You can substitute a = 2ˣ and b = 5ʸ to make both equations linear.
The first equation becomes
a - b = 3
In the second equation, first simplify the exponents:
2ˣ ⁻³ = 2ˣ × 2⁻³ = 1/8 × 2ˣ
5ʸ ⁻² = 5ʸ × 5⁻² = 1/25 × 5ʸ
so the second equation changes to
a/8 + b/25 = 21
Multiply both sides of this by 200 (the LCM of 8 and 25) to eliminate the fractions:
25a + 8b = 4200
Multiply both sides of the first equation by 8, then add the corresponding sides of both equations. This eliminates b and you can solve for a :
8 (a - b) + (25a + 8b) = 8 (3) + 4200
(8a - 8b) + (25a + 8b) = 24 + 4200
33a = 4224
a = 128
Plug this into the first equation to solve for b :
128 - b = 3
b = 125
Now solve for x and y. Notice that
128 = 2⁷
and
125 = 5³
so it follows that x = 7 and y = 3.
Alternatively, you can use logarithms. For example,
a = 2ˣ → log₂(a) = log₂(2ˣ ) → x = log₂(128) = 7
Find the errors and correct the following mathematical sentences.
Answer:
Step-by-step explanation:
18). 3x + 2 ÷ 3x = [tex]\frac{2}{3x}[/tex]
Since, 3x + 2 ÷ 3x = 3x + [tex]\frac{2}{3x}[/tex]
Therefore, right hand side of the equation will be = 3x + [tex]\frac{2}{3x}[/tex]
20). [tex]\frac{4x+3}{3}=x+1[/tex]
Since, [tex]\frac{4x+3}{3}=\frac{4x}{3}+\frac{3}{3}[/tex]
= [tex]\frac{4}{3}x+1[/tex]
Therefore, right hand side of the equation should be [tex]\frac{4}{3}x+1[/tex].
Which graph represents the function f (x) = 3 x minus 2 Over x minus 2?
Answer:
C
Step-by-step explanation:
7% interest on a loan of $800 for a year. how much will you receive?
Answer:
$56
Step-by-step explanation:
Here's an easy way to figure out this and any percentage question. One per cent (1 dollar out of $100) of $800 would be $8. So, if the man received 7 per cent out of $800, then just multiply $8 times 7, which is 56...so $56!
Hope it helps
Please mark me as the brainliest
Thank you
Step-by-step explanation:
Here's an easy way to figure out this and any percentage question. One per cent (1 dollar out of $100) of $800 would be $8. So, if the man received 7 per cent out of $800, then just multiply $8 times 7, which is 56...so $56
A grocery store counts the number of customers who arrive during an hour. The average over a year is 10 customers per hour. Assume the arrival of customers follows a Poisson distribution. (It usually does.) Find the probability that at least one customer arrives in a particular one minute period. Round your answer to 3 decimals. Find the probability that at least two customers arrive in a particular 4 minute period. Round your answer to four decimals.
Answer:
0.1535 = 15.35% probability that at least one customer arrives in a particular one minute period.
0.1443 = 14.43% probability that at least two customers arrive in a particular 4 minute period.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Find the probability that at least one customer arrives in a particular one minute period.
The average is of 10 customers per hour(60 minutes), so for this case, [tex]\mu = \frac{10}{60} = \frac{1}{6}[/tex]
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-\frac{1}{6}}*(\frac{1}{6})^{0}}{(0)!} = 0.8465[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.8465 = 0.1535[/tex]
0.1535 = 15.35% probability that at least one customer arrives in a particular one minute period.
Probability that at least two customers arrive in a particular 4 minute period.
The average is of 10 customers per hour(60 minutes), so for this case, [tex]\mu = \frac{10*4}{60} = \frac{4}{6} = \frac{2}{3}[/tex]
This probability is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-\frac{2}{3}}*(\frac{2}{3})^{0}}{(0)!} = 0.5134[/tex]
[tex]P(X = 1) = \frac{e^{-\frac{2}{3}}*(\frac{2}{3})^{1}}{(1)!} = 0.3423[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.5134 + 0.3423 = 0.8557[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.8557 = 0.1443[/tex]
0.1443 = 14.43% probability that at least two customers arrive in a particular 4 minute period.
Please help me I don’t get it
Answer:
The number is 4
Step-by-step explanation:
We set up the equation given the conditions listed. Since it says 5 times the difference between a number and 7, we can use x as a placeholder for the number.
(x-7) is the difference between the number and 7. The question asks for 5 times that difference thus we multiply the entire thing by 5 giving us 5(x-7. The question says that it all equals -15 so we set that expression equal to -15.
Thus we get the equation and solve:
5(x-7)= -15 (distributive property)
5x-35= -15 (add 35 to both sides)
5x=20 (divide by 5)
x=4; so the number is 4
i need help <3 <3 < 3 <3 <3 <3 <3 <3 <3 <3
Answer:
I have study up to 8 class hahahahahah
Answer:
owo - well uh
Last year, 120 new houses were built in a neighborhood. So far this year, 2/3
of them have been sold. How many new houses have been sold this year?
Write your answer in simplest form.
Multiply the total number of houses built by the fraction sold:
120 x 2/3 = (120 x 2)/3 = 240/3 = 80
80 houses were sold.
please help me i really need help please
Answer:
39°
Step-by-step explanation:
180-90-51=39
Answer:
its 39
Step-by-step explanation:
you know that a right triangle already has the angle 90 so 51 plus 90 equals 141
180-141=39
10. Find the volume of the prism.
3 ft
7 ft
2 ft
please help what is the value of
tan^2(180-tetha)
Answer:
1/cos^2(180-theta) - 1
Step-by-step explanation:
According to trigonometry identity
tan^2 theta + 1 = sec^2 theta
tan^2 theta = sec^2 theta - 1
hence tan^2(180-tetha) = sec^2 (180 -theta) - 1
tan^2(180-tetha) = 1/cos^2(180-theta) - 1
Hence the value of tan^2(180-tetha) is 1/cos^2(180-theta) - 1
Justin has $7.50 more than Eva, and Emma has $12 less than Justin. Together, they have a total of $63.00. How much money does each person have?
i only have 5 min help fast
Answer:
To make it easier, lets say Justin = J, Eva = E, and Emma = M. Then, J = E + 7.50 M = J -12 J + E + M = 63 You can substitute for M in the third equation using the second equation, and you get: J + E + J - 12 = 63 Clean it up a little bit and you get: 2J + E = 75 You know J = E + 7.50, so substitute that for J and you get: 2(E + 7.50) + E = 75 2E + 15 + E = 75 3E + 15 = 75 3E = 60 E = 20 ; meaning that Eva has $20. Justin has $7.50 more than Eva, so he has $27.50. Emma has $12 less than Justin, so Emma has $15.50. Double check your answer by making sure they all add up to 63, which they do.
here's a graph of a linear function write the equation that describes that function
Answer:
y=3/4x+2
Step-by-step explanation:
Each of the four graphs represents a function. Which function has an inverse that is also a function?
8
40
6
6
4
+
-8
-6 -4
4
-8
-6
-2
-2
-4
6
8
-4
-6
-6
-8
Ο Α
Ов
x
8
8
x
8
-8
-6
-4
6
-8
-6-4
6
8
U
-4
4
6
с
D
Answer124
Step-by-step explanation:
Answer: The answer is C
Step-by-step explanation: Graph C passes the horizontal line test and becomes a function as the horizontal line does not cut the curve more than once along any line drawn.
Also, the curve passes the vertical line test as well, if a vertical is drawn, it does not cut the curve more than once if drawn any where vertically.
Thus, graph C passes both the horizontal and vertical line test. So the curve has both function and inverse function.
The physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 47 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 47 and 68
Answer:
The approximate percentage of lightbulb replacement requests numbering between 47 and 68 is 49.85%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 47
Standard deviation of 7
What is the approximate percentage of lightbulb replacement requests numbering between 47 and 68?
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% of the above.
Between 47 and 68:
68 = 47 + 7*3
So 68 is three standard deviations of the mean.
Of the 50% above the mean, approximately 99.7% are between the mean of 47 and 3 standard deviations above the mean, which is 68. So
0.5*0.997 = 0.4985
0.4985*100 = 49.85%
The approximate percentage of lightbulb replacement requests numbering between 47 and 68 is 49.85%.
Which of the following graphs are identical?
Answer:
second part is a,c,d
Answer: they are correct
Step-by-step explanation:
correct
A mother bottlenose ate about 220 pounds of food in one week. About how much food did she eat in a day?
She ate about
pounds of food in a day.
Find the circumference of the circle.
Answer:
25.12ft
Step-by-step explanation:
C=2πr
C = 2(3.14)(4)
C = 25.12ft
Answer:
25.12
Step-by-step explanation:
The circumference of a circle is equal to [tex]2\pi r[/tex]. So, to find the circumference plug in 4 for r and solve the expression. [tex]2\pi 4[/tex], where [tex]\pi[/tex] equals 3.14 is 25.12.
8increase by 3 times a number (t).
Answer:
8 + 3n
Step-by-step explanation:
Answer:
8 + 3t
Explanation:
Penny makes 5 liters of applesauce. She saves 0.24 liter for dinner and puts the rest in jars. If each jar holds 0.68 liter, how many jars can she fill?
Answer:
Penny can fill eight jars.
Answer:
Penny can fill 8 jars.
Step-by-step explanation:
Step one: Multiply the divisor by a power of 10 to make it a whole number. Then, multiply the dividend by the same power of 10. Step two: Write the decimal point in the quotient above the decimal point in the new dividend. Step three: Divide!
A brick measures 15 cm in length, 8 cm in breadth and 5 cm in height. How many bricks will be used to make a wall of length 15 cm, breadth 10 cm and height 8 cm
1. 2 bricks
2. 5 bricks
3. 9bricks
4. 4bricks
Answer:
2bricks
Step-by-step explanation:
volume of cuboid = length × breadth ×height
step 1 : calculate the first one
v= 15cm ×8cm× 5cm = 1200cm^3
step 2 calculate the 2nd one
v= 15cm ×10cm×8cm = 600cm^3
number of bricks
1200cm^3 × 1bricks/ 600cm^3 = 2 bricks
Please help will give brainliest
Answer:
25 is the area because5 times 5 equals 25
Step-by-step explanation:
hope this helps
Answer:
25
Step-by-step explanation:
The dot plot shows the number of books Melanie's classmates have read. Approximately what percent of Melanie’s classmates have read more than 7 books
Answer:
.30
Step-by-step explanation:
in the coordinate plain the point located at (-3,4) was reflected and is now located at (3,4). how was the point reflected
Answer:
they reflect thru the y-axis
Step-by-step explanation:
Robin made a cuboid of plasticine. Length, breadth, and height of the cuboid are
3 cm, 2cm, 3 cm respectively. How many such cuboids will he need to make a
perfect cube?
will need 18cm^3
Step-by-step explanation:
volume of cuboid = length × base × height
so v= 3cm ×2cm×3cm
v=18cm^3
if you subtract 17 from my number and multiply the difference by -6 the results is -138 what is Sarah's number
Answer:
40
Step-by-step explanation:
let the unknown be y (x is used as times(multiplication) )
(y-17)x-6=-138
add /-6 to both sides
y-17x-6/-6=-138/-6
y-17=23
make y independent/add 17 to both sides
y-17+17=23+17
y=40
or in an easier way
-138/-6 =23
23+17=40
simply reversing the question to get the answer
Can you help me please it has to be harry potter and the philosopher's stone movie
Answer and Step-by-step explanation:
Divide each side by 2.
x [tex]\geq[/tex] 5
This is the correct answer for getting the x by itself.
#teamtrees #PAW (Plant And Water)
Answer:
4
Step-by-step explanation:
2x10=20
I think...
Please find the area of of the shaded polygon
Answer:
8
Step-by-step explanation:
Triangle PQR IS SIMILAR TO Triangle KLM.
What is the value of x in inches?
A 7 in.
B 148 in.
C 92 in.
D 168 in.
How many bags of topsoil does Betsy need to cover her flower bed?
Answer:
3 bags of topsoil is needed
Step-by-step explanation:
base = 20m
height = 6 m
Area of flower bed = [tex]\frac{1}{2}*base*height\\[/tex]
[tex]= \frac{1}{2}*20*6\\\\= 10*6\\= 60 square feet[/tex]
Number of bags= Total area of flower bed ÷ 20
= 60 ÷ 20
= 3
PLEASE HELP PLESD PLEDmoon