-3√48n
I have to solve this using perfect squares, is anyone familiar with those?

Answer: B

Step-by-step explanation:

You are combining like terms

12y+4y=16y

16y+2x

The function that best approximates f(x) as h approaches 0 is c. tan(x)/x.

For values of h very close to 0, the function that best approximates f(x) = tan(x) is option c. tan(x)/x.

To understand why, let's examine the behavior of each function as h approaches 0:

a. sin(x): As h approaches 0, sin(x+h) - sin(x) / h approaches the derivative of sin(x), which is cos(x). Therefore, sin(x) is not the best approximation for f(x) as h approaches 0.

b. sin(x)/x: As h approaches 0, sin(x+h) - sin(x) / h approaches the derivative of sin(x), which is cos(x). Dividing by x helps to account for the change in slope as x approaches 0. Therefore, sin(x)/x provides a better approximation for f(x) as h approaches 0.

c. tan(x)/x: As h approaches 0, tan(x+h) - tan(x) / h approaches the derivative of tan(x), which is sec^2(x). Dividing by x helps to account for the change in slope as x approaches 0. Therefore, tan(x)/x provides the best approximation for f(x) as h approaches 0.

d. sec(x): The secant function is the reciprocal of the cosine function, and it does not provide a good approximation for f(x) as h approaches 0.

e. sec^2(x): As h approaches 0, sec(x+h) - sec(x) / h approaches the derivative of sec(x), which is sec(x) * tan(x). Therefore, sec^2(x) does not provide the best approximation for f(x) as h approaches 0.

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In one min Charlie can read is \(2\frac{1}{7}\) pages at a constant rate.

A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilize this technique for math computations.

In the unitary technique, the value of a unit or one quantity is always counted first, and the values of additional or less quantities are subsequently determined. This approach is known as the unitary method for this reason. Due to the fact that they generate two distinct sorts of variations, there are two different types of unitary approaches.

In \(\frac{2}{3}\) min Charlie can read \(1\frac{3}{7} = \frac{10}{7}\) pages

In one min Charlie can read is: \(\frac{10}{7}*\frac{3}{2} = \frac{30}{14} = 2\frac{2}{14} =2\frac{1}{7}\)

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Answer: 61

Step-by-step explanation: Basic addition. : )

Answer:

The answer is 43

Step-by-step explanation:

You just had to add

Answer:a

Step-by-step explanation:

The total area under the frequency polygon for a continuous random variable equals 1 is True.

A frequency polygon is very similar to a histogram, which is used to compare data sets or to depict a cumulative frequency distribution. A line graph is used to show quantitative data.

Statistics is concerned with the collecting of facts and information for a certain goal. The computation of each run for each ball in cricket provides game statistics. Tables, graphs, pie charts, bar graphs, histograms, polygons, and other graphical representations of statistical data are employed.

Frequency polygons are a visually appealing way of expressing quantitative data and frequency distributions. Let's look at how to draw a frequency polygon.

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Answer:

About 270

Step-by-step explanation:

Since the kg goes up by 40kg so 240-280. So the line in between would be 260, since 500 would be a little higher 270 would be a decent answer.

Answer:

Our two numbers are:

\(2+4\sqrt{2} \text{ and } 4\sqrt{2}-2\)

Or, approximately 7.66 and 3.66.

Step-by-step explanation:

Let the two numbers be a and b.

One positive real number is four less than another. So, we can write that:

\(b=a-4\)

The sum of the squares of the two numbers is 72. Therefore:

\(a^2+b^2=72\)

Substitute:

\(a^2+(a-4)^2=72\)

Solve for a. Expand:

\(a^2+(a^2-8a+16)=72\)

Simplify:

\(2a^2-8a+16=72\)

Divide both sides by two:

\(a^2-4a+8=36\)

Subtract 36 from both sides:

\(a^2-4a-28=0\)

The equation isn't factorable. So, we can use the quadratic formula:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

In this case, a = 1, b = -4, and c = -28. Substitute:

\(\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-28)}}{2(1)}\)

Evaluate:

\(\displaystyle x=\frac{4\pm\sqrt{128}}{2}=\frac{4\pm8\sqrt{2}}{2}=2\pm4\sqrt{2}\)

So, our two solutions are:

\(\displaystyle x_1=2+4\sqrt{2}\approx 7.66\text{ or } x_2=2-4\sqrt{2}\approx-3.66\)

Since the two numbers are positive, we can ignore the second solution.

