The customer had a 3-hour repair when paying $96 without a coupon.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
With a coupon, the customer paid $66 for a 3-hour repair.
The coupon gives a 40% discount on the inspection fee, so let's call the original inspection fee "x". Then the customer paid 0.6x + 14*3 = $66.
Solving for x, we get x = $30.
Without a coupon, the customer paid $96.
We want to find out how many hours of repair were done for $96.
Let's use a similar equation to solve for the number of hours:
Let's call the number of hours "h". Then the customer paid 30*0.6 + 14h = $96.
Solving for h, we get h = 3.
Therefore, the customer had a 3-hour repair when paying $96 without a coupon.
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Dont really understand. Algebra 1 class
The equation of line r is x = -3/2y + 5/2.
What is the equation of the line?A line's equation is typically expressed in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. A line's equation expresses the y coordinate of any point on the line in terms of its x coordinate. In other terms, a line equation is a formula that can be used to compute the y coordinate of any point on a line given its x coordinate.
In the given question,
The equation of line r is y = -1/3x + 7.
Line r is perpendicular to line q, so the slopes of the two lines must be opposite reciprocals of one another. The slope of line q is 3, so the slope of line r must be -1/3.
To find the equation of line r, we can use the point-slope formula. The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
In line r, (x1, y1) is (1, 3). The slope, m, is -1/3.
Substituting values into the point-slope formula, we have y - 3 = -1/3(x - 1).
Solving for y, we have y = -1/3x + 7.
This equation is written in slope-intercept form, which is the form y = mx + b, where m is the slope and b is the y-intercept.
In line r, the slope is -1/3 and the y-intercept is 7.
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Can someone help a stoned brotha out
4x-(6x+1)≤ 8x + 2(x-3)
Answer:
-1/6
Step-by-step explanation:
To solve the inequality 4x-(6x+1)≤ 8x + 2(x-3), we can simplify both sides of the inequality and isolate x on one side:
4x - (6x + 1) ≤ 8x + 2(x-3)
4x - 6x - 1 ≤ 8x + 2x - 6
-2x - 1 ≤ 10x - 6
Subtract 10x from both sides:
-12x - 1 ≤ -6
Add 12x to both sides:
-1 ≤ 6x
Divide both sides by 6:
-1/6 ≤ x
The solution to the inequality is x ≥ -1/6. This means that x is greater than or equal to -1/6, so any value of x that is greater than or equal to -1/6 will satisfy the inequality.
there is a severe shortage of critical care doctors and nurses to provide intensive-care services in hospitals. to offset this shortage, many hospitals, such as emory hospital in atlanta, are using electronic intensive-care units (eicus) to help provide this care to patients (emory university news center). eicus use electronic monitoring tools and two-way communication through video and audio so that a centralized staff of specially trained doctors and nurses - who can be located as far away as australia - can provide critical care services to patients located in remote hospitals without fully staffed icus. one of the most important metrics tracked by these eicus is the time that a patient must wait for the first video interaction between the patient and the eicu staff. consider the following sample of patient waiting times until their first video interaction with the eicu staff. click on the datafile logo to reference the data. wait time (minutes) 40 46 49 44 45 45 38 51 42 46 41 45 49 41 48 42 49 40 42 43 43 42 41 41 55 43 42 40 42 40 49 43 44 45 61 37 40 37 39 43 a. compute the mean waiting time for these patients (to decimals). 42.83 minutes b. compute the median waiting time (to decimals). 43 minutes c. compute the mode (to decimal). minutes d. compute the first and third quartiles (to decimals). first quartile: minutes third quartile: minutes
The mean waiting time for 40 patients is 44.10 minutes. The median waiting time is 43.5 minutes. The mode waiting time is 42 minutes.
The mean waiting time for these 40 patients is calculated by adding up all the waiting times and dividing by the number of patients, which gives:
(mean) = (46+49+40+44+45+45+38+51+45+42+46+41+41+48+42+49+49+40+43+42+41+43+42+41+55+43+42+40+42+40+49+43+44+45+61+37+49+40+42+43+43+42+41+41+55+43+42+40+42+40+49+43+44+45+61+37+43+40+37+39)/40 = 44.10
Therefore, the mean waiting time is 44.10 minutes.
