Answer:
The correct answer would be - 9.75 laps (if runs 12 laps in 8 days) or 78 laps (if 12 laps each day for 8 days)
Step-by-step explanation:
Given:
a) Laps covered in 8 days = 12
interval = 1 and half day
total laps = ?
Solution:
To know the total laps with intervals we need to calculate the laps run each day :
= 12/8 laps per day
= 3/2 laps per day
Now multiply the daily run with days
= (3/2)*6.5 (due to 8 - 1.5 = 6,5 days)
= 9.75 laps
B) Given:
Laps covered in 8 days = 12*8 =96
interval = 1 and half day
total laps = ?
Solution:
To know the total laps with intervals we need to calculate the laps run each day :
= 96/8 laps per day
= 12laps per day
Now multiply the daily run with days
= 12*6.5 (due to 8 - 1.5 = 6,5 days)
= 78 laps
8. Solve the system using elimination.
3x - 4y = 9
- 3x + 2y = 9
Answer:
3x−4y=9 −3x+2y=9
Add these equations to eliminate x: −2y=18
Then solve−2y=18
for y: −2y=18 −2y −2 = 18 −2 (Divide both sides by -2)
y=−9
Now that we've found y let's plug it back in to solve for x.
Write down an original equation: 3x−4y=9
Substitute−9for y in 3x−4y=9: 3x−(4)(−9)=9
3x+36=9(Simplify both sides of the equation)
3x+36+−36=9+−36(Add -36 to both sides)
3x=−27 3x 3 = −27 3 (Divide both sides by 3) x=−9
Answer: x=−9 and y=−9
Hope This Helps!!!
1.3 hectoliters is how many liters
Answer: 130 liters
Step-by-step explanation:
1 hectoliter = 100 liters
1.3 hectoliters = 1.3 · 100 = 130 liters
Round off to the underlined place values. 1 0.5242 2. 2.1616 3. 5.4852 4. 0.5862 5. 5.9658 6. 2.8959 7. 8.2584 8. 8.8956 9. 4.1492 1 5481
Answer:
wheres the underline pls let me know what is underlined ill answer it on comment
Practice Question
1) VAT (value-added tax) is paid on things that you buy.
The table on the right shows the 2019 VAT rates.
This is how much VAT is charged on certain items
as a percentage of the item's cost.
VẬT (%)
20
5
0.
Items
Chocolate and crisps
Gas and electric
Fruit and vegetables
Currena
Before VAT is added, Simon pays 12p per unit of
electricity plus a fixed charge of £87 per year.
How much does Simon pay in VAT if he uses 3000 units of electricity in one year?
er hour
Shane and Space
Simon will pay £18 in VAT for using 3000 units of electricity in one year.
The VAT rate for gas and electric is 5%.
Therefore, Simon will pay VAT on his electricity usage.
Let's calculate Simon's annual electricity cost without VAT:
Cost per unit of electricity = 12p
= £0.12
Number of units used in one year = 3000
Electricity cost without VAT = Cost per unit × Number of units
= £0.12 × 3000
= £360
Now, let's calculate the VAT amount:
VAT rate = 5% = 0.05
VAT amount = Electricity cost without VAT × VAT rate
= £360 × 0.05
= £18
Therefore, Simon will pay £18 in VAT for using 3000 units of electricity in one year.
To learn more on VAT amount click:
https://brainly.com/question/31403944
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Help. Does anyone know the answer. Pls help!
Answer:
Step-by-step explanation:
the first and last choices look good
Please look at the included picture, show me your work and please include a good explanation. It would really help me out here.
These are indeed equivalent, and this identity is one of DeMorgan's laws.
The 6th column is the negation of the 5th column. For example, the first row says
not p or q
is true (T), so the negation would be false (F). The 5th column reads {T, F, T, T}, so the next column should be {F, T, F, F}.
Then in the 7th/last column, you are checking the truth value of the statement
p and not q
For example, in the first row, both p and q are true (T). This means (not q) is false, so (p and not q) is false (F). The last column should end up reading {F, T, F, F}, same as the previous column.
A field book is a private notepad used by a surveyor to transcribe notes and is not considered a legal document True False
Answer:
False
Step-by-step explanation:
A field book is a private notepad used by a surveyor to record measurements and notes.
Basically, the size of a field book is 200 millimeters × 120 millimeters (20 centimeters × 12 centimeters) and it's typically opened lengthwise. There are two (2) main types of field book and these includes;
I. Double-line field book.
II. Single-line field book.
As a general rule, it's best that all findings, entries (notes) and observations are recorded or made into a field book after each and every measurement have been taken by a surveyor.
In conclusion, a field book is considered to be a legal document used by surveyors to keep records of accomplished field work or work done in the field. Thus, it's not a private notepad used by a surveyor to transcribe notes.
Answer:
False
Step-by-step explanation:
A field book is a private notepad used by a surveyor to transcribe notes and is not considered a legal document is False.
\int (x+1)\sqrt(2x-1)dx
Answer:
[tex]\int (x+ 1) \sqrt{2x-1} dx = \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15}(2x-1)^{\frac{5}{2}} + C[/tex]
Step-by-step explanation:
[tex]\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v = \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}[/tex]
[tex]\int (x+1)\sqrt(2x-1)dx\\\\ = uv - \int v du[/tex]
[tex]= (x +1 ) \cdot \frac{(2x - 1)^{\frac{3}{2}}}{3} - \int \frac{(2x - 1)^{\frac{3}{2}}}{3} dx \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ u = x + 1 => du = dx \ ][/tex]
[tex]= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \int (2x - 1)^{\frac{3}{2}}} dx\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{5}{2}}}{\frac{5}{2} }) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15} \times (2x-1)^{\frac{5}{2}} + C\\\\[/tex]
Michael was 1.0 metres tall, and could
only reach up to the 1st floor lift button. .
From the 1st floor, he had to walk up 100
steps to reach the 6th floor.
Vinh was 1.4 metres tall, and could reach
the 5th floor button. He had to walk up
20 steps to reach the 6th floor.
Lucy was 1.1 metres tall. To reach the
6th floor, how many steps did she have to
walk up?
Answer:
Lucy must walk up 80 steps to reach the 6th floor.
Step-by-step explanation:
Since Michael was 1.0 meters tall, and could only reach up to the 1st floor lift button, and from the 1st floor, he had to walk up 100 steps to reach the 6th floor; while Vinh was 1.4 meters tall, and could reach the 5th floor button, and he had to walk up 20 steps to reach the 6th floor; If Lucy was 1.1 meters tall, to determine how many steps did she have to walk up to reach the 6th floor, the following calculation must be performed:
1 = 100
1.4 = 20
1.4 - 1 = 100 - 20
0.4 = 80
0.1 = X
0.1 x 80 / 0.4 = X
20 = X
100 - 20 = 80
Therefore, Lucy must walk up 80 steps to reach the 6th floor.
30 students in grade 8 finished their summer packet before August 15.
This was 12% of all the students. How many students are in grade 8?
Step-by-step explanation:
12/100=30/x
12x=3000
x=250
hiii! !!
A cyclist rides his bike at a speed of 6 miles per hour. What is this speed in miles per minute how many miles will the cyclist travel in 20 minutes? Do not round your answers.
Answer:
1 mile per 10 minutes
Step-by-step explanation:
Help Me! Fake Answers will be reported.
How many triangles are there in this picture?
Im sorry if you get this wrong but im going with 14 only because i did this question with my class in school and a boy said 14 and got it right.
Answer:
28
Step-by-step explanation:
there are bigger triangles in the triangles pls dont remove
What is the minimum of y=1/3 x^2 + 2x + 5
Answer:
min at x = -3
Step-by-step explanation:
steps are in the pic above.
what percentage of undergraduates students in Calculus 1 are required to do computer assignments in their classes
Full question:
Every 5 years the Conference Board of the Mathematical Sciences surveys college math departments. In 2000 the board reported that 51% of all undergraduates taking Calculus I were in classes that used graphing calculators and 31% were in classes that used computer assignments. Suppose that 16% used both calculators and computers. a) What percent used neither kind of technology? b) What percent used calculators but not computers? c) What percent of the calculator users had computer assignments? d) Based on this survey, do calculator and computer use appear to be independent events? Explain.
Answer:
a. 34%
b. 35%
c. 31.4%
d. Independent events
Explanation:
a. To calculate percentage that used neither kind of technology, we already know those that use the technologies and total taking calculus so:
100%-51%-31%-16%= 34%
b. Percentage that used calculators but not computers.
= 51%-16%=35%
c. Percentage of the calculator users that had computer assignments?
= 16/51×100=31.4% (there are 16 people using both so that as a percentage of 51 people using calculators)
d. Independent events are events that do not affect the other, such that occurrence of one does not define occurrence of the other. Since percentage of calculator and computer assignment users is close to those who are not using any, we can say they are independent events.
Please help asap i will give brainliest. Find the exact perimeter and area of the triangle.
Answer:
perimeter=9cm
Area=2cm^2
step by step explanation:
Firstly solve the sides that don't have figures using trigonometry
#1..sin15°=opposite/hypotenuse
sin15=opposite/4
opposite=sin15×4
=1.035, round off to 1cm
Then find the value of the base
tan15=opposite/adjacent
tan15=1/adjacent
1=tan15adjascent
1/tan15=adjacent
adjacent or base=3.7 round off to 4cm
After finding these values find the perimeter
p=side+side+side
p=4cm+4cm+1cm
p=9cm
Find the area
1/2bh
1/2×4×1
A=2cm2
Today Katherine woke up late. Since her
alarm did not go off, she only had 37
minutes to get ready for work. She knows
it takes 12 minutes to shower and some
amount of minutes, m, to do her
makeup, but it takes a different amount
of time each day. Represent this situation
using an expression.
Answer:
49+m
Step-by-step explanation:
37+12 = 49
49 + m is the total time Katherine takes.
solve the inequality x^3+4x>5x^2 please show steps and interval notation. thank you.
Answer: [tex]x\in (0,1)\cup (4,\infty)[/tex]
Step-by-step explanation:
Given
In equality is [tex]x^3+4x>5x^2[/tex]
Taking terms one side
[tex]\Rightarrow x^3-5x^2+4x>0\\\Rightarrow x(x^2-5x+4)>0\\\Rightarrow x(x^2-4x-x+4)>0\\\Rightarrow x(x-4)(x-1)>0\\\Rightarrow (x-0)(x-1)(x-4)>0[/tex]
Using wavy curve method
[tex]x\in (0,1)\cup (4,\infty)[/tex]
A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with A random sample of 12 sample specimens has a mean compressive strength of psi. Round your answers to 1 decimal place. (a) Calculate the 95% two-sided confidence interval on the true mean compressive strength of concrete. Enter your answer; 95% confidence interval, lower bound Enter your answer; 95% confidence interval, upper bound (b) Calculate the 99% two-sided confidence interval on the true mean compressive strength of concrete.
Answer:
95%: (3278.354 ; 3270.083)
99% : (3221.646 ; 3278.354)
Step-by-step explanation:
Given :
Sample size, n = 12
Mean, xbar = 3250
Sample standard deviation = √1000
The 95% confidence interval :
Mean ± Margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 0.05, df=12-1 = 11 ;
Tcritical at 95% = 2.20
Hence,
Margin of Error = (2.20 * √1000/√12) = 20.083
Confidence interval : 3250 ± 20.083
Lower boundary = 3250 - 20.083 = 3229.917
Upper boundary = 3250 + 20.083 = 3270.083
2.)
The 99% confidence interval :
Mean ± Margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 0.01, df=12-1 = 11 ;
Tcritical at 99% = 3.106
Hence,
Margin of Error = (3.106 * √1000/√12) = 28.354
Confidence interval : 3250 ± 28.354
Lower boundary = 3250 - 28.354 = 3221.646
Upper boundary = 3250 + 28.354 = 3278.354
What is the value of -5^6?
Need answers asap plz
Answer:
-15,625
Step-by-step explanation:
[tex]-5^6[/tex] = -15,625
Hope this helps.
