Answer:
Step-by-step explanation:
$1,250,000 in current assets (cr) and $500,000 in current liabilities(cl)
current ratio (cr)=1250000/500000=2.5
Δ note payable ( change in note payable NP)
minimum current=2.2
2.2=(1250000+ΔNP)/(500000+ΔNP)
2.2(500000+ΔNP)=1250000+ΔNP
1100000+2.2ΔNP=1250000+ΔNP
2,2ΔNP-ΔNP=1250000-1100000
1.2ΔNP=150000
ΔNP=150000/1.2=125000
Nelson's short-term debt (notes payable) increase without pushing its current ratio below 2.2=125000
assuming this amount used to increase the inventory
new inventory=335000+125000=360000
current asset= 1250000+125000=1375000
the new ratio=(1375000-360000)/500000+125000
new ratio = 1.624
George has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x2−3x+4 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r−c)(3) mean about George's new store?
This is a great question!
When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -
[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]
____
Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,
[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]
Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,
( 1. The new store will have a profit of $3400 after its third month in business.
( 2. The new store will have a profit of $2400 after its third month in business.
( 3. The new store will sell 2400 items in its third month in business.
( 4. The new store will sell 3400 items in its third month in business.
The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
Substitution:The substitution method is the algebraic method to solve simultaneous linear equations.
Given function is,
[tex]r(x) = x^2+5x+14[/tex]...(1)
And [tex]c(x) = x^2-4x+5[/tex]...(2)
Now, substituting the value into the equation (1) and (2).
[tex]r(5) = (5)^2+5(5)+14=64[/tex]
[tex]c(5) = (5)^2-4(5)+5=10[/tex]
Therefore,
[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]
Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
Learn more about the topic Substitution:
https://brainly.com/question/3388130
How many bits does it take to identify uniquely every person in the United States (the current population is about 300 million)?
Answer:
what's a bit
Step-by-step explanation:
The function defined by w(x)=-1.17x+1260 gives the wind speed w(x)(in mph) based on the barometric pressure x (in millibars,mb). a) Approximate the wind speed for a hurricane with the barometric pressure of 900mb. b) Write a function representing the inverse of w and interpret its meaning in context. c) Approximate the barometric pressure for a hurricane with speed 90 mph.
Answer:
a) 207 mph
b) x = (1260-w)/1.17
c) 1000 mb
Step-by-step explanation:
a) Put the pressure in the equation and solve.
w(900) = -1.17(900) +1260 = 207
The wind speed for a hurricane with a pressure of 900 mb is 207 mph.
__
b) Solving for x, we have ...
w = -1.17x +1260
w -1260 = -1.17x
x = (1260 -w)/1.17 . . . . inverse function
__
c) Evaluating the inverse function for w=90 gives ...
x = (1260 -90)/1.17 = 1170/1.17 = 1000 . . . millibars
The approximate barometric pressure for a hurricane with a wind speed of 90 mph is 1000 millibars.
Find a solution to the linear equation y=12x−24
Answer:
I didn't know which one you wanted...
Step-by-step explanation:
1. Finding the x an y-intercepts
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (2,0)
y-intercept(s): (0,−24)
2. Finding the slope and y-intercept
Use the slope-intercept form to find the slope and y-intercept.
Slope: 12
y-intercept: −24
Write the equation in the form Ax + By = C. Find an equation of a line passing through the pair of points (4,7) and (3,4).
Answer:
[tex] 3x - y = 5 [/tex]
Step-by-step explanation:
The two pint equation of a line:
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
We have
[tex] x_1 = 4 [/tex]
[tex] x_2 = 3 [/tex]
[tex] y_1 = 7 [/tex]
[tex] y_2 = 4 [/tex]
[tex] y - 7 = \dfrac{4 - 7}{3 - 4}(x - 4) [/tex]
[tex] y - 7 = \dfrac{-3}{-1}(x - 4) [/tex]
[tex] y - 7 = 3(x - 4) [/tex]
[tex] y - 7 = 3x - 12 [/tex]
[tex] 5 = 3x - y [/tex]
[tex] 3x - y = 5 [/tex]
Figure ABCDE was reflected across the line y=x to create figure A’B’C’D’E’. What are the coordinates of the pre image of E?
Answer
so I need to know the coordinates for me to tell you the answer but I think I can still help you by explaining.
In order for E to become E' the rule for reflection over y=x is (y, x) so you basically switch the x and the Y to have E'. so for you to be able find out E, you need to witch the x and the y.
for example:
if E' was (-2, 3)
E in the pre image would be (3, -2)
hope this helps :)
Answer:
(-2,6)
Step-by-step explanation:
Just did it edge 2021
State if the triangles in each pair are similar. If so, State how you know they are similar and complete the similarity statement.
Answer:
Answer is option 2
Step-by-step explanation:
We know that Angle M = Angle G (given in diagram)
We also know that Angle L in triangle LMN is equal to Angle L in triangle LGH
As two angles are equal in both triangles they are similar.
But why is it Triangle LGH instead of Triangle HGL?
As we know M=G therefore they should be in the same place in the name Of the triangle. In triangle LMN M is in the middle therefore Angle G should also be in the middle
A man is twice the age of his son,in 20 years time, the son's age will be 2/3 of that his father. what is the son's present age?
Answer:
20 years old.
Step-by-step explanation:
Let us say that the man's age is represented by x and the son's age is represented by y.
As of now, x = 2y.
In 20 years, both ages will increase by 20. We can have an equation where the son's age increased by 20 equals 2/3 of the man's age plus 20.
(y + 20) = 2/3(x + 20)
Since x = 2y...
y + 20 = 2/3(2y + 20)
3/2y + 30 = 2y + 20
2y + 20 = 3/2y + 30
1/2y = 10
y = 20
To check our work, the man's age is currently double his son's, so the man is 40 and the son is 20. In 20 years, the man will be 60 and the son will be 40. 40 / 60 = 2/3, so the son's age is 2/3 of his father's.
So, the son's present age is 20 years old.
Hope this helps!
Translate into an equation: The cost of V ounces at $2 per ounce equals $56.
Answer:
V = number of ounces
56 = 2V
Step-by-step explanation:
Answer:28
Step-by-step explanation:V times 2= 56
if the line〈3 + 2t,1 +t,2−t〉intersects the unit sphere inR3given byx2+y2+z2= 1,and if so, at what points.
Answer:
[tex]( x_1 , y_1 , z_1 ) = < -7 + 4\sqrt{3} , -4 + 2\sqrt{3} , 7 - 2\sqrt{3} >\\\\( x_2 , y_2 , z_2 ) = < -7 - 4\sqrt{3} , -4 - 2\sqrt{3} , 7 + 2\sqrt{3} >\\[/tex]
Step-by-step explanation:
Solution:-
- We are given a parametric form for the vector equation of line defined by ( t ).
- The line vector equation is:
L: < 3 + 2t , t + 1 , 2 -t >
- The same 3-dimensional space is occupied by a unit sphere defined by the following equation:
[tex]S: x^2 + y^2 + z^2 = 1[/tex]
- We are to determine the points of intersection of the line ( L ) and the unit sphere ( S ).
- We will substitute the parametric equation of line ( L ) into the equation defining the unit sphere ( S ) and solve for the values of the parameter ( t ):
[tex]( 3 + 2t )^2 + ( 1 + t )^2 + ( 2 - t)^2 = 1\\\\( 9 + 12t + 4t^2 ) + ( t^2 + 2t + 1 ) + ( 4 + t^2 -4t ) = 1\\\\t^2 + 10t + 13 = 0\\\\[/tex]
- Solve the quadratic equation for the parameter ( t ):
[tex]t = -5 + 2\sqrt{3} , -5 - 2\sqrt{3}[/tex]
- Plug in each of the parameter value in the given vector equation of line and determine a pair of intersecting coordinates:
[tex]( x_1 , y_1 , z_1 ) = < -7 + 4\sqrt{3} , -4 + 2\sqrt{3} , 7 - 2\sqrt{3} >\\\\( x_2 , y_2 , z_2 ) = < -7 - 4\sqrt{3} , -4 - 2\sqrt{3} , 7 + 2\sqrt{3} >\\[/tex]
The world’s population is currently estimated at 7,125,000,000. What is this to the nearest billion? billion
Answer:
7,000,000,000
Step-by-step explanation:
since the closest number is less than 5 (1<5) you round down making the nearest billion 7
Answer:
7,000,000,000 OR 7 Billion
Step-by-step explanation:
Since the 1 is millions place and its less than 5, you need to round down meaning that 7,125,000,00 rounded to the nearest billion is 7 billion.
if g (x) = 2x + 2, find g (a + h) - g (a)
Answer:
[tex] g(x) = 2x+2[/tex]
Let's find g(a+h):
[tex] g(a+h)=2*(a+h) +2= 2a +2h +2[/tex]
And now let's find g(a)
[tex] g(a)= 2a+2[/tex]
And now finally:
[tex] g(a+h) = 2a +2h +2 -2a-2 = 2h +2-2= 2h[/tex]
Step-by-step explanation:
We have the following function given:
[tex] g(x) = 2x+2[/tex]
Let's find g(a+h):
[tex] g(a+h)=2*(a+h) +2= 2a +2h +2[/tex]
And now let's find g(a)
[tex] g(a)= 2a+2[/tex]
And now finally:
[tex] g(a+h) = 2a +2h +2 -2a-2 = 2h +2-2= 2h[/tex]
of the boxes of cruncho cereal on a supermarket shelf 25 percent contain a prize and the other 75 percent contain no prize.if Gerry buys two boxes of cruncho cereal which of the following is closest to the probability that neither box contain a prize??
Answer:
The probability that neither box contains a prize is 0.5625 or 56.25%
Step-by-step explanation:
It's referred as to the case when the probability of success (or failure) of the event A doesn't interfere with the probability of B. In this question we'll assume there are enough boxes of cereal of each type to make the choosing of one of them affect very little the choosing of the other one.
Let's call p=0.25 to the probability of getting a cereal box with a prize, and q=0.75 to the negation of p, i.e. the probability of getting a ceral box without a prize. There are four possible combinations: {pp,pq,qp,qq}. We need to find the probability of the combination qq. We compute it as the product of the individual probabilities
In other words, the probability that neither box contains a prize is 0.5625 or 56.25%
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In ABC,if sin A=4/5 and tan A=4/3, then what I s cos A?
2(x + 25) HELPPPPP MEEEEE
Answer:
2x+50
Step-by-step explanation:
Distributive property: 2(x)+2(25)
Simplify: 2x+50
Answer: 2x + 50
Step-by-step explanation: In this problem, the 2 distributes through the parenthses, multiplying by each of the terms inside.
So we have 2(x) + 2(25) which simplifies to 2x + 50.
An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pmf:
Answer:
a) E(X) = 16.09 ft³
E(X²) = 262.22 ft⁶
Var(X) = 3.27 ft⁶
b) E(22X) = 354 dollars
c) Var(22X) = 1,581 dollars
d) E(X - 0.01X²) = 13.470 ft³
Step-by-step explanation:
The complete Correct Question is presented in the attached image to this solution.
a) Compute E(X), E(X2), and V(X).
The expected value of a probability distribution is given as
E(X) = Σxᵢpᵢ
xᵢ = Each variable in the distribution
pᵢ = Probability of each distribution
Σxᵢpᵢ = (13.5×0.20) + (15.9×0.59) + (19.1×0.21)
= 2.70 + 9.381 + 4.011
= 16.092 = 16.09 ft³
E(X²) = Σxᵢ²pᵢ
Σxᵢ²pᵢ = (13.5²×0.20) + (15.9²×0.59) + (19.1²×0.21)
= 36.45 + 149.1579 + 76.6101
= 262.218 = 262.22 ft⁶
Var(X) = Σxᵢ²pᵢ - μ²
where μ = E(X) = 16.092
Σxᵢ²pᵢ = E(X²) = 262.218
Var(X) = 262.218 - 16.092²
= 3.265536 = 3.27 ft⁶
b) E(22X) = 22E(X) = 22 × 16.092 = 354.024 = 354 dollars to the nearest whole number.
c) Var(22X) = 22² × Var(X) = 22² × 3.265536 = 1,580.519424 = 1,581 dollars
d) E(X - 0.01X²) = E(X) - 0.01E(X²)
= 16.092 - (0.01×262.218)
= 16.0926- 2.62218
= 13.46982 = 13.470 ft³
Hope this helps!!!
IZ OT 50
Mathematics is the science of patterns and is the foundation for
algebra.
a. True
b. False
Answer:True
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Because it can but does not
Pls help me help me pls guys
Answer:
C
Step-by-step explanation:
[tex]-5x-49\geq 113[/tex]
[tex]-5x\geq 162[/tex]
[tex]x\leq -32.4[/tex]
(Multiplying or dividing by a negative flips the sign).
An object of height 2.50cm is placed 20.0cm from a converging mirror of focal length 10.0cm. What are the height and the magnification of the image formed?
First find the distance it is reflected:
D = 20.0 x 10.0 /(20-10) = 200/10 = 20cm away.
Now calculate the magnification: -20/ 20 = -1
Now calculate the height:
-1 x 2.50 = -2.50
The negative sign means the image is inverted.
The mirrored image would be inverted, 2.50 cm tall and 20 cm in front of the mirror.
Not sure how to solve
Answer:
(x, y, z) = (13/7, 19/7, 25/7)
Step-by-step explanation:
You know that the vector whose components are the coefficients of the equation of the plane is perpendicular to the plane. That is (1, 2, 3) is a vector perpendicular to the plane.
The parametric equation for a line through (1, 1, 1) with this direction vector is ...
(x, y, z) = (1, 2, 3)t +(1, 1, 1) = (t+1, 2t+1, 3t+1)
The point of intersection of this line and the plane will be the point in the plane closest to (1, 1, 1). That point has a t-value of ...
(t +1) +2(2t +1) +3(3t +1) = 18
14t +6 = 18
t = 12/14 = 6/7
The point in the plane closest to (1, 1, 1) is ...
(x, y, z) = (6/7+1, 2(6/7)+1, 3(6/7)+1)
(x, y, z) = (13/7, 19/7, 25/7)
The formula to convert Fahrenheit to Celsius is C - 5 (F - 32). Convert 30°C to
Fahrenheit. Round to the nearest degree.
A. 30°F
B. -1°F
C. 112°F
D. 86°F
Answer:
D. *6F
Step-by-step explanation:
C=(F-32)*5/9
30=(F-32)*5/9
F = (30*9)/5+32
F = 86
5x +3y=210 x+y=60 Witch can represent a linear equation
Answer:
both
Step-by-step explanation:
Both of the equations shown here are linear equations in standard form.
5x + 3y = 210
x + y = 60
Joan's Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of planting trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for planting of a medium-sized tree. Actual times from a sample of 10 plantintings during the past month follow (times in hours):
1.7, 1.5, 2.6, 2.2, 2.4, 2.3, 2.6, 3.0, 1.4, 2.3
With a 0.05 level of significance, test to see whether the mean tree-planting time differs from two hours.
A. State the null and alternative hypotheses.
B. Compute the sample mean.
C. Compute the sample standard deviation.
D. What is the p-value?
E. What is your conclusion?
Answer:
A) Null and alternative hypothesis
[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]
B) M = 2.2 hours
C) s = 0.52 hours
D) P-value = 0.255
E) At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean tree-planting time significantly differs from two hours.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]
The significance level is 0.05.
The sample has a size n=10.
The sample mean is M=2.2.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.52.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.52}{\sqrt{10}}=0.1644[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.2-2}{0.1644}=\dfrac{0.2}{0.1644}=1.216[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
This test is a two-tailed test, with 9 degrees of freedom and t=1.216, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t>1.216)=0.255[/tex]
As the P-value (0.255) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.
Sample mean and standard deviation:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(1.7+1.5+2.6+. . .+2.3)\\\\\\M=\dfrac{22}{10}\\\\\\M=2.2\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((1.7-2.2)^2+(1.5-2.2)^2+(2.6-2.2)^2+. . . +(2.3-2.2)^2)}\\\\\\s=\sqrt{\dfrac{2.4}{9}}\\\\\\s=\sqrt{0.27}=0.52\\\\\\[/tex]
Express it in slope-intercept form.
Hey there! :)
Answer:
y = 1/4x - 3.
Step-by-step explanation:
Use the slope-formula to find the slope of the line:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in two points from the line. Use the points (-4, -4) and (0, 3):
[tex]m = \frac{-3 - (-4)}{0 - (-4)}[/tex]
Simplify:
m = 1/4.
Slope-intercept form is y = mx + b.
Find the 'b' value by finding the y-value at which the graph intersects the y-axis. This is at y = -3. Therefore, the equation is:
y = 1/4x - 3.
Which of the following theorems verifies that HIJ MLN?
Answer:
HL (try HL, I believe that's the right answer)
Answer:
HL
Step-by-step explanation:
BRO TRUST ME
Human body temperatures are normally distributed with a mean of 98.2oF and a standard deviation of 0.62oF. Find the temperature that separates the bottom 12% from the top 88%.
Answer:
The temperature that separates the bottom 12% from the top 88% is 97.5°F.
Step-by-step explanation:
We are given that human body temperatures are normally distributed with a mean of 98.2°F and a standard deviation of 0.62°F.
Let X = human body temperatures
So, X ~ Normal([tex]\mu= 98.2,\sigma^{2} = 0.62^{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] = mean human body temperature = 98.2°F
[tex]\sigma[/tex] = stnadard deviation = 0.62°F
Now, we have to find the temperature that separates the bottom 12% from the top 88%, that means;
P(X < x) = 0.12 {where x is the required temperature}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-98.2}{0.62}[/tex] ) = 0.12
P(Z < [tex]\frac{x-98.2}{0.62}[/tex] ) = 0.12
Now, the critical value of x that represents the bottom 12% of the area in the z table is given as -1.1835, that is;
[tex]\frac{x-98.2}{0.62} = -1.1835[/tex]
[tex]{x-98.2}= -1.1835\times 0.62[/tex]
[tex]x = 98.2 -0.734[/tex] = 97.5°F
Hence, the temperature that separates the bottom 12% from the top 88% is 97.5°F.
The number 128 is divided into two parts in the ratio 7:9. Find the absolute difference between the two parts.
Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69 bpm. For a random sample of 147 adult males, the mean pulse rate is 69.5 bpm and the standard deviation is 11.2 bpm. Find the value of the test statistic.
Answer:
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{69.5-69}{\frac{11.2}{\sqrt{147}}}=0.541[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=69.5[/tex] represent the sample mean
[tex]s=11.2[/tex] represent the sample standard deviation
[tex]n=69[/tex] sample size
[tex]\mu_o =69[/tex] represent the value that we want to test
t would represent the statistic (variable of interest)
Hypothesis to test
We want to check if the true mean is 69, the system of hypothesis would be:
Null hypothesis:[tex]\mu =69[/tex]
Alternative hypothesis:[tex]\mu \neq 69[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{69.5-69}{\frac{11.2}{\sqrt{147}}}=0.541[/tex]
If A and B are independent events, P(A) = 0.25, and P(B) = 0.3, what is P(AB)?
O A. 0.25
B. 0.3
C. 0.15
O D. 0.075
Answer:
[tex] P(A) = 0.25, P(B= 0.3[/tex]
And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :
[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]
And the best option would be:
[tex] P(A \cap B) =0.075[/tex]
Step-by-step explanation:
For this case we have the following events A and B and we also have the probabilities for each one given:
[tex] P(A) = 0.25, P(B= 0.3[/tex]
And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :
[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]
And the best option would be:
[tex] P(A \cap B) =0.075[/tex]
Can anyone please explain? Need some help :)
A regular hexagon is inscribed in a circle with a diameter of 12 units. Find the area of the hexagon. Round your answer to the nearest tenth. (there's no picture included)
Answer:
93.5 square units
Step-by-step explanation:
Diameter of the Circle = 12 Units
Therefore:
Radius of the Circle = 12/2 =6 Units
Since the hexagon is regular, it consists of 6 equilateral triangles of side length 6 units.
Area of the Hexagon = 6 X Area of one equilateral triangle
Area of an equilateral triangle of side length s = [tex]\dfrac{\sqrt{3} }{4}s^2[/tex]
Side Length, s=6 Units
[tex]\text{Therefore, the area of one equilateral triangle =}\dfrac{\sqrt{3} }{4}\times 6^2\\\\=9\sqrt{3} $ square units[/tex]
Area of the Hexagon
[tex]= 6 X 9\sqrt{3} \\=93.5$ square units (to the nearest tenth)[/tex]