The pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers is number line.
What is meant by pedagogical tool?
In math, pedagogical tool refers designed to convey important lessons and allow people to improve their understanding of a problem or undertaking.
Here we need to find the research recommends that teachers use the following pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers.
While we looking into the given question, here we need to find the tool that is used to find the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers that is none other than number line because it uses the visual representation of the number that gives better understanding of number.
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Evaluate the expression 6x +4 9/10 when x=2/3
Answer:
8 [tex]\frac{9}{10}[/tex]
Step-by-step explanation:
substitute x = [tex]\frac{2}{3}[/tex] into the expression
(6 × [tex]\frac{2}{3}[/tex] ) + 4 [tex]\frac{9}{10}[/tex]
= (2 × 2) + 4 [tex]\frac{9}{10}[/tex]
= 4 + 4 [tex]\frac{9}{10}[/tex] ( add the whole numbers )
= 8 [tex]\frac{9}{10}[/tex]
sara correctly solves a system of two linear equations and finds that the system has no solution. if one of the two equations is -
When two system of linear equations solved by Sara represents the lines parallel to each other then the equations have no solution.
Step by Step explanation:
Given system of two linear equations :
Let us consider system of two linear equation with Sara has :
y = 3x + 7
y = 3x + 9
Here both the lines have same slope = 3
Lines are parallel to each other.
Solve the equation by elimination method :
y = 3x + 7
y = 3x + 9
0 = 0x - 2
⇒ -2 = 0 which is not possible and has no solution.
Therefore, when the system of linear equations with Sara has no solution it represents lines are parallel to each other.
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The box below is opened by pressing any two buttons
whose numbers multiply together to give 12√6.
Select all of the numbers on buttons that can be used
as part of a pair to open the box.
3√2
4√3
3
√6
4√6
4√2
3√4
4
12√2
The multiplication that will give a value of 12✓6 from the numbers will be:
3✓2 × 4✓3
3 × 4✓6
How to illustrate the expression?It should be noted that addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case, it should be noted that:
3✓2 × 4✓3 = 12✓6
3 × 4✓6 = 12✓6
It should be noted both scenarios highlight the given value of 12✓6.
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organizations interested in making sure that accused persons have a trial of their peers often compare the distribution of jurors by age, education, and other socioeconomic variables. one such study in a large southern county provided the following information on the ages of 1,000 jurors and the age distribution countywide. Soc. Age 21-40 41-50 51-60 Over 60 Total 399 212 Number of jurors Age % countywide 231 158 1,000 42.1 22.9 15.7 19.3 100 a. Display the above data using appropriate graphs. b. Is this significant evidence of a difference between the age distribution of jurors and the countywide age distribution? c. Does there appear to be an age bias in the selection of jurors?
Yes, it is significant evidence of a difference between the age distribution of jurors and the countrywide age distribution.
No, there is no age bias in the selection of jurors.
P Oi Ei ( Oi-Ei) ^2/Ei
0.421 399 421 1.149643705
0.229 231 229 0.017467249
0.157 158 157 0.006369427
0.193 193 193 1.870466321
1 1000 1000 3.043946702
The above can be represented in graphs.
Now,
Ei = n × pi
TS = 3.04394672
From TS < value
Value (7.81472)
We fail to reject the null hypothesis at 5% value of significance
No, there is no age bias in the selection of jurors.
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Solve the following system of equations graphically on the set of axes below.
y=-x-6
x-2y=-6
Plot two lines by clicking the graph.
Click a line to delete it.
Convert from point slope form to slope intercept form.
Slope U/D, (5,0)
Please help me!!!!!!!
Answer:
x = 5
Step-by-step explanation:
assuming you mean the slope of the line id undefined and passes through (5, 0 )
A line with an undefined slope is a vertical line parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (5, 0 ) with x- coordinate 5 , then
x = 5 ← equation of line
A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary. The sample information is submitted to Minitab with the following results: Analysis of Variance Source Factor df Ss MS F 3 28.17 9.39 5.37 0.133 15 26.26 1.75 18 54.43 Total What is the decision rule? (Round your answer to 2 decimal places.) eject H0 if F> At the 0.01 level of significance, is there a difference in the mean number of months before a raise was granted among the four CPA firms? Do not reject O Reject
Treatment remains the same. Do not Reject.
Test Statistics:
[tex]f = \frac{\text{treatment}}{\text{error}} = 5.37[/tex]
Reject Null Hypothesis if [tex]f > f(a, a-1, N-a)[/tex]
Critical Value [tex]f(0.01, 3, 15) = 5.42 \text{ (From F Table)}[/tex]
[tex]\because 5.37 < 5.417[/tex]
We fail to Reject [tex]H0[/tex]
[tex]\therefore[/tex] Do not Reject.
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Please help!!!!!!!!!!
Answer: [tex]6^{\frac{1}{12} }[/tex]
Step-by-step explanation:
A tank is full of water. The tank is a right circular cylinder lying on its side (length is parallel to horizon), with radius 2 m, and length 5 m. Find the work required to pump the water out of a spout that rises 2 m above the tank. Set up the integral, but do NOT evaluate. The base of a solid is a circular disk with radius
The integral for the work required to pump the water out of a spout that rises 2 m above the tank is
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex] dx
Integral
An integral in mathematics is either a numerical value equal to the area under the graph of a function for some interval or a new function, the derivative of which is the original function (indefinite integral).
Given that:
r = 2m
l = 5m
sinθ = [tex]\frac{x}{r}[/tex]
dv = 2l [tex]\sqrt{r^{2} + x^{2} }[/tex] dx
Let p be the density of water and g be the acceleration due to gravity.
dm = p dv
dw = dmg (h + r - x)
dw = pg (h + r - x) dx
dw = 2l pg (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex] dx
w = ∫dw
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex] dx
Therefore, the integral for the work required to pump the water out of a spout that rises 2 m above the tank is
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex] dx
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78 POINTS BRANLIEST CHECK WILL DELETE U IF WRONG ANSWER
Answer:
Below
Step-by-step explanation:
For the boxes:
the sum of all three angles = 180 for a triangle
soooo : 28 + x-4 + 2x = 180
then x = 52 via algebra
100 points
Pls pls pls help
What is the measure of angle R in this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the hundredths place (2 decimal places).
m∠R=
Answer:
m∠R = 61.92°------------------------------------
Use trigonometry.
Since all three sides are known, you may choose either sine, cosine or tangent.
We'll use sine here:
sine = opposite leg / hypotenusesin ∠R = TS/TRsin ∠R = 60/68sin ∠R = 0.8823m∠R = arcsin 0.8823m∠R = 61.92°1.25y-0.35y=585
Solve for y
Answer:
y = 650
Step-by-step explanation:
0.9y = 585
y = 650
Answer:
[tex]y = 650[/tex]
Step-by-step explanation:
[tex]1.25y-0.35y=585[/tex]
[tex]0.9y=585[/tex]
[tex]y = \frac{585}{0.9}[/tex]
[tex]y = 650[/tex]
revie
the blanks.
Leo and his friends like to collect and trade cards from a certain combat card game. Leo used
his allowance to purchase 9 booster packs and 5 premade decks, which included a total of
253 cards. For his birthday, he received 7 booster packs and 5 premade decks, which
included a total of 229 cards. How many cards come in every booster pack and every
premade deck?
Find a formula for the general term an of the geometric sequence:
{ 10/3, 10/9, 10/27, 10/81, 10/243}
Express the common ratio r as a fraction and place in parentheses!
an = __________
Answer: [tex]\displaystyle \frac{10}{3}\left(\frac{1}{3}\right)^{n-1}[/tex]
======================================================
Explanation:
a = 10/3 is the first term
r = 1/3 is the common ratio
Multiply each term by r = 1/3 to get the next term.
Example:
(10/3)*(1/3) = 10/9
We then plug those two items into the formula
[tex]a_n = a(r)^{n-1}[/tex]
to end up with the answer shown above.
The value of n is a positive integer.
The graph represents Tamira's motion detector walk. Complete the following sentences based on the graph.
Note that:
For 1) To compute the average rate (AR), divide the change in y-values by the change in x-values. That is:
AR = (5-2)/5-4)
= 3/1
= 3ft/sec.
For 2) we must use the same formula above:
(2-5)/(10-7)
= -1 ft/sec.
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Full Question:
See attached graph
The graph shows the elevation of a hiker compared to ground level.
What is the y-intercept?
Answer:
-15
Step-by-step explanation:
State if the three side lengths form an acute, obtuse or right triangle. 9m, 12m, 15m
The three side lengths; 9m, 12m, 15m as given in the task content would form a right triangle.
What type of triangle is formed by the three side lengths as given in the task content?It follows from the task content that the type of triangle formed by the side lengths given is to be determined.
On this note, recall that given three side lengths, a, b and c where c is the longest of all three side-lengths;
if; c² > a² + b² .....Obtuse triangle.
if; c² < a² + b².......Acute triangle.
if; c² = a² + b²........Right triangle.
On this note, since;
15² = 12² + 9²
225 = 144 + 81
225 = 225.
The three side lengths in discuss would form a right triangle.
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Put the slope intercept form
Which statement is true about the functions f(x)=-15x^2+32 and g(x)=-17x^2+5x+32? a. f(x) and g(x) have the same zeros. b. f(x) has a higher maximum than g(x). c. f(x) and g(x) have the same y intercept. d. f(x) and g(x) are odd functions.
None of the Options are true both the given functions are parabolic functions.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given function are, f(x)=-15x²+32 and g(x)= -17x²+5x+32,
Zeros for the functions are,
x = ± 1.461 and x = -1.233 and 1.527,
Where g(x) has a higher maximum than f(x), the Intercept of f(x) is greater than g(x). As shown in the graph.
Thus, none of the options are true because both of the supplied functions are parabolic.
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The University is conducting a similar analysis on how much of the 80-minute TR class sessions are used for instruction. There is evidence from a previous study that the population standard deviation for duration time is
2.1
minutes. A random selection of 83 class sessions this semester yields an average duration time of 78 minutes. (a) Calculate a
90%
confidence interval the parameter of interest. (No interpretation needed in your final answer; just the numeric interval.) (a) [5 pts] (b) What is the minimum sample size required to estimate the mean duration time of TR classes to within
0.5
of a minute with
99%
confidence? (b) [5 pts] (c) Suppose that the sample standard deviation for duration times in this study is
2.6
minutes. Calculate a
95%
confidence interval for
σ 2
, the population variance.
The minimum sample size required to estimate the mean duration time of TR classes is t distribution confidence interval.
The confidence interval is 75.0694 and 76.9306.
Given that
(a) This is t-distribution confidence interval because sample standard deviation is given and also sample size is less than 30.
(b)
CI for 95%
n 28
mean 76
value of 95% CI and df = 27 (using table) 2.0518
std. dev. 2.4
SE = standard deviation/n² 0.45356
ME = t*SE 0.93062
Lower Limit = Mean - ME 75.06938
Upper Limit = Mean + ME 76.93062
95% CI (75.0694 , 76.9306 )
95% CI=75.0694 , 76.9306
(c)The 95% confidence interval estimate of the population mean is within 75.0694 and 76.9306 (lower bound and upper bound)
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Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) 5 f(x) a = 2 1 + x
The first four nonzero terms of the series for f(x) from the taylor series is F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....
Given that,
We have to get the first four nonzero terms of the series for f(x), centering at the specified value of a, use the definition of a Taylor series. (Separate your responses into a list using commas.)
f(x)=5/1+x and a=2
We know that,
Take
f(x)=5/1+x and a=2
f(2)=5/1+2=5/3
f'(x)=-5/(1+x)² f'(2)=-5/(1+2)²=-5/9 (differentiating)
f''(x)=10/(1+x)³ f''(2)=10/(1+2)³=10/27
f'''(x)=-30/(1+x)⁴ f'''(2)=-30/(1+2)⁴=-30/81=-10/27
Using the taylor series
F(x)=f(a)-(x-a)f'(a)+(x-a)²/2!f''(a)-(x-a)³/3!f'''(a)+....
F(x)=f(2)-(x-2)f'(2)+(x-2)²/2f''(2)-(x-2)³/3!f'''(2)+....
F(x)=5/3-(x-2)(5/9)+(x-2)²/2(10/27)-(x-2)³/6(-10/27)+....
F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....
Therefore, The first four nonzero terms of the series for f(x) from the taylor series is F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....
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On the grid above, flag F is rotated around point S. Which of the images does NOT result from this transformation?
A.
image 3
B.
image 2
C.
image 1
D.
All of the images result from this transformation
.
A figure in the flag has rotational symmetry if the figure can be mapped onto itself by a rotation between 0° and 360° about the center of the figure.
What is symmetry?Symmetry in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Something is symmetrical when it is the same on both sides. A shape has symmetry if a central dividing line (a mirror line) can be drawn on it.To learn more about symmetry refer to:
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Given the matrix [2 5 5 13], (a) does the Inverse of the matrix exist? Your answer is (Input Yes or No): (b) If your answer is yes, write it as [a_11 a_12 a_21 a_22], find a_11 = a_12 = a_21 = a_22 =
Yes, the inverse of the matrix exist and a11 = 13 , a12 = -5 , a21 = -5 and a22 = 2
The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity.
The matrix whose determinant is non-zero and for which the inverse matrix can be calculated is called an invertible matrix.
According to the question,
The matrix given is [tex]\left[\begin{array}{cc}2&5\\5&13\end{array}\right][/tex]
Let Matrix be A
To check if its inverse exist , We have to find out the determinant
|A| = 13(2) - 5(5)
=> 26 - 25
=> 1
Determinant is non zero
Hence , Inverse exist
(b) To find the inverse , we have to find the adjoint of A
adj A = [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex]
Inverse is ratio of adj A and determinant A
A⁻¹ = adj A / |A|
=> [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex] / 1
=> A⁻¹ = [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex]
a11 = 13 , a12 = -5 , a21 = -5 and a22 = 2
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order these numbers for least to greatest -4,5,-2,1,0
Answer: 0, 1, 5, -2 ,-4
Step-by-step explanation: hope it helps
Question 29 The Valley of Ashes symbolizes the emotional turmoil and feelings of the characters the working class who enable the lifestyles of the wealthy the negative economic impact of prohibition laws Gatsby's fears
The Valley of Ashes symbolizes the emotional turmoil and feelings of the characters the working class who enable the lifestyles of the wealthy the negative economic impact of prohibition laws Gatsby's fears organized crime
What is the Valley of Ashes?On the north shore of Long Island, the valley of ashes was a two to three thousand acre marshland that encircled the Flushing River mouth. This small river primarily serves as an inlet into Flushing Bay, which is an arm of the East River, with tidal water flowing through it rather than fresh water.
It is a metaphor for the moral and societal decay brought on by the unrestrained pursuit of wealth, as the wealthy indulge in only their own pleasure. The emotional turmoil and feelings of the characters from the working class that support the lifestyles of the wealthy are symbolized by The Valley of Ashes. the damaging effects of prohibition laws on the economy Gatsby worries about organized crime.
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If a nonlinear system depends on a parameter, then the equilibrium points can change as the parameter varies. In other words, as the parameter changes, a bifurcation can occur. Consider the one-parameter system family of systems dx = x2 – a =-y(+2+1), where a is the parameter.(a) Show that the system has no equilibrium points if a < 0. (b) Show that the system has two equilibrium points if a > 0. (c) Show that the system has exactly one equilibrium point if a = 0. (d) Find the linearization of the equilibrium point for a = 0 and compute the eigenvalues of this linear system.
If a<0, then there is no x-null lines, the system has no equilibrium points.
If a=0, it has only one equilibrium points.
If a>0, the system has two equilibrium points.
Points are (-√a,0) and (√a,0)
The system changes from no fixed points to two fixed points when it increases through a=0.
a is a bifurcation point.
The Jawbian matrix,
J = [tex]\left[\begin{array}{ccc}2x&0\\-2xy&x^{2}-1\\\end{array}\right][/tex]
Now,
J[0,0] = [tex]\left[\begin{array}{ccc}0&0\\0&-1\\\end{array}\right][/tex] =0
J[-√a,0] = [tex]\left[\begin{array}{ccc}-2\sqrt{a} &0\\0&-a-1\\\end{array}\right][/tex] = 2a√a + 2√a
If a=0, then it will be a live equilibrium, one of the values are 0, For a>0, the point (-√a,0) is sink and (√a,0) is a saddle points.
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a recipe asks for 223cups of raisins. how many cups of raisins are needed to make 12of a recipe? multiply. express the answer in simplest form. enter the answer in the box.
The anwer of number of cups of raisins required for 12 recipes needing 223 cups of raisins each are 2676.
Multiplication operation will be required to find the number of cups of raisins. The expression to be formed for calculation is-
Total number of cups = number of recipes × number of cups for one recipe
Keep the values in formula to find the total number of cups
Total number of cups = 12 × 223
Performing multiplication on Right Hand Side of the equation
Total number of cups = 2676
Thus, 2676 cups are required for recipe.
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Find an explicit description of Nul A by listing vectors that span the null space. 1 2 3 0 A = 0 0 1 0 A spanning set for Nul A is (Use a comma to separate answers as needed.)
An explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.
What is the explicit description of a null space matrix?
To find an explicit description of the null space of matrix A, we can find a spanning set of vectors that span the null space.
The null space of matrix A, denoted Nul A, is the set of all vectors x that satisfy the equation Ax = 0. In other words, the null space consists of all vectors that are mapped to the zero vector by the matrix A.
To find a spanning set for Nul A, we can use the following steps:
Row reduces the matrix A to a reduced row-echelon form using elementary row operations.
Identify the free variables in the row-reduced matrix.
For each free variable, create a vector with a 1 in the position corresponding to the free variable and 0's in all other positions.
The set of vectors created in step 3 form a spanning set for Nul A.
For example, consider the matrix A = [1, 2, 3, 0; 0, 0, 1, 0]. To find a spanning set for Nul A, we can row reduce the matrix to reduced row-echelon form:
[1, 2, 3, 0] -> [1, 2, 3, 0]
[0, 0, 1, 0] -> [0, 0, 1, 0]
The matrix is already in reduced row-echelon form, so there are no more elementary row operations to perform. The free variables in this matrix are the third and fourth columns, which correspond to the variables x3 and x4, respectively. Therefore, we can create the following vectors:
x3 = [0, 0, 1, 0]
x4 = [0, 0, 0, 1]
These vectors form a spanning set for Nul A, as they are linearly independent and span the null space.
Hence, an explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.
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Which linear function has the greatest rate of change?
A. The Equation
B. The Table
C. The graph
Answer:
The graph
Step-by-step explanation:
The graph has a slope of 4, the equation has a slope of 3, the table has a slope of 2.
manny has just filled out his deposit ticket for his savings account. he hands it to the teller and the teller hands it back to manny. the teller explains to manny that the deposit ticket cannot be accepted in its current form. what must manny do to the deposit ticket in order for the teller to process the deposit ticket? a deposit ticket. the ticket has not been signed for cash back. the date is december 16. a. manny forgot to sign the deposit ticket for less cash back
The manny must do his signature on the deposit ticket in order to get deposited the cashback ticket.
What is cashback?
Cashback is a type of reward program offered by some retailers and online merchants that gives customers money back for making purchases. It is a way for retailers to reward customers for their loyalty and encourage them to keep coming back to their store. Cashback can be offered in the form of a fixed amount, a percentage of the purchase price, or a combination of both. Cashback rewards may be paid in cash or as credits to the customer's account, and they may be used to purchase additional items from the store or to offset future purchases.
When teller sees the deposit ticket he must have seen that it is not signed by manny hence he returned this to manny now manny just have to do one work that to sign that deposit ticket after that teller will accept that deposit ticket and manny will get his required cashback easily in his bank account
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Answer:
a edge
Step-by-step explanation: