A single card is drawn from a standard deck. Find the probability of the following event.
Drawing a king or a face card

Answer:

O a=0

Step-by-step explanation:

#1

No

See in first one the angle included is in between the two similar sides( corresponding to other triangle)

In second one the angle marked is not between the corresponding similar sides .

So not congruent

#2

Yes

Three angles of both are equal

The linear function that represent this problem is 7y = 22x + 127, and the temperature at 11:15am is 53.19 degrees

a.

We can take two points from this to find the slope and y - intercept to determine the linear function.

A(6, 59)

B(13, 81)

The slope of a linear equation has a formula of ;

m = y₂ - y₁ / x₂ - x₁

m = 81 - 59 / 13 - 6

m = 22/7

Using the slope to find the y - intercept, we need just one point;

y = mx + c

59 = 22/7(13) + c

59 = 286/7 + c

c = 59 - 286/7

c = 127/7

The equation can be written as;

y = 22/7x + 127/7

rewriting this;

7y = 22x + 127

b. The temperature at 11.15am

Substituting this into the equation;

7y = 22(11.15) + 127

7y = 372.3

y = 53.19 degrees Fahrenheit

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Translation:

The room temperature at 6 am was 59 degrees Fahrenheit. It was increasing linearly until 1 pm when the thermometer marked 81 degrees. a) Write a linear equation that shows the temperature as a function of time in that interval. b) Calculate with this equation the temperature at 11:15 am. Round to the nearest tenth of a degree Fahrenheit if necessary.

The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.

The reciprocal of the divisor: Reciprocal and division of fractions are two different methods. When the numerator and denominator of a fraction are interchanged, then it is said to be its reciprocal. Suppose a fraction is a/b, then its reciprocal will be b/a. A fraction is a numerical quantity that is not a whole number.

The reciprocal of the divisor 5 1/5 divided by 1/10

To the reciprocal of the divisor.

Equation: 5 1/5 divided by 1/10

1st: Flip the 1/10 to become 10/1

2nd: Change division to multiplication

New equation: 5.1/5.10/1

⇒ 50/5

       ⇒ 10.

The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.

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The interquartile range of the data that is represented on the dot plot is: 2 chocolate chips.

Interquartile range (IQR) = upper quartile - lower quartile.

Upper quartile (Q3) = center of the second half of the data = 5

Lower quartile (Q1) = center of the first half of the data = 3

Interquartile range (IQR) = 5 - 3

Interquartile range (IQR) = 2 chocolate chips.

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Answer:

D

Step-by-step explanation:

why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.

x²

-x²

-x -x

x x x x (clearly that means 4x)

-1 -1 -1

1 1

so, we see it is D.

The coordinates of the y-intercept are (0, 3.5) and the coordinates of the x-intercepts are (-17.5, 0). Using these coordinates, the graph of the equation is shown below.

From the question, we are to graph the given linear equation.

To graph the equation,

We will determine the coordinates of the x-intercepts and y-intercepts.

When x = 0

y = 1/5x + 3.5

y = 1/5(0) + 3.5

y = 3.5

(0, 3.5)

When y = 0

y = 1/5x + 3.5

0 = 1/5x + 3.5

Multiply through by 5

0 = x + 17.5

x = -17.5

(-17.5, 0)

Using the coordinates of the x-axis and y-axis, the graph of the equation is shown below.

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Answer:

75 Degrees

Step-by-step explanation:

A triangle is equal to 180 degrees

32+73+Y=180

subtract 32 and 73 from 180

32+73 is 105

180 - 105 is 75

we are left with Y=75

We want to find the equation of the line that passes through the points:

(4 , -8) and (9 , 11)

First, we're going to find the slope between these points using the fact that:

If we have two points that lie on a line:

The slope between them can be found using the formula:

If we replace our values:

The slope will be:

Now, we could apply the point-slope equation. This equation tells us that we can find the equation of the line if we got a point (x1,y1) on the line, and the slope m:

Replacing our values:

This, is the general form. We want to express the last equation as a standard form like this:

If we re-write:

Therefore, the standard for the equation of the line that passes through (4 , -8) and (9, 11) is:

19x-5y=116

Answer:

The mean number of radioactive atoms that decay per day is 81.485.

Answer:

    x ≓ 3.242593855

Step-by-step explanation:

Hey there!

2/3 + 1/4
= 2 × 4/3 × 4 + 1 × 3/4 × 3

= 8/12 + 3/12

= 8 + 3 / 12 + 0

= 8 + 3 / 12

= 11/12

Therefore, your answer is: 11/12

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

14

Step-by-step explanation:

From the given information:

suppose, Y is the number of times a coin is being flipped.

If the coin is flipped for the first time and we get H, then we have:

TTT = \(\dfrac{1}{2}(Y+1)\)

Afterward, if we get H, then we waste two times plus the probability of this event \(\dfrac{1}{4}\).

Therefore, we have : \(\dfrac{1}{4}(Y+2)\)

Afterward, if we get H, then we waste three times plus the probability of this event \(\dfrac{1}{8}\).

Therefore, we have : \(\dfrac{1}{8}(Y+3)\)

If we got T at the third time, then;

T = \(\dfrac{1}{8}(3)\)

Thus, average number of headsthat you’ll see until gettingTTT can be expressed as:

\(= \dfrac{1}{2}(Y+1)+ \dfrac{1}{4}(Y+2)+ \dfrac{1}{8}(Y+3)+ \dfrac{1}{8}(3)\)

= 14

Answer:

12

Step-by-step explanation:

We find the LCM which is simply 12.

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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The recursive rule is f(n) = f(n - 1) * 2; f(1) = 9 and the explicit rule is f(n) = 9(2)^n-1

The recursive rule

From the question, we have the following parameters that can be used in our computation:

The table

The table definitions imply that we simply multiply 2 to the previous term to get the current term

This means that

f(n) = f(n - 1) * 2

Where

f(1) = 9

The explicit rule

The table definitions imply that we simply multiply 2 to the previous term to get the current term

a = 9

r = 2

So we have

f(n) = a * r^n-1

This gives

f(n) = 9(2)^n-1

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Answer:

w÷319= 342

Step-by-step explanation:

w divided by 319 is equal to 342

Answer:

The area is changing at the point of  \(\mathbf{61200 m^2/year}\)

Step-by-step explanation:

From the given information:

Let's recall from our previous knowledge that the formula for finding the area of a rectangle = L × w

where;

L = length and w = width of the rectangle

Suppose the Length L is twice the width w

Then L = 2w --- (1)

From The area of a rectangle

A = L  × w

A = 2w  × w

A = 2w²

Taking the above differentiating with respect to time

\(\dfrac{dA}{dt }= 4w \times \dfrac{dw}{dt} --- (2)\)

At the time t

\(\dfrac{dw}{dt}= 34 m \ per \ year ; w = 450 \ m\)

Replacing the values back into equation 2, we get:

\(\dfrac{dA}{dt }= 4 \times 450 \times 34\)

\(\mathbf{\dfrac{dA}{dt }= 61200 m^2/year}\)

Answer:

The correct fraction is 13/20.

Step-by-step explanation:

\(.65 = \frac{65}{100} = \frac{13}{20} \)

Answer:

4 cookies

Step-by-step explanation:

The remainder of (7x12)/5 is your answer.

Answer:

a. y(t) = 0

Step-by-step explanation:

There are two axis on the graph. One is x-axis which is horizontal line on the graph and the other is y-axis which is vertical side of the graph. The point where x-axis and y-axis meet is origin which has value 0. The equation to write the points of the graph is represented by y(x) = 0. In the given equation there is t variable used in the values.

Answer:

3(7) + 2* |7 - 8| - 12 = 11

Step-by-step explanation:

3(7) + 2* |7 - 8| - 12

21 + 2* |-1| - 12

21 + 2* 1 - 12

21 + 2 - 12

23 - 12 = 11

Hope this helps! :)

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

3*(root3)

Step-by-step explanation:

square root of 75 = sq. root of ( 5 × 5 × 3 )= 5root3

now 5root3 - 2root3 = (5-2)root3 = 3root3

Answer:

86=y

Step-by-step explanation:

129=y+43

-43    -43

86=y

or

y=86

Answer: 21

Step-by-step explanation:  im not guessing im a certified expert at calculus and have a masters degree in mathmatics so yeah

Answer:

21

Step-by-step explanation:

I did the test

Hope this helps :)

The coordinates of the vertices for the image of the triangle U′V′W′ is

U′(1, 1), V′(−4, 0), W′(−1, 4)

To rotate a point 90 ° clockwise about the origin, we can apply the transformation (x, y) → (y, -x)

So applying this transformation to each vertex of triangle UVW we get

U(−1, 1) → U' = (1, 1)

V(0, −4) → V' = ( -4, 0)

W(−4, −1) → W' = (-1, 4)

Therefore the coordinates of the vertices for the image triangle U'V'W' are U′(1, 1), V′(−4, 0), W′(−1, 4)

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Answer:

\(Pr =\frac{1}{38955840}\)

Step-by-step explanation:

Given

\(n = 35\) ---- 1 to 35

\(r = 5\) -- selection

Required

The probability of winning

The probability of getting the first number correctly is:

\(P(1) = \frac{1}{35}\)

At this point, the remaining numbers are 34

So, the second selection has the following probability

\(P(2) = \frac{1}{34}\)

Following the above sequence, we have:

\(P(3) = \frac{1}{33}\)

\(P(4) = \frac{1}{32}\)

\(P(5) = \frac{1}{31}\)

So, the required probability is:

\(Pr =P(1) * P(2) * P(3) * P(4) * P(5)\)

\(Pr =\frac{1}{35} *\frac{1}{34}*\frac{1}{33}*\frac{1}{32}*\frac{1}{31}\)

\(Pr =\frac{1}{35*34*33*32*31}\)

\(Pr =\frac{1}{38955840}\)

After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.

So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)

The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.

The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:

Midpoint of JK: (1, -4)

Midpoint of J'K': (4, 1)

The slope of the vector: 3/5

(x₁ + x₂)/2, (y₁ + y₂) /2

Point-slope formula: y - y₁ = m(x - x₁)

Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)

Applying simplification , we get: y = (- 3/5)x - 1.2

To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:

y - 1 = (7/3)( x - 4)

Apply simplification , we get: y = (7/3)x - 17/3

To evaluate the intersection point, we can solve the system of equations:

y =(- 3/5)x - 1.2 = (7/3)x - 17/3

Evaluating for x and y, we get x = -6 and y = -1.

Therefore, the center of rotation is (-6, -1).

√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)

Distance between image points and center of rotation

√( ( 6 - (-6))² + ( 3 - (-1))² = 13

The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).

The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':

Angle of vector: arctan(5/3) = 59.04 degrees

Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

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D (94)

Hoped I help :]