Answer: This is a binomial distribution problem with parameters n = 17 and p = 0.3, where n is the sample size and p is the probability of a defective bulb. We need to find the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective.
Let X be the number of defective bulbs in the sample. Then X has a binomial distribution with parameters n = 17 and p = 0.3, i.e., X ~ B(17, 0.3).
We want to find P(3 ≤ X ≤ 6). Using the binomial probability formula, we have:
P(3 ≤ X ≤ 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
= (17 choose 3)(0.3^3)(0.7^14) + (17 choose 4)(0.3^4)(0.7^13) + (17 choose 5)(0.3^5)(0.7^12) + (17 choose 6)(0.3^6)(0.7^11)
≈ 0.1566 (rounded to four decimal places)
Therefore, the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective is approximately 0.1566.
Step-by-step explanation:
Help pleasee. I have no idea how to do this
Simple linear regression results ______ sensitive to mild departures from the underlying assumptions.
Simple linear regression results are indeed sensitive to mild departures from the underlying assumptions.
The assumptions underlying simple linear regression include:
Linearity:
The relationship between the independent variable (x) and the dependent variable (y) is linear.
Independence: The observations are independent of each other.
Normality:
The residuals (the difference between the observed values of y and the predicted values of y) are normally distributed.
Equal variance (homoscedasticity):
The residuals have equal variance for all values of x.
If any of these assumptions are violated, it can lead to biased and inefficient estimates of the regression coefficients, inaccurate standard errors, and incorrect statistical inference.
Even mild departures from these assumptions can affect the accuracy of the results.
It is important to check for these assumptions and, if necessary, use alternative methods such as robust regression or nonparametric regression to obtain more accurate results.
For similar questions on linear
https://brainly.com/question/24275089
#SPJ11
given the following scenario, would you use the wilcoxon rank sum or the mann whitney test? determining if there is a difference in ratings in maintenance quality at two tirezone locations. forty customers were randomly selected from the location on 13th street, and forty five customers were randomly selected from the newberry road location. group of answer choices wilcoxon rank sum test mann whitney test
The appropriate statistical test for comparing the difference in maintenance quality ratings at two tirezone locations, where there are two independent groups of customers, would be the Mann-Whitney test or Wilcoxon rank-sum test.
The Mann-Whitney test would be appropriate for this scenario because it is used to compare the difference between two independent groups. In this case, we have two independent groups of customers from different locations, and we want to determine if there is a significant difference in their ratings of maintenance quality.
The test compares the ranks of the observations in the two groups and uses that information to determine if there is a significant difference between them. The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is another name for the same test.
Therefore, the Mann-Whitney test or Wilcoxon rank-sum test is the appropriate statistical test to use in this scenario.
To know more about Mann-Whitney test:
https://brainly.com/question/28069693
#SPJ4
help please
A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 8 feet. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water will it take to fill up the pool completely? Use π = 3.14 and round to the nearest gallon.
2,255 gallons
1,127 gallons
301 gallons
40 gallons
To fill the entire pool we will 2,255 need gallons of water.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.
Given, A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 8 feet.
From the general formula of the volume of a cylinder,
Volume = pi × radius² × height
In our case,
radius = 8/2 = 4
Height = 6
Thus, Volume = 3.14 × 4 × 4 × 6
The volume of the Pool = 301.44 Cubic foot
Since there are 7.48 gallons of water in a cubic foot
Thus,
The volume of the pool in gallons = 301.44 × 7.48
The volume of the pool in gallons = 2,254.77
Therefore, to fill the entire pool we will 2,255 need gallons of water.
Learn more about Volume here:
brainly.com/question/1578538
Answer:
To fill the entire pool we will 2,255 need gallons of water.
Step-by-step explanation:
The mean and the standard deviation of the sample of 100 bank customer waiting times are x⎯⎯ = 5.33 and s = 2.207. Calculate a t-based 95 percent confidence interval for µ, the mean of all possible bank customer waiting times using the new system. Are we 95 percent confident that µ is less than 6 minutes?. Assume normality.
95% confidence that the population mean is less than 6 minutes since the upper limit of the confidence interval is below 6 minutes.
95% confidence that the population mean is within the range of 4.897 to 5.763 minutes.
The t-based 95 percent confidence interval for the population mean:
CI =[tex]\bar x\pm t\alpha/2 \times (s/\sqrt n)[/tex]
[tex]\bar x[/tex] is the sample mean, s is the sample standard deviation, n is the sample size, tα=/2 is the t-value corresponding to the desired level of confidence and (s/√n) is the standard error of the mean.
The sample size is 100, the sample mean is 5.33, and the sample standard deviation is 2.207, the standard error of the mean is:
s/√n
= 2.207/√100
= 0.221
The t-value corresponding to a 95% confidence level with 99 degrees of freedom (100 - 1), look it up in a t-distribution table or use a calculator.
The t-value is approximately 1.984.
The 95% confidence interval for the population mean is:
CI = 5.33 ± 1.984 × 0.221
= [4.897, 5.763]
For similar questions on Population Mean
https://brainly.com/question/28103278
#SPJ11
Whether has a saving acc he depos the same amount of money each month after 3 month had 150 in the acc after 5 month he had 300 in the acc make a table values interesting the two points
Regularly depositing the same amount into a savings account can lead to a large rise in the account balance over time with the appropriate plan and dedication.
What is amount?An undefined number or quantity of something is referred to as an amount and can be used in a variety of different settings. Any number, quantity, length of time, or amount of data can be referred to as an amount. Amount in terms of money refers to the total amount being paid or received. The quantity of physical items is the total number of those items. The length or duration of a work or event can be referred to as the amount in terms of time. The entire quantity of data points or pieces of information is referred to as the amount in terms of data.
Here in the question:
Month | Amount Deposited | Account Balance
1 | 150 | 150
2 | 150 | 300
3 | 150 | 450
4 | 150 | 600
5 | 150 | 750
As seen in the table above, after five months, a 150 initial deposit into a savings account can grow to a balance of 750 with monthly deposits of the same amount for the next four months. This demonstrates that consistent saving can have a considerable impact on a savings account's overall balance.
Since interest is calculated using the compounding principle, regular deposits can enhance the amount that can be earned over time. This indicates that interest may be accumulated on both the initial deposit and any prior interest in the account. So, by consistently contributing the same amount of money to a savings account, it is feasible to dramatically raise the account's overall balance.
In conclusion, it is clear that consistent contributions to a savings account can be an excellent strategy to build wealth. Regularly depositing the same amount into a savings account can lead to a large rise in the account balance over time with the appropriate plan and dedication.
To know more about amount, visit:
brainly.com/question/25720319
#SPJ1
Rent expense in Volusia Company's 2014 income statement is $420,000. If Prepaid Rent was $70,000 at December 31, 2013, and is $95,000 at December 31, 2014, the cash paid for rent during 2014 is:A. $480,000B. $445,000C. $395,000D. $420,000
As per the mentioned informations, the cash paid for rent during 2014 is calculated to be $395,000. So, the correct answer is option (C) i.e. $395,000.
To calculate the cash paid for rent during 2014, we need to use the information given in the problem and apply the following formula:
Cash paid for rent = Rent expense + Prepaid rent at the beginning of the period - Prepaid rent at the end of the period
Substituting the values given in the problem, we get:
Cash paid for rent = $420,000 + $70,000 - $95,000
Cash paid for rent = $395,000
Therefore, it can be concluded that the correct answer is (C) $395,000.
Learn more about Cash :
https://brainly.com/question/13226199
#SPJ4
What is ¨the surface area of a tissue box¨ unit of measurement
A - Square meters
B - Yards
C - Cubic inches
D - Cubic feet
E - Square centimeters
The surface area of a tissue box is a measure of the total area that the surface of the box occupies. Out of the options given, A - Square meters and E - Square centimetres are both square units and could be used to measure the surface area of a tissue box.
Explain surface area
The surface area is the total area that covers the outer surface of a three-dimensional object. It is calculated by adding the areas of all the faces or surfaces of the object.
Explain area
The area is the measure of the size of a two-dimensional surface or region. It is expressed in units of square units (e.g., square meters, square inches).
According to the given information
The surface area of a tissue box is a measure of the total area that the surface of the box occupies. Since area is measured in square units, the correct unit of measurement for the surface area of a tissue box would be a square unit. Out of the options given, A - Square meters and E - Square centimeters are both square units and could be used to measure the surface area of a tissue box.
To know more about surface area visit
brainly.com/question/29298005
#SPJ1
Jim's family recently moved to a new
city. The city's population has been
growing, and based on recent trends,
Jim expects it to continue growing
exponentially. This table shows the
expected population in the next two
years.
Time (years)
Population
840,000
882,000
Time (years)
1
2
Find an expression for P(t), the city's
population t years from now. Write your
answer in the form P(t) = a(b)t, where a
and b are integers or decimals. Do not
round.
P(t) =
To find an expression for P(t), we can use the two given data points to create a system of equations. We can assume that the population is growing exponentially, which means that the population at time t is given by:
P(t) = a(b)^t
where a and b are constants that we need to determine.
Using the first data point, we have:
840,000 = a(b)^1
which simplifies to:
840,000 = ab
Using the second data point, we have:
882,000 = a(b)^2
We can solve for a in terms of b by dividing the second equation by the first equation:
882,000/840,000 = (a(b)^2)/(ab)
Simplifying, we get:
1.05 = b
Substituting this value of b into the first equation, we get:
840,000 = a(1.05)
Solving for a, we get:
a = 800,000
Therefore, the expression for P(t) is:
P(t) = 800,000(1.05)^t
This means that the city's population t years from now can be calculated by multiplying the initial population of 800,000 by 1.05 raised to the power of t.
Answer:
Step-by-step explanation:
city. The city's population has beengrowing, and based on recent trends,Jim expects it to continue growingexponentially. This table shows theexpected population in the next twoyears.Time (years)Population840,000882,000Time (years)12Find an expression for P(t), the city'spopulation t years from now. Write youranswer in the form P(t) = a(b)t, where aand b are integers or decimals. Do notround.P(t) =
show that,for all value for x
(2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2
Answer:
Therefore, the answer is: (2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2
Step-by-step explanation:
To prove that (2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2 for all values of x, we can simply expand the left-hand side of the equation and simplify it to match the right-hand side.
Expanding the left-hand side using the distributive property, we get:
(2x-1)(x+2)(3x-1) = (2x^2+3x-2)(3x-1)
= 6x^3 + 7x^2 - 9x + 2
This matches the right-hand side of the equation, so we have proven that (2x-1)(x+2)(3x-1)=6x^3+7x^2-9x+2 for all values of x.
At a local store, 2 bagels and 2 cups of coffee cost $4.40. The cost of 3 bagels and 4 cups of coffee is $7.80.
Part A:
Write a system of equations to represent this situation.
Part B:
Solve the system of equations by substitution and interpret its meaning.
How do I go about solving this? (Teacher got sick mid-lesson & still wanted us to finish the worksheet but he never went over how to solve this kind of equation) Any kind of help is greatly appreciated.
[tex]g(a) = 4a-2\\h(a) = 3a\\Find: g(h(8))[/tex]
The composite function g(h(8)) when evaluated is 94.
Evaluating the composite functionsFrom the question, we have the following parameters that can be used in our computation:
g(a) = 4a - 2
h(a) = 3a
To find g(h(8)), we need to first evaluate h(8), and then plug that result into g(a) and simplify.
h(a) is defined as 3a, so h(8) = 3(8) = 24.
Now we can plug in 24 for a in g(a) and simplify:
g(a) = 4a - 2
g(h(8)) = g(24) = 4(24) - 2 = 94
Therefore, g(h(8)) = 94.
Read more about composite function at
https://brainly.com/question/10687170
#SPJ1
a farmer has 350 feet of fencing and wants to construct 3 pig pens by first building a fence around a rectangular region, then subdividing the region into three smaller rectangles by placing two fences parallel to one side of the rectangle. what dimensions of the region maximizes the total area? what is the maximum area?
To begin solving this problem, we need to determine the dimensions of the rectangular region that the farmer will fence in. Let's say the length of thr uses, is given by the equation:
e rectangle is L and the width is W. The perimeter of the rectangle, which will be the length of fencing the farme
2L + W = 350
Solving for W, we get:
W = 350 - 2L
Next, we need to divide the rectangular region into three smaller rectangles by placing two parallel fences. Let's say the two fences are placed along the length of the rectangle, dividing it into three sections with widths of x, y, and z. Therefore, we have:
L = x + y + z
Now, we can determine the area of the entire fenced-in region by summing the areas of the three smaller rectangles. The area of a rectangle is given by the equation:
Area = Length x Width
Therefore, the total area of the fenced-in region is:
Area = (xW) + (yW) + (zW)
Substituting W = 350 - 2L and L = x + y + z, we get:
Area = (x(350-2(x+y+z))) + (y(350-2(x+y+z))) + (z(350-2(x+y+z)))
Simplifying this equation, we get:
Area = 350(x+y+z) - 2(x^2 + y^2 + z^2)
To maximize the area, we need to take the derivative of this equation with respect to one of the variables (x, y, or z), set it equal to zero, and solve for the variable. This process is too complicated to do by hand, so we will use a calculator or computer program to find the maximum area.
After finding the maximum area, we can determine the dimensions of the region that give us this maximum area. We do this by using the equations we derived earlier:
W = 350 - 2L
L = x + y + z
With the maximum area and these equations, we can solve for the dimensions of the region that give us the maximum area.
In summary, the farmer should fence in a rectangular region with dimensions that maximize the total area of three smaller rectangles created by placing two parallel fences. The maximum area can be found by taking the derivative of the area equation and setting it equal to zero. The dimensions of the region that give us the maximum area can be found by using the equations we derived earlier.
learn more about dimensions here : brainly.com/question/28688567
#SPJ11
Martin is building a wire-screen chicken coop in the shape of a rectangular prism. The coop has a height of 42 inches, a width of 36 inches, and a length of 48 inches. Martin wants to determine the total surface area of the coop in order to purchase the correct amount of wire screening.
Which of the following expressions represents the total surface area of the right rectangular prism with the dimensions given above?
The total surface area of the wire-screen chicken coop is 10512 square inches.
What is surface area?The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area
According to the given information:the total surface area of the right rectangular prism, we use the formula:
2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
We are given the height, width, and length of the wire-screen chicken coop, which are 42 inches, 36 inches, and 48 inches, respectively.
Substituting these values in the formula, we get:
2(36)(48) + 2(36)(42) + 2(48)(42)
Multiplying out, we get:
= 3456 + 3024 + 4032
Adding these terms, we get the total surface area:
= 10512
Therefore, the total surface area of the wire-screen chicken coop is 10512 square inches.
To know more about surface area visit :
https://brainly.com/question/16519513
#SPJ1
find the surface area of the trapezoid
The surface area of the trapezoid is calculated to be equal to 731 square feet
How to evaluate for the surface area of the trapezoidarea of a trapezoid is calculated using the formula: 1/2 × (A + B) × height where A is and B are the parallel base. Also the trapezoid have four rectangle sides and two same trapezoid sides.
A = 10ft
B = 13ft
height = 7ft
area of two trapezoid side = 2[1/2 × (10 + 13) ft × 7 ft = 161 ft²
area of rectangle with length 15ft and width 8ft = 8 ft × 15 ft = 120 ft²
area of rectangle with length 15ft and width ft = 15 ft × 105 ft = 105 ft²
area of rectangle with length 15ft and width 13ft = 15 ft × 13 ft = 195 ft²
area of rectangle with length 15ft and width 10ft = 15 ft × 10 ft = 150 ft²
surface area of the trapezoid = 161 ft² + 120 ft² + 105 ft² + 195 ft² + 150 ft² = 731 ft².
Therefore, the surface area of the trapezoid is calculated to be equal to 731 square feet
Read more about trapezoid here:https://brainly.com/question/2234926
#SPJ1
Geometry Pleeeeeease help !!!!Find the values of x and y. Write your answer in simplest form.
The values of x and y in the simplest form in the triangles are computed and listed below
Finding the values of x and y in the simplest form.Figure (1)
Using the proportion of similar triangles, we have
x/6 = 6/9
So, we have
x = 36/9
This gives
x = 4
Next, we have
y^2 = 6^2 + 4^2
y^2 = 52
y = 2√13
Figure (2)
Using the proportion of similar triangles, we have
x/6 = 6/2
So, we have
x = 36/2
This gives
x = 18
Next, we have
y^2 = 6^2 + 18^2
y^2 = 360
y = 6√10
Figure (3)
Using the pythagoras theorem of right triangles, we have
y^2 = 40^2 - 32^2
y^2 = 576
y = 24
Next, we have
x^2 = 30^2 - 24^2
x^2 = 324
x = 18
Read more about right triangles at
https://brainly.com/question/2437195
#SPJ1
identify the values of a, h, and k in the given function, and choose the correct transformation.
The correct transformation is - "a is a stretch by a factor of 5, while h moves the graph to the left by 6, and k moves the graph up by 7".
Explain about the algebraic transformation:A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location. Every point in a reflection is equally spaced from a fixed line
The line of symmetry is another name for this curve. The Image and Pre-Image share the same size in a reflection.
General form for the member of the reciprocal family:
y = a /(x - h) + k ..eq 1
For the given function:
y = 5/(x + 6) + 7 ...eq 2
On comparing eq 1 and eq 2
a = 5
h = -6
k = 7
Now,
As, -6 is added to the x value, it shows the shift to left on x axis.5 is multiplied with the value of x, which represents the stretch with factor.At last 7 is added to the function, shows that there is a upward shift by unit 7.Thus, the correct transformation is - "a is a stretch factor of 5, while h moves the graph to the left by 6, and k moves the graph up by 7".
Know more about the transformation
https://brainly.com/question/1548871
#SPJ1
what does the equal 2,000,005,679,876=?
Answer:
N/A
Step-by-step explanation:
If you're looking for a significance or interpretation of the number 2,000,005,679,876, it's just a number. Unless utilized in a certain mathematical, financial, or another applicable context, it has no meaning or relevance. It is a big number with thirteen digits that can signify a quantity, amount, or value in a variety of scenarios depending on the context.
Dana has 9 CDs. She has 1/5 as many as Sonya. How many CDs does Sonya have?
Answer:
Usemos la variable s para representar la cantidad de CD que tiene Sonya.
Luego, dado que Dana tiene 1/5 de la cantidad que tiene Sonya, podemos escribir la siguiente ecuación y resolverla para s:
1 s = 9
5
Multiplica ambos lados de la ecuación por 5 para resolver:
5 * 1 s = 9 * 5
5
s = 45
Sonya tiene 45 CD.
Ms. Ouzts wants to by a purse for $100. Sales tax in SC is 8.5%. If she has $125 to spend on the purse, will she have enough to purchase it? Why or why not?
Yes, Ms. Ouzts will have enough to purchase the purse as $125 is greater than the total cost of the purse including tax, which is $108.50.
The sales tax in South Carolina is 8.5%, which means that the total cost of the purse including tax will be
= Cost of purse + Sales tax
Substitute the values in the equation
= $100 + (8.5% of $100) = $100 + $8.50 = $108.50
If Ms. Ouzts has $125 to spend on the purse, then she will have enough to purchase it because $125 is greater than $108.50.
In fact, she will have $125 - $108.50 = $16.50 left over after buying the purse.
Learn more about sales tax here
brainly.com/question/29442509
#SPJ4
Sovle each of the followig eqations and mark it on a number line
|3z-2|=1
The solutions to the equation are z = 1 and z = 1/3. We can mark these solutions on a number line is {1/3, 1}.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
We can solve this equation by considering two cases:
Case 1: 3z-2 = 1
Solving for z, we get:
3z-2 = 1
3z = 3
z = 1
Case 2: 3z-2 = -1
Solving for z, we get:
3z-2 = -1
3z = 1
z = 1/3
Therefore, the solutions to the equation are z = 1 and z = 1/3. We can mark these solutions on a number line as follows:
The solution set is {1/3, 1}.
To learn more about algebra from the given link:
https://brainly.com/question/24875240
#SPJ4
High clouds are those that form at altitudes of at least:
65,617 ft (20,000 m).
32,800 ft (10,000 m).
6500 ft (2000 m).
20,000 ft (6000 m).
High clouds are those that form at altitudes of at least 20,000 ft (6000 m).
At high altitudes, ice crystals form due to which cloud formation occurs. Cirrus, cirrostratus, and cirrocumulus clouds are a few types of clouds. Cirrostratus clouds frequently form a thin, white layer that resembles a veil and covers the entire sky. Small, spherical, white clouds called cirrocumulus develop in long rows. Because they can provide information about changes in atmospheric pressure, temperature, and moisture levels in the upper atmosphere, these high clouds are crucial for meteorologists to investigate.
For more info on clouds refer,
https://brainly.com/question/31557527
#SPJ4
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
The best measure of variability for the data is A. The range is the best measure of variability, and it equals 8.
How to find the range ?The range is the difference between the highest value and the lowest value in the dataset. In this case, the highest number of rose bouquets is 9, and the lowest is 1. This is the data shown on the line plot.
Range = Highest Value - Lowest Value
Range = 9 - 1
Range = 8
The range is the best measure of variability, and it equals 9. The IQR is used when there are outliers that can affect the data.
Find out more on range at https://brainly.com/question/28084761
#SPJ1
Select the correct answer.
Scatter plot graph in quadrant 1 of a coordinate plane. 12 points are plotted approximated at (2, 3), (4, 5), (5.8, 4), (5.9, 6.1), (3, 13), (4.9, 7.9), (5.5, 9.1), (6.5, 8), (6.5, 10), (7.5, 7.1), (8, 9), and (8.1, 10.1).
Which point represents the outlier?
A.
(2, 3)
B.
(4, 5)
C.
(3, 13)
D.
(8, 9)
Answer:
d
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
c
Matt is painting the trim in his living room. He leans a ladder against the wall so that it forms an angle
elevation with the floor of 56°. If it is a 12-foot ladder, how high up on the wall does it reach? Round to
the nearest tenth.
Answer:
9.9 inches
Step-by-step explanation:
Visualize the scenario for a second. If the ladder is leaning against the wall, we can assume that it is the hypothenuse of the triangle that is forming here. The angle of elevation in this scenario is the angle formed by the ladder and ground.
Next, recall each trig function and determine which best belongs. We have the hypothenuse and we need the side opposite the angle. Therefore, we use sine. (probably using a calculator for trig questions)
Therefore, we can now set up our equation and solve. (x is the height of the wall)
sin 56 = [tex]\frac{x}{12}[/tex] Initial equation
12 sin 56 = x Multiply each side by 12 so that we get x by itself.
x ≈ 9.9 Punch 12 sin 56 into a calculator and your done!
Therefore, the answer is about 9.9 inches. (If you got something different, make sure that your calculator is in degrees and not radians! Some calculators abbreviate it as DEG and RAD respectively.)
I don't get it... please help thanks in advance
Answer:
Set your calculator to degree mode.
[tex] \tan( \alpha ) = \frac{23}{35} [/tex]
[tex] \alpha = {tan}^{ - 1} \frac{23}{35} = 33.31[/tex]
The angle of elevation of the sun is about 33°.
Triangle ABC is similar to triangle DEF. What is DE?
The measure of DE, given that Triangle ABC is similar to Triangle DEF, is 53. 09 units .
How to find the measure of DE ?To find the measure of DE, you need to use the corresponding sides of BC and EF to find the scale factor that shows the difference in the sizes of corresponding sides.
The scale factor is:
= 31 / 8
= 3. 875
Now, since the value of the corresponding side of AB is 13.7 units, the measure of DE would be :
= 13. 7 x 3. 875
= 53. 09 units
Find out more on Triangles at https://brainly.com/question/9329173
#SPJ1
Function f is a logarithmic function with a vertical asymptote at x=0 and an x-intercept at (4,0). The function is decreasing over the interval (0, ∞)
The interval over which both functions are positive is (4, ∞).
How to write an equation for the transformed logarithm?In Mathematics and Geometry, the general form of a logarithm function is represented by the following mathematical equation:
f(x) = alog(±x + h) + k
Where:
a represent the scale factor of the logarithmic graphh represent a horizontal translation.k represent a vertical translation.x represent the base.Based on the given logarithm function g(z) = log₂(z + 3) - 2, we can reasonably infer and logically deduce that it is a vertical translation of this logarithmic function f(z) = log₂(z + 3).
Additionally, the logarithm function g(z) has a vertical asymptote at z = -3 and would be positive on the interval (-3, ∞). This ultimately implies that, an intersection of the intervals over which each function is positive is given by;
Intersection of intervals = (4, ∞) ∪ (-3, ∞).
Positive interval = (4, ∞).
Read more on logarithm function here: https://brainly.com/question/31288200
#SPJ1
If the distance between opposite numbers on a line is 8 units, what are the opposite numbers
The opposite numbers that have a distance of 8 units between them on a number line are: -4 and 4.
We have,
The distance on a number line between two numbers is the number of units that separates both numbers.
Opposite numbers have the same distance to point zero on a that lies between them. For example, 4 on a number line is 4 units from point 0. -4 is also 4 units. 4 is the opposite number of -4.
Distance between -4 and 4
= |-4 - 4|
= |-8|
= 8 units.
Therefore, the opposite numbers that have a distance of 8 units between them on a number line are: -4 and 4.
Learn more about the number line on:
brainly.com/question/24644930
#SPJ1
Solve the quadratic equation graphically using at least two different approaches. When necessary, give your solutions to the nearest hundredth. 16 x squared minus 400 = 0 a. x = -1.1 or x = -1 c. x = 5 or x = -5 b. x = 1.12 or x = -0.82 d. x = 1 or x = -1 Please select the best answer from the choices provided
By factoring and finishing the square , C is the right response. x = -5 or x =5
What are factoring and the square method's definitions?There are two ways to resolve quadratic equations: factoring and solving the square. A quadratic equation is factored when it is divided into two linear equations with the same solution. A method for rewriting quadratic equations in the form (x+a)²+b (x +a)² +b is known as "completing the square." This method enables us to change a quadratic expression or equation in the form an x² + b x + c to a (x - h) ² + k²from a provided quadratic expression or equation. This method can be applied to ease the process of solving complex quadratic equations .
The following techniques can be used to graphically solve the quadratic equation using at least two separate approaches:
Technique 1: Factoring
- Step 2: Finish the square
- Technique 3: Quadratic equation
- Step Four: Graphing
16x² - 400 = 0 is the quadratic equation that is provided.
First approach: factoring
The quadratic equation presented can be factored as follows:
16x²- 400 = 0
16(x² - 25) = 0
16(x + 5)(x - 5) = 0
Because of this, x = -5 or x = 5.
completing the square using method two
The square of the given quadratic equation can be completed as follows:
16x² - 400 = 0
16x² = 400
x² = (400/16)
x² = 25
x = ±√25
Because of this, x = -5 or x = 5.
To know more about factoring visit:
brainly.com/question/1863222
#SPJ1