The sum of two numbers is 11. Twice the first number minus the second number is 7
Find the numbers.​

The ordered pair that could be the image point is (a) (2.5,1)

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

Point C = (5, 2)

This means that

C = (5, 2)

The point is dilated using the origin as a center of the origin

So, the image point is

C = k(5, 2)

Let k = 1/2

So, we have

C = 1/2(5, 2)

Evaluate

C' = (2.5, 1)

Hence, the ordered pair that could be the image point is (a) (2.5,1)

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Question

Triangle ABC is dilated with the origin as the center of the dilation. Which ordered pair could represent the image of point C(5, 2) after the dilation?

A (2.5,1)

B (5,−2)

C (7.5,4.5)

D (−1,−4)

Let x be women and y men.

x + y = 65 equation 1.

y = x - 7 equation 2.

Now we need to solve the equation system, as follows:

- on eq. 2 y is already solved, so we can replace y on eq. 1:

x + x - 7 = 65

2x - 7 = 65

2x = 65 + 7

2x = 72

x = 72/2

x = 36 women

Finally, we replace x on eq 2:

y = 36 - 7

y = 29 men

False. the number of levels of observed x-values must be equal to the order of the polynomial in x that you want to fit.

The number of levels of observed x-values does not have to be equal to the order of the polynomial in x that you want to fit. The order of the polynomial determines the degree of the polynomial, which indicates the highest power of x in the equation. The number of levels of observed x-values represents the distinct values or categories of x that are observed in the data. In polynomial regression, you can fit a polynomial of any order to the data, regardless of the number of levels of observed x-values. However, it is important to note that fitting a polynomial of higher order than necessary may lead to overfitting and may not provide meaningful or reliable results.

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The value of the given expression will be 4.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that the expression is 2⁴ / ( 3.2 x 0.8 0 + 1.44 ). SOlve the expression as below,

E = 2⁴ / ( 3.2 x 0.8 ) + 1.44 )

Solve the denominator by mathematical operation.

E = 16 / ( 2.56 + 1.44 )

Divide the numerator by denominator,

E = 16 / 4

E = 4

Therefore, the solution of the expression is 4.

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The number of relations according to given condition are  (a) \(2^{(n^2 - n)\) , (b) \(2^{(n^2 - n)\) , (c) \(2^{((n - 1) * n)\) , (d) \(2^{(n^2 - n){ - 2^{((n - 1) * n)\) and (e) \(2^{((n - 1) * (n - 1))\).

What is a relation?

In mathematics, a relation is a set of ordered pairs that establishes a connection or association between elements from different sets.

(a) For the relation R to contain the ordered pair (a, b), there are two possibilities: either (a, b) is in R or it is not in R. This means that there are \(2^{(n^2 - n)\) total relations that satisfy this condition. The exponent \((n^2 - n)\)represents the total number of possible ordered pairs in the set S excluding (a, a) pairs.

(b) For the relation R to exclude the ordered pair (a, b), we need to consider all possible pairs (x, y) where x and y are distinct elements in S. The total number of such pairs is  \((n^2 - n)\). For each pair, there are two possibilities: either (x, y) is in R or it is not in R. Hence, there are \(2^{(n^2 - n)\)  total relations that satisfy this condition.

(c) For no ordered pair in R to have a as its first element, we need to consider all possible pairs (x, y) where x is any element in S except for a. The total number of such pairs is (n - 1) * n since there are (n - 1) choices for the first element and n choices for the second element. For each pair, there are two possibilities: either (x, y) is in R or it is not in R. Therefore, there are \(2^{((n - 1) * n)\) total relations that satisfy this condition.

(d) To have at least one ordered pair in R with a as its first element, we can exclude the case where no ordered pair in R has a as its first element. Hence, the total number of relations satisfying this condition is \(2^{(n^2 - n)} - 2^{((n - 1) * n)\)

(e) To have no ordered pair in R with a as its first element or b as its second element, we need to consider all possible pairs (x, y) where x is any element in S except for a, and y is any element in S except for b. The total number of such pairs is (n - 1) * (n - 1). For each pair, there are two possibilities: either (x, y) is in R or it is not in R. Therefore, there are \(2^{((n - 1) * (n - 1))\) total relations that satisfy this condition.

Note: The above calculations assume that a relation can contain both (a, a) and (b, b) pairs, as the conditions specified for a and b to be distinct elements of S.

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Answer:

C and D is the answer.

Step-by-step explanation:

If m∠5 = x°, according to the Corresponding Angle Theorem, m∠9 will equal the same, and because 9 and 12 are vertical angles, both of these will be the same measure.

The congruency statement that is correct is that ABCD ≅ A'B'C'D'

It should be noted that a quadrilateral simply means a closed shape that has four sides, four vertices, and four angles.

Two figures are congruent if they have the same shape and size and they mirror each other.

Therefore, congruency statement that is correct is that ABCD ≅ A'B'C'D'

Which congruency statement is correct?

ABCD ≅ A'B'C'D'

ABCD ≅ A'D'C'B'

CDAB ≅ A'D'C'B'

CDAB ≅ C'B'A'D'

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Answer:

ABCD ≅ A'B'C'D'

Step-by-step explanation:

The answer would be

A. ABCD ≅ A'B'C'D'

Your welcome <3

Answer:

2a2 - 6a + 29

Step-by-step explanation:

The curve joining the points P1, P2, P3, and so on is called the involute of a circle.

To construct the locus of the free end of the coir for unwinding through an angle of 360 degrees, as well as the normal and tangent at any point on the curve.

Here are the steps for construction:

1. Draw a line PQ that is tangent to the circle and is equal to the circumference of the circle. This line represents the coir being unwound.

2. Divide both the circle and the tangent line into the same number of equal parts. Label these divisions on the circle as 1, 2, 3, and so on. Similarly, label the divisions on the tangent line as 1', 2', 3', and so on.

3. Draw tangents at points 1, 2, 3, and so on on the circle. Mark the points where these tangents intersect the tangent line as P1, P2, P3, and so on.

The distance from each point Pi to the corresponding point i' on the tangent line should be the same as the distance from the center of the circle to the point i on the circle.

4. The curve joining the points P1, P2, P3, and so on is called the involute of a circle. This curve represents the locus of the free end of the coir as it unwinds.

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The process involves creating an initial circle that represents the drum, then using this to draw a horizontal line that's the same length as your first circle's circumference. Divide both into segments and draw lines (tangents) from one set of segments to the other. Points along these lines represent an unwound thread and create the involute when joined up. Tangents and normals can also be drawn onto this curve.

This question pertains to the mathematical concept of a curve locus, specifically the spiral curve produced by unwinding a coir from a drum. To draw this spiral curve (or 'involute'), start by sketching a circle representing the drum (with diameter 30mm). Next, calculate the circumference of this circle and draw a horizontal line of equivalent length. Then, divide this line and the circumference of your circle into the same number of equal sections. For each section in your circle, draw a line from the point of division to an equivalent point on your horizontal line. These lines are your tangents. Mark points on these lines which correspond to the distances covered by the unwound thread. Finally, join these points to create the involute of the circle.

For the part about drawing a normal and a tangent at any point on the curve: Pick a point on the curve. Remember that the tangent at a point on an involute is perpendicular to the line from the point to the centre of the original circle. A normal at any point on a curve is simply a line drawn perpendicular to the tangent at that point.

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Construct a 95% confidence interval for the expected difference in average test scores between the small class (Classroom A) and the regular class (Classroom B),

a. You can follow these steps:
1. Refer to column (4) of Table 13.2 and find the results for the regressors.
2. Calculate the standard error of the difference in average test scores using the formula:
  SE(difference) = sqrt[SE(Classroom A)^2 + SE(Classroom B)^2]
  where SE(Classroom A) and SE(Classroom B) are the standard errors for each class.
3. Calculate the margin of error (ME) by multiplying the critical value (z*) corresponding to a 95% confidence level by the standard error (SE).
4. Finally, construct the confidence interval by subtracting the margin of error from the difference in average test scores and adding it to the difference in average test scores.

b. To construct a 95% confidence interval for the expected difference in average test scores between the small class with a teacher with 5 years of experience (Classroom A) and the regular class with a teacher with 10 years of experience (Classroom B), you can follow similar steps as in part a. However, this time you need to account for the difference in teacher experience as a regressor.

c. To construct a 95% confidence interval for the expected difference in average test scores between the small class with a teacher with 5 years of experience (Classroom A) and the regular class with a teacher with 10 years of experience (Classroom B), you can follow similar steps as in part a. However, this time you need to consider both the class type and teacher experience as regressors.

d. The intercept is missing from column (4) because it represents the expected average test score when all the regressor variables are equal to zero. In this case, the intercept is not relevant to the question being asked, so it is not included in the table.

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An angle's supplement is the angle that adds up to 180 degrees. As a result, 129° would be the measure of the supplement of an angle with a measure of 51°.

An angle's supplement is the angle that, when combined with the original angle, yields a total of 180°. By deducting the original angle's measurement from 180°, one can determine the supplement angle's measurement. As a result, the measure of the supplement for an angle with a measure of 51° would be 129°. Due to the fact that 180° - 51° Equals 129°. With this knowledge, it is clear that c. 129° is the correct answer. It is significant to remember that, regardless of the size of the original angle, the supplement of an angle always has the same size. As a result, each angle's supplement is always equal to 180° minus the size of the original angle.

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Answer:

129

Step-by-step explanation:

Answer:

In the given figure, Triangle LMN is an isosceles triangle with angle m = angle n and angle p bisects angle NLQ. Prove that angle P is parallel to MN.

Answer:

Step-by-step explanation:

I guess 6%?

In this case, the highest degree term is n^7 in the numerator and n^3 in the denominator. Therefore, as n approaches infinity, the sequence grows without bound and diverges. So the answer is "diverges".

To determine if the sequence converges or diverges and find the limit, we'll analyze the given sequence a_n = n^4 / (n^3 - 9n).
Step 1: Identify the highest power of n in both the numerator and the denominator. In this case, it's n^4 in the numerator and n^3 in the denominator.
Step 2: Divide both the numerator and the denominator by the highest power of n found in the denominator, which is n^3.
a_n = (n^4 / n^3) / ((n^3 - 9n) / n^3)
Step 3: Simplify the expression.
a_n = (n) / (1 - (9/n^2))
Step 4: Take the limit as n approaches infinity.
lim n→∞ a_n = lim n→∞ (n) / (1 - (9/n^2))
As n approaches infinity, the term (9/n^2) approaches 0 since the denominator grows much faster than the numerator.
lim n→∞ a_n = lim n→∞ (n) / (1 - 0)
Step 5: Evaluate the limit.
lim n→∞ a_n = ∞

Since the limit goes to infinity, the sequence diverges. Therefore, the answer is "diverges." To determine whether the sequence converges or diverges, we can look at the highest degree term in the numerator and denominator.

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Answer:

2

Step-by-step explanation:

2x^2 -3xy^3

Let x=-2 and y =-1

2 ( -2)^2 -3 (-2) (-1)^3

Using PEMDAS, we do exponents first

2 ( 4) - 3(-2) (-1)

Multiply nexy

8 - 6

2

In this question, we are required to find

\(2 {x}^{2} - 3x {y}^{3} \)

When, x = -2 and y = -1

We just need to plug the values of x and y in the given polynomial to get our required answer.

Given, Polynomial in variable x and y,

\(2 {x}^{2} - 3x {y}^{3} \)

Plugging values of x and y,

\(2 {( - 2)}^{2} - 3( - 2)( - 1) {}^{3} \)

According to PEMDAS, we need to do the exponents first, So let's simplify the exponents,

\(2(4) - 3( - 2)( - 1)\)

Opening the parantheses and finding the answer,

\(2 \times 4 - 3 \times - 2 \times - 1\)

\(8 -6\)

\( \boxed{ \red{2}}\)

This is our required answer !!

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A. A sample size of 62 should be taken for a 95% level of confidence.

B. The sample size of 107 should be taken for a 99% level of confidence.

a. To estimate the sample size needed to estimate the mean time a staff member spends with each patient, we can use the formula for sample size calculation:

n = (Z^2 * σ^2) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired level of confidence

σ = population standard deviation

E = desired margin of error

For a 95% level of confidence:

Z = 1.96 (corresponding to a 95% confidence level)

E = 2 minutes

σ = 8 minutes (population standard deviation)

Substituting these values into the formula:

n = (1.96^2 * 8^2) / 2^2

n = (3.8416 * 64) / 4

n = 245.9904 / 4

n ≈ 61.4976

Since we can't have a fraction of a sample, we round up the sample size to the nearest whole number. Therefore, a sample size of 62 should be taken for a 95% level of confidence.

b. For a 99% level of confidence:

Z = 2.58 (corresponding to a 99% confidence level)

E = 2 minutes

σ = 8 minutes (population standard deviation)

Substituting these values into the formula:

n = (2.58^2 * 8^2) / 2^2

n = (6.6564 * 64) / 4

n = 426.0096 / 4

n ≈ 106.5024

Rounding up the sample size to the nearest whole number, a sample size of 107 should be taken for a 99% level of confidence.

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The probability of either A or B occurring (or both) is  0.11. The correct answer is A.

We know that:

P(A) = 0.58

P(B) = 0.44

P(A ∩ B) = 0.25

We can use the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

to find P(A ∪ B), which is the probability of either A or B occurring (or both). Substituting the given values, we get:

P(A ∪ B) = 0.58 + 0.44 - 0.25

= 0.77

We also know that:

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

Substituting the values we know, we get:

0.25 = 0.58 + 0.44 - P(A ∪ B)

Solving for P(A ∪ B), we get:

P(A ∪ B) = 0.58 + 0.44 - 0.25

= 0.77

Therefore, we have:

P(A ∩ B) = 0.25

P(A ∪ B) = 0.77

Using the formula:

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

we can find P(A ∩ B) as:

0.25 = 0.58 + 0.44 - 0.77 - P(A ∩ B)

Solving for P(A ∩ B), we get:

P(A ∩ B) = 0.11

Therefore, the answer is (a) 0.11.

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The values of x for which the expression can be further simplified are given as follows:

The expression in the context of this problem is defined as follows:

\(\sqrt{71x}\)

71 is a prime number, hence the expression can be simplified when x has a prime factor factorization with numbers that have powers greater than 1.

Hence the values of x are given as follows:

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The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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If the value of a polynomial is 0 when x = 5, then the expression x - 5 must be a factor of the polynomial.

To understand why, let's consider the process of evaluating a polynomial at a specific value of x.

When we substitute x = 5 into the polynomial, if the result is 0, it means that (x - 5) is a factor of the polynomial. This is because when we divide the polynomial by (x - 5), the remainder is 0.

In other words, if the polynomial evaluates to 0 when x = 5, it indicates that (x - 5) divides evenly into the polynomial, making it a factor.

Thus, the other expressions (-5x, 5x, x + 5) are not necessarily factors of the polynomial when the value of x is 5.

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Answer:

I got x<2 but that's not an option

Step-by-step explanation:

5(x+5) <35

5x+25<35

5x<10

x<2

Answer:

  D.  (-2, -7)

Step-by-step explanation:

I find the easiest way to locate the vertex or x-intercepts is to use a graphing calculator (see below). The vertex is the extreme point on the graph. For this function, it is (-2, -7), choice D.

__

The axis of symmetry of the graph is the vertical line such that every point on the left is a mirror image of the corresponding point on the right. Here, that axis of symmetry is x=-2. (It is shown as a dashed orange line on the graph.)

The location of the axis of symmetry for quadratic ...

  y = ax^2 +bx +c

is x = -b/(2a).

For your function,

  y = 2x^2 +8x +1

the coefficients are a = 2, b = 8, c = 1. This means the axis of symmetry is ...

  x = -b/(2a) = -8/(2(2)) = -2

The vertical line at x=-2 is the axis of symmetry.

The vertex is on the axis of symmetry. Its y-value is found by evaluating the function for x = -2 (the x-value of the axis of symmetry).

  y = 2·(-2)^2 +8(-2) +1 = 2·4 -8·2 +1 = 8 -16 +1

  y = -7 . . . . at the vertex

So, the (x, y) coordinates of the vertex are (-2, -7).

Answer:

D. (-2, -7)

Step-by-step explanation:

y= 2x²+8x+1

The vertex is max or min of the graph, for the given function it is

x = -b/2a for a>0

so x= - 8/4= -2

for the point of x= -2

y= 2*4 - 16 + 1 = - 7

So vertex is  (-2, -7), choice D.

Answer:

21 3/5

Step-by-step explanation:

I think the answer is 21 3/5 because

6×3 3/5=21 3/5 but I'm not positive.

Answer:

For sure, A and C. However, I cannot fully read the last one.

Step-by-step explanation:

Be sure to mark me Brainliest!

Answer:

Maybe try 'A'..good luck

Answer:

The answer is b

Answer:

319

Step-by-step explanation:

So, to find the surface area, first we find the base area, which is: 11 x 11 = 121

Then, we have to find the area of the other faces. Since each face is a triangle, we can use the formula A = 1/2 x b x h.

So,

b = 11

h = 9

1/2 x 11 x 9 = 49.5

The, we multiply by 4, the number of sides: 49.5 x 4 = 198

Then, we add the 2, values: 121 + 198,

Which gives us: 319.

Hope this helped!