Six identical circles fit inside the rectangle as shown below. If the rectangle has a width of 15
units and a height of 10 units, what is the radius of each circle?

The correct dosage to be administered is 5 ml.

To calculate the correct dosage to be administered, we can use the following formula:

Dose = (Desired dose / Stock strength) x Stock volume

In this case, the desired dose is 15 mg and the stock strength is 10 mg/0.5 ml. Therefore:

Dose = (15 mg / 10 mg/0.5 ml) x Stock volume

Simplifying this expression, we get:

Dose = 3 x Stock volume

To find the stock volume needed, we can rearrange this formula as follows:

Stock volume = Dose / 3

Substituting the values we have, we get:

Stock volume = 15 mg / 3 = 5 ml

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Answer:Therefore, the total number of players on the team is 21.

Step-by-step explanation:Let's start by using algebra to represent the information given in the problem.

Let p be the total number of players on the team.

The number of players who chose water is given as 14.

This is also equal to 2/3 of the total number of players, so we can write:

14 = (2/3) * p

To solve for p, we can isolate it on one side of the equation by multiplying both sides by the reciprocal of 2/3, which is 3/2:

14 * (3/2) = (2/3) * p * (3/2)

21 = p

Answer:

( 6 + s ) ÷ 4

Step-by-step explanation:

MUST KNOW WHAT S IS TO SOLVE EQUATION

Answer:

  BD = √97 cm ≈ 9.849 cm

Step-by-step explanation:

Diagonal BD of rectangle ABCD is the hypotenuse of right triangle ABD. Opposite sides of the rectangle are the same length, so we have ...

  AB = 4 cm

  AD = 9 cm

The sides are related to the diagonals by the Pythagorean theorem.

The Pythagorean theorem tells you the relation between sides and hypotenuse of a right triangle:

  AB² +AD² = BD²

  4² +9² = BD² = 16 +81 . . . . . evaluating the squares

  BD = √97 . . . . . take the square root

The length of BD is √97 cm, about 9.849 cm.

Answer:

Step-by-step explanation:

(–5g^5 h^6)^2 × (g^4 h^2)^4        the ^ carot symbol means raised to power X

 (25 g^10 h^12) × (g^16 h^8)         exponents raised to powers MULTIPLY

  -5² = 25   g^5² = g^10  h^6² = h^12     do the same thing with   (g^4 h^2)^4

  25 g^(10+16) h^(12+8)                 collecting terms powers ADD

  25 g^26 h^20                         Which letter is the answer?  

                                                  Did you follow my explaination?

Answer:

B. –25g26h20

Step-by-step explanation:

The blanks are -2 and 0.5 respectively, by solving the expression (8 - 2x) *(-0.25x)

What does the term Algebraic Expression means?

In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.

Solution:

Given the expression, we need to solve it by using the properties of basic multiplication.

= (8 - 2x)*(-0.25x)

= (8*(-0.25x)) + (-2x * (-0.25x))

= -2x + 0.5\(x^{2}\)

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Answer:

$33,600

Step-by-step explanation:

2,800 x 12

Answer:

9

Step-by-step explanation:

because the shape is equal and 106 minus 97 is 9.

Answer:

9

Step-by-step explanation:

Those two angles should be equal to each other, so turn that into an equation.

106=x+97

Now solve for x

108-97 = 9

x=9

\(4( \frac{1}{5} x + 7) = 2x - 2\)

\(x = 25\)

confidence interval: This tells us the degree of certainty or uncertainty that is existent in a sampling method.

To construct a 95% confidence interval for the population mean cholesterol level, we can use the following formula:

CI = x ± t*(s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, and t is the t-value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%.

Substituting the given values, we have:

CI = 224 ± t*(12/√21)

Using a t-table with 20 degrees of freedom (since n-1=20), we find that the t-value for a 95% confidence interval is approximately 2.086.

Thus, the confidence interval is:

CI = 224 ± 2.086*(12/√21)

CI = (219.60, 228.40)

Therefore, the answer is option (c) (219.60, 228.40).

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Answer:

\(\{8,-8\}\)

Step-by-step explanation:

\(~~~-|x| = -8\\\\\implies |x| = \dfrac{-8}{-1}\\\\\implies |x| = 8\\\\\implies x = \pm 8\\\\\text{Hence, the solution set is}~ \{8,-8\}\)

Answer:

Step-by-step explanation:

y = k x

Total cost = y

number of pounds = x

constant = 0.59

Equation

y = 0.59 x

The first- and second order partial derivatives of the function f(x,y) = 3xy - 2xy² - x²y are:

∂f/∂x = 3y - 4xy - x², ∂f/∂y = 3x - 4xy - x²∂²f/∂x² = -4y, ∂²f/∂y² = -4x and ∂²f/∂y∂x = -4y.

Given function:

f (x,y) = 3xy - 2xy² - x²y

Let's find the first order partial derivatives.

1. First order partial derivative with respect to x.

Keep y constant and differentiate with respect to x.∂f/∂x = 3y - 4xy - x²2.

First order partial derivative with respect to y

Keep x constant and differentiate with respect to y.

∂f/∂y = 3x - 4xy - x²

Let's find the second order partial derivatives.

1. Second order partial derivative with respect to x.

Keep y constant and differentiate ∂f/∂x with respect to x.∂²f/∂x² = -4y2. Second order partial derivative with respect to y.Keep x constant and differentiate ∂f/∂y with respect to y.∂²f/∂y² = -4x3. Second order partial derivative with respect to x and y.

Keep x and y constant and differentiate ∂f/∂y with respect to x.∂²f/∂y∂x = -4y

From the above steps, we can say that the first order partial derivatives are:∂f/∂x = 3y - 4xy - x²and ∂f/∂y = 3x - 4xy - x²The second order partial derivatives are:

∂²f/∂x² = -4y∂²f/∂y² = -4x

and ∂²f/∂y∂x = -4y

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15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

Answer:

B

Step-by-step explanation:

Each successive shape in the sequence has one more side than the preceding shape. Therefore, the 6th shape in the sequence, an octagon, has 8 sides,beginning with a triangle which has 3 sides

The 6th shape in this pattern is an octagon, which has 8 sides. This pattern follows a sequence of shapes, beginning with a triangle which has 3 sides, followed by a square which has 4 sides, then a pentagon which has 5 sides, and so on. Each successive shape in the sequence has one more side than the preceding shape. Therefore, the 6th shape in the sequence, an octagon, has 8 sides.

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Answer:

Step-by-step explanation:

x + 2) = 2(x + 2)2 - 6(x + 2)

           = 2(x2 + 4x + 4) - 6(x + 2)

           = 2x2 + 8x + 8 - 6x - 12

           = 2x2 + 2x - 4

Answer:

39 miles per hour

Step-by-step explanation:

The equation is

Speed = distance/time

We take

117 / 3 = 39 miles per hour

So, the average speed is 39 miles per hour.

The equation to represent the percent h the day he spent doing homework on Monday is \(\frac{h}{100} = \frac{3}{24}\)

David spent 3 hours doing his homework on Monday. The equation that can be used  to find h, the percent of the day he spent doing homework on Monday can be found as follows:

We have 24 hours in a day. So, on Monday she uses 3 hours for her homework.

Therefore, the equation to represent the percentage h is as follows:

h = 3 / 24 × 100

h = 300 / 24

24h = 300

h = 300 / 24

h = 12.5%

Hence, the equation is as follows;

\(\frac{h}{100} = \frac{3}{24}\)

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Answer:

b = n + n

Step-by-step explanation:

Answer:

5x+12=36

Step-by-step explanation:

Answer:13

Step-by-step explanation:

Answer: He has 47 chairs

Step-by-step explanation:

if he has 7 left over from 8 rows, and 17 from 6 rows of the same length, thats 5 chairs per row that where taken away, 8-6=2, 17-7=10 10/2= 5

5 chairs per row x8 rows +7 extra chairs=47 chairs total

\(I \approx [1/(2^5\times 20) - 1/(2^7\times42) + 1/(2^9\times72)...]\)

This series provides an approximation for the definite integral I within the desired accuracy.

To approximate the definite integral \(I = \int_{0}^{1/2} x^3 arctan x dx\) within the indicated accuracy, we can use a series expansion for the function arctanx.

The series expansion for

arctanx = x - x³/3 + x⁵/5 - x⁷/7...............

Substituting this series expansion into the integral, we get:

\(I = \int_{0}^{1/2} x^3 (x - x^3/3 + x^5/5 - x^7/7....) dx\)

Expanding the expression and integrating each term, we obtain:

\(I = [x^5/20 - x^7/42 + x^9/72 - x^{11}/110....]^{1/2}_0\)

Evaluating the upper and lower limits, we have:

\(I = [(1/2)^5/20 - (1/2)^7/42 + (1/2)^9/72 - (1/2)^{11}/110....] - [0^5/20 - 0^7/42 + 0^9/72 - 0^{11}/110....]\)

Simplifying the expression, we get:

\(I \approx [1/(2^5\times 20) - 1/(2^7\times42) + 1/(2^9\times72)...]\)

This series provides an approximation for the definite integral I within the desired accuracy.

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Making "a" the subject of the formula would give us: a = 8 - b - c/2

Given the formula, 8 = a+b+c/2, to make a the subject of the formula, we would isolate a in the equation.

8 = a+b+c/2

8 = (2a + 2b + c)/2

2(8) = 2a + 2b + c

16 = 2a + 2b + c

16 - 2b - c = 2a

Divide both sides by 2

16/2 - 2b/2 - c/2 = 2a/2

8 - b - c/2 = a

a = 8 - b - c/2

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The variance-stabilizing transformation of Yi in linear regression can be found using the Fisher transformation. By taking the square root of the variance of Yi and dividing it by the expectation of Yi, we can apply the inverse hyperbolic tangent function to obtain the transformed Yi.

This results in the expression: tanh^-1(sqrt(V ar(Yi))/E[Yi]). This transformation is useful because it stabilizes the variance of Yi, making it easier to analyze and model. It allows us to make more accurate predictions and inferences about the relationship between the predictors and the response variable in linear regression.

We can find the variance-stabilizing transformation of Yi as follows:

1. Take the square root of both sides of the equation:
sqrt(V ar(Yi)) = sqrt((E[Yi])^2)

2. Simplify the equation:
sqrt(V ar(Yi)) = E[Yi]

3. Define the transformation function, T(Yi), which transforms Yi into the square root of its variance:
T(Yi) = sqrt(Yi)

So, the variance-stabilizing transformation of Yi is T(Yi) = sqrt(Yi). By applying this transformation, the relationship between predictors and Yi should exhibit more constant variance, improving the performance of the linear regression model.

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Answer: 10

Step-by-step explanation:

parenthesis first 9 - 15 + 8 x 2

multiply 8 x 2

you now have 9 - 15 + 16

subtract first because addition and subrtaction go in the order they're in the equation: 9 - 15 = -6

then add -6 + 16 = 10

The degrees of freedom for the numerator would be 4.

In a balanced single-factor ANOVA, the degrees of freedom for the numerator, also known as the treatment or between-group degrees of freedom, can be calculated as (number of groups - 1).

In this case, the ANOVA has 5 groups, so the degrees of freedom for the numerator would be 5 - 1 = 4.

The numerator degrees of freedom represent the variability between the group means. It indicates the number of independent pieces of information available to estimate the treatment effect. In other words, it measures the extent to which the groups differ from each other.

Having a larger degrees of freedom for the numerator allows for a more precise estimation of the treatment effect and increases the power of the statistical test. With 4 degrees of freedom for the numerator, we have more statistical information to assess the significance of the differences among the group means.

In summary, in a balanced single-factor ANOVA with 5 groups and each group having the same number of subjects (n = 10), the degrees of freedom for the numerator would be 4, representing the variability between the group means.

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The points that lie in the feasible region of this maximization problem are (-1,1) and (1,1).

The given constraints are: 14X + 4Y ≤ 28 and X − Y ≤ 2

In order to determine which of the points belong to the feasible region of this maximization problem, we need to check each point one by one. Let's evaluate each point and check which of the points lie in the feasible region. The points are given as below:x = −1, y = 2.5

The two constraints are:14X + 4Y ≤ 28 and X − Y ≤ 2

For the point (x,y) = (-1,2.5), we have:

14(-1) + 4(2.5) = 7 > 0;

Therefore, the point (-1,2.5) satisfies the first constraint.

Next, we need to check whether the point (-1,2.5) satisfies the second constraint:X − Y = -1 - 2.5 = -3.5 < 2

Since the second constraint is not satisfied, (-1,2.5) is not in the feasible region.

x = −1, y = 1

For the point (x,y) = (-1,1), we have:14(-1) + 4(1) = 10 > 0;

Therefore, the point (-1,1) satisfies the first constraint

.Next, we need to check whether the point (-1,1) satisfies the second constraint:X − Y = -1 - 1 = -2 < 2

Since the second constraint is satisfied, (-1,1) is in the feasible region.

x = 4, y = 2For the point (x,y) = (4,2), we have:14(4) + 4(2) = 64 > 0;

Therefore, the point (4,2) satisfies the first constraint.Next, we need to check whether the point (4,2) satisfies the second constraint:X − Y = 4 - 2 = 2 < 2

Since the second constraint is not satisfied, (4,2) is not in the feasible region.

x = 2, y = 1

For the point (x,y) = (2,1), we have:

14(2) + 4(1) = 32 > 0;

Therefore, the point (2,1) satisfies the first constraint.Next, we need to check whether the point (2,1) satisfies the second constraint:X − Y = 2 - 1 = 1 < 2

Since the second constraint is satisfied, (2,1) is in the feasible region.

x = 1, y = 1

For the point (x,y) = (1,1), we have:

14(1) + 4(1) = 18 > 0;

Therefore, the point (1,1) satisfies the first constraint.

Next, we need to check whether the point (1,1) satisfies the second constraint:X − Y = 1 - 1 = 0 < 2

Since the second constraint is satisfied, (1,1) is in the feasible region.

Hence, the two points that belong to the feasible region are (-1,1) and (1,1).

Therefore, the correct answer is: The points that lie in the feasible region of this maximization problem are (-1,1) and (1,1).

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