x = 15/2
Step-by-step explanation:
Step 1: Add 1 to both sides.
2/3x − 1 + 1 = 4 + 1
2/3x = 5
Step 2: Multiply both sides by 3/2.
(3/2) * (2/3x) = (3/2) * (5)
x = 15/2
How many different 10-letter arrangements are possible using the letters in the word AUTOMOBILE?
Answer:
1,814,400
Step-by-step explanation:
the formula would be: nPr / x_1 ! x_2!....
since there are 2 O's and it is a 10-LETTER ARRANGEMENT, the equation would now be:
10P10 / 2!
10P10 would simplify down to 10! so you would have :
10! / 2!
if you simplify this above: you would get 1,814,400
Please Help. Lateena solved the equation below. Is her solution correct? Explain why or why not?
I've attached the picture for the problem.
Answer:
Not correct
Step-by-step explanation:
Given:
x² - 6x - 7 = 0
The following equation can be solved correctly by factoring Thus,
x² - x + 7x - 7 = 0
x(x - 1) +7(x - 1) = 0
(x - 1)(x + 7) = 0
(x - 1) = 0
x - 1 = 0
x - 1 + 1 = 0 + 1
x = 1
Or
(x + 7) = 0
x + 7 = 0
x + 7 - 7 = 0 - 7
x = -7
Therefore, the solution would be x = 1 or x = -7
Lateena solution is therefore NOT CORRECT because she used a wrong method.
Lee's goal is to log more
than 10,000 steps each day. If
she is awake 16 hours a day,
how many steps does she need
Ito take each hour?
Answer: 625 steps per hour
Step-by-step explanation:
10,000/16=625
3x + 7y = 21 –3x – 7y = 42
Solve the system of equations?
9514 1404 393
Answer:
no solution
Step-by-step explanation:
The equations describe parallel lines. There are no values of x and y that will satisfy both equations.
In standard form, the two equations are ...
3x +7y = 21
3x +7y = -42 . . . . . with positive leading coefficient
If (x, y) values satisfy the first equation, they cannot satisfy the second equation, and vice versa.
A survey showed that 40% of students would select the Ferris Wheel as their favorite ride in the amusement park. How many students out of 5,000 would you predict would prefer the Ferris Wheel?
Group of answer choices
2,400
3,000
2,000
1,250
Answer:
2000
Step-by-step explanation:
40/100 * 5000 = 2000
In a histogram, the ________
consists of intervals or ranges.
I really should pay more attention in class....
The height corresponding to the longest side of the triangle whose sides are 42cm,
34cm and 20cm in length is ?
plz help me urgently
Answer:
sdufbjdfjkwjhevjhvdwhdvbj tsm thank you for the points
e
Step-by-step explanation:
Answer:
ty for the points.
Step-by-step explanation:
find the principle of money if intrest in 3 years with 5 percent per annum is rs 300
Answer:
HI from Nepal
Answer:
let principal be x
interest =Rs300
time=3 years
rate=5%
To find principal use formula,
Interest=P*T*R/100
Rs300=x*3*5/100
Rs300*100=15x
Rs30000=15x
Rs30000/15=x
Rs2000=x
Step-by-step explanation:
therefore principal=Rs 2000
you start driving east with 14 miles turn left and Drive North for another 10 miles at the end of driving what is your straight line distance from your starting point
Answer:
17.205 miles
Step-by-step explanation:
Since these directions form a 90-degree angle, we can use the Pythagorean Theorem.
14^2 + 10^2 = c^2
196 + 100 = c^2
296 = c^2
It doesn't have a perfect square root, you can either say that it is [tex]\sqrt{296}[/tex] or approximately 17.205 miles.
The maintenance department at the main campus of a large state university receives daily requests to replace fluorescent light bulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 43 and a standard deviation of 11. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 10 and 43
Answer:
The approximate percentage of lightbulb replacement requests numbering between 10 and 43 is of 49.85%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 43
Standard deviation = 11
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above the mean.
What is the approximate percentage of lightbulb replacement requests numbering between 10 and 43?
43 is the mean
10 = 43 - 3*11
So 10 is 3 standard deviations below the mean.
Of the 50% of measures below the mean, 99.7% are between 3 standard deviations below the mean(10) and the mean(43). So
0.5*0.997 = 0.4985.
0.4985*100% = 49.85%.
The approximate percentage of lightbulb replacement requests numbering between 10 and 43 is of 49.85%.
An elevator has a placard stating that the maximum capacity is 1600 lb�10 passengers. So, 10 adult male passengers can have a mean weight of up to 1600/10=160 pounds. If the elevator is loaded with 10 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 160 lb. (Assume that weights of males are normally distributed with a mean of 166 lb and a standard deviation of 29 lb.)
1.The probability the elevator is overloaded is?
*-Please show work to help me understand-*
2. Does this elevator appear to be safe?
A.Yes, there is a good chance that 10 randomly selected people will not exceed the elevator capacity.
B. No, 10 randomly selected people will never be under the weight limit.
C.Yes, 10 randomly selected people will always be under the weight limit.
D.No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.
Answer:
1. 0.7421 = 74.21% probability the elevator is overloaded.
2. D.No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Assume that weights of males are normally distributed with a mean of 166 lb and a standard deviation of 29 lb.
This means that [tex]\mu = 166, \sigma = 29[/tex]
Sample of 10.
This means that [tex]n = 10, s = \frac{29}{\sqrt{10}}[/tex]
1.The probability the elevator is overloaded is?
Probability that the sample mean is above 160 pounds, which is 1 subtracted by the p-value of Z when X = 160. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{160 - 166}{\frac{29}{\sqrt{10}}}[/tex]
[tex]Z = -0.65[/tex]
[tex]Z = -0.65[/tex] has a p-value of 0.2579.
1 - 0.2579 = 0.7421
0.7421 = 74.21% probability the elevator is overloaded.
2. Does this elevator appear to be safe?
High probability of the elevator being overloaded, so not safe. Correct answer is given by option D.
In which quadrant of the coordinate plane is the point (−7,−212) located?
1. Quadrant I
2. Quadrant II
3. Quadrant III
4. Quadrant IV
Answer:
Quadrant 3
Step-by-step explanation:
Please help
Find the Arc Length of arc b, given the radius is 5 cm.
Answer:
Arc length= 180/360 ( 2 pi × 5cm)180/360 (2 ×22/7×5cm)
18/36=1/2× 2×22/ 7 ×5cm
1×22/7×5cm
22/7×5cm
110/7
=15.715cm
HELP ME PLEASEEEEEEEEEEEE
Answer:
20 feet
Step-by-step explanation:
[tex]1)\ A = \frac{b * h}{2}[/tex]
[tex]2)\ 120 = \frac{12b}{2}[/tex]
[tex]3)\ 12b = 240[/tex]
[tex]4)\ b = 20[/tex]
Parker Moore is single and pays into an HMO. The total cost is $8,550 annually and the employer pays 90 % of the total cost . Parker also pays 50% of the optional annual dental premium of $782. How much is deducted each week from his paycheck ?
Answer:23.96
Step-by-step explanation:
100-90=10%
10/100=0.10
0.10(8550)=855
100-50=50%
50/100=0.50
0.50(782)=391
855+391=1246
1246/52=23.96
I need help graphing the right points so please send a picture of the graph also
In the xy-coordinate plane, the graph of the equation y = 3x2 - 12x – 36 has zeros
at x = a and x = b, where a
Part A: Graph the function.
Answer:
you cant send pictures unless created on a graphing website but ill try to help. you first have to simplify y, and if you could comment a clearer equation that would be nice because your equation is confusing(cant tell if its all together
Convert x^2+ (y + 8)^2= 64 to a polar equation that
expresses r in terms of theta.
Answer:
their graphed
Step-by-step explanation:
A rectangular prism that has a width of 3 1/2 what is the width of the prism in terms of cubes?
Answer:
84 cubes :)
Step-by-step explanation:
What is the surface area of the triangular prism? 1 5ft 3 ft 5 ft 4 ft
Answer:
134
Step-by-step explanation:
What is the volume of a cylinder with a base area of 23 cm2 and a height of 15 cm
Answer:
V =345 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = Bh where B is the base and h is the height
V= 23 * 15
V =345 cm^3
Answer:
345cm³
Step-by-step explanation:
AB h = 23 x15
= 345cm³
Your welcome!
902
If the probability that a person will die in the next year is
what is the
100,000'
probability that the person will not die in the next year?
A. 0.902%
B. 99.098%
C. 0.098%
D. 99.902%
Answer:
B. 99.098%
Step-by-step explanation:
The probability that the person will not die in the next year is 99.098% .
Correct option is B.
What is probability?Measure of the likelihood of an event happening is called Probability. Probability can be between 0 to 1. 0 means the event cannot happen, 1 indicates the specific event. The sum of the probabilities of all events in the sample space is 1.
Probability can be defined as the ratio between the number of favorable outcomes and the total number of outcomes of an event. For a trial with “n” number of results, the number of favorable outcomes can be denoted by x. The formula for calculating the probability of an event is as follows.
Probability (Event) = Favorable Outcome/Total Outcome = x/n
Given,
Probability of a person will die next year = 902/100000
sum of the probabilities of all events in the sample space is 1.
Then probability of the person will not die in the next year
= 1 - 902/100000
= 1 - 0.00902
= 0.99098
= 0.99098 × 100/100
= 99.098%
Hence, 99.098% is the probability that the person will not die in the next year.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ7
5. Michelle sells flowers for weddings. The
price she charges (P) can be approximated by
the equation: P = 40 + 12d , where d
represents how many dozens of flowers are
ordered. Ann paid Michelle $400 for the
flowers at her wedding. How many dozens of
flowers did Ann order?
A. 37
B. 30
C. 25
D. 22
Answer:
B. 30
Step-by-step explanation:
since Ann paid $400, you set the equation equal to 400
400=40+12d
Then you solve for d to find how many dozen of flowers Ann ordered.
400-40=12d
360=12d
360/12=d
d=30
Which expressions correctly represent the area of the triangle XYZ?
Answer:
Options (2) and Option (1)
Step-by-step explanation:
Area of the ΔXYZ = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(XZ)h[/tex]
= [tex]\frac{1}{2}(18)h[/tex]
By applying sine rule in the ΔYPZ,
sin(38°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sin(38°) = [tex]\frac{h}{14}[/tex]
h = 14[sin(38°)]
Therefore, area of the given triangle = [tex]\frac{1}{2}(18)(14)sin(38)[/tex]
By applying sine rule in ΔYPZ,
sin(58°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sin(58°) = [tex]\frac{h}{10}[/tex]
h = 10sin(58°)
Area of ΔXYZ = [tex]\frac{1}{2}(18)(10)sin(58)[/tex]
Therefore, Options (2) and Option (1) are the correct options.
Write the slope intercept form of this equation 7x-5y=35
a ladybug moves 1/25 of a mile in 3/5 of an hour. if the lady bug continues at this pace how far in miles doesbit move in one hour
Answer:
1/15 mile
Step-by-step explanation:
(1/25) / (3/5)
When dividing by a fraction flip it over and multiply
(1/25) * (5/3) = 5/75
Reduce
1/15 mile
Please help me with this
Answer:
1.) The quotient of a number and 2 = x ÷ 2
2.) A number decreased by 2 = x - 2
3.) 2 times a number = 2x
4.) 2 increased by a number = 2 + x
Step-by-step explanation:
Let's look for key words hidden in these sentences:
1.) The quotient of a number and 2 = The word quotient refers to division
2.) A number decreased by 2 = The word decreased refers to subtraction
3.) 2 times a number = the word times refers to multiplication
4.) 2 increased by a number = the word increased refers to addition
Hope this helps!
HELPP FAST!! Will mark brainliest
Answer:
No
Step-by-step explanation:
Because it is not going up by the same amount everytime
negative x plus 1 is less than 5
Answer:
-x+1 < 5
Step-by-step explanation:
Not sure what the question is?
Answer:
-x + 1 < 5
Step-by-step explanation:
negative x plus 1 is less than 5
-x + 1 < 5
-TheUnknownScientist
A pharmaceutical sale representative gets paid $50,000 annually plus 3.5% commissions on total sales. This year he sold $420,000 in pharmaceuticals. What are his annual total earnings? someone help pls
Answer:
[tex] \frac{3.5}{100} \times 420000 = 14700commission \\ total \: earnings = 50000 + 14700 \\ = 64700[/tex]
3. Find the value of x.
(2x-71
Answer:
33
Step-by-step explanation:
2x-7 = 73
2x = 73-7
2x = 66
x = 66÷2
x = 33
Therefore, the value of x is 33