The number of bacteria in a certain population increases Accor to a continuous growth model,with a growth parameter of 9.6% per hour. How many hours does it take for the size of the sample to double
Answers
The required number of hours does it take for the size of the sample to double is 11 hours.
What is percentage?Percentages are basically divisions where the denominator is 100. To show that a number is a percent, we utilize the percent image (%) close to the number. For instance, in the event that you got 75 inquiries right out of 100 on a test (75/100), you would have scored 75%.
According to question:Let initial population be x.
As question says number of bacteria increases by 9.6% per hours.
9.6% of x takes 1 hours,
So, in 11 hours size of sample become 105.6%, means almost double of initial size.
Thus, 11 hours will be taken to make size double.
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Related Questions
The following figure is made of 1 triangle and 1 rectangle.
7,2,11 find the area for each part of the figure and the whole figure
Answers
The area of the figures is shown:
Rectangle A: 54 units²
Rectangle C: 21 units²
Triangle B: 3 units²
What is the area?The measurement that expresses the size of a region on a plane or curved surface is called an area.
Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
The area of rectangle A:
Area = l*b
Area = 9*6
Area = 54 units²
Area of rectangle C:
Area = l*b
Area = 3*7
Area = 21 units²
Area of triangle B:
Area = 1/2 * b * h
Area = 1/2 * 3 * 2
Area = 1 * 3
Area = 3 units²
Therefore, the area of the figures is shown:
Rectangle A: 54 units²
Rectangle C: 21 units²
Triangle B: 3 units²
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Which property is shown in the matrix addition below?
-6
9
15 -2
0
-3
+
6
-9
-15 2
0
3
commutative property
associative property
Oinverse property
Oidentity property
0 0 0
0 0 0
Answers
For the given matrix the additive inverse property is shown.
What is additive inverse of matrix?
The matrix that is created by changing the sign of each matrix element is known as the additive inverse. -(-A)=A is the notation for the additive inverse of the matrix A.
Rows and columns serve as a measure of a matrix's dimensions. Given that it has three rows and three columns, for instance, the matrix below has a dimension of 3 x 3. Three by three can be read off as the matrix's dimension. We consequently obtain the additive inverse of the matrix
M = - M.
Consider the given matrix,
[tex]\left[\begin{array}{ccc}-6&15&-2\\9&0&-3\end{array}\right] + \left[\begin{array}{ccc}6&-15&2\\-9&0&3\end{array}\right] = \left[\begin{array}{ccc}0&0&0\\0&0&0\end{array}\right][/tex]
Here each element in first matrix is negative of the element of second matrix.
That is each element is inverse of the element in second matrix.
And the addition of elements is 0.
Hence, for the given matrix the additive inverse property is shown.
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PLEASEEEEE HELP MEEEEEE!
Answers
$9/1lb
The owner of a landscaping business wants to know how much time, on average, his workers spend mowing one lawn. Which is the most appropriate rate with which to calculate an answer to his question?
lawns per employee
hours per lawn
employee per lawn
lawns per day
Answers
The mowing takes hours hence, the best rate is hours per lawn. Hence the correct option is option 1. It can be solved by rate of work.
The rate lawns per employee gives the lawns mowed by one employee.
The rate hours per lawn gives the number of hours required to mow one lawn.
The rate employee per lawn gives how many employees are required to mow one lawn.
The rate lawns per day gives the number of lawn mow in one day.
Since the mowing takes hours hence, the best rate is hours per lawn. Hence the correct option is option 1.
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Find The value of my coins. If i have p pennies, n nickels and twice as many quarters as pennies.
Translate into an algebraic expression and simplify if possible.
Answers
The value of p pennies, n nickels and twice as many quarters as pennies is (51p + 5n) cents or $(51p + 5n)/100.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).
Given that you have p number of coins of pennies, n number of coins of nickels and twice as many quarters as pennies.
Thus the number of coins of quarters is 2p.
The value of penny, nickel, and quarter are
1 penny = 1 cent
1 nickel = 5 cents
1 quarter = 25 cents
The value of p number of pennies is p cents.
The value of n number of nickels is (n×5) =5n cents.
The value of 2p number of quarter is (2p × 25) = 50p cent.
The total value is p + 5n + 50p = (51p + 5n) cents
Divide 51p + 5n by 100 to convert it into dollar:
(51p + 5n) cents = $(51p + 5n)/100
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Need help with math question
Answers
A vertex with degree 2 in a graph has an edge that loops around itself. The graph is therefore a cycle graph.
What is Euler circuit?Every edge of a graph is used precisely once in an Euler circuit. An Euler path has two distinct vertices where it begins and finishes. A vertex serves as the beginning and conclusion of an Euler circuit.In an Eulerian path, we pass over two unvisited edges with one end point, v, each time we visit a vertex. As a result, the degree of each middle vertex in the Eulerian Path must be even. Since any vertex can be the central vertex in an Eulerian cycle, all vertices must have an even degree.All of a graph G's vertices must be even if it has an Euler circuit. Or, to put it another way, G cannot have an Euler circuit if the number of odd vertices is more than 0.To learn more about Euler circuit refer :
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A mason is a person who builds structures with bricks, stone, cement block, or wee. A mason usually uses, mortar to hold the bricks together. A general rule of thumb in masonry is that 2 1/2 bags of mortar are needed for every 100 cement blocks. Use a double number line to determine each answer.
Answers
By using the concept of unitary method, it can be calculated that
a) For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required
b) For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, unitary method will be used
The double number line has been shown below-
a) For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required
For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required
For 350 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 350[/tex] bags of mortar are required
For 350 blocks of cement, [tex]\frac{35}{4}[/tex] bags of mortar are required
For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required
b) For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required
For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required
For 50 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 50[/tex] bags of mortar are required
For 50 blocks of cement, [tex]\frac{5}{4}[/tex] bags of mortar are required
For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required
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Use the following table to find the rate of change. Remember the below equation rise/ run
X 2 4 6 8 10
Y 4 8 12 16 20
pls help :)
Answers
The rate of change of the function that is defined by the table:
X: 2 4 6 8 10
Y: 4 8 12 16 20
is r = 2
How to find the rate of change?For a function with two known points (x₁, y₁) and (x₂, y₂), the rate of change between these two points is written as:
r = ( y₂ - y₁)/(x₂ - x₁)
Here we have the table that defines a function:
X: 2 4 6 8 10
Y: 4 8 12 16 20
Here we can use any pair of two points on the table, for example, if we use the first pair and last pair:
(2, 4) and (10, 20)
The rate is:
r = (20 - 4)/(10 - 2) = 16/8 = 2
If we use the first two pairs (2, 4) and (4, 8) we get:
r = (8 - 4)/(4 - 2) = 4/2 = 2
So the rate of change of the function is r = 2.
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Assume that females have pulse rates that are normally distributed with a mean of 76.0 beats per minute and a standard deviation of 12.5 beats per minute. A) If 4 adult female is randomly selected, find the probability that her pulse rate is less than 80 beats per minute.
Answers
The probability that their mean pulse rate is less than 80 beats per minute is of:
0.7389 = 73.89%.
How to obtain a probability using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 76, \sigma = 12.5, n = 4, s = \frac{12.5}{\sqrt{4}} = 6.25[/tex]
The probability that their mean pulse rate is less than 80 beats per minute is the p-value of Z when X = 80, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (80 - 76)/6.25
Z = 0.64
Z = 0.64 has a p-value of 0.7389.
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Choose ALL correct answers
(1, -3)
(4, 1)
(6, 3)
(2, -2)
Answers
Answer:
(a) (1, -3)
(b) (2, -2)
Step-by-step explanation:
You want to identify two points on the line through (3, -1) that has a y-intercept of -4.
GraphGraphing the line and points is suggested. The attached shows that graph, and identifies the two points on the line as ...
(1, -3) and (2, -2)
__
Additional comment
The equation of the line is x-y=4, so you can tell if the points fall on the line by seeing if they have that difference.
Pls help what this is
Stem-and-leaf plots
Answers
Answer:
C is the answer
Step-by-step explanation:
Stem and leaf plots were also confusing to me at first, but once you understand they are actually easy!
Look at the first column where it says 2,3,4,5 and 6. Those are the tens place. The columns next to it with 2,3,8,9,etc are the ones place. For example, the first column has two, so we know that the number has a two in the tens place.
2_
Look at the numbers next to it, there's 2,3, and 8.
Since there's 3 numbers, that means that there are three numbers that have a two in the ones place. 2,3 and 8 are the numbers that go in the ones place.
So in the graph there is 22,23 and 28.
If you look at your choices, you can find all of them except 38, since on the row with the 3, next to it is the number 9 and not the number 8.
Put the following values in order from greatest to least.
Justify your answer.
0.388
3/8
38.38%
0.39
Answers
Answer:
0.39, 0.388, 38.38%, 3/8
Step-by-step explanation:
Which scale factors produce a contraction under a dilation of the original image? Select each correct answer. Responses −6 , negative 6, −0.5 , negative 0.5, 0.5 0.5 6
Answers
The set of scale factors that would produce a contraction under a dilation of the original image are:
B. -0.5
C. 0.5
What is scale factor?A scale factor can be defined as the ratio of two corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, quadrilaterals, and other types of polygons.
In Mathematics, the following rules are applied to interpret and understand the dilation of a geometric figure:
A geometric figure is enlarged when the scale factor is greater than 1 (k > 1).A geometric figure is reduced or contracted when the scale factor is less than 1 (k < 1).A geometric figure will remain the same when the scale factor is equal to 1 (k = 1).For a contraction under a dilation of the original image, the scale factor (k) must either be negative or less than one (1). Therefore, the required values are -0.5 and 0.5 respectively.
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LaShonda is buying tickets for a group of families going to a ballet. She wants to have at least 25 tickets. Each adult ticket costs $22.50 and each child ticket costs $17.50. LaShonda wants to spend no more than $400. Which system of inequalities can LaShonda use to find the number of tickets she can buy?
Answers
Answer: You Like Big Black Men and You love them dancing on you
Step-by-step explanation:
I have your search history ;)
The system of inequalities can LaShonda use to find the number of tickets she can buy will be;
⇒ x + y ≤ 25
⇒ 22.50x + 17.50y < 400
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
She wants to have at least 25 tickets. Each adult ticket costs $22.50 and each child ticket costs $17.50.
LaShonda wants to spend no more than $400.
Now,
Let the number of adult tickets = x
And, The number of child tickets = y
Here, She wants to have at least 25 tickets.
So, We get;
⇒ x + y ≤ 25
And, Each adult ticket costs $22.50 and each child ticket costs $17.50.
LaShonda wants to spend no more than $400.
So, We get;
⇒ 22.50x + 17.50y < 400
Thus, The system of inequalities can LaShonda use to find the number of tickets she can buy are;
⇒ x + y ≤ 25
⇒ 22.50x + 17.50y < 400
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Select the correct location on the expression.
Mateo uses this exponential expression to determine the balance of his savings account. Which value in the expression represents the
annual interest rate for his savings account?
100(1+0,02)
12t
Answers
Answer:
0,02
Step-by-step explanation:
i got it correct
A water tank initially contained 111 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.
How many minutes have passed, m, when the tank contains 194 liters? Round to the nearest hundredth.
Answers
Answer:
9.22 minutes
Step-by-step explanation:
You could use the form y=mx + b to find this equation
y will represent the total liters
x will represent the total number of minutes
b will represent the initial number of liters in the beginning
1. Plug 194 in for y, plug 9 in for m, put 111 in place of b
The equation should look be: [tex]194 = 9x + 111[/tex]
2. Solve the equation
3. Subtract 111 on both sides. The equation would now be: [tex]83 = 9x[/tex]
4. Divide both sides by 9 (to get x by itself). [tex]\frac{83}{9} = 9.22222222[/tex]
5. Round to the nearest hundredth place to get 9. 22 minutes
Mark and Aly were selling slices of pizza for a school event. Mark had 2 1/3
of a pizza pie left over. Aly had 1 5/9 left.
Together, how much pizza did Mark and Aly have left?
Answers
Answer:
11/9
Step-by-step explanation:
If this is an addition question then this is your answer.
If a sum of $500 were shared among a group of people in the following ratios, how much would each person receive?
