Evaluate the expression. Give the answer as a mixed number in simplest form.

212 ÷ 1310

Answer:

length of each edge = (x + 3)

Step-by-step explanation:

The surface area of each face of the cube = (\(x^{2}\) + 6x + 9) \(m^{2}\). But the surface of a cube has the shape of a square. So that,

Area of a square = length x length

                            = \(l^{2}\)

By factorizing the area,

\(x^{2}\) + 6x + 9 = \(x^{2}\) + 3x + 3x + 9

                  = (\(x^{2}\) + 3x) (3x + 9)

                  = x(x +3) + 3(x + 3)

                  = (x + 3)(x + 3)

                  = \((x + 3)^{2}\)

\(x^{2}\) + 6x + 9 = \((x + 3)^{2}\)

Thus,

\((x + 3)^{2}\) = \(l^{2}\)

find the square root of both sides

l = (x + 3)

length of each edge = (x + 3)

Answer:

Each girl has 5 pill bugs each.

The length of each pill bug should be 9 millimeters

Step-by-step explanation:

100 divided by 20 equals 5

900 divided by 100 equals 9

Answer:

Step-by-step explanation:

\((sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA\)

we take the LHS so here goes,

\((sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA\\(\frac{1}{cosA} -\frac{1}{sinA})(1+\frac{sinA}{cosA}+\frac{cosA}{sinA})\\\\(\frac{sinA-cosA}{sinAcosA})(\frac{sinAcosA+sin^2A+cos^2A}{sinAcosA})\\\)

since , \(sin^2A+cos^2A=1\)

the identity becomes,

\((\frac{sinA-cosA}{sinAcosA})(\frac{1+sinAcosA}{sinAcosA})\\\\(\frac{sinA+sin^2AcosA-cosA-cos^2AsinA}{sin^2Acos^2A})\\\\\)

now, we know,

\(sin^2A=1-cos^2A\) and \(cos^2A=1-sin^2A\)

the identity becomes,

\((\frac{sinA+(1-cos^2A)cosA-cosA-(1-sin^2A)sinA}{sin^2Acos^2A} )\\\\\)

\((\frac{sinA+cosA-cos^3A-cosA-sinA+sin^3A}{sin^2Acos^2A})\)

sin A and cos A cancel out it becomes zero

\(\frac{sin^3A-cos^3A}{sin^2Acos^2A} \\\\\)

Splitting the denominator the identity becomes

\(\frac{sin^3A}{sin^2Acos^2A}-\frac{cos^3A}{sin^2Acos^2A} \\\\\frac{sinA}{cos^2A} - \frac{cosA}{sin^2A} \\\\\frac{sinA}{cosA}(\frac{1}{cosA})-\frac{cosA}{sinA}(\frac{1}{sinA})\\\\\)

Hence,

\(tanAsecA-cotAcosecA\)

The equation ,\(-2x^2+5xy-7y^2+9x-7y+13=0\) represents a conic. The discriminant is is -31 , so the represents an ellipse .

A curve obtained by a cone and a plane is called conic .

Here given equation is

\(-2x^2+5xy-7y^2+9x-7y+13=0\)

we know that discriminants of equation

\($$A x^{2}+B x y+C y^{2}+D x+E y+F=0$$\)

is \($$D=B^{2}-4 A C$$\)

and if

D<0  it's ellipse

D=0 it's parabola

D>0 It's  hyperbola

Here, the is

\($$D=5^{2}-4(-2)(-7)=-31$$\)

Hence it's an ellipse

The equation ,\(-2x^2+5xy-7y^2+9x-7y+13=0\) represents a conic. The discriminant is is -31 , so the represents an ellipse .

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Answer:

-31 and ellipse

Step-by-step explanation:

on edge :)

When more than one adjustment is required on a worksheet, the adjustment can be added to a blank line and the adjustment can be combined into one adjustment amount. Option b and d is correct.

The adjustment can be added to a blank line if there is an available blank line on the worksheet, each adjustment can be separately added to its own line, ensuring clarity and organization.

The adjustment can be combined into one adjustment amount instead of listing each adjustment separately, it is also possible to combine them into a single adjustment amount. This is appropriate when the individual adjustments are related or impact the same account.

So the correct options are B and D.

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Answer:

GCF = 5x^3

Step-by-step explanation:

25x^3/5x^3 = 5

10x^4/5x^3 = 2x

The multiplication model represented by the image is given as follows:

12(4 x 10) + (3 x 10) + (6 x 10) + 18.

A multiplication operation is equivalent to consecutive additions.

For the green squares, the following addition is obtained:

10 + 10 + 10 + 10 + 6.

(which is the number of squares painted green).

Considering a multiplication with consecutive additions, it is written as follows:

4 x 10 + 6.

For the red squares, the expression is:

4 + 4 x 10 + 2 = 4 x 10 + 6.

For the blue squares, the expression is:

8 + 3 x 10 + 8

3 x 10 + 16

For the white squares, the expression is:

2 + 6 x 10

Hence the total model is calculated as follows:

4 x 10 + 6 + 4 x 10 + 6 + 3 x 10 + 16 + 2 + 6 x 10

(4 x 10)(6 + 6) + (3 x 10) + (6 x 10) + 18.

12(4 x 10) + (3 x 10) + (6 x 10) + 18.

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Answer:

The radius of the cylinder is 2.52 cm.

Step-by-step explanation:

The formula for the volume of a cylinder of radius r and height h is

V = πr²h.  We can solve this for r² by dividing both sides of the equation by πh:

r² = V / (πh)

Then the desired radius is found by taking the square root of this.

r = √{V / [πh]}

                  200 cm^2

Here, r² = ------------------- = 6.37 cm^2

                   3.14(10 cm)

and so r = √6.37 cm^2 = 2.52 cm

The radius of the cylinder is 2.52 cm.

Answer:

radius = 2.52 cm

Step-by-step explanation:

\(Volume = \pi r^2 h\\\\200 = \pi r^2 \times 10\\\\\frac{200}{10 \times \pi} = r^2 \\\\6.332 = r^2 \\\\\sqrt{6.332} = r \\\\r = 2.52 \ cm\)

Answer:

Read Exp:

Step-by-step explanation:

Exponents are like a simpler way to multiply something by itself a certain amount of times.

So like if you were to see 7^4 on a test or assignment you would solve it like this:

- 7x7x7x7.

It just means 7 times itself 4 times. NOT 7 times 4.  

Answer:

The average rate of change in that interval is 1.99

Step-by-step explanation:

Here we have that the difference quotient for g(x) is:

\(\frac{6^{x + h} - 3 - 6^x + 3}{h}\)

Remember that for a general function f(x), the difference quotient is:

\(\frac{f(x + h) - f(x)}{h}\)

So if we look at the difference quotient for g(x), we can conclude that:

\(g(x) = 6^x - 3\)

Also remember that the average rate of change in an interval (a, b) is just:

\(\frac{g(b) - g(a)}{b - a}\)

So here we want the average rate of change of g(x) in the interval from x = -2 to x = 1, this is:

\(R = \frac{(6^1 - 3) - (6^{-2} - 3)}{1 - (-2)} = \frac{6 - 6^{-2}}{3} = 1.99\)

The average rate of change in that interval is 1.99

Answer:

                                                                                 59360

Step-by-step explanation:

Answer:

n=9M, when m is 6,n=18

Step-by-step explanation:

If n is proportional to M

n=kM

27=3k

k=27/3

k=9

the formula on terms of n and M is

n= 9M

2) If m= 6,

n= 3M

n=3(6)

n=18

Answer:

n = 108

Step-by-step explanation:

given n is proportional to m² then the equation relating them is

n = km² ← k is the constant of proportion

to find k use the condition n = 27 when m = 3 , then

27 = k × 3² = 9k ( divide both sides by 9 )

3 = k

n = 3m² ← equation of proportion

when m = 6 , then

n = 3 × 6² = 3 × 36 = 108

Answer:

3.2

Step-by-step explanation:

Answer:

pythagorean theorem !!!!!!

Step-by-step explanation:

0.8²+1.6²=3.2²

0.64+2.56=10.24

THAT means the distance is

\( \sqrt{10.24} \)

=3.2miles

Answer:

6

5

3

pt 2

6+5+3+1=15

plz wait till someone else answers cuz ion know if this is what the question is asking for

Answer:

An angle is in standard position, if its vertex is located at the origin and one ray is on the positive x-axis.

Step-by-step explanation:

Mike comes to a stop 105.3 feet above sea level while trekking on a mountain. The vertical separation between Mike and the mountain's base is 101.5 feet .

Given that,

Mike comes to a stop 105.3 feet above sea level while trekking on a mountain. There are 3.8 feet of sea level below the mountain's base.

We have to find what is the vertical separation between Mike and the mountain's base.

The Mike comes to a stop 105.3 feet above sea level while trekking on a mountain.

3.8 feet of sea level below the mountain's base.

We just have to do the difference of the above sea level feet and below sea level feet.

=105.3-3.8

=101.5

Therefore, the vertical separation between Mike and the mountain's base is 101.5 feet .

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Step-by-step explanation:

31+27+19+18+22+21+25+29+34+30 divided by 10

Answer:

A. area of larger rectangle: 18x^2

area of smaller rectangle: 8x^2

B. area of shaded region: 10x^2

Step-by-step explanation:

Larger rectangle: A = lw = (6x)(3x) = 18x^2

Smaller rectangle: A = lw = (4x)(2x) = 8x^2

The shaded region = larger rectangle - smaller rectangle

=> 18x^2 - 8x^2 = 10x^2

Answer:

8 fishes are in each tank

Step-by-step explanation:

53-29= 24

24÷3= 8

the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined which shape is formed as Square

When the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined, a square is formed. The sides are equal length and the angles are all 90 degrees.The coordinates (1,1), (7,3), (8,0) and (2,-2) are points on a two-dimensional plane. When the points are connected, a square is formed. A square is a four sided shape with four 90 degree angles and four equal length sides. The length of each side can be calculated by finding the distance between the two points. For example, the distance between (1,1) and (7,3) is 6 units. Therefore, the length of each side of the square is 6 units.

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Answer:

x = 68

Step-by-step explanation:

17/ 30 = x / 120

To get from 30 to 120 in the denominator, we multiply by 4

30*4 = 120

We must do the same in the numerator

17 * 4 = 68

x = 68

Answer:

It would take you 4.8 hours to reach to New York and it would take you 4 hours if your speed was 10 mph faster.

Step-by-step explanation:

240÷50=4.8

240÷(50+10)=x

240÷60=4

Answer:

4.8

Step-by-step explanation:

Answer:

671921 * 79719

= 53,564,870,199

Answer:

53564870199

Step-by-step explanation:

671921*79719=53564870199

The probabilities to the given problem are as follows:

a) To find the probability that the mobile phone will need to be recharged in less than 1.5 days, we can use the cumulative distribution function (CDF) of the Exponential distribution. The CDF of an Exponential distribution with mean μ is given by:

CDF(x) = 1 - e^(-x/μ)

Substituting the given values, we have:

CDF(1.5) = 1 - e^(-1.5/2.5) ≈ 0.432

Therefore, the probability that the mobile phone will have to be recharged in less than 1.5 days is approximately 0.432.

b) Now, let's consider a new model of phone where the probability of needing to be recharged in less than 1.5 days is 0.4061. We have 15 of these new phones, all put into usage on the same day and working independently of each other. We want to find the probability that at least 7 of these phones will need to be recharged in less than 1.5 days.

This scenario can be modeled using the binomial distribution, which describes the number of successes in a fixed number of independent Bernoulli trials. Each phone either needs to be recharged in less than 1.5 days (success) or doesn't need to be recharged (failure), with a probability of success given as 0.4061.

Using Matlab or a similar statistical software, we can calculate the probability of at least 7 successes out of 15 trials. In Matlab, we can use the binocdf function to calculate the cumulative binomial probability.

The probability of at least 7 successes out of 15 trials can be calculated as follows:

P(X ≥ 7) = 1 - binocdf(6, 15, 0.4061) ≈ 0.251

Therefore, the probability that at least 7 out of 15 new phones will need to be recharged in less than 1.5 days is approximately 0.251.

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Answer:

19.5 ft squared

Step-by-step explanation:

Area of a triangle is (b*h)/2 so its is 39/2 or 19.5

Let the unkown be x. the given proportion would be

20/3 = x/6

By crossmultiplying, it becomes

x * 3 = 20 * 6

3x = 120

x = 120/3

x = 40

The correct option is C

The probability P(n < 10 | n is prime) is 4/6, which simplifies to 2/3 or approximately 0.67 (rounded to the nearest hundredth).

To find the probability P(n < 10 | n is prime), we need to determine the number of prime integers less than 10 and divide it by the total number of integers from 1 to 15 that are prime.

The prime numbers less than 10 are 2, 3, 5, and 7. So, there are 4 prime numbers less than 10.

The total number of integers from 1 to 15 that are prime is 6 (2, 3, 5, 7, 11, and 13).

As a result, the chance P(n 10 | n is prime) is 4/6, which can be expressed as 2/3 or, rounded to the nearest hundredth, as around 0.67.

Thus, 0.67 is the answer.

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To solve the equation cos(theta) = 1/4, we will find the values of theta that satisfy the equation.The general solution for the given equation is theta = 1.32 + 2πk, 4.96 + 2πk, where k is any integer.

Step 1: Determine the principal angle.
Find the angle whose cosine is 1/4 in the range of 0 to 2π.
theta = cos^(-1)(1/4) ≈ 1.32 rad (rounded to two decimal places)
Step 2: Determine the second angle in the range of 0 to 2π.
Since cosine is an even function, its value is the same for both positive and negative angles. Thus, the second angle in this range is -1.32 rad, which is equivalent to 2π - 1.32 ≈ 4.96 rad (rounded to two decimal places).
Step 3: General solution
Cosine is periodic with a period of 2π, so we can express the general solution as:
theta = 1.32 + 2πk or theta = 4.96 + 2πk, where k is any integer.
Step 4: Write the final answer.
The general solution for the given equation is theta = 1.32 + 2πk, 4.96 + 2πk, where k is any integer.

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