Answer:
Y = 0
X= 1/2
Z = -1/2
Step-by-step explanation:
4x-y+ 2z=-1
-x+y-3z= 1
-x+2y + 5z = 2
Solving simultenously
Y= 4x + 2z -1
Y =1+ 3z+ x
Y =x/2 -( 5z/2) - 1
Equating y will give two equations
3x-z = 2
3x + 11z = -4
Subtracting the equations
-12z =6
Z= -1/2
Substituting z
3x +1/2 = 2
3x = 3/2
X= 1/2
Substituting x and z to find y in
-x+y-3z= 1
-1/2 + y +3/2 = 1
Y = 1-1
Y = 0
Answer: b) is answer
Step-by-step explanation:
Suppose that a storm front is traveling at 33 mph. When the storm is 13 miles away a storm chasing van starts pursuing an average speed of 54 mph. How long does it take for the van to catch up with the storm? How far have they driven? (Hint: we can let our two variables be x= distance and t= time. Additionally, [speed x time= distance]. Won’t the van catch up when the distances are equal?
Please make it easy to understand your answer :)
Answer:
Time = X = 37.14 minutes
Distance they covered= 33.42 miles.
Step-by-step explanation:
Distance= speed * time
And the distance traveled by the two need to be equal.
Speed of storm = 33 mph
Speed of van = 54 mph
But storm is 13 miles away from van.
So
54*x = 33*x+ 13
54x-33x = 13
21x = 13
X= 0.62 hours
X = 37.14 minutes
54 *0.62= 33.42 miles.
Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 18 specimens of a particular species, 5 resprouted after fire. Estimate with 99.5% confidence the proportion of all shrubs of this species that will resprout after fire.
Answer:
The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 18, \pi = \frac{5}{18} = 0.2778[/tex]
99.5% confidence level
So [tex]\alpha = 0.005[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.005}{2} = 0.9975[/tex], so [tex]Z = 2.81[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 - 2.81\sqrt{\frac{0.2778*0.7222}{18}} = -0.01 = 0[/tex]
We cannot have a negative proportion, so we use 0.
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 + 2.81\sqrt{\frac{0.2778*0.7222}{18}} = 0.5745[/tex]
The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).
How many 3-letter codes can be formed if the second letter must be a vowel (a, e, i, o, u)?
Answer:
3,380 combinations
Step-by-step explanation:
26*5*26= 3,380
Answer:
3380
Step-by-step explanation:
Since there are 26 letters, it would be
26*5*26
This is 3380
Solve 4x+5≥-23. show your work
Answer:
x≥-7
Step-by-step explanation:
4x+5≥-23
Subtract 5 from each side
4x+5-5≥-23-5
4x≥-28
Divide each side by 4
4x/4≥-28/4
x≥-7
Answer:
X≥-7
Step-by-step explanation:
Step 1: Subtract 5 from both sides.
4x+5-5≥-23-5
4x ≥-28
Step 2: Divide both sides by 4.
4x/4 ≥-28/4
X ≥-7
An amount was invested at r% per quarter. What value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places
Answer:
25.75 % interest rate
Step-by-step explanation:
Given:
Amount was invested = r% per quarter
Amount invested = P
Rate of interest = r % per quarter
Time (n) = 4 Quarters
Computation:
A = P(1 + r/100)ⁿ
According to question.
⇒ A = P + 1.5P = 2.5P
⇒ 2.5P = P(1 + r/100)⁴
⇒ 2.5 = (1 + r/100)⁴
⇒ 1 + r/100 = 1.2575
⇒ r/100 = 0.2575
⇒ r = 25.75
25.75 % interest rate
You play a game that requires rolling a six sided die then randomly choosing a card from a deck containg 8 red cards ,6 blue cards and 8 yellow cards whats the probability that younroll a 3 on the due and choose a red card
Answer:
2/33
Step-by-step explanation:
Probability that a 3 is rolled on the die = 1/6 (equal chance of rolling any number)
Probability of choosing a red card = 8/22 (8 red cards, 22 cards in total)
8/22 = 4/11
Probability of rolling a 3 AND choosing a red card = 1/6 x 4/11
= 4/66
= 2/33
Suppose Carol Danvers invested $1,000 into an account paying 6% annual interest compounded
annually.
How much is in her account at the end of one year?
Answer:
$ 1,060.00
Step-by-step explanation:
A = $ 1,060.00
A = P + I where
P (principal) = $ 1,000.00
I (interest) = $ 60.00
Compound Interest Equation
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
Which expression best represents the situation?
Select the expression that best matches the scenario.
O4 + x + 3
4(x + 3)
4.3
4x + 3
Tyson bought a burger for himself and
each of his 3 friends. He left a tip of $3.
Which expression could represent
the amount of money Tyson spent?
Explain your thinking.
Help plz
Answer:509
Step-by-step explanation:600
A store has 80 modems in its inventory, 30 coming from Source A and the remainder from Source B. Of the modems from Source A, 20% are defective. Of the modems from Source B, 8% are defective. Calculate the probability that exactly two out of a sample of five modems selected without replacement from the store’s inventory are defective.
Answer:
0.102
Step-by-step explanation:
The number of defective modems in the inventory is 20% * 30 + 8% * 0.50 =10 (out of 80)
Note that the number of defectives in the inventory is fixed i.e. we are told that there is 1/8 probability that a modem in the inventory is defective, but rather that exactly 1/8 of all modems are defective.
The probability that exactly two modems in a random sample of five are defective is :
(10↓2)(70↓3) / (80↓5) = 0.102
Rachel owns as twice as many beanie babies as Kaye. Alexia owns 1/3 as many beanie babies as Rachel. If Kaye owns 63 beanie babies,how many does Alexia owns?
Answer:
42
Step-by-step explanation:
Let the number of beanie babies Kaye has be x
according to question
Rachel owns as twice as many beanie babies as Kaye
number of beanie babies Rachel has : 2*x = 2x
Also,
Alexia owns 1/3 as many beanie babies as Rachel
number of beanie babies Alexia has : 1/3(2x) = 2x/3
It is given that Kayes has 63 beanie babies
thus x = 63
Thus,
Number of beanie babies Alexia has = 2x/3 = 2*63/3 =2*21 = 42
Please help meee
Which number line model represents the expression -2/5 + 4/5:
The number line model that represents the expression -2/5 + 4/5 is: Option B
How to solve Inequality on number line?
To plot an inequality, such as x > 2, on a number line, first draw a circle over the number (e.g., 2). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in.
Now, in this case, the operation to solve is:
-2/5 + 4/5
Solving this gives 2/5
Now, since the operation shows a negative and positive fraction with the solution being positive, then we can easily say that Option B is the correct answer to the problem
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Which of the following are solutions to the quadratic equation? Check all that apply x^2 + 12x + 36 = 7
Answer:
x = -6 + [tex]\sqrt{7}[/tex], x = -6 - [tex]\sqrt{7}[/tex]
Step-by-step explanation:
(x + 6)² = 7
x + 6 = + or - [tex]\sqrt{7}[/tex]
x = -6 + [tex]\sqrt{7}[/tex], x = -6 - [tex]\sqrt{7}[/tex]
The solution of the quadratic equation is x = -6 +√7, x = -6 - √7.
What is a quadratic equation?A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Completing the square entails writing a quadratic in the form of a squared bracket and, if necessary, adding a constant. Finding the maximum or minimum value of the function and when it occurs is one application of completing the square.
Given that the quadratic equation is x² + 12x + 36 = 7.
(x + 6)² = 7
x + 6 = ±√7
x = -6 + √7 , x = -6 - √7
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Please help this is urgent!
Answer:
Isosceles
Obtuse
Step-by-step explanation:
1) When two sides of a triangle are the same length, the triangle is an isosceles triangle.
2) When one angle of the triangle is greater than 90 degrees, the triangle is an obtuse triangle.
I hope this helps! Have a great day!
Answer:
Isosceles, obtuse
Step-by-step explanation:
There are three types of triangles based on their sides:
Equilateral: a triangle with 3 equal sidesIsosceles: a triangle with 2 equal sidesScalene: a triangle with no equal sidesThis triangle here as sides of 28 cm, 16 cm, and 16 cm
This triangle has two equal sides of 16 cm, indicating it is an isosceles triangleThere are three types of triangles based on their angles:
Acute: when all angles are less than 90° Right: when the triangle has one angle that is 90° Obtuse: when one of the angles is greater than 90°This triangle has angles of 26°, 26°, and 128°
This triangle has one angle that is greater than 90° → 128°, indicating that this is an obtuse triangleAccording to the U.S. Census Bureau, the mean of the commute time to work for a resident of Boston, Massachusetts, is 27.3 minutes with a standard deviation of 8.1 minutes. What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean
Answer:
By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean
By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean
95% of commuters in Boston has a commute time within 2 standard deviations of the mean
Empirical ruleEmpirical rule states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean.
Hence, 95% of commuters in Boston has a commute time within 2 standard deviations of the mean
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An appliance repairman charges $25 plus $40 per hour for house calls. Write the rule as an equation that relates hours worked x and his fee y.
To get the total fee, you need to multiply the hourly rate by number of hours worked and add that to the flat fee of $25.
The equation would be y = 40x + 25
A textile manufacturer has historically found an average of 0.1 flaws per square meter of cloth. Let X be the number of flaws in a bolt of 2000 square meters of cloth. How is X distributed
Answer:
Poisson distribution
Step-by-step explanation:
Given that :
There is an average of 0.1 flaws per square meter of cloth
So X = the number of flaws in a bolt of 2000 square meters of cloth.
The objective is to deduce how is X distributed.
Well, we can say X undergoes Poisson distribution.
Because, the flaw can be randomly positioned on the cloth and also dictate how many times the event is likely to occur within a specified period of time.
Most time Poisson distribution is majorly used for independent events.
An independent is an event which contains two types of events occuring at a time say event [tex]E_1[/tex] and event [tex]E_2[/tex] and the event [tex]E_1[/tex] does not in any way affects the occurrence of the event [tex]E_2[/tex] .
Bob has 54 more five-dollar bills than ten-dollar bills. The number of five-dollar bills he has
is 7 times that of ten-dollar bills. How many dollars does Bob have in all?
Answer:5000 sum
Step-by-step explanation:
Solve x for the diagram below.
Answer:
20°
Step-by-step explanation:
These angles add up to 90° so we have:
x + 2x + x + 10 = 90
4x + 10 = 90
4x = 80
x = 20°
express 0.8342 as a fraction A: 8342/10 B: 8342/1000 C: 8342/10000
Answer:
[tex]\frac{8342}{10000} \\ [/tex]
Answer C is correct
Step-by-step explanation:
[tex]0.8342 = \frac{8342}{10000} [/tex]
To check whether this correct or wrong.
[tex]0.8342 \times 10000 = 8342[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The decimal 0.8342 expressed as a fraction is (c) 8342/10000
How to express the decimal 0.8342 as a fraction.From the question, we have the following parameters that can be used in our computation
The decimal 0.8342
Express the decimal 0.8342 as a fraction
So, we have the following representation
Fraction = 8342/10000
When the fraction is simplified, we have
Fraction = 8342/10000
Hence, the decimal 0.8342 as a fraction is (c) 8342/10000
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Use the 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an interval that is expected to contain about 95% of the data values. A bell-shaped distribution with mean 1050 and standard deviation 7.
The interval is to:_______.
Answer:
Intervals = (1,064) , (1,036)
Step-by-step explanation:
Given:
Use 95% method
Mean = 1,050
Standard deviation = 7
Find:
Intervals.
Computation:
95% method.
⇒ Intervals = Mean ± 2(Standard deviation)
⇒ Intervals = 1,050 ± 2(7)
⇒Intervals = 1,050 ± 14
⇒ Intervals = (1,050 + 14) , (1,050 - 14)
⇒ Intervals = (1,064) , (1,036)
The Intervals = (1,064) , (1,036)
Given that:
Use 95% methodMean = 1,050Standard deviation = 7Based on the above information, the calculation is as follows:
Intervals = Mean ± 2(Standard deviation)
Intervals = 1,050 ± 2(7)
Intervals = 1,050 ± 14
Intervals = (1,050 + 14) , (1,050 - 14)
Intervals = (1,064) , (1,036)
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Joseph places $5,500 in a savings
account for 30 months. He earns $893.75
in interest. What is the annual interest
rate?
Answer: About 6.2%
Step-by-step explanation:
He starts with 5500 and gains 893.75 in 2.5 years.
The equation is then 5500*(x)^2.5 = 5500+893.75, or
5500*x^2.5 = 6393.75.
x is about 1.0621, or about 6.2% because it's interest.
Hope that helped,
-sirswagger21
Answer: 137.5%
Step-by-step explanation
Solve 5x^2+3x-4=0 for x using quadratic formula
Answer:
Step-by-step explanation:That would be the answer
What’s the correct answer for this?
Answer:
(2,-2)
Step-by-step explanation:
In the attached file
Aurora saved $850. Ahe used 35% of her savings on a new TV. How much did the TV cost?
Multiply her savings by the percent spent:
850 x 0.35 = 297.50
The tv cost $297.50
Answer:
the price of TV is = 297.5$
Step-by-step explanation:
all money= 850$
purchased money= 35% of all money ==> 850 ( 35%) = 297.5$
When Ravi brought 3 friends to his house after school, his mother gave them a box of pretzels and a box of crackers. She told them to share the snacks equally among themselves and to give her any that were leftover.
The boys opened the boxes and found a total of 26 pretzels and 35 crackers.
How many pretzels and crackers did the boys give to Ravi's
Answer:
6 pretzels and 8 crackers
Step-by-step explanation:
Since his mom told him to give her the remaining, 6*4= 24 giving to his mom 2 pretzels and 8*4=32 so he has to give his mom 3 crackers. This way him and his friends have the same amount of snacks.
Hope you find it useful. Good night
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
7.1
Step-by-step explanation:
d = sqrt(7^2 + -1^2)= sqrt(50)=7.1
Answer:
by using distance formula
putting values
d=√(-1-6)²+(-4--5)²
d=√(-7)²+(1)²
d=√49+1
d=√50
d=5√2=7.1
6500 rounded to the nearest thousand is __. Enter your answer without commas
Answer:
7000
Step-by-step explanation:
If the hundreds place is higher than 5, then add 1 to the thousands place.
Maddie is packing moving boxes. She has one 3 cubic-foot box and one 6 cubic-foot box. How many cubic feet of clothing can she fit in the two boxes?
8 9 10 12
Answer:
She can fit 9 cubic feet of clothing in the two boxes.
Step-by-step explanation:
She can fit a total of 3 cubic feet of clothing in one box, and the other she can fit a total 6 cubic feet.
3 + 6 = 9
Answer:
9 cu ft.
Step-by-step explanation:
That is the sum of the capacities of the 2 boxes
= 3 + 6
= 9 cu ft.
The table represents an exponential function. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 0.25, 0.125, 0.0625, 0.03125. What is the multiplicative rate of change of the function? 0.2 0.25 0.5 0.75
Answer:
0.5 or C on edge2021
Step-by-step explanation:
The multiplicative rate of change of the function will be:
0.5What is a Multiplicative rate of change?The multiplicative rate of change is the common factor that the numbers can be multiplied with to get the succeeding figures.
For instance, if 0.25 is multiplied by 0.5, the result will be 0.125. Also, if 0.125 is multiplied by 0.5, the result will be 0.0625.
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How can you use mathematics to help scientists explore Martian Craters ?
Answer:
Mathematics could make scientists to have a preliminary understanding of the dimensions, perimeters, areas and volumes of different craters on Mars.
Step-by-step explanation:
Martian Craters are series of craters formed on the surface of Mars. The study of a planets crater gives an understanding of the properties of matter that lies under the crater.
Mathematics can be applied to determine the dimensions, perimeter, area and volume of the features of a crater using appropriate conversions and theorems.
The Pi in the sky theorem can be applied to determine the area and perimeter, even volume of different craters on the Mars surface. Also, eingenfunction expansion theorem gives a preliminary knowledge of the craters.
By measurements and conversions processes, the features of Martian crater could be studied from images.