Solve the system of equations using elimination: -x-2y=19 and -x-y=12.

Theo should expect the spinner to land on "Action" 12 times.

Probability refers to a possibility that deals with the occurrence of random events.

Given: A spinner with 5 sections labeled action, drama, sci-fi, horror, and comedy.

Theo spins the spinner 60 times.

We need to find the number of times, out of 60, the spinner lands on "Action".

Here, a total number of outcomes= 5

A number of favorable outcomes = 1

So, the probability that the spinner lands on "Action" = 1/5

Theo spins the spinner 60 times.

So, the number of times the spinner lands on "Action"

= 1/5 x 60 = 12

Hence, Theo should expect the spinner to land on "Action" 12 times.

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We have the sum of cubes identity

[tex]a^3 + b^3 = (a + b) (a^2 - ab + b^2)[/tex]

and observing that 1 + 4 = 2 + 3, we have

[tex]1^3 + 4^3 = (1 + 4) (1^2 - 4 + 4^2) = 5 \times 13[/tex]

and

[tex]2^3 + 3^3 = (2 + 3) (2^2 - 6 + 3^2) = 5 \times 7[/tex]

Then

[tex]\sqrt{1^3+2^3+3^3+4^3+5^3} = \sqrt{5\times13 + 5\times7 + 5\times5^2} = \sqrt{5 \times (20 + 25)} \\\\ ~~~~~~~~ = \sqrt{5^2 \times (4 + 5)} = \sqrt{5^2\times9} = \sqrt{5^2\times3^2} = 5\times3 = \boxed{15}[/tex]

Alternatively, we have the well-known sum of cubes formula

[tex]\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4[/tex]

The sum under the square root is this sum with [tex]n=5[/tex]. Then

[tex]1^3+2^3+3^3+4^3+5^3 = \dfrac{5^2\times6^2}4 = 225 = 15^2[/tex]

and so the square root again reduces to 15.

Using proportions, it is found that both can be right, as the amounts found from each operation are the same.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering you have 73 cards, and your cousin says that you have 7 less than half the cards he has, his amount is found as follows:

0.5x - 7 = 73

0.5x = 80

x = 160.

Then, one-fourth of his amount is:

(1/4) x 160 = 40.

33 more than this is:

33 + 40 = 73.

Both operations have results (73,160), hence the both can be right.

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The value of the given logarithm using calculator is 2.031

Logarithm are inverse of exponential functions. Given the following logarithm expression;

log(7)52

This can also be expressed as:

log(7)52 = log52/log7

log(7)52 = 0.5399/0.9804

log(7)52  = 2.031

Hence the value of the given logarithm using calculator is 2.031

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The relative frequency for the range 16 - 20 is 0.27.

The frequency of a data set refers to the number of times a data or an event is occurring.

From the given information:

Range         Number of values

1 - 5                       3

6 - 10                     1

11 - 15                    4

16 - 20                  5

21 - 25                   2

Total                     15          

Relative Frequency = Subgroup frequency/ Total frequency

Relative Frequency for the range 16 - 20:

= 4/15

= 0.27

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Answer:

.27

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

The linear equation modeling the given function is P(t)=1700t+45000.

Step-by-step explanation:

In the question it is given that a town's population has been growing linearly. In 2003, the population was 45000, and the population has been growing by 1700 people each year.

It is required to write an equation P(t), for the population t years after 2003.

To solve this question, substitute the given slope , or change in population in the equation with the initial population . Thus, formulate the equation modeling the given function.

Step 1 of 1

Formulate the equation in the slope-intercept form.

[tex]$$\begin{aligned}&y=m x+b \\&P(t)=1700 t+45000\end{aligned}$$[/tex]

Answer:

probably B

Step-by-step explanation:

Using the formula pi*r^2, we plug in our values
pi*49=49pi mi^2
but, we still have one more step, as we are calculating for three quarters of a circle, not a full circle.
To find the area for 3/4 of a circle, we just multiply 3/4 by the area of the circle

49pi*3/4=147pi/4

A quick way (though not always accurate) to guess the answer in a multiple choice like this is to see that someone might find the area of the full circle as their final answer, not multiplying by 3/4, so there's a good chance that 49pi mi^2 would be an answer in the multiple choice. since we know that there is a correct answer that is exactly 3/4 of that answer, we can take the ratios of the answers and check if any of them equal 3/4. indeed, after checking a bit, answer B divided by answer A equals 3/4 exactly, and no other answer combination equals 3/4 (D/B is about equal to 4/5). So, we can guess that B is the answer.

Still better to actually do the problem though

For question 1 option C is the correct answer and for question 2 option A is the correct answer.

We need to find which transformation from the graph of a function f(x) describes the graph of 10f(x).

Here the transformation that describes the graph of g(x) is a vertical dilation of scale factor k = 10 of f(x).

We can start by defining the general vertical dilation.

For a given function f(x), a vertical dilation stretches or contracts the graph vertically, depending on the scale factor k.

And it is written as:

g(x) = k*f(x).

Then here we have:

g(x) = 10*f(x)

It is easy to see that this is a vertical dilation of scale factor k = 10. Therefore, option C is the correct answer.

We need to check from the given options which information is sufficient to prove that quadrilateral ABCD is a parallelogram.

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Therefore, option A is the correct answer.

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The confidence interval for the true mean number of reproductions per hour is (7.5,7.7)

Given mean of 7.6 , standard deviation of 2.2, n=707 and 90% confidence level.

We have to find the confidence interval for the true mean number of reproductions per hour for the bacteria.

α=0.90

μ=7.6

σ=2.2

m=707

α/2=0.45

We have to calculate z value for the p value of 0.45 which is z=1.64.

Margin of error=z*μ/[tex]\sqrt{n}[/tex]

=1.64*2.2/[tex]\sqrt{707}[/tex]

=0.13

Lower level=mean -m

=7.6-0.13

=7.47

after rounding upto 1 decimal

=7.5

Upper level= mean +m

=7.6+0.13

=7.73

after rounding upto 1 decimal

=7.7

Hence the confidence interval is (7.5,7.7) for the true mean number of reproductions per hour.

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Answer:

2x-9=0

2x-9+9=0+9.add the inverse of subtraction /addition/ (+9)

2x=9....then divide by 2

x=9/2

x=4.5. will the final answer

Answer:

y = - 6x + 7.5

Step-by-step explanation:

the perpendicular bisector of BC passes through the midpoint of BC at right angles to BC.

calculate the slope m of BC using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = B (- 2, 1 ) and (x₂, y₂ ) = C (4, 2 )

[tex]m_{BC}[/tex] = [tex]\frac{2-1}{4-(-2)}[/tex] = [tex]\frac{1}{4+2}[/tex] = [tex]\frac{1}{6}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{6} }[/tex] = - 6

the midpoint of BC is the average of the x and y coordinates

midpoint = ( [tex]\frac{-2+4}{2}[/tex] , [tex]\frac{1+2}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex] , [tex]\frac{3}{2}[/tex] ) = ( 1, 1.5 )

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 6 , then

y = - 6x + c ← is the partial equation

to find c substitute (1, 1.5 ) into the partial equation

1.5 = - 6 + c ⇒ c = 1.5 + 6 = 7.5

y = - 6x + 7.5 ← equation of perpendicular bisector of BC

Answer: (–∞, –6)

Step-by-step explanation:

From the given information, the function is never non-negative over (-8,-6), which is the only subset of the interval that is given.

On the number line after 10 moves frog is at the integer -96.

Given that, a frog starts at 0 on a number line.

It jumps 100 units to the right then jumps 200 units to the left=+100-200=-100 (2 moves).

It then jumps 199 units to the right followed by 198 units to the left =-100+199-198=-99 (2 moves).

It then jumps 197 units to the right followed by 196 units to the left =-99+197-196=-98 (2 moves).

It then jumps 195 units to the right followed by 194 units to the left =-98+195-194=-97 (2 moves).

It then jumps 193 units to the right followed by 192 units to the left =-97+193-192=-96 (2 moves).

Hence, on the number line after 10 moves frog is at the integer -96.

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Answer:

AED 3

Step-by-step explanation:

Let tacos: t

Let burritos: b

1) Set up equations.

2t + 3b = 18

4t + 2b = 20

2) Solve the system of equations using substitution.

2t = 18 - 3b

t = 18/2 - 3b/2

t = 9 - 3b/2

Substitute this into the second equation and simplify.

4(9 - 3b/2) + 2b = 20

36 - 12b/2 + 2b = 20

36 - 6b + 2b = 20

36 - 4b = 20

-4b = 20 - 36

-4b = -16

b = -16/-4

b = 4

3) Substitute the found answer in any one of the two equations.

2t + 3(4) = 18

2t + 12 = 18

2t = 18 - 12

2t = 6

t = 6/2

t = 3

Therefore, a soft taco costs AED 3.

The inverse of the given function is y = [tex]\rm \sqrt {x/2}[/tex].

A function is a mathematical statement used to relate a dependent and an independent variable.

The function given is

y = 2x²

To find the Inverse of a function ,

The x and y are interchanged and the function is again written in terms of x

Here

x = 2y²

y² = x/2

y = [tex]\rm \sqrt {x/2}[/tex]

Therefore the inverse of the given function is y = [tex]\rm \sqrt {x/2}[/tex].

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Answer:

22

Step-by-step explanation:

The correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent. Option A is correct.

For two triangles to be similar, the ratio of the measure of similar sides of the triangle must be equal to a constant known as a scale factor.

From the given figures, the expression that can be used to prove that the triangles are similar is as shown;

HL/JL = IL/KL = HI/JK

Hence the correct option is to show that the ratios HL/JL = IL/KL = HI/JK are equivalent

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I can Confirm A is correct

Step-by-step explanation:

The required probability is 0.45

We have total 26 letters in english, of which 21 are consonants and 5 are vowels.

According to the question, we have to select 5 of them of which 4 will be consonants and 1 will be vowel.

Suppose we want to have the vowel in the first selection, so the probability of picking a vowel is equal to the quotient between the number of vowels and the number of total number of letters.

So the probability is 5/26

Now, a letter has been selected, so in the set, we have 25 letters left.

In the next 4 selections, we must select consonants.

In the second selection the probability is 21/25

In the third selection the probability is 20/24

In the fourth selection the probability is 19/23

In the last selection the probability is 18/22

So, the probability is (5/26)×(21/25)×(20/24)×(19/23)×(18/22)

Now, remember that we take that the vowel must be in the first place, but it can be in any five places, so if we add the permutations of the vowel letter we have,

P = 5×(5/26)×(21/25)×(20/24)×(19/23)×(18/22) = 0.45

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-0.5244 will separates the highest 70% of the scores in a normal distribution from the lowest 30%

Normal Distribution is bell shaped and symmetrical in nature.

We use standard normal to find probabilities of normal distribution.

Fig 1 represents Graph of standard normal

and Fig 2 is % points Table for standard normal distribution.

From % points Table the value separates the highest 70% of the scores in a normal distribution from the lowest 30% is 0.5244 since 30% lies left side from 0 it will be negative

⇒  value separates the highest 70% of the scores in a normal distribution from the lowest 30% is -0.5244

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The value of x from the given equation is ±√10

Linear equations are equation that has a leading degree of 1. Given the equation below:

Given the equation below;

x² = 10

Take the square root of both sides

√x² = ±√10

x = ±√10

Hence the value of x from the given equation is ±√10

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Answer:

D .2

Step-by-step explanation:

3-(-9)

5-(-1)

=3+9

5+1

12

6

= 2

The exponential equation for the growth is f(x)=57[tex]e^{0.51x}[/tex] where x is the number of days and the population on 21st march is 2069983.5 of microbes.

Given:

Days                   population

0                                57

1                                 95

5                               700

10                               8525

We have to form exponential equation which shows the growth of microbes.

We know that exponential equation which shows the sum is as under:

f(x)=P[tex]e^{rt}[/tex] where r is the rate of growth and x is the number of days, months or years depending on how things grows.

In the question when x=0 population is 57.

f(0)=57

P[tex]e^{0}[/tex]=57

P=57

When x=1, population is 95.

f(1)=95

P[tex]e^{r}[/tex]=95

57 [tex]e^{r}[/tex]=95

57=95/[tex]e^{r}[/tex]----1

when x=5,population is 700.

f(5)=700

P[tex]e^{5r}[/tex]=700

57[tex]e^{5r}[/tex]=700

57=700/[tex]e^{5r}[/tex]-----2

Equating 1&2

95/[tex]e^{r}[/tex]=700/[tex]e^{5r}[/tex]

[tex]e^{5x} /e^{x} =700/95[/tex]

[tex]e^{5r-r}[/tex]=7.36

[tex]e^{4r}[/tex]=7.36

[tex](2.7182)^{4r}[/tex]=[tex](2.7182)^{2}[/tex]

equating both sides

4r=2

r=0.5

put the value of t=21 in the exponential equation

f(21)=57[tex]e^{0.5*21}[/tex]

=57[tex]e^{10.5}[/tex]

=57*36315.5

=2069983.5

Hence the population on 21st march is 2069983.5.

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Answer:

[tex]x = - 4[/tex]

[tex]y = - 4[/tex]

Step-by-step explanation:

Looking at these equations, we can see neither x or y have the same coefficient. Therefore, we need to multiply or divide, to make either the x or the y the same. It's less of a hassle to make the Xs the same, so let's do that. Taking the top equation and multiplying it by 4, we get:

[tex]4x - 20y = 64[/tex]

Now let's subtract the top equation from the bottom equation, leaving us with a third equation:

[tex] - 18y = 72[/tex]

Divide 72 by -18 to get

[tex]y = - 4[/tex]

Now let's substitute into our first equation to find X:

[tex]x + 20 = 16[/tex]

Leaving us with:

[tex]x = - 4[/tex]

Now let's substitute into the second equation to check our solution is correct:

[tex] - 16 + 8 = - 8[/tex]

This is correct, so the answer is X and Y are both equal to -4

Steps 4 and 5 describe the errors Stephen made.

Stephen evaluated [tex](6.34\times 10^{-7})(4.5\times 10^3)[/tex].  

His work is shown below.

Step 1 - [tex](6.34\times 10^{-7})(4.5\times 10^3)[/tex]

Step 2 - [tex]=(6.34\times 4.5)(10^{-7} \times 10^3)[/tex]

Step 3 - [tex]=(28.53)(10^{-4})[/tex]

Step 4 - [tex]20.53\times 10^4[/tex]

Error is the step as 4 sign is negative.

So correct step is [tex]=(28.53)(10^{-4})[/tex]

Step 5 - [tex]=(28.53)(10^{-4})[/tex]

Error is the step as there are 4 in place of 3.

So correct step is [tex]=(28.53)(10^{-4})[/tex]

Steps 4 and 5 describe the errors Stephen made.

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The coefficient of the last term in the binomial expansion is 1.

Given term is (x + 1)⁹.

The algebraic expansion of a binomial's powers is expressed by the binomial theorem or binomial expansion. The process of expanding and writing terms that are equal to the natural number exponent of the sum or difference of two terms is known as binomial expansion.

The binomial expansion formula for (a + b)ⁿ= ⁿC₀(aⁿb⁰)+ⁿC₁(aⁿ⁻¹b¹)+ⁿC₂(aⁿ⁻²b²)+ⁿC₃(aⁿ⁻³b³)+...............+ⁿCₙ(a⁰bⁿ)

Here, a = x, b = 1 and n = 9.

Substituting the values in the formula,

⁹C₀(x⁹{1}₀)+⁹C₁(x⁹⁻¹{1}¹)+⁹C₂(x⁹⁻²{1}²)+⁹C₃(x⁹⁻³{1}³)+......+⁹C₉(x⁰{1}⁹)

The last term is ⁹C₉(x⁰{1}⁹)

The coefficient of the last term = ⁹C₉ = 1.

Hence, the coefficient of the last term in the binomial expansion of (x+1)⁹ is 1.

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Answer:

In interval notation, the solution of |3 x-2|<7 is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex].

Step-by-step explanation:

The given absolute value function is |3 x-2|<7.

It is required to solve the inequality and express the solution using interval notation. -B<x-A<B and solving them separately for x

Step 1 of 3

Given absolute value equation is |3 x-2|<7.

It can be written as -7<3 x-2<7.

To solve for the equality, 3x-2=7 and

[tex]$$3 x-2=-7$$[/tex]

First, solve the equation 3x-2=7, then add 2 on both sides.

[tex]$$\begin{aligned}&3 x=7+2 \\&3 x=9\end{aligned}$$[/tex]

Step 2 of 3

Simplify 3x=9 further, by dividing each side with 3 .

[tex]$$\begin{aligned}&\frac{3 x}{3}=\frac{9}{3} \\&x=3\end{aligned}$$[/tex]

Step 3 of 3

Similarly, 3x-2=-7

From the above term 3x-2=-7,

Add 2 on each side.

[tex]$$\begin{aligned}&3 x=-7+2 \\&3 x=-5\end{aligned}$$[/tex]

Simplify $3 x=-5$ further, by dividing each side with 3 .

[tex]$$\begin{aligned}&\frac{3 x}{3}=-\frac{5}{3} \\&x=-\frac{5}{3}\end{aligned}$$[/tex]

Therefore, the solution is [tex]$-\frac{5}{3} < x < 3$[/tex] or [tex]$\left\{-\frac{5}{3}, 3\right\}$[/tex]

By inclusion/exclusion,

[tex]n(P' \cup Q) = n(P') + n(Q) - n(P' \cap Q)[/tex]

We have

[tex]n(\xi) = n(P) + n(P') \implies n(P') = 28 - n(P)[/tex]

so that

[tex]n(P'  \cup Q) = (28 - n(P)) + n(Q) - 2n(P) = 28 - 3n(P) + n(Q)[/tex]

Now,

[tex]n(\xi) = 28 \implies n(P \cup Q) = 28 - 7 = 21[/tex]

and by inclusion/exclusion,

[tex]n(P \cup Q) = n(P) + n(Q) - n(P \cap Q)[/tex]

Decompose [tex]Q[/tex] into the union of two disjoint sets:

[tex]Q = (P \cap Q) \cup (P' \cap Q)[/tex]

Since they're disjoint,

[tex]n(Q) = n(P\cap Q) + n(P'\cap Q) \implies n(Q) = n(P\cap Q) + 2n(P)[/tex]

[tex]\implies n(P \cup Q) = n(P) + (n(P\cap Q) + 2n(P)) - n(P \cap Q)[/tex]

[tex]\implies 21 = 3n(P)[/tex]

[tex]\implies n(P) = 7[/tex]

From the Venn diagram, we see there are 3 elements unique to [tex]P[/tex] - by the way, this is the set [tex]P \cap Q'[/tex] - so [tex]n(P\cap Q) = 7-3 = 4[/tex], and it follows that

[tex]n(Q) = n(P\cap Q) + 2n(P) = 4 + 2\times7 = 18[/tex]

Finally, we get for (a)

[tex]n(P' \cup Q) = 28 - 3n(P) + n(Q) = 28 - 3\times7 + 18 = \boxed{25}[/tex]

For (b), we have by inclusion/exclusion that

[tex]n(P \cup Q') = n(P) + n(Q) - n(P \cap Q') = 7 + 18 - 3 = \boxed{22}[/tex]

Answer: 17 players

Step-by-step explanation: 1780.50-1151.50=629, 629/37 = 17

The number of players the team can bring to the tournament is 17.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given,

Budget = $1780.50

Fixed cost (bus rent) = $1151.50

Variable cost = $37 per player.

For n number of players.

Total cost = 1151.50 + 37n

Total cost ≤ total budget

1151.50 + 37n ≤ $1780.50

37n ≤ 629

n ≤ 17

Hence "The number of players the team can bring to the tournament is 17".

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