Answer:
x = 14
y = -7
z = -3
but this is none of the provided answer options !
Step-by-step explanation:
it's really easy by principle. it's just some work to do.
we try to find equations to express one variable in terms of the others.
but one thing there is : your teacher made a mistake.
the right solution is x = 14, y = -7, z = -3
your teacher made a typo at d.
but the right answer should be d.
just to give you an idea how this can be done (and also to prove that there is a mistake by the teacher):
we can directly try to transform one expression into one that describes x by y and z.
and then another to describe e.g. z by y. and then solve the third one just for y. and then we get the other 2 by these other expressions.
or we can e.g. add or subtract one equation to/from another. this is one of these cases, because we can find really simple expressions that way :
we do
5x + 6y + 7z = 7
- (3x + 4y + 3z = 5)
- (2x + 2y + 3z = 5)
---------------------------
0x + 0y + z = -3
=> z = -3
3x + 4y - 3×3 = 5
3x = -4y + 14
x = (-4y + 14)/3
2×(-4y + 14)/3 + 2y - 9 = 5
(-8y + 28)/3 + 2y = 14
-8y + 28 + 6y = 42
-2y = 14
y = -7
x = (-4×-7 + 14)/3 = (28+14)/3 = 42/3 = 14
Amit makes a cuboid having sides 3cm, 2cm & 3cm. How many such cuboids will be required to form a cube.
Start with a volume of a cuboid,
[tex]V=abc=3\cdot2\cdot3=18\mathrm{cm^3}[/tex]
The side of the cube we need equals to the LCM of the cubiod's sides,
[tex]\mathrm{LCM}(a,b,c)=\mathrm{LCM}(3,2,3)=6[/tex]
Now compute the volume of such cube,
[tex]V=\mathrm{LCM}(a,b,c)^3=6^3=216\mathrm{cm^3}[/tex]
Divide the volumes to get how many cubiods are in such cube,
[tex]\dfrac{V_{\mathrm{cube}}}{V_{\mathrm{cubiod}}}=\dfrac{216}{18}=\boxed{12}[/tex]
Hope this helps :)
Answer:
Hi,
Answer: 12
Step-by-step explanation:
lcm(3,2,3)=6
Volume of a cuboid=3*2*3=18 (cm³)
Volume of the cube=6³=216 (cm³)
Number of cuboids=216/18=12.
The number of cubic feet of water in a curved container can be approximated by V=0.95h^2.9 find the amount of water in the container when h=8 feet round to the nearest tenth
Answer choices:
A. 0.9
B. 358.4
C. 395.1
D. 314.9
Answer:
C. 395.1
Step-by-step explanation:
Substitute the value for x:
[tex]V=0.95(8)^{2.9}\\V=395.1[/tex]
The graph shown is the solution set for which of the following inequalities?
Answer:
b is your answer hope it is helpful
Answer:
b is the correct answer
Step-by-step explanation:
the answer is b
Complete the Similarity statement below only if the triangles are similar.
Which of the following is a geometric sequence? a. 5,-25,125,-625 b.2,4,16,48 c. 13,16,19,22 d. 100,50,0,-50
Answer:
a
Step-by-step explanation:
B isn't a geometric sequence as it's last term doesn't follow the rule
C is an arithmetic sequence
D is an arithmetic sequence too
help please i’ll give brainliest
Answer:
b
Step-by-step explanation:
b intercepts the y axis
Find the formula for the geometric sequence 1, 5, 25, 125, .
A study was performed to determine the percentage of people who wear life vests while out on the water. A researcher believed that the percentage was different for those who rode jet skis compared to those who were in boats. Out of 400 randomly selected people who rode a jet ski, 86.5% wore life vests. Out of 250 randomly selected boaters, 92.8% wore life vests. Using a 0.10 level of significance, test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat. Let jet skiers be Population 1 and let boaters be Population 2.
Step 2 of 3:
Step 1 of 3:
State the null and alternative hypotheses for the test. Fill in the blank below.
H0Ha: p1=p2: p1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯p2H0: p1=p2Ha: p1_p2
Step 3 of 3:
Draw a conclusion and interpret the decision.
Compute the value of the test statistic. Round your answer to two decimal places.
From the test the person wants, and the sample data, we build the test hypothesis, find the test statistic, and use this to reach a conclusion.
This is a two-sample test, thus, it is needed to understand the central limit theorem and subtraction of normal variables.
Doing this:
The null hypothesis is [tex]H_0: p_1 - p_2 = 0 \rightarrow p_1 = p_2[/tex]The alternative hypothesis is [tex]H_1: p_1 - p_2 \neq 0 \rightarrow p_1 \neq p_2[/tex]The value of the test statistic is z = -2.67.The p-value of the test is 0.0076 < 0.05(standard significance level), which means that there is enough evidence to conclude that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.-------------------
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
-------------------------------------
Proportion 1: Jet-ski users
86.5% out of 400, thus:
[tex]p_1 = 0.865[/tex]
[tex]s_1 = \sqrt{\frac{0.865*0.135}{400}} = 0.0171[/tex]
Proportion 2: boaters
92.8% out of 250, so:
[tex]p_2 = 0.928[/tex]
[tex]s_2 = \sqrt{\frac{0.928*0.072}{250}} = 0.0163[/tex]
------------------------------------------------
Hypothesis:
Test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.
At the null hypothesis, it is tested that the proportions are the same, that is, the subtraction is 0. So
[tex]H_0: p_1 - p_2 = 0 \rightarrow p_1 = p_2[/tex]
At the alternative hypothesis, it is tested that the proportions are different, that is, the subtraction is different of 0. So
[tex]H_1: p_1 - p_2 \neq 0 \rightarrow p_1 \neq p_2[/tex]
------------------------------------------------------
Test statistic:
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis.
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_1 - p_2 = 0.865 - 0.928 = -0.063[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0171^2 + 0.0163^2} = 0.0236[/tex]
The value of the test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.063 - 0}{0.0236}[/tex]
[tex]z = -2.67[/tex]
The value of the test statistic is z = -2.67.
---------------------------------------------
p-value of the test and decision:
The p-value of the test is the probability that the proportion differs by at at least 0.063, which is P(|z| > 2.67), given by 2 multiplied by the p-value of z = -2.67.
Looking at the z-table, z = -2.67 has a p-value of 0.0038.
2*0.0038 = 0.0076.
The p-value of the test is 0.0076 < 0.05(standard significance level), which means that there is enough evidence to conclude that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.
A similar question is found at https://brainly.com/question/24250158
PLEASE HELP ME
An expression is shown below:
6x^2y − 3xy − 24xy^2 + 12y^2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
9514 1404 393
Answer:
(3y)(2x^2 -1x -8xy +4y)(3y)(x -4y)(2x -1)Step-by-step explanation:
Part A: All of the coefficients have a common factor of 3. All of the variable products have a common factor of y, so the greatest common factor of all terms is 3y. The expression can be written as ...
(3y)(2x^2 -1x -8xy +4y)
__
Part B: The remaining factor can be factored pairwise:
3y(x(2x -1) -4y(2x -1)) = 3y(x -4y)(2x -1)
what is the volume of the solid?
9514 1404 393
Answer:
(9√3 -3π/2) ft^3 ≈ 10.88 ft^3
Step-by-step explanation:
The area of the hexagon is given by the formula ...
A = (3/2)√3·s^2 . . . . for side length s
The area of the hexagonal face of this solid is ...
A = (3/2)√3·(2 ft)^2 = 6√3 ft^2
__
The area of the circular hole in the hexagonal face is ...
A = πr^2
The radius is half the diameter, so is r = (2 ft)/2 = 1 ft.
A = π(1 ft)^2 = π ft^2
Then the area of the "solid" part of the face of the figure is ...
A = (6√3 -π) ft^2
__
The volume is ...
V = Bh . . . . . where B is the area of the base of the prism, and h is its height
V = ((6√3 -π) ft^2)(3/2 ft) = (9√3 -3π/2) ft^3 ≈ 10.88 ft^3
Desde cierto paradero se transportan 300 pasajeros en
4 microbuses. ¿Cuántos micros se deben aumentar para
que por cada 3 micros se transporten 90 pasajeros?
Se necesitan 10 micros si queremos que cada 3 micros transporten 90 pasajeros.
En principio, sabemos que 300 pasajeros pueden transportarse en 4 microbuses.
Entonces, el numero de pasajeros que va por cada micro será el cociente entre el numero de pasajeros y el numero de micros:
N = 300/4 = 75
Queremos responder:
¿Cuántos micros se deben aumentar para que por cada 3 micros se transporten 90 pasajeros?
Definamos X como el numero de grupos de 3 micros que tendriamos en esta situación.
Entonces 300 sobre X, debe ser igual a 90 (el numero de pasajeros que va en cada grupo de 3 micros)
300/X = 90
300 = 90*X
300/90 = X = 3.33...
Notar que el número total de micros sera 3 veces X:
3*X = 3*3.33.... = 10
Se necesitan 10 micros.
Si queres leer más sobre el tema, podes ver.
https://brainly.com/question/23854869
Line L has a slope of 1/2 . The line through which of the following pair of points is perpendicular to L?
The line which crosses through L must have an intersect point with L to become perpendicular.
Gien slope is positive 1/2.
What is a straight line graph?The graph follows a straight line equation shows a straight line graph.equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the lineslope(m)=tan∅=y axis/x axis.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.
Learn more about the straight lines here:-https://brainly.com/question/14323743
#SPJ2
I need help on this 20 points
Answer:
4^15
Step-by-step explanation:
We know a^b^c = a^(b*c)
4^3^5
4^(3*5)
4^15
A gift box shown below is packed with small cubic 1/2 inch blocks. The blocks are packed tightly with no spaces between them.
A. How many blocks are in the gift box?
B. What is the volume of the gift box?
C. Find how much wrapping paper will be needed to wrap the gift box (hint: find surface area).
Step-by-step explanation:
the box is
9 in × 3.5 in × 4.5 in = 141.75 in³
each block is
0.5 in × 0.5 in × 0.5 in = 0.125 in³ (1/8 in³)
so, we can fit
141.75 / 0.125 = 1134
blocks into the box.
and they fit neatly, as the dimensions of the box and the cubes allow a tight packing without any empty left over space in the box.
please help! Here are the shopping times(in minuts) of nine shoppers at a local grocery store. complete the grouped frequency distribution for the data. in the distribution, the frequency of a class is the number of shopping times in that class.( Note that we are using a class width of 6.)
Answer:
The shopping time (in minutes) of the nine shoppers are:
15, 16, 18, 20, 22, 25, 27, 28, 29 (just to make it easier to read, I rearranged everything from least to greatest.)
We can see, that 3 shoppers shopped for 15-20 minutes.
And, 3 shoppers shopped for 21-26 minutes.
And finally, 3 shoppers shopped for 27-32 minutes.
So the answer for all 3 of the boxes is 3.
Let me know if this helps.
resolver utilizando la regla de clamer
Answer:
pordondede donde eres?
Step-by-step explanation:
........................
Help me pls ASAP I WILL GIVE BRAINLIEST
-3 = -e/75
9514 1404 393
Answer:
e = 225
Step-by-step explanation:
To eliminate the coefficient of e, multiply both sides of the equation by its reciprocal. The reciprocal of -1/75 is -75.
(-75)(-3) = (-75)(-e/75)
225 = e
Cars arrive at a toll booth according to a Poisson process with mean 90 cars per hour. Suppose the attendant makes a phone call. How long, in seconds, can the attendant's phone call last if the probability is at least 0.1 that no cars arrive during the call
Answer:
92.12 seconds
Step-by-step explanation:
According to the poisson probability relation :
P(X =x) = (e^-λ * λ^x) / x!
For no calls to be reveived during the period, x = 0
P(X = 0) = (e^-λ * λ^0) / 0!
P(X = 0) = 0.1
0.1 = (e^-λ * λ^0) / 0!
0.1 = e^-λ
Take the In of both sides
In(0.1) = - λ
-2.303 = - λ
λ = 2.303
The length of call in second, l
l = λ / r ; r = arrival rate
r = 90 per hour ; this means ;
90 / 3600 = 0.025
l = 2.303 / 0.025
l = 92.12 seconds
Three research departments have 6, 9,
and 7 members, respectively. Each
department is to select a delegate
and an alternate to represent the
department at a conference. In how
many ways can this be done?
Answer:
I don't know because I don't understand what you mean
What unit of measurement would you use to measure the capacity of a juice box?
Juice in a juice box is usually measured in ounces.
A line passes through the point (-2,4) and has a slope of 7. Write an equation for this line
Answer: y = 7x + 18
Step-by-step explanation:
y = mx + b, (-2,4), m = 7
4 = 7(-2) + b
4 = -14 + b
b = 18
y = 7x + 18
Many individuals over the age of 40 develop intolerance for milk and milk-based products. A dairy has developed a line of lactose-free products that are more tolerable to such individuals. To assess the potential market for these products, the dairy commissioned a market research study of individuals over 40 years old in its sales area. A random sample of 250 individuals showed that 86 of them suffer from milk intolerance. Based on the sample results, calculate a 90% confidence interval for the population proportion that suffers milk intolerance. Interpret this confidence interval. a) First, show that it is okay to use the 1-proportion z-interval. b) Calculate by hand a 90% confidence interval. c) Provide an interpretation of your confidence interval. d) If the level of confidence was 95% instead of 90%, would the resulting interval be narrower or wider
Answer:
a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.
b) See step by step explanation
CI 90 % = ( 0,296 ; 0,392)
c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392)
d) the CI 95 % will be wider
Step-by-step explanation:
Sample Information:
Sample size n = 250
number of people with milk intolerance x = 86
p₁ = 86 / 250 p₁ = 0.344 and q₁ = 1 - p₁ q₁ = 0,656
To calculate 90 % of Confidence Interval α = 10% α/2 = 5 %
α/2 = 0,05 z(c) from z-table is: z(c) = 1.6
Then:
CI 90 % = ( p₁ ± z(c) * SE )
SE = √ (p₁*q₁)/n = √ 0,225664/250
SE = 0,03
CI 90 % = ( 0,344 ± 1,6* 0,03 )
CI 90 % = ( 0,344 - 0,048 ; 0,344 + 0,048)
b) CI 90 % = ( 0,296 ; 0,392)
a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.
c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392) .
d) CI 95 % then significance level α = 5 % α/2 = 2.5 %
α/2 = 0,025 z(c) = 1.96 from z-table
SE = 0,03
And as 1.96 > 1.6 the CI 95 % will be wider
CI 95% = ( 0,344 ± 1.96*0,03 )
CI 95% = ( 0,344 ± 0,0588 )
CI 95% = ( 0,2852 ; 0,4028 )
9. What is m JKM? A 28° C 90° B 58.5° D 117°
Step-by-step explanation:
her it Go i think it is helpful for u
-3x > 12
What is the value of x? Use substitution to support your answer.
Answer:
x < -4
Step-by-step explanation:
-3x > 12
----- ----
-3 -3
12 ÷ -3 = -4
Which means:
x < -4
(The sign changes because the equation is divided by a negative number)
Hope this helped.
Answer:
x <-4
Step-by-step explanation:
-3x > 12
Divide each side by -3. remembering to flip the inequality
-3x/-3 > 12/-3
x <-4
What is the more formal name used for describing the corporate-finance decision concerning which projects to invest in?
Answer:
i hope it will help you
Step-by-step explanation:
Working capital management is how companies are able to manage finances and continue operations.
represent (-12)+(-8)+14 on a number line
Answer:
-6
Step-by-step explanation:
(-12)+(-8)= -20
-20+14= -6
look at the image below
On his recent free-throw attempts, Lamar made 4 shots and missed 6 shots. Considering this
data, how many of his next 20 free-throw attempts would you expect Lamar to miss?
Answer:
12 free throw attempts
Step-by-step explanation:
First, find what percent of free throw attempts he misses:
6/10
= 0.6
So, he misses 60% of the time. Multiply 20 by 0.6 to find how many you would expect Lamar to miss out of 20 attempts:
20(0.6)
= 12
So, you would expect Lamar to miss 12 free throw attempts
Mr Makgato sells his car for R42 000.00. The total commission is 7.2% of the selling price of which the broker receives 2 thirds and the salesperson receives the rest. How much does the broker receive?
Answer:
2016
Step-by-step explanation:
using USA dollars:
$42000 x .072 (7.2%) = 3024 total commission
3024 x 2/3 = 2016 brokers amount
Find the value of x.
