Answer:
Paul is the youngest at 17 years old. Fiona is 20 years old, Sara is 23 years old
Step-by-step explanation:
Assign variables to the ages.
S = sara's age
F = Fiona's age
P = Paul's age.
S + F + P = 60
S = 3 + F
P = F - 3
(3 + F) + F + (F - 3) = 60
3 + 3F - 3 = 60
3F = 60
F = 20
S = 23
P = 17
Consider the functionf:R→Rdefined viaf(x) =|x|.(a) Give a functiongwith domainRsuch thatg◦fis one-to-one, or describe why it is not possible.(b) Give a function with domain such that◦fis onto, or describe why it is not possible.(c) Give a functiongwith rangeRsuch thatf◦gis one-to-one, or describe why it is not possible.(d) Give a functiongwith rangeRsuch thatf◦gis onto, or describe why it is not possible.
Answer:
(a) Is not possible
(b) It is possible
(c) It is possible
(d) Is NOT possible.
Step-by-step explanation:
(a)
Is not possible, notice that for any function [tex]g[/tex] such that
[tex]g : \mathbb{R} \rightarrow \mathbb{R}[/tex]
you would have that
[tex](g\circ f)(x) = g(f(x)) = g(|x|)[/tex]
And for, lets say -3,3 you have that
[tex]g(|-3|) = g(|3|) = g(3)[/tex] therefore is not possible to find a function that is one to one.
(b)
It is possible. Take the following function
[tex]g(x) = x\sin(x)[/tex] since [tex]\sin[/tex] is periodic it will take positive and negative numbers and if you multiply by [tex]x[/tex] each period will become bigger and bigger.
(c)
It is possible. Take the function
[tex]g(x) = \sqrt{x}[/tex]
Then
[tex](f \circ g )(x) = | \sqrt{x} | = \sqrt{x}[/tex] and [tex]\sqrt{x}[/tex] is one to one.
(d)
It is NOT possible because [tex](f\circ g)(x) = f(g(x)) = |g(x)|[/tex] and that will always be positive.
PLEASEE HELPP MEE IN MATH WITH THIS PROBLEM PLEASEEE!!!!
We have been given a graph. We are asked to find the values of x,y and z.
We will use parallel line's angles to solve our given problem.
We know that corresponding angles of parallel lines are equal.
We can see that angle [tex]2x+3[/tex] and 67 are corresponding angles, so we can set an equation as:
[tex]2x+3=67[/tex]
[tex]2x+3-3=67-3[/tex]
[tex]2x=64[/tex]
[tex]\frac{2x}{2}=\frac{64}{2}[/tex]
[tex]x=32[/tex]
Therefore, the value of x is 32.
We know that interior angles on same side of transversal are supplementary.
We can see that [tex]3y+5[/tex] and 67 are interior angles, so we can set an equation as:
[tex]3y+5=67[/tex]
[tex]3y+5-5=67-5[/tex]
[tex]3y=62[/tex]
[tex]\frac{3y}{3}=\frac{62}{3}[/tex]
[tex]y=\frac{62}{3}[/tex]
Therefore, the value of y is [tex]\frac{62}{3}[/tex].
We can set an equation for angle z as:
[tex]4z+13=2x+3[/tex]
[tex]4z+13-13=2x+3-13[/tex]
[tex]4z=2x-10[/tex]
Upon substituting value of z, we will get:
[tex]4z=2(32)-10[/tex]
[tex]4z=64-10[/tex]
[tex]4z=54[/tex]
[tex]\frac{4z}{4}=\frac{54}{4}[/tex]
[tex]z=13.5[/tex]
Therefore, the value of z is 13.5.
I need help with this math problem
Teh value of x is 23° (D)
Step-by-step explanation:
Total of angel = 360°
The value of x :
(2x + 15)° + 119° + 99° + 81° = 360°
2x + (15 + 119 + 99 + 81)° = 360°
2x + 314° = 360°
2x = 360° - 314°
2x = 46
x = 46 ÷ 2
x = 23°
So, the value of x is 23° (D)
Hope it helpful and useful :)
bill drove 315 miles in 7 hours, Alisha drove 235 mile sin 5 hours, and Joanna drove 414 miles in 9 hours. which person drove at an average speed of 47 miles per hour? (and can u explain what mph each person has thx :3) if u has roblox my username is zaw1031
Answer:
Alisha
Step-by-step explanation:
Speeds:
Bill:
315/7 = 45 mph
Alisha:
235/5 = 47 mph
Joanna:
414/9 = 46 mph
Answer:
The answer is Alisha.
Step-by-step explanation:
235 mph divided by 5 is equal to 47 mph.
In one study, the correlation between the educational level of husbands and wives in a certain town was about 0.50; both averaged 12 years of schooling completed, with an SD of 3 years. (a) Predict the educational level of a woman whose husband has completed 18 years of schooling. (b) Predict the educational level of a man whose wife has completed 15 years of schooling. (c) Apparently, well-educated men marry women who are less well educated than themselves. But the women marry men with even less education. How is this possible
Answer:
a) Predicted value =0.5×18+6= 15
b) Predicted value =0.5×15+6= 13.5
c) Since least square equation has the tendency to regress the outcome toward mean value , as both the explanatory variable (in part a and b) are above mean value , the response variable are smaller then them.
Step-by-step explanation:
[ Find the attachments for explanation]
Final answer:
Explaining how to predict the educational level of a spouse based on correlation, and discussing why well-educated individuals may marry partners with different education levels.
Explanation:
The questions can be answered as -
(a) Predicting the educational level of a woman whose husband has completed 18 years of schooling:
Given that the correlation between the educational levels of husbands and wives is 0.50, we can use this correlation to predict the wife's educational level.
Educational level of wife = correlation * (wife's SD / husband's SD) * husband's years of schooling + wife's average years of schooling.
(b) Predicting the educational level of a man whose wife has completed 15 years of schooling:
Apply the same formula as in (a) but with the wife's years of schooling given as 15 years.
(c) Explanation of why well-educated men marry women less educated than themselves:
This can occur due to various factors such as social dynamics, career aspirations, or personal preferences.
I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 30 miles per hour instead, then I would have arrived 20 minutes later. How many miles did I drive?
Answer:
40 miles
Step-by-step explanation:
Let's set x to the number of miles driven, and t to the number of hours it took to drive.
We know that 40t is equal to x.
We also know that 40t is equal to 30(t + 1/3).
Solve for t:
40t = 30(t+1/3)
40t = 30t + 10
Subtract 30t from both sides:
10t = 10
Divide 10 from both sides:
t = 1
40t = 40 x 1 = 40 miles
I drove 40 miles.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.
Suppose, I drove n number of miles and it took me x time in hours.
We know that 40x is equal to n.
Since it would take 20 more minutes, so we have the division of 20/60 = 1/3
Then, 40x is equal to 30(x+ 1/3).
Solve for t:
40x = 30(x+1/3)
40x = 30x + 10
10x = 10
Now , divide by 10 on both sides,
x = 1
40x = 40 x 1 = 40 miles
Therefore, I drove 40 miles.
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What’s the correct answer for this?
Answer:
RT ≈ 7.82
Step-by-step explanation:
tan θ = opposite / adjacent
tan 41 = RT / 8
RT = tan 41 × 8
RT = 0.869 × 8
RT = 7.821
RT ≈ 7.82
A bag contains 5 blue marbles, 2 black marbles, and 3 red marbles. A marble is randomly drawn from the bag.
The probability of not drawing a black marble is______
robability of drawing a red marble is_____
Answer:
4/5 (not drawing a black marble)
3/10 (drawing a red marble)
Step-by-step explanation:
Each of six jars contains the same number of candies. Alice moves half of the candies from the first jar to the second jar. Then Boris moves half of the candies from the second jar to the third jar. Then Clara moves half of the candies from the third jar to the fourth jar. Then Dara moves half of the candies from the fourth jar to the fifth. Finally, Ed moves half of the candies from the fifth jar to the sixth jar. At the end, 30 candies are in the fourth jar.
How many candies are now in the sixth jar?
Answer:
The number of candies in the sixth jar is 42.
Step-by-step explanation:
Assume that there are x number of candies in each of the six jars.
⇒ After Alice moves half of the candies from the first jar to the second jar, the number of candies in the second jar is:
[tex]\text{Number of candies in the 2nd jar}=x+\fracx}{2}=\frac{3}{2}x[/tex]
⇒ After Boris moves half of the candies from the second jar to the third jar, the number of candies in the third jar is:
[tex]\text{Number of candies in the 3rd jar}=x+\frac{3x}{4}=\frac{7}{4}x[/tex]
⇒ After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the fourth jar is:
[tex]\text{Number of candies in the 4th jar}=x+\frac{7x}{4}=\frac{15}{8}x[/tex]
⇒ After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fifth jar is:
[tex]\text{Number of candies in the 5th jar}=x+\frac{15x}{16}=\frac{31}{16}x[/tex]
⇒ After Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the sixth jar is:
[tex]\text{Number of candies in the 6th jar}=x+\frac{31x}{32}=\frac{63}{32}x[/tex]
Now, it is provided that at the end, 30 candies are in the fourth jar.
Compute the value of x as follows:
[tex]\text{Number of candies in the 4th jar}=40\\\\\frac{15}{8}x=40\\\\x=\frac{40\times 8}{15}\\\\x=\frac{64}{3}[/tex]
Compute the number of candies in the sixth jar as follows:
[tex]\text{Number of candies in the 6th jar}=\frac{63}{32}x\\[/tex]
[tex]=\frac{63}{32}\times\frac{64}{3}\\\\=21\times2\\\\=42[/tex]
Thus, the number of candies in the sixth jar is 42.
There are now 33.75 candies in the sixth jar.
Let's denote:
- x as the initial number of candies in each jar.
After Alice moves half of the candies from the first jar to the second jar, the number of candies in the first jar becomes [tex]\( \frac{x}{2} \)[/tex], and the number of candies in the second jar becomes [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .
After Boris moves half of the candies from the second jar to the third jar, the number of candies in the second jar becomes [tex]\( \frac{3x}{4} \)[/tex], and the number of candies in the third jar becomes [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .
After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the third jar becomes [tex]\( \frac{x}{2} \)[/tex], and the number of candies in the fourth jar becomes [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .
After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fourth jar becomes [tex]\( \frac{3x}{4} \)[/tex], and the number of candies in the fifth jar becomes [tex]\( \frac{3x}{4} + \frac{3x}{8} = \frac{9x}{8} \).[/tex]
Finally, after Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the fifth jar becomes [tex]\( \frac{9x}{16} \)[/tex], and the number of candies in the sixth jar becomes [tex]\( \frac{9x}{16} + \frac{9x}{32} = \frac{27x}{32} \).[/tex]
Given that 30 candies are now in the fourth jar, we can set up the equation:
[tex]\[ \frac{3x}{4} = 30 \][/tex]
Solving for x :
[tex]\[ x = \frac{4 \times 30}{3} = 40 \][/tex]
Now, we can find the number of candies in the sixth jar:
[tex]\[ \frac{27 \times 40}{32} = \frac{1080}{32} = 33.75 \][/tex]
So, there are now 33.75 candies in the sixth jar.
A baker has 6.8 kilograms of flour. She buys another 1.5 kilograms of flour. She uses 1.2 kilograms to make cupcakes and 0.8 kilograms to make cookies.
How much flour does the baker have left?
Answer:6.3
Step-by-step explanation: 6.8 +1.5 -1.2 -0.8=6.3
The amount of flour left is 6.3 kg.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total flour = 6.8 + 1.5 = 8.3 kg
Amount of flour used = 1.2 + 0.8 = 2 kg
The amount of flour left.
= 8.3 - 2
= 6.3 kg
Thus,
6.3 kg of flour is left.
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A math class has 3 girls and 9 boys in the seventh grade and 7 girls and 3 boys in the eighth grade. The teacher randomly selects a seventh grader and an
eighth grader from the class for competition. What is the probability that the students she selects are both girls?
Write your answer as a fraction in simplest form.
Final answer:
To calculate the probability that both a seventh grader and an eighth grader selected at random are girls, multiply the probability of selecting a girl from each grade. For the seventh grade, it's 1/4, and for the eighth grade, it's 7/10. The overall probability of both being girls is therefore 7/40.
Explanation:
The question involves determining the probability that both students selected for a competition from different grades are girls. To find this, we need to consider the number of girls in each of the two grades separately.
In the seventh grade, there are 3 girls out of 12 students. So, the probability of selecting a girl from the seventh grade is 3/12, which simplifies to 1/4. In the eighth grade, there are 7 girls out of 10 students. Therefore, the probability of selecting a girl from the eighth grade is 7/10.
To find the overall probability of selecting girls from both grades, we multiply the probabilities of each event since they are independent: (1/4) * (7/10) = 7/40.
Thus, the probability that both selected students are girls is 7/40.
Juan and Rob Are selling cookie dough for a school fundraiser Juan Has t Cookie dough Orders Rob has 40 cookie dough orders they have a total of 75 cookie dough orders all together
Answer:
Juan has 35 orders
Step-by-step explanation:
you subtract 40 from 75 to get 35
Juan has 35 cookie dough orders for the school fundraiser
The question involves solving a simple algebra problem related to a school fundraiser involving cookie dough orders. Juan and Rob have a total of 75 cookie dough orders together. Juan has t orders and Rob has 40 orders. The problem can be represented by the equation t + 40 = 75. To find out how many cookie dough orders Juan has, we subtract 40 from both sides of the equation, which gives us t = 35. So, Juan has 35 cookie dough orders.
Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%. How long will it take for her
money to reach $105,000? Round to the nearest tenth of a year.
In need of help !!
Answer:
It will take 36.1 years for her money to reach $105,000.
Step-by-step explanation:
The amount of money earned after t years in continuous interest is given by:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial investment and r is the interest rate, as a decimal.
Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%.
This means that [tex]P(0) = 7000, r = 0.075[/tex]
How long will it take for her money to reach $105,000?
This is t for which P(t) = 105000.
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]105000 = 7000e^{0.075t}[/tex]
[tex]e^{0.075t} = \frac{105000}{7000}[/tex]
[tex]e^{0.075t} = 15[/tex]
[tex]\ln{e^{0.075t}} = \ln{15}[/tex]
[tex]0.075t = \ln{15}[/tex]
[tex]t = \frac{\ln{15}}{0.075}[/tex]
[tex]t = 36.1[/tex]
It will take 36.1 years for her money to reach $105,000.
Which is the correct calculation for the volume of the
pyramid?
(36)(7)= 84 units
(36)(7) = 126 units
36(7) = 252 units
3617)(3) = 756 units
Answer:
(A)One-third(36)(7)= 84 cubic units
Step-by-step explanation:
Volume of a Pyramid = [tex]\frac{1}{3}X$Base Area X Height[/tex]
The base is a rectangle
Base Area = 9 X 4=36 Square Units
Height =7 Units
Therefore:
Volume [tex]=\frac{1}{3}(36)(7)[/tex]
=84 Cubic Units
Answer:
Step-by-step explanation:
a single number between 0 and 9 occurring either alone or in a larger number is called a _________
Answer:
The answer is digit
Step-by-step explanation:
A single number between 0 and 9 is a digit, which often makes up larger numbers.
Students sometimes suspect that studying more isn't worth it for "harder" math and science classes: either you understand it, or you don't. To find out whether more studying actually transferred to higher grades, one enterprising student surveyed randomly selected students and asked them the number of hours they had spent studying for a final exam in a core math or science class, and their grade on the final exam. The student wanted to know the average increase in points scored on the final for every additional hour spent studying. What statistical procedure should be performed?
ANSWER: The statistical procedure that should be performed is REGRESSION.
Step-by-step explanation: Regression is a statistical procedure that is used to estimate the relationship between an independent variable and a dependent variable using their mean values.
The independent variable in this case is the hours each student spend in studying, while the dependent variable is the students grade.
Since the researcher wants to determine if the hours a student spend in studying maths and science has any significant effect on their grades. The researcher should use regression, because it will show if the two variables are related and how it relates, by showing how far the points are from the trend lines of the graph.
6th grade math please help ! c;
Answer:
$19.99
Step-by-step explanation:
Take the price for 2 pairs and divide by 2 to get the price for one pair
39.98 /2
19.99 for one pair
Do you want brainlyest
Answer:
I mean I guess sure
Step-by-step explanation:
Anyway hope you have a good day!!
ig..
Is 80 a multiple of 10 why or why not
Answer:
Yes because 10 times 8 is 80.
Step-by-step explanation:
Answer: 80 IS a multiple of 10 because 8 times 10 is 80.
Step-by-step explanation:
What is a food that provides energy to perform activitie in a food chain
Answer: The Sun is the major source of energy for organisms and the ecosystems of which they are a part. Producers such as plants, algae, and cyanobacteria use the energy from sunlight to make organic matter from carbon dioxide and water. This establishes the beginning of energy flow through almost all food webs.
Hope you understood : )Problem:
An old coin is kept in a cubic box in such a way that the outline of the coin touches the 4 walls of the box, if the base of the box has a 24 cm perimeter, what is the area of the coin?
Answer:
28.27 cm^2 (2 decimal places)
Step-by-step explanation:
side of box = 24/4 = 6
diameter of coin would be 6 too
area of coin = pi x (6/2)^2 = 28.2743
What is the surface area of the triangular prism shown
Answer:
C
Step-by-step explanation:
A. 558 m2
B. 976 m2
C. 1,680 m2
D. 1,750 m2
Answer:
1064.64
Step-by-step explanation:
Name four possible solutions to the inequality; X > -1
Final answer:
Four possible solutions to the inequality X > -1 are 0, 1, 2, and 2.5, as each of these values is greater than -1. The solution set in interval notation is (-1, ∞).
Explanation:
The inequality in question is X > -1. To provide four possible solutions, we are essentially looking for any four numbers that are greater than -1. Remember, there are an infinite number of solutions since X can be any value greater than -1, but here are four specific examples:
0122.5Each of these values satisfies the inequality X > -1, because they are all greater than -1. It is important to note that solutions to inequalities like this one are often represented in interval notation, in this case, it would be (-1, ∞), meaning any number greater than -1 but less than infinity.
Carlos used 6 boards to build 2/3 of a front porch. How many boards will Carlos use to build the whole porch? Express your answer in simplest form.
Answer:
9 boards
Step-by-step explanation:
2/3 of the porch= 6 boards
so to figure out how much one third of the porch needs you find half of what it takes to fill in 2/3 of the porch and you get 3.
so 3=1/3 of the porch
then you simply do 3times 3 or 3+3+3 and you get 9
so it takes 9 boards to fill the whole porch
Olivia has taken an initial dose of a prescription medication.
The relationship between the elapsed time T, in hours, since she took the first dose, and the amount of medication M(t), in milligrams (mg), remaining in her bloodstream is modeled by the following function.
M(t)=50 (e^-0.75t)
How many milligrams of the medication will be remaining in Olivia's bloodstream after 6 hours?
Round your answer, if necessary, to the nearest hundredth.
Answer:
0.56 mg
Step-by-step explanation:
Put 6 where t is and do the arithmetic.
M(6) = 50(e^(-0.75·6)) = 50e^-4.5 ≈ 0.56
Olivia will have about 0.56 mg of medication remaining in her blood.
find the zeros of the polynomial 12x^2+31x+20
Answer:
-5/4; -4/3
Step-by-step explanation:
12x^2 + 31x + 20 =
(4x + 5)(3x + 4) -->
x = -5/4 OR -4/3
What’s the correct answer for this?
Answer:
D
Step-by-step explanation:
Because their slopes are equal. Rest of the step-by-step explanation is in the attached file!!
Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 900 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion to be within .02 of the true proportion (i.e., between .18 and .22)? (Hint: Use the sampling distribution of the sample proportion in this case.)
Answer:
86.64% probability that the resulting sample proportion is within .02 of the true proportion.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For the sampling distribution of a sample proportion p in a sample of size n, we have that [tex]\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this problem:
[tex]\mu = 0.2, \sigma = \sqrt{\frac{0.2*0.8}{900}} = 0.0133[/tex]
How likely is the resulting sample proportion to be within .02 of the true proportion (i.e., between .18 and .22)?
This is the pvalue of Z when X = 0.22 subtracted by the pvalue of Z when X = 0.18.
X = 0.22
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.22 - 0.2}{0.0133}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a pvalue of 0.9332.
X = 0.18
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.18 - 0.2}{0.0133}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
0.9332 - 0.0668 = 0.8664
86.64% probability that the resulting sample proportion is within .02 of the true proportion.
Andre drew a plan of a courtyard at a scale of 1 to 60. On his drawing, one side of the courtyard is 2.75 inches. if Andre made another courtyard scale drawing at a scale of 1 to 12, would this drawing be smaller or larger than the first drawing? explain your reasoning
Answer: The new drawing would be larger than the first drawing.
Step-by-step explanation:
A scale factor greater that one is an enlargement, but one smaller than one is a reduction
The second drawing will be 5 times bigger than the first one.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
The scale factor is done due to the unpractical measurement of any figure.
Given in the first drawing scale factor is 1:60
So Andre takes 60 units as 1
For example, it is 60 inches to 1 inch.
In the second drawing, Andre took 1:12
So he took 12 units as 1
For example 12 inches to 1
Now multiply by 5 then 5:60
So 60 inches to 5 inches means the second drawing is 5 times bigger the first one.
Hence "The second drawing will be 5 times bigger than the first one".
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Please help me with this 15+0.50=25+0.25 *
Answer:
15.50=25.25
Step-by-step explanation:
15+0.50=15.50
25+0.25=25.25
So 15+0.50=25.25 = 9.75 because you subract 25.25-15.50=9.75
Hope this helps