For extra fun, groups of student in a class are tasked to create algebraic expression to satisfy the measures of the angles of their triangular picture frame project. If the measure of the angles are as follows:m∠A = 5x - 3, m∠C = 2x + 5, m∠E = 3x - 2, arrange the sides of the frame in increasing order.

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Answer:

2x+1

Step-by-step explanation:

f(g(x))= (2x)+1

(2)x+1

Answer:

36.8 i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

4^-3

=1/4^3

=1/64

Answer:

[tex]\frac{1}{64}[/tex]

Step-by-step explanation:

[tex]4^{-3} = 0.015625[/tex]

[tex]0.015625 = \frac{1}{64}[/tex]

Answer:

V=147

Step-by-step explanation:

V=whl

V=6 inches*3.5 inches*7 inches

V=147

Solution :

The probability of winning when you choose n is =  [tex]$^nC_2\left(\frac{1}{2}\right)^n$[/tex]

[tex]$n\left(\frac{n-1}{2}\right)\times \left(\frac{1}{2}\right)^n = n(n-1)\left(\frac{1}{2}\right)^{n+1}$[/tex]

Apply log on both the sides,

[tex]$f(n) = \log\left((n)(n-1)\left(\frac{1}{2}\right)^{n-1}\right) = \log n +\log (n-1)+(n+1) \ \log\left(\frac{1}{2}\right)$[/tex]

Differentiation, f(x) is [tex]$f'=\frac{1}{x}+\frac{1}{(x-1)}+\log\left(\frac{1}{2}\right)$[/tex]

Let us find x for which f' is positive and x for which f' is negative.

[tex]$\frac{1}{x}+\frac{1}{(x-1)} > 0.693$[/tex]       , since [tex]$\log(1/2) = 0.693147$[/tex]

For x ≤ 3, f' > 0 for [tex]$\frac{1}{x}+\frac{1}{x-1}+\log\left(\frac{1}{2}\right)>0$[/tex]

[tex]$\frac{1}{x}+\frac{1}{x-1}-0.6931470$[/tex]

That means f(x) is increasing function for n ≤ 3

[tex]$\frac{1}{x}+\frac{1}{x-1}< 0.693147 $[/tex] for x > 4

f' < 0 for n ≥ 4, that means f(n) is decreasing function for n ≥ 4.

Probability of winning when you chose n = 3 is [tex]$3(3-1)\left(\frac{1}{2}\right)^{3+1}=0.375$[/tex]

Probability of winning when you chose n = 4 is [tex]$4(4-1)\left(\frac{1}{2}\right)^{4+1}=0.375$[/tex]

Therefore, we should chose either 3 or 4 to maximize chances of winning.

The probability of winning with an optimal choice is n = 0.375

Answer:

D

Step-by-step explanation:

It’s correct

[tex]\frac{1}{3} *\pi *6^{2}*27[/tex]

[tex]=324\pi[/tex]

Step-by-step explanation:

hi, this looks complicated, however, let's deal with it.

using sine rule,

we have,

a/sin A= c/sin C

4.83/sin 46= 5.5/sin C

cross multiply

4.83sin C=5.5sin 46

sin C= (5.5sin46)/4.83

sin C= 0.8191

C=sin inverse of 0.8191

C=54.99 approximately 55

since we have C, we can now find B to get b or rather AC

A+B+C=180. (sum of angles in a triangle)

46°+ B + 54.99°=180°

B+ 100.99°=180°

B°=180°-100.99°

B=79°

since we have B, we can find b or rather AC

using cosine rule,

b²=c²+a²-2 x c x a x cos B

b²= 5.5² + 4.83² - 2 x 5.5 x 4.83 x cos 79°

b²=30.25+23.33-53.13cos79

b²=53.58-10.14

b²=43.44

b=6.59 approximately 6.6

Answer:

the probability is a fraction or a percentage, some times even a decimal

Solution :

LD50 is a test that used by the scientist and by the medical practitioners to determine the toxicity of any chemical compounds. It involves introducing the different dose levels of the chemical compound that is to be tested to the group of the experimental subjects.

The LD50 graph of the Drugs X is attached below.

From the graph, we can see that the LD50 level of the drug X is 10 mg/kg.

Answer:

=========================================

Explanation:

The perimeter around the circle, aka circumference, is found through this formula

C = 2*pi*r

That's for a full circle. However, we're dealing with semicircles here, so we cut that in half to get pi*r to represent the curved distance around half the circle.

For the outer larger semicircle, that curved distance is exactly 14pi

For the inner smaller semicircle, that curved distance is 7pi, since 7 is half of 14.

The total curved portions is 14pi+7pi = 21pi

Then we add on the last straight line portion that's 14 cm long to get a total perimeter of 21pi+14

This is the exact perimeter in terms of pi.

The last thing to do is replace pi with 3.14 and simplify

21pi+14 = 21*3.14+14 = 79.94

This value rounds to 80

Answer:

96

Step-by-step explanation:

3^4 = 81

3 * 5 = 15

81 + 15 = 96

Answer:

a) 84th percentile.

b) The 25th percentile is of 67 inches.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

The heights of the men age 18 and over in HANES5 averaged 69 inches; the SD was 3 inches.

This means that [tex]\mu = 69, \sigma = 3[/tex]

Such a man that is 6 feet tall is at the percentile of this height distribution.

6 feet = 6*12 inches = 72 inches. So this percentile is the p-value of Z when X = 72. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{72 - 69}{3}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.84, so 84th percentile.

What is the 25th percentile, to the nearest inch

X when Z has a p-value of 0.25, so X when Z = -0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.675 = \frac{X - 69}{3}[/tex]

[tex]X - 69 = -0.675*3[/tex]

[tex]X = 67[/tex]

The 25th percentile is of 67 inches.

Answer:

1

Step-by-step explanation:

a it is 1 because

can u see perpedicular symbol

Answer:

1 line.

A perpendicular line is a line that meets another line and forms a 90° angle.

If you look at the diagram, only the middle line forms a 90° angle when it meets line AB

Answer:

1 miles= 1.609km

so, 25x1.609 = 40.225km

Answer:

[tex] \frac{13}{20} [/tex]

Answer:

a1 = 1, a2 = 2Step-by-step explanation:

Algebra

The inverse of -9n is dividing by -9.

[tex]n = - 5[/tex]

Answer:

n=−5

Step-by-step explanation:

what we have −9n=45

we divide -9 on both sides:

−9n/-9 =45/-9

n=−5

Hope this is right!

Step-by-step explanation:

Guess "This afternoon l,he has the same number of annuals and perennials left to plant will take more time to plant.

Answer:

23 years

Step-by-step explanation:

Step 1: Calculate the rate constant (k) for the radioactive decay

A radioactive substance with initial concentration [A]₀ decays to 97% of its initial amount, that is, [A] = 0.97 [A]₀, after t = 1 year. Considering first-order kinetics, we can calculate the rate constant using the following expression.

ln [A]/[A]₀  = - k.t

k = ln [A]/[A]₀ / -t

k = ln 0.97 [A]₀/[A]₀ / -1 year

k = 0.03 year⁻¹

Step 2: Calculate the half-life of the substance

We will use the following expression.

[tex]t_{1/2}[/tex] = ln2/ k = ln 2 / 0.03 year⁻¹ = 23 years

Answer:

Solution given:

cscθ -cscθcos²θ

taking common

cscθ(1-cos²θ)

we have

1-cos²θ=sin²θ and cscθ=1/sinθ

now

1/sinθ*sin²θ

=sinθ

so

D)

sin θ is a required answer.

Answer:

19.2m

Step-by-step explanation:

"Slice" the rectangle into two right triangles (slice along the diagonal). Now you can use the Pythagorean theorem to calculate the length of the diagonal:

[tex]a^{2} +b^{2} =c^{2} \\12^{2}+15^{2} =c^{2} \\144+225=c^{2} \\\sqrt{369} =\sqrt{c^{2} }\\19.2m =c[/tex]

Answer:

x ≥6

Step-by-step explanation:

Given the product:

√(x-6)*√(x+3)

The function has to be defined if x ≥0

Hence;

√(x-6)*√(x+3)≥0

Find the product

√(x-6)(x+3)≥0

Square both sides

(x-6)(x+3)≥0

x-6≥0 and x+3≥0

x≥0+6 and x ≥0 - 3

x ≥6 and x ≥-3

Hence the required inequality is x ≥6

Answer:

Step-by-step explanation:

Perpendicular means opposite reciprocal as far as the slope goes. The thing we need to know without prompting is that the given slope of x = -2 is a perfectly vertical line with an undefined slope, and that a line perpendicular to this one would have to be a perfectly horizontal line. Slopes of perfectly horizontal lines is always 0. Therefore, filling in the point-slope form of a line using the slope of 0 and the given point:

y - 6 = 0(x -(-5)) and

y - 6 = 0(x + 5) and

y - 6 = 0x + 0 so

y - 6 = 0 and

y = 6.

Answer:

Factorizing 4x2 - 9y2, we get

(2x)2 - (3y)2, by using the identities of a2 - b2.

= (2x + 3y) (2x - 3y)

Step-by-step explanation: