In the initial list, there were 4 integers.
We have the following system if the mean is m, x is the list's initial sum, and n is the number of integers in the list:
m = x/n , m + 2 = (x + 15) / (n + 1) and m + 1 = (x + 16) / (n + 2).
The initial equation is x = mn.
Therefore, changing x in the other two equations:
m + 2 = (mn + 15) / (n + 1) ..............(1)
m + 1 = (mn + 16) / (n + 2)...............(2)
Based on equation (1):
(m + 2)(n + 1) = mn + 15
mn + m + 2n + 2 = mn + 15
m + 2n + 2 = 15
m + 2n = 13
m = 13 - 2n.
Now change m in equation (2) to:
13 - 2n + 1 = ( n(13 - 2n) + 16) / (n + 2)
14 - 2n = (13n - 2n^2 + 16) / (n + 2) Through-multiplication by n + 2:
(14 - 2n)(n + 2) = 13n - 2n^2 + 16
14n + 28 - 2n^2 - 4n = 13n - 2n^2 + 16
10n + 28 = 13n + 16
12 = 3n
n = 4.
Hence, there were 4 integers in the original list.
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Juliana makes a prism 4 inches across and 4 inches wide but only 1 inch tall. She then decides to create
layers equal to her first one. Fill in the chart below, and explain how you know the volume of each new
prism.
Number of
Layers
3
5
7
Volume
Explanation
The volume of prism with 1 layer=16 inch³; The volume of prism with 3 layer=48 inch³;The volume of prism with 5 layer=80 inch³;The volume of prism with 7 layer=112 inch³.
What is volume?The total amount of space an object occupies in three dimensions is indicated by its volume. The term "capacity" describes something's ability to hold, absorb, or receive by an object .
Here,
Since each layer is of 1 inch.
So the volume of first prism,
=4*4*1
=16 inch³
When there is 3 layer, so the height is 3 inch,
=4*4*3
=48 inch³
When there is 5 layer, so the height is 5 inch,
=4*4*5
=80 inch³
When there is 7 layer, so the height is 7 inch,
=4*4*7
=112 inch³
The volume of a prism with one layer is equal to 16 inch³; with three layers, it is 48 inch³; with five layers, it is 80 inch³; and with seven layers, it is 112 inch³.
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help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The length of the shorter leg is 9 mm.
The length of the longer leg is 12 mm.
The length of the hypotenuse is 15 mm.
Pythagoras theory applies to every right triangle. If
The shorter leg = aThe longer leg = bThe hypotenuse = c[tex]a^2 + b^2 = c^2[/tex]Step-by-step explanation:
Known
Longer leg = shorter leg +3 mmAsked
a?b?c?Answer
[tex]a^2 + b^2 = c^2[/tex]
[tex]a^2 + (a+3)^2 = (a+6)^2[/tex]
[tex]a^2 + a^2 + (2 \times a \times 3) + 3^2 = a^2 + (2 \times a \times 6) + 6^2[/tex]
[tex]2a^2 + 6a + 9 = a^2 + 12a + 36[/tex]
[tex]2a^2 - a^2 + 6a - 12a + 9 - 36 = 0[/tex]
[tex]a^2 - 6a - 27 = 0[/tex]
[tex]a^2 - 9a + 3a - 27 = 0[/tex]
[tex]a \times (a - 9) + 3 \times (a - 9) = 0[/tex]
(a-9) (a+3)=0
a-9=0 or a+3= 0
a=9 or a=-3 (impossible)
Shorter leg
a=9 mm
Longer leg
b = a+3
b = 9+3
b = 12 mm
Hypotenuse
c = a+6
c = 9+6
c = 15 mm
Which statement is an example of deductive reasoning?
Responses
Quadrilaterals DEFG and JKLM have four congruent sides and no right angles. Therefore, any quadrilateral with four congruent sides has no right angles.
Quadrilaterals cap d cap e cap f cap g and cap j cap k cap l cap m have four congruent sides and no right angles. Therefore, any quadrilateral with four congruent sides has no right angles.
Triangle XYZ is an isosceles right triangle. Triangle CDE is an isosceles right triangle. Therefore, all right triangles are isosceles right triangles.
Triangle cap x cap y cap z is an isosceles right triangle. Triangle cap c cap d cap e is an isosceles right triangle. Therefore, all right triangles are isosceles right triangles.
All rulers in geometry class are 12 inches long. The biology class also uses rulers. Therefore, the rulers in biology class are 12 inches long.
All rulers in geometry class are 12 inches long. The biology class also uses rulers. Therefore, the rulers in biology class are 12 inches long.
All squares are parallelograms. Quadrilateral ABCD is a square. Therefore, quadrilateral ABCD is a parallelogram.
Answer:
Step-by-step explanation:
Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job. How much total money would Taub have after 7 weeks of saving? Also, write an expression that represents the amount of money Taub would have saved in w weeks.
Total savings after 7 weeks:
Total savings after w weeks:
Total savings after 7 weeks : $140
Total savings after w weeks : $(70 + 10w)
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a phrase : Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job.
Taub will have a total of -
70 + 7 x 10 = $140
The expression that represents the amount of money Taub would have saved in [w] weeks is -
y = 70 + 10w
Therefore -
Total savings after 7 weeks : $140
Total savings after w weeks : $(70 + 10w)
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At Sascha's Salad Bar, customers make their own salads and pay by the ounce. Jenny paid $6.16 for a 22-ounce salad. Seth spent $7.28 on a salad. How much did his salad weigh?
The weight of the salad at the cost of $7.28 will be 31.9 ounces.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that at Sascha's Salad Bar, customers make their own salads and pay by ounce. Jenny paid $6.16 for a 22-ounce salad. Seth spent $7.28 on a salad.
$6.16 ⇒ 22 ounces
$1 ⇒ 22 / $6.16
$7.28 ⇒ ( 22 x 7.28 ) / $6.16
$7.18 ⇒ 31.9 ounces
Therefore, the weight of the salad at the cost of $7.28 will be 31.9 ounces.
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Determine the length of the line segment shown.
line segment from negative 5 comma 5 to 3 comma negative 1
6 units
8 units
10 units
36 units
The length of the line segment from negative 5 comma 5 to 3 comma negative 1 is 10 Units.
How to find the length of a line segment?
A line segment is defined as a line bounded by two points on a line.
The line segment from negative 5 comma 5 to 3 comma negative 1
is found by using the formula
square root of (x2-x1)² +(y2-y1)²
[tex]\sqrt{(3+5)^{2} +(-1-5)^{2} }^[/tex]
[tex]\sqrt{8^{2}+6^{2} }[/tex]
[tex]\sqrt{100}[/tex]
=10 units
therefore the length of the line segment is 10 units
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Can anyone write the equation of the graph?
The equation of the graph is f(x) = |x - 3| + 5
How to determine the equation of the graph?The graph represents the given parameter
From the graph, we have the following highlights:
The graph is an absolute value graphThe graph has its minimum point at (3, 5)This means that
Vertex = (3, 5)
Rewrite the vertex as
(h, k)
An absolute value function is represented as
f(x) = a|x - h| + k
Substitute the known values in the above equation
So, we have the following equation
f(x) = a|x - 3| + 5
On the graph, we have
(x, f(x)) = (2, 6)
So, we have
6 = a|2 - 3| + 5
This gives
a = 1
So, we have
f(x) = 1 * |x - 3| + 5
Evaluate
f(x) = |x - 3| + 5
Hence, the graph has an equation of f(x) = |x - 3| + 5
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c=0.325g+p ,solve for g
Solving for g in the equation g = (c - p)/0.325
What is an equation?An equation is a mathematical expression that show the relationship between two variables.
How to solve for g in the given equation?Since we are given the equation c = 0.325g + p, we desire to make g subject of the formula.
To do this, we perform some mathematical operations on it.
So, c = 0.325g + p
Now, to isolate 0.325g on the right hand side, we subtract p from both sides of then equation.
So, c = 0.325g + p
c - p = 0.325g + p - p
c - p = 0.325g
Now to isolate g, we divide both sides of the equation by 0.325. So, we have
c - p = 0.325g
(c - p)/0.325 = 0.325g/0.325
g = (c - p)/0.325
So, we have g = (c - p)/0.325
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having driven a hybrid car for 4.5 years, a driver believes the car gets more than 33 miles per gallon (mpg). the driver kept records of all car fill-ups and taking a sample of 15 found a sample average of 32.84 mpg and sample standard deviation of 1.86 mpg. assuming that the underlying distribution is normal, what can be concluded at the 0.05 level of significance?
By probability, There is insufficient evidence to conclude that the gas mileage is greater than 33 mpg.
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.p value is calculated using online p value calculator (you will find it by searching online).
p value interpretation: if the null hypothesis is true then the probability that the sample average is greater than 33 mpg is 0.373143.
[ the p value associated with a test is the probability that we obtain the observed value of the test statistic or a value that is more extreme in the direction given by the alternative hypothesis, when H0 is true ].
decision: accept H0 at 5% level of significance as p value >0.05
[level of significance is chosen as 5 %= 0.05]
conclusion : there is insufficient evidence to conclude that the gas mileage is greater than 33 mpg.
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What is the sum of the zeros of the function y = x² - 9x-10?
Answer: 9
Step-by-step explanation:
Finding the zeros is the same as solving. Then, we will add the two solutions together.
Given:
y = x² - 9x - 10
Solving by Quadradic Formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\displaystyle x=\frac{-(-9)\pm\sqrt{(-9)^2-4(1)(-10)} }{2(1)}[/tex]
[tex]\displaystyle x=\frac{9\pm\sqrt{81+40} }{2}[/tex]
[tex]\displaystyle x=\frac{9\pm\sqrt{121} }{2}[/tex]
[tex]\displaystyle x=\frac{9+11}{2},\;\;x=\frac{9-11}{2}[/tex]
x = 10, -1
Adding them together:
10 + -1 = 9
regression analysis is a statistical procedure for developing a mathematical equation that describes how . a. none of the answers is correct b. one dependent and one or more independent variables are related c. several independent and several dependent variables are related d. one independent and one or more dependent variables are related
In regression analysis, there is one dependent variable and there can be one or more independent variables among which a relationship has to be established.
Given that;
Regression analysis is a statistical procedure for developing a mathematical equation that describes;
Finding the variables that have an effect on an interest issue can be done with accuracy using regression analysis. You can confidently establish which elements are most important, which ones can be ignored, and how these factors interact when you do a regression. You must specify a dependent variable that you believe is influenced by one or more independent variables before you can do a regression analysis.
The next step is to create an extensive dataset to work with. A great technique to create this dataset is by sending surveys to your target audiences. Questions covering each of the independent variables in which you are interested should be included in your survey.
Hence, Regression analysis requires establishing a link between one or more independent variables and one dependent variable.
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402 students were surveyed about their preferences of sports. 140 students like football, 144 students like baseball, and 42 students like both sports. how many students like exactly one of the two sports? a) 200 b) 140 c) 284 d) 98 e) 102 f) none of the above.
The students that will like exactly one of the two sports out of football and baseball is 200.
What is set theory?These are the fundamental set of set theory formulas. When there are two sets P and Q, the number of elements in one of the sets P or Q is denoted by n(P U Q). The number of elements in both sets P and Q is represented by the expression n(P ⋂Q). n(P U Q) is equal to n(P) + n(Q) - n (P Q).
Here,
F=140
B=144
F∩B=42
F-B=n(F)-n(F∩B)
=140-42
F-B=98
B-F=n(B)-n(F∩B)
=144-42
=102
So, the students that will like exactly one of the two sports,
=102+98
=200
There are 200 students who will only enjoy one of the two sports—football or baseball.
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Which criterion can be used to prove ABC and ADC are congruent? select the correct answer
ΔABC and ΔADC are congruent by angle-side-angle (ASA) postulate of triangle congruence.
In this question we have been given a quadrilateral ABCD and diagonal AC.
We need to prove triangle ABC and ADC are congruent.
In ΔABC and ΔADC,
∠BAC ≅ ∠ACD ...........(Given)
AC ≅ AC ...........(Common side)
∠ACB ≅ ∠DAC ..........(Given)
ΔABC ≅ ΔADC ..........(ASA postulate of triangle congruence)
Therefore, ΔABC and ΔADC are congruent by angle-side-angle (ASA) postulate of triangle congruence.
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Write an equation of the parabola in vertex form that has a vertex (-3, 7) and passes through (-4, 8).
y = 4/3 ( x + 3 )² + 7 is equation of the parabola .
In math, what is a parabola?
A right circular cone and a plane perpendicular to one of the cone's elements intersect to form a parabola, also known as an open curve.The shape of Banana is resembling a parabola. A parabola is emerging from the Rainbow. The shape of a parabola is being assumed by parabolic dish antennas. Mirror's concave surface.The h and k of the above vertex form are the coordinates of the vertex. So our function has the following form
y = a ( x- h )² + k
y = a ( x - ( - 3 ))² + 7
8 = a ( -4 - ( -3 ) + 7
8 = a ( 6 )
a = 8/6
a = 4/3
the a value we can write the final vertex form
y = a ( x - ( - 3 ))² + 7
y = 4/3 ( x + 3 )² + 7
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Dados os polinomios:
X-2=
X-3=
X+1=
X+5=
Answer:
X-2=1
X-3=2
X+1=2
X+5=6
a family has 5 natural children and has adopted 2 girls. each natural child has equal probability of being a girl or a boy, independent of the other children. find the pmf of the number of girls out of the 7 children.
PMF probability mass function:
2 - 0.03125, 3 - 0.15625, 4 - 0.3125, 5 -0.3125, 6 - 0.15625, 7 - 0.03125.
Define the term Probability?The probability of such a function is the degree to which an event will occur as a rational number.
A family has 2 adopted girls and 5 biological daughters.
Each naturally occurring child does have an equal chance of being a boy or a girl.
Out of the seven offspring, the probability mass function for girls is as follows:
B should stand for Boy, and G should stand for G.
Consequently, this is the probability mass function:
P(GGBBBBB) = ⁵C₀ x (0.5)⁰ x (0.5)⁵
= 0.03125
P(GGGBBBB) = ⁵C₁ x (0.5)¹ x (0.5)⁴
= 0.15625
P(GGGGBBB) = ⁵C₂ x (0.5)² x (0.5)³
= 0.3125
P(GGGGGBB) = ⁵C₃ x (0.5)³ x (0.5)²
= 0.3125
P(GGGGGGB) = ⁵C₄ x (0.5)⁴ x (0.5)¹
= 0.15625
P(GGGGGGG) = ⁵C₀ x (0.5)⁵ x (0.5)⁰
= 0.03125
Thus, the probability mass function for girls out of the 7 children is obtained.
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I”M GIVING BRAINLIEIST OR WHATEVER TO WHO EBER EXPLAINS THE BEST
Answer:-3
Step-by-step explanation:
a store is designing the space for rows of nested shopping carts. each row has a starting that is 4 feet long, followed by the nested carts (so 0 nested carts means there’s just the starting cart). the store measured a row of 13 nested carts to be 23.5 feet long and a row of 18 nested carts to be 31 feet long. each nested cart adds 1.5 feet to the row. if the store design allows for 43 feet for each row, how many total carts fit in a row?
Plot these points on a graph and draw a line connecting them beginning at (0, 4) and ending at (18, 31). The graph is plotted below.
What is meant by Plotting the points?Plotting is the process of putting a point on a coordinate plane using X and Y coordinates. In a nutshell, a plot point is anything that happens to a character, good or bad, that significantly alters their life. So, if a character is fired, thrown out of the house, mugged, or wins the lottery, all of these are significant events that would be included in the outline of a novel. Begin by plotting a point at the origin, which is the center of the graph (the point (0,0)). The x-coordinate will then tell you how many units you need to move left or right, and the y-coordinate will tell you how many units you need to move up or down.Given:
Starting cart denotes that the number of nested carts is zero.
So, let the x axis represent the number of nested carts and the y axis represent the height of the nested carts.
As per question,
When x = 0 , the height is y = 4 ft
When x = 13, the height is y = 2.5 ft
When x = 18, the height is y = 31 ft
So, the points on the graph are (0,4), (13, 23.5) and (18, 31).
Plot these points on a graph and draw a line passing through all these points starting at (0, 4) and ending at (18, 31).
The graph is shown below.
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You and your friends go camping and put up a tent on camp grounds. the tent is shaped like an isosceles triangle. the sides of the tent are 5 feet each and the opening of the tent is 6 feet wide. how tall is the tent
the student council at a local college has 8 seniors, 7 juniors, 5 sophomores and 3 freshmen. if 3 of them are randomly chosen to be on a committee, what is the probability that none of them are seniors?
The probability is 0.6 that if randomly choosen none of them are senior.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .acc to our question-
total people in council= 23The number of committees that have no seniors: In this case, we have to select 5 people from a group of 1+3+4=8 people. This can be done in 8C5 ways.The number of committees that have no seniors: In this case, we have to select 5 people from a group of 1+3+4=8 people. This can be done in 8C5 ways.Hence,the probability is 0.6 that if randomly choosen none of them are senior.
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quick help me please
Answer:
calculate the difference ere
(3-22)+5
remove unnecessary parentheses
-19+5
calculate the sum
= -14
draw the full decision tree for the parity function of four boolean attributes, a, b, c, and d. is it possible to simplify the tree? g
The diagramfull decision tree for the parity function of four boolean attributes, a, b, c, and d is shown below picture and it is possible to simplify the tree.
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rearrange the formula below to make 'a' the new subject:
[tex]c + \frac{1}{2}a^{2}b = d[/tex]
is the bottom answer correct for this question? :
[tex]a = \sqrt{2(\frac{d-c}{b} )}[/tex]
Step-by-step explanation:
c + 1/2 × a²b = d | - c on both sides
1/2 × a²b = d - c | ×2 on both sides
a²b = 2(d - c) | /b on both sides
a² = (2/b) × (d - c) | sqrt on both sides
a = sqrt(2(d - c)/b)
yes, the given answer is correct.
The graph shows how many bottles a machine caps in a certain number of seconds.
(shown in the picture below)
Part A
What is the constant of proportionality, and what does it mean in this situation?
Use the drop-down menus to show and explain your answer.
The constant of proportionality is __ (Choices: 15, 30, 20) ; the machine caps __ (Choices: 30, 20, 15) bottles in ____________ (Choices: 1 second, 1 minute, 15 seconds)
Part B
Which of the following is an ordered pair on the graph? What does it represent in this situation?
A. ) (45, 90); the machine caps 45 bottles in 90 seconds.
B. ) (45, 900); the machine caps 45 bottles in 900 seconds.
C. ) (45, 900); the machine caps 900 bottles in 45 seconds.
D. ) (900, 45); the machine caps 900 bottles in 45 seconds.
Considering the proportional relationship graphed, it is found that:
A. The constant is of 20.
B. A pair on the graph is given as follows: C. ) (45, 900); the machine caps 900 bottles in 45 seconds.
What is a proportional relationship?A proportional relationship is a linear function with intercept zero in which the output variable y is given by the multiplication of the input variable x and the constant k, as follows:
y = kx.
Considering point (15, 300) on the graph presented, the constant is calculated as follows:
300 = 15k
15k = 300
k = 300/15
k = 20.
The input and the output are given as follows:
Input: number of seconds.Output: number of bottles capped.Hence option C is the correct option for item 2.
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41.153 to the nearest tenth
Answer: 41.2
Step-by-step explanation: The rules of rounding are you round up if the number you're rounding is 5 or higher than five, and you keep the same number if it is 4 or lower. For this problem, the 1 is the digit being rounded, so to round it, look at the number to the right of the 1, which is a 5, which means we would round up.
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What is the area of â–³mnp? 40 m2 60 m2 68 m2 127.5 m2
The area of MNP triangle is 60 m².
Based on the congruency of triangles, the value of MP and QS will be the same. Hence, the value of side MP will be 8 m.
Now, the formula to calculate right angled triangle is 1/2 × base × height.
Keep the values in formula to find the value of area of triangle MNP.
Area = 1/2 × 8 × 15
Performing multiplication and division on Right Hand Side of the equation to find the area of triangle MNP
Area = 4 × 15
Area = 60 m²
Thus, the area of right angled triangle is 60 m².
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how large are hamster litters? among 47 golden hamster litters recorded, there were an average of 7.72 baby hamsters, with a standard deviation of 2.5 hamsters per litter.
We are 90% certain that the average number of hamsters per litter is between 7.1077 and 8.3323.
What exactly is a confidence interval?A confidence interval is a range of values that includes a population value with a high degree of certainty. When a population mean falls between an upper and lower interval, it is frequently expressed as a percentage. The confidence level is the long-run proportion of corresponding CIs that contain the parameter's true value. For example, 95% of all intervals computed at the 95% level should contain the true value of the parameter.
Given, n=47
[tex]\bar{x}[/tex]=7.72
s=2.5
c=90%=0.90
To find the t-value, look in the row that starts with degrees of freedom.
df=n-1
df=47-1
df=46>45 and in the column with c=90% in the table
=1.679
Now, the margin of error is then:
E=[tex]t_{\alpha/2}\times \dfrac{s}{\sqrt{n}}=1.679\times \dfrac{2.5}{\sqrt{47}}\approx 0.6123[/tex]
The confidence interval's boundaries are thus:
[tex]\overline{x}-E[/tex]=7.72-0.6123=7.1077
[tex]\overline{x}+E[/tex]=7.72+0.6123= 8.3323
The average number of hamsters per litter is between 7.1077 and 8.3323, and we are 90% certain of this.
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You want to buy some noodles. A 9-ounce package costs $3.15. A 12-ounce package costs $4.44 A 22-ounce package costs $7.26. Which package is the best buy?
Answer: A 22-ounce package costs $7.26 is best to buy
Step-by-step explanation:
A 9-ounce package costs $3.15 = 35 cents an ounce
A 12-ounce package costs $4.44 = 37 cents an ounce
A 22-ounce package costs $7.26 = 33 cents an ounce making it the cheapest by ounce
a random sample of 2,000 members of a union reveals that 1,600 would vote yes on a merger proposal. what is the 95% confidence interval for the population proportion of members who would vote yes?
The 95% confidence interval for the population proportion of members who vote yes is (0.782, 0.818).
What is Random Sample?A choice that is made at random (purely by chance, with no predictability). They tapes of samples are:
Convenient: Sample taken from a pool that is easily accessible.
Random: Put all the possibilities into a hat, then pull some of them at random. Every kth element is taken in a systematic manner. If you wanted to survey anything on the street, for instance, you may interview every fifth person.
Cluster: The population is divided into groupings, or clusters, and every component of each cluster is surveyed.
Stratified: Additionally stratifies the people into several groupings. But only a small portion of the group is questioned after that.
Now, finding the sample proportion,
[tex]p=\frac{x}{n} \\\\=\frac{1600}{2000}\\\\ =0.8[/tex]
The confidence level is given as,
[tex]C=p\pm[z(\frac{\alpha}{2})\times\sqrt{\frac{p(1-p)}{n} } ][/tex]
The value of [tex]z(\frac{\alpha}{2})[/tex] is 1.96
Putting the values, we get
[tex]C=0.8\pm[1.96\times\sqrt{\frac{0.8(1-0.8)}{2000} } ]\\\\C=0.8\pm[1.96\times\sqrt{\frac{0.8(0.2)}{2000} } ]\\\\C=0.8\pm0.018\\\\C=(0.782,0.818)[/tex]
Therefore, the 95% confidence interval is (0.782,0.818).
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The given question is incomplete. Here is the complete question.
a random sample of 2,000 members of a union reveals that 1,600 would vote yes on a merger proposal. what is the 95% confidence interval for the population proportion of members who would vote yes?
a) 0.782 to 0.818
b) 0.754 to 0.799
c) 0.690 to 0.713
d) 0.799 to 0.951
A dilation with scale factor 0.25 is performed on triangle 1 to produce triangle 2. Which statement MUST be true about the two triangles?
O Their corresponding sides have equal lengths, and their corresponding angles have equal measures.
• Their corresponding sides are parallel, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
O Their corresponding sides are parallel, and their corresponding angles have equal measures.
O Their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
The correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
What is property of similar triangle?
If the corresponding sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are similar.
They have parallel corresponding sides, and they have angles with the same measure.
hence, the correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
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