find the area of a rectangle with the length 4/6cm and breadth 24/3

Answer:

47 students in each bus

Step-by-step explanation:

243-8= 235

235/5=47

Answer:

Option D: \(y= -\frac34x+14\)

Step-by-step explanation:

In order for two lines to be perpendicular, the product of the slopes has to be \(-1\). That allows you to rule out A and C. Let's plug the coordinate of the point in B. If the equality holds, we found or line. Else, it's D.

\(11 =-\frac34(4) +8 \rightarrow 11 = -3+8 \rightarrow 11=5\) Which is obviously impossible. Our line has to be D

The margin of error at 95% confidence is approximately 2.16.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To find the margin of error at 95% confidence, we need to use the following formula:

Margin of error = z * (σ/√n)

where:

z = the z-score associated with the desired level of confidence (in this case, 95% confidence corresponds to a z-score of 1.96)

σ = the population standard deviation

n = the sample size

Given that the population variance is 441, the population standard deviation is the square root of 441, which is 21.

So, the margin of error is:

Margin of error = 1.96 * (21/√361)

= 1.96 * (21/19)

= 2.16 (rounded to two decimal places)

Therefore, the margin of error at 95% confidence is approximately 2.16.

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The above equation equals -27

If 830 grams = 1 day.

23.24 kilograms = 4 weeks.

23.24 kilograms were used by Sebastian in those 4 weeks.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 3x = 4 is an equation.

We have,

830 grams is used each day.

830 grams = 1 day ___(1)

1 week = 7 days

Multiply 4 on both sides.

4 weeks = 28 days ___(2)

From (1) and (2) we get,

4 weeks = 28 days

4 weeks = 28 x 1 day

4 weeks = 28 x 830 grams

4 weeks = 23240 grams ____(3)

1000 grams = 1 kg

Multiply both sides by 23240/1000.

23240 grams = 23.24 kilograms _____(4)

From (3) and 94) we get,

4 weeks = 23.24 kilograms

Thus,

23.24 kilograms were used by Sebastian in those 4 weeks.

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Answer:

6w

Step-by-step explanation:

Multiply the constant by the coefficient.

2 times 3 is 6 and since there's a w beside 3, you'd have 6w.

The fraction that satisfies the problem is 20/24.

Equivalent fractions are fractions that have the same value, but different numerators and denominators.

If the fraction is equivalent to 5/6, then the numerator and denominator of the fraction is a multiple of 5 and 6, respectively.

Let x be the factor

fraction = 5x / 6x

If the sum of my numerator and my denominator is 44, then:

5x + 6x = 44

11x = 44

x = 4

fraction = 5x / 6x = 20/24

The final statement says that the sum of the digits in the denominator is 6.

2 + 4 = 6

Hence, the fraction is 20/24.

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Answer:

\(y=-3x+8\)

Step-by-step explanation:

\(-2x+6y=-4\\6y=2x-4\\y=\frac{1}{3}x+\frac{2}{3}\\\)

if two lines perpendicular,

\(m_{1} .m_{2}=-1\\ \frac{1}{3} .m_{2}=-1\\m_{2}=-3\)

the line perpendicular to this line is

\(y=-3x+k\) ; k ∈ R

the line passes through the point (5,-7)

so,

\(-7=-3.(5)+k\\-7=-15+k\\k=8\)

∴the equation of a line that passes through the point (5,-7) and is perpendicular to the line -2x+6y=-4 is

\(y=-3x+8\)

Answer:

Distance between Jackson and Symphony stations is 2.2 miles.

Step-by-step explanation:

From the given map,

Location of two stations can be represented by the ordered pairs Jackson(2, 4) and Symphony(1, 2)

Every unit of the map represents the distance of 1 mile.

Distance between two points is measured by the formula,

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)

Therefore, distance between the given stations will be,

d = \(\sqrt{(2-1)^2+(4-2)^2}\)

  = \(\sqrt{1+4}\)

  = \(\sqrt{5}\)

  = 2.236

  ≈ 2.2 miles

Distance between Jackson and Symphony stations is 2.2 miles.

Answer:

Exact form:

25/9

Decimal form:

2.(7)

Mixed fraction form:

2 7/9

Step-by-step explanation:

Hope you found this helpful

Answer:

(-5/3)² = 25/9

Step-by-step explanation:

(a/b)ⁿ = aⁿ / bⁿ

(-5/3)² = -5² / 3² = 25 / 9

On a postsynaptic membrane, the opening of K+ ion channel induces an IPSP (Inhibitory Postsynaptic Potential).

The potential changes in a neuron after the receptor and ion channel activation is called synaptic potential. This potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP).EPSP is a depolarizing potential that results from the opening of the Na+ ion channel. It causes a change in the potential of the neuron towards threshold level that may trigger an action potential.Ion channels and pumps in a postsynaptic neuron regulate the internal potential of the cell. In a typical postsynaptic cell, the resting potential (Vrest) is -70 mV, the threshold value is -55 mV, the reversal potential for Cl- ion (Ec) is -63 mV, the reversal potential for K+ ion (Ex) is -90 mV, and the reversal potential for Na+ ion (ENa) is 60 mV.The opening of Cl- ion channel leads to an inward flow of negative ions and thus results in hyperpolarization. The opening of K+ ion channel leads to an outward flow of K+ ions, and the membrane potential becomes more negative. Thus, it also results in hyperpolarization. The opening of a Na+ ion channel leads to inward flow of Na+ ions, which makes the cell more positive, and it is depolarization. Therefore, the opening of K+ ion channel leads to an IPSP, and it hyperpolarizes the neuron.

The postsynaptic potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP). The opening of the K+ ion channel leads to an outward flow of K+ ions, which makes the cell more negative and hyperpolarizes it, leading to IPSP.

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The probability of having one white ball is 1/20 or approximately 0.05.

To find the probability of selecting one white ball out of three balls, you need to know the number of white balls in the box and the total number of balls in the box. You also need to know whether the balls are being selected randomly or not.

Assuming that there is only one white ball in the box and the rest are some other color, and that the balls are being selected randomly.

The probability of selecting one white ball out of three would be:

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Since there is only one white ball, there is only one way to select one white ball out of three. The total number of ways to select three balls out of six is 6 choose 3, which is equal to 20.

Therefore, the probability of selecting one white ball out of three would be

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Probability = 1/20

Probability = approximately 0.05.

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Answer:

x ≤ -3

Step-by-step explanation:

3 - 5x ≥ 18

-5x ≥ 18 - 3

-5x ≥ 15

x ≤ -3

The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

The proportion of voters that approve the mayor's work is of 70%.

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Answer:

x = 2-√13/3

Step-by-step explanation:

In a standard normal distribution, the mean and the standard deviation are both 0 and 1, so  the correct answer to the given question is option b. 0 and 1.

Standard normal distribution: The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation

In a standard normal distribution, the correct answer to the given question is option b. 0 and 1. The standard normal distribution is a normal distribution curve where the values of the mean and standard deviation are 0 and 1 respectively

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The answer is that regression analysis is the most appropriate method.

The most appropriate statistical method to justify building a new elementary school in the district would be regression analysis. This method can be used to examine the relationship between the expected number of students and the capacity of the schools in the district.



Regression analysis is a statistical method that helps to determine the relationship between two or more variables. In this case, the expected number of students would be the independent variable, while the capacity of the schools in the district would be the dependent variable. By analyzing the relationship between these variables, the school district can make predictions about how many students will need to be accommodated in the future and whether a new elementary school is necessary.

In contrast, binomial distribution is a statistical method that is used to calculate the probability of a specific number of successes in a set of trials, which would not be suitable for this situation. Confidence intervals and hypothesis tests are statistical methods used to draw conclusions about populations based on sample data, but may not be the most appropriate method for this situation.

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The inequality representing the number of backpacks, x, that need to be sold each week for the factory to meet the profit goal is:

30x - 12,000 ≥ 980

To represent the situation, we need to consider the revenue and expenses associated with selling backpacks.

Let's break down the components:

Selling price per backpack: $40.00

Cost to make one backpack: $10.00

Operating expenses per week: $12,000.00

Profit goal per week: $980.00

To calculate the profit, we subtract the total cost (including both the cost to make the backpacks and the operating expenses) from the revenue obtained by selling the backpacks. The number of backpacks sold is denoted by 'x.'

Revenue from selling x backpacks: $40.00 × x

Total cost (including operating expenses) for x backpacks: $10.00 ×x + $12,000.00

The profit is given by the difference between revenue and cost:

Profit from selling x backpacks: Revenue - Total Cost

Profit from selling x backpacks: $40.00× x - ($10.00× x + $12,000.00)

To meet the factory's profit goal of at least $980.00, we set up the following inequality:

$40.00× x - ($10.00× x + $12,000.00) ≥ $980.00

Now we simplify the inequality:

$40.00× x - $10.00 × x - $12,000.00 ≥ $980.00

$30.00 × x - $12,000.00 ≥ $980.00

Thus, the inequality representing the number of backpacks, x, that need to be sold each week for the factory to meet the profit goal is:

30x - 12,000 ≥ 980

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The probabilities will be 0.1081 , 0.676, 0.863, 0.605 respectively.

let us consider, the chances of getting stem be a success(S) and not getting it be a failure(F) , and the total probability be 1 .

as per the statement 26% students are major in stem

total students selected randomly are 36.

∴ P(S) = 0.26

P( F)  = 1 - 0.26 = 0.74

Now the binomial probability of success is given by

\(P(x) = C^{n} _{x} S^{x} F^{n-x}\)

where C is for the combination formula

S is changes of success

F is chances of failure

x = no. of times success

n = total times the experiment done

From the provided information we can solve each case as follows :

A) exactly 7 of them major in stem

P(7) = \(C^{36} _{7} (0.26)^{7} (0.74)^{29}\)

   = 0.1081

B)at most 10 of them major in stem

it means P(0,1,2...10)

∴ P = P(0) + P(1) +......+P(10)

P = 0.676

C) at least 7 of them major in stem.

it means P(7,8,9...36)

∴ P = P(7) + P(8) + ...+ P(36)

P = 0.863

D) between 9 and 15 (including 9 and 15) of them major in stem.

In this case we subtract P(0,1,2...8) from P(0,1,2,...15)

and get P(9,10,11,...15)

∴ P(9,10,11,...15) =  P(0,1,2,...15)  -   P(0,1,2...8)

                        =  0.987  -  0.382

                        = 0.605

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The measure of a central angle is equal to the measure of the intersected arc.

Then, arc CD is equal to 55º

Arc EDC is equal to the sum of ars CD and DE:

Answer:

rate of change is 4.

Step-by-step explanation:

rate of change is the slope, so, pick any two relations given to us in the table.

(-3, -14) and (-1, -6).

slope = y2 - y1/ x2 - x1

slope = -6 - (-14)/-1-(-3)

slope = 8/2 = 4.

the rate of change is 4.

Answer:

9042.85 pounds

Step-by-step explanation:

12000×0.91^3

12000×0.753571

9042.85 pounds

Statement I is correct, while statements II and III are false. The longer-term bond (Bond L) fluctuates more due to its higher interest rate risk compared to the shorter-term bond (Bond S).

To calculate the value of Bond L and Bond S, we need more information, specifically the interest rate or yield associated with these bonds.

a. Bond prices are influenced by various factors, including the bond's face value, coupon payments, time to maturity, and prevailing interest rates. Without the interest rate or yield, we cannot determine the exact values of Bond L and Bond S.

The bond price can be calculated using the present value formula, which discounts the future cash flows of the bond to their present value.

b. The longer-term bond (Bond L) tends to fluctuate more when interest rates change compared to the shorter-term bond (Bond S) due to interest rate risk. Interest rate risk refers to the impact of changes in interest rates on the value of a bond.

I. Longer-term bonds have more interest rate risk than shorter-term bonds. This statement is true. Longer-term bonds are exposed to changes in interest rates for a more extended period, which makes their prices more sensitive to interest rate movements. When interest rates rise, the value of longer-term bonds tends to decrease more than shorter-term bonds.

II. Longer-term bonds have less reinvestment rate risk than shorter-term bonds. This statement is false. Reinvestment rate risk refers to the risk of reinvesting coupon payments at lower interest rates when the bond matures. Longer-term bonds have a higher reinvestment rate risk because they have more coupon payments to reinvest over the bond's longer lifespan.

III. Longer-term bonds have less interest rate risk than shorter-term bonds. This statement is false. As mentioned earlier, longer-term bonds have more interest rate risk because their prices are more sensitive to changes in interest rates compared to shorter-term bonds.

In summary, statement I is correct, while statements II and III are false. The longer-term bond (Bond L) fluctuates more due to its higher interest rate risk compared to the shorter-term bond (Bond S).

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The equations that describe the projection of the region R onto the xy plane are: x² + y² ≤ 1 So, the integral becomes∫`0^1 ∫0 ^8∫e^(2e)r dz dy dr  which gives the final answer as 126(1 - e⁻²)

we have to evaluate the triple integral and integral with the mentioned parameters:

(1) Evaluate the triple integral ∭(x, y, z) dV over the region R={(x, y, z)| 0 ≤ ≤ x² + y² ≤ 1, 0 ≤ ≤ 2 - x - y}

The given triple integral can be solved by conversion to cylindrical coordinates as

x = r cos θ, y = r sin θ, and z = z ∬R f(r, θ)r dr dθ

where R is the projection of the region R onto the xy-plane

The equations that describe the projection of the region R onto the xy plane are:

x² + y² ≤ 1 and x + y ≤ 2or r ≤ 1 and r cos θ + r sin θ ≤ 2, or equivalently, r ≤ 1 and r ≤ 2/√(2 sin θ + cos θ)

So, the integral becomes∫0 ^(2π)∫`0 ^1 ∫`0 ^(2/√(2 sin θ + cos θ)) r³ cos θ sin θ dz dr dθ which gives the final answer as `(π/12)(4 + √2)`(2)

Evaluate the triple integral ∭(x, y, z) dV over the region R={(x, y, z)| 0 ≤ y ≤ 8, e ≤ z ≤ 2e, x² + y² ≤ 1}`The given integral can be solved by conversion to cylindrical coordinates as: x = r cos θ, y = y, and z = z ∬R f(r, θ)r dr dy where R is the projection of the region R onto the `xy` plane

The equations that describe the projection of the region R onto the xy plane are: x² + y² ≤ 1 So, the integral becomes∫`0^1 ∫0 ^8∫e^(2e)r dz dy dr  which gives the final answer as 126(1 - e⁻²)

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multiply Start Fraction 5 Over 7 End Fraction by 3.

What do math fractions mean?

An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.

                                Whether it is in the numerator or denominator, a complex fraction contains a fraction.

                             The numerator and denominator of a correct fraction are opposite each other.

What is basic fraction theory?

Every fraction has two components: the numerator, which is the actual number of parts, and the denominator, which is the total number of parts.

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Answer:

c is the answer i took the test

Step-by-step explanation:

Using the given data on the number of live multiple-delivery births for women aged 15 to 54, we need to calculate probabilities related to the age groups of the mothers. The probability of a randomly selected multiple birth involving a mother aged 30 to 39 will be determined, as well as the probabilities of not being in the age range, being less than 45, and being at least 40. Finally, we need to interpret whether a multiple birth involving a mother aged at least 40 is unusual.

(a) To calculate the probability of a randomly selected multiple birth involving a mother aged 30 to 39, we sum the number of multiple births in that age group and divide it by the total number of multiple births for women aged 15 to 54.

P(30 to 39) = 2822 / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

(b) To find the probability of a randomly selected multiple birth involving a mother who is not aged 30 to 39, we subtract the probability found in part (a) from 1.

P(not 30 to 39) = 1 - P(30 to 39)

(c) To determine the probability of a randomly selected multiple birth involving a mother aged less than 45, we sum the number of multiple births for age groups below 45 and divide it by the total number of multiple births for women aged 15 to 54.

P(less than 45) = (89 + 508 + 1631 + 2822 + 1855 + 374) / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

(d) To find the probability of a randomly selected multiple birth involving a mother aged at least 40, we sum the number of multiple births for age groups 40-44 and 45-54, and divide it by the total number of multiple births for women aged 15 to 54.

P(at least 40) = (374 + 119) / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

Interpretation: The answer to part (d) will determine whether a multiple birth involving a mother aged at least 40 is unusual. If the probability is less than 0.05, it can be considered unusual. Therefore, we need to compare the calculated probability to 0.05 and select the correct choice.

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The crucial value (z) relies on the desired level of confidence and is predicated on a normal distribution when creating a confidence interval for a proportion (p) with a confidence level of 93%.

A 93% confidence level in this instance translates to an alpha level of 0.07 (1 - 0.93 = 0.07) that is split evenly between the two tails. In the usual normal distribution table, we search for the value that falls within the range of 0.07 to find the proper z-value. A 93% confidence level corresponds to a z-value of roughly 1.81. The confidence interval for the proportion p may be calculated using this number and provides a range where the genuine proportion is like to fall.

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The measure of side length AB in the triangle is approximately 13.8 units.

The sine rule is expressed as:

\(\frac{c}{sinC} = \frac{b}{sinB}\)

From the diagram:

Angle B = 50 degrees

Angle C = 62 degrees

Side AC = b = 12

Side AB = c =?

Plug these values into the above formula and solve for c.

\(\frac{c}{sinC} = \frac{b}{sinB}\\\\\frac{c}{sin62^o} = \frac{12}{sin50^o}\\\\c = \frac{12 * sin62^o}{sin50^o}\)

c = 10.595 / 0.766

c = 13.832

c = 13.8

Therefore, side AB measures 13.8 units.

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