8/9 - 1/3
To subtract these two fractions, first find a common denominator.
The common denominator will be the
least common multiple for the two denominators.
In this case, the least common multiple of 9 and 3 is 9.
So to subtract, a denominator of 9 is needed in each fraction.
8/9 already has 9 in the denominator so it stays the same.
To get a 9 in the denominator of 1/3, multiply top and bottom by 3.
This gives us 3/9.
So we have 8/9 - 3/9 which is 5/9.
Answer:
Five-ninths
Step-by-step explanation:
Since the denominators are different (9 and 3) we need to change one of them.
9 is divisible by 3 therefor we do not need to change Eight-ninths.
3 times 3 = 9, nine becomes the new denominator, but remember, whatever we do to the bottom (denominator), we must also do to the top (numerator).
1 times 3 = 3
Now the equation is 8/9 - 3/9, we must only subtract the numerators. The answer is 5/9.
I need help with the following questions. Help would be very much appreciated! :D
Step-by-step explanation:
a) 12:40 = 3: 10
b) 40:12 = 10:3
c)
[tex]1. \: \frac{non \: fiction}{graphic \: novels} [/tex]
[tex]2. \: \frac{science \: fiction}{graphic \: novels} \: \: \: \: \: \: \: 3. \frac{science \: fiction}{non \: fiction} [/tex]
d)
Fiction books is 80.
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 9 phones from the manufacturer had a mean range of 1260 feet with a standard deviation of 24 feet. A sample of 12 similar phones from its competitor had a mean range of 1230 feet with a standard deviation of 37 feet. Do the results support the manufacturer's claim? Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed.
a. State the null and alternative hypotheses for the test.
b. Compute the value of the t test statistic. Round your answer to three decimal places.
c. Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.
d. State the test's conclusion.
Answer:
a
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex] (Manufacturers claim)
b
[tex]t = 2.114[/tex]
c
Decision rule
Reject the null hypothesis
d
There is sufficient evidence to support the claim that the calling range (in feet) of Manufacturers 900-MHz cordless telephone is greater than that of its leading competitor
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 9[/tex]
The second sample size is [tex]n_2 = 12[/tex]
The first sample mean is [tex]\= x_1 = 1260 \ feet[/tex]
The second sample mean is [tex]\= x_2 = 1230[/tex]
The first standard deviation is [tex]\sigma_1 = 24[/tex]
The second standard deviation is [tex]\sigma_2 = 37[/tex]
The significance level is [tex]\alpha = 0.10[/tex]
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex] (Manufacturers claim)
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 -2[/tex]
[tex]df = 9 + 12 - 2[/tex]
[tex]df = 19[/tex]
Generally the pooled standard deviation is mathematically represented as
[tex]\sigma_p = \sqrt{ \frac{(n_1 - 1)\sigma_1^2 + (n_2-1 )\sigma_2^2 }{ (n_1 - 1 ) + (n_2 - 1 )} }[/tex]
[tex]\sigma_p = \sqrt{ \frac{(9 - 1)24^2 + (12-1 )37^2 }{ (9 - 1 ) + (12 - 1 )} }[/tex]
[tex]\sigma_p =32.17[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x_1 - \= x_2 }{\sqrt{\frac{\sigma_p^2}{n_1 } +\frac{\sigma_p^2}{n_2 } } }[/tex]
[tex]t = \frac{1260 - 1230 }{\sqrt{\frac{32.17^2}{9 } +\frac{32.17^2}{12 } } }[/tex]
[tex]t = 2.114[/tex]
Generally the p-value is obtained from the student t distribution table and the value is
[tex]p-value = P(t > 2.11) = t_{2.11 , 19} = 0.024173[/tex]
Given that the [tex]p-value < \alpha[/tex]
The null hypothesis is rejected
Hence we can conclude that there is sufficient evidence to support the claim that the calling range (in feet) of Manufacturers 900-MHz cordless telephone is greater than that of its leading competitor
What is the solution set of the equation 2z+6z+2=3−1z
Note: z≠0,−2
Answer:
z = 1/9
Step-by-step explanation:
2z + 6z + 2 = 3 - 1z
2z + 6z + 1z = 3 - 2 (on rearranging)
9z = 1 (on solving)
z = 1/9
HOPE IT HELPS (✿^‿^)
i need help asap !!!!!!!!!!!
Answer:
3 a : YES
3 b : NO
4:
F
D
E
5:
IH
GH
IG
Step-by-step explanation:
3 a) Yes The sum of any two sides is larger than the third side
3 b). NO The sum of 3 ft + 4 ft gives 7ft which is not larger than 10 ft
4 Recall that larger angles opposite larger sides, and smaller angles oppose smaller sides in the triangle. Therefore, the smallest angle must be that opposite the 1 1/4 side that is angle [tex]\angle F[/tex] then angle d must follow (opposes side of length 2) and lastly angle E (since it opposes the largest side of length 2 1/8
5:
Notice that the third angle which is not given must verify the following:
[tex]\angle I = 180^o-59^o-61^o=60^o[/tex]
Therefore following the same concept as explained in the previous problem the order of these angles from smallest to largest must be:
IH
GH
IG
Does a point have a location?
A point in geometry is a location.
It has no size, width, length or depth. A point is shown by a dot. A line is defined as a line of points that extends infinitely in two directions.
simplify 2(3x+7)-4(7+x)
Answer:
[tex] \boxed{ \bold { \huge{ \boxed{ \sf{2x - 14}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{2(3x + 7) - 4(7 + x)}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{6x + 14 - 4(7 + x)}[/tex]
Distribute 4 through the parentheses
⇒[tex] \sf{6x + 14 - 28 - 4x}[/tex]
Collect like terms
⇒[tex] \sf{6x - 4x + 14 - 28}[/tex]
⇒[tex] \sf{2x + 14 - 28}[/tex]
Calculate
⇒[tex] \sf{2x - 14}[/tex]
Hope I helped!
Best regards!!
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2(3x + 7) - 4(7 + x)}}\\\\{\mathsf{= 2(3x) + 2(7) - 4(7) - 4(x)}}\\\\\mathsf{= 6x + 14 - 28 - 4x}\\\\\mathsf{= (6x - 4x) + (14 - 28)}\\\\\mathsf{= 2x - 14}\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{2x - 14}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the value of each of the following quantities.
(a) C(5, 4)
(b) C(5, 0)
(c) P(5, 1)
(d) P(5, 5)
Answer: (a) 5 (b)1 (c)5 (d)120
Step-by-step explanation:
Formula for combinations: [tex]C(n,r)=\dfrac{n!}{r!(n-r)!}[/tex]
Formula for permutations: [tex]C(n,r)=\dfrac{n!}{(n-r)!}[/tex]
(a) C(5, 4) = [tex]\dfrac{5!}{4!(5-4)!}=\dfrac{5\times4!}{4! (1)}=5[/tex]
(b) C(5, 0) = [tex]\dfrac{5!}{0!(5-0)!}=\dfrac{5!}{5! }=1[/tex]
(c) P(5, 1) = [tex]\dfrac{5!}{(5-1)!}=\dfrac{5\times4!}{4! }=5[/tex]
(d) P(5, 5) = [tex]\dfrac{5!}{(5-5)!}=\dfrac{5!}{1}=5!= 5\times4\times3\times2\times1=120[/tex] [as 0!=1]
Hence, the required answer is
(a) 5 (b)1 (c)5 (d)120
3 times the sum of 1/3 of
a number and 8 is 11
Answer:
I guess this is how to do it....
3×(1/3 of x + 8)=11.
use the 3 to multiply the numbers in the bracket.
3x+24=11.
3x=11-24.
3x=-13.
x= -13/3.
x= -4.33.
please help for this question. Thank you
Answer:
A. 8.3
B.18.7
C. 10.4
D. 1.04
Step-by-step explanation:
p(x) = 0.03x² + 0.56x + 6.35
A. Determination of p(3)
p(x) = 0.03x² + 0.56x + 6.35
x = 3
p(3) = 0.03(3)² + 0.56(3) + 6.35
p(3) = 0.03(9) + 1.68 + 6.35
p(3) = 0.27 + 1.68 + 6.35
p(3) = 8.3
B. Determination of p(13)
p(x) = 0.03x² + 0.56x + 6.35
x = 13
p(13) = 0.03(13)² + 0.56(13) + 6.35
p(13) = 0.03(169) + 7.28 + 6.35
p(13) = 5.07 + 7.28 + 6.35
p(13) = 18.7
C. Determination of p(13) – p(3)
From A and B above,
p(13) = 18.7
p(3) = 8.3
p(13) – p(3) = 18.7 – 8.3
p(13) – p(3) = 10.4
D. Determination of p(13) – p(3) / 13 – 3
From C above,
p(13) – p(3) = 10.4
p(13) – p(3) / 13 – 3 = 10.4/ 13 – 3
= 10.4 / 10
= 1.04
A = 1 −7 −1 2 , B = 3 7 −1 0 , C = 1 0 −1 1 Find: a) BC, b) 5A − 2C, c) A + C,
Answer:
b
Step-by-step explanation:
The price of a cup of coffee was $2.10 yesterday. Today, the price rose to $2.25. Find the percentage increase. Round your answer to the nearest tenth
of a percent.
Answer:
Easy-peasy.
Step-by-step explanation:
2.45/2.10 = 1.167 (rounded to the nearest tenth of a cent).
That is, 2.45 is 116.7% of 2.10
Since $2.10 is 100% of 2.10,
2.45 is a 16.7 increase.
The solution is 7.1 %
The percentage increase in the price of the coffee is 7.1 %
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
Let the percentage increase in the price of the coffee be represented as A
Now , the value of A is calculated by
Let the initial price of the coffee be = P
The value of P = $ 2.10
The increased price of the coffee be = Q
The value of Q = $ 2.25
Now , the equation will be
The percentage increase in the price A = ( increased price of the coffee - initial price of the coffee / initial price of the coffee ) x 100
Substituting the values in the equation , we get
The percentage increase in the price A = ( ( 2.25 - 2.10 ) / 2.10 ) x 100
The percentage increase in the price A = ( 0.15 / 2.10 ) x 100
The percentage increase in the price A = 0.0714 x 100
The percentage increase in the price A = 7.14 %
Therefore , the percentage increase is 7.1 %
Hence , the percentage increase in the price is 7.1 %
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Question 4
Given the following definitions:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4,5)
B = {1, 3, 5, 7)
How many elements are in A u B?
Answer:
A union B = { 1, 2, 3, 4, 5, 7 }
The A∪B will be {1,2,3,4,5,7}. Then the number of the terms in A∪B will be 6.
What are Sets?Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
The union of A and B is given as all the terms in A and B.
Given the following information:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4,5)
B = {1, 3, 5, 7)
Then the A∪B will be given as,
A∪B = 6{1, 2, 3, 4, 5, 7}
Thus, the A∪B will be {1,2,3,4,5,7}.
Then the number of the terms in A∪B will be 6.
More about the Sets link is given below.
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Hannah and Zach together earn $950 for an
advertising drop. They earn equal hourly rates
of pay. If Hannah worked for 10 hours and
Zach for 9 hours, how much
did Zach earn?
Answer:
$450
Step-by-step explanation:
First, write out an equation. We know that Hannah and Zach together earnes $950 and they get payed in equal hourly rates, so for now, in this step of solving the problem, we will be adding the number of hours each person worked together.
Hannah worked 10 hrs and Zach worked 9 hrs, so add 10+9 to get 19 hrs worked in all between the two of them.
Let "x" represent the amount of money made each hour, and form your equation.
Your equation would be: [tex]19x=950[/tex]
Then, just solve for "x". Divide both sides by 19.
[tex]\frac{19x}{19}=\frac{950}{19}\\x=50[/tex]
The "x=50" means that Hannah and Zach each earn $50 per hour.
Now, the question asks us to find the amount of money that Zach made. So, multiply 50 by only the number of hours Zach worked, which is 9.
[tex]50*9=450[/tex]
That means that Zach made a total of $450.
If 3s = t + 5 and se = 4, then t =
Answer:
t must be 7
Step-by-step explanation:
Replace s with 4 and solve for t in the original equation:
3 s = t + 5
3 (4) = t + 5
12 = t + 5
12 - 5 = t
7 = t
So t must be 7
The square of a number is 3 less than four times the number. Which values could be the number?
Answer:
The numbers are 1 and 3Step-by-step explanation:
Let the number be x
The statement
The square of a number is 3 less than four times the number is written as
x² = 4x - 3
Solve the quadratic equation
We have
x² - 4x + 3 = 0
Write - 4x as a difference
That's
x² - x - 3x - 3 = 0
Factorize the expression
That's
x( x - 1) - 3( x - 1) = 0
( x - 1)( x - 3) = 0
x - 1 = 0 x - 3 = 0
x = 1 x = 3
The numbers are 1 and 3
Hope this helps you
Answer:
1 and 3
Step-by-step explanation:
Find the value of x. Picture below
Answer:
x=6
Step-by-step explanation:
BD is bisecting of <B
x/3=8/4 the theorem of the bisecting
4*x=3*8
4x=24
x=24/4
x=6
what is the slope of the line?
Answer:
Step-by-step explanation:
(1,15) and (2,30)
(30-15)/(2-1)= 15/1 = 15
Find the product. (3p–2)(2p^2–p+3)
Answer:
6p^3−7p^2+11p−6
Step-by-step explanation:
1. You would want to foil it, which means multiplying one number from each parentheses to the next parentheses, like so:
3p * 2p ^ 2 = 6p^3
3p * -p = -3p
3p * 3 = 9p
-2 * 2p^2 = -4p^2
-2 * -p = 2p
-2 * 3 = - 6
2. Now add all of the numbers we foiled together, thus getting you:
6p^3−7p^2+11p−6
James works in a post office and is paid $8 per hour. Last week, he worked
32 hours and this week he worked 33.25 hours. How much should his
biweekly (every 2 weeks) paycheck be for?
Answer:
James will receive a paycheck in the amount of $522.
Step-by-step explanation:
There are 2 ways you can go at finding the answer. The first way is by adding 32 hours and 33.25 hours together to get a total of 65.25 hours. Then multiply 65.25 hours by $8 to get $522. The second way is multiplying 32 hours by $8 and get $256. Then multiply 33.25 hours by $8 to get $266. Finally add $256 and $266 up and you get $522. I hope this helps you!
For the diagram, calculate; the radius of the smaller section and the perimeter of the shape of the and;
Answer:
a). Radius r of the small sector= 12cm
b). Perimeter of the shape= 68 cm
c). Angle= 47.7°
Step-by-step explanation:
a). Radius of the big sector= 24 cm
Arc if the big sector= 20 cm
Arc of the small sector= 10 cm
For the radius r of the small sector
r/10 = 24/20
r=(10*24)/20
r= 24/2
r= 12 cm
Radius r of the small sector= 12cm
b). Perimeter of the shape
= Total length of the shape
Let's note that the other side of the sector is also the radius= 24 cm
Perimeter= 20+24+24
Perimeter of the shape= 68 cm
c) the angle
Length of arc = 2πr*(angle/360)
Let angle = b
Length of arc = 20cm
20= 2*3.14*24*(b/360)
(20*360)/(2*3.14*24)= b
47.7°= b
Angle= 47.7°
Tyrion can invest in an account earning 2.5% interest compounded monthly. If he invests $5000, ow much will he have in 7 years?
Answer:
$5925.51Step-by-step explanation:
We are going to be using the compound interest formula
Given data
principal P= $5000
N is time = 7 years
rate r= 2.5%= 0.025
compounded monthly k= 112
final amount A=?
The expression for the compound interest is
[tex]A= P(1+\frac{r}{K} )^K^N[/tex]
substituting into the expression we have
[tex]A= 5000(1+\frac{0.025}{12} )^1^2^*^7\\\\ A= 5000(1.002 )^1^2^*^7\\\\ A= 5000(1.002 )^8^7\\\\A= 5010*1.18273815853 \\\\ A= 5925.51[/tex]
in seven years he will have $5925.51
A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711 , the explained variation is 18.592 , and the unexplained variation is 2.119 . Find the coefficient of determination.
Answer:
0.898
Step-by-step explanation:
The formula for the Coefficient of determination = ratio of explained variation to Total variation
From the above question, we have the following values
Explained variation = 18.592
Total variation = 20.711
The coefficient of determination = 18.592 : 20.711
= 18.592/20.711
= 0.8976872194
Approximately ≈ 0.898
Therefore, the coefficient of determination is 0.898
PLLLSSSS HELP which one is greater a or b. ?
Answer:
The rate of change for A is 4. For B, it is 2
Step-by-step explanation:
the slope of A is 4 and for B it is 2. Slope is the same as rate of change.
Many smoke detectors contain:
A. Carbon-14
B. Americium-241
C. Strontium-90
D. Iodine
Answer:
Option B, Americium-241, is the right answer.
Step-by-step explanation:
A device which senses smoke usually as an indicator of fire is known as a smoke detector.The two most common types of smoke detectors are the Ionization chamber and photoelectric smoke indicators. Many of these smoke detectors comprise some amount of americium-241, which is a radioactive substance. These smoke detectors respond immediately to fires that give off some smoke.what is the formula for the area of a triangle?
a. a^2 + b^2 = c^2
b. A= 1/2acosB
c. A= 1/2bcsinA
d. a^2 = sin^2 + cos^2c
Answer: c. (1/2) bc sin A
Step-by-step explanation:
You can find the area of a triangle using trigonometry if you know the lengths of two sides and the measure of the included angle using the following formula:
[tex]A=\dfrac{1}{2}ab\sin C[/tex]
Answer:
[tex]\Large \boxed{\mathrm{\bold{C} }}[/tex]
Step-by-step explanation:
We can find the area of the triangle when two sides are given and the angle in between the two sides.
[tex]\displaystyle A=\mathrm{\frac{1}{2} bc \cdot sinA}[/tex]
b and c are the sides and A is the angle in between b and c.
Consider the following repeating decimal. 0.619
(a) Write the repeating decimal as a geometric series.
0.619 = _______ + n=0 summation infinity _______
(b) Write the sum of the series as the ratio of two integers
Answer:
a. 0.6[tex]\overline {19}[/tex] = [tex]0.6 + \ \sum \limits ^{\infty}_{n=0} \ 0.019 \ ( \dfrac{1}{100})^n[/tex]
b. 0.6[tex]\overline {19}[/tex] = [tex]\mathbf{\dfrac{613}{990}}[/tex]
Step-by-step explanation:
Consider the following repeating decimal. 0.6[tex]\overline {19}[/tex]
a) Write the repeating decimal as a geometric series.
0.6[tex]\overline {19}[/tex] is being expressed as 0.6191919...
0.6[tex]\overline {19}[/tex] = 0.6 + 0.019 + 0.00019+ 0.0000019 + ...
0.6[tex]\overline {19}[/tex] =[tex]0.6 + \dfrac{19}{1000}+ \dfrac{19}{100000}+ \dfrac{19}{10000000}+ ...[/tex]
0.6[tex]\overline {19}[/tex] = [tex]0.6+ \dfrac{19}{1000} \begin {bmatrix} 1 + \dfrac{1}{100} + \dfrac{1}{10000}+ ... \end {bmatrix}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]0.6 + \ \sum \limits ^{\infty}_{n=0} \ 0.019 \ ( \dfrac{1}{100})^n[/tex]
(b) Write the sum of the series as the ratio of two integers
0.6[tex]\overline {19}[/tex] = [tex]0.6 + 0.019 ( \dfrac{1}{1-0.01})[/tex]
0.6[tex]\overline {19}[/tex] =[tex]0.6 + \dfrac{19}{1000}\times \dfrac{100}{99}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]0.6 + \dfrac{19}{990}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]\dfrac{594+19}{990}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]\mathbf{\dfrac{613}{990}}[/tex]
What is 0.000345 expressed in scientific notation?
O 3.45 x 102
O 3.45 x 10
0 3.45 x 102
0 3.45 x 10 4
Answer:
The answer is D 10 to the power of -4.
Step-by-step explanation:
When the decimal point moves left, the power of becomes negative. Therefor the answer is D.
Have a good day.
If 3s = t + 5 and s
= 4, then t = ?
3s=t+5
s=4
we substitute 4 for s in the equation
3*4=t+5
12=t+5
t=12-5
t=7
Answer:
Brainliest!
Step-by-step explanation:
3s = t+5
s = 4
so...
3 (4) = t+5
12 = t+5
t = 7
Simplify (x + 3)(x − 3)
Answer:
x^2 -9
Step-by-step explanation:
(x + 3)(x − 3)
FOIL
first x*x =x^2
outer -3x
inner 3x
last -3*-3 =-9
Add together
x^2 -3x+3x -9
Combine like terms
x^2 -9
Dione has 3 rolls of pennies containing 50 coins each, 4 rolls of nickels
containing 40 coins each, 5 rolls of dimes containing 50 coins each, and 6
rolls of quarters containing 40 coins each. How much money does she have?
Answer:
$94.50
Step-by-step explanation:
3(50)=150 $1.50
4(40)=160 160(5)=800 $8.00
5(50)=250 250(10)=2500 $25.00
6(40)=240 240(25)=6000 $60.00
60+25+8+1.5=$94.50