Negating a statement in terms of quantifiers means expressing the opposite of the statement using quantifiers such as "for all" (∀) and "there exists" (∃) instead of using negation symbols like "not". The key to negating a statement using quantifiers is to switch the quantifiers and negate the predicate.
For example, the negation of the statement "For all x, P(x)" is "There exists x such that not P(x)" because we have switched the universal quantifier "for all" to the existential quantifier "there exists" and negated the predicate P(x). On the other hand, the negation of the statement "There exists x such that P(x)" is "For all x, not P(x)" because we have switched the existential quantifier to the universal quantifier and negated the predicate.
Similarly, the negation of a statement involving "and" or "or" can be found by negating each component and switching the connective. For example, the negation of "P(x) and Q(x)" is "P(x) or not Q(x)" or "not P(x) or Q(x)".
In this context, the negation statements are:
a) There exists x such that x <= 1
b) There exists x such that x > 2
c) For all x, x < 4
d) For all x, x >= 0
e) There exists x such that x >= -1 and x <= 2
f) For all x, x >= 4 and x <= 7
The complete question is given below:
"
Express the negation of each of these statements in terms of quantifiers without using the negation symbol.
a) ∀x(x>1)
b) ∀x(x≤2)
c) ∃x(x≥4)
d) ∃x(x<0)
e) ∀x((x<−1)∨(x>2))
f) ∃x((x<4)∨(x>7))
"
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7 = x + 12 helllllllllllllpppppppppppppppp plllsssssssssssssss
Answer: -5
Step-by-step explanation:
To solve for x, you must use inverse operations.
We must move the 12 from the right, to the left in order to solve for x.
The inverse of addition, is subtraction.
Subtract 12 from both sides
7 - 12 = x + 12 - 12
To subtract a bigger number from a smaller number, flip it around, and make your answer negative
12 - 7 = 5
7 - 12 = -5
Something minus itself is 0
-5 = x + 12 - 12
-5 = x + 0
We like to have x on the left, and the = is symetrical. Just flip it around
x = -5 + 0
x = -5
Verify
7 = -5 + 12
7 = 12 - 5
7 = 7
true
Pre-Algebra - MA3119 B-CR
Translations
Pre-Test Active
Which rule describes the translation below?
S
4
H
77
3
2
4
-5-1-3-1₁
2 ? †
5 6
1
23 4 5 X
The rule of translation is: (x, y) → (x - 5, y - 3)
Option A is the correct answer.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The coordinates are:
S = (1, 5)
T = (1, 1)
U = (4, 1)
And,
S' = (-4, 2)
T' = (-4, -2)
U' = (-1, -2)
We see that,
(1, 5) = (1 - 5, 5 - 3) = (-4, 2)
(1, 1) = (1 - 5, 1 - 3) = (-4, -2)
(4, 1) = (4 - 5, 1 - 3) = (-1, -2)
This is a translation of 5 units to the left and 3 units down.
Thus,
(x, y) → (x - 5, y - 3) is the rule of translation.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
Answer:
The probability of landing on purple is equal to the probability of landing on blue.
This is because each color covers the same number of sections (2 for purple, 3 for blue) and each section has the same size, so the probability of landing on each color is equal.
Probability = Number of successful outcomes / Total number of outcomes
For purple and blue, the number of successful outcomes is the same (2 and 3, respectively) and the total number of outcomes is 8, so the probability of landing on either color is equal.
Probability of landing on purple or blue = 2 / 8 = 3 / 8 = 0.25
Can you help please
Answer: Yes.
Step-by-step explanation:
Proportional relationships are relationships between two variables where their ratios are equivalent. In other words, a proportional relationship is one side is always multiplied/divided by the same value. In this case, the value is 2.
Hope this helps!
Graph the function f(x) = cube root x+1
what are the minimum and maximum values on the intervals [-2, 0]?
There is no maximum and minimum values.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is f(x)=∛(x+1)
Find where the first derivative is equal to 0 to find the local maxima and minima.
By differentiating the given function we get
[tex]f(x)=(x+1)^{\frac{1}{3} }[/tex]
[tex]f'(x)=\frac{1}{3(x+1)^{\frac{2}{3} }}[/tex]
For maxima f'(x)=0
0= [tex]\frac{1}{3(x+1)^{\frac{2}{3} }}[/tex]
No local maxima or minima
Therefore, there is no maximum and minimum values.
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Please help dont know how to do this
The glide reflection maps triangle ABC to triangle A'B'C' is (x, y) -> (x + 8, -y)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The rule for the glide reflection is to first reflect the point across the y-axis and then translate the point 8 units to the right. Mathematically, this can be written as:
(x, y) -> (x + 8, -y)
So, to apply this rule to the vertices of triangle ABC, we would do the following:
A(-4, -2) -> (A(-4, -2) + 8, -(-2)) = A'(4, 2)
B(-2, 6) -> (B(-2, 6) + 8, -(6)) = B'(6, -6)
C(4, 4) -> (C(4, 4) + 8, -(4)) = C'(12, -4)
And so, the glide reflection maps triangle ABC to triangle A'B'C'.
Hence, the glide reflection maps triangle ABC to triangle A'B'C' is (x, y) -> (x + 8, -y)
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The functions f(x) and g(x) are graphed below.
Determine (f+g)(-4)=
Determine (f-g)(3)=
Determine (fg)(0)=
Determine (f/g) (2)=
The numeric values of each expression are given as follows:
(f + g)(-4) = 1.(f - g)(3) = -3.(fg)(0) = -2.(f/g)(0) = -2/3.How to obtain the numeric values of the function?At x = -4, the numeric values are given as follows:
f(-4) = 0, g(-4) = 1.
Hence the addition is given as follows:
f(-4) + g(-4) = 0 + 1 = 1.
At x = 3, the numeric values are given as follows:
f(3) = -1, g(3) = 2.
Hence the subtraction is given as follows:
f(3) - g(3) = -1 - 2 = -3.
At x = 0, the numeric values are given as follows:
f(0) = 2, g(0) = -1.
Hence the product is given as follows:
(fg)(0) = f(0) x g(0) = 2 x -1 = -2.
At x = 2, the numeric values are given as follows:
f(2) = -2, g(2) = 3.
Hence the quotient is given as follows:
(f/g)(0) = f(0)/g(0) = -2/3.
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HURRY WILL MARK BRAINLIEST!
this is a triangular pyramid. all three sides of the base are congruent select all figures that can be formed by the verticals slice perpendicular to the base of the triangular pyramid equilateral triangle isosceles triangle obtuse angle right angle
The figures that will be formed are isosceles triangle and right angle.
option B and D.
What is a triangular pyramid?
A triangular pyramid is a geometric shape that has a triangular base and three triangular faces.
If all three sides of the base are congruent, then a verticals slice perpendicular to the base of the triangular pyramid will form the following figures;
Isosceles triangle ( two equal sides )right angle ( due to perpendicular bisection with the base )Thus, the isosceles triangle will be formed because all three sides of the base are congruent, and third side will be from the vertical slice to the base creating a third unequal side.
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The principal of a large high school is concerned about the number of absences for students at his school. To investigates, he prints a list showing the number of absences during the last month for each of the 2500 students at the school. For this population of students, the distribution of absences last month is skewed to the right with a u = 1.1 and a o = 1.4. If a random sample of 50 students is selected from the list printed by the principal and the sample mean number of absences is calculated, then there is about a 95% chance that the sample mean will fall in which of these intervals. .902 to 1.298 .704 to 1.496 1.1 to 1.694 0 - 3 to 2.5 .506 to 1.1
The mean number of absences for the sample of 50 students will fall within this range.
The 95% confidence interval for the mean number of absences for the sample of 50 students can be calculated using the formula: X ± z*(σ/√n), where X is the sample mean, z is the critical value of the normal distribution at a 95% confidence level (1.96), σ is the population standard deviation (1.4), and n is the sample size (50). The confidence interval can be calculated as follows: X ± 1.96 (1.4/√50) = X ± 0.246. Therefore, the 95% confidence interval for the mean number of absences for the sample of 50 students is 0.902 to 1.296.
