Answer:
Option d: The data are continuous because the data can take on any value in an interval.
Step-by-step explanation:
The data are continuous if they can take on any value within a range. In this case study, there are different elephants including small/young ones and big ones/old ones.
Thus, their heights will vary and can take on any value within a particular range.
Given that 243√3 =3^a, find the value of a
Answer:
a=11/5 OR 5.5
Step-by-step explanation:
Line AB and Line CD are parallel lines. Which translation of the plane can we use to prove angles x and y are congruent, and why?
Answer:
Option C.
Step-by-step explanation:
In the given figure we have two parallel lines AB and CD.
A transversal line FB intersect the parallel lines at point B and C.
We know that the if a transversal line intersect two parallel lines, then corresponding angles are congruent.
[tex]\angle ABC=\anle ECF[/tex]
[tex]x=y[/tex]
To prove this by translation, we need a translation along the directed line segment CB maps ine CD onto line AB and angle y onto angle x.
Therefore, the correct option is C.
The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. What is the probability of a weight between 415 pounds and the mean of 400 pounds
Answer:
The probability is [tex]P(x_1 \le X \le x_2 ) = 0.4332[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 400[/tex]
The standard deviation is [tex]\sigma = 10[/tex]
The considered values are [tex]x_1 = 400 \to x_2 = 415[/tex]
Given that the weight follows a normal distribution
i.e [tex]\approx X (\mu , \sigma )[/tex]
Now the probability of a weight between 415 pounds and the mean of 400 pounds is mathematically as
[tex]P(x_1 \le X \le x_2 ) = P(\frac{x_1 - \mu }{\sigma } \le \frac{X - \mu }{\sigma } \le \frac{x_2 - \mu }{\sigma } )[/tex]
So [tex]\frac{X - \mu }{\sigma }[/tex] is equal to Z (the standardized value of X )
Hence we have
[tex]P(x_1 \le X \le x_2 ) = P(\frac{x_1 - \mu }{\sigma } \le Z \le \frac{x_2 - \mu }{\sigma } )[/tex]
substituting values
[tex]P(x_1 \le X \le x_2 ) = P(\frac{400 - 400 }{10 } \le Z \le \frac{415 - 400}{415 } )[/tex]
[tex]P(x_1 \le X \le x_2 ) = P(0\le Z \le 1.5 )[/tex]
[tex]P(x_1 \le X \le x_2 ) = P( Z < 1.5) - P( Z < 0)[/tex]
From the standardized normal distribution table [tex]P( Z< 1.5) = 0.9332[/tex] and
[tex]P( Z < 0) = 0.5[/tex]
So
[tex]P(x_1 \le X \le x_2 ) = 0.9332 - 0.5[/tex]
[tex]P(x_1 \le X \le x_2 ) = 0.4332[/tex]
NOTE : This above values obtained from the standardized normal distribution table can also be obtained using the P(Z) calculator at (calculator dot net).
A manufacturer knows that on average 20% of the electric toasters produced require repairs within 1 year after they are sold. When 20 toasters are randomly selected, find appropriate numbers x and y such that (a) the probability that at least x of them will require repairs is less than 0.5; (b) the probability that at least y of them will not require repairs is greater than 0.8
Answer:
(a) The value of x is 5.
(b) The value of y is 15.
Step-by-step explanation:
Let the random variable X represent the number of electric toasters produced that require repairs within 1 year.
And the let the random variable Y represent the number of electric toasters produced that does not require repairs within 1 year.
The probability of the random variables are:
P (X) = 0.20
P (Y) = 1 - P (X) = 1 - 0.20 = 0.80
The event that a randomly selected electric toaster requires repair is independent of the other electric toasters.
A random sample of n = 20 toasters are selected.
The random variable X and Y thus, follows binomial distribution.
The probability mass function of X and Y are:
[tex]P(X=x)={20\choose x}(0.20)^{x}(1-0.20)^{20-x}[/tex]
[tex]P(Y=y)={20\choose y}(0.20)^{20-y}(1-0.20)^{y}[/tex]
(a)
Compute the value of x such that P (X ≥ x) < 0.50:
[tex]P (X \geq x) < 0.50\\\\1-P(X\leq x-1)<0.50\\\\0.50<P(X\leq x-1)\\\\0.50<\sum\limits^{x-1}_{0}[{20\choose x}(0.20)^{x}(1-0.20)^{20-x}][/tex]
Use the Binomial table for n = 20 and p = 0.20.
[tex]0.411=\sum\limits^{3}_{x=0}[b(x,20,0.20)]<0.50<\sum\limits^{4}_{x=0}[b(x,20,0.20)]=0.630[/tex]
The least value of x that satisfies the inequality P (X ≥ x) < 0.50 is:
x - 1 = 4
x = 5
Thus, the value of x is 5.
(b)
Compute the value of y such that P (Y ≥ y) > 0.80:
[tex]P (Y \geq y) >0.80\\\\P(Y\leq 20-y)>0.80\\\\P(Y\leq 20-y)>0.80\\\\\sum\limits^{20-y}_{y=0}[{20\choose y}(0.20)^{20-y}(1-0.20)^{y}]>0.80[/tex]
Use the Binomial table for n = 20 and p = 0.20.
[tex]0.630=\sum\limits^{4}_{y=0}[b(y,20,0.20)]<0.50<\sum\limits^{5}_{y=0}[b(y,20,0.20)]=0.804[/tex]
The least value of y that satisfies the inequality P (Y ≥ y) > 0.80 is:
20 - y = 5
y = 15
Thus, the value of y is 15.
An insect population in a lab has 2 ¹² insect. If the population double how many insect will be there?
Answer:
8192
Step-by-step explanation:
2 ¹²= 4096
4096 x 2 = 8192
Suppose that f(x,y) is a smooth function and that its partial derivatives have the values, fx(8,5)=2 and fy(8,5)=2. Given that f(8,5)=−2, use this information to estimate the value of f(9,6).
Answer:
f(9,6) = 2
Step-by-step explanation:
We know df = (df/dx)dx + (df/dy)dy
From the question, df/dx = fx(8,5) = 2 and df/dy = fy(8,5) = 2
Since we need to find f(9,6) and f(8,5) = -2
dx = 9 - 8 = 1 and dy = 6 - 5 = 1
f(9,6) = f(8,5) + df
df = (df/dx)dx + (df/dy)dy
df = fx(8,5)dx + fy(8,5)dy
Substituting the values of fx(8,5) = 2, fy(8,5) = 2, dx = 1 and dy = 1
df = 2 × 1 + 2 × 1
df = 2 + 2
df = 4
f(9,6) = f(8,5) + df
substituting the value of df and f(8,5) into the equation, we have
f(9,6) = -2 + 4
f(9,4) = 2
The value of f(9,6) = 2
Rewrite the equation in =+AxByC form. Use integers for A, B, and C. =−y6−6+x4
Answer:
6x + y = -18
Step-by-step explanation:
The given equation is,
y - 6 = -6(x + 4)
We have to rewrite this equation in the form of Ax + By = C
Where A, B and C are the integers.
By solving the given equation,
y - 6 = -6x - 24 [Distributive property]
y - 6 + 6 = -6x - 24 + 6 [By adding 6 on both the sides of the equation]
y = -6x - 18
y + 6x = -6x + 6x - 18
6x + y = -18
Here A = 6, B = 1 and C = -18.
Therefore, 6x + y = -18 will be the equation.
The function ƒ(x) = 2x is vertically translated 5 units down and then reflected across the y-axis. What's the new function of g(x)?
Answer:
g(x) = -2x - 5
2x becomes -2x as a reflection across the y-axis
add on -5 to shift the function 5 units down
Reflection Over Parallel Lines Please complete the attached reflection. Thanks!
Answer: A(3, -5)
B(6, -2)
C(9, -2)
Step-by-step explanation:
If we have a point (x, y), and we do a reflection over the axis y = a, then the only thing that will change in our point is the value of x.
Now, the distance between x and a must remain constant before and after the reflection.
so if x - a = d
then the new position of the point will be:
(a - d, y) = (2a - x, y).
I will use that relationship for the 3 points
A)
We start with the point (1, -5)
The reflection over y = -1 leaves.
The distance between 1 and -1 is = 1 - (-1) = 2.
Then the new point is (-1 - 2, -5) = (-3, -5)
Now we do a reflection over y = 1, so D = -3 - 1 = -2
Then the new point is:
A = (1 -(-2), -5) = (3, -5)
B) (2, -2)
Reflection over y = -1.
distance, d = 2 - (-1) = 3
the point is (-1 - 3, -2) = (-4, -2)
Now, a reflection over y = 1.
The distance is D = -4 - 1 = -5
The new point is (1 - (-5), 2) = (6, -2)
C) (5, -2)
reflection over y = -1
Distance: D = 5 - ( - 1) = 6
New point: (-1 - 6, -2) = (-7, -2)
Reflection over y = 1.
Distance D = -7 - 1 = -8
New point ( 1 - (-8), -2) = (9, -2)
. What is the percentage of VanArsdel's manufactured goods sold in Alberta? (to two decimal places in the format 00.00, without the % sign)
Answer:
Revenue : 47.77
Units Sold : 28.91
Step-by-step explanation:
The revenue is the amount that is received after selling the goods manufactured. VanArsdel's sold good of manufactured in Alberta. Goods manufactured by VanArsdel's is considered as 100 percent out of which it sold 28.91 % of units in Alberta. The revenue percentage is 47.77%.
One grade of tea costing $3.20 per pound is mixed with another grade costing $2.00 per pound to make 20
pounds of a blend that will sell for $2.72 per pound. How much of the $3.20 grade is needed? Formulate an
equation and then solve it to find how much of the $3.20 grade is needed.
Answer:
X+y = 20... equation 1
3.2x + 2y = 54.4...equation 2
X= 12
12 of $3.2 grade is needed
Step-by-step explanation:
Let x = grade containing$ 3.2 per pound
Let y = grade containing $2.00 per pound
X+y = 20... equation 1
X3.2 +2y = 20(2.72)
3.2x + 2y = 54.4...equation 2
Multiplying equation 1 by 2
2x +2y = 40
3.2x + 2y = 54.4
1.2x = 14.4
X= 12
If x= 12
2x +2y = 40
2(12) + 2y = 40
2y = 40-24
2y = 16
Y= 8
Find the least common multiple of $6!$ and $(4!)^2.$
Answer:
The least common multiple of $6!$ and $(4!)^2.$
is 6×4! or 144
In the given figure, find AB, given thatAC = 14 andBC = 9.
Answer:
Given:
AC = 14 and BC = 9
AB = ?
Solution:
From the fig:
AC = AB + BC
Putting the values
14 = AB + 9
AB = 14 - 9
AB = 5
(you can also take AB = x or any other variable)
Step-by-step explanation:
Using traditional methods it takes 109 hours to receive an advanced flying license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher believes the new technique may lengthen training time and decides to perform a hypothesis test. After performing the test on 190 students, the researcher decides to reject the null hypothesis at a 0.02 level of significance.
What is the conclusion?
a. There is sufficient evidence at the 0.020 level of significance that the new technique reduces training time.
b. There is not sufficient evidence at the 0.02 level of significance that the new technique reduces training time.
I think the answer is option B.
Because while researchers research they believed that it will lengthen the time and it don't reduced the time.
Hope it's correct..
Simplify the expression.
16 • 4^-4
A. 256
B. -256
C. 1/16
D. -4,096
Answer:
C. 1/16
Step-by-step explanation:
[tex]16 * 4^{-4}[/tex]
16 can be written as a power of 4.
[tex]4^2 * 4^{-4}[/tex]
The bases are same, add exponents.
[tex]4^{2+-4}[/tex]
[tex]4^{-2}[/tex]
Simplify negative exponent.
[tex]\frac{1}{4^2 }[/tex]
[tex]\frac{1}{16}[/tex]
Which is the value of this expression when p = 3 and q = negative 9? ((p Superscript negative 5 Baseline) (p Superscript negative 4 Baseline) (q cubed)) Superscript 0 Negative one-third Negative StartFraction 1 Over 27 EndFraction StartFraction 1 Over 27 EndFraction One-third Edge 2020
Answer:
I am pretty sure that the answer is D. The value should be 1.
Step-by-step explanation:
Answer:
Answer is D
Step-by-step explanation:
On Edge 2020
6. Look at the figure below.
Are triangles ABC and DEC congruent?
Explain why or why not.
Answer:
Yes
Step-by-step explanation:
They are congruent by the AAS postulate.
∠A corresponds to and is congruent to ∠D
Side BC corresponds to and is congruent to side EC
∠C is congruent to ∠C by the Vertical Angles Theorem.
So, ΔABC ≅ ΔDEC
The circle graph shows the percentage of numbered tiles in a box. If each numbered tile is equally likely to be pulled from the box, what is the probability of pulling out a tile with a 6 on it? (Hint: Remember that percents are based out of 100% and probability is represented as a fraction of 100%)
Answer: [tex]\dfrac{1}{5}[/tex]
Step-by-step explanation:
From, the circle graph in the attachment below,
The percentage of portion taken by 6 (dark blue) = 20%
So, the probability of pulling out a tile with a 6 on it = percentage of portion taken by 6 (dark blue) = 20% [Probability can also be written as a percentage]
[tex]=\dfrac{20}{100}\\\\=\dfrac{1}{5}[/tex] [we divide a percentage by 100 to convert it into fraction]
Hence, the probability of pulling out a tile with a 6 on it = [tex]\dfrac{1}{5}[/tex]
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's standard deviation
Answer:
15
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
30 hcchxfifififififfud7dd7d
Find the value of y.
[tex]y^2 = 9(9+3)\\\\y^2 = 9(12)\\\\y^2 =3^2\cdot3\cdot2^2\\\\y = 6\sqrt{2}[/tex]
One stats class consists of 52 women and 28 men. Assume the average exam score on Exam 1 was 74 (σ = 10.43; assume the whole class is a population). A random sample of 16 students yielded an average of a 75 on the first exam (s=16). What is the z-score of the sample mean? Is this sample significantly different from the population? (Hint: Use the z-score formula for locating a sample mean)
Answer:
(A) What is the z- score of the sample mean?
The z- score of the sample mean is 0.0959
(B) Is this sample significantly different from the population?
No; at 0.05 alpha level (95% confidence) and (n-1 =79) degrees of freedom, the sample mean is NOT significantly different from the population mean.
Step -by- step explanation:
(A) To find the z- score of the sample mean,
X = 75 which is the raw score
¶ = 74 which is the population mean
S. D. = 10.43 which is the population standard deviation of/from the mean
Z = [X-¶] ÷ S. D.
Z = [75-74] ÷ 10.43 = 0.0959
Hence, the sample raw score of 75 is only 0.0959 standard deviations from the population mean. [This is close to the population mean value].
(B) To test for whether this sample is significantly different from the population, use the One Sample T- test. This parametric test compares the sample mean to the given population mean.
The estimated standard error of the mean is s/√n
S. E. = 16/√80 = 16/8.94 = 1.789
The Absolute (Calculated) t value is now: [75-74] ÷ 1.789 = 1 ÷ 1.789 = 0.559
Setting up the hypotheses,
Null hypothesis: Sample is not significantly different from population
Alternative hypothesis: Sample is significantly different from population
Having gotten T- cal, T- tab is found thus:
The Critical (Table) t value is found using
- a specific alpha or confidence level
- (n - 1) degrees of freedom; where n is the total number of observations or items in the population
- the standard t- distribution table
Alpha level = 0.05
1 - (0.05 ÷ 2) = 0.975
Checking the column of 0.975 on the t table and tracing it down to the row with 79 degrees of freedom;
The critical t value is 1.990
Since T- cal < T- tab (0.559 < 1.990), refute the alternative hypothesis and accept the null hypothesis.
Hence, with 95% confidence, it is derived that the sample is not significantly different from the population.
Write the equation of the line in slope intercept form that is perpendicular to the line y=-(3/2)x +7. Show your work
Answer:
the answer is y= 2/3x - 5
WILL GIVE BRAINLIEST IF CORRECT!! Please help ! -50 POINTS -
Answer:
i think (d) one i think it will help you
Evaluate the expression
Answer: C) tan(pi/56)
=============================================
Explanation:
I recommend using a trig identity reference sheet. The specific identity we will be using is [tex]\frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)} = \tan(A-B)[/tex]
What we are given is in the form [tex]\frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)}[/tex] with A = pi/7 and B = pi/8
A-B = (pi/7)-(pi/8)
A-B = pi(1/7-1/8)
A-B = pi(8/56 - 7/56)
A-B = pi*(1/56)
A-B = pi/56
Therefore,
[tex]\frac{\tan\left(\pi/7\right)-\tan(\pi/8)}{1+\tan(\pi/7)\tan(\pi/8)} = \tan\left(\pi/56\right)[/tex]
Which two points are on the graph of y=-x+ 3?
(-1,-2), (1,4)
(1, 2), (0, -3)
(0, 3), (4, -1)
(4, -1), (1, 3)
Answer:
(0, 3), (4, -1)
(1, 2)
Step-by-step explanation:
If the answers that have been provided to you are only in pairs then it'd just be the first answer I wrote. The points (1, 2) also are on the graph of y=x+3 but if the answers aren't individual than I'd just stick with the (0, 3), (4, -1). Does that make sense? I used a graphing calculator online called Desmos, it's very good. I highly recommend it for problems like these.
I hope this helps:) Select as brainliest because I actually put work into this and tried.
Please answer this correctly without making mistakes
Answer:
Centerville is 13 kilometers away from Manchester
Step-by-step explanation:
26.1 - 13.1 = 13
A data set is summarized in the frequency table below. Using the table, determine the number of values less than or equal to 6.
Answer:
18
Step-by-step explanation:
Given the above table of the data set, the number of values less than or equal to 6 would be the sum of the frequencies of all values that is equal to or less than 6.
From the table above, we would add up the frequencies of the values of 6 and below, which is:
2 + 3 + 6 + 4 + 3 = 18
Answer = 18
The number of values less than or equal to 6 is 18
Calculation of the number of values:Here the number of values should be less than or equivalent to 6 represent the sum of the frequencies i.e. equal or less than 6
So, here the number of values should be
= 2 + 3 + 6 + 4 + 3
= 18
Hence, we can conclude that The number of values less than or equal to 6 is 18
Learn more about frequency here: https://brainly.com/question/20875379
Find the distance between the points (-3, -2) and (-1, -2). 2 √6 4
Answer:
Let the distance be AB.
So, by using distance formula, we get
AB=√(x^2-x^1)^2+(y^2-y^1)^2
AB=√[-1-(-3)]^2+[-2-(-2)]^2
AB=√(-1+3)²+(-2+2)²
AB=√2²+0²
AB=√4
AB=2 units
hope it helps u...
plz mark as brainliest...
Answer: The distance between the points (-3, -2) and (-1, -2). is 2
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 8% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 4% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
a. What percentage of the employees will experience lost-time accidents in both years?
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?
Answer:
a) percentage of the employees that will experience lost-time accidents in both years = 1.2%
b) percentage of the employees that will suffer at least one lost-time accident over the two-year period = 10.8%
Step-by-step explanation:
given
percentage of lost time accident last year
P(L) = 8% = 0.08 of the employees
percentage of lost time accident current year
P(C) = 4% = 0.04 of the employees
P(C/L) = 15% = 0.15
using the probability
P(L ∩ C) = P(C/L) × P(L)
= 0.08 × 0.15 = 0.012 = 1.2%
percentage of the employees will experience lost-time accidents in both years = 1.2%
b) Using the probability of the event
P(L ∪ C) = P(L) + P(C) - P(L ∩ C)
= 0.08 + 0.04 -0.012 = 0.108 = 10.8%
percentage of the employees will suffer at least one lost-time accident over the two-year period = 10.8%
f(x)=x^2+12x+7 f(x)=(x+_)^2+_ Rewrite the function by completing the square
Answer:
f(x) = (x + 6)² - 29
Step-by-step explanation:
Given
f(x) = x² + 12x + 7
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² + 12x
x² + 2(6)x + 36 - 36 + 7
= (x + 6)² - 29, thus
f(x) = (x + 6)² - 29
answers are 6, and -29