Annie time running the race was 4.08 seconds less than karen time her goal was to complete the race in less than 39.50 seconds did she meet her goal

The total value of Thuli's investment after 3 years is R6200

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

principal, P = 5000

Rate = 8%

Time = 3 years

Using the above as a guide, we have the following:

Amount = P * (1 + RT)

Substitute the known values in the above equation, so, we have the following representation

Amount = 5000 * (1 + 8% * 3)

Evaluate

Amount = 6200

Hence, the amount is R6200

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The constant acceleration equations are:

The position equation: x = x0 + v0t + 1/2at^2

The velocity equation: v = v0 + at

The acceleration equation: a = (v - v0)/t

Constant acceleration equations describe the motion of an object that is experiencing a constant acceleration. When an object experiences a constant acceleration, its velocity changes by the same amount in equal time intervals. The equations that describe this motion are as follows:

The position equation: x = x0 + v0t + 1/2at^2

where x is the position of the object at time t, x0 is the initial position of the object, v0 is the initial velocity of the object, a is the constant acceleration of the object, and t is the time elapsed.

The velocity equation: v = v0 + at

where v is the velocity of the object at time t, v0 is the initial velocity of the object, a is the constant acceleration of the object, and t is the time elapsed.

The acceleration equation: a = (v - v0)/t

where a is the constant acceleration of the object, v is the velocity of the object at time t, v0 is the initial velocity of the object, and t is the time elapsed.

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The probability that at most three bottles will be sold on a randomly selected day is about is 0.569

The probability of an event is a number that indicates how likely the event is to occur.

Given that, the number x of bottles of garden plant fungicide sold by a garden center each day was recorded, we need to find the probability that at most three bottles will be sold on a randomly selected day is about,

The possible values of x is 0, 1, 2, 3, 4, 5, 6 and 7

The probability that at most three bottles will be sold on the randomly selected day will be =

P(x≤3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

= 0.135 + 0.141 + 0.150 + 0.143

= 0.569

Hence, the probability that at most three bottles will be sold on a randomly selected day is about is 0.569

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1 year has  31,536,000 seconds.

1 year = 365days

1 day = 24 hours

1 hours = 3600 second

1 year =  365*24*3600 =31,536,000

A year is the orbit of a planetary body, such as Earth, moving in  orbit around the Sun. Due to the tilt of the earth's axis, the seasons change at the turn of the year, characterized by changes in weather, daylight hours, and thus vegetation and soil fertility. In the temperate and subpolar regions of the planet, four seasons are generally known: spring, summer, autumn and winter. In tropical and subtropical regions, several geographic sectors do not have defined seasons. but in the seasonal tropics, an annual wet and dry season is identified and observed.

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The missing information in the square is option(b) x = 4y = 4 √(2) and y = 4.

Given square PQRS, the task is to determine the missing information. A square is a quadrilateral with four equal sides and four equal angles.

The coordinates of the vertices of a square are (x,y), (x+4,y), (x+4,y+4) and (x,y+4).

The missing information, x and y, can be found by solving the equations that represent the sides of the square. We can start by solving for x.

The equation for the side PQ is x + 4y = 2 √(2). Solving this equation for x gives x = 4y - 8 √(2).

Similarly, the equation for the side RS is x + 4y = 4 √(2). Solving this equation for x gives x = 4y = 4 √(2).

Therefore, the missing information is x = 4y = 4 √(2) and y = 4.  

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The required number line is typically drawn from left to right to show all of the possible solutions that make the inequality true.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
The number line is typically drawn from left to right to show all of the possible solutions that make the inequality true.

The inequality may involve a variable x, and the number line would represent all possible values of x that satisfy the inequality. The solutions could be, for example, all values of x greater than 3, in which case the number line would start at 3 and extend to the right to represent all values of x greater than 3. Alternatively, the solutions could be all values of x less than or equal to -2, in which case the number line would start at -2 and extend to the left to represent all values of x less than or equal to -2.

