The commutative property in mathematics says that the order in which numbers are multiplied doesn't change the product. For example, using the commutative property, the product of 13 x 7 x 21 will be the same as 7 x 21 x 13, which is 1911.
Explanation:The commutative property is a fundamental concept in Mathematics which states that for multiplication and addition, numbers can be moved around (or commuted) without changing the result. For example, if you have the multiplication problem 13 * 7 * 21, thanks to the commutative property, you can rearrange this problem to: 7 * 21 * 13 or 21 * 13 * 7 or any other arrangement of these three numbers, and the result will remain the same.
Let’s see this in action:
Original arrangement: 13 * 7 * 21 = 1911
Changed arrangement: 7 * 21 * 13 = 1911
As you can see, regardless of how the terms were rearranged, the answer remained the same, thus demonstrating the commutative property.
https://brainly.com/question/5637942
#SPJ11
The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to represent the first three terms, respectively.] The three number are __, __, and __
Answer:
2r²-5r+2=0
a=2
b=-5
c=2
Step-by-step explanation:
if you throw a rubber ball toward the ground at an angle, it will bounce up feom the ground at the same angle. find the unknown angle measure in the drawing at the right.
Experts/ace/geniuses helppp asapp
look at clock blair arrived a the bus stop at 45 minutes ago what time did blaire arive at the bus stop?
Find the general form of the complete partial fraction decomposition of the integrand. use it to determine whether or not a term of each type listed below occurs in the complete partial fraction decomposition. select true if it does occur and false if it does not.
What is the sum of the numbers in the series below? 15 + 11 + 7 + . . . + (–129)
The sum of the numbers in the series is -8208.
Explanation:The sum of a series can be found using the formula for the sum of an arithmetic series, which is given by:
Sum = (n/2)(first term + last term),
where n is the number of terms and the first and last terms are provided in the series. In this case, the first term is 15 and the last term is -129. The common difference between each term is -4.
Using the formula, we have:
Sum = ([-129 - 15]/2)(15 + -129) = (-144/2)(-114) = 72 * -114 = -8208.
Therefore, the sum of the numbers in the series is -8208.
A car rental agency charges $50 per week plus $0.50 per mile to rent a car. What is the weekly cost to rent the car, f, as a function of the number of miles driven during the week, x. How many miles did you drive during the week if the weekly cost to rent the car was $100?
The weekly cost to rent the car, f, as a function of the number of miles driven during the week, x, is f = 50 + 0.50x. If the weekly cost to rent the car was $100, the number of miles driven during the week is 200 miles.
Explanation:The weekly cost to rent the car, f, as a function of the number of miles driven during the week, x, can be calculated using the formula f = 50 + 0.50x. This is because the car rental agency charges $50 per week plus $0.50 per mile. To find the number of miles driven during the week if the weekly cost to rent the car was $100, we can substitute f = 100 into the formula and solve for x:
100 = 50 + 0.50x
50 = 0.50x
x = 100/0.50
x = 200
Therefore, the number of miles driven during the week is 200 miles.
Learn more about Calculating weekly cost and miles driven here:https://brainly.com/question/34287171
#SPJ3
20 pt question on angles plz help
Find the slope and y-intercept fotv
# 12 Q please find the volume
The equation of a hyperbola is 5x2 − y2 = 25. What is the area of the asymptote rectangle?
If w = <3.5, -6> and z = <-1.5, -4>, what is the resulting vector for 2w − z?
Answer:
C. <8.5, -8>
Step-by-step explanation:
for PLATO users
find the surface area of the solid formed by the net
What are the relationships among radii, chords, tangents, and inscribed angles?
Hey can you please help me posted picture of question
For the data set below, compute the standard deviation. Round to the nearest hundredth. 2, 3, 5, 8 2.03 2.20 2.6 4.5
To calculate the standard deviation, compute the mean, subtract it from each data point, square the results, average those and take the square root. Round to the nearest hundredth, and for one standard deviation below the mean, subtract the standard deviation from the mean.
Explanation:To calculate the standard deviation of a data set, you can use a calculator or a computer. The formula for standard deviation is the square root of the variance, which is the average of the squared differences between each data point and the mean of the data set. Let's compute the mean and standard deviation of the provided data set: 2, 3, 5, 8, 2.03, 2.20, 2.6, 4.5.
Calculate the mean (average) of the data.Subtract the mean from each data point and square the result.Find the average of these squared differences.Take the square root of this average to get the standard deviation.
You may round the standard deviation to the nearest hundredth as requested.
To find the value that is one standard deviation below the mean, subtract the standard deviation from the mean.
icole wants to buy a pair of jeans. The original cost of the jeans is $42.50, and the markup is 10 percent. How much will she have to pay for the jeans? $44.50 $46.75 $52.50
The length of the shorter base in an isosceles trapezoid is 4 in, its altitude is 5 in, and the measure of one of its obtuse angles is 135°. Find the area of the trapezoid.
Answer:
45
Step-by-step explanation:
The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. she performs a two-tail test of the null hypothesis that the mean for the stressed oak furniture is 650. the calculated value of the z test statistic is a positive number that leads to a p-value of 0.080 for the test. 22 referring to scenario 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650. what would be the p-value of this one-tail test? 0.040 0.960 0.840 0.160
Final answer:
The p-value for the one-tailed test, with the alternative hypothesis that the mean is greater than 650, is half the two-tailed p-value. Hence, the one-tailed p-value is 0.040.
Explanation:
The quality control engineer initially performed a two-tailed test with the null hypothesis that the mean force necessary to produce cracks in stressed oak furniture is 650. The calculated z-test statistic led to a two-tailed test p-value of 0.080. If the engineer had chosen an alternative hypothesis that the mean was greater than 650, the test would have been a one-tailed test. In a one-tailed test, you would only consider the probability on the side of the distribution that corresponds to the alternative hypothesis. Therefore, since the original two-tailed p-value was 0.080, for the one-tailed test, we would take half of that value which results in a p-value of 0.040.
A statistician observes the number of heads that occur when a coin is tossed 1000 times
HOW CAN YOU WRITE THE EQUATION OF A LINE THAT IS PARALLEL AND/OR PERPENDICULAR TO ANOTHER LINE USING A POINT ON THAT LINE.?
A map has the scale 2 centimeters = 1 kilometer. on a map, the area of a forest preserve is 3.8 square centimeters. what is the area of the actual forest preserve
To find the actual area of the forest preserve, the map area of 3.8 cm² is multiplied by the scale ratio squared (0.25 km²/cm²), resulting in an actual area of 0.95 km².
Explanation:The area of the actual forest preserve can be calculated by using the scale given, which is 2 centimeters = 1 kilometer. First, we need to convert the area on the map into the actual area using this scale. Since the scale is linear and the area is measured in square units, we need to square the scale ratio to convert the area on the map to the actual area.
To do this conversion we consider that the scale of 2 cm : 1 km means that every 1 cm on the map is equivalent to 0.5 km (since 2 cm is 1 km). Therefore, for the area, we get the following ratio: (1 cm² = 0.5 km) × (1 cm² = 0.5 km), which simplifies to 1 cm² = 0.25 km². Now, we can find the actual area of the forest preserve by multiplying the 3.8 cm² area on the map by the value of each square centimeter in real-life units, which is 0.25 km².
Actual area = Map area × Scale ratio squared
= 3.8 cm² × 0.25 km²/cm²
= 0.95 km².
Therefore, the forest preserve has an actual area of 0.95 square kilometers.
To date, Ty has cumulative earnings of $107,600. This week he is paid $3,000. What's the total amount of social security tax for this week? Assume a rate of 6.2% on $110,100 for social security and 1.45% for Medicare.
A. $186.00
B. $155.00
C. $180.00
D. $57.66
Final answer:
The total Social Security tax for Ty's earnings this week, given his total earnings are now $110,600, is $155.00. This calculation considers the Social Security tax rate of 6.2% up to the income threshold of $110,100. Thus, option B is correct.
Explanation:
The question involves calculating the Social Security tax for Ty's earnings this week. With cumulative earnings to date at $107,600 and an additional $3,000 this week, Ty's total earnings for the year are now $110,600.
Since the Social Security tax rate is 6.2% and applies only up to an income of $110,100, we will only apply the tax rate to the $110,100 threshold, not the full $110,600. The week's Social Security tax is then:
0.062 × $110,100 = $6,826.20 (for the entire year so far)
Since we only need to find out the tax for this week's earnings, we need to calculate the tax that was already paid on the first $107,600:
0.062 × $107,600 = $6,671.20
The additional Social Security tax for this week is the difference between the two:
$6,826.20 - $6,671.20 = $155.00
Therefore, the total Social Security tax for this week is $155.00, which corresponds to option B.
The total amount of Social Security tax for Ty this week is $155.00. Hence, the correct option is B.
To calculate the total amount of Social Security tax for Ty this week, we must apply the 6.2% rate to his weekly pay of $3,000. However, since his cumulative earnings to date are $107,600 and the Social Security tax applies only up to $110,100, we need to determine how much of his $3,000 weekly salary is subject to this tax.
To find this, we subtract his current earnings from the maximum amount that is subject to Social Security tax: $110,100 - $107,600 = $2,500. Only $2,500 of Ty's $3,000 salary is taxable for Social Security purposes since he has reached the threshold beyond which Social Security tax is not levied on additional income.
Therefore, this week's Social Security tax is 6.2% of $2,500, which equals $155.00. As the rate for Medicare does not cap, the full $3,000 is subject to the Medicare tax at a rate of 1.45%, leading to a Medicare tax amount of $43.50. However, as the question only asks for the Social Security tax, the answer is B. $155.00.
10q-3r=14 write a formula for g (r) in terms of r
Answer:
3/10r +7/5
Step-by-step explanation:
10q−3r=14
10q=3r-14
10q=3r/10 +14/10
q=3/10r+7/5
To find g(r) in terms of r, the equation 10q-3r=14 is manipulated algebraically to isolate q as g(r)=(14+3r)/10.
Explanation:The student's question involves solving a linear equation for a variable. This is a standard algebraic task often encountered in high school mathematics. The student is given the equation 10q-3r=14 and is asked to write a formula for g(r) in terms of r, implying a need to solve for q as a function of r, which can be named g(r).
To isolate q, we perform algebraic manipulations:
First, add 3r to both sides of the equation to get 10q = 14 + 3r.Next, divide both sides of the equation by 10 to solve for q, which gives us q = (14 + 3r) / 10.Last, we rename q as g(r) which results in the final function: g(r) = (14 + 3r) / 10.This function represents q in terms of r, and g(r) is thereby defined.
hey can you please help me posted picture of question
hey can you please help me posted picture of question
In a random sample survey of 80 students at Torrey’s middle school, 24 students said that math was their favorite subject. There are a total of 300 students at this middle school. Based on the survey, which value is the BEST estimate for the number of students who would say that math is their favorite subject?
Final answer:
Based on the survey where 30% of 80 students favored math, the best estimate for the total number of students preferring math out of 300 at the middle school is 90 students.
Explanation:
In a random sample survey of 80 students at Torrey's middle school, 24 students said that math was their favorite subject. This represents 30% of the surveyed group (24 out of 80 students). To estimate the number of students who would say that math is their favorite subject throughout the entire middle school, we can use this percentage.
To find the estimated number of students who favor math in the whole school, which has 300 students, we apply the 30% to the total school population:
Total number of students: 300Percentage favoring math: 30%Estimated number of students favoring math: 300 students * 0.30 = 90 studentsTherefore, the best estimate for the number of students who would say that math is their favorite subject at this middle school is 90 students.
The circle shown here has area πr2. If its radius is tripled in length its new area will be
20 points math pls help brainliest.
Which table matches the function shown in the graph?
Which table matches the function shown in the graph?
number 1 is a
number 2 d
What is the domain of the step function f(x) = ⌈2x⌉ – 1?
The domain of the given step function is:
The set of all the real numbers.
Step-by-step explanation:Ceiling function--
The ceiling function also known as the least integer function is the function which takes the largest value of the integer for a non-integer number which lie between the two integers , and gives the integer itself if the number is integer.
and it is given by:
[tex]f(x)=\left \lceil x \right \rceil[/tex]
(
For example--
if x= 0.5
then f(x)=1 since x lie between 0 and 1
if x= -2.5
Then f(x)= -2
since x lie between -3 and -2.
if x=3
then f(x)=3 )
Also, the function is defined for all real values of x.
i.e. The domain of such a function is: All real numbers.
The function f(x) is given by:
[tex]f(x)=\left \lceil 2x \right \rceil-1[/tex]
Hence, the domain is all the real numbers.