In the marching band at Hometown High, there are 77 woodwinds and 88 brass. If there is an equal number of woodwind and brass musicians in each row, what is the greatest number of rows in a performance? A) 9 rows B) 11 rows C) 13 rows D) 15 rows

Probabilities are used to determine the chances of an event

The value of P(a and b) is 0.21

The given parameters are:

P(a) = 0.62

P(b) = 0.47

P(a or b) = 0.88

P(a and b) is calculated using the following formula

P(a and b) = P(a) + P(b) - P(a or b)

So, we have:

P(a and b) = 0.62 + 0.47 - 0.88

P(a and b) = 0.21

Hence, the value of P(a and b) is 0.21

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Final answer:

To find the remainder when dividing x^4-3x^2-9x+4 by x-3, substitute x=3 into the polynomial and calculate the expression.

Explanation:

To find the remainder when dividing x^4-3x^2-9x+4 by x-3, we can use the Remainder Theorem. According to the theorem, if we substitute the opposite of the divisor into the polynomial, the remainder will be the value we get.

So, substitute x = 3 into the polynomial:

3^4 - 3(3)^2 - 9(3) + 4

Calculating this expression, we find that the remainder is 142.

To calculate this, firstly we need the initial lead of the robbers in miles before the police starts to chase, which is the product of the speed of the robbers and the time before the police starts to chase. Given that the speed of robbers is 66 mph and the time before the police chase is 0.5 hours, multiplying these gives a robber lead of 33 miles.

Next, to determine how quickly the police can close this gap, we need to calculate the relative speed of the police helicopter compared to the robbers. The speed of the police is 132 mph and the speed of the robbers is 66 mph, the difference between these two speeds is the relative speed. So, 132 mph - 66 mph gives a relative speed of 66 mph.

Finally, the time it will take for the police to catch up to the robbers - the catchup time - is the ratio of the initial lead of the robbers to the relative speed of the police. Here it is 33 miles divided by 66 mph, this yields a catchup time of 0.5 hours.

Therefore, it will take the police 0.5 hours to overtake the robbers.

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48/75

 both numbers are divisible by 3

 so it simplifies to 16/25

Answer:

90 and 283

Step-by-step explanation:

0.7/10 = 0.07

1.05 / 15 = 0.07

1.40 / 20 =0.07

1.75/25 = 0.07

 yes it is proportional ( they all equal the same when divided)

 proportion =  0.07

 Part B) y = 0.07x

The end behavior of the function f(x) = 2x³ – 26x – 24 can be described as:

As x → -∞, y →-∞ and as x→∞, y →∞.

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

To determine the end behavior of the polynomial function f(x) = 2x³ – 26x – 24, we need to examine the degree of the polynomial and the sign of its leading coefficient.

The degree of the polynomial is 3, which means it is an odd-degree polynomial.

The sign of the leading coefficient is positive (+2). These two pieces of information tell us that the end behavior of the graph will be as follows:

As x becomes very large in the positive direction, the values of the function will also become very large in the positive direction.

As x becomes very large in the negative direction, the values of the function will become very large in the negative direction.

Therefore, as x → -∞, y →-∞ and as x→∞, y →∞.

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The ratio which is used to convert 2.5 centimeters to meters is : (d) 1 meter/100 centimeter.

To convert 2.5 centimeters to meters, we choose the ratio that relates centimeters to meters,

The correct ratio to use in this case is 1 meter/100 centimeters,

This ratio states that there are 100 centimeters in 1 meter.

To convert centimeters to meters, we divide the given measurement (2.5 centimeters) by the ratio of 1 meter/100 centimeters.

Using this ratio, we have:

2.5 centimeters × (1 meter/100 centimeters) = 2.5/100 meters

2.5/100 = 0.025 meters,

So, 2.5 centimeters is equal to 0.025 meters.

Therefore, The correct answer is (d) 1 meter/100 centimeter.

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Answer:

You can display data in a histogram by labeling the x and y axis with your numbers provided. Then you put in the amount of numbers.

Answer:

Sample response: To create a histogram, first label the x-axis and choose the interval. Then calculate the frequency of each interval. Next, label the y-axis and determine the scale. Now create the bars. Draw bars the height of the frequency for each interval. Last, give the graph a title.

Step-by-step explanation:

Answer:

[tex]\frac{4}{5}\frac{cup}{liter}.[/tex]

Step-by-step explanation:

The problem says that Angela uses 2/3 cup strawberries to make 5/6 liter of smoothies. Then, to find the unit rate in cups of strawberrry per liter, that is cup/liter we need to divide both fractions:

[tex]\frac{\frac{2}{3}cup}{\frac{5}{6}liter} = \frac{2*6}{3*5}\frac{cup}{liter} = \frac{12}{15}\frac{cup}{liter}= \frac{4}{5}\frac{cup}{liter}.[/tex]

Then, the unit rate in cups of strawberry per liter is [tex]\frac{4}{5}\frac{cup}{liter}.[/tex] That is, Angela uses 4/5 cups of strawberry to do 1 liter of smoothie.

there are 4 9's in a deck

 so first pick = 4/52 reduces to 1/13

second pick there would be 3 9's left and 51 cards so it would be 3/51 reduces to 1/17

probability of both happening = 1/13 * 1/17 = 1/221 (fraction form)

 if you need it in decimal it = 1/221 = 0.00452, rounded to 0.005

Final answer:

To identify a basis for the row and column spaces of a matrix and determine its rank, one uses row reduction to reach REF or RREF. The non-zero rows of the RREF are the basis for the row space, the corresponding columns in the original matrix form the basis for the column space, and the rank is the number of these basis vectors. In statistics, the degrees of freedom for the Test of Independence is calculated as (number of columns - 1)(number of rows - 1).

Explanation:

To find a basis for the row space and column space of a matrix as well as the rank, you follow specific procedures. First, perform row reduction on the matrix to bring it to row echelon form (REF) or reduced row echelon form (RREF). The non-zero rows of the RREF correspond to a basis for the row space. The columns in the original matrix that correspond to the leading 1s in the RREF form a basis for the column space. The rank of the matrix is equal to the number of leading 1s in the RREF form, which is also the number of basis vectors for either the row space or column space since they have the same dimension.

The Test of Independence in statistics uses a contingency table to determine if two categorical variables are independent. The number of degrees of freedom for the test is given by the formula: (number of columns - 1)(number of rows - 1). This is critical when referencing the chi-squared distribution table to determine the p-value for the hypothesis test.

let x = hours

6x + 14x = 40

20x=40

x = 40/20 = 2 hours

1 pm + 2 hours = 3 pm

eastbound trains is going 14 miles per hour, 14 mph x 2 hours = 28 miles

 Answer is A. 3 pm and 28 miles

The eastbound train has traveled 28 miles and they met at 3:00 pm

Speed is the ratio of total distance to total time taken. It is given by:

Speed = distance / time

Let both cargo trains meet each other at time t.

For the train traveling west:

6 = d₁ / t

d₁ = 6t

For the train traveling east:

14 = d₂ / t

d₂ = 14t

Since both trains are 40 miles apart, hence:

d₁ + d₂ = 40

6t + 14t = 40

20t = 40

t = 2 hours

t = 3:00 pm (1:00 pm + 2 hours)

Distance travel by east bound train = d₂ = 14t = 14(2) = 28 miles

The eastbound train has traveled 28 miles and they met at 3:00 pm

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it would take 84 hours,or 3.5 days,hope this helps

The quadratic equation that can be used to find x the smaller number is x^2 + x - 272 = 0.

A quadratic equation is a polynomial which has the highest degree equal to two. It is a second-degree equation of the form ax² + bx + c = 0, where a, b, are the coefficients, c is the constant term, and x is the variable.

For the given situation,

Let the integer be x and the consecutive next integer be  x+1.

