if
a manufacturer of basketballs can tolerate that the volumes of the
balls can have a 5 % error in the volume of the basketballs, what
is the maximum error we can tolerate for the basketball radius?

Answer:

x=-4

Step-by-step explanation:

-6x=17+7

-6x=24

x=-4

Answer:

x = -4

Step-by-step explanation:

Add 7 to each side of the equation (left and right of the equal sign) which should get you to -6x = 24. Then multipy both sides by -1 to make the -6x positive and turn the 24 negative. That should leave you with 6x = -24, then divide by 6 on each side and your answer should be x = -4

The probability that at most one corporation makes charitable contributions is approximately 0.4816, or 48.16%

Explanation: Let's denote the event that a corporation makes a charitable contribution as C, and the event that it does not make a charitable contribution as C'. The probability that a corporation makes charitable contributions is given as 0.72, which means the probability of not making a charitable contribution is 0.28 (1 - 0.72).

We can use the binomial probability formula to calculate the probability of exactly one corporation making charitable contributions. The formula is P(X = k) = (nCk) * p^k * q^(n-k), where n is the number of trials (2 corporations in this case), k is the number of successful trials (1 corporation making charitable contributions), p is the probability of success (0.72), q is the probability of failure (0.28), and (nCk) represents the number of combinations.

\(P(X = 1) = (2C1) * (0.72)^1 * (0.28)^(2-1) = 2 * 0.72 * 0.28 = 0.4032\)

Similarly, the probability of no corporations making charitable contributions can be calculated using

\(P(X = 0) = (2C0) * (0.72)^0 * (0.28)^(2-0) = 1 * 1 * 0.28^2 =0.0784.\)

To find the probability that at most one corporation makes charitable contributions, we sum up the probabilities of exactly one corporation and no corporations making charitable contributions:

P(at most one corporation) = P(X = 1) + P(X = 0) ≈ 0.4032 + 0.0784 ≈ 0.4816. Therefore, the probability that at most one corporation makes charitable contributions is approximately 0.4816, or 48.16%.

Learn more about event here:

https://brainly.com/question/15063914

#SPJ11

The smallest number of eggs that could have been in the basket = 301

Given that the basket is filled with an unknown number of eggs.

Let N be the smallest number of eggs in the basket.

When eggs are removed 2, 3, 4, 5, or 6 at a time, one egg is left over at the end which means (N-1) is divisible by 2, 3, 4, 5, or 6, i.e. (N-1) is the least common multiple of 2, 3, 4, 5, and 6.  

Since LCM (2, 3, 4, 5, 6) = 60

So, (N-1) should be a multiple of 60, then only (N-1) will be divisible by 2, 3, 4, 5, and 6. Therefore N is of the form 60k+1 (where k is an integer).

Since no egg is left over when they are removed 7 at a time, N should be a multiple of 7. Smallest multiple of 7 that is of the form 60k+1 (where k is an integer) is 301.

Hence the smallest number of eggs that could have been in the basket = 301.

To learn more about LCM visit : https://brainly.com/question/16054958

#SPJ11

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

To know more about maximizes visit:

https://brainly.com/question/30072001

#SPJ11

According to the rules of significant figures:



1.25 × 200 = 300

the answer is

TRue

Answer:

C Because the evolution of wasted numbers is incorrect

Answer:

b

Step-by-step explanation:

Answer:

B) (x + 1)2 + (y + 2)2 = 25

Step-by-step explanation:

In trigonometry, it should be noted that the value of sin(-5pi/6) is -0.5.

In order to find the value, we can use the following steps:

Draw a unit circle and mark an angle of -5pi/6 radians.

The sine of an angle is represented by the ratio of the opposite side to the hypotenuse of the triangle formed by the angle and the x-axis.

In this case, the opposite side is 1/2 and the hypotenuse is 1.

Therefore, sin(-5pi/6) will be:

= 1/2 / 1

= -0.5.

We can also use the following identity to find the value of sin(-5pi/6):

sin(-x) = -sin(x)

Therefore, sin(-5pi/6)

= -sin(5pi/6)

= -0.5.

Learn more trigonometry on

https://brainly.com/question/24349828

#SPJ1

Answer:

2.4 hr. = time working together

Step-by-step explanation:

Let x = time working together

x/6 = work done by Martin

x/4 = work done by Victor

Martin's part + Victor's part = 1 jog done

x/6 + x/4 = 1  Multiply thru by 12

2x + 3x = 12

5x = 12

x = 2.4 hr.

The time taken to pour concrete on the walkway using their combined rate is 2 hours 24 minutes.

To solve :

Time taken by Martin = 6 hours

Time taken by Victor = 4 hours

Recall :

Rate = 1 ÷ time

Hence ;

Working together :

Therefore, the time taken if they work together will be :

Therefore, The time taken if they work together will be 2.4 hours.

Learn more : https://brainly.com/question/18112348

Answer: I don’t know if this will help, but I do know that the function for that equation is -7

Step-by-step explanation:

In this case, the y-values for x = 3 and x = 2.9 are -14 and -13.6, respectively. Therefore, the change in y, or dy, is 0.4.

To compute dy using the function y = -4x - 2 as x goes from 3 to 2.9, we can calculate the difference in y-values between these two x-values.

First, we substitute x = 3 into the equation y = -4x - 2:

y = -4(3) - 2

y = -12 - 2

y = -14

Next, we substitute x = 2.9 into the equation y = -4x - 2:

y = -4(2.9) - 2

y = -11.6 - 2

y = -13.6

The change in y (dy) is the difference between the two y-values:

dy = -13.6 - (-14)

dy = -13.6 + 14

dy = 0.4

To calculate dy, we need to find the change in y-values corresponding to the change in x-values.

By substituting the given x-values into the equation y = -4x - 2, we find the corresponding y-values. The difference between these two y-values represents the change in y, which is denoted as dy.

Therefore, the value of dy, when x goes from 3 to 2.9 using the function y = -4x - 2, is 0.4.

To know more about value click here

brainly.com/question/30760879

#SPJ11

Answer:

The given expression is not a complete equation or function. It seems like a linear function, but it is missing an input variable and an equal sign.

A linear function in the form of y = mx + b, where y is the output, x is the input, m is the slope, and b is the y-intercept.

Without the input variable, we cannot evaluate the function. Can you please check if you have provided the complete equation or function?

Step-by-step explanation:

Since the subsequence {an} = 1, 2, 3, 4, 5, 6, 7, … is convergent to the limit ∞, thus the original sequence {an} = 1, 2, 3, 4, 5, 6, 7, … must also be unbounded.

If every term of the sequence is either greater than or equal to (≥) some number M or less than or equal to (≤) some number N (finite numbers), then the sequence is said to be bounded.

Otherwise, the sequence is said to be unbounded. And, if a sequence has a convergent subsequence, then the sequence is called bounded.

Let’s look at the example to answer the question.

Example of an unbounded sequence that has a convergent subsequence:

Let {an} = 1, 2, 3, 4, 5, 6, 7, …It is an unbounded sequence since there is no number that can be defined as M or N, that will make every term of the sequence less than or equal to (≤) or greater than or equal to (≥) this number (M or N).

However, {an} = 1, 2, 3, 4, 5, 6, 7, … has a convergent subsequence which is {an} = 1, 2, 3, 4, 5, 6, 7, … itself.

And, since the subsequence {an} = 1, 2, 3, 4, 5, 6, 7, … is convergent to the limit ∞, thus the original sequence {an} = 1, 2, 3, 4, 5, 6, 7, … must also be unbounded.

Know more about limit  here:

https://brainly.com/question/282767

#SPJ11

Answer:

a

Step-by-step explanation:

triangles are pyramids and it has 6 sides

Answer:

Hexagonal prism

Step-by-step explanation:

We can rule out B and D because if it was a pyramid, there would be a triangle in the net (The net of a 3D shape is what it looks like if it is opened out flat). We can also rule on C because it it was a cylinder, there would be a circle in the net. Therefore, our remaining answer is A.

61mm has to be converted to cm.

Simply divide by 10 [ 10mm = 1cm ]

61 mm = (61/10) = 6.1 cm

5.5 + 6.1 = 11.6cm

OR...

Convert 5.5cm to mm by multiplying by 10

5.5cm = (5.5×10) = 55mm

55+61 = 116mm

116mm = (116/10) = 11.6cm

The answer for this question is 11.6 cm or 116 mm.

You need to convert either millimeter to centimeter or vice versa

1 cm = 10 mm

converting 5.5 cm to mm :

5.5 X 10 = 55 mm

Now, add both the values of millimeter:

55 + 61 = 116 mm

If we need answer in centimeter

we can convert 116 mm into cm

116/10 = 11.6 cm

To know more about mm to cm conversion you can refer to:

https://brainly.com/question/4083211?referrer=searchResults

The correct question is :

Add 5.5 cm to 61mm

Answer:

Step-by-step explanation:

5x7=35 hours(Gary’s total free time per week)

7+8=15 hours(Gary is spending his time on the internet+Playing video games)

35h.....100%

15.........x%

x=42,8%=>43%

The compound inequality for the graph shown above include the following:

x < -4.

x ≤ 5.

In Mathematics, a number line is a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.

Since the first point is at -4 and the arrow points to the left of the number line, it represents the less than (<) inequality symbol and should be written as x < -2.

Additionally, the second point is located at 5 and the arrow points to the left of the number line with a shaded circle, it represents the greater than (>) inequality symbol and should be written as x ≤ 5.

Read more on number line here: brainly.com/question/16482555

#SPJ1

The value of x is 8.5 cm

The complete question is in the image

The given parameters are:

y = 12 cm

\(\theta = 45^o\)

The value of x is calculated using the following sine ratio

\(\sin(\theta) = \frac xy\)

This gives

\(\sin(45^o) = \frac x{12}\)

Multiply by 12

\(x = 12 * \sin(45^o)\)

Evaluate

x = 8.5

Hence, the value of x is 8.5 cm

Read more about right triangles at:

https://brainly.com/question/2437195

#SPJ1

a ball of radius 13 has a round hole of radius 3 drilled through its center. then the volume of the resulting solid is 8.5528 x 10³  units³

The radius of the ball is 13 units.

Its volume is

V₁ = (4π*13³)/3

    = 9.2028 x 10³ units³

The drilled hole has the approximate shape of a solid cylinder with radius = 3 and length = 26. Its volume is

V₂ = π*(3²)*26

    = 0.650 x 10³ units³

The volume of the resulting solid is

V₁ - V₂ = 8.5528 x 10³

Answer: 8.5528 x 10³  units³

learn more about of volume here

https://brainly.com/question/4672503

#SPJ4

The company's profits on June 1, 2002 is $4500 and the company's profits many years into the future is $1000 per month.

The equation f(t) = (t^2 + 9) / (t^2+2) provides the monthly profits, in thousands of dollar, where t refers to months after June 1, 2002.

The company’s profit on June 1, 2002 using the equation is when t = 0 months

f(0) = (0^2 + 9) / (0^2+2) = 9/2 = 4.5 or $4500.

The company’s profit on many years into the future using the equation is given by:

Limit(t→∞)((t^2+9)/(t^2+2))= Limit(t→∞)(2t/2t)=1

Hence the monthly profit is $1,000.

Learn more about Profits:

https://brainly.com/question/1078746

#SPJ4

Answer:

\(let \: the \: angle \: be \: \alpha \\ \tan( \alpha ) = \frac{p}{b} \\ \tan(16.8) = \frac{2.7}{x} \\ x = \frac{2.7}{0.30 } \\ x = 9 \\ now \: by \: using \: pythagoras \: theorem \: \\ h = \sqrt{p {}^{2} } + b {}^{2} \\ h = \sqrt{ {2.7}^{2} } + {9 }^{2} \\ h = 9.396\)

A random sample of approximately 1067 registered voters is needed to estimate the proportion of voters planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

To estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence and a

margin of error no greater than 0.03, we need to determine the sample size. We can use the following formula for

sample size calculation:

\(n = (Z^2 × p × (1-p)) / E^2\)
Where:
- n is the sample size
- Z is the Z-score (1.96 for 95% confidence)
- p is the estimated proportion of voters planning to vote for Chavez
- E is the margin of error (0.03 in this case)

Since we don't know the true proportion of voters planning to vote for Chavez, we can use the most conservative

estimate (p = 0.5) to ensure the required margin of error:

\(n = (1.96^2 × 0.5 × (1-0.5)) / 0.03^2\)
n = (3.8416 × 0.25) / 0.0009
n = 0.9604 / 0.0009
n ≈ 1067

Therefore, a random sample of approximately 1067 registered voters is needed to estimate the proportion of voters

planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

for such more question on  random sample

https://brainly.com/question/24466382

#SPJ11

The double integral ∫∫x(\(sec^2\))(y) dA over the region R = {(x, y) | 0 ≤ x ≤ 6, 0 ≤ y ≤ π/4} is equal to 3π/8.

To evaluate the given double integral ∫∫x(sec^2)(y) dA over the region R = {(x, y) | 0 ≤ x ≤ 6, 0 ≤ y ≤ π/4}, we follow the process of integrating with respect to one variable at a time.

First, we integrate with respect to x. Since the bounds of x are from 0 to 6, the integral becomes:

∫[0, π/4] ∫[0, 6] x(sec^2)(y) dx dy

Integrating x with respect to x, we get:

(1/2)x^2(sec^2)(y) |[0, 6]

Plugging in the limits of integration, we have:

(1/2)(6^2)(sec^2)(y) |[0, π/4]

Simplifying, we get:

(1/2)(36)(sec^2)(y) |[0, π/4]

= 18(sec^2)(y) |[0, π/4]

Next, we integrate the remaining expression with respect to y. The integral of sec^2(y) is tan(y), so we have:

18(tan(y)) |[0, π/4]

Evaluating the limits of integration, we get:

18(tan(π/4) - tan(0))

= 18(1 - 0)

= 18

Therefore, the double integral ∫∫x(sec^2)(y) dA over the given region R is equal to 18.

To learn more about integral refer here:

https://brainly.com/question/31059545#

#SPJ11

Answer: m = 2; b = 6

y = mx + b

because the line  parallel to  y = 2x + 3

=> \(\left \{ {{m=2} \atop {b\neq 3}} \right.\)

the line passes through  the point (0,6) => 6 = b

Step-by-step explanation:

Answer:

The given function is an Absolute value function because its expression is contained within the absolute value symbol.

Explanation:

Given the function;

Recall that Absolute value functions are functions that contains it algebraic expression within the absolute value symbol.

Such as;

Therefore, the given function is an Absolute value function because its expression is contained within the absolute value symbol.

Answer:

180

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

Because 20x9=180

Please MARK BRAINLEST!!

The resulting direction field will give a visual representation of the behavior of the solutions to the given differential equation y' = 25x cos(πy).


1. Identify the given differential equation: y' = 25x cos(πy). This is a first-order differential equation, where y' represents the first derivative of y with respect to x. The equation is a first-order differential equation because it only involves the first derivative of y with respect to x. The presence of the cosine function makes it a non-linear differential equation.

2. To sketch the direction field for this equation, we'll plot small line segments (or arrows) that show the slope of the solution at each point (x, y) on the xy-plane.

To find the actual solution curves to this differential equation, we would need to solve the equation using techniques such as separation of variables or an integrating factor. The direction field can help us visualize the general behavior of the solutions, but to get specific information about individual solutions we would need to solve the equation.

3. For each point (x, y), calculate the slope using the given differential equation. The slope at point (x, y) will be m = 25x cos(πy).

4. Plot the small line segments (or arrows) at various points (x, y) with the calculated slopes. The length and direction of these segments represent the slope of the solution curve at that point.
The differential equation tells us that the slope of the tangent line to a solution curve at any point (x,y) is equal to 25x cos(πy). This means that the direction of the solution curve at any point is given by the direction of the tangent line at that point, which is indicated by the arrows in the direction field.

The cosine function in the equation has a period of 2π, which means that the slope of the tangent line repeats every time y increases by 2π. This can be seen in the direction field by the repeating patterns of the arrows.

5. The resulting direction field will give a visual representation of the behavior of the solutions to the given differential equation y' = 25x cos(πy).

Learn more about differential equation:

brainly.com/question/31583235

#SPJ11