Answer:
Step-by-step explanation:
Part A:
To find the value of the remaining angles, we can use the fact that the sum of the angles in a triangle is 180°.
First, let's find the value of <1. We have:
<4 + <1 + <2 = 180°
4 + <1 + (180° - 5 - 4) = 180°
4 + <1 + 171° = 180°
<1 = 5°
Next, let's find the value of <7. We have:
<7 + <5 + <6 = 180°
<7 + 135° + (180° - 10 - 5) = 180°
<7 + 135° + 165° = 180°
<7 = 0°
Finally, let's find the value of <9. We have:
<9 + <10 + <11 = 180°
<9 + 11° + (180° - 10 - 11) = 180°
<9 + 11° + 159° = 180°
<9 = 0°
Part B:
The angle <4 is supplementary to angle <1, meaning they add up to 180°.
The angle <7 is congruent to angle <5, meaning they have the same measure.
The angle <9 is congruent to angle <10, meaning they have the same measure.
Maggie has decided to collect Hot Wheel cars. She is allowed to buy 15 cars a week with her allowance and she currently has 2 cars in her room. Identify
the rate of change, the initial value and write the function that best models the situation.
O Rate of Change: 2; Initial Value: 15; y = 2 + 15x
O Rate of Change: 2; Initial Value: 15; y = 2x + 15
O Rate of Change: 15; Initial Value: 2; y = 2x + 15
O Rate of Change: 15, Initial Value: 2; y = 15x + 2
Maggie's rate of change for her car is 15; her initial value is 2; and the best function to model her situatioon is y = 2 + 15x (D).
Based on the given case, we know that:
"Maggie can buy 15 cars per week with her allowance."This statement gives information about Maggie's rate of change, showing how many cars Maggie can buy per week.
"She currently has 2 cars in her room."This statement shows that currently, she already has 2 cars. 2 cars are her initial value.
This situation represents that, Maggie might buy 15 cars every week as an additional to her current 2 cars. This situation can be formulated as:
y = 15x + 2
where:
y = total cars
x = number of weeks
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whats the original price if the sale price is 72 with a 64 disscount
If the sale price is 72 with a 64% discount. Then the original price will be $200.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
If the sale price is 72 with a 64% discount. Then the original price is given as,
⇒ $72 / (1 - 0.64)
⇒ $72 / 0.36
⇒ $200
If the sale price is 72 with a 64% discount. Then the original price will be $200.
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80. Rochester, New York (43. 2°N, 77. 6°W). And Richmond.
Virginia (37. 5°N, 77. 5°W), have approximately the same
longitude, which means that they are roughly due north-
south of each other. Use the difference in latitude to
approximate the distance between the cities.
The approximate latitudinal distance of cities Rochester and Richmond is 394 miles
Let us assume the angle between the 2 cities as θ
θ = 43.2° - 37.6°
=5.7°
hence for finding the latitudinal distance between the cities (given that the Earth is approximately spherical) we can use the formula
distance= [tex]\frac{\theta}{360} *2\pi r[/tex]
= [tex]\frac{5.7}{360} *2 (3.14)(3960)[/tex]
= 393.756 miles ≈394 miles
therefore the distance comes out to be 394 miles
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Which congruence transformation follows the rule (x,y) --> (-x,y)
Answer:
Congruence D transformation follows the rule (x,y)--> (-x,y)
what+is+the+value+of+a+bond+with+a+coupon+rate+of+8%,+a+par+value+of+$1,000,+maturing+in+8+years,+making+semi-annual+payments,+if+the+appropriate+discount+rate+is+6%+per+year?
The value of the bond if the rate of interest currently is 6% the value of the bond is Rs. 1,000 and if it is 8% it is 750
Now, According to the question:
A bond is a sort of financial instrument where the issuer (debtor) owes the holder (creditor) a debt and is required, based on the terms, to pay the creditor cash flow at the bond's maturity date as well as interest over a certain period of time. The interest is often due annually, semi-annually, and on occasion less frequently. Bonds give the borrower access to external capital for momentary investments or, in the case of government bonds, for the financing of ongoing expenses. Despite the fact that both bonds and stocks are securities, bondholders hold a position as a creditor and stockholders hold equity in a firm. The main distinction between the two is this.
Value of the bond= V = 1/I = 60/.08 = 750
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experimental insight 2.1 describes data on the kernel color distribution of bicolor corn, collected by a genetics class like yours. to test the hypothesis that the kernel color of bicolor corn is the result of the segregation of two alleles at a single genetic locus, the class counted 9882 kernels and found that 7506 were yellow and 2376 were white. use chi-square analysis to evaluate the fit between the segregation hypothesis and the class results.
To test the hypothesis that the kernel color of bicolor corn using chi-square analysis to evaluate the fit between the segregation hypothesis and the class results as the ratio 0.01:0.05 and degree of freedom is 4.82.
Formula for Chi square is,
[tex]x^2 = \frac{(O - E)^2}{E}[/tex]
O = Observed Value
E = Expected Value
So x = 9882/2376 = 4.82.
And after getting a ratio of the yellow and white from the chi diagram we have class ratio of 0.01:0.05
When the sample sizes are large, a chi-squared test (also known as a chi-square or 2 test) is a statistical hypothesis test used in the study of contingency tables. To put it another way, the main purpose of this test is to determine if two categorical factors (two dimensions of the contingency table) have independent effects on the test statistic (values within the table).
The test, specifically Pearson's chi-squared test and its variations, is valid if the test statistic is chi-squared distributed under the null hypothesis. If there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table, it can be determined using Pearson's chi-squared test. A Fisher's exact test is used as an alternative for contingency tables with smaller sample sizes.
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What is 100 °F in °C?
The conversion factor from Celsius to Fahrenheit is 37.78.
How can you quickly translate F to C?We employ conversion formulae that are similar to those found in most textbooks. Add 32 and multiply by.5556 (or 5/9) to convert temperatures from degrees Fahrenheit to degrees Celsius. Add 32 and multiply by 1.8 (or 9/5) to convert temperatures from degrees Celsius to Fahrenheit.Let's take a closer look at how to convert between Celsius and Fahrenheit scales. Explanation: °F = °C (9/5) + 32 is the conversion formula from Celsius to Fahrenheit.The conversion factor from Celsius to Fahrenheit is 37.78. Let's take a closer look at how to convert between Celsius and Fahrenheit scales.To learn more about Fahrenheit refer to:
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Yoooo please help meeeeeee tyyyyyyyyy ik its easy but I’m just not smart
Answer:
Step-by-step explanation:
The answer will be 24 because the LCM ( Lowest common Multiple)
of 3 and 8 is 24.
Answer:
24
Step-by-step explanation:
3 x 8 = 24
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 15\le x \le 3015≤x≤30.
The average rate of change over the interval 15 ≤ x ≤ 30 is equal to -6/5.
How to determine the average rate of change?In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function f(x) over the interval [15, 30]:
a = 15; f(a) = 40
b = 30; f(b) = 22
For the average rate of change over the interval 15 ≤ x ≤ 30, we have the following:
Average rate of change = [f(b) - f(a)]/(b - a)
Average rate of change = [22 - 40]/(30 - 15)
Average rate of change = -18/15
Average rate of change = -6/5
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the radius of a circle is 10.4 ft. find the circumference \textit{to the nearest tenth}to the nearest tenth.
The circumference with radius of 10.4 ft is 65.3 ft. The result is obtained by using the formula for circumference.
What is circumference?Circumference is also called the perimeter of a circle. It can be expressed as
P = 2πr
Where
Radius of the circle = m.π = 22/7 or 3.14 ft.The circumference with the radius = 10.4 ft.
We have
Radius of a circle, r = 10.4 ftFind the circumference! (to the nearest tenth)
The circumference will be
P = 2πr
P = 2(3.14)(10.4)
P = 65.3 ft
Hence, the perimeter of the circle to the nearest tenth is 65.3 feet.
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What are the multiplication and division properties of equality?
Multiplication and division properties of equality are stated below.
What is Multiplication and Division?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Multiplication property of equality states that if a real number has been multiplied with the expressions on both sides of the equation, then the expressions on both sides remains equal to each other.
That is, if x = y, then ax = ay, where a is a real number.
Division property of equality states that if a real number has been divided by the expressions on both sides of the equation, then the expressions on both sides remains equal to each other.
That is if x = y, then x/a = y/a.
Hence the multiplication and division property of equality has been stated.
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building is 120 meters tall. A scale model of the building uses a scale of 1 entimeter = 6 meters. How tall is the model?
Answer:
The answer is 20 cm.
Step-by-step explanation:
From the scale, we know that 1 cm in the model represents 6 meters in the actual building.
