Explanation is there for your question
We can desribe 15x-10 as an expression.
We would describe 6x-2<35 as an
We can describe 15x-10 as an expression.
We would describe 6x-2<35 as an inequality.
What is an inequality?In mathematics, inequalities characterize the connection between two non-equal numbers. Inequality means being unequal. If two values are not equal, we use the "not equal symbol". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare two numbers on the number line based on their size. In the illustration above, there's a less than sign. This means that it's an inequality.
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yellowstone national park is a popular field trip destination. this year the senior class at high school a and the senior class at high school b both planned trips there. the senior class at high school a rented and filled 14 vans and 11 buses with 531 students. high school b rented and filled 7 vans and 7 buses with 315 students. every van had the same number of students in it as did the buses. how many students can a van carry? how many students can a bus carry?
The van contains 12 students and the bus contain 33 students.
The given information is:
The senior class at the high school rented and filled 14 vans and 11 buses with 531 students.
For this, we have to convert it into an equation:
14v+11b=531---------(1)
A High school b rented and filled 7 vans and 7 buses with 315 students.
For this, we have to convert it into an equation:
7v+7b=315----------(2)
To, find the number of students in the van and bus we have to solve two equations :
14v+11b=531
7v+7b=315*2
---------------------
14v+11b=531
14v+14b=630
----------------
-3b=-99
b=33
The total number of students on the bus is 33 members.
Now substitute the b value in any equation, and substitute in equation(2) we get the v value:
7v+7(33)=315
7v+231=315
7v=84
v=12
The total number of students in the van is 12 members.
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A rental company charges $85 a day and 30 cents a mile for renting a truck. Michael rents a truck for 2 days, and his bill comes to $290. How many miles did he drive?
Answer:
400 miles
Step-by-step explanation:
Let m be the number of miles.
\(85(2) + .30m = 290\)
\(170 + .30m = 290\)
\(.30m = 120\)
\( m = 400\)
a lambert quadrilateral can be "doubled" to form a saccheri quadrilateral; a saccheri quadrilateral can be "halved" to form a lambert quadrilateral.
T/F
True. A lambert quadrilateral can be "doubled" to form a saccheri quadrilateral; a saccheri quadrilateral can be "halved" to form a lambert quadrilateral. So, the statement is true.
A Lambert quadrilateral is a type of quadrilateral that has three right angles and one acute angle.
To double a Lambert quadrilateral means to construct a new quadrilateral with twice the area but with the same shape.
This can be done by drawing a line through the acute angle of the original quadrilateral and constructing a new square on each side of the line.
The resulting shape is a Saccheri quadrilateral, which has two right angles and two acute angles.
To halve a Saccheri quadrilateral means to construct a new quadrilateral with half the area but with the same shape.
This can be done by drawing a line through one of the acute angles of the original quadrilateral and constructing a new square on one side of the line. The resulting shape is a Lambert quadrilateral.
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which equation represents the graph of a circle
y=x^2
x^2+y^2=9
x=4
y=x
An equation that represents the graph of a circle include the following:
What is the equation of a circle?In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.From the information provided above, we have the following equation of a circle has the only correct answer option:
x² + y² = 9
x² + y² = 3²
Therefore, the center (h, k) is (0, 0) and the radius is equal to 3 units.
Also, we can determine the diameter of this circle;
Diameter = 2r
Diameter = 2(3)
Diameter = 6 units.
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At a conference, there are 90 math teachers and 75 science teachers. write the ratio of math teachers to science teachers in simplest form.
Answer:
6:5 or \(\frac{6}{5}\)
Step-by-step explanation:
\(\frac{90}{75}\) Divide by \(\frac{15}{15}\)
\(\frac{6}{5}\) or 6:5
Jon drove 240 miles to get to the Grand Canyon. If the drive took 4 hours, what is Jon's average rate of speed?
Answer:
60 miles per hour
Step-by-step explanation:
Average speed = miles drove/ hours
=> 240/4
=> 60 miles per hour
Answer:
Jon drove 60 miles per hour.
Step-by-step explanation:
Since john drove 240 miles in 4 hours that means you need to divide 240 by 4, which is 60. An easier example can be 60 x 4.
when the integer is negative , the cube of the integer is ?
When an integer is negative, its cube is also negative because the exponent is odd.
find x and what type of angle is this?
Answer:
a) x = 12
b) right triangle
Step-by-step explanation:
a) 2x + 1 + 5x + 5 + 90 = 180
7x + 96 = 180
180 - 96 = 84
84 / 7 = 12
x = 12
b) you can tell that it is a right triangle because of the square in the corner that indicates it is a right triangle
let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b) find sin (θ+y)
In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement
\(\sin (\theta)=\frac{3}{5}\)Describes the following triangle
To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation
\(x^2+3^2=5^2\)Solving for x, we have
\(\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}\)The missing length of the first triangle is equal to 4.
For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression
\(\tan (y)=\frac{12}{5}\)Describes the following triangle
Using the Pythagorean Theorem again, we have
\(5^2+12^2=h^2\)Solving for h, we have
\(\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}\)The missing side measure is equal to 13.
Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.
The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles
\(\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}\)To calculate the sine and cosine of the sum
\(\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}\)We can use the following identities
\(\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}\)Using those identities in our problem, we're going to have
\(\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}\)
can someone answer page 3 question 3, page 5 question 3, all of page 6
The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7
What is trigonometrical ratios?Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle. There are three common trigonometric ratios: sine, cosine, and tangent
For page 3 question 3,
a) <A + <B = 90 since <C = right angle
b) SinA = BC/AB and CosB = BC/AB
The ratio of the two angles BC/AB ÷ BC/AB = 1
I notice that the ratio of sinA and cosB gives 1
b) The ratio of CosA and SinB will give
BC/AB ÷ BC/AB
= BC/AB * AB/BC = 1
For page 5 number 3
Tan28 = g/i
g/12.2 = tan28
cross multiplying to have
g = 12.2*tan28
g = 12.2 * 0.5317
g = 6.5
b) the angle I is given as 90-28 degrees
<I = 62 degrees
To find the side h we use the Pythagoras theorem
h² = (12.2)² + (6.5)²
h² = 148.84 +42.25
h²= 191.09
h=√191.09
h= 13.8
For page 6
1) Sin42 = x/18
x=18*sin42
x = 18*0.6691
x = 12.0
2) cos28 = 6/x
xcos28 = 6
x = 6/cos28
x [= 6/0.8829
x = 6.8
3) Tan63 = x/34
x = 34*tan63
x= 34*1.9526
x = 66.4
4) Sin50 123/x
xsin50 = 123
x = 123/sin50
x = 123/0.7660
x =160.6
5) Sin57 = P/8
Pole = 8sin57
the pole = 8*0.8387
The pole = 6.7
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A state health department was considering a new policy that would require all school-age children to receive the varicella (Chicken Pox) vaccine. In order to evaluate the need for such a requirement, health department epidemiologists were asked to determine the incidence of varicella in a randomly-selected fifth-grade class. During the previous school year, the class had 20 students, 5 of whom had varicella before entering fifth grade and 2 of whom developed varicella during fifth grade. What was the incidence of varicella during the fifth grade
The incidence rate of varicella is 13 per 100 if there were 20 students and 5 of whom got vaccinated before fifth grade.
Given Total students of 100 in which 5 had varicella before entering fifth grade and 2 of whom developed varicella during fifth grade.
We have to find the incidence rate of varicella means requirement of vaccine in proportion form.
So we want the incidence rate, which is the number of people who caught the disease who were at risk to it. So we have 20 people in the class in total. But we said that five of them already had it and they were told that they are immune. So we have 15 people in the class who are at risk, then two people caught it. and so the incidence rate is going to be two divided by 15, which you can check is Not .13 recurring. And so as a percentage We just times by 100 this is going to be 13/ 100.
Hence the incidence of varicella during the fifth grade is 13/100.
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write 270/450 as a fraction in its simplest form
Answer:
The answer is 3/5
Step-by-step explanation:
Step-by-step explanation:
270 / 450
Dividing both numerator and denominator by 90 we get
= 3 / 5
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Is 4/5 greater or less than 45/100 how do you know
Answer:
4/5 is grater than 45/100
Step-by-step explanation:
Why?
because in percentage you make the bottom # a 100 one of them already has that and when it has 100 on the bottom it tells you that the top # is the percentage so 45/100 is 45%
now to make 4/5 a percentage what times 5 = 100?
20 does
so you times the top and bottom by 20
4*20= 80
now your fraction is 80/100 (top # tells you the %)
it's 80%
80% is grater than 45%
Answer:
4/5 is greater than 45/100.
Step-by-step explanation:
In order to figure it out, you need to make both fractions have common denominators. In order to do that, you figure out this:
5 times what equals 100? It's 20.
With fractions in this situation, whatever you do to the top, you have to do to the bottom. So, you multiply 4 times 20, which is 80.
In the end, you would end up with these two fractions:
80/100 and 45/100.
Obviously, 80/100 is greater than 45/100. In the beginning, 80/100 was originally 4/5. Therefore, 4/5 is greater than 45/100.
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Expand the following using the distributive property.
6(-3w + 1/3)
A) -18w + 2
B) 18w + 2
C) 18w – 2
D) -18w – 2
Answer:
A
Step-by-step explanation:
6(-3w+1/3)
-18w+2
Answer:
A
Step-by-step explanation:
6(-3w +1/3)
to distribute you multiply everything inside the parentheses by 6
so
6(-3w) + 6(1/3)
-18w + 6/3
-18w +2
Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil. Jason decides to test the land for oil. He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil. What is the probability that the land has no oil and the test shows that there is no oil? A. 0. 09 B. 0. 11 C. 0. 44 D. 0. 36.
The probability that the land has no oil and the test shows that there is no oil is C. 0.44.
To find the probability, we consider two independent events: the land having no oil and the test correctly indicating no oil.
The probability that the land has no oil is 1 - 0.45, which equals 0.55.
The probability that the test shows no oil, given that there is no oil, is 0.80 based on the kit's claimed accuracy rate.
To calculate the overall probability, we multiply the individual probabilities:
Probability = (Probability of no oil) * (Probability of test indicating no oil)
Probability = 0.55 * 0.80
Probability = 0.44
Hence, the probability that the land has no oil and the test shows that there is no oil is 0.44.
The correct answer is C. 0.44.
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=
O RIGHT TRIANGLES AND TRIGONOMETRY
Word problem involving the Pythagorean Theorem
3000 as
Madisyn V
A 13-ft ladder leans against the side of a house. The bottom of the ladder is 10 ft from the side of the house. How high is the top of the ladder from the ground?
If necessary, round your answer to the nearest tenth.
Answer:
8.3 ft
Step-by-step explanation:
You want the height of the top of a 13 ft ladder whose base is 10 ft from the side of a house.
Pythagorean theoremThe ladder represents the hypotenuse of a right triangle with legs of 10 ft and the height up the side of the house.
a² +b² = c² . . . . . . . . Pythagorean relation
a² +10² = 13² . . . . . . . known values filled in
a² = 169 -100 = 69 . . . . subtract 10²
a = √69 ≈ 8.3 . . . . . . . . . . . take the square root
The top of the ladder is about 8.3 feet from the ground.
monique has a blog with her website and wants to evaluate the engagement of her readers. her blog posts usually take at least 4 minutes to read, and she wants to track the percentage of users who read an entire blog post. she should set up a(n) goal.
Monique has a blog with her website and wants to evaluate the engagement of her readers. her blog posts usually take at least 4 minutes to read, and she wants to track the percentage of users who read an entire blog post. she should set up time-on-site goal.
The total amount of time a user spends on your website, also referred to as session duration, is the term "time on site." It is calculated by noting the timestamps of when a visitor accesses your landing page via a search engine or link and when they leave your website.
52 seconds is a decent average time on page benchmark across several industries. B2B websites have the highest Average Time On Page, which is roughly 82 seconds, according to data from 20 billion user sessions. The type of target audience, industry, and device type are just a few of the variables that affect a decent average time on page.
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100 points! Which statements are correct interpretations of this graph?
Select each correct answer.
Responses
1.3 boxes are filled per minute.
0.75 boxes are filled per minute.
.
3 boxes are filled every 4 min.
4 boxes are filled every 3 min.
Answer: 3 boxes every 4 minutes, and 0.75 boxed every minute. And 0.75 boxes are filled per minute.
Step-by-step explanation: Hope This Helps!
there is 892 red balloons and there are 742 Blue balloons about how many balloons are there in all ?
Answer: 1634 ballons
Step-by-step explanation:
892+742=1634
5x – 18 > 2(4x – 15).
The solution to the inequality 5x - 18 > 2(4x - 15) is x < 4.
To solve the inequality 5x - 18 > 2(4x - 15), we can simplify the expression and isolate the variable x.
First, distribute the 2 to the terms inside the parentheses:
5x - 18 > 8x - 30
Next, we want to isolate the x terms on one side of the inequality.
Let's move the 8x term to the left side by subtracting 8x from both sides:
5x - 8x - 18 > -30
Simplifying further, we combine like terms:
-3x - 18 > -30
Now, let's isolate the variable x.
We can start by adding 18 to both sides of the inequality:
-3x - 18 + 18 > -30 + 18
Simplifying further:
-3x > -12
To isolate x, we need to divide both sides of the inequality by -3. However, when we divide by a negative number, we need to flip the inequality sign:
(-3x) / (-3) < (-12) / (-3)
Simplifying gives us:
x < 4.
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Which expression is equivalent to 8 (a minus 6)?
8 a minus 48
2a
8 a minus 6
48a
Answer:
8 a minus 48
Step-by-step explanation:
you need to distribute!!
so you distribute the 8 to both the a and 6
8 times a equals 8 a
8 times 6 equals 48
and so that’s how you get 8 a minus 48 c:
Answer:
8 a minus 48
Step-by-step explanation:
Please help with this area question!
Answer:
Step-by-step explanation:
i thinks its 6 (im sorry if im wrong)
Marsha gets a job that pays 15$ per hour and she started the week with 20$
The answer is y=15x+20
Brittany stamps 20 letters in 1
hour. How many hours will it
take her to stamp 380 letters?
According to Thomson Financial, last year the majority of companies reporting profits had beaten estimates. A sample of 162 companies showed that 98 beat estimates, 29 matched estimates, and 35 fell short. (a) What is the point estimate of the proportion that fell short of estimates
If required, round your answer to four decimal places. pshort = (b) Determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates. If required, round your answer to four decimal places. ME = (c) How large a sample is needed if the desired margin of error is 0.05?
To the nearest foot, what is the diameter of a circle whose circumference is 47.1 feet?
Answer:
94.2
Step-by-step explanation:
Suppose a large chain of home improvement stores has a computer located near the front entrance of each of their stores to allow prospective employees to submit employment applications. Suppose that between the hours of 9 a.m. and 12 noon on non-holiday weekdays, people arrive at the computer to submit applications uniformly, and that the mean time each computer sits idle is 10 min. Determine the probability that on a random non-holiday weekday, the computer will sit idle for more than 15 min during the hours of 9 a.m. and 12 noon. Give your answer in decimal form, precise to three decimal places.
Probability=
we need to use the exponential distribution, which is a probability distribution that models the time between events that occur at a constant rate.
In this case, the rate is 1/10 (since the mean time each computer sits idle is 10 min), and we want to find the probability that the computer will sit idle for more than 15 min. The probability that the computer will sit idle for at least 15 min is given by:
P(X >= 15) = e^(-15/10) = 0.2231
where X is the time between arrivals of applicants at the computer. We use the formula for the exponential distribution, which is: f(x) = lambda * e^(-lambda * x), where lambda is the rate (1/10) and x is the time between events (in this case, the time the computer sits idle).
To get the probability that the computer will sit idle for more than 15 min, we need to subtract this probability from 1: P(X > 15) = 1 - P(X >= 15) = 1 - 0.2231 = 0.7769, Therefore, the probability that on a random non-holiday weekday, the computer will sit idle for more than 15 min during the hours of 9 a.m. and 12 noon is 0.7769, or approximately 0.777 (rounded to three decimal places).
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9. D(-3, -8), E(1, -2)
Midpoint
find an example of functions f and g such that f ◦g is a bijection, but g is not onto and f is not one-to-one.
f(2) = f(-2) = 4,
f ◦ g is a bijection, but g is not onto and f is not one-to-one.
Let f(x) = x^2 and g(x) = sign(x) where sign(x) is the signum function, which returns -1 for negative values of x, 0 for x = 0, and 1 for positive values of x. Then f ◦ g(x) = f(g(x)) = f(sign(x)) = sign(x)^2 = 1 for all values of x, since the square of any real number is positive.
Now, g(x) is not onto since there is no x such that g(x) = -1. And f(x) is not one-to-one since f(2) = f(-2) = 4, for example.
Therefore, f ◦ g is a bijection, but g is not onto and f is not one-to-one.
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