Find the union and interesection of each of the following A={3,6,9,12}, B ={6,8,9}

Answer:

25

Step-by-step explanation:

Let x represent the number of $50 jackets that were sold, and let y represent how many $30 jackets were sold.

50x + 30y = 2360

y = x + 12

Solve by substitution by substituting the second equation into the first one. Then, solve for x:

50x + 30y = 2360

50x + 30(x + 12) = 2360

50x + 30x + 360 = 2360

80x + 360 = 2360

80x = 2000

x = 25

So, 25 $50 jackets were sold.

Answer:

Step-by-step explanation:

a) First differences of the f(x) values in the table are ...

  19 -13 = 6, 37 -19 = 18, 91 -37 = 54, 253 -91 = 162

The second differences are not constant:

  18 -6 = 12, 54 -18 = 36, 162 -54 = 108

But, we notice that both the first and second differences have a common ratio. This is characteristic of an exponential function. The common ratio is 18/6 = 3, so the parent function is 3^x.

__

b) Translating a function down 4 units subtracts 4 from each y-value. The values of f(x) in the table would be ...

  9, 15, 33, 87, 249

__

c) The x-values of the function stay the same for a vertical translation, so the points in the table of the transformed function are ...

  (x, f(x)) = (1, 9), (2, 15), (3, 33), (4, 87), (5, 249)

Answer: I think this is it:

The parent function of the function represented in the table is exponential. If function f was translated down 4 units, the f(x)-values would be decreased by 4. A point in the table for the transformed function would be (4,87)

Step-by-step explanation: I got it right on Edmentum!

Answer: 72

Step-by-step explanation:

no. of family pizzas-  2

cost of one family pizza - 24 each

total cost for family pizza -48

one family pizza's cost equals to 3 small pizzas

which is cost of 3 small pizzas = 24

therefore, total cost= 24+48

=72

Step-by-step explanation:

csc θ sin θ

(1 / sin θ) sin θ

1

The simplified value of the given expression comes to be 1.

The given expression is:

[tex]cosec\theta.sin\theta[/tex]

The trigonometric ratio [tex]cosec\theta[/tex] is the ratio of the hypotenuse to the opposite side. It is the inverse of [tex]sin\theta[/tex].

[tex]cosec\theta=\frac{1}{sin\theta}[/tex]

We know that [tex]cosec\theta=\frac{1}{sin\theta}[/tex]

So [tex]cosec\theta.sin\theta[/tex]

[tex]=\frac{1}{sin\theta} .sin\theta[/tex]

=1

So, the simplified value is 1.

Hence, the simplified value of the given expression comes to be 1.

To get more about trigonometric ratios visit:

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What's the question? I can try and help..

Answer:

9

Step-by-step explanation:

The mean squared error (MSE)of a set of observations can be calculated using the formula :

(1/n)Σ(Actual values - predicted values)^2

Where n = number of observations

Steps :

Error values of each observation (difference between actual and predicted values) is squared.

Step 2:

The squared values are summed

Step 3:

The summation is the divided by the number of observations

The difference between the actual and predicted values is known as the ERROR.

(1/n)Σ(ERROR)^2

n = 3

Error = +3, +3, - 3

MSE = (1/3)Σ[(3)^2 + (3)^2 + (-3)^2]

MSE = (1/3) × [9 + 9 + 9]

MSE = (1/3) × 27

MSE = 9

Answer: Midline equation: y = -7

Step-by-step explanation: This function is a sinusoidal function of the form:

y = a.cos(b(x+c))+d

Midline is a horizontal line where the function oscillates above and below.

In the sinusoidal function d represents its vertical shift. Midline is not influenced by any other value except vertical shift. For that reason,

Midline, for the function: [tex]h(x) = -4cos(5x-9) - 7[/tex] is y=d, i.e., [tex]y=-7[/tex]

Answer:

y=-7

Step-by-step explanation:

Answer:

$546

Step-by-step explanation:

Given

Amount, P = $650

Rate, R = 12%

Period, T = 7 months

Required

Determine the amount paid.

We'll solve this using simple interest formula, as thus

[tex]I = \frac{PRT}{100}[/tex]

Substitute values for T, R and P

[tex]I = \frac{\$650 * 12 * 7}{100}[/tex]

[tex]I = \frac{\$54600}{100}[/tex]

[tex]I = \$546[/tex]

Hence, Henry's withdrawal is $546

Answer:

1526.04

Step-by-step explanation:

the formula for calculating the volume of cone is

V=πr^2(h/3)

Thus,

V = (3.14)(9)^2(18/3)

V = (3.14)(81)(6)

V = 1536.04 yd^3

Rounding off to the nearest tenth, we get

V = 1536 yd^3

Answer:

$540.98

Step-by-step explanation:

future value= $ 50,000

number of deposits (n)= 8*12 = 96

rate (r) = 4% per month

= 4÷12 per annum

= 0.33% p.a

i = 0.33÷100

= 0.0033

We know,

Future value of annuity = P÷i [ (1 + i)^n - 1 ]

$50,000 = P÷ 0.0033 [ ( 1+0.0033)^96 - 1]

$50,000 * 0.0033=P [ (1.0033)^96 - 1 ]

$165 = P*0.305

P = $165÷0.305

P = $ 540.98

Rough::

let x= 1.0033)^96

log x = 96 * log (1.0033)

log x = 0.1156

x = Antilog (0.1156)

= 1.305

1.305 - 1 = 0.305

Answer:

x = 66.74715005725

Step-by-step explanation:

First you bring over the added variable. 0.194185, and subtract it from 66. Then you divide your difference by 0.985897. This gives you 66.74715005725

Answer:

Step-by-step explanation:

The first one is true. There can't be any other choice.

a = 5959599949 b = 0 then a*b = 0 because b = 0

The Second one is also true, although you may stall trying to figure out what is meant.

Suppose the angle to start with is 30 degrees

There are two angles that are supplementary to this angle. They can only be 180 - 30 = 150 each. Therefore they are equal to each other. This happens because supplementary angles must add to 180 and nothing else.

The third one is false. You can think of states like Montana which has 3 syllables and Wyoming which also has 3. Texas has two. But guess what? Maine only has 1.

The last one is also false. If you square an even number, you get an even number. Add 1 and you get an odd number. 4^2 = 16 Add 1 you get 17. Seventeen is odd.

Answer:

5*sqrt3

Step-by-step explanation:

The vector AB= (0-(-1), 4-2,6-3) AB= (1,2,3)

The modul of AB is sqrt(1^2+2^2+3^2)= sqrt14

The vector AC is (1-(-1), 1-2, 2-3)= (2,-1,-1)

The modul of B is sqrt (2^2+(-1)^2+(-1)^2)= sqrt6

AB*AC= modul AB*modul AC*cosA

cosA=( 1*2+2*(-1)+3*(-1))/ sqrt14*sqrt6= -3/sqrt84=

sinB= sqrt (1- (-3/sqrt84)^2)= sqrt75/84= sqrt 25/28= 5/sqrt28

s= modul AB*modul AC*sinA= sqrt14*sqrt6* 5/ sqrt28= 5*sqrt3

Answer:

A. 70.69 is the correct answer.

Step-by-step explanation:

Given:

Two lines:

[tex]3x - 4y + 5 = 0 \\2x + 3y -1 = 0[/tex]

To find:

Angle between the two lines = ?

Solution:

Acute Angle between two lines can be found by using the below formula:

[tex]tan \theta = |\dfrac{(m_1 - m_2)}{ (1 + m_1m_2)}|[/tex]

Where [tex]\theta[/tex] is the acute angle between two lines.

[tex]m_1, m_2[/tex] are the slopes of two lines.

Slope of a line represented by [tex]ax+by+c=0[/tex] is given as:

[tex]m = -\dfrac{a}{b }[/tex]

So,

[tex]m_1 = -\dfrac{3}{- 4} = \dfrac{3}{4}[/tex]

[tex]m_2 = -\dfrac{2}{ 3}[/tex]

Putting the values in the formula:

[tex]tan \theta = |\dfrac{(\dfrac{3}{4}- (-\dfrac{2}{3}))}{ (1 + \dfrac{3}{4}\times (-\dfrac{2}{3 }))}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{3}{4}+\dfrac{2}{3}}{ (1 -\dfrac{1}{2})}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{17}{12}}{ \dfrac{1}{2}}|\\\Rightarrow tan \theta = \dfrac{17}{6}\\\Rightarrow \theta = tan^{-1}(\frac{17}{6})\\\Rightarrow \theta = \bold{70.69^\circ}[/tex]

So, correct answer is A. 70.69

Answer:

-1 8/9

Step-by-step explanation:

w + ( - x)

w = -5/9

z = 4/3

Input:

-5/9 + ( -4/3)

-5/9 - 4/3

-4/3 * 3/3 = -12/9

-5/9 - 12/9 = -17/9 = -1 8/9

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

Total expected amount = $0.04375

Step-by-step explanation:

We need to calculate probability of getting heads on every combination of coin tosses

HHH = 1/8 = 3 heads

HHT = 1/8 = 2 heads

HTH = 1/8 = 2 heads

HTT = 1/8 = 1 head

THH = 1/8 = 2 heads

THT = 1/8 = 1 head

TTH = 1/8 = 1 head

TTT = 1/8 = 0 head

So the probability of 3 heads is 1/8 and the amount is (1/8)* 0.14 = $0.0175

Probability of 2 heads is 3/8 and the amount is (3/8) * 0.06 = $0.0225

Probability of 1 head is 3/8 and amount is (3/8) * 0.01 = $0.00375

Total expected amount = 0.00375 + 0.0225 + 0.0175

Total expected amount = $0.04375

Answer:

11.422

Step-by-step explanation:

[tex]78.2 - 66.778 \\ = 11.422[/tex]

y=mx+b is the general formula of linear equation

y=-2x+5+3x+2

y=1x+7

m=1

b=7

Linear equation given in the question is,

2 + 3x + 5 - 2x = y

To simplify this equation further,

        (2 + 5) + (3x - 2x) = y

         7 + x = y

Now compare this linear equation with the slope-intercept form of the linear equation,

y = mx + b

Here, m = slope of the line'

b = y-intercept

By comparing the equations,

m = 1

b = 7

Learn more,

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Answer:

Step-by-step explanation:

102-8= 94

94/2= 47

Jiri is 47 years old.

We have 26 letters and 3 slots to fill. We can reuse a letter if it has been picked, so we have 26^3 = 26*26*26 = 17,576 different three letter "words". I put that in quotes because a lot of the words aren't actual words, but more just a sequence of letters.

Based on the fact that you asked this three times and got the same answer three times, I suspect the interpretation made by the users that posted those answers was incorrect, and that you meant to ask about dividing in base 2.

We have

111001₂ = 1×2⁵ + 1×2⁴ + 1×2³ + 1×2⁰ = 57

1101₂ = 1×2³ + 1×2² + 1×2⁰ = 13

and 57/13 = (4×13 + 5)/13 = 4 + 5/13.

4 = 2² is already a power of 2, so we have

111001₂/1101₂ = 1×2² + 5/13

we just need to convert 5/13. To do this, we look for consecutive negative powers of 2 that 5/13 falls between, then expand 5/13 as the sum of the smaller power of 2 and some remainder term. For instance,

• 1/4 < 5/13 < 1/2, and

5/13 - 1/4 = (20 - 13)/52= 7/52

so that

5/13 = 1/4 + 7/52

or

5/13 = 1×2 ⁻² + 7/52

Then a partial conversion into base 2 gives us

111001₂/1101₂ = 1×2² + 1×2 ⁻² + 7/52

111001₂/1101₂ = 100.01₂ + 7/52

Continuing in this fashion, we find

• 1/8 < 7/52 < 1/4, and

7/52 = 1/8 + 1/104

==>   111001₂/1101₂ = 100.011₂ + 1/104

• 1/128 < 1/104 < 1/64, and

1/104 = 1/128 + 3/1664

==>   111001₂/1101₂ = 100.0110001₂ + 3/1664

• 1/1024 < 3/1664 < 1/512, and

3/1664 = 1/1024 + 11/13312

==>   111001₂/1101₂ = 100.0110001001₂ + 11/13312

• 1/2048 < 11/13312 < 1/1024, and

11/13312 = 1/2048 + 9/26624

==>   111001₂/1101₂ = 100.01100010011₂ + 9/26624

• 1/4096 < 9/26624 < 1/2048, and

9/26624 = 1/4096 + 5/53248

==>   111001₂/1101₂ = 100.011000100111₂ + 5/53248

and so on.

It turns out that this pattern repeats, so that

[tex]\displaystyle \frac{111001_2}{1101_2} = 100.\overline{011000100111}_2[/tex]

Answer:

y = -1/6x - 1.

Step-by-step explanation:

I  am assuming that the point id (6, -2).

The slope of the required line = -1/6.

y - y1 = m(x - x1) where m = slope and x1,y1 is a point on the line so we have

y - (-2) = -1/6( x- 6)

y + 2 = -1/6x + 1

y = -1/6x - 1.

Answer:

[tex]\boxed {\boxed { \sf 12 \ inches}}[/tex]

Step-by-step explanation:

The area of a triangle can be calculated using the following formula.

[tex]a=\frac{1}{2} bh[/tex]

The area of the triangle is 24 square inches and the base is 4 inches long.

Substitute the values into the formula.

[tex]24 \ in^2 = \frac {1}{2} * 4 \ in * h[/tex]

Multiply on the right side of the equation.

[tex]24 \ in ^2 = ( \frac{1}{2} * 4 \ in ) * h[/tex]

[tex]24 \ in ^2 =2 \ in *h[/tex]

We are solving for the height of the triangle, so we must isolate the variable h. It is being multiplied by 2 inches. The inverse of multiplication is division, so we divide both sides by 2 inches.

[tex]\frac { 24 \ in ^2 }{2 \ in }= \frac{ 2 \ in *h}{ 2 \ in}[/tex]

[tex]\frac { 24 \ in ^2 }{2 \ in }= h[/tex]

[tex]12 \ in = h[/tex]

The height of the triangle is 12 inches.

Answer:

The value of x= 20

Step-by-step explanation:

I believe the question is ,"60% of x is us, find x"

So , if the percentage of x to 60 is 12.

60/100 * x = 12

0.6 *x = 12

Dividing both sides by 0.6

X= 12/0.6

X= (12/6) *(10)

X= 2*10

.x= 20

The value of x= 20

Answer:

The 99% confidence interval is  [tex]71.67 < \mu < 78.33[/tex]

Step-by-step explanation:

From the question we are told that

     The sample  size  is  [tex]n = 15[/tex]

      The  sample  mean is  [tex]\= x = 75[/tex]

        The  standard deviation is  [tex]s = 5[/tex]

 Given that confidence is  99%  then the level of significance is mathematically represented as

              [tex]\alpha = 100 - 99[/tex]

             [tex]\alpha = 1\%[/tex]

             [tex]\alpha = 0.01[/tex]

Next we obtain the critical values of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table

   The  value is

                  [tex]Z_{\frac{ \alpha }{2} } = 2.58[/tex]

Generally the margin for error is mathematically represented as

            [tex]E = Z_{\frac{ \alpha }{2} } * \frac{ s}{ \sqrt{n} }[/tex]

=>         [tex]E = 2.58 * \frac{ 5}{ \sqrt{15} }[/tex]

=>         [tex]E = 3.3307[/tex]

   The  99% confidence interval is mathematically represented as

             [tex]\= x -E < \mu < \= x +E[/tex]

=>          [tex]75 - 3.3307 < \mu <75 + 3.3307[/tex]

=>          [tex]71.67 < \mu < 78.33[/tex]

Answer:

{-3, 1, 5, 6}

Step-by-step explanation:

The domain of a relation is the x-values represented in that function. In a coordinate pair, the x-value comes first, so all of the first numbers in each of the pairs are part of the domain. When writing domain, it should always be in the least to greatest order. Therefore, the domain is {-3, 1, 5, 6}. Since this relation is a function, none of the x-values will repeat.

Answer:

A. 6²¹

Step-by-step explanation:

When you have a number raised to the power in that form, you have to multiply the powers:

(6⁷)³

7×3 = 21

(6⁷)³ = 6²¹

Answer:

A. 6 raise to 21

Step-by-step explanation:

its a formula if:

a raise to m whole raise to n = a raise to m×n

so here

          6 raise to 7 × 3

         that is 6 to the power of 21

Answer:

$18.37

Step-by-step explanation:

$16.70 × 1.10 = $18.37

or

$16.70 × 0.10 = $1.67

$16.70 + 1.67 = $18.37

Without knowing what Juan's exact steps were, it's hard to say what he did wrong. The least you could say is that his solution is simply not correct.

4 sin²(θ) - 1 = 0

==>   sin²(θ) = 1/4

==>   sin(θ) = ±1/√2

==>   θ = π/4, 3π/4, 5π/4, 7π/4