The possible values of two consecutive even integers, of which the sum of their squares is 1684, are 28 and 30 for positive integers, while for negative integers, they are -28 and -30.
The difference between two consecutive even integers is 2.
Let the integers be a and (a+2). Then,
a² + (a + 2)² = 1684
a² + a² + 4a + 4 = 1684
2a² + 4a - 1680 = 0
a² + 2a -840 = 0
Hence, we get a quadratic equation.
There are three methods of solving a quadratic equations: by factoring, completing the square, and by using the abc formula.
Use the factoring method:
a² + 2a -840 = (a - 28) (a + 30)
a = 28 and a = -30
Hence, if the integers are positive, they are: 28 and 30.
If the integers are negative, they are -28 and -30.
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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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Amy wins a $200 gift card from a local store during its grand opening. If the card is not used within the year, a 10% fee is deducted from the balance at the end of each year. The following table shows Amy's gift card balances (y) for an inactive gift card at the end of year x
Answer:
20 dollars will be deducted if the card is not used. I am not sure what your question is but this is what I understood sorry it it isn't what you are asking for
(2 points) match the slope fields shown below with the differential equations a 1. y′=cos(x) d 2. y′=4−y c 3. y′=x e 4. y′=y f 5. y′=x−y b 6. y′=sin(x)
The differential equations a) y' = cos(x), b) y' = sin(x), c) y' = 4-y, d) y' = x, e) y' = y, and f) y' = x-y all match the corresponding slope fields shown in figures A-F respectively.
a. y'=cos(x): This differential equation describes the slope field shown in figure A. To calculate the slope of a given point (x,y), we can use the formula y'=cos(x). For example, if x=π/2 and y=1, the slope of the line at that point is y'=cos(π/2)=-1.
b. y'=sin(x): This differential equation describes the slope field shown in figure B. To calculate the slope of a given point (x,y), we can use the formula y'=sin(x). For example, if x=0 and y=1, the slope of the line at that point is y'=sin(0)=0
c. y'=4-y: This differential equation describes the slope field shown in figure C. To calculate the slope of a given point (x,y), we can use the formula y'=4-y. For example, if x=0 and y=2, the slope of the line at that point is y'=4-2=2.
d. y'=x: This differential equation describes the slope field shown in figure D. To calculate the slope of a given point (x,y), we can use the formula y'=x. For example, if x=3 and y=2, the slope of the line at that point is y'=3.
e. y'=y: This differential equation describes the slope field shown in figure E. To calculate the slope of a given point (x,y), we can use the formula y'=y. For example, if x=3 and y=4, the slope of the line at that point is y'=4.
f. y'=x-y: This differential equation describes the slope field shown in figure F. To calculate the slope of a given point (x,y), we can use the formula y'=x-y. For example, if x=2 and y=1, the slope of the line at that point is y'=2-1=1.
The differential equations a) y' = cos(x), b) y' = sin(x), c) y' = 4-y, d) y' = x, e) y' = y, and f) y' = x-y all match the corresponding slope fields shown in figures A-F respectively.
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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!!
a survey is conducted and the following results are recorded 360 students are taking a math course 280 are taking a physics course 300 are taking a biology course 100 are taking math and physics 120 are taking math and biology 110 are taking physics and biology 40 are taking math, physics and not biology 40 are not taking any of the courses a. how many are taking only math? b. how many are in the survey? c. how many are taking exactly two of the courses?
A) The total no. of students taking only maths is 220 students.
let's say the total no. of students taking only maths = M
M = 360 - (100 + 40) = 220 students.
B) The total no. of students in the survey is 960 students.
let's say the total no. of students in the survey = S
S = 360 + 280 + 300 - (100 + 120 + 110) + 40 = 960 students.
C) The total no. of students who are taking exactly two of the courses is 330 students.
let's say the total no. of students who are taking exactly two of the courses = T
T = 100 + 120 + 110 = 330 students.
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You own a hat shop. Your total monthly cost
is $1,850. Each hat costs $50. How many hats
must you sell to break even each month?
Answer:
The Answer is 37
Step-by-step explanation:
Just do 1850/50 and then do 50*37 to confirm
Lat week, Zachary' Diner old 28 milkhake with whipped cream on top and 72 milkhake without whipped cream. What percentage of the milkhake had whipped cream?
Zachary' Diner old 28 milkshake with whipped cream on top and 72 milkshake without whipped cream, percentage of the milkshake had whipped cream is 28%.
Zachary ordered 28 milkshake with whipped cream on top and 72 milkshake without whipped cream.
So total number of milkshake is 100
So percentage of milkshake had whipped cream will be,
28/100 x 100
=28%
A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied.Learn more about Percentages:
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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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find each value of k for which the lines y=9kx-1 and kx 4y=12 are perpendicular
The value of k in the equations is 2/3
How to determine the value of kFrom the question, we have the following parameters that can be used in our computation:
y = 9kx - 1
kx + 4y = 12
This can be expressed as
y = 9kx - 1
y = -kx/4 + 3
The slopes of perpendicular lines are opposite reciprocal
This means that
9k * -k/4 = -1
So, we have
k^2 = 4/9
Evaluate
k = 2/3
Hence, the value of k is 2/3
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For numbers 3-6 state if the triangles are congruent and if so what method proves they are congruent?
The congruence postulates used for each triangle are as follows;
3) AAS
4) None
5) HL congruence
6) None
How to Identify the triangle congruence postulate?Some of the triangle congruence postulate in geometry are;
SAS; Side Angle Side Congruence Postulate
SSS; Side Side Side Congruence Postulate
ASA; Angle Side Angle Congruence Postulate
AAS; Angle Angle Side Congruence Postulate
HL; Hypotenuse Leg Congruence Postulate
3) W e can see that we are given two triangles with two corresponding congruent angles and corresponding non-included side. Thus, the congruence postulate used is AAS.
4) We are given two triangles with two corresponding congruent angles but the sides given are not congruent to each other and so the triangles are not congruent.
5) We are given two triangles with their corresponding hypotenuse and leg being congruent and so the HL congruence postulate is used.
6) The angles shown don't match each other. It is just two congruent sides and this is insufficient to conclude the triangles are congruent.
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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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jamie drove 61 miles jamie car used 4 gallons of gas, how many miles per gallon did jamie car get
The number of miles per gallon that Jamie's car get will be 15.25 miles per gallon.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Jamie drove 61 miles Jamie's car used 4 gallons of gas.
The number of miles per gallon that Jamie's car get will be given as,
Rate = 61 / 4
Rate = 15.25 miles per gallon
The number of miles per gallon that Jamie's car get will be 15.25 miles per gallon.
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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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(-3,9) (4,6) (6,-3)
find the fourth vertex of the parallelogram
Answer: (-1, 0)
not sure
Step-by-step explanation:
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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in the number 652.12, how does the value of the 2 in the hundredths place compare to the value of the 2 in the ones place?
In the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.
In the number 652.12, the value of the 2 in the hundredths place is much smaller than the value of the 2 in the ones place. In this number, the 2 in the hundredths place represents 0.02, which is two hundredths of a unit. On the other hand, the 2 in the ones place represents 2 units.
To understand the difference in value, consider that the decimal point separates the number into its integer part (to the left of the decimal point) and its fractional part (to the right of the decimal point). The place value of each digit depends on its position relative to the decimal point. The rightmost digit is the ones place, the digit to its left is the tens place, and so on. The place value of the digits to the right of the decimal point is determined by powers of 10 that are negative, starting from -1 for the hundredths place, -2 for the thousandths place, and so on.
Therefore, in the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.
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In the number 652.12, the 2 in the hundredth place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.
In the number 652.12, the value of the 2 in the hundredths place is much smaller than the value of the 2 in the ones place. In this number, the 2 in the hundredths place represents 0.02, which is two hundredths of a unit. On the other hand, the 2 in the ones place represents 2 units.
To understand the difference in value, consider that the decimal point separates the number into its integer part (to the left of the decimal point) and its fractional part (to the right of the decimal point). The place value of each digit depends on its position relative to the decimal point. The rightmost digit is the ones place, the digit to its left is the tens place, and so on. The place value of the digits to the right of the decimal point is determined by powers of 10 that are negative, starting from -1 for the hundredths place, -2 for the thousandths place, and so on.
Therefore, in the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.
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What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?
a) 3127
b) 3133
c) 3137
d) 3139
e) 3149
The smallest positive integer that is neither prime nor square and that has no prime factor less than 50 is 3137.
This can be determined by using the prime factorization method. Prime factorization is a process of breaking down a number into its prime factors. The prime factors of a number are the factors that are only divisible by one and itself. For 3137, the prime factors are 3, 7, 17 and 37 since these are the only prime numbers that can divide 3137 evenly. Since none of the prime factors are less than 50, 3137 is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50.
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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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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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solve for h.
h/6 - 1 = -3
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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Find the perimeter of triangle FGL, if the perimeter of triangle MHQ is 70.4 centimeters.
Answer:
The perimeter of triangle FGL is unknown.
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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HELP EMERGENCY A printing company charges $8.95, plus an additional $.15 for each print over 50. Write an equation that can be used to determine the cost, C, to print an order of p, prints
Answer choices:
c (p) =.15 (x+50) +. 8.95
c (p) = 8.95 (x + 50) + 0.15
c (p) =.15 (x- 50) + 8.95
c (p) = 8.95 (x- 50) +0.15
Answer:
(c) C(p) =.15 (p- 50) + 8.95
Step-by-step explanation:
You want an equation for the cost of prints that are $0.15 for each print over 50 plus an additional $8.95.
Translating EnglishThe number of prints over 50 will be (p -50). At $0.15 for each of these, their cost will be ...
0.15(p -50)
When the $8.95 charge is added, the total comes to ...
c(p) = 0.15(p -50) +8.95
__
Additional comment
The problem statement asks for the function to be written C(p). The answer choices use c(p) with the variable x in the equation where p should be. In effect, none of the answer choices is correct.
a hospital director believes that 46% of the lab reports contain errors. a sample of 250 tubes found 95 errors. is there sufficient evidence at the 0.05 level to refute the hospital director's claim? state the null and alternative hypotheses for the above scenario.
Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.
What is null hypothesis ?
The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.
To test if there is sufficient evidence to refute the hospital director's claim, we would perform a hypothesis test. The test statistic in this case would be the sample proportion of lab reports with errors (95 errors out of 250 total lab reports), and we would compare this to the null hypothesis value of 46%. The p-value for this test represents the probability of observing a sample proportion as extreme or more extreme than the observed proportion, given that the null hypothesis is true.
If the p-value is less than the significance level of 0.05, we would reject the null hypothesis, which means we have sufficient evidence to conclude that the proportion of lab reports with errors is not equal to 46%. On the other hand, if the p-value is greater than or equal to the significance level of 0.05, we would fail to reject the null hypothesis, which means we do not have sufficient evidence to conclude that the proportion of lab reports with errors is different from 46%.
Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.
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Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.
The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.
To test if there is sufficient evidence to refute the hospital director's claim, we would perform a hypothesis test. The test statistic in this case would be the sample proportion of lab reports with errors (95 errors out of 250 total lab reports), and we would compare this to the null hypothesis value of 46%. The p-value for this test represents the probability of observing a sample proportion as extreme or more extreme than the observed proportion, given that the null hypothesis is true.
If the p-value is less than the significance level of 0.05, we would reject the null hypothesis, which means we have sufficient evidence to conclude that the proportion of lab reports with errors is not equal to 46%. On the other hand, if the p-value is greater than or equal to the significance level of 0.05, we would fail to reject the null hypothesis, which means we do not have sufficient evidence to conclude that the proportion of lab reports with errors is different from 46%.
Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.
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Q. Mr X had income from salary of 200000. Income from Capital Gain of
150000 and income from other sources is 250000. Contribution to PF
is *40000, PPF 70000, and LIC is 40000. Calculate Income Tax Liability of mr x
The income tax liability of Mr. X is 450,000 rupees.
What is subtraction?Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.
Given:
Mr X had income from salary of 200000.
Income from Capital Gain of, 150000 and income from other sources is 250000.
Contribution to PF is 40000, PPF 70000, and LIC is 40000.
Income Tax liability = total income - total deductions
= 600,000 - 150,000
= 450,000
Therefore, the tax liability is 450,000 rupees.
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Determine whether the following statement is true or false. Every graph represents a function. Choose the correct answer below. A. The statement is true because every graph associates a unique y-value for each x-value. B. The statement is false because a graph that crosses the x-axis two times does not represent a function. C. The statement is true because every graph associates a unique x-value for each y-value. D. The statement is false because a graph that crosses the y-axis two times does not represent a function.
"Every graph represents a function" - statement is false.
Correct option: D
What is function?The vertical line test is used to verify function. That is, a graph must have a unique y value for it to be referred to as a function for a certain (unique) value of x.
If for a particular x, and y values are coming it means it is not a function.
Hence, every graph is a function is false.
Because if it crosses y axis twice it means for a particular x value , two different value of y will exist. And that is not possible for a function
Hence option D is correct: The statement is false because a graph that crosses the y-axis two times does not represent a function.
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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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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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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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