1. Eduardo runs 6 laps around the track at Lincoln Park School. Then he runs 3 miles to get home. How far will he run in all? Show your work.​

Answer:

[tex]{ \sf{a = \frac{0.012}{0.633 -0.063 } }} \\ \\ { \sf{a = \frac{0.012}{0.57} }} \\ \\ { \sf{a = 0.021 \: (2 \: s.f)}}[/tex]

The solution to the compound inequality -3+b> 7 OR b +9 <17 is given as follows:

b < 8 or b > 10.

The inequality for this problem is defined as follows:

-3+b> 7 OR b +9 <17.

The or operation means that the we must solve each operation separately, and then the solution set to the compound inequality is given by the union of the solution set of each of the inequalities.

The solution set for the first inequality is given as follows:

-3+b> 7

b > 10.

The solution set for the second inequality is given as follows:

b + 9 < 17

b < 8.

Hence the solution for the entire inequality is of:

b < 8 or b > 10.

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Answer:

6

Step-by-step explanation:

We know that a dozen is the value of 12 so to find half a dozen we simply need to half it!

This means that there are 6 eggs in a half dozen.

FUN FACT:

A baker's dozen is 13, one more than a regular dozen!

Hope this helps, have a lovely day!

Answer:

Relating SSE to Other Statistical Data



The estimated volume of the coffee cup is approximately 152.8 cubic centimeters.

It is the perimeter of the circle, which can be found by multiplying the diameter of the circle by pi (π), a mathematical constant that is approximately equal to 3.14.

The volume of a right cylinder is:

V = πr²h

We are given the height of the coffee cup as h = 8.3 cm. To find the radius,

C = 2πr

We are given the circumference of the coffee cup as C = 14.9 cm. Solving for r, we have:

14.9 = 2πr

r = 14.9 / (2π) ≈ 2.372 cm

Now we can substitute these values into the formula for the volume of a cylinder:

V = πr²h

V = π(2.372)²(8.3)

V ≈ 152.8 cubic centimeters

Therefore, the estimated volume of the coffee cup is approximately 152.8 cubic centimeters.

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The perimeter of the given figures is: Triangle = 4x - 2. Rectangle = 8x - 8, and square = 12x - 8y.

The whole distance encircling a form is referred to as its perimeter. It is the length of any two-dimensional geometric shape's border or outline. Depending on the size, the perimeter of several figures can be the same. Consider a triangle built of an L-length wire, for instance. If all the sides are the same length, the same wire can be used to create a square.

The perimeter of a figure is the sum of all the segments of the figure.

The perimeter of triangle is:

P = 2x - 5 + x + x + 3 = 4x - 2

The perimeter of rectangle is:

P = 2(l + b)

P = 2(3x + 1 + x - 5)

P = 2(4x - 4)

P = 8x - 8

The perimeter of square is:

P = 4(s)

P = 4(3x - 2y)

P= 12x - 8y

Hence, the perimeter of the given figures is: Triangle = 4x - 2. Rectangle = 8x - 8, and square = 12x - 8y.

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Answer:

7.  300 miles

8. 60 miles

9. 5 miles

10. 1000 meters

Step-by-step explanation:

7.

We Take

60 x 5 = 300 miles

So, Ruth drives 300 miles in 5 hours.

8.  

5 miles = 10 minutes

1 mile = 2 minutes

2 hours = 120 minutes

We Take

120 / 2 = 60 miles

So, Carl drive 60 miles in 2 hours

9.

1 hour and 25 minutes = 85 minutes

We Take

85 / 17 = 5 miles

So, Nick travels 5 miles in an hour and 25 minutes.

10.

100 meters = 2 minutes

50 meters = 1 minute

We Take

50 x 20 = 1000 meters

So, Stan swims 1000 meters in 20 minutes.

Answer:

7. 300 miles/hours
8. 60 miles in 2 hours
9. 5 miles in 2 hours and 25 mins.

10. 1000 meters in 20 minutes.

Step-by-step explanation:

7. 60 x 5= 300 miles/hours

8. 5 miles in 10 minutes so in 2 hours it will be 5 x 12 = 60 miles in 2 hours

9.  5 miles in 2 hours and 25 mins.

10. 1000 meters in 20 minutes.

As a result, the probability of a 45-54-year-old motorist becoming involved in an accident is 5.38%, rounded to two decimal places.

Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.

To determine the likelihood that a driver aged 45-54 was involved in an accident, divide the number of drivers in that age group who were engaged in an accident by the total number of drivers in that age group:

Probability = Number of 45-54-year-old drivers involved in an accident / Total number of 45-54-year-old drivers

We can observe that 7 drivers aged 45 to 54 were engaged in an accident, with a total of 130 drivers in that age group:

The probability is 7/130 = 0.0538.

To convert this to a percentage, multiply by 100:

Probability = 0.0538 * 100 = 5.38 percent

As a result, the likelihood of a 45-54-year-old motorist becoming involved in an accident is 5.38%, rounded to two decimal places.

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Answer:

(f - g)(x) = -4x² + x - 8

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

            = x - 8 - (4x²)

            = -4x² + x - 8

Answer:

6188 ways

Step-by-step explanation:

there ate 5 objects to be choosen and there is no replacement of the object therefore you got

17 choices for the first selection of the object and 16 objects for the selection of the second object and so on until you get 13 objects for the last selection

totally you have 5 selections also arrangement does not matter there fore you have 17!/12!5! which is 6188

note we used 5! cause there are 5 placed objects and 12! are unplaced objects

note

that you have used one so you have to deduct one every time you use one

Answer:

invertible

Step-by-step explanation:

If A is invertible then ∣A∣ =0

Your question is incomplete. The complete question is: Which of the graphs below illustrates water boiling in Denver, Colorado? (Altitude 1,600 meters.)

Answer:

Explanation:

The normal boiling point of water is 100°C. That is the temperature at which water boils when the atmospheric pressure is 1 atm, i.e. at sea level.

The liquids boil when its vapor pressure equals the atmospheric pressure; so the higher the atmospheric pressure the higher the boiling point, and the lower the atmospheric pressure the lower the boiling point.

Since, it is stated that the altitude of Denver, Colorado is 1,600 m, the atmospheric pressure (the pressure exerted by the column of air above the place) is lower than 1 atm (atmospheric pressure at sea level).

Hence, water boiling point in Denver is lower than 100°C.

The graphs shown represent the temperature (T °C) as water is heated. Since when liquids boil their temperature remains constant during all the phase change, the flat portion of the graph represents the time during which the substance is boiling.

In the graph A, the flat portion is below 100°C; in the graph B, the flat portion is at 100 °C; in the graph C the flat part is above 100ªC, and, in graph D, there is not flat part. Then, the only graph that can illustrate water boiling in Denver, Colorado is the graph A.

Using the correct order of operations, the value is 13

PEDMAS is simply described as a mathematical acronym that represents the different arithmetic operations in order from least to greatest of application.

The alphabets represents;

From the information given, we have;

15-(4-3)2

solve the parentheses first

15 - (1)2

Multiply the values

15 - 2

Subtract the values

13

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The complete question:

Solve using the correct order of

operations of PEMDAS

15 - (4-3)2

Answer:

54°

Step-by-step explanation:

AB = BC = CD = AD (Because all sides of a rhombus are equal)

Let's consider the triangle DBC:

BC = DC => ∠DBC = 36°

The angle DCB is equal to:

180° - 36*2 = 180° - 72° = 108°

In a parallelogram, opposite angles are equal.

Then the angle DAB = DCB = 108°

Also, we know that the diagonals of a rhombus are the bisectors of the angles from which they come.

So, the angle DAE = EAB = 108° / 2 = 54°

Answer:

C) 60º, 60º, 120º, 120º

Step-by-step explanation:

We know the sum of all the angles in a rectangle is 360 degrees, whether it's irregular or not.

Given: x + 2x + 2x + x = 360

Calculate the linear equation, to find x.

x + 2x + 2x + x = 360

3x + 3x = 360

6x = 360  (Divide both sides by 6)

x = 60 degrees.

Then you can calculate the polygons.

x + 2x + 2x + x

For the first x, = 60.

Then for 2x, 60 * 2 = 120.

Then for 2x again, = 120.

Finally for the last x, = 60.

Therefore, the answer is C) 60º, 60º, 120º, 120º.

Answer:

2.

a) log base 10 of 100

b) The expression means that 10 to the 2nd power equals 100.

c) 2

3.

4. It would make sense that the value is between 1 and 2 because 10 to the 1st power is 10, and 10 to the 2nd power is 100. 50 is between 10 and 100 so the value would have to be between 1 and 2. This works because logs are the inverse function to exponentiation.

a) 2.6021

b) 3 and the value is exact because the base 10 in the log expression is technically the exponent when you convert it to exponent form. This works because logs are the inverse function to exponentiation. So 10 to the 3rd power would give you exactly 1000.

Answer:

150

Step-by-step explanation:

Using the formulas

A=6a2

V=a3

Solving forA

A=6V⅔=6·125⅔ ≈150

Answer:

Step-by-step explanation:

If the volume of a cube is 125 cm³, it means that each side of the cube measures 5 cm (since 5 x 5 x 5 = 125).

To find the surface area of the cube, we need to calculate the area of each of the six faces and add them together.

The area of each face is simply the length of one side squared (or side x side).

So, the surface area of the cube would be:

6 x (5 cm x 5 cm) = 6 x 25 = 150 cm²

Therefore, the surface area of the cube is 150 cm².

Answer:

13/8

Step-by-step explanation:

You first find the lcm of 8 and 4 which is 8

Then make a dividing line (/) with the lcm as the numerator.

After which you start diviing the lcm by each denominator of the two terms, and then multiplying with their numerators:

8/8 x 7 + 8/4 x 3 all over the lcm which is 8

(1 x 7 + 2 x 3)/8

(7 + 6)/8

13/8

The ordered pairs of given equation are (3/2,4), (1/3, -3),(5/6,0)

An ordered pair is composed of the ordinate and the abscissa of the x coordinate, with two values supplied in parentheses in a specified sequence. Placing a point on the Cartesian plane could be beneficial for visual comprehension.

for example, the ordered pair (x, y) signifies an ordered pair in which 'x' is referred to as the first element and 'y' is referred to as the second element. These items, which can be either variables , have distinct names depending on the context in which they are used. In an ordered pair, the element order is quite significant.

Given Equation of Y=6x−5

First Ordered pair;(,4)

y=4

x=4+5/6

x=3/2

First Ordered pair;(, -3)

y=-3

x=-3+5/6

x=1/3

First Ordered pair; (,0)

y=0

x=5/6

The ordered pairs of given equation are

(3/2,4), (1/3, -3),(5/6,0)

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The complete question is:

For The Equation, Y=6x−5

Complete The Given Ordered Pairs (,4), (, -3), (,0)

By answering the presented questiοn, we may cοnclude that Since a line equatiοn parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.

When twο expressiοns are equal, a mathematical equatiοn is a statement stating that equality. Twο sides are jοined by the algebraic symbοl (=), and tοgether they make up an equatiοn. Fοr instance, the claim that "2x + 3 = 9" means that "2x plus 3" equals the number "9" is made in this argument. Finding the value(s) οf the variable(s) necessary fοr the equatiοn tο be true is the gοal οf sοlving equatiοns.

There are variοus types οf equatiοns, including regular and nοnlinear οnes with οne οr mοre elements. "x² + 2x - 3 = 0" is an equatiοn that raises the variable x tο the secοnd pοwer. Mathematical disciplines like algebra, calculus, and geοmetry all make use οf lines.

the given equatiοn:

[tex]$\begin{array}{c}{{5x-6y=30}}\\ {{-6y=-5x+30}}\\ {{y=(5/6)x-5}}\end{array}$[/tex]

Sο the slοpe οf the given line is 5/6.

Since a line parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.

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Initially, while maintaining the very same [tex]x-[/tex]coordinates, the negative reflect across the [tex]x-axis[/tex] modifies the signs of all locations' [tex]y-[/tex]coordinates.

A negative value is one that always has a value lower than zero and is denoted by the minus (-) symbol. In a number line, negative values are displayed just left of zero.

If a number is higher than zero, it is considered positive. Or less zero numbers are referred to as negative numbers. If a number is bigger than that or equal to zero, it is not negative. If a number falls below or equal to zero, it is non-positive.

This transforms Figure [tex]1[/tex] into a new figure with points [tex](-2, -5), (-2, -4), (-3, -4), (-3, -2), (-5, -2), (-5, -5)[/tex].

Next, the [tex]180^{0}[/tex] rotation about the origin swaps the signs of both [tex]x[/tex] and [tex]y[/tex] coordinates of each point. This results in the final figure with points [tex](2, -5), (2, -4), (3, -4), (3, -2), (5, -2), (5, -5)[/tex].

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The aquarium has six rectangular faces, four of which are identical (two sides and two ends), and two of which are identical to each other but different from the others (top and bottom).

a) We can use the formula for the volume of a rectangular prism, which is given by V = lwh, where l is the length, w is the width, and h is the height. In this case, we have  [tex]V = 12 ft^3 and h = 1.5 ft[/tex] . We want to express y as a function of x, so we need to eliminate w from the equation.

We can rearrange the equation for the volume to get  [tex]w = V/(lh)[/tex] , and substitute in h [tex]= 1.5 ft[/tex] :

[tex]w = V/(1.5lx)[/tex]

Now we can substitute y for w to get:

[tex]y = V/(1.5lx)[/tex]

b)  To find the total surface area, we need to find the area of each face and add them up.

The area of one of the identical sides or ends is lw, so the total area of these four faces is:

[tex]4lw = 4xy[/tex]

The area of the top and bottom faces is lx, so the total area of these two faces is:

[tex]2lx[/tex]

Therefore, the total surface area S is given by:

[tex]S = 4xy + 2lx[/tex]

We can express y in terms of x using the equation from part a):

[tex]y = V/(1.5lx)[/tex]

Substituting this into the expression for S, we get:

[tex]S = 4x(V/(1.5lx)) + 2lx[/tex]

Simplifying, we get:

[tex]S = (8/3)V/x + 2lx[/tex]

So the total surface area S is a function of x, and we can use this equation to find the value of S for any given value of x.

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Answer:

Step-by-step explanation:

For Diane's account:

Year 1: Interest = $70,000 x 0.03 = $2,100

Year 2: Interest = ($70,000 + $2,100) x 0.03 = $2,163

Year 3: Interest = ($70,000 + $2,100 + $2,163) x 0.03 = $2,227.89

For Henry's account:

Year 1: Interest = $70,000 x 0.03 = $2,100

Year 2: Interest = $70,000 x 0.03 = $2,100

Year 3: Interest = $70,000 x 0.03 = $2,100

For the first year, both Diane and Henry earn the same interest of $2,100. However, for the second and third years, Diane earns more interest than Henry. Therefore, Diane earns more interest for each year after the first year

Distance from a point in space to the moon is a continuous random variable and Number of coins in a stack is a discrete random variable.

A discrete random variable is one that has a finite number of possible values or one that can be countably infinitely numerous. A discrete random variable is, for instance, the result of rolling a die because there are only six possible outcomes.

A continuous random variable, on the other hand, is one that is not discrete and "may take on uncountably infinitely many values," like a spectrum of real numbers.

1. The Name of the people in the car that crosses the bridge - Not a Variable

2. Continuous random variable measuring the interval between each car crossing the bridge.

3. The Categorical Random Variable for the type of vehicles crossing the bridge

4. The number of cars that use the bridge in one hour - Continuous Random Variable

For Question 2:

1. Type of coin - Categorical Random Variable

2. The distance from a given location in space to the moon - Continuous Random Variable

3. Number of coins in a stack - Discrete Random Variable

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Complete question is:

Label each of the following as Discrete Random Variable, Continuous Random Variable, Categorical Random Variable, or Not a Variable.

1. The Name of the people in the car that crosses the bridge Not a Variable

2. The time between each car crossing the bridge Continuous Random Variable

3. The type of cars that cross the bridge Categorical Random Variable

4. The number of cars that use the bridge in one hour Continuous Random Variable

Question 2: Which of these are Continuous and which are Discrete Random Variables?

1. Type of coin

2. Distance from a point in space to the moon

3. Number of coins in a stack

The total amount of money Carol originally invested is £22,000 in the bank account.

Compound interest is interest that is calculated not only on the initial amount of money invested or borrowed, but also on any accumulated interest from previous periods.

This results in exponential growth or accumulation of interest over time.

Let X be the amount that Carol originally invested in the account.

After 1 year, the amount of money in the account will be X(1+0.025) = X(1.025).

After Carol withdrew £1000, the amount of money in the account will be X(1.025) - £1000.

After 2 years (i.e. on 1st January 2016), the amount of money in the account will be (X(1.025) - £1000)(1+0.025) = (X(1.025) - £1000)(1.025).

We know that the amount of money in the account on 1st January 2016 was £23,517.60, so we can write the equation:

(X(1.025) - £1000)(1.025) = £23,517.60

Expanding the left-hand side and simplifying, we get:

X(1.025)² - £1000(1.025) = £23,517.60

X(1.025)² = £24,567.63

Dividing both sides by (1.025)², we get:

X = £22,000 (rounded to the nearest pound)

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The complete question is -

On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On the 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?

Descriptive statistics are the most useful in life. Descriptive statistics provide information about a data set and can help to summarize and interpret data. Specifically, I find the mean and median to be the most useful.

Descriptive statistics involves the use of measures such as the mean, median, mode, and range, as well as graphical representations of the data, such as histograms, box plots, and scatter plots.

The mean is the average of a set of data and is useful for summarizing and interpreting data. For example, when I am studying for a test, I often use the mean of my practice test scores to understand my overall performance.

The median is the middle value of a set of data and is useful for understanding the spread of the data. For example, when I am tracking my monthly expenses, I often use the median to understand how much I am spending each month. By taking the median of my monthly expenses, I can get an idea of which expenses are taking up the most of my budget.

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Answer:

going from left to right:

AA

BD

CB

DC