Answer: Solution: [tex]a=\dfrac{-19}{3}[/tex] and [tex]b=\dfrac{1}{3}[/tex] .
Step-by-step explanation:
The given pair of equations:
[tex]a-8b= -9\ ...(i)\\\\ a-2b= -7\ ...(ii)[/tex]
Eliminate equation (i) from (ii) , we get
[tex]-2b-(-8b)=-7-(-9)\\\\\Rightarrow\ -2b+8b=-7+9\\\\\Rightarrow\ 6b=2\\\\\Rightarrow\ b=\dfrac{1}{3}[/tex]
Put value of b in (ii) , we get
[tex]a-2\times\dfrac{1}{3}=-7\\\\\Rightarrow\ a=-7+\dfrac{2}{3}\\\\\Rightarrow\ a=\dfrac{-21+2}{3}\\\\\Rightarrow\ a=\dfrac{-19}{3}[/tex]
Solution: [tex]a=\dfrac{-19}{3}[/tex] and [tex]b=\dfrac{1}{3}[/tex] .
On a number line if point A lies -3 and point B lies on 4, what is the length of AB
Answer:
7
Step-by-step explanation:
4-(-3)=
4+3=
7
Answer:
7
Step-by-step explanation: take the absolute value of both numbers and add them together so -3 becomes 3 and 4 stays the same they add up to 7.
A VERTICAL POLE OF CAST A SHADOW OF 4.5m LONG AT THE SAME TIME A TREE OF HEIGHT 24m LONG CAST A SHADOW OF 6m LONG. FIND THE HEIGHT OF THE POLE.
Answer:
18 metres
Step-by-step explanation:
4.5/6 = x/24
¾= x/24
x = 18 m
help me please ;))) (yes im very rich that's why I'm giving out lots of points -_- (and brainly ;))
Answer:
(I) 17.25 miles
(ii) 1hr56mins20seconds
(III) 4hrs47mins38seconds
Step-by-step explanation:
(I) read from the lowest distance given
(ii) read from the longest time given
(III) added all times together to get total cycling time
Step-by-step explanation:
here,
shortest distance is 17.25 miles
the longest time is 1:56:20 hrs:mins:secs
total time is 4:47:38
Convert 25 feet per second to miles per hour.
1 mile = 5,280 feet
1 hour = 3600 seconds
3600/5280 = 0.681818 feet per second
25 ft per second x 0.681818 = 17.045 miles per hour
Round the answer as needed.
Answer:
The correct answer is 17.045 miles per hour.
On Thursday, 40 trains left the station. Eight left late. On Saturday 50 trains left the station. Nine left late. What percentage of trains were not late on each day?
Answer:
Thursday=80%
Saturday=82 %
Step-by-step explanation:
Thursday trains not late=40-8=32
% trains not late=32/40×100=80
Saturday trains not late=50-9=41
% trains not late on Saturday=41/50×100=82
The mean amount purchased by a typical customer at Churchill's Grocery Store is $23.50 with a standard deviation of $5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions.
(a) What is the likelihood the sample mean is at least $25.00? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
(c) Within what limits will 90 percent of the sample means occur? (Round your answers to 2 decimal places.)
Answer:
a. [tex]\mathtt{P(X \geq 25) =0.0170}[/tex] ( to four decimal places)
b. [tex]P(22.5<X<25) = 0.9043[/tex] ( to four decimal places )
c. The limits will be between the interval of ( 22.33,24.67 )
Step-by-step explanation:
Given that :
mean = 23.50
standard deviation = 5.00
sample size = 50
The objective is to calculate the following:
(a) What is the likelihood the sample mean is at least $25.00?
Let X be the random variable, the probability that the sample mean is at least 25.00 is:
[tex]P(X \geq 25) = 1 - P(\dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{25- 23.50}{ \dfrac{5}{\sqrt{ 50}} })[/tex]
[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5}{ \dfrac{5}{7.07107}} })[/tex]
[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5 \times 7.071}{ {5}})[/tex]
[tex]P(X \geq 25) = 1 - P(Z< 2.1213)[/tex]
[tex]P(X \geq 25) = 1 - P(Z< 2.12)[/tex] to two decimal places
From the normal tables :
[tex]P(X \geq 25) = 1 - 0.9830[/tex]
[tex]\mathtt{P(X \geq 25) =0.0170}[/tex] ( to four decimal places)
(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00?
[tex]P(22.5<X<25) = P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{25-23.5}{\dfrac{5}{\sqrt{50}}} ) - P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{22.5-23.5}{\dfrac{5}{\sqrt{50}}} )[/tex]
[tex]P(22.5<X<25) = P(Z<\dfrac{1.5}{\dfrac{5}{7.071}} ) - P(Z<\dfrac{-1}{\dfrac{5}{7.071}} )[/tex]
[tex]P(22.5<X<25) = P(Z<2.12) - (Z<-1.41 )[/tex]
[tex]P(22.5<X<25) = (0.9830 ) - (0.0787)[/tex]
[tex]P(22.5<X<25) = 0.9043[/tex] to four decimal places
(c) Within what limits will 90 percent of the sample means occur?
At 90 % confidence interval, level of significance = 1 - 0.90 = 0.10
The critical value for the [tex]z_{\alpha/2} = 0.05[/tex] = 1.65
Standard Error = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
Standard Error = [tex]\dfrac{5}{\sqrt{50}}[/tex]
Standard Error = 0.7071
Therefore, at 90 percent of the sample means, the limits will be between the intervals of : [tex](\mu \pm z_{\alpha/2} \times S.E)[/tex]
Lower limit = ( 23.5 - (1.65×0.707) )
Lower limit = ( 23.5 - 1.16655 )
Lower limit = 22.33345
Lower limit = 22.33 (to two decimal places).
Upper Limit = ( 23.5 + (1.65*0.707) )
Upper Limit = ( 23.5 + 1.16655 )
Upper Limit = 24.66655
Upper Limit = 24.67
The limits will be between the interval of ( 22.33,24.67 )
PLEASE help me solve this question! No nonsense answers please!
Answer:
10x -24 ft^2
Step-by-step explanation:
The area of the square is x^2
The area of the flower garden is lw
( x-4) ( x-6)
x^2 -6x-4x +24
x^2 -10x +24
Subtract the flower garden from the square to find the area of the patio
x^2 - ( x^2 -10x +24)
Distribute the minus sign
x^2 -x^2 +10x -24
10x -24
Answer:
c. 10x -24 sq. ft
Step-by-step explanation:
area of lot = x * x
area of garden = (x-4)(x-6) = x^2-10x+24
Area of patio
= area of lot - area of patio
= x^2 -(x^2-10x+24)
= 10x-24 sq.ft
8(4k - 4) = -5k - 32
Answer:
k=0
Step-by-step explanation:
8(4k-4)=5k-32
32k-32=-5k-32
32k-32+32=-5k-32+32
32k=-5k
32k+5k=-5k+5k
37k=0
37k/37=0/37
k=0
Answer:
k=0
Step-by-step explanation:
To solve for k, we need to first distribute the 8 through the parenthesis.
32k-32=-5k-32
Lets add 5k to both sides.
37k-32=-32
add 32 to both sides
37k=0
divide 37 from both sides
k=0
I need help with five math questions please help
Answer:
-5X+2Y-2
Step-by-step explanation:
-5X-7-2+2Y+7
-5X-2+2Y
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Fachorise completely
x^2y^2-1
Answer:
[tex](xy+1)(xy-1)[/tex]
Step-by-step explanation:
x²y²-1
=(xy)²-(1)²
=(xy+1)(xy-1)
What are all the numbers of Pi? I need this now please
Thank you!! ♥︎
Answer:
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 ...
Step-by-step explanation:
If two angles are complements of each other then each angle is
Answer:
each angle is less than 90 degrees. angle 1+angle2=90 degrees
Step-by-step explanation:
Which polynomial is a factor of both expressions? x – 8 x + 7 x – 2 (x – 2)2
Answer:
C. x-2
Step-by-step explanation:
edge
Answer: the 3rd the answer c
x-2
Step-by-step explanation:
how many are 9 raised to 3 ???
Answer:
[tex]\huge \boxed{729}[/tex]
Step-by-step explanation:
9 raised to 3 is the base 9 with an exponent of 3.
[tex]9^3[/tex]
9 is being multiplied by itself 3 times.
[tex]9^3 =9 \times 9 \times 9 = 729[/tex]
Solve the equation for x. the square root of the quantity x plus 4 end quantity minus 7 equals 1
Answer:
x = 60Step-by-step explanation:
I hope it helps :)
[tex]\sqrt{x+4} -7=1\\\mathrm{Add\:}7\mathrm{\:to\:both\:sides}\\\sqrt{x+4}-7+7=1+7\\\sqrt{x+4}=8\\\mathrm{Square\:both\:sides}\\\left(\sqrt{x+4}\right)^2=8^2\\x+4=64\\x = 64-4\\x = 60[/tex]
There are 4 colas, 1 ginger, 7 root beers, and 6 cherry sodas in a cooler. What are the odds of choosing a ginger ale? Give your answer in a proportion in lower terms.
Answer:
Step-by-step explanation:
the odds of choosing a ginger ale is 1/21
Samuel has $20 in his savings account before he makes a deposit of $160 after two weeks he withdraws $160 how did Samuel savings account balance change
The table below shows the number of cars Jing sold each month last year.
What is the median of the data in the table.
13
16
19
20.5
23.5
Other:
Answer:
The median of the data in the table is 19.
Step-by-step explanation:
We are given the following data that shows the number of cars Jing sold each month last year below;
Number of cars Jing sold: 13, 16, 19, 20.5, 23.5
For calculating the median, firstly we have to observe that the number of observations (n) in our data is even or odd because;
If n is odd, then the formula for calculating median is given by;Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]
If n is even, then the formula for calculating median is given by;Median = [tex]\frac{(\frac{n}{2} )^{th} \text{ obs.} + (\frac{n}{2}+1 )^{th} \text{ obs.} }{2}[/tex]
Here, the number of observations in our data is odd, i.e. n = 5.
So, Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{5+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{6}{2} )^{th} \text{ obs.}[/tex]
= 3rd obs. = 19
Hence, the median of the data in the table is 19.
Please solve these questions on the topic of exponents
Answer/Step-by-step explanation:
Recall: [tex] x^{-a} = \frac{1}{x^a} [/tex]
a. [tex] 4^{-3} = \frac{1}{4^3} = \frac{1}{64} [/tex]
b. [tex] 13^{-2} = \frac{1}{13^2} = \frac{1}{169} [/tex]
c. [tex] (-3)^{-2} = \frac{1}{-3^2} = \frac{1}{9} [/tex]
how many terms are there in the expressions 1 + 2k - j
Answer:
3 terms
Step-by-step explanation:
A term in mathematics, especially in Algebra, could be a number, a variable, variable together with a number or variables multiplied together as a single whole. Terms are usually separated with either negative or positive sign in an expression.
In the expression, [tex] 1 + 2k - j [/tex] , there are 3 terms here spared by either the negative sign or the positive.
The 3 terms are: [tex] 1, 2k, j [/tex].
PLEASE ANSWER QUICKLY ASAP
COMPLETE QUESTION B
Answer:
Sector
Step-by-step explanation:
A sector of a circle is the portion of circle enclosed by two radii and arc
the first four terms of the sequence an=2n+3are
answer
5,8,11,14
3,5,7,9
1,3,5,7
5,7,9,11
Step-by-step explanation:
Hey, there!!!
Your required answer is optionD.
checking,
The 1st sequences are,
5,8,11,14
here,
now, use formula,
(an = 2n+3) in the sequences,
a1 = 2×1+3=5 = matching
a2= 2×2+3=7 = not matched
a3= 2×3+3= 9 = not matched
a4= 2×4+3=11 = not matched.
For 2nd sequences
3,5,7,9
Use the formula of an term,
a1 = 2×1+3=5 = not matched
a2 =2×2+3=7not matched
a3 = 2×3+3=9= not matched.
For 3rd sequences,
1,3,5,7
a1=2×1+3=5= not matched
a2=2×2+3=7= not matched
a3=2×3+3=9= not matched
a4=2×4+3=11= not matched
Now, for 4th sequences,
5,79,11
a1=2×1+3=5= matching
a2=2×2+3=7= matching
a3= 2×3+3=9= matching
a4=2×4+4=11= matching
Therefore, the answer is option D.
Hope it helps..
A student uses his place value chart to show number after the teacher instructed him to divide a number by 100 the charge of 28.003 what was the chart look like first
Step-by-step explanation:
A student divided the given number by 100 that resulted to 28.003 in his chart. So what we are looking for in the given situation is that the value of the number before it was divided by 100.
To get the desired value, we can simply multiply the obtained result by 100
=> 28.003 x 100
=> 2800.3
So, by dividing 100 to the given number, we simply move the value to the right in a value of hundreds.
Find the term of each sequence.
32, 80, 200, ...5th term
Answer:
t5 = 1250
Step-by-step explanation:
Each term is derived by multiplying the previous term by 2.5
t2 = t1 * 2.5
t2 = 32 * 2.5
t2 = 80
===========
tn = a*b^(n - 1)
t3 = 32*2.5^2
t3 = 200
That's just to test the formula. It does work.
===============
t5 = 32*2.5^(5 -1)
t5 = 32*2.5^4
t5 = 1250
A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint. If a can of paint contains 75 ounces of white paint, how many ounces of blue paint are in the can?
Answer:
60 ounces.
Step-by-step explanation:
Given:
A mixture contains 5 parts of white paint for every 4 parts of blue paint.
i.e. Ratio of white paint : blue paint = 5 : 4
Quantity of White paint = 75 ounces
To find:
How many ounces of blue paint = ?
Solution:
Here, we are given the ratio of white and blue paint in the mixture.
Also, we are given the quantity of white paint in the paint can.
And we have to find the quantity of other paint in the can.
Let us use all the given statements to find the unknown quantity of blue paint.
Ratio of white paint : blue paint= Ratio of quantity of white paint: blue paint
[tex]\dfrac{5}{4} = \dfrac{75}{\text{Quantity of blue paint}}\\\Rightarrow \text{Quantity of blue paint} = 15 \times 4\\\Rightarrow \text{Quantity of blue paint} = 60\ ounces[/tex]
So, the quantity of blue paint in the can is 60 ounces.
1 1/3 minus 5/6 please help me out
Answer:
17/6
So this is the answer. If you want to convert to decimal... The answer will be 2.83..hope it is right
We can calculate E, the amount of euros that has the same value as D U.S. dollars, using the equation e=17/20d. How many U.S. dollars have the same value as 1 euro?
Answer:
1.18 dollar.
Step-by-step explanation:
E = 17/20D
E => The amount in euros.
D => The amount in dollars.
From the question given,
E = 1
D =?
E = 17/20D
1 = 17/20D
Cross multiply
20 x 1 = 17D
20 = 17D
Divide both side by 17
D = 20/17
D = 1.18
Therefore, 1.18 dollar is equivalent to 1 euro.
Answer:
How many Euros have the same value as 1 U.S. dollar?
17/20 euros
How many U.S. dollars have the same value as 1 euro?
59/50 dollars
(or 0.85 either one is correct)
Step-by-step explanation:
Khan Academy
Hope this helps! ;)
What is the distance between the points (5,1) and (-3,-5)?
Answer
[tex] \boxed{10 \: \: units}[/tex]
Step by step explanation
Let the points be A and B
A ( 5 , 1 ) ⇒ ( x₁ , y₁ )
B ( -3 , -5 )⇒ ( x₂ , y₂ )
Now, let's find the distance between theses two points:
Distance = [tex] \mathsf{ \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }[/tex]
Plug the values
[tex] \mathsf{ \sqrt{ {( - 3 - 5)}^{2} + {( - 5 - 1)}^{2} } }[/tex]
Calculate
[tex] \mathsf{ \sqrt{ { ( - 8)}^{2} + {( - 6)}^{2} } }[/tex]
Evaluate the power
[tex] \mathsf{ \sqrt{64 + 36} }[/tex]
Add the numbers
[tex] \mathsf{ \sqrt{100} }[/tex]
Write the number in exponential form with a base of 10
[tex] \mathsf {\sqrt{ {10}^{2} } }[/tex]
Reduce the index of the radical and exponent with 2
[tex] \mathsf{10 \: units}[/tex]
-------------------------------------------------------------------------------
The distance formula is used to determine the distance ( d ) between two points. If the co-ordinates of the two points are ( x₁ , y₁) and ( x₂ , y₂ ) , the distance equals the square root of x₂ - x₁ squared + y₂ - y₁ squared.
Hope I helped!
Best regards!
Can someone please help!! ****This problem is multiple choice!
Answer:
I believe it's A) 302.94
Step-by-step explanation:
There are 360 degrees in a circle. So I enetered 360/112 in a calculator and got 3.214.
Then I multiplied 3.214 by 30pi and got 302.939 AKA 302.94. I did this because I looked at it like a ratio problem but idk if thats correct.
At the end of the day, a bakery gives everything that is unsold to food banks for the needy. If it has 12 apple pies left at the end of a given day, in how many different ways can it distribute these pies among 6 food banks for the needy?
Answer:
462 ways
Step-by-step explanation:
The formula to use in solving this problem is given as the Combination formula
The Combination formula is given as
C(n , r) = nCr = n!/r! (n - r)!
We are told that a food bakery has 12 pies unsold at the end of the day which they intend to share to 6 food banks
n = 12, r = 6
In order to ensure that at least 1 food bank gets 1 pie, we have:
n - 1 = 12 - 1 = 11
r - 1 = 6 - 1 = 5
Hence,
C(11, 5) = 11C5
= 11!/ 5! ×(11 - 5)!
= 11!/5! × 6!
= (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/ (5 × 4 × 3 × 2 × 1) ×( 6 × 5 × 4 × 3 × 2 × 1)
= 462 ways
