Answer:
log(1/10) = -1
Step-by-step explanation:
Use the law of exponents and the meaning of logarithm.
1/10 = 10^-1
log(10^x) = x
So, you have ...
log(1/10) = log(10^-1)
log(1/10) = -1
If f(x)=ax+b/x and f(1)=1 and f(2)=5, what is the value of A and B?
Answer:
[tex]\huge\boxed{a=9 ; b = -8}[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{ax+b}{x}[/tex]
Putting x = 1
=> [tex]f(1) = \frac{a(1)+b}{1}[/tex]
Given that f(1) = 1
=> [tex]1 = a + b[/tex]
=> [tex]a+b = 1[/tex] -------------------(1)
Now,
Putting x = 2
=> [tex]f(2) = \frac{a(2)+b}{2}[/tex]
Given that f(2) = 5
=> [tex]5 = \frac{2a+b}{2}[/tex]
=> [tex]2a+b = 5*2[/tex]
=> [tex]2a+b = 10[/tex] ----------------(2)
Subtracting (2) from (1)
[tex]a+b-(2a+b) = 1-10\\a+b-2a-b = -9\\a-2a = -9\\-a = -9\\a = 9[/tex]
For b , Put a = 9 in equation (1)
[tex]9+b = 1\\Subtracting \ both \ sides \ by \ 9\\b = 1-9\\b = -8[/tex]
Consider the following ordered data. 6 9 9 10 11 11 12 13 14 (a) Find the low, Q1, median, Q3, and high. low Q1 median Q3 high (b) Find the interquartile range.
Answer:
Low Q1 Median Q3 High
6 9 11 12.5 14
The interquartile range = 3.5
Step-by-step explanation:
Given that:
Consider the following ordered data. 6 9 9 10 11 11 12 13 14
From the above dataset, the highest value = 14 and the lowest value = 6
The median is the middle number = 11
For Q1, i.e the median of the lower half
we have the ordered data = 6, 9, 9, 10
here , we have to values as the middle number , n order to determine the median, the mean will be the mean average of the two middle numbers.
i.e
median = [tex]\dfrac{9+9}{2}[/tex]
median = [tex]\dfrac{18}{2}[/tex]
median = 9
Q3, i.e median of the upper half
we have the ordered data = 11 12 13 14
The same use case is applicable here.
Median = [tex]\dfrac{12+13}{2}[/tex]
Median = [tex]\dfrac{25}{2}[/tex]
Median = 12.5
Low Q1 Median Q3 High
6 9 11 12.5 14
The interquartile range = Q3 - Q1
The interquartile range = 12.5 - 9
The interquartile range = 3.5
A local mattress manufacturer wants to know if its manufacturing process is in or out of control and has hired you, a statistics expert in the field, to analyze its process. Specifically, the business has run 20 random samples of size 5 over the past month and has determined the mean of each sample.
a. Determine the estimate of the mean when the process is in control.
b. Assuming the process standard deviation is .50 and the mean of the process is the estimate calculated in part a, determine the Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process.
c. Explain the results to the vice-president of the mattress manufacturer focusing on whether, based on the results, the process is in or out of control.
Sample no. Mean of Sample
1 95.72
2 95.44
3 95.40
4 95.50
5 95.56
6 95.72
7 95.60
8 95.24
9 95.46
10 95.44
11 95.80
12 95.20
13 94.82
14 95.78
15 95.18
16 95.32
17 95.08
18 95.22
19 95.04
20 95.
Answer:
Answer to question a = 95.4
Answer to question b = UCL = 96.07
LCL = 94.73
Answer to question c = Process is still in control
Step-by-step explanation:
a. The computation of estimate mean is as shown below:-
= 95.4
b. The computation of Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process is shown below:-
= 95.4 + 0.67082
= 96.07
= 95.4 - 0.67082
= 94.73
c. The explanation is shown below:-
From the above calculation we can see that the sample lies between LCL AND UCL that is (94.73 ,96.07) ,
The Process is still in control
Sherina wrote and solved the equation. x minus 56 = 230. x minus 56 minus 56 = 230 minus 56. x = 174. What was Sherina’s error?
Answer:
subtracting 56 instead of adding (or adding wrong)
Step-by-step explanation:
She wrote ...
x - 56 = 230
x - 56 - 56 = 230 -56 . . . . correct application of the addition property*
x = 230 -56 . . . . . . . . . . . . incorrect simplification
Correctly done, the third line would be ...
x -112 = 174
This would have made Sherina realize that the error was in subtracting 56 instead of adding it. The correct solution would be ...
x - 56 + 56 = 230 + 56 . . . using the addition property of equality
x = 286 . . . . . . . . . . . . . . . . correct simplification on both sides
__
There were two errors:
1) incorrect strategy --- subtracting 56 instead of adding
2) incorrect simplification --- simplifying -56 -56 to zero instead of -112
We don't know whether you want to count the error in thinking as the first error, or the error in execution where the mechanics of addition were incorrectly done.
_____
* The addition property of equality requires the same number be added to both sides of the equation. Sherina did that correctly. However, the number chosen to be added was the opposite of the number that would usefully work toward a solution.
Answer:
D: Sherina should have added 56 to both sides of the equation.
Step-by-step explanation:
I got a 100% on my test.
I hope this helps.
if f(x)=3x-3 and g(x)=-x2+4,then f(2)-g(-2)=
Answer:
3
Step-by-step explanation:
f(x)=3x-3
g(x)=-x^2+4,
f(2) = 3(2) -3 = 6-3 =3
g(-2) = -(-2)^2+4 = -4+4 = 0
f(2)-g(-2)= = 3-0 = 3
the difference of 8 and 2, added to x"
Answer:
see below
Step-by-step explanation:
Difference is subtract
(8-2)
Then add this to x
(8-2) +x
6+x
The expression −50x+100 represents the balance, in dollars, of a bank account after x months. What is the rate of change, in dollars per month, of the bank account balance?
Answer:
-50
Step-by-step explanation:
Basically get two slopes -50(1)+100 will get you 1,50 (1 is x and 50 is y since its the answer)
-50(0)+100 (0,100) Y₂-Y₁/X₂-X₁ 50-100/1-0
Rate of change per month = -$50
The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side length of 6 centimeters? Do not include units in your answer.
Answer:
36
Step-by-step explanation:
formula of area for square:
A=s^2
s=6
A=6^2
A=36
Answer:
36
Step-by-step explanation:
I got it right
Solve for 2 in the diagram below.
120°
32°
T=
Step-by-step explanation:
Hello, there!!!
It's so simple here,
Here,
we have is 1 angle is 120°and other is 3x°.
now,
3x°=120° {because when two st.line intersects eachother then the opposite angle formed are equal}
so, 3x°=120
or, x=120°/3
=40°
Therefore, the value of x is 40°.
Hope it helps....
What is 5 feet and 11 inches in inches
Answer:
60
Step-by-step explanation:
5 is 60 inch
Consider F and C below.
F(x, y) = x2 i + y2 j
C is the arc of the parabola y = 2x2 from (−1, 2) to (2, 8)
(a) Find a function f such that F = ∇f. f(x, y) =
(b) Use part (a) to evaluate C ∇f · dr along the given curve C.
(a)
[tex]\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)[/tex]
[tex]\dfrac{\partial f}{\partial y}=\dfrac{\mathrm dg}{\mathrm dy}=y^2\implies g(y)=\dfrac{y^3}3+C[/tex]
[tex]\implies f(x,y)=\dfrac{x^3+y^3}3+C[/tex]
(b)
[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\mathbf r=f(2,8)-f(-1,2)=\boxed{171}[/tex]
100 students are interviewed to see which of biology, chemistry or physics they prefer.
59 of the students are girls. 35 of the girls like biology best.
2 of the boys prefer physics.
6 out of the 30 who prefer chemistry are girls.
What percentage of the students prefer biology?
Answer:
50%
Step-by-step explanation:
Girls Boys
total: 59 total: 41
- Chemistry 35 - Physics 2
= 24 = 39
- Chemistry ( 30 - 6 ) 24
= 15
Total boys and girls for Biology = 35 + 15 = 50
% = 50/100*100
= 50%
Hope it helps and also mark it as brainliest!!!!Find the length of AB¯¯¯¯¯¯¯¯ A. 19.56 B. 51.86 C. 42.99 D. 34.98
Answer:
Apllying cos on the triangle
cos(angle)= Base/ Hyp
cos(34)= 29/ AB
AB= 29/0.8290
AB=34.98
Step-by-step explanation:
The length of AB is 34.98 units which the correct answer would be an option (D).
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
Given that ΔABC
∠C = 90°
Here base = BC = 29 units and hypotenuse = AB
To determine the length of AB
Apply the cosine on the given right triangle
⇒ cos(θ) = Base/hypotenuse
⇒ cos(34) = 29/ AB
∴ cos(34°) = 0.8290
⇒ 0.8290 = 29/ AB
⇒ AB= 29/0.8290
⇒ AB = 34.98 units
Hence, the length of AB is 34.98 units
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write a thirdthird-degree polynomial expression that has only two terms with a leading term that has a coefficient of five and a constant of negative two
Answer:
5x^3-2
[tex]ax^{3} +bx^{2} +cx+d\\5x^{3}-given\\ d=-2-given\\5x^{3} -2[/tex]
Explanation:
The two terms are [tex]5x^3[/tex] and [tex]2[/tex]. Terms are separated by either a plus or minus.
We can write it as [tex]5x^3+(-2)[/tex] which is an equivalent form. Here the two terms are [tex]5x^3[/tex] and [tex]-2[/tex]. This is because adding a negative is the same as subtracting.
The coefficient is the number to the left of the variable.
The degree is the largest exponent, which helps form the leading term.
The third degree polynomial written above is considered a cubic binomial. "Cubic" refers to the third degree, while "binomial" means there are 2 terms.
We can write something like [tex]5x^3[/tex] as 5x^3 when it comes to computer settings.
What is the difference? Complete the equation. -1 2/5 - (-4/5) = ?
Answer:
First convert them which will be
-7/5 - (-4/5)
so when you subtract a negative number from negative number they actually subtract ex = -4-(-2) = -2
so its simply 7/5-4/5 then add a negative sign
so
3/5
now add negative sign so
-3/5
A cabinet door has a perimeter of 76 inches. Its area is 357 square inches. What are the dimensions of the door?
Answer:
17 by 21 inches
Step-by-step explanation:
The perimeter is twice the sum of the dimensions, and the area is their product, so you have ...
L + W = 38
LW = 357
__
Solution:
W(38 -W) = 357 . . . . . substitute for L
-(W^2 -76W) = 357 . . expand on the left
-(W^2 -38 +19^2) = 357 -19^2 . . . . complete the square
(W -19)^2 = 4 . . . . . . . write as a square
W -19 = ±√4 = ±2 . . . take the square root; next, add 19
W = 19 ±2 = {17, 21} . . . . if width is one of these, length is the other
The dimensions are 17 by 21 inches.
Megan has 12 pounds of cheesecake. On Monday, she and her friends eat 4 pounds. On Tuesday, she and her friends eat another 3 pounds. On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. On Friday, she gives 3 pounds to her dog. On Saturday, her mom gives her one more pound. On Sunday, how many pounds of cheesecake does Megan have left?
Answer:
Step-by-step explanation:
First we start with 12 pounds
On Monday, she and her friends eat 4 pounds. So we have 8 now.
On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.
On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15
On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.
On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.
On Saturday, her mom gives her one more pound. 2 + 1 = 3.
On Sunday, she finally has 3 pounds.
Answer:
nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Step-by-step explanation:
How should a musician effectively convey emotions or ideas in a performance?
Answer:
Within the factors hindering expression in music, tempo is the most important number of factors such as your mood.
Step-by-step explanation:
If one wants to convey a message, they should try these:
a) Use real life
b) introduce symbolism
c) convey sensory disruption, e.t.c.
Hope these helps.
The chart shows a certain city's population by age. Assume that the selections are independent events. If 8 residents of this city are selected at random, find the probability that the first 2 are 65 or older, the next 3 are 25-44 years old, the next 2 are 24 or younger, and the last is 45-64 years old.
Answer:
0.000014
Step-by-step explanation:
The chart is not provided so i will use an example chart to explain the answer. Here is a sample chart:
City X's Population by Age
0-24 years old 33%
25-44 years old 22%
45-64 years old 21%
65 or older 24%
In order to find probability of independent events we find the probability of each event occurring separately and then multiply the calculated probabilities together in the following way:
P(A and B) = P(A) * P(B)
probability that the first 2 are 65 or older
Let A be the event that the first 2 are 65 or older
The probability of 65 or older 24% i.e. 0.24
So the probability that first 2 are 65 or older is:
0.24(select resident 1) * 0.24(select resident 2)
P(A) = 0.24 * 0.24
= 0.0576
P(A) = 0.0576
probability that the next 3 are 25-44 years old
Let B be the event that the next 3 are 25-44 years old
25-44 years old 22% i.e. 0.22
So the probability that the next 3 are 25-44 years old is:
0.22 * 0.22* 0.22
P(B) = 0.22 * 0.22 * 0.22
= 0.010648
P(B) = 0.010648
probability that next 2 are 24 or younger
Let C be the event that the next 2 are 24 or younger
0-24 years old 33% i.e. 0.33
So the probability that the next 2 are 24 or younger is:
0.33 * 0.33
P(C) = 0.33 * 0.33
= 0.1089
P(C) = 0.1089
probability that last is 45-64 years old
Let D be the event that last is 45-64 years old
45-64 years old 21% i.e. 0.21
So the probability that last is 45-64 years old is:
0.21
P(D) = 0.21
So probability of these independent events is computed as:
P(A and B and C and D) = P(A) * P(B) * P(C) * P(C)
= 0.0576 * 0.010648 * 0.1089 * 0.21
= 0.000014
What is the result of question?
Answer:
B
Step-by-step explanation:
x can not be greater than (1,325-270)/26 because $270 is fixed for the rental
Find the number of pieces of floor tiles each measuring 26cm long and 10cm wide needed to lay a floor measuring 260m long and 15m wide
Answer:
150,000
Step-by-step explanation:
1 m = 100 cm
260 m = 260 * 100 cm = 26000 cm
15 m = 15 * 100 cm = 1500 cm
area of floor = LW = 26000 cm * 1500 cm = 39,000,000 cm^2
area of 1 tile = 26 cm + 10 cm = 260 cm^2
number of tiles needed = 39,000,000/260 = 150,000
Answer: 150,000 tiles
How do you find x when knowing the probability?
Answer:
x
Step-by-step explanation:
probability is the branch of mathematics concerning numeral descriptions of how likely an event is to occur or how likely it is that a proposition is true
What is the volume of a cube with a side length of
of a unit?
Brian needs to paint a logo using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle?
Answer:
7.5 cm²
Step-by-step explanation:
Dimensions of the large ∆:
[tex] base (b) = 3cm, height (h) = 9cm [/tex]
[tex] Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 [/tex]
Dimensions of the small ∆:
[tex] base (b) = 2cm, height (h) = 6cm [/tex]
[tex] Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 [/tex]
Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²
Find the Vertical asymptotes of the graph of f
[tex]f(x) = \frac{x + 2}{ {x}^{2} - 4}[/tex]
Answer:
x = 2 and x = -2
Step-by-step explanation:
To find the vertical asymptotes, set the denominator equal to zero and solve for x:
vertical asymptotes are x = 2 and x = -2
On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negative 3) and (4, 0). Which statement best explains the relationship between lines AB and CD? They are parallel because their slopes are equal. They are parallel because their slopes are negative reciprocals. They are not parallel because their slopes are not equal. They are not parallel because their slopes are negative reciprocals.
Answer:
A. they are parallel because their slopes are equal.
Step-by-step explanation:
edge 2020
Answer:
its A in egde
Step-by-step explanation:
Transform the polar equation to a Cartesian (rectangular) equation: r= 4sinθ
options include:
x^2+y^2 = 4y
x^2+y^2 = -4
x^2+y^2 = 4
x^2+y^2 = -4y
Answer:
x^2 +y^2 = 4y
Step-by-step explanation:
Using the usual translation relations, we have ...
r^2 = x^2+y^2
x = r·cos(θ)
y = r·sin(θ)
Substituting for sin(θ) the equation becomes ...
r = 4sin(θ)
r = 4(y/r)
r^2 = 4y
Then, substituting for r^2 we get ...
x^2 +y^2 = 4y . . . . . matches the first choice
. A discount brokerage selected a random sample of 64 customers and reviewed the value of their accounts. The mean was $32,000 with a population standard deviation of $8,200. What is a 90% confidence interval for the mean account value of the population of customers
Answer:
The 90% confidence interval is [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 64
The sample mean is [tex]\= x = \$ 32, 000[/tex]
The standard deviation is [tex]\sigma= \$ 8, 200[/tex]
Given that the confidence interval is 90% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table , the value is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{ \sqrt{n} }[/tex]
=> [tex]E = 1.645 * \frac{ 8200 }{ \sqrt{64} }[/tex]
=> [tex]E = 1686.13[/tex]
The 90% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]32000 - 1689.13 < \mu < 32000 + 1689.13[/tex]
=> [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]
The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. A 2-row table with 10 columns. The first row is labeled time (seconds), x with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.6. The second row is labeled height (meters), h with entries 100, 98.8, 95.1, 89.0, 80.4, 69.4, 55.9, 40.0, 21.6, 0. A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table? According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground. According to the line of best fit, the object was dropped from a lower height. The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds. The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.
Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have a line of best fit:
h = –21.962x + 114.655
As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.
Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
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Give the domain and range of each relation using set notation
Answer:
See below.
Step-by-step explanation:
First, recall the meanings of the domain and range.
The domain is the span of x-values covered by the graph.
And the range is the span of y-values covered by the graph.
1)
So, we have here an absolute value function.
As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:
[tex]\{x|x\in\textbb{R}\}[/tex]
(You are correct!)
For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:
[tex]\{y|y\leq 7\}[/tex]
2)
We have here an ellipse.
First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:
[tex]-4\leq x\leq 6[/tex]
So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:
[tex]\{x|-4\leq x\leq 6\}[/tex]
For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:
[tex]-5\leq y\leq 1[/tex]
This represents all the y-values between -5 and 1, including -5 and 1.
In set notation, thi is:
[tex]\{y|-5\leq y\leq 1\}[/tex]
