Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0
The equation of the line passing through (-1, 2) and (1, -8). Then the equation of the line will be
y + 8 = [(-8 - 2) / (1 + 1)] (x - 1)
y + 8 = -5x + 5
y = - 5x - 3
The equation that best represents a line perpendicular will be y = - 5x - 3.
A large community college has professors and lecturers. The total number of faculty members is 228. The school reported that they have 5 professors every 14 lecturers How many of each type of faculty member does the community college employ?
There are 60 professors and 168 lecturers according to the given information.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.
Main BODY:
Let X be the number of professors and Y be the number of lecturers. As the total of both is 228:
X + Y = 228
Then, as there are 5 professors for every 14 lecturers:
5 X = 14 Y or X = (14/5) Y
Replacing this last value of X on the first equation:
(14/5) Y + Y = 228
(14/5) Y + (5/5) Y = 228
(19/5) Y = 228
Y = 228 * (5/19)
Y = (228*5)/19
Y = 1140 / 19
Y = 60
Then we can find X:
X = (14/5) Y = (14/5) * 60 = 168
X = 168
Hence thre are 60 professors and 168 lecturers.
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You decide to contribute to a mutual fund that averages 3.7% return per year. If you contribute $575 quarterly.
Round all answers to the nearest cent as needed.
a) How much will be in the account after 10 years? $
b) How much of this money did you deposit? $
c) How much of this money is interest earned? $
a) After 10 years, the amount (future value) in the mutual fund will be $27,679.22.
b) The total amount deposited in the mutual fund is $23,000.
c) The amount of interest earned on the quarterly deposits is $4,679.22.
What is the future value?The future value is the compounded present value of periodic deposits.
The future value is compounded at an interest rate per period.
We can compute the future value using an online finance calculator, which also shows the total deposits and interest earned.
N (# of periods) = 40 quarters (10 years x 4)
I/Y (Interest per year) = 3.7%
PV (Present Value) = $0
PMT (Periodic Payment) = $575
Results:
Future Value (FV) = $27,679.22
Sum of all periodic payments = $23,000 ($575 x 40 quarters)
Total Interest = $4,679.22
Thus, making a quarterly deposit of $575 for 10 years at 3.7% APR will yield a future value of $27,679.22.
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1. The population of a city increases by 4%, Find the increase in the population after 3 years if the original population is 22,000
Answer: 2640
Steps:
There are different ways you can solve this
METHOD 1
1. Find what 4% of 22,000 is
0.04 × 22,000 = 880
You do this so that you can find out the increase from the original number of people in the city
2. Find out what 3 years of increase is
880 = 1 year's worth of increase
880 × 3 = 3 year's worth of increase
2640 = 3 year's worth of increase
Therefore the population increase is 2640 ( 12% )
METHOD 2
1. Find out what 12% of 22,000 is
4% = 0.04
12% = 3 × 0.04
12% = 0.12
12% of 22,000 = 0.12 × 22000
12% of 22,000 = 2640
Therefore the population increase is 2640 ( 12% )
A cone has a radius of 4 cm and a height of 12 cm. What is the volume of the cone, to the nearest whole centimeter?
Volume = 201 cm
Step-by-step explanation:How do I find the volume of a cone?Here is an equation to help you find the volume of a cone:
V=πr²[tex]\frac{h}{3}[/tex]=π·4²·[tex]\frac{12}{3}[/tex] ≈ 201.06193cm³
This equation is what I used to solve your question. The answer is 201.06193, but is says round to the nearest whole number, so the answer is actually 201 cm.
In the equation:
V means Volume
π means Pi (3.14)
r² means radius squared
[tex]\frac{h}{3}[/tex] means height divided by 3
4² means 4 · 4
[tex]\frac{12}3}[/tex] means 12 ÷ 3
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Will give brainliest!!!
What is the value of x?
Use the provided picture
y = 3x +2
y = 3x - 3
These lines are...
Answer:
Step-by-step explanation:
Calculate the volume of water that runs off the Shoppes at Fremont parking lot after a 5 cm rainfall event. Assume that all water that falls on the parking lot runs off.[200m x 100m = 20,000m2[5cm x 1m/ 100cm = 0.05m]20,000m2 x 0.05m = 1000m3
The volume of water that runs off the Shoppes at Fremont parking lot after a 5 cm rainfall event is [tex]1000m^{3}[/tex].
Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.
Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.
Basically, the volume of a liquid is measured in liters, where 1 liter is equal to 1000 cubic centimeters.
1 liter = 1000 cubic centimeters = 0.001 cubic meters
Hence,
1 cubic meters = 1000 liters
Given,
[200m x 100m = [tex]20000m^{2}[/tex]]
[5cm x 1m/ 100cm = 0.05m]
20,000m2 x 0.05m = [tex]1000m^{3}[/tex]
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Weight of an empty carton is 8.350 kg. Apples weighing 21.475 kg are packed into it. Find the total weight of the carton
The total weight of the carton after packing the apples is 29.825 kg.
Step-by-step explanation:1. Write the individual weights.Empty carton: 8.350 kg
Apples: 21.475 kg
2. Do an addition.Since we are placing the apples inside the empty carton, now the carton will also contain the weight of the apples, additional to its own weight.
8.350 kg + 21.475 kg= 29.825 kg.
3. Express the result.The total weight of the carton after packing the apples is 29.825 kg.
Graph the line with the equation y = -x - 2.
The required graph is as follows.
What is graph of an equation in x and y?The graph of an equation in x and y is the value of y for the
corresponding value of x.
Given,
y = -x - 2
or x + y = -2
The line cuts x axis when y = 0 and cuts y axis when x = 0.
Therefore, the line cuts x axis at x = -2
the line cuts y axis at y = -2
Hence, required graph is:
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The difference between two same side interior angles of two paralell lines is 35 degrees. Find the measures of the two angles.
Draw a model for 1.8 divided by 0.6
Answer: 1.8 divided by 0.6 is 3
The equation of the model for 1.8 is divided by 0.6 will be E = 1.8 / 0.6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the number 1.8 is divided by the number 0.6. The mathematical model for the division can be written as:-
E = 1.8 / 0.6
Hence, the equation of the model for 1.8 is divided by 0.6 will be E = 1.8 / 0.6.
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Credit card disclosure: "Your due date is at least 25 days after the end of the billing cycle. We will not
charge you interest on new purchases provided that you have paid your previous balance in full by the due
date each month." Identify the true statement.
The 25 days after the end of the billing cycle is referred to as the grace period
If you pay your previous balance in full after the due date, the credit card company will not charge you
interest
days is an exceptionally long period without paying a credit card bill
If you make the minimum payment on your card within the 25 day period, the credit card company will
not charge you interest
If you make the minimum payment on your card within the 25-day period, the credit card company will not charge you interest. Option D is correct.
What is the investment?Investment is defined as when an individual spends money on something that returns him or her higher money than the money they or invest.
Here,
According to the statment, "Your due date is at least 25 days after the end of the billing cycle. We will not charge you interest on new purchases provided that you have paid your previous balance in full by the due date each month"
Since al the option are wrong except option D
Option D is true. because the statement mentioned the same statement as mentioned in the given statment.
Thus, Option D is correct.
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Kennedy High School is going to select a committee. The committee will have a faculty member, a male student, a female student, and a parent. Here are the positions and the people interested in each.
Based on this list, how many ways are there to fill the four committee positions?
There are 160 ways to fill the four committee positions.
What is Combination?
The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words means "Selection of things," where the order of the items is irrelevant.Faculty members can be selected in A = 2 ways
Male student can be selected in B= 4 ways
Female student can be selected in C = 4 ways
One parent can be selected in D = 5 ways.
Total number of ways to select committee of four = A*B*C*D
= 2* 4 * 4 * 5
= 160 Ways
Hence, there are 160 ways to fill the four committee positions.
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An animal shelter has 8 puppies. If the puppies are 32% of the total dog and cat population, how many dogs and cats are in the animal shelter?
Answer:
25
Step-by-step explanation:
32/100=8/x
cross multiply
32x=100(8)
32x=800
/32. /32
x=25
hopes this helps please mark brainliest
Question 1 of 10, Step 1 of 1
Correct
An economist wants to estimate the mean per capita Income (in thousands of dollars) for a major city in California. He believes that the mean Income is $21.3, and the
variance is known to be $32.49. How large of a sample would be required in order to estimate the mean per capita income at the 99 % level of confidence with an
error of at most $0.39? Round your answer up to the next integer.
n=1422 is the sample that would be required in order to estimate the mean per capita income at the 99 % level of confidence with an error of at most $0.39.
What is meant by confidence level?The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The parameter's true value, for instance, should be present in 95% of all intervals computed at the 95% level. The range of values within the 95% confidence interval represents the population's actual mean, with 95% confidence. The sample mean (the center of the CI) will differ between samples due to natural sampling variability. The process itself, not a certain CI, is what inspires confidence. According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, hence to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.
At 99% confidence interval the critical value is [tex]z_{0.005}[/tex]=2.58
Margin of error=0.39
Or, [tex]z_{0.005}[/tex](σ/√n)=0.39
Or, 2.58(5.7/√n)=0.39
Or, n=(2.58×(5.7/0.39)²
Or, n=1422
n=1422 is the sample that would be required in order to estimate the mean per capita income at the 99 % level of confidence with an error of at most $0.39.
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Use the given conditions to find the values of all six trigonometric functions. (If an answer is undefined, enter UNDEFINED.) sec(x) = − 9/5, tan(x) < 0sin(x)=cos(x)=tan(x)=csc(x)=sec(x)=ot(x)=
The given conditions to find the values of all six trigonometric functions is cos (x) =-5/9, sin (x) = 2 root(14)/9, tan(x)= - 2 root(14)/5 and cot(x)= - 5 (2 root 14), csc(x)= 9 /2root (14).
What is trigonometric functions ?
Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the angles and sides of a triangle.
[tex]$\sec (x)=-\frac{9}{5} < 0$[/tex]and [tex]$\tan (x) < 0$[/tex]
so, x is in the second quadrant.
So, [tex]$\cot (x), \cos (x)$[/tex]are negative and [tex]$\sin (x), \csc (x)$[/tex] are positive.
Hence,
[tex]$$\begin{aligned}\cos (x) & =\frac{1}{\sec (x)}=-\frac{5}{9} \\\sin (x) & =\sqrt{1-\cos ^2(x)}=\sqrt{1-\frac{25}{81}}=\frac{2 \sqrt{14}}{9} \\\tan (x) & =\frac{\sin (x)}{\cos (x)} \\& =-\frac{2 \sqrt{14}}{5} \\\cot (x) & =\frac{1}{\tan (x)}=-\frac{5}{2 \sqrt{14}} \\\csc (x) & =\frac{1}{\sin (x)}=\frac{9}{2 \sqrt{14}}\end{aligned}$$[/tex]
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Name
Chapter
4
Test B (continued)
8. You deposit $300 in an account that earns simple interest at an annual rate of 5%.
How much money is in the account after 6 years?
Answer:
90
Step-by-step explanation:
To solve, you have to use the formula
I=Prt
I is the dollars of of simple interest earned
P is principal in dollars
R is the annual interest rate (decimal form)
T is the time in years
I=Prt
I =300*0.05*6
I = 90
Answer:
we use bodmas!
Step-by-step explanation:
how do you say hi in spanish
Answer:
hola
Step-by-step explanation:
Answer: You say Hola
Step-by-step explanation:
Which sounds like (Ohw·laa) = This means Hi or Hello
If 7 is added to twice a number and
this sum is multiplied by 2, the result is
the same as if the number is multiplied by
13 and 9 is added to the product. What is
the number?
Answer: x= -5
Step-by-step explanation:
2(7+2x) = 3x+9
14+4x=3x+9
isolate x
x=-5
Find the missing angles:
X=_________
Y=_________
Answer:
See below!
Step-by-step explanation:
Statement:When a quadrilateral (shape with 4 sides) in inscribed in a circle, the opposite angles of the quadrilateral add up to 180 degrees.Solution:From the statement, we get:
108 + x = 180
Subtract 108 to both sides
x = 180 - 108
x = 72°Also,
y + 88 = 180
Subtract 88 to both sides
y = 180 - 88
y = 92°[tex]\rule[225]{225}{2}[/tex]
Answer:
X= 72
y= 92
Step-by-step explanation:
108 + x = 180
x = 180 - 108
x = 72°
y + 88 = 180
y = 180 - 88
y = 92
help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of hurricane.
How to solve function?A function having the formula f(x) = ax' + b is said to be linear.
It appears to be a standard linear equation, except the linear function symbol is f rather than y. (x).
You would be given the value of f(x) and asked to locate x when solving a linear function.
F(x) is the barometric air pressure in inches of mercury.
x is the distance in miles from the eye of a severe hurricane.
It is given pressure 28inches of mercury
Put F(x) equal to 28
F(x) = 0.48ln(x+2) +27
28 = 0.48ln(x+2)+ 27
28-27= 0.48ln(x+2)
1= 0.48ln(x+2)
1/0.48= ㏑(x+2)
25/12= ㏑(x+2)
x+2= e^(25/12)
x+2=8.03119
x=8.03119-2
x= 6.03119
x = 6(round off)
Therefore, for 28 inches of mercury occurs about 6 miles from the eye of hurricane.
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El perímetro de un jardín rectangular es 376 m.
Si la longitud del jardín es 99 m, ¿cuál es su anchura?
Answer:
89 m
Step-by-step explanation:
p/2 = 376/2 = 188 m
l + a = 188
a = 188 - l
a = 188 - 99
a = 89 m
A single card is drawn from a standard 52 card deck fund the conditional probability that the card is a spade given that it is a 10
When the card is a jack, there is a 0.25 probability that you will receive a spade.
What is probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability.
The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application. Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
According to our question-
P(Spade) = 13/52 = 1/4 P(Jack) = 4/52
= 1/13 P(Spade and Jack)
= (1/4)(1/13) = 1/52 P(Spade/Jack)
= P(Spade and Jack)/P(Jack)
= (1/52)/(1/13) = (1/52)(13/1)
= 13/52 = 1/4 = 0.25
Hence, When the card is a jack, there is a 0.25 probability that you will receive a spade.
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Complete question-
A single card is drawn from a standard 52- card deck. Find the conditional probability that the card is a spade, given that it is a jack.?
A recipe recommends cooking a roast between 35 and 45 minutes per pound. Which of the following cooking times for a 10-pound roast follows the recommendation?
Answer:
If one of the answers is 5 hours and 50 minutes, that. If its 7 hours and 30 minutes, that. In between is 6 hours and 40 minutes.
Step-by-step explanation:
Problem Solving Strategy: Write an
Equation
Write an equation for each problem using the variable -n. Then solve and check the equation.
6) Allan has 84 baseball cards. This is 19 fewer cards than Mike. How many baseball cards does Mike have?
7) Jamie can ride her bike 3 times as fast as Michelle can jog. If Jamie rides her bike at a rate of 12 miles per hour, how fast can Michelle jog?
Problem Solving Strategy: Mental Math
Hence, the equation for the question (7) is [tex]n + 19 = 84[/tex] and equation for (8) is [tex]3n = 12[/tex]. It can be solved by linear equation in one variable.
What is a linear equation in one variable?
A linear equation in one variable is written as [tex]ax+b = 0[/tex]. Here, [tex]a[/tex] and [tex]b[/tex] are constants and [tex]x[/tex] is a variable.
(7)
Consider n number of baseball cards does Mike have. Since this is 19 less then the cards Allan have hence, as you add 19 in n then it will give 84.
[tex]n + 19 = 84[/tex]
(8)
Consider the speed of Michelle is n. As, it is 3 times less than the speed of the Jamie hence, it you multiply 3 with n then it will give 12.
[tex]3n = 12[/tex]
Hence, the equation for the question (7) is [tex]n + 19 = 84[/tex] and equation for (8) is [tex]3n = 12[/tex].
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If the following data were transformed, and points with the coordinates
(x, log(y)) were plotted, what points would be plotted? Round log(y) to three
decimal places.
A. (1.690, 49), (2.535, 343), (3.380, 2401)
B. (49, 1.690), (343, 2.535), (2401, 3.380)
C. (1.690, 2), (2.535, 3), (3.380, 4)
D. (2, 1.690), (3, 2.535), (4, 3.380)
The points that would be plotted are (2, 1.690), (3, 2.535), and (4, 3.380).
What are the coordinates?
Any one of a group of numbers used to describe where a point is on a line, a surface, or in space coordinates of latitude and longitude
Here, we have
If the following data were transformed and points with coordinates (x, log(y)) were plotted then we have to find what points would be plotted.
