Maddie wrote six different equations based on the triangle below.
60°
Four of the six equations that Maddie wrote are correct. Which four of the equations are correct?
sin 30 = 1
cos 60
12
1/201
tan 60 = √3
sin 60
tan 30-
=
cos 30 =
√2
2
√√2
2

Answer:

where represents the time two hours later than the current time. represents the time one hour later than current time. Henceforth, the time at present is 9 pm.

Step-by-step explanation:

Answer:

give me more instructions so i can actually help

Step-by-step explanation:

3268760 different samples of size 10 people are possible to be selected.

15818400 different license plates are possible.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

The combination formula aids in determining the number of possible combinations that may be created by selecting a portion of a bigger collection of objects.

We need the number of possible combinations of choosing 10 people out of 25 (any order). The 25 binomial coefficient, (10) gives the number. Possible number of combinations are:

²⁵C₁₀ =  25! / (25-10)!(10!)

²⁵C₁₀ = 3268760

We want 3 letters and 3 digits but the first digit can't be zero. There are 26 alphabets and 10 digits. Since repetition is allowed we can use any of the 26 alphabets in place of all 3 letters.

This gives us 26 x 26 x 26 = 26³ ways to choose the first three letters.

For digits, since the first digit can't be 0, we can choose the rest 9 digits. For the next two digits, we can choose any one digit from 10. This gives us 9 x 10 x 10 ways to choose digits.

Finally, by law of multiplication, the total number of ways of choosing license plates is :

number of license plates = 26³ × 9 × 100

= 15818400

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3268760 different samples of size 10 people are possible to be selected.

15818400 different license plates are possible.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

The combination formula aids in determining the number of possible combinations that may be created by selecting a portion of a bigger collection of objects.

We need the number of possible combinations of choosing 10 people out of 25 (any order). The 25 binomial coefficient, (10) gives the number. Possible number of combinations are:

²⁵C₁₀ =  25! / (25-10)!(10!)

²⁵C₁₀ = 3268760

We want 3 letters and 3 digits but the first digit can't be zero. There are 26 alphabets and 10 digits. Since repetition is allowed we can use any of the 26 alphabets in place of all 3 letters.

This gives us 26 x 26 x 26 = 26³ ways to choose the first three letters.

For digits, since the first digit can't be 0, we can choose the rest 9 digits. For the next two digits, we can choose any one digit from 10. This gives us 9 x 10 x 10 ways to choose digits.

Finally, by law of multiplication, the total number of ways of choosing license plates is :

number of license plates = 26³ × 9 × 100

= 15818400

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Answer:

An inequality in mathematics is a statement that compares two values, with the use of inequality symbols like < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), and ≠ (not equal to). For example, the inequality "5 > 2" states that 5 is greater than 2. Inequalities can be used to represent real-world situations, such as expressing constraints or limitations.

Step-by-step explanation:

The coordinates can be determined by using mid point formula. Here the coordinates vertex C is (2,8), vertex A is (0,2) and vertex T is (6,4)

Here the midpoints are (1,5) , (4,6), (3,3).

By using mid point equation, x₁+x₂/2 = 1

So x₁+x₂ = 2  --------------------> eq 1

x₂+x₃/2 = 3

x₂+x₃ = 6   -----------------------> eq 2

x₁+x₃/2 = 4

x₁+x₃ = 8 -----------------------> eq 3

Adding equations 1,2,3

2( x₁+x₂+x₃) = 16

 x₁+x₂+x₃ = 8 ---------------> 4

Determining x-coordinates

Subtracting equation 1 from 4

x₁+x₂+x₃ -(x₁+x₂) = 8-2

 x₃ = 6

Similarly subtracting equation 2 from 4

x₁+x₂+x₃ -(x₂-x₃) = 8-6

x₁ = 2

Subtracting 3 from 4

x₁+x₂+x₃ -(x₁+x₃) = 8-8

x₂ = 0

Determining y coordinates

y₁+y₂/2 = 5

y₁+y₂ = 10 ----------------> 5

y₁+y₃/2 = 6

y₁+y₃ = 12 ----------------> 6

y₂+y₃/2 = 3

y₂+y₃ =6   -------------->  7

Adding equations 5,6 and 7

2(y₁+y₂+y₃) = 28

y₁+y₂+y₃ = 14 -----------------> 8

Subtracting equations 5,6 and 7 from 8

y₁+y₂+y₃ -(y₁+y₂) =14 - 10

y₃ = 4

y₁+y₂+y₃ -( y₂+y₃) = 14- 6

y₁ = 8

y₁+y₂+y₃-(y₁+y₃) = 14- 12 = 2

So the coordinates are (x₁ , y₁) =(2,8)

                                       (x₂, y₂) = (0, 2)

                                       (x₃, y₃) = (6,4)

So the coordinates of C,A and T are (2,8) , (0,2) and (6,4) respectively.

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A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

If the ratio is 5: 3, (girls: boys) we can use this equation to figure out how many boys there are if there are 35 girls:

We can see that in the ratio 5: 3, 5 is being multiplied by 0.6 to get three. If the relationship between the numbers 5 and 35 stays proportional, we multiply 35 by 0.6.

Therefore, the ratio of girls to boys is 35: 21, meaning there are 21 boys.

Answer: x = -3/2 , x = -1 1/2 , x = -1.5

Step-by-step explanation:

6/-4.5 = 8/4x

first determine the defined range --> x ≠ 0

cancel out the common factor 4 --> 6/-4.5 = 2/x

the convert the decimal into a fraction --> 6/-9/2 = 2/x

now use -a/b = a/-b = -a/b to rewrite the fraction --> 6/-9/2 = 2/x

then simplify the complex fraction --> -4/3 = 2/x

simplify the equation using cross-multiplication --> -4x=6

divide both side of the equation by -4 --> x = -3/2 , x ≠ 0

lastly, check if the solution is in the defined range --> x = -3/2

solution : x = -3/2

Alternative form: x = -1 1/2 , x = -1.5 (simplified)

Answer:

As P(M) = 0.45

P(F) = 1-0.45 = 0.55

P(Both students are male) = 0.45 x 0.45 = 0.2025 = 0.203 (cor to 3 dp)

P(Both students are female) = (1-0.45) x (1-0.45) = 0.55 x 0.55 = 0.3025 = 0.303 (cor to 3 dp)

P(First student male and second female) = 0.45 x 0.55 = 0.2475 = 0.248 (cor to 3 dp)

hope this helps!!!

The height of the right cylinder is 0.011 inches approximately.

Volume Definition:

Every three-dimensional object occupies some space. It is being determined how big this area is. Volume is the term used to describe the area contained within an object's three-dimensional boundaries. It is referred to as the object's capability on sometimes.

‘Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Now in the given question,

Circumference,

[tex]2\pi r[/tex] = [tex]\frac{41}{4}[/tex]

[tex]r=\frac{41}{8\pi }[/tex]

V = 9 cubic inches

volume of cylinder = πr²h = 3.14×[tex]\frac{41}{8\pi }^2[/tex]×h

h = (9)÷(3.14×[tex]\frac{41}{8\pi }^2[/tex]) = 0.011 inches

therefore the height of the cylinder is 0.011 inches approximately.

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Answer:

27.52

Step-by-step explanation:

1m =1.09 yards

30/1.09 = 27.52

Answer: Let x be the number of servings of Designer Whey and y be the number of servings of Muscle Milk.

We know that:

x + y = 7 (because you want 7 days of supply)

And the protein content per serving of Designer Whey is 18g and the protein content per serving of Muscle Milk is 20g. So:

18x + 20y = 412 (because you want 412g of protein)

And the carbohydrate content per serving of Designer Whey is 4g and the carbohydrate content per serving of Muscle Milk is 8g. So:

4x + 8y = 108 (because you want 108g of carbohydrates)

We can now use the above two equations to solve for x and y. We'll start by solving for x in terms of y:

18x + 20y = 412

18x = 412 - 20y

x = (412 - 20y)/18

Now we can substitute this expression for x into the equation for the carbohydrates:

4x + 8y = 108

4((412 - 20y)/18) + 8y = 108

1664 - 80y + 8y = 1080

1664 = 1080 + 80y

584 = 80y

y = 7.3

Since y must be an integer, we'll round it down to 7. So y = 7. We can now use either equation to find x:

18x + 20y = 412

18x + 20 * 7 = 412

18x = 412 - 140

18x = 272

x = 15.1

Since x must be an integer, we'll round it up to 15. So x = 15.

Therefore, you should combine 15 servings of Designer Whey and 7 servings of Muscle Milk in order to meet your requirements.

Step-by-step explanation:

There are 2518 sets of five marbles that include either the lavender one or exactly one yellow one, but not both.

To solve this problem, we need to find the number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both colors. Here's one way to approach the problem:

Number of sets of five marbles that include the lavender one: There is only one lavender marble, so we can choose any 4 other marbles to go with it.

There are a total of 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 7 x 6 x 5 x 4 = 840 possible sets of five marbles that include the lavender one.

Number of sets of five marbles that include exactly one yellow one: There are two yellow marbles,

So there are 2 possible choices for the yellow marble. For each choice, we can choose any 4 other marbles to go with it.

As before, there are 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 2 x (7 x 6 x 5 x 4) = 1680 possible sets of five marbles that include exactly one yellow one.

Number of sets of five marbles that include both the lavender one and exactly one yellow one:

We need to subtract these sets from the total number of sets that include either the lavender one or exactly one yellow one.

We have already found that there are 840 sets of five marbles that include the lavender one, and 1680 that include exactly one yellow one.

To find the number of sets that include both, we can choose any one yellow marble and the lavender one.

There are 2 choices for the yellow marble and 1 choice for the lavender one,

So there are 2 x 1 = 2 possible sets of five marbles that include both the lavender one and exactly one yellow one.

Number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both:

Finally, we need to subtract the number of sets that include both the lavender one and exactly one yellow one from the total number of sets that include either the lavender one or exactly one yellow one.

The total number of sets that include either the lavender one or exactly one yellow one is 840 + 1680 = 2520. The number of sets that include both is 2,

So the number of sets that include either the lavender one or exactly one yellow one, but not both, is 2520 - 2 = 2518.

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Answer:

  D. y = x² +7x +10

Step-by-step explanation:

You want the function that describes a graph showing a quadratic with roots of -5 and -2.

The factored form of the equation can be written from the x-intercepts (roots) by considering that a root of p means (x -p) is a factor. The factored equation is ...

  y = (x -(-5))(x -(-2)) = (x +5)(x +2) . . . . . doesn't match A or B

When this is multiplied out, it becomes ...

  y = x² +5x +2x +10 = x² +7x +10 . . . . . . matches choice D

The equation is y = x² +7x +10.

Answer:

see below

Step-by-step explanation:

170*70=11900

after one year 170*80 = 13600
gain on paper = 13600-11900 = 1700

80/70 = 1.14 so 14% if you had paid out of pocket

but then you bought on margin meaning you only used

15% of your money = 11900* 15% = 1785

but your gain was 1700, so your return = 1700/1785 = 95%

45% of your money = 11900* 45% = 5355

but your gain was 1700, so your return = 1700/5355 = 32%

85% of your money = 11900* 85% = 10115

but your gain was 1700, so your return = 1700/10115 = 17%

Answer:

[tex]240\pi cm^{2}[/tex]

Step-by-step explanation:

Lateral area of a cylinder is the curved surface area, (which connects the top with the base)

Curved Surface Area= [tex]2\pi rh[/tex]

where  r = radius of base

           h =  height of cylinder

Substituting the provided values:

Lateral area of cylinder = [tex]2\pi (6 cm)(20 cm)[/tex]

                                        = [tex]240\pi cm^{2}[/tex]

The expression with exactly two terms for the amount of money the club

will make for selling 'f' frames is 7f- 36.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression.

Given:

Price of frame= $13

Material cost = $6

Renting both cost = $36

For selling 'f' frames the amount of money the club make

= (13f - 6f) - 36

= (13-6)f- 36

= 7f- 36

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Answer:

B and C

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

Verify each statement.

A) 2⁻³ raised to the third power equals 1.

B) 2⁻³ is less than 1.

C) 2⁻³ is greater than 3⁻².

D) 2⁻³ multiplied by -1 equals 2³.

E) 2⁻³ is equal to -8.​

The cost of one candy bar is $2.35.

The meaning of unit price is a price quoted in terms of so much per agreed or standard unit of product or service.

Given that, there are 30 king-sized candy bars in a box and the box sells for $70.50, we need to find that how much does each candy bar in the box cost,

Since, the cost of all 30 candies is given collectively, i.e. $70.50,

We will divide the cost of the whole box by the number of candies to find the unit price of the candies,

Unit price = $70.50 / 30

= $2.35

Hence, the cost of one candy bar is $2.35.

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Answer:

y = -140x + 1400

Step-by-step explanation:

First, we'll find the slope, m, using the formula:

m = (160 - 780) / (8 - 4) = -620 / 4 = -155

Next, we'll use one of the points and the slope to find the y-intercept, b:

b = y - mx

We'll use the point (4, 780) to find b:

b = 780 - (4 * -155) = 1400

So the equation that models the balance, y, after x months is:

y = -155x + 1400

And since -155 can be simplified to -140, the equation becomes:

y = -140x + 1400

Any value of k greater than 0 will work, since the limit will be 1 as x approaches 0, regardless of the value of k. Other values of k can also work.

The limit in question is 3*_4limX-0 ekx+1. For any limit to exist, the expression must approach a finite number as x approaches 0. In this case, that number is 1. As long as the exponent k is greater than 0, the exponential expression will approach 0 as x approaches 0, and the limit will be 1. Therefore, any value of k greater than 0 will work. It is worth noting, however, that other values of k can also work. For example, if k is equal to 0, then the expression reduces to 3/4 as x approaches 0, and the limit still exists and is equal to 1. Similarly, if k is less than 0, then the expression will approach infinity as x approaches 0, and the limit will still exist and be equal to 1.

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The probability of getting exactly 7 heads when a fair coin is tossed 9 times is 0.164 to the nearest thousandth.

To calculate the probability of getting exactly 7 heads when a fair coin is tossed 9 times, we can use the binomial probability formula below:

P(X = k) = [tex]^nC_k * p^k * (1 - p)^{n - k}[/tex]

where;

p is the probability of success on a single trial = 0.5

n is the number of trials = 9

k is the number of desired successes = 7

Substituting:

P(X = 7) = ⁹C⁷ * (0.5)⁷ * (1 - 0.5)²

P(X = 7) ≈ 0.164

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Given the set of data used, This is an observational study because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured.

An observational study draws conclusions from a sample of a population in disciplines like epidemiology, social sciences, psychology, and statistics when the independent variable is not under the researcher's control due to ethical considerations or practical limitations.

With this in mind, the set of data presented is conducted in a way that doesn't change the response or the variable being measured.

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Answer:

3/4 servings

Step-by-step explanation:

Each serving = 1/2

There are 3/8 cookies.

How many times 1/2 "fits" into 3/8 = how many servings.

3/8 / 1/2

= 3/8 * 2

= 3/4 servings

Based on their contribution ratios, the amount each will get from the winnings is as follows:

A ratio shows the relative size of a variable, quantity, or value when compared to another.

Ratios are fractional values expressed as decimals, percentages, or fractions.

The cost of a ticket = R60

Contributions by:

Hanna = R15

Sarah = R21

Mthunzi = R24

Ratio = 5: 7: 8

Sum of ratios = 20 (5 + 7 + 8)

Hanna = R1,000 (5/20 x R4,000)

Sarah = R1,400 (7/20 x R4,000)

Mthunzi = R1,600 (8/20 x R4,000)

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Bistro’s food cost percent is 35.83%

Food cost percentage is calculated by taking the cost of goods sold and dividing that by the revenue or sales generated from that finished dish.

Food cost percent is calculated using the following formula:

Total Food Cost Percentage = (Total Cost of Goods Sold / Total Revenue) x 100

From the parameters in the question,

Total Food Cost Percentage = 67,000/187,000 x 100

Total Food Cost Percentage = 6,700,000/187000

Total Food Cost Percentage = 35.73%

Hence, the Bistro’s food cost percent is 35.83%

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Answer:

The area of the irregular figure is 8.1 ft² (rounded to the nearest tenth).

Step-by-step explanation:

The irregular figure is made up of:

[tex]\boxed{\begin{aligned}\sf Area\;of\;triangle&=\sf \dfrac{1}{2} \times base \times height\\\\&=\sf \dfrac{1}{2} \times 2.8 \times 3.6\\\\&=\sf 1.4 \times 3.6\\\\&=\sf 5.04 \; ft^2\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}\sf Area \; of\;semicircle&= \sf \dfrac{1}{2} \pi r^2\\\\&= \sf \dfrac{1}{2}\times 3.14 \times (1.4)^2\\\\&= \sf \dfrac{1}{2}\times 3.14 \times1.96\\\\&= \sf 1.57 \times1.96\\\\&= \sf 3.0772\; ft^2\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}\sf Area \;of\;irregular\;figure&=\sf Area\;of\;triangle+ Area\;of\;semicircle\\\\&=\sf 5.04+3.0772\\\\&=\sf 8.1172\\\\&=\sf 8.1\; ft^2\;(nearest\;tenth)\end{aligned}}[/tex]

Therefore, the area of the irregular figure is 8.1 ft² rounded to the nearest tenth.

There are 45697600 number of different license plates can be manufactured for this state.

The combination is a mathematical technique that is the number of ways to arrange the n number of collections where the order of selection does not matter.

ⁿCₐ= n!/(n-a)!a!

Here given in the question is,

On the license plate, there are 4 letters and 2 numbers.

Since, There are 26 alphabets in English from A to Z for which at position 1, there are 26 possibilities of alphabets at every position by,

²⁶C₁ = 26!/(26-1)!1!

       = 26!/25!1!

       = 26!/25!

        = 26

So, for 4 different positions of letters,

Then, The number of ways is,

⇒ 26×26×26×26 = 26⁴= 456976

And, There are 10 numbers in math for which at position 1, there are 10 possibilities of numbers at every position by,

¹⁰C₁ = 10!/(10-1)!1!

       = 10!/9!1!

       = 10!/9!

        = 10

So, for 2 different positions of numbers, the number of ways is,

= 10×10 = 10²= 100

Thus, The total number of ways the license can be manufactured = 456976 × 100= 45697600

Therefore, 45697600 different license plates can be manufactured for this state.

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