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Problem (a): \(\textsf{Rate of change = \$100 per year, Initial value = \$350}\)
Problem (b): \(\textsf{y = 100x + 350}\)
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The first step that we must take before attempting to solve the problem is to understand what the problem is asking us to do and what is given to us to help do so. So in the first part we are asked what the rate of change and initial value for Sarah's business. Using that information we would be able to complete the second part which asks us to write an equation in slope-intercept form. In this problem we are given two points which resemble how much Sarah charged each customer for the given years.
Now that we know what we must accomplish, we can move onto actually solving the problem. So first we must determine what the rate of change is and this is basically like finding the slope. This can be done by subtraction the y-values in the numerator and the x-values in the denominator.
Determine the rate of change
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)\(m = \frac{750 - 350}{2014 - 2010}\)\(m = \frac{400}{4}\)\(m = 100\)Now we can see that the rate of change would be an increase of $100 per year after calculating the slope. The next part was to determine the initial value for Sarah's business and this can be easily done because we know that she has had this business since 2010 and we are given that the price in 2010 was $350.
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We now have completed part (a) and we can move onto the next part which is to create an equation in slope-intercept form to represent the fees that Sarah charges each year.
So we know that the slope is an increase of $100 per year which means that we will have a positive slope. We also know the initial price that Sarah charged in her first year which will represent the y-intercept or the first point on the graph.
m ⇒ This represents the slope of the line that is being written.b ⇒ This represents the y-intercept of the line that is being written.Plug in the values
\(y = mx + b\)\(y = 100x + 350\)After plugging in the values we have a finished expression in slope-intercept form which represents the scenario that is going on with Sarah's business. We see that that initial price was 350 and we increase that by 100 each year. Therefore, the final equation in slope-intercept form is y = 100x + 350.
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Match the ones on the left to the right
Answer/Step-by-step explanation:
\( (4 + 5) + 2 = 4 + (5 + 2) \) => any combination of numbers were formed or grouped when adding. The associative property of addition was applied.
\( 2(2x + 4) = 4x + 8 \) => the sum of two terms (addend) are multiplied by by a number separately (I.e., a(b + c) = a(b) + a(c) = ab + ac). The property applied is distributive property.
\( (7x * x) * 3 = 7 * (x * 3) \) => the numbers were grouped in any combination to arrive at same result when multiplying. Associative property of multiplication was applied.
\( (8 * x * 2) = (x * 8 * 2) \) => the numbers where ordered in any manner to arrive at same result when multiplying. Cummutative property of multiplication was applied.
\( (7 + 3) + 1 = (1 + (7 + 3) \) => the order in which the nnumbers in the were arranged doesn't matter, as same result is arrive at. This is Cummutative property of addition.
Graph the solution to the equations below. y = 1 4 x + 2 and y = −2x −7
Over the last three evenings, Lucy received a total of 107 phone calls at the call center. The second evening, she received 3 times as many calls as the third evening. The first evening, she received 7 more calls than the third evening. How many phone calls did she receive each evening?
Answer:
1st evening = 7 + 20 = 27 calls
2nd evening = 3 (20 ) = 60 call
3rd evening = 20 calls
Step-by-step explanation:
total calls for the last three evenings = 107 phone calls
2nd evening = 3x as many calls as the 3rd evening
1st evening = 7 more calls than the 3rd evening.
find:
how many calls did she receive each evening?
let T (total) = 107
let x = 3rd evening.
let 2nd = 3x
let 1st = (7 + x)
T = 1st + 2nd + 3rd
107 = (7 + x) + 3x + x
107 - 7 = 5x
100 = 5x
x = 100 / 5
x = 20
therefore,
1st evening = 7 + 20 = 27 calls
2nd evening = 3 (20 ) = 60 call
3rd evening = 20 calls
Answer:
1st = 27 calls
2nd = 60 call
3rd = 20 calls
Step-by-step explanation:
total calls = 107 phone calls
2nd = 3x
1st = 7 + 3x
T (total) = 107
T = 1st + 2nd + 3rd
107 = (7 + x) + 3x + x
107 - 7 = 5x
100 = 5x
x = 100 / 5
x = 20
so,
1st = 7 + 20 = 27 calls
2nd = 3 (20 ) = 60 call
3rd = 20 calls
What is the answer to this combination lock
Answer: 375
Step-by-step explanation:
Ruling out each number:
6: In the first two rows, the 6's placement did not change but the clue did, meaning that it is talking about a different number. Otherwise, it would say it's in the right place twice or in the wrong place twice.
