To convert the exponential equation 4c = 256 into a logarithmic form, one can apply the logarithm to both sides, simplifying using the property that the logarithm of a power is the exponent times the logarithm of the base, yielding the equivalent equation c = 4.
The question requires us to convert the exponential equation 4c = 256 into a logarithmic form. To achieve this, we need to recognize that a logarithm function is the inverse of an exponential function. Therefore, applying a logarithm to both sides of the equation will allow us to solve for the variable c.
It's important to note that any logarithmic base can be used, but common practice is to use either base 10 (common logarithm) or the natural base e (natural logarithm).
Since 256 is 4 raised to the 4th power (4⁴), we can write the equation as 4c = 4⁴. By applying the logarithm, we then get the equivalent logarithmic equation log(4c) = log(4⁴).
Using the property of logarithms that states the logarithm of a number raised to an exponent will be the product of the exponent and the logarithm of the number, we can simplify this to c*log(4) = 4*log(4). Since log(4) is a common factor on both sides, dividing by log(4) gives us c = 4.
Given that jklm is a rhombus, find kjm.
a. 37°
c. 106°
b. 74°
d. 143°
Answer:
C.
Step-by-step explanation:
A company makes triangular plates for individual slices of pizza. For each plate, the base is 7 inches and the height is 12 inches. The area of the top of the plate is ____ inches squared.
Answer:
42 Inches squared ( hope that helps) ;)
The area of the top of the plate will be 42 inches squared.
What is the area of the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,
A = (1/2) × h·b
A company makes triangular plates for individual slices of pizza. For each plate, the base is 7 inches and the height is 12 inches.
Then the area of the triangle is given as,
Area = 1/2 x 12 x 7
Area = 6 x 7
Area = 42 square inches
The area of the top of the plate will be 42 inches squared.
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Identify the function that best models the given data.
Answer: W(i) = 3.125x^2 − 14.5x + 208.5
Step-by-step explanation:
4/101.78 do long divison for this problem
How many distinguishable 7 letter "words" can be formed using the letters in alabamaalabama?
Final answer:
The number of distinguishable 7-letter words that can be formed using the letters in alabamaalabama is 5040.
Explanation:
The number of distinguishable 7-letter words that can be formed using the letters in alabamaalabama can be calculated using permutations. In this case, we have 12 letters, but some of them are repeated. To calculate the total number of permutations, we need to divide the total number of permutations by the factorial of the number of times each repeated letter appears. The word alabamaalabama has 7 distinct letters, so there are no repeated letters in this case. Therefore, the number of distinguishable 7-letter words that can be formed is simply 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.
Which graph best represents the solution to the system of equations shown below?
y = -2x + 14
y = 2x + 2
Answer:
solution is (3,8)
option A
Step-by-step explanation:
[tex]y = -2x + 14[/tex]
[tex]y = 2x + 2[/tex]
Lets graph each equation
Given equation is in the form of y=mx+b
LEts graph each equation using a table
[tex]y = -2x + 14[/tex]
x y
0 14
1 12 points are (0,14) and (1,12)
[tex]y = 2x + 2[/tex]
x y
0 2
1 4 points are (0,2) and (1,4)
Graph both the table
The graph is attached below. both graph intersects at (3,8)
A television station would like to measure the ability of its weather forecaster. Past data have been collected that indicate the following:
Probability of sunshine on sunny days is 0.8
Probability of sunshine on rainy days is 0.4
Probability of a sunny day is 0.6
Find the probability of
(I)sunshine
(II)sunny given that the forecaster has predicted sunshine
Final answer:
The probability of sunshine on any given day is 0.64, and the probability that it is sunny given that sunshine has been forecasted is 0.75.
Explanation:
To address the question, we'll first define the given probabilities:
Probability of sunshine on sunny days (P(S|Sunny)) = 0.8Probability of sunshine on rainy days (P(S|Rainy)) = 0.4Probability of a sunny day (P(Sunny)) = 0.6Probability of a rainy day is the complement of a sunny day (P(Rainy)) = 0.4, since P(Sunny) + P(Rainy) = 1
Part I: Finding the probability of sunshine
To find the overall probability of sunshine, we use the law of total probability:
P(S) = P(S|Sunny) × P(Sunny) + P(S|Rainy) × P(Rainy)P(S) = 0.8 × 0.6 + 0.4 × 0.4 = 0.48 + 0.16 = 0.64Part II: Finding the probability of sunny given sunshine
To find the probability of sunny given that the forecaster has predicted sunshine, we use Bayes' theorem:
P(Sunny|S) = [P(S|Sunny) × P(Sunny)] / P(S) = (0.8 × 0.6) / 0.64 = 0.48 / 0.64 = 0.75The x-intercept of the graph of f(x)= 3log(x-5)+2 is:
Answer: [tex]\frac{1}{e^{\frac{2}{3}}}+5[/tex] or 5.51
Step-by-step explanation:
The given function : [tex]f(x)= 3\log(x-5)+2[/tex]
We know that , the x-intercept is the point on graph( basically intersection of graph and x-axis) where y coordinate is zero.
I.e. for x-intercept of function , f(x) =0
i.e. [tex]0= 3\log(x-5)+2[/tex]
[tex]\Rightarrow\ \log(x-5)=\dfrac{-2}{3}[/tex]
Taking exponent on both sides , we get
[tex]x-5=e^{\frac{-2}{3}}\\\\\Rightarrow\ x=e^{\frac{-2}{3}}+5\ \ or\ \ x=\dfrac{1}{e^{\frac{2}{3}}}+5[/tex]
On simplification , [tex]\frac{1}{e^{\frac{2}{3}}}+5\approx5.51[/tex].
Hence , the x-intercept of the graph f(x)= [tex]\dfrac{1}{e^{\frac{2}{3}}}+5[/tex] or 5.51.
Answer:
10^-2/3 +5
Step-by-step explanation:
How much money will you have at the end of one year if interest is compounded semiannually at 10% on a $600 deposit? A. $661.50 B. $662.00 C. $660.00 D. $659.50
Compound interest on a principal of $600.00 at a rate of 10% per year compounded twice per year over a period of one year results in an accumulated total of $661.50 (principal plus interest).
What is compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
A = P(1 + r/n[tex])^{nt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
Given:
P = principal (the initial deposit amount) = $600
r = annual interest rate = 10%
n = the number of compounding periods per unit of time = 2
t = 1
First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n[tex])^{nt}[/tex]
A = 600.00(1 + 0.1/2[tex])^{(2)(1)}[/tex]
A = 600.00(1 + 0.05[tex])^{(2)}[/tex]
A = $661.50
Therefore, the amount is $661.50.
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What is the volume of a right circular cone with a diameter of 21 centimeters and a height of 87 centimeters? Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
Suppose that f(x)=x^2 and g(x)= -4/5x^2 which statement best compares the graph of g(x) with the graph of f(x)
Answer: the graph of g(x) is the graph of f(x) compressed vertically
Step-by-step explanation:
a) 7.02 is 10.4% of what number?
b) 152.5 is what percent of 61?
There are 36 students on the bus. There are 2 times as many girls than boys on the bus. On your paper, write a system of liner equations and solve for the number of girls and boys on bus. How many girls are on the bus. A-12 B-24 C-17 D-19
Final answer:
To find the number of girls and boys on the bus, create a system of linear equations and solve for the variables. In this case, there are 12 boys and 24 girls on the bus.
Explanation:
To solve for the number of girls and boys on the bus:
Let G represent the number of girls and B represent the number of boys.
From the problem, G = 2B and G + B = 36.
Substitute G = 2B into the second equation to get 2B + B = 36, which gives B = 12. Therefore, there are 12 boys and 24 girls on the bus.
Joo-Eun wants to draw a triangle with sides measuring 6 mm, 8 mm, and 11 mm. Which is true about Joo-Eun’s plan? Joo-Eun cannot draw a triangle with these side lengths. Joo-Eun can only draw one unique triangle with these side lengths. Joo-Eun can draw exactly two triangles with these side lengths. Joo-Eun can draw more than one triangle with these side lengths.
Answer:
Option 2 is correct .i.e., Joo-Eun can only draw one unique triangle with these side lengths.
Step-by-step explanation:
Measures of sides of triangles are 6 mm , 8 mm and 11 mm
We use a result which states that if sum of two sides of a triangle is greater than 3rd side then triangle with those measures exist.
here,
6 + 8 = 14 > 11
6 + 11 = 17 > 8
8 + 11 = 19 > 6
Therefore, triangle With given measures exist.
Now we use another result which says that a triangle with given measurement can only be drawn as one unique triangle and the angles would be unique for the particular triangle.
Therefore, Option 2 is correct .i.e., Joo-Eun can only draw one unique triangle with these side lengths.
The statement that is true about Joo-Eun’s plan is: Joo-Eun can only draw one unique triangle with these side lengths.
What is a Unique Triangle?A unique triangle is a congruent triangle that remains the same no matter how it is flipped.
The conditions for a unique triangle include;
The presence of three side lengths as is the case in the triangle Joo-Eun wants to draw, The presence of two angles and any side condition.The triangle in the above question meets the first condition.
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A 12 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building. How far up the building does the ladder reach ?
A. 24√2
B.6√2
C. 6 feet
D.12√2
Answer:
The answer is B. 6 square root 2
Step-by-step explanation:
A grab bag contains 8 football cards and 2 basketball cards. an experiment consists of taking one card out of the bag, replacing it, and then selecting another card. determine whether the events are independent or dependent. what is the probability of selecting a football card and then a basketball card? express your answer as a decimal.
Answer:
Independent - 0.16
Step-by-step explanation:
A city’s annual rainfall totals are normally distributed, and the probability that the city gets more than 43.2 inches of rain in a year is given by P(z≥1.5)=0.0668. If the standard deviation of the city’s yearly rainfall totals is 1.8 inches, what is the city’s mean annual rainfall?
Answer: 40.5 inches
Step-by-step explanation:
Given: A city’s annual rainfall totals are normally distributed.
The probability that the city gets more than 43.2 inches of rain in a year is given by P(z≥1.5)=0.0668
Thus, X=43.2 inches
z=1.5
Standard deviation [tex]\sigma[/tex]=1.8 inches
We know that [tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]\Rightarrow\mu=X-z\sigma\\\Rightarrow\mu=43.2-1.5\times1.8\\\Rightarrow\mu=43.2-2.7\\\Rightarrow\mu=40.5\ inches[/tex]
Hence, the city’s mean annual rainfall is 40.5 inches.
How would you convert the repeating, nonterminating decimal into a fraction? Explain the process as you solve the problem. 0.1515
Answer:
5/33
Step-by-step explanation:
x = 0.1515
100 x = 15.1515
100 x - x = 15.1515 - 0.1515
99 x = 15
x = 15 / 99 = 3 ∙ 5 / 3 ∙ 33 = 5 / 33
0.15165 = 5 / 33
question is in the image
A model rocket is launched with an initial upward velocity of 67/ms. The rocket's height h (in meters) after t seconds is given by the following.
h= 67t-5t^2
Find all values of t for which the rocket's height is 30 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Step-by-step explanation:
The rocket's height h (in meters) after t seconds is given by:
[tex]h=67t-5t^2[/tex]
67 m/s is the initial upward velocity of the rocket. We need to find the values of t for which the rocket's height is 30 meters. So equation (1) becomes :
[tex]67t-5t^2=30[/tex]
[tex]67t-5t^2-30=0[/tex]
The above equation is a quadratic equation. We need to find the value of t.After solving the quadratic equation, we get the values of t are :
t = 0.464 seconds = 0.46 seconds
or
t = 12.936 seconds = 12.94 seconds
Hence, this is the required solution.
The rocket's height is 30 meters at t = 3.79 seconds or t = 0.54 seconds after launch, when solved using the quadratic formula applied to the given equation.
Explanation:To find all values of t for which the rocket's height is 30 meters according to the given quadratic equation h = 67t - 5t2, we need to set the equation equal to 30:
30 = 67t - 5t2
Moving all terms to one side, we obtain:
0 = 5t2 - 67t + 30
Now, we can solve this quadratic equation using the quadratic formula:
t = (-b ± sqrt(b2 - 4ac)) / (2a)
Here, a = 5, b = -67, and c = 30. Plugging these values into the formula we get:
t = (67 ± sqrt(672 - 4 * 5 * 30)) / (10)
Calculating the discriminant and then computing the values for t:
t = 3.79 or t = 0.54
Therefore, the rocket is at 30 meters at approximately t = 3.79 seconds or t = 0.54 seconds after launch, rounded to the nearest hundredth.
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what is the reciprocal of 8-3i
The reciprocal of the complex number 8-3i is found by dividing its complex conjugate (8+3i) by the modulus squared of 8-3i, which is 73. The result is 8/73 + 3i/73.
Explanation:The reciprocal of a complex number is the complex conjugate of that number divided by the modulus squared of the original number. In the case of the complex number 8-3i, its complex conjugate is 8+3i. To find the reciprocal of 8-3i, you would divide this complex conjugate by the modulus squared of 8-3i.
First, calculate the modulus squared of 8-3i:
Modulus of 8-3i = sqrt(82 + (-3)2) = sqrt(64 + 9) = sqrt(73).Modulus squared = (sqrt(73))2 = 73.Then, divide the complex conjugate by this modulus squared to get the reciprocal:
Reciprocal of 8-3i = (8+3i) / 73 = 8/73 + 3i/73.
Find the values of x and y. Show your work.
Answer:
the value of x and y are, 5 and 4
Step-by-step explanation:
SSS(Side Side Side) postulate states, that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.
In given triangle ABC and triangle CDE as shown in attachment , by above theorem ,we have
[tex]AB\cong BC[/tex]
⇒ [tex]7x-4=31[/tex]
[tex]7x=35[/tex]
∴ [tex]x=5[/tex]
also, [tex]BC\cong DE[/tex]
⇒ [tex]4y+8=24[/tex]
simplify:
[tex]4y=16[/tex]
∴ [tex]y=4[/tex]
Hence, the value of x=5 and y=4.
The price of bananas is $6.50 for 5 pounds. What is the price as a unit rate?
$6.50/1lb
$1.30/1lb
$1/30/3lb
$1.05/1lb
There are 4! (or 24) "words" that can be formed using each of the letters a, b, c and d once. if these "words" are alphabetized, which one is 17th?
What is 3/2 - 1 equal
930 miles to travel with a car that gets 22 miles per gallon. How much will it cost to travel if gas costs 2.03 a gallon?
the polynomial (x - 2) is a factor of the polynomial 3x2 - 8x + 2.
First, let's factor 3x²-8x+2
Looking at wee can see that the first term is and the last term is where the coefficients are 3 and 2 respectively.
Now multiply the first coefficient 3 and the last coefficient 2 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient -8? Let's list all of the factors of 6:
Factors of 6:
1,2,3,6
-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 6
1*6
2*3
(-1)*(-6)
(-2)*(-3)
note: remember two negative numbers multiplied together make a positive number
Now, which of these pairs add to -8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -8
None of these pairs of factors add to -8.
So the expression 3x²-8x+2 cannot be factored.
So (x - 2) is NOT a factor of 3x²-8x+2
So the statement is false
Answer:
B.false
Step-by-step explanation:
apexs
Question 3 (Essay Worth 10 points)
(03.06 MC)
Part A: Eveline rented a car at $180 for 4 days. If she rents the same car for 9 days, she has to pay a total rent of $325.
Write an equation in the standard form to represent the total rent (y) that Eveline has to pay for renting the car for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
To which real number subset(s) do the following real numbers belong?
-4, -2, 1, 3, 5
A. whole numbers
B. natural numbers
C. integers and rational numbers
D. natural and irrational numbers
A circle is drawn in the xy-coordinate plane. if there are n different points (x, y) on the circle such that xy = 0, then the possible values of n are