The exponential function that models the relationship between the two points is [tex]y = 41.62 (1.0824)^x.[/tex]
We have,
To write an exponential model given two points (6,85) and (7,92), we can use the general exponential function form:
y = a[tex]b^x[/tex]
where y is the dependent variable, x is the independent variable, a is the initial value (when x = 0), and b is the base of the exponential function.
To find the values of a and b, we can use the two given points as follows:
When x = 6, y = 85:
85 = a b^6
When x = 7, y = 92:
92 = a b^7
We now have a system of two equations with two unknowns (a and b).
We can solve for a by dividing the second equation by the first equation:
92/85 = (ab^7) / (ab^6)
1.0824 = b
Substitute this value of b into one of the equations to solve for a:
85 = a (1.0824)^6
a = 41.62
Therefore,
The exponential function that models the relationship between the two points is [tex]y = 41.62 (1.0824)^x.[/tex]
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dividing 1/9 is equal to multiplying by
Answer: 9
Step-by-step explanation: To divide we need to flip the second fraction we are dividing by. For example:
10/1 divided by 1/4 = 10/1 times 4/1. So in this case, the answer is 40.
Now lets try it with 1/9.
X divided by 1/9 = X times 9/1.
So dividing by 1/9 is equal to multiplying by 9.
A dog runs 100 feet in 30 seconds. How many meters per hour is this? Use the fact that 1 meter is about 3.28 feet.
Answer:
60.96 meters per hour.
Answer:
3658.53658537 meter per hour
Step-by-step explanation:
[tex]\frac{100ft}{30sec}[/tex] · [tex]\frac{1meter}{3.28feet}[/tex] · [tex]\frac{60sec}{1min}[/tex] ·[tex]\frac{60min}{hour}[/tex] You can cross cancel works like you can numbers
[tex]\frac{100}{30}[/tex] · [tex]\frac{1meter}{3.28}[/tex] · [tex]\frac{60}{1}[/tex] · [tex]\frac{60}{1hour}[/tex]
[tex]\frac{360000meters}{98.4hours}[/tex]
3658.53658537 meter per hour
$6,000 dollars is invested in two different accounts earning 3% and 5% interest. at the end of one year, the two accounts earned $220 in interest. how much money was invested at 3%
The amount of money is 4000 was invested at 3%.
Let x be the amount of money invested at 3%.
Then, the amount of money invested at 5% is 6000 - x.
The interest earned on the amount invested at 3% is 0.03x.
The interest earned on the amount invested at 5% is 0.05(6000 - x) = 300 - 0.05x.
The total interest earned is given as $220.
So, we can write the equation:
0.03x + (300 - 0.05x) = 220
Simplifying and solving for x, we get:
0.03x + 300 - 0.05x = 220
-0.02x + 300 = 220
-0.02x = -80
x = 4000
Therefore, $4000 was invested at 3%.
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Use substitution!!!
Pt. a
truck a costs $20,345. You can expect to pay an average of $1230 per year for repairs. truck b costs about 16,000. It will cost an average of $1425 for repairs per year. After how many years are the total costs for cars the same?
(I can solve it, can you just turn the words into an equation for me?)
Pt. B
You have 56 coins that are all nickles and dimes. The value of the coins is $2.05. Find the number of nickels and dimes.
(Can you also just make an equation out of this for me?)
The system of equations are t = 22.28 years , number of nickles and dimes are solved
Given data ,
a)
Let the number of years be represented as t
For truck A, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:
Total cost for truck A = 20345 + 1230t
For truck B, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:
Total cost for truck B = 16000 + 1425t
when the total costs are equal , we get
20345 + 1230t = 16000 + 1425t
On simplifying , we get
195t = 4,345
t = 22.28 years
b)
Let the number of nickels be n and number of dimes be d
The total value of nickels is 0.05n (since the value of one nickel is $0.05) and the total value of dimes is 0.10d (since the value of one dime is $0.10)
The total value of the coins = $ 2.05
And , the total number of coins = 56
0.05n + 0.10d = 2.05
And , n + d = 56
Hence , the system of equations are solved
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Look at the scatter plot below.
Which statement is true about data?
A The data shows a strong linear association
B There is no association
C There is a nonlinear association
D There is week negative association
Answer:
there is no associstaion
Step-by-step explanation:
Line 1: y=x
System A
1 9
Line 2: y=-- x+
2
12.5
This system of equations is:
O consistent dependent
O consistent independent
O inconsistent
This means the system has:
O a unique solution
Solution:
D
O Infinitely many solutions
Ono solution
Line 1: y=-
Line 2: y=-
System B
This system of equations is:
O consistent dependent
O consistent independent
inconsistent
This means the system has:
O a unique solution
Solution: D
Infinitely many solutions
Ono solution
System C
Line 1: y=-
-x-1
Line 2: -x+4y=-4
This system of equations is:
O consistent dependent
consistent independent
O inconsistent
This means the system has:
O a unique solution
Solution: D
Infinitely many solutions
no solution
The equations are classified as follows
System A
consistent and independent this means that the system as a unique solution at (3, 3)
How to classify system B and CSystem B
inconsistent this means that the system as a no solution
A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.
System C
consistent and dependent this means that the system as infinitely many solution
A consistent system is dependent if there are an infinitely many solutions. The two equations represent the same line when you graph them.
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Suppose Manuela flips a coin three times. What is the theoretical probability of flipping tails at least two times? Express your answer as a fraction in simplest form.
The probability of flipping tails at least two times in three flips is 1/2.
When flipping a coin, there are two possible outcomes: heads or tails. Each flip is independent of the previous flips, so the probability of getting tails on any given flip is always 1/2 (assuming the coin is fair).
To find the theoretical probability of flipping tails at least two times in three flips, we can use the binomial probability formula:
P(x ≥ k) = 1 - P(x < k)
where P(x < k) is the probability of getting tails fewer than k times in three flips.
To find P(x < k), we can add up the probabilities of getting tails 0 times and getting tails 1 time:
P(x < 2) = P(0 tails) + P(1 tail)
P(0 tails) = (1/2)⁰ x (1/2)³ = 1/8
P(1 tail) = 3 x (1/2) (1/2)² = 3/8 (since there are three ways to get exactly one tail: TTH, THT, HTT)
P(x < 2) = 1/8 + 3/8 = 1/2
Therefore, the probability of flipping tails at least two times in three flips is:
P(x ≥ 2) = 1 - P(x < 2) = 1 - 1/2 = 1/2
So the theoretical probability of flipping tails at least two times in three flips is 1/2 or 0.5 as a decimal.
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12. You start the day left with 3 assignments due tomorrow. Your work load seems to double every period!
That means you would have how many assignments due tomorrow by 1st period? 4th period? 8th period?
Write an equation for this scenario & answer all questions.
The equation for the scenario of the work load doubling every period would be Assignments due = 3 x 2^(number of periods)
The assignments due would be:
1 st period - 6 assignments 4 th period - 48 assignments 8th period - 768 assignments How to find the assignments due ?Assignments start at 3 assignments and then double per period so the best equation is:
Assignments due = 3 x 2^(number of periods)
After 1 period:
Assignments due = 3 x 2^(number of periods)
= 3 x 2
= 6 assignments
After 4 periods:
= 4 x 2⁴
= 48 assignments
After 8 periods:
= 4 x 2 ⁸
= 768 assignments
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Olga Semargl's medical care bills for a recent illness were $4,620. Her major medical policy did not
cover $312 of the bill. Olga's policy had a coinsurance feature that paid 80% of all covered expenses
over a $500 deductible. What was the amount paid by the major medical policy?
The amount paid by the major medical policy is $3,046.40.
First, we need to calculate the covered expenses before the coinsurance feature comes into play. Since Olga's major medical policy did not cover $312 of the bill, the covered expenses will be:
Covered expenses = Total bill - Amount not covered
Covered expenses = $4,620 - $312
Covered expenses = $4,308
Next, we need to calculate the amount of the covered expenses that is subject to the coinsurance feature. Since Olga's policy has a $500 deductible, the covered expenses subject to coinsurance will be:
Covered expenses subject to coinsurance = Covered expenses - Deductible
Covered expenses subject to coinsurance = $4,308 - $500
Covered expenses subject to coinsurance = $3,808
The coinsurance feature pays 80% of the covered expenses subject to coinsurance, so the amount paid by the major medical policy will be:
Amount paid = Coinsurance rate x Covered expenses subject to coinsurance
Amount paid = 0.8 x $3,808
Amount paid = $3,046.40
Therefore, the amount paid by the major medical policy is $3,046.40.
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In the figure, m<1 = (3x + 12) degrees, m<2 = (3x + 18) degrees and m<3 = (7x + 10) degrees. What is m<3 in degrees?
The measure of the angle m∠3 of the triangle is m∠3 = 150°
Given data ,
Let the triangle be represented as ΔABC
Now , the measures of the angles are
m∠1 = ( 3x + 12 )°
m∠2 = ( 3x + 18 )°
m∠3 = ( 7x + 10 )°
m∠3 = 180° - ( m∠1 + m∠2 )
Now , for a triangle , the total angles = 180°
So , m∠1 + m∠2 = m∠3
On simplifying , we get
( 3x + 12 ) + ( 3x + 18 ) = ( 7x + 10 )
6x + 30 = 7x + 10
Subtracting 6x on both sides , we get
x + 10 = 30
Subtracting 10 on both sides , we get
x = 20
m∠3 = 150°
Hence , the measure of m∠3 = 150°
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The complete question is attached below :
In the figure, m<1 = (3x + 12) degrees, m<2 = (3x + 18) degrees and m<3 = (7x + 10) degrees. What is m<3 in degrees?
Rotations : If the point (6,2) was on a figure that was rotated 180 degrees clockwise what would be the coordinates of the new point on this figure
The coordinates of the new point is (-6, -2)
What would be the coordinates of the new pointFrom the question, we have the following parameters that can be used in our computation:
Point = (6, 2)
Rule: 180 degrees rotation
The rule of 180 degrees rotation is
(x, y) = (-x -y)
Substitute the known values in the above equation, so, we have the following representation
image = (-6, -2)
Hence, the image is (-6, -2)
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Find each angle and arc measure.
mBC⌢ = degrees
(60 POINTs will give BRAINIEST FOR EFFORT)
The angle is 47 degrees while the arc measure is solved to be 94 degrees
How to find the arc measureThe arc measure of the figure labelled AC is solved using the relationship between arcs and inscribed angles.
The relationship goes with formula below
angle B = 1/2 arc measure AC
where
angle B is the inscribed angle and it is equal to 47 degrees
arc measure AC is the unknown
plugging in the values will result to
47 degrees = 1/2 arc measure AC
arc measure AC = 2 * 47 degrees
arc measure AC = 94 degrees
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convert 1324 base 5 to base 8
In conclusion 1324 base 5 = 326 base 8.
To convert the number 1324 in base 5 to base 8, you can follow these steps:
Step 1: Write the given number in expanded form with powers of 5.
1324 base 5 = 1 × 5² + 3 × 5¹ + 2 × 5⁰ + 4 × 5⁻¹
Step 2: Simplify the expression to obtain the decimal equivalent.
1324 base 5 = 25 + 15 + 2 + 0.4 = 42.4
Step 3: Convert the decimal equivalent to base 8 by successive multiplication by 8.
0.4 × 8 = 3.2 (0)
0.2 × 8 = 1.6 (1)
0.6 × 8 = 4.8 (4)
0.8 × 8 = 6.4 (6)
0.4 × 8 = 3.2 (3)
0.2 × 8 = 1.6 (1)
The integer parts obtained in order give the equivalent representation of the number in base 8.
Therefore, 1324 base 5 = 42163 base 8.
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complete question:
How can I convert the number 1324 in base 5 to its equivalent representation in base 8?
4. Marcy makes $19 an hour working as a librarian. She gets a 5% raise.
Which of the following statements are true about Marcy's new rate of pay? Select the 3 correct answers.
A Marcy will make an additional 1/20 of her salary an hour.
B Marcy will make an additional $0.95 an hour.
C Marcy’s new hourly rate is $19.50 an hour.
D After working 10 hours at the new rate, Marcy will make $195.
E After working 15 hours at the new rate, Marcy willmake $299.25.
What is the value of x?
Enter your answer in the box.
x =
A ladder measures 6 feet. If the top of the ladder is placed 4 feet up on a wall, how many feet from the base of the wall is the bottom of the ladder?
Answer:
4.47214
Step-by-step explanation:
-3(w+5)+4(3w-5) simplify
Answer:
9w - 35
Step-by-step explanation:
-3(w + 5) + 4(3w - 5)
(Use the distributive property to multiply -3 by w + 5.)
-3w - 15 + 4(3w - 5)
(Use the distributive property to multiply 4 by 3w - 5)
-3w - 15 + 12w - 20
(Combine -3w and 12w to get 9w.)
Subtract 20 from -15 to get -35.
9w - 35.
Answer:
[tex]\mathrm{9w-35}[/tex]Step-by-step explanation:
[tex]\mathrm{-3(w+5)+4(3w-5) }[/tex]
Expand (Apply the distributive property) :-
[tex]\mathrm{-3w-15+12w-20}[/tex]
Combine like terms:-
[tex]\mathrm{-3w+12w=\bf 9w}[/tex]
[tex]\matherm{-15-20=\bf-35}[/tex]
[tex]\mathrm{9w-35}[/tex]
______________________
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The ratio of the sides of rectangle LMNP to the sides of rectangle TUVW is 1:4. The length of LM is 3.6 in, and the length of UV is 16 in.
What is the difference between the areas of the two rectangles?
A. 226 in2
B. 172.8 in2
C. 211 in2
D. 216 in2
Find the volume of the composite solid
6 cm.
14 cm.
120 cm*
460 cm³
1462 cm³
980.2 cm³
The volume of the composite solid is 980.2 cm³.
What is a composite solid?
A composite solid is a solid made of two or more well-defined solid objects.
To calculate the volume of the composite solid, we use the formula below
Formula:
V = (πr²h/3)+(2πr³/3)...................... Equation 1Where:
V = Volume of the composite solidr = Radius of the cone and the hemisphereh = Height of the coneFrom the question,
Given:
r = 6 cmh = 14 cmπ = 22/7Substitute these values into equation 1
V = (6²×14×22/7)/3+(2×6³×22/7)/3V = 528+452.2V = 980.2 cm³Learn more about composite shape here: https://brainly.com/question/8370446
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You are given an image of a panda to create a custom shirt. The original image is 9mm tall and 16mm wide. You need to enlarge the image by a scale factor of 6. What is the new height?
The height of the image after the dilation with scale factor of 6 is given by the relation H = 54 mm
Given data ,
Let the image be an image of a panda to create a custom shirt
Now , original image is 9mm tall and 16mm wide
Let the dilation scale factor of enlargement be k = 6
So , the new image is 6 ( 9mm tall and 16mm wide )
On simplifying the equation , we get
The new image is 54 mm tall and 96 mm wide
Hence , the height of the image is 54 mm
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how long would it take a car going 20 mph to real 528 feet?
The time will take the car to reach it's destination is 0.005 hours
The first step is to convert 528 feet to miles
1 foot= 0.000189394 miles
528= x
cross multiply
= 528 × 0.000189394
= 0.1
Time= distance/speed
distance= 0.1 miles
speed= 20
Time= 0.1/20
= 0.005 hours
Hence it will take the car 0.005 hours to reach its destination
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A parallelogram has one side that is 4 centimeters long and one side that is 6 centimeters long. What is the perimeter of the parallelogram? Explain.
How can you find the perimeter of a parallelogram??
Answer:
20
Step-by-step explanation:
2L + 2W = P :))
HELP PLS ILL PUT MAX POINTS AS I CAN ALSO CHECK PICTURE
The expression which has the greatest value is 1 7/8 divided by 1/12
• For the first question, [tex]\frac{3}{4} /\frac{1}{3} =2 \frac{1}{4}[/tex]
• For the second question, [tex]\frac{3}{4} / \frac{1}{12} = 9[/tex]
• For the third question, [tex]1 \frac{7}{8} =\frac{15}{8}[/tex] so [tex]\frac{15}{8} /\frac{1}{12} = 22 \frac{1}{2}[/tex]
• For the fourth question, [tex]1 \frac{7}{8} =\frac{15}{8}[/tex] so [tex]\frac{15}{8} /\frac{1}{3} = 5 \frac{5}{8}[/tex]
—————
Please remember to revise this and make it in your own words if you want! I tried to speed this up a lot! I hope this helps you. -Doodle
—————
Answer:
1 7/8 / 1/ 12 has the greatest value
Step-by-step explanation:
Compound Area mathsss
Answer:
The answer for Area is 189.29in²
Step-by-step explanation:
Area of compound =Area of semi circle +Area of rectangle
r=d/2=10/2=5in
A=1/2pir² + L×B
A=1/2×5² + 10×15
A=25pi/2+150
A=39.29+150
A=189.29in²
Mia and Allen have been married for 3 years. They both have well-paying jobs
that allow them to live comfortably and pay their bills. They are trying to live on
a budget. They have a $1,000 emergency fund, and they are paying down $28,000
worth of combined student loan debt. Each year for the past 3 years, they have
received a large tax refund -- which they call their "celebration fund" - and use it
to take a nice vacation each summer. They are receiving a large refund, rather
than one close to zero. Why is this kind of tax refund problematic?
Receiving a large tax refund is problematic because it means overpaying taxes and missing out on the opportunity to use that money throughout the year for paying down debt, building an emergency fund, or investing.
We have,
While receiving a large tax refund each year may seem like a positive thing, it actually means that Mia and Allen are overpaying their taxes throughout the year.
This means that they are essentially giving the government an interest-free loan by allowing them to hold onto their money instead of having it available to them throughout the year to use for things like paying down debt or investing in their future.
By overpaying their taxes,
Mia and Allen are essentially missing out on the opportunity to use their money in ways that could benefit them in the long run.
Additionally, the large tax refund they receive each year may create a sense of false security, leading them to believe that they are in a better financial situation than they actually are.
Rather than receiving a large tax refund each year, it may be more beneficial for Mia and Allen to adjust their tax withholdings so that they are receiving more money in each paycheck.
This way, they can use the extra money to pay down debt, build up their emergency fund, or invest in their future, rather than giving the government an interest-free loan.
Thus,
Receiving a large tax refund is problematic because it means overpaying taxes and missing out on the opportunity to use that money throughout the year for paying down debt, building an emergency fund, or investing.
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James Abbott McNeill Whistler's Nocturne in Black and Gold: The Falling Rocket (c. 1875) is an example of "art-for-art's sake" of the
________ movement.
O Color Field
Aesthetic
Impressionist
Avant-Garde
James Abbott McNeill Whistler's Nocturne in Black and Gold: The Falling Rocket (c. 1875) is an example of "art-for-art's sake" of the Aesthetic movement is: B. Aesthetic.
What is The Falling Rocket?The art for art's sake movement which began to form in the late 19th century as a response against the utilitarian and moralistic attitude to art that had predominated in previous centuries is exemplified by The Falling Rocket.
The movement emphasized the value of art as a self sufficient and independent field, free from politics, religion and other outside influences.
Therefore the correct option is B.
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Help its urgent i need to get these done
The planes that are parallel in the cube shown would be C. NOR and LMP.
What are parallel planes ?Two planes that are located on a cube and are always opposite and never intersect; they remain continuously at the same distance from each other. A cube consists of three pairs of parallel planes in correspondence with its triplet of opposing faces.
From the given options, the only parallel planes would be NOR and LMP. One of the reasons for this, is that these planes have no point of intersection unlike the planes in the other options.
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Simply 4(2y-4)-11y????
Answer:
[tex]\mathrm{-3y-16}[/tex]Step-by-step explanation:
[tex]\mathrm{4(2y-4)-11y}[/tex]
Apply the distributive property:-
[tex]\mathrm{8y-16-11y}[/tex]
Combine like terms:-
[tex]\mathrm{8y-11y=\bf-3y}[/tex]
[tex]\mathrm{-3y-16}[/tex]
_________________________
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Sarah has 14 cupcakes she gives 3/7 away how many cupcakes did she give away
Answer:
she gave away 6 cupcakes
Step-by-step explanation:
3/7 is the same as 6/14.
if she gave away 6/14 cupcakes, she gave away 6 cupcakes
if P = (4,2), Find: Rx=3 (P). Pls help!!
The coordinates of the reflected point P' will be (4, -3).
When a point is reflected over the x-axis, its y-coordinate changes sign.
In this case, the point P has coordinates (4,3).
To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.
So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.
Therefore, the coordinates of the reflected point P will be (4, -3).
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Answer:
Step-by-step explanation: