The ratio of oranges sold to bananas sold is 3 to 10. If a total of 30 bananas were sold,then how many oranges were sold ?

Answer:

Any value of x makes the equation true -> All Real Numbers (-∞, ∞)

Step-by-step explanation:

#a

\(\\ \rm\Rrightarrow f(-4)\)

\(\\ \rm\Rrightarrow 3(-4)+2\)

\(\\ \rm\Rrightarrow -12+2\)

\(\\ \rm\Rrightarrow -10\)

#b

#1

\(\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}\)

\(\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}\)

Find y

\(\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}\)

Inverse is

\(\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}\)

#2

\(\\ \rm\Rrightarrow gof(x)\)

\(\\ \rm\Rrightarrow g(f(x))\)

\(\\ \rm\Rrightarrow g(3x+2)\)

\(\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}\)

\(\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}\)

\(\\ \rm\Rrightarrow \dfrac{6x+3}{3}\)

If we factor out

\(\\ \rm\Rrightarrow \dfrac{2x+1}{1}\)

\(\\ \rm\Rrightarrow 2x+1\)

#c

\(\\ \rm\Rrightarrow f(x)=g(x)\)

\(\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}\)

\(\\ \rm\Rrightarrow 3(3x+2)=2x-1\)

\(\\ \rm\Rrightarrow 9x+6=2x-1\)

\(\\ \rm\Rrightarrow 7x=-7\)

\(\\ \rm\Rrightarrow x=-1\)

Answer:

Given functions:

\(f(x)=3x+2\)

\(g(x)=\left(\dfrac{2x-1}{3}\right)\)

Part (a)

\(\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}\)

Part (b)(i)

\(\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}\)

Part (b)(ii)

\(\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}\)

Part (c)

\(\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}\)

Answer:

9.013 square units

Step-by-step explanation:

Answer:

6x+8y = 3

Step-by-step explanation:

we have 3x + 4y = 7

4y = -3x + 7

y = -3/4 x + 7/4

so slope is -3/4

2 parallel lines always have same slope

so the slope of our new line is -3/4

so y = -3/4 x + C

for c,

we have (x,y) = (-2/3,7/8)

7/8 = -3/4 * -2/3 + C

C = 3/8

so equation is

y = -3/4 x + 3/8

simplyfyig,

8y = -6x + 3

or, 6x+8y = 3

The value of a Chi-Square goodness-of-fit test at a 5% significance level is 13.45

We need to perform a Chi-Square goodness-of-fit test at a 5% significance level.

First we need to calculate the expected count

expected value = ∑(x)/n

= (40 + 33 + 35 + 32 + 60)/5

= 200/5

= 40

Now we need tocalculate the test statistic value

Observed  expected  O - E    (O - E)^t/E       %

40                40             0            0                   0

33                40             -7          1.225          9.11

35                40             -5          0.625         4.65

32                40             -8         1.6                11.90

60                40             20        10                 74.35

Chi square test is 13.45

Therefore, the value of test statistics is 13.45.

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Josue used 150 square centimeters of wrapping paper to cover the cube-shaped gift box

To determine the amount of wrapping paper used by Josue for the cube-shaped gift box, we need to calculate the surface area of the cube.

The net of the gift box consists of six squares, each representing a face of the cube. The dimensions provided in the figure show that each side of the squares is 5 cm.

Since a cube has six faces, we need to calculate the total surface area by multiplying the area of one square face by six.

The formula to find the area of a square is side length squared, so we can calculate the area of one square face as 5 cm * 5 cm = 25 cm².

Now, to find the total surface area, we multiply the area of one face by six: 25 cm² * 6 = 150 cm².

Therefore, Josue used 150 square centimeters of wrapping paper to cover the cube-shaped gift box.

It's worth noting that this calculation assumes that there is no overlap or excess wrapping paper used while wrapping the gift box. Additionally, we have assumed that the dimensions provided are accurate and refer to the side length of the squares in the net.

Overall, the amount of wrapping paper used can vary based on the wrapping technique employed and any additional decorations or folds added to the gift box.

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Answer: -2

Step-by-step explanation:

Answer:

2 and 3\4

Step-by-step explanation:

hope that is right

The inclined end of the ramp is 7.27 inches above the ground.

The ramp needs to run 10 inches horizontally for every 1 inch of rise.

Let's denote the length of the inclined end of the ramp (the rise) as "x" inches.

Since the ramp needs to run 10 inches horizontally for every 1 inch of rise, the horizontal distance covered by the ramp (the run) can be calculated as 10x inches.

We are also given that the surface of the ramp is 80 inches long.

This surface includes both the rise and the run of the ramp.

