Armando found the volume of the figure below by using the steps shown.
A rectangular prism with a length of 18 inches, width of 5 inches, and height of 8 inches. A triangular prism with a base of 18 inches and height of 6 inches. The prism has a height of 5 inches.
What mistake, if any, did Armando make?
Armando determined the volume correctly.
Armando used the wrong formula for the total volume.
Armando used the wrong dimensions for the triangular prism.
Armando did not apply the order of operations correctly.

Answer:

180.48[tex]ft^{2}[/tex]

Step-by-step explanation:

The area of a rectangle = bh

Area of a circle = π[tex]r^{2}[/tex]

Rectangle = 8 x 10 = 80

Circle = 3.14([tex]8^{2}[/tex]) = 200.96

But because it's a hlaf circle, divide the number by 2

100.48

Now add the numbers together

180.48[tex]ft^{2}[/tex]

Answer & Step-by-step explanation:

[tex]K(5,4)[/tex]

Remember this:

[tex](x,y)[/tex]

[tex](5_{x},4_{y})[/tex]

When you are going to graph a point, you always start along the x-axis (the horizontal), then you move on to the y-axis (vertical). Both of the numbers in K are positive, so we will stay in Quadrant I.

For x, starting at (0,0) move to the right to point 5. From here, move up to the line that has value 4. Mark this spot with a dot and label if needed.

*If the x value is positive, you move to the right. If it is negative, you move to the left.

If the y value is positive, you move up. If it is negative, you move down.

Final answer:

To graph point K at (5,4), draw axes, locate 5 on the x-axis, 4 on the y-axis, and mark the point at the intersection.

Explanation:

To graph point K at (5,4), you start by drawing a set of perpendicular lines representing the x-axis (horizontal) and y-axis (vertical), usually with arrows on each end to indicate that they extend infinitely.

Each axis should be marked with evenly spaced intervals. Locate the number 5 on the x-axis (the horizontal axis) and then move vertically until you're level with the number 4 on the y-axis (the vertical axis).

Plot point K at the intersection of these two points.

This gives you the coordinates of point K where the first number in the parentheses is the position on the x-axis and the second number is the position on the y-axis.

The outlier in the data set {12, 15, 20, 44, 18, 20} is 44. It significantly increases the mean and range of the data set, but the median and mode are less affected. The outlier highlights sampling variability and induced variability.

The student has asked to identify the outlier in the data set {12, 15, 20, 44, 18, 20} and assess how it affects the mean, median, mode, and range of the data. Considering the provided data, it's apparent that the number 44 is the outlier since it is significantly higher than the rest of the numbers in the set. To confirm, we can calculate the interquartile range (IQR) and use it to detect outliers, but since the data set is small, a visual inspection is sufficient.

Without the outlier (44), the data set is {12, 15, 18, 20, 20}. The mean (or average) is calculated by adding all the numbers and dividing by the count of numbers, which results in a mean of (12 + 15 + 18 + 20 + 20) / 5 = 17. The median, which is the middle number when the data is sorted, is 18. The mode, the number that appears most often, is 20 in this case. As for the range, which is the difference between the largest and smallest number, it's 20 - 12 = 8.

With the outlier included, the mean becomes (12 + 15 + 18 + 20 + 20 + 44) / 6 = 21.5, the median remains 18, the mode is still 20, and the range expands to 44 - 12 = 32. Clearly, the outlier has a significant effect on the mean and range, causing them to increase, while the median and mode are less impacted due to their nature of being more resistant to extreme values. The presence of an outlier shows some degree of sampling variability and may introduce induced variability in the analysis of data.

Answer:

x^2-3x-7=0. x2−3x−7=0 x 2 - 3 x - 7 = 0.

Step-by-step explanation:

x^2-3x-7=0. x2−3x−7=0 x 2 - 3 x - 7 = 0. Use the quadratic formula to find the solutions. −b±√b2−4(ac)2a - b ± b 2 - 4 ( a c ) 2 ...

Answer:

x=3/2 ±  √37/2

Step-by-step explanation: the answer

Answer:

View answer in the photo.

Step-by-step explanation:

Answer:

y = 5x - 18

Step-by-step explanation:

Points:

Equation of the line:

y = ax + b

(5; 7) and (8; 22)

(5; 7)

7 = 5a + b

(8; 22)

22 = 8a + b

a and b are the same values:

{- 5a - b = - 7

{8a + b = 22

3a = 15

a = 5

5a + b = 7

5.5 + b = 7

25 + b = 7

b = 7 - 25

b = - 18

Equation:

y = 5x - 18

I Hope I've helped you.

Final answer:

The slope-intercept form equation of the line that passes through the points (5, 7) and (8, 22) is y = 5x + 18, found by first calculating the slope and then using the point-slope form to solve for y.

Explanation:

To find the slope-intercept form of the equation of the line that passes through the points (5, 7) and (8, 22), we first need to calculate the slope (m). The slope is given by the formula:

m = (y2 - y1) / (x2 - x1)

Using our points, this becomes:

m = (22 - 7) / (8 - 5) = 15 / 3 = 5

Now, we use one point and the slope in the point-slope form of the equation, y - y1 = m(x - x1), which becomes:

y - 7 = 5(x - 5) => y - 7 = 5x - 25

Solving for y to get the slope-intercept form, y = mx + b:

y = 5x + (25 - 7) = 5x + 18

So, the correct slope-intercept form equation of the line is y = 5x + 18.

Answer:

what is the question

Step-by-step explanation:

plsss give brainliest

The correct answer is  Calvin is correct because he correctly applied the quotient of powers rule.

The correct option is (D).

Calvin is correct because he correctly applied the quotient of powers rule.

According to the quotient of powers rule, [tex]\( \frac{a^m}{a^n} = a^{m - n} \).[/tex]

So, in this case:

[tex]\[ \frac{r^{-5}s^{-3}}{r^8s^{-2}} = r^{-5 - 8}s^{-3 - (-2)} = r^{-13}s^{-1} \][/tex]

Then, when you raise this expression to the power of -4:

[tex]\[ (r^{-13}s^{-1})^{-4} = r^{-13 \times -4}s^{-1 \times -4} = r^{52}s^4 \][/tex]

Nadine's approach would result in:

[tex]\[ \left( \frac{r^{-5}s^{-3}}{r^8s^{-2}} \right)^{-4} = \left( \frac{e^{-20}s^{-12}}{r^{32}s^8} \right) \][/tex]

Which is incorrect.

So, the correct answer is D. Calvin is correct because he correctly applied the quotient of powers rule.

complete question given below:

Nadine and Calvin are simplifying the expression ( (r^(-5)s^(-3))/r^8s^(-2) ). Nadine claims the first step to simplify the expression is to raise the numerator and denominator to the power (e^(-20)s^(-12))/r^(32)s^8 . Calvin claims the first step to simplify the expression is to apply the quotient of powers to get (r^(-13)s^(-1))^-4.

Who is correct and why?

A.Nadine is incorrect because she should have applied the quotient of powers rule first.

B.Nadine is correct because she correctly applied the power of a product rule.

C.Calvin is incorrect because he should have applied the power of a product rule first.

D.Calvin is correct because he correctly applied the quotient of powers rule

Answer:

A

Step-by-step explanation:

Answer:

The answer is 15

Step-by-step explanation:

i took the test

Answer: B

Step-by-step explanation:

Answer:

Answer is x = 100 degrees.

Step-by-step explanation:

Vertically opposite angles are equal.

Then value of x is 100 degrees.

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

Step-by-step explanation:

[tex]x = 100 \: \: degrees[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

80 inches

Step-by-step explanation:

Pythagorean theorem

Answer:

-3+1/3=-8/3 or-2.6,    5+6+7x+3=7x+14

Step-by-step explanation:

Answer:

-3+1/3= -2.66666666667      

Step-by-step explanation:

Answer:

48π or 150.72

Step-by-step explanation:

The radius of the big circle is 8.

We can use that to find the area of the big circle.

Area is πr^2

π(8)^2

64π

Now, we can find the area of the small circle.

The diameter of that is 8, meaning the radius is 4.

πr^2

π(4)^2

16π

Now we subtract the area of the small circle from the area of the big circle to get the area of the shaded region.

64π-16π=48π

As a decimal: 48*3.14=150.72

Answer:

Hope this answers the question.

Step-by-step explanation:

Factoring a number: If you use the number 10, for example, you have to find all the factors to factor it. 1, 2, 5, 10.

Factoring a trinomial: If you use the trinomial x^2 + 16 + 64, for example, to factor it you need to first find what numbers multiply up to 64 and also add up to 16. In this case, those numbers are 8, and so you get (x + 8)^2.

Final answer:

Factoring a number involves breaking it down into its prime factors, a straightforward process within the real number system. Factoring a trinomial, particularly in algebra, requires finding binomials that, when multiplied, return the original trinomial and can extend to complex numbers, guided by the fundamental theorem of algebra.

Explanation:

Factoring a trinomial and factoring a number are two very different processes within the realm of mathematics. When we talk about factoring a number, we refer to breaking it down into its prime factors, which are the prime numbers that multiply together to give the original number. For instance, factoring the number 10 would give us 2 and 5, since 2 x 5 = 10. This process is straightforward and applies to the number system.

On the other hand, factoring a trinomial involves finding two binomials that, when multiplied together, result in the original trinomial. This is more commonly encountered in algebra, especially when dealing with second-order polynomials (quadratics). For example, factoring the trinomial x² + 5x + 6 involves finding two binomials (x + 2) and (x + 3), since (x + 2)(x + 3) = x² + 5x + 6. Furthermore, factoring trinomials can extend into complex numbers where every nth-order polynomial can be factored into n linear factors in the complex number system, according to the fundamental theorem of algebra.

In summary, factoring a number focuses on prime factorization within the real number system, while factoring a trinomial involves algebraic manipulation that can extend into handling complex numbers and requires an understanding of both real and complex number systems.

Answer:

B

Step-by-step explanation:

You have to evaluate the power and calculate the sum or difference in order to get the answer

Answer:

(-4y,+12y), (z,19z)

Step-by-step explanation:

i got the same question.

Answer:

k  =  y/x

as a fraction for both

Answer: B

Step-by-step explanation:

The answer is 32.2102.

In June, Cory begins to save money for a video game and a TV he wants to buy in December.

He starts with $22. Each month he plans to save 10% more than the previous month.

How to find how much money will he have at the end of December?

the given scenario is an application of a geometric sequence with

a1=$20 and  r= 22/2 *100 = 1.1

. Since December is 6 months from June, then to find out the 6th term.

As, a2 = a1 * r = 20 × 1.1 = 22

a3= a2 *r = 22 * 1.1 = 24.2

a4= a3 * r = 24.2 * 1.1 = 26.62

a5=a3 * r = 26.62 *1.1 = 29.282

a6= a4*r = 29.282 * 1.1 = 32.2102.

Learn more about equations on : https://brainly.com/question/16175490

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Answer:

1.8333

Step-by-step explanation:

12x-2=20

Add 2 to both sides:

12x=22

Divide both sides by 12:

[tex]x=\frac{22}{12}\approx 1.8333[/tex]

Hope this helps!

Answer:

x= -12

Step-by-step explanation:

Assuming this is a direct variation

y = kx

When y = -16 x =4  we can find k

-16 = k*4

Divide each side by 4

-16/4 = 4k/4

-4 =k

So

y = -4k

Y = 48

48 = -4x

Divide each side by -4

48/-4 = -4x/-4

-12 =x

Answer:

6.75 dm²

Step-by-step explanation:

All the side edges in the regular triangular prism are 3 dm long. Then, the base of the triangular plate is 3 dm long, and the other two sides are: √[3² + 3²] = 4.24 dm long (a right triangle is made and Pythagorean theorem is applied).

The height of the triangular plate is: √[4.24² + 1.5²] = 4.5 dm long (again Pythagorean theorem is applied)

Area of the triangular plate is: base*height/2 = 3*4.5/2 = 6.75 dm²

Step-by-step explanation:

Hope it helps.

Please rate and mark as brainlist.

Answer:

I'm not sure

Step-by-step explanation:

sorry

Answer:

  (b)  $880

Step-by-step explanation:

You want the cost of an 8-inch by 11-inch ad at the rate of $10 per square inch.

The area of the ad is the product of its dimensions:

  A = LW

  A = (11 in)(8 in) = 88 in²

The cost is $10 for each of those square inches:

  ($10/in²)×(88 in²) = $880

The cost of the full-page ad is $880, choice B.

Answer:

B. $6,870

Step-by-step explanation:

Calculate how much money they earned from tickets then subtract the cost of making and that's their balance:

(1007×10)-3200=

10070-3200=

$6,870

B. $6,870

Final answer:

After calculating the total proceeds from selling tickets to 1,007 attendees at $10 each, the balance of the line of credit used to fund the play's production ($3,200) will be a positive $6,870.

Explanation:

The question pertains to a fundraiser calculation for Betsy's high school play. To determine the balance of the bank account after ticket sales, we must calculate the total proceeds from selling tickets to the attendees and then adjust the balance of the line of credit that was originally used to fund the production.

The production cost is $3,200.00, and tickets are sold at $10 each. With 1,007 people attending, the total ticket proceeds will be 1,007  imes $10 = $10,070. Since the school used a line of credit to pay for the play, the proceeds will pay off this balance. Hence, after depositing the ticket sales, the balance is:

Balance after deposit = Ticket proceeds - Production costs
= $10,070 - $3,200
= $6,870 (Credit balance)

The correct balance of the bank account after the play's opening night is therefore $6,870 (Option B).

Answer:

The answer would be 13.3.

Step-by-step explanation:

Use the Pythagorean theorem to find the other distances in the 5, 3, x triangle and the 7, 3, y triangle and add those two answers together plus 3 to get your answer.

Answer:

13.3 kilometers

Step-by-step explanation:

You need to use Pythagorean theorem for x+3+y.

The distance you would be looking for is 4+3+6.3=13.3

Answer:

(a)Time taken to reach the ground, x=6 seconds

(b)Maximum height of the arrow during its flight =101.25 feet

Step-by-step explanation:

Given the quadratic function which models the flight of the arrow:

[tex]y=-5x^2+15x+90[/tex]

Where:

(a)Positive Zero

[tex]-5x^2+15x+90=0\\-5(x^2-3x-18)=0\\-5(x^2-6x+3x-18)=0\\-5(x(x-6)+3(x-6))=0\\-5(x+3)(x-6)=0\\x+3=0\:or\:x-6=0\\x=-3,x=6[/tex]

In 6 seconds, the arrow will hit the horizontal plane, i.e. the ground.

(b)

[tex]y=-5x^2+15x+90\\y-90=-5(x^2-3x)\\y-90-5(\frac{9}{4}) =-5(x^2-3x+(\frac{3}{2} )^2)\\y-101.25=-5(x-\frac{3}{2} )^2\\y=-5(x-\frac{3}{2} )^2+101.25[/tex]

Comparing with the vertex form:

[tex]y=a(x-h)^2+k[/tex]

Our vertex, (h,k)=(1.5, 101.25)

Maximum Value of y=101.25

The maximum value of y represents the maximum height of the arrow during its flight, which is 101.25 feet.