x and y are integers, y>_ 2, x +y <_ 4 and y <_ 2x +2

Answer:

Is to place a ' or a prime

ΔA'B'C'

Answer:

One way to name a transformed figure is to place a apostrophe after each letter in the

name of the original figure. For example, a reflection of ΔABC is named ΔA'B'C' (pronounced A prime B prime C prime).

Step-by-step explanation:

Answer:

the answer is 40:45

Step-by-step explanation:

i did the test and got it right

The difference of the expression will be;

⇒ 4 - i

Option A is true.

What is mean by Subtraction?

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ (11 - 5i) - (7 - 4i)

Now,

Solve the expression as;

The expression is,

⇒ (11 - 5i) - (7 - 4i)

Thus. The difference of the expression is,

⇒ (11 - 5i) - (7 - 4i) = 11 - 5i - 7 + 4i

                          = 4 - i

Therefore, The difference of the expression will be;

⇒ 4 - i

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The correct choice is A. x = π/6 + nπ (where n is an integer).

The given equation is sin3x+sinx+ √3 cosx = 0. We need to solve the equation on the interval (0, 2π). Using the trigonometric identity, we can write sin3x = 3sinx - 4sin³x. Substitute this in the given equation. 3sinx - 4sin³x + sinx + √3 cosx = 0.

Combine the like terms. 3sinx + sinx - 4sin³x + √3 cosx = 0 .Simplify the equation. 4sinx(1 - sin²x) + 4cosx(sin60°) = 0sinx(1 - sin²x) + cosx(sin60°) = 0sinx(1 - sin²x) + cosx(√3/2) = 0. Divide throughout by cos x.sin x(1 - sin²x)/cos x + (√3/2) = 0tan x(1 - sin²x) = - (√3/2)tan x = - (√3/2) / (1 - sin²x).

Now, we know that the interval lies between 0 to 2π. That is 0 ≤ x < 2π.To find the solution, we need to find all the possible values of x. Thus, let's solve the equation for x as follows. tan x = - (√3/2) / (1 - sin²x)tan x = - (√3/2) / cos²xUse the identity, tan²x + 1 = sec²x.

We get sec²x = cos²x + sin²x/cos²x. We can write tan x as sin x / cos x.tan²x + 1 = sin²x/cos²x + 1sin²x/cos²x + cos²x/cos²x = sec²xsin²x + cos²x = 1sin²x = 1 - cos²x. Now, substitute this in the equation. We get, tan²x + 1 = sin²x/cos²x + 1tan²x = (1 - cos²x)/cos²x + 1tan²x = 1/cos²x.

Thus, we have, tan x = - (√3/2) / cos²xWe know, tan²x = 1/cos²xOn substituting, we get, (1/cos²x) = 3/4cos²x = 4/3. Taking the square root on both sides, cos x = ± 2 / √3sin x = ± √(1 - cos²x) = ± √(1 - 4/3) = ± √(−1/3). Note that sin x cannot be positive.

Thus,sin x = - √(1/3)cos x = 2/√3. The possible value of x is thus,π/6 + nπ, where n is an integer.Thus, the solution is given by,x = π/6 + nπ (where n is an integer)Hence, the correct choice is A. x = π/6 + nπ (where n is an integer).

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Answer:

The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve.

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

factors are numbers that divide exactly into a number , leaving no remainder.

then the only factor of 27 from the list is 27

The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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If mark and Alexis work together on a particular truck, they can load all of the packages in 90 minutes.

It will take 90 minutes for both Mark and Alexis to load all of the products.

Given,

that Mark can load a truck with items in 120 minutes and Alexis can do the same in 240 minutes, the average time for the two of them is as follows:

Average = (120 + 240) ÷ 2

= 360 ÷ 2

= 180

In this case, the term "Average" refers to the value that should be used to represent the sample. By dividing the total number of values in a particular set by the sum of all the values in that set, the average is determined. also known as the arithmetic mean.

Since there were two parties engaged, our calculation is 180 ÷ 2 = 90.

Hence, in this case, it is concluded that the correct answer is option B. 90 minutes.

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We can conclude that for any natural number n,\(n^2\)= 1 (mod 4) depending on the remainder of n when divided by 4.

The statement "For any natural number n, it is true that in=1,i,â1, depending on the remainder of n when divided by 4" is not true.

In fact, the statement is not well-defined because it is unclear what "in" refers to.

However, if the statement is intended to be "For any natural number n, it is true that \(n^2\)=1 (mod 4) depending on the remainder of n when divided by 4," then this statement is true.

To see why, note that any natural number can be written as 4k, 4k+1, 4k+2, or 4k+3 for some integer k.

If n = 4k, then \(n^2 = (4k)^2 = 16k^2\), which is divisible by 4 and hence is congruent to 0 (mod 4). Therefore, \(n^2\) = 1 (mod 4).

If n = 4k + 1, then \(n^2 = (4k + 1)^2 = 16k^2 + 8k + 1 = 4(4k^2 + 2k) + 1\), which is congruent to 1 (mod 4). Therefore, \(n^2\) = 1 (mod 4).

