Given the function f(x)=4x²-14x+12, which of the following expressions is equivalent to f(x)?

Answer:

4394

5200 X 0.12 = 624 --> 5200 - 624 = 4576

5200 X 0.035 = 182

4576 - 182 = 4394

Given that

The height of the tent is 4 feet and the length of the rope is 8 feet.

We have to find the distance of the rope from the tent.

Explanation -

The given diagram is

Here the given diagram is making a right-angled triangle.

So we will use the Pythagoras theorem to find the required length.

The Pythagoras theorem is given as

Here Hypotenuse = H = 8 feet, Base = B = ?, and Perpendicular = P = 4 feet.

Then,

So the required distance will be 6.928 feet.

Hence, C is the correct option.

Final answer -

Answer:hey! ur picture shows nothing :(

Step-by-step explanation:

I think u can creat a new question or edit this one, i can help if i see the problem

Answer:

rgre5ydytye453efdfe45fgs4terwt

Step-by-step explanation:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbvbcn

Answer:1. 0.889, 2. −0.4, 3. 0.636 (i rounded the answers to the nearest thousandths)

Step-by-step explanation: the thing is when you are changing them from fraction to decimal you use long division for example

let us say the fraction is a half.

we put the numerator inside and the denominator outside.

so in this case 2 is outside and 1 is inside.

(forgive my drawing)

So after the zero we put a point if it is any number we still put a point after the first division answer.

We also put a zero next to 1 even though it is any other number a the answer on top we still put a zero if the number is over like in this case.

so 10 divide by 2 is 5 we put it on top.

Since we got an answer with no reminder our answer is 0.5.

Answer:

WHERES THE PICTURE???

Step-by-step explanation:

Answer:

I think it is 22000 bc u place the 10 in the x spot and multiply.

Answer:

54a6b2+9ab2 factored is

9ab2(6a⁵+ 1)

Answer:

\(y=\frac{7}{3}-\frac{2}{3}x\)

Step-by-step explanation:

To solve for y, we will have to get y by itself on one side of the equation, with all of the other variables and values on the other side.

2x + 3y = 7

Subtract 2x to both sides of the equation.

3y = 7 - 2x

Divide both sides by 3.

\(y=\frac{7}{3}-\frac{2}{3}x\)

And now we have solved for y.

I hope you find my answer helpful.

Answer: 4

Step-by-step explanation: Arrange them in number order and cross one off on the left then the right to find the middle value which should be 4

Hello, sorry for taking half an hour to respond.

a) If x represents the number of students in her class, we have :

The cost of a calculator on website C : 480 : x
The cost of a calculator on website D : 480 : (x+4)

b) We call the price of a calculator on website C as a, and the price on website D is a-6
Let's also call the amount of calculators if we buy on website C as d, and the amount of calculators if we buy on website D as d + 4

We have :

a.d = (a-6)(d+4)
Break the brackets out : ad = ad-6d + 4a - 24
=> -6d + 4a - 24 = 0
Divide both sides by 2
=> -3d + 2a - 12 = 0

=> 2a = 3d + 12

So, d is divisible by 3, and a is divisible by 2 => ad is divisible by 6.

And ad x the amount of students = 480

So, we can conclude that the amount of students is a factor of 80

Let's list out all of them : 1,2,4,5,8,10,16,20,40,80.

If there was 20 students :

The price of each calculator would be : 480 : 20 = 24

If it's 6 cheaper, it would be 24-6 = 18

And she would've gotten 480 : 18 (not divisible)

If you keep replacing like that, you'll eventually get the answer. I don't have time left, so the answer is 16 students. Hope it helps.

Answer:

750

Step-by-step explanation:

150 is bigger than 100 so we know the answer has to be bigger than 500. 150/100*500=150*5=750

Answer: 750

Step-by-step explanation:

150% is 1.5  500(1.5)=750

By solving the given equation, d = -4

           To find d in the equation -14d + 12d + 11d + 18 = -18, we need to combine similar terms on the left side of the equation and isolate the variable.

Combining similar terms, we get:

(-14 + 12 + 11)d + 18 = -18

9d + 18 = -18

           We can then extract the variable by shifting the constant term to the other side of the equation:

9d = -18 - 18

9d = -36

Finally, we can find d by dividing both sides of the equation by 9:

d = -36/9

d = -4

Therefore, the solution of the equation is d = -4. When d equals -4, the equation is balanced and both sides of the equation are equal.

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Answer:

Therefore any set of data that satisfies the 5-Number summary: 16,18,22,26 and 28 can be represented with the box plot.

Step-by-step explanation:

Interpreting Box Plots

We use a box plot to present the 5-Number summary of a set of data.

The values contained in the 5-Number summary are:

In the box plot, the following rules apply:

Using these, we interpret the given box plot

A left whisker extends from 16 to 18, therefore:

The box extends from 18 to 26 and is divided into 2 parts by a vertical line segment at 22.

