Answer:
x = 4 and y = 1
Step-by-step explanation:
4x + y = 17
2x + y = 9
Solve for x in the second equation.
2x = 9 - y
x = 9/2 - y/2
Put x as 9/2 - y/2 in the first equation.
4(9/2-y/2) + y = 17
36/2 - 4y/2 + y = 17
18 - 2y + y = 17
18 - y = 17
- y = -1
y = 1
Put y as 1.
2x + 1 = 9
2x = 8
x = 4
Answer:
x = 4, y = 1
Step-by-step explanation:
=> 4x+y = 17 -----------(1)
=> 2x+y = 9 -----------(2)
Subtracting both equations
=> 4x+y-2x-y = 17-9
=> 2x = 8
=> x = 4
Now, putting x = 4 in eq (1)
=> 4(4) + y = 17
=> 16 + y = 17
=> y = 17-16
=> y = 1
What is the solution to arccos 0.5 express answer in radians
Answer:
arccos (0.5) is [tex]\frac{\pi}{3}[/tex]
Step-by-step explanation:
With the arccos(0.5) in this problem, you are asked which angle renders its cosine equal to 0.5 (or 1/2).
Recall that there are special angles in the unitary circle that render well know values like 1/2. There are two angle values between 0 and the full circle ([tex]2\pi[/tex] radians), that render cosine function equal 1/2, and they are: [tex]\frac{\pi}{3}[/tex], and [tex]-\frac{\pi}{3}[/tex].
The arccos uses just the first one as answer over the restricted domain between 0 and [tex]\pi[/tex], since otherwise it will not be considered a function.
So the answer is that the arccos (0.5) is [tex]\frac{\pi}{3}[/tex]
What is the range of this function?
Answer:
c
Step-by-step explanation:
outputs are on the right, which are the y-values.
Pleaseeee hheeelppp mmmeee
Answer:
A
90 degrees
anticlockwise.
Step-by-step explanation:
It looks much more complicated than it really is. I don't know how to explain this in any other form but to give the answers.
1 A
The center of rotation is where the 90 degree angle has its vertex. So that would be A.
1 B
Follow x. It rotates 90 degrees. So every point must rotate 90 degrees.
1 C
The direction is against the way the clock tells time, so the direction of rotation is anticlockwise.
According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 emails per day.† Suppose for a particular office the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is three. (Round your answers to four decimal places.) (a) What is the probability of receiving no emails during an hour? (b) What is the probability of receiving at least three emails during an hour? (c) What is the expected number of emails received during 15 minutes? (d) What is the probability that no emails are received during 15 minutes?
Answer:
Step-by-step explanation:
The interval of interest is per hour. This means 60 minutes. Since the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is three, it means that
Mean, μ = 3
x is a random variable representing the number of mails received per hour
a) The probability of receiving no emails during an hour is expressed as
P(x = 0)
From the Poisson distribution calculator,
P(x = 0) = 0.0498
b) the probability of receiving at least three emails during an hour is expressed as P(x ≥ 3).
P(x ≥ 3) = 0.577
c) the expected number of emails received during 15 minutes is
3 × 15/60 = 0.75
d) mean = 0.75
From the poisson distribution calculator, P(x = 0) = 0.47
Find the intersection point for the following linear functions. f(x) = 2x + 3 g(x) = -4x − 27
Answer:
(- 5, - 7 )
Step-by-step explanation:
Equate f(x) and g(x), that is
2x + 3 = - 4x - 27 ( add 4x to both sides )
6x + 3 = - 27 ( subtract 3 from both sides )
6x = - 30 ( divide both sides by 6 )
x = - 5
Substitute x = - 5 into either of the 2 functions for y- coordinate
Substituting into f(x)
f(- 5) = 2(- 5) + 3 = - 10 + 3 = - 7
Thus point of intersection = (- 5, - 7 )
A quantity, T , Varies inversely with a quantity, r. If t=6 then r=5 what is the constant of variation
Answer:
t varies inversely to 30/r
Step-by-step explanation:
t varies inversely to r
(lol I can't seem to find the variation sign in the keyboard)
when you introduce the constant K the sign changes to =
t=k/r
if t=6, r=5
substitute the values
6=k/5
k= 6×5
k=30
we have found the constant so we add it to our initial equation
t inversely varies to 30/r
Which function is graphed below?
Answer:
Piecewise function;
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5
Step-by-step explanation:
Function graphed represents the piecewise function.
1). Equation of the line with y-intercept (-2) and slope 'm'.
Since, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{1}[/tex]
= 2
Therefore, equation of this segment will be in the form of y = mx + b,
⇒ y = 2x - 2 where x < 2
2). Equation of a horizontal line,
y = 4 where 2 ≤ x ≤ 5
3). Equation of the third line in the interval x > 5
Let the equation of the line is,
y = mx + b
Where m = slope of the line
b = y-intercept
Here, slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{2}[/tex]
= 1
Equation of this line will be,
y = 1(x) + b
y = x + b
Since, this line passes through (5, 6),
6 = 5 + b
b = 6 - 5 = 1
Therefore, equation of this line will be,
y = x + 1 where x > 5
Graphed piecewise function is,
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5
the instantaneous growth rate r of a colony of bacteria t hours after the start of an experiment is given by the function r=0.01t^3-0.07t^2+0.07t+0.15 for 0≤t≤7. find the times for which the instantaneous growth rate is zero.
Answer:
t = 5,-1,3
Step-by-step explanation:
r=0.01t^3-0.07t^2+0.07t+0.15
For simplification let's multiply the equation by 100
100r = t³ - 7t² + 7t + 15
When r= 0
t³ - 7t² + 7t + 15= 0
Let's look for the value of t.
Let's try a possible division
(t³ - 7t² + 7t + 15)/(t-5) = t² -2t -3
So we've gotten one as t-5
Let's factorize t² -2t -3
= t² +t -3t -3
= t(t+1) -3(t+1)
= (t+1)(t-3)
So we have
(t-5)(t+1)(t-3)
What it means is that the possible values are when
t = 5,-1,3
These are also called the roots of the equation
Answer:I don’t know
Step-by-step explanation: fruit flys are weird
Complete the following exercises by applying polynomial identities to complex numbers. Show your work. Factor x^2 + 64. Check your work. Factor 16x^2 + 49. Check your work. Find the product of (x + 9i)^2. Find the product of (x − 2i)^2. Find the product of (x + (3+5i))^2.
Answer:
Step-by-step explanation:
Hello,
Factor x^2 + 64.
[tex]\boxed{x^2+64=x^2+8^2=x^2-8^2i^2=(x-8i)(x+8i)}[/tex]
Factor 16x^2 + 49.
[tex]\boxed{16x^2+49=(4x)^2-(7i)^2=(4x-7i)(4x+7i)}[/tex]
Find the product of (x + 9i)^2.
[tex]\boxed{(x+9i)^2=x^2+18xi+(9i)^2=x^2+18xi-81=x^2-81+18xi}[/tex]
Find the product of (x − 2i)^2.
[tex]\boxed{(x-2i)^2=x^2-4xi-4=x^2-4-4xi}[/tex]
Find the product of (x + (3+5i))^2.
[tex]\boxed{(x + (3+5i))^2=x^2+(3+5i)^2+2x(3+5i)=x^2+9-25+30i+6x+10xi}\\\boxed{=x^2+6x-16+(30+10x)i}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the value of x in the figure
(X+5)* 90*
Answer:
x = 85 deg
Step-by-step explanation:
We can see that there are two straight lines that intersect and that the two angles given are opposite angles.
Because they are opposite angles, the two angles have the same value, i.e
(x + 5) = 90 (subtract 5 from each side)
x = 90 - 5
x = 85 deg
A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples of 16 people ages 30 dash 40 who do not exercise regularly and 12 people ages 30 dash 40 who do exercise regularly were selected, and the resting pulse rate (in beats per minute) of each person was measured. The summary statistics are to the right. Apply the nonpooled t-interval procedure to obtain a 95% confidence interval for the difference, mu 1 minus mu 2, between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise. Assume that the requirements for using the procedure are satisfied and round to two decimal places.
Answer:
We Reject H₀ if t calculated > t tabulated
But in this case,
0.83 is not greater than 2.056
Therefore, we failed to reject H₀
There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.
Step-by-step explanation:
Refer to the attached data.
The Null and Alternate hypothesis is given by
Null hypotheses = H₀: μ₁ = μ₂
Alternate hypotheses = H₁: μ₁ ≠ μ₂
The test statistic is given by
[tex]$ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } } $[/tex]
Where [tex]\bar{x}_1[/tex] is the sample mean of people who do not exercise regularly.
Where [tex]\bar{x}_2[/tex] is the sample mean of people who do exercise regularly.
Where [tex]s_1[/tex] is the sample standard deviation of people who do not exercise regularly.
Where [tex]s_2[/tex] is the sample standard deviation of people who do exercise regularly.
Where [tex]n_1[/tex] is the sample size of people who do not exercise regularly.
Where [tex]n_2[/tex] is the sample size of people who do exercise regularly.
[tex]$ t = \frac{72.7 - 69.7}{\sqrt{\frac{10.9^2}{16} + \frac{8.2^2}{12} } } $[/tex]
[tex]t = 0.83[/tex]
The given level of significance is
1 - 0.95 = 0.05
The degree of freedom is
df = 16 + 12 - 2 = 26
From the t-table, df = 26 and significance level 0.05,
t = 2.056 (two-tailed)
Conclusion:
We Reject H₀ if t calculated > t tabulated
But in this case,
0.83 is not greater than 2.056
Therefore, We failed to reject H₀
There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.
kiran scored 223 more points in a compouter game than tyler. if kiran scored 409 points, how many points did tyler score
Answer:
223=409−z
409=223+z
Step-by-step explanation:
A politician who is running for the office of mayor of a city with 25,000 registered voters commissions a survey. In the survey, 48% of the 200 registered voters interviewed say they plan to vote for her. a. What is the population of interest?
Answer:
The 25,000 registered voters
Step-by-step explanation:
Population includes the entirety of the set of data, it consists of all the elements of a data set. For example all the students in a school, all the citizens of a country etc.
While the sample is the elements of the population from which observations are drawn from.
Therefore, for the case above, the population is the entirety of the registered voters in the city, that is all the 25,000 registered voters.
LM=9, NR=16, SR=8. Find the perimeter of △SMP.
HURRY FIRST ANSWER I WILL MARK YOU AS BRAINLILIST PROMISE
Answer:
perimeter of △SMP = 25Step-by-step explanation:
The perimeter of the triangle △SMP is the sum of al the sides of the triangle.
Perimeter of △SMP = ||MS|| + ||MP|| + ||SP||
Note that the triangle △LRN, △LSM, △MPN and △SRP are all scalene triangles showing that their sides are different.
Given LM=9, NR=16 and SR=8
NR = NP+PR
Since NP = PR
NR = NP+NP
NR =2NP
NP = NR/2 = 16/2
NP = 8
From △LSM, NP = PR = MS = 8
Also since LM = MN, MN = 9
From △SRP, SR = RP = PS = 9
Also SR = MP = 8
From the equation above, perimeter of △SMP = ||MS|| + ||MP|| + ||SP||
perimeter of △SMP = 8+8+9
perimeter of △SMP = 25
A 1-inch rise for a 16-inch run makes it easier for the wheelchair rider to ascend a ramp. How long must a ramp be to easily accommodate a 24-inch rise to the door?
Answer: The ramp must be 32 feet long. In inches, 384.
Step-by-step explanation:
For each 16 inches of run, there is one inch of rise. To get 24 inches of rise, multiply 16 by 24 to get 384 inches. To convert to a more useful measurement, convert to feet. 12 inches per foot. 384/12 = 32
Measurement is the process of assigning numbers to physical quantities and phenomena.
If a 1-inch rise for a 16-inch run makes it easier for the wheelchair rider, this can be expressed as:
1inch rise = 16-inch run
In order to determine how long must a ramp be to easily accommodate a 24-inch rise to the door, we can write:
24in rise = x
Divide both expressions:
[tex]\dfrac{1}{24}=\dfrac{16}{x}\\[/tex]
Cross multiply:
[tex]x=16 \times 24\\x=384inches[/tex]
Hence the ramp must be 384inches long in order to easily accommodate a 24-inch rise to the door.
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what is 1/4 x 1/4 x 1/4
Answer:
1/64
Step-by-step explanation:
1/4 × 1/4 × 1/4
Multiply the fractions.
1/4³
= 1/64
Answer:
The answer is 1/64.
Step-by-step explanation:
1/4 x 1/4 x 1/4 = 1/64
In other ways, you can write this as: 1/4³
Hope this helped!
The triangle ABC formed by AB = 13cm, BC=5cm and
AC = 12cm is
Answer:
Right-angle triangle
Step-by-step explanation:
What is the value of n in the numerical sentence?
Answer: n = -2
Step-by-step explanation:
answer:
-2
step by step explanation:
Ben owns a townhome valued at $195,000, but still owes $120,000 on the loan, Ben has $5,000 in savings and a balance of $1,400 on his credit cards. There is a balance of $20,000 owed on Ben's car which is valued at $38,000. What is Ben's net worth?
Answer:
$96,600
Step-by-step explanation:
Answer:
A on edge
Step-by-step explanation:
What are the steps for constructing a copy of an angle using only a compass and
a straightedge?
Answer:
1. Use a straightedge
2. Draw dots on the line to mark the starting point
3. Place the point of the compass on the point you made or was given
4. Extend the compass so that the pencil is on the 2nd point & make a an arc thru point B
5. Place the compass point on the starting point dot on the line and draw w/ the pencil to create an arc crossing the line.
Answer:
Step 1: Mark the point that will be the vertex of the new angle, and label it P.
Step 2: Draw a ray from P in any direction, with any length. This ray will be one of the sides of the new angle.
Step 3: Place the compass point on the vertex of the original angle, and adjust the compass width to a convenient size.
Step 4: Use the compass to draw an arc intersecting both rays of the original angle at two points, J and K.
Step 5: Move the compass (without changing the width) to point P, and make an arc intersecting the existing ray of the angle. Mark the intersection point, and label it M.
Step 6: Set the compass point on the original angle at point J, and set its width to the length of line segment JK.
Step 7: Move the compass point to M on the new angle, and draw an arc cutting the previous arc. Mark the intersection point and label it L.
Step 8: Draw a ray from point P through point L. The new angle is a copy of the original angle.
Step-by-step explanation:
edmentum
Solve the system of linear equations.
Answer:
work is shown and pictured
Assume that the probability of the binomial random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. Find the probability that at leastat least 3535 households have a gas stove.
This is not the correct question, the correct question is;
Assume that the probability of the binomial random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. Find the probability that at least 35 households have a gas stove.
Answer: p ( x > 34.5 ) The area to the right of 34.5
Step-by-step explanation:
Given that, x = 35
when using normal approximation
Using continuity correction
so
p ( x ≥ 35 ) = p ( x > 34.5 )
More than means the area is towards the right.
Therefore, the area under the normal curve is,
p ( x > 34.5 ) The area to the right of 34.5
solving the equation 2x+3(3x-5)=51 for x gives x = 6 what is the complete solution
Answer:
x = 6
Step-by-step explanation:
2x + 3(3x - 5) = 51
Expand the brackets.
2x + 9x - 15 = 51
Add like terms.
11x - 15 = 51
Add 15 on both sides.
11x = 51 + 15
11x = 66
Divide both sides by 11.
x = 66/11
x = 6
The solution to the equation 2x+3(3x-5)=51 is x = 6
How to determine the complete solution?The equation is given as:
2x+3(3x-5)=51
Expand
2x + 9x - 15 = 51
Evaluate the like terms
11x = 66
Divide both sides by 11
x = 6
Hence, the solution to the equation 2x+3(3x-5)=51 is x = 6
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Immediately after filling my gas tank, I drove 237.1 miles to my favorite campground. I filled my tank again at the campground, and computed that I got 28.7 miles per gallon on the trip. How many gallons of gas did I use on the trip to the campground
Answer:
57,838.4 - 57,491.9 = 346.5 miles
346.5/17.5 = 19.8 miles per gallon.
Hope this helps :-)
Step-by-step explanation:
Please help roght now very rushed
Answer:
c
Step-by-step explanation:
The salary scale for a senior officer starts at N57000
per annum. A rise of N2800 is given at the end of each
Find the total amount of money that the officer will
year.
earn in 14 years.
Answer:
N1,052,800.
Step-by-step explanation:
The starting salary of the officer = N57,000
Increase per annum =N2,800
The given pattern forms an arithmetic sequence since the annual salary increases by a fixed amount.
We are to determine the total amount of money that the officer will earn in 14 years.
Sum of an arithmetic sequence, [tex]S_n=\frac{n}{2}[2a+(n-1)d]$ ,where: \left\{\begin{array}{lll}$First term, a=57,000\\$Common difference, d=2,800\\$Number of terms, n=14\end{array}\right[/tex]
[tex]S_{14}=\frac{14}{2}[2(57,000)+(14-1)(2,800)]\\=7[114,000+13*2800]\\=7[150,400]\\=1,052,800[/tex]
At the end of 14 years, the total amount earned by the officer will be N1,052,800.
What is the solution to the system of equations?
y=-3x – 2
5x + 2y = 15
0 (-40. 19)
(-19.55)
(19-40)
(55.-19)
Answer:
Step-by-step explanation:
y = -3x - 2
5x + 2y = 15
5x + 2(-3x -2) = 15
5x -6x - 4 = 15
-x - 4 = 15
-x = 19
x = -19
y = -3(-19) - 2
y = 57 - 2
y = 55
(-19, 55)
solution is b
Find the equation of the line with slope m=1/2 that contains the point (4,6)
Answer:
y = 1/2x + 4
Step-by-step explanation:
Use the formula for the equation of a line.
y = mx + b
Where m is the slope, and b is the y-intercept.
The slope is given.
y = 1/2x + b
The points (x, y) are given.
(4, 6)
Put y as 6 and x as 4, solve for b.
6 = 1/2(4) + b
6 = 2 + b
6 - 2 = b
4 = b
The y-intercept is 4 or (0, 4).
The equation of the line is y = 1/2x + 4.
Which statement is true about the graphs of the two lines y = –6 and x = ?
The lines are perpendicular to each other because the graph of y = –6 is a horizontal line with a slope that is undefined, and the graph of x = is a vertical line with a slope of 0.
The lines are perpendicular to each other because the graph of y = –6 is a vertical line with a slope that is undefined, and the graph of x = is a horizontal line with a slope of 0.
The lines are perpendicular to each other because the graph of y = –6 is a vertical line with a slope of 0, and the graph of x = is a horizontal line with a slope that is undefined.
The lines are perpendicular to each other because the graph of y = –6 is a horizontal line with a slope of 0, and the graph of x = is a vertical line with a slope that is undefined.
Answer:
if x is positive the answer is the 4th statement and if it is negative the answer is the 3rd statement
Step-by-step explanation:
We have the statement that tells us: "the graphs of the two lines y = –6 and x =?" x, we do not know it, but from the y coordinate we can do it by discard.
In the case of y-coordinate we have that y = -6 is a horizontal line with a slope of 0, therefore of the 4 statements it is reduced to 2, the third and the fourth.
Depending on the sign that has the value of x, if it is positive or negative it would be the 3rd and 4th answer.
if x is positive it is a vertical line with a slope that is undefined, but if it is negative it is a horizontal line with a slope that is undefined.
A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is
A. 0.100
B. 0.010
C, 0.001
D. 0.002
Answer:
D. 0.002
Step-by-step explanation:
Given;
total number of sample, N = 500 elements
50 elements are to be drawn from this sample.
The probability of the first selection, out of the 50 elements to be drawn will be = 1 / total number of sample
The probability of the first selection = 1 / 500
The probability of the first selection = 0.002
Therefore, on the first selection, the probability of an element being selected is 0.002
The correct option is "D. 0.002"
On the first selection, the probability of an element being selected is 0.002. Option D is correct.
Given information:
A population consists of 500 elements. so, the total number of samples will be [tex]N = 500[/tex] .
We want to draw a simple random sample of 50 elements.
The probability is defined as the preferred outcomes divided by the total number of samples.
So, the probability of first selection will be calculated as,
[tex]P=\dfrac{1}{500}\\P=0.002[/tex]
Therefore, on the first selection, the probability of an element being selected is 0.002.
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