Answer:
Here's the exponential equation to model the card's value:
y = 98.70 * 2^x
where x is the number of years after Mr. Olsen purchased the card.
To find the value of the card after 5 years:
x = 5
y = 98.70 * 2^5 = 98.70 * 32 = $3162.40
So, Mr. Olsen can expect the card's value to be $3162.40 5 years after he purchased it.
Step-by-step explanation:
Answer:
Step-by-step explanation:
m
in the morning, the train went 170 miles. in the afternoon the train went 50 more miles. how far did the train end up going?
In the morning, the train went 170 miles. in the afternoon the train went 50 more miles. The Train ended up going 220 miles in total.
In the morning, the train traveled 170 miles.
In the afternoon, it traveled an additional 50 miles.
To find the total distance traveled by the train, we need to add the distance traveled in the morning and the distance traveled in the afternoon:
Total distance = Distance traveled in the morning + Distance traveled in the afternoon
Total distance = 170 miles + 50 miles
Total distance = 220 miles
So, the train ended up traveling a total of 220 miles.
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3. for questions 3-5, complete the missing values in each table below using the graph
The missing values are derived from the graph as follows:
3 ) 7, 14, 21, 28, 35
4) 3, 7, 10, 14, 17
5) 1, 21, 10, 49, 19
What is a graph?In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.
In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:
F(y) = 3.5x
In the first table, where x = 2
y= 3.5 *2
= 7
This iteration goes on and on and is consistent for all the values.
In the second table,
Where F(y) is known, for example 10.5, then x is derived as:
10.5 = 3.5x (divide both sides by 3.5)
x = 3
This iteration goes on and on and is consistent for all the values.
In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.
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The shaded part of the diagram below shows the top surface of an engine part.
5
Diagram not drawn to scale
The measurements taken by a motor engineer are:
• reflex angle BÔC = 240°,
• AO=OD= 6 cm,
• BO=OC=3 cm.
The top surface of the engine part is to be painted.
The paint costs 15p per cm².
75
Using = 3, calculate how much it costs to paint the top surface of 20 engine parts.
Give your answer in pounds.
(1 mark)
Answer:
To calculate the cost of painting the top surface of 20 engine parts, we need to find the surface area of one engine part and then multiply it by 20.
To find the surface area, we need to find the length of the curved surface. We can do this by using the Pythagorean theorem to find AB and then use that to find the circumference of the curved surface.
AB^2 = BO^2 + AO^2 = 9 + 36 = 45
AB = sqrt(45) = 3 sqrt(5)
Circumference = 2 * pi * AB = 2 * pi * 3 sqrt(5) = 6 pi sqrt(5)
Using the fact that the reflex angle BÔC is 240 degrees, we can find the length of the curved surface:
240° / 360° = 2/3 of the circumference
Curved surface length = 2/3 * 6 pi sqrt(5) = 4 pi sqrt(5)
Finally, we can find the surface area of one engine part:
Surface area = (2 * 6 * 3) + (4 pi sqrt(5) * 6) = 36 + (24 pi sqrt(5))
To paint 20 engine parts, the cost would be:
20 * surface area * 15p = 20 * 36 + 20 * 24 pi sqrt(5) * 15p = 720 + (24 * 20 * 15 * pi * sqrt(5)) p = 720 + 720 pi sqrt(5) p
Since 1 pound is equal to 100 pence, the cost in pounds would be:
720 + 720 * pi * sqrt(5) / 100 = 720 + 720 * 0.177 / 100 = 720 + 1.264
So, the cost to paint the top surface of 20 engine parts would be 721.264 pounds.
Wyatt bought a pair of sunglasses online for $56. He used a coupon code to get a 10% discount. The website also applied a 10% processing fee to the price after the discount. How much did Wyatt pay, in the end? Round to the nearest cent.
Answer:
$55.44 is the price of the sunglasses
Step-by-step explanation:
Price Of Sunglasses = $56
10% Discount = $5.6
So, $56-$5.6 = $50.4 <------ Applying Discount
10% of $50.4 = $5.04 <------ Price of Processing Fee for Discounted Price
$50.4+$5.04 = $55.44 <------ Total Price
The discounted price is $50.4 and we take 10% of that [discounted price] and we add it to the discounted price. 10% of that is $5.04. = $55.44
Answer:
$55.44
Step-by-step explanation:
56 - 56(0.10) = 50.40 price with 10% off
50.40 + 50.40(0.10) = 55.44 10% processing fee added to discounted price
Three people are playing near the water. Person A stands on the dock. Person B starts at the top of a pole and ziplines into the water. Person C climbs out of the water and up the zipline pole. Match the people to the graphs where the horizontal axis represents time in seconds and the vertical axis represents height above the water level in feet.
The correct match for the people given their position near the water and the graph, is :
Line 1 - Person C Line 2 - Person A Line 3 - Person B How to match the graphs ?Line 1 is Person C because Line 1 starts from under the level of the water and Person C climbs out of the water then goes up the zipline. Line 2 represents Person A because Line 2 is a stright line which is elevated above the water. Person A stood on the dock and did not move so they are most likely the person on Line 2.
Person B is on Line 3 because they stood on a pole at first which is higher than the dock that Person A was on. They then ziplined into the water which is why Line 3 went below water level.
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6. Find the volume of a cone with a radius of 5 ft and a height of 12 ft. (1 point)
O 300 ft³
O 314 ft³
O 100 ft³
O224 ft³
Answer:
314 ft^3
Step-by-step explanation:
The equation that needs to be set up is 1/3 × pi × r^2 ×h which r is the radius and h is the height. If we substitute 1/3 × pi × 5 × 12= 100 × pi. Once you finish the equation out by multiplying 100 and pi (3.14) It can be rounded to 314 ft ^3
Hey, I need help what is 12+3s+9s+2=?
Answer:
Below
Step-by-step explanation:
12 + 3s + 9s + 2 =
(3s+9s) + (12+2) =
12s + 14 ( or 2 (6s+7) )
evaluate
2-6/-2-4-12/6x-3
the / is division
please show step by step
The simplified expression 2-6/-2-4-12/6x-3 is given as follows:
-2 - 2x.
How to simplify the expression?The expression for this problem is defined as follows:
[tex]2 - \frac{6}{-2} - 4 - \frac{12x}{6} - 3[/tex]
The division operation has a higher precedence over the subtraction operations, hence:
6/-2 = -3.12x/6 = 2x.Hence the expression can be written as follows:
2 - (-3) - 4 - 2x - 3 = 2 + 3 - 4 - 2x - 3.
Then combining the like terms, which are the constant, the simplified expression is given as follows:
-2 - 2x.
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The graph show the population of beavers in a forest for different numbers of years after
1995. The beaver population is growing exponentially.
Explain why we can think of the beaver population as a function of time in years.
2. What is the meaning of the point labeled Q in this context?
3. Write an equation using function notation to represent this situation.
Answer:
1. We can think of the beaver population as a function of time in years because it shows how the population changes over time. The graph shows a direct correlation between the number of years after 1995 and the number of beavers in the forest, indicating that the population of beavers is dependent on the number of years that have passed since 1995.
2. The point labeled Q represents the exponential growth rate of the beaver population.
3. An equation using function notation to represent this situation would be: P(t) = P0 * e^kt, where P(t) is the population at time t (in years after 1995), P0 is the initial population of beavers in 1995, and k is the constant exponential growth rate.
16. For the following graph:
label the x and y intercepts
label the transformations
define the domain and range
For the function,
y = log(x + 3), all the required values are given below.
What is transformation on the graphs?Let the function f(x) and g(x) are two real functions.
The function provided by the basic function f(x) and the constant
g(x) = f(x - k),
may be drawn by horizontally moving the f(x) k unit coordinates.
The shift's direction depends on the value of k. Specifically,
The base graph moves k units to the right if k > 0, and
The base graph moves k units to the left if k < 0.
Given:
A graph of the function.
The function is y = log(x + 3)
The x-intercept is (-2, 0) and y-intercept is (0, 0.477).
The transformation is,
-3 units to the left.
The domain is,
(−3, ∞), {x|x>−3}
Range: (−∞, ∞), {y|y∈R}
Hence, all the required values are given above.