From the table:
At x = 2 and y = 49 ⇒ (x,log(y)) = ( 2 , log 49 ) = (2, 1.690)
At x = 3 and y = 343 ⇒(x,log(y)) = ( 3 , log 343) = (3, 2.535)
At x = 4 and y = 2401 ⇒(x,log(y)) = ( 4 , log 2401) =(4, 3.380)
Hence, The points that would be plotted are (2, 1.690), (3, 2.535), and (4, 3.380).
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A list of brownies for chocolate brownies given at the right will make 16 brownies. Use the list to decide how much each ingredient needed to make 20 brownies, one cup butter, 6 ounces unsweetened chocolate, 2 cup sugar, 1/2 teaspoon vanilla, four eggs half cup flour.
The ingredients for 4 brownies would be: 1/2 cup butter, 15/4 ounces unsweetened chocolate, 9/8 cup sugar, 3 teaspoons vanilla, 3 eggs, and 3/4 cup flour.
What exactly is a proportion?A percentage is a component of a total amount, and the measures are related by the rule of three.
Keep in mind that in a particular ratio, such as: a/b=c/d a*d=b*c
Create the following ratio for each ingredient:1/8 cup butter, 5/8 ounces of unsweetened chocolate, 1/4 cup sugar, 1/8 teaspoon vanilla, 1/2 egg, and 3/16 cup flour.
Explanation:
Given that the original recipe calls for 16 brownies;
Butter:
(1/8)/16=b/12
(2/3)(12)=16b
8=16b
b=1/2
Chocolate:
5/16=c/12
60=16c
c=60/16
c=15/4
Sugar: (3/2)/16=s/12
(3/2)(12)=16s
18=16s
s=18/16
s=9/8
Vanilla: 2/16=v/12
24=16v
v=3/2
Eggs: 2/16=e/12
e=3/2
Flour:1/16=f/12
f=3/4
As a result, the following would be the components for four brownies,
3/4 cups flour, 1/2 cups butter, 15/4 ounces unsweetened chocolate, 9/8 cups sugar, 3/2 teaspoons vanilla, and 3/2 eggs.
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A 99% confidence interval of 3.551 < p <7.989
means that:
Since the formula for P only applies to positive z, the minus sign must be removed if z is negative.We change 1.96 to 1.65 for a CI of 90%, and we use 2.57 for a CI of 99%.
What is the 99% confidence interval's p value? If z is negative, we omit the minus sign because the formula for P only works for positive z.We substitute 1.65 for 1.96 for a CI of 90%, and 2.57 for a CI of 99%.Similar relationships exist between significance at the 0.01 level and the 99% confidence interval.When an effect is significant, the confidence interval's values will all fall on the same side of zero (either all positive or all negative).Simply said, p-values establish a threshold at which we claim that the results are "statistically significant" (p0.05 being the standard). According to a confidence interval that includes the value of no difference between treatments, the investigated therapy is not substantially different from the control.To learn more about confidence interval refer
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5. Can a triangle be drawn with side lengths of 7.3 meters, 4.6 meters, and 11 meters? Explain.
Yes, a triangle can be drawn with side lengths of 7.3 meters, 4.6 meters, and 11 meters this is in the case whereby the lengths of any two sides combined is longer than the length of the 3rd side.
What is triangle inequality?Triangle inequality, in Euclidean geometry, theorem can be described as the theorem that states that the sum of any two sides of a triangle is greater than or equal to the third side.
This can be represented using the symbols, {a + b ≥ c.} and this can be explained that the the shortest distance between two points is a straight line.
Then cherck this illustration to confirm that we are right:
7.3 + 4.6 > 11
7.3 + 11 > 4.6
4.6 + 11 > 7.3
Hence from this we can see that triangle can be drawn
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Difference between 246 and 31 tripled
The difference between 246 and 31 tripled is
246 - 31³ = -29545How to calculate the difference between 246 and 31 tripledThe problem is solved using subtraction
the term difference is similar to subtraction in mathematics
Then tripling is raise to power 3 or exponents of 3, hence after subtraction then exponents is applied to the end result of subtraction to give the answer
The subtraction
= 246 - 31
= 215
The exponents
= 215³
= 215 * 215 * 215
= 9938375
'
On the second thought, we have a different answer in this case
= 246 - 31³
= 346 - 31 * 31 * 31
= -29545
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