beyond struggling pls help
FIND THE FOLLOWING MEASUREMENTS

Beyond Struggling Pls HelpFIND THE FOLLOWING MEASUREMENTS

Answers

Answer 1

Check the picture below.

well, ∡CED is the same as ∡CEA and those are right-angles so those are pretty much given, now

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{29}\\ a=\stackrel{adjacent}{20}\\ o=\stackrel{opposite}{CE} \end{cases} \\\\\\ CE=\sqrt{ 29^2 - 20^2}\implies CE=\sqrt{ 841 - 400 } \implies CE=\sqrt{ 441 }\implies \boxed{CE=21} \\\\\\ \stackrel{\textit{since we know the radius CB=29}}{CB-CE = EB\implies }\boxed{EB=8}[/tex]

Beyond Struggling Pls HelpFIND THE FOLLOWING MEASUREMENTS
Answer 2

Answer:

angle CED 90°. CE = 21. EB = 8.

Step-by-step explanation:

angle CED = 90° (right angle).

the radius (centre to edge) is the same right around the circle.

so that means that distance CD = 29.

draw a line from C to D. notice how that has just become an hypotenuse?

we know that DE = 20.

we have a right-angled triangle.

CE² = hypot² - DE²

       = 29² - 20²

       = 841 - 400

       = 441

CE = √441 = 21.

EB must be radius subtract CE. that is, 29 - 21 = 8.


Related Questions

A person who owns a 2/3 of a land sells 1/4 of it express the land sold as a fraction of the whole land

Answers

If a person owns 2/3 of a land and sells 1/4 of it, the fraction of the whole land sold can be expressed as 1/4 divided by 2/3.

To divide fractions, we invert the second fraction and multiply. Therefore, we have:

1/4 ÷ 2/3 = 1/4 × 3/2 = 3/8

So, the fraction of the whole land sold is 3/8. This means that the person has 2/3 - 3/8 = 5/24 of the original land remaining after selling 1/4 of it.

To see why this is the case, we can visualize the original land as a pie chart. If the person owns 2/3 of the land, then 1/3 of the land belongs to someone else. If the person sells 1/4 of their share, they are effectively selling 1/4 of 2/3 of the land, or 2/12 of the land. This represents a portion of the pie chart that is 2/12 of the total pie, or 1/6. Therefore, the person now owns 5/6 of the pie chart, or 5/24 of the original land.

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Kai uses an entire can of paint on a square backdrop for the school play. The label on the can states that one can covers 27 m2 of wall surface. Estimate the backdrop’s side length, to one decimal place.

Answers

If one can of paint covers 27 m², then the area of the square backdrop must be 27 m². To find the length of one side of the square, we need to take the square root of the area. The square root of 27 is approximately 5.2. Therefore, the side length of the square backdrop is approximately 5.2 meters.

<
←+
-6
6
4
U ←
2
-4
-6-
2
6
→x
Write an equation that represents the line.
Use exact numbers.

Answers

To find the equation in slope-intercept form, y = mx + b, we need to first find the slope using
    [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

 

In this case we have the two points (1,2) and (4,4), so our calculation looks like:

    [tex]m=\dfrac{4-2}{4-1} = \dfrac{2}{3}[/tex]
Notice this is the same "rise over run" that we can count out on the graph.  If we start at (1,2) and go "up 2 units, right 3 units", then we end up at the point (4,4).

 

Now we need to find b.  We have [tex]y = \frac{2}{3}x+b[/tex], so we need to substitute in one of the points to find b.  Let's use (1,2):

           [tex]2 = \frac{2}{3}\cdot 1+b[/tex]

           [tex]2 = \frac{2}{3}+b[/tex]

    [tex]2 - \frac{2}{3} =b[/tex]

           [tex]\frac{4}{3} =b[/tex]

 

This gives us our equation: [tex]y = \frac{2}{3}x+\frac{4}{3}[/tex]

help please. thank you bro. ​

Answers

The area of the small and large sectors are about 11,760 feet² and 23,520 feet² respectively.

We have to given that;

A circle is shown in image.

Here, We have;

For small sector,

Angle = 120 deg

Radius = 14 feet

Since, Area of sector of circle is,

⇒ A = 1/2 (θr²)

Hence, For small sector,

Area = 1/2 (120 × 14²)

Area = 11,760 feet²

For large sector is,

Area = 1/2 (θr²)

Area = 1/2 (360 - 120) × 14²

Area = 1/2 × 240 × 14²

Area = 23,520 feet²

Thus, The area of the small and large sectors are about 11,760 feet² and 23,520 feet² respectively.

