The solutions to the equation are (1. 5) and (4.6, -2.2)
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
x^2 + y^2 = 26
2x + y = 7
The above expression is a system of equation that implies that:
One linear equation and one circle equation
Next, we plot the graph to solve graphically
The points of intersection are (1. 5) and (4.6, -2.2)
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to estimate the average annual expenses of students on books and class materials, a sample of size 36 is taken. the sample mean is $850 and the sample standard deviation is $54. a 99 percent confidence interval for the population mean is group of answer choices $823.72 to $876.28 $832.36 to $867.64 $826.82 to $873.18 $825.48 to $874.52
Answer: $826.82 to $873.18
Step-by-step explanation:
a stock market drops by 1.38 what rational number represents the drop in index
The drop in the index is - 69/50 (-1.38)
- A stock market index drops by 1.38 points
- We need to find the rational number represents the change in
the index
∵ Drop means the stock is become less
∴ The value of change will be negative
∵ The stock is drops by 1.38
∴ -1.38 = -1.38/1
- Multiply up and down by 100 because there are 2 digits right the
decimal point
∴ -1.38 = -138/100
- Divide up and down by 2
∴ -1.38 = - 69/50
∴ The drop in the index is - 69/50 (-1.38)
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What is 2/5 of a book to 1/2 of an hour as a unit rate?
Answer: 4/5 book per hour
Step-by-step explanation: in this question, we are to rewrite (2/5)/(1/2) as unit rate.
To write this as a unit rate, what we need to do is to divide 2/5 by 1/2.
That means 2/5 divided by 1/2
Removing the division and replacing with multiplication will give 2/5 * 2/1 = 4/5 books/hour
On a feild trip, the ratio of teachers to students must be 2:9. If there are 81 students on the feild trip, how many teachers must there be?
Answer:
18
Step-by-step explanation:
If they are 18 teachers on the field trip the ratio would be 18 : 81. this in the simplest form is 2 : 9
PLEASEEEE SOMEONE HELP I GIVE AS MUCH POINTS :’( Thank you!
The approximate area of the trapezoid is determined as 13.95 unit².
What is the approximate area of the trapezoid?The approximate area of the trapezoid is calculated as follows;
Area = ¹/₂(b₁ + b₂)h
Where;
b₁ and b₂ are the lengths of the parallel sidesh is the heightThe y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;
y(3/2) = - (3/2)²/2 + 3/2 + 5
y(3/2) = -9/8 + 3/2 + 5
y(3/2) = 5.375
y(4) = -4²/2 + 4 + 5
y(4) = -8 + 9
y(4) = 1
h = 5.375 - 1 = 4.375
The approximate area of the trapezoid is calculated as;
Area = ¹/₂(5.375 + 1) x 4.375
Area = 13.95 unit²
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pls helpppppppppqjhg
Answer:
Step-by-step explanation:
It is the 3rd or 1st one.
Based on the 2017 American Community Survey, the proportion of the California population aged 15 years old or older who are married is p = 0.482. Suppose n = 1000 persons are to be sampled from this population and the sample proportion of married persons (p) is to be calculated. What is the probability that more than 50% of the people in the sample are married? Round your answer to three decimal places.
Therefore, the probability that more than 50% of the people in the sample are married is approximately 0.115 (rounded to three decimal places).
To solve this problem, we can use the normal approximation to the binomial distribution since the sample size is large (n = 1000) and the proportion of married persons (p) is not too close to 0 or 1.
The mean of the sample proportion can be calculated as:
μ = p = 0.482
The standard deviation of the sample proportion can be calculated as:
σ = sqrt((p * (1 - p)) / n) = sqrt((0.482 * (1 - 0.482)) / 1000) ≈ 0.015
To find the probability that more than 50% of the people in the sample are married, we need to calculate the z-score and find the area under the normal curve to the right of this z-score.
The z-score can be calculated as:
z = (x - μ) / σ = (0.5 - 0.482) / 0.015 ≈ 1.200
Using a standard normal distribution table or a calculator, we can find that the area to the right of z = 1.200 is approximately 0.1151.
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While gaming, a Playstation 4 uses about 140 Watts of energy. A flat-screen TV uses about 150 Watts. If you are gaming for 4 hours a day 5 times a week for a year, how much will that cost you if you pay 5 cents/kWh? Your answer should have $/kWh as the unit. *
9514 1404 393
Answer:
regardless of the time used your energy will cost $0.05/kWhyour annual energy use will cost $15.08Step-by-step explanation:
The problem statement tells you the cost of energy is $0.05/kWh. If those are the units required for the answer, that is the answer.
__
The question, "how much will that cost you?" suggests the units of the answer should be dollars (not dollars per kWh). In that case, we need to know the number of kWh used during the year. The total annual cost will be ...
(0.14 kW +0.15 kW)(4 h/day)(5 day/wk)(52 wk/yr)(1 yr)($0.05/kWh)
= (0.29)(4)(5)(52)($.05) = $15.08
Your cost will be $15.08 for the electricity for a year.
While gaming, a Playstation 4 uses about 140 Watts of energy. A flat-screen TV uses about 150 Watts. If you are gaming for 4 hours a day 5 times a week for a year, how much will that cost you if you pay 5 cents/kWh? Your answer should have $/kWh as the unit. *
\(\huge\star{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}\star\)
regardless of the time used your
energy will cost $0.05/kWh
your annual energy use will cost
$15.08
The problem statement tells you the cost
of energy is $0.05/kWh. If those are the
units required for the answer, that is the
answer.
The question, "how much will that cost
you?" suggests the units of the answer
should be dollars (not dollars per kWh). In
that case, we need to know the number
of kWh used during the year. The total
annual cost will be..
(0.14 kW +0.15 kW)4 h/day)(5 day/wk)(52
wk/yr)(1 yr)($0.05/kWh)
= (0.29) 4) (5)(52)($.05) = $15.08
Your cost will be $15.08 for theelectricity for a year.
Which of the following is a correct way to solve 4 = 13 – 3x ?
A. 4 + 13 = 13 - 3x + 13. 17 = -3x. 17/-3 = -3x/-3. x = -17/3.
B. 4 - 13 = 13 - 13 - 3x. -9 = -3x. -9/-3 = -3x/-3. x = 3.
C. 4 - 13 = 13 - 13 - 3x. -9 = -3x. -9/-3 = -3x/-3. x = -3.
D. 4 - 13 = 13 - 13 - 3x. -9 = -3x. -9/3 = -3x/3. x = -3.
The solution of the equation 4 = 13 – 3x is x = 3 which is the correct answer would be an option (B).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
We have been given an equation as
4 = 13 – 3x
Rearrange the terms non-variables and variables,
3x = 13 - 4
Apply the subtraction operation,
3x = 9
x = 9/3
Apply the division operation, and we get
x = 3
Therefore, the correct answer would be an option (B).
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A recipe requires 1/4 of a cup of cranberries for 1 batch of scones. How many batches of scones can be made using 6 1/2 of cranberries?
A 13/8 Batches
B 24Batches
C 24 1/2 Batches
D 26 Batches
If you need the pic to it let me know it's due soon and I can't figure it out bc I'm not good at math what so ever
Answer:
Im pretty sure its 26, sorry if im wrong.
Need help with this!
The output of the function call doWork(30) is given as follows:
9.
How to obtain the output of the function?The input of the function is given as follows:
n = 30.
Hence we apply the recursion as follows:
doWork(30) -> return 1 + doWork(15).doWork(15) -> return 1 + doWork(7) -> integer part of the division is 7.doWork(7) -> return 7 -> less than 10.Now we apply the inverse procedure, as follows:
doWork(15) -> return 1 + 7 = 8.doWork(30) -> return 1 + 8 = 9.More can be learned about recursive functions at https://brainly.com/question/30645557
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What is the area of ABC?
This value is approximate.
=========================================================
Work Shown:
area = 0.5*side1*side2*sin(included angle)
area = 0.5*AB*AC*sin(A)
area = 0.5*11*18*sin(55)
area = 81.0960523846101
area = 81.1 cm^2
The cm^2 refers to "square cm".
Notice that the angle must be between the two sides, hence the "included".
Convert the angle measures.
17. 120° to radians.
After conversion we get,
17. 120° = 0.2988 radian.
The given measure is,
17.20 degree
A radian is a unit of measurement for angles. Angles are measured using two units: degrees and radians. You may have been using degrees to measure the sizes of angles up to this point. Angle measures in advanced mathematics, on the other hand, are typically described using a unit system other than the degree system for a variety of reason.
A single radian, as seen here, is about equal to 57.296 degrees. When we wish to compute the angle in terms of radius, we use radians instead of degrees. In the same way that '°' is used to denote a degree, rad or c is used to represent radians. 1.5 radians, for example, is written as 1.5 rad or 1.5c.
Then 1 degree = 0.0175 radian
Now,
17.120 degree = 0.0175x17.120
= 0.2988 radian.
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thankssss plzzz helpp
PLEASE HELP I WILL GIVE BRAINLIEST!!!
1. Inconsistent
2. Consistent
3. The graph of the system of equations is at B
4. The graph of the system of equations is at C
5. The solution of the equation is b
How to solve using opposite coefficients methodThe system of equation required to be solved are
x - 9y = 2 ----1
3x - 3y = -10 ----2
Multiplying (1) by 3 and subtracting 2 from it
3x - 27y = 6
3x - 3y = -10
0 - 24y = 16
solving for y
y = 16 / -24 = -2/3
solving for x by substituting y into 1
x - 9 * -2/3 = 2
x + 6 = 2
x = -4
hence the solution is (-4, -2/3)
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A normally distributed quality characteristic is monitored through the use of an ¯x and
an R chart using rational subgroups of size 4. The center line for the ¯x chart is CL = 151:0
and that for the R chart is CL = 4:1. Both charts exhibit control.
a) What are the estimated mean and standard deviation of the process?
b) What are the UCL and LCL for both charts?
c) Suppose the specifications are 1505. What is the estimated fraction nonconforming?
d) Assuming that the process mean can be easily adjusted but the standard deviation
can’t, what can the fraction nonconforming be reduced to?
e) Calculate the out-of-control ARL assuming the mean shifts to 153.0
a. The estimated mean is the center line of the ¯x chart CL= 151.0 and standard deviation of the process is 1.992
b. The UCL and LCL for ¯x chart is 153.37 and 148.63, for the R chart 9.322 and 0, respectively
c. The estimated fraction nonconforming is 41.8%.
d. The fraction nonconforming be reduced to 146.03
e. The out-of-control ARL assuming the mean shifts to 153.0 is 73.4 subgroups
a) The estimated mean of the process is the center line of the ¯x chart, which is CL = 151.0. The estimated standard deviation of the process can be calculated using the R chart. From the R chart, the average range is 4.1. Since the subgroup size is 4, we can estimate the standard deviation of the process as:
sigma = Rbar/d2 = 4.1/2.059 = 1.992
b) The UCL and LCL for the ¯x chart can be calculated using the formula:
UCL = CL + A2Rbar = 151.0 + 0.5774.1 = 153.37
LCL = CL - A2Rbar = 151.0 - 0.5774.1 = 148.63
The UCL and LCL for the R chart can be calculated using the formula:
UCL = D4Rbar = 2.2824.1 = 9.322
LCL = D3Rbar = 04.1 = 0
c) The estimated fraction nonconforming can be calculated using the process capability index Cp, which is the ratio of the specification width to the process width:
Cp = (USL - LSL)/(6sigma) = (150 - 145)/(61.992) = 0.418
The estimated fraction nonconforming is approximately 41.8%.
d) Since the standard deviation cannot be reduced, the only way to reduce the fraction nonconforming is to shift the process mean. The new Cp can be calculated using the formula:
Cp' = (USL - μ)/(3sigma) = (150 - μ)/(31.992)
We want to find the mean μ that will result in a Cp' of 2.0, which is considered to be a reasonable target for process capability. Therefore:
2.0 = (150 - μ)/(3*1.992)
μ = 146.03
The process mean would need to be shifted to 146.03 to achieve a fraction nonconforming of 0.0027, which corresponds to a Cp' of 2.0.
e) The out-of-control average run length (ARL) can be calculated using the following formula:
ARL = \([1/(1-\alpha )][(1-\alpha )^{(k-1)}][(1+\alpha /2)^h]\)
where α is the Type I error rate, k is the number of standard deviations from the center line, and h is the number of points beyond the control limits. Assuming a 3-sigma shift, k = 3 and h = 1. For a standard α = 0.05, the ARL is:
ARL = [1/(1-0.05)][(0.05/0.95)²][(1+0.05/2)¹] = 73.4
Therefore, on average, it would take 73.4 subgroups or 293.6 individual measurements to detect an out-of-control condition.
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What is the area of square DEFG?ILL GIVE BRAINLIEST
Answer:
4 sq units
Step-by-step explanation:
2 un x 2 un = 4 sq uints
mixed in a drawer are blue socks, white socks, and gray socks. you pull out two socks, one at a time, without looking. find the probability of getting 2 socks of the same color.
The probability of getting 2 socks of the same color given by the following solution is 65/132.
Beginning with the first sock, we have three options: blue, white, or grey. If we wanted to know the likelihood of drawing only one blue sock, we might divide the number of blue socks in the drawer by the total number of socks (2 / 12).
We have three options for the second sock: blue, white, or grey. Keep in mind that we are drawing without replacement, so there is now one fewer sock in the drawer. Thus, with three alternatives for the first sock and three options for the second sock, the total number of combinations is three times three, or nine. The following are all of the potential combinations: (blue, blue), (blue, white), (blue, grey), (white, blue), (white, white), (white, grey), (white, blue), (white, white), (white, grey), (grey, blue), (grey, white) (gray, gray).
So the probability of 2 socks of the same color is, in equation form:
P(2 socks of same color) = P(blue sock first) * P(blue sock second) + P(white sock first) * P(white sock second) + P(gray sock first) * P(gray sock second).
= 2/12*1/11 + 4/12*3/11 + 6/12*5/11
= 65/132
Therefore, the probability of getting 2 socks of the same color 65/132.
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Complete question:
Mixed in a drawer are 2 blue socks, 4 white socks, and 6 gray socks. You pull out two socks, one at a time, without looking. Find the probability of getting 2 socks of the same color.
Find the equation of the linear function x 0 1 2 3 4 y -4 -2 0 2 4
Answer:
its counting down
Step-by-step explanation:
because it was in the positives and went down to the negatives
What is the sum of 15 and the square root of 144?
Answer:
27 pls mark me branilest
Answer:
27
Step-by-step explanation:
Hi there!
\(15+\sqrt{144}\)
The square root of 144 is 12:
\(= 15+12\)
\(= 27\)
I hope this helps!
Simplify.
4727 + 6V75
Answer:
1+1
Step-by-step explanation:
During gym , your "friend" is standing 5 meters from you and throws a ball at your face. It hits you in approximately 1. 2 seconds. What is the velocity of the ball?
The velocity of the ball thrown by your friend is approximately 4.17 meters per second.
To ascertain the speed of the ball, we want to utilize the condition of movement that relates distance, time, and speed increase. For this situation, we expect that the ball goes in an orderly fashion, and its speed increase is because of the power applied by your companion's toss. We can utilize the recipe:
distance = speed x time
We realize that the distance among you and your companion is 5 meters, and the time taken for the ball to travel that distance is 1.2 seconds. Hence, we can revise the equation to tackle for the speed:
speed = distance/time
Subbing the qualities, we get:
speed = 5/1.2 = 4.17 meters each second (approx.)
So the speed of the ball tossed by your companion is around 4.17 meters each second.
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A department store sells a pair of shoes with an 87% markup. If the original price of the shoes was $103, what is the selling price of the shoes
Answer:
Step-by-step explanation:
103x.87=89.61
103+89.61=192.61
Write an equation in point slope form for the line that passes through the point with the given slope (-7,-3) m=2
8−4(−x+5) A: 4x-12 B: -4x- 12 C: 4x + 13 D: 4x + 5
Step-by-step explanation:
8-4(-x + 5)
8 + 4x - 20
4x - 12
Where did the formula for summing finite geometric series come from? Suppose the geometric series has first term a₁ and constant ratio r , so that S n= a₁ + a₁r+ a₁ r²+ . . +a₁ rⁿ⁻¹
b. Use part (a) to show that S n -r S n = a₁ - a₁ rⁿ .
The formula for summing a finite geometric series is derived through algebraic manipulations and telescoping series. Sₙ - rSₙ = a₁ - a₁rⁿ.
The formula for summing finite geometric series can be derived using algebraic manipulations and properties of geometric progressions. Here's how we can derive the formula:
Let's consider a geometric series with the first term a₁ and a common ratio r. The series can be expressed as:
Sₙ = a₁ + a₁r + a₁r² + ... + a₁r^(n-1)
Now, let's multiply both sides of this equation by the common ratio r:
rSₙ = a₁r + a₁r² + a₁r³ + ... + a₁rⁿ
Next, subtract the second equation (rSₙ) from the first equation (Sₙ):
Sₙ - rSₙ = (a₁ + a₁r + a₁r² + ... + a₁r^(n-1)) - (a₁r + a₁r² + a₁r³ + ... + a₁rⁿ)
If we look closely at the terms on the right side, we can see that they form a telescoping series. The terms cancel out except for the first term (a₁) and the last term (a₁rⁿ). Therefore, the right side simplifies to:
Sₙ - rSₙ = a₁ - a₁rⁿ
Now, let's factor out Sₙ on the left side:
Sₙ(1 - r) = a₁ - a₁rⁿ
Finally, divide both sides by (1 - r) to solve for Sₙ:
Sₙ = (a₁ - a₁rⁿ) / (1 - r)
This is the formula for summing a finite geometric series.
In part (b) of the question, we are asked to use part (a) to show that Sₙ - rSₙ = a₁ - a₁rⁿ. By substituting the formula for Sₙ from part (a) into the left side of the equation, we have:
(a₁ - a₁rⁿ) / (1 - r) - r(a₁ - a₁rⁿ) / (1 - r)
To simplify further, we can factor out a common term of (a₁ - a₁rⁿ) from both fractions:
(a₁ - a₁rⁿ) * [(1 - r) - r] / (1 - r)
Simplifying the numerator:
(a₁ - a₁rⁿ) * (1 - r - r) / (1 - r)
(a₁ - a₁rⁿ) * (1 - 2r) / (1 - r)
Now, we have the expression (a₁ - a₁rⁿ) * (1 - 2r) / (1 - r) which is equal to the right side of the equation. Therefore, we have shown that Sₙ - rSₙ = a₁ - a₁rⁿ using the formula derived in part (a).
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Under her cell phone plan, Julieta pays a flat cost of $61.50 per month and $5 per gigabyte. She wants to keep her bill at $78 per month. Write and solve an equation that can be used to determine gg, the number of gigabytes of data Julieta can use while staying within her budget.
find the length of the diagonals of rectangle QRST
Answer: 11: 26
12: 111
Step-by-step explanation:
Answer:
11:
since diagonal are equal of rectangle
QS=RT
4x+6=6x-4
6+4=6x-4x
2x=10
x=10/2
x=5
now
diagonal :4x+6=4*5+6=26
12.
again
QS=RT
9x+12=11x-10
12+10=11x-9x
2x=22
x=11
now
diagonal=9*11+12=99+12=111
A new car is purchased for $23,000 and over time its value depreciates by one half every 3 years. How long, to the nearest tenth of a year, would it take for the value of the car to be $7,800 (25 PTS)
It take for the value of the car is 4.7 years.
Now, According to the question:
A new car is purchased for $23,000
and, over time its value depreciates by one half every 3 years.
It take for the value of the car to be $7,800.
According to the statement :
The equation will be :
y = 23,000 × \((\frac{1}{2} )^n\)
7,800 = 23,000 × \((\frac{1}{2} )^n\)
By simplification, we get:
n = 1.56
Over time its value depreciates by one half every 3 years.
So, 1.56 × 3 = 4.68 ≈ 4.7 years.
Hence, It take for the value of the car is 4.7 years.
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Name an outcome that has a probability between 0 and 0.5.