the solution to the equation log2x + log4x + log16 = 7 the logarithms using the properties of Logarithms is x ≈ 53.408.
To solve the equation log2x + log4x + log16 = 7, we can simplify the logarithms using the properties of logarithms.
First, we can use the property loga + logb = log(ab) to combine the logarithms:
log2x + log4x + log16 = log(2x * 4x * 16)
Next, we simplify the expression inside the logarithm:
log(2x * 4x * 16) = log(32x^3)
Now, our equation becomes:
log(32x^3) = 7
To eliminate the logarithm, we can rewrite the equation in exponential form:
32x^3 = 10^7
Simplifying further:
32x^3 = 10,000,000
Now, we can solve for x by dividing both sides of the equation by 32:
x^3 = 10,000,000 / 32
x^3 = 312,500
To find the value of x, we take the cube root of both sides:
x = ∛312,500
x ≈ 53.408
Therefore, the solution to the equation log2x + log4x + log16 = 7 is x ≈ 53.408.
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A baseball player earns $3 million in 2015. During the next 15 years, the earning increase 4% each year.
Write an exponential growth model giving the earning y (in millions of dollars) t years after 2015. Write the base of the model as a decimal
The exponential growth model for the baseball player's earnings, in millions of dollars, t years after 2015 is[tex]y = 3 \times (1.04)^t,[/tex] with a base of 1.04.
To model the exponential growth of the baseball player's earnings, we can use the formula:
[tex]y = a \times (1 + r)^t[/tex]
where:
y represents the earning in millions of dollars
a represents the initial earning in millions of dollars (in this case, $3 million)
r represents the growth rate per year (4%, which can be expressed as 0.04)
t represents the number of years after 2015
In this case, we want to find the earning y (in millions of dollars) t years after 2015.
Since the initial earning in 2015 is $3 million, we can substitute a = 3.
Therefore, the exponential growth model for the player's earnings is:
[tex]y = 3 \times (1 + 0.04)^t[/tex]
Simplifying the expression further, we have:
[tex]y = 3 \times 1.04^t[/tex]
The base of the model is 1.04, which is the decimal representation of the growth rate (4%).
Using this model, we can calculate the player's earnings for any year after 2015 by plugging in the value of t.
For example, if we want to find the earnings 5 years after 2015, we substitute t = 5 into the equation:
[tex]y = 3 \times 1.04^5[/tex]
This will give us the projected earnings in millions of dollars for that particular year.
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Subtract (8n-5)-(-2n-3)
Answer:
Step-by-step explanation:
( 8n - 5 ) - ( -2n - 3 )
( 8n - 5 ) + ( 2n + 3 )
8n - 5 + 2n + 3
10n - 2
Will mark it brilliant
40. What is mzWXY? How do you know?
W
X
69°
Z
Y
The value of the angle m<WXY is 69 degrees
How to determine angleWe need to know that the shape given is a parallelogram.
The properties of a parallelogram are given as;
Opposite sides of the shape are parallel.Opposite sides of the shape are congruent.Opposite angles of a parallelogram are equal.Same-Side interior angles are supplementary, that is sum up to 180 degrees.Each diagonal of a parallelogram separates it into two equal trianglesThe diagonals of a parallelogram bisect each other.From the information given, we have that;
Angel WZY and Angle WXY are opposite angles of the parallelogram
Then,
m<WXY = 69 degrees
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What is the strength of the association between the two
variables in the scatter plot?
Select from the drop-down menu to correctly complete the
statement.
The strength of association is Choose...
Strong or weak
a cube with a surface area of 6 square inches is removed from the corner of a cube with a surface area of of 96 square inches.
questions
a. what do you think removing the smaller cube from largers cubes has on its surface area? explain your answer
b. find the surface area of the new solid.
a. The surface area of the cube is reduced .
b . The new surface area of the new solid is 90 in²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
a. The surface area of the original cube is 96 in² and a cube of another 6 in² is removed from the old cube.
This means that the surface area of the cube is reduced.
The surface area of a cube is expressed as;
SA = 6l²
where l is the side length of the cube.
b. The surface area of the new solid = surface area of big cube - surface area of old cube = 96-6
= 90 in²
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Graph the circle (x - 3)^2 + (y + 3)^2= 36.
The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.
To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.
The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.
Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.
Using this information, we can proceed to plot the circle on a graph:
Plot the center point: (3, -3).
From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.
Up: (3, -3 + 6) = (3, 3)
Down: (3, -3 - 6) = (3, -9)
Left: (3 - 6, -3) = (-3, -3)
Right: (3 + 6, -3) = (9, -3)
Connect the plotted points to form a circle.
The resulting graph should look like this:
| • (3, 3)
|
| •
| •
__|_____________________________
|
|
|
|
| • (3, -3)
The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.
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Which statements is true and justify your answer
Answer:
Step-by-step explanation:
sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2
Answer:
sin( 3pi/4 ) = -√2/2
So, B.
100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, and period of the function. Then graph the function. Thank you!
The amplitude and the period of the function f(x) = 2cos[3(θ + 45)] + 2 are 2 and 2π/3
The Phase shift is 45 and the vertical shift is 2
How to determine the amplitude and period of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2cos[3(θ + 45)] + 2
A sinusoidal function is represented as
f(x) = Acos(B(x + C)) + D
Where
Amplitude = A
Period = 2π/B
Phase shift = C
vertical shift = D
Using the above as a guide, we have the following:
Amplitude = 2
Period = 2π/2
Next, we have
Phase shift = 45
vertical shift = 2
Hence, the amplitude is 2 and the period is 2π/3
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Suppose you're making a soup that uses 5 cups of chicken broth for 8 servings. You need to make 12 servings of the soup. How much broth do you need?
A) 7.5 cups
B) 2.5 cups
C) 8.7 cups
D) 10 cups
A bag has 6 blocks in it.
Jerry picks a block out of
the bag 60 times. He gets
the green block 43 times.
Based on these results how
many blocks to you expect
to be green? Explain your
reasoning.
We can expect 258 blocks in the bag to be green.
We have to given that,
A bag has 6 blocks in it. Jerry picks a block out of the bag 60 times. He gets the green block 43 times.
Since, We know that Jerry picked a block out of the bag 60 times, and got the green block 43 times.
So the probability of picking a green block is:
P = 43/60
P = 0.7167
This means that out of every 60 blocks picked, there are 43 green.
Now, For this probability to estimate the number of green blocks in the bag.
since, Jerry picked 60 blocks 6 times
When, we assume that the bag contains a total of 360 blocks , we can multiply this total by the probability of getting a green block:
360 x 0.7167 = 258.012
Thus, We can expect 258 blocks in the bag to be green.
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What is the strength of the association between the two
variables in the scatter plot?
Select from the drop-down menu to correctly complete the
statement.
The strength of association is Choose...
Strong or weak
A weak correlation between the two variables is depicted by the scatter plot in the supplied image.
The trend line's points are widely dispersed, which suggests that there is little correlation between the variables.
In a scatter plot, the degree of connection between the two variables can be classified as strong or weak.
A weak correlation indicates that there is a lot of scatter around the trend whereas a high relationship indicates that there is very little scatter in comparison to the trend's movement.
Thus, the given association is weak correlation.
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please help me out with explanation
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
Answer:
891 cm³
Step-by-step explanation:
Since they are the same shape with only their sizes different, that means they have a proportionate ratio so:
2673 / 9 = V / 3
Now make V the formula of the subject:
V = 2673 / 9 TIMES 3 = 891.
Simplify.
√n/18.
Answer choices:
A 1/6n √2.
B √1/9
C 1/6 √2n
Please explain the answer my radical calculator doesn't work on anything with letters in it.
Answer: C 1/6*√2n
Step-by-step explanation:
• Simplify √n/18 as (1/3)^2*n/2
• Multiply them under the radical so the squares 1/3 cancels out to 1/3*√n/2
• Multiply the √n/2 on both sides as √2*n/√2*√2 so it comes out to √2n/2
• Multiply √2n/2 with 1/3 to make √2n/6
√2n/6 is equal to 1/6*√2n
The radical expression √n/18 when simplified is 1/3√n/2
Simplifying the radical expressionFrom the question, we have the following parameters that can be used in our computation:
√n/18
Express 18 as 9 * 2
So, we have the following representation
√n/18 = √n/(9 * 2)
Rewrite as
√n/18 = √n/(2 * 9)
Take the square root of 9
This gives
√n/18 = 1/3 * √n/2
Evaluate the products
√n/18 = 1/3√n/2
Hence, the expression when simplified is 1/3√n/2
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please help! thank uu ~ :)
Answer: It has ans an equal chance of 50-50
Step-by-step explanation: There are 10 of each type, leaving 20 total, half of the candy is Cherry, the other half is Strawberry.
Explain each step and answer 50 points
1 Yes the set of rational expressions is closed under subtraction
2. Yes the set of rational expressions is closed under multiplication
3. No the set of rational expressions is not closed under division
How to determine if the expression is closed
1. The subtraction of two rational expressions results in another rational expression.
= p(x)/q(x) - r(x)/s(x)= ((p(x)s(x) - r(x)q(x))/(q(x)s(x)))
this is also a rational expression.
2. The multiplication of two rational expressions results in another rational expression.
=(p(x)/q(x)) * (r(x)/s(x)) = ((p(x)r(x))/(q(x)s(x)))
this is a rational expression.
3. Division of two rational expressions may result in an expression that is not a rational expression.
= (p(x)/q(x)) / (r(x)/s(x)))
= ((p(x)s(x)) / (q(x)r(x)))
this may not be a rational expression if q(x)r(x) equals zero at some point, causing division by zero
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Need help with pie chart
a. The category that was chosen as approximately 1/4 will be Cat.
b. The percentage that choose other or cat will be 35%.
c. The percentage that choose dog is 16%
a. It should be noted that to determine the category chosen by approximately one-fourth of the community, we need to look for the corresponding section of the pie chart. This shows the cat.
b. The percentage that choose other or cat will be:
= 10% + 25%
= 35%.
c. The percentage that choose dog is:
= 32% / 2
= 16%
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15% of what number is 3?
Answer:
Step-by-step explanation:
15 % of x = 3
[tex]\frac{3x}{20} = 3\\ x = 20[/tex]
Answer:
20
Step-by-step explanation:
Find 1% 3 : 15 = 0.2Find 100% 0.2 × 100 = 20%or solve with an expression
3 : 15 × 100 =
0.2 × 100 =
20
or solve with an equation3 : 15 = x : 100
x = 3 × 100 : 15
x = 20
Which of these contexts describes a situation that is certain?
Rolling an even number on a standard six-sided die, numbered from 1 to 6.
Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on red or yellow or green or blue.
Winning a raffle that sold a total of 100 tickets if you bought 0 tickets.
Reaching into a bag full of 5 strawberry chews and 15 cherry chews without looking and pulling out a pineapple chew.
The context which describes a certain situation from the given is spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on red or yellow or green or blue.
Certain probability or certain situation is defined as the situation where the event is sure to happen.
Rolling an even number on a standard six-sided die, numbered from 1 to 6.
The die can be rolled to odd number. Soo it is uncertain.
Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on red or yellow or green or blue.
This is a certain situation since the spinner will surely land on any of the four colors.
Winning a raffle that sold a total of 100 tickets if you bought 0 tickets.
This is not possible.
Reaching into a bag full of 5 strawberry chews and 15 cherry chews without looking and pulling out a pineapple chew.
This is also not possible.
Hence the certain situation is spinning a spinner.
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The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that exactly 10 flights arrive on time.
Probability that exactly 10 flights arrive on time is 53.33%.
Given that,
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation.
Recently, Southwest Air had the best rate with 80% of its flights arriving on time.
Total number flights in sample = 15
Probability that exactly 10 flights arrive on time is,
P = 10/15 × 80%
= 0.5333
= 53.33%
Hence the required probability is 53.33%.
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I need help right now can someone help me ple
The Area of Rhombus QRST is 78.32 in².
We know the formula of Area of Rhombus
= 1/2 x product of diagonals
We have, QS = 8.8 and RT = 17.8
So, Area of Rhombus QRST
= 1/2 x QS x RT
= 1/2 x 8.8 x 17.8
= 78.32 in²
Thus, the Area of Rhombus QRST is 78.32 in².
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Consider polygon ABCD, shown below.
B
C
E
A
G
F
D
Select all the ways that describe rigid transformations that take AEFD to CFEB.
The rigid transformations that can take AEFD to CFEB are translation, rotation, and reflection.
To describe the rigid transformations that take polygon AEFD to CFEB, we need to identify the transformations that preserve the shape and size of the polygon. Here are some possibilities:
Translation: A translation involves moving the entire polygon without changing its orientation or shape. If we shift polygon AEFD to the right, it will align with polygon CFEB. Therefore, translation is one way to achieve this transformation.
Rotation: If we rotate polygon AEFD around a fixed point, such as the center of the polygon or a vertex, by a certain angle, it can align with polygon CFEB. A rotation preserves the shape and size of the polygon.
Reflection: A reflection involves flipping the polygon across a line, resulting in a mirror image. If we reflect polygon AEFD across a line of reflection, it can match polygon CFEB.
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In one part of a rainforest in South America, 3/5 of the frogs are poisonous. What fraction of the frogs are not poisonous?
2/5 of the frogs in that portion of the South American rainforest are not poisonous.
How to calculate the fraction of frogs that are not poisonous in South American rainforestOn the off chance that 3/5 of the frogs in a rainforest in South America are poisonous, at that point, the remaining division speaks to the frogs that are not poisonous.
To discover this division, we subtract the division of poisonous frogs from 1 (which speaks to the complete):
1 - 3/5 = 5/5 - 3/5 = 2/5
Hence, 2/5 of the frogs in that portion of the rainforest are not poisonous. This fraction represents the parcel of frogs that don't have poisonous characteristics.
It is important to note that this calculation expects that all frogs within the rainforest are either poisonous or notpoisonous, and there are no other conceivable outcomes or middle states.
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Simplify the expression 5x2+6x+4+x2+x
.
Thank You!
The simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.
The given expression is 5x²+6x+4+x²+x
Simplifying the given expression
5x²+6x+4+x²+x
Firstly, put the similar terms together
5x²+x²+6x+x+4
Adding the similar terms
6x²+7x+4
∵ The expression cannot be solved further, 6x²+7x+4 is the final solution.
Therefore, the simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.
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What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 5.6 cm? Enter your answer as a decimal in the box. radians
Answer:
The measure of the central angle in radians is 5.6/8 = 0.7 radians.
Write x2 + 6x − 3 = 0 in the form of (x − a)2 = b, where a and b are integers. (1 point)
(x + 6)2 = 3
(x + 6)2 = 12
(x + 3)2 = 6
(x + 3)2 = 12
Answer:
Step-by-step explanation:
The time (t) required to do a job varies inversely as the number of people (p) working on the job.
It takes 9 hours for 4 roofers to complete a certain job. How long would it take 6 roofers to complete the same job?
hours
Answer:
6 hours
Step-by-step explanation:
Varying inversely simply means using the "inverse proportion" methodSo therefore,
4 roofers= 1 hour
1 roofer= 9 * 4
= 36 hours
Why? Because the lesser amount of workers you have, the more time will be needed so as to complete the work.6 roofers= 36/6=6 hours
The more people you have, the lesser amount of time will be spent on completing the work.Find an angle in each quadrant with a common reference angle with 311°, from 0°≤θ<360°
Angles in each quadrant with common reference angle as 311° are :
First quadrant = 49°, second quadrant = 131°, third quadrant = 229° and fourth quadrant = 311°.
Given that,
Reference angle = 311°
We have to find an angle in each quadrant with this reference angle.
311° is in the fourth quadrant.
The equivalent angle on the first quadrant is,
360° - 311° = 49°
Equivalent angle on second quadrant is,
180° - 49° = 131°
Equivalent angle on third quadrant is,
360° - 131° = 229°
Hence the angles are found.
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25. Solve for the missing variables.
The missing angles in the cyclic quadrilateral are as follows:
a = 101°
b = 67°
c = 84°
d = 80°
How to find the angles in a cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.
Opposite angles of a cyclic quadrilateral is supplementary.
c = 180 - 96
c = 84 degrees
d = 180 - 100
d = 80 degrees
100 = 1 / 2 (a + 99)
100 = 0.5a + 49.5
0.5a = 50.5
divide both sides by 0.5
a = 50.5 / 0.5
a = 101 degrees
84 = 1 / 2 (101 + b)
84 = 50.5 + 0.5b
84 - 50.5 = 0.5b
0.5b = 33.5
b = 33.5 / 0.5
b = 67 degrees
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The quadratic functions f(x) and g(x) are described in the table.
x f(x) g(x)
−6 36 4
−5 25 1
−4 16 0
−3 9 1
−2 4 4
−1 1 9
0 0 16
1 1 25
2 4 36
In which direction and by how many units should f(x) be shifted to match g(x)?
Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units
The direction that the quadratic function f(x) is to be translated is to the left and the units is 4.
Here given two functions, f(x) and g(x).
General form of the quadratic function is,
ax² + bx + c.
It is clear that, f(x) is simply the square of the x values.
f(x) = x²
Since g(x) is the translation of the function f(x) and the value of g(x) = 0, when x = -4,
g(x) = (x + 4)²
That is,
g(x) = f(x + 4).
So f(x) is shifted left by 4 units.
Hence f(x) is shifted left by 4 units.
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