is
In 5-8, apply Laws of Exponents to write
expressions.
5, efo
e²f
7.3j4k-2.7j5k9
uiva
-3
6. (2x)-3. (y)-³
8. aº.b6.b-3
Answers
By using the concept of law of exponents,the required answers are: 5) [tex]e^{-1} f^{-1}[/tex] and 8) [tex]b^{3}[/tex]
What is the law of exponents?According to this law of exponents, exponents of numbers are added, subtracted, multiplied, and divided when numbers get multiply, divide, and number raised by another exponents.
What are exponents?Exponents are the power of numbers, which tells us how many time a number multiply by itself.
we have,
5) [tex]\frac{ef^0}{e^2f}[/tex]
⇒ [tex]e^{1-2}f^{0-1}[/tex]
⇒ [tex]e^{-1} f^{-1}[/tex]
8) [tex]a^{0}b^{6} b^{-3}[/tex] ( [tex]a^{0}[/tex]=1 )
⇒ [tex]b^{6-3}[/tex]
⇒ [tex]b^{3}[/tex]
Hence, final answer are [tex]e^{-1} f^{-1}[/tex] and [tex]b^{3}[/tex]
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Related Questions
Josie makes fruit punch by mixing fruit juice and lemonade in the ratio
She needs to make 35 litres of punch for a party.
How much of each ingredient does she need?
Fruit juice
7 litres
Lemonade =
28 litres
During the party Josie decides to make some more.
She has 3 litres of fruit juice left and plenty of lemonade.
How much xtra punch can she make?
litres
To make the second batch of punch go further Josie
adds 2 more litres of lemonade.
What is the ratio of fruit juice to
lemonade in the second batch?
Answers
Let the lemonade and fruit be Mixed in x ratio.
[tex]\therefore[/tex] Total mixture of fruit punch [tex]= 1\times x \ + \ 3\times x = 4x[/tex]
She needs to make 35 liters of punch.
Requirement of ingredients :
Fruit juice to be added [tex]= \frac{x}{4x} \times 35 = 8.75[/tex] liters of fruit juice
If 8.75 liters of fruit juice is to be added,
then,
lemonade required[tex]=35\ litres - 8.75\ litres = 26.25\ litres .[/tex]
Now ,
According to question she wants to make more fruit punch,
so , given that she had 2 liters of fruit juice.
Here ,
⇒x become 2.
⇒Lemonade required =[tex]2\times x[/tex]
⇒Lemonade required = [tex]2\times3 = 6\ liters[/tex]
There total fruit punch = [tex]6 + 3=9\ liters[/tex]
[tex]\therefore\\[/tex] ratio of fruit juice to lemonade in the second batch = 6:9 = 2:3.
What is ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
What is Proportion?
A proportion is an equation in which two ratios are set equal to each other.
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Please help!! 10 points
Answers
Answer:
y = - 2x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, - 4) ← 2 points on the line
m = [tex]\frac{-4-2}{4-1}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = - 2x + 4 ← equation of line
Given that
7
x
−
3
y
=
23
Find
x
when
y
=
−
2
Answers
Answer: [tex]\frac{17}{7}[/tex]
Step-by-step explanation:
7x - 3y = 23
3y = -2 × 3 = -6
7x + 6 = 23
7x = 23 - 6
7x = 17
x = [tex]\frac{17}{7}[/tex]
convert 730 hours into minutes
Answers
Answer:
730 hours = 43800 minutes
Step-by-step explanation:
Formula = multiply the time value by 60
Answer:
43,800 minutes
Step-by-step explanation:
convert 730 hours into minutes
there are 60 minutes in 1 hour so:
730 * 60 = 43,800 minutes
Convert this Slope Intercept Form equation into Standard Form. y=2x-12
Answers
Answer: -2x+y=-12
Step-by-step explanation:
After what I did this is what i got. Can't really explain it
Hope this helps :)
Swimming pool A holds 215 gallons
213 gallons of water. How many times as many gallons does pool a hold
than pool B? (Example 5)
Answers
2B times as many gallons does pool A hold than pool B.
What is gallons?
The gallon is a volumetric unit that is used in both imperial and American customary measurements.
The imperial gallon (imp gal), which is equal to 4.54609 liters and was once used in various Caribbean nations as well as the United Kingdom, Ireland, Canada, Australia, and Australia.
Given:
Swimming pool A has 2^15 gallons of water.
Swimming pool B has 2^13 gallons of water.
We have to find the number of times pool A hold than pool B.
It is obvious that Swimming Pool A holds more water than Swimming Pool B.
Consequently, we must determine how many times as many gallons Pool A holds as Pool B:
2^15 > 2^13.
Therefore,
A = 2^15, B = 2^15
[tex]A = (\frac{2^1^5}{2^1^3}) B = 2B\\ A = 2B[/tex]
Hence the proof.
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Henry Bonnacio deposited 1,000 in a new savings account at First National Bank. He made no other deposits or withdrawls. After 6 months the interset was computed at an annual rate of 6 1/2%. How much simple interst did his money earn.
Answers
* Applying this to the principle of 1000 we calculate:
* 1000 * 0.0325 = 32.50.
I fill the 42 l tank in my car and take a 360 km trip. if my car consumes gasoline at a rate of 8 l per 100 km, how much farther can i go before i run out of gasoline?
Answers
Using the principle of proportional relationship, you can go 165km farther after the trip of 360km with 42L gasoline in the tank.
Consumption rate =[tex]8L[/tex] for [tex]100 km[/tex]
So, per number of Km per Litre is
[tex]8L = 100km[/tex]
[tex]1 L = x[/tex]
so,
[tex]8x = 100[/tex]
[tex]x=8 \div 100\\[/tex]
[tex]x= 12.5[/tex] kilometer per Litre
Number of kilometers for [tex]42 L[/tex]
[tex]12.5 km = 1 L[/tex]
[tex]y=42L[/tex]
On, Cross multiplying
[tex]y = 12.5\times42[/tex]
[tex]y = 525 km[/tex]
The difference in the distance [tex]= 525 - 360 = 165 km[/tex]
Therefore, the gas can go for a further [tex]165 km[/tex]
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20 4/0 - 3 1/10
Give answer as mixed number
Answers
The solution to the difference 20 4/10 - 3 1/10 is 17 3/10
We have been given two fractions.
20 4/10 and 3 1/10
We need to find the difference 20 4/10 - 3 1/10
First we write improper fraction as a proper fraction.
20 4/10 = 204/10
3 1/10 = 31/10
So, the difference would be,
20 4/10 - 3 1/10
= 204/10 - 31/10
= 173/10
= 17 3/10
Therefore, the solution to the difference 20 4/10 - 3 1/10 is 17 3/10
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-8x-7=33 ''solve it ''
Answers
Answer:
Step-by-step explanation:
-8x-7=33
+7 +7
-8x=40
x=-5
¿Alguien sabe como resolver esta acertijo ?
Un conductor conduce una guagua/autobús de 56 personas, en una parada bajan 31 personas, en la siguiente suben 18 y en la siguiente bajan 16
¿ cuantos años tiene el conductor ?
Answers
Con base en el uso de simbología para el acertijo, la edad del conductor es 27 años.
¿Cómo determinar la edad del conductor según el acertijo?
Los acertijos no deben ser entendidos literalmente, sino simbólicamente. Cada elemento representa algo figurativo.
Este acertijo parece incoherente debido a estar incompleto y es preciso añadir un criterio adicional que permita brindar sentido al contenido, este criterio es asumir que un pasajero simboliza un año, que el autobús simboliza al conductor, que el ingreso de un pasajero implica sumar un año a la edad del conductor, que el egreso de un pasajero implica restar un año a la edad del conductor y que la población resultante dentro del autobús es la edad del conductor.
En consecuencia, efectuamos la siguiente operación para determinar la edad del conductor:
x = 56 - 31 + 18 - 16
x = 27
El conductor tiene una edad de 27 años.
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45 g and 60 b will go on a field trip. What is the maximum number of groups we can form where each group has the same number of g and the same number of b? How many g and how many b will each group have? Thank you.
Answers
Answer:
17
Step-by-step explanation:
First, add up the total and find a number divisible for your total which is 105. The next step will be to divide by a number that can go into it easily, like 3 for example. then you would get 35. Since we want the most groups try a number *2 of 3 and that will be 6. After you divide you'll get 17.5 . and since there isn't .5 of a person you go to the lowest number ( not rounding ) and that'll be 17 since 105 divide another multiple of 3 would get you 11.66 repeated.
Suav has a loyalty card good for a discount at his local grocery store. The item he wants to buy is priced at $21, before discount and tax. After the discount, and before tax, the price is $19.53. Find the percent discount.
Answers
The percent discount given to Suav in the local grocery store is
How to find the the percent discountinformation given in the problem
The item Suav wants to buy in the grocery store is priced at $21
After the discount, and before tax, the price is $19.53
The discount is found by subtraction as follows
discount = price at the store - price before tax
discount = $21 - $19.53
discount = 1.47
Discount in percent
the problem is discount of the price at the store
percentage deals with a fraction hundred and used as follows
= 1.47/21 * 100
= 7/100 * 100
= 7%
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There are 9 adults waiting in line to get the newly released "grown-up" happy meal. What is the probability that
hey are lined up from shortest to tallest?
Answers
not an answer, but ik the probability that they'll get one - 0% because they have been discontinued already :D
esearchers performed a study on the effects of a nonsteroidal anti-inflammatory drug (nsaid) given before and after arthroscopic knee surgery. a sample of 67 patients undergoing elective knee arthroscopy was randomly divided into three treatment groups. researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery, and the f value obtained was 4.79. which statement is false?
Answers
The F-test is used in regression analysis to test the hypothesis that all model parameters are zero. It is also used in statistical analysis when comparing statistical models.
Statistical models that have been fitted using the same underlying factors and data set to determine the model with the best fit. That is:
H₀ : B₁ = B₂ = ............. = Bₓ =0
H₁: Bₙ ≠ 0 for at least one j.
The F-test was developed by Ronald A. Fisher (hence F-test) and is a measure of the ratio of variances. The F-statistic is defined as:
F = [tex]\frac{explained variables}{unexplained variables}[/tex]
A general rule of thumb that is often used in regression analysis is that if
F > 2.5then we can reject the null hypothesis. We would conclude that there is a least one parameter value that is nonzero.
The F-distribution is generally a skewed distribution and also related to a chi-squared distribution. The f distribution is the ratio of X1 random chi-square variable with degrees of freedom ϑ1 and X2 random chi-square variable with degrees of freedom ϑ2. (In other words each of the chi-square random variable has been divided by its degrees of freedom)
The F-distribution is generally a skewed distribution and also related to a chi-squared distribution. The f distribution is the ratio of X1 random chi-square variable with degrees of freedom ϑ1 and X2 random chi-square variable with degrees of freedom ϑ2. (In other words each of the chi-square random variable has been divided by its degrees of freedom)
F =[tex]\frac{x_{1}/v_{1} }{x_{2}/v_{2} }[/tex]
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At maria's auto shop, it takes her 9 minutes to do an oil change and 12 minutes to do a tire change. let x be the number of oil changes she does. let y be the number of tire changes she does. using the values and variables given, write an inequality describing how many oil changes and tire changes maria can do in less than 3 hours (180 minutes).
Answers
The inequality describing oil and tyre change within 180 minutes is 3x + 4y > 60.
Taking each information seperately followed by summing them for a complete equation.
1 oil change taken amount of time = 9 minutes
So, x oil change will take amount of time = 9x
Similarly, y number of tire changes will take amount of time = 12y
Adding these values to form the equation -
Number of oil and tyre changes in less than 180 minutes
Keep the value of each and symbol for 'less than'
9x + 12y > 180
Dividing the inequality by 3
3x + 4y > 60
Hence, the required inequality is 3x + 4y > 60.
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He makes a total of $500 for every 3 clients he
acquires.
How much money will 21 clients bring in?
Answers
3 thousand 500 dollars
Step-by-step explanation:3x7=21
About 1 percent of the population has a particular genetic mutation. 100 people are randomly selected. find the standard deviation for the number of people with the genetic mutation in such groups of 100.
Answers
Answer:
1/100 or just 1
Step-by-step explanation:
$$$$$$$$$$$$$$$$$$$$$$$$
as discussed in the wall street journal story, weighting is designed to adjust poll results to give more weight to people whose demographic characteristics are under-represented in the sample and less weight to people whose demographic characteristics are over-represented. think about how certain demographic groups might end up being under or over-represented (that is, there are too many or too few people in the sample from that group, compared to the population as a whole). weighting can therefore potentially help fix which types of bias? (check all that apply.)
Answers
Using the concepts of weighting, we got that demographic groups helps in fixing difference between the levels of different people if there are many or too few people in the sample from that group, compared to the population as a whole.
Demographic segmentation examples actually explain how researchers divide a market into the smaller groups according to age, gender, family income, race and ethnicity, qualification, marital status, nature of the employment, etc.
It is an extremely tedious task to the accommodate customers belonging to different demographics and develop the exhaustive marketing plan. Demographic examples ease creating the strategy for a marketer. Thus, they are one of most commonly implemented marketing segmentation methods compared to the other techniques such as geographic segmentation, behavioral segmentation, or the psychographic segmentation.
Hence, certain demographic groups might end up being under or over-represented means that there are too many or too few people in the sample from that group, compared to the population as a whole, in that case weighting can therefore potentially helps in fixing the difference in the levels of different people.
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PLS HELPP TYSM I NEED HELP ASAPPPP
Answers
Answer:
x = 7
Step-by-step explanation:
(10x+30)° and (17x-19)° are
EQUAL TO EACH OTHER
10x+30 = 17x-19
7x = 49
x = 7
desmos
M a t h (look at image)
Answers
Answer:
241
Step-by-step explanation:
9 x 12 = 108 m (area of square)
19 x 14 = 266 / 2 = 133 (area of triangle)
108 + 133 = 241
PLEASE HELP ASAP! (QUESTION IN IMAGE + 15 Points)
One angle of an isosceles triangle measures 128°. What measures are possible for the other two angles? Choose all that apply.
Answers
Answer:
Hmm I am not sure, but I think you should try 44 and 26!
Step-by-step explanation:
Reply back if its right :)
A textbook store sold a combined total of 382 chemistry and biology textbooks in a week. The number of biology textbooks sold was 58
less than the number of chemistry textbooks sold. How many textbooks of each type were sold?
Number of chemistry textbooks sold:
Number of biology textbooks sold:
Answers
Answer:
chemistry books is 220 and number of biology books is 220
Step-by-step explanation:
let y be biology books
let x be the number of chemistry books
x-58=y
equation 1 ) x+y=382
sub in x-58 for y
2. x+(x-58)=382
3. 2x-58= 382
4. 2x=382-58
5. 2x = 324
6. x/2 =324/2
7. x = 162
for x=y+58
y=162
x 220
220+162=382
y+x=382
Using your academic vocabulary and writing at least 5-7 sentences, give the (x, y) solution to the system and explain how to
solve it using the SUBSTITUTION METHOD. If your explanation uses any other method (graphing calculator or linear combination), you will not receive credit for this writing assignment.
y - 3x + 7
5x-y-5
Answers
y = 3x + 7
5x - y = 5
To solve by substitution method, substitute the value of y from the 1st equation into the y of the 2nd equation and solve
5x - (3x +7) = 5
Distributive property
5x -3x -7 =5
Combine like terms
2x -7 = 5
Add 7 to each side to isolate constants
2x -7 +7 = 5 + 7
Addition property of equity
2x = 12
Divide both sides by 2 to solve for x
2/2 x = 12/2
Division property of equity
x = 6
Now substitute value of x into equation 1 to solve for y
y = 3x + 7
y = (3)(6) + 7
y = 18 + 7
y = 25
Now substitute x and y values into equations to see if the solution is true
x= 6, y= 25
y = 3x + 7
25 = (3)(6) + 7
25 = 18 + 7
25 = 25
Solution is true ✅
5x - y = 5
(5)(6) - 25 = 5
30 - 25 = 5
5 = 5
Solution is true ✅
a conical tent is to accommodate 11 persons. each person must have 4 m2 of the space on the ground and 20 m3 of air to breathe. find the height of the cone.
Answers
The height of the conical tent is 15 metres.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc toour question-
Let the radius of the base of the conical tent be r metres and its height be h metres. Area of the base = ( 4 × 11 ) m 2 = 44 m 2 ⇒ π r 2 = 44 m 2 =(4×11)m2=44m2⇒πr2=44m2(i) Volume of the cone = ( 20 × 11 ) m 3 = 220 m 3 =(20×11)m3=220m3 ⇒ 1 3 π r 2 h = 220 m 3 ⇒ π r 2 h = 660 m 3 ⇒13πr2h=220m3⇒πr2h=660m3.(ii) On dividing (ii) by (i), we get π r 2 h π r 2 = 660 m 3 44 m 2 ⇒ h = 15 m πr2hπr2=660m344m2⇒h=15m Hence, the height of the tent is 15 metreslearn more about unitary method click here:
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(Constant of Proportionality MC)
The table shows a proportional relationship
X 1 2 3
y 14 28 42
Write an equation that represents the proportional relationship. Pls help
Answers
The equation that represents the proportional relationship is y = 14x.
We are given a table. The table contains the values for "x" and "y". The first row contains the data for the variable "x". The values of "x" are 1, 2, and 3. The second row contains the data for the variable "y". The corresponding values of "y" are 14, 28, and 42. We know that the table shows a proportional relationship between the values of "x" and "y". Let the constant of proportionality be represented by the variable "k".
y ∝ x
y = k*x
k = y/x
The value of k must be the same for each corresponding pair of values of "x" and "y".
k = 14/1 = 28/2 = 42/3 = 14
Hence, the equation is y = 14x.
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Answer:
y = 14x.
Step-by-step explanation:
Write the standard form of the equation of the line passing through (-5, 1) and is parallel to y = -2/5x -5
Answers
The equation of the line passing through (-5, 1) and is parallel to y = -2/5x -5 in standard form is 5y + 2x = -5
How to find the equation of a line?The equation of a line can be represented in standard form or slope intercept form as follows;
Slope intercept form,
y = mx + b
where
m = slopeb = y-interceptLine are parallel when they have the same slope.
Therefore, the slope of the equation has a slope of - 2 / 5 x.
The line passes through (-5, 1).
Hence, let's find y-intercept.
y = - 2 / 5 x + b
1 = - 2 / 5 (-5) + b
1 - 2 = b
b = -1
Therefore, y = -2 / 5x - 1.
The equation in standard form should be in the form Ax + By = C.
Hence,
y + 2 / 5 x = -1
5y + 2x = -5
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ben sat outside his school in cambridge and made a note of the colour of the first 100 cars that passed .
27 of them were red.
in britain there were around 35 million cars on the road.
use bens findings to give pout an estimate of how many cars on the road are red
Answers
The estimate for the number of cars that are red will be 9450000.
What is the estimate of the number of cars?From the information, when Ben sat outside his school in Cambridge and made a note of the colour of the first 100 cars that passed, he found out that 27 of them were red.
Based on the above, the ratio of red cars to total cars is 27:100.
Therefore, if thee are 35 million cars, the red cars will be:
= Ratio of red cars × Total cars
= 27/100 × 3500000
= 9450000
The number of red cards is 9450000.
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10) Determine the value of 10 - t when t = 4.
11) Determine the value of 12 + m when m = 6.
12) Determine the value of a + 5.2 when a = 1.9.
13) Determine the value of 3.4 - b when b = 2.1.
Answers
Answer:
10) 6
11) 18
12) 7.1
13) 1.3
Step-by-step explanation:
all you have to do is substitute
10 - 4 = 6
12 + 6 = 18
1.9 + 5.2 = 7.1
3.4 - 2.1 = 1.3
Please help me (see attachment)
Answers
explanation: