what is the area of the long triangle

If the spherical snowball is melting , then the rate at which the radius changing after 6.5 hours is 0.208 ft/h  .

A spherical snowball has volume = 260 ft³ that is melting at a rate of 11 cubic feet per hour, while remaining spherical.

We have to find the rate at which the radius is changing after 6.5 hours.

So , let "V" = volume of snowball, "r" = radius of snowball, and "t" = time.

Volume Of Sphere is  V = (4/3)πr³ and dV/dt = -11 ft³/h ;

So,  dr/dt when t = 6.5 hours. is dV/dt = (dV/dr)×(dr/dt)  ;

derivative of volume formula with respect to "r", we get:

⇒ dV/dr = 4πr²   ;

Substituting the given values in chain rule equation, we get:

⇒ -11 = (4/3)πr² × dr/dt  ;

⇒ dr/dt = -11/((4/3)πr²)

For  rate of change of the radius when t = 6.5 hours, we find the radius at that time.

The initial volume of the snowball = 260 ft³.

After 6.5 hours of melting at a rate of 11 ft³/h, the remaining volume will be:  V = 260 - (11 × 6.5) = 188.5 ft³   ;

So , V = (4/3)πr³

⇒ 188.5 = (4/3)πr³

⇒ r³ = (188.5 × 3 / (4π))   ;

≈ 3.55ft

Now we substitute r = 3.55 feet

⇒ dr/dt = -11/[(4/3)π(3.55)²]  ;

⇒ dr/dt ≈ -0.208 ft/h  ;

Therefore , the rate at which radius is changing after 6.5 hours is approximately 0.208 feet per hour and negative sign represents that radius is decreasing  .

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The probability the math majors are seated together is 0.028 and all seated togeather with their group is 0.0047.

Probability is the probability that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics.

Probability determines the likelihood of an event occurring.

P(A) = f / N. Odds and probabilities are related, but odds depend on probabilities. Before we can determine the probability that an event will occur, we first need the probability.  

total number of teacher is 10

so number of ways total 10 teacher seat = 10!/(6!*4!)

= 210

and

the number of ways  the math majors are seated together

= 6

probability = 6/210 = 0.028

the number of ways the math majors are seated together and the computer science majors are seated together

= 1

probability = 1/210

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Answer:

The length is [tex]9[/tex] inches and the width is [tex]30[/tex] inches.

Step-by-step explanation:

The perimeter of the rectangle is [tex]2x + \frac{4x}{3} = 30[/tex]. We multiply [tex]3[/tex] by both sides which will give us [tex]6x + 4x = 90[/tex]. Adding, we have [tex]10x = 90[/tex]. Dividing [tex]10[/tex] by both sides will give us [tex]x = 9[/tex]. The length of the rectangle is [tex]9[/tex], and the width is [tex]\frac23 \cdot 9 = 6.[/tex] Checking our answer, we have [tex]6 + 6 + 9 + 9 = 30.[/tex] Therefore, the length of the rectangle is [tex]\boxed{9 \text{ inches}}[/tex] and the width of the rectangle is [tex]\boxed{30 \text{ inches}}[/tex].

Hope that helps!

Answer: The equation of a line in the form y = mx + b can be found using the slope-intercept form, where m is the slope of the line and b is the y-intercept. To find the equation of BC, we need to find the slope of the line and one point on the line.

The slope of the line can be found using the two points A and B. The slope of the line can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively. Plugging in the values, we get:

m = (4 - (-1)) / (4 - (-3)) = 5 / 7

So the slope of the line BC is 5/7.

One point on the line BC is B = (4, 4), so we can use this point and the slope to find the y-intercept:

b = y - mx

where y and x are the y and x coordinates of point B, respectively. Plugging in the values, we get:

b = 4 - (5/7) * 4 = 4 - 20/7 = -16/7

So the equation of line BC in the slope-intercept form is:

y = (5/7)x - 16/7

Step-by-step explanation:

Answer:

The expression is a summation, or the sum of a sequence of terms. Each term is equal to 900 * (1.04)^n+1, where n starts at 1 and goes up to infinity.

To calculate this sum, we would need to find the limit of the sequence as n approaches infinity. However, finding the exact value of this sum is not possible and would require the use of mathematical tools like mathematical analysis.

To estimate the value, we can use a calculator or spreadsheet to calculate the sum for a finite number of terms and then see how the sum changes as we increase the number of terms. For example, if we calculate the sum for n = 1 to 100, we would get an estimate of the value. If we then calculate the sum for n = 1 to 200, we would get a closer estimate.

In this case, we can round the expression to the nearest integer, which would be 53.

Step-by-step explanation:

Answer:

Let the number of $2 notes be x, while that of $10 notes be y.

Set two equations

x + y = 21     y = 21 - x ------- 1

2x + 10y < 110  ------ 2

Sub 1 into 2

2x + 10(21-x) < 110

2x + 210 - 10x < 110

-8x < -100

x > 12.5

Minimum number of $2 notes in the envelope = 13

Answer:

Not Possible

Step-by-step explanation:

No answer choices are shown however, we can solve for some that are equivalent so we know which ones are not.

Here are some that are equivalent:

20(2+1)

2(20+10)

40+20

60

Answer: 4x2

Step-by-step explanation:

Answer:

[tex]4x^2[/tex]

Step-by-step explanation:

[tex](2x)(2x)=(2*2)(x*x)=4x^2[/tex]

The term "difference" os the result of subtracting one number from another.

So in other terms you want to know what would be the result of subtracting -4.6 from 13.5 :

13.5 - -4.6 = Difference between the two temperatures

Two minus signs turn into a positive sign so :

13.5 - -4.6 =

13.5 + 4.6 =

18.1 = Difference between the two temperatures

Your answer is : The difference between the two temperatures is 18.1

To solve the given equations multiply equation 1 with - 2 and the solutions are x = 1 and y = 2.

In mathematics, the Elimination method is about deleting one of the words containing any of the variables to make the calculations easier.
To solve the equations, multiply or divide a number by the equation(s) until all of the variable terms' coefficients are the same.

The term is then eliminated or removed from the result by adding or subtracting from both equations.

Here we have

Equation 1: 2x - 5y = -8

Equation 2: 4x + 5y = 14  

We can multiply given equations as follows

To eliminate 'x' terms multiply the multiply equation 1 with -2

-2 × Equation 1 =>  - 4x + 10y = 16  ---- (Equation 3)  

Now add Equation (2) and Equation (3)

=> 4x + 5y - 4x + 10y = 14 + 16

=> 15y = 30

=> y = 2

Now substitute y = 2 in equation (2)

=> 2x - 5(2) = -8

=> 2x - 10 = -8

=> 2x = 2

=> x = 1  

Therefore,

To solve the given equations multiply equation 1 with - 2 and the solutions are x = 1 and y = 2.

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The length of PC and GC is 4.4 and 6.6 respectively.

What is centroid of a triangle?

A centroid of a triangle is defined as a equidistant from all the point present on the triangle. It is always lies on the interior of the triangle. The centroid divided the median in the ratio 2:1

Given ABC is the triangle.

In which G, H, J are the midpoints on AB, BC, AC sides respectively.

Then, AH, CG, BJ are the medians and they are intersect at the point P.

P is the centroid of the triangle.

Given, GP =2.2 we have  to find the PC and GC.

We know that the centroid divided the median in 2:1 ratios.

i.e., AP:PH = CP:PG = BP:PJ = 2:1

We know , GP = 2.2, then, [tex]\frac{CP}{PG} = \frac{2}{1}[/tex]

⇒CP= 2(2.2)= 4.4then, GC = GP+PC= 2.2 + 4.4= 6.6.

Hence, the length of PC and GC is 4.4 and 6.6 respectively.

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Answer:

Step-by-step explanation:

Since the side lengths are proportional, the ratio of the width to length in the old phone will be equal to the ratio of the width to length in the new phone. That is:

(width of old phone) / (length of old phone) = (width of new phone) / (length of new phone)

We know the length of the old phone is 1.41.4 inches, and the width is 2.82.8 inches, so we can use that information to solve for the width of the new phone:

(2.82.8 inches) / (1.41.4 inches) = (width of new phone) / (1.611.61 inches)

Cross multiplying, we get:

(width of new phone) = (2.82.8 inches) * (1.611.61 inches) / (1.41.4 inches)

Using a calculator, we can find that the width of the new phone is approximately 3.23.2 inches.

Answer:

-19 > k

Step-by-step explanation:

-4 > k + 15

Subtract 15 from each side.

-4-15 > k + 15-15

-19 > k

Any value less than -19 would make this statement true

Answer:

- 19 > k

Step-by-step explanation:

- 4 > k + 15

Subtract 15 from both sides.

- 4 - 15 > k

- 19 > k

Answer:

32 markers

Step-by-step explanation:

Ty has 8 x 3 = 24 markers.

Together, they have 8 + 24 = 32 markers.

Answer:

-2,-4,-8,-16

common ratio of geometric sequence shown is -2

this sequence is in the decreasing form.

the next number in this sequence is -32

I hope that helps.

The area and perimeters of the shapes are: (1) Area = 702 ft², perimeter = 96 ft (2): Area = 20 in² Perimeter = 21 in

Perimeter is the distance round the object while the area is the floor space the object occupies

1) Area =  (l*w) + (L*W)

Area = (6*9)  + (24*27)

Area = 54 + 648

Area = 702 ft²

ii) perimeter = 24+27+30+9+6= 96 ft

2)  Area =  (l*w) + (L*W)

Area = (2*3) +( 7*2)

Area = 6+14 = 20 in²

ii) perimeter =2+7+2+2+3+2+3 = 21 in

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With an area of 11,224 square feet and the dimensions of the screen if it is 30 feet longer than it is wide, the width of the screen is 91.5 feet, and the length of the screen is 121.5 feet.

Let's call the width of the screen "w". Then, the length of the screen would be "w + 30". The area of the screen is 11,224 square feet, so we can set up an equation:

w * (w + 30) = 11,224

Expanding the right side of the equation, we get:

w^2 + 30w - 11,224 = 0

We can use the quadratic formula to solve for w:

w = (-b ± √(b^2 - 4ac)) / 2a

Where a = 1, b = 30, and c = -11,224.

Plugging in the values, we get:

w = (-30 ± √(30^2 - 4 * 1 * -11,224)) / 2 * 1

= (-30 ± √(900 + 44,896)) / 2

= (-30 ± √(45,796)) / 2

= (-30 ± 213) / 2

Taking the positive solution, we get:

w = (183 / 2) = 91.5 feet

So the width of the screen is 91.5 feet, and the length of the screen is 91.5 + 30 = 121.5 feet.

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Hexagonal prism A has a surface area of 43 cm2.

A three-dimensional shape's surface area is the total area on its surface. A cuboid's surface area is calculated by adding the areas of each of its six rectangular sides. The cuboid's length, width, and height may all be identified, and the formula SA=2lw+2lh+2hw can be used to determine its surface area (SA).

The surface area of a hexagonal prism is given by the formula:

SA = 2B + PH

where B is the base's surface area, P is its perimeter, and H is the prism's height.

Since prism B is a dilation of prism A with a scale factor of 2, its surface area is four times the surface area of prism A. So we can write:

SA_B = 4×SA_A

where SA_B is the surface area of prism B and SA_A is the surface area of prism A

We are given that SA_B = 172 cm², so we can substitute this value into the equation above to find SA_A:

172 = 4×SA_A

SA_A = 43 cm²

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Answer:

Os = {W, X, Y, Z}

Step-by-step explanation:

The sample space for the experiment is the set of all possible outcomes, in this case, W, X, Y, and Z. It represents all the outcomes that can occur in a single trial of an experiment. The sample space is usually denoted as a set, and the elements in the set are the individual outcomes. In this case, the sample space is the set {W, X, Y, Z}.

Answer:

the answer is the last one

Step-by-step explanation:

os= {w, x, y, z}

Answer: 11.7 in.

Step-by-step explanation:

I don't really know this stuff myself since I'm in 8th grade, but I can say that AA is 12in. long. I measured the length of A'C, and it was a little shorter than AA. So therefore, I think the answer is 11.7 in. I just wanted to help you out.

I'm sorry, but I'm not sure what you mean by "Imagine math - item 92070." Can you please provide more context or clarification so I can assist you better?

Answer:

the slope is -6/-5

The equivalent to the ratio 1:2 is 2 : 4

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

Ratio = 1 : 2

To determine the equivalent expression, we multiply each proportion of the ratio by the same number (say 2)

Using the above as a guide, we have the following:

Ratio = 2 * 1 : 2 * 2

Evaluate

Ratio = 2 : 4

Hence, the ratio is 2 : 4

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The possible values of the length of the rectangle is x > 34, the correct option is A.

For a rectangle with length and width L and W units, we get:

Area of the rectangle = [tex]L \times W \: \rm unit^2[/tex]

Perimeter of the rectangle = [tex]2(L + W) \: \rm unit[/tex]

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Given that width is 8 inches less than the length x

Sum of length and width more than 60

Now, the length is x

Width is x-8

x-8+x>60

2x>60

x>30

Therefore, the length of rectangle will be  x > 34

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Answer:x=251

Step-by-step explanation:

Step 1: Subtract 8 from both sides of the equation.

Explanation: Subtracting 8 from both sides of the equation keeps the equality balanced.

Step 2: x = 251

Explanation: Subtracting 8 from both sides of the equation gives us

x = 259 - 8 = 251.

Answer:

Step-by-step explanation:

x = -251

The work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.

We can use Hooke's law to find the force required to stretch the spring 4 inches from its natural length:

[tex]F = kx[/tex]

where F is the force in pounds, x is the displacement in inches, and k is the spring constant in pounds per inch (which we want to find).

Since 18 foot-pounds of work is required to stretch the spring 4 inches, we know that the work done is equal to the potential energy stored in the spring:

[tex]W = (1/2) k x^2[/tex]

Solving for k, we get:

[tex]k = (2W) / x^2[/tex]

Plugging in the values for W and x, we get:

[tex]k = (2 * 18) / (4^2) = 2.25[/tex]

So the spring constant is 2.25 pounds per inch.

Now we can use Hooke's law again to find the force required to stretch the spring an additional 3 inches:

[tex]F = kx[/tex]

= [tex]2.25 * 3[/tex]

= 6.75 pounds

Finally, we can find the work required to stretch the spring an additional 3 inches:

[tex]W = (1/2) k x^2[/tex]

= [tex](1/2) * 2.25 * 3^2[/tex]

= 10.125 foot-pounds

Therefore, the work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.

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The length of town from the base of the cliff is 848.25 feet

Concept of height and distance

You can use trigonometry formulas to find height and distance from anything. If you know the distance from the Qutub Minar to your current location and the angle at which you can see the top of the Minar, you can find the altitude of the Qutub Minar. Use trigonometry to find the elevation. This is because the ground, minaret elevation, and contour lines all combine to form a 90 degree right triangle between the minaret and the ground.

The distance is usually the "base" of the right triangle formed by the minar's elevation and line of sight. The length of the horizontal plane also forms the base of a triangle parallel to the ground at a given height, so we know the distance. The line of sight forms the "hypotenuse" of a right triangle. Lines perpendicular to the ground form the "height" of the triangle.

To calculate elevation or depression you can use the following formulas:

sinθ = hypotenuse /height.

cosθ = hypotenuse /base,

tanθ = base /height

where θ is the elevation or depression angle.

and in this question the angle of depression is 23 degree and height is 360 feet and we have to calculate the base

tan 23 degree = 360/base

base  = 360/tan 23

=360/0.4244

= 848.25 feet.

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Answer: If there is a proportional relationship between the number of pitchers of lemonade Karen wants to make, x, and the number of lemons she needs, y, and the equation modeling this relationship is y = 5x, then we can find the number of pitchers Karen can make with 15 lemons by solving for x:

15 = 5x

Dividing both sides by 5:

3 = x

So Karen can make 3 pitchers of lemonade with 15 lemons.

Step-by-step explanation:

Range, interquartile range, standard deviation, and variance are four measures of variability that can be used to compare two data sets.

area:

Difference between highest and lowest values.

Range is the straightforward allowance to calculate variability. To asset the area, follow these steps:

Sort all the values ​​in the dataset from lowest to highest.

Subtract the lowest value from the highest value. Interquartile range:

area of ​​the middle half of the distribution

standard deviation:

mean distance from mean

Standard deviation is a useful measure of the variance of a normal distribution.

A normal distribution distributes data symmetrically without skew. Most of the values ​​are clustered around the central region, with values ​​tapering away from the center. Standard deviation indicates how far the data are, on average, from the center of the distribution.

deviation:

mean squared distance from mean 

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