answer the following question and show your work.A spherical scoop of ice cream 6. with a diameter of 5 cm rests on top of a sugar cone that is 12 cm deep and has a diameter of 5 cm. If all of the ice cream melts into the cone, what percent of the cone will be filled? Round to the nearest percent.

1. 13 hamsters

2. 66 legs

1. From the question, we are told that a hamster has 4 legs

Given that there are a total of 52 legs, so to find the total number of hamsters present, we simply go on to divide the number of total legs by the number of legs a hamster has

Mathematically; that would be 52/4 = 13 hamsters

2. Here, we want to the total number of legs present in a house where we have 4 bettles , 5 hamsters and 11 birds

1 bettle has 6 legs

so 4 bettles will have 4 * 6 = 24 legs

1 hamster has 4 legs

so 5 hamsters will have 5 * 4 = 20 legs

1 bird has two legs

so 11 birds will have 11 * 2 = 22 legs

So the total number of legs present in the house will be the addition of all the legs

That will be 24 + 20 + 22 = 66 legs

3. Here, we have a total of 32 legs , we now want to find the different combination of all the animals present

What is important here is that at any point, for any combination, the total number of legs must be eual to exactly 32

We proceed as follows;

1 bird

1 bettle

6 hamsters

Another can be;

2 birds

2 bettles

4 hamsters

Another combination can be

3 hamsters

3 bettles

1 bird

and so on

Answer:

The actual area of the basketball court is;

Explanation:

Given that the scale of the drawing is;

And the dimension of the basketball court on the scale drawing is;

The actual dimension will be;

Therefore, the actual area of the basketball court will be;

The actual area of the basketball court is;

Hence, Six ( 6 ) alarms are used to certain that a burglar is trying to enter and get detected by at least one alarm.

Given;

There are many automatic burglar alarms in a sizable bank vault.

The likelihood that a burglar will be discovered by a single alarm is 0.55.

We need to get;

How many of these alarms should be installed to be 99% confident that at least one alert will detect a thief attempting to enter

The probability of one alarm has a likelihood of failing to detect a burglar is

1 - 0.55 = 0.45

Let's say there are ' n ' alerts.

The likelihood that not one of the ' n ' alarms will sound is 0.45ⁿ.

The likelihood that at least one of the alarms catches the intruder is then just 1 - 0.45ⁿ.

This probability should be 99%, as desired.

In other words, if we solve for n and get

1 - 0.45ⁿ = 0.99

n = 5.76

n ≅ 6

Therefore, 6 alarms were utilized.

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The asset's variance is approximately 0.0358, and its standard deviation is approximately 0.1891.

To calculate the variance and standard deviation of the asset's returns, we'll follow the steps mentioned earlier using the given probability distribution:

⇒ Calculate the expected return (μ):

μ = (0.27 * 0.25) + (0.18 * 0.25+) + (0.10 * 0.30) + (0.04 * 0.20+)

  = 0.0675 + 0.045 + 0.03 + 0.008

  = 0.1505

⇒ Calculate the variance (σ^2):

σ^2 = [(0.27 - μ)^2 * 0.25] + [(0.18 - μ)^2 * 0.25+] + [(0.10 - μ)^2 * 0.30] + [(0.04 - μ)^2 * 0.20+]

Substituting the values and simplifying:

σ^2 = [(0.27 - 0.1505)^2 * 0.25] + [(0.18 - 0.1505)^2 * 0.25+] + [(0.10 - 0.1505)^2 * 0.30] + [(0.04 - 0.1505)^2 * 0.20+]

    = [(0.1195)^2 * 0.25] + [(0.0295)^2 * 0.25+] + [(-0.0505)^2 * 0.30] + [(-0.1105)^2 * 0.20+]

    = 0.017972 + 0.00021617 + 0.0030309025 + 0.01459516

    = 0.0358141325

⇒ Calculate the standard deviation (σ):

σ = √(σ^2)

  = √(0.0358141325)

  ≈ 0.1891

Therefore, the asset's variance is approximately 0.0358 and the standard deviation is approximately 0.1891.

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Thus, the total area of composite figure (circle on a rectangle) is found as  29.91 m².

Area of sector of the circle = (Ф/360°) *π*r²

r is the radius = 5.5 m

π = 3.14

Area =  (30/360°) *3.14 * 5.5²

Area = 7.91 m²

Area of rectangle = width × length

Area = 4 × 5.5 = 22 m²

Total area of composite figure = area of the circle's sector + area of the rectangle

Total area of composite figure =  7.91 m² + 22 m² = 29.91 m²

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The probability that the sample mean will be between 295 to 305 is  0.99921

Since we are given that the mean is 300  and the standard deviation of  18 and we were given a total of 144 observations.A z-score gives you a thought of how distant from the mean a data point is. A z-score can be put on a normal distribution curve. Z In arrange to utilize a z-score, you wish to know the mean μ additionally the population standard deviation σ.

The formula  we are referring to for calculating the  Zscore is :

Zscore = (x - mean) ÷ σ/√n

At first, let x be = 295, so  the

Zscore = (295 - 300) / (18/12) = - 3.33

The probability for zscore for z<-3.33  is,

=>P(Z< - 3.33) = 0.00039

Similarly for the  second part x  305, Sp

The Zscore will be  (305 - 300) / (18/12) = 3.33

so the probability of z<3.33

=>P(Z< 3.33) = 0.9996

so the probability of mean between the range 295 to 305

P(Z < 3.33) - P(Z < - 3.33)

=0.9996-0.00039

= 0.99921

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At a significance level of 0.03, the critical value is 1.711 (found using a t-distribution table with degrees of freedom equal to 20 and a significance level of 0.015). Since the calculated test statistic (2.568) is greater than the critical value, we reject the null hypothesis at a significance level of 0.03.

The degrees of freedom for the unequal variance test can be calculated using the formula:

\(df = [(s1^2/n1 + s2^2/n2)^2] / [((s1^2/n1)^2)/(n1-1) + ((s2^2/n2)^2)/(n2-1)]\)

Substituting the given values, we get:

\(df = [(15^2/27 + 9^2/15)^2] / [((15^2/27)^2)/(27-1) + ((9^2/15)^2)/(15-1)]\)

= 20.37

≈ 20 (rounded down to nearest whole number)

The decision rule for the 0.025 significance level and a right-tailed test is to reject the null hypothesis if the test statistic exceeds the critical value. The critical value can be found using a t-distribution table with degrees of freedom equal to 20 and a significance level of 0.025. From the table, we find the critical value to be 1.734.

The test statistic for the two-sample t-test with unequal variances can be calculated using the formula:

\(t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2)\)

Substituting the given values, we get:

\(t = (114 - 106) / sqrt(15^2/27 + 9^2/15)\)

= 2.568

Using a significance level of 0.025 and degrees of freedom equal to 20, the critical value is 1.734. Since the calculated test statistic (2.568) is greater than the critical value, we reject the null hypothesis.

At a significance level of 0.03, the critical value is 1.711 (found using a t-distribution table with degrees of freedom equal to 20 and a significance level of 0.015). Since the calculated test statistic (2.568) is greater than the critical value, we also reject the null hypothesis at a significance level of 0.03. Therefore, we can conclude that there is evidence to suggest that the population mean of the first population is greater than that of the second population.

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Answer:

I believe the correct answer would be

\(y = x - \frac{3}{20} \)

Step-by-step explanation:

Isolate the y

Answer:

~ 340

Step-by-step explanation:

A = pi * r^2

The big circle is r1 = 12cm so the small r2=6cm

A= A1 - A2 = (pi * r1^2)-( pi*r2^2) = 339,29 ~ 340 square cm

If the radius of the small circle is 12cm then: r1 = 24cm and r2 = 12cm and calculate it the same way

Answer:

\(1290 = \frac{h}{10} + \frac{h}{5} \\ 12900 = h + 2h \\ 3h = 12900 \\ h = 4300\)

Answer:

this is the answer of this question

The percent yield of Cu(OH)2 obtained in the reaction is 70.29%.

To calculate the percent yield of Cu(OH)2, we need to compare the actual yield of Cu(OH)2 obtained in the reaction to the theoretical yield of Cu(OH)2 that could have been obtained if all the CuSO4 reacted completely.

The balanced equation for the reaction is:

CuSO4 + 2NaOH → Cu(OH)2 + Na2SO4

The molar mass of CuSO4 is 159.61 g/mol, and its mass is 5.6 g. So, the number of moles of CuSO4 used in the reaction is:

5.6 g CuSO4 × (1 mol CuSO4/159.61 g CuSO4) = 0.035 mol CuSO4

According to the balanced equation, 1 mol of CuSO4 reacts with 1 mol of Cu(OH)2. Therefore, the theoretical yield of Cu(OH)2 that could have been obtained is:

0.035 mol Cu(OH)2

The molar mass of Cu(OH)2 is 97.56 g/mol, and its mass is 2.4 g. So, the actual yield of Cu(OH)2 obtained in the reaction is:

2.4 g Cu(OH)2 × (1 mol Cu(OH)2/97.56 g Cu(OH)2) = 0.0246 mol Cu(OH)2

Now, we can calculate the percent yield of Cu(OH)2:

percent yield = (actual yield / theoretical yield) × 100%

= (0.0246 mol / 0.035 mol) × 100%

= 70.29%

Therefore, the percent yield of Cu(OH)2 obtained in the reaction is 70.29%.

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The value of the infinite series as n tends to 0 is: 0

Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.

From the infinite series, we want to find the value of the series as n tends to 0.

We are given the series as:

x/2ˣ

At x = 0, we have:

0/2⁰ = 0/1 = 0

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a. Because the longest side can only be the sum of the other two sides, only (i) and (ii) are feasible (but not equal to the sum). b. Swap the pipe with length 3 and the pipe with length 4 as necessary.

