1 point Convert an angle of 55° into radians. Round your answer to the nearest hundredth
1 point On a circle of radius 5 trace out an angle of 6 radians. What arc length have you just traced? Round your answer to the nearest hundredth.

The amounts of 30% pure silver and 45% pure silver that should be mixed to obtain 14 grams of 43% pure silver are approximately 1.867 grams and 12.133 grams, respectively.

To determine the amounts of 30% pure silver and 45% pure silver that should be mixed to obtain 14 grams of 43% pure silver, we can set up a system of equations based on the given information.

Let's assume x represents the amount (in grams) of the 30% pure silver and y represents the amount (in grams) of the 45% pure silver.

Equations based on the amounts of silver:

x + y = 14 -- equation (1) (total amount of silver is 14 grams)

Equations based on the percentages of silver:

(0.30x + 0.45y) / (x + y) = 0.43 -- equation (2) (overall purity of the mixture is 43%)

To solve the system of equations, we can use substitution or elimination method. In this case, let's use the substitution method.

From equation (1), we can express x as 14 - y and substitute it into equation (2):

(0.30(14 - y) + 0.45y) / (14 - y + y) = 0.43

Simplifying the equation:

(4.2 - 0.3y + 0.45y) / 14 = 0.43

(4.2 + 0.15y) / 14 = 0.43

4.2 + 0.15y = 0.43 * 14

4.2 + 0.15y = 6.02

0.15y = 6.02 - 4.2

0.15y = 1.82

y = 1.82 / 0.15

y ≈ 12.133

Now, substitute the value of y back into equation (1) to find x:

x + 12.133 = 14

x = 14 - 12.133

x ≈ 1.867

Therefore, the amounts of 30% pure silver and 45% pure silver that should be mixed to obtain 14 grams of 43% pure silver are approximately 1.867 grams and 12.133 grams, respectively.

Please note that the answers have been rounded to three decimal places for convenience, but you can use the exact decimal values for more precise calculations if needed.

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According to the characteristics of ticket sales and the resulting system of linear equations we find that 122 children bought each one a ticket on Sunday.

In this question we have a word problem, whose information must be translated into algebraic expressions to find a solution. Let be x and y the number of children and adults that went to the movie theatre, respectively.

We need two linear equations, one for the number of people assisting to the theatre and another for the total sales:

x - 4 · y = 0     (1)

6.30 · x + 9.50 · y = 1063.20     (2)

By algebraic procedures the solution to this system is: x = 122.559, y = 30.639. Since the number of tickets sold are integers, then we truncate each result: x = 122, y = 30.

According to the characteristics of ticket sales and the resulting system of linear equations we find that 122 children bought each one a ticket on Sunday.

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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The angle <AOB has a measured angled of 144 degrees.

The given diagram is a circle geometry. The triangle in the circle is an isosceles triangle since it is projected from a circumference.

Since the sum of angle in a triangle is 180 degrees, hence;

<A + <B + <O = 180

Since <A + <B = 18 degrees, hence;

18 + 18 + <O = 180

36 + <O = 180

<O = 180 - 36

<O = 144 degrees

Hence the measure of the angle AOB is 144 degrees.

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Differentiate a Power Series is g(z) = Σ (-3)^n * n * z^(n-1), for n=1 to infinity, and -1/3 < z < 1/3.

To differentiate the power series representation of f(x) = ln(1-3z) to find g(z), first recall the power series representation for ln(1-x):

f(x) = ln(1-x) = -Σ (x^n)/n, for n=1 to infinity, and |x| < 1.

Now, we have f(x) = ln(1-3z). Replace x with -3z:

f(x) = ln(1-(-3z)) = ln(1+3z) = -Σ ((-3z)^n)/n, for n=1 to infinity, and |-3z| < 1.

To find the power series representation for g(z), differentiate f(x) with respect to z:

g(z) = d/dz[-Σ ((-3z)^n)/n] = Σ (-3)^n * n * z^(n-1), for n=1 to infinity, and |-3z| < 1.

However, the question asks for the power series representation on the interval (-1, 1):

Since |-3z| < 1, we have -1/3 < z < 1/3. Thus, g(z) = Σ (-3)^n * n * z^(n-1), for n=1 to infinity, and -1/3 < z < 1/3.

Differentiating the power series representation for g(z), f(x) = ln(1-3z) gives: f'(z) = -3/(1-3z)

Now, we can find the power series representation for f'(z) as follows:

f'(z) = -3(1+3z+9z^2+...) = -3∑n=0^∞(3z)^nHence, the power series representation for g(z) is:g(z) = ∫f'(z)dz = ∫(-3(1+3z+9z^2+...)dz= -3(z+3z^2+3*3z^3/3+...) = -3∑n=1^∞3^(n-1)z^n The power series representation of g(z) is therefore given by ∑n=1^∞-3*3^(n-1)z^n  

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A. \(\bold{\boxed{\green{2^{12}}}}\)

Answer:

Solution given:

\(2^6 x (2^2)^3\)

we know that

product of power and power is added and power to power is multiplied for same base only.

I.E.

product of same base but different power:\(a^b+a^c=a^(b+c)\)

power to power :\( (a^b)^c=a^(b*c)\)

By using above property

\(2^6+2^{2*3}\)

\( 2^6+2^6\)

\(2^{[6+6]}=2^{12}\)

Answer: I think it is 364.80

Center point of dilation is a fixed point in a plane about which all the points of the figure expanded or contract. And scale factor of a dilation is the ratio of new formed image to the old given image.

Explanation:

Therefore, the center of the dilation can be find using the translation and scale factor can be calculated using the ratio of the new to the old images.

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The vertex of the function defined as g(x) = f(x+2) is (8, 4).

From the question, we have the following parameters that can be used in our computation:

Vertex of f(x) = (6, 4)

For the function defined as g(x) = f(x+2), we have

Vertex = (x + 2, y)

Where

x = 6 and y = 2

Substitute the known values in the above equation, so, we have the following representation

Vertex = (6 + 2, 4)

Evaluate

Vertex = (8, 4)

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Answer: a

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

-2x^3+4x

To decrease the width of the confidence interval, the researcher can take the following steps:

1. Decrease the confidence level: The confidence interval width is inversely proportional to the confidence level. By decreasing the confidence level, the researcher can have a narrower interval. However, it is important to note that decreasing the confidence level also increases the chance of the interval not capturing the true population mean.

2. Increase the sample size: The sample size affects the precision of the estimate. Increasing the sample size reduces the standard error, which leads to a narrower confidence interval. This is because a larger sample provides more information about the population.

Therefore, the researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a narrower interval, providing a more precise estimate of the mean fat content of hen's eggs.

The researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a more precise estimate of the mean fat content of hen's eggs.

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Answer:

I attached answer list respectively

Answer:

width=5.5

Length=12

Step-by-step explanation:

L = 1+2W       [eq2; “length of the rectangle is 1 yd more than twice the width”]

(1+2W)(W)=66      [substitute eq2 for L in eq1]

W + 2W2= 66       [distribute]

2W2+ W – 66 = 0     [put all term on left side]

(2W-11)(W+6) = 0      [factor or use Quadratic Formula]

Substitute for W in either formula:

L = 1 + 2(5.5)

(i don't know if you understand this)

Answer:

Daniel is 8 years old now

Step-by-step explanation:

Let Kevin's age now be K and let Daniel's age now be D

"Kevin is 3 times as old as Daniel"

Translation: K = 3D

"4 years ago, Kevin was 5 times as old as Daniel"
4 years ago Kevin's age = K - 4
4 years ago Daniel's age = D - 4
4 years ago, Kevin was 5 times as old as Daniel.

Translation: K - 4 = 5(D - 4)
K - 4 = 5D - 20

Simplify this equation:
Add 4 to both sides:
K - 4 + 4 = 5D - 20 + 4

K = 5D - 16

Substitute K = #D:
3D = 5D - 16

Subtract 5D from both sides:
3D - 5D = - 16
-2D = -16

or

2D = 16   (multiply by - 1)

D = 16/2 = 8

and

K = 3D = 3 x 8 = 24

Now, Kevin is 24 years old and Daniel is 8 years old

Verify
If Kevin is 3x older than Daniel who is 8 now,
Kevin's age now = 3 x 8 = 24  Check

4 years ago, Daniel was 8 - 4 = 4 years
4 years ago, Kevin was 24 - 4 = 20
Kevin's age 4 years ago = 5 x 4 = 20 Check

Derek's total income from selling 31 bags of popcorn at the first game is $62 and he sold 322 bags of popcorn over the whole season.

It is a branch of mathematics that deals with the occurrence of a random event.

a. Independent variable: Bags of popcorn (X)

Dependent variable: Income (I)

b. If the function is I(X) = 2X, we can find Derek's total income by plugging in the number of bags he sold at the first game, which is X = 31:

I(31) = 2(31) = 62

Therefore, Derek's total income from selling 31 bags of popcorn at the first game is $62.

c. To find out how many bags of popcorn Derek sold over the whole season, we need to rearrange the function to solve for X:

I(X) = 2X

X = I(X) / 2

We know that Derek made a total income of $644 over the whole season, so we can plug this in to find X:

X = 644 / 2 = 322

Therefore, Derek sold 322 bags of popcorn over the whole season.

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Answer:

C

Step-by-step explanation:

If 1472cm² of wrapping paper is needed to cover the smaller box, approximately 1672cm² of wrapping paper is needed to cover the larger box (assuming the surface area is directly proportional to the length).

Since the smaller and larger boxes have exactly the same shape, we can assume that their dimensions are proportional.

Let's denote the width and height of the smaller box as "w" and "h," respectively, and the width and height of the larger box as "W" and "H," respectively.

We know that the length of the smaller box is 16 cm, so we have:

Length of smaller box = 16 cm

Width of smaller box = w

Height of smaller box = h

To find the dimensions of the larger box, we can set up a proportion based on the lengths of the boxes:

16 cm / 18 cm = w / W

From this proportion, we can solve for W:

\(W = (18 cm \times w) / 16 cm\)

Now, let's consider the surface area of the boxes.

The surface area of a box is given by the sum of the areas of its six faces. Since the boxes have the same shape, the ratio of their surface areas will be equal to the square of the ratio of their lengths:

Surface area of smaller box / Surface area of larger box = (16 cm / 18 cm)^2.

We know that the surface area of the smaller box is 1472 cm^2, so we can set up the equation:

\(1472 cm^2\) / Surface area of larger box \(= (16 cm / 18 cm)^2\)

To find the surface area of the larger box, we rearrange the equation:

\(Surface $area of larger box = 1472 cm^2 / [(16 cm / 18 cm)^2]\)

Now we can substitute the value of W into the equation to find the surface area of the larger box:

Surface area of larger box \(= 1472 cm^2 / [(16 cm / 18 cm)^2] = 1472 cm^2 / [(18 cm \times w / 16 cm)^2]\)

\(= 1472 cm^2 / [(18 \times w / 16)^2] = 1472 cm^2 / [(9w / 8)^2]\)

\(= 1472 cm^2 / [(81w^2 / 64)]\)

Simplifying further:

Surface area of larger box \(= (1472 cm^2 \times 64) / (81w^2)\)

So the amount of wrapping paper needed to cover the larger box is given by the surface area of the larger box, which is:

\((1472 cm^2 \times 64) / (81w^2)\)

Note that we don't have enough information to calculate the exact value of the wrapping paper needed to cover the larger box since we don't know the width "w" of the smaller box.

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The probability that the second card is a spade given the first one is a spade is 12/51.

To find the probability that the second card drawn is a spade given that the first one is a spade, we need to use conditional probability.

Let's first find the probability of drawing a spade on the first draw. Since there are 13 spades in a standard deck of 52 cards, the probability of drawing a spade on the first draw is 13/52 or 1/4.

Now, since we are drawing without replacement, there are only 51 cards left in the deck for the second draw and only 12 spades left. So, the probability of drawing a spade on the second draw given that the first one was a spade is 12/51.

Therefore, the probability that the second card is a spade given that the first one is a spade is 12/51 or approximately 0.235.

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Answer:

1) The download speed for AT&T is 1,800

2) The download speed for Bidmore is 1,500

3) The download speed for Comcast is 1,680

4) AT&T has the best download speed out of the three.

5) They will go through the origin and be a proportional line.

Step-by-step explanation:

The equation 3+7+2=+2 is actually not true, but false.

The equation 3+7+2=+2 is actually not true, but false. This is because the sum of 3, 7, and 2 is 12, not 2.

In general, an equation is considered true if the expressions on both sides of the equal sign are equivalent in value. In this case, the expressions on the left-hand side (3+7+2) and the right-hand side (+2) are not equivalent, and therefore the equation is false.

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Answer:

Hi there.....

Step-by-step explanation:

This is ur answer......

1, 3, 5, 7, 9, 11, 13, 15.................39

Therefore the total sum = 400

hope it helps you,

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Answer:

400

Step-by-step explanation:

These are the first 20 odd numbers

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35 + 37 + 39

Put them in a calculator and you get: 400

Answer:

36 girls are in the choir

Step-by-step explanation:

answer:

36

sbs:

divide 56 by 3 and multiply it 2

Answer:

35 1/2 Miles divied by 1 1/4=28.4 gallons

Step-by-step explanation:

Answer:

16. C

17. B

Step-by-step explanation:

All you have to do is plug in the numbers into the pythagorean theorem. The Pythagorean Theorem is: \(a^2+b^2=c^2\) Now I encourage you to try these problems out for yourself and see why they're correct. Doing these will help you solve other propblems like this. Remember the hypotenuse is alays the longest side. ;)

Answer:

Lena can buy candy in infinite no of ways with the possible amounts:-

1 pound of candy = $7

1.1 pound of candy = $7.7

2 pounds of candy = $14

3 pounds of candy = $21

4 pounds of candy = $28

5 pounds of candy = $35

6 pounds of candy = $42

7 pounds of candy = $49

8 pounds of candy = $56

9 pounds of candy = $63

10 pounds of candy = $70

11 pounds of candy = $77

11.9 pounds of candy = $83.3

With Square Payments, you can easily and safely accept all forms of payment. You can collaborate with customers rather than competing with them when it comes to how they want to pay for goods and services when you use Square Payments.

Through Square, you can accept credit cards, Apple Pay, Android Pay, and a lot of other payment options. A client is an individual or company who purchases goods or services from another company. Customers are essential because they produce income. Without them, companies would cease to exist. A customer is the recipient of a good, service, product, or idea in sales, commerce, or economics that they have purchased from a seller, vendor, or supplier in exchange for money or another useful consideration. When a customer buys something and uses it themselves, they are considered a consumer. Although they might not be the final users, customers always buy goods or services. Although they might not have paid for it, consumers are always the ones who use a good or service in the end.

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