Step-by-step explanation:
The prime factorization of 12 is
12 = 2²×3
To find denominators suitable for your purpose, you need to group the factors
{1, 2, 2, 3}
into two groups with different products that share at least one of the numbers that is not 1.
For example, your grouping could be (2, [2), 3], where a 2 is shared. That is, your denominators could be 2*2=4 and 2*3=6.
Another possible grouping is (1, [2), 2, 3], giving rise to denominators of 2 and 12.
Yet another is (1, [3), 2, 2], for denominators of 3 and 12.
Using the first grouping, a pair of mixed numbers matching your requirement might be
1 3/4, 5 1/6
a boat rental company charges a fee per hour. The charge is the same per hour . The ordered pairs(2,14.50) and (5,36.25) represent the corresponding hours,x,and the cost,y. What is the rate of change expressed as a unit rate?
Answer: One hour costs 7.25 $
Step-by-step explanation:
The charge for 2 hours is 14.50 $, then 14.50 $ / 2 hours = 7.25 $ / hour
The charge for 5 hours is 36.25 $, then 36.25 $ / 5 hours = 7.25 $ / hour
Answer: One hour costs 7.25 $
[tex]\textit{\textbf{Spymore}}[/tex]
can someone help me with my math?
I can try it depends on what the question is
PLEASE ANSWER QUICK!!!
A cube-shaped container has an edge length of 12 inches. The container is filled with smaller plastic cubes that each have an edge length of 3 inches. How many cubes are needed to fill the container?
27
64
1728
16
Answer:
64 cubes
Step-by-step explanation:
The square is 12x12x12 inches, meaning it is 1,728 cubic inches in volume. A 3x3x3 inch cube is 27 cubic inches in volume. Divide 1,728 by 27 and you'll find that 64 3x3x3 cubes can fit inside one of the 12x12x12 cubes.
Final answer:
To fill a cube-shaped container with an edge length of 12 inches, 64 small cubes with an edge length of 3 inches each are required.
Explanation:
The student is asking how many small cubes, with an edge length of 3 inches, are required to fill a larger cube-shaped container with an edge length of 12 inches. First, we calculate the volume of the large cube which is 12 inches x 12 inches x 12 inches, resulting in 1728 cubic inches. Then, we find the volume of one small cube which is 3 inches x 3 inches x 3 inches, resulting in 27 cubic inches. To determine the number of small cubes that can fit into the larger cube, we divide the large cube's volume by the small cube's volume: 1728 cubic inches / 27 cubic inches which equals 64. Therefore, 64 small plastic cubes are needed to fill the container.
over the weekend statton and Taylor drove to Montana to go hunting. now they're preparing to go home. Tyler needs gas for his jeep, which gets 30 miles per gallon for gas mileage. When he stops at the gas station, he already has 8 gallons of gas in his tank. he buys more gas for $1.50 per gallon
If Tyler spends $16.50 on gas, what is the total distance the boys could travel? round, if necessary, the nearest tenth.
Answer:
Step-by-step explanation:
Givens
His tank contains 8 gallons
He spends 16.50 on gas
A gallon of gas costs 1.50 dollars
Millage = 30 mpg
Find the gas added.
Total gas (in gallons) added = amount spent / cost per gallon
Total gas (in gallons) added = 16.50 / 1.50
Total gas (in gallons) added = 11 gallons.
Find the total number of gallons in his tank.
Total = what was there + What he bought.
Total = 8 + 11
Total = 19 gallons.
Find the distance he can travel
Total distance = gallons * miles / gallon
Total distance = 19 * 30
Total distance = 570 miles.
Tyler and Statton could potentially travel a total distance of 570 miles with the amount of gas they have.
Explanation:The question is asking for the total distance that the boys could travel on the bought gas. Tyler bought $16.50 worth of gas at $1.50 per gallon, which means he bought 11 gallons ($16.50/$1.50). Tyler initially had 8 gallons of gas in his tank. Therefore, he now has a total of 8 + 11 = 19 gallons of gas. His Jeep gets 30 miles for every gallon of gas. Therefore, the total distance they can travel is 19 gallons * 30 miles/gallon = 570 miles.
So, "Tyler and Statton could potentially travel 570 miles with the gas in the tank".
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Define circle.
A)A round line
B)A set of points that is round
C)A set of points centered around a point
D)A set of points equidistant from a point
Answer:
Option D is correct
Step-by-step explanation:
According to Geometry, A circle is a round plane figure whose boundary (that is the circumference) consists of points equidistant from a fixed point (that is the centre).
Thus, according to the definition of circle in geometry, option D is correct because it gives the correct description about circle while all other options are not correct because they are giving the incorrect description of circle.
Your client has saved $1,860 for a down payment on a house. A government loan program requires a down payment equal to 3% of the loan amount. What is the largest loan amount that your client could receive with this program?
Answer:
5,580
Step-by-step explanation:
1860*3=5,580
Find the area of the kite. The figure is not drawn to scale.
Answer:
The area of the kite is [tex]42\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of a kite is half the product of the diagonals
so
[tex]A=\frac{1}{2}(D1*D2)[/tex]
we have
[tex]D1=2*(3)=6\ units[/tex]
Find the length side of diagonal D2
Applying the Pythagoras Theorem
[tex]D2=\sqrt{5^{2}-3^{2}} +10\\ \\D2=4+10\\ \\D2=14\ units[/tex]
Find the area of the kite
we have
[tex]D1=6\ units[/tex]
[tex]D2=14\ units[/tex]
substitute
[tex]A=\frac{1}{2}(D1*D2)[/tex]
[tex]A=\frac{1}{2}(6*14)=42\ units^{2}[/tex]
QUICK !
What is the image point of (5,-5) after a translation right 2 units and up 3 units ?
Answer:
(7,-2)
Step-by-step explanation:
First, you move to the right of y-axis like 5 to 7,
then you movie to the up of x-axis like -5 to -2.
So the answer was (7,-2)
Final answer:
The image point of (5,-5) after a translation right 2 units and up 3 units is (7, -2).
Explanation:
The image point of (5,-5) after a translation right 2 units and up 3 units can be found by adding the respective translation values to the x and y coordinates of the original point. To move the point right by 2 units, you add 2 to the x-coordinate, and to move the point up by 3 units, you add 3 to the y-coordinate.
Therefore, the new coordinates after the translation will be:
Add 2 to the x-coordinate: 5 + 2 = 7.Add 3 to the y-coordinate: -5 + 3 = -2.So the image point after the translation is (7, -2).
find the explicit formula for 5, 9, 13, 17
ASAP
The explicit formula for the sequence 5, 9, 13, 17 is an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
Explanation:The given sequence is 5, 9, 13, 17. To find the explicit formula, we need to determine the pattern or rule that generates these numbers. In this case, the pattern can be observed by adding 4 to the previous term to get the next term. So, the explicit formula for this sequence is:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term (5 in this case), n is the position of the term in the sequence, and d is the common difference (4 in this case).
Using this formula, we can find any term in the sequence by plugging in the values for n and a1.]
5.) I'm having trouble doing my homework right now. Please show work so I know how to do the next one.
she worked one hour at the store and ten hours tutoring
store money is 9 an hour so thats $9
tutoring is 15 an hour so 15x10 is $150
so 9+150=159
A box of pancake mix requires 1 cup of mix and
2/3 cups of water to make 6 to 7 pancakes. Arjun is
making pancakes for his family of 6, and he wants every-
one to have at least 3 pancakes. How much pancake mix
will Arjun need? How much water will he need?
Answer:
3 cups of pancake mix and 2 cups of water
Step-by-step explanation:
For the family of 6 to have 3 pancakes each, Arjun must make at least 18 pancakes. If 1 cup of pancake mix makes at least 6 pancakes, Arjun would need three cupes of pancake mix to make at least 18 pancakes.
Now if each cup of pancake mix requires 2/3 cups of water, the amount of water needed for 3 cups of pancake mix would be
3 x 2/3 = 2 cups of water
Hope this helps!Answer:
3 cups of pancake mix and 2 cups of water
Step-by-step explanation:
We are given that a box of pancake mix requires 1 cup of mix and 2/3 cups of water which makes at least 6 cupcakes.
If each person in Arjun's family of 6 wants to have 3 pancakes, it means that he needs to make 18 cupcakes.
To make 18 cupcakes, we need [tex]1 \times 3 =[/tex] 3 cups of pancake mix and [tex]3 \times \frac{2}{3} =[/tex] 2 cups of water.
How much voltage is required to run 1.6 A of current through a 240 0 resistor?
Here, current (I) = 1.6A
resistance(R) = 240 ohm
we know, voltage(v) =I×R
=1.6×240
=384 VOLTS
Hope i am clear and correct
Answer:
380 V
Step-by-step explanation:
Explain and show work
Answer:
330
Step-by-step explanation:
For Rectangles and Squares:
13x9=117
12x9=108
9x5=45
For Triangles:
12x5=60 divided by 2=30
12x5=60 divided by 2=30
How to get answer:
Add all the answers up:
117+108+45+30+30=330
A six-sided number cube is rolled
What is the probability of getting a 2 and then a 1, given that the first number rolled was 2?
Final answer:
The probability of getting a 2 and then a 1, given that the first number rolled was 2, is 1/5 or 0.2 (20%).
Explanation:
The probability of getting a 2 and then a 1, given that the first number rolled was 2, can be calculated using the concept of conditional probability.
Since we know that the first number rolled was a 2, the sample space is reduced to {2, 3, 4, 5, 6}. The probability of rolling a 2 from this reduced sample space is 1/5.
Now, since we want to find the probability of rolling a 1 after rolling a 2, the reduced sample space is further reduced to {1}. The probability of rolling a 1 from this reduced sample space is 1/1, since there is only one outcome.
Therefore, the probability of getting a 2 and then a 1, given that the first number rolled was 2, is 1/5 * 1/1 = 1/5 or 0.2 (20%).
The probability of rolling a 2 and then a 1 on a six-sided number cube, given that the first number rolled was a 2, is [tex]\(\frac{1}{6}\)[/tex].
To solve this problem, we need to consider the probability of each event separately and then combine them, keeping in mind that the outcome of the first roll affects the probability of the second roll.
1. The probability of rolling a 2 on the first roll is [tex]\(\frac{1}{6}\)[/tex], since there is only one '2' on a six-sided die and there are six possible outcomes.
2. Given that the first roll is a 2, the probability of rolling a 1 on the second roll is still [tex]\(\frac{1}{6}\)[/tex]. This is because the die has no memory, and each roll is independent of the previous one. The fact that a 2 was rolled first does not change the probability of rolling a 1 on the second roll.
3. Since the rolls are independent events, we multiply the probabilities of the two events to find the combined probability:
[tex]\[ P(\text{2 and then 1} | \text{first roll is 2}) = P(\text{first roll is 2}) \times P(\text{second roll is 1}) \][/tex]
4. Substituting the probabilities we found:
[tex]\[ P(\text{2 and then 1} | \text{first roll is 2}) = \frac{1}{6} \times \frac{1}{6} \][/tex]
5. Multiplying these probabilities:
[tex]\[ P(\text{2 and then 1} | \text{first roll is 2}) = \frac{1}{36} \][/tex]
However, since we are given that the first number rolled was a 2, we do not need to consider the probability of rolling a 2 on the first roll. We only need to consider the probability of rolling a 1 on the second roll, which is [tex]\(\frac{1}{6}\)[/tex].
Therefore, the probability of getting a 2 and then a 1, given that the first number rolled was a 2, is [tex]\(\frac{1}{6}\)[/tex].
k=13t-2 find the output of k when the of t is 3
Answer:
= 37
Step-by-step explanation:
k=13t-2
k=13(3)-2
13*3
39-2
37
37
because 13(3)= 39
39-2=37
a teacher read part of a book to class. The graph shows the number of pages read by the teacher over the next several days. Find and interpret the rate of change and the initial value.
The rate of change on a graph represents how fast or slow the changes are happening, while the initial value is the starting point. To find these on a graph, you determine the slope of the line for the rate of change, and look at the intercept on the y-axis for the initial value. These values give us insights into the reading pace and starting point of the teacher.
Explanation:The rate of change in a graph represents the slope of the line. It tells us how the quantity being measured changes over time. If the graph is a straight line, the rate of change is constant, but if the line is curved, the rate of change varies.
To find the rate of change, you need to select two points on the graph and find the difference in the page numbers divided by the difference in the corresponding time points. That is (pages end - pages start) / (time end - time start).
The initial value is the point where the teacher started reading the book. This point is seen as the intercept on the y-axis of the graph.
The interpretation of these values would be that the rate of change tells us how quickly the teacher is reading the book, and the initial value tells us at what page number the teacher started reading.
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Initial value: The teacher initially read 150 pages. Rate of change: The teacher read 100 pages per day. The graph shows that the teacher is reading at a consistent pace and is making good progress on the book.
The initial value of the graph is the y-intercept, which is 100 pages. This means that the teacher had already read 100 pages before the graph starts.
The rate of change of the graph is the slope, which is calculated as (change in y) / (change in x). In this case, the slope is (750 - 100) / (5 - 1) = 130 pages/day.
This means that the teacher is reading 130 pages per day.
Interpretation:
The teacher is reading at a rate of 130 pages per day. This means that each day, the teacher is reading 130 more pages than the previous day.
The initial value of 100 pages means that the teacher had already read a significant portion of the book before the graph starts. It is possible that the teacher was reading ahead, or that the teacher was reading a chapter book to the class and had already finished the first chapter.
Overall, the graph shows that the teacher is reading at a consistent pace and is making good progress on the book.
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Choose the correct translation for the following statement. It is a minimum of three. x < 3 x ≤ 3 x > 3 x ≥ 3
Answer: [tex]x \ge 3[/tex] (choice D)
===========================================
Explanation:
Saying "a minimum of 3" means that the lowest you can go is 3. You can pick 3 or pick any value larger than this. Therefore we can say that x is greater than or equal to 3.
The correct mathematical translation for 'It is a minimum of three.' is 'x ≥ 3'. This means that 'x' can be three or any number greater than three.
Explanation:The correct translation for the English statement 'It is a minimum of three.' is x ≥ 3. This means 'x' can be equal to three or any number greater than three.
This is because in mathematical language, the term 'minimum' refers to the lowest possible value that a variable like 'x' can take. Since it's specified that 'x' has a minimum value of three, it can't be less than three.
The notation 'x ≥ 3' effectively means that 'x' is equal to three or 'x' is greater than three, which fits the criteria that it's a minimum of three.
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Add 5/6 + 3/4 + 2/3 simplify the answer write it as a mixed number if possible
Answer: 27/12 or 2 3/12
Step-by-step explanation: First off we would need to find a common denominator, so all the fractions could be added together easily, and we could use a denominator of 12 because 6 times 2 equals 12, 4 times 3 equals 12, and 3 times 4 equals 12. So 5/6 would become 10/12, 3/4 would become 9/12, and 2/3 would become 8/12. So adding them all together would give you a sum of 27/12 or 2 3/12. Hope this helped!
4(x + 5) > 10(x - 1)
Answer:
x < 5
Step-by-step explanation:
Solve the inequality by using the distributive property and inverse operations.
4(x + 5) > 10(x - 1)
4x + 20 > 10x - 10
20 > 10x - 4x - 10
20 > 6x - 10
20 + 10 > 6x
30 > 6x
5 > x
confused someone help
Answer:
y = -5x - 21
Step-by-step explanation:
Given in the question,
equation of a parallel line
y = -5x + 6
point through which it passes
(-4,-1)
Step1
Find the gradient of the equation given, as it is parallel so it will have same gradient
equation of straight line
y = mx + c
where m is gradient
c is y intercept
y = -5x + 6
m =-5
Step2
Find y-intercept
-1 = -5(-4) + c
-1 = 20 + c
c = -20 - 1
c = -21
Step3
form the equation
y = -5x - 21
Answer:
[tex]y=-5x-21[/tex]
Step-by-step explanation:
The given line has equation;
[tex]y=-5x+6[/tex]
This line is in the form [tex]y=mx+c[/tex], where [tex]m=-5[/tex]
[tex](x_1,y_1)=(-4,-1)[/tex]
The required equation can be found using the formula;
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the given point and slope to get,
[tex]y+1=-5(x+4)[/tex]
Expand
[tex]y=-5x-20-1[/tex]
[tex]y=-5x-21[/tex]
A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true? Check all that apply.
The angular velocity is 10π rad/sec.
The angular velocity is 10π rad/min.
The angular velocity is 60π rad/min.
The angular velocity is 600π rad/sec.
The angular velocity is 600π rad/min.
Answer:
The angular velocity is 10π rad/s or 600 rad/min.
Step-by-step explanation:
angular velocity = angle/time
0.5 revolution = 0.5 × 2π = π rad
ω = θ/t = π rad/0.1 s = 10π rad/s
Convert time to minutes
ω = 10π rad/1 s × (60 s/1 min) = 600π rad/min
Chord AB subtends two arcs with measures in the ratio of 1:5. Line l is tangent to a circle at point A. Find the measure of the angle between the tangent and secant AB .
The measure of the angle between tangent and secant AB in a circle with arcs in a 1:5 ratio is 120°, calculated using arc measures.
Let's denote the measures of the arcs subtended by chord AB as x and 5x, where x is the measure of the smaller arc.
Now, according to the properties of angles formed by a tangent and a secant, the measure of the angle formed between the tangent and the secant AB is equal to half the difference of the measures of the intercepted arcs.
So, the measure of the angle [tex]\( \angle A \)[/tex] formed between the tangent and the secant AB is:
[tex]\[ \angle A = \frac{1}{2} \left|5x - x\right| \\\[ \angle A = \frac{1}{2} \left|4x\right| \][/tex]
Now, since x represents the measure of the smaller arc, it must be greater than 0. Thus, the expression simplifies to:
[tex]\[ \angle A = 2x \][/tex]
Now, we need to find the value of x. Since the sum of the measures of the arcs in a circle is 360°, we have:
[tex]\[ x + 5x = 360^\circ \\\[ 6x = 360^\circ \\\[ x = \frac{360^\circ}{6} \\\[ x = 60^\circ \][/tex]
Now, we can find the measure of the angle [tex]\( \angle A \)[/tex]:
[tex]\[ \angle A = 2x \\\[ \angle A = 2(60^\circ) \\\[ \angle A = 120^\circ \][/tex]
So, the measure of the angle between the tangent and secant AB is 120°.
Answer:
The measure of the angle between the tangent and secant AB is [tex]\(120\°\).[/tex]
Explanation:
To solve this problem, let's denote the measures of the two arcs subtended by chord AB as [tex]\(x\)[/tex] and [tex]\(5x\)[/tex], respectively.
We know that when a tangent line intersects a secant line, the angle formed between the tangent and the secant is equal to half the difference of the measures of the intercepted arcs.
So, the angle between the tangent and secant AB, let's call it [tex]\(\theta\)[/tex], is given by:
[tex]\[ \theta = \frac{1}{2}(5x - x) = \frac{1}{2}(4x) = 2x \][/tex]
Now, let's find the value of [tex]\(x\).[/tex]
Since chord AB subtends two arcs with measures in the ratio of [tex]\(1:5\)[/tex], the total angle around the circle is [tex]\(1x + 5x = 6x\)[/tex], which is [tex]\(360\°\)[/tex](since the total angle around a circle is [tex]\(360\°\)[/tex]).
So, we have:
[tex]\[ 6x = 360\° \][/tex]
Solving for [tex]\(x\):[/tex]
[tex]\[ x = \frac{360\°}{6} = 60\° \][/tex]
Now, we can find the measure of the angle [tex]\(\theta\):[/tex]
[tex]\[ \theta = 2x = 2 \times 60\° = 120\° \][/tex]
So, the measure of the angle between the tangent and secant AB is [tex]\(120\°\).[/tex]
Find the zero(s) of this function: y=x^2-17x+52
here are the answers to this question
Answer:
The zeroes are {-4, 13}
Step-by-step explanation:
Your best bet here is to determine the zeros using the quadratic formula or "completing the square."
Completing the square,
y = x² - 17x +52, or
y = (x - 17/2)² - (17/2)² +52, or
y = (x - 17/2)² - 289/4 +208/4, or
y = (x - 17/2)² - 81/4
We set this = to 0, as we want the zeros. Then:
(x - 17/2)² - 81/4 = 0, or
x - 17/2 = ±9/2, after having taken the square root of both sides.
Thus, one root is x = 17/2 + 9/2, or 26/2, or 13, and the other is
x = 1/2 - 9/2, or -8/2, or -4.
The zeroes are {-4, 13}.
how do i factor 8g^2-10g-12
Answer:
(4g+3)(g-2)
Step-by-step explanation:
well they all have a common factor of 2
so divide all of it by two 2[(4g^2-5g-6)]
then factory that to get (4g+3)(g-2)
Hopefully this helps you :)
{-4x + 4y = -8
{ x - 4y = -7
what is long and yellow and never rings worksheet
Answer:
A banana my dude.
Step-by-step explanation:
The answer to the riddle 'what is long and yellow and never rings' is likely a banana, as this is an example of the type of playful thinking and language interpretation often encouraged in English exercises.
Explanation:
The question "what is long and yellow and never rings" might be referring to a type of riddle or a joke commonly found in English language or creative thinking exercises. Since it mentions something that is long and yellow but never rings, a possible answer could be a banana. This is because a banana is indeed long and yellow, yet it certainly cannot ring like a telephone or bell could. Such tasks are designed to engage students in out-of-the-box thinking and interpreting language in a playful manner.
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Kristy wanted to divide her paint evenly into two-3 1/2-gallon containers. She had 5 1/4 gallons of paint. How much paint did she pour into each container? (HELP NEEDED)
Answer:
[tex]2\frac{5}{8}\ gal[/tex]
Step-by-step explanation:
step 1
Convert mixed number to an improper fraction
so
[tex]5\frac{1}{4}\ gal=\frac{5*4+1}{4}=\frac{21}{4}\ gal[/tex]
step 2
Divide the total gallons of paint by two
[tex]\frac{(21/4)}{2}=\frac{21}{8}\ gal[/tex]
step 3
Convert improper fraction to mixed number
[tex]\frac{21}{8}\ gal=\frac{16}{8}+\frac{5}{8}=2+\frac{5}{8}=2\frac{5}{8}\ gal[/tex]
What is the y-intercept in the equation y=4x-3?
➷ Equations come in the form y = mx + c
'c' is the y intercept
In this equation, the y intercept is -3
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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The y-intercept of the given equation y = 4x-3 is -3.
What is y-intercept?The y-coordinate of a point where a line, curve, or surface intersects the y-axis is called y-intercept.
According to the given question.
We have an equation y = 4x -3.
To find the y-intercept substitute x = 0 in the above equation y = 4x -3.
[tex]\implies y = 4x -3\\\implies y = 4(0) - 3\\\implies y = -3[/tex]
Hence, the y-intercept of the given equation y = 4x-3 is -3.
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They are the same because the central angle measure is the same. The arc lengths are proportional: . The arc lengths are proportional: . The arc lengths are proportional:
Is this an answer? I don’t think this is a question buddy
PLEASE HELP ME!!!!! THIS IS DUE IN LIKE 10 MINS!!! PLEASE DO IT QUICKLY!!! I WILL BE MARKING BRAINLIEST!!
(The answers you can chose from are in the screen shot)
All sides are equall
Answer:
side a is less then a sum of the other two
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. If you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side.