The sum of two numbers is 67. The smaller number is 21 less than the larger number. What are the numbers?
The equations are x + y = 67 and x = y + 21. Then the two numbers are 44 and 23.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The sum of the two numbers is 67. The smaller number is 21 less than the larger number.
Let the two numbers be 'x' and 'y' and x > y. Then the equations are given as,
x + y = 67 ...1
x = y + 21 ...2
From equations 1 and 2, then we have
y + 21 + y = 67
2y = 46
y = 23
Then the value of 'x' is given as,
x = 23 + 21
x = 44
The equations are x + y = 67 and x = y + 21. Then the two numbers are 44 and 23.
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Two seventh grade math classes are competing in an academic challenge. Each class will randomly select one class member to compete each week. Each class has 26 students, and half of the students in each class are boys.
The classes want to design a simulation that will give the probability of both class members participating in the academic challenge being girls. Two possible simulations are given below.
Simulation 1: Flip a coin 26 times. If it lands on heads, count the flip as a girl. If it lands on tails, count the flip as a boy. Count how many times the coin lands on heads.
Simulation 2: Use two standard decks of cards. Randomly draw one card from each deck. Each diamond or heart drawn will represent a girl. Each spade or club drawn will represent a boy. After the two cards are drawn, they are replaced and the decks are shuffled. Count how many times a heart or diamond is drawn from both decks for 100 trials.
(Simuation 1 or Simulation 2) would be best to use to simulate a girl being randomly selected from each class to participate in the academic challenge. Based on this simulation, the probability that two girls will be selected is about (15%, 50%, 25%, or 75%).
The best simulation for the probability of selecting two girls is Simulation 2, which uses two standard decks of cards, with hearts and diamonds representing girls. The probability that both selected members are girls is 25%.
To simulate the probability that both class members participating in the academic challenge are girls, Simulation 2 would be more appropriate. Since each class has half boys and half girls, just like a standard deck of cards has half red suits (hearts and diamonds representing girls) and half black suits (spades and clubs representing boys), this simulation effectively mirrors the class demographics.
To calculate the probability of selecting a girl from both classes, consider the probability of drawing a heart or diamond from one deck, which is 1/2 or 0.5. Since the events are independent (what happens in one draw does not affect the other), we can multiply the probabilities for the two events: 0.5 (probability of a girl from Class A) * 0.5 (probability of a girl from Class B) = 0.25. Therefore, the probability of both selected members being girls is 25%.
Lan pays a semiannual premium of $700 for automobile insurance, a monthly premium of $145 for health insurance, and an annual premium of $450 for life insurance.
the monthly expense is $
Answer:
$300
Step-by-step explanation:
1.automobile insurance : $700 semiannual premium
Annual premium = $700×2=$1400
2.
Health insurance :$145 per month
Annual premium= $145×12=$1740
3. Life insurance: $450 annual
Total annual premium
$1400+$1740+$450=$3590
Hence his monthly expenses on premium =
[tex]\frac{3590}{12}[/tex]
=$299.16
=$300 Approximately
The rectangular poster shown measures 2w-30 by w. The poster has an area of 5400 cm2. What is the value of w?
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!
the sum of two integers is 9 and the sum of their squares is 53. Find the integers.
A triangle has side lengths of 14 cm, 48 cm, and 55 cm.
The perimeter of parallelogram ABCD is equal to 10 cm. Find the length of diagonal
BD if you know that the perimeter of triangle ABD is 8 cm.
how do you solve it??? thanks
What is the name of the line of reflection for the pair of figures?
A student who was ineligible for financial aid needed to borrow 775,000 for tuition,books,and living expenses. Some money was borrowed at 8%, some at 9%, and some at 10%. How much was borrowed at each interest rate if the annual interest owed was 67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%.
8%:
9%:
10%:
Pepper Jackie has 12 picks. 1 out of every 4 picks is orange . The rest are green. How many picks are orange?
Noah spent some of his allowance on Monday. He spent 1/6 of his allowance on Tuesday and 3/6 of it on Friday. Noah has none of his allowance money left. What fraction of his allowance did he spend on Monday?
Let us represent the allowance spent by Noah on Monday by the letter "x".
We know that all the fractions must always add up to 1 in such questions.
Thus, if Noah spent 1/6 of his allowance on Tuesday and 3/6 of it on Friday and he spend x amount on Monday, then these spendings must add up to 1.
In other words,
[tex] x+\frac{1}{6}+\frac{3}{6}=1 [/tex]
[tex] x+\frac{1+3}{6}=1 [/tex]
Thus, [tex] x+\frac{4}{6}=1 [/tex]
[tex] \therefore x=1-\frac{4}{6}=\frac{6-4}{6}=\frac{2}{6}=\frac{1}{3} [/tex]
Thus Noah spent a third or [tex] \frac{1}{3} [/tex] of her allowance on Monday.
find the area of an equilateral triangle (regular 3-gon) with the given measurement 9-inch A=sq. in.
The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. on a certain day, 308 people entered the park, and the admission fees collected totaled 812 dollars. how many children and how many adults were admitted?
if 10/4 = 14/x what is x?
The prices of six different types of cell phones, in dollars are 49, 189, 79, 250,125,85. how many data points are closer ti the center than the mean absolute deviation?
Verify the identity. Show your work. (1 + tan^2u)(1 - sin^2u) = 1
120 meals to 52 meals
Trey graphs the equations y = –x2 + 2x + 3 and y = x2 – 2x + 3 to solve the equation –x2 + 2x + 3 = x2 – 2x + 3. His graph is shown below.
mc011-1.jpg
What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?
The solution of the equation [tex]-x^2+2x+3=x^2-2x+3[/tex] are the x-coordinates of common points on the graphs of the function [tex]y=-x^2+2x+3[/tex] and [tex]y=x^2-2x+3.[/tex]
As you can see from the attached diagram these graphs intersect at points (0,3) and (2,3), then the solutions of the previous equation are x=0 and x=2.
Answer: x=0, x=2.
You are thinking about building a home. You are told that for a particular area, the construction costs for the home should be about four times the cost of the land and the landscaping costs should be about one-third of the cost of the land. If your total budget is $250,000, calculate your budget for the land.
Using synthetic division, find (x4 − 2) ÷ (x + 1).
Answer:
Step-by-step explanation:
We have given:
x^4-2/x+1
Put x+1 = 0
x= 0-1
x= -1
-1 | 1 0 0 0 -2
| -1 1 -1 1
_______________
1 -1 1 -1 -1
Thus it makes the expression:
x^3-x^2+x-1 - 1/x+1
You can further confirm this expression by solving the expression:
(x4 − 2) ÷ (x + 1).
x^4 - 1 -1/x+1
x^4-1/x+1 - 1/x+1
(x^2-1) (x^2+1)/x+1 - 1/x+1
(x-1)(x+1) (x^2+1)/x+1 - 1/x+1
x+1 n the numerator will be cancelled out by x+1 in the denominator.
(x-1) (x^2+1) - 1/x+1
Multiply (x^2+1) by x-1
x(x^2+1) -1(x^2+1) - 1/x+1
x^3+x-x^2-1 - 1/x+1
x^3-x^2+x-1 - 1/x+1 ....
Two jets leave an airport at the same time, flying in opposite directions. The first jet is traveling at three hundred seventy-seven mph and the other at two hundred seventy-five mph. How long will it take for the jets to be 9128 miles apart?
Final answer:
To find the time it takes for two jets to be 9128 miles apart, calculate their combined speed and divide the total distance by this speed, resulting in approximately 14 hours.
Explanation:
To find the time taken for the jets to be 9128 miles apart:
Calculate the combined speed of the two jets by adding their speeds together: 377 mph + 275 mph = 652 mph.
Divide the total distance of 9128 miles by the combined speed of the jets to get the time taken: 9128 miles ÷ 652 mph ≈ 14 hours.
If 5/9 of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank ?
If 5/9 of a tank can be filled in 2 minutes, it would take 3.6 minutes to fill the whole tank by setting up a proportion and solving for the time.
Explanation:If 5/9 of a tank can be filled in 2 minutes, then to find the time it takes to fill the whole tank, we can set up a proportion. Since time is directly proportional to the amount of the tank filled, we have the following relationship:
Fraction of tank filled / Time to fill that fraction = 1 (whole tank) / x minutes
So, 5/9 of the tank is to 2 minutes as 1 whole tank is to x minutes:
(5/9) / 2 = 1 / x
Cross-multiplying gives us:
5x = 18
Dividing both sides by 5:
x = 18/5
x = 3.6 minutes
Therefore, it would take 3.6 minutes to fill the whole tank.
Final answer:
To find out how long it takes to fill the entire tank, set up the proportion of (5/9) of the tank in 2 minutes to (9/9) of the tank in x minutes, which gives x = 3.6 minutes for the whole tank to be filled.
Explanation:
If 5/9 of a tank can be filled in 2 minutes, we can set up a direct proportion to find out how long it would take to fill the entire tank. We are trying to find the time required to fill 9/9 (or the whole tank) if 5/9 takes 2 minutes. To solve this, we calculate:
Set up the proportion where the fraction of the tank filled is directly proportional to the time taken: (5/9) / 2 = (9/9) / x minutes.
Now we solve for x, which represents the total time to fill the tank: x = (2 minutes * 9/9) / (5/9).
Simplify the right side: x = 2 minutes * (9/5).
Calculate the value of x: x = 3.6 minutes.
Therefore, it will take 3.6 minutes to fill the entire tank.
What is an atom? GIVING BRAINLIEST 30 POINTS PLEASE HELP
Question 1 options:
an indivisible particle
one of the three particles that make up all matter
an element without an electrical charge
the basic particle that makes up matter
Question 2 (1 point) Question 2 Unsaved
What is a neutron?
Question 2 options:
a subatomic particle with no electric charge, found in the electron cloud
a subatomic particle with no electric charge, found in the nucleus of an atom
a subatomic particle with no electric charge, found in the neutron cloud
a subatomic particle with either a positive or negative electric charge, found in the nucleus of an atom
Question 3 (1 point) Question 3 Unsaved
What is a proton?
Question 3 options:
a subatomic particle with a -1 negative electric charge, found in the proton cloud
a subatomic particle with a +1 positive electric charge, found in the nucleus of an atom
a subatomic particle with a -1 negative electric charge, found in the nucleus of an atom
a subatomic particle with a +1 positive electric charge, found in the proton cloud
Question 4 (1 point) Question 4 Unsaved
What is an electron?
Question 4 options:
a subatomic particle with a +1 positive electric charge, found in the electron cloud
a subatomic particle with a -1 negative electric charge, found in the nucleus of the atom
a subatomic particle with a +1 positive electric charge, found anywhere in an atom
a subatomic particle with a -1 negative electric charge, found in the electron cloud
Question 5 (1 point) Question 5 Unsaved
What is an electron cloud?
Question 5 options:
the area surrounded by the nucleus of an atom, where electrons and neutrons can be found
the area that surrounds the nucleus of an atom, where electrons can be found
the area that surrounds the nucleus of an atom, where electrons and neutrons can be found
the area surrounded by the nucleus of an atom, where electrons can be found
Question 6 (1 point) Question 6 Unsaved
What is an ion?
Question 6 options:
an atom with either more or fewer electrons than protons, giving the atom either a positive or negative charge
an atom with either more or fewer neutrons than protons, giving the atom a different atomic mass
an atom with either more or fewer electrons than protons, giving the atom a significantly different atomic mass
an atom with either more or fewer neutrons than protons, giving the atom either a positive or negative charge
Question 7 (1 point) Question 7 Unsaved
What are isotopes?
Question 7 options:
atoms of the same element that have different atomic masses because they have different numbers of protons
atoms of the same element that have different atomic masses because they have different number of electrons
atoms of the same element that have different electric charges because they have different numbers of neutrons
atoms of the same element that have different atomic masses because they have different numbers of neutrons
Question 8 (1 point) Question 8 Unsaved
Which statement is FALSE?
Question 8 options:
An ion can be either positively or negatively charged
Isotopes are caused by different numbers of neutrons in the electron cloud
Question 9 (1 point) Question 9 Unsaved
Look at the timeline below. What is missing from the timeline?
Question 9 options:
1913 CE: Bohr proposed that electrons can change their orbit with a change of energy. He calls the orbits valence shells.
Question 10 (1 point) Question 10 Unsaved
What is the overall charge of an atom’s nucleus?
Question 10 options:
positive
neutral
negative
It depends on how many protons are in the nucleus.
It depends on how many neutrons are in the nucleus.
Question 11 (1 point) Question 11 Unsaved
Where is most of the mass in an atom?
Question 11 options:
electrons
nucleus
electron cloud
protons
neutrons
Answer:
1. Option 4
2. Option 2
3. Option 2
4. Option 4 (not completely sure)
5. Option 2
6. Option 1 (not completely sure)
7. Option 4
8. Isotopes are caused by different numbers of neutrons in the electron cloud
9. Not sure of the question
10. Positive charge
11. nucleus
Step-by-step explanation:
Give the guy above me brainliest.
Nancy has nine books and she has read 8 total books Sally has two times more books the Nancy how many books does Sally have
Sally has 18 books, as she has two times more books than Nancy, who has 9 books. The equation used is Sally's books = 2 × Nancy's books. Therefore, 2 × 9 = 18.
To determine how many books Sally has, we need to understand that she has two times more books than Nancy. Nancy has a total of 9 books.
The equation we use here is:
Sally's books = 2 × Nancy's booksGiven Nancy's books = 9:
Sally's books = 2 × 9 = 18Therefore, Sally has 18 books.
mark's soup recipe makes 6 servings and uses 4 carrots and 2 potatoes. Drag carrots and potatoes into the box to show how many Mark needs for 15 servings.
Answer:
10 carrots and 5 potatoes
Step-by-step explanation:
If 6 servings uses 4 carrots and 2 potatoes we can determine how many carrots and potatoes must be used per serving.
Lets look at the carrots:
[tex]=4/6=0.67[/tex]
Therefore for 15 servings:
[tex]=0.67×15=10.05≈10[/tex]
Lets look at potatoes:
[tex]=2/6=0.33[/tex]
Therefore for 15 servings:
[tex]=0.33×15=4.95≈[/tex]
Sandra used benchmark fractions to describe some insects she collected she said the ladybug is about 1/4 inch long and the cricket is about 2/3 inch long which insect is longer
The length of cricket is longer than ladybug.
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
We have to given that;
Sandra used benchmark fractions to describe some insects she collected she said the ladybug is about 1/4 inch long and the cricket is about 2/3 inch long.
Here, The length of ladybug = 1/4 inch
And, The length of cricket = 2/3 inch
Now, By comparing we get;
⇒ 1/4 and 2/3
⇒ 3/12 and 8/12
⇒ 3/12 < 8/12
Hence, The length of cricket is longer than ladybug.
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Find the midpoint of side EF. Figure EFGH is shown. E is at negative 2, 3. F is at 1, 6. G is at 4, 3. H is at 1, 0. (−1, 4) (−0.75, 4.25) (−0.5, 4.5) (−0.25, 4.75)
Hence, the mid-point of side EF is located at:
(-0.5,4.5)
Step-by-step explanation:We know that the coordinates of a mid-point C(e,f) of a line segment AB with vertices A(a,b) and B(c,d) is given by:
[tex]e=\dfrac{a+c}{2},\ f=\dfrac{b+d}{2}[/tex]
Here we have to find the mid-point of side EF.
E(-2,3) i.e. (a,b)=(2,3)
and F(1,6) i.e. (c,d)=(1,6)
Hence, the coordinate of midpoint of EF is:
[tex]e=\dfrac{-2+1}{2}\ ,\ f=\dfrac{3+6}{2}\\\\\\e=\dfrac{-1}{2}\ ,\ f=\dfrac{9}{2}\\\\\\e=-0.5\ ,\ f=4.5[/tex]
Hence, the mid-point of side EF is:
(-0.5,4.5)
Find all the zeros of the equation.
-3x^4+27x^2+1200=0
I don't really understand this. Please show me the steps! Thanks!
Final answer:
The zeros of the equation -3x^4+27x^2+1200=0 are x = 16 and x = -25.
Explanation:
To find the zeros of the equation -3x^4+27x^2+1200=0, we can use the quadratic formula. Let's set our equation equal to zero:
-3x^4+27x^2+1200=0
Now, we can use the quadratic formula, which states that for an equation in the form ax^2+bx+c=0, the solutions are given by:
x = (-b ± sqrt(b^2-4ac))/(2a)
Applying this formula to our equation, we get:
x = (-27 ± sqrt(27^2-4(-3)(1200)))/(2(-3))
Simplifying further, we have:
x = (-27 ± sqrt(729+14400))/(-6)
x = (-27 ± sqrt(15129))/(-6)
x = (-27 ± 123)/(-6)
So the two solutions are:
x = (-27 + 123)/(-6) = 16
x = (-27 - 123)/(-6) = -25
paul graphed the equation y=x which point does the graph not pass? 0,0 5,5 10,15