Answer:
x= 2, y= 2, and z= 6
Step-by-step explanation:
If this is a Diophantine equation, add 35 to both sides and factor the left:
(3x+1)(2y+7)(z+5) = 847 = 7 times 112
Each integer factorization of 847 into 3 factors leads to a different number/value of x, y, and z. If the first factor, (3x+1), is 1 more than a multiple of 3, and the second factor, (2y+7), is odd, then x, y, and z will be integers.
For example:
847 = 121 times -7 times -1 gives (x, y, z) = (40, -7, -6) because 121 times -7 times -1 is 847 as well, it checks out.
If x, y, and z need to be positive, then the three numbers/factors need to be greater than 1, 7, and 5. The only combination that works is 7 times 11 times 11, which gives (x, y, z) = (2, 2, 6).
:)
Consider a graph of the equation y = −3x + 4. What is the y-intercept? Answers: −3, 3, 4, −4
Answer:
When finding the y-intercept it indicates that the x-coordinate will be zero.
So,when letting x=0 you will get
y=-3(0)+4
Hence,
y=4
Step-by-step explanation:
m∠C= step by step thank you so much
Answer:
please mark my answer brainliest
Step-by-step explanation:
in tri ABD and bcd...
AD =DC ...given
AB =BC.....given
BD =BD.....common
therefore...both tri are congruent...by SSS CRITERION
therefore angle adb...and angle bdc are equal...cpct...
therefore angle bdc =32°
angle dbc =90°
therefore angle bcd =angle C=180- (90 +32) =58°
angle C=58°....answer
The following table shows scores obtained in an examination by B.Ed JHS Specialism students. Use the information to answer the questions that follow: Score 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 Frequency 10 4 10 20 30 15 3 2 1 5.a. Construct a cumulative frequency curve for the data. b. Find the; i. inter-quartile range. ii. 70th percentile class scores. iii. probability that a student scored at most 50 on the examination
Answer:
(a) The cumulative frequency curve for the data is attached below.
(b) (i) The inter-quartile range is 10.08.
(b) (ii) The 70th percentile class scores is 0.
(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.
Step-by-step explanation:
(a)
To make a cumulative frequency curve for the data first convert the class interval into continuous.
The cumulative frequencies are computed by summing the previous frequencies.
The cumulative frequency curve for the data is attached below.
(b)
(i)
The inter-quartile range is the difference between the third and the first quartile.
Compute the values of Q₁ and Q₃ as follows:
Q₁ is at the position:
[tex]\frac{\sum f}{4}=\frac{100}{4}=25[/tex]
The class interval is: 34.5 - 39.5.
The formula of first quartile is:
[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
Here,
l = lower limit of the class consisting value 25 = 34.5
(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 24
f = frequency of the class interval = 20
h = width = 39.5 - 34.5 = 5
Then the value of first quartile is:
[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
[tex]=34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75[/tex]
The value of first quartile is 34.75.
Q₃ is at the position:
[tex]\frac{3\sum f}{4}=\frac{3\times100}{4}=75[/tex]
The class interval is: 44.5 - 49.5.
The formula of third quartile is:
[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
Here,
l = lower limit of the class consisting value 75 = 44.5
(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 74
f = frequency of the class interval = 15
h = width = 49.5 - 44.5 = 5
Then the value of third quartile is:
[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
[tex]=44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83[/tex]
The value of third quartile is 44.83.
Then the inter-quartile range is:
[tex]IQR = Q_{3}-Q_{1}[/tex]
[tex]=44.83-34.75\\=10.08[/tex]
Thus, the inter-quartile range is 10.08.
(ii)
The maximum upper limit of the class intervals is 69.5.
That is the maximum percentile class score is 69.5th percentile.
So, the 70th percentile class scores is 0.
(iii)
Compute the probability that a student scored at most 50 on the examination as follows:
[tex]P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}[/tex]
[tex]=\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89[/tex]
Thus, the probability that a student scored at most 50 on the examination is 0.89.
Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the 0.05 significance level, test the claim that the sample of 100 subjects has a distribution that agrees with the distribution of state populations.
Answer:
Step-by-step explanation:
H₀ : The distribution of the sample agrees with the population distribution.
H₁ : the distribution of the does not agree with the population distribution.
Using the Chi-square test statistics
we will compute the expected frequencies
Now expected frequency for Washington will be
Fe = Npi = 1000×51% = 5100
expected frequency for Oregon
Fe = Npi = 1000×30% = 300
expected frequency for Idaho
Fe = Npi = 1000×11% = 110
expected frequency for Montana
Fe = Npi = 1000×8% = 80
The Chi=square test statistics is;
x² = ∑ [ (Fo - Fe)² / Fe )
now we substitute
Given our Fo ( 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana) from the question
x² = (450-510)²/510 + (340-300)²/300 + (150-110)²/110 + (60-80)²/80
x²= 31.9376
so the chi-square test statistics is 31.9376
Now the chi-square critical value
first we compute for degree of freedom
d.f = k -1 = 4 - 1 = 3
So from the critical value table, degree of freedom 3 and significance level 0.05,
the chi-square critical value is 7.8147
Therefore chi-square test statistics 31.9376 is greater than the chi-square critical value 7.8147, so NULL HYPOTHESIS IS REJECTED at 5% significance.
There is sufficient evidence to warrant rejection of the claim that the distribution of the sample agrees with the distribution of the state populations.
A card is randomly selected from a standard
deck of playing cards. Find the probability
that it is a face card, given that a black card
is drawn.
Answer:
3 / 13
Step-by-step explanation:
Hello!
There are 52 cards in a deck with half being red and half being black. The question ask for when a black card is drawn so we divide the total by 2
52/ 2 = 26
There are 6 black face cards in a deck so to get the probability one will be drawn we put how many there are over the total amount
6/26 we can simplify this
3 / 13
The answer is 3 / 13
Hope this helps!
Answer:
3/13
Step-by-step explanation:
In a standard 52-card deck, there are 26 black cards and 26 red cards. Of the 26 black cards, 13 are spades and 13 are clubs. Each suit has 3 face cards, Jack, Queen, and King. Therefore, there are 6 black face cards out of a total of 26 black cards.
p(face given black) = 6/26 = 3/13
Darren picked 25 flowers that he plans to divide evenly into 3 vases. He will use as many flowers per vase as he can, but may have flowers left
Answer:
He will use flowers per vasebut will have one leftStep-by-step explanation:
In this problem we are required to place flowers evenly across 3 flower vases.
Given that we have 25 flower to collect from and distribute evenly.
we are going to divide 25 by 3
We have
[tex]= \frac{25}{3}\\\\ =8\frac{1}{3}[/tex]
From the result in the improper fraction we can see the Darren can place 8 flowers evenly of the 25 flowers and there will be just one left over
Your anula salary of $42,500 is about to he increased by 2%.Explain the steps you would take to determine your new salary.What will your new salary be?
Answer:
$43,350
Step-by-step explanation:
To find the increase in the salary we need to find the percentage.
2 percent of $42,500 = $850.
$42,500 + $850 = $43,350.
New salary = $43,350.
t takes one person 2 hours to grade 1 exam and it takes another 4 hours to grade 1 exam. If both work together, how many exams they can grades in 8 hours
Answer:
4
Step-by-step explanation:
2×4 equals 8 4 papers in 8 hours
What is another name for AC
Answer:
air conditioning or air cooling or climate control
hope this helps :)
A box contains 9 red and 2 blue marbles. If you select one marble at random from the box, determine the odds against selecting a blue marble.
Answer:
2/11 or approx. 18%
Step-by-step explanation:
There are 2 blue marbles out of 11 total marbles, so the probability will be 2/11.
2/11 = 0.18, or 18%
So, the odds are 2/11 or approx. 18%
Answer:
9:2
Step-by-step explanation:
9 red and 2 blue
ways that an outcome cannot occur : how many ways it can occur
9 : 2 are the odds against a blue marble
DUE TONIGHT !! determine whether the statement is true or false. justify your answer. A line with a slope of -5/7 is steeper than a line with a slope of -6/7
False.
Slope is the "rise over run" (y/x) in a linear equation. Because the denominators are the same in both fractions, it means you can just focus on the numerator with the larger number as that one will be the steeper line.
Round to the nearest thousand.
64,473
64,473 rounded to the nearest thousand is ?
Answer:
64000
Step-by-step explanation:
Answer:
64000
Step-by-step explanation:
The stem-and-leaf plot shows the number of words in the classified ads in a newspaper one day.
How many ads had at least 20, but fewer than 45, words?
1 0 3 3 5 7 9
2 0 0 1 4 5
3 3 8 8
4 7
5 2
key:1|0 = 10
A. 6
B. 3
C. 10
D. 8
Answer:
D. 8
Step-by-step explanation:
We can see the numbers from 20 (inclusive) to 45 on the plot:
20, 20, 21, 24, 25, 33, 38, 38In total 8 adsCorrect answer choice is: D. 8
PLEASE HELP!!!! I will award brainliest!! Look at the figure shown below. A student made the table shown below to prove that PQ is equal to RQ. 1. Provide the missing statement and justification in the proof. 2. Using complete sentences, explain why the proof would not work without the missing step.
Answer:
See below.
Step-by-step explanation:
1.
Statement 8. triangle SQR is congruent to triangle TQP
Reason 8. ASA
2.
The only way to prove those two sides are congruent is to first prove that the triangles that contain those sides are congruent. Then you can use CPCTC to prove those sides congruent.
As the sample size for a t-distribution increases, the differences between the t-distribution and the standard normal distribution ______.
Answer:
The differences become smaller
Step-by-step explanation:
Normally, we use the t-distribution table rather than the normal distribution when the population standard deviation is unknown and when the sample size is small i.e. less than 30.
Now, as the sample size gets bigger, we will be getting closer to the point where we have to use the normal distribution.
This means that as the sample size increases, the values of the t-distribution will be getting close to that of the normal distribution because normal distribution is used when sample is more than 30.
For example the t-value for a sample of 25 people would be closer to the normal distribution value for a sample of 35 people while a t-value for a sample of 15 people will be far away from the normal distribution value for a sample of 35 people.
Thus, as the sample size increases, the differences between the t-distribution and standard normal distribution becomes smaller.
please help!!!!
what is the least common denominator of 1/6, 10/11, 5/12?
===================================================
Work Shown:
LCM = least common denominator
List out the prime factorization of each denominator
6 = 2*311 = 1*1112 = 2*2*3So we have the list of primes 2,3, and 11 that help form the denominators when we multiply some of them together.
The prime 2 shows up at most twice, so 2*2 = 4 is a factor of the LCM
The prime 3 shows up at most one time, meaning 3 is also a factor
The prime 11 shows up at most one time, so 11 is another factor
Multiply these factors to get 4*3*11 = 12*11 = 132
The LCM is 132
---------------------
Another Approach:
Focus on 1/6 and 10/11 for now. The LCM is 66 because 6*11 = 66. We simply multiply the denominators together. Then we divide over the GCF 1 to get 66/1 = 66.
The LCM of 1/6 and 10/11 is 66
The fractions 1/6 and 10/11 are equivalent to 11/66 and 60/66 respectively
The original list of fractions updates to 11/66, 60/66, 5/12
We've gone from 3 different denominators to now 2 different denominators.
Repeat the steps of multiplying the denominators and dividing by the GCF
66*12 = 792
792/(gcf of 66 and 12) = 792/6 = 132
So the LCM of all the fractions is 132.
Find the equation of the line that contains the points (4,2) and (6,10). Write the equation in the form y=mx+b and identify m and b.
(5)
(5) = 3, then (10) =???
,
3
Step-by-step explanation:
If (5) = 3
Then (10) = 6
Because 5 x 2 = 10 so 3 x 2 = 6
△ABC = △DBC, AB= 10, AC=7 DC= ?
Answer:DC=7
Step-by-step explanation:
As it is written △ABC = △DBC. So the corresonding legs (the legs which are equal ) are as follows:
AC=DC AB=DB BC= BC
So DC=7 the same like AC
Plz HELP ASAP (algebra)
Answer:16
Step-by-step explanation:
Given: 15% of 60 is 9.
so 9 kids are 15 year old.
and 1 other kid is 16 year old.
Thus, there are total of (15+1) kids that are either 15 or 16 year old. you can also draw venn diagram to find that.
A norman window has the shape of a square with a semicircle mounted on it. Find the width of the window if the total area of the square and the semicircle is to be 190 ft squared?
Answer:
11.68ft or 11.68 feet
Step-by-step explanation:
From the above question, we are told that:
Area of the square and the Area semicircle is to be 190 ft squared.
We are also told in the question that:
The window has the shape of a square with a semicircle mounted on it.
Hence, the Diameter of the semicircle = Width of the Square
Let the Width of the square = x
Area of a square = Width²
= x²
Let the Diameter of the semi circle = x
Radius of the semi circle = Diameter of the semi circle/2 = x/2
Area of a semicircle = πr²/2
Area of a the semi Circle = π ×(x/2)² /2
= (πx²/4)/2
= πx²/8
Therefore,
Area of a square + Area of a semicircle = 190ft²
= x² + πx²/8 = 190
Cross Multiply
x² + πx² = 190
= x² ( 1 + π/8) = 190
x² = (190)/(1 + π/8)
x² = 136.42573798
x = √136.42573798
x = 11.680142892ft
Approximately x ≈ 11.68ft
Therefore, the width of the window = 11.68ft
Given: 2x + 3y= 6.
What is the y-intercept?
(0,3)
(2,0)
(0,2)
no intercept
a=3i+4j, b=5i+4j. find a+b
Answer:
8i+8j
Step-by-step explanation:
3i+4j+5i+4j
i(3+5) + j(4+4)
Therefore 8i +8j
HAPPY TO HELP YOU
Answer:
Step-by-step explanation:
we have :
a=3i+4j
b=5i+4i
so that : a+b=3i+4j+5i+4j
=(3i+5i)+(4j+4j)
so a+b=8i+8j=8(i+j)
Find the slope of the line graphed below?
Answer:
7/5
Step-by-step explanation:
rise over run
start at the bottom point and count up along y axis and then count over along x axis
factorise : 64a cube minus 27b cube minus 144a square b plus 108ab square .
Plz Answer this question
Answer:
[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]
Step-by-step explanation:
The question is not properly formatted, here is a good format for proper understanding and readability
[tex]64a^3-27b^3-144a^2+108ab^2[/tex]
let us first collect/ group like terms
[tex]64a^3-144a^2+108ab^2-27b^3[/tex]
we can now bring out the common factors we have
[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]
The simplified expression is
[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]
Please help. I’ll mark you as brainliest if correct
Answer: He doesn't have any money left that period point blank
Step-by-step explanation
7-6=1
1-3= you cant do that
so he doesn't get soda at all.
7 -6 =1. . . . . . . - . . . . . . = . 1-3= nope. - . . . = nahhh
Picture 1
Soap, Face, cream, Fragrance mist
Common
What’s the answer please
Answer:
C. [tex] \sqrt {149} [/tex]
Step-by-step explanation:
Coordinates of the endpoints of the segment are (4, 4) & (-6, - 3)
By distance formula
Length of segment
[tex] = \sqrt {(4+3)^2 +(4+6)^2} [/tex]
[tex] = \sqrt {(7)^2 +(10)^2} [/tex]
[tex] = \sqrt {49 +100} [/tex]
[tex] = \sqrt {149} [/tex]
What is the equation of the line: * parallel to the line y = -¼x + 5 and * passing through the point (2, -1) y = -¼x + 4 y = ¼x + 2 y = ¼x - 1 y = -¼x - 1/2
Answer:
y=-1/4x-1/2
Step-by-step explanation:
When two lines are parallel, they have the same slope.
So for this line, we already know that the slope (m) has to equal -1/4x.
Slope intercept form is y=mx+b, where m is the slope and b is the y intercept.
in order to find the equation, we must plug in x and y to solve for b, the y intercept (the value of y when x=0).
Now, let's plug in 2 for x and -1 for y and solve for b:
-1=-1/4(2)+b=-1=-1/2+b=-1+1/2=b
b=-1/2
Hence, the answer is y=-1/4x-1/2
Answer:
The answer is -1/4x - 1/2
Step-by-step explanation:
Just took the Unit Session
Which fraction is equal to k in the equation below?
1\3 / 2= k
Answer:
0_10 =0_2
Step-by-step explanation:
Convert the following to base 2:
0_10
Hint: | Starting with zero, raise 2 to increasingly larger integer powers until the result exceeds 0.
Determine the powers of 2 that will be used as the places of the digits in the base-2 representation of 0:
Power | \!\(\*SuperscriptBox[\(Base\), \(Power\)]\) | Place value
0 | 2^0 | 1
Hint: | The powers of 2 (in ascending order) are associated with the places from right to left.
Label each place of the base-2 representation of 0 with the appropriate power of 2:
Place | | | 2^0 |
| | | ↓ |
0_10 | = | ( | __ | )_(_2)
Hint: | Divide 0 by 2 and find the remainder. The remainder is the first digit.
Determine the value of 0 in base 2:
0/2=0 with remainder 0
Place | | | 2^0 |
| | | ↓ |
0_10 | = | ( | 0 | )_(_2)
Hint: | Express 0_10 in base 2.
The number 0_10 is equivalent to 0_2 in base 2.
Answer: 0_10 =0_2