What's the probability of rolling a number less than 5 and a head when rolling a die and then tossing a coin?

Answer:

98.5 degrees

Step-by-step explanation:

To find the angle measurement between two vectors use: cos(theta)=(u dot v)/(|u|*|v|)

The vectors are u=sqrt(5)i-8j and v=sqrt(5)i+1j .

So find the dot product of u and v.  u dot v=sqrt5*sqrt(5)+(-8)*(1)=5-8=-3.

Second step: Find the magnitude of both vectors.  So to find the magnitude of a vector, let's call it t when t=ai+bj, you just do |t|=sqrt(a^2+b^2).

|u|=sqrt(5+64)=sqrt(69) and |v|=sqrt(5+1)=sqrt(6)

Now multiply your magnitudes of your vectors: sqrt(69)*sqrt(6)=sqrt(414).

So now we have:

cos(theta)=-3/sqrt(414)

Now arccos( ) or cos^(-1) to find the angle theta.

theta=cos^(-1)[-3/sqrt(414)] which is approximately 98.5 degrees.

Answer:

Ans 1) The correct option is B) 98.5

Ans 2) The correct option is C) [tex]\sqrt{5}[/tex]

Step-by-step explanation:

The angle measurement between two vectors by:

[tex]cos(\theta)=\frac{(u.v)}{(|u|\times |v|)}[/tex]

Magnitude of vector t=ai+bj, calculated by:

[tex]|t|=\sqrt{a^{2}+b^{2}}[/tex]

The given vectors are [tex]u=\sqrt{5}i-8j[/tex] and [tex]v=\sqrt{5}i+1j[/tex]

First find the dot product of u and v;

[tex]u.v=(\sqrt{5}i-8j)(\sqrt{5}i+1j) = 5-8= - 3[/tex]

Now,  Find the magnitude of both vectors u and v.  

[tex]|u|=\sqrt{(\sqrt{5})^{2}+8^{2}}[/tex]

[tex]|u|=\sqrt{5+64}[/tex]

[tex]|u|=\sqrt{69}[/tex]

and

[tex]|v|=\sqrt{(\sqrt{5})^{2}+1^{2}}[/tex]

[tex]|v|=\sqrt{5+1}[/tex]

[tex]|v|=\sqrt{6}[/tex]

Now, put the all values in  [tex]cos(\theta)=\frac{(u.v)}{(|u|\times |v|)}[/tex]

[tex]cos(\theta)=\frac{-3}{\sqrt{69} \times \sqrt{6}}[/tex]

[tex]=\frac{-3}{414}[/tex]

take arc cos both the sides,

[tex]\theta=cos^{-1} \frac{-3}{\414}[/tex]

[tex]\theta=98.5 \degree[/tex]   (approx)

Therefore, the correct option is B) 98.5

Ans 2)  calculate IvI by

If t= ai +bj then magnitute is [tex]\sqrt{a^{2}+b^{2}}[/tex]

Given : v = (-2,-1)

it means v = -2i -1 j

[tex]|v| =\sqrt{(-2)^{2}+(-1)^{2}}[/tex]

[tex]|v| =\sqrt{4+1}[/tex]

[tex]|v| =\sqrt{5}[/tex]

Therefore, the correct option is C) [tex]\sqrt{5}[/tex]

Answer:

  x +2y = 12

Step-by-step explanation:

Try the given points in the given equations and see what works.

  -2x + 5y at (2, 5) is -2(2) +5(5) = 21 ≠ 12

) +)   2x + y at (2, 5) = 2(2) +(5) = 9 ≠ 12

  x + 2y at (2, 5) = 2 +2(5) = 12 . . . . . goes through first point

  x + 2y at (4, 4) = 4 + 2(4) = 12 . . . . goes through second point

__

You know the answer at this point, so the next check is just for "completeness." It is not necessary to properly answer the question.

  -x +2y at (2, 5) = -(2) +2(5) = 8 . . . . goes through first point

  -x +2y at (4, 4) = -(4) + 4(4) = 4 ≠ 8 . . . does not go through second point

Answer:

A

Step-by-step explanation:

it has to do with the people's ethnics or standard or values.

The statement is not ambiguous so it has no language barrier

Answer:

  C.  use of language

Step-by-step explanation:

The descriptor "childish" will likely influence results. Most Grade 9 students prefer not to be thought of as "childish."

For this case we have that by definition:

Two angles are complementary if their sum is 90 degrees.

Then, assuming that the variable "x" represents the complement of 22, we have:

[tex]x + 22 = 90\\x = 90-22\\x = 68[/tex]

Thus, the complement of 22 degrees is 68 degrees.

Answer:

Option A

For this case we have by definition, that the electrical power is given by:

[tex]P = I ^ 2 * R[/tex]

Where:

P: It's the power

I: It's the current

R: It's the resistance

Clearing the current:

[tex]I ^ 2 = \frac {P} {R}\\I = \pm \sqrt {\frac {P} {R}}[/tex]

We choose the positive value:

[tex]I = \sqrt {\frac {500} {25}}\\I = \sqrt {20}\\I = 4.47A[/tex]

ANswer:

Option A

Given two sets X and Y, a relation between X and Y freely associates elements of X with elements of Y, with no restrictions.

A function is a relation with some restrictions: there must be exactly one element of Y connected with each element of X.

The set X is called the domain of the function, and it represents all the possible inputs that we can feed the function with. As we just said, every element of the domain must have a correlated element in Y.

The set Y is called the range of the function, and it represents all the possible outputs that the function can return.

The difference between function and relation and the relationship between the domain and the range of a function is discussed below

The domain of a function is the set of values that we are allowed to plug into our function.

The range of a function is the set of values that the function assumes.

Let there be an X set and a Y set. An ordered pair (x,y) is called a relation in x and y. The first element in an ordered pair is called the domain, and the set of second elements is called the range of the relation.

A function is a particular kind of relation between sets. A function takes every element x in a starting set, called the domain, and tells us how to assign it to exactly one element y in an ending set, called the range.

For example, each person is in the following table is paired with a number representing his or her height:

Alex → 180 Claudia → 165 Gilbert → 204 Judith → 165

The given relation {(Alex, 180), (Claudia, 165), (Gilbert, 204), (Judith, 165)} is a function as every person is pairs with exactly one number, their height. The domain is (Alex, Claudia, Gilbert, Judith). The range is (165, 180, 204).

The domain is the input, the independent value—it's what goes into a function. The range is the output, the dependent value—it's what comes out. Domain and range may be limited to a few discrete values, or they may include all numbers everywhere, to infinity and beyond.

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Answer:

15

Step-by-step explanation:

The mean of the first graph comes to be the point at which the graph reaches its highest point.

The mean of the blue graph is: μ = 30

The mean of the blue graph is: μ = 45

The difference of the means of the distributions is: 45 - 30 = 15

Answer:

15

Step-by-step explanation:

Answer:

50, 52, and 54

Step-by-step explanation:

The three even integers are x, x+2, and x+4.  The sum of the least two is 48 more than the greatest:

x + x+2 = x+4 + 48

2x + 2 = x + 52

x = 50

So the three integers are 50, 52, and 54.

Answer: B) plane symmetry and symmetry about an axis

Step-by-step explanation: Please see the image below!

The figure has plane symmetry and symmetry about an axis option second “plane symmetry and symmetry about an axis” is correct.

It is defined as the line which will make exactly two halves with similar shape and size in the geometry. For two-dimensional shape there is a line of symmetry, and for the three-dimensional shapes there is a plane of symmetry. In other words, if we make a mirror image of the shape around the line of symmetry, we will get exactly the same half portion.

We have a three-dimensional figure shown in the figure.

If a plane can divide a three-dimensional figure into two congruent mirrored halves, the figure possesses plane symmetry.

As a result, there are two plane symmetries in the provided figure.

If there is a line around which a three-dimensional figure may be rotated by an angle higher than 0° but less than 360° so that the image coincides with the preimage, the figure has symmetry at that axis.

As a result, the following figure displays axis symmetry. As a result, the figure features plane symmetry as well as axis symmetry.

Thus, the figure has plane symmetry and symmetry about an axis option second “plane symmetry and symmetry about an axis” is correct.

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Answer:

f(x) = 7 sin 8x + 3 ⇒ 1st answer

Step-by-step explanation:

* Lets revise the trigonometry translation  

- If the equation is y = A sin (B x + C) + D  

* A is the amplitude  

- The amplitude is the height from highest to lowest points and  

  divide the answer by 2  

* The period is 2π/B  

- The period is the distance from one peak to the next peak

* C is the horizontal shift  

- The horizontal shift is how far the function is shifted to left  

  (C is positive) or to right (C is negative) from the original position.  

* D is the vertical shift  

- The vertical shift is how far the function is shifted vertically up

  (D is positive) or down (D is negative) from the original position.  

- The equation of the mid-line is y = D

* Now lets solve the problem

∵ f(x) = A sin(Bx + C) + D

∵ The amplitude is 7

∴ A = 7

∵ The period is 2π/B

∵ The period is π/4

∴ 2π/B = π/4 ⇒ divide both sides by π

∴ 2/B = 1/4 ⇒ Use cross multiplication

∴ B × 1 = 2 × 4

∴ B = 8

∵ The equation of the mid-line is y = D

∵ The equation of the mid-line is y = 3

∴ D = 3

- There is no mention for C

∴ C = 0

∴ f(x) = 7 sin 8x + 3

Answer:

52

Step-by-step explanation:

you divide 60 by 3120

Answer:

  7.  B) 26–35

  8.  C) 31/77

Step-by-step explanation:

7. It's a matter of writing the fractions in a way that lets you compare their values. It is usually convenient to convert them to decimal:

(age group, healthy fraction)

(18–25, 9/48 = 0.1875)

(26–35, 16/98 ≈ 0.1633)

(36–45, 19/94 ≈ 0.2021)

(> 45, 12/60 = 0.2000)

The group with the smallest percentage of healthy blood sugar is 26–35.

__

8. There are 94+60 = 154 study participants who are at least 36. Of those, 35+27 = 62 are at risk for diabetes. That ratio is ...

  62/154 = 31/77

Answer:

First of all , 12000 multiply with 1.5 percent and with the answer times it with 2 and with the answer add with 360

#hope it helps

Step-by-step explanation:

12000×1.5%

=180

180×2

=360

12000+360

= 12360

#hope it helps

Answer:

0

y = -2

Step-by-step explanation:

The formula for the slope is (in general) Δy / Δx Since the value of y does not change (I'm assuming we are talking about AB), the slope is (-2 - - 2) / (2 - -2) = 0/4 = 0

So the equation of the line is

y = mx + b

m = 0

y = 0*x - 2

y = - 2  <<<< Equation

Answer:

Slope = 0

Equation:

[tex]y = -2[/tex]

Step-by-step explanation:

Note that the diagonal AB is a horizontal line parallel to the x axis. The Slope m of a line is a measure of how the function f(x) changes when x increases or decreases.

Note, however, that horizontal lines such as segment AB do not change and their value of y does not depend on the value of x. Therefore all horizontal lines have slope m = 0.

Finally, the equation of line AB is

[tex]y = -2[/tex]

Answer:

  -6/5

Step-by-step explanation:

The slope is computed from ...

  slope = (change in y)/(change in x)

  = (-2 -4)/(3 -(-2)) = -6/5

Answer:

[tex]-\frac{6}{5}[/tex]

Step-by-step explanation:

We are given the points (-2,4) and (3, -2).

We want to find the slope (m) of this line.

The slope can be found using the following formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points.

Even though we are already given the points, we can label the values of them to avoid confusion and mistakes.

[tex]x_1=-2\\y_1=4\\x_2=3\\y_2=-2[/tex]

Now, substitute the values of the points into the formula. Remember that we have negative numbers.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-2-4}{3--2}[/tex]

[tex]m=\frac{-6}{3+2}[/tex]

[tex]m=\frac{-6}{5}[/tex]

The slope of the line is [tex]-\frac{6}{5}[/tex].

Answer:

0,-2,-4,-6,-8, ...

Step-by-step explanation:

In order to find the sequence represented by the given explicit formula we have to plug in the values of n

Given formula is:

[tex]a_n=2-2n\\a_1=2-2(1)\\=2-2=0\\a_2=2-2(2)\\=2-4\\=-2\\a_3=2-2(3)\\=2-6\\=-4\\a_4=2-2(4)\\=2-8\\=-6\\a_5=2-2(5)\\=2-10\\=-8[/tex]

So the explicit sequence is:

0,-2,-4,-6,-8,..........

Answer:

kmkmlklm

Step-by-step explanation:

Answer:

  T = 88 -(7/2000)A

Step-by-step explanation:

The table values have a constant difference of +2000 ft and -7 degrees, so the slope of the linear equation is -7/2000 degrees per ft. The temperature is 88 at an altitude of 0, so we can write the requested equation in slope-intercept form as ...

  T = 88 -(7/2000)A

_____

The slope-intercept form of the equation for a line is ...

  y = mx + b

where m is the slope and b is the y-intercept. In this equation, y is the dependent variable and x is the independent variable. For our temperature equation, the dependent variable is T, and the independent variable is A.

Area of 3400 decreases by 7.25%.

Rewrite 7.25% as a decimal.

This leads to 0.0725.

So, (3400)(0.0725) = 246.5.

Now (246.5)(13 years) = 3,276.

The area after 13 years will be

3,276 km^2.

Answer:

(h.g)(x) = 4x^2 + 5x - 6

Step-by-step explanation:

Given the following: f(a) = x^2 - 8x + 4; g(x) = 4x – 3; and h(x) = x + 2.

(h.g)(x) = (4x – 3)(x + 2)

(h.g)(x) = 4x^2 + 8x - 3x - 6

(h.g)(x) = 4x^2 + 5x - 6

The value of (h . g)(x) is 4x² + 5x - 6.

A function whose values are found from two given functions by applying one function to an independent variable and then applying the second function to the result and whose domain consists of those values of the independent variable for which the result yielded by the first function lies in the domain of the second.

Given:

f(x) = x² - 8x + 4; g(x) = 4x – 3; and h(x) = x + 2.

Now,

(h . g)(x) = (4x – 3)(x + 2)

(h . g)(x) = 4x² + 8x - 3x - 6

(h . g)(x) = 4x² + 5x - 6

Hence, (h . g)(x)=  4x² + 5x - 6.

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Answer: B. 36

The complete square is (x+6)^2. It's missing the third term, which is 36 because 6 x 6 is 36.

ANSWER

B. 36

EXPLANATION

The given quadratic expression is:

[tex] {x}^{2} + 12x = 16[/tex]

To complete the square we add the square of half the coefficient of x.

The coefficient of x is 12.

Half of it is 6.

The square of 6 is 36.

Therefore we add 36 to both sides of the equation to complete the square.

The correct answer is B.

Answer:

C. increases rapidly.

Step-by-step explanation:

tan(θ) =  sin(θ)/cos(θ)

Now, when sin 90 = 1

and cos 90 = 0

so, tan(90) = 1/0 = not defined.

(1/0 is infinity and its value is not defined)

So, when angle θ increases to 90°, then the value of tan(θ) increases rapidly, as shown in the figure below.

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The hole which was initially 8 feet deep and then extended by 3 more feet got partially filled by 4 feet of dirt by a tractor, resulting in a total remaining depth of 7 feet.

Your question is a simplifying numerical values scenario. First, you dug a hole that was 8 feet deep. Next, you dug an additional 3 feet, so you would add these two values together to get a total depth of 11 feet (8 + 3). Finally, a tractor accidentally filled 4 feet of the hole with dirt. Subtracting this from the total depth of the hole means your hole is now 7 feet deep (11 - 4).

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Answer:4

Step-by-step explanation: 6 times 6 divide by 9

Multiply the denominators across and Multiply the numerators across

x/6= 6/9

9x= 36

x= 4

Check answer by using substitution method

x/6= 6/9

4/6= 6/9

Divide by 2 for 4/6

Divide by 3 for 6/9

2/3= 2/3

Answer is x= 4

Answer:

It will take 8 hours to drive 400 miles

Step-by-step explanation:

The millers drive 50 miles an hour. So we can write the proportion 1/50 = x/400. Then we solve for x and get 8 hours.

Answer:

The answer is 8!

Step-by-step explanation:

It will take 8 hours to drive 400 miles

The millers drive 50 miles an hour. So we can write the proportion 1/50 = x/400. Then we solve for x and get 8 hours.

Answer:

  one solution: (x, y) = (1, 0)

Step-by-step explanation:

See below for a graph with the one solution identified.

Answer:

The system has one solution at (1,0).

Step-by-step explanation:

Consider the provided system of equations

y=-6x+6

Substitute x = 0 in above equation.

y=-6(0)+6

y=6

The coordinate is (0,6)

Now substitute y=0 in the above equation.

0=-6x+6

-6=-6x

x=1

The coordinate is (1,0)

Now use the coordinates (0,6) and (1,0) in order to draw the graph.

The graph of y= -6x + 6 is shown in figure 1.

Similarly, consider the second equation y= 3x - 3

Substitute x = 0 in above equation.

y=3(0)-3

y=-3

The coordinate is (0,-3)

Now substitute y=0 in the above equation.

0=3x-3

3=3x

x=1

The coordinate is (1,0)

The graph of y= 3x - 3 is shown in figure 2.

Now draw the graph of both equation as shown in figure 3.

By observing the graph it can be concluded that the system has one solution at (1,0)

Hence, the system has one solution at (1,0).

Answer:

TRUE

Step-by-step explanation:

APE-X

The statement is true. Three points are collinear if they lie on the same line. Since a line exists within a plane, those points would also exist within that plane, making them coplanar.

The statement 'If three points are collinear they are also coplanar' is indeed true.

Here's why: Points are said to be collinear if they lie on the same line. A line, by definition, exists within a plane, so any points on that line would also exist within that same plane, which means they are coplanar.

For example, imagine a piece of paper. This paper represents a plane. Draw a line across the paper and mark three points on that line. The three points are collinear because they are on the same line. Since the line is on a plane (the paper), the points are also coplanar.

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Answer:

I think it's -5, 3

Step-by-step explanation:

since it's four units down that would be 5, 3

next, since you need to reflect on the other side of the y axis, it would be -5, 3

hope this helps :)

Answer:

(-5, 3)

Step-by-step explanation:

We are given a point [tex] ( 5 , 7 ) [/tex].

When we translate this given point four units down, it means that its x coordinate will remain the same while 4 units will be subtracted from the y coordinate to get:

[tex] ( 5 , 7 ) \times (5, 3) [/tex]

Now this point [tex] ( 5 , 3 ) [/tex] is to be reflected over the y axis so the y coordinate will remain the same but the x coordinate will change its sign.

So we get:

(-5, 3)

Answer:

m= 4, -2

Step-by-step explanation:

move everything to one side.

m^2-2m-8=0

then factor

(m-4)(m+2)

then

m= 4, -2

hope this helps!

Answer:

Step-by-step explanation:

Answer:

Option D) x = 2

Step-by-step explanation:

(4-2)(x-2) = 4x - 8

Distribute and simplify 4-2

2(x-2) = 4x - 8

2x-4 = 4x -8

Subtract 2x on both sides and add 8 on both sies

4x - 8 = 2x-4

2x= 4

Divide 2 on both sides

x = 2

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