The correct option e) 94.29%, for the probability that among the next 166 responses there will be at most 43 correct answers.
Explain the term Normal approximation?The normal curve is roughly followed by the sample distribution of averages and proportions from numerous independent experiments. The population value that corresponds to a sampling distribution or average is its expectation.If we use a normal distribution to simulate any binomial distribution with p = 0.24 for n = 166 results, then:
There should be 43 correct responses, or
μ = np = 166*0.24
μ = np = 34.86
The number of accurate responses has a standard deviation of
σ = √(np(1-p))
σ = √(34.86*0.76)
σ = 5.14
43 correct responses have a z-value;
z = (x - μ)/σ
z = (43 - 34.86)/5.14
z = 1.58
The likelihood that 43 accurate responses are provided is:
N(1.58) = 0.9429
Thus, the probability that among the next 166 responses there will be at most 43 correct answers is 94.29%.
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The complete question is-
Use the normal distribution to approximate the desired probability. A certain question on a test is answered correctly by 24.0 percent of the respondents. Estimate the probability that among the next 166 responses there will be at most 43 correct answers.
a) 74.56870% b) 74.30203% c) 75.20203% d) 94.95% e) 94.29%
Solve the inequality 3(x-2) + 1 ≥x + 2(x + 2).
O A. x≤ 4
OB. x ≥-5
OC. no solution
OD. all real numbers
Answer: no solution
Step-by-step explanation:
1. distribute through both sides to get 3x-6+1 ≥ x+2x+4
2. then combine like terms to get 3x-5 ≥ 3x+4
3. then make sure like terms are together on either side -> 3x -3x ≥ 4+5 ->
4. since the 3x-3x = 0, there are no solutions
*URGENT*
The sin (theta) = -2/5, and theta lies in quadrant IV. Find the exact values of the sine and cosine of 2 theta.
Answer: first choice!
sin2Theta= -4rt21/25
cos2Theta = 17/25
Step-by-step explanation:
Use Double Angle Formulas.
You can find cos2Theta immediately because one of the formulas needs only sin(theta) and that was given.
Cos2Theta =
1 - 2(sinTheta)^2
= 1 - 2(-2/5)^2
= 1 - 2(4/25)
= 1 - 8/25
= 25/25 - 8/25
= 17/25
The only answer with cos2theta=17/25 is the first choice.
Use a simple graph and Pythagorean Theorem to find cos(theta). Then you can use the Double Angle Formula for sin2theta. This would kinda be a double check if you have time. Since the first part of the solution eliminated all choices except the first choice, if you're pressed for time just do cos2theta calculation and pick the first choice.
See image for sin2theta calculation.
uppose we wanted the margin of error for the 90% confidence level to be about 1.5%. how large of a survey would you recommend?
confidence level to be about 1.5%. Then the survey would you recommend is 1537
The first thing is to apply the corresponding formula of this case, it is the calculation of a sample size without knowing the population. The equation is as follows, let n be the sample size:
n = (z * s / E) ^ 2
We know that z the corresponding z score of 95% of the confidence level, that this case is 1.96.
s, is the standard deviation and has a heat of 10.
Finally E, would be the error that is 0.5.
Now it's just replace in the formula:
n = (1.96 * 10 / 0.5) ^ 2 = 1536.64, that is approximately the sample must be 1537.
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an agriculturalist working with australian pine trees wanted to investigate the relationship between the age and the height of the australian pine. a random sample of australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the australian pine based on the age, in years, of the tree. Predicted height = 0.29 + 0.48(age) Which of the following is the best interpretation of the slope of the regression line?
The height increases by 0.48 meters each year.
The available regression equation is: Predict height= 0.29 + 0.48 (age).
Here, the predict height is dependent variable and the age is in-dependent variable.
Intercept = 0.29
Slope = 0.48
The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.
The height increases, an average, by 0.48 m per year.
Because co-efficient of slope variable indicate the positive sign and we increase 1 year in age then automatically height increased is 0.48 m.
The height increases, on average, by 0.48 meter each year.
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The available regression equation is: Predict height= 0.29 + 0.48 (age).
Here, the predict height is dependent variable and the age is in-dependent variable.
Intercept = 0.29
Slope = 0.48
The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.
question a polynomial p(x) has a relative maximum at (-2,4) , a relative minimum at (1,1) , a relative maximum at (5, 7) and no other critical points. how many zeros does p(x) have?
The polynomial p(x) must have at least two zeros, since it has three relative extrema.
What is polynomial?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x²- 4x + 7 is an illustration of a polynomial with a single indeterminate x.
Here i would think that since there are only 3 critical points given and no other information other than that those are the only critical points that p(x) would not have any real zeros.
At each of the relative extrema, the value of the function changes from increasing to decreasing or vice versa, meaning that the function crosses the x-axis at that point, which is a zero. Therefore, p(x) must have at least two zeros.
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PLEASE HEP ASAP GOT TEN MINS LEFT TILL DUE
Answer:
a ≈ 3.009075116
Step-by-step explanation:
cos(α) = adj/hyp
cos(53°) = a/5
a = 5 * cos(53°)
a ≈ 3.009075116
What is the answer to this question
Answer:
Step-by-step explanation:
a because if you divide everything under the fraction number you get answer a
The solution for the given expression is x = 4³/₅. The correct option is B.
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 the expression is x - 17⁴/₅ = -13¹/₅. The given expression will be solved as,
x - 17⁴/₅ = -13¹/₅
x = 17⁴/₅ -13¹/₅
x = 89 / 5 - 66 / 5
x = 23 / 5
x = 4³/₅
The expression will be equivalent to x = 4³/₅.
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PLS HELP
What is the range of f(x) = |x| + 7?
−7 ≤ y < ∞
−∞ < y ≤ −7
0 ≤ y < ∞
7 ≤ y < ∞
The range of the function f(x) = |x| + 7 is given by the option presented as follows:
7 ≤ y < ∞.
How to obtain the range of a function?The range is composed by the set containing all the values assumed by the output of the function, that is, all the numeric values assumed by the function.
In the context of this problem, the function is defined as follows:
f(x) = |x| + 7.
The parent function is the absolute value function g(x) = |x|, which gives the distance of a point x from the origin, assuming real values of at least 0, as a distance cannot be negative.
The addition by 7 means that the parent function was translated up seven units, meaning that the minimum value assumed by the range is seven, and the range of the function is given by the last option given as follows:
7 ≤ y < ∞.
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Lucy wants to plant 218 flowers in her garden. If there are 32 flowers in a box, how many boxes of flowers will Lucy need to order?
Answer:
Step-by-step explanation:
She could order 7 boxes. if each box has 32 flowers, then you would multiply 6 by 32 which is 192. If you subtract 218 from 192 you get 26. meaning that if she orders 6 boxes of 32 flowers then she would only have 192 flowers and there would be 26 flowers remaining, so then it's better for her to order 7 boxes it's better to have more than what she wants instead of having less than what she wants... that way she is able to plant 218 flowers even if there are some left.
Can someone help? Please?
Answer:
D. 66 cm
Step-by-step explanation:
You have parallelogram MNPR with diagonals that cross at E, and ME = 7x-30, and PE = 5x-12. You want to know the length of MP.
DiagonalsThe diagonals of a parallelogram bisect each other this means point E is the midpoint of diagonal MP, and ...
ME = PE
7x -30 = 5x -12
2x = 18 . . . . . . . . . add 30-5x
x = 9
Then the length of the half-diagonal is ...
ME = 7x -30 = 7(9) -30 = 33
So, the full diagonal is ...
MP = 2·33 = 66 . . . . . cm
Read the following statement: If A is an acute angle, then m2A = 30°. This statement demonstrates:
the substitution property.
the reflexive property. the symmetric property. the transitive property.
Answer:
Its been a minute since I've done this math
Step-by-step explanation:
This statement demonstrates the substitution property.
The substitution property states that if two expressions are equal, then we can substitute one expression for the other in any equation or inequality. In this case, "A" is an acute angle, and "m2A" is the measure of twice that angle. The statement says that if we double the measure of an acute angle, the result will be 30 degrees. Therefore, we can substitute "m2A" for 30 degrees in any equation or inequality.
The reflexive property states that any number or object is equal to itself. The symmetric property states that if a = b, then b = a. The transitive property states that if a = b and b = c, then a = c. None of these properties are demonstrated in the given statement.
PLEASE HURRY!
Write and solve the inequality that represents negative one eighth is less than the product of negative two thirds and a number.
A: negative one eighth is less than negative two thirds y where y is less than three sixteenths
B: negative one eighth is less than or equal to negative two thirds y where y is greater than negative three sixteenths
C: negative two thirds is less than negative one eighth y where y is less than one twelfth
D: negative two thirds is greater than negative one eighth y where y is greater than negative one twelfth
The solution to the inequality statement is x < 3/16
How to determine the solution to the inequality?From the question, we have the following parameters that can be used in our computation:
negative one eighth is less than the product of negative two thirds and a number.
Express as numbers and operators
So, we have
-1/8 < -2/3x
Divide both sides by -2/3
So, we have the following representation
1/8* 3/2 > x
Evaluate the produdts
3/16 > x
Rewrite as
x < 3/16
Hence, the solution is x < 3/16
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Decrease by
15 %
Increase by
85 %
Determine the Input
A number went into this machine and 50 came out.
What number went in?
To determine the input number, we can use the following steps:
Calculate the change in the input number as a percentage of the input number. In this case, the input number decreased by 15%, so the change is -0.15 * input number.
Add the change to the output number to find the input number. In this case, the output number is 50, so the input number is 50 + (-0.15 * input number).
Solve for the input number. In this case, we can solve for the input number by rearranging the equation and solving for x:
input number = 50 / (1 - 0.15)
input number = 50 / 0.85
input number = 58.82
Therefore, the input number is 58.82.
Note that this process can also be used to determine the output number given the input number and the percentage change. For example, if the input number is 100 and it increases by 85%, the output number would be:
output number = 100 * (1 + 0.85)
output number = 100 * 1.85
output number = 185
Answer:
[tex]x \times \frac{85}{100} \times \frac{185}{100} = 50[/tex]
[tex]x = 50 \times \frac{ {100}^{2} }{85 \times 185} [/tex]
[tex]31.8[/tex]
it seems to be a long number so I rounded
There might be a mistake because I wasn't able to check.
What is a written description of x − 14?
Answer: The written description of x - 14 is given as the difference of variable x and integer 14 gives x -14.
Step-by-step explanation:
Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
Let x be a variable,
And 14 is an integer.
By using mathematical operations,
The difference of x and 14 can be given as,
x - 14.
a new chemotherapy drug was tested in a randomized controlled trial (rct) on 822 cancer patients. of the 344 patients randomly assigned to receive the new drug, 101 survived for at least five years. of the 478 patients randomly assigned to the placebo, 299 survived for at least five years. determine the conditional probability of randomly selecting a study participant who survived for at least five years, given drug assignment.
We determined the conditional probability of drug assigned people who survived at least 5 years = 101/344
What is conditional probability?The possibility of occurring an event connected to the previous other event. That means occurring of two events is related to each other.
How to determine conditional probability of the question?We determine the probability by the following way.
At first, we will make a chart with the given data.
survived 5yrs get other result total
Drug assign 101 243 344
placebo 299 179 478
total 400 422 822
We need to determine the probability of 5 years survived persons from drug assigned
Let, it is denoted by P(Sr/Dr)
As per conditional probability P(Sr/Dr) = P(Sr and Dr)/P(Dr)
= 101/344
As from the above chart, we find P (Sr and Dr) =101 and
P(Dr) = total drug assigned = 344
hence, P(Sr/Dr) = 101/344
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which of the three methods of assigning probabilities is used when we are dealing with sampling (as a method of determining probabilities)? no need to explain.
Random sampling methods of assigning probabilities is used when we are dealing with sampling.
Random sampling is a method of assigning probabilities used when dealing with samples of a population. It involves randomly selecting a sample from the population and then using that sample to estimate the probabilities of different outcomes. This is done by calculating the proportion of the sample that falls into each category. For example, if you are trying to determine the probability of a certain outcome, you would randomly select a sample from the population and then count how many of the individuals in the sample fall into that category. The probability of the outcome would then be calculated by dividing the number of individuals in that category by the total number of individuals in the sample.
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What is the slope of the line that passes through the points (-7,-2) and
(-15, -14)? Write your answer in simplest form.
Answer:
Step-by-step explanation:
To find the slope of a line that passes through two points, we can use the slope formula, which is written as follows:
slope = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
Given the points (-7, -2) and (-15, -14), we can substitute their coordinates into the slope formula to find the slope of the line:
slope = (-14 - (-2)) / (-15 - (-7))
= -12 / -8
= 3/2
Therefore, the slope of the line that passes through the points (-7, -2) and (-15, -14) is 3/2. In simplest form, this is equal to 1.5.
Kala's parents give her simple interest on any money she saves for college. Which equation and solution represents the total interest, T, earned when the principal amount is $100, the
annual simple interest rate is 1%, and the number of years is 10
Answer:
The interest earned is $10.00
Step-by-step explanation:
Interest = principal x rate x time
I= 100(.01)(10)
I = 10
Graph the image of this figure after a dilation with a scale factor of 3 centered at
(−7, −6). Use the polygon tool to graph the dilated figure. *picture Below*
Answer:
See the picture below
Step-by-step explanation:
You start from the center given (-7,-6), then count how many spaces from the center to that point. Take that number and triple it to find the new point. I drew lines so that you could see the path of two of the points.
The path that I did not draw was from the point (-3,-2). If you start at (-7,-6) you will have to move 4 spaces to the right and 4 spaces up to get to (-3,-2) Now triple that. You will move 12 spaces to the right and 12 spaces up for the new point of (5,6)
Three years ago Joseph was three times older than Agnes in 2 years times the sum of their ages will be 75 years. Determine their present ages
Answer:
Hey, answer is attached.
Step-by-step explanation:
Hope this helps.
Joe asked a bank teller to cash a $570 check using $20 bills and $50 bills, If the teller gave him a total of 15 bills, how many of each type of bill did he receiver
Answer:
9 $50 bills and 6 $20 bills
Step-by-step explanation:
Let f = number of $50 bills.
Let t = number of $20 bills.
f + t = 15
50f + 20t = 570
f = 15 - t
50(15 - t) + 20t = 570
750 - 50t + 20t = 570
-30t = -180
t = 6
f + t = 15
f + 6 = 15
f = 9
Answer: 9 $50 bills and 6 $20 bills
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
[tex] \sf \: x = 25[/tex]
Step-by-step explanation:
Given equation,
→ (x - 7)2 = 36
Now the value of x will be,
→ 2(x - 7) = 36
→ (2 × x) - (2 × 7) = 36
→ 2x - 14 = 36
→ 2x = 36 + 14
→ 2x = 50
→ x = 50/2
→ [ x = 25 ]
Hence, the value of x is 25.
Answer:
x = 25
Step-by-step explanation:
(x-7)2 = 36
divide both sides by 2
x-7 = 18
add 7 to both sides
x = 25
Can someone please help me
The equivalent expressions of 9/7x-3/4 are 9/7x+(-3/4) and -3/4+9/7x.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 9/7x-3/4.
Nine by seven times of x minus three by four.
x is the variable of expression.
The equivalent expression is an expression whose value is same but looks different.
9/7x-3/4.
By commutative property
-3/4+9/7x is an equivalent expression of 9/7x-3/4.
9/7x+(-3/4).
When we simplify we get 9/7x-3/4.
-9/7x+3/4 is also a equivalent expression we get it by multiplying with negative.
Hence, 9/7x+(-3/4) and -3/4+9/7x are equivalent expressions of 9/7x-3/4.
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6. The discount price of a hat is $18. What is the regular price?
The store offers a 20% discount btw .
Answer:$22.50 regular price
Step-by-step explanation: RP=Regular Price
RP-20%of RP=18
RP-0.20RP=18........RP =1RP
1RP-0.20RP=18
0.80RP=18
RP=18/0.80
RP=$22.50
Answer:
22.50
Step-by-step explanation:
other answer is cryptic so here is a full explaination
To find the regular price of the hat, we need to determine the amount of the discount and then add that amount to the discount price.
The discount on the hat is 20% of the regular price, or 20/100 * regular price. The discount price is $18, so we can set up the equation:
discount price = regular price - (20/100 * regular price)
Substituting the known values into the equation, we get:
$18 = regular price - (20/100 * regular price)
Solving for the regular price, we find that the regular price is $22.50. This is the price of the hat before the discount.
what is sue's position x if her home is the origin? assume the positive direction is to the right.
If Sue's home is the origin and the positive direction is assumed to the right, then her position is 2 mi.
Therefore, the answer is 2mi.
Origin depends on the frame of reference, it depends on from where the observer is viewing.
From the figure, distance between home and Sue = 2 - 0 = 2mi
and the distance between Cinema and Sue = 5 - 2 = 3mi
Sue's position is 2mi right to her home and 3mi left to the Cinema. So if her home is the origin and positive direction is to the right x is +2 mi.
--The question is incomplete without the figure, answering to the figure attached--
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If f(x)=|x−5| 2, find f(3). responses 10 10 6 6 4 4 0
If the function f(x) = |x-5| + 2, then the value of f(3) is 4
The function
f(x) = |x-5| + 2
The function is defined as the mathematical statement that shows the relationship between the independent variable and the dependent variable. The function consist of different variables, numbers and mathematical operators
Here the function consist of the absolute value symbol.
|-a| = a
The absolute value of the positive and the negative number will be always positive.
The function is f(x) = |x-5| + 2
Then,
f(3) = |3-5| + 2
= |-2| + 2
= 2 + 2
= 4
Therefore, the value of f(3) is 4
I have answered the question in general, as the given question is incomplete
The complete question is:
If f(x)=|x−5| + 2, find the value of f(3).
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Draw a line PQ and take a point A outide it. Uing ruler and compa , draw a line through A parallel to PQ
Using a ruler and compass, draw a line through point A parallel to line PQ by first drawing a line segment from A to any point on PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. Finally, use the ruler to draw a line through the arc, parallel to PQ.
Drawing a line parallel to an existing line can be done using a ruler and compass. First, draw a line segment from point A to any point on line PQ. Then, use the compass to draw an arc from the other end of the line segment to the other point on PQ. This arc should intersect with the first line segment. Finally, use the ruler to draw a line through the arc, parallel to PQ. This line will be parallel to PQ since it is the same distance from each point on the original line. The use of the compass ensures that the resulting line is the same distance away from the original line throughout, thus resulting in a line parallel to PQ.
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What i the equation of the line that pae through the point (-1,5)(−1,5) and ha a lope of -3
The equation of the line is y = -3x + 2.
What is the slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are represented by Δy and Δx, respectively.
As a result, m = change in y/change in x = Δy/Δx is the formula for the change in y-coordinate with respect to the change in x-coordinate.
where "m" represents a line's slope.
Given that, the line passes through the point (-1,5) with slope of -3.
The equation of line passes through (x₁, y₁) with slope m is
y - y₁ = m(x - x₁)
Putting x₁ = -1, y₁ = 5 and m = -3.
y - 5 = -3(x - (-1))
y - 5 = -3x - 3
y = -3x + 2
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What transformation took place to get from triangle ABC to triangle A’B’C’? Be specific.
What transformation took place to get from triangle A’B’C’ to triangle A”B”C”? Be specific.
We can see two transformations.
1) ΔABC → ΔA'B'C', it is a translation 10 units left and 2 units up.
T(-10, 2)2) ΔA'B'C' → ΔA''B''C'', it is a reflection across the x-axis.
R(x-axis)Rida writes a fitness blog. At a certain point, she has 6,218 followers. Then the following events happen, in order:
92 people stop following Rida's blog.
417 people start following Rida's blog.
The number of followers doubles.
Use the drop-down menus to answer the questions below.
CLEAR CHECK
An expression that models this series of events is
.
Zuberi also writes a fitness blog. His current number of followers is equal to 3(945−120)+312. A possible series of events that led to this number of followers would be:
An expression that models the series of events is 2(6,218 - 92 + 417).
The possible events are:
120 followers stop following Zuberi's blog.
The number of followers triples.
312 followers start following Zuberi's blog.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
At a certain point, she has 6,218 followers.
Events happened in order:
92 people stop following Rida's blog.
417 people start following Rida's blog.
The number of followers doubles.
An expression that models this series of events.
= 2(6,218 - 92 + 417)
The current number of followers.
= 3 (945 - 120) + 312
The possible events.
120 followers stop following Zuberi's blog.
The number of followers triples.
312 followers start following Zuberi's blog.
Thus,
An expression that models the series of events is 2(6,218 - 92 + 417).
The possible events are given above.
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