the third one i think

Step-by-step explanation:

Find the slope of the line?

Answers

Answer:

m=3/4

Step-by-step explanation:

First, let us remind ourselves of the slope formula: m=rise/run=([tex]y_{2}[/tex]-[tex]y_{1}[/tex])/([tex]x_{2}[/tex]-[tex]x_{1}[/tex])

Let's pick two points from the graph to work with. Let's do (3,-6) and (-1,-9).

And let 3=[tex]x_{1}[/tex], -6=[tex]y_{1}[/tex], -1=[tex]x_{2}[/tex], -9=[tex]y_{2}[/tex].

1. Substitute the values into the slope formula: [-9-(-6)]/(-1-3)

2. simplify the expression: [-9-(-6)]/(-1-3)=(-9+6)/-4=-3/-4=3/4

3. As a result, the slope of the line is 3/4

suppose a hand of four cards is drawn from a STANDARD DECK of playing cards with replacement , determine the probability of exactly one card is jack:

Answers

Therefore, the probability of exactly one card being jack when a hand of four cards is drawn from a standard deck of playing cards with replacement is 0.073 or 7.3%.

Suppose a hand of four cards is drawn from a standard deck of playing cards with replacement, the probability of exactly one card being jack can be determined using the following steps:Step 1: Determine the total number of possible outcomes when four cards are drawn from a standard deck of 52 cards with replacement. The total number of possible outcomes = 52 × 52 × 52 × 52 = 7,311,616.Step 2: Determine the total number of ways in which exactly one card can be a jack. There are four jacks in a standard deck of 52 cards, so the total number of ways in which exactly one card can be a jack = 4 × 48 × 48 × 48 = 53,333,632.Step 3: Determine the probability of exactly one card being jack. Probability of exactly one card being jack = Total number of ways in which exactly one card can be a jack / Total number of possible outcomes= 53,333,632/ 7,311,616 = 7.28 ≈ 0.073 or 7.3%.Therefore, the probability of exactly one card being jack when a hand of four cards is drawn from a standard deck of playing cards with replacement is 0.073 or 7.3%.

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The probability of event A is Pr(A)=1/3 The probability of the union of event A and event B, namely A UB, is Pr(AUB)=5/6 Suppose that event A and event B are disjoint. Pr(B) = [....]

Answers

Given that the probability of event A is Pr(A) = 1/3 and the probability of the union of event A and event B, namely AUB, is Pr(AUB) = 5/6. The probability of event B is Pr(B) = 2/3.

Suppose that event A and event B are disjoint.

The probability of event B is Pr(B) = 1/2.

To find the probability of event B.

For disjoint events A and B, we know that A ∩ B = Φ (empty set).

Thus, we can express the union of A and B as: AUB = A + B, where A and B are disjoint.

In general, the probability of the union of two events can be expressed as: P(AUB) = P(A) + P(B) - P(A ∩ B).

For disjoint events, the intersection of the events is always an empty set.

Thus, P(A ∩ B) = 0.

Using this information, we can write:

P(AUB) = P(A) + P(B) - P(A ∩ B)

= P(A) + P(B) - 0

= P(A) + P(B)

Given P(A) = 1/3 and P(AUB) = 5/6, we can solve for P(B) as follows:

5/6 = P(A) + P(B)

=> P(B) = 5/6 - P(A)

=> P(B)  = 5/6 - 1/3

=> P(B)  = 2/3

Thus, the probability of event B is Pr(B) = 2/3.

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What is the solution to the equation below?



0.5n = 6

Answers

It's 12 because if you divide 6 by 0.5 you should get 12, so basically use the opposite operation.

Hope that helps!

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Find the area of the figure to the nearest tenth. Complete the equation of this circle:Please help will mark brainliest!! the profit margin is the amount of net profit earned for every $1 of: Pls help ASAP Imagine that Maritans launch a rocket toward the Earth at a great speed. While therocket is traveling toward us, it will appearthan it actually is.O more bluedarkerlargermore red What effect does planting trees and bushes on a steep hill have?A- It makes the hill a good habitat for animals.B- It provides oxygen to the soil.C- Over time, it will help the hill grow taller.D- It helps stop erosion. What was the primary motivation for the draining of lake beds in Mexico City? A. to reduce the risk of flooding B. to prevent the spread of diseases C. to protect the city from invaders D. to mine for gold under the lake beds Please select the best answer from the choices provided. A B C D HELPPPPPPPPPPPPPppppppppp number 4 How did people in rural areas get access to new products? ill mark brainliest, question is attached Was Manifest Destiny a positive or negative event? What does the author's use of the pronoun "we" suggest about the document he's written? A)It's supposed to be seen as a secondary source document. B)It's a new solution to an old mystery.C) It's supposed to be seen as a primary source document. D)It's accurate about for the outcome of the historical event. Find the slope plz help ASAP!! The building blocks of DNA are Which of the following figures has a length, width, and height?A. SquareB. Line segmentC. PointD. Pyramid P l e a s e a n s w e r t h i s Which of the following contains an element in a +1 oxidation state?CO2, PbO2, CaO, N2O5, Cu2O what is the term for when the fire inspector must identify a date for reinspection of the property? Assume the following information appears in the standard cost card for a company that makes only one product: Standard Quantity or Hours Standard Price or Rate Standard Cost Direct materials 5 pounds $ 11.00 per pound $ 55.00 Direct labor 2 hours $ 18.30 per hour $ 36.60 Variable manufacturing overhead 2 hours $ 3.00 per hour $ 6.00 During the most recent period, the following additional information was available: 20,000 pounds of material was purchased at a cost of $10.50 per pound. All of the material that was purchased was used to produce 3,900 units. 8,000 direct labor-hours were recorded at a total cost of $132,000. What is the direct labor rate variance 1. Based on the examples in the table, how do opinions differ from facts? 2. How do facts differ from theories?3. Although they're different, what relationship exists between facts and theories?4. What do all the theories in the table have in common?5. How do laws differ from theories?6. If someone told you that plate tectonics is just a theory and that it hasn't been accepted as a law yet, how would thisinformation conflict with what you understand about theories and laws? Discrete math proofTheorem: 0.1 Let a and n be positive natural numbers. Then the following statements are equivalent. GCDa, n) = 1 (Relatively Prime) a is not a zero divisor. (ab = 0) b=0) There exists a natural nu