Here are the first four terms of a number sequence.
2 7 12 17
Here are the first five terms of another number sequence.
-4 -1 2 5 8
Find two numbers that are in both number sequences.
Two numbers that are in both sequences are the numbers 17 and 32.
What is a sequence?A sequence can be described as a set of numbers each with a defined interval between one another. For example, in the sequence 2, 4, 6, 8, 10, the interval is 2.
What numbers do these sequences have in common?To find two common numbers, let's expand the sequences as it is shown below:
First sequence: In this sequence, the interval is 5.
2 7 12 17 22 27 32
Second sequence: In this sequence, the interval is 3.
-4 -1 2 5 8 11 14 17 20 23 26 29 32
Learn more about sequences in https://brainly.com/question/30262438
#SPJ1
The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 400 grams and a standard deviation of 20grams. Find the weight that corresponds to each event.
(Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.)
a. Highest 20 percent
b. Middle 60 percent to
c. Highest 80 percent
d. Lowest 15 percent.
Answer:
a. To find the weight corresponding to the highest 20 percent of coffees, we need to find the z-score that corresponds to the 0.8 cumulative probability.
Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.8 is 0.8416.
Next, we use the z-score formula to find the weight:
Weight = Mean + (z-score * Standard Deviation)
Weight = 400 + (0.8416 * 20) = 448.32 g
So, the weight corresponding to the highest 20 percent of coffees is approximately 448.32 g.
b. To find the weight corresponding to the middle 60 percent of coffees, we need to find the z-scores that correspond to the cumulative probabilities of 0.2 and 0.8.
Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.2 is -0.8416, and the z-score corresponding to a cumulative probability of 0.8 is 0.8416.
Next, we use the z-score formula to find the weights:
Weight Lower Bound = Mean + (z-score * Standard Deviation)
Weight Lower Bound = 400 + (-0.8416 * 20) = 351.68 g
Weight Upper Bound = Mean + (z-score * Standard Deviation)
Weight Upper Bound = 400 + (0.8416 * 20) = 448.32 g
So, the weight corresponding to the middle 60 percent of coffees ranges from approximately 351.68 g to approximately 448.32 g.
c. To find the weight corresponding to the highest 80 percent of coffees, we use the same process as in (a) to find the z-score that corresponds to the cumulative probability of 0.8, which is 0.8416.
Next, we use the z-score formula to find the weight:
Weight = Mean + (z-score * Standard Deviation)
Weight = 400 + (0.8416 * 20) = 448.32 g
So, the weight corresponding to the highest 80 percent of coffees is approximately 448.32 g.
d. To find the weight corresponding to the lowest 15 percent of coffees, we need to find the z-score that corresponds to the cumulative probability of 0.15.
Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.15 is -0.9332.
Next, we use the z-score formula to find the weight:
Weight = Mean + (z-score * Standard Deviation)
Weight = 400 + (-0.9332 * 20) = 346.64 g
So, the weight corresponding to the lowest 15 percent of coffees is approximately 346.64 g.
Step-by-step explanation:
The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 2 and roots of multiplicity 1 at x = 0 and x = -2 . It goes through the point (5,189).
If "a" is a root of a polynomial, then (x-a) is a factor of the polynomial.
If the multiplicity of a root a is "p", then (x-a)^p is a factor of the polynomial.
Based on the roots and multiplicity, we have:
P(x) = k · (x-2)^2 · (x-0) · (x - (-2))
P(x) = k · (x-2)^2 · (x-0) · (x+2)
We need that "k" up front to account for any vertical stretch or compression to hit the exact point (5,189).
To find "k", we plug in that point and solve for "k":
189 = k · (5-2)^2 · (5-0) · (5+2)
189 = k · (3)^2 · (5) · (7)
189 = k · 315
0.6 = k
So the final answer is: P(x) = 0.6 · (x-2)^2 · (x-0) · (x+2)
Select the correct answer.
A fantasy board game makes use of four dice. The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each. If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist?
A.
30
B.
240
C.
2,400
D.
3,000
Answer:
The total possible outcomes that exist are:
2400
Step-by-step explanation:
We are given four dices:
first is a standard 6-faced die.
The second die has 4 faces.
Third dice has 10 faces.
Fourth dice has 10 faces.
Now when all the dice are thrown together then the total number of possible outcomes are:
( Since there are 4 numbers possible for the first die, 6 for second and 10 each for third and fourth)
The answer is:
2400
BRAINLIEST if correct, 5th grade geometry
Answer:
EF, GH
Step-by-step explanation:
both go on forever from one point
Answer:
A and B
Step-by-step explanation:
Because they go infinitly in one direction and end in another.
Find the area of the figure pictured below.
The area of the composite figure is 41 ft square.
How to find the area of a figure?The figure is a composite figure. A composite figure is a figure that has two or more shapes.
Therefore, the area of the composite figure is the sum of the individual area of the shapes.
Therefore,
area of the figure = area of rectangle 1 + area of rectangle 2
area of rectangle 1 = lw
where
l = lengthw = widthTherefore,
area of rectangle 1 = 2 × 4 = 8 ft²
area of rectangle 2 = 11 × 3 = 33 ft²
Hence,
area of the figure = = 8 + 33
area of the figure = 41 ft²
learn more on area here: https://brainly.com/question/23718948
#SPJ1
A magician shuffles a standard deck of playing cards and allows an audience member to pull out a card, look at it, and replace it in the deck. Three additional people do the same. Find the probability that of the 4 cards drawn, at least 1 is a face card. (Round your answer to one decimal place.
The probability that at least 1 of the 4 cards drawn is a face card is 0.6.
How to find probability of 4 cards drawn?A typical deck contains 52 cards in total. There are 51 cards left in the deck after the first spectator draws a card. The replacement card leaves 52 cards in total, which is the same as before. The number of cards remains 52 for all four draws since each succeeding audience member will draw a card and replace it.
Finding the likelihood that none of the four cards are face cards and subtracting it from one will give us the chance that at least one of the four cards is a face card.
A deck of cards has 12 face cards (4 jacks, 4 queens, and 4 kings). Consequently, the likelihood that a single draw will not provide a face card is:
P(not a face card)=(52 - 12)/(52)=(40/(52)=(10/13).
The likelihood that none of the four draws will produce a face card is:
P(no face cards are present) = (10/13)4 = 0.432
As a result, the likelihood that at least 1 of the four cards revealed is a face card is as follows:
P(none are face cards) = 1 - P(at least one is a face card) = 1 - 0.432 = 0.568
The chance, rounded to one decimal place, is roughly 0.6.
Consequently, there is a 0.6 percent chance that at least one of the four cards will be a face card.
To know more about Standard Deck visit:
brainly.com/question/13935092
#SPJ1
Enter each answer as a whole number or a faction, or DNE forDoes Not Exist
The values of the piecewise functions at the indicated limits using the equations obtained from the graph are;
[tex]\lim \limits_{x \to2^+}\frac{f(x) - 4}{f(x+ 3)} = \underline{-\frac{2}{3} }[/tex]
[tex]\lim \limits_{x\to 3^-}[/tex] f(f(x) + 4) = 7
[tex]\lim\limits_{h\to 0} \frac{f(2+ h)-f(2)}{h}[/tex] DNE
What is a piecewise function?A piecewise function is a function that has rules or definition based on the interval of reference of the function.
The graphed function, f(x), comprising of several piecewise functions, indicates that as x → 2⁺, we get;
The points on the line of the graph are;
(1, 1), and (3, 3)
The slope of the graph as x tends to 2⁺ is therefore;
Slope = (3 - 1)/(3 - 1) = 1
The equation of the line is therefore;
y - 1 = x - 1
y = f(x) = x
Therefore;
f(x) - 4 = x - 4
f(x + 3) = x + 3
[tex]\lim \limits_{x\to 2^+} \frac{f(x) -4}{f(x + 3)} = \frac{x - 4}{x + 3} | x = 2[/tex]
[tex]\lim \limits_{x\to 2^+} \frac{f(x) -4}{f(x + 3)} = \frac{2 - 4}{2 + 3} =\underline{-\frac{2}{5}}[/tex]The piecewise function for the interval, x → 3⁻ is; f(x) = x, therefore;
f(f(x) + 4) = f(x + 4) = x + 4
[tex]\lim \limits_{x\to 3^-}f(f(x) + 4)[/tex] = x + 4, where; x = 3, therefore;
[tex]\lim \limits_{x\to 3^-}f(f(x) + 4)[/tex] = 3 + 4 = 7[tex]\lim \limits_{h\to 0} = \frac{f(2 + h)-f(2)}{h}[/tex], can be found as follows;
The equation of the function at x = 2 is; y = f(x) = x
f(2 + h) = 2 + h
f(2) = 2
Therefore;
[tex]\frac{f(2 + h)-f(2)}{h}[/tex] = (2 + h - 2)/h = h/h
[tex]\lim \limits_{h\to 0} \frac{f(2 + h)-f(2)}{h} = \frac{0}{0}[/tex] DNE (Does Not Exist)Learn more about the piecewise functions here: https://brainly.com/question/14390119
#SPJ1
Which of the following shows a correct method to calculate the surface area of the cylinder?
cylinder with diameter labeled 2.6 feet and height labeled 4.4 feet
SA = 2π(2.6)2 + 2.6π(4.4) square feet
SA = 2π(2.6)2 + 1.3π(4.4) square feet
SA = 2π(1.3)2 + 1.3π(4.4) square feet
SA = 2π(1.3)2 + 2.6π(4.4) square feet
Option D is correct, SA = 2π(1.3)2 + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that cylinder with diameter labeled 2.6 feet and height labeled 4.4 feet
The surface area of cylinder is given by the formula =2πrh+2πr²
The radius is Diameter/2
2.6/2=1.3
The radius is 1.3
Surface area =2π(1.3)(4.4)+2π(1.3)²
So =2.6π(4.4)+2π(1.3)²
Hence, Option D is correct, SA = 2π(1.3)² + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ1
Answer:
Step-by-step explanation:
Qué fracción restada a 1/2 da como resultado 4/10?
-1/10 should be subtracted from 1/2 to get 4/10.
How can you represent a fraction? Are fractions and ratios same?A fraction is of the form → (x/y).
For example, we can write fractions as → 2/3.
Fractions and ratios represent the same aspect. We can write -
2 : 3 = 2/3
4 : 7 = 4/7
Given is to solve the expression -
(1/2) - ? = 4/10
We can write the expression as -
(1/2) - (x) = (4/10)
(x) = 4/10 - 1/2
(x) = 4/10 - 5/10
(x) = -1/10
Therefore, -1/10 should be subtracted from 1/2 to get 4/10.
To solve more questions on subtracting fractions, visit the link below
https://brainly.com/question/30489902
#SPJ9
{Question in English -
What fraction subtracted from 1/2 equals 4/10?}
What is the measure of each angle in a regular polygon with 14 sides? If necessary, round your answer to the nearest tenth.
The measure of each angle in the regular polygon is 154.3 degrees
How to determine the measure of each angle in a regular polygonFrom the question, we have the following parameters that can be used in our computation:
Number of sides, n = 14
The measure of each angle is calculated as
Angle = ( n − 2 ) × 180/n
substitute the known values in the above equation, so, we have the following representation
Angle = (14 − 2) × 180/14
Evaluate
Angle = 154.3
Hence, the angle is 154.3
Read more about angles at
https://brainly.com/question/25716982
#SPJ1
Rewrite the equation in Ax+By=C form
y-6=5(x+2)
Scenario #1: Raul.
raul is a saver. he sets aside $100 per month during his career of 40 years to prepare for retirement. He does not like the idea of investing because he prefers to minimize his risk as much as possible so he puts his money in a savings account, which earns 1.5% interest per year.
1. what is the total balance in the account after 40 years?
2. how much of a total did Raul contribute himself?
3. how much money did Raul make through compound interest in this savings account?
4. identify one way Raul could have increased the total amount of money he made over 40 years. Explain your reasoning..
After 40 years, the account has a total balance of $49.450.80.
Why is there an interest?Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.
Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.
The total contributions would be $100 x 480 = $48,000.
The interest earned on the account balance can be calculated as follows:
Interest = Account balance * Interest rate
At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:
Year 1: $48,000 * 1.5% = $720
Balance = $48,000 + $720 = $48,720
Year 2: $48,720 * 1.5% = $730.80
Balance = $48,720 + $730.80 = $49,450.80
To know more about interest visit:-
https://brainly.com/question/11339060
#SPJ1
For each value of y , determine whether it is a solution to 10 < y
If a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.
What is inequality?
In mathematics, an inequality is a statement that describes a relationship between two values, expressing that one value is greater than, less than, or equal to the other value. Inequalities are denoted by symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).
The inequality 10 < y means that "y" is greater than 10. To determine whether a given value of "y" is a solution to this inequality, we simply need to check whether that value is indeed greater than 10.
For example:
If y = 11, then 10 < y is true, because 11 is greater than 10.
If y = 10, then 10 < y is false, because 10 is not greater than 10 (they are equal).
If y = 9, then 10 < y is false, because 9 is not greater than 10.
Hence, if a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.
To learn more about the inequalities, visit:
https://brainly.com/question/25275758
#SPJ1
I need help answering this
The domain of the function for this situation is given as follows:
B. All whole numbers greater than or equal to 0 and less than or equal to 7.
How to obtain the domain of a function?The domain of a function is the set that contains all the values assumed by the input of the function.
Hence, on a graph, the domain is given by the values assumes on the horizontal axis of the graph.
The values that compose the domain of the graph are given as follows:
0, 1, 2, 3, 4, 5, 6 and 7.
Which is best described by option B.
More can be learned about domain of functions at https://brainly.com/question/30348593
#SPJ1
what is the equation of a line that is parallel to the line that is given by the equation x=-4?
The equation of the line which is parallel to the line x = -4 will be x = -3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the equation of the line is x = -4. The y-intercept is zero for the line.
The equation of the line parallel to the equation will be,
x = -3
To know more about an equation of the line follow
https://brainly.com/question/18831322
#SPJ9
what happend if you do rise over run
PLEASE GIVE BRAINLIEST
thank you and have a good day :)
Answer:
You figure out the slope
Step-by-step explanation:
Rise/Run is a formula that calculates the slope. This determines the direction of the line and how steep it is.
Answer:
its a math term yw my boy
Step-by-step explanation:
The figure below is dilated by a factor of 4 centered at the origin. Plot the resulting image
The resulting image of the dilated figure has vertices at (-8, -4), (8, -8), and (4, 8).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.
To dilate the given figure by a factor of 4 centered at the origin, we need to multiply the coordinates of each vertex by 4.
The new coordinates of B will be:
x-coordinate: 4 x (-2) = -8
y-coordinate: 4 x (-1) = -4
So the new vertex B' is (-8, -4).
The new coordinates of C will be:
x-coordinate: 4 x (2) = 8
y-coordinate: 4 x (-2) = -8
So the new vertex C' is (8, -8).
The new coordinates of D will be:
x-coordinate: 4(1) = 4
y-coordinate: 4(2) = 8
So the new vertex D' is (4, 8).
Therefore, the image of the resultant figure is given in the image below.
To learn more about the dilation in geometry;
https://brainly.com/question/10713409
#SPJ2
Identify the y- intercept of the graph below
b= -4
b=6
b=4
b= -10
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
What is Variability of data?Data variation can be caused by a variety of sources. Variability is also known as data spread. The standard deviation is a measure of variability since it measures the spread of data.
The range is the best measure of variability for the data shown, and its value is 45.
The range is defined as the difference between the largest and smallest values in a set of data.
In this case, the largest score is 88 and the smallest score is 20, so the range is 88 - 20 = 68.
The IQR (interquartile range) is another measure of variability, but it is not the best measure for this data set because the data set has only a few values and does not form a normal distribution. The IQR is a more appropriate measure for larger data sets that form a normal distribution.
To Know more about Variability of data visit,
https://brainly.com/question/12872866
#SPJ1
How much time will it take to earn $760.00 in interest if you deposit $3,200.00 into a simple interest account earning 4.5% annum Simple interest
Using the formula of simple interest, the time it will take to accumulate to $3200 at a rate of 4.5% is 71.35 years
What is Simple InterestSimple interest is a method of calculating the interest charge on a loan or deposit. It is based on the principle of earning interest only on the initial amount (principal) that was borrowed or deposited.
The formula for simple interest is:
I = P * r * t
where:
I is the interest amount
P is the principal amount
r is the interest rate (expressed as a decimal)
t is the time period (in years)
Substituting the values into the formula;
A = P(1 + rt)
3200 = 760(1 + 0.045(t))
3200 = 760 + 34.2t
34.2t = 3200 - 760
34.2t = 2440
t = 2440 / 34.2
t = 72.35 years
Learn more on simple interest here;
https://brainly.com/question/20690803
#SPJ1
What is 7/8 of sixteen times a half of 30
7/8 of sixteen times a half of 30 is 210.
What is a PEMDAS rule?
PEMDAS is an acronym that stands for the order of operations in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
To calculate this, we can follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):
Start with the expression inside the parentheses: half of 30 is 15.
Multiply 16 by 15: 16 times 15 is 240.
Find 7/8 of 240:
7/8 of 240 = (7/8) x 240
= 210
Hence, 7/8 of sixteen times a half of 30 is 210.
To learn more about the PEMDAS rule, visit:
https://brainly.com/question/23385237
#SPJ1
someone pls help with this question
a² y² - 2aby + b²
I will give brainliest and ratings if you get this correct
The short-run total cost is TC is wL + rK and short-run average cost curve is TC/Q. The SMC is 4.01 and the SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost.
What is the firm short-run total cost curve and short-run average cost curve functionA. To calculate the firm’s short-run total cost curve, we need to calculate the total cost at each level of output. The short-run total cost can be represented as follows:
TC = wL + rK,
where w is the wage rate, L is the labor used, r is the interest rate, and K is the capital used. In this case, w = $4 and r = $1.
To calculate the short-run average cost curve, we need to divide the total cost by the level of output:
SAC = TC / Q
Where Q is the level of output.
B. The short-run marginal cost function can be calculated as the change in total cost for a small change in the level of output:
SMC = dTC / dQ
At a level of output of 25, the labor used is L = 25 / 2 = 12.5. The total cost can be calculated as follows:
TC = 4 * 12.5 + 1 * 100 = 50 + 100 = 150
So, the short-run average cost is SAC = 150 / 25 = $6 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:
Q = 2 * sqrt(KL)
Taking the derivative with respect to L, we get:
dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))
Substituting the values, we get:
SMC = 4 + (1 / (sqrt(100 * 12.5)))
At a level of output of 200, the labor used is L = 200 / 2 = 100. The total cost can be calculated as follows:
TC = 4 * 100 + 1 * 100 = 400
So, the short-run average cost is SAC = 400 / 200 = $2 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:
Q = 2 * sqrt(KL)
Taking the derivative with respect to L, we get:
dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))
Substituting the values, we get:
SMC = 4 + (1 / (sqrt(100 * 100)))
SMC = 4.01
C. To draw the graph for the SAC and SMC, we need to calculate the SAC and SMC for different levels of output. We can then plot the SAC and SMC against the level of output to obtain the graphs.
D. The SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost. When the level of output is low, the marginal cost is high and the fixed cost is a large portion of the total cost. As the level of output increases, the marginal cost decreases and the fixed cost becomes a smaller portion of the total cost. As a result, the average cost decreases and reaches a minimum at the point where the marginal cost intersects the average cost.
Learn more on short-run total cost curve here;
https://brainly.com/question/13694840
https://brainly.com/question/25109150
https://brainly.com/question/13743514
#SPJ1
Is 8 a solution to 3/4x=6?
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
YES, x = 8
Step-by-step explanation:
plug in 8 for x and see if both sides are equal
3/4 times 8 = 24/4 or 6
Answer:
Yes, 8 a solution to 3/4 x=6 !Step-by-step explanation:
If we solve it as....
[tex]\mathrm{\cfrac{3}{4}x=6}[/tex]
[tex]\mathrm{4\times\cfrac{3}{4}x=6\times\:4}[/tex]
[tex]\mathrm{3x=24}[/tex]
[tex]\mathrm{\cfrac{3x}{3}=\cfrac{24}{3}}[/tex]
[tex]\mathrm{x=8}[/tex]
Yes, 8 would be the solution!
___________________
Hope this helps!
NAME
12. Ling wants to buy a sleeping bag.
The sale price is $9. What was the
original price if the sale price was 30?
How do I find the answer to this question?
Answer:
you see
Step-by-step explanation:
Grayson is going to invest in an account paying an interest rate of 4% compounded
continuously. How much would Grayson need to invest, to the nearest dollar, for the
value of the account to reach $15,000 in 5 years?
Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.
What is continuously compounded interest?
Continuous compounded interest indicates that an account balance is constantly earning interest and reinvesting that money so that it, too, earns interest.
The formula for continuous compounding is given by:
[tex]A = Pe^{rt}[/tex]
where A is the amount in the account after t years, P is the principal amount (the amount invested), r is the annual interest rate, and e is the base of the natural logarithm.
We want to find P when A = $15,000, r = 0.04, and t = 5 years.
Substituting these values into the formula, we get:
[tex]15000 =Pe^{0.04*5}[/tex]
Simplifying the right-hand side, we get:
[tex]15000 =Pe^{0.2}[/tex]
Dividing both sides by e^(0.2), we get:
[tex]P= \frac{15000}{e^{0.2}}[/tex]
Using a calculator, we get:
P ≈ $10,994
Therefore, Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.
To know more about continuously compounded interest visit,
https://brainly.com/question/14303868
#SPJ1
answer all pls get 100 pointa
a).The function1 changes at greater rate of 45.
b). At x = 1; the function1 = 45 and function2 = 50.
c).The functions are equal to 90 at x = 2.
What is a function in the form y = mx + cA function in the equation form "y = mx + c" represents a straight line in a two-dimensional coordinate system. "y" and "x" are variables representing the coordinates of points on the line, "m" is the slope of the line, and "c" is the y-intercept, which is the point at which the line crosses the y-axis.
The slope "m" represents the rate at which the line rises or falls as x increases. The y-intercept "c" determines the location of the line along the y-axis. This equation is known as the slope-intercept form of a linear equation.
For the function1, when y = 0 and x = 0, we can solve for c and m as follows:
0 = 0m + c
c = 0
when y = 90 and x = 2;
90 = 2m + 0
m = 45
Hence, the function1 with y = 45x changes at a greater rate of 45.
At x = 1:
for function1;
y = 45(1) + 0 = 45
for function2;
y = 40(1) + 10 = 50.
At the point when x = 2:
for function1;
y = 45(2) + 0 = 90
for function2;
y = 40(2) + 10 = 90.
Therefore, the function1 changes at greater rate of 45. At x = 1; the function1 = 45 and function2 = 50. The functions are equal to 90at x = 2.
Know more about function here:https://brainly.com/question/24148225
#SPJ1
A bag of garden soil weighs 42 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the volume of 15 bags in cubic yards.
Answer:
285.76 kilograms 1.1 cubic yard
Step-by-step explanation:
Answer:
1.11121 cubic yards.
Step-by-step explanation:
First, let's convert the weight of 1 bag of garden soil from pounds to kilograms:
1 lb = 0.45359237 kg
42 lbs = 42 * 0.45359237 kg = 19.05 kg
So, the weight of 1 bag of garden soil is 19.05 kilograms.
Next, let's find the weight of 15 bags of garden soil:
15 bags * 19.05 kg/bag = 285.75 kg
So, 15 bags of garden soil weigh 285.75 kilograms.
Next, let's find the volume of 15 bags of garden soil in cubic yards:
1 cubic foot = 0.037037 cubic yards
2 cubic feet * 15 bags = 30 cubic feet
30 cubic feet = 30 * 0.037037 cubic yards = 1.11121 cubic yards
So, 15 bags of garden soil have a volume of 1.11121 cubic yards.
