Answer:
Option C.
Step-by-step explanation:
The given logarithmic equation is
[tex]\log_2(x+11)=4[/tex]
It can be written as
[tex](x+11)=2^4[/tex] [tex][\because log_ax=y\Leftrightarrow x=a^y][/tex]
[tex]x+11=16[/tex]
[tex]x=5[/tex]
Now, to check whether [tex]x=5[/tex] is a true solution or not. Substitute [tex]x=5[/tex] in the LHS of given equation.
[tex]LHS=\log_2(5+11)[/tex]
[tex]LHS=\log_2(16)[/tex]
[tex]LHS=\log_22^4[/tex]
[tex]LHS=4[/tex] [tex][\because log_aa^x=x][/tex]
[tex]LHS=RHS[/tex]
Hence, [tex]x=5[/tex] is a true solution because [tex]\log_2(16)=4[/tex].
Therefore, the correct option is C.
Answer:
C on edge2021
Step-by-step explanation:
The manager of the motor pool wants to know if it costs more to maintain cars that are driven more often. Data are gathered on each car in the motor pool regarding number of miles driven (X) in a given year and maintenance costs for that year (Y) in thousands of dollars. The regression equation is computed as: Y-60+0.08X, and the p-value for the slope estimate is 0.7. What conclusion can we draw from this study? a. Cars that are driven more tend to cost more to maintain. b. There's no statistically significant linear relationship between the number of miles driven and the maintenance cost c. The correlation between the response variable and independent variable is significant. d. The slope estimate is significantly different from zero.
Answer:
b. There's no statistically significant linear relationship between the number of miles driven and the maintenance cost
Step-by-step explanation:
The p-value for the slope estimate show us how strong is the certainty that there are a linear relationship between both variables. In this case, the p-value for the slopes shows if there is a significant relationship between the number of miles driven and the maintenance cost.
If we have a high p-value like 0.7 we can said that there is no certainty in the linear relationship. it means that there's no statistically significant linear relationship between the number of miles driven and the maintenance cost.
What are the next two numbers in the pattern of numbers;
45, 15, 44, 17, 40, 20, 31, 25, …
Answer:
Next two numbers are 15 and 32 respectively.
Step-by-step explanation:
The given pattern is
45, 15, 44, 17, 40, 20, 31, 25, …
Here, we have two patterns.
Odd places : 45, 44, 40, 31,...
Even places : 15, 17, 20, 25,...
In series of odd places, we need to subtract square of integers.
[tex]45-(1)^2=45-1=44[/tex]
[tex]44-(2)^2=44-4=40[/tex]
[tex]40-(3)^2=40-9=31[/tex]
So, 9th term of given pattern is
[tex]31-(4)^2=31-16=15[/tex]
In series of even places, we need to add prime numbers.
[tex]15-2=17[/tex]
[tex]17+3=20[/tex]
[tex]20+5=25[/tex]
So, 10th term of given pattern is
[tex]25+7=32[/tex]
Therefore, the next two numbers in the pattern of numbers are 15 and 32 respectively.
The currency in Bolivia is the Boliviano. The exchange rate is approximately $1 = 8 Bolivianos. At this rate, how many Bolivianos would you get if you exchanged $3?
Answer:
24 bolivianos
Step-by-step explanation:
$1=8b
$3=?
Cross multiply: ($3*8)/1 =24
Dan earns £8.10 per hour how much will he earn for 7 hours work
linear function for f(-11)=5, slope of f= -2/3
Answer:
f(x) = -2/3(x +11) +5
Step-by-step explanation:
The point-slope form of the equation of a line will give you the desired linear function:
y = m(x -h) +k . . . . . for slope m through point (h, k)
You are give point (x, f(x)) = (-11, 5) = (h, k), and you are given slope m = -2/3. Putting these values into the function form gives ...
f(x) = -2/3(x +11) +5
What is the perimeter of the shape below?
Answer:
I think it is 288.6 ft. Lol hope this helps
Step-by-step explanation:
The mean of the data set(9,5,y,2,x)is twice the data set (8,x, 4,1,3).What is (y-x)
Answer:
y - x = 16
Step-by-step explanation:
Explanation:-
Step(i):-
Given data set A is 9,5,y,2,x
Mean of the Data set A
= [tex]\frac{9 + 5 + y + 2 +x}{5}[/tex]
= [tex]\frac{16 +x+y}{5}[/tex]
Given data set B is 8, x, 4, 1, 3
Mean of the Data set B
= [tex]\frac{8+ x+4+1+3}{5}[/tex]
Step(ii):-
Mean of the Data set A = 2 X Mean of the Data set B
[tex]\frac{16 +x+y}{5} = 2 X \frac{16+x}{5}[/tex]
On simplification , we get
16 +x + y = 2( 16 +x)
16 + x + y = 32 + 2 x
16 + x + y - 32 - 2 x = 0
y - x -16 =0
y - x = 16
x^2 + 5x - 24 = 0 How do I solve by factoring
Answer:
x = -8 or x = 3
Step-by-step explanation:
To factor ax² + bx + c, use AC method.
a times c is 1 × -24 = -24.
Factors of ac (-24) that add up to b (5) are 8 and -3.
Divide by a and reduce: 8/1 and -3/1.
Therefore, the factors are x + 8 and x − 3.
x² + 5x − 24 = 0
(x + 8) (x − 3) = 0
x = -8 or 3
When writing expressions for complex numbers, what does i represent?
Answer: See below
Step-by-step explanation:
[tex]i[/tex] is an imaginary number.
[tex]i=\sqrt{-1}[/tex]
[tex]i^2=-1[/tex]
The probability of randomly selecting a white flower from a garden that has green, pink, yellow, and white flowers is 6%.
Which of the following describes the likelihood of selecting a white flower?
A.
likely
B.
unlikely
C.
neither unlikely nor likely
Answer:
b. unlikely
Step-by-step explanation:
I don't really know a step by step explanation :( sry
Let $A_1 A_2 A_3 A_4$ be a regular tetrahedron. Let $P_1$ be the center of face $A_2 A_3 A_4,$ and define vertices $P_2,$ $P_3,$ and $P_4$ the same way. Find the ratio of the volume of tetrahedron $A_1 A_2 A_3 A_4$ to the volume of tetrahedron $P_1 P_2 P_3 P_4.$
Answer:
27 : 1
Step-by-step explanation:
The faces of a regular tetrahedron are equilateral triangles. The incenter, circumcenter, and centroid are all the same point, located 1/3 of the distance from the edge to the opposite vertex of the face. The vertical height of the point that is 1/3 the slant height from the base is 1/3 of the height of the tetrahedron.
Then the "inscribed" tetrahedron has 1/3 the height of the original. The ratio of volumes is the cube of the ratio of linear dimensions, so the ratio of the larger volume to the smaller is ...
3³ : 1³ = 27 : 1
Please help! Correct answer only, please! Find the following product if possible. Explain if it is not possible. A. B. C. D.
Answer: A
Step-by-step explanation:
To multiply matrices, multiply each term in Row 1 of the first matrix with each term in Column 1 of the second matrix and then find their sum. Repeat for Row1×Column2, Row2×Column1, and Row2×Column2.
[tex]\left[\begin{array}{ccc}1&4&-1\\3&2&2\end{array}\right] \times \left[\begin{array}{cc}2&-1\\0&3\\5&2\end{array}\right] \\\\\\=\left[\begin{array}{ccc}1(2)+4(0)-1(5)&1(-1)+4(3)-1(2)\\3(2)+2(0)+2(5)&3(-1)+2(3)+2(2)\end{array}\right] \\\\\\=\left[\begin{array}{cc}-3&9\\16&7\end{array}\right][/tex]
maths
Ella mixes cordial and water in the ratio of 1:4 how much water should be mixed with 50ml or cordial
calculate the
Simple interest on a
7,500,00 for 4 years
at 4½
per
annum
Step-by-step explanation:
S.i =principal x rate x time/100
7,50000x4x4.5/100
13500000/100
135000
On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day.
x 25 50 75 100 Total
P(x) 0.16 0.36 0.38 0.10 1.00
Find the probability expressions: (Round your answers to 2 decimal places.)
a. P(X=50)P(X=50).
b. P(X≤75)P(X≤75).
c. P(X>50)P(X>50).
d. P(X<100)P(X<100).
Answer:
a. P(X=50)= 0.36
b. P(X≤75) = 0.9
c. P(X>50)= 0.48
d. P(X<100) = 0.9
Step-by-step explanation:
The given data is
x 25 50 75 100 Total
P(x) 0.16 0.36 0.38 0.10 1.00
Where X is the variable and P(X) = probabililty of that variable.
From the above
a. P(X=50)= 0.36
We add the probabilities of the variable below and equal to 75
b. P(X≤75) = 0.16+ 0.36+ 0.38= 0.9
We find the probability of the variable greater than 50 and add it.
c. P(X>50)= 0.38+0.10= 0.48
It can be calculated in two ways. One is to subtract the probability of 100 from total probability of 1. And the other is to add the probabilities of all the variables less than 100 . Both would give the same answer.
d. P(X<100)= 1- P(X=100)= 1-0.1= 0.9
Which expression is equivalent to 3(x-6)+5(x-4)
Answer:
[tex]8x-38[/tex]
Step-by-step explanation:
[tex]3(x-6)+5(x-4)\\3x-18+5x-20\\3x+5x-18-20\\8x-38[/tex]
Describe the solutions of the following system in parametric vector form,and provide a geometric comparison with the solution set .
x1 + 3x2- 5x3 = 4
x1+ 4x2 - 8x3 = 7
-3x1- 7x2 +9x3 =6
Answer:
The equations are linearly independent so there is no parametric vector form
Step-by-step explanation:
I attached the solution.
$17,500,000 is what percent of $70,000,000?
Answer: 1/4 of 70,000,000
Step-by-step explanation: 17,500,000 / 70,000,000 = 0.25
Answer:
[tex]25\%[/tex]
Step-by-step explanation:
[tex]\frac{17,500,000}{70,000,000}[/tex]
[tex]\frac{1}{4}=0.25=25/100=25\%[/tex]
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Enter the correct answer.
Answer:
Step-by-step explanation:
The formula is y = mx + b
m being the slope, rise over run. And b being the y-intercept. Right off the bat we can visually see the y-intercept is -4.
To find slope, we need to take two sets of coords and apply the slope fomula. The slope fomula is change in y divided by the change in x. The function itself is straight, so that means the slope will be the exact same no matter which points you choose.
(4, -1) and (8, 2) are coords on the line. Do 2 - (-1) to get 3. then do 8 - 4 to get 4. Finally, we just gotta do 3/4 which is simply [tex]\frac{3}{4}[/tex].
We have the slope of 3/4 and we have the y-intercept of -4. Just plug it in the standard formula of y = mx + b to get:
[tex]y=\frac{3}{4} x-4[/tex]
A college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of hours they watch per week. The results are provided below. Calculate the 80% confidence interval of the true average number of hours of TV watched per week.
P.S: excel formola needed only. For lower and Upper Bound
CBB K-6 4 3 6 6 0 9 4 5 5 8 8 7 4 8 89265 123456789 0123456789 20 2
Answer:
80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].
Step-by-step explanation:
We are given that a college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of hours they watch per week. The results are provided below;
Hours of TV per week (X): 6, 14, 13, 6, 16, 10, 19, 4, 5, 5, 18, 8, 7, 14, 8, 8, 9, 12, 6, 5.
Firstly, the Pivotal quantity for 80% confidence interval for the true average is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean number of hours of TV watched per week = [tex]\frac{\sum X}{n}[/tex] = 9.65
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex] = 4.61
n = sample of people = 20
[tex]\mu[/tex] = true average number of hours of TV watched per week
Here for constructing 80% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.
So, 80% confidence interval for the true average, [tex]\mu[/tex] is ;
P(-1.33 < [tex]t_1_9[/tex] < 1.33) = 0.80 {As the critical value of t at 19 degrees of
freedom are -1.33 & 1.33 with P = 10%}
P(-1.33 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.33) = 0.80
P( [tex]-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80
P( [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80
80% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]9.65-1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] , [tex]9.65+1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] ]
= [8.28 hours, 11.02 hours]
Therefore, 80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].
While filing your income tax, you report annual contributions of $100 to a public radio station, $300 to PBS (television station), $150 to a woman’s shelter, and $450 to other charitable organizations.
Find your monthly expense.
Hey there! I'm happy to help!
Let's add up all of these contributions.
100+300+150+450=1000
However, this is annual. We want monthly. So, we simply divide by 12.
1000/12≈83.33
Therefore, the monthly expense is $83.33
I hope that this helps! Have a wonderful day!
Suppose parts are of two varieties: good (with probability 90/92) and slightly defective (with probability 2/92). Parts are produced one after the other. What is the probability that at least 3 parts must be produced until there is a slightly defective part produced
Answer:
95.69%
Step-by-step explanation:
We have X is the number of parts produced up to (and including) the first slightly defective part. So, X is Geometric (2/92), which would be the following:
P (X => 3) = Summation i = 3, up to infinity of {[(90/92)^(i-1)] * (2/92)}
We replace and solve and we are left with:
P (X => 3) = (2/92) * (90/92)^(3-1) * 1/(1 - 90/92)
P (X => 3) = 0.9569
Which means that the probability that at least 3 parts must be produced until there is a slightly defective part produced is 95.69%
The probability that an event will happen is P(E)=34. Find the probability that the event will not happen.
Answer:
.66
Step-by-step explanation:
1minus .34
Correct me if I am wrong
Please answer this correctly
Answer:
538
Step-by-step explanation:
l x w
7x39
12x20
5x5
538
write this small number in standard form. 0.00078
Answer:
78/100000
Hope it helps you
i have a daily allowance of 70grm but have only used 48 what percentage do i have left
Answer:
You have 31.43% of your allowance left.
Step-by-step explanation:
This question can be solved using a rule of three.
Your initial amount, of 70, is 100%.
The remaining amount, of 70 - 48 = 22, is x%. So
70 - 100%
22 - x%
[tex]70x = 100*22[/tex]
[tex]x = \frac{100*22}{70}[/tex]
[tex]x = 31.43[/tex]
You have 31.43% of your allowance left.
I need help with solving this
Answer:
49
Step-by-step explanation:
Positive 49 not -49
Which of the following numbers are in setA? Check all that apply.
A = {x | x is a positive, odd integer less than 7}
0
1
2
5
3
Answer:
1, 3, 5.
Step-by-step explanation:
The members of the set are {1, 3, 5}.
Note 0 is an even integer so is not included in the set.
Also 0 is neither negative or positive.
Solve Systems of Algebraic Equations in Two Variables
Hello I need some help on setting up 2 equations of this problem. The answers are cheeseburger costs $1.55 and the milkshake $0.85
Four cheeseburgers and two chocolate milkshakes cost a total of $ 7.90. Two
Shakes cost 15 cents more than a hamburger with
cheese so What is the price of a cheeseburger?
And the price of a shake?
Answer:
4c+ 2m = 7.90
2m -.15 = c
Step-by-step explanation:
Let c = cheese burger
m = milkshake
4c+ 2m = 7.90
2m -.15 = c
Substitute into the first equation
4( 2m -.15) +2m = 7.90
Distribute
8m -.6 +2m = 7.90
Combine like terms
10m - .6 = 7.90
Add .6 to each side
10m = 7.90+.6
10m = 8.50
Divide by m
10m = 8.50/10
m = .85
Now find c
2m -.15 = c
2(.85) - .15=c
1.70-.15 = c
1.55 =c
PLEASE HELP ?
The range is the set of
A: first coordinates
B: ordered pairs
C:second coordinates
Answer:
C:second coordinates
Step-by-step explanation:
A range is the set of output coordinates
The domain is the input coordinates
Domain is the x, range is the y
Answer: its definitly c
Step-by-step explanation:
