Construct rectangle ABCD in which b) BC = 5.4 cm and BCA = 45°​

The equation of the transformed function is f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3.

Given that,

The f(x) = square root of X base function is transformed by a reflection in the x-axis, a vertical stretch by a factor of 3, a horizontal compression by a factor of 1/2, a vertical translation by a factor of 3, a vertical translation by a factor of 3 down, and then a horizontal translation by a factor of 6 right.

We have to verify the changed function's equation.

Take the function

f(x)=√x

The function reflection in the x-axis,

f(x)=-√x

The function is vertical stretch by a factor of 3.

f(x)= -1/3√x

The function is horizontal compression by a factor of 1/2.

f(x)= -1/3[tex]\sqrt{2x}[/tex]

The function is vertical translation by a factor of 3 down,

f(x)=  -1/3[tex]\sqrt{2x}[/tex] -3

The function is horizontal translation by a factor of 6 right.

f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3

Therefore, The equation of the transformed function is f(x)= -1/3[tex]\sqrt{2(x-6)}[/tex] -3.

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a) Refer to the attachment for graph:

The ellipse in counter clockwise direction starting from the point (1,0)

b) Cartesian equation for a curve that contains the parametrized curve is

  x²+ y/4=1

What are trigonometric expressions?

Trigonometric identities are, by definition, reciprocal. These formulas show the connections between the sine/cosine functions and tangents.

a) Given: x= cost , y= 2 sin t,  0<t≤2π

y= 2 sin t,

sin t= y/2

we know that,

cos²t + sin²t=1

x²+ y/4=1

b)  The point (x,y) moves on the ellipse x²+ y/4=1

   t increases from 0 to 2π.  The point (x,y)  moves around the ellipse around the ellipse in counter clockwise direction starting from the point (1,0)

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According to the given standard deviation, the bag that the student brought has more than 1 gram of potato chip than the average chip bag.

Standard deviation:

Standard deviation refers the measure of how scattered the data is in relation to the mean.

Given,

The student wanted to know if the bags of potato chips they were buying contained the correct weight of chips compared to the listed weight on the bag of 42.5 grams.

And the student collected a sample of 30 bags of chips and weighed each bag. Here the average weight of the bags they collected was 41 grams with a standard deviation of 1.6 grams. assume a 95% level of confidence.

Now, we have to find the confidence interval for this situation.

From, the given details, we have obtained the following things,

Bag weight = 42.5 gram

Number of samples = 30

Average weight = 41 grams

Standard deviation = 1.6 grams

Confidence level = 95%

So, according to the formula of confidence interval,

The value of it is calculated as,

=> CI = x ±  Z × s / √n

When we apply the values on the formula, then we get,

=> CI = 41 ± 1.9600 × 1.6 / √30

=> CI = 41 ± 0.573

Therefore, Confidence Interval 41 ±0.573 (±1.4%) [40.427 – 41.573].

While we compare this one with the given bag weight we get the difference of,

=> 42.5 - 41.5

=> 1

Therefore, the bag that the student brought has more than 1 gram of potato chip than the average chip bag.

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Answer:

5

Step-by-step explanation:

Answer:

The answer for the question is five!

Answer: Answer is below

Step-by-step explanation:

Angles 1 and 5 and 8 are the same.

Angles 2 and 3 and 6 and 7 are the same.

180-138=42 degrees

So the obtuse are 138 and the acute are 42.

Angle 1 is 138 degrees

Angle 2 is 42 degrees

Angle 3 is 42 degrees

Angle 5 is 138 degrees

Angle 7 is 42 degrees

Angle 8 is 138 degrees

Angle 6 is 42 degrees

Hope it helped and have a nice weekend!

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Answer:

Angle 4 is 138 and opposite angles are the same! That makes angle 1, 5, and 8 the same as 4 which is 138!

We need to subtract to find the other 4 angles!

180 - 138 = 42 degrees

Angles 2, 3, 6 and 7 will be 42 degrees!

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Answer:

Step-by-step explanation:

m just means measure. So the question is asking you what is the MEASURE of the ANGLE AEB.

Since angles AEB and CED are vertical angles, you can set the two expressions equal to each other and solve for X.

1) 3x + 54 = 7x - 30

2) 54 = 4x - 30

3) 84 = 4x

4) x = 21

3(21) + 54 = 117

m∠AEB = 117°

The solution for y and x in the expressions given as 2/5(10y-5) =2y + -10 and x − 3.28 = −5.34 are y = 6 and x = -2.06, respectively

Variable y

From the question, the algebraic expression is given as

2/5(10y-5) =2y + -10

Open the brackets

This gives

4y - 2 = 2y + -10

Collect the like terms in the above equation

So, we have the following representation

4y - 2y = 10 + 2

Evaluate the like terms

2y = 12

Divide by 2

y = 6

Variable x

Here, we have

x − 3.28 = −5.34

There is a constant to add to or subtract from the expression

So, we add 3.28 to both sides

x = 3.28 − 5.34

Evaluate the like terms

x = -2.06

Hence, the solution is x = -2.06

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The probable percentage of complete and usable observation is 18.87%

Probable percentage is probability of a certain event which can be written as percentage

Total number of variables in data set = 20 variables

percentage of randomly spread missing observation in data set = 8%

percentage of non missing observation in data set = 100% - 8%

= 92%

changing percentage into number = 92 / 100

= 0.92

Probable percentage of complete and usable observation =

(0.92)²⁰ × 100

solving the power

0.18869 × 100

= 18.87

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Using the concepts of Application of derivative, we got that 1657.92inches³/sec rate  of the  volume of the cone changing when the radius is 40 inches and the height is 40 inches for a right circular cone.

We know that volume of right circular cone is given by =(1/3πr²h)

We are given rate of change of radius(dr/dt) and rate of change of the height(dh/dt)

Therefore ,differentiating the volume with respect to time and applying the chain rule.

dV/dt = [(1/3)πr²×(dh/dt)+ (1/3)π·2·r·(dr/dt)·h]

=>dV/dt=[(1/3)× π×r × [(r×dh/dt)+2h×(dr/dt)]]

We are given that dr/dt=2inc/sec and dh/dt= -5inc/sec

So, on putting the values, we get

=>dV/dt=[ ( (1/3)×3.14×40)×[40×(-5)+2×40×2]]

=>dV/dt=[0.33×3.14×40×[-200+160]

=>dV/dt=[0.33×3.14×40×(-40)]

=>dV/dt= -1657.92inches³/sec(negative sign denote volume is decreasing)

Hence, if the radius of a right circular cone is increasing at the rate of 2 inches per second and its height is decreasing at the rate of 5 inches per second.  the rate of  the volume of the cone changing when the radius is 40 inches and the height is 40 inches is 1657.92inches³/sec.

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Raja can make 7 perfume samples from a 2.8 ounce bottle of perfume.

According to the question,

We have the following information:

Raja manages a perfume store. She makes 0.4-ounce samples from a 2.8- ounce bottle of perfume.

So, we have the following expressions:

1 bottle of perfume sample = 0.4 ounce

Total ounces of perfume in the bottle = 2.8 ounce

Now, we can easily find the number of perfume samples that can be made from this perfume by dividing the total ounces of perfume in bottle by the ounces of perfume sample.

Number of perfume samples = 2.8/0.4

Number of perfume samples = 7

Hence, Raja can make 7 perfume samples from a 2.8 ounce bottle of perfume.

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Answer: n = 31.66666667

Step-by-step explanation:

Add '-12n' to each side of the equation.

500 + -12n = 120 + 12n + -12n

Combine like terms: 12n + -12n = 0

500 + -12n = 120 + 0

500 + -12n = 120

Add '-500' to each side of the equation.

500 + -500 + -12n = 120 + -500

Combine like terms: 500 + -500 = 0

0 + -12n = 120 + -500

-12n = 120 + -500

Combine like terms: 120 + -500 = -380

-12n = -380

Divide each side by '-12'.

n = 31.66666667

Simplifying

n = 31.66666667

The distance from the entrance which is located at (-3,7) to the garden at points (3,-2) is [tex]3\sqrt{13}[/tex].

First, let us understand the distance formula:

The distance formula is the measurement of the distance between 2 points. It calculates the straight line distance between the given points.

The distance formula is given by:

Distance = [tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]

Where A(a, b) and B(c, d) are the coordinates.

We are given;

The park entrance is located at (-3, 7).

Another point at (3, -2).

We need to find the distance from the entrance to the garden at another given point.

Substitute the given values in the distance formula, we will get;

Distance = [tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]

Distance = [tex]\sqrt{(-3-3)^2+(7-(-2))^2}[/tex]

Distance = [tex]\sqrt{(6)^2+(9)^2}[/tex]

Distance = [tex]\sqrt{36+81}[/tex]

Distance = [tex]\sqrt{117}[/tex]

Distance = [tex]3\sqrt{13}[/tex]

So, the distance between the given points is [tex]3\sqrt{13}[/tex].

Thus, the distance from the entrance which is located at (-3,7) to the garden at points (3,-2) is [tex]3\sqrt{13}[/tex].

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Answer: florist a is cheaper than florist b

Step-by-step explanation: the price of florist B's flowers are 5.20$ more than florist A's

Answer:

Step-by-step explanation:

or

Answer:

[tex]\left(\dfrac{12}{5}\right)^2=\left(2\frac{2}{5}\right)^2[/tex]

Step-by-step explanation:

Given mixed number:

[tex]5 \frac{19}{25}[/tex]

Rewrite the given mixed number as an improper fraction:

[tex]\implies 5 \frac{19}{25}=\dfrac{5 \times 25+19}{25}=\dfrac{125+19}{25}=\dfrac{144}{25}[/tex]

Rewrite 144 as 12² and 25 as 5²:

[tex]\implies \dfrac{144}{25}=\dfrac{12^2}{5^2}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^c}{b^c}=\left(\dfrac{a}{b}\right)^c:[/tex]

[tex]\implies \dfrac{12^2}{5^2}=\left(\dfrac{12}{5}\right)^2[/tex]

Convert 12/5 to a mixed number:

[tex]\implies \left(\dfrac{12}{5}\right)^2=\left(\dfrac{10+2}{5}\right)^2=\left(\dfrac{10}{5}+\dfrac{2}{5}\right)^2=\left(2\frac{2}{5}\right)^2[/tex]

Required correct statement is n+ 8 could be positive or negative or zero.

What is a negative number?

A negative number is any number less than zero. For example, -8 is a number that is seven less than 0. It may seem odd to say that a number is less than 0. After all, we often think that zero means nothing.

Option A: n + 8 is always positive is not correct since n is negative and adding a positive number (8) to a negative number will give a negative or zero result.

Option B: n + 8 is always negative is not correct since adding a positive number (8) to a negative number will give a negative or zero result, not always negative.

Option C: n + 8 cannot be zero is a wrong statement, if we put value of n = -8 then we will get zero as answer.

Option D: n + 8 could be positive or negative or zero is correct since it depends on the value of n.

If n is a large negative number, n + 8 could still be negative. If n is a small negative number or zero, n + 8 could be positive or zero.

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Correct question is "n is a negative number.

Which statement is correct?

Choose only one answer.

A) n +8 is always positive

B) n +8 is always negative

C) n + 8 cannot be zero

D) n+ 8 could be positive or negative or zero"

The equation which represents the population, P after t months is:

y = 1600(1+ 0.25)^t.

Given,

A population of beetles grows by 25% every month.

the beetle population starts with 1,600 beetles,

we are asked to determine the equation which represents the population, P after t months.

