2. Cornerstone High School has 1860 students.
45% of the students bike or walk to school.
372 students drive to school.
•The remaining students travel to school by bus.
How many students travel to school by bus?
a.651
6.837
c.1209
d.1443

El par ordenado (90, 60) tiene la misma pendiente que la línea y forma una relación proporcional con el punto dado.

El par ordenado que formaría una relación proporcional con el punto que se muestra a continuación es (90, 60). Para encontrar una relación proporcional en un plano coordenado, debemos encontrar dos puntos que tengan la misma pendiente.

La pendiente de una línea se calcula utilizando la fórmula (y2 - y1) / (x2 - x1).

Usando los puntos dados (0, 0) y (45, 30), podemos calcular la pendiente de la línea:

Pendiente = (30 - 0) / (45 - 0)

= 30 / 45

= 2 / 3

Ahora, podemos calcular la pendiente de cada uno de los pares ordenados dados y compararlos con la pendiente de la línea:

(10, 10):

Pendiente = (10 - 0) / (10 - 0)

= 10 / 10

= 1 (no es proporcional)

(25, 35):

Pendiente = (35 - 0) / (25 - 0)

= 35 / 25 = 7 / 5 (no es proporcional)

(70, 50):

Pendiente = (50 - 0) / (70 - 0)

= 50 / 70 = 5 / 7 (no es proporcional)

(90, 60):

Pendiente = (60 - 0) / (90 - 0)

= 60 / 90 = 2 / 3 (es proporcional)

Por lo tanto, el par ordenado (90, 60) tiene la misma pendiente que la línea y forma una relación proporcional con el punto dado.

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The binomial probability distribution is a ​Discrete probability distribution that describes probabilities for experiments in which there are two​ mutually exclusive outcome.

Discrete Probability Distribution:

A discrete probability distribution can be defined as a probability distribution that gives the probability that a discrete random variable has a given value. These distributions represent data with a finite number of possible outcomes. There are two conditions that a discrete probability distribution must satisfy.

1) 0 ≤ P(X = x) ≤ 1. This means that the probability of a discrete random variable X taking the exact value x is between 0 and 1.

2) ∑P(X = x)=1. The sum of all probabilities must be 1.

Mutually exclusive outcome:

Mutual Exclusive Outcome is a statistical term that describes two or more events that cannot occur simultaneously. It is commonly used to describe a situation where one result is replaced by another. For example, war and peace cannot coexist at the same time. This makes them mutually exclusive.

The concept of mutual exclusivity is often used in capital budgeting. A company may have to choose from several projects that, when completed, will add value to the company. Some of these projects are mutually exclusive.

For example, suppose a company has a budget of $50,000 for an expansion project. Projects A and B are mutually exclusive if available projects A and B each cost $40,000 and project C costs $10,000.

If a company is pursuing A, it cannot afford to bully B, and vice versa. Project C can be considered independent. Even if other projects go ahead, the company can still afford to do C. If neither A nor B accepts, the viability of C is not affected, and accepting C does not affect the viability of other projects.

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Answer: 34

Step-by-step explanation:

The result of multiplying the numbers 17 by 2 is 34.

When you multiply two numbers, you are essentially adding the first number to itself a certain number of times, determined by the second number.

In this case, when you multiply 17 by 2, you are adding 17 to itself two times:

17 + 17 = 34

Therefore, the result of multiplying 17 by 2 is 34.

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Answer:

81 2/3

Step-by-step explanation:

69 2/9 - ( - 12 4/9)

= 69 2/9 + 12 4/9

Add the whole parts to get 69 + 12 = 81

Add the fractional parts: 2/9 + 4/9 = 6/9 = 2/3

So
69 2/9 - (-12 4/9) = 81 2/3

a. The hypothesis test is right-tailed.

b. The P-value is 0.2525.

c. Using a significance level of a = 0.01, we fail to reject the null hypothesis .

a) The hypothesis test is right-tailed because the alternative hypothesis is p > 0.4.

b) To find the P-value, we need to use a standard normal distribution table or a calculator. Since the test statistic is positive, we look for the area to the right of z = 0.67. Using a standard normal distribution table or a calculator, we find that the area to the right of z = 0.67 is 0.2525. This is the P-value.

c) Using a significance level of a = 0.01, we compare the P-value to the significance level. The P-value is greater than the significance level, so we fail to reject the null hypothesis . There is not enough evidence to support the claim that p > 0.4 at the 1% significance level.

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The given question is incomplete, the complete question is :

The test statistic of z = 0.67 is obtained when testing the claim that p>0.4. a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the P-value. c. Using a significance level of a = 0.01, should we reject null hypothesis or should we fail to reject null hypothesis?

The compound interest at the end of 6 years is $1725.14

Compound interest is a type of interest that is calculated not only on the initial principal amount but also on any accumulated interest that has been added to the principal. In other words, the interest that is earned on the principal is added to the principal, and then interest is calculated on the new total.

The formula for compound interest compounded continuously is

A = Pe^rt

A = 1100e^(0.075 * 6)

A = $1725.14

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The equation of linear function which relate y to x is,

⇒ y = - 4x - 2

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 2, 6) and (- 1, 2).

Now,

Since, The equation of line passes through the points (- 2, 6) and (- 1, 2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (2 - 6) / (- 1 - (-2))

m = - 4 / 1

m = - 4

Thus, The equation of line with slope - 4 is,

⇒ y - 6 = - 4 (x - (-2))

⇒ y - 6 = - 4 (x + 2)

⇒ y = - 4x - 8 + 6

⇒ y = - 4x - 2

Therefore, The equation of linear function which relate y to x is,

⇒ y = - 4x - 2

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Answer:

it just dots that all

Step-by-step explanation:

no step need

The substitution method calculator online shows the substitution method's result for the pair of linear equations.

One way to solve a system of linear equations with one or more unknown variables in mathematics is the substitution method. For the purpose of solving simultaneous equations, the substitution method is regarded as an algebraic technique. By resolving the equations, this method allows one variable's value to be determined. Any of the preceding equations can be solved by replacing the first variable's value for another variable.

The substitution technique calculator should be used as follows:

Step 1: Type the linear equations' coefficients into the input field.

Step 2: Then, select "Solve" to see the outcome.

Step 3: Lastly, the output field will show the value of the variables x and y in the linear equations solved using the substitution approach.

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1)

The area of the electronic board on the scale drawing is 1800 cm².

2)

Using the scale factor 5:1.

Length:

1 = 50

5 = 250 cm

Width:

1 = 36 cm

5 = 180 cm

3)

The area of the actual electronic board is 45000 cm²

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

Scale factor = 5 : 1

Now,

Electronic board dimensions:

Length = 50 cm

Width = 36 cm

Now,

Area of the electronic board on the scale drawing.

= length x width

= 50 x 36

= 1800 cm²

Now,

Actual dimensions:

Length = 250 cm _____(1)

Width = 180 cm _____(2)

Using the scale factor 5:1.

1 = 50

5 = 250 cm

And,

1 = 36 cm

5 = 180 cm

Area of the actual electronic board.

From (1) and (2)

= 250 x 180

= 45000 cm²

Thus,

The area of the electronic board on the scale drawing is 1800 cm².

The area of the actual electronic board is 45000 cm²

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ABCD is rhombus with  m 25 = 3x+33 and m/2 = 4x-44, the value of the x is 14.4.

In a rhombus, opposite angles are equal, and the measure of an angle is half the measure of its intercepted arc. Therefore, we have:

m ∠B = m ∠D = 2(m ∠A) = 2(m ∠C)

Also, the sum of the measures of the angles in a quadrilateral is 360 degrees, so we have:

m ∠A + m ∠B + m ∠C + m ∠D = 360

Since ABCD is a rhombus, its diagonals bisect each other at right angles. Therefore, we have:

m ∠BAC + m ∠CBD = 90

Substituting the given angle measures, we get:

2(4x-44) + 2(3x+33) = 360 (using the fact that m/2 = 2m∠A)

8x - 88 + 6x + 66 = 180

14x - 22 = 180

14x = 202

x ≈ 14.4 (rounded to the nearest tenth)

Therefore, x ≈ 14.4.

