Answer:length=16, width=4
Step-by-step explanation:
P=40m
L=4W
P=L+L+W+W
40=4W+4W+W+W
40=10W
W=4
L=4W
L=4(4)
L=16
3 Coffee 5.85
1 Diet Bev. – lg. 3.38
1 Sparkling Water 2.50
3 Ranch Chicken Sandwich 44.97
1 Classic Burger 12.95
1 Thai Stir-fry Special 11.50
2 Club Sandwich 22.98
Subtotal 104.13
Tax (13%) 13.54
Total 117.67
1. The receipt is for lunch for five students. Each student will pay 1/5 of the bill.
What will each student pay, excluding taxes and tip?
The amount of money each student will pay, excluding taxes and tip, $23.534
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
Given that,
3 Coffee 5.85
1 Diet Bev. – lg. 3.38
1 Sparkling Water 2.50
3 Ranch Chicken Sandwich 44.97
1 Classic Burger 12.95
1 Thai Stir-fry Special 11.50
2 Club Sandwich 22.98
Subtotal 104.13
Tax (13%) 13.54
Total 117.67
The receipt is for lunch for five students. Each student will pay 1/5 of the bill
The amount of money each student will pay = ?
⇒ 1/5x117.67
⇒ 23.534
Therefore, the amount each student will pay, $23.534
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One month Lashonda rented 5 movies and 3 video games for a total of $29. The next month she rented 7 movies and 9 video games for a total of $73. Find the
rental cost for each movie and each video game.
Rental cost for each movie: s
Rental cost for each video game: s
The rental cost for each movie and each video game is $ 1 and $8 respectively.
How do you find the equality of a equation?We have 2 variables (cost of movie and cost of video game) and we need 2 equations to find them. Let's say the cost of movies is M and the cost of video games is V. In the first month, Lashonda rented 5 movies (5M) and 3 video games (3V) for $29.
5M + 3V = 29 (equation 1)
The next month, he rented 7 movies and 9 games for $73.
7M + 9V = 73 (equation 2)
Let's isolate one of the variables. I choose to isolate M in equation 2:
M = (73-9V)/7
Now, substitute our new equation 2 into equation 1.
5*(73 - 9V) + 3V = 29
365 - 45V + 3V = 29
365-29 = 45V - 3V
336 = 42V
V = $8
Now, substitute the value of V into one of our earlier equations to find M.
M = $1
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Need help solving these two questions
Answer: 34 on both?
Step-by-step explanation:
(3x+2y=20
1x-7y=22
X
Simplify the expression. Write the answer with positive exponents. Assume all variables represent positive numbers. (x2z)1/4/x-1/2z1/2
We can simplify the expression as follows:
(x2z)1/4/x-1/2z1/2 = (x2z)1/4 * (x1/2z-1/2)
Using the property of exponents: (a^b)^c = a^(bc)
x2z = x^(2 * 1) * z^(1 * 1) = x^2 * z
x1/2z-1/2 = x^(1/2 * 1) * z^(-1/2 * 1) = x^(1/2) * z^(-1/2)
Substituting back into the expression:
(x^2 * z)^(1/4) * (x^(1/2) * z^(-1/2))
= x^ (2 * 1/4) * z^(1 * 1/4) * x^(1/2) * z^(-1/2) = x^(1/2) * z^(1/4) * x^(1/2) * z^(-1/2)
Combining like terms:
x^(1/2) * z^(1/4) * x^(1/2) * z^(-1/2) = x^(1/2 + 1/2) * z^(1/4 - 1/2) = x^1 * z^(-1/4) = x * z^(-1/4)
So, the simplified expression is x * z^(-1/4) with positive exponents.
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An expression is shown below.
143-35
33
What is the value of the expression?
A 4
B 9
с12
D 18
Answer:
4?
Step-by-step explanation:
(143-35)/3^3
108/27
4
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{143 - 35}{3^3}}[/tex]
[tex]\mathsf{= \dfrac{108}{3^3}}[/tex]
[tex]\mathsf{= \dfrac{108}{3 \times 3 \times 3}}[/tex]
[tex]\mathsf{= \dfrac{108}{9 \times3}}[/tex]
[tex]\mathsf{= \dfrac{108}{27}}[/tex]
[tex]\mathsf{= 4}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{4}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Find the restricted values of x for the following rational expression.
Simplify the following union and/or intersection.
(−∞,−12]∩[−12,18)
The restricted values of x for the given rational expression are all real numbers except for x = −12.
Find the restricted values of x for the following rational expression?The restricted values of x for the rational expression are x ≠ -12.The simplified union and/or intersection is (−∞,−12).The simplified union and/or intersection is (−12, 18). This is called an open interval because it does not include the endpoints.The restricted values of x for the given rational expression are all x-values that make the expression undefined.This includes any values of x that make the denominator of the expression equal to 0, as this would result in a division by 0.The given union and intersection is (−∞,−12]∩[−12,18).This is known as the intersection of two intervals, and the result of this expression is (−12,18).This means that the set of values that satisfy the expression are all real numbers greater than -12 and less than 18.To learn more about intersection of two intervals refer to:
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The hotel room tax in Junction City is calculated using the function T(x)=0.06x+4.5, where x = the cost in dollars of the room and T(x) = the tax in dollars. What is the tax on a room that costs $120? Please look at the screenshot for the answer options. I am in a rush. Someone answer pls. Thx.
Tax on hotel room that costs $120 = $11.7
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
Given,
Function for tax of hotel room
T(x)=0.06x+4.5
where x is the cost in dollars of the room
T(x) = the tax in dollars.
Cost of the room = $120
Tax of the room
= 0.06(120) + 4.5
= 7.2 + 4.5
= $11.7
Hence, $11.7 is the tax on room that costs $120.
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joyce wants to survey a simple sample of 10 people from members of a gym list which of the following sample methods are not
The sampling methods here that are not examples of simple random sampling are;
A) Select the first 10 people from a list of members.
B) Ask 10 members in the gym on a Monday morning
E) Select every 20th person from a list of members until she has 10 .
F) Ask all members of the gym
What is the importance of simple random sampling?A subset of a certain population chosen at random is referred to as a simple random sample. You'll see that each person in the population has an exact equal probability of getting chosen using this sampling technique.
Simple random sampling is significant because it eliminates all prejudice because each member has an equal probability of being chosen. As a result, it will provide a good illustration of the topic of our investigation.
A) Choose the top 10 individuals from a list of members; this is not a straightforward random sampling because the selection is targeted rather than random.
B) This is not random because it is particular to one day of the week—a Monday morning—and we have no idea who might show up on other days.
C) Pick 10 people at random from a list using a random number generator; this is known as basic random sampling.
D) Without looking, choose the names of 10 members at random from a box; this method is random since each member has an equal chance of being chosen.
E) Choose 10 members at a time from a list of members; this is not a random process because not all members have an equal probability of getting chosen.
F) Consult with every gym patron; this is not a random pick.
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36÷9643 what is the solution and answer
Answer:
[tex] \frac{36}{9643} = 0.003733278[/tex]
ava says i think that 3/7
929
Step-by-step explanation:
yes sorry i cant do this
NEED HELP ASAP!!! What is 2/5 written as a percentage?
A. 4%
B. 400%
D. 0.40%
C. 40%
Answer: C. 40%
Step-by-step explanation:
To convert a fraction to a percentage, we multiply it by 100. So 2/5 can be written as (2/5) * 100 = 40%.
2/5= .40
To convert into a percentage move the decimal point two places to the left.
2/5= 40% (C)
Can anyone help with this?
For given parallelogram, x = 4.
What are a parallelogram's four characteristics?There are six crucial parallelogram characteristics to be aware of:
Congruent sides are those when AB = DC.
Congruent opposite angels are D = B.
(A + D = 180°) Consecutive angles are supplementary.
All angles are correct if just one of them is.
A parallelogram's diagonals cut each other in half.
In Geometry, a parallelogram is a type of quadrilateral. It is a two-dimensional figure with four sides. The most important properties of a parallelogram are that the opposite sides are parallel and congruent and the opposite angles are also equal.
Find the value of x in parallelogram?5x-1=19
⇒5x=19+1
⇒5x=20
x=20/5
x=4
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Evaluate the line integral ∫ 4xy dx + 2x
2 − 3xy dy, where C is the arc of
the circle x
2 + y
2 = 1, from (1, 0) to (0, 1) in the counterclockwise direction.
The line integral can be evaluated using Green's Theorem.
How can we evaluate the line integral?Green's Theorem states that for a simply connected region D with continuous partial derivatives, the line integral of the curl of a vector field around a closed path C is equal to the double integral of the curl over the region enclosed by C.
In this case, the curl of the vector field (4xy, 2x^2 - 3xy) is (3, -4), so the line integral is equal to the double integral of (3, -4) over the region enclosed by the circle x^2 + y^2 = 1.
The double integral can be calculated using polar coordinates, and the result is (-π/2, π/2) = π.
Therefore, the line integral ∫ 4xy dx + 2x^2 - 3xy dy, where C is the arc of the circle x^2 + y^2 = 1, from (1, 0) to (0, 1) in the counterclockwise direction, is equal to π.
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factor and simplify the expression
(x+5)^-1/5 -(x+5)^-6/5
type in exponential form with positive exponents
Answer:
Step-by-step explanation:
THIS SOLUTION IS x=15
Use the drawing tools to form the correct answers on the graph.
Complete the
function table for the given domain, and plot the points on the graph.
f (z) = -- + 2c + 5
T
f(c)
The function table for the given domain should be completed as follows;
x 2 3 4 5 6
f(x) 10 5 2 1 2
How to complete the function table for the given domain?In order to use the given quadratic function to complete the table, we would have to substitute each of the values of x (domain or x-values) into the quadratic function and then evaluate as follows;
When the value of domain x = 2, the quadratic function is given by;
f(x) = (x - 5)² + 1
f(2) = (2 - 5)² + 1
f(2) = (-3)² + 1 = 10
When the value of domain x = 2, the quadratic function is given by;
f(x) = (x - 5)² + 1
f(3) = (3 - 5)² + 1
f(3) = (-2)² + 1 = 5
When the value of domain x = 4, the quadratic function is given by;
f(x) = (x - 5)² + 1
f(4) = (4 - 5)² + 1
f(4) = (-1)² + 1 = 2
When the value of domain x = 5, the quadratic function is given by;
f(x) = (x - 5)² + 1
f(5) = (5 - 5)² + 1
f(5) = (0)² + 1 = 1
When the value of domain x = 6, the quadratic function is given by;
f(x) = (x - 5)² + 1
f(6) = (6 - 5)² + 1
f(6) = (1)² + 1 = 2
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Water covers 70.7%, or about 3.61 x 10⁸ km², of the Earth's surface. Approximate the total surface area of the Earth. (Round your answers to the nearest million.)
_____________ km²
Answer:
511 million km²
Step-by-Step Explanation:
Let the total surface area of the Earth be x.
Water covers 70.7% of the total surface area of the Earth, i.e.,
70.7% of x = 3.61 x 10⁸ km²
or, 70.7x /100 = 3.61 x 10⁸ km²
or, 707x/1000 = 3.61 x 10⁸ km²
or, 707x = 3.61 x 10⁸ x 1000km²
or, 707x = 3.61 × 10^11 km²
or, x = 0.0051 × 10^11 km²
or, x = 5.1 × 10⁸ km² = 511 million km²
Hope it helps.
If you have any query, feel free to ask .
Answer:
511 million km²
Step-by-step explanation:
Let x be the approximate total surface area of the Earth.
Given water covers 70.7%, or about 3.61 × 10⁸ km², set up an equivalent ratio of percent (in decimal form) to area:
[tex]\implies 0.707:3.61 \times 10^8=1:x[/tex]
Solve for x:
[tex]\implies\dfrac{0.707}{3.61 \times 10^8}=\dfrac{1}{x}[/tex]
[tex]\implies0.707x=3.61 \times 10^8[/tex]
[tex]\implies x=\dfrac{3.61 \times 10^8}{0.707}[/tex]
[tex]\implies x=\dfrac{3.61 }{0.707}\times 10^8[/tex]
[tex]\implies x=5.10608203...\times 10^8[/tex]
One million has 6 zeros and can be written in scientific notation as:
1 × 10⁶Therefore, to write x in millions as x × 10⁶, subtract 2 from the exponent and move the decimal point to the right by 2 places:
[tex]\implies x=510.608203...\times 10^6[/tex]
Therefore, the approximate surface area of the Earth is 510.608203... million km², which is 511 million km² to the nearest million.
5x +9y = 18+ (x + y)
Answer:
2x=9-4y
Step-by-step explanation:
5x+9y=18+x+y
5x-x=18+y-9y
4x=18-8y
2x=9-4y
a uniform solid sphere of mass m1 and radius r1 is inside and concentric with a spherical shell of mass m2 and radius r2 (fig. p14.48). find the gravitational force exerted by the spheres on a particle of mass m located at (a) (b) and (c) where r is measured from the center of the spheres.
The gravitational force exerted by the spheres on a particle of mass m located at (a)r=a,(b)r=b, and (c)r=c are
[tex]F=\frac{Gm_1m_a}{R_1^2}\\\\F=\frac{Gm_1m}{b^2}}\\\\F=m(\frac{Gm_1}{c^2} +\frac{Gm_2}{c^2} )[/tex]
Total gravitational Field at r=a
Total gravitational Field at r=a=Field due to solid sphere+ field due to spherical shell
we know the gravitational field inside the spherical shell is zero.
and gravitational field due to the solid sphere inside = [tex]\frac{GMr}{R^2}[/tex]
so here
Total gravitational Field=Field due to solid sphere+ field due to spherical shell
[tex]G=\frac{Gm_1a}{R_1^2} +0\\\\G=\frac{Gm_1a}{R_1^2}[/tex]
Force exerted on particle F=mG
[tex]F=\frac{Gm_1m_a}{R_1^2}[/tex]
when r=b:
we know the gravitational field inside the spherical shell is zero.
and gravitational field due to a solid sphere outside at a distance:
[tex]r=\frac{GM}{r^2}[/tex]
so here
Total gravitational Field=Field due to solid sphere+ field due to spherical shell
[tex]G=\frac{Gm_1}{b^2}}+0\\\\G=\frac{Gm_1}{b^2}}[/tex]
Force exerted on particle F=mG
[tex]F=\frac{Gm_1m}{b^2}}[/tex]
gravitational field due to a hollow sphere outside at a distance:
[tex]r=\frac{GM}{r^2}[/tex]
and gravitational field due to a solid sphere outside at distance:
[tex]r=\frac{GM}{r^2}[/tex]
so here
Total gravitational Field=Field due to solid sphere+ field due to spherical shell
[tex]G=\frac{Gm_1}{c^2} +\frac{Gm_2}{c^2}[/tex]
Force exerted on particle F=mG
[tex]F=m(\frac{Gm_1}{c^2} +\frac{Gm_2}{c^2} )[/tex]
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(42
5
+ (-1
4
)) ÷ (3
4
− (-1.75)) =
Answer:
= 11.496503
Step-by-step explanation:
Based on the histogram, estimate the mean commute distance (in miles) for the students in the sample. Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.
The mean commute distance (in miles) for the students in the sample is given as follows:
7.9 miles.
How to obtain the mean?The mean of a data-set is calculated as the sum of all observations in the data-set divided by the number of observations.
The histogram gives the number of observations in each range.
Hence, to obtain the sum of the observations, we consider the midpoint of each range, as follows:
S = 20 x 2 + 20 x 6 + 14 x 10 + 7 x 14 + 4 x 18 + 3 x 22
S = 536.
The number of people is given as follows:
20 + 20 + 14 + 7 + 4 + 3 = 68.
Hence the mean is of:
536/68 = 7.9 miles.
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2x + 2y = 8, x + y = -2
Answer:
X=-2-y
2(-2-y)+2y=8
-4-2y+2y=8
Step-by-step explanation:
-4-8=0
=-12
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A consulting engineer's time is billed at $40 per hour, and her assistant's is billed at $10 per hour. A customer received a bill for $425 fir a certain job. If the assistant worked 5 hours less than the engineer, how much time did each bill on the job?
Engineer: _____ hr
Assistant: ______ hr
Answer:
Engineer: 9.5 hr
Assistant: 4.5 hr
Step-by-step explanation:
To solve this problem, we can create and solve a system of equations.
Define the variables:
Let x be the number of hours the engineer worked.Let y be the number of hours the assistant worked.Given the engineer's time is billed at $40 per hour, and her assistant's is billed at $10 per hour, and a customer received a bill for $425 for a certain job:
[tex]40x+10y=425[/tex]Given the assistant worked 5 hours less than the engineer:
[tex]y=x-5[/tex]Therefore, the system of equations that represents the problem is:
[tex]\begin{cases}40x+10y=425\\ \quad \qquad \;\;\;y=x-5\end{cases}[/tex]
Substitute the second equation into the first equation to eliminate y:
[tex]40x+10(x-5)=425[/tex]
Solve the equation for x to find the number of hours the engineer worked:
[tex]\begin{aligned}40x+10(x-5)&=425\\40x+10x-50&=425\\50x-50&=425\\50x&=475\\x&=9.5\end{aligned}[/tex]
Therefore, the engineer worked 9.5 hours.
Substitute the found value of x into the second equation and solve for y to find the number of hours the assistant worked:
[tex]\begin{aligned}y&=x-5\\y&=9.5-5\\y&=4.5\end{aligned}[/tex]
Therefore, the assistant worked 4.5 hours.
The total cost of 5 kg rice and 6 kg sugar is Rs 940. If the
rate of rice increases by 20% and the rate of sugar decreases
by 10%, the total cost of 4 kg rice and 3 kg sugar will be
Rs 627. By what percent the cost of 1 kg rice is more or less
than the cost of 1 kg sugar. Find it.
The percent cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.
What is percent increase?We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage.
Let the cost price of rice is R and cost price of sugar is S.
Case 1 : total cost of 5 kg rice and 6 kg sugar is Rs. 940.
5R + 6S = 940 ...(1)
Case 2 : rate of rice increased by 20% and the rate of sugar decreased by 10%.
The new cost price of rice = R + 20% of R = 1.2R
The new cost price of sugar = S - 10% of S = 0.9S
So, the total cost of 4 kg rice and 3 kg sugar will be Rs. 627.
Thus,
4 × 1.2R + 3 × 0.9S = 4.8R + 2.7S = 627 ..(2)
From equations (1) and (2) we have,
(5R + 6S)/(4.8R + 2.7R) = 940/627
R/S = 8/9
Hence, if the price of rice is 8 then the price of sugar is 9.
It is clear that the price of sugar is more than that of rice.
The percent cost by which cost of rice is less than sugar is:
(9 - 8)/ 9 (100) = 11 1/9%.
Hence, the cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.
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Two workers in a holiday boutique are filling stockings with small gifts and candy. Lisa has already filled 2 stockings and will continue to fill them at a rate of 1 stocking per hour. Jake, who just arrived to help, can fill 3 stockings per hour. At some point, Jake will catch up with Lisa and they will have completed the same number of stockings. How many stockings will each worker have filled by then? How long will that take?
Based on the information, it can be inferred that after one hour Jake and Lisa will have filled 3 socks each.
How to find the time necessary for both of them to have filled the same number of socks?To find the time necessary for both of them to have filled the same number of socks, we must take into account the speed at which each one fills the socks.
Jack 3 socks / hourSmooth 1 half / hourAdditionally, when Jake arrives at work, Lisa has already filled two stockings. According to the above, after one hour Lisa will complete all 3 socks and Jake will have filled the first 3 socks for him.
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In a blind ESP test, a person correctly identifies whether a tossed coin comes up heads or tails in 63 trials out of 100. Use the normal approximation (without the continuity correction) to calculate the probability of correctly identifying 63 or more.
P(z > -5.233): Not the usual approximation, but the exact binomial computation is used for the computation of the the probability of correctly tossed 63 or more.
Define the term binomial distribution?The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take is among two independent values given a particular set of conditions or hypotheses.The fundamental presumptions of the binomial distribution include that each trial has only one possible outcome, that each trial shares the same success probability, that every trial is independent of the others or mutually exclusive.As opposed to just a continuous distribution, like the normal distribution, the binomial distribution is a frequent discrete distribution for use in statistics.For the stated question:
In 63 out of 100 trials inside a blind ESP test, the person accurately determines whether a coin will land on its head or tail.
Thus, P(z > -5.233) is the normal approximation.
Not the usual approximation, but the exact binomial computation is used for the computation of the the probability of correctly tossed 63 or more.
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please i need help with this trigonometry
Answer: √15
Step-by-step explanation:
AB²+BC²=AC²
(√8)²+(√6)²=AC²
AC²=14
AC=√14
Write the fraction or mixed number as a percent 21/25
Answer:
84%
Step-by-step explanation:
21/25*100%
21*4
84%
The inverse Laplace transform ofF left parenthesis s right parenthesis equals fraction numerator 5 s plus 2 over denominator s squared open parentheses s squared minus 1 close parentheses end fractionis
O minus 5 plus 2 t plus fraction numerator 7 e to the power of t over denominator 2 end fraction plus fraction numerator 3 e to the power of minus t end exponent over denominator 2 end fraction
O minus 5 plus 2 t minus fraction numerator 7 e to the power of t over denominator 2 end fraction plus fraction numerator 3 e to the power of minus t end exponent over denominator 2 end fraction
O 5 minus 2 t plus fraction numerator 7 e to the power of t over denominator 2 end fraction plus fraction numerator 3 e to the power of minus t end exponent over denominator 2 end fraction
O 5 minus 2 t minus fraction numerator 7 e to the power of t over denominator 2 end fraction plus fraction numerator 3 e to the power of minus t end exponent over denominator 2 end fraction
O minus 5 minus 2 t plus fraction numerator 7 e to the power of t over denominator 2 end fraction plus fraction numerator 3 e to the power of minus t end exponent over denominator 2 end fraction
The inverse Laplace transform of F(s) equals 5 minus 2 t plus fraction numerator 7 e to the power of t over denominator 2 end fraction plus fraction numerator 3 e to the power of minus t end exponent over denominator 2 end fraction.
The function's representation in the time domain is the supplied function's inverse Laplace transform. The function in this problem has the denominator s2 (s2 - 1) and the numerator 5s + 2. The outcome of the inverse Laplace transform is a function of time t with a constant term of -5, a linear term of 2t, two exponential terms (7et and 3e-t) split by 2, and a constant term of 7et.
These words are combined to form the final response, which provides the supplied function's time-domain representation. The answer options' divergent interpretations of the constant and linear terms show that there are several correct ways to calculate the inverse Laplace transform.
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Problem is the attached image.
The reasoning represent by the both of the students for congruent of vertical angle are correct but the reasoning of student 1 is more suitable and cleared than student 2.
What is the vertical angle?The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal. Additionally, a vertical angle and the angle to which it is adjacent are supplementary angles, meaning their sum is 180 degrees.
In this, ∠1 and ∠2 are adjacent angle so the sum of the measure of these two angles are 180°
∠1 + ∠2 = 180 ⇒ ∠1 = 180 -∠2
like this ∠2 and ∠3 are adjacent angle so the sum of the measure of these two angles are 180°
∠2 + ∠3 = 180 ⇒ ∠3 = 180 -∠2
from the above equation;
∠1 = ∠3
or, we can say that the vertically opposite angles are equal in measure.
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