Step-by-step explanation:
y = [tex]{\log_b x}[/tex]
if x =4 then y = [tex]{\log_b 4}[/tex] =-1 --> [tex]b^{-1}[/tex] =4 --> b= 1/4
Answer:
b = 1/4
Step-by-step explanation:
It has to be a log because for x=0, b⁰ should be 1 for every b and that is not the case here.
Remember that [tex]y = \log_bx[/tex] means that [tex]b^y=x[/tex].
Since the point (4,-1) seems to be on the line, we can solve:
b⁻¹ = 4
so b = 1/4
if 4x/2=4, then................
Answer:
x=2
Step-by-step explanation:
4x /2 = 4
Simplify the left side
2x = 4
Divide each side by 2
2x/2 = 4/2
x = 2
Jaleel and Lisa are simplifying the expression 2 (x minus 2) + 2 as shown. Jaleel’s Method 2 (x minus 2) + 2 = 2 x minus 4 + 2 = 2 x minus 2 Lisa’s Method 2 (x minus 2) + 2 = 2 x minus 2 + 2 = 2 x Whose method is correct and why? Lisa’s method is correct because 2 (x minus 2) equals 2 x minus 2. Lisa’s method is correct because 2 (x minus 2) equals 2 x. Jaleel is correct because 2 (x minus 2) equals 2 x minus 2. Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.
Answer:
(D)Jaleel's method is correct because 2(x-2)=2x-4.
Step-by-step explanation:
Jaleel and Lisa are simplifying the expression 2(x-2)+2 as shown.
[tex]J$aleel's Method: \left\{\begin{array}{ccc}2 (x -2) + 2 \\= 2 x - 4 + 2 \\= 2 x - 2\end{array}\right[/tex]
[tex]L$isa's Method: \left\{\begin{array}{ccc}2 (x-2) + 2 \\= 2 x -2 + 2 \\= 2 x\end{array}\right[/tex]
We can see that Jaleel's method is correct because:
2(x-2)=2x-4.
When you expand, you must multiply the term outside by all the terms inside the bracket.
The correct option is D.
Answer:
Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.
D is correct
Step-by-step explanation:
i just took the quiz.
According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The wall street journal, June 26, 2008). Suppose eight individuals are randomly selected.
The probability no one delays or goes without medical care is ____________ ;
The probability only one person delays or goes without medical care is ____________.
Please keep three decimals.
Answer:
The probability no one delays or goes without medical care is 0.168;
The probability only one person delays or goes without medical care is 0.336.
Step-by-step explanation:
This problem can be modeled with a binomial random variable, with sample size n=8 and probability of success p=0.2.
The probability that exactly k Americans delay or go without medical care because of concerns about cost within the sample of eight individuals can be calculated as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{8}{k} 0.2^{k} 0.8^{8-k}\\\\\\[/tex]
The probability no one delays or goes without medical care (x=0) is:
[tex]P(x=0) = \dbinom{8}{0} p^{0}(1-p)^{8}=1*1*0.168=0.168\\\\\\[/tex]
The probability only one person delays or goes without medical care (x=1) is
[tex]P(x=1) = \dbinom{8}{1} p^{1}(1-p)^{7}=8*0.2*0.21=0.336\\\\\\[/tex]
what is the slope of a line of duty hat is parallel to the line whose equation is 5y+2x=12
Answer:
-2/5
Step-by-step explanation:
The slope of two parallel lines will be the same.
Here, our equation is 5y + 2x = 12. Let's find the slope by isolating y:
5y + 2x = 12
5y = -2x + 12
y = (-2/5)x + 12/5
So, the slope is -2/5.
Thus, the slope of the line parallel to the given one will be -2/5.
~ an aesthetics lover
Answer:
-2/5
Step-by-step explanation:
5y+2x=12
Solve for y
Subtract 2x
5y = -2x+12
Divide by 5
5y/5 = -2/5 x +12/5
y = -2/5x +12/5
The slope is -2/5
Parallel lines have the same slope
The U.S. Department of Agriculture (USDA) uses sample surveys to obtain important economic estimates. One USDA pilot study estimated the price received by farmers for corn sold in January from a sample of 20 farms. The mean price was reported as $3.64 per bushel with a standard deviation of $0.0835 per bushel. Give a 95% confidence interval for the mean price received by farmers for corn sold in January.
Answer:
{$3.60; $3.68}
Step-by-step explanation:
The confidence interval for a sample of size 'n', with mean price 'X' and standard deviation 's' is determined by:
[tex]X\pm z*\frac{s}{\sqrt n}[/tex]
The z-score for a 95% confidence interval is 1.96.
Applying the given data, the lower and upper bounds of the confidence interval are:
[tex]3.64\pm 1.96*\frac{0.0835}{\sqrt 20} \\L=\$3.60\\U=\$3.68[/tex]
The confidence interval for the mean price received by farmers for corn sold in January is:
CI : {$3.60; $3.68}
The manager of a computer retail store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.5 years and a standard deviation of 0.4 years. He then randomly selects records on 45 laptops sold in the past and finds that the mean replacement time is 4.4 years. Assuming that the laptop replacment times have a mean of 4.5 years and a standard deviation of 0.4 years, find the probability that 45 randomly selected laptops will have a mean replacment time of 4.4 years or less.
Answer:
The probability that 45 randomly selected laptops will have a mean replacment time of 4.4 years or less is P(M<4.4)=0.0468.
Step-by-step explanation:
We have a population normally distributed with mean 4.5 years and standard deviation of 0.4 years.
Samples of size n=45 are selected from this population.
We have to calculate the probability that a sample mean is 4.4 years or less.
Then, we calculate the z-score for the sample mean M=4.4 and then calculate the probability using the standard normal distribution:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{4.4-4.5}{0.4/\sqrt{45}}=\dfrac{-0.1}{0.06}=-1.677\\\\\\P(M<4.4)=P(z<-1.677)=0.0468[/tex]
The probability that 45 randomly selected laptops will have a mean replacment time of 4.4 years or less is P(M<4.4)=0.0468.
Find the slope through each pair of two points. Report answers in simplest form.
(0,0) and (0.5,0.25)
m =
Answer:
m = 0.5
Step-by-step explanation:
m = (y2 - y1) / (x2 - x1)
= (0.25 - 0) / (0.5 - 0)
= 0.25/0.5
= 0.5
Please find the missing side of the triangle and round the answer to the nearest tenth. Thanks.
Answer:
x = 74.3
Step-by-step explanation:
Using the trigonometric ratio formula, the missing side, x, of the right angled triangle, can be found as follows:
Ѳ = 22°,
adjacent side length = x
Opposite side length = 30
Thus, we would apply the formula:
tan Ѳ = opposite length/adjacent length
[tex] tan 22 = \frac{30}{x} [/tex]
Multiply both sides by x
[tex] tan 22*x = \frac{30}{x}*x [/tex]
[tex] tan 22*x = 30 [/tex]
[tex] 0.4040*x = 30 [/tex]
Divide both sides by 0.4040 to make x the subject of the formula
[tex] \frac{0.4040*x}{0.4040} = \frac{30}{0.4040} [/tex]
[tex] x = \frac{30}{0.4040} [/tex]
[tex] x = 74.26 [/tex]
x ≈ 74.3 (to the nearest tenth)
if you make $2710.00 a month and must spend 89% of that on recurring and variable expenses, how much money can you potentially save in one year?
Answer:
$3577.20
Step-by-step explanation:
You can save 11% of your income each month, so in 12 months, you can save ...
12×0.11×$2710 = $3577.20
What is the answer? ACB ~ EFD
Answer:
z = 60°
Step-by-step explanation:
In ΔABC
Sum of all angles of triangle = 180
65 + 55 +∠A = 180
120 +∠A = 180
∠A = 180 - 120
∠A = 60
In similar triangles, corresponding angles are congruent
z = ∠A
z = 60°
Please answer this question now in two minutes
Answer:
the slope equation is y2 - y1 divided by x2 - x1
Step-by-step explanation:
so the answer would be 3 over 2 because of this method
Answer:
3/2
Step-by-step explanation:
Use the easy rise over run method.
start at the point (50,20) then go up 3 units and 2 units to the right to get the next point.
3/2 should be the slope.
Hope I helped you!
REALLY NEED HELP PLS
CAN U HELP Xx
Answer:
0
Step-by-step explanation:
There are no green counters in the bag.
The decay constant for 14C is 0.00012. A 4050-year-old wooden chest is found by archaeologists. What percentage of the original 14C would you expect to find in the wooden chest? (Express your answer as a percentage rounded to one decimal place.)
Answer:
The radioactive decay constant or k = ln (.5) / Half-Life
Half-Life = -.693147 / .00012
Half-Life = -5,776.225 years
We'll call beginning amount as 100%
Ending Amount = Beginning Amount / 2^n (where n = # of half-lives)
n = 4,050 / 5,776.225 = 0.7011499725
Ending Amount = 100% / 2^0.7011499725
Ending Amount = 100% / 1.625800202
Ending Amount = 61.5081729452%
Ending Amount = 61.5 % (rounded)
Step-by-step explanation:
empt 1
Find the equation in slope-intercept form of a line with slope - 2 and y-intercept 4.
a) y = -2x
Ob) y - 2x-4
c) y = -2x+4
d) y - 4x -2
Question 12 (5 points)
Answer:
y = -2x +4
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -2x +4
Identify the statement as true or false.
New Jersey is a state if and only if Florida is not a state.
Is the statement true or false?
O true
O false
6th term in the sequence -1,4,-16,64
6th term in the sequence is 1024
Answer:
1024
Step-by-step explanation:
I hope this helps!
Two planes travel toward each other from cities that are about 1725 km apart at rates of 360 km/hr and 330 kr/hr. They started at the same time. In how many hours
will they meet?
hours.
The two planes will meet after
(Simplify your answer.)
Answer: 2 1/2 or 2.5 hours
Step-by-step explanation:
Add 360 and 330
360 + 330 = 690
Divide 1,725 by 690
1,725 / 690 = 2.5
The two planes will meet in 2.5 hours
The speed is the distance covered by an object at a particular time. The time it will take for the two planes to meet is 2.5 hours.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Given that the speed of the two planes is 360 km/hr and 330 km/hr. Therefore, the relative speed of the two planes with respect to each other is,
Relative speed = 360 km/hr + 330 km/hr
= 690 km/hr
Now, since the total distance between the two cities is 1725 km. Therefore, the time it will take for two planes to meet is,
Time = Distance /Speed
= 1725 km / 690 km/hr
= 2.5 hour
Hence, the time it will take for the two planes to meet is 2.5 hours.
Learn more about Speed:
https://brainly.com/question/15100898
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Which best compares the volumes of the two cylinders? Geometry
Answer:
The correct answer would be C
Step-by-step explanation:
please mark brainliest
The choice which best compares the volume of the cylinders is; Choice B; The volume of cylinder B is the same as that of cylinder A.
Which best compares the volumes of the two cylinders?From geometry, It can be concluded that the volume of a solid shape is the product of its cross sectional area and the height over which the area spans. On this note, since the volume of a cylinder is dependent on the radius and height of the cylinder, both cylinders have equal volumes.
Read more on cylinders;
https://brainly.com/question/9554871
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Give a recursive definition of each of these sets of ordered pairs of positive integers. (Hint: plot the points in the set in the plane and look for lines containing points in the set. 1. S={(a, b) I a E Z+, b Ñ Z+ , and a | b}2. S={(a, b) I a E Z+, b Ñ Z+ , and 3 | a + b} 3. S={(a, b) | a Ñ Z+ , b Ñ Z+ , and a + b is odd) a) (1,2) S, (2, 1) E S and if (a, b) S then (a + 2, b) E S, (a, b + 2) E S and (a + 1, b + 1) E S b) (1,2) es, (2, 1) Ñ Sand if (a, b) Ñ S then (a + 3, b) Ñ s, (a, b + 3) Ñ s, (a+1, b + 2) ES and (a + 2, b + 1) Ñ s c) (1,1) Ñ Sand if (a, a) Ñ Sthen (a + 1, a + 1) Ñ S and if (a, b) Ñ S, then (a, b + a) Ñ s
Answer:
1. s=gfcgj sdgc
gzgixxhcxc
vxtuixzdfhvxxgjknn
jfhujhgcxvjkmvcghj
mvhuiknbb5542698755
8423675369
8823
Perform the indicated operation and simplify the result.
Answer:
7/ (3a-1)
Step-by-step explanation:
3a^2 -13a +4 28+7a
------------------ * --------------------
9a^2 -6a+1 a^2 -16
Factor
(3a-1)(a-4) 7(4+a)
------------------ * --------------------
(3a-1) (3a-1) (a-4)(a+4)
Cancel like terms
1 7
------------------ * --------------------
(3a-1) 1
Leaving
7/ (3a-1)
What is the discriminant of the quadratic equation 0 = –x2 + 4x – 2?
Answer:
Discriminant=8
Step-by-step explanation:
-x²+4x-2=0
here a=-1,b=4 and c=-2
Discriminant=b²-4ac
Discriminant=(4)²-4(-1)(-2)
Discriminant=16-8
Discriminant=8
i hope this will help you :)
Answer the following True or False:
If the p-value is 0.13 and the level of significance , a , is 0.05 in a hypothesis test for a mean, then we
accept the null hypothesis.
O false
O true
Answer:
false.
I think .???
a null hypothesis doesn't matter regardless
What is the solution to the system of equations?
y = 3x - 10
h
2x + y = 4
04-8. 6)
O (-6, 16)
O (6.-8)
O (16.-6)
Answer:
The answer is option C
y = 1/3x - 10 ........ 1
2x + y = 4 .......... 2
Substitute the first equation into the second one
That's
2x + 1/3x - 10 = 4
7/3x = 14
Multiply through by 3
That's
7x = 42
Divide both sides by 7
x = 6
Substitute x = 6 into any of the Equations
y = 1/3x - 10
y = 1/3(6) - 10
y = 2 - 10
y = - 8
Therefore
x = 6 y = - 8
Hope this helps
The Foot Locker is having a 60% off sale on shorts. John paid $18 for a pair of shorts. What was the original price of the shorts?
Answer:
$30 is the price of the original pair of sneakers.
Step-by-step explanation:
You wanna cross multiply so you put :
18. 60
_ = _
x. 100
You multiply 18 the cost of the sneakers by 100 and then divide the product (1800) by 60 and you get $30.
MARK ME AS BRAINLIEST!
slope of line passes through (7/20, 8/3) and (3/8, 7/9)
Answer:
[tex]slope = \dfrac{-680}{9}[/tex]
Step-by-step explanation:
We are given coordinates of two points:
Let the points be A and B respectively:
[tex]A(\dfrac{7}{20}, \dfrac{8}{3})\\B(\dfrac{3}{8}, \dfrac{7}{9})[/tex]
To find the slope of line AB.
Formula for slope of a line passing through two points with coordinates [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:
[tex]m = \dfrac{y_2- y_1}{x_2- x_1}[/tex]
Here, we have:
[tex]x_2 = \dfrac{3}{8}\\x_1 = \dfrac{7}{20}\\y_2 = \dfrac{7}{9}\\y_1 = \dfrac{8}{3}\\[/tex]
Putting the values in formula:
[tex]m = \dfrac{\dfrac{7}{9}- \dfrac{8}{3}}{\dfrac{3}{8}- \dfrac{7}{20}}\\\Rightarrow m = \dfrac{\dfrac{7-24}{9}}{\dfrac{15-14}{40}}\\\Rightarrow m = \dfrac{\dfrac{-17}{9}}{\dfrac{1}{40}}\\\Rightarrow m = \dfrac{-17\times 40}{9}\\\Rightarrow m = \dfrac{-680}{9}[/tex]
So, the slope of line AB passing through the given coordinates is:
[tex]m = \dfrac{-680}{9}[/tex]
NEED UGANT HELP really stuck xx
Answer:
0.6
Step-by-step explanation:
3+2=5
P (white) = 3/5 = 0.6
(Hopefully this works, if not, on hearty maths you can go back to your assigned tasks page and go back onto the task to get a new question if that makes sense)
Define f(0,0) in a way that extends f(x,y)=x^2 - y^2/x^2 + y^2 to be continuous at the origin.
Answer:
It cannot be extended.
Step-by-step explanation:
Consider the function [tex]f(x,y) = \frac{x^2-y^2}{x^2+y^2}[/tex]. To extend this functions so it is continous at (0,0) we must define [tex] f(0,0) = \lim_{(x,y)\to(0,0)\frac{x^2-y^2}{x^2+y^2}[/tex]. However, this implies that the limit exists. So, we should find if the limit exists or not.
In this case, consider the case in which y =0. When y=0 then
[tex]\lim_{(x,y)\to(0,0) \frac{x^2-0^2}{x^2+0^2} = \lim_{x\to 0}\frac{x^2}{x^2}= 1[/tex]
But, when x=0, we get
[tex]\lim_{(x,y)\to(0,0) \frac{0^2-y^2}{0^2+y^2} = \lim_{y\to 0}\frac{-y^2}{y^2}=-1[/tex].
So, since the limit depends on how we approach to the point (0,0) the limit does not exist. So we can't extend f(x,y) so it is continous.
5x + 7y = -29 y = x + 1
Answer:
(x, y) = (-3, -2)
Step-by-step explanation:
Perhaps this is a system of equations you want the solution for.
Since you have an expression for y, substitution is a viable approach.
5x +7(x+1) = -29 . . . . . . substitute for y
12x = -36 . . . . . . subtract 7 and simplify
x = -3 . . . . . . . . . divide by 12
y = (-3) +1 = -2 . . . use the expression for y
The solution is (x, y) = (-3, -2).
What is the value of p?
Answer:
Step-by-step explanation:
The angle next to 90 degrees is also 90 degrees and it's supplementary
the angle next to 133 degrees is 47 degrees and it's also supplementary
p + 90 + 47 = 180
p + 137 = 180
p = 43 degrees
the solution is d
A smart phone manufacturer is interested in constructing a 99% confidence interval for the proportion of smart phones that break before the warranty expires. 97 of the 1750 randomly selected smart phones broke before the warranty expired. Round your answers to three decimal places. A. With 99% confidence the proportion of all smart phones that break before the warranty expires is between and .
Answer:
With 99% confidence the proportion of all smart phones that break before the warranty expires is between 0.041 and 0.069.
Step-by-step explanation:
We have to calculate a 99% confidence interval for the proportion.
The sample proportion is p=0.055.
[tex]p=X/n=97/1750=0.055[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.055*0.945}{1750}}\\\\\\ \sigma_p=\sqrt{0.00003}=0.005[/tex]
The critical z-value for a 99% confidence interval is z=2.576.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=2.576 \cdot 0.005=0.014[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.055-0.014=0.041\\\\UL=p+z \cdot \sigma_p = 0.055+0.014=0.069[/tex]
The 99% confidence interval for the population proportion is (0.041, 0.069).