Determine the domain of the function. f as a function of x is equal to the square root of x plus three divided by x plus eight times x minus two.

All real numbers except -8, -3, and 2
x ≥ 0
All real numbers
x ≥ -3, x ≠ 2

Answer:

1/6

Step-by-step explanation:

The probability of even number is 1/2. The probability of number greater than 4 is 1/3, because only 5 and 6 are greater than 4.

Multiply these two values

1/2*1/3= 1/6

Answer:

Step-by-step explanation:

An equilateral triangle is a triangle that has all of its sides equal. Let a, b and c be the sides of the equilateral triangle. Since all the sides are equal, then

a = b = c.

The perimeter of the triangle is the sum of all the sides of the triangle.

P  = a + b+ c

GIVEN THE PERIMETER OF THE EQUILATERAL TRIANGLE AS P = 15 x + 30 units and a = b = c, then;

15 x + 30 = a + b + c

15 x + 30 = a + a + a (since all sides are equal)

15 x + 30 = 3a

3a = 15 x + 30

3a = 3(5x+10)

Dividing both sides by 3 will give;

3a/3 =   3(5x+10)/3

a = 5x+10

Hence, the length of one side of the equilateral triangle is 5x + 10 units.

Answer:

D.

Step-by-step explanation:

Edge 2020

Answer:  103 adult tickets

Step-by-step explanation:

Adult tickets (a) = a

Student tickets (s) = 2a

Total = 309

a + 2a = 309

     3a = 309

      a = 103

Answer:

Step-by-step explanation:

Total tickets sold = 309

Let the number of adult tickets sold be x

Let the number of student tickets sold be 2x

Adult tickets + student tickets = 309

[tex]x + 2x = 309[/tex]

Collect like terms

[tex] 3x = 309[/tex]

Divide both sides of the equation by 3

[tex] \frac{3x}{3} = \frac{309}{3} [/tex]

Calculate

[tex]x = 103[/tex]

Hence, 103 adult tickets were sold.

Hope this helps..

Good luck on your assignment...

Answer:

1/6

Step-by-step explanation:

As we already know that selected bulb is defective the required probability doesn't depend on functional bulbs at all.

The probability, that selected defective bulb is from Box2 is number of defective bulbs in Box 2  divided by total number of defective bulbs.

P(defective in box 2)= N(defective in box 2)/N(defective total)

As we know there is only 1 defective lamp in box 2.

So N(defective in box 2)=1

Total number of defective bulbs is Box1- 2 defective  bulbs,  box2- 1 defective bulbs, box3 - 3 defective bulbs. Total are 6 defective bulbs.

So N(defective total)=6

So P(defective in box 2)=1/6

Answer:

( A -c) /B =t

Step-by-step explanation:

A=Bt+c

Subtract c from each side

A-c=Bt+c-c

A -c = Bt

Divide each side by B

( A -c) /B = Bt/B

( A -c) /B =t

Answer:

Hey there!

A=Bt+c

A-c=Bt

t=(a-c)/B

Hope this helps :)

Answer:

The level of significance to be used is α = 0.0025

Step-by-step explanation:

Here, we are interested in calculating the the level of significance which at most must be used for each of the hypothesis test

We proceed as follows;

P(type 1 error) = α

From the question, n = number of hypotheses = 20

P( of one or more type one error) ≤ 0.05

1- P(no type one error) ≤ 0.05

Hence;

1- (1-α)^20 ≤ 0.05

(1-α)^20 ≥ 0.95

1- α ≥ 0.997438621223

α ≤ 0.00256

Thus α = 0.0025

Answer:

[tex]12 {y}^{9} - 6 {y}^{5} + 4 {y}^{2} + 21[/tex]

Step-by-step explanation:

divide each term by 2y^3

Multiply through by the least common denominator.

Answer: { 0.5995, 0.8025 }

Step-by-step explanation:

Given that

                   Estimates          Std. Error         t value            Pr(>/t/)

Intercept:         -90.020          16.702           -5.390             0.000

length    :           0.701             0.044            15.798              0.000

Now using the given information to compute a 95% confidence interval for the slope:

We use the formula

β₁ ± tₐ/₂, ₙ₋₂ × ∝β₁

So we know that number of values (n) = 10

therefore error of degree of freedom df = n -2 = (10-2) = 8

Level of significance α ( 1 - 0.95 ) = 0.05

so tₐ/₂, ₙ₋₂ = t ₍₀.₀₅/₂, ₁₀₋₂

t ₀.₀₂₅, ₈ = 2.306 (critical value)

From the given table ( regression analysis output)

slope regression β₁ = 0.701

The standard error of the slope is Sβ₁  = 0.044

Let “the maximum size of salmonids consumed by a northern squaw fish” be the response variable and “squawfish length” be the explanatory variable.

The 95% confidence interval for the slope of the regression is:

β₁ ± tₐ/₂, ₙ₋₂ × ∝β₁ = 0.701 ± 2.306 (0.044)

= 0.701 ± 0.101464

= { 0.701 - 0.101464, 0.701 + 0.101464 }

= { 0.599536, 0.802464 } ≈  {0.5995, 0.8025 }

The confidence interval of the slope is (0.599, 0.803)

The sample size is given as:

[tex]\mathbf{n = 10}[/tex]

The confidence interval is given as:

[tex]\mathbf{CI = 95\%}[/tex]

Start by calculating the degrees of freedom

[tex]\mathbf{df = n - 2}[/tex]

So, we have:

[tex]\mathbf{df = 10 - 2}[/tex]

[tex]\mathbf{df = 8}[/tex]

The level of significance is calculated as:

[tex]\mathbf{\alpha = 1 - CI}[/tex]

So, we have:

[tex]\mathbf{\alpha = 1 - 95\%}[/tex]

[tex]\mathbf{\alpha = 0.05}[/tex]

The critical value at 0.05 level of significance and 8 degrees of freedom is:

[tex]\mathbf{t_{\alpha} =2.306}[/tex]

The confidence interval of the slope is then calculated as:

[tex]\mathbf{CI = \beta_1 \pm t_\alpha \times S\beta_1}[/tex]

From the question, we have:

[tex]\mathbf{S\beta_1 = 0.044}[/tex] --- standard error of the slope

[tex]\mathbf{\beta_1 = 0.701}[/tex] -- the slope

So, the equation becomes

[tex]\mathbf{CI = \beta_1 \pm t_\alpha \times S\beta_1}[/tex]

[tex]\mathbf{CI = 0.701 \pm 2.306 \times 0.044}[/tex]

[tex]\mathbf{CI = 0.701 \pm 0.102}[/tex]

Split

[tex]\mathbf{CI = (0.701 - 0.102,0.701 + 0.102)}[/tex]

[tex]\mathbf{CI = (0.599,0.803)}[/tex]

Hence, the confidence interval of the slope is (0.599, 0.803)

Read more about confidence intervals at:

https://brainly.com/question/24131141

Answer:

Graph is attached below

Step-by-step explanation:

You first need to plot any two points on the coordinate plane(you can also do more than two points to make it more accurate). Then, using a ruler connect the points and extend the line outwards.

The plotted straight line is as shown in below graph.

Given straight line equation is y = x + 2

To plot a straight line, take two different values of x which output different values of y. Then plot those points in the graph.

After plotting those two points, you connect both dots with straight line and extend that line infinitely from both endpoints.

Example, take x = 1 and x = 2 for straight line y = x + 2

Then we get:

For x = 1, y = 1 + 2 = 3

For x = 2, y = 2 + 2 = 4

The plot of points (1,3) and (2,4) and the straight line y = x + 2 is shown below.

Learn more here:

https://brainly.com/question/959487

Answer:

7.7cm

Step-by-step explanation:

Area of a rectangle is expressed as

A = Length × Width

A = LW

Let dL and dW be the errors in the measurements.

If there is an error of at most 0.1cm each in the measurement, then dL = dW = 0.1cm.

The area of the rectangle with error will be expressed as A = LdW + WdL

Given L = 27cm and W = 50cm

A = 27(0.1)+50(0.1)

A = 2.7+5.0

A = 7.7cm

Hence, the maximum error in the calculated area of the rectangle is 7.7cm

Answer:

The answer is A.

Step-by-step explanation:

In a linear equation, y = mx + b, m is represented as gradient (slope) and b is the y-intercept.

So for this question, m is 2/3 and b is 1.

Answer:

x=7

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

The given system of equations has one solution.

Hence option A is correct.

The given system is

4x-2y=8

2x+y=2

Since we know that,

For system

a₁x + b₁ y = c₁

a₂x + b₂y = c₂

If

a₁/a₂ = b₁/b₂ = c₁/c₂   then it has an infinite solution

a₁/a₂ ≠ b₁/b₂              then unique solution

a₁/a₂ = b₁/b₂ ≠ c₁/c₂   then no solution

Here we have

a₁ =  4, b₁ = -2 and c₁ = 8

a₂ = 2, b₂ = 1  and  c₂ = 2

Now since

a₁/a₂ ≠ b₁/b₂   ⇒ 4/2  ≠ -2/1

                      ⇒ 2 ≠ -2

Hence, the given system has a unique solution.

Learn more about system of equations at:

brainly.com/question/14323743

#SPJ2

Answer:

a. k = 3

b. N = 27

c. n = 9

Step-by-step explanation:

Given that,

Source :          sS                 dF            mS                F

Between:                            k -1        sSB/k-1             mSB

within                                  N-K        sSw/N-K           mSw

total                                     N-1

Therefore F ( 2, 24 ) = F ( K - 1, N - K )

so K - 1 = 2

K = 2 + 1

K = 3

N - K = 24

N - 3 = 24

N = 24 + 3

N = 27

married, single and divorced are equal sizes

so n = N/3

n = 27 / 3

n = 9

a. k = 3

b. N = 27

c. n = 9

Answer:

Hello There!

~~~~~~~~~~~~~~~~~~~`

3 − x = 2 =

X = 1

Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helped you. Brainliest would be nice!

Answer: x = 1 / 1 = x.

Step-by-step explanation:

3 - x = 2

First, since you can't subtract x from 3, we find ways to subtract 2 from 3.

So, we write the 3 and attach (-) minus/negative sign to the 3 with 2. Because when a number crosses the equal sign and it is negative, it becomes positive and when it is positive, it becomes negative.

And 2 will cross the equal sign so,it will be (-) just like: -2. And -x will cross the equal sign so it will be x. Let's solve it with the steps above:

3 - x = 2

3 - 2 = x

1. = x

OR

3 - x = 2

-x = 2 - 3

-x/- = -1/-

So, negative will cancel negative.

x =1.

Please mark me as the brainliest!!

Thanks!!

Notice that C has a clockwise orientation. By Green's theorem, we have

[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\iint_D\left(\frac{\partial(xy+x\cos x)}{\partial x}-\frac{\partial(y\cos x-xy)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]

where D is the triangule region with C as its boundary, given by the set

[tex]D=\{(x,y)\mid0\le x\le2\land0\le y\le8-4x\}[/tex]

So we have

[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}((y+\cos x-x\sin x)-(\cos x-x\sin x))\,\mathrm dy\,\mathrm dx[/tex]

[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}y\,\mathrm dy\,\mathrm dx=\boxed{-\dfrac{64}3}[/tex]

Answer:

7

Step-by-step explanation:

Take the amount of money and divide by the cost per fish

46/6 =7 with 4 dollars remaining

She can buy 7 goldfish

Answer:

7

Step-by-step explanation:

7 x 6 = 42

Greetings from Brasil...

X = 2 liter container

Y = 3 liter container

the total of containers are:

X + Y = 400

the capacity of the containers is

2X + 3Y = 1100

Assembling the equation system

2X + 3Y = 1100

X + Y = 400       x(-2)

2X + 3Y = 1100

-2X  -2Y = - 800    

X + Y = 400    so

X + 300 = 400

X = 400 - 300

----------------------------------------------------------

BR:

Observe que:

1 vasilha de 2L = 1 × 2 = 2L

2 vasilhas de 2L = 2 × 2 = 4L

3 vasilhas de 2L = 3 × 2 = 6L

X vasilhas de 2L = X × 2 = 2X litros

.....

1 vasilha de 3L = 1 × 3 = 2L

2 vasilhas de 3L = 2 × 3 = 4L

3 vasilhas de 3L = 3 × 3 = 6L

X vasilhas de 3L = X × 3 = 3X litros

Logo 2X + 3Y = 1100

Existem X e Y vasilhas que num total sao 400, logo

X + Y = 400

Answer:

A: (–0.3, 2.1)

Answer:a

Step-by-step explanation:

Answer:

15 people

Step-by-step explanation:

since Raul and his friends each weigh 1/20 ton,

and the total weight reads 3/4 ton

The total number pf people on the scale will be:

The total weight of Raul and his friends divided by their individual weight

==> (3/4 ton) ÷ (1/20 ton)

= 3/4 X 20/1 = 15 people

Answer:

I can find the total number of people by dividing the total weight by the weight of one person.

This is the plato answer, I hope this is the answer youre looking for! :))

Answer:

10

Step-by-step ex1planation:

Answer:

[tex]w=\frac{t+8}{3}[/tex]

Step-by-step explanation:

[tex]3w - 8 = t[/tex]

Add 8 on both sides.

[tex]3w - 8 + 8 = t + 8[/tex]

[tex]3w = t + 8[/tex]

Divide both sides by 3.

[tex]\frac{3w}{3} =\frac{t+8}{3}[/tex]

[tex]w=\frac{t+8}{3}[/tex]

The value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.

It is defined as the combination of constants and variables with mathematical operators.

We have an equation:

3w - 8 = t

To solve for w in terms of t

Make the subject as w

In the equation:

3w - 8 = t

Add 8 on both sides:

3w - 8 + 8 = t + 8

3w = t + 8

Divide by 3 on both sides:

3w/3 = (t + 8)/3

w = (t + 8)/3

The equation represents a function of w in terms of t

As we know, the function can be defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Thus, the value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.

Learn more about the expression here:

brainly.com/question/14083225

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Answer:

the first blank is 2, the second one is 1

Answer:

Yellow box #1=2

Yellow box #2=1

Step-by-step explanation:

#1) 8-6=2

#2)8-7=1

I believe the value is negative 4. If not, well, try any negative below that, such as -5,6,7,8, etc.

Answer:

y is less than -3

Step-by-step explanation:

To do this you would just subtract 9 from both sides so you get -y is greater than 3. Since you cannot have y as a negative number you will divide -1 from both sides but when you do that you will have to flip the sign so you get y is less than -3.

Step-by-step explanation:

Hey, there !!!

According to your question,

total c.p = 532.50

tax rate =6%

let original price be x.

now,

total c.p = x + tax rate of x.

or, 532.50= x+ (6/100) × x

or, 532.50 = 106x/100

or, 53200 = 106x

or, x= 53200/106

Therefore, the original price was 501.88.

Hope it helps...

Answer:

try 3x=30 or 10

Step-by-step explanation:

Answer:

f(x) = -(x + 1)² - 2

Step-by-step explanation:

f(x) = a(x - h)² + k

-6 = a(1 - -1)² + -2

-6 = a(4) -2

-4 = 4a

a = -1

f(x) = -(x + 1)² - 2

Answer:

Step-by-step explanation:

Using chain rule to find the partial deriviative of z with respect to s and t i.e ∂z/∂s and ∂z/∂t, we will use the following formula since it is composite in nature;

∂z/∂s = ∂z/∂x*∂x/∂s +  ∂z/∂y*∂y/∂s

Given the following relationships z = x⁸y⁹, x = s cos(t), y = s sin(t)

∂z/∂x = 8x⁷y⁹, ∂x/∂s = cos(t), ∂z/∂y = 9x⁸y⁸ and ∂y/∂s = sin(t)

On substitution;

∂z/∂s = 8x⁷y⁹(cos(t)) + 9x⁸y⁸ sin(t)

∂z/∂s = 8(scost)⁷(s sint)⁹(cos(t)) + 9(s cost)⁸(s sint)⁸ sin(t)

∂z/∂s = (8s⁷cos⁸t)s⁹sin⁹t + (9s⁸cos⁸t)s⁸sin⁹t

∂z/∂s = 8s¹⁶cos⁸tsin⁹t + 9s¹⁶cos⁸tsin⁹t

∂z/∂s = 17s¹⁶cos⁸tsin⁹t

∂z/∂t =  ∂z/∂x*∂x/∂t +  ∂z/∂y*∂y/∂t

∂x/∂t = -s sin(t) and ∂y/∂t = s cos(t)

∂z/∂t  = 8x⁷y⁹*(-s sint) + 9x⁸y⁸* (s cos(t))

∂z/∂t = 8(scost)⁷(s sint)⁹(-s sint) + 9(s cost)⁸(s sint)⁸(s cos(t))

∂z/∂t = -8s¹⁷cos⁷tsin¹⁰t + 9s¹⁷cos⁹tsin⁸t

∂z/∂t = -s¹⁷cos⁷tsin⁸t(8sin²t-9cos²t)

Step-by-step explanation:

8.x×8-12=50

8x-12=50

9.1/2x>or=100

10.2 whole number5/9-x=31

Answer: Franklin could end at 4 different points.

Step-by-step explanation:

Given: Franklin the fly starts at the point (0,0) in the coordinate plane.

At each point, Franklin takes a step to the right, left, up, or down.

i.e. there are 4 choices of directions [A coordinate plan has 4 quadrants]

If he moves 10 steps, then the number of different points Franklin could end up at =  choices of directions

= 4

Hence, Franklin could end at 4 different points.