Answers
The Interpret (N · T)(t) is \(N[T(t)] = 20t^{2}+92t+205.\)
The number of bacteria after 5 hours will be 1165.
It will take for the bacteria count to reach 2221.
As per the question statement, the number of bacteria "N" in a refrigerated food is given by [N(T) = (5T² - 4T +100)], where "T" is the temperature of the food in degrees Celsius,
And when the food is removed from the refrigerator, the temperature of the food is given by [T(t) = (2t+5)].
First we are required to find out (N · T)(t), which is N[T(t)] which can be expressed as
\(N[T(t)] = 5[T(t)]^{2} - 4T +100\\or, N[T(t)] = 5(2t+5)^{2} -4(2t+5)+100\\or, N[T(t)] = 5(4t^{2}+25+20t)-8t-20+100\\ or, N[T(t)] = 20t^{2} +125+100t-8t+80\\ or, N[T(t)] = 20t^{2}+92t+205.\)
Then, the number of bacteria after 5 hours will be N[T(5)], i.e.,
\(N[T(5)] = 20(5^{2})+(92*5)+205\\or, N[T(5)] = (20*25)+460+205\\or, N[T(5)] = 500+665\\or, N[T(5)]=1165\)
And finally, the time required for the bacteria count to reach 2221 can be calculated by solving the quadratic equation \([2221 = 20t^{2}+92t+205]\), i.e.,
\([20t^{2}+92t+205 = 2221]\\or, 20t^{2}+92t+(205-2221)=0\\or,20t^{2}+92t-2016=0\\or, 5t^{2}+23t+504=0\)
And the formula to calculate the solutions of a standard quadratic equation [ax² + bx +c = 0] goes as
\(x=\frac{-b+\sqrt{(b^{2}-4ac) } }{2a}, \frac{-b-\sqrt{(b^{2}-4ac) } }{2a}\)
Comparing [ax² + bx +c = 0] with [5t² + 23t + 504=0], we get
(a = 5), (b = 23) and (c = -504), and using these values in the above mentioned formula to calculate the solutions of quadratic equations, we get, [t = 8, (-12.6)].
Since time (t) cannot be negative, thus [t ≠ (-12.6)].
Hence, (t = 8) or, the time required for the bacteria count to reach 2221 is 8 hours.
Quadratic Equation: In algebra, any polynomial equation whose highest degree is two and can be rearranged to the standard form of [ax² + bx + c = 0], where (a ≠ 0), is known as a quadratic equation.To learn about Quadratic Equations, click on the link below.
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Related Questions
What is the percentage difference between 1982802.91786170.42
Answers
Given:
Two numbers are given as
\(\begin{gathered} 1982802.9 \\ 1786170.42 \end{gathered}\)Required:
We need to find the percentage difference between both numbers
Explanation:
Consider
\(\begin{gathered} a=1982802.9 \\ b=1786170.42 \end{gathered}\)The formula to find the percentage difference is
\(100*\frac{\text{ la-bl}}{\frac{(a+b)}{2}}\)put the values
\(\)The following are rational expression in simplified form EXCEPT.
Answers
Answer:
D
Step-by-step explanation:
Since D is 18x/9 , you can divide 18 by 9 and you end up with 2x
Combine Like Terms : 4x-8-8
Answers
Answer:
4x-16
Step-by-step explanation:
When combining like terms you combine the constant terms (the terms without a variable) and the x terms. Since the only variable term is 4x we can leave in at that.
But there are two constant terms -8 and -8, together they make -16 so, the simplified expression would be 4x-16
Due May 4Attendance Question (5/4/21) A cab company charges a$5 boarding rate in addition to its meter which is $3 forevery mile. What equation represents the rate of thiscompany?
Answers
Explanation
Step 1
Let x represents the number of hours
Let y represents the rate of the company
and
cost per hour = $3
so, the total cost per time is
cost per time= 3* number of hours
cost per time==3x
now, the company charges a $5 boarding rate
so, the rate is
\(\begin{gathered} \text{rate= boarding rate}+\text{cosper times} \\ reaplce \\ y=\text{ \$5+\$3x} \\ \text{reorder} \\ y=\text{ \$3x}+\text{\$5} \end{gathered}\)I hope this helps you
6x-18=51 solve for x
Answers
6x=51+18
6x=69
divide both sides by 6
6x divide by 6 and 69 divide by 6
x=11.5
Answer:
11.5
Step-by-step explanation:
add 18 to both sides
divide by 6
How many times could you expect to roll a number that is not 5 if you rolled a standard die 360 times?
Answers
The number of times I would expect to roll a number that is not a 5 is 300 times.
What is the number of times a 5 won't be rolled?A standard die has 6 faces. There are 5 numbers that are not 5 on a standard die. They are 1, 2, 3, 4, 6.
The number of times a 5 won't be rolled = (5/6) x 360
5 x 60 = 300 times
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Pls help me !!!!!
Find the value of x. Then classify the triangle.
Answers
Answer:
6.
x = 13 isosceles
7.
x= 60 equilateral
Step-by-step explanation:
6.
154 + 13 = 167
180 - 167 = 13
x = 13 degrees
7. 180 / 3 = 60
Mallory will donate 1 7/ 10% of her income at the end of the year to charity. Mallory’s employer will match her donations by donating 3/4% of her income to the same charity.
Answers
Mallory would donate $1,335.25 to charity
What is the equivalent of 1 7/10% in decimals?
In the first place, 7/10% is the same as 0.70% when added to 1%, it becomes 1.70% and the match-up donation is 0.75% (i.e 3/4%) is the portion of her Income that the employer would contribute to the charity in addition to Mallory's contribution.
Mallory's contribution=1.70%*$54,500
Mallory's contribution=$926.50
The employer's contribution which is 0.75% of her salary is determined thus:
employer's matchup contribution=0.75%*$54,500
employer's matchup contribution=$408.75
In essence, the total amount that she would donate to charity, hers and employer's is the sum of $926.50 and $408.75
total donation to charity=$926.50+ $408.75
total donation to charity=$1,335.25
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Full question:
Mallory will donate 1 7/ 10% of her income at the end of the year to charity. Mallory’s employer will match her donations by donating 3/4% of her income to the same charity.. If Mallory earned $54,500 this year how much
will she donate to charity?
for a standard normal distribution, find: p(-1.62 < z < 2.01)
Answers
The probability of the interval -1.62 < z < 2.01 in a standard normal distribution is approximately 0.9262 or 92.62%.
In a standard normal distribution, the mean is 0 and the standard deviation is 1. The z-score represents the number of standard deviations a data point is from the mean. To find the probability of a specific interval, we calculate the area under the curve between the corresponding z-values.
Given the interval -1.62 < z < 2.01, we need to find the area under the standard normal curve between these two z-values. This can be done using a standard normal distribution table or by using a statistical software or calculator.
By looking up the z-values in the table or using software, we find the corresponding probabilities: P(z < -1.62) = 0.0526 and P(z < 2.01) = 0.9788.
To find the probability of the interval -1.62 < z < 2.01, we subtract the probability of the lower bound from the probability of the upper bound: P(-1.62 < z < 2.01) = P(z < 2.01) - P(z < -1.62 = 0.9788 - 0.0526 = 0.9262.
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Given the following functions, find each of the values: f(x)=x^2 − 4x − 12
g(x)=x−6
(f+g)(−2)= __________ (f−g)(2)= __________
(f . ⋅g)(0)= __________
(f/g)(−1)= __________
Answers
The values of (f+g)(-2), (f-g)(2), (f . ⋅g)(0), and (f/g)(-1) are -8, -12, 72, and 1, respectively, the functions f(x) and g(x) are given as follows f(x) = x^2 − 4x − 12 and g(x) = x−6.
To find the value of (f+g)(-2), we simply evaluate f(-2) and g(-2) and add the results.
f(-2) = (-2)^2 - 4(-2) - 12 = 4
g(-2) = -2 - 6 = -8
Therefore, (f+g)(-2) = 4 + (-8) = -4.
The other values can be found similarly. For example, to find the value of (f-g)(2), we evaluate f(2) and g(2) and subtract the results.
f(2) = 2^2 - 4(2) - 12 = -8
g(2) = 2 - 6 = -4
Therefore, (f-g)(2) = -8 - (-4) = -4.