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Factorise the following


1.1. 6a-21


1.2.
[tex]6 {x}^{2} + 9x[/tex]

Answers

Answer:

1.1. 3(2a-7)

1.2. 3x(2x+3)

Step-by-step explanation:

Put the common factor on the outside of the parentheses.

1.1. 6a-21

The lowest common factor for 6a and -21 is 3.

     3(2a-7)

1.2. [tex]6x^{2} +9x[/tex]

The lowest common factor for [tex]6x^{2}[/tex] and 9x is 3x.

      3x(2x+3)

11. 6x^2-9x
12. 3x(2x+3)
Hope it helps

how to find the first term of arithmetic sequence given the number of terms, the last term and the common differnece

Answers

To find the first term of an arithmetic sequence, use the formula: first term = last term - (number of terms - 1) * common difference.

To find the first term of an arithmetic sequence given the number of terms, the last term, and the common difference, you can use the following formula

First term = Last term - (Number of terms - 1) * Common difference

Here's how to use this formula

Identify the number of terms, the last term, and the common difference of the arithmetic sequence.

Plug these values into the formula.

Simplify the formula using order of operations (PEMDAS) to find the first term.

For example, let's say we have an arithmetic sequence with 10 terms, a last term of 50, and a common difference of 5. Using the formula above, we get

First term = 50 - (10 - 1) * 5

First term = 50 - 9 * 5

First term = 50 - 45

First term = 5

Therefore, the first term of the arithmetic sequence is 5.

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TANK A large tank is currently holding 12,000 gallons of water. The water will drain at a constant rate of 100 gallons per minute until the volume of water in the tank is 4,000 gallons. Write an equation to find the number of minutes m it will take for the specified amount of water to drain.

Answers

The equation to find the number of minutes m is 12000 - 100m = 4000

Writing an equation to find the number of minutes m

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

Initial volume  = 12000 gallons

Rate of draining = 100 gallons per minute

Final volume of water = 4000 gallons

The equation to find the number of minutes m is represented as

f(m) = Initial volume - Rate of draining * m

So, we have

f(m) = 12000 - 100m

When the volume is at 4000 gallons, we have

12000 - 100m = 4000

Hence, the equation to find the number of minutes m is 12000 - 100m = 4000

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Perform the following area application.
Compute the number of vinyl tiles, measuring 8 in. each side, needed to tile a kitchen measuring 24 ft. by 18 ft.
__________tiles

Answers

To find the number of vinyl tiles needed to tile a kitchen measuring 24 ft. by 18 ft. with tiles measuring 8 in. each side, we need to convert all measurements to the same units.

First, we need to convert the kitchen measurements from feet to inches:

- 24 ft. = 24 x 12 = 288 in.
- 18 ft. = 18 x 12 = 216 in.

Next, we need to divide the length and width of the kitchen by the length of each tile to find the number of tiles needed in each direction:

- Length: 288 in. ÷ 8 in. = 36 tiles
- Width: 216 in. ÷ 8 in. = 27 tiles

Finally, we multiply the number of tiles needed in each direction to find the total number of tiles needed:

- Total tiles: 36 tiles x 27 tiles = 972 tiles



To tile a kitchen, it is important to accurately calculate the number of tiles needed to ensure that there is enough material to complete the job. In this case, we converted all measurements to the same units and then used division and multiplication to find the total number of tiles needed.



To tile a kitchen measuring 24 ft. by 18 ft. with vinyl tiles measuring 8 in. each side, we need a total of 972 tiles.

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PLEASE HELP I AM GROUNDED AND DONT UNDERSTAND

Answers

Answer:

46°

Step-by-step explanation:

180-136= 44

x = 180 -90-44

x = 46

On monday 5/8 inches of rain fell in 2/3 hour. What is the value of the excretion?

Answers

The value of the excretion is equal to 15 / 16 inches of precipitation per hour.

How to find the value of the excretion

In this question we find that a precipitation of 5 / 8 inches of rain is registered in a time of 2 / 3 hour and we are asked to find how many precipitation is registered in a time of an hour, that is, the value of the excretion. The excretion can be found by cross multiplication:

r = (5 / 8 in) / (2 / 3 h)

r = 15 / 16 in / h

A precipitation of 15 / 16 inches in a time of an hour is the value of the excretion.

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PROBLEM SOLVING: Write the answer corresponds to the problem. REMINDERS

If the answer requires decimals, express your answer in 2 decimal places. If your answer is more than 3 digits, DO NOT INCLUDE THE COMMA. Compute for the mean expenses of the XYZ Corporation given the following:



Name Total Sales Total Expenses
Quezon City 14,950. 00 4,933. 50
Caloocan City 18,290. 00 6,035. 70
Marikina City 37,200. 00 12,276. 00
Cebu City 18,900. 00 6,237. 00
Davao City 45,000. 00 14,850. 00
Mandaluyong City 23,000. 00 7,590. 00
Cavite 22,000. 00 7,260. 00
Laguna 21,000. 00 6,930. 00
Manila 66,000. 00 21,780. 00
Iloilo 34,000. 00 11,220. 0

Answers

The mean expenses of the XYZ Corporation is 9,811.22.

To compute for the mean expenses of the XYZ Corporation, we need to add up all the total expenses of each city and divide it by the total number of cities.

Total Expenses = 4,933.50 + 6,035.70 + 12,276.00 + 6,237.00 + 14,850.00 + 7,590.00 + 7,260.00 + 6,930.00 + 21,780.00 + 11,220.00
Total Expenses = 98,112.20

Number of Cities = 10

Mean Expenses = Total Expenses / Number of Cities
Mean Expenses = 98,112.20 / 10
Mean Expenses = 9,811.22

The mean expenses of the XYZ Corporation is 9,811.22. Since the answer does not require decimals, we do not need to express it in two decimal places. However, we need to follow the reminder that if the answer is more than three digits, we should not include the comma.

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Subtract the polynomials
(3x² + 2x − 5) – (4x² – 3x − 4)


A:-7x²+5x-9

B:7x²-x-9

C:x²-x-9

D:-x²+5x-1

please helpppp asap​

Answers

Answer:

-x² + 5x - 1

Step-by-step explanation:

separate the x², the x, and the constants (numbers without any x).

3x² - 4x² = -x²

2x - -3x = 2x + 3x = 5x

-5 - -4 = -5 + 4 = -1.

we have -x² + 5x - 1

Pincushion circumference=8

Answers

If circumference of circle is 8 units then the radius of circle is 1.27 units

The circumference of the circle is 8 units.

We have to find the radius of the circle.

The formula for circumference of cirlce is two times of pi and radius.

Circumference = 2πr.

Where r is the radius of the circle.

The value of radius we have to find.

The circumference is 8 units.

Plug in the values of circumference to find r:

8=2×3.14 r

When 2 is multiplied with three point one four we get six point two eight.

8=6.28 r

Divide both sides by 6.28:

r = 8/6.28

When eight is divided by six point two eight we get one point two seven.

r=1.27 units

Hence,  the radius of circle is 1.27 units when circumference is 8 units.

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Complete question

If circumference of circle is 8 units then find the radius of circle?

Jan creative a pattern using the rule ""add 3."" Bill creates a pattern using the rule ""add 6."" Which describes the relationship between Jan sand Bill’s patterns?

Answers

Jan created a pattern using the rule "add 3," and Bill created a pattern using the rule "add 6." In arithmetic sequences, the nth term is given by the formula a + (n-1)d, where a is the first term and d is the common difference between any two consecutive terms.

The common difference is the difference between each pair of consecutive terms in a sequence. Because Jan's pattern has a common difference of 3, the nth term in her sequence is given by a + (n-1)3, and because Bill's pattern has a common difference of 6, the nth term in his sequence is given by a + (n-1)6.The nth term in both Jan and Bill's sequence is a linear function of n. The slope of a line is the common difference between any two consecutive terms in a sequence.

As a result, the slopes of Jan and Bill's patterns are 3 and 6, respectively. In general, two patterns are in a linear relationship if their slopes are constant multiples of one another. In this case, Bill's pattern is the result of multiplying Jan's pattern by a factor of 2. As a result, their patterns have a linear relationship. Answer: The patterns have a linear relationship because Bill's pattern is the result of multiplying Jan's pattern by a factor of 2.

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If each serving of the stew will contain pound of meat, how many servings of the stew can the club
make?
Enter your answer in the box.

Answers

The number of servings of the stew the club can make is 24

Calculating the servings of the stew the club can make?

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

The dot plot

From the dot plot, we have

Total = 4/8 * 2 + 6/8 + 1 * 3 + 1 2/8 * 1

Evaluate

Total = 6


Each serving can take 1/4 pounds

So, we have

Total = 6/(1/4)

Evaluate

Total = 24

Hence, the servings of the stew the club can make is 24

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In a scatter plot, if all data points were aligned along a 45° angle, your correlation would be:
A) Of medium strength
B) Of weak strength
C) Perfect
D) 0
E) None of the above

Answers

Answer:

C) Perfect correlation

if a car is speeding down a road at 50 miles/hour ( mph ), how long is the stopping distance d50 compared to the stopping distance d25 if the driver were going at the posted speed limit of 25 mph ?

Answers

The stopping distance of D40 is 2.56 times the stopping distance of D25.

Given that are two initial velocities: 40 mph and 25 mph, with which the car's stopping distance is D40 and D25.

The final velocity for both is 0 mph (as the car to a stops).

We need to compare the stopping distance D40 to the stopping distance D25.

Use the third equation of motion for both cases to get the comparison.

The equation is given by:

[tex]v^2 - u^2 = 2as.[/tex]

Case 1)

[tex]0 - 40^2 = 2a(D40)[/tex]

Case 2)

[tex]0 - 25^2 = 2a(D25)[/tex]

Comparing the obtained expressions.

[tex]\frac{40^2}{25^2} = \frac{2a(D40)}{2a(D25)}[/tex]

[tex]2.56 = \frac{D40}{D25}[/tex]

[tex]2.565 \times D25 = D40[/tex]

Hence the stopping distance of D40 is 2.56 times the stopping distance of D25.

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You spin a spinner that is equally divided into 9 parts. 3 parts are white, 3 parts are black, and 3 parts are yellow.
What is the probability of the spinner not stopping at a black section? Write your answer as a percent rounded to the nearest whole number.

(Thank you!!)

Answers

Answer:

6/9 67%

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

66,6% are 2/3 -> 67%

From the 9 parts are 6 left - > 9/6 = 2/3

Finding an angle measure given a triangle and parallel lines

Answers

Answer:

We have congruent alternate interior angles.

39° + 96° + x° = 180°

135° + x° = 180°

x = 45

In the Northwest Bank waiting line system, assume that the service times for drive-up teller follow an exponential probability distribution with a mean of 100 customers per hour. Use the exponential probability distribution to answer the following questions:
a. What is the probability that the service time is one minute or less?
b. What is the probability that the service time is two minutes or less?
c. What is the probability that the service time is more than two minutes?
d. What is the probability that the service time is between three and seven minutes?

Answers

Calculating this expression, we find that the probability of the service time being one minute or less is approximately 0.6321.

Calculating this expression, we find the probability of the service time being between three and seven minutes is approximately 0.1849.

To answer the questions, we will use the exponential probability distribution formula:

f(x) = λ * e^(-λx)

Where λ is the rate parameter (mean service rate) and x is the service time.

a. To find the probability that the service time is one minute or less, we substitute x = 1 and λ = 100/60 (since there are 60 minutes in an hour and the mean service rate is given per hour):

P(X ≤ 1) = λ * e^(-λx)

P(X ≤ 1) = (100/60) * e^(-(100/60) * 1)

b. To find the probability that the service time is two minutes or less, we substitute x = 2 and λ = 100/60:

P(X ≤ 2) = λ * e^(-λx)

P(X ≤ 2) = (100/60) * e^(-(100/60) * 2)

Calculating this expression, we find that the probability of the service time being two minutes or less is approximately 0.8647.

c. To find the probability that the service time is more than two minutes, we subtract the probability of the service time being two minutes or less from 1:

P(X > 2) = 1 - P(X ≤ 2)

Calculating this expression, we find that the probability of the service time being more than two minutes is approximately 0.1353.

d. To find the probability that the service time is between three and seven minutes, we subtract the probability of the service time being less than three minutes from the probability of the service time being less than seven minutes:

P(3 ≤ X ≤ 7) = P(X ≤ 7) - P(X < 3)

P(3 ≤ X ≤ 7) = (100/60) * e^(-(100/60) * 7) - (100/60) * e^(-(100/60) * 3)

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Rey is checking the distance between two rooms on a blueprint. The
blueprint uses a scale in which 3 inches equals 4 feet. If the distance
on the blueprint is 11 inches, how far is it between the rooms, in feet?
Your answer can be exact or rounded to two decimal places.

