Answer:
[tex]log_5125=3[/tex]
Step-by-step explanation:
Given : [tex]log_5125[/tex]
We have to find the value of [tex]log_5125[/tex]
Consider the given expression [tex]log_5125[/tex]
Rewrite 125 in power- base form, [tex]125=5^3[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]
[tex]\log _5\left(5^3\right)=3\log _5\left(5\right)[/tex]
[tex]=3\log _5\left(5\right)[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1[/tex]
[tex]\log _5\left(5\right)=1[/tex]
[tex]3\log _5\left(5\right)=3[/tex]
Thus, [tex]log_5125=3[/tex]
The value of log_5 125 is 3.
We have,
To find the value of log base 5 of 125, we need to determine the exponent to which we need to raise 5 to obtain 125.
In other words,
What power do we need to raise 5 to in order to get 125.
So,
By evaluating 5³ (5 raised to the power of 3), we find that 5³ = 125.
So, log base 5 of 125 is equal to 3, as log base 5 of 125 = 3.
So,
log base 5 of 125 equals 3 because 5 raised to the power of 3 gives us 125.
Thus,
The value of log_5 125 is 3.
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Two standardized tests, a and b, use very different scales of scores. the formula upper a equals 40 times upper b plus 50a=40×b+50 approximates the relationship between scores on the two tests. use the summary statistics for a sample of students who took test b to determine the summary statistics for equivalent scores on test
a. lowest score equals= 2121 mean equals= 2929 standard deviation equals= 22 q3 equals= 2828 median equals= 2626 iqr equals= 66 find the summary statistics for equivalent scores on test
a. lowest scoreequals= nothing meanequals= nothing standard deviationequals= nothing q3equals= nothing medianequals= nothing iqrequals= nothing
Final answer:
Using the transformation formula a = 40×b + 50, we calculated equivalent scores on Test A based on the given summary statistics of Test B, demonstrating the effects of linear transformation on statistical measures.
Explanation:
Using the formula a = 40×b + 50, we can calculate the equivalent scores on test A from the given summary statistics for test B. This formula allows us to transform the scores from one scale to another, maintaining the distribution's shape but adjusting the scale and location.
Lowest score on Test A = 40×(21) + 50 = 890Mean score on Test A = 40×(29) + 50 = 1,210Standard deviation remains unchanged as we are scaling and shifting the data. So, it is 40×(22) = 880.Q3 (third quartile) on Test A = 40×(28) + 50 = 1,170Median on Test A = 40×(26) + 50 = 1,090IQR (Interquartile range) remains constant as it's a measure of spread, not affected by linear transformations. So, it would be 40×(6) = 240.By applying linear transformation to the test scores, we can effectively compare results from tests using different scales, making it easier for educational institutions and researchers to evaluate data cohesively.
solve w = 9x + 5y for y
To solve the equation w = 9x + 5y for y, subtract 9x from both sides to get w - 9x = 5y. Then, divide every term by 5 to obtain y = (w - 9x) / 5
Explanation:To solve the equation w = 9x + 5y for y, you should first isolate y on one side of the equation. This involves a series of steps.
Start by subtracting 9x from both sides of the equation. This will give you w - 9x = 5y.Next, divide every term in the equation by 5 to solve for y. This would give you (w - 9x) / 5 = y or y = (w - 9x) / 5.Now, the equation has been solved for y, meaning you can now substitute any values for w and x into this equation to find the corresponding value for y.
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Is y=4x+x a linear equation
If p = .9, what is the frequency of the heterozygote? .81+(2)(.9)(.1) + (.01) .10 .81 + .18 .18
Approximately how many years are needed to double a $500 investment when interest rates are 13.50 percent per year? (Round your answer to 2 decimal places)
Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax), while employers paid another 6.2%. How much will someone earning $45,000 a year pay towards social security out of their gross wages?
Answer:
The answer is $1890.
Step-by-step explanation:
Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax)
While employers paid another 6.2%.
So, someone earning $45000, will pay [tex]0.042\times45000=1890[/tex] dollars in FICA.
The question says only individual. The earnings are exclusive to employees, so they will only pay from earnings. The employer will not pay from employee's earnings.
The answer is $1890.
The number of earnings towards social security should be $1,890.
Given that,
The employers in 2012 paid 4.2%.The employer should paid 6.2%.And, the earning should be $45,000.Based on the above information, the calculation is as follows:
[tex]= 4.2\% \times \$45,000[/tex]
= $1,890
Therefore we can conclude that the number of earnings towards social security should be $1,890.
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Write a word problem for the absolute value
The absolute value is useful in solving problems involving distance, temperature, and error in measurement. The word problem is described below.
A word problem involving absolute value is as following:
John lives 3 blocks away from his school.
One day, he walked to school and noticed that he accidentally left his backpack at home.
He decided to go back home to get it. When John got back home, he realized that he forgot his backpack was actually in his car.
John's car is parked 5 blocks away from his house. How far did John walk in total?
To solve this problem, we need to use absolute value.
John walked 3 blocks to school, then back home, and then 5 blocks to his car.
The total distance he walked would be the absolute value of the difference between the distance from school to home and the distance from home to car:
|3 - 5| = 2
Therefore, John walked a total of 2 blocks that day.
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Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
she gets 145 every week, but paid every other week
so 145 *2 = 290
her pay check will increase by $290
The linear function c = 2 y + 29 models the average cost of a haircut in a certain city, where c, is the average price of a haircut y years after 1995. find the slope for the model. then describe what this means in terms of the rate of change in the average cost of a haircut over time
The rate of change implies that the city's haircut prices are consistently going up over time.
The given linear function is c=2y+29, where c represents the average cost of a haircut y years after 1995.
The slope of the linear function, 2, reflects the rate of change in the average cost of a haircut over time.
This means that for each year after 1995, the average cost of a haircut increases by $2. In other words, the slope indicates that the cost of haircuts is rising at a constant rate of $2 per year. This steady increase implies that the city's haircut prices are consistently going up over time.
The positive slope signifies that the average cost is consistently moving upward as the year progresses. Customers can expect to pay, on average, $2 more for a haircut each year compared to the previous year.
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The slope of the linear function c = 2y + 29 is 2, indicating that the average cost of a haircut increases by 2 units for every 1 increase in the number of years after 1995.
Explanation:The slope of a linear function represents the rate of change. In the given linear function c = 2y + 29, the slope is the coefficient of y, which is 2. This means that for every 1 increase in y (number of years after 1995), the average cost of a haircut will increase by 2 units.
A bridge club had 22 members with a mean age of 68. Then two new members joined. One was 62 years old, and the other was 80 years old. How did the mean age change after they joined?
5x + 20 = y 5x + 20 = 70 5x = 50 x = 10 Jack has a business mowing lawns and charges a flat fee of $20 per yard, plus an additional $5 an hour. He wants to make sure that he makes at least $70 doing yard work for a client with a very large yard. He sets up and solves the equation above. What does his solution of 10 mean? A) He needs to mow at least 10 yards. B) He needs to work for at least 10 days for this client. C) He needs to work at least 10 hours in the client's yard. D) He needs to charge and additional $10 an hour for this client.
Answer:
C
Step-by-step explanation:
$74.95 jacket; 5% tax
the selling price of a refrigerator, is $471.45. if the markup is 5% OF THE DEALER cost, what is the dealers cost of the refrigerator
What type of number is -12.123 repeating?
Choose all that apply.
Whole number
Integer
Rational
Irrational
Answer:
Rational
Step-by-step explanation:
The following diagram shows that all whole numbers are integers, and all integers are rational numbers. Numbers that are not rational are called irrational.
Hint #22 / 4
\green{\text{Whole numbers}}Whole numbers start color #28ae7b, start a text, W, h, o, l, e, space, n, u, m, b, e, r, s, end text, end color #28ae7b are numbers that don't need to be represented with a fraction or decimal. Also, whole numbers cannot be negative.
\blue{\text{Integers}}Integersstart color #6495ed, start a text, I, n, t, e, g, e, r, s, end text, end color #6495ed are whole numbers but can also be negative.
\purple{\text{Rational numbers}}Rational numbersstart color #9d38bd, start text, R, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end text, end color #9d38bd are numbers that can be expressed as a fraction of two integers. Keep in mind that the denominator cannot be equal to 000!
\pink{\text{Irrational numbers}}Irrational numbersstart color #ff00af, start text, I, r, r, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end text, end color #ff00af are numbers that cannot be expressed as a fraction of two integers.
Hint #33 / 4
Now, let's answer the question.
-0.\overline{12}−0.
12
minus, 0, point, start overline, 12, end overline is not a whole number because it needs to be represented with a fraction or decimal.
For this same reason, -0.\overline{12}−0.
12
minus, 0, point, start overline, 12, end overline is not an integer.
-0.\overline{12}−0.
12
minus, 0, point, start overline, 12, end overline is a rational number because it can be represented as a fraction of two integers \left(-\dfrac{4}{33}\right)(−
33
4
)left parenthesis, minus, start fraction, 4, divided by, 33, end fraction, right parenthesis.
Hint #44 / 4
The following number type applies to -0.\overline{12}−0.
12
minus, 0, point, start overline, 12, end overline :
Rational
The number -12.123 repeating is rational
What is Number system?A number system is defined as a system of writing to express numbers.
-12.123 repeating is a rational number.
A rational number is any number that can be expressed as a ratio of two integers (i.e. a fraction), where the denominator is not zero.
In this case, we can express -12.123 repeating as the fraction:
-12.123... = -12123/1000
Since -12123 and 1000 are both integers, and the denominator is not zero, -12.123 repeating is a rational number.
Hence, the number -12.123 repeating is rational
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The probability that a corporation made profits in 2005 is 0.78 and the probability that a corporation made charitable contributions in 2005 is 0.23. assuming that these two events are independent, the probability (rounded to 4 decimal places) that a corporation made profits in 2005 or made charitable contributions in 2005, but not both is:
(×2+1)(x3+2x)(x2+4x-16i-4xi) Solve for the roots in equation
A submarine took 16 minutes to reach a depth of 96 meters below the surface of the water. Which integer best represents the rate of the submarines dive
List five staple convenience goods that you or your household buys on a regular basis. (you do not need to use complete sentences. 2.5 points)
The five staple convenience goods are:
Food items,
Petrol,
Detergents,
Drinking water, and
Fruits.
Staple convenience goods are those items that are purchased by consumers on a regular basis because they are constantly used by them.
These items are readily available nearby a domestic environment because they are always on a high demand by consumers.
These goods listed above are called staple convenience goods because they share some common features which include:
These goods can be bought in small quantity especially when needed.These goods doesn't require a purchase plan before they are bought.They are bought frequently and regularly.Learn more here:
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Find the exact circumference of a circle with the given radius. 3½ cm C = 7.5π cm 7π cm 6.25π cm
Answer:
(B) [tex]7{\pi}cm[/tex]
Step-by-step explanation:
We are given the radius of the circle that is equal to [tex]3\frac{1}{2}cm[/tex].
Now, circumference of circle is given as:
[tex]C=2{\pi}r[/tex]
[tex]C=2{\pi}(3\frac{1}{2})[/tex]
[tex]C=2{\pi}(\frac{7}{2})[/tex]
[tex]C=7{\pi}cm[/tex]
Therefore, the circumference of the circle is [tex]7{\pi}cm[/tex].
Hence, option B is correct.
Nate went on a trip, and he used a table of values to repeatedly record the time he had been traveling and the distance from his destination. The function represented by the table of values is linear, and the rate of change is 50 miles per hour. Which of these statements is correct?
Answer: b. with any pair of values for time and distance, it is possible for Nate to determine the initial value by repeatedly subtracting 50, if necessary.
Step-by-step explanation: i took the unit test. hope this helps<33
Answer:
B
Step-by-step explanation:
edge 2021
Helen's preferences over cds (c) and sandwiches (s) are given by u(s,
c.= sc + 10(s + c), with muc = s + 10 and mus = c + 10. if the price of a cd is $9 and the price of a sandwich is $3, and helen can spend a combined total of $30 each day on these goods, find helen's optimal consumption basket.
A container holds 5 gallons of juice. How much is this in pints?
5 gallons is 40 pints.
Hope this helps!
The table of values below represents a linear function and shows the amount of money in a tip jar at a dry cleaners since the dry cleaners opened for the day. How much was in the tip jar when the dry cleaners opened?
A linear equation has a standard form of:
y = mx + b
where in this case,
y = amount of money in tip jar, m = slope, x = number of hours, b = y intercept
We select any two paired data to calculate for the slope:
m = (y2 – y1) / (x2 – x1)
m = (18.25 – 15.50) / (5 – 4)
m = 2.75
y = 2.75x + b
Choosing any one data pair to calculate for b the y-intercept:
15.50 = 2.75 (4) + b
b = 4.5
Therefore there was $4.50 in the tip jar during the opening.
Answer: $4.50
Answer:
4.50
Step-by-step explanation:
from the table, we can tell the tip increases by 2.75 per hour
the 3rd hour: 15.50-2.75=12.75
the second hour: 12.75-2.75=10.00
the 1st hour: 10.00-2.75=7.25
the 0 hour: 7.25-2.75=4.50
so there was 4.50 in the jar
When an opinion poll calls landline telephone numbers at random, approximately 30% of the numbers are working residential phone numbers. the remainder are either non-residential, non-working, or computer/fax numbers. you watch the random dialing machine make calls. x is the number of calls until the first working residential number is reached. does x have a binomial distribution? give your reasons?
The measures of a sphere with a volume of 972pi in^3 are multiplied by 1/3.
What is the volume of the sphere?
A) 324pi in^3
B) 108pi in^3
C) 54pi in^3
D 36pi in^3
you are a geologist assigned to estimate the density of the Earth. look at picture for the full question:
The ladybugs are planting a garden. They have 25-cm-by-10 cm rectangle for flowers. Each flower needs exactly 1 square centimeter for space. How many flowers can they plant?
Answer: They can plant 250 flowers.
Step-by-step explanation:
Given : The dimension of the rectangular garden = 25-cm-by-10 cm
[i.e. length by width]
Area of rectangle = length x width
⇒ Area of rectangular garden = 25 x 10 = 250 square centimeter .
Area required by each flower = 1 square centimeter
Then, the number of flowers they can plant = [tex]\dfrac{\text{Area of garden}}{\text{Area of needed by each flower}}[/tex]
[tex]=\dfrac{250}{1}=250[/tex]
Hence, they can plant 250 flowers.
The boy : Girl ratio is 4:5. If there are 225 students, how many girls are in the school? answer and proportion answer and proportion breakdown please
(b) the water level drops at a rate of 0.1 cm per hour. at what rate is the radius of the water decreasing when the depth is 4 cm? round your answer to four decimal places.
The rate at which the radius of the water is decreasing when the depth is 4 cm is 0.6949 cm/hr.
Explanation:To find the rate at which the radius of the water is decreasing, we can use the chain rule from calculus. Let's denote the depth of the water as 'h' and the radius as 'r'. We are given that the water level drops at a rate of 0.1 cm per hour, so dh/dt = -0.1 cm/hr. We want to find dr/dt when h = 4 cm. Using the formula for the volume of a cone, V = (1/3)πr^2h, we can find the relationship between r and h: r = √((3V)/(πh)). Taking the derivative of this equation with respect to time, we have: dr/dt = (√((3V)/(πh)))' = -(3/2)(√((3V)/(πh^3)))(dh/dt). Plugging in the given values and solving for dr/dt when h = 4 cm, we get:
dr/dt = -(3/2)(√((3(350))/(π(4)^3)))(-0.1) = 0.6949 cm/hr
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Name the property illustrated be each statement. (3x+2)-5=(3x+2)-5