The properties that were used to derive the properties of logarithms are the properties of exponent because logarithms are exponents. The properties of exponents are: product of powers, power to a power, quotient of powers, power f a product and power of a quotient.
As an example, the log property log(a^k) = k log (a) can be derived from the exponential property (b^a)^k = b^(ak).
Likewise,
log (ab) = log (a) + log (b) comes from c^(a+b) = c^a*c^b
Proof:
Let x = c^a and y=c^b
Then,
log (x) = a and log (y) =
b (base c)
log (xy) = log (c^a * c^b) = log (c^(a+b)) = a+b = log(x) + log (y)
Curt is installing a picket fence around his garden which is 45.45 ft by 14.63 ft. When he gets to the hardware store he finds that each picket fence slat is two feet wide. If Curt does not want any spaces between each slat, use estimation to determine how many slats of fencing he should buy.
Tank 1 initially contains 50 gals of water with 10 oz of salt in it, while tank 2 initially contains 20 gals of water with 15 oz of salt in it. water containing 2 oz/gal of salt flows into tank 1 at a rate of 5 gal/min and the well-stirred mixture flows from tank 1 into tank 2 at the same rate of 5 gal/min. the solution in tank 2 flows out to the ground at a rate of 5 gal/min. if x1(t) and x2(t) represent the number of ounces of salt in tank 1 and tank 2, respectively, set up but do not solve an initial value problem describing this system.
What if the atom has no charge
If 3/2 divided by 1/4 =n, then n is between
Compare the value of the
4 in 40 and 400
Susie is paying $502.33 every month for her $150,000 mortgage payment. If this is a 4.5% 30 year mortgage, how much interest will she pay over the 30 years of payments?
Answer:
$30838.80
:3 simply it pls
Lena bought 10 pounds of potatoes for $5.50 write the cost as cents per pound
let A and B be nxn matrices such that AB is singular prove that either A or Bis singular
Linear regression describes the extent to which _______ predicts ________.
Linear regression describes the extent to which an independent variable predicts a dependent variable through a linear relationship.
Explanation:Linear regression describes the extent to which an independent variable (x) predicts a dependent variable (y) through a linear relationship.
For example, if we have data that shows the number of hours studied (x) and the test score (y) of students, linear regression can help us determine how well the number of hours studied predicts the test score.
The regression line is used to model the linear relationship between the independent and dependent variables in the population.
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A flagpole cast a shadow 16 feet long at the same time a pole 9 feet high casts a shadow 6feet long what is the height in feet of the flagpole
Estimate then find the product 7×7956
Final answer:
To estimate the product of 7 and 7956, round 7956 to 8000 and then multiply by 7 to get 56,000. The exact product, calculated using the multiplication algorithm, is 55,692.
Explanation:
To estimate the product of 7×7956, we can round 7956 to the nearest thousand which gives us 8000. Then, we multiply 7×8000 to get an estimated product of 56,000. To find the exact product, we multiply 7 by 7956 to get 55,692.
When calculating such a product, we use the multiplication algorithm where we multiply each digit of the second number by the first number and then add up the resulting values.
Here's how you would perform the multiplication step by step:
7×7 = 49, add the carried over 6 to get 55, write down 5 and carry over the 5.
After placing the digits in their correct positions, we get the final answer: 55,692. Therefore, the exact product of 7×7956 is 55,692.
Can you help me solve this 2/3 (5 x 4) ÷ 3 + 6/7 =
To put up several tents for a camping trip, you need several pieces of rope each 6 2/3 feet long. If you have a rope that is 43 feet, how many pieces can you cut for the tents?
box contains 15 items,4 of which are defective and 11 are good. Two items are selected. What is probability that the first is good and the second defective?
Final answer:
The probability that the first item selected is good and the second item is defective is 22/105.
Explanation:
To find the probability that the first item selected is good and the second item is defective, we need to consider the total number of items, the number of good items, and the number of defective items.
The total number of items is 15, with 11 being good and 4 being defective. When we select the first item, there are 15 options, out of which 11 are good. Therefore, the probability of selecting a good item first is 11/15.
After selecting the first item, there are now 14 items left in the box, with 10 being good and 4 being defective. When we select the second item, there are 14 options, out of which 4 are defective. Therefore, the probability of selecting a defective item second is 4/14, which simplifies to 2/7.
To find the probability that both events occur, we multiply the probabilities: (11/15) * (2/7) = 22/105.
what is the value of x in the equation 5(4x-10)+10x=4(2x-3)+2(x-4) ?
-7/4
-1/4
3/20
3/2
Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Here, the given expression is,
[tex]5(4x-10)+10x=4(2x-3)+2(x-4)[/tex]
By distributive property,
[tex]20x - 50 + 10x = 8x - 12 + 2x - 8[/tex]
By combining like terms,
[tex]30x -50=10x-20[/tex]
Adding 50 on both sides,
[tex]30x=10x-20+50[/tex]
[tex]30x = 10x + 30[/tex]
Subtracting 10x on both sides,
[tex]20x = 30[/tex]
Divide both sides by 20,.
[tex]x=\frac{3}{2}[/tex]
Hence, LAST option is correct.
Will someone please answer this question?
surface area = 5ab +5bh
a = 4
b=7
h=18
5*4*7 = 140
5*7*18 = 630
630+140 = 770 square meters
There are 12 more toy cars than toy trucks in a toy box. With a total of 38 toy cars and trucks.How many toy trucks are in the toy box?
Answer:
Hui
Step-by-step explanation:
For each function, use the slope formula to calculate the rate of change between the points. In your final answer, include all of your calculations.
f(x):
(a, f(a) and (b,f(b)
1.) f(x)=x - 3 (0,f(0)) and (6,f(6))
2.) f(x) = -x (-4,f(-4)) and(2,f(2))
3.) f(x)=x2 (-2,f(-2)) and (0,f(0))
4.) f(x)=x3 (-1,f(-1)) and (1,f(1))
5.) f(x)=2x (0,f(0)) and (4,f(4))
The equation of the line of best fit of a scatter plot is y = −4x − 6. What is the slope of the equation?
−6
−4
4
6
Hello, I'm working on a project and I've been stumped.
How would I find the central ark of a ferris wheel? I'm using the London Eye ferris wheel for my project, and so far I know it has a diameter of 120 meters and 32 cars. It has a circumference of 377m and an area of 11,310m.
How can that information help me? Please include all steps and a clear explanation, and give the answer in degrees. Thank you.
a circle has 360 degrees
the ferris wheel has 32 cars so the circle is broken up into 32 sections
the central angle would be the angle between 2 of the cars
so divide 360 by 32
360/32 = 11.25 degrees
If cba represents three numbers multiplied together, what property allows you to rearrange the factors to read abc?
The commutative property allows you to rearrange the factors of a multiplication problem.
Explanation:The property that allows you to rearrange the factors of a multiplication problem is the commutative property. This property states that the order of the factors can be changed without changing the product. In this case, if cba represents three numbers multiplied together, you can rearrange the factors to read abc because multiplying in any order will give you the same product.
For example, if c = 2, b = 3, and a = 4, then cba = 2 * 3 * 4 = 24. Rearranging the factors to abc gives abc = 4 * 3 * 2 = 24, which is the same product.
For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is
P(X≤−1.9)=0.0287165598160018P(X≤−1.9)=0.0287165598160018
P(X≥1.7)=0.044565462758543P(X≥1.7)=0.044565462758543
P(−1.95996398454005≤X≤1.95996398454005)=0.95
Answer:
92.67% probability of obtaining a z value between -1.9 to 1.7.
Step-by-step explanation:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is
This probability is the pvalue of z = 1.7 subtracted by the pvalue of z = -1.9.
z = 1.7 has a pvalue of 0.9554.
z = -1.9 has a pvalue of 0.0287.
So there is a 0.9554-0.0287 = 0.9267 = 92.67% probability of obtaining a z value between -1.9 to 1.7.
the formula I=square root w/r gives the electric current I amperes that flows through an appliance, where W is the power in watts and R is the resistance in ohms. which set of numbers best describes the value of I for the given values of W and R? ( 42.) W=100,R=25 ( 43.)W=100,R=50
Final answer:
The value of I for the given values of W and R can be calculated using the formula I = [tex]\sqrt{(W/R)[/tex]. For W = 100 and R = 25, the value of I is 2 amperes. For W = 100 and R = 50, the value of I is approximately 1.41 amperes.
Explanation:
The formula I = [tex]\sqrt{(W/R)[/tex] gives the electric current in amperes that flows through an appliance, where W is the power in watts and R is the resistance in ohms.
To determine the value of I for the given values of W and R, we can simply substitute the values into the formula. For the first set of numbers, W = 100 and R = 25:
[tex]I = \sqrt{(100/25)} = \sqrt{(4)} = 2[/tex] amperes.
For the second set of numbers, W = 100 and R = 50:
[tex]I = \sqrt{(100/50)} = \sqrt{(2) }[/tex]≈ 1.41 amperes.
Therefore, the value of I for the first set of numbers (W = 100, R = 25) is 2 amperes, and the value of I for the second set of numbers (W = 100, R = 50) is approximately 1.41 amperes.
EASY 5 POINTS REALLY NEED HELP RN!!!! Which expression finds the length of side x in this right triangle?
Answer:
Top right one
Step-by-step explanation:
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Angle BCA is congruent to angle DAC, and angle BAC is congruent to angle DCA by:
the vertical angle theorem.
the alternate interior angles theorem.
the reflexive property.
None of the choices are correct.
Angle BAC is congruent to angle DCA by the alternate interior angles theorem. Option B is correct.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
here,
The pro[perty of parallel lines states that when two parallel lines intersect by the same transversal line the alternate interior angle will be equal as also the alternate exterior angles.
So,
Line BC and AB are parallel lines and AC is a transversal line,
So,
Angle BAC = angle DCA
Thus, angle BAC is congruent to angle DCA by the alternate interior angles theorem. Option B is correct.
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If m and n are positive integers such that the greatest common factor of [tex] m^{2} n^{2}[/tex] and [tex] m n^{3}[/tex] is 45, then which of the following could n equal?
(A) 3
(B) 5
(C) 9
(D) 15
(E) 45
There is a value of a such that subtracting a-4 from 4a+16 gives an answer of -25. What is that value of a?
Look at the radian measure for every 30 degrees and 45 degrees in the Unit Circle. Explain how finding the exact measure in quadrant one can help you determine the remaining exact radian measures.
Suppose there is a test for esophageal cancer that is 95% accurate both on those that do and those that do not have esophageal cancer. if 0.7 percent of the population has esophageal cancer, compute the probability that a person has this cancer, given that his or her test results indicates so.
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