Answer:
y = 45,121,040×1.027^t
Step-by-step explanation:
An exponential growth equation is generally of the form ...
value at time t = (initial value)(growth factor)^t
where the growth factor is the multiplier for a period equal to one time unit.
Here, the initial value (in 2014) is 45,121,040. The growth factor is given as 1.027 (2.7% added per year), and we can define t as the number of years after 2014. Then our equation is ...
y = 45,121,040×1.027^t . . . . where t = years after 2014
Cube: Find the surface area of a cube with side 5 inches.
Answer:
We are given the dimension of the side being 5 inches and it states that we need to determine the surface area. The first step that we must do is find the area of one side and then we multiply it by 6 because we have 6 same sides.
[tex]A = s^2[/tex]
[tex]A = (5\ in)^2[/tex]
[tex]A = 25\ in^2[/tex]
Now that we have the area of one side we can multiply it by 6 to get the total surface area.
[tex]A = 25\ in^2 * 6[/tex]
[tex]A = 150\ in^2[/tex]
Therefore, our final answer is that the surface area is 150 inches squared
Hope this helps!
Answer:
150 square inches
Step-by-step explanation:
find the area of 1 square face
5*5=25
multiply by 6 faces
25*6=150
4. In a women's professional tennis tournament, the money a player wins depends on her finishing place in the
standings The first-place finisher wins half of $1.500.000 in total prize money. The second-place finisher wins half of
what is left then the third-place finisher wins half of that, and so on.
al Write a rulle to calculate the actual prize money in dollars won by the player finishing in nth place, for any positive
b) What type of relationship exists between the two variables?
Using geometric sequence concepts, it is found that:
a) The rule is: [tex]P_n = 750000(0.5)^{n-1}[/tex].
b) An exponential relationship exists between the two variables.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
A geometric sequence represents an exponential relationship between the variables.
In this problem, considering that the first-place finisher wins half of $1.500.000 in total prize money, and each finisher earns half of the one who finished above, the first term and the common ratio are given by:
[tex]a_1 = 750000, q = 0.5[/tex].
Hence the nth term of the sequence is given by:
[tex]P_n = 750000(0.5)^{n-1}[/tex]
More can be learned about geometric sequence concepts at https://brainly.com/question/11847927
#SPJ1
so i am just gonna technically give u all points for these questions
Answer:
It should move three places to the left :3
Step-by-step explanation:
A person can read 24 pages of a book in 1/3 of an hour. What is this person's reading rate in pages per hour?
72
48
12
8
Which statements about the cone are true? check all that apply. the radius is double the diameter. the radius is 9 mm. the base area is calculated using the radius. the volume is one-third the volume of a cylinder with the same height and diameter. the volume of the cone is 297 pi millimeters cubed.
To solve this problem, we have to understand and establish some basic mathematical facts on a cone.
The answer to this question are option b and c only.
ConeThis is a solid figure that has the base of a circle and the top is made up round triangle.
The formula of volume of a cone is given as
[tex]v = \frac{1}{3}\pi r^2 h[/tex]
where;
r = radiush = heightIn the given question, the first fact given is if the radius doubles the diameter and that false.
[tex]diameter = 2 * radius[/tex]
If we have the value of the the radius, we can calculated the base area using area of a circle
[tex]area = \pi r^2[/tex]
The volume of a cone is actually one-third the volume of a cylinder
we can only calculate the volume of the cone is we have the value of the height of the cone.
The answer to this question are option b and c only.
Learn more on volume of a cone here;
https://brainly.com/question/12004994
#SPJ4
Answer:
B, C, D, E
Step-by-step explanation:
Got it wrong the first time.
PLEASE HELP!!!!!!!!!!!!!!!!
Using a calculator, it is found that the correlation coefficient for this data is given by:
B. -0.901.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.To find the coefficient, which has symbol r², we input in a calculator the values of x and the values of y, hence:
r² = -0.901.
Which means that option B is correct.
More can be learned about correlation coefficients at https://brainly.com/question/25815006
#SPJ1
Find the missing value (x)
Answer:
y=14; x=72
Step-by-step explanation:
y=(21×2)/3; x=(48×21)/14
Given the system below:
f(x) = 2x
g(x) = 2x
Which value(s) of x make f(x) = g(x) a true statement? If necessary, you may choose more than one
answer.
1
4
3
2
9
0
All real numbers
1. f(x) = 2x
2. g(x) = 2x
Substitute g(x) to the 2x in the first statement.
You'll get: f(x) = g(x)
Therefore, x ∈ all real numbers (any value of x would make it a true statement)
You roll a number cube twenty times and it lands on a 3 five times. What is the
experimental probability that it ends on a 3 the next time you roll?
Answer:
Hence, a fair dice has a probability of 16 to land on any predetermined number 1 through 6. Therefore, to land on 3 the probability is 16
Step-by-step explanation:
christian is trown into a swimming pool his mass is 62,000g and his volume is 68,000cm3 what would his density be? (Show solution)
Answer:
0.91 g/cm³
Step-by-step explanation:
Density Formula
Density = Mass/VolumeSolving
Density = 62,000 g / 68,000 cm³Density = 31/34 g/cm³Density = 0.91 g/cm³Question 12 of 14
The perimeter of a rectangle is 32 inches. The length is 1 foot. What is the width of the rectangle in inches?
A.
4 inches
B.
10 inches
C.
15 inches
D.
20 inches
If h = 3.5u, what is the value of h when u = 17?
Give any decimal answers to 1 d.p.
Put u=17
h=3.5(17)h=51+8.5h=59.5Answer:
59.5.
Step-by-step explanation:
h = 3.5u
When u = 17,
h = 3.5*17
= 59.5
-7-3 log₂ (-n + 10) = -16
Answer:
2
Step-by-step explanation:
-3 log₂ (-n + 10) = -16+7
-3 log₂ (-n + 10) = -9
log₂ (-n + 10) = -9/-3
log₂ (-n + 10) = 3
-n + 10 = 2^3
-n + 10 = 8
n=2
Help pls
Two digits of the 6-digit number X = 345 * 8* are missing. Fill in the missing digits
so that the number obtained is the smallest possible number that is divisible by 45.
Find X.
The smallest possible number that is divisible by 45 when the blanked place of the number is filled is 345285.
What is the divisible rule of 9 and 5?The divisible rule of 9 and 5 are:
Divisible rule of 9- When the addition of all number is divisible by 9, then that number also divisible by 9.Divisible rule of 5- When a number has a digit 0 or 5 in the last of it, then that number also divisible by 5.Two digits of the 6-digit number are missing.
[tex]X = 345 * 8*[/tex]
The smallest possible number from this is divisible by 45. The factors of 45 are 9 and 5.
[tex]45=9\times5[/tex]
Thus, the 6-digit number which is divisible by 45, must be divisible by 9 and 5.
To be divisible with 5, the number has 0 or 5 in last. So the numbers can be,
[tex]X = 345 * 85\\X=345 * 80[/tex]
For first number, when the blank is filled with number 2 to make sum 9 and for second the blank number should be 7. Thus, the numbers,
[tex]X = 345 285\\X=3457 80[/tex]
Thus, the smallest possible number that is divisible by 45 when the blanked place of the number is filled is 345285.
Learn more about the smallest common factor here;
https://brainly.com/question/16054958
#SPJ1
Which is the equation of a trend line that passes through the points (7, 450) and (14, 401)? y = negative 7 x 499 y = negative startfraction 1 over 7 endfraction x 451 y = startfraction 1 over 7 endfraction x 449 y = 7 x 401
The equation of the line that passes through the points (7, 450) and (14, 401) is y + 7x = 499
How to find equation of a line?The equation of a line can be represented as follows:
y - y₁ = m(x - x₁)
where
m = slopeTherefore, (7, 450)(14, 401)
m = 401 - 450 / 14 - 7 = -49 / 7 = -7
Therefore, using (7, 450)
y - 450 = -7(x - 7)
y - 450 = -7x + 49
y + 7x = 49 + 450
y + 7x = 499
learn more on equation of a line here: https://brainly.com/question/3649177
#SPJ4
(1) a) Why is 8x²y + 5x³y² - 2 considered as an expression and not an equation?
Answer & step-by-step explanation:
An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign. As you can clearly see here, there is no equal sign connecting anything here, thus, it is an expression.
Because for it to be called an equation you need to have the equal symbol (=) comparing two epressions.
Example of expression:
2x - 4y + 14
Example of equation:
-3y - 2 = -2x - 8
⇔ -3y = -2x + 6
⇔ -y = -[tex]\frac{2}{3}[/tex]x + 2
⇔ y = [tex]\frac{2}{3}[/tex]x - 2
Instructions
For this activity, you will need two different coins. First, you will determine the theoretical probability of events. Then, you will flip the coins 100 times and determine the experimental probability of the events.
Flip two different coins 100 times, and record the results of each coin toss in a table like the one below:
Result
Frequency
Two heads 30
Two tails 40
One head, one tail 70
Answer the following questions based on the data you gathered. You must show your work to receive credit.
What is the theoretical probability that a coin toss results in two heads showing?
What is the experimental probability that a coin toss results in two heads showing?
What is the theoretical probability that a coin toss results in two tails showing?
What is the experimental probability that a coin toss results in two tails showing?
What is the theoretical probability that a coin toss results in one head and one tail showing?
What is the experimental probability that a coin toss results in one head and one tail showing?
Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference?
The experimental probability that a coin toss results in two heads showing is 3/14
The theoretical probability of two headsThe sample space of two coins is:
S = {HH, HT, TH, TT}
In the above sample space, we have:
n(HH) = 1 i.e. number of two headsTotal = 4 i.e. the sample sizeThe theoretical probability of two heads is calculated as:
P = n(HH)/Total
This gives
P = 1/4
Hence, the theoretical probability of two heads is 1/4
The experimental probability of two heads?To do this, we make use of the table in the question
The table is given as:
Result Frequency
Two heads (HH) 30
Two tails (TT) 40
One head, one tail (HT) 70
Total 140
The experimental probability of two heads is calculated as:
P = n(HH)/Total
This gives
P = 30/140
Simplify
P = 3/14
Hence, the experimental probability of two heads is 3/14
The theoretical probability of two tailsUsing the sample space in (a), we have:
n(TT) = 1 i.e. number of two tailsTotal = 4 i.e. the sample sizeThe theoretical probability of two tails is calculated as:
P = n(TT)/Total
This gives
P = 1/4
Hence, the theoretical probability of two tails is 1/4
The experimental probability of two tailsFrom the table in the question, we have:
Two tails (TT) =40
Total = 140
The experimental probability of two tails is calculated as:
P = n(TT)/Total
This gives
P = 40/140
Simplify
P = 2/7
Hence, the experimental probability of two tails is 2/7
The theoretical probability of one head and one tailUsing the sample space in (a), we have:
n(HT) = 2 i.e. number of one head and one tailTotal = 4 i.e. the sample sizeThe theoretical probability of one head and one tail is calculated as:
P = n(HT)/Total
This gives
P = 2/4
Simplify
P = 1/2
Hence, the theoretical probability of one head and one tail is 1/2
The experimental probability of one head and one tailFrom the table in the question, we have:
One head one tail (HT) = 70
Total = 140
The experimental probability of one head one tail is calculated as:
P = n(HT)/Total
This gives
P = 70/140
Simplify
P = 1/2
Hence, the experimental probability of one head one tail is 1/2
Why are there difference between the theoretical probabilities and the experimental probabilities?The reason for the difference between the probability types is because one is as a result of an actual experiment, while the other is an estimate of the experiment.
Read more about probability at:
https://brainly.com/question/251701
#SPJ1
#94 will give brainliest to best answer!
Answer:
5/8
Step-by-step explanation:
There are 8 sections, and 4 sections that are 1, and 1 pink section. So adding these up, we get 5/8.
Hope this helped! :)
Find the lcd of the given rational equation
The LCD of the rational equation [tex]-\frac{3}{x + 2} + \frac{5x}{x - 1} = \frac{x + 2}{x^2 -3x + 2}[/tex] is (x + 2) (x -1)(x - 2)
How to determine the LCD?The rational equation is given as:
[tex]-\frac{3}{x + 2} + \frac{5x}{x - 1} = \frac{x + 2}{x^2 -3x + 2}[/tex]
Factorize the quadratic denominator
[tex]-\frac{3}{x + 2} + \frac{5x}{x - 1} = \frac{x + 2}{(x -1)(x - 2)}[/tex]
Write out the denominators
(x + 2), (x - 1) and (x -1)(x - 2)
Remove the repetition
(x + 2) (x -1)(x - 2)
Hence, the LCD of the rational equation is (x + 2) (x -1)(x - 2)
Read more about LCD at:
https://brainly.com/question/10749076
#SPJ1
Someone please Help me please
In this question, we are presented with two triangles are required to find he missing sides in them. the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively
Trigonometric RatioIn the first triangle, we need to use trigonometric ratio to find the missing side in the triangle
Data;
Angle = 45hypothenuse = [tex]8\sqrt{2}[/tex]adjacent = xTo find the adjacent side, we need to use cosine rule on this problem.
[tex]cos\theta = \frac{adjacent}{hypothenuse} \\cos45 = \frac{x}{8\sqrt{2} } \\x = 8[/tex]
The adjacent side is equal to 8 units
In the second triangle, we also need to use trigonometric ratio, but let's write down our data
angle = 30hypothenuse = 10opposite = ?adjacent = ?We can use both cosine and sine rule here or use one and use Pythagoras's theorem to find the other side.
[tex]cos \theta = \frac{adjacent}{hypothenuse} \\cos 30 = \frac{x}{10} \\x = 8.660[/tex]
The adjacent side is equal to 8.660, let's find the opposite side using sine rule
[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 30 = \frac{y}{10} \\y = 5[/tex]
And lastly, the value of the other angle is
[tex]90 + 30 + z = 180\\z = 180 - 120\\\\z = 60[/tex]
From the calculations above, the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively
Learn more on trigonometric ratios here;
https://brainly.com/question/11967894
#SPJ1
The doctor told my dad he should drink 72 ounces of water every day.
How many cups of water should he drink per day? (There are 8 ounces in a cup.) Write and solve an equation to represent this problem.
How many quarts of water is that? Write and solve an equation to represent this problem.
Answer: 9 cups
Step-by-step explanation: 8 multiply it by 9 .
(A-5)² + (B- 3)² = 18 B=A-2 A = ?, B = ?
Answer:
A = 8 and B = 6
Step-by-step explanation:
Since (B = A - 2), we can substitute (A - 2) in for the "B" variable in the first equation to isolate "A".
(A - 5)² + (B - 3)² = 18 -----> Original equation
(A - 5)² + ((A - 2) - 3)² = 18 -----> Plug in B = A - 2
(A - 5)² + (A - 5)² = 18 -----> Subtract
(A² - 10A + 25) + (A² - 10A + 25) = 18 -----> Expand parentheses
2A² - 20A + 50 = 18 ------> Add like terms
2A² - 20A + 32 = 0 -----> Subtract 18 from both sides
2(A² - 10A + 16) = 0 -----> Remove common factor
2(A - 2)(A - 8) = 0 -----> Factor within parentheses
A = 2 -----> Find A - 2 = 0
A = 8 -----> Find A - 8 = 0
Since "A" gave two possible values, we need to plug them into both equations to see which value gives reasonable "B" values.
When A = 2:
B = A - 2 -----> Original equation
B = 2 - 2 -----> Plug in A = 2
B = 0 -----> Subtract
(A - 5)² + (B - 3)² = 18 -----> Original equation
(2 - 5)² + (B - 3)² = 18 ------> Plug in A = 2
(-3)² + (B - 3)² = 18 -----> Subtract within first parentheses
9 + (B - 3)² = 18 -----> Square value within first parentheses
(B - 3)² = 9 -----> Subtract 9 from both sides
B - 3 = 3 -----> Take square root of both sides
B = 6 -----> Add 3 to both sides
When A = 8:
B = A - 2 -----> Original equation
B = 8 - 2 -----> Plug in A = 8
B = 6 -----> Subtract
(A - 5)² + (B - 3)² = 18 -----> Original equation
(8 - 5)² + (B - 3)² = 18 ------> Plug in A = 8
(3)² + (B - 3)² = 18 -----> Subtract within first parentheses
9 + (B - 3)² = 18 -----> Square value within first parentheses
(B - 3)² = 9 -----> Subtract 9 from both sides
B - 3 = 3 -----> Take square root of both sides
B = 6 -----> Add 3 to both sides
As you can see, when A = 2, there are two possible values of "B" depending on the equation. However, when A = 8, both equations give a "B" value of B = 6. Therefore, A = 8 and B = 6 are the answers.
A bag of colored paper clips contains 3 red clips
and 6 green clips. What's the probability of
pulling out a red clip and then a green clip?
(Assume that you don't put the first red paper
clip back in the bag.) Write your answer as a
fraction.
Answer:
1/5
Step-by-step explanation:
solution [ calculation of probability ]
P= (3/3+6) × (6/3+6-1)
=3/9×6/10
=1/5
In a random sample of 200 items, 5 items were defective. An estimate of the percentage of defective items in the population is Group of answer choices 2.5% 200 5.0% 10.0%
An estimate of the percentage of defective items in the population if 5 of 200 items were defective is 2.5%.
How to calculate percentage?The percentage of a defective item out of a total item can be calculated as follows:
% defective item = no of defective item/total no of items × 100
According to this question, in a random sample of 200 items, 5 items were defective.
% defective item = 5/200 × 100
% defective item = 2.5%
Therefore, an estimate of the percentage of defective items in the population if 5 of 200 items were defective is 2.5%.
Learn more about percentage at: https://brainly.com/question/13450942
#SPJ1
Helppppppppppp meeeeeeeeee pleaseeeeeee
A rectangle has a perimeter of 48 inches. If twice the length decreased by three is equal to three times the width, the find the length and the width
Answer:
Length= 15, width= 9Step-by-step explanation:
perimeter of a rectangle P= 2(L+W)
L= length
W= width
48=2(L+W)---------------(1)
twice the length= 2×L= 3L
decreased by three= 2L-3
three times the width= 3×W= 3W
twice the length decreased by three is equal to three times the width
2L-3= 3W-------------------(2)
solving equation one and two simultaneously
from equation (2)
3W= 2L-3
W=2L/3-3/3
W= 2L/3 - 1----------(3)
substitute equation (3) into equation (1)
48=2(L+2L/3-1)
48=2L+4L/3-2
48×3=6L+4L-6
144=10L-6
10L=144+6
10L=150
dividing bothsides by 10
L= 15
substitute L= 15 into equation (2)
2L-3=3W
2(15)-3=3W
30-3 = 3W
27= 3W
3W= 27
dividing bothsides sides 3
3W=27/3
W=9
therefore, Length= 15, width= 9need help asap, much appreciated!!!!!!!!!!!
Step-by-step explanation:
there are 13 out of 52 diamond cards.
and there are 26 out of 52 black cards.
so, for the first card to be diamond the probability is
13/52 = 1/4 = 0.25
but now, he does not put the card back.
he pulls the second card out of 51 possible cards.
the desired cases are still 26.
so, the probability to pull a black card as the second card under the restriction that the first card was a diamond is
26/51 = 0.509803922...
the probability for that combined event is then
1/4 × 26/51 = 26/204 = 13/102 = 0.12745098...
so, c. is the right answer.
what is the volume of an equilateral triangular pyramid with base side length of 9 cm, base
height of 7.8 cm, and height of 5 cm? round your answer to the nearest tenth.
e Structure What is the length of a pool with a perimeter
6 feet? Explain how you found the answer. Then describe
You can use a feature of the pattern to find the length.
Answer:
To begin to answer this question, you will want to determine the equation for the volume of a rectangular prism. In this case, the equation is length times width times height or:
V = l * w * h
In the question, you are given several pieces of information that you can then plug into the equation. For example, you know the volume is 21,904 ft3 because they tell you that directly. You also know that the pool is 8 feet deep. I consider the depth to be the same as the height. With that information, you now have the equation:
21,904 ft3 = l * w * (8ft)
You are also told that the length is 2 times the width. Written as an equation, you would say that
l = 2w
Now, you can substitute that 2w for l to get the equation:
21,904 ft3 = (2w) * w * 8ft
We know that when you multiply a variable times itself, you get a squared variable, so 2w * w = 2w2 and that
21,904 ft3 = 2w2 * 8ft
Now, you can solve the equation to find w. At this point, it is easiest to drop the units of feet on the numbers to do the math. As long as all your numbers are in the same units (i.e. feet), you are good to go. Start by dividing each side by 8 to get
2738 = 2w2
Then divide both sides by 2 to get
1369 = w2
Finally, for this portion, take the square root of 1369 to get
w = 37 feet.
But you're not done yet. You know the width, and you know that l = 2w. Plug the value for w (37) into this equation to get the length, which is 74 feet.
The final answer is that the width of the pool is 37 feet and the length is 74 feet.
You can check your answer by plugging the length, width, and height (depth) into the equation for volume to see if you get 21,904ft3.
If you take 8 ft x 37 ft x 74 ft, you get 21,904 ft3 and you know that you answer is correct.
Step-by-step explanation:
what is 16/18 and 4/18 in its simplest form ?
Answer:
in fractions
16/18 = 8/9
4/18 = 2/9
Answer:
8/9 and 2/9
Step-by-step explanation:
for 16/18
divide the numerator and denominator by 2 to option it's simplest form
16/18÷2/2 = 8/9
for 4/18
also divide the numerator and denominator by 2 to get the simplest form.
4/18 ÷2/2= 2/9