The complete results are as follows:
(f+g)(-2) = -4
(f-g)(2) = -4
(f . ⋅g)(0) = 72
(f/g)(-1) = 1
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The shadow length
of the factory
chimney is 32.5 m,
and the shadow
length of a nearby
pole with a height of
2.4 m is 2.72 m.
Calculate the height
of the chimney.
Answers
Answer:
18.2
Step-by-step explanation:
32.5÷2.72=11.9
32.5-11.9=20.6
20.6-2.4m=18.2
y varies inversely with x. y=15 when x=10, find y when x=5
Answers
=
25
Explanation:
y
=
k
x
;where
x
and
y
are variables and
k
is constant
or
5
=
k
10
or
k
=
5
(
10
)
or
k
=
50
So Equation becomes
y
=
50
x
When
x
=
2
y
=
50
2
or
y
=
25
Midge makes six payments each year of $115 for her auto insurance. Howmuch must she budget weekly to cover this fixed expense?a. $14.38b. $19.17C. $27.13d. $13.27
Answers
Given
Six payments each year
$ 115
Procedure
If 6 payments are made in one year then each payment is made every two months.
We now know that a year has a total of 52 weeks.
Therefore, the monthly budget should be as follows:
\(\begin{gathered} W_b=\frac{6\cdot115}{52} \\ W_b=13.27\text{ } \end{gathered}\)The answer would be $13.27
Help me with this!!!
Answers
A right triangular prism and its net are shown below.
(All lengths are in centimeters.)
Answers
Answer:
A=4
B=8
C=6
D=10
SA=208
Surface area=bh+(s1+s2+s3)H
=6×8+(4+6+10)(8)
=208
Step-by-step explanation:
Answer:
Step-by-step explanation:
In a survey 34% of population was found to know hindi 46% to know english and 23% to know both languages.What is the percentage of those knowing neither hindi nor english
Answers
The percentage of population of those knowing neither Hindi nor English is 43%.
What is percentage?The outcome of multiplying a given number by a percentage is the percentage. Since a percentage is a portion of a number or quantity, they are typically smaller than the actual number. There are instances, though, where the percentage exceeds the number. If the percentage is greater than 100%, this would occur.
A percentage is simply a certain proportion of a number.
Typically, the phrase "percent of" comes after the quantity.
So, 70% of 50 is 35, for instance.
50 is the quantity, 35 is the percentage, and 70% is the percent in this sentence.
The total percentage of population is represented by 100%, so let the population be 100
No. of population that knows only Hindi = 34 - 23
= 11
No. of population that knows only English = 46 - 23
= 23
No. of population that knows both = 23
The sum = 11 + 23 + 23
= 57
No. of population that knows neither Hindi nor English = 100 - 57
= 43
And percentage = 43%
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after fitting a linear regression model to a dataset, the model's slope and intercept are -3 and 0 respectively. now, if we change our independent variable by adding 4.5 units to x, what is the absolute value of the change in the predicted value of dependent variable y?
Answers
The absolute value of change in the predicted value of dependent variable Y is 18.
Any variable whose value is influenced by an independent variable is said to be dependent. The thing that is measured or assessed in an experiment or mathematical equation is the dependent variable. The phrase "the outcome variable" is another name for the dependent variable.
Slope = b = -4
Intercept = a = -2.8
So, the equation of the regression line is
y = a + bx
y = -2.8 - 4x ...Equation 1
Now suppose the value of x is changed by adding 4.5
i.e. put x = x + 4.5
So,
y = -2.8 - 4(x + 4.5)
y = -2.8 -4x - 18 ...Equation 2
Comparing 1 and 2 ,
We get the predicted value of dependent variable Y as 18
Therefore The absolute value of change in the predicted value of dependent variable Y is 18
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55.563 the nearest hundredth
Answers
Answer:
55.56
Step-by-step explanation:
If its 5 or mor add one more if its four or less let it rest
Write
(4-√√
√5)(4+√√5
2√11
where a and b are integers.
a =
b
Find the values of a and b.
a=
b=
Answers
Answer:
The expression given as (4-√5)(4+ √ 5) + 2√11 when rewritten is 11 + 2√11
How to rewrite the expression
From the question, we have the following parameters that can be used in our computation:
(4-√5)(4+ √ 5)
2√11
Rewrite the expression properly
So, we have the following representation
(4-√5)(4+ √ 5) + 2√11
Apply the difference of two squares to open the bracket
This gives
(4-√5)(4+ √ 5) + 2√11 = 16 - 5 + 2√11
Evaluate the like terms
So, we have the following representation
(4-√5)(4+ √ 5) + 2√11 = 11 + 2√11
Hence, the solution of the expression is 11 + 2√11
Step-by-step explanation:
For what type of triangle is the orthocenter always a vertex of the triangle?
Answers
Answer:
A.) Right triangle
Step-by-step explanation:
In a right triangle, the altitude from each acute angle coincides with a leg and intersects the opposite side at (has its foot at) the right-angled vertex, which is the orthocenter.
Answer:
right triangle
step explanation:
In a right triangle, the altitude from each acute angle coincides with a leg and intersects the opposite side at (has its foot at) the right-angled vertex, which is the orthocenter. The altitudes from each of the acute angles of an obtuse triangle lie entirely outside the triangle, as does the orthocenter H.
have a great day / night
also so may i have brainlst it will be my first one ever but if not thats fine as well
Oct 24, 6:34:22 PM
Write two numbers that multiply to the value on top and add to the value on botton
42
-17
Answers
14 and 3 are two numbers for multiplication and addition.
What is multiplication ?
The four fundamental operations in mathematics are addition, subtraction, division, and multiplication. In mathematics, multiply refers to the repetitive addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two groups of this nature, and each group has ice cream.Multiplying in math is equivalent to adding like groups. The number of items in the group grows as we multiply. An example of a multiplication problem would be the product and the two factors. The factors and the product in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, respectively.The two numbers are 14 and 3.
14 + 3 = 17
14 * 3 = 42
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Help plss my math thinking are going away and plss explain:A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280 pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad?
Answers
Answer:
40
Step-by-step explanation:
Let's call blueberries, raspberries, grapes and cherries b, r, g, and c respectively. We can write:
b + r + g + c = 280 (1)
r = 2b (2)
g = 3c (3)
c = 4r (4)
We can plug (2) into (1) to get b + 2b + g + c = 280. Then, we can re-write (4) into r = c / 4 and plug that into (2) which gets us c / 4 = 2b, and when we re-write that we get c = 8b (5). Let's plug that into (1) to get b + 2b + g + 8b = 280. Next, we'll re-write (3) to get g / 3 = c, and we can plug that into (5) to get g / 3 = 8b so then g = 24b and plug that into (1) to get b + 2b + 24b + 8b = 280 → 35b = 280 → b = 8. We can plug this into (5) to get c = 8 * 5 = 40. Hope this helps!
Can you guys help me with this problem
It’s in the picture
Answers
Answer:
74
Step-by-step explanation:
Answer:
do length x with for both shapes then add together
Step-by-step explanation:
hope this helps
Triangle CDE is translated down into the right forming triangle C’D’E’. Which congruency statement is correct?
Answers
Answer:
B: DCE=D'C'E'
I hoped this helped you!
The required Triangle DCE is congruent to triangle D'C'E'. Option B is correct.
What is congruent geometry?In geometry, two figures are congruent if they have the same shape and size, and all their corresponding parts (sides, angles, and vertices) are congruent. Congruent figures can be moved, rotated, or reflected without changing their shape or size.
Here,
Triangle DCE is congruent to triangle D'C'E'.
This is because a translation is a type of transformation that preserves the shape and size of the original figure, so the two triangles are congruent with each other.
Thus, the required Triangle DCE is congruent to triangle D'C'E'. Option B is correct.
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PLEASE HELP!! I need all the work shown please!!
APH hows the heart rate of a runner during a 4 minute interval.
Please describe the following:
1. The range of the runner's heart rate
2. The intervals where the runner's heart rate is increase
3. The interval where the runner's heart rate is decreasing.
4. The interval where the runner's heart rate is staying the same.
5. Create an equation to represent the linear portions between 2 and 3 minutes AND the range between 3 and 4 minutes.
6. Explain what you think is happening to cause these changes in heart rate.
Please explain all steps and show all work!
Answers
Answer:
1- The range of the runner's heart rate is 60 to 110.
2- The interval where the runner's heart rate is increasing is from second 0 to second 2.
3- The interval where the runner's heart rate is decreasing is not mentioned in the given information.
4- The interval where the runner's heart rate is staying the same is from second 2 to second 4.
5- To create an equation to represent the linear portions between 2 and 3 minutes, we need to first determine the slope of the line. The slope is the change in heart rate (y-value) divided by the change in time (x-value). In this case, the change in heart rate is 80 - 60 = 20 and the change in time is 2 - 0 = 2. Therefore, the slope of the line is 20/2 = 10.
To find the equation of the line, we can use the point-slope form of a linear equation, which is: y - y1 = m(x - x1). In this case, y1 is the starting heart rate of 60 at time x1 = 0. Substituting these values into the equation, we get: y - 60 = 10(x - 0). Simplifying this equation, we get: y = 10x + 60.
To find the equation of the range between 3 and 4 minutes, we can use the same method. The starting heart rate at time x1 = 3 is 80 and the ending heart rate at time x2 = 4 is above 110. The change in heart rate is 110 - 80 = 30 and the change in time is 4 - 3 = 1. Therefore, the slope of the line is 30/1 = 30. Using the point-slope form of a linear equation, we get: y - 80 = 30(x - 3). Simplifying this equation, we get: y = 30x + 50.
6- It is difficult to determine what is causing the changes in heart rate without more information. Heart rate can be affected by many factors, including physical activity level, age, fitness level, and underlying medical conditions. It is possible that the runner's heart rate increased at the beginning of the interval due to the increased physical activity, and remained constant for the next two minutes because the activity level was sustained. The sudden increase in heart rate at the end of the interval could be due to a variety of factors, such as a burst of energy or a reaction to some external stimulus.
Simplify the expression 4( 3/2f+1)−7(f+5).
Please help!
Answers
Answer:
\(-f-31\) or \(-(f+31)\)
Step-by-step explanation:
Distribute,
6f+4-7f-35
Simplify
-f-31
Explanation-
You remove the parentheses and add like terms
What is the decimal equivalent to 5/8 inch
Answers
Answer:
0.625
Step-by-step explanation:
Find the value of x
Answers
Answer:
x=43 degrees
Step-by-step explanation:
The ratio of boys to girls in Ms. Cunningham’s class is 2 to 3. There are 18 girls in the class.
What is the total number of students in Ms. Cunningham’s class?
Answers
Answer:
30
Step-by-step explanation:
18 / 3 = 6
6 x 2 = 12
18 + 12 = 30
Shape 1 and shape 2 are plotted on a coordinate plane. Which rigid transformation can you perform on shape 2 to show that shape 2 is congruent to shape 1?
Answers
By using any of the above rigid transformations, you can show that shape 2 is congruent to shape 1.
What is coordinates?Coordinates are numerical values used to locate a point in space. They are usually expressed as a set of two or three numbers, called the x-coordinate, y-coordinate, and z-coordinate. The x-coordinate represents the point's location along the horizontal axis, the y-coordinate represents its location along the vertical axis, and the z-coordinate represents its location along the depth axis. Coordinates are used to locate specific points on maps and in other applications.
A rigid transformation is a transformation where the size and shape of the object remain unchanged. A translation, rotation, and reflection are all types of rigid transformations that can be used to show congruence between two shapes.
To show that shape 2 is congruent to shape 1, a translation can be performed. This is where both shapes are moved the same distance in the same direction. For example, if both shapes are moved two units to the right, the shapes remain unchanged and the relative position of each point in the shapes is preserved.
In addition to a translation, a rotation can also be performed. This is where both shapes are rotated the same angle around the origin. For example, if both shapes are rotated 90 degrees counterclockwise, they will remain unchanged and the relative position of each point in the shapes is preserved.
Finally, a reflection can be performed. This is where both shapes are reflected across a line or plane. For example, if both shapes are reflected across the line y=x, they will remain unchanged and the relative position of each point in the shapes is preserved.
By using any of the above rigid transformations, you can show that shape 2 is congruent to shape 1.
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