Answers
If a sum of $500 were shared among a group of people in the following ratios,
a) 6:4 then, 6x = 300 and 4x = 200.
b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.
c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50
d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.
What is ratio?
Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.a) 6:4
Let it be 6x , 4x
6x + 4x = 500
10x = 500
x = 50
Then, 6x = 300 and 4x = 200.
b) 1:4:5
Let be x, 4x, 5x
x + 4x + 5x = 500
10x = 500
x = 50.
Then x = 50 , 4x = 200 and 5x = 250.
c) 1 : 8 : 1
x + 8x + x =500
10x = 500
x = 50
Then, x =50 , 8x = 400 and x = 50
d) 10 : 5: 4: 1
10x + 5x + 4x + x = 500
20x = 500
x = 25
Then, 10x = 250 , 5x = 125, 4x = 100, x = 25.
Hence, If a sum of $500 were shared among a group of people in the following ratios,
a) 6:4 then, 6x = 300 and 4x = 200.
b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.
c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50
d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.
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Simplify by combining like terms.
3a +15-2a²+5a²-7+5a
Answers
Answer:
8a + 3a^2 + 8
Find the area of the circle with a diameter of 6.1
Answers
Find the value of each trigonometric ratio.
Answers
Answer:
sinA = 7/25
tanX = 35/12
Step-by-step explanation:
Trigonometric ratio for:
sinA = perpendicular/hypotenuse = 14/50 = 7/25
tanX = perpendicular/base = 35/12
For the functions f(x)=2x3 and g(x)=3x3−2, find (f∘g)(1) and (g∘f)(1).
Answers
Value of composite function (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.
What is composite function?
Function composition is associate operation ∘ that takes 2 performs f and g, and produces a perform h = g ∘ f such h(x) = g. during this operation, the perform g is applied to the results of applying the perform f to x
Main body:
according to question;
f(x) = 2x³
g(x) = 3x³ -2
we need to find composite function:
f o g (x) = 2(3x³-2)
{to find composite function , we replace one function as value of x in another}
f o g(x) = 6x³ -4
= 6x³ -4
f o g(1) = 6*1 -
= 2
g o f(x) = 3(2x³)-2
g o f(x) = 6x³ -2
= 6x -2
g o f(1) = 6*1 -2
= 5
Hence value of (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.
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The ratio of top dogs to fat cats was 24 to 19. if they were 152 fat cats, how many top dogs were there?
Answers
The ratio shows how many times one value is contained in another value.
The number of top dogs is 192.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of top dogs to fat cats was 24 to 19.
if they were 152 fat cats.
This means,
Number of top dogs = 24x
Number of fat cats = 19x
Now,
Number of fat cats = 152
This means,
152 = 19x
x = 8
Now,
Number of top dogs = 24x
= 24x
= 24 x 8
= 192
Thus,
The number of top dogs is 192.
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Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modeled by the function y=3.5x+5 where y is the total miles jogged and x is the number of hours Shirley continues to jog. Identify the rate of change and the initial value of the function. Express your answers as decimals if necessary.
Answers
The rate of change of the modelled equation is 3.5 and the initial value is 5.
How to find the rate of change in a slope intercept equation?Linear equation can be represented in different form such as slope intercept form, point slope form, general form and standard form.
Equation in slope intercept form is as follows:
y = mx + b
where
m = slope = rate of changeb = y-intercept = initial valueTherefore, Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modelled by the function y = 3.5x + 5 where y is the total miles jogged and x is the number of hours.
The equation is modelled in slope intercept form.
Therefore,
rate of change = 3.5
initial value = 5
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Rahim is saving for a new bike which will cost $1600. Rahim earns $3000 per month. Rahim spends his money on bills, food and extras in the ratio 6:4:2. Of the money he spends on extras, and puts 20% into his savings account to buy his bike. How long will it take rahim to save for his new bike
Answers
Answer:
it will take rahim 16 months
Step-by-step explanation:
6:4:2
3000÷12=250
1500:1000:500
20% 100
100×16=1600
You can play a game for $1. In the game, you roll an 8-sided die. If you roll an 8, you get $9. If
roll an odd number, you get $1. Otherwise, you gain nothing.
(a) What is the expected value of this game?
