What’s the square root of 12?

Answer:

A)

15 hours

B)

108 hours

C)

2074.29 miles

Step-by-step explanation:

Under the assumption the earth is a perfect circle, then in one complete rotation about its axis ( 24 hours) the Earth will cover 360 degrees or 2π radians.

A)

In every 24 hours the earth rotates through 360 degrees ( a complete rotation). We are required to determine the length of time it will take the Earth to rotate through 225 degrees. Let x be the duration it takes the earth to rotate through 225 degrees, then the following proportions hold;

(24/360) = (x/225)

solving for x;

x = (24/360) * 225 = 15 hours

B)

In 24 hours the earth rotates through an angle of 2π radians (a complete rotation) . We are required to determine the length of time it will take the Earth to rotate through 9π radians. Let x be the duration it takes the earth to rotate through 9π radians, then the following proportions hold;

(24/2π radians) = (x/9π radians)

Solving for x;

x = (24/2π radians)*9π radians = 108 hours

C)

If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;

circumference = 2*π*R = π*D

                         = 7920*3.142

                         = 24891.43 miles

Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;

(24891.43miles)/(24 hours) = 1037.14 miles/hr

The distance covered by the point in 2 hours will thus be;

1037.14 * 2 = 2074.29 miles

Answer: Option b

b. x greater or equal than 1.8

Step-by-step explanation:

In this problem we have the following inequality:

[tex]2x\leq 3(x-0.6)[/tex]

To solve it we must group the x on one side and the constants on the other side

[tex]2x\leq 3(x-0.6)[/tex]

Apply distributive property on the right side of the inequality

[tex]2x\leq 3x-3*0.6[/tex]

[tex]2x\leq 3x-1.8[/tex]

Subtract 3x on both sides of the inequality

[tex]2x-3x\leq 3x-3x-1.8[/tex]

[tex]-x\leq-1.8[/tex]

Multiply by -1 both sides of the inequality

[tex]x\geq 1.8[/tex]

The answer is the option b

Answer:

the answer is option B

Step-by-step explanation:

Answer: 3/5=0.60

Step-by-step explanation:

The p(a/b) is 3/5 = 0.6

The Bayes theorem predicts the likelihood that an event connected to any condition would occur. Use the concept of the conditional probability formula, P(Ei|A)=P(Ei∩A)P(A), to demonstrate the Bayes theorem (A). The Bayes' Theorem describes the likelihood that an event connected to any condition would occur.

Given

P(a) = P(student in karate ) = 3

P(b) =P(student in chess) = 5

P(a|b) = 3/5 = 0.60

To know more about Bayes theorem refer to :

https://brainly.com/question/14989160

#SPJ2

Answer:

A

Step-by-step explanation:the lines do not cross therefor the two equations do not share a solution.

Answer:

A

Step-by-step explanation:

Answer:

$0.75 tax

Step-by-step explanation:

1. Find total cost of meal: $10.50 + $1.50 + $0.50 = $12.50

2. Find tax of meal: $12.50 * 6% = 12.5 * 0.06 = $0.75

Answer:

C. 48,5 cm²

Step-by-step explanation:

The area is 8×4 + 3×3 + 5×3/2 = 32+9+15/2 = 41+7,5 = 48,5 cm²

Answer:

A = 13 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh  where b is the length of the base and h is the height

A = 1/2 (6.5) * 4

A = 13 cm^2

For this case we must find an expression equivalent to:

[tex](x ^ {\frac{1}{4}} * y ^ {16}) ^ {\frac {1} {2}}[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Then, rewriting the expression:

[tex](x ^ {\frac {1 * 1} {4 * 2}} * y ^ {\frac {16 * 1} {2}}) =\\x ^ {\frac {1} {8}} * y ^ {\frac {16} {2}}) =\\x ^ {\frac {1} {8}} * y ^ {8}[/tex]

Answer:

Option B

ANSWER

B. 10

EXPLANATION

We need to find the value of x first.

It was given that the perimeter of triangle XYZ is 24.

This means that:

XY+YZ+XZ=24

we substitute the expression in terms of x to get;

[tex](5x - 1) + (13 - x) = 24[/tex]

This implies that

[tex]5x - x = 24 - 13 + 1[/tex]

[tex]4x = 12[/tex]

Divide both sides by 4 to get;

[tex]x = 3[/tex]

|WY|=|ZX|=13-3=10

Answer:

WY = 10 units

Step-by-step explanation:

From the figure we can see a rectangle WXYZ.

Diagonals of rectangle are equal.

It is given that, Perimeter of triangle XYZ = 24

XY + YZ = 5x - 1 and XZ = 13 - x

To find the value of x

Perimeter of ΔXYZ = XY + YZ + XZ

24 = 5x - 1 + 13 - x

4x + 12 = 24

4x = 12

x = 12/4 = 3

x = 3

To find the value of WY

We have WY = XZ

XZ = 13 - x

 = 13 - 3 = 10

Therefore WY = XZ = 10 units

Answer:

Shravan's age is 40 years old

Gaurav’s age is 30 years old

Step-by-step explanation:

Let

x-----> Shravan's age

y-----> Gaurav’s age

we know that

x=y+10 -----> equation A

(1/7)(x-5)=(1/5)(y-5) ----> equation B

substitute equation A in equation B and solve for y

(1/7)(y+10-5)=(1/5)(y-5)

(1/7)(y+5)=(1/5)(y-5)

5(y+5)=7(y-5)

5y+25=7y-35

7y-5y=25+35

2y=60

y=30 years

Find the value of x

x=y+10  ----> x=30+10=40 years

therefore

Shravan's age is 40 years old

Gaurav’s age is 30 years old

Answer: x÷(2÷5y)

Step-by-step explanation: this is because you have to first do the quotient of 2 and try then the answer will be divided by 5

Answer:

The quotient of x and the quotient of 2 and 5y.

Expression:

x/(2/5y)

Explanation:

The quotient means to divide the numbers. The “and” after quotient is what the number is dividing with. So, x us dividing with the division of 2 and 5y.

The conjugate of the complex number 2 - 8i is 2 + 8i, found by changing the sign of the imaginary part from negative to positive.

The conjugate of a complex number is found by changing the sign of the imaginary part.

For a complex number with a real part of 2 and an imaginary part of -8i, the complex number is represented as 2 - 8i. To find its conjugate, we change the sign of the imaginary part, resulting in 2 + 8i.

The general form of a complex number is a + bi, where a is the real part and bi is the imaginary part.

The conjugate is then written as a - bi. Therefore, if we have the complex number z = 2 - 8i, the conjugate, denoted as [tex]\( \overline{z} \)[/tex], is 2 + 8i.

Hello There!

The value of the number "5" in the number 15,406 would be the value of 5,000

Answer:

13/6

Step-by-step explanation:

-6 1/3 + 5 5/6

1. You can reduce the first equation to 2

-6 1/3, becomes -2 x 1/1. This is because 3 goes into itself 1 time, and it goes into 6, -2 times. Your new equation: -2 + 5 5/6

2. Multiply the 5's in 5 5/6 by each other to get...

25/6

Your new equation: -2 + 25/6

3. Multiply 6 by -2 to get -12

4. Now add the numerators(remember -12 is basically, -12/1) together to get your answers

-12 + 25/6 = 13/6

Hello There!

If we add -6 1/3 and 5 5/6 together, we will get a sum of -1/2

STEP 1 First, I like to convert mixed numbers into improper fractions because they are easier to work with. So, I would change -6 1/3 to -19/3. Then, I would change 5 and 5/6 to 35/6.

STEP 2 Applying the fraction formula for addition. (-19x6) + (35x3) and then i would put this over 6x3

STEP 3   -114+105

                      18

STEP 4

-9/18 = -1/2

Answer: It can not be a mixed number because if you divide -27 by 50 you get -0.54, so then if you turn -0.54 in fraction form it would be -27/50, so the fraction would stay the way it is. -27/50 is not an improper fraction. To be improper, the numerator must be greater than the denominator!

* Hopefully this helps:) Mark me the brainliest:)!!!

Answer:

y = - 3x + 16

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{3}[/tex] x + 8 ← is in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3, so

y = - 3x + c ← is the partial equation of the perpendicular line

To find c substitute (6, - 2) into the partial equation

- 2 = - 18 + c ⇒ c = - 2 + 18 = 16

y = - 3x + 16 ← equation of perpendicular line

Answer:

The trip will take more than one hour

Step-by-step explanation:

The complete question is

A straight road connects the towns of Winridge and Upper Lansbury. On a map on which each unit represents 10 miles, the coordinates of Winridge are (8,4) and the coordinates of Upper Lansbury are (6,10). If Ty drives from Winridge to Upper Lansbyet at an average speed of 40 miles per hour, will the trip take more than an hour? Explain your reasoning

we know that

The speed is equal to divide the distance by the time

so

s=d/t

Solve for t

t=d/s ----> the time is equal to divide the distance by the speed

step 1

Find the distance

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

(8,4), (6,10)

substitute

[tex]d=\sqrt{(10-4)^{2}+(6-8)^{2}}[/tex]

[tex]d=\sqrt{(6)^{2}+(-2)^{2}}[/tex]

[tex]d=\sqrt{40}[/tex]

[tex]d=2\sqrt{10}\ units[/tex]

Convert to miles

[tex]d=2\sqrt{10}*10=20\sqrt{10}\ miles[/tex]

[tex]d=63.2\ miles[/tex]

step 2

Find the time

we have

s=40 miles/hour

d=63.2 miles

t=d/s -----> t=63.2/40=1.58 hours

1.58 hours > 1 hour

therefore

The trip will take more than one hour

The complement of A would be the elements in U that are not in A.

A is 2, 4, 6, 8

Remove those numbers from U for the complement.

The complement would be {1, 3, 5, 7, 9, 10}

Answer: The complement is 1, 3, 5, 7, 9, 10

I hope that this helps! :3

Step 1: Convert [tex]\frac{5\pi }{12}[/tex], which is in radians into degrees. To convert it multiply by [tex]\frac{180}{\pi }[/tex]

[tex]\frac{5\pi }{12} =\frac{180}{\pi }[/tex]

900/12

75

Step 2: 75 degrees isn't on the unit circle but 45 degrees and 30 degrees is. Since 45 + 30 = 75 you can use the cosine of 45 and 30 to find the exact value

cos45 = [tex]\frac{\sqrt{2} }{2}[/tex]

cos30 =[tex]\frac{\sqrt{3} }{2}[/tex]

Step 3: Add the cos45 and cos30 to get cos5pi/12

[tex]\frac{\sqrt{2} }{2} +\frac{\sqrt{3} }{2} = \frac{\sqrt{2}+\sqrt{3}}{2}[/tex]

Hope this helped!

Answer:

y = 9 + 19x

Step-by-step explanation:

To find the equation matching a set of data, you simply try a few values for x and see if by solving that side of the equation you get the value of y.  If you do, you found your equation.

You have a big advantage here... since you have the value of y when x = 0.

When x = 0, y = 9, that's a very important data to have to simplify your research.

Let's try the value of 0 for x in each of the given equations:

y = 18 + 10 (0) = 18  --- NO

y = 9 + 19 (0) = 9 --- YES!  We can confirm with another value of x:

y = 9 + 19 (1) = 28 --- YES! Confirmed!

y = 9 + 19x is your answer!

Answer:

see explanation

Step-by-step explanation:

The rule (x + 3, y + 2) means add 3 to the original x- coordinate and add 2 to the original y- coordinate, that is

A(- 2, 2) → A'(- 2 + 3, 2 + 2) → A'(1, 4)

B(- 2, 4) → B'(- 2 + 3, 4 + 2) → B'(1, 6)

C(0, 0) → C'(0 + 3, 0 + 2) → C'(3, 2)

Answer:

24649-17424=7225 UNITS

Step-by-step explanation:

This step implies that Lara was using the Pythagoras theorem to find the missing length of the right triangle.

a²+b²=c², taking a and b to be the  two lengths adjoined by the right angle and c the hypotenuse.

Laura's step represents the step above.

157²=24649

132²=17424

157²-132²=c²

24649-17424=7225

Answer:

Final answer is c=-7.

Step-by-step explanation:

Given equation is [tex]0=-x^2+4x-7[/tex].

Now question says that Misha wrote the quadratic equation 0=-x2+4x-7 in standard form. Now we need to find about what is the value of c in her equation.

We know that standard form of quadratic equation is given by [tex]ax^2+bx+c=0[/tex].

compare given equation with the standard form, we find that -7 is written in place of +c

so that means +c=-7

or c=-7

Hence final answer is c=-7.

James will have $32,270.13 after 6 years

Answer:

[tex]y=20000(1.083)^6[/tex]

Step-by-step explanation:

Let y represents the amount James have after 6 years,

Given,

Principal amount, P = $ 20,000,

Compound rate of interest per year, r = 8.3 %,

Thus, the amount after x years would be,

[tex]A=P(1+\frac{r}{100})^x[/tex]

[tex]=20,000(1+\frac{8.3}{100})^x[/tex]

[tex]=20000(1.083)^x[/tex]

Therefore, the amount after 6 years would be,

[tex]y=20000(1.083)^6[/tex]

Which is the correct equation that represents the amount, James will have after 6 years.

Answer: The graph is attached.

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

You can solve for "y":

[tex]2y<5x-10\\\\y<\frac{5}{2}x-\frac{10}{2}\\\\y<\frac{5}{2}x-5[/tex]

You need to rewrite the expression:

[tex]y=\frac{5}{2}x-5[/tex]

You can identify that the slope of this line is:

[tex]m=\frac{5}{2}[/tex]

And the y-intercept is:

[tex]b=-5[/tex]

Substitute [tex]y=0[/tex] and solve for "x" to know the x-intercept:

[tex]0=\frac{5}{2}x-5\\\\5*2=5x\\\\x=2[/tex]

Now you know that the line passes through the points (0,-5) and (2,0).

Since the inequality is "<", you know that the line must be dashed and the shaded region must be below the line [tex]y=\frac{5}{2}x-5[/tex].

Knowing this, you can graph it (Observe the graph attached)

[tex]\cos(15^\circ) = \cos(45^{\circ}-30^{\circ}) = \cos(45^{\circ})\cos(30^{\circ})+\sin(45^{\circ})\sin(30^{\circ}) = \\ \\ =\dfrac{\sqrt 2}{2}\cdot \dfrac{\sqrt 3}{2}+\dfrac{\sqrt 2}{2}\cdot \dfrac{1}{2} = \dfrac{\sqrt 6 +\sqrt 2}{4}[/tex]

Answer:

[tex]\cos (15)=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Step-by-step explanation:

We want to find the exact value of

[tex]\cos 15\degree[/tex]

We rewrite this expression using compound angles  

[tex]\cos (45\degree-30\degree)[/tex]

Recall that:

[tex]\cos (A-B)=\cos A\cos B+\sin A\sin B[/tex]

We apply this property to obtain:

[tex]\cos (45-30)=\cos 45\cos 30+\sin 45\sin 30[/tex]

[tex]\cos (15)=\frac{\sqrt{2}}{2} \times \frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2} \times \frac{1}{2}[/tex]

[tex]\cos (15)=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Answer:

The correct answer option is D. 0.42.

Step-by-step explanation:

We are given the results of a survey in which people were asked if they prefer reading books or e-books.

We are to find the marginal frequency of the number of people who prefer to read books.

For that, we will divide the total number of people who prefer reading books by the total number of people surveyed.

Marginal frequency = 105/250 = 0.42

Answer:

The slope of this line is 1/5

Answer:

25.5%

Step-by-step explanation:

% error = | estimate - actual | / actual × 100%

% error = | 59 - 47 | / 47 × 100%

% error ≈ 25.5%

Answer:

20.3%

Step-by-step explanation:

The formula for percent error is the experimental value minus the theoretical value divided by the theoretical value all times 100.

Experimental - Theoretical

------------------------------------------ x 100

         Theoretical

−12

------- ×100

59

=−0.20339×100

=−20.339

=20.339%

=20.3% error

Answer:

The correct answers are:

Question 4: the first step Keisha should take is: log to the power of x equals log 9.

Question 5: step 4 could be n ln 2 equals ln 86

Question 6: the exact solution is x=ln(7)

Step-by-step explanation:

Ok,

Question 4: the equation that shows the first step Keisha should take is:

[tex]7^{x}=9[/tex]

[tex]log(7^{x} )=log(9)[/tex]

[tex]x(log(7))=log(9)[/tex] (applying the properties of logarithms)

[tex]x=\frac{log(9)}{log(7)} =1.129[/tex]

Solution: the first step Keisha should take is: log to the power of x equals log 9.

Question 5: Her first three steps are:

[tex]2^{n}-3=83[/tex]

[tex]2^{n}-3+3=83+3[/tex] (adding 3 to both sides)

[tex]2^{n}=86[/tex]

[tex]2^{n}-3+3=83+3[/tex]

[tex]nln(2)=ln(86)[/tex]

Solution: step 4 is: [tex]nln(2)=ln(86)[/tex] (applying the properties of logarithms)

Question 6: The exact solution of 2 e to the power of x equals 14 is:

[tex]2e^{x}=14[/tex]

[tex]\frac{2e^{x} }{2} =\frac{14}{2}[/tex] (dividing both sides by 2)

[tex]e^{x}=7[/tex]

[tex]xln(e)=ln7[/tex] (ln(e)=1)

[tex]x=ln(7)[/tex]

Solution: [tex]x=ln(7)[/tex]

For Keisha's equation, the first step involves taking the logarithm of both sides, and for Mary's equation, the fourth step involves taking the natural logarithm. The exact solution for the third equation is x = ln 7.

Question 4:

Keisha is solving the equation [tex]\(7^x = 9\)[/tex]. The correct first step is:

[tex]\[ \log(7^x) = \log(9) \][/tex]

So the correct option is:

[tex]\[ \text{log } 7^x = \text{log } 9 \][/tex]

Question 5:

For Mary's equation [tex]\(2^n - 3 = 83\)[/tex], Step 4 involves taking the natural logarithm:

[tex]\[ n \ln 2 = \ln 86 \][/tex]

So the correct option is:

[tex]\[ n \ln 2 = \ln 86 \][/tex]

Question 6:

The equation [tex]\(2e^x = 14\)[/tex] can be solved by taking the natural logarithm:

[tex]\[ x = \ln \left(\frac{14}{2}\right) \][/tex]

Simplifying this gives:

[tex]\[ x = \ln 7 \][/tex]

So the correct option is:

[tex]\[ \ln 7 \][/tex]