Answers
A quadratic equation in standard form to represent the data in the table is as follows;
y = 0.5x² - 4x + 9
How to determine an equation of the line of best fit for the data?In order to determine a quadratic equation in standard form for the line of best fit that models the data points described above, we would use a scatter plot (graphing calculator).
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a quadratic equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the data set, a quadratic equation for the line of best fit is given by:
y = 0.5x² - 4x + 9
Read more on scatter plot here: brainly.com/question/28605735
#SPJ1
Related Questions
Help! ASAP!! figure rst on the graph is reflected over the y axis creating figure r's't'. figure r's't' is translated down 2 units and left 1 unit creating r"s"t". tyler knows rst = r's't' because reflections produce congruent figures. he also knows that r's't' = r"s"t" because translations produce congruent figures. what can tyler determine based on these two statements? check all that apply. 1. RST = R’’S’’T’’
2. RS = ST = TR
3. R = S = T
4. R = R’ = R’’
5. TS = T’S’ = T’’S’’
Answers
Reflections and translations do not guarantee that all corresponding sides of the figures will be equal.
What is translation and reflection?
The translation is when we slide a figure in any direction. Reflection is when we flip a figure over a line.
Based on these two statements, Tyler can determine the following:
1. RST = R’’S’’T’’
4. R = R’ = R’’
5. TS = T’S’ = T’’S’’
Tyler cannot determine that RS = ST = TR, because reflections and translations do not necessarily produce congruent figures. Similarly, Tyler cannot determine that R = S = T, because reflections and translations do not guarantee that all corresponding sides of the figures will be equal.
Hence, Reflections and translations do not guarantee that all corresponding sides of the figures will be equal.
To know more about Reflections and translations visit:
https://brainly.com/question/29615465
#SPJ1
The ratio of games lost to games won by
netball team is 2:3. The team has won 18
games How many games did they lose.
Answers
Answer:12
Step-by-step explanation:
the 7th-grade class wants to collect empty soda pop cans to earn $50.00. If pop cans earn $0.25 per pound how many cans will they need to collect to earn the $50.00?
Answers
200 pounds need to collect to earn the $50.00. Divide the cost per pound from the total amount needed, [tex]\frac{50.00}{0.25}[/tex]= 200 pounds.
Is the British pound?The official money of the U.k. and its regions is the GBP, or British pound sterling. The Pound is the earliest currency that is still accepted as legal tender in the entire world. The GBP, represented by pound sign (£), has one of the greatest trade volumes worldwide.
What makes something a "pound"?The development of the pounds sterling -The Latin word "libra," which means balance and weight, is where the name "pound sterling" comes from. During the years, the pound banknotes underwent various revisions before being initially printed by the Bank of England and over 300 years ago.
To know more about pound visit:
https://brainly.com/question/29181271
#SPJ1
based on the data in the graph, by approximately what percent did the sea ice decrease from 1980 to 2005 ?
Answers
Answer:
Step-by-step explanation:
Blood Pressure
The pressure P (in millimeters of mercury) against the walls of
the blood vessels of a patient is modeled by
P(t) = 100-20cos ((8•(pie))/3)
where t is time (in seconds).
1) Graph the model and state any important key features in
context of the problem. Period, Ascontops, Doman, Range. Amplitude
What does the period tell
2) What is the period of the model?
you about this situation? The Change
3) What is the amplitude of the model? What does it tell you
about this situation?
4) If one cycle of this model is equivalent to one heartbeat,
what is the pulse of this patient?
5) A physician wants this patient's pulse rate to be 64 beats
per minute or less. What should the period be? What
should the coefficient of t be?
6) what
ar Some ways we can use this
Function to help others/benefit
Society?
Explain.
Answers
The solution is, the correct option is, A.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
The translation of a sin function can be modeled by the form: P(t)=Asin(Bx+C)+D
Where:
A = the curve's amplitude (highest and lowest points)
The period = (2[pi])/ |B|
The phase shift (horizontal shift) = (-C)/B
D = vertical shift
By looking at the function we are given: P(t)=30sin(2[pi]t)+100,
We can see that the amplitude (the curve's highest and lowest points) = 30.
The phase shift (C) or in this case 't' = 0 (so there is no horizontal shift)
The period = 1
And D (the vertical shift) = 100
To learn more on function click:
brainly.com/question/21145944
#SPJ9
Use the graphs of f and g to find (fg)(−1).
Answers
Answer:
-1
Step-by-step explanation:
g(-1)=-1
348 hamburgers and cheeseburgers were sold on Tuesday. The number of cheeseburgers sold was 3 times the number of hamburgers sold. How many hamburgers were sold?
Answers
Answer:
There were 261 Cheeseburgers and 87 Hamburgers sold on Tuesday
Step-by-step explanation:
Let's write some equations where H=Hamburgers and C=Cheeseburgers:
1) H+C=348
2) C=3H
1) Substitute 3H as C in the first equation:
3H+H=348
2) Combine alike terms:
4H=348
3) Divide both sides by 4:
H=87
4) Now, substitute 87 as H in the first equation:
87+C=348
5) Subtract 87 from both sides:
C=261
The U.S. Department of Health and Human Services wants to know whether the healthcare system is achieving its goals in Virginia. Much information about healthcare comes from patient records, but that source doesn't allow us to compare people who use health services with those who don't. Therefore, the U.S. Department of Health and Human Services conducted the Virginia Health Survey, which was used to interview a random sample of 48,548 people who live in Virginia.
Part A: What is the population for this sample survey? What is the sample? (3 points)
Part B: Describe a method that could have been used to obtain the random sample. (3 points)
Part C: The survey found that 71% of individuals over age 25 and 88% of individuals ages 25 and younger in the sample had visited a general practitioner at least once during the past year. Do you think these estimates are close to the truth about the entire population? Explain. (4 points)
Answers
Answer:
Step-by-step explanation:
Part A: The population for this sample survey is all people who live in Virginia, and the sample is the random group of 48,548 people who were interviewed for the survey.
Part B: One method that could have been used to obtain the random sample is simple random sampling. This involves selecting individuals from the population at random, so that each person in the population has an equal chance of being selected. This can be done using a random number generator or by selecting names from a list of the population.
Part C: It's difficult to say whether the estimates are close to the truth about the entire population without more information about the survey methodology and potential sources of bias. However, assuming that the survey was conducted using sound sampling techniques and that the sample is representative of the population, it's possible that the estimates are reasonably accurate. Nevertheless, it's important to keep in mind that survey estimates always have some degree of sampling error, so the true population values could be slightly different from the survey results. Additionally, the survey may not capture people who don't have access to healthcare or who choose not to seek medical care, so the estimates may not be fully representative of the entire population.
Answer: Part A: The population for this sample survey is all people who live in Virginia, while the sample is the 48,548 people who were interviewed in the Virginia Health Survey.
Part B: One method that could have been used to obtain the random sample is simple random sampling. This involves randomly selecting individuals from the population using a random number generator or other randomization method to ensure that each member of the population has an equal chance of being selected. Another method could be stratified random sampling, which involves dividing the population into strata based on relevant characteristics (such as age or income), and then randomly selecting individuals from each stratum in proportion to their representation in the population.
Part C: It is difficult to determine whether these estimates are close to the truth about the entire population without additional information. However, if the sample was selected using appropriate sampling methods (such as simple random sampling or stratified random sampling) and had a large enough sample size, then the estimates are likely to be relatively accurate. The margin of error, which depends on the sample size and variability in the population, can also be calculated to provide an estimate of the range in which the true population value is likely to fall. Overall, the accuracy of the estimates will depend on the quality of the sampling method used, the size of the sample, and the representativeness of the sample in relation to the population.
Determine the z-critical value associated with each of the following confidence intervals. Hint: Using the link to the tool provided, select two tails and find the z-score associated with a certain probability (area in tails) corresponding to a particular confidence interval. For instance for a 80% confidence interval you would enter in a 0.20 area or probability because that is the area in the two tails. You can leave the mean as 0 and standard deviation as 1 in the tool when calculating z- critical values. Each z-critical value is rounded to 2 decimal places. https://www.webassign.net/csalt/index.html#/toolset/distributions A) A 99% confidence interval B) A 95% confidence interval C) A 90% confidence interval D) An 80% confidence interval
Answers
A) the z-critical value associated with a 99% confidence interval is 2.58. B) the z-critical value associated with a 95% confidence interval is 1.96. C) the z-critical value associated with a 90% confidence interval is 1.64. D) the z-critical value associated with an 80% confidence interval is 1.28.
Describe z- critical value?The z-critical value (or the critical z-value) is the number of standard deviations from the mean that corresponds to a given level of significance in a two-tailed z-test. It is used in statistical hypothesis testing to determine whether to reject or fail to reject the null hypothesis.
A) For a 99% confidence interval, the area in each tail is (1-0.99)/2 = 0.005. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:
z-critical value = 2.58
Therefore, the z-critical value associated with a 99% confidence interval is 2.58.
B) For a 95% confidence interval, the area in each tail is (1-0.95)/2 = 0.025. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:
z-critical value = 1.96
Therefore, the z-critical value associated with a 95% confidence interval is 1.96.
C) For a 90% confidence interval, the area in each tail is (1-0.90)/2 = 0.05. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:
z-critical value = 1.64
Therefore, the z-critical value associated with a 90% confidence interval is 1.64.
D) For an 80% confidence interval, the area in each tail is (1-0.80)/2 = 0.10. Using the provided tool and selecting "two tails", we can find the z-critical value associated with this probability:
z-critical value = 1.28
Therefore, the z-critical value associated with an 80% confidence interval is 1.28.
To know more about area visit:
https://brainly.com/question/30612393
#SPJ1
How do u solve this and whays the answer
Answers
Answer:
4095 yd³
What is volume of any figure?The volume of any figure is the total space enclosed inside of any figure. For example, the total space inside the cube is the volume of the cube. The formula to find the volume of a cube is (side)³ or (side)(side)(side) Please also note that volume is usually labelled in cubic units.
Discussing the PLAN to solve!Here, we are given a figure that is 3-dimensional. Therefore, the volume of this 3-dimensional figure must be in cubic units. We can also see that the figure has been split into two 3-dimensional figures. Thus, the sum of those divided 3-dimensional figures will result in the volume of the figure.
Finding the volume of the figure:Step-1) Find the volume of both 3-dimensional figures:
Volume of cuboid = Length × Width × Height
Volume of cuboid = 30 yd × 9 yd × 7 yd = 30 yd × 63 yd² = 1890 yd³Volume of trapezoidal prism = Area of base × Length
Volume of trapezoidal prism = (30 + 19)(10)/2 × 9 = (49)(45) = 2205 yd³Step-2) Add the volumes of both prisms.
Volume of figure = Volume of cuboid + Volume of trapezoidal prism
Volume of cuboid = 1890 yd³Volume of trapezoidal prism = 2205 yd³Volume of figure = 1890 yd³ + 2205 yd³ = 4095 yd³
Learn more about volumes: https://brainly.com/question/22907480
the function is increasing on the interval (s):
Answers
The function graphed above is:
Increasing on interval: (-3 0.5),
Decreasing on interval(s): (-∞ -3) and (0.5 ∞)
What is decreasing and increasing interval?
Real number intervals with growing and decreasing real-valued functions are referred to as increasing and decreasing intervals.
We apply the first-order derivative test to examine the sign of the derivative in each interval and identify the growing and decreasing intervals.
For the graph attached, the decreasing interval is
from negative infinity to -3 and
0.5 to positive infinity
While the increasing interval is from -3 to 0.5
Learn more about increasing interval at:
brainly.com/question/30460486
#SPJ1
Middle school students were asked whether they receive an allowance and whether they have a cell phone. The results are shown in the table.
cell phone No cell phone
Allowance 45 21
NO Allowance 35 49
What is the approximate percent of total students that receive no allowance and do not have a cell phone?
The outlined content above was added from outside of Formative.
23%
33%
47%
49%
Answers
The approximate percent of total students that receive no allowance and do not have a cell phone is this:
C. 47%
How to get the approximate percentageFirst, we are given some figures that stand for the number of students who receive no allowance and have no cell phones. We have to calculate the total number of students as follows:
45 + 21 + 35 + 49 = 150
The number of students who receive no allowance = 49
The number of students who have no cell phones =21
So, the percentage is = The Total number of students that receive no allowance and have no cell phones / Total number of students.
= 49 + 21 = 70
70/150 × 100
= 46.6%
Approximately this is 47%.
Learn more about approximation here:
https://brainly.com/question/28802280
#SPJ1
A speech class has five freshmen and four sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that at least four of the freshmen are standing next to each other?
Answers
The stated statement states that there are 360000 different ways to arrange them all in a line without any freshman standing close to one another.
What exactly is a standing position?Standing, also known as nov. 2, is a posture when the body is only supported by the feet while being held in an upright (orthostatic) position. The body moves slowly back and forth between the leg in the sagittal plane, although appearing to be immobile.
The total amount of ways they can position in a line without any further restrictions and the total amount of times they are standing in a line can both be included, but no undergraduates actually standing next to one another.
The answer we seek in accordance with the inclusion-exclusion principle is the difference between the two.
Furthermore take note of the phrase "Everyone is identifiable" in the issue, which suggests that "order matters."
The total number of configurations in which they can line up is the iteration of nine persons, which is:
P⁹ * 9 = 9! = 362880
The amount of different ways they can be in a line without standing close to one other is the next thing we take into account.
The sophomores will be taken into consideration initially. We have strategies for lining up the sophomores.
P⁴ * 4= 4! =24
But we haven't yet taken into account the freshman. Currently, we are not allowed to place two freshmen in front of or behind two sophomores, or between two freshmen. We shall take into account any location the freshman might possibly fit inside the line.
In the figure below, B stands for sophomores, and X for an open spot.
The line appears as follows once the sophomores have been taken into account:
X B X B X B X B X
Each freshman must move to an open area since no two undergraduates can fit in the exact same X place.
This is how the line will appear. (B stands for sophomores, G for freshmen)
G B G B G B G B G
The freshmen's order, however, has not been taken into account. They can be arranged in several ways.
P⁵ * 5 = 5!= 120 ways.
The number of sophomore arrangements and indeed the number of freshman arrangements are multiplied:
There are several methods to arrange them all in a line without any freshman standing near to one another.
Add it to the total variety of ways, and you'll have our needed response: 362880-2880=360000.
To know more about Standing visit:
https://brainly.com/question/26726050
#SPJ1
Which ordered pair is a solution to the system of inequalities shown on the graph?
Responses.
A(3, 3)
B (1, −2)
C (1, 2)
D(−2, 1)
Answers
Based on the graph, the point that is a solution to the system of inequalities is C(1,2).
What is inequality ?
An inequality is a mathematical statement that describes a relationship between two values or expressions that are not necessarily equal. Inequalities use symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) to compare the values or expressions.
The graph shows a system of linear inequalities. The shaded region represents the solution set of the system.
Therefore, Based on the graph, the point that is a solution to the system of inequalities is C(1,2).
To learn more about Inequality from given link.
https://brainly.com/question/30231190
#SPJ1
Type an equation for the
following pattern.
1
2
3
4
5
21/2
9
15/2 y = - x + []
3
?
6
9/2
Enter the number that belongs in the green box. Make sure
the fraction is in simplest form.
Answers
y = -3/2 x + 24. is the equation of the line in slope intercept form.
Equation of a line in point slope formThe formula for calculating the equation of a line in point slope form is expressed as:
y - y0 = m(x - x0)
where:
m is the slope
(x0, y0) is the point on the line
Using the coordinate points (2, 9) and (4, 6). The slope is calculated as:
Slope = 6-9/4-2
Slope = -3/2
The required equation will therefore be expressed as:
y - 9 = -3/2(x - 2)
2y - 18 = -3x + 6
2y = -3x + 24
y = -3/2 x + 24
Hence the slope-intercept form of the equation is y = -3/2 x + 24.
Learn more on equation of a line here: https://brainly.com/question/13763238
#SPJ1
b. 3 and b= b- Let A= Show that the equation Axb does not have a solution for some choices of b, and describe the set of all b for which Ax b does have a solution. -6 -2 How can it be shown that the equation Ax=b does not have a solution for some choices f b? O A. Row reduce the matrix A to demonstrate that A has a pivot position in every row. O B. Find a vector b for which the solution to Ax b is the identity vector. O C. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row. O D. Find a vector x for which Ax b is the identity vector. O E. Row reduce the augmented matrix o demonstrate that A bhas a pivot position in every row. A b Describe the set of all b for which Ax b does have a solution. b does have a solution is the set of solutions to the equation 0=2b, +b2. The set of all b for which Ax (Type an integer or a decimal.)
Answers
The way it can be shown that the equation Ax=b does not have a solution for some choices is A. Row reduce the matrix A to demonstrate that A has a pivot position in every row
How to solve thisA us 2 x 2 matrix, then Ax =b will not have a solution fot some B if rank(A) <2
This implies A does not have pivot position in every row in its reduced row echelon form.
This shows that option A is correct.
The augmented matrix [A b] is
[tex]\left[\begin{array}{ccc}1&4&b1\\3&-12&b2\end{array}\right][/tex]
Perform R2 = R2 +3 R1
[tex]\left[\begin{array}{ccc}-1&4&b1\\0&0&b2 = 3b1\end{array}\right][/tex]
New solutions exist if [tex]b_2 + 3b_i = 0[/tex]
0 = [tex]3b_1 + b_2[/tex]
Thus, the equation Ax = b have the solution if rank(A) = rank([A b])
Read more about matrices here:
https://brainly.com/question/94574
#SPJ1
Si una pelota más un bate cuesta 1.10 dólares su precio del bate es 1 dólar más que la pelota cuánto cuesta el bate.cuánto cuesta el bate?
Answers
Answer:
Step-by-step explanation:
If a ball plus a bat costs 1.10 dollars and the price of the bat is 1 dollar more than the ball, what is the cost of the bat?
If we represent the price of the ball as "p", then the price of the bat will be "p + 1", since the problem tells us that the price of the bat is 1 dollar more than the price of the ball.
We also know that the sum of the price of the ball and the bat is 1.10 dollars. We can write this as an equation:
p + (p + 1) = 1.10
Simplifying and solving for p, we get:
2p + 1 = 1.10
2p = 0.10
p = 0.05
Therefore, the price of the ball is 0.05 dollars. To calculate the price of the bat, we can add 1 dollar to the price of the ball:
p + 1 = 0.05 + 1 = 1.05
So, the price of the bat is 1.05 dollars.
What is the answer to this problem?
-4(x-5)+6(x+1)+4x-20+3x+12+-1(x-9)+-x-12+8-x+-2x+7(2x+1)=?
Answers
18x+30
Step-by-step explanation:
O think That's the answer...
Find non-invertible matrices A,B such that A+B is invertible. Choose A,B so that (1) neither is a diagonal matrix and (2) A,B are not scalar multiples of each other.A = [_____ _____][_____ _____]B = [_____ _____][_____ _____]
Answers
Matrices A and B are non-invertible matrices that can be added together to form an invertible matrix. To find these matrices, we can use the following steps:
Step 1: Choose a matrix A that is not a diagonal matrix and is not invertible. One example of such a matrix is
[tex]A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right][/tex]
Step 2: Choose a matrix B that is not a diagonal matrix, is not invertible, and is not a scalar multiple of matrix A. One example of such a matrix is
[tex]B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right][/tex]
Step 3: Add the matrices A and B together to form the matrix A+B. This matrix will be invertible, as shown below:
[tex]A+B = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]+\left[\begin{array}{ccc}0&0\\1&1\end{array}\right]=\left[\begin{array}{ccc}1&1\\1&1\end{array}\right][/tex]
Step 4: Verify that the matrix A+B is invertible by finding its determinant. The determinant of a 2x2 matrix is given by:
det(A+B) = (1)(1) - (1)(1) = 0
Since the determinant of the matrix A+B is not equal to zero, the matrix is invertible.
Therefore, the matrices [tex]A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right][/tex] are non-invertible matrices that can be added together to form an invertible matrix [tex]A+B =\left[\begin{array}{ccc}1&1\\1&1\end{array}\right][/tex].
https://brainly.in/question/8463680
#SPJ1
On a certain hot summers day, 685people used the public swimming pool. The daily prices are$1.75 for children and$2.00 for adults. The receipts for admission totaled $1.282.50 How many children and how many adults swam at the public pool that day?
Answers
By making and solving the equations we know that the number of children and adults that swam at the pool is 350 and 335 respectively.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others. Let's learn more about math equations in this tutorial.
For instance, a formula might be 3x - 5 = 16.
After solving this equation, we learn that the value of the variable x is 7.
So, make equations as follows:
c + a = 685 (1)
c = 685 - a
Now, substitute c = 685 - a in the 2nd equation as follows:
1.75c + 2a = 1.282.50 (2)
1.75(685 - a) + 2a = 1,282.50
1,198.75 - 1.75a + 2a = 1,282.50
0.25a = 83.75
a = 83.75/0.25
a = 335
Then, the children:
c = 685 - a
c = 685 - 335
c = 350
Therefore, by making and solving the equations we know that the number of children and adults that swam at the pool is 350 and 335 respectively.
Know more about equations here:
https://brainly.com/question/2972832
#SPJ1
Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x.
Answers
This shows that y is proportional to x with a constant of proportionality r.
Therefore, the constant of proportionality in the equation y = rx is r.
Which one of these is an equation?Two expressions joined by the equal sign constitute an equation, which is a statement in mathematics. An illustration of a formula is 3x - 5 = 16. After resolving this equation, we discover that the value of x is 7.
The given equation is y = rx.
To find the constant of proportionality, we can use the definition of proportionality, which states that two variables are proportional to each other if they have a constant ratio.
In this case, we can write:
y/x = r
This shows that y is proportional to x with a constant of proportionality r.
Therefore, the constant of proportionality in the equation y = rx is r.
To know more about equation visit:
https://brainly.com/question/29657988
#SPJ1
Mr. Smith is putting a brick border around his irregular shaped yard. Before installing the border, he must cut the bricks to fit the angles of the garden. Use the given measures to answer the question.
Answers
The angle measures are given as follows:
m < A = 184º.m < B = 156º.m < C = 137º.m < D = 177º.m < E = 34º.m < F = 128º.How to obtain the angle measures?First we must obtain the value of x, considering the total sum of the interior angle measures of the polygon, and then with the value of x we obtain each angel measure.
The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:
S(n) = 180 x (n - 2).
The polygon has six vertices, hence the sum is given as follows:
S(6) = 180 x 4
S(6) = 720.
We then add all the angle measures to obtain the value of x as follows:
7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720
28x = 768
x = 768/28
x = 27.43.
Then each angle measure is rounded as follows:
m < A = 7(27.43) - 8 = 184º.m < B = 4(27.43) + 46 = 156º.m < C = 5(27.43) = 137º.m < D = 6(27.43) + 12 = 177º.m < E = x + 7 = 34º.m < F = 5(27.43) - 9 = 128º.More can be learned about the sum of the interior angle measures of a polygon brainly.com/question/224658
#SPJ1
There are 2 blueberries for every 7 strawberries. If there are 49 strawberries, how many blueberries are there?
Answers
Answer:
14
Step-by-step explanation:
So, 49 divided by 7 is 7 so there are 7 groups of 7 strawberries. With each of those 7 groups there are 2 blueberries. So, you are then going to multiply 7 by 2 and that gives you 14 blueberries.
The function h(x)
f(x) is defined as:
f(x)=
=
1
x-3
<
>
can be expressed in the form f(g(x)) where g(x) = (x − 3) and
-
Answers
Answer:
[tex]f(x)=\frac{1}{x}[/tex]
Step-by-step explanation:
You are looking for a function that when you plug g(x) into f(x), you get the result of h(x).
If we define f(x) as 1/x then that would mean when we plug in g(x) we would get h(x) = 1 / (x-3), which is what we're looking for.
Then, write the result as a binomial squared. a2+a
Answers
Answer:
The result can be written as (a + 1)².
what is the rate of change of y= -1025x + 30,750?
Answers
Answer:
Step-by-step explanation:
The rate of change is dy/dx=-1025
13. The table below gives air pressures in kPa at selected altitudes above sea level measured in
kilometers.
X
y
Altitude (km)
0
1
Air Pressure (kPa) 101 90
2
79
3
70
durma
4
62
5
54
Write an exponential regression equation that models these data rounding all values to the nearest
thousandth.
Use this equation to algebraically determine the altitude, to the nearest hundredth of a kilometer,
when the air pressure is 29 kPa.
Answers
Answer:
I don't know yet bye
Step-by-step explanation:
The exponential regression equation that models the data is y = 101 × (0.899)ˣ and when the air pressure is 29 kPa, the altitude is 6.09 km.
To find an exponential regression equation that models the given data, we can use the general form:
y = abˣ
where y is the air pressure and x is the altitude.
Using the provided data, we can substitute the values of x and y into the equation to obtain a system of equations:
When x = 0, y = 101:
101 = ab⁰
101 = a
When x = 1, y = 90:
90 = ab¹
90 = ab
90=101b
Divide both sides by 101:
b=90/101
b= 0.899
Therefore, the exponential regression equation that models the data is:
y = 101 × (0.899)ˣ
To determine the altitude when the air pressure is 29 kPa, we can substitute y = 29 into the equation and solve for x:
29 = 101 × (0.899)ˣ
Dividing both sides by 101:
0.287 = (0.899)ˣ
log(0.287) = log((0.899)ˣ)
log(0.287) = x × log(0.899)
x = log(0.287) / log(0.899)
x = 6.093.
Hence, when the air pressure is 29 kPa, the altitude is 6.09 km.
To learn more on Exponential regression equation click:
https://brainly.com/question/14200896
#SPJ2
The table below gives air pressures in kPa at selected altitudes above sea level measured in
kilometers.
x Altitude 0 1 2 3 4 5
y Air pressure 101 90 79 70 62 54
Write an exponential regression equation that models these data rounding all values to the nearest
thousandth.
Use this equation to algebraically determine the altitude, to the nearest hundredth of a kilometer,
when the air pressure is 29 kPa.
What is the volume of this figure?
Answers
Answer:
112cm³
Step-by-step explanation:
Let us ignore the bottom part of the figure and first find only the volume of the cuboid at the top
from the figure we know that
length of the cuboid is 10 cm
Width is 2 cm
height is 5 cm
now the formula for Volume of cuboid is Length×Width×Height
so,
Volume of the Upper Cuboid = 10×2×5= 100cm³ ---(1)
Now we will ignore the cuboid on top and find the volume of the one at the bottom
From the figure, we know that its dimensions are
length = 2cm
height = 3cm
width = 2cm
Volume of the lower cuboid = 2×2×3 = 12cm³ ---(2)
Adding (1) and (2)
100cm³ + 12 cm³ = 112cm³
Therefore the volume of the given figure is 112cm³
The volume of the box is 112 cm³.
We have,
The figure can be considered as two boxes.
Now,
One box:
Volume.
= Length x Width x height
= 10 x 2 x 5
= 100 cm³
Another box:
Volume.
= Length x Width x height
= 2 x 2 x 3
= 12 cm³
Now,
The volume of the box.
= 100 + 12
= 112 cm³
Thus,
The volume of the box is 112 cm³.
Learn more about volume of box here:
https://brainly.com/question/13913076
#SPJ6
A car was stopped at a red light. When the light turns green, the car reaches a speed of 47 miles per hour in 4 seconds. What is the acceleration, to 1 decimal place?
feet/s2.
Answers
Answer:
275.7 ft/s^2 appr.
Step-by-step explanation:
47mi*5280=248160 feet per hour.
4 seconds = 4/(60*60)=1/900 of an hour.
1/900*248160=275.7 feet/s^2 approx.
Answer:
The car's acceleration is 17.2 ft/s².
Step-by-step explanation:
First we need to do some unit conversions.
Unit Conversions
There is 60 seconds in 1 minute.
There is 60 minutes in 1 hour.
So therefore there is 3600 seconds in 1 hour.
There is 5280 feet in 1 mile.
Now we can create an expression convert mph to ft/s
Multiply the speed value in mph by [tex]\frac{5280}{3600}[/tex] to get the speed in ft/s
We can simplify [tex]\frac{5280}{3600}[/tex] to [tex]\frac{22}{15}[/tex].
Multiply the speed value in mph by [tex]\frac{22}{15}[/tex] to get the speed in ft/s.
We are given a speed of 47 mph.
[tex]47*\frac{22}{15}=68.93[/tex]
Numerical Evaluation of Acceleration
Now we can solve for the acceleration.
The formula for acceleration is
[tex]a=\frac{v_f-v_i}{t}[/tex]
In this example we are given
[tex]v_f=68.93\\v_o=0\\t=4[/tex]
Substituting our values into the equation for acceleration yields
[tex]a=\frac{68.93-0}{4}[/tex]
Evaluate [tex]\frac{68.93-0}{4}[/tex]
[tex]a=17.23[/tex]
Rounding to 1 decimal place gives us
[tex]a=17.2[/tex]
Learn more about acceleration here
https://brainly.com/question/24857145
stuck on standard deviation have never done it before
Answers
The standard deviation of the given data set above would be = 6.97.
How to calculate the standard deviation of the given data set above?The mean is first calculate as follows;
= 8.9+1.4+14.2+24.1+6.1+1.7+9.2+5.2/8
= 70.8/8
=8.86
find the square of the difference between each data and the mean. That is;
8.9-8.86 = 0.04² = 0.0016
1.4-8.86 = −7.46² = 55.6516
14.2-8.86 = 5.34² = 28.5156
24.1-8.86 = 15.24² = 232.2576
6.1 -8.86 = −2.76² = 7.6176
1.7-8.86 = −7.16² =51.2656
9.2-8.86 = 0.34² = 0.1156
5.2 -8.86 = −3.66² = 13.3956
Sum the whole variables derived, divide it by number of variables and square the result.
= 0.0016+55.6516+28.5156+232.2576+7.6176+51.2656+0.1156+13.3956
= 388.8208/8
= √48.6026
= 6.97.
Learn more about division here:
https://brainly.com/question/25289437
#SPJ1