Answer:
Part a) The estimate amount of medicine is 30.0 grams
Part b) The actual amount of medicine is 29.925 g. The difference between the estimate and the actual amount, is 0.075 g
Part c) 5.985 grams
Part d) 6 grams
Step-by-step explanation:
The complete question is
Dr. Mann mixed 10.357 g of chemical A, 12.062 g of chemical B, and 7.506 g of chemical C to make 5 doses of medicine.
a. About how much medicine did he make in grams? Estimate the amount of each chemical by rounding to the nearest tenth of a gram before finding the sum. Show all your thinking.
b. Find the actual amount of medicine mixed by Dr. Mann. What is the difference between your estimate and the actual amount?
c. How many grams are in one dose of medicine? Explain your strategy for solving this problem.
d. Round the weight of one dose to the nearest gram
Part a) round to the nearest tenth of a gram first
Chemical A
10.357 g -----> 10.4 g
Chemical B
12.062 g -----> 12.1 g
Chemical C
7.506 g -----> 7.5 g
To find out the estimate amount of medicine sum the three values
10.4+12.1+7.1=30.0 g
therefore
The estimate amount of medicine is 30.0 grams
Part b)
The actual amount of medicine is
10.357+12.052+7.506=29.925 g
To find out the difference between your estimate and the actual amount, subtract the actual amount from the estimate
30.0-29.925=0.075 g
Part c) To find out how many grams are in one dose of medicine, divide the actual amount of medicine by five
29.925 g/5=5.985 g
Part d) Round the weight of one dose to the nearest gram
we have
5.985 g ------> 6 g
Can someone explain to me what is n? I was very confused about this problem and my teacher didn’t review it in class! (Don’t mind the answer choice that appears on the document)
Answer:
n = 5
Step-by-step explanation:
5 * (n/5) = 5 / (n/5)
(5 * n) /5 = 5 * (5/n)
n = ( 5*5) / n
n = 25/n
n² = 25
n = 5
Two children are selling lemonade they are charging 1$ for a cup they only sell 10 cups
Answer:
Well this isn't a grammatically correct question but if you're asking how they would split the money it would be $5 for each person.
Step-by-step explanation:
1. The 10 people buy the cups of Lemonade.
2. One cup of lemonade is $1, so that means 10 cups would be $10.
3. Then you would give half to your friend which would be $5.
Use function notation to represent how much the volume of the box (in cubic inches) changes by if the cutout length increases from 0.3 inches to 1.2 inches.
To calculate the change in volume of a box when cutout length increases from 0.3 inches to 1.2 inches using function notation, use the formula ΔV=f(l2)-f(l1), where f(l) represents the volume of the box given the length of the edge.
Explanation:The change in volume when the cutout length increases from 0.3 inches to 1.2 inches can be represented in function notation as ΔV=f(l2)-f(l1), where f(l) represents the volume of the box as a function of the length (l) of the edge. Here, l1=0.3 and l2=1.2.
Given the formula for the volume of the box V = Length x Width x Height. Let's assume Width and Height remain constant. If initially the volume was V1=f(l1) and finally it became V2=f(l2), the change in volume will be ΔV=V2-V1 which equals f(l2)-f(l1).
For example, if the width and height of the box are 6 inches and 3 inches respectively, then the initial volume is V1 = 0.3 x 6 x 3 cubic inches and the final volume is V2 = 1.2 x 6 x 3 cubic inches. Therefore, ΔV = (1.2 x 6 x 3) - (0.3 x 6 x 3) cubic inches.
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The change in the volume of the box when the cutout length increases from 0.3 inches to 1.2 inches can be calculated using the function ΔV = V(1.2) - V(0.3). Assuming the rest of the box's dimensions are constant, this results in a change in volume of 16.2 cubic inches.
To use function notation to represent how the volume of the box changes by if the cutout length increases from 0.3 inches to 1.2 inches, let us first define a function V(l) that represents the volume of the box as a function of the cutout length 'l'. If the initial cutout length is 0.3 inches and the final cutout is 1.2 inches, the change in length Δl would be 1.2 inches - 0.3 inches = 0.9 inches. We can express the change in volume, ΔV, as the function of the change in cutout length as follows: ΔV = V(1.2) - V(0.3).
Given that the volume of a rectangular box can be calculated by the formula volume = length × width × height, and assuming other dimensions of the box do not change, the function V(l) becomes:
V(l) = length × width × l
Let's consider an example where the dimensions of the box remain constant at 6 inches by 3 inches. The volume function would then be:
V(l) = 6 in. × 3 in. × l in.
The change in volume for an increase in cutout from 0.3 to 1.2 inches is then:
ΔV = V(1.2) - V(0.3) = (6 × 3 × 1.2) - (6 × 3 × 0.3) = 21.6 in.³ - 5.4 in.³ = 16.2 in.³.
f+13/4=4 solve for f
Answer:
f= .75 or 3/4
Step-by-step explanation:
13/4 = 3 1/4 or 3.25
4-3.25= .75
Or
3/4
Answer:
f = 3/4
Step-by-step explanation:
f+(13/4)= 4
subtract (13/4) from both sides
⇒f + (13/4)- (13/4) = 4 -(13/4)
⇒f =(16-13) /4
∴f = 3/4
Lucas and Brianna read three books each last month. a.
b.
Which of the tables, if any, shows a proportional relationship?
Both Lucas and Brianna had specific reading goals they needed to accomplish. What different strategies did
each person employ in reaching those goals?
Answer:
Please read the answer to Parts A and B below.
Correct statement, question and data:
Lucas and Brianna read three books each last month. The table shows the number of pages in each book and the length of time it took to read the entire book.
Pages Lucas Read 208 156 234
Time (hours) 8 6 9
Pages Brianna Read 168 120 348
Time (hours) 6 4 12
a. How many observations can you make about any similarities or difference that exist between the reading rates of the two students.
b. Both Lucas and Brianna had specific reading goals they needed to accomplish. What different strategies did each person employ in reaching those goals?
Source:
Grade 7, Module 1 - Student material of New York State
Step-by-step explanation:
Part A.
We notice that Lucas read at a constant reading rate of 26 pages per hour and he read for a total of 23 hours. On the other hand, Brianna, does not follow a constant reading rate, she read the first book at a rate of 28 pages per hour, the second at a rate of 30 pages per hour and the third book at a rate of 29 pages per hour, adding up to 22 hours.
Part B.
Lucas followed at a constant rate of 26 pages per hour and Brianna was not constant but she reads faster than Lucas with an average rate of 29 pages per hour (636 pages in 22 hours).
Determine the unit rate
Answer:
52.50/5.8= $9 per hour
What is the solution to this equation
x-4=17
Answer:
21
Step-by-step explanation:
x-4=17
x=17+4
x=21
that's the solution
What Is
-(v-1)=-6v+16
Answer:
[tex]v = 3[/tex]
Step-by-step explanation:
-(v-1)=-6v+16
-v+1=-6v+16
grouping like terms
-v+6v=16-1
5v=15
dividing through by 5
[tex] \frac{5v}{5} = \frac{15}{5} [/tex]
[tex]v = \frac{15}{5} [/tex]
[tex]v = 3[/tex]
-2.4 divided by 5 1/3
Answer:
[tex]-0.45[/tex]
Step-by-step explanation:
Factor the numerator and denominator and cancel the common factors. you'll get your answer as [tex]-\frac{9}{20}=-0.45[/tex]
How do I answer this question I don’t understand it
Answer:
4. Tell your interviewer what you do know.
If you do have some knowledge of the question, then take the time to tell your interviewer what you do know of the situation. Saying everything out loud can start you on the process of figuring out the problem.
Step-by-step explanation:
Answer:
[tex] u = -\dfrac{vx}{w} [/tex]
Step-by-step explanation:
You are allowed to multiply and divide both sides of an equation by the same non-zero number or non-zero variable. Do the appropriate operations to isolate the u.
[tex] x = -\dfrac{1}{v}uw [/tex]
We are solving for u, so first, switch sides.
[tex] -\dfrac{1}{v}uw = x [/tex]
Multiply both sides by v.
[tex] -\dfrac{1}{v}uw \times v = x \times v [/tex]
[tex] -uw = x \times v [/tex]
Divide both sides by -w.
[tex] \dfrac{-uw}{-w} = \dfrac{xv}{-w} [/tex]
[tex] u = -\dfrac{vx}{w} [/tex]
what is 7765 to the nearest hundred
Answer:
7800
add 1 to the tens place as grater than 5
7765 rounded to the nearest hundred would be 7800
40pts! Completely factor this quadratic expression: 4x^2+12x-72
Answer:
=4(x−3)(x+6)
Step-by-step explanation:
4x^2+12x-72
=4(x−3)(x+6)
The factorized form of the equation 4x² + 12x - 72 is
A = 4 ( x + 6 ) ( x - 3 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be A = 4x² + 12x - 72
Now , the equation can be simplified by
A = 4 ( x² + 3x - 18 )
Now , on simplifying the equation , we get
A = 4 ( x² - 3x + 6x - 18 )
Now , on grouping the similar terms in the equation , we get
A = 4 ( x ( x - 3 ) + 6 ( x - 3 ) )
A = 4 ( x + 6 ) ( x - 3 )
So , the factorized form of the equation is
A = 4 ( x + 6 ) ( x - 3 )
Hence , The factorized form of the equation 4x² + 12x - 72 is
A = 4 ( x + 6 ) ( x - 3 )
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Evaluate
2^-2 •(12•3) - 5^3
Answer:
The answer to your question is: -116
Step-by-step explanation:
2⁻²(12 x 3) - 5³
= 1 /2² (36) - 125
= 1/4 (36) -125
= 36/ 4 -125
= 9 - 125
= - 116
6x4=8xN
how do i solve this equation
Answer:
whats equivelent to 6x4?
Step-by-step explanation:
6 x 4 = 24
8 x 2 = 16 so 8 x 3 = 24 because 8 x 4 would be
8 x 2 = 16
16 x 2 =
6 + 6 = 12
carry the one.
2
1 + 1 + 1 (We now have three ones from carrying that 1) and our answer is
32.
So N = 3
Answer:
6x4=8xN N=8x3
Step-by-step explanation: N=8x3 because 6x4=24 so if you multiply 8x3 it =
24
$546,322 is greater than less than or equal to 540997
Answer:
greater than
Step-by-step explanation:
it is largee
Answer: greater then
Step-by-step explanation:
cause 546 is greater then 540
the sum of two numbers is 45 and its difference is 5
Final answer:
The student's question can be solved by setting up a system of equations from the given information and finding that the two numbers are 25 and 20.
Explanation:
Solution to the Given Problem
The student's question involves solving a system of equations. They are given that the sum of two numbers is 45 and their difference is 5. To solve this, we can set up two equations based on the information given:
Let the two numbers be x and y.
The sum of the two numbers is 45: x + y = 45
The difference of the two numbers is 5: x - y = 5
To find the values of x and y, we can solve this system of equations. By adding the two equations, we cancel out y, giving us:
2x = 50
Dividing both sides by 2, we find that x = 25. Substituting x = 25 into one of the original equations, for instance, x + y = 45, we get:
25 + y = 45
Subtracting 25 from both sides gives us y = 20.
Therefore, the two numbers are 25 and 20.
which of these is the third step in an addition problem
Answer:
solving
Step-by-step explanation:
Write the number with the lest value using the digit 1 through 9. Use each digit 1 through 9.use each digit only once. Please it do tomorrow I need help please
Answer:The number should be 123456789.
Step-by-step explanation:
The total digits should be 9 i.e. 1, 2, 3, 4,5, 6,7, 8, and 9.
The largest number should be at the unit place, the 2nd largest number should be at the tenth place, and the 3rd largest number should be at the 100th place, and so on.
So in this way, the 1 number should be written at the left-most position.
Therefore we can conclude that The number should be 123456789.
help please!(picture)
Answer:
7a - 2
Step-by-step explanation:
A perimeter is just the sum of all sides added together, so just put all the expressions together into a big equation.
2a - 3 + 2a + 3a + 1
Combine like terms
7a - 2
Find how many yard are in 1 mild. A mile is 5280 feet, a yard is 3 feet
Answer: 1760
Step-by-step explanation:
[tex]\dfrac{5280\ feet}{1\ mile}\times \dfrac{1\ yard}{3\ feet}\quad =\dfrac{5280\ yard}{3\ feet}\quad =\large\boxed{1760\ yard\ per\ mile}[/tex]
Roses are red
Violets are blue
u probably wont get this question right
but i trust u
question-
make 3/8 into a decimal
What is the equation that is parallel to the equation
-9x + 3y = 8 and crosses through the point (14, 2)?
5(x+2)-7=5(x-3) ??? Thanks!
Step-by-step explanation:
5(x+2)-7=5(x-3)
5x + 10 -7 = 5x -15
5x - 5x ..... this question must have an error
Answer:
Undefined
Step-by-step explanation:
5(x+2)-7=5x-3
5x+10-7=5x-3
5x+3=5x-3
5x=5x
can't solve, so it is undefined.
What’s 3/8×1/9 in the simplest form
Answer:
1/24
Step-by-step explanation:
First, multiply the two fractions together.
3/8 * 1/9
Multiply the numerators:
3*1=3
And the denominators:
8*9=72
So, the fraction ends up being 3/72.
I need simplify the fraction by dividing both the numerator and the denominator by 3:
3/3=1
72/3=24
Simplified fraction is 1/24.
Answer: [tex]\frac{1}{24}[/tex]
Step-by-step explanation: To multiply fractions, first multiply across the numerators and then multiply across the denominators.
[tex](\frac{3}{8}) (\frac{1}{9}) = \frac{3}{72}[/tex]
[tex]\frac{3}{72} = \frac{1}{24}[/tex]
What is the justification for the step taken from line 2 to line 3? 5 lines of math. The first line has, 3 x plus 9 minus 7 x equals x plus 10 plus x. The second line has, negative 4 x plus 9 equals 2 x plus 10. An arrow pointing from the front of the second line to the front of the third line. The third line has, negative 6 x plus 9 equals 10. The fourth line has, negative 6 x equals 1. The last line has x equals negative StartFraction 1 Over 6 EndFraction. the subtraction property of equality the multiplication property of equality combining like terms on one side of the equation the distributive property
Answer:
The subtraction property of equality
Step-by-step explanation:
it just is
The justification for the step taken from line 2 to line 3 is the subtraction property of equality
What are equations?Equations are expressions that have equal values when compared using the "=" sign
The equation on line 2 is given as:
[tex]-4x + 9 = 2x + 10[/tex]
The equation on line 3 is given as:
[tex]-6x + 9 = 10[/tex]
2x is subtracted from both sides of the equation in step 2 to get the equation in step 3
Hence, the justification for the step taken from line 2 to line 3 is the subtraction property of equality
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If it is known that a+b/a−b =c, find the following:
3a+3b/2a−2b
Answer:
[tex]\frac{3}{2}[/tex] c
Step-by-step explanation:
Given
[tex]\frac{3a+3b}{2a-2b}[/tex] ← factor numerator and denominator
= [tex]\frac{3(a+b)}{2(a-b)}[/tex]
= [tex]\frac{3}{2}[/tex] × [tex]\frac{a+b}{a-b}[/tex] ← this = c
= [tex]\frac{3}{2}[/tex] × c = [tex]\frac{3}{2}[/tex] c
how do you find the median
Answer:
Step-by-step explanation:
You first rearrangel all of numbers from least to greatest, then you cross out the smallest and bigest number untill you meet in the middle. If you there two numbers in the middle then you find the average of those numbers.
Combine like terms to create an equivalent expression. 7/8 * m + 9/10 - 2m - 3/5
Plz
Answer: -3(15m-4)/40
(All the numbers are above the fraction bar, then 40 is under the fraction bar)
- 9/8 m + 3/10
Answer
If ST = 12 and RT = 49, find RS.
Given ST = 12 and RT = 49, we apply the basic principle of part-whole relationships in a line to find RS. By subtracting the length of ST from RT, we determine that RS equals 37.
Explanation:The question asks to find the length of RS given that ST = 12 and RT = 49. To find the length of RS, we can apply the concept that in a linear situation, if S is a point between R and T, then RS + ST = RT. This concept is based on the principle of the sum of parts of a whole.
Given:
ST = 12RT = 49To find RS, we use the equation:
RS + ST = RT
Plugging in the given values:
RS + 12 = 49
Solving for RS, we subtract 12 from both sides:
RS = 49 - 12
RS = 37
Therefore, the length of RS is 37.
which two points should you use to find the equation of the model? a linear model for the data in the table shown in the scatter plot ? please help with question A and B
Answer:
a. (1,14) and (7,7)
b. slope = -1.2
Step-by-step explanation:
a. Use the points that are actually on the drawn line
(1,14) and (7,7)
b. Slope formula is :
[tex]slope = ( y_{2} - y_{1}) \div ( x_{2} - x_{1})[/tex]
It doesnt matter which one is 1 or 2. I will take (1,14) as (x1, y1) and (7,7) as (x2, y2)
[tex]slope = \frac{(7 - 14)}{(7 - 1)} \\ = \frac{ - 7}{6} = - 1.1667 = - 1.2[/tex]
Answer:
(A) (1, 14) and (7, 7)
(B) -1.17
Step-by-step explanation:
(A) the 2 points that should be used are: (1, 14) and (7, 7). The reason is that these 2 points are the closest to the trend line.
(B) With 2 points - (x1, y1) and (x2, y2) - a linear equation can be obtained. The slope (m) of the line is computed as follows:
m = (y2 - y1)/(x2 - x1)
m = (7 - 14)/(7 - 1) = -1.17