Answer:
Step-by-step explanation:
3x - 2y = –9
3x−2y+2y=−9+2y
3x=2y−9/3x^3
=2y−9/3
x=2/3y−3
4x + 3y = 22
4x+3y+−3y=22+−3y
4x=−3y+22
4x4
=−3y+22/4
x=−3/4y+11/2
The solution of the given system of equations are x=1 and y=6
What is Linear equation?An equation between two variables that gives a straight line when plotted on a graph.
Given,
3x - 2y = -9
4x + 3y = 22
Consider the first linear equation
3x-2y = -9
3x= -9+2y
x= [tex]\frac{-9+2y}{3}[/tex]
x=[tex]\frac{2}{3}y-3[/tex]
Substitute the values in the second linear equation
4([tex]\frac{2}{3}y-3[/tex])+3y=22
[tex]\frac{8}{3} y-12+3y=22\\\frac{17}{3}y=22+12\\ \frac{17}{3}y=34\\y=6[/tex]
Substitute the value of y in the first linear equation
3x-2y= -9
3x-2×6=-9
3x-12=-9
3x=3
x=1
Hence, Solution of the given system of equations are x=1 and y=6
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Mariah is studying the life cycle of the monarch butterfly. She must choose one stage in the cycle to present in science class: egg, caterpillar, chrysalis, or adult. She plans to make her choice randomly using a custom spinner divided into four sections. First, however, she spins the spinner 50 times to see the frequencies it generates.
Stage Times Landed On
egg 10
caterpillar 12
chrysalis 15
adult 13
The relative frequency of landing on egg is .
The relative frequency of landing on caterpillar is .
The relative frequency of landing on chrysalis is .
The relative frequency of landing on adult is .
All the outcomes be considered equally likely.
The relative frequency of landing on an egg, caterpillar, chrysalis and adults are 0.2, 0.24, 0.3 and 0.26.
What is the relative frequency?"Relative frequency represents the ratio of the number of times a value of the data occurs in a dataset".
For the given situation,
Number of times egg landed on spin, x1 = 10
Number of times caterpillar landed on spin, x2 = 10
Number of times chrysalis landed on spin, x3 = 15
Number of times adult landed on spin, x4 = 13
Total number of times, n = 50
The formula for relative frequency = [tex]\frac{x}{n}[/tex]
The relative frequency of landing on an egg = [tex]\frac{10}{50}[/tex]
⇒ [tex]0.2[/tex]
The relative frequency of landing on caterpillar = [tex]\frac{12}{50}[/tex]
⇒[tex]0.24[/tex]
The relative frequency of landing on chrysalis = [tex]\frac{15}{50}[/tex]
⇒ [tex]0.3[/tex]
The relative frequency of landing on adults = [tex]\frac{13}{50}[/tex]
⇒ [tex]0.26[/tex]
Hence we can conclude that the relative frequency of landing on an egg, caterpillar, chrysalis, and adults are 0.2, 0.24, 0.3 and 0.26.
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Answer:
The relative frequency of landing on egg is 0.2.The relative frequency of landing on caterpillar is 0.24.The relative frequency of landing on chrysalis is 0.3.The relative frequency of landing on adult is 0.26.All the outcomes can be considered equally likely.Step-by-step explanation:
Ready to help you all any time
Which expression is equivalent to 5(2+7)
A. 2(5+7)
B. 2+7(5)
C. 5(2)+7
D.5(2)+5(7)
Answer:
D
Step-by-step explanation:
So 5(2+7) equals 45
A. 2(5+7)=24
B. 2+7(5)=37
C. 5(2)+7=17
D.5(2)+5(7)=45
Only D equals 45
Hope I helped :D
Can y’all answer this or not !?
Answer:
b
Step-by-step explanation:
Answer:
x=417.6
Step-by-step explanation:
Let's solve your equation step-by-step.
0.5x+78.2=287
Step 1: Subtract 78.2 from both sides.
0.5x+78.2−78.2=287−78.2
0.5x=208.8
Step 2: Divide both sides by 0.5.
0.5x divided by 0.5
208.08 divided by 0.5
Find the length of the right triangle’s other leg. Round to the nearest tenth.
leg = 10 ft
hypotenuse = 12 ft
Answer: 17.32
Step-by-step explanation:
What are the roots of y = x2 – 3x – 10?
0-3 and -10
-2 and 5
X 2 and -5
3 and 10
Answer:
x = 5 x = -2
Step-by-step explanation:
y = x^2 – 3x – 10
Set the equation equal to zero
0= x^2 – 3x – 10
Factor
What 2 numbers multiply to -10 and add to -3
-5 *2 = -10
-5+2 = -3
0=(x-5) ( x+2)
Using the zero product property
x-5 = 0 x+2 = 0
x = 5 x = -2
Answer:
-2 and 5
Step-by-step explanation:
trust
Need help solving this
Answer:
c: no solution
Step-by-step explanation:
Solve for a,b,and/or c
Help solve ASAP!
Answer:
a=90-67=23°
.................
Given: 5(x + 2) - 3 = 4(x - 1)
Prove: x = -11
Statement Reason
5(x + 2) - 3 = 4(x - 1) given
5x + 10 - 3 = 4x - 4 [?]
5x + 7 = 4x - 4 addition
5x = 4x - 11 subtraction
x = -11 subtraction
Answer:-11 proved
Step-by-step explanation:
5(x+2)-3=4(x-1)
Open brackets
5x+10-3=4x-4
Collect like terms
5x-4x=-4+3-10
x=-11
A class of 64 students was given 320 book how many will each students take home
Each student will take=320/64
=5
So the answer is 5.
Hope it will be helpful to you...
✧◝(⁰▿⁰)◜✧
A math class is having a discussion on how to determine if the expressions 4x-x+5 and 8-3x-3 are equivalent using
substitution. The class has suggested four different methods.
Which describes the correct method?
O Both expressions should be evaluated with one value. If the final values of the expressions are both positive, then the two
expressions must be equivalent.
Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two
expressions must be equivalent.
Both expressions should be evaluated with two different values. If for each substituted value, the final values of the
expressions are positive, then the two expressions must be equivalent.
O Both expressions should be evaluated with two different values. If for each substituted value, the final values of the
expressions are the same, then the two expressions must be equivalent.
6:55 PM
5/15/2020
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Answer:
Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
Step-by-step explanation:
Both expressions are linear expressions. It takes 2 points to define a line. If the lines defined by each expression go through the same two points, then the expressions are equivalent.
If the expressions have the same value for two different variable values, they are equivalent. (choice D)
_____
Additional comment
One more point is needed than the degree of the polynomial expression. That is, quadratic (degree 2) expressions will be equivalent if they go through the same 2+1 = 3 points.
The vertices of ΔDEF have coordinates D(–1, 2), E(3, 3), and F (2, –4).What are the coordinates of the vertices of r(90°, O)(ΔDEF)?
Answer:
D,E
Step-by-step explanation:
hope I helped
A radio station claims that the amount of advertising per hour of broadcast time has an average of 13 minutes and a standard deviation equal to 1.2 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 17 minutes. Calculate the z-score for this amount of advertising time.
Answer:
[tex]Z = 3.33[/tex]
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 13, \sigma = 1.2[/tex]
You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 17 minutes. Calculate the z-score for this amount of advertising time.
We have to find Z when X = 17. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17 - 13}{1.2}[/tex]
[tex]Z = 3.33[/tex]
What is 7/10 divided by 12 simplified
Answer:
7 /120
Step-by-step explanation:
7/10 ÷ 12
Copy dot flip
7/10 * 1/12
7 /120
Answer:
0.058333
Step-by-step explanation:
12 divided by 9 tenths and hundredths
Find the volume of the cylinder. Round your answer to the nearest tenth.
Please help!
Answer:1236.4 ft^3
Step-by-step explanation:
height=h=7ft
Diameter=15ft
Radius=r=15/2=7.5ft
Volume of cylinder=π x r^2 x h
Volume of cylinder=3.14 x (7.5)^2 x 7
Volume of cylinder=3.14x7.5x7.5x7
Volume of cylinder=1236.375
Volume of cylinder=1236.4 ft^3
What does 2 + 2 = ?
Answer:
4
Step-by-step explanation:
1+1+1+1 or 2 + 2
Apple exist in the world. This particular tree only have 4 perfect apples total. Because you only have one friend, they help you pick 2 out of the 4 apples. Then you pick 2 of the other apple. Without dropping or eating them, he gave both of his apple to you . How many apple do you have without dropping or eating them?
Answer:
4
Step-by-step explanation:
Suppose the following set of random numbers is being used to simulate the event of a basketball player making 3 free throws in a row. How should the numbers be arranged?
Answer:
860 583 785 814 010 122 337 198 621 549 034 076 796 495 978 078 433 330 333 153
Step-by-step explanation:
a p e x :))
Answer: 860 583 785 814 010 122 337 198 621 549 034 076 796 495 978 078 433 330 333 153
Step-by-step explanation:
State the domain and range for the function. f(x)= -tan x
Answer:
domain: (-∞, ∞) \ (kπ+π/2 for integers k)range: (-∞, ∞)Step-by-step explanation:
The tangent function is undefined at odd multiples of π/2. It can take on any value.
The domain is all real numbers except odd multiples of π/2.
The range is all real numbers.
Answer: it’s b
Step-by-step explanation:
edge
Suppose r⃗ (t)=cos(πt)i+sin(πt)j+5tkr→(t)=cos(πt)i+sin(πt)j+5tk represents the position of a particle on a helix, where zz is the height of the particle. (a) What is tt when the particle has height 2020? t=t= (b) What is the velocity of the particle when its height is 2020? v⃗ =v→= (c) When the particle has height 2020, it leaves the helix and moves along the tangent line at the constant velocity found in part (b). Find a vector parametric equation for the position of the particle (in terms of the original parameter tt) as it moves along this tangent line.
Answer:
a) t = 4
b) v = pi j + 5 k
c) rt = 1i + (pi t) j + (20 +5t )k
Step-by-step explanation:
You have the following vector equation for the position of a particle:
[tex]r(t)=cos(\pi t)\hat{i}+sin(\pi t)\hat{j}+5t\hat{k}[/tex] (1)
(a) The height of the helix is given by the value of the third component of the position vector r, that is, the z-component.
For a height of 20 you have:
[tex]5t=20\\\\t=\frac{20}{5}=4[/tex]
(b) The velocity of the particle is the derivative, in time, of the vector position:
[tex]v(t)=\frac{dr(t)}{dt}=-\pi sin(\pi t)\hat{i}+\pi cos(\pi t)\hat{j}+5\hat{k}[/tex] (2)
and for t=4 (height = 20):
[tex]v(t=4)=-\pi sin(\pi (4))\hat{i}+\pi cos(\pi (4))\hat{j}+5\hat{k}\\\\v(t=4)=-0\hat{i}+\pi\hat{j}+5\hat{k}[/tex]
(c) The vector parametric equation of the tangent line is given by:
[tex]r_t(t)=r_o+vt[/tex] (3)
ro: position of the particle for t=4
[tex]r_o=cos(\pi (4))\hat{i}+sin(\pi (4))\hat{j}+20\hat{k}\\\\r_o=\hat{i}+0\hat{j}+20\hat{k}[/tex]
Then you replace ro and v in the equation (3):
[tex]r_t=(1\hat{i}+20\hat{k})+(\pi \hat{j}+5\hat{k})t\\\\r_t=1\hat{i}+\pi t \hat{j}+(20+5t)\hat{k}[/tex]
Part(a): The value of [tex]t=4[/tex]
Part(b): Required vector [tex]L(t)=(1\widehat{i}+0\widehat{j}+10\widehat{k})+(t-4)(0\widehat{i}+\pi \widehat{j}+5\widehat{k})[/tex]
Given vector equation is,
[tex]r(t)=cos(\pi t)\widehat{i}+sin(\pi t)\widehat{j}+5t\widehat{j}[/tex]
Vector equation:
A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector, and with an arrow indicating the direction.
Part(a):
When the particle has a height of 20
[tex]5t=20\\t=4[/tex]
Part(b):
The point on the curve is [tex](cos(4\pi),sin(4\pi),20) =(1,0,20)[/tex]
Differentiating the given equation with respect to [tex]t[/tex].
[tex]r'(t)=- \pi sin(\pi t)\widehat{i}+\pi cos(\pi t)\widehat{j}+5\widehat{k}\\r'(t)=- \pi sin(4\pi t)\widehat{i}+\pi cos(4\pi t)\widehat{j}+5\widehat{k}\\r'(4)=0\widehat{i}+\pi \widehat{j}+5\widehat{k}\\L(t)=r(4)+(t-4)r'(4)\\L(t)=(1\widehat{i}+0\widehat{j}+10\widehat{k})+(t-4)(0\widehat{i}+\pi \widehat{j}+5\widehat{k})[/tex]
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Which of the following are perfect squares? Check all that apply.
Answer: 16, 64, and 49
Step-by-step explanation: Perfect squares are products made by squaring or multiplying a whole number by itself twice.
11 is not a perfect square since nothing can
be multiplied by itself to give us 11.
The same is true for 62 and 15.
16 is a perfect square since it's possible to find a whole number that can be multiplied by itself to give us 16.
That number is 4 since 4 × 4 = 16.
64 is also one since 8 can be multiplied by itself twice to give us 64.
49 is also one since 7² or 7 × 7 is 49.
Answer:D,E and F
Step-by-step explanation:
Perfect squares are numbers in which their square roots are whole numbers.
From the options
√16 =4
√64 =8
√49 =7
Two forces are acting on an object at the same point. Determine the angle between the two forces. (-2,7) and (3,-1)
Answer:
It is 124 degrees.
Step-by-step explanation:
You square each coordinate like this:
sqrt(x^2+y^2 )
You will end up getting sqrt(53 and sqrt(10.
Then find the dot product which is -6+-7=-13.
Then cos^-1(-13/sqrt53*sqrt10)
=124 degrees
The estimate obtained from a sample of which of the following sizes would most likely be closest to the actual parameter value of a population?
A.15
B. 75
c. 45
d. 150
Answer:
d 150
Step-by-step explanation:
Answer:
150
Step-by-step explanation:
If ItsAkelia (me) had 1M subs and M00dybear had 1M who had more?
(not real sub count but just asking)
Answer:
If you both have 1M subs then its the same, not one person has more
g(x) = 9x plug in g(9)
Answer:
81
Step-by-step explanation:
replace x with 9 so it's 9x9 which is 81
Answer:
g(9) = 81
Step-by-step explanation:
g(x) = 9x
g(9) = 9(9) = 81
Pls help with these questions I can give brainliest thank you all! 9 a and b
Answer:
A. 8 1/4 * 11 1/2 * 14=1328 1/4 ft^2
OR
8 1/4 height times 11 1/2 width times 14 in length equals 1328 1/4 feet squared
B. 8 1/4 * 14 1/2 * 14=1674 3/4
OR
8 1/4 height times 11 1/2 width plus 3 so 14 1/2 width times 14 equals 1674 3/4 feet squared
Step-by-step explanation:
Tell the measure of the angles In degrees 1/4
Answer:
so 1/4 of a circle is 90 degrees 1/4 is equal to 90 over 360 C it's 90 parts of 360. so here we go with this one. this angle is 20 degrees remember that's 90 alright the square one and this little part would be 20 degrees each angle appears wider as the Rays get longer.
Step-by-step explanation:
Let me know if this help's you lol :)
Need Help ASAP !!!!!
Answer:
Luke worked 7 hours and Joshua worked 4 hours
Step-by-step explanation:
Let's call the number of hours that Luke worked l, and the number of hours that Joshua worked j. Since we know that Luke worked for 3 more hours than Joshua, we can express the amount of hours he worked as (j+3). Now, you can set up the following equation:
25j+35(j+3)=345
Expand parentheses:
25j+35j+105=345
Subtract 105 from both sides and combine like terms:
60j=240
j=4
Since Luke worked 3 more hours, he worked 7 hours. Hope this helps!
!!!!!!WILL MARK BRAINLIEST I need answer quickly!!!!!!!!
For males in a certain town, the systolic blood pressure is normally distributed with a mean of 105 and a standard deviation of 5. Using empirical rule, determine the interval of systolic blood pressures that represent the middle 99.7 of males
Answer:
Average systolic blood pressure = x = 130
Standard deviation = s = 6
Step-by-step explanation:
We are to find interval that represents the systolic blood pressure of middle 99.7% of the males.
According to the empirical rule:
a) 68% values lie within 1 standard deviation of the mean
b) 95% values lie within 2 standard deviation of the mean
c) 99.7% values lie within 3 standard deviation of the mean
So, 99.7% value will lie within 3 standard deviations from the mean.
We can express this range as:
( x - 3s, x + 3s)
= (130 - 3(6), 130 +3(6))
= ( 130 - 18, 130 + 18)
= ( 112, 148 )
Thus the interval from 112 to 148 contains the systolic blood pressure of middle 99.7% of the males in the certain town
Hope this helps!!!
The interval of systolic blood pressures that represent the middle 99.7 of males is (90, 120).
What is Empirical Rule?Empirical rule is a rule for normally distributed data which defines that almost all the data observed ranges between three standard deviations from the mean.
Given that,
For males in a certain town, the systolic blood pressure is normally distributed.
Mean, μ = 105
Standard deviation, σ = 5
Using empirical rule, we can say that 99.7% of males having the systolic blood pressures observed following a normal distribution lies within 3 standard deviations of the mean.
So the interval is (μ ± 3σ).
That is, (105 - 3×5, 105 + 3×5) = (90, 120)
Hence the required interval is (90, 120).
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Assume the average weight of an American adult male is 180 pounds with a standard deviation of 34 pounds. The distribution of weights follows a normal distribution. What is the probability that a man weighs somewhere between 120 and 155 pounds?
Answer:
Step-by-step explanation:
Find a-score of both
z-score = (x-mean)/SD
for 120
z =( 120- 180)/34 = -1.765
For 155
z = (155-180)/34 = -0.735
The probability to look for using z-score table is;
P(-1.765<z<-0.735) = 0.19239
a reading teacher recorded the number of pages read in an hour by each of her students. The numbers are shown below: 54,39,29,43,60,44,35,49,51. for this data, which summary statistic is not correct?
Answer: The answer is 29, because that 29 would be the outlier of the numbers.
Step-by-step explanation:
