what is the ratio of basketball score to all scores right the simplest form. the baseball score is 45 the basketball score is 14 the football score is 21 the soccer score is 20

Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).

The statement about function g which is true is that: function g is exponential because g(x) changes by equal factors over equal intervals of x.

The slope of a line simply refers to the gradient of a line and it's typically used to describe both the ratio, direction and steepness of an equation of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

\(Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Slope = (40 - 10)/(2 - 1)

Slope = 30/1

Slope = 30

Slope = (160 - 40)/(3 - 2)

Slope = 120/1

Slope = 120.

Factor = 40/10 = 4

Factor = 160/40 = 4

Factor = 640/160 = 4.

Therefore, function g is exponential because g(x) changes by equal factors over equal intervals of x.

Read more on slope here: https://brainly.com/question/18028474

#SPJ1

Answer:

Step-by-step explanation:To solve this problem, we can use similar triangles. Let the side length of the cube be s, and let the midpoints of AB, AC, and BC be P, Q, and R, respectively. Then OP, OQ, and OR are the diagonals of the faces of the cube, and so they are equal to .Consider triangle AOB. By the Pythagorean theorem, we have , so . Since angle AOB is 90 degrees, we can use similarity to see that triangle OAP is similar to triangle OAB, so . Solving, we find that .Using similar triangles, we can find that . Since the sum of the squares of the lengths of the diagonals of a cube is equal to three times the square of the side length, we have

$$(0P2 + 0Q? + OR?) = 35388 Substituting the values we found for $OP$, $OQ$, and $OR$, we haveSimplifying and solving for , we find that . Thus, the side length of the cube inscribed in the tetrahedron is .

The annual interest is $22.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Given;

Amount invested= $550

Annual interest= 4%

SI= 550*4*1/100

=5.5*4

=22

Therefore, the simple interest will be $22.

Learn more about simple interest here;

https://brainly.com/question/1548909

#SPJ1

Step-by-step explanation:

100 nsmzmsmsmsmsmsmsnsnnsnsbsnjsjjsjsjsj

Answer:

[B]. (1,-5)

Step-by-step explanation:

Given:

\(\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}\)

Solve:

\(\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}\)        Since 2y - 2y = 0 we take that away now we have;

\(4x=-6\\3x=13\)        Add 4x + 3x = 7x

\(\frac{7x}{7} =\frac{7}{7}\) Divide both sides by 7.

\(x=1\)

Now substitute x to find y.

\(4(1)+2y=-6\)

\(4 + 2y =-6\)  Add 6 to the other side.

\(10 = 2y\) Divide both sides by 2.

\(\frac{10}{2} =\frac{2y}{2}\)

\(y = 5\)

Hence, the answer is [B]. (1,-5)

RevyBreeze

The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

For similar questions on set

https://brainly.com/question/13458417

#SPJ8

Answer:

Solving the expression \(\frac{3}{4}n=-1\frac{3}{4}n-18\) we get \(\mathbf{n=-\frac{36}{5} }\)

Step-by-step explanation:

We need to solve the expression: \(\frac{3}{4}n=-1\frac{3}{4}n-18\)

Solving:

\(\frac{3}{4}n=-1\frac{3}{4}n-18\)

First we convert mixed fraction into improper fraction

\(\frac{3}{4}n=-\frac{7}{4}n-18\)

Now adding 7/4 n on both sides

\(\frac{3}{4}n+\frac{7}{4}n=-\frac{7}{4}n-18+\frac{7}{4}n\\\frac{3}{4}n+\frac{7}{4}n=-18\)

Now, taking LCM on left side

LCM of 4 and 4 is 4

\(\frac{3}{4}n+\frac{7}{4}n=-18\\\frac{3*1n+7*1n}{4}=-18\\\frac{3n+7n}{4}=-18\\\frac{10n}{4}=-18\)

Now, multiply both sides by 4/10

\(\frac{10n}{4}\times \frac{4}{10} =-18\times \frac{4}{10}\\n=-\frac{36}{5}\)

So, solving the expression \(\frac{3}{4}n=-1\frac{3}{4}n-18\) we get \(\mathbf{n=-\frac{36}{5} }\)

Answer:

Quantity of juice = 300 milliliters

Step-by-step explanation:

Given the following data;

Total quantity of juice = 3 liters

Number of students = 10 students

To find the quantity of orange juice each student can get;

First of all, we would have to convert the total quantity (volume) of juice into a unit that's divisible by 10 i.e liters to milliliters.

Conversion:

1 liter = 1000 milliliters

3 liters = 3 * 1000 = 3000 milliliters

Next, we determine the quantity each student get;

Quantity of juice = 3000/10

Quantity of juice = 300 milliliters

Answer:

A.

tip: $6.12

total amount: $40.12

Answer:

A

Step-by-step explanation:

34.00 x .18 = 6.12

Take 18 and put a decimal in front of it and multiply it by the cost (34.00)

example if it were 20.00 and the tip was 5%

20.00 x .05

Answer:

178.5 actually

Step-by-step explanation:

Given:

The population is given as, P = 198,714.

The objective is to round off the digits and provide the required explanation.

Explanation:

1. If the population is rounded to the nearest ten thousand,

2. The digit placed in the ten thousands place is 9.

3. To round off the the digit placed in ten thousand, then the digit present before it, which is in thousands place must be considered.

4. In the given number 198,714, the digit present in thousands place is 8.

5. If the preceding digit is 5 or greater than 5, then the digit required to round off will increase up by 1.

6. If the number 9 is rounded up, it will increase by 1 and become 10.

7. If the value of the place is 10 or more, insert the once value of the two digit number at the same place and add the tens value of the two digit number to the successive digit of the given place value.

8. Since, the current value placed in ten thousands is 9 and the preceding value in thousands is more than 5, then the value 9 will increase by 1 and become 10.

9. The number 198714 rounded to nearest ten thousand is, 20000.

Given the condition regarding B and C being nonnegative real numbers, we can conclude \(|A|^2\) ≤ BC.

The given condition states that 0 ≤ B - 2 Re(λA) + |λ|^2 C for all complex numbers λ, which means that the real part of the expression is nonnegative. If C ≠ 0, we can choose λ = A/C and simplify the expression as follows:

Dividing both sides by C, we get

Multiplying both sides by C, we obtain

This means that |A|^2 is nonnegative and cannot be greater than BC.

Learn more about Complex Numbers:

https://brainly.com/question/5564133

#SPJ4

Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

Answer:

The 99% confidence interval is = 0.37 +/- 0.070

= (0.300, 0.440)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 37% = 0.37

Number of samples n = 315

Confidence interval = 99%

z value(at 99% confidence) = 2.58

Substituting the values we have;

0.37 +/- 2.58√(0.37(1-0.37)/315)

0.37 +/- 2.58√(0.00074)

0.37 +/- 2.58(0.027202941017)

0.37 +/- 0.070183587825

0.37 +/- 0.070

= (0.300, 0.440)

The 99% confidence interval is = 0.37 +/- 0.070

= (0.300, 0.440)

Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

Learn more about real return and stocks here: https://brainly.com/question/32228847

#SPJ1

Answer:

249.24

Step-by-step explanation:

Year Interest Total

Interest Balance

0 -- -- £200.00

1 £9.19 £9.19 £209.19

2 £9.61 £18.80 £218.80

3 £10.05 £28.85 £228.85

4 £10.51 £39.36 £239.36

5 £11.00 £50.36 £250.36

The computation shows that the number of pans needed will be 5/6.

From the information given, it should be noted that it was stated that 1/6 of a pan will be needed for one person.

Therefore, the pans that will be needed for the 5 friends will be:

= 1/6 × 5..

= 5/6

Learn more about computations on:

brainly.com/question/4658834

#SPJ1

The request dimensions of the rectangle for maximum area are,

Length of perimeter is, \(l = 41 m . ,\)

Width of perimeter is, \(w = 41m\)

The perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.

Let \(l\) and \(w\) denote the length and width of the Rectangle.

Its Perimeter is \(2(l+w)\), which is given to be, 164.

\(l+w\) = 164/2

\(l+w\) =82                         (Equation-1)

Now, Area \(A\) of the Rectangle, is, given by,

\(A = lw\)

We can substitute equation-1,

\(A = l(82-l)\)

\(A = 82l-l^{2}\)

which is a function of \(l\),

So let us,

Write it as,

\(A(l) = 82l-l^{2}\)                 (Equation-2)

We are request to maximize \(A\).

We know that, for \(A_{max}\), \(A^{|}l\) = 0 , and \(A^{||} l\) < 0

We can equation-2,

\(A^{|}l\) = 0 ⇒ \(82-2l = 0\)

\(l = \frac{82}{2}\)

\(l = 41\)

Further,

\(A(l) = -2\) < 0, ∀\(l\) , and  in particular, for \(l = 41\) , too.

Thus, \(l = 41\) gives \(A_{max}\)

Hence, the request dimensions of the rectangle for maximum area are,

\(l = 41 m . ,\) and \(w = 82 -l = 41m\)

Therefore,

The request dimensions of the rectangle for maximum area are,

Length of perimeter is, \(l = 41 m . ,\)

Width of perimeter is, \(w = 41m\)

To learn more about Perimeter visit :

brainly.com/question/6465134

#SPJ4

Answer:

a49%, 1/2,0.55,3/5

b)0.2,1/4,27%,3/10

c)9/10,95%,0.99,97/100

d)30%,1/3,0.6,2/3

e)0.09,10%,11/100,0.125

Answer:

below

Step-by-step explanation:

that is the procedure above

The expectation values are <x> = 1.25 x 10⁻¹⁰ ,  <x²>  =  2.07 x 10⁻²⁰

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

We need to find expectation value of <x> and < x²>

average value for <x>   is given by a/2   where a = length of box

hence <x> = ( (2.5 x 10⁻¹⁰) /2) = 1.25 x 10⁻¹⁰

hence <x²> = (1.25 x 10⁻¹⁰)²  = 1.56 x 10⁻²⁰

<x²> = ( a/2 x 3.14 x n)²   x ( 4 x 3.14² x n² /3  -2)

hence <x²>  = ( 2.5 x 10⁻¹⁰ / 2 x 3.14 x 5)²   x ( 4 x 3.14² x 5² /3  -2)

  <x²>  =  2.07 x 10⁻²⁰

<x²>  is not equal to <x>²

The expectation values are <x> = 1.25 x 10⁻¹⁰,  <x²>  =  2.07 x 10⁻²⁰

To learn more about the average from the given link

https://brainly.com/question/1136789

#SPJ4

Answer: The only solution to this is x = 0. Therefore, g(1) = 0 and g' (1) = g' (1) = 1/f ' (0) = 1/2.

Step-by-step explanation: Since, f(x) = 3x3 + 2x + 1, it follows that f ' (x) = 9x2 + 2.  So by the above theorem,

g' (1) = 1/f ' (g(1)) where f ' (g(1)) = 9 · g(1)2 + 2.

It remains to figure out what g(1) equals. Since g(x) = f -1 (x),  g(1) is the solution to

3x3 + 2x + 1 = 1 <----> (3x2 + 2)x = 0