A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

a. Because the longest side can only be the sum of the other two sides, only (i) and (ii) are feasible (but not equal to the sum).

b. Swap the pipe with length 3 and the pipe with length 4 as necessary.

c. Always place the biggest angle across from the longest side.

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We added 9 to both sides of the equation to complete the square for the x-term.

To find the standard equation of the sphere, we need to apply the formula:

(x - h)² + (y - k)² + (z - l)² = r², where (h, k, l) is the center of the sphere and r is its radius.

We are given the center of the sphere as (-6, 1, 4), and it is tangent to the yz-plane, which means its x-coordinate will be -6 + r.

Therefore, the center of the sphere will be (-6 + r, 1, 4).

Since it is tangent to the yz-plane, its radius will be the distance from the center to the yz-plane, which is 6 units (distance from -6 to 0).

So, the standard equation of the sphere is:

(x - (-6 + r))² + (y - 1)² + (z - 4)² = 6²

We need to find r to complete the equation.

To do this, we will use the fact that the sphere is tangent to the yz-plane.

This means that its x-coordinate is equal to -6 + r.

Therefore,-6 + r + r = 0 ⇒ 2r = 6 ⇒ r = 3

So, the standard equation of the sphere is:

(x + 9)² + (y - 1)² + (z - 4)² = 36

Note that we added 9 to both sides of the equation to complete the square for the x-term.

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The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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Answer:

C) 1/5

Step-by-step explanation:

rise/run

Hope this helps. Pls give brainliest.

Answer:

Change in Y over change in X. So down 8 and over 2. Simplified it would be 4/1

The value of arc PQ is 110°

The circumference of a circle is the length of the 360 degree arc of that circle. Therefore the sum of the arc on a circumference of a circle is 360°

Therefore ,

8x-10+ 6x + 10x+10 = 360

24x -10+10 = 360

24x = 360

divide both sides by 24

x = 360/24

x = 15

therefore the value of x is 15

Arc PQ = 8x -10

substitute 15 for x

ArcPQ = 8×15-10

= 120-10

= 110°

therefore the value of arc PQ is 110°

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Now we have the constant of proportionality, we can fill the table in (1)

if t=6,

6 = 1/6 x d

d = 36 ft

if d = 60 ft

t = 1/6 x 60

t = 10 mins

If d =18 ft

t = 1/6 x 18

t = 3 mins

If t = 1

1= 1/6 x d

d = 6 ft

Now let me draw the table and insert the values we just got

Answer: C. 13/3

Step-by-step explanation:

\(slope=\frac{rise}{run} =\frac{y}{x} =\frac{13}{3}\)

Answer:

(0, -8)

Step-by-step explanation:

The distance must be equal from C to A and points B to D.

Max and Earl work 8 hours per week. Since Earl works 2 more hours, Earl works 8 + 2 = 10 hours per week.

Let's assume that both Max and Earl work x hours per week.

Since Max earns P50 per hour, his total weekly earnings can be calculated as:

Max's weekly earnings = P50 * x

Similarly, since Earl earns P40 per hour and works 2 more hours than Max, his total weekly earnings can be calculated as:

Earl's weekly earnings = P40 * (x + 2)

According to the given information, Max and Earl earn the same amount per week. So we can set up an equation:

Max's weekly earnings = Earl's weekly earnings

P50 * x = P40 * (x + 2)

Simplifying the equation,

50x = 40(x + 2)

Expanding:

50x = 40x + 80

Subtracting 40x from both sides:

10x = 80

Dividing both sides by 10:

x = 8

Therefore, Max and Earl work 8 hours per week. Since Earl works 2 more hours, Earl works 8 + 2 = 10 hours per week.

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Answer:

q= 10

Step-by-step explanation:

9q - 10q = -10

-q = -10

q= -10/-1 = 10

Answer:

q=10

Step-by-step explanation:

subtract 10q from both sides than divide-10 by -1

Hi there!

The substitutions are 10 and 0.

The relative frequency for the event of spin a 2 is P = 0.16

Given data ,

Let the total number of times the event occurs = 50

Now , the number of times the spin of 2 occurs = 8 times

So , the relative frequency is given by

Relative Frequency = Subgroup frequency / Total frequency

P = 8 / 50

P = 0.16

Hence , the relative frequency is 0.16

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The complete question is attached below :

If the table shows the results for spinning the spinner 50 times. What is the relative frequency for the event "spin a 2"

In order to find the perimeter of this figure, let's calculate the length of the semicircle at the top of the figure.

The diameter of the semicircle is equal to 5 meters, so the radius (which measures half the diameter) is equal to 2.5 meters.

Now, to calculate the length of the semicircle, we can use the formula below:

Calculating the perimeter of the figure, we have:

Rounding to the nearest tenth (half even method), we have a perimeter of 30.8 meters.