12 inches of snow fell in 26 hours.At that rate how much snow fell during school hours?
(6 hours approximately)

Answer:

2001

Step-by-step explanation:

First, let us find the circumference of the wheel ( circle ) using the below formula.

C = 2πr

Here,

r ⇒ radius ⇒ 28 cm

Let us solve it now.

C = 2 × π × 28

C = 175.93 cm

And now let us covert the travelling distance to centimeters.

( For that, multiply km by 100000 )

3.52km = 352000 cm

Now, to find the number of revolution, divide the total distance travelled by its circumference.

352000/175.93 = 2000.79

Approximately, 2001 revolutions

The number of revolutions made by a wheel of 28cm radius covering a distance of 3.52km is 2000.8.

Given,

Radius, r = 28cm

Circumference = 2πr = 56π cm

Circumference = Distance traveled in one revolution

The distance traveled by wheel = 3.52km = 3520m = 352000cm

Let N = number of revolution

Now we know that,

Total distance = Number of revolutions × 1 revolution distance(circumference)

or 352000 = N × 56π

or N = 352000/56π

or N = 2000.8

Therefore, the number of revolutions made by a wheel of 28cm radius covering a distance of 3.52km is 2000.8.

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The quantity of the surullitos left over is 7.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a chef makes 750 surulfitos and donates half of them to a soup kitchen. The rest are divided equally among 16 plates.

The leftover surulfitos are,

E =  750 / ( 2 x 16 )

E = 375 / 16

E = 23⁷/₁₆

The remainder is 7 so the leftover surullitos are 7.

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The value of x of the quadrilateral using the concept of similar quadrilaterals is; x = 1.5

Two quadrilaterals are referred to as similar quadrilaterals when the three corresponding angles are the same and as a result the fourth angles automatically become the same due to the fact that the interior angles of a quadrilateral sum up to 360 degrees and two adjacent sides have equal ratios.

Thus, we can say by the concept of similar quadrilaterals that;

AB/LM = BC/MN

Thus;

14/(x + 9) = 10/(x + 6)

14(x + 6) = 10(x + 9)

14x + 84 = 10x + 90

14x - 10x = 90 - 84

4x = 6

x = 1.5

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(a) The impulse of the car of mass 1200 kg is 12000 Ns.

(b) The change in velocity of the car is 10 m/s.

Impulse is the product of force and time.

(a) To calculate the impulse of the force, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

(b) To calculate the change in velocity of the car, we use the formula below

Where:

From the question,

Given:

Substitute these values into equation 2

Hence the change in velocity of the car is 10 m/s.

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Answer:

------------------------------------

100 dozen add 20% is:

312%, 312' 4', 13, 9, 4.2 x 10-2. This is a decending order.

What is meant by decending?

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We can find the discount by taking the product between the price of the couch and the decimal form of the percentage, the discount on the couch is equal to $258.75

We know that for a couch whose price is $1,725, we apply a discount of the 15%.

Then we just need to find the 15% of $1,725, to do so, we need tu multiply the number by the decimal form of that percentage.

To get the decimal form, you need to take the quotient between the percentage and 100%, you will get:

15%/100% = 0.15

Then the discount is:

0.15*$1,725 = $258.75

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Answer:

It is 63 cm

Step-by-step explanation:

Take 28/4 = 7. That is what1 equals in the proportion. So, we take 2 x 7, 3 x 7, and 4 x 7. Then you just add the sides together and it equals 63 cm.

Answer: 63

Step-by-step explanation:

In the ratio, the longest side is 4. 4x7 is 28, so to make the ratios proportional again, you multiply all the sides by 7, getting 14:21:28.

These are the side lengths of the triangle, and to find the perieter you add all of them up, getting 63.

Hope this helps :)

The probability that a two-digit number selected at random has a tens digit less than its units digit is 0.2667 (4/15).

What is a probability simple definition?

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%

P= A/B

  = 4/15

There are 90 two-digit numbers (99-9). Of these, six numbers are divisible by 15 (15, 30, 45, 60, 75, 90). This is also divisible by 5. Therefore, the preferred case is 30-6 = 24. Therefore, the required probability is 24/90 = 4/15.

The probability of an event can be calculated by simply dividing the number of favorable results by the total number of possible results using a probabilistic expression. Whenever you are uncertain about the outcome of an event, you can talk about the probability of a particular outcome, that is, its potential.

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The domain of (f/g)(x) in interval notation is [-3, 6].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the graph,

f(x) has x values from x = -1 to x = 6

g(x) has x values from x = -3 to x = 5

The function f(x) is f(x) = mx + c

Find two coordinates from the graph of f(x).

= (-1, 3) and (6, 4)

m = (4 - 3) / (6 + 1) = 1/7

Now,

3 = (1/7) x -1 + c

3 = -1/7 + c
c = 3 + 1/7

c = 22/7

f(x) = (1/7)x + 22/7  _____(1)

The function g(x) is f(x) = mx + c

Find two coordinates from the graph of g(x).

= (-3, 2) and (5, 4)

m = (4 - 2) / (5 +3) = 2/8 = 1/4

Now,

2 = 1/4 x (-3) + c

2 = -3/4 + c
c = 2 + 3/4

c = 11/4

g(x) = (1/4)x + 11/4  _______(2)

Now,

From (1) and (2)

(f/g)(x)

= f(x)/g(x)

= ((1/7)x + 22/7) / ((1/4)x + 11/4)

The domain of f(x) and g(x) will include the domain of both f(x) and g(x).

So,

x = -1 to x = 6 and x = -3 to x = 5

This can be written as,

[-3, 6]

Thus,

The domain of (f/g)(x) is [-3, 6].

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The square feet of the garden that could contain flowers, given the side lengths of the stepping stone and the garden, is C. 16 ft².

To find the portion of the garden that could contain flowers, first find the total area of the entire garden ;

= Length of garden x Width

= 4 x 6

= 24 ft ²

The stepping stones will not contain flowers so their area should be deducted from the area of the garden :

= 24 - ( 2 x ( 2 x 2 ))

= 24 - ( 2 x 4 )

= 24 - 8

= 16 ft²

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Jim will need to sail 4 miles across the lake from the marina to Kingston.

Miles is a unit of measurement used to measure the distance between two locations. It is equal to 1.609 kilometers and is commonly used in the United States and the United Kingdom. Miles are frequently used to measure the distance between two cities, the distance a person has traveled, or the length of a road or highway. It is also sometimes used to measure the distance of a flight.

Since he is driving 16 miles from the boat launch to the marina, he will have covered a total of 20 miles by the time he arrives at the marina. From there, it is 4 more miles to Kingston. Therefore, he will need to sail a total of 4 miles to reach his destination.

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The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) is y = -2x - 18.

Therefore, the answer is b) y = −2x − 18.

The slope-intercept form of a line's equation is y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

To find the equation of a line that is perpendicular to another line, we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other. This means that if the slope of one line is m, the slope of a line perpendicular to it is -1/m.

The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) can be found by first finding the slope of the line 2x – 4y = 17. We can do this by rearranging the equation to the slope-intercept form:

2x – 4y = 17

-4y = -2x + 17

y = (1/2)x - (17/4)

The slope of the line 2x – 4y = 17 is (1/2). Therefore, the slope of a line perpendicular to it is -2.

To find the equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2), we can use the slope-intercept form of a line's equation and plug in the slope (-2) and the coordinates of the point p(-8, -2):

y = -2x + b

-2 = -2×(-8) + b

b = -18

--The question is incomplete, the complete question is given below--

"Give the slope-intercept form of the equation of the line that is perpendicular to 2x – 4y = 17 and contains p(–8, –2).

a. y = −2x + 8

b. y = −2x − 18

c. y = −2x − 12

d. y = −2x + 2"

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The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) is y = -2x – 18

y = mx + b is the slope intercept form of a line’s equation. Here, m = slope of the line and b = y-intercept.

The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) can be found by first finding the slope of the line 2x – 4y = 17. We can do this by rearranging the equation to the slope-intercept form:

2x – 4y = 17

-4y = -2x + 17

y = (1/2)x - (17/4)

The slope of the line is 1/2. Hence m = ½

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The area of triangle will be 140 square units.

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

K is the scaling factor for x in the equation y = Kx. This expression can also be visualised in terms of proportionality:

y ∝ x

K can therefore be regarded as a proportionality constant in this context.

Given the area of triangle = 35 sq. units

and scale factor is 2

The base times the height of a triangle equals its area. Triangle ABC's base and height each double when a scale factor of 2 with centre A is used, increasing the area by a factor of 4 as a result.

area of triangle = 1/2bh

where b = base and h = height

given 1/2bh = 35

when scale factor is 2

new base = 2b

new height = 2h

area will be 1/2(2b)(2h) = 4/2bh

so  1/2bh = 35

4/2bh = 35 x 4 = 140 square units.

Hence the area is 140 square units.

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Answer:

1_ones and 2 _tenth

Step-by-step explanation:

the number in front of the point they start from ones continues

Answer:

i think it's true am a 6 grader i really try

Step-by-step explanation:

For given parametric curve the equations of both tangents at point where it crosses itself are: y = ± (√15x + 2√15)

The graph of parametric curve x = cos t + 2 cos 2t, y = sin t + 2 sin 2t (t ∈ [0, 2π]) is as shown below.

From the graph we can observe that, the curve crosses itself at (-2, 0).

Let x = -2

cos t + 2 cos 2t = -2,

and y = 0

sin t + 2 sin 2t = 0

sin t + 2 (2 sin(t) cos(t)) = 0

sin t + 4 sin t cos t = 0

sin t(1 + 4 cos t) = 0

sin(t) = 0   OR   1 + 4 cos(t) = 0

sin(t) = 0   OR   cos(t) = -1/4

From sin(t) = 0

⇒ t = 0 or t = π,

but for these values of t, cos t + 2 cos 2t = -2 is not true.

This means, the point (-2, 0) must corresponds to cos(t) = -1/4

[tex]\Rightarrow t=cos^{-1}(\frac{1}{4} )[/tex]

When cos(t) = -1/4,

sin(t) = [tex]\frac{\sqrt{15} }{4}[/tex]                ..............(by identity sin²(t) + cos²(t) = 1)

And

[tex]sin(2t) = 2sin(t)cos (t)\\sin(2t) = 2\times \frac{\sqrt{15} }{4} \times (\frac{-1}{4} )\\\\sin(2t) = -\frac{\sqrt{15} }{8}[/tex]

[tex]\\\\cos(2t)=2cos^2{t} - 1\\\\cos(2t)=2(\frac{-1}{4} )^2 - 1\\\\cos(2t)=\frac{1}{8}-1\\\\ cos(2t)=\frac{-7}{8}[/tex]

Now we find derivative of given parametric equations with respect to t.

for x = cos t + 2 cos 2t,

dx/dt = -sin(t) -4 sin(2t)

y = sin t + 2 sin 2t

dy/dt = cos(t) + 4 cos(2t)

Consider dy/dx

[tex]= \frac{\frac{dy}{dt} }{\frac{dx}{dt} }\\\\= \frac{cos(t) + 4 cos(2t) }{-sin(t) -4 sin(2t)}\\\\=\frac{\frac{-1}{4}+4~\frac{-7}{8} }{-\frac{\sqrt{15} }{4}-4~\frac{\sqrt{15} }{8} }\\\\=-\sqrt{15}[/tex]

This means, slope m = -√15

We have the point (−2,0)

Using equation of line y=mx+b the y-intercept would be,

0 = -√15 (−2) + b

b = -2√15

So, the equation for this tangent line :

y = -√15x - 2√15

And the equation of other tangent would be,

y = √15x + 2√15

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The location of B such that the ratio of AB to BC is given as follows:

B = 28.

The location of B in the context of this problem is obtained applying the proportion, which is the ratio between the locations.

The coordinates of each point in this problem are given as follows:

The length of each segment in this problem is given as follows:

The ratio of AB to BC is 3 to 1, hence the following proportional relationship is established:

AB/BC = 3.

(x - 4)/(36 - x) = 3.

Applying cross multiplication, we can solve to obtain the value of x, representing the location of B, as follows:

x - 4 = 108 - 3x

4x = 112

x = 112/4

x = 28.

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The number of revolution each wheel make is 5605.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is given as πr².

We have,

Diameter of the wheel = 36 inches

The radius of the wheel = 18 inches

The circumference of the wheel = 2πr.

The total distance traveled = Circumference of the wheel x Number of revolutions (N).

Now,

10 miles = 10 x 5280 ft = 10 x 5280 x 12 inches

10 miles = 2πr x N

N = (10 x 5280 x 12) / (2 x 3.145 x 18)

N = 633600 / 113.04

N = 5605

Thus,

The number of revolutions is 5605.

