Answer:
x > -4
Step-by-step explanation:
— 3х + 7 < 19
Subtract 7 from each side
— 3х + 7-7 < 19-7
-3x < 12
Divide each side by -3, remembering to flip the inequality
-3x/-3 > 12/-3
x > -4
Just like any of your two-step equations, in this inequality,
start by isolating the x term which in this case is -3x by
subtracting 7 from both sides.
This gives us -3x < 12.
Solving from here, we divide both sides by -3.
However, when solving inequalities, you need to watch out.
When you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign.
Please give this idea your full attention. Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when dividing both sides of an inequality by a negative.
So we end up with x > -4.
Tori needs to make some house repairs in three years that will cost $9,000. She has some money in an account earning 9% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs
Answer:
She needs to have approximately $6950 on that account.
Step-by-step explanation:
Since the account has an interest rate of 9% annually, then it's compounded and the earnings can be found by the following expression:
[tex]M = C*(1 + r)^t[/tex]
Where M is the final amount, C is the initial amount, r is the interest rate and t is the time elapsed in years.
She needs the money in 3 years, therefore t = 3. Applying this to the problem we have:
[tex]9000 = C*(1 + 0.09)^3\\9000 = C*(1.09)^3\\C*1.295 = 9000\\C = \frac{9000}{1.295}\\C = 6949.81[/tex]
She needs to have approximately $6950 on that account.
According to 2013 report from Population Reference Bureau, the mean travel time to work of workers ages 16 and older who did not work at home was 30.7 minutes for NJ State with a standard deviation of 23 minutes. Assume the population is normally distributed.
Required:
a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?
b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.
c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?
Answer:
a) 48.80% probability that his travel time to work is less than 30 minutes
b) The mean is 30.7 minutes and the standard deviation is of 3.83 minutes.
c) 13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes
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 normally distributed samples are solved using the z-score formula.
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.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this question, we have that:
[tex]\mu = 30.7, \sigma = 23[/tex]
a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?
This is the pvlaue of Z when X = 30. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 30.7}{23}[/tex]
[tex]Z = -0.03[/tex]
[tex]Z = -0.03[/tex] has a pvalue of 0.4880.
48.80% probability that his travel time to work is less than 30 minutes
b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.
[tex]n = 36[/tex]
Applying the Central Limit Theorem, the mean is 30.7 minutes and the standard deviation is [tex]s = \frac{23}{\sqrt{36}} = 3.83[/tex]
c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?
This is 1 subtracted by the pvalue of Z when X = 35. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{35 - 30.7}{3.83}[/tex]
[tex]Z = 1.12[/tex]
[tex]Z = 1.12[/tex] has a pvalue of 0.8687
1 - 0.8687 = 0.1313
13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes
help solve the above equation
Answer:
[tex]\dfrac{1}{27}[/tex]
Step-by-step explanation:
[tex]n^{-\frac{2}{3}}=9[/tex]
Rewrite:
[tex]\dfrac{1}{\sqrt[3]{n^2}}=9\\\\9\sqrt[3]{n^2}=1[/tex]
Cube both sides:
[tex]729n^2=1[/tex]
Divide both sides by 729:
[tex]n^2=\dfrac{1}{729}[/tex]
Take the square root of both sides:
[tex]n=\sqrt{\dfrac{1}{729}}=\dfrac{1}{27}[/tex]
Hope this helps!
Bonita said that the product of 5/6 x 1 2/3 is 7/3. How can you tell that her answer is wrong.
Answer:=
1 7/18
Step-by-step explanation:
Turn the improper fraction into a mixed fraction.
the sum of the three numbers in 2003,two of the numbers are 814 and 519 what is the third number
Answer:
idk dont ask me
Step-byi-step explanation:
Answer:
a+b+c=2003
a+b=814
2003-819=189
Step-by-step explanation:
You are at a playground with a see-saw and a large merry-go-round. You put your phone on the see-saw and find it slides when it is tilted at an angle of 38 degrees. How far can you put your phone from the center of the merry-go-round (in m) when it makes one rotation every 3 s
Answer: r_max = 1.75m
Step-by-step explanation:
Below is a rather brief analysis to solving this problem.
The phone starts sliding when along incline,
when F_net = m g sin(theta) - fs_max = 0
and fs_max = us N = us m g cos(theta)
m g sin(theta) - us m g cos(theta) =
us = tan(theta) = tan38 = 0.781
On merry - go - round,
fs_max = us N = us m g
Using F = m a
fs_max = m w^2 r_max and w = 2pi / T
us m g = m (2 pi / T)^2 (r_max)
0.781 x 9.81 = (2 pi / 3)^2 (r_max)
r_max = 1.75 m
cheers i hope this helped !!
One number is 4 plus one half of another number. Their sum is 31. Find the numbers.
Answer:
18, 13
Step-by-step explanation:
x=4+1/2y
x+y=31
4+1/y+y=31
3/2y=27
y=18
x=31-18=13
Answer:
13 & 18
Step-by-step explanation:
Create the formulas:
0.5x+4=y
x+y=31
0.5x+4=y
Multiply both sides by 2
x+8=2y
x+y=31
Subtract 31 from both sides
x+y-31=0
Subtract y from both sides
x-31= -y
Multiply both sides by -1
-x+31=y
Multiply both sides by 2
-2x+62=2y
Combine equations:
-2x+62=x+8
Add 2x to both sides
62=3x+8
Subtract 8 from both sides
3x=54
Divide both sides by 3
x=18
0.5x+4=y
Subtract y from both sides
0.5x-y+4=0
Subtract 0.5x from both sides
-y+4= -0.5x
Multiply both sides by -1
y-4=0.5x
Multiply both sides by 2
2y-8=x
x+y=31
Subtract y from both sides
x= -y+31
Combine equations:
2y-8= -y+31
Add y to both sides
3y-8=31
Add 8 to both sides
3y=39
Divide both sides by 3
y=13
An analysis of 8 used trucks listed for sale in the 48076 zip code finds that the power model ln(\hat{price})=3.748-0.1395ln(miles)ln(price^)=3.748−0.1395ln(miles), for price (in thousands of dollars) and miles driven (in thousands), is an appropriate model of the relationship. If a used truck has been driven for 47,000 miles, which of the following is closest to the predicted price for the truck?(A) $9.46(B) $24.80(C) $3,210.00(D) $9,460.00(E) $24,800.00
Answer:
(E) $24,800.00
Step-by-step explanation:
[tex]ln(\hat{price})=3.748-0.1395ln(miles)[/tex]
If a used truck has been driven for 47,000 miles
Miles=47 (in thousands)
We therefore have:
[tex]ln(\hat{price})=3.748-0.1395ln(47)\\ln(\hat{price})=3.2109\\$Take the exponential of both sides\\e^{ln(\hat{price})}=e^{3.2109}\\Price=e^{3.2109}\\$Price=24.80 \\Since the price is in thousands of dollars\\Price=24.80 X \$1000\\Predicted Price=\$24800.00[/tex]
The correct option is E.
Researchers want to compare the effectiveness of an extract of St. John's Wort with placebo in outpatients with major depression. They recruited 200 adult outpatients diagnosed as having major depression and having a baseline Hamilton Rating Scale for Depression (HAM-D) score of at least 20. Participants were randomly assigned to receive either St. John's Wort extrat, 900 milligrams per day (mg/day) for 4 weeks, increased to 1200 mg/day in the absence of an adequate response thereafter, or a placebo for 8 weeks. The response variable was the change on the HAM-D over the treatment period. After analysis of data, it was concluded that St. John's Wort was not effective for treatment of major depression.
Required:
a. What type of experimental design this is?
b. What is the population that is being studied?
c. What is the response variable in this study?
d. What are the treatments?
e. Identify the experimental units.
f. What is the control group in this study?
Answer:
a) Experimental Design: Randomised Experimental Design
b) Population : All Adult outpatients diagnosed with major depression
c) Responsive Variable : Effectiveness of extracts on depression patients' HAM-D rating
d) Treatments : John Wart extracts or Placebo
e) Experimental units : 200 adult outpatients diagnosed with major depression having HAM-D score > 20
Step-by-step explanation:
a) Randomised Experimental Design is being used : As experimental units are randomly assigned to any of the experimental groups, each receiving different treatments
b) Population refers to the entire group of objects or individuals, to whom the experiment research can be applied. So, all adult outpatients diagnosed with major depression as per HAM-D depression score are population
c) Responsive variable is the dependent variable being affected by independent variables. It is effectiveness of extracts on depression patients, ie change in change on the HAM-D depression rating
d) Treatments are the ways or objects with which experimental units are treated. These are John wart extracts or Placebo
e) Experimental units are the selected sample people or objects for experiment conduct. These are '200' adult outpatients diagnosed with major depression, having a baseline Hamilton Rating Scale for Depression (HAM-D) score > 20
Suppose that a large mixing tank initially holds 100 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 4 lb/gal, determine a differential equation (in lb/min) for the amount of salt A(t) (in lb) in the tank at time t > 0. (Use A for A(t).)
Answer:
dA/dt = 12 - 2A/(100 + t)
Step-by-step explanation:
The differential equation of this problem is;
dA/dt = R_in - R_out
Where;
R_in is the rate at which salt enters
R_out is the rate at which salt exits
R_in = (concentration of salt in inflow) × (input rate of brine)
We are given;
Concentration of salt in inflow = 4 lb/gal
Input rate of brine = 3 gal/min
Thus;
R_in = 4 × 3 = 12 lb/min
Due to the fact that solution is pumped out at a slower rate, thus it is accumulating at the rate of (3 - 2)gal/min = 1 gal/min
So, after t minutes, there will be (100 + t) gallons in the tank
Therefore;
R_out = (concentration of salt in outflow) × (output rate of brine)
R_out = [A(t)/(100 + t)]lb/gal × 2 gal/min
R_out = 2A(t)/(100 + t) lb/min
So, we substitute the values of R_in and R_out into the Differential equation to get;
dA/dt = 12 - 2A(t)/(100 + t)
Since we are to use A foe A(t), thus the Differential equation is now;
dA/dt = 12 - 2A/(100 + t)
334% of what number is 33,400
Answer:
10000
Step-by-step explanation:
3.34x=33400
x=10000
The number is x=10000.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
let, the number = x
now, we get,
3.34x=33400
x=10000
Hence, The number is x=10000.
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What is the equation of the line perpendicular to y = 2/3 x +1 that passes through the point (12, – 6)?
Answer:
y= -3/2x+12
Step-by-step explanation:
the slope of perpendicular lines multiplied together would be -1, so the slope of the perpendicular line is -3/2. y=-3/2x+b, so -6=-18+b, so b= 12. the equation of the line is y=-3/2x+12.
Express 1.8meter in seconds given answer in scientific notation
Answer:
Dear user,
Answer to your query is provided below
Scientific notation = 1.8x10^0
Step-by-step explanation:
This is usually expressed simply as 1.8 (Recall that 10^0 = 1.)
1.8×10^0
Solve for B. R = x(A + B)
Answer:
B = R/x -A
Step-by-step explanation:
[tex]\text{Divide the equation by x:}\\\\\dfrac{R}{x}=A+B\\\\\text{Subtract A:}\\\\\dfrac{R}{x}-A = B\\\\\text{The solution is ...}\\\\\boxed{B=\dfrac{R}{x}-A}[/tex]
Answer:
[tex] b = \frac{r - ax}{x} \\ [/tex]
Step-by-step explanation:
[tex]r = x(a + b) \\ r = ax + bx \\ r - ax = bx \\ \frac{r - ax}{x} = b[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
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 triangleUse the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below.
60
25
Answer:
65
Step-by-step explanation:
C^2= A^2 + B^2
C^2 = (60)^2 + (25)^2
C^2 = 4225
Take the square root of C
C = 65
Answer:
65
Step-by-step explanation:
Use the Pythagorean Theorem to find the length of the hypotenuse.
[tex]a^2+b^2=c^2[/tex]
I'm assuming that '60' and '25' are measures of the legs, since the question asks to find the hypotenuse.
[tex]60^2+25^2=c^2\\\rightarrow 60^2=3600\\\rightarrow 25^2 = 625\\3600+625=c^2\\4225=c^2\\\sqrt{4225}=\sqrt{c^2}\\\boxed{65=c}[/tex]
The hypotenuse should measure 65 units.
Assume that when adults with smartphones are randomly selected, 53% use them in meetings or classes. If 7 adult smartphone users are randomly selected, find the probability that exactly 5 of them use their smartphones in meetings or classes.
Answer:
[tex]P(X=5)=(7C5)(0.53)^5 (1-0.53)^{7-5}=0.194[/tex]
Then the probability that exactly 5 of them use their smartphones in meetings or classes is 0.194
Step-by-step explanation:
Let X the random variable of interest "number of adults with smartphones", on this case we now that:
[tex]X \sim Binom(n=7, p=0.53)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=5)[/tex]
Using the probability mass function we got:
[tex]P(X=5)=(7C5)(0.53)^5 (1-0.53)^{7-5}=0.194[/tex]
Then the probability that exactly 5 of them use their smartphones in meetings or classes is 0.194
What are the names for the sides of a triangle?
Answer:
there are none
Step-by-step explanation:
a triangle its is own shape and does not have any name for each side.
Which of the following linear equations has the steepest slope?
A. Y = -2x +11
B. y=+x+4
C. y - x +7
D. y - 7+2
Answer:
A --- unless d is supposed to be "y= -7x + 2"
Step-by-step explanation:
The slope is m in y=mx + b
So:
a. y= -2x + 11 slope= -2
b. y= x + 4 slope= 1
c. y= -x + 7 slope= -1
d. y= -7 + 2 (I don's see an x but if there were an x I assume that the slope would equal -7)
The higher the m value, the steeper the slope because it is m/1
So, -2/1 is steeper than 1/1 or -1/1
The perimeter of the rectangle playing field is 432 yards the length of the field is 4 yards less than triple the width The perimeter of the rectangle playing field is 432 yards the length of the field is 4 yards less than triple the width. What is the length and width in yards?
Answer:
160 yards
Step-by-step explanation:
P=2l+2w
P=2(3w-8)+2(w)
432=2(3w-8)+2(w)
432=6w-16+2w
432=8w-16
432+16=8w
448=8w
w=448/8
w=56yards
l=3(56)-8
l=168-8=160yards
16 of 22
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Sample Space: Tutorial
Activity
In this exercise, you'll use the formula for the probability of the complement of an event.
Another game you've set up at casino night involves rolling a fair six-sided die followed by tossing a fair coin. In this game, players earn points
depending on the number they get on the die and which side of the coin turns up. For example, the player earns 5 points for getting (2, tails).
Question 1
Find the total number of possible outcomes in each trial of this game.
Answer:
The number of possible outcomes in each trial of this game is 12
Step-by-step explanation:
Given
Rolling of a 6 sided die followed by tossing of a fair coin
Required
Number of possible outcomes
The first step is to list out the possible outcomes of rolling a die and tossing a coin
Rolling a fair die = {1,2,3,4,5,6}
Tossing a coin = {Head, Tail}
Let Head be represented by H and Tail be represented by T;
So,
Rolling a fair die = {1,2,3,4,5,6}
Tossing a coin = {H, T}
The question states that a roll of a 6 sided die is followed by a toss of a fair coin
This means that each trial is {A roll of die and A toss of coin}
So, the sample space is as follows
Sample Space = {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}
Number of outcomes in the sample space is 12.
Hence, the number of possible outcomes in each trial of this game is 12
Answer:
the total number of possible outcomes in each trial of this game is 12
Step-by-step explanation:
uhhhhhh none :) kk bye <3
Please answer this correctly
Mark all of the values that are between 61 and 80. See the diagram below. You should mark exactly 6 values.
Which of the following is the solution to 4 | X+32 8 ?
A. XS-5 or x 2-1
B. X25 or x 2-1
C. $-5 and x-1
D. -1
SUBMIT
Answer:
A
Step-by-step explanation:
x + 3 must be 2 or greater, or -2 or less
So x must be ≥ -1 or ≤ -5
Suppose you buy a CD for $500 that earns 3% APR and is compounded quarterly. The CD matures in 3 years. Assume that if funds are withdrawn before the CD matures, the early withdrawal fee is 3 months' interest. What is the early withdrawal fee on this account?
Answer:
$3.75
Step-by-step explanation:
I = Prt
I = $500·0.03·(3/12) = $3.75
The early-withdrawal fee is $3.75 for the first quarter.
_____
Each quarter after that, the principal amount will be larger, so the interest penalty will be larger. The fee would be the amount of interest that would be credited at the end of the next quarter, or at the end of the quarter currently in progress.
A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes. How long to finish filling the remaining jugs
Answer:
Step-by-step explanation:
=20
This take 30 minutes to finish filling the remaining jugs.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes.
Now,
Let the time to finish filling the remaining jugs = x
Since, A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes.
Hence, By definition of proportion we get;
⇒ 20 / x = 2 / 3
⇒ 20 × 3 / 2 = x
⇒ x = 30
Thus, The time to finish filling the remaining jugs = 30 minutes
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Which expression is equivalent to 36 a minus 27?
9 (4 a minus 3)
3 (18 a minus 9)
9 (4 a minus 27)
3 (12 a minus 6)
Answer:
[tex]9(4a)-9(3)[/tex]
Step-by-step explanation:
[tex]36a-27[/tex]
[tex]9(4a)-9(3)[/tex]
[tex]9(4a-3)[/tex]
Answer:
it is 9(4a-3)
Step-by-step explanation:
find the equation ( in form of y = mx+c) of line which has a gradient of -3 and a y intercept of -2
Answer:
The answer is y = -3x - 2.
Step-by-step explanation:
Given that in slope-form equation, m represents gradient and c is y-intercept. So you have to sbustitute the values into the equation :
[tex]y = mx + c[/tex]
[tex]let \: m = - 3 \\ let \: c = - 2[/tex]
[tex]y = - 3x - 2[/tex]
what is the positive solution for the equation
Answer:
x=3
Step-by-step explanation:
4x^2 - 36 = 0
Add 36 to each side
4x^2 -36 +36 = 0+36
4x^2 = 36
Divide each side by 4
4x^2/4 =36/4
x^2 = 9
Take the square root of each sdie
sqrt(x^2) = ±sqrt(3)
x = -3,+3
We want the positive square root
x=3
what is 0.035 as a simplified reduced fraction
Answer:
7/200
Step-by-step explanation:
0.035= 35/1000= 7*5/200*5=7/200
Find the nth term and the 150th term of the following sequence 7,11,15,19,23,...
Answer:
for the 9th it is 39 for the 150th it is 607
