A photograph measuring 4" wide × 6" long must be reduced in size to fit a space four inches long in an advertising brochure. How wide must the space be so that the picture remains in proportion?
Answer:
The proportion of the width to the length of the original photograph is 4:6, which can be simplified to 2:3. To maintain the same proportion, the width of the reduced photograph must also be 2/3 of the length.
Since the length of the space in the brochure is 4 inches, the width of the space must be:
width = (2/3) x length
width = (2/3) x 4
width = 8/3
width ≈ 2.67 inches
Therefore, the width of the space in the brochure should be approximately 2.67 inches to maintain the proportion of the photograph.
ANSWER ASAP. 50PTS. BRAINLIEST ANSWER.
What is the area of Triangle PQR on the grid?
A triangle PQR is shown on a grid. The vertex P is on ordered pair 1 and 4, vertex Q is on ordered pair 3 and 1, and the vertex R is on ordered pair 5 and 4.
(1 point)
5 square units
6 square units
10 square units
12 square units
The Area of given triangle is 8 square units.
Area of Triangle:Area of triangle is the total area occupied by the triangle or the area enclosed within the three sides of the triangle.
The formula for calculating area of triangle is,
A = 1/2 bh
where b and h represent the base and height of the triangle, respectively.
This formula can be used to calculate triangles of any shape, including scalene, isosceles, and equilateral triangles. Remember that the base and height of a triangle are perpendicular to one another.
Now in the given question,
P(1,4), Q(3,1), R(5,4)
We have PR parallel to the x axis. We'll call that the base,
b = 5 - 1 = 4
The altitude is then the y difference h = 5 - 1 = 4
Then area of given triangle is,
[tex]A=\frac{1}{2}bh\\\\\\A=\frac{1}{2} (4)(4)\\\\A=\frac{1}{2} (16)\\\\A=8[/tex]
Hence, the area of given triangle is 8 square units.
To know more about triangles, visit:
https://brainly.com/question/2773823
#SPJ1
6-3) the turkalike rug company buys medium grade carpet in 100-foot rolls. the average number of defects per roll is 2.0. assuming that these data follow a poisson distribution, use the poisson spreadsheet template to answer the following questions. a. what is the probability of finding exactly 6 defects in a carpet roll chosen at random? b. what is the probability of finding 3 or fewer defects in carpet roll? using the poisson distribution.
The probability of finding exactly 6 defects in a carpet roll is 0.0435 and the probability of finding 2 or fewer defects in a carpet roll is 0.405.
a. To find the probability of finding exactly 6 defects in a carpet roll chosen at random, we can use the Poisson formula:
P(X = 6) = (e^-λ * λ ^6) / 6!
putting λ = 2.0, we get:
P(X = 6) = (e^-2 * 2^6) / 6! = 0.0435
So the probability of 6 defects in a carpet roll chosen at random is 0.0435.
b. To find the probability of finding 2 or fewer defects in a carpet roll, we can use the cumulative distribution function of the Poisson distribution:
P(X <= 2) = 1 - P(X > 2)
Using the Poisson formula, we can calculate P(X > 2) as follows:
P(X > 2) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
Plugging in λ = 2.0, we get:
P(X > 2) = 1 - (0.135 + 0.27 + 0.54) = 0.595
So P(X <= 2) = 1 - 0.595 = 0.405
So the probability of finding 2 or fewer defects in a carpet roll is 0.405.
To know more about Probability:
https://brainly.com/question/16722133
#SPJ4
___The given question is incorrect, the correct question is given below:
The Turkalike Rug Company buys medium grade carpet in 100-foot rolls. The average number of defects per roll is 2.0. Assuming that these data follow a Poisson distribution, use the Poisson spreadsheet template to answer the following questions.
a) What is the probability of finding exactly 6 defects in a carpet roll chosen at random?
b) What is the probability of finding 2 or fewer defects in a carpet roll?
Cuantos frascos de perfume de 12 cl se llenan con un bidón de 15 l?
Using the method of unit conversion, the number of bottles that can be filled is obtained as 125.
What is unit conversion?
Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding.
We can start by unit converting the volume of the drum from liters to centiliters, as the volume of the perfume bottles is given in centiliters -
15 liters = 1500 centiliters
Now we can find the number of 12 cl perfume bottles that can be filled with the drum by dividing the volume of the drum by the volume of each bottle -
Number of bottles = volume of drum / volume of each bottle
Number of bottles = 1500 cl / 12 cl
Number of bottles = 125
Therefore, 125 12 cl perfume bottles can be filled with a 15 l drum.