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The fraction of the group who had a score of 35 or more is 20%.

A histogram is a graphical representation of the distribution of numerical data. It consists of a series of bars (or rectangles) that are aligned along an axis, typically the x-axis, with the area of each bar proportional to the frequency or count of data points that fall within a specific interval or bin on that axis. Histograms are commonly used in statistics and data analysis to show the frequency distribution of a dataset. They allow you to visualize the shape of the distribution, including the central tendency (mean, median, mode) and the spread (variance, standard deviation). Histograms can also be used to identify outliers, gaps, and patterns in the data. They are often used in quality control to identify defects, in finance to analyze stock prices, in biology to analyze population distribution, and in many other fields where numerical data needs to be analyzed and understood visually.

Here,

First, you need to determine the range of scores represented in the histogram. This should be indicated by the x-axis of the histogram. Next, you need to identify the bin or bins in the histogram that correspond to scores of 35 or more. A bin is a group or interval of scores. The height of each bin represents the frequency or count of scores in that interval. Once you have identified the bin(s) that correspond to scores of 35 or more, you need to sum the heights of those bins to get the total count or frequency of scores that are 35 or higher. Finally, you can divide the total count or frequency of scores that are 35 or higher by the total count or frequency of scores in the entire histogram to get the estimated fraction of the group who had a score of 35 or more.

For example, if the histogram represents the happiness scores of 100 people and the bin or bins that correspond to scores of 35 or more have a total count of 20, then the estimated fraction of the group who had a score of 35 or more is 20/100 = 0.2 or 20%.

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45 is 5 times as many as 9 and is 9 times as many as 5.

We have the following statement -

45 is x times as many as 9 and is y times as many as 5

We have to find x and y.

A number 'n' is 'a' times as many as 'b'. Then n equals to ?

n will be equal to -

n = ab

According to the question -

45 is x times as many as 9 and is y times as many as 5. Using the method shown above we can write two equations -

45 =  x 9     ---(1)

and

45 = y x 5     ---(2)

Now -

Solving both, we get -

x = 5 and y = 9

Hence, 45 is 5 times as many as 9 and is 9 times as many as 5.

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Answer: Half the side of NL from the original figure.

Step-by-step explanation:

When it is a scale factor of 1/2 all the sides are halved there fore nl is halved.

Answer:

Step-by-step explanation:

An equilateral right-angled triangle is impossible to draw. Equilateral means all the sides measure the exact same length. In a right triangle, by definition, the hypotenuse is longer than either of the other sides. so the last choice is the one you want.

Answer:

an equilateral right triangle cannot exist, all angles are 60° and therefore NOT right

Step-by-step explanation:

an equilateral right triangle cannot exist, all angles are 60° and therefore NOT right

With regards to the probabilities of getting each color in the game played by Larry and Jessica, the correct answer is B. No, the probabilities are NOT equally likely.

In the game being played by Larry and Jessica, the colors that can be picked by either person include:

The probability of picking blue is:

= Number of blue sections / Total sections

= 3 / 8

The probability of picking red is :

= 3 / 8

The probability of picking green is:

= 2 / 8

= 1 / 4

The probabilities are therefore not equally likely.

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In this case, when you have a subtraction of -7a^2 and then an addition of +10a^2, you can simplify the expression by adding the coefficients of the two terms that have the same literal and exponent.

So, you have:

-7a^2 + 10a^2

To add or subtract these terms, we need to have the same literal and exponent, which is the case here. The coefficients of the terms are -7 and 10, so we can add them to get:

-7a^2 + 10a^2 = 3a^2

Therefore, the simplified expression is 3a^2.

