Answer:
So now,
you know the formula for simple interest is P×R×T divided by a hundred?
So 2500 times 3.55 times 2.75 divided by 100
Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is adding 5 CDs a month to her collection. Write a system to find the number of months after which they will have the same number of CDs. Let x represent the number of months and y the number of CDs.
Answer:
3 months
Step-by-step explanation:
Let x be the number of months CDs are added at Tom and Nita's respective rates of 1 and 5 CDs/month.
Tom's collection after x months is = 30 + 1x
Nita's collection after x months is = 18 + 5x
At some point they will have equal numbers of CD's, so set the equations equal to each other:
30 + 1x = 18 + 5x
4x = 12
x = 3 months
At 3 months both Tom and Nita will have the same number of CDs.
Tom: 30 + 1*3 = 33 CDs
Nita: 18 + 5*3 = 33 CDs
x = 3
Step-by-step explanation:We can create a system of equations to represent the situation we have been given.
Creating the Equations
In this system, we can create an equation to represent both people's collections.
First, we can create Nita's.
To create the equation we can start with the constant. We are told she starts with 18 CDs. So, this will be one of the terms.Next, we can multiply x by 5. We can do this because x represents the number of months that have passed and 5 is the number of CDs she adds per month. This means 5x will be another term.Finally, the constant and variable will add up to the total number of CDs, which is represented by y. So, the expression will be set equal to y.All of this creates the equation: 5x + 18 = y.
Next, we can do the same to find Tom's equation.
Tom starts out with 30 CDs. So this will be the constant term.Each month he adds 1 CD. This means that we can multiply 1 by x to make the term 1x.Finally, like with Nita's this expression will be set equal to y.This creates the second equation: 1x + 30 = y.
The system is:
5x + 18 = y
1x + 30 = y
Solving the System of Equations
One method to solve a system of equations is substitution. Substitution is when you substitute an expression for a variable. Since both expressions are set equal to y, we can substitute the expressions for y and set them equal to each other.
This creates the new equation: 5x + 18 = 1x + 30. Then, solve normally.
First, subtract 1x from both sides4x + 18 = 30
Next, subtract 18 from both sides.4x = 12
Finally, divide both sides by 4x = 3
This means after 3 months the number CDs will be equal.
Mrs. Taylor is planning a pizza party for her students. She plans to purchase cheese pizza and pepperoni pizza for her students to enjoy. Cheese pizzas cost $8 each and pepperoni pizzas cost $11 each. She needs to purchase at least 12 pizzas, while spending no more than $180.
Let x represent the number of cheese pizzas purchased and y represent the number of pepperoni pizzas purchased.
What are two combinations of cheese and pepperoni pizzas that Mrs. Taylor can purchase without exceeding her spending limit?
Verify the combinations, graphically.
Verify the combinations, algebraically.
What is one combination of cheese and pepperoni pizzas that does not meet the criteria?
Verify the combination, graphically.
Verify the combination, algebraically.
The two combinations of cheese and pepperoni pizzas that Mrs. Taylor can purchase without exceeding her spending limit are; x + y ≥ 12 and
8x + 11y < 180
How to solve linear programming problems?We are told that she needs twelve pizzas. The equation below represents the number of pizzas of the type she needs to buy;
x + y ≥ 12
Where;
x represents the number of pepperoni pizzas she can buy while keeping her limit of 12 pizzas.
y represents the number of cheese pizzas she can buy while keeping her limit of 12 pizzas.
We are told that she cannot spend more than 180 dollars. Thus, our inequality is now;
8x + 11y < 180
Where;
8x represents the amount of dollars per pepperoni pizza.
11y represents the amount of dollars per cheese pizza.
These equations show all possible solutions.
The purple area in the graph attachment is verified to show the possible combinations.
Read more about Linear Programming at; https://brainly.com/question/14309521
#SPJ1
anybody know the answer, i dont understand U_U
A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.
What is the inverse of a function?Suppose that the given function is
[tex]f:X\rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
[tex]f^{-1}: Y \rightarrow X[/tex]
such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]
(and vice versa).
It simply means, the inverse of 'f' is undone operator, that takes back the effect of 'f'
The graph that represents the inverse of the given function is option A because graph A is showing more rapid growth as compared to the given graph.
Hence, the correct option is A.
Learn more about Inverse function:
https://brainly.com/question/19425567
#SPJ1
5. Verbal
Explain how to find a line perpendicular to a linear function that passes through a given point.
Answer:
The required line can be found by substituting the slope and the given point in the slope intercept form of a line and is given by y=mx+c, where m is the slope and c is the y intercept.
Step-by-step explanation:
In the given question, it is given that a linear function passes through a given point.It is required to find a line perpendicular to the function.When two functions are perpendicular, the product of their slopes is equal to -1.Thus, substitute the slope and the given point in the slope intercept form of a line and is given by y=mx+c, where m is the slope and c is the y intercept.The equation of a parallel line to a linear function that passes through a point can be explained using the examples below.
We have,
The parallel line to a linear function that passes through a point can be explained using the examples below.
Example:
Let's find a line parallel to the linear function y = 3x - 2 that passes through the point (2, 5).
Step 1: Given linear function and point
Linear function: y = 3x - 2
Point: (2, 5)
Step 2: Determine the slope of the given linear function
The slope (m) of the given function y = 3x - 2 is 3.
Step 3: Use the slope to find the equation of the parallel line
Since the parallel line has the same slope (3), its equation will be
y = 3x + b, where "b" is the y-intercept that we need to find.
Step 4: Substitute the coordinates of the given point into the equation of the parallel line
Using the coordinates (2, 5) of the given point, we can solve for "b":
5 = 3(2) + b
5 = 6 + b
b = 5 - 6
b = -1
So, the equation of the line parallel to y = 3x - 2 and passing through the point (2, 5) is:
y = 3x - 1.
Thus,
The equation of a parallel line to a linear function that passes through a point can be explained using the examples above.
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ7
A company produces packets of soap powder labeled Giant Size 32 Ounces. The actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz. and a standard deviation of 0.7 oz. To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight. How heavy does a box have to be for it to be labeled overweight
In order to be labeled overweight the weight of box should be of 34.15 ounces.
Given mean of 33 ounces, standard deviation=0.7 ounces. Production of packets of 32 ounces.
Because it is normally distributed samples are solved using the z score formula.
In this Z=X-meu/st
meu is sample mean and st is population standard deviation.
We have to find the z score and then p value from the z table.
meu =33 and st=0.7
Top 5% so X when Z has a p value of 1-0.05=0.95. So X when Z=1.645.
Z=(X-meu)/st
1.645=(X-33)/0.7
X-33=0.7*1.645
X-33=1.1515
X=1.1515+33
X=34.1515 ounces.
Hence to be labeled overweight the box must have 34.15 ounces weight.
Learn more about z test at https://brainly.com/question/14453510
#SPJ4
If a researcher counting how many seconds each bystander helps a stranger Struggling to pick up a heavy box
Answer:
You didn't finish the whole question.
Step-by-step explanation:
We have to calculate mean of the data.
Mean is the sum of numbers divided by total numbers included.
Mean=∑X/n
where n is the number.
Mean =(10+15+10)/3
=35/3
=11.67
What do you understand by mean ?in mathematics, a quantity that has a value intermediate between those of the extreme members of some set. numerous types of manner exist, and the method of calculating an average depends upon the relationship known or assumed to control the alternative members.
The mean, or average, is calculated by adding up the scores and dividing the whole by the number of scores. consider the following number set: 3, 4, 6, 6, 8, 9, 11. The mean is calculated in the following way: 3 + 4 + 6 + 6 + 8 + 9 + 15 = 51
Learn more about mean here
https://brainly.com/question/12892403
#SPJ2
Please Help Asap!!!!
Express 16.927 in standard form correct to 3 significant figures
The standard form to 3 significant figure of 16.927 is 1. 69 × 10^-1
How to determine the standard formGiven the value;
16.927 to convert to three significant figure
= 1. 69 × 10 ^ -1
Note that "2" cannot add up as 1 to '9'
Thus, the standard form to 3 significant figure of 16.927 is 1. 69 × 10^-1
Learn about standard form here:
https://brainly.com/question/1708649
#SPJ1
What does it mean to "model with mathematics"?
Answer:
See below. To model with mathematics is to test ideas using math and computer programs to simulate an object or action.
Step-by-step explanation:
To "model with mathematics" means that equations and mathematical relationships will be employed to simulate an object or action instead of using the actual object or action. One example would be the design of a roller coaster. The forces inherent on a roller coaster design can be predicted using Newton's laws and other principles of physics. F=ma may be used to predict the force pulling the car down the initial incline and that can be used to calculate speed at the bottom. A change in the car's direction will also produce forces that may be calculated, One might ask "Will this turn produce more force than the seat belt can safely handle?" Rather than building a coaster and testing it with your business partner in the seat, a mathematical model can be used to determine the risks and maximum forces. You'll have a much better chance of keeping your friend intact on the actual coaster. Mathematical models are also used to predict weather, the impact of monetary policy of the economy, and even which Netflix movie you are most likely to enjoy. The design of aircraft, ships, cars, and many other items are done using computer-aided design programs where the various forces can be modeled to determine optimum design without actually building the item. This can save enormous amounts of time and money to be able to test ideas on the computer before starting actual assembly.
Simplify completely:
√320x2y³
simplify the radical by breaking the radicand up into a product of known factors,assuming positive real numbers.
Sorrry i cant write answer is that form but
the answer is 8 then square root of 5x rais to power 2 then write y raise to power3.
Keira and Nathan are dragging a box across a floor, as shown in the diagram on the left. Kiera pulls at an angle of 30below the horizontal and with a force of 80 poundsNathan pulls at an angle of 50 degrees above the horizontal and with a force of 85 pounds. The diagram on the right shows the triangle that represents this situation . What is the magnitude of the resultant force acting on the box ?
Answer:
165.0
30 plus 50 plus the 85 equals 165
The magnitude of the resultant force acting on the box is 126.4 pounds.
Hence the correct answer is C.
Given that Kiera pulls at an angle of 30below the horizontal and with a force of 80 pounds Nathan pulls at an angle of 50 degrees above the horizontal and with a force of 85 pounds.
We need to determine the magnitude of the resultant force acting on the box.
To find the magnitude of the resultant force acting on the box, we can use the law of cosines.
The law of cosines states that for any triangle with sides of lengths a, b, and c, and an angle θ opposite to side c, the following equation holds:
c² = a² + b² - 2ab × cos(θ)
In this case, we have a triangle formed by the two forces exerted by Keira and Nathan, and we want to find the magnitude of the resultant force, which corresponds to side c.
Let's assign the following values:
a = 80 pounds (force exerted by Keira)
b = 85 pounds (force exerted by Nathan)
θ = 180° - 30° - 50° (angle opposite to the resultant force)
θ = 100°
Now we can plug these values into the law of cosines equation:
[tex]F = \sqrt{80^2 + 85^2 -2\times 80 \times 85\times \cos100}[/tex]
Solving we get,
F = 126.4
Hence the magnitude of the resultant force acting on the box is 126.4 pounds.
Learn more about law of cosines click;
https://brainly.com/question/21634338
#SPJ4
Use the regression line for the data in the scatterplot to answer the question. on average, how many more goals will a player score for every additional hour of practice?
On average the more goals will a player scores for every additional hour of practice is 3/4.
Given a regression line for the data in the scatterplot which is shown in figure.
This question can be solved by finding the slope of the line.
Slope is the ratio of vertical change to horizontal change between two points on the line.
Here, we can find the slope by taking the two points which is on the line.
Let us take the two points be A(1.5,2) and B(6.5,6)
Now, we will find the slope using the formula, we get
m=(y₂-y₁)/(x₂-x₁) where (x₁,y₁)=(1.5,2) and (x₂,y₂)=(6.5,6)
Substitute the values in the formula, we get
m=(6-2)/(6.5-1.5)
m=4/5
The slope which we find is near to the slope 3/4.
Hence, the more goals will a player score for every additional hour of practice from the regression line is 3/4.
Learn more about Slope of line from here brainly.com/question/3493733
#SPJ4
How do I do the distribution table and the proccess plss help
Answer + Step-by-step explanation:
p(X=3) = the probability that X is equal to 1 or 2 or 3 minus (the probability that X is equal to 2 plus the probability that X is equal to 1)
Because ,when X = 2 or X = 1 the largest number is not 3 so we have to subtract those values .
……………………………………………………………
the probability that X is equal to 1 or 2 or 3 is :
[tex](\frac{3}{6} )^4 = \frac{81}{1296}[/tex]
Then
[tex]p\left( X=3\right) =\frac{81}{1296} -(\frac{1}{1296} +\frac{15}{1296}) =\frac{65}{1296}\\\\p\left( X=4\right) =\frac{4^4}{1296} -(\frac{1}{1296} +\frac{15}{1296}+\frac{65}{1296}) =\frac{175}{1296}\\\\p\left( X=5\right) =\frac{5^4}{1296} -(\frac{1}{1296} +\frac{15}{1296}+\frac{65}{1296}+\frac{175}{1296}) =\frac{369}{1296}[/tex]
Verification:
1+15+65+175+369+671 = 1 296
A boat can travel 408 miles on 204 gallons of gasoline how far can it travel on 169 gallons
Answer:
338 milesStep-by-step explanation:
If a boat can travel 408 miles on 204 gallons, this means that for every 2 miles, it requires 1 gallon.
So, for 169 gallons, there are 2 miles for every gallon.
So, multiply 169 * 2.
The answer is 338
Hope this helps!
Explain when the solution set of an inequality will be the empty set or the set of all real numbers. Show an example of each.
Answer:
There are two cases when the solution set of an inequality will be the empty set or the set of all real numbers.
The first case is when the inequality is always false no matter what value is chosen for the variable. For example, the inequality x > 5 has no solution because there is no value of x that is greater than 5. In this case, the solution set is the empty set.
The second case is when the inequality is always true no matter what value is chosen for the variable. For example, the inequality x > -∞ has infinitely many solutions because there is no value of x that is not greater than -∞. In this case, the solution set is the set of all real numbers.
Step-by-step explanation:
During the snow storm your pipes burst you called preston the plumber who charges $50 for a serice call and $5 per hour. if your bill was for $120 total,how long did it take preston to repair your broken pipes
It takes Preston 14 hours to repair the broken pipes.
Given Information
Cost of service call charged by Preston, the plumber, S = $50
Preston charges $5/hour.
Preston's charge per hour, P = $5
The total bill, B = $120
We have to calculate the number of hours Preston take to repair the broken pipes.
Calculating the Number of Hours
Total service charge of Preston = Total bill - Service Call Charge
= B - S
∴ Number of hours Preston took to mend the broken pipe is given by,
H = (B - S)/P
H = $(120 - 50)/$5
H = 70/5
H = 14 hours
Therefore, Preston took 14 hours to repair the pipes.
Learn more about hours here:
https://brainly.com/question/3913939
#SPJ4
Fossils of Lystrosaurus, a dinosaur without the ability to swim or fly, can be found across Africa, India, and Antarctica.
What does this indicate?
A. That those continents were all connected during the time Lystrosaurus lived.
B. That they went extinct because they could not adapt.
C. That they later evolved either the ability to swim or the ability to fly.
D. Those continents were separated at the time Lystrosaurus lived.
Answer:
A
Step-by-step explanation:
Pangaea is the name for the land mass before the continents split. The continents would have been connected during that species life time.
What is the range of f?
Answer: [tex][-3,7][/tex]
Step-by-step explanation:
The range of a function is the set of y-values
x + 7 = -9 expressions
Answer:
x = -16Step-by-step explanation:
x + 7 = -9
Subtract 7 from both sides
x + 7 - 7 = -9 - 7
Simplify
x = -16
Answer:
x=-16
Step-by-step explanation:
x+7=-9
x=-9-7
x=-16
pls help.... Natalie plans to run 5 miles every week for 3 weeks. The first day of the first week she ran 1 1/5 miles. How mant miles does she need to run the rest of the first week?
Answer:
3 4/5
Step-by-step explanation:
If Natalie runs 5 miles each week and she already ran 1 1/5 then she will need to run 3 4/5.
5 - 1 1/5 = 3 4/5
What is the value of sin 0 given that (3-4) is a point on the terminal side of 0
Using trigonometric relations, we will see that:
sin(θ ) = -0.8
How to get the sine of the angle?
For any point (x, y), the angle between the positive x-axis and the ray that connects the origin with the point (x, y) is:
θ = Atan(y/x)
In this case, the point is (3, -4), then the angle is:
θ = Atan(-4/3) = -53.13°
Then the sine of theta is:
sin(θ = -53.13°) = -0.8
If you want to learn more about trigonometric functions:
https://brainly.com/question/8120556
#SPJ1
A tablet at a local electronics store is in high demand and will only be available to customers for a limited time. The store initially has 4 cases of the tablet on hand. The store manager receives new supplies of the tablet each week. At the beginning of week 1, the store manager receives an additional order from the distributor of 5 cases of tablets. At the beginning of week 6, the manager receives another order of 10 cases. Which of the following equations best models the scenario for how many cases of the tablet the store can expect to receive each week?
Answer:
y = x + 4
Explanation:
Initially (at week 0) = 4 cases
now (at week 1) = 5 cases
now (at week 6) = 10 cases
turn them into points:
(0, 4), (1, 5), (6, 10)Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) : \dfrac{5-4}{1- 0 } = 1[/tex]
Find equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf \rightarrow y-4 =1(x -0)[/tex]
[tex]\sf \rightarrow y = x +4[/tex]
PLEASE HELP MEE.
measure of angle B = 27 degrees, measure of angle C = 82 degrees, b = 14. Find the length of c to the nearest
tenth.
=======================================================
Work Shown:
[tex]\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\\\\\frac{\sin(27)}{14}=\frac{\sin(82)}{c}\\\\c\sin(27) = 14\sin(82)\\\\c=\frac{14\sin(82)}{\sin(27)}\\\\c\approx 30.5375398\\\\c\approx \boldsymbol{30.5}\\\\[/tex]
I used the law of sines. Make sure your calculator is in degree mode.
The confirmation diagram shown below was made with GeoGebra. It is a free geometry and algebra app that I use all the time.
If gasoline costs $ 3.77 per gallon when you pay with a credit card, but $0.08 per gallon less if you pay with cash, how much do you save by filling up a 8-gallon tank and paying for it with cash?
Answer:
$0.64
Step-by-step explanation:
Cost for 8 gallons of gas
Credit Card at $3.77/gal
Cash at $(3.77 - 0.08)/gal: $3.69/gal
(8 gal)*($3.77/gal) = $30.16
(8 gal)*($3.69/gal) = $29.52
Savings is $0.64
Which type of rigid transformation is shown? Identifying the Type of Rigid Transformation
The transformation is translation
What is Translation?Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.
The figure is attached below:
As per the definition the figure shows that size hasn't changed.
Hence, the transformation is translation.
Learn more about this concept here:
https://brainly.com/question/1761538
#SPJ1
The quotient of 7 more than three times a number m and the number 27 less than n
The given statement can be modeled as an algebraic expression (3m+7)/27 < n.
What is an Expression?In mathematics, an expression is a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The statement is given as "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression.
(3m+7)/27 < n
Hence, the given statement can be modeled as an algebraic expression (3m+7)/27 < n.
Learn more about Expression:
brainly.com/question/13947055
#SPJ1
2 triangles are shown. They have one congruent side. The first triangles has angle measures of 98 degrees and 35 degrees. The second triangle has angle measures of 35 degrees and 47 degrees.
Are the triangles congruent? If so, how do you know?
yes, because all the angles of the triangles are acute
yes, because the triangles have three congruent, corresponding angles
yes, because of ASA or AAS
not enough information given
Answer:
215 is the answer of the 2 triangles
Answer: Yes because of ASA or AAS (C)
Step-by-step explanation:
Got it right on edge ")
Does this table represent a function? Why or why not?
X
2234
5
y
1
4
4
2
5
OA. No, because one x-value corresponds to two different y-values.
B. Yes, because every x-value corresponds to exactly one y-value.
OC. No, because two of the y-values are the same.
D. Yes, because there are two x-values that are the same.
No, because one x-value corresponds to two different y-values.
How to determine the true statement about the table?The table of value is given as:
x 2 2 3 4 5
y 1 4 4 2 5
From the above table, we have:
When x = 2, y = 1 and 4
This means that 1 value of x points to multiple values of y
The above means that the table does not represent a function
Read more about functions at:
https://brainly.com/question/2253924
#SPJ1
A bake shop sells twenty different kinds of pastries. Twelve of them were chocolate. Zack randomly buys eight kinds of pastries. What is the chance that four of them will be chocolate
Answer:
Just look at the other answer
Step-by-step explanation:
Clara did not want to tell Carl how old she was. All she said was that every year on her birthday, her Mom puts as many coins in her money box as how old she turned that day. Carl roughly estimated the number of coins in the box as not less that 110 but not more than 130 coins. How old is Clara?
Clara is 15 years old, and there are 120 coins on the box.
How old is Clara?Each year her mom puts as many coins in her money box as how old she turns that day.
So on her first birthday, 1 coin is put in the box.
On her second birthday, 2 coins are put in the box
And so on.
So we have the simple summation:
[tex]\sum_{n = 1} n[/tex]
We know that the outcome of that summation is a number in the interval [110, 130]
If we know that the sum goes from n = 1 to n = N (N is the age of Clara) then we can rewrite the summation as:
[tex]N*(N + 1)/2[/tex]
Now we can solve:
[tex]N*(N + 1)/2 = 110\\\\N^2 + N = 220\\\\N^2 + N - 220 = 0[/tex]
The two solutions of the quadratic equation are:
[tex]N = \frac{-1 \pm \sqrt{1^2 - 4*1*(-220)} }{2} \\\\N = (-1 \pm 29.7) /2[/tex]
If we take only the positive solution:
N = (-1 + 29.7)/2 = 14.35
Now, notice that we got this number by taking the smallest possible number of coins (110) So we can round this to the next whole number, which is 15.
If N = 15, then the number of coins in the box is:
15*(15 + 1)/2 = 120
Which lies on the wanted interval.
If you want to learn more about summations:
https://brainly.com/question/542712
#SPJ1