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Answer:

y=mx+c

Step-by-step explanation:

The charge for the t-shirt earlier than the cut price of 25 percent is $20.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, the 25% discount, the price of a t-shirt was 15$.

Since, After 25% discount price of t-shirt = 15

Thus

Original price of t-shirt = 15 * 100/75

Original price of t-shirt = 20

Therefore, the price before the discount of 25 percent is $20.

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Answer:

[tex]y=1[/tex]

Step-by-step explanation:

Adding the equations yields [tex]4y=4[/tex]. Therefore, [tex]y=1[/tex].

Answer: 4 pie chart

Step-by-step explanation:

Each pie chart  [tex]\pi[/tex] wil have 4 parts to it  depending on  how the shape of the pie  is

Answer:

You know that x = -9, and 3 or The first number is 3, the other -9

Step-by-step explanation:

First number: x

Second: x + 6

(x)^2 + (x + 6)^2 = 90

x^2 + x^2 + 6x + 6x + 36 = 90

Simplify more

2x^2 + 12x + 36 = 90

2x^2 + 12x - 54 = 0

2(x + 9)(x - 3) = 0

Answer: it's not its  [tex]\frac{1}{27}[/tex]

Step-by-step explanation:

Because the negative in the exponent moves it to the denominator then just cube 3 in the denominator

[tex]\frac{1}{3^{3} }[/tex]

[tex]\frac{1}{27}[/tex]

But [tex]2^{-3} =\frac{1}{8}[/tex]

because [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]

Therefore the numerical order of the dimensions of rectangular prism is 8, 12

The minimal set of coordinates required to represent any point inside a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one since a point on it may be specified by a single coordinate, such as the point at 5 on a number line.

We have a minimum set when a group of words can all be distinguished from one another by altering one phoneme (always in the same location in the word). feat, fit, fat, fate, and foot were used. Big, Pig, Rig, Fig, Dig, and Wig might be included in another minimum list based on consonant phonemes.

The equation for the volume of a rectangular prism:

V = l × w × h

Given dimensions are x, x-2, and x+8

V = (x)(x-2)(x+8) = 96

x^3 - 2x^2 + 8x = 96

x^3 - 2x^2 + 8x - 96 = 0

(x-12)(x+4)(x-8) = 0

Therefore, x = 12, -4, 8

As the dimension of prism can't be negative, we can discard -4 as one of the dimension.

Thus, the numerical order of the dimensions of rectangular prism is 8, 12

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The integral, ∫ [ (9ˣ - eˣ )/3ˣ ] dx evaluate value is 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3). So, the correct answer is option (c).

Integration is defined as the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up all their areas. If d/dx(F(x) = f(x), then ∫ f(x) dx = F(x) + C, where C is integration constant and indefinite integrals. We have an integral, say , I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

and we have to determine its value.

I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

=> I = ∫ [ (9ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3ˣ - eˣ/3ˣ ] dx

=> I = ∫ 3ˣ dx - ∫ eˣ3⁻ˣ dx

=> I = 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3) + C

( since, ∫aˣ dx = aˣ/ln a)

where C --> integration constant

So, the required value is 3ˣ/ln(3)-eˣ/3ˣ(1 - ln 3).

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Complete question:

Find integral ∫ [ (9ˣ - eˣ )/3ˣ ] dx .

a) 3ˣ - eˣ/(1 - ln 3) + C

b) 9ˣ/2ln3 - eˣ/(3ˣ ln 3) + C

c) 3ˣ/ln3 - eˣ/3ˣ(1 - ln 3) + C

d) 3ˣ/ln3 - eˣ/3ˣ + C

[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3(ab^2)^2}{6a^3b^{-3}}\implies \cfrac{3}{6}\cdot \cfrac{(ab^2)^2}{a^3b^{-3}}\implies \cfrac{1}{2}\cdot \cfrac{(a^2b^4)}{a^3b^{-3}}\implies \cfrac{1}{2}\cdot \cfrac{b^4 b^3}{a^{-2}a^3} \\\\\\ \cfrac{1}{2}\cdot \cfrac{b^{4+3}}{a^{-2+3}}\implies \cfrac{1}{2}\cdot\cfrac{b^7}{a^1}\implies \cfrac{b^7}{2a}[/tex]