The biologist is studying Black Carp invasiveness in Lake Ontario next. He doesn't have time to sample the fish himself, so instead he instead asks a fisherman who has been fishing off of one of Toronto's piers all morning about his catch. The fisherman responds that, of the 75 fish he has caught, 47 have been Black Carp. What is the lower bound of a 99% confidence interval for the true proportion of fish that are Black Carp in Lake Ontario

Tan(x/2) = (1 + cosx)/sinx is equivalent to the trigonometric identity cscx

An equation is an expression that can be used to show the relationship between variables and numbers.

Trigonometric identities are based on the six trigonometric ratios. They are sine, cosine, tangent, cosecant, secant, and cotangent.

It is given as:

tanФ = sinФ/cosФ, cotФ = 1/tanФ = cosФ/sinФ, cosecФ = 1/sinФ and secФ = 1/cosФ

According to half angle formula:

tan(x/2) = (1 + cosx)/sinx

Hence:

tan(x/2) + cotx = [(1 - cosx)/sinx] + (cosx/sinx)

tan(x/2) + cotx = (1 - cosx + cosx)/sinx

= 1/sinx

= cscx

Therefore tan(x/2) = (1 + cosx)/sinx is equivalent to cscx

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The probability that neither student and parent don't get picked is equal to the value 2/5.

Probability is simply the likelihood of something occurring. When we are uncertain about the outcome of an event, we can discuss the probabilities of various outcomes—how likely they are. Statistics is the study of events governed by probability.

Given, there are 5 students 7 parents and 8 teachers in a room.

Total members in the room = 5+7+8

Total members in the room = 20

Total mem = 20

Probability of neither student and parent get picked = Probability of Teacher getting picked

Probability = Needed ones / Total members

Probability = 8 / 20

Probability = 2/5

Therefore, the probability that neither student and parent don't get picked is equal to the value 2/5.

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Answer:

9

Step-by-step explanation:

I'm going to solve this question by expanding the logarithm (note that you can also solve this equation by solving for a, b, and c)

We know the following

\(log(ab)=log(a)+log(b)\)

Which means we can split the numerator into

\(log(b^{1/2})+log(c^{3/2})\)

We also know that

\(log(a^{x})=x*log(a)\)

Which means that we can rewrite the following as

\(\frac{log(b)}{2}+\frac{3log(c)}{2}\)

We can evaulate this and get

-1+12= 11

for the numerator

Now we need to take care of the denominator

we know the following

\(log(\frac{x}{y})=log(x)-log(y)\)

which means that we have

11-2log(a)

solve and get

11-2

9

Answer:

Step-by-step explanation:

.

The best way for Anthony to plan his garden is to create a rectangular plot. He can use the side of the barn as one side of the rectangle, and then measure out the other three sides. The total length of the three sides will be 176 feet. He can divide this into two sides that are 88 feet long and two sides that are 44 feet long. This will give him a rectangular plot that is 176 square feet.

Once Anthony has the dimensions of the plot, he can build a fence around it to protect it from rabbits. He can use a variety of materials such as wood, wire, or plastic mesh to build the fence. The fence should be at least four feet tall and buried at least six inches deep to be effective. If he chooses to use wire, he should use thick, galvanized wire to make sure that the rabbits cannot chew through it.

Once the fence is in place, Anthony can begin planting his garden. He should also consider adding a layer of mulch or straw around the outside of the fence to discourage the rabbits from digging underneath it. With the right planning and protection, Anthony should be able to enjoy a successful garden.

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;

C² = a²+b²

Where:

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Answer:

t - 7/8 is the answer

hope it helps

Answer:

B \(1/4^2\) and A \(4^1/4^3\)

Step-by-step explanation:

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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Answer:

16 \(\pi\) cm

Step-by-step explanation:

C = 8 * 2 * pi = 16 \(\pi\) cm

Answer:C≈50.27cm

Step-by-step explanation:

C=2πr=2·π·8≈50.26548cm

Answer:

27

Step-by-step explanation:

2x9/2x3=27

The percentage of the data values are between 110 and 170 = 37.5%

We know that in the box plot, the first quartile is nothing but 25% from smallest to largest of data values.

The second quartile is nothing but between 25.1% and 50% (i.e., till median)

The third quartile: 51% to 75% (above the median)

And the fourth quartile: 25% of largest numbers.

In the attached box plot, we can observe that between two numbers on the number line there are 5 equal parts.

So, each unit length measures 10 units.

Also, the median of the data = 110

We need to find the percentage of the data values are between 110 and 170.

i.e., the percentage of the data values are in the third quartile.

The range of this box plot is: 190 - 30 = 160

The data values are between 110 and 170 = 60

Using percentage formula,

P = (60/160) × 100

P = 37.5%

This is the required percentage.

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Find the complete question below.

Answer:

2^4   * 9^4

Step-by-step explanation:

(2*9)^4

We can take the power to each term inside the parentheses

2^4   * 9^4

Answer:

Step-by-step explanation:

(y - 3) = -2(x - 4)

y = -2x + 8 + 3

y = -2x + 11

pls give brainliest

Answer:

The the linear equation in point-slope form is

\(y-3 = -2 (x-4)\)

Step-by-step explanation:

Given

We know that the point-slope form of the line equation is

\(y-y_1=m\left(x-x_1\right)\)

Here:

substituting the values m = -2 and the point (4, 3) in the point-slope form

\(y-y_1=m\left(x-x_1\right)\)

\(y-3 = -2 (x-4)\)

Thus, the the linear equation in point-slope form is

\(y-3 = -2 (x-4)\)

Note: This equation could be further simplified to write it in the slope-intercept form

\(y=mx+b\)

where m is the slope and b is the y-intercept

so writing the equation in the slope-intercept form

\(y-3 = -2 (x-4)\)

\(y-3 = -2x+8\)

\(y=-2x+8+3\)

\(y=-2x+11\)

Thus, the equation is the slope-intercept form is

Step-by-step explanation:

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The composition of functions is solved and ( f - g ) ( x ) = x² + 8

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the first function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 2x² + 1

Let the second function be represented as g ( x )

Now , the value of g ( x ) is

g ( x ) = x² - 7

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

On simplifying , we get

( f - g ) ( x ) = 2x² + 1 - ( x² - 7 )

( f - g ) ( x ) = x² + 8

Hence , the function is ( f - g ) ( x ) = x² + 8

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Answer:

(a) A(0)= 0 (kg)

(b) \(R_{in}=0.28\dfrac{kg}{min}\)

(c) \(C(t)=\dfrac{A(t)}{2840}\)

(d) \(R_{out}=\dfrac{A(t)}{710}\)

(e) \(\dfrac{dA}{dt}=0.28-\dfrac{A(t)}{710}\)

Step-by-step explanation:

A tank contains 2840L of pure water.

A solution that contains 0.07 kg of sugar per liter enters a tank at the rate 4 L/min. The solution is mixed and drains from the tank at the same rate.

(a) Amount of sugar initially in the tank.

Since the tank initially contains pure water, the amount of sugar in the tank

A(0)= 0 (kg)

(b) Rate at which the sugar is entering the tank. (kg/min)

\(R_{in}\)=(concentration of sugar in inflow)(input rate of the solution)

\(=(0.07\dfrac{kg}{liter}) (4\dfrac{liter}{min})\\R_{in}=0.28\dfrac{kg}{min}\)

(c) Concentration of sugar in the tank at time t

Volume of the tank =2840 Liter

Concentration c(t) of the sugar in the tank at time t

Concentration, C(t)= \(\dfrac{Amount}{Volume}\)

\(C(t)=\dfrac{A(t)}{2840}\)

(d) Rate at which the sugar is leaving the tank

\(R_{out}\)=(concentration of sugar in outflow)(output rate of solution)

\(=\dfrac{A(t)}{2840})( 4\dfrac{Liter}{min})=\dfrac{A}{710}\\R_{out}=\dfrac{A(t)}{710}\)

(e) Differential equation representing the rate at which the amount of sugar in the tank is changing at time t.

\(\dfrac{dA}{dt}=R_{in}-R_{out}\\\dfrac{dA}{dt}=0.28-\dfrac{A(t)}{710}\)

Answer:

l

Step-by-step explanation:

Answer:

i think that to many but the answer is 5

Step-by-step explanation:

qwerty

The probability that one or more of the children is a carrier of the recessive allele is 0.988.

The probability that one or more of the children is a carrier of the recessive allele can be calculated using the binomial theorem. The binomial theorem states that the probability of a success in a given trial is the sum of all probabilities of success minus the probability of none of the successes.

For the given scenario, we can assume that the probability of each child being a carrier is 0.25 (since each parent is known to be a carrier). The probability of one or more of the children being a carrier is then\((1-0.25^4) = 0.988.\)

To calculate this, we first calculate the probability of none of the children being a carrier, which is \((1-0.25)^4 = 0.316\). We then subtract this from 1 to get the probability of one or more of the children being a carrier:\((1-0.25)^4 = 0.316\)

Therefore, the probability that one or more of the children is a carrier of the recessive allele is 0.988.

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Answer:

yes

Step-by-step explanation:

3.68-3=0.68 (SHE HAS ENOUGH!!!)

Answer:

u > 7

Step-by-step explanation:

-2u -6 < -20  Add 6 to both sides

-2u - 6 + 6 < -20 + 6

-2u < -14  Divide both sides by -2.  When you multiply or divide both sides by a negative number, you must flig the sign.

\(\frac{-2u}{-2}\) > \(\frac{-14}{-2}\)

u > 7

Helping in the name of Jesus.

The answer is:

u > 7

In-depth explanation:

You haven't told me what the values of u are, but I'll solve the equation for u.

Add 6 on each side:

\(\bf{-2u-6 < -20}\)

\(\bf{-2u < -14}\)

Divide each side by -1 and reverse the sign:

\(\bf{2u > 14}\)

Now divide each side by 2

\(\bf{u > 7}\)

The equation of a line parallel to 2x - 5y = 10 with a y-intercept of (0,1) is 2x - 5y = -5 in standard form.

Equation of a line passing through (2,6) and (2,4) in slope-intercept form:

To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).

Given points:

Point 1: (2,6)

Point 2: (2,4)

Since the x-coordinate is the same for both points, we can conclude that the line is vertical, and its equation will be in the form x = c, where c is the x-coordinate of any point on the line.

In this case, x = 2 is the equation of the line passing through the points (2,6) and (2,4).

Equation of a line parallel to 2x - 5y = 10 with a y-intercept of (0,1) in standard form:

To determine the equation of a line parallel to a given line, we need to keep the same slope. The given line has the equation 2x - 5y = 10, which can be rearranged to the slope-intercept form y = (2/5)x - 2.

Since the parallel line has the same slope, the equation will be in the form y = (2/5)x + b, where b is the y-intercept.

Given y-intercept: (0,1)

Substituting the values into the equation, we have y = (2/5)x + 1.

To convert the equation into standard form (Ax + By = C), we multiply through by 5 to eliminate the fraction:

5y = 2x + 5

Rearranging the terms:

2x - 5y = -5

Therefore, the equation of a line parallel to 2x - 5y = 10 with a y-intercept of (0,1) is 2x - 5y = -5 in standard form.

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Answer: ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

-3√2

The response choice that include the true statements based on the number line is the second option;

Point B represents \(-2\frac{1}{2}\), Point C represents 1, and 1 > \(-2\frac{1}{2}\)

A number line is a line that contains (equally spaced) markings, which is then used to illustrate mathematical operations.

The number line in the question is presented as follows;

<________|_____|_____|__|__|____|____|____|___|_|____|_____|____>

                -5          A               B                     0       C      D                     5  \({}\)

Therefore, based on the number line, we get;

The location of the point A is 4 units to the left of the point 0, taking the points to the right of zero as positive, we get;

Each unit to the left of point O, is -1 larger than the previous value, moving from right to left.

The coordinates of the point A is therefore, -1 × 4 = -4

The location of the point C is one unit to the right of 0, therefore, the coordinates of the point C is 1

The location of the point C = 1 is further right to 0 than the point B = -2 1/2

Therefore;

The correct option is; Point B represents -2 1/2, Point C represents 1, and 1 > -2 1/2

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Answer:

737 747 4

Step-by-step explanation:

74747747

The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

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Find the required table attached

Since the speed of the Cheetah is constant, this means that the speed must be the same all through in the table.

To get the unknown time and distance, we will have to use the formula below:

Speed = 120/4 = k

Speed = 30m/s = k

We are to get the distance when the time is 25secs

Speed = Distance/Time

30 = d₂/25

d₂ = 30 × 25

d₂ = 750 m

To get the time in the third column

Time = Distance/Speed

t₃ = 270/30

t₃ = 9seconds

Find the completed table attached:

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