Answer: 1/52
Step-by-step explanation:
There is a 13/52 chance of drawing a hearts card and then there is a 4/52 chance of drawing a 6
(13/52)(4/52)=1/52
There is a 1/52 chance of Marlin drawing a hearts card and then a 6
Try it
Evaluate the step function for the given input values.
-4, -3 ≤ x < -1
-1,
-1 ≤ x < 2
2 ≤ x < 4
X24
g(x) =
g(2) =
g(-2) =
g(5) =
lating a Step Function Us
3,
5,
4
The value of g(x) = [x] At, 2 ≤ x < 3, g(x) = 2, It is also known as the greatest integer function.
What is a step function?A function on real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals.
Informally speaking, a step function is a piecewise constant function having only finitely many pieces.
A step function f(x) = [x] is called a step function where the output is the greatest integer less than or equal to the input.
The function is g(x) = [x].
At, - 1 ≤ x < 0, g(x) = 0.
At, 1 ≤ x < 2, g(x) = 1.
At, 2 ≤ x < 3, g(x) = 2.
learn more about step functions here :
https://brainly.com/question/29003617
#SPJ9
Match the following equations with their direction field. Clicking on each picture will give you an enlarged view. While you can probably solve this problem by guessing, it is useful to try to predict characteristics of the direction field and then match them to the picture. Here are some handy characteristics to start with -- you will develop more as you practice.
A. Setyequal to zero and look at how the derivative behaves along thex-axis.
B. Do the same for they-axis by settingxequal to0
C. Consider the curve in the plane defined by settingy'=0-- this should correspond to the points in the picture where the slope is zero.
D. Settingy'equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and can be used to construct the direction field picture by hand.
1.y'= e^{-x} + 2y
2.y'= 2\sin(x) + 1 + y
3.\displaystyle y'= -\frac{(2x+y)}{(2y)}
4.y'= y + 2
sps3-Q-stmarys-ca-Q-edu-1991-sethw4-7pro sps3-Q-stmarys-ca-Q-edu-1991-sethw4-7pro
A B
sps3-Q-stmarys-ca-Q-edu-1991-sethw4-7pro sps3-Q-stmarys-ca-Q-edu-1991-sethw4-7pro
C D
My answers are correct I just need someone to show me the work on how to get there
The option (b) set y equal to a constant other than zero to get the curve of points where the slope is that constant.
A slope field is a visual representation of the slopes of a function's derivative at different points on the xy-plane. The slope at a particular point in the xy-plane is given by the derivative of the function at that point.
To match the given equations with their corresponding slope fields, you need to analyze the behavior of the slopes and isoclines. An isocline is a curve in the plane along which the slope of a function is constant. Isoclines are useful in constructing slope fields by hand, as they help in determining the slope at different points.
To start with, set y equal to zero and observe how the derivative behaves along the x-axis. Similarly, set x equal to zero and observe the behavior of the derivative along the y-axis. These observations will give you an idea of the direction and magnitude of the slope at different points in the xy-plane.
Next, consider the curve in the plane defined by setting y' = 0. This curve represents the points in the picture where the slope is zero. These points are known as critical points or equilibrium points. They are essential in analyzing the stability and behavior of a system.
These curves are called isoclines and can be used to construct the slope field picture by hand.
To know more about slope here.
https://brainly.com/question/3605446
#SPJ4
Complete Question:
Match the following equations with their slope field. Clicking on each picture will give you an enlarged view. While you can probably sove this problem by guessing, it is useful to try to predict characteristics of the slope field and then match them to the picture Here are some handy characteristics to start with- you will develop more as you practice. Set y equal to zero and look at how the derivatiwe behaves along the x axis. Do the same for the y axis by setting x equal to 0. Consider the curve in the plane defined by setting y' = 0-this should correspond to the points in the picture where the slope is zero. Setting y equal to a constant other than zero gives the curve of points where the slepe is that constant. These are called isoclines, and can be used to construct the slope field picture by hand.
students were surveyed about what summer camp they would be attending of the students that stated they would be going to camp redwood 15% did not go to camp of the students that stated they would be going to camp arrowhead 20% did not go to camp how many more students went to camp redwood than cam arrowhead?
The number of students who went to Camp Redwood was 23% more than the number of students who went to Camp Arrowhead.
What is percentage ?
A percentage is a way of expressing a number as a fraction of 100. The symbol for percentage is "%". For example, 50% means 50 out of 100 or 0.5 as a decimal.
Percentages are commonly used to represent proportions, rates, and changes in quantities. They can be used to compare quantities of different sizes, or to express how much one quantity has changed relative to another quantity.
Given by the question:
Let's assume that there are a total of 100 students who were surveyed.
If 15% of the students who planned to go to Camp Redwood did not go, then 85% of them did go:
0.85 x (number of students who planned to go to Camp Redwood) = number of students who actually went to Camp Redwood
Similarly, if 20% of the students who planned to go to Camp Arrowhead did not go, then 80% of them did go:
0.80 x (number of students who planned to go to Camp Arrowhead) = number of students who actually went to Camp Arrowhead
Let's say that x students planned to go to Camp Redwood and y students planned to go to Camp Arrowhead. Then we can write two equations based on the above percentages:
0.85x = number of students who actually went to Camp Redwood
0.80y = number of students who actually went to Camp Arrowhead
We want to find the difference between the number of students who went to Camp Redwood and the number of students who went to Camp Arrowhead, so we can subtract the second equation from the first:
0.85x - 0.80y = (number of students who actually went to Camp Redwood) - (number of students who actually went to Camp Arrowhead)
We can substitute the values from the percentages into the equation:
0.85x - 0.80y = 0.85(0.85x) - 0.80(0.80y)
0.85x - 0.80y = 0.7225x - 0.64y
0.13x = 0.16y
We can solve for one of the variables in terms of the other:
x = (0.16/0.13)y
x = 1.23y
So if y students planned to go to Camp Arrowhead, then 1.23y students planned to go to Camp Redwood. The difference between the number of students who went to Camp Redwood and the number of students who went to Camp Arrowhead is:
1.23y - y = 0.23y
So the number of students who went to Camp Redwood was 23% more than the number of students who went to Camp Arrowhead.
To know more about percentage visit:
https://brainly.com/question/29116686
#SPJ1
an education reform lobby is compiling data on the state of education in the united states. in their research they looked at the percent of people who graduate high school in 10 different states. the data are provided below. use a ti-83, ti-83 plus, or ti-84 to calculate the sample standard deviation and the sample variance. round your answers to one decimal place. high school graduation rate (%) 77.1 82.9 90 91.3 81.9 83.3 84.9 82.5 84.6 helpcopy to clipboarddownload csv provide your answer below: $$standard deviation
The sample variance and standard deviation are given as follows:
Variance = 87.22 %².Standard deviation = 9.34%.How to obtain the measures?To obtain the variance and the standard deviation, first we must obtain the mean, which is given by the sum of all observations divided by the number of observations, hence:
Mean = (77.1 + 82.9 + 90 + 91.3 + 81.9 + 83.3 + 84.9 + 82.5 + 84.6)/10
Mean = 75.85.
Then we must obtain the sum of the differences squared between each observation and the mean, as follows:
(77.1 - 75.85)² + (82.9 - 75.85)² + (90 - 75.85)² + (91.3 - 75.85)² + (81.9 - 75.85)² + (83.3 - 75.85)² + (84.9 - 75.85)² + (82.5 - 75.85)² + (84.6 - 75.85)² = 784.9825
The sample variance is given by the above sum divided by one less than the sample size, hence:
Variance = 784.9825/9
Variance = 87.22 %².
The standard deviation is the square root of the variance, hence:
Standard deviation = sqrt(87.22)
Standard deviation = 9.34%.
More can be learned about standard deviation at https://brainly.com/question/30240469
#SPJ1
Which statement correctly describes the relationship between △ABC and △A′B′C′ ?
a . △ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a reflection across the y-axis, which is a rigid motion.
b . △ABC is not congruent to △A′B′C′ because there is no sequence of rigid motions that maps △ABC to △A′B′C′.
c . △ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 6 units to the left, which is a rigid motion.
d . △ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 6 units to the right, which is a rigid motion.
The correct option is (d): △ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 6 units to the right, which is a rigid motion.
In option (a), a reflection across the y-axis is not a rigid motion, as it changes the orientation of the triangles, and therefore cannot be used to show congruence.
In option (b), if there is no sequence of rigid motions that maps △ABC to △A′B′C′, then the triangles are not congruent.
In option (c), a translation 6 units to the left does not map △ABC to △A′B′C′. However, a translation 6 units to the right would map △ABC to △A′B′C′, because translations are rigid motions that preserve distance and angle measures.
Therefore, option (d) is the correct statement that describes the relationship between the two triangles.
Learn more about congruency at
https://brainly.com/question/7888063
#SPJ4
Each column of AB is a linear combination of the columns of B using weights from the corresponding column of A. Choose the correct answer below.A.)The statement is true. The definition of AB states that each column of AB is a linear combination of the columns of A using weights from the corresponding rows of B.B.)The statement is true. The definition of AB states that each column of AB is a linear combination of the columns of B using weights from the corresponding column of A.C.) The statement is false. The definition of AB states that each column of AB is a linear combination of the columns of A using weights from the corresponding column of B.D.)The statement is false. The definition of AB states that each column of AB is a linear combination of the columns of A using weights from the corresponding rows of B.
C)The statement is false. The definition of AB states that each column of AB is a linear combination of the columns of B using weights from the corresponding column of A.(C)
To see why this is the case, let A be an m x n matrix and let B be an n x p matrix. Then the product AB is an m x p matrix whose (i,j)-th entry is given by the dot product of the i-th row of A with the j-th column of B:
(AB){i,j} = \sum{k=1}^n a_{i,k} b_{k,j}
This means that the j-th column of AB is obtained by taking a linear combination of the columns of B using the weights from the j-th column of A.
In other words, the statement "each column of AB is a linear combination of the columns of B using weights from the corresponding column of A" is true, but the statement in answer choice C is false.
For more questions like Linear combination click the link below:
https://brainly.com/question/25867463
#SPJ4
I need help with the volume of the following rectangular prism of 16 1/4 and 1/2
Answer:
To find the volume of a rectangular prism, you need to multiply its length, width, and height.
Assuming that the dimensions are in inches, we have:
Length = 16 inches + 1/4 inch = 16.25 inches
Width = 1/2 inch
Height = some unknown value (not given in the question)
So, if we know the height, we can calculate the volume of the rectangular prism. If the height is, for example, 10 inches, then:
Volume = Length x Width x Height
Volume = 16.25 inches x 0.5 inches x 10 inches
Volume = 81.25 cubic inches
Therefore, the volume of the rectangular prism depends on its height, which is not given in the question.
Let n be the outer unit normal of the elliptical shell. S: 4x²+9y²+36z²= 36
The outer unit normal vector at any point (x, y, z) on the surface of the ellipsoid is given by:
n = <8x, 18y, 72z> / sqrt((8x)² + (18y)² + (72z)²)
What is expression ?In mathematics, an expression is a combination of one or more values, variables, operators, and/or functions that are evaluated to produce a single result.
For example, 3 + 4 is an expression that evaluates to 7, and (x + 2) / (y - 1) is an expression that can be evaluated for different values of x and y.
Expressions can be simple or complex, and can involve arithmetic operations (addition, subtraction, multiplication, division), algebraic operations (such as factoring or expanding), trigonometric functions, logarithmic functions, and many other mathematical operations.
Expressions are often used in mathematical modeling and problem solving, and can be written in a variety of formats, including symbolic notation, numerical values, or verbal descriptions.
According to given condition :The equation you provided, 4x² + 9y² + 36z² = 36, represents an ellipsoid centered at the origin (0,0,0) with semi-axes of length 3, 2, and 1 in the x, y, and z directions, respectively.
The outer unit normal vector, n, at a given point on the surface of the ellipsoid is perpendicular to the tangent plane at that point. To find the normal vector at a given point (x, y, z) on the surface, we can take the gradient of the function 4x² + 9y² + 36z², which gives us:
∇(4x² + 9y² + 36z²) = <8x, 18y, 72z>
At any point on the surface of the ellipsoid, this gradient vector is proportional to the normal vector, and the constant of proportionality is the reciprocal of the length of the gradient vector:
n = k<8x, 18y, 72z>
To find the value of k, we need to normalize n so that its length is 1. That is,
|n| = sqrt((8x)² + (18y)² + (72z)²) = 1
Solving for k, we get:
k = 1 / sqrt((8x)² + (18y)² + (72z)²)
Thus, the outer unit normal vector at any point (x, y, z) on the surface of the ellipsoid is given by:
n = <8x, 18y, 72z> / sqrt((8x)² + (18y)² + (72z)²)
To know more about expression visit :
https://brainly.com/question/1859113
#SPJ1
The realized demand valuesAtand forecast valuesFtfor periodst=1,2,3,4,5are provided in the table below. Round only the final measure of forecast accuracy to two decimals. The cumulative sum of the forecast errors (CSE) is (Round to two decimals.) The mean absolute deviation value (MAD) is (Round to two decimals.) The mean squared error value (MSE) is (Round to two decimals.) The mean absolute percent error value (MAPE) is (Round to two decimals.)
The final measures of forecast accuracy are: CSE = -46, MAD = 18.4, MSE = 462.8, MAPE = 12.44
The forecast errors can be calculated as follows:
Period 1: 751 - 751 = 0
Period 2: 741 - 751 = -10
Period 3: 728 - 749 = -21
Period 4: 773 - 745 = 28
Period 5: 718 - 751 = -33
The cumulative sum of the forecast errors (CSE) is: 0 - 10 - 21 + 28 - 33 = -46
The mean absolute deviation (MAD) can be calculated as follows:
MAD = (abs(0) + abs(-10) + abs(-21) + abs(28) + abs(-33)) / 5
MAD = (0 + 10 + 21 + 28 + 33) / 5
MAD = 92 / 5 = 18.4
The mean squared error (MSE) can be calculated as follows:
MSE = (0^2 + (-10)^2 + ( -21)^2 + 28^2 + (-33)^2) / 5
MSE= ( 0+ 100+ 441 + 784 + 1089)/5
MSE = 2314/ 5 = 462.8
The mean absolute percent error (MAPE) can be calculated as:
MAPE = (abs(0/751) + abs(-10/741) + abs(-21/728) + abs(28/773) + abs(-33/718)) / 5 * 100
MAPE = (0 + 1.34 + 2.89 + 3.63 + 4.58) / 5 * 100
MAPE = 12.44
The final measures of forecast accuracy are:
CSE = -46
MAD = 18.4
MSE = 462.8
MAPE = 12.44
To know more about Forecast accuracy:
https://brainly.com/question/28231988
#SPJ4
_______The given question is incorrect, the correct question is given below:
The realized demand values A= 751, 741, 728, 773, 718
and forecast values F = 751, 751, 749, 745, 751
for periods = 1,2,3,4,5
are provided in the table below. Round only the final measure of forecast accuracy to two decimals. The cumulative sum of the forecast errors (CSE) is (Round to two decimals) The mean absolute deviation value (MAD) is (Round to two decimals) The mean squared error value (MSE) is (Round to two decimals) The mean absolute percent error value (MAPE) is (Round to two decimals.)
calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of american adults. if necessary, round to one more decimal place than the largest number of decimal places given in the data. heart rates in beats per minute class frequency 61 - 66 4 67 - 72 8 73 - 78 5 79 - 84 7 85 - 90 13
Sample Mean _______________
Sample Variance _________________
The sample mean of the given frequency distribution of heart rates is 77.59 and the sample variance is 27.543.
To calculate the sample mean and sample variance of the given frequency distribution of heart rates, we must first calculate the mid-points of each class (i.e. 63.5, 69.5, 76.5, 82.5, 87.5). Then, we must calculate the mid-point multiplied by the frequency of each class [tex](4x63.5, 8x69.5, 5x76.5, 7x82.5, 13x87.5)[/tex]. Finally, we must add up all of these values together and divide by the total frequency. This gives us the sample mean.
To calculate the sample variance, we must first calculate the squared differences of each midpoint multiplied by the frequency from the sample mean [tex](4x63.5, 8x69.5, 5x76.5, 7x82.5, 13x87.5)[/tex]. Then, we must add up all of these values together and divide by the total frequency minus one. This gives us the sample variance.
Therefore, the sample mean of the given frequency distribution of heart rates is 77.59 and the sample variance is 27.543.
Learn more frequency distribution here:
https://brainly.com/question/14926605
#SPJ4
7. The total of 13 cherries, 8 more cherries, and 2 more cherries is c.
The value of c is given as follows:
c = 23.
How to obtain the value of c?The problem states that the total of 13 cherries, 8 more cherries, and 2 more cherries is c, hence the value of c is obtained with the addition of these amounts, as follows:
c = 13 + 8 + 2.
Adding these three amounts, the numeric value of c is given as follows:
c = 23.
Missing InformationThe problem asks for the numeric value of c.
More can be learned about addition of amounts at https://brainly.com/question/17301989
#SPJ1
let a and as be the events that a person is left- eve dominant or right-eve dominant, respectively.when a person folds his or her hands, let by and b2 be the events that the left thumb and right thumb, respectively, are on top. a survey in one statistics class yielded the following table:
If the student is selected randomly, the probabilities for the following is given as:
P (A1∩B1) = 0.1163P(A1∪B1) = 0.7209P(A1|B1) = 0.2273P(B2'∪A1') = 0.2814Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
P (A1∩B1) = 5/43 = 0.1163
P(A1∪B1) = 14/43 + 22/43 - 5/43 = 31/43 = 0.7209
P(A1|B1) = 5/22 = 0.2273
P(B2'∪A1') = (1-21/43) + (1-14/43) - 26/43
= 25/43 = 0.2814
P(A2∩B1) = 17/43 = 0.3953
P(A2∩B2)= 12/43 = 0.2791
P(A2∩B1) is more i.e. student with left thumb on top is more .Hence, student selects left thumb on top.
Learn more about Events:
https://brainly.com/question/11789412
#SPJ4
Complete question:
Let A1 and A2 be the events that a person is left-eye dominant or right-eye dominant, respectively. When a person folds his/her hands, let B, and B2 be the vents that the left thumb and right thumb, respectively, are on top. A survey in one statistics class yielded the table below: B B2 Totals A 5 9 14 17 12 29 Totals 21 If a student is selected randomly, find the following probabilities: a) P(A, NB) b) P(AUB) c) P(A1B1) d) P(B' UA) e) If the students had their hands folded and you hoped to select a right-eye-dominant student, would you select a "right thumb on top” or a “left thumb on top” student? Why?
I will give brainlist for the right answer!!
use one of these equations to solve!
1. Separation of variables
2.Homogeneous equation
3. Exact equation
I need answer ASAP please!
Answer:
the solution to the differential equation is:
y + (1/3)y^3 = e^x + 1/3.
Step-by-step explanation:
We can use the equation e^x=(1/(1+y^2))dy/dx to solve this differential equation using separation of variables.
First, we can rewrite the equation as:
(1+y^2)dy = e^x dx
Next, we can separate the variables:
(1+y^2)dy = e^x dx
∫ (1+y^2)dy = ∫ e^x dx
y + (1/3)y^3 = e^x + C
where C is the constant of integration.
Now we can use the initial condition to solve for C. Let's say the initial condition is y(0) = 1, then we have:
1 + (1/3)(1)^3 = e^0 + C
4/3 = 1 + C
C = 1/3
Therefore, the solution to the differential equation is:
y + (1/3)y^3 = e^x + 1/3.
St=4x-4,Tu=4x-10 and SU=5x+1
Work Shown:
ST + TU = SU .... segment addition postulate
(4x-4) + (4x-10) = 5x+1
8x-14 = 5x+1
8x-5x = 1+14
3x = 15
x = 15/3
x = 5
Then use this x value to determine the segment lengths.
ST = 4x-4 = 4*5-4 = 16TU = 4x-10 = 4*5-10 = 10 is the final answerSU = 5x+1 = 5*5+1 = 26As a check: ST+TU = 16+10 = 26 which matches with SU = 26. This confirms ST+TU = SU is the case and it confirms the final answer.
determine the number of solution for the equation shown below? 4x+6=4-6
Answer: X= -8
Step-by-step explanation: 4 minus 6 equals to -2. So for 4x + 6 to equal -2 you have to do 4x times -8 to get -8 then add it by 6 to get -2.
4 times 8 = -8 + 6 = -2
Which sign makes the statement true?
792 3/20
792 1/2
The sign that makes the statement true is 792 3/20 ≠ 792 1/2.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
There are two types of fractions: proper fractions in which the numerator is less than the denominator and,
Improper fractions in which the numerator is larger than the denominator.
Given, Are two fractions 792 3/20 and 792 1/2.
The sign that makes the statement true is 792 3/20 ≠ 792 1/2.
Some other signs, for example, Inequalities can also make the statement true.
learn more about fractions here :
https://brainly.com/question/10354322
#SPJ9
Show that in any parallelogram the sum of the squares of the lengths of the four sides equals the sum of the squares of the lengths of the two diagonals.
The statement "parallelogram the sum of the squares of the lengths of the four sides equals the sum of the squares of the lengths of the two diagonals." is proved.
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are congruent, meaning they have the same length. Similarly, the opposite angles of a parallelogram are congruent, meaning they have the same measure.
Now, let's consider a parallelogram ABCD with sides AB, BC, CD, and DA. We want to show that:
AB² + BC² + CD² + DA² = AC² + BD²
where AC and BD are the diagonals of the parallelogram.
First, let's draw the diagonals AC and BD. This divides the parallelogram into four triangles: triangle ABC, triangle BCD, triangle CDA, and triangle DAB.
Next, let's use the Pythagorean theorem in each of these triangles. Recall that the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In triangle ABC, we have:
AC² = AB² + BC²
Similarly, in triangle CDA, we have:
AC² = CD² + DA²
Adding these two equations together, we get:
2AC² = AB² + 2BC² + CD² + 2DA²
Now, let's look at triangle ABD. We have:
BD² = AB² + DA²
Similarly, in triangle BCD, we have:
BD² = BC² + CD²
Adding these two equations together, we get:
2BD² = AB² + 2BC² + CD² + 2DA²
Finally, adding the two equations we obtained for AC² and BD², we get:
2AC² + 2BD² = 2AB² + 4BC² + 2CD² + 2DA²
Simplifying this expression, we get:
AC² + BD² = AB² + BC² + CD² + DA²
Therefore, we have proven that in any parallelogram, the sum of the squares of the lengths of the four sides is equal to the sum of the squares of the lengths of the two diagonals.
To know more about parallelogram here.
https://brainly.com/question/29147156
#SPJ4
Differentiate Y = 1/x
Evaluate z- (y-z) if z= 4 and y =6
Answer: 2
4 – (6-4) = 2
Answer: 2- (y= 6 , z=2)
Step-by-step explanation:
If z = 4 and y = 6, then we can substitute these values into the expression:
z - (y - z) = 4 - (6 - 4)
Expanding the subtraction in the parentheses, we get:
z - (y - z) = 4 - (6 - 4) = 4 - (2) = 4 - 2
Finally, solving for the subtraction:
z - (y - z) = 4 - 2 = 2
So, the value of the expression z - (y - z) when z = 4 and y = 6 is 2.
Let f(x) = −|x−3|+3 and g(x) = 12x−3. Graph the functions in the same coordinate plane.
What are the solutions to f(x)=g(x)?
The graph of the functions f(x) and g(x) on the same coordinates plane and the solution is (0 , 0.818).
What is a function?
A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Two functions:
f(x) = -|x - 3| + 2
g(x) = 12x - 3
Now,
The graph is given below.
The intersection of the graph of f(x) and g(x) is the solution to f(x) = g(x).
So,
for x> 3 , we can say that
-|x - 3| + 3 = 12x -3
-x + 3 +3 = 12x -3
Therefore , x = 9/11 = 0.818
for x< 3 , we can say that
-|x - 3| + 3 = 12x -3
x - 3 = 12x - 3
x = 0
The solution is (0 , 0.818).
Thus, the solution is (0 , 0.818).
Learn more about functions here:
brainly.com/question/28533782
#SPJ1
A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true proportion of families who own at least on DVD player. Place your limits, rounded to 3 decimal places, in the blanks. Do not use any labels or symbols other than the decimal point. Simply provide the numerical values. For example, 0.123 would be a legitimate entry.
Lower limit (first blank) = __________, Upper limit (second blank) = ___________.
For example, 0.123 would be a legitimate entry. Lower limit (first blank) = 0.285, Upper limit (second blank) = 0.562.
The confidence interval for proportions is
p±z *√p(1-p)/n.
In this case, p = 36/85 = .4235, and z* = 2.575 (the value of the standard normal distribution corresponding to 99%).
so,
0.4235 ± 2.576 * √0.4235*0.5765/85
0.4235 ± 0.13804
= (0.285, 0.562)
Therefore, Lower limit is 0.285 and Upper limit 0562.
A confidence interval is the mean of your estimate plus and minus the variation in that estimate. This is the range of values you anticipate your estimate to fall between if you redo your test, within a certain position of confidence.
Confidence, in statistics, is another way to describe probability. For illustration, if you construct a confidence interval with a 95 confidence position, you're confident that 95 out of 100 times the estimate will fall between the upper and lower values specified by the confidence interval.
Learn more about Confidence Interval:
https://brainly.com/question/2847372
#SPJ4
Consider the curve defined parametrically by f(t) = t , - [infinity] < t < [infinity]t² - 4e^t-2 Let g(x,y,z) be a real-valued differentiable function of three variables. If a = (2,0,1) and∂g/∂x (a) = 4, ∂g/∂y(a) = 2, ∂g/∂z(a) = 2, find d (g o f)/dt at t = 2.
The value of the d(g o f)/dt at t = 2 is 14.
We can start by computing the composition (g o f)(t) and then finding its derivative with respect to t using the chain rule.
(g o f)(t) = g(f(t)) = g(t, t^2 - 4e^(t-2))
At t = 2, we have f(2) = 2 and f'(2) = 2t - 4e^(t-2) evaluated at t = 2 gives f'(2) = 0.
To find d(g o f)/dt at t = 2, we first need to evaluate (g o f)(2):
(g o f)(2) = g(f(2)) = g(2, 0) = g(a)
Next, we use the chain rule to find the derivative of (g o f) with respect to t:
[tex](d/dt) (g o f)(t) = (∂g/∂x)(a) (df/dt) + (∂g/∂y)(a) (d/dt) (t^2 - 4e^{(t-2)}) + (∂g/∂z)(a) (dg/dz)(a)[/tex]
Since f(t) = t, df/dt = 1. Also, since g(x,y,z) is differentiable, we can write dg/dz(a) as ∂g/∂z(a) = 2.
Substituting the values we have and evaluating at t = 2, we get:
[tex](d/dt) (g o f)(2) = (4)(1) + (2)(2t - 4e^{(t-2)})(t=2) + (2)(2)[/tex]
= 4 + 2(4-4e^0) + 4
= 14
For more questions on Chain Rule
https://brainly.com/question/26731132
#SPJ4
how to write
526.8- 318.05
Answer:208.75
Step-by-step explanation:
Bill will run at least 31 miles this week. So far, he has run 16 miles. What are the possible numbers of additional miles he will run? Use t for the number of additional miles he will run. Write your answer as an inequality solved for t.
Answer:
The inequality to set up is [tex]t+16 \ge 31[/tex]
It solves to [tex]t \ge 15[/tex]
Bill needs to run at least 15 more miles.
================================================
Explanation:
He has run 16 miles so far. Add on another t miles to get 16+t or t+16 to represent the total amount he runs. This expression must be 31 or larger
Either t+16 > 31 or t+16 = 31
Those two items condense to [tex]t+16 \ge 31[/tex]
To solve for t, we subtract 16 from both sides to undo the +16.
[tex]t+16 \ge 31\\\\t+16-16 \ge 31-16\\\\t \ge 15\\\\[/tex]
Bill needs to run at least 15 more miles.
Meaning that t = 15, t = 16, t = 17, etc.
(6.82x-2.53y - 5.72)-(-5.72 +9.45y-8.11x)
A mathematical statement known as an equation is created by joining two expressions with an equal sign. For instance, 3x - 5 = 16 is an equation. This equation may be solved, and the result shows that the value of the variable x is 7.
What is meant by mathematical equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal." Equations are collections of variables, constants, and mathematical operations such as addition, subtraction, multiplication, or division. Each equation is balanced by an equal sign.The left-hand side (LHS) of the equation is on the left, while the right-hand side is on the right (RHS).A mathematical equation is a claim that the values of two expressions are equal. A mathematical equation essentially states that two things are equal.Given,
(6.82x - 2.53y - 5.72) - (-5.72 + 9.45y - 8.11 x)
Simplifying the above equation,
= 6.82x - 2.53y - 5.72 - (-5.72 + 9.45y - 8.11 x)
= 6.82x - 2.53y - 5.72 + 5.72 - 9.45y + 8.11 x
Simplify
6.82x - 2.53y - 5.72 + 5.72 - 9.45y + 8.11 x : 14.93x - 11.98y
Then we get,
= 14.93x - 11.98y
To learn more about mathematical equation, refer to:
https://brainly.com/question/2228446
#SPJ1
Given the expression -12x² + 3-4x-10, answer the questions below.
BTP THIEMESLA
MATERIANGELOOS!
CREARES Y RECREINAGE
En Menasgitteell
paleta balia
CARE SEGN 400
MASHIL MOTEL EGTE
MODEJMLE 25000
SEAR
HUNG TRUE
& PE
l
the
N
a warm
TENT
230 5000-640
S
TRARON SE Shiptare
7500
A. In the expression -12x² + 3-4x -10, what are the terms?
Type the constant terms in the box below.
Tans Slide
B. In the expression -12x² + 3-4x -10, what are variable terms?
Type the variable terms in the box below.
Answer:
Step-by-step explanation:
12x2 +3-4-10
Express each set in roster notation. Express the elements as strings, not n-tuples.
(a) A^2, where A = {+, -}.
(b) A^3, where A = {0, 1}.
The expression of a function is
(a) {"++", "+-", "-+", "--"}
(b) {"000", "001", "010", "011", "100", "101", "110", "111"}
(a) Roster notation is used to express a set of elements in a compact form. In this case, A is the set {+, -}, and A^2 is the set of all possible ordered pairs of elements from A. This set can be expressed using roster notation as {"++", "+-", "-+", "--"}. The double symbols indicate the two elements of each ordered pair.
(b) Here, A is the set {0, 1}, and A^3 is the set of all possible ordered triplets of elements from A. This set can be expressed using roster notation as {"000", "001", "010", "011", "100", "101", "110", "111"}. The triple symbols indicate the three elements of each ordered triplet.
Learn more about expression here
https://brainly.com/question/14083225
#SPJ4
consider a sample with a mean of 500 and a standard deviation of 100. what are the z-scores for the following data values: 520, 640, 500, 470, and 320? z-score for 520 __z-score for 640 __z-score for 500 __z-score for 470 __z-score for 320 __
The z-scores for the given data values 520, 640, 500, 470, and 320 are:
0.2, 1.4. 0, -0.3, -1.8
To calculate the z-scores for each data value, we can use the formula:
z = (x - μ) / σ
where:
x is the data value
μ is the population mean (in this case, 500)
σ is the population standard deviation (in this case, 100)
Let's calculate the z-scores for each data value:
For x = 520:
z = (520 - 500) / 100 = 0.2
For x = 640:
z = (640 - 500) / 100 = 1.4
For x = 500:
z = (500 - 500) / 100 = 0
For x = 470:
z = (470 - 500) / 100 = -0.3
For x = 320:
z = (320 - 500) / 100 = -1.8
Therefore, the z-scores for the given data values are:
z-score for 520: 0.2
z-score for 640: 1.4
z-score for 500: 0
z-score for 470: -0.3
z-score for 320: -1.8
To know more about z-scores:
https://brainly.com/question/15016913
#SPJ4
a retailer's shipping guidelines prohibit shipping more than 10 pounds worth of merchandise in one medium-sized shipping box. each pair of adult-sized jeans weighs about 1 pound and each pair of adult-sized athletic shoes weighs about 2 pounds.
The limit of 10 pounds per shipment of medium-sized box and the 1 pound weight per jeans and 2 pound weight per pair of shoes, indicates that the graph and ordered pair of inequality are as follows;
13. Please find attached the required graph of the inequality, created with MS Excel
14. 5 pairs of jeans and 4 pairs of shoes weigh more than 10 pounds and can not be packaged in the same medium box.
What is an inequality?An inequality is relationship that compares expressions with different values.
13. The inequality in the question, x + 2·y ≤ 10, indicates that we get;
x + 2·y ≤ 10
2·y ≤ 10 - x
y ≤ (10 - x)/2 = 5 - x/2
y ≤ 5 - x/2
The graph of the inequality, x + 2·y ≤ 10 can be created using the above inequality. Please find attached the required graph created using with the inequality expressed as an equation, followed by shading the feasible region, using MS Excel.
14. The point on the graph that corresponds to 5 pairs of jeans and 4 pairs of shoes, (5, 4), is not in the feasible region. Based on the point (5, 2.5) on the graph, when 5 pairs of jeans are packed in the box, only 2 pairs of shoes can be included. Therefore;
5 pairs of jeans and 4 pairs of jeans can not be packaged in the same medium boxLearn more about inequalities here: https://brainly.com/question/29189207
#SPJ1
What is the degree of 124 - 8x + 4x² - 3? A. 8 B. 12 C. 4 D. 3
The polynomial degree of 12x^4 - 8x + 4x^2 - 3 is option C. 4 .
What is polynomial degree?The highest or greatest power of a variable in a polynomial equation is referred to as the degree of the polynomial. The degree denotes the polynomial's highest exponential power (ignoring the coefficients).
The highest degree of a polynomial's monomials with non-zero coefficients is referred to as the polynomial's degree in mathematics. A term's degree is a non-negative integer and is calculated by adding the exponents of all the variables that occur in it.
To know the degree we will arrange as
12x^4 - 8x + 4x^2 - 3
12x^4+ 4x^2 - 8x - 3
Then we can see that the highest degree is 4.
Learn more about polynomial at:
https://brainly.com/question/2833285
#SPJ1