Rosa ran the hurdles in 58.32 seconds. maya ran the hurdles in 54.078 seconds. what is the difference between the two times? 3.954 seconds 4.242 seconds 4.258 seconds 5.758 seconds

324 is the maximum value of the product of these three numbers

What is maxima and minima?

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, and minima will be its lowest.

The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.

Let the three nonnegative numbers are x,y,z

According to the question

x+y+z=36

and y=2x

therefore, 3x+z=36--------------------------------------------------(1)

z=36-3x

Let 3xz= u--------------------------------------------------------------(2)

differentiating equation 2

du/dx=3z + 3xdz/dx

or

du/dx= z + xdz/dx

differentiating equation 1

3 + dz/dx = 0

dz/dx = -3

du/dz = 36-3x + x(-3)

du/dx = 12 - 2x--------------------------------------------------------------(3)

for maxima put du/dx = 0

x=6-------------------------------------------------------------------------------(4)

again differentiating du/dx = 12 - 2x

d2u/dx2=-2

which means 3xz= u is maximum at x=6

from equation 1 and 4

we get 18+z=36

z=18

Therefore 3xz= 3(6)(18)=324

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Answer:

The slope of line m can be found using the slope formula:

m = (y2 - y1)/(x2 - x1)

m = (1 - 3)/(5 - (-2))

m = (-2)/(7)

m = -0.286

To find the slope of a line perpendicular to line m, we need to take the negative reciprocal of m:

slope = -1/m

slope = -1/(-0.286)

slope = 3.496

Therefore, the slope of a line perpendicular to line m is 3.496.

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

use binomial multiplication method

Answer:

(9π - 18) m²

Step-by-step explanation:

Area of sector = (angle / 360) X area of circle

Length of arc = (angle / 360) X circumference of circle

Area of circle = π r ²

= π (6) ²

= 36π

angle TSR = 90° (the little square means 90). there are 360° in a full circle.

area of sector (the triangle including the shaded part) = (90/360) X 36π

= 9π.

now we need to find the area of the triangle.

ST and SR will be same length (both are radius).

this means that angles STR and SRT will be equal.

there are always 180° in a triangle.

if TSR is 90°, then  STR and SRT combined will be 180 - 90 = 90°.

since they are both equal, STR = 45° and SRT = 45°.

Area of triangle = ½ ab sin C  (where a and b are the side lengths, ie both are 6, C is the angle between them. ie 90°)

= 1/2 (6) (6) Sin 90

= 18.

we now have the area of our sector (9π) and area of our triangle (18).

the shaded section is the difference between the two.

so we just subtract the area of the triangge from the area of the sector:

9π - 18 = (9π - 18) m²    ........ this roughly = 10.27 m²

We can compute various descriptive statistics such as the mean, median, mode, range, variance, standard deviation, sum of values, and sum of squared deviations.

The sample mean, also known as the average, provides information about the central tendency of the variable X. It represents the typical or average number of coupons used by the shoppers in the sample. In this case, calculating the mean of the given data would provide an estimate of the average number of coupons used over the 6-month period.

The sample standard deviation measures the dispersion or variability of the data points around the mean. It indicates how much the individual observations deviate from the mean value. A higher standard deviation implies greater variability, indicating a wider range of coupon usage among the shoppers in the sample.

By computing the sample mean and standard deviation, we can understand the average coupon usage and the degree of variability in the data. These statistics help us summarize and interpret the characteristics of the variable X, allowing us to make comparisons, identify outliers, assess the spread of the data, and make inferences about the larger population from which the sample was drawn.

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Answer

$128

Step-by-step explanation:

Okay well if $80 is 100% then 60% is 48 dollars.

so 80 +48=128

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

The answer I think would be 7. Hope this helped!!

Answer:

0.53 hours

Step-by-step explanation:

D = (r)(t), Where

‘D’ is the distance covered

‘r’ is the approach rate

‘t’ is the total time spent

Distance covered, ‘D’ = 4 miles

Approach rate, “r” = 3.5mph + 4mph

r = 7.5mph.

t is unknown

Solving for t,

D = (r)(t)

4 = 7.5t

t = 4/7.5

t = 0.53 hours (to the nearest hundredth)

Therefore, it will take Amanda and Alexis 0.53 hours to meet

The rational function graphed below is: \(\(f(x) = \frac{1}{(x + 3)(x - 3)}\)\)

To determine the rational function graphed below, let's analyze the key features of the graph.

The graph appears to have two vertical asymptotes at \(\(x = -3\)\) and \(\(x = 3\)\) since the denominator \(\((x + 3)(x - 3)\)\) becomes zero at those points, and division by zero is not defined. Vertical asymptotes are represented by vertical lines that the graph approaches but never touches.

The graph also seems to cross the x-axis at \(\(x = -3\)\) and \(\(x = 3\)\) since the numerator 1 is nonzero at those points, causing the function to have y-intercepts at those locations.

Furthermore, the graph appears to be symmetrical with respect to the vertical line x = 0 because the rational function is an even function. This is evident from the fact that the terms \(\((x + 3)\) and \((x - 3)\)\) in the denominator are identical except for the sign. Therefore, the function has symmetry about the y-axis.

Considering all these characteristics, the rational function that matches the given graph is:

\(\(f(x) = \frac{1}{(x + 3)(x - 3)}\)\).

This function has vertical asymptotes at \(\(x = -3\) and \(x = 3\)\), crosses the x-axis at \(\(x = -3\) and \(x = 3\)\), and is symmetric with respect to the y-axis. The graph should resemble a hyperbola centered at the origin.

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Answer:

1, 4, and 7

Step-by-step explanation:

The rest are equal to angle 2

The maximum area of the rectangle inside the ellipse is 2ab.

Given that,

Ellipse = x2 / a2 + y2 / b2 = 1

we know the general coordinates of any point in an ellipse of the equation

x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)

So, we take general vertices of rectangles as

(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)

So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ

So, its area will be ab4sinθcosθ (Length x Breadth)

Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A

Now A=2absin2θ

Now as the area is the maximum given in the question, we have to differentiate it with respect to θ

dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)

Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ =  π / 2 and θ=π / 4

So now we to put θ=π / 4 in the equation of area which is A=2absin2θ

We get as A=2absin2π / 4=2absinπ / 2=2ab

Hence the max area of the rectangle inside the ellipse is 2ab.

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Both -5 and 1 are extraneous solution to the equation

A quadratic equation is a second-order polynomial equation in a single variable x ax2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

c²+2c-4-1-2c = 0

c²+2c-2c -4-1 = 0

c²-5 = 0

Therefore both -5 and 1 are extraneous solution in the equation.

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To find the 90% confidence interval for the mean amount of drug in all the pills manufactured by the company, we can use the following formula: CI = X ± Zα/2 * (σ/√n).

Where:

X = sample mean = 325.5 mg
σ = sample standard deviation = 10.3 mg
n = sample size = 80
Zα/2 = the critical value of the standard normal distribution corresponding to a 90% confidence level, which is 1.645.

Plugging in the values, we get:

CI = 325.5 ± 1.645 * (10.3/√80)
CI = 325.5 ± 2.38
CI = (323.12, 327.88)

Therefore, we can say with 90% confidence that the mean amount of drug in all the pills manufactured by the company is between 323.12 mg and 327.88 mg.


1. Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size:
SE = 10.3 mg / √80 ≈ 1.15 mg

2. Find the critical value (z) for a 90% confidence interval using a standard normal distribution table or calculator. In this case, the critical value is approximately 1.645.

3. Calculate the margin of error (ME) by multiplying the critical value (z) by the standard error (SE):
ME = 1.645 × 1.15 mg ≈ 1.89 mg

4. Determine the confidence interval by adding and subtracting the margin of error from the sample mean:
Lower Limit = 325.5 mg - 1.89 mg ≈ 323.61 mg
Upper Limit = 325.5 mg + 1.89 mg ≈ 327.39 mg

Thus, the 90% confidence interval for the mean amount of drug in all the pills manufactured by the company is approximately 323.61 mg to 327.39 mg.

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Answer:

x=1/6

Step-by-step explanation:

Answer:

Option B - Darin scores in a basketball game is 19 Points

Step-by-step explanation:

Darin scores in a basketball game = 3s + 2t + u

where s is the number of three-point field goals made,

t is the number of two-point field goals made,

u is the number of free throws made.

Darin scores in a basketball game = 3(2) + 2(5) + 3

= 6 + 10 + 3

= 19 Points

Hope this helps!

Answer:

m = -9 and x = (0, 9)

Explanation: its not c its actually x

It will take approximately 35.1 years for the sample of the substance to decay to 78% of its original amount.

The formula for exponential decay model is A = A0e^-kt where A is the final amount, A0 is the initial amount, k is the decay constant and t is the time interval.

Given that the half-life of a certain substance is 22 years and we have to determine how long it will take for a sample of this substance to decay to 78% of its original amount.

We know that the half-life of a certain substance is 22 years.

So, the initial amount will be halved every 22 years or the amount is reduced to 50% every 22 years.

This information is given by the formula A = A0e^-kt

Since the initial amount will be halved after every 22 years, this means that A0/2 = A0e^-k*22.

Simplifying the equation we get, 1/2 = e^-k*22

Dividing by e^22 both sides we get,

e^22/2 = e^k*22Log_e

e^22/2 = k*22

So, k = ln 2/22 = 0.0315

So, A = A0e^-kt becomes A = A0e^(-0.0315t)

Let's say t = T, then we have A = 0.78A0A0e^(-0.0315T) = 0.78A0

Dividing by A0 both sides we get, e^(-0.0315T) = 0.78

Taking natural log both sides we get, ln e^(-0.0315T)

= ln 0.78-0.0315T

= ln 0.78T

= -ln 0.78/0.0315T

≈ 35.1 years

Therefore, it will take approximately 35.1 years for the sample of the substance to decay to 78% of its original amount (Round to one decimal place as needed).

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Answer:

x ≈ 39.5°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos x = \(\frac{adjacent}{hypotenuse}\) = \(\frac{OP}{NP}\) = \(\frac{64}{83}\) , then

x = \(cos^{-1}\) ( \(\frac{64}{83}\) ) ≈ 39.5° ( to the nearest tenth )

Answer:

6

Step-by-step explanation:

If you were scaling it by 1/6 it would be smaller.

Answer:

Step-by-step explanation:

As per equation, the initial amount is:

Sample amount left after 50 years:

Answer:

C. 45,257

Step-by-step explanation:

5280 * 60 = 316,800

316,800 ÷ 7 = 45,257

The distance between two consecutive rest stops is 45257 feet.

Division is the process of dividing a number by a given number.

Given that, the 60-mile road is divided into 7 equal parts.

The length of each part is:

60/7 mile

Given that;

1 mile = 5280 feet

Therefore;

60/7 mile = (60/7)5280 feet

60/7 mile ≈ 45257 feet

Hence, the distance between two consecutive rest stops is 45257 feet.

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Solution,

2x-56=8

or,2x=8+56

or,2x=64

or,X=64/2

X=32

Hope it helps

Good luck on your assignment

Answer:

x=32

Step-by-step explanation:

First I put the 56 on the other side by doing the opposite to it, so adding 56 to both sides.

2x - 56 = 8

   +56      +56

2x=64

Then divide both sides by two to single out the x and know it's value

2x=64

/2     /2

x=32

Answer: Reflect the shape A in the line: y = -1 An investment has been growing in value at a rate of 8% per year and now has a value of $8200. Find the value of the investment in 5 years. Step by St …

explanation:

Answer:

x = -9/2 - 1/2y

Step-by-step explanation:

2x + y = -9

2x = -9 - y

x = -9/2 - 1/2y

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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Answer:

156

Step-by-step explanation:

200 minus 22 percent is 44.

200 minus 44 is 156.

Therefore the reduced version has 156 calories.

The new snack has 156 calories.

To find the number of calories in the new snack, we can start by calculating the 22% reduction in calories compared to the old version.

The old version of the snack has 200 calories.

To determine the reduction, we calculate 22% of 200 calories:

22% of 200 = (22/100) * 200 = 0.22 * 200 = 44 calories.

This means that the new snack has 44 fewer calories than the old version.

To find the number of calories in the new snack, we subtract the reduction from the old version's calories:

200 calories - 44 calories = 156 calories.

Therefore, the new snack has 156 calories.

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Answer:

7/2 cups of milk.

Step-by-step explanation:

1 3/4=7/4

2(7/4)=14/4=7/2

Answer:

7/2 cups of milk.

Step-by-step explanation:

If you want double the pancakes You must double the amount of milk:

First change it into an improper fraction:

1 3/4=7/4

then multiply it by two and simplify:

2(7/4)=14/4=7/2