Mateo is studying a human hair with a diameter of 6.5 x 10^-4 inches and a horse hair with a diameter of 1.3 x 10^-3 inches. Which statement is true?
A.The horse hair is 2 times as thick as the human hair.
B.The horse hair is 5 times as thick as the human hair
C.The human hair is 2 times as thick as the horse hair
D.The human hair is 5 times as thick as the horse hair
Answers
A.The horse hair is 2 times as thick as the human hair.
Answer:
A.The horse hair is 2 times as thick as the human hair.
Step-by-step explanation:
We have been given that Mateo is studying a human hair with a diameter of [tex]6.5\times 10^{-4}[/tex] inches and a horse hair with a diameter of [tex]1.3\times 10^{-3}[/tex] inches.
Since proportions states that two fractions are equal, So we will use proportions to solve our given problem.
[tex]\frac{\text{Diameter of horse hair}}{\text{Diameter of human hair}}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}\times \text{Diameter of human hair}[/tex]
Now we will quotient rule of exponents to simplify our given problem.
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3--4}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3+4}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{1}}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=\frac{13}{6.5}\times \text{Diameter of human hair}[/tex]
[tex]\text{Diameter of horse hair}=2\times \text{Diameter of human hair}[/tex]
We can see that the diameter of horse hair is 2 times the diameter of human hair. Therefore, the horse hair is 2 times as thick as the human hair and option A is the correct choice.
Related Questions
A cone is a solid that has one circular base and only one face. true or false
Answers
The cone is made by rotating a right triangle for 360°
The base is a circle, formed by one of the leg. The other leg makes the only one face.
one teaspoon equals 0.5 centimeters. how many liters equals 50 teaspoons? Round the answer to the nearest hundredth.
Answers
50 teaspoons would equal 50*0.5 = 25 centimeters
1 cm = 0.001 liter
25*0.001 = 0.025 liters
how many different ways can an after school club of 13 students line up
Answers
Answer: 6227020800
Step-by-step explanation:
Solve this quadratic equation by completing the square.
x^2+10x=7
Answers
take 1/2 of the linear coefient and square it
10/2=5, (5)^2=25
add that to both sides
x^2+10x+25=7+25
factor perfect square trionomial
(x+5)^2=32
squaer root both sides
x+5=+/-4√2
minus 5
x=-5+/-4√2
x=-5+4√2 and -5-4√2
What is the algebraic expression for "the difference between seven times a number and three times that number"?
7 - 3x
7x - 3
7x - 3x
Answers
"difference"= -
"three times a number" = 3x so
7x-3x
Answer:
(C)7x-3x
Step-by-step explanation:
The given algebraic expression is:
"The difference between seven times a number and three times that number"
Let the number be equal to =x, then according to the statement, we have
seven times a number=7x and three times that number=3x
The difference between seven times a number and three times that number=7x-3x
which is the required algebraic expression.
Hence, option C is correct.
?? Please help answer and solve, showing the steps you took
Answers
n = 20t² - 20t +120
dn/dt = 0 = 40t - 20 + 0
40t - 20 = 0
40t = 20
t = 20/40
t = 1/2 or 0.5
Therefore, the number of bacteria would be minimal at 0.5°C.
Find the coordinates of point S that lies along the directed line segment from R(-14, -1) to T(4, -13) and partitions the segment in the ratio of 1:5.
Answers
I'd like to point out, is 1:5 from R to T, since that matters, that way we know the ratio from RS is the 1 and the ratio ST is the 5.
[tex]\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ R(-14,-1)\qquad T(4,-13)\qquad \qquad 1:5 \\\\\\ \cfrac{RS}{ST} = \cfrac{1}{5}\implies \cfrac{R}{T} = \cfrac{1}{5}\implies 5R=1T \implies 5(-14,-1)=1(4,-13)\\\\ -------------------------------\\\\[/tex]
[tex]\bf { S=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\ -------------------------------\\\\ S=\left(\cfrac{(5\cdot -14)+(1\cdot 4)}{1+5}\quad ,\quad \cfrac{(5\cdot -1)+(1\cdot -13)}{1+5}\right)[/tex]
Answer: The required co-ordinates of the point S are (-11, -6).
Step-by-step explanation: We are given to find the co-ordinates of the point S that lies along the directed line segment from R(-14, -1) to T(4, -13) and partitions the segment in the ratio of 1:5.
We know that
the co-ordinates of a point that divides the line segment joining the points (a, b) and (c, d) in the ratio m : n is given by
[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).[/tex]
According to the given information, we have
(a, b) = (-14, -1), (c, d) = (4, -13) and m : n = 1 : 5.
Therefore, the co-ordinates of the point S are given by
[tex]\left(\dfrac{1\times4+5\times(-14)}{1+5},\dfrac{1\times(-13)+5\times(-1)}{}\right)\\\\\\=\left(\dfrac{4-70}{6},\dfrac{-13-5}{6}\right)\\\\\\=\left(\dfrac{-66}{6},\dfrac{-18}{6}\right)\\\\=(-11,-3)[/tex]
Thus, the required co-ordinates of the point S are (-11, -6).
Your little brother just learned how to flip and catch a coin. He believes that by catching the coin in mid-air, he can influence the probability that it will land heads up. Based on your understanding of theoretical probability, explain to your little brother why his theory of influence is false.
Answers
If a coin is fair then it has two faces , one is heads and the another is tails.
The probability getting any favorable outcomes is given by the formula :-
[tex]\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}[/tex]
So the factor effecting probability is just the number of favorable outcomes and total outcomes.
If a coin is tossed then the probability of getting heads will be :-
[tex]P(H)=\dfrac{1}{2}=0.5=50\%[/tex]
To get heads always this should be 1 , which can be happen if number of favorable outcomes is equal to total outcomes.
i.e. Number of heads = Number of total outcomes, this means coin should be biased.
Catching the coin in mid-air can never be a factor for this.
Therefore, the little brother's theory is false.
Answer:
Sample Response: The probability of a coin landing heads up is 1/2, or 50%. That fact will not change if the coin is caught in midair.
Step-by-step explanation:
someone answer and explain how to do this plz
Answers
Here height = 4 and base = 13
area = the height times the base divided by 2
13*4=52
52/2 = 26
area = 26 sq. units
An expression is shown below:
square root of 32 plus square root of 2
Which statement is true about the expression?
It is rational and equal to 4.
It is rational and equal to 5.
It is irrational and equal to 5 multiplied by square root of 2.
It is irrational and equal to 4 multiplied by square root of 2.
Answers
The answer is "It is irrational and equal to 5 multiplied by square root of 2."
Answer:
It is irrational and equal to [tex]5[/tex] multiplied by square root of [tex]2[/tex]
Step-by-step explanation:
we have
[tex]\sqrt{32}+\sqrt{2}[/tex]
Remember that
[tex]32=2^{5}[/tex]
substitute in the expression
[tex]\sqrt{2^{5}}+\sqrt{2}=4\sqrt{2}+\sqrt{2}=5\sqrt{2}[/tex]
therefore
It is irrational and equal to [tex]5[/tex] multiplied by square root of [tex]2[/tex]
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 5 and 625, respectively.
Answers
so (a1r^4) / (a1r) = r^3 = 625/5
r^3 = 125
r = 5
so a1* 5 = 5 giving a1 = 1
explicit rule is an = 5^(n-1)
you borrow $90 from your grandmother. you pay back $15 each week.
a. write an equation in standard for that represents the amount owed y after x weeks.
b. find the y intercept of the graph. what does this represent?
c. find the x intercept of the graph. what does this represent?
Answers
b. y = 90, The money you owe her initially, or after 0 weeks.
c. x = 6, The number of weeks until you pay her back all $90.
Answer: a) y = 90-15x
b) y = 90
c) x = 6
Step-by-step explanation:
Since we have given that
Amount borrowed from his grandmother = $90
Amount he pay back each week = $15
Let the number of weeks be 'x'.
Let total amount owed be 'y'.
So, it becomes
[tex]y=90-15x[/tex]
a) write an equation in standard for that represents the amount owed y after x weeks.
Our equation is [tex]y=90-15x[/tex]
b. find the y intercept of the graph. what does this represent?
For this , we put x = 0.
[tex]y=90-15(0)\\\\y=90[/tex]
So, the y-intercept of the graph is 90.
It represents that the graph intersect y-axis at (0,90)
c. find the x intercept of the graph. what does this represent?
For this, we put y = 0.
[tex]0=90-15x\\\\90=15x\\\\x=\dfrac{90}{15}\\\\x=6[/tex]
So, the x intercept of the graph is 6.
It represents that the graph intersect the x-axis at (6,0)
The length of a rectangle is 3 mm greater than the width. the area is 154 mm squared. find the length and the width.
Answers
area = l x w
l = w+3
sqrt(154) = 12.4 round o 12
12-1 = 11
11+3 = 14
11 * 14 = 154
width = 11
length = 14
Answer the questions that aren't covered please? Thanks
Answers
5. Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work. a. 3in, 4in, 5 in b. 5in, 6in, 7in c. 8in, 9in, 12in
Answers
The triangle with measures 3 in., 4 in. and 5 in. made up right angle triangle.
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
a) Given that, 3 in., 4 in. and 5 in.
By using Pythagoras theorem, we get
5²=3²+4²
25=9+16
25=25
So, the triangle is right triangle.
b) The given sides of triangle measures 5 in., 6 in. and 7 in.
To determine whether the triangle is acute, right, or obtuse, add the squares of the two smaller sides, and compare the sum to the square of the largest side.
7²<5²+6²
49<25+36
49<61
So, the triangle is acute angle triangle.
c) The given sides of triangle measures 8 in., 9 in. and 12 in.
12²>8²+9²
144>64+81
144>125
So, the triangle is obtuse angle triangle.
Therefore, the triangle with measures 3 in., 4 in. and 5 in. made up right angle triangle.
Learn more about the triangle here:
brainly.com/question/2773823.
#SPJ7
How to simplify all this numbers to make one equation?
Answers
6-x-2-4x, then you must combine like terms
(-x-4x)+(6-2)
-5x+4
Determine the equation of the graph and select the correct answer below.
y = (x + 1)2 + 3
y = (x + 1)2 − 3
y = (x − 1)2 − 3
y = (x − 1)2 + 3
Answers
vertex form is y = (x-h)^2 + k
where h,k) is the vetex
so here we have y = (x - 1)^2 - 3
Its C
You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. find the probability that the first card is a king and the second card is a queen.
Answers
there are 4 kings and 4 queens in a deck
chance of getting a king is 1/52
chance of getting a queen without the king being put back would be 1/51
1/52 x 1/51 = 1/2652 probability
The probability of drawing first a king and then a queen from a standard deck without replacement is 0.603%, which is calculated by multiplying the individual probabilities of drawing a king and then a queen (1/13 * 4/51).
The student is asking about how to calculate the probability of drawing two specific cards from a deck of cards in succession without replacement. In a standard deck of 52 cards, the probability of drawing a king first is 4/52 since there are four kings in the deck. After drawing a king, there are 51 cards left, and the probability of drawing a queen next is 4/51 because there are four queens in the deck. These events are dependent because the outcome of the second draw depends on the first.
To find the combined probability of both events happening, we multiply the probabilities of each event:
P(first card is a king) = 4/52
P(second card is a queen after drawing a king) = 4/51
So, the probability is (4/52) * (4/51), which simplifies to 1/13 * 4/51.
Combined probability = (1/13) * (4/51) = 4/663 = 0.006033182503770739, or about 0.603% when expressed as a percentage.
Find the surface area of a hemisphere with a diameter of 26 cm. Round your answer to the nearest tenth.
Answers
Hence, the surface area of a hemisphere is half that, [tex]2 \pi r^{2} [/tex].
If the base is also included then the surface area will be [tex]3 \pi r^{2} [/tex].
Given,
Diameter = 26 cm
Therefore, Radius = [tex] \frac{26}{2} [/tex] = 13 cm
Thus,
Area = [tex]3 * \pi * 13^{2} = 3 * \pi * 169 = 507 \pi = [/tex] = 1592.8 [tex] cm^{2} [/tex] [approx.]
The following is a geometric sequence.
1, 2, 6, 24
TRUE
FALSE
Answers
Which of the following is the coefficient in the algebraic expression 8x+z^2
Answers
Answer:
The coefficients are 8 and 1.
Step-by-step explanation:
In order to determine the answer, we have to know about algebraic expressions.
An algebraic expression is conformed by terms or only one term.
A term is just a variable with a coefficient. Also similar terms have the same variable but no always the same coefficient. Therefore if the algebraic expression has two terms, so there are two coefficients. The coefficient with value "1" is not necessary write it.
In this case, we have two terms:
"x" variable."z" variable.So, we have two coefficients:
For x, the coefficient 8.For z, the coefficient 1.Finally, the coefficients are 8 and 1.
Choose the linear inequality that describes the graph. The gray area represents the shaded region
Answers
slope = (-2-3) / (1 - 0) = -5
y int is (0,3)
line is dashed, means no equal sign....shading above the line, means greater then
ur inequality is : y > -5x + 3
Answer:
y > -5x + 3
Step-by-step explanation:
Based on the graph, what are all of the solutions to f(x) = x3 − 7x − 6? x = −6 x = −2, −1 x = −2, −1, 3 x = −6, −2, −1, 3
Answers
x = −2, −1, 3 are solutions of equation : f(x) = 0
because : f(-2) = f(-1) = f(3) = 0
Which sequence of transformations creates a similar but not congruent triangle?
A. Dilation and reflection
B. Reflection and rotation
C.Reflection and translation
D.Translation and rotation
Answers
dilation will make bigger or smaller therefore it cannot be congruent
Answer:
A
Step-by-step explanation:
Can someone help me please ? Thanks!
Answers
a. 3, 4, 5
3^2+4^2?5^2
9+16?25
25=25
right
b. 5, 6, 7
5^2+6^2=7^2
25+36=49
61>49
acute
c. 64+81=144
145>144
acute
hope this helps!
Assume 3 vertices are a,b,c
if a^2 + b^2 < c^2 ->it's obtuse
a^2 + b^2 = c^2 ->it's right
a^2 + b^2 > c^2 ->it's acute
First one is right apparently, similar combination of right triangle include 6,8,10
A collection of 24 coins, consisting of nickels, dimes, and quarters, has a value of $3.40. if there are twice as many quarters as nickels, and one-third as many nickels as dimes, how many coins of each kind are there?
Answers
8x.25=2
12x.1=1.2
4x.05=.2
2+1.2+.2=3.4
HELP ME!!!! PLEASE!!!! Ughhh
Answers
Opposite =12
Adjacent = 5
tan(67°) = 12/5
Solve for h: a = 1/2bh
h = A over 2b
h = A/b (1 /2)
h = 2Ab
h = 2A/b
Answers
NEED HELP!!!!
Which of the following types of statement cannot be used to explain the steps of a proof? Check all that apply.
1.Postulate
2.Theorem
3.Conjecture
4.Guess
Choose more then 1
Answers
Answer:
Please don't use the answer that was given ,,, the correct answer is GUESS and Conjecture
Step-by-step explanation:
Jorani flips two standard american quarters. how many ways can she get at least one head?
Answers
she can get
1 head 1 tail
1 tail 1 head
2 tails
2 heads
3 of the ways has at least 1 head
3 ways