There are 104 cars in the parking lot.
According to statement there are between 90 and 115 cars on the lot.
So, {X| 90 < x < 115} (This renders an infinite solution set finite)
AND exactly one eight of them have a sticker on the back, so the total number of cars must be evenly divisible by eight.
X ∈ {96, 104, 112,}
AND exactly one fourth of the cars are green, so the number of cars must be evenly divisible by 4. Here all above written numbers are divisible by 4. So, find the mean to calculate the number of cars in the parking lot.
x = (96+104+112)/3
x = 104
There are 104 cars in the parking lot.
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Aria is paddling a canoe at a constant speed. She starts a timer when she is 40 feet from her starting position. After 30 seconds, Aria is 130 feet from her starting position. Write a linear equation in slope-intercept form to find the distance d of Aria from her starting position after t second.
Answer:
[tex]y = 3x + 40[/tex]
Step-by-step explanation:
The slope-intercept equation takes the form
[tex]y = mx + c[/tex]
Where m is the gradient, and c is the y-intercept.
If we assume we are plotting a graph where the X axis is time, and the y axis is distance, and we know our time value starts at 40, then we can say that our y intercept value is 40.
Next, let's figure out how far she has travelled. 130-40 = 90, and she has travelled this distance in 30 seconds, so dividing 90 by 30, we know that she is travelling 3 feet a second. This leaves us with a gradient of 3.
Putting these two values together, we can find the final form of the equation to be:
[tex]y = 3x + 40[/tex]
Answer:
d = 3t + 40
Step-by-step explanation:
So, since you have a constant speed you're going to have a linear equation, which was also stated in the question. So it's asking for slope-intercept form which is expressed as: y=mx+b, where m=slope, and b=y-intercept. So it's important to know what these two things mean in certain contexts. In every single case, the slope is how much the y-value is changing as x increases by 1, and in this specific case, the distance is what is changing as time goes by. So this means that the distance would be the y-value, and x would be the t variable (time). And remember how it mentioned "constant speed", this means as one second passes, the distance increases by a constant distance. We can solve for this by using the given information.
She's already 40 feet from her starting position, and after 30 seconds she's 130 feet from her starting position. This means she traveled (130 - 40) feet, because she was already 40 feet away from her starting position. This means she traveled 90 feet. Now to find how much she travels in a second, divide it by the time which is 30 seconds, and you get: 90 feet / 30 seconds = 3 ft/s, this is her constant speed. This is the slope of the equation. So now we have the equation: d = 3t + b. Now all we need to find is the y-intercept
The y-intercept in this context, is how far away she is from her starting position initially. This is given in the problem, it's 40 feet. She's already 40 feet away when 0 seconds have passed. So this gives us the equation: d = 3t + 40
Work out the mean for the data set below: 3 , 5 , 4 , 3 , 5
Answer:
4
Step-by-step explanation:
The mean is the average of the numbers.
if you rearrange the data, you will get the order, 3,3,4,5,5.
you add all of them together to get the number twenty, then you divide 20 by the total number of data plots which is five. Then you get the number 4 which is your answer
3+3+4+5+5 = 20
20/5 = 4
Can some one put the answers out
Step-by-step explanation:
1. -5(a - 9) = -5a + 45
2. [tex]\frac{-8.3-(+2.7)}{\frac{1}{5} } = \frac{-8.3-2.7}{0.2} =\frac{-11}{0.2}=-55[/tex]
3.13p + 13 - p = (13p - p) + 13 = 12p + 13
4. -11b - 3(-4b + 1) = -11b + 12b - 3 = b - 3
5.
[tex]-2n+\frac{1}{6}-4\frac{1}{2}n = (-2n-4\frac{1}{2}n)+\frac{1}{6} = [-\frac{4}{2} n-(\frac{8}{2}+\frac{1}{2} )n]+\frac{1}{6} = -\frac{4}{2} n- \frac{9}{2} n+\frac{1}{6} =-\frac{13}{2}n\\+ \frac{1}{6}[/tex]
6. It didn't show all the information on the question.
7. [tex]-\frac{3}{5}(20r-5)-(-6r) =-12r+3+6r = (-12r+6r)+3=-6r+3[/tex]
8. [tex]-\frac{5}{6}x+\frac{4}{9}+\frac{2}{3}x+\frac{1}{3}=(-\frac{5}{6}x+\frac{2}{3}x)+(\frac{4}{9}+\frac{1}{3})=(-\frac{5}{6}x+\frac{4}{6}x)+(\frac{4}{9}+\frac{3}{9})=-\frac{1}{6}x+\frac{7}{9}[/tex]
9.It didn't show all the information on the question.
which is a stretch of an exponential decay function ?
Using translation concepts, a stretch of a decay exponential function is given by:
[tex]f(x) = 5\left(\frac{1}{5}\right)^x[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
An exponential decay function is given by:
[tex]y = ab^x[/tex]
In which |b| < 1.
A stretch means that the function is multiplied by a factor with absolute value greater than 1, hence the function would be given by:
[tex]f(x) = 5\left(\frac{1}{5}\right)^x[/tex]
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Quick factorisation question… can someone pls help and also provide a step by step explanation? Thank you!
Hello,
Answer:
C. (b - c)(a + b)
Step-by-step explanation:
A = (b - c)(a - c)
A = ba - bc - ac - c² ≠ ab + b² - ac - bc
B = (b + a)(b + c)
B = b² + bc + ab + ac ≠ ab + b² - ac - bc
C = (b - c)(a + b)
C = ba + b² - ca - cb
= ab + b² - ac - bc
→ That is answer C
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas.During
one particular week, the two cars went a combined total of 1400 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of
the two cars that week
20 gallons is consumed from the first car and 25 gallons is consumed from the second car.
What is an Equation ?A mathematical statement that relates two algebraic expression using an equal sign is called an equation.
It is given that
Fuel Efficiency of the first car is 20 miles per gallon of gas
Fuel Efficiency of the second car is 40 miles per gallon of gas
Total miles travelled = 1400 miles
Total gas consumption = 45 gallons
Let the gallons consumed from the first car is x
then the gallons consumed by the second car is (45 - x)
The equation formed will be
20* x + 40 * (45 -x) = 1400
20x +1800 - 40x = 1400
-20x = -400
x = 20
Therefore 20 gallons is consumed from the first car and
45-20 = 25 gallons is consumed from the second car.
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expand and simplify(2x-3)(3x-5)
Answer:
6[tex]x^{2}[/tex] - 19x + 15
Step-by-step explanation:
(2x - 3) (3x - 5)
2x(3x-5) - 3 (3x-5)
6[tex]x^{2}[/tex] - 10x - 3 (3x - 5)
6[tex]x^{2}[/tex] - 10x - 9x + 15
6[tex]x^{2}[/tex] - 19x + 15
Answer:
6x² - 19x + 15
Step-by-step explanation:
(2x - 3)(3x - 5)
each term in the second factor is multiplied by each term in the first factor, that is
2x(3x - 5) - 3(3x - 5) ← distribute parenthesis
= 6x² - 10x - 9x + 15 ← collect like terms
= 6x² - 19x + 15
7. License Plate Laws The Chapter Problem involved passenger cars in Connecticut and passenger cars in New York, but here we consider passenger cars and commercial trucks. Among 2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticut trucks, 45 had only rear license plates (based on samples collected by the author). A reasonable hypothesis is that passenger car owners violate license plate laws at a higher rate than owners of commercial trucks. Use a 0.05 significance level to test that hypothesis. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval
Yes it is true that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars because null hypothesis is rejected.
Given among 2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticut trucks, 45 had only rear license plates.
let [tex]p_{1}[/tex] be the probability that commercial cars have rear license plates and [tex]p_{2}[/tex] be the probability that connected trucks have rear license plates.
Cars Trucks Total
Total 2049 334 2383
x 239 45 284
p 0.1166 0.1347 0.1191
α=0.05
Hypothesis will be :
[tex]H_{0}:p_{1} =p_{2}[/tex]
[tex]H_{1} :p_{1} < p_{2}[/tex]
It is a left tailed test at 0.05 significance.
Standard errors of p=[tex]\sqrt{p(1-p)/n}[/tex]
=[tex]\sqrt{(0.1191*0.8809)/2383}[/tex]
=[tex]\sqrt{0.1049/2383}[/tex]
=0.0066
Test statistic Z=p difference/standard error
=(0.1166-0.1347)/0.0066
=-0.0181/0.0061
=-2.967
p value=0.001505<5%
Since p is less than 5% we reject null hypothesis.
We cannot calculate standard deviation so we cannot calculate confidence interval.
Hence there is statistical evidence at 5% significance level to support that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
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A ferris wheel has 32 passenger cabins. if you are sitting in cabin 14 which is currently at the top of the wheel, what is the number of the cabin at the bottom of the wheel?
Answer:
30Step-by-step explanation:
A ferris wheel has 32 passenger cabins. if you are sitting in cabin 14 which is currently at the top of the wheel, what is the number of the cabin at the bottom of the wheel?
from the top to the base you have a semicircle, so 16 cabins, if at the top there is the 14 below you will have the 30.
32 : 2 + 14 = 30
Answer:
Number of the cabin at the bottom of the wheel is 30
Step-by-step explanation:
Since there are 32 passenger cabins, each half of the wheel has:
32/2 = 16 cabinsIt means the opposite cabins on the Ferris wheel have number difference of 16.
If one of the cabins has a number 14, the opposite cabin has number of:
14 + 16 = 30Could you guys help meee
1. y= 2x
2. (0, 5)
3. y = 3x + 12
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
1. let us take (0,0) and (1, 2)
m= 2-0/1-0
m= 2
So equation of line
y- 0 = 2(x-0)
b
2. y= 3x+5
passes through (0, 5)
3. y= 3x+5
m = 3
We need the equation of a line with slope 3 that passes through point (0, 12).
y - y1 = m(x - x1)
y - 12 = 3(x - 0)
y - 12 = 3x
y = 3x + 12
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Triangle abc is a right triangle with leg lengths of 5 and 12 inches. find the length of the hypotenuse. round answer to the nearest hundredth if necessary. 4.12 in 10.91 in 13 in 17 in
The hypotenuse of the right triangle ABC, with legs of 5 and 12 inches is 13 inches, computed using the Pythagoras Theorem. Hence, the 3rd option is the right choice.
The Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is always equal to the sum of the squares of the other two legs.
If the hypotenuse is taken as a, and the two legs are taken as b and c, then by the Pythagoras Theorem, we can write that:
a² = b² + c².
In the question, we are given that the right triangle ABC, has legs of lengths 5 and 12 inches each, and we are asked to find the length of the hypotenuse.
Thus, taking b = 5 and c = 12, in the above equation, we get:
a² = 5² + 12²,
or, a² = 25 + 144,
or, a² = 169,
or, a² = 13²,
or, a = 13.
Thus, the hypotenuse of the right triangle ABC, with legs of 5 and 12 inches is 13 inches, computed using the Pythagoras Theorem. Hence, the 3rd option is the right choice.
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PLEASE HELP THIS IS TIMEDDDD PLS DONT GUESS
What is the sum of f° + g°?
360°
120°
180°
110°
Answer: 180
Step-by-step explanation:
i got you!!!!!!! Hope u pass
Answer:
180
Step-by-step explanation:
<f and <g are on a straight line and they are supplementary angles which means their sum is equal to 180.
Ten friends want to play a game. They must be divided into three teams with three people in each team and one field judge. In how many ways can they do it?
Using the combination formula, it is found that there are 16,800 ways for them to do it.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
For the judge, one is taken from a set of 10.For the first team, 3 are taken from a set of 9.For the second team, 3 are taken from a set of 6.For the third team, 3 are taken from a set of 3.Hence the number of ways is:
[tex]N = C_{10,1}C_{9,3}C_{6,3}C_{3,3} = \frac{10!}{1!9!} \times \frac{9!}{3!6!} \times \frac{6!}{3!3!} \times \frac{3!}{3!0!} = 16800[/tex]
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A plane flies at 350 mph in the direction 40° north of east, with a wind blowing at 40 mph in the direction 30° south of east. what is the plane’s drift angle?
Lets simplify the given problem,
The speed with which the plane flies = 350 mph
The direction of flight of the plane = N 40° E
The speed with which the wind blows = 40 mph
The direction in which the wind blows = S 40° E
Therefore, we have;
The resolution of the components of the motion of the plane, given as follows;
= 350 × sin(40°)·i + 350 × cos(40°)·j
The resolution of the components of the motion of the wind, given as follows;
= 40 × sin(40°)·i - 40 × cos(40°)·j
The resultant motion of the plane is given as follows;
= 262.563·i + 254.435·j
The direction of motion of the plane = tan⁻¹(262.563/254.435) ≈ N 45.9° E
Therefore, the plane's drift = Plane's Track - Plane's Heading = N 45.9° E - N 40° E ≈ 5.9° ≈ 5.89°
Drift Angle of the plane is 5.89 degree.
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Answer: A 5.9
Step-by-step explanation:
cuz i said so
In a recent survey of 1002 people, 701 said that they voted in a recent presidential election. voting records show that 61% of eligible voters did not vote. how would the confidence interval change if we increased the confidence level to 99%? find the 99% confidence interval estimate to support your answer.
The 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623,0.7369).
Given sample size=1002 and confidence level of 99%.
In a sample with a number n of people surveyed with a probability of a success of π and a confidence level of 1-α, we have the following confidence interval of proportions.
π±z[tex]\sqrt{}[/tex]π(1-π)/n
in which z is the z score that has a p value of 1-α/2
n=1002,π=701/1002
So α=0.01, z is the value of Z that has a p value of 1-0.01/2=0.995, so Z=2.575.
Lower limit=π-[tex]z\sqrt{}[/tex]π(1-π)/n
=0.6996-2.575[tex]\sqrt{0.6996*0.3004/1002}[/tex]
=0.6623
Upper limit=π+[tex]z\sqrt{}[/tex]π(1-π)/n
= 0.6996+2.575[tex]\sqrt{0.6996*0.3004/1002}[/tex]
=0.7369
Hence the 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623,0.7369).
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What is 88=10y + 30 - 4y?
Answer:
y = [tex]\frac{29}{3}[/tex]
Step-by-step explanation:
88 = 10y + 30 - 4y , that is
88 = 6y + 30 ( subtract 30 from both sides )
58 = 6y ( divide both sides by 6 )
[tex]\frac{58}{6}[/tex] = y , that is
y = [tex]\frac{29}{3}[/tex]
Find the surface area. Round your answer to the nearest hundredths, if necessary. Leave your answer in terms of for answers that contain .
Answer:
I don't know how to answer this, sorry!
Step-by-step explanation:
What is the gradient of the graph shown?
Answer:
1
Step-by-step explanation:
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The steps used to solve the quadratic equation are
8(x2 + 2x) = –3
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
How to determine the stepsGiven the equation;
8x² + 16x + 3 = 0
Collect like terms
8x² + 16x = -3
Take the common factors, we have
8(x² + 2x) = -3
Completing squares in the brackets and balancing the equation in the right side
8(x² + 2x + 1) = -3 + 8
Factoring the perfect square
[tex]8(x + 1)^2} = 5[/tex]
Make 'x' subject
[tex](x + 1)^2= \frac{5}{8}[/tex]
[tex](x + 1) =[/tex] ±[tex]\sqrt{\frac{5}{8} }[/tex]
[tex]x =[/tex] -1 ±[tex]\sqrt{\frac{5}{8} } }[/tex]
Thus, we can clearly see the steps used to solve the quadratic equation are
8(x2 + 2x) = –3
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
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If The Area Of Triangle MNO Is 24cm2 Find The Area Of Triangle PNO
Answer:
24 cm^2
Step-by-step explanation:
The three sides are equal (SSS: side, side, side) so the triangles are congruent.
Find the area of the trapezoid
Answer:
337.5Ft
Step-by-step explanation:
Find the length of the 40 degree arc shown in red. Round your
answer to the nearest whole number. (Enter only a number as your
answer.)
The radius or any additional information related to the circle to assist in calculating the length of the 40-degree arc.
To find the length of a 40-degree arc, to know the radius or diameter of the circle to which the arc belongs. Once you have that information, use the formula to find the arc length:
Arc Length = (θ / 360) × 2 ×π ×r
Where:
θ = Central angle in degrees (40 degrees in this case)
r = Radius of the circle
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Pls, can someone help me with this problem?
Answer:
1 ÷ 3
Step-by-step explanation:
You want 1/3 written as a quotient.
QuotientThe quotient of A and B is "A divided by B." There are two ways to write this using math symbols:
A/B
A÷B
The fraction 1/3 is already written as a quotient. This set of symbols can be read as either of ...
"one-third""one divided by three".The other way to write the quotient is ...
1 ÷ 3
__
Additional comment
When you learn about exponents, you learn another way to write the quotient of A and B is ...
A·B⁻¹
<95141404393>
Divide 54 into the ratio 11:7
Answer:
33:21
Step-by-step explanation:
The way I look at it is that 11:7 is 18 parts of 54. So I divide 54 by 18 and get 3 per. Then multiply, 11 * 3 is 33 and 7 * 3 is 21.
The expression is 12 x 2 / 7 will be 24/7. And the number 54 into the ratio 11:7 will be 33 and 21.
What is the ratio?The utilization of two or more additional numbers that compares is known as the ratio.
The expression is given below.
⇒ 12 x 2 / 7
⇒ 24 / 7
Divide 54 into the ratio 11:7.
⇒ 54 x 11 / (11 + 7)
⇒ 594 / 18
⇒ 33
⇒ 54 x 7 / (11 + 7)
⇒ 378 / 18
⇒ 21
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Can you help me find the answer to it pls and ty <3 .
The expression that represent the area of the cut off part is 81π / 4
How to find area?The area of the cut off part can be found as follows:
Area of a circle = πr²
where
r = radiusTherefore, the cut off part is like 1 / 4th of a circle.
Hence,
area of the cut off region = πr² / 4
r = 9 inches
area of the cut off region = π9² / 4
area of the cut off region = 81π / 4
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A survey was conducted to determine which type of lunch was more popular among the school’s football team. For this purpose, the number of each type of lunch sold to the players was tracked. How many more pizza lunches than hot dog lunches were sold? A. 3 B. 4 C. 7 D. 5
The number of pizza lunches sold more based on the survey is 5.
How to compute the value?The information is incomplete and an overview will be given.
Let the number of pizza lunches sold be 24.
Let the number of hot dog lunches be 19.
Therefore, the number of pizza lunches sold more will be:
= 24 - 19
= 5
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Answer: C, 7
Step-by-step explanation:
Question 4(Multiple Choice Worth 2 points)
(02.04 MC)
Beginning with the graph of f(x) = x², what transformations are needed to form g(x) = 3(x + 2)2-1?
The transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units
Transformation of functionsTransformation is the technique used to change the position of a figure on an xy-plane.
Given the parent function f(x) = x², the transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units
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-6. The area of trapezium in cm² is A. 276 C. 207 B. 240 D. 225
Answer:
276 cm²
Step-by-step explanation:
Area of trapezium:Construct a line DE parallel to AB.
DE = 13 cm
So, ABED is a parallelogram
In ΔDEC,
DE = a = 13 cm
EC = AB - BE
= 30 - 16
EC = b = 14 cm
DC = c = 15 cm
Use Heron's formula to find the area of triangle.
[tex]\sf s = \dfrac{a+b+c}{2}\\\\=\dfrac{13+15+14}{2}\\\\=\dfrac{42}{2}\\\\s = 21[/tex]
s-a = 21 - 13 = 8
s - b = 21 - 14 = 7
s - c = 21 - 15 = 6
[tex]\sf \boxed{\bf Area \ of \ triangle = \sqrt{s(s-a)(s-b)(s-c)} }[/tex]
[tex]\sf = \sqrt{21 * 8 * 7* 6}\\\\=\sqrt{3 * 7 * 2* 2 * 2 * 7 * 2 * 3}\\\\= 3 * 7 * 2 * 2\\\\= 84 \ cm^2[/tex]
Area of ΔDEC = 84 cm²
[tex]\sf \dfrac{1}{2}*base * height = 84\\\\ \dfrac{1}{2}*14*height = 84[/tex]
[tex]\sf height =\dfrac{84*2}{14}\\\\[/tex]
= 6 *2
height = 12 cm
Now we know the height of the trapezium. h = 12 cm
The length of the parallel sides are a = 30 cm & b =16 cm
[tex]\sf \boxed{Area \ of \ trapezium = \dfrac{(a +b)*h}{2}}[/tex]
[tex]\sf =\dfrac{(30+16)*12}{2}\\\\=\dfrac{46*12}{2}\\\\= 23 * 12\\\\= 276 \ cm^2[/tex]
Come up with two examples of ratio relationships that are interesting to you.
In mathematics a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other
Let's take an mathematical example
Let's find the ratio of volume of a cone and cylinder if radius and height are same for both .
See
V for cone=1/3πr²hV for cylinder=πr²hThe ratio is 1:3
#Example 1
Gems Ram has=3Gems Kane has=4Ratio of gems=3:4
#Example 2
Total continents in world=7Total oceans in world=5Ratio of ocean to continents=5:7
Note:-
Two examples are already provided on your another question .You may refer there
Which exponential equation with base of 2, has been reflected on y -axis, vertically compressed by a factor of 1/3 and vertically translated up 2 units:
*
By applying the rigid transformations of reflection on y-axis, vertical compression and vertical translation, we find the transformed function based on f(x) = 2ˣ is f''(x) = (1/3) · 2⁻ˣ + 2.
How to derive a function by using rigid transformations
Rigid transformations are transformations applied on functions such that their Euclidean distance is conserved. In this problem we must use the following rigid transformations to determine an expression based on f(x) = 2ˣ.
Reflection on y-axis
f'(x) = f(-x) (1)
f'(x) = 2⁻ˣ
Vertical compression
f''(x) = k · f'(x) (2)
f''(x) = (1/3) · 2⁻ˣ
Vertical translation
f'''(x) = f''(x) + c (3)
f''(x) = (1/3) · 2⁻ˣ + 2
By applying the rigid transformations of reflection on y-axis, vertical compression and vertical translation, we find the transformed function based on f(x) = 2ˣ is f''(x) = (1/3) · 2⁻ˣ + 2.
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