The length of the sides of a rectangle are 60 and 91 centimeters. The is the length of the diagonal?

The volume of the quarter-sphered sized tank is approximately 490,490 cubic feet.

To find the volume of the quarter-sphered sized tank, we need to first calculate the volume of a sphere and then divide it by 4.

The formula for the volume of a sphere is V = (4/3) * π *\(r^3\), where V represents volume and r represents the radius.

Given that the radius of the main tank is 70 feet, we can substitute this value into the formula.

V = (4/3) * π * \(70^3\)
V = (4/3) * π * 343,000

Now we can calculate the volume.

V = (4/3) * 3.14 * 343,000
V ≈ 1.43 * 343,000
V ≈ 490,490

Since we want the answer rounded to the nearest whole number, the volume of the quarter-sphered sized tank is approximately 490,490 cubic feet.

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Answer: Because of the total number of DVDs given (36)the number of  individual type of DVD are coming in decimals such that

Number of comedy films =11.07

Number of Action films =22.15

and Number of horror  films =2.78

I also solved using total number of DVDs as 26 and the results were as follows

Number of comedy films =8

Number of acton films =16

and Number of horror  films =2

Step-by-step explanation:

Total number of DVD collection = 36

ratio of the type of DVD =comedy films to action to horror = 4:8: 1

Total ratio =4+8+1 = 13

Number of comedy films = ratio of comedy films/ total ratio x Total DVD collection

= 4/13 x 36= 11,.07 rounded to 11 comedy films

Number of action films = ratio of action films/ total ratio x Total DVD collection

= 8/13 x 36= 22.15 rounded to 22 action films

Number of horror films = ratio of horror films/ total ratio x Total DVD collection

1/13 x 36=2.78 rounded t0 3 Horror movies .

The numbers of each DVD are giving decimal numbers .

Using

Total number of DVD collection  as 26.

we have that

Number of comedy films= 4/13 x 26 = 8

Number of action films= 8/13 x 26= 16

Number of Horror films = 1/13 x 26 = 2

Answer:

y = 2x + 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x50=100

2x30=60

100x2=200

To determine which function grows faster between f(n) = (nlogn)^2 and g(n) = n^3, we can compare the rates of growth by analyzing the limits as n approaches infinity.

We will prove our answer by taking the limit of the ratio of the two functions. First, let's calculate the limit as n approaches infinity for the ratio f(n)/g(n). Using L'Hôpital's rule, we can differentiate both the numerator and denominator to simplify the expression. Taking the derivative of (nlogn)^2 results in 2nlogn(1 + logn), and differentiating n^3 gives 3n^2.

Now, we can evaluate the limit as n approaches infinity of the ratio (2nlogn(1 + logn))/(3n^2). By canceling out the common factor of n from the numerator and denominator, we are left with the limit of (2logn(1 + logn))/(3n). As n approaches infinity, the term 2logn(1 + logn) grows at a slower rate than n, while the denominator grows at a faster rate. Therefore, the limit of the ratio is 0.

Since the limit of f(n)/g(n) is 0, it implies that the function g(n) = n^3 grows faster than the function f(n) = (nlogn)^2 as n approaches infinity. In other words, the growth rate of n^3 surpasses the growth rate of (nlogn)^2, proving that g(n) grows faster than f(n).After evaluating the limit of the ratio f(n)/g(n) using L'Hôpital's rule and simplifying the expression, we determined that g(n) = n^3 grows faster than f(n) = (nlogn)^2. The proof is established by showing that the limit of the ratio is 0, indicating that g(n) outpaces the growth of f(n) as n approaches infinity.

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For the statement to happen, the number should be 2.

An algebraic expression is is defined as the combination of numbers and variables in solving a particular mathematical question. Variable, usually letters, are used to denote the unknown quantity.

Let x = number

Based on the information given, add the number to the numerator of 11/35 and add twice the number to the denominator of 11/35, and the result should be equal to 1/3.

Hence, (11 + x) / (35 + 2x) = 1/3.

Simplify and solve for the value of x.

3(11 + x) = (35 + 2x)

33 + 3x = 35 + 2x

3x - 2x = 35 - 33

x = 2

number = 2

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Answer:

1530 x 2.6

Step-by-step explanation:

Just multiply, 90 divided by 1530, multiply 1530 x 2.6

The volume of Ganymede is approximately 3.48 times the volume of the Moon, based on the given diameters of the two moons and the formula for the volume of a sphere.

The volume of a sphere is the amount of space occupied by the sphere in three-dimensional space. It can be calculated using the formula V = (4/3)πr³, where V is the volume of the sphere, r is the radius of the sphere, and π (pi) is a mathematical constant approximately equal to 3.14159. This formula states that the volume of a sphere is four-thirds of the product of pi and the cube of the sphere's radius.

In the given question,

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. Since we are given the diameters of the two moons, we can calculate their radii by dividing the diameters by 2. Therefore, the radius of Ganymede is 3,388/2 = 1,694 km, and the radius of the Moon is 1,245/2 = 622.5 km.

Now, we can calculate the volumes of the two moons:

V_Ganymede = (4/3)π(1694)³ ≈ 7.66 x 10^10 km³

V_Moon = (4/3)π(622.5)³ ≈ 2.2 x 10^10 km³

To find how many times larger Ganymede's volume is compared to the Moon's volume, we can divide the volume of Ganymede by the volume of the Moon:

V_Ganymede / V_Moon ≈ (7.66 x 10¹⁰) / (2.2 x 10¹⁰) ≈ 3.48

Therefore, the volume of Ganymede is approximately 3.48 times the volume of the Moon.

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By evaluating the polynomial, we will see that the sign on the interval [-4, 2] is negative.

Here we have the polynomial:

f(x) = (x - 2)*(x + 4)*(x + 5).

You can see that the roots of the polynomial are at:

x = 2

x = -4

x = -5.

Then, on the interval [-4, 2], the sign of the polynomial don't change. So to get the sign of f(x) on that interval we can just evaluate it in any value of x that belongs to the interval, for example, x = 0.

f(0) = (0 - 2)*(0 + 4)*(0 + 5) = -2*4*5 = -40

With this, we can conclude that the sign of f(x) on the given interval is negative.

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Answer:

always negative

Step-by-step explanation:

Given statement solution is :- The t-statistic associated with the test is approximately -0.28.

The t-statistic, which is used in statistics, measures how far a parameter's estimated value deviates from its hypothesised value relative to its standard error. Through the Student's t-test, it is utilised in hypothesis testing. In a t-test, the t-statistic is used to decide whether to accept or reject the null hypothesis.

To find the t-statistic associated with the test, we need to calculate the test statistic using the estimated slope coefficient, the null hypothesis, and the standard error.

The estimated slope coefficient is 4.93.

The null hypothesis is H₀: β₁ ≥ 5.14 (stating that the true slope coefficient is greater than or equal to 5.14).

The predicted slope's standard error is 0.74.

The formula to calculate the t-statistic is:

t = (estimated slope - hypothesized slope) / standard error

Plugging in the values:

t = (4.93 - 5.14) / 0.74

t = -0.21 / 0.74

t ≈ -0.28 (rounded to two decimal places)

Therefore, the t-statistic associated with the test is approximately -0.28.

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The constant of variation between time and speed is 22.

The time it would take to drive the fixed distance at a speed of 23 km/h is approximately 0.96 hours or 57.6 minutes.

Given that,

The time required to drive a fixed distance varies inversely as the speed.

It takes 1 hour to drive a fixed distance at a speed of 22 km/h.

The question asks for the time it will take to drive the same distance at a speed of 23 km/h.

Use the formula for inverse variation:

t = k/r,

Where t is the time,

r is the speed, and

k is the constant of variation.

We know that when r = 22 km/h,

t = 1 hour.

So we can plug in these values and solve for k:

1 = k/22

k = 22

Now use this value of k to find the time it takes to drive the same distance at a speed of 23 km/h:

t = 22/23

t ≈ 0.96 hours, or about 57.4 minutes.

So the answer is approximately 0.96 hours or 57.4 minutes.

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Answer:

m∠1 is 49° and m∠3 is 49°

Step-by-step explanation:

In the given figure

∵ There are 2 parallel lines

∵ A transversal cuts them

∴ ∠4 and ∠8 are corresponding angles

→ Corresponding angles are equal in measures

∴ m∠4 = m∠8

∵ m∠8 = 131°

∴ m∠4 = 131°

∵ ∠1 and ∠4 formed a pair of linear angle

∵ The sum of the measures of the linear angles is 180°

∴ m∠1 + m∠4 = 180°

→ Substitute ∠4 by 131°

∴ m∠1 + 131° = 180°

→ Subtract 131 from both sides

∵ m∠1 + 131 - 131 = 180 - 131

∴ m∠1 = 49°

∵ ∠1 and ∠3 are vertically opposite angles

∴ m∠1 = m∠3

∵ m∠1 = 49°

∴ m∠3 = 49°

The number of blueberries sold is B = 171 blueberries

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number of blueberries sold be B

Now , the total number of muffins = 380 muffins

The total percentage of chocolate chunk = 15 % of the total

So , the number of muffins that were chocolate chunk = ( 15/100 ) x 380

The number of muffins that were chocolate chunk = 57 chocolate chunk

The number of muffins that were banana nut = ( 2/5 ) of the total

The number of muffins that were banana nut = 152 banana nuts

And , the remaining trees were blueberry

So , on simplifying the equation , we get

The number of blueberries = 380 - number of muffins that were banana nut - number of muffins that were chocolate chunk

The number of blueberries = 380 - 152 - 57

The number of blueberries = 171 blueberries

Hence , the number of blueberries is 171

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The solution to the literal equation is y = x - 2.

To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.

From the given information:

4x + 1 = 9 + 4y

To solve for y, we have to switch the sides:

9 + 4y = 4x + 1

Subtract 9 from both sides

9 - 9 + 4y = 4x + 1 - 9

4y = 4x - 8

Divide both sides by 4

\(\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}\)

y = x - 2

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To send the frequency distribution data to Excel, you can follow these steps:

1. Open Excel on your computer.

2. Create a new worksheet or open an existing one where you want to import the data.

3. Label the first column as "Number of Tests Performed" and the second column as "Number of Patients".

4. In the first column, enter the values 0, 1, 2, 3, and 4 or more in separate cells, corresponding to the number of tests performed.

5. In the second column, enter the corresponding values 14, 8, 4, 4, and 2, which represent the number of patients for each category of tests.

6. Select both columns by clicking and dragging over the cells.

7. Go to the "Copy" option in the Excel toolbar or use the Ctrl+C keyboard shortcut to copy the selected data.

8. Switch to the Excel worksheet where you want to paste the data.

9. Select the first cell where you want to paste the data.

10. Right-click on the cell and choose the "Paste" option or use the Ctrl+V keyboard shortcut to paste the data.

Now, the frequency distribution data from the emergency room tests should be successfully transferred to Excel.

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Answer:

Step-by-step explanation:

3x+ 50= 6x-10

50+10=6x-3x

60=3x

x=20

Answer:

x = 20

Step-by-step explanation:

you can notice that those two are identical, so it's a basic equation

3x + 50 = 6x - 10

and now we can solve it by moving x'es to one side and number to the other (remembering that when you do that you need to change the sign, so if there is "-" then change to "+"):

50 = 6x - 10 - 3x

50 = 3x - 10

50 + 10 = 3x

60 = 3x

20 = x

Answer:

(z+7)*(z+4)

Step-by-step explanation:

The first term is,  z2  its coefficient is  1 .

The middle term is,  +11z  its coefficient is  11 .

The last term, "the constant", is  +28

Step-1 : Multiply the coefficient of the first term by the constant   1 • 28 = 28

Step-2 : Find two factors of  28  whose sum equals the coefficient of the middle term, which is   11 .

     -28    +    -1    =    -29

     -14    +    -2    =    -16

     -7    +    -4    =    -11

     -4    +    -7    =    -11

     -2    +    -14    =    -16

     -1    +    -28    =    -29

     1    +    28    =    29

     2    +    14    =    16

     4    +    7    =    11    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  4  and  7

                    z2 + 4z + 7z + 28

Step-4 : Add up the first 2 terms, pulling out like factors :

                   z • (z+4)

             Add up the last 2 terms, pulling out common factors :

                   7 • (z+4)

Step-5 : Add up the four terms of step 4 :

                   (z+7)  •  (z+4)

            Which is the desired factorization

Rounding off the 1004.8 into 3 significant figures will give 1000.

Since significant figures are established as digits, they are also known as significant digits. By counting all of the values beginning with the first non-zero digit on the left, it is possible to determine the number of significant digits.  

For example, the number of significant figures in 567 is 3.
The number of significant figures in 2.671 is 4.  

Here we have a number    

1004.8 need to be rounded off for 3 significant figures  

Since 4 is less than 5 then the resultant number = 1000  

[ 4 and 8 neglected since 4 < 5]

Therefore,

Rounding off the 1004.8 into 3 significant figures will give 1000.

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The unit of measurement used is A. Standard deviation is the unit of measurement used to describe how far a set of values are from the mean.

The degree of variation of data from the average, or mean, is gauged by the standard deviation. It provides us with information on the average amount by which each data point diverges from the mean.

A lesser standard deviation suggests that the data points gather closely around the mean, whereas a greater standard deviation signifies that the data points are further dispersed. To standardize a value, we subtract the mean from the value and then divide by the standard deviation.

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The inequality expression 9|x - 8| < 36 when solved for x is 4 < x < 12

To solve the inequality 9|x - 8| < 36, we can divide both sides by 9:

|x - 8| < 4

This means that the distance between x and 8 is less than 4. So, the solution can be expressed in two parts:

x is less than 4 units away from 8 to the left:

x < 8 - 4 = 4

x is less than 4 units away from 8 to the right:

x > 8 + 4 = 12

Therefore, the solution is 4 < x < 12, or in interval notation: (4, 12).

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Answer:

y = - 3x + 13

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, 4 ) and (x₂, y₂ ) = (5, - 2 )

m = \(\frac{-2-4}{5-3}\) = \(\frac{-6}{2}\) = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 4 )

4 = - 9 + c ⇒ c = 4 + 9 = 13

y = - 3x + 13 ← equation of line

Answer:

sin R = 20 / 29

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin R = opp / hyp

sin R = 20 / 29

Answer:

not trying to be mean i have no idea  please do not get mad at me i am 9 years old i want points so i am trying to awnser but it is hard for me i am in 4th grade.

Step-by-step explanation:

Answer:

-x + 1

Step-by-step explanation:

There are 3 terms in the given expression.  Apply the Distributive Property for Multiplication to the first and third:

2x + 4  - 7 - 3x + 4

Combining like terms, we get:  -x + 1

Answer:

x = 4

Step-by-step explanation:

Given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

To find k use the condition y = 24 when x = 6 , then

24 = 6k ( divide both sides by 6 )

4 = k

y = 4x ← equation of proportion

When y = 16, then

16 = 4x ( divide both sides by 4 )

4 = x

Answer:

Susan.

Step-by-step explanation:

If we find a common denominator for both fractions we can find the answer. 6 and 8 both go into 24 so,

5/6 x 4/4 = 20/24

5/8 x 3/3 = 15/24

From doing this we see Susan read more.

The value of P0.05 < 0.19658. We do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years.

According to the question we will set up Hypothesis

Null,  H0: U=26

Alternate, H1: U<26

Test Statistic

Population Mean(U)=26

Sample X(Mean)=24.4

Standard Deviation(S.D)=9.2

Number (n)=25

we use Test Statistic (t) = x-U/(s.d/√(n))

to =24.4-26/(9.2/√(25))

to =-0.87

| to | =0.87

Critical Value

The Value of |t α| with n-1 = 24 d.f is 1.711

We got |to| =0.87  & | t α | =1.711

According to this, we have to make a decision

Hence Value of  |to | < | t α |

P-Value: Left Tail -Ha : ( P < -0.8696 ) = 0.19658

Hence Value of P0.05 < 0.19658

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