Answer:
The formula that represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A) is [tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex] .
Step-by-step explanation:
We are given the area of an Equilateral triangle which is A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex] . And we have to represent the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).
So, the area of an equilateral triangle = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]
where, s = side of an equilateral triangle
A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]
Cross multiplying the fractions we get;
[tex]4 \times A = \sqrt{3} \times \text{s}^{2}[/tex]
[tex]\sqrt{3} \times \text{s}^{2}= 4\text{A}[/tex]
Now. moving [tex]\sqrt{3}[/tex] to the right side of the equation;
[tex]\text{s}^{2}= \frac{4 \text{A}}{\sqrt{3} }[/tex]
Taking square root both sides we get;
[tex]\sqrt{\text{s}^{2}} = \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]
[tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]
Hence, this formula represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).
conditinal probability question. please help! :)
Answer:
P(A|B) = 1 / 6
Step-by-step explanation:
Assuming two fair sided dice with faces numbered 1 to 6.
By intuition, there can only be 6 possible outcomes, so probability is 1/6.
Illustration how to use conditional probability.
Given two events A, B, following is the equation of conditional probability
that A happens given B has already happened and observed.
P(A|B) = P( A intersect B ) / P(B)
In the given problem,
A = casting a double-six
B = casting a double
P(A) = (1 / 6) * (1 / 6) = 1/36
P(B) = (6/6) * (1/6) = 1/6
P(A|B) = 1/36 / (1/6) = 1/6
Determine the values of \theta if sec\;\theta=-\frac{2}{\sqrt{3}}.
Answer:
See below.
Step-by-step explanation:
So, we have:
[tex]\sec(\theta)=-2/\sqrt{3}[/tex]
Recall that secant is simply the reciprocal of cosine. So we can:
[tex]\cos(\theta)=(\sec(\theta))^{-1}=(-2/\sqrt{3})^{-1}\\\cos(\theta)=-\sqrt{3}/2[/tex]
Now, recall the unit circle. Since cosine is negative, it must be in Quadrants II and/or III. The numerator is the square root of 3. The denominator is 2. The whole thing is negative. Therefore, this means that 150 or 5π/6 is a candidate. Therefore, due to reference angles, 180+30=210 or 7π/6 is also a candidate.
Therefore, the possible values for theta is
5π/6 +2nπ
and
7π/6 + 2nπ
Please answer this correctly without making mistakes
Answer:
1.2 miles
Step-by-step explanation:
5.3 - 4.1 = 1.2 miles
Answer:
1.2 milesStep-by-step explanation:
5.3 - 4.1 = 1.2
1.2 miles difference.
This is because from Washington to Lanberry it is 4.1 miles. From Washington to Newberry it is 5.3., SO, if you subtract it you will get 1.2 miles difference.
Hope this helped,
kavitha
Which graphs represent functions?
6 ≤ x+ 15 plzzzzz helpppp
Answer:
[tex]\large \boxed{\sf \ \ x \geq -9 \ \ }[/tex]
Step-by-step explanation:
Hello, please find below.
[tex]6\leq x+15\\\\\text{*** subtract 15 from both sides ***}\\\\6-15=-9\leq x \\\\x \geq -9[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Please help me with this
I would really appreciate it
thank you
Answer:
1) x=58, y=109
2) x=72, y=36
3) x=60, y=48
Step-by-step explanation:
1) 58 and x are so-called "F-angles" (a.k.a "corresponding angles), so x=58°
The angle on the other side of the 58 is 180-58 = 122 because they are supplementary. We need this one to calculate y.
The sum of angles in a quadrilateral is 360°, so 71 + 58 + 122 + y = 360, so y = 109
2) There are two isosceles triangles. Due to the symmetry, the bottom left angle is also 72, leaving 180-72-72 = 36 for y. The top triangle is the same triangle rotated, so x = 72.
3) Due to the parallel lines, the left angle of the top triangle is also 72, making the supplementary angle below it 180-72=108. The sum in the quadrilateral must be 360, so 72+108+2x+x=360, so 3x=180, x=60.
The sum in the outer triangle must be 180, so 72+y+x = 180, leaving y = 180-72-60 = 48
What is the vertex of this parabola y=-5x^2-10x-13
Step-by-step explanation:
Vertex for your equation is (-1, -8)
How many ways can 3 boys and 2 girls stand in a row so that the two girls are not next to each other?
Answer:
3 ways← key b=boy g=girlStep-by-step explanation:
b g b gg b b gg b g bgive brainllest please °∩°
Solve the quadratic equation x2 + 2x – 20 = 0 by completing the square.
Answer:
x^2 + 2x - 20 = 0
x^2 + 2x - 20 + 20 = 0 + 20 ( add 20 to both sides)
x^2 + 2x = 20
x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)
( x + 1 )^2 = 21
x = [tex]\sqrt{21}-1[/tex]
x = [tex]-\sqrt{21}-1[/tex]
Answer:
A) x = –1 ± square root 21
is the answer:)
which formulas can be used to find the surface area of a regular pyramid where p is the perimeter of the base, s is the slant height, BA is the base area, and LA is the lateral area click all that apply options: A. SA= 1/2BA + 1/2ps B. SA= BA-LA C. SA= BA+LA D. SA= BA • LA E. SA= BA + 1/2ps
Answer:
C and E
Step-by-step explanation:
He got it on ap.ex
The area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.
What is a square pyramid?In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a pyramid with a square base:
The perimeter of the base is p
The slant height is s.
The base area is BA
The lateral area is LA.
We can find the area of the pyramid as follows:
SA = BA + LA
SA= BA + 1/2ps
Thus, the area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.
Learn more about the pyramid here:
brainly.com/question/13057463
#SPJ5
determine both the lower and upper limits of a 90% z-confidence interval for µ , the mean score for all students in the school district who are enrolled in gifted and talented programs.
Answer:
CI = ( μ - 1,64 * σ /√n ; μ + 1,64 * σ /√n )
Step-by-step explanation:
We assume Normal Distribution
For Confidence Interval, CI = 90 % and α = 10 %
α = 0,1 and α/2 = 0,05
So we will look for z score reciprocate to these values, at the two tails of the bell
z(α/2) = 1,64 at th right tail and -1,64 at the left
CI = ( μ ± 1,64 * σ /√n )
CI = ( μ - 1,64 * σ /√n ; μ + 1,64 * σ /√n )
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps
Answer:
123 domestic stamps
89 foreign stamps
Step-by-step explanation:
Answer:
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
Which equation represents the total number of stamps Malik collected?
✔ x + y = 212
Which equation represents the difference in the number of foreign and domestic stamps Malik collected?
✔ x – y = 34
Which system of linear equations represents the situation?
✔ x – y = 34 and x + y = 212
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
This system of equations models the given information for both stamp types.
x – y = 34
x + y = 212
Solve the system of equations.
How many foreign stamps does Malik have?
✔ 89 foreign stamps
How many domestic stamps does Malik have?
✔ 123 domestic stamps
Step-by-step explanation:
its right on 2021 edge! :) hope this helps
how many two third ounce slice of cheese in twenty four ounce package
Answer: 36
Step-by-step explanation:
Simply do 24/(2/3) to get 36 2/3 ounce slices.
Hope it helps <3
Question 14 (5 points)
Which of the following gives the correct intercept points and vertex point for the function f(x) = x2 + 3x - 18?
A. y-intercept: (0,18); vertex point: ( – ; – 20_); xintercepts: (-3, 0) and (6,
0)
B. y-intercept: (0, -18); vertex point: (-1, – 19); x-intercepts: (-3, 0) and (-6,
0)
C. y-intercept: (0, -18); vertex point: ( - 2/3, - 20 1/4); x-intercepts: (3, 0) and (-
6,0)
D. y-intercept: (0, 18); vertex point: (-1, – 19); x-intercepts: (3,0) and (6, 0)
Answer:
C. y-intercept: (0, -18); vertex point: ( [tex]-\frac{2}{3}[/tex], [tex]-20\frac{1}{4}[/tex]); x-intercepts: (3, 0) and (-
6,0)
Step-by-step explanation:
Hope it helped
Answer:
C. y-intercept: (0, -18); vertex point: ( - 2/3, - 20 1/4); x-intercepts: (3, 0) and (-
6,0)
Step-by-step explanation:
It's a positive parabola, so that means it opens upward. Crossing the x-axis at -6 and 3 it's minimum is -20 and crosses the Y-axis at -18.
The population of a city can be modeled with a linear equation Y equals -80 X +3450 where X is the number of years after 2000 and why is the cities population by the description of the cities population based on equation
Answer:
retype that im not understanding .
Step-by-step explanation:
A survey of the average amount of cents off that coupons give was done by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20cents; 70cents; 50cents; 65cents; 30cents; 55cents; 40cents; 40cents; 30cents; 55cents; $1.50; 40cents; 65cents; 40cents. Assume the underlying distribution is approximately normal.
Construct a 95% confidence interval for the population mean worth of coupons .
What is the lower bound? ( Round to 3 decimal places )
What is the upper bound? ( Round to 3 decimal places )
What is the error bound? (Round to 3 decimal places)
Answer:
The lower bound = 35.443
The upper bound = 71.697
The error bound = 18.127
Step-by-step explanation:
We are given that a survey of the average amount of cents off that coupons gives was done by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News.
The following data were collected (X): 20cents; 70cents; 50cents; 65cents; 30cents; 55cents; 40cents; 40cents; 30cents; 55cents; 150 cents; 40cents; 65cents; 40cents.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean worth of coupons = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{750}{14}[/tex] = 53.57 cents
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 31.40 cents
n = sample size = 14
[tex]\mu[/tex] = population mean worth of coupons
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.16 < [tex]t_1_3[/tex] < 2.16) = 0.95 {As the critical value of t at 13 degrees of
freedom are -2.16 & 2.16 with P = 2.5%}
P(-2.16 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.16) = 0.95
P( [tex]-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}{[/tex] < [tex]2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]53.57-2.16 \times {\frac{31.40}{\sqrt{14} } }[/tex] , [tex]53.57+2.16 \times {\frac{31.40}{\sqrt{14} } }[/tex] ]
= [35.443, 71.697]
Therefore, a 95% confidence interval for the population mean worth of coupons is [35.443, 71.697].
what’s the opposite of negative two
Answer: The answer is two
Step-by-step explanation: If you look for opposites of a number its either negative or positive. So when the answer is negative, the opposite is positive and if the answer is positive, the opposite is negative.
Answer:
[tex]\boxed{2}[/tex]
Step-by-step explanation:
The opposite of a number is the number that is the same distance from 0 on the number line.
-2 opposite is 2.
72 students choose to attend one of three after school activities: football, tennis or running.
There are 25 boys.
27 students choose football, of which 17 are girls.
18 students choose tennis.
24 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
Answer:
P = 0,3749 or P = 37,49 %
Step-by-step explanation:
17 girls play football 10 boys do ⇒ 27 students
24 girls running 3 boys do ⇒ 27 students
then 6 girls play tennis and 12 boys do ⇒ 18 students
Probability of student running P is equal to P1 (probability of student (boy) running ) plus P2 (probability of student (girl) running )
P = P1 + P2
P1 (probability of girl running ) is equal to choose a girl out of 72 students, times the probability of the girl running
Probability of girl 47/72 = 0,6528
Probability of running is equal to 24/47 = 0,5106
Then the probability of girl running is equal to
P2 = 0,6528*0,5106 = 0,3333 or 33,33 %
P2 = 0,3333 or P2 = 33,33 %
Now we have 72 students 25 boys, then the probability of choosing a boy is = 25/72 = 0,3472
And the probability of running is 3/25 = 0,12
Then
P1 = 0,3472*0,12
P1 = 0,04166 and
P = P1 + P2
P = 0,04166 + 0,3333
P = 0,3749 or P = 37,49 %
Which of the following is represented by MN ?
A.
Radius of the circle
B.
Diameter of the circle
C.
A chord of the circle
D.
Circumference of the circle
Answer:
A
Step-by-step explanation:
That is the radius. Since its half of the diameter.
Answer:
A. Radius of the circle
Step-by-step explanation:
A line segment that has as endpoints the center of a circle and a point on the circle is called a radius.
Answer: A. Radius of the circle
Choose the correct equation for the parabola based on the given information. Given: Focus:(2,8) Directrix: y = 4 a. 2(y-2)= (x- 6)^2 b. 8(x -2) = (y -6)^2 c. 8(y - 6)= (x-2)^2 d. 2(x-2)= (y-8)^2
Explanation:
The directrix is horizontal, so the axis of symmetry is vertical. We'll have an x^2 term. The vertical distance from y = 4 to y = 8 is 4 units. Cut this in half to get 2, which is the focal distance p = 2.
The point (2,4) is directly below (2,8), and the point is on the directrix. The midpoint between (2,4) and (2,8) is (2,6). This is the vertex.
(h,k) = (2,6)
4p(y-k) = (x-h)^2
4*2(y-6) = (x-2)^2
8(y-6) = (x-2)^2
Which expressions are equivalent to: 3(−2a - 4)+3a? A: -6a - 12 +3a B: 3a+12 C: none of the above smh
Answer:
AStep-by-step explanation:
3(−2a - 4)+3a
=-6a - 12 +3a
A: -6a - 12 +3a
[tex]hope \: this \: helps[/tex]
Answer:
the answer is A
Step-by-step explanation:
you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a
What is the density of a brownie the shape of a cube weighing 15 grams measuring 5 cm on a side?
Answer:
0.12 g/cm³
Step-by-step explanation:
Density is the ratio of mass to volume. The volume of the brownie is the cube of its side dimension:
V = s³ = (5 cm)³ = 125 cm³
Then the density is ...
ρ = M/V = (15 g)/(125 cm³) = 0.12 g/cm³
The density of the brownie is 0.12 g/cm³.
(6/22 + 5/77) ^2 equalviant to in fraction form
Answer:
676/5929
Step-by-step explanation:
Help with finding the slope of the line and graph find the slope 1.) (1, 6) (3,8) 2.) (7,10) (5,6) 3.) (1,-2) (3,4) 4.) (10,5) (4,7) 5.) (-2,6) (0,5) 6.) (-9,9) (7,5) 7.) (-3, 5) (0,0) (8, 10) (-7, 14) 9.) (-12, -5) (0, -8)
Answer:
1 is 1.
2 is 2.
3 is 3. (this is not a joke, keep going)
4 is -1/3.
5 is -1/2.
6 is -1/4.
7 is -5/3.
8 is -4/15, if you meant that the points are (8,10) and (-7,14). You might have typed wrong.
9 is -1/4.
10 is 1/3. Take a look at it. It goes up by 1 and it goes over 3. 1 divided by 3 is 1/3.
11 is 1. It rises 2 and goes across by 2. 2 divided by 2 is 1.
12 is -3/4, because it goes down 3 and over 4.
13 is -3/2. Do you see why?
14 is 1. It's super easy, since it only goes up 1 and over 1.
15 is easy. You have to figure this one out, but I'll give you a hint. It goes down by 3 .
If mZNOM = 30°, then what is the length of the minor arc
NM?
Answer:
Option (B)
Step-by-step explanation:
To determine the length of arc of a circle we use the formula,
Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]
Where θ = measure of the central angle subtended by the arc
r = radius of the circle
For the circle given in the picture attached,
Length of arc NM = [tex]\frac{30}{360}(2\pi)(2)[/tex]
= [tex]\frac{4\pi }{12}[/tex]
= [tex]\frac{\pi }{3}[/tex]
Therefore, length of [tex]\widehat{NM}=\frac{\pi }{3}[/tex]
Option (B) will be the answer.
Answer: C
Step-by-step explanation:
4#/12 = #
How many real roots and how many complex roots exist for the polynomial
F(x) - X4+ x2 - 5x2 + x -- 6?
O A. 2 real roots and 2 complex roots
B. O real roots and 4 complex roots
O c. 3 real roots and 1 complex root
D. 4 real roots and 0 complex roots
Answer:
D. 4 real roots and 0 complex roots
Step-by-step explanation:
If I assume that the function you are saying is
[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]
There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.
[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]
There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.
Suppose that f(x,y) is a smooth function and that its partial derivatives have the values, fx(8,5)=2 and fy(8,5)=2. Given that f(8,5)=−2, use this information to estimate the value of f(9,6).
Answer:
f(9,6) = 2
Step-by-step explanation:
We know df = (df/dx)dx + (df/dy)dy
From the question, df/dx = fx(8,5) = 2 and df/dy = fy(8,5) = 2
Since we need to find f(9,6) and f(8,5) = -2
dx = 9 - 8 = 1 and dy = 6 - 5 = 1
f(9,6) = f(8,5) + df
df = (df/dx)dx + (df/dy)dy
df = fx(8,5)dx + fy(8,5)dy
Substituting the values of fx(8,5) = 2, fy(8,5) = 2, dx = 1 and dy = 1
df = 2 × 1 + 2 × 1
df = 2 + 2
df = 4
f(9,6) = f(8,5) + df
substituting the value of df and f(8,5) into the equation, we have
f(9,6) = -2 + 4
f(9,4) = 2
The value of f(9,6) = 2
If y>0, which of these values of x is NOT in the domain of this equation? y=x2+7x
Answer:
[tex]\boxed{\sf \ \ \ [-7,0] \ \ \ }[/tex]
Step-by-step explanation:
Hello
[tex]y=x^2+7x=x(x+7) >0\\<=> x>0 \ and \ x+7 >0 \ \ or \ \ x<0 \ and \ x+7<0\\<=> x>0 \ \ or \ \ x<-7\\[/tex]
So values of x which is not in this domain is
[tex]-7\leq x\leq 0[/tex]
which is [-7,0]
hope this helps
If (x+1) is the factor of polynomial p(x) = ax²+x+1, then find a.
Answer:
a = 0
Step-by-step explanation:
p(x) = ax²+x+1
Let x+1 = 0 => x = -1
Putting in the above polynomial
=> p(-1) = a(-1)^2+(-1)+1
By Remainder Theorem, Remainder will be zero
=> 0 = a(1) -1+1
=> 0 = a
OR
=> a = 0
Answer:
a = 1Step-by-step explanation:
Factors are what we can multiply to get the number.
x² + x + 1
Factor the polynomial.
x(x+1) + 1
ax² + x = x(x + 1)
ax² + x = x² + x
[tex]a=\frac{x^2 +x}{x^2 +x}[/tex]
a = 1
from the top of a building 10m high the angle of depression of a stone lying on the horizontal ground is 60° . calculate the distance of the stone from the foot of the building
Answer:
14.29cm
Step-by-step explanation:
Height of the building=10cm
Angle of depression=60°
We are therefore asked to find the distance from the stone to the
the foot of the building;Therefore we use Tan ratio which is opp/adj;
Let the distance from the stone to the foot of the building be x;
10/x=Tan60°
10/x=1.7/1
We then cross multiply to get 1.7x=10
x=10/1.7
=10*10/1.7*10
=100/17
=14.29cm.
