Answer:
Richard= 16 years old
Teo= 7 years old
Step-by-step explanation:
Let Richard's and Teo's age be R and T years old respectively.
[tex]\textcolor{steelblue}{\text{Form 2 equations based on given information:}}[/tex]
R +T= 23 -----(1)
R= 2T +2 -----(2)
[tex]\textcolor{steelblue}{\text{Solving by substitution:}}[/tex]
Substitute (2) into (1):
(2T +2) +T= 23
3T +2= 23
3T= 23 -2
3T= 21
T= 21 ÷3
T= 7
Substitute T= 7 into (2):
R= 2(7) +2
R= 14 +2
R= 16
Thus, Richard is 16 years old and Teo is 7 years old.
The following table summarizes a sample of the wait times at two branches of a bank. The district manager wants to construct a two-sample t test to see if there is a significant difference between the average wait times at the two branches.
Branch A B
Mean (minutes) 4.77 5.13
Standard deviation (minutes) 1.45, 45 1.36
Number of observations 20 20
Which of the following are conditions for this type of test?
Choose all answers that apply:
A. The samples are both randomly selected.
B. The wait times within each sample are independent of each other.
C. The wait times within each group are approximately symmetric without outliers.
The conditions for this type of sampling test regarding the wait times at two branches of a bank include:
The samples are both randomly selected.The wait times within each group are approximately symmetric without outliers.What is sampling?It should be noted that sampling simply means a statistical process where a predetermined number of observations are taken from a larger population.
In this case, the samples are both randomly selected and the wait times within each group are approximately symmetric without outliers. When there's a symmetric distribution with no outliers, the mean and standard deviation will be used.
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The ratio of men to women working for a company is 4 to7. If there are 198 employees total, how many men work for the company
Answer:
Step-by-step explanation:
find the angle between vectors a =(1,2) and b = (1,-1/2). Brainliest for correct answer. Look at photo.
Answer:
90°
Step-by-step explanation:
The angle between the vectors can be found any of several ways. Here, we observe that the segments from the origin to the two points are at right angles to each other. (Their slopes are opposite reciprocals.) Hence the angle between the vectors is 90°.
__
The slope to point 'a' is y/x = 2/1 = 2.
The slope to point 'b' is y/x = (-1/2)/1 = -1/2.
The product of these slopes is (2)(-1/2) = -1, indicating the vectors are perpendicular. The angle between them is 90°.
__
We can also use the trig formula for the tangent of the difference of angles.
tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))
The tangents are the slopes, calculated above, so we have ...
tan(α -β) = (2 -(-1/2))/(1 +(2)(-1/2)) = (5/2)/0 = undefined
The tangent is undefined for angles that are odd multiples of 90°. The angle between the vectors is 90°.
Given vectors
ā=(-1,-2), b=(-2,3), C = 3,-1),d =(-3,2)
find the dot product of b and c.
3
0-3
09
0-9
Answer:
-9
Step-by-step explanation:
b={-2,3)
c=(3,-1)
dot product b.c
=(-2×3) + (3×-1)
=-6+(-3)
=-6-3
=-9
Guys please help! i will mark brainliest to the right answers
Note: in order for me to mark a brainliest 2 people need to answer
Answer: [tex]\frac{3}{2}x+y=-\frac{17}{2}[/tex]
Step-by-step explanation:
The standard form of a linear equation is [tex]ax+by=c[/tex]
So we need to solve for c
Start by simplifying everything in the equation
[tex]y+7=-\frac{3}{2} (x+1)[/tex]
Use the Distributive Property
[tex]y+7=-\frac{3}{2}x-\frac{3}{2}[/tex]
Now subtract 7 from both sides
[tex]y+7=-\frac{3}{2}x-\frac{3}{2}\\y+7-7=-\frac{3}{2}x-\frac{3}{2}-7\\y=-\frac{3}{2}x-\frac{17}{2}[/tex]
Add [tex]\frac{3}{2} x[/tex] to both sides
[tex]y+\frac{3}{2}x=-\frac{3}{2}x+\frac{3}{2}x-\frac{17}{2}\\\frac{3}{2}x+y=-\frac{17}{2}[/tex]
NOTE: [tex]-\frac{17}{2}[/tex] simplifies to -8.5 if you find that more desirable
PLEASE HELP BEFORE MIDNIGHT
Answer:
Step-by-step explanation:
Variance=0.0016
Standard deviation is the square root of variance.
sigma=sqrt(0.0016)=0.04
mean=0.9 inch
Calculating z for 0.936 inch
z = (0.936 - 0.9)/0.04
= 0.036/0.04
= 0.9
Using normal distribution table
P(x<=0.936 inch)
= P(0.9)
= 0.81594
P(x>0.936) + P(x<=0.936) = 1
P(x>0.936)
= 1 - P(x<=0.936)
= 1 - 0.81594
= 0.18406
= 0.1841
Maya sells candles to her 5 neighbors. Each neighbor buys 2 boxes of candles. There are 6 candles in each box. What is the total number of candles that all of her neighbors will get?
A.
16 candles
B.
30 candles
C.
40 candles
D.
60 candles
Answer:
D. 60 Mark brainliest<3
Step-by-step explanation:
Each neighbor buys 2 boxes which contains 6 candles meaning they in total contain 12.
5x12 = 60
please help:
A box in the shape of a right rectangular prism has a length of 8 . 58.5 inches, a width of 4 . 54.5 inches, and a height of 3 . 753.75 inches. What is the volume, in cubic inches, of the box? Do not round your answer.
Answer:
Step-by-step explanation:
Use the volume formula of a right rectangular prism!
V=whl
Just plug the values in and throw them in your calculator.
w stands for width
h stands for height
l stands for length
Hope that helps. Since it is part of a quiz, I can't give you the answer, but I believe in you!
Which symbol < > = will make the comparison true 4/6 and 4/8
Answer:
4/6 > 4/8
Step-by-step explanation:
To see if the following is true:
We can cross multiply:
[tex]\frac{4}{6}\neq \frac{4}{8}[/tex] {4* 8 = 32} {4*6=24}
Thus,
[tex]\frac{4}{6}=32[/tex]
[tex]\frac{4}{8}=24[/tex]
Hence, [tex]\frac{4}{6} > \frac{4}{8}[/tex]
We can also turn them into decimal:
[tex]\frac{4}6=0.6667[/tex]
[tex]\frac{4}{8}=0.5[/tex]
0.5 is NOT greater than 0.6667 which also means that 4/8 is NOT greater than 4/6.
~lenvy~
Answer this frequency distribution Question. I will make Brainelist + 50 points
Answer:
(i) 41-45 mins
(ii) 40 mins
(iii) 75 workers
(iv) Rs10500
Step-by-step explanation:
(i) The modal class is the class with the highest frequency.
Therefore, from inspection of the frequency table, the modal class is 41-45 mins since if has the highest frequency of 14.
(ii) As the data is grouped, to find an estimate of the mean, assume that every worker takes the value of the class mid-point. As the data is discrete, there are gaps between the classes, and so we also have to use lower and upper class boundaries to calculate the mid-points.
Class 21-25 : lower 20.5 | upper 25.5 | mid-point 23
Class 26-30 : lower 25.5 | upper 30.5 | mid-point 28
Class 31-35 : lower 30.5 | upper 35.5 | mid-point 33
Class 36-40 : lower 35.5 | upper 40.5 | mid-point 38
Class 41-45 : lower 40.5 | upper 45.5 | mid-point 43
Class 46-50 : lower 45.5 | upper 50.5 | mid-point 48
Class 51-55 : lower 50.5 | upper 55.5 | mid-point 53
Class 56-60 : lower 55.5 | upper 60.5 | mid-point 58
Mean = (sum of frequency x class mid-point) ÷ total frequency
⇒ Mean = (2 x 23 + 5 x 28 + 7 x 33 + 10 x 38 + 14 x 43 + 8 x 48 + 3 x 53 + 1 x 58) ÷ 50
⇒ Mean = 40 mins
(iii) 8 hours = 8 x 60 = 480 mins
Total time ÷ average time to make one doll = 480 ÷ 40 = 12
If the mean time to make a doll is 40 minutes, then one person can make 12 dolls in 8 hours.
Therefore, to calculate the number of workers required to make 900 dolls in 8 hours, divide the total number of dolls needed by 12:
900 ÷ 12 = 75
So 75 workers will be needed to make 900 dolls in 8 hours, given the mean time for a worker to make a doll is 40 mins.
(iv) Overtime is paid in excess of 6 hours. Therefore, each worker will be working 2 hours overtime.
Total amount of overtime pay = hours x rate x workers
= 2 x Rs70 x 75
= Rs10500
An aircraft (at Z) is spotted by two observers (at X and Y) who are L=1750 feet apart . As the airplane passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane, as indicated in the figure. If If A=30 degrees and B=20 degrees how high is the airplane?
Answer:
at aircraft(at z) sported by
As a cold front passed, the temperature dropped steadily
2 degrees each hour. It dropped a total of 10 degrees. How
many hours did it take for the temperature to drop this far?
Answer:
5
Step-by-step explanation:
because 10 divided by 2 is 5
A school band sold 432 tickets for their upcoming spring concert. This represents about 85.5% of the number of tickets sold last year. How many tickets were sold last year? (Round to the nearest whole number)
The recent price of a car is Rs.10,00,000. If its price reduces by 10% yearly, after how many years it's price will be Rs. 7,29,000? Find it.
Answer:
hope it helps
also do write the givens
Solve for y.
-3y + 7 = 34
What does y equal?
Answer:
y = -9
Step-by-step explanation:
-3y + 7 = 34
-3y = 34 - 7
-3y = 27
3y = -27
y = (-27)/3
y = -9
Are the ratios 5:4 and 20:16 equivalent?
Answer:
yes
Step-by-step explanation:
If you take 20 and divide by 4 you get 5. if you take 16 and also divide by 4, you will get 4.
Solve | x + 6| - 7 = 8
A: x= -9 and x = -21
B: x = 9 and x = -9
C: x = -9 and x = 21
D: x = 9 and x = -21
Answer:
x = 9,-21
Step-by-step explanation:
Given:
[tex]\displaystyle \large{|x+6|-7=8}[/tex]
Transport -7 to add 8:
[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]
Cancel absolute sign and add plus-minus to 15:
[tex]\displaystyle \large{x+6=\pm 15}[/tex]
Transport 6 to subtract ±15:
[tex]\displaystyle \large{x=\pm 15-6}[/tex]
Consider:
[tex]\displaystyle \large{x= 15-6}[/tex] or [tex]\displaystyle \large{x = -15-6}[/tex]
[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
Solution:
[tex]\displaystyle \large{x = 9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
__________________________________________________________
Second Method
Given:
[tex]\displaystyle \large{|x+6|-7=8}[/tex]
Transport -7 to add 8:
[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]
Absolute Function Property:
[tex]\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}[/tex]
Consider both intervals:
When x ≥ a then:
[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{x+6=15}[/tex]
Transport 6 to subtract 15:
[tex]\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}[/tex]
When x < a then:
[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}[/tex]
Transport -6 to add 15:
[tex]\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}[/tex]
Transport negative sign to 21:
[tex]\displaystyle \large{x=-21}[/tex]
Solution:
[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
__________________________________________________________
Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!
you roll two fair dice, a green one and a red one.
(a) are the outcomes on the dice independent?
(b) find p(1 on green die and 2 on red die)
(c) find p(2 on green die and 1 on red die)
(d) find p[(1 on green die and 2 on red die) or (2 on green die and 1 on red die)]
Answer:
(a) yes
(b) 1/36
(c) 1/36
(d) 1/18
Step-by-step explanation:
(a) yes they are independent as the outcome of one does not affect the outcome of the other.
(b) As the dice are fair, each possible number (1 through 6) has the same probability of being rolled.
P(1 on green die) = 1/6
P(2 on red die) = 1/6
Therefore, P(1 on green die) AND P(2 on red die) = 1/6 × 1/6 = 1/36
(c) Again, as the dice are fair, each possible number (1 through 6) has the same probability of being rolled.
P(2 on green die) = 1/6
P(1 on red die) = 1/6
Therefore, P(2 on green die) AND P(1 on red die) = 1/6 × 1/6 = 1/36
(d) p[(1 on green die and 2 on red die) OR (2 on green die and 1 on red die)
= 1/36 + 1/36
= 2/36
= 1/18
make r the subject of this formula t=2r/r-1
[tex]t= \dfrac{2r}{r-1}\\\\\implies tr-t= 2r\\\\\implies tr -2r = t\\\\\implies r(t-2) = t\\\\\implies r = \dfrac{t}{t-2}[/tex]
The formula of r is t/t-2 for equation t=2r/r-1.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is t = 2r/r-1
t equal to two times of r divided by r minus one
We need to find the formula for r
t = 2r/r-1
Apply cross multiplication
t(r-1)=2r
Apply distributive property on left side
tr-t=2r
Subtract 2r on both sides
tr-2r=t
r(t-2)=t
Divide both sides by t-2
r=t/t-2
Hence, the formula of r is t/t-2 for equation t=2r/r-1.
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this urgent pls
thank you
Answer:
x is less or equal to 30
the last Choice is correct.
Answer:
Last option D.
Step-by-step explanation:
IF it can be no more than 30, the 4th one says it can be equal to 30 or less than thirty.
Write the word sentence as an inequality.
1. A number x divided by 3 is at most 5
An inequality that represents this word sentence is ____ .
[tex]\boxed{ \dfrac{x}{3} \leq 5}[/tex]
Explanation:A number {x} {divided by} {3} is {at most} {5}.
↧ ↧ ↧ ↧ ↧
x ÷ 3 ≤ 5
[tex]\text{Inequality formed} \rightarrow \boxed{ \dfrac{x}{3} \leq 5}[/tex]
Answer:
[tex]\sf \dfrac{x}{3}\leq 5[/tex]
Step-by-step explanation:
x divided by 3 = x/3
at most 5 means "equal or less than 5" = ≤ 5
Final solution
[tex]\sf \dfrac{x}{3}\leq 5[/tex]
------------------------------------------------------------------------------------------------
Extra information
Alternative ways of writing the inequality:
x ÷ 3 ≤ 5
[tex]\sf \dfrac13x\leq 5[/tex]
1. y= x+ 12 Y= -18
2. y = x — 10 y=-12
Answer:
1) x=-30 2) x=-2
Step-by-step explanation:
1) y=x+12.
Y= -18
x+12=-18
x=-18-12
x=-30
2) y=x-10
y= -12
x-10=-12
x=-12+10
x=-2
It is a widely held belief that a typical piece of printer paper with a thickness of 0.1 mm can go through at most 7 folds. When folding a piece of paper in half, the number of layers doubles with each fold, which also doubles the thickness. Sylvia is testing this theory and employing a hydraulic press in order to ensure each fold is as tight as possible. If Sylvia is successful in folding the paper completely, determine the thickness of her piece of printer paper after being folded in half 7 times.
12.8mm
Step-by-step explanation:[tex]0.1\times2^7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left\{2^7\right.=2\times2\times2\times2\times2\times2\times2\\ =0.1\times128\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\left.\ 128\right\}\\ =12.8mm[/tex]
I hope this helps you
:)
UNDERSTAND VOLUME
When water is poured from the graduated cylinder below into a rectangular
prism, the rectangular prism is completely filled.
How many 1-cm unit cubes can be packed into the rectangular prism with no gaps
or overlaps?
Answer____ 1-cm unit cubes
Explain your answer.
Check the picture below.
liquid always take the shape of the container that contains it, so 25 cm³ from a beaker or pitcher or a curvy pipe dumped into another container, will always have 25 cm³ as its volume.
In this case it went from the cylinder to a prism, same 25 cm³.
notice in the picture, the volume of a green cube with those dimensions is just 1 cm³.
Part 014 The credit card with the transactions described in the popup below uses the average daily balance method to calculate interest. The monthly interest rate is 1.4% of the average daily balance. Calculate parts a-d using the statement in the popup Click the icon to view the credit card statement a Find the average daily balance for the billing period. Round to the nearest cent. The average daily balance for the billing period is $ (Round to the nearest cent as needed.)
The average daily balance of the transactions given for the billing period will be $1798.
How to calculate the average daily balance?From the complete question, the average daily balance is completed below:
Billing date = 2645.92 × 5 = $13229.6
Repayment on June 6 = $1345.92 × 2 = $2691.84
June 8 = $1381.85
June 9: = $1518.53 × 8 = $12148.24
Gas = $1560.90
Groceries = $1687.37 × 10 = $16873.70
Clothing = $1902.49 × 4 = $7609.96
Total = $53935.19
Therefore, the average daily balance will be:
= $53935 / 30
= $1798
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Solve the following quadratic by completing the square.
Answer:
[tex]x = -5 \pm \sqrt{26}[/tex]
Step-by-step explanation:
[tex]x^2+10x-1=0\\\\\implies x^2+2\cdot 5 x +5^2-5^2-1=0\\\\\implies (x+5)^2-25-1=0\\\\\implies (x+5)^2 -26=0\\\\\implies (x+5)^2 = 26\\\\\implies x +5 = \pm\sqrt{26}\\\\\implies x = -5 \pm \sqrt{26}[/tex]
Natalie randomly answered the last three
true-or-false questions on her math quiz.
What is the probability that she got at least
two correct?
The probability that Natalie got at least two correct on the last three
true-or-false questions is 1/4.
What is the probability that Natalie got at least two correct?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The sample space is 2. The question is either correct or wrong.
The probability that Natalie got at least two correct = 1/2 x 1/2 = 1/4
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A perfect score on a test with 25 questions is 100. Each question is worth the same number of points. How many points is each question on the test worth
Answer:
4
Step-by-step explanation:
100 divided by 25 equals 4.
Rosa invests $1100 in one account and $1300 in an account paying 3 % higher interest. At the end of one year she had earned $255 in interest. At what rates did she invest?
$1100 invested at __%
$1300 invested at __%
Answer:
$1100 at 9%$1300 at 12%Step-by-step explanation:
The amount of interest earned in one year is the product of the interest rate and the amount invested at that rate. The total interest earned is the sum of the amounts of interest earned on each investment.
Let x represent the lower interest rate. Then the higher rate is x+0.03 and the total interest earned is ...
1100x +1300(x+0.03) = 255
2400x +39 = 255 . . . simplify
2400x = 216 . . . . . . subtract 39
x = 216/2400 = 0.09 = 9% . . . . divide by the coefficient of x
Rosa invested $1100 at 9%, and $1300 at 12%.
What is the answer for B