select true statement​

Answer:

\(6\ lb = 2.724\ kg\)

\(11\ kg = 24.2\ lb\)

Step-by-step explanation:

Given

\(1\ kg = 2.2\ lb\)

\(1\ lb = 0.454\ kg\)

Required

- Convert 6 lb to kg

- Convert 11kg to lb

To solve for (a), we make use of the second conversion unit:

\(1\ lb = 0.454\ kg\)

Multiply both sides by 6

\(6 * 1\ lb = 0.454\ kg * 6\)

\(6\ lb = 2.724\ kg\)

Hence, a 6lb backpack weighs 2.724kg

Solving (b): 11 kg to lb

Here, we make use of the first conversion unit

\(1\ kg = 2.2\ lb\)

Multiply both sides by 11

\(11 * 1\ kg = 2.2\ lb * 11\)

\(11\ kg = 24.2\ lb\)

Hence, the cat weighs 24.2lb

Based on the angle of the seesaw and the height off the ground, the maximum length of the seesaw is 2 meters.

This can be found as:

Sin 30° = 1 / Maximum length

Solving gives:

Sin 30° = 1 / Maximum length

Ml = 1 / Sin 30°

= 1 / 0.5

= 2 meters

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Answer: 26.3

Step-by-step explanation:

Therefore, the correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

Based on the given information, D represents the null hypothesis (H₀) and E represents the alternative hypothesis (Hₐ).

The null hypothesis (H₀) is a statement that there is no significant difference between the observed data and the expected results. In this case, the null hypothesis is that the population mean (μ) is greater than or equal to 1000.

The alternative hypothesis (Hₐ) is a statement that there is a significant difference between the observed data and the expected results. In this case, the alternative hypothesis is that the population mean (μ) is less than 1000.

Correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

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Answer:

read.

Step-by-step explanation:

The popularity of the Gutenberg press in Europe made books more accessible and motivated people want to learn how to READ.

This is evident in the fact that Johannes Gutenberg who was widely known as a printer was famous for inventing a means of producing books at a cheaper cost and portable size that is also durable and easy for distribution.

The result of this invention led to an increase in the availability of books and thereby enhance and motivate more people, not just the elites, to have access to books and READ them.

Answer:

Read

Step-by-step explanation:

cause

Answer:

Step-by-step explanation:

I don’t know

We want to find the opening price of the stock in the beginning of the day. We will find that the solution is $89.50.

Let's say that the opening price of the stock was X.

Then, it is increased 6% to get to $94.87

This means that the 106% of X is equal to $94.87, then we can solve:

1.06*X = $94.87

Where we wrote 106% in decimal form, now we can just solve this for X:

X  = $94.87/1.06 = $89.50

This means that the price of the stock in the beginning of the day was $89.50

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Answer: 52 seconds.

Step-by-step explanation:

|-3| + 23 = 26. 26 x 2 = 52.

The conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. Generally, insurance companies use the number of traffic violations and/or the number of claims a driver has had within a certain time period as indicators of their riskiness.

As Eric has had no accidents or traffic violations, the probability that he is a high-risk driver is very low. However, this does not mean that the probability is zero. There are many other factors which can contribute to a driver's risk, such as age, gender, experience, and location.

If Eric is an experienced driver, who has been driving for many years with no traffic accidents, then the probability of him being a high-risk driver will be lower than the average driver. On the other hand, if Eric is a new driver, or is located in an area with a high rate of traffic accidents, then the probability of him being a high-risk driver may be higher than the average driver.

Overall, the conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. However, this probability can change depending on other factors, such as his age, experience, and location.

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The vertex where the line segment x and y intersect  is v.

The name of one side of the angle below is line segment WV and XW

The angle below can be named with three letters as ∠STU or ∠UTS.

Vertex is the point of intersection of edges or line segments.

Therefore, the vertex where the line segment x and y intersect  is vertex v.

The name of one side of the angle below is line segment WV and XW.

Lastly, the angle below can be named with three letters as follows:

The middle letter usually indicates the actual angle of the vertex.

Therefore, the angle below can be named with three letters as ∠STU or ∠UTS.

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Answer: 6.56, 13.12 are the correct answers

Step-by-step explanation:

Answer:

4x² - 12x + 9

4a² - 10a + 25

Step-by-step explanation:

If you want to have some fun with math, you should try to find perfect square trinomials. These are polynomials that look like this:

a² + 2ab + b² = (a + b)²

or

a² - 2ab + b² = (a - b)²

They are called perfect square trinomials because they are the squares of binomials. For example, x² + 2x + 1 is a perfect square trinomial because it is the same as (x + 1)².

How do you spot a perfect square trinomial? Here are some tips:

- The first and last terms must be perfect squares. For example, 4x² and 9 are perfect squares because they are 2x times 2x and 3 times 3.

- The middle term must be double the product of the square roots of the first and last terms. For example, 6x is double of 2x times 3, which are the square roots of 4x² and 9.

Let's practice with some examples:

4x²- 12x + 9

This is a perfect square trinomial because:

- The first and last terms are perfect squares: 4x² = (2x)² and 9 = (3)²

- The middle term is double the product of the square roots of the first and last terms: -12x = 2 * -2x * 3

We can write this polynomial as (2x - 3)².

16x² + 24x - 9

This is not a perfect square trinomial because:

- The first and last terms are perfect squares: 16x² = (4x)² and 9 = (3)²

- The middle term is not double the product of the square roots of the first and last terms: 24x ≠ 2 * -4x * -3

We cannot write this polynomial as a square of a binomial.

4a² - 10a + 25

This is a perfect square trinomial because:

- The first and last terms are perfect squares: 4a² = (2a)² and 25 = (5)²

- The middle term is double the product of the square roots of the first and last terms: -10a = 2 * -2a * -5

We can write this polynomial as (2a - 5)².

36b² - 24b - 16

This is not a perfect square trinomial because:

- The first and last terms are perfect squares: 36b² = (6b)² and 16 = (4)²

- The middle term is not double the product of the square roots of the first and last terms: -24b ≠ 2 * -6b * -4

We cannot write this polynomial as a square of a binomial.

Now you know how to find perfect square trinomials. They are fun, right?

The polynomials that are perfect square trinomials are:

a. 4x² - 12x + 9 = (2x - 3)^2 c. 4a² - 10a + 25 = (2a - 5)²

By mathematical induction, we have proved that cn = 4 · 2 n − 5 n for all integers n ≥ 1.

We will prove by mathematical induction that cn = 4 · 2 n − 5 n for all integers n ≥ 1.

Base case: When n = 1, we have c1 = 3 and 4 · 2^1 − 5^1 = 3. Therefore, the base case holds.

Inductive hypothesis: Assume that cn = 4 · 2 n − 5 n for some integer n ≥ 1.

Inductive step: We need to show that the hypothesis holds for n + 1, i.e., cn+1 = 4 · 2 n+1 − 5 n+1.

From the recurrence relation, we have:

cn+1 = 7cn − 10cn−1

Substituting the inductive hypothesis, we get:

cn+1 = 7(4 · 2 n − 5 n) − 10(4 · 2 n−1 − 5 n−1)

Simplifying the expression, we get:

cn+1 = 4 · 2 n+1 − 5 n+1

Therefore, the inductive step holds.

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To produce 200 watts of power, the speed of wind must be about 11 miles per hour for the windmill.

The relationship between power generated by a windmill and wind speed can be expressed as:

P = k * V^3

where P is the power generated in watts, V is the wind speed in miles per hour, and k is the variation constant.

We are given that k = 0.15, and we need to find the wind speed V that produces 200 watts of power. We can solve for V as follows:

200 = 0.15 * V^3

V^3 = 200 / 0.15

V^3 = 1333.33

V = (1333.33)^(1/3)

V ≈ 10.68

Rounding to the nearest mile per hour gives a wind speed of 11 miles per hour. Therefore, the wind needs to be blowing at about 11 miles per hour for the windmill to produce 200 watts of power.

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The overall relapse rate from this study would be =58.3%.

To calculate the relapse rate , the the proportion of all the individuals that have a relapse should be converted to a percentage as follows:

The total number of individuals that has relapse= 28

The total number of individuals under study = 48

The percentage = 28/48 × 100/1

= 58.3%

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To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.

Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.

Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.

(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.

Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.

Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.

(3) Show that HK=G.

To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.

Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.

Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.

(4) Show that G is a cyclic group.

Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.

Therefore, G is not a cyclic group.

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To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.

Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.

Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.

(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.

Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.

Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.

(3) Show that HK=G.

To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.

Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.

Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.

(4) Show that G is a cyclic group.

Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.

Therefore, G is not a cyclic group.

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Answer:

\(\frac{x+3}{x}\)

Step-by-step explanation:

Factorise numerator and denominator

x² - 9 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

x² - 9

= x² - 3² = (x - 3)(x + 3)

x² - 3x ← factor out x from each term

= x(x - 3)

Then

\(\frac{x^2-9}{x^2-3x}\)

= \(\frac{(x-3)(x+3)}{x(x-3)}\) ← cancel common factor (x - 3) on numerator/denominator

= \(\frac{x+3}{x}\)

Approximately -0.602 is the operating leverage for this project.

We must apply the following formula to determine a project's degree of operational leverage (DOL):

DOL is calculated as (percentage change in operating cash flow) / (change in sales).

In this instance, we can determine the DOL using the fixed expenses and operational cash flow since we just have one set of predicted statistics.

DOL is equal to operating cash flow divided by fixed costs.

DOL = $82,706 / ($82,706 - $220,000)

DOL = $82,706 / -$137,294

DOL ≈ -0.602

Approximately -0.602 is the operating leverage for this project. The project's operating cash flow and fixed costs are inversely correlated, which means that when fixed costs rise, operating cash flow decreases. This relationship is indicated by a negative DOL.

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Answer:

10 cm

Step-by-step explanation:

Answer:

\(P(B) = \frac{4}{18} = \frac{2}{9} = 0.2\)

Step-by-step explanation:

Sample space 2+5+7+4=18

Answer:

4/18 or 2/9

Step-by-step explanation:

The total number of balls = 2 + 5 + 7 + 4 = 18

4 out of the 18 balls are blue ∴ the probability is 4/18 or 2/9

Hope this helps!

$6.60 because 6.00 + 0.60 = 6.60

Answer:

sec(x) = sqrt(10)

Step-by-step explanation:

We know that tan(x) = 3.

Using the identity tan^2(x) + 1 = sec^2(x), we can solve for sec(x).

First, let's square both sides of the equation tan(x) = 3:

tan^2(x) = 3^2

tan^2(x) = 9

Next, we can substitute this expression for tan^2(x) into the identity:

tan^2(x) + 1 = sec^2(x)

9 + 1 = sec^2(x)

10 = sec^2(x)

Finally, we can take the square root of both sides to solve for sec(x):

sqrt(10) = sec(x)

Therefore, sec(x) = sqrt(10).

- When your car's speedometer reads 45 mph with the 4.65-inch tires, your tires rotate approximately 4.525 times per second.
- When you have the new 5.35-inch tires and your speedometer reads 45 mph, your car is actually traveling at approximately 3.93 rotations per second.
- When you have the new 3.75-inch tires and your speedometer reads 45 mph, your car is actually traveling at approximately 5.614 rotations per second.

Step 1: Convert the tire size to radius
To find the radius of the tire, we divide the diameter by 2. So the radius of the 4.65-inch tire is 2.325 inches.

Step 2: Find the circumference of the tire
The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius. Plugging in the radius, we get C = 2π(2.325) = 14.579 inches.

Step 3: Calculate the number of rotations per second
To find the number of rotations per second, we need to know the linear velocity of the car. We are given that the car is traveling at 45 mph.

To convert this to inches per second, we multiply 45 mph by 5280 (the number of feet in a mile), and then divide by 60 (the number of minutes in an hour) and 60 again (the number of seconds in a minute). This gives us a linear velocity of 66 feet per second.

Next, we need to calculate the number of rotations per second. Since the circumference of the tire is 14.579 inches, for every rotation of the tire, the car moves forward by 14.579 inches. Therefore, to find the number of rotations per second, we divide the linear velocity (66 inches/second) by the circumference of the tire (14.579 inches). This gives us approximately 4.525 rotations per second.

So, when your car's speedometer reads 45 mph, the tires should rotate approximately 4.525 times per second.

Now, let's consider the scenario where you buy new 5.35-inch tires and drive with your speedometer reading 45 mph.

Step 4: Calculate the new linear velocity
Following the same steps as before, we find that the new tire has a radius of 2.675 inches (half of 5.35 inches). The circumference of the new tire is approximately 16.795 inches.

Using the linear velocity of 45 mph (66 inches/second), we divide by the new circumference of the tire (16.795 inches) to find the number of rotations per second. This gives us approximately 3.93 rotations per second.

Therefore, when you have the new 5.35-inch tires and your speedometer reads 45 mph, your car is actually traveling at approximately 3.93 rotations per second.

Lastly, let's consider the scenario where you replace your tires with 3.75-inch tires and your speedometer reads 45 mph.

Step 5: Calculate the new linear velocity
Again, using the same steps as before, we find that the new tire has a radius of 1.875 inches (half of 3.75 inches). The circumference of the new tire is approximately 11.781 inches.

Dividing the linear velocity of 45 mph (66 inches/second) by the new circumference of the tire (11.781 inches), we find that the number of rotations per second is approximately 5.614 rotations per second.

Therefore, when you have the new 3.75-inch tires and your speedometer reads 45 mph, your car is actually traveling at approximately 5.614 rotations per second.

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Answer:

(0,-1)

(1,-5)

(2,-9)

Step-by-step explanation:

y = −4x −1

Let x=0

y = 0-1 = -1  (0,-1)

Let x = 1

y = -4(1) -1 = -4-1 =-5  (1,-5)

Let x = 2

y = -4(2) -1 = -8-1 =-9 (2,-9)

a) Four-digit strings with 10⁴ characters are available.

b) A string that finishes in an odd number has 10 options for the first three digits and 5 options for the last digit.

c) The fourth digit has nine alternatives.

Given,

We have to find the number of strings of four decimal digits for the following conditions;

a) Do not use the same numeral more than once.

There are 10⁴ strings with four decimal digits.

We have 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and 7 options for the fourth digit when creating a string with 4 different digits. We deduce from the product rule that there are 10 9 8 7 = 5040 four decimal digits with no duplicate digits.

b) End with an odd digit

There are 10 choices (ranging from 0 to 1, 2,..., 9) for the first three digits of a string that ends in an odd number, and 5 possibilities (ranging from 1, 3, 5, 7,.., 9) for the last digit. According to the product rule, there are 5000 strings that terminate in an even number, or 10 × 10 × 10 × 5.

c) Have exactly three digits that are 8

There is one non-8 digit in the 4-decimal string, which includes exactly 3 digits that are 8. Therefore, there are 9 options for the fourth digit (ranging from 0 through 1, 2, 3, 4, 5, 6, and 9). The non-digit may appear in the string at positions 1, 2, 3, or 4. The sum rule leads us to the conclusion that there are 36 four decimal digits with exactly three 8s, which equals 9 + 9 + 9 + 9 = 36.

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Question is incomplete. Completed question is given below;

How many strings of four decimal digits

a) Do not contain the same digit twice

b) End with an odd digit?

c) Have exactly three digits that are 8

Answer: it is table "a"

explanation:

as the equation is y= 2x + 5 you should substitute each of the x values from -2 to 4 in order to get the y value which will help you decide which table should be used by Cindy to graph the equation.

now, this is how you should substitute the values into the equation and simplify it so that you get the "y" value.

the first x value given is -2 therefore:

you put -2 in the equation instead of putting x, this will allow you to find the y value which you can compare with the choices given.

y= 2x+5 (this is the equation)

y= 2(-2)+5 (here I have replaced the x with -2)

y= -4+5 (you should multiply 2 and -2)

y= 1 (therefore the answer is 1)

you should further continue this way and get the y values which will help you decide which is the correct table to be used. Now you already know that table "a" is the answer.

Answer:

The answer is table A

Step-by-step explanation:

Given:

Form the table of values from x = -2 to x = 4

Hence,

Therefore, the table that can be used for the graph of the equation is;

Table A

1. x=9

2. x=1

3. s=2

4. s= 2.5

5. s=6

6. T=5/6

7. x=1

8. y=2

9. x=120

10. x=16/13

11. x=-4

12. s=7

13. x=2

14. x=2

15. t=97/5

16. x=5/2

17. x=-70/3

Answer: obtuse scalene triangle

Step-by-step explanation:

A scalene triangle has three different sides.

An isosceles triangle has 2 of the same sides and 1 different side.

Answer:

Its a obtuse scalene triangle!

The function f(x) = 8x + 3x^(-1) has a local maximum at x = 2 with a value of f(2) = 19, and a local minimum at x = -2 with a value of f(-2) = -19.Explanation:

To find the local extrema of a function, we need to find the critical points of the function, which are the points where the derivative is either zero or undefined. In this case, the derivative of f(x) is f'(x) = 8 - 3x^(-2), which is undefined at x = 0.Setting the derivative equal to zero, we get:8 - 3x^(-2) = 0Solving for x, we get:x = ±2

These are the critical points of the function. To determine whether each critical point is a local maximum or a local minimum, we need to examine the second derivative of the function.

The second derivative of f(x) is f''(x) = 6x^(-3), which is negative for x > 0 and positive for x < 0.Therefore, x = 2 is a local maximum of the function with a value of f(2) = 19, and x = -2 is a local minimum of the function with a value of f(-2) = -19. These are the only local extrema of the function, since the function is increasing for x < -2 and decreasing for -2 < x < 0, and then increasing again for x > 0.

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