In total 6 weeks, the saved money by both Sadio and Thoma will be in the ratio of 2:1.
Define the term ratios?When two or so more numbers are compared, the ratio shows how big one is in relation to the other. The dividend and number being divided is referred to as the antecedent, and the divisor for number that also is dividing is referred to as the consequent. A ratio compares two numbers by division.For the given question.
Initial money owned by each is-
Sadio = $15
Thoma = $0.
Let the number of weeks passed be 'x'.
Then, present money after x weeks.
Sadio = $3.50x + 15
Thoma = $3x
The number of weeks , when ratio becomes 2:1
(3.50x + 15)/3x = 2/1
3.50x + 15 = 6x
6x - 3.5x = 15
x = 15/2.5
x = 6
Thus, in total 6 weeks, the money held by both Sadio and Thoma will be in the ratio of 2:1.
To know more about the ratios, here
https://brainly.com/question/12024093
#SPJ4
a company has three corporate offices and wishes to determine if there is a difference in the average age of the corporate executives at the three locations. the ages were recorded for the five top executives at each location. the appropriate test statistic is the test and the degrees of freedom for this problem are
The appropriate statistic test should be ANOVA and The degree of freedom is 12.
What are Statistical tests?
An instrument for making quantitative judgments about a process or processes is a statistical test. The goal is to decide whether there is sufficient data to "reject" a theory or hypothesis on the process.
In the given problem the average age of the corporate executives at the three locations is being calculated, it means more than two groups are being compared. hence, The appropriate statistic test would be ANOVA.
In order to calculate the degree of freedom, we must know the no. of observations.
here, no. of observations are 15 ( 3 × 5 ) and the no. of groups are 3.
∴ Degree of freedom = no. of observations - no. of groups
= 15 - 3 = 12.
Learn more about Statistical tests from the link given below:
https://brainly.com/question/15980493
#SPJ4
the height of chance's beanstalk decreases by 50% per day when he stops feeding it. chance's beanstalk is 20 inches tall when he stops feeding it.
When Chance stops feeding the beanstalk, it loses half its height every day. Chance's beanstalk grows to a height of 20 inches after he stops feeding it= 20.5^t
What is unitary method?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Consider your square as being composed of smaller unit squares.
The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.
Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.
Hence, When Chance stops feeding the beanstalk, it loses half its height every day. Chance's beanstalk grows to a height of 20 inches after he stops feeding it= 20.5^t
learn more about unitary method click here:
brainly.com/question/24587372
#SPJ4
A soap maker wants to ship as many bars of soap as she can to a store. Each bar of soap weighs 1/5 pound. The box that she will use to ship the soap can hold a maximum of 18 pounds of soap.
How many bars of soap can the soap maker ship to the store?
The number of bars of soap that the soap maker ship to the store is 90.
How to calculate the number of bars?From the information, the soap maker wants to ship as many bars of soap as she can to a store. Each bar of soap weighs 1/5 pound.
Since the box that she will use to ship the soap can hold a maximum of 18 pounds of soap. The number of soaps will be:
= 18 ÷ 1/5
= 18 × 5
= 90
The number of soaps is 90.
Learn more about fractions on:
brainly.com/question/78672
#SPJ1
Find equations of the tangents to the curve x = 9t2 + 3, y = 6t3 + 3 that pass through the point (12, 9). (enter your answers as a comma-separated list. ).
y - 9 = 1(x - 15) is the required equation for the tangent.
What are equations?Equations come in two varieties: identities and conditional equations.
All possible values of the variables result in an identity.
Only certain combinations of the variables' values make a conditional equation true.
Two expressions joined by the equals symbol ("=") form an equation.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance.
When this equation is solved, we discover that the value of the variable x is 7.
So, the equation of the tangent is:
First, with respect to t, differentiate the function as follows:
dx/dt = d(9t² + 6)/dt
dx/dt = 18t
Like this, we have:
dy/dt = d(6t³ + 3)/dt
dy/dt = 18t²
Now, we will obtain:
dy/dx = 18t²/18t
dy/dx = t
We know that (15, 9) occurs on the curve, so we got:
d(9t² + 6)/dt and d(6t³ + 3)/dt ⇒ t = ±1 and t = 1 ⇒ t = 1
So, (15, 9) is the slope.
y - 9 = 1(x - 15) is the equation of the tangent.
Therefore, y - 9 = 1(x - 15) is the required equation for the tangent.
Know more about equations here:
https://brainly.com/question/28937794
#SPJ4
Correct question:
Find the equations of the tangents to the curve x = 9t2 + 6, y = 6t3 + 3 that passes through the point (15, 9).
Which of the following pairs of correlation coefficients most closely corresponds to the observed correlations between the intelligence scores of adopted children and those of their adoptive or biological parents?
a. child-adoptive: 0.20; child-biological: 0.40
b. child-adoptive: 0.40; child-biological: 0.40
c. child-adoptive: 0.20; child-biological: 0.20
d. child-adoptive: 0.50; child-biological: 0.50
correlation coefficients most closely corresponds to the observed correlations between the intelligence scores of adopted children is a. child-adoptive: 0.20; child-biological: 0.40
Children for adoption
Adoption is the social, emotional, and legal process in which children who will not be raised by their birth parents become full and permanent legal members of another family while maintaining genetic and psychological connections to their birth family.
learn more about of biological here
https://brainly.com/question/14510435
#SPJ4
The glee club has $90 to spend on pens and pencils. Each pen costs $0. 75 and each pencil costs $0. 15. Write an equation that describes the numbers of pens, x, and pencils, y, that the glee club can buy. What is the greatest number of each type of writing tool that the club can buy?.
Part a: 0.75x + 0.15y = 90 is the equation that indicates how many club pens and pencils the glee club can purchase.
Part B: The maximum number of pens and pencils the club can purchase is 120 and 600 respectively.
Define the term linear equation?First order equations include linear equations. In the coordinate system, the linear equations get defined for lines. When a homogeneous factor of degree 1 is present in the equationThe stated values in the questions are-
Cost of one pen = $0.75
Let total number of pens be x.
Cost of one pencil = $0.15
Let total number of pencils be y.
Total cost (pens and pencils) = $90
Total cost = (Cost of one pen) x (Number of pens) + (Cost of one pencil)x(Number of pencils)
The equation modelling number of club pens and pencils is:
0.75x + 0.15y = 90
For the greatest number of pens ;
0.75x = 90
x = 90/0.75
x = 120
Thus, the greatest number of pens bought by club is 120.
For greatest number of pencils;
0.15y = 90
y = 90/0.15
y = 600
Thus, the greatest number of pencils bought by club is 600.
To know more about the linear equation, here
https://brainly.com/question/2030026
#SPJ4
a newsletter publisher believes that 29% of their readers own a personal computer. a testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. after performing a test at the 0.02 level of significance, the testing firm fails to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
There's not enough evidence to refute the publisher's claim.
Here, we are given that a newsletter publisher believes that 29% of their readers own a personal computer.
The testing firm believes this is inaccurate and hence conducts hypothesis testing to verify the claim.
They take a significance level of 0.02 and fail to reject the null hypothesis.
The null hypothesis of the testing firm would be- 29% of the readers own a personal computer because this is what is established by the publisher.
They fail to reject this null hypothesis which means that there is not enough evidence at 0.02 significant level that the percentage is not 29%.
Thus, there's not enough evidence to refute the publisher's claim.
Learn more about hypothesis testing here-
https://brainly.com/question/29576929
#SPJ4
2. Tyler has written an incorrect proof to show that quadrilateral ABCD is a
parallelogram. He knows segments AB and DC are congruent. He also knows
angles ABC and ADC are congruent. Find the mistake in his proof.
Segment AC is congruent to itself, so triangle ABC is congruent to triangle ADC by
Side-Angle-Side Triangle Congruence Theorem. Since the triangles are congruent, so
are the corresponding parts, and so angle DAC is congruent to ACB. In
quadrilateral ABCD, AB is congruent to CD and AD is parallel to CB. Since AD is
parallel to CB, alternate interior angles DAC and BCA are congruent. Since
alternate interior angles are congruent, AB must be parallel to CD. Quadrilateral
ABCD must be a parallelogram since both pairs of opposite sides are parallel.
Answer: specific analyze is as it follows
Step-by-step explanation:
Which statements are true about the ordered pair (−1, 5) and the system of equations? {x+y=4x−y=−6 Select each correct answer. Responses The ordered pair (−1, 5) is a solution to the first equation because it makes the first equation true. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the first equation because it makes the first equation true. The ordered pair (−1, 5) is a solution to the second equation because it makes the second equation true. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the second equation because it makes the second equation true. The ordered pair (−1, 5) is not a solution to the system because it makes at least one of the equations false. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is not a solution to the system because it makes at least one of the equations false. The ordered pair (−1, 5) is a solution to the system because it makes both equations true. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the system because it makes both equations true.
The statements that are true about the ordered pair (−1, 5) and the system of equations include the following;
A. The ordered pair (−1, 5) is a solution to the first equation because it makes the first equation true.
B. The ordered pair (−1, 5) is a solution to the second equation because it makes the second equation true.
D. The ordered pair (−1, 5) is a solution to the system because it makes both equations true.
How to determine the true statement?In order to determine if this ordered pair is a true solution based on the given system of linear equations, we would have to test the ordered pair (-1, 5) by substituting it into each of the linear equation as follows;
For the first linear equation, we have the following:
x + y = 4
-1 + 5 = 4
4 = 4 (True).
For the first linear equation, we have the following:
x - y = -6
-1 - 5 = -6
-6 = -6 (True).
Read more on ordered pairs here: brainly.com/question/12179097
#SPJ1
Which picture has an area equivalent to 3/4 shaded?
Answer:
ITS A
Step-by-step explanation:
Harper runs 2200 meters in 10 minutes. How many meters can Harper run in one minute?
Answer: 220 meters in 1 minute
Step-by-step explanation:
if harper can run 2200 meters in 10 min then that means you can run 220 in 1 min
2200/10 = 220
Answer:
220
Step-by-step explanation:
2200/10 is 220
Starting at 1:00 p.m., the temperature changes −4
degrees Fahrenheit per hour. Write and solve an equation to find how many hours x
it will take to reach −1°
F.
Answer: 9 hours
Step-by-step explanation:
here are a couple of things to notice here. You don’t have a starting temperature, so that will be an unknown. I will call it S.
The next thing to notice is that the current temperature (C) at any given time is just the starting temperature minus 4 times the number of hours (H) that have passed since 1 PM.
C = S – 4*H
We want to solve this for H when the current temperature (C) is -1.
-1 = S – 4*H
You can rearrange this by adding 4*H to both sides and adding 1 to both sides:
4*H = S + 1
Then you divide both sides by 4
H = (S+1)/4
This will tell you the number of hours PAST 1 PM that it takes to get to -1 degrees. Of course, you need to know the starting temperature, S, in order to get a numeric answer.
Let’s check this with an example. If the starting temperature were exactly 4 degrees above -1, then it should take exactly 1 hour. So let S = -1 + 4 = 3. If you plug 3 in for S, you do see that H becomes 1 hour PAST 1 PM (2 PM).
suppose you want to perform a test to compare the mean gpa of all freshmen with the mean gpa of all sophomores in a college? what type of sampling is required for this test?
The type of sampling required for this test is Independent sampling with quantitative data.
Randomly chosen samples are known as independent samples since their results are independent of other observations' values. The premise that samples are independent underlies many statistical analyses.
In the hypothetical situation, independent sampling is required since the researcher needs two distinct samples: one from freshmen and one from sophomores. These samples are independent since there would be no relationship between them.
The information would be quantitative in nature. Student GPAs are the dependent variable in this study. Since GPA is a qualitative indicator, the kind of data being collected is also quantitative.
To learn more about sampling, visit the link below:
brainly.com/question/29314866
#SPJ4
the height of a cylinder is increasing at a constant rate of 2 centimeters per second, and the volume is increasing at a rate of 1152 cubic centimeters per second. at the instant when the height of the cylinder is 33 centimeters and the volume is 403 cubic centimeters, what is the rate of change of the radius? the volume of a cylinder can be found with the equation v
Answer:
about 2.758 cm/s
Step-by-step explanation:
You want the rate of change of a cylinder's radius, when its height is 33 cm increasing at 2 cm/s, and its volume is 403 cm³ increasing at 1152 cm³/s.
Rate of changeThe volume of a cylinder is given by the equation ...
V = πr²h
Solving for the radius gives ...
r = √(V/(πh))
Differentiating, we have ...
[tex]r'=\dfrac{1}{\sqrt{\pi}}\left(\dfrac{1}{2}V^{-\frac{1}{2}}h^{-\frac{1}{2}}V'-\dfrac{1}{2}V^{\frac{1}{2}}h^{-\frac{3}{2}}h'\right)=\dfrac{hV'-Vh'}{2h\sqrt{\pi Vh}}[/tex]
Filling in the values V = 403, V' = 1152, h = 33, h' = 2, we have ...
r' = (33·1152 -403·2)/(2·33·√(π·403·33)) = 37210/(66√(13299π))
r' ≈ 2.758 . . . . . cm/s
The rate of change of the radius is about 2.758 cm/s.
the top 5% of applicants on a test will receive a scholarship. if the test scores are normally distributed with a mean of 76 and a standard distribution of 12, what is the lowest test score that still qualifies for a scholarship?
As per the standard distribution, the lowest test score is 27.76%
Standard distribution:
In statistics, standard distribution means a normal distribution with a mean of zero and standard deviation of 1.
Given,
The top 5% of applicants on a test will receive a scholarship. if the test scores are normally distributed with a mean of 76 and a standard distribution of 12.
Here we need to find the lowest test score that still qualifies for a scholarship.
As per the given question, we have identified the value of
=> μ = 76 (mean)
=> σ = 12 (standard deviation)
Then we need to take the value of x as,
x < 5% (find the probability)
Now, converting the problem in standard form
=> Z = (5 − 76) / 12
=> Z = -5.91
Then as per the z table the value is 0.2786
To know more about standard distribution here.
https://brainly.com/question/29509087
#SPJ4
the volume of a sample of nitrogen is 6.00 liters at 35oc and 0.974 atm. what volume will it occupy at stp?
5.152 L volume will it occupy at STP.
What is ideal gas law?
The equation of state for an ideal gas, in theory, is known as the ideal gas law. Even though it has a number of shortcomings, it provides a good approximation of the behavior of several gases under various circumstances. Theoretical point particles that move randomly and only collide in elastic ways make up an ideal gas.
Using the ideal gas equation PV=nRT, where n is the number of moles, it is possible to determine the volume that will be present at STP as follows.
n= PV/RT
p=0.974 atm
V=6.0 L
R = 0.0821 L.atm/k.mol
T= 35 +273= 308k
n= (0.974 atm x 6.0 L)/( 0.0821 L.atm/k.mol x 308 k)= 0.178 moles
STP 1 mole= 22.4 L what obout 0.23 moles
=22.4 x0.178moles/ 1moles =5.152 L
Hence, 5.152 L volume will it occupy at STP
Learn more about ideal gas law, by the following link
https://brainly.com/question/9779722
#SPJ4
I spent $2000 to get
Brownie Town up and running. We make all sorts of brownies. Some have peanuts, some have chocolate chips, and others have icing.
Every month I earn $200
from Brownie Town sales.
The equation form as per the statement in the question will be y = -200x - 2000.
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the given information in the question,
They spent $2,000 therefore that would be -2,000, and they make $200 per month selling brownies.
So simply add -2,000 each time on the chart under "Income made," and the final amount should be 600.
So, the equation will be,
y = -200x - 2000.
To know more about Equation:
https://brainly.com/question/29657983
#SPJ1
(x+2)(x+1) expand and simplify
Hello!
To expand:
==> we must multiply each variable with each other
[tex](x+2)(x+1)=x*x+x*1+2*x+2*1=x^2+x+2x+2=x^2+3x+2[/tex]
Thus: when (x+2)(x+1) is expanded and simplified
==> [tex]x^2+3x+2[/tex]
Answer:
Step-by-step explanation: First we will expand so
x times x = x^2
x times 1 = x ( don’t need to put 1 in front)
2 times x is = 2x
2 times 1 = 2
Now we line them all up and look out if there are any like terms.
x^2 + x + 2x + 2 = x^2 +3x + 2
Please help i am so confused
The domain and the range of the functions are given by the images at the end of the answer.
How to obtain the domain and the range of the function?The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, on the graph, it will be given by the values of x of the graph, the values assumed by the horizontal axis of the graph.
The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, on the graph, it will be given by the values of y of the graph, the values assumed by the vertical axis of the graph.
The notations are given as follows:
Discrete functions -> composed by dots -> the domain and the range are given by the {}, as only the values are assumed, not intervals.Continuous functions -> continuous functions -> domain and range are given by intervals.More can be learned about the domain and range of functions at brainly.com/question/2264373
#SPJ1
Drag statements and reasons to each row to show why the slope of the line between D D and E E is the same as the slope between E E and F F , given that triangles A A and B B are similar.
By definition of slope , we have seen that Slope = 4/3 and 4/3 = 16/12
How to find the slope of a Line?The slope of a line is basically a measure of its steepness. Mathematically, the slope is calculated as rise over run.
To find the slope, we divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points. This is change in y divided by change in x.
From definition of slope, we know that;
Slope between line D and E is; Slope = 4/3
Similarly, by definition of slope, we know that;
Slope between line D and E is; Slope = 16/12
Now, 16/12 can be reduced to 4/3 and as such;
4/3 = 16/12
Read more about Slope of Line at; https://brainly.com/question/3493733
#SPJ1
aclub is hosting an ice cream sundae party with four different flavors of ice cream and six different toppings available. how many sundaes are possible using one flavor of ice cream and three different toppings?
There are 80 sundaes possible using one flavor of ice cream and three different toppings.
Here, we are given that a club is hosting an ice cream sundae party with four different flavors of ice cream and six different toppings.
For choosing 1 flavor of ice cream from 4, we have 4 ways.
Now, we need to choose 3 different toppings from the given 6.
This can be done in 6C3 ways
6C3 = 6! / (3! × 3!)
= (6 × 5 × 4) / (3 × 2)
= 120/ 6
= 20
Thus, we have 20 ways of choosing 3 different toppings.
Now, the number of ways of making the sundaes would be-
4 × 20
= 80
Thus, there are 80 sundaes possible using one flavor of ice cream and three different toppings.
Learn more about combination here-
https://brainly.com/question/11732255
#SPJ4
52=2(x+19)
Please help me
divide the following polynomials (9x^4+3x^3y−5x^2y^2+xy3 ) ÷ (3x^2+2x^2y−xy^2)
Hence, the remainder is [tex]0[/tex] and the quotient is [tex]3x-y[/tex].
What is the polynomial?
A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Here given polynomial is
[tex]\frac{9x^4+3x^3y-5x^2y^2+xy^3}{3x^3+2x^2y-xy^2}[/tex]
[tex]3x-y[/tex]
[tex]\sqrt[3x^3+2x^2y-xy^2]{9x^4+3x^3y-5x^2y^2+xy^3} \\\\[/tex]
[tex]9x^4+6x^3y-3x^2y^2+0[/tex]
-----------------------------------------
[tex]-3x^2y-2x^2y^2+y^3x[/tex]
[tex]-3yx^3-2y^2x^2+y^3x[/tex]
------------------------------------------
[tex]0[/tex]
Hence, the remainder is [tex]0[/tex] and the quotient is [tex]3x-y[/tex].
To know more about the polynomial
https://brainly.com/question/11154053
#SPJ1
Ray has $1600 in his bank account. How much interest will the money earn in one year at 2%. What will his balance be?
Answer: 32 every month or day. if its every month the answer is 384, if its every day it would be 11680
Step-by-step explanation:
Given:
Initial amount = $1600,Interest rate = 2%,Time = 1 year.Find the amount of interest:
$1600*2/100 = $32Find the balance after one year:
$1600 + $32 = $1632a survey of a group of 116 tourists was taken in st. louis. the survey showed the following: 66 of the tourists plan to visit gateway arch; 50 plan to visit the zoo; 10 plan to visit the art museum and the zoo, but not the gateway arch; 14 plan to visit the art museum and the gateway arch, but not the zoo; 18 plan to visit the gateway arch and the zoo, but not the art museum; 9 plan to visit the art museum, the zoo, and the gateway arch; 14 plan to visit none of the three places. how many plan to visit the art museum only?
12 People plan to visit the art museum only.
What is Set Theory?
We study sets and their characteristics in the area of mathematical logic known as set theory. A set is a collection of things or a group of things. These things are frequently referred to as elements or members of a set. A set is, for instance, a group of cricket players. A set is a clearly defined collection of things or people, as we already learnt in the introduction. Numerous examples from everyday life, such as the number of rivers in India and the colors in a rainbow, can be used to relate sets.
Given,
Total no of people =116
No of people visiting any of the three places = total - people visiting none of the places
= 116 -14 = 102
No of people visiting only Gateway arch = total people visiting gateway arch - (people visiting all the three + people visiting Gateway ans museum butnot zoo +people visiting gateway and zoo butnot museum)
= 66 - (18+9+14) = 25
Similarly, people visiting only zoo = 14
Total no of people plan to visit Art Museum only = 102 - (25+14+9+18+10+14) = 112
12 People plan to visit the art museum only.
Learn more about Set Theory, by the following link.
https://brainly.com/question/13458417
#SPJ4
The square on the right is a scaled copy of the square on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
The scale factor of the figure of the two squares is 1.5
How to find the scale factorThe scale factor is determine using division
The formula involve:
let the scale factor be r then we say
area of square A * r = area of square B
8 * 8 * r = 12 * 12
64r = 144
r = 144 / 64
r = 1.5
using the dimensions
8r = 12
r = 12 / 8
r = 1.5
Learn more on scale factor :
https://brainly.com/question/29010530
#SPJ1
Lennon uses 5 1/2 cups of flour for every 2 batches of cookies she bakes. What is the unit rate per batch of cookies?
The unit rate per batch of cookies is 2.75 as Lennon uses 5 1/2 cups of flour for every 2 batches of cookies she bakes.
What is meant by unit rate?To calculate the unit rate, divide the denominator by the numerator so that the denominator equals 1. For example, if 50 kilometers are reached in 5.5 hours, the unit rate is 50 kilometers/5.5 hours = 9.09 kilometers per hour.
When expressed as a fraction, a unit rate has a denominator of one unit. To write a rate as a unit rate, divide the rate's numerator and denominator by the rate's denominator.
Based on the given conditions, formulate:
(5 1/2)/2
We have to find the common denominator and write the numerators above the common denominator.
(((5×2)/2)+(1/2))/2
Now, we have to calculate the product or quotient:
((10/2)+(1/2))/2
Now, write the numerators over common denominator,
((10+1)/2)/2
Then, calculate the sum or difference:
(11/2)/2
=11/4
=2.75 (or) 2 3/4
Therefore, the unit rate per batch of cookies is 2.75.
To know more about unit rate, visit:
https://brainly.com/question/13795269
#SPJ1
HELPPPPP ME SLAY PEOPLEEEEEEE
The solutions are given below.
What is angle?An angle is the formed when two straight lines meet at one point, it is denoted by θ.
Given that,
lines u and v are parallel,
And ∠ 9 = 80° and ∠ 5 = 68°
(a)
Angle 12 is supplementary angle of angle 9,
Therefore, ∠12 = 180 - 80 = 100
(b)
Angle 1 and angle 9 are corresponding angle and are equal.
∠ 1 = ∠ 9 = 80
(c)
Angle 1 is supplementary angle of angle 4,
Therefore, ∠ 4 = 180 - 80 = 100
(d)
Angle 3 and angle 1 are vertically opposite angles,
Therefore, ∠ 3 = ∠ 1 = 80°
(e)
Angle7 and angle 5 are vertically opposite angles,
Therefore, ∠ 7 = ∠ 5 = 68°
(f)
Angle 16 and 7 are supplementary angles,
Therefore, ∠16 = 180 - 68 = 112
To learn more about Angle on:
https://brainly.com/question/28451077
#SPJ1
please answer the question (ratios)
The following are the amount each person receive:
a. 6 : 4 = $300 : $200b. 1 : 4 : 5 = $50 : $200 : $250c. 1 : 8 : 1 = $50 : $400 : $50d. 8 : 9 : 8 = $160 : $180 : 160e. 10 : 5 : 4 : 1 = $250 : $125 : $100 : $25How to find the amount each person receive?Amount of money = $500a. 6 : 4
Total ratio = 6 + 4
= 10
6/10 × 500
= $300
4/10 × 500
= $200
b. 1 : 4 : 5
Total ratio = 1 + 4 + 5
= 10
1/10 × 500
= $50
4/10 × 500
= $200
5/10 × 500
= $250
c. 1 : 8 : 1
Total ratio = 1 + 8 + 1
= 10
1/10 × 500
= $50
8/10 × 500
= $400
1/10 × 500
= $50
d. 8 : 9 : 8
Total ratio = 8 + 9 + 8
= 25
8/25 × 500
= $160
9/25 × 500
= $180
8/25 × 500
= $160
e. 10 : 5 : 4 : 1
Total ratio = 10 + 5 + 4 + 1
= 20
10/20 × 500
= $250
5/20 × 500
= $125
4/20 × 500
= $100
1/20 × 500
= $25
Read more on ratio:
https://brainly.com/question/2328454
#SPJ1
Jay is trying to simplify the following expressions 3x (3 +12 divided by 3) -4. What should be his first step in solving this problem
Jay is incorrect in doing addition first.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given the expression as;
3x (3 +12 divided by 3) -4.
To simplify this expression, then must follow PEMDAS.
3x(3+12÷3)
3x(3+4)
3x(7)
21x
Which means that Jay is incorrect in doing addition first.
To know more about an expression follow;
brainly.com/question/19876186
#SPJ1