The formula can be interpreted as follows: the sample mean is likely to fall within the interval of 0.902 to 1.296, plus or minus 1.96 times the standard deviation of the population divided by the square root of the sample size. Since the population standard deviation is 1.4 and the sample size is 50, the interval is 0.902 to 1.296. This interval gives us a 95% confidence that the mean number of absences for the sample of 50 students will fall within this range.
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e highest possible measurement scale (nominal, ordinal, interval, ratio) for each of the variables listed in question 1. write your answers in sentence or lower case. do not write anything else in addition to the scale of measurement. only nominal, ordinal, etc. please check your spelling before submitting!! credit will not be given for missing, or misspelled answers. age in years
The measurement scale for "age in years" is ordinal, meaning the values have a specific order or ranking, but no notion of equal distances between them.
The "age in years" measurement scale is ordinal. An ordinal scale is a type of measurement scale that has a specific order or ranking to its values, but there is no notion of equal distances between the values. In the case of "age in years," the values have a clear order (e.g., 25 years old is younger than 30 years old), but it doesn't make sense to say that a difference of 5 years is the same as a difference of 1 year. This is why age in years is considered to be measured on an ordinal scale.
Additionally, with an ordinal scale, the values can only be compared in terms of their order or ranking, and not in terms of the actual differences between them. For example, we can say that someone who is 25 years old is younger than someone who is 30 years old, but we cannot say that a person who is half as old as someone who is 50 years old at the age of 25. This is because an ordinal scale does not have a meaningful zero point and does not allow for meaningful comparisons of the absolute size of differences between values. An ordinal scale is the second highest measurement scale, below interval and ratio scales, which provide more information about the magnitude of the values being measured.
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List in order from least to greatest all the whole number factors of 28.
Which reason justifies the second statement in the proof below?
Given: parallelogram L E N S and parallelogram N G T H
Prove: Angle L is congruent to angle T.
A. In a parallelogram, consecutive angles are supplementary.
B. Alternate Interior Angles Theorem
C. In a parallelogram, opposite angles are congruent.
D. Corresponding Angles Postulate
SOMEONE PLEASE HELP!
The reason that justifies the second statement "Angle L is congruent to angle T" is:
In a parallelogram, opposite angles are congruent.
Option C is the correct answer.
What is a parallelogram?A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
Parallelogram LENS and parallelogram NGTH
Now,
Parallelogram LENS:
∠L = ∠N _____(1)
Opposite angles are equal.
Parallelogram NGTH:
∠N = ∠T ______(2)
Opposite angles are equal.
Now,
∠ENS = ∠GNH
Vertical angles are equal.
So,
From (1) and (2).
∠L = ∠T
Angle L is congruent to angle T
Thus,
Angle L is congruent to angle T
[ In a parallelogram, opposite angles are congruent ].
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What percent of a 120-gallon tank is full if it contains 90 gallons?
Answer:
The vertical tank is basically a cylinder that is sometimes referred to as a V-120 cylinder. Both 120-gallon tanks can hold up to 96 gallons of propane when full (not 120 gallons). That’s due to the 80% rule; all propane tanks can be filled up to 80% of their maximum capacity.
Answer:
75%
Step-by-step explanation:
twenty-five randomly selected students were asked the number of movies they watched the previous week. the results are as follows:
Step 1: To construct
The box plot for the given data.
Step 2 : Explanation
Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot.
Use a horizontal or vertical number line and a rectangular box to make a box plot. The axis's ends are labelled by the smallest and largest data values. One end of the box is marked by the first quartile, while the other end is marked by the third quartile. Approximately half of the data is included within the box. From the box's ends to the smallest and greatest data values, the "whiskers" extend. The median or second quartile can be in the middle of the first and third quartiles, or it can be either one or the other.
The box plot's five numerical summaries are as follows:
# of movies Frequency Cumulative frequency
0 5 5
1 9 14
2 6 20
3 4 24
4 1 25
N=25
in a boxplot, the dashed vertical line in the middle of the box represents which of the following measures of location?
Box plot is the use of a rectangle to represent data where the vertical sides of the rectangle represents the lower and upper quartile.
From the box plot,
The minimum is 153 cm
The first quartile is 168.4 cm
The second quartile is 174.2 cm
The third quartile is 183.9
The maximum is 195 cm
See attachment for the missing box plot.
There are 5 vertical lines in a box plot
The first represents the minimum value
The second represents the first quartile
The third represents the second quartile i.e. the median
The fourth represents the third quartile
The last represents the maximum quartile
From the attached box plot.
The first vertical line is 153 cm
The second vertical line is 168.4 cm
The third vertical line is 174.2 cm
The fourth vertical line is 183.9 cm
The firth vertical line is 195 cm
Hence:
The minimum is 153 cm
The first quartile is 168.4 cm
The second quartile is 174.2 cm
The third quartile is 183.9
The maximum is 195 cm
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What is 67% as a fraction
Answer:
67/100
Step-by-step explanation:
Hi can someone please help me with these questions I'm really struggling with them!!!
Answer:
Step-by-step explanation:
∠ EGF=180-∠FGH
= 180-(180-112)
= 112°
∠LKM= 90= 8X -6
2(4X-3)=90
4X-3=45°
3)
22=4X-10
X=8
NR= 3(8) +6
= 30
Element X is a radioactive isotope such that its mass decreases by 51% every day. If
an experiment starts out with 150 grams of Element X, write a function to represent
the mass of the sample after t days, where the hourly rate of change can be found
from a constant in the function. Round all coefficients in the function to four decimal
places. Also, determine the percentage rate of change per hour, to the nearest
hundredth of a percent.
The percentage rate of change per hour to the nearest hundredth is 3%.
Function to represent decay is A(t)= 150×([tex].97^{t}[/tex]).
What is percentage?Percentage means out of hundred. If we want to calculate percentage the we have to make the fraction out of hundred.
It means that if same thing is distributed among 100 people how much a single person would get.
Now for the given question:
For radioactive decay the mathematical equation is
A(t) = A(0)[tex](1-r)^{t}[/tex]
where A(0) is the initial quantity = 150 gm. and r is the rate of decay = 51%
For hourly decay,
A(24)= A(0)(1-0.51) as 1 day has 24 hour and each day substance decay by 51%.
A(24)= A(0)×0.49
but,
A(24)= A(0)[tex](1-r)^{24}[/tex]
0.49A(0)=A(0)[tex](1-r)^{24}[/tex] (we do this to calculate r)
.049= [tex](1-r)^{24}[/tex]
1-r = [tex]\sqrt[24]{.49}[/tex]
1-r= 0.97
r = 1- 0.97
r= 0.03
r = 3%
Function for hourly decay,
A(t) = 150 ×[tex](1-r)^{t}[/tex]
A(t) = 150 ×[tex](1-0.03)^{t}[/tex]
A(t)= 150×([tex].97^{t}[/tex])
Hence, Hourly rate of decay is 3% and the equation for hourly rate o decay is A(t)=150×[tex].97^{t}[/tex].
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based on the table, do the data support the use of a normal model to approximate population characteristics?
Yes, as the relative frequency distribution closely resembles the empirical criterion for normal models.
Frequency tables or charts are used to represent frequency distributions. Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range. The distribution is known as a relative frequency distribution in the latter case.
What is the relative frequency distribution formula?
Subgroup Count / Total Count: Relative Frequency
Because they let us determine how frequent a certain value is in a dataset in comparison to all other values, relative frequency distributions are helpful.
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3. Let g(x) be the elevation in feet of the Mississippi river x miles from its source.
a. What does g(10)=62 mean in the context of this application?(What are the units here?)
b. What does g'(10)=-2.4 mean in the context of this application? (What are the units here?)
c. Use this information to estimate the elevation of the Mississippi 11 miles from its source.
a)
g(10) = 62 means at 10 miles from the source, the elevation of the Mississippi river is 62 feet.
b)
The rate of change of the elevation with distance from the source is -2.4.
c)
The elevation of the Mississippi 11 miles from its source is 59.6 feet.
