Let \( \alpha \) and \( \beta \) be first quadrant angles with \( \cos (\alpha)=\frac{\sqrt{5}}{10} \) and \( \sin (\beta)=\frac{\sqrt{10}}{10} \). Find \( \cos (\alpha+\beta) \).

Answer:

0.00007

Step-by-step explanation:

Answer:

0.00035

Step-by-step explanation:

0.0005×0.007 ×100

—————-------

1

0.0000035 ×100

0.00035

Given the following question:

We have 60 balloons in total

4/12 of the balloons are black

3/12 of the balloons are white

We are trying to find the amount of red balloons Carter has:

Let...

B = black

W = white

R = red

[tex]B=(\dfrac{4}{12}) \times60=20[/tex]

         [tex]B=20[/tex]

[tex]W=(\dfrac{3}{12}) \times60=15[/tex]

     [tex]20+15=35[/tex]

     [tex]60-35=25[/tex]

         [tex]R=25[/tex]

Carter has 25 red balloons

The shares of Eno and Musa in gained dividends are: R 110 and R 165 respectively.

Total amount : R 275.00

Ratio of Eno to Musa = R 2.00 / R3.00

So,

Total ratio: 2 + 3 = 5

Then,

Eno's share = 2/5*275

Eno's share = R 110

Similarly,

Musa's share = 3/5*275

Musa's share = R 165

Thus, the shares of Eno and Musa in gained dividends are: R 110 and R 165 respectively.

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It takes Martha `4` hours to knit each hat and `13` hours to knit each pair of mittens.

What is meant by hours?

Hours are a unit of time used to measure the duration of an event or activity. An hour is equal to 60 minutes or 3,600 seconds. It is often used to indicate the time of day or to schedule appointments or events.

What is a pair?

A pair is a set of two things that go together or belong together, like a pair of shoes, socks, or gloves. It can also refer to a pair, a duo, or a twosome.

According to the given question

Let's assume that each hat takes `h` hours to knit and each pair of mittens takes `m` hours to knit.

From the given information, we know that:

- 3 hats and 3 pairs of mittens took a total of 51 hours. This means that 3h + 3m = 51.

- 3 hats and 5 pairs of mittens took a total of 77 hours. This means that 3h + 5m = 77.

We can use these two equations to solve for `h` and `m`.

First, let's solve for `h` by multiplying the first equation by 5 and the second equation by 3, and then subtracting the second equation from the first:

15h + 15m = 255

9h + 15m = 231

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

6h = 24

h = 4

So each hat takes Martha `4` hours to knit.

Now we can use either of the original equations to solve for `m`. Let's use the first one:

3h + 3m = 51

3(4) + 3m = 51

12 + 3m = 51

3m = 39

m = 13

So each pair of mittens takes Martha `13` hours to knit.

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Answer:

population: 2,900,904.279

Step-by-step explanation:

You need to calculate the total area first. The figure is made from 2 smaller figures.

Area for the top figure = 159 x (345 - 276) = 159 x 69 = 10971

Area for the bottom figure = 265 x 276 = 73140

Total are = 10971 + 73140 = 84111 mi^2

so you have 34.489 people/mi^2 =>

34.489 x 84111 = 2,900,904.279 people

Answer: diffrent form so i can help you better

Step-by-step explanation:

Answer:

525 units

Step-by-step explanation:

firsat find a 1% increase

25/100 = 0.25

multiply this by 20 (per 5 years) and add to the original amount

0.25 x 20 = 500

500+25 = 525

This is your answer, and you just repeat this process for each year

To find the angle in radians, we need to convert the given angle from degrees to radians. We know that 180 degrees = π radians.

So,

34 degrees = (34/180) * π radians

= 0.1885 * 3.14

= 0.591 radians

Therefore, the answer is (C) 0.59 radians.

The area of the sector (the slice you eat) can be calculated using the formula:

Area = (n/360) * πr^2

where n is the central angle in degrees, and r is the radius of the slice.

Plugging in the given values, we get:

Area = (34/360) * 3.14 * 8^2

= 0.1 * 3.14 * 64

= 20.096 square inches

Rounding to the nearest tenth, the answer is 20.1 square inches.

The arc length of the pizza you have eaten can be calculated using the formula:

Arc Length = (2πr * Ø)/360

where Ø is the angle in degrees, and r is the radius of the slice.

Plugging in the given values, we get:

Arc Length = (2 * 3.14 * 8 * 34)/360

= 4.776 inches

Therefore, the answer is 4.776 inches.

It is nοt pοssible that fοr sοme v, the equatiοn cx = v has mοre than οne sοlutiοn if c is invertible.

Inverse οperatiοns are οppοsite οperatiοns that undο each οther. Fοr example, 5 ✕ 2 = 10 and 10 ÷ 2 = 5 are inverse οperatiοns.

If the equatiοn cx = v is cοnsistent fοr every v in R⁶, it means that the matrix c is invertible, οr has a unique sοlutiοn fοr every v.

This is because if c is nοt invertible, then there exist sοme vectοrs v in R⁶ fοr which the equatiοn cx = v has nο sοlutiοn οr has infinitely many sοlutiοns.

If c is invertible, then fοr any vectοr v in R⁶, the equatiοn cx = v has a unique sοlutiοn given by

[tex]x = c^{( 1 )} v[/tex], where [tex]c^{(1)}v[/tex]

is the inverse οf c.

Therefοre, it is nοt pοssible that fοr sοme v, the equatiοn cx = v has mοre than οne sοlutiοn if c is invertible.

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The probability that the person selected is a tall, left-handed woman is 0.02.

Given that, The probability that the person selected is a woman is P(W) = 38% = 0.38

The probability that the person selected is tall is P(T) = 54% = 0.54

The probability that the person selected is left-handed is P(L) = 11% = 0.11

It is given that the events W, T, and L are independent of each other. Therefore, their joint probability is given by:

P(W ∩ T ∩ L) = P(W) × P(T) × P(L) = 0.38 × 0.54 × 0.11 = 0.02292

Now, the probability that the person selected is a tall, left-handed woman is given by:

P(T ∩ L ∩ W) = P(W ∩ T ∩ L) = 0.02292 = 0.02

Therefore, the probability that the person selected is a tall, left-handed woman is 0.02.

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14 by 16

I just know it :DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

The probability of the complement of choosing an orange juice box is 17/18. (option d)

The complement of an event is the probability of that event not occurring. In this case, the event is choosing an orange juice box, so the complement is choosing any other juice box (i.e., an apple juice box or a fruit punch juice box).

The total number of juice boxes in the cooler is:

4 + 8 + 6 = 18

The number of juice boxes that are not orange juice boxes is:

4 + 6 = 10

Therefore, the probability of choosing a juice box that is not an orange juice box (i.e., the complement of choosing an orange juice box) is:

10/18 = 5/9

But the question asks for the probability of the complement, which is the probability of not choosing a juice box that is not an orange juice box. This is simply:

1 - 5/9 = 4/9

However, the question asks for the probability of the complement of choosing an orange juice box, not the complement of not choosing an orange juice box. These two probabilities are equal, since the event and its complement always add up to 1. Therefore, the probability of the complement of choosing an orange juice box is:

1 - 8/18 = 10/18 = 17/18

Therefore, the probability of the complement of choosing an orange juice box is 17/18.

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i cant fully answer it but i know the steps,

(the link is how you would set it up)

you can replace x with 20 or 27, i would start 20

Answer:

exact form: [tex]\frac{18}{5}[/tex]

decimal form: 3.6

mixed number form: [tex]3\frac{3}{5}[/tex]

Answer:

y=18/5

Step-by-step explanation:

6=5y/3

multiply both sides:

6*3=5y

simplify 6*3 to 18:

18=5y

divide both sides by 5:

18/5=y

answer: y=18/5

Answer:

_2⁵b⁴*⁵a⁵

Answer=_32b²⁰a⁵

The triangle fοrmed by J(7,2), K(-4,9), and L(-3,-1) is a scalene οbtuse triangle.

A triangle is said tο be οbtuse scalene in geοmetry if οne οf its angles is larger than 90 degrees but less than 180 degrees, while the οther twο angles are bοth less than 90 degrees. Measurements fοr the three sides and angles vary.

Tο classify the triangle fοrmed by the pοints J(7,2), K(-4,9), and L(-3,-1), we need tο find the lengths οf its sides and apply the triangle classificatiοn criteria.

Using the distance fοrmula, we can find the lengths οf the sides:

[tex]JK = \sqrt{[(7 - (-4))^2 + (2 - 9)^2]} \\JK =\sqrt{ (11^2 + (-7)^2)} \\ JK =\sqrt{170} \\KL = \sqrt{[(-4 - (-3))^2 + (9 - (-1))^2]} \\KL =\sqrt{ (1^2 + 10^2) } \\KL = \sqrt{101} \\LJ = \sqrt{[(-3 - 7))^2 + ((-1) - 2)^2]} \\LJ=\sqrt{ (10^2 + (-3)^2)} \\LJ = \sqrt{109}[/tex]

Since all three sides have different lengths, the triangle is scalene.

Therefοre, the triangle fοrmed by J(7,2), K(-4,9), and L(-3,-1) is a scalene οbtuse triangle.

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Two shapes would have equal volumes if the areas of their corresponding cross-sections are equal at every height.

According to Cavalieri's principle, two shapes have equal volumes if for every pair of parallel cross-sections taken at the same height, the areas of the cross-sections are equal.

1. Two cylinders with the same height and different radii.

  As long as the cross-sectional areas of the cylinders at each height are the same, the volumes will be equal. The radii of the cylinders can vary.

2. Two cones with the same height and different base radii.

  Similar to cylinders, as long as the cross-sectional areas of the cones at each height are the same, the volumes will be equal.

3. Two prisms with the same height and different base shapes.

  If two prisms have the same height and the cross-sectional areas at each height are equal, then the volumes will be equal.

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Answer:

-7 and 3

-5 and 1

-3 and -1

Step-by-step explanation:

-7 + 3 = -4

-5 + 1 = -4

-3 + -1 = -4

The probability that a randomly selected bicycle from a bicycle shop will have either a water bottle holder or a kickstand is 95%, calculated by adding the probabilities of each component being present and subtracting the probability of both being present.

The probability that a randomly selected bicycle from a bicycle shop will have either a water bottle holder or a kickstand is 95%. To calculate this, we first need to consider the probability that a bicycle has a water bottle holder, which is 60%. The probability that the bicycle has a kickstand is 55%. Then, the probability of a bicycle having both a kickstand and a water bottle holder together is the product of the individual probabilities, which is 34%. Thus, the probability that a randomly selected bicycle will have either a water bottle holder or a kickstand is 60% + 55% - 34% = 95%.

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The money is Noah wants to share  with people if each person still gets the same amount is 4.

The algebraic approach to solving simultaneous linear equations is known as substitution method.

Let the total amount Noah have be'y'.

The initial amount shared by Noah among 10 people be 'x'.

Then,

y = 10x

But,

Amount shared is decreased by 20, ans sharing with 5 people.

Then,

y - 20 = 5x

Put value of y.

10x = 5x + 20

On solving;

x = 20/5

x = 4

Thus, money is Noah wants to share  with people if each person still gets the same amount is 4.

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The coordinates of the midpoint of the given segment is; (-15, 4)

For any specific line segment, it is well known that the midpoint is defined as the halfway between its two endpoints. The expression that is used to find the x-coordinate of that midpoint is expressed as: [(x)1 + (x)2]/2, which denotes the average of the x-coordinates. Similarly, the expression that is used to find the y-coordinate of that midpoint is expressed as: [(y)1 + (y)2]/2, which is the average of the y-coordinates.

We are given the coordinates of the endpoints of the line as;

K(-11, 2) and L(-19, 6)

Thus;

Midpoint Coordinate = (-11 - 19)/2, (2 + 6)/2

= (-15, 4)

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If P represents the number of pounds of your package, and C is the total cost of shipping your package, the equation that represents the relationship between P and C is C = 3 + 0.63P.

To write an equation that represents the relationship between the weight of the package (P) and the total cost of shipping (C), we need to use the information given in the problem. The shipping company charges a fixed base cost of $3 per package plus an additional $0.63 per pound.

We can represent the additional cost per pound as 0.63P, since the cost increases by $0.63 for every additional pound. Therefore, the equation that represents the relationship between P and C is:

C = 3 + 0.63P

This equation gives us the total cost of shipping a package based on its weight. We can use this equation to calculate the cost of shipping a package of any weight by simply plugging in the weight (in pounds) for P and then solving for C.

For example, if a package weighs 5 pounds, we can substitute P = 5 into the equation to get:

C = 3 + 0.63(5)

C = 3 + 3.15

C = 6.15

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Yes, they will reach their goal of $45.00 by selling 12 cups of lemonade on Sunday.

Yes, they will reach their goal. To calculate this we can use the following formula:

Total Sales = (Number of cups sold on Saturday × Price per cup) + (Number of cups sold on Sunday × Price per cup)

Total Sales = (37 × 0.75) + (12 × 0.75)

Total Sales = 27.75 + 9

Total Sales = 36.75

Since 36.75 is greater than the goal of 45.00, they will reach their goal. This can be further verified by looking at the total cost of the cups they sold. 37 cups sold on Saturday at $0.75 each will cost $27.75. Adding the 12 cups sold on Sunday at $0.75 each will cost $9, bringing the total cost of the cups sold to $36.75. This is the same amount that was calculated using the formula above. Therefore, they will reach their goal by selling 12 cups of lemonade on Sunday.

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The total simple interest earned by Liz at the end of 5 years is found as: $28.5

A straightforward but effective idea. Very simply: interest is the benefit for saving - and the penalty of borrowing.

Principal P = $570

Interest r = 1%

Time t = 5 years.

SI = P*R*t / 100

SI = 570*1*5 / 100

SI = 28.5

Thus, the total simple interest earned by Liz at the end of 5 years is found as: $28.5.

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The complete question is-

Liz spent her summer break working at Wild Lakes waterpark. At the end of the summer, she put $570 of her earnings into a savings account that earns 1% interest each year. Find her simple interest after 5 years.

We can confirm that each person should receive exactly 224 Pokémon cards, and there won't be any cards left over.

To split the 1,792 Pokémon cards equally between 8 people, including yourself and your 7 friends, you need to divide the total number of cards by the number of people:

1,792 cards ÷ 8 people = 224 cards per person.

So each person should get 224 Pokémon cards.

However, we should also check if there is a remainder after the division. To do that, we can multiply the number of cards each person is getting by the number of people and subtract it from the total number of cards:

224 cards/person x 8 people = 1,792 cards

1,792 cards - 1,792 cards = 0 remainder

Since there is no remainder, we can confirm that each person should receive exactly 224 Pokémon cards, and there won't be any cards left over.

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A graph that would display the narrowest parabola is f(x) = -4x² - 30x.

In Mathematics, the standard equation of the directrix lines for any parabola can be modeled or represented by the following mathematical expression:

y = a(x - h)² + k.

Where:

Generally speaking, the larger the absolute value of the leading coefficient of a quadratic function, the narrower would be graph of its parabola.

In this context, we have the following:

y = -2x²+x+3; a = -2

f(x) = -4x² - 30x; a = -4

|a| = |-2| = 2

|a| = |-4| = 4

Therefore, |-2| is less than |-4|.

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Answer: 32.2 cubic inches

Step-by-step explanation:

 The volume of one coin can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.

Substituting the given values, we get:

V = π(1.4)^2(0.0625)

V ≈ 0.14 cubic inches (rounded to the nearest hundredth)

To find the total volume of all the coins, we can multiply the volume of one coin by the number of coins:

Total volume = 230 × 0.14

Total volume ≈ 32.2 cubic inches (rounded to the nearest hundredth)

Therefore, the coins take up approximately 32.2 cubic inches of the treasure chest.

The correct option for this question is C. arrangement of the body.

Why it is?

Based on the given passage, the word "lines" most likely refers to the arrangement of the body in ballet dancing. The passage states that "Ballet places a lot of emphasis on the lines of the body" and that "Good lines" in ballet are a combination of the body alignment and artistic expression.

It also mentions that proper positioning of the feet is important for achieving good lines and that turnout, which is the outward rotation of the hips and knees, is the basis for all ballet movements.

Therefore, "lines" in this context is referring to the visual lines created by the dancer's body and limbs in ballet dance, which are essential to proper technique and artistic expression.

Therefore, the correct answer is C. arrangement of the body.

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Relation 2 and 3 are actual functions with proper domain, co domain, range.

A function can be represented in several ways, including using algebraic expressions, tables, graphs, or even words. For example, the function f(x) = 2x + 1 defines a relationship between the input x and the output 2x + 1. If we input x = 3 into this function, the output would be f(3) = 2(3) + 1 = 7.

Functions can have different properties, such as being continuous or discontinuous, being differentiable or nondifferentiable, or having maximum or minimum values. Functions can also be classified according to their types, such as linear, quadratic, exponential, logarithmic, trigonometric, or piecewise-defined functions.

Functions are used extensively in mathematics, science, engineering, economics, and many other fields to describe real-world phenomena and to solve practical problems. They are also studied in their own right, as objects of mathematical interest and beauty, with deep connections to many other areas of mathematics, such as calculus, analysis, and algebra

Relation 2 and 3 are actual functions with proper domain, co domain, range.

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