There is each person holding the sign for 3/4 hours.
What is the rate?
A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The 4 members of a robotics team held a car wash to raise money. To attract customers, each person held a sign by the road for an equal portion of the car wash, which lasted 3 hours in all.
If the car wash lasted 3 hours in all and there are 4 members in the robotics team, each person held the sign for 3 hours / 4 = 3/4 hours.
Hence, there are each person held the sign for 3/4 hours.
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The sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores. What is the variance for this sample?
The variance for the sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores is 5.
The formula for the variance of a sample is:
[tex]s^2[/tex] = SS / (n - 1)
where SS is the sum of squared deviation scores, n is the sample size, and [tex]s^2[/tex] is the variance.
In this case, SS = 20 and n = 5, so we can substitute these values into the formula:
[tex]s^2[/tex] = 20 / (5 - 1)
[tex]s^2[/tex] = 5
Therefore, the variance for this sample is 5.
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3. You purchase a car using a $30,000 loan with a 6% simple interest rate.
(a) Suppose you pay the loan off after 6 years. How much interest do you pay on your loan? Show your work.
(b) Suppose you pay the loan off after 3 years. How much interest do you save by paying the loan off sooner? Show your work.
Answer:
(1) if the loan is paid off after 6 years, the interest paid on the loan is $10,800. (2) $5,400 in interest will be conserved if the debt is repaid in 3 years as opposed to 6 years.
What, using an illustration, is simple interest?Simple Interest (S.I.) is a technique for figuring out how much interest will accrue on a specific initial sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a cost of ten p.a. for 2 years, they will pay S.I. on the loaned money for those two years.
(a) Using the straightforward interest calculation, we can determine the amount of interest paid on the debt if it is repaid after six years:
I = Prt
where P represents the loan's capital, r represents the interest rate, and t represents the quantity of time (in years).
P is $30 000, r is 6%, and t is 6 years in this example. With these numbers entered into the algorithm, we obtain:
I = 30,000 * 0.06 * 6 = $10,800
Therefore, if the loan is paid off after 6 years, the interest paid on the loan is $10,800.
(b) To calculate the interest saved by paying off the loan after 3 years instead of 6 years, we can calculate the interest paid in both scenarios and then subtract the interest paid at 3 years from the interest paid at 6 years.
If the loan is paid off after 3 years, the total interest paid can be calculated using the same formula as before:
I = 30,000 * 0.06 * 3 = $5,400
By deducting the interest costs at 3 years from of the interest charged at 6 years, we can determine the amount of interest that would have been paid had the debt been repaid after 3 years:
Interest saved = Interest paid at 6 years - Interest paid at 3 years
= 10,800 - 5,400
= $5,400
Therefore, $5,400 in interest will be conserved if the debt is repaid in 3 years as opposed to 6 years.
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A ceramic paperweight is shaped like a square pyramid. The length of the square base and the slant height is shown. What is the height of the paperweight? Round to the nearest tenth of an inch.
4in 3in
A ceramic paperweight is shaped like a square pyramid. the height of the paperweight is 1 inch.
What is Pythagorean Theorem?
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base, and Hypotenuse.
To find the height of the paperweight, we can use the Pythagorean Theorem, which relates the lengths of the sides of a right triangle.
In this case, the height of the paperweight, which is the unknown side, forms a right triangle with one of the slant heights and half the length of the square base, as shown in the diagram below:
/\
/ \
/ \
/ \
/_ _ _ _\
4 in
To apply the Pythagorean Theorem, we can write:
height² + (1/2 * 4 in)² = 3 in²
Simplifying, we get:
height² + 8 in² = 9 in²
Subtracting 8 in² from both sides, we get:
height² = 1 in²
Taking the square root of both sides, we get:
height = 1 in
Therefore, the height of the paperweight is 1 inch.
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Select the correct answer from each drop down menu.
the graph of the function f(x) = 5/4sin(x)+1 is shown. what are they key features of this function?
Answer:
The maximum value of the function is 9/4.
The minimum value of the function is -1/4.
On the interval (0, pi/2), the function is strictly increasing.
The range of the function is [-1/4, 9/4].
Given function is:
y=5/4sin x + 1
:
Are all isosceles triangles always similar?
No, not all isosceles triangles are always similar. Two triangles are considered similar if their corresponding angles are congruent and their corresponding sides are in proportion. While all equilateral triangles are also isosceles triangles, not all isosceles triangles have congruent angles and proportional sides.
Any triangle with any two sides that have the same length is known as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides. Triangles are three-sided polygons in geometry that can be divided into three groups based on their sides, such as:
Scalene triangle (All three sides are unequal)Isosceles triangle (Only two sides are equal)Equilateral triangle (All three sides are equal)For example, consider an isosceles triangle with base angles of 70 degrees and a third angle of 40 degrees, and another isosceles triangle with base angles of 80 degrees and a third angle of 20 degrees. These triangles have different angles and are therefore not similar, even though they are both isosceles triangles.
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The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is
recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been
found to be 69 with a standard deviation of 7.6. Assume that the distribution is approximately normal.
Find the probability that an elite athlete has a maximum oxygen uptake of at least 84.2 ml/kg.
Find the probability that an elite athlete has a maximum oxygen uptake of at most 58.36 ml/kg.
Find the probability that an elite athlete has a maximum oxygen uptake of 58.36 ml/kg.
We are given that the distribution of maximum oxygen uptake for elite athletes is approximately normal with mean 69 and standard deviation 7.6.
To find the probability that an elite athlete has a maximum oxygen uptake of at least 84.2 ml/kg, we need to standardize the value using the formula:
z = (x - μ) / σ
where,
x = the value of 84.2 ml/kg
μ = the mean of 69 ml/kg
σ = the standard deviation of 7.6 ml/kg.
Plugging in the values, we get:
z = (84.2 - 69) / 7.6
= 2.03
Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being greater than or equal to 2.03 is 0.0217. Therefore, the probability that an elite athlete has a maximum oxygen uptake of at least 84.2 ml/kg is 0.0217.
To find the probability that an elite athlete has a maximum oxygen uptake of at most 58.36 ml/kg, we again need to standardize the value:z = (58.36 - 69) / 7.6
= -1.36
Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being less than or equal to -1.36 is 0.0869. Therefore, the probability that an elite athlete has a maximum oxygen uptake of at most 58.36 ml/kg is 0.0869.
Finally, to find the probability that an elite athlete has a maximum oxygen uptake of exactly 58.36 ml/kg, we need to use the fact that the normal distribution is a continuous distribution, which means that the probability of a specific value is zero. Therefore, the probability that an elite athlete has a maximum oxygen uptake of exactly 58.36 ml/kg is 0.Learn more Probabilities on
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If there were two runners running a race, one along the inside and one along the outside, how far apart they start so the race is fair?
Answer:
I would believe inside of a race track is smaller than the outside. They are staggered so the runners all run the same distance.
Step-by-step explanation:
y=(6x-5)(x+4) in standard form (Ax+By=C) and please provide steps! ;)
The quadratic equation y = 6x²+ 19x -20 has the same standard form as Ax+By +C = 0.
what is quadratic equation ?
A quadratic polynomial in an independent condition is represented by the expression x ax²+bx+c=0. a 0. Since this equation is of second order, the Fundamental Theory of Algebra requires that it has at best one solution. There can be both simple and complex solutions.
A quadratic equation is just that—quadratic. This indicates that which has at least yet another word that has to be squared. One of the often cited solutions for differential calculus is "ax² + bx + c = 0." where X is an undefined parameter and a, b, and c are mathematical coefficients or constants.
y=(6x-5)(x+4)
y = 6x² - 5x + 24x - 20
y = 6x² + 19x -20
The quadratic equation y = 6x² + 19x -20 has the same standard form as Ax+By +C = 0.
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HELP ME math DIVIDE 28 BY 25,704 USING LONG DIVISION
Answer:
918
Step-by-step explanation:
simplifying radicals
Answer:9√2
Step-by-step explanation:
you divide 1134 and 7 in square root and it equals sqrt(162)
Then you simplify by taking out numbers out of the square root.
sqrt(162)=9√2Find the conditional probability calculator
Conditional probability can be calculated by using Bayes' theorem, P(A|B) = P(B|A) × P(A) / P(B)
To find the conditional probability, we need to know the probability of two events: the probability of the event we're interested in, and the probability of the condition. Then, we can use Bayes' theorem to calculate the conditional probability.
Bayes' theorem states that the probability of an event A given that event B has occurred is equal to the probability of B given A, multiplied by the probability of A, divided by the probability of B:
P(A|B) = P(B|A) × P(A) / P(B)
The steps to find the conditional probability:
1) Identify the events A and B.
2) Determine the probabilities of A and B.
3) Determine the conditional probability P(B|A)
4) Substitute the values into Bayes' theorem to find P(A|B)
5) Interpret the result.
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how to convert 147 cm in feet?
The conversion of the unit centimeters to feet is written as 147 centimeters = 4.82283 feet.
Centimeters and feet are the units that are used for measuring the length of the any given parameter.
Conversion of the unit centimeter into feet is written as :
Value of one centimeter = 0.0328084 feet.
To convert the given value 147 centimeters substitute in the given relation we have,
⇒ ( 147 × 1 ) centimeters = ( 147 × 0.0328084 ) feet
⇒ 147 centimeters = ( 4.822835 ) feet
⇒ 147 centimeters = ( 4.8228 ) feet ( Round upto four decimals )
Therefore, after conversion the measurements centimeters to feet we have 147 cm is equal to ( 4.8228 ) feet ( Round upto four decimals ) .
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What is the initial value of the function Y=17(1.124)^x ?
Answer:
y = 17
Step-by-step explanation:
the initial value of the function is obtained when x = 0
• note that [tex]a^{0}[/tex] = 1
then
y = 17[tex](1.24)^{x}[/tex] ← substitute x = 0
y = 17[tex](1.24)^{0}[/tex] = 17 × 1 = 17
initial value of the function is y = 17
a car dealership pays $8,350 for a car. ther mask up the price by 17.4% to get the retail price. what is the retail price of the car at this dealership?
The retail price of the car at the dealership is $9,803.90. This means that the dealership is adding a markup of $1,453.90, or 17.4% of the cost, to sell the car to customers.
To find the retail price of the car at the dealership, we need to add 17.4% to the dealership's cost of $8,350. Here are the steps to do this calculation:
Multiply the cost of the car by the percentage markup as a decimal. To convert a percentage to a decimal, divide it by 100. So 17.4% as a decimal is 0.174.
Markup = $8,350 x 0.174 = $1,453.90
Add the markup to the cost of the car to get the retail price.
Retail Price = $8,350 + $1,453.90 = $9,803.90
It's important to note that the final selling price of the car may be negotiable, and that other fees and taxes may also be added to the retail price.
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A circle is centered at the origin, and point (9,−12)
lies on the circumference of the circle. Which two points also lie on the circumference of the circle
The two points that also lie on the circumference of the circle are approximately (-9.2, -12.5) and (11.8, -7.1).
Describe circumference of the circle?The circumference of a circle is the distance around its outer edge, also known as its perimeter. It is a key measurement in geometry, and is defined as the product of the circle's diameter and pi (π), a mathematical constant approximately equal to 3.14.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, r is the radius of the circle, and π is the mathematical constant pi.
C = πd
The circumference of a circle is proportional to its radius or diameter, which means that if you double the radius or diameter of a circle, its circumference will also double. This relationship is fundamental to many mathematical and scientific applications, such as calculating the area or volume of a circle or sphere.
The circumference of a circle can be measured using a variety of tools, including rulers, compasses, and string. In practice, it is often measured indirectly by measuring the diameter or radius of the circle and using the formula above to calculate its circumference.
In summary, the circumference of a circle is the distance around its outer edge or perimeter, and is calculated using the formula C = 2πr or C = πd. It is a key measurement in geometry and has many practical applications in mathematics, science, and engineering.
To find two more points on the circumference of the circle, we can use the fact that the distance between the center of the circle and any point on its circumference is equal to the radius of the circle.
The radius of the circle can be found using the distance formula, which gives:
radius = sqrt((9-0)^2 + (-12-0)^2) = sqrt(225) = 15
So the circle has a radius of 15.
Now, to find two more points on the circumference, we can use the fact that any point on the circle can be represented as (r cos θ, r sin θ), where r is the radius of the circle and θ is the angle that the line connecting the point and the origin makes with the positive x-axis.
Since we already know one point on the circle, (9,-12), we can find the angle θ that this point makes with the positive x-axis by using the inverse tangent function:
θ = arctan(-12/9) = -53.13 degrees (or -0.93 radians)
Now we can find two more points on the circle by adding or subtracting multiples of 360 degrees (or 2π radians) to the angle θ and using the formula (r cos θ, r sin θ). For example:
Point (15 cos (-53.13), 15 sin (-53.13)) ≈ (-9.2, -12.5)
Point (15 cos (306.87), 15 sin (306.87)) ≈ (11.8, -7.1)
Therefore, the two points that also lie on the circumference of the circle are approximately (-9.2, -12.5) and (11.8, -7.1).
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What is the conversion of 31c to f ?
The value of conversion from Celsius to Fahrenheit for the value 31 Celsius is equal to 87.8 Fahrenheit.
Standard measuring units for the temperature is known as Celsius and Fahrenheit.
Formula used to convert the temperature from Celsius to Fahrenheit is written as
°F = 9 /5 ( ° C ) + 32.
Convert 31 Celsius to Fahrenheit by substituting the given value in the above formula :
= 9 /5 ( 31° ) + 32
= (1/5) (279° ) + 32
= 55.8° + 32
= 87.8°F
Therefore, the values after conversion for the 31Celsius to Fahrenheit is given by 87.8 Fahrenheit.
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determine if the columns of the matrix form a linearly independent set.[1 4 -3 0 -2 -2 4 1 -4 -5 7 5]
What is the conversion of 23/32 in inches ?
The conversion of 23/32 cm in inches is 0.283464844 inches.
Centimeter (cm) and inch are both units of measurement used to express length or distance.
Centimeter is a metric unit of length used in the International System of Units (SI) and is equal to one hundredth of a meter.
To convert 23/32 centimeters (cm) to inches, we can use the conversion factor of 1 cm = 0.393701 inches.
First, we can convert 23/32 cm to cm as a decimal by dividing the numerator (23) by the denominator (32):
23/32 cm = 0.71875 cm
Then, we can use the conversion factor to convert 0.71875 cm to inches:
0.71875 cm × 0.393701 inches/cm = 0.28346484375 inches (rounded to nine decimal places)
Therefore, 23/32 cm is approximately equal to 0.283464844 inches.
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Correct Question:
What is the conversion of 23/32 cm in inches ?
Which value for x will result in the greatest relative frequency given discrete random variable X, when [tex]X \sim B(4, \frac{1}{10})?[/tex]?
x=5
x=1
x=0
x=3
The value x = 3 will result in the greatest relative frequency given discrete random variable X.
What is relative frequency?
A frequency is the number of times an event takes place. It's experimental, not theoretical, to study relative frequency. As it is an experimental one, it is likely that when we repeat the trials, we will get different relative frequencies.
The relative frequency of a discrete random variable increases with decreasing variable value.
This implies that,
A variable with x = 0 would occur more frequently than one with x = n, where n > 0.
So, the greatest relative frequency given discrete random variable X, when X ∼ B (4, 1/10) is x = 3.
Hence, the value x = 3 will result in the greatest relative frequency given discrete random variable X.
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Write an expression that is equivalent to 734+356 − 134that uses addition instead of subtraction.
The expression that is equivalent to 734 + 356 - 134 using addition instead of subtraction is:
734 + 356 + (-134)
Answer:
706+350 = 956
write 5 x 5 x 5 x 5 using exponets
Answer:5 and a tiny 4 in the corner of that 5
Step-by-step explanation:
there are four 5s so u do 5 with little 4
Find the highest concentration after how many hours
Using the derivative of the function, we cannot approximate the time when the concentration is highest since it does not exist.
What is the time of highest concentrationTo find the time when the concentration is highest, we need to find the maximum of the concentration function. We can do this by finding the derivative of the function and setting it to zero, and then solving for t.
First, let's find the derivative of c(t):
c'(t) = [d/dt](120t / (3t^2 + 90))
c'(t) = (120(3t^2 + 90) - 120t(6t)) / (3t^2 + 90)^2
c'(t) = (360t^2 + 10800 - 720t^2) / (3t^2 + 90)^2
c'(t) = 10800 / (3t^2 + 90)^2
Now, we set c'(t) to zero and solve for t:
10800 / (3t^2 + 90)^2 = 0
10800 = 0 (since the denominator cannot be zero)
There is no solution to this equation, which means that c'(t) never equals zero, and therefore there is no maximum or minimum value for the concentration.
However, we can use the second derivative test to confirm this result. Taking the derivative of c'(t), we get:
c''(t) = d/dt
c''(t) = [d/dt](10800 / (3t^2 + 90)^2)
c''(t) = (-2 * 10800 * 3 * 2t) / (3t^2 + 90)^3
c''(t) = -129600 / (3t^2 + 90)^3
At any value of t, the denominator is positive, so the sign of the second derivative is determined by the numerator. Since the numerator is negative for all values of t, the second derivative is negative and therefore the function is concave down for all values of t. This means that there is no maximum value for the concentration, only a minimum value of 0.
Therefore, we cannot approximate the time when the concentration is highest since it does not exist.
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What does it mean if a function is continuous?
The absence of unexpected values or discontinuities is referred to as a function's continuous nature.
A continuous function is one in which a shift in the argument causes a continuous change in the value of the function, which is a change without a noticeable jump. This shows that there are no abrupt changes in value or discontinuities. More exactly, a function is continuous if it is possible to guarantee that, even with arbitrarily small changes to its parameter, its value won't change dramatically. Any function that is discontinuous is referred to as such.
A function is referred to as continuous if it is constant for all values of x inside its domain. The ability to simulate and evaluate physical occurrences and mathematical relationships involving smoothly varying numbers makes continuous functions crucial in many branches of mathematics and science.
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A taxi makes 56 trips between two cities which are 492 km apart. How much distance does the taxi cover in all?
Answer:
Step-by-step explanation:
25,584km
how much is 140 cm in inches
Answer:
Step-by-step explanation:
140 cm to inches is 55.1181 or roughly 55 inches.
what is 35km in miles?
Based on the conversion factor, 35km is equivalent to approximately 21.75 miles.
Kilometers and miles are units of distance measurement used in different parts of the world. While kilometers are the standard unit of distance in most countries, miles are widely used in the United States, the United Kingdom, and a few other countries.
A kilometer is approximately 0.621371 miles, which means that 1 mile is roughly 1.609344 kilometers.
To convert 35km to miles, we need to use this conversion factor. We can start by setting up a proportion:
35 km = x miles
1 km = 0.621371 miles
Multiplying both sides by the conversion factor, we get:
35 km x 0.621371 miles/1 km = x miles
Simplifying this expression, we get:
21.748485 miles = x miles
In conclusion, measurements are essential in our daily lives, and knowing how to convert one measurement to another can be beneficial. In this article, we explored what 35km in miles means and how we can convert kilometers to miles. Remember that 1km is approximately 0.621371 miles, and we can use this conversion factor to convert any distance measurement from kilometers to miles or vice versa.
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What is a factor tree for 78?
The factor tree shows how 78 can be factored into its prime factors.
78 = [tex]2 \times 3 \times 13.[/tex]
The first step in creating a factor tree for the number 78 is to identify two factors of 78 that sum up to 78. One such pair of factors is 6 and 13. After we reach prime numbers, we can carry on breaking down each component.
Prime factorization is the process of converting a composite number into the product of its prime factors. A prime factor is a prime number that divides the original integer by itself with no remainder.
The prime factorization of the number 78 is
78 = 6 x 13
78 = 2 x 3 x 13.
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a. Find the perimeter of a triangle whose side
lengths are 5 cm, 8√3 cm, and √27 cm. Give
the answer as a radical expression in simplest
form.
Answer:
[tex]5+11\sqrt{3}[/tex]
---------------
Perimeter is the sum of side lengths:
[tex]P=5+8\sqrt{3}+\sqrt{27} =5+8\sqrt{3}+\sqrt{3^2*3} =5+8\sqrt{3}+3\sqrt{3}=5+11\sqrt{3}[/tex]Also need help with this one girlys or boys
The equivalent expression is 0.7 - 1.8h.
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
2.1 + (-3.7h) + 1.9h - 1.4
Combine the like terms.
2.1 - 1.4 - 3.7h + 1.9h
0.7 - 1.8h
Thus,
0.7 - 1.8h is the equivalent expression.
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What is the conversion of 1500 meters in miles ?
To convert meter into miles we simply have to divide meter by 1609.34 so we have 1500 m as 0.9321 miles.
Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.
The SI base unit of length is the metre (or metre; US spelling), which is denoted by the letter m.
first described in 1793 as a ten millionth of the distance between the equator and the North Pole, but was later redefined in 1799 to refer to a prototype metre bar (this bar was changed again in 1889).
The imperial unit system uses the symbol mi to designate the mile as a unit of length.
Although it was initially an English unit, it was adopted by numerous nations, each of which had a somewhat different definition. However, the English mile is 63,360 inches, 5280 feet, or 1760 yards.
Miles = meter x 0.000621
= 1500 x 0.000621
= 0.9321 miles
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