3 & 5: Since we know 6 is already ruled out, both 5 & 3 would have to be correct.
2 & 4 & 8: Is proven wrong in the 4th clue.
7: 7 would have to be in the middle since the second clue says it's in the wrong place. If it was 1, it would say it's in the right space.
1: Is proven wrong after 7 is proven true.
Figuring out placement:
5: For the first clue, it says that it's in the correct place meaning that 5 is the last digit.
3: For both of the times 3 appears, it is in the wrong spot, revealing that it's the first digit.
7: In the second clue, it could either be 1 or 7. However, since 3 took the first spot and 5 took the last spot, 7 would have to be in the middle since the clue says it's in the wrong place. If it was 1, it would say it's in the right space.
Cuantas Escuelas de administración hay ?
help!!!!! Friends from Galilea gave him a skydiving class for his birthday. Her helicopter took off from the skydiving center at an angle of 20 ° and traveled 3.4 kilometers before she jumped in a direction perpendicular to the ground. How far from the skydiving center did Alexa land?
Answer:
5
Step-by-step explanation:
5555
Sharon tried to solve an equation step by step.
9
9
15
5
=−3(e−2)
=−3e+6
=3e
=e
Step 1
Step 2
Step 3
Find Sharon's mistake.
Choose 1 answer:
Choose 1 answer:
Answer:
step 2
Step-by-step explanation:
9 = -3(e - 2)
9 = -3e + 6
9-6 = -3e
3 = -3e
divide both sides by -3
-1 = e
HELP ME PLEASE!!!!!!
ZEARN!!!!
The expression 1 2/5 + 2 2/3 using fifteenths is 3 + 6/15 + 10/15
How to rewrite the expression using fifteenthsFrom the question, we have the following parameters that can be used in our computation:
1 2/5 + 2 2/3
3 + 2/5 + 2/3
To rewrite the expression using fifteenths, we multiply the numerator and the denominator of the fractions by the same number
In this case, we use 3 and 5
So, we have
3 + 2/5 * 3/3 + 2/3 * 5/5
Evaluate the products
3 + 6/15 + 10/15
Hence, the expression using fifteenths is 3 + 6/15 + 10/15
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Which expressions describe the end behaviors of the function, f(x)= (3.25)^x+6, modeled by the graph? An exponential curve on a coordinate plane with horizontal x axis ranging from negative 10 to 10 in increments of 1. The vertical y axis ranges from negative 4 to 14 in increments of 1. The curve begins infinitely close to the line y equals 6 in the second quadrant. The curve increases through begin ordered pair 0 comma 7 end ordered pair. The curve passes through begin ordered pair 1 comma 9.25 end ordered pair and exits the first quadrant.
The expression that describe the end behavior of the expression f(x)= (3.25)^x + 6 is The curve begins infinitely close to the line y equals 6 in the second quadrant.
What is end behavior as used in math?The behavior of the graph of a function at its "ends" on the x-axis is referred to as the end behavior of a function, f.
For example, if we look at the right end of the x-axis (as x approaches + ∞) and the left end of the x-axis (as x approaches - ∞), the end behavior of a function explains the trend of the graph.
The graph of the function is attached and from the graph it shows that the graph continued to tend towards towards line y = 6
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The radius of a circle is 4 millimeters. What is the circle's area? Use 3.14 for pi.
(The answer MUST BE ONE OF THE ANSWERS BELOW)
Answer:
50.24 mm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
A = 3.14 ( 4)^2
= 50.24 mm^2
Answer:
c. 50.24 square millimeters
Step-by-step explanation:
Radius of circle = 4 milimeters.
Area of a circle = πr²
Area = 3.14 × 4² (π = 3.14)
= 50.24 square millimeters
positive continous random variable with disbution and density we define in class the expected value to be prove, that given this definition:
Continuous random variable is a random variable that can take on a continuum of worth. In alternative words, a random variable is said to be continuous if it supposes a value that falls between a particular interval.
A continuous random variable can be described as a random variable that can take on an infinite number of possible values. Due to this, the probability that a continuous random variable will take on a fixed value is 0.
The probability density function of a continuous random variable can be explained as a function that gives the probability that the value of the random variable will drop between a range of values. Let X be the continuous random variable, then the formula for the pdf, f(x).
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Please Help!
Car X travels 174 miles in 3 hours.
Answer:
The graph =
y = 58xStep-by-step explanation:
(a)
distance covered (y) = 174 miles
time taken (x) = 3 hours
Therefore the points = (3, 174) and (0, 0) = stationary position
Find the gradient (m)
m = 174-0 / 3-0
m = 58
Therefore the equation =
y = 58x(distance = 58 × time)
For the distance = 174 and time = 3 hours, the equation to find either distance or time = y = 58x
(b) the graph is constant, because the time and distance are also contant when the speed used is the same.
____________________
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Savannah needs to buy a bag of dog food that will last for 2 weeks (14 days). She
estimates that a 20 lb bag will be enough. Is she correct?
Answer:
if it is a chihuahua, then it will be just fine with 20lb
TIME REMAINING
44:54
The table below shows the number of cars sold each month for 5 months at two dealerships.
Cars Sold
Month
Admiral Autos
Countywide Cars
Jan
4
9
Feb
19
17
Mar
15
14
Apr
10
10
May
17
15
Which statements are supported by the data in the table? Check all that apply.
The mean number of cars sold in a month is the same at both dealerships.
The median number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The range of the number of cars sold is the same for both dealerships.
The data for Admiral Autos shows greater variability.
The statements supported by the data in the table are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
To determine which statements are supported by the data in the table, let's analyze the given information:
The mean number of cars sold in a month is the same at both dealerships.
To calculate the mean, we need to find the average number of cars sold each month at each dealership.
For Admiral Autos:
(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13
For Countywide Cars:
(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13
Since both dealerships have an average of 13 cars sold per month, the statement is supported.
The median number of cars sold in a month is the same at both dealerships.
To find the median, we arrange the numbers in ascending order and select the middle value.
For Admiral Autos: 4, 10, 15, 17, 19
Median = 15
For Countywide Cars: 9, 10, 14, 15, 17
Median = 14
Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.
The total number of cars sold is the same at both dealerships.
To find the total number of cars sold, we sum up the values for each dealership.
For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65
For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65
Since both dealerships sold a total of 65 cars, the statement is supported.
The range of the number of cars sold is the same for both dealerships.
The range is determined by subtracting the lowest value from the highest value.
For Admiral Autos: 19 - 4 = 15
For Countywide Cars: 17 - 9 = 8
Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.
The data for Admiral Autos shows greater variability.
To determine the variability, we can look at the range or consider the differences between each data point and the mean.
As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.
Based on the analysis, the statements supported by the data are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
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Find the slope of the line that passes through (3, 12) and (6, 18)
. Read the paragraph and choose a sentence that describes it best. On the way across the Aegean Sea, Caesar was kidnapped by pirates and held prisoner. He maintained an attitude of superiority throughout his captivity. The pirates demanded a ransom of 20 talents of silver, but he insisted that they ask for 50. After the ransom was paid, Caesar raised a fleet, pursued and captured the pirates, before imprisoning them. He had them crucified on his own authority, as he had promised while in captivity—a promise that the pirates had taken as a joke.
a) Caesar was a vane man who thought 20 talents is too little of a ransom
b) Caesar was very brave and kept to his word to kill the pirates
c) Pirates didn’t believe Caesar will kill them because he was their prisoner
d) The pirates didn’t kill Caesar not only because he was promised to be paid for, but because he made them respect him
The sentence that best describes the paragraph is: "The pirates didn't believe Caesar would kill them because he was their prisoner." So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.
The paragraph recounts the events of Caesar's kidnapping by pirates while crossing the Aegean Sea. Despite being held captive, Caesar maintained an attitude of superiority. The pirates demanded a ransom of 20 talents of silver, but Caesar insisted they ask for 50. This indicates that Caesar saw himself as more valuable than the initial ransom amount suggested by the pirates.
After the ransom was paid, Caesar did not forget the pirates' actions. He raised a fleet, pursued the pirates, and captured them. The sentence implies that the pirates didn't believe Caesar would actually kill them because he was their prisoner and they likely saw his promises as mere jest.
However, Caesar, true to his word, had the pirates crucified on his own authority.
This sequence of events highlights Caesar's determination, strategic thinking, and his ability to command respect even in dire circumstances. Despite being initially taken prisoner, he managed to turn the tables on the pirates, assert his authority, and exact his revenge. So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.
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Analyze the diagram below and complete the instructions that follow.
8
45°
Find the value of x.
A. 4
B. 8√√2
2
C. 4√2
DG
45°
Save and Exit
Next
Subr
Answer:
Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.
Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:
x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)
So the value of x is option B: 8√2 / 2 or simplified, 4√2.
What is the answer to this question?
Answer:
20 3/4
Step-by-step explanation:
21 4/8 or 21.5- 3/4 or .75= 20.75 or 20 3/4
Answer:
look at the photo I have sent
Please, help me find the answer
The probability values for the questions posed are :
11/20probability of Public speaking given that student is majoring in Business Administration1/3A.)
Number of students Taking a public speaking class majoring in business administration.
10 + 45 = 55P(PS or BA) = 55/100 = 11/20
Therefore, the probability of PS or BA is 11/20
B.)
For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.
Hence, as inferred from P(A|B) ; probability of A given B.
C.)
P(PS|BA) = n(PSnBA) / n(BA)
n(PS) = 10+20 = 30
n(PSnBA) = 10
P(PS|BA) = 10/30 = 1/3
Therefore , the probability of PS|BA is 1/3.
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When you reverse the digits in a certain two-digit number you decrease its value by 45. What is the number if the sum of its digits is 9?
Answer:
72
Step-by-step explanation:
x+y=9 possible numbers
1 and 8
2 and 7
3 and 6
4 and 5
9 and 0
so
81-18=63
72-27=45 so this is the right number
63-36=27
54-45=9
90-9=81
Question content area top Part 1 Write a recursive definition for the sequence. -4,16,-64 256 -1024
The recursive formula for the given sequence is:
A(n) = -4*A(n - 1)
How to find the recursive formula?Here we have the sequence:
-4, 16, -64, 256, -1024
We can see that these are just powers of 4 such that each consecutive term the sign changes.
Then if we start at -4, we have:
-4*-4 = 16
16*-4 = -64
-64*-4 = 256
And so on, then the general formula is:
A(n) = -4*(-4)ⁿ⁻¹
And the recursive one is:
A(n) = -4*A(n - 1)
That is the n-th term of the sequence.
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JJM Corporation recently issued 10-year bonds at a price of $1,000. These bonds pay $60 in interest each six months. Their price has remained stable since they were issued, that is, they still sell for $1,000. Due to additional financing needs, the firm wishes to issue new bonds that would have a maturity of 10 years, a par value of $1,000, and pay $40 in interest every six months. If both bonds have the same yield, how many new bonds must JRJ issue to raise $2,000,000?
Answer:
2,596
Step-by-step explanation:
Calculation to determine how many new bonds must JRJ issue to raise $2,000,000
Given,
Coupon rate = 8.0%
Face value = 1000
Year to maturity = 10
NPER = 20
First step is to calculate the PMT using this formula
PMT = Face value × Coupon rate / 2
Let plug in the formula
PMT=(1000 × 0.08) / 2
PMT= 80/2
PMT= 40
Second step is to calculate the Rate using this formula
Yield = 12%
Rate = Yield / 2
Let plug in the formula
Rate= 12% / 2
Rate= 6%
Third step is to calculate the net proceeds using this formula
Net proceeds= PV(rate, NPER, PMT, FV)
Let plug in the formula
Net proceeds= PV(6%, 20, 40, 1000)
Net proceeds= $770.60
Now let calculate how many new bonds must JRJ issue to raise $2,000,000
New bonds needed= $2,000,000 / 770.60
New bonds needed= 2,596 bonds
Therefore how many new bonds must JRJ issue to raise $2,000,000 will be 2,596 bonds
Please help!! Will give thanks
Question is in photo!
Answer:
linear
Step-by-step explanation:
its increasing at a steady rate each year. hope it helps!!!!
i need help
can you look over this picture and see what the answer is
Answer:
AC = 12
Step-by-step explanation:
If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore
ΔABC is similar to ΔADE.
The sides of smaller triangle are in proportion with sides of bigger triangle.
Therefore we have the equation:
AC/AE = AB/AD
Substitute the given numbers:
x/x+15 =8/18
18x= 8(x+15)
18x = 8x+120
10x = 120
x = 12
AC=12
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How many zero pairs can be created in the model below?
O- 0
O- 1
O- 2
O- 3
Answer: -x because its more than one zero
Step-by-step explanation:
Functions f(4) determine what f(x)=40
The value of the function at 4, f(4) = 74 and the then value of x when f(x) = 40 is 6.
What are Functions?Functions are defined as the relation between two sets such that elements of a set is mapped to the elements of the other set and no element in the first set has more than one image in the other set.
Given values of x and the function values on those x in the table.
x values are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
f values on these x are 60, 64, 42, -5, 74, -4, 40, -29, 3, 47
Clearly we can see that x = 4 maps to 74.
So f(4) = 74.
Similarly we have an f value of 40 at x = 6.
Hence f(4) = 74 and the x = 6 when f(x) = 40.
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is 16.0 identified as a whole number?
Answer:
it is a rational number
Step-by-step explanation:
Another group held a dance to raise money for charity. Pre-sale tickets were $2.00 less than ticketspurchased at the event.They sold 54 pre-sale tickets and 82 tickets at the event. The group raised $980 from total ticket sales.How much did they charge for each ticket?Write and solve an equation to answer this question.
To solve this question let's represent our situation by an expression.
If we consider "x" as the value for tickets at the event, so "x-2" represent the value for pre-sale tickets. And once we have the number of each tickets (54 units for pre-sale and 82 units for tickets at the event) we have sold and also the amount the group raised ($980), now we can create our expression and find "x":
Now we have:
Tickets at the event : x = $8
Pre-sale: x-2 = 8-2 = $6
And those are the final answers.
A Triangle has a height that is half of 28 yards and an area of 56 yards^2. What is the length of the base of the trangle?
The length of the base of the triangle is 8 yards whose height is half of 28 yards.
What is triangle?A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.
According to question:The following formula provides the area of a triangle:
Area = (1/2) x base x height
We are given that the height of the triangle is half of 28 yards, which is:
height = 1/2 x 28 = 14 yards
We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:
56 = (1/2) x base x 14
Simplifying this equation, we get:
56 = 7 x base
Dividing both sides by 7, we get:
base = 8
Therefore, the length of the base of the triangle is 8 yards.
The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.
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Does this table represent a function? Why or why not?
O
X
2
3
3
4
5
y
1
4
3
2
5
A. Yes, because there are different y-values.
B. Yes, because every x-value corresponds to exactly one y-value.
C.
No, because the y-values are positive.
D. No, because one x-value corresponds to two different y-values.
SUBMIT
The given table does not represent a function. The correct answer is D. No, because one x-value corresponds to two different y-values.
To determine if the table represents a function, we need to check if every x-value corresponds to exactly one y-value. Let's analyze the given table:
x | y
-------
O | 1
X | 4
2 | 3
3 | 2
3 | 5
4 |
5 |
From the table, we can see that the x-values are not unique. Both the values 3 and 4 appear twice in the x-column, but they have different corresponding y-values.
This violates the definition of a function, which states that each input (x-value) should have only one output (y-value).
Therefore, the given table does not represent a function.
The correct answer is D. No, because one x-value corresponds to two different y-values.
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