In summary, when you have terms with the same literal and exponent, you can add or subtract their coefficients to simplify the expression.

Answer:

1 cake

Step-by-step explanation:

12 slices = 2 cakes

6 slices = 1 cake

Ivan ran a total distance of 550 meters during football practice.

To calculate the total distance Ivan ran, we need to add up the distances he covered in each direction:

To find the total distance, we can add up the absolute values of each distance, since distance is a scalar quantity and is always positive:

Total distance = |300 m| + |(200 m)| + |50 m|

= 300 m + 200 m + 50 m

= 550 m

So Ivan ran a total distance of 550 meters during football practice.

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The reminder of F(x)  when it is  divided by x-3 by using the factorizing method is equal to 8.

The Remainder Theorem is a method to Euclidean polynomial division. According to this theorem, dividing a polynomial P(x) by a factor (x - a), which is not an element of the polynomial, yields a smaller polynomial and a remainder.

"f(x) is divided by (x - 3)" is the mathematical expression for the statement.

[tex]\frac{x^4 -5x^2-6x-10}{x-3}[/tex]

factorize the numerator in the above expression.

[tex]\frac{x^4-3x^3+3x^3-9x^2+4x^2-12x+6x-18+18-10}{x-3}[/tex]

Further simplify the above expression.

[tex](x^3+3x^2+4x+6) + \frac{8}{x-3}[/tex]

Thus, when f(x) is divided by (x - 3), the remaining is 8.

The Remainder Theorem starts with a polynomial, say p(x), where "p(x)" is a polynomial p with x as a variable. Then, according to the theorem, divide that polynomial p(x) by some linear factor x - a, where an is just some number. A lengthy polynomial division is performed here, yielding some polynomial q(x) (the variable "q" stands for "the quotient polynomial") and a polynomial remainder is r. (x). It may be stated as follows:

q(x) + r = p(x)/x-a (x)

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The spherical tanks of Eindhoven can hold a maximum of approximately 14,137 cubic meters of water.

The maximum amount of water that one of the spherical tanks of Eindhoven will hold can be found using the formula for the volume of a sphere:

V = (4/3) * π * [tex]r^3[/tex]

where V is the volume of the sphere, r is the radius of the sphere, and π is a constant equal to approximately 3.14159.

According to the Eindhoven website, the diameter of each spherical tank is 30 meters. The radius, therefore, is half of the diameter, which is:

r = 30/2 = 15 meters

Substituting this value into the formula for the volume of a sphere, we get:

V = (4/3) * π * [tex](15)^3[/tex]

V ≈ 14,137 cubic meters

When we round this to the closest integer, we obtain:

Maximum amount of water = 14,137 cubic meters

Therefore, one of the spherical tanks of Eindhoven can hold a maximum of approximately 14,137 cubic meters of water.

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Answer:

4.5%

Step-by-step explanation:

The total percentage decrease in the investor's stock account was 4.5%. This is calculated by taking the decrease in Company A (3%) and Company B (6%) and adding them together to get a total decrease of 9%. This percentage is then divided by two (since there are two companies) to get 4.5%.

Answer:4320

Step-by-step explanation:8% interest =108% which is equivalent to x1.08

4000 x 1.08 = 4320

The given sequence is an arithmetic sequence.

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed constant called the common difference to the previous term. A geometric sequence is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed constant called the common ratio.

In the given sequence

103.8 - 111 = -7.2

96.6 - 103.8 = -7.2

Similarly we can observe that each term is obtained by subtracting 7.2 from the previous term. Therefore, the common difference is -7.2, and the sequence is an arithmetic sequence.

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Factors of 47 are 1 and 47 which implies that it can only be divided by one and itself.

The number 47 is a prime number, which implies that it can only be divided by one and itself. As a result, the components of 47 are 1 and 47.

Generally, a number's factors are the positive integers that divide it evenly with no residual. The factors of 12 are, for example, 1, 2, 3, 4, 6, and 12, since each of these numbers can be divided into 12 without leaving a leftover.

Yet, there are only two elements in the case of prime numbers, such as 47, which are always 1, and the number itself. This is because, by definition, prime numbers have no divisors other than 1 and themselves.

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a) The economic order quantity is 300 units.

b) The annual holding costs are 3,750.

c) The annual ordering costs are 3,750.

d) The reorder point is 117 units.

To solve this problem, we can use the Economic Order Quantity (EOQ) model, which helps determine the optimal order quantity to minimize total inventory costs. The formula for EOQ is:

[tex]EOQ = \sqrt{((2DS/H)}[/tex]

where D is the annual demand, S is the setup cost per order, and H is the annual holding cost per unit.

a) Find the economic order quantity:

D = 15,000 units

S = 75 per order

H = 25 per unit per year

Substituting into the formula for EOQ:

[tex]EOQ = \sqrt{((2\times15000\times75)/25)} = \sqrt{90000} = 300 units[/tex]

Therefore, the economic order quantity is 300 units.

b) Find the annual holding costs:

To find the annual holding costs, we need to multiply the average inventory level by the holding cost per unit. Half of the EOQ can be used to compute the average inventory level.

Average inventory level = [tex]EOQ/2 = 300/2 = 150 units[/tex]

Annual holding costs = Average inventory level x Annual holding cost per unit

= [tex]150 \times25 = 3,750[/tex]

Therefore, the annual holding costs are 3,750.

c) Find the annual ordering costs:

To find the annual ordering costs, we need to divide the annual demand by the EOQ and then multiply by the setup cost per order:

Number of orders per year = Annual demand / EOQ =[tex]15,000 / 300 = 50[/tex] orders per year

Annual ordering costs = Number of orders per year x Setup cost per order

=[tex]50 \times75 = 3,750[/tex]

Therefore, the annual ordering costs are 3,750.

d) What is the reorder point?

The inventory level at which a new order ought to be placed is known as the reorder point. It is calculated as the lead time demand plus safety stock. The lead time demand is the demand during the lead time, which is 2 working days in this case. We can assume that the demand is evenly distributed over the 300 working days per year, so the lead time demand is:

Lead time demand = (Annual demand / 300) x Lead time = [tex](15,000 / 300) \times 2 = 100 units[/tex]

The safety stock is the buffer inventory kept to cover unexpected demand during the lead time. The safety stock depends on the desired service level and the variability of demand and lead time. Assuming a 95% service level and a normal distribution of demand and lead time, we can use the z-score corresponding to a 95% service level, which is 1.645. The standard deviation of demand during the lead time can be estimated as the square root of the lead time demand:

Standard deviation of demand during lead time = [tex]\sqrt{100}[/tex] = 10 units

The safety stock is then:

Safety stock = z-score x Standard deviation of demand during lead time

= [tex]1.645 \times 10 = 16.45[/tex] units (rounded up to 17 units)

Therefore, the reorder point is:

Reorder point = Lead time demand + Safety stock

= [tex]100 + 17 = 117[/tex]units

Therefore, the reorder point is 117 units.

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The length of the leg of the 45-45-90 triangle is 6.

In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle.

The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

In a 45-45-90 triangle, the length of each leg is equal to x, and the length of the hypotenuse is √2 times the length of a leg.

So if the hypotenuse is 6√2, then each leg has length:

x = (6√2)/√2 = 6

Hence, the length of the leg of the 45-45-90 triangle is 6.

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The value of x after the following code 'int x = 10; for (int y=5; y<20; y = 5) x = y' is executed will be 5.

The given for loop initializes the variable y to 5, then checks if y is less than 20, and then sets y to 5 again in each iteration. This means that the loop will execute only once with the value of y being 5, and after that, the loop condition will always be false because y is never incremented or changed in any way.

During the execution of the loop, the value of y is assigned to the variable x. Therefore, after the loop, the value of x will be 5.

So, the final value of x will be 5.

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