Using proportions, it is found that the original sample weighed [tex]8.28 \times 10^{-9}[/tex] grams.
This question is solved by proportions, using a rule of three.The weight of 1 batch, in grams, is of [tex]6.9 \times 10^{-10}[/tex]. How much do the sample of 12 batches weigh?The rule of three is:
1 batch - [tex]6.9 \times 10^{-10}[/tex] grams.
12 batches - x grams
Applying cross multiplication:
[tex]x = 12 \times 6.9 \times 10^{-10} = 82.8 \times 10^{-10}[/tex]
Applying scientific notation:
[tex]8.28 \times 10^{-9}[/tex]
The original sample weighed [tex]8.28 \times 10^{-9}[/tex] grams.
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Answer please................................
Answer:
1 and 4
Step-by-step explanation:
scores on a test have a mean of 66 and Q3 is 80. The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth.
A) 10.5
B) 20.9
C) 9.4
D) 18.7
A teacher wants to give each student 2 pencils. A store is selling pencils in boxes of 24. If the teacher has a total of 125 students, how many boxes of pencils should he buy?
Answer:
10.41
Step-by-step explanation:
hehe
Answer:
11
Step-by-step explanation:
Total number of pencils needed = 125 × 2 = 250
Total number of boxes = [tex]\frac{250}{24}[/tex] = 10.416
the teacher need to buy 11 boxes
How many inflection point(s) do you see ?
Answer:
7
Step-by-step explanation:
There is a point of inflection at each point where the graph crosses the line y=2. There are 7 points of inflection shown.
__
A point of inflection is where the graph changes from being concave downward to concave upward, or vice versa. For a sine function, that is everywhere the function crosses its midline.
Answer:
7 inflection points
Step-by-step explanation:
The given function [tex]f(x)=sinx+2[/tex] has a midline of y=2 where each point of the function that intersects the line is an inflection point. Inflection points are where the concavity changes, defined by when the second derivative is equal to 0 or undefined.
[tex]f(x)=sin(x)+2[/tex]
[tex]f'(x)=cos(x)[/tex]
[tex]f''(x)=-sin(x)[/tex]
[tex]0=-sin(x)[/tex]
[tex]x=\pi n[/tex] for any integer [tex]n[/tex]
From [tex][-10,10][/tex], there are 7 inflection points, which are[tex]x=-3\pi,-2\pi,-\pi,0,\pi,2\pi,3\pi[/tex]
please answer!!!!!!!!!!!
If a team won 2/3 of its games and lost the rest. what was the team's win-loss ratio
Answer: 2 wins to 1 loss
Step-by-step explanation:
Add the expression. (3x + 2) + (2x + 5) *
Answer:
5x+7
Step-by-step explanation:
If ARST = ANPQ, which of the following is true?
Answer:
T=Q
Step-by-step explanation:
They are in te same position on the comparison
Write an expression to model each situation.
Sandra picked 10 blue flowers and 16 red flowers. Then she divided the flowers equally into 2 bouquets. _______________
A recipe called for 2/3 cup flour. Kyle doubled the recipe. Then he added 1/4 cup more flour to make the dough less sticky. ________________
For the given conditions expressions 1 and 2 are obtained as (10 + 16) ÷ 2 and 2/3 x 2 + 1/4 respectively.
What is a mathematical expression?A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: Number/variable, mathematical operator, and expression
It is given that the expression is,
Sandra selected 16 red flowers as well as 10 blue blooms. She then equally split the flowers into 2 bouquets.
The expression for the given condition is,
=(10 + 16) ÷ 2
If a recipe required 2/3 cup of flour. The recipe was quadrupled by Kyle. He then increased the flour by 1/4 cup to make the dough less sticky. The expression for the given condition is,
=2/3 x 2 + 1/4
Thus, the obtained expressions are (10 + 16) ÷ 2 and 2/3 x 2 + 1/4.
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Which statement about the following equation is true? 3x2 â€"" 8x 5 = 5x2.
The discriminant is greater than 0, so there are two real roots and it can be determined by using nature of roots.
Given that,
Equation; [tex]\rm 3x^2 - 8x + 5 = 5x^2[/tex]
We have to determine,
Which statement about the following equation is true?
According to the question,
To determine the true statement about the equation following all the steps given below.
Equation; [tex]\rm 3x^2-8x+5=5x^2[/tex]
Simplify the equation for the roots of the equation,
[tex]\rm 3x^2-8x+5=5x^2\\\\\rm5x^2- 3x^2+8x-5=0\\\\ 2x^2+8x-5=0\\\\ 2x^2+8x-5=0\\\\2x^2+8x=5\\\\2x(x+4)=5\\\\Then, \ 2x = 5, \ \ x = \dfrac{5}{2} \\\\And\ \ x+4=5, \ \ x=5-4, \ \ x=1[/tex]
The equation has two real roots and x is 1 and 5/2.
Hence, The discriminant is greater than 0, so there are two real roots.
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Points A, B and C lie on a circle, centre O.
Angle AOC = 142°.
Find the value of y.
The value of y in the cyclic quadrilateral with ∠AOC(142°) is 38°
The diagram above represents a cyclic quadrilateral.
A cyclic quadrilateral has all it vertices on the circumference of the circle.
Therefore,
Opposite angles are supplementary. This means they add up to 180 degrees.
Therefore,
142° + y° = 180°
subtract 142 from both sides of the equation
142 - 142 + y = 180 - 142
y = 38°
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If 3x-2=11, what is the value of 6x+5? PLS HELP
Answer:
approximately 31
Step-by-step explanation:
3X-2=11
3x=13
x=13/3 = 4.3
then 6X+5=6×4.3+5 = 30.8 or approximately
Determine the domain and range of the function f(x) = â€""|x| 2. The domain of the function is. The range of the function is.
The domain of the function f(x) = |x|² is the set of all real numbers (-∞ < x < ∞)
The range of the function f(x) = |x|² is the set of all real numbers greater than or equal to zero ( f(x) ≥ 0)
The given function is:
f(x) = |x|²
This can also be expressed as:
f(x) = x²
This is because the square operator cancels the effect of the absolute value
The function f(x) = x² is valid for all real values of x. Therefore, the domain of the function f(x) is -∞ < x < ∞
The range of the function f(x) is all positive real numbers. This is because the square of all numbers gives a positive number.
Range = f(x) ≥ 0
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Answer:
1. all the real numbers
2. all numbers less than or equal to 2.
Step-by-step explanation:
There are 222 red marbles in a box. Amit takes out 6 red marbles and replaces them with 12 blue
marbles. He continues doing this till all the red marbles are replaced with blue marbles.
Which of the following expressions gives the total number of blue marbles he put in the box?
A (222 + 6) = 12 B (222 - 6) + 12 C (222 - 6) + 12 D (222 + 6) x 12
Answer:
(222 - 6) + 12
Step-by-step explanation:
You put B and C as the same thing but the correct option is this because first you take away 6 (subtract 6) from the 222 marbles then you replace them with 12 (add 12).
find possible lenth and breadth of the rectangle whose area is given by the expression x power 2 +6x +8
[tex]x^2 +6x +8\\\\=x^2 + 4x +2x +8\\\\=x(x+4) +2(x+4)\\\\=(x+2)(x+4)\\\\\text{Possible length and breadth of the rectangle are (x+4) and (x+2) respectively.}[/tex]
Which table matches the equation y= 8x + 20
Answer:
The first table
Step-by-step explanation:
x y
7 76
10 100
13 124
16 148
HOPE THIS HELPS :)
What's the Answer ~
[tex] \sf \tiny{14 + 14 \div 7}[/tex]
Step-by-step explanation:
remember the priorities of the different mathematical operations
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
so,
14 + 14/7 = 14 + 2 = 16
Hey there!
14 + 14 ÷ 7
14 ÷ 7 = 2
= 14 + 2
= 16
Therefore, your answer is: 16
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
ABC is a triangle. AC=19cm, BC=17cm and angle BAC=60
Answer:
In the picture
Step-by-step explanation:
it's an acute triangle
more information in the picture
Solve the expression then name the polynomial
If f(x) = 2x – 3 and g(x) = 3x2
– 2x + 6 then what is (f + g)(x)?
50 POINTS PLEASE HELPP
For which of the following inequalities, is 4
part of the solution set? Select all that
apply.
I A. x > -5
I B. 2 > x
C. 3x + 4 >-8
O D. 5x < 2x - 3
E. -6 < 4 - 2x
Answer:
a
Step-by-step explanation:
Answer:
A, C, and E
Step-by-step explanation:
Replace the x with 4 and do the math
The surface area of a box is 160 square inches. The length of the box is twice its width, and is 4 inches less than its height. What is the height of the box, in inches?
the height of the box is 9 inches
Answer:
solution given:
total surface area of a box=160 square inches
let length, width, and height be l,b, and h respectively.
according to the question:
l=2b
∴b =[tex]\frac{l}{2}[/tex]
l=h-4
∴ h=l+4
we have
total surface area of a box=160 square inches
2(lb+lh+bh)=160
[tex]2(l*\frac{l}{2}+l(l+4)+\frac{l}{2}*(l+4))=160[/tex]
[tex]2*\frac{l^2+2l^2+8l+l^2+4l}{2}=160[/tex]
[tex]4l^2+12l=160[/tex]
[tex]4(l^2+3l)=160[/tex]
[tex]l^2+3l=\frac{160}{4}[/tex]
[tex]l^2+3l-40=0[/tex]
doing middle term factorization
[tex]l^2+(8-5}l-40=0[/tex]
[tex]l^2+8l-5l-40=0[/tex]
taking common from each two terms
l(l+8)-5(l+8)=0
(l+8)(l-5)=0
either
l=-8[neglected as length is always positive]
or
l=5
now
b=[tex]\frac{5}{2} =2.5[/tex]
h=5+4=9
Step-by-step explanation:
Triangle NLM is reflected over the line segment as
shown, forming triangle ABC. Which congruency
statement is correct?
NLM - CAB
NLM -CBA
NLM - BCA
NLM - BAC
Triangle NLM is reflected over the line segment as shown, forming triangle ABC then the correct congruency statement is NLM ≅ CAB
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Triangle NLM is reflected over the line segment and form the triangle ABC.
Triangle NLM is reflected over the line segment to form triangle ABC. This means that the corresponding sides and angles of the two triangles are congruent.
The reflection over a line segment preserves the orientation of the triangle, so the order of the letters in the names of the triangles should remain the same.
Therefore, triangle NLM is reflected over the line segment as shown, forming triangle ABC then the correct congruency statement is NLM ≅ CAB
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3 1/8 - b = 1 3/4
how do I figure out what b is?
What property was used in step 1 to arrive at step 2?
Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18.
Answer:
Distributive Property
Step-by-step explanation:
5(x - 7) = 55 ⇒ 5x - 35 = 55
The 5 was distributed in 5(x-7) to get 5x - 35.
Solve for x:
7 |x - 2| + 7 = -2 |x - 2| + 2
Answer:
It is a fraction -5/9
Step-by-step explanation:
Solving Quadratic Equations by Factoring
Answer:
are those 4 all answers or are they separate?
Step-by-step explanation:
PLS SHOW ME HOW U GET THE ANSWER AND WILL GIVE BRAINLYEST
Answer:
38 degrees
Step-by-step explanation:
all triangles length added up are 180 degrees.
add 52 and 90 to get 142. Subtract to get 38 degrees.
Write all the factors of 9 . Use commas to separate them.rtth
Answer:
1, 3, 9
Step-by-step explanation:
the nine can be divided by those three numbers and no more
Answer:
1,3,9
Step-by-step explanation:
Estimate the quotient of 57.87 ÷ 5 A) 9 B) 10 C) 11 D) 12
Answer:
C, 11
Step-by-step explanation:
how to calculate fractions without a calculator
Answer:
Step-by-step explanation:
all you need to do is divide that number by the denominator of the fraction, then multiply your result by the numerator of the fraction