To learn more about unit conversion from the given link
https://brainly.com/question/97386
#SPJ1
How many 12 cl perfume bottles are filled with a 15 l drum?
It is said that 60% of college students have a job outside of school. The college admissions office is investigating on whether this claim is true or not.a) If a test of hypothesis is conducted, describe in in the context of the problem, what would be the type I error:b) If a test of hypothesis is conducted, describe in the context of the problem what would be the type II error:
The type I error, in the context of the problem, would be the incorrect rejection of the null hypothesis. This would mean that the college admissions office would incorrectly conclude that the claim is true, when in fact it is not.
The type II error, in the context of the problem, would be the incorrect acceptance of the null hypothesis. This would mean that the college admissions office would incorrectly conclude that the claim is false, when in fact it is true.
The college admissions office sets up a hypothesis test with the claim being 60% of college students have a job outside of school.
The null hypothesis would be that the claim is false, or that less than 60% of college students have a job outside of school.
The alternative hypothesis would be that the claim is true, or that at least 60% of college students have a job outside of school.
The type I error would be if the college admissions office incorrectly rejected the null hypothesis, that is, if they concluded that the claim is true and at least 60% of college students have a job outside of school when in fact the claim.
For more questions like Hypothesis visit the link below:
https://brainly.com/question/13378539
#SPJ4
Please help me urgently
Answer:
Below
Step-by-step explanation:
25 oo pass / hr
# passengers for H hours would be 2500H
f (H) = 2500 H
Answer:
a) 2500H
b) 20,000
Step-by-step explanation:
Algebraic equation:To find the number of passengers carried, multiply the number of passengers carried in an hour by the total hours.
a) Passengers carried in an hour = 2500
Passengers carried in 'H' hours = 2500 * H = 2500H
b) H = 8 hours
Passengers carried in 8 hours = 2500 * 8
= 20,000
Listed below are brain volumes (cm3) of unrelated subjects used in a study. Use the sample data to construct a 99% confidence interval estimate of the mean of the brain volume of the population. 963 1027 1272 1079 1070 1173 1067 1347 1100 1204
The 99% confidence interval estimate of the mean of the brain volume of the population is given as follows:
(1009.5, 1250.9).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 10 - 1 = 9 df, is t = 3.2498.
Using a calculator, the parameters are given as follows:
[tex]\overline{x} = 1130.2, s = 117.45, n = 10[/tex]
The lower bound of the interval is of:
1130.2 - 3.2498 x 117.45/sqrt(10) = 1009.5.
The upper bound of the interval is of:
1130.2 + 3.2498 x 117.45/sqrt(10) = 1250.9.
More can be learned about confidence intervals at https://brainly.com/question/25890103
#SPJ1
Calculating angle of elevation of sun at different times of the day using your height and the length of shadow cast
At noon on a clear day, with a height of 6 feet and a length of the shadow of 6 feet, the angle of elevation of the sun is approximately 45 degrees.
What is the angle of elevation?An angle of elevation is defined as the angle formed between the horizontal plane and the line of sight from the observer's eye to anything above.
Let's assume a height of 6 feet and a length of the shadow of 6 feet.
We'll also assume that we are measuring the angle of elevation at noon on a clear day.
Using the tangent formula, we have:
tan θ = h / s
tan θ = 6/6
θ = tan⁻¹(6 / 6)
θ = tan⁻¹(1)
θ = 45°
Therefore, the angle of elevation of the sun is approximately 45 degrees.
Learn more about the angle of elevation here:
https://brainly.com/question/24083809
#SPJ9
1853
1854
1850
1851
1852
YEAR
1841
1847
1848
1849
8:59
NUMBER
OF IRISH
IMMIGRANTS
37,772
105,536
112,934
159,398
164,004
221,253
159,548
162,649
101,606
Which of the following statements mos
accurately describes patterns of Irish
immigration in the mid-19th century?
O It remained relatively unchanged.
O
It continually increased between
1847 and 1854.
The statement that most accurately describes patterns of Irish immigration in the mid-19th century is: its peaked in approximately 1851. The Option D is correct.
What was pattern of Irish immigration to US in mid 19th century?Irish immigration to the United States in the mid-19th century was characterized by several factors:
Timing: Irish immigration to the United States peaked in the mid-19th century, particularly in the decades following the Great Famine of 1845-1852. During this time, millions of Irish fled to the United States to escape poverty and famine at home.Destination: Irish immigrants tended to settle in cities, particularly in the Northeast, such as Boston, New York, and Philadelphia. These cities offered employment opportunities and a supportive Irish-American community.Employment: Many Irish immigrants in the mid-19th century worked in manual labor jobs, such as construction, manufacturing, and domestic service. They faced significant discrimination and prejudice from the American-born population, who often considered them to be inferior and less capable.Read more about Irish immigration
brainly.com/question/27970047
#SPJ1
How do I solve y = 2x + 7
y=-3x+17
Answer:
Make the expressions equal to each other.
2x + 7 = -3x + 17
Use subtraction, division, and addition to isolate the variable.
2x + 3x + 7 = -3x + 3x + 17
5x + 7 = 17
5x + 7 - 7 = 17 - 7
5x = 10
5x/5 = 10/5
x = 2
y = 11
Step-by-step explanation:
27. A man is climbing down from 225 feet high descending 25 feet per minute. Write an
equation/function that models this situation.
Consider the curve C parametrized by x= t and y (`6-t^2)^1/2 for -4≤ t ≤ 4 write an equation relating x and y but without t and without square roots. write it so variable terms are on one side and any constant on the other side.
An equation relating x and y but without t and square roots is represented by x² + y² = 16, here variable terms are present on one side and any constant on the other side.
A function is represented in the cartesian form, such as, f(x,y)=0 or expressed in the form of parametric equations, written as
r(t) = ⟨x(t),y(t)⟩, α ≤ t ≤ β
the position vector, x(t) and y(t) helps to determine the location of a particular point on the curve with respect to a third independent parameter or varible t. We have, a curve C with parametrized equation, x = t and y = √(6-t²) for -4≤ t ≤ 4. We have to write eqution related to x and y without t and square roots. So,
substitute t = x in y
=> y = √(16 − x²)
squaring on both sides
=> y² = (16 - x²)
=> x² + y² = 16
Hence, the required equation is x² + y² = 16.
To learn more about parametric equation , refer:
https://brainly.com/question/16814415
#SPJ4
Determine the lateral area and the surface area of each triangular prism by determining the area of the shape’s net.
Btw: They are all 1
The lateral area of the triangular prism is 3 cm².
The surface area of the triangular prism is 4 cm².
How to find the lateral and surface area of a triangular prism?The diagram above is a triangular prism. The lateral area can be found as follows:
lateral area of the triangular prism = perimeter of the base × height
Therefore,
lateral area of the triangular prism = (1 + 1 + 1) × 1
lateral area of the triangular prism = 3 × 1
lateral area of the triangular prism = 3 cm²
Therefore,
surface area of the triangular prism = perimeter of the base × height + 2(base area)
Therefore,
surface area of the triangular prism = 3 + (1 × 1)
surface area of the triangular prism = 4 cm²
learn more on triangular prism here:https://brainly.com/question/30147220
#SPJ1
Math help needed, within 30 minutes please :)
34.) If a fruit punch is made using 3 parts strawberries, 2 parts blueberry, 2 parts lime juice, 3 parts simple syrup, and 6 parts I’ve. How many ounces of each ingredient do you need to make five gallons? (Note: 1 gal=128 oz.)
Show with steps please! It’s a practice problem and I’m trying to learn. :)
120 ounce of strawberry, 80 ounce of blueberry, 80 ounce of lime juice, 120 ounce of simple syrup and 240 ounce of sugar is needed to make five gallons (640 ounces) of fruit punch
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
1 gal = 128 oz. Hence:
5 gal = 5 gal * 128 oz. per gal = 640 ounces
If a fruit punch is made using 3 parts strawberries, 2 parts blueberry, 2 parts lime juice, 3 parts simple syrup, and 6 parts sugar. Hence. of 5 gallons:
Amount of strawberry = [3/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (3/16) * 640 = 120 ounces
Amount of blueberry = [2/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (2/16) * 640 = 80 ounces
Amount of lime juice = [2/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (2/16) * 640 = 80 ounces
Amount of simple syrup = [3/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (3/16) * 640 = 120 ounces
Amount of sugar = [6/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (6/16) * 640 = 240 ounces
120 ounce of strawberry, 80 ounce of blueberry, 80 ounce of lime juice, 120 ounce of simple syrup and 240 ounce of sugar is needed
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Paying into a retirement savings plan will increase taxable income, true or false
Answer:
true
Step-by-step explanation:
what is the point group for each of the following substituted cyclobutanes? assume that the four-membered ring is flat and that replacing h with x or y changes no other structural parameters.
The point group of a substituted cyclobutene can be determined by examining its symmetry elements.
In group theory, point groups are used to describe the symmetry of a molecule. The point group of a molecule can be determined by examining its symmetry elements, such as rotation axes, reflection planes, and inversion centers.
In the case of substituted cyclobutene, we can assume that the four-membered ring is flat and that replacing hydrogen atoms with other substituents, such as X or Y, does not affect any other structural parameters.
Now, let's consider the point groups for two substituted cyclobutene: 1,1-dimethylcyclobutane and 1,2-dimethylcyclobutane.
1,1-dimethylcyclobutane has two methyl groups attached to the same carbon atom. The symmetry elements of this molecule include a C2 axis that passes through the two methyl groups and perpendicular to the plane of the ring. There are also two perpendicular mirror planes that bisect the ring and pass through the carbon atom with the two methyl groups.
Using the point group flowchart, we can determine that the point group for 1,1-dimethylcyclobutane is C2v.
On the other hand, 1,2-dimethylcyclobutane has two methyl groups attached to adjacent carbon atoms. This molecule has a C2 axis that passes through the two methyl groups and the ring, as well as two perpendicular mirror planes that bisect the ring and pass through the carbon atoms with the methyl groups.
Using the point group flowchart, we can determine that the point group for 1,2-dimethylcyclobutane is Cs.
To know more about cyclobutene here.
https://brainly.com/question/29115552
#SPJ4
What is the meaning of "coefficients"?
A coefficient is a quantity or number that is related to a variable. The variable is frequently followed by an integer that has been multiplied by the variable.
Define Coefficient.In mathematics, a coefficient is a quantity that is multiplied by a variable in a single term or in a polynomial's terms. Any sign that represents a constant value can be used, including numbers. It is often a number, however in other situations it could be a letter. In the formula: ax² + bx + c, for instance, x is the variable and a and b are the coefficients.
Therefore, a coefficient can be actual or hypothetical, expressed as a fraction or decimal, positive or negative, and real or imaginary. According to another definition, a coefficient is "Any number we multiply a variable by." For instance, the coefficient of the variable x in the expression 9.3x is 9.3, whereas the coefficient of the expression -5z is -5.
To know more about coefficients, visit:
https://brainly.com/question/30066987
#SPJ1
The following data show the ages of recent award-winning male actors at the time when they won their award. Make a frequency table for the data, using bins of 20-29, 30-39, and so on.
Click the icon to view the ages of male actors.
Complete the table below.
Age
20-29
30-39
40-49
50-59
60-69
70-79
No. of actors
Here is the frequency table for the data, using bins of 20-29, 30-39, and so on:
Age
20-29: 14 actors30-39: 14 actors40-49: 14 actors50-59: 7 actors60-69: 4 actors70-79: 1 actorWhat is a Frequency Table?A table that is created to display the distribution of a characteristic's frequency of occurrence in accordance with a specific set of class intervals.
With the ages and data sets given, we are able to compute the frequency of occurrence in the data set using the specific class interval given.
Read more about frequency tables here:
https://brainly.com/question/16148316
#SPJ1
Mount Fuji in Japan can be modeled as a cone with a diameter of 25 miles and a height of 2.35 miles. Which measurement is closest to the volume of Mount Fuji in cubic miles?
The measurement which is closest to the volume of Mount Fuji in cone shape is 385 miles³.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex.
A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.
Christmas trees, carrots, party hats, ice cream cones, and traffic cones are five instances of cones in everyday life (used as road dividers).
Let's look at some actual code examples.
Explanation: A cone is a three-dimensional solid shape with a circular base at one end and one pointy edge serving as a vertex.
So, the formula for the volume of the cone is:
Volume = πr² h/3
Now, insert values and calculate as follows:
Volume = πr² h/3
Volume = π12.5² 2.35/3
Volume = 384.51785
Rounding off: 385 miles³
Therefore, the measurement which is closest to the volume of Mount Fuji in cone shape is 385 miles³.
Know more about cones here:
https://brainly.com/question/1082469
#SPJ1
Mount Fuji in Japan can be modeled as a cone with a diameter of 25 miles and a height of 2.35 miles. Which measurement is closest to the volume of Mount Fuji in cubic miles?
Answer:
385mi
Which cross sections is possible in cylinders and cones
The cross-section of the cylinders and cones is always round.
What is a cross-section area?The cross-sectional area is the region of a two-dimensional shape produced when a three-dimensional object, such as a cylinder, is cut perpendicular to a preset axis at a point.
A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been solid in three dimensions. In elementary geometry, it is regarded as a prism with a circle as its basis.
A three-dimensional geometric shape known as a cone has a flat base and a smooth, tapering vertex. A cone is made up of several line segments, half-lines, or lines that connect to a single point.
As a result, the cross sections of the cones and cylinders are always round.
To know more about the cross-section area follow
https://brainly.com/question/3436750
#SPJ9
Trig ratios, pls hurry
The person is 36m away from the boat.
Applying simultaneous equations to solve angle of depressionThe given figure is triangular in nature. In order to determine the distance of the person from the boat, we will use the pythagoras theorem.
Given the following parameters
GH = 20m
GK = 30m
The measure of the length HK (The distance of the person from the boat,) is calculated as:
HK^2 = GH^2 + GK^2
HK^2 = 20^2+ 30^2
HK^2 = 400+900
HK^2 = 1300
HK = 36m
Hence the distance of the person from the boat is approximately 36m
Learn more on angle of depression here: https://brainly.com/question/17193804
#SPJ1
2. By using a truthtable determine whether the following argument is valid or not If 10,836 is divisible by 12 then 10836 is divisible by 3. If 10,836 is divisible by 3 then the sum of the digits of 10836 is divisible by 3. Therefore, if 10,836 is divisible by 12 then the sum of the digits of 10836 is divisible by 3. (10 marks)
Based on the truth table constructed, the premises and conclusions are true, hence, the argument is valid.
What is the validity of the argument?The validity of the argument is determined as follows:
First statement, S1:
10836/12 = 903
10836/3 = 3612
Second statement, S2:
10836/3 = 3612
1 + 0 + 8 + 3 + 6 = 18
18/3 = 6
Statement 3, S3:
10836/12 = 903
1 + 0 + 8 + 3 + 6 = 18
18/3 = 6
The truth table is given below
Premise 1 Premise 2 Conclusion
S1. T T T
S2. T T T
S3. T T T
Since all the premises and conclusions are true, the argument is valid.
Learn more about truth table at: https://brainly.com/question/1485606
#SPJ1
PLEASE HELP
“Simplify the following using the properties of exponents”
A). (3x^-3y^5)^4
B). 5x^0
Answer:
[tex]A) 81x^{-12}y^{20}[/tex]
B) 5
Step-by-step explanation:
[tex]A) (3x^{-3}y^5)^4=(3)^4 \,\cdot\, (x^{-3})^4\,\cdot\,(y^5)^4=81x^{-12}y^{20}\\\\B) 5x^0=5(1)=5[/tex]
What is 16⅐% of 48? Show work
What is the physical significance of the slope of a position vs time graph?
Answer:
The slope of a position vs. time graph has a physical significance as it represents the velocity of an object. If the graph is a straight line, then the velocity is constant. If the graph is curved, then the velocity is changing, which means the object is either accelerating or decelerating. The direction of the slope (positive or negative) indicates the direction of the velocity.
We choose a number from the set {1, 2, 3, . . . , 100} uniformly at random and denote this number by X.
For each of the following choices decide whether the two events in question are independent or not
(a) A = {X is even}, B = {X is divisible by 5}.
(b) C = {X has two digits}, D = {X is divisible by 3}.
(c) E = {X is a prime}, F = {X has a digit 5}. Note that 1 is not a prime number.
(a) Not independent, as the occurrence of X being even affects the probability of X being divisible by 5 and vice versa.
(b) Not independent, as the occurrence of X having two digits affects the probability of X being divisible by 3 and vice versa.
(c) Independent, as the occurrence of X being a prime does not affect the probability of X having a digit 5, and vice versa.
Two occurrences are often considered independent if their occurrence has no impact on the likelihood of their occurrence. The occurrences in (a) and (b) are not independent since one event's occurrence affects how likely the other is. Because the chance of one event in (c) is unaffected by the likelihood of the other, the occurrences are independent in (c).
Read more about Events:
https://brainly.com/question/22881926
#SPJ4
1
A reforestation drive is conducted in a town. The town had 2,022 trees at the start of the drive. Four months after the start of the
reforestation drive, the town had 4,897 trees.
If n represents the number of months and T represents the number of trees, which of the following equations can be used to model
this situation?
OA. T 718.75 - 2,022
OB. T = 2,022n + 718.75
OC. T 718.75 + 2,022
OD. T = 2875 + 2,022n
Answer: OD. T = 2875 + 2,022n
Step-by-step explanation: What makes the most sense is
OD. T = 2875 + 2,022n
because they added 2875 to the trees already there and 4,897 was the new total after four months, I also want to point out it has nothing to do with decimals or a 700 number.
MTH 115 – Principles of Mathematics
Assignment 8.3 – Journal 8
First, complete Technology Assignment 8 before attempting these problems.
You can afford a loan payment of $1200 a month. You have put an offer of $175,000 on a house. You are considering three different loans.
Loan A. P = $175,000 at a rate of 5% with monthly payments for 30 years.
Loan B. P = $175,000 at a rate of 4% with monthly payments for 15 years.
Loan C. P = $175,000 at a rate of 4.5% with monthly payments for 20 years.
Find the payment and total interest for each loan.
Loan A: Payment = Total Interest =
Loan B: Payment = Total Interest =
Loan C: Payment = Total Interest =
Choose the loan you will use and clearly state why you chose that one.
Using the given information, we can use the PMT function in Excel or a financial calculator to find the monthly payment and total interest for each loan.
Loan A:
P = $175,000
r = 5%/12 = 0.004167 (monthly interest rate)
n = 30 years x 12 months/year = 360 months
Payment = $966.45
Total Interest = $153,522.05
Loan B:
P = $175,000
r = 4%/12 = 0.003333 (monthly interest rate)
n = 15 years x 12 months/year = 180 months
Payment = $1,297.53
Total Interest = $33,555.64
Loan C:
P = $175,000
r = 4.5%/12 = 0.00375 (monthly interest rate)
n = 20 years x 12 months/year = 240 months
Payment = $1,095.09
Total Interest = $66,022.37
Based on the information given, I would choose Loan B because it has the lowest total interest and a reasonable monthly payment that fits within my budget of $1200 per month. While Loan A has a lower interest rate, the longer repayment period results in a significantly higher total interest. Loan C has a lower monthly payment, but the longer repayment period also results in a higher total interest.
The variables x and y are connected by the equation y=(x-3)(x - 5)(x+2).Some corresponding values of x and y are shown in the table below. X -2 0 1 y 0 30 24 (i) Calculate the value of k -1 24 2 12 3 0 4 -6 5 0 (0) 6 k [1] avis
The value of k is given as follows:
k = 24.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
From the table, we have that when x = 6, y = k, hence the value of k is found replacing each of the three instances of x by 6, as follows:
k = (6 - 3)(6 - 5)(6 + 2)
k = 3 x 1 x 8
k = 24.
Learn more about the numeric values of a function at brainly.com/question/28367050
#SPJ1
Referring to the Fig. in Question #23, find the cosine of angle S. Reduce the answer to the lowest terms.
The Cosine of angle S in the given triangle is
[tex]\frac{8}{10} =\frac{4}{5}[/tex] .
Trigonometric Identities:Trigonometric Identities are equality claims that apply the principles of trigonometry and are valid for all possible values of the variables in the equation.
Many particular trigonometric identities can be used to express the relationship between a triangle's side length and angle.Only the right-angle triangle is consistent with the trigonometric identities.
All trigonometric identities are built upon the foundation of the six trigonometric ratios. Some of their names are sine, cosine, tangent, cosecant, secant, and cotangent. Each of these trigonometric ratios is defined using the adjacent side, opposite side, and hypotenuse side of the right triangle. All fundamental trigonometric identities are derived from the six trigonometric ratios.
The Cosine of an angle ∅ in a right triangle is given as ,
Cosine (∅) = [tex]\frac{base}{hypotenuse}[/tex]
Now in the given triangle .
[tex]Cosine (S)=\frac{8}{10} =\frac{4}{5}[/tex]
Learn more about trigonometric identities, visit:
https://brainly.com/question/14746686
#SPJ1