To find the sum of 5 consecutive integers, use the formula (n + n+1 + n+2 + n+3 + n+4), where n is the first integer. The consecutive integers are 99, 100, 101, 102, and 103.
Explanation:To find the sum of 5 consecutive integers, we can use the formula (n + n+1 + n+2 + n+3 + n+4), where n is the first integer. In this case, the sum is 505, so we have the equation: n + (n+1) + (n+2) + (n+3) + (n+4) = 505. Simplifying this, we get: 5n + 10 = 505. Subtracting 10 from both sides gives 5n = 495. Dividing both sides by 5, we find that n = 99.
Therefore, the 5 consecutive integers are 99, 100, 101, 102, and 103.
The expression 9x^2 -5x -7 has ___ terms and a constant of ___.
A. 3, -7
B. 5, -7
C. 3, 7
D. -5, 7
Between what 2 integers does √89 fall?
Question 5 options:
9 and 10
10 and 11
11 and 12
12 and 13
Two scientists are measuring lava temperatures. One scientist records temperature of 1725 degrees Fahrenheit. The other scientist records a temperature of 950 degrees Celsius. Which is the greatest temperature? (Use C= 5/9(F - 32)
Final answer:
To compare temperatures, convert them to the same unit. In this case, 1725°F is the greatest temperature between 1725°F and 1742°F.
Explanation:
Converting temperatures: To compare temperatures, we must convert them to the same unit. The first scientist recorded 1725°F, and the second scientist recorded 950°C. Converting 950°C to Fahrenheit, we get 1742°F. Therefore, 1725°F is the greatest temperature.
denna is four more than three times older than ted. the sum of their ages is 60. how old is ted?
The pine tree in George's front yard is 8.83 meters tall. What is that number rounded to the nearest tenth?
Debra started a babysitting business. She purchased toys, snacks, and other supplies. She charged an hourly rate for each child. The expression −145+6y−145+6y represents the profit Debra has earned from her babysitting business. Which expression represents the total amount Debra earns from babysitting?
A) y
B) −145
C) 6y
D) 6
The ratio of clownfish to angelfish at a pet store is 5:4 the ratio of angelfish to goldfish is 4:3 there are 60 clownfish at the pet store .
The number of angelfish and goldfish are required.
The number of angelfish is 48 and goldfish is 36.
The ratio of clownfish to angelfish is
[tex]\dfrac{c}{a}=\dfrac{5}{4}[/tex]
Ratio of angelfish to goldfish is
[tex]\dfrac{a}{g}=\dfrac{4}{3}[/tex]
Number of clownfish is [tex]c=60[/tex]
From the given ratios
[tex]\dfrac{60}{a}=\dfrac{5}{4}\\\Rightarrow a=\dfrac{60\times 4}{5}\\\Rightarrow a=48[/tex]
[tex]\dfrac{48}{g}=\dfrac{4}{3}\\\Rightarrow g=\dfrac{48\times 3}{4}\\\Rightarrow g=36[/tex]
The number of angelfish is 48 and goldfish is 36.
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Two containers, A and b begin with equal volumes of liquid. 120 mL is then poured from a to B. Container b now contains four times as much liquid as A. Find the volume of liquid left in container a at the end
The volume of liquid left in container a at the end is 80 mL.
Let's denote the initial volume of each container as ( V ) mL. After pouring 120 mL from A to B, the volume of liquid in A decreases to ( V - 120 ) mL and the volume in B increases to ( V + 120 ) mL.
We're given that after this transfer, the volume in B is four times the volume in A:
[tex]\[ V + 120 = 4(V - 120) \][/tex]
Now, we solve for ( V ):
V + 120 = 4V - 480
120 + 480 = 4V - V
600 = 3V
V = [tex]\frac{600}{3}[/tex] = 200
So, the initial volume in each container was 200 mL. After pouring, A has ( 200 - 120 = 80 ) mL left.
The process of arriving at an approximate answer to a computation such as 0.79 times 403 is called
Select the expressions that are equivalent to 5(w+5)
Here are two shapes with the same area. Work out the perimiter of the rectangle.
8+3(16-12) I got 16 but I want to make sure I'm correct
What is 5 4/7 / -1/5
What is a high school Academic Decathlon?
The High School Academic Decathlon is a competition involving ten academic events where students compete individually and as a team in subjects like mathematics, science, and social science. The competition promotes teamwork, public speaking, and scholastic excellence. Teams are categorized based on GPA, and all participants take part in each event.
The High School Academic Decathlon is a rigorous academic competition where students compete in a series of ten events covering various subjects. These events include mathematics, science, economics, social science, literature, art, music, and speech. The competition is designed to encourage scholastic excellence, public speaking, and teamwork.
Teams are usually composed of nine students, divided into three categories based on their GPA: Honors, Scholastic, and Varsity. Each student participates in all ten areas of the competition, contributing to both individual and team scores.
Participating in the Academic Decathlon not only boosts students' academic achievements but also helps them develop important skills such as time management, critical thinking, and public speaking. For example, a student who is teased by her basketball team for her academic award is navigating the balance between athletic and academic achievements, showcasing the multifaceted nature of high school life.
what time will it be 20 minutes after 3:30p.m
What is 15/24 as a decimal?
sandra plans to excersise the same number of minutes m each of the remaning three days this week in order for sandra to excersise for exactly 150 minutes this week what is the
value of m
Mia's cat weighs 13 pounds ,7 ounces .about what is that weight in kilograms ?
Which is an equation in point-slope form of the line that passes through the points (4, 5) and (−3, −1) ?
a. y−1=6/7(x−3)
b. y+1=6/5(x+3)
c. y+3=7/6(x+1)
d. y+1=6/7(x+3)
what is the positive solution to the equation 0=1/3x^2-3
You can use the simplified equation to find the solution.
The positive solution of given equation is x = 3
What is a positive solution of given equation?
When we find the solution of the equation, we find the values of the variables for which the given equation is correct. Sometimes the values of the solutions comes out negative and sometimes positive and sometimes both or can be 0 too.
To find positive solutions, we only consider those solutions which are positive.
Simplification of the given equation[tex]0 = \dfrac{1}{3}x^2 - 3\\ \\ \text{Adding 3 on both sides}\\ \\ 3 = \dfrac{1}{3}x^2\\ \\ \text{Multiplying 3 on both sides}\\\\ 9 = x^2\\ \\\\ \text{taking square root}\\ 3 = \pm x\\ x = \mp 3 \\ (x = 3), (x = -3)[/tex]
Thus, x = 3, and x = -3 are the solutions to given equation.
The positive solution to the given equation is x = 3.
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List the hierarchy of organization in a snowy owl.
The hierarchy of biological organization in a snowy owl involves various nested levels from the most inclusive, the biosphere, to the least complex, atoms. Each level, from biomes to molecules, represents a stage of increasingly specific categorization.
Hierarchy of Biological Organization in a Snowy Owl
The hierarchy of biological organization describes the levels of biological world organization from the most inclusive to the least complex levels. When considering a snowy owl or any other organism, this involves the following hierarchy:
Biosphere - The global ecological system integrating all living beings and their relationships.
Biome - A large community of plants and animals that occupies a distinct region such as tundra where snowy owls may be found.
Ecosystem - The community of living organisms in conjunction with the nonliving components of their environment interacting as a system.
Community - An assembly of different species within a defined area.
Population - A group of individuals of the same species that live in the same area.
Organism - An individual living entity such as a single snowy owl.
Organ Systems - A group of organs that work together to accomplish specific functions.
Organs - Composed of tissues that perform a specific function or group of functions.
Tissues - An ensemble of similar cells from the same origin that carry out a specific function.
Cells - The smallest unit of life.
Organelles - A subunit within a cell that has a specialized function.
Molecules - A group of atoms bonded together, representing the smallest fundamental unit of a chemical compound that can take part in a chemical reaction.
Atoms - The smallest unit of a chemical element.
The snowy owl, as an organism, falls into this hierarchy at the organism level, but is also part of each of these nested levels up to the biosphere.
PLEASE HELP I WILL GIVE 99 POINTS
Aida applied the distributive property to write the equivalent expressions below.
15 + 21 = 3(4 + 8)
What is Aida’s error?
Aida used 3 as the factor, which is not common to 15 and 21.
Aida did not correctly divide by the common factor to get (4 + 8).
Aida did not apply the correct operations to the expressions.
Aida wrote two expressions that are not equivalent.
PLEASE HELP I WILL GIVE POINTS
Which correctly shows how to use the GCF and the distributive property to find an expression equivalent to 45 + 72?
3(15 + 24)
9(5 + 8)
(5)(9) + (2)(36)
(3)(15) + (8)(9)
Set up and solve a system of equations to solve the problem.
Casey wants to buy a gym membership. one gym has a $150 joining fee and costs $35 per month. Another gym has no joining fee and costs $60 per month. When would Casey pay the same amount to be a member of either gym? How much would he pay?
Answer:6 months 360
Ft: 150+35t=60 t
G(t): 60t
Step-by-step explanation:
Dana loves rocks! She has 6 pieces of granite, 3 pieces of marble, 14 pieces of sandstone, and 1 piece of slate. What is the ratio of pieces of sandstone to pieces of marble in Dana's collection?
The ratio of pieces of sandstone to pieces of marble in Dana's collection is 14 : 3.
What is the ratio?A ratio indicates how many times one number contains another. If a and b are to objects then ratio of a to the b is given as a : b.
Now the given number of stones in Dana's collection are,
granite- 6 pieces
marble- 3 pieces
sandstone- 14 pieces
slate- 1 piece
Now to find the ratio of pieces of sandstone to pieces of marble we have,
pieces of sandstone/pieces of marble = 14/3
⇒pieces of sandstone : pieces of marble = 14 : 3
Hence,The ratio of pieces of sandstone to pieces of marble in Dana's collection is 14 : 3.
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Dana's collection contains a 14:3 ratio of sandstone to marble fragments. So option (c) is correct.
To find the ratio of pieces of sandstone to pieces of marble in Dean's collection, we need to compare the number of sandstone pieces to the number of marble pieces.
Step 1: Count the pieces of sandstone and marble.
Sandstone: 14 pieces
Marble: 3 pieces
Step 2: Write down the ratio in the form of sandstone : marble".
Sandstone : Marble
Step 3: Substitute the counts into the ratio.
Sandstone: Marble = 14:3
Thus, the ratio of pieces of sandstone to pieces of marble in Dean's collection is 14:3.
Complete Question:
Dean loves rocks! He has 6 pieces of granite, 3 pieces of marble, 14 pieces of sandstone, and 1 piece of slate. What is the ratio of pieces of sandstone to pieces of marble in Dean's collection?
Choose 1 answer:
14:6
3:24
14:3
24:3
9,540,00 in expanded for in exponents
Evaluate the expression 3x + 4y/2 for x = 1.5 and y = 2.5 .
A. 2
B. 4.25
C. 6.25
D. 7.25
Using this how do you solve the equation: f(g(3))
i do not get number 8... can someone help me?
wade purchased 3 videos and one music CD, the CD cost wade $12.99 if he paid the same amount of each video and spent a total of $42.96,how much did each video cost?
Final answer:
To find the cost of each video, subtract the cost of the CD from the total amount spent, and then divide by the number of videos. Each video cost Wade $9.99.
Explanation:
The student's question involves a basic algebra problem where Wade purchased 3 videos and one music CD. The cost of the music CD was $12.99, and the total spent was $42.96. We need to determine how much each video cost.
Firstly, subtract the cost of the music CD from the total spent to find the total cost of the videos:
$42.96 - $12.99 = $29.97.
This means the total cost for the 3 videos is $29.97. Since Wade paid the same amount for each video, we divide the total cost of the videos by the number of videos:
$29.97 ÷ 3 videos = $9.99 per video.
Therefore, each video cost Wade $9.99.