Sum of interior angles in quadlateral (trapezoid) is 360 degrees.
\(5y+2+8y+73+2y=360\).
Simplify by collecting y terms and subtracting 73 on the other side.
\(15y+75=360\implies y=285/15=\boxed{19}\).
Hope this helps.
joel finished the race in 8.04 seconds. ray finished the race in 8.40 seconds. which statement is true? responses joel and ray finished the race in the same amount of time. joel and ray finished the race in the same amount of time. ray had the faster time. ray had the faster time. joel had the faster time.
The statement "Ray had the faster time" is true because comparing the times, Joel completed the race in 8.04 seconds, while Ray completed the race in 8.40 seconds.
Since the race is a competition where the objective is to complete it in the shortest amount of time, the athlete with the smaller time is considered the faster runner.
In this case, Ray's time of 8.40 seconds is greater than Joel's time of 8.04 seconds. Therefore, Joel had the faster time.
It's important to note that even though the time difference between them is relatively small, Ray's time is greater, indicating that it took him longer to complete the race compared to Joel.
Thus, the statement "Ray had the faster time" accurately describes the situation, highlighting that Joel achieved a quicker completion time than Ray in the race.
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Identify the y-intercept. Write as an ordered pair.
Answer: Its y-intercept is obtained when the x coordinate is 0, so that the function crosses the y-axis. Therefore, it means that x=0 . Note that the y value that corresponds to this intercept is y=f(0) y = f ( 0 ) . Thus, an ordered pair that represents the y-intercept is (0,f(0)) ( 0 , f ( 0 ) )
Step-by-step explanation:
how many pattern block triangles would create 2 hexagons
Answer:
Step-by-step explanation:
twelve triangles make 2 hexagons, which means there are 12 groups of in 2
Write the equation for the line in point slope form that passes through (-2,3) and has a slope of 4.
Answer:
y-3=4(x+2)
Step-by-step explanation:
Once you know how the point slope form equation is laid out this question is actually quite easy. Point slope form looks like this
y-y2=slope(x-x2)
I put the y in the front and the slope (4) comes after the equal sign. Then x is subtracted from x. But I put a plus sign because when you subtract a negative number, it is the same as adding a negative number. This is why the ending part of the equation is (x+2) instead of (x--2). Hopefully this makes sense...
Which word is associated with multiplication when computing probabilities? Choose the correct answer below Disjoint O And O Not
When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.
According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .
According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.
The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.
Therefore,
When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.
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In 2012 a dolphin named M007 was tracked as he swam through the Atlantic waters.
He swam 600 miles in 67 days. For 26.4 miles, M007 was tracked off the eastern
coast of Florida. How long did M007 spend near the coast of Florida? Round your
answer to nearest tenth of a day if necessary.
Answer:
2.9 days
Step-by-step explanation:
Need days / mile
67 days / 600 mi = .1116666 day/mile
.1116666 day/mi * 26.4 mi = 2.948 day ~ 2.9 days
OR
Miles per day
600 mi / 67 day = 8.9552 mi / day
26.4 mi / (8.9552 mi/day) = 2.948 ~ 2.9 day
A group of hikers tracked how long it took to hike a 10-mile trail. They hiked 2.5 miles in 2 hours, 7.5 miles in 6 hours, and 8.75 miles in 7 hours.
Determine if the relationship between the hikers' distance and time is proportional.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 0.8 miles per hour.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour.
No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 8.75 miles in 7 hours.
No, it is not proportional because 2.5 miles in 2 hours is not equivalent to 7.5 miles in 6 hours.
Option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that:
A group of hikers tracked how long it took to hike a 10-mile trail. They hiked 2.5 miles in 2 hours, 7.5 miles in 6 hours, and 8.75 miles in 7 hours.
From the data given:
Ratio = distance/time
2.5 / 2 = 1.25 miles per hour
7.5 / 6 = 1.25 miles per hour
8.75 / 7 = 1.25 miles per hour
Thus, option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.
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Find the slope and the equation of the tangent line to the graph of the function at the given value of x. y=x 4
−10x 2
+9;x=1 The slope of the tangent line is (Simplify your answer.) The equation of the tangent line is
The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.
The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.
Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:
dy/dx = 4x^3 - 20x
To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:
dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16
Therefore, the slope of the tangent line is -16.
To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:
y - y(1) = -16(x - 1)
Expanding the equation and simplifying, we have:
y - y(1) = -16x + 16
Rearranging the equation, we obtain the equation of the tangent line:
y = -16x + (y(1) + 16)
To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.
In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.
The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.
To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.
Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).
The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.
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what is the answer to -4/22t -5/22t
Answer:
-9/22tStep-by-step explanation:
Just do -4/22-5/22 = 9/22 and just add a t, which is 9/22t.
if f(x) = 3x2 + 10, what is f( - 7)?
The value of function f(-7) is 157.
What is a function?Functions have the property that each input is related to exactly one output. The function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
For the given situation,
The function is f(x) = 3 x^2 + 10
Then f( - 7) becomes,
⇒ \(f(-7)=3(-7 )^{2} +10\)
⇒ \(f(-7)=147+10\)
⇒ \(f(-7)=157\)
Hence we can conclude that the value of function f(-7) is 157.
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if sat scores are normally distributed with a mean of 500 and standard deviation of 100, what is minimum score is needed to ensure that you are ni the top 7
To determine the minimum score needed to ensure that you are in the top 7%, we need to find the z-score associated with the top 7% and then convert it back to the raw score.
The top 7% corresponds to an area of 0.07 under the standard normal distribution curve. To find the z-score associated with this area, we can use a standard normal distribution table or a calculator.
Using a standard normal distribution table or calculator, we find that the z-score corresponding to an area of 0.07 is approximately 1.4051.
To convert this z-score back to the raw score, we can use the formula:
x = z * standard deviation + mean
Substituting the values into the formula, we get:
x = 1.4051 * 100 + 500
x ≈ 140.51 + 500
x ≈ 640.51
Therefore, the minimum score needed to ensure that you are in the top 7% is approximately 640.51.
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Write a recursive definition and an explicit formula for each sequence. Then find a₁₂. 10,20,40,80,160, . . . .
Geometric Progression is a type of recursive mathematical sequence in which the next term is generated by multiplying the previous term with a fixed number that is called the Common Ratio represented by 'r'.It is calculated by the ratio of two consecutive terms.
The formula to calculate the 12th term of a Geometric Progression is :
=> \(a_{12} = a.r^{(12-1)}\)
Here a = first term, r = common ratio calculated by => r=(a2/a1), and n = \(n^{th}\) term to find
In the given question, First term a = 10, n = 12, and calculating r,
=> r = (a2/a1) => r = (20/10) = 2
Calculating,
\(a_{12\\} = (10).(2^{(12-1)})\) => \((10).(2048)\)
\(a_{12} = 20480\)
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A businesswoman bought a refrigerator from a manufacturer for $1378 calculate the selling price if she incurs a loss of 3%
Answer:
Step-by-step explanation:
Amount of loss = 3% of $1378
\(=\frac{3}{100} \times 1,378\)
\(=\$41.34\)
Selling price \(=\$1,378-\$41.34\)
\(=\$1,336.66\)
Dylan's cow produces 21 1/3 liters of milk per day.The milk is put into bottles with a volume of 2 1/3 liters.How many bottles does Dylan need each week to bottle all the milk?
The amount of bottles that Dylan needs each week to bottle all the milk is; 64 bottles
How to work with Algebra?
We are given;
Amount of Milk produced by Dylan's cow per day = 21 ¹/₃ liters
Thus, amount of liters of milk produced in a week = 21 ¹/₃ liters * 7 = 448/3 liters.
Then, number of bottles required in a week = 448/3 ÷ 2¹/₃ = 448/7
Number of bottles required in a week = 64 bottles
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Suppose you are conducting a study of reaction times for a group of 10 depressed individuals and 10 non-depressed individuals. You want to compare mean reaction times but in order to use a pooled t test you need to make sure the variances for the two groups are not significantly different. Let var1=8 and var2=25. Are the variances similar enough so you can use the pooled t test to evaluate differences in the means?
Yes or no?
No, the variances are not similar enough to use the pooled t test. The ratio of the two variances (25/8) is greater than 3, which is the typical cutoff for determining similarity of variances. Therefore, an alternative method such as the Welch's t-test or a non-parametric test should be used to compare the means.
To determine if the variances are similar enough to use a pooled t-test, you can perform an F-test for equality of variances. Follow these steps:
1. Calculate the F statistic by dividing the larger variance by the smaller variance: F = var2 / var1 = 25 / 8 = 3.125.
2. Determine the degrees of freedom for each group: df1 = 10 - 1 = 9 and df2 = 10 - 1 = 9.
3. Check the F critical value for the given degrees of freedom and chosen significance level (e.g., 0.05) using an F-distribution table or a calculator. For df1 = 9 and df2 = 9 at a 0.05 significance level, the F critical value is approximately 3.18.
4. Compare the calculated F statistic to the F critical value: 3.125 < 3.18.
Since the F statistic is less than the F critical value, we fail to reject the null hypothesis that the variances are equal. Therefore, the variances are similar enough to use the pooled t-test to evaluate differences in the means. The answer is yes.
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Using simple moving averages and the following time series data, respond to each of the items.
Period Demand
1 130
2 122
3 121
4 112
5 141
6 105
7 116
8 118
9 142
10 125
Click here for the Excel Data File
b. Compute all possible forecasts using a six-period simple moving average model. (Round your answers to 1 decimal place. )
c. Compute the MAD. (Round your answer to 1 decimal place. )
d. What is the forecast demand for period 11? (Round your answer to 1 decimal place. )
e. What is the error associated with the eleventh-period forecast? (Round your answer to 1 decimal place. )
To calculate the error associated with the eleventh-period forecast using simple moving averages, we need to first determine the forecasted value for the eleventh period. We can do this by taking the average of the previous 10 periods, which gives us a forecast of 65.7.Next, we need to compare this forecasted value with the actual value for the eleventh period. Let's say the actual value for the eleventh period is 70. The error associated with the eleventh-period forecast would then be the difference between the forecasted value and the actual value, which is 70 - 65.7 = 4.3.
Therefore, the error associated with the eleventh-period forecast is 4.3.
This means that the simple moving average model has a deviation of 4.3 units from the actual value for the eleventh period. In summary, simple moving averages can be useful in forecasting future values based on historical data. However, it is important to keep in mind that there may be errors associated with the forecasts. The error associated with the eleventh-period forecast can be calculated by finding the difference between the forecasted value and the actual value for that period. It is essential to monitor these errors to ensure the accuracy of the forecasting model.
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The question asks for the calculation of the simple moving average, forecasted demand, and associated error for a series of time period demands. The methods for these calculations are described, but without actual demand for period 11, we can't compute its associated error.
Explanation:To compute a six-period simple moving average for the forecast, we need to average the demand for the last six periods. We can't calculate it for the first five periods as we don't have enough previous data points.
For period 6, the 6-period SMA = (130+122+121+112+141+105) / 6 = 121.8 (rounded to 1 decimal place).
Continue this for the remaining periods. This method will give us the forecasts.
MAD (Mean Absolute Deviation) is a measure of forecast accuracy. It can be arrived at by taking the average of the absolute differences between the actual and forecasted values.
The forecast demand for period 11 should be the SMA based on the demand of periods 5-10.
The error associated with the eleventh-period forecast is the difference between the actual demand in period 11 and our forecast for it. As we do not have the actual demand for period 11 in the data provided, we cannot calculate this error.
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The scalar k is equal to 6. Vectors vì and v2 are defined as
vi = <-3, 6 > and v2 4, -8>
Evaluate: kvi + U.
a survey of over 7{,}0007,0007, comma, 000 randomly selected employees in 151515 nations recently showed that employees who work in a digital workplace tended to be happier than those who don't work in a digital workplace. can we conclude that working in a digital workplace caused employees to be happier? why?
We cannot conclude that working in a digital workplace caused employees to be happier from the survey.
How is the conclusion from the survey explained?
A survey is a technique for acquiring data which could be considered as an information and not be considered as a conclusion.Surveys are statistical tools which are insufficient to generalize the entire population.A formal questionnaire is developed, and the questions are then asked in a specific order, according to the structured method of data gathering used in surveys , which doesn't include any scientific research or proof.Experimental research is not conducted in surveys which include only descriptive research.Scientific evidences from experiments are required to conclude that working in a digital workplace caused employees to be happier.To learn more about surveys, refer:
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The volume of a cube is 500 cubic feet. What is the length of each edge of the cube?
Answer:
About 7.94
Step-by-step explanation:
The formula to find the edge of each side is V^1/3. And 500^1/3 is about 7.94
Answer:
i keep getting a different answer every time _-_ I'M LOSING MY MIND!!!
Use the Law of Sines to find the missing angle of the triangle.
Find m∠B to the nearest tenth.
Answer:
m∠B = 70.0° (nearest tenth)
Step-by-step explanation:
Sine Rule for Angles
\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Given:
a = 13c = 19A = 40°Substituting the given values into the formula to find m∠C:
\(\implies \sf \dfrac{\sin 40^{\circ}}{13}=\dfrac{\sin C}{19}\)
\(\implies \sf \sin C=\dfrac{19\sin 40^{\circ}}{13}\)
\(\implies \sf C=\sin^{-1}\left(\dfrac{19\sin 40^{\circ}}{13}\right)\)
\(\implies \sf m \angle C=69.96086904^{\circ}\)
Interior angles of a triangle sum to 180°
\(\implies \sf m \angle A+ m \angle B+m \angle C=180^{\circ}\)
\(\implies \sf 40^{\circ} + m \angle B+69.960...^{\circ}=180^{\circ}\)
\(\implies \sf m \angle B=70.03913...^{\circ}\)
Therefore, m∠B = 70.0° (nearest tenth)
Could you help me with this geometry question?
The value of <RQZ has been calculated as 21 from the solution we have below.
How to solve for RQZWe have
< PZQ= <PQZ
PQR - PRQ = 42
Let < PZQ = y⁰
PQZ = y⁰
Let PRQ = x⁰
< PQR = x + 42⁰
< QpZ + y + y = 180⁰
such that
QPZ + 2y = 180⁰
<QPZ = 180⁰ - 2y
<(QPZ + PQR + PRQ) = 180
Adding these equations, we would have
180 - 2y + x + 42 + x = 180⁰
180 would cancel out
We have
2x - 2y + 42 = 0
x- y +21 = 0
We have to add 21 to both sides of the equation
x- y + 42 = 21
(x + 42) - y = 21
(x + 42) = <PQR and y = < PQZ
Hence 21 = <RQZ
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In Ms. March's class, 7/10 of the students walk to school. Another 1/5 of the students ride thier bikes. The other students ride on the school bus. What fraction of the class rides on the school bus?
A. 1/10
B. 1/5
C. 2/5
D. 1/2
(I will mark brainliest!)
Answer:
1/10 of the class
Step-by-step explanation:
We already know:
Total students: 10/10Determining the fraction of the total students rides on school bus
\(\implies\dfrac{7}{10} = \text{Walk}\) \(\dfrac{10}{10} - \dfrac{7}{10} = \boxed{\dfrac{3}{10}} \ \text{students remain}\)
\(\implies\dfrac{1}{5} = \dfrac{2}{10} = \text{Ride bikes}\) \(\dfrac{3}{10} - \dfrac{2}{10} = \boxed{\dfrac{1}{10} }\ \text{student remain}\)
Thus, 1/10 of the class rides on the bus.
Help me with this please
Answer:
(-12, -18)
Step-by-step explanation:
https://www.omnicalculator.com/math/endpoint
A concave shaving mirror has a radius of curvature of +31.5 cm. It is positioned so that the (upright) image of a man's face is 3.40 times the size of the face. How far is the mirror from the face? Number i Units
The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.
Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40
We know that the formula for magnification is given by:
m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :
f = r/2where,f = focal length of the mirror
Using the mirror formula:1/f = 1/v - 1/u
We know that a concave mirror has a positive focal length, so we can replace f with r/2.
We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u
Also, from the given data, we have :m = v/u
Substituting the value of v/u in terms of m, we get: u/v = 1/m
So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u
Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm
Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.
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A researcher describes the characteristics of three groups of subjects in a study. What statistics should the researcher use to analyze this demographic data
These statistical measures help the researcher summarize, describe, and understand the data collected from the study participants.
As the researcher is describing the characteristics of the subjects, the appropriate statistical analysis would be descriptive statistics.
Descriptive statistics is a method that summarizes and describes the data collected in a study. It includes measures such as mean, median, mode, standard deviation, range, and frequency distribution.
These measures can provide a clear picture of the demographic data of the three groups of subjects and help in drawing meaningful conclusions.
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Five state officials are listed to the right. a. List the 10 possible samples (without replacement) of size 3 that can be obtained from the population of five officials. Governor (Upper G) Lieutenant Governor (Upper L) Secretary of State (Upper S) Representative (Upper R) Press Secretary (Upper P) b. If a simple random sampling procedure is used to obtain a sample of three officials, what are the chances that it is the first sample on your list in part (a)? the second sample? the tenth sample? a. List all 10 possible samples (without replacement) of size 3. Use the letter abbreviation for each official.
Answer:
All possible are:
(G,L,S)
(G,L,R)
(G,L,P)
(G,S,R)
(G,S,P)
(G,R,P)
(L,S,R)
(L,S,P)
(S,R,P)
{L,R,P)
Probability of 1st/2nd/10th sample = 1/10
Step-by-step explanation:
All the possible combinations of the 3 size samples from a 5 size population have been listed without repetition.
Total Numbers of Samples = 10
To find the probability of finding the first sample from random sampling procedure,
Probability = Number of desired outcomes/ Total number of outcomes
Where Number of desired outcome is 1 and total number of outcomes is 10.
Probability = 1/10
Similarly, to find 2nd sample or 10th sample, the number of desired outcomes is same i.e 1, hecne the probability remains the same i.e 1/10
Possible samples:
(G,L), (G,S), (G,A), (G,P), (L,S), (S,A), (A,P), (L,P), (S,P), (A,L).
a) Given:
Population size \(N=5\).
Sample size \(n=2\)
Possible sample (without replacement)
\(\Rightarrow 5C_{2}=\frac{5!}{2!\times 3!}\)
\(=\frac{5\times 4}{2}\)
\(=10\)
\(10 samples:-\)
Governor, Lieutenant Governor, secretary of state, Attorney General, Press (P)
Possible samples:
(G,L), (G,S), (G,A), (G,P), (L,S), (S,A), (A,P), (L,P), (S,P), (A,L).
b) Event: \(E\to\)choosing sample second and tenth.
\(E=\left\{\left ( G,S \right ),\left ( A,L \right ) \right\}\\n\left ( E \right )=2\\n(S) =10\)
The Probability of that it is the first sample.
Second and tenth sample\(=\frac{n\left ( E \right )}{n(S)}\)
\(=\frac{2}{10}\)
\(=\frac{1}{5}\)
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What’s the inequality for the equation 3m - 4 > 11
Answer: m > 5
Step-by-step explanation:
3m-4 > 11
+5 +5
3m > 15
Divide by 3
m > 5
Help plz.
................
Answer:
-2, 14 is your answer. Hope this helps!
Step-by-step explanation:
If k(-5, 10) is midpoint and (-8, 6) is one side then you add -3 and subract 4 to get L. That means subtract 3 from -5 and add 4 to the 10.
Open with
What is the value of 3-1 +3-2?
Answer:
3
Step-by-step explanation:
p = 8 x10 and q = 4 X10
Work out the value of each expression,
P - Q
Answer:
p = 80 and q = 40
so p - q = 80 - 40 = 40
Hey there!
If.........
p = 8 • 10
q = 4 • 10
8 • 10 – 4 • 10
8 • 10 = 80
4 • 10 = 40
80 – 40 = 40
Answer: 40 ☑️
Good luck on your assignment and enjoy your day!
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