Order these numbers from least to greatest.

3/4, -1/5, -5/16, 0.90, -0.52

0.90, 3/4, -5/16 , -0.52, -1/5
-1/5 , -5/16 , -0.52, 3/4, 0.90
0.90, 3/4, -0.52, -5/16 , -1/5
-0.52, -5/16 , -1/5 , 3/4, 0.90

There are 10 keychains were made from 180 beads.

What is keychain?

A metal ring or chain known as a keychain, sometimes known as a key fob or keyring, is used to hang multiple keys on.

You can keep your keys organized on a key ring, which is a metal ring. Through the slots in your keys, you pass the ring.

Typically, it will be bigger than the split ring, and the polished stainless steel style is perfect for adding some lovely colors. The paint, which is a charming keychain in and of itself, gives the Carabiner Clip its lovely color.

Given:

The members of the art club are making keychains that require 18 beads a piece.

The art club adviser brought a bag with 250 beads for them to use.

There are 70 beads left in the end.

That is there are 250 - 70 = 180 beads are used.

Since each keychain requires 18 beads.

So, there are 180 / 18 = 10 keychains were made.

Here, there are 18 keychain were made.

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The expression represents the number of coins Arthur is x + 80 cents.

The term expression in math refers a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that Arthur has x pennies. His father gave him 6 dimes, and his mother gave him 4 nickels.

And we need to find expression represents the number of coins Arthur has now.

From the given question, here we have to convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

AS we know that one penny = 1 cent, one dime = 10 cents, one nickel = 5 cents and

Therefore, x pennies = x cents

Then 6 dimes = 60cents

Then 4 nickels = 20 cents

Therefore, the Arthur's coins in total is written as,

=> (x + 60 + 40) cents

=> (x + 80) cents.

Therefore, the resulting expression is written as (x + 80) cents.

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Triangle ABC was reflected over the y axis and then translated 2 units left to form triangle A'B'C'.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Triangle ABC was reflected over the y axis and then translated 2 units left to form triangle A'B'C'.

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Answer: translation 2 units to the right and reflection across the y-axis

Step-by-step explanation:

i took the test and got it correct, i also added a picture :)

Answer:

y = 7

Step-by-step explanation:

The equation: 2y+5=3y-2

-

Solving the equation:

1) We have to move 2y to the other side while also moving the -2 to the other side.

The equation will now be 5+2=3y-2y

2) Now we can add and subtract the values.

So, it'll  be 7 = y.

Therefore, Y is equal to 7.

Proof of identity tanθ = secθ/cscθ is shown below.

We have to give that,

Verify the identity,

tanθ = secθ/cscθ

Now, We can prove as,

Since,

sec θ = 1 / cos θ

csc θ = 1 / sin θ

tan θ = sin θ / cos θ

LHS,

tan θ = sin θ / cos θ

RHS,

secθ/cscθ = (1 / cos θ) / (1 / sin θ)

secθ/cscθ = (sin θ / cos θ)

secθ/cscθ = tan θ

Hence, We prove that,

tanθ = secθ/cscθ

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Answer:

Multiply the height by 2, and divide the result by the object's acceleration due to gravity. If the object fell from 5 m, the equation would look like this: (2*5 m)/(9.8 m/s^2) =1.02 s^2. Take the square root of the result to calculate the time it takes for the object to drop.

Answer:

it may bee

10y²-15y+5

=10y²-10y-5y+5

=10y(y-1)-5(y-1)

=(y-1)(10y-5) ans

The solution of the differential equation y'' + y' + y = 0 is,

\(y = C_{1} e^{\frac{(- 1 + \sqrt{3}i) }{2} } + C_{2} e^{\frac{(- 1 - \sqrt{3}i) }{2} }\)

We have to give that,

Solve the following differential equation,

y'' + y' + y = 0

Now, the auxiliary equation is,

m² + m + 1 = 0

Solve the equation for m,

m = (- 1 ± √(1² - 4)) / 2

m = (- 1 ± √- 3i) /2

m = (- 1 ± √3i)/2

Hence, the solution of the differential equation,

\(y = C_{1} e^{\frac{(- 1 + \sqrt{3}i) }{2} } + C_{2} e^{\frac{(- 1 - \sqrt{3}i) }{2} }\)

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Answer:

117 in²

Finding the area of the trapezoid:

First, we need to find the area of the trapezoid formed by the dotted lines. The formula for finding the area of the trapezoid is "(a₁ + a₂)h/2".

[Where, a₁ = shorter parallel side; a₂ = longer parallel side]

⇒ (a₁ + a₂)h/2 = Area of trapezoid

⇒ (14 + 26)15/2 = Area of trapezoid

⇒ Area of trapezoid = (40)15/2 = (20)15 = 300 in²

Reviewing on how to find the area of the unshaded region:

To find the area of the shaded region, we need to subtract the area of the unshaded region from the area of the trapezoid. In this case, the unshaded region is a triangle whose base is 26 inches. To find the area of the triangle, we need to use the formula 1/2 x Base x Height. We are given the base, but the height is unknown.

Determining the height:

We are given a small side length "6 inches" and the height of the trapezoid "15 inches". If we subtract the small side length from the height of the trapezoid, we will obtain the height of the triangle.

⇒ Height of trapezoid - Small side length = Height of triangle

⇒ 15 - 6 = Height of triangle

⇒ 9 in = Height of triangle

Determining the area of the unshaded region:

Now, let's substitute the base and the height in the formula to find the area of the triangle

⇒ 1/2 x Base x Height

⇒ 1/2 x 26 x 9

⇒ 13 x 9

⇒ 117 in²

Determining the area of the shaded region:

Finally, let's subtract the area of the unshaded region from the area of the trapezoid to obtain the area of the shaded region.

⇒ Area of trapezoid - Area of unshaded region = Area of shaded region

⇒ 300 - 117 = Area of shaded region

⇒ 183 in² = Area of shaded region

1) Multiply the given equation

2) Simplifying the equation

______________________

Answer:

1/12

Step-by-step explanation:

probability of tails is 1/2

probability of 1 out of 6 is 1/6

so 1/2 x 1/6 = 1/12

Answer:

y=4x-22

Step-by-step explanation:

Answer:

95%

Step-by-step explanation:

The 68-95-99.7 rule to find the percentage of people is also know as the empirical rule.

The empirical rule formula states that:

68% of data falls within 1standard deviations from the mean - between μ – σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

From question:

Mean (μ) = 505

Standard deviation (σ) = 146

Hence, we are to find the number of standard deviation which is represented as x

The score is between 213 and 797

μ - xσ

= 505 - 146x = 0

= 505 - 146x = 213

146x = 505 - 213

146x = 292

x = 292/146

x = 2

μ + xσ

505 +146x = 797

146x = 797 - 505

146x = 292

x = 292/146

x = 2

Hence, the percentage falls within 2 standard deviation from the mean.

Thus, from the formula above:

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Therefore, the percentage of people taking the test who score between 213 and 797 is 95%

The solution for the given problem is (a) P(X ≥ 20,000) = 0.4493, P(X ≤ 30,000) = 0.7769, P(20,000 ≤ X ≤ 30,000) = 0.3276. (b) P(X > 75,000) = 0.0821, P(X > 100,000) = 0.0183.

Solution: a) To find the probability that a randomly selected fan will last at least 20,000 hours. P(X ≥ 20,000). Now, Mean time until failure is 25,000 hours which is given and is represented by µ. Hence, µ = 25,000 hrs. The parameter used for the Exponential distribution is λ.λ = 1 / µλ = 1 / 25,000 hrs. λ = 0.00004. Therefore, the probability that a randomly selected fan will last at least 20,000 hours. P(X ≥ 20,000) =  e -λt = e -0.00004 × 20,000 ≈ 0.4493The probability that a randomly selected fan will last at least 20,000 hours is 0.4493.

To find the probability that a randomly selected fan will last at most 30,000 hours. P(X ≤ 30,000) = 1 - e -λt = 1 - e -0.00004 × 30,000 ≈ 0.7769. The probability that a randomly selected fan will last at most 30,000 hours is 0.7769.

To find the probability that a randomly selected fan will last between 20,000 and 30,000 hours. P(20,000 ≤ X ≤ 30,000) = P(X ≤ 30,000) - P(X ≤ 20,000)P(20,000 ≤ X ≤ 30,000) = (1 - e -λt) - (1 - e -λt)P(20,000 ≤ X ≤ 30,000) = e -0.00004 × 20,000 - e -0.00004 × 30,000 ≈ 0.3276. The probability that a randomly selected fan will last between 20,000 and 30,000 hours is 0.3276.

b) To find the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations.

z = (X - µ) / σZ = (X - µ) / σ = (X - 25,000) / (25,000)λ = 1 / µλ = 1 / 25,000 hrs. λ = 0.00004

The formula for z is z = (X - µ) / σ => X = z σ + µ

The standard deviation of the Exponential distribution is σ = 1 / λσ = 1 / 0.00004 = 25,000 hrs

Z = (X - µ) / σ = (X - 25,000) / (25,000)Z > 2z > 2 => (X - 25,000) / (25,000) > 2 => X > 75,000 hrs.

Now, the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations.

P(X > 75,000) = e -λt = e -0.00004 × 75,000 ≈ 0.0821

The probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations is 0.0821

To find the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations.

Z > 3z > 3 => (X - 25,000) / (25,000) > 3 => X > 100,000 hrs.

Now, the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations P(X > 100,000) = e -λt = e -0.00004 × 100,000 ≈ 0.0183

The probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations is 0.0183.

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Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

Step-by-step explanation:

ax +by+c

i.e. 1x +1/8y +4

therefore a=1 b=1/8 c=4

Answer:

x = 48

Step-by-step explanation:

It is a 90 degree angle. So first you would subtract 42 from 90 degrees. Then you'd get your answer! Hope this helped

Answer:

x = 3

Step-by-step explanation:

10 + 2(7 - 9x) = 5(2x - 12)

10 + 14 - 18x = 10x - 60

24 - 18x = 10x - 60

+60                 +60

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

84 - 18x = 10x

     +18x    +18x

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

84 = 28x

/28    /28

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

3 = x

Answer:

x = 3

Step-by-step explanation:

Do multiplication for the parenthesis terms, then add and subtract accordingly.

Answer:

X intercepts (-30,0)

Y intercepts (0,-3)

To evaluate the integral by reversing the order of integration, we first need to draw the region of integration. From the given limits of integration, we can see that the region is a rectangle with vertices at (0,4), (0,12), (11,4), and (11,12).

Now, we can reverse the order of integration by integrating with respect to y first, and then x. The new limits of integration will be y = 4 to y = 12 and x = 0 to x = 11e^(2y/3).

So, the new integral will be:

∫(0 to 11) ∫(4 to 12) 3y e^(2x/3) dy dx

We can evaluate this integral using integration by parts. Integrating with respect to y gives us:

∫(0 to 11) [3y^2/2 e^(2x/3)] from y = 4 to y = 12

Simplifying this expression gives us:

∫(0 to 11) [36e^(2x/3) - 6e^(8x/3)]/2 dx

Now, integrating with respect to x gives us:

[27e^(2x/3) - 9e^(8x/3)] from x = 0 to x = 11

Substituting these values and simplifying gives us the final answer:

(27e^22/3 - 9e^88/3) - (27 - 9) = 27e^22/3 - 9e^88/3 - 18

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Answer:

w = \(\frac{p -2l}{2}\)

Step-by-step explanation:

p = 2l + 2w  Subtract 2l from both sides of the equation

p - 2l = 2p  Divide both sides by 2

\(\frac{p -2l}{2}\) = w

The sum of the first 7 terms of the series is,

⇒ S = 14.91

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The series is,

8, 6, 9/2, …

Now, We can find the common ratio as;

Common ratio = 6 / 8 = 3 / 4

And, 9/2 ÷ 6 = 3/4

Hence, The series is geometric series.

So, The sum of nth term of geometric series is,

S = a₁ (1 - rⁿ) / (1 - r)

Where, 'a₁' is first term and 'r' is common ratio.

Here, a = 8, r = 3/4

Hence, The sum of 7th term of geometric series is,

S = a₁ (1 - rⁿ) / (1 - r)

S = 8 (1 - (3/4)⁷) / (1 - 3/4)

S = (8 (4096 - 2187) / 4096 ) / (1/4)

S = 8 × 1909 × 4 / 4096

S = 14.91

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The value of the missing lengths are;

x = 4

y = 3. 5

It is important to note that trigonometric identities are described as equalities that shows the certainty of all the values that are found the in the trigonometric functions in an equation.

There are distinct identities, such as;

From the information given, we have that;

sin θ = opposite/ hypotenuse

Now, substitute the values

sin 30 = 2/x

Find the sine value

0.5x = 2

x = 4

Using the Pythagorean theorem, we have;

4² - 2² = y²

y² = 16 - 4

y² = 12

Find the square root

y = 3. 5

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Answer:

No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. ... Note that we have variables on both sides of the equation.

Step-by-step explanation:

Answer:

Do you have a picture or the graph or equation? Also if this helps, I included a picture with an example of solutions on graphs. If you have any further questions feel free to ask me! (:

Answer:

The area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h. Hence, to find the area of a tri-sided polygon, we have to know the base (b) and height (h) of it.

Step-by-step explanation:

hope this help .

The number of ways to arrange the books when one shelf is left empty is m * (m-1)^(n-1).To solve this problem, we need to use the permutation formula since the order of books on shelves matters.

We can start by finding the total number of ways to arrange n books on m shelves, where n is the number of books and m is the number of shelves.

If we have n books and m shelves, the number of ways to arrange the books on the shelves without any restrictions is m^n. However, since we have the additional restriction that each shelf must contain at least one book, we need to subtract the number of arrangements where one or more shelves are left empty.

The number of ways to arrange the books when one shelf is left empty is m * (m-1)^(n-1), since we can choose the empty shelf in m ways, and then arrange the remaining n-1 books on the (m-1) non-empty shelves in (m-1)^(n-1) ways. However, we need to be careful not to double-count the arrangements where two shelves are left empty, so we add back in the number of arrangements where two shelves are empty, which is m choose 2 * (m-2)^(n-1). We continue this process until we've accounted for all the possible combinations of empty shelves.

Therefore, the total number of arrangements with at least one book on each shelf is:

m^n - m*(m-1)^(n-1) + m choose 2 * (m-2)^(n-1) - m choose 3 * (m-3)^(n-1) + ...

This expression can be simplified using the principle of inclusion-exclusion, but it still depends on the values of n and m.

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Answer: (x+4)(x-9)=0 is zero product property, you're correct on the second one

Step-by-step explanation:

Answer:

a) 10 per for 4 min means 150 per hour. so more hamburgers are sold per hour.

b) see attachment

Answer:

The solution to the equation is x = 0.38 or -18.38

Step-by-step explanation:

x^2+18x=7 can be properly written as

\(x^{2} +18x =7\)

To solve by completing the square, divide the coefficient of x by 2, square and then add to both sides

i.e 18/2 = 9

Then add 9² to both sides of the equation

\(x^{2} +18x + 9^{2} = 7 + 9^{2}\)

This becomes

\((x+9)^{2} = 7 + 81\)

\((x+9)^{2} = 88\)

\(x+9 = \pm \sqrt{88}\)

\(x = -9 \pm\sqrt{88}\)

\(x = -9 \pm 9.38\)

∴ \(x = -9+9.38 or -9-9.38\)

\(x = 0.38 or -18.38\)

Hence, x = 0.38 or -18.38

The analysis  on the above students will be Positive analysis on 50% tax reduction cause 12 % smoking reduction in teenagers ,Normative analysis federal government should spend more on AIDS research ,Positive analysis on Rising paper prices will increase textbook prices and Normative analysis on coffee at Starbucks is too high.

Positive analysis is a way of analyzing things that rely on the facts that are available, such as observable behaviors. The aforementioned statement is an example of positive analysis because it contains a cause-and-effect connection.b.

Normative analysis is an analysis based on opinions or values.

Positive analysis is an analysis based on facts, while normative analysis is an analysis based on opinions, which statement represents positive analysis and which represents normative analysis, based on the following statements are explained below:

a. A 50-cent-per-pack tax on cigarettes will lead to a 12 percent reduction in smoking by teenagers: Positive analysis

b. The federal government should spend more on AIDS research: Normative analysis

c. Rising paper prices will increase textbook prices: Positive analysis

d. The price of coffee at Starbucks is too high: Normative analysis

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