If n = 4k + 2, then \(n^2 = (4k + 2)^2 = 16k^2 + 16k + 4 = 4(4k^2 + 4k + 1)\), which is congruent to 0 (mod 4). Therefore, n^2 = 0 (mod 4), which is not equal to 1 (mod 4).

If n = 4k + 3, then\(n^2 = (4k + 3)^2 = 16k^2 + 24k + 9 = 4(4k^2 + 6k + 2)\) + 1, which is congruent to 1 (mod 4). Therefore, \(n^2 = 1\) (mod 4).

Therefore, we can conclude that for any natural number n,\(n^2 =\)1 (mod 4) depending on the remainder of n when divided by 4.

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If f(x) is a continuous function on a closed interval [a,b] then:

f(x) is riemann integrable on [a,b]

If a function's lower and higher integrals are identical, the function is said to be Riemann integrable. We define ∫baf(x)dx=L(f,a,b)=U(f,a,b)

Integrability Follows from Continuity: If a function f is integrable on [a,b], it follows that it is continuous on the closed interval [a.b]. The Definite Integral as a Region's Area If the closure has no negative values and f is continuous.

The existence of a number L R such that for each sampled partition that satisfies it holds that indicates that the function f: [a, b] R is Riemann integrable.

Hence we get the required answer.

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Answer:

  y = (x -1)² -3

Step-by-step explanation:

A quadratic with a vertex at (h, k) will have an equation of the form ...

 y = a(x -h)² +k

You have (h, k) = (1, -3), and a vertical scale factor* of 1. So, the equation of the graphed curve is ...

  y = (x -1)² -3

_____

* One way to determine the value of "a" in the form shown is to look at the vertical difference between the vertex and the points 1 unit right or left of the vertex. Here, those points are 1 unit above the vertex, so the vertical scale factor "a" is 1.

(a) The Null And Alternate hypothesis are stated below,

(b) The value of test-statistic is 3,

(c) The "p-value" is 0.0013,

(d) The hypothesis is rejected because p-value is less than 0.025.

Part (a) : The appropriate null and alternative hypotheses are:

Null hypothesis (H₀): The average LSAT score at the University of Pennsylvania is equal to or less than the national average of 1,300.

Alternative hypothesis (Hₐ): The average LSAT score at the University of Pennsylvania is significantly higher than the national average of 1,300.

Part (b) : To calculate the test-statistic, we use formula : t = (x' - μ)/(s / √n),

where x' = sample mean, μ = hypothesized population mean, s = sample standard deviation, and n = sample size.

Substituting the given values,

We get,

t = (1375 - 1300)/(125 / √25) = 3;

So, the value of the test statistic is 3.

Part (c) : To calculate "p-value", we need to find the probability of getting a t-value as extreme or more extreme than 3, assuming that the null hypothesis is true.

We know that for a two-tailed test at a significance level of 0.03, the p-value is approximately 0.0013.

Part (d) : To test the hypotheses using the p-value, we compare it to the significance-level.

Since the p-value is less than 0.025 (half of the significance level for a two-tailed test), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim.

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The given question is incomplete, the complete question is

The admissions officer for the graduate programs at the university of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300. an accepted standard deviation for LSAT scores is 125. random sample of 25 scores had an average of 1,375.

(a) State the appropriate null and alternative hypotheses.

(b) Calculate the value of the test statistic

(c) Calculate the p-value.

(d) Use the p-value to test the hypotheses and conduct the test at the 0.025 level.

The function f(x)=√x with f:R→R is injective and surjective but not bijective.

Injective (or one-to-one): f(x) is injective, which means that if f(x1) = f(x2), then x1 = x2. In other words, if the square root of x1 is equal to the square root of x2, then x1 and x2 are equal.

Surjective (or onto): f(x) is surjective, which means that for every y in the codomain (R), there exists an x in the domain (R) such that f(x) = y. In other words, the square root of any real number can always be expressed as a real number.

Bijective: f(x) is not bijective. The square root function is not bijective because it is not defined for negative values of x.

Function: A function f is a function if for every x in the domain of f, there is exactly one y in the codomain of f such that f(x) = y. In other words, each x in the domain is mapped to exactly one y in the codomain.

In the case of f(x) = √x, it is a function. For every x in the domain of f, which is [0,∞), there is exactly one y in the codomain of f, which is [0,∞), such that f(x) = y.

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Answer: i think its c

hope its right

:)

To make the risks of fatality by car equal to the risk of fatality by rock climbing, a certain number of hours must be traveled by car for each hour of rock climbing.

Let's calculate how many hours must be traveled by car for each hour of rock climbing to make the risks of fatality by car equal to the risk of fatality by rock climbing.

Given that the risk of fatality by rock climbing is 1 in 320,000 hours and the risk of fatality by car is 1 in 8,000 hours

To make the risks of fatality by car equal to the risk of fatality by rock climbing:320,000 hours (Rock climbing) ÷ 8,000 hours (Car)

= 40 hours

Therefore, for each hour of rock climbing, 40 hours must be traveled by car to make the risks of fatality by car equal to the risk of fatality by rock climbing.

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Given,

Sample mean = ±3 of true mean

Standard error = 1.8

Therefore,

Required probability of sample mean being within 3 units of the true mean is,

P ( sample mean - 3 < mean < sample mean + 3 )

= P [( sample mean - 3 ) - mean / 1.8 ] < mean - sample mean / 1.8 < [ ( sample mean + 3 ) - mean / 1.8 ]

= P ( - 1.67 < ∉ < 1.67)

= P (∉ < 1.67) - P( ∉ < 1.67)

= 0.952 - 0.047

= 0.905

Hence, the probability that the sample mean is within 3 units of the true mean if the standard error is 1.8 is 0.905.

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Answer: the second option |y^5|

Step-by-step explanation:

The values of the expression \(\sqrt{y^{10}}\) is \(|y^5|\).

Option B is the correct answer.

We have,

Expression:

\(\sqrt{y^{10}}\)

This can be written as,

Simplifying the powers.

\(\sqrt{y^{2 \times 5}}\)

Square root can be written as,

\(\sqrt{x} = x^{1/2}\)

So,

The expression can be written as,

\(y^{(2 \times 5) \times\frac{1}{2}\)

Simplifying the powers.

2 x 5 x 1/2 = 5

So,

\(y^5\) or \(|y^5|\)

Thus,

The values of the expression \(\sqrt{y^{10}}\) is \(|y^5|\).

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Answer:

I think the answer is 169 because of the exponent

On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -

1 - A

2 - C

3 - B

4 - D

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Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

answer:

statements

1. BD ≅ DE

2. CD ≅ DF

3. ∠BDC ≅ ∠EDF

4. ▲BDC = ▲EDF

5. BC ≅ EF

reasons

1. given

2. given

3. definition of vertical angles

4. SAS

5. CPCTC

step-by-step explanation:

Answer:

100%

glass.......x

ceramic....y

x:y = 2:3

x/y = 2/3

after the increase in both jars:

3x:ny = 1:1

3x/ny = 1

3/n × x/y = 1

3/n × 2/3 = 1

3/n = 3/2

n = 2

volume of vater in the ceramic (y) is two times larger than before

2y = y + y = y + 100%y

you increased one more time the original volume of water or 100% of the original volume

Using the properties of an arithmetic sequence we can conclude that the total number of match boxes is 66.

There is a consistent distinction between the words in a sequence of numbers known as a "arithmetic progression" or "arithmetic sequence" (AP).

We know that the bottom row of the pyramid has 11 matchboxes .

As we can see in the figure that the each succeeding step has one matchbox less.

Therefore the number of matchboxes in each row is in an AP.

Therefore the AP has a common difference of  -1 and the first term is 11

The last term of the AP is 1.

Therefore

aₙ = a + (n-1)d

or, 1 = 11 + (n-1)(-1)

or, n = 11

We know that the sum of all terms of an AP is given by

S=n/2{2a+(n-1)d}

or, S = 11/2 {2×11 + (10)(-1)}

or, S = 66

Therefore from the arithmetic progression we calculate that the total number of match boxes is 66.

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The exact value of sin(π/6) is 1/2.

To find the exact value of sin(π/6), we can use the unit circle or the trigonometric identity for the sine function. In the unit circle, π/6 corresponds to an angle of 30 degrees, which lies in the first quadrant.

At this angle, the y-coordinate of the corresponding point on the unit circle is 1/2. Since sin(θ) represents the ratio of the opposite side to the hypotenuse in a right triangle, for an angle of 30 degrees, sin(π/6) is equal to 1/2.

Alternatively, we can use the trigonometric identity sin(θ) = cos(π/2 - θ). Applying this identity, we have sin(π/6) = cos(π/2 - π/6) = cos(π/3). Now, π/3 corresponds to an angle of 60 degrees, which lies in the first quadrant.

At this angle, the x-coordinate of the corresponding point on the unit circle is 1/2. Therefore, cos(π/3) = 1/2. Substituting this value back into sin(π/6) = cos(π/3), we get sin(π/6) = 1/2.

In both approaches, we find that the exact value of sin(π/6) is 1/2, indicating that the sine function of π/6 radians is equal to 1/2.

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The probability that a group of four siblings includes all XY is 1/16 (6.5%), while the probability all XX offspring is 1/16 (6.5%). It is a simple genetic probability calculation.

Genetic probabilities and chromosomes

Females inherit two chromosomes X, whereas males inherit one chromosome X and one chromosome Y.

The probabilities of inherent two chromosomes X (females) are 1/2 (50%), while the probabilities of inherent one chromosome X and one chromosome Y (males) are also 1/2.

In consequence, the probability that a group of four siblings includes all XY is 1/16 (because it is equal to 1/2 x 1/2 x 1/2 x 1/2 = 1/16), the same for the probability all XX offspring (1/16).

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There are 15 rows of seats in the theater

The given parameters are:

The number of rows is calculated as:

Rows = Total number of people/People per row

This gives

Rows = 357/24

Evaluate the quotient

Rows = 14.875

Round up the number

Rows = 15

Hence, there are 15 rows of seats in the theater

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