Write the following sentence as an equation.
The quotient of 120 and twice 20 is equal to 3.

Answer:

10 : 6

Step-by-step explanation:

1km / min = 1000m / 60 sec = 100/6 m/s

Ratio :

100/6 : 10

10/6 : 1

10 : 6

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A tangent meets with the radius to form a right angle

Thus, we can use Pythagoras' theorem

b^2 = c^2 - a^2

Sub the values in:

b^2 = 5^2 - 3^2

b^2 = 16

Square root for the answer:

b = 4

Thus, the answer is option A.

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Answer:

option 1 is the answer

Step-by-step explanation:

IN A CIRCLE , THE TANGENT IS THE PERPENDICULAR TO THE RADIUS DRAWN TO THE POINT OF CONTACT

SO AC ⊥ BC

ie angle ACB= 90 degree

therefore in triangle ABC , ACB = 90 DEGREE

By applying pythagorus theorem ,

AB^2 = AC^2 + BC^2

5^2 = r^2 + 3^2

25 -9 = r^2

16 = r^2

r = square root o f 16

therefore r= 4

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Answer: d) determinant cannot be found

Step-by-step explanation:

You can only find the determinant of a SQUARE matrix.

In other words, the dimensions must be 2 × 2 or  3 × 3 or ... n × n

The dimensions of the given matrix is 2 x 3, so the determinant cannot be calculated.

Answer:

x = 12

Step-by-step explanation:

Since they are equidistant from the centre, they are equal in length i.e.

JK = LM

4x+37 = 5(x+5)

4x+37 = 5x+25

37-25 = 5x-4x

12 = x

OR

x = 12

Answer:

1/2

Step-by-step explanation:

The formula that relates two independent events is provided as below:

P(A) x P(B) = P(A⋂B)

=> P(A) x (1/3) = 1/6

=> P(A) = (1/6) x 3

=> P(A) = 3/6 = 1/2

=> Option D is correct

Hope this helps!

Answer:

x = 7

Step-by-step explanation:

<ACF = 90° (since AB is the diameter and it is perpendicular to EF)

But <ACF = 2(7x-4)

So

2(7x-4) = 90

14x-8 = 90

14x = 90+8

14x = 98

Dividing both sides by 14

x = 7

Answer:

a, b

Step-by-step explanation:

a and b  cause  all  the data are  not in a form of a line

Answer:

Step-by-step explanation:

The rectangular form of a complex number is expressed as z = x+iy

where the modulus |r| = [tex]\sqrt{x^{2}+y^{2}[/tex] and the argument [tex]\theta = tan^{-1}\frac{y}{x}[/tex]

In polar form, x = [tex]rcos\theta \ and\ y = rsin\theta[/tex]

[tex]z = rcos\theta+i(rsin\theta)\\z = r(cos\theta+isin\theta)[/tex]

Given the complex number, [tex]z = -6+6\sqrt{3} i[/tex]. To express in trigonometric form, we need to get the modulus and argument of the complex number.

[tex]r = \sqrt{(-6)^{2}+(6\sqrt{3} )^{2}}\\r = \sqrt{36+(36*3)} \\r = \sqrt{144}\\ r = 12[/tex]

For the argument;

[tex]\theta = tan^{-1} \frac{6\sqrt{3} }{-6} \\\theta = tan^{-1}-\sqrt{3} \\\theta = -60^{0}[/tex]

Since tan is negative in the 2nd and 4th quadrant, in the 2nd quadrant,

[tex]\theta =180-60\\\theta = 120^{0}[/tex]

z = 12(cos120°+isin120°)

This gives the required expression.

Answer:

StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U

Step-by-step explanation:

The expression below means RS/VU = ST/UT

See the attachment for better explanation.

Answer:

A

Step-by-step explanation:

I took the test

Range of the given function  y=-x-5 includes -4

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

For the given function,

y = -x-5

Wen we put x = -1

we get y = -4

Also,

The range of this function is (-∞, ∞)

Hence,

The function  y = -x-5 includes the -4.

To learn more about function visit:

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Answer:

[tex] y^2 -4y +6=0[/tex]

[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

Where [tex] a = 1, b= -4 ,c =6[/tex]

And replacing we got:

[tex] y = \frac{-(-4) \pm \sqrt{4^2 -4(1)(6)}}{2*1}[/tex]

And solving we got:

[tex] y = \frac{4 \pm \sqrt{-8}}{2} =2 \pm 2\sqrt{2} i[/tex]

Where [tex] i =\sqrt{-1}[/tex]

And the possible solutions are:

[tex] y_1=2 + 2\sqrt{2} i , y_2 = 2 - 2\sqrt{2} i [/tex]

Step-by-step explanation:

For this case we use the equation given by the image and we have:

[tex] -y^2 +4y -6=0[/tex]

We can rewrite the last expression like this if we multiply both sides of the equation by -1.

[tex] y^2 -4y +6=0[/tex]

Now we can use the quadratic formula given by:

[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

Where [tex] a = 1, b= -4 ,c =6[/tex]

And replacing we got:

[tex] y = \frac{-(-4) \pm \sqrt{4^2 -4(1)(6)}}{2*1}[/tex]

And solving we got:

[tex] y = \frac{4 \pm \sqrt{-8}}{2} =2 \pm 2\sqrt{2} i[/tex]

Where [tex] i =\sqrt{-1}[/tex]

And the possible solutions are:

[tex] y_1=2 + 2\sqrt{2} i , y_2 = 2 - 2\sqrt{2} i [/tex]

14. Was the perimeter calculated correctly?

We know that,

Perimeter of rectangle = 2 ( l + b )

= 2 ( 4 + 7 / 5 )

= 2 ( 20 + 7 / 5 )

= 2 × 27/5

= 54 / 5

= 1 * 4/5

No ...

Answer:

x=0.5355 or x=-6.5355

First step is to: Isolate the constant term by adding 7 to both sides

Step-by-step explanation:

We want to solve this equation: [tex]2x^2 + 12x - 7 = 0[/tex]

On observation, the trinomial is not factorizable so we use the Completing the square method.

Step 1: Isolate the constant term by adding 7 to both sides

[tex]2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7[/tex]

Step 2: Divide the equation all through by the coefficient of [tex]x^2[/tex] which is 2.

[tex]x^2 + 6x=\frac{7}{2}[/tex]

Step 3: Divide the coefficient of x by 2, square it and add it to both sides.

Coefficient of x=6

Divided by 2=3

Square of 3=[tex]3^2[/tex]

Therefore, we have:

[tex]x^2 + 6x+3^2=\frac{7}{2}+3^2[/tex]

Step 4: Write the Left Hand side in the form [tex](x+k)^2[/tex]

[tex](x+3)^2=\frac{7}{2}+3^2\\(x+3)^2=12.5\\[/tex]

Step 5: Take the square root of both sides and solve for x

[tex]x+3=\pm\sqrt{12.5}\\x=-3\pm \sqrt{12.5}\\x=-3+ \sqrt{12.5}, $ or $x= -3- \sqrt{12.5}\\$x=0.5355 or x=-6.5355[/tex]

Answer:

Step-by-step explanation:

Step 1: Isolate the constant term by adding 7 to both sides of the equation.

Step 2: Factor 2 from the binomial.

Step 3: 9

Step 3 b: 18

Step4: write the trinomial as the square root of a binomial.

Step 5: divide both sides of the equation by 2 Step

6: Apply the square root property of equality Step

7: subtract 3 from both sides of the equation.

Answer:

a) 0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less

b) 0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c) 0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours

d) 86 should have a battery life of at least 9 hours.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

The probability of being higher than x is:

[tex]P(X > x) = \frac{b - x}{b-a}[/tex]

The probability of being between c and d is:

[tex]P(c \leq X \leq d) = \frac{d-c}{b-a}[/tex]

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

This means that [tex]a = 8.5, b = 12[/tex]

a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

[tex]P(X \leq 10) = \frac{10 - 8.5}{12 - 8.5} = 0.4286[/tex]

0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less.

b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

[tex]P(X > x) = \frac{b - x}{b-a}[/tex]

[tex]P(X > 11) = \frac{12 - 11}{12 - 8.5} = 0.2857[/tex]

0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

[tex]P(c \leq X \leq d) = \frac{d-c}{b-a}[/tex]

[tex]P(9.5 \leq X \leq 11.5) = \frac{11.5 - 9.5}{12 - 8.5} = 0.5714[/tex]

0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours.

d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

Proportion of iPad Minis with a battery life of at least 9 hours.

[tex]P(X > 11) = \frac{12 - 9}{12 - 8.5} = 0.8571[/tex]

Out of 100:

0.8571*100 = 85.71

To the nearest whole number

86 should have a battery life of at least 9 hours.

Answer:

Total time of flight= 6.3 s

Total Max height= 60.87ft

Step-by-step explanation:

Height above ground = 15ft

Velocity=30ft/sec

Angle = 90°

Max height traveled= U²Sin²tita/2g

Max height traveled= ( 30²*1²)/(2*9.81)

Max height traveled= 900/19.62

Max height traveled= 45.87 ft

Total Max height= 15+45.87= 60.87ft

Time travel to Max height

=( usin90)/g

Time travel to initial position

= (30*sin90)/9.81

= 3.1 s

Time to travel to the ground from Max height

H = 1/2gt²

60.87= 1/2 * 9.81*t²

(60.87*2)/9.81= t²

3.5 = t

Total time of flight = 3.5+3.1

Total time of flight= 6.3 s

Step-by-step explanation:

a. If x is the total numbers of students in school, 35%x = 140.

0.35x = 140

x = 140/0.35 = 400

b. Since there are 400 kids in the school, 15% of them take the bus which is 0.15 * 400 = 60 kids.

Answer:

(a) The probability mass function of X is:

[tex]P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...[/tex]

(b) The most likely value for X is 1.32.

(c) The probability that at least two of the four selected have earthquake insurance is 0.4015.

Step-by-step explanation:

The random variable X is defined as the number among the four homeowners  who have earthquake insurance.

The probability that a homeowner has earthquake insurance is, p = 0.33.

The random sample of homeowners selected is, n = 4.

The event of a homeowner having an earthquake insurance is independent of the other three homeowners.

(a)

All the statements above clearly indicate that the random variable X follows a Binomial distribution with parameters n = 4 and p = 0.33.

The probability mass function of X is:

[tex]P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...[/tex]

(b)

The most likely value of a random variable is the expected value.

The expected value of a Binomial random variable is:

[tex]E(X)=np[/tex]

Compute the expected value of X as follows:

[tex]E(X)=np[/tex]

         [tex]=4\times 0.33\\=1.32[/tex]

Thus, the most likely value for X is 1.32.

(c)

Compute the probability that at least two of the four selected have earthquake insurance as follows:

P (X ≥ 2) = 1 - P (X < 2)

              = 1 - P (X = 0) - P (X = 1)

              [tex]=1-{4\choose 0}\ (0.33)^{0}\ (1-0.33)^{4-0}-{4\choose 1}\ (0.33)^{1}\ (1-0.33)^{4-1}\\\\=1-0.20151121-0.39700716\\\\=0.40148163\\\\\approx 0.4015[/tex]

Thus, the probability that at least two of the four selected have earthquake insurance is 0.4015.

Answer:

Options (c) and (f)

Step-by-step explanation:

In the given triangle,

Measure of one angle is 90°.

Therefore, it's a right angle triangle.

Since two angles of the given triangle are equal, opposite sides of this triangle will be equal.

Therefore, the given right triangle is an isosceles triangle.

Options (c) and (f) will be the answer.

Answer:

x= -6 broo

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

Given the following parameters;

Time, T = 150mins

Cooker setting, H = 7

Since the time for a pot of water to boil is inversely proportional to the cooker setting;

[tex]T * 1/H[/tex]

[tex]T = K/H[/tex] ........equation 1

Where, K is the constant of proportionality.

Substituting the parameters into the equation 1, we have;

150 = K/7

K = 150*7

K = 1050

To find the cooker setting at 7mins;

[tex]T = K/H[/tex]

H = K/T

H = 1050 ÷ 7

H = 150.

Hence, the cooker setting must be at 150.

Answer: 16875x³-13500x²+3600x-320

Step-by-step explanation:

[gοfοh](x) means g(f(h(x))). So you plug in h(x) into f(x) and that into g(x).

f(3x)=5(3x)-4=15x-4

g(f(3x))=5(15x-4)³

g(f(3x))=5(3375x³-2700x²+720x-64)

g(f(3x))=16875x³-13500x²+3600x-320

Answer:

A

Step-by-step explanation:

Answer:

a. Attached.

b. Mean = 0.5

Step-by-step explanation:

This random number generator con be modeled with an uniform continous random variable X that has values within 0 and 1, each with the same constant probability within this range.

The probability for the values within the interval [a,b] in a continous uniform distribution can be calculated as:

[tex]f(x)=\dfrac{1}{b-a}\;\;\;x\in[0; 1][/tex]

In this case, b=1 and a=0, so f(x)=1.

The sketched curve of the probability distribution of this random variable is attached.

The mean of this distribution can be calculated as the mean for any uniform distribution:

[tex]E(X)=\dfrac{a+b}{2}=\dfrac{0+1}{2}=0.5[/tex]

Answer:

All Lake Tahoe Community College math students

Step-by-step explanation:

From the question itself it is clear that the instructor is interested in the average number of days Lake Tahoe Community College math students are absent from class during a quarter that lasts 9 weeks, which clearly indicates that the teacher is interested in population of all Lake Tahoe Community College math students.

Answer:

Step-by-step explanation:

We assume your intended attendance equation is ...

  A = -1.95x^3 +70.1x^2 -188x +2150

a. For x=0 (corresponding to 1985), the first three terms are 0, so we have ...

  A = 2150 . . . . the initial value of the function

__

b. For x=13 (corresponding to 1985) we have ...

  A = ((-1.95(13) +70.1)(13) -188)(13) +2150 = (44.75(13) -188)(13) +2150

  = 393.75(13) +2150 = 7268.75

Attendance in the year 1998 is modeled to be about 7269.

Answer:

y+8 = 3(x-3)

Step-by-step explanation:

The point slope form of the equation for a line is

y-y1 = m(x-x1)

y- -8 = 3(x -3)

y+8 = 3(x-3)

*The question is incomplete. Attached below is the diagram of the box plots being referred to followed by the complete question and options.

Answer:

D. The median for town A, 20 degrees, is less than the median of town B, 30 degrees

Step-by-step Explanation:

From the given diagram of the box plots showing the daily low temperatures for town A and B, the median of town A and B is shown on the box plots by the line that divides the box. Therefore, the median of town A is where the line that divides the box is. Median for town A is 20⁰. Same applies for town B. Town B median is 30⁰.

Therefore, option D is the most appropriate comparison of the centers. Median of town A is less than median of town B.

Answer:

8  5/648

Step-by-step explanation:

y = 5x ^ -3 + 4x^2

dy /dx = 5 * -3 x^ -4 + 4 * 2x ^ 1

           = -15 x ^ -4 + 8x

Now take the second derivative

dy^2/ dx^2 = -15  * -4 x^-5 +8

                   = 60 x^ -5 +8

                   = 60 /x^5   +8

Evaluate at x = 6

                   = 60 / 6^5  +8

                    60/7776 +8

                   5/648 + 8

                  8  5/648

Step-by-step explanation:

Hope you understand this

Answer:

The ball is at a maximum height when t = 0.125s.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]

In this question:

[tex]h(t) = -32t^{2} + 8t + 3[/tex]

So [tex]a = -32, b = 8[/tex]

When is the ball at a maximum height

[tex]t_{v} = -\frac{8}{2*(-32)} = 0.125[/tex]

The ball is at a maximum height when t = 0.125s.