Bob’s average speed was 72 miles/hr and the Mean Value Theorem can be used to prove that he was traveling faster than 55 miles per hour at some point between the two toll readers.
How to determine the true statementWe have the following parameters
Rate = 50 miles per hour
Time = 12:00 to 12:10 where he passed the second reader after 12 miles
This means that he drove 12 miles in 10 minutes or 1/6 hour
The speed within this interval is calculated as
Speed = 12/(1/6)
Evaluate
Speed = 72 miles
So, at a point t, Bob was driving at an instantaneous speed of 72 miles per hour, which is faster than 55 miles per hour.
Therefore, Bob was traveling faster than 55 miles per hour at some point between the two toll readers.
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Find the point (x, y) on the unit circle that corresponds to the real number t. t = 7/4
The point on the unit circle that corresponds to the real number t = 7/4 is given as follows:
(-0.1782, 0.9840).
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
With parameter t, the coordinates of the point are given as follows:
(cos(t), sin(t)).
Hence the x-coordinate when t = 7/4 is given as follows:
cos(7/4) = -0.1782.
The y-coordinate when t = 7/4 is given as follows:
sin(7/4) = 0.9840.
Meaning that the coordinates are:
(-0.1782, 0.9840).
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Kevin hiked up Lamb's Canyon in 3 hr and then ran back down in 2 hr. His speed running downhill was 1.8 mph greater than his speed hiking uphill. How far up the canyon did he hike?
Kevin hiked (blank) mi up the canyon.
Kevin hiked up Lamb's Canyon with the goal of making it to the top.
How far up the canyon did he hike?To solve it, you need to set up two equations - one for hiking and one for running.Let x be the distance Kevin hiked up the canyon.
For hiking: 3 hr = x / h
For running: 2 hr = (x + 1.8) / r
Where h is the speed at which Kevin hiked uphill and r is the speed at which he ran downhill.Solving the two equations for x yields:
x = (3h * r) / (h + r)
To find the distance Kevin hiked up the canyon, you need to plug in the values for h and r.Therefore, Kevin hiked (3h * r) / (h + r) mi up the canyon.
For the distance that Kevin hiked uphill, the equation would look like this:Distance = (x mph) * (3 hr)
For the distance that Kevin ran downhill, the equation would look like this:Distance = (x + 1.8 mph) * (2 hr)
We can combine these two equations by setting them equal to each other and solving for x. We get:(x mph) * (3 hr) = (x + 1.8 mph) * (2 hr)
Solving for x, we get x = 2.4 mph.
Now that we know x, we can plug it back into our original equation for the distance that Kevin hiked uphill. We get:Distance = (2.4 mph) * (3 hr) = 7.2 mi. Therefore, Kevin hiked 7.2 mi up the canyon.To learn more about to find the distance refer to:
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The proportional relationship between the number of inches a candle has burned away, b, at any time in hours, t, can be represented by the equation b = 1.5tb=1.5t. At what rate does the candle burn, in inches per hour?
The rate at which the candle burns is 1.5 inches per hour.
At what rate does the candle burn, in inches per hour?We know that the proportional relation between the number of inches that the candle has burned away, b, and the time in hours, t, is:
b = 1.5*t
The rate at which the candle burns is the amount burned in one unit of time, in this case, hours, then:
So, after t = 1 (one hour)
b = 1.5
In one hour, the candle burns 1.5 inches.
That is the rate at which the candle burns, it should be written as:
rate = 1.5 inches burned per hour.
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Use the converse of the Pythagorean theorem to determine whether the triangle is
right, obtuse or acute.
9 m
15 m
10 m
The given triangle is obtuse triangle according to the corollary to the converse of the Pythagorean Theorem.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The triangle's longest side measures 15 units in length.
Compare the sum of the squares on the other two sides to the square that is the length of the longest side.
The square of the longest side is 15², which equals 225.
9² + 10² = 181 square units make up the sum of the squares on the other two sides.
Thus, 181 < 15².
As a result, the triangle is an obtuse triangle according to the corollary to the converse of the Pythagorean Theorem.
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There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple? (Give your answer as a fraction in simplest form.)
The probability that the next fruit out of the bag is an apple is P = 4/5
How to find the probability?We want to fnind the probability of randomly selecting an apple from the bag, where we assume that all the fruits have the same probability of being randomly selected.
Remember that the probability is equal as the quotient between the number of apples and the total number of fruit on the bag.
Originally, there are:
4 apples.3 peaches2 plums.The checkout person takes 2 plums and 1 peach, so now there are:
4 apples.1 peach.For a total of 4 + 1 = 5 fruits
Then the probability of randomly grabing an apple is:
P = 4/5
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Is 4.259462364423... Rational or irratioL
DUE REALLY SOON SOMEONE PLEASE HELP ME WITH THIS!
how to solve 9x-3y=5 & 2x -3y=7 using the elimination method
The solution to the system of equations 9x - 3y = 5 and 2x - 3y = 7 is (-2/7, -53/21)
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Given the equations:
9x - 3y = 5 (1)
2x - 3y = 7 (2)
To solve by elimination method, subtract equation 2 from 1, hence:
7x = -2
Dividing by 2:
x = -2/7
Put x = -2/7 in equation 2:
2(-2/7) - 3y = 7
y = -53/21
The solution is (-2/7, -53/21)
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x-2y+z=9
2x + 3y - 2z = -12
x+y=3z = - 13
Answer:
what to find in this question ?
Write the first five terms of the sequence that is represented by the recursive function
f(1) =3
f(n) = f(n-1) = 4, where n is an integer and n > 1.
The first five terms of the arithmetic sequence are given as follows:
3, -1, -5, -9, -13.
How to model the arithmetic sequence?An arithmetic sequence is a sequence for which the difference between consecutive terms is constant, being called common difference d.
The recursive definition is given as follows:
f(n) = f(n - 1) + d.
For this problem, the definition is given as follows:
f(n) = f(n - 1) - 4.
Meaning that the common difference is of 4, and hence each term is obtained subtracting the first term by 4, starting with the first term given by f(1) = 3.
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what is the y-intercept in the following equation y=-4x-5
Answer:
y intercepts : (0, -5)
Step-by-step explanation:
hope it helps<3Answer:
(0,-5)
Step-by-step explanation:
Solve for x round to the nearest tenth
The solved for x round to the nearest tenth is x≈ 14.
What is meant by round ?
A spherical item. a circuitous or repetitive course; rounds in the hospital.A large-scale outburst at a gathering from a crowd of people.A song that is sung by multiple groups, each of which begins singing at a separate moment.Making a number simpler while maintaining a value that is close to what it was is known as rounding. Although less accurate, the outcome is simpler to utilize.For instance, 73 equals 70 when rounded to the closest 10, since 70 is closer to 73 than 80 is.Rounding numbers maintains the value of the original number while also making them "easier" to use or comprehend.Remember Sine of an angle is = opposite side /hypotenuse
So let the hypotenuse be x :
sin(54°) = opposite side / x
sin(54°) = 12 / x
To solve for x, divide sin(54°) by 12:
x = 12 / sin(54°)
x≈14
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find $53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} 1\frac{2}{3} \right)$. express your answer as a mixed number.
The result of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex] is[tex]$-56\frac{13}{20}$[/tex]
A mixed number is a combination of a whole number and a fraction, like [tex]3\frac{1}{2}[/tex], expressing numbers greater than one whole unit. It can be converted to an improper fraction.
To find the solution of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex]
We can first simplify the inner parenthesis
[tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right)=53\cdot(-1\frac{1}{10})=-53\frac{11}{10}$[/tex]
Then simplify the denominator, The denominator is the bottom part of a fraction, which represents the total number of parts in the whole. It is used to indicate the size of the fraction's unit or whole. It is also used to divide the numerator (top part of a fraction) by in order to determine the fraction's value.
[tex]$2\frac{3}{4} - 1\frac{2}{3} = \frac{11}{4} - \frac{5}{3} = \frac{44}{12} - \frac{20}{12} = \frac{24}{12} = 2$[/tex]
Now we can divide -53 and 11/10 by 2
[tex]$-53\frac{11}{10} \div 2 = -53\frac{11}{20} = -\frac{1133}{20} = -56\frac{13}{20}$[/tex]
So, the answer is [tex]$-56\frac{13}{20}$[/tex]
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when performing an addition or subtraction calculation, significant figures in the calculated result are dictated by the decimal places of the measured numbers. the calculated result should have choose... the measured number in the calculation with the fewest
The number with the fewest Decimal point will determine the number of significant figures in the calculated result.
The significant figures in the estimated result of an addition or subtraction calculation are determined by the decimal places of the measured values. This is so that the computed result can accurately reflect the precision of the measurement, which is shown by the decimal points in the measured values. Therefore, in the calculation with the fewest decimal places, the calculated result should have the same number of decimal places as the measured value. The result should have two decimal places, for instance, if one number has two decimal places and the other has four. By doing this, it is ensured that the result is not given a higher level of precision than the measured data utilized in the computation warrant.
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Suppose that a wholesaler expects that his monthly revenue, in dollars, for an electronic game will be R(x) = 170x -0.13x^2, 0 < x < 800 where x is the number of units sold. Find his marginal revenue and interpret it when the quantity sold is the following. (a) X = 200 $ Interpret the marginal revenue. O This is the additional revenue from the 201st unit. O This is the additional revenue from the 200th unit. O The sale of the 200th unit results in a loss of revenue of this amount O The sale of the 201st unit results in a loss of this amount. (b) 800 $ Interpret the marginal revenue. O This is the additional revenue from the 101st unit. O This is the additional revenue from the 200th unit. O The sale of the 101st unit results in a loss of this amount O The sale of the 800th unit results in a loss of revenue of this amount
The total monthly revenue when 200 units were sold is $28800 and the monthly revenue when 800 units were sold is $52800.
Given,
The equation for monthly revenue, [tex]R(x)= 170x - 0.13x^{2}[/tex] [tex](0 < x < 800)[/tex]
where [tex]x[/tex] is the number of units sold
(a) Total number of units sold, [tex]x = 200[/tex]
Monthly revenue, [tex]R(200)= 170x- 0.13x^{2}[/tex]
[tex]= 170*200 - 0.13*200^{2}[/tex]
[tex]= 34000 - 0.13* 40000[/tex]
[tex]= 34000 - 5200[/tex]
[tex]= 28800[/tex]
Hence , monthly revenue = $28800
(b) Total number of units sold, [tex]x = 800[/tex]
Monthly revenue, [tex]R(800)= 170x- 0.13x^{2}[/tex]
[tex]= 170*800 - 0.13*800^{2}[/tex]
[tex]= 136000 - 0.13*640000[/tex]
[tex]= 136000- 83200[/tex]
[tex]= 52800[/tex]
Hence , monthly revenue = $52800
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what is the length q and r
The correct order of bond lengths P, Q, and R in the above diagram is P > Q > R. The correct option is A.
What is the bond length?The bond length is the distance between the centers of two bound atoms. Consider the fact that a homonuclear diatomic molecule's bonded atoms are separated by half their element's atomic radius (sometimes referred to as the covalent or bonding atomic radius).
Less percentage of s character in a bond means the length of orbitals of the molecule is more, and also the bond length is more.
Therefore, the correct option is A. P > Q > R.
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The question is incomplete. Your most probably complete question is given below:
Which is the correct order of bond lengths P, Q, and R in the above diagram?
P > Q > R
R > Q > P
Q > P > R
Q > R > P
ara sells apples at a farmers market she begins the day with 35 1/2 pounds of apples she sells half of the apples in the mornning 4/19 of the apples in the afternoon and 1/4 of the apples in the evening how many pounds of apples dose she have left
Using mathematical operations, Ara's remaining pounds of apples are 1.405 pounds.
What are mathematical operations?The four basic mathematical operations are addition, subtraction, division, and multiplication.
In this situation, we applied the mathematical operations of multiplication, addition, and subtraction to determine the difference (or the quantity of apples left) between the quantity brought to the market and the quantity sold.
The total quantity of apples = 35¹/₂ pounds
The quantity sold in the morning = ¹/₂ of 35¹/₂ pounds = 17.75 pounds
The quantity sold in the afternoon = ⁴/₁₉ of 35¹/₂ pounds = 7.47 pounds
The quantity sold in the evening = ¹/₄ of 35¹/₂ pounds = 8.875 pounds
The total quantity sold = (¹/₂ + ⁴/₁₉ + ¹/₄) = ³⁶/₃₈ of 35¹/₂ pounds = 34.095 pounds
The remaining pounds of apples = 1.405 pounds (35.5 - 34.095)
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A tumor is injected with 0.6
grams of Iodine-125, which has a decay rate of 1.15%
per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after t
days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60
days.
Enter the exact answer.
Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, c*exp(h)
or c*ln(h)
.
Answer:
The exponential model representing the amount of Iodine-125 remaining in the tumor after t days would be:
Iodine-125(t) = 0.6 * e^(-0.0115t)
To find the amount of Iodine-125 that would remain in the tumor after 60 days, we would plug in t = 60 into the model:
Iodine-125(60) = 0.6 * e^(-0.0115(60))
= 0.6 * e^(-0.69)
= 0.6 * 0.5032
= 0.3019
So after 60 days, there would be approximately 0.3019 grams of Iodine-125 remaining in the tumor.
If I helped you, could you please make my answer best?
Which expression is the least absolute value ?
|-28|
|-1|
|6|
|15|
Answer:
|-28|
Step-by-step explanation:
-28 is the least value in the expression given
NEED HELP ASAP Select from the drop-down menu to correctly complete the statement.
The product of 7 and 58 is
Choose...
because 58 is less than 1.
Drop downs: greater than 7
less than 7
equal to 7
The product of 7 and ⁵/₈ is less than 7 because ⁵/₈ is less than 1
How to find the product of fractions?We want to find the product of 7 and ⁵/₈.
Now, this will be expressed as;
7 * ⁵/₈.
Now, we are multiplying a whole number by a proper fraction that is less than 1 and as such, it means that the product will be lesser than 7 simply because ⁵/₈ is less than 1.
Thus;
7 * ⁵/₈ = 35/8
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a wooden deck of a house needs paint. the function C(n)=24n+5 represents the cost of painting the deck as a function of the number of cans of paint used.The function n(A)=A/6 represents the number of cans of paint needed as a function of area in square ft of the deck. Write a function for the cost of painting the deck as a function of the area in square ft of the deck.
Answer: C(n)=24n+5 =24
(A)=A/6 =0
Step-by-step explanation:
There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple?
According to the information, the probability that the next pice of fruit out of the bag will be an apple is 0.66.
How to calculate the probability that the next piece of fruit out of the bag will be an apple?To calculate the probability that the next piece of fruit out of the bag will be an apple we have to perform the following mathematical operation:
We have to calculate how many fruits there are in the bag.
4 apples, 3 peaches, and 2 plums less 2 plums and 1 peach = 4 apples, 2 peaches.So, we have 4 apples and 2 peaches, so we have 6 fruits in total. Now, we have to divide the number each fruit in the bag by the total number of fruits as shown.
4 / 6 = 0.66
2 / 6 = 0.33
According to the above, the probability that the next pice of fruit out of the bag will be an apple is 0.66.
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HELP!!! You go out to dinner and the bill comes to $40.94. How much should you tip if you want the tip to be 15.0% of the bill? Express the dollar amount to the nearest cent
Answer: 6.14for the tip
Step-by-step explanation:
Answer:
$6.14
Step-by-step explanation:
Well, first step is to divide 15.0% by $40.94.
Then you get 6.141
Translate that to money, rounding off, you get:
$6.14!
I hope this helps! Great to be of service to you!
please help. solve the inequality
Answer:
x ≤ - 2 ; 0 ≤ x ≤ 7
Step-by-step explanation:
x ≤ - 2
0 ≤ x ≤ 7
the distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. suppose the company hires a 28th employee at a salary of $120,000. which of the following claims about the new salary distribution is supported?
The range is not likely to vary, which is one of the claims regarding the new salary distribution that is supported.
What is standard deviation?Standard deviation is significant because it facilitates comprehension of measurements when data is scattered. The data's standard deviation will increase in proportion to how widely spread the data is. How dispersed the data is is indicated by the standard deviation. Any distribution will have roughly 95% of its values within two standard deviations of the mean. A large standard deviation doesn't necessarily mean something is wrong; rather, it only indicates that the group under study has a lot of variety, according to Rumsey in Statistics for Dummies.Therefore,
Given that a small company's salary distribution of 27 employees has a mean of $35,000 and a standard deviation of $2,000,
When a highly unusual value, such as 120000, is taken into account for the 28th employee, we discover that the mean increases.
The new median would be the average of items 14 and 15, as the prior median was the 14th item. Thus, the median may alter.
Because the maximum has been raised up to 120000, the range will undoubtedly vary.
so that we can say
Range changes, median changes, and mean increases.
Thus, we determine that Option B is correct.
The complete question is:
The distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. Suppose the company hires a 28th
28th employee at a salary of $120,000. Which of the following claims about the new salary distribution is supported?
The median is not likely to change. I
The range is not likely to change. II
The mean is likely to increase. III
A) I only
B) III only
C) I and II only
D) I and III only
E) I, II, and III
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Some values of functions f, g, h, and k are provided in the table on the right.
Find a possible equation of each function Verify your results with a graphing
calculator table. (HINT Use linear or exponential equations]
The equation of function f is f(x) =?
Without any values of the functions f, g, h, and k, it is not possible to find the equation of each function. The equation of a function can be determined by analyzing the values of the function. Based on the given values, a possible equation can be found and then verified by plotting the points on a graph and seeing if they align with the equation.
It's important to note that the equation can be a linear or exponential equation but it's impossible to determine it without any values.
The local coffee shop ran a summer special. With the purchase of an $8.75 reusable mug, the cost of a coffee would only be $1.95 per cup for every visit through out the entire month. If Bre spent a total of $41.90 in the month of July, how many cups of coffee did she purchase?
PLS HELP
Answer: X = 17
Step-by-step explanation:
8.75 + 1.95x = 41.9
1.95x = 41.9 - 8.75
1.95x = 33.15
x = 33.15/1.95
x = 17
When given a circle with a radius of 4, how do you find the following? explain why.
a. Diameter
b. Circumference
Answer:
Diameter is 8
Circumference is 8pi ~= 25.13
Step-by-step explanation:
The diameter is double the radius. So the given radius is 4 and double is 8.
The Circumference is given by C = pi•d or C = 2pi•r
Both of these equations will give the circumference.
C = pi•d
= pi•8
= 8pi ~= 25.13
OR
C = 2pi•r
= 2pi•4
= 8pi ~= 25.13
For finding the diameter, I multiply the radius by 2:
Diameter = 2 × radius
= 2 × 4
= 8
So the diameter is 8. As for the circumference, we can use two ways : either multiply pi times the diameter, or multiply 2 times pi times the radius.
The formulas are
C = πd and C = 2πr
To find the circumference, stick in 8 for d:
C = π × 8
C = 25.13 units
can you help me with my math today
One of the legs of a right triangle measures 11 cm and the other measures 14 cm
The measure of hypotenuse of the triangle whose sides are given would be = 17.80cm
How to find the hypotenuse of triangle?The formula used to calculate the hypotenuse of a triangle is the Pythagorean formula= C²= a² + b²
Where c = hypotenuse = ?
a² = 11 cm
b² = 14 cm
Substitute the given values into the formula to find hypotenuse.
c² = 11² + 14²
c² = 121+196
c² = 317
C = √317
C = 17.80cm.
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Complete question:
One of the legs of a right triangle measures 11 cm and the other leg measures 14 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
