Final answer:
The function y=230(0.98)ˣ is an exponential decay model depicting how a quantity decreases over time. The graph starts at 230 (the initial value) and decreases at a decay rate of 0.98 each step. To express small or large numbers succinctly, standard exponential form is used.
Explanation:
The exponential equation given, y=230(0.98)ˣ, represents a mathematical function known as an exponential decay model. To draw the appropriate graph for this function, you would plot the y-value against x on a Cartesian plane. The x-axis would indicate the time or trial number, and the y-axis would represent the value of y at that time. The decay rate in this equation is 0.98, which means that with each step in x (assuming x is a time interval), the quantity y decreases to 98% of its previous amount. The initial value, or mean, of the equation is 230, which is the starting point of the graph at x=0.
The mentioned exponential curve would start at y=230 and decrease gradually as x increases. If you were to shade the area for the probability that a student has less than $0.40 in his or her pocket, you would first need to solve for x when y=0.40, and then shade under the curve to the left of the corresponding x-value on your graph. This would visually represent P(x < 0.40).
To express numbers in standard exponential form, you use a coefficient between 1 and 10 multiplied by a power of 10. For example, converting 9.3 times 10 to the power of 7 is an example of expressing a very large number in exponential form. For small values of x, the exponential curve will show slower change, which increases rapidly for larger values of x.
If you were going to use the quadratic formula to solve the following equation and b=15, what number would you use as the value for the variable ‘a’?
-15x+22=12x^2
Answer:
You would use a = 12
Step-by-step explanation:
The b value is the coefficient that is in front of the x term, that does not have an exponent of 2. It's simply the x term (not the x^2 term)
We're told that b = 15 is used, but we see that -15 is in front of the x term. To fix this contradiction, add 15x to both sides so that you move the x term to the right side
-15x+22 = 12x^2
-15x+22+15x = 12x^2+15x
22 = 12x^2+15x
Now subtract 22 from both sides to move that term over as well
22-22 = 12x^2 + 15x - 22
0 = 12x^2 + 15x - 22
12x^2 + 15x - 22 = 0
12x^2 + 15x + (-22) = 0
The last equation is in the form ax^2 + bx + c = 0 with
a = 12, b = 15, c = -22
PLEASE HELP! Screenshot attached
Answer:
( x - 6 ) ( x - 3 ) (x + 4)
Step-by-step explanation:
In trapezoid ABCD with bases AB and DC , diagonals intersect at point O. Find the length of diagonal BD , if BO=6 cm and: AO/OC = 3/1
Answer:
BD = 8 cm
Step-by-step explanation:
Diagonals of trapezoid divides each other in equal ratio.
if ABCD is a trapezoid and the diagonals AC and BD intersect at point O
then we have
[tex]\frac{AO}{OC} =\frac{OB}{OD}[/tex]
it is given that
[tex]\frac{AO}{OC} =\frac{3}{1}[/tex] and BO=6 cm
so we can write
[tex]\frac{3}{1} =\frac{6}{OD}[/tex]
cross multiply
[tex]3 OD=6[/tex]
divide both side by 3
OD= 2 cm
now we have
BD = BO +OC
BD = 6 cm + 2 cm
BD= 8 cm
Step-by-step explanation:
The ratios of the sides is the same.
3OD=OB
Let y be the length of OD
Therefore,
3y=6
y=2,
meaning OD is 2.
OB+OD=DB
BD=6
ANSWER:
BD=8
solve for m 1/3=12-m
Answer:
m = 35/3 or 11 2/3
Step-by-step explanation:
1/3=12-m
Subtract 12 from each side
1/3 - 12 = -m
Get a common denominator
1/3 - 12*3/3 = -m
1/3 - 36/3 = -m
-35/3 = -m
Multiply by -1
-1* -35/3 = -1 *-m
35/3 = m
Changing to a mixed number
3 goes into 35 11 times with 2 left over
11 2/3
[tex]12-m=\dfrac{1}{3}\qquad\text{subtract 12 from both sides}\\\\-m=-11\dfrac{2}{3}\qquad\text{change the signs}\\\\\boxed{m=11\dfrac{2}{3}}[/tex]
simplify
a/5x−10 + a/6x−12
To simplify the expression, find the common denominator, distribute the 'a' to each term, and combine like terms.
