the environmental protection agency (epa) rates the mean highway gas mileage of the 2013 ford edge to be 27 miles per gallon. assume the standard deviation is 3 miles per gallon. a rental car company buys 60 of these cars, 0.2979 is the probability that the average mileage of the fleet is less than 26 miles per gallon.
What is probability?Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A probability value between 0 and 1 represents an occurrence.
The four primary categories of probability are axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you might argue that it is the likelihood that a specific event will occur.
Given that,
μ = 27
σ = 3
n = 60
As we know,
= p ( 26 < x(avg.) < 26.8 )
= p (26 - 27 / 0.3873 ) < ( x(avg.) - μ(avg.)x /σx(avg.) ) < (26.8- 27/0.3873)
= p ( -1/ 0.3873 < z < -0.2 / 0.3873 )
= p ( -2.5820 < z < -0.5164 )
= p ( z < -0.5164) - p ( z < -2.5820 )
Using z table, we get -
= 0.3028- 0.0049
= 0.2979
Thus, probability = 0.2979
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Aeris reads the temperature of a liquid in a lab experiment. The temperature of the liquid is 7.2ºF. After 5 hours, she reads the temperature of the liquid again. The temperature of the liquid is now −1.6°F.
Aeris plots the points on a number line to determine the temperature change between these two readings.
How much did the temperature decrease?
Enter your answer as a decimal in the box.
[ ]
Answer: 8.8 (-8.8'F)
Step-by-step explanation:
What we know:
Temperature started as 7.2
Temperature ended as -1.6
We need to find the difference
How to solve:
By doing simple subtraction, we can solve this.
Process:
Write equation 7.2 - (-1.6) = ?
Simplify 7.2 + 1.6 = ?
Solve = 8.8
Solution: {8.8 (-8.8'F)}
The temperature decreased by 8.8'F, but it increased/changed by -8.8'F.
A person standing close to the edge on top of a 96-foot building throws a ball vertically upward. The quadratic function h(t) = - 16t^2 + 116t + 96 models the balls height about the ground, h(t), in feet, t seconds after it was thrown.
a) What is the maximum height of the ball? __ feet
b) How many seconds does it take until the ball hits the ground? __ seconds
Answer:
the answer is 306.25 feet and b is 8 sec
Step-by-step explanation:
Explanation
The height of the ball as a function of the time is given by the following formula:
A. Maximum height of the ball
To find the value of the maximum height, we maximum the function h(t) computing its first derivative and equalling the result to zero:
Solving the last equation for t, we get time t when the height is maximum:
So the maximum height is given by the value of h(t) when t = 2.5:
The maximum height is 196ft.
B. Time until the ball hits the ground
The ball will hit the ground when h(t) = 0. So we must find the value of t such that:
Solving this equation is equivalent to finding the roots of a second-order polynomial:
Where:
• a = -16,
,
• b = 80,
,
• c = 96.
The roots of this polynomial are given by the following formula:
s
Answer
A. The maximum height of the ball is 196 ft.
Mr.green is putting lights around 8 windows each window is 3 and 1/2 feet wide and 5 feet long how many feet of lights does he need
The number of fests of light that Mr Green needs 140 feet of lights
What is a perimeter?The perimeter is the distance around the object. For example, your house has a fenced yard. The perimeter is the length of the fence.
From the formula for perimeter L x W which will give us.L being 5 and W being 3.5
The equation is 5 × 3.5 = 17.5.
With that being said I just need to multiply that answer by 8 which gives us 140. This means that he will need 140 feet of light in order to put light around each window.
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what is 5,821 g = ___ dag
Answer:
582.1
Step-by-step explanation:
Colette ha 5/6 of a pitcher of water. She ue 3/5 of the water to water her plant. How much water doe he ue (in term of pitcher)? b) How much water i left (in term of pitcher)?
[tex]\frac{7}{30}[/tex] of water is left in the pitcher
What is Least common multiple ?Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
According to the given information
Total water in container = [tex]\frac{5}{6}[/tex]
Total water used to water the plants = [tex]\frac{3}{5}[/tex]
Water left in pitcher = [tex]\frac{5}{6} - \frac{3}{5}[/tex]
Taking LCM we will get
= [tex]\frac{25-18}{30}[/tex]
= [tex]\frac{7}{30}[/tex]
[tex]\frac{7}{30}[/tex] of water is left in the pitcher
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Mariel and Sam Trent's savings account had a balance of $9,544 on May 1. The account earns interest at a rate of 5.25% compounded
vide. More than f U.S. banking
monthly until the end of August.
Answer: its around 25,000 during the end of august
Step-by-step explanation:
can somebody please help
Answer:
(4,12) Quadrant l
(-5,2) Quadrant ll
(-9,-4) Quadrant lV
(3,-3) Quadrant lll
Step-by-step explanation:
hope this helps!
How do I solve this?
Answer:
Step-by-step explanation:
can you send a much clear image its to blurry I can not read it.
Solve for X using Trigonometry Will give thanks and five stars
Answer:
x= 19.5
Step-by-step explanation
sin58 = x/23
x = 23×sin58
x = 19.5
Mr. Tazari bought 4 new plants for his garden. Each plant cost $7. The store
gave him a discount, so he only paid of the regular price for each plant.
Use the properties of multiplication to find the total cost for all the plants.
Answer:
21
Step-by-step explanation:
u/5 = 17/11 Solve the following proportion for u. Round your answer to the nearest tenth.
On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.
What do you think about proportionality?We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
What is proportionality?When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.
Here,
[tex]\frac{U}{5} = \frac{17}{11} \\\\[/tex]
[tex]U = \frac{17}{11} X 5\\[/tex]
[tex]U = \frac{85}{11}\\ U = 7.72[/tex]
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Identify the common difference: d=
Identify the zero term(starting amount) a=
The formula to find the common difference of an arithmetic sequence is: d = a(n) - a(n - 1), where a(n) is a term in the sequence, and a(n - 1) is its previous term in the sequence
What is arithmetic sequence?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. For instance, the number sequence 5, 7, 9, 11, 13, and 15 has a common difference of 2 in arithmetic.
Sequences can in fact begin at any number that we choose. A sequence with the general word an is commonly notated as ann=1 a n n = 1.
or d = (an + 1 - an) (an – an-1). AP reduces if the common difference is negative. For instance, the AP drops in these numbers: -4, -6, -8.
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9. If one-sixth is one-half of three-fourths of a certain number, what is that number?
A. [tex] \frac{3}{16} [/tex]
B. [tex] \frac{4}{9} [/tex]
C. [tex] \frac{5}{4} [/tex]
D. [tex] \frac{3}{2} [/tex]
E. [tex] \frac{9}{4} [/tex]
Answer:
B) 4/9---------------------------
Convert the statement into equation, considering the number as x, and solve:
1/6 = 1/2×3/4×x Equation 1/6 = 3/8×x Simplify the RHSx = 1/6 ÷ 3/8 Divide both sides by 3/8x = 1/6 × 8/3 Change division to multiplication x = 4/9 AnswerCorrect choice is B.
What’s the value of z ?
Answer:
z = 7
Step-by-step explanation:
We know that, sum of the exterior angles of a quadrilateral is added up to 360°.
Accordingly,
115 + 7z + 12z + 16z = 360
Combine like terms.
115 + 35z = 360
Subtract 115 from both sides.
35z = 360 - 115
35z = 245
Divide both sides by 35.
z = 7
6% of 33.00
some one help
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6\%\ of\ 33.00}[/tex]
[tex]\mathsf{= \dfrac{6}{100}\ of\ 33.00}[/tex]
[tex]\mathsf{= \dfrac{6}{100}\times33.00}[/tex]
[tex]\mathsf{= \dfrac{6}{100}\times 33}[/tex]
[tex]\mathsf{= \dfrac{6}{100}\times \dfrac{33}{1}}[/tex]
[tex]\mathsf{= \dfrac{6\div2}{100\div2}\times \dfrac{33}{1}}[/tex]
[tex]\mathsf{= \dfrac{3}{50}\times\dfrac{33}{1}}[/tex]
[tex]\mathsf{= \dfrac{3\times 33}{50 \times1}}[/tex]
[tex]\mathsf{= \dfrac{99}{50}} \mathsf{\rightarrow 1 \dfrac{49}{50}}[/tex]
[tex]\huge\text{Answer: }[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{99}{50} \ or\ 1\dfrac{49}{50}}}\huge\checkmark[/tex]
[tex]\uparrow\large\text{Either those should work because they are equivalent to (equal to)}\\\large\text{each other}\uparrow[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Find the measure of ∠c given the information below.
A = 155
E= 69
The image is below giving brainliest for whoever answers correctly + explaining !
Answer:
c=65
Step-by-step explanation:
a=115
180-115=b
b=65
b=c
c=65
Pete has 3 puppies. The puppies' names are Jack, Buster, and Coco. Pete's three puppies share 1 whole bone. Jack ate 2/16 of the bone Buster ate 5/8 of the bone. What fraction of the bone did Coco eat?
Answer: 2/8
Step-by-step explanation: 2/16 can be simplified to 1/8, 1/8 + 5/8 = 6/8, since a whole bone is 8/8, or 1. 8/8 - 6/8 = 2/8
so, once more, the answer is 2/8.
Water is being from a pool. The volume of water in the pool t minutes after begin draining is given by the function V(t)=4522(0.94)^t. Which of the following is the closest to the percent volume that has drained out of the pool after 10 minutes
The closest percentage volume that has drained out is 46%
How to determine the percentage volume?From the question, we have the following parameters that can be used in our computation:
V(t) = 4522(0.94)^t
The initial volume is calculated when t = 0
So, we have
V(0) = 4522(0.94)^0
Evaluate
V(0) = 4522
The new volume is calculated when t = 10
So, we have
V(10) = 4522(0.94)^10
Evaluate
V(10) = 2435.62
The percentage is then calculated as
Percentage = (V(10) - V(0))/(V(0))
So, we have
Percentage = (2435.62 - 4522)/4522
Evaluate
Percentage = -46%
Hence, the percentage is 46%
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In a tidal river, the time between high and low tide i 7. 8 hour. At high tide the depth of water i 19. 2 feet, while at low tide the depth i 5. 1 feet. Aume the water depth a a function of time can be expreed by a trigonometric function (ine or coine). Write an equation for the depth f(t) of the tide (in feet) t hour after 12:00 noon. *I have tried to figure thi problem out o many time and all my anwer end up wrong. Cloe, but wrong, any help i greatly appreciated. *
the time between high and low tide i 7. 8 hour. At high tide the depth of water i 19. 2 feet, while at low tide the depth i 5. 1 feet. So roughly 2 hours and 15 minutes, the depth will be 12 feet
What is depth?
a measurement made through an object or body of material, typically horizontally inward from an outer surface, upward from an upper surface, or upward from the top of something considered to be one of multiple layers. deepness, the property of being deep.
(0,6)
(8,20)
(16,6)
y = C*sin( k*pi*x) + 6 since (0,6) is given
C(sin(k*pi*8) + 6 = 20
C(sin(k*pi*8) = 14 <--- label this equation ALPHA
Also,
C(sin(k*pi*16) + 6 = 6
C(sin(k*pi*16) = 0
since C cannot be zero, k*pi*16 must be 180 = pi
k*16 = 1
k = 1/.16
C(sin( (1/16)*pi*8) = 14
C ( sin (pi/2) ) = 14
C = 14
D(t) = 14 sin( (pi/16) t ) + 6 where D is the depth and t is time
12 = 14 sin((pi/16)t) + 6
6/14 = sin((pi/16)t)
arcsin(3/7)*16/pi = t
t = 2.25572...
So roughly 2 hours and 15 minutes, the depth will be 12 feet
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Hi! I need this answer very quickly but I don't understand this math problem hope you can help! I need to know if it has no solution or one or two and can you show work with it, please? TYYYYY
7b + 3 - 4b = 3 - 3(b + 4)
Answer:
b=-2
Step-by-step explanation:
I dont have the steps srry :(
Answer:
b = -2
Step-by-step explanation:
7b + 3-4b= 3 - 3 (b +4)
a and b are vectors that are not parallel.
FG = 2a − 3b
-
Choose all of the vectors below which are parallel to
FG.
a-b10a-15
3a-2b-4a+6b 2a + 3b
2a-3b-4a 2a-12b +4a + 3b
Answer:
[tex]\boxed{\textbf{a}-\dfrac{3}{2}\textbf{b}}[/tex]
[tex]\boxed{10 \textbf{a}-15\textbf{b}}[/tex]
[tex]\boxed{-4 \textbf{a}+6\textbf{b}}[/tex]
[tex]\boxed{2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}}[/tex]
Step-by-step explanation:
Given vector:
[tex]\overrightarrow{\rm FG}=2 \textbf{a}-3\textbf{b}[/tex]
Two vectors are parallel if one can be written as a scalar multiple of the other.
Therefore, the following vectors are parallel to FG:
[tex]\textbf{a}-\dfrac{3}{2}\textbf{b}=\dfrac{1}{2}(2 \textbf{a}-3\textbf{b})[/tex]
[tex]10 \textbf{a}-15\textbf{b}=5(2 \textbf{a}-3\textbf{b})[/tex]
[tex]-4 \textbf{a}+6\textbf{b}=-2(2 \textbf{a}-3\textbf{b})[/tex]
[tex]2\textbf{a}-12\textbf{b}+4\textbf{a}+3\textbf{b}=6\textbf{a}-9\textbf{b}=3(2 \textbf{a}-3\textbf{b})[/tex]
Write a linear function f with f (5)=7 and f(-2)=0
Without multiplying, order the following products from least to greatest.
1 1/6 x 310 8/8x310 4/7x310
One of the factors is present in all of the items mentioned. The order of the value of the other factor will match the order of the value of the product.
A multiplication comparison: What does that mean?When two amounts are compared, a multiplicative comparison determines which can be created when the other is multiplied by a specific number. Like Sam, who has twice as many balloons than Sid. Three balloons are in Sid's possession.Every single one of the previously named things contains one of the elements. Both the order of the other factor's value and the order of the product's value will be the same. A fraction that is equal to 1 multiplied by a number produces a number as the result. A positive whole number can be multiplied by a fraction greater than one, and the resulting number will always be larger than the initial whole number.To learn more about Multiplicative comparison refer to:
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Use the following function rule to find f(5). f(x) = –4 |x| − 3 f(5) = \
A function is a relationship between inputs where each input is related to exactly one output.
The value of f(x) at x = 5 is -23.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = -4 |x| - 3
The value of f(x) at x = 5.
f(5) = -4 |5| - 3
f(5) = -4 x 5 - 3
f(5) = -20 - 3
f(5) = -23
Thus,
The value of f(x) at x = 5 is -23.
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In each of the follwing, find:
a. (fg)(x)
b. (f-g)(x)
c. (f *g )(x)
d. (f/g) (x)
1. F(x) = 3x 4; g(x) = 2x - 1
2. F(x) = x-1/ x2, g(x) = 1/x
The solution to the following functions are 1) 6x5-3x4, 3x4+1, 6x5-3x4, 3x4 / (2x-1), 2)(x-1)/x3, (x-1)/x2 - 1/x, (x-1)/x3, x-1
What are functions?The relationship between two sets of numbers is described mathematically by a function. It is a mathematical equation that assigns a unique output value to each input value inside a specific domain. Functions are frequently expressed by a letter, such as F(x) = 3x+ 4 or g(x), where the letter indicates the function and the input value is represented by the variable x.
Functions can be either linear or nonlinear, and they can have a single or numerous outputs for each value of the input. They are frequently employed to simulate real-world situations and generate predictions based on available information. Functions can be graphed on a coordinate plane to visualise their behavior, and they can be combined or transformed using various mathematical operations.
How to solve?
1)a. (fg)(x) = (3x4)(2x-1) = 6x5-3x4
b. (f-g)(x) = (3x4) - (2x-1) = 3x4+1
c. (f *g )(x) = (3x4) * (2x-1) = 6x5-3x4
d. (f/g) (x) = (3x4) / (2x-1) = 3x4 / (2x-1)
2)a. (fg)(x) = (x-1/x2) * (1/x) = (x-1)/x3
b. (f-g)(x) = (x-1/x2) - (1/x) = (x-1)/x2 - 1/x
c. (f *g )(x) = (x-1/x2) * (1/x) = (x-1)/x3
d. (f/g) (x) = (x-1/x2) / (1/x) = (x-1)/x2 / (1/x) = (x-1)/x2 * x = x-1
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Which box-and-whisker plot represents this data: 6, 9, 13, 13, 18, 20, 22, 25, 26, 28, 30, 30 ?
The box and whisker plot that represents the data given is option D (see attachment below).
How to Determine the Box and Whisker Plot that Represents a Data Set?The box and whisker plot that represents a data set will display the five-number summary of the data, which include minimum and maximum values, upper quartiles and lower quartiles, and the median of the data.
Given the data set, 6, 9, 13, 13, 18, 20, 22, 25, 26, 28, 30, 30, the five-number summary that would be displayed on the box and whisker plot include:
Minimum: 6 (at the beginning of the whisker to the left)
First Quartile: 13 (at the beginning of the edge of the box)
Median: 21 (at the middle line on the box)
Third Quartile: 27 (at the end of the edge of the box)
Maximum: 30 (at the end of the whisker to the right)
Therefor, the box and whisker plot would be the option D (see image below).
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The graph below shows the number of hours Dario
worked and the amount he earned.
Earnings (in dollars)
100
90
80
70
60
50
40
30
DARIO'S EARNINGS
(2, 24)
(5, 60)
(8, 96)
0 1 2 3 4 5 6 7 8 9 10
Time (in hours)
What was Dario's hourly wage?
A $10
B $12
$24
D $54
Answer: answer is b 12$.
Step-by-step explanation:
A deli is trying out new labels for their cylindrical-shaped wheels of cheese. The label covers the entire wheel except the circular top and bottom.
If the wheel has a radius of 30 centimeters and a height of 20 centimeters, how many square centimeters of the wheel does the label cover? (Approximate using pi equals 22 over 7)
A: 792,000 over 7 square centimeters
B: 66,000 over 7 square centimeters
C: 26,400 over 7 square centimeters
D: 2,640 over 7 square centimeters
The cylindrical wheels covers about 9428.7 squared centimeter
Area of CylinderThis is the total area covering the entire body of the cylinder.
The formula of surface area of a cylinder is given as;
A = 2πrh + 2πr²
A = Area of cylinderh = height of cylinderr = radius of cylinderA = 2(22/7) × 30 × 20 + 2(22/7)×30²
A = 9428.57 cm²
The area of the wheel is 9428.7cm²
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Answer:
Step-by-step explanation:
Find the midpoint of AC is at -2 and C is at 3 on a number line
The midpoint of AC is 0.5 where A is at -2 and C is at 3 on the number line.
What is number line?A number line is a line on which numbers are pointed at some intervals, it is used to show numerical operations.
Given that,
A and C are two points on number line.
A is at -2 and C is at 3
The midpoint of AC can be given by finding average of both the points,
Midpoint of AC = (-2 + 3) / 2
= 1 /2
= 0.5
The required midpoint of AC where A is at -2 and C is at 3 is 0.5.
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I need help, what does y equal?
In the provided figure, the value of y is 5.5 units.
What is trigonometric ratios?Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilized in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more. The values of all trigonometric functions depending on the ratio of sides of a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.
Here,
cos 30°=b/15
b=15*cos 30°
b=13 units
since this is square so all sides are equal.
sin 30°=p/15
p=15*sin 30°
p=7.5 units
required difference=13-7.5
=5.5 units
The value of y in the given figure is 5.5 units.
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