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Related Questions
Factor 3/4 out of 3/4z + 6
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[tex] \frac{3}{4} z + 6 = \frac{3}{4} (z + 8 )[/tex]
EXPLANATION
We want to factor
[tex] \frac{3}{4} [/tex]
out of
[tex] \frac{3}{4} z + 6[/tex]
The first term is already having a factor of
[tex] \frac{3}{4} [/tex]
The constant term which is the second term is not having a factor of
[tex] \frac{3}{4} [/tex]
so we need to use a trick of multiplying and dividing by the same factor to obtain,
[tex] \frac{3}{4} z + 6 = \frac{3}{4} z + \frac{3}{4} \times \frac{6}{ \frac{3}{4} } [/tex]
We can now factor
[tex] \frac{3}{4} [/tex]
out of the right hand side to obtain,
[tex] \frac{3}{4} z + 6 = \frac{3}{4} (z + \frac{6}{ \frac{3}{4} } )[/tex]
Let us rewrite the right most fraction using the normal division symbol.
[tex] \frac{3}{4} z + 6 = \frac{3}{4} (z + 6 \div \frac{3}{4} )[/tex]
We simplify to obtain,
[tex] \frac{3}{4} z + 6 = \frac{3}{4} (z + 6 \times \frac{4}{3} )[/tex]
This further gives us,
[tex] \frac{3}{4} z + 6 = \frac{3}{4} (z + 2 \times 4 )[/tex]
[tex] \frac{3}{4} z + 6 = \frac{3}{4} (z + 8 )[/tex]
Forty people were randomly sampled and surveyed as to the number of pets in their household. The results are listed below. 1 1 0 4 1 0 1 2 3 5 2 0 2 0 3 1 2 0 0 1 0 4 0 0 3 1 0 0 2 1 0 0 4 0 1 3 5 0 2 1 What is the mean, median, and mode of the household pet data?
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1.4
1
0
Answer : The mean, median, and mode of the household pet data is, 1.4, 1 and 0 respectively.
Step-by-step explanation :
Mean : It is determine by adding all the numbers then divided by how many numbers there are.
[tex]Mean=\frac{\text{Sum of outcomes}}{\text{Number of outcomes}}[/tex]
Median : It is the middle term that is sorted by the list of numbers. It is determine by placing the numbers in increasing order.
For odd observations the formula will be: [tex]\frac{n+1}{2}[/tex]
For even observations:
First find the value at position [tex]\frac{n}{2}[/tex]
Second find the value at position [tex]\frac{n+1}{2}[/tex]
Then find that average of two values to get the median.
Mode : It is defined as the value that appears most in a set of data.
As we are given that the set of data:
1, 1, 0, 4, 1, 0, 1, 2, 3, 5, 2, 0, 2, 0, 3, 1, 2, 0, 0, 1, 0, 4, 0, 0, 3, 1, 0, 0, 2, 1, 0, 0, 4, 0, 1, 3, 5, 0, 2, 1
First we have to placing the numbers in increasing order.
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5
Now we have to determine the mean.
[tex]Mean=\frac{\text{Sum of outcomes}}{\text{Number of outcomes}}[/tex]
Sum of outcomes = 1+1+0+4+1+0+1+2+3+5+2+0+2+0+3+1+2+0+0+1+0+4+0+0+3+1+0+0+2+1+0+0+4+0+1+3+5+0+2+1 = 56
[tex]Mean=\frac{56}{40}=1.4[/tex]
The mean of the household pet data is, 1.4
Now we have to determine the median.
For even data:
[tex]\frac{n}{2}[/tex] and [tex]\frac{n+1}{2}[/tex]
Here, n = 40
[tex]\frac{40}{2}[/tex] and [tex]\frac{40+1}{2}[/tex]
20 and 20.5
The number of pets at 20th position and 21th position is, 1 and 1 respectively.
Then we have to take an average of two values.
[tex]\frac{1+1}{2}=1[/tex]
The median of the household pet data is, 1
Now we have to determine the mode.
In the given set of data, 0 appears 15 times, 1 appears 10 times, 2 appears 6 times, 3 appears 4 times, 4 appears 3 times and 4 appears 2 times.
The value that appears most in a set of data is, 0
The mode of the household pet data is, 0
half of a number (or a number divided by2)
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(I dont really get what you are asking lol)
it costs $100 to rent the bowling alley, plus $4 per person. The cost for any number (n) of people can be found using the expression 100 + 4n. The cost for 15 people equals $ ___. (Input whole number only.)
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Answer:
160
Step-by-step explanation:
100 + 4 (15)
100 + 60
160
if m∠1 = 50, then m∠5 =
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2. angle 1 and angle 5 are corresponding angles [Given]
3..Therefore angle1=angle 5 [ Corresponding angles are =]
4..Therefore angle 5 = 50 degrees [= angles have same measure]
The above assumes that we are talking about corresponding angles of congruent or similar polygons or corresponding angles forme when a transversal intersects two parallel lines
The angle measure of angle 5 is m∠5 = 130 degrees.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given information:
The two lines m and n are parallel lines.
And line l intersects lines m and n.
m∠1 = 50.
angle 1 and angle 3 are opposite angles.
Therefore, m∠1 = m∠3.
Angle 3 and angle 5 represent a pair of supplementary angles.
So,
m∠3 + m∠5 = 180
m∠5 = 180 -50
m∠3 = 130.
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The complete question:
If m∠1 = 50, then m∠5 = ?
The image is given below.
The sum of 19.3 and a number is 30.4. Which equation can be used to solve the problem?
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Answer:
YOUR CORRECT ANSWER'S (B.)Step-by-step explanation:
I TOOK THE TEST.ordering numbers from greatest to least is called putting them in *blank* order
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sorry it took me so long to answer it
i space out a lot due to ADHD lol
i was thinking about slime
yay slime
Express 105 as a mixed number in simplest form. -
4 20
A.5 -
20
1
B.4 -
4
5
C.4 -
20
1
D.5 -
4
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I can’t really understand them sorry
give an example of two principal amounts and two periods of time for which the simple interest turned at 2.42 percent would be equal
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Graph the equation on the coordinate plane.
How would I graph it?
y=12x
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12 on the x axis you stay on the x axis, because you dont have a Y intercept. Then draw a vertical line from the point
What is graph?The graph of a function is the representation in the Cartesian plane of an algebraic expression.
Let us consider the equation y=12x.
x 0 1 2 3
y=12x 0 12 24 36
Now plot the values of (x,y) on the graph.
y=12 x has slope 12 and it does not have y intercept.
So 12 on the x axis you stay on the x axis, because you dont have a Y intercept. Then draw a vertical line from the point
Hence the graph is given in the attachment.
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marcel bought a,new hat for $21.99 and 2 pairs of socks for 3.99 each. what is the total price, including a 7.5% sales tax?
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A can of orange and a chocolate bar cost £1.30 together. Two cans of orange and a chocolate bar cost £2.15 together. How much would three cans of orange and four chocolate bars cost?
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Solving the system of linear equations provided, we find that the cost of a can of orange is £0.85 and a chocolate bar costs £0.45. Therefore, three cans of orange and four chocolate bars would cost £4.35.
The student's question involves solving a system of linear equations to find the individual prices of a can of orange and a chocolate bar. Once the individual prices are determined, the student wants to know the total cost of three cans of orange and four chocolate bars. Here's a step-by-step approach to solve this problem:
Let the price of a can of orange be 'O' and the price of a chocolate bar be 'C'.
The first equation from the given information would be O + C = £1.30.
The second equation would be 2O + C = £2.15.
Subtract the first equation from the second to find the price of an additional can of orange, which gives us O = £0.85.
Substitute the value of O in the first equation to find C, which yields C = £0.45.
Now, calculate the cost of three cans of orange and four chocolate bars: 3O + 4C = 3(£0.85) + 4(£0.45) = £2.55 + £1.80 = £4.35.
So, three cans of orange and four chocolate bars would cost £4.35 together.
Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $275.
Write an equation in the standard form to represent the total rent (y) that Marguerite has to pay for renting the truck for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
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Remember that the equation of a straight line passing through points is ( x_{1} , y_{1} ) and the points ( x_{2} , y_{2} ) is given by
y - y_{1} / x - x_{1} = y - y_{2} / x - x_{2}
Knowing that Marguerite rented a truck at $125 for 2 days, we know if she rents the exact same truck for 5 days, she has to pay a total of $275 for the rent.
This means that the line modeling this situation crosses points at (2, 125) and (5, 275).
The equation modeling the total rent (y) that Marguerite has to pay for renting the truck for x days is given by
y - 125 / x - 2 = 275 - 125 / 5 - 2 = 150 / 3 = 50
But if you are writing the equation in standard form it would be
50x - y = -25
Part B:
When writing the function using function notation it means you are making y the subject of the formula and then replacing the y with f(x).
