Answer:
Step-by-step explanation:
2x + 3y = 6
2x = 6-3y
x = (6-3y)/2
x - 3y = 9
(6-3y)/2 -3y = 9
(6-3y)/2 -6y/2 = 9
(6-9y)/2 = 9
6 - 9y = 9×2
-9y = 18-6
y = 12/-9
y = -4/3
2x + 3y = 6
2x + 3(-4/3) = 6
2x -4 = 6
2x = 6+4
2x = 10
x = 10/2
x = 5
Therefore x = 5 and y = (-4/3)
I used subsitution method
please click thanks and mark brainliest if you like :)
Answer:
x = 5; y = -4/3
Step-by-step explanation:
One equation has 3y. The other equation has -3y. Add the equations to eliminate y and solve for x.
2x + 3y = 6
(+) x - 3y = 9
---------------------
3x = 15
x = 5
2x + 3y = 6
2(5) + 3y = 6
3y + 10 = 6
3y = -4
y = -4/3
Answer: x = 5; y = -4/3
50% of 80
50% of 48
50% of 15
25% of 120
25% of 90
If you rent a car for one day and drive it for 100 miles the cost is 40 dollars if you drive it 220 miles the cost is 46 dollars what is the linear equation for this
Answer:
[tex] y = \dfrac{1}{20}x + 35 [/tex]
Step-by-step explanation:
Let y = cost.
Let x = number of miles.
We have two (x, y) points: (100, 40) and (220, 46).
Now we find the equation of the line that passes through those two points using the two-point form of the equation of a line.
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
[tex] y - 40 = \dfrac{46 - 40}{220 - 100}(x - 100) [/tex]
[tex] y - 40 = \dfrac{6}{120}(x - 100) [/tex]
[tex] y - 40 = \dfrac{1}{20}(x - 100) [/tex]
[tex] y - 40 = \dfrac{1}{20}x - 5 [/tex]
[tex] y = \dfrac{1}{20}x + 35 [/tex]
The histogram shows that nine students had grades of 80 or higher.
The histogram shows there were 22 students in the class.
The histogram shows there were 25 students in the class.
The histogram is symmetrical.
The histogram has a peak.
The histogram shows the data is evenly distributed.
The histogram shows a gap in the data
Answer:
bde
Step-by-step explanation:
Answer:
B: The histogram shows there were 22 students in the class.
D: The histogram is symmetrical.
E:The histogram has a peak.
F: The histogram shows the data is evenly distributed.
Step-by-step explanation:
edg 2020
Which of the following statements about sets of numbers is true? (1 point)
All integers are whole numbers.
O All irrational numbers are integers.
O All rational numbers are natural numbers.
O All integers are rational numbers.
Answer:
-All integers are whole numbers.
-All rational numbers are natural numbers.
Step-by-step explanation:
The statement which is correct about the sets of numbers is:
All integers are rational numbers.
Option D is the correct answer.
What is a rational number?A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.
We have,
Natural number:
Natural numbers are positive integers or non-negative integers which start from 1 and end at infinity.
Integer:
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Whole number:
Whole numbers include all natural numbers and 0.
It does not include fractions, decimals, and negative integers.
Irrational numbers:
An irrational number is a type of real number which cannot be represented as a simple fraction.
It cannot be expressed in the form of a ratio.
Rational number:
A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.
From the above definition, we can say that,
- Some integers are whole numbers but not all integers are whole numbers.
- No irrational numbers are integers.
-Some rational numbers are natural numbers but not all rational numbers are natural numbers.
- Yes, all integers are rational numbers.
Thus the statement which is correct about the sets of numbers is:
All integers are rational numbers.
Option D is the correct answer.
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WILL GIVE BRAINLEST PLEASE!!!!!!!! Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table: Color of Tile Purple Pink Orange Number of times the tile is drawn 6 18 26 What is the experimental probability that Jenny will pull out a purple tile? fraction 6 over 50 fraction 44 over 50 fraction 6 over 44 fraction 18 over 44
Answer:
6/50
Step-by-step explanation:
There are 50 tiles
6 purple
18 pink
26 orange
P( purple) = purple/ total
= 6/50
3. Find F(3).
F(x)=-x^3+4x^2-2x
Answer:
To Find F(3) you just have to replace x=3 so:
F(3)= -3^3 + 4×3^2 -2×3 = -27 +4×9 - 6 = -33 + 36 = 3
Determine whether the samples are independent or dependent. A data set included the daily number of words spoken by 210 randomly selected women and 210 randomly selected men.a. The samples are independent because there is a natural pairing between the two samples. b. The samples are dependent because there is a natural pairing between the two samples. c. The samples are dependent because there is not a natural pairing between the two samples. d. The samples are independent because there is not a natural pairing between the two samples.
Answer:
The correct answer is:
The samples are independent because there is not a natural pairing between the two samples. (d.)
Step-by-step explanation:
Paired samples or dependent samples are samples in which natural matching or coupling occur, thus creating a data set where data from one sample is uniquely paired to another sample because they are from related groups. Examples are: pre-test/post-test data gotten before and after an intervention, samples from siblings, twins, couples etc.
On the other hand, independent or unpaired samples are those data sets that are gotten from unrelated groups, these type of samples are gotten by matching randomly sampling two unrelated groups without first matching the subjects. In our example, the sample from randomly selected women and men are not paired and unrelated, hence they are independent samples.
The samples are independent because there is not a natural pairing between the two samples. Hence, option (D) is correct.
Let us understand both the events in a systematic manner to answer this question.
Independent Events:
The simple way to understand the events, If the events are not related to each other, then the events are independent of each other. If one event is dependent on another then it is not an independent event.
Example:
Event 1: Toss a coin.
Event 2: Roll a die.
Both the events are independent of each other.
Dependent Events:
The simple way to understand the events, If the events are related to each other, then the events are independent of each other. If one event is dependent on another then it is not an independent event.
Example:
Event 1: Toss a coin.
Event 2: If head appears then roll a die.
Both the events are dependent on each other.
Thus, the samples are independent because there is not a natural pairing between the two samples.
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Consider the following theorem. Theorem If f is integrable on [a, b], then b a f(x) dx = lim n→[infinity] n i = 1 f(xi)Δx where Δx = b − a n and xi = a + iΔx. Use the given theorem to evaluate the definite integral. 9 (x2 − 4x + 6) dx 1
Split up the interval [1, 9] into n subintervals of equal length (9 - 1)/n = 8/n :
[1, 1 + 8/n], [1 + 8/n, 1 + 16/n], [1 + 16/n, 1 + 24/n], …, [1 + 8 (n - 1)/n, 9]
It should be clear that the left endpoint of each subinterval make up an arithmetic sequence, so that the i-th subinterval has left endpoint
1 + 8/n (i - 1)
Then we approximate the definite integral by the sum of the areas of n rectangles with length 8/n and height [tex]f(x_i)[/tex] :
[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx \approx \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right)[/tex]
Take the limit as n approaches infinity and the approximation becomes exact. So we have
[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx = \lim_{n\to\infty} \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right) \\\\ = \lim_{n\to\infty} \frac8n \sum_{i=1}^n \left(1+\frac{16}n(i-1)+\frac{64}{n^2}(i-1)^2-4-\frac{32}n(i-1)+6\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=1}^n \left(64(i-1)^2-16n(i-1)+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=0}^{n-1} \left(64i^2-16ni+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(64\sum_{i=0}^{n-1}i^2 - 16n\sum_{i=0}^{n-1}i + 3n^2\sum{i=0}^{n-1}1\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{64(2n-1)n(n-1)}{6} - \frac{16n^2(n-1)}{2} + 3n^3\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{49n^3}3-24n^2+\frac{32n}3\right) \\\\= \lim_{n\to\infty} \frac{8\left(49n^2-72n+32\right)}{3n^2} = \boxed{\frac{392}3}[/tex]
What is the volume of a rectangular prism with a length, width,
2
1
5
and height of
cm, -
cm, and
cm, respectively?
3
4
6
Step-by-step explanation:
Hey, there!!
It's so simple,
Given,
length (l)= 2/3cm
Breadth (b) = 1/4cm
and height (h)=5/6cm
now, we use the formula for volume of rectangular prism is,
v = l× b× h
or, v= (2/3 × 1/4 × 5/6)^3
By simplifying it we get,
The volume is 5/36cm^3.
Hope it helps...
Plzzz help me on this question
This is Additional mathematics IGCSE
Answer:
[tex] \alpha = 7[/tex]
Step-by-step explanation:
[tex]a(vector) = 4i - 2j[/tex]
[tex]b(vector) = \alpha i + 2j[/tex]
[tex]ab(vector) = ( \alpha - 4)i \: + 4j[/tex]
Now,
Let K * ab (unit vector) = ab (vector)
(0.4 * k) j = 4 j Thus, K = 10[tex](0.3 \times k)i = ( \alpha - 4)i[/tex]Solving further :
[tex] \alpha = 7[/tex]
An ice cream store makes 144 quarts of ice cream in 8 hours. How many quarts could be made in 12 hours?
Hey there! I'm happy to help!
We know that the ice cream store makes 144 quarts in eight hours. What about in one hour? Let's divide this by eight to find out.
144/8=18
So, they make 18 quarts every hour. We want to figure out how many can be made in 12 hours. So, we just multiply 18 by 12!
18(12)=216
Therefore, 216 quarts of ice cream could be made in 12 hours.
Have a wonderful day! :D
The ice cream store will make 216 quarts of ice cream in 12 hours.
What is division?Division is breaking a number up into an equal number of parts.
Given that, An ice cream store makes 144 quarts of ice cream in 8 hours.
Since, they make 144 quarts of ice cream in 8 hours
Therefore, in 1 hour they will make = 144/8 = 18 quarts
So, in 12 hours = 18x12 = 216 quarts.
Hence, The ice cream store will make 216 quarts of ice cream in 12 hours.
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The population of Jacksonville is 836,507. What is the population rounded to the
nearest hundred thousand?
A. 900,000
O
B. 850,000
C. 840,000
o D. 800,000
Answer:
D. 800,000
Step-by-step explanation:
It is D because you find the hundred thousand place which is the 8, the you go to the number next door which is 3, if the 3 is 5 or greater the 8 will become a 9 or if it is not then it will stay the same. And everything to the left stays the same, everything to the right turns into zeros.
144 is the same as 379 less than c
How can this be wrote in a equation
Answer:
144 = c - 379
Step-by-step explanation:
"144 is the same as 379 less than c"
144 = c - 379
Answer and Step-by-step explanation:
This can be written in an equation like this:
144 = c - 379
The question is saying that 144 is the same answer as the result of 379 less than c (or c minus 379). This is why we equal 144 to the result of c minus 379.
#teamtrees #PAW (Plant And Water)
If you’re good at statistics please help
Answer:
Step-by-step explanation:
probabilty distribution= interval of x/total area of the distribution
OR P(x)= frequency of x/total frequency(N)*the interval of x(w)
x f probabilty f/N*w
16 10 0.2
17 16 0.32
18 20 0.4
19 4 0.08
w is the width of the bar( interval) 17-16=1
N=10+16+20+4=50
( only need to draw histogram)
Solve the equation 3(2x + 2) = 3x − 15.
Hi there! :)
Answer:
x = -7.
Step-by-step explanation:
Starting with:
3(2x + 2) = 3x - 15
Begin by distributing '3' with the terms inside of the parenthesis:
3(2x) + 3(2) = 3x - 15
Simplify:
6x + 6 = 3x - 15
Isolate the variable by subtracting '3x' from both sides:
6x - 3x + 6 = 3x - 3x - 15
3x + 6 = -15
Subtract 6 from both sides:
3x + 6 - 6 = -15 - 6
3x = -21
Divide both sides by 3:
3x/3 = -21/3
x = -7.
Answer:
x = -7
Step-by-step explanation:
3(2x+2) = 3x - 15
First, we should simplify on the left side.
6x + 6 = 3x - 15 ; Now we subtract six from both sides.
-6 -6
6x = 3x - 21 ; next we just subtract 3x from both sides.
-3x -3x
3x = -21
Finally, we divide 3 from both sides to separate the three from the x.
x = -7
Hope this helps!! <3 :)
(Algebra) HELP ME ASAP PLZ
Answer:
no solution because the answer will be p=2
10 - [ 8p + 3 ] = 9 [ 2p - 5 ]
10 - 8p - 3 = [ 2p - 5 ]
-8p + 10 - 3 = [ 2p - 5 ]
p = 2 We need to get rid of expression parentheses.
If there is a negative sign in front of it, each term within the expression changes sign.
Otherwise, the expression remains unchanged.
In our example, the following 2 terms will change sign:
8p, 3
Step-by-step explanation:
What is the value of x for the given equation?
4 – 2(x + 7) = 3(x + 5)
X=
Answer:
-5
Step-by-step explanation:
Eight gardeners equally share 1/2 of a pile of pine needles. What fraction of the pile does each gardener receive?
Answer:
Each gardner will get 1/16 of a pile of pine needles.
Step-by-step explanation:
1/2 ÷ 8
*Switch the division to multiplication and flip the 8 (or 8/1) upside-down.
= 1/2 · 1/8
= 1/16
The function f is defined by f(x) = 2x^2+5.
Find f(3a)
Find the side of a square whose diagonal is of the given measure.
Given = 15.2 cm
Answer:
15cm
Step-by-step explanation:
First, a square's diagonal is basically the hypotenuse of a 45-45-90 triangle. a 45-45-90 triangle has a really special relationship, where the side length is x, and the diagonal is x [tex]\sqrt{2}[/tex]. So, the side length is 15.
Answer:
15cm
Step-by-step explanation:
Each corner of the square would be a 90° angle so half of that would be 45°.
[tex] \sin(45) \times 15 \sqrt{2} = 15cm[/tex]
Need help please thank you
Answer:
first term (a1) = 3/2
common difference (d) = 7/4-3/2 = 1/4
Two friends compete with each other and five other, equally good, violinists for first and second chair in an orchestra, in a blind competition What is the probability that the two friends end up as first and second chair together?
Answer: 0.0476
Step-by-step explanation:
Given : Two friends and 5 other people compete with each other for first and second chair in an orchestra.
Total people in this competition= 2+5=7
By permutation , Number of ways to arrange 7 people= 7!
Also, number of ways for two friends end up as first and second chair together= 2 × 5! [ 2 ways to arrange friends on first and second chair and 5! ways to arrange others]
I.e. Required probability = [tex]\dfrac{2\times5!}{7!}[/tex]
[tex]=\dfrac{2!\times5!}{7\times6\times5!}\\\\=\dfrac{1}{7\times3}\\\\=\dfrac{1}{21}\\\\=0.0476[/tex]
Hence, the probability that the two friends end up as first and second chair together = 0.0476
Find two numbers nearest to 8888888 which are exactly divisible by 2915 explain step by step
Four randomly chosen Nevada students were asked how many times they drove to Arizona last year. Their replies were 4,5,6,7. The geometric mean is
Group of answer choices
5.31
5.38
4.98
3.95
The geometric mean of the numbers is 5.38
Given the values a, b, c and d
The geometric mean of the values will be expressed as:
[tex]GM = (abcd)^{1/4}[/tex]
Given the values 4, 5, 6, and 7, the geometric mean will be expressed as:
[tex]GM = (4\times5\times6\times7)^{1/4}\\[/tex]
[tex]GM = (840)^{1/4}\\GM=\sqrt[4]{840} \\GM = 5.38[/tex]
Hence the geometric mean of the numbers is 5.38.
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Solve
0.9(7x + 14) = 1.5 - (x + 2)
[tex]\\ \sf\longmapsto 0.9(7x+14)=1.5-(x+2)[/tex]
[tex]\\ \sf\longmapsto 6.3x+12.6=1.5-x-2[/tex]
[tex]\\ \sf\longmapsto 63x+12.6=-x-0.5[/tex]
[tex]\\ \sf\longmapsto 63x+x=-0.5-12.6[/tex]
[tex]\\ \sf\longmapsto 64x=-13.1[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-13.1}{64}[/tex]
[tex]\\ \sf\longmapsto x=0.2[/tex]
The average age of a college is 21.8 years. The average age of students of college is 24.2 years and average age of lecturers of college is 20.6 years. Find the ratio of the number of students to that of lecturers?
Answer:
22,2
Step-by-step explanation:
average also known as mean
so you find it by adding all the numbers together and dividing them by how many there are
so 21,8 + 24,2 + 20.6 = 66,6 divided by 3 equals 22,2
PLS HELP ASAP:Find all the missing elements:
Answer:
b ≈ 9.5, c ≈ 14.7
Step-by-step explanation:
Using the Sine rule in Δ ABC, that is
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values
[tex]\frac{7}{sin23}[/tex] = [tex]\frac{b}{sin32}[/tex] ( cross- multiply )
b × sin23° = 7 × sin32° ( divide both sides by sin23° )
b = [tex]\frac{7sin32}{sin23}[/tex] ≈ 9.5 ( to the nearest tenth )
Also
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]
[tex]\frac{7}{sin23}[/tex] = [tex]\frac{c}{sin125}[/tex] ( cross- multiply )
c × sin23° = 7 × sin125° ( divide both sides by sin23° )
c = [tex]\frac{7sin125}{sin23}[/tex] ≈ 14.7 ( to the nearest tenth )
find terminal points on the unit circle determines by 5pi/3
9514 1404 393
Answer:
(x, y) = (1/2, -√3/2)
Step-by-step explanation:
The coordinates on a unit circle of the intersection of the terminal ray of angle α are ...
(x, y) = (cos(α), sin(α))
For α = 5π/3, the point on the unit circle is ...
(x, y) = (cos(5π/3), sin(5π/3)) = (1/2, (-√3)/2)
Consider the following case and determine whether there is sufficient information to solve the triangle using the low of sines. Two angles and the side included between them are known.
A. There is insufficient information because to use the law of sines, one side and the angle opposite it must be known.
B. There is sufficient information because if two angles and a side included between them are known, the third angle and the remaining two sides can be determined using the law of sines.
C. There is insufficient information because to use the law of sines, two angles and a side opposite one of them must be known.
D. There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.
Answer:
D. There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.
Step-by-step explanation:
A triangle is a plane shape that consists of 3 sides and 3 angles. There are different ways of solving for any unknown sides or angles of a triangle.
If any two angles and just one side of a triangle are known, then other angles and sides can also be determined using the sine rule.
For example, if a, b and c are the sides of the triangle and <A, <B and <C are the angles. The sine law is expressed as shown;
a/sinA = b/sinB = c/sinC
Any two can be equated to get any unknown sides and angles.
Also, if two of the angles are known, the third angle can be determined since the sum of angle in a triangle is 180°. If <A and <B are known for example, the third angle <C can be determined using the expression.
<C = 180°-(<A+<B)
Based on the explanation, option D is therefore the correct option i.e There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.
The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet. When the water was 4 feet from the end of the hose, what was its height above the ground? 3.2 feet 4.8 feet 5.6 feet 6.8 feet
Answer: 3.2 feet.
Step-by-step explanation:
Given: The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation[tex]f(x) = -0.3x^2 + 2x[/tex], where [tex]f(x)[/tex] is the height of the path of the water above the ground, in feet, and [tex]x[/tex] is the horizontal distance of the path of the water from the end of the hose, in feet.
At x= 4 , we get
[tex]f(x) = -0.3(4)^2 + 2(4)=-0.3(16)+8 =-4.8+8=3.2[/tex]
Hence, when the water was 4 feet from the end of the hose, its height above the ground is 3.2 feet.
Answer:
3.2 feet.
Step-by-step explanation: