Dennis cutting 4.7 foot length of twine from a 240 foot spool of twine he needs to cut 42 lenghts and says that 45 feet of twine will remain. Show that this is reasonable
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Related Questions
A worker can assemble 3 shelf units each hour. the same worker can assemble 6 tv stands each hour. if x = hours assembling shelf units, y = hours assembling tv stands, and 24 = total number of furniture pieces made, write a function in standard form modeling the situation.
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What is the r (common ratio) for the geometric sequence: -3, -15, -75, -375, -1875...
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hope this helps
3 x 5 = 15
15 x 5 = 75
75 x 5 = 375
etc
There is a box full of toys. There are four Lego sets, six video games, and five remote control cars. You randomly choose a toy. Find the probability of choosing a remote control car. A. 1/7 B. 7/24 C. 1/3 D. 11/24
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There is a box full of toys. There are four Lego sets, six video games, and five remote control cars. You randomly choose a toy. Find the probability of choosing a remote control car.
Probability means occurrence of chance.
Step 1) Add all the toys
[tex]4+6++5=15[/tex]
There are 5 control cars
[tex]5/15[/tex]
The simplified form would be [tex]1/3[/tex]
Thus, your answer is option C.
Hope I helped (:
Have a great day!
The probability of choosing a remote control car from the box is 1/3, which is calculated by dividing the number of remote control cars (5) by the total number of toys (15).
Explanation:To find the probability of choosing a control car from the box, we use the formula for probability, which is:
Probability = Number of favorable outcomes / Total number of possible outcomes
The number of favorable outcomes is the quantity of remote control cars which is 5. The total number of toys is the sum of all the toys, which are 4 Lego sets + 6 video games + 5 remote control cars = 15 toys in total.
The probability is therefore calculated as:
Probability of choosing a remote control car = 5 (number of remote control cars) / 15 (total number of toys) = 1/3
Hence, the correct answer is C. 1/3.
To solve the literal equation 5x = 7t + 6, what is the first step that you must do?
Can anyone help me?
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In the number 12,005,999 what is the value of the 2
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A student has two test scores. the difference between the scores is 44 and the mean, or average, of the scores is 8484. what are the two test scores?
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.help me please thanks
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Jim and Sarah are running for class president. Cayla and Daniel are running for Vice President. What combinations of president and Vice President could there be?
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Simply the product -7x/5y * 5x/-7
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= x^2/y
(-) times(-) = positive
and canceled out 7, 5
so answer is
x^2/y
what we do is, we form a single fraction where the numerator is the product of the numerators, and the denominator is the product of the denominators, that is:
[tex] \frac{-7x}{5y} \cdot \frac{5x}{-7}= \frac{-7\cdot5 \cdot x \cdot x}{5 \cdot(-7) \cdot y} [/tex]
simplify the common numbers and terms in the numerator and denominator:
[tex]\frac{-7\cdot5 \cdot x \cdot x}{5 \cdot(-7) \cdot y}=\frac{5 \cdot x \cdot x}{5 \cdot y}=\frac{x \cdot x}{y}= \frac{ x^{2} }{y} [/tex]
Answer: [tex]\frac{ x^{2} }{y} [/tex]
What is the measure of <JHG?
The measure of <JHG is _____ degrees
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The measure of ∠JHG is 70 degree.
What is an Angle?An angle is formed by two rays called the arms of the angle meeting at a common endpoint called the vertex of the angle.
There are three types of angles, acute angle, right angle and obtuse angle.
Protractor is used to measure angles, it is of semicircular shape with degrees of angles engraved upon it.
Acute Angle : The angle whose measure is less than 90 degree is called the acute angle.
Right Angle : The angle whose measure is equal to 90 degree is called right angle.
Obtuse Angle: The angle whose measure is greater than 90 degree is called obtuse angle.
The ∠JHG has JH and HG are the arms of the angle.
The measure of ∠JHG = 70 degree, it is less than 90 degree, it is an acute angled triangle.
To know more about Angle
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andre placed 7/8 gallon of water in a pot near his wood burning stove 1/5 gallon of water evaporates each hour how many hours would it take for the entire pot of water to evaporate
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To divide, you just want to reverse the second fraction and then multiply.
1/5 reversed is 5/1.
7/8 * 5/1 = 35/8
35/8 converted to a mixed number would be 4 3/8.
So it would take 4 3/8 hours for the entire pot of water to evaporate.
Find the distance between the points 6 + 5i and 1 – 2i.
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let : z = 6+5i z' = 1-2i
the distance between the points 6 + 5i and 1 – 2i is : |z - z' |
|z - z' | = |6+5i -1+2i| = |5+7i | =√(5²+7²) =√74
Answer:
Approximately 8.6
Step-by-step explanation:
The two numbers with a product of 30 and a sum of 17 are
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_____________________________________________
15 * 2 = 30 .
15 + 2 = 17 .
______________________________________________
The required numbers are "15" and "2".
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
Let the first number would be x and the second number would be y
We have been given that the two numbers with a product of 30,
So, x × y = 30
x = 1/y .....(i)
And the sum of 17, then x + y = 17 .....(ii)
Take both equations, then solves them and we get the values that are:
x = 15 and y = 2
So, 15 × 2 = 30 and 15 + 2 = 17
Thus, the required numbers are "15" and "2".
Learn more about the number system here:
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Five cans of tomatoes cost $6.50. At this rate, how much will nine cans of tomatoes cost?
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The cost of one can of tomatoes is $1.30, so nine cans at this rate would cost $11.70.
If five cans of tomatoes cost $6.50, to find the cost of nine cans, we first need to find the cost of one can of tomatoes. We do this by dividing the total cost by the number of cans.
Cost per can = Total cost / Number of cans
Cost per can = $6.50 / 5
Cost per can = $1.30
Now that we know how much one can costs, we can find out how much nine cans will cost by multiplying the cost per can by nine.
Total cost for nine cans = Cost per can × Number of cans
Total cost for nine cans = $1.30 × 9
Total cost for nine cans = $11.70
Therefore, nine cans of tomatoes will cost $11.70.
A balloon is released on top of a building. The graph shows the height of the balloon over time. What does the slope and y-intercept reveal about the situation?
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1.5/10=3/20=0.15. Since it's based off of 1000 feet, we multiply 0.15 by 1000 to get 150 as the rate of change for every x value. In addition, since we start at 0.5, 1000*0.5=500 and we therefore start at 500 ft. Using the information we have, we therefore have C as our answer
Answer:
C. The balloon starts at a height of 500 ft and rises at a rate of 150 ft.
Step-by-step explanation:
We have been given a graph which represents the height of the balloon over time.
We can see from our graph that y-intercept, which represents the height of the balloon (in thousand feet) at time equals zero, is 0.5. To find the correct y-intercept we will multiply 0.5 by 1000 as height of the balloon is given in thousand feet.
[tex]\text{y-intercept}=(0.5\times 1000)\text{ feet}=500\text{ feet}[/tex]
Therefore, y-intercept represents that the balloon starts at a height of 500 feet.
Now let us find slope of our given line using slope formula.
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_2-y_1[/tex] is vertical change or rise.
[tex]x_2-x_1[/tex] is horizontal change or run.
Upon substituting given values in above formula we will get,
[tex]\text{Slope}=\frac{3.5-0.5}{20-0}[/tex]
[tex]\text{Slope}=\frac{3}{20}[/tex]
[tex]\text{Slope}=0.15[/tex]
Now let us multiply 0.15 by 1000 as height of balloon is given in thousand feet.
[tex]\text{Slope}=0.15\times 1000=150[/tex]
Therefore, slope of our line is 150 which means that height of balloon is increasing 150 feet per second or balloon is rising at a rate of 150 feet per second.
Upon looking at our given options we can see that option C is the correct choice.
A gumball machine has just been filled with 50 black, 150 white, 100 red, and 100 yellow gumballs that have been thoroughly mixed. sue and jim each purchase one gumball. what is the likelihood that both sue and jim will get red gumballs?
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Final answer:
To calculate the likelihood of both Sue and Jim getting red gumballs, we multiply the probability of each event occurring sequentially. After Sue gets a red gumball, the chances are 1/4, and then 99/399 for Jim. The final probability of both getting red gumballs is 99/1596 or about 6.203%.
Explanation:
The likelihood that both Sue and Jim will get red gumballs from the gumball machine can be calculated using basic probability principles. First, we need to determine the total number of gumballs in the machine. This is the sum of black, white, red, and yellow gumballs, which are 50, 150, 100, and 100 respectively, making a total of 400 gumballs.
The probability that Sue gets a red gumball is the number of red gumballs divided by the total number of gumballs in the machine, which is 100/400, simplifying to 1/4. When Sue takes a gumball, assuming she gets a red one, there are now 399 gumballs left with 99 being red. Therefore, the probability that Jim also gets a red gumball is 99/399. To find the likelihood of both events occurring, we multiply these probabilities:
P(Both Sue and Jim get red gumballs) = P(Sue gets a red gumball) × P(Jim gets a red gumball after Sue) = (1/4) × (99/399).
Now we simplify and multiply these fractions to get the final probability. After simplifying, the final probability is 99/1596, which is approximately 0.06203 or 6.203% chance that both Sue and Jim will get red gumballs.
What is the result of dividing x^3-4 by x+2
A. x^2-2x+4+12/x+12
B. x^2-2x+4+4/x+2
C. x^2-2x+4-4/x+2
D. x^2-2x+4-12/x+2
What is the result of dividing 2x^3+x^2-2x+8 by x+2
A. 2x^2+5x+8
B. 2x^2-3x+16
C. 2x^2-3x+4
D. 2x^2+5x-8
What is the remainder when the polynomial 6x^2+11x-3 is divided by 2x-1
Jorge wasnt to divide 3x^2-x-2 by x+4 using synthetic division. (has picture)
Which answer shows the correct process?
What is the remainder when the polynomial 6x^2+11x-3 is divided by x+2
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Write x^3-4 as 1x^3 + 0x^2 + 0x + (-4)x^0
The coefficients here are 1, 0, 0, and -4
note how the exponents step down one at a time (3, 2, 1, 0)
Write the coefficients 1, 0, 0, -4 in that order along a single row. Write the test root x = -2 in a box off to the left of the row of coefficients. See Figure1A (attached) to see how the set up is done so far.
-------------------------
Now we will follow the steps to perform synthetic division. The first step is to drop the first coefficient (which is 1) down below the horizontal line. This is shown by the letter A in red. See Figure1B (attached).
We then multiply that dropped value (1) by the test root (-2) to get 1 times -2 = -2. This result of -2 is placed where you see the red letter B (Figure1B)
Now add straight down: 0 plus -2 = -2
The result -2 is placed just below the previous result. It is placed where you see the red letter C
-------------------------
Repeat these steps over and over until the bottom row is filled out. By that, I mean we have the bottom row terms line up with the right most value in the top row. See figure1C to have a look at what I mean. We stop once we get to -12 in the bottom row as there are no more terms to fill out.
The last term in the bottom row (-12) is the remainder. The other terms help construct the quotient.
In this case, the quotient is 1x^2 + (-2)x + 4x^0 which simplifies to x^2 - 2x + 4
The remainder is -12
Put this all together and we have the final answer of [tex]x^2 - 2x + 4 - \frac{12}{x+2}[/tex]
So the final answer is choice D
===================================================================================================
Problem 2)
Follow the same kind of steps shown in problem 1. This time we'll have the synthetic division table you see in the image Figure2 (attached)
The last value in the bottom row is the remainder. The remainder of 0 indicates (x+2) is a factor of 2x^3+x^2-2x+8
The quotient is the other values in the bottom row. The other values in that bottom row are (in order) 2, -3, 4 so the quotient is 2x^2 - 3x + 4
This makes the final answer to be choice C
===================================================================================================
Problem 3)
We can use the remainder theorem and skip synthetic division
2x-1 = 0 leads to x = 1/2 = 0.5
Plug x = 0.5 into the function f(x) = 6x^2 + 11x - 3 to get
f(x) = 6x^2 + 11x - 3
f(0.5) = 6(0.5)^2 + 11(0.5) - 3
f(0.5) = 4
So the remainder is 4
Answer: 4
Side Note: if you wish to use synthetic division, then check out "Figure3" in the attachments
===================================================================================================
Problem 4)
The answer is choice with the bottom row of 3, -13, and -54. This looks to be choice C. The same steps are followed as done in problems 1 through 3.
===================================================================================================
Problem 5)
Plug x = -2 into f(x) = 6x^2 + 11x - 3
f(x) = 6x^2 + 11x - 3
f(-2) = 6(-2)^2 + 11(-2) - 3
f(-2) = -1
Final Answer: -1
What's the principal square root of 169
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The principal square root of 169 is 13.
The principal square root of a number is the non-negative square root.
The principal square root of 169 is the non-negative number that, when multiplied by itself, equals 169.
We are looking for a number such that when it is squared (multiplied by itself), it equals 169.
This can be expressed mathematically as:
x² = 169
The solution to this equation is
x = √169.
169 is a perfect square, and its square root is 13 because:
13 × 13 = 169.
Therefore, the principal square root of 169 is 13.
E bisects DF, DE=2y, and EF=8y-3. Find DE, EF, and DF
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DF=2
EF=1
DE=1
What is the distance in km between two cites that are 7.5 cm apart on a 1:24 000 scale
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7.5 cm on the map represents 7.5 x 24000 = 180000 cm on the ground.
180000 cm = 1800 m (dividing by 100 cm per m)
1800 m = 1.8 km (dividing by 1000 m per km)
Those "cities" are really close together!
The answer to this question
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Use substitution to go from
Angle T = Angle R
to
3x+36 = 6x-9
Now let's solve for x
3x+36 = 6x-9
3x+36-3x = 6x-9-3x
36 = 3x-9
36+9 = 3x-9+9
45 = 3x
3x = 45
3x/3 = 45/3
x = 15
Since x = 15, we can say,
Angle T = 3x+36
Angle T = 3*x+36
Angle T = 3*15+36 ... x is replaced with 15 (since x = 15; found above)
Angle T = 45+36
Angle T = 81
The final answer is 81 degrees
A single little brown bat can eat up to 1,000 mosquitoes in a single hour. Express in scientific notation how many mosquitoes a little brown bat might eat in 10.5 hours.
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I hope this helps!
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 3 small boxes has a total weight of 110 kilograms. A delivery of 2 large boxes and 6 small boxes has a total weight of 74 kilograms. How much does each type of box weigh?
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5x + 3y = 110 .....multiply by -2
2x + 6y = 74
------------------
-10x - 6y = - 220 (result of multiplying by -2)
2x + 6y = 74
-----------------add
-8x = - 146
x = -146/-8
x = 18.25 <== large box weighs 18.25 kg
2x + 6y = 74
2(18.25) + 6y = 74
36.50 + 6y = 74
6y = 74 - 36.50
6y = 37.50
y = 37.50/6
y = 6.25 <=== small box is 6.25 kg
Solve the following equation, answer as a reduced, mixed number.
4(7x - 1) = 3(2x + 1) - 4(x + 6)
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28x-4= 6x+3-4x-24
then we combine like terms and move like terms to the different sided
28x-4=2x-21
26x=-17
x= -17/26
:)
How many ounces of gold are in anan 18-karat gold chain that weighs 2.7 ounces?
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A karat is a measure of the amount of gold in the gold chain. The karat has a maximum value of 24 karats. This means that an 18 karat of gold chain contains 18 parts of pure gold for every 24 parts of gold chain. Therefore:
gold = (18 / 24) * 2.7 ounces
gold = 2.025 ounces
12x > 9(2x-3) -15
solve the inequality for x. show each step of the solution.
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-6x>-42
x<7
12x > 18x - 27 -15 (distribute)
12x > 18x - 42 (simplify)
12x - 18x > 18x - 18x - 42 (subtract -18x from each side)
-6x/-6 > -42/-6 (divide, isolate the x)
x < 8 (answer, when you divide a negative, flip the sign)
hope this helps
An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. The boundary of the closed airspace starts at the vertex at (10, 6) and passes through the point (12, 7). A commuter jet has filed a flight plan that takes it along a linear path from (–18, 14) to (16, –13). Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?
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Answer:
third option
Step-by-step explanation:
I just got a 100
Answer:
C
Step-by-step explanation:
A bag contains eight green marbles and four blue marbles. what is the probability of drawing a green marble on the second draw?
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ann took a taxi home from the airport. the taxi fare was $2.10 per mile and she gave the driver a $5 tip. Ann paid a total of $49.10. What is an equation to determine the distance in miles from Anns home to the airport?
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(49.1/5)/2.1 = amount of miles it takes to reach Ann's home
Hope this helps!
A jet travels 500 miles in 2 hours. At this rate, how far could the jet fly in 8 hours? What is the rate of speed of the jet?
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500 / 2 = 250 miles per hour ( rate of speed)
250 * 8 = 2,000 miles in 8 hours