So, our first number is:

\(a=2+4\sqrt{2}\)

And since the second number is four less, our second number is:

\(b=(2+4\sqrt{2})-4=4\sqrt{2}-2\approx 3.66\)

Answer:

\(2+4\sqrt{2}\text{ and }4\sqrt{2}-2\)

Step-by-step explanation:

Let the large number be \(x\). We can represent the smaller number with \(x-4\). Since their squares add up to 72, we have the following equation:

\(x^2+(x-4)^2=72\)

Expand \((x-4)^2\) using the property \((a-b)^2=a^2-2ab+b^2\):

\(x^2+x^2-2(4)(x)+16=72\)

Combine like terms:

\(2x^2-8x+16=72\)

Subtract 72 from both sides:

\(2x^2-8x-56=0\)

Use the quadratic formula to find solutions for \(x\):

\(x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\) for \(ax^2+bx+c\)

In \(2x^2-8x-56\), assign:

Solving, we get:

\(x=\frac{-(-8)\pm \sqrt{(-8)^2-4(2)(-56)}}{2(2)},\\x=\frac{8\pm 16\sqrt{2}}{4},\\\begin{cases}x=\frac{8+16\sqrt{2}}{4}, x=\boxed{2+4\sqrt{2}} \\x=\frac{8-16\sqrt{2}}{4}, x=\boxed{2-4\sqrt{2}}\end{cases}\)

Since the question stipulates that \(x\) is positive, we have \(x=\boxed{2+4\sqrt{2}}\). Therefore, the two numbers are \(2+4\sqrt{2}\) and \(4\sqrt{2}-2\).

Verify:

\((2+4\sqrt{2})^2+(4\sqrt{2}-2)^2=72\:\checkmark\)

Answer:

Example 1 : Convert 2 feet into inches. Solution : Here, we convert bigger unit into smaller unit. So we have to multiply. 2 feet = 2 x 12 inches = 24 inches Example 2 : Convert 3.5 yards into inches. Solution : Here, we convert bigger unit into smaller unit…

Answer: The first hour is free, and the rest charges is $2.50

Let x be the time.

Let y be the total

Your equation will look like

When x < 2, y = 0

When x > 1, y = $2.50(x)

So:

1 < x < ∞ for hours, then equation will look like:

y = total amount

$2.50 is cost (remember that the first hour is for free, and so you subtract $2.50 from the total.

$2.50x - $2.50 = y should be your equation.

hope this helps

Step-by-step explanation:

i would first multiply your 4 so you get 4q-32=7q+5 than add 32 to both sides so ypu get 4q=7q+5+32 than subtract 7q from both sides you should end up with 4q-7q=5+32 which = -3q=37 than divided by -3 to get q =

\( \frac{ - 37}{3} \)

or about -12.33333 going on for ever

The estimated probability of an amateur golfer hitting at least 6 times in his next 10 attempts is 20%. The Option A.

To simulate the situation, we can use the table of random numbers by selecting the first two digits of each number as a random sample. Let's consider hitting the ball as a success, and missing it as a failure.

So, the amateur golfer has a probability of success of 0.48 and a probability of failure of 0.52. We want to calculate the probability of having at least 6 successes in 10 attempts, which means we need to add up the probabilities of having 6, 7, 8, 9, or 10 successes.

Using binomial probabilities, we can calculate these probabilities as follows:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10); X is the number of successes in 10 attempts.

Using the binomial formula, we can calculate each probability as:

P(X = k) = (10 choose k) * (0.48)^k * (0.52)^(10-k). By adding up these probabilities, we get P(X ≥ 6) = 0.196 or approximately 20%.

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Answer:

Step-by-step explanation:

Use the table to find the required data:

The probability that a student selected at random is a graduate student is 31%.

The probability of an event happening is represented by a number. The ratio of favourable outcomes to all outcomes is how probability is defined.

The total number of students is 6101, out of which 1879 are graduate students. Therefore, the probability that a student selected at random is a graduate student is:

P(graduate student) = number of graduate students / total number of students

P = 1879 / 6101

P = 0.3078

Therefore, the probability that a student selected at random is a graduate student is 31%.

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Answer:

Step-by-step explanation:

the balloon starts at a height of 0 ft and rises at a rate of 100 ft.

Answer:

You cab try to divide it evenly as best you can into 5 different sections and then mark them

Step-by-step explanation:

you go in between 1 and -1 and make them go up by fifths to show you work and then just use the numbee line as you know how to

the average weight of 4boys 39.6 is Wight

Answer:

c: Fugitive Slave Act

Step-by-step explanation:

Search on Google.

Answer:

answer is (A) the Kansas Nebraska Act

Step-by-step explanation:

Answer:

B) 146 ≥ 9c+10

Step-by-step explanation:

$9 per yoga class can be represented with 9c, and then we have 9c+10 to represent the additional $10 yoga mat bought.

Since she can't use more than $146, then we have the inequality 9c+10≤146, which is the same as 146≥9c+10, so option B is correct.

The measure of angle BAD in the rhombus ABCD can be determined as 116 degrees. The angle bisector of angle ACD forms a 64-degree angle with the diagonal BD.

To explain further, in a rhombus, the diagonals bisect each other at right angles. Let's consider the angle bisector of angle ACD. Since the angle bisector forms a 64-degree angle with the diagonal BD, the other half of the angle bisector (angle BAD) will also measure 64 degrees. Since angle BAD and angle BCD are adjacent angles that share the same vertex, the sum of their measures is 180 degrees. Therefore, angle BCD measures 180 - 64 = 116 degrees. Hence, the measure of angle BAD is 116 degrees.

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The interest rate is 10.89%

1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..

The size of the nominal money supply in the new short-run equilibrium is 121.07.

2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.

Real exchange rate will remain unchanged.

3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.

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The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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116 years it take  for the account value to reach 26500 dollars

percentage, a relative value indicating hundredth parts of any quantity.

Given that 7700 dollars is placed in an account with an annual interest rate of 5.5%.

We need to find the time it  take for the account value to reach 26500 dollars

\(A=P(1+r)^{t}\)

A = final amount=26500

P = initial amount (7700)

r = annual interest rate (5.5%)

n = number of times interest is compounded per year

t = time in years

Solving for t, we get:

\(25600=7700(1+5.5/100)^{t}\)

\(25600=7700(1.055)^{t}\)

Divide both sides by 7700

\(25600/7700=1.055^{t}\)

3.32=tlog1.055

3.32=0.02t

t=116 years

Hence, 116 years it take  for the account value to reach 26500 dollars

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The following are the true statements are

m<4 is greater than m<2

m<4 is greater than m<1

m<1 + m<2= m<4

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

As, by property

m<1 + m<2= m<4

and, the measure of each individual angle is less than angle 4.

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Answer:

Step-by-step explanation:

Whats the question?

Answer:

x= 11.25, y=5.29

Step-by-step explanation:

Since I can only guess what subject this is off the picture, I've concluded by dividing 90 with the bigger triangle's side will give you your hidden answer. For example, 90/15 = 6 so I'd presume the rest are like that. 90/17 = 5.29, 90/8 = 11.25

Rico found a hailstone after a recent thunderstorm and calculated its volume to be 9.2 × 10 gallons, instead of gallons, among the following units the cubic meter would be the most appropriate unit for measuring the volume of Rico's hailstone.

As Rico found a hailstone after a recent thunderstorm and calculated its volume to be 9.2 × 10 gallons.

We know that,

The hailstone is in form of a sphere.

So, the volume of the sphere will be \(\left(\frac{4}{3}\right) \pi r^3\)

So, \(\text { Volume of hailstone }=\left(\frac{4}{3}\right) \pi r^3\)

From above, we can conclude that,

The unit of volume of hailstone depends on the value of the radius of the hailstone. (As here the other value is 4/3 and \(\Pi\) is constant.

The most appropriate unit for measuring the value of the radius of the hailstone is the meter.

Hence, among the given, he should use the cubic meters for measuring the volume of the hailstone.

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Answer:

113.04

Step-by-step explanation:

Given:V = 324 cu

cmh = 9 cm

Since the formula for the volume of a cylinder is V = AreaBase*heightAreaBase = V/height = 324cu cm/ 9 cmAreaBase = 113.04 square centimetresTherefore, the area of the pillar in square centimeters is 113.04

The base area of the cylindrical pillar would be; 113.04 cm²

The volume of the cylinder is the product of the height, pie, and square of the radius.

v = πr²h

where, r = radius, h = height

Therefore,

v = 324π cm³

h = 9cm

Consider find the radius;

324π = 9πr²

r² = 324π  /9π

r² = 36

r = √36

r = 6 cm

Base area of the pillar = πr²

Base area of the pillar = 36π

Base area of the pillar = 36 × 3.14

Base area of the pillar is 113.04 cm²

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Answer: -3

Step-by-step explanation:

The midpoint is basically the average of two points

-6+0=-6
-6/2=-3