Find all intervals on which the function f(x) = (e^(2x^2+5)/-6x is decreasing.

Amount to be repaid for Bank A is $2,696.625 and Amount to be repaid for Bank B is $2,741.25. However, I will choose Bank B because it offers a lower interest rate.

The formula to calculate the simple interest is;

I = PRT

Where;

P is principal

R is rate

T is time

Now, we are given that;

Bank A;

Principal amount; P = $2550

Interest rate; R = 11.5% = 0.115

Time; t = 6 months = 0.5 years

Thus;

I = (2550 * 0.115 * 0.5)

I = $146.625

Amount to be repaid = 2550 + 146.625

Amount to be repaid = $2,696.625

Bank B;

Principal amount; P = $2550

Interest rate; R = 7.5% = 0.075

Time; t = 12 months = 1 year

Thus;

I = (2550 * 0.075 * 1)

I = $191.25

Amount to be repaid = 2550 + 191.25 = $2,741.25

Thus, bank B offers a more favorable interest rate and as such would be the preferred bank.

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Answer: the person has high blood sugar Levels

Step-by-step explanation:

\(s = \frac{cardinality(s)}{cardinality( \omega)} = \frac{15}{100} = \frac{1.5}{100} \)

The shaded region represents 1.5 grids

\(1.5 = 1 \frac{0.5}{1} = 1 \frac{5}{10} = 1\frac{1}{2} \)

Answer:

D

Step-by-step explanation:

The answer and work is in the attached screenshot! :)

We know that

• The radius is 17 feet.

First, we find the circular area

This means the square flower bed will have an area of 615.44 square feet. So, we find its sides with the formula for squared areas

The critical value and the conclusion are mathematically given as

z_{0.05}=1.960 and  z<Zcritical, therefore we Reject H_o

a)Test statistic  z=-3.32

Claim: p< 0.5

a=0.05

critical value z_{0.05}

z_{0.05}=1.960

b)

z<Zcritical,

Beause z=-3.32< z_{0.05}=1.960 Reject H_o

In conclusion,

z_{0.05}=1.960 and  z<Zcritical, therefore we Reject H_o

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Answer:

To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.

First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.

Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.

Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.

However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.

In this case the answer is very simple . .

Step 01:

Data

Initial earnings

1 hour ===> $10

20 hours / week

New earnings

+ 15% hour

$10 * (1.15)

Step 02:

Inicial earnings

New earnings

The difference would be:

New earnings - Inicial earnings = $ (230 - 200) = $30

The answer is:

The difference in money you will earn is $ 30.

The equation will be 6x - 4= 8.

Solve the equation: 6x - 4 = 8 + 4 + 4.

6x = 12. 6 6. x = 2

Hopefully, that helps

Answer:

x=89

×=60

cab=180

cba=180

The height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

We have given a table:

Time     height

2                8

4               12

6                16

8               20

10              24

The slope of the line = (12-8)/(4-2) = 4/2 = 2

The value of the slope is positive we can say,  the height of water increases as time passes.

Thus, the height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.

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the answer is A: The height of the water increases 2 inches per minute.

hope this helped :)

Answer:

the answer is 11

Step-by-step explanation:

if you take 18 divided by 3 and then 2 times that plus 2 and minus 25 it is 11

The difference between the circumference of the circle and the perimeter of the triangle is 28.2 units. (Option B)

To find the length of each side of triangle, the distance is calculated between the vertices using the formula:

d = √((x2 – x1)^2 + (y2 – y1)^2)

Hence,

AB =√((-4 – 0)^2 + (9 – 0)^2) = 9.85 units

AC = √((9 – 0)^2 + (4 – 0)^2) = 9.85 units

BC = √((9 – (-4))^2 + (4 –9)^2) = 13.93 units

Hence, the perimeter of the triangle = 9.85 + 9.85 + 13.93 = 33.6 units

As AB and AC is the radius of the circle, the circumference of the circle is:

C = 2πr = 2π(9.85) = 61.8 units.

Hence, the difference between the circumference of the circle and the perimeter of the triangle = 61.8 – 33.6 = 28.2 units.

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Answer:

<

Step-by-step explanation:

0.27 is less than 0.3. < is the less than symbol because the "mouth" is pointing towards to the larger number.

The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

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Answer:

I believe it is 10e or in decimal form 27.18

Answer:

-3,671.68187

Step-by-step explanation:

-1.93273(2018) + 228.56727 = -3671.68187

Answer:

Write a linear model in slope-intercept form, then substitute 18 for x and solve for y.

Step-by-step explanation:

Answer:
10 Probability of blue is 2/10%

Step-by-step explanation:

Therefore, nine rabbits will need 7.5 sacks of food for one week.

The unitary method is a mathematical technique that involves finding the value of a single unit to determine the value of a given number of units. It is a method of solving mathematical problems that involve proportional relationships between quantities. The unitary method is commonly used in various areas of mathematics, such as algebra, arithmetic, and geometry. It is also used in everyday life to solve problems related to money, time, distance, and other quantities.

Here,

To solve this problem, we can use proportionality. We know that the number of sacks of food needed is directly proportional to the number of rabbits.

Let x be the number of sacks needed for 9 rabbits. Then, we can set up the following proportion:

6/10 = 9/x

Cross-multiplying, we get:

6x = 90

Dividing both sides by 6, we get:

x = 15/2 or 7.5

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Complete question:

If six rabbits need 10 sacks of food per week, how many sacks will nine rabbits need to eat for one week?

Answer:

ANYTHING EXCEPT 3x²-48

Step-by-step explanation:

Answer:

3(x2-8x+16)

Step-by-step explanation:

I got it wrong Bc of the other answer

Answer:

true

Step-by-step explanation:

There are 1048576 different telephone numbers in city A have 774 as the first three digits.

Permutation with repetition is used to calculate all of the possible combinations of telephone numbers.

For the N different types and we have to choose (a) of the different types, the number of possible combinations would be :

\(P = N^(i)\)

From the given problem, we have

The total number = 7 digits

The constant number = 3 digits

Thus, i = 7 - 3 = 4 digits

Now the characters = {0,1, 2, 3, 4, 5, 6, 7, 8, 9}

N = 10

Substituting the parameter, we can find the number of possible combinations of a telephone number in the city a which is;

P = 4¹⁰

P = 1048576

Hence, there are 1048576 different telephone numbers in city A have 774 as the first three digits.

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Answer:

They are the same.

Step-by-step explanation:

The degree of the polynomial is 5 and the leading coefficient is -1.

The given polynomial is f(x)

f(x) = \(-x^{5} +2x^{4} +3x^{3} +2x^{2} -8x +9\)

The degree of the polynomial is the term with the highest power,

So, in the given polynomial, the term with the highest term is \(-x^{5}\)

The highest power is 5,

So, its degree is 5.

The leading coefficient is the coefficient of the term with the degree,

So, the leading coefficient is -1.

Hence, the degree of the polynomial is 5 and the leading coefficient is -1.

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Therefore, we can see that 10 kilometers is greater than 9 miles (10 km > 14.48 km), and so the comparison "10 kilometers < 9 miles" is false.

A kilometer (km) is a unit of measurement for length, commonly used in the metric system. It is equal to 1000 meters or approximately 0.62 miles. Kilometers are often used to measure longer distances, such as the distance between two cities or countries.

by the question.

To explain this, we can convert kilometers to miles or miles to kilometers to compare them in the same unit.

1 mile is approximately equal to 1.61 kilometers. So, 9 miles would be approximately equal to 14.48 kilometers.

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Answer:

length= 3.7 ft.

Step-by-step explanation:

T= (square root of length) * k

1.8 seconds = (square root of 3) * k

k= 1.8 seconds / (square root of 3)

a.) T= (square root of 11) k

substituting k:

T=(square root of 11) * 1.8 seconds / (square of 3)

T= 3.4 seconds

b.) 2 seconds = (square root of length) k

substituting k:

2 seconds =(square root of length) 1.8 seconds / (square root of 3)

Divide the equation by 1.8 seconds / (square root of 3):

2 seconds / [1.8 seconds / (square root of 3)] = (square root of length)

10(square root of 3) / 9 = (square root of length)

square both sides:

100/7 ft= length

length= 3.7 ft.

Hope this helps.

The powers, (index) and coefficients of the polynomial indicates;

(A) The standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

(B) 4

(C) Positive zeroes; 2 or 0, negative zeroes; 0 or 2, complex zeroes; 0 or 2 or 4

(D) ±1/2, ±1, ±3/2, ±2, ±3, ±6

(E) Please find attached the graph of the polynomial created with MS Excel

(F) Four complex roots

A polynomial is a mathematical expression that consists of variables and coefficients joined together by addition, subtraction and multiplication, with the exponents of the variables consisting of positive integer values.

Part A) The polynomial in standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

Part B) The degree of the polynomial is 4, as the highest power of the polynomial is 4

Part C) The use of the Rule of Signs, to determine the options for the number of positive zeroes, negative zeroes and complex zeroes, can be presented as follows;

Positive zeroes options; The number of time the signs coefficients of the expression; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6, changes are two as follows;

+6 to -12, and from -12 to +9, therefore, the number of possible positive zeroes are 2 or 0, positive zeroes

The negative zeroes options; The negative zeroes options can be found by changing the sign of all the coefficients as follows; -2·x⁴ - 3·x³ - 9·x² + 12·x - 6, therefore, the number of times the sign of the coefficients change are again from -6 to +12, and from +12 to -9, which is 2 times, therefore;

The possible number of negative zeros are 2 or 0, negative zeroes

Whereby there are possibly 0 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 4

Whereby there are 2 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Whereby there are possibly 0 negative zeros and 2 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Part D) The rational roots theorem indicates that for a polynomial the rational roots are in the form p/q, where p is a factor of the constant term, and q is a factor of the leading coefficient.

The constant term is 6, and the leading coefficient is 2. The factors of 6 are ±1, ±2, ±3, and ±6 and the factors of 2 are; ±1, ±2 therefore;

p/q = ±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±2/2, ±3/2, ±6/2, which can be summarized as; ±1/2, ±1, ±3/2, ±2, ±3, ±6

Part E) Please find attached a screenshot of the graph of the polynomial created with MS Excel

Part F) The attached graph of the polynomial, created with MS Excel, indicates that there are no real zeros of the polynomial, therefore, there are four complex zeroes of the polynomial

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