Is 81 in the sequence with the nth term 4n+1?
Explain
The independent variable of a function belongs to the domain or range?
Use rounding or compatible numbers to estimate each product or quotient.
5x2 3/5
about 10
about 10 3/5
about 12
about 15
2. use rounding or compatible numbers to estimate each product or quotient
25 7/8 divided by 2 8/9
about 9
about 10
about 11
about 12
3. Mr. Garcia's class at 3 2/3 pizzas, Mrs Rizzoli's class ate 4 1/8 pizzas, and Mrs. Tindal's class ate 3 1/4 pizzas. Use benchmarks to estimate the total number of pizzas eaten by all three classes.
about 9
about 10
about 11
about 12
To estimate the product or quotient, round numbers to the nearest whole or compatible number: 5 multiplied by 2 3/5 is about 15; 25 7/8 divided by 2 8/9 is about 9; and the total pizzas eaten by all classes is about 11.
Estimation with Rounding and Compatible Numbers
The estimation of products or quotients using rounding or compatible numbers involves adjusting values to simpler, more manageable numbers before performing the calculation. Here's how to estimate each of the provided examples:
For estimating the product of 5 by 2 3/5, you can round 2 3/5 to 3, which is a compatible number since 5 times 3 equals 15. Hence, the estimated product is about 15.To estimate the quotient of 25 7/8 divided by 2 8/9, round 25 7/8 to 26 (as 7/8 is close to a whole) and 2 8/9 to 3 (since 8/9 is close to 1), resulting in an estimated quotient of about 9 when you divide 26 by 3.For the total pizzas eaten by all three classes, use benchmarks: 3 2/3 rounds to 4, 4 1/8 rounds to 4, and 3 1/4 rounds to 3. Adding these gives 4+4+3 which equals 11. So, the total estimated number of pizzas is about 11.These estimations use the concept of rounding to the nearest whole number or to a fractions compatibility and demonstrate the importance of not over-representing the precision in your answer. Moreover, estimations are especially useful in mental math and when an approximate answer is sufficient.
Consider a civilization broadcasting a signal with a power of 2.0×104 watts. The Arecibo radio telescope, which is about 300 meters in diameter, could detect this signal if it is coming from as far away as 141 light-years. Suppose instead that the signal is being broadcast from the other side of the Milky Way Galaxy, about 70000 light-years away.
For light: Inverse Square Law
The signal is weaken by the inverse square of the
difference of distances this means that one over the square of the
difference.
Therefore, 70000LY / 141 LY =496.45 and that squared =246462.602 times less signal, or 1/246462.602.
2 For a circular telescope like the
Arecibo radio telescope that equals Pi times the radius squared. Sensitivity
of the telescope depends on its area.
The new telescope needs 246462.60 times that area to have
enough sensitivity
(150 x 150 x Pi) = 70 685 sq m area for the Arecibo telescope
and that times 246462.60
= 1.74212 x 10^10
What is the diameter of a circle with that area?
1. Divide the area by Pi = 5.548156 x 10^9
2. Take the square root of the result to find the radius = 74485.94293
3. Multiply by 2 to find the diameter = 148971.886
-7x= -56
Is the answer A or B
A city ordinance in River City requires that there be a police officer for every 470 residents. If the population of River city is 410,300, what is the minimum number of police officers needed?
To meet the city ordinance's requirement, River City needs at least 874 police officers, determined by dividing the population of 410,300 by 470 and rounding up to the nearest whole number.
To determine the minimum number of police officers needed for the population of River City, we simply divide the city's population by the number of residents per officer as required by the ordinance. In this case, we divide 410,300 residents by the ordinance's requirement of one officer for every 470 residents.
Calculation: 410,300 residents / 470 residents per officer = approximately 873.19.
Since we cannot have a fraction of a police officer, we round up the number to the nearest whole number to ensure that we meet the minimum requirement. Therefore, River City needs at least 874 police officers.
Write an equation that represents this comparison sentence 32 is 8 times as many as 4
Answer:
[tex]32=8\times 4[/tex]
Step-by-step explanation:
We have been given a word phrase. We are asked to write an equation for the given word phrase.
8 times 4 would be [tex]8\times 4[/tex].
We have been given that 32 is 8 times as many as 4. This means that 32 is equal to 8 times 4. We can represent this information in an equation as [tex]32=8\times 4[/tex]
Therefore, our required equation would be [tex]32=8\times 4[/tex].
All of the following expressions have the same value, when x = -2 and y = 4, except _____.
a. x 2y
b. (-2) 2y
c. -4 x 2
d. -2 xy
-2 *2(4) = -2 *8 = -16
(-2) *2(4) = -2 *8 = -16
-4(2)*2 = -8*2 = -16
-2*(-2*4) = -2 *-8 = 16
D is the only one that is positive so D is the answer
C. -4 x^2
next time add the ^ it doesnt copy the small numbers
Jake got the expression 7x plus 1 and then wrote his answer as 1 plus 7x. Is his answer an equivalent expression? How do you know?
4. This panel screen is an excellent example of how harmony is created in
artwork. What is the most obvious concept that has helped to create harmony
in this piece?
abstract shapes and themes
representation of historic scenes
realistic portraits
scenes of nature
Answer:
realistic portraits
Step-by-step explanation:
i did it
Which story represents the graph below?
A student slowly walks to a bus stop, waits, and then rides the bus.
A car accelerates, then maintains its speed before speeding up again.
both of the above
neither of the above
Your answer would be B: A car accelerates, then maintains its speed before speeding up again.
it will cost $73 per hour to rent a sailboat and 88 per hour to rent a ski boat. how much more will it cost to rent a ski boat than a sailboat for 4 hours
Find (7 × 106) − (4 × 104). A) 6.096 × 104 Eliminate B) 6.096 × 106 C) 6.96 × 104 D) 6.96 × 106
Item 2 Find the unit rate. 6 2/5 revolutions in 2 2/3 seconds The unit rate is revolutions per second.
a large aquarium has 6 more fish than a small aquarium. There are 19 fish in a large aquarium. How many fish are in a small aquarium
The number of fish in the small aquarium is 13 fish.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
The number of fish in the large aquarium = 19
A large aquarium has 6 more fish than a small aquarium.
The number of fish in the small aquarium is
⇒ [tex]19-6[/tex]
⇒ [tex]13[/tex]
Hence we can conclude that the number of fish in the small aquarium is 13 fish.
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Colin drove 45 minutes to the air port. He arrived 90 minutes before his flight departed and then he spent 70 minutes in the air. Once he landed Colin spent 20 minutes gathering his language and the. He drive 35 minutes to his hotel what must be true of any expression that represents the hotel time Collin spent traveling from his house to the hotel.
Given: The time taken to do each activity from Colin's house to his hotel in given.
he drove to the airport for 45 minuteshe waited at the airport for the flight to depart for 90 minuteshis fight duration was 70 minutesupon landing, he gathered his luggage for 20 minuteshe drove to the hotel for 35 minutesTo Find: what is true of any expression that represents the total time Collin spent traveling from his house to the hotel
Solution: Any expression will involve the sum of all the durations of his various activities i.e., 260 minutes or 4 hours and 20 minutes.
Explanation:
As each of the activities described is an independent activity that does not overlap, we can easily sum up the durations of each to find the total time Collin took from his house to the hotel.
We add it as follows :
he drove to the airport for 45 minutes + he waited at the airport for the flight to depart for 90 minutes + his fight duration was 70 minutes + upon landing, he gathered his luggage for 20 minutes + he drove to the hotel for 35 minutes.
So, 45+90+70+20+35 = 260 minutes
which means it took a total of 260 minutes or 4 hours and 20 minutes from Collin's house to his hotel.
Answer:
the answer is A
Step-by-step explanation:
I got a 90 and I got it right and so will u so trust me
Simplify.
9y+11z+7y−4z
What is the answer?
Please Troy to help me understand this example
Rachel bought 6 1/4 pounds of dried fruit. If 1/3 of the fruit was dried apricots, how many pounds of dried apricots did she buy?
Rachel bought 6 1/4 pounds of dried fruit. If 1/3 of the fruit was dried apricots, then the pounds of dried apricots which she bought was 25/12 or 2.08pounds.
What is Arithmetic operation?This basically comprises of operations such as Addition, Subtraction, Multiplication and Division.
Operations such as 'of ' are usually represented with the multiplication sign which is ( × ). In this scenario we were told that 1/3 of the 6 1/4 pounds of dried fruit was dried apricot.
This therefore means that 1/3 of 25/4 = 1/3 × 25/4 = 25/12.
This means that 25/12 or 2.08pounds was bought by her.
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how do you write 4.7 repeating as a fraction in simplest form
4.7 (repeating 7's) as a fraction would be 4 7/9
Hannah borrowed $2,000 from a bank. She agreed to pay back the bank $2,180 after 2 years. What was the simple interest rate of the loan? A. 9% B.4.5 % C.0.9% D. 5.45%
Graph y<1−3x .
A graph with y axis ranging from negative 4 to 2 and x axis ranging from negative 1 to 4. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point 3. The graph is shaded above the line.
Number graph with x axis ranging from negative one to five, and y axis ranging from negative four to two. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line.
Number graph with y axis ranging from negative 4 to 2, and x axis ranging from negative 2 to 6. A solid line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded above the line.
Number graph x axis ranging from negative one to five, and y axis ranging from negative four to two. A solid line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line.
The correct answer is B. Number graph with x axis ranging from negative one to five, and y axis ranging from negative four to two. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line. I took the test and this answer was correct, I'm 100% sure!
The correct option is (B) which represents the linear inequality y ≤ 1 - 3x as shown in the picture.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The inequality is:
y ≤ 1 - 3x
As we can see the above expression represents the linear inequality:
After plotting the linear inequality on the coordinate plane.
From the graph, a straight line is drawn and the shaded region represents the solution to the linear inequality.
Thus, the correct option (B) Number graph with an x-axis ranging from a negative one to five, and a y-axis ranging from negative four to two. A dotted line with arrows at both ends passes through the y-axis at one and the x-axis at point three. The graph is shaded below the line is correct.
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The largest number that rounds to 2,500 when rounded to the nearest ten?
Round 0.078 to the nearest thousandths
Rounding 0.078 to the nearest thousandths gives us 0.078.
We have,
To round 0.078 to the nearest thousandths, we look at the digit in the thousandth place, which is the third decimal place.
The digit in the thousandth place is 8.
Now,
We will look at the digit preceding the digit in the thousandth place.
We see that,
The digit is zero which is less than 5.
So,
0.078 rounding to the nearest thousandth is 0.078 itself.
Therefore,
Rounding 0.078 to the nearest thousandths gives us 0.078.
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find the coordinates of the missing endpoint if E is the midpoint of df. f=(5,8) E=(4,3)
Coordinates of the midpoint [tex](h,k)[/tex] of a segment with endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
[tex]h=\frac{x_1+x_2}{2}[/tex]
[tex]k=\frac{y_1+y_2}{2}[/tex]
If the coordinates of the endpoints D, F and midpoint E are [tex](x_1,y_1)[/tex], [tex](5,8)[/tex] and [tex](4,3)[/tex] respectively,
Coordinates of the endpoint D,
[tex]4=\frac{x_1+5}{2}[/tex]
[tex]x_1+5=8[/tex]
[tex]x_1=3[/tex]
[tex]3=\frac{8+y_1}{2}[/tex]
[tex]y_1+8=6[/tex]
[tex]y_1=-2[/tex]
Therefore, coordinates of the endpoint D are [tex](3,-2)[/tex].
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We have that the coordinates of the missing endpoint is
d=(13,14)
From the question we are told that
The coordinates of the missing endpointE is the midpoint of df. f=(5,8) E=(4,3)Generally the equation for the df is mathematically given as
For X
[tex]\frac{(x_1-x-2)}{2}= x_m\\\\\frac{(x_1-5)}{2}= 4[/tex]
x_1-5=8
x_1=13
For Y
[tex]\frac{(y_1-y-2)}{2}= y_m\\\\\frac{(y_1-8)}{2}= 3[/tex]
y_1-8=6
y_1=14
Therefore the coordinates of the missing endpoint
d=(13,14)
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The ice-cream truck had 112 ice-cream bars when it went out on its afternoon route. The driver sold 76 ice cream bars at the first stop. At the next stop, the Smith family and the Allen family bought the remaining ice-cream bars, divided equally between the two families. Each ice-cream bar cost $1.50.
How much did the Smith family pay for their ice-cream bars?
The correct answer is $27.00
Ten students went to a pizza parlor together. They ordered 8 small pizzas. How much pizza will each student get if they share the pizzas equally? Express your answer as a fraction and a decimal.
What is the product of any integer and –1?
A.The product is the opposite of the integer.
B.The product is the integer unchanged.
C.The product is positive.
D.The product is negative.
Solve this problem in your notebook using all four steps. Harvey is 3 times as old as Jane. The sum of their ages is 48 years. Find the age of each. Jane is _____ a0 years old. Harvey is ____ a1 years old.
Answer:
Jane is 12 and Harvey is 36
Step-by-step explanation:
Answer: The jane is 12 years old and Harvey is 36 years old.
Explanation:
Let jane's age is defined by J and Harvey's age is defined by H.
It is given that the Harvey is 3 times as old as Jane. It means the age of Harvey is 3 times of the age of jane.
H = 3J ..... (1)
It also given that the sum their ages is 48.
H + J = 48 ..... (2)
Using equation (1), Put H = 3J,
3J + J =48
4J = 48
J = 12
Substitute this value is equation (1).
H = 3(12)
H = 36
Therefore, the Jane's age is 12 and the Harvey's age is 36.
need help finding D=___