Marsha deposited $6,000 into a savings account 4 years ago. The simple interest rate is 5%. How much money did Marsha earn in interest?
A scout troop took a camping trip to the dunes that lasted for 97 minutes. Along the way, they stopped
at 10:48AM for a break. The troop didn't check the time when they left, but when they arrived a park
ranger said it was 11:37AM. What time did they start the trip?
Answer:
they started trip at 10:00 am
Step-by-step explanation:
Let's call the starting time "S".
The arrival time is 11:37AM,
difference in time after break to park arrived : 11:37 am - 10:48 am = 49 minutes
remaining time : 97-49= 48 minutes
starting time= 10:48 am -48 minutes = 10:00 am
There are 16 more sophomores and juniors in an 8 AM algebra class if there are 54 students in this class find the number of sophomores and number of juniors in the class
The number of sophomores in the class is 35.
The number of Juniors in the class is 19.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of sophomores = x + 16
Number of Juniors = x
Now,
Number of students in the class = 54
This means,
x + x + 16 = 54
2x + 16 = 54
2x = 54 - 16
2x = 38
x = 19
Thus,
Number of sophomores = 19 + 16 = 35
Number of Juniors = 19
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A private museum charges $40 for a group of 10 or fewer people. A group consisting of more than 10 people must, in
addition to the $40, pay $2 per person for the number of people above 10. For example, a group of 12 pays $44. The
maximum group size is 50.
a) How much does a group of 16 pay?
b) Find a formula for the cost function.
c) What are the domain and range of the cost function? (Hint: Use the graph on the calculator)
Answer:
i hope this helpes
Step-by-step explanation:
a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.
b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.
c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.
Answer:
a) $52
b) C(x) = 40 + 2x, if x > 10 and x ≤ 50
C(x) = 40, if x ≤ 10
c) Domain = {x ≥ 1 and x ≤ 50}
Range = { from 40 to 140}
A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final
answer to four decimal places and intermediate z-value calculations to two decimal places
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:
0.5874 = 58.74%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953[/tex]
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (18.1 - 17.2)/0.3953
Z = 2.28
Z = 2.28 has a p-value of 0.9887.
Z = (17.1 - 17.2)/0.3953
Z = -0.25
Z = -0.25 has a p-value of 0.4013.
Hence:
0.9887 - 0.4013 = 0.5874 = 58.74%.
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Please help! i have no clue what the answers are!
Answer:
1) 9
2) 27
3) Read explanation below!
Step-by-step explanation:
1) Use the Pythagorean theorem to find AD. Show your working
Pythagorean theorem = a²+b²=c²Where a = 12 and c=15 = 12²+?²=15²To find '?' we first have to expand the indices...
12² = 14415² = 225144 + ?² = 225Now work out '?'
225 - 144 = 81√81 = 92) Find AC. Show your working
We have found out that AD is 9 and to find AC we have to add 18!
9 + 18 = 273) Is ΔABC a right triangle? Explain
We can that ΔABC is not a right angle as none of the angles in the triangle are 90°! If it was a right angled triangle we would see the ∟sign on one of the angles. Even though there are two of those in the middle it does not count as the question is asking about ΔABC!!
Have a lovely day :)
If 2 equals m then what is 3m+5
Answer: 11
Step-by-step explanation:
3x2=6
6+5=11
What the a round the the nearest thousand 802957
David is tracking the amount of water he drinks each day.
On Thursday, he drinks 15
cups of water.
On Friday, he drinks 12
cups of water.
What is the percent change in his water intake?
The original amount of water is 15 cups.
The change in David's water intake is 3 cups.
And, The percent change is 20%. This is a percent decrease.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
David is tracking the amount of water he drinks each day.
Here, On Thursday, he drinks 15 cups of water.
And, On Friday, he drinks 12 cups of water.
Hence, We get;
The original amount of water = 15 cups.
And, The change in David's water intake = 15 - 12
= 3 cups
And, The percent change in his water intake is,
⇒ Percent = 3 / 15 × 100
⇒ Percent = 20%
Thus, The original amount of water is 15 cups.
The change in David's water intake is 3 cups.
And, The percent change is 20%. This is a percent decrease.
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You work for a rock-climbing gym and need to purchase 330 feet of climbing rope to arrive in three days for an event. The online retailer SportsStuff.com charges $5.50 per yard of rope and offers free three-day shipping. The same rope at OutdoorHaven.com costs $5.20 per yard, plus a $12.25 rush delivery fee. What is the cheapest price you can pay for the rope you need for your gym?
Answer:pls brainly award
Step-by-step explanation:
The 330 feet of rope is equivalent to 330/3 = 110 yards.
The cost of the rope at SportsStuff.com is 110 * $5.50 = $605.
The cost of the rope at OutdoorHaven.com is 110 * $5.20 + $12.25 = $604.45.
Therefore, the cheapest price you can pay is $604.45.
Dawn is ordering 1 veggie sandwich for every 3 ham sandwiches. She needs 12 sandwiches in all. How many veggie sandwiches did she order, and how many ham sandwiches did she order.
which of these shapes below is an enlargement of shape x by a scale factor of 2
A scale factor consists of two or more shapes who look the same but have different scales or measures. A scale factor of 2 means that the new triangle is two times the size of the original.
If we look at shape x, we can see it has a base of 4, and a height of 3. If we also know that a scale factor of two means that the new shape will be twice as large, we can use an equation that looks like this:
(Base/height × scale factor = new base length)
4 × 2 = 8 (b)3 × 2 = 6 (h)Now that we have these numbers, we can take them and see which shape matches the new length.
Shape A has a base of 6, and a height of 5.Shape B has a base of 6, and a height of 8.Shape C has a base of 8, and a height of 8.Shape D has a base of 8, and a height of 6.Shape E has a base of 6, and a height of 6.Shape F has a base of 8, and a height of 6.Shape D has a base of 8 and a height of 6, meaning that it has a scale factor 2 compared to shape x.
Therefore Shape D is the answer.
if f(x)=3x-4,find f (4)
Answer:
8
Step-by-step explanation:
f(4) = 3(4) - 4
f(4) = 12 - 4
f(4) = 8
18. In a game, you draw a card with three consecutive numbers on it. You
choose one of the numbers and find the sum of its prime factors. Ther
you can move that many spaces. You draw a card with the numbers
25, 26, 27. Which number should you choose if you want to move as
many spaces as possible? Explain.
Answer:
The number with the highest sum of prime factors is 27, as it has only two prime factors: 3 and 3. The sum of its prime factors is 6, so if you choose 27, you can move 6 spaces. The number 25 has two prime factors as well, but only 5 + 5 = 10. 26 is not a prime number, so it wouldn't be the best choice. So, if you want to move as many spaces as possible, you should choose 27.
Choose the solution to this inequality.
9
1/2 ≥b + 2/1/2
O
10
O
A. b2²/
B. b≤11/100
O C. bs-²/
O D.
D. b < 2 ²1/1
Answer:
[tex]\text{Choice C: }\boxed{b\le 1 \dfrac{7}{10}\\\\}[/tex]
Step-by-step explanation:
We are given inequality:
[tex]\dfrac{7}{2}\ge \:b\:+\:\dfrac{9}{5}[/tex]
Switch sides:A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Answer:
The length of the train can be calculated using the formula:
Length of the train = Speed x Time / 2
Where,
Speed = 60 km/hr = 60 x 1000/60 = 1000 m/min
Time = 9 sec = 9 / 60 min = 0.15 min
So,
Length of the train = 1000 x 0.15 / 2 = 75 m
Therefore, the length of the train is 75 meters.
Answer:
Length of the train shold be 75m
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!
Answer:
0.2
Step-by-step explanation:
as 0.2 is greater than 1
Answer:
0.2
Step-by-step explanation:
The diagram = 0.1
0.1 < 0.2
You deposit $3000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 25 years?
The amount that will be in the account in 25 years is $16,282.298.
What is Compound Interest?Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.
Given that,
Principal amount, P = $3000
Rate of interest, r = 7% = 0.07
Number of years, n = 25
The final amount in a compound interest where the interest is compounded annually is,
A = P (1 + r)ⁿ
Substituting the given values,
A = 3000 (1 + 0.07)²⁵
= 3000 (1.07)²⁵
= 16,282.298
Hence the final amount after 25 years is $16,282.298.
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lydia has money in two savings accounts one rate is 8% and the other is 12% if she has $350 more in 12% account and the total interest is $336 how much is invested in each savings account
The required amount invested in accounts with 8% and 12% are $1470 and $1820 respectively.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Lydia has money in two savings accounts one rate is 8% and the other is 12% and the total interest is $336. Let the amount invest in accounts be x and y respectively.
According to the question,
0.08x + 0.12y = 336 - - - - - -(1)
Again,
she has $350 more in 12% account
y = x + 350 - - - - - -(2)
Put y in equation 1,
0.08x + 0.12[x + 350] =336
0.08x + 0.12x + 42 = 336
0.20x = 336 - 42
x = 294/0.20
x = $1470
Now
y = 1470 + 350
y = $1820
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48) A woman has $1.70 in dimes and nickels. She has 5 more dimes than nickels. How many nickels does she have?
What is the least number that two whole numbers can have as the LCM? A. the greater of the two numbers the lesser of the two numbers B. C. the product of the two numbers D. the sum of the two numbers
Answer:
b
Step-by-step explanation:
:)
Interpret Linear Function Equations What is the slope-intercept form of the function described by this table? X y y=0 1 Enter your answer by filling in the boxes. X + 1 2 -2 3 -5 K 1 2
The slope-intercept form of the function described by this table is y = x + 1
How to determine the slope intercept formFrom the question, we have the following parameters that can be used in our computation:
x y
0 1
From the above table of values, we can see that
The difference between the x and the y value is 1
Mathematicallly, this can be represeted as
y - x = 1
Add x to both sides
y = x + 1
The above equation is in the slope intercept form, y = mx + c
Hence, the equation is y = x + 1
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Which statements about the reflection are true? Check all that apply.
Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will remain in the same location as C because it is on the line of reflection.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.
The statements that are true are:
Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.
Options A, B, D, E, and F.
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
Clayton could use the relationship (x, y) → (y, x) to find the points of the image.
This is the y = x reflection rule.
This is true.
Clayton could negate both the x and y values in the points to find the points of the image.
Reflection of (x, y) along the x-axis and y-axis consecutively will give us
(-x, -y).
This is true.
C’ will remain in the same location as C because it is on the line of reflection.
This is not true.
C’ will move because all points move in a reflection.
This is true.
The image and the pre-image will be congruent triangles.
This is true.
The image and pre-image will not have the same orientation because reflections flip figures.
This is true.
Thus,
All statements are true except the statement:
C’ will remain in the same location as C because it is on the line of reflection.
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Which is the factored form of -3n6 +12n4 - 6n²?
Factored form of -3n⁶ +12n⁴ - 6n² would be, (n² + 1)(-3n² + 6).
What is factorization?
The process of writing a number or any mathematical object as a product of several factors, usually smaller or simpler objects of the same kind, is known as factorization or factoring.
In mathematics, factorization is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number.
The factored form of -3n^6 +12n^4 - 6n² is:
-3n² (n⁴ - 2) + 6n² (1 - n²)
= -3n² (n⁴ - 2) + 6n² - 6n⁴
= -3n² (n⁴ - 2 + 2n²) + 6n²
= -3n² (n² + 1)² + 6n²
= (n² + 1)(-3n² + 6).
So, Factored form of -3n⁶ +12n⁴ - 6n² would be, (n² + 1)(-3n² + 6).
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You own Company X. When you started the company, you Initially invested $12,000. You also borrowed $12,000 through a five-year (long-term) loan, of which you have paid back $2,018. You have retained $1,291 in earnings to be reinvested in the company, and you decided to put $1,000 of it aside for a long-term investment. The company owns land and a building worth $8,878 and equipment worth $4,230. As of today, the company has $8,250 in cash, $1,225 in Inventory, and is due to receive accounts worth $675. However, the company owes its suppliers $485 and has a $500 loan to pay off in the next six months.
The equity of Company X's is $13,291.
What is the equity?The difference between assets and liabilities is the equity.
The equity is the portion of assets belonging to the owners.
Analysis:Initial investment = $12,000
Retained Earnings = $1,291
Long-term loan = $9,982 ($12,000 - $2,018)
Land and building = $8,878
Equipment = $4,230
Cash $8,250
Inventory = $1,225
Accounts Receivable = $675
Accounts Payable = $485
Short-term loan = $500
Company X
Balance SheetAs of current date
Current Assets:Cash $8,250
Inventory 1,225
Accounts Receivable 675 $10,150
Long-term Assets:Long-term investment $1,000
Land and building 8,878
Equipment 4,230 $14,108
Total Assets $24,258
Current Liabilities:Accounts Payable $485
Short-term loan 500 $985
Long-term Liabilities:Long-term loan $9,982
Total liabilities $10,967
Equity:Initial capital $12,000
Retained earnings 1,291 $13,291
Total liabilities and equity $24,258
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Question Completion:Determine Company X's equity?
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The following figure is made of 3 triangles and 1 rectangle!
The area for each part of the figure is given as follows:
Triangle A: 20 square units.Triangle D: 6 square units.Whole figure: 32 units squared.How to obtain the areas?The area of a right triangle is given by half the multiplication of it's sides.
Triangle A has the side lengths given as follows:
4 units.2 + 2 + 6 = 10 units.Hence the area is given as follows:
A = 0.5 x 4 x 10 = 20 units squared.
Triangle D is has the side lengths given as follows:
2 units 6 units.Hence the area is given as follows:
D = 0.5 x 2 x 6 = 6 units squared.
The total area is given by the sum of the areas of each part of the figure, hence:
20 + 2 + 4 + 6 = 32 units squared.
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Help
Problems 3.1–3.2
Starting at noon, the temperature changed steadily at a rate of −0.8°C every hour.
At 3 p.m., the temperature was −2.5°C.
What was the temperature at noon?
The temperature at noon is equal to -0.1°C.
What is the slope-intercept form?Mathematically, the standard form or slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Note: Let x represent the time.
Next, we would write an equation that models the situation based on the rate of change (slope) and y-intercept (initial value) as follows;
y = mx + c
y = -0.8x - 2.5
y = -0.8(3) - 2.5
y = -2.4 - 2.5
y = -0.1°C
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Yuki and Roman are photographers for the yearbook. Yuki starts with 20 photos. She then takes 60 photos each week. Roman starts with 110 photos. He then takes 35 photos each week. After how many weeks will Yuki and Roman have taken the same number of photos? Write a system of equations that can be used to solve the problem. Write your answers in the blanks.
p = ____________w + ______________
p= ____________w + ______________
After 3 3/5 weeks, they will have the same number of pictures.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, Yuki and Roman are photographers for the yearbook. Yuki starts with 20 photos. She then takes 60 photos each week. Roman starts with 110 photos. He then takes 35 photos each week.
Let "w" the number of weeks they collected the pictures
For Yuki,
The total picture he has after 0 weeks = is 20
The total picture he has after 1 week = 20 + 60
The total picture he has after 2 weeks = 20 + 60*2
The total picture he has after w weeks = 20 + 60*w
For Roman,
The total picture he has after 0 weeks = is 110
The total picture he has after 1 week = 110 + 35
The total picture he has after 2 weeks =110 + 35*2
The total picture he has after w weeks = 110 + 35*w
To calculate the number of weeks when they have equals pictures:
20 + 60*w = 110 + 35*w
25w = 90
w = 3 3/5
Therefore, After 3 3/5 weeks, they will have the same number of pictures.
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Solve this system of equations by
using the elimination method.
2x - 2y = 2
5x + 2y = 12
The ordered pair of solutions
is written in the format (x, y).
([?], [])
The ordered pair of solutions is (11/5, 2).
What is the linear equations?
A linear equation is a mathematical equation that represents a straight line when graphed on a coordinate plane. It has the form of ax + b = y, where a and b are constants and x and y are variables. The coefficient "a" determines the slope of the line, and the constant "b" determines the y-intercept.
The elimination method is a method of solving a system of linear equations by adding or subtracting the equations to eliminate one of the variables.
Here is the solution for the system of equations 2x - 2y = 2 and 5x + 2y = 12 using the elimination method:
Multiply the first equation by 5: 10x - 10y = 10
Add the two equations: 15x - 8y = 22
Solve for x by dividing both sides of the equation by 15: x = 22/15 = 11/5
Substitute the value of x back into one of the original equations to solve for y:
2x - 2y = 2
2(11/5) - 2y = 2
22/5 - 2y = 2
22/5 - 2y = 2
22/5 = 2 + 2y
22/5 - 2 = 2y
20/5 = 2y
10/5 = y
The solution to the system of equations is (x, y) = (11/5, 10/5) = (11/5, 2).
So, the ordered pair of solutions is (11/5, 2).
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The ordered pair of solutions is written in the format (x, y) is (11/5, 2) .
What do linear equations mean?When plotted on a coordinate plane, a linear equation is a mathematical equation that resembles a straight line. It takes the form axe + b = y, with a and b acting as constants and x and y as variables. The line's slope is determined by the coefficient "a," whereas the y-intercept is determined by the constant "b."
A system of linear equations can be solved using the elimination approach by adding or removing equations to get rid of one of the variables.
Here is the elimination technique solution for the system of equations 2x - 2y = 2 and 5x + 2y = 12:
The first equation is multiplied by 5: 10x - 10y = 10.
Equational sum: 15x - 8y = 22
Divide both sides of the equation by 15 to find the value of x: x = 22/15 = 11/5
To find the value of y, add the value of x back into one of the initial equations:
2x - 2y = 2
2(11/5) - 2y = 2
22/5 - 2y = 2
22/5 - 2y = 2
22/5 = 2 + 2y
Simplify the equation
22/5 - 2 = 2y
20/5 = 2y
10/5 = y
The system of equations has a solution of (x, y) = (11/5, 10/5) = (11/5, 2).
The pair of answers that are in order is (11/5, 2).
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If tan\alpha =-(2)/(5) and \alpha is in Quadrant IV, find cos\alpha .
The value of cosα is 2/5.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, tanα= -2/5 and α is quadrant IV.
We know that, tan(−θ) = − tan(θ)
α= 2/5
As we know cos(−θ) = cos(θ)
cosα =2/5
Therefore, the value of cosα is 2/5.
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