The area of each of the given triangle is:
4. 21 units²; 5. 12 units²; 6. 12 units²
7. 35 ft²; 8. 8 in.²; 9. 24 cm²
What is the Area of a Triangle?To find the area of a triangle, find one-half the product of the height and the base length of the triangle.
Therefore, area = 1/2(base * height).
4. A = 1/2 * 6 * 7 = 21 units²
5. A = 1/2 * 4 * 6 = 12 units²
6. A = 1/2 * 6 * 4 = 12 units²
7. A = 1/2 * 7 * 10 = 35 ft²
8. A = 1/2 * 8 * 8 = 8 in.²
9. A = 1/2 * 6 * 8 = 24 cm²
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3x + 5 + 5x + 15=x=3x + 5 =5x + 15=we are using sumplementary angles to find the answer.
Sum of a supplementary angle is 180 degrees
3x +5 + 5x +15 = 180
8x + 20 = 180
8x = 180 -20
8x = 160
divide both sides by x
8x/8 = 160/8
x = 20 degrees
3x + 5 = 3(20) + 5
3x +5 = 60 + 5
3x +5 = 65 degrees
5x +15 = 5(20) + 15
5x +5 = 100 +15
5x +5 = 115 degrees
seven distinct pieces of candy are to be distributed among three bags. the red bag and the blue bag must each receive at least one piece of candy; the white bag may remain empty. how many arrangements are possible?
Using combination, there are 1932 arrangments possible.
A combination is a mathematical approach that counts the number of potential configurations in a box containing objects, regardless of their order.
In combinations, we can select items in any order. In combinations, the order doesn’t matter.
The combination formula of given as: n! / r!(n-r)!
Each candy would be distributed in three different ways if there were no limits on how many candies might fit in a bag. 3⁷ different ways to distribute the sweets in this scenario. However, only empty blue and red bags count in this scenario.
There are 2⁷ methods to distribute candy if the red bag is left empty.
Similarly, for the blue bag.
Hence there are 2⁷ +2⁷ – 1 ways to distribute candy such that either blue or red bag is empty.
The total amount of circumstances and ways to deliver the sweets
= 3⁷ – (2⁷ + 2⁷ -1)
= 1932
Therefore, there are a total of 1932 arrangements possible.
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you wish to calculate the growth rate of a population but you have no idea whether the population grows continuously or not. which would be the best model to use?
Logistic growth is the module to calculate the growth rate of a population but you have no idea whether the population grows continuously or not.
Two types of growth modules:
logistic growth and exponential growth.
In logistic growth, a population's per capita growth rate decreases when population size approaches a maximum imposed by finite environmental resources.
Because it is based on boundless resources, exponential development is not a particularly sustainable condition of affairs (those are uncommon in the actual world).
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One number is 3 more than twice another. Their sum is 24. Find the numbers.
show work
Answer:
it easy 3 times 4 times 2
Step-by-step explanation:
Answer:
7, 17
Step-by-step explanation:
Let the first number be x
Let the second number be 3 + 2x
Sum of two numbers = 24
x + 3 + 2x = 24
3x = 24 - 3
3x = 21
x = 21 ÷ 3
x = 7
First number = x = 7
Second number = 3 + 2x = 17
Pam has ridden her new bike 7.2 miles. Dale has ridden his new bike 12.5 times as far as Pam.
How far has Dale ridden his bike? Enter your answer in the box.
Answer:
He has ridden 90 miles
Step-by-step explanation:
7.2 X 12.5 = 90
Help pls :c
Need help with this calculus graph question
Answer: see photo below
Convert the following into Vertex form
y=-3x^2 +1
n + 2 = -14 -n Show work
Answer:
n = -8
Step-by-step explanation:
n + 2 = -14 -n
Add n to each side
n+n + 2 = -14 -n+n
2n+2 = -14
Subtract 2 from each side
2n+2-2 = -14-2
2n = -16
Divide by 2
2n/2 = -16/2
n = -8
Two cylinders are shown below. Which cylinder has the greater volume? Use 3.14 for π. Round to the nearest hundredth. Use the drop-down menus to show your answer
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
Please have a look at the attached photo.
My answer:
To find which cylinder has the greater volume, we need to find out the volume of each one.
As we all know that the formula used to determine the volume of a cylinder is:
V = The base area*the height
<=> V = π\(r^{2}\)h (cubic units)
For example, in my attached photo, we will use this formula to find the volume of each one.
1. Cylinder A:The base area = π\(r^{2}\) = π\(3.5^{2}\) = 38.46 square in
The height = 8.5 in
=> the volume of Cylinder A
= The base area*the height
= 38.46*8.5
= 326.91 cubic in
2. Cylinder B:The base area = π\(r^{2}\) = π\(2.7^{2}\) = 22.89 square in
The height = 11 in
=> the volume of Cylinder A
= The base area*the height
= 22.89*11
= 251.79 cubic in
Hence, Cylinder B has the greater volume
What is the answer to 1/4×4/5
Answer:
1/5 or 0.2
Step-by-step explanation:
1/4 x 4/5 =
=1x4/4x5
=4/20 -OR- 1/5 -OR- 0.2
Indicate whether each relation is a function or not a function. Answers may be used more than once.
A relation is a set of ordered pairs that relate the elements of two sets. A function is a special type of relation where each element of the first set (domain) is paired with only one element of the second set (range).
To determine if a relation is a function or not, we need to check if there are any repeating values in the first coordinate (domain) of the ordered pairs. If there are, then the relation is not a function.
For example, consider the relation {(1,2), (2,4), (3,6), (1,5)}. The first coordinate 1 appears twice, and is paired with two different second coordinates 2 and 5. Therefore, this relation is not a function.
On the other hand, the relation {(1,2), (2,4), (3,6)} is a function, because there are no repeating values in the first coordinate. In summary, a relation is a function if each element in the domain is paired with only one element in the range. If there are any repeating values in the domain, then the relation is not a function.
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Log x + log 6= log(2x+1)
In logarithm , value of function is 1/4.
How should log be defined?
The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e.Log x + log 6= log(2x+1)
use log property log m + log n = log ( mn)
log ( 6x) = log (2x + 1)
6x = 2x + 1
4x = 1
x = 1/4
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Use proportional reasoning to find 45% of 200
Answer:
90 i think :)
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
By reasoning, we can say 50% of 200 is 100
We can say 10% of 200 is 20
We divide 20 by 2 to get 5%
20/2
= 10
Subtract 100 by 10
100 - 10
= 90
45% of 200 is 90
in a marketing research study, one-half of a sample received a coupon in a direct mail; the other half did not. a researcher wants to compare money spent at the store between the two groups. what statistical technique should be used? group of answer choices one-sample t test paired-samples t test independent-samples t test pearson correlation coefficient
The appropriate statistical technique to compare money spent at the store between two groups in a marketing research study is the independent-samples t-test.
The independent-samples t-test is used to compare the means of two independent groups. In this case, the groups are the ones who received the coupon and the ones who did not, and they are independent because the participants were randomly assigned to each group.
The null hypothesis for the independent-samples t-test is that there is no difference between the means of the two groups. The alternative hypothesis is that there is a significant difference between the means of the two groups.
By conducting an independent-samples t-test on the data, the researcher can determine whether the difference in money spent at the store between the two groups is statistically significant or simply due to chance. If the p-value is less than the significance level (usually 0.05), the researcher can reject the null hypothesis and conclude that there is a significant difference between the two groups in terms of the money spent at the store.
Therefore, the independent-samples t-test is an appropriate statistical technique to compare the means of two independent groups and test for significant differences between them.
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A 95% confidence interval for the mean body mass index (BMI) of young American women is 26.8 +0.6. One of your classmates interprets this interval in the following way: "The mean BMI of young American women cannot be 28." Is your classmate's interpretation correct? If not, what is the correct interpretation of the confidence interval? Incorrect. We are 95% confident that future samples of young women will have mean BMI between 26.2 and 27.4.
Incorrect. We are 95% confident that the interval from 26.2 and 27.4 captures the BMI of all young American women.
Correct. The interval states that the mean BMI of young American women is between 26.2 and 274, so the mean cannot be 28. Incorrect. We are 95%confident that the interval from 26.2 and 274 captures the true mean BMI of all young American women. Incorrect. If we take many samples, the population mean BMI will be between 26.2 and 27.4 in about 95% of those samples.
