Algebra 1
Function Notation Worksheet Alternate
Name
For #I-8: Evaluate the following expressions given the functions below:
f(x) = x2 – 7
g(x) = -3x - 1
j(x)=2x-9
h(x) = 1
X=
1. g(10) =
2. What is the value of x if g(x) = 16
3. f(3) =
4. What is the value of x if f(x) = 23
X
5. h(-2) =
6. What is the value of x if h(x) = -2
X =
7. |(7) =
8. h(a) =
For #9-12: Translate the following statements into coordinate points:
9. S(-1) = 3
10. g(4) = -1
11. h(2) = 8
12. k(2) = 9​

Answer:

p value is 0.1343

Step-by-step explanation:

Null: u>= 442

Alternative: u < 442

Using the formula for z score:

(x - u)/sd/√n

Where x is 438, u = 442 sd can be determined from the variance = √variance =√576 = 24 and n = 44

z score = 438-442 / (24/√44)

z score = -4/(24/6.6332)

z = -4/3.6182

z =-1.1055

Now let's find the p value at 0.1 significance level using a z score of -1.1055, using a p value calculator, p value is 0.1343 which greatest than 0.1 meaning the day is not sufficient enough to conclude that the machine is underfilling the bags.

Answer:

[tex]z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347[/tex]      

The p value for this case would be given by"

[tex]p_v =2*P(z>2.347)=0.0189[/tex]  

For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications

Step-by-step explanation:

Information given

[tex]\bar X=6.6[/tex] represent the sample mean

[tex]s=\sqrt{0.49}= 0.7[/tex] represent the population deviation

[tex]n=270[/tex] sample size      

[tex]\mu_o =6.5[/tex] represent the value that we want to test    

[tex]\alpha=0.1[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value for the test

Hypothesis to verify

We want to verify if the true mean for this case is equal to 6.5 lbs/square inch or not , the system of hypothesis would be:      

Null hypothesis:[tex]\mu= 6.5[/tex]      

Alternative hypothesis:[tex]\mu \neq 6.5[/tex]      

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

And replacing we got:

[tex]z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347[/tex]      

The p value for this case would be given by"

[tex]p_v =2*P(z>2.347)=0.0189[/tex]  

For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications

Answer:

Option 4.

Step-by-step explanation:

Reciprocal of the second fraction turns the product into the division of the two fractions, which equals to 1.

[tex]a/3(a/3)[/tex]

[tex]a/3 \div 3/a=1[/tex]

Two fractions are said to be the reciprocal or multiplicative inverse of each other, if their product is 1.

Answer:

D. a/3 divided by 3/a = 1

Step-by-step explanation:

edge

Answer:

Area = 108 cm^2

Perimeter = 44 cm

Step-by-step explanation:

Area, -->

24 + 30 + 24 + 30 -->

24(2) + 30(2)

48 + 60 = 108 cm^2

108 = area

10 + 12 + 10 + 12, -->

10(2) + 12(2) = 44 cm

44 = perim.

Hope this helps!

Answer:

Step-by-step explanation:

Draw the diagram.

This time put in the only one line for the height. That is only 1 height is 8 cm. That's it.

The base is 6 +  6 = 12 cm.

The slanted line is 10 cm

That's all your diagram should show. It is much clearer without all the clutter.

Now you are ready to do the calculations.

Area

The Area = the base * height.

base = 12

height = 8

Area = 12 * 8 = 96

Perimeter.

In a parallelagram the opposite sides are equal to one another.

One set of sides = 10 + 10 = 20

The other set = 12 + 12 = 24

Both sets = 20 + 24

Both sets = 44

Answer

Area = 96

Perimeter = 44

Answer:

The answer is -4.

Step-by-step explanation:

You should get this answer if you do 3 - 7.

Answer:

340

Step-by-step explanation:

If x is the amount of pages in the book we can write:

1/4x + 5 + 3/5(x - (1/4x + 5)) + 10 + 12 + 24 = x

1/4x + 51 + 3/5(3/4x - 5) = x

1/4x + 51 + 9/20x - 3 = x

7/10x + 48 = x

3/10x = 48

x = 160

Answer:

1. C

2. A

3. A

Step-by-step explanation:

1. It is the Symmetric Property of Congruence because the definition is literally what it says.

2. Incomplete sentences don't matter as long as you have the right stuff.

3. Step 2 is wrong because it should be Definition of Midpoint.

If Curtis is attempting to defend a step in his proof paragraph. He should apply the symmetric property of congruence so that he can demonstrate that AB=BC and that BC=AB. It's best to choose C.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.

A)If Curtis is trying to justify a step in his paragraph proof. Symmetric Property of Congruence that he should use as a result he can show AB=BC therefore BC=AB. Option C is correct.

B)All of the following would make a formal proof incomplete except Incomplete sentences. Option A is correct.

C)Step 2 in the proof has a flaw Because it is not a symmetric property while they show congruency because it must be a midpoint definition. Option A is correct.

Thus, if Curtis is trying to justify a step in his paragraph proof. Symmetric Property of Congruence that he should use as a result he can show AB=BC therefore BC=AB. Option C is correct.

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The correct answer is A

Explanation:

An orthographic drawing shows a three-dimensional figure from different perspectives or sides. Indeed, the orthographic drawing in the question shows how the object looks if you see this the front, side, and top of this. This implies the foundation drawing needs to match the figures of the orthographic drawing.

According to this, the correct figure is A because this is the only one that has a rectangle shape, and due to this, if you look at this from any different sides you will always see a rectangle. For example, the top view shows a rectangle of approximately 2x3 squares, and this view only fits with option A because B and C are not complete rectangles and therefore their top view is not a rectangle.

Answer:

d = 234.6 m

Step-by-step explanation:

You can consider a system of coordinates with its origin at the beginning of the walk of the student.

When she start to walk, she is at (0,0)m. After her first walk, her coordinates are calculated by using the information about the incline and the distance that she traveled:

[tex]x_1=60cos28\°=52.97m\\\\y_1=60sin28\°=28.16m[/tex]

she is at the coordinates (52.97 , 28.16)m.

Next, when she walks 180m to the east, her coordinates are:

(52.97+180 , 28.16)m = (232.97 , 28.16)m

To calculate the distance from the final point of the student to the starting point you use the Pythagoras generalization for the distance between two points:

[tex]d=\sqrt{(x-x_o)^2+(y-y_o)^2}\\\\x=232.97\\\\x_o=0\\\\y=28.16\\\\y_o=0\\\\d=\sqrt{(232.97-0)^2+(28.16-0)^2}m=234.6m[/tex]

The displacement of the student on her complete trajectory was of 234.6m

Answer:

6 pizzas

Step-by-step explanation:

At least 10 and fewer than 20 makes it 10-19

So,

10-19 => 6 pizzas

6 pizzas have at least 10 pieces of pepperoni but fewer than 20 pieces of pepperoni.

Answer

its -1

Step-by-step explanation:

ED 2020 boiiiii

The residual value of the line of the best fit when x = 2 is -1

The equation of the line is given as:

y = 0.5x + 1

When x = 2, we have:

y = 0.5 * 2 + 1

Evaluate

y = 2

The residual is the difference between the actual value and the predicted value.

From the complete graph, the actual value is 1.

So, we have:

Residual = 1 - 2

Evaluate

Residual = -1

Hence, the residual value when x = 2 is -1

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Answer:

n=N-1

Step-by-step explanation:

You can start by imagining this scenario on a small scale, say 5 squares.

Assuming it starts on the first square, the grasshopper can cover the full 5 squares in 2 ways; either it can jump one square at a time, or it can jump all the way to the end and then backtrack. If it jumps one square at a time, it will take 4 hops to cover all 5 squares. If it jumps two squares at a time and then backtracks, it will take 2 jumps to cover the full 5 squares and then 2 to cover the 2 it missed, which is also 4. It will always be one less than the total amount of squares, since it begins on the first square and must touch the rest exactly once. Therefore, the smallest amount n is N-1. Hope this helps!

The smallest value of n is N-1.

Square is a quadrilateral of equal length of sides and each angle of 90°.

Here given that there are 1×N squares i.e. N numbers of squares in one row.

The grasshopper can jump either one square or two squares to land on the next square.

Let's assume the scenario of 5 squares present in a row.

Let the grasshopper starts from the first square,

so the grasshopper can cover the full 5 squares in 2 methods;

one method is that it will jump one square at a time and reach at last square.

another method is it will jump all the squares to the finish and then backtrace.

If the grasshopper jumps one square at a time, it will take 4 jumps to cover all 5 squares.

Similarly, If a grasshopper jumps two squares at a time and then backtrace, it will take 2 jumps to reach the 5th square and then it will jump 1 square and then 2 squares to cover the 2 squares it missed, for which the number jump is also 4.

From the above it is clear that the number of jumps will always be one less than the total number of squares if the grasshopper begins from the first square and touch every square exactly once.

Therefore, the smallest value of n is N-1.

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Answer: 38 23/24

Step-by-step explanation:

Turn the mixed numbers into improper fractions

5 * 3 = 15

15 + 2 = 17

17/3

————————

6 * 8 = 48

48 + 7 = 55

55/8

————————

Now multiply the improper fractions

17/3 * 55/8

17 * 55 = 935

3 * 8 = 24

Divide 935 by 24 to get the answer as a mixed number.

935 / 24 = 38.95833

0.95833/1 = 23/24

935/24 as a mixed number is 38 23/24

Answer: 119 / 4

Step-by-step explanation:

5 2/3 x 6 7/8

= 17/3 x 6 x 7/8

= 17 x 2 x 7/8

= 17 x 2 x 7/8

= 17 x 7/4

= 119 / 4

Answer:

V = 137.2

Step-by-step explanation:

We are given the volume equation. Simply plug in your r into the equation and calculate and you should get 137.189 as your answer.

Answer:

The number of ways is  [tex]\left 9}\atop } \right. P _5 = 15120[/tex]

Step-by-step explanation:

From the question we are told that

   The number of factories visited is  [tex]n = 9[/tex]

    The number of factories to be visited by a representative  r = 5

The number of way to visit the 5 factories is mathematically represented as

         [tex]\left 9}\atop } \right. P _5 = \frac{9!}{(9-5)!}[/tex]

Where P represents  permutation

  =>   [tex]\left 9}\atop } \right. P _5 = \frac{9 \ !}{4\ !}[/tex]

 =>     [tex]\left 9}\atop } \right. P _5 = \frac{9 *8*7 * 6 * 5 * 4!}{4\ !}[/tex]

=>    [tex]\left 9}\atop } \right. P _5 = 15120[/tex]

Answer:

Triangular Prism

volume 748

Answer:

27.11% probability that 2 of them have blue eyes

Step-by-step explanation:

For each person, there are only two possible otucomes. Either they have blue eyes, or they do not. The probability of a person having blue eyes is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

8% of all people have blue eyes.

This means that [tex]p = 0.08[/tex]

Random sample of 20 people:

This means that [tex]n = 20[/tex]

What is the probability that 2 of them have blue eyes?

This is P(X = 2).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{20,2}.(0.08)^{2}.(0.92)^{18} = 0.2711[/tex]

27.11% probability that 2 of them have blue eyes

The probability that 2 of them have blue eyes is 27.11%.

Given that,

Approximately 8% of all people have blue eyes.

Out of a random sample of 20 people,

We have to determine,

What is the probability that 2 of them have blue eyes?

According to the question,

People having blue eyes p = 8% = 0.08

Sample of people n = 20

For each person, there are only two possible outcomes. Either they have blue eyes, or they do not.

The probability of a person having blue eyes is independent of any other person.

The probability that 2 of them have blue eyes is determined by using a binomial probability distribution.

[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}[/tex]

Therefore,

The probability that 2 of them have blue eyes is,

[tex]\rm P (X = x) =n_C_x\times p^x \times (1-p)^{n-x}}\\\\ \rm P (X = x) = \dfrac{n!}{(n-x)! \times x!} \times p^x \times (1-p)^{n-x}}\\\\[/tex]

Substitute all the values in the formula,

[tex]\rm P (X = 2) = \dfrac{20!}{(20-2)! \times 2!} \times (0.08)^2 \times (1-0.08)^{20-2}}\\\\ P (X = 2) = \dfrac{20!}{(18)! \times 2!} \times (0.0064) \times (0.92)^{18}}\\\\ P (X = 2) = \dfrac{19\times 20}{ 2} \times (0.0064) \times (0.222)\\\\ P(X = 2) = {19\times 10}\times (0.00142)\\\\P(X = 2) = 0.2711\\\\P(X = 2) = 27.11 \ Percent[/tex]

Hence, The required probability that 2 of them have blue eyes is 27.11%.

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Answer:

50%

OR

1/2

Step-by-step explanation:

The box and whisker plot shows the time spent from 4 to 6 hours is Quartile 1 to 3 which makes it 50%.

Answer:

Step-by-step explanation:

The vertical asymptotes of the rational expression are the places where the denominator is zero:

  x^2 -16 = 0

  (x -4)(x +4) = 0 . . . . . true for x=4, x=-4

  x = 4, x = -4 are the equations of the vertical asymptotes

__

The zeros of a rational expression are the places where the numerator is zero:

  4x = 0

  x = 0 . . . . . . divide by 4

Answer:

0.637

Step-by-step explanation:

The average value of a whole sinusoidal waveform over one complete cycle is zero as the two halves cancel each other out

Answer:

Both piecewise functions have a linear portion and a quadratic portion.  The y-intercepts of both linear pieces are the same, 2.  The quadratics are both open upward, but have different y-intercepts (one at 1, one at 2).  The linear portion of the first function is decreasing, while the linear portion of the second function is increasing.

Step-by-step explanation:

Comparing and contrast of the functions are shown in below.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The given piecewise functions are;

⇒ f (x) = { - x + 2 ; x < 0

         = { x² + 1 ; x > 0

Now, Comparison and contrast of the above piecewise functions are,

The similarities are;

1) Both piecewise functions are linear when x < 0.

2) Both piecewise functions are quadratic when x > 0.

3) The magnitude the slope of the linear part both function are equal.

4) The leading coefficient of the quadratic function are the same.

5) The y-intercept of the linear function are equal, therefore, the linear functions in f(x) and g(x) intersect on the y-axis.

6) The domain of the linear and quadratic functions are the same.

The contrasts (differences) in the function are;

1) The slope of the linear function of g(x) is positive and the slope of the linear function of f(x) is negative.

2) The y-intercept of the quadratic function in f(x) is +1, while the y-intercept of the quadratic function in g(x) is +2.

3) The quadratic function in f(x) and g(x) have graphs that do not intersect.

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Answer:

18 pounds of cashews are needed.

Step-by-step explanation:

Given;

A manager bought 12 pounds of peanuts for $30.

Price of peanut per pound P = $30/12 = $2.5

Price of cashew per pound C = $5

Price of mixed nut per pound M = $4

Let x represent the proportion of peanut in the mixed nut.

The proportion of cashew will then be y = (1-x), so;

xP + (1-x)C = M

Substituting the values;

x(2.5) + (1-x)5 = 4

2.5x + 5 -5x = 4

2.5x - 5x = 4 -5

-2.5x = -1

x = 1/2.5 = 0.4

Proportion of cashew is;

y = 1-x = 1-0.4 = 0.6

For 12 pounds of peanut the corresponding pounds of cashew needed is;

A = 12/x × y

A = 12/0.4 × 0.6 = 18 pounds

18 pounds of cashews are needed.

Answer: H - 46

Step-by-step explanation:

Primeter = 2(l + w)

50 = 2{(3m+2) + (m-5)}

25 = 3m+2 +m -5

25 = 4m -3

m = 28/4 = 7

l = 3m+2 = 23 cm

w = m-5 = 2 cm

Area = l x b

= 23 x 2 = 46 sq. cm.

Answer:

  5

Step-by-step explanation:

To put the equation in standard form, add 6 to both sides.

  x^2 +4x -1 +6 = -6 +6

  x^2 +4x +5 = 0

The new value of "c" (the constant) is 5.

Answer:

C or 5 for me

Step-by-step explanation:

Answer:

  a[1] = 4

  a[n] = -3·a[n-1]

Step-by-step explanation:

The sequence given is not a geometric sequence, since the ratios of terms are -3, -3, 3 -- not a constant.

If we assume that the last given term is supposed to be -108, then the common ratio is -3 and each term is -3 times the previous one. That is expressed in a recursive formula as ...

  a[1] = 4 . . . . . . . . . . .  first term is 4

  a[n] = -3·a[n-1] . . . . . each successive term is -3 times the previous one

Answer:

m = -2/3

Step-by-step explanation:

Slope Formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex]

So,

[tex]m = \frac{-1-1}{9-6}[/tex]

m = -2/3

Answer:

[tex] P(X>8)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] F(x) = 1- e^{-\lambda x}[/tex]

And if we use this formula we got:

[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]

Step-by-step explanation:

For this case we can define the random variable of interest as: "The life of an electric component " and we know the distribution for X given by:

[tex]X \sim exp (\lambda =\frac{1}{8.9}) [/tex]

And we want to find the following probability:

[tex] P(X>8)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] F(x) = 1- e^{-\lambda x}[/tex]

And if we use this formula we got:

[tex] P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070[/tex]

Answer:

Step-by-step explanation:

                              Y

p(x,y)            0          1            2

           0      0.10     0.04     0.02

x          1       0.08     0.2     0.06

            2       0.0      0.14     0.30

a) What is P(X = 1 and = 1)

From the table above we have

P(1,1) = 0.2

b)  Compute P(X ≤ 1 and Y ≤ 1).

[tex]=p(0,0)+p(0,1)+p(1,0)+p(1,1)\\\\=0.1+0.04+0.08+0.2\\\\=0.42[/tex]

C)

Let A ={X ≠ 0 and Y ≠ 0}

p{X ≠ 0 , Y ≠ 0}

= p(1,1) + p(1,2) + p(2,1) + p(2,2)

= 0.20 + 0.06 + 0.14 + 0.30

=0.7

d) The possible X values are in the figure 0,1,2

[tex]p_x(0)=p(0,0)+p(0,1)+p(0,2)\\\\=0.1+0.04+0.02\\\\=0.16\\\\p_x(1)=p(1,0)+p(1,1)+p(1,2)\\\\=0.08+0.2+0.06\\\\=0.34\\\\p_x(2)=p(2,0)+p(2,1)+p(2,2)\\\\=0.06+0.14+0.3\\\\=0.5[/tex]

The possible Y values are in the figure 0,1,2

[tex]p_y(0)=p(0,0)+p(1,0)+p(2,0)\\\\=0.1+0.08+0.06\\\\=0.24\\\\p_y(1)=p(0,1)+p(1,1)+p(2,1)\\\\=0.04+0.2+0.14\\\\=0.38\\\\p_y(2)=p(0,2)+p(1,2)+p(2,2)\\\\=0.02+0.06+0.3\\\\=0.38[/tex]

So the probability of x ≤ 1 is

[tex]p(x\leq 1)=p_x(0)+p_x(1)\\\\=0.34+0.16\\\\=0.50[/tex]

e) From the table

[tex]p_x(x=1,y=1)=p(1,1)\\\\=0.2\\\\p_x(1)=0.34\\\\p_y(1)=0.38[/tex]

we multiply both together

0.34  x 0.38

=0.1292

Therefore p(1,1) is not equal px(1), py(1)

Hence x and y are not independent it is not equal

Answer:

1/12 of a dozen is 1

Step-by-step explanation:

One dozen means 12. If you ask for 1/12 of 12, you multiply 12 and 1/12. You should get 1 as your answer.