For any positive numbers a, b, and d, with b + 1, logo
= d.logy a.
A. da
B. ad. logo ad
оооо
c. logo a + logo d
+
D. ad
Answers
For any positive numbers a, b, and d, with b ≠ 1, \(d*log_ba=lob_ba^d\)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given:
\(d*log_ba\\\\Using\ law\ of\ logarithms:\\\\d*log_ba=lob_ba^d\)
For any positive numbers a, b, and d, with b ≠ 1, \(d*log_ba=lob_ba^d\)
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Related Questions
How much would you need to deposit in an account now in order to have $3000 in the account in 15 years? Assume the account earns 3% interest compounded monthly.
Answers
Answer:
Principal = Total ÷ (1 + Rate)^years
That formula is found here: http://www.1728.org/compint2.htm
Principal = 3.000 / (1.03) ^ 15
Principal = 3.000 / 1.5579674166
Principal = $1,925.59
Step-by-step explanation:
A study of the career paths of hotel general managers sent questionnaires to an SRS of 160 hotels belonging to major U.S. hotel chains. There were 103 responses. The average time these 103 general managers had spent with their current company was 11.7 years. Give a 99% confidence interval for the mean number of years general managers of major-chain hotels have spent with their current company. (Take it as known that the standard deviation of time with the company for all general managers is 3.6 years.)
Answers
Answer:
(10.78483, 12.61517)
Step-by-step explanation:
It is given that the genera mangers of few hotels were sent some questionnaires for conducting a study for the career paths in the major hotel chains of the United States.
Number of hotels = 160
Number of response received = 103
The average number of years these general mangers was in their current hotels, \($\bar x$\) = 11.7 years
Confidence Interval, CI = 0.99
Therefore,
a = 0.01, |Z(0.005)| (from standard normal table)
∴ 99% of CI = \($\bar x \pm Z \times \frac{s}{\sqrt n}$\)
\($= 11.7 \pm 2.58 \times \frac{3.6}{\sqrt {103}}$\)
\($(10.78483, 12.61517)$\)
Is the data set approximately periodic?
If so, what are its period and amplitude?
Hour
Number of cars
1 2 3
4
5
6
7 8 9 10 11 12
52 76 90 75 91 104 89 105 119 103 121 135
Answers
The data set is approximately periodic with a period of 3 and an amplitude of about 7.5.
How to explain the valueThe period is the length of time it takes for the data to repeat itself. In this case, the data repeats itself every 3 hours. The amplitude is the distance between the highest and lowest values in the data set. In this case, the amplitude is about 7.5 cars.
Hour | Number of cars
------- | --------
1 | 90
2 | 52
3 | 76
4 | 75
5 | 91
6 | 104
7 | 89
8 | 105
9 | 119
10 | 103
11 | 121
12 | 135
As you can see, the data repeats itself every 3 hours. The highest value in the data set is 135 cars, and the lowest value is 52 cars. The difference between these two values is 83 cars, which is about 7.5 times the average number of cars (90 cars). Therefore, the amplitude of the data set is about 7.5 cars.
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Question 8: The equation of motion of a particle is
s = t^3 4t^2 + 2t + 8
Where s is in meters
and t is in seconds
Find the acceleration after t=5 seconds.
Answers
Answer:
D) \(22\:\text{m/s}^2\)
Step-by-step explanation:
Acceleration is the derivative of velocity, which is the derivative of position, so we must differentiate the function twice:
Position of Particle: \(s(t)=t^3-4t^2+2t+8\)
Velocity of Particle: \(v(t)=3t^2-8t+2\)
Acceleration of Particle: \(a(t)=6t-8\)
After \(t=5\) seconds, the acceleration of the particle is \(a(5)=6(5)-8=30-8=22\:\text{m/s}^2\)
The acceleration of the particle after 5 seconds is 38 m/s².
What is acceleration?Acceleration is the rate of change of velocity or the slope of velocity.
We know that the first derivative of motion or speed is velocity and the second derivative of motion or speed is acceleration.
∴ We have to take the derivative of s = t³ + 4t² + 2t + 8 twice to obtain the equation of acceleration and replace t with 5 to get the acceleration value after 5 seconds.