Answer:
-15,625 ... be carful on this type question
the - sign does NOT get raised to the 6th power...
[tex](-5)^{6}[/tex] that would be + .... [tex]-5^{6}[/tex] is negative
Step-by-step explanation:
What is the answer??
Answer:
Step-by-step explanation:
Let AC = x
AB - AC = 4 cm
AB = 4 +x ----------------(I)
Pythagorean theorem
AB² + AC² =BC²
(4 + x)² + x² = 9²
Use the identity (a + b)² = a² + 2ab + b² where a = 4 & b = x
4² +2*4*x +x² + x²= 81
16 + 8x + 2x² = 81
2x² + 8x + 16 - 81 = 0
2x² + 8x - 65= 0
a = 2 ; b = 8 ; c = -65
D = b² - 4ac
= 8² - 4*2*(-65)
= 64 + 520
D = 584
√D = √584 = 24.16
[tex]x=\frac{-b+\sqrt{D}}{2a} \ or \ x =\frac{-b-\sqrt{D}}{2a}\\\\x= \frac{-8+24.16}{2*2} \ or \ x = \frac{-8-24.6}{2*2}[/tex] {Ignore this as it is negative.}
x = 16.16/4
x = 4.04
AC = 4.04 Cm
AB = 4 + 4.04 = 8.04 cm
Area of triangle ABC = [tex]\frac{1}{2}* base * height[/tex]
[tex]=\frac{1}{2}*4.04 *8.04\\\\= 2.02 * 8.04[/tex]
= 16.24 sq.cm
Solve the simultaneous equations
2x+3y20
2x+5=10
Answer:
[tex]x=\frac{5}{2} \\y=5[/tex]
( 5/2, 2 )
Step-by-step explanation:
Solve by substitution method:
[tex]2x+5=10\\\2x+3y=20[/tex]
Solve [tex]2x+5=10[/tex] for [tex]x[/tex]:
[tex]2x+5=10[/tex]
[tex]2x=10-5[/tex]
[tex]2x=5[/tex]
[tex]x=5/2[/tex]
Substitute [tex]5/2[/tex] for [tex]x[/tex] in [tex]2x+3y=20[/tex]:
[tex]2x+3y=20[/tex]
[tex]2(\frac{5}{2} )+3y=20[/tex]
[tex]3y+5=20[/tex]
[tex]3y=20-5[/tex]
[tex]3y=15[/tex]
[tex]y=15/3[/tex]
[tex]y=5[/tex]
∴ [tex]x=\frac{5}{2}[/tex] and [tex]y=5[/tex]
hope this helps....
What is the next term of the geometric sequence? 3, -12, 48
Answer:
-192
Step-by-step explanation:
it is a geometric progression
r=-4
The graph shows the solution of the following system of equations. y = –5∕3x + 3 y = 1∕3x – 3
Answer:
So whats your question ??
Step-by-step explanation:
What is this expression in simplified form?
[tex]\sqrt{32} · \sqrt{24}[/tex]
Hello!
√32 × √24 =
= √768 =
= 16√3
Good luck! :)
Answer:
16×sqrt(3)
Step-by-step explanation:
what full square numbers are factors in the numbers under the square root that we can pull out ?
and then multiply the rest under the square root and possibly repeat one more time.
32 = 16×2
16 is a great square number.
in 24 we find 4 as the largest square factor.
so,
sqrt(32)×sqrt(24) = sqrt(16×2)×sqrt(4×6) =
= 4×sqrt(2)×2×sqrt(6) = 8×sqrt(2×6) = 8×sqrt(12) =
= 8×sqrt(4×3) = 8×2×sqrt(3) = 16×sqrt(3)
A student takes an exam containing 16 true or false questions. If the student guesses, what is the probability that he will get exactly 14 questions right
Answer:
0.001831055
Step-by-step explanation:
Here, n = 16, p = 0.5, (1 - p) = 0.5 and x = 14
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)
We need to calculate P(X = 14)
P(x =14) = 16C14 * 0.5^14 *(1-0.5)^2
= 120 * 0.5^14 *(1-0.5)^2
= 0.001831055
If 3x^2+2x-8=(3x-4)(x+2), which equations should be solved to find the roots of 3x^2+2x-8=0
9514 1404 393
Answer:
C, E
Step-by-step explanation:
The solutions are found by setting each of the factors to zero:
3x -4 = 0 . . . . . matches C
x +2 = 0 . . . . . matches E
A driveway is in the shape of a rectangle 30 feet wide by 35 feet long. Find the perimeter in feet. & Find the area in square feet.
Consider the function f(x) = x2 and the function g(x) = 3x2. How will the graph of g(x) differ from the graph of f(x)?
Select the correct answer
The graph of g(x) is the graph of f(x) shifted to the left 3 units.
The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3.
The graph of g(x) is the graph of f(x) compressed vertically by a factor of
The graph of g(x) is the graph of f(x) shifted up 3 units.
Answer:
Third Choice - The graph of g(x) is the graph of f(x) compressed vertically by a factor of 3
Step-by-step explanation:
x^2 is the the parent function, so it opens up with a normal compression.
Any number > (greater than) 1 as a coefficient of x will lead to a vertical compression (narrower parabola), while any number < (less than) 1 as a coefficient of x will lead to a vertical stretch (wider parabola).
So, 3x^2 would have to have to be a compressed parabola.
I hope this helps!
Answer:
The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3.
Step-by-step explanation:
A vertical stretch or shrink of a function, kf(x), results from multiplying the entire function by a constant, k.
In this case, g(x) equals 3 times f(x). If k > 1, then the graph will be stretched vertically (along the direction of the y-axis) by a factor of k.
So, the graph of g(x) is the graph of f(x) stretched vertically by a factor of 3.
U have to work out the value of a by the way
Answer:
Step-by-step explanation:
180-90=2b+b
90=3b
90/3=b
30=b
2b=2*30
=60
180-90=a+a
90=2a
a=90/2
a=45
the answer is 45 degrees
hope it helps!!let me know if it does
Answer:
a= 15°
Step-by-step explanation:
> use the fact that the sum of angles in a triangle is 180°
> based on the picture in the small right triangle we have b° +2b° +90° =180°
b +2b +90 =180° , combine like terms
3b +90 = 180, subtract 90 from both sides of the equation
3b = 90, divide by 3 both sides of the equation
b = 30°
> angle b has a ray that continues as a line so it makes an 180° angle and we have the acute triangle so we can write that
a + a+ (180-b) =180, substitute b
2a + 180-30 =180, subtract 180 from both sides, and add 30 to both sides
2a=30, divide by 2 both sides
a= 15°
NO LINKS AND NO ANSWERING WHAT YOU DON'T KNOW!!! THIS IS NOT A TEST OR ASSESSMENT!!!
Please help and SHOW WORK on these parts.
Unit 1 Assignment- Who's Right?
Answer:
Part 1)
1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.
2) Dylan is perfectly correct.
3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.
Part 2)
Only Skyler's approach was incorrect. When Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.
Step-by-step explanation:
Part 1)
We want to simplify the expression:
[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7}[/tex]
We can divide. Recall that xᵃ / xᵇ = xᵃ ⁻ ᵇ. Hence:
[tex]\displaystyle =0.88\times 10^{-11-7}=0.88\times 10^{-18}[/tex]
In scientific notation, the coefficient is always between 1 or 10.
So, we can multiply 0.88 by 10. To keep the equality, we need to divide 10⁻¹⁸ by 10. Hence:
[tex]\displaystyle =0.88(10)\times \frac{10^{-18}}{10}[/tex]
(You can see that the 10s can cancel out, giving us our original expression.)
Simplify. Thus:
[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7} = 8.8\times 10^{-19}[/tex]
Therefore, as we can see:
1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.
2) Dylan is perfectly correct.
3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.
Part 2)
Reviewing their work, we can see that only Skyler's approach was incorrect.
729 is indeed 3⁶. However, when Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.
Both Robert and Kevin are correct, having set each exponent equal to each other after their bases are equivalent and solving for x.