If you remember that from part A, we have that the equation for the total rent which is y that Marguerite has to pay for renting the truck for x amount of days is given by
y = 50x + 25.
Writing the equation using the function notation would give us this
f(x) = 50x + 25
Part C:
To graph the function, we name the x-axis the number of days and name the y-axis total rent. The x-axis is numbered using the intervals of 1 while the y-axis is numbered using the intervals of 50.
The points of (2,125) and of (5,275) are marked on the coordinate axis and a straight line is drawn to pass through these two points.
Answer:
Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $275.
Write an equation in the standard form to represent the total rent (y) that Marguerite has to pay for renting the truck for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
(10 points)
Step-by-step explanation:
Loudness, or the intensity of sound, is measured in decibels. The sound level of a television is about 70 decibels, which is considered a safe hearing level. A food blender runs at 20 decibels higher than a TV, and a jet engine's decibel reading is 40 less than twice that of a blender. At this level, exposure can cause hearing loss. Find the intensity of the sound of a jet engine.
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The number of students is 7 more than 5 times the number of teachers. There are 12 teachers. How many students are there?
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12 x 5 = 60
And since it says there are 7 more than 5 times the amount we need to add 7 to 60 which would be 67.
So, there are 67 students :D
Divide. 5/6÷ −2/3 please help asap
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5/6 x (-3/2)
-15/12
-5/4 is your answer
hope this helps
Hope this answer is correct ☺
Certain clouds form when temperatures fall below minus−64°C. What is this temperature in degrees Fahrenheit?
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-64 Celsius =
-64 * 9/5 + 32 = minus 83.2 degrees Fahrenheit
Clouds form when temperatures drop below -64°C.
To convert temperatures from Fahrenheit to Celsius, subtract 32, multiply by 5, and divide by 9. -64°C is equal to -83.2°F, the temperature at which certain clouds form.
To convert from Fahrenheit to Celsius:
Subtract 32 from the Fahrenheit temperature.Multiply the result by 5.Divide by 9 to get the temperature in Celsius.For this specific question:
Minus 64°C is equal to -83.2°F.
Clouds form when temperatures drop below -64°C.
What is the LCD of the fractions 1/3 and 11/15
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The LCD of the fractions [tex]\frac{1}{3} ,\frac{11}{15}[/tex] is 15
What is fraction?"It is a part of a whole number and a way to split up a number into equal parts."
What is LCD of the fractions?"The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions."
For given question,
We have been given two fractions [tex]\frac{1}{3} ,\frac{11}{15}[/tex]
We need to find the least common denominator of [tex]\frac{1}{3} ,\frac{11}{15}[/tex]
The denominator of fraction [tex]\frac{1}{3}[/tex] is 3.
and the denominator of fraction [tex]\frac{11}{15}[/tex] is 15.
Multiples of 3 are 3, 6, 9, 12, 15, 18,...
Multiples of 15 are 15, 30, 45,...
The least common multiple of 3 and 15 is 15.
Therefore, the LCD of the fractions [tex]\frac{1}{3} ,\frac{11}{15}[/tex] is 15
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what is fourteen thousand and two hundred eight thousandths in standard form?
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The standard form of fourteen thousand and two hundred eight thousandths is 1.4208 x 10⁴.
What is a standard form of the number?Standard form refers to any number that can be written as a decimal number between 1.0 and 10.0 multiplied by a power of ten. 1.23 108; If you look closely, 1.23 is a decimal number between 1.0 and 10.0, so the standard form of 123,000,000 is 1.23 108.
Given that the number is fourteen thousand and two hundred eight thousandths.
The standard form of the number will be written as,
14208 = 1.4208 x 10⁴
The standard form is 1.4208 x 10⁴.
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Graph the inequality: –2(y – 2) < 2(y – 4)
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y>3y>3 is your answer for that problem.
Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)} (F - G) (6) =
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G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
F(6) = 8
G(6) = 9
so
(F - G) (6) = 8 - 9 = -1
Answer:
The value of (F-G)(6) is -1.
Step-by-step explanation:
The given functions are defined as
[tex]F = \{(0, 1), (2, 4), (4, 6), (6, 8)\}[/tex]
[tex]G = \{(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)\}[/tex]
We need to find the value of (F-G)(6).
Using subtraction of two function property, we get
[tex](F-G)(6)=F(6)-G(6)[/tex] .... (1)
From the given functions it is cleared that the value of function F is 8 at x=6 and the value of function G is 9 at x=6. It means
[tex]F(6)=8[/tex]
[tex]G(6)=9[/tex]
Substitute F(6)=8 and G(6)=9 in equation (1).
[tex](F-G)(6)=8-9[/tex]
[tex](F-G)(6)=-1[/tex]
Therefore the value of (F-G)(6) is -1.
Jill’s front door is 42” wide and 84” tall. She purchased a circular table that is 96 inches in diameter. Will the table fit through the front door?
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Simplify the product. 8x2(4x2 + 4y6)
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Answer:
32x^4+32x^2y^6
Step-by-step explanation:
The root symbol was forgotten in the provided question. It should look like this:
Simplify the product. 8x^2(4x^2 + 4y^6)
3y + 5z + 8y - 3z
A: 11y + 5z
B: 14y + 2z
C: 14y + 8z
D: 16yz
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[tex]3y + 5z + 8y - 3z = (3y + 8y) + (5z - 3z) = 11y + 2z[/tex]
So you would choose A confidently
solve for the variable k.
m/k=x
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m = xk <==
The equation m/k = x solved for k will be k = m / x.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
m/k = x
Simplify the equation for k, then we have
x = m / k
kx = m
k = m / x
The equation m/k = x solved for k will be k = m / x.
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A building is 1 ft from a 12-ft fence that surrounds the property. A worker wants to wash a window in the building 1515 ft from the ground.ground. He plans to place a ladder over the fence so it rsts against the building. (See the figure.) He decides he should place the ladder 9 ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need?
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Using the Pythagorean Theorem for the given right triangle, we calculated that the worker would need a ladder of at least 25 feet in length to reach the window.
Explanation:The problem described can be solved by using the Pythagorean Theorem, which is appropriate for any right triangle. In the given problem, we have a right triangle - one side is the distance from the fence to where the ladder touches the building (12ft + 1ft + 9ft = 22ft), the other side is the height of the window from the ground (15ft), and the hypotenuse is the length of the ladder we need to find.
According to the Pythagorean theorem: [tex]A^2 + B^2 = C^2[/tex]. If we plug in our values, it would look like [tex]15^2 + 22^2 = C^2[/tex]. After carrying out the operations, we find that C^2 = 625.
To find the length of the ladder (C), we take the square root of 625, which is 25ft. So, the worker needs a ladder that is at least 25 feet long.
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There are two sizes of trucks available: larger truck with a 2.5-ton payload, and smaller trucks with 1.5-ton payload. To unload a freight train 21 larger trucks are needed . How many smaller trucks would be needed for the same job?
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Answer:
35 smaller trucks.
Step-by-step explanation:
Given:
i) The larger truck with a 2.5-ton payload, and smaller trucks with 1.5-ton payload.
ii) To unload a freight train 21 larger trucks are needed .
Total load of the freight train = 21 times 2.5 tons
= 21 × 2.5
= 52.5 tons
To find the number of small trucks needed, we need to divide 52.5 by 1.5
= 52.5 ÷ 1.5
= 35 small trucks needed.
So, to unload the freight, we need 35 smaller trucks.
To convert 5 square meters to square yards, multiply 5 by 1.196
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This equation is true/correct.
Daniel is completing a home project. He needs 13 pieces of wood, each 1 1/2 feet long, to complete the project. How much wood does Daniel need to complete his home project?
8 2/3 ft
11 1/2 ft
14 1/2 ft
19 1/2 ft
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Answer:
Daniel will need [tex]19\frac{1}{2}[/tex] feet wood to complete his home project.
Step-by-step explanation:
We are told that Daniel needs 13 pieces of wood, each [tex]1\frac{1}{2}[/tex] feet long, to complete his home project.
To find total amount of wood needed we will multiply number of wood pieces by length of each wooden piece.
First of all we will convert our mixed fraction to improper fraction as: [tex]1 \frac{1}{2} =\frac{3}{2}[/tex]
Now let us multiply our values.
[tex]13*\frac{3}{2} =\frac{39}{2}[/tex]
Now we will convert this improper fraction to mixed fraction to find our final answer.
[tex]\frac{39}{2}=19\frac{1}{2}[/tex]
Therefore, Daniel needs [tex]19\frac{1}{2}[/tex] feet wood to complete his home project.
If you're currently making $8.75 per hour and you're offered a new job that pays $9.47 per hour, how much more would you make per hour at the new job?