The equation for the population is:

Pf = Pi(1-r)^t

where pf = final value

pi = initial value

r = growth factor

t = time in years.

substitute the values in the equations.

let y represent the final population after t years.

r = 25%

convert percentage to decimal.

r = 0.25

y = 1600(1+ 0.25)^t

Hence we get the required answer.

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The expression below using the MathQuill function is 2x^3+42^3-\sqrt\left(49\right).

Given expression:

= 2x³+42³-√49

Expression:

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

After using MathQuill function:

2x³+42³-√49 = 2x^3+42^3-\sqrt\left(49\right).

Therefore The expression below using the MathQuill function is 2x^3+42^3-\sqrt\left(49\right).

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Answer:30

Step-by-step explanation:6 times 4 is24 and to the nearest 100 it will be 30

Step-by-step explanation:

The lengths of the sides of the rectangular field should be 40 ft (smaller value) and 60 ft (larger value) respectively.

Let L = length of rectangle area and W = width of rectangle area.

Let the length of the side that divides the area be parallel to the width of the area.

The total length of fencing F = 2L + 2W + W

F = 2L + 3W

Since the area is a rectangle, its area is A = LW

Since the area = 2400 square feet,

LW  = 2400 ft²

So, L = 2400/W

Substituting L into F, we have

F = 2L + 3W

F = 2(2400/W) + 3W

F = 4800/W + 3W

To find the value at which F is minimum, we differentiate F with respect to W.

So, dF/dW = d(4800/W + 3W)/dW

dF/dW = -4800/W² + 3

Equating dF/dW to zero, we have

-4800/W² + 3 = 0

-4800/W² = - 3

W² = -4800/-3

W² = 1600

W = √1600

W = 40 ft

To determine if this is a value that gives minimum F, we differentiate F twice to get

d²F/dW² = d(-4800/W² + 3)/dW

d²F/dW² = 14400/W³ + 0

d²F/dW² = 14400/W³

substituting W = 40 into the equation, we have

d²F/dW² = 14400/(40)³

d²F/dW² = 14400/64000

d²F/dW² = 0.225

Since d²F/dW² = 0.225 > 0, W = 40 is a minimum point for F

Since L = 2400/W

So, L = 2400/40

L = 60 ft

So, the lengths of the sides of the rectangular field should be 40 ft (smaller value) and 60 ft (larger value) respectively.

The expression that can be used to find the change in temperature each hour would be 27 h.

It is given that the temperature dropped 27°F in h hours. The temperature dropped the same number of degrees each hour.

We have to find the change in temperature each hour.

We can express this mathematically:

27 h

Then the equation would be 27 h.

Therefore, The temperature dropped the same number of degrees each hour would be 27 h.

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Answer:

Step-by-step explanation:

Its the last two and the first one

The perimeter of the rectangle is 16 feet.

The correct answer is an option (C)

In this question, the length of the rectangle is,

l = 1 yard 2 feet 1 inch

l = 3 feet + 2 feet + 0.0833 feet

l = 5.0833 feet

And the width of the rectangle is,

w = 2 feet 11 inches

w = 2 feet + 0.9167 feet

w = 2.9167 feet

So, the perimeter of the rectangle would be,

P = 2(l + w)

P = 2 * (5.0833 + 2.9167)

P = 16 feet

Therefore, the perimeter of the rectangle is 16 feet.

The correct answer is an option (C)

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Jason can check his answer isolate the variable, solving the operations and substituting the (x) value in the equation.

The clearance rules to solve the problem are the following:

The sign rules to solve the problem are the following:

Solving the equation we have:

-8. 5x – 3. 5x = –78

Two like signs add the values and keep the common sign.

-12x = -78

What is multiplying goes to the other side of the equality by dividing.

x = -78 / -12

x = 6.5

Substituting the (x) value in the equation we can check the answer and we get:

-8. 5x – 3. 5x = –78

-8.5(6.5) - 3.5(6.5) = -78

-55.25 - 22.75 = -78

- 78 = - 78

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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The equation in vertex form would be y = [tex]2(x+5)^{2}[/tex] -6

The vertex of a parabola is the point where the parabola crosses its axis of symmetry.  If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape.  If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.