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1.5 x ? = 0.6. What value of ? makes this number sentence correct? Please show working out.
Answer:
x = 0.4
Step-by-step explanation:
1.5 * x = 0.6
x = 0.6 / 1.5
x = 0.4
Answer:
0.4
Step-by-step explanation:
To solve the equation 1.5 * ? = 0.6 for the value of ?, we need to isolate the variable ? on one side of the equation.
First, we can divide both sides of the equation by 1.5 to isolate the variable:
1.5 * ? / 1.5 = 0.6 / 1.5
Simplifying, we get:
? = 0.4
Therefore, the value of ? that makes the equation 1.5 * ? = 0.6 true is 0.4.
9) Find the value of x and y
Step-by-step explanation:
Let’s start with y.
Because they are opposite angles on 2 180 degrees lines 102 = y-17
Now solve
102 = y - 17
Now add 17 to both sides
119 = y
For x
Because it is on a 180 degree line
102 + 3x = 180
Now subtract 102 from both sides
3x = 78
Now divide each side by 3 to get x alone
x = 26
This proves the answer is in fact A
Please answer ASAP!!!
Solve by elimination
-16y=22+6x and -11y-4x=15
The solution of the equations will be x = 241 and y = -89.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two equations are -16y=22+6x and -11y-4x=15. The equations by elimination method will be calculated as:-
-16y=22+6x
-11y-4x=15
Write the equations in the following way:-
6x + 16y = -22
-4x - 11y = 15
24x + 64y = 88
-24x - 66y = 90
____________
0 - 2y = 178
y = 89
The value of x will be:-
-11y-4x=15
-11 x -89 - 4x = 15
979 - 4x = 15
-4x = -964
x = 241
Therefore, the value of x is 241 and the value of y is -89.
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In a direct variation, y=16 when x=2. Write a direct variation equation that shows the relationship between x and y.
y=8x is the direct variation equation that shows the relationship between x and y.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
In a direct variation, y=16 when x=2.
y=kx
We have to find the relationship between x and y.
16=2k
Divide both sides by 2
k=8
Now plug in the value of k in the above equation.
y=8x
Hence, y=8x is the direct variation equation that shows the relationship between x and y.
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The measure of an angle is 8 degrees less than three times the measure another angle. If the two angles are supplementary, what is the measure or the larger angle?
Answer:
Let's call the measure of the first angle "x". Then, the equation can be written as:
x = 3y - 8
Since the angles are supplementary, their measures add up to 180 degrees, so:
x + y = 180
We can substitute the first equation into the second equation to solve for y:
3y - 8 + y = 180
4y = 188
y = 47
Now that we know the measure of y, we can substitute it back into the first equation to find x:
x = 3(47) - 8 = 133
So the measure of the larger angle is 133 degrees.
What is geometry in mathematics ?
Answer:
Geometry in Mathematics is the study of shape and figures.
Answer:
Geometry refers to a branch of mathematics which is focused on the measurement and relationship of lines, angles, surfaces, solids and points. For instance, the calculation of a triangle's angles is an example of geometry.
Given rectangle C D E F below, DG = 15 If CG = 3x+6, solve for x
can u help me out i could get 100%
Step-by-step explanation:
x+4y=0
2x−y=18
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
x+4y=0,2x−y=18
Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign.
x+4y=0
Subtract 4y from both sides of the equation.
x=−4y
Substitute −4y for x in the other equation, 2x−y=18.
2(−4)y−y=18
Multiply 2 times −4y.
−8y−y=18
Add −8y to −y.
−9y=18
Divide both sides by −9.
y=−2
Substitute −2 for y in x=−4y. Because the resulting equation contains only one variable, you can solve for x directly.
x=−4(−2)
Multiply −4 times −2.
x=8
The system is now solved.
x=8,y=−2
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Your Best,EdwinDebby is a real estate agent and recently sold a $155,000 home. Five percent commission will be taken from the sale. Two percent will go to the broker, one percent will go the office assistant, and Debby will profit the remaining two percent. How much money will Debby profit for herself?
Answer:
$150.35
Step-by-step explanation:
Total commission taken from sale = $155,000 * 5% = $7,750.
Broker = $7,750 * 2% = $155.
Office assistant = $7,750 * 1% = $77.5.
Debby's profit = $7,750 - $155 - $77.5 = $7,517.5 * 2% = $150.35.
You manage a call center. You are reviewing wages for 25 phone operators and 5 supervisors. Phone operators
earn $22.85 per hour, and supervisors earn $27.25 per hour.
What, approximately, is the mean hourly wage for the 30 employees?
$23.02
$23.58
$25.05
$26.52
$27.21
Answer: To find the mean hourly wage, you need to sum up the total wages of all employees and then divide by the number of employees. The total hourly wage for 25 phone operators is 25 * $22.85 = $571.25. The total hourly wage for 5 supervisors is 5 * $27.25 = $136.25. The combined total is $571.25 + $136.25 = $707.50. The mean hourly wage for the 30 employees is $707.50 / 30 = $23.58. So, the answer is approximately $23.58.
Step-by-step explanation:
6x + y = 9 3x -4y = -18
Answer:
x = 2/3
y = 5
Step-by-step explanation:
6x + y = 9
3x -4y = -18
Times the second equation by -2
6x + y = 9
-6x + 8y = 36
9y = 45
y = 5
Now put 5 in for y and solve for x
6x + 5 = 9
6x = 4
x = 2/3
Let's check
6(2/3) + 5 = 9
4 + 5 = 9
9 = 9
So, x = 2/3 and y = 5 is the correct answer.
Three years ago, the sum of the ages of the father and son was 48 years. After three years the ratio of the ages of the father and son will be 3: 1, then how much old is the father than his son? Find it.
Step-by-step explanation:
Solution: Let the current ages of the father be F and that of the son, S.
Three years ago their ages were (F-3) and (S-3) and the sum was 48, or
F+S = 48+3+3 = 54, or
F = 54-S …(1)
(F+3) : (S+3) = 3:1, or
F+3 = 3S+9, or
F = 3S+6 …(2)
Equate (1) and (2): 54-S = 3S+6, or
4S=48, or S = 12 and So F = 42.
The father is 42 years and the son 12 years,
Answer:
+3 year after now Dad = 45; Son = 15 ====> 30 years old
now Dad = 42; Son = 12 ====> 30 years old
-3 year after now Dad = 39; Son = 9 =====> 30 years old
Step-by-step explanation:
Before 3 year is 48 so after 3 year is + 6 right???
so ==> 48 + 6(father and son so it's 2) + 6(same same) ==> 60
the ratio is 3:1 so son gets 1 dad gets 3 right?
==> 4 is the sum
So son is 60/4x1 = 15
Dad is 60/4x3(dad have three remember?) = 45
so now dad and son will be:
Dad = 45 -3 (only dad ok?) = 42
Son = 15-3(only son) = 12
so you can find the before to by minus 3 again ok??
Thanks for seeing
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if jack has three packs of gum and sam has 4 packs of gum. how much do they have in total
If jack has three packs of gum and sam has 4 packs of gum, then the total amount of gum they have together is 7 packs.
What is the addition?
The addition is putting numbers together to make a sum or total. The plus sign + tells you to add two numbers. = is an equals sign. It shows that things on either side of it are equal.
We have given,
Jack has 3 packs of gum and Sam has 4 packs of gum.
To find the total number of packs of gum they have together, we simply add their individual amounts:
3 packs (Jack) + 4 packs (Sam) = 7 packs
Therefore, the total amount of gum they have together is 7 packs.
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Madhu's father is 26 years younger than Madhu's grandfather and 29 years older than Madhu. The sum of the ages of all three is 135 years.
There, ages are as follows:
Madhu's grandfather age = 72 years
Madhu father's age = 46 years
Madhu age = 17 years
How to find there ages?Madhu's father is 26 years younger than Madhu's grandfather and 29 years older than Madhu.
The sum of the ages of all three is 135 years.
