A pattern has 12 red squares to every 84 blue circles
The ratio is shown below;
[tex]\begin{gathered} \text{Ratio}=\frac{12}{84} \\ \text{Divide all through and reduce to the simplest form and you now have;} \\ \text{Ratio}=\frac{1}{7} \end{gathered}[/tex]Solve the following inequality for n. Write your answer in the simplest form.9n + 4 ≤ 6n - 6
Given,
The expression is,
[tex]9n+4\le6n-6[/tex]Substracting 4 from both sides then,
[tex]\begin{gathered} 9n+4-4\le6n-6-4 \\ 9n\le6n-10 \end{gathered}[/tex]Substracting 6n from both sides then,
[tex]\begin{gathered} 9n\le6n-10 \\ 9n-6n\le6n-6n-10 \\ 3n\le-10 \end{gathered}[/tex]Multiplying both sides by 1/3 then,
[tex]\begin{gathered} 3n\le-10 \\ 3n\times\frac{1}{3}\le-10\times\frac{1}{3} \\ n\le-\frac{10}{3} \end{gathered}[/tex]Hence, the solution for n is n<= (-10/3).
An ice cream store has the pricing shown below. You want to determine the best value. The height of the cone is 4.5 in and the diameter is 2 in. The diameter of each scoop is 3 in. Assume the cone is stuffed full with ice cream.Question: Which size is the best value? Explain your reasoning using complete sentences.
Solution:
Step 1:
We will calculate the volume of ice cream in the single scoop
The volume of the ice cream will be
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3 \\ r=\frac{2in}{2}=1in(cone) \\ h=4.5in \\ r=\frac{3in}{2}=1.5in(radius\text{ of the hemisphere\rparen} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} V=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^{3} \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+\frac{2}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{14} \\ V=\frac{165}{14} \\ V=11.79in^3 \end{gathered}[/tex]Step 2:
We will use the formula below to calculate the volume of the two scoops of ic cream
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{4}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5in+\frac{4}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{7} \\ V=\frac{132}{7} \\ V=18.86in^3 \end{gathered}[/tex]Step 3:
We will use the formula below to calculate the volume of the three scoops of ic cream
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{6}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+2\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{297}{14} \\ V=\frac{363}{14} \\ V=25.93in^3 \end{gathered}[/tex]For the first ice cream with one scoop
[tex]\begin{gathered} 1in^3=\frac{3.50}{11.79} \\ 1in^3=\text{ \$}0.30 \end{gathered}[/tex]For the second ice cream with two scoops
[tex]\begin{gathered} 1in^3=\frac{4.50}{18.86} \\ 1in^3=\text{ \$}0.24 \end{gathered}[/tex]For the third ice cream with three scoops
[tex]\begin{gathered} 1in^3=\frac{5.50}{25.93} \\ 1in^3=\text{ \$}0.21 \end{gathered}[/tex]Hence,
The final answer is
The triple sold at $5.50 has the best value because it has the lowest price of $0.21 per cubic inch of the ice cream
This graph shows how fast the international space station travels in orbit around Earth What is the meaning of the point with an x-coordinate of 3?A. In 1 second, the space station travels 3 miles B. In 3 seconds, the space station travels 3 miles in 15 miles.C. The space station travels 3 miles in 15 seconds D. It takes the space st 3 seconds to go 5 miles.
From the graph, x coordinate 3 mean it takes 3 seconds to travels 15 miles.
Option B is the correct answer.
If f(x) = 4x - 1 and g(x)=2x-4, what is (fog)(x)?
The value of the composite function (f o g)(x) is 8x - 17
How to evaluate the function?The definition of the functions are given as
f(x) = 4x - 1
g(x) = 2x - 4
The composite function definition is given as
(f o g)(x)
This composite function is calculated using the following composite function formula
(f o g)(x)= f(g(x))
Substitute the known values in the above equation
So, we have the following equation
(f o g)(x) = 4(g(x)) - 1
So, we have the following equation
(f o g)(x) = 4(2x - 4) - 1
Open the brackets
(f o g)(x) = 8x - 16 - 1
Evaluate
(f o g)(x) = 8x - 17
Hence, the composite function is (f o g)(x) = 8x - 17
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The greatest common factor of 36 and 60 is 12. Explain what this means.
For 12 to be the GCF (Greatest common factor) between 36 and 60, means that the greatest number that can divide both 36 and 60 at the same time is 12.
Can someone explain to me how to find the answers
Part a: The missing length = 28 units.
Part b: The missing length = 25 units, for the given similar triangle.
What is termed as the similarity of the triangle?If two triangles' corresponding angles seem to be congruent and their corresponding sides are proportional, they are said to be similar. In other phrases, similar triangles have the same shape but may or may not be the same size. The triangles have been congruent if their side lengths are also of equal length.Part a: For the similar triangles.
Let the unknown value be x.
The, using the similarity of the triangle,
63/x = 27/12
x = (63×12)/27
x = 28 units.
The missing length is 28 units.
Part b: For the similar triangles.
Let the unknown value be x.
The, using the similarity of the triangle,
21/15 = (10 + x)/x
21x = 150 - 15x
6x = 150
x = 25
The missing length is 25 units.
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Bismuth-210 has a half-life of about 6 days. After 21 days, how many milligrams of a1,220 mg sample will remain? Round answer to the nearest tenth place. If answerdoes not have tenths place use a zero so that it does.
SOLUTION:
Step 1:
In this question, we are given the following:
Bismuth-210 has a half-life of about 6 days.
After 21 days, how many milligrams of a 1,220 mg sample will remain?
Round answer to the nearest tenth place.
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} We\text{ have that:} \\ 0.5\text{ = e}^{-6k} \\ Taking\text{ In of both sides, we have that:} \\ ln\text{ 0.5 = -6k} \\ That\text{ means that:} \\ k\text{ =}\frac{-ln\text{ 0. 5}}{6} \end{gathered}[/tex][tex]Let\text{ the number to remain, A=1220e}^{-(-\frac{ln0.5}{6})(21)}[/tex][tex]\begin{gathered} 107.83378\text{ mg} \\ \approx\text{ 107. 8 mg \lparen to the nearest tenth\rparen} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]107.\text{ 8 mg \lparen to the nearest tenth\rparen}[/tex]I bought a suit that was on sale for 40% off the original price the original price of the suit was 260. How much did I save? and how much did I pay for the suit not including tax to the nearest dollar?
I saved 104
I payed 156
Explanations:% Discount = 40%
Original Price = 260
The amount I saved is the discount given
[tex]\begin{gathered} \text{Discount = }\frac{\%\text{ Discount}}{100}\times\text{ 260} \\ \text{Discount = }\frac{40}{100}\times260 \\ \text{Discount = 0.4}\times260 \\ \text{Discount = }104 \end{gathered}[/tex]Therefore, I saved 104
The amount payed = Original Price - Amount saved
Amount payed = 260 - 104
Amount payed = 156
Dude I need help so if anyone can answer this for me that would be great!
5/6 ÷ -2/3
A -5/4
B -5/9
C 5/9
D 5/4
A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
The final expression for this division of fraction 5/6 ÷ (-2/3) is -5/4.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
The division of two fraction:
5/6 ÷ (-2/3)
= (5/6) / (-2/3)
= 5/6 x (-3/2)
= (5 x (-3)) / (6 x 2)
= -5 x 3 / 6 x 2
= -5 / 4
Thus,
The final expression for this division of fraction 5/6 ÷ (-2/3) is -5/4.
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If M is a centroid of triangle WOR and YR =16, what is the length of WR
If M is a centroid of triangle WOR and YR =16, the length of WR
side will be WR = 48.
What is the triangle's centroid?The centroid of the thing represents its center. A triangle's centroid is the point at which its three medians intersect. It can also be described as the point at which the three medians intersect.The median is a line that connects the midpoints of two sides and the opposite vertex of a triangle. A triangle is a two-dimensional shape with three sides. The three angles add up to 180 degrees.The centroid of a triangle divides the triangle's medians in a 2: 1 ratio.The ratio of the two sides will be given here as:
WY/ YR = 2/1
Determine the value of YR to determine the value of WR.
WY/16 = 2/1
WY = 32
WR will have the following value:
WR = WY+ YR
WR = 32+ 16
WR = 48
As a result, the value of the side WR is 48.
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Which expression is equivalent to 10x – 6?
Answer:
1. -6 + 10x
Step-by-step explanation:
The expression 10x – 6 is the same as adding -6 to 10x, or 10x + -6. Since addition equations can be rearranged, 10x + -6 can also be written as -6 + 10x.
Answer:
[tex] \sf{ \large{ - 6 + 10x}}[/tex]
Step-by-step explanation:
10x - 6
note: there is a plus sign at 10x
+10x - 6
so when you switch it will be like this
-6 + 10x
Which of the following are true?
A.-2.7<- 4.6
B.-7.3 1.2
C.-5.2 - 2.9
D. 4.7 3.4
O A and D
O B and C
OC and D
O A and B
Answer:
B and C are correct
Step-by-step explanation:
Write the number in standard notation.5.8 × 10−3
0.0058
Explanation:The given scientific notation is:
[tex]5.8\times10^{-3}[/tex]This can also be written as:
[tex]\begin{gathered} 5.8\times\frac{1}{1000} \\ \\ =\frac{5.8}{1000} \\ \\ =0.0058 \end{gathered}[/tex]Therefore 5.8 x 10^-3 in standard form is 0.0058
what is the probability that Glenn will get a yellow marble
The bag has 5 marbles
3 yellow marbles
2 red marbles
"Glen chooses a marble first and then Kris chooses one" You have to determine the probability of Kris choosing a yellow marble if Glen chooses a yellow one first.
1. First you have to determine the probability that Glen choose a yellow marble first.
To do so, you have to calculate the quotient between the number of yellow marbles on the bag and the total number of marbles on the bag:
[tex]\begin{gathered} P(Y_1)=\frac{nº\text{yellow}}{\text{total}} \\ P(Y_1)=\frac{3}{5} \end{gathered}[/tex]2. and 3.
After Glen takes the first yellow marble from the bag, the total number of marbles is reduced by one and so is the number of yellow marbles on the bag, so:
New total: 4 marbles
Number of yellow marbles: 2
4.
To determine the probability of Kris choosing a yellow marble, you have to use the data on the remaining marbles on the bag. And calculate the quotient between the remaining number of yellow marbles and the remaining number of marbles:
[tex]\begin{gathered} P(Y_2)=\frac{2}{4} \\ P(Y_2)=\frac{1}{2} \end{gathered}[/tex]A laptop computer consumes about 40 watts of electricity per hour when operating. At $0.20 per kilowatt-hour, how much does a laptop cost to operate for 10 hours?A )8 centsB )800 centsC )40 centsD) 200 cents
A) 8 cents
Explanation
Step 1
find the rate
[tex]\begin{gathered} \text{rate}=\text{ 40 }\frac{\text{w}}{h} \\ \end{gathered}[/tex]cost
[tex]\begin{gathered} \text{ Cost= 0.20 per 1000 wats hour} \\ \end{gathered}[/tex]hence
total cost = time*rate*consume
[tex]\begin{gathered} \text{ Total cost = 10 hours}\cdot40\frac{w}{h}\cdot0.2\frac{\text{ \$}}{1000\text{ w}} \\ \text{ Total cost =}0.08\text{ dollars} \end{gathered}[/tex]now, to convert from dollars to cents, multply by 100
[tex]\text{ Total cost =}0.08\text{ dollars}\cdot(\frac{100\text{ cents}}{1\text{ dollar}})=8\text{ cents}[/tex]I hope this helps you
Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.
How many numbers are greater than 64?
There are 35 natural numbers that are greater than 64.
Natural numbers:
Natural number are the numbers that start from 1 and end at infinity. In other words, they are counting numbers and they do not include 0 or any negative values.
Given,
Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.
Here we need to find the numbers that satisfied the given condition and that is also greater than 64.
We know that, two digit natural numbers range from 10 to 99.
Since there are replacement take place, then each number formed from 10 to 99 is valid in this exercise.
Now, we have to move on to the other thing that is, those number are greater than 64,
Then we have to calculate it as,
=> 99-64 = 35 are greater than 64.
And those number are 65,66,67,68,69,...,98,99.
Finally, we have identified that there are 35 number are greater than 64.
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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each. There are 135 boxes in all. If the truck is carrying a total of 4350 pounds in boxes, how many of each type of box is it carrying?
Number of large boxes:
Number of small boxes:
Number of large boxes will be 65.
Number of small boxes will be 70.
What is mathematical expression?
Expression in math is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each.
There are 135 boxes in all.
If the truck is carrying a total of 4350 pounds in boxes.
Let number of large boxes = x
Number of small boxes = y
Since, There are 135 boxes in all.
So, We get;
x + y = 135 ... (i)
And, The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each and the truck is carrying a total of 4350 pounds in boxes.
So, we can formulate;
40x + 25y = 4350 ... (ii)
Solve equation (i) and (ii) as;
Multiply 40 by (i) and subtract by (ii) we get;
40x + 40y - 40x - 25y = 5,400 - 4,350
15y = 1,050
y = 70
And, x + y = 135
x + 70 = 135
x = 135 - 70
x = 65
Thus, Number of large boxes will be 65.
Number of small boxes will be 70.
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Pythagorean TheoremFor the following right triangle, find the side length x. Round your answer to the nearest hundredth.18Х11
Solution
For this case we can use the Pythagoras theorem and we have:
[tex]18^2=11^2+x^2[/tex]And solving for x we got:
[tex]x=\sqrt[]{18^2-11^2}=\sqrt[]{324-121}=\sqrt[]{203}=14.25[/tex]Then the answer is:
14.25
use nPr formula 11P0=
we know that
the formula is equal to
P(n,r) = n! / (n-r)!
we have that
nPr = n!/(n-r)!
we have
11P0
so
n=11
r=0
= 11!/(11-0)!
=11!/11!
=1
answer is 1Solve Each system of equations.
-r + t = 5
-2r+t=4
Higher Order Thinking Veronica needs to buy 13 pounds of cheese. When the clerk places some cheese in a container and weighs it, the scale shows 1 pounds. The container weighs pound. How many more pounds of cheese should be added to the scale to get the amount that Veronica needs? Explain how you solved the problem.
After calculating some basic arithmetic we have come to find that, 12 pounds of more cheese should be added to the scale to get the amount that Veronica needs which 23 pounds.
What is arithmetic?Using the four operations, arithmetic is a branch of mathematics that deals with the characteristics of numbers.
Division, multiplication, and subtraction are the four operations. The rules for each operation are very detailed.
As an illustration of arithmetic, one of the rules of addition and subtraction is that addition increases the overall value of a number while subtraction decreases the overall value of a number.
Veronica needs to buy 13 pounds of cheese
Cheese in a container weighs = 1 pounds
Mass of cheese clerk needs to add = 13 - 1
= 12 pounds
(as 1 pound is already there)
Thus, 12 pounds of more cheese should be added to the scale to get the amount that Veronica needs which 23 pounds.
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Write an phrase that would translate into the following mathematical expression: 8z- 2 ?
The mathematical expression 8z - 2 can be phrased as:
The difference between 8 times the variable z and 2.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Any mathematical object has a symbol, and that symbol is called a variable. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
Consider the mathematical expression,
8z - 2
The expression can be defined as 2 less than the product of 8 and variable z.
The expression can also be rephrased as:
The difference between 8 times the variable z and 2.
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Can someone help me with this geometry question? My instructor said I was wrong?
4 years ago Lena won some money in the lottery and put it in a bank account that earns 6% interest compounded annually if Lena currently has $5,000 00 in the bank account how much interest has she earned round your answer to the nearest cent
Solution
For this case we can use the compound interest formula given by:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]and for this case A= 5000, r = 0.06, t= 4 and n = 1 ( compounded yearly)
[tex]A=5000(1+\frac{0.06}{1})^{1\cdot4}=6312.38[/tex]and the interest would be:
[tex]i=6312.38-5000=1312.38[/tex]Which of the following graphs shows the preimage P(x)=|x| and the image I(x)=1/2⋅P(x)?
Given,
The expression for function P(x) is | x |.
The expression for function I(x) is | x |/2.
Required:
The graph of the function.
The graph of the function is,
The function P(x) is represented by black line.
The function I(x) is represented by Red line.
Hence, option A is correct.
What is the inverse of the function y = 2(x + 1)³?
Answer:
[tex]\sqrt{x}[/tex][tex]\sqrt[3]{1/2(x)}[/tex] - 1 = y
Step-by-step explanation:
Inverse: swap x and y
y =2(x+1)^3
x = 2(y + 1)^3
now put it in a y = mx + b form
x = 2(y + 1)^3
1/2(X) = (y+1)^3
[tex]\sqrt{x}[/tex][tex]\sqrt[3]{1/2(x)}[/tex]= y + 1
[tex]\sqrt{x}[/tex][tex]\sqrt[3]{1/2(x)}[/tex] - 1 = y
need help with this problem.
[tex]\cfrac{6^3\cdot 15^3}{(7^0)^3}\implies \cfrac{(6\cdot 15)^3}{(1)^3}\implies \cfrac{90^3}{1}\implies 729000[/tex]
what is the least common multiple of 62 and 31?
Answer:
there is none so it would be 62
Step-by-step explanation:
Can u help me answer question 24 BTW this is lesson 6 the distributive property 24. 5(2x+7) = __________
We have the following:
[tex]5\mleft(2x+7\mright)=_{}[/tex]We apply the distributive property that tells us that the multiplication of a number by a sum is equal to the sum of the multiplications of said number by each of the addends.
Therefore:
[tex]5(2x+7)=_{}10x+35[/tex]I need to find the inequality 5-12x<29
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x > −2
Interval Notation:
(−2, ∞)
X is greater than -2
