I'm assuming the given log equation is [tex]\log_{\text{x}}(49) = \text{x}[/tex]
If so, then the exponential form is [tex]\text{x}^{\text{x}} = 49[/tex]
This is because the general form [tex]\log_{\text{b}}(\text{x}) = \text{y}[/tex] transforms into [tex]\text{y} = \text{b}^{\text{x}}[/tex]
For both equations, the 'b' is the base.
Keisha has two dogs. The larger dog weighs 1.2 pounds more than the smaller dog. The combined weight of the two dogs is 13.6 pounds. What is the weight, in pounds, of the smaller dog?
Answer:
x = 6.2
Step-by-step explanation:
let ‘x’ denotes the weight of a smaller dog.
“1.2″ + x” be the weight of the larger dog
combined weight = 13.6
smaller dog weight =
x+x+1.2 = 13.6
2x + 1.2 = 13.6
2x = 13.6–1.2
2x = 12.4
x = 12.4/2
x = 6.2 pounds.
Hope you understood it, Happy Learning.
What is the total amount that Matthew's bank will receive after lending him $8,000 for four years at an interest rate of 6 percent, compounded annually? TA= P (1+i)^t
Answer:
10,099.80
Step-by-step explanation:
Given: The principal amount (P)= $8,000
The rate of interest (i)= 6 % = 0.06
Time = 4 years
The formula to calculate the compound amount in x years is given by :-
Then the compound amount received by Matthew after 4 years will be:_
Hence, the total amount that Matthew's bank will receive afeter 4 years =$10,099.80
Answer:
$10,099.82
Step-by-step explanation:
Given formula: [tex]\sf TA = P (1+i)^t[/tex]
where:
TA = total amountP = principal amounti = interest rate (in decimal form)t = time (in years)Given:
P = $8,000i = 6% = 0.06t = 4 yearsSubstituting the given values into the formula:
[tex]\implies \sf TA=8000(1+0.06)^4[/tex]
[tex]\implies \sf TA=10099.81568[/tex]
Therefore, the total amount the Matthew's bank will receive is $10,099.82
You chose an EXPONENTIAL model with the equation:
y=4.04·0.56x
In the context of the tennis balls:
(1) What does 4.04 mean?
(2) What does 0.56 mean?
Equation: y = 4.04·0.56^x
(1) What does 4.04 mean?Solution: Here in the exponential model, the height is 4.04 feet when the bounce number is 0. It represents the initial height. (original, starting value)
(2) What does 0.56 mean?Solution: 0.56 represents the represents the growth rate of how much the height will decrease with the amount of bounces. (growth factor)
Extra's :x represents the unit of measure of bounces.
General equation
y=ab^x#1
Here
a is 4.04So it represents the initial value where x is 0 as any number⁰ is 1#2
0.56 is bit's the rate of change with respect to xComposite Figures
Find the volume of the composite figure.
First, find the volume of the cylinder.
Use 3.14 for TT.
Cylinder
8 cm
Volume = [?] cm³
5 cm
4 cm
Rectangular prism
Volume = [] cm³
8 cm
1,005.44
Pir^2h
3.142*8*8*5
1,005.44
Work out the surface area of this cylinder
Diameter is 12 cm
Height is 25 cm
Answer:
The surface area of this cylinder is 1168.67
Step-by-step explanation:
To find the surface area of a cylander use this formula
A = 2π[tex]\frac{d}{2}[/tex]h+2π([tex]\frac{d}{2}[/tex])²Plug in
A = 2 × π × [tex]\frac{12}{2}[/tex] × 25 + 2 × π × [tex]\frac{12}{2}[/tex]²Answer is 1168.67
Write the slope-intercept form of the equation of the line through the given points.
through: (0,4) and (5,-2
Answer:
Step-by-step explanation:
(-2-4)/(5-0)= -6/5
y - 4 = -6/5(x - 0)
y - 4 = -6/5x + 0
y = -6/5x + 4
I really need help!! Imagine you bought a car that is valued at $20,000 but depreciates at a rate of 15% per year. How much is the car worth after 5 years? What is your classmate’s error, what is the correct equation, and what is the value of the car after 5 years?
thanks
Answer:
[tex]20000 \times 0.15 \times 5 = 15000 \\ 20000+15000=35000
Step-by-step explanation:
20000 times (0.15 is rate) times years (5)
Answer you get is 15000 , then you have to take 20000+15000=35000
Marcia has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. the table below shows the information about the two credit cards marcia currently uses. card a card b amount $1,389.47 $1,065.32 apr 16% 12% monthly payment $39.38 $28.05 after 4 years, approximately how much will marcia have saved in interest by consolidating the two balances? a. $1,890.24 b. $133.92 c. $543.84 d. $1,346.40 please select the best answer from the choices provided. a b c d
The amount save by Marcia in interest by consolidating the two balances is $133.92.
What is the total payment for APR of 16%?
The total monthly payment for APR of 16% is calculated as follows;
Total monthly payments for 16% =$39.38x48 = $1890.24
What is the total payment for APR of 12%?Total monthly payments for 12% APR = $36.59*48 = $1756.32
Amount saved by MarciaA = $1890.24 - $1756.32
A = $133.92
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3. Ramu finishes 1/3 part of a work in 1 hour. How much part of the work will be finished in 1 2/5 hours?
Which of the following can represent the three angles in an obtuse, scalene triangle?
-50, 30, 100
-40, 50, 90
-30, 30, 120
-50, 50, 80
Answer:
30, 30, 120
Step-by-step explanation:
Answer:
•50, 30, 100
Step-by-step explanation:
One side (100) is much bigger than the rest (over 90), and the other two are not alike or the same, making it scalene.
16
20
Х
Solve for x.
Answer:
im assuming 24?
Step-by-step explanation:
bc 16 plus four is 20 so i did the same for 20 i like 96 % that this could be wrong
Passengers, who are travelling in a car west along a road that runs east-west, see a mountain 9 km away on a bearing of 290°. When they have travelled a further 5 km west along the road, what will be the distance to the mountain?
What is the value of the expression below when t = 6?
Answer:
C. -18
I hope that this helped you.
Answer:
C. -18
Step-by-step explanation:
The value of the expression is found by substituting the given value for the variable and following the Order of Operations to evaluate it.
__
[tex]\dfrac{2(4(6-t)^2+t-3(t+5))}{3}\qquad\text{given}\\\\=\dfrac{2(4(6-6)^2+6-3(6+5))}{3}=\dfrac{2(4(0^2)+6-3(11))}{3}=\dfrac{2(6-33)}{3}\\\\=\dfrac{2(-27)}{3}=\dfrac{-54}{3}=\boxed{-18}[/tex]
_____
Additional comment
In this instance, the Order of Operations can be shortcut a bit by factoring 3 from the numerator and denominator early in the evaluation.
= 2(2 -11) = 2(-9) = -18
The area of a DVD is 36π cm.2. What is the diameter of the DVD?
Answer:
i had done this before so thats your answer, pls follow
The diameter of the DVD is 12 units.
What is Surface Area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. It is the overall area that the object's surface occupies.
As per the given data:
The area of the DVD is equal to 36π cm².
We have to find out the diameter of the DVD.
As we know that a DVD is having a circular shape:
Area for a circle is given by πr², where r is the radius of the circle.
From the given data in the question:
πr² = 36π
r² = 36
r = √36
r = 6 units
The diameter of a circle is double the radius of the circle.
Diameter = 2r = 2 × 6 = 12 units
The diameter of the DVD is 12 units.
Hence, the diameter of the DVD is 12 units.
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helppppppppppppppppppp!!!!!!!!
The answer is C.
Step-by-step explanation:
I can't explain but I literally just did this question and I got it right
Can someone help me with this question?
A bag contains 12 movie tickets and 8 concert tickets. You randomly choose 1 ticket and do not replace it. Then you randomly choose another ticket. Find the probability that both events A and B will occur. Round your answer to the nearest tenth.
Event A: The first ticket is a concert ticket.
Event B: The second ticket is a concert ticket.
about ___%.
To solve this problem, we have to understand probability without replacement and consider the two events happening. The probability that both events occurs is 14%
Probability without replacementTo solve this problem, let's write down the data given;
Data;
Movie Ticket = 12Concert Ticket = 8But we are asked to calculate the probability that both times we pick both tickets, it would be a concert ticket.
Total number of tickets =
[tex]12 + 8 = 20[/tex]
Let's proceed for the first event
[tex]P = \frac{8}{20}= \frac{2}{5}[/tex]
The probability the second event occurs will be
[tex]P = \frac{7}{20}[/tex]
The probability both events occur will be
[tex]P = P_a * P_b = \frac{2}{5} * \frac{7}{20} = \frac{7}{50} =0.14 = 14\%[/tex]
The probability that both events occurs is 14%
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Make sure your answer is in degrees. you should be able to find this without a calculator.
sin-1 -1/2 = ?
Answer:
Below.
Step-by-step explanation:
sin-1 1/2 = 30 degrees in the first quadrant.
As the sin is negative in Quadrants 3 and 4,
sin01 -1/2
= 210, 330 degrees, in the range 0-360 degrees
Answer: -30°
Step-by-step explanation:
right on acellus
What is the probability of pulling a card from a deck of 52 cards and getting a king and a queen?
Answer:
4/52 or 1/13
Step-by-step explanation:
In a standard deck of 52 cards, there are 4 suits and each suit has 13 cards.
There are 4 kings, 4 queens, 4 aces, and 4 jacks.
So the probability of drawing a king would be:
4/52 = 1/13
Answer:
The probability of drawing a King is 4/52 or about . 0769, which is also the probability of drawing a Queen. The probability that a card drawn from the deck will be both a King and a Queen is zero. The probability that a card will be either a King or a Queen is 8/52.
Step-by-step explanation:
52 cards in a deck 4 queens and 4 kings
Jodie started washing her car at 10:15 am she finished at 10:50 am how long did it take jody to wash her car.
Answer:
35 minutes
Step-by-step explanation:
this requires us to find out how long it took and because both times given to figure this out are within the same hour it is easy to figure out in this case, 50 - 15 = 35. This is not as simple with all problems like this but because of the times given in this problem its much easier.
evaluate the expression when m=5 and n=29 n-4m
Answer:
9
Step-by-step explanation:
substitute m = 5 and n = 29 into the expression
n - 4m
= 29 - 4(5)
= 29 - 20
= 9
(I will give brainlist ) What is the equation of the following graph?
Answer: y=1/3x+2
Step-by-step explanation:
Solve pls i give brainlist to correct answer.
Answer:
Maggie can run faster by 0.85 minutes.
Maggie runs in 5.20 minutes, Olivia runs in 4.35 minutes.
Step-by-step explanation:
Maggie = can run a mile in 5.2 minutes (1.3/0.25)
Olivia = can run a mile in 4.35 minutes (2.9/0.666666667)
5.2-4.35= 0.85 minutes
Can someone explain the right answer? The question and answer is below.
Answer:
x -3y +4Pythagorean theoremStep-by-step explanation:
You want to find the horizontal and vertical distances between two points, and you want to know how to use those to find the distance between those points.
__
horizontal distanceThe x-coordinate of a point is its horizontal distance from the y-axis. The horizontal distance between two points will be the difference of their x-coordinates.
If the points are (3, -4) and (x, y), the x-coordinates are 3 and x. The difference between those coordinates can be written as x-3. (Usually, we subtract the first point from the second one.)
The horizontal distance from (3, -4) to (x, y) is (x -3).
__
vertical distanceIn like fashion, the y-coordinate of a point is its vertical distance from the x-axis. The vertical distance between two points will be the difference of their y-coordinates.
For the points (3, -4) and (x, y), the y-coordinates are -4 and y. The difference between those coordinates is y -(-4) = y +4.
The vertical distance from (3, -4) to (x, y) is (y +4).
__
total distanceAs the attachment shows, the horizontal and vertical distances between the two points can be considered to be the legs of a right triangle. The "total" distance between the points is the straight-line distance. It is the hypotenuse of that triangle.
The Pythagorean theorem gives the relation between the sides and hypotenuse of a right triangle. In this context, the Pythagorean theorem can be used to create an equation showing the relationship between the legs of the triangle and the distance from (x, y) to the center. (That distance is the radius.)
In particular, the equation created is ...
(x -3)² +(y +4)² = 7²
_____
Additional comment
For right triangle legs 'a' and 'b', and hypotenuse 'c', the Pythagorean theorem tells you ...
a² +b² = c²
The sum of the squares of the sides is equal to the square of the hypotenuse.
Explain how to solve this problem:
A credit card company charges 12.9% annual interest. If they
compound interest monthly, how much will you owe for every dollar
you do not pay off for a year?
"every dollar" means P = 1
compounded monthly interest means 12
1(1+(.129/12)^(12(1)) =
in calculator do pemdas
1. .129/12 = 0.01075
2. 0.01075 + 1 = 1.01075
3. (1.01075)^12 = 1.136907156 =
answer = 1.14
Mayfield schools
lcps
Fake records usually have fewer first digits 1, 2, and 3. What is the approximate probability, if Benford's law holds, that among 1500 randomly chosen invoices there are 843 or fewer amounts with first digit 1, 2, or 3
The probability that there are 843 or fewer amounts with first digit 1, 2, or 3 is 0.562
How to determine the probability?The given parameters are:
Fewer digits = 843
Total = 1500
The probability is then calculated as:
P = 843/1500
Evaluate the quotient
P = 0.562
Hence, the probability that there are 843 or fewer amounts with first digit 1, 2, or 3 is 0.562
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What is the sum of the following equation: (9+5)*43x(23,550-32)*655
Answer:
1,012,632....I'm sure that's is answerConstruct a 90% confidence interval for the population mean, . assume the population has a normal distribution. a sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78
Answer:
[tex]CI=\{2.5053,3.2147\}[/tex]
Step-by-step explanation:
Assuming the conditions for constructing a t-confidence interval are true, we use the formula [tex]\displaystyle CI=\bar{x}\pm t^*\biggr(\frac{s}{\sqrt{n}}\biggr)[/tex] where our sample mean is [tex]\bar{x}=2.86[/tex], our sample standard deviation is [tex]s=0.78[/tex], our sample size is [tex]n=15[/tex], and a 90% confidence level is equivalent to a critical value of [tex]t^*=1.7613[/tex],
[tex]\displaystyle CI=\bar{x}\pm z^*\biggr(\frac{s}{\sqrt{n}}\biggr)\\\\CI=2.86\pm 1.761\biggr(\frac{0.78}{\sqrt{15}}\biggr)\\\\CI=2.86\pm0.3547\\\\CI=\{2.5053,3.2147\}[/tex]
Hence, we are 90% confident that the true population mean of a student's grade point average is between 2.5053 and 3.2147
4. Write an expression to find the perimeter
of the rectangle below. 6x
3x-5
Answer:
Down below
Step-by-step explanation:
If I am correct, it would be 6x + 6x + 3x - 5 + 3x - 5. I am almost positive this is what they are asking for. If I am incorrect, I will answer three questions for free, on any topic of your choosing. In advance, sorry if I'm incorrect.
julie buys a bike for $2700 and sells it a year later, making a 15% profit
How much profit did Julie make?
Answer:
$405.
Step-by-step explanation:
That would be 15% of $2700
= 2700 * 0.15
= $405
What is the product? startfraction x squared minus 16 over 2 x 8 endfraction times startfraction x cubed minus 2 x squared x over x squared 3 x minus 4 endfraction
The product of the given expression is [tex]\frac{x(x-1)(x-4)}{2(x+4)}[/tex] OR [tex]\frac{x(x^{2} -5x+4)}{2x+8}[/tex] OR [tex]\frac{x^{3} -5x^{2} +4x}{2x+8}[/tex]
Simplifying fractionsFrom the question, we are to determine the product of the given expressions
The given expressions are
[tex]\frac{x^{2} - 16}{2x+8}\times \frac{x^{3}-2x^{2} +x}{x^{2} +3x-4}[/tex]
[tex]\frac{(x+4)(x-4)}{2(x+4)}\times \frac{(x^{2} -x)(x-1)}{(x-1)(x+4)}[/tex]
[tex]\frac{(x-4)}{2}\times \frac{(x^{2} -x)}{(x+4)}[/tex]
[tex]\frac{(x-4)}{2}\times \frac{x(x-1)}{(x+4)}[/tex]
[tex]\frac{x(x-1)(x-4)}{2(x+4)}[/tex]
OR
[tex]\frac{x(x^{2} -5x+4)}{2x+8}[/tex]
OR
[tex]\frac{x^{3} -5x^{2} +4x}{2x+8}[/tex]
Hence, the product of the given expression is [tex]\frac{x(x-1)(x-4)}{2(x+4)}[/tex] OR [tex]\frac{x(x^{2} -5x+4)}{2x+8}[/tex] OR [tex]\frac{x^{3} -5x^{2} +4x}{2x+8}[/tex]
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Here is the complete and correct question:
What is the product? StartFraction x squared minus 16 Over 2 x + 8 EndFraction times StartFraction x cubed minus 2 x squared + x Over x squared + 3 x minus 4 EndFraction
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Answer:
A. StartFraction x (x minus 4) (x minus 1) Over 2 (x + 4) EndFraction
Step-by-step explanation:
correct on edge :)
