The given triangle is obtuse triangle according to the corollary to the converse of the Pythagorean Theorem.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The triangle's longest side measures 15 units in length.
Compare the sum of the squares on the other two sides to the square that is the length of the longest side.
The square of the longest side is 15², which equals 225.
9² + 10² = 181 square units make up the sum of the squares on the other two sides.
Thus, 181 < 15².
As a result, the triangle is an obtuse triangle according to the corollary to the converse of the Pythagorean Theorem.
To learn more about Pythagorean Theorem from given link
https://brainly.com/question/343682
#SPJ1
help please she didn’t teach us thistle
Answer:
12x^4y^7
Step-by-step explanation:
base(b)=8x^3y^5
height(h) =3xy^2
Area= (b x h)/2 =12x^4y^7
Answer:
[tex]A = 12x^4y^7[/tex]
Step-by-step explanation:
The formula for the area of a triangle is:
[tex]A = \dfrac{1}{2}bh[/tex]
where [tex]b[/tex] is the length of the triangle's base and [tex]h[/tex] is the length of the triangle's height.
In this problem, we are given the length of the base of the triangle as [tex]8x^3y^5[/tex] and the length of the height of the triangle as [tex]3xy^2[/tex].
Thus, the area of the given triangle is:
[tex]A = \dfrac{1}{2} \cdot 8x^3y^5 \cdot 3xy^2[/tex]
We can simplify this by combining like terms and using the exponent addition rule ([tex]x^a \cdot x^b = x^{a+b}[/tex]).
[tex]A =\left(\dfrac{1}{2} \cdot 8 \cdot 3 \right)(x^3 \cdot x)(y^5 \cdot y^2)[/tex]
[tex]A = (4 \cdot 3)(x^{3 + 1})(y^{5+2})[/tex]
[tex]A = 12x^4y^7[/tex]
Use a graphing utility to graph the function to approximate (to two decimal places) any relative minima or maxima of the function. (If an answer does not exist, enter DNE.)
h(x) = x3 − 6x2 + 16
Answer:Use a graphing utility to graph the function and approximate (to two decimal places) any relative minima or maxima. (If an answer does not exist, enter DNE.)
f
(
x
)
=
x
3
−
3
x
2
−
x
+
3
relative minimum
(
x
,
y
)
=
c
Step-by-step explanation:
there's a simple rule that allows us to convert a number from the binary system to the decimal. for example, 42
The rule for converting a binary number to Decimal point is to multiply each binary digit by two to the power of its position from the right, and add all the resulting values together. For example, 42 in binary is 101010, so the conversion is 1*2^5 + 0*2^4 + 1*2^3 + 0*2^2 + 1*2^1 + 0*2^0 = 32 + 8 + 2 = 42.
1. Start with the rightmost binary digit (the ones place) and multiply it by 2^0.
2. Move to the next digit to the left (the twos place) and multiply it by 2^1.
3. Continue this process until you reach the leftmost binary digit.
4. Add all the products together to get the decimal equivalent.
For example, 42 in binary is 101010, so the calculations are: 0*2^0 + 1*2^1 + 0*2^2 + 1*2^3 + 0*2^4 + 1*2^5 = 0 + 2 + 0 + 8 + 0 + 32 = 42.
The rule for converting a binary number to decimal is to multiply each binary digit by two to the power of its position from the right, and add all the resulting values together. To do this, start with the rightmost binary digit (the ones place) and multiply it by 2^0. Then move to the next digit to the left (the twos place) and multiply it by 2^1. Continue this process until you reach the leftmost binary digit. Add all the products together to get the decimal equivalent. For example, 42 in binary is 101010, so the calculations are:
0*2^0 + 1*2^1 + 0*2^2 + 1*2^3 + 0*2^4 + 1*2^5 = 0 + 2 + 0 + 8 + 0 + 32 = 42.
Learn more about Decimal point here
https://brainly.com/question/20753759
#SPJ4
What proportion of the variation iny can be explained by the variation in the values of x? Report answer as percentage accurate to one decimal place: (If the answer is 0.84471 _ then it would be 84. 5%6 .. syou would enter 84.5 without the percent symbol:) r^2 =
A. To find the correlation coefficient, we can use the formula:
r = (n * Σxy - Σx * Σy) / √ ((n * Σx² - (Σx)²) * (n * Σy² - (Σy)²))
Where n is the number of data points.
Plugging in the values for the given data set:
r = (12 * 712.94 - 1451.9 * 511.6) / √ ((12 * 1297.14 - 1451.9²) * (12 * 636.35 - 511.6²))
r = -0.636
So, the correlation coefficient is -0.636.
B. To find the proportion of the variation in y that can be explained by the variation in x, we can use the formula:
r² = r²
r² = (-0.636) ²
r² = 0.40496
So, 40.5% of the variation in y can be explained by the variation in the values of x.
C. To find the regression line,we can use the formula:
y = a + bx
Where a is the y-intercept and b is the slope of the line.
To find b, we can use the formula:
b = (n * Σxy - Σx * Σy) / (n * Σx² - (Σx)²)
Plugging in the values for the given data set:
b = (12 * 712.94 - 1451.9 * 511.6) / (12 * 1297.14 - 1451.9²)
b = -0.856
To find a, we can use the formula:
a = (Σy - b * Σx) / n
Plugging in the values for the given data set:
a = (511.6 - -0.856 * 1451.9) / 12
a = 55.54
So, the regression line is:
y = 55.54 - 0.856x
The negative slope of -0.856 means that as x increases, y decreases, which is consistent with the negative correlation coefficient of -0.636. The y-intercept of 55.54 means that when x is 0, y is predicted to be 55.54.
Complete question:
Run a regression analysis on the following bivariate set of data with y as the response variable.
x y
43.8 54.1
41.3 51.2
35.3 60.1
48.1 44.9
42.8 51.8
44.7 50.8
39.4 56.6
38.2 56.6
40.7 53.5
45.3 51.1
45 46.7
41.1 52.2
A. Find the correlation coefficient and report it accurate to three decimal places.
r = ________________
B. What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.)
r² =_______________ %
C. Based on the data, calculate the regression line (each value to three decimal places)
y =___________ x + _______________
To learn more about correlation coefficient:
https://brainly.com/question/4219149
#SPJ4
please help due tn!!
Answer:
Step-by-step explanation:
Answer:
244.5
Step-by-step explanation:
Use A Budgeting Calc This Anwser Is Correct
3xsquared minus 5 equals negative 5x minus 3
Answer:
see below
Step-by-step explanation:
3²-5 = -5x-3
9-5 =- 5x-3
-5x = 7
so x= -7/5
Charisse is adding a weather protective stain to the exterior of her shed. She measures the walls to be 8 feet long and 6 feet high. There are no windows on the shed, and the roof and the bottom do not need the protective stain. Additionally, the front door, which is 3 feet wide and 6 feet high, does not need to be stained. What is the total surface area Charisse needs to stain? Multiple choice question. cross out A) 66 ft2 cross out B) 144 ft2 cross out C) 174 ft2 cross out D) 192 ft2
Charisse needs to stain an area of 174 square feet.
How to calculate the total surface area Charisse needs to stain?
The total surface area of the shed's walls that needs to be stained is the sum of the areas of the four walls, minus the area of the front door.
The area of one wall is 8 feet × 6 feet = 48 square feet.
Since there are 4 walls, the total area of all walls is 48 square feet × 4 = 192 square feet.
The area of the front door is 3 feet × 6 feet = 18 square feet
Now we can subtract the area of the door from the total area of all walls:
192 square feet - 18 square feet = 174 square feet
Learn more about total surface area on:
brainly.com/question/16519513
#SPJ1
Explain how the commutative property is applied when finding GCF using factor trees
Answer: The commutative property is applied when finding the GCF by taking the factor that has more than 1 factor other than itself(composite) and multiply them until you can no longer multiply. You then take the factors that are in common and multiply them.
Step-by-step explanation: my teacher made me use this way.
A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 6 in. and a base of 10 in. The area of the hexagonal base is 259.8 in².
What is the surface area of the pyramid?
The surface area of the hexagonal pyramid is S = 575.9 inches²
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
Let the surface area of the hexagonal pyramid be S
Now , the equation will be
The base of the hexagonal pyramid a = 10 inches
The height of the lateral face h = 6 inches
The base area of the pyramid = ( 3√3 / 2 )a²
The lateral surface area of the pyramid = 3a √ ( ( 3a²/4 ) + h² )
So , The total surface area of hexagonal pyramid is S
S = ( 3√3 / 2 )a² + 3a √ ( ( 3a²/4 ) + h² )
Substituting the values in the equation , we get
The base area of the pyramid = 259.8 inches²
The lateral surface area of the pyramid = 3 ( 10 ) √ ( 3 ( 100/4 ) + 36 )
On simplifying the equation , we get
The lateral surface area of the pyramid = 316.1 inches²
Total surface area of hexagonal pyramid S = 259.8 inches² + 316.1 inches²
The total surface area of hexagonal pyramid S = 575.9 inches²
Hence , the surface area of the pyramid is 575.9 inches²
To learn more about surface area of pyramid click :
https://brainly.com/question/15050758
#SPJ1
Your bag of rice says to mix 1 cup of rice to 2 cups of water. How many cups of water would be needed to mix with 1/3 cup of rice?
Jenna earned $125 of interest by leaving her money in the bank for 4 years at a 5% interest rate. What was the principle amount that Jenna put in the bank
The principal amount that Jenna put in the bank is $625.
What is simple interest?Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.
Given interest earned = $125
time = 4 years
rate = 5%
let the principal be p
this is the case of simple interest,
SI = (p*r*t)/100
substitute the values
125 (p* 5 * 4)/100
125 x 100 = p x 20
p = 12500/20
p = $625
Hence principal amount is $625.
learn more about simple interests;
https://brainly.com/question/25845758
#SPJ1
the sampling distribution of the sample mean based on samples of size 2 for the population was simulated, and a histogram of the results was produced. whifh of the following histograms is most likely the histogram of the sampling distribution
The sampling distribution of the sample mean based on samples of size 2 for a population can be approximated by a normal distribution.
The histogram of the sampling distribution would therefore look like a bell-shaped curve. The mean of the sampling distribution is equal to the population mean, and the standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size (in this case, 2).
Therefore, the formula for the sampling distribution of the sample mean for a population of size 2 is:
Mean = Population Mean
Standard Deviation = Population Standard Deviation / √2
The histogram of the sampling distribution would look like a bell-shaped curve with the mean and standard deviation determined by the formula above.
Therefore, the histogram most likely representing the sampling distribution of the sample mean based on samples of size 2 for the population is a bell-shaped curve with the mean and standard deviation determined by the formula above.
Learn more about sampling distribution here:
https://brainly.com/question/29375938
#SPJ4
1.
6х6х7х7x7x7
Write using exponents
2.
-104 x -104 x -104
Write using exponents
According to the solving the exponential form of the given number is as follows:
= 6² × 7⁴
= (-104)³
How Do I Write a Formula in Exponential Form?Bases and powers are employed in the exponential form to write numbers. It informs us of the amount of times we must actually multiply a number in order to obtain the answer. When we write the number 125 as 53, for instance, we can see that it is the third power of 5, or the number 125, which looks to be a typical three-digit number when observed.
What does exponential form mean?When a single integer is multiplied by itself a certain number of times, x, the equation y takes on the base component b to the power of x, which is the quantity being multiplied, and is known as the exponential form.
According to the given information:The exponential form of the given number is :
= 6х6х7х7x7x7
= 6² × 7⁴
The exponential form of the given number is :
= -104 x -104 x -104
= (-104)³
To know more about exponential form visit:
https://brainly.com/question/30278502
#SPJ1
refer to exhibit 26-5. the data illustrate that the firm in question is a group of answer choices price taker (perfectly competitive firm). factor price taker. price searcher (monopolist, oligopolist, etc.). factor price searcher.
According to the given data, the firm in question must be a price-taker, which is a perfectly competitive firm.
A price-taker is basically an individual or a particular company that must accept prices that are prevailing in a market and lacks the market share to be able to influence the market price on its own. All the economic participants can be considered to be price-takers in a market consisting of perfect competition.
In the given data set, the marginal revenue is constant which is very typical for competitive firms. This happens because the market decides the optimal price level and companies do not have much say over the price. This is a way by which they can maximize profits.
To know more about price-taker here
https://brainly.com/question/29218058
#SPJ4
In 2007, there were 120 houses in a subdivision. The number of houses in the subdivision increased by approximately 8% per year from 2007-2017. Enter the BEST estimate of the number of houses in the subdivision in 2017.
Answer:
216
Step-by-step explanation:
2017-2007=10
8*10=80
80% of 120= 96
120+96=216
a new restaurant is interested in determining the best time-temperature combination for roasting a five-pound cut of lamb. the times to be tested are 45 minutes, 60 minutes, and 90 minutes at temperatures of 350 degrees fahrenheit and 425 degrees fahrenheit for each time, with the exception of the 90 minute - 425 degree combination. that combination is being eliminated because it will overcook the lamb, which leaves five combinations remaining. from 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. the quality of the finished product is evaluated for each roast. which of the following is true?
The two cuts that are being roasted for each time-temperature combination are an example of replication.
Option (c) is correct.
What is temperature?
Temperature is a measure of the average thermal energy of the particles in a substance. It is a scalar quantity, meaning it has only a magnitude and not a direction. The most commonly used unit of temperature measurement is the degree Celsius (°C) or the degree Fahrenheit (°F), but it can also be measured in Kelvin (K) in scientific and engineering applications.
Given options are:
(a) The two cuts that are being roasted for each time-temperature combination are an example of conduction
(b) The two cuts that are being roasted for each time-temperature combination are an example of convection
(c) The two cuts that are being roasted for each time-temperature combination are an example of replication
(d) None of the above
(c) The two cuts that are being roasted for each time-temperature combination are an example of replication.
In the question it is given that From 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. Here it is an act of copying the exact sahpe size of the lamb in all cuts, which is nothing but replication. Moreover, this replication can help in proper comparision.
Hence, The two cuts that are being roasted for each time-temperature combination are an example of replication.
Option (c) is correct.
To learn more about the temperature, visit:
https://brainly.com/question/14054025
#SPJ4
HELP ASAP! FIND LINEAR EQUATION PARALLEL TO Y = -3/4X + 1 THROUGH POINTS (8,-6)
Answer:
y = [tex]-\frac{3}{4}[/tex] x
Step-by-step explanation:
y = mx + b , where "m" is a slope and "b" is an y-intercept.
If a║b ⇒ [tex]m_{a}[/tex] = [tex]m_{b}[/tex] and [tex]b_{a}[/tex] ≠ [tex]b_{b}[/tex]
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~
y = [tex]-\frac{3}{4}[/tex] x + 1
( 8 , - 6 )
y - ( - 6 ) = [tex]-\frac{3}{4}[/tex] ( x - 8 )
y + 6 = [tex]-\frac{3}{4}[/tex] x + 6
y = [tex]-\frac{3}{4}[/tex] x
In a population of bats living in a certain region, 30 percent have a wingspan greater than 10 inches. In a random sample of 80 bats living outside of the region, 20 had a wingspan greater than 10 inches. Consider a one-sample z-test to investigate whether there is evidence that the proportion of bats with a wingspan greater than 10 inches living outside the region is different from that of the bats living in the region. Which of the following is the correct test statistic?
answer choices
z=\frac{0.30-0.25}{\sqrt{\frac{\left(0.25\right)\left(0.75\right)}{80}}}
z= 80
(0.25)(0.75)
0.30−0.25
z=\frac{0.30-0.25}{\sqrt{\frac{\left(0.30\right)\left(0.70\right)}{80}}}
z= 80
(0.30)(0.70)
0.30−0.25
z=\frac{0.25-0.30}{\sqrt{\frac{\left(0.25\right)\left(0.75\right)}{80}}}
z= 80
(0.25)(0.75)
0.25−0.30
z=\frac{0.25-0.30}{\sqrt{\frac{\left(0.25\right)\left(0.75\right)}{80}}}
z= 80
(0.25)(0.75)
0.25−0.30
z=\frac{0.25-0.30}{\sqrt{\frac{\left(0.30\right)\left(0.70\right)}{80}}}
z= 80
(0.30)(0.70)
0.25−0.30
The correct static test is [tex]$z=\frac{0.30-0.25}{\sqrt{\frac{0.30(0.70)}{80}}}$[/tex]
What is static test?Without actually running the software application's code, static testing is a type of software testing technique used to check for errors in software. The code is run to find the flaws in Dynamic Testing tests, though. To automate static testing, static testing technologies can be employed. Following are a few instances: A static testing tool like Source Eter is an example that can help with the analysis of Python, C, C++, Java, and other programming languages' code. Other static testing tools like PMD or Find Bugs can be integrated with it as well.Number of residents in a certain area with wingspan measurements larger than 10 inches = =30% = 0.30
[tex]$=p_o=30 \%=0.30$[/tex]
20 of the 80 bats in a n=80 random sample from outside the area have wingspan measurements larger than 10 inches to ascertain whether there is any variation in the proportion of bats with a wing span more than 10 inches that live outside the region and those that do.
In response to the query;
an investigation using a one-sample z-test,
The following definition applies to the hypothesis:
[tex]$p=\frac{x}{n}$[/tex]
[tex]$p=\frac{20}{80}$[/tex]
H0: The fraction of bats with a wingspan larger than 10 inches that reside outside of the region and those that do so are equal.
= p - p₀ = 0.
Ha! There is a discrepancy between the percentage of bats with a wingspan larger than 10 inches that reside outside of the region and those that do.
= p - p₀ ≠ 0.
n = 80 , X = 20 , p₀ = 0.30
The analysis will be conducted using the z-test for a single proportion.
Following is a sample of the percentage of bats residing outside the area whose wingspan is larger than 10 inches:
The test statistic is,
[tex]& z=\frac{p-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}} \\[/tex]
[tex]& z=\frac{0.25-0.30}{\sqrt{\frac{0.30(1-0.30)}{80}}}[/tex]
The correct test statistic is
[tex]$=\frac{0.30-0.25}{\sqrt{\frac{0.30 \times 0.70)}{80}}}$[/tex]
To learn more about static test refer to:
https://brainly.com/question/29337608
#SPJ4
On a 800km trip, Ryan's family travelled at 90km/h for the first 600km and 100km/h for
the remainder of the journey. If they had travelled 90km/h for the entire journey, how
much longer would the trip have taken?
The trip would have taken 8.89 hours instead of 8 hours.
How to calculate distance traveled?Distance traveled can be calculated by multiplying the speed at which the object is traveling by the amount of time the object has been in motion.
For example, if a car is traveling at 60 miles per hour for two hours, the distance traveled would be 120 miles.
To calculate distance more accurately, you can use the formula d = rt, where d is the distance, r is the rate of speed, and t is the time in which the object has been in motion.
It is important to note that this formula assumes a constant speed throughout the duration of the journey.
It is also important to remember that the unit of measurement used for both the speed and the time must be the same. Therefore, if the speed is in miles per hour, the time must also be in hours.
