Solve each equation.
1. r-38= 9 _____
2. h+17=40 _____
3. n + 75= 155 ____
4. q - 17= 18 _____

Answer:

Vertical angles theorem

Step-by-step explanation:

f

Answer: the right side subtracted 4 when they were supposed to add in the row before the solution.

Step-by-step explanation: you have to subtract or add from both sides, they have to be the same, when solving equations like these. the answer should be 5.

The function f(x) is a periodic function with oscillations, while g(x) is an exponential function that decreases rapidly.

The function f(x) is a periodic function that oscillates between 1/4 - 1 and 1/4 + 1 with a period of 2.

It starts at 1/4 - 1, reaches a maximum of 1/4 + 1, then returns to 1/4 - 1, and so on. The sine function sin(πx) generates these oscillations, and the constant 1/4 shifts the graph vertically.

The function g(x) is an exponential function with a base of 4 raised to the power of -x. As x increases, the exponent becomes more negative, causing the function to decrease rapidly.

Similarly, as x decreases, the exponent becomes less negative, causing the function to increase rapidly. The function approaches zero as x approaches infinity.

In summary, f(x) is a periodic function with oscillations, while g(x) is an exponential function that decreases rapidly.

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Answer: B, 42,068

Step-by-step explanation:

Since there's 52 weeks in a year and you make 809 cars each week, you have to multiply 52 by 809.

52 x 809 = 42068.

The Detroit Ford factory makes 42068 cars each year.

Number of dimes collected by Rosalyn = \(250\)

How to calculate the number of dimes by Rosalyn?

Let D = # of dimes ,  Q = # of quarter.

We have

A dime is \(10\) pennies , a quarter is \(25\) pennies and $\(82.50\) is \(8250\) pennies.

Now this leads to the equation:

\(10D + 25 Q =8250\)

If Rosalyn collected \(50\) more quarters than dimes,

Then \(Q=D+50\)

\(10D+25(D+50)=8250\)

\(35D+1250=8250\)

\(35D=7000\)

\(D=\frac{7000}{35}\)

\(D = 200\)

So there are \(200\) dimes.

And since there are \(50\) more quarters than dimes , hence there are \(250\) quarters.

So Rosalyn collected \(250\) dimes.

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The odds of the employee passing the test are 0.25. Alternatively, we can say that the employee has a 1 in 4 chance of passing the test if the probability is 0.20

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents impossibility (an event that cannot occur) and 1 represents certainty (an event that is certain to occur).

For example, if you toss a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 0.5 (or 1/2) because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

The odds of an event happening are defined as the ratio of the probability of the event occurring to the probability of the event not occurring. Mathematically, odds can be expressed as:

odds = P(event happening) / P(event not happening)

In this case, the probability of the employee passing the test is 0.20, so the probability of the employee not passing the test is 0.80 (since the sum of probabilities of all possible outcomes must be 1).

Therefore, the odds of the employee passing the test can be calculated as:

odds = 0.20 / 0.80 = 0.25

So the odds of the employee passing the test are 0.25. Alternatively, we can say that the employee has a 1 in 4 chance of passing the test (since 0.25 can be written as a fraction of 1/4).

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Answer:x value is 25

Answer:

30

Step-by-step explanation:

x=30

2x=60

3x=90

30+60+90=180 degrees

Answer:

  a) 151

  b) 160₉

  c)i) 30

  c)ii) 21

Step-by-step explanation:

(a) The value of the digits 3 and 4 is the value of the number with the other digits set to zero.

  304₇ = 3×7² +0×7¹ +4×7⁰ = 3×49 +4 = 151₁₀

The total value of the digits 3 and 4 is 151.

__

(b) We can make a short table for conversions.

  10₁₀ = 11₉

  100₁₀ = (11₉)² = 121₉

So,

  135₁₀ = 1×121₉ +3×11₉ +5 = 121₉ +33₉ +5 = 154₉ +5 = 160₉

The base-9 equivalent of 135 is 160₉.

__

(ci) 110₅ = 1×5² +1×5¹ +0×5⁰ = 25 +5 = 30₁₀

Lisa is 30 in base 10.

(cii) 110₅ -14₅ = 41₅ = 4×5¹ +1×5⁰ = 20+1 = 21₁₀

Lisa's younger brother is 21 in base 10.

Alternate solution

14₅ = 5+4 = 9₁₀ . . . now we can find the difference in base 10:

30 -9 = 21

_____

Additional comment

It helps to understand place value and how the digit positions relate to the powers of the number base. I find "expanded form using exponents" to be helpful, as you can see in the answers above. The relationships between place value and powers of the base hold true for any number base, and they extend to either side of the "decimal point."

The percentage of her commission from the sales was 2.2%

percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Commission = $58,399

sales = $2,654,500

Percentage commission = \(\frac{commission}{sales}\) x 100%

Percentage commission = \(\frac{58399}{2654500}\) x 100%

Percentage commission = 2.2%

In conclusion, the percentage commission is 2.2%

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We can find the probabilities of ever transiting from states 4, 5, and 6 to a transient state by looking at the fourth, fifth, and sixth rows of F, respectively.

To find the mean time spent by the Markov chain in any transient states of the chain which starts at any transient state, we need to first identify the transient states. In this case, we can see that states 1, 3, and 7 are transient states since there is a non-zero probability of reaching an absorbing state (states 4, 5, and 6) from these states.

Next, we need to find the expected time spent in each of the transient states before reaching an absorbing state. We can set up a system of equations to solve for these expected times using the fact that the expected time spent in a state is equal to 1 plus the sum of the expected times spent in each possible next state, weighted by their transition probabilities.

For example, for state 1, we have:

E(T1) = 1 + 0.5E(T2) + 0.25E(T3)

where E(Ti) is the expected time spent in state i before reaching an absorbing state.

Similarly, for state 3, we have:

E(T3) = 1 + 0.4E(T2) + 0.2E(T4)

And for state 7, we have:

E(T7) = 1 + 0.2E(T5) + 0.5E(T6)

Solving these equations, we get:

E(T1) = 5

E(T3) = 5.5

E(T7) = 4

Therefore, the mean time spent by the Markov chain in any transient state is:

(E(T1) + E(T3) + E(T7))/3 = (5 + 5.5 + 4)/3 = 4.83

To find the probability that the Markov chain will ever transit to one of the transient states starting from another transient state, we can use the concept of fundamental matrix. The fundamental matrix F is defined as the matrix (I-Q)^-1, where Q is the submatrix of P consisting of the transition probabilities between transient states.

In this case, we have:

Q = [0 0.25 0.2;

0.4 0 0.2;

0.2 0.2 0]

Using a calculator or software to calculate the inverse of (I-Q), we get:

(I-Q)^-1 = [1.25 0.625 1;

0.625 1.25 1;

1 1 1.5]

The (i,j)-th entry of F represents the expected number of times the Markov chain will visit state j starting from state i before reaching an absorbing state. Therefore, the probability of ever transiting to a transient state starting from another transient state is simply the sum of the corresponding entries in F.

For example, to find the probability of ever transiting from state 2 to a transient state, we look at the second row of F:

[0.625 1.25 1]

The sum of these entries is 0.625 + 1.25 + 1 = 2.875, so the probability of ever transiting from state 2 to a transient state is 2.875.

Similarly, we can find the probabilities of ever transiting from states 4, 5, and 6 to a transient state by looking at the fourth, fifth, and sixth rows of F, respectively.

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The equation of the circle that meets the specified requirements is x^2 + y^2 = 89, with the center at the origin and going through P(5, 8).

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The equation of a circle with center at the origin (0,0) and passing through the point (x1,y1) can be found using the distance formula.

The distance between a point (x1, y1) and the origin (0,0) is given by:

sqrt((x1-0)^2 + (y1-0)^2) = sqrt(x1^2 + y1^2)

Let's call the radius of the circle r. We know that the distance between the point (x1,y1) and the origin is equal to r. So, we can set up the equation:

sqrt(x1^2 + y1^2) = r

Substituting the values x1 = 5 and y1 = -8, we have:

sqrt(5^2 + (-8)^2) = r

Solving for r, we get:

r = sqrt(5^2 + (-8)^2) = sqrt(25 + 64) = sqrt(89)

Finally, we can write the equation of the circle in standard form using the center (0,0) and radius r:

(x - 0)^2 + (y - 0)^2 = r^2

x^2 + y^2 = r^2

x^2 + y^2 = 89

The  equation of the circle that satisfies the stated conditions that is center at the origin, passing through P(5, −8) is x^2 + y^2 = 89.

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Answer:

59

Step-by-step explanation:

Given: a = 13, b = 6, and c = 5

(13-6)^2+2 x 5 (=10)

(13-6)^2+10

=59

Answer:

59

Step-by-step explanation:

Given,

a = 13

b = 6

c = 5

To find : ( a - b )^2 + 2c

Answer : -

( a - b )^2 + 2c

= ( 13 - 6 )^2 + 2 ( 5 )

= ( 7 )^2 + 10

= 49 + 10

= 59

Therefore,

the value of ( a - b )^2 + 2c is 59.

Answer:

x-(-0.9)

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation::3*x+7*x-(9-18)=0

Solve::10x+9 = 0

Subtract 9 from both sides of the equation::10x = -9

Divide both sides of the equation by 10::x = -9/10 = -0.900

Answer:

Step-by-step explanation:

3x+7x=9-18

10x = -9

x = -9 / 10

x = -0.9

The function g tells us the amount of remaining water.

The variable x gives us how much time has passed.

Given g(840) = 0,

We can see that the variable x is 840 and the functional value of g is 0.

This means at after 840 minutes the amount of water in the pool will be zero.

Looking at the choices, the correct answer is >>>

The expressions are given as;

1. The factored form of g(x) is g(x) = 1/(x-6)

2. The LCD of g(x) and h(x) is (x-6)(x+8)

3. The LCD of h() and p(x) is (x-6)(8x + 32)

Functions are simply defined as laws, equations or rules showing the relationship between two variables.

These variables are termed;

From the information given, we have that;

g(x) = (x + 8)/x² + 2x - 48

Factorize the denominator of the function;

x²+ 8x - 6x - 48

group in pairs

x(x + 8) - 6(x + 8)

Then,

g(x) = x + 8/(x-6)(x+ 8)

g(x) = 1/(x-6)

The lowest common denominator of the functions g(x) and h(x) is;

g(x) = x + 8/(x-6)(x+ 8)

h(x) = 6x - 36/x-6

LCD = (x-6)(x+8)

The LCD of h(x) and p(x) is given as;

p(x) = x² - x - 20/8x + 32

= (x-6)(8x + 32)

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Answer:

y=0.25x^2−2x

Step-by-step explanation:

You have to use the disruptive property.

There are a total of 12870 paths that stay outside or on the boundary of the square.

To go from (-4, -4) to (4, 4) with each step increasing either the x-coordinate or the y-coordinate by 1, you can only move diagonally upwards or diagonally to the right. This means that you can only move in one of two directions at each step.

In order to stay outside or on the boundary of the square -2 < x < 2, -2 < y < 2 at each step, you need to make sure that you don't move too far in either direction. Since there are 16 steps in total, you need to choose 8 steps to move in the x-direction and the remaining 8 steps to move in the y-direction.

The number of ways to choose 8 steps out of 16 to move in the x-direction is given by the binomial coefficient "16 choose 8" which can be calculated as C(16, 8) = 12870. Similarly, the number of ways to choose 8 steps out of 16 to move in the y-direction is also 12870.

Therefore, there are a total of 12870 paths that stay outside or on the boundary of the square -2 < x < 2, -2 < y < 2 at each step.

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The riddle mentioned in the question is about a farmer who is traveling along with a sack of rye, a goose, and a mischievous dog.

He comes to a river that he must cross from east to west, and there is a boat available to do so.  Therefore, the farmer takes the goose back to the east side and leaves it there. He then takes the sack of rye across the river, drops it off with the dog, and goes back to the east side to pick up the goose. In this manner, all of the farmer's possessions can be safely transported across the river without any of them being lost to the dog or the goose.This riddle is a classic example of a type of logical puzzle known as a "transport problem."

The goal of a transport problem is to determine how to transport one or more objects from one location to another while satisfying certain constraints, such as the size of the transport vehicle or the safety of the objects being transported.

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Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

Answer:

w = 1

Step-by-step explanation:

10(w+5) = 60

w+5 = 6

w = 6-5

w = 1

Answer: w is 1!

Step-by-step explanation: 5 plus 1 is 6. 6 times 10 is 60! Good luck! :D

Answer:

2x^3 + 3x^2 -11x -6

Step-by-step explanation:

(2x + 1)(x-2)(x + 3) ​

(2x^2 -4x + x - 2)(x + 3)

(2x^2 -3x - 2)(x + 3)

2x^3 - 3x^2 - 2x + 6x^2 - 9x - 6

2x^3 + 3x^2 -11x -6

Answer:

\(2x^{3} + 3x^{2} - 11x - 6\)

Step-by-step explanation:

(2x + 1)(x - 2)(x + 3)

Since there is multiplication i between all of these, I will multiply the first 2, then multiply it with the last one:

(2x + 1) (x - 2) = \(2x^{2} -3x - 2\)

(\(2x^{2} -3x - 2\) ) (x + 3) =   \(2x^{3} +3x^{2} -11x - 6\)

Answer:

$5.50

Step-by-step explanation:

1.) The first step is finding what 45% of $10 is. We can do this by turning 45% into a decimal number (45%=0.45). We then multiply 0.45 by the $10.

2.) 0.45×$10=$4.50 ; We just found that 45% of $10 is $4.50

3.) Because the shirt is 45% less than the original price (45% off), we need to subtract the 45% (which is equal to $4.50) from the original price, $10

4.) $10-$4.50=$5.50, the new price

Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

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Answer:

The sum is $10

Step-by-step explanation:

Since Tony got $5 on Monday and $5 on Tuesday, we can add them together by doing 5+5. We can add 5 and 5 together to get a total of $10 that Tony has earned. This means that it isn't a sum of 0 but a sum of 10.

(hope this helped)

Answer:

a. standard deviation

Step-by-step explanation:

Standard deviation measures the variation (how spread out the data is from the mean) of a data set.  

Answer:

Step-by-step explanation:

990 x 70% = 693 people

Therefore , the solution of the given problem of equation comes out to be cost of one pair of pants is $40.

The similar symbol (=) is used in mathematical equations to variables denote equality between two propositions. Mathematical formulae, which are abstractions of reality, are used to demonstrate how different numerical factors can be compared. For instance, the equal sign splits the integer 12 or perhaps the equation y + 6 = 12 to two separate halves. One can compute how so many characters each side of the a character has. Contradictory meanings are common in symbols.

Here,

Given :

Mathew bought 5 shirts and 2 pairs of pairs is $165.

Toby bought 3 shirts and 5 pairs of pants for $251.

x is the shirt of price ,

y is the pants of price .

Thus,

=> 5x + 2y = 165

=> 3x + 5y = 251

So,

=> x = 165 -2y/5

=> 3(165 - 2y/5) + 5y = 251

=> 3(165 - 2y /5) + 5y = 251

=>  495 - 6y  + 25y = 251 *5

=>  495 + 19y = 1255

=> 19y = 1255 - 495

=> 19 y =  760

=> y =760/19

=> y = 40

and

=> x = 165 - 2*40 /5

=> x = 165-80/5

=> x = 85/5

=> x =17

Thus , cost of one pair of pants is $40.

Therefore , the solution of the given problem of equation comes out to be cost of one pair of pants is $40.

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The correct simplification would be \(18x^4 - 36x^3 + 9x^2\) (option a).

To simplify the expression \(9x^2(4x - 2x^2\) - 1), we need to perform the multiplication and combine like terms.

1. Start by distributing the 9x^2 to each term inside the parentheses:

  \(9x^2 * 4x = 36x^3 9x^2 * (-2x^2) = -18x^4 9x^2 * (-1) = -9x^2\)

2. Now we can combine the terms obtained from the distribution:

\(36x^3 - 18x^4 - 9x^2\)

3. Rearranging the terms in descending order of exponents:

\(-18x^4 + 36x^3 - 9x^2\)

4. However, we can simplify this expression further by factoring out a common factor of \(-9x^2\):

\(-9x^2(2x^2 - 4x + 1)\)

5. Thus, the final simplified expression is:

\(18x^4 - 36x^3 + 9x^2\)

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