A soft drink can has a height of 16cm and a radius of 3cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can). Give your answer rounded DOWN to the nearest cm, to ensure it fits inside the can.

The value of x is (-∞, -5) ∪ (1, ∞).

Given is a polynomial, \(x^4+2x^3-12x^2+14x-5 > 0\),

Solving for x,

Factors =

\(x^4+2x^3-12x^2+14x-5\\ \\= \quad \left(x-1\right)^3\left(x+5\right)\)

Therefore,

\(\left(x-1\right)^3\left(x+5\right) > 0\)

\(x < -5\quad \mathrm{or}\quad \:x > 1\)

Hence the value of x is (-∞, -5) ∪ (1, ∞).

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Hopefully, you'll get answers as good as the ones you're giving.

For this question, you would need to spend whatever you have left after you bail out your daughter and her math teacher.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

x1 = -8, x2= 2

Step-by-step explanation:

1. Write 6x as a difference

= x^2 + 8x - 2x - 16 = 0

2. Factor the expressions

= x ( x + 8 ) - 2x - 16 = 0

= x ( x + 8 ) - 2 ( x + 8 ) = 0

Factor out x + 8 from the expression

= ( x + 8 ) ( x - 2 ) = 0

3. When the product of factors = 0, at least one factor is 0

x + 8 = 0

x - 2 = 0

4. Solve the equation for x

x = - 8

x = 2

Therefore, the equation has 2 solutions :

x1 = -8, x2 = 2

Answer:

x = 100

Step-by-step explanation:

1 and 2 are a linear pair and sum to 180° , that is

x + \(\frac{4}{5}\) x = 180 ( multiply through by 5 to clear the fraction )

5x + 4x = 900

9x = 900 ( divide both sides by 9 )

x = 100

The values of the trigonometry functions are sin(θ) = 3/√13, cos(θ) = 2/√13, tan(θ) = 3/2, csc(θ) = √13/3, sec(θ) = √13/2 and cot(θ) = 2/3

from the question, we have the following parameters that can be used in our computation:

The right triangle

The hypotenuse of the right triangle is calculated as

h² = 2² + 3²

When evaluated, we have

h = √13

The values of the trigonometry functions are then evaluated as

sin(θ) = 3/√13

cos(θ) = 2/√13

tan(θ) = 3/2

csc(θ) = √13/3

sec(θ) = √13/2

cot(θ) = 2/3

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Answer:

Art

Step-by-step explanation:

...................

Answer:

Music

Step-by-step explanation:

Have a good rest of your day!

Answer:

\(Width: \frac{3in}{8ft} = \frac{5in}{x} (cross multiply)\)

   = \(40\) ÷3 ≈ 13.3ft

\(Width: \frac {3in}{8ft} = \frac{6.5in}{x}\)

   = 17.3

\(A=e\) × \(w\)

   \(= 13.3\) × \(17.3\) ≈ \(230.09\) ≈ \(230.1\)

Answer:

i will not give you the exact answer but i will tell you how to get the answer you need to add all the costs of everything and divide it by the number of tickets and that is how you get profit

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

Answer:

The rate is 6 for all of them

Step-by-step explanation:

The rate would be the price for one taco, so you divide the cost by the number of tacos you're getting.

Answers: Well 1 taco is 6$. 4 tacos is 24$. 5 tacos is 30$. 6 tacos is 36$.

Answer:

5-2(-4x+10)-5x----open brackets and multiply

5+8x-20-5x----combine like terms

8x-5x+5-20

3x-15

3(x-5)

Answer:

Simplified : 3x - 15

Step-by-step explanation:

5 - 2(-4x + 10) - 5x

5 + 8x - 20 - 5x

5 + 3x - 20

3x - 15

Answer:

The best option for him would be a real interest rate of 5%.

Step-by-step explanation:

The nominal interest rate is the one that represents the percentage of increase of the money that is in a certain investment, without discounting the depreciation due to inflation or the payment of taxes.

On the other hand, the real interest rate is the one that represents the real increase in the money invested, after discounting inflation and any taxes to be paid.

Therefore, the best option for Oscar would be to invest his $ 4,000 in a savings account with a real interest rate of 5% per year.