In order to calculate this, we need to first calculate the time it took for the family to travel the first 600km at 90km/h. This can be calculated using the formula:
Time = Distance / Speed
So, the time it took for the family to travel the first 600km is:
Time = 600km / 90km/h = 6.67 hours
Then, we can calculate the time it would have taken for the family to travel 800km at 90km/h using the same formula:
Time = 800km / 90km/h = 8.89 hours
Therefore, the trip would have taken 8.89 hours, which is 0.89 hours longer than the original trip which took 8 hours.
To learn more about distance refer to:
brainly.com/question/26046491
#SPJ1
answer now for brainliest its my last one
The missing length is given as follows:
LN = 44.
How to obtain the missing length?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
The parallel lines for this triangle are given as follows:
VU and LM.
Hence the proportional relationship regarding the remaining side lengths is given as follows:
x/24 = 11/8
Applying cross multiplication, we have that:
8x = 24 x 11
x = 3 x 11
x = 33.
Hence the missing length is given as follows:
LN = 33 + 11
LN = 44.
More can be learned about similar triangles at https://brainly.com/question/30233764
#SPJ1
you have found the following ages( in years)of 5 porcupines?
what is the standard deviation? round your answers to the nearest tenth
The standard deviation is 4.0, while mean is 10.2.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Mean = 10.2
The standard deviation is 4.0.
Age in the mean is the average age.
Mean = (16 + 10 + 5 + 7 + 13)/5
Mean = 51/5 = 10.2
The variance's square root will reveal the standard deviation.
(16 - 10.2) + (10 -10.2) + (5-10.2) + (7-10.2)+( 13-10.2) ( 13-10.2)
5.8 + 0.2 -5.2 - 3.2 + 2.8
each number into squares
33.64 + 0.04 + 27.04 + 10.24 + 7.84
Variation: 78.8/5 = 15.76
Standard deviation = 3.969 = 4.0.
To learn more about standard deviation refer to:
brainly.com/question/24298037
#SPJ1
The complete question is,
16, 10, 5, 7, 13
What is the porcupines' typical age based on your sample? Where can I find the standard deviation? in a circle tenths of a percent, closest.
5 in thick slice is cut off the top of a cube resulting in a rectangular box that has volume 135in^3. find the side length of the original cube
The side length of the original cube is 8.90 inches
How to find the side length of the original cube?Let x be the side length of the original cube. After cutting off the top, the remaining rectangular box has dimensions of x-5, x-5, and x.
The volume of this rectangular box is:
(x-5)(x-5)(x) = x³ - 10x² + 25x
x³ - 10x² + 25x = 135
x³ - 10x² + 25x -135 = 0
Use cubic formula.
x =8.90
Therefore, the side length of the original cube is 8.90 inches
Learn more about volume of cube on:
brainly.com/question/1972490
#SPJ1
Is d = 6 a solution to the inequality below?
13 < d + 3
Answer:
Step-by-step explanation:
d = 6 would not be a solution to the inequality below because it would make the inequality untrue! Plugging in, we get:
13 < d + 3
13 < 6 + 3
13 < 9
We know that 9 is not a solution to the inequality!
To solve, we isolate the d, and from there we can find all values that are a solution to the inequality to the solution!
[tex]13 < d + 3\\\\13 - 3 < d\\\\10 < d[/tex]
Thus, one can say that the solutions to the inequality are: [R, d > 10]!
a father is now four times as old as his son. five years ago, he was exactly one and a half times as old as his son ten years from now. find the sum of their present ages
Answer:
sum of their present ages is 5 + 20 = 25 years.
Step-by-step explanation:
The father's current age is 4x (because he is four times as old as his son)
Five years ago, the father's age was (4x - 5) and the son's age was (x - 5)
Ten years from now, the father's age will be (4x + 10) and the son's age will be (x + 10)
From the second statement, we know that:
(4x - 5) = 1.5(x - 5)
And from the third statement, we know that:
(4x + 10) = 1.5(x + 10)
We can solve these equations simultaneously to find the present ages of the father and the son.
Solving the first equation:
4x - 5 = 1.5x - 7.5
2.5x = 12.5
x = 5
So the son's current age is 5 years old.
The father's current age is 4x = 4(5) = 20 years old.
So, the sum of their present ages is 5 + 20 = 25 years.
Kristin is the manager of a local bank where there are currently 6,700 checking accounts. She wants to collect a sample of checking accounts in order to compile information about customer behavior at the bank. Several different sampling scenarios are described below. Identify the type of sample used in each scenario. Choose from:A. Simple random sample (SRS)B. Stratified sampleC. Cluster sampleD. Systematic sampleE. Convenience sample
Selecting elements from an ordered sampling frame is a statistical approach used in survey methodology known as systematic sampling and in the given situation (D) systematic sampling would be the best.
What is a Systematic sample?Systematic sampling is a statistical technique used in survey methodology that involves choosing components from an ordered sampling frame.
An equiprobability approach is the most typical type of systematic sampling.
This method treats the list's evolution in a cyclical manner, returning to the top after it has been completed.
The sampling process begins with the random selection of one element from the list, followed by the selection of every kth element in the frame, where k is the sampling interval, also known as the skip, and is equal to:
k = N/n.
Therefore, in the given situation (D) systematic sampling would be the best.
Know more about a Systematic sample here:
https://brainly.com/question/28505229
#SPJ4
Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors.
if b is the span of the given vectors, so we can express b as the linear combination of the other given two vector.
given that,
[tex]a_{1} =\left[\begin{array}{ccc}-1&\\3&\\-1\end{array}\right] , a_{2} =\left[\begin{array}{ccc}-2\\-3\\6\end{array}\right] , b=\left[\begin{array}{ccc}-6\\9\\2\end{array}\right] \\\\\\\\\\\\\\\\\\\\\\\\[/tex]
We have determined that b is span of given vector a1 and a2.
we can write. [tex]a_{1} =(-1,-3,-1) ,a_{2}=(-2,-3,6) , b=(-6,9,2)[/tex] .
A vector is a quantity that has magnitude and direction.
if x,y,z...., v are vectors and a,b,c....k are scalars then the linear combination is ax+by+cz+......+kv
The set of linear combinations is called span for set of vectors.
So, b is span of given vector.
[tex]b=(c)a_{1} +(d)a_{2}[/tex] ...... equation (A)
where c and d are scalars.
Now,
[tex](-6,9,2)=c(-1,3,-1)+d(-2,-3,6)\\(-6,9,2)=(-c,3c,-c)+(-2d,-3d,6d)\\(-6,9,2)=(-c-2d,3c-3d,-c+6d)\\[/tex]
equating the equations,
[tex]-c-2d=-6\\3c-3d=9\\-c+6d=2\\[/tex]
now we shall solve the above linear equations.[tex]subtract \\-c-2d-(-c+6d) = -6-2\\-8d=-8\\d=1\\now, \-c=-6+2d\\c=6-2=4\\c=4[/tex]
So, value of scalars c, d satisfied equation A,
thus, b is span of given vector a1 and a2.
The complete question is.
Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors. a1=[-1 3 -1], a2=[-2 -3 6]= [-6 9 2]
learn more about vector.
https://brainly.com/question/29740341
#SPJ4
Using separation of variables, solve the differential equation,
(3+x^10)(????y/????x) = x^9/y
Use C to represent the arbitrary constant.
y^2=_____________
The value of y² is 1/5 ln(3+x¹⁰) + C
What is the separation of variables?
Separation of variables, in mathematics, is any of several strategies for rewriting equations so that each of two variables appears on a different side of the problem. These strategies are used to solve ordinary and partial differential equations.
Here, we have
Given: (3+^10)(/) = ^9/
We have to solve the differential equation by using the separation of variables.
Rewrite as y dy = x⁹/3+x¹⁰ dx
As (3+x¹⁰)' = 10x⁹, we solve
y²/2 = 1/10 ln(3+x¹⁰) + C
y² = 1/5 ln(3+x¹⁰) + 2C
Since C is any constant, y² = 1/5 ln(3+x¹⁰) + C
Hence, the value of y² is 1/5 ln(3+x¹⁰) + C
To learn more about the separation of variables from the given link
https://brainly.com/question/14289293
#SPJ4
The picture shows two ladders propped against
facing walls. The end of the first ladder is 5m
above the base of the second wall. The second
ladder is 5m above the base of the first wall.
5m
Can you work out at what height the
ladders cross?
Are you surprised that we don't need to know
the distance between the two walls?
5m
5m
10m
This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
What is equal angles ?
Equal angles can be defined as the angles which are equal .
Given ,
The picture shows two ladders propped against facing walls. The end of the first ladder is 5m above the base of the second wall. The second
ladder is 5m above the base of the first wall.
the angles ∠BAD and ∠ADC are alternate angles, and therefore equal. Likewise, angles ∠ABC and BCD are also alternate and therefore equal.
∠BEA and ∠CED are opposite, which means that they are equal. You can see these equal angles in the diagram on the right.
This means that the triangles ABE and DCE have the same angles as each other, and are therefore similar.
so,
This means:
AE/ED=AB/DC=5m/10m=1/2
Therefore AE=1/3 AD.
This means E is 1/3 of the way up from the floor to D, so is at a height of
This means E is 13 of the way up from the floor to D, so is at a height of 10m/ 3=3 1/3m
If instead B is a metres above the floor, then:
AE/ED=AB/DC=a/10
Therefore AE=a/10+a AD.
This means E is the same fraction of the 10m above the floor, so is 10a/10+a metres above the floor.
If instead D is b metres above the floor, then:
AE/ED=AB/DC=a/b
Therefore AE=a/a+b AD.
This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
Therefore, This means E is the same fraction of the b metres above the floor, so is ab/a+b metres above the floor.
To learn more about Equal angles from the given link.
https://brainly.com/question/3946145
#SPJ1
Showing the amount of each monthly payment that goes toward principal and interest for the first three months of the loan.
A home mortgage of $140,000 with a fixed APR of 6% for 30 years.
For each month, you will pay $700 in interest.
What is simple interest?
Simple interest is a method of calculating the interest on a loan or investment where the interest is determined based on the initial principal (the original amount of the loan or investment) and a fixed interest rate. The interest is calculated based on the amount of time the principal is invested or borrowed.
The formula for simple interest is:
I = Prt
Where:
I is the interest
P is the principal
r is the annual interest rate (expressed as a decimal)
t is the time (in years)
For example, if you have a home mortgage of $140,000 with a fixed APR of 6% for 30 years, the simple interest calculation for each month will be:
I = (140,000 x 0.06) / 12 = $700
Hence, for each month, you will pay $700 in interest.
To learn more about the simple interest, visit:
https://brainly.com/question/25793394
#SPJ1
A principal of $5000 is invested in an account paying an annual rate of 7%. Find the amount in the account after 6 years if the account is compounded semiannually,quarterly, and monthly
The amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly is 6724.4, 6736.7, and 6664.9.
What is compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Here, we have
Given: A principal of $5000 is invested in an account paying an annual rate of 7%.
We have to find the amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly.
A) Compounded semi-annually:
= 5000*(1 + 0.05/2)^(2*6) = 6724.4
B) Compounded quarterly:
= 5000*(1 + 0.05/4)^(4*6) = 6736.7
C) Compounded monthly:
= 5000*(1 + 0.05/12)^(12*6) = 6664.9
Hence, the amount in the account after 6 years if the account is compounded semiannually, quarterly, or monthly is 6724.4, 6736.7, and 6664.9.
To learn more about the compound interest the given link
https://brainly.com/question/24274034
#SPJ1
