POSSIBLE POINTS:
Jaedin invests $12,000 in an account that compounds interest annually. After three years, the account is worth $13,343.22. Use the function A = P(1 +
r), where r is the annual interest rate, P is the principal, and A is the amount of money after t years. What is the interest rate of the account?

Answer:

this is your answer

\( {9}^{4} \)

\(\large{\sf \boxed{(\sf -3)^8}}\)

\(\rightarrow \sf ((-3)^2)^4\)

apply exponent rule: \(\sf \bf \left(a^b\right)^c=a^{bc}\)

\(\rightarrow \sf (-3)^8\)

The length of the panel is 0.5 meter.

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

Given that,

Area of the panel = 0.8 \(m^{2}\)

width of the panel = 1.6 meter

Here, solar panel is in the form of rectangle.

Area of rectangle = length× width

                     0.8 =   1.6 × length

                   length = \(\frac{0.8}{1.6}\)

                   length = 0.5 meter

Hence, The length of the panel is 0.5 meter.

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Karen has 8 different ways to cast the film considering the given options for the female and male lead roles.

In mathematical terms, this can be expressed as "C(2,1)" or "2C1" which represents choosing 1 actor out of 2. The formula for combinations is:

C(n, r) = n! / (r!(n-r)!)

where "n" is the total number of options available and "r" is the number of options to be chosen.

In this case, C(2,1) = 2! / (1!(2-1)!) = 2.

Therefore, Karen has 2 different ways to cast the female lead role.

For the male lead role:

With four actors interested in the male lead role, Karen has four options to choose from. This is equivalent to calculating the number of combinations of 4 actors taken 1 at a time. Again, using the combination formula:

C(4, 1) = 4! / (1!(4-1)!) = 4.

Therefore, Karen has 4 different ways to cast the male lead role.

To find the total number of different ways Karen can cast the film, we multiply the number of options for each role together:

Total ways = Number of ways for the female lead role × Number of ways for the male lead role

= 2 × 4

= 8.

So, the combinations for each role (2 for the female lead and 4 for the male lead) and then multiply them together, resulting in a total of 8 different ways.

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Answer:

y=3x+2

Step-by-step explanation:

slope intercept form

y=mx+b

y=y coordinate

m=slope

x=x coordinate

b= y-intercept

Answer:

y=4

Step-by-step explanation:

The x axis is a horizontal line ( y=0)

A line parallel would also be of the form y= something  and be a horizontal line

The only answer of the form y=   is y=4

Answer: There will be 8 balloons left over.

Step-by-step explanation: A total of 580 balloons to be distributed equally among 26 students means 580 ÷ 26.

The division is not exact, since 580 are not divisible by 26, it will result in a rest, so

580 ÷ 26 = 22 and has rest 8

Therefore, there will be 8 balloons left over.

It will represent the change in temperature between midnight and 6, the correct option is C.

H(t) is the rate at which the temperature changes. So, if we integrate H(t), we will get the change of temperature.

In this case, we have:

\(\int\limits^6_0 {H(t)} \, dt\)

This will give the change in temperature between 6:00 AM (represented by the 6) and midnight (represented with the 0).

So the correct option is C.

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Answer:

x = 66°

Step-by-step explanation:

First, you can use exterior angle theorem to say that

\(m<JIH = m<JDI + m<DJI\)

and you can substitute to get:

105° = 39° + m<DJI

m<DJI = 66°

m<DJI and m<AJF are vertical angles, so they equal each other:

m<DJI = m<AJF

m<AJF = x = 66°

Answer:

See explanation below

Step-by-step explanation:

Volume = (11)(10)(7) = 770 cubic centimeters

Surface area = (2)(10)(7) + (2)(11)(7) + (2)(11)(10) = 1774 square centimeters

b) Surface area (How much wax can cover the cube)

c) Volume (How much juice will be inside the cube)

Answer:

Yes it looks correct but that is just me

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This is the correct solution.

5 + 14a = 9a -5

14a - 9a = -5 -5

5a = -10

a=-10/5 = -2

Therefore, a = -2

Answer:

x=68

>ADC= 133

Step-by-step explanation:

90+2x+1+2x-3=360

4x+88=360

4x=272

x=68

>ADC= 2(68)-3= 133

Marta's theory lacks practical significance or real-world applicability.

Marta's theory suggests that filling out a job application in crayon leads to a lower probability of being hired.

However, she mentions that almost nobody fills out an application in crayon.

This means that the finding or theory has no practical significance because it doesn't affect a significant number of people or have a real impact in real-world scenarios.

If the vast majority of job applicants do not use crayon to fill out their applications, Marta's theory becomes inconsequential because it doesn't provide any meaningful insight or guidance for job seekers.

The theory lacks practical significance because it doesn't have any practical implications or relevance in the context of job applications and hiring processes.

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The complement of set A, denoted by ​ A`, is the collection of all elements that belong to the universal set but are not part of set A. It's not necessary to mention the universe (also known as U) if it's understood which set of elements is being referred to.

The complement of a set A is the collection of all elements that belong to the universal set but not to set A. It is denoted as ​ A` and does not include any elements that are already in set A. The universal set, also known as U, contains all possible elements and is assumed to be known. Therefore, when referring to the complement of a set, it is not necessary to mention the universal set explicitly. The complement of a set is useful in determining the set of elements that are not part of a particular set, and it can be used in various mathematical operations.

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The required change-of-coordinates matrix from A to B is B = [1 1 0; 0 1 4; 0 0 -5]. The required coordinates of [x]s for x = 3a + 4a2 + a3 is [70, -277, 15].

Given information:

Let 47 {1,22,23} and B = {b,,b2,b3} be bases for a vector space V, and suppose a1 2b1-b2a2b+4b2 + b3 a3 = b2 - 5b3 a.

Find the change-of-coordinates matrix from A to B.

b. Find [x]s for x = 3a +4a2 + a3.a1 2b1 - b2a2b + 4b2 + b3 a3 = b2 - 5b3 aIn matrix form, this becomes

A [a1, a2, a3] = B [b1, b2, b3]

where A = [1, 22, 23] and

B = [b1, b2, b3].

We need to solve this matrix equation for B which gives the change-of-coordinates matrix from A to B. The given equation can be rewritten as a1

[1, 22, 23] + a2 [2, -1, 4] + a3 [0, 1, -5] = b2 [0, 1, 0] + b3 [0, 0, -5]

This implies that the coordinates of b2 and b3 in terms of A are b2 = a1 + a2b3 = -a1 + 4a2 - 5a3

Thus, the change-of-coordinates matrix from A to B is

B = [1 1 0; 0 1 4; 0 0 -5]

To find [x]s for x = 3a + 4a2 + a3, we first find its coordinates in A.

3a + 4a2 + a3 = 3[1, 22, 23] + 4[2, -1, 4] + [0, 1, -5]= [11, 81, -3]

Thus, [x]a = [11, 81, -3].Now, we can find the coordinates of x in B as follows:

[x]b = B[x]a= [1 1 0; 0 1 4; 0 0 -5][11; 81; -3]= [70, -277, 15]

Therefore, [x]s = [70, -277, 15].

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Answer:

\(482.5\:\mathrm{in^2}\)

Step-by-step explanation:

The area of the figure consists of a rectangle with a triangle removed from the corner of it. Therefore, the area of the composite of the figure can be found by subtracting the area of the triangle from the area of the rectangle.

Area of the rectangle: \(25\cdot 20=500\:\mathrm{in^2}\)

Area of the triangle: \(\frac{1}{2}\cdot 5\cdot 7=17.5\:\mathrm{in^2}\)

Thus, the area of the figure is \(500-17.5=\boxed{482.5\:\mathrm{in^2}}\)

The area of the trapezoid is 13 meters.

The area of a trapezoid is calculated by taking the sum of the two bases and multiplying that by the height, then dividing that by two. In this case, the sum of the two bases is 4 meters + 2.5 meters = 6.5 meters. Multiplying this by the height of 4 meters gives us a result of 26 meters. Finally, we divide that by two to get the final area of 13 meters.

To calculate the area of a trapezoid, you first need to calculate the sum of its two bases. The two bases are the bottom and the top lengths of the trapezoid, which in this case are 4 meters and 2.5 meters respectively. Once you have the sum of the two bases, you can then multiply that sum by the height of the trapezoid, which in this case is 4 meters. This will give you the total area of the trapezoid. Lastly, you divide this total area by two to get the final area.

In summary, to calculate the area of a trapezoid with a base length of 4 meters and 2.5 meters, and a height of 4 meters, you need to first calculate the sum of its two bases, which in this case is 6.5 meters. Multiply this by the height of 4 meters to get the total area of 26 meters. Finally, divide this by two to get the final area of the trapezoid, which is 13 meters.

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The measure of ∠ABC in the triangle ABC is approximately 59.804 degrees.

To find the measures of the angles of the triangle ABC, we can use the angle formula based on the coordinates of the vertices. Let's calculate the angles step by step:

Find the length of each side of the triangle using the distance formula:

AB = √[(x2 - x1)² + (y2 - y1)²] = √[(3 - (-2))² + (2 - 0)²] = √[5² + 2²] = √(25 + 4) = √29

BC = √[(x2 - x1)² + (y2 - y1)²] = √[(3 - 3)² + (-3 - 2)²] = √[0² + (-5)²] = √25 = 5

AC = √[(x2 - x1)² + (y2 - y1)²] = √[(-2 - 3)² + (0 - 2)²] = √[(-5)² + (-2)²] = √(25 + 4) = √29

Use the law of cosines to find the measures of the angles:

Let's calculate ∠ABC:

cos(∠ABC) = (AB² + BC² - AC²) / (2 * AB * BC)

cos(∠ABC) = (29 + 25 - 29) / (2 * √29 * 5)

cos(∠ABC) = 25 / (2 * √29 * 5)

∠ABC = cos⁻¹(25 / (2 * √29 * 5))

Using a calculator, we can find the value of ∠ABC as approximately 59.804 degrees.

Therefore, the measure of ∠ABC in the triangle ABC is approximately 59.804 degrees.

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Answer:

what is mathematics in freshman course

The value of the k in the dimension of rectangle is 6 .

Rectangle 1 : 18 by 3

Rectangle 2 : 9 by 6

Given, that two rectangles have same area.

Area of rectangle = Length × Breadth

Perimeter of rectangle = 2(l+b)

Here the dimension of rectangles are,

Rectangle 1 : 3k by 3

Area of rectangle 1 = 3k × 3

Area of rectangle 1 = 9k

Area of rectangle 2 = (k+3) × 6

Area of rectangle 2 = 6k + 18

Moreover the area of two rectangles are same. So equate the areas.

6k + 18 = 9k

3k = 18

k = 6

Thus the value of k in the dimensions of rectangle is 6.

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Answer:

Pyramid A had a lateral area of 100 and Pyramid B has a Lateral area of 225

so 100:225 or 4:9, due to the fact that both have square bases just muliply the lateral edge by itself

Step-by-step explanation:

Answer:

\(\frac{14x}{9}-5\)

Step-by-step explanation:

14 times a number x :  14* x = 14x

Quotient of 14 times a number x  an 9 :   \(\frac{14x}{9}\)

5 less the quotient of 14 times a number x and 9 :

\(\frac{14x}{9}-5\)

To determine the ratio of the heights of two similar pentagonal prisms with a volume ratio of 27:125, we need to consider the relationship between the volumes and dimensions of similar prisms. Since the prisms are similar, their corresponding linear dimensions (height, width, and length) have the same ratio.

Let's denote the ratio of their heights as h₁ : h₂. The volume ratio can be expressed as:

(Volume of Prism 1) / (Volume of Prism 2) = 27/125

For a prism, the volume can be calculated as:

Volume = Base Area × Height

Since the prisms are similar, the ratio of their base areas is the square of the ratio of their linear dimensions. Therefore, the ratio of their base areas is (h₁/h₂)².

Now, we can express the volume ratio in terms of their heights:

(h₁ × Base Area 1) / (h₂ × Base Area 2) = 27/125

Since the base areas are proportional, we can substitute the base area ratio with the height ratio squared:

(h₁ × (h₁/h₂)²) / h₂ = 27/125

We can cancel out one h₁ from both the numerator and denominator:

(h₁/h₂)² = 27/125

Now, take the square root of both sides to find the height ratio:

h₁/h₂ = √(27/125) = √(3³/5³) = 3/5

So, the ratio of their heights is 3:5.

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The probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

The given probability distribution table shows the probabilities of having 1, 2, or 3 computers in a randomly selected home in Queens. However, the probability of having 4 or more computers is not given in the table.

To find the probability of having 4 or more computers in a randomly selected home, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is having 4 or more computers in a home, and the complement of this event is having 1, 2, or 3 computers in a home.

So, the probability of having 4 or more computers in a randomly selected home in Queens can be calculated as:

P(4 or more) = 1 - P(1 or 2 or 3)

P(1 or 2 or 3) = P(1) + P(2) + P(3) = 0.4 + 0.3 + 0.2 = 0.9

P(4 or more) = 1 - 0.9 = 0.1

Therefore, the probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

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Answer:

EBC and ABE, as well as ABD and ABE

Step-by-step explanation:

Supplementary angles form an 180 degree angle. In other words, they form a straight line.

EBA and DBC are each greater than 90 degrees and are vertical angles, not supplementary angles.

EBC and ABE form a straight line. So they are supplementary angles.

ABD  and ABE form a straight line. So  they are also supplementary angles.

CBE and ABD are each less than 90 degrees and are vertical angles, not supplementary angles.

So, EBC and ABE, as well as ABD and ABE are the correct choices.

Answer:  35 is the answer for the given problem

Step-by-step explanation:

Answer:

\(x^2-y^2=\pm35\)

Fast and loose:

The difference being positive tells you that \(x>y\). Now try staring at the product for a while, and think of all possible combinations. It's either 6,1 and 3,2, -2,-3, -1,-6 Now, the 3/2 pair both give  1, so no good. 6-1 and \(-1-(-6)\) are indeed 5.

Rigorously:

if \(x-y=5\) it means \(x=5+y\), let's replace in the second

\((y+5)y=6\\y^2+5y-6= (y-1)(y+6)=0\)

From this we get either \(y=1; x=6\) or \(y=-6; x=-1\) . At this point is just replacing either pairs to get the result.

The result!

At this point we just have to crunch numbers:

\(6^2-1^2= 36-1=35\) OR

\((-1)^2-(-6)^2=1-36=-35\)

Answer:

I hope you got it.

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

245 divided by 7 = 35

Answer:

Yeah if she has 245 glue sticks and put the glue sticks in 7 bins ofc we are going to be dividing.

Step-by-step explanation:

245 divided by 7 = 35

Answer:

0

Step-by-step explanation:

i^2+1

We know that i^2 = -1

-1 +1

0