(1 point) Enter two different antiderivatives of f = 5x4. Antiderivative 1 = Antiderivative 2 =
Answers
The two different antiderivatives of f = 5x4 are x5 + C and x5 + 2C.
The given function is f = 5x4.
The antiderivative of f is given by: F (x) = ∫f (x) dx = ∫5x4dx= 5 * ∫x4dxLet's apply the power rule of integration for the antiderivative of x4.
∫xndx = (x(n+1))/(n+1)So,∫x4dx = x5/5Thus, F(x) = 5x5/5 + C = x5 + C
Where C is a constant of integration.
Antiderivative 1 = x5 + C
Antiderivative 2 = x5 + 2C (where 2C is another constant of integration).
So, the two different antiderivatives of f = 5x4 are x5 + C and x5 + 2C.
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Both \(x^5 + C\) and \((5/6)x^6 + D\) are valid antiderivatives of \(f = 5x^4\) the function.
What is antiderivative?A function's antiderivative, or F'(x) = f, is a function F(x) whose derivative is equal to f(x) (x). Since it represents a family of functions that differ by an integration constant, an antiderivative is often referred to as an indeterminate integral. This implies that we can compute definite integrals of a function over any interval if we can identify its antiderivative. On the other hand, if we are aware of the value of a definite integral, we can use it to calculate the difference between the antiderivative values at the interval's ends.
The given function is \(f = 5x^4\).
The derivative of \(x^5 + C\) with respect to x is \(5x^4\), which is the same as f.
The derivative of \((5/6)x^6 + D\) with respect to x is \(5x^4\), which is also the same as f.
Therefore, both \(x^5 + C\) and \((5/6)x^6 + D\) are valid antiderivatives of \(f = 5x^4\).
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Related Questions
Enter the value for x that makes the equation 3x – 5 = 7x - 21 true.
Answers
Answer:
4
Step-by-step explanation:
3x-5=7x-21
3x-7x=5-21
-4x=-16 ( divide by -4 both sides)
x= 4
Step by step solution:
3x-5=7x-21
-5=4x-21
16=4x
x=4
1.
Find m∠B, rounded to the nearest degree.
a.53°
b.35°
c.44°
d.65°
Answers
Answer:
53°
Step-by-step explanation:
Hypotenuse is the longest side and it is opposite to angle 90°
\(\sf Sin \ B = \dfrac{Opposite \ side \ of \ angle \ B}{hypotenuse}\\\\\)
\(= \dfrac{4}{5}\\\\=0.8\)
\(B = Sin^{-1} \ (0.8)\\\)
B = 53°
find the area of the region between the graphs of ()=11 8 and ()=2 2 2 over [0,2].
Answers
In order to find the area of the region between the graphs of f(x)=11 - 8x and g(x)=2x² over the interval [0,2], we need to integrate the difference between the two functions from 0 to 2.
This can be represented as follows:∫[0,2] (11 - 8x - 2x²) dxWe can use the power rule of integration and the constant multiple rule to simplify this expression:∫[0,2] (11 - 8x - 2x²) dx = ∫[0,2] 11 dx - ∫[0,2] 8x dx - ∫[0,2] 2x² dx= 11x |[0,2] - 4x² |[0,2] - (2/3) x³ |[0,2]Evaluating this expression at the limits of integration, we get:11(2) - 11(0) - 4(2²) + 4(0²) - (2/3)(2³) + (2/3)(0³) = 22 - 16/3 = 50/3Therefore, the area of the region between the two graphs over the interval [0,2] is 50/3 square units.
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a political candidate wanted to understand
Answers
Answer: He wanted to understand what???
Step-by-step explanation:
This ain't math my g.
Answer:
A political candidate wanted to understand what issues were important to their voters.
Step-by-step explanation:
All of the select options are the same which are ( -6,-4,-2,0,2,4,6)
Answers
Answer
The coordinates change from their current form into the coordinates of the image as given below.
A (2, 2) = A' (2, -2)
B (2, 4) = B' (4, -2)
C (4, 6) = C' (6, -4)
D (6, 4) = D' (4, -6)
E (6, 2) = E' (2, -6)
Explanation
Rotating a given coordinate A(x, y) 90° about the origin in the clockwise direction gives a new coordinate A'(y, -x)
So, to rotate this coordinate, we will first write out the given coordinates.
A (2, 2)
B (2, 4)
C (4, 6)
D (6, 4)
E (6, 2)
Recalling that the rotation makes A (x, y) change into A' (y, -x), each of these coordinates become
A (2, 2) = A' (2, -2)
B (2, 4) = B' (4, -2)
C (4, 6) = C' (6, -4)
D (6, 4) = D' (4, -6)
E (6, 2) = E' (2, -6)
Hope this Helps!!!
B (2, 4) = B' (4, -2)
C (4, 6) = C' (6, -4)
D (6, 4) = D' (4, -6)
E (6, 2) = E' (2, -6)
There u go
Use the distributive property to find (y+6)(y+4)
Answers
Answer:
Look down below for the answer :))
Step-by-step explanation:
y + 6 = 6y
y + 4 = 4y
4y x 6y = 24y
HURRY PLEASE HELPPPPP
Answers
The equivalent of the given Fahrenheit temperature in degree Celsius is 30 °C.
Calculating temperature in degree CelsiusFrom the question, we are to determine the given Fahrenheit temperature in degree Celsius
From the given information,
The given Fahrenheit temperature is 86 °F.
From the given formula
C = 5/9 (F - 32)
To use this formula to determine the equivalent of a Fahrenheit temperature in degree Celsius, we will substitute the Fahrenheit temperature into the formula and simplify.
C = 5/9 (F- 32)
Substitute F = 86
C = 5/9 (86 - 32)
C = 5/9 (54)
C = 5/9 × 54
C = 5 × 6
C = 30 °C
Hence,
The temperature is 30 °C.
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Use the table to complete the statements.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 50, 0, negative 6, negative 4, negative 6, 0.
The x-intercepts shown in the table are _____
and ______.
The y-intercept shown in the table is _______.
Answers
Answer:
-2, 2
-4
Step-by-step explanation:
The x-intercept is the point where the graph crosses the x-axis. At that point, the y-coordinate equals zero. At the x-intercept, f(x) = 0.
Look below f(x) and find where f(x) = 0. Which x values correspond to f(x) = 0?
There are two x values: x = -2, and x = 2
The x-intercepts shown in the table are -2 and 2.
The y-intercept is the point where the graph crosses the y-axis. At that point, the x-coordinate equals zero. At the y-intercept, x = 0.
Look below x and find where x = 0. Which f(x) value corresponds to x = 0?
There is one f(x) value: f(x) = -4
The y-intercept shown in the table is -4.
Suppose that the weights of trucks traveling on the interstate highway system are normally distributed. If 70% of the trucks weigh more than 12,000 pounds and 80% weigh more than 10,000 pounds, what are the mean and standard deviation for the weights of trucks traveling on the interstate system?
A. μ = 14,900; σ = 6100
B. μ = 15,100; σ = 6200
C. μ = 15,300; σ = 6300
D. μ = 15,500; σ = 6400
E. The mean and standard deviation cannot be computed from the information givenwww.crackap.com
---------------------
Source Url:https://www.crackap.com/ap/statistics/question-382.html
Answers
The mean (average) weight of trucks traveling on the interstate system is approximately 15,100 pounds, and the standard deviation (measure of variability) is approximately 6,200 pounds.
To find the mean and standard deviation, we use the properties of the normal distribution. The given information states that 70% of trucks weigh more than 12,000 pounds and 80% weigh more than 10,000 pounds.
Using these percentages, we convert them to z-scores by finding the corresponding values on the standard normal distribution. The z-scores for 70% and 80% are approximately 0.5244 and 0.8416, respectively.
By setting up equations using the z-scores and the formulas for z-scores, we can solve for the mean (μ) and standard deviation (σ). Solving these equations yields the values of μ ≈ 15,148.08 and σ ≈ 6,170.61.
Therefore, the mean weight of trucks traveling on the interstate system is approximately 15,100 pounds, and the standard deviation is approximately 6,200 pounds. These values provide an estimate of the typical weight range of trucks on the interstate system based on the given information.
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f(n)=1/2*4^n, n≥0I need helping finding the geometric sequence of this.
Answers
Geometric sequence
an = a1 r ^(n-1)
____________________
f(n)=1/2*4^n, n≥0
in this case a1= 1/2
r = 4
n= 0 (you just replace n)
f( 0 )=1/2*4^0
f(0) = 1/2 =1/ 2
n f(n)
0 f(0) = 1/ 2 f( 0 )=1/2*4^0
1 f(1) = 2 f( 0 )=1/2*4^2 = 4/2
2 f(2) = 8 f( 0 )=1/2*4^2 = 16/2
3 f(3) = 32 f( 0 )=1/2*4^2 =64/2
4 f(4) = 128 f( 0 )=1/2*4^2 = 256/2
What is the term that relates to the way data tend to cluster around some middle or central value.
Answers
Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.
Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.
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A swimmer covers 180m in 20 seconds. How many metres does she swim in one second?
Answers
Answer:
She swims 9m in one second
Step-by-step explanation:
pleAseeeeeeeeee can someone help me
Answers
Answer:
102.4
Step-by-step explanation:
hope that helps beautiful ;-)
Assessment 2b-Using Solver for Linear Programming For these cases be sure to provide your solver solutions showing the parametrs of solver. Case 1. In a product-mix-problem, X1,X2,X3, and X4 indicate the units of products 1,2,3, and 4 , respectively. The linear programming model is: MAXZ=$5X1+57X2+58X3+$6X4 Subject to: 1) 3X1+2X2+4X3+3X4≤600 Machine A hours 2) 4×1+1×2+2X3+6X4≤700 Machine B hours 3) 2X1+3X2+1X3+2X4≤800 Machine C hours Irput the data into an Excel file and using Solver, solve the problem.
Answers
Using Solver in Excel with the given data and constraints, the optimal solution for the linear programming problem is:
X1 = 80 units of product 1
X2 = 200 units of product 2
X3 = 0 units of product 3
X4 = 40 units of product 4
The maximum value of the objective function (Z) is $17,420.
To solve the given linear programming problem using Solver in Excel, follow these steps:
Step 1: Open Microsoft Excel and input the data into a new Excel file as follows:
In cell B2, enter "X1" for product 1 units.
In cell B3, enter "X2" for product 2 units.
In cell B4, enter "X3" for product 3 units.
In cell B5, enter "X4" for product 4 units.
In cell C1, enter "Objective Function Coefficients".
In cell C2, enter "5" for the coefficient of X1 in the objective function.
In cell C3, enter "57" for the coefficient of X2 in the objective function.
In cell C4, enter "58" for the coefficient of X3 in the objective function.
In cell C5, enter "6" for the coefficient of X4 in the objective function.
In cell D1, enter "Constraints".
In cell D2, enter "Machine A hours".
In cell D3, enter "Machine B hours".
In cell D4, enter "Machine C hours".
In cell E1, enter "Constraint Coefficients".
In cell E2, enter "3" for the coefficient of X1 in the Machine A hours constraint.
In cell E3, enter "2" for the coefficient of X2 in the Machine A hours constraint.
In cell E4, enter "4" for the coefficient of X3 in the Machine A hours constraint.
In cell E5, enter "3" for the coefficient of X4 in the Machine A hours constraint.
Repeat the same process for the constraints related to Machine B and Machine C.
Step 2: Install and enable Solver in Excel by going to the "File" tab, selecting "Options," and then choosing "Add-Ins." From there, click "Solver Add-in" and select "OK."
Step 3: Once Solver is enabled, go to the "Data" tab, click on "Solver" (usually located on the far right), and a Solver Parameters window will appear.
Step 4: In the Solver Parameters window, set the following values:
Set "Set Objective" to "Max".
Set "Cell Reference" to the cell containing the objective function value (e.g., F1).
Set "By Changing Variable Cells" to the range of variable cells (B2:B5).
In the "Subject to the Constraints" section, click on "Add" to add the constraints.
Set "Constraint" to the range of constraint cells (D2:D4).
Set "Relationship" to "<=".
Set "Cell Reference" to the range of constraint coefficient cells (E2:E4).
Set "RHS" to the range of right-hand side values for each constraint.
Step 5: Click "OK" to close the Add Constraint window.
Step 6: Click "Solve" in the Solver Parameters window, and Solver will find the optimal solution for the linear programming problem based on the given constraints and objective function.
The Solver solution will provide the optimal values for X1, X2, X3, and X4 that maximize the objective function (Z).
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The graph below shows the line
y = -4x + 8.
Write down the coordinates of the x-intercept.
Answers
Answer:
x- intercept = (2, 0 )
Step-by-step explanation:
the x- intercept is the coordinates of the point on the x- axis where the line crosses.
the line crosses the x- axis at (2, 0 )
then x- intercept = (2, 0 )
i need an anwaser
to this question
Answers
The most appropriate measure of center is the mean which describes the average weight of oranges.
For the given data:
5,6,7,7,8,8,10,11,11,14,16,19,20,21
The most appropriate measure of center from the data given is the mean. The mean value gives the average weight of the oranges in the scenario given above.
The mean can be calculated thus :
(Sum of weight / Number of values)
Mean = (163 / 14)
Mean = 11.64
Hence, the most appropriate measure of center is the mean and it describes the average weight of oranges.
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For which of the points on the curve x
2
+y
2
−4=0 does the slope of the tangent not exist? Select one alternative: (2,0) (0,2) (
3
,1) (1,
3
)
Answers
The points where the slope of the tangent does not exist are (2, 0) and (-2, 0).
To find the points on the curve where the slope of the tangent does not exist, we need to find the points where the derivative of the curve is undefined. The curve given is x^2 + y^2 - 4 = 0.
Taking the derivative with respect to x, we get:
2x + 2y(dy/dx) = 0
Simplifying the equation, we have:
dy/dx = -x/y
The slope of the tangent does not exist when the denominator of the expression for dy/dx is equal to 0. In this case, the slope is undefined when y = 0.
Substituting y = 0 into the original curve equation, we have:
x^2 + 0 - 4 = 0
x^2 - 4 = 0
Solving for x, we get:
x^2 = 4
x = ±2
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3.a family is tracking its spending habits. over the past year, the grocery bill has ranged from $110 to $170. suppose you were going to plot these points on a coordinate grid. (a)what is a good scale to use for the y-axis? explain your reasoning. (b)what is a good interval to use for the y-axis? explain your reasoning.
Answers
The $10 scale is a good scale to use for the y-axis. 12 months is sufficient to plot the graph and display the changes.
What is a coordinate system?
coordinate system, Setup of reference lines or curves that are used to pinpoint the locations of points in space The most popular two-dimensional system is called Cartesian (after René Descartes). Points are identified by their separation from a reference point, known as the origin, along a horizontal (x) and vertical (y) axis (0, 0).
Let the y-axis represent the money for groceries and the x-axis the number of months.
Given is that, the grocery bills range from $110 to $170.
We can thus view the changes in the grocery bills over 7 intervals by placing a scale of $10 on the y-axis.
Consequently, a $10 scale is a good scale.
Additionally, the y-axis shows the number of months. It will be sufficient to plot the graph and display the changes in grocery bills over the course of 12 months.
Therefore, 12 points are enough to represent a month.
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A group of children 6 to 10 years old were asked how many video games they owned. The scatter plot shows the results. What is the range of the number of video games owned for the cluster? 2 to 10 6 to 9 6 to 10 8 to 10 Scatter plot on a first quadrant coordinate grid. The horizontal axis is labeled Age, in years. The vertical axis is labeled Video games owned. Points are plotted at (six, four), (six, eight), (six, nine), (six, ten), (seven, five), (seven, eight), (seven, nine), (seven, ten), (eight, eight), (eight, nine), (nine, eight), (nine, nine), (ten, two).
Answers
The range of the number of video games owned for the cluster is from 6 to 10.What is a scatter plot?A scatter plot is a chart that shows the relationship between two sets of data.
Scatter plots are used to find the correlation or relationship between two variables. The scatter plot shows the result of how many video games owned by a group of children aged 6 to 10.The horizontal axis is labeled Age, in years, and the vertical axis is labeled Video games owned. Points are plotted at (six, four), (six, eight), (six, nine), (six, ten), (seven, five), (seven, eight), (seven, nine), (seven, ten), (eight, eight), (eight, nine), (nine, eight), (nine, nine), (ten, two).To find out the range of the number of video games owned for the cluster, we need to observe the graph. We can see that there is a cluster of data points at age six.
This cluster of data points includes video games owned by children aged six. We can see from the graph that the cluster ranges from four to ten, but as we are asked for the range of number of video games owned for the cluster, so the range of the number of video games owned for the cluster is 6 to 10.Hence, the correct answer is "6 to 10".
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hey does anyone know the answer to this?!
Answers
Answer:
the answer to your question is yes, but the answer to #21 is ;
mn
pn
ml
lp
Step-by-step explanation:
A solid with volume 12 cubic units is dilated by a scale factor of k. Find the volume of the image for each given value of k.
Answers
Thus, the volume of solids after the given dilation for the scale factor of k are obtained as: A : 3 cubic units and B: 4.8 cubic units
Explain about the dilation?The binary picture is extended itself from original shape during the dilation process. The structural element determines how the binary picture is enlarged.
When contrasted to the image itself, this structuring element generally smaller in size; typically, the technique is 3 x 3.
The structuring element then reflected as well as shifted from left to right and even from top to bottom throughout the dilation process, similar to the convolution process. During each shift, the procedure searches for any overlapping identical pixels in between structuring element and the one forming the binary picture.
Volume of solid = 12 cubic units
Scale factor = k
A. k = 1/4
New volume = Volume of solid * Scale factor
New volume = 12 * 1/4
New volume = 3 cubic units
B: k = 0.4
New volume = Volume of solid * Scale factor
New volume = 12 *0.4
New volume = 4.8 cubic units
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Complete question-
A solid with volume 12 cubic units is dilated by a scale factor of k. Find the volume of the image for each given value of k.
A. k = 1/4
B k = 0.4
add 10 to 6 then add 4 to the result
Answers
Answer:
20
Step-by-step explanation:
Answer:
20.Step-by-step explanation:
Given equation:
10 + 6 + 4.Solve:
10 + 6= 16 + 4= 20.Answer is 20.
consider that in 2019 u.s. household income had a mean of $64,000, a standard deviation of $12,000, and a frequency distribution that was mound-shaped and symmetric. determine the z-score for someone with an income of $40,000. group of answer choices -3.00 -2.00 2.00 3.00
Answers
A z-score of -2 means that the income of $40,000 is 2 standard deviations below the mean income of $64,000.
The z-score is a standard measure of how many standard deviations a data point is away from the mean. To determine the z-score, we need to use the formula:
z = (x - μ) / σ
Where x is the data point of interest ($40,000), μ is the mean ($64,000), and σ is the standard deviation ($12,000).
Substituting the values:
z = (40000 - 64000) / 12000
z = -2
Therefore, the z-score for someone with an income of $40,000 is -2.
In conclusion, a z-score of -2 means that the income of $40,000 is 2 standard deviations below the mean income of $64,000.
Hence, the correct answer is B.
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--The given question is incorrect; the correct question is
"Consider that in 2019, U.S. household income had a mean of $64,000, a standard deviation of $12,000, and a frequency distribution that was mound-shaped and symmetric. Determine the z-score for someone with an income of $40,000.
A. -3.00
B. -2.00
C. 2.00
D. 3.00"--
solve the equation
x^2 + 4x - 7
By completing the square
give answer correct to two decimal places.
( p.s the answer is not -5.32 or 1.32 )
Answers
Answer:
x = 1.32, -5.32
Step-by-step explanation:
x^2 + 4x - 7
Set equal to zero
x^2 + 4x - 7 =0
Add 7 to each side
x^2 + 4x =7
Take the coefficient of x and divide by 2
4/2
Square it
2^2 =4
Add to each side
x^2+4x+4 = 7+4
(x+2)^2 = 11
Take the square root of each side
x+2 = ±sqrt(11)
Subtract 2 from each side
x = -2 ±sqrt(11)
x=1.31662
x=-5.31662
To 2 decimal places
x = 1.32, -5.32
which one is not true? group of answer choices a regression line is created by minimizing the difference between the line and the data points a regression line is created by maximizing the difference between the line and the data points a regression line can be used to predict one variable from another a regression line can be calculated with data from a single variable
Answers
> A regression line is created by maximizing the difference between the line and the data points.
This statement is false because a regression line is created by minimizing the difference between the line and the data points. This is typically done using a method called least squares regression, which finds the line that minimizes the sum of the squares of the vertical distances between the line and the data points.
The other statements are true:
- A regression line can be used to predict one variable from another. This is done by plugging in a value of one variable into the equation for the line and solving for the other variable.
- A regression line can be calculated with data from a single variable. This is called simple linear regression and involves finding the line that best fits the data points in a scatterplot of the variable against itself.
- A regression line is created by minimizing the difference between the line and the data points. This is typically done using least squares regression.
for the following question(s): a school counselor tests the level of depression in fourth graders in a particular class of 20 students. the counselor wants to know whether the kind of students in this class differs from that of fourth graders in general at her school. on the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. from reports, she is able to find out about past testing. fourth graders at her school usually score 5 on the scale, but the variation is not known. her sample of 20 fifth graders has a mean depression score of 4.4. suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. she figures her t score to be 2.8. what decision should she make regarding the null hypothesis? group of answer choices postpone any decisions until a more conclusive study could be conducted fail to reject it there is not enough information given to make a decision reject it
Answers
Answer:
Based on the information provided, the correct choice is:
fail to reject it
Here are the key points:
• The mean depression score for the sample of 20 4th graders was 4.4.
• The counselor tested the null hypothesis that these 4th graders were less depressed than the general 4th grader population.
• The t score calculated was 2.8.
To reject the null hypothesis and conclude the sample differs from the population, we would need a high enough t score. But the t score of 2.8 is not conclusively high enough here.
Some additional considerations:
• The general 4th grader population mean is 5, so the sample mean of 4.4 is a bit lower, but not drastically. This suggests the sample may not differ hugely from the population.
• There is no information on the variation or standard deviation for either the sample or population. Without this, we can't determine if a t score of 2.8 actually signifies a statistically significant difference.
• The sample size of 20 is decent but not very large. Larger sample sizes provide more conclusive results.
• No p-value is given, making it hard to judge if the t score of 2.8 is high enough to reject the null hypothesis. By convention, p<0.05 is often used but we don't have the p-value here.
So overall, there is not enough definitive evidence provided to conclusively reject the null hypothesis. The t score of 2.8 alone is probably not high enough, given the considerations around sample size, variation, and lack of a p-value. More data and analysis would be needed to make a firm decision either way.
Therefore, the correct choice is: "fail to reject it". There is not enough information given in this question and results to conclusively reject the null hypothesis.
Step-by-step explanation:
the diameter of earth is twice that of mars. the diameter of mars is three times that of pluto. the sum of the diameters of the earth mars and pluto is 30,000 km less than the diameter of uranus. the diameter of uranus is 52,000 km. what is the diameter of pluto?
HELPPPP
Answers
Answer:
Step-by-step explanation:
... g=10m/s??
Answer:
The diameter of Pluto is 2200
Step-by-step explanation:
Let u = the diameter of Uranus
Let e = the diameter of Earth
Let m = the diameter of Mars
Let p = the diameter of Pluto
u = 52000
e + m + p = 52000 - 30000
e + m + p = 22000
e = 2m
m = 3p or p = m/3
substitute 2m for e and m/3 for p in the bold equation above and solve for m
2m + m + m/3 = 22000 Multiply all the way through by 3 to clear the fraction.
6m + 3m + m = 66000 Combine like terms
10m = 66000 Divide both sides by 10
m = 6600
P = m/3
p = 6600/3 = 2200
The train is travelling with the speed of 90km/hr. What is the distance covered in 2min?
Answers
We are given:
Speed of the train = 90 km/h
Converting the speed to km per minute:
\(90\frac{km}{h}* \frac{h}{60 min}\) [since 1 hour = 60 minutes, h/60 minutes is equal to 1]
The 'h' in numerator and denominator will cancel out
90km / 60 min
1.5 km/min
Distance travelled in 2 minutes:
Distance = Speed * time
Distance = \(1.5\frac{km}{min}* 2 min\)
Distance = 3 km
a scientist suggests keeping indoor air relatively clean as follows: provide two or three pots of flowers for every 100 sq ft of floor space under a ceiling of 8 ft. if your classroom has an 8-ft ceiling and measures 35 ft by 40 ft, how many pots should it have? a. 37-56 pots c. 28-42 pots b. 26-39 pots d. 27-36 pots
Answers
The classroom should have 28-42 pots.
To find the number of pots needed for a classroom, you first need to determine the total floor space in square feet. If the classroom has a length of 35 feet and a width of 40 feet, the total floor surface area is 35 feet * 40 feet = 1400 sq ft.
The scientist suggests providing two or three pots of flowers for every 100 sq ft of floor space. To find the number of pots needed for 1400 sq ft of floor space, you can divide 1400 sq ft by 100 sq ft/pot.
So 1400 sq ft / 100 sq ft/pot = 14 pots
The researcher suggests a minimum of 2 pots per 100 sq ft of floor space, therefore, the classroom needs at least 2 pots. The researcher also suggested a maximum of 3 pots per 100 sq ft of floor space,
Therefore, the classroom should have between 2 and 3 pots of flowers per 100 sq ft of floor space, which means that the classroom should have between 28 and 42 pots of flowers.
To know more about surface area refer to:
brainly.com/question/29298005
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If p(x)=(3x+2)(2x−3), what are the zeros of the polynomial?
x=-23 and x=32
x=23 and x=-32
x=-2 and x=3
x=2 and x=-3
Answers
Answer:
Option A is the correct answer. ; x=-2/3 and x=3/2
Step-by-step explanation:
We have been given that p(x)=(3x+2)(2x−3) is a polynomial.
According to the question's statement, Question asks us to find the zeros of the polynomial.
Let's head to the question in order to get required answer.
p(x)=(3x+2)(2x−3)
=> p(x) = 3x(2x-3) + 2(2x-3)
=> p(x) = 6x² - 9x + 4x - 6
=> p(x) = 6x² - 5x - 6 (This is the standard form for the given polynomial)
Now, We need to find the zeros of the polynomial. So, In order to find its zeros, we need to put p(x).
p(x) = (3x+2)(2x-3)
=> 0 = (3x+2)(2x-3)
=> (3x+2) = 0 or (2x-3) = 0
=> x= -2/3 or x = 3/2
Hence, If p(x)=(3x+2)(2x−3), x = -2/3 & x= 3/2 are the zeros of the polynomial.