Find the critical numbers of the function. (Enter your answers as a comma-separated list.)

The statement when 12 is divided by 2/3 has no remainder is true.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, 12 is divided by 2/3 which is,

= (12)/(2/3).

= 12×(3/2)                            (we can flip the divisor to make it a multiplier)

= 36/2.

= 18.

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Answer:

each of them need to save 24013813120321312331313131 cents

Step-by-step explanation:

Answer:

The probability that one marble drawn at random is not blue is 70%

Answer and Step-by-step explanation:

Solution:

Given:

Let A is the event of a person over 50 diagnosed by health service.

B1 is the event that an adult over 50 actually has diabetes.

B2 is the event that an adult over 50 does not have diabetes.

P (B1) = 8% = 0.08

And P (B2) = 1 – P (B1)

                  = 1 – 0.08

                  = 0.92

Correctly diagnose of all persons with diabetes= 95%

P (A/B1) = 0.95

Incorrectly diagnose of all persons without diabetes=   2%

P (A/B2) = 0.02

(a) ) the community health service will diagnose an adult over 50 as having diabetes.

P (B1) P (A/B1) = (0.08) (0.95) = 0.076

P (B2) p (A/B2) = (0.92) (0.02) =0.0184

P (B1) P (A/B1) + P (B2) p (A/B2) =  0.076 + 0.0184

                                                     = 0.0944

(b)  A person over 50 diagnosed by the health service as having diabetes actually has the disease.

By using formula:

P (B1/A) = P (B1) P (A/B1) / P (B1) P(A/B1) + P (B2) P (A/B2)

Put all the given values:

= (0.08) (0.95) / (0.08) (0.95) + (0.92) (0.02)

=0.076 / 0.076 + 0.0184

=0.076 / 0.0944

= 0.8050

Using conditional probability, it is found that there is a:

a) 0.0944 = 9.44% probability that the community health service will diagnose an adult over 50 as having diabetes.

b) 0.8051 = 80.51% probability that a person over 50 diagnosed by the health service as having diabetes actually has the disease.

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

Item a:

The percentages of a positive test is:

Hence:

\(P(A) = 0.95(0.08) + 0.02(0.92) = 0.0944\)

0.0944 = 9.44% probability that the community health service will diagnose an adult over 50 as having diabetes.

Item b:

From item a, \(P(A) = 0.0944\).

The probability of both a positive test and having the disease is:

\(P(A \cap B) = 0.95(0.08)\)

Hence, the conditional probability is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.95(0.08)}{0.0944} = 0.8051\)

0.8051 = 80.51% probability that a person over 50 diagnosed by the health service as having diabetes actually has the disease.

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Answer:

2(x² + 5)

Step-by-step explanation:

To factor 2x² + 10, we can first factor out the greatest common factor of the terms, which is 2:

2x² + 10 = 2(x² + 5)

We can't factor anymore, so the answer is:

2(x² + 5)

Answer:

2(x² + 5)

Step-by-step explanation:

To factorise this, do the distributive property backwards. In other words:

2x² + 10

2x² ÷ 2 + 10 ÷ 2

x² + 5

2(x² + 5)

∴ 2(x² + 5) is the answer

The expression (-9x)^4 can be represented as -6561x^3 without using exponents.

To express the expression (-9x)^4 without using exponents, we can expand it by multiplying the base (-9x) four times using the multiplication property.

(-9x)^4 = (-9x) * (-9x) * (-9x) * (-9x)

To simplify this expression, we can multiply the terms together, taking care to apply the rules of multiplication:

(-9x) * (-9x) = (-9 * -9) * (x * x) = 81 * x^2 = 81x^2

So, by substituting this result back into the original expression, we get:

(-9x)^4 = 81x^2 * (-9x) = -6561 x^3

Therefore, the expression (-9x)^4 can be represented as -6561x^3 without using exponents.

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The value of x is 6 or 3.5.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

We have,

Radius = (x-2)

CB= 2x -9

Using Pythagoras theorem

AB² + CB² = AC²

(x-2)² + (2x-9)² = (x-2+1)²

x² + 4  -4x + 4x² + 81 - 36x = x² + 1 -2x

4x² -38x + 84 = 0

Solving the quadratic equation we get

x= 6 or 3.5

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13.1% of the recent graduates read exactly one book.

We can solve this problem using set theory and the Principle of Inclusion-Exclusion (PIE).

Let's define the following sets:

We want to find the number of students who read exactly one book, which is equivalent to finding the number of students who are in exactly one of the sets A, B, or C.

By PIE, we can find the number of students who read exactly one book as follows:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

We already have the values of |A|, |B|, and |C| from the given information:

To find |A ∩ B|, we can use the given information that 193 students read both To Kill A Mockingbird and Gone with the Wind, but not Lord of the Flies:

|A ∩ B| = 193

Similarly, to find |A ∩ C| and |B ∩ C|, we can use the given information that 163 students read Lord of the Flies and To Kill A Mockingbird, and 74 students read only Lord of the Flies:

|A ∩ C| = 0 (since the students who read both A and C would have read all three books, but only 113 students are known to have read all three books)

|B ∩ C| = 163

Finally, we have the value of |A ∩ B ∩ C| from the given information:

|A ∩ B ∩ C| = 113

Putting all this information together, we have:

|A ∪ B ∪ C| = 892 + 472 + 582 - 193 - 0 - 163 + 113 = 1848

Thus, the number of students who read exactly one book is:

1848 - (|A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|) = 1848 - (892 + 472 + 582) + 193 + 0 + 163 - 113 = 1848 - 2046 + 243 = 243

Finally, the percentage of students who read exactly one book is:

(243 / 1848) * 100 = 13.1% (rounded to the nearest tenth)

So, 13.1% of the recent graduates read exactly one book.

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The purpose of the SUBSET-SUM issue is to determine whether a subset from a list of integers may add up to a certain value.

A dynamic programming approach that takes repeating, positive, and negative numbers into account. The purpose of the SUBSET-SUM problem is to determine whether a subset of a list of integers may add up to a certain value. As an example, consider the list of numbers [1, 2, 3, 4]. If the target is set to that number, there are two subsets, 3, and 1, 2, 4, that both add up to 7. If the target is equal to 11, there are no solutions.

If there are t integers in the sums list, then there are usually (t -1) subsets that need to be checked to see if there are even any solutions to SUBSET-SUM. This post will look at a technique for using dynamic programming to solve issues more successfully. though, in contrast

Let is SUBSET-SUM (arr, t, sum/2) be the function that returns true if there is a subset of arr [0..t-1] with sum equal to sum/2

The is SUBSET-SUM problem can be divided into two subproblems

is SUBSET-SUM() without considering last element (reducing t to t-1)

is SUBSET-SUM considering the last element (reducing sum/2 by arr[t-1] and t to t-1)

If any of the above subproblems return true, then return true.

is SUBSET-SUM (arr, t, sum/2) = is SUBSET-SUM (arr, t-1, sum/2) || is SUBSET-SUM (arr, t-1, sum/2 – arr[t-1])

Therefore,

The purpose of the SUBSET-SUM issue is to determine whether a subset from a list of integers may add up to a certain value.

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The coordinates of vertices U(1 , -3) , V(4 , -3) , T(1 , -4) , W(4 , -4) becomes

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4) after the reflection across x-axis occurs.

In the question given 4 coordinates,

U(1 , -3)

V(4 , -3)

T(1 , -4)

W(5 , -4)

the reflection across x-axis

U(1 , -3) →U' (1, 3)

V(4 , -3) → V'(4 , 3)

T(1 , -4) → T'(1 , 4)

W(5 , -4) → W'(5 , 4)

so  after the reflection across the x axis the coordinates of the vertices becomes ,

U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4)

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Hi there!  

»»————-　★　————-««

I believe your answer is:  

4 students.  

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(30 * \frac{1}{3} =10\)

⸻⸻⸻⸻

⸻⸻⸻⸻

\(10 * (2/5) = 4\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer: The total number of people is 138 and each team has 12 people in it:

Total teams:

Therefore there are 11 teams:

And the people in a small group are 6 or the remainder:

The value of k is 18.

If x + 2 is a factor of f(x) = x^3 + 5x + k, it means that when x = -2, the expression f(x) becomes zero.

Substituting x = -2 into f(x), we have:

f(-2) = (-2)³ + 5(-2) + k

= -8 - 10 + k

= -18 + k

Since f(-2) should equal zero, we have:

-18 + k = 0

k = 18

Therefore, the value of k is 18.

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Answer:

x = 14

Step-by-step explanation:

Given

\(\frac{2}{5}\) x - \(\frac{3}{2}\) = \(\frac{1}{4}\) x + \(\frac{3}{5}\)

Multiply through by 20 ( the LCM of 5, 2 and 4 ) to clear the fractions

8x - 30 = 5x + 12 ( subtract 5x from both sides )

3x - 30 = 12 ( add 30 to both sides )

3x = 42 ( divide both sides by 3 )

x = 14

The theoretical probability of spinning red is given as follows:

1/3.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the spinner in this problem, 2 out of 6 regions are red, hence the theoretical probability is given as follows:

2/6 = 1/3.

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Answer:

Step-by-step explanation:

8.008.009

The volume of the given triangular prism is 384 cm³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, the area of the base is

Area of a rectangle = 1/2 ×Base×Height

= 1/2 ×12×4

= 24 cm²

Now the volume is 24×16

= 384 cm³

Therefore, the volume of the given triangular prism is 384 cm³.

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Answer:

y = 3. last option is correct answer for 2nd question.

Step-by-step explanation:

f(x) just means y.

horizontal asymptote is y = 'something.'

the graph crosses y = 4, so y = 4 cannot be asymptote.

y = 3 is since the graph never quite touches it.

as for ∞, we see that as x approaches -∞, y almost reaches 3. but not quite. also, as x approaches +∞, y approaches +∞.

so the last option is the correct answer.

Given:

Vertices of a parallelogram ABCD are A(7,-4), B(-1,-4), C(-1,-12), D(7, -12).

To find:

Whether the parallelogram ABCD is a rhombus, rectangle or square.

Solution:

Distance formula:

\(D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Using distance formula, we get

\(AB=\sqrt{(-4-(-4))^2+(-1-7)^2}\)

\(AB=\sqrt{(-4+4)^2+(-8)^2}\)

\(AB=\sqrt{0+64}\)

\(AB=8\)

Similarly,

\(BC=\sqrt{(-1-(-1))^2+(12-(-4))^2}=8\)

\(CD=\sqrt{(7-(-1))^2+(-12-(-12))^2}=8\)

\(AD=\sqrt{(7-7)^2+(-12-(-4))^2}=8\)

All sides of parallelogram are equal.

\(AC=\sqrt{(-1-7)^2+(-12-(-4))^2}=8\sqrt{2}\)

\(BD=\sqrt{(7-(-1))^2+(-12-(-4))^2}=8\sqrt{2}\)

Both diagonals are equal.

Since, all sides are equal and both diagonals are equal, therefore, the parallelogram ABCD is a square.

We know that, a square is special case of rectangles and rhombus.

So, parallelogram ABCD is a rhombus, rectangle or square. Therefore, the correct option is c.

Answer:

50 yards

Step-by-step explanation:

6 in by 4 in would represent 3x5 by 2x5 yards, or 15 by 10

P = 2(15) + 2(10)

P = 30 + 20

Answer:

A

Step-by-step explanation:

X can only have 1 input buy Y can have many

Answer:

Point G

Step-by-step explanation:

The mapping rule for a 90° counterclockwise rotation is:

Therefore, if A = (4, 1):

The point that represents A' after A(4, 1) is rotated 90° counterclockwise is:

The amount more that Khalil would have in his account more than Charlotte is $250.

The formula for calculating future value when there is continuous compounding is :

FV = A x e^r x N

Where:

Future value of Charlotte's account = $730  x 2.718^0.035 x 8 = $756

The formula for calculating future value when there is daily compounding:

FV = P (1 + r)^nm

Where:

FV = 730 x (1 + 0.00011)^(365 x 8) = 1006.49.

Difference in the amounts  = 1006.49 - $756 = 250.49 ≈ $250

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Answer:

29 is correct  (the 250 is wrong)

Step-by-step explanation:

Rate 1:

3

1

2

%

=

3

+

1

/

2

=

Rate 1: 3

2

1

​

%=3+1/2=

3.5

%

→

0.035

3.5%→0.035

Rate 2:

3

7

8

%

=

3

+

7

/

8

=

Rate 2: 3

8

7

​

%=3+7/8=

3.875

%

→

0.03875

3.875%→0.03875

Calculate Final Amount for Charlotte

Calculate Final Amount for Charlotte

‾

Calculate Final Amount for Charlotte

Compounded Continuously:

Compounded Continuously:

�

=

�

�

�

�

A=Pe

rt

�

=

730

�

=

0.035

�

=

8

P=730r=0.035t=8

Given values

�

=

730

�

0.035

(

8

)

A=730e

0.035(8)

Plug in

�

=

730

�

0.28

A=730e

0.28

Multiply

�

=

965.8848

A=965.8848

Use calculator (with e button)

Calculate Final Amount for Khalil

Calculate Final Amount for Khalil

‾

Calculate Final Amount for Khalil

Compounded Daily:

Compounded Daily:

�

=

�

(

1

+

�

�

)

�

�

A=P(1+

n

r

​

)

nt

Compound interest formula

�

=

730

�

=

0.03875

�

=

8

�

=

365

P=730r=0.03875t=8n=365

Given values

�

=

730

(

1

+

0.03875

365

A=730(1+

365

0.03875 )

365(8)

Plug in values

�

=

730

(

1.0001062

)

2920

A=730(1.0001062)

2920

Simplify

�

=

995.284

A=995.284

How much more money Khalil has:

995.284

−

965.8848

995.284−965.8848

29.3992

$29

Round to the nearest dollar

Answer: 253

Step-by-step explanation:

The measure of side n is √(m^2 - 64).

According to the given question.

We have a right angle triangle.

Here, we have to find the measure n.

Since, the given triangle is divided into two right angle triangles.

Now in the right angled triangle with the side measure m, n and 8.

By the Pythagoras theorem we can say that

m^2 = 8^2 + n^2

⇒ m^2 = 64 + n^2

⇒ m^2 -64 = n^2 ...(i)

⇒ n = √(m^2 - 64)

Hence, the measure of side n is √(m^2 - 64).

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The x-axis should be the number of pounds of tomatoes bought.

The y-axis should be the total cost of x pounds of tomatoes.

The slope of each line represents the cost of tomatoes/pound.

The y-intercept of each line represents the bus fare.

To determine which point would not be found on the line, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

As per the given data:

Tomatoes from Grandiose Grocers = $2.50/pound

Tomatoes from EconoFoods = $2/pound

Bus fare for EconoFoods = $3

The x-axis should be the number of pounds of tomatoes bought.

The y-axis should be the total cost of x pounds of tomatoes.

For Grandiose Grocers:

y = 2.50x

For EconoFoods:

y = 2x + 3

From comparing with the slope-intercept form of a line, y = mx + c

m(Grandiose Grocers) = 2.50 {cost of tomatoes per pound}

m(EconoFoods) = 2 {cost of tomatoes per pound}

c is the y intercept:

c(Grandiose Grocers) = 0 {bus fare is $0}

c(EconoFoods) = 3 {bus fare is $3}

Hence, The x-axis should be the number of pounds of tomatoes bought.

The y-axis should be the total cost of x pounds of tomatoes. The slope of each line represents the cost of tomatoes/pound. The y-intercept of each line represents the bus fare.

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The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.

1. The given function is f(x) = \(-2(x+4)^2\) + 1.

2. To find the maximum of the function, we need to determine the vertex of the parabola.

3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.

4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.

5. The x-coordinate of the vertex is given by h = -4.

6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.

7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.

8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).

9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.

10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.

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The solution is,  the original number in the work force is 190.76.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

A 35% decrease resulted in a new work force number of 124.

let, the original number in the work force is  x

then,

x - x*35% = 124

or, x - 0.35 x = 124

or, 0.65 x = 124

or, x = 190.76

Hence, The solution is,  the original number in the work force is 190.76.

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