Answers

To find the actual distance between the rooms, set up a proportion using the given scale:

3 inches / 4 feet = 11 inches / x feet

Now, solve for x:

3/4 = 11/x
x = (4 * 11) / 3
x ≈ 14.67 feet

The actual distance between the rooms is approximately 14.67 feet.

find the length of the curve y=ln(cosx) from 0 to pi/3

Answers

To find the length of the curve y = ln(cos(x)) from 0 to π/3, we can use the arc length formula for a curve defined by a function y = f(x):

L = ∫[a to b] √(1 + (f'(x))²) dx.

In this case, the function is y = ln(cos(x)). Let's first find the derivative:

y' = d/dx ln(cos(x)).

Using the chain rule, we have:

y' = -tan(x).

Now we can calculate the arc length:

L = ∫[0 to π/3] √(1 + (-tan(x))²) dx.

Simplifying the integrand, we have:

L = ∫[0 to π/3] √(1 + tan²(x)) dx.

Using the trigonometric identity tan²(x) + 1 = sec²(x), we can rewrite the integrand as:

L = ∫[0 to π/3] √(sec²(x)) dx.

Taking the square root of sec²(x), we have:

L = ∫[0 to π/3] sec(x) dx.

Integrating sec(x), we get:

L = ln|sec(x) + tan(x)| [0 to π/3].

Evaluating the integral at the upper and lower limits, we have:

L = ln|sec(π/3) + tan(π/3)| - ln|sec(0) + tan(0)|.

Simplifying further, we have:

L = ln|2 + √3| - ln|1 + 0|.

Since ln|1| = 0, the second term on the right-hand side becomes 0, and we are left with:

L = ln|2 + √3|.

Therefore, the length of the curve y = ln(cos(x)) from 0 to π/3 is ln|2 + √3|.

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monthly total production costs and the number of units produced at a local company over a period of 10 months are shown in the data set productioncost. use a simple linear regression model to develop an estimated regression equation to best describes the relationship between x and y. construct a standardized residual plot. based upon the standardized residual plot, does a simple linear regression model appear to be appropriate?

Answers

It's important to note that without the actual data, I cannot provide a definitive assessment of the model's appropriateness. I recommend conducting the analysis with the provided dataset to draw accurate conclusions about the suitability of the linear regression model.

To develop an estimated regression equation and assess the appropriateness of a simple linear regression model, we need the specific data from the "productioncost" dataset. Since the data is not provided, I cannot perform the analysis or construct the standardized residual plot.

However, I can provide you with a general approach to determine the appropriateness of a simple linear regression model based on a standardized residual plot. After fitting the regression model, you can calculate the standardized residuals by dividing the residuals by their estimated standard deviation. Plotting these standardized residuals against the predicted values can help assess the model's appropriateness.

In a standardized residual plot, if the residuals exhibit random scatter around the horizontal line at zero, with no discernible patterns or trends, it suggests that the linear regression model is appropriate. On the other hand, if there are systematic patterns or trends in the residuals, such as a curved shape or unequal spread, it indicates that the linear regression model may not adequately capture the relationship between the variables.

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Find the volume of the following solids.
The base of the solid is the region between the curve y=2√sin x and the interval [0,π] on the x-axis. The cross-sections perpendicular to the x-axis are
a. equilateral triangles with bases running from the x-axis to the curve.
b. squares with bases running from the x-axis to the curve.

Answers

To find the volume of the solid with equilateral triangular cross-sections, we need to integrate the area of each equilateral triangle over the interval [0,π]. The area of an equilateral triangle with side length s is given by (s^2√3)/4. Since the triangles have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x. Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2√3/4 dx

Simplifying, we get:

V = √3∫[0,π] sin x dx

Using the substitution u = cos x, we get:

V = √3∫[-1,1] √(1 - u^2) du

Using the formula for the integral of the half-circle, we get:

V = (√3/2)π

Therefore, the volume of the solid is (√3/2)π.

To find the volume of the solid with square cross-sections, we need to integrate the area of each square over the interval [0,π]. Since the squares have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x.

Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2 dx

Simplifying, we get:

V = 4∫[0,π] sin x dx

Using the identity ∫sin x dx = -cos x + C, we get:

V = -4cos x ∣[0,π]

Since cos π = -1 and cos 0 = 1, we get:

V = -4(-1 - 1) = 8

Therefore, the volume of the solid is 8.

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Need help with first four

Answers

Answer:

For 1 is it 1 hour and 15 mins?

Step-by-step explanation:

6 by 32 = 30 mins

12 by 32 = 1 hr

13 by 32 = 15

1hr + 15 mins = 1hr 15 mins

Sorry if incorrect

what is the lower quartile of the numbers 1 5 6 6 7 7 8 8 8 8 9 9 18 20 20 20 20 20 24 32 50 50 68 100

Answers

To find the lower quartile of a set of numbers, we need to determine the value that separates the lowest 25% of the data from the rest. In the given set of numbers, the lower quartile can be found by arranging the data in ascending order and identifying the value at the 25th percentile.

First, let's arrange the data in ascending order: 1 5 6 6 7 7 8 8 8 8 9 9 18 20 20 20 20 20 24 32 50 50 68 100.

To find the lower quartile, we need to determine the position of the 25th percentile. Since there are 23 data points, the 25th percentile corresponds to the value at the (25/100) * 23 = 5.75th position.

Since the position is not a whole number, we need to find the value between the fifth and sixth data points. The fifth data point is 7, and the sixth data point is also 7. Therefore, the lower quartile is 7.

The lower quartile represents the value below which 25% of the data lies. In this case, 25% of the data points are less than or equal to 7. It indicates that a quarter of the values in the dataset are smaller than or equal to 7, while the remaining 75% are larger.

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a net for the gift box.
14 m
15.65 m
15.65 m
I
I
7m
15 m
1
14 m

Answers

what do u need help with

i don't get it pls i need help pls pls pls

Answers

Answer:

IDONTKNOW  but your answer might be 35 .

Step-by-step explanation:

i think the answer is

5 x 7

So basically you have 4 and 3 so you want to multiply that and idontrealyknow the rest. eh sorry idontknow i tried.

if $\&x$ is defined as $\&x = x + 5$ and $\#x$ is defined as $\#x = x^2$ , what is the value of $\#(\&4)$?

Answers

The value of $\#(\&4)$ is 81. We first evaluated $\&4$ using the definition given, which gave us the value 9. Then, we substituted this value into the definition of $\#x$ to find the final answer of 81.

To find the value of $\#(\&4)$, we first need to evaluate $\&4$. Using the given definition of $\&x$, we have:

$$\&4 = 4 + 5 = 9$$

Now, we can substitute this value into the definition of $\#x$:

$$\#(\&4) = \#9 = 9^2 = 81$$

Therefore, the value of $\#(\&4)$ is 81. We first evaluated $\&4$ using the definition given, which gave us the value 9. Then, we substituted this value into the definition of $\#x$ to find the final answer of 81.
To find the value of #(&4), let's first compute &4.

According to the definition, &x = x + 5. So, &4 = 4 + 5 = 9.

Now we need to find the value of #9. The definition of #x is x², which means #9 = 9² = 81.

Therefore, the value of #(&4) is 81.

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smith is in jail and has 3 dollars; he can get out on bail if he has 8 dollars. a guard agrees to make a series of bets with him. if smith bets a dollars, he wins a dollars with probability .4 and loses a dollars with probability .6. find the probability that he wins 8 dollars before losing all of his money if

Answers

Therefore, the probability that Smith wins 8 dollars before losing all of his money is approximately 0.0479.

To solve this problem, we can use a probability tree diagram to visualize the different possible outcomes.

At each stage, Smith either wins a dollars or loses a dollars, until he either reaches 8 dollars (and wins) or 0 dollars (and loses). We can calculate the probability of each outcome by multiplying the probabilities of the branches leading to that outcome.

Starting with 3 dollars, there are two possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 4 dollars.

Smith loses a dollar with probability 0.6, leaving him with 2 dollars.

From 4 dollars, there are three possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 5 dollars.

Smith loses a dollar with probability 0.6, leaving him with 3 dollars.

Smith wins 4 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 7 dollars.

From 5 dollars, there are two possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 6 dollars.

Smith wins 3 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 8 dollars.

From 6 dollars, there are two possible outcomes:

Smith wins 2 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 8 dollars.

Smith loses a dollar with probability 0.6, leaving him with 5 dollars.

From 7 dollars, there is one possible outcome:

Smith wins 1 dollar with probability 0.4, leaving him with 8 dollars.

Therefore, the probability that Smith wins 8 dollars before losing all of his money is the sum of the probabilities of the outcomes that lead to winning 8 dollars, which is:

0.4 * 0.6 * 0.4 * 0.4 + 0.4 * 0.6 * 0.4 * 0.6 * 0.4 + 0.4 * 0.6 * 0.4 * 0.4 * 0.6 * 0.16 + 0.4 * 0.6 * 0.4 * 0.4 * 0.4 * 0.4 * 0.16 = 0.047872

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