Answers
The expected value of the game, given the amounts to be made when a number is rolled, is $ 1.25
How to find the expected value ?First, find the probability of rolling an 8 :
= Number of eights / Number of sides
= 1 / 8
= 0.125
The the probability of rolling an odd number :
= Odd numbers from 1 to 8 / Number of sides
= 4 / 8
= 0.5
The expected value of the game is:
= ( Probability of getting an 8 x Amount if you get 8 ) + ( Probability of getting an odd x Amount if you get an odd ) + ( Probability of not getting an 8 or odd x Loss )
= ( 0.125 x 9 ) + ( 0.5 x 1 ) + ((1 - 0.125 - 0.5) x -1)
= $ 1.25
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Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the area under the graph using first two then four rectangles.f(x)=x^3 between x=0 and x=1
Answers
The area under the graph using the first two and then four rectangles = 0.221 unit square
According to the graphs given in the below figure,
Given in the question,
f(x) = [tex]x^{3}[/tex] when x = 0 and x = 1
The first rectangle of the first graph goes from 0 to 0 .6,
Width = 0.6
Height measured from the middle point = 0.3
f( 0.3) = [tex]( 0.3)^{3}[/tex]
f(0.3) = 0.027 units.
Area of first rectangle = 0.6 x 0.027 = 0.0162 unit square
Now taking the second rectangle of the first part,
It is going from 0.6 to 1.0,
Width = 0.4 units
height = 0.8 units
Height measured from the middle-
f(0.8) = [tex](0.8)^{3}[/tex] = 0.512
Area of the second part of the rectangle = 0.512 x 0.4
= 0.2048 unit square
Final area = 0.2048 + 0.0162 = 0.221 square units
Therefore, the same could be done with the second part rectangle of 4
For the given first part of four rectangles = width = 0.6 units and height = 0.1 unit
so f(0.1) = [tex]0.1^{3}[/tex]
= 0.001 units
Therefore, the area under the graph using the first two and then four rectangles = 0.221 unit square
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Jason drops a tennis ball outside of his hotel balcony. He is standing 52 feet above the street. If the ball hits the hotel canopy 12 feet above street-level, how long after Jason releases the ball will it hit the canopy. Use the function h(t) = -16t2 + 52. Round your answer to the nearest tenth.
Jason drops a tennis ball outside of his hotel balcony. He is standing 52 feet above the street. If the ball hits the hotel canopy 12 feet above street-level, how long after Jason releases the ball will it hit the canopy. Use the function h(t) = -16t2 + 52. Round your answer to the nearest tenth.
1.6 seconds
2.0 seconds
0.4 seconds
4.0 seconds
Answers
1.6 seconds. The ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.
How to find time ?To find the time it takes for the ball to hit the canopy, we need to solve the equation h(t) = 12 for t.
The given equation for h(t) is h(t) = -16t^2 + 52, so we can substitute this into the equation h(t) = 12 to get:
12 = -16t^2 + 52
To solve this equation, we can move all the terms to one side of the equation to get:
-16t^2 + 40 = 0
We can then divide both sides of the equation by -16 to get:
t^2 - 2.5 = 0
We can then use the quadratic formula to solve for t:
t = +/- sqrt(2.5)
t = +/- 1.58
Thus, the ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.
Rounding this answer to the nearest tenth gives us 1.6 seconds, so the correct answer is 1.6 seconds.
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URGENT!!!!!!!!!!
identify the conic section represented by the equation x+2=-2(y-3)^2
circle
ellipse
hyperbola
parabola
Answers
Step-by-step explanation:
[tex] - \frac{x}{2} - 1 = (y - 3) {}^{2} [/tex]
[tex] - 0.5(x + 2) = (y - 3) {}^{2} [/tex]
A parabola with a vertex (-2,3)
A production line estimates that 1.50% of the items it produces is defective. In a package containing 200 items, find the probability that no item is defective
Answers
The probability of the defective items is given as 0.015.
Given that,
A production line estimates that 1.50% of the items it produces is defective. In a package containing 200 items,
Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
Number of the item = 200
1.5% of the item is defective, = 0.015 [200]
Probability of the defective item = 0.015[200] / 200 = 0.015
Thus, the probability of the defective items is given as 0.015.
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