Johnny currently owns fewer than 200 records.
Let's denote:
- \( x \) as the number of records Johnny currently owns.
Given:
- Gina has 400 records.
- Johnny would still have fewer than Gina has if he were to double the number of records he owns.
We can set up the following inequality:
[tex]\[ 2x < 400 \][/tex]
To find the maximum value of \( x \), we solve for it:
[tex]\[ x < \frac{400}{2} \]\[ x < 200 \][/tex]
So, Johnny currently owns fewer than 200 records.
My sister’s birthday is in a few weeks and I would like to buy her a new vase to keep fresh flowers in her house. She often forgets to water her flowers and needs a vase that holds a lot of water. In a catalog, there are three vases available and I want to purchase the one that holds the most water. The first vase is a cylinder with diameter 10 cm and height 40 cm. The second vase is a cone with base diameter 16 cm and height 45 cm. The third vase is a sphere with a diameter of 18 cm.
1. Find the volume for each vase.
2. Which vase should I purchase?
3. How much more water does the largest vase hold than the smallest vase?
4. Suppose the diameter of each vase decreases by 2 cm. Which vase would hold the most water?
Answer:
1. 392, 20.83, 4/3
2. 16 cm and 45 cm cone
3. 0.9 Fl oz
4. the cone still
Step-by-step explanation:
The volume of each vase can be determine by using volume formula of sphere, cone and cylinder.
(1) The volume of sphere is [tex]972\pi[/tex], volume of cone is [tex]960\pi[/tex] and volume of cylinder is [tex]1000\pi[/tex].
(2) You should purchase the cylinder vase.
(3) The largest vase hold [tex]40 \pi \:{\rm cm}^3[/tex] more than smallest vase.
(4) If the diameter decreases by 2 cm, then cone holds more water.
Given:
Diameter of cylinder is [tex]d=10 \:\rm cm[/tex].
Height of cylinder is [tex]h=40\:\rm cm[/tex].
Diameter of cone is [tex]d=16 \:\rm cm[/tex].
Height of cylinder is [tex]h=45\:\rm cm[/tex].
Diameter of sphere is [tex]d=45 \:\rm cm[/tex].
(1)
Calculate the volume of cylinder.
[tex]\begin{aligned}\mbox{Cylinder Volume} &= \pi r^2 h\\& = \pi(5)^2(40) \text{ cm}^3\\&= 1000 \pi \text{ cm}^3.\end{align}[/tex]
Calculate the volume of Cone.
[tex]\begin{aligned}\mbox{Cone Volume} &= \frac13 \pi r^2 h\\&= \frac13 \pi(8)^2(45) \text{ cm}^3\\&= 960 \pi \text{ cm}^3.\end{align}[/tex]
Calculate the volume of sphere.
[tex]\begin{aligned}\mbox{Sphere Volume} &= \frac43 \pi r^3\\&= \frac43 \pi (9)^3 \text{ cm}^3\\&= 972 \pi \text{ cm}^3.\end{align}[/tex]
(2)
Since the volume of cylinder is higher than the volume of sphere and cone. So, you should purchase cylinder vase.
(3)
The largest vase hold water more than the smallest vase is,
[tex]\text{Cylinder Volume} - \text{Cone Volume} = 1000 \pi \text{ cm}^3 - 960 \pi \text{ cm}^3 = 40 \pi \text{ cm}^3[/tex]
(4)
As per the question if diameter of each vase decreases by 2 cm then radius decreases by 1 cm.
Calculate the volume of cylinder.
[tex]\begin{aligned}\mbox{Cylinder Volume} &= \pi r^2 h\\&= \pi(4)^2(40) \text{ cm}^3\\&= 640 \pi \text{ cm}^3.\end{align}[/tex]
Calculate the volume of Cone.
[tex]\begin{aligned}\mbox{Cone Volume}&= \frac13 \pi r^2 h\\&= \frac13 \pi(7)^2(45) \text{ cm}^3\\&= 735 \pi \text{ cm}^3.\end{align}[/tex]
Calculate the volume of sphere.
[tex]\begin{aligned}\mbox{Sphere volume} &= \frac43 \pi r^3\\&= \frac43 \pi (8)^3 \text{ cm}^3\\&= 682 \frac23 \pi \text{ cm}^3.\end{align}[/tex]
Since the volume of cone is more the sphere and cylinder. So cone hold most water.
Learn more about volume here:
https://brainly.com/question/8667621
Anyone good with Box Plots? Please help! 15 pt!!!
And Brainiest Answer!!
Find the spread for both by subtracting the hlowest number from the highest number:
Basketball: 85-67 = 18
Baseball: 76 - 64 = 12
Now subtract the two to find their difference:
18-12 = 6
The answer would be C. The spread of data for basketball players is 6 inches greater than baseball players.
Answer:
a
Step-by-step explanation:
(w-w^2)^4=?
.......................
Answer:
w^8 - 4w^7 + 6w^6 - 4w^5 + w^4 .
Step-by-step explanation:
(w - w^2)^4
= w^4 ( 1 - w)^4
By the binomial theorem:
= w^4( 1 - 4w + 6w^2 - 4w^3 + w^4)
= w^4 - 4w^5 + 6w^6 - 4w^7 + w^8
= w^8 - 4w^7 + 6w^6 - 4w^5 + w^4 ( Standard form).
Bacteria X has a growth rate of 180 % per hour. Some amount of bacteria X are accidentally introduced into some egg salad. Three hours after contamination, there were 35,000 bacteria X in the egg salad.
Find the initial number of bacteria X introduced into the egg salad?
Estimate the number of bacteria in the food 4 hours after contamination?
There were about 6001 bacteria X bring introduced into the egg salad. The number of bacteria in the food 4 hours after contamination is 63000.
To find the initial number of bacteria X introduced into the egg salad, divide the final number by (1 + growth rate)^time. For estimating the number of bacteria in the food 4 hours after contamination, multiply the initial number by (1 + growth rate)^time.
Explanation:To find the initial number of bacteria X introduced into the egg salad, we can use the formula:
Initial Number = Final Number / (1 + Growth Rate)^Time
Plugging in the given values, we have:
Initial Number = 35,000 / (1 + 180%)^3 = 35,000 / (1 + 1.8)^3 = 35,000 / 3.027 = 11,542.52
To estimate the number of bacteria in the food 4 hours after contamination, we can use the same formula:
Number after 4 hours = Initial Number * (1 + Growth Rate)^Time
Plugging in the values, we have:
Number after 4 hours = 11,542.52 * (1 + 180%)^4 = 11,542.52 * (1 + 1.8)^4 = 11,542.52 * 10.4044 = 120,108.83
Learn more about Bacteria growth here:https://brainly.com/question/34853242
#SPJ11
How do I find the Axis of Symmetry for a parabola
Answer:
Explanation given below.
Step-by-step explanation:
The first step is to put the parabola in the form [tex]ax^2+bx+c[/tex] , which is the standard form of a parabola
Note: a is the coefficient before x^2 term, b is the coefficient before x term, and c is the independent constant term
The axis of symmetry divides the parabola symmetrically. The axis of symmetry has the equation [tex]x=-\frac{b}{2a}[/tex]
Where a and b are the respective values shown above
So, that is how you get the axis of symmetry of any parabola.
Answer:
The equation of the axis of symmetry of the parabola is x = h,
where h is the x-coordinate of the vertex point
Step-by-step explanation:
* The axis of symmetry is the line which divides the
shape into two congruent parts
* The general form of the quadratic equation is:
ax² + bx + c = 0
* The quadratic equation is represented graphically by parabola
∵ The parabola has minimum point or maximum point
∴ The axis of symmetry of the parabola is passing through this point
This point is called the vertex point or the turning point
- Lets find this point:
* the x-coordinate of this point calculated from the equation
x- coordinate of the vertex point h = -b/2a
- where b is the coefficient of x and a is the coefficient of x²
∴ The equation of the axis of symmetry of the parabola is x = -b/2a
EX:
- If ⇒ x² - 4x + 4 = 0
∵ a = 1 , b = -4
∴ h = -(-4)/2(1) = 2
∴ The equation of the axis of symmetry of the parabola is x = 2
The graph show you the axis of symmetry
How do you Determine the median of a data set
Answer: The meadian of a data set is the number in between all of the numbers.
Step-by-step explanation: For example, you havent put any numbers so ill just use 1-10. so you first list all the numbers in order, grom smallest to biggest. then find the muddle number
Final answer:
To determine the median of a data set, arrange the data in ascending order and find the middle value for an odd number of data, or the average of the two middle numbers for an even number of data. The median is resistant to outliers and splits the data set into two equal halves.
Explanation:
To determine the median of a data set, you need to arrange the data in ascending order first. If the number of data values is odd, the median is the middle value. For example, in a set of 11 data values, the 6th number would be the median. If the number of data values is even, the median is the average of the two middle values. For instance, if a data set has 14 values, you would take the average of the 7th and 8th values after arranging the data.
To find the median in a data set with even number of values, such as 14, add the two middle values, 6.8 and 7.2, together and then divide by two, yielding a median of 7.0. It's important to note that the median separates the data into two equal halves, where half the values are same or smaller than the median, and the other half are same or larger.
When a data set contains extreme values or outliers, the median can be particularly useful as it is not influenced by these extreme values, unlike the mean.
If the two triangles shown are congruent, what is true of the two triangles?
they’re the same shape and size
Answer:
They are going to have a congruent match of sides and angles
Step-by-step explanation:
This is because congruent parts of congruent triangles are congruent.
Please mark Brainliest
a triangle has an area of 32 square feet centimeters and a base of 8 centimeters. what is the width of the rectangle
Area = Base x Width ÷ 2
Area = 32cm^2
Base = 8cm
32 ÷ 8 = 4
4 × 2 = 8
Answer = 8
To check our answer:
8 x 8 = 64
64 ÷ 2 = 32
:)
To find the height of a triangle with an area of 32 square centimeters and a base of 8 centimeters, we use the formula A = 1/2 × base × height. The height is calculated to be 8 centimeters.
The student has asked about finding the width of a triangle, given its area in square centimeters and the length of its base. There seems to be a confusion with the terminology; the width of a rectangle is being referred to instead of the triangle's height. However, to provide assistance with the appropriate concept, we will focus on finding the height of a triangle.
The area of a triangle is calculated by the formula A = 1/2 ×base× height. When we know the area and the base length, we can rearrange the formula to solve for the height. For a triangle with a base of 8 centimeters and an area of 32 square centimeters, the calculation would be as follows:
Area = 1/2 × base × height
32 = 1/2 × 8 × height
32 = 4 × height
height = 32 / 4
height = 8 centimeters
Therefore, the height of the triangle would be 8 centimeters.
How many times larger than 0.005 is 0.625
Answer:
Step-by-step explanation:
0.005 * x = 0.625 Divide both sides by 0.005
0.005x/0.005 = 0.625/0.005 Do the division
x = 125
So what that means is 0.625 is 125 times larger than 0.005
What is the following sum? 4(5√x^2 y) +3(5√x^2 y) help meeee
4(5√x^2y)+3(5√x^2y)=7(5√x^2y)
Find the distance d. (2,4) and (7,2)
Answer:
[tex]\large\boxed{d=\sqrt{29}}[/tex]
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (2, 4) and (7, 2). substitute:
[tex]d=\sqrt{(7-2)^2+(2-4)^2}=\sqrt{5^2+(-2)^2}=\sqrt{25+4}=\sqrt{29}[/tex]
A fair six-sided die is rolled 54 times. Theoretically, about how many times should a roll of "4" occur?
-9
-4
-14
-no way to tell
➷ First calculate the probability of getting it for each roll
As there is only one '4', the probability would be 1/6
Multiply this by the number of rolls:
1/6 x 54 = 9
The correct option would be 9.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
9
Step-By-Step-Solution
Which system will have an infinite number of solutions?
A.
–4y = –6x + 8
B.
–4x + 5y = 8
5y = –4x + 6
C.
–2x + 4y = 3
D.
2x – 6y = 9
5y = –4x + 6
Answer:
do you still need an answer
can u guys please help?
Answer:
9.42 square meters i think
Step-by-step explanation:
Answer:
the answer is 28.26
9. What’s the answer to this question?
The right option is (D) 5
Step-by-step explanation:−2x²+wx−4−(x²+5x+6)=−3x²−10
Step 1:Add 3x^2 to both sides.
wx−3x²−5x−10+3x²=−3x²−10+3x²
wx−5x−10=−10
Step 2:Add 5x to both sides.
wx−5x−10+5x=−10+5x
wx−10=5x−10
Step 3:Add 10 to both sides.
wx−10+10=5x−10+10
wx=5x
Step 4:Divide both sides by x.
wx /x = 5x/x
w=5
David and Karen have a goal to read 10,000 pages together by the end of summer.
David reads 80 pages every day.
Karen reads 25% more pages every day than David reads.
David and Karen agree that the model 180d = 10,000 will tell them how many days it will take them to read 10,000 pages, together, by the end of summer.
They invite Rick to read with them to get to their goal faster. Rick reads 35% fewer pages per day than Karen.
Which equation can be used to find how many days it will take David, Karen, and Rick to read 10,000 pages, together, by the end of summer?
David reads 80 pages every day.
Karen reads 25% more pages every day than David reads.
So, Karen reads [tex]\frac{25}{100}*80= 20[/tex] more pages. She reads a total of 80 + 20 =100 pages.
Rick reads 35% fewer pages per day than Karen. So, Rick reads [tex]\frac{35}{100}*100=35[/tex] less pages than Karen. He reads 100 - 35 =65 pages
So, in total the tree friends read = 80+100+65=245 pages.
So, equation becomes [tex]245d=10000[/tex]
Which equation graph passes through the points (5,6) and (0,3)
Answer:
A. y = 3/5 x + 3
Step-by-step explanation:
(5, 6) and (0,3)
slope = (6 - 3)/(5-0) = 3/5
and y-intercept b = 3
Equation
y = 3/5 x + 3
Answer:
A. y = 3/5 x + 3
4+(-4)=0 what property is this?
Answer:
Zero property
Step-by-step explanation:
We are making a equation equal 0
which label could replace A in the diagram below.
The only label that could replace "A" in the diagram is Rational Numbers only.
The correct answer is A. Rational Numbers only.
Here's a breakdown of the diagram and the reasoning behind the answer:
Real Numbers: This is the largest set of numbers, encompassing all possible numbers, including positive, negative, whole, decimal, rational, and irrational numbers.Whole Numbers: These are the counting numbers (1, 2, 3, ...) and zero. They are a subset of the real numbers.Rational Numbers: These are numbers that can be expressed as a fraction of two integers (e.g., 1/2, 3/4, -5/6). They include all whole numbers, as well as fractions and terminating or repeating decimals.Integers: These are whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3, ...). They are a subset of both rational numbers and whole numbers.Irrational Numbers: These are numbers that cannot be expressed as a fraction of two integers. They include numbers like pi (π), the square root of 2 (√2), and many other non-repeating, non-terminating decimals.The diagram shows that "A" is a subset of real numbers but not a subset of whole numbers.
This means that "A" must include some numbers that are not whole numbers.
Of the given options, only rational numbers fit this description. Integers are a subset of whole numbers, and irrational numbers are not a subset of real numbers.
Complete Question:
Which label or labels could replace "A" in the diagram below?
A. Rational Numbers only
B. Rational Numbers or Integers
C. Integers only
D. Irrational Numbers
Suppose you had d dollars in your checking account. You spent $20 but have at least $55 left. How much money did you have initially? Write, solve, and graph an inequality that represents this situation.
Answer:
Step-by-step explanation:
55-20 is less than or equal to (d)
i think...
Answer:
The solution would be d ≥ 75
Step-by-step explanation:
To find this we know that we have at least 55, which can be modeled as:
d ≥ 55
And then we need to add 20
d ≥ 55 + 20
d ≥ 75
1. Casey set a personal goal to drink at least 84 fluid ounces of water each day this week. Given that 1 cup is equivalent to 8 fluid ounces, how many cups of water is Casey hoping to drink each day?
2. On a coordinate plane, the public swimming pool can be represented by the point (-6,5) and Tim's house can be represented by the point (1,5). If each unit on the graph represents 0.5 miles, how many miles is Tim's house from the pool?
3. Dr. Woods saw 22 patients in the last month who tested positive for the flu. If this number represents 40% of the patients that she saw, how many total patients did Dr. Woods see in the last month?
Plz help me out fams
Answer: for #1. 10.5 cups of water. For #3. 55 people
Step-by-step explanation:
You must take the total amount of fluid ounces and divide it by how many ounces in a cup, which is 8.
You must divide the amount of people that tested positive by the percentage (as a decimal) of people tested. In this case, it would be 22 divided by 0.4.
Greta is making a patio
Answer:
Step-by-step explanation:
Can you give more information?
Write the first three multiples of each number 6,11 and 14 please comment
A multiple of a number is a number multiplied by another number.
Considering this definition, the first three multiples of 6 are 6, 12, and 18 because it is six multiplied by 1, 2, and 3.
Similarly, the multiples of 11 are 11, 21, and 33 and the multiples of 14 are 14, 28, and 42.
The first three multiples of 6 are 6, 12, and 18, the first three multiples of 11 are 11, 22, and 33, and the first three multiples of 14 are 14, 28, and 42.
Explanation:The first three multiples of a number are obtained by multiplying that number by 1, 2, and 3, respectively. For the given numbers:
The first three multiples of 6 are: 6, 12, and 18.The first three multiples of 11 are: 11, 22,33.The first three multiples of 14 are: 14, 28, 42.
These calculations are made by simply multiplying the original number by 1, then 2, then 3. It's foundational multiplication, a key concept in Mathematics.
Learn more about Multiples here:https://brainly.com/question/24327271
#SPJ2
Shannon's hair is 121 /2 inches long. She wants to shorten it by 3 1/2 inches. How long will her hair be after she has it cut?
Answer:
57 inches
Step-by-step explanation:
divide 121/2 = 60.5 .. make the 3 1/2 inches into a decimal: 3.5 and then subtract 60.5 - 3.5 = 57 inches.. hope this helps
Her hair would be 57 inches after the haircut.
Hope this helps!
ari made a fruit salad with 1/2 cup of blueberries, 3/8 cup strawberries, and 3/4 cup raspberries. how many total cups of fruit salad did ari make?
Ari made 1 and 5/8 total cups of fruit salad
If the greatest value of n is 9, which inequality best shows all the possible values of n? (5 points)
n > 9
n < 9
n ≥ 9
n ≤ 9
The answer to this is the last one as it shows that not is not larger than 9 but it can equal to it. This makes the original statement true
Answer: The correct option is
(D) [tex]n\leq 9.[/tex]
Step-by-step explanation: We are given that the greatest value of n is 9.
We are to select the inequality that best shows all the possible values of n.
Since the greatest value of n is 9, it means that the value of n is less than or equal to 9.
But the values of n cannot be greater than 9.
So, we will be using the sign of less than or equal to in the inequality.
Therefore, the required inequality that best shows all the possible values of n is given by
[tex]n\leq 9.[/tex]
Thus, (D) is the correct option.
Can somebody please help with this (Will mark Brainliest) 30 Points!
Algebra 1
Answer:
H
Step-by-step explanation:
Let a represent Ann's height, and let j represent Jay's height
Break up the sentence into the key parts.
"The difference between Ann's and Jay's heights" "is" "half of Jay's height"
"The difference between Ann's and Jay's heights" becomes the expression:
a - j
"is" is math means an equal sign '='
"half of Jay's height" becomes the expression: (1/2)j
Put the 3 parts together and get the equation:
a - j = (1/2)j,
Since all the equations in the answer choices are in terms of a, solve the above equation for a...
a = (1/2)j + j, which is answer H
An old house has a basement stairway that has steps with 7.25 inch vertical risers and 10 inch horizontal treads. What is the slope of the stairway? Round to two decimal places.
Answer:
Final answer is slope = 0.73
Step-by-step explanation:
Given that an old house has a basement stairway.
Stairway has steps with 7.25 inch vertical risers and 10 inch horizontal treads. Now we need to find about what is the slope of the stairway. Also round the answer to two decimal places.
[tex]slope=\frac{rise}{run}=\frac{7.25}{10}=0.725[/tex]
Now round that value to two decimal places gives 0.73
Hence final answer is slope = 0.73
Item 1 A bag contains 7 blue cards, 4 green cards, 6 red cards, and 8 yellow cards. You randomly choose a card. a. How many possible outcomes are there?
Answer:
4 possible outcomes
Step-by-step explanation:
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
Let
x------> size of the event space
y-----> size of the sample space
so
[tex]P=\frac{x}{y}[/tex]
In this problem
The probability of choose a blue card is
[tex]x=7[/tex]
[tex]y=7+4+6+8=25[/tex]
substitute
[tex]P=\frac{7}{25}[/tex]
The probability of choose a green card is
[tex]x=4[/tex]
[tex]y=7+4+6+8=25[/tex]
substitute
[tex]P=\frac{4}{25}[/tex]
The probability of choose a red card is
[tex]x=6[/tex]
[tex]y=7+4+6+8=25[/tex]
substitute
[tex]P=\frac{6}{25}[/tex]
The probability of choose a yellow card is
[tex]x=8[/tex]
[tex]y=7+4+6+8=25[/tex]
substitute
[tex]P=\frac{8}{25}[/tex]
The sum of the probabilities of the 4 possible outcomes is equal to
[tex]\frac{7}{25}+\frac{4}{25}+\frac{6}{25}+\frac{8}{25}=\frac{25}{25}[/tex] ----> represent the 100%
0.5 as hundredths in fraction form and decimal form
Answer:
5/100, .05
Step-by-step explanation:
The decimal form remains 0.5, but when expressed with a denominator of 100, it becomes 50.0%.
To express 0.5 as hundredths in fraction form, you convert the decimal to a fraction with a denominator of 100. Since 0.5 is equivalent to 50%, you would write this as 50/100. This fraction can also be simplified to 1/2 by dividing both the numerator and the denominator by 50.
In decimal form, 0.5 is already represented as a decimal and does not require conversion. However, if we are to express it with a denominator of 100, we simply move the decimal point two places to the right (multiplying by 100), yielding 50.00, which can then be represented as 50.0% when expressing as a percent.