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Answer:

An algebraic expression is a statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations.

Step-by-step explanation:

An example could include x^3 + 1, or something more complicated, like (y^4x^2 + 2xy – y)/(x – 1) = 12

Answer:

Step-by-step explanation:

These are equations which have an = sign and have a variable that needs to be found.

E.g x + 3 = 24

Answer:

              Teresa has 994 songs on her MP3 player.

Step-by-step explanation:

              We know that Rosanne has 142 songs on her MP3 player, and that Teresa has 7 times more songs than Rosanne does. Therefore, we can conclude that the number of songs that Teresa has 142 × 7 = 994 songs on her MP3 player.

Have a great day! Feel free to let me know if you have any more questions :)

The inequality describing Chau's goal to earn more than $1500 total this month is, $9b + $8u > $1500

This inequality represents Chau's goal to earn more than $1500 in total this month by working as a busboy and a theater usher.

The first term, $9b, represents the earnings from Chau's hours worked as a busboy, where $9 is his hourly rate as a busboy, and b is the number of hours worked as a busboy.

The second term, $8u, represents the earnings from Chau's hours worked as a theater usher, where $8 is his hourly rate as an usher, and u is the number of hours worked as an usher.

Total earnings = (hourly rate as busboy x number of hours as busboy) + (hourly rate as usher x number of hours as usher)

So, we can write the inequality for Chau's goal as follows:

$9b + $8u > $1500

where b is the number of hours worked as a busboy and u is the number of hours worked as an usher.

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54 centimetres, rounded to two decimal places, is comparable to around 21.26 inches.

The Imperial and US Customary measuring systems both utilise the inch as their unit of measurement.

It is the unit of length.

Furthermore, length is measured in centimetres,

Used in the International System of Units,

This is the metric system's present configuration.

There are 21.26 inches in 54 cm (centimeters).

To convert centimeters to inches,

You can use the following conversion:

1 inch = 2.54 cm

Therefore,

To convert 54 cm to inches,

You can divide 54 by 2.54:

54 cm / 2.54 = 21.26 inches

So 54 cm is equivalent to approximately 21.26 inches,

Rounded to two decimal places.

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The slope of each line on the given graph is:

Figure 1: -1/4

Figure 2: 0

Figure 3: -4

Figure 4: 4

The slope (m) of a linear relationship is calculated as rise/run = change in y / change in x.

Figure 1:

Slope (m) = change in y / change in x = -1/4 (the line declines, so the slope will be negative).

Figure 2:

Slope (m) = 0 (this is because there is no rise but run), thus, the slope of any horizontal line is always 0.)

Figure 3:

Slope (m) = change in y / change in x = -4/1 = -4 (the line declines, so the slope will be negative).

Figure 4:

Slope (m) = change in y / change in x = 4/1 = 4 (the line rises, so the slope will be positive).

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The age of Jane is 22 years.

Janes age is 10 more than three times her son's age. In two years, her age will be 12 less than the square of her son's age. Therefore, let's find Jane's age as follows:

Hence, using equation,

let

son's age = x

Jane age = 3x + 10

In two years,

(x + 2)² - (3x + 10 + 2)  = 12

(x + 2)(x + 2) - 3x - 12 = 12

x² + 2x + 2x + 4 - 3x - 24 = 0

x² + x - 20 = 0

x² - 4x + 5x  - 20 = 0

x(x - 4) + 5(x - 4) = 0

(x + 5)(x - 4) = 0

Therefore,

x = -5 and x = 4

We can only use positive numbers.

Therefore,

Jane's age = 3x + 10

Jane's age = 3(4) + 10

Jane's age = 12 + 10

Jane's age = 22

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The lithosphere's reservoir of carbon is approximately 10^5.25 or about 177,828 times greater than the biosphere's reservoir of carbon. Rounding this to the nearest order of magnitude gives an answer of (b) 10⁶.

Carbon is one of the most important elements on Earth as it forms the building blocks for life and plays a crucial role in regulating the planet's climate. The carbon cycle is a complex process that involves the exchange of carbon between different reservoirs such as the atmosphere, oceans, biosphere, and lithosphere.

To compare the size of the carbon reservoirs in the biosphere and lithosphere, we can take the ratio of the two reservoirs:

Lithosphere/Biosphere = 100,005,500/560

Simplifying the expression on the right-hand side gives:

Lithosphere/Biosphere = 178,933.93

To convert this ratio to orders of magnitude, we can take the logarithm base 10 of the ratio:

log10(Lithosphere/Biosphere) = log10(178,933.93)

log10(Lithosphere/Biosphere) ≈ 5.25

Therefore, the lithosphere's reservoir of carbon is approximately 10^5.25 or about 177,828 times greater than the biosphere's reservoir of carbon.

Rounding this to the nearest order of magnitude gives an answer of (b) 10⁶.

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Answer: -15

Step-by-step explanation:

In 2004, as per the run, the distance to the nearest tenth of a mile is 3.11 miles.

The distance that Kenenisa Bekele of Ethiopia ran in 2004 is equal to 5,000 meters, which is equivalent to 3.11 miles to the nearest tenth of a mile. To calculate this distance, you can use a simple conversion formula.

To convert meters to miles, you need to divide the number of meters by 1609.34.

In this case, we would divide 5,000 meters by 1609.34, which gives us 3.11 miles.

=> 5000/ 1609.34 = 3.11 miles.

This is the total distance that Kenenisa Bekele ran in 2004 to the nearest tenth of a mile.

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Answer:

Step-by-step explanation:

Use the Pythagorean theorem a^2 +b^2 =c^2

So 15^2 + 5^2 = c^2

sqrt c = sqrt 250

A nondirectional hypothesis using the t-score of -.493, degrees of freedom of 14, and a p-value of .629 could be:

"There is no significant difference between the two groups on the variable being measured."

This hypothesis is nondirectional because it does not specify which group would have a higher or lower score. The t-score and p-value indicate that the difference between the two groups is not statistically significant at the 95% confidence level.

"For the variable being measured, there is no significant difference between the two groups."

Because it does not state which group would have a greater or lower score, this hypothesis is nondirectional. The difference between the two groups is not statistically significant at the 95% confidence level, according to the t-score and p-value.

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Answer:

D

Step-by-step explanation:

step by step... solved

A man claims to be capable of extrasensory perception. A fair coin is flipped 25 times as just a test, and the man is asked to predict the outcome ahead of time. He gets 17 of the 25 questions right.

What is the likelihood that he could have performed at least as well if he didn't have ESP?

Let X = the number of correct responses he receives without using ESP (25, 0.5)

p(X = 17) = 1 - p(X = 16)

With n = 25 and p = 0.5, p(X = 16) = 0.9461.

As a result, p(X = 17) = 1 - 0.9461 = 0.0539.

If you don't have Binomial tables, a normal approximation to the Binomial can be used.

X is roughly equal to N(np, npq) = N. (12.5, 6.25)

p(X = 17) = 1 - p(X < 16.5) with a continuity correction = 1 - p(Z (16.5 - 12.5) / v6.25) = 1 - F(1.6) = 1 - 0.9452 = 0.0548

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It would take 11.25 hours after leaving his house until the phone's battery level got down to 31.5%.

According  to given conditions :

To determine how many hours after leaving his house it would take until the phone's battery level got down to 31.5%, we need to use the information provided in the table to find the equation of the line that represents the relationship between B and t. We can then use this equation to solve for the value of t when B is 31.5%.

To find the equation of the line, we can use the two points (1.5, 38.25) and (9, 9). The slope of the line is:

slope = (B2 - B1) / (t2 - t1) = (9 - 38.25) / (9 - 1.5) = -29.25 / 7.5 = -3.9

The equation of the line in point-slope form is:

B - 38.25 = -3.9(t - 1.5)

Simplifying, we get:

B = -3.9t + 44.1

Now we can solve for the value of t when B is 31.5%. Setting B to 31.5% (or 0.315) and solving for t, we get:

0.315 = -3.9t + 44.1

-3.9t = -43.785

t = 11.25

Therefore, it would take 11.25 hours after leaving his house until the phone's battery level got down to 31.5%.

What is percentage ?

A percentage is a number or ratio expressed as a fraction of 100. The symbol used to represent percentages is "%". Percentages are used to compare values and express proportions. For example, if a group of 100 people includes 60 men and 40 women, we can say that the percentage of men in the group is 60%, and the percentage of women is 40%.

To calculate a percentage, we divide the value we want to express as a percentage by the total value, and then multiply by 100. For example, if we want to express 25 as a percentage of 100, we divide 25 by 100 to get 0.25, and then multiply by 100 to get 25%. Similarly, if we want to find what percentage of 200 is 50, we divide 50 by 200 to get 0.25, and then multiply by 100 to get 25%.

Percentages are used in many different fields, including finance, science, and statistics, as well as everyday life. For example, we might use percentages to calculate the amount of tax on a purchase, to compare the results of scientific experiments, or to track the progress of a fundraising campaign.

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The correct answer is (c) Understate change in the cost of living because consumers substitute toward goods whose relative prices are declining.

consumers do substitute toward goods whose relative prices are declining. This means that they are able to maintain their standard of living even if the overall cost of living increases. Therefore, the CPI tends to understate changes in the cost of living because it does not fully account for consumer substitution.  

The other options are not correct because:

a. The CPI does take into account quality changes by adjusting prices for changes in quality.

b. The CPI adjusts for changes in relative prices, so it does not overstate changes in the cost of living due to substitution effects.

d. The CPI includes services, but it may understate changes in the cost of living if the prices of services are increasing faster than the prices of goods.

e. The CPI includes a wide range of items, including volatile items such as fruit, vegetables, and petrol. However, the weights assigned to these items may change over time to reflect changes in consumer spending patterns.

The correct answer is (c) Understate change in the cost of living because consumers substitute toward goods whose relative prices are declining.

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70 °C is equal to 158 °F.

A temperature unit developed from the SI (International System of Units) is the Celsius (symbol: °C).

Prior to the adoption of the metric system, the Fahrenheit (symbol: °F) was a commonly used measurement of temperature.

To convert a temperature from Celsius (°C) to Fahrenheit (°F),

We can use the following formula:

°F = (°C x 1.8) + 32

Where

°F is the temperature in Fahrenheit

°C is the temperature in Celsius.

Substituting 70 for °C,

We get:

°F = (70 x 1.8) + 32

Simplifying the expression:

°F = 126 + 32

°F = 158

Therefore, 70 degrees Celsius is equal to nearly 158 degrees Fahrenheit.

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Answer:

Step-by-step explanation:

0.14285714285714286

A glass case is in the shape of a rectangular prism where the volume of the case is 4/125 cubic foot. The number of cubic blocks with a side length of 1/5 foot required to find the volume of glass case is option C: 4.

What is the rectangular prism?

A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional solid shape that has six faces, where each face is a rectangle.

The volume of the glass case is 4/125 cubic foot. We can write this as:

V = l × w × h = 4/125

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

To find how many cubic blocks with a side length of 1/5 foot would be required to find the volume of the glass case, we need to find the number of cubic blocks that can fit in the rectangular prism. Since the side length of each block is 1/5 foot, the volume of each block is (1/5)^3 = 1/125 cubic foot.

Therefore, the number of cubic blocks required is:

number of blocks = V / volume of one block

number of blocks = (4/125) / (1/125)

number of blocks = 4

So, we would need 4 cubic blocks with a side length of 1/5 foot to find the volume of the glass case.

Hence, the answer is 4.

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Answer: 62

Step-by-step explanation:

The result of multiplying the numbers 31 by 2 is 62.

When you multiply two numbers, you are essentially adding the first number to itself a certain number of times, determined by the second number.

In this case, when you multiply 31 by 2, you are adding 31 to itself two times:

31 + 31 = 62

Therefore, the result of multiplying 31 by 2 is 62.

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Answer:

Length = 16 feet, width = 12 feet

Step-by-step explanation:

Scale is 2 cm = 4 feet

Therefore 1 cm = 4/2 = 2 feet

8 cm length = 8 x 2 = 16 feet

6 cm width = 6 x 2 = 12 feet

So the room size is Length = 16 feet, width = 12 feet

Answer: In the scale drawing, each 2 cm represents 4 feet. So, 1 cm represents 2 feet (since 2 cm is twice 1 cm). Therefore, the length of the room in feet is:

8 cm x (2 feet/1 cm) = 16 feet

Similarly, the width of the room in feet is:

6 cm x (2 feet/1 cm) = 12 feet

So, the actual dimensions of the room are length = 16 feet and width = 12 feet.

Answer: Length = 16 feet, width = 12 feet

Step-by-step explanation:

The answer is t = (2 - 3Q)/(4+Q).

To make t the subject of the given equation:

(2-4t)/(t+3)

We can start by cross-multiplying both sides by (t+3) to eliminate the denominator on the left-hand side:

(2 - 4t) = (t+3) * Q

where Q is an unknown value that is the result of the cross-multiplication.

Next, we can distribute the right-hand side:

2 - 4t = Qt + 3Q

Then, we can rearrange the equation by moving all the terms with t to one side and the constant terms to the other side:

2 - 3Q = t(4+Q)

Finally, we can divide both sides by the coefficient of t to isolate t:

t = (2 - 3Q)/(4+Q)

Therefore, the equation in terms of t is:

t = (2 - 3Q)/(4+Q)

In mathematics, an equation is a statement that two expressions are equal to each other. It consists of two sides: the left-hand side and the right-hand side, which are connected by an equals sign (=). An equation typically contains one or more variables, which are represented by symbols such as x, y, or z, and the goal is often to solve for these variables in order to find their values that make the equation true.

For example, the equation x + 2 = 5 is an algebraic equation that states that the sum of x and 2 is equal to 5. Solving this equation for x gives us x = 3, which means that the value of x that makes the equation true is 3.

Equations are used to model many real-world problems in mathematics, science, engineering, economics, and other fields, and they are an important tool for understanding and solving complex problems.

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Answer:

use a calculator online

Step-by-step explanation:

Calculating the Molecular Mass

Gather the necessary tools for solving a chemistry problem. Having everything you need easily accessible will simplify the process of solving the assigned problem. You will need the following:

A pencil and paper. Calculations are easier to solve when you write them out. Be sure to show all your steps to get full credit.

A periodic table. You will need to be able to find atomic weight of elements using the periodic table.

A calculator. Calculators are necessary to simplify calculations of complex numbers.

Answer:

34/5

Step-by-step explanation:

Option A. In observational studies, the variable of interest can be either numerical or categorical, so it does not have to be numerical.

Observational studies are a type of study in which researchers observe and record data on variables of interest without manipulating them directly. These studies are often used in fields such as epidemiology, social sciences, and psychology to investigate relationships between variables and identify potential risk factors for diseases or other outcomes.

The variable of interest in an observational study can be either numerical or categorical. Numerical variables are those that can be measured and expressed as a numerical value, such as age, height, weight, or blood pressure. Categorical variables are those that are qualitative or nominal in nature, such as gender, race, or smoking status.

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In observational studies, the variable of interest ____

A. cannot be numerical.

B. must be numerical.

C. is controlled.

D is not controlled.