Which equation provides the best estimate for 35.78 ÷ 12.31?
30 ÷ 15 = 2
36 ÷ 12 = 3
30 ÷ 10 = 3
40 ÷ 10 = 4

If the pth term of an arithmetic progression is q and qth term is p then the (p+q) th term is 0.

Given that the p th term of an A.P is q aand q th term is p.

We are required to find the (p+q) th term of that A.P.

Arithmetic progression is a sequence in which all the terms have common difference between them.

N th term of an A.P.=a+(n-1)d

p th term=a+(p-1)d

q=a+(p-1)d-------1

q th term=a+(q-1)d

p=a+(q-1)d---------2

Subtract equation 2 by 1.

q-p==a+(p-1)d-a-(q-1)d

q-p=pd-qd-d+d

q-p=d(p-q)

d=(p-q)/(q-p)

d=-(p-q)/(p-q)

d=-1

Put the value of d in 1.

q=a+(p-1)(-1)

q=a-p+1

a=q+p-1

(p+q) th term=a+(n-1)d

=q+p-1+(p+q-1)(-1)

=q+p-1-p-q+1

=0

Hence if the pth term of an A.P is q and qth term is p then the (p+q) th term is 0.

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Answer:

7

Step-by-step explanation:

Because the parts of the circle are congruent, the segments are as well, we can use that to make an equation then solve it like normal

9x-34=4x+1

-1 on both sides

9x-35=4x

-9x on both sides

-35=-5x

x=7

Answer:

Leo stop at 1339. 3 feet tall and Leo almost reach the top of the building

Answer:

1232

Step-by-step explanation:

1232 6th grades went on the trip because 160p multiplied by .77, the amount of chaired covered by 6th graders, is equal to 1232.

Answer:

t/7

Step-by-step explanation:

Since the ratio between the amount of water and the time should be the same, 84/12 = 7.

Hence, the ratio is t/7.

Hope this helped!

The volume of the given prism is 168 cubic meters. It's important to note that the units of the measurements provided (m) are in meters. So the resulting volume is in cubic meters (m³).

To find the volume of a prism, we need to multiply the area of the base by the height. In this case, the given prism has a base that measures 7 m by 4 m and a height of 6 m.

Step 1: Calculate the area of the base. The base of the prism is a rectangle, so the area is found by multiplying the length (7 m) by the width (4 m).

Area of the base = length × width

              = 7 m × 4 m

              = 28 m²

Step 2: Multiply the area of the base by the height of the prism to find the volume.

Volume of the prism = Area of the base × height

                  = 28 m² × 6 m

                  = 168 m³

Therefore, the volume of the given prism is 168 cubic meters.

It's important to note that the units of the measurements provided (m) are in meters. So the resulting volume is in cubic meters (m³). The volume represents the amount of space enclosed by the prism. In this case, the prism has a length of 7 m, width of 4 m, and height of 6 m, resulting in a volume of 168 cubic meters.

Remember to always include the appropriate unit of measurement when expressing the volume or any other quantity.

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Answer:

(C) The sum of the measures of ∠P, ∠Q, and ∠R is 180°

Step-by-step explanation:

All triangles, when their three angles are added up, gets us 180°.

This goes without saying, even with scalene triangles.

Additionally, the angles in squares add up to 360°, the angles in a pentagon add up to 540°.

Hope this helped!

The text is asking for the slope-intercept form of a linear equation that passes through two given points, (-5,5) and (4,-1). The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Once we find the slope, we can use it to write the equation in point-slope form: y - y1 = m(x - x1). Finally, we can rearrange the point-slope form to get the slope-intercept form.

PEASE MARK BRAINLIEST

4 minutes and 30 seconds go into 2 hours 26 times

119

Answer:

???? i dont understand

Step-by-step explanation:

i think yes

Answer:

???

Step-by-step explanation:

Answer:

y = −14x + 3

Step-by-step explanation:

Parallel lines have the same slope

The equation y = −14x + 7 is put in slope intercept form ( y = mx + b )

Where m = slope

-14 takes "m's" place meaning that the slope = -14

If parallel lines have the same slope than the equation of a line parallel to y = −14x + 7 must have a slope of -14

The only equation that has a slope of -14 is D

So, the probability of ending up with a three-digit number that is divisible by 4 is 1/24.

To find the probability of ending up with a three-digit number that is divisible by 4 when spinning the spinner three times, we need to consider the possible outcomes that satisfy this condition and divide it by the total number of possible outcomes. Let's analyze the given spinner and its possible outcomes:

Spinner: [1, 2, 3, 4, 5, 6]

To form a three-digit number, the hundreds digit will be determined by the first spin, the tens digit by the second spin, and the units digit by the third spin. A number is divisible by 4 if the last two digits (tens and units digits together) form a number divisible by 4. Therefore, we need to find the number of possible outcomes for the tens and units digits that satisfy this condition.

Possible outcomes for the tens digit: [2, 4, 6]

Possible outcomes for the units digit: [2, 4, 6]

Combining the possible outcomes for the tens and units digits, we have a total of 9 (3 possibilities for the tens digit multiplied by 3 possibilities for the units digit) favorable outcomes. The total number of possible outcomes for each spin is 6 (since there are 6 numbers on the spinner). Since we are spinning the spinner three times independently, the total number of possible outcomes for spinning it three times is 6^3 = 216. Therefore, the probability of ending up with a three-digit number divisible by 4 is:

Probability = favorable outcomes / total outcomes

Probability = 9 / 216

Probability = 1 / 24

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Answer:

10 girls

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Answer:19

Step-by-step explanation:

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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Answer:

a)  $16,122

b) $4,246

c) $112,357

Step-by-step explanation:

What is depreciation

We should calculate the depreciation using the declining balance method
This uses the technique of computing the depreciation on the previous year's depreciated value

As an example
If the original cost is $100 and depreciation rate is 10%( 0.10 in decimal)

Depreciation Year 1 = 100 x 0.10 = $10

Depreciated value at end of year 1 = 100 - 10 = $90

For the second year, the depreciation amount is computed on $90
= 90 x 0.10 = $ 9

Depreciated amount at end of year 2 = 90 - 9 = $81

The depreciated value of an asset valued at $A at time of purchase at a depreciation rate of r (in decimal) for n years is given by the formula
A' = A(1 - r)ⁿ

We are given
A = $34,145
r = 8/100 = 0.08 therefore 1 - r = 1 - 0.08 = 0.92

a) Depreciated value after 9 years:
A' = 34145(0.92)⁹
    = 16121.95

Rounded to the nearest dollar that would be $16,122 ANSWER

b) Depreciated Value after 25 years

A' = 34145(0.92)²⁵

    = $4,246  rounded to the nearest dollar

c) Car's value after 50 years

At the end of 25 years, the Mustang has become a classic with a value of $4, 246

Then it starts to appreciate at the rate of 14% (0.14 in decimal)

The appreciated value each year after 25 years is given by
A'' = A'( 1 + r)ⁿ

where r is the rate of appreciation and n is the number of years

We are given r = 14% = 0.14

1 + r = 1.14

n = 25

A' = 4,246 the value after 25 years from purchase

Car value after 50 years = car value after 25 years appreciated for the next 25 years

= 4246(1.14)²⁵

= $112,357 rounded to the nearest $

So you can really make a killing after 25 years. As an interesting side note, the value of the car will reach the original value 16 years after 25 years or a total of 41 years after purchase

We can plot the vector r(t) and the vector N(T) at the given value of t = T.

To find the principal unit normal for the vector-valued function r(t) = sin(t)i + tcos(t)j + tk, we need to compute the derivative of r(t) with respect to t and then normalize it to obtain a unit vector.

First, let's find the derivative of r(t):

r'(t) = cos(t)i + (cos(t) - tsin(t))j + k

Next, we'll normalize the vector r'(t) to obtain the unit vector:

||r'(t)|| = sqrt((cos(t))^2 + (cos(t) - tsin(t))^2 + 1^2)

Now, we can find the principal unit normal vector by dividing r'(t) by its magnitude:

N(t) = r'(t) / ||r'(t)||

Let's evaluate the principal unit normal at t = T:

N(T) = (cos(T)i + (cos(T) - Tsin(T))j + k) / ||r'(T)||

To sketch the situation, we can plot the vector r(t) and the vector N(T) at the given value of t = T.

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Answer:

9/50

Step-by-step explanation:

Answer:

she saved 6$ because 15% off 40=34 40-34=6

The volume of the solid formed by rotating the region inside the first quadrant enclosed by the curves y = x and y = 5x about the x-axis is (250π/7) cubic units. When finding the volume of a solid of revolution, we use the method of cylindrical shells.

To calculate the volume, we integrate the area of each cylindrical shell formed by rotating an infinitesimally small strip about the x-axis. The height of each shell is the difference between the y-values of the two curves, which is (5x - x²). The circumference of each shell is given by 2πx, and the thickness is dx. Therefore, the volume of each shell is 2πx(5x - x²)dx.

To find the total volume, we integrate this expression over the interval where the two curves intersect. Setting\(y = x^2\)and y = 5x equal to each other, we get x² = 5x. Solving this equation, we find two intersection points: x = 0 and x = 5. Thus, the limits of integration are from 0 to 5.

Integrating the expression \(2\pi x(5x - x^2)dx\) from 0 to 5 gives us the volume of the solid formed by rotating the region inside the first quadrant. Evaluating this integral, we find the volume to be (250π/7) cubic units.

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Answer: 8 six packs because its cheaper

Step-by-step explanation:

8x2.1=$16.80 and 6x3.12=$18.72

Answer:

first is some and second is all

Step-by-step explanation:

PLEASE GIVE BRAINLIEST!!!!!!!!!!

Answer:

1. All

2. Some

Step-by-step explanation:

I belive this awnser is correct

Answer:

Yes, it's c.

Step-by-step explanation:

3 to the 0th power is 3x3 zero times. It's zero. 0 to the 26th power is just 0x0 26 times. It's just 3x3 0 times multiplied with 0x0 26 times.

The dimensions for the maximum possible area that is 6.25 m² are L = 2.5 m and W = 2.5 m.

Area is the measure of the surface enclosed by a closed two-dimensional figure. It is typically measured in square units, such as square meters, square feet, or square inches. The formula for finding the area of various shapes depends on their geometrical structure. For example, the area of a rectangle is given by multiplying its length and width, the area of a triangle is given by multiplying its base and height and dividing by 2, and the area of a circle is given by π times the square of its radius.

Here,

To find the maximum area of the rectangular exercise area, we need to use the given amount of fencing to enclose the largest possible area.

a) Let the length of the rectangle be L and the width be W. We know that the perimeter of the rectangle is 10 m, so:

2L + 2W = 10

Simplifying, we get:

L + W = 5

We want to maximize the area of the rectangle, which is given by:

A = LW

Using the equation L + W = 5, we can solve for L in terms of W:

L = 5 - W

Substituting into the area equation, we get:

A = (5 - W)W = 5W - W²

To find the maximum area, we need to take the derivative of A with respect to W, set it equal to zero, and solve for W:

dA/dW = 5 - 2W = 0

Solving for W, we get:

W = 2.5

Substituting this value back into the equation L + W = 5, we get:

L = 2.5

So the maximum possible area is:

A = LW = (2.5)(2.5) = 6.25 square meters

b. To find the dimensions of the maximum possible area, we can use the fact that the maximum area occurs when the rectangle is a square.

Let x be the length and y be the width of the rectangle. We know that the perimeter is 10m, so:

2x + 2y = 10

Simplifying this equation, we get:

x + y = 5

To maximize the area, we want to find the values of x and y that satisfy this equation and also make the area as large as possible. Since we know that the rectangle is a square, we can set x = y:

x + y = 5

x + x = 5

2x = 5

x = 2.5

Therefore, the dimensions of the maximum possible area are 2.5m by 2.5m.

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Logan's swimming average is 2.25 kilometers per hour.

Mila's swimming average swimming speed is 34.44 m/min.

The distance swam by Logan = 750 m

The distance swam by Mila =  of Logan's distance =   × 750 = 2 × 250 = 500.

The probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, we have a population of marks on a biology final test that is normally distributed with a mean of 78 and a standard deviation of 6. We want to know the probability that a class of 50 has an average score that is less than 77.
Using the central limit theorem, we can calculate the standard error of the mean as follows:
standard error of the mean = standard deviation / square root of sample size
standard error of the mean = 6 / √50
standard error of the mean = 0.8485
Next, we need to calculate the z-score for a sample mean of 77:
z-score = (sample mean - population mean) / standard error of the mean
z-score = (77 - 78) / 0.8485
z-score = -1.18
We can use a standard normal distribution table or calculator to find the probability associated with a z-score of -1.18. The probability of a sample mean less than 77 is approximately 0.1190 or 11.90%.
Therefore, the probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

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Answer:

12

Step-by-step explanation:

You need the GCF of 48 and 60

48 = 2 x 2 x 2 x 2 x 3

60 = 2 x 2 x 3 x 5

Both have 2 x 2 x 3, so the answer is 12

The Total surface of triangular prism  is 112 inches.

To calculate the surface area of a triangular prism, you need the measurements of the base and the height of the triangular faces, as well as the length of the prism.

The given measurements are;

Base ; 5 inches and  4 inches

height is 8 inches

Length of the prism is 2 inches.

To find the total surface area, we sum up the areas of all the faces:

Total surface area = area of triangular  faces + area of rectangular faces + area of lateral faces.

area of triangular faces = 5 inches × 4 inches = 20 inches.

area of the two faces = 20 ×2 =40

Area rectangular faces = 5 inches × 8 inches/ 2 = 40 inches.

Area of lateral faces = 8 inches ×2 = 16 square inches

for the two lateral faces is 16 × 2 = 32 square inches.

Total surface area = 40 square inches + 40 inches + 32 square inches = 112 square inches.

The Total surface of triangular prism  is 112 inches.

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