Explanation:To simplify the expression a/5x-10 + a/6x-12, we need to find a common denominator for the two terms. The common denominator is 30x(x-2). We then multiply each term by the appropriate factor to get a common denominator. This simplifies the expression to:
a(6x-12) + a(5x-10) / 30x(x-2)
Now, we can distribute the 'a' to each term:
6ax - 12a + 5ax - 10a / 30x(x-2)
Combining like terms, we get a(11x - 22) / 30x(x-2).
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Mr. Potts, the college Pastry Chef, baked three apple pies, two blueberry pies, five cherry pies, and six key lime pies for the student fundraiser. What percent of the pies were apple, round to one decimal place?
Answer: 18.8%
Step-by-step explanation:
[tex]\dfrac{\text{quantity of APPLE pies}}{\text{quantity ot TOTAL pies}}[/tex]
[tex]=\dfrac{3}{3+2+5+6}[/tex]
[tex]=\dfrac{3}{16}[/tex]
= 0.1875
= 18.75%
≈ 18.8% rounded to one decimal place
Whats the value of 6 in 3.6?
6 is in the tenths place.
Written Form: 0.6
PLZ HELP i neeed these problems done before there due
will give brainlyest
Answer:
Q 1 = answer is B
Q 2 = answer is A
Step-by-step explanation:
the perimeter of a 5-sided figure is 45.56 meters two of the sides have the same length. the sum of the other three side lengths is 24.2 meters how long is each of the same length sides explain
Answer:
The two equal (same length) sides are 10.68 metres each.
Step-by-step explanation:
45.56 - 24.2 = 21.36 m (length of the 2 equal sides)
21.36 ÷ 2 = 10.68 metres
Answer:
10.68 m
Step-by-step explanation:
We are given that a perimeter of 5-sided figure =45.56 m
Two side of same length
Sum of three sides of given figure=24.2 m
We have to find the length of each side of the same length and explain.
Let x be the length of each side of same length
We know that
Perimeter of 5- sided figure=Sum of length of five sides
Therefore,
x+x+24.2=45.56
[tex]2x+24.20=45.56[/tex]
[tex]2x=45.56-24.2[/tex]
[tex]x=\frac{21.36}{2}=10.68[/tex]
Hence, length of each side of same length=10.68 m
Hari's weekly allowance varies depending on the number of chores he does. He received $20 in allowance the week he did 22 chores, and $12 in allowance the week he did 6 chores. Write an equation for his allowance in slope-intercept form.Hari's weekly allowance varies depending on the number of chores he does. He received $20 in allowance the week he did 22 chores, and $12 in allowance the week he did 6 chores. Write an equation for his allowance in slope-intercept form.
The slope-intercept form of the equation, which represents how much allowance Hari receives based on the number of chores he does, is y = 0.5x + 9. Here, the slope of 0.5 represents the amount Hari earns per chore, and 9 is the base amount Hari receives irrespective of the chores.
Explanation:The given scenario provides us with two points (22, $20) and (6, $12) where the number of chores is the x-coordinate and the allowance is the y-coordinate. We can use these points to find the slope of the line:
Slope (m) = (y2 - y1) / (x2 - x1)= ($20 - $12) / (22 - 6) = $8 / 16 = $0.5,
Next, we use the slope and one of the points to find the y-intercept: y = mx + b so $20 = ($0.5 * 22) + b, solving for b gives us b = $20 - $11 = $9, which is our y-intercept.
So, the equation of the line in slope-intercept form is y = 0.5x + 9
This equation states that Hari earns $0.5 per chore and gets a guaranteed $9 even if he does no chores.
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Two fair coins are flipped at the same time. What is the probability that both will display tails?
Answer:
2 out of 4. 2/4
Step-by-step explanation:
There are 2 sides to each coin, there are two coins so all sides add up to 4.
The probability that both coins will display tails is:
P = 0.25
How to get the probability?
A fair coin has two possible outcomes, tails and heads, both with the same probability.
Then the probability of getting tails is:
p = 0.5
So, the probability for each coin (of getting tails) is:
p₁ = 0.5
p₂ = 0.5
The joint probability (this is, the probability that both of the above events happen at the same time) is the product between the individual probabilities:
P = p₁*p₂ = 0.5*0.5 = 0.25
If you want to learn more about probability, you can read:
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A car dealer Purchased a car for $2000 and then sold it for $3200.right and solve an equation to find the profit.
Answer: $1200 profit
Step-by-step explanation: $3200 - $2000 = $1200
Suki rode her bike 4/5 mile. Claire rode her bike 1/3 mile. they want to compare how far they each rode their bikes using the Benchmark 1/2
Suki rode her bike a longer distance than Claire because when comparing each of their distances to the benchmark of 1/2 mile, Suki's distance (4/5 mile) is greater than the benchmark (1/2 mile), while Claire's distance (1/3 mile) is less than the benchmark. Therefore, Suki rode a longer distance than Claire in relation to the benchmark.
Suki's Distance with Benchmark (1/2):
Suki rode her bike for 4/5 miles.
The benchmark is 1/2 mile.
Comparison: [tex]\frac{4}{5} > \frac{1}{2}[/tex]
Interpretation: Suki's distance ( 4/5 miles) is greater than the benchmark 1/2 mile.
Claire's Distance with Benchmark (1/2):
Claire rode her bike for 1/3 mile.
The benchmark is 1/2 mile.
Comparison: [tex]\frac{1}{3} < \frac{1}{2}[/tex]
Interpretation: Claire's distance ( 1/3 mile) is less than the benchmark 1/2 mile.
Overall Comparison:
Suki's distance (4/5) is greater than Claire's distance (1/3).
Interpretation: Suki rode her bike a longer distance than Claire.
In summary, both Suki and Claire are comparing their distances to the benchmark of 1/2 mile. Suki's distance is greater than the benchmark, while Claire's distance is less than the benchmark. Therefore, Suki rode a longer distance than Claire.
What is the next number in the arithmetic sequence below
Answer:
D
Step-by-step explanation:
The common difference d, between the terms is
d = - 9 - 3 = 3 - 15 = 15 - 27 = - 12
To find the next term in the sequence subtract 12 from the previous term
⇒ - 9 - 12 = - 21 ← is the next term in the sequence
The next term of the sequence after -9 is -21
What is an Arithmetic Sequence?An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant term. This constant term is called Common difference.If the first term of a sequence is a and the common difference is d then the nth term can be written as a + (n-1)dHow to find what is the next number in the arithmetic sequence ?The given sequence is 27, 15, 3, -9 and so on.Common difference can be found by subtracting a term from its previous term.∴ Common difference of the given problem = (15 - 27) = -12
∴ Each term of the sequence gets decreased by 12
∴ The term after -9 will be ( -9 - 12) = -21
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is y=5/3x+3,20x+12y=12 a parallel, perpendicular.or a neither pair equation
Answer:
Neither
Step-by-step explanation:
y = 5/3 x + 3, this line has slope = 5/3
20x + 12y = 12
12y = -20x + 12
y = -20/12 x + 1
y = - 5/3 x + 1, this line has slope = - 5/3
Parralel ; same slopes
Perpendicular; slopes are opposite and reciprocal
So answer is neither pair parallel nor perpendicular
The pair of equations y = 5/3x + 3 and 20x + 12y = 12 are parallel because they both have the same slope of 5/3 once the second equation is put into slope-intercept form.
To determine if the pair of equations y = 5/3x + 3 and 20x + 12y = 12 are parallel, perpendicular, or neither, we must first put both equations into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. The equation y = 5/3x + 3 is already in slope-intercept form with a slope of 5/3. To convert the second equation into slope-intercept form, we can rewrite it as 12y = -20x + 12, and then y = (-20/12)x + 1, which simplifies to y = -5/3x + 1.
Now, comparing the slopes of these two lines, we see that both slopes are equal, meaning the lines are parallel to each other since they have the same slope but different y-intercepts.
Travis can afford a $260-per-month car payment, and he is interested in either a compact car, which costs $10800, or a coupe, which costs 11,300. If he is being offered a 4-year car loan with and APR of 6%, compounded monthly, which car can Travis afford?
Answer: travis can afford the compact car but not the coupe
Step-by-step explanation:
Answer:
Travis can afford the compact car.
Step-by-step explanation:
The EMI formula is :
[tex]\frac{p*r*(1+r)^{n} }{(1+r)^{n}-1 }[/tex]
In first case:
p = 10800
r = 6/12/100=0.005
n = 4*12 = 48
Putting values in the formula we get:
[tex]\frac{10800*0.005*(1+0.005)^{48} }{(1+0.005)^{48}-1 }[/tex]
= $254
We can see that Travis can afford the compact car because the EMI is less than $260.
In second case:
p = 11300
r = 6/12/100=0.005
n = 4*12 = 48
Putting values in the formula we get:
[tex]\frac{11300*0.005*(1+0.005)^{48} }{(1+0.005)^{48}-1 }[/tex]
= $265.75
We can see that the coupe will have an EMI of $265.75 which is higher than the amount that Travis can afford.
Hence, Travis can afford a compact car.
If you took a true “if then” statement and instead a not in each clause the new statement would also be true
Answer:
True
Step-by-step explanation:
If it snows today, I will have to go out and clean the driveway.If it does not snow today, I will not have to out and clean the driveway.Without going into p's and q's and true false tables, I believe the negation is also true.Answer:
Step-by-step explanation:
If a then b is true then not b = not a is true. This is called the contrapositive.
which of the following is not a possible value for a probability? A.10/100. B.1/16. C.0.82. D.1.001
Answer:
D.1.001
Step-by-step explanation:
You cannot have a probability greater than 1. 1 is it will happen ( 100%)
Area and Perimeter of a rectangle that is 92 meters long and 18 meters wide
a= 92(18) =1656
Area= 1656m
p= 2(92+18) =220
Perimeter= 220m
are the following figures similar
Answer:
Yes, they are similar. The answer you would click is Yes, the corresponding sides are proportional.
Step-by-step explanation:
The second figure is a dilation of the first, making them similar. The dilation is by a factor of 2 and a half.
An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall, and the initial velocity of the ball is 40 ft per sec. The height s of the ball in feet is given by the equation s equals negative 2.7 t squared plus 40 t plus 6.5s=−2.7t2+40t+6.5 , where t is the number of seconds after the ball was thrown. Complete parts a and b. a. After how many seconds is the ball 12 ft above the moon's surface?
Answer:
0.14 s
Step-by-step explanation:
s = -2.7 t² + 40t + 6.5
Let s = 12
12 = -2.7t² + 40t + 6.5 Subtract 12 from each side
-2.7t² + 40t + 6.5 - 12 = 0
-2.7t² + 40t - 5.5 = 0
Apply the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = -2.7; b = 40; c = -5.5
[tex]x = \frac{-40\pm\sqrt{40^2 - 4\times (-2.7) \times (-5.5)}} {2(-2.7)}[/tex]
[tex]x = \frac{-40\pm\sqrt{1600-59.4}}{-5.4}[/tex]
[tex]x = \frac{-40\pm\sqrt{1540.6}}{-5.4}[/tex]
[tex]x = \frac{-40\pm 39.25}{-5.4}[/tex]
x = 7.41 ± 7.27
x₁ = 0.14; x₂ = 14.68
The graph below shows the roots at x₁ = 0.134 and x₂ = 14.68.
The Moon’s surface is at -12 ft. The ball will be 12 ft above the Moon’s surface (crossing the x-axis) in 0.14 s.
The second root gives the time the ball will be 12 ft above the Moon’s surface on its way back down.
Divide. 1/3 ÷ 4/5 Express your answer in simplest form.
To calculate 1/3 ÷ 4/5, switch the division operation to multiplication by flipping the second fraction. This gives us 1/3 * 5/4, which simplifies to 5/12.
Explanation:In mathematics, when we're asked to divide fractions, we often use the method of multiplying by the reciprocal of the second fraction.
In this case, the question asks you to perform the division operation of 1/3 ÷ 4/5.
To do this, you would first flip (or find the reciprocal) of the second fraction, which results in 5/4 instead of 4/5. Next, we perform the operation of 1/3 multiplied by 5/4 rather than division. Multiplication of these fractions gives us 5/12. Thus, 1/3 ÷ 4/5 = 5/12 is your answer in simplest form.Learn more about Divide Fractions here:https://brainly.com/question/18511795
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A 3.5 ft by 5.5 ft mirror is placed in a wooden frame. What is the area of the frame
Answer:
19.25ft
Step-by-step explanation:
area = length x width so 3.5 x 5.5 = 19.25
Answer:
The area of the frame is 19.25 feet.
Step-by-step explanation:
We can see from the information that the wooden frame is a rectangle since length and breadth are unequal.
breadth = 3.5 ft
length = 5.5 ft
The formula for area of a rectangle is = A = L x b
Area = 3.5 * 5.5
Area = 19.25 feet
what equation results from completing the square and then factoring? x^2+2x=9
A.(x+2)²=8
B.(x+1)²=10
C.(x+2)²=10
D. (x+1)²=8
Answer: (x+1)^2=10
Step-by-step explanation:
PLZ HELP ASAP (10 points)
Answer:
<DAB= 98
Step-by-step explanation:
Remark
I think you are supposed to assume that this is a parallelogram. In that case the two labeled angles are intended to be equal (one of the properties of a parallelogram).
Equation
2x + 36 = 3x - 5 Add 5 to both sides
2x + 36 + 5 = 3x - 5 + 5 Combine
2x + 41 = 3x Subtract 2x from both sides
2x - 2x + 41 = 3x - 2x Combine
41 = x
Answer
<DAB = 2x + 36
<DAB = 2*41 + 36
<DAB = 82 + 36
<DAB = 98
How many ounces of iodine worth 30 cents an ounce must be mixed with 50 ounces of iodine worth 18 cents an ounce so that the mixture can be sold for 20 cents an ounce?
Answer:
10 ounces
Step-by-step explanation:
10 ounces of iodine are worth 30 cents so the mixture can be sold for 20 cents an ounce.
What are arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Let n be the ounces of 30 cents worth of iodine.
To determine the mixture to be worth 20 cents per ounce.
The value of 50 ounces of 18-cent iodine is
⇒ (50)(18) = 900 cents of iodine.
A (50+n) mixture of iodine is produced by combining 50 ounces of 18-cent iodine with n ounces of 30-cent iodine.
Similarly, n ounces of 30-cent iodine is worth 30n.
So, the price of 50+n ounces of 20-cent iodine (50+n)20
⇒ 30x + 900 = 1000 + 20x
Rearrange the likewise terms and apply the arithmetic operations,
⇒ 10x = 100
⇒ x = 10
We can estimate that in order to sell the mixture for 20 cents per ounce, we should combine 10 ounces of iodine worth 30 cents.
Hence, 10 ounces of iodine are worth 30 cents so the mixture can be sold for 20 cents an ounce.
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A roller coaster starts from a deck at an elevation of 20 feet above the ground on the first Hill Climb 78 Feet and then drops 85 feet. on the second Hill the coaster climbs is 103 ft and then drops 110 ft how far below or above the deck is the coaster after the second Hill?
Answer:
6 feet above the deck
You and your mom enter a drawing with 3 different prizes. A total of 9 people entered the drawing, and prizes are awarded randomly. There are 504 ways to reward the prizes. What is the probability that you win first prize and tour mom wins second prize?
Answer:
[tex]\frac{1}{72}[/tex]
Step-by-step explanation:
We have been given that there are total 9 people who entered the drawing competition. There are 3 prizes to be distributed to the winners. The total number of ways that 3 prizes can be awarded to the 9 people can be determined as 9*8*7 = 504.
The total number of ways in which I win the first prize and my mom wins the second prize would be 1*1*7 = 7.
Therefore, the probability that I win the first prize and my mom wins the second prize would be: [tex]\frac{7}{504}=\frac{1}{72}[/tex]
Answer:
it’s 7
Step-by-step explanation:
The area of a rectangular classroom is 420 square feet. If the length and width of the classroom are multiplied by 3, what will be the area of the new classroom?
A:1640 ft B:1720 ft C:2840 ft D:3780 ft
Answer:
D: 3780 square feet
Step-by-step explanation:
Let the length be L. Let the width be W.
The area of a rectangle is length times width, so
A = LW
The area is 420 square feet, so
LW = 420
Now you multiply the length by 3 and multiply the width by 3.
The length is now 3L, and the width is now 3W.
The area of the new rectangle is the new length times the new width.
new area = 3L * 3W
new area = 3 * 3 * LW
new area = 9 * LW
LW was the original area, and it is 420 square feet, so the new area is 9 times the old area.
new area = 9 * 420 square feet
new area = 3780 square feet
Calculate: 0.3 of 14
100% --> 14
30% --> x
100x = 420
x= 420/100
x=4.2
Answer:
The answer is 4.2
Step-by-step explanation:
Always remember that when they use the word of, it means you have to multiply. So 14 times 0.3 is 4.2