The connection between 1 mL and 1 cm3 is useful to know because they are equivalent in volume. This means that 1 mL of a substance occupies the same amount of space as 1 cm3 of the same substance.
What is the volume?Knowing this connection can simplify calculations involving volume measurements and make them easier to convert between the two units.
To displace 1 L of water, you would need to use 1000 cubic centimetres of water. This is because 1 L is equivalent to 1000 mL, and since 1 mL is equivalent to 1 cm3, then 1000 mL (or 1 L) is equivalent to 1000 cm3.
A 1 m3 object would displace 1000 L of water. This is because 1 m3 is equivalent to 1000 L, and when an object is submerged in water, it displaces the same amount of water as its own volume.
It's not possible to determine the area of the base of the prism based solely on the information provided. The number of linking cubes only tells us the volume of the prism, not the shape or size of the base.
To find the area of the prism's base, we can use the formula:
Base Area = Volume / Height
Therefore, a) Base Area = 51 cm3 / 3 cm = 17 cm2
b) Since the height is negative, it doesn't make sense to find the area of the base in this case.
c) Base Area = 375 cm3 / 4 cm = 93.75 cm2
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Guys please helppppppppppppppppppppppppppppp
Answer:
the 2nd one is the answer
Answer:
the second one is the answer is correct
Jewel completed 12 out of 20 of her homework questions last night. What percent did she complete?
Answer:
60%
Step-by-step explanation:
12/20 = 3/5 = 0.6 = 60%
Hey there! To find out how much of her homework Jewel completed, all we need to do is a little math. First, let's divide the number of questions she did by the total number of questions. That's 12 divided by 20 which equals 0.6.
Now, we just need to turn that decimal into a percentage. To do that, we simply multiply 0.6 by 100, which gives us 60. And voila! Jewel completed 60% of her homework.
Use the quadratic formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a, to solve the equation 2x2 + 10x − 6 = 0. Round to the nearest hundredths place.
x = −5.54 and x = 0.54
x = −0.54 and x = 5.54
x = −4.30 and x = −0.70
x = −22.17 and x = 2.17
Using the quadratic formula we can see that the correct option is the first one:
x = −5.54 and x = 0.54
How to find the solution of the quadratic equation?Here we want to solve the quadratic equation:
2x² + 10x - 6 = 0
To solve it, we need to use the quadratic formula, the solutions for x will be:
\(x = \frac{-10 \pm \sqrt{10^2 - 4*2*-6} }{2*2} \\\\x = \frac{-10 \pm 12.2}{4}\)
then the two solutions of the quadratic equations are:
x = (-10 + 12.2)/4 = 0.55
x = (-10 - 12.2)/4 = -5.55
Then the correct option (by approximation) is the first one, where the difference in the last digit is due to rounding.
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You deposit $5000 in an account earning 5% interest compounded continuously. How much will you have in the account in 5 years? Round to the nearest cent.
Decide whether the rates are equivalent. Maria saves $50 in 4 months.
Ralph saves $60 in 5 months
Answer:
The rates are not equivalent since Maria saves $0.50 more per month than Ralph.
Step-by-step explanation:
We can determine if two rates are equivalent by comparing the rates at which they save per month.
Maria's savings per month:
Both 50 and 4 can be divided by 2, which gives us 25/2. As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.
Ralph's savings per month:
Both 60 and 5 can be divided by 5, which gives us 12. Thus, Ralph saves $12 per month.
Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.
Does anyone know this answer??
Approximately 99.7% of scores lie in the shaded region.
We have,
The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.
According to this rule:
Approximately 68% of scores lie within 1 standard deviation of the mean.
Approximately 95% of scores lie within 2 standard deviations of the mean.
Approximately 99.7% of scores lie within 3 standard deviations of the mean.
Now,
In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.
This encompasses the area within 3 standard deviations of the mean.
And,
Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.
Therefore,
Approximately 99.7% of scores lie in the shaded region.
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(x-2x³-29x² - 43x+8)÷(x-7)
Answer:
-2x^2 - 43x - 343 - 2393/x-7
Shania
Determine the value of x if the two lines are parallel.
5x+15 7
1. (1,-1) parallel to y=2/5x-3
2. (-3,1) perpendicular to y= -2/5x - 4
STEP BY STEP PLEASE
The answers are :
1. The equation of line parallel to y = \(\frac{2}{5}\) x - 3 will be y = \(\frac{2}{5}\) x - \(\frac{7}{5}\) .
2. The equation of line perpendicular to y = - \(\frac{2}{5}\) x - 4 will be y = \(\frac{5}{2}\) x + \(\frac{13}{2}\) .
What is the slope intercept form of a line ?
The equation of line that can be written as y = mx + c, where m is the slope and c is the line's y-intercept, is known as a slope intercept form.
1.
It is given that equation is : y = 2/5x - 3.
So , the slope here is 2/5 and a parallel line will have the same slope.
We know that the slope intercept form of a line is :
y = mx + c
Put , slope(m) = 2/5 in above equation.
Given , (1,-1) i.e., x = 1 and y = -1
Now we substitute these values to find value of c.
-1 = 2/5(1) + c
-1 = 2/5 + c
-1 - 2/5 = c
(-5 - 2)/5 = c
-7/5 = c
Putting m = 2/5 and c = -7/5 , we get :
So, the equation of parallel line is :
y = \(\frac{2}{5}\) x - \(\frac{7}{5}\)
2.
We know that the product of the slope of two perpendicular lines is -1.
Given that equation is : y = -2/5x - 4 i.e., slope = -2/5
So , slope of a line perpendicular to this line is -1/(-2/5) = 5/2
And this line passes through the point (-3,1).
Equation of a line that passes through a point (x1 , y1) and slope (m) is :
(y-y1) = m (x-x1)
Here ;
x1 = -3 , y1 = 1 and m = 5/2
So , the equation of perpendicular line will be :
(y - 1) = \(\frac{5}{2}\) (x - (-3))
(y - 1) = \(\frac{5}{2}\) (x + 3)
y - 1 = \(\frac{5}{2}\) x + \(\frac{15}{2}\)
y = \(\frac{5}{2}\) x + \(\frac{15}{2}\) + 1
y = \(\frac{5}{2}\) x + \(\frac{13}{2}\)
Therefore , the answers are :
1. The equation of line parallel to y = \(\frac{2}{5}\) x - 3 will be y = \(\frac{2}{5}\) x - \(\frac{7}{5}\) .
2. The equation of line perpendicular to y = - \(\frac{2}{5}\) x - 4 will be y = \(\frac{5}{2}\) x + \(\frac{13}{2}\) .
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Please help with this question asap
Answer:
36/5
Step-by-step explanation:
Did it in my head, hopefully its correct
City there are 244,000 48-year-olds. Based on the table below howmany are not expected to be alive in a year?
SOLUTION:
Case: Number of deaths
Method:
First, we add the total number of deaths
\(\begin{gathered} 63+79+91+99+103+106+110+113+115+117+118+120+123+127+132+315+341+371+405+443 \\ =3491 \end{gathered}\)Next, we subtract from the total number of people alive
\(\begin{gathered} 2000000-3491 \\ =1996509 \end{gathered}\)If there were 244,000 48-year olds,
The scale factor will be:
\(\begin{gathered} =\frac{244000}{100000} \\ =2.44 \end{gathered}\)Hence the number of people expected NOT to be alive is:
\(\begin{gathered} 3491\times2.44 \\ =8518.04 \end{gathered}\)Final answer:
8519 people approximately
\(22y = 11(3 + y)\)I need help with my homework cause I'm sorta slow
Given the expression:
\(22y=11(3+y)\)First we need to get rid of the parenthesis by multiplying 11 by 3 and by y:
\(\begin{gathered} 22y=11(3+y) \\ \Rightarrow22y=33+11y \end{gathered}\)Now we solve for y:
\(\begin{gathered} 22y=33+11y \\ \Rightarrow22y-11y=33 \\ \Rightarrow11y=33y \\ \Rightarrow y=\frac{33}{11}=3 \\ y=3 \end{gathered}\)Therefore, y=3
a number has the digits 2, 5, and 4. To the nearest 100, the number rounds to 200. What is the number?
Answer:
245
Step-by-step explanation:
if you're rounding to the nearest 100, 245 would be the only one that would round to 200. if it were 250 or above, it would round to 300, so 245 is the only one that would round to 200 because 245 is less than 250
Find the solution(s) for the equation below: |3x – 2| - 5 = -1
A.no solution
B.x = 2
C.x = 4/3 or x = 2
D.x = -2/3 or x = 2
Answer:
It would be D.x = -2/3 or x =2
Answer:
B
Step-by-step explanation:
(3x-2) - 5 = -1
⇒(3x-2)-4=0
⇒3x-6=0
⇒3x=6
⇒x=6/3
⇒x=2
Round 5.165 to 4 decimal places
Answer:
5.17
Step-by-step explanation:
Hello, I need help graphing with y = x+4,
Multiply 3 1/3 x 1 1/7
write the answer in simplest form.
Equipment was acquired on January 1, 2018 at a cost of $77,100. The equipment was originally estimated to have a salvage value of $5,370 and an estimated life of 10 years. Depreciation has been recorded through December 31, 2021 using the straight-line method. On January 1, 2022, the estimated salvage value was revised to $7,420 and the useful life was revised to a total of 9 years.
Determine the depreciation expense for 2022. (Round answer to 0 decimal place, e.g. 1500)
the depreciation expense for 2022 is $4,968. By solving with New annual depreciation expense = (Book value - Revised salvage value) / Revised useful life
How to determine the depreciation expense?
To determine the depreciation expense for 2022, we need to first calculate the book value of the equipment as of January 1, 2022.
Book value as of January 1, 2022 = Cost of equipment - Accumulated depreciation
Accumulated depreciation as of December 31, 2021 = (Cost of equipment - Salvage value) / Useful life x Number of years depreciated
Accumulated depreciation as of December 31, 2021 = ($77,100 - $5,370) / 10 x 4 = $25,956
Book value as of January 1, 2022 = $77,100 - $25,956 = $51,144
Next, we need to determine the new annual depreciation expense based on the revised estimated salvage value and useful life.
New annual depreciation expense = (Book value - Revised salvage value) / Revised useful life
New annual depreciation expense = ($51,144 - $7,420) / 9 = $4,968
Therefore, the depreciation expense for 2022 is $4,968.
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Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
The complete question is attached in the diagram.
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Which of the four is it?
Answer:
option 1 i believe
Step-by-step explanation:
just worked it out
i hope this is right and helps <3
A local city park rents kayaks for $3.75 per hour. If a customer rents for four or more hours, the cost is only $3.25 per hour, plus a $5 processing fee. If C(x) represents the total cost and x represents the number of rental hours, which of the following functions best models this scenario?
C of x equals 3.75 times x if x is less than 6 and 3.25 plus 5x if x is greater than 6.
C of x equals 3.75 times x if x is less than or equal to 5 and 3.25x minus 5 if x is greater than 6.
C of x equals 3.75 times x if x is less than 6 and 3.25x plus 5 if x is greater than or equal to 6.
C of x equals 3.75 times x if x is less than 5 and 3.25x minus 5 if x is greater than or equal to 6.
The function that best models this scenario is C of x equals 3.75 times x if x is less than 5 and 3.25x plus 5 if x is greater than 6.
How to calculate the value?Let the number of hours be illustrated as x. In this situation, local city park rents kayaks for $3.75 per hour. This will be:
= 3.75 × x
= 3.75x
Also, customer rents for four or more hours, the cost is only $3.25 per hour, plus a $5 processing fee. This will be illustrated as:
= 5 + (3.25 × x)
= 5 + 3.25x
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Angle X = 45° and Angle Y = 45°. Find the measure of angle Z.
Answer:
90°
Step-by-step explanation:
sum of angle in triangle =180
Angle X +Angle Y +Angle Z =180
45 + 45 + Angle Z =180
Angle Z =180-(45+45)
Angle Z = 90°
Keeyn has a bag of Joly Ranchers. Keevyn gaveof the bag to Zavion and of the bag to Qeisha
Then Keewyn gave of the remaining candy to hes favorite teacher, Mr. Won How much of the tota
candy bag did Keevyn give to Mr. Wonk?
Answer:
Half maybe?
sorry it would have been easier if it told us how much exactly
How many hours will it take to complete a 45-km bike ride if you go 12km per hour the whole time?
Answer:
3.75 hours
Step-by-step explanation:
d = rt
where d is the distance, r is the rate and t is the time
45 = 12 t
Divide each side by 12
45/12 = t
3.75 hours = t
12.) Given the following information, determine which lines, if any, are parallel. State the converse that justifies your answer. Pleaseee helppp
Answer:
Step-by-step explanation:
Given Parallel lines Converse
a. ∠13 ≅ ∠17 a║c Corresponding angles
b. ∠4 ≅ ∠9 d║e Exterior alternate angles
c. m∠20 + m∠21 = 180° a║b Consecutive interior angles
d. ∠8 ≅ ∠19 Vertical angles
e. ∠10 ≅ ∠23 b║c Interior alternate angles
f. m∠14 + m∠17 = 180° a║c Consecutive interior angles
From the given diagram and information, it can be concluded that lines a, b, and c are parallel, and lines d and e are parallel.
The given lines in the diagram are a, b, c, d, and e.
a. It is given that the measure of angle 13 is equal to that of angle 17.
Now, these two angles are made by lines a, c, and d. Now, the angles are corresponding and equal, and hence, lines a and c will be parallel.
b. It is given that the measure of angle 4 is equal to that of angle 9.
These two angles are made by lines d, e, and b. Now, the angles are alternate exterior and equal, and hence, lines d and e will be parallel.
c. It is given that the sum of the measure of angles 20 and 21 is equal to 180 degrees.
These two angles are made by lines a, b, and e. Now, the angles are supplementary and their sum is 180 degrees, and hence, lines a and b will be parallel.
d. It is given that the measure of angle 8 is equal to that of angle 19.
These two angles are vertically opposite angles between lines a and e.
e. It is given that the measure of angle 10 is equal to that of angle 23.
These two angles are made by lines b, c, and e. Now, the angles are alternate interior and equal, and hence, lines b and c will be parallel.
f. It is given that the sum of the measure of angles 14 and 17 is equal to 180 degrees.
These two angles are made by lines a, c, and d. Now, the angles are supplementary and their sum is 180 degrees, and hence, lines a and c will be parallel.
Therefore, it can be concluded that lines a, b, and c are parallel, and the lines d and e are parallel.
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As the CAPS document outlines, the Content Specification and Content Clarification for Patterns, Functions, and Algebra shows sequenced mathematics content topics and a content area spread. In the Intermediate Phase, select one topic and report on the topic sequence and content area spread. Your report should demonstrate mathematics concepts and procedures’ hierarchical and logical progression.
Answer:
Step-by-step explanation:
In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."
The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:
Introduction to Variables and Expressions:
Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.
Solving One-Step Equations:
Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.
Solving Two-Step Equations:
Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.
Writing and Graphing Linear Equations:
Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.
Systems of Linear Equations:
Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.
Word Problems and Applications:
Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.
The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.
By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.
The sets of ordered pairs below represent the cost to fix a plumbing issue based on the number of hours. The first coordinate represents the hours and the second coordinate the cost.
We can say that after answering the offered question For instance, if equation fixing a plumbing problem takes an hour, the cost would be $75. If the repair takes two hours, it will cost $125, and so on.
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
{(1, 75), (2, 125), (3, 175), (4, 225), (5, 275)}
The cost to repair a plumbing issue based on the number of hours is represented by these sets of ordered pairs. For instance, if fixing a plumbing problem takes an hour, the cost would be $75. If the repair takes two hours, it will cost $125, and so on.
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Without graphing, determine how many x-intercepts the function has.
y=3x^2 + 3x +4
y = 2x^2 + 3x + 3 has 0 x intercepts
y = 3x^2 + 3x + 4 has 0 x intercepts
Solve the following system of equations. 4x + 3y = -5
- 3x + 7y=13
Answer: 13
Step-by-step explanation:
4x+3y=-5 solve x :
4x = -3y + -5 | -3y
1x = -0.75y + -1.25 | : 4
-3x + 7y = 13 solve x :
-3x + 7y = 13 | -7y
-3x = -7y = 13 | : (-3)
Equalization Method Solution: -0.75y+-1.25=2.333y+-4.333
-0, 75y - 1,25 = 2,333y - 4, 333 solve y:
-0, 75y - 1,25 = 2,333y -4, 333 | -2,333y
-3, 083y - 1,25 = -4,333 | + 1, 25
-3. 083y = -3,088 | : (-3, 083)
y = 1
Plug y = 1 into the equation 4x + 3y = -5 :
4x + 3 · 1 | Multiply 3 with 1
4x + 3 = -5 | -3
4x = -8 | : 4
x = -2
So the solution is:
y = 1, x = -2
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Solve each equation for x. If your answer is a decimal, found your the nearest hundredth.
Given:
Equation is
\(3^{x+3}+4=85\)Required:
Solve equation for x.
Explanation:
We will use here
\(\begin{gathered} a^b=a^c \\ b=c \end{gathered}\)Now,
\(\begin{gathered} 3^{x+3}+4=85 \\ 3^{x+3}=81 \\ 3^x=27 \\ 3^x=3^3 \\ x=3 \end{gathered}\)Answer:
Hence, the value of x = 3.