The maximum number of guests that Marshall can invite with a total budget cost of $81.90 is 63 guests.
What does the cost mean?Cost can refer to a variety of measures used to quantify the expense or effort required to solve a problem or perform a task.
For example, in optimization problems, the cost function represents a mathematical function that measures the objective or goal that needs to be minimized or maximized, subject to certain constraints.
According to the given informationFirst, we can find the cost per guest for the retirement party, which is $15.60 ÷ 12 guests = $1.30 per guest.
Next, we can use this unit rate to find the maximum number of guests that Marshall can invite with a total budget of $81.90:
Maximum number of guests = Total budget ÷ Cost per guest
Maximum number of guests = $81.90 ÷ $1.30 per guest
Maximum number of guests = 63 guests (rounded down to the nearest whole number)
Therefore, the maximum number of guests that Marshall can invite with a total budget of $81.90 is 63 guests.
To know more about the Cost visit:
brainly.com/question/29489686
#SPJ1
in a survey of 464 registered voters, 133 of them wished to see mayor waffleskate lose her next election. the waffleskate campaign claims that no more than 34% of registered voters wish to see her defeated. does the 98% confidence interval for the proportion support this claim? (hint: you should first construct the 98% confidence interval for the proportion of registered voters who wish to see waffleskate defeated.)
The Waffleskate campaign's claim that less than 34% of registered voters wish to see her defeated is not supported by the data, as the 98% confidence interval (0.236 to 0.336) for the proportion of voters who want her to lose does not include 0.34.
Why the 98% confidence interval for the proportion does not support this claim?To determine if the 98% confidence interval supports the Waffleskate campaign's claim that no more than 34% of registered voters wish to see her defeated, we need to construct the confidence interval and see if 34% falls within the interval.
The sample proportion of registered voters who wished to see Waffleskate lose her next election is 133/464 ≈ 0.286. To construct the 98% confidence interval for the true proportion, we can use the formula p ± Z√(pq/n), where p is the sample proportion, q is the complement of p, n is the sample size, and Z is the standard normal value corresponding to the desired confidence level.
Plugging in the values, we get:
p ± Z√(pq/n) = 0.286 ± 2.33√((0.2860.714)/464) ≈ 0.236 to 0.336
Therefore, the 98% confidence interval for the proportion of registered voters who wish to see Waffleskate lose her next election is 0.236 to 0.336. Since this interval does not include 0.34, the Waffleskate campaign's claim that no more than 34% of registered voters wish to see her defeated is not supported by the 98% confidence interval for the proportion.
Learn more about Waffleskate campaign's
brainly.com/question/14553449
#SPJ11
consider all undergraduate students at a local university to be a population. in this population, the proportion of students who live on campus is 0.23. in a random sample of 300 students from this population, the proportion who live on campus is 0.19. we would call the number 0.19 a a. z-score. b. p-value. c. parameter. d. statistic. e. significance level.
The number 0.19 is a d. statistic, which represents a numerical summary of a sample. The z-score would be calculated by (0.19 - 0.23) / sqrt((0.23 * 0.77) / 300) and would indicate how many standard deviations the sample proportion is from the population proportion.
The p-value and significance level would be used in hypothesis testing to determine the likelihood of obtaining a sample proportion as extreme or more extreme than the observed proportion, assuming the null hypothesis is true.
The parameter is the true proportion of all undergraduate students at the local university who live on campus, which is estimated by the sample statistic.
Learn more about statistic:
https://brainly.com/question/30915447
#SPJ11
___________ is the number of individual buy orders and the total number of shares that wish to buy.
Buy-side order flow is the number of individual buy orders and the total number of shares that wish to buy.
This is a crucial metric that is used by traders, investors, and analysts to gauge the demand for a particular security or asset.
The buy-side order flow refers to the number of shares that market participants want to purchase at a given time, and it provides valuable insights into the sentiment of the market. If there are more buy orders than sell orders, then there is a higher demand for the security, which can lead to an increase in the price of the asset. On the other hand, if there are more sell orders than buy orders, then there is a higher supply of the security, which can lead to a decrease in the price of the asset.
Traders and investors use buy-side order flow data to help them make informed decisions about when to buy or sell a security. By analyzing the number of buy orders and the total number of shares that wish to buy, they can identify trends and patterns in the market, and adjust their strategies accordingly. Additionally, buy-side order flow data can be used to help identify potential support and resistance levels for a security, which can be useful in setting stop-loss orders and other risk management measures.