So we can write the following equation:

x + 10x = 80

11x = 80

Dividing both sides of the equation by 11:

x = 80 / 11

x = 7.27 inches

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54 people from the region will need to be selected to find one person who carries the genetic trait

47 percent of the people living in a certain region carry a certain genetic trait.

since 47% carry genetic trait

therefore 53% didn't carry genetic trait

because every time we get person not carry genetic trait but after 54 person surety carry genetic trait

people from the region will be selected at random one at a time until someone is found who carries the genetic trait.

0.47 would be your probability of randomly selecting but your'e solving geometrically so think how many trials until successful.

use u x(mean)= 1/.47 to get around 2.13

54 people from the region will need to be selected to find one person who carries the genetic trait

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The probability that a dancer performs first in the talent competition can be calculated by dividing the number of favorable outcomes (a dancer performing first) by the total number of possible outcomes (all possible orderings of the acts). The answer is a simplified fraction.

There are a total of 20 acts consisting of 4 instrumentalists, 10 singers, and 6 dancers. Since we want to find the probability of a dancer performing first, we can consider the first act as the dancer, and the remaining acts can be arranged in any order.

The total number of possible orderings of the 20 acts is 20!, which represents the factorial of 20 (20 factorial).

The number of favorable outcomes is 6 * 19!, which means fixing one dancer as the first act and arranging the remaining 19 acts in any order.

Therefore, the probability can be calculated as:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

= (6 * 19!) / 20!

The expression (6 * 19!) / 20! can be simplified by canceling out the common factors:

Probability = 6 / 20

Hence, the probability that a dancer performs first is 6/20, which simplifies to 3/10.

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Answer:

uhhh

Step-by-step explanation:

Answer:

IT IS ALSO ISOSCELES !!

Step-by-step explanation:

2 sides are the same

if it was scalene all sides would be different

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Answer:

3.1415926

Step-by-step explanation:

3.1415926 * 1 = 3.1415926

Answer:

g4 bk.58i

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sadie's tower is the one of the left.

A)  Since the blocks are the same the

For 1 block

length = 6           >from image

width = 6             >from image

height = 7            > height for 1 block = height/4 = 28/4   divide by

                               4 because there are 4 blocks

For Evan's tower of 3:

length = 6

width = 6

height = 7*3

height = 21

Volume = length x width x height

Volume = 6 x 6 x 21

Volume = 756 m³

B)  Sadie's tower of 4:

Volume = length x width x height

Volume = 6 x 6 x 28

Volume = 1008 m³

Difference in volume = Sadie's Volume - Evan's Volume

Difference = 1008-756

Difference = 252 m³

C) He knocks down 2 of Sadie's and now her new height is 7x2

height = 14

Volume = 6 x 6 x 14

Volume = 504 m³

The effective annual rate (EAR) for the investment account with a return of 14.00% (APR) compounded quarterly can be calculated using the formula:

EAR = (1 + (APR / n))^n - 1

Where APR is the annual percentage rate and n is the number of compounding periods per year. In this case, since interest is compounded quarterly (every 3 months), n would be 4.

Plugging in the values, we have:

EAR = (1 + (0.14 / 4))^4 - 1

Calculating this expression, we find that the effective annual rate is 14.62%.

The effective annual rate (EAR) is a measure of the true annual interest rate taking into account the effects of compounding. It allows for easy comparison of different interest rates that compound over different periods.

In this scenario, the investment account has an annual percentage rate (APR) of 14.00%, which represents the nominal interest rate per year. However, the interest is compounded quarterly, meaning it accrues and is added to the account balance every 3 months. To determine the actual annual rate accounting for compounding, we calculate the effective annual rate (EAR).

By using the formula mentioned above and plugging in the values, we can calculate the EAR. The APR is divided by the number of compounding periods per year (4, in this case), and then 1 is added to this result. The entire expression is raised to the power of the number of compounding periods per year (4) and then subtracted by 1.

The resulting EAR is 14.62%, indicating the equivalent annual rate considering the effects of compounding on the investment account.

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The given problem can be exemplified in the following diagram:

Applying the Pythagorean theorem we get:

Solving the squares:

Solving the operations:

Now we take the square root to both sides:

Solving the operations:

Therefore, the height of the tree is 35.8 feet.

Answer:

Step-by-step explanation:

The notation means that wherever you see an x on the right, you let it equal 2.

g(x) = 3x^2 + 4x - 36

x = 2

g(2) = 3*2^2 + 4*2 - 36

g(2) = 3*4 + 8 - 36

g(2) = 12 + 8 - 36

g(2) = 20 - 36

g(2) = - 16

Answer:

7,8

Step-by-step explanation:

The cost of endless chicken wings at Restaurant X is $5. So cost equation for n chicken wings at Restaurant X is,

The cost of chicken wings at Restaurant Z is 20 cents and $1.40 for sauce. So cost equation for Restaurant Z is,

So answer is,

Restaurant X: c = 5

Restaurant Z: 0.20n + 1.40

(b)

Plot the system of equation on the graph.

(c)

The lines of two restaurant X and restaurant Z intersect each other at point (18,5). This means that restaurant X and restaurant Z has same cost 5 at n = 18. So both restanurant has same cost for 18 chicken wings.

Answer: 18

Answer:

  2820 no votes

Step-by-step explanation:

The fraction of votes that were 'no' is ...

  no/total = (5)/(8+5) = 5/13

The number of votes that were 'no' is ...

  (5/13)(7332) = 2820 . . . no votes

The value of x from the given supplementary angles is 42°.

Find the value of x using the measures of the two given adjacent supplementary angles.

The two angles are 3x and 54

3x+ 54=180

Supplementary angles measure is equal to 180°.

hence we frame it as:

3x+ 54=180

now arrange the like terms:

⇒ 3x = 180-54

⇒ 3x=126

⇒ x=126/3

⇒ x=42

hence x value is 42°

now 3x=3(42)

= 126

the two angles are 126° and 54°

Hence we get the required answer.

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Answer:

360 degrees divided by that order

TRUNCATED to one decimal place, it's 50.2

ROUNDED to one decimal place, it's 50.3

The round-off of 50.272 to 1 decimal place using rules of rounding

numbers are 50.3.

Rounding off numbers means making a number simpler by adjusting it to its nearest place according to certain rules.

Rounding a number to one decimal place means keeping only the first digit after the decimal point and neglecting the rest. In this case, the digit in the second decimal place is 7, which is greater than or equal to 5. As per the rounding rules, if the digit is greater than 5, the preceding digit is increased by 1.

So, 50.272 becomes 50.3 when rounded to one decimal place.

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Answer:

the product of the 2 numbers is 22

Step-by-step explanation:

x² + y² = 80

(x - y)² = 36

=>

x - y = 6

or y - x = 6

let's start with the first one x-y=6

x = 6 + y

=>

(6+y)² + y² = 80

y² + 6y +6y + 36 + y² = 80

2y² + 12y + 36 = 80

2y² + 12y - 44 = 0

y² + 6y - 22 = 0

the solution of a quadratic equation

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case here we have an squadron in y.

a=1

b=6

c=-22

(-6 ± sqrt(36 + 4×22))/2 = (-6 ± sqrt(36+88))/2 =

= (-6 ± sqrt(124))/2 = (-6 ± sqrt(4×31))/2 =

= (-6 ± 2×sqrt(31))/2 = -3 ± sqrt(31)

y1 = -3 + sqrt(31)

y2 = -3 - sqrt(31)

=>

x1 = 6 + -3 + sqrt(31) = 3 + sqrt(31)

x2 = 3 - sqrt(31)

control :

(-3 + sqrt(31))² + (3 + sqrt(31))² = 80

9 - 3 sqrt(31) - 3 sqrt(31) + 31 + 9 +3 sqrt(31) + 3 sqrt(31) + 31 = 80

9 + 31 + 9 +31 = 80

18 + 62 = 80

80 = 80 correct

solving now for y-x=6

delivers exactly the same calculations, just with x and y trading places.

so, the resulting 2 number pairs are the same.

the product of the 2 numbers :

(3 + sqrt(31))(-3 + sqrt(31)) = -9 - 3 sqrt(31) + 3 sqrt(31) + 31 =

= -9 + 31 = 22

(3 - sqrt(31))(-3 - sqrt(31)) = -9 + 3 sqrt(31) - 3 sqrt(31) + 31 =

= 22

so, the product is the same in both cases.

Answer:

-10

Step-by-step explanation:

∛-1000=-10

Answer:

-10

Step-by-step explanation:

First...

A cube root is to find a number that if multiplied three times by its self equals this number. (sorry a little confusing)

Next...

Forget about the negative for a little bit and look at it.

10*10*10=1000

Finally...

If 10 cubed is positive 1000 then -10 cubed is -1000.

So the answer is -10.

Answer: It means Undo

Step-by-step explanation:

The probability that the lifetime of at least one component exceeds 2 is 0.135.

Given that the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image.

We want to find the probability that the lifetime of at least one component exceeds 2.

The probability that the lifetime of at least one component exceeds 2 is P(X>2).

\(\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}f(x,y)dydx\end\)

Now, we will substitute the given function, we get

\(\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}xe^{-x(1+y)}dydx\end\)

Further, we will simplify this, we get

\(\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\left[-e^{-x(1+y)\right]_{0}^{\infty}dx\\ &=\int_{x=2}^{\infty}e^{-x}dx\\ &=\left[-e^{-x}\right]_{2}^{\infty}\\ &=e^{-2}\\ &=0.135\end\)

Hence, the probability that the lifetime of at least one component exceeds 2 for the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image is 0.135.

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