3.8 x[tex]10^3[/tex] is 169 times smaller than 6.422x [tex]10^5[/tex].
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq[/tex] a < 10. Scientific notations have some of the profits as:
Better readability due to compact representation Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
We need to find out how many times 3.8 x 10^5 is greater than 3.8 x 10^-7.
To do that, we have to divide 3.8 x 10^5 by 3.8 x 10^-7 and then find the answer.
Let us do that:
[tex]\begin{gathered} \frac{3.8\cdot10^3}{6.422\cdot10^{5}}\text{ = }\frac{3.8}{6.422}\cdot\text{ }\frac{10^3}{10^{5}} \end{gathered}[/tex]
= 169
According to the division law of indices states that if a numerator and a denominator have the same base (e.g. 10), then the power of the numerator can subtract of the denominator.
Therefore, 3.8 x[tex]10^3[/tex] is 169 times smaller than 6.422x [tex]10^5[/tex].
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The graph of a quadratic function with the vertex 2,3 is shown in the figure below.Find the domain in the range. Write your answers as inequalities, using X or Y as appropriate. Or, you may instead write “empty set” or “all reals” as the answer.domain=range=
From the graph, we are asked to find the domain and randge./.
First lets know what domain and range.
Domain of a function is the set of values that are allowed is the plug into our function.
The domain and rang of the function written in an inequality form are:
Domain:
-1 < x < 4
Range:
-10 < y < 3
Can you help me understand the steps to number 21 I think I got it wrong
The probability of an event is determined a follows;
[tex]P\lbrack E\rbrack=\frac{\text{Number of required outcomes}}{Number\text{ of possible outcomes}}[/tex]We shall begin with the probability of selecting an even number as shown below;
[tex]\begin{gathered} P\lbrack\text{even\rbrack}=\frac{6}{12} \\ P\lbrack\text{even\rbrack}=\frac{1}{2} \end{gathered}[/tex]Next we shall calculate the probability of selecting a number less than 5 as shown below;
[tex]\begin{gathered} P\lbrack\text{less than 5\rbrack=}\frac{4}{12} \\ P\lbrack\text{less than 5\rbrack=}\frac{1}{3} \end{gathered}[/tex]The probability of event A OR event B occuring is calculated a follows;
[tex]\begin{gathered} P\lbrack A\rbrack\text{ OR P\lbrack{}B\rbrack=P\lbrack{}A\rbrack+P\lbrack{}B\rbrack} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{1}{2}+\frac{1}{3} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{3+2}{6} \\ P\lbrack\text{even\rbrack OR P\lbrack{}less than 5\rbrack=}\frac{5}{6} \end{gathered}[/tex]The probability of selecting an even number or a number less than 5 is therefore
[tex]\frac{5}{6}[/tex]The correct answer is option A
Enter the missing values in the area model to find 2(5n+1)
First box: 10n
2
10n + 2
Explanations:The area model = 2 (5n + 1)
Thsi can expanded into:
2 (5n) and 2(1)
In the first box:
2 (5n) = 10n
In the second box:
2(1) = 2
In the third box:
2 (5n + 1) = 10n + 2
hi, I would like help with this please and ty
You can use number line or inequalities to compare the temperatures of this three different cities.
Using number line to compare the temperatures 2.5, -3.5 F and -5 F
Using inequality
[tex]\begin{gathered} 2.5>-3.5 \\ -3.5>-5 \end{gathered}[/tex]=In AABC, the measure of ZC=90°, CB = 35, AC = 12, and BArepresents the cosine of ZA?37. What ratio
ANSWER:
[tex]\frac{12}{37}[/tex]STEP-BY-STEP EXPLANATION:
The first thing is to draw the triangle ABC:
We have that the trigonometric cosine ratio is given as follows
[tex]\begin{gathered} \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \text{For A, we have} \\ \text{adjacent = 12} \\ \text{hypotenuse = }37 \\ \text{replacing:} \\ \cos A=\frac{12}{37} \end{gathered}[/tex]determine the ratio of surface area to volume of the triangular prism
Solution
The surface area of a Triangular prism is given as;
[tex]SA=bh+(s_1+s_2+s_3)H[/tex]The volume of a triangular prism is given as;
[tex]V=\frac{1}{2}bhl[/tex]The ratio of surface area to volume of the triangular prism
[tex]\text{ratio}=\frac{SA}{V}=\frac{bh+(s_1+s_2+s_3)H}{\frac{1}{2}bhl}[/tex]I need help on this
You consider each parittion of the axis represents 1 unit.
You can notice that in the given image, the coordinates of the points A, B, C and D are the following:
A(-6,4)
B(-2,1)
C(2,3)
D(-1,-4)
where you have taken into account that point left side of the origin have negative x valuesand points right side have positive x values. Point down side of origin have negative y values and points above origin has positive y values.
Use the table of values for f and g below to find the indicated compositions. (f \circ g)(8) =Answerg(f(3))=Answerf(f(1))=Answer (g \circ g)(6) =Answer
In order to find the value of a composition of functions at x = a, (f º g)(a), we first find the value of g(a), then find the value of f(x) at x = g(a).
(f º g)(a) = f(g(a))
In this problem, the values of f(x) and g(x) are shown in the table, for integer values of x from 0 to 9.
So, we have:
1. (f º g)(8) = f(g(8))
From the table, we see that
g(8) = 4 (value of g(x) in the line corresponding to x = 8)
Then:
f(g(8)) = f(4) = 4 (value of f(x) in the line corresponding to x = 4)
Thus:
[tex]\mleft(f\circ g\mright)\mleft(8\mright)=4[/tex]2. g(f(3))
f(3) = 8
g(8) = 4
Thus:
[tex]g(f(3))=4[/tex]3. f(f(1))
f(1) = 6
f(6) = 2
Thus:
[tex]f(f(1))=2[/tex]4. (g º g)(6) = g(g(6))
g(6) = 7
g(7) = 3
Thus:
[tex]\mleft(g\circ g\mright)\mleft(6\mright)=3[/tex]
An online auction company charges sellers a commission fee of 5.25% of an items final selling price. If you sell an item for 55$ what fee will you pay to the auction company ?
The selling price of the item is $55.
The money charged by the auction company is;
[tex]\begin{gathered} 5.25\text{ \% of \$55} \\ \frac{5.25}{100}\times55 \\ =\text{ \$2.89} \end{gathered}[/tex]The fee paid to the auction company is $2.89
The total area of a polygon is 176 sq.ft. Find the value of x in the drawing
Answer:
x=6 ft
Explanation:
The given polygon is a trapezium in which:
• The parallel sides are a=16 ft and b=(16+2x) ft
,• The height, h = 8 ft
,• Area = 176 sq.ft.
The area of a trapezium is calculated using the formula:
[tex]\begin{gathered} A=\frac{1}{2}(a+b)h \\ a,b\text{ are the parallel sides} \\ h\text{ is the perpendicular height} \end{gathered}[/tex]Substitute all the known values:
[tex]\begin{gathered} 176=\frac{1}{2}\times8(16+16+2x) \\ 176=4(32+2x) \end{gathered}[/tex]Divide both sides by 4.
[tex]\begin{gathered} \frac{176}{4}=32+2x \\ 44=32+2x \end{gathered}[/tex]Subtract 32 from both sides:
[tex]\begin{gathered} 44-32=32-32+2x \\ 12=2x \end{gathered}[/tex]Divide both sides by 2.
[tex]\begin{gathered} \frac{12}{2}=\frac{2x}{2} \\ x=6\text{ feet} \end{gathered}[/tex]The value of x in the drawing is 6 feet.
Answer:
X=6
Step-by-step explanation:
First multiply 8 by 16 to get 128. Then subtract that from 176 to get 48. Then divide by to because there are two triangles to get 24, so each triangle is 24 square feet. Find a number that multiplied by 8 equals 48 (this will be x). The reason that I did this is because of the formula for area of a triangle (B*H/2=A). After you divide by 48 by 2 you will get 24. The number that was multiplied by 8 is x (x=6).
How would I create a logic proof for this question?
Let us represent the premises given:
[tex]\begin{gathered} \text{Let } \\ A=\text{John is aardvark} \\ C=\text{Charles has a blue eye} \\ B=\text{Bob counts} \\ E=\text{Edna drives a truck} \\ D=\text{Dan edits} \end{gathered}[/tex]Then
We can subdivide the argument into substatement
Statement 1: If John is an aardvark then either Charlene has blue eyes or Bob counts
[tex]A\Rightarrow(C\lor B)[/tex]Statement 2: If Charlene has a blue eye then Edna drives a truck
[tex]C\Rightarrow E[/tex]Statement 3: Either John is an aadvark or Dan edits
[tex]A\lor D[/tex]Statement 4: Moly claims that either Bob counts or Edna drives a truck, but Moly is wrong
[tex]\begin{gathered} (B\lor E),\text{ But} \\ \sim(B\lor E) \end{gathered}[/tex]Therefor D
[tex]\therefore D[/tex]The above hypothesis and conclusion can be summarized below as;
Using a truth table calculator, the validity of the above arguments is shown below
Hence, we can conclude that the above is a valid argument.
Can you just help me with this it is hurt
A horizontal line is in the form
y =
This means the x component changes and the y component stays the same
( -7, 10)
The line is in the form
y = 10
x can be any value
The slope is zero since it is horizontal
The point ( 3,10) is on the line
The equation of the line is y = 10
The y intercept is 10 not -7
how do I create equal groups that represent the division fact 28÷4=7?
So to make equal groups just create the number of groups (divisor, in this case: 4) and insert into that the number of the quotient( in this case: 7)
1) Let's make equal groups for that division since 7 added 4 times is equal to 28:
2) Since 7 x 4 is the same as adding 7 four times, we have above four groups with seven balls that added up yields 28, in each group we have 7 balls.
3) So to make equal groups just create the number of groups (divisor) and insert into that the number of the quotient. Note that this is valid just for exact divisions.
The probability of picking an odd prime number is . The probability of picking a number greater than 0 that is also a perfect square is
we know that
total blocks=10
total odd prime numbers------> 3,5,7------> 3 numbers
so
Part 1
The probability of picking an odd prime number is
P=3/10 or P=0.3Part 2
total blocks=10
total numbers greater than zero also a perfect square ------>1,4,9---> 3 numbers
so
The probability is
P=3/10 or P=0.3Angle AED is 146 degrees. Ray EC bisects angle AED. What is the measure of angle AEC?
STEP 1
We draw a diagram to represent the information.
[tex]\begin{gathered} <\text{AEC}=\frac{In conclusion, the answer is 73 degreesSimple random sampling uses a sample of size from a population of size to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of bank accounts, we want to take a random sample of four accounts in order to learn about the population. How many different random samples of four accounts are possible?
There will be 1,215,450 different random samples of four accounts are possible.
What is combination and permutation?There are two methods to calculate the number of ways a certain event can happen. Both are used in different circumstances, such as, when the order of arrangement does not matter we use the combination and when the order matters we use permutation.
Given,
Population size, N = 75
Sample size, n = 4
We have selected a random sample of 4 accounts in order to learn about the population because these accounts can not be repeated and can be in any order, so we will use combination without repetition. According to this, the number of ways by which n subjects can be chosen from N subjects are given by,
[tex]\frac{N}{n}[/tex] = [tex]\frac{N!}{n!(N-n)!}[/tex]
Therefore, required number of ways are,
= 75!/4!(75-4)!
= 75!/4!*71!
= 75*74*73*72*/4*3*2
= 1,215,450
Hence, There will be 1,215,450 different random samples of four accounts are possible.
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Please solve #24 for me.I’m struggling badly with systems of equations and need some help solving problems with it.Please explain the steps of it as best and basic as possible.
Data
• Small cones (s): $2
,• Large cones (L): $3.50
,• Total sold (T): $163
,• The number of L sold was 12 more than the number of ,s.
Procedure
We have to build a system of equations based on the information given.
• Equation 1:, she sold $163 of small and large cones
[tex]2s+3.50L=163[/tex]• Equation 2: ,the number of L sold was 12 more than the number of ,s.
[tex]L=s+12[/tex]As we have L isolated in the second equation, it is convenient to use this expression in the first equation to have it in terms of one variable:
[tex]2s+3.50\times\left(s+12\right)=163[/tex]Simplifying the parenthesis we get:
[tex]2s+3.50s+42=163[/tex]As we have two terms with an s we can group in each side of the equation the common terms and simplify them as follows:
[tex]2s+3.50s=163-42[/tex][tex]5.50s=121[/tex][tex]s=\frac{121}{5.50}[/tex][tex]s=22[/tex]Now that we have s, we just have to replace this value in equation 2:
[tex]L=22+12=34[/tex]Answer:
• Small snow cones: 22
,• Large snow cones: 34
What is the component form of the vector represented by 8a when a=(-4,2)
Given the vector represented by:
[tex]8a[/tex]You know that:
[tex]a\langle-4,2\rangle[/tex]By definition, the Component Form of a vector is:
[tex]\vec{V}=\langle x,y\rangle[/tex]In this case, you only need to multiply the coordinates of "a" by 8, in order to find the Component Form of:
[tex]8a[/tex]Therefore, you get:
[tex]=\langle(8)(-4),(8)(2)\rangle=\langle-32,16\rangle[/tex]Hence, the answer is:
[tex]\langle-32,16\rangle[/tex]i need help doing number 34 and 35 if you can please :(
The tangent of an angle, we will follow the steps below
Step 1: Write out the trigonometric ratio to obtain the tangent of an angle
[tex]\tan \emptyset=\frac{opposite}{adjacent}[/tex]From question 35
Step 2: Apply the tangent ratio
[tex]\begin{gathered} \tan A=\frac{\text{opposite}}{\text{adjacent}}=\frac{60}{100}=\frac{6}{10}=\frac{3}{5} \\ \tan A=\frac{3}{5}=0.6000 \end{gathered}[/tex]For tan B
[tex]\begin{gathered} \tan B=\frac{\text{opposite}}{\text{adjacent}}=\frac{100}{60}=\frac{5}{3} \\ \tan B=\frac{5}{3}=1.6667 \end{gathered}[/tex]a. a grade that is 12 points lower than a grade of x can be represented as Options: x-12both x-12 and 12-x 12-x
a. If a friend says his grade is 12 points lower than your grade, it means your grade is greater than his grade, if your grade is represented by x, then the grade of your friend can be found by subtracting 12 from your grade, this can be written as:
[tex]x-12[/tex]b. If x represents your friend's grade instead of yours, then to find your grade you need to add 12 to his grade, it can be represented as:
[tex]\begin{gathered} x+12 \\ 12+x \end{gathered}[/tex]The correct answers are B. and D.
Help find the slope of the lined graph
The slope of the line graph is -1.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
The slope is rise over run.
Therefore,
slope = y₂ - y₁ / x₂ - x₁
Using (3, -3) and (-2, 2)
Therefore,
x₁ = 3
x₂ = - 2
y₁ = -3
y₂ = 2
Hence,
slope = 2 + 3 / -2 - 3
slope = 5 / -5
Therefore,
slope = - 1
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what do you do after you multiply an equation in the elimination method?2x -3y=-11x+3y = 8
1) Let's multiply the second equation by -2, to eliminate x
2x -3y=-11
x+3y = 8
2) Now let's add both equations
2x -3y=-11
-2x-6y = -16
--------------------
-9y = -27
3) Divide both by -9
y=3
4) Plug y=3 into the simpler original equation, to make calculations easier:
x +3y=8
x+3(3) =8
x +9 =8 Subtract 9 from both sides
x = 8-9
x=-1
So, after multiplying it we add both equations to eliminate one variable either x or y.
sue writes three different numbers. the numbers are all between 30 and 60 . the numbers all have 6 ones . what numbers does sue write
EXPLANATION
The three numbers are 36, 46 and 56. This is because the only three numbers that have 6 ones and wich are included between 30 and 60 are 36, 46 and 56, no other number can comply that condition.
What’s your question represents our relationship shown in the graph
Given the graph of a line
As shown the line passes through the point (0, 0)
So, the relation has the form:
[tex]y=kx[/tex]We will find the value of k using one point lying on the line
As shown the line passes through the point (4, 14)
So, when x = 4, y = 14
Substitute with x and y into the equation: y = k * x
so,
[tex]\begin{gathered} 14=k\cdot4 \\ \\ k=\frac{14}{4}=3.5 \end{gathered}[/tex]so, the answer will be option C) y = 3.5x
Supposed to go out to a dinner and you spend $42 you want to leave a 20% tip how much money should you leave for a tip round your answer to the nearest cent
Answer:
$8.4
Explanation:
To find how much money you should leave for a tip, we need to find how much is 20% of $42. So, to calculate this, we need to multiply 42 by 20 and then divide by 100, so:
$42 x 20% = 42 x 20 / 100 = 840 / 100 = 8.4
Therefore, the answer is $8.4
Can you please help me out with a question
Step 1 :
We use the Intersecting Chord Theorem which states that :
When two chords intersect each other inside a circle, the products of their segments are equal.
This theorem states that A×B is always equal to C×D
(no matter where the chords are).
From the question, A = 15, B = 12, C = ? , D = 18
Step 2 :
Using the equation, where AB = CD
[tex]\begin{gathered} 15\text{ x 12 = C x 18} \\ 180\text{ = 18 C} \\ \text{Divide both sides by 18, we have that:} \\ C\text{ = 10 units.} \end{gathered}[/tex]CONCLUSION :
The value of C = 10 units
Given BD bisects ∠ABC, complete the flowchart proof below. Note that the last statement and reason have both been filled in for you.
In order to prove that the triangles are congruent, we can write the following statements and reasons:
first box in the first row:
statement: BD bisects angle ABC
reason: given
first box in the second row:
statement: angle ABD congruent to angle DBC
reason: A segment bisector divides a segment into two congruent segments.
second box in the second row:
statement: angle ADB congruent to angle BDC
reason: given
third box in the second row:
statement: side AB congruent to side BC
reason: given
Since we have two pairs of congruent angles and one pair of congruent sides that are not between the angles, we can prove the triangles congruent by case AAS.
If an object is shot upward with an initial velocity, vo, in feet per second (fu/s), the velocity, v, in fus is given by the formula v = vo - 321,where ris time in seconds. Find the initial velocity of an object if the velocity after 2 seconds is 38 ft/s.
The final velocity function is given to be:
[tex]v=v_0-32t[/tex][tex]\begin{gathered} We\text{ are to find the initial velocity;} \\ v_0,\text{ given final velocity v to be 38ft/s and time t to be 2secs} \end{gathered}[/tex]Thus, we have:
[tex]\begin{gathered} v=v_0-32t \\ 38=v_0-32(2) \\ 38=v_0-64 \\ 38+64=v_0 \\ 102=v_0 \\ v_0=102\text{ft/s} \end{gathered}[/tex]Hence, the initial velocity of the object is 102ft/s
100_0.22 help me please
Given the expression :
[tex]100-0.22[/tex]The answer will be as follows, add the decimal point and two zeros
[tex]100-0.22=100.00-0.22[/tex]See the following picture:
Tell whether the following statement is always, sometimes, or never true for numbers greater than zero. Explain. In equivalent ratios, if the numerator of the first ratio is greater than the denominator of the first ratio, then the numerator of the second ratio is greater than the denominator of the second ratio.
Answer
The statement is always true.
Explanation
Since equivalent ratios reduce to essentially the same fundamental ratios, if the numerator of one of the ratios is greater than its denominator, then the numerator of each of the equivalent ratios must be greater than each of their corresponding denominators too.
So, this statement is always true!
Hope this Helps!!!