A restaurant offers a $12 dinner special that has 5 choices for an appetizer, 13 choices for an entrée, and 4 choices for a dessert. How many different meals are available when you seject an appetizer, an entrée, and a dessert?

Answer:

Step-by-step explanation:

Perimeter is the sum of side lengths

Let's find the sides first

Perimeter is

Answer:

8

Step-by-step explanation:

18(4/3)=24

6(4/3)=h

h=8

Answer:

h = 8

Step-by-step explanation:

These shapes are similar, so you can set up a proportion to solve for h:

\(\frac{24}{18}= \frac{h}{6}\)

Cross multiply:

\(\frac{144}{18h}\)

Divide 144 by 18:

h = 8

Answer:

\(x = \frac{15}{2} \\\\x =7\frac{1}{2}\)

Step-by-step explanation:

\(3\left(2x-1\right)=4x+12\\\\\mathrm{Expand\:}3\left(2x-1\right):\quad 6x-3\\6x-3=4x+12\\\\\mathrm{Add\:}3\mathrm{\:to\:both\:sides}\\6x-3+3=4x+12+3\\\\Simplify\\6x=4x+15\\\\\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}\\6x-4x=4x+15-4x\\\\Simplify\\2x =15\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\frac{2x}{2}=\frac{15}{2}\\\\Simplify\\x = 15/2\)

Answer:

\(7\frac{1}{2}\)

Step-by-step explanation:

\(3(2x-1)=4x+12\\\)

Use 3 to open the bracket

\(3(2x-1) = 6x -3\\\\ 6x-3 = 4x+12\\\)

Collect like terms and simplify

\(6x-4x = 12+3\\2x = 15\)

Divide both sides of the equation by 2

\(\frac{2x}{2} = \frac{15}{2} \\\\x = \frac{15}{2} = 7\frac{1}{2}\)  

Answer:

The answer is 2

Step-by-step explanation:

Edge 2021

Answer: (-4, -3)

Step-by-step explanation:It is a linear line

X started at 2, went to the left 3 to negative 1.  Go to the left another 3 to get to -4.

Y started at 3, went down 3 to 0.  Go down another 3 to -3.

Answer:

47×2

Step-by-step explanation:

this is not the answer thank you

Answer:

Step-by-step explanation:

6

The surface area of the cylindrical pottery vase is 177.55 in².

Given that a cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches, we need to find the surface area of the vase,

SA of a cylinder = 2π×radius(h+r)

= 2×3.14×2.15(2.15+11)

= 177.55 in²

Hence, the surface area of the cylindrical pottery vase is 177.55 in².

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Answer:

Building and solving an equation, it is found that the coordinates are: (9,0).

We are given two points: A(-9,3) and B(21, -2).

We also want point C(x,y).

C is 3/5 of the way from A to B, thus:

This is used to find both the x-coordinate and the y-coordinate of C.

First, the x-coordinate, considering .

Then we get 9,0

Step-by-step explanation:

Answer:

To find the equation of the ellipse, we need to use the standard form of the equation for an ellipse centered at the origin:

((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1

where (h, k) is the center of the ellipse, a is the distance from the center to the end of the major axis, and b is the distance from the center to the end of the minor axis.

Step 1: Find the center of the ellipse

The center of the ellipse is halfway between the two foci:

center = ((2+2)/2, (4-8)/2) = (2,-2)

Step 2: Find the length of the major axis

The distance between the two foci is 12 units (the absolute value of the difference in the y-coordinates):

c = 12

The length of the minor axis is the distance between the two co-vertices, which is 16 units:

2b = 16

b = 8

To find the length of the major axis, we use the relationship between a, b, and c in an ellipse:

c^2 = a^2 - b^2

a^2 = b^2 + c^2

a^2 = 8^2 + 12^2

a^2 = 256

a = 16

Step 3: Plug in the values to the standard form of the equation

((x-2)^2)/16^2 + ((y+2)^2)/8^2 = 1

Therefore, the equation of the ellipse is:

((x-2)^2)/256 + ((y+2)^2)/64 = 1

The z-intercept is at 500, the domain of the function is all non-negative real numbers, or [0, ∞) and the maximum revenue is 500

1. The graph of the function is attached below;

2. The z-intercept is where the graph intersects the x-axis, which occurs when the revenue is 0. In this situation, the z-intercept represents the maximum price that the company can charge for the cell phone and still expect to sell some units. So, the z-intercept is $500, meaning if the company charges more than $500, it will not sell any cell phones and its revenue will be 0.

3. No, 0≤x≤ 600 is not an appropriate domain for the function. The company can charge any price, not just prices between 0 and 600 dollars. The domain of the function should be all non-negative real numbers, or [0, ∞).

4. The maximum revenue occurs at the point where the slope of the function changes from negative to positive, which is the vertex of the parabola. In this case, the function r(x) is a linear function, so there is no vertex. The maximum revenue occurs at the endpoint of the domain, which is x=500, since the company cannot charge more than $500 without reducing the number of phones sold to 0. Therefore, the company should charge $500 to get the maximum revenue.

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Answer:

$405

Step-by-step explanation:

2700 x 0.15 = 15% of 2700

Answer:

What do you mean by combining terms?

If you have an equation like y=3(2+x), then you would need to substitute for x before you combined the terms "2" and "x"

The volume of the cylinder is 1020.5 cu.yards .

A cylinder is a three dimensional figure , wit no vertices and edges , it as two similar circular bases and a curved surface.

It is given that :

Radius of the cylinder is 5 yards

Height = 13 yards

The volume of the cylinder is given by

V = π R²h

V = 3.14 *(5 *5) * 13

V = 1020.5 cu.yards

The volume of the cylinder is 1020.5 cu.yards .

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EXPLANATION

Given the system of equations

Isolate x for -2x -3y = 12

Add 3y to both sides:

-2x -3y +3y = 12 +3y

Simplify:

-2x = 12 + 3y

Divide both sides by -2

-2x/-2 = 12/-2 + 3y/-2

Simplify:

x = -12/2 + 3y/2

Substitute x = - (12+3y)/2

3(-(12+3y)/2)+2y = 7

Simplify:

(-36-5y)/2 = 7

Isolate y for (-36-5y)/2 = 7

Multiply both sides by 2:

2(-36-5y)/2 = 7*2

Simplify:

-36 -5y = 14

Add 36 to both sides:

-36 -5y + 36 = 14 + 36

Simplify:

-5y = 50

Divide both sides by -5:

-5y/-5 = 50/-5

Simplify:

y= - 10

For x = -(12+3y)/2

Substitute y= -10

x = -(12+3(-10))/2

-(12+3(-10))/2

Remove the parentheses:

= - (12-3*10)/2

Simplifying:

12 - 3* 10 = -18

= -(-18)/2

Apply the fraction rule: (-a)/b = -(a/b)

=-(-18/2)

Divide the numbers

= -(-9)

Apply rule -(-a)=a

=9

So, x=9

The solutions to the system of equations are x=9, y =-10

Answer:

\( \huge\mathcal\colorbox{red}{\color{pink}{ᶛɲƧཡэʀ}}\)

Value of x & y when

equations are

is

x = 1.5

y = 8

a. The integral converges and its value is 3.

b. The integral converges and its value is -1.

c. The integral diverges.

d. The integral converges and its value is 1/5 ln(5/2).

e. The integral converges and its value is 1/9 ln 2.

f.  Integral diverges because 1/0 is undefined.

a.

\(\int_0^ \infty (1 + 2x) e^{(-x)} dx\)

Applying limit

= limₐ→∞ \(\int _0^a (1 + 2x) e^{(-x)} dx\)

= limₐ→∞ \((-e^{(-a)}(a+3) - 2e^{(-a)} + 3)\)

= 3

b.

\(\int_-\infty^1 (1 + 2x) e^{(-x)} dx\)

= limₐ→-∞ \(\int_a^1 (1 + 2x) e^{(-x)} dx\)

= limₐ→-∞ \((e^{(-a)}(2a+3) - 2e^{(-a)} - 1)\)

= -1

c.

\(\int _{-\infty}^4\sqrt{(6 + y)} dy\)

= limₐ→-∞ ∫a⁴ √(6 + y) dy

= limₐ→-∞ \([2/3 (6 + y)^(3/2)]_a^4\)

= ∞

d.

\(\int_2^\infty 1/(x^2 + x - 6) dx\)

= limₐ→∞ \(\int_2^a 1/(x^2 + x - 6) dx\)

= limₐ→∞ \([1/5 ln|a-3| - 1/5 ln|a+2|]\)

Using natural log

= 1/5 ln(5/2)

e.

\(\int_3^\infty e^{-3x} / (9 + e^{-3x}) dx\)

= limₐ→∞ \(\int_3^a e^{(-3x)} / (9 + e^{(-3x)}) dx\)

= limₐ→∞ \([-1/3 \:ln|a^3 - 27| - 1/9 \:ln|9 + e^{(-3a)}| + 1/9\: ln\: 18]\)

= 1/9 ln 2

f.

∫₀¹ 1/√(x - x) dx

= ∫₀¹ 1/0 dx

Hence it is undefined.

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Question :-

determine if the following integrals converge or diverge. if the integral converges, determine its value. show your work carefully, writing the improper integral as a limit of an intermediate ordinary integral. you must evaluate the intermediate integral, and you must use proper limit notation, to obtain credit here.

a.

\(\int_0^ \infty (1 + 2x) e^{(-x)} dx\)

b.

\(\int_-\infty^1 (1 + 2x) e^{(-x)} dx\)

c.

\(\int _{-\infty}^4\sqrt{(6 + y)} dy\)

d.

\(\int_2^\infty 1/(x^2 + x - 6) dx\)

e.

\(\int_3^\infty e^{-3x} / (9 + e^{-3x}) dx\)

f.

∫₀¹ 1/√(x - x) dx

Answer:

B)65 g/m2

Step-by-step explanation:

I did it on usa test prep

Answer:

C

Step-by-step explanation:

I did it on USATestPrep

Answer:

The exact value of the other leg is 10.

Step-by-step explanation:

Finding the exact value of x given a 45 degree angle and a side length of 10 can be done using trigonometry. In a 45-45-90 right triangle, the two legs are congruent and the hypotenuse is equal to the square root of 2 times the length of the legs.

Therefore, if one leg is 10, the hypotenuse is 10 times the square root of 2. To find the length of the other leg, we can use the Pythagorean theorem:

c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the legs of the right triangle.

Substituting known values, we get:

(10√2)^2 = 10^2 + b^2

200 = 100 + b^2

b^2 = 100

b = 10

Therefore, the exact value of the other leg is 10.

Answer: 18 and 99 degrees

Step-by-step explanation:

The sum of the measures of the other 2 angles is 360 - 219 - 24 = 117 degrees.

So the other two angles measure (2/13)(117)=18 degrees and (11/13)(117)=99 degrees

The locations of the points on the number line are:

point 1: 1 step to the right of 0.

point 4: 4 steps to the right of 0.

point -3:  3 steps to the left of 0

A number lines is an horizontal straight line in which the integers are placed in equal intervals.

All positive numbers on the number line are on the right side of zero while the negative numbers are on the left side of zero.

To locate 1: starting from 0, count 1 step to the right.

To locate 4: starting from 0, count 4 steps to the right.

To locate -3: starting from 0, count 3 steps to the left.

Check the attached image to see the points.

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Answer:

z=  0.278

Step-by-step explanation:

Given data

n1= 60 ; n2 = 100

mean 1= x1`= 10.4;     mean 2= x2`= 9.7

standard deviation  1= s1= 2.7 pounds ;  standard deviation 2= s2 = 1.9 lb

We formulate our null and alternate hypothesis as

H0 = x`1- x`2 = 0 and H1 = x`1- x`2 ≠ 0 ( two sided)

We set level of significance α= 0.05

the test statistic to be used under H0 is

z = x1`- x2`/ √ s₁²/n₁ + s₂²/n₂

the critical region is z > ± 1.96

Computations

z= 10.4- 9.7/ √(2.7)²/60+( 1.9)²/ 100

z= 10.4- 9.7/ √ 7.29/60 + 3.61/100

z= 0.7/√ 0.1215+ 0.0361

z=0.7 /√0.1576

z= 0.7 (0.396988)

z= 0.2778= 0.278

Since the calculated value of z does not fall in the critical region so we accept the null hypothesis H0 = x`1- x`2 = 0  at 5 % significance level. In other words we conclude that the difference between mean scores is insignificant or merely due to chance.

Step-by-step explanation:

sin A = opposite/ Hypotenuse

Sin A = 5/7

Hello !

sin(A) = opposite/hypotenuse = 5/7

arcsin(5/7)  ≈ 45,58°

sin(A) = 5/7

the angle A ≈ 45,58°

The areas of the trapezoid is 50 units².

The trapezoid PQRS have bases 10 and 12 units respectively. The height of the trapezoid is unknown. Let's find the area of the trapezoid as follows:

area of trapezoid = 1 / 2 (a + b)h

where

Therefore,

a = 10 units

b = 15 units

Using Pythagoras's theorem,

5² - 3² = h²

h = √25 - 9

h = √16

h = 4 units

area of trapezoid = 1 / 2 (10 + 15)4

area of trapezoid = 1 / 2 × 25 × 4

area of trapezoid = 100 / 2

area of trapezoid = 50 units²

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Answer:

49 students passed the test

Step-by-step explanation:

70/100=0.07 - 1%

0.07*70=49

Answer:

a.2

Step-by-step explanation:

72=(9x8)

72 / 2 = 36

The margin of error is ±2%

A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.

Let x be margin of error and y be the percentages of the population.  

So,

y-x =33%

y +x = 37%

Solving above equations

2y= 70

y= 35%

and x= 2%

Hence, the margin of error is ±2%.

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