A parabola can be drawn given a focus of (−4,5) and a directrix of y=−9. what can be said about the parabola?

Answer: It's A if not put B

Step-by-step explanation:

Since correlative conjunctions are used to connect parts of a sentence with equal value, we only need to use a comma when two independent clauses are being connected with correlative conjunctions.Correlative conjunctions include pairs such as “both/and,” “either/or,” “neither/nor,” “not/but” and “not only/but also.

Answer:

9

Step-by-step explanation:

Since the absolute value of -9 is 9.

By using the concept of testing of hypothesis, it can be calculated that

The required test statistic is t = 0.918

What is testing of hypothesis?

Suppose, there is a hypothesis and there is a data at hand. Testing of hypothesis is a method of inferencing which is used to decide whether the given hypothesis is true or not based on the statistical data given

From the table attached here, it can be calculated that

\(\bar{x}_{2012}=365.4667\\s^{2}_{2012}=27133.66364\\\bar{x}_{2013}=331.775\\s^{2}_{2013}=29750.53782\\n_{2012}=45\\n_{2013}=40\\\)

So the test statistic t is

\(\large t=\frac{\bar{x}_{2012}-\bar{x}_{2013}}{\sqrt{\frac{s^{2}_{2012}}{n_{2012}}+\frac{s^{2}_{2013}}{n_{2013}}}}\)

\(t=\frac{365.4667-331.775}{\sqrt{\frac{27133.66364}{45}+\frac{29750.53782}{40}}}\)

\(t \large =\frac{33.6917}{36.6978711}\)

t = 0.918

The value of the test statistic is 0.918

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The Area of the Faces are:

Face A: 93.5 square inches

Face B: 93.5 square inches

Face C: 46.75 square inches

Face D: 46.75 square inches

Face E: 93.5 square inches

Face F: 93.5 square inches

Face A:

Since the dimensions of the base sheet are 8.5 inches by 11 inches, the area of Face A is:

Face A = 8.5 inches x 11 inches

= 93.5 square inches

Face B:

Since the dimensions of the whole sheet are 8.5 inches by 11 inches, the area of Face B is:

Face B = 8.5 inches x 11 inches

= 93.5 square inches

Face C:

Since the dimensions of the half sheet are 8.5 inches by 5.5 inches (half of 11 inches), the area of Face C is:

Face C = 8.5 inches x 5.5 inches

= 46.75 square inches

Face D:

It has the same dimensions as Face C, so the area is also:

Face D = 8.5 inches x 5.5 inches = 46.75 square inches

Face E:

They have the same dimensions as the whole sheet, so the area of Face E is:

Face E = 8.5 inches x 11 inches = 93.5 square inches

Face F: This is the top face of the prism, which is the same as Face B. So the area of Face F is also:

Face F = 8.5 inches x 11 inches = 93.5 square inches

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The area in square meters will the oil slick cover is 9.5×10⁶ m².

15 barrels of diesel spilt into the ocean, where each barrel contains 42 gallons. Thereby the total volume of the oil spilt by 15 barrels is calculated as follows:

The total volume of the oil spilt by 15 barrels = 15× 42 gallons.

=630 gallons

1 gallon = 3.78541 liters

Volume in L = 630 gallons × 3.78541 liters/ 1 gallon

= 2384.8083 L

1 L = 10⁻³ m³

2384.8083  L = 2384.8083 × 10⁻³ m³

= 2.3848083 m³

The area covered by the oil spill has to be determined, where the thickness of the oil spill is given to be 2.5×10² nm.

1 nm = 10⁻⁹ m

Thereby, 2.5×10² nm = 2.5×10²×10⁻⁹ m

= 2.5×10⁻⁷ m

Area (m²) = volume (m³)/thickness (m)

= 2.3848083 m³/ 2.5×10⁻⁷ m

= 0.95392×10⁷ m²

= 9.5×10⁶ m²

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The measure of the inscribed angle is equal to 90 degrees

The inscribed angle theorem mentions that the angle inscribed inside a circle is always half the measure of the central angle or the intercepted arc that shares the endpoints of the inscribed angle's sides. In a circle, the angle formed by two chords with the common endpoints of a circle is called an inscribed angle and the common endpoint is considered as the vertex of the angle.

In this problem, the side length of the square is 5 which forms 90 degrees to all the other sides.

The measure of the circumscribed angle is 90 degree

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The correct answer is 113. To forecast the sales of the ice rink on day 4 using the trend method, we need to determine the trend equation based on the given data points.

The trend equation represents the overall pattern or trend in the sales data and allows us to make predictions for future values.

First, we need to calculate the average increase in sales per day. The average increase is obtained by dividing the total increase in sales over the three days (102 - 80 = 22) by the number of days (3 - 1 = 2). Therefore, the average increase in sales per day is 22 / 2 = 11.

Next, we can use the average increase to forecast the sales for day 4. Starting from the last known sales value (102), we add the average increase to project the sales for the next day. Thus, the forecasted sales for day 4 would be 102 + 11 = 113.

Therefore, the correct answer is 113.

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The postulate that can be used to prove the two triangles are congruent is (c) None of the other answers are correct

The figure represents the given parameter

There are two triangles in the figure

Such that the triangles are similar triangles or congruent

From the question, we understand that the triangles are congruent

Also, we know that

UQ ≅ AC and QD ≅ AU

There is no point C on any of the triangles

This means that we cannot ascertain the congruency of the triangles

Hence, the true statement is (c)

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We can use the substitution $u=x^2+9$ to find the indefinite integral of the given expression. We have:

\(∫�2�2+9��=\)\(12∫2��2+9���∫ x 2 +9​\)

\(x 2\)

​

\(dx= 21​ ∫ x 2 +9​ 2x​ xdx\)

Let $u=x^2+9$, then $\frac{du}{dx}=2x$ and $dx=\frac{du}{2x}$, so we have:

\(12∫2��2+9���=12∫1���21​ ∫ x 2 +9​ 2x​ xdx= 21​ ∫ u​ 1​ du\)

Integrating with respect to $u$, we get:

\(12∫1���=�+�=�2+9+�21​ ∫ u​ 1​ du= u​ +C= x 2 +9​ +C\)

where $C$ is a constant of integration. Therefore, the indefinite integral of $\frac{x^2}{\sqrt{x^2+9}}$ is $\sqrt{x^2+9} + C$, where $C$ is a constant.

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There is a graph image below.

Answer:

Ok, if we start with a number n, then we can write the consecutive numbers of n as:

n + 1

n + 2

n + 3..

etc.

Now, suppose that we have an integer x, and we want to write it as a sum of consecutive numbers.

There is a really trivial way.

We know that x + 0 = x.

now, we can write:

0 = (x - 1) + (x - 2) + ... + 1 + 0 + (-1) + (-2) + ..... + (-x + 2) + (x - 1)

Then we wrote zero as a sum of consecutive numbers.

Now we can write:

x = x + 0 = x + (x - 1) + (x - 2) + .... + 1 + 0 - 1 - 2 - ... - (x - 1) = x

Then we show that for any integer x, we can write it as a sum of consecutive integers.

Then it must work for all the integers x, then we prove that all the integers can be written as a sum of consecutive integers.

Answer:

The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.

To find the probability, we need to calculate n(E) and n(S).

In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.

This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.

Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.

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By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).

Herein we must apply a rigid transformation into a given point to determine an image. Rigid transformations are transformations applied on a geometric locus such that Euclidean distance is conserved. Dilations are a kind of rigid transformations such that:

(x, y) → (k · x, k · y), for k > 0

If we know that Q(x, y) = (0, 2) and k = 0.5, then the coordinates of Q' are:

Q'(x, y) = (0.5 · 0, 0.5 · 2)

Q'(x, y) = (0, 1)

By applying the definitions of rigid transformation ((x, y) → (0.5 · x, 0.5 · y)) and dilation, we conclude that the coordinates of Q'(x, y) are (0.1).

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Answer: Q' = (0,1)

Step-by-step explanation: just did it on edge

The statement that best describes "willing suspension of disbelief" is: A dynamic in which the audience agrees to accept the fictional world of the play on an imaginative level while knowing it to be untrue.

The concept of "willing suspension of disbelief" is an essential element in experiencing and appreciating works of fiction, particularly in theater, literature, and film. It refers to the voluntary act of temporarily setting aside one's skepticism or disbelief in order to engage with the fictional narrative or performance. It involves consciously accepting the imaginative world presented by the creator, even though it may contain unrealistic or fantastical elements. By willingly suspending disbelief, the audience allows themselves to become emotionally invested in the story and characters, making the experience more enjoyable and meaningful. This dynamic acknowledges the inherent fictional nature of the work while acknowledging that the audience is aware of its fictional status. It creates a mutual understanding between the audience and the creators, enabling the audience to fully immerse themselves in the narrative and connect with the intended emotions and themes of the work.

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Answer:

Step-by-step explanation:

If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology

The roots are 14.09, 0.30 and -0.39 to nearest hundredth.

Answer:

You start with 720 grams of element X, which has a half life of 9 minutes. How much time will it take until only 255 grams remain?

elapsed time = half life * log (beginning amount / ending amount) / log 2

elapsed time = 9 * log (720 / 255) / log (2)

elapsed time = 9 * log (2.8235294118 ) / log (2)

elapsed time = 9 * 0.450792316 / 0.30102999566

elapsed time = 9 * 1.4974996595

elapsed time = 13.4774969355  minutes

Since the problem wants this rounded to the nearest tenth of a minute:

elapsed time = 13.5 minutes

Step-by-step explanation:

The correctly formatted scientific notations are:
B. 8 × 10^6
C. 6.1 × 10^12
D. 0.802 × 10^4 (which can be simplified to 8.02 × 10^3)
F. 4.532 × 10^−9 .

Scientific notation has the general form a × 10^b, where a is a number between 1 and 10 (inclusive) and b is an integer. In option A, 6/10^6 is not in scientific notation because the numerator is not between 1 and 10. In option E, 9.31 × 100^-7 is not in scientific notation because 100^-7 is not an integer power of 10.

Scientific notation is a way to express very large or very small numbers in a more compact and convenient form. In scientific notation, a number is expressed as a product of a decimal number between 1 and 10 (inclusive) and a power of 10. The power of 10 indicates the number of places the decimal point needs to be moved to obtain the original number.

For example, the number 8,000,000 can be written in scientific notation as 8 × 10^6. The decimal number 8 is between 1 and 10, and the exponent 6 indicates that the decimal point needs to be moved six places to the right to obtain the original number.

Similarly, the number 0.000000004532 can be written in scientific notation as 4.532 × 10^-9. The decimal number 4.532 is between 1 and 10, and the exponent -9 indicates that the decimal point needs to be moved nine places to the right to obtain the original number.

Scientific notation is widely used in fields such as science, engineering, and mathematics, where very large or very small numbers are frequently encountered. It allows these numbers to be expressed concisely and accurately, without the need for many zeros or long strings of digits.

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The four corners of a square are 90 degrees.

They are evenly split by the diagonal lines, so each corner is now two 45 degree angles.

The lines form triangles, which have 3 angles that need to equal 180 degrees.

Two of the angles are 45, so 45 + 45 = 90 degrees.

X = 180 -90 = 90 degrees.

Answer:

90 degrees

By 90 * 4 is 360

Step-by-step explanation:

The 15th term in the sequence a (n) = 9n - 12 as required to be determined in the task content is; 123.

It follows from the task content that the 15th term in the sequence whose nth term is defined by the equation; a (n) = 9n - 12 is to be determined.

Since tye formula for the nth term of the sequence is; a (n) = 9n - 12.

To determine the 15th term, we must substitute 15 for n in the equation as follows;

a (15) = 9 (15) - 12

a (15) = 135 - 12

a (15) = 123.

In conclusion, the 15th term of the sequence whose nth term is as defined is; 123.

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Answer:

c 6 d 4 I hope it will help you please follow me

This is true, we can verify that the equation n(A∪B)=n(A)+n(B) holds for the given disjoint sets A={a,e,i,o,u} and B={g,h,k,l,m}.

Since A and B are disjoint sets, meaning they have no common elements, we can say that A∩B=∅. Therefore, the equation n(A∪B)=n(A)+n(B) becomes:
n({a,e,i,o,u,g,h,k,l,m}) = n({a,e,i,o,u}) + n({g,h,k,l,m})
Counting the elements, we see that n({a,e,i,o,u,g,h,k,l,m})=10, n({a,e,i,o,u})=5, and n({g,h,k,l,m})=5.
Substituting these values back into the equation, we get:
10 = 5 + 5
Hi! To verify the equation n(A∪B) = n(A) + n(B) for the given disjoint sets A = {a, e, i, o, u} and B = {g, h, k, l, m}, we first need to find the union of sets A and B.
Since A and B are disjoint (meaning they have no elements in common), the union of A and B, denoted as A∪B, simply combines the elements of both sets. So, A∪B = {a, e, i, o, u, g, h, k, l, m}.
Now, let's find the number of elements (n) in each set:
n(A) = 5 (as there are 5 elements in set A)
n(B) = 5 (as there are 5 elements in set B)
n(A∪B) = 10 (as there are 10 elements in the union of A and B)
Now, we can verify the equation:
n(A∪B) = n(A) + n(B)
10 = 5 + 5

The equation holds true for the given disjoint sets A and B.

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Given:

The water leaks from the faucet at a rate of 1/2 gal/hr

The total water leaks after (x) hours will be = 1/2 * x

We will find the number of gallons when x = 1, 2, 3, and 4

The table will be as follows:

Hours Gallons

1 1/2 * 1 = 1/2

2 1/2 * 2 = 1

3 1/2 * 3 = 3/2

4 1/2 * 4 = 2

To calculate Evan's AGI (Adjusted Gross Income) and taxable income if he files as a single taxpayer, we need to consider his income and deductible expenses.

Calculate Evan's total income:
  - Salary: $73,650
  - Part-time hourly pay: $700

  Total income = Salary + Part-time pay = $73,650 + $700 = $74,350

Deductible expenses:
  - Moving expenses: $1,200
  - Student loan interest: $2,890
  - Uniform cost: $1,490
  - Cash contribution: $1,345

  Total deductible expenses = $1,200 + $2,890 + $1,490 + $1,345 = $6,925

Calculate AGI:
  AGI = Total income - Total deductible expenses
  AGI = $74,350 - $6,925 = $67,425

Evan's taxable income is equal to his AGI since there were no other deductions mentioned in the question.

Therefore, Evan's AGI is $67,425, and his taxable income is also $67,425.

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Evan's AGI is $67,425 and his taxable income is $54,875 if he files as a single taxpayer.

We have,

Income:

Salary: $73,650

Part-time work pay: $700

Total income: $73,650 + $700 = $74,350

Deductible Expenses:

Cost of moving possessions: $1,200

(This deduction applies if the move meets certain distance and time requirements. Since the move was 125 miles away, it meets the distance requirement.)

Interest paid on student loans: $2,890

Cost of purchasing a delivery uniform: $1,490

Cash contribution to State University deliveryman program: $1,345

Total deductible expenses:

$1,200 + $2,890 + $1,490 + $1,345

= $6,925

Now we can calculate Evan's AGI and taxable income:

AGI (Adjusted Gross Income)

= Total income - Deductible expenses

AGI = $74,350 - $6,925 = $67,425

Taxable Income = AGI - Standard Deduction

For a single filer in 2022, the standard deduction is $12,550.

Taxable Income = $67,425 - $12,550 = $54,875

Therefore,

Evan's AGI is $67,425 and his taxable income is $54,875 if he files as a single taxpayer.

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Answer:

3/10

Step-by-step explanation:

3/25 / 2/5

For large enough x, exponential functions like 2ˣ will always dominate a polynomial of any degree. This is to say the denominator will always be larger than the numerator (again, for sufficiently large x). So the limit in this case would be 0. (I'll leave a link in comments to a variety of answers regarding this detail.)

But if you've been introduced to L'Hopital's rule: we have

\(\displaystyle \lim_{x\to\infty}\frac{5x^3+10}{6\times2^x-1} = \lim_{x\to\infty}\frac{15x^2}{6\ln(2)\times2^x} = \lim_{x\to\infty}\frac{30x}{6\ln^2(2)\times2^x} = \lim_{x\to\infty}\frac{30}{6\ln^3(2)\times2^x} = \frac1\infty = 0\)

A moderately intense, wide peak in the 3200-3400 cm⁻¹ region is indicative of the presence of hydroxyl (-OH) functional groups.

Identification of Hydroxyl Functional Groups Using Infrared Spectroscopy

One specific region of the infrared spectrum that can provide valuable information is the 3200-3400 cm⁻¹ region. If an unknown compound displays a moderately intense, wide peak in this region, it is highly likely that it contains a hydroxyl (-OH) functional group.

Infrared spectroscopy is a powerful tool in the identification of functional groups in unknown compounds.

The presence of hydroxyl groups can be further confirmed by looking for other characteristic peaks in the IR spectrum, such as a broad peak in the 1600-1700 cm⁻¹ region for the bending vibrations of the -OH bond. Overall, infrared spectroscopy can be an effective method for identifying hydroxyl functional groups in unknown compounds.

Infrared spectroscopy is a powerful tool in the identification of functional groups in unknown compounds.  This is because the stretching vibration of the -OH bond falls in the range of 3200-3400 cm⁻¹ and the hydroxyl group is characterized by a broad, intense peak due to the high density of vibrational modes.

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Answer:

the answer is -10

Step-by-step explanation:

-2 × 5 = -10