Answer:
1/100
Step-by-step explanation:
Since the numerators are all the same, the lowest value will depend on the denominators. The greater the denominator, the lower the value. Thus, the answer is 1/100
If it takes 7lb of flour to make 3 loaves of bread, how much flour is needed to make 4 loaves of bread?
Answer:
28/3 or 9 1/3 pounds
Step-by-step explanation:
Let's set up a proportion using the following setup:
pounds/loaves=pounds/loaves
We know that 7 pounds of flour is needed for 3 loaves. We don't know how many pounds are needed for 4 loaves, therefore we can say x pounds are needed for 4 loaves.
7 pounds/ 3 loaves= x pounds/ 4 loaves
7/3=x/4
We want to find out what x (flour needed for 4 loaves) is. We have to get x by itself.
x is being divided by 4. We need to perform the inverse operation. The opposite of division is multiplication. Therefore, we should multiply both sides of the equation by 4.
4*(7/3)=(x/4)*4
4*7/3=x
9.333333=x
x=9.33 or 28/3 or 9 1/3
It will take 28/3 or 9 1/3 pounds of flour to make 4 loaves of bread.
Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.0 millimeters (mm) and a standard deviation of 1.7 mm. For a randomly found shard, find the following probabilities.
a. the thickness is less than 3.0 mm
b. the thickness is more than 7.0 mm
c. the thickness is between 3.0 mm and 7.0 mm
Answer:
(a) The probability that the thickness is less than 3.0 mm is 0.119.
(b) The probability that the thickness is more than 7.0 mm is 0.119.
(c) The probability that the thickness is between 3.0 mm and 7.0 mm is 0.762.
Step-by-step explanation:
We are given that thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.0 millimeters (mm) and a standard deviation of 1.7 mm.
Let X = thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village.
So, X ~ Normal([tex]\mu=5.0,\sigma^{2} =1.7^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean thickness = 5.0 mm
[tex]\sigma[/tex] = standard deviation = 1.7 mm
(a) The probability that the thickness is less than 3.0 mm is given by = P(X < 3.0 mm)
P(X < 3.0 mm) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{3.0-5.0}{1.7}[/tex] ) = P(Z < -1.18) = 1 - P(Z [tex]\leq[/tex] 1.18)
= 1 - 0.8810 = 0.119
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
(b) The probability that the thickness is more than 7.0 mm is given by = P(X > 7.0 mm)
P(X > 7.0 mm) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{7.0-5.0}{1.7}[/tex] ) = P(Z > 1.18) = 1 - P(Z [tex]\leq[/tex] 1.18)
= 1 - 0.8810 = 0.119
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
(c) The probability that the thickness is between 3.0 mm and 7.0 mm is given by = P(3.0 mm < X < 7.0 mm) = P(X < 7.0 mm) - P(X [tex]\leq[/tex] 3.0 mm)
P(X < 7.0 mm) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{7.0-5.0}{1.7}[/tex] ) = P(Z < 1.18) = 0.881
P(X [tex]\leq[/tex] 3.0 mm) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{3.0-5.0}{1.7}[/tex] ) = P(Z [tex]\leq[/tex] -1.18) = 1 - P(Z < 1.18)
= 1 - 0.8810 = 0.119
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
Therefore, P(3.0 mm < X < 7.0 mm) = 0.881 - 0.119 = 0.762.
Mary is running a marathon which is a total of 26 miles. She is running at a pace of 7.5 miles per hour and
has already run 8 miles. If she stays at the same pace, how much time in hours does she have left?
Answer:
2.4 hours
Step-by-step explanation:
If Mary is running 26 miles at a pace of 7.5 miles per hour, it will take her 3.47 hours to run the full course.
26/7.5 = 3.466666...
If she has run 8 miles, 1.07 hours have passed.
8/7.5 = 1.06666666...
Subtract the total time from the time that has already passed to find the time left.
3.47 - 1.07 = 2.4
Mary has 2.4 hours left.
Solve the linear equality 4x-7 <5
Answer:
X<3
Step-by-step explanation:
4x-7 <5
4x < 5+7
4x < 12
X < 12/4
X < 3
Hope this helps..
Good Luck!
Blake is going to invest in an account paying an interest rate of 1.5% compounded quarterly. How much would Blake need to invest to the nearest dollar, for the value of the account to reach $910 in 10 years
Answer:
$783.46
Step-by-step explanation:
Compounded interest rate (quarterly) formula: A = P(1 + r/4)^4t
Simply plug in our known variables and solve:
910 = P(1 + 0.015/4)^4(10)
910 = P(1.00375)^40
910 = 1.16151P
P = 783.464
Answer: 783
Step-by-step explanation:
Cynthia grandpa says that his first simple calculator cost 80 Cynthia knows she just bought a new Calculator for four dollars what is the percent decrease in the price of a calculator
Answer:
0.16
Step-by-step explanation:
turning into.a decimal to.find you answer
Price of calculator is 95% decreased.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given,
Price of the Grandpa's calculator = $80
Price of new calculator = $4
Price decreased = $80 - $4 = $76
Price decrease in percentage = ($76/$80) × 100
= 0.95 × 100
= 95 %
Hence, there is 95% of decrease in price of calculator.
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Find the volume of the cone.
Diameter: 20 m, Slant Height: 26 m
Round to the nearest whole number.
Volume
=
[?] m3
Answer:
2513the step-by-step explanation for height first :
[tex]h=\sqrt{h^{2} } +r^{2} =26[/tex]
[tex]h=\sqrt{h^{2} } +10^{2} =676[/tex]
[tex]h=\sqrt{h^{2} } + 100 = 676[/tex]
[tex]100-100 = 0[/tex]
[tex]676-100=576[/tex]
[tex]\sqrt{576}[/tex]
[tex]height =[/tex] 24 m
________________
step-by-step explanation for the problem :
FORMULA : [tex]v = \frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]
v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]10^{2}[/tex] · [tex]24[/tex] = [tex]800\pi[/tex] = [tex]2513.27412[/tex] = 2513
The State of Nevada has seatbelt laws for drivers. It is known that 68 % of the drivers wear seatbelts. A sample of six drivers is selected.The average number of people you should expect to find wearing their seatbelt is
A. 4.08
B. 3.34
C. 6.68
D. 4.26
Answer:
A . 4.08
The average number of people you should expect to find wearing their seat belt is
μ= n p = 4.08
Step-by-step explanation:
Step(i):-
Given the probability that drivers wear seat belts
p = 68% =0.68
Given sample size 'n' =6
we will use binomial distribution
mean of the binomial distribution μ= n p
step(ii):-
The average (0 r) mean of the binomial distribution
μ= n p = 6 X 0.68 = 4.08
The standard deviation of the binomial distribution
σ = √npq
= [tex]\sqrt{6 X 0.68 X 0.32} = 1.142[/tex]
Final answer:-
The average number of people you should expect to find wearing their seat belt is
μ = 4.08
The standard deviation of the people you should expect to find wearing their seat belt is
σ = 1.142
If the endpoints of AB have the coordinates A(9, 8) and B(-1, -2), what is the AB midpoint of ?
Answer:
(4, 3)
Step-by-step explanation:
Use the midpoint formula: [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2} )[/tex]
Given the following functions f(x) and g(x), solve f[g(6)]. f(x) = 6x + 12 g(x) = x − 8
Answer:
Answer:
Option 2nd is correct.
=0.
Step-by-step explanation:
Given the function:
Solve:
First calculate:
f[g(x)]
Substitute the function g(x)
Replace x with x-8 in the function f(x) we get;
The distributive property says that:
Using distributive property:
⇒
Put x = 6 we get;
Therefore, the value of is 0.
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
f(x) = 6x + 12
g(x) = x − 8
f(g(6))=?
g(6)=6-8= -2
f(-2)= -2*6+12= -12+12=0
f(g(6))= f(-2)=0
Which describes how to calculate density? .mass divided by volume .volume divided by mass .mass added to volume .volume subtracted from mass added to volume volume subtracted from mass
Answer:
mass divided by volume
Step-by-step explanation:
The density can be calculated as the mass divided by volume. So, the correct option is A.
How to find the density?Density is like rate. It tells you how much of a thing is available for each unit other thing which contains the first thing.
Density = (Total amount available)/(total space which contains that amount)
Suppose that a finite amount of substance is there having its properties as:
The mass of substance = m kg
The density of substance = d kg/m³
The volume of that substance = v m³
Then, they are related as:
[tex]d = \dfrac{m}{v}[/tex]
Therefore, the density can be calculated as the mass divided by volume. So, the correct option is A.
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If school A is ahead of school B on day 6 which I statement might be true ?
Answer:
The third answer should be correct :)
What two numbers is the square root of 74 between?
Answer:
8 and 9
Step-by-step explanation:
√64 = 8
√81 = 9
√74 falls inbetween those 2
A triangle has side lengths of $10,$ $24,$ and $26.$ Let $a$ be the area of the circumcircle. Let $b$ be the area of the incircle. Compute $a - b.$
Answer:
a-b = 156πStep-by-step explanation:
For the inscribed circle
Formula for calculating the radius of an inscribed circle in a triangle r = Area of the triangle/0.5 of its perimeter
Given a triangle of side 10, 24 and 26.
Area of the triangle = 1/2 * base * height
Area of the triangle = 1/2*10*24
Area of the triangle = 120
Perimeter of the triangle = 10+24+26 = 60
radius of the inscribed circle = 120/0.5(60)
r = 120/30
r = 4
Area of the incircle b = πr² = π(4)² = 16π
For the circumcircle
Formula for calculating the radius of a circumcircle outside a triangle
R = abc/4√s(s-a)(s-b)(s-c)
s = a+b+c/2
a, b and c are the length of the 3 sides
s = 10+24+26/2
s = 60/2 = 30
R = 10(24)(26)/4√30(20)(6)(4)
R = 6240/4*120
R = 13
radius of the circumcircle = 13
Area of the circumcircle a = πR² = π(13)² = 169π
a - b = 169π - 16π
a-b = 156πAnswer:
It's 153 pi.
Step-by-step explanation:
Solution:
Let the triangle be $ABC,$ with $AB = 10,$ $BC = 24,$ and $AC = 26.$
Since $10^2 + 24^2 = 26^2$, we know that $\triangle ABC$ is a right triangle with hypotenuse $\overline{AC}$. The hypotenuse of a right triangle is a diameter of the triangle's circumcircle, so the area of the circumcircle of $ABC$ is $(26/2)^2\pi = 169\pi$.
Turning to the incircle, we start with the fact that $[ABC] = rs$, where $r$ is the inradius and $s$ is the semiperimeter of the triangle. We have $[ABC] = (10)(24)/2 = 120$ and $s = (10+24+26)/2 = 30$, so $r = [ABC]/s = 120/30 = 4$. Therefore, the area of the incircle is $4^2\pi = 16\pi$.
Finally, the area of the circumcircle is $169\pi - 16\pi = \boxed{153\pi}$ greater than the area of the incircle.
12x - y = -4
4x - 3y = -6 (1 point)
Answer:
Step-by-step explanation:
12x - y = -4 ----------------------(I)
4x - 3y = -6 ---------------------(II)
Multiply equation (I) by (-3)
(I)*(-3) -36x + 3y = 12
(II) 4x - 3y = - 6 {Add and y will be eliminated}
- 32x = 6
x = 6/-32
x = -3/16
Plugin the value of x in equation (I)
[tex]12*\frac{-3}{16} -y=-4\\\\3*\frac{-3}{4}-y=-4\\\\\frac{-9}{4}-y = -4\\\\-y=-4+\frac{9}{4}\\\\-y=\frac{-4*4}{1*4}+\frac{9}{4}\\\\-y=\frac{-16}{4}+\frac{9}{4}\\\\-y=\frac{-7}{4}\\\\y=\frac{7}{4}\\\\y=1\frac{3}{4}[/tex]
Which explains how to find the radius of a circle whose equation is in the form x2 + y2 = z?
Answer:
z would be your radius
Step-by-step explanation:
Equation: (x - h)² + (y - k)² = r²
Simply take √r² to find r, your radius.
Answer:
The radius is the square root of the constant term, z.
Step-by-step explanation:
option C on edgenuity 2020
hope this helps!
Which statement represents a true conclusion, based on the Venn diagram? All real numbers are even numbers. All numbers that are multiples of three are even numbers. Some numbers that are multiples of three are also even numbers. No numbers that are multiples of three are also even numbers.
Answer:
Some number that are multiples of three are also even numbers
Step-by-step explanation:
In the picture
The statement represents a true conclusion, based on the Venn diagram is option A) Some numbers that are multiples of three are also even numbers
What are real numbers?The numbers which are not imaginary and can be quantified are real numbers.Real numbers can be positive or negative, and include the number zero. Imaginary numbers are numbers that cannot be quantified, like the square root of -1-2,-1.1 etc.What are even numbers?They are whole numbers that can be be divided by two into two equal value. examples 2,4,6,8 etc.
According to the question:-
A) All real numbers are even numbers.
B) All numbers that are multiples of three are even numbers.
C) Some numbers that are multiples of three are also even numbers
D) No numbers that are multiples of three are also even numbers.
OPTION C is the answer of the given question example 4*3,6*3 etc.
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if 25% or the person'so salary is $135.75 then what is the amount of his full salary?
Answer:
543
Step-by-step explanation:
let x= total salary
0.25x=135.75
x=543
Answer:
[tex]\$ \: 543.00[/tex]
Step-by-step explanation:
[tex]25\% \times x =135.75[/tex]
[tex]1/4 \times x =135.75[/tex]
[tex]0.25 \times x =135.75[/tex]
[tex]x=135.75 \times 4[/tex]
[tex]x=543[/tex]
A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer to the same household). Suppose P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8. Compute the following.a. P(A ∩ B).b. The probability that the lifeline usage amount is exceeded in exactly one of the two months.
Complete question is;
A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer to the same household). Suppose P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8. Compute the following.
a. P(A ∩ B).
b. The probability that the lifeline usage amount is exceeded in exactly one of the two months.
Answer:
A) 0.4
B) 0.4
Step-by-step explanation:
We are given;
P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8
A) To solve this question, we will use the the general probability addition rule for the union of two events which is;
P(A∪B) = P(A) + P(B) − P(A∩B)
Making P(A∩B) the subject of the equation, we have;
P(A∩B) = P(A) + P(B) − P(A∪B)
Thus, plugging in the relevant values, we have;
P(A∩B) = 0.7 + 0.5 - 0.8
P(A∩B) = 0.4
B)The probability that the lifeline usage amount is exceeded in exactly one of the two months can be described in terms of A and B as:
P(A but not B) + P(B but not A) = P(A∩B') + P(B∩A')
where;
A' is compliment of set A
B' is compliment of set B
Now,
P(A∩B') = 0.7 − 0.4 = 0.3
P(B∩A') = 0.5 − 0.4 = 0.1
Thus;
P(A but not B) + P(B but not A) = 0.1 + 0.3 = 0.4
8x+7-3=-20 solve for equation
What is provided won't really end up being an equation... however. you can just solve for x if you wanted
8x+7-3=-20
8x+4=-20
8x=-24
x=-3
Answer:
x=-3
Step-by-step explanation:
The speed of cars passing through the intersection of Blossom Hill Road and the Almaden Expressway varies from 14 to 35 mph and is uniformly distributed. None of the cars travel over 35 mph through the intersection.Required:a. What is the probability that the speed of a car is at most 26 mph?b. What is the probability that the speed of a car is between 18 and 22 mph?c. What is the probability that the speed of a car is below 19 given that it is below 56 mph?d. What is the probability that the speed of a car is exactly 19 or 56 mph
Answer:
a)[tex] P(14\leq X \leq 26) = \frac{12}{21}[/tex]
b) [tex]P(18\leq X \leq 22) = \frac{4}{21}[/tex]
c) [tex]P(X\leq 19) = P(14\leq X \leq 19) = \frac{5}{21}[/tex]
d) [tex]P(\{X=19\}\cup\{X=56\}) = 0[/tex]
Step-by-step explanation:
Let X be the speed of a car. So, we know that X is distributed uniformly over the interval [14,35]. Recall that if X is distributed uniformly over the set [a,b] then the density function of X is
[tex] f(x) = \frac{b-a}[/tex if x is in the set [a,b] and 0 otherwise.
So in our case, the density function is [tex] f(x) = \frac{1}{21}[/tex]. Using this function we have that
[tex]\text{P}(a \leq X\leq b) = \int_{a}^{b} f(x) dx[/tex]. In this case
[tex]P(a\leq X \leq b = \int_{a}^{b} \frac{1}{21}dx = \frac{b-a}{21}[/tex] when a,b are in [14,35].
a).We are asked for [tex]P(X\leq 26) = P(14\leq X \leq 26) = \frac{26-14}{21}=\frac{12}{21}[/tex]
b) [tex]P(18\leq X \leq 22) = \frac{4}{21}[/tex]
c) Note that since 35 < 56 it is always true that the speed is under 56. So, the probability that the speed of the car is less than 19 given that the speed is below 56 is the same as having the probability that the speed is less than 19. That is
[tex]P(X\leq 19) = P(14\leq X \leq 19) = \frac{5}{21}[/tex]
d) It is impossible that the speed is 19 and 56 at the same time, so the probability that the speed is 19 and 56 is 0. Since the speed is at most 35, it is impossible that the speed is 56. So the probability of having that the speed is 56 is 0. Recall from the definition that
[tex] P(X=19) = P(19\leq X \leq 19) = \frac{19-19}{21} = 0[/tex]
So, using the following formula for events A,B
[tex]P(A\cup B) = P(A)+P(B) - P(A\cap B) [/tex]
then,
[tex]P(\{X=19\}\cup\{X=56\}) = 0[/tex]
Scores on a recent national statistics exam were normally distributed with a mean of 82.2 and a standard deviation of 5.If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award
Answer:
The lowest score eligible for an award is 92.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 82.2, \sigma = 5[/tex]
If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award
The lowest score is the 100 - 2.5 = 97.5th percentile, which is X when Z has a pvalue of 0.975. So X when Z = 1.96. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 82.2}{5}[/tex]
[tex]X - 82.2 = 5*1.96[/tex]
[tex]X = 92[/tex]
The lowest score eligible for an award is 92.
Ten years ago 53% of American families owned stocks or stock funds. Sample data collected by the Investment Company Institute indicate that the percentage is now 44%. (a) Choose the appropriate hypotheses such that rejection of H0 will support the conclusion that a smaller proportion of American families own stocks or stock funds this year than 10 years ago. H0: p - Select your answer - Ha: p - Select your answer - (b) Assume the Investment Company Institute sampled 300 American familie
Answer:
a) The null and alternative hypothesis are:
[tex]H_0: \pi=0.53\\\\H_a:\pi<0.53[/tex]
b) If 300 families were sampled, for a significance level of 5%, there is enough evidence to support the claim that a smaller proportion of American families own stocks or stock funds this year than 10 years ago (P-value = 0.001).
Step-by-step explanation:
The claim that we want to have evidence to support is that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.
The hypothesis for this test should state:
- For the null hypothesis, that the population proportion is not significantly different from 53%.
[tex]H_0:\pi=0.53[/tex]
- For the alternative hypothesis, that the population proportion is significantly less than 53%.
[tex]H_a: \pi<0.53[/tex]
If 300 families are sampled, we can perform a hypothesis test for a proportion.
The claim is that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.53\\\\H_a:\pi<0.53[/tex]
The significance level is 0.05.
The sample has a size n=300.
The sample proportion is p=0.44.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.53*0.47}{300}}\\\\\\ \sigma_p=\sqrt{0.00083}=0.029[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.44-0.53+0.5/300}{0.029}=\dfrac{-0.088}{0.029}=-3.065[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-3.065)=0.001[/tex]
As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.
On one episode of his show, a radio show host encouraged his listeners to visit his website and vote in a poll about proposed tax increases. Of the 4821 people who vote, 4277 are against the proposed increases. To which of the following populations should the results of this poll be generalized?
(a) All people who have ever listened to this show
(b) All people who listened to this episode of the show
(c) All people who visited the show host's website
(d) All people who voted in the poll
(e) All people who voted against the proposed increases
Answer:
(d) All people who voted in the poll.
Step-by-step explanation:
The poll can only be generalized to the people who voted in the poll.
Out of this poll we get a estimation of the population proportion. But about the people who listen to the show but did not vote in the poll or even the ones that visit the website but did not vote, we can not infere nothing using the results of the poll as we don't know if they are against the proposed increases or not.
If the people who voted in the poll were a representative sample of certain group, then we could generalize the results for this group.
In a class⅗ of the children are going to special event If there are 30 children in the class,how many are going
Answer:
18
Step-by-step explanation:
3/5 x 30
(3 times 30)divided by 5
= 18 children are going.
Hope this helps:-)
Find the distance from the point (1, 4) to the line y = 1/3x – 3. A) 2(square root) 10 units B) 4 units C) 4(square root) 2 units D) 20 units
Answer:
Distance between line and point =
4√5 -3/2√10
Step-by-step explanation:
Distance between the line is
= √ ((9-0)²+(0+1)²)
= √ (89+1)
= √90
= 3√10
Half of the line = 3/2√10
Distance of one side of the line and the point.
= √((9-1)²+(0-4)²)
= √((8)²+(-4)²)
=√64+16
= √80
= 4√5
Distance between line and point =
4√5 -3/2√10
Answer: 2 square root 10 units
Step-by-step explanation: A
Which expression is equivalent to 8√6
a √14
b √48
c √96
d √384
The equivalent expression of 8√6 is √384, because when it is simplified, it gives the same value.
What is Equivalent ExpressionA mathematical expression that can be streamlined or reorganized to have the same value as the original expression but with a different form is known as an equivalent expression. The commutative, associative, and distributive qualities of arithmetic, as well as the properties of operations like simplifying fractions, combining like terms, and manipulating the order of operations, are used to create equivalent expressions.
For instance, regardless of the value of x, the equations 2x + 3x and 5x reflect the same value and are therefore identical. The like phrases 2x and 3x can be combined to make both expressions simpler to 5x.
A mathematical expression that can be streamlined or reorganized to have the same value as the original expression but with a different form is known as an equivalent expression. The properties of arithmetic, as well as the properties of operations like simplifying fractions, combining like terms, and manipulating the order of operations, are used to create equivalent formulations.
In the expression given;
The expression 8√6 have an equivalent of √384.
This is because the simplified form of √384 is 8√6
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Answer:
D.) √384
Step-by-step explanation:
200 × 65 inches and feet
Answer:
200x65=13000
Step-by-step explanation:
What do u mean by inches and feet?
Answer:
200*65=13000
but i have no clue what the inches and feet are about...
Step-by-step explanation:
help asap plz zzzzzz
Answer:
Area of the triangle = 10 m²
Step-by-step explanation:
If you flip the triangle upside down, You get a triangle with a base of 5 and height of 4. You can use the triangle area formula [tex]\frac{1}{2} *b*h[/tex] to solve.
[tex]\frac{1}{2} *5*4=\\\\\frac{1}{2} *20=\\\\10[/tex]
The triangle's area is 10
Stevin product Calculate (x + 9) (x + 12): a)x² - 21x - 108 b)x² - 21x + 108 c)x² + 21x + 108 d)x² + 21x - 108 e)x² - 21x - 108
Answer:
The answer is C.
Step-by-step explanation:
You have to apply Distributive Law :
[tex]a(m + n) = am + an[/tex]
So for this question :
[tex](x + 9)(x + 12) [/tex]
[tex] = x(x) + x(12) + 9(x) + 9(12)[/tex]
[tex] = {x}^{2} + 12x + 9x + 108[/tex]
[tex] = {x}^{2} + 21x + 108[/tex]