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,
g(x) is the elevation in feet of the Mississippi river x miles from its source.
a)
g(10) = 62
This means,
At 10 miles from the source, the elevation of the Mississippi river is 62 feet.
b)
g'(10 = -2.4
This means,
The rate of change of the elevation with distance from the source is -2.4.
It is negative because the river flows downward.
The unit is feet per mile.
c)
We can make g(x) = mx + c
m = -2.4
(10 , 62) = (x, g(x))
So,
62 = -2.4 x 10 + c
62 = -24 + c
c = 62 + 24
c = 86
And,
g(x) = -2.4x + 86
So,
At x = 11 miles
g(11) = -2.4 x 11 + 86
g(11) = -26.4 + 86
g(11) = 59.6
Thus,
g(10) = 62 means at 10 miles from the source, the elevation of the Mississippi river is 62 feet.
The rate of change is -2.4.
The elevation of the Mississippi 11 miles from its source is 59.6 feet.
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If $23,000 is invested for 1 yr at 4% simple interest, how much interest is earned?
Answer:$920
Step-by-step explanation:
Step-by-step explanation:
The interest earned is $920.
On saturday, the ratio of the amount of water sued by Household A to the amount of water used by Household B is 13:5. Household A uses 975 litres of water. Determine the total amount of water used by the two households on Saturday.
Answer:
1350
Step-by-step explanation:
A:B = 13:5 = 975:x
x=975/13*5 =375
total =975+375 = 1350
We use the proportional method
Let A = water used in household A.
Let B = water used in household B.
A to B = 13 to 5
A = 260 gal
260 to B = 13 to 5
260/B = 13/5
13B = 5 * 260
B = 100
A + B = 260 + 100 = 360
The total is 360 gallons.
Graph the function f(x)=\root(3)(x+1). What are the minimum and maximum values on the interval [−2, 0]? Write your answers in the boxes.
The minimum and the maximum values of the function f(x) = ∛(x+1) on the interval [−2, 0] are
maximum = 1minimum = -1How to find the minimum and the maximum valuesThe maximum and minimum values are pointed out from the graph by tracing the lowest point within the range and the highest point within the range to the graph, then to the output of the graph
The minimum point was at -2 and this gave an output of -1
The maximum point was at 0 and this gave an out put value of 1
The graph is attached
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a car complets a journey of 1330km in 14 hours.What is the average speed in km per hour?
Answer:
95km/h
Step-by-step explanation:
Divide 14km/h by 1330km to find out the equally distributed km/h per km:
1330km/14km/h
[95km/h]
Is this correct pls help meee
Answer:
No the answer is
[tex]14 - 7y[/tex]
Find the exact perimeter of quadrilateral ABCD plotted below.
A(-3,2)
D(0,-6)
B(6,-2)
C(3,-6)
Perimeter of quadrilateral is 26.39 unit.
What is the distance between two points?Distance between two points with coordinates (x₁ , y₁) and (x₂ , y₂). is given by
D = √[(x₁ - x₂)² + (y₁ - y₂)²]
This formula is derived from the Pythagoras Theorem, as the points form a right triangle in plane, with the hypotenuse representing the distance between them.
Given,
Quadrilateral ABCD
A(-3,2)
D(0,-6)
B(6,-2)
C(3,-6)
Perimeter = distance between A and B + distance between B and C + distance between C and D + distance between D and A
Perimeter =
√[(-3 -6)² + (2 - -2)²] + √[(6 - 3)² + (-2 - -6)²] +
√[(3 - 0)² + (-6 - -6)²] + √[(0 - -3)² + (-6 - 2)²]
Perimeter = √[(-9)² + (4)²] + √[(3)² + (4)²] + √[(3)² + (0)²] + √[(3)² + (-8)²]
Perimeter = √[81 + 16] + √[9 + 16] + √[9 - 0] + √[9 + 64]
Perimeter = √[97] + √[25] + √9 + √[73]
Perimeter = 9.85 + 5 + 3 + 8.54
Perimeter = 26.39 unit
Hence, 26.39 unit is the perimeter of quadrilateral ABCD.
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A researcher conducted an experiment on the effect of caffeine on memory in college students in the United States. The researcher randomly assigned each of 100 students to one of two groups. received caffeinated coffee followed by a memory test. The second group received decaffeinated coffee followed by a memory test. The researcher calculated the aver- age number of items correctly recalled in each group. a. What is the population? b. What is the sample? c. The group that received decaffeinated coffee is a(n) d. The group that received caffeinated coffee is a(n) e. The sample contains -participants. The population contains f. The averages calculated after the memory test is a
The sample has 100 participants, the population has all college students. Averages after the memory test represent mean effect of caffeine on memory for the sample.
a. The population in this experiment is all college students in the United States.
b. The sample in this experiment is the 100 students who participated in the study.
c. The group that received decaffeinated coffee is the control group.
d. The group that received caffeinated coffee is the experimental group.
e. The sample contains 100 participants. The population contains all college students in the United States.
f. The averages calculated after the memory test are the mean number of items correctly recalled in each group. These means represent the average effect of caffeine on memory for the sample of 100 college students who participated in the study. The results of the study can be used to make inferences about the population of all college students in the United States. However, it is important to keep in mind that the sample may not be representative of the entire population and further studies may be needed to make stronger conclusions about the effect of caffeine on memory in college students.
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A physical education teacher uses a pedometer to record the number of steps that a student completes in a 40-minute physical education class. Differentiate among the test, measurement, and evaluation characteristics reflected in this activity
The physical education teacher is using a pedometer to measure the number of steps taken by a student in a 40-minute physical education class, which can then be used to evaluate the student’s performance and physical fitness level.
Test: A test is a tool used to collect data by which a physical education teacher can assess the physical fitness of their students. In this case, the physical education teacher is using a pedometer to measure the number of steps taken by a student in a 40-minute physical education class. This data can be used as a measure of physical fitness.
Measurement: Measurement is the process of assigning a numerical value to a physical education student’s performance. The pedometer is the tool used to measure the number of steps taken by a student in a 40-minute physical education class. This numerical value serves as an indicator of the student’s physical fitness level.
Evaluation: Evaluation is the process of assessing the physical education student’s performance in relation to the expected performance standards. The teacher will use the numerical data collected by the pedometer to evaluate the student’s performance and physical fitness level. The teacher will then use this information to make changes to the physical education program and to provide feedback to the student.
In conclusion, the physical education teacher is using a pedometer to measure the number of steps taken by a student in a 40-minute physical education class, which can then be used to evaluate the student’s performance and physical fitness level. This is a great example of how test, measurement, and evaluation can be used to assess student performance.
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Add adverb clauses to these sentences
(1 ) Mrs. Pan was unhappy.
(2 ) Mrs. Pan went to the store
The complete statements are:
(1) Although Mrs. Pan was unhappy, she tried to hide it.(2) After she finished her chores, Mrs. Pan went to the store.How to determine the complete statementAs a general rule, an adverbial clause, sometimes referred to as an adverb clause, is a group of words that, together, functions as an adverb.
They are introduced to a statement by words such as although, though, etc
Using the above as a guide, we have the following:
(1) Although Mrs. Pan was unhappy, she tried to hide it.(2) After she finished her chores, Mrs. Pan went to the store.Read more about adverb at
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The complement of an angle is 30 less than twice the angle. Find the
larger angle.
Answer:
50 degrees. Complementary angles are any two angles that add up to 90 degrees. In this case, if the complement is 30 less than its bigger angle, and the bigger angle is twice the size of its complementary angle, then that would mean you take the unknown angle as x.(WORK SHOWN BELOW)
Step-by-step explanation:
[tex]x=2\times (\left90-x)\right-30\\[/tex]
Then regroup
[tex]x= 180-2x-30[/tex]
Work with like terms. For example, a whole's like term is another whole.
[tex]x+2x=(\left180-30)\right\\180-30=150\\x+2x=1+2\\x+2x=3x\\3x=150[/tex]
If 3x is the same as 150, then 150 divided by 3 is also x. We know this because almost any correct equation with some form of a constant or variable can be flipped into the opposite of itself.
[tex]x=\frac{150}{3}[/tex]
And lastly, 150 divided by 3 is 50.
Hope this helps!