The probability that emission of both CO and hydrocarbon is in excess is 0.8.
What is probability?The proportion of favorable cases to all possible cases used to determine how likely an event is to occur.
Let, A be the event in which cars are emitting excess CO:
P(A) = 0.12
Let, B be the event in which cars are emitting excess hydrocarbons:
P(B) = 0.15
The cars which emit both CO and Hydrocarbons in:
P(A∩B) = 0.8
The probability that emission of both CO and hydrocarbon is in excess is 0.8.
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A track-and-field coach recorded the length of each student's standing long jump. The data is summarized in the box plot.
Standing Long Jumps
0
+
2
4
+
Feet
6
8
10
Choose all of the statements that can be concluded from this data.
A. The median jump length is 5 feet, which is the average length of a standing long jump for the students represented in the box plot.
B. The median jump length is 5 feet, which is the length of the middle student's long jump if the students were ordered by the length of
their long jump.
C. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 4 feet of the
median.
D. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 2 feet of the
median.
A
Answer:
A because of the average length showed
Jamie is ordering cupcakes for an office party. The top three flavors are chocolate/chocolate (x), strawberry/vanilla (y), and peanut butter/chocolate (z). 18 total cupcakes are purchased for $55.75. The chocolate/chocolate are $3 each, the strawberry/vanilla are $2.75 each, and the peanut butter/chocolate are $3.50 each. There are twice as many chocolate/chocolate cupcakes purchased as peanut butter/chocolate cupcakes. How many of each type of cupcake did Jamie purchase
Jamie purchases 4 chocolate (3.57), 7 strawberry/vanilla, and 7 peanut butter cupcakes for an office party.
How to write the given information as an expression or an equation?The steps involved are:
Observe the given data and notice the variable termsUse operators like multiplication or fraction if it consists of terms like twice or thrice or one fourth etc.Use the operators like addition or subtraction (more or less/greater or smaller) in between those variablesSolve those equations for the required values.Calculation:Given that,
Jamie is ordering cupcakes for an office party.
There are three flavors - Chocolate, Strawberry/vanilla, and peanut flavors.
Jamie purchased a total of 18 cupcakes for $55.75
The cost for a single cupcake of each flavor is as follows:
Chocolate - $3
Strawberry - $2.75
Peanut - $3.50
Consider the number of cupcakes of each flavor as x, y, and z respectively.
So, the equations we can write from this data are,
x + y + z = 18 and
3x + 2.75y + 3. 50z = 55.75
But it is given that,
There are twice as many chocolate cupcakes purchased as peanut butter cupcakes.
So, z = 2x
Then the above two equations become,
3x + y = 18 and
10x + 2.75y = 55.75
By solving these two equations we get,
x = 3.57 ≅ 4
y = 7.28 ≅ 7
Since we know that z = 2x,
⇒ z = 2 × 3.57 = 7.14 ≅ 7
So,
There are 4 chocolate, 7 strawberry, and 7 peanut cupcakes.
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Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y=-2x+5
Step-by-step explanation:
For every increase in x, y decreases by 2
so the slope is -2
You can solve for the y-intercept by going backward, 1-1=0, 3+2=5
the y-intercept is (0,5)
Using the slope intercept equation format, the answer is y-2x+5
PLEASE HELP QUICK!!!!
Bernie borrowed b books from his friend Grant's collection of 29 books. What does the expression 29 - b represent?
If the price of gas started at $2.56 per gallon and increased at a rate of 4% per year, after how many years will the price of gasoline per gallon reach or exceed $5?
The price of gas is modeled by f(x) = 2.56(1.04)x.
Use logarithms to find the answer to the question.
Answer: 18 years
Work Shown:
[tex]f(\text{x}) = 2.56(1.04)^\text{x}\\\\5 = 2.56(1.04)^\text{x}\\\\5/2.56 = (1.04)^\text{x}\\\\1.953125 = (1.04)^\text{x}\\\\\log(1.953125) = \log(1.04^\text{x})\\\\\log(1.953125) = \text{x}*\log(1.04)\\\\\text{x} = \frac{\log(1.953125)}{\log(1.04)}\\\\\text{x} \approx 17.0682937693249\\\\[/tex]
The steps above show f(x) replaced with 5. Then you'd use logarithms to isolate the variable x. The relevant useful log rule is [tex]\log(A^B) = B\log(A)[/tex] so we can pull down the exponent.
From here it seems your teacher wants you to round up to the nearest integer.
If we plugged in x = 17, then f(x) = 4.99 which is one cent too small.
While x = 18 leads to f(x) = 5.19
Therefore, x = 18 has the price reach or exceed $5
What is the slope of the line through (-3, 3) and (-1, -1)?
(-3, 3)
-3 -2 -1
(-1,-1)
4
3
2
You
1
-1
2.
y
1 2
3
4
X
Answer:
The slope is -2
Step-by-step explanation:
To find the slope, we can use the slope formula
m = ( y2-y1)/(x2-x1)
= (-1 -3)/(-1 - -3)
= ( -1-3)/(-1+3)
= -4/2
= -2
The slope is -2
A car-making factory has 480 wheels. how many cars can be completed with the wheels?
Answer:
See below
Step-by-step explanation:
If the car has 4 wheels 480/4 = 120 cars
If the car has 3 wheels 480/3 = 160 cars
If the car has 6 wheels ( like a dual truck) 480 / 6 = 80
pls help tysm!!!!!!!!!
Answer:
Second choice
Step-by-step explanation:
Analyse each sentences: The sum of x and y is 5 can be mathematically expressed as [tex]\displaystyle{x+y = 5}[/tex] since both are sum together and equal to 5.
Next, the value of y is one more than value of x can be mathematically expressed as [tex]\displaystyle{y=x+1}[/tex] because value of y is one more than value of x so y will be the value of x add with 1.
Therefore, form the simultaneous equation:
[tex]\displaystyle{\left \{ {{x+y=5} \atop {y=x+1}} \right}[/tex]
Hence, the answer is second choice.
For the function F defined by F(x)=x2−2x+4, find F(|−4|)
By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.
How to evaluate a quadratic equation with an absolute value
Herein we must apply the definition of absolute value prior to evaluating the quadratic equation defined in the statement. From algebra we know that absolute values are defined as:
|x| = x, when x ≥ 0 or - x, when x < 0. (1)
Then, we apply (1) on the quadratic equation:
F(|x|) = |x|² - 2 · |x| + 4
As x < 0, by absolute value properties:
F(|x|) = x² + 2 · x + 4
F(|- 4|) = (- 4)² + 2 · (- 4) + 4
F(|- 4|) = 16 - 8 + 4
F(|- 4|) = 12
By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.
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A desk is on sale for $595, which is 32% less than the regular price. What is the regular price?
Answer:
875
Step-by-step explanation:
1-0.32=0.68 so its 0.68 of its original price.
x*0.68=595 x is the original price
x=595/0.68
x=875
To study the population of consumer perceptions of new technology, sampling of the population is preferred over surveying the entire population because ______.
Because It is quicker and fast.
Sampling:
Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed, but it may include simple random sampling or systematic sampling.
Sampling is the selection of a subset of the population of interest in a research study. In the vast majority of research endeavors, the participation of an entire population of interest is not possible, so a smaller group is relied upon for data collection.
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Which of the following is a geometric sequence?
A. 7, 4, 1, -2, …
B. 2, 4, 6, 8, …
C. 1, 1/2, 1/4, 1/8, …
D. 1, 1, 2, 3, 5, …
Answer: C
Step-by-step explanation:
Each term is half the previous term.
Michael rode on the train 168.45 miles the first week of work and 149.85
miles the second week. ABOUT how many miles did he ride on the train
during the two weeks?
a.) a little less than 320
b.) a little more than 320
c.) a little less than 330
d.) a little more than 330
Answer:
A little less than 320
Step-by-step explanation:
Round the miles to 168 and 150
Add together 168 + 150 = 318
Answer: a. a little less than 320
Let [tex]sin\beta =\frac{2\sqrt[]{2} }{5} \\[/tex] and [tex]\frac{\pi }{2} \leq\beta \leq \pi \\[/tex].
Determine the exact value of [tex]sin(\frac{\beta }{2} )[/tex]
Since beta is in the first quadrant, the final answer will be positive.
To find cos(beta) so we can use the half angle identity, we can substitute into the Pythagorean identity. Doing so gives us that
[tex] \sin( \beta ) = \frac{ \sqrt{17} }{5} [/tex]
So, this means that
[tex] \sin( \frac{ \beta }{2} ) = \sqrt{ \frac{1 - \frac{ \sqrt{17} }{2} }{2} } = \sqrt{ \frac{2 - \sqrt{17} }{4} } = \frac{ \sqrt{2 - \sqrt{17} } }{2} [/tex]
One of the criticisms of the Social Readjustment Rating Scale is that it does NOT take into account:
What is one major limitation of the Social Readjustment Rating Scale?
The Social Readjustment Rating Scale has severe limitations, despite being a helpful tool for the research of life transition and disease. The current measure cannot be used to assess the impact of various life changes (such as positive or negative ones) on the development of sickness.Learn more about Social Readjustment Rating Scale brainly.com/question/13044228
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Janice bought 30 items each priced at 30 cents, 2 dollars, or 3 dollars. If her total purchase price was $\$$30.00, how many 30-cent items did she purchase
she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
According to the statement
Janice bought total items = 30
Price of items are 30 cents, 2 dollars, or 3 dollars.
Total purchase price of Janice = 30$
If we let she bought 10 items at price of 3$, Then it is not possible
So, Number of items which are bought by her at price of $3 is less than 10. Similarly Number of items which are bought by her at price of $2 is less than 10.
we know that 1 CENT = 0.01 $
We also know that 10 30-cents will worth 3 dollars, so the number of cents which are bought by her at price of $0.01 is greater than 10.
Now, Let she bought 20 items at price of 0.01$
Then 20*0.3 = 6$
It means 30$-6$ = 24$
24$ are left to purchase the things which are at price of 2$ and 3$.
If we let she purchase 4 items at cost $3 then
Then 4*$3 = 12$
It means 24$-12$ = 12$
Now, with remaining money she bought 6 items at cost $2.
So, she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
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she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
According to the statement
Janice bought total items = 30
Price of items are 30 cents, 2 dollars, or 3 dollars.
Total purchase price of Janice = 30$
If we let she bought 10 items at price of 3$, Then it is not possible
So, Number of items which are bought by her at price of $3 is less than 10. Similarly Number of items which are bought by her at price of $2 is less than 10.
we know that 1 CENT = 0.01 $
We also know that 10 30-cents will worth 3 dollars, so the number of cents which are bought by her at price of $0.01 is greater than 10.
Now, Let she bought 20 items at price of 0.01$
Then 20*0.3 = 6$
It means 30$-6$ = 24$
24$ are left to purchase the things which are at price of 2$ and 3$.
If we let she purchase 4 items at cost $3 then
Then 4*$3 = 12$
It means 24$-12$ = 12$
Now, with remaining money she bought 6 items at cost $2.
So, she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
Create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem.
For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.
How can the distance formula prove SSS Triangle Congruence Theorem?Given that the distance formula =
[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]
Let say that Angle ABC has the vertices of A (-4, -2), B (-5,1). C (0,2) and Angle DEF has the vertices of D (7, -4), E (4,-5), F (3,0)
So lets prove it:
AC = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]
=[tex]\sqrt{(-4-0)^2 + (-2-2)^2}[/tex]
=[tex]\sqrt{32}[/tex]
= 4[tex]\sqrt{2}[/tex]
Do the same for DF:
DF = [tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} - y_{1}^{2} )}[/tex]
= [tex]\sqrt{(7-3)^2 + (-4-0)^2}[/tex]
=[tex]\sqrt{32}[/tex]
= 4[tex]\sqrt{2}[/tex]
Looking at the above, one can see the values are the same and as such this proves that AC is the same to DF. If you do the same for the other part of the angles, you will see that they are congruent.
Therefore, For a person to be able to create a coordinate proof to show that the two triangles are congruent by the SSS Triangle Congruence Theorem one can simply use the distance formula.
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give the volume and surface area of the sphere shown
Answer:
V≈3053.63
A≈1017.88
Step-by-step explanation:
V=[tex]\frac{4}{3}[/tex]π [tex]r^{3}[/tex]=[tex]\frac{4}{3}[/tex]·π·[tex]9^{3}[/tex] ≈3053.62806
A=4π[tex]r^{2}[/tex]=4·π·[tex]9^{2}[/tex] ≈1017.87602
How many miles is it across the united states from the east coast to the west coast.
The thousand of miles across the United states from the east coast to the west coast.
In order to find the number of miles across the United states from the east coast to the west coast.
Hence, the thousand of miles across the United states from the east coast to the west coast.
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1 point
Calculate the rate of change for each function over the interval [0, 3], then tell which function is
growing faster.
f(x) = 2x + 3
g(x) = 2² +3
Of(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
f(x) has a rate of change of 6
g(x) has a rate of change of 7
So g(x) is growing faster
f(x) has a rate of change of 6
g(x) has a rate of change of 7
So f(x) is growing faster
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So f(x) is growing faster
If f(x) = 2x + 3 then Δy/Δx = 2 and g(x) = 2² +3 then Δy/Δx = 2.33.
The correct answer is option A.
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
How to estimate the rate of change of a function over the interval [0, 3]?Let f(x) = 2x + 3 and g(x) = 2² +3
Let, ∆y /∆x denotes the ratio of y change and x change when x change exists relatively large.
If f(x) = 2x + 3
Δy/Δx = [f(3) - f(0)]/3 - 0
f(3) [tex]= 2*3+3 = 9[/tex]
f(0) [tex]= 2*0+3 = 3[/tex]
[f(3) - f(0)]/3 - 0 = (9 - 3)/3
= 6/3 = 2
g(x) = 2² +3
Δy/Δx = [g(3) - g(0)]/3 - 0
[tex]$= (2^3 +3)-(2^0 +3)/3[/tex]
[tex](2^3 +3)-(2^0 +3) = 7[/tex]
[tex](2^3 +3)-(2^0 +3)/3[/tex] = 7/3 = 2.33
Therefore, the correct answer is option A.
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
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Carla left the bookstore traveling 12 mph. Then, 3 hours later, Zari left traveling the same direction at 18 mph. How long does Zari have to travel before catching up with Carla
Answer:
6 hours.
Step-by-step explanation:
Speed = distance / time.
Carla travels 3 * 12 = 36 miles before Zari leaves the shop.
So Zari travels x miles in the same time as Carla travels x- 36 miles.
So 18 = x/t and 12 = (x - 36)/t
From first equation x = 18t so we have the equation
12 = (18t - 36/t
18t - 36 = 12t
6t = 36
t = 6 hours.
Ryan is cleaning out his room. his sister gives him 4 boxes of books to put with the 3 books he already had. when he finishes cleaning he discovers he now has 35 books on his shelves. how many books were in each box?
Answer:
8 books per box.
Step-by-step explanation:
One must assume that the books are evenly distributed among the boxes. Ryan has 3 books already and adds 4 boxes to reach a total of 35 books:
3 books + 4 boxes = 35 books
4 boxes = 35 books-3 books
4 boxes = 32 books
1 box = 8 books
There are 8 books per box.
A new toy comes in the shape of a regular hexagonal pyramid. The base has side lengths of 10 inches and the apothem is 5√3 inches. If the surface area is 420 + 150√3 square inches, what is the slant height?
A. 11 inches
B. 14 inches
C. 7 inches
D. 28 inches
The slant height of the hexagonal pyramid is: B. 14 inches.
What is the Area of a Regular Hexagon?Area of a regular hexagon = 3√3/2(s²)
First, find the area of the regular hexagon:
Area = 3√3/2(s²) = 3√3/2(10²) = 150√3 in.².
Surface area is given as 420 + 150√3 in.².
Area of the 6 triangles = surface area - area of hexagonal base = 420 + 150√3 - 150√3
Area of the 6 triangles = 420 in.²
Area of 1 triangle = 420/6 = 70 in.²
Use the area of a triangle to find the slant height (h):
70 = 1/2(10)(h)
2(70) = 10(h)
140/20 = h
h = 14 in.
The answer is B. 14 inches.
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Select all that apply.
Which functions have a range of {y ∈ all real numbers | -∞ < y < ∞}?
f(x) = -(x + 1)^2 - 4
f(x) = -4x + 11
f(x) = 2/3x - 8
f(x) = 2^x+3
f(x) = x^2 + 7x - 9
The functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the range of {y ∈ R | -∞ < y < ∞}.
What are the domain and range of a function?The domain is the set of all the possible values of x that are taken as inputs for the function.The range is the set of all the values(output) that are obtained for the domain of x.So, domain = {input values(x)} and range = {output values(y)}Calculation:Step 1: Finding the range for the function f(x) = -(x + 1)² - 4
The given function is quadratic in the form of a(x - h)² + k,
So, the range of the function is y ≤ k if a < 0 or y ≥ k if a > 0
For the given function, a = -1 so, a < 0. thus, the range of the given function is y ≤ k, where k = -4
∴ Range of f(x) = -(x + 1)² - 4 is: (-∞ -4], {y | y ≤ -4}
Step 2: Finding the range for the function f(x) = -4x + 11
This is a linear function. So, the range is R.
∴ Range of f(x) = -4x + 11: (-∞, ∞), { y | y ∈ R}
Step 3: Finding the range for the function f(x) = 2/3x - 8
This is also a linear function. So, the range is R.
∴ Range of f(x) = 2/3x - 8: (-∞, ∞), { y | y ∈ R}
Step 4: Finding the range for the function f(x) = 2^x + 3
This is an exponential function. So, the range is y > k
Here k = 3.
∴ Range of f(x) = 2^x+3: (3, ∞), {y | y > 3}
Step 5: Finding the range for the function f(x) = x² + 7x - 9
This is a quadratic function.
we can write it as,
f(x) = x² + 2 × x × (7/2) + (7/2)² - (7/2)² - 9
= (x + 7/2)² - 85/4
This is in the form of a(x - h)² - k. where a = 1 > 0 and k = -85/4
Since a > 0, the range of the function is y ≥ -85/4
∴ Range of f(x) = x² + 7x - 9: [-85/4, ∞), {y | y ≥ -85/4}
Therefore, the functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the given range {y ∈ R, -∞ < y < ∞}
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Use the given information to find the unknown value. Y varies inversely with the cube of x. When x=5, then y=1. Find y when x=1
Answer:
125
Step-by-step explanation:
y = 1k/x^3 I am trying to find the constant k. I will use the information that I have been given to find k
1 = k/5^3
1 = k/125 Multiply both sides by 125
125 = k
Now, we will find y when x = 1
y = 125/1^3
y = 125
The value of y is 125 when x is 1.
Write the function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.
y = 1k/x^3 I am trying to find the constant k. I will use the information that I have been given to find k
1 = k/5^3
1 = k/125
Multiply both sides by 125
125 = k
Now, we will find y when x = 1
y = 125/1^3
y = 125
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Jean estimates that her friend complete a new level of a game on the first try 20% of the time. she conducts a simulation to predict how manytimes out of 80 her friend would complete a new level on the first try. jin uses a random number generator. every digit that is eight or nine representatives complete in the level. what is the problem ability that her friend completes a new level on the first try written as a percent
The friend's probability of beating the next level on her first attempt are 22.5 percent.
Describe probability.
To forecast how likely occurrences are to occur, probability has been introduced in mathematics. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment.
This idea is used to discuss the probability or likelihood of an event happening.
The frequency of the number 8 is seven.
The frequency of the number 9 is 11.
The full list of frequencies is provided as
10 + 9 + 6+ 7 + 8 + 12 + 4 + 6 + 7 + 11 = 80
7 + 11 = 18
18/80 is the probability.
= 0.225 x 100
22.5 percent
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AABC is an isosceles triangle. AB is the longest side with
length 9x+3, BC = 4x+6 and CA = 3x+9. Find AB.
Answer:
30
Step-by-step explanation:
Since ABC is isosceles, BC = CA.
4x + 6 = 3x + 9x = 3So, AB = 9(3)+3 = 30.
If a is an obtuse angle in a triangle and sin a = , calculate the exact value of sin 2a.
Answer:
Step-by-step explanation:
cos A = √( 1 - (5/13)²) = √( 1 - 25/169) = √(144/169) = - 12 /13
in 2 A = 2 sin A cos A
sin 2 A = 2 *5/13 ( - 12/13 ) = - 120 / 169
the answer is -120/169
Adding and Subtracting Functions
F(x)=x^2+4
G(x)=x-1
Find (g+f)(x)
Answer:
Step-by-step explanation:
[tex](g+f)(x)=g(x)+f(x)=x-1+x^2 +4=x^2 +x+3[/tex][tex]x^2 +x+3[/tex]
slope:
y-intercept:
PLSPLSPLS HELP
Answer:
Slope: 1
Y-intercept: -1
Step-by-step explanation:
The line passes the y-axis at -1, the rise/run, which is used to calculate the slope is 2/2, and it equals to 1, so the slope is 1.
I hope it helps! Have a great day!
bren~