Answer:

-2

Step-by-step explanation:

9 - [4^2 - (3 + 2)]

PEDMAS says parentheses first

Work from the inside out

9 - [4^2 - (5)]

9 - [16-5]

9 - [11]

Subtract

9-11

-2

The relation between the probability of its complement is that their sum is 1.

Complement in probability theory is an essential concept that helps us understand the likelihood of an event not occurring. It is a mathematical term that refers to the opposite or negation of an event.

Complement refers to the probability of an event not occurring, given the probability of it occurring. It is often denoted as the complement of an event A and is represented by A’.

The complement of an event A is defined as the set of all outcomes in the sample space that are not in A.

The probability of the complement of A is equal to the probability of all the outcomes in the sample space that are not in A.

The most important properties of the complement of an event is that the probability of an event and its complement always add up to 1. This is known as the law of complementary probability, and is expressed as:

P(A) + P(A’) = 1

This means that if we know the probability of an event occurring, we can easily calculate the probability of its complement by subtracting the probability of the event from 1.

For example, if the probability of event A is 0.7, then the probability of its complement, A’, is 1 – 0.7 = 0.3.

Hence the relation between the probability of its complement is that their sum is 1.

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Answer:

2W + 56 = 78 , W = 10

Step-by-step explanation:

perimeter of rectangle = 2*the Length + 2*the Width

Answer:

The last option line DG is congruent to line GE

Step-by-step explanation:

Median: a segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side

So basically G is the midpoint of DE because FG is the median.

The last option, we can conclude that line DG is congruent to line GE

Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong same number of observations.

Median is a line segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side.

We are given that FG is an median.

Thus, basically G becomes the midpoint of DE because FG is the median.

So, DG = GE

Hence,

The last option, we can conclude that line DG is congruent to line GE

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Answer:

odd

Step-by-step explanation:

a function is even when f(-x) =f(x) and a function is odd

when f(-x)= -f(x)

so let's substitute -x into our function

f(-x)= (-x)^3 -(-x)

= -x^3 +1

so, f(-X)= -f(x)

therefore our function is odd

Answer:

8×p≈c

Step-by-step explanation:

Because if each is 8 dollars you would multpy the number (Or Letter) by how many you want or have.

Answer:

$840.77

Step-by-step explanation:

According to the question,The share would need to increase by 400% to reach its original value.

The value of something is the worth of it in terms of money or goods. It is the amount of goods or services that one can exchange for something else. Values are subjective and depend on the individual's perception and situation. Some values are determined by the market, while others are intrinsic, such as the value of family and friendship.

This is calculated by taking the percentage lost (80%) and subtracting it from 100% (original value). 100%- 80% = 20%. To reach the original value, the share would need to increase by 400%, which is calculated by multiplying the amount of percentage it has to increase (20%) by the factor of 4. 20% x 4 = 400%.

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The function is never negative.

option D is the correct answer.

A negative function is a function in which the resulting y value is negative.

Also, a negative function is a function that has y values that are less than zero for any x values. In other words, a negative function has a negative sign in front of its output.

From the given graph, the x and y values started from 0 and increases into the positive direction, so we can conclude that the function can never be negative.

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Answer:

31

Step-by-step explanation:

Step 1

5 1/3 + 5 1/3 + 10 1/6 + 10 1/6

Step 2

5 1/3 + 5 1/3 = 10 2/3

Step 3

10 1/6 + 10 1/6 = 20 2/6 or 20 1/3

Step 4

20 1/3 + 10 2/3 = 30 3/3 or 31

Answer:

180°

Step-by-step explanation:

A whole circle is 360°, therefor an straight line is half of that, so 360/2=180.

Answer

First one is A

Second one is B

Third one is D

Problem 1

Answer: Choice A

(30, 225); Rocket reaches max height of 225 ft after 30 seconds.

-------------------

Explanation:

Distribute the 0.25 through to get

y = 0.25(60x-x^2)

y = 15x - 0.25x^2

y = -0.25x^2 + 15x

This is in standard form y = ax^2+bx+c with a = -0.25, b = 15 and c = 0.

The first two values mentioned lead to this x coordinate of the vertex.

h = -b/(2a)

h = -15/(2*(-0.25))

h = -15/(-0.5)

h = 30

This tells us the answer is between A and C.

If you were to plug x = 30 into the original equation, you'll get y = 225. It means that after x = 30 seconds, the rocket has reached its max height of 225 feet. Therefore, the answer must be choice A.

===========================================================

Problem 2

Answer:  Choice B

(x-3)^2 = -8(y-6)

-------------------

Explanation:

vertex = base of the bulb = (3,6)

focus = top of the bulb = (3,4)

This flashlight is pointed downward, which forms a downward opening parabola.

The distance from the vertex to the focus is p = 2 units. This is known as the focal distance.

We'll plug that in along with the vertex (h,k) = (3,6) in the formula below

4p(y-k) = (x-h)^2

4*2(y-6) = (x-3)^2

8(y-6) = (x-3)^2

Unfortunately that equation above produces a parabola that opens upward. To fix things, we stick a negative out front on either side, which will reflect the parabola over the x axis to make the parabola open downward. That leads us to choice B.

===========================================================

Problem 3

Answer:  D) square

-------------------

Explanation:

We can form a point by intersecting the plane through the point where the two cones meet. The plane needs to be parallel to the base of each cone.

We can also form a line. To do so, we intersect the plane at exactly  along the edge of the cone. Make the plane tangent to the cone.

Lastly, we can form a circle by intersecting any plane parallel to the cone's base. This plane cannot pass through the meeting point of the two cones. Rather, the plane passes through one of the cones.

Those three previous paragraphs mean that we can rule out choices A,B,C. The only thing we can't form is a square. We can form straight lines, but we cannot form perpendicular lines needed to get a square. Nice work on selecting the correct answer.

Patterns are used to represent arithmetic or geometric progressions

The pattern of the progression is 22n - 40

The sequence is given as:

-18,4,26

The above sequence is an arithmetic progression with the following parameters:

Initial value (a) = -18

Common difference (d) = 22

So, the pattern is calculated as:

\(T_n = a + (n - 1)d\)

This gives

\(T_n = -18 + (n - 1)22\)

Open the bracket

\(T_n = -18 -22 +22n\)

\(T_n = 22n - 40\)

Hence, the pattern of the progression is 22n - 40

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Answer:

We conclude that there is no difference in potential mean sales per market in Region 1 and 2.

Step-by-step explanation:

We are given that a random sample of 12 supermarkets from Region 1 had mean sales of 84 with a standard deviation of 6.6.

A random sample of 17 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 8.5.

Let \(\mu_1\) = mean sales per market in Region 1.

\(\mu_2\)  = mean sales per market in Region 2.

So, Null Hypothesis, \(H_0\) : \(\mu_1-\mu_2\) = 0      {means that there is no difference in potential mean sales per market in Region 1 and 2}

Alternate Hypothesis, \(H_A\) : > \(\mu_1-\mu_2\neq\) 0      {means that there is a difference in potential mean sales per market in Region 1 and 2}

The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;

                            T.S.  =  \(\frac{(\bar X_1 -\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+ {\frac{1}{n_2}}} }\)   ~  \(t__n_1_+_n_2_-_2\)

where, \(\bar X_1\) = sample mean sales in Region 1 = 84

\(\bar X_2\) = sample mean sales in Region 2 = 78.3

\(s_1\)  = sample standard deviation of sales in Region 1 = 6.6

\(s_2\)  = sample standard deviation of sales in Region 2 = 8.5

\(n_1\) = sample of supermarkets from Region 1 = 12

\(n_2\) = sample of supermarkets from Region 2 = 17

Also, \(s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }\)  = \(s_p=\sqrt{\frac{(12-1)\times 6.6^{2}+(17-1)\times 8.5^{2} }{12+17-2} }\) = 7.782

So, the test statistics =  \(\frac{(84-78.3)-(0)}{7.782 \times \sqrt{\frac{1}{12}+ {\frac{1}{17}}} }\)  ~   \(t_2_7\)

                                   =  1.943  

The value of t-test statistics is 1.943.

Now, at a 0.02 level of significance, the t table  gives a critical value of -2.472 and 2.473 at 27 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that there is no difference in potential mean sales per market in Region 1 and 2.

Answer:

42

Step-by-step explanation:

[ ( 7 - 3 ) * 2 + 6 ] * 3

= [ 4 * 2 + 6 ] * 3

= [ 8 + 6 ] * 3

= 14 * 3

= 42