The right whisker extends from 26 to 28.

Therefore any set of data that satisfies the 5-Number summary: 16,18,22,26 and 28 can be represented with the box plot.

Box plot has boxes with some lines ( called whiskers ).

Box plot on the graphical level tells about 5 points:

There is starting whisker or left whisker denoting point minimum (Q0) and extends from there the line to Q1 ( first quartile).

Then the box starts which starts from Q1 and touched Q3. In the middle it passes through Q2 ( The median of the data ), and thus has a line in it.

At last, there is end whisker or right whisker denoting end quantile or Q4 (the maximum point).

Given data:

Left whisker extends from 16 to 18.

     Thus Q0 = 16

              Q1 = 18

Box plot starts from 18 and extends to 26, and is split by a vertical line segment at 22.

    Thus Q2 = 22

             Q3 = 26

The right whisker or end whisker extends from 26 to 28

    Thus Q4 = 28.

Thus the description of data is given as:

\(Q_0 = Minimum = 16\\Q_1 = First\: quartile = 18\\Q_2 = Second \:quartile = Median= 22\\Q_3 = Third\: quartile = 26\\Q_4 = Maximum = 28\\\)

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In calculating chi-square test statistics, we use the squared difference between the observed (O) and expected (E) values in each cell, divided by the expected value (E). This is referred to as the squared difference, denoted as option C.

The expected number of successes for the Rosi treatment group is given as 126.12, which corresponds to option C.

Regarding the statement, if the three treatments are not equally effective, to reject the null hypothesis, the chi-square statistic for this example will be larger. This statement is true. When the treatments are not equally effective, there will be larger differences between the observed and expected values, leading to a larger chi-square statistic. This increased statistic indicates a greater deviation from what would be expected under the null hypothesis, providing evidence to reject it.

In the given table for testing independence in 2-way tables, the observed values are presented alongside the expected values (in parentheses) for each category. The total counts for each row and column are also provided.

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The value of f(-3) in the function is -3

The graph represents the given parameter

From the graph, we have the function to be

Function = f(x)

This means that the value of x in f(-3) is

x = -3

So, we look up to the function value when x = -3

On the graph, we have

f(x) = -3 when x = -3

Hence, the value is -3

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Answer:

the answer is $17.98

Step-by-step explanation:

....

Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

To calculate the future value of a three-year uneven cash flow given below, using an 11% discount rate, we need to use the formula;

Future value of uneven cash flow = cash flow at year 1/(1+discount rate)¹ + cash flow at year 2/(1+discount rate)² + cash flow at year 3/(1+discount rate)³ + cash flow at year 4/(1+discount rate)⁴

Given the cash flows;

Year 0: $0

Year 1: $600

Year 2: $500

Year 3: $400

Then the Future value of uneven cash flow

= $600/(1+0.11)¹ + $500/(1+0.11)² + $400/(1+0.11)³

= $600/1.11 + $500/1.23 + $400/1.36

=$540.54 + $405.28 + $293.00

=$1,238.82

Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

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The Cp and Cpk values indicate that the process is capable of meeting the specifications for relative humidity in the greenhouse.

The amount of water vapor in the air as compared to the maximum amount that it can contain at a certain temperature is known as relative humidity. It is computed as a percentage by dividing the actual amount of water vapor in the air by the maximum amount of water vapor the air can contain at the same temperature, then multiplying the result by 100. For instance, if the air can hold 10 grams of water vapor at a certain temperature and there are only 5 grams of water vapor present, the relative humidity would be 50%. High relative humidity can be uncomfortable and promote the development of mold and other microorganisms.

How to solve?

The mean is (60+78+70+84+81+80+85+60+88+75)/10 = 76.8

The standard deviation is sqrt(((60-76.8)^2+(78-76.8)^2+(70-76.8)^2+(84-76.8)^2+(81-76.8)^2+(80-76.8)^2+(85-76.8)^2+(60-76.8)^2+(88-76.8)^2+(75-76.8)^2)/10) = 6.9

Cp = (85-65)/(66.9) = 0.56

Cpk = min((85-76.8)/(36.9), (76.8-65)/(36.9)) = min(0.86, 0.71) = 0.71

The Cp and Cpk values indicate that the process is capable of meeting the specifications for relative humidity in the greenhouse.

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Answer: 6

Step-by-step explanation:

Just some simple ratios

P = Pizza People = Pl

P: Pl

2 : 9

x: 27

We want to find x.

Since 27/9 is equal to 3, we multiply 2 by 3 as well!

2x3=6, our desired amount.

Answer:

So first add the perimeter lengths together.

65+45=110

Then do 110 because there are 2 backyards.

110x2= 220

Then we need to see how many 8ft panels of fencing we need for that much perimeter length so do 220/8.

220/8=27.5

You need 27 and 1/2 panels to enclose the yards.

Without knowing the size of the outer circle, it is impossible to determine the exact area of the shaded region. However, we can use the circumference of the inner circle (125.6 inches) to find its radius, and then use that to calculate the area of the shaded region as a fraction of the area of the outer circle.

The formula for the circumference of a circle is C = 2πr, where r is the radius. We can rearrange this formula to solve for r:

r = C/2π

Plugging in the given circumference of the inner circle, we get:

r = 125.6/2π
r ≈ 19.998 inches

Since both circles have the same center, we know that the radius of the outer circle must be at least 19.998 inches longer than the radius of the inner circle. Let's call the radius of the outer circle R. Then:

R = r + 19.998
R ≈ 39.996 inches

The area of a circle is given by the formula A = πr^2. So the area of the inner circle is:

A_inner = πr^2
A_inner ≈ 1256.64 square inches

And the area of the outer circle is:

A_outer = πR^2
A_outer ≈ 5023.27 square inches

The area of the shaded region is the difference between these two areas:

A_shaded = A_outer - A_inner
A_shaded ≈ 3766.63 square inches

So the area of the shaded region is approximately 3766.63 square inches, but this answer depends on the radius of the outer circle, which is not given in the problem.

Answer:

44

Step-by-step explanation:

because it looks like a square tilted

The final expression is given as ln|S| = 8t / √πS(0) + ln|S(0)|.

A spherical weather balloon is being inflated at a rate of 5 cm/s. If we want to express the surface area of the balloon as a function of time t (in seconds), then we have to use the formula for the surface area of a sphere which is given as S = 4πr².

Here, the radius of the balloon is increasing at the rate of 5 cm/s.

So we can say that dr/dt = 5 cm/s, where dr is the rate of change of radius with respect to time.

We can differentiate the formula of surface area of the sphere w.r.t time, we get: dS/dt = d/dt (4πr²) => dS/dt = 8πr (dr/dt)We know, r = (1/2)Sqrt(S/π)So, we can substitute the value of r in the above expression, dS/dt = 4πS (ds/dt) / Sqrt(πS)

On simplifying this, we get: dS/dt = 4S (ds/dt) / √πSNow, if S = S(0) at t = 0, then we can integrate both sides of the equation to get the surface area of the balloon as a function of time t.S(0) is the initial surface area of the balloon.

Substituting, we get:∫ dS/S = ∫ 4(dt/√πS(0))We get:ln|S| = 8t / √πS(0) + CWhere C is the constant of integration.At t = 0, S = S(0),

so we get:ln|S(0)| = CBy substituting this value of C in the above expression, we get:ln|S| = 8t / √πS(0) + ln|S(0)|

On simplifying this expression, we get the surface area of the balloon as a function of time t.

We derived the expression of surface area of the balloon as a function of time t when the radius of the balloon is increasing at the rate of 5 cm/s. We used the formula of surface area of a sphere and the derivative of radius w.r.t time to derive the expression of surface area. The final expression is given as ln|S| = 8t / √πS(0) + ln|S(0)|.

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The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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The 98% confidence interval for the population mean (μ) is approximately (2.711, 3.009).

1: Identify the given data

Sample size (n) = 150 students

Sample mean (x) = 2.86

Population standard deviation (σ) = 0.78

Confidence level = 98%

2: Find the critical z-value (z*) for a 98% confidence level

Using a z-table or calculator, you'll find that the critical z-value for a 98% confidence level is 2.33 (approximately).

3: Calculate the standard error (SE)

SE = σ / √n

SE = 0.78 / √150 ≈ 0.064

4: Calculate the margin of error (ME)

ME = z* × SE

ME = 2.33 × 0.064 ≈ 0.149

5: Construct the confidence interval

Lower limit = x - ME = 2.86 - 0.149 ≈ 2.711

Upper limit = x + ME = 2.86 + 0.149 ≈ 3.009

The 98% confidence interval is approximately (2.711, 3.009).

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Answer: 112 degrees

Explanation:

By the alternate interior angles theorem, m<CAD=40 and m<ACD=28. The quadrilateral is divided into two triangles. The sum of the angles of a triangle is equal to 180 degrees. Now that you know the measurements of two out of the three angles, you can add them up and subtract them from 180.

180-(40+29)=112

Answer:

x < -5

Step-by-step explanation:

Answer:

B. y= 6x2, y= -4.5x2, y= -x2

Step-by-step explanation:

y = 6x2, y = −4.5x2, y = −x2

This should be correct )

To solve this problem you must keep on mind the following information: By definition, a quadratic function has the following form:  

 y=ax^{2}+bx+c&#10;

Where a&#10; is the leading coefficient.

If the leading coeficient is closer to zero, the parabola is widest,if it has a larger positive or negative value, the parabola is narrowest.

Therefore, by knowing the information above, you have that the answer is:

y=- x^{2}  \\ y=-4.5 x^{2}  \\ y=6 x^{2}

Answer:

The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

Step-by-step explanation: