How many mathematicians discovered the Law of Sines?

Answer:

There were 120 questions on the test.

Step-by-step explanation:

It is given that:

Number of questions answered = 54

Grade percent = 45%

Let,

x be the total number of questions

45% of x = 54

[tex]\frac{45}{100}x=54\\0.45x = 54[/tex]

Dividing both sides by 0.45

[tex]\frac{0.45x}{0.45}=\frac{54}{0.45}\\x=120[/tex]

Therefore,

There were 120 questions on the test.

Answer:

94 cm²

Step-by-step explanation:

= 2 × (5×3 + 5×4 + 3×4)

= 2 × (15 + 20 + 12)

= 2 × 47

= 94 cm²

To answer the questions, we need to understand the utility functions and budget constraints for both Joey and Jim. Let's break it down step by step:

Joey's Utility Function and Budget Constraint:

Joey's utility function for whisky (w) and beer (b) is given by: U(w, b) = 5 + (w^0.3 * b^0.7)

w: The quantity of whisky (in bottles) consumed by Joey

b: The quantity of beer (in cans) consumed by Joey

Joey spends £75 in total on drink. The cost of beer is £2 per can, and the cost of whisky is £6 per bottle.

To find how many cans of beer and bottles of whisky Joey consumes, we need to maximize his utility function while staying within his budget constraint.

Joey's Budget Constraint:

Joey's total expenditure on drink (E) is given by: E = 2b + 6w

And we know that E = £75.

So, the budget constraint is: 2b + 6w = 75

Now, we can solve this problem using optimization techniques. However, without specific numerical values for the utility function and budget constraint, it's not possible to determine the exact quantities of beer and whisky consumed by Joey. We can only find the optimal consumption bundle if the specific values are given.

Joey's Indifference Curve and Budget Constraint Diagram:

To illustrate Joey's optimal consumption bundle, we would need to plot his indifference curve (representing his preferences) and his budget constraint (showing all possible affordable combinations of beer and whisky). However, without the exact values, we cannot draw the diagram.

Jim's Utility Function and Consumption:

Jim's utility function for beer (b) and whisky (w) is given by: U(b, w) = min{5, (w^0.3 * b^0.7)}

Jim's utility function shows that he insists on drinking beer and whisky together, and his utility is the minimum of 5 and the product of whisky and beer raised to certain powers.

Again, without specific numerical values for the utility function, we cannot determine the exact quantities of beer and whisky consumed by Jim.

In summary, to fully answer the questions, we would need the specific numerical values for the utility function and the budget constraint. With those values, we could then calculate the optimal consumption bundles for both Joey and Jim.

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Answer:

(2,3)

Step-by-step explanation:

you go up 3 and forward 2 so it would be positive positive.

Given:

Increase 386.3 by  4%.

To find:

The value for given statement.

Solution:

We have,

Initial value = 386.3

Increasing rate = 4%

The increased value is

[tex]\text{New value}=\text{Initial value + Increasing rate }\times \text{Initial value}[/tex]

[tex]\text{New value}=386.3+\dfrac{4}{100}\times 386.3[/tex]

[tex]\text{New value}=386.3+15.452 [/tex]

[tex]\text{New value}=401.752[/tex]

Therefore, the required value is 401.752.

Step-by-step explanation:

Acceleration = g = 32.17ft/s²

Initial velocity = 0ft/s

Time taken = 6.7s

Using Kinematics,

we have s = ut + 0.5at².

=> s = (0)(6.7) + 0.5(32.17)(6.7)²

=> s = 722.06ft.

Answer: The population in 2025 will be 7669

Step-by-step explanation:

a) When we have an initial quantity A, and we have an increase of the X%, the new quantity is written as:

new quantity = A + A*(X%/100%) = A*(1 + X%/100%)

In this case, our initial quantity is 3500, the town's population in 2005.

And X% = 4%.

We know that each year, the population increases by 4%.

Then if P(1) is the population one year after 2005, this is:

P(1) = 3500*(1 + 4%/100%) = 3500*(1.04)

After another year, the population increases again:

P(2) = (3500*(1.04))*(1 + 4%/100%)) = 3500*(1.04)*(1.04) = 3500*(1.04)^2

Well, we already can see the pattern here, the population N years after 2005 will be:

P(N) = 3500*(1.04)^N

b) Now we want to know the population in 2025.

N represents the number of years after 2005, then we will have:

N = 2025 - 2005 = 20

2025 is 20 years after 2005.

Then the population in 2025 will be:

P(20) = 3500*(1.04)^20 = 7,668.9

And we can not have a 0.9 of a person, so we should round it up to the next whole number, then the population in 2025 will be 7669

Answer:

imma say 12 pages

Step-by-step explanation: sorry if wrong

Answer:

3

Step-by-step explanation:

Answer:

y-intercept: 11

which means the baby weighs 11 lb when it is born (t=0).

Step-by-step explanation:

We are dealing with an equilateral triangle which has 3 equal sides.

length of a side = 3 ft

Since the three sides of an equilateral triangle are equal and we are given two sides to have lengths of 3x - 9 and 23 - 5x , it means that;

3x - 9 = 23 - 5x

Rearranging this gives;

3x + 5x = 23 + 9

8x = 32

x = 32/8

x = 4

putting 4 for x in 3x - 9, we have;

3(4) - 9 = 3 ft

Thus,

length of a side = 3 ft

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Answer:

∠CFD = 60°

Step-by-step explanation:

Along line CE:

∠AFE + ∠AFB + ∠BFC = 180° (sum of angles on a straight line)

(7x + 4) + (8x + 6) + (6x + 2) = 180

collecting alike terms:

7x + 8x + 6x + 4 + 6 + 2 = 180

21x + 12 = 180

21x = 168

x = 8°

We could find the  measure of CFD using:

a) Along line AD:

∠AFB + ∠BFC + ∠CFD = 180° (sum of angles on a straight line).

(8x + 6) + (6x + 2) + ∠CFD = 180

14x + 8 + ∠CFD = 180

∠CFD = `180 - (14x + 8)

∠CFD = 172 - 14x

b) ∠CFD = ∠AFE (vertical opposite angles are equal)

∠CFD = 7x + 4

To find value of ∠CFD, substitute x = 8

∠CFD = 7(8) + 4

∠CFD = 60°

Answer:

15% chance

Step-by-step explanation:

The required probability is 0.0166 that you will dress all in a brown shirt, pants, socks, and shoes.

The probability that you will dress all in brown is the product of the probability of selecting each brown item.

There is only one choice of brown shirt out of a total of 5 shirt choices, so the probability of selecting a brown shirt is 1/5.

Similarly, there is only one choice of brown pants out of a total of 3 pant choices, so the probability of selecting brown pants is 1/3.

There is also only one choice of brown socks out of a total of 4 sock choices, so the probability of selecting brown socks is 1/4.

Finally, there is also only one choice of brown shoes out of a total of 3 shoe choices, so the probability of selecting brown shoes is 1/3.

To find the overall probability of dressing all in brown, you need to multiply these probabilities together: (1/5) × (1/3) × (1/4) × (1/3) = 1/60.

This means the probability of dressing all in brown is approximately 0.0166, or about 1.7%.

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Answer:

11.65$ : 100% = x : 94

94 because 100 - 6

Step-by-step explanation:

Do this:

11.65 x 94 = ?

divide the answer by 100

and that is your answer

Answer:

x=3

Step-by-step explanation:

I did a 2-column proof for the explanation :)

Answer:

Step-by-step explanation:

Here you go mate

∴Use PEMDAS

Parenthesis,Exponent,Multiplication,Division,Addition,Subtraction

Step 1

5x-19=2(x-5)  Equation/Question

Step 2

5x-19=2(x-5)  Remove parenthesis

5x=2x+9

Step 3

5x=2x+9  Subtract 2x from sides

3x=9

Step 4

3x=9  Divide sides by 3

Answer

x=3

Hope this helps

Answer:

y = 3x - 1

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

5 * 8 = 40

300/40 = 7.5

Answer:

(a) median = 6

(b) median = 14

(c) median = 37

(d) median = 19

(e) median = 4.5

(f) median = 15

(g) median = 126

(h) median = 345

(i) median = 50

(j) median = 75

Step-by-step explanation:

The median of the ungrouped data is obtained by arranging the numbers from the lowest to the highest number, then select the middle number. If you have two numbers in the middle, sum the two numbers and divide it by 2.

(a) in order: 3    4    4     6   7     8      8

median = 6

(b) in order:  11        11           12           14           15       16          17

median = 14

(c) in order:    31         31          34            37         38          41        42

median = 37

(d) in order:   17       17         18       19      19       21      23

median = 19

(e) in order:   3         3        3         4       5        6      7     9

median = (4 + 5) / 2 = 4.5

(f) in order:  12        14       14       14        16      18          19     20

median = (14 + 16)/2 = 15

(g) in order:   120       121         124      128       129        131

median = (124 + 128)/2 = 126

(h) in order:  321      339      342      345    352        358       362

median = 345

(i) in order: 43      46       49      49     51       51      51      52

median = (49 + 51)/2 = 50

(j) in order:   68     70       73     74      76      77      77       81

median = (74 + 76)/2 = 75

Answer:

We know that the area of a square of sidelength L, is:

Area = L^2

In this case, we have:

L = 2cm + x cm

And we know that the area of the square is 7cm, then:

Area = 7cm^2 = (2cm + x cm)^2

7cm^2 =  4cm^2 + 4cm*xcm + (x cm)^2

7cm^2 = 4cm^2 + (4*x)cm^2 + x^2 cm^2

Now we can remove all the "cm^2" and just get the numbers:

7 = 4 + 4*x + x^2

We can subtract 4 in both sides to get

7 - 4 = 4 + 4*x + x^2 - 4

3 = 4*x + x^2

This is what whe wanted to prove.

similar it is just 3 times bigger but similar

Answer:

1.5 hours = 1 hour 30 mins

Step-by-step explanation:

3/4 = 0.75

0.75 x 2 = 1.5

Answer:

seee I won the waaaarrrrrr.... [:

Answer:

126

Step-by-step explanation:

cause it's the smallest