Incorrect. We are 95% confident that the interval from 26.2 and 27.4 captures the BMI of all young American women is the correct interpretation of the confidence interval.
A 95% confidence interval is a range of values that we can be 95% sure contains the true mean of the population. The 95% confidence interval for the mean body mass index (BMI) of young American women is 26.8 ± 0.6.
This means that we are 95% confident that the true mean BMI of young American women is between 26.2 and 27.4.
Consequently, the statement, "The mean BMI of young American women cannot be 28" is incorrect as the confidence interval does not include the value 28.
However, this does not imply that the true mean BMI of young American women cannot be 28.
A confidence interval is a statistical range that provides an estimate of the possible values for an unknown population parameter, such as a mean or proportion, based on a sample from that population. It provides a range of values within which the true population parameter is likely to fall, along with a specified level of confidence.
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What is the value of x? Show logical steps to solve for x
(x+22)+x=90
Answer:
x=34
Step-by-step explanation:
Remove the redundant parentheses
x+22+x=90
Simplify
2x+22=90
Solve
2x=68
x=34
What is the answer for 1,2,3?
Answer:
1: A (Function)
2: B {(3,2), (2,1), (8,2), (5,7)}
3: C (Domain)
Step-by-step explanation:
Domains are the x values that go right or left.
Ranges are the y values that go up or down.
If the domain repeats when given a set of points, it is not a function.
The domain (x value) CAN'T repeat.
A fair six-sided die is rolled 66 times. Theoretically, about how many times should a roll of "6 occur?
Answer:
11
Step-by-step explanation:
On a fair six-sided die, there is a \(\frac{1}{6}\) chance of rolling each number. Therefore, for each of the rolls, the number 6 has a \(\frac{1}{6}\) chance of being rolled. This can be read as for every 6 rolls, one 6 should appear.
Since the die is being rolled 66 times, we have the following proportion:
\(\frac{1}{6}=\frac{x}{66}\), where \(x\) is the theoretical number of times a roll of "6" occurs.
Multiply both sides by 66:
\(x=\frac{1}{6}\cdot 66=\boxed{11}\)
Question 3[20 Points] a) [10 points] If a=2, b=5 and m=10, then find F(s) for the following function: f(t)=ate-bt sin(mt) u(t) b) [10 points] Explain the time shift property in Laplace transform and give an example about it.
The time shift property tells us that if we shift the function f(t) = u(t - a) by 'a' units to the right, the Laplace transform F(s) will be multiplied by \(e^{(-as)}\), which represents the time delay.
a) To find F(s) for the given function \(f(t) = ate^{(-bt)} sin(mt)u(t)\), where u(t) is the unit step function, we can use the Laplace transform.
- The Laplace transform of a is A/s, where A is the value of a.
- The Laplace transform of \(e^{(-bt)}\) is 1/(s + b).
- The Laplace transform of sin(mt) is \(m/(s^2 + m^2)\), using the property of the Laplace transform for sine functions.
- The Laplace transform of u(t) is 1/s.
Now, using the linearity property of the Laplace transform, we can combine these transforms:
\(F(s) = (A/s) \times (1/(s + b)) \times (m/(s^2 + m^2)) \times (1/s)\)
\(= Am/(s^2(s + b)(s^2 + m^2))\)
b) The time shift property in the Laplace transform states that if the function f(t) has a Laplace transform F(s), then the Laplace transform of the function f(t - a) is \(e^{(-as)}F(s)\).
This property allows us to shift the function in the time domain and see the corresponding effect on its Laplace transform in the frequency domain. It is particularly useful when dealing with time-delay systems or when we need to express a function in terms of a different time reference.
For example, let's consider the function f(t) = u(t - a), where u(t) is the unit step function and 'a' is a positive constant. This function represents a step function that starts at t = a. The Laplace transform of this function is F(s) = \(e^{(-as)}/s.\)
The time shift property tells us that if we shift the function f(t) = u(t - a) by 'a' units to the right, the Laplace transform F(s) will be multiplied by \(e^{(-as)}\), which represents the time delay. This property allows us to analyze and solve problems involving time-delay systems in the Laplace domain.
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Alguien me ayuda cuanto es un cuarto de 180??
Answer:
45
Step-by-step explanation:
usa una calculadora
Set up the triple integral needed to compute the volume of the tetrahedron bounded by the plane 140 + 35y + 102 - 70 = 0 and the coordinate planes.
The equation 140 + 35y + 102 - 70 = 0 can be simplified to 35y = -172, which gives y = -4.914.
The tetrahedron is bounded by the coordinate planes (x = 0, y = 0, z = 0) and the plane 140 + 35y + 102 - 70 = 0, which can be written as 35y = -172 or y = -4.914. Since the plane intersects the y-axis, it cuts off a triangular pyramid from the octant. The height of this pyramid is 4.914 units and its base is a right triangle with legs of length 140 and 102 units. Thus, the volume of this pyramid is given by:
V = (1/3) * (base area) * (height)
V = (1/3) * (140 * 102)/2 * 4.914
V = 14237.04 cubic units
To find the volume of the entire tetrahedron, we need to integrate over the region that the tetrahedron occupies. Since the tetrahedron is located in the first octant and bounded by the coordinate planes, we can set up the following triple integral:
∫∫∫E dV
where E is the solid region bounded by x = 0, y = 0, z = 0, and the plane 140 + 35y + 102 - 70 = 0. We can rewrite this equation as:
140 + 35y + 102 - 70 = 0
35y = -172
y = -4.914
Thus, the integral becomes:
∫∫∫E dV = ∫0^102 ∫0^(140-7/5y) ∫0^(-7/10y + 35/10) dz dx dy
The limits of integration for z are obtained from the equation of the plane, while the limits of integration for x and y are the limits of the triangular base of the tetrahedron.
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Tom bought a bag full of coal. After one week the bag was 2|3 full. During the next week he used of the remaining coal What fraction was left in the bag?
Answer:
None
Step-by-step explanation:
When he first bought the coal, it was full. After one week, he used 1/3, leaving the bag 2/3 full. If he used the remaining coal in the bag, that means he used all of the coal - all two thirds of it.
The fraction of coal left in the bag was zero or none since Tom used the remaining coal.
What is the reasoning?The procedure of utilizing logical reasoning to analyze a condition to determine the best problem-solving approach for a particular issue, then using this approach to create and explain a resolution.
The reasoning is a tricky but interesting problem in mathematics that requires relations of variables to solve.
As per the given,
After one week the bag was 2|3 full
Now remaining coal = 1 -2/3 = 1/3 part
Now, Tom used this remaining amount.
So, 1/3 - 1/3 = 0 part.
Hence "The fraction of coal left in the bag was zero or none since Tom used the remaining coal".
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Calculate the area of the parallelogram
Answer:
28 square inches
Step-by-step explanation:
Area = b * h
To find the height, you first have to solve the triangle.
\(a^{2} +b^{2} =c^{2} \\\\3^{2} +h^{2} =5^{2} \\h^{2} =5^{2} -3^{2} \\h=4\)
Now use that for your area
Area = 7 * 4
Bill wants to save for his son’s college expenses. He knows what tuition will cost in 18 years and knows the interest rate on the bank account. What he doesn’t know is how much to deposit each month to save enough for his son’s college expenses. Which Excel formula would you use?
The Excel formula that Bill would use is PMT.
How to illustrate the information?From Bill's situation, he has the following information:
time = NPER = number of periods = 18 years
RATE of the bank
FV = future value = cost of tuition
PMT, is a financial function, computes the loan payment based on constant payments and a constant interest rate. The Excel PMT function is a financial function that computes loan payments based on a fixed interest rate, the number of periods, and the loan amount. The function's name is derived from the acronym "PMT," which stands for "payment."
In conclusion, the correct option is PMT.
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Complete question
Bill wants to save for his son’s college expenses. He knows what tuition will cost in 18 years and knows the interest rate on the bank account. What he doesn’t know is how much to deposit each month to save enough for his son’s college expenses. Which Excel formula would you use? Choose from FV, PV, PMT, NPER, or RATE.
HELP PLEASE 14 POINTS
Answer:
To my knowledge of congruency, I would say the answer is A,
Step-by-step explanation:
Hope this helped!!!
Someone help fast!!! Easy points!!!
I couldn’t understand this it’s due tonight
Answer:
2A/h - b2= b1
Step-by-step explanation:
A = 1/2 ( b1+ b2) h
Multiply each side by 2
2*A = 2*1/2 ( b1+ b2) h
2A = ( b1+ b2) h
Divide each side by h
2A/h = ( b1+ b2) h/h
2A/h = ( b1+ b2)
Subtract b2 from each side
2A/h - b2= b1+ b2-b2
2A/h - b2= b1
if 2100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
The dimensions of the box that maximize the volume are x = √700 and h = 100 / √700.
To find the largest possible volume of the box, we need to optimize the dimensions of the box. Let's denote the length of each side of the square base as x and the height of the box as h.
The surface area of the box consists of the area of the square base (x^2) and the four sides of the box (4xh). Since the box has an open top, we do not consider the top surface. The total surface area is given as 2100 square centimeters, so we have:
x^2 + 4xh = 2100
To maximize the volume, we need to express the volume of the box (V) in terms of a single variable. The volume of a rectangular prism is given by V = x^2h.
We can rewrite the equation for the surface area to solve for h:
h = (2100 - x^2) / (4x)
Now we can substitute this expression for h in the volume equation:
V = x^2 * [(2100 - x^2) / (4x)]
Simplifying, we have:
V = (1/4) * (2100x - x^3)
To find the maximum volume, we need to find the critical points of this function. We take the derivative of V with respect to x and set it equal to zero:
dV/dx = 2100/4 - (3/4)x^2 = 0
Solving this equation, we find:
2100/4 = (3/4)x^2
x^2 = 700
x = √700
Substituting this value back into the equation for h, we find:
h = (2100 - 700) / (4 * √700) = 1400 / (4 * √700) = 100 / √700
Therefore, the largest possible volume of the box is:
V = (1/4) * (2100 * √700 - 700 * √700) = 350√700 cubic centimeters.
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Suppose vanguard brokerage services developed new software to increase their speed of execution rating. if the new software is able to increase their speed of execution rating from the current value of to the average speed of execution rating for the other brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating?
It's generally reasonable to assume that enhancing the speed of execution can positively impact customer satisfaction. Quicker order executions can lead to reduced slippage, improved trade efficiency, and a better overall trading experience. Customers often value fast and reliable execution when it comes to brokerage services.
To determine the potential impact on overall satisfaction rating, several factors would need to be considered, including but not limited to:
Other aspects of the brokerage service: Speed of execution is just one aspect of brokerage services. Factors like customer support, platform usability, account management features, pricing, research tools, and investment options also contribute to overall satisfaction. Improving one aspect may not guarantee a significant increase in overall satisfaction if other areas remain unchanged.
Individual preferences and priorities: Different customers prioritize different features in their brokerage services. While some might highly value speed of execution, others may focus on different aspects such as cost-effectiveness, available investment options, or educational resources. The impact on overall satisfaction would depend on how important speed of execution is to the customer base as a whole.
Competitors' performance: The competitiveness of the market plays a role in shaping customers' expectations. If the average speed of execution rating for other surveyed brokerage firms is relatively high, matching that average may positively impact satisfaction. However, if the sector's overall speed of execution rating is generally low, merely reaching the average might not suffice to significantly boost satisfaction.
It's essential for brokerage firms to consider these factors comprehensively and conduct customer surveys or market research to assess the potential impact on overall satisfaction accurately.
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neka cases a check for $245. The teller gave him two 50- dollar bills, six 20-dollar bills and f 5 dollar bills. determine the value of f.
There 5 5 dollars in the amount given by the teller to Neka
What is the total value of a single denomination?
The total value of a single denomination is the number of that denomination received by Neka multiplied by the value of each denomination
In other words, the total value of 50-dollar is $50 multiplied by 2 since there 2 50- dollar bills, the same applies all other bills.
Total amount=($50*2)+($20*6)+($5*f)
total amount=$245
$245=($50*2)+($20*6)+($5*f)
$245=$100+$120+($5*f)
$245=$220+($5*f)
$245-$220=$5*f
$25=$5*f
f=$25/$5
f=5
In essence, there are 5 5 dollar bills
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I have an exam tomorrow, wish me luck.
Answer:
good luck
Step-by-step explanation:
Answer:
Good luck on your exam!