Convert this identity to one using sine term(s) only.
1-2cos(r)^2

Final answer:

The odds against rolling a sum of 6 with the roll of two dice are 31:5, as there are 5 favorable outcomes for a sum of 6 and 36 total possible outcomes when rolling two dice.

Explanation:

The question is asking about the odds against rolling a sum of 6 with two dice. To calculate this, first, we need to find all the possible combinations of two dice that sum up to 6. Those combinations are (1,5), (2,4), (3,3), (4,2), and (5,1), therefore there are 5 ways to achieve a sum of 6.

The total number of possible outcomes when rolling two dice is 6 * 6 = 36, since each die has 6 faces. So, there are 36 - 5 = 31 ways to not roll a sum of 6. The odds against rolling a sum of 6 are therefore the number of ways not to roll a 6 to the number of ways to roll a 6, which is 31:5.

Odds against rolling a sum of 6 with two dice = 31:5.

Answer:a=2A/p

Step-by-step explanation:

Answer is D Use the distributive property to simplify.  

The answer provides the total number of combinations of ice cream cones based on flavors, cone types, and toppings.

The number of different combinations of ice cream cones that can be created considering different flavors of ice cream, types of cones, and toppings:

The answer is 7 on e2020.

Answer:

the perimeter is [tex]8\sqrt{2} +2\sqrt{10}[/tex]

Step-by-step explanation:

It is given that PQRS is a parallelogram

with sides SR=[tex]4\sqrt{2}[/tex]  and QR = [tex]\sqrt{10}[/tex]

We know that the opposite sides in a parallelogram are equal

so we have

PQ= SR= [tex]4\sqrt{2}[/tex]

PS= QR= [tex]\sqrt{10}[/tex]

Now to find the perimeter of parallelogram we add all the sides

perimeter = [tex]PQ+SR+PS+QR[/tex]

                =[tex]4\sqrt{2} +4\sqrt{2} +\sqrt{10} +\sqrt{10}[/tex] ( plug the values)

                =[tex]8\sqrt{2} +2\sqrt{10}[/tex]

hence the perimeter is [tex]8\sqrt{2} +2\sqrt{10}[/tex]

Answer: 39,075 is the answer

Step-by-step explanation:

Answer:

The area of the clock face is [tex]79\ m^{2}[/tex]

Step-by-step explanation:

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=5\ m[/tex]

[tex]\pi=3.14[/tex]

substitute

[tex]A=(3.14)(5^{2})=78.5\ m^{2}[/tex]

Round to the nearest square meter

[tex]78.5\ m^{2}=79\ m^{2}[/tex]

Mrs. Cunningham travels at a speed that is 20mph faster than Mr. Cunningham. Given that Mr. Cunningham has a 165-mile head start, Mrs. Cunningham would need 8.25 hours to cover this distance and catch up with him.

This question can be approached by analysing the relative speeds and the initial advantage Mr. Cunningham had. Mr. Cunningham travels for three hours at 55 mph before Mrs. Cunningham leaves, giving him a 165 mile head start. To determine how long it will take Mrs. Cunningham to overtake Mr. Cunningham, it's necessary to calculate how long it will take her to make up this 165-mile deficit at her faster speed.

Mrs. Cunningham travels 75mph, which is 20mph faster than Mr. Cunningham's speed. Thus, each hour, she closes the distance between them by 20 miles. To find out how many hours it takes her to close the 165 mile distance between them, divide this distance by her relative speed, so: 165miles / 20mph equals 8.25 hours.

Thus, it will take Mrs. Cunningham 8.25 hours to overtake Mr. Cunningham.

https://brainly.com/question/14362959

#SPJ12

Answer:

B.) $307.60 ; C.) $252 ; B.) $1644

Step-by-step explanation:

1.) Since the employer pays 70% of the premium, this leaves Ms. Everett with 100-70=30% of the cost.

30% = 30/100 = 0.3; this makes her part of the cost

0.3(12304) = 3691.2

She gets paid monthly, so we divide this by 12:

3691.2/12 = 307.6

This means she has $307.60 deducted monthly.

2.) Since the insurance company pays 80% of the costs, this leaves Peter with 100-80 = 20% of the cost.

We take his deductible out of the cost first:

1060-50 = 1010

20% = 20/100 = 0.2; this makes his part of the cost

0.2(1010) = 202+50 = 252, since we have to count the deductible as part of his cost.

3.) The total cost of all visits would be

305(12) = 3660

The insurance company pays 60% of the cost; this means she is left with 100-60 = 40%.  40% = 40/100 = 0.4;

0.4(3660) = 1464

Mattie also pays 12 $15 copays; this adds 12(15) = 180 to this:

1464+180 = $1644

Ms. Everett's monthly deduction for her health insurance premium is $307.60. Peter paid $202 for his nutritional counseling after accounting for the deductible and insurance payment. Mattie paid a total of $1,644 for her chiropractor visits, considering the co-pays and her share of the visit costs after insurance.

1. To determine the amount deducted from Ms. Everett's paycheck for her health insurance premium, we calculate 30% of the total annual premium (since her employer pays 70%) and then divide by 12 to get the monthly deduction.

Total annual premium: $12,304
Employer's share (70%): $12,304 × 0.70 = $8,612.80
Ms. Everett's share (30%): $12,304 × 0.30 = $3,691.20
Monthly deduction: $3,691.20 / 12 = $307.60

2. To find out how much Peter paid for his nutritional counseling, we subtract the $50 deductible from the total cost and then calculate 20% of the remaining amount (since the insurance pays 80%).

Total cost of counseling: $1,060
Deductible: $50
Amount after deductible: $1,060 - $50 = $1,010
Peter's share (20%): $1,010 × 0.20 = $202

3. To determine the total amount Mattie paid for her chiropractor visits, we multiply the co-pay by the number of visits and add to it the total amount of her share for the visits after insurance contribution.

Cost per visit: $305
Insurance pays (60%): $305 × 0.60 = $183
Mattie's share per visit (40%): $305 × 0.40 = $122
Co-pay per visit: $15
Total co-pay: $15 × 12 = $180
Total Mattie's share for visits: $122 × 12 = $1,464
Total amount Mattie paid: $1,464 + $180 = $1,644

i put C and it was correct !

To find JL, we simply add the lengths of JK and KL together which gives us 22 units.

If K is the midpoint of JL, it means that JK is equal in length to KL.

Thus, we can set up the equation 5x + 1 (for JK) equal to 7x - 3 (for KL) since these expressions represent the lengths of JK and KL respectively.

Solving the equation 5x + 1 = 7x - 3 for x, we find that x = 2. Substituting x back into the expression for either JK or KL yields the length of one segment, which in this case is 11 units for both JK and KL.

Final answer:

Aaliyah ate 1/8 more of the mini-pizza than James after converting their consumed amounts to a common denominator and subtracting James's share from Aaliyah's.

Explanation:

To calculate how much more Aaliyah ate compared to James, we need to compare the fractions of the mini-pizzas they each consumed. Aaliyah ate 7/8 of her mini-pizza, while James ate 3/4 of his mini-pizza. To make a comparison, we have to ensure both fractions have the same denominator.

Since the least common denominator for 4 and 8 is 8, we convert James's fraction from 3/4 to 6/8 by multiplying both the numerator and the denominator by 2. Now we can compare the amounts:

To find out how much more Aaliyah ate, we subtract James's portion from Aaliyah's:

7/8 - 6/8 = 1/8

Therefore, Aaliyah ate 1/8 more of the mini-pizza than James.

Answer:

  f(0) = -1

Step-by-step explanation:

Any scientific or graphing calculator can help you do this. According to the Order of Operations, the exponent is evaluated first, then the sign is applied:

  f(0) = -2^0 = -(2^0) = -1

Answer:

[tex]\large\boxed{\tt x \ and \ y = 4}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to solve for x and y of a 45-45-90 degree triangle.}[/tex]

[tex]\large\underline{\textsf{What is a 45}^{\circ}\textsf{- 45}^{\circ} \textsf{- 90}^{\circ} \textsf{Triangle?}}[/tex]

[tex]\textsf{A 45}^{\circ} \textsf{- 45}^{\circ} \textsf{- 90}^{\circ} \ \textsf{triangle is a special right triangle with legs that are congruent.}[/tex]

[tex]\textsf{These kinds of Triangles are considered "Special Right Triangles" as first they're}[/tex]

[tex]\textsf{Right Triangles, and secondly they have special side lengths that can be figured}[/tex]

[tex]\textsf{out with only one side length given.}[/tex]

[tex]\underline{\textsf{What are the Ratios between the sides?}}[/tex]

[tex]\tt Leg : Leg : Hypotenuse[/tex]

[tex]\tt x : x : x \sqrt2[/tex]

[tex]\textsf{If we are given a leg, the other leg will equal the same since these kinds of triangles}[/tex]

[tex]\textsf{have 2 equal sides, which are considered \underline{Isosceles Triangles}. Given that 4 is one}[/tex]

[tex]\textsf{leg, this means that the other leg is 4, and the Hypotenuse is 4} \tt \sqrt 2. \ \textsf{The}[/tex]

[tex]\textsf{Hypotenuse is always multiplied by} \ \tt \sqrt 2 \ \textsf{to equal the sum of the legs. Finding}[/tex]

[tex]\textsf{the legs are different however, as we need to divide the Hypotenuse by} \ \tt \sqrt2.[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{We are given the Hypotenuse, and a 45}^{\circ} \ \textsf{angle to show that it's a 45}^{\circ}\textsf{- 45}^{\circ} \textsf{- 90}^{\circ}[/tex]

[tex]\textsf{triangle. Let's divide the Hypotenuse by} \ \tt \sqrt 2 \ \textsf{to find the value of x and y. Remember}[/tex]

[tex]\textsf{that the legs are equal to each other.}[/tex]

[tex]\tt \frac{Hypotenuse}{\sqrt2} = Leg.[/tex]

[tex]\tt \frac{4 \sqrt{\not2}}{\sqrt{\not{2}}} = x \ and \ y.[/tex]

[tex]\large\boxed{\tt x \ and \ y = 4}[/tex]