Overall, the buy-side order flow is an important metric that provides valuable insights into the sentiment of the market and helps traders and investors make informed decisions about their investments.
To learn more about number here:
https://brainly.com/question/29595846
#SPJ4
Can someone help me asap? It’s due tomorrow. I will give brainiest if it’s all correct.
Answer:
1.a
2.c
3.d
4.b
Step-by-step explanation:
Which inequality is true when the value of w is -3?
find the equation that is parallel to the line y=-5x-8 and passes through the point (7,-2).Write the equation in slope intercept form
An equation of a line that is parallel to the line y=-5x-8 and passes through the point (7, -2) is y = -5x + 33.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Since the line is parallel to y=-5x-8, the slope is equal to -5.
At data point (7, -2) and a slope of -5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-2) = -5(x - 7)
y + 2 = -5x + 35
y = -5x + 35 - 2
y = -5x + 33
Read more on point-slope here: brainly.com/question/24907633
#SPJ1
The equation of the line that is parallel to y = -5x - 8 and passes through the point (7,-2) is y = -5x + 33, in slope intercept form.
How to find the the equation in slope intercept form
To find an equation that is parallel to the line y = -5x - 8, we know that it must have the same slope. So the slope of the new line is -5.
Now we use the point-slope form of a linear equation to find the equation of the line passing through (7,-2) with slope -5:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Substituting the values we get:
y - (-2) = -5(x - 7)
Simplifying and solving for y, we get:
y + 2 = -5x + 35
y = -5x + 33
Therefore, the equation of the line that is parallel to y = -5x - 8 and passes through the point (7,-2) is y = -5x + 33, in slope intercept form.
Learn more about slope intercept form at https://brainly.com/question/22057368
#SPJ1
CAN SOMEONE PLEASE HELP ME WITH THIS :((
What is the value or arc PQ? Only enter numerical values.
The value of arc PQ is 110°
What is circumference of a circle?The circumference of a circle is the length of the 360 degree arc of that circle. Therefore the sum of the arc on a circumference of a circle is 360°
Therefore ,
8x-10+ 6x + 10x+10 = 360
24x -10+10 = 360
24x = 360
divide both sides by 24
x = 360/24
x = 15
therefore the value of x is 15
Arc PQ = 8x -10
substitute 15 for x
ArcPQ = 8×15-10
= 120-10
= 110°
therefore the value of arc PQ is 110°
learn more about circumference from
https://brainly.com/question/29644055
#SPJ1
What is the width of the pool?
Answer:
249 feet
Step-by-step explanation:
Hello!
Let the missing side be x.
We can use a trigonometric ratio to solve this question. The one we are going to use is Tangent.
There are 3 trigonometric ratios: Sin (Opposite/Hypotenuse), Cos (adjacent/hypotenuse), and Tan(Opposite/Adjacent).
We need to use the ratio that involves the 2 sides, 144 and x. That would be Tan, as x is opposite to 60°, and 144 is adjacent to 60°.
Solve for x:tan(60) = x/144tan(60) * 144 = x => Plug tan(60) into a calculator, and multiply the result by 144.The missing side is 249 feet.
What is 2. 803 rounded to the nearest half
Answer: 3
Step-by-step explanation:
an expression is well-defined if you can compute its value without any illegal operations. examples of expressions that are not well-defined include $1/0$ and $\sqrt{-10}$. for what values of ${}x$ is the expression \[\frac{\sqrt{x 1} \sqrt{1 - x}}{\sqrt{x}}\]well-defined? express your answer in interval notation.
To exclude the value [tex]$x=0$[/tex] since division by zero is not allowed.
The expression is well-defined for [tex]$x \in (0,1]$[/tex].
Expression is well-defined for [tex]$0\leq x\leq 1$[/tex].
In interval notation, we can write this as [tex]$[0,1]$[/tex].
Therefore, the expression [tex]$\frac{\sqrt{x\cdot 1} \sqrt{1 - x}}{\sqrt{x}}$[/tex] is well-defined for [tex]$ x\in [0,1]$[/tex].
Expression to be well-defined, we need to ensure that we do not perform any illegal operations.
This means that we cannot take the square root of a negative number, and we cannot divide by zero.
Let's consider each of the factors in the expression separately.
The first factor is.
[tex]$\sqrt{x\cdot 1}=\sqrt{x}$[/tex].
To ensure that this is well-defined, we need.
[tex]$x\geq 0$[/tex] since we cannot take the square root of a negative number.
The second factor is
.[tex]$\sqrt{1-x}$[/tex].
To ensure that this is well-defined, we need.
[tex]$1-x\geq 0$[/tex], or equivalently, [tex]$x\leq 1$[/tex], since we cannot take the square root of a negative number.
The denominator is.
[tex]$\sqrt{x}$[/tex].
To ensure that this is well-defined, we need.
[tex]$x\geq 0$[/tex], since we cannot divide by zero.
For similar questions on value
https://brainly.com/question/28159917
#SPJ11
can someone answer my new math questions please
Answer:
yes
Step-by-step explanation:
Dilate point S by a scale factor of 1/2
PLEASE JUST TELL WHERE THE POINT MUST BE LOCATED DONT GIVE A LONG EXPLANATION AND IF U CAN UPLOAD A PIC OF THE ANSWER
The position of point S after dilating will be half of the original. The dilated point S' has been shown below.
What is dilation?
Using a modification known as dilation, an object can be resized. Through dilatation, the objects can be resized or enlarged. This transformation results in a shape that is a perfect replica of the original image. The form's dimensions do vary, though. An expansion or contraction of the original form is required for a dilatation. This shift is referred to as a scale factor.
We are given a graph showing position of point S.
Now, on dilating the point by a scale factor of [tex]\frac{1}{2}[/tex], we get that the point will be located at half of the original.
The point has been located and attached in the image below.
Hence, the required solution has been obtained.
Learn more about dilation from the given link
https://brainly.com/question/30240987
#SPJ1
two pollsters will canvas a neighborhood with 20 houses. each pollster will visit 10 of the houses. how many different assignments of pollsters to houses are possible?
There are 92,378 different assignments of pollsters to houses where two pollsters will canvas a neighborhood with 20 houses.
There are 20 houses to choose from for the first pollster, and then 19 houses remaining for the second pollster.
However, since the order in which the pollsters visit the houses does not matter, we need to divide by the number of ways of arranging the 10 houses that each pollster will visit evaluated using probability.
Therefore, the total number of different assignments of pollsters to houses is:
(20 choose 10) * (10 choose 10) / 2! = (184,756) * (1) / 2 = 92,378
So there are 92,378 different assignments of pollsters to houses.
learn more about probability
brainly.com/question/30034780
#SPJ4
you are in charge of conducting a very important study on the efficacy of imitrex on migraine sufferers. you ask 25 women to test this drug. each of the 25 women is given 'excedrin for migraines' immediately after the onset of their first migraine, after which you measure the time it takes for the headache to subside. after the onset of their second migraine, you give them imitrex and again measure the time it takes for the headache to subside. assuming the data are normally distributed, which is the most appropriate statistical test to determine if imitrex works better than excedrin at eliminating migraines?
If the p-value obtained from the paired t-test is less than the predetermined level of significance (usually 0.05), then it can be concluded that there is a statistically significant difference between the two treatments, and that imitrex is more effective than excedrin at eliminating migraines.
To determine if Imitrex works better than Excedrin at eliminating migraines in your study, the most appropriate statistical test to use is the Paired Samples t-test.
This test is suitable because:
We have two related samples: the same 25 women are given both Excedrin and Imitrex, so their response times are paired.
We're comparing the mean response times between two treatments, which requires a t-test.
The data is assumed to be normally distributed.
To conduct the Paired Samples t-test, follow these steps:
Calculate the difference in response times for each woman (Imitrex time - Excedrin time).
Calculate the mean of these differences.
Calculate the standard deviation of the differences.
Determine the degrees of freedom (25 women - 1 = 24).
Using the mean, standard deviation, and degrees of freedom, calculate the t-statistic.
Compare the t-statistic to the critical value from the t-distribution table, using your chosen significance level (e.g., 0.05).
If the t-statistic is greater than the critical value, reject the null hypothesis, concluding that there's a significant difference between the effectiveness of Imitrex and Excedrin for migraine relief.
For similar question on t-distribution.
https://brainly.com/question/24277447
#SPJ11
To determine if Imitrex works better than Excedrin, the most appropriate statistical test to use would be a "paired t-test."
We are comparing the efficacy of Imitrex and Excedrin for Migraine in the same group of 25 women, with each woman acting as her own control. You are measuring the time it takes for the headache to subside after administering each drug. To determine if Imitrex works better than Excedrin, the most appropriate statistical test to use would be a "paired t-test."
Step-by-step explanation:
1. Record the time it takes for the headache to subside after administering Excedrin and Imitrex to each woman.
2. Calculate the difference in time for each woman between the two drugs.
3. Compute the mean and standard deviation of these differences.
4. Perform a paired t-test to compare the mean difference to 0 (no difference between the two drugs).
5. Assess the p-value obtained from the t-test. If the p-value is less than the significance level (usually 0.05), then you can conclude that there is a statistically significant difference between the two drugs, suggesting that Imitrex works better than Excedrin in eliminating migraines.
Learn more about statistical test here:
https://brainly.com/question/14128303
#SPJ11
Can someone help me out fast please!?!?!
Pamela purchased a new laptop for her schoolwork. She plans to sell it sometime in the future; however, its value depreciates monthly. The expression below shows the depreciated sales value of the laptop. What does the second term of the expression represent?
A. The number of months Pamela will wait to sell the laptop.
B. The original value of the laptop.
C. The total depreciation value of the laptop.
D. The monthly depreciation value of the laptop.
The second term of the expression represent the total depreciation value of the laptop. Therefore, the answer is C.
How to find the terms of an expression?Pamela purchased a new laptop for her schoolwork. She plans to sell it sometime in the future; however, its value depreciates monthly.
The expression below shows the depreciated sales value of the laptop.
856 - 17mTherefore, the meaning of the second term in the expression can be calculated as follows:
Therefore,
856 = The amount she bought the laptop
The second term 17m is the total depreciation value of the laptop where m = number of months.
learn more on expression here: brainly.com/question/29001350
#SPJ1
5. This solid was created by joining two right rectangular prisms.
4½ cm
8 cm
4 cm
-9 cm
10½ cm
Enter the volume of the solid, in cubic centimeters.
The volume of the solid as shown in the diagram is 540 cm².
What is volume?Volume is the space occupied by a solid shape.
To calculate the volume of the of the solid, we use the formula below
Formula:
V = LWH+lwh............................ Equation 1Where:
V = Volume of the solid L = Length of the bigger prismW = Width of the bigger prismH = Height of the bigger prisml = Length of the smaller prismw = Width of the smaller prismh = Height of the smaller prismFrom the diagram in question,
Given:
L = 10.5 cmW = 9 cmH = 4 cml = 9 cmw = 4.5 cmh = 4 cmSubstitute these values into equation 1
A = (10.5×9×4)+(9×4.5×4)A = 378+162A = 540 cm³Hence, the volume is 540 cm³.
Learn more about volume here: https://brainly.com/question/1331127
#SPJ1
the slope of a graphed line is -8/7. Write the standard-form equation of the line using the coordinates of the labeled point.
The standard-form equation of the line using the coordinates of the labeled point is: B. 8x + 7y = 60.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.At data point (4, 4) and a slope of -8/7, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = -8/7(x - 4)
By multiplying all through by 7, we have:
7(y - 4) = -8(x - 4)
7y - 28 = -8x + 32
7y + 8x = 32 + 28
8x + 7y = 60.
Read more on point-slope here: brainly.com/question/24907633
#SPJ1
Help
Please show your work .
Answer:
QR=8
Step-by-step explanation:
When two lines are perpendicular, they form two 90-degree angles. So:
m∠QSR = m∠QSP = 90°
We also know that the line segment PS is congruent to the line segment SR.
Lastly, by the reflexive property, QS is congruent to itself.
Thus, ΔPSQ ≅ ΔRSQ by SAS (side-angle-side).
Now that we know these triangles are congruent, we can further state that PQ is congruent to QR by CPCTC (corresponding parts of congruent triangles are congruent).
If PQ is congruent to QR, then their measures are also congruent, and we can get this equation (by using substitution and algebra):
[tex]3n-1=5n-7=\\6=2n=\\n=3[/tex]
Plug in n to the length of QR:
[tex]5n-7=\\5(3)-7=\\15-7=\\8[/tex]
So, QR=8.
farmers use herbicides to limit the growth of weeds among their crops. do you think it would be appropriate to display these data in a histogram without first plotting them in a time plot? explain why or why not.
Whether to use a histogram or a time plot depends on the specific objective of your analysis. A histogram
is suitable for analyzing the distribution of herbicide usage, while a time plot is better for analyzing trends over time.
It would be appropriate to display these data in a histogram without first plotting them in a time plot if you are looking
to analyze the distribution or frequency of herbicide usage across different amounts or categories.
A histogram can provide a clear visualization of the distribution and help identify any patterns or trends in the data.
However, if your goal is to analyze the trend of herbicide usage over time, then it would be more appropriate to use a
time plot.
A time plot will show changes in the usage of herbicides over a specific time period and help identify any seasonal
patterns or trends in the data.
In summary, whether to use a histogram or a time plot depends on the specific objective of your analysis. A histogram
is suitable for analyzing the distribution of herbicide usage, while a time plot is better for analyzing trends over time.
for such more question on histogram
https://brainly.com/question/28164315
#SPJ11
3(6+X) = 24
SOLVE THE EUATION
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Answer:
[tex]3(6+x)=24[/tex]
[tex]3x+18=24[/tex]
[tex]3x=6[/tex]
[tex]x=2[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Help with algebra 2 homework
a) The inverse function is given as follows: [tex]r = \sqrt{\frac{3v}{40\pi}}[/tex]
b) The radius of the cone with a volume of 4190 cubic inches is given as follows: r = 10 inches.
How to obtain the inverse function?The function for this problem is defined as follows:
v(r) = 40/3πr²
We want to find the radius as a function of the volume for the inverse function, hence:
[tex]r^2 = \frac{3v}{40\pi}[/tex]
[tex]r = \sqrt{\frac{3v}{40\pi}}[/tex]
Then the radius of the cone with a volume of 4190 cubic inches is given as follows:
[tex]r = \sqrt{\frac{3 \times 4190}{40\pi}}[/tex]
r = 10 inches.
More can be learned about inverse functions at https://brainly.com/question/3831584
#SPJ1
Sky Launch Trampoline Park charges customers $9.50 per hour they spend jumping. Each customer must
also pay $2.50 for grip socks. Create a table or t-chart. Write an equation in slope-intercept form to represent this linear function.
Answer:
2.50 + 9.50h
Step-by-step explanation:
Sky Launch Trampoline Park charges customers $9.50 per hour they spend jumping. Each customer must also pay $2.50 for grip socks.
Let the number of hours be h.
The equation will be:
= 2.50 + (9.50 × h)
= 2.50 + 9.50h
assume that for some statistic 1000 tests were performed. to avoid the situation of the incorrectly found significance, bonferroni correction was applied. the resulting p-value is 0.00013. what significance level was chosen for the tests? the significance level was:
The significance level chosen for the tests with total number of test performed as 1000 for given p-value is equal to 0.87 or 87%.
Total number of test performed = 1000
p-value is equal to 0.00013
The Bonferroni correction involves ,
Adjusting the significance level for multiple comparisons by dividing it by the number of comparisons performed.
Here, 1000 tests were performed and the resulting p-value is 0.00013.
The significance level that was chosen for the tests,
Reverse the Bonferroni correction by multiplying the p-value by the number of comparisons,
adjusted p-value = p-value / number of comparisons
number of comparisons = 1000
adjusted p-value = 0.00013
p-value = adjusted p-value x number of comparisons
⇒p-value = 0.00013 x 1000
⇒p-value = 0.13
So the original p-value before the Bonferroni correction was 0.13.
The significance level, we subtract the p-value from 1,
significance level = 1 - p-value
⇒significance level = 1 - 0.13
⇒significance level = 0.87
Therefore, the significance level chosen for the tests was 0.87 or 87%
learn more about significance level here
brainly.com/question/3487014
#SPJ4
I need a bit of help please
The slope of the line in the reduced form is 4 / 7.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
Therefore,
slope = m = change in y / change in x
slope = m = y₂ - y₁ / x₂ - x₁
P = (2, 3)
Q = (9, 7)
x₁ = 2
x₂ = 9
y₁ = 3
y₂ = 7
Therefore,
slope = 7 - 3 / 9 - 2
slope = 4 / 7
learn more on slope here: https://brainly.com/question/26578510
#SPJ1
Write the point-slope form of the equation of the line that passes through the points (6, -9) and (7, 1). Include your work in your final answer. Type your answer in the box provided to submit your solution.
Therefore , the solution of the given problem of equation comes out to be 10x - y = 51 is the point-slope form of the equation of the line passing through the points (6, -9) and (7, 1).
Explain the equation.Variable words are frequently used in complex algorithms to show consistency between two arguments that are opposed to one another. Academic expressions called equations are used to show the equality of various academic figures. Take into account the details in the z + 7 proposals.
Here,
The equation for the line passing between the points (6, -9) and (7, 1) must be found in the point-slope form.
Using the equation m = (y2 - y1) / (x2 - x1), find the slope (m) of the line, where (x1, y1) and (x2, y2) are the coordinates of the two points.
=> (x1, y1) = (6, -9)
=> (x2, y2) = (7, 1)
=> m = (1 - (-9)) / (7 - 6)
=> m = 10 / 1 m = 10
Consequently, the line's slope is 10.
=> y - y1 = m(x - x1)
=> m = 10 (x1, y1) = (6, -9)
=> y - (-9) = 10(x - 6)
=> y + 9 = 10x - 60
=> 10x - y = 51
Therefore, 10x - y = 51 is the point-slope form of the equation of the line passing through the points (6, -9) and (7, 1).
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Consider a sequence whose first five terms are:-1.75, -0.5, 0.75, 2, 3.25
Which explicit function (with domain all integers n ≥ 1) could be used to define and continue this sequence?
Step-by-step explanation:
+ 1.25
every new term is the previous term + 1.25.
with starting value -1.75
f(n) = 1.25n - 1.75
A circle with center O and radius 5 has central angle XOY. X and Y are points on the circle. If the measure of arc XY is 90 degrees, what is the length of chord XY?
The length of chord XY is 5√2.
What is the length of the chord?
It is described as the line segment that connects any two points on the circle's circumference without going through the circle's center. As a result, the diameter is the chord of a particular circle that is the longest and goes through its center. In mathematics, determining the chord's length can be crucial at times.
Here, we have
Given: A circle with center O and radius 5 has a central angle XOY. X and Y are points on the circle. If the measure of arc XY is 90 degrees.
We have to find the length of chord XY.
∠XOY = 90°
OX = OY = 5
We draw a perpendicular from the center to chord XY bisect XY at D.
Now, since OD bisects ∠XOY
∠XOD = ∠YOD = 90°/2 = 45°
Now, in ΔXOD
sin45° = XD/OX
1/√2 = XD/5
5/√2 = XD...(1)
In ΔYOD
sin45° = YD/OY
5/√2 = YD...(2)
Adding (1) and (2), we get
XD + YD = 5/√2 + 5/√2
XY = 5√2
Hence, the length of chord XY is 5√2.
To learn more about the length of the chord from the given link
https://brainly.com/question/26094865
#SPJ1
Verify that the segments are parallel.
10. CD || AB
This means that the corresponding sides of the two triangles are in proportion, and therefore CD is parallel to AB, as required.
What is triangle?A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is often used in mathematics, science, engineering, and art. Triangles can be classified into different types based on the length of their sides and the size of their angles. Triangles are used in various applications, such as in the construction of buildings, bridges, and other structures, as well as in navigation and surveying. They are also important in various fields of mathematics, including trigonometry and geometry.
Here,
To use similarity theorems to show that CD is parallel to AB, we need to first establish that triangles AEB and CED are similar. If we can show that these triangles are similar, then we can use the corresponding angles theorem, which states that if two pairs of corresponding angles are congruent, then the lines containing the sides are parallel.
Let's compare the two triangles AEB and CED:
Angle AEB is congruent to angle CED (both are vertical angles).
Angle EAB is congruent to angle ECD (both are alternate interior angles formed by a transversal cutting parallel lines AB and CD).
Angle BAE is congruent to angle DCE (both are alternate interior angles formed by a transversal cutting parallel lines AB and CD).
Therefore, we have established that triangles AEB and CED are similar by the angle-angle-angle similarity theorem.
Now that we have shown that the triangles are similar, we can use the corresponding sides theorem, which states that the corresponding sides of similar triangles are in proportion, to find out if CD is parallel to AB.
The corresponding sides of AEB and CED are:
AE/CE = AB/CD
Substituting the given values, we have:
AC + CE / CE = AB / BD
4 + 12 / 12 = AB / (14/3)
16/12 = AB / (14/3)
AB = (16/12) x (14/3)
= 56/9
Now we can use the corresponding sides theorem to find the length of CD:
AE/CE = AB/CD
Substituting the values we have found, we get:
4/12 = (56/9)/CD
CD = (56/9) x (12/4)
= 14
Since we have found that AB = 56/9 and CD = 14, we can see that:
AB/CD = (56/9)/14
= 4/3
This means that the corresponding sides of the two triangles are in proportion, and therefore CD is parallel to AB, as required.
To know more about triangle,
https://brainly.com/question/28600396
#SPJ1
Mr. K drove to Milwaukee, Wisconsin for spring break. He left at 1:25pm and arrived at 3:00pm. How long did it take him to get there? Also, he spent $285 on basketball game tickets, $5 on parking, $15.90 on concessions at the game, $20 on dinner after the game, $26.69 in UBER rides to and from the game, and $35 in gas. How much money did he spend IN ALL? and if he started the trip with $400, how much money does he have left over?
Answer:
A.) 1 hour and 35 minutes
B.) $387.59
C.) $12.41
Step-by-step explanation:
Question 1 answer — 1 hour and 35 minutes
Question 2 answer — $387.59
Question 3 answer — $12.41
Hope my answer helps you.
:)
Please mark my answer as the BRAINLIEST. Plssssssssssssssssssss
A two-bedroom house in Seattle was worth $400,000 in 2005. Its appreciation rate is 3.5% each year.
a. How much is the house worth in 2015?
b. When will it be worth $800, 000?
c. In Jacksonville, houses are depreciating at 2% per year. If a house is worth $200, 000 now, how much value
will it have lost in 10 years?
Answers:
(a) $564,239.50
(b) 2026
(c) $36,585.44
==========================================
Explanation:
Part (a)
One template for exponential equations would be
y = a*b^x
Another template is
y = a(1+r)^x
which is a bit more descriptive. I'll use the second template.
a = 400000 = starting valuer = 0.035 = growth rate in decimal formr is positive for exponential growth or appreciation.
The equation y = a(1+r)^x updates to y = 400000*(1+0.035)^x and then simplifies to y = 400000*(1.035)^x
From here we plug in x = 10 because the year 2015 is ten years after 2005.
So,
y = 400000*(1.035)^x
y = 400000*(1.035)^10
y = 564239.504248449
y = 564239.50
The house is worth about $564,239.50 in the year 2015.
------------
Part (b)
We work the process of part (a) in reverse.
This time we know what y is and we want to solve for x.
Use logarithms to isolate the exponent.
y = 400000*(1.035)^x
800000 = 400000(1.035)^x
800000/400000 = (1.035)^x
2 = (1.035)^x
Log(2) = Log( (1.035)^x )
Log(2) = x*Log( 1.035 )
x = Log(2)/Log(1.035)
x = 20.1487916840008
If x = 20, then,
y = 400000*(1.035)^x
y = 400000*(1.035)^20
y = 795,915.545386338
y = 795,915.55
We're short of the goal of $800,000.
If x = 21, then
y = 400000*(1.035)^x
y = 400000*(1.035)^21
y = 823,772.589474859
y = 823,772.59
We've gone over the goal.
Somewhere between x = 20 and x = 21 is when the house will be worth exactly $800,000.
It's better to side with x = 21 since x = 20 comes up short.
21 years after 2005 is 2005+21 = 2026
------------
Part (c)
Go back to the template: y = a(1+r)^x
This time we have
a = 200,000r = -0.02The r value is negative to indicate exponential decay or depreciation.
y = a(1+r)^x
y = 200000(1+(-0.02))^x
y = 200000(1-0.02)^x
y = 200000(0.98)^x
The 0.98 means the house keeps 98% of its value from year to year.
Plug in x = 10.
y = 200000(0.98)^x
y = 200000(0.98)^10
y = 163,414.56137751
y = 163,414.56
The house starts off at $200,000 and ten years later it's $163,414.56
Subtract the values to determine how much home value was lost.
200,000 - 163,414.56 = 36,585.44
The home value will have lost $36,585.44 over the 10 year period.