Answer:
the square root function stretched by 2 and shifted so that its turning point is located at (3,-5) is h(x) = 2 * sqrt(x + 3) - 5.
Step-by-step explanation:
random samples of size 100 are drawn. from the population to generate a sampling distribution of sample means
The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.
The population propose will match the pattern mean's proposal. The population trendy deviation divided by the rectangle root of the sample length yields the same results as the standard deviation of the distribution of the sample means, also known as the same old mistakes of the proposed (n).
The general sample recommends factors to be included in the pattern mean calculation.
The population suggest is calculated using the sum of all values within the population denoted with the aid of the summation of X divided by the number of values in the population that is denoted with the aid of N. The population suggest is the mean or average of all values within the given population.
Therefore,
The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.
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Find the value of csc for the angle 0 in standard position having 5,-12) on its terminal side
The cosecant of the angle is 0.2
How to determine the cosecant of the angle?From the question, we have the following parameters that can be used in our computation:
(5,-12)
This means that
(x, y) = (5,-12)
The csc(θ) is calculated as
csc(θ) = 1/x
Substitute the known values in the above equation, so, we have the following representation
csc(θ) = 1/5
Evaluate
csc(θ) = 0.2
Hence, the value of csc(θ) is 0.2
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PLEASE HURRY WILL GIVE BRAINLIEST
whats 2 + 2?
Answer
[tex]2 + 2 = 4[/tex]
Answer:
4
Step-by-step explanation:
2+2
4
hope it helps. Nice time
The table represents a linear function. Find the missing values to complete the table.
A) x = 1, y=17/3
B) x= 1, y = 21/3
C) x = 5, y = 17/3
D) x = 5, y = 21/3
The value of missing x = 5
The value of missing y = 17 / 3
How to find the Slope ?The standard line equation, y = mx + b, or the slope formula, m = (y2 - y1)/(x2 - x1), can both be used to find the slope, m.
According to the given information
Let two points be [tex](x_{1} , y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] are ( 3 , 8 ) and ( 6 , 15 )
Slope of the two points = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
= [tex]\frac{15-8}{6-3}[/tex]
= 7 / 3
Let the equation passing through points ( 3 , 8 ) be
[tex]( y - y_{1}) = m(x - x_{1})[/tex]
y - 8 = 7/3( x - 3 )
3y - 24 = 7x - 21
3y = 7x - 21 + 24
3y = 7x + 3
When x = 2
3y = 14 + 3
y = 17 / 3
When y = 38/5
114/3 = 7x + 3
7x = 114/3 - 3
21x = 114 - 9
x = 5
So
The value of missing x = 5
The value of missing y = 17 / 3
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I company sells concrete in batches of 5 yd.³ the probability distribution of X the number of cubic yard sold in the single order for concrete from this company shown in the table below the expected value of the probability distribution of X is 19.25 and the center deviation is 5.76 there's a fixed cost to deliver the concrete The Profit why in dollars for to particular order can be described by Y equals 70 5X -100 what is the standard deviation of why
432
The standard deviation of Y is 432.
A company sells concrete in batches of 5 yd³.The probability distribution of X, the number of cubic yards sold in a single order for concrete in batches from this company, is shown in the table below.The expected value of the distribution of X is 19.25 and the standard deviation is 5.76.There is a fixed cost to deliver the concrete in batches. The profit Y, in dollars, for a particular order in a company can be described by(Y = 75X - 100)
The formula of the standard deviation is :
SD(Y) = SD(75X - 100)
Substituting the value of SD(X) and SD(100) in the above expression.
SD(Y) = 75SD(X) - SD(100)
SD(Y) = 75 SD(X) - 0
SD(Y) = 75 × 5.76
SD(Y) = 432
Hence, the standard deviation of Y is 432.
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4.) BLACK
Calculate the volume
of 500 g of salt
Density of Salt is 2.16
Answer: 2 170 kilograms [kg] of Salt fit into 1 cubic meter. 135.46867 pounds [lbs] of Salt fit into 1 cubic foot. Salt weighs 2.17 gram per cubic centimeter or 2 170 kilogram per cubic meter, i.e. density of salt is equal to 2 170 kg/m³; at 20°C (68°F or 293.15K) at standard atmospheric pressure . In Imperial or US customary measurement system, the density is equal to 135.469 pound per cubic foot [lb/ft³], or 1.254 ounce per cubic inch [oz/inch³] .
Step-by-step explanation:
record the angular velocity w. calculate the total moment of inertia of the cylinder-person system. (hint: treat the person as a single particle.) calculate the total angular momentum of the system.
For recording the angular velocity we will use
angular velocity, ω = dθ /dt
Angular velocity:
Angular velocity is a vector quantity, expressed as the angular velocity or rotational speed of an object and the rate of change of angular displacement that specifies the axis about which the object rotates. The amount of change in a particle's angular displacement over time is called its angular velocity. The trajectory of the angular velocity vector is usually perpendicular to the plane of rotation in the direction given by the right-hand rule.
Total Moment of Inertia:
The total moment of inertia is the sum of the moments of inertia of the mass elements in the body.
Unlike mass, which is a constant for a given body, the moment of inertia depends on the location of the center of rotation. In general, the moment of inertia is calculated by using integral calculus.
Thin cylindrical shell open at both ends, radius r, mass m.
This formula assumes that the thickness of the shell is negligible. This is a special case of a thick-walled cylindrical tube with r1=r2. A point mass m at the end of a rod of length r has the same moment of inertia and the value r is called the radius of gyration.
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One number is twelve less than another. If their sum is increased by seven, the result is 83
please help me
Answer:
x=44
y=32
Step-by-step explanation:
Given numbers x and y:
y=x-12
x+y+7=83
x+x-12+7=83
2x=88
x=44
y=32
HEPPPP ASPP!!! PLEASE I BEG YOU !!
John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours john’s brother works, and c, the total cost of the project ?
According to the given questions the answer is for 3 hour $560, for 8 hour cost $685 and for 12 hour cost $785.
What are time and work?A crucial concept that time and labour have in common with some other mathematical topics is the concept of proportionality. Because efficiency grows inversely linked to the amount of time needed when the quantity of work is constant.
What is work time problem in math?The fundamental equation for solving is 1/r+1/s=1/h. Let's choose Hrithik as our example. Let's assume that Hrithik completes 1/20 of something like the work in a day and Dhoni completes 1/30 of the work in a day. They will accomplish 1/20 + 1/30 = 5/60 = 1/12th of something like the work in a day if they collaborate.
Briefing:Given that John paid $485 to build a deck.
And he will pay $25 per hour to his brother for building the deck.
one hour of work costs John $25 + $485 .
Total cost of building deck = $25 × h number of hours + $485
3 hour of work costs $25 × 3 = $75 + $485 = $560
8 hour of work costs = $25 × 8 = $200 + $485 = $685
12 hour of work costs = $25 × 12 = $300 + $485 = $785
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The complete question is-
John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project?
h c
0 485
3 510
8 535
12 560
h c
0 510
3 535
8 560
12 585
h c
0 485
3 560
8 685
12 785
h c
0 510
3 585
8 710
12 810
what is the width of 1 book, if the bookshelf is 3 feet 9 inches wide?
Answer:
2.5
Step-by-step explanation:
Step-by-step explanation:
Given
Shelf Width = 3ft 9in
Copies = 18
Required
Determine the width of each book
This is calculated by dividing the shelf width by the number of copies.
Width = Shelf Width ÷ Copies
Width = (3 ft 9in) ÷ (18)
[Convert with to inches]
Width = (3 * 12 + 9) ÷ (18)
Width = (36 + 9) ÷ (18)
Width = 45 ÷ 18
Width = 2.5 inches
The Bay Area Online Institute (BAOI) has set a guideline of 60 days for the time it should take to complete an independent study course. In analyzing the times taken to complete the course for 16 random students, BAOI found the average time it took to complete the course was 72 hours with a standard deviation of 20 hours. Consider the possible inferences BAOI can make about the time it takes to complete this course if they assume that the time it takes is normally distributed: i. At the 5% level, BAOI can infer that the average time to complete exceeds 60 hours. ii. At the 1% level, BAOI can infer that the average time to complete exceeds 60 hours. What is true about i. and it: O Only (l) is true O There is insufficient information to determine which of the other answers shown here is correct. O Neither (1) nor (ii) is true O Both (1) and (ii) are true O Only ) is true
As per the given standard deviation, only (i) is true.
The term standard deviation refers the measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Here have given that the Bay Area Online Institute (BAOI) has set a guideline of 60 days for the time it should take to complete an independent study course.
Here by analyzing the times taken to complete the course for 16 random students, BAOI found the average time it took to complete the course was 72 hours with a standard deviation of 20 hours.
So, let us consider the possible inferences BAOI can make about the time it takes to complete this course if they assume that the time it takes is normally distributed:
i. For the 5% level, BAOI can infer that the average time to complete exceeds 60 hours.
ii. For the 1% level, BAOI can infer that the average time to complete exceeds 60 hours.
Here we are trying to determine if they should spend at least 480 minutes a day studying.
Now, our knoll is that the mean is 480 and then we are looking for evidence that they are studying less than 480.
Here we don't know the population standard deviation so we're going to use a distribution.
In the given, critical values are going to be a distribution with degrees of freedom.
So, if we look at a chart 11 of freedom, we can see our critical value. I'm going to center to zero if I draw our T.
Therefore, the tail probability of.05 and the rest of it is.95%.
Based on these value we have conform that option (1) is correct.
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AXY is similar to ABC
Which of the following expressions could be used to determine the length of segment AB?
The expression that could be used to determine the length of segment AB in the triangles given is: A. AB = AX * AC/AY.
What are Similar Triangles?When two triangles are stated to be similar to one another, it means both triangles have equal corresponding angles, but their corresponding sides have proportional lengths or have ratios that are equal.
This means similar triangles have the same shape but different sizes, since their corresponding side lengths have proportional length.
Given that triangle AXY is similar to triangle ABC, it means that:
m<A = m<A
m<X = m<B
m<Y = m<C
AX/AB = AY/AC = XY/BC
To find the length of AB, we could use the following expression derived from the ratios stated above:
AX/AB = AY/AC
Cross multiply:
(AB) * (AY) = (AX) * (AC)
Divide both sides by AY
(AB) * (AY) / AY = (AX) * (AC) / AY
AB = AX * AC/AY
The expression to use is: A. AB = AX * AC/AY
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over the past 30 years, the sample standard deviations of the rates of return for stock x and stock y were 0.20 and 0.12, respectively. the sample covariance between the returns of x and y is 0.0096. the correlation of the rates of return between x and y is the closest to .
The correlation of the rates of return between x and y is the closest to = 0.4
What is Correlation?Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect.
Calculation for the correlation of the returns,
Using this formula,
Covariance of the returns = Correlation coefficient between the returns*Stock returns standard deviation*Mod T Stock returns standard deviation
The sample standard deviations of the rates of return for stock x and stock y were 0.20 and 0.12
The sample covariance between the returns of x and y is 0.0096.
Let plug in the formula
Covariance of the returns = Correlation * (0.20) * (0.12)
0.0096 = Correlation * (0.20) * (0.12)
0.0096 = Correlation * 0.024
0.0096 / 0.024 = Correlation
0.4 = Correlation
Correlation = 0.4
Therefore,
The correlation of the rates of return between x and y is the closest = 0.4
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Find the x- and y-intercepts of the graph of -8x+y=21−8x+y=21
The y-intercept is 21 and the x-intercept is -21/8 for the equation -8x +y = 21.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given the equation is -8x + y = 21. The x and y-intercepts will be calculated as below,
For the y-intercept substitute, the value x=0 in the equation,
-8x + y = 21
0 + y = 21
y = 21
For the x-intercept substitute the value of y=0 in the equation,
-8x + y = 21
-8x = 21
x = -21 / 8
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Which graph represents the solution set of the system of inequalities?
y < -3x-2
y ≤ x-2
The graph that represents the solution to the system of inequalities is graph (a).
What is system of inequality?
A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem requires a variety of solutions and those solutions must satisfy multiple constraints, systems of inequalities are used.
The given system of inequalities is,
y < -3x - 2
y ≤ x - 2
y < -3x - 2 means that the left-hand side of the inequality will be shaded, and the line of the inequality will be a dotted line.
y ≤ x - 2 means that the left-hand side of the inequality will be shaded, and the line of the inequality will be a closed line.
The above highlights means that the shaded region that represent the solution to the system of inequalities will be at the left-hand side
Hence, graph (a) represents the system of inequalities.
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A random sample of 30 male college students was selected, and their heights were
measured. The heights (in inches) are given below
(a) Complete the frequency distribution for the data. Make sure to enter your answers for
the relative frequency as decimals, rounded to the nearest tenth.
Height Frequency Relative Frequency
68
69
70
71
73
1244
70 7368
66 73 70 23 23 64
74
The decimal equivalent of the relative frequency, rounded to the closest tenth, is 1.
How does relative frequency work?The proportion of outcomes when a certain event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
Thirty male college students at random were chosen.
The following table lists their heights in inches. These heights are 12 44 70 73 68 66 73 70 23 23 64 74 and 68 69 70 71 73.
Therefore, the frequency of any height value in the data set is just its count. A value's relative frequency is simply the ratio of its corresponding frequency to the total frequency.
So, the frequency table is
Height(xi) Frequency(fi) Relative frequency
66 3 3/30=0.1
67 3 3/30=0.1
68 4 4/30=0.13
69 3 3/30=0.1
70 2 2/30=0.06
71 4 4/30=0.13
72 2 2/30=0.06
73 6 6/30=0.2
74 3 3/30=0.1
Total 30 1
the frequency distribution for the data is given above.
The relative frequency as decimals, rounded to the nearest tenth is 1
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The length of four rivers in Africa is shown in the table below.
How is the length of the Zambezi river written in scientific notation?
Move the correct answer to each box. Not all answers will be used.
The length of the Zambezi river is 838 × 10⁵ or 83.8 × 10⁶ or 8.38 × 10
What is scientific notation?
Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.
For example, 750,000,000 can be written in scientific notation as 7.5 ✕ 10⁸.
The length of the Zambezi river 83,800,000 feet.
Rewrite 83,800,000:
83,800,000 = 838 × 100000
83,800,000 = 838 × 10⁵ [Since the number of zeros is 5]
Multiply and divide 10:
83,800,000 = 838 × 10⁵ × (10/10)
83,800,000 = (838/10) × 10⁵ × 10
83,800,000 = 83.8 × 10⁵ × 10
83,800,000 = 83.8 × 10⁶
Multiply and divide 10:
83,800,000 = 83.8 × 10⁶ × (10/10)
83,800,000 = (83.8/10) × 10⁶ × 10
83,800,000 = 8.38 × 10⁷
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Help me please just 5-8
Answer:
listed below
Step-by-step explanation:
5.) x=77 and y=63
6.)y=60 and x= 1230
7.)y=65 and x=92
8.)y=69 and x=175
Instructor Celsius looked at her class data from Quiz 3. She recorded the students' amount of study time (in minutes) and quiz score (out of 100) She made scatterplot of her data and saw that it had linear pattern. She computed that r = 0.80.After telling the class about these results one student figures this means that if they study _ very long time they will make very high quiz score: What Is the wrong with this conclusion? The teacher is using the wrong type of plot; thc efore the results are invalid. Since 8 you know the slope will be negative 50 studying long time will give vou a lower score The student is assuming that correlation implics causation and are correct
For the given scatter plot of the data, the wrong with the conclusion was shown by option B. Since r = 0.80 slope will be negative 50 studying long time will give you lower score is incorrect.
As given in the question,
Based on the class data of quiz3,
Teacher made scatterplot to represent the linear relation between amount of study time and quiz score
Pattern form was linear.
Using which correlation coefficient was computed to r = 0.8.
From the data scatterplot as it was linear the more time students study the good will the score.
Therefore, from the information of scatterplot option B. Since r = 0.80 slope will be negative 50 studying long time will give you lower score is incorrect answer.
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A box contains 2 red marbles and 3 black marbles. Two marbles are drawn in succession without replacement. Find the following: a. Find the probability the second marble is red? b. Find the probability that both marbles are the same color? c. Find the probability that the second marble is black given the first marble is red? d. Find the probability that first marble red given that the second marble is red?
a. The probability that the second marble is red is 2/5, since there are 2 red marbles and a total of 5 marbles.
b. The probability that both marbles are the same color is 4/15, since there are two ways that this could happen (both red or both black) and there are 15 possible outcomes in total.
c. The probability that the second marble is black given the first marble is red is 3/4, because out of the 4 possible outcomes (RR, RB, BR, BB) the only way to get a black marble on the second draw is if it is BR.
d. The probability that the first marble is red given that the second marble is red is 2/3, because out of the 3 possible outcomes (RR, RB, BR) the only way to get a red marble on the first draw is if it is RR or RB.
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Given the conditional statement ~p → q, which statement is logically equivalent?
p → ~q
~p → ~q
~q → ~p
~q → p
Answer:
~q → pStep-by-step explanation:
Given the conditional statement ~p → q, the statement logically equivalent is ~q → p.
7. Evaluate the expression below if a = 64,
b = 9, and c = 5
A. 19
B. 19/2
C. 49/4
D.49/2
The given expression can be simplified to get the value as 19. The correct option is (A).
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given expression is as below,
[tex](12b - 2^{c}) /\sqrt[3]{a}[/tex]
Substitute a = 64, b = 9 and c = 5 to obtain the value as below,
⇒ (12 × 9 - 2⁵)/∛64
⇒ (108 - 32)/4
⇒ 76/4
⇒ 19
Hence, the value of the given expression is obtained as 19.
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The image of the complete problem is attached here.
Suppose that, in a hypothesis test, the null hypothesis is in fact false.
a. Is it possible to make a Type I error?
A. Yes, it is possible. A Type I error is not rejecting the null hypothesis when it is in fact false.
B. No, it is not possible. A Type I error is not rejecting the null hypothesis when it is in fact false.
C. No, it is not possible. A Type I error is rejecting the null hypothesis when it is in fact true.
D. Yes, it Is possible. A Type I error is rejecting the null hypothesis when it is in fact false.
b. Is it possible to make a Type II error?
A. No, it is not possible. A Type II error is rejecting the null hypothesis when it is in fact true.
B. Yes, it is possible. A Type II error is rejecting the null hypothesis when it is in fact false.
C. No, it is not possible. A Type II error is not rejecting the null hypothesis when it is in fact false.
D. Yes, it is possible. A Type II error is not rejecting the null hypothesis when it is in fact false.
a) No, it is not possible. A Type I error is rejecting the null hypothesis when it is in fact true.
b)Yes, it is possible. A Type II error is not rejecting the null hypothesis when it is in fact false.
A false positive conclusion in statistics is known as a Type I error, and a false negative conclusion is known as a Type II error.
The significance level, or alpha, determines the likelihood of a Type I error, whereas beta determines the likelihood of a Type II error. These dangers can be reduced by carefully designing the layout of your study.
If your results show statistical significance, that means they are very unlikely to occur if the null hypothesis is true. In this case, you would reject your null hypothesis. But sometimes, this may actually be a Type I error.
If your findings do not show statistical significance, they have a high chance of occurring if the null hypothesis is true. Therefore, you fail to reject your null hypothesis. But sometimes, this may be a Type II error.
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Write the relation as a set of ordered pairs. A relation. An arrow goes from negative 2 to 4, 0 to 0, 2 to 4. a. ordered pairs: {(4, –2), (0, 0), (2, 4)} b. ordered pairs: {(–2, 4), (0, 0), (4, 2)} c. ordered pairs: {(–2, 4), (0, 0), (2, 4)} d. ordered pairs: {(4, –2), (0, 0), (4, 2)} Please select the best answer from the choices provided A B C D Mark this and return
The required relation as a set of ordered pairs is (C) {(–2,4), (0,0), (2,4)}.
What are the Ordered pairs in the set?A set of ordered pairs is any pair of components that appear in a specific sequence and are wrapped in brackets.
If there are two elements, "a" and "b," then the two distinct pairings are "(a, b)" (b, a).
A is referred to as the first element and B is referred to as the second element in an ordered pair (a, b).
A pair of numbers in a particular order is known as an ordered pair.
The ordered pairings (1, 2) and (-4, 12) are two examples.
It matters which of the two numbers comes first: (2, 1) and (1, 2) are not the same thing (2, 1).
So, an arrow in a relationship travels from -2 to 4, 0 to 0, and 2 to 4.
Consequently, by virtue of ordered pairs.
The ordered pairings are obtained:
(-2, 4)
(0, 0)
(2, 4)
Hence, the pairs are (-2, 4), (0, 0), and (-2). (2, 4)
Therefore, the required relation as a set of ordered pairs is (C) {(–2, 4), (0, 0), (2, 4)}.
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Correct question:
Write the relation as a set of ordered pairs.
A relation. An arrow goes from negative 2 to 4, 0 to 0, 2 to 4.
a. ordered pairs: {(4, –2), (0, 0), (2, 4)}
b. ordered pairs: {(–2, 4), (0, 0), (4, 2)}
c. ordered pairs: {(–2, 4), (0, 0), (2, 4)}
d. ordered pairs: {(4, –2), (0, 0), (4, 2)}
Please select the best answer from the choices provided
A
B
C
D
Need Help with this question.
Answer:
x=5
Step-by-step explanation:
If p and q are parallel, then the two angles in question should be equal to one another.
So,
(3x+15)°=(8x-10)°
(3x+15)°+10°=(8x-10)°+10°
(3x+25)°=(8x)°
(3x+25)°-(3x)°=(8x)°-(3x)°
25°=5x°
5=x
So, the two angles should be (8(5)-10)° and (3(5)+15)°. Both of these expressions equal 30°. This makes sense, as the illustration shows that the two angles are acute.
Fully simplify.
(3x^2y^2)^3
(3x
2
y
2
)
3
Answer:
[tex]27x^6y^6[/tex]
Step-by-step explanation:
The formatting of the question is a bit confusing, but if the expression is [tex](3x^2y^2)^3[/tex], use the power of a product exponent rule [tex](ab)^m=(a)^m(b)^m[/tex]. So,
[tex](3x^2y^2)^3=(3)^3(x^2)^3(y^2)^3[/tex].
Next, use the power of a power exponent rule [tex](a^m)^n=a^{m*n}[/tex]. So,
[tex](3)^3(x^2)^3(y^2)^3=27(x^{2*3})(y^{2*3})=27x^6y^6[/tex]
Create a table showing all the tasks you and your family do around the house that use water and how often those tasks happen. Leave space for one more column.
A distribution of values is normal with a mean of 200 and a standard deviation of 19. From this distribution, you are drawing samples of size 33. Find the interval containing the middle-most 86% of sample means: Enter your answer using interval notation. In this context, either inclusive [] or exclusive () intervals are acceptable. Your numbers should be accurate to 1 decimal places.
The interval containing the middle-most 86% of sample mean in the interval notation is is (196.4, 203.5)
The 50 +/- 86/2 percentile will make up the center 86% of the sample means' distribution.
The 86th percentile's z-score is 1.08
sample mean population mean = 200
standard deviation from mean = 19
sample size = 33.
Standard error (SE) is equal to 19 / sqrt(33) = 3.3077.
86th percentile x can be located using the formula z = (x - population mean)/sample error.
1.08 = (x - 200)/3.3077
x = 3.3077* 1.08 + 200 = 203.57
that is the interval's upper bound.
it is 3.5721 over the population mean (203.57 - 200).
Due to the symmetry of the normal distribution, the interval's bottom bound will be 1.66 standard deviations below the population mean (200 - 3.572 = 196.428).
then the interval is (196.4, 203.5).
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the temperature of city changed by total of -12 degrees Celsius over 2 weeks period. the temperature changed by the same amount each week. Part A write an expression to show the average change in the temperature of the city each week. Part B simply the expression and explain, using words, what your answer mean
Answer:
The number of degrees Celsius goes down 6 every week. (-6)
Step-by-step explanation:
If the city's temperature changed the same every week, and over the period of 2 weeks it changed -12 degrees Celsius, we need to figure out how much it changed every week (c). We can do this by dividing the number of weeks (w), by the total number of Celsius it changed (t).
The equation will look something like this:
w ÷ t = c
Fitting the numbers into this equation will look something like this:
2 ÷ -12 = -6
Every week, it changed -6 degrees Celsius.
Simplifying the expression, every week it changed -6 degrees Celsius. We know this because the temperature changes the same amount every week. So if the total amount is -12, we have to divide that by 2 to get -6.
Suppose that DEF is isosceles with base DE.
Suppose also that mZD=(5x+26)° and mZF = (3x+63)°.
Find the degree measure of each angle in the triangle.
k
D
(5x + 26)
-(3x + 63)°
E
mZD=
mZE=
mZF =
X
O
The degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
What is an isosceles triangle?
In an isosceles triangle, the two base angles are congruent, or equal in measure.
In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:
m∠D + m∠F + m∠E = 180 degrees
Substituting the given values for the measures of angles D and F, we get:
(5x+26) + (3x+63) + m∠E = 180
Combining like terms and solving for m∠E, we find that:
m∠E = 180 - (5x+26) - (3x+63)
= 180 - 8x - 89
= 91 - 8x
Therefore, the measure of angle E is 91 - 8x degrees.
To find the measure of angles D and F, we can substitute this value back into the equation:
m∠D + m∠F + m∠E = 180
(5x+26) + (3x+63) + (91-8x) = 180
Solving for x, we find that x = 6.
m∠D =5(6) + 26 = 30 + 25 = 56°
m∠F = 3(6) + 63 = 18 + 63 = 81°
m∠E = 91 - 8(6) = 91 - 48= 43°
Therefore, the degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
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https://brainly.com/question/1475130
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The degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
What is an isosceles triangle?
In an isosceles triangle, the two base angles are congruent, or equal in measure.
In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:
m∠D + m∠F + m∠E = 180 degrees
Substituting the given values for the measures of angles D and F, we get:
(5x+26) + (3x+63) + m∠E = 180
Combining like terms and solving for m∠E, we find that:
m∠E = 180 - (5x+26) - (3x+63)
= 180 - 8x - 89
= 91 - 8x
Therefore, the measure of angle E is 91 - 8x degrees.
To find the measure of angles D and F, we can substitute this value back into the equation:
m∠D + m∠F + m∠E = 180
(5x+26) + (3x+63) + (91-8x) = 180
Solving for x, we find that x = 6.
m∠D =5(6) + 26 = 30 + 25 = 56°
m∠F = 3(6) + 63 = 18 + 63 = 81°
m∠E = 91 - 8(6) = 91 - 48= 43°
Therefore, the degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
To learn more about the isosceles triangles, visit:
brainly.com/question/1475130
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