A restaurant offers a​ $12 dinner special that has 7 choices for an​ appetizer, choices for an​ entrée, and 3 choices for a dessert. How many different meals are available when you select an​ appetizer, an​ entrée, and a​ dessert?

Answer:

  GJ and HI

Step-by-step explanation:

No line through K is parallel to any other in the diagram. That eliminates the last three choices.

Opposite sides of the square base are parallel, so GJ║HI.

Answer:

The right answer is the last option, 12,12.

Step-by-step explanation:

[tex]GI^2=FI*IH\\ GI^2 = 7*21\\ GI = \sqrt{147}[/tex]

[tex]\sqrt{147} = 12,124... = 12,12[/tex]

Answer:

1.88

Step-by-step explanation:

8-2√5=3.527864045

square root of 3.527864045=1.87826090972

the question will probably want it to 2d.p (decimal places) which means the answer would be 1.88

Answer:

The square root of 8 - 2√5 is

[tex] \sqrt{4 + \sqrt{11} } \: - \sqrt{4 - \sqrt{11} } [/tex]

Step-by-step explanation:

To find the square root

8-2√5 must be in the form √a - √b where a > b

√ 8 - 2√5 = √a - √b

Square both sides

8 - 2√5 = (√a - √b)²

That's

8 - 2√5 = (a + b) - 2√ab

Since the two surd expressions are equal we can equate them

That's

8 = a + b ........ 1

a = 8 - b ........ 2

2√5 = 2√ab

Simplify

Divide both sides by 2

√5 = √ab

square both sides

We have

5 = ab ....... 3

Substitute a = 8 - b into equation 3

5 = ( 8 - b)b

5 = 8b - b²

b² - 8b + 5 = 0

After solving

b = 4 + √ 11 or 4 - √ 1

Since b is less than a

b = 4 - √11

a = 4 + √11

So the square root of 8 - 2√5 is

[tex] \sqrt{4 + \sqrt{11} } \: - \sqrt{4 - \sqrt{11} } [/tex]

Hope this helps you.

Answer:

d. t ≈ 5m

e. y ≈ 44°

f. x = 36°

Step-by-step explanation:

We'd apply the trigonometry function to solve for all missing sides and angles as follows:

d. Adjacent length = t

Hypothenuse = 11.1m

θ = 62°

Use Cos θ = adjacent/hypothenuse

Cos(62) = t/11.1

Multiply both sides by 11.1

11.1*cos(62) = t

11.1*0.4695 = t

t = 5.21 ≈ 5 m

e. Opposite = 7m

Hypotenuse = 10m

θ = y°

Use sine θ = opposite/hypotenuse

Thus,

sine θ = 7/10

sine θ = 0.7

θ = sin-¹(0.7) = 44.4

y ≈ 44° (nearest whole number)

f. Opposite = 4.2cm

Adjacent = 5.8cm

θ = x°

Use tan θ = opposite/adjacent

tan θ = 4.2/5.8

tan θ = 0.7241

θ = tan-¹(0.7241) = 35.91

θ = x ≈ 36°

Answer:

Its B

Step-by-step explanation:

B is the proper answer in scientific notation and scientific notation is only one decimal placed

The most common form of scientific notation inserts a decimal point after the first significant digit

Step-by-step explanation:

Kaytee's total points are WX + 2S − L.  The total number of exams is W − Y + 2.  Therefore:

G = (WX + 2S − L) / (X − Y + 2)

The total number of exams is W − Y + 2.

We have given that,

In professor Hoepker's class, there are X tests and a final. At the end of the semester, the lowest Y test scores are dropped and the remaining test scores and the final (which has twice the weight of a test) are averaged to compute the average score for the entire class. The final cannot be dropped.

Going into the final, student Kaytee has an average of W on the X tests. The sum of her lowest Y test scores is L. Her final exam score is S.

The sum brings two or more numbers together to make a new total.

We have to determine her average score of G in the class in terms of X, Y, W, L, and S.

Kaytee's total points are WX + 2S − L.  

The total number of exams is W − Y + 2.

Therefore:G = (WX + 2S − L) / (X − Y + 2)

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Answer:

Step-by-step explanation:

To find the answer to Part A we can do (97 - 42) + 1 = 56. The reason we do + 1 is because 97 - 42 is just counting the numbers in between 42 and 97 but it leaves out 42 and since it's inclusive we need to include 42.

Part B: We can do (200 / 2) - 1 = 99. The reason we do - 1 is because 200 / 2 includes the endpoint of the line but since we don't want to include the endpoint of the line we do - 1.

Answer:

Part A = 56 Integers

Part B = 99 Points

Step-by-step explanation:

Part A ~ Since it's inclusive, at the end we must put n + 1 -->

97 - 42 = 55 => 55 = n => 56 Integers

Part B ~ n - 1  Since it is exclusive. so, =>

200/2 = 100, 100 = n (n-1) => 99 Points

Hope this helps!

Answer:

2.89

Step-by-step explanation:

just do 1.7×1.7=2.89

Answer:

(B ) .  34.2cm^2

Step-by-step explanation:

[tex]A = \frac{\alpha }{360} \times \pi r^2\\\alpha=20 \\r = 14\\\\A =\frac{20}{360} \times 22/7\times 14^2\\A = 1/18 \times4312/7\\A =34.2 cm^2[/tex]

Answer:

2

Step-by-step explanation:

[tex]\sqrt{((\sqrt{2} - 0)^2 + (0 - (-\sqrt{2}))^2)[/tex]

Answer:

Mean value of the ACT scores

x⁻  = 18.66

Step-by-step explanation:

Explanation:-

Given data

Student scores were as follows: 20, 18, 16, 15, 23, 20.

Mean value or Expected value

  x ⁻ = ∑x/n

  [tex]x^{-} = \frac{20+18+16+15+23+20}{6}[/tex]

 [tex]x^{-} = \frac{112}{6} = 18.66[/tex]

Mean value = 18.66

Final answer:-

Mean value of the ACT scores

                           x⁻  = 18.66

Answer:

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the men and women who own cats respectively. The population proportion of men and women who own cats would be p1 and p2 respectively.

p1 - p2 = difference in the proportion of men and women who own cats.

The null hypothesis is

H0 : p1 = p2

p1 - p2 = 0

The alternative hypothesis is

Ha : p1 ≠ p2

p1 - p2 ≠ 0

it is a two tailed test

Sample proportion = x/n

Where

x represents number of success

n represents number of samples

For men

n1 = 80

p1 = 55/100 = 0.55

x1 = p1n1 = 0.55 × 80 = 44

For women,

n2 = 100

p2 = 30/100 = 0.3

x2 = p2n2 = 0.3 × 100 = 30

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (44 + 30)/(80 + 100) = 0.41

1 - pc = 1 - 0.41 = 0.59

z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.55 - 0.3)/√(0.41)(0.59)(1/80 + 1/100) = 3.39

Test statistic = 3.39

Answer:

C

Step-by-step explanation:

Tan = opposite / adjacent

= 1 / √3

= √3 / 3

Answer:

C.

Step-by-step explanation:

Tangent= opposite over adjacent.

Tangent = 1/√3

Answer:

E

Step-by-step explanation:

Substitute each point into the equation to test whether they would equate to 2. Point a equates to 141, point b to -120, c to 27 and d to -54. Therefore, none of the points would correctly balance/be solutions to the equation

The solutions to the equation 3x + 12y = 2 is the option E. none of the above.

Equations are the mathematical expressions which consist of two expressions including one or more variables connected with an equal to sign.

We have to find the solution of the equation 3x + 12y = 2.

Substitute each ordered pairs given.

A. (7, 10)

(3 × 7) + (12 × 10 ) = 21 + 120 ≠ 2

B. (-8, -8)

(7 × -8) + (12 × -8) ≠ 2

C. (-7, 4)

(3 × -7) + (12 × 4) = -21 + 48 ≠ 2

D. (-2, -4)

(3 × -2) + (12 × -4) ≠ 2

So none of the ordered pairs satisfies the given equation.

Hence there is no solutions for the given equation in the options.

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Answer:

(-0.5, 0)

Step-by-step explanation:

Coordinates of endpoints of segment are:

A= (-2, 1)

B= (1, - 1)

By mid-point formula:

The midpoint of [tex] \overline{AB} [/tex]

[tex] = \bigg(\frac{ - 2 + 1}{2}, \: \: \frac{1 + ( - 1)}{2} \bigg) \\ \\ = \bigg(\frac{ - 1}{2}, \: \: \frac{0}{2} \bigg)\\ \\ = \bigg(\frac{ - 1}{2}, \: \: 0 \bigg)\\ \\ = ( - 0.5, \: \: 0 )[/tex]

Answer:

sinR = 0.7184

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

sin∅ = opposite/hypotenuse

Step 1: Find missing leg length

16² + b² = 23²

b² = 23² - 16²

b = √273

Step 2: Find sinR

sinR = √273/23

sinR = 0.718379

Answer:

no solution

Step-by-step explanation:

4x+3y = 6

8x + 6y = 5

Multiply the first equation by -2

-2(4x+3y) = 6*-2

-8x -6y = -12

Add this to the second equation

-8x-6y = -12

8x + 6y = 5

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

0x + 0y = -7

0 = -7

Since this is never true there is no solution

Answer:

X = 8/3, y= -14/9

Step-by-step explanation:

using elimination method:

subtract equation 1 from equation 2

8x-4x + 6y-3y = 5-6

4x+3y= -1

4x= -1-3y

divide both sides by 4

x = -1-3y÷4

substitute x = -1-3y/4 in equation 2

8(-1-3y)/4 +6y = 5

-8-24y/4+ 6y =5

-8-24y+6y/4 =5

-8-18y/4 = 5

Cross multy

-8-18y × 1 = 4×5

-8-18y = 20

collect like terms

-18y = 20+8

-18y = 28

divide both sides by-18

y = 28/-8

y = -14/9

put y = -14/9 in equation 1

4x+3(-14/9) = 6

4x-42/9 = 6

42/9 = 14/3

so, 4x=6+14/3

LCM =3

4x = 18+14/3

4x= 32/3

cross multiply

4x×3 = 32

12x = 32

divide both sides by 12

12x/12= 32/12

x = 8/3

so, x = 8/3, y = -14/9

check:

first equation:

4(8/3) + 3(-14/9)

32/3 - 14/3( 3 cancels 9 rem 3)

LCM= 3

32 - 14/3

= 18/3

= 6

Answer: C

Step-by-step explanation:

This is a 45-45-90 triangle. In a 45-45-90 triangle, the hypotenuse is x√2 in length. The legs are equal to each other. They have the length of x. X is consistent throughout all 3 sides of the triangle. Since we have the hypotenuse, we can set it equal to x√2 to find x that will let us know the length of the legs.

7√2=x√2                             [divide both sides by √2]

x=7

Now that we know the length is x=7, the legs are 7 in length each.

Answer:

  1600 boxes of cookies; 350 boxes of chocolates

Step-by-step explanation:

Let x and y represent the numbers of boxes of cookies and chocolates to order, respectively. The constraints seem to be ...

The objective function we want to maximize is ...

  p = 2.70x +2.45y

_____

Looking at the problem, we see that cookies yield the most profit, so we'd like to maximize the boxes of cookies sold within the allowed limits.

There are two limits on x:

  x ≤ 550 +3y

  x ≤ 1950 -y

x will be as large as it can be if it bumps up against these limits simultaneously:

  550 +3y = 1950 -y

  4y = 1400 . . . . . . . . . add y-550

  y = 350

  x = 1950 -350 = 1600

Profit will be maximized for an order of 1600 boxes of cookies and 350 boxes of chocolates.

_____

The "feasible region" of the solution is where the three constraint inequalities overlap. It is a quadrilateral with vertices at (0, 0), (550, 0), (1300, 650), and (1600, 350). We can reject the ones with x or y being 0. Per our analysis above, the solution of interest is (x, y) = (1600, 350), since it maximizes x.

The usual protocol for solving a linear programming model like this is to evaluate the objective function at each of the vertices. With a little thought about the problem, we have saved some evaluation effort.

Answer:

z= 56°

hope u understood it...

Answer:

Z=56

Step-by-step explanation:

Because i said so

Answer:

D) Standard deviation, because there are no outliers that affect the center

Answer:

12.1 km

Step-by-step explanation:

350 * 2 = 700

200 * 2 = 400

700 + 400 = 1100

1100 * 11 = 12100

12100 / 1000 = 12.1

12.1 km

Answer:

There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.

Standard error sm = 1.634

Test statistic t = 1.102

P-value = 0.28

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that women who exercise daily have a significantly different duration of labor than all women.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=16\\\\H_a:\mu\neq 16[/tex]

The significance level is 0.05.

The sample has a size n=29.

The sample mean is M=17.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√77.4=8.8.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{8.8}{\sqrt{29}}=1.634[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.8-16}{1.634}=\dfrac{1.8}{1.634}=1.102[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=29-1=28[/tex]

This test is a two-tailed test, with 28 degrees of freedom and t=1.102, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>1.102)=0.28[/tex]

As the P-value (0.28) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.

Answer:

5(2a -5 + b)

Step-by-step explanation:

(10a - 25 + 5b) = 5( 2a - 5 + b)

5(b +  2a  - 5) = 5(2a - 5 + b)

Answer:

5(2a -5 + b)

Step-by-step explanation:

Answer:

1 can sing but cannot play keyboard.

Step-by-step explanation:

There are six members in the rock band. We need to identify how many person can sing, play guitar and play keyboard. To identify this we will find out number of member for each activity,

Total 6 members

4 can play guitar

3 can pay keyboard

All singers play guitar but one guitarist cannot sing.

There will be 1 singer who cannot play keyboard.

Answer:

70>t+55

Step-by-step explanation:

The way you wrote the options were somewhat confusing.

She is looking to beat her time, so we are looking at one that is 70> because the new time must be below 70

Since she has already ran 55 minutes, we're looking at her remaining time she still has to run for

We could suppose t is the remaining time left, so 70>t+55

Answer:

D

Step-by-step explanation:

70>t+55 /edge.

Answer: Apothem

Step-by-step explanation: Half of an octagon is called an apothem

The dashed line shown in the regular octagon is called an apothem.

Octagon is an eight-sided two-dimensional geometrical figure. An octagon consists of 8 interior angles and 8 exterior angles. The sum of the interior angles of an octagon is 1080°, and the sum of its exterior angles is 360°.

Given is a regular octagon, we need to determine the asked part of the given octagon is called what,

So, the part asked is called the apothem.

A line from the center of a regular polygon at right angles to any of its sides is called an apothem.

Hence, the dashed line shown in the regular octagon is called an apothem.

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Hey there! :)

Answer:

(7x +5)(x - 3)

Step-by-step explanation:

Starting with:

7x² - 16 - 15

Find two numbers that add up to -16 and multiply to form -15. Remember the coefficient of 7 in the front of the equation.

The numbers '5' and '-3' can be derived. Put these into factored form:

(7x +5)(x - 3)

Answer:

R = V₀² Sin 2θ₀/g

Step-by-step explanation:

Consider a projectile motion with following properties:

R = range of projectile

V₀ = Launch Velocity of Projectile

θ₀ = Launch Angle

V₀ₓ = V₀ Cos θ₀ =  x - component of launch velocity

V₀y = V₀ Sin θ₀ =  y - component of launch velocity

t = time to reach maximum height

T = 2t = total time of flight

First we use 1st equation of motion in vertical direction to find value of "t":

Vfy = V₀y + gt

where,

Vfy= final vertical velocity at highest point = 0 m/s

g = -g (for upward motion)

V₀y = V₀ Sin θ₀

Therefore,

0 = V₀ Sin θ₀ - gt

t = V₀ Sin θ₀/g

Now the total time of flight will be:

T = 2t = 2 V₀ Sin θ₀/g

Since, the horizontal velocity of the projectile remains uniform throughout the motion. Therefore:

x - x₀ = V₀ₓ T

where,

x - x₀ = R = Range of Projectile

V₀ₓ = V₀ Cos θ₀

Therefore,

R = (V₀ Cos θ₀)(2 V₀ Sin θ₀/g)

R = V₀² (2 Sin θ₀Cos θ₀)/g

since, 2 Sin θ Cos θ = Sin 2θ

Therefore,

R = V₀² Sin 2θ₀/g