Q1 - Find the circumference of following circle. Take π = 3.14

A-18.84 units
B-47.3 units
C-72.22 units
D-47:1 units

Answer:

1/9

Step-by-step explanation:

Answer:

1/9

Step-by-step explanation:

Answer:

Explanation:

Given the expression:

In the expression:

Rearrange the expression to bring the like terms together:

Next, combine the like terms:

An equivalent expression is:

The limit value does not exist.

To estimate the limit numerically, we can plug in values of x that are close to 9 and see what the function approaches.

When x = 8.9, the function is (8.9 - 3) / (8.9 - 9) = 5.9 / -0.1 = -59

When x = 8.99, the function is (8.99 - 3) / (8.99 - 9) = 5.99 / -0.01 = -599

When x = 9.01, the function is (9.01 - 3) / (9.01 - 9) = 6.01 / 0.01 = 601

When x = 9.1, the function is (9.1 - 3) / (9.1 - 9) = 6.1 / 0.1 = 61

As we can see, the function is approaching infinity as x approaches 9 from both the left and the right. Therefore, the limit does not exist and the answer is DNE (does not exist).

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The sailcloth having vertices of 0, 0), (4, 0), and (3, 6), with a sailcloth cost  of $11.75 per square yard is $141

The given parameters;

Cost of the sailcloth per square yard = $11.75

Vertices of the sailcloth are; (0, 0), (4, 0), and (3, 6)

The cost of purchasing the sailcloth = The area of the sailcloth × Cost per square yard

Taking the base length as; 4 - 0 = 4

The height = The distance from the x-axis to the highest point on the sailcloth = The highest y-value = 6

Which gives;

The area of the sailcloth = Area of a triangle = \(\dfrac{1}{2} \times 4 \times 6 = 12\)

The area of the sailcloth = 12 yard²

The cost of purchasing the sailcloth = 12 yard² × $11.75/yard² = $141

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The researcher should sample approximately 409 students in order to be 98% confident that the true mean GPA is within 0.1 of the sample mean.

To estimate the average GPA of all UCF students with a 98% confidence level and a margin of error of 0.1, we can use the formula:
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-score for the desired confidence level (98% confidence level corresponds to a Z-score of 2.33)
σ = standard deviation
E = margin of error
Given that the margin of error (E) is 0.1 and the standard deviation (σ) is 0.85, we can substitute these values into the formula:
n = (2.33 * 0.85 / 0.1)^2
Calculating this expression gives us:
n ≈ 20.22^2
n ≈ 408.48

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Answer:

52%

Step-by-step explanation:

I am assuming it  asking what is the chance a boy is picked.

13+12 = 25 total kids

100/25 = 4% chance for each kid to be picked

13 boys x 4 % = 52% chance for a boy to be picked.

The measurement of BC in the given figure is 4√2.

Given is figure we need to find the measurement of BC,

∠GBC = ∠CDF = 45° [alternate angles]

So, in triangle DCF,

Cos 45° = DF/DC

1/√2 = DF/12√2

DF = 12

Now we see that the triangles DCF and BCG are similar triangles by AA rule,

So, according to the definition of similar triangles,

DC/BC = DF/BG

12√2/BC = 12/(7-3)

12√2/BC = 12/4

12√2/BC = 3

3BC = 12√2

BC = 4√2

Alternatively, you can find the value of BC, using the trigonometric ratios in triangle GBC,

Cos 45° = GB/BC

GB = 7-3 = 4

Therefore,

Cos 45° = 4/BC

1/√2 = 4/BC

BC = 4√2

Hence the measurement of BC in the given figure is 4√2.

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The radii and the centers are explained below.

Given that are equations of circles we need to find the center and the radius of each circle.

1) x² + 6x + y² - 4y = -9

x² + 2·3·x + y² - 2·2·y = -9

Add 13 to both side,

x² + 2·3·x + y² - 2·2·y + 13 = -9 + 13

x² + 2·3·x + y² - 2·2·y + 9 + 4 = 4

(x+3)² + (y-2)² = 4

The center = (-3, 2) and the radius = 2

2) x² + 10x + y² - 8y = -31

x² + 2·5·x + y² - 2·4·y = -31

Add 41 to both sides,

x² + 2·5·x + y² - 2·4·y + 41 = -31 + 41

x² + 2·5·x + y² - 2·4·y + 25 + 16 = 10

(x+5)² + (y-4)² = 10

The center = (-5, 4) and the radius = √10

3) x² - 2x + y² + 4y -11 = 0

x² - 2x + y² + 4y = 11

x² - 2·1·x + y² - 2·2·y = 11

Add 5 to both sides,

x² - 2·1·x + y² - 2·2·y + 5 = 11 + 5

x² - 2·1·x + y² - 2·2·y + 4 + 1 = 16

(x-1)² + (y-2)² = 4²

The center = (1, 2) and the radius = 4

4) x² + 9x + y² = 0

\(\left(x-\left(-\frac{9}{2}\right)\right)^2+\left(y-0\right)^2=\left(\frac{9}{2}\right)^2\)

The center = (-9/2, 0) and the radius = 9/2

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The expressions that can be used to describe how many milligrams of vitamin C are in the salad are:

(Choice A) 200b + (300s + 42d)

(Choice E) 300s + 200b + 42d

So, the correct answers are A and E.

The milligrams of vitamin C in the salad can be determined by considering the quantities of spinach, berries, and dressing used in the salad, along with their respective vitamin C content.

In the given scenario, the salad includes 300 milliliters (mL) of spinach, 200 mL of berries, and 42 mL of dressing. The vitamin C content is measured in milligrams per milliliter (mg/mL), with values denoted as s for spinach, b for berries, and d for dressing.

To calculate the milligrams of vitamin C in the salad, we can use the expressions provided:

(Choice A) 200b + (300s + 42d)

(Choice E) 300s + 200b + 42d

In Choice A, the expression 200b represents the milligrams of vitamin C in the berries, while (300s + 42d) represents the combined vitamin C content of spinach and dressing.

In Choice E, the expression 300s represents the milligrams of vitamin C in the spinach, 200b represents the milligrams of vitamin C in the berries, and 42d represents the milligrams of vitamin C in the dressing.

By substituting the respective values of s, b, and d into either expression, we can calculate the total milligrams of vitamin C in the salad.

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The price of a ticket exceeds its expected value by $0.75.

In this raffle scenario, we need to find out by how much the price of a ticket exceeds its expected value.

Step 1: Determine the probability of winning each prize.
- The probability of winning the first prize: 1/1000 (1 winning ticket out of 1000)
- The probability of winning a second prize: 3/1000 (3 winning tickets out of 1000)
- The probability of not winning any prize: 996/1000 (996 losing tickets out of 1000)

Step 2: Calculate the expected value of each outcome.
- Expected value of winning the first prize: (1/1000) * $100 = $0.10
- Expected value of winning a second prize: (3/1000) * $50 = $0.15
- Expected value of not winning any prize: (996/1000) * $0 = $0

Step 3: Add the expected values together.
- Total expected value: $0.10 + $0.15 + $0 = $0.25

Step 4: Determine the difference between the price of a ticket and its expected value.
- Difference: $1.00 (ticket price) - $0.25 (expected value) = $0.75

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Answer:

-976,563.

Step-by-step explanation:

The common ratio is 15/-3 = -75/15 = 375/-75 = -5.

Sum of n terms = a1. (r^n - 1) / (r - 1)

so S9 = -3 * ((-5)^9 - 1)) /  (-5 - 1)

= -976,563.

As a result of answering the given question, we may state that radicals \(\sqrt(27x^5) + \sqrt(48x^6) = 3x^2\sqrt(3x) + 4x^3\sqrt3\) And that's the simplified expression.

A radical is a symbol denoting the square root or nth root. Root expressions are ones that contain square roots. A number or word that appears there is a radical's radicand. Examples include the radicals 7 and 2y+1. Radicals can also be defined by the following terms: Radial equations are equations that contain radicals. A "root expression" is the expression located within the square root. The numbers 2, 372, 2x+7, and 41p are examples of radical representations. The word "root expression" refers to the expression located within the square root. The numbers 2, 372, 2x+7, and 41p are all radical representations.

\(\sqrt(27x^5) + \sqrt(48x^6)\)

First, let's factor out any perfect squares from under the radicals:

\(\sqrt(27x^5) = \sqrt(9x^4 * 3x) = 3x^2\sqrt(3x)\\\sqrt(48x^6) = \sqrt(16x^6 * 3) = 4x^3\sqrt3\)

Now we can substitute these simplifications back into the original expression and combine like terms:

\(\sqrt(27x^5) + \sqrt(48x^6) = 3x^2\sqrt(3x) + 4x^3\sqrt3\)

And that's the simplified expression.

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Answer:

x≤3

Step-by-step explanation:

Hi there!

4x≤12

Divide both sides by 4 to isolate x

4x/4≤12/4

x≤3

I hope this helps!

Thus, the part of the trinomial that's equal to the product of p and q is the constant

term!

B: The Constant Term

Step-by-step explanation:

A statement that not true about the Mann Whitney U test. The correct answer is B. The two samples are equal in size.

The Mann Whitney U test, also known as the Mann-Whitney-Wilcoxon test or the Wilcoxon rank-sum test, is a nonparametric test that is used to compare two independent samples to determine whether they come from the same population. It is often used when the data is not normally distributed or when the assumptions of the t-test are not met.

The Mann Whitney U test involves ranking the observations from both samples, calculating the sum of the ranks for each sample, and then comparing these sums to determine whether the samples are significantly different from each other.

The statement that is not true about the Mann Whitney U test is that the two samples are equal in size. This is not a requirement for the test, as it can be used with samples of different sizes.

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Answer:

Youngest child: $2

oldest child: $6

Second oldest: $2.50

Step-by-step explanation:

Youngest child= x

oldest child= 3x

Second oldest: .50+x

x+3x+.50+x=10.5

5x+.50=10.5

    - .50= - .50

5x=10

divided both numbers by 5 and x is equal to 2. So, the youngest child is $2 and you add .50, which is $2.50, and thats for the second child. Last, you do 2 times 3 equals $6 which is the oldest child.

The youngest contributed $1.90, the oldest contributed $5.27, and the second oldest contributed $2.85.

Three children each contributing to their mother's birthday present. The eldest gave three times more than the youngest, while the second oldest contributed 50 cents more. If the gift costs $10.50 which is given in the question.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

Let the youngest sibling contribute the amount of x dollars

As per the given information,

3x + 0.50 x + x + x = 10.50

Apply the addition operation,

4.50x = 10.50

x = 10.50 / 6.50

Apply the division operation to get

x = 1.90

So the youngest sibling contributed = $1.90

The oldest contributed 1.90 × 3 = $5.27

And the second oldest contributed (1.50)1.90= $2.85

Therefore, the youngest contributed $1.90, the oldest contributed $5.27, and the second oldest contributed $2.85.

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As per the congruence theorem, we have proved that ΔABC ≅ΔDEF.

In math congruence theorem states that if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other.

Here we need to prove ΔABC ≅ΔDEF by using the congruence theorem.

Here we have given that ΔABC and ΔDEF,

=> ∠B≅∠E [right angle]

So, we have obtained that

=> ∠A≅∠D

As we know that there is two angles and one non included side of ΔABC is congruent the two corresponding angles and one non- included side of ΔDEF, therefore, by AAS congruence rule.

So, based on the given fact we have identified that

=> ΔABC ≅ΔDEF

Therefore, the AAS congruence postulate defined that the triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

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Answer:

1. 256 bacteria cells 2. y=2^x 3. 2 bacteria cells

Step-by-step explanation:

Answer:

- 11r³ + 3r + 16

Step-by-step explanation:

( 8r - 4r³ + 8 ) - ( 5r - 8 + 7r³ ) =

= 8r - 4r³ + 8 - 5r + 8 - 7r³ =

= - 11r³ + 3r + 16

The line integral of $2x^2 \mathrm{~d}y$ along the curve $C$ is equal to 486 according to the given information.

To calculate the line integral $\int_C 2x^2 \mathrm{~d}y$, we need to parameterize the curve $C$ and express $x$ and $y$ in terms of the parameter $t$. The given curve is defined as $\mathbf{r}(t) = \langle 3t-3, 3t \rangle$, where $0 \leq t \leq 4$.

Differentiating $\mathbf{r}(t)$ with respect to $t$, we have $\mathbf{r}'(t) = \langle 3, 3 \rangle$. Integrating $2x^2$ with respect to $y$ along the curve $C$ gives us:

$\int_C 2x^2 \mathrm{~d}y = \int_0^4 2(3t-3)^2 (3 \mathrm{~d}t) = 2 \int_0^4 (27t^2 - 54t + 27) \mathrm{~d}t$.

Evaluating the integral, we get $\int_C 2x^2 \mathrm{~d}y = [9t^3 - 27t^2 + 27t]_0^4 = 486$.

Therefore, the line integral $\int_C 2x^2 \mathrm{~d}y$ along the curve $C$ is equal to 486.

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Answer:

$5

Step-by-step explanation:

if 5 leis are worth $25, each lei would be 25/5

25/5 is 5/1, when the denominator is one, that is unit price

the unit price is $5

Answer:

"Games played in a workplace environment to achieve status, advancement and money"

The Answer is (x+9)^2

Answer:

-81/20

Step-by-step explanation:

The chance of the event B is 0.4 when using the probability for the two independent two event formula.

In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).

Events classified as independent do not depend on other events for their occurrence.

Event A's likelihood of happening is P(A)=0.65.

The likelihood of the two events A and B intersecting is P(A∩B)=0.26.

Given that the likelihood of the two independent events is:

P(A∩B) = P(A)⋅P(B)

Then the probability of the event B will be,

P(B) = P(A)/P(A∩B)

P(B) = 0.65/0.26

P(B) =0.4

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The given set of functions {f_1(x) = x, f_2(x) = x^2, f_3(x) = 3x - 6x^2} is linearly independent on the interval (-infinity, infinity).

Linear independence of a set of functions means that no function in the set can be expressed as a linear combination of the other functions. In other words, for the set to be linearly independent, the only solution to the equation c_1f_1(x) + c_2f_2(x) + c_3f_3(x) = 0 should be c_1 = c_2 = c_3 = 0, where c_1, c_2, and c_3 are constants.

To determine if the given set is linearly independent, we need to check if there exist non-zero constants c_1, c_2, and c_3 such that c_1f_1(x) + c_2f_2(x) + c_3f_3(x) = 0 for all x in the interval (-infinity, infinity).

By substituting the functions into the equation and equating the coefficients of the terms with the same powers of x, we can solve for c_1, c_2, and c_3. If the only solution is c_1 = c_2 = c_3 = 0, then the set is linearly independent. In this case, the given set is indeed linearly independent as there is no non-zero solution to the equation, confirming that the functions are not dependent on each other.

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Categorical charts are useful in displaying nominal data or numerical data that splits nicely into different categories so you can quickly see comparative results and trends.

The type of chart that is useful in displaying nominal data or numerical data that splits nicely into different categories is called a categorical chart. Categorical charts allow you to quickly see comparative results and trends by displaying data in separate categories or groups. This makes it easier to identify patterns and trends in the data and to draw conclusions about the relationships between different variables.

Examples of categorical charts include bar charts, column charts, and pie charts. Bar charts and column charts are commonly used to display numerical data, while pie charts are often used to display proportional data. Categorical charts can be used in a variety of contexts, such as business, education, and scientific research, to help communicate complex data in a clear and concise manner.

Overall, categorical charts are a powerful tool for organizing and displaying data in a way that makes it easy to identify patterns and trends. By using these charts, you can quickly and accurately visualize complex data sets and draw conclusions about the relationships between different variables.

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Answer:

5.2776558e+14

Step-by-step explanation:

\(a_{n} =a_{1} *r^{n-1}\)

15, 30, 60

\(a_{46} =15(2)^{46-1}\)

\(a_{46}\) = 5.2776558e+14

hope it helps :)

mark brainliest!

Based on the transformation of the given parent function f(x), the function g(x) is: C. g(x) = ∛(x) + 2

In Mathematics, the translation of a geometric figure to the right is a type of transformation which simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure up is a type of transformation that simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

Translating the parent function f(x) = ∛(x) two (2) units up, would produce an image of function f(x):

g(x) = f(x) + 2

g(x) = ∛(x) + 2

In this context, we can reasonably infer and logically deduce that the parent function f(x) was shifted 2 units up to produce function g(x).

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