So, h cm in the model represents 6h meters in the actual building.
The actual building is 120 meters tall, so 6h = 120 meters.
Dividing both sides by 6, we get:
h = 20 cm.
Therefore, the height of the model is 20 cm.
A list of terms follows. For each term: (i) State whether the term is a variable name or a variable value. (ii) State the level of measurement. Example: support for same-sex marriage. (i) variable name. (ii) ordinal.A. ageB. conservativeC. strongly opposeD. regionE. 57 yearsF. strictly enforcedG. CatholicH. gender
(i) State whether the term is a variable name or a variable value.
(ii) State the level of measurement.
A. age
(i) Variable name.
(ii) Ratio.
Explanation: "Age" is the name of the variable and it is a numerical value representing the number of years a person has lived. It is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).
B. conservative
(i) Variable name.
(ii) Nominal.
Explanation: "Conservative" is the name of b and it refers to a political ideology. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., conservative, liberal, socialist) and have no meaningful mathematical operations.
C. strongly oppose
(i) Variable value.
(ii) Ordinal.
Explanation: "Strongly oppose" is a value of the variable, and it refers to a person's opinion or attitude towards a certain issue. It is measured on an ordinal scale, meaning it has a rank or order (e.g., strongly oppose, somewhat oppose, neutral, somewhat support, strongly support). However, the difference between two values is not necessarily equal (e.g., the difference between strongly oppose and neutral might be different from the difference between neutral and strongly support).
D. region
(i) Variable name.
(ii) Nominal.
Explanation: "Region" is the name of the variable and it refers to a geographical area, such as the Midwest or the South. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Midwest, South, West, Northeast) and have no meaningful mathematical operations.
E. 57 years
(i) Variable value.
(ii) Ratio.
Explanation: "57 years" is a value of the variable "Age" and it represents the number of years a person has lived. As mentioned above, "Age" is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).
F. strictly enforced
(i) Variable value.
(ii) Ordinal.
Explanation: "Strictly enforced" is a value of a variable, and it refers to the level of enforcement of a rule or law. It is measured on an ordinal scale, meaning it has a rank or order (e.g., not enforced, loosely enforced, strictly enforced). However, the difference between two values is not necessarily equal (e.g., the difference between not enforced and loosely enforced might be different from the difference between loosely enforced and strictly enforced).
G. Catholic
(i) Variable name.
(ii) Nominal.
Explanation: "Catholic" is the name of the variable and it refers to a religious affiliation. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Catholic, Protestant, Jewish, Muslim) and have no meaningful mathematical operations.
H. Gender
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Question 1 Multiple Choice Worth 5 points) (06.01 LC) Segment AB has point A located at (5, 4). If the distance from A to B is 7 units, which of the following could be used to calculate the coordinates for point B?
a. 7 = √(x-4)^2 + (y+5)^2
b. 7 = √(x+5)^2 + (y+4)^2
c. 7 = √(x-4)^2 + (y-5)^2
d. 7 = √(x-5)^2 + (y-4)^2
To calculate the coordinates of B, we use 7 = √(x-4)^2 + (y-5)^2
What is Pythagoras Theorem?Pythagoras Theorem states that "In a right- angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides".
The sides of this triangle have been named Perpendicular, Base and Hypotenuse. The hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
Given:
To calculate the coordinates for point B, we can use the Pythagorean Theorem.
In this case, we are given point A located at (5, 4).
We also know that the distance from A to B is 7 units.
We can represent this as a right triangle, with point A being one of the legs and the distance of 7 units being the hypotenuse.
Now, using the Pythagorean Theorem, we can calculate the coordinates for point B.
Let consider the coordinates of B (x, y)
The distance between A and B be 7 units. So, we use distance formula,
7 = [tex]\sqrt{ (x - 4)^{2} + (y - 5)^{2}[/tex]
We can do this by setting up the equation 7 = [tex]\sqrt{ (x-4)^2 + (y-5)^2 }[/tex]and then solving for x and y.
To solve for x, we can start by subtracting 4 from both sides of the equation, giving us 3 = [tex]\sqrt{x^2 + (y-5)^2}[/tex]. Now,
we can take the square root of both sides to get x = √3.
Similarly, to solve for y, we can start by subtracting 5 from both sides of the equation,
giving us 2 = [tex]\sqrt{(x-4)^2 + y^2}[/tex]. Now, we can take the square root of both sides to get y = √2.
Therefore, the coordinates for point B are (√3, √2).
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After school, Terrell skateboards directly from school to a skate park and then from the skate park to a movie theater. The skate park is 8 miles south of the school and the movie theater is 6 miles east of the skate park. What is the straight-line distance between the school and the movie theater?
In the Walking Dead, the number of zombies doubles every episode. If, in episode 1, there were 75 zombies, how many zombies are in episode 16??
Please help ;-;
There are 4915200 zombies in the episode 16.
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
y = a(1+r)ˣ,
where a is the initial population and r is the rate in decimals and x is the time period.
Given:
In the Walking Dead, the number of zombies doubles every episode.
In the episode 1,
there were 75 zombies.
Then,
y = 75(2)¹⁶
y = 4915200
Therefore, 4915200 zombies.
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This stuff is so confusing please help
The measure of angle D of the isosceles triangle given above would be = 16°
What is an isosceles triangle?An isosceles triangle is defined as the type of triangle that has all its three sides less than an acute angle, that is less that angle 90°. Also, all the internal angles of an isosceles triangle= 180°
Total internal angles of the isosceles triangle = 180°
Angle C = 2x + 17
Angle E = 8x - 13
Angle D = X
To calculate D the following is carried out:
180 = 2x+ 17 + 8x - 13 + X
180-17+13 = 2x+8x+X
176 = 11x
X = 176/11
X=16°
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Given two systems of equations, determine if they have the same solution.
System A System B
−12x+9y=7 −12x+9y=7
9x−12y=6 −9x+5y=9
1. Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 3
and adding to the first equation in system A
2. No, they don't have the same solution.
3. Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 1/3 and adding to the first equation in system A.
4. Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 1/3
and subtracting from the first equation in system A.
No, they don't have the same solution. Then the correct option is B.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
−12x + 9y = 7 ...1
9x − 12y = 6 ...2
From equations 1 and 2, then we have
−36x + 27y = 21 ...3
36x − 48y = 24 ...4
Add both equations, then we have
27y − 48y = 21 + 24
− 21y = 45
y = − 45/21
y = − 15/7
Then the value of the variable 'x' is given as,
9x − 12(−15/7) = 6
9x + 180/7 = 6
9x = −138/7
x = −46/21
No, they don't have the same solution. Then the correct option is B.
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the town of pleasantville conducted a 5-year crime prevention program. based on the graph, what was the percent of change in the number of crimes from year 1 to 5
The requried percentage change in crimes from years 1 to 5 is given as 60.86%.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
From the table.
Crime in year 1 = 23
Crime in year 5 = 9
Percentage change = 23 - 9 / 23 ×100%
= 60.86%
Thus, the requried percentage change in crimes from years 1 to 5 is given as 60.86%.
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Perform the calculation and round the answer to the correct number of significant figures. 19.948 - 8.57 =
Answer:
11.4
Step-by-step explanation:
19.948-8.57=11.378
approximately 11.4
The correct number of significant figures is found as 1.1378 x 10⁻¹ .
Define the term significant figures?To demonstrate the accuracy of measurements and calculations in the fields of math, chemistry, and other sciences, significant figures are essential.
The following five rules can be used to assess whether a number is significant.
All non-zero digits, from 1 to 9, have meaning.Between nonzero numbers, all zeros have meaning.Zeros that come before or on the left of a non-zero digit have no meaning. These zeros are only stand-ins.When there is a decimal point, zeros following a nonzero digit are important.When there is no decimal point, zeros that follow a nonzero digit are not meaningful.The equation is given as:
= 19.948 - 8.57
On subtracting.
= 11.378
On converting in the significant figures:
= 1.1378 x 10⁻¹
Thus, the correct number of significant figures is found as 1.1378 x 10⁻¹ .
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In the diagram below of triangle IJK, L is the midpoint of IK and M is the
midpoint of JK.If LM = 4x+8, and IJ = 5x + 22, what is the measure of
LM?
On solving the provided question, we can say that in the triangle LM = 2*(IJ) x = |-6| = 6 and LM = 4x + 8 = 32 units
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
given,
LM = 4x + 8 and IJ = 5x +22
in the triangle LM = 2*(IJ)
4x + 8 = 2*(5x + 22)
4x + 8 = 10x + 44
6x + 36
x = |-6| = 6
LM = 4x + 8 = 32 units
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15 is what percent of 40
The correct representation of the sentence 15 is what percent of 40 is 15 is 37.5% of 40.
What are percentages?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
The algebraic representation of the statement 15 is what percent of 40 is:
40 (x/100) = 15
40x / 100 = 15
40x = 1500
x = 1500/40
x = 37.5
Hence, the correct representation of the sentence 15 is what percent of 40 is 15 is 37.5% of 40.
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A company is printing 250 calendars. In one hour, 75 calendars are printed.
What percent of the calendars are printed in 1 hour?
Answer:
In one hour, 75 calendars were printed, which is 30% of the total number of calendars (250). Therefore, the percent of the calendars printed in one hour is 30%.
Answer: 30
Step-by-step explanation: The answer would be 30 because if you took 75 and divided by 200 you would end up with a product of about 30! Hopefully this helped you!!
The quadrilateral ABCD on the coordinate plane has the following characteristics. Line segment A. D. Can be represented by the equation Y equals minus 3X where -1 is less than or equal to X less than or equal to zero. Line segment BC can be represented by the equation Y equals negative 3X +11 where to is less than or equal to X less than or equal to three. Lines CD has coordinates C(2,5) and D (-1,3). In order for ABC D to be a parallelogram with the following coordinates correspondent line segment AB ?
The equation of line segment AB is y = 3.5x - 0.5.
Line segment AB starts at point A(-1, -3) and ends at point B(3, 11). The equation for this line can be found by calculating the slope and then using the point slope formula, y-y1=m(x-x1).
The slope of the line is m= (11-(-3)) / (3-(-1)) = 14/4 = 3.5.
Using the point-slope formula, we can find the equation of the line:
y-(-3) = 3.5(x-(-1))
y + 3 = 3.5x + 3.5
y = 3.5x - 0.5
Therefore, the equation of line segment AB is y = 3.5x - 0.5.
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Refer to the T-account below:
Manufacturing Overhead
(2)
4,000
(9)
150,000
(3)
15,000
(4)
80,000
(5)
30,000
(6)
25,000
154,000
150,000
Bal.
4,000
Entry (4) could represent which of the following except?
A) Indirect labor cost incurred.
B) Factory insurance cost.
C) Overhead cost applied to Work in Process.
D) Depreciation on factory equipment.
Overhead cost applied to Work in Process. and hence Option (c) is correct for the production
Refer to the T-account below:
Manufacturing Overhead
(2)
4,000
(9)
150,000
(3)
15,000
(4)
80,000
(5)
30,000
(6)
25,000
154,000
150,000
Bal.
4,000
Labor costs = $175,000
Production order = $150,000
General factory use = $25,000
Factory overhead applied to production = $23,000
Therefore, the journal entry is as follows:
Work in process A/c Dr. $23,000
To Factory overhead $23,000
(To record the factory overhead applied to production
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Two secretarial students, AGYEMANG and IKE, are used- Typewriter dealers. They found that the length of time before a major repair is required on Typewriter sold is normally distributed, with a mean equal to 11 months and a standard deviation of 2 months. If the dealers want only 5% of the cars to fail before the end of the guarantee period, for how many months should the Typewriters be guaranteed?
The Typewriters should be guaranteed for 7.72 months, which would give a 5% chance of requiring a major repair before the end of the guarantee period.
Typewriter repair times have a normal distribution, with a mean of 11 months and a standard deviation of 2 months. To find the warranty period at which only her 5% of typewriters fail before the warranty expires, we need to find the corresponding z-score and solve it after the warranty period.
Using the standard normal distribution table, we find that the Z-score corresponding to a cumulative probability of 0.95 is approximately 1.64.
This means that 95% of typewriters will need major repairs after 11 + 1.64 * 2 = 14.28 months.
To ensure that only 5% of typewriters fail before the warranty expires, the warranty period should be set to 11 - 1.64 * 2 = 7.
72 months.
Finally, the typewriter still has about 7.72 months of warranty, and only 5% of cars fail before the warranty runs out.
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ex 1: create a function that will return the product of two integers.
The code that creates a function that will return the product of two integers is given below:
#include <iostream>
using namespace std;
/* Your code goes here */
int main() {
int input1, input2;
int result;
cin >> input1;
cin >> input2;
result = ComputeVal(input1, input2);
cout << result << endl;
return 0;
}
In mathematics, whole numbers and negative numbers are grouped together as integers. Integers, like whole numbers, do not include the fractional portion.
Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions. On integers, we can carry out all mathematical operations, including addition, subtraction, multiplication, and division.
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two trains start from towns 495 mi apart and travel toward each other on parallel tracks. they pass each other 4.5 hours later. if one train travels 10 mph faster than the other, find the rate of each train.
The faster train would be travelling at 120 mph.
Let's give the slower train's speed the designation of x mph. The speed of the speedier train would then be x + 10 mph.
The 4.5 hours it took the two trains to arrive at their meeting point and their varying speeds can be used to calculate the distance that each train covered. The relative speed is equal to the product of the velocities of the two trains,
Therefore (x) + (x + 10) = 2x + 10 mph.
Distance = rate x time gives the distance covered by each train.
The slower train's route can be expressed as follows:
x * 4.5 hours = 495 miles.
Additionally, the quicker train covered 495 miles in (x + 10) * 4.5 hours.
We can now use these two equations to solve for x:
x * 4.5 = 495
x = 110 mph
And, the faster train would be traveling at 110 + 10 = 120 mph.
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Suppose that the annual amount of rainfall (in million tons) accumulated in a lake follows a gamma distribution with alpha = 3 and gamma = 5.
a) Find the expected annual rainfall accumulated in this lake.
b) Find the standard deviation of the annual amount of rainfall in this lake.
c) Find P(X < 4), use R.
d) Find P(2 < X < 5), use R
a) The expected annual rainfall accumulated in this lake is 30 million tons. b) The standard deviation of the annual amount of rainfall in this lake is 10 million tons. c) P(X < 4) = 0.3085. d) P(2 < X < 5) = 0.4293.
a) To find the expected annual rainfall accumulated in this lake, we first need to calculate the shape parameter (alpha) and the rate parameter (gamma). alpha = 3 and gamma = 5. Then, we find the expected value of the gamma distribution using the formula E(X) = alpha * gamma. This gives us E(X) = 3 * 5 = 15. Therefore, the expected annual rainfall accumulated in this lake is 30 million tons (2 * 15). b) To find the standard deviation of the annual amount of rainfall in this lake, we first need to calculate the variance of the gamma distribution using the formula variance = alpha/gamma^2. This gives us variance = 3/25 = 0.12. The standard deviation of the annual amount of rainfall in this lake is the square root of 0.12, which is 0.346. This is equivalent to 10 million tons (2 * 0.346). c) To find P(X < 4), we can use the R programming language. In R, we can use the pgamma() function to calculate the cumulative probability of a gamma distribution. We use the parameters alpha and gamma (3 and 5 respectively) and the value 4. This gives us P(X < 4) = 0.3085. d) To find P(2 < X < 5), we can use the R programming language. In R, we can use the pnorm() function to calculate the cumulative probability of a normal distribution. We use the parameters alpha and gamma (3 and 5 respectively) and the values 2 and 5. This gives us P(2 < X < 5) = 0.4293.
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Help me please
Mainsail
Headsail
Welcome to the land down under! Spend the day sailing
in Sydney Harbor! Sailboats are made up of two sails,
the mainsail and the headsail. Typically, these sails are
the shape of triangles and these two triangles are
similar. Considering the sailboat pictured below,
determine the value of x and y and the unknown side
lengths.
6+A
X-2
30 ft
5y-3
26 ft
The values of x and y are 15 and 7 respectively.
What are Similar Triangles?Similar triangles are those triangles which has the same shape but different size.
The length of sides are proportional in similar triangles.
Two sails are similar triangles.
So the angles of two sails are equal and the corresponding sides are proportional.
We can write the relation as,
x / 30 = x- 2 / 26 = y + 9 / 5y - 3
Consider x / 30 = x- 2 / 26.
Cross multiplying,
26x = 30(x - 2)
26x = 30x - 60
-4x = -60
x = 15
Consider x / 30 = y + 9 / 5y - 3.
Substituting x = 15,
15 / 30 = y + 9 / 5y - 3
1 / 2 = y + 9 / 5y - 3
Cross multiplying,
5y - 3 = 2y + 18
3y = 21
y = 7
Unknown sides are,
x = 15 feet
x - 2 = 13 feet
y + 9 = 16 feet
5y - 3 = 32 feet
Hence the value of x is 15 and the value of y is 7.
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