Answer:
12
Step-by-step explanation:
We can factor out 10! on the numerator and the denominator,.
This gives: 10! (1 + 11 + (11 * 12)) / 10! (1 + 11)
This is because 10! * 11 is equal to 11! meaning we can factor out 10!.
10! * 11 * 12 also equals 12! which is why we can factor 10! out of that too.
Seeing as 10! is at the top and bottom we can cancel those out.
This leaves us with: 144 / 12 which is equal to 12.
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 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]
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
Is 6/16 greater or less than 4/10
Answer:
Less than 4/10
Step-by-step explanation:
First lets convert both fractions to a common denominator:
16 and 10 can both go into 80 equally.
Now lets convert the fractions so they have a denominator of 80:
(6/16) *5 = 30/80
(4/10) *8 = 32/80
we can multiply the fractions to get just the numerator (*80)
Now compare 30 to 32. As you can see 32 is greater meaning that 6/16 is less that 4/10.
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.
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
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]
. 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 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.
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]
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.
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
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
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:
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]
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
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).
Explain the connection between the chain rule for differentiation and the method of u-substitution for integration.
Answer:
Chain rule: [tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex], u-Substitution: [tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
Step-by-step explanation:
Differentiation and integration are reciprocal to each other. The chain rule indicate that a composite function must be differentiated, describing an inductive approach, whereas u-substitution allows integration by simplifying the expression in a deductive manner. That is:
[tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex]
Let integrate both sides in terms of x:
[tex]f[u(x)] = \int {\frac{df}{du} \frac{du}{dx} } \, dx[/tex]
[tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]
This result indicates that f must be rewritten in terms of u and after that first derivative needs to be found before integration.
WILL GIVE BRAINLIEST IF CORRECT!! Please help ! -50 POINTS -
Answer:
i think (d) one i think it will help you
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
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
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%
Suppose that Vera wants to test the hypothesis that women make less money than men doing the same job. According to the Bureau of Labor Statistics (BLS), the median weekly earnings for men in the professional and related occupation sector in 2015 was $1343. Vera collected median weekly earnings data for women in 2015 from a random subset of 18 positions in the professional and related occupation sector. The following is the sample data. $1811, $728, $1234, $966, $953, $1031, $990, $633, $796, $1325, $1448, $1125, $1144, $1082, $1145, $1256, $1415, $1170 Vera assumes that the women's median weekly earnings data is normally distributed, so she decides to perform a t-test at a significance level of α = 0.05 to test the null hypothesis, H0:µ=1343H0:μ=1343 against the alternative hypothesis, H1:µ<1343H1:μ<1343 , where µμ is the population mean. If the requirements for performing a t-test have not been met, only answer the final question. Otherwise, answer all five of the following questions. First, compute the mean, x⎯⎯⎯x¯ , of Vera's sample. Report your answer with two decimals of precision.
Answer:
There is sufficient evidence to conclude that women make less money than men doing the same job.
Step-by-step explanation:
The hypothesis for the test can be explained as follows:
H₀: Women does not make less money than men doing the same job, i.e. [tex]\mu\geq \$1343[/tex].
Hₐ: Women make less money than men doing the same job, i.e. [tex]\mu<\$1343[/tex].
From the provided data compute the sample mean and standard deviation:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{18}[1811+728+...+1170]=1125.11\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{18-1}\times 1322541.86}=278.92[/tex]
Compute the test statistic as follows:
[tex]t=\frac{\bar x-\mu}[\s/\sqrt{n}}=\frac{1125.11-1343}{278.92/\sqrt{18}}=-3.143[/tex]
The test statistic value is -3.143.
Compute the p-value as follows:
[tex]p-value=P(t_{n-1}<-3.143)=P(t_{17}<-3.143)=0.003[/tex]
*Use a t-table.
The p-value of the test is 0.003.
The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.
Conclusion:
There is sufficient evidence to conclude that women make less money than men doing the same job.
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
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
Given that 243√3 =3^a, find the value of a
Answer:
a=11/5 OR 5.5
Step-by-step explanation:
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.
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..
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
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)