Members of the Robotics team are making 3-d prints of animals. One animal takes 3.742 grams of material. The 3-d printer has made 12.5 animals so far. How many grams of materials have they used so far?

Answer:

\(y=-\frac{2}{5} x+\frac{36}{5}\)

Step-by-step explanation:

→ Find the gradient

\(\frac{4-6}{8-3}= \frac{-2}{5} =-\frac{2}{5}\)

→ Write into y = mx + c format

\(y=-\frac{2}{5} x+c\)

→ Substitute in ( 3 , 6 )

\(6 = -\frac{6}{5} +c\)  ∴ \(c = 6+\frac{6}{5} =\frac{36}{5}\)

→ Rewrite into y = mx + c format

\(y=-\frac{2}{5} x+\frac{36}{5}\)

The value of a is 5/9 if  y = a(x - 2)(x + 6) and (3,5) is a point on the graph.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

It is given that:

A quadratic relation has the equation y= a(x - s )(x – t).

y = a(x - 2)(x + 6) and (3,5) is a point on the graph

Plug x = 3 and y = 5

5 = a(3 - 2)(3 + 6)

a = 5/9

The parabola has zeros of 4 and -2 and a y-intercept of 1

y= a(x - s )(x – t)

0= a(4 - s )(4 – t)

0= a(-2 - s )(-2 – t)

1= a(0 - s )(0 – t)

No solution.

Similarly, it can find the equation of the parabola in the remaining part,

Thus, the value of a is 5/9 if  y = a(x - 2)(x + 6) and (3,5) is a point on the graph.

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Answer:

Perry's claim is correct while Karina is incorrect

Step-by-step explanation:

Question is incomplete (See Attachment)

First, we need to determine the area covered by Karina and Perry

For Karina, there are 9 square boxes each of which has an area of 1 unit sq

So:

\(Karina = 9 * 1\ unit^2\)

\(Karina = 9\ unit^2\)

For Perry:

There are 18 square boxes, each of which has an area of 1 unit sq.

So:

\(Perry = 18 * 1\ unit^2\)

\(Perry = 18\ unit^2\)

Comparing both areas, we can conclude that Perry's claim is correct while Karina is incorrect

Answer:

a) 293 units

b) 5795p

Step-by-step explanation:

First, determine how many units used

Take the new reading and subtract the old reading

6538 - 6245

293 units

The first 200 is at 22p

200 * 22 p =4400p

293 -200 = 93 units at the remaining unit price.

93 * 15 p =1395p

Add the two totals together

4400p + 1395p =5795p

Answer:

Step-by-step explanation:

All it's saying is that the 12% of the people are 35 and the 82% of people who did not submitted data is 175 people

The calculated test statistic (2.08) is greater than the critical value (1.96), we reject the null hypothesis and conclude that there is evidence to suggest that the contest has increased participation in the box tops for education program.

To determine if the contest has increased participation in the box tops for the education program, we need to conduct a hypothesis test.

We will use a significance level of 0.05, which means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true).

Null Hypothesis: The proportion of students submitting box tops for education is still 12% (or has decreased) after the contest.

Alternative Hypothesis: The proportion of students submitting box tops for education has increased after the contest.

To test this hypothesis, we will use a one-sample proportion test. We will use the sample proportion, p' = 35/210 = 0.1667, as an estimate of the population proportion, p. The test statistic is calculated as:

z = (p' - p) / √(p x (1-p)/n)

where n is the sample size.

Under the null hypothesis, the expected value of the test statistic is 0, and the standard deviation of the test statistic is sqrt(p*(1-p)/n).

Using p = 0.12 and n = 210, we have:

z = (0.1667 - 0.12) / √(0.12 x 0.88/210) ≈ 2.08

The critical value for a significance level of 0.05 and a two-tailed test is ±1.96.

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The graph of the function y = 5|x - 4| is added as an attachment

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

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

0.9, 0.89, 0.81, 0.8, 0.79, 0.09, 0.08

Step-by-step explanation:

Answer: 0.09 , 0.89 , 0.81, 0.08, 0.79 , 0.9, 0.8

Step-by-step explanation:

First find the greatest

0.09, 0.89,0.81, 0.08, 0,79

Then the least

0.9 .0.8

Now put it all together  

0.09, 0.89. 0.81 , 0.08, 0.79 , 0.9, and lastly 0.8

Answer:

x=9

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

12=x+3

Step 2: Flip the equation.

x+3=12

Step 3: Subtract 3 from both sides.

x+3−3=12−3

Question

Which division problem does the diagram below best illustrate?

A diagram with 5 ovals containing 7 squares.

30 divided by 5 = 6

35 divided by 7 = 5

21 divided by 7 = 3

40 divided by 5 = 8

Answer:

B

The division which correctly illustrates a diagram with 5 ovals containing 7 squares is: 35 divided by 7 = 5

"It is the process of breaking a number up into equal parts."

"It is a statement which consists of equal symbol between two algebraic expressions."

For given example,

A diagram with 5 ovals containing 7 squares,

This means, there is an unknown number X such that:

⇒ X/7 = 5

Now, we can solve the equation for X.

⇒ X/7 = 5

⇒ (X/7) × 7= 5 × 7

⇒ X = 35

Therefore, the division which correctly illustrates a diagram with 5 ovals containing 7 squares is: 35 divided by 7 = 5

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Answer:

The set M of all square numbers less than 80 is:

M = {0, 1, 4, 9, 16, 25, 36, 49, 64}

The set N of all non-negative even numbers that are under 30 is:

N = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

Answer:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Step-by-step explanation:

A square number, also known as a perfect square, is a non-negative integer that is obtained by multiplying an integer by itself. In other words, it is the result of squaring an integer.

The square numbers less than 80 are:

An even number is an integer that is divisible by 2 without leaving a remainder.

The non-negative even numbers that are under 30 are:

Therefore:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Both men are committing fallacies in their reasoning. The occurrence of a hurricane on that land cannot be predicted with certainty, and making decisions based on fallacious reasoning can lead to poor outcomes.

A fallacy refers to the statement in an argument that makes an error in logic. Fallacies are very dangerous because they lead to incorrect thinking about certain topics and may lead to an incorrect conclusion about that topic most of the time.

The fallacy in Poindexter's uncle's reasoning is known as the fallacy of induction. This fallacy occurs when someone assumes that because a certain event has happened in the past, it is likely to happen again in the future. While it is true that the land has been hit by hurricanes 160 times in the past, it doesn't necessarily mean that it will happen again in the near future.

On the other hand, Poindexter's nephew is committing the fallacy of the Gambler's Fallacy. This fallacy occurs when someone assumes that because something hasn't happened in a while, it is more likely to happen soon. In this case, the nephew assumes that a hurricane must be due soon simply because it hasn't happened in the past 13 years. However, the occurrence of a hurricane is not influenced by the time that has passed since the last one. Each hurricane is a unique event that is not influenced by previous occurrences.

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The correct answer is (j - k)(x) = 10 + x.

To find the difference in the amount of money between Joel's and Kevin's accounts, we subtract the value of Kevin's account (k(x)) from Joel's account (j(x)).

(j - k)(x) = (25 + 3x) - (15 + 2x)

            = 25 - 15 + 3x - 2x

            = 10 + x

This expression represents how much more money is in Joel's account compared to Kevin's account after x weeks.

Therefore, the correct function is (j - k)(x) = 10 + x.

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Answer: A. 1.2

Step-by-step explanation:

The principal, real, root of:

2^√1.44

=1.2

All roots:

1.2

−1.2

1.44 is not a perfect square

We know that cos(45) = sin(45) = √2/2.

Substituting these values, we can simplify the expression as follows:

4cos(45) - 2sin(45)

= 4(√2/2) - 2(√2/2) (substituting cos(45) and sin(45) values)

= 2√2 - √2

= √2

Therefore, the answer is √2.

Answer:

30: 100

31: -13

32: -45

33: 14

34: -32

35: -22

36: 17

Answer:

x - 4 yards.

Step-by-step explanation:

Given:

Area of rectangle = 3x^2 - 12x square yards

Width = 3x yards

To find:

Length of rectangle

Solution:

The area of a rectangle is equal to the product of its length and width.

Area of rectangle = Length * Width

Substituting the given values, we get:

3x^2 - 12x = Length * 3x

Length =( 3x^2 - 12x )3x

Length = x-4

Therefore, the length of the rectangle is x - 4 yards.

Answer: The length of the rectangle is x - 4 yards.

Step-by-step explanation:

We can create an equation to solve this word problem, where the variable L = length.

3x  ×  L  = \(3x^2 - 12x\)

We need to solve for the variable L, to find the length of the rectangle.

First lets factor the right side of the equation to make it easier to divide with.

3x  ×  L  = \(3x^2 - 12x\)

We can factor out 3x from the right side of the equation.

3x  ×  L  = 3x(x - 4)

Now we need to get the variable L by itself (isolating the variable). In order to do that, we can divide both sides by 3x.

3x ×  L  = 3x(x - 4)

/3x           /3x

L = x - 4

The length of the rectangle is x - 4 yards.

The amount in the account at the end of 1 year is $5400.

The amount in the account at the end of 2 year is $5832.

What do you mean by interest rate?

The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.

According to data in the given question,

We have:

Deandre places $5000 in an account that pays 8% interest compounded each year.

And no withdrawals are made from the account.

Now, we need to determine the amount of 8% interest on the $5000,

\(=\frac{5000}{100}*8\\ =400\)

Then, the amount in the account at the end of 1 year =$5000+$400

=$5400.

Now, we need to determine the amount of 8% interest on the $5400,

\(=\frac{5400}{100}*8\\ =432\)

So, the amount in the account at the end of 2 year =$5400+$432

=$5832.

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Step-by-step explanation:

12^2 x 3.14=452.16

452.16 x 28=12,660.48

12,660.48/3=4,220.16

4,220.16 is the answer

Answer:

Sure, I can help with that! Here are the steps to solve each problem:

a) Since sin A = 0.6018, we can use the inverse sine function (sin^-1) to find the measure of angle A. Taking the inverse sine of 0.6018 gives us 37.19 degrees rounded to the nearest degree.

b) Since cos B = 0.9205, we can use the inverse cosine function (cos^-1) to find the measure of angle B. Taking the inverse cosine of 0.9205 gives us 23.06 degrees rounded to the nearest degree.

c) Since tan C = 0.0349, we can use the inverse tangent function (tan^-1) to find the measure of angle C. Taking the inverse tangent of 0.0349 gives us 2.00 degrees rounded to the nearest degree.

I hope that helps! Let me know if you need any further assistance.

Answer:

3021

Step-by-step explanation:

Answer:

Your answer is: Estimated is: 3,000

The real answer was:

↓

3,021.

Step-by-step explanation:

Hope this helped : )

Answer:

about 8 hours

Step-by-step explanation:

8 hours. It is Five hours plus Three hours.

Answer:

x= -2

Step-by-step explanation:

2(x+3)=5x+10-x (we need to distribute first)

2x+6=4x+10   (then add like terms)

-2x=4    (now divide)

x= -2

Answer:

1.99677419355

Step-by-step explanation:

Answer:

1.996 rounds to 2

Step-by-step explanation:

\(-21x^{2}-588\)

let me know if anything is unclear, I'm happy to help!

Answer:

AC = 17.8

Explanation:

to figure out the length of AC, you want to put the values into the tangent function:

tan 64° = AC/8.7

Now to solve:

first swap them so you have AC/8.7 = tan 64°

Multiply both sides by 8.7 to get AC = 8.7 tan 64°

then calculate it

AC = 8.7 x 2.0503...

AC = 17.8376

AC = 17.8 (3 Significant Figures)

Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

CONCLUSION:

The final answer is: