Answers
Answer:
A) [tex]x = \dfrac{\log_6(46) + 6}{4}[/tex]
B) [tex]x = \dfrac{\ln(11)}{2}[/tex]
C) [tex]x = \dfrac{11}{5}[/tex]
Step-by-step explanation:
A) We can solve for x by taking log base 6 of both sides.
[tex]\log_6(6^{4x-6}) = \log_6(46)[/tex]
[tex]4x - 6 = \log_6(46)[/tex]
[tex]4x = \log_6(46) + 6[/tex]
[tex]\boxed{x = \dfrac{\log_6(46) + 6}{4}}[/tex]
B) First, we have to divide both sides by 2.
[tex]2e^{2x} / 2= 22 / 2[/tex]
[tex]e^{2x} = 11[/tex]
Then, we can solve for x by taking the natural log (log base e) of both sides.
[tex]\ln(e^{2x})= \ln(11)[/tex]
[tex]2x= \ln(11)[/tex]
[tex]\boxed{x = \dfrac{\ln(11)}{2}}[/tex]
C) We can solve for x by raising 2 to the power of each side.
[tex]2^{\log_2(5x + 5)} = 2^4[/tex]
This cancels the log base 2 on the left.
[tex]5x + 5 = 16[/tex]
[tex]5x = 11[/tex]
[tex]\boxed{x = \dfrac{11}{5}}[/tex]
Related Questions
The value of the expression 0.738 divided by 8.2 is between which two numbers?
A) 0.06 and 0.08 B) 0.08 and 0.1 C) 0.1 and 0.5 D) 0.7 and 1
Answers
0.738 ≈ 0.7
8.2 ≈ 8.0
Then we can divide 0.7 by 8.0:
0.7 / 8.0 ≈ 0.0875
So the value of the expression is approximately 0.0875. This is between the values in answer choice B, 0.08 and 0.1. Therefore, the answer is B) 0.08 and 0.1.
Answer:
B) 0.08 and 0.1
The answer was 0.09, which is between 0.08 and 0.1
What happens to a consistent slope when the y value starts to decrease and the x value remains the same over time?
A. Y decreases and X decreases
B. Y decreases and X increases
C. Y increases and X increases
D. Y increases and X decreases
Answers
The correct answer is option B:
⇒ Y decreases and X increases.
Given that;
the y value starts to decrease and the x value remains the same over time.
Now, We know that;
the slope remains constant, but the y value decreases as you move along the slope in the negative y direction, while the x value increases.
Hence,
If the y value starts to decrease while the x value remains the same over time on a consistent slope,
Thus, The correct answer is option B:
⇒ Y decreases and X increases.
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How do I do my calculations?
Answers
The area of the shaded region for the normal distribution is approximately 0.6985.
We have,
To find the area of the shaded region under the standard normal distribution curve between z = -0.87 and z = 1.24, we can use a standard normal distribution table or a calculator with a standard normal distribution function.
Using a standard normal distribution table, we look up the area to the left of z = -0.87 and the area to the left of z = 1.24 and then subtract the smaller area from the larger area to find the area between z = -0.87 and z = 1.24.
The table value for z = -0.87 is 0.1949, and the table value for z = 1.24 is 0.8934.
The area between z = -0.87 and z = 1.24 is:
= 0.8934 - 0.1949
= 0.6985
So the area of the shaded region is approximately 0.6985.
Thus,
The area of the shaded region for the normal distribution is approximately 0.6985.
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Give me the domain and range
Tell me if the graph is a function or not
Answers
The domain and range of the graph are domain = [-2, 5] and range is [-6, 2] and the graph is not a function
Calculating the domain and range of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the x values to be
x = -2 to 5
On the graph, we have the y values to be
y = -6 to 2
This means that domain = [-2, 5] and range is [-6, 2]
If the graph is a function or notThe graph is the graph of a circle
A circle does not represent a function
Hence, the graph is not a function
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Solve for x, y and z
2x – y + 3z = 10
x + 3y – 2z = 5
3x – 2y + 4z = 12
Answers
The solution to the system of equations is:
x = 3, y = 2, z = 2
To solve for x, y, and z, we can use the elimination method or substitution method. Here, we will use the elimination method.
First, we will eliminate y from the equations by multiplying the first equation by 3 and the second equation by 1, and then adding them:
(3) (2x – y + 3z = 10)
6x – 3y + 9z = 30
(1) (x + 3y – 2z = 5)
x + 3y – 2z = 5
Adding the two equations gives:
7x + 7z = 35
Simplifying, we get
x + z = 5 (Equation 1)
Next, we will eliminate y again by multiplying the second equation by 2 and the third equation by 3, and then adding them:
(2) (x + 3y – 2z = 5)
2x + 6y – 4z = 10
(3) (3x – 2y + 4z = 12)
9x – 6y + 12z = 36
Adding the two equations gives:
11x + 8z = 46
Substituting x + z = 5 from Equation 1 into the above equation, we get:
11(x + z) + 8z = 46
11x + 19z = 46
Solving for z, we get:
z = 2
Substituting z = 2 into x + z = 5 from Equation 1, we get:
x + 2 = 5
x = 3
Finally, substituting x = 3 and z = 2 into any of the original equations, we can solve for y:
2x – y + 3z = 10
2(3) – y + 3(2) = 10
6 – y + 6 = 10
y = 2
Therefore, the solution to the system of equations is:
x = 3
y = 2
z = 2
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I can prove that 2=1, where is the error?
X = 1
X+X = 1+X
2x = 1+X
2x = X+1
2X-2 = X+1-2
2x-2 = X-1
2 (x-1)/(x-1) = X-1/X-1
2 times 1 = 1 1-1 / 1-1
2 = 1
I subtracted -2
because thats the # I chose to subtract with.
Answers
Answer:The algebraic steps you have taken are incorrect, leading to an invalid conclusion. Let's go through each step and see where the mistake is made:
X = 1 (given)
X+X = 1+X (adding X to both sides)
2X = 1+X (combining like terms)
2X = X+1 (rearranging terms)
2X-2 = X+1-2 (subtracting 2 from both sides)
2X-2 = X-1 (simplifying)
2(x-1)/(x-1) = (x-1)/(x-1) (dividing both sides by x-1, note that x cannot be 1 as it would result in division by 0)
2 = 1 (canceling out the (x-1)/(x-1) on both sides)
The error lies in dividing both sides by (x-1) in step 7. Although (x-1) appears on both sides of the equation, it is not equal to zero as x cannot be 1 due to division by zero. Dividing by (x-1) effectively cancels it out, leading to the incorrect result of 2=1.
Step-by-step explanation:
Olympic size swimming pools are 50 meters long and 25 meters wide with a minimum depth of 2 meters. If the swimming pool is a rectangular prism and water weighs 1000 kilograms per cubic meter, what is the weight of the water in the smallest possible full Olympic size pool in kilograms?
Answers
Answer:
660,430 gallons AKA 2499.9995045071 kilograms
you would proably round it to 2500 kilograms
Step-by-step explanation:
looked it up, had the same measurements as you gave
The coordinate of the points below represents the vertices of a rectangle what is the perimeter in units of the rectangles WXYZ
Answers
The perimeter of the rectangle is P = 18 units
Given data ,
Let the rectangle be represented as ΔWXYZ
Now , the coordinates of the triangle are
W ( 3 , 3 ) , X ( 8 , 3 ) , Y ( 8 , 7 ) and Z ( 3 , 7 )
The perimeter of the rectangle = 2 ( length + width )
The width of the rectangle W = ( 7 - 3 ) = 4 units
The length of the rectangle L = ( ( 8 - 3 ) = 5 units
So , P = 2 ( 4 + 5 )
P = 2 x 9
P = 18 units
Hence , the perimeter is 18 units
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3. Olivia is constructing a monument to honor the heroes in her community. It will be in
the shape of a regular pentagonal prism and stand 10 feet tall. She will need 5,119.5
cubic feet of concrete to fill the prism. Olivia will run lights across the top of the
monument from the center to the midpoint of one side.
17.25 ft
SCRATCHPAD
10 ft
Answers
The height will be 61.8 ft
How to solve for the heightFind the volume of prism
Volume = Base Area × Height
since height = 10 feet
5,119.5 ft³ / 10 ft
= 511.95 ft²
formula for the area of a regular polygon is:
Area = (Perimeter × Apothem) / 2
ide length of the pentagon as 's' and the apothem as 'a'
511.95 ft² = (5s × a) / 2
angle at the center of the pentagon is 360° / 5 = 72°
72 / 2 = 36 degrees
tan(36°) = (s/2) / 17.25
solve for the value of s
s = 2 × 17.25 × tan(36°)
= 12.36 ft
5 s =
5 x 12.36 ft
= 61.8 ft
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PLEASE HELP (WILL GIVE BRAINLIEST)
Answers
Answer:
$5.50(2/3)π(6.5^3) = $3,163.45
$5.50(2/3)(3.14)(6.5^3) = $3,161.85
$3,161.85 is the correct answer.
Select all of the values of x that make the inequality -x+6 ≥ 10 true.
Answers
Which expression is equivalent to -√324?
A. -(32)4/5
B. -(32)5/4
C. (-32)4/5
D. (-32)5/4
Answers
In an election, the median number of votes a candidate received in 6 towns was 250. Which statement MUST be true about this election?
OA. The total number of votes the candidate received in the election was 1500.
OB. The candidate received at least 250 votes in half of the 6 towns.
OC. The candidate received exactly 250 votes in at least two of the towns.
O D. The total number of votes received by all the candidates in the election was 1500.
Answers
Answer:
B. The candidate received at least 250 votes in half of the 6 towns.
This is because the median number of votes is the middle value when all the vote counts are put in order. This means that at least three towns gave the candidate more than 250 votes, and at least three towns gave the candidate fewer than 250 votes. So, the candidate received at least 250 votes in half of the 6 towns. The total number of votes the candidate received in the election cannot be determined from this information. Similarly, the number of votes received in individual towns cannot be determined.
What are the coordinates of the vertex of the graph of:
f(x) = 2 lx - 3l
Enter your answer in the boxes.
( ), ( )
Answers
Answer:
(3, 0)
Step-by-step explanation:
It might be first helpful to think about the function [tex]|x-3|[/tex], we will call this [tex]g(x)[/tex]. So, [tex]g(x)=|x-3|[/tex].
The modulus (absolute value) function reflects any points on a graph that go below the x-axis up into the positive x region.
We know that the graph of [tex]y=x-3[/tex], will cross the x-axis at (3,0). We can work this out by setting y to 0 and rearranging for x. At the x-axis, y = 0.
Therefore, when the modulus comes in, a vertex will be created at (3,0).
But that is the vertex of [tex]g(x)[/tex].
Using basic algebra we can derive from previous working that [tex]f(x)=2g(x)[/tex].
Graphically, the multiplier of 2 on the outside of [tex]g(x)[/tex] stretches the graph in y-axis, and does so by the scale factor of 2.
With our vertex (3,0), the y value is 0. And if you multiply 0 and 2 together, 0 is produced. The x value will remain unchanged as a result of this transformation.
Therefore, the vertex of [tex]f(x)[/tex] is (3,0).
So I still don’t understand.
Answers
An equation for the height of the rocket after t seconds is h(t) = -16t² + 352t.
The time it takes for the rocket to reach a height of 0 is 22 seconds.
The time it takes to reach the top of its trajectory is 11 seconds.
The maximum height is 1,936 feet.
The time it takes to reach a height of 968 feet is 18.8 or 3.2 seconds.
How to determine the time when the rocket would hit the ground?Based on the information provided, we can logically deduce that the height (h) in feet, of this rocket above the ground is related to time by the following quadratic function:
h(t) = -16t² + Vit
When the initial velocity is 352 feet per seconds, the height function becomes;
h(t) = -16t² + 352t
Generally speaking, the height of this rocket would be equal to zero (0) when it hits the ground. Therefore, we would equate the height function to zero (0) as follows:
0 = -16t² + 352t
352t = 16t²
Time, t = 352/16
Time, t = 22 seconds.
Next, we would determine the maximum height of this rocket by taking the first derivate in order to determine the time (t) it takes;
h(t) = -16t² + 352t
h'(t) = -32t + 352
352 = 32t
t = 352/32 = 11 seconds.
h(11) = -16(11)² + 352(11)
h(11) = 1,936 feet.
At a height of 968 feet, the time is given by;
968 = -16t² + 352t
16t² - 352t + 968 = 0
t² - 22t + 60.5 = 0
Time, t = 18.8 or 3.2 seconds.
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A marketing research company desires to know the mean consumption of milk per week among people over age 30 . They believe that the milk consumption has a mean of 3.5 liters, and want to construct a 85% confidence interval with a maximum error of 0.07 liters. Assuming a standard deviation of 1.4 liters, what is the minimum number of people over age 30 they must include in their sample? Round your answer up to the next integer.
Answers
The minimum number of people over age 30 they must include in their sample is: 829 people
How to calculate the standard error?The formula for calculating the standard error is:
SE = μ ± Z(σ/√N)
Where:
σ = the standard deviation,
N = the sample size,
Z = the Z value for the percent confidence level desired.
We must find the Z value, at the 85% confidence level from a Cumulative Standardized Normal table for the 99% confidence level. This gives us the value of Z = 1.44
σ = 1.4 liters
N = 0.07
Thus:
0.07 = 1.44(1.4/√N)
0.07/1.44 = 1.4/√N
1.4/√N = 0.04861
√N = 1.4/0.04861
N = (1.4/0.04861)²
N = 829 people
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A house is infested with mice and to combat this the householder acquired four cats cyd, Greg, Ken, and Rom, The householder observes that only half of the creatures caught are mice. A fifth are voles and the rest are birds. 20% of the catches are made by Cyd, 45% by Greg, 10% by Ken and 25% by rom. a) What is the probability of a randomly selected catch being a mouse caught by Cyd? b) Bird not caught by Cyd? c) Greg's catches are equally likely to be a mouse, a bird or a vole. What is the probability of a randomly selected d) The probability of a randomly selected catch being a mouse caught by Ken is 0.05 . What is the probablity that a catch being a mouse caught by Greg? e) Given that the probability of a randomly selected catch is a mouse caught by Rom is 0.2 verify that the catch made by Ken is a mouse? probability of a randomly selected catch being a mouse is 0.5 . f) What is the probability that a catch which is a mouse was made by Cyd?
Answers
Note that the probabilities are given below.
What are the probabilities?
a) the probability of a randomly selected catch being a mouse caught by Cyd
p(Catching a mount) x p(Cyd made the catch)
= 0.5x .2
= 0.1
b) the probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.
Thus
P(that a catch is a bird) x p(the Cyd didn't make the catch)
= 0.3 x 0.8
=0.24
c) The probability of a randomly selected catch being caught by Greg is 0.45
To calculate, we say
(0.5 x0.45) + (0.3 x 0.45) + (0.2 x .45)
= 0.45.
d)
P (mouse caught by Greg) = (0.45 x 0.5) / 1
= 0.225.
e) P(catch is a mouse caught by Ken and catch is a mouse)
= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)
= 0.05 x 0.1
= 0.005
f)
P (catch made by Cyd | catch is a mouse)
= 0.1 x 0.2 / 0.5
= 0.04
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Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h. A. h(2) = 16 B. h(8) = 21 C. h(13) = 18 D. h(-3) = -1
Answers
The statement that could be true for h is h(2) = 16.
Option A is the correct answer.
We have,
The function h has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25, and we know that h(8) = 19 and h(-2) = 2.
To determine which statement could be true for h, we can use the given domain and range, along with the two known function values, to narrow down the possible values of h(x) for different values of x.
h(2) = 16
We do not have enough information to determine whether this statement could be true or not.
It is possible that h(2) = 16, but it is also possible that h(2) could be a different value within the range of 1 ≤ h(x) ≤ 25.
h(8) = 21
This statement cannot be true, as we already know that h(8) = 19.
h(13) = 18
This statement cannot be true, as 13 is outside the given domain of -3 ≤ x ≤ 11.
h(-3) = -1
This statement cannot be true, as -1 is outside the given range of 1 ≤ h(x) ≤ 25.
Therefore,
The statement that could be true for h is h(2) = 16.
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(Please help in image)
Answers
Answer:
[tex] {x}^{2} + 11x + 18 = [/tex]
[tex](x + 2)(x + 9)[/tex]
The two numbers are 2 and 9.
2 + 9 = 11, and 2 × 9 = 18.
Oliver did the high jump three times. His scores were 7.016 feet, 5.42 feet, and 8.308 feet. How many feet did he jump in total? pleas help im in test
Answers
The total height of the three jumps is A = 20.744 feet
Given data ,
1st high jump score: 7.016 feet
2nd high jump score: 5.42 feet
3rd high jump score: 8.308 feet
On adding the scores , we get
7.016 + 5.42 + 8.308 = 20.744 feet
On simplifying the equation , we get
A = 20.744 feet
Hence , Oliver jumped a total of 20.744 feet in the three high jumps
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When Emilia looked at her cell phone bill for the month, she saw that she had spent 1/12 of her minutes talking to her mother and 5/12 of her minutes talking to her best friend. What fraction of the minutes did Emilia spend talking to either her mom or her best friend?
Answers
Answer:
The answer to your problem is, She spend more talking to her friend then her mother
Step-by-step explanation:
The question asking:
What fraction of the minutes did Emilia spend talking to either her mom or her best friend?
So we can see that she talks to her friend instead of her mother shown;
[tex]\frac{1}{12} < \frac{5}{12}[/tex]
The total equals to [tex]\frac{6}{12} or\frac{1}{2}[/tex]
So, She spend more talking to her friend then her mother
Thus the answer to your problem is, She spend more talking to her friend then her mother
The insurance premium of a new bus is GH¢93.30 plus 15% of the insured value. What is the insurance premium of a bus whose insured value is GH¢250.00?
Answers
The requried insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.
The insurance premium of a bus is GH¢93.30 plus 15% of the insured value.
Let's first calculate 15% of¢250.00:
15% of GH¢250.00 = 0.15 x 250.00 = GH¢37.50
Now, we can add this amount to the base premium of GH¢93.30 to find the total insurance premium for the bus:
GH¢93.30 + GH¢37.50 = GH¢130.80
Therefore, the insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.
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What has no solutions in common with 6x+2y=12
Answers
Answer:
-6x - 2y = 12
Step-by-step explanation:
Work out and simplify where possible. A) 3/4 + 5/6. B) 4/7 - 1/3
Answers
3/4 + 5/6 = 9/12 + 10/12 = (9 + 10)/12 = 19/12
B) To subtract 1/3 from 4/7, we also need a common denominator. The least common multiple of 3 and 7 is 21. We can convert both fractions to have a denominator of 21:
4/7 = (4/7) * (3/3) = 12/21
1/3 = (1/3) * (7/7) = 7/21
Now we can subtract the fractions:
4/7 - 1/3 = 12/21 - 7/21 = 5/21
The sum of four consecutive integers is 250. What is the greatest of these integers?
Answers
The greatest of the given integers is 64.
Given that, the sum of four consecutive integers is 250. We need to find what is the greatest of these integers.
Let the consecutive integers be = x, x+1, x+2, x+3
Therefore,
x + x+1 + x+2 + x+3 = 250
4x + 6 = 250
2x + 3 = 125
2x = 122
x = 61
Therefore, the greatest integer = 61 + 3 = 64
Hence, the greatest of the given integers is 64.
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Anna took a job that paid $116 the first week. She was guaranteed a raise of 7% each week. How much money will she make in all over 10 weeks? Round the answer to the nearest cent, and number answer only.
Answers
Anna will make $1602.71 in all over 10 weeks.
Here, the first week salary of Anna = $116
i.e., the initial salary a = $116
She was guaranteed a raise of 7% each week.
so, her salary in the next week would be,
116 + 7% of 116
7 percent of 116 is:
116 × 7/100 = 8.12
so, her salary will be $124.12
So, the equation for the salary after 'm' weeks would be,
[tex]n = 116\times (1 + 0.07)^{m - 1}\\\\n = 116\times (1 .07)^{m - 1}[/tex]
Using this equation , the salary in the second week m = 2 would be,
n = 124.12
Salary in the third week m = 3 would be,
n = 116 × [tex](1.07)^{3-1}[/tex]
n = 132.81
Salary in the fourth week m = 4 would be,
n = 116 × [tex](1.07)^{4-1}[/tex]
n = 142.11
Salary in the fifth week m = 5 would be,
n = 116 × [tex](1.07)^{5-1}[/tex]
n = 152.05
Salary in the sixth week m = 6 would be,
n = 116 × (1.07)⁶⁻¹
n = 162.7
Salary in the seventh week m = 7 would be,
n = 116 × (1.07)⁷⁻¹
n = 174.08
Salary in the eighth week m = 8 would be,
n = 116 × (1.07)⁸⁻¹
n = 186.27
Salary in the nineth week m = 9 would be,
n = 116 × (1.07)⁹⁻¹
n = 199.31
And the salary after the tenth week m = 10 would be,
n = 116 × (1.07)¹⁰⁻¹
n = 213.26
The total money after 10 weeks would be,
T = 116 + 124.12 + 132.81+ 142.11 + 152.05 + 162.7 + 174.08 + 186.27 + 199.31 + 213.26
T = $1602.71
This is the required amount.
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The circumference of a circle is 43.96 m. What is the approximate area of this circle? Use 3.14 for TT.
O 153.86 m²
O 164.32 m²
O 138.03 m²
O 615.44 m²
Answers
Answer:
43.96 = 2πr
r = 21.98/π
A = π(21.98/π)^2 = 483.1204/π = 153.78 square meters
A = 483.1204/3.14 = 153.86 square meters
Filipe practiced 12 fewer hours than Bianca. If Filipe practiced for 16 hours, how long did Bianca practice?
Bianca practiced for
____
hours.
Answers
Answer:
28 hours
Step-by-step explanation:
Let's use "B" to represent the number of hours Bianca practiced.
From the problem, we know that Filipe practiced 12 fewer hours than Bianca, which means:
Filipe's practice time = Bianca's practice time - 12
We are also told that Filipe practiced for 16 hours, so we can substitute that into the equation:
16 = B - 12
To solve for B, we can add 12 to both sides:
16 + 12 = B
So, Bianca practiced for a total of 28 hours.
A girl is three years older than her brother. If their combined age is 35 years, how old is each?
Answers
Answer: The brother is 16 and she is 19.
Step-by-step explanation:
35 - 3 = 32
32 / 2 = 16
16 + 3 = 19
The two tables show the number of copies of album x y and z sold in outlets A , B C and D of w company.
Which outlet sold the greatest amount of copies of album x in July and august
Answers
Outlet A: 80 + 90 = 170
Outlet B: 60 + 70 = 130
Outlet C: 70 + 80 = 150
Outlet D: 90 + 80 = 170
Outlets A and D both sold the greatest amount of copies of album X in July and August, with 170 copies sold each. Therefore, the answer is either A or D.