How many kilobytes are in a megabyte if a kilobyte is 10^3 and a megabyte is 10^6

Step-by-step explanation:

as x intercepts are -8 and 72 we realize that f(x)=a(x+8)(x-72)

we know that f(62)=-490 so a= -0.7

so f(x)= -0.7(x+8)(x-72)

True. The double integral can be used to compute the area of a region d in a plane by integrating the function f(x,y). In fact, the double integral of f(x,y) over a region D in the xy-plane gives the volume of the solid between the surface z=f(x,y) and the xy-plane over the region D.

However, if we take the function f(x,y) to be the constant function 1, then the double integral of f(x,y) over the region D is simply the area of the region D. Therefore, we can compute the area of a region D in a plane by integrating the constant function 1 over the region D using the double integral. Integrating over two variables requires calculating two separate integrals, so the answer is more than 100 words.
True. A double integral can be used to compute the area of a region D in a plane by integrating the function f(x, y). To find the area, you would integrate the function f(x, y) = 1 over the region D, as the double integral represents the sum of the function values over the entire area. The double integral can be thought of as a generalization of single-variable integration, allowing us to find the area in two dimensions.

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Answer:

Perimetro = 4 cm + 7 cm + 12 cm

                = 23 cm

Step-by-step explanation:

Answer:

The iPhone is cheapest in Paris, where it costs £701.75.

Step-by-step explanation:

Divide each price by the conversion factor.

\(\text{London: } \£750\\\text{Paris: } \text{EUR }800/1.14=\£701.75\\\text{New York: } \$1050/1.39=\£755.40\)

A function is a function that represents the area under a curve. In this case, f is the curve being considered. The function a(x) represents the area under the curve of f from x=0 up to x.

So, if we want to find the area under the curve of f from x=0 up to x=3, we would evaluate a(3) - a(0). This would give us the total area under the curve of f from x=0 to x=3. Similarly, if we have another area function, say b(x), that represents the area under the curve of f from some other starting point (e.g. from x=1), we would use b(x) to find the area under the curve of f from x=1 up to some other x value.
The graph of f, displayed in the figure to the right, represents a function that can be analyzed using various mathematical concepts. In this case, we can consider two area functions for f, denoted as A(x) and B(x), which would allow us to evaluate the areas under the curve of the graph with respect to the x-axis. These area functions can be used to understand properties and behaviors of the function f in different regions of the graph.

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The solution is: we created a cumulative frequency table of the data and, the bakery sell less than 30 loaves in 16.

Here, we have,

we know that,

Cumulative frequency is used to determine the number of observations that lie above (or below) a particular value in a data set. The cumulative frequency is calculated using a frequency distribution table, which can be constructed from stem and leaf plots or directly from the data.

now, we have,

given that,

12, 19, 27, 24, 19, 44, 8, 32, 21, 37, 15, 6, 16, 48, 26, 5, 14, 23, 6, 35, 37, 28, 47, 40

if we create a cumulative frequency table of the data, we get,

Class interval  Frequency     Cumulative frequency

0-10                       4                               4

10-20                    6                               10

20-30                   6                               16

30-40                   5                                21

40-50                   3                                24

so, from the table we get,

the bakery sell less than 30 loaves in 16.

Hence, The solution is: we created a cumulative frequency table of the data and, the bakery sell less than 30 loaves in 16.

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Proportionality constant of p is = 14 t

The constant proportional relationship between two variables. The proportionality constant, k, is defined as k = y/x. This is equivalent to the equation for the slope of a line through the origin, m = y/x. The value of m, which will be the same as the value of k, or the constant or proportionality, can be discovered using the equation for the slope of the line.

y = kx

The rate k = 210 ÷ 15 = 14 gel pens per minute

"p" is number of pens, "t" is number of minutes

p = 14t

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Answer:

See below

Step-by-step explanation:

Slope intercept form is

Slope= -3 passes through point (15, -50)

Slope = 1/2 with and x-intercept of (28,0)

Slope = 7 passes through (1,2)

Slope = -4 passes through (-2,5)

Slope = -2 with x-intercept of (-3,0)

Slope = 34 passes through the origin

Answer:

Step-by-step explanation:

Let x = no. of books

:

Cost = 12.50x + 54150

:

Revenue = 25x

:

Rev = cost

25x = 12.5x + 54150

25x - 12.50x = 54150

12.5x = 54150

x = 54150%2F12.5

x = 4332 books need to be sold to cover production costs

:

:

Check:

c = 12.50(4332) + 54150

c = 54150 + 54150

c = 108300

:

r = 25(4332)

r = 108300

Answer:

35

Step-by-step explanation:

5 x 7 = 35

Answer:

35

Step-by-step explanation:

The equation is 5x. When the value of x is 7, you multiply 5*x or 5*7. This gives you 35.

The option that is true based on the equation is that B. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

This is the degree of the hotness and the coldness that's in a body.

In this case, based on the information, the conversion of Celcius to Fahrenheit is simply by multiplying by 1.8.

Therefore, 1°C to F will be:.

= 1 × 1.8

= 1.8°F

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The volume of the cylinder is 2797.74 cubic meters whose radius is 9m and height is 11m

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Given that radius is 9m and height is 11m

The formula for volume is πr²h

Plug in the values of radius and height

Volume = π(9)²(11)

=3.14×81×11

=2797.74 cubic meters

Hence, the volume of the cylinder is 2797.74 cubic meters whose radius is 9m and height is 11m

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Answer:

8 months

Step-by-step explanation:

194-3m = 217-6m

3m = 23

m=7.666666.....  (8 months

The surface area of the softball is approximately 254.34 square centimeters.

To calculate the surface area of a softball, we can use the formula for the surface area of a sphere, which is S.A. = 4πr².

Given that the diameter of the softball is 9 cm, we can find the radius (r) by dividing the diameter by 2:

r = 9 cm / 2 = 4.5 cm

Now we can substitute the value of the radius into the surface area formula:

S.A. = 4π(4.5 cm)²

Simplifying further:

S.A. = 4π(20.25 cm²)

S.A. = 81π cm²

To calculate the numerical value, we can use an approximation for π, such as 3.14:

S.A. ≈ 81 * 3.14 cm²

S.A. ≈ 254.34 cm²

It's important to note that the result is an approximation due to using an approximation for π. Using more decimal places for π would yield a more precise value.

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The equation of the straight line passing through the points (-1,1) and (2,-4) is  y = -5/3x - 2/3.

To find the equation, we can use the point-slope form of a linear equation, which is y - y₁ = m(x - x₁), where (x₁, y₁) are the coordinates of a point on the line and m is the slope of the line.

We have,

Point 1: (-1, 1) with coordinates (x₁, y₁)

Point 2: (2, -4) with coordinates (x₂, y₂)

Let's calculate the slope (m):

m = (y₂ - y₁) / (x₂ - x₁)

 = (-4 - 1) / (2 - (-1))

 = -5 / 3

Now, substituting one of the points and the slope into the point-slope form, we have:

y - y₁ = m(x - x₁)

y - 1 = (-5/3)(x - (-1))

y - 1 = (-5/3)(x + 1)

Expanding the equation:

y - 1 = (-5/3)x - 5/3

To simplify the equation, let's multiply both sides by 3 to eliminate the fraction:

3(y - 1) = -5x - 5

Expanding and rearranging the equation, we get:

3y - 3 = -5x - 5

3y = -5x - 5 + 3

3y = -5x - 2

y = (-5/3)x - 2/3

Thus, the equation of the straight line passing through the points (-1,1) and (2,-4) is y = -5/3x - 2/3.

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Answer:

Step-by-step explanation:

y=mx+b   is the standard form

m= slope

If the slopes are the same they are parallel

If the slopes are Opposite signed and reciprocals, then they are perpendicular

both of the slopes are 5, so the lines are parallel

Step-by-step explanation:

1) To draw triangle ABC, we start by drawing a line segment BC of length 6 cm. Then we draw an angle of 40° at point B, and an angle of 60° at point C. We label the intersection of the two lines as point A. This gives us triangle ABC.

```

C

/ \

/ \

/ \

/ \

/ \

/ \

/ \

/_60° 40°\_

B A

```

2) To find the measure of angle BAC, we can use the fact that the angles in a triangle add up to 180°. Therefore, angle BAC = 180° - 40° - 60° = 80°.

3) To show that ABD is an isosceles triangle, we need to show that AB = AD. Let E be the point where the bisector of angle BAC intersects AB. Then, by the angle bisector theorem, we have:

AB/BE = AC/CE

Substituting the given values, we get:

AB/BE = AC/CE

AB/BE = 6/sin(40°)

AB = 6*sin(80°)/sin(40°)

Similarly, we can use the angle bisector theorem on triangle ACD to get:

AD/BD = AC/BC

AD/BD = 6/sin(60°)

AD = 6*sin(80°)/sin(60°)

Since AB and AD are both equal to 6*sin(80°)/sin(40°), we have shown that ABD is an isosceles triangle.

4) To show that MD is the perpendicular bisector of AB, we need to show that MD is perpendicular to AB and that MD bisects AB.

First, we can show that MD is perpendicular to AB by showing that triangle AMD is a right triangle with DM as its hypotenuse. Since M is the midpoint of AB, we have AM = MB. Also, since ABD is an isosceles triangle, we have AB = AD. Therefore, triangle AMD is isosceles, with AM = AD. Using the fact that the angles in a triangle add up to 180°, we get:

angle AMD = 180° - angle MAD - angle ADM

angle AMD = 180° - angle BAD/2 - angle ABD/2

angle AMD = 180° - 40°/2 - 80°/2

angle AMD = 90°

Therefore, we have shown that MD is perpendicular to AB.

Next, we can show that MD bisects AB by showing that AM = MB = MD. We have already shown that AM = MB. To show that AM = MD, we can use the fact that triangle AMD is isosceles to get:

AM = AD = 6*sin(80°)/sin(60°)

Therefore, we have shown that MD is the perpendicular bisector of AB.

5) Finally, to show that DM = DN, we can use the fact that triangle DNM is a right triangle with DM as its hypotenuse. Since DN is the orthogonal projection of D on AC, we have:

DN = DC*sin(60°) = 3

Using the fact that AD = 6*sin(80°)/sin(60°), we can find the length of AN:

AN = AD*sin(20°) = 6*sin(80°)/(2*sin(60°)*cos(20°)) = 3*sin(80°)/cos(20°)

Using the Pythagorean theorem on triangle AND, we get:

DM^2 = DN^2 + AN^2

DM^2 = 3^2 + (3*sin(80°)/cos(20°))^2

Simplifying, we get:

DM^2 = 9 + 9*(tan(80°))^2

DM^2 = 9 + 9*(cot(10°))^2

DM^2 = 9 + 9*(tan(80°))^2

DM^2 = 9 + 9*(cot(10°))^2

DM^2 = 9 + 9*(1/tan(10°))^2

DM^2= 9 + 9*(1/0.1763)^2

DM^2 = 9 + 228.32

DM^2 = 237.32

DM ≈ 15.4

Similarly, using the Pythagorean theorem on triangle ANC, we get:

DN^2 = AN^2 - AC^2

DN^2 = (3*sin(80°)/cos(20°))^2 - 6^2

DN^2 = 9*(sin(80°)/cos(20°))^2 - 36

DN^2 = 9*(cos(10°)/cos(20°))^2 - 36

Simplifying, we get:

DN^2 = 9*(1/sin(20°))^2 - 36

DN^2 = 9*(csc(20°))^2 - 36

DN^2 = 9*(1.0642)^2 - 36

DN^2 = 3.601

Therefore, we have:

DM^2 - DN^2 = 237.32 - 3.601 = 233.719

Since DM^2 - DN^2 = DM^2 - DM^2 = 0, we have shown that DM = DN.

