Jack spends 300 minutes in two weeks riding his skateboard to and from his friend's house Monday through Friday.
Time taken by Jack to ride his skateboard down the hill to his friend's house = 10 minutes
Time taken by Jack to ride his skateboard up the hill to his friend's house = 20 minutes
Total time combined = 30 minutes
Total days in a week Monday through Friday= 5 days
Total days in 2 weeks = 10 days
Therefore, time spent by jack riding his skateboard up and down the hill to his friend's house in two weeks Monday through Friday = 10*30 = 300 minutes
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Multiplying polynomials
(5p - 5)(7p + 6)
What is the sign of
−289 + 311?
Answer:
it is positive
Step-by-step explanation:
-289+311=22 which is a positive number
Solve the recurrence relation: t(n) = 3t(n-1) 1, with initial condition of t(0) = 1
A linear recurrence relation is a function or sequence in which each term is a linear combination of the terms that came before it.
The recurrence relation exists [tex]$T(n)=\Theta\left(3^n\right)$[/tex].
What is meant by "recurrence relation"?Recurrence relations are used to simplify complex problems by reducing them to an iterative process based on simpler versions of the problem.
Using the substitution method, we find out that
[tex]T(n) &=n+3 T(n-1) \\[/tex]
[tex]&=n+3(n-1)+3^2 T(n-2) \\[/tex]
[tex]&=n+3(n-1)+3^2(n-2)+3^3 T(n-3) \\[/tex]
[tex]&=\cdots \\[/tex]
[tex]&=n+3(n-1)+3^2(n-2)+\cdots+3^{n-1}(n-(n-1))+3^n T(0) \\[/tex]
simplifying the above equation, we get
[tex]$&=\frac{3^{n+1}-2 n-3}{4}+3^n T(0) \\[/tex]
[tex]&=\Theta\left(3^n\right)[/tex]
Even without doing the full calculation it is not hard to check that [tex]$T(n) \geq 3^{n-1}+3^n T(0)$[/tex], and so [tex]$T(n)=\Omega\left(3^n\right)$[/tex].
A cheap way to obtain the corresponding upper bound is by considering
[tex]$S(n)=T(n) / 3^n$[/tex], which satisfies the recurrence relation
[tex]$S(n)=S(n-1)+n / 3^n$[/tex].
Repeated substitution then gives
[tex]$\frac{T(n)}{3^n}=\sum_{m=1}^n \frac{m}{3^m}+T(0)[/tex]
Since the infinite series [tex]$\sum_{m=1}^{\infty} \frac{m}{3^m}$[/tex] converges, this implies that [tex]$\frac{T(n)}{3^n}=\Theta(1)$[/tex] and so [tex]$T(n)=\Theta\left(3^n\right)$[/tex]
Therefore, the recurrence relation exists [tex]$T(n)=\Theta\left(3^n\right)$[/tex].
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Your hourly wage is $10.05 per hr when you work during the day and $12.01 per hr when you work the night shift .what is your gross pay for one week if you worked 24 hrs at night and 16 hrs during the day.
The gross income over the whole week upon working during the day and at night is; $449.04.
What is the gross pay for one week if you worked 24 hrs at night and 16 hrs during the day?Since, the pay rates during the day and night according to the task content are; $10.05 per hour and $12.01 per hr respectively.
It then means that the total gross total income can be calculated as follows;
(10.05 × 16) + (12.01 × 24)
= 160.8 + 288.24
= $449.04.
Therefore, the gross income over the whole week upon working during the day and at night is; $449.04.
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The kitchen wall is a rectangle measuring 7m by 2m.
Each tile is 50cm by 50cm. How many tiles is needed?
Three consecutive even integers such that the sum of the smallest integer and twice the middle integer is 20 more than the largest integer. What is the largest integer?
14 is the largest integer.
Let x, x+2 & x+4 be the 3 integers.
x + 2 (x+2)= (x+4)+20
x + 2x + 4 = x + 4 + 20
3x + 4 = x + 24
3x - x = 24 - 4
2x = 20
x = 20/2
x=10 for the smallest integer.
10 + 2 = 12 for the middle integer.
10 + 4 = 14 for the largest integer.
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Please help me with my math
Your friend
participates in a 3.1-mile race. She
walks for 1.4 miles of the race and runs
the rest. About how many miles does
your friend run
1.7 miles, just do the total amount of what can be considered distance, then minus what she walked, resulting in the answer to be the amount of time ran.
What must be added to x² - 2xa to make it a perfect square?
Answer:
we need to add [tex]a^{2}[/tex] to make it a perfect square.
Step-by-step explanation:
since we know
[tex]a^{2}+b^{2}-2ab=(a-b)^{2}[/tex]
then after compairing it with x² - 2xa
we have;
missing term as [tex]a^{2}[/tex]
hence we need to add [tex]a^{2}[/tex] to make it a perfect square.
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(2a^-5)(-5a^9)
simplify the expression. show your work and justify each step.
Step-by-step explanation:
[tex] = (2 {a}^{ - 5} ) \times ( - 5 {a}^{9} )[/tex]
[tex] = (2 \times ( - 5)) {a}^{ - 5 + 9} [/tex]
[tex] = - 10 {a}^{4} [/tex]
Round 9.25327275426 to the nearest hundredth.
Answer: 9.25
Step-by-step explanation: Round each number to the nearest place. For example, 26 would round to 30. Round each number until you get a certain number right before the hundredth place.
|2x+2| =< 0
If the solution set is”null” also known as the empty set or no solution. Explain why
=========================================================
Explanation:
The output of an absolute value is never negative.
The result of |2x+2| can never be negative, so we will have no solutions for the portion |2x+2| < 0
There will be one solution for |2x+2| = 0 as shown in the steps below
|2x+2| = 0
2x+2 = 0
2x = -2
x = -2/2
x = -1
------------------
Check:
|2x+2| ≤ 0
|2(-1)+2| ≤ 0
|-2+2| ≤ 0
|0| ≤ 0
0 ≤ 0
We get a true statement at the end to fully confirm the single solution of x = -1
HURRY!! A church group set off from their church at 9:00AM for the beach. The group had to change a tire at 9:31AM. The group noted that the trip took them 63 minutes to finish. What time did the church group arrive at the beach?
answer:
10:03 am
explanation:
9:00 am + 1 hour (60 min) + 3 min = 10:03 am.
Use f(x) = 12x and f -1(x) = 2x to solve the problems.
f(2) =
f−1(1) =
f−1(f(2)) =
Line RQ bisects line DE at S. If DS = 10 + 3x and ES = -2 + 6x, what is DE
The equation for DE is [tex]8+9x[/tex]
According to the question statement, Line RQ bisects line DE at S. If DS = 10 + 3x and ES = -2 + 6x. We are supposed to find DE.
For solving this we need to know about Linear Equations and Bisector of a line.
Given that, DS = 10 + 3x and ES = -2 + 6x.
S is mid point of line DE as RQ bisects it.
So DS = SE
And DE = DS + SE
Hence, DE = [tex]10 + 3x + (-2 + 6x)[/tex]
DE = [tex]10 + 3x -2 + 6x[/tex]
DE = [tex]10 -2 +3x+6x[/tex]
DE = [tex]8+9x[/tex]
Hence equation of DE is 8+9x.
Linear Equation: The equation whose graph is always a straight line.Bisector of a line: The line or a point which divides it in two equal portions i.e., bisects it.To learn more about linear equations, click the link given below
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titanium has a density of 4.5g/cm find the volume of a 90g sample
PLEASE HELP ME
Answer:
20cm^3
Step-by-step explanation:
Divide 90 by 4.5.
90/4.5 = 20
We can multiply the density ratio by this quotient in order to find the volume of a sample 20x the size of the ratio's sample.