Therefore, let's find their ages as follows:
Let
Madhu's grandfather age = x
Madhu father's age = x - 26
Madhu age = x - 26 - 29 = x - 55
Therefore,
x + x - 26 + x - 55 = 135
3x = 135 + 81
3x = 216
divide both sides by 3
x = 216 / 3
x = 72
Hence,
Madhu's grandfather age = 72 years
Madhu father's age = 72 - 26 = 46 years
Madhu age = x - 26 - 29 = 72 - 55 = 17 years
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the graph of a quadric function moves through the point (0,-2) and (4,0) what is the zero of the function
The zeroes of the quadratic function 2x² - 7x - 4 is 1 and 4,
known as roots.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
itsA quadratic equation has two roots as it's degree is two.
We know, The general form of a quadratic equation is x² + bx + c.
Let, y = x² + bx + c.
At, (0, - 2).
- 2 = 0 + 0 + c.
c = - 2.
At, (4, 0).
0 = 4² + 4b - 2.
0 = 14 + 4b.
b = - 7/2.
So, It is x² - (7/2)x - 2 = 0.
2x² - 7x - 4 = 0.
2x² - 8x + x - 4 = 0.
2x(x - 4) - 1(x - 4) = 0.
(x - 4)(x - 1) = 0.
So, the zeroes of the function are 4 and 1.
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Help mee please!!!!1
Answer:
rectangular prism has 6 faces, 8 vertices (or corners) and 12 edges.
Step-by-step explanation:
hopefully this is the answer you are looking for.
Answer:
Step-by-step explanation:
Lin counts 5 bacteria under a microscope. She counts them again each day for four days, and finds that the number of bacteria doubled each day—from 5 to 10, then from 10 to 20, and so on.
Is the population of bacteria a function of the number of days? If so, is it linear? The population of bacteria is a function. The relationship is linear.
sampling repeatedly from a small population without replacement leads the outcomes in our sample to be
Repeatedly sample variance from a small population without replacement leads to the outcomes in our sample being non-independent, as the same individuals may be chosen multiple times.
Repeatedly sample variance from a small population without replacement can lead to skewed results, as the same individuals may be chosen multiple times. This can be problematic when the sample size is small, as the same individuals may be overrepresented in the sample. This can lead to outcomes that are not representative of the population and can lead to inaccurate results. As the same individuals are chosen multiple times, the outcomes in the sample are not independent; the outcomes of one individual can influence the outcomes of other individuals in the sample. This can lead to bias in the results and should be avoided when possible. When sampling from a small population without replacement, it is important to ensure that the sample size is large enough that the same individuals are not chosen multiple times, otherwise the results may be skewed or biased.
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Sampling repeatedly from a small population without replacement leads the outcomes in our sample to be dependent.
What does dependent sample means?In dependent samples, subjects in one group do provide information about subjects in other groups.
When 32 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.
The two solutions of the quadratic equations are 8,-4 and the negative solution -4
What are quadratic equations?A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
Given here: when 32 subtracted from the square of a number and the result is 4 times the number.
Let x be the number then we have
x²-32=4x
x²-4x-32=0
x²-8x+4x-32=0
x(x-8)+4(x-8)=0
(x-8) (x+4) =0
Thus the two solutions of the quadratic equations are 8,-4
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Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -5, -1, 2
The polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -5, -1, 2 is,
⇒ f (x) = x³ + 4x² - 7x - 10
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
For a polynomial,
A leading coefficient = 1,
And, the given zeros = -5, -1, 2
Now, We know that;
The standard polynomial is given by:
⇒ f (x) = a (x - p) (x - q) ...
Where, 'a' is leading coefficient and p, q, .. are zeroes.
Here, A leading coefficient = 1,
And, the given zeros = -5, -1, 2
Hence, The polynomial is,
⇒ f (x) = 1 (x - (-5)) (x - (- 1)) (x - 2)
⇒ f (x) = (x + 5) (x + 1) (x - 2)
⇒ f (x) = (x + 5) (x² - 2x + x - 2)
⇒ f (x) = (x + 5) (x² - x - 2)
⇒ f (x) = x³ - x² - 2x + 5x² - 5x - 10
⇒ f (x) = x³ + 4x² - 7x - 10
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Hi everyone can someone please help me find the area and perimeter of these following shapes
Check the picture below.