To find the median waiting time, we first need to order the waiting times from lowest to highest:
37, 37, 38, 39, 40, 40, 40, 40, 41, 41, 41, 42, 42, 42, 42, 42, 43, 43, 43, 43, 44, 44, 45, 45, 45, 46, 46, 48, 49, 49, 49, 49, 51, 55, 55, 61, 61
We can see that there are 40 waiting times in this sample, which is an even number. The median is the average of the two middle values, which are 43 and 44. Therefore, the median waiting time is:
(median) = (43+44)/2 = 43.5
The median waiting time is 43.5 minutes.
The mode is the most common value in the data set. In this case, we can see that the waiting time of 42 minutes appears most frequently in the data set, occurring 6 times. Therefore, the mode waiting time is:
(mode) = 42
The mode waiting time is 42 minutes.
The first quartile (Q1) is the value below which 25% of the waiting times fall, and the third quartile (Q3) is the value below which 75% of the waiting times fall. To find these values, we first need to order the waiting times from lowest to highest (as we did in part b):
37, 37, 38, 39, 40, 40, 40, 40, 41, 41, 41, 42, 42, 42, 42, 42, 43, 43, 43, 43, 44, 44, 45, 45, 45, 46, 46, 48, 49, 49, 49, 49, 51, 55, 55, 61, 61
There are 40 waiting times in the data set, so to find the first quartile, we need to find the value below which 25% of the waiting times fall. This means we need to find the waiting time that is at the 25th percentile. We can do this by finding the index of the waiting time that is at the 25th percentile:
25th percentile = (25/100) * 40 = 10
This means that the waiting time at the 10th index in the ordered list is the value at the first quartile. In this case, the waiting time at the 10th index is 41 minutes.
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____ The given question is incorrect, the complete question is given below:
There is a severe shortage of critical care doctors and nurses to provide intensive care services in hospitals. To offset this shortage, many hospitals, such as Emory Hospital in Atlanta, are using electronic intensive care units (eICUS) to help provide this care to patients (Emory University News Center). eICUs use electronic monitoring tools and two-way communication through video and audio so that a centralized staff of specially trained doctors and nurses - who can be located as far away as Australia - can provide critical care services to patients located in remote hospitals without fully staffed ICUs. One of the most important metrics tracked by these elcus is the time that a patient must wait for the first video interaction between the patient and the eICU staff. Consider the following sample of 40 patient waiting times until their first video interaction with the eſcu staff. Click on the datafile logo to reference the data. DATA fill Wait Time (minutes) 46 49 40 44 45 45 38 51 45 42 46 41 41 48 42 49 49 40 43 42 41 43 42 41 55 43 42 40 42 40 49 43 44 45 61 37 49 40 42 43 43 42 41 41 55 43 42 40 42 40 49 43 44 45 61 37 43 40 37 39 a. Compute the mean waiting time for these 40 patients (to 2 decimals). minutes b. Compute the median waiting time (to 2 decimals). minutes c. Compute the mode (to 2 decimal). minutes d. Compute the first and third quartiles (to 2 decimals). minutes First Quartile: Third Quartile: minutes.
Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x
The constant of proportionality (r) in the equation y = rx represents the rate of change of y with respect to x, indicating the factor by which x and y are related.
The constant of proportionality (r) in the equation y = rx is simply the coefficient in front of the x term. In this case, r is the constant of proportionality, and it represents the rate at which y changes as x changes. In other words, it gives the relationship between x and y, such that y is directly proportional to x with a constant of proportionality of r.
So, in the equation y = rx, the value of r is the constant of proportionality.
In a direct proportion, if x increases, then y also increases, and if x decreases, then y decreases as well. The constant of proportionality (r) gives us the factor by which x and y are related.
For example, if y is equal to twice x (y = 2x), then the constant of proportionality (r) is 2. If x increases by 1 unit, y increases by 2 units, and if x decreases by 1 unit, y decreases by 2 units. The constant of proportionality in this case is 2.
In the equation y = rx, the variable x represents the input and y represents the output. The constant of proportionality (r) tells us how much y changes for a unit change in x. It can be thought of as the ratio of the change in y to the change in x. The constant of proportionality can also be expressed as the slope of a line that represents the relationship between x and y.
In summary, the constant of proportionality (r) in the equation y = rx gives us the factor by which x and y are related and represents the rate of change of y with respect to x.
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Which equation correctly represents the statement shown?
The value of t is 41 more than 24.
A.
t = 41 + 24
B.
t = 41 × 24
C.
24 = t ÷ 24
D.
41 = t − 24
Answer:
option A is the correct answer.
new flowers are being planted in a circular flwoer bed with a 14-foot diameter. if each flower requires 2 square feet of space, about how many flowers can be planted? (1 point) 308 flowers, 154 flowers, 77 flowers, 66 flowers
A total of 77 new flowers can be planted on the flower bed.
New flowers has to be planted in a circular flower bed that has a diameter of 14 ft.
Each one of the flower requires to square feet of the space.
The radius of the flower bed will be 7 feet.
The area of the flower bed can be calculated by using the formula,
A = πr²
Where r is the radius.
Put in the value of radius to find the area of the flower bed,
A = 3.14 x 7 x 7
A = 153.86 ft²
Now, let us say that N number of floors can be planted,
So,
N)(2) = 153.82
N = 76.93
So we can say that about 77 flowers can be planted on the flower bed.
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Solve for k:
k-
-
k =
I
96
Answer: look it up frfr
Step-by-step explanation:
for safety reasons, 5 different alarm systems were installed in the vault containing the safety deposit boxes at a beverly hills bank. each of the 5 systems detects theft with a probability of 0.82 independently of the others. the bank, obviously, is interested in the probability that when a theft occurs, at least one of the 5 systems will detect it. what is the probability that when a theft occurs, at least one of the 5 systems will detect it?
The probability that when a theft occurs, at least one of the 5 systems will detect it is approximately 0.9997.
How likely something is to occur is known as its probability. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
We can solve this problem using the complement rule. The probability that none of the 5 systems detect the theft is given by:
(1 - 0.82)^5 = 0.00033124
So the probability that at least one system detects the theft is:
1 - 0.00033124 = 0.99966876
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Find the inverse of the function. y = 2^x2 –4
Answer: The inverse of the function y = 2^x^2 - 4 is not a function because it is not a one-to-one function.
Step-by-step explanation:
The inverse of a function is a reflection of the original function over the line y = x. To find the inverse of the function y = 2^x^2 - 4, we need to switch the variables x and y and then solve for x.
y = 2^x^2 - 4
x^2 = log2(y + 4)
x = sqrt(log2(y + 4))
However, this expression is not the inverse of the original function because it is not a one-to-one function, meaning that the same output can have multiple inputs. For example, log2(10) = 3 and log2(14) = 3.5, so sqrt(log2(10)) = sqrt(3) = sqrt(log2(14)) = sqrt(3.5). This means that for y = 10, x can be either sqrt(3) or sqrt(3.5), which is not allowed in a function.
Therefore, the inverse of the function y = 2^x^2 - 4 is not a function.
(-8x²y²-27xy³ + 12x³y²)÷(−3x²y4)
Answer:
(- 12x ^ 2 + 8x + 27y)/(3x * y ^ 2)
Step-by-step explanation:
which expression is equal to 45 4 5 responses 4 x 15 1 5 4 x 1 fifth 4 x 51 5 1 4 x 5 over 1 5 x 14 1 4 5 x 1 fourth 5 x 41 4 1 5 x 4 over 1
Option A, which is 4 x 15 + 1 - 5 x 4 x 1, is the correct expression that is equal to 45 x 4 + 5.
To show this, we can simplify the expression as follows:
4 x 51 + 1 - 5 x 4 x 1
= 204 + 1 - 20
= 205 - 20
= 184
Then, we can check if 185 is equal to 45 x 4 + 5:
45 x 4 + 5
= 180 + 5
= 185
Since 185 is equal to 185, it is concluded that an expression that is "equal to" 45 x 4 + 5, is held by option A.
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SOMEBODY PLEASE HELP ME ASAP I WILL LOVE YOU FOREVER
By determining the value of x when y = 0, (x, 0), and the value of y when x = 0, respectively, the x-intercept and y-intercept are determined (0, y).
What is linear equation?A two-variable equation with a line-shaped graph is referred to as a linear equation. A collection of coordinate plane points that are all the solutions to the linear equation make up the graph. If all of the variables have true numerical values, the equation can be graphed by first drawing a sufficient number of points to identify a pattern, then connecting those points to include all of the points.
A linear equation is represented in standard form as
Ax+By=C,A,B≠0
The equation for y must first be solved before you may graph a linear equation in its usual form.
The x-intercept is found by finding the value of x when y = 0, (x, 0), and the y-intercept is found by finding the value of y when x = 0, (0, y).
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how many 3-digit numbers have exactly one zero?
Answer:
162
Step-by-step explanation:
Whether the zero is in the ones position or the tens position, there are only 9 possibilities for each of the other two digits and they can occur (with possible repetition) in either order. That’s 81 for each zero position for a total of 162.
There are 171 three-digit numbers that have exactly one zero. The zero can be in either the tens or units places, yielding 90 and 81 possibilities respectively.
Explanation:To determine how many 3-digit numbers have exactly one zero, we need to consider the possible placements of the zero. A 3-digit number has three positions: the hundreds place, tens place, and units place. The zero cannot be in the hundreds place, as that would make it a 2-digit number. So, the zero can only have two possible positions: the tens or units place.
For each case:
The zero in the tens place: In this case, we have 9 options (1-9) for the hundreds place, 1 option for the tens place (0), and 10 options (0-9) for the units place. This gives 9 * 1 * 10 = 90 numbers.The zero in the units place: Similarly, we have 9 options for the hundreds place, 9 options (1-9) for the tens place, and 1 option for the units place (0). This gives 9 * 9 * 1 = 81 numbers.So, in total, we have 90 + 81 = 171 3-digit numbers with exactly one zero.
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Terrell decides to buy some strawberry jam for his grandmother at the Berrien County Farmer's Market. The jars are cylinders.
Terrel has enough money to either
buy one large jar has which has a diameter of 8 cm, and a height of 16 cm.
or
buy three small jars of jam which have a diameter of 6 cm, a height of 7 cm.
Which option will give him the most jam to give to his grandmother? Please explain your answer and your reasoning in complete sentences. Be sure to explain each step that requires a computation. Use key vocabulary like "volume of a cylinder."
Answer:
A large container is a better deal because for a large container the amount of jam per dollar is greater thank that in the three smaller containers.
Step-by-step explanation:
What is the volume of a cylinder?
The volume of a cylinder is given by -
V[c] = πr²h
Given is Terrel who has to buy either one large jar or three small jars of jam. A small jar has a diameter of 6 cm, a height of 7 cm, and costs $4. A large jar has a diameter of 8 cm, a height of 16 cm, and costs $12.
For one large container, its volume will be -
V[L] = πr²h = 22/7 x 4 x 4 x 16 = 804.56 cm³
Amount of jam per dollar = V[1] = 804.56 / 12 = 67.04 cm³
For three small containers, the total volume will be -
V[S] = πr²h = {22/7 x 3 x 3 x 7} x 3 = 594 cm³
Amount of jam per dollar = V[2] = 594 / 12 = 49.5 cm³
It can be seen that for a large container the amount of jam per dollar is greater than that in the three small container. Hence, a big container would be a better deal for Terrell.
Therefore, a large container is a better deal because for a large container the amount of jam per dollar is greater than that in the three small container.
Answer:
Step-by-step explanation:
buy one large jar has which has a diameter of 8 cm, and a height of 16 cm.
4 ×(1 × – 10–3) Evaluate the expression.
How many envelopes can be made from a sheet of paper measuring 324 cm by 172 cm, if
each envelope requires a piece of paper of size 18 cm by 12 cm?
Answer: 258 envelopes
Step-by-step explanation:
Pls help me help me fast
Answer:
Step-by-step explanation:
Part A
First find the measure of angle C which is 52° due to it being next to angle D
Next add 52 to angle B to get 142
Subtract 142 from 180 to get 38°
Angle A is 38°
Part B
The fourth option is correct
What is the area of the figure?
(NEED THE ANSWER ASAP. PLEASE DONT PUT ANYTHING NONSENSE OR I'LL REPORT U. THANK U FOR UR HELP)
The area of the given figure is 12 square meters
The given figure is a parallelogram
Parallelogram is a geometric figure that has both pair of opposites parallel sides and opposite sides are equal . Number of vertices and edges are four
The height of the parallelogram = 2 meters
The base length of the parallelogram = 6 meters
The area of the parallelogram = The height of the parallelogram × The base length of the parallelogram
Substitute the values in the equation
The area of the parallelogram = 2 × 6
Multiply the numbers
= 12 square meters
Therefore, the area is 12 square meters
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I have solved the question in general , as the given question is incomplete
The complete question is :
What is the area of the figure ?
Given f(x) = 5(x-6)³ + 4, classify each statement about f-1(x) as t
as true or false.
The point of symmetry on f-1 (x) is (4, 6).
The domain of f(x) is (-∞0, 4).
The graphs of f(x) and f(x) are reflections across the x axis.
The range of f-1(x) is (-∞, ∞).
The point of symmetry on f⁻¹(x) is (4, 6) which is false.
The domain of f(x) is (-∞, 4) which is false.
The graphs of f(x) and f(x) are reflections across the x-axis which is also false.
The range of f⁻¹(x) is (- ∞, ∞) which is true.
What is the inverse function?Let the function f is given as
y = m(x + a) + c
Then the inverse function of the function f will be given by swapping x with y and y with x.
The function is given below.
f(x) = 5(x - 6)³ + 4
The inverse function of the function f(x) is given as,
x = 5(y - 6)³ + 4
y = ∛[(x - 4) / 5] + 6
f⁻¹(x) = ∛[(x - 4) / 5] + 6
The graph of the function and inverse function is given below.
The point of symmetry on f⁻¹(x) is (4, 6) which is false.
The domain of f(x) is (-∞, 4) which is false.
The graphs of f(x) and f(x) are reflections across the x-axis which is also false.
The range of f⁻¹(x) is (- ∞, ∞) which is true.
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factors other than the independent variable may also act on the dependent variable. if these factors vary systematically with the independent variable, they are called:
Factors other than independent variables which may act on the dependent variable , when these factors vary systematically with independent variable they are known as confounds variables or extraneous variable.
Factor which is other than the independent variable and might produce an effect in the given experiment.Manipulation of independent variable which has an effect on the expressions dependent variable.Other variables which has impact on changing the dependent variables are known as extraneous variable.Extraneous variables are also known as confounding variables.Confounding variables or extraneous variables these are the factors which does not manipulate and are part of the given experiment.Therefore, factors which vary systematically with the given independent variable is called confounds variables or extraneous variable.
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i need help
schoology
question1
The measure <h = 45 degree, <g= 135 degree, <h = 55 degree and
<k = 125 degree.
What is Vertical Angles?When two lines converge, vertical angles are created. Because the angles are opposite one another, vertical angles are also known as vertically opposite angles. They are constantly on par.
Given:
As, from the Figure
<h + 135 = 180 (Linear Pair)
<h = 180 - 135
<h = 45
and, <g = 135 (Vertical Opposite Angle)
Now, <m + 125 = 180 (Linear Pair)
<m = 180 - 125
<h = 55
and, <k = 125 (Vertical Opposite Angle)
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2. Choose one of the pair of starting angles in the table below:: each table has () over them
(a = 50 degrees
y = 110 degrees )
(a= 30 degrees
b=70 degrees)
(c =30 degrees
y=120 degrees)
Please note you are only using 1 of the the selections above, and they will give different results
(a) What is the angle measurement of first unknown angle? Explain the angle relationship you used.
(b) What is the angle measurement of second unknown angle? Explain the angle relationship you used.
Hint: Remember to start with a relationship where you have one unknown.
Answer:
If A=30 and B= 70 the first unknown angle Y would be 100. When using the E.A.T (exterior angle theorem) you add the 2 remote interior angles to get the exterior angle. (Y)
Unknown angle 2 is a interior angle, so we know all 3 of the interior angles must equal 180.
30+70=100
180-100=80
C=80
Step-by-step explanation:
which of the following statements best explains the steps to solve the pair of equations graphically
y= -x+1
y=2x+4
The following statements best explains the steps to solve the pair of equations graphically is Option D.
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
The first equation is:
y = -x +1
so the slope is -1, and the y-intercept is +1.
The second equation is:
y = 2x +4
so the slope is 2, and the y-intercept is 4.
The slopes and intercepts are properly described in the last selection.
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The complete question:
A pair of linear equations is shown below:
y = -x + 1
y = 2x + 4
Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)
On a graph, plot the line y = -x + 1, which has y-intercept = -1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of
Intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept - 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of
intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = -2 and slope = 2, and write the coordinates of the point
of intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of
intersection of the two lines as the solution.
identify the zeros and asymptotes of
f(x)=
X²-9
x²-16
The zeros of f(x)= x²-9 is +3 and -3
The zeros of f(x) = x²-16 is +4 and -4
What are zeros and asymptotes?An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity. There are three types of asymptotes: vertical, horizontal and oblique. Vertical Asymptotes.
The zeros of a function are defined as the values of the variable of the function such that the function equals 0.
Therefore when f(x) =0
x²-9 = 0
x² = 9
x =√9
x = ±3
therefore the zeros of x²-9 is ±3
The vertical asymptote is 0 and horizontal asymptote is infinity.
x²-16 = 0
x² = 16
x = √16
x = ±4
the vertical asymptote is 0 and horizontal asymptote is infinity.
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when the temperature is 35°C there are 7 million bacteria. How many millions of bacteria are there when the temperature is 38°C 
The number of millions of bacteria when the temperature is 38°C is 7, 600, 000 bacteria
What is proportion?Proportion can simply be defined as a mathematical comparison of numbers.
The different types of proportion in mathematics are;
Direct ProportionInverse ProportionCompound ProportionContinued ProportionFrom the information given, we have that;
When the temperature was 35 degree Celsius, the number was 7 million
Then, we have the representation given as;
35°C = 7, 000, 000
Then 38°C = x
cross multiply, we get;
x = 7, 000, 000 × 38/35
divide the values
x = 7, 600, 000 bacteria
Hence, the value is 7, 600, 000 bacteria
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round 0.1347 to the nearest tenth
The rounding off the value 0.1347 to the nearest tenth is 0.1
What is rounding off?
When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.
The act of rounding off is merely an estimation. Rounding off is the process of estimating an actual number to a close number.
Given, 0.1347 round to the nearest tenth
While rounding to the nearest tenth, the value after the digit has been noticed.
In the number 0.1347, rounding to the nearest tenth, digit 3 should play a role to round the digit 1 which is in the tenth position. 3 is not equal to 5 and less than 5.
So, 0.1347 becomes 0.1
Hence, the required answer is 0.1
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a dye is injected into the pancreas during a certain medical procedure. a physician injects 0.3 grams of the dye, and a healthy pancreas will secrete 4% of the dye each minute. predict the amount of dye remaining, to the nearest hundredth of a gram, in a healthy pancreas 30 minutes after the injection.
The estimated quantity of dye left in a healthy pancreas 30 minutes after the injection, rounded to the closest hundredth of a grams, is 0.07 grams.
As per the question given,
After the dye is injected, a healthy pancreas will secrete 4% of the remaining amount of dye each minute. Let's use exponential decay to model the amount of dye remaining in the pancreas over time.
The amount of dye remaining after t minutes can be expressed as:
R(t) = 0.3 * (1 - 0.04)^t
We want to find the amount of dye remaining after 30 minutes, so we can substitute t=30 into the equation and calculate:
R(30) = 0.3 * (1 - 0.04)^30
R(30) = 0.3 * (0.96)^30
R(30) = 0.3 * 0.2312
R(30) = 0.0694
Rounding to the nearest hundredth of a gram, the predicted amount of dye remaining in a healthy pancreas 30 minutes after the injection is 0.07 grams.
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Answer:
0.09 g
Step-by-step explanation:
You want to know the amount remaining of 0.3 g of dye after 30 minutes if the amount decreases by 4% per minute.
Exponential functionThe amount can be modeled by the exponential function ...
q = a·b^t
where q is the quantity remaining, 'a' is the initial quantity, b is the growth factor per minute, and t is the number of minutes.
The growth factor is related to the growth rate by ...
b = 1 + growth rate
ApplicationHere, the growth rate is -4% per minute, so the growth factor is ...
b = 1 +(-0.04) = 0.96
The initial quantity is 0.3 grams, so the remaining quantity after 30 minutes is ...
q = 0.30·0.96^30 ≈ 0.08816 ≈ 0.09 . . . . grams
The amount of dye remaining after 30 minutes is predicted to be 0.09 g.
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Find the output, y, when the input, a, is 7
Answer: Y would be 4
If you look at the graph and find 7 on the x axis where the inputs are, you can see that if you go up, the only output for 7 is 4.
If five bags of mulch covers 32 square feet,
how many square feet could 16 bags cover?
Answer:
102.4 square feet
Step-by-step explanation:
1. divide 32 by 5 to find how much square feet one bag of mulch covers
2. multiply that number (6.4) by 16 to find how many square feet 16 bags of mulch would cover
Answer:102.4 ft
Step-by-step explanation: do the math 32/5 = 6.4 6.4x16=102.4 ft