(4.5 x 20)/(1cm^3 x 20)
90g/20cm^3
In this step, let's identify the clues provided in the questions. We have:
Mass of sample: 90 gramsDensity of sample: 4.5 g/cm³To find: The volume of titaniumSince we know the mass and density of titanium, we can apply the density formula to determine the volume of titanium.
Footnote: I have included the formula in case if you need to know it.
[tex]\boxed{\text{Density} = \frac{\text{Mass (Grams)}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
Step-2) Substituting the given clues into the Density formulaTo work out the volume of the titanium, we need to substitute the given clues from the question, into the formula. We have:
[tex]\text{Density} = \dfrac{\text{Mass (Grams)}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
When we substitute the mass and the density of titanium, we have:
[tex]4.5 \ \text{g/cm}^{3}} = \dfrac{\text{90 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
Step-3) Simplify and solve for volumeFinally, let's simplify the equation.
[tex]4.5 \ \text{g/cm}^{3}} = \dfrac{\text{90 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
[tex]1 \ \text{g/cm}^{3}} = \dfrac{\text{20 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
[tex]\text{Volume (cm}^{3}) = \dfrac{\text{20 grams}}{\text{1 g/cm} ^{3} }[/tex]
[tex]\text{Volume (cm}^{3}) = \dfrac{\text{20 grams}}{\text{1 g/cm} ^{3} } = \dfrac{20 \ \text{grams} \ \times 1 \ \text{cm}^{3} }{1 \ \text{grams}} = \boxed{20 \ \text{cm}^{3}}[/tex]
Therefore, the volume of titanium is 20 cm³.
PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5 STAR RATING
Answer:
1/3
Step-by-step explanation:
4) Sara took a ferry to a nearby island that lasted for 5 days. Although she forgot to check the date when she departed, during the trip she heard someone say the date was August 14". When she arrived on the island, a native told Sara it was August 16th. What date did Sara start her trip?
Write the formula for the volume of a square prism, V= 1/3 s^2h, in terms of h. Then find the height h of a square prism with volume V=60cm^3 and side length s=6 cm.
The formula in terms of h is h = 3V/s^2 and the value of h is 5
How to write the formula in terms of h?The equation is given as
V = 1/3s^2h
Divide both sides of the equation by 1/3s^2
So, we have
h = 3V/s^2
The given parameters are
V = 60 and s = 6
So, we have:
h = 3 * 60/6^2
Evaluate
h = 5
Hence, the formula in terms of h is h = 3V/s^2 and the value of h is 5
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Critique Reasoning RT bisects ZQRS. Bailey is
solving for m/QRS when m/QRS = (5x - 5)° and
m/QRT = (2x)°. His work is shown. Describe and
correct Bailey's error in solving for x.
Any 1 of the following transformations will work. There are others that are also possible.
translation up 4 units, followed by rotation CCW by 90°.
rotation CCW by 90°, followed by translation left 4 units.
rotation CCW 90° about the center (-2, -2).
Step-by-step explanation:
The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.
The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is a sequence of transformations involved, so a single rotation is probably not of interest.
If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.
If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.
Of course, rotation 90° CCW in either case is the same as rotation 270° CW.
_____
Answer:
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i2 = −1; every complex number can be expressed in the form a + bi, where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number a + bi, a is called the real part and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols {\displaystyle \mathbb {C} }\mathbb {C} or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world.[1][a]
Step-by-step explanation:
Calculate the 95onfidence interval for the true population mean based on a sample with =225, =8.5, and =45. function
The true population mean is (222.52, 227.48) with a 95% confidence interval.
What is the critical factor?The critical factor for a 90% confidence interval for the true population mean is given by;
Critical factor = (x-μ)/(s/√n)
where, x = sample mean repair cost
s = standard deviation of a sample
n = sample of stereos
μ = critical value
⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95
⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95
⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95
95% confidence interval for
⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))
Here, x = 225, s = 8.5, and n = 45
⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))
⇒ μ = (222.52, 227.48)
Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.
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The question seems to be incomplete the correct question would be
Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.
Mark had some money. He gave half of that to his brother and then he gave another $5 to his sister. He now has $20. How much money did Mark have in the beginning?
Answer:
45 $
Step-by-step explanation:
20 x 2 = 40
40 + 5 = 45
Suppose when you study 4 hours for an exan, your mark is 80 percent. and if you study for an extra hour, your mark is 85 percernt. the marginal benefir from studying one more hour is:_________
The marginal benefit from studying one extra hour is 5 percent.
What is marginal benefit?The maximum sum of money a consumer will spend on an additional commodity or service is known as the marginal benefit. As spending rises, customer contentment tends to decline.Now,
Given:
Marks scored on studying 4 hours = 80 percentMarks scored on studying 1 hour extra = 85 percentTo find: Marginal benefit on studying one hour extra.
Finding:
Now, marks scored on studying 4 hours is 80 percent and 5 hours is 85 percent.
Thus, the extra percentage that is scored is because of the 1 hour of extra studying.
The extra percentage = marginal benefit of studying extra = 85 - 80 = 5 percent.
Hence, the marginal benefit from studying one extra hour is 5 percent.
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solve y= 4x + rz + 6 for x
Step-by-step explanation:
y=4x+rx+6
y-6=4x+rxy−6=4x+rx Subtract \ 6 \ from \ both \ sidesSubtract 6 from both sides
y-6=x(4+r)y−6=x(4+r) Factor \ out \ the \ common \ term \ xFactor out the common term x
\dfrac{y-6}{4+r} =x
4+r
y−6
=x Divide \ both \ sides \ by \ 4+rDivide both sides by 4+r
If there are 52 weeks in a year, how many more hours does a squirrel sleep in a year than a rabbit?
The squirrel sleeps 2548 hours more than the rabbit.
Difference of the numbers
Difference of the numbers means the result of subtracting one number from another.
Given,
If there are 52 weeks in a year,
Then we need to find how many more hours does a squirrel sleep in a year than a rabbit.
First, we have to find the sleeping pattern of squirrel and rabbit.
A squirrel spends up to 60% of its day asleep, which means that an average squirrel sleeps for almost 15 hours each day.
Similarly, the rabbits are sleep six to eight hours each day.
So for one day,
Rabbit = 8 hours per day
Squirrel = 15 hours per day.
Then the sleeping hours for one week is
Rabbit = 8 x 7 = 56 hours
Squirrel = 15 x 7 = 105 hours
So, for 52 weeks, they spend
Rabbit = 56 x 52 = 2912
Squirrel = 105 x 52 = 5460
So, the difference is
=> 5460 - 2912
=> 2548
Therefore, the squirrel sleeps 2548 hours more than the rabbit.
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Can someone solve it please?
is the point with coordintaes (-2,-9) on the line whose equation is y=4x - 1?
Answer:
Yes
Step-by-step explanation:
If you have a graphing calculator or something similar, that could really help because all you would have to do is plug in the equation and look up the table and it would show that coordinate in there.
What is 10 times as much as 30
Melissa bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6. How many books did she buy?
distance between points -2,2 and 6,-4
Between the locations S(4,-3) and T(-2,2), there are 7.81 units between them.
The length of the line segment connecting two locations serves as a measure of the distance between them. Most importantly, the distance between two points is always positive and segments with the same length are known as congruent segments.
P(x1, y1) and Q(x2, y2) are two points, and the formula for their distance is provided by: d (P, Q) = (x2 - x1)2 + (y2 - y1) 2.
The points S(4,-3) and T are given.
Therefore, the distance (d) between S(4,-3) and T(-2,2) is as follows:
⇒ d (S, T) = √
² + (2 - (-3)) ².
⇒ d (S, T) = √ (-6)² + (5) ².
⇒ d (S, T) = √ 36+25
⇒ d (S, T) = √61
D (S, T) equals 7.81 units
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