What value of x makes the equation 7^15⋅7^4=7x true?
Answers
Answer:
To find the value of x that makes the equation 7^15 * 7^4 = 7^x true, you can use the properties of exponents.
In this case, you can apply the rule that when you multiply two numbers with the same base, you can add their exponents. So, for the equation:
7^15 * 7^4 = 7^x
You can combine the exponents on the left side:
7^(15 + 4) = 7^x
Now, you have:
7^19 = 7^x
For these two exponential expressions to be equal, the exponents must be equal:
x = 19
So, the value of x that makes the equation true is x = 19.
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The average sales per customer at a home improvement store during the past year is $75 with a standard deviation of $12. The probability that the average sales per customer from a sample of 36 customers, taken at random from this population, exceeds $78 is:
Answers
Answer:
sin(A-B) = 24/25
Step-by-step explanation:
The trig identity for the differnce of angles tells you ...
sin(A -B) = sin(A)cos(B) -sin(B)cos(A)
We are given that sin(A) = 4/5 in quadrant II, so cos(A) = -√(1-(4/5)^2) = -3/5.
And we are given that cos(B) = 3/5 in quadrant I, so sin(B) = 4/5.
Then ...
sin(A-B) = (4/5)(3/5) -(4/5)(-3/5) = 12/25 + 12/25 = 24/25
The desired sine is 24/25.
$150 table; 40% discount
Answers
Answer:
$60
Step-by-step explanation:
40% of 150=60
40 × 150= $60
100 1
150 - 60 = $90 (discounted price) [Answer]
Answers
Answer:
$5.50
Step-by-step explanation:
so if its $3 for an ice cream plus .50 cents per ounce all you have to do is 11 x 0.50 witch would equal $ 5.50.
logb 3 ≈ 0.5646,
and
logb 5 ≈ 0.8271.
(Round your answer to four decimal places.)
㏒b(2b^3)
Answers
Final answer:
By using the properties of logarithms, namely ㏒b(a * c) = ㏒b(a) + ㏒b(c) and ㏒b(a^p) = p * ㏒b(a), we find the approximation of the logarithm ㏒b(2b^3) to be 3.3562.
Explanation:
To approximate the value of ㏒b(2b^3), we can use the properties of logarithms. The first one is that ㏒b(a * c) = ㏒b(a) + ㏒b(c), where a and c are the numbers we wish to find the logarithm of. We can apply this property to your given expression as follows:
- ㏒b(2b^3) = ㏒b(2) + ㏒b(b^3).
The second logarithmic property we need is that ㏒b(a^p) = p * ㏒b(a), where a is the base, and p is the exponent. We can apply this property to the second term on the right side:
- ㏒b(b^3) = 3 * ㏒b(b).
- Since ㏒b(b) is equal to 1 (because b raised to the power of 1 is b), then our equation becomes:
- ㏒b(2b^3) = ㏒b(2) + 3.
Now, we can substitute the values given for ㏒b(2), which is 0.3562:
- ㏒b(2b^3) = 0.3562 + 3 = 3.3562.
So, approximating ㏒b(2b^3) to four decimal places, we get 3.3562.
Learn more about Logarithms here:
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que representa Laos hombres con relacion al total
Answers
Answer:
There would be 20 ounces of almonds in the bag
Step-by-step explanation:
System of Equations
To solve the problem, we'll set up these two variables:
x = ounces of almonds
y = ounces of raisins
The ratio of almonds to raisins in the trail mix is 5:7, thus:
Cross-multiplying:
7x=5y [1]
A 3-pound bag of this trail mix contains 3*16=48 ounces that include almonds and raisins, thus:
x + y = 48 [2]
Multiplying [2] by 5:
5x + 5y = 240
Substituting from [1]:
5x + 7x = 240
12x = 240
x = 240/12
x = 20
There would be 20 ounces of almonds in the bag
children and how many adults were admitted?
Your answer is
number of children equals____
number of adults equals____