Complete the table to determine the total number of possible outcomes.

Nothing tricky here:

[tex]\displaystyle \int_{-\infty}^0 \sqrt{1+2^2} \, e^{2\theta} \, d\theta = \sqrt5 \int_{-\infty}^0 e^{2\theta} \, d \theta \\\\ ~~~~~~~~ = \frac{\sqrt5}2 \left(e^0 - \lim_{\theta\to-\infty} e^{2\theta}\right) \\\\ ~~~~~~~~ = \frac{\sqrt5}2[/tex]

Recall that

[tex]\phi = \dfrac{1+\sqrt5}2[/tex]

and this is exactly 1/2 more than the value of the integral.

Answer: y-intercept is 12

Step-by-step explanation:

y = mx +b

m = slope

b = y-intercept

y | = | x | + | b

f(x) | = | 4x | + | 12

b = y-intercept

Answer:

  x = 8

Step-by-step explanation:

You want the value of x for a right triangle with side lengths (x+1) and (x-3) and an area of 22.5 cm².

The area of a triangle is given by the formula ...

  A = 1/2bh

Then the area of this triangle is ...

  22.5 = 1/2(x -3)(x +1)

  45 = x² -2x -3

  48 = x(x -2) . . . . . . . add 3 and factor out x

We know that 48 can be factored as (8)(6). Comparing this to x(x-2), we see that x=8.

__

Additional comment

x could also be -6, but that would make the side lengths be negative. The only applicable solution for this geometry is x=8.

ive n

lan A

Plan B

Monday: 3 clients - Plan A

5 clients - Plan B

Total 10 hours

Tuesday

6 clients - Plan A

2 clients - Plan B

Total 10 hours

rocedure

Let's define a system of linear equations that represents the above problem.

A: Number of hours of workout in plan A

B: Number of hours of workout in plan B

The goal here is to solve

3A+5B=10 and

6A+2B=10 for the variables A and B.

The solutions to your equations are:

A = 5/4 hour

B = 5/4 hour

EXPLANATION:

Solution first(a) exercise part b:

All the internal angles of a right triangle must add up to 180, so to order the internal angles from least to greatest we must find the missing angle;

The exercise is as follows:

Now we must order them from lowest to highest, the order is as follows:

7r³ + 11r²s  -9rs² - 8s³ is the simplification of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).

The process of writing an expression in the most effective and compact way possible without affecting the original expression's value is known as simplification of an algebraic expression.

Collecting similar terms is the process, which entails expanding or contracting the terms in an expression.

Let's review some of the crucial words used during expression simplification:

In an algebraic expression, a variable is a letter with an undetermined value.

We have been asked to simplify the expression

(7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)

Let's simplify

⇒ (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)

⇒ 7r³ + 10r²s  −3rs² − 8s + r²s -6rs²

⇒ 7r³ + 11r²s  -9rs² - 8s³

Thus, 7r³ + 11r²s  -9rs² - 8s³ is the simplified form of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).

Learn more about simplification

https://brainly.com/question/13742517

#SPJ13

Probability that first three price winners are omar, kira and elsa is     [tex]\frac{1}{84}[/tex]

Probability that omar is first prize winner and kira is second prize winner and elsa is third price winner is  [tex]\frac{1}{504}[/tex]

When things are of diverse kinds, the term "permutation" is used to describe the various arrangements that could be made. Combination, meanwhile, is the quantity of smaller groups or sets that can be created from the components of a bigger set.

(i)First 3 prizes must be given to 3 persons regardless of order

Hence they can also be arranged in 3! ways.

est 6 can be arranged in 6! ways.

positions                   ___ ___ ___ ___ ___ ___ ___ ___ ___

number of ways         3     2       1     6     5    4       3     2     1

total number of ways to arrange 9 people = 9!

[tex]P(A)= \frac{(3)(2)(1)(6)(5)(4)(3)(2)}{(9).(8).(7).(6).(5).(4).(3).(2))}[/tex][tex]P(A)=\frac{6}{9.8.7}[/tex][tex]P(A)= \frac{1}{84}[/tex]

(ii)Event A

In event A three positions are fixed .

Omar -1 Kira -2 Elsa -3

Therefore there is only 1 way to fill the 1st,2nd and 3rd position

Permutations can only be made among the other positions.

Positions -           ___  ___ ___ ___ ___ ___ ___ ___  ___

Number of ways-  1        1      1       6     5     4      3      2    1

Total number of ways of arranging  9 people =9×8×7×6×5×4×3×2×1

Number of ways to satisfy event A =1×1×1×6×5×4×3×2×1

P(A)=   [tex]\frac{(6)(5)(4)(3)(2)(1)}{(9)(8)(7)(6)(5)(4)(3)(2)(1)}[/tex]

P(A)= [tex]\frac{1}{504}[/tex]

To learn more about permutation and combination visit :

brainly.com/question/24887778

#SPJ9

Answer:

400 < m< 430 kg

Step-by-step explanation:

the mass of horse is 429 kg

estimated to the nearest hundred is 400  kg

estimated to the nearest  tens is 430 kg

thus the value of m mass lies between 400 to 430

therefore

400 < m< 430 kg

The answer is 400 < m< 430 kg

The total possible outcome for the experiment is 36.

The ossible outcomes for same number on each dice is 6.

So probability for the same number on dice is,

So probability for the same number on dice is 1/6. So first statement "The probability of rolling the same digit with each die is 1/4" is false.

So, 13 games were played each month, if each month had the same number of games.

Compared to multiplication, division is the opposite. If three groups of four add up to 12, then division of 12 into three groups of equal size yields four in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division. It is referred to as a method of division to divide anything. According to the degree of difficulty, there are three different sorts of division procedures. These include the bus stop approach, the chunking method, and the long division method. The chunking method is also known as division by repeated subtraction.

Given Data

A total of 117 football games in the season, and 33 were played at night.

The season was nine months long.

Each month same numbers of game were played.

So,

117 ÷ 9

13

So, 13 games were played each month, if each month had the same number of games.

To learn more about division, visit:

https://brainly.com/question/21416852

#SPJ9

a. It should be noted that the equation illustrates that the value of 6a + 9b is 24.

b. The value of 2x + 5y is 25.

a. From the information, 2a + 3b = 8. The value of 6a + 9b will be:

6a + 9b = 3(2a + 3b)

This implies that the value will be multiplied by 3. Therefore, 8 × 3 = 24

(ii) What is the value of 2x + 5y?

4x + 10y = 50

It should be noted that this can be divided through by 2. This will be;

(4x + 10y = 50) / 2

2x + 5y = 25

The value is 25.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Answer:

x=-1/4 or -.25

Step-by-step explanation:

I took the test and double checked it

The scale is 1/2 to 7 feet. That means that for each half of an inch of the original picture, the scaled figure will have 7 feet.

Now,

That means that 1 inch corresponds to 7ft +7ft= 14ft.

Therefore, if my original figure is 1 inch in height the scaled picture will be 14 ft in height.

Answer: The scaled figure will fit in the billboard.

Let the price of black and white brouchers be x

The price of color brochures be y.

A/q,

4x+4y=148.....(1)

4x+3y=125 .....(2)

The equation (1) becomes,

x+y=37

y=37-x.......(3)

Putting (3) in (2) we have,

4x+3(37-x)=125

4x+111-3x=125

x=14

Putting the value of x in (3) we have,

y=37-14=23

The price of black and white brouches is $14

The price of color brouchers is $23.

The dilated polygon image is attached below under a dilation with a scale factor of 3 and center of dilation (0,0)​

In geometry, a polygon is a two-dimensional closed shape with straight sides that is flat or plane. It doesn't have any curved edges. A polygon's sides are also known as its edges. The vertices (or corners) of a polygon are the points where two sides meet.

Transformation is the movement of a point from one location to another. Transformations include rotation, reflection, translation, and dilation.

Dilation is the process of increasing or decreasing the size of a figure by a factor k. If a point A(x, y) is dilated about the origin by a factor k, the new point is A' (kx, ky).

Assume the polygon has vertices at A(0, 0), B(3, 3) and C. (-3, 3). If the polygon is dilated by a factor of three with the center of dilation at (0, 0), the new vertices are as follows:

A'(0,0), B'(1, 1) and C'(-1, 1)

Therefore, the polygon graph is attached in which the polygon is dilated by a factor of three with the center of dilation at (0, 0),

Learn more about polygon here:

https://brainly.com/question/1592456

#SPJ9

Step-by-step explanation:

Two friends, Grayson and Santiago, had just bought their first cars. The equation y=31.9xy=31.9x represents the number of miles, yy, that Santiago can drive his car for every xx gallons of gas. Grayson uses 8 gallons of gas to drive 328.8 miles in his car.

How many miles less does Santiago's car travel on one gallon of gas than Grayson's car?

..

please post full questions

Answer: CD<AD

Step-by-step explanation:

Just got it right on the test.

Answer: CD<AD

Step-by-step explanation:

Took the test!

a) g(3) = -182

b) g(0) = 7

c) g(-1) = 70

a) g(3): To get this, we will substitute 3 for x in the function g(x)

b) g(0): To get this, we will substitute 0 for x in function g(x)

c) g(-1): To get this, we will substitute -1 for x in function g(x)

The z-score of the given expression P(-a < z < a) = 0.4314 is; 0.55

We are told that P(-a < z < a) = 0.4314. Thus;

P(-a < z < a) = 0.4314 is represented by the area about mean. This means that; 0.4314/2 = 0.2157 is the area each on the left side and right side of mean.

Now, from online z-score calculator, we see that the z value corresponding to 0.2157 is 0.55.

Assume that ​z-scores are normally distributed with a mean of 0 and a standard deviation of 1, if P(-a < z < a) = 0.4314, then it means that the z score is 0.55.

Read more about Normal Distribution at; https://brainly.com/question/27275125

#SPJ1

Complete question is;

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(−a < z < a) = 0.4314, find d a. Round to two decimal places

Answer:

578.0 yd^2

Explanation:

The formula for finding the surface area of a cylinder is given as;

where A = surface area

pi = 3.14

r = radius of the base of the circle = diameter/2 = 8/2 = 4 yd

h = height = 19yd

Let's go ahead and substitute these values into our formula and solve for A;

SOLUTION

Step1:

hence from the diagram above, the dimension of the rug is

Since we have area of the rug,

then we have

We now solve the equation above quadratically

Then we have

Solve using factor method we obtain

Equating each factor to zero we have

Since x can not be 28, the value of x is 1

The Dimension of the rug becomes

Hence the dimension of the rug is 32 ft by 22ft (22,32)

You cook a turkey in an oven for 3 hours and 45 minutes. Let f(t) be the temperature (in degrees Fahrenheit) of the turkey t hours after being placed in the oven.

a) At t = 0

temperature of turkey is 67 degree  Fahrenheit

b) At t = 3.75

temperature of turkey is 165 degree  Fahrenheit

c) t = 3

temperature of turkey is 4 degree  Fahrenheit

d) at t = 3.75

temperature of turkey is 169 degree  Fahrenheit

Algebra is a branch of mathematics that facilitates the description of problems or situations into mathematical statements. It involves variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a valid mathematical statement. All branches of mathematics, such as coordinate geometry, calculus, and trigonometry, employ algebra. An elementary algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations on variables and constants, such as addition, subtraction, multiplication, division, etc., are done.

Given that : You cook a turkey in an oven for 3 hours and 45 minutes. Let f(t) be the temperature (in degrees Fahrenheit) of the turkey t hours after being placed in the oven.

a) At t = 0

temperature of turkey is 67 degree  Fahrenheit

b) At t = 3.75

temperature of turkey is 165 degree  Fahrenheit

c) t = 3

temperature of turkey is 4 degree  Fahrenheit

d) at t = 3.75

temperature of turkey is 169 degree  Fahrenheit

To learn more about basic algebra visit :

brainly.com/question/15167098

#SPJ9

The solution to the system of equations are,  x + 2y = 8  and -3x-2y = 12 is: X = -10 ,  Y = 9

The given system of equations:

x  +  2y  =  8              (Equation - 1)

-3x - 2y  =  12            (Equation - 2)

This can be written in matrix form as shown:

[tex]\left[\begin{array}{ccc}1&2&\\-3&-2&\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]  [tex]= \left[\begin{array}{ccc}8\\12\\\end{array}\right][/tex]

Let us assume, D = [tex]\left[\begin{array}{ccc}1&2\\-3&-2\\\end{array}\right][/tex]

We can use cross multiplication,

= (-2)(1) - (-3)(2)

= -2 + 6

= 4 ≠ 0

So the system has a unique solution,

Then,

[tex]D_{1} = \left[\begin{array}{ccc}8&2\\12&-2\\\end{array}\right][/tex]

We can use cross multiplication,

[tex]D_{1} = (8)(-2)-(12)(2)\\D_{1} = -16-24\\D_{1} = -40[/tex]

[tex]D_{2} =\left[\begin{array}{ccc}1&8\\-3&12\\\end{array}\right][/tex]

We can use cross multiplication,

[tex]D_{2} = (12)(1)-(-3)(8)\\D_{2} = 12+24\\D_{2} = 36[/tex]

So, they can solve the X and Y values,

X = D1 / D

X = -40/4

X = -10

Y = D2 / D

Y = 36/4

Y = 9

Therefore,

The solution to the system of equations are,  x + 2y = 8  and -3x-2y = 12 is: X = -10 ,  Y = 9

To learn more about information Matrix :

brainly.com/question/24955126

#SPJ1

The classified balance sheet for Alpha Co. at the end of Year 1 is illustrated below.

A financial statement incorporating classifications as current assets and liabilities, long-term liabilities, and other things is called a classified balance sheet. It may be simpler to read and extract the information you need by categorizing the information than if it were just listed in a lot of line items.

It is a financial report that includes totals for all of the different revenue and expense classifications and displays revenues, expenses, and profits.

The balance sheet is illustrated below:

Current Assets  

Accounts Receivable  26500

Cash    20500

Merchandise Inventory  26300

Total Current Assets  73300

Property, Plant and Equipment  

Land    10000

Total Property, Plant and Equipment 10000

Total Assets   83300

Current Liabilities    

Accounts Payable   12200

Long Term Liabilities  

Long-Term Notes Payable  17500

Stockholders' Equity  

Common Stock  30000  

Retained Earnings  23600  

Total                                 53600

Total Liabilties          83300

Learn more about balance sheet on:

https://brainly.com/question/1113933

#SPJ1

Answer: 87, 295,000,000 or eighty-seven two hundred ninety-five Billion

Im pretty sure

Answer:

Similarity: Both are geometry terms, used in proofs.

Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.

Step-by-step explanation:

ASA: Angle, Side, Angle

AAS: Angle, Angle, Side

Similarity: Both are geometry terms, used in proofs.

Difference: When to use, in the ASA we have two angles and one included side, while the AAS we have two angles, but we want to find a relation involving the non-involved size.

I am going to use the drawer to show the differences: