Rewrite
6 3/4
as an improper fraction.

Answer:

28.07°

Step-by-step explanation:

use SohCahToa

in this case we use tan^-1 to get the angle x°

tan^-1(8/15)=28.07248694

to the nearest hundredth

=28.07°

The given triangle is rotated about 180 degrees and as such, we can say that the triangle CBF is congruent to the triangle EDF.

From the attached image, we see that CB is parallel to ED. We also see that the transversal lines are  BD and CE.

The point E will become the image of point C by a rotation of 180° around the point F.

Now, the point D will be the image of point B by a rotation of 180° around the point F.

Rotation is a type of transformation and as such  ΔEDF will be the image of  ΔCBF.

Therefore we can conclude that ΔCBF ≅ ΔEDF

The second way to prove this congruency is as follows;

∠B = ∠D  (Due to the fact that alternate angles are congruent)

∠C = ∠E  (Due to the fact that alternate angles are congruent)

Now, since CB ≅ ED , then it means that ΔCBF ≅ ΔEDF by SAS congruency postulate

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Let's denote the amount Jolene invested at 3 percent interest as 'x' dollars. Since she put twice as much in the lower-yielding account, the amount she invested at 9 percent interest would be '2x' dollars.

To calculate the interest earned from each account, we'll use the formula: Interest = Principal × Rate × Time.

For the 3 percent interest account:

Interest_3_percent = x × 0.03

For the 9 percent interest account:

Interest_9_percent = 2x × 0.09

We know that the total annual interest is $3120, so we can set up the equation:

Interest_3_percent + Interest_9_percent = 3120

Substituting the above equations, we have:

x × 0.03 + 2x × 0.09 = 3120

Simplifying the equation:

0.03x + 0.18x = 3120

0.21x = 3120

Dividing both sides of the equation by 0.21:

x = 3120 / 0.21

x = 14857.14

Therefore, Jolene invested approximately $14,857.14 at 3 percent interest and twice that amount, $29,714.29, at 9 percent interest.

Answer:

Step-by-step explanation:

X is the amount invested at 6%

Y is the amount invested at 9%

0.06X + 0.09Y = 4998

X = 2Y

0.06(2Y) + 0.09Y  = 4998

.12Y + 0.09Y = 4998

0.21Y = 4998

21Y = 499800

Y = 499800/21 = 23800

So X = 2*23800 = 47600

$47,600 is invested at 6% and $23800 is invested at 9%

Answer:

y = 3.75x + 300

Step-by-step explanation:

hope it was in time :)

Answer:

56

Step-by-step explanation:

56

9514 1404 393

Answer:

  -2

Step-by-step explanation:

The rise between adjacent points (left to right) is -6, while the run is 3. Then the slope is ...

  m = rise/run = -6/3 = -2

The slope of the line is -2.

Hence the correct option is to translate down 2 unit

Transformations can be non-rigid (when the preimage's size or shape is unaltered) or stiff (where the size is changed but the shape remains the same). These are the fundamental guidelines that this concept abides by. It is a straightforward approach to alter 2D forms.

Planar transformations and spaces can be distinguished from one another using the dimensions of the operand sets.

We have the parent function f(X)= x

and transformed function is g(x)= -3f(x+5)-2

the parent function f(x) is translated dawn 2 units and stretched by 5 .

Hence the correct option is to translate down 2 unit

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The solution of the function 3f(1) - 4g(-2)  is -19.

The functions can be solved as follows;

f(x) = 7x - 4

g(x) = 11 - x²

Therefore, let's solve the composite function as follows:

A composite function is generally a function that is written inside another function.

Hence,

3f(1) - 4g(-2) = ?

f(1) = 7(1) - 4 = 7 - 4 = 3

g(-2) = 11 - (-2)² = 11 - 4 = 7

Therefore,

3f(1) - 4g(-2) = 3(3) - 4(7) = 9 - 28 = -19

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Answer:

it’s SAA

Step-by-step explanation:

ur wlcm, i am sure of my answer

brainliest please?

Answer:

I don't really know what the question is but..

Step-by-step explanation:

Since total of 92 people in the trip including student and chaperon, add groups of 23 to become 92 or use this equation

(20+3)xy=92

23y=92

y=92/23

y=4

therefore,

20x4=80 (students)

3x4=12 (chaperons)

Answer:

15 chaperones

Step-by-step explanation:

1. Okay, First you're going to see how many times 20 can feet into 92. Which is 4.5 times. However, you cannot cut someone in half. So the answer would actually be 5. Then. Just do 5*3, because remember, there are THREE chaperones for every 20 students.

Answer:

7 hours

Step-by-step explanation:

here,

270/18=105/x

x=(105*18)/270

x=7

Chau made $270 for 18 hours of work. At the same rate,  Therefore Chau would have to work 7 hours at the same rate to make $105.

To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:

Let x be the number of hours Chau needs to work to make $105.

We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:

Rate = Total earnings / Number of hours

Rate = $270 / 18 hours

Rate = $15 per hour

Now, we can set up the proportion:

$15 per hour = $105 / x hours

To find x, we can cross-multiply:

$15 × x = $105

Now, solve for x:

x = $105 / $15

x = 7 hours

So, Chau would have to work 7 hours at the same rate to make $105.

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There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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The probability of getting 21, when first card is an ace and the second card is a queen = 0.024133.

The term blackjack means that you get a value of 21 with only two cards.

Number of cards in a deck of cards = 52

There are 4 types of cards in a deck of cards - spades, clubs, hearts, and diamonds, out of which spades and clubs are black in colour.

Given that first card is Ace and second one is a Queen.

Odds of getting an Ace are 4/52, odds of the next being Queen is 16/51.

P(blackjack)=4×16/(52/2).

where P is used for probability .

Probability: Probability is simply how likely something is to happen. Whenever we are unsure about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events governed by probability is called statistics.

Probability of getting an ace followed by a queen card: 4/52 * 16/51 = 0.024133.

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Answer:

6.5

Step-by-step explanation:

\(a^{2} + b^{2} = c^{2}\) means that the two shorter legs (a and b) squared and added together equal the hypotenuse (c) you square \(6^{2} + 2.5^{2} = 42.25\) then find the square root of 42.25 which is 6.5

Answer:

39.0625

Step-by-step explanation:

Answer:

39.0625

Step-by-step explanation:

Answer:

A. $1 less

Step-by-step explanation:

24 divided by 8 (unit rate) = $3

28 divided by 7 = $4

4-3=1

The Gini coefficient is 2(−13/30) = -13/15.

The Lorenz curve L(p) can be expressed as the cumulative distribution function of a random variable X. The Gini coefficient is then given by the area between the diagonal line (representing perfect equality) and the Lorenz curve L(p).

In other words, the Gini coefficient is the ratio of the area between the diagonal line and the Lorenz curve to the total area under the diagonal line.

The Lorenz curve for the state can be given as L(p)=p^4/3.Ron can compute the Gini coefficient by finding the area between the diagonal line and the Lorenz curve.

The diagonal line goes from (0,0) to (1,1).The area under the diagonal line is 1/2.

The area between the diagonal line and the Lorenz curve is given by∫[0,1](L(p)−p)dp=

∫[0,1](p^4/3−p)dp

=(1/15)−(1/2)

= -13/30

The Gini coefficient can be negative when the Lorenz curve lies above the diagonal line, which indicates that the distribution is more equal than the hypothetical distribution of perfect equality.

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Answer:

The trip is 50 miles

Step-by-step explanation:

30 = (60/100)T

T = (10/6)(30) = (5/3)(30) = 50 miles

We have to find in a total spent of $2000 how much represents $120

first divide both 2000/120= 200/12= 100/6= 16.667

but that means

100 = 16.667x 6

so 16.667 represents the 6%

Step-by-step explanation:

bence 3 günde 80 tavuk aldıgı icin 240 mı oluyor

In choosing Fran's company over Shirley's company, the customer saves $160

What is Algebra?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)

As per the given details:

Fran charges f(h) = 25 +135h

Shirley charges s(h) = 65 + 150h

h = number of hedges

Cost in Fran's company for 8 hedges = 25 + 135(8)

= $1105

Cost in Shirley's company for 8 hedges = 65 + 150(8)

= $1265

Cost saved by the customer in choosing Fran's company:

Cost in Shirley's company - Cost in Fran's company

=  $1265 - $1105

=  $160

A customer saves $160 in choosing Fran's company over Shirley's company.

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Answer:

7

Step-by-step explanation:

Answer:

\(\sqrt{15}\)

Step-by-step explanation:

a^2+b^2=c^2

7^2+b^2=8^2

49+b^2=64

b^2=15

b=\(\sqrt{15}\)

Answer:

14.61111 Celsius.

That is the answer.

Answer:

Step-by-step explanation:

The given function is  :  

Here , x= independent variable where we place the input value and f(x) = dependent variable where we get the output value.

Now , when we put x= 3 , we get

That means , the value of f(3) in the given function is 8.

Hence, the correct answer is B=8.

Answer:

$26,986.29

Step-by-step explanation:

We can use the formula for calculating the depreciation of an asset over time:

wor

\(\bold{D = P(1 - \frac{r}{100} )^t}\)

where:

D= the current value of the asset

P = the initial purchase price of the asset

r = the annual depreciation rate as a decimal

t = the number of years the asset has been in use

In this case, we have:

P = $39,600

r = 12% = 0.12

t = 3 years

Substituting these values into the formula, we get:

\(D= 39,600(1 - \frac{12}{100})^3\\D= 39,600(1 - 0.12)^3\\D= 39,600*0.88^3\\D= 39,600*0.681472\\D=26986.2912\)

Therefore, the car is worth approximately $26,986.29 after 3 years of depreciation at a rate of 12% per annum.

Answer:

$26,986.29

Step-by-step explanation:

As the car's value depreciates at a constant rate of 12% per annum, we can use the exponential decay formula to create a function for the value of the car f(t) after t years.

\(\boxed{f(t)=a(1-r)^t}\)

where:

In this case, the initial value is $39,600, and the rate of depreciation is 12% per year. Therefore, the function that models the value of the car after t years is:

\(f(t)=39600(1-0.12)^t\)

\(f(t)=39600(0.88)^t\)

To calculate the value of the car after 3 years, substitute t = 3 into the function:

\(\begin{aligned} f(3)&=39600(0.88)^3\\&=39600(0.681472)\\&=26986.2912\\&=26986.29\;(\sf 2\;d.p.)\end{aligned}\)

Therefore, the car is worth $26,986.29 after 3 years.

1 From the given information, no determination can be made as to whether the parallelogram is a rhombus, a rectangle, or a square.

2 The reason for the determination made in the previous step is A. From the given information, no determination can be made as to whether the parallelogram is a rhombus, a rectangle, or a square.

The diagonals of a parallelogram bisect each other, but this is true for all parallelograms, regardless of whether they are squares, rectangles, or rhombuses.

Therefore, the given information is not sufficient to determine whether the parallelogram is a rhombus, a rectangle, or a square.

In conclusion, from the given information, no determination can be made as to whether the parallelogram is a rhombus, a rectangle, or a square.

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Simplifying this fraction gives us 1/4. The answer is (D) 1/4.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

Let's start by finding the fraction of Michelle's patients who are under 12 or over 65. We know that one-third of her patients are under 12, so two-thirds must be 12 or older. Similarly, five-twelfths of her patients are over 65, so seven-twelfths must be 65 or younger.

Now, we want to find the fraction of Michelle's patients who are between 12 and 65. To do this, we need to subtract the fraction of patients who are under 12 or over 65 from 1 (since these are the only two age groups we're considering).

Fraction of patients under 12: 1/3

Fraction of patients over 65: 5/12

Fraction of patients 12 to 65: 1 - 1/3 - 5/12

We can simplify this expression by finding a common denominator:

Fraction of patients 12 to 65: 12/12 - 4/12 - 5/12

Fraction of patients 12 to 65: 3/12

Simplifying this fraction gives us 1/4. Therefore, the answer is (D) 1/4.

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Answer: 9x^2+15x-6

Step-by-step explanation: I did my test an it said this was right (Plato )

The solution of the function is 9x² + 15x -6. The correct option is C.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

Given function is F(x) = x² + 7x and g(x) = 3x - 1. The value of the function  (fg)(x) will be calculated as,

(fg)(x) =  x² + 7x

(fg)(x) = ( 3x - 1)² + 7(3x - 1)

(fg)(x) = 9x² -6x + 1 + 21x - 7

(fg)(x) = 9x² + 15x - 6

Therefore, the solution of the function is 9x² + 15x -6. The correct option is C.

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