Miles, Sam, Laney, and Ella each walked from their houses to the mall. Miles walked 4\5 mile, Sam walked 2\3 mile, Laney walked 1\2 mile, and Ella walked 7\8 mile. Order the people based on who walked the farthest.

The distribution of test scores shows that most students did not do well on the test; some did fine and only a few did exceedingly well. The distribution is likely to be skewed.

What is a skewed distribution?

A skewed distribution is one in which the data is not uniformly distributed but rather concentrated on one side. In simple words, a skewed distribution is one in which one tail has a greater number of observations than the other tail, with the majority of data falling in the tail with the greater number of observations.

In a symmetric distribution, the data is uniformly distributed on both sides of the median, with half of the data lying to the right and half to the left.

Thus, the distribution of test scores shows that most students did not do well on the test; some did fine and only a few did exceedingly well. The distribution is likely to be skewed.

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For numbers less than 0.1, such as 0.06, the zeros to the right of the decimal point but before the first nonzero digit are called leading zeros.

When we have a decimal number less than 0.1, there may be one or more zeros between the decimal point and the first nonzero digit. These zeros are known as leading zeros. In the example of 0.06, the zero before the 6 is a leading zero. It indicates that the number is less than 0.1 but greater than 0.01. The leading zero helps establish the position of the decimal point and provides clarity about the magnitude of the number.

Leading zeros are significant in decimal notation because they affect the place value of the digits. Each leading zero shifts the decimal point one place to the right, indicating a smaller value.

It's important to recognize and include leading zeros when working with decimal numbers to maintain accuracy and precision. They contribute to the overall value and understanding of the number's magnitude, especially when comparing and performing calculations involving decimal quantities.

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Answer:

1,620,000 meters

Step-by-step explanation:

Speed-   450 meter----- 1 second

1 minute = 60 seconds

60 minutes (1 hour) = 3600 seconds

Distance in 1 hour

1 ------ 450

3600---- X

X= 3600 x 450

x= 1,620,000 meters

Answer:

?????????

Step-by-step explanation:

What are u asking

Answer:

They sold 60 muffins and 60 cookies yesterday

It is a LCM problem

Step-by-step explanation:

6 muffins together

20 cookies together

To sell the same amount of muffins and cookies,

Find the lowest common multiple of 6 muffins and 20 cookies

6 muffins = 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78

20 cookies = 40, 60, 80

The lowest common multiple of 6 muffins and 20 cookies is 60

Therefore,

They sold 60 muffins and 60 cookies yesterday

It is a LCM problem

The solution to the inequality are the region in the shaded area and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

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Answer:14.58 miles.

Step-by-step explanation:

Matthew is training to participate in a half marathon.

The distance covered by Matthew on the first day is 12.5 miles.

The distance covered by Matthew on the second day is 13.5 miles.

The distance increased on the second day is, 13.5-12.5=1 mile.

The percentage will be,

=\dfrac{1}{12.5}\times 100\%

=0.08\times 100\%

=8\%

Hence, each day he runs 8% more. So the distance covered by him on day 3 will be,

=13.5+\left(13.5\times \dfrac{8}{100}\right)

=13.5+1.08

=14.58 miles

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Step-by-step explanation:

Answer:

Basic consensus is that that other answer is wrong. The actual answer is 19.22

Step-by-step explanation:

To find the common ratio you just do this, last number = 15.5, and first number = 12.5.

15.5/12.5 equals 1.24.

^That's the common ratio.^

using A(n) = a * r ^ n - 1,

you get 12.5 * 1.24 ^ 3 - 1, or just 12.5 * 1.24 ^ 2

and solving that problem, you get 19.22.

Confirm this by doing the same thing earlier, 19.22/15.5 is 1.24. Which is the ratio found earlier. So it checks out.

Answer:

The 95% confidence interval based on this sample is =

[6.41, 7.79]

Step-by-step explanation:

The formula for Confidence Interval =

Mean ± z × standard deviation/√n

Sample mean = 7.1 hours

Standard deviation = 5 hours

n = 200 students

z = 95% confidence interval z score

= 1.96

C.I = 7.1 ± 1.96 × 5/√200

C.I = 7.1 ± 0.693

Hence, Confidence Interval

= 7.1 - 0.693

= 6.407

Approximately = 6.41

= 7.1 + 0.693

= 7.793

Approximately = 7.79

Therefore, the 95% confidence interval based on this sample is

[6.41, 7.79]

Understanding:

[Q1] f(x) represents the money Philip owes his friend while x being the time in months. When x was zero, Philip owed his friend a total of $1080. Therefore, the answer is D.

[Q2] You can calculate the slope by using the following formula \(m=\frac{y_2-y_1}{x_2-x_1}\), by using any 2 points on the graph we can easily calculate the slope.

\(m=\frac{810-1080}{6-0}=\frac{-270}{6}=-45\)

Solutions:

[Q1] D. Philip paid a total of $1080 for the car

[Q2] \(m=-45\)

[Q3] The slope represents the amount Philips pays his friend monthly.

Answer:

c=35 + 25m

Step-by-step explanation:

Sorry, that's all I got

Answer:

D

Step-by-step explanation:

The 1220 feet is positive because the plane is above her.

The 14 feet is negative because the tree is below her.

Because you're comparing distances, you need the absolute value of both distances.

The absolute value of 1220 is 1220 and the absolute value of -14 is 14, so the absolute value of 1220 is greater than the absolute value of -14. The answer is D.

The increase in your savings, and the annual interest rate mean that the savings in a year would be $121.20.

To find the total savings in a year, you first need to find the increased savings amount. The original savings were $100, so the increased savings would be:

= 100 x (1 + 20%)

= 100 x 1.20

= $120

Your total savings at an annual rate of 1% would therefore be:
= Increased savings x ( 1 + rate)

= 120 x ( 1 + 1%)

= 120 x 1.01

= $121.20

In conclusion, in a year, you would have a total savings amount of $121.20.

Rest of the question is:

You have savings of $100 which you deposited into a savings account.

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Explanation:

x = amount she travels on each of those three remaining days

3x = total amount traveled over those three remaining days

3x+24 = total amount traveled over the four days

3x+24 = 120 miles total

This equation is in the form px+q = r where:

Let's solve for x. We follow PEMDAS in reverse to undo what's happening to x, so we can isolate it.

3x+24 = 120

3x+24-24 = 120-24 .... subtract 24 from both sides

3x = 96

3x/3 = 96/3 .... divide both sides by 3

x = 32

Triana must travel 32 miles per day for those remaining three days.

Doing so means she travels 3x = 3*32 = 96 miles over those three remaining days. Then add on those 24 miles traveled on the first day to get 96+24 = 120 miles total. This helps confirm the answer.

Another way to confirm the answer is to plug x = 32 into 3x+24 = 120. After simplifying both sides, you should get 120 = 120 which is a true statement.

Answer:

y= -4

Step-by-step explanation:

The weight of the astronaut with gear on the moon is 80 pounds.

The pull of gravity is different on Earth than on the Moon as gravity depends on factors such as the mass of the celestial body, the radius of the celestial body, and the density of the celestial body.

The pull of gravity on Earth = 10 m/s²

Thus, Given:

Weight of object on Earth: 25 pounds

Weight is described as the product of mass and the acceleration due to gravity

Thus, 25 = 10 * mass

mass = 2.5 unit

Weight of the object on the Moon: 4 pounds

4 = 2.5 * acceleration due to gravity on the moon

Acceleration due to gravity on the moon = 1.6 m/s²

Weight of astronaut with gear on earth = 500 pounds

500 = mass * 10

mass = 50 units

Weight of astronaut with gear on earth = 50 * 1.6

= 80 pounds

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The force on the first charge is directed at an angle of 81.8° counter clockwise from the positive x-axis.

The total force on the first charge can be found using Coulomb's law and the superposition principle. According to Coulomb's law, the force between two charges is given by:

F = k * (q1 * q2) / r^2

where F is the force,

k is Coulomb's constant (9.0 × 10^9 N · m^2/C^2),

q1 and q2 are the charges of the two objects, and

r is the distance between them.

In this case, there are three charges involved, so we need to find the force on the first charge due to the other two charges. We can do this by finding the force between the first and second charges and the force between the first and third charges, and then adding them together using vector addition.The force between the first and second charges is:

F12 = k * (q1 * q2) / r12^2

where r12 is the distance between the first and second charges.

We can find r12 using the Pythagorean theorem:

r12^2 = (0.2 m)^2 + (0 m)^2 = 0.04 m^2r12 = 0.2 m

The force between the first and third charges is:

F13 = k * (q1 * q3) / r13^2

where r13 is the distance between the first and third charges.

We can find r13 using the Pythagorean theorem:

r13^2 = (0 m)^2 + (0.2 m)^2 = 0.04 m^2r13 = 0.2 m

Now we can use Coulomb's law to find the magnitudes of the two forces:

F12 = (9.0 × 10^9 N · m^2/C^2) * (-3.8 × 10^-4 C) * (8.1 × 10^-4 C) / (0.2 m)^2F12 = -1.202 N (attractive force)F13 = (9.0 × 10^9 N · m^2/C^2) * (-3.8 × 10^-4 C) * (2.8 × 10^-4 C) / (0.2 m)^2F13 = -0.266 N (repulsive force)

The total force on the first charge is the vector sum of F12 and F13. To find the direction of this force, we can use the tangent function:

tan θ = Fy / Fx

where Fy is the vertical component of the force and

Fx is the horizontal component of the force.

We can find these components using trigonometry:

Fy = F12 sin 90° + F13 sin 270° = -1.202 N + (-0.266 N) = -1.468 NFx = F12 cos 90° + F13 cos 270° = 0 N + (0.266 N) = 0.266 N

θ = tan^-1 (Fy / Fx) = tan^-1 (-1.468 N / 0.266 N) = -81.8°

The force on the first charge is directed at an angle of 81.8° counter clockwise from the positive x-axis.

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Answer:

Step-by-step explanation:

Translation right or left means change of the x-coordinate.  

Translation up or down means change of the y-coordinate.

Translation right or up means adding.

Translation left or down means  subtracting.

\(A=(x_A, y_A)\quad\rightarrow\quad B=(x_A+4,\,y_A-4)\\\\x_A+4=12\qquad\qquad y_A-4=-7\\\\x_A=12-4\qquad\qquad y_A=-7+4\\\\x_A=8\qquad\qquad\qquad y_A=-3\\\\A=(8,-3)\)

Answer:

(D) Chey has a gift card with a balance of $26.58 and bought a hat that cost $15.85. The sum is the balance on his gift card.

Step-by-step explanation:

Which real-world story is represented by the problem (-15.85) + 26.58?

Comparing the options given below,

The correct option is

(D) Chey has a gift card with a balance of $26.58 and bought a hat that cost $15.85. The sum is the balance on his gift card.

This is because, buy a hat that cost $15.85 = -15.85

He has a balance is $26.58 on his credit card.

Hence: $26.58 - $15.85

Hence, option D is correct

Answer:

B & D

Step-by-step explanation:

Phil's final debt after 20 years will be around $320,679.

To purchase a home, Phil borrowed $150,000 from a bank at a 3.5% annual interest rate.

The annual compounding of interest causes the amount of interest for each year to rise in proportion to the debt. Phil will be required to pay the initial sum plus interest after the first year, which comes to

$150,000 + 3.5% of $150,000 = $155,250.

Since interest is charged on the new amount owed for the second year, Phil will owe

$155,250 + 3.5% of $155,250, which

= $160,551.75.

For the next 20 years, this procedure is repeated, with the amount owed rising yearly by the sum of the year before plus interest. Phil's debt after 20 years will be around $320,679.

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The number of first class tickets bought by Sarah is 6

The number of coach tickets bought by Sarah is 3

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

let x people be for coach ticket and y be for first class ticket

Sarah a total of 9 people took the trip.

x + y = 9

She was able to purchase coach tickets for ​$200 and first class tickets for ​$1010. She used her total budget for airfare for the​ trip, which was ​$6660

$200x + $1010y = $6660

The simultaneous equation

x + y = 9

$200x + $1010y = $6660

solving the simultaneous equation gives

x = 3 and y = 6

Hence the number of coach tickets = 3 and the number of first class tickets = 9

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For this particular question, the method that is not used to test hypotheses is the survey method.

What are the methods used to test hypotheses?                                                                                                                                                                       In statistics, hypothesis testing is a method of statistical inference that compares two hypotheses about a population. The following are methods used to test hypotheses:

Traditional (computed value) method:This method compares the test statistic to a critical value based on a predetermined alpha level, which is a value set to determine if the null hypothesis should be rejected.

P-value method: The P-value approach compares the test statistic to the p-value to determine if the null hypothesis should be rejected or not.

Confidence interval method: The confidence interval approach compares the test statistic to the lower and upper bounds of the confidence interval to determine if the null hypothesis should be rejected or not.

Survey method: The survey method is not used to test hypotheses, but it is a way of collecting data from a group of individuals to understand their opinions or attitudes.

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9514 1404 393

Answer:

  208

Step-by-step explanation:

The order of operations requires that the multiplication be done before addition or subtraction.

  40 + 40 - 20×0 + 3 + 125

  = 40 + 40 - 0 + 3 + 125

  = 80 - 0 + 3 + 125

  = 80 + 3 + 125

  = 83 + 125

  = 208

__

The calculator shown in the attachment can be relied upon to perform calculations according to the order of operations. (It adds parentheses to show the order in which it is doing the calculation.)

Answer:

208

40 plus 40 minus 20 times 0 plus 125 in written form:

40 + 40 - 20 × 0 + 3 + 125

In order to get our answer 208, we must do it step by step:

First, we need to put 40 plus 40 into an equation:

40 + 40 = 80

Now that we have 80, we need to find 20 times 0:

20 x 0 = 0

Since 20 times 0 equals 0, we can now add 80 plus 3:

80 + 3 = 83

Now what we have left is to add 83 plus 125 which will give us our answer:

83 + 125 = 208!

The answer will be 208.

            Hope this helps!

     ~Hocus Pocus

Out of the given differential equations, only equation 3 is separable, and equation 4 is linear. The rest are nonlinear and neither separable nor linear.

The first-order differential equation dy/dx + exy = x2y2 is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term x2y2 in the equation makes it nonlinear, and the term exy makes it non-separable.

The differential equation y + ex * sin(x) = x3y' is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term ex * sin(x) and the term y' (derivative of y) make it nonlinear, and the term y makes it non-separable.

The differential equation ln(x) - x2y = xy' is separable but not linear. The terms ln(x) and x2y make it nonlinear, but it can be separated into two parts, one containing x and y and the other containing x and y'. Therefore, it is separable.

The differential equation dy/dx + cos(y) = tan(x) is linear but not separable. The terms cos(y) and tan(x) make it nonlinear, but it can be written in the form dy/dx + P(x)y = Q(x), where P(x) = cos(y) and Q(x) = tan(x). Therefore, it is a linear differential equation.

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Answer:

see explanation

Step-by-step explanation:

\(\frac{1}{3}\) a³ - \(\frac{3}{4}\) a² - \(\frac{5}{2}\) - ( \(\frac{5}{2}\) a² + \(\frac{3}{2}\) a³ + \(\frac{a}{3}\) - \(\frac{6}{5}\) ) ← distribute parenthesis by - 1

= \(\frac{1}{3}\) a³ - \(\frac{3}{4}\) a² - \(\frac{5}{2}\) - \(\frac{5}{2}\) a² - \(\frac{3}{2}\) a³ - \(\frac{a}{3}\) + \(\frac{6}{5}\) ← collect like terms

= (\(\frac{1}{3}\) a³ - \(\frac{3}{2}\) a³ ) + (-\(\frac{3}{4}\) a² - \(\frac{5}{2}\) a² ) - \(\frac{a}{3}\) + (- \(\frac{5}{2}\) + \(\frac{6}{5}\) ) ← change to common denominators

=   (\(\frac{2}{6}\) a³ - \(\frac{9}{6}\) a³ ) + (- \(\frac{3}{4}\) a² - \(\frac{10}{4}\) a² ) - \(\frac{a}{3}\) + (- \(\frac{25}{10}\) + \(\frac{12}{10}\) ) ← simplify

= - \(\frac{7}{6}\) a³ - \(\frac{13}{4}\) a² - \(\frac{1}{3}\) a - \(\frac{13}{10}\)

Answer:

Step-by-step explanation:

\(\sf \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\left[\dfrac{5}{2}a^2+\dfrac{3}{2}a^3+\dfrac{a}{3}-\dfrac{6}{5}\right]=\)

               \(\sf = \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\dfrac{5}{2}a^2-\dfrac{3}{2}a^3-\dfrac{a}{3}+\dfrac{6}{5}\\\\\\( Combine \ like \ terms)\\\\= \dfrac{1}{3}a^3 -\dfrac{3}{2}a^3 -\dfrac{3}{4}a^2-\dfrac{5}{2}a^2-\dfrac{a}{3}-\dfrac{5}{2}+\dfrac{6}{5}\\\\=\left[\dfrac{1*2}{3*2}-\dfrac{3*3}{2*3}\right]a^3 + \left[-\dfrac{3}{4}-\dfrac{5*2}{2*2}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{5*5}{2*5}+\dfrac{6*2}{5*2}\right]\\\\\\\)

               \(\sf ==\left[\dfrac{2}{6}-\dfrac{9}{6}\right]a^3+\left[-\dfrac{3}{4}-\dfrac{10}{4}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{25}{10}+\dfrac{12}{10}\right]\\\\=\dfrac{2-9}{6}a^3+\dfrac{(-3-10)}{4}a^2-\dfrac{a}{3}+\dfrac{(-25+12)}{15}\\\\\)

               \(\sf = \dfrac{-7}{6}a^3+ \dfrac{(-13)}{4}a^2-\dfrac{a}{3}+\dfrac{(-13)}{15}\\\\=-\dfrac{7}{6}a^3-\dfrac{13}{4}a^2-\dfrac{a}{3}-\dfrac{13}{15}\)

(a) The area of parallelogram ABCD as a function of c can be found using the cross product of the vectors AB and AD. The magnitude of the cross product gives the area of the parallelogram.

(b) For c = -2, the parametric equations of the line passing through D and perpendicular to the parallelogram ABCD can be determined by finding the direction vector of the line, which is orthogonal to the normal vector of the parallelogram, and using the point D as the initial point.

(a) To find the area of parallelogram ABCD, we first calculate the vectors AB = B - A and AD = D - A. Then, we take the cross product of AB and AD to obtain the normal vector of the parallelogram. The magnitude of the cross product gives the area of the parallelogram as a function of c.

(b) To find the parametric equations of the line passing through D and perpendicular to the parallelogram ABCD, we use the normal vector of the parallelogram as the direction vector of the line. We start with the point D and add t times the direction vector to get the parametric equations, where t is a parameter representing the distance along the line. For c = -2, we substitute the value of c into the normal vector to obtain the specific direction vector for this case.

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Triangle:

Procedure:

The interior angles of a triangle add up to 180°. As we know two angles, we can get the third as follows:

Isolating for m∠J

Replacing the values given:

Then using the trigonometric functions, we can get the sides.

Answer:

• m∠J, = 22°

• JL = 19.01

• KL = 7.99

Answer:

Step-by-step explanation: 4 numbers

30,50,70,90