The product of two consecutive integers is 272,

⇒ [tex]x(x+1)=272[/tex]

⇒ [tex]x^{2} +x=272[/tex]

⇒ [tex]x^{2} +x-272=0[/tex]

Hence we can conclude that the quadratic equation that can be used to find x the smaller number is x^2 + x - 272 = 0.

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Answer:

The answer is A. -2.50

Step-by-step explanation:

Answer:

67.307 feet of rope per team

Step-by-step explanation:

The probability that the sample mean of 90 test takers falls within 10 points of the population mean of 502 is approximately 0.6578.

To find the probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the critical reading part of the test, we need to calculate the probability using the standard normal distribution.

Given:

- Population mean [tex](\(\mu\))[/tex]: 502

- Sample size[tex](\(n\))[/tex]: 90

- Standard deviation [tex](\(\sigma\))[/tex] of the population (assumed known or provided): Let's assume it is 100 (for example purposes).

We are looking for the probability that the sample mean[tex](\(\bar{X}\))[/tex] falls within 10 points of the population mean (502 ± 10).

Step 1: Calculate the standard error of the mean (SEM):

[tex]\[ SEM = \frac{\sigma}{\sqrt{n}} \][/tex]

[tex]\[ SEM = \frac{100}{\sqrt{90}} \][/tex]

[tex]\[ SEM = \frac{100}{9.4867} \][/tex]

[tex]\[ SEM \approx 10.548 \][/tex]

Step 2: Convert the deviation of ±10 points from the mean into a z-score using the standard normal distribution:

[tex]\[ z = \frac{\text{sample mean} - \mu}{SEM} \][/tex]

For the upper bound:

[tex]\[ z_{\text{upper}} = \frac{502 + 10 - 502}{10.548} \][/tex]

[tex]\[ z_{\text{upper}} = \frac{10}{10.548} \][/tex]

[tex]\[ z_{\text{upper}} \approx 0.9497 \][/tex]

For the lower bound:

[tex]\[ z_{\text{lower}} = \frac{502 - 10 - 502}{10.548} \][/tex]

[tex]\[ z_{\text{lower}} = \frac{-10}{10.548} \][/tex]

[tex]\[ z_{\text{lower}} \approx -0.9497 \][/tex]

Step 3: Find the cumulative probabilities using the standard normal distribution table or a calculator:

[tex]\[ P(-0.9497 \leq Z \leq 0.9497) \][/tex]

Using a standard normal distribution table or a calculator, find:

[tex]\[ P(Z \leq 0.9497) \approx 0.8289 \][/tex]

[tex]\[ P(Z \leq -0.9497) \approx 0.1711 \][/tex]

Step 4: Calculate the probability that the sample mean falls within 10 points of the population mean:

[tex]\[ P(-0.9497 \leq Z \leq 0.9497) = 0.8289 - 0.1711 \][/tex]

[tex]\[ P(-0.9497 \leq Z \leq 0.9497) = 0.6578 \][/tex]

Therefore, the probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 is approximately [tex]{0.6578} \).[/tex]

Answer:

Scientific notation of [tex](2.3\times 10^{-3})\times (3\times 10^{8})[/tex] is [tex]6.9\times 10^{5}[/tex] .

Step-by-step explanation:

As given the expression in the question be as follow .

[tex]= (2.3\times 10^{-3})\times (3\times 10^{8})[/tex]

Simplify the above terms

[tex]= 2.3\times 10^{-3}\times 3\times 10^{8}[/tex]

[tex]= 2.3\times 3\times 10^{-3}\times 10^{8}[/tex]

Now by using the exponent property

[tex]x^{a}\times x^{b} = x^{a + b}[/tex]

Thus apply this property in the above

[tex]= 6.9\times 10^{-3+8}[/tex]

[tex]= 6.9\times 10^{5}[/tex]

Therefore  scientific notation of [tex](2.3\times 10^{-3})\times (3\times 10^{8})[/tex] is [tex]6.9\times 10^{5}[/tex] .