The two missing angles of the diagram are:

∠HDG = 117°

∠FDG = 180°

We know that sum of angles on a straight line is 180 degrees.

We also know that two angles that sum up to 180 degrees are referred to as supplementary angles.

From the given image, we see that:

∠HDF is given as 63°.

Thus:

∠HDG = 180 - 63

∠HDG = 117°

Thus, it means that ∠FDG is 180 degrees

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Answer:

c

Step-by-step explanation:

the second triangles dimensions are 1.5 times greater than the first one.

Answer:

thirty thousand, six hundred and eighty-two!

Step-by-step explanation:

Answer:

thirty thousand six hundred eighty two

Answer:

y=4x+1

Step-by-step explanation:

7=4(2)+c

c=1

y=4x+1

Answer:

D

Step-by-step explanation:

(the line is a / shape, so the slope is positive)

(the line crosses the y axis at (0,-2)

(using the above information, the equation is y=2x-2)

Answer:

y = 2x - 2

Step-by-step explanation:

Start with

y = mx + b

The graph shows the y-intercept -2.

We have y = mx - 2

slope = m = rise/run

The slope is rise of 2 and run of 1, so m = 2.

y = 2x - 2

Answer:

Karma worked for 7 1/2 hours. She spent 2/3 of the time on her computer. To find out how long she was on her computer, we can multiply the total time she worked by the fraction of time she spent on her computer.

Step-by-step explanation:

7 1/2 hours * 2/3 = (15/2) * (2/3) = 30/6 = 5 hours.

Therefore, Karma was on her computer for 5 hours.

Answer:

5

Step-by-step explanation:

We want to multiply a mixed number by a fraction.

7 1/2 * 2/3

Change the mixed number to an improper fraction.

(2 * 7 + 1)/2 = 15/2

15/2 * 2/3

Simplify.

15/3 * 2/2

5 * 1

5

Therefore, to ensure with probability 0.9 that the class average would be within 5 of 60, the professor would need 118 students to take the final exam.

The Central Limit Theorem states that the distribution of the sum or average of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution.

Therefore, in this example we can use the Central Limit Theorem to approximate the mean of the test scores of the students taking the final exam. If the professor knows that the mean of the test scores is 60 and the standard deviation is 16, then the professor can calculate the sample size necessary to ensure that the class average is within 5 of 60 with a probability of 0.9.

Using the formula \(n = (zα/2 * σ/ε)2\), where zα/2 is the z-score associated with a confidence level of 0.9, σ is the standard deviation of the population, and ε is the margin of error desired, we can calculate the sample size necessary for this professor.

\(n = (1.645 * 16/5)2 = 118.03\)
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Answer:

              a₁ = -5, d = 7,  a₂ = 2, a₃ = 9, a₄ = 16

equation of sequence:    \(\boxed{\bold{a_n=7n-12}}\)

Step-by-step explanation:

a₁ + a₂ + a₃ = 6    

a₁ + a₁ + d + a₁ + 2d = 6

3a₁ + 3d = 6

a₁ + d= 2     ⇒ a₁ = 2 - d

a₄ = 16

a₁ + 3d = 16

2 - r + 3d = 16

2d = 14

d = 7

a₁ = 2-7 = -5

a₁ = -5, d = 7   ⇒  a₂ = -5+7 = 2, a₃ = 2+7 = 9, a₄ = 9+7 = 16

equation of arithmetic sequence:

\(a_n=a_1+d(n-1)\\\\a_n=-5+7(n-1)\\\\\underline{a_n=7n-12}\)

Answer:Look Down 0D

Step-by-step explanation:I am sorry if this doesn't help but I dont know the answer???

a) The angle between vectors A and B is approximately 154.68 degrees.To find the angles between the vectors A and B,

we can use the dot product formula and the fact that the dot product of two vectors A and B is given by:

A · B = |A| |B| cos(θ)

where |A| and |B| represent the magnitudes of vectors A and B, respectively, and θ is the angle between them.

Let's calculate the angles for each case:

(a) A = 2î − 7ĵ, B = -5î + 3ĵ:

Using the dot product formula:

A · B = (2)(-5) + (-7)(3) = -10 - 21 = -31

The magnitude of A:

|A| = √(2^2 + (-7)^2) = √(4 + 49) = √53

The magnitude of B:

|B| = √((-5)^2 + 3^2) = √(25 + 9) = √34

Now, we can calculate the angle θ using the formula:

-31 = (√53)(√34)cos(θ)

Simplifying:

cos(θ) = -31 / (√53)(√34)

Using inverse cosine (arccos) to find θ:

θ = arccos(-31 / (√53)(√34))

The angle between vectors A and B is approximately θ = 154.68 degrees.

(b) A = 6î + 4ĵ, B = 3î − 3ĵ:

Using the dot product formula:

A · B = (6)(3) + (4)(-3) = 18 - 12 = 6

The magnitude of A:

|A| = √(6^2 + 4^2) = √(36 + 16) = √52 = 2√13

The magnitude of B:

|B| = √(3^2 + (-3)^2) = √(9 + 9) = √18 = 3√2

Now, we can calculate the angle θ using the formula:

6 = (2√13)(3√2)cos(θ)

Simplifying:

cos(θ) = 6 / (2√13)(3√2) = 1 / (√13)(√2)

Using inverse cosine (arccos) to find θ:

θ = arccos(1 / (√13)(√2))

The angle between vectors A and B is approximately θ = 23.38 degrees.

(c) A = 7î + 5ĵ, B = 5î − 7ĵ:

Using the dot product formula:

A · B = (7)(5) + (5)(-7) = 35 - 35 = 0

The magnitude of A:

|A| = √(7^2 + 5^2) = √(49 + 25) = √74

The magnitude of B:

|B| = √(5^2 + (-7)^2) = √(25 + 49) = √74

Now, we can calculate the angle θ using the formula:

0 = (√74)(√74)cos(θ)

Since the dot product is zero, it indicates that the vectors are orthogonal (perpendicular) to each other. In this case, the angle between vectors A and B is θ = 90 degrees.

Therefore, for the given cases:

(a) The angle between vectors A and

B is approximately 154.68 degrees.

(b) The angle between vectors A and B is approximately 23.38 degrees.

(c) The angle between vectors A and B is 90 degrees.

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Answer:

Polynomials can have constants (3, -9), variables (x, y), and exponents (\(x^{2}\)). One thing you can't have is a variable in the denominator. For example: \(\frac{2}{x+3}\)

Or fractional exponents.

Step-by-step explanation:

a)   \(y=x^{2} +2^{x}\)

Is not a polynomial because \(2^{x}\) does not have the standard form, where variable is the base. e.g. \(x^{2}\)

b)   \(y^{2}=(x-2)^{2}-1\)

Is not a polynomial because \(y^{2} =\sqrt{y} =y^{\frac{1}{2} }\) has fractional exponents

c)   \(y=\frac{1}{x^{2} } +\frac{1}{x+\frac{1}{2} }\)

Is not a polynomial because our variable x is in the denominator

Answer:

4.14815 CUBIC YARDS

Step-by-step explanation:

28*12*(0.333333...)   you need to convert 4 inches to feets

112 ft3

then to convert to CUBIC YARDS

112=  4.14815 CUBIC YARDS