The standard equation of a parabola is

y=a[tex]x^{2}[/tex]+bx+c .

But the equation for a parabola can also be written in "vertex form":

y= a(x-h)² +k

if the curve passes through (-3, 2) and the coordinates of vertex h = -5, K= -6, then we can find a by simple substitution

2 = a[tex](-3 + 5)^{2}[/tex] - 6

2 = a([tex]2^{2}[/tex]) - 6

2 = 4a - 6

collecting like terms

4a = 2 + 6

4a = 8

dividing both sides by 4

a = 8/4

a = 2.

So the equation of parabola in vertex form is y = 2[tex](x+5)^{2}[/tex] - 6

In conclusion, the equation of parabola in vertex form is 2[tex](x+5)^{2}[/tex] - 6

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Answer: 41 miles per gallon

Step-by-step explanation: Divide 256 by 6 and you get 41

The probability the mean of his sample will be between $45.00 and $65.00 is 0.6826.

Given:

A delivery driver has an average daily gasoline expense of $55.00. the standard deviation is $10.00. the owner takes a sample of 54 bills.

n = 54

standard error = 10/[tex]\sqrt{54}[/tex]

= 2.205

when x = 45,

z score = 45 - 55 / 10

= -10/10

= -1

probability at z = -1 is 0.3413

z score for x = 65

z = 65 - 55 / 10

= 10/10

= 1

probability at z = 1 is 0.3413

Total probability = 0.3413+0.3413

= 0.6826

Therefore the probability the mean of his sample will be between $45.00 and $65.00 is 0.6826.

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The evaluation of the inverse of the function, f(x) = -0.086·x + 2.92 are;

a. The inverse of the function is f⁻¹(x)  = -11.63·x + 33.95

B. The inverse function gives the number of year after 2000 when the percentage of children taking antidepressants is equal to x

b. The percentage of children taking antidepressant is 2.3% in 2007

The inverse of a function is a function that gives the input from the output such that it undoes the function's effect.

The function that indicates the percentage of children taking that take antidepressants from from the year 2004 to the year 2009 is presented as follows;

f(x) = -0.086·x + 2.92

x = The number of years after the year 2000

The inverse of the function can be obtained by making x the subject of the function formula as follows;

f(x) = -0.086·x + 2.92

f(x) - 2.92 = -0.086·x

x = (f(x) - 2.92)/(-0.086) ≈ -11.63·f(x) + 33.95

x  ≈ -11.63·f(x) + 33.95

Which through plugging in f⁻¹(x) = x, and f(x) = x,

Indicates;

f⁻¹(x) = -11.63·x + 33.95

In the inverse function, the argument is the percentage, while the output is the number of years, f⁻¹(x)

When x = 2.3,

f⁻¹(2.3) = -11.63×2.3 + 33.95 ≈ 7.2

The inverse when the percentage is 2.3% is 7.2 years

a. The inverse function is f⁻¹(x) = -11.63·x + 33.95

The output of the inverse function represents the number of years since 2000 when the percentage of the children taking antidepressants is x. The correct option is option B

b. The year in which the number of children taking antidepressant equals 2.3% is 2,000 + 7 = 2007

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The probability that a pupil selected uses the tennis courts only is the fraction 11/50 or 0.22

The probability of an event occurring is the ratio of the number of required outcome divided by the total number of possible outcomes.

From the question,

The pupils that uses only tennis courts = 92 - (30+19+10) { where 30 is the number of pupils that uses all three, 19 is the number of pupils that uses only swimming pool and 10 is the number of pupils that uses only gym and tennis court}

The pupils that uses only Tennis courts = 92 - 59

The pupils that uses only Tennis courts = 33

The probability of selecting a pupil who uses only the tennis court = 33/150

Therefore by simplification, the probability that only a pupil selected uses only the tennis court is the fraction 11/50

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