The ratio of students who wear glasses to the total class is 2: 5. If there
are 30 students in total, how many students wear glasses?

Answer:

B

Step-by-step explanation:

If the 2 lines were parallel, then

5x - 10 = 70 ( alternate angles )

Add 10 to both sides

5x = 80 ( divide both sides by 5 )

x = 16

For the 2 lines to be parallel then x = 16

Answer:

B.16

Step-by-step explanation:

First I would Make an equation:

For example set (5x-10)=70

Add 10 to both sides:

5x-10+10=70+10

Simplify:

5x=80

Divide both sides by 5:

5x/5=80/5

simplify:

x=16

In conclusion the answer is B.16

Thus, the area of new kite with its diagonal doubled is found as: 140 sq. cm.

The area a kite encloses is known as its area of flight. A quadrilateral with two sets of neighbouring sides that are equal is referred to as a kite. A kite is made up of four angles, four sides, and two diagonals.

The product of a lengths of a kite's diagonals divides its area in half.

The area of the kite ABCD = 35 cm square.

The formula for the area of kite = 1/2*(d)*(D)

d - length of small diagonal

D - length of large diagonal.

Then,

35 =  1/2*(d)*(D)

(d)*(D) = 35*2

(d)*(D) = 70 cm sq.  ..eq 1

Now, the length of diagonals of new kite are doubles that is 2d and 2D.

Area of new kite = 1/2 *(2d)*(2D)

Area of new kite = 1/2 *4*(d)*(D)

Area of new kite = 2 *(d)*(D)

Put the value of (d)*(D) from eq 1.

Area of new kite = 2*70

Area of new kite = 140 sq. cm

Thus, the area of the new kite with its diagonal doubled is found as: 140 sq. cm.

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and that is how you are supposed to do

The domain of the function is defined as 0 ≤  x ≤ 4.

option A is the correct answer.

A domain of a function refers to "all the values" that can go into a function without resulting in undefined values.

So the domain of a function is the set of x values, while the range of a function is the set of y values.

From the given statement, the range of the function is defined as;

y = vt

where;

y = 60 mph x 4 hr

y = 240 miles

From the given statement, the domain of the function is defined as;

0 ≤  x ≤ 4

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Answer:

80%

Step-by-step explanation:

If you do 4 divided by 5 it equals 0.8, which is 80%

Answer:

The answer is 80%

Step-by-step explanation:

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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  To rewrite a quadratic function in the form f(x) = a(x-h)² + k, we need to complete the square. The process involves finding the values of h and k that shift the vertex of the parabola to a desired position.

Starting with the quadratic function f(x) = -x² + 6x, we want to rewrite it in the form f(x) = a(x-h)² + k. To do this, we complete the square by following these steps:
Group the x-terms together: f(x) = -(x² - 6x).
Factor out the coefficient of x² from the x-terms: f(x) = -1(x² - 6x).
Complete the square by adding and subtracting the square of half the coefficient of x: f(x) = -1(x² - 6x + 9 - 9).
Rearrange the terms: f(x) = -1[(x - 3)² - 9].
Distribute the negative sign: f(x) = -(x - 3)² + 9.
Now the quadratic function is in the desired form f(x) = a(x-h)² + k, where a = -1, h = 3, and k = 9. The vertex of the parabola is shifted to the point (3, 9). The term (x - 3)² determines the horizontal shift, while the constant term 9 determines the vertical shift.

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The Simplification of the expression  \(\frac{8(x+3)^2}{2(x+3)}\) is

4 x+12

This is further explained below.

Generally, the required expression is

\(\frac{8(x+3)^2}{2(x+3)}\)

Cancel the common factor of 8 and 2.

\(\frac{4(x+3)^2}{x+3}\)

Cancel the common factor of (x+3)^2 and x+3.

Factor x+3 out of 4(x+3)^2.

\(\frac{(x+3)(4(x+3))}{x+3}\)

Cancel the common factors.

4(x+3)

Apply the distributive property.

4 x+4 *3

Multiply 4 by 3.

4 x+12

In conclusion, The expression's (\(\frac{8(x+3)^2}{2(x+3)}\))condensed form

4 x+12

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Answer:

Step-by-step explanation:

1.y=5/3x+5

2.y=x-7

3.y=x-6

Answer

2

Step-by-step explanation:

x+y=-7+2x

Reorder the terms:

y = -7+ 2x

Solving

y = -7 + 2

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.Simplifying

y = 7 + 2x

The complement of the empty set is the set of all possible elements in the universal set U, which is the English alphabet in this context.

The universal set U is defined as the set of all possible elements or values under consideration for a given context. On the other hand, the complement of a set A is defined as the set of all elements that are not in A but are in U.

The complement of the empty set is defined as the set of all elements in U since the empty set is a subset of every set.

Therefore, the complement of the empty set in this context would be the entire set of all letters in the English alphabet.

This is because the empty set contains no elements, and therefore, its complement would be the set of all possible elements in U, which in this case is the English alphabet.

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The scenario would be represented by a given right angle triangle as shown below

Looking at the triangle,

BC = x represents the height of the tree

AC = x + 4 represents the length of the wire

AB = x - 28 represents the distance from the base of the tree to the wire.

We would solve for x by applying pythagorean theorem which states that

Hypotenuse^2 = shorter leg^2 + longer leg^2

hypotenuse = x + 4

shorterleg = x - 28

Longer leg = x

Thus, we have

We would solve the quadratic equation by applying the general formula for solving quadratic equations which is expressed as

The limitations of using the Fundamental Counting Principle when determining the probability of an outcome is that it is not simple and it does not apply to non-uniform probability distribution

Probability is the likelihood or chance of an event happening or not.

Probability values helps in decision-making in day-to-day activities.

The Fundamental Counting Principle in probability is a way to determine the number of outcomes in a probability problem. It states that if there are p ways to do one thing and q ways to do another, the number of way to do both things is p × q.

However, this principle is limited for non-uniform probability distribution and for larger samples space.

Therefore, the limitations of using the Fundamental Counting Principle when determining the probability of an outcome is that it is not simple and it does not apply to non-uniform probability distribution.

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Describe four common ways in which individuals respond to perceived inequity are -

Equity, also known as shareholders' equity (or shareholders' equity for private companies), is the sum of money which would be handed back to a company ’s creditors if each of its assets have been liquidated and all of its debt was paid off in the event of liquidation.

Some key features regarding the equity are-

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Answer:

C

Step-by-step explanation:

a number is only divisible by 4, if the number formed by the last 2 digits is divisible by 4.

Answer:

(b)

Total frequencies:

Multiples of 3 or 5:

Required probability:

(c)

(i) Good limes = GL = 10

(ii) Good fruits = GF = 10 + 8 = 18

(iii) Good apple = GA = 8, Bad lime = BL = 6

Answer:

(a^2+2)(a+2)

Step-by-step explanation:

Factor a^3+2a+2a^2+4.

Using Factoring by grouping

a^3+2a   +    2a^2+4

Factor out a from the first two terms and 2 from the last two terms.

a( a^2 +2) + 2 ( a^2+2)

Factoring out a^2+2.

(a^2+2)(a+2)

The general solution is given by: y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

The most general solution to the original nonhomogeneous differential equation can be found by adding the homogeneous solution and the particular solution together. That is,

y = y_h + y_p

= c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the most general solution to the original nonhomogeneous differential equation. We can use the arbitrary constants c1 and c2 to find specific solutions for different initial conditions. The general solution is given by:

y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the final answer. Note that we have used the terms "general solution" and "arbitrary constants" in our answer, as instructed.

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a)There are \(2^m^n\) possible relation

b)Similarly \(n^m\)

c)\(\frac{n^m}{2^m^n}\)

a)Set A has m elements and set B has n elements

Firstly determine the number of elements A*B by using the multiplication rule

Number of elements\(=A*B=m*n=mn\)

For each element, \(A*B\) we have two option

First element 2 ways

Second element 2 ways

mn element 2 ways

By using the multiplication rule

\(2*2*2......=2^m^n }\)

Then there are \(2^m^n\) possible relation

b)Similarly \(n^m\)

c)\(\frac{n^m}{2^m^n}\)

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Factoring integers with sublinear resources on a superconducting quantum processor can be achieved using quantum approximate optimization algorithm" (QAOA) or quantum phase estimation algorithm (QPE) approach.

Factoring large integers is a problem of significant importance in the field of cryptography.

Classical computers have limited efficiency in solving this problem, and their performance is expected to decline further as the size of the integers to be factored increases.

In contrast, quantum computers are expected to have exponential speedup in factoring large integers, thanks to Shor's algorithm.

Recently, researchers have been exploring the possibility of using superconducting quantum processors to factor integers with sublinear resources.

One approach is to use a so-called "quantum approximate optimization algorithm" (QAOA), which maps the problem of factoring integers to a problem of finding the ground state of a certain Hamiltonian.

The QAOA can be implemented using a superconducting quantum processor, with the problem Hamiltonian implemented by a set of two-qubit gates.

Another approach is to use the quantum phase estimation algorithm (QPE) to estimate the eigenvalues of the problem Hamiltonian.

This can be used to factor integers by finding the period of a certain function using the quantum Fourier transform, as in Shor's algorithm. QPE can be implemented on a superconducting quantum processor using phase estimation circuits, which require only polynomial resources.

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We can find the general term of the sequence using the formula for arithmetic sequence.The formula for the nth term of an arithmetic sequence is given by:an = a1 + (n-1)d wherean is the nth term of the sequence,a1 is the first term of the sequence, and is the common difference between any two consecutive terms of the sequence.

Given that the first term of the sequence is -10 and the second term is 6. Therefore, a1 = -10 and

a2 = 6.We can find the common difference by subtracting any two consecutive terms of the sequence. Using the first two terms, we get:

d = a2 - a1

= 6 - (-10)

= 16

Therefore, the general term of the sequence is: an = -10 + (n-1)16

an = 16n - 26 Now, we can substitute

Therefore, the general term of the sequence is: an = -10 + (n-1)16

n = 82 to get the 82nd term of the sequence:

a82 = 16(82) - 26

= 1306

Therefore, the 82nd term of the given sequence is 1306.

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Answer:

Commutive Property

Step-by-step explanation:

The numbers switched that's all

Answer:

Commutative property

Step-by-step explanation:

Change

Order

m

m

u

t

a

t

i

v

e

so basically you’re not changing the group ( associative ) and you’re not multiplying into the groups ( Distribuative ) so the only other option would be Commutative, and you’re changing the order of the numbers so it would be commutative.

The annual scholarship payment for a perpetual scholarship with a $100,000 endowment and a 7% discount rate would be $7,000.

To calculate the annual scholarship payment, we need to determine the amount that can be withdrawn from the endowment each year while still preserving its value over time. The discount rate of 7% represents the college's desired rate of return on investments.

Using the concept of present value, we can calculate the annual payment as a percentage of the initial endowment. The formula for present value is:

Present Value = Annual Payment / Discount Rate

In this case, we want to find the annual payment, so we rearrange the formula:

Annual Payment = Present Value * Discount Rate

Since the present value is the initial endowment of $100,000, and the discount rate is 7%, the calculation is as follows:

Annual Payment = $100,000 * 0.07 = $7,000

Therefore, to maintain the perpetual scholarship, the college would need to make an annual payment of $7,000. This amount is determined by the combination of the initial endowment and the discount rate, ensuring that the scholarship remains sustainable over time.

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Answer:

C ≈ 31.4 units

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( r is the radius ) , then

C = 2π × 5 = 10π ≈ 31.4 units ( to the nearest tenth )

Answer:

$135

Step-by-step explanation:

180÷4=45

45×3=135

Answer:

$135

Step-by-step explanation:

180÷4=45

45×3=135

Hope this helps! :)

Answer:

(a) 40

(b) 15% per week, to the nearest percent.

Step-by-step explanation:

Given:

old production,

P(w) = 230(1.1^w)

(a) At week 0, w=0, so

P(0) = 230(1.1^0) = 230

Difference (old - new) = 230-190 = 40

(b) about 15% per week

(c) from the 4th week on

approximate growth rate of new factory

N(w) = 190(R^w)

we know

w=0, N(0) = 190

w=7, N(7) = 505

so R=(505/190)^(1/7) = 1.1499 = 1.15 approx.

(c)

The old production tabulated:

w P(w) New

0 230 190

1 253 220

2 278 252

3 306 290

4 337 337

5 370 380

6 407 440

7 448 505

So we see that at the end of the 4th week, the two productions match, and new factory begins to exceed old production.

Answer:

40 is

But it is not an

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\(\huge\text{Question \#1}\)

\(\huge\textsf{3y - z}\)

\(\huge\textsf{= 3(6) - 2}\)

\(\huge\textsf{= 18 - 2}\)

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\(\boxed{\boxed{\huge\textsf{Answer: 16}}}\huge\checkmark\)

\(\huge\text{Question \#2}\)

\(\huge\textsf{y + 5z}\)

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\(\huge\textsf{\boxed{\star\underline{\underline{16 = 16}}\star}\star}\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

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Answer:

in edg is B

Step-by-step explanation:

Answer:

It's B

Step-by-step explanation: