Answer:
[tex]A.\ 16\sqrt3\ cm^2[/tex] is the correct answer.
Step-by-step explanation:
Given that:
Side of an equilateral triangle = 8 cm
To find:
Area of the triangle will be:
[tex]A.\ 16\sqrt3\ cm^2[/tex]
[tex]B.\ \dfrac{32}{3} cm^2[/tex]
[tex]C.\ 48\ cm^2[/tex]
[tex]D.\ 36\sqrt3\ cm^2[/tex]
Solution:
First of all, let us have a look at the formula for area of an equilateral triangle:
[tex]A =\dfrac{\sqrt3}{4}a^2[/tex]
Where [tex]a[/tex] is the side of equilateral triangle and an equilateral triangle is a closed 3 sided structure in 2 dimensions which has all 3 sides equal to each other.
Here, we are given that side, [tex]a=8\ cm[/tex]
Putting the value in formula:
[tex]A =\dfrac{\sqrt3}{4}\times 8^2\\\Rightarrow A =\dfrac{\sqrt3}{4}\times 64\\\Rightarrow A =\sqrt3\times 16\\OR\\\Rightarrow \bold{A =16\sqrt3\ cm^2}[/tex]
Hence, [tex]A.\ 16\sqrt3\ cm^2[/tex] is the correct answer.
Simplify.
√20
v
Assume that the variable represents a positive real number.
Answer:
[tex]2\sqrt{5v}[/tex]
Step-by-step explanation:
We can treat 20v as a regular number and not a term.
To simplify this square root, we need to break it down into parts which can be squared.
[tex]\sqrt{20v} = \sqrt{4\cdot5v}[/tex]
Square root of 4 is 2, so that goes outside the radical.
[tex]2\sqrt{5v}[/tex].
Hope this helped!
Answer:
2 sqrt(5)
Step-by-step explanation:
sqrt(20)
sqrt(4*5)
We know that sqrt(ab) = sqrt(a) sqrt(b)
sqrt(4) sqrt(5)
2 sqrt(5)
let p and p+2 be prime numbers (i.e they are twin primes) with p>3. Show that 6|(p+1)
from the well known theorem that, primes are multiple of 6 ±1 ( eg 5,7,11,13,17,19...)
and one of them has [tex]-1[/tex] and other has $+1$ from the multiple of 6
let , $p=6n-1$, so $p+2=6n+1$
$\implies p+1=6n$
$\therefore 6|(p+1)$
QED
h(x) = x2 + 1 k(x) = x – 2
Evaluate 3h(2) + 2k(3) =
Answer:
17
Step-by-step explanation:
[tex]h(x) =x^2 +1\\k(x)=x-2\\\\3h(2)+2k(3)\\\\h(2)= ?\\k(3)=?\\\\h(2) = (2)^2 +1\\= 4+1\\h(2)=5\\\\\\k(3)= 3-2\\k(3) = 1\\\\3h(2) +2k(3)\\\\= 3(5)+2(1)\\=15+2\\3h(2)+2k(3) = 17[/tex]
5, 9, and 17
Step-by-step explanation:
please help
Determine if the relation is a function. Explain your reasoning.
y=3×
Answer:
yes for each input there is exactly one output.
Step-by-step explanation:
phone pictures is given by y equals 0.25 x where X is the number of 32 y equals 3x + 2y
A helicopter is at a cruising height of 1,200 feet. Suppose the angle of depression to the landing pad is 15°, which is located on top of a building that is 64 feet high. If the helicopter continues at the current cruising height, how far does the helicopter need to travel to be directly above the landing pad? Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest foot.
Answer:
we have a right triangle and to get the internal angle of the right triangle formed at the helicopter we subtract 62 degrees from 90 which equals 28 degrees
we now use the cosine to find the distance (d) from the helicopter
cosine 28 = 85/d
d = 85 / cosine 28 = 85 / 0.8829 = 96.2736 = 96 feet
Answer Both Questions
Answer:is the first answer 15.875 and the second answer 17 x 28 ÷5
Step-by-step explanation:
I cant seem to get the second one right...
Rx=1 means to reflect the given point on the line of x= 1
The mapping for the reflection on line x is x = k
(-2,7) = (-2(1) - -2,7) = (4,7)
The missing value is 7
which expression have a value of 2/3
A: 8+(24 divided by 12) X 4
B:8+24 divided by (12X4)
C: 8+24 divided 12X4
D: (8+24) divided (12X4)
Solve this and I’ll give u 5 stars and brainleist
Answer:
notice: temperature rises quickly at sunrise, and drops before sunsetwonder: whether this location is shaded by mountains later in the dayStep-by-step explanation:
notice
The temperature starts off below zero in the early morning and stays cold until the sun comes up. Then it warms rapidly to an above zero temperature that peaks in early afternoon. Once the sun gets lower, the temperature starts cooling off again. (The daily temperature range of 25-27 degrees is pretty typical for partly-cloudy sky conditions and stable weather.)
wonder
We wonder if this isn't a location that is on the east- or north-side of a mountain, or in a mountain valley, where the sun hits it early and is shaded later in the day. (The topo map attached seems to show it is in such a location.)
which operation should you perform first when evaluating the expression 3²+ 2
Answer:
You should calculate 3² first.
Step-by-step explanation:
In PEMDAS, E (which stands for exponents) comes before A (which stands for addition) so therefore you should calculate 3² first.
Explanation:
The acronym PEMDAS helps determine the order of operations
P = parenthesis
E = exponents
M = multiplication
D = division
A = addition
S = subtraction
With the expression [tex]3^2+2[/tex] we have two operations going on here: exponents and addition.
Since exponents comes before addition (E comes before A in PEMDAS), this means we evaluate [tex]3^2[/tex] first, then add later.
A farmer decides to try out a new fertilizer on a test plot containing 10 stalks of corn. Before applying the fertilizer, he measures the height of each stalk. Two weeks later, after applying the fertilizer, he measures the stalks again. He compares the heights of these stalks to 10 stalks that did not receive fertilizer. Did the fertilizer help? Use a significance level of 0.10 to test whether the height of the stalks increased.
The differences are calculated and the mean difference is found to be -3.36 inches with a standard deviation of 1.05 inches. Set up the appropriate hypothesis test and find the standardized test statistic.
t* = -14.31
t* = 3.2
t* = -3.2
t* = -10.12
Answer:
d) t = -10.12
Step-by-step explanation:
Explanation:-
Given sample size 'n'=10
Given the differences of mean x⁻ -μ = -3.36
Standard deviation of the sample 'S' =1.05 inches
We will use t-statistic
[tex]t = \frac{x^{-}-Mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t= \frac{-3.36}{\frac{1.05}{\sqrt{10} } }[/tex]
t = -10.12
Answer: D
Step-by-step explanation:
A sandman earns a commission of 26%. One week he had sales of $24400. Find the commission for the week.
Answer:
6344
Step-by-step explanation:
Find 26% of 24400
24400 * 26%
24400 * .26
6344
Plzz help i really need help..
Answer:
D. neither.
Step-by-step explanation:
A function is when one x-value only has one corrisponding y-value.
The answer it's D. Neither
what number must be added to the sequence of 7,13 and 10 to get an average of 13
Answer:
22
Step-by-step explanation:
We can write an equation:
(7+13+10+x)/4=13
x represents the number that needs to be added to get an average of
(7+13+10+x)/4=13
(30+x)/4=13
30+x=52
x=22
The number is 22
Hope this helps! Have a wonderful day :)
What is the volume of a cube with a side length of
of a unit?
Use Lagrange multipliers to minimize the function subject to the following two constraints. Assume that x, y, and z are nonnegative. Question 18 options: a) 192 b) 384 c) 576 d) 128 e) 64
Complete Question
The complete question is shown on the first uploaded image
Answer:
Option C is the correct option
Step-by-step explanation:
From the question we are told that
The equation is [tex]f (x, y , z ) = x^2 +y^2 + z^2[/tex]
The constraint is [tex]P(x, y , z) = x + y + z - 24 = 0[/tex]
Now using Lagrange multipliers we have that
[tex]\lambda = \frac{ \delta f }{ \delta x } = 2 x[/tex]
[tex]\lambda = \frac{ \delta f }{ \delta y } = y[/tex]
[tex]\lambda = \frac{ \delta f }{ \delta z } = 2 z[/tex]
=> [tex]x = \frac{ \lambda }{2}[/tex]
[tex]y = \frac{ \lambda }{2}[/tex]
[tex]z = \frac{ \lambda }{2}[/tex]
From the constraint we have
[tex]\frac{\lambda }{2} + \frac{\lambda }{2} + \frac{\lambda }{2} = 24[/tex]
=> [tex]\frac{3 \lambda }{2} = 24[/tex]
=> [tex]\lambda = 16[/tex]
substituting for x, y, z
=> x = 8
=> y = 8
=> z = 8
Hence
[tex]f (8, 8 , 8 ) = 8^2 +8^2 + 8^2[/tex]
[tex]f (8, 8 , 8 ) = 192[/tex]
It always travels at 3×108 m/s.
Answer:
it's electromagnetic radiatum
A farmer has 6 buckets of blueberries and wants to sell them at a market stall. The farmer will charge $1.50 per pint. If each bucket can hold half a bushel of blueberries, how much will the farmer make in selling all of the blueberries?
Answer:
$96
Step-by-step explanation:
6(1/2) = 3 bushels of berries total
3(4) = 12 pecks of berries total
4(8) = 32 quarts of berries total
32(2) = 64 pints of berries total
64 x $1.50 = $96
Answer:
The farmer will make a total of $96 from selling 6 buckets of blueberries.
Step-by-step explanation:
The total price is determined by multiplying the 12 pecks down into pints. Each pint sells for 1.50 and he has 64 pints of blueberries.
64 x $1.50 = $96
What Number is equivalent to 4^3
A. 7
B. 12
O C. 64
D. 81
Answer:
C
Step-by-step explanation:
4³ means 4 multiplied by itself 3 times, that is
4 × 4 × 4
= 16 × 4
= 64 → C
find the perimeter of a square of sides 10.5cm
Answer:
42 cm
Step-by-step explanation:
A square has 4 equal sides. To find the perimeter, add all side lengths together.
1. Set up the equation and solve
10.5 + 10.5 + 10.5 + 10.5 = 42
A triangle has a base that is increasing at a rate of 18 mm per minute with the height being held constant. What is the rate of change of the area of the triangle if the height is 7 mm
Answer:
63mm/minStep-by-step explanation:
Area of a triangle = 1/2 * base * height
A = 1/2bh
Rate of change of area is expresssed as dA/dt = dA/db * db/bt
db/dt is the rate at which the base is increasing.
Given db/dt = 18mm/min
A = 1/2*7b
A = 7b/2
dA/db = 7/2
The rate at which the area is changing dA/dt = dA/db * db/bt
dA/dt = 7/2 * 18
dA/dt = 7*9
dA/dt = 63mm/min
Hence the rate at which the area of the triangle is changing is 63mm/min
You are an assistant director of the alumni association at a local university. You attend a presentation given by the university’s research director and one of the topics discussed is what undergraduates do after they matriculate. More specifically, you learn that in the year 2018, a random sample of 216 undergraduates was surveyed and 54 of them (25%) decided to continue school to pursue another degree, and that was up two percentage points from the prior year. The Dean of the College of Business asks the research director if that is a statistically significant increase. The research director says she isn’t sure, but she will have her analyst follow up. You notice in the footnotes of the presentation the sample size in the year of 2017 was 200 undergraduates, and that 46 of them continued their education to pursue another degree.
There is a short break in the meeting. Take this opportunity to answer the dean’s question using a confidence interval for the difference between the proportions of students who continued their education in 2018 and 2017. (Use 95% confidence level and note that the university has about 10,000 undergraduate students).
Answer:
(0.102, -0.062)
Step-by-step explanation:
sample size in 2018 = n1 = 216
sample size in 2017 = n2 = 200
number of people who went for another degree in 2018 = x1 = 54
number of people who went for another degree in 2017 = x2 = 46
p1 = x1/n1 = 0.25
p2 = x2/n2 = 0.23
At 95% confidence level, z critical = 1.96
now we have to solve for the confidence interval =
[tex]p1 -p2 ± z*\sqrt{((1-p1)*p1)/n1 + ((1-p2)*p2/n2}[/tex][tex]0.25 -0.23 ± 1.96*\sqrt{((1 - 0.25) * 0.25)/216 + ((1 - 0.23) *0.23/200}[/tex]
= 0.02 ± 1.96 * 0.042
= 0.02 + 0.082 = 0.102
= 0.02 - 0.082 = -0.062
There is 95% confidence that there is a difference that lies between - 0.062 and 0.102 on the proportion of students who continued their education in the years, 2017 and 2018.
There is no significant difference between the two.
Which algebraic expression means “three more than a number squared”? 2 n + 3 2 n minus 3 n squared + 3 n squared minus 3
The algebraic expression that means "three more than a number squared" is n² + 3, where n is the number.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The statement is given in the question, as follows:
“three more than a number squared”
The expression n² represents the square of the number, and the expression + 3 represents the addition of three more to the square of the number.
So, n² + 3 represents the value of the square of the number plus three.
Thus, the algebraic expression that represents "three more than a number squared" is n² + 3.
Learn more about the algebraic expression here :
brainly.com/question/21751419
#SPJ6
Theresa bought 2 pineapples for $6. She wants to find the constant of proportionality in terms of dollars per pineapple. She modeled this proportional relationship on a number line diagram, as shown.
Part B
How much would 4 pineapples cost?
The yellow bar is the total cost of 2 pineapples. The black line in the middle of the yellow splits it equally in half and is located at the 3.
The constant bod proportionality would be 3, which means each pineapple cost $3
Answer:
first of all, brainly better not delete my answer again. (the answer is 3)
Step-by-step explanation:
you have to multiply to find the number of pineapples. but unlike me i did skip count and write down my number's and I tried to find "what number skips until it ends to 6?'' i found 3 as my answer! 3,6,9,12,15,18,21 etc..
Find the sum of 1 + 3/2 + 9/4 + …, if it exists. This is infinite series notation. The answer is NOT 4.75.
Answer:
D
Step-by-step explanation:
First, this looks like a geometric series. To determine whether or not it is, find the common ratio. To do this, we can divide the second term and the first term, and then divide the third term and the second term. If they equal to same, then this is indeed a geometric series.
[tex](3/2)/(1)=3/2\\(9/4)/(3/2)=(9/4)(2/3)=18/12=3/2[/tex]
Therefore, this is indeed a geometric series with a common ratio of 3/2.
With just this, we can stop. This is because since the common ratio is greater than one, each subsequent value is going to be bigger than the previous one. Because of this, the series will not converge. Therefore, the series has no sum.
To see this more clearly, imagine a few more terms:
1, 1.5, 2.25, 3.375, 5.0625...
Each subsequent term will just increase. The sum will not converge.
Answer:
No Sum --- it doesn't exist.
Step-by-step explanation:
The partial sums get arbitrarily large--the go to infinity.
The geometric series you are trying to sum has common ratio = 3/2.
The sum of the infinite series exists only when |common ratio| < 1.
The formula for the partial sum of n terms is (r^(n+1) - 1) / (r - 1) = (1.5^(n+1) - 1) / 0.5, or in decimals instead of fraction.. i.e. 1 + 1.5 + 2.25 + 5.0525 + 25.628 + 656.840..... therefore It would take a long time but you'd be adding up forever and goes to infinity.
Given a dataset with the following properties:
mean = 50
median = 40
standard deviation = 5
What is the shape of the distribution?
Answer:
The distribution is positively skewed.
Step-by-step explanation:
A measure of skewness is defined in such a way that the measure should always be zero when the distribution is symmetric and measure should be a pure number i.e independent of origin and units of measurement.
The shape of the distribution can be found by finding the coefficient of skewness.
The coefficient of skewness can be found by
Sk= 3(Mean-Median)/ Standard Deviation
Sk= 3( 50-40)5= 30/5=6
The shape will be positively skewed.
In a positively skewed distribution the mean > median > mode. It has a long right tail.
Using the skewness formula, it is found that the distribution is right-skewed.
------------------
The skewness of a data-set with mean M, median [tex]M_e[/tex] and standard deviation s is given by:[tex]S = \frac{3(M - M_e)}{s}[/tex]
If |S| < 0.5, the distribution is said to be symmetric.If S <-0.5, the distribution is left-skewed.If S > 0.5, the distribution is right-skewed.------------------
Mean of 50, thus, [tex]M = 50[/tex]Median of 40, thus [tex]M_e = 40[/tex]Standard deviation of 5, thus, [tex]s = 5[/tex]The coefficient is:
[tex]S = \frac{3(M - M_e)}{s} = \frac{3(50 - 40)}{5} = \frac{30}{5} = 6[/tex]
Thus, the distribution is right-skewed.
A similar problem is given at https://brainly.com/question/24415645
Find the missing side or angle.
Round to the nearest tenth.
Answer:
b=2.7
Step-by-step explanation:
using sine rule,,,
Step-by-step explanation:
So for this problem, we need the missing angle A. From there, we can use the law of sines to compute length of b.
So the sum of the interior angles of a triangle is 180. With that in mind, we can make an equation to fine the measure of angle A.
53 + 80 + A = 180
133 + A = 180
A = 47
Now that we have the angle of A, we can use the law of sines to fine the length of b.
b / sin(B) = a / sin(A)
b = sin(B) * a / sin(A)
b = sin(80) * 2 / sin(47)
b = 2.693
Now round that to the nearest tenth to get
b = 2.7
Cheers.
solve this equation 4log√x - log 3x =log x^2
Answer:
[tex]x = \frac{1}{3} [/tex]
Step-by-step explanation:
*Move terms to the left and set equal to zero:
4㏒(√x) - ㏒(3x) - ㏒(x²) = 0
*simplify each term:
㏒(x²) - ㏒(3x) - ㏒(x²)
㏒(x²÷x²) -㏒(3x)
㏒(x²÷x² / 3x)
*cancel common factor x²:
㏒([tex]\frac{1}{3x}[/tex])
*rewrite to solve for x :
10⁰ = [tex]\frac{1}{3x}[/tex]
1 = [tex]\frac{1}{3x}[/tex]
1 · x = [tex]\frac{1}{3x}[/tex] · x
1x = [tex]\frac{1}{3}[/tex]
*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:
x = [tex]\frac{1}{3}[/tex]
Find the value of x.
A. 3
B. 9
C. 0
D. 12
Answer:
x=3
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
3x(x+1) = 4x(x)
Divide each side by x
3x(x+1)/x = 4x(x)/x
3(x+1) = 4x
Distribute
3x+3 = 4x
Subtract 3x
3x+3-3x= 4x-3x
3 =x
Answer:
x = 3
Step-by-step explanation:
0 is a rediculas answer 9 and 12 are to big.
The lines are supposed to have a simular length:
3(3) + 4 = 13
4(3) + 3 = 15
These are the best answers that fit.
A table has five bowls. None of the quantities in the bowls are prime, though the last two bowls are empty. Two of the quantities are squares, and when added to the remaining number, the sum is 21. What are the amounts in the first three bowls?
Since two of the quantities are squares and the sum of all of three is equal 21, then the possible values of those two quantities are: 1,4,9,16
Let's consider each possibility
1 and 4
21-1-4=16, but 16 is also square and there can be only two square so NO
1 and 9
21-1-9=11, but 11 is prime, so NO
1 and 16
21-1-16=4... 4 is a square ,so NO
4 and 9
21-4-9=8 , 8 is not prime and not a square, so YES
4 and 16
21-4-16=1, but 1 is a square ,so NO
9 and 16
9+16=25>21 so.. NO
Therefore, the amounts in the first three bowls are 4,8,9.
