100 students are interviewed to see which of biology, chemistry or physics they prefer.
29 of the students are girls. 9 of the girls like biology best.
20 of the boys prefer physics.
9 out of the 27 who prefer chemistry are girls.
What percentage of the students prefer biology?

Answer: C = 25.1 yards

Step-by-step explanation: The circumference formula is as follows C = 2[tex]\pi[/tex]r^2 C being circumference, [tex]\pi[/tex] Being pi or 3.14, and r^2 The radius squared

The radius is given to us in the image being the midsegment from the center of the circle or 4 and we will input all our values into the equation.

C = 2 x 3.14 x 4^2 ≅ 25.13

We round to the nearest tenth to get

C = 25.1 yards

The complementary angle is x= 36 degrees.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question-

The complementary angle is x

Complementary angles total to a straight angle (90 degrees) (90 degrees).

x + (2/3)x = 90

(3/3)x + (2/3)x = 90

(5/3)x = 90

x = 90(3/5)

x = 54 degrees

The angle is 2/3 of this

The angle is (2/3)54 = 36 degrees

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The minimum sample size needed in order for us to be 90% confident that our estimate is within 1.2 hours per week of is 55.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Assuming that the standard deviation of the number of hours worked by college graduates is 6.30 hours per week

We need to find the minimum sample size needed in order for us to be 90% confident that our estimate is within 1.4 hours per week of.

The formula to determine sample size is n = [zs/E]²

z is standardization value indicating confidence level.

s is sample standard deviation.

E is acceptable acceptance error.

n = [invNorm(0.95)×6.3/1.4]²

n = [1.645×6.3/1.4]²

n=54.79=55

Hence, 55 is the minimum sample size needed in order for us to be 90% confident that our estimate is within 1.2 hours per week of.

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The value of x in the absolute value equation |3x + 12| = 0 is -4

From the question, we have the following parameters that can be used in our computation:

|3x + 12| = 0

The above equation is an absolute value equation

So, we start by removing the absolute brackets

So, we have the following representation

3x + 12 = 0

Evaluate the like terms

This gives

3x = -12

Divide both sideso of the equation by 3

x = -4

Hence. the solution is -4

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95% confidence interval is wider than 90% confidence interval.

Given as that unknown mean and a known variance.

let's suppose parameter for mean as µ and

for standard deviation σ.

we have sample of size n  as x1,x2,x3,x4.......xn.

Confidence means what degree of assurance do we desire that the interval estimate contains the  populace mean µ.

The likelihood that the interval falls within the level of confidence c

The population parameter is contained in estimate.

If the level of confidence is 90%, this means that we are 90%

confident that the interval contains the population mean, µ

The corresponding z-scores for 90% confidence interval are ± 1.645.

If the level of confidence is 95%, this means that we are 95%

confident that the interval contains the population mean, µ

The corresponding z-scores for 95% confidence interval are ± 1.96.

So In comparison to a 95% Confidence Interval, a 90% Confidence Interval would be narrower. This happens because the reliability of an interval containing the actual mean declines as the confidence interval's precision rises (i.e., CI width decreases) (less of a range to possibly cover the mean). Consider the case of 100% confidence; the interval must contain all possible values in order to guarantee that the mean is captured with 100% certainty.

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Among both teenage boys and adult men, delinquency, hard drug use, and aggressive-bullying responses to frustration have been linked with higher-than-average levels of Testosterone.

The sex hormone testosterone has significant physiological functions. It is thought to control the creation of sperm, red blood cells, muscle mass, fat distribution, and sex drive (libido) in men.

Males and females may both have diminished bone mass and sex drive if a man has low testosterone, which can cause symptoms like erectile dysfunction.

Low sperm counts, testicular shrinkage, and impotence are issues connected to males having abnormally high testosterone levels. Cardiac attack risk is elevated when heart muscle is damaged. enlarged prostate and urination problems.

Therefore , Drug use and aggressive to frustration are licked with higher-than-average levels of Testosterone.

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A parametrization of path C is x= 4t and y = 8t

Line segments on nearly trivial to parametrize. It is often it easiest to do in interval t∈ [0,1]

Then we just need to think about what we need to add to each first coordinate to get the second

Since, 0+ 4 = 4  and 0+ 8 = 8

So, parametrization is

=> x = 4t

y = 6t

(b) To evalute the line integral, we have to derivate parametrize

dx/dt = 4

dy/dt = 8

So, the differential line element is

[tex]ds = \sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2}[/tex]

=> √(4)²+(8)²

=> 4√5

Integrating ,

[tex]\int\limits_{c} {x^2 + y^2} \, ds\\ = \int\limits^1_0 {(4t)^2 + (8t)^2 } 4\sqrt{5} \,dt\\=4\sqrt{5} [\frac{80}{3} t^3]^{1}_{0}\\[/tex]

Putting the limits

=> 285.51

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If to approximate the length of a marsh, a surveyor walks x = 420 meters. The Approximate the length AC of the marsh is 420.7m.

Using this formula to find the length of Ac of the march

b² = a²+c² -2ac Cos B

Where:

a²=220

c²= 420

Cos B = 180°  - 75° = 105°

Let plug in the formula

b² = 220² + 420² - 2(220)( 420) Cos  105°

b² = 220² + 420² - 2(220)( 420) (-0.258819045)

b² = 48,400 + 176,400 - 47,829.76

b² = 224,800 -  47,829.76

b = √176,970.24

b = 420.7m

Therefore the length is 420.7m

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Polynomial with integer coefficients that cannot be factored into polynomials of lower degree, also with integer coefficients, is called a prime polynomial.

A polynomial is an algebraic expression made up of at least one algebraic term. An algebraic term is the product of a variable or variables and constant, where the variable can have no rational or negative exponents. A polynomial that has a single term is called a monomial, binomials have two terms and a trinomial has three terms.

A polynomial with integer coefficients that cannot be factored is called an irreducible or prime polynomial .

In order to identify whether a polynomial is prime or not, try factoring it. If it can be factored, then it is not prime but if it cannot be factored then it is prime.

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1. The equation of the line is:

y=-2x/3 + 5

2. The equation of the line in slope intercept form is:

y=3x+5

1. Given:

we have two points:

(-3,7) = (x₁,y₁)

(9,-1) = (x₂,y₂)

equation of the line is:

y - y₁ = m(x-x₁)

₁first calculate slope m = y₂-y₁/x₂-x₁

m = -1-7/9-(-3)

m = -8/12

m = -2/3

now, y - 7 = -2/3 (x-(-3)

y-7=-2/3(x+3)

y-7=-2x/3-2

y=-2x/3-2+7

y=-2x/3 + 5

hence equation of the line is y=-2x/3 + 5

2. Given two points:

(2, 11) and (4, 17)

(2, 11) = (x₁,y₁)

and (4, 17) = (x₂,y₂)

slope intercept form:

y=mx+c

we need to calculate the m value:

m = 17-11/4-2

m = 6/2

m=3

now substitute in the given form:

y - 11 = 3(x-2)

y-11=3x-6

y=3x-6+11

y=3x+5

Hence we get the required answer.

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Answer:

So a circle with diameter 17 m has a circumference of 53.4 m

Step-by-step explanation:

Divide the circumference by π, or 3.14 for an estimation. The result is the circle's diameter.

Divide the diameter by 2.

There you go, you found the circle's radius

the measure of the value a is 24°

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angles of triangle = 180

Here given 3 angles are 2a, 3a and a+36°

So the sum of all the angles should be 180°

⇒2a+ 3a +a+36° = 180

⇒6a = 180-36

⇒a = 144/6= 24

Hence the measure of the value a is 24°

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The value of the function f(x) which is differentiable at all x, at x = 2

Or f(2) = b. 4.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, The function 'f' is differentiable for all x.

Now, f(1) = 2 and f(4) = 8, So, f(x) can be 2x as it is satisfying the conditions.

∴ At x = 2 or f(2) = 2(2) = 4.

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Answer:

83

Step-by-step explanation:

30+54=83

Answer:

The number is 6.

Step-by-step explanation:

30+54 = (?)(5+9)

30+54=80

5+9=14

30+54=80=(?)(5+9)

14x6=84

The area of cheese is 38 square centimeters.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given that the height of the cheese is 2.5 inches and the base is 4.75 inches.

The value of 1 inch is 2.54 centimeters.

Now convert 2.5 inches and 4.75 inches into centimeter:

2.5 inches = (2.5 × 2.54) centimeters = 6.35 centimeters

4.75 inches = (4.75 × 2.54) centimeters = 12.065 centimeters

The area of triangle is (1/2) × base × height

The area of the cheese is [(1/2) × 6.35 × 12.065] square centimeter

=38.31 square centimeter

= 38 square centimeters (nearest square centimeter)

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Probability mass function of H and X is,

P(X=m∣H=1)P(H=1) =[tex]\left[\begin{array}{c\alpha }n\\m\end{array}\right][/tex] b^N (1-b)^(n-s) q (Since, q=(1-p))

Let X be the number of successful surgeries.

From the question, we have

it is observed that H∈{0,1}

P(H=1) =E(H)

=p

Next, observe that X∈{0,1,…n}, Now, we want to find following:

f(h,m) =P(H=h,X=m)

=P(X=m∣H=h)P(H=h)

Probability mass function of H and X is,

P(X=m∣H=1)P(H=1)=[tex]\left[\begin{array}{c\alpha }n\\m\end{array}\right][/tex] a^n (1-a)^(n-k) p

P(X=m∣H=0)P(H=0)= [tex]\left[\begin{array}{c\alpha }n\\m\end{array}\right][/tex]b^N (1-b)^(n-k) (1-p)

=[tex]\left[\begin{array}{c\alpha }n\\m\end{array}\right][/tex] b^N (1-b)^(n-s) q (Since, q=(1-p))

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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We want to see for which one of the given functions, the inverse derivate evaluated in x = 20 is equal to 1/5.

The correct option is B:  f(x) = x^3 + 5x + 20

What is inverse derivative?

The inverse function rule in calculus is a formula that converts the derivative of the inverse of a bijective and differentiable function, f, into the derivative of f.

Remember that two functions f(x) and g(x) are inverses if:

f( g(x)) = g( f(x))) = x

And for the inverse derivate of a function, we have the rule:

[tex]\frac{d}{dx}[f^{-1} (f(x))]=\frac{1}{{f^'}(x)}[/tex]

So first we need to find for what value of x each function is equal to 20, and then we need to see if the derivate of the function evaluated in that same value of x is equal to 5.

For example, for the first option we have:

A: f(x) = x + 5

We find the x-value such that the function is equal to 20.

f(15) = 15 + 5 = 20

We derivate the function.

f'(x) = 1

We evaluate the function in the x-value we got above.

f'(15) = 1

This is not the correct option, as this is not 5.

Now we need to do that for all the given options.

The only correct option will be the second one:

B: f(x) = x^3 + 5x + 20

First we find the x-value such that this is equal to 20

f(0) = 0^3 + 5*0 + 20 = 20

Then the x-value is x = 0.

Now we find the derivate of f(x).

f'(x) = 3*x^2 + 5

Now we evaluate that in the x-value we got before:

f'(0) = 3*0^2 + 5 = 5

As wanted, this is equal to 5.

Then we have:

[tex]\frac{d}{dx}[f^{-1} (f(0))]=\frac{1}{{f^'}(0)}[/tex]

[tex]\frac{d}{dx} [f^{-1} (20)]=\frac{1}{5}[/tex]

As wanted.

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The answer will be [tex]a^{-20-12a}[/tex] that can be find out using exponential function.

What are exponential function ?

Exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change.

Like, f(x) = [tex]x^{a}[/tex]

x is base and a is power.

Basic rules to solve this function :

1. If we take the product of two exponentials with the same base, we simply add the exponents:

x^ a * x^ b = x^ a + b.

2. If we take the quotient of two exponentials with the same base, we simply subtract the exponents:

x^ a / x^ b =  x^ a-b

3. We can raise exponential to another power, or take a power of a power. The result is a single exponential where the power is the product of the original exponents:

x^ (a)^ b = x^ (ab).

In given equation, [tex]{a^{2^{-2^5}}/{a^{4a^3}}[/tex]

So the answer is a^(-20-12a).

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Answer:

1/3

Step-by-step explanation:

15/5=3

21/7=3

Answer: 3:1

Step-by-step explanation:

We can model this problem using ratios, we start with a ratio of 15:21 and we know we went down to a 5:7. To make both equivalent we divide both 15 and 21 by 3, meaning the ratio between the two is 3:1.

False. The orthogonal projection of y onto a subspace W is never reliant on any particular basis and always depends simply on W.

The term "orthogonality" can be used when the vector space contains an inner product and is complete (i.e., wh

en it's a Hilbert space). When the range and the null space are orthogonal subspaces, the projection is said to be orthogonal.

In order to portray three-dimensional objects in two dimensions, orthographic projection (also known as orthogonal projection and analemma) is used. Every plane of the picture appears in an affine transformation on the viewing surface thanks to orthographic projection, a type of parallel projection in which all of the projection lines are orthogonal to the projection plane. An oblique projection, also known as a parallel projection in which the projection lines are not orthogonal to the projection plane, is the reverse of an orthographic projection.

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The value of x is 17

Define Angle

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Define Mid-line in Triangle

In a triangle, a midline (or a midsegment) is any of the three lines joining the midpoints of any pair of the sides of the triangle.

We know, the x+6 is mid-line of 46.

So, according to that make it a half of 46 is 23

Now, equate the value and find x

23 = x + 6

23 - 6 = x

17 = x

swap the sides

x = 17

Hence, the value of x is 17

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The term 3x2 in the quotient is the result of dividing 3x4 by x^2.

Divide the dividend by the divisor to determine the quotient of a division problem.

First, take the dividend's first digit from the left.

Second step: After dividing it by the divisor, write the result as the quotient on top.

Step 3: Deduct the outcome from the digit and write the difference below.

Step 4: Bring down the dividend's next digit (if present).

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he term 3x2 in the quotient is the result of dividing 3x4 by x² (A)

The polynomial −2x3 − x2 + 13x in the last line is the result of subtracting 3x4 + 9x3 + 3x2 from the dividend and bringing down 13x . (B)

Complete the division.

The quotient is 3x2 + -2x + 5

.

Heres all three. Hope i helped.

Answer:

her sales would be 56.9

Step-by-step explanation:

Answer:

56.9

Step-by-step explanation:

There are 3 more days will it take her to plant all the trees.

What is rate?

The numerator of a ratio in mathematics represents the rate of change in the other (dependent) variable if the denominator of the ratio is expressed as a single unit of one of the related quantities and it is assumed that this quantity can be changed systematically (i.e., is an independent variable).

Given:

Tamika must plant 432 trees.

In the past 6 days Tamika planted 288 trees.

She continues the planting tree at the same rate.

As she planted 288 trees in 6 days.

That means she plant 288 / 6 = 48 trees in a day.

The remaining trees are 432 - 288 = 144.

So, 144 trees will be planted in 144 / 48 = 3 days.

Hence, there are 3 more days will it take her to plant all the trees.

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A linear equation is an algebraic equation with two or more variables in which the highest degree of the variables is one. Linear equations can be written in the form ax + b = c, where a, b, and c are all constants.16. x = 32

To solve the equation 8x - 5 = 257, we need to isolate the variable x. We can do this by adding 5 to both sides.

8x - 5 + 5 = 257 + 5

8x = 262

Then, we can divide both sides by 8 to isolate x.

8x/8 = 262/8

x = 32

To solve the equation 8x - 5 = 257, we can add 5 to both sides to isolate the variable x. This gives us 8x = 262. Dividing both sides by 8 then gives us x = 32. This is the solution to the equation.

The complete question is :

algebra 2: cc 2015 > chapter 7: solving rational equations > section exercises 7.5 > exercise 16 previous 16 answer sheet .What is the solution to the equation 8x - 5 = 257?

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The given expression can be simplified to obtain the quotient and remainder as 3x + 4 and -4 respectively.

The polynomial p(x) divided by the other polynomial g(x) gives remainder r(x) and quotient as q(x) such that degree of r(x) is not greater than g(x).

The given expression is (3x²+ 22x + 27)/(x+6).

The division can be done as follows,

First take the quotient as 3x so that that the remainder is,

3x²+ 22x - 3x(x + 6)

= 4x

Now, the new dividend is 4x + 6.

Take the quotient as 4 to get the remainder as,

4x + 6 - 4(x + 6)

= -18

It cannot be further divided because the degree of -18 is less than x + 6.

Which implies that the quotient is 3x + 4 and the remainder is -18.

Hence, the quotient and remainder for the given division of polynomials is 3x + 4 and -4 respectively.

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The systems of equations to solve for this quadratic function to model the values in the table is y =  -2x^2 + 4x - 2

The general form of a quadratic function is --> y = ax2 + bx + c

-2 = a(0)2 + b(0) + c

-2 = 0 + 0 + c

-2 = c

substitute c value

(-1 , -8) substitute

-8 = a ( -1 )2 + b ( -1 ) - 2

-8 = a - b - 2

-6 = a - b

( 3 , -8)

-8 = a ( 3 )2 + b ( 3 ) - 2

-8 = 9a + 3b - 2

-6 = 9a + 3b

a - b = -6

9a + 3b = -6

on solving :

9 ( b - 6 ) + 3b = -6

9b - 54 + 3b = -6

12b - 54 = -6

12b = 48

b = 4

a - 4 = -6

a = -2

The quadratic equation for this table is y = -2x^2 + 4x - 2

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Full question:

set up the systems of eqautions to solve for this quadratic function to model the values in the table.

x | y

-1 | -8

0 | -2

3 | -8

Answer:

a.

Step-by-step explanation:

it is not clear what your teacher discussed and wants from you here.

formally, all triangles are similar, as the description says. and the sequence of the vertexes in the "name" does not make any difference in identifying the triangle. this would be only important when identifying a specific angle (the center letter). in other words : a triangle is identified by naming its three corners in any sequence. simply because for the similarity concern you can twist and turn the triangle until it has the same orientation as the other triangle to compare.

so, again, a very strange question from your teacher. many greetings from me.

as explained, formally all 4 statements are correct.

but in order to identify one, it has to be a.

because the sequence of the corners are the same.

in QTS the side QT (the shortest of the 3 sides) is named first. and TS (the longest of the 3 sides) is named last.

in PQT we have the same sequence. PQ is the shortest side first, and QT is the longest side last.

no other answer option has the same sequence on the left and the right side.

but again, this is actually irrelevant for the similarity relation.

e.g. triangle RQS = triangle SQR, they are just twisted and turned images of the same triangle.

The slope intercept form is given as  y = 1/6x - 3.

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The given equation is y + 2 = 1/6(x - 6).

It can be written in terms of slope-intercept form y = mx + c as below,

y + 2 = 1/6(x - 6)

=> 6(y + 2) = x - 6

=> 6y + 12 = x - 6

=> 6y = x - 6 - 12

=> y = 1/6(x - 18)

=> y = 1/6x - 3

Hence,  slope-intercept form of the given equation is y = 1/6x - 3.

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