Perform the addition or subtraction and use the fundamental identities to simplify. There is more than one correct form of the answer: cos(x) 1 + sin(x) cos(x) 1 - sin(x) 2tan

To get 36 as a result, you can add different numbers, some examples that can work are 18+18, 24+12, 12+12+12, and 8+12+16.

This is a basic mathematical operation that involves calculating the total of two, three, or more numbers. This implies in addition you combine or add numbers and in most cases you get a bigger number. Here are some examples:

5 + 6 = 11

254 + 25 = 279

0.2 + 1.2 = 1.4

Use substraction to find possible numbers. Here is an example:

36 -18 = 18  which means 18 + 18 = 36

36 - 20 = 16 which means 20+16 = 36

Add small numbers until you get to the total. Here is an example:

2 + 4 + 8 + 6 + 3 + 7 + 5+ 1 = 36

Based on this, some numbers that you can use to get 36 are

18+18

24+12

12+12+12

8+12+16

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The value of the function f(x) which is differentiable at all x, at x = 2

Or f(2) = b. 4.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, The function 'f' is differentiable for all x.

Now, f(1) = 2 and f(4) = 8, So, f(x) can be 2x as it is satisfying the conditions.

∴ At x = 2 or f(2) = 2(2) = 4.

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Check the picture below, so that's the triangle hmmmm a bit non-right-triangle or irregular per se, so let's use Heron's formula on this one, so we'll have to first find the length of each side

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ J(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill JK=\sqrt{(~~ 0- (-2)~~)^2 + (~~ 3- 1~~)^2} \\\\\\ ~\hfill JK=\sqrt{( 2)^2 + ( 2)^2} \implies JK=\sqrt{ 8 }[/tex]

[tex]K(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad L(\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill KL=\sqrt{(~~ 3- 0~~)^2 + (~~ -4- 3~~)^2} \\\\\\ ~\hfill KL=\sqrt{( 3)^2 + ( -7)^2} \implies KL=\sqrt{ 58 } \\\\\\ L(\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\qquad J(\stackrel{x_2}{-2}~,~\stackrel{y_2}{1}) ~\hfill LJ=\sqrt{(~~ -2- 3~~)^2 + (~~ 1- (-4)~~)^2} \\\\\\ ~\hfill LJ=\sqrt{( -5)^2 + (5)^2} \implies LJ=\sqrt{ 50 }[/tex]

now let's use those three lengths for Heron's

[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{8}\\ b=\sqrt{58}\\ c=\sqrt{50}\\ s=\frac{\sqrt{8}+\sqrt{58}+\sqrt{50}}{2}\\\\ \qquad \frac{\sqrt{58}+7\sqrt{2}}{2} \end{cases}[/tex]

[tex]A=\sqrt{\frac{\sqrt{58}+7\sqrt{2}}{2}\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{8} \right)\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{58} \right)\left(\frac{\sqrt{58}+7\sqrt{2}}{2}-\sqrt{50} \right)} \\\\\\ ~\hfill {\Large \begin{array}{llll} A=10 \end{array}}~\hfill[/tex]

If the domain of f(x) = x² - 4 is limited to {-1, 0, 1, 2} the greatest value of the range is 0

The range represents the output values

Using the given expression to solve it can be found that the output values are

for x = -1, f(x) = x² - 4 = -1² - 4 = -3

for x = 0,  f(x) = x² - 4 = 0² - 4 = -4

for x = 1, f(x) = x² - 4 = 1² - 4 = -3

for x = 2, f(x) = x² - 4 = 2² - 4 = 0

The greatest value of the range is 0

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The complement of set A is-

A' = {2, 4, 5, 6, 7, 8, 9, 10}

We have -

A' = U - A

A' = {1,2,3,4,5,6,7,8,9,10} - {1,3,5,7}

A' = {2, 4, 5, 6, 7, 8, 9, 10}

Therefor, the complement of set A is -

A' = {2, 4, 5, 6, 7, 8, 9, 10}

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The point estimate for sales when advertising is $3000 is $5412.

Based on the given information, the estimated regression equation is Ŷ = 12 + 1.8x, where Ŷ is the estimated value of the dependent variable (sales), x is the value of the independent variable (advertising), and the constants 12 and 1.8 are the coefficients of the regression equation.

If advertising is $3000, then the point estimate for sales (in dollars) is the value of Ŷ when x = 3000. Substituting this value into the estimated regression equation, we get:

Ŷ = 12 + 1.8 * 3000 = 12 + 5400 = 5412

So, the required amount is $5412.

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The probability distribution of rolling a die is

P(1) = 1/6, P(2) = 1/6, P(3) = 1/6, P(4) = 1/6, P(5) = 1/6, P(6) = 1/6

Given that,

Let T be the outcome of a roll with a fair die.

Then

T = {1, 2, 3, 4, 5, 6}

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability of getting 1 P(1) = 1/6

The probability of getting 2 P(2) = 1/6

The probability of getting 3 P(3) = 1/6

The probability of getting 3 P(3) = 1/6

The probability of getting 4 P(4) = 1/6

The probability of getting 5 P(5) = 1/6

The probability of getting 6 P(6) = 1/6

Therefore, the probability distribution of rolling a die has been found

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Answer:

  f(x) = x³ -9x² +28x -30

Step-by-step explanation:

You want a monic polynomial f of least degree with zeros 3 and 3-i.

For zero x=a, the polynomial has a factor (x -a). Complex zeros come in conjugate pairs, so another one is 3+i. This means the factored form is ...

  f(x) = (x -3)(x -3 +i)(x -3 -i)

  f(x) = (x -3)(x² -6x +9 +1) . . . . . combine the two right factors

  f(x) = x³ -9x² +28x -30

__

Additional comment

When multiplying polynomials mentally, it can be useful to consider the coefficients of the product terms in order of decreasing powers:

  f(x) = (1)x³ +(-3 -6)x² +(10 +(-3)(-6))x +(-3)(10)

Answer:

Write in Standard Form

1. The standard form of a linear equation is

Ax + By = Cx-y=-1

2. x = 16

Ig?

I'm not sure.

The table with the absolute guessing errors should be completed as follows;

Guess                                  2    15   10   8    12   19   20   5    7    9

Absolute guessing error   12    1      4    6    2     5    6    9    7    5

A graph of the guess and absolute guessing error is shown in the image attached below.

Yes, the absolute guessing error is a function of the guess because every guess (input value) has one absolute guessing error (output value).

In Mathematics, the margin of error (MOE) is sometimes referred to as an absolute guessing error and it can be defined as a measure of the difference that exist between an observed value and a true value of the population parameter.

Mathematically, the absolute guessing error for the guesses made by these group of ten friends with respect to the actual number of 14 as follows;

Absolute guessing error = 14 - 2 = 12

Absolute guessing error = 14 - 15 = 1

Absolute guessing error = 14 - 10 = 4

Absolute guessing error = 14 - 8 = 6

Absolute guessing error = 14 - 12 = 2

Absolute guessing error = 14 - 19 = 5

Absolute guessing error = 14 - 20 = 6

Absolute guessing error = 14 - 5 = 9

Absolute guessing error = 14 - 7 = 7

Absolute guessing error = 14 - 9 = 5

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The equation of the regression line of the given data is y = 1.28x + 3.69. By using a scatter plot, the required equation is calculated.

A regression line describes the relationship between the dependent and independent variables of a set of data.

It is given by y = mx + b; where m is the estimated slope of the data and b is the estimated y-intercept of the data.

To find the regression line, we need to draw the scatter plot for the given data.

The coordinates paired from the given data are:

(12, 18.11), (7, 14.08), (11, 17.97), (8, 15.55), (13, 17.93), (4, 7.71), (3, 4.93), (5, 10.77), and (9, 16.68).

The scatterplot for these points is shown below:

From the plot, consider any two points on the line.

Such as (x1, y1) = (3.35, 7.99) and (x2, y2) = (9.61, 16.02)

So, the equation of the regression line is

(y - y1) = {(y2 - y1)/(x2 - x1)} (x - x1)

⇒ (y - 7.99) = {(16.02 - 7.99)/(9.61 - 3.35)} (x - 3.35)

⇒ y - 7.99 = (8.03/6.26)(x - 3.35)

⇒ y - 7.99 = 1.282(x - 3.35)

⇒ y - 7.99 = 1.282x - 4.2947

⇒ y = 1.282x + 3.695

When rounded to two decimals, we get

y = 1.28x + 3.69

Therefore, the equation of the regression line of the given data is y = 1.28x + 3.69.

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1. ZX ≅WY; WXYZ is a parallelogram.           1. Given

2. ZY≅  WX                                                     2. The opposite sides of the                

                                                                      parallelogram are ≅  

There are 4 different kinds of parallelograms, including 3 unique kinds. The four types are rhombuses, squares, parallelograms, and rectangles.

There are not equal sides on a parallelogram. A parallelogram only has equal sides on its opposite sides.

A line segment bisector splits a line segment into two equally sized pieces. It passes through the segment's halfway.

The following justifications are given for the choice made above:

The following is how the two-column proof is presented.

Statement Motive

1. ZX ≅WY; WXYZ is a parallelogram.           1. Given

2. ZY≅  WX                                                     2. The opposite sides of the parallelogram are ≅

3. YX ≅ YX                                                   3. The reflexive quality

4. Δ ZYX ≅ΔWXY                                      4. The SSS thm.

5 . ∠ZYX ≅ ∠WXY                                       5 . CPCTC

6  . m∠ZYX ≅m∠WXY                                 6. Def. of ≅

7.    m∠ZYX + mWXY equal 180°        7. Parallelograms with consecutive s are additional

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The probability that at most 2 of the next 10 callers have to wait more than 8 minutes is the sum of the probabilities of 0, 1, or 2 callers having to wait for more than 8 minutes which is 0.810

The probability that at most 2 of the next 10 callers having to wait can be defined using the expression :

P(X ≤ 2) = P(0) + P(1) + P(2)

Using the individual probabilities given by the histogram attached :

P(X ≤ 2) = 0.181 + 0.345 + 0.284

P(X ≤ 2) = 0.810

Therefore, the probability that at most 2 callers have to wait more than 8 minutes is 0.810

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The following list has six more terms than the preceding one. What does x+z equal if it is -10?

A series of numbers is an ordered list. The three dots signify moving forward in the set pattern. Each digit with in sequence is referred to as a word. The first term in the list is 1, followed by the second by 3, the third by 5, and so on.

t1=X\st2=y\st3=Z

t4=7\st5=13

common distinction Since d=6, t4=t3+d 7=t3+6 t3=7-6 t3=1=Z

Z=1\st3=t2+d

X + Z= (-11) + 1 X+Z = -10 because 1 = t2+6 t2= 1-6 t2= -5 = y y= -5 t2= t1+d -5= t1+6 t1= -5 -6 t1= -11 =X X = -11

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Answer: m= 6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

because slope is the amount of times your changing the line

Not agree with the Mr. Chin's conjecture, because there may be space for the desk in the room but Mr. Chin not have the actual measurement, it may or may not fit the  desk in room of given length and width.

A good guess or an idea about a pattern is a conjecture. Speculate (about something) We can only speculate about the killer's thoughts. speculate that... He speculated that the population might double within a decade. speculate about something She speculated about the existence of a brand-new species.

A mathematical assertion that has not yet been thoroughly established is known as a conjecture. When one observes a pattern that is consistent across many cases, speculations result. However, just because a pattern applies to a lot of cases does not mean that it applies to all of them. To fully accept the mathematical observation, conjectures must be demonstrated. A theorem is formed when a conjecture is thoroughly demonstrated.

A crucial step in solving a problem is making a guess; It's more than just a tool for professionals in math. It is extremely uncommon for a problem's solution to be immediately apparent in everyday problem solving. Instead, the process of solving problems involves looking at the problem structure, looking at the cases, making a guess about the solution, and then proving that guess.

Hence, not agree with Mr. Chin's conjecture.

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The appropriate conclusion at the 5% significance level is b. Reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.

[tex]\bar{x_1}[/tex] = pounds per batch distributor A = 23

[tex]\bar{x_2}[/tex] = pounds per batch distributor B = 18

[tex]\sigma_{1}[/tex] = standard deviation distributor A = 4

[tex]\sigma_{2}[/tex] = standard deviation distributor B = 5

n = sample size = 4

α = significance level = 5% = 0.05

Test statistic is using z test to find the z value from two population, after that we can search p-value and then comparing the p-value with significance level.

If p-value is lower than significance level, the null hypothesis (H0) is accepted. But, if p-value is higher than significance level, the H0 is rejected.

Calculate test statistic by this formula,

Z = [tex]\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma^2_1 + \sigma^2_2}{n}}}[/tex]

= [tex]\frac{23-18}{\sqrt{\frac{4^2 + 5^2}{4}}}[/tex]

= [tex]\frac{5}{\sqrt{\frac{16 + 25}{4}}}[/tex]

= 1.56

Using z table for 1.56, we get 0.9406. Since is right tailed test. So, p value is

p-value = 1 - 0.9406

= 0.0594

Then, p-value is 0.0594 is higher than significance level 0.05. So, H0 is rejected.

Thus, the conclusion is reject H0, we cannot conclude the mean amount of fertilizer per batch distributor A is greater than distributor B.

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35% of the fuel Capacity did not use on this flight.

Step 1: Calculate the change i.e., subtract old value from the new value

Step 2: Divide that change by the old value.

Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

 Percentage change = ((final value - initial value) ÷final value) ×100

Given: Total capacity in a fuel tank of a jet = 200000 liters

Used fuel =130000 liters

% Of fuel which is not used = ((total capacity of fuel tank - used fuel) ÷total capacity of fuel tank) ×100

[tex]=\frac{200000-130000}{200000}*100\\=\frac{70000}{2000}[/tex]

=35%

Therefore, 35% of the fuel capacity did not used in this flight.

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A GENERAL NOTE: CHARACTERISTICS OF THE GRAPH OF THE PARENT FUNCTION  [tex]f(x) = b^{x}[/tex]

-It’s a one-to-one function

-The graph passes through y-intercept of the point (0,1)

-x-intercept: none

-The domain is all real numbers: (−∞,∞)

-The range is y > 0 or (0,∞)

-The graph is increasing

-The graph is asymptotic to the x-axis as x approaches negative infinity

-Horizontal asymptote: y=0

-The graph increases without bound as x approaches positive infinity

-Increasing if b > 1

-Decreasing if b < 1

-The graph is continuous

-The graph is smooth

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Answer:

30 bowls

Step-by-step explanation:

 9 lb   /   (3/10 lb/bowl)   =   9 * 10/3  bowls = 30 bowls

The relationship between x and y is and the constant of variation is 24.

What is inversely proportional?

One kind of proportionality relationship is inverse proportion. If two quantities are inversely related, one will increase while the other will decrease. Building a wall would be an example of an inverse proportion in action.

Given that x and y are inversely proportion.

Assume that the relationship between x and y is

y = k/x where k is constant of variation.

Putting x = 3 and y = 8 in y = k/x :

8 = k/3

Multiply both sides by 3:

k = 8 × 3

k = 24

Putting x = 4 and y = 6 in y = k/x :

6 = k/4

Multiply both sides by 4:

k = 6 × 4

k = 24

The relationship is y = 24/x and the constant of variation is 24.

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Answer:

x and y are not inversely proportional.

Image:

The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.

Given that,

36 local middle school kids were chosen at random to take part in a taste test to choose a new menu item for a cafeteria. The Cajun potato barrels or the macaroni and cheese were the options offered to each pupil. 20 pupils chose the macaroni and cheese from the sampling, while 16 selected the Cajun potato barrels. On a scale from 1 (very dislike) to 9 (very much like), each student was asked to rank the object they selected (extremely like).

We have to find which of the following keeps this study from being an experiment with a sound design.

Each student was given the option of choosing either the macaroni and cheese or the Cajun potato barrels. Because the students' treatments were not distributed at random, those who preferred their cuisine chose it and gave it high marks. As a result, the study has selection bias.

Therefore, The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.

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6/8 is an equivalent fraction to 3/4; 2/6 is equivalent to 1/3; 6/9 is equivalent to 2/3; 10/25 is equivalent to 2/5; 4/16 is equivalent to 1/4; the fraction of 1/3 is equivalent to 2/6; 8/16 is an equivalent fraction to 2/4.

A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. The fractions equivalent to each other have been mentioned above.

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Answer:

See explanation.

Step-by-step explanation:

Given quadratic:

[tex]x^2+140x-1500[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], first find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].

As  a = 1, b = 140 and c = -1500, then:

[tex]\implies a \cdot c=1 \cdot -1500=-1500[/tex]

[tex]\implies b=140[/tex]

Therefore, the two numbers are 150 and -10 as:

[tex]\implies 150 \cdot -10 = -1500[/tex]

[tex]\implies 150+(-10)=140[/tex]

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies x^2+(150-10)x-1500[/tex]

Distribute:

[tex]\implies x^2+150x-10x-1500[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x+150)-10(x+150)[/tex]

Factor out the common term  (x + 150):

[tex]\implies (x+150)(x-10)[/tex]

Therefore you can use midpoint to find the other endpoint  (x2,y2), then by rewriting the (x2,y2)= (2a-x1,2b-y1) .

The exact midpoint between two other plane points needs to be found on occasion. For example, you might seek out a line that splits a particular line segment into two equal halves. This central region is known as the "halfway."

Here,

If you are aware of one endpoint (x1, y1) and the midpoint (a, b), but are unaware of the second endpoint (x2, y 2), you can solve the problem by rewriting the

=> a=[tex]\frac{x1+x2}{2}[/tex]

=> 2a=x1+x2

=>2a-x1=x2

=> b=[tex]\frac{y1+y2}{2}[/tex]

=>2b=y1+y2

=> 2b-y1=y2

So, the unknown endpoint can be found by

(x2,y2)=(2a-x1,2b-y1)

Therefore you can use midpoint to find the other endpoint  (x2,y2), then by rewriting the (x2,y2)= (2a-x1,2b-y1) .

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Liam can conclude that the price and monthly rate of both the gyms are equal.

Given, Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee.

Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75.

we have to mention that what Lian can conclude,

As, substituting the first equation in the second one Liam got the price which is same in both the gyms.

So, Liam can conclude that the price and monthly rate of both the gyms are equal.

Hence, Liam can conclude that the price and monthly rate of both the gyms are equal.

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Answer:

y=x^2 + 1

Step-by-step explanation: the second parabola is only raised by 1 unit up, therefore the entire function shifts upwards by 1.