Now, s = t³ + 4t² + 2t + 8 meters.
ds/dt = 3t² + 8t + 2 m/s.
d²s/dt² = 6t + 8m/s²
Now, at t = 5 seconds d²s/dt² = 6t + 8 is,
d²s/dt² = 6(5) + 8 m/s².
d²s/dt² = 38 m/s².
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you are helping your sister plan her sweet 16. the venue you want to host it at charges $75 for every 3 guest as well as a rental deposit of $200 write an equation to determine the total party cost
Answers
Answer:
y = 25x + 200
Step-by-step explanation:
y = the total cost of the party
x = the number of guests
75/3 = 25
25 is the cost per guest.
Helping in the name of Jesus.
which of these 3 curves drawn matches the graph of y=2x^2+x
Answers
Answer:
Slope: 1
y-intercept: 8
Step-by-step explanation:
x, y
-8,0
0,8
A vector in standard position has its terminal point at (0,0).O TrueO False
Answers
It is False that
Explanation:
A vector in standard position has its starting point at (0, 0), and its terminal point at (a, b)
It is False
Jerome solved the equation below using the steps shown. Step 1: 3x + 6 = 18 step 2: 3x = 12 step 3: x = 4 what operation did her perform to get from step 2 to step 3
Answers
Answer:
divided both sides of the equation by 3
Step-by-step explanation:
Use implicit differentiation to find an equation of the tangent line to the curve
sin(x+y)=4x−4y at the point (π,π)
Answers
Answer:
The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.
Step-by-step explanation:
o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:
Differentiate both sides of the equation with respect to x:
cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx
Simplify by grouping the terms with dy/dx on one side and the rest on the other side:
cos(x+y) * (1 + dy/dx) + 4dy/dx = 4
Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):
cos(2π) * (1 + dy/dx) + 4dy/dx = 4
Simplify:
-5dy/dx = 4 - cos(2π)
dy/dx = -4/5
Use the point-slope form of the equation of a line to write the equation of the tangent line:
y - π = (-4/5)(x - π)
Simplify:
y = (-4/5)x + (8/5) + π
The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.
Help please!! I will mark brainilist and give a lot of points.
This is Pythagorean theorem.
Formula: a^2+b^2=c^2
When I say ^2 I mean to the power of 2.
The question is asking me to solve for a.
Then give me b and c which is b = 17 1/3 and c = 16.
How do I solve for a when b is greater than c? Won’t that give me a negative a? You can’t have a negative a right?
Unless I’m wrong.
Please help my solve this!!!!! :D
Answers
Answer:
a = 23.588
Step-by-step explanation:
a^2 = 17 1/3^2 + 16^2
a^2 = 300.4 + 256
a^2 = 556.4
a = 23.588 (I rounded to thousandths but you can round to whatever)
Hello there,
I just looked into the question and you are absolutely right whatever you inferred.I think the question might be wrong.The value of c should be greater than b.I guess it will like this:\(b = 16 \: \: \: c = 17 \frac{1}{3} \)The values should be like this.I am solving the equation by this:\( {a}^{2} = {c}^{2} - {b}^{2} \\ = > {a}^{2} = {(17 \frac{1}{3}) }^{2} - {(16)}^{2} \\ = > {a}^{2} = {( \frac{52}{3} )}^{2} - {(16)}^{2} \\ = > {a}^{2} = ( \frac{52}{3} - 16)( \frac{52}{3} + 16) \\ = > {a}^{2} = ( \frac{52 - 48}{3} )( \frac{52 + 48}{3} ) \\ = > {a}^{2} = \frac{4}{3} \times \frac{100}{3} \\ = > {a}^{2} = \frac{400}{9} \\ = > a = \sqrt{ \frac{400}{9} } \\ = > a = \frac{20}{3} \\ = > a = 6 \frac{2}{3} \)So, the value of a is \(a = 6 \frac{2}{3} \)Hope you could get an idea from it.
Doubt clarification - use comment section.
(Elimination Strategies) Which of these strategies would eliminate a variable in the system of equations? x - 2y = 115x + 3y = -11Choose all that apply : A) Add the equations B) Multiply the top equation by 5 , then add the equations . C) Multiply the top equation by -5, then add the equations .
Answers
As we can see the only one is the option C
-5*(x-2y=11)=-5x+10y=-55
5x+3y=-11
then we add the equations
13y=-66
y=-66/13=-5.07
as we can see C is the correct answer
which describes the correct order of steps for constructing an angle bisector of ABC using only a straightedge and compass
Answers
Constructing an angle bisector using only a straightedge and compass involves drawing the Angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle.
To construct an angle bisector using a straightedge and compass, there are several steps that you need to follow. The correct order of steps for constructing an angle bisector of ABC using only a straightedge and compass are listed below:
Step 1: Draw the angle ABC with a straightedge.
Step 2: Place the point of the compass on point B and swing an arc that intersects both lines that make up the angle. Label the two points where the arc intersects the angle as points D and E.
Step 3: Without changing the compass width, place the point of the compass on point D and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point F.
Step 4: Without changing the compass width, place the point of the compass on point E and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point G.
Step 5: Draw the line segment FG with a straightedge. This line segment is the angle bisector of angle ABC.
In summary, constructing an angle bisector using only a straightedge and compass involves drawing the angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle. Following these steps will allow you to construct the angle bisector of ABC accurately.
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In an orchard, there are 15 apple trees, 26 orange trees, and a cherry tree. What is the ratio of apple trees to cherry trees?
A: 41:1
B: 15:14
C: 1:15
D:15:1
NO LINKS
Answers
Answer:
D 15:1
Step-by-step explanation:
15 apple trees
26 orange trees
1 cherry tree
apple trees : cherry trees
15 : 1
Answer: D 15:1
In hopes of encouraging healthier snacks at school, Zack brought in a tray of carrot sticks and apple slices to share. The tray had a total of 25 snacks, of which 12 were carrot sticks.
What percent were carrot sticks?
What percent were apple slices?
Answers
Answer:
48% were carrot sticks.
52% were apple slices.
Step-by-step explanation:
Given that:
Total number of snacks in the tray = 25
Number of carrot sticks = 12
Number of apple slices = 25 - 12 = 13
Percent of carrot sticks = \(\frac{Number\ of\ carrot\ sticks}{Total\ Number}*100\)
Percent of carrot sticks= \(\frac{12}{25}*100\)
Percent of carrot sticks = 0.48 * 100 = 48%
Percent of apple slices = \(\frac{13}{25}*100\)
Percent of apple slices = 52%
Hence,
48% were carrot sticks.
52% were apple slices.
What is 1+57327392393629323
Answers
Answer:
57327392393629324
Step-by-step explanation:
rational number between 2 and 3 ?
Answers
Answer:
2:3
Step-by-step explanation:
It’s easy
Answer:
2.5
Step-by-step explanation:
i think
EXERCISE Carlos is jogging at a constant speed. He starts a timer when he is 12 feet from his starting position. After 3 seconds, Carlos is 21 feet from his starting position. Write a linear equation to represent the distance d of Carlos from his starting position t seconds after starting the timer.
Answers
The linear equation that represent the distance d of Carlos from his starting position is d=3t+12 where d denotes the distance and t denotes the time.
What is the meaning of speed?
The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined.
Given that when Carlos is 12 feet from his starting position, starts a timer.
He is 21 feet from his starting position after 3 s.
He covers (21 - 12) = 9 feet in 3 second.
The speed of an object is the distance that covers in unit time.
The Carlos's speed is 9/3 = 3 feet/s.
After t seconds, he covers (3×t) = 3t feet.
The distance of his from his starting position after t seconds is (3t + 12) feet.
The linear equation is d = 3t + 12.
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Please look at the graphs in the photo. Thank you!
Answers
(a). The graph of y = -f(x) is shown in the image below.
(b). The graph of y = g(-x) is shown in the image below.
How to draw the graph of the transformed functions?By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;
y = -f(x)
y = -|x + 2| - 4
Part b.
In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = rise/run
Slope (m) = -2/4
Slope (m) = -1/2
At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -1/2(x - 0)
g(x) = -x/2 + 5, -4 ≤ x ≤ 4.
y = g(-x)
y = x/2 + 5, -4 ≤ x ≤ 4.
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Angela's effective federal tax rate is 17%. Last year, she was able to reduce taxable income by
contributing $250.00 per semi-monthly paycheck to her tax -deferred retirement account and $72.07 per
semi-monthly paycheck to her flexible spending account. How much did she reduce her federal taxes by if
her gross semi-monthly pay is $2,819.96?
Answers
Answer:
Step-by-step explanation:
work out the area of the circle
take pi to be 3.142 give your answer to 1 decimal place
radius 8
Answers
The area of the circle with the given radius is 201.088 square units.
What is area of a circle?The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.
Given that, the radius of a circle is 8 units.
Here, area of a circle
= 3.142×8²
= 3.142×64
= 201.088 square units
Therefore, the area of the circle is 201.088 square units.
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Simplify the following expression:
√-36+√-100+ 7
O A. 7+ 16i
OB. 7+√136i
O C. 16
C. 16 - 7i
O D. 23 + 0i
Answers
√-36 + √-100 + 7
To simplify this expression, we need to first remove the negative radicals. We can do this by squaring both sides of the equation:
√-36 = -6
√-100 = -10
Substituting these values back into the expression, we get:
-6 + -10 + 7 = -19 + 7 = -12
So, the simplified expression is:
-12
Since the expression is already in its simplified form, there is no need to factor it further.
simply your answer someone help
Answers
Hope it helps.
Are the triangles below right, obtuse or acute?
Answers
can someone please help me with this one question!
Answers
Answer:
RST≈TSR FOR YOU PLAESE RANK ME HELPING HAND
Find the difference: 4.203 - 0.01
Answers
Answer:
4.193
Step-by-step explanation:
you line up the decimals then subtract to get 4.193
75 points Dilations of Segments and Angles
CD is dilated by a scale factor of 3/4 to form C ′ D ′ . CD measures 2. What is the measure of C ′ D ′ ?
Answers
Answer
0.823742
Step-by-step explanation:
just a genius
A cereal box has dimensions of 12 inches, (7)3/4 inches, and 2 inches. A pastry box has a dimensions of (3)2/3 inches, (3)1/2 inches, and (2)1/3 inches. What is the difference in volume, cubic inches, between the two boxes. show your work
Answers
The difference in volume between the two boxes would be = 156in³
How to calculate the difference in volume between the boxes?To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;
Volume = length×width×height.
For box 1 = length = 12in, width = 7¾in, height= 2in
Vol = 12×7¾×2 = 186in³
For box 2; length = 3⅔in, width = 3½in, height= 2⅓in
Volume = 3⅔×3½×2⅓ = 30
The difference = 186-30 = 156in³
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4. Amy, Betty and Carol have 96 books altogether. Betty has 6 books less than Amy and Carol has half as many as Betty. How many books does each girl have?
Answers
The Amy has 42 books, Betty has 36 books, and Carol has 18 books.
Let's set up equations to represent the given information:
Let A represent the number of books Amy has.
Let B represent the number of books Betty has.
Let C represent the number of books Carol has.
Let's say Amy has x books.
Betty has 6 books less than Amy, so Betty has (x - 6) books.
Carol has half as many books as Betty, so Carol has (x - 6)/2 books.
According to the problem, the total number of books they have is 96.
So, we can write the equation:
x + (x - 6) + (x - 6)/2 = 96
To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:
2x + 2(x - 6) + (x - 6) = 192
2x + 2x - 12 + x - 6 = 192
5x - 18 = 192
5x = 210
x = 42
Amy has 42 books.
Betty has (42 - 6) = 36 books.
Carol has (36)/2 = 18 books.
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Least to greatest (sorry I’m horrible at simple math)
Answers
Step-by-step explanation:
Least to greatest
= 0.919, 0.99, 1.09
Answer:.919,099,1.09
Step-by-step explanation:
6. The angle relationship shown is-
مرا
60°
30°
O complementary angles
O supplementary angles
O vertical angles
O angle bisector
Answers
Answer:
60+30=90 degrees = complementary angles.
Step-by-step explanation: