Answers
Answer:
x=8
Step-by-step explanation:
log4( x-6) +log4(x) = 2
We know that loga + log b = log (ab)
log4( x-6)(x) = 2
Raise each side to the base of 4
4^log4( x-6)(x) = 4^2
( x-6)(x) = 16
Distribute
x^2 -6x = 16
Subtract 16 from each side
x^2 -6x-16 = 0
Factor
(x-8) (x+2) =0
Using the zero product property
x-8=0 x+2 =0
x=8 x=-2
Checking, we cannot have the log of a negative number so -2 is not a solution
Answer:
x = 8
Step-by-step explanation:
log4(x - 6) + log4(x) = 2
log4[(x - 6) × x] = 2
x² - 6x = 4²
x² - 6x - 16 = 0
x² - 8x + 2x - 16 = 0
x(x - 8) + 2(x - 8) = 0
(x + 2)(x - 8) = 0
x = 8, -2
Log of negative numbers do not exist, so x is only 8
Related Questions
log 10(x + 3) – log 10(x-3) = 1
Answers
Answer:33/9
Step-by-step explanation:
Log10(x+3)-Log10(x-3)=1
Log10((x+3)/(x-3))=1
(x+3)/(x-3)=10^1
(x+3)/(x-3)=10
Cross multiply
x+3=10(x-3)
Open brackets
x+3=10x-30
Collect like terms
10x-x=30+3
9x=33
Divide both sides by 9
9x/9=33/9
x=33/9
What is 1 2/3 - 2 1/3?
Answers
Step-by-step explanation:
First it will be easer if you turn both sides into improper fractions
5/3-7/3
Now do 5-7
5-7=-2
The bottom of the fraction stays the same
-2/3 is your answer.
Which expression shows a way to find 25% of 1000?
Answers
Answer:250
Step-by-step explanation:
25% of 1000
25/100 x1000
(25 x 1000)/100
25000/100=250
A large company that produces a "fat-burner" pill claims an average loss of 20 pounds in the first month. A consumer advocacy group believes that this claim is actually just "hype" intended to sell more of the compound. The advocacy group would like to obtain statistical evidence about this issue and takes a random sample of 100 consumers who responded that they had purchased the pill but didn't know what the survey was about. They find that these 100 people lost an average of 18 pounds with a standard deviation of 7.5 pounds. What are the null and alternative hypothesis in this situation
Answers
The null and alternative hypothesis for the tests are:
H0: μ = 20
Ha: μ < 20
Given data:
In this situation, the null and alternative hypotheses can be formulated as follows:
Null Hypothesis (H0): The average weight loss of consumers who take the "fat-burner" pill is equal to 20 pounds.
Alternative Hypothesis (Ha): The average weight loss of consumers who take the "fat-burner" pill is less than 20 pounds.
In symbolic notation:
H0: μ = 20
Ha: μ < 20
where μ represents the population mean weight loss of consumers who take the "fat-burner" pill.
The null hypothesis assumes that the claim made by the company is accurate and that the average weight loss is indeed 20 pounds. The alternative hypothesis challenges this claim and suggests that the actual average weight loss may be less than 20 pounds, implying that the "hype" around the pill's effectiveness might be exaggerated.
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In the data set below, what is the upper quartile?
3344466889
Answers
Answer:8
Step-by-step explanation:
3 3 4 4 4 6 6 8 8 9
data in upper quartile section are 6 8 8 9
We therefore find the median of 6 8 8 9
The median is the upper quartile
Upper quartile=(8+8)/2
Upper quartile=16/2
Upper quartile=8
Question 4:
Nathan has three quarters, two nickels, and eleven pennies. How much money does he have?
Answers
Answer:
96Step-by-step explanation:
quarters = 25 cents so 3 quarters is 75
nickels= 5 cents so 10
pennies= 11
11+10+75
Answer:
96¢
Step-by-step explanation:
25+25+25=75
75+5+5=85
85+1+1+1+1+1+1+1+1+1+1+1=96
Therefore Nathan has 96¢
Hope that helps! If you have any further questions comment down below or message me! Good luck!
write it as a product: -[tex]ax^{6}[/tex]+[tex]\frac{1}{8}[/tex]
Answers
Answer:
[tex]\frac{-abx^{6}+1 }{b}[/tex]
Step-by-step explanation:
Which ordered pair (x,y) is a solution to the following?
y = 2x + 5
O(-2,1)
O(2,7)
O(1,6)
O(-3,11)
Answers
Answer:
(-2,1)
Step-by-step explanation:
Which property justifies the following statement? If ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3.
Answers
Answer:
transitive property
Step-by-step explanation:
The given statement is an example of transitive property.
What is transitive property?The transitive property states that “if two quantities are equal to the third quantity, then we can say that all the quantities are equal to each other”.
Given that, ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3.
This is an example of transitive property.
Transitive property states that, if a = b and b = c then a = c
Hence, the given statement is an example of transitive property.
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How many groups of 7 are in 21?
Answers
To find that divide 7 from 21
What is 5/4 divided 9/4
Answers
Answer: [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
[tex]\frac{\frac{5}{4} }{\frac{9}{4} }[/tex]
When multiplying by fractions, invert the fraction in the denominator and multiply it by the numerator.
[tex]\frac{5}{4}*\frac{4}{9}[/tex]
Simplify 4.
[tex]\frac{5}{9}[/tex]
Answer:5/9
Step-by-step explanation:
5/4 ➗ 9/4
The division sign would change to multiplication,and the numerator and denominator in the right hand fraction would be inverted
5/4 x 4/9
Multiply both fractions
(5x4)/(4x9)
20/36
Reduce the fraction to the lowest term by dividing both numerator and denominator by 4
(20 ➗ 4)/(36 ➗ 4)=5/9
The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 7 minutes and a standard deviation of 3 minutes. Based upon the above information and numerically justified, would you be surprised if it took less than one minute to find a parking space?
a. Yes
b. No
c. Unable to determine.
Answers
Answer:
a. Yes
Step-by-step explanation:
Problems of normally distributed samples can be 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.
If the absolute value of the z-score is 2 or larger, X is considered a surprising outcome.
In this question:
[tex]\mu = 7, \sigma = 3[/tex]
Would you be surprised if it took less than one minute to find a parking space?
We have to find the z-score when X = 1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1 - 7}{3}[/tex]
[tex]Z = -2[/tex]
Since Z = -2, the correct answer is:
a. Yes
The square of a number decreased by twice the number is equal to 28 more than the number. Find all possible values for the number
Answers
Answer:
-4 or 7
Step-by-step explanation:
Let x represent the number. Then the problem statement tells us ...
x^2 -2x = 28+x
x^2 -3x = 28 . . . . . subtract x
x^2 -3x +2.25 = 30.25 . . . . add the square of half the x coefficient
(x -1.5)^2 = 30.25 . . . . . . . . write the left side as a square
x -1.5 = ±5.5 . . . . . . . . . . . . take the square root
x = 1.5 ±5.5 = {-4, 7} . . . . . . . add 1.5
The number may be either -4 or 7.
To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75° from the horizontal. an observer at a distance d = 560 m away measures the angle of elevation to the spot of light to be 45°. find the height h of the cloud cover,
Answers
Answer:
The height of the cloud cover is 441.66 meters
Step-by-step explanation:
Distance = 560 m
The height of the cloud cover = h meters
According to the diagram, the worker stands at point R,
Let RT = x
tan 45⁰ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{x}[/tex]
therefore, 1 = [tex]\frac{h}{x}[/tex], h = x
Then tan 75⁰ = [tex]\frac{h}{560-x}[/tex], substituting x = h, we have
3.732 = [tex]\frac{h}{560-h}[/tex]
3.732(560 - h) = h
3.732 × 560 = 3.732h + h
2089.92 = 4.732h
h = 441.66 m
The height of the cloud cover is 228.62 meters
The given parameters are:
[tex]\mathbf{\alpha = 75^o}[/tex]
[tex]\mathbf{\theta = 45^o}[/tex]
[tex]\mathbf{d = 560m}[/tex]
See attachment for the image of the cloud cover.
From the attached image, we have the following sine ratios:
[tex]\mathbf{sin(75) = \frac hx}[/tex]
[tex]\mathbf{sin(45) = \frac h{560 - x}}[/tex]
Make h the subject in both equations
[tex]\mathbf{ h = xsin(75)}[/tex]
[tex]\mathbf{ h = (560 - x) sin(45)}[/tex]
So, we have:
[tex]\mathbf{ xsin(75) = (560 - x) sin(45)}[/tex]
Open brackets
[tex]\mathbf{ xsin(75) = 560sin(45) - x sin(45)}[/tex]
Collect like terms
[tex]\mathbf{ xsin(75) + x sin(45)= 560sin(45) }[/tex]
Evaluate sine 45 and 75
[tex]\mathbf{ 0.9659x + 0.7071x= 560 \times 0.7071}[/tex]
[tex]\mathbf{ 1.673x= 395.976}[/tex]
Divide both sides by 1.673
[tex]\mathbf{ x= 236.69}[/tex]
Recall that:
[tex]\mathbf{ h = xsin(75)}[/tex]
So, we have:
[tex]\mathbf{h = 236.69 \times 0.9659}[/tex]
[tex]\mathbf{h = 228.618871}[/tex]
Approximate
[tex]\mathbf{h = 228.62}[/tex]
Hence, the height of the cloud cover is 228.62 meters
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-3b+7=13 solve for b
Answers
Answer:
b = -2
Step-by-step explanation:
Start with your given:
-3b + 7 = 13
Subtract 7 on both sides:
-3b = 6
Then, divide -3 on both sides and solve:
b = -2
Answer:
b = -2
Step-by-step explanation:
You start by subtracting the 7 on the left and move it to the other side. Then you have 6 on the right and -3b on the left. Then you divide the -3 on each side and that gives you b= -2.
Hope this helps.
1. Terry made $53
washing cars. She made
some money selling
cookies. In total she has
$67. How much money
did she make selling
cookies?
Answers
Answer:
Terry made $14 selling cookies.
Step-by-step explanation:
[tex]67-53=14[/tex]
Answer:
$14
Step-by-step explanation:
She made $14 selling cookies.
$67-$53=$14
write an equation of a line that is parellel to x=8 and that passes through the point -3,-2
Answers
Since the line is parallel to x = 8, the slope doesn't change.
In this case, the slope is undefined so nothing changes.
All we need to do is find the x-coordinate in (-3, -2). The x-coordinate is -3.
So, the equation will be x = -3
Best of Luck!
If ab is parallel to cd and the slope of cd is -5, what is the slope of ab?
Answers
Answer:
The slope of AB is -5.
Step-by-step explanation:
Parallel lines copy the same slope, so if CD and AB are parallel lines, they will both have the same slope of -5.
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.The equation ex = 6 − 5x is equivalent to the equation f(x) = ex − 6 + 5x = 0. f(x) is continuous on the interval [0, 1], f(0) = ____, and f(1) = ____. Since f(0) < 0 < f(1), there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation ex = 6 − 5x, in the interval (0, 1).
Answers
Answer:
f(c)=4f, left parenthesis, c, right parenthesis, equals, 4 for at least one ccc between -2−2minus, 2 and 11
Step-by-step explanation:
hope this helps
There is a root in the given equation ex = 6 − 5x, in the interval (0, 1).
It is required to find the functions has f(0) and f(1).
What is function?A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given:
Using Intermediate value Theorem we have
If F(x) is continuous and f(a) and f(b) have opposite signs then there will be at a point (a ,b) whereby F(c) = 0
The equation is
[tex]f(x) = e^{x} - 6 + 5x = 0[/tex] on interval [0, 1],
This shows that the F(x) is continuous on (0,1).
[tex]f(0) = e^{0} - 6 + 5*0 = -5\\ \\f(1) = e^{1} - 6 + 5*1 = e-1[/tex]
e = 2.7182
since the functions has f(0) and f(1) have opposite signs then there is at a point whereby F(c) = 0 ( intermediate value theorem fulfilled )
Hence, there is a root in the given equation ex = 6 − 5x, in the interval (0, 1).
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A movie theater decreased the size of its popcorn bags by 20%. If the old bags held 15 cups of popcorn, how much do the new bags hold
Answers
Answer:
Your answer will be [tex]12[/tex] cups of popcorn.
Step-by-step explanation:
To find out how much the new bags hold, you need to find out the discount.
[tex]\frac{20}{100 } = .2[/tex]
[tex]15 * .2 = 3[/tex]
We know that the discount is [tex]3[/tex].
To figure out how much the new bags hold, subtract by the old bags.
[tex]15 - 3 = 12[/tex]
The new bags hold 12 cups of popcorn.
Bob and Cheryl are taking a road trip that is 188.20 miles. Bob drove 1/4 of the total distance. How many miles did Bob drive
Answers
Answer:47.05 miles
Step-by-step explanation:
Divide 188.20 by 4 be careful of where you put the decimal point. It is also possible to multiply 188.20 by .25 and get the same answer.
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answers
Answer:
True
Step-by-step explanation:
You should always check just in case a mistake or miscalculation was made. To check, substitute the value you got for the variable into the equation and solve.
For example,
x=2
8x-2=14
Substitute 2 in for x
8(2)-2=14
16-2=14
14=14
Since this is true, we know that 2 is the correct solution.
1 hour is equal to how many seconds
Answers
Answer: 3600 seconds
Step-by-step explanation:
60 seconds in a minute
60 minutes in an hour
(60)(60) = 3600
Answer:
3600
Step-by-step explanation:
There are 60 seconds in 1 minute
30 minutes equal 1800
So, 1800 + 1800 is 3600.
Hope this helps! :)
sam has 356 stuffed animals all of wich are either cats or eliphants the number of elephants he owns is 17 more than twice the number of cats.
how many of each type of stuffed animal does he own.
Answers
Answer:
113 cats243 elephantsStep-by-step explanation:
If Sam subtracts 17 elephants from his collection, he has 339 stuffed animals that are 2/3 elephants and 1/3 cats.
The number of cats is 339/3 = 113.
The number of elephants is 356 -113 = 243 = 2·113 +17.
Sam has 113 cats and 243 elephants.
what is the probability that a data value and a normal distribution is between a z score -1.32 and a z score of 0.94
Answers
Answer:
0.733
Step-by-step explanation:
Using a calculator or table:
P(-1.32 < Z < 0.94) = P(Z < 0.94) − P(Z < -1.32)
P(-1.32 < Z < 0.94) = 0.8264 − 0.0934
P(-1.32 < Z < 0.94) = 0.733
What is the area of the triangle
Answers
Answer:
A. 6 inchesssssssss
Answer:
6
Step-by-step explanation:
if a line is perpendicular to y=-2/3x+2, will it be perpendicular to 2x+3y=12?
Answers
Answer:
3x + 2y = -2
Step-by-step explanation:
Given Equation is − 2 x + 3 y = 12
3 y = 2 x + 12
y = ( 2 /3 ) y + 12
Slope of this line is m = 2/ 3
Slope of Line A m a = 2
Slope of Line B m b = 2/ 3
Slope of Line C m c = − ( 2 /3 )
Slope of Line D m d = − ( 3 /2 )
since m d = − 1 /m , D is perpendicular to the given line
A pediatrician randomly selected 10 parents of his patients. Then he surveyed the parents about their opinions of different kinds of diapers. Identify the population and sample in this setting. Choose 1 answer
Answers
Answer:
c) The population is the parents of the pediatrician's patients; the sample is the
10
1010 parents of patients selected.
Step-by-step explanation:
Answer:
c) The population is the parents of the pediatrician's patients; the sample is the
10
1010 parents of patients selected.
Step-by-step explanation:
Find the mean, median, and mode(s) of the data. Choose the measure that best represents the data. 31, 35, 2, 32, 27, 35
Please Answer Quickly :^)
Answers
median : 31.5
mode : 35
Daniel has $5000 in a savings account, has $7000 in investments, owns a
$10,000 car, and owns a $32,000 house. What is the total value of his large
assets?
O A. $42,000
B. $22,000
C. $12,000
D. $54,000
Answers
Answer:$42,000
Step-by-step explanation:
The total value of his large assets is $42,000.
What is large assest value?Asset size is the total market value of the securities in a fund. It can also be referred to as assets under management.
Daniel has $5000 in a savings account, has $7000 in investments, owns a $10,000 car, and owns a $32,000 house.
The total value of his large assets is determined in the following steps given below.
[tex]\rm Large \ assest = House + Car\\\\ Large \ assest = 32000+10000\\\\ Large \ assest = 42000[/tex]
Hence, the total value of his large assets is $42,000.
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