The 3-4-5 right triangle is a commonly used right triangle. Use the inverse sine function to determine the measure of the angle opposite the side of length 3.

The equation for the growth of the number of bacteria is x(t) = 10000t - 550t² + 110000

The growth rate of the number of bacteria is given as:

V = 10000 - 100mt,

Such that

t = time in hours,

m = 11.

To find the equation for the growth of the number of bacteria x(t), we can integrate this formula with respect to t.

Using the initial condition x(0) = 10000*m, we have

x(t) = ∫V dt + C

Substitute the known values in the above equation, so, we have the following representation

x(t) = ∫(10000 - 100mt) dt + C

Integrate

x(t) = 10000t - 50mt² + C

Recall that x(0) = 10000*m.

So, we have

10000m = 10000 * 0 - 50 * m * 0² + c

Evaluate

c = 10000m

c = 10000 * 11

c = 110000

So, the equation is

x(t) = 10000t - 50mt² + 110000

Since m = 11, we have

x(t) = 10000t - 550t² + 110000

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After 8 months both Boden and Camden will have the same number of CDs.

The given data:

Let 'n; be the total number of months, when both have the same amount of CDs.

Thus,

For 4 new CDs each month bought by Boden: 45 + 4n.

For 2 new CDs each month bought by  Camden : 61 + 2n.

Then, the equation becomes:

45+ 4n = 61 + 2n

45 + 2n = 61

2n = 16

n = 8

Thus, after 8 months both Boden and Camden will have the same number of CDs.

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The probability of obtaining at least one tail is equal to one minus the probability of getting all heads when a coin is tossed five times.

The probability of obtaining at least one tail is equal to one minus the probability of getting all heads when a coin is tossed five times.

3/8

The probability of obtaining at least one tail is equal to 1 minus the probability of obtaining all heads. The probability of obtaining all heads is 1/2^5 = 1/32. Therefore, the probability of obtaining at least one tail is 1 - 1/32 = 31/32. This simplifies to 3/8.

The probability of obtaining at least one tail is equal to one minus the probability of getting all heads when a coin is tossed five times. The probability of obtaining all heads is one out of two to the power of five, which is equal to one out of thirty-two. Therefore, the probability of obtaining at least one tail is one minus one out of thirty-two, which is equal to thirty-one out of thirty-two. This simplifies to three out of eight.

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Answer:

51 questions she answered correctly.

Step-by-step explanation: 85/100 x 60

= 510/10

= 51

Answer:

51 questions

Step-by-step explanation:

To do this we need to realize that 85% is equal to 85/100. This can be simplified in fraction form to .85.

Looking at the question, we see that it says "Briley answered 85% of the 60 quiz..." A key word here is of. Of always means multiply. So we can see if we were going to form an equation, we would be multiplying.

Briley answered correctly = (85%) times (60 questions)

Mathematically, ?=(.85)x(60)=51

So we know she answered 51 correctly, and that 51 is 85% of 60.

I hope this helps you!

The cost of the guitar string is given by the equation b = $ 1.30

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the cost of one guitar pick be = c

Let the cost of one guitar string be = b

And , Patrick bought 25 guitar picks and 25 guitar strings for = $ 40

Substituting the values in the equation , we get

25c + 25b = 40   be equation (1)

Now , cost of one guitar string = 1 + c

b = 1 + c   be equation (2)

Substituting the value of b in equation (1) , we get

25c + 25 ( 1 + c ) = 40

On simplifying the equation , we get

25c + 25 + 25c = 40

Subtracting 25 on both sides of the equation , we get

50c = 15

Divide by 50 on both sides of the equation , we get

c = $ 0.30

So , the cost of one guitar string = $ 1 + $ 0.30 = $ 1.30

Hence , the cost of one guitar string is $ 1.30

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Answer:

Step-by-step explanation:

By the way you've worded this, I'm guessing that you're looking for how much money Chris made at the end of the year.

When we're dealing with annual income, we must always consider how much was already present in savings before actually performing any operation, because that will give us the final answer.

Since Chris started with $5200, we do [tex](0.07)($5200) = $364[/tex] to find that Chris made $364 by the end of the year.

Lastly, to find his total income at the end of the year, we add [tex]5200 + 364 =[/tex] $5,564 at the end of the year.

$656.25 is the difference between the investor paying for the share and the investor selling the share.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that At the beginning of 2017, the share was worth $1050.

From the beginning of 2015 to the beginning of 2017 the value of the share halved each year.

In 2017 it is 1050.

In 2016, it is 2100

In 2015, it is 4200

Beginning of 2017 to the beginning of 2019, the value of the share increased by 1.5 times each year.

In 2017, 1050×1.5=1575

In 2018, 1575×1.5=2362.5

In 2019, 2362.5×1.5=3543.75

The investor paid for the share 4200 and the investor sold 3543.75.

Difference =4200-3543.75

=656.25

Hence, $656.25 is the difference between the investor who paid for the share and the investor who sold the share.

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f(x)=5x−3f(x)=5x-3 g(x)=x2−3g(x)=x2-3

Set up the composite result function. g(f(x))g(f(x))Evaluate g(5x−3)g(5x-3) by substituting in the value of f(5x−3)=(5x−3)2−3g(5x-3)=(5x-3)2-3

Simplify each term: g(5x−3)=25x2−30x+9−3g(5x-3)=25x2-30x+9-3 Subtract 33 from g(5x−3)=25x2−30x+6

To find the value of the function g(x) = 5x - 3 at x = -2, substitute -2 for x. This gives g(-2) = -13.

The function given is g(x) = 5x - 3. To find the value of this function when x = -2, you substitute -2 for x in the equation. This yields:

g(-2) = 5(-2) - 3

Which simplifies to:

g(-2) = -10 - 3

So, g(-2) = -13.

In summary, you substituted -2 for x in the function g(x)=5x−3 and then performed the arithmetic operations to find that g(−2) equals -13.

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Question 1 : find x intercept

y=0

0=3x+6
subtract 6 from both sides, after doing that, the equation would be : -6=3x

Then divide by -3 on both sides, the answer would be : x=3

Therefore the x intercept as a coordinate is (3,0)

Question 2 : find the y intercept

x=0

y=3(0)+6

y=6

Therefore the y intercept as a coordinate would be (0,6)

Hope this helped =)

-YinAhara

The price of first 3 video games is $57.3 and the other 2 videos games is $34.2 in the given arithmetic problem.

The study and use of numbers, mathematical relationships between numbers, and mathematical observations are all covered by the branch of mathematics known as arithmetic.

The core ideas in number theory, measurement, and computation are typically referred to as "arithmetic" (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots). It hasn't always meant the same thing, though, in the mathematical community.

Susan bought total 5 games

Lets the higher price be x

and lower be y

3x + 2y = $91.50

and

x - y = $2

x = 2 + y

Putting the value of x in first formula

3(2 + y) + 2y = 91.50

6 + 3y + 2y = 91.50

3y + 2y = 91.50 - 6

5y = 85.5

y = 85.5/5

y = 17.1

2y = 34.2

Putting the value of y in x

x = 2 + (17.1)

x = 19.1

3x = 57.3

Thus, the price of first 3 video games is $57.3 and the other 2 videos games is $34.2.

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c From the graph, it appears that around 50% of seniors had used alcohol in 2015.

d.This gives us: A=-0.8(25)+63=50%. So, both the line graph and the formula estimate that around 50% of seniors had used alcohol in 2015.

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Three degrees of freedom remain after applying five equations to eight variables. The other five variables may theoretically be solved for by specifying any three of them.

Five equations link these eight variables together. There are two equations given by the Pythagorean Theorem.

[tex]a^ 2=x^ 2+w^2 \ b^2=y^2+w^{\} 2[/tex]\

Two more are provided by the side ratios of similar triangles.

[tex]x/w=c/v[/tex]

[tex]y/w=c/u[/tex]

The two triangles are connected by the fifth equation, which is a straightforward linear relationship.

[tex]w=u+v[/tex]

Three degrees of freedom remain after applying five equations to eight variables. The other five variables may theoretically be solved for by specifying any three of them. But it might or might not be simple. What comes next will involve two distinct circumstances.

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The flavors that have chocolate as one of the ingredients will be 10 and the flavors that don't have chocolate as one of the ingredients will be 30.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

In this case, the bakery makes 40 different flavors of muffins. 25% of the flavors have chocolate as one of the ingredients

The flavors that have chocolate as one of the ingredients will be:

= 25% × 40

= 10

The flavors that don't have chocolate as one of the ingredients will be:

= 40 - 10

= 30

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The number of pounds of the chemical container can hold with given dimension is,  3600 pounds

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

Given that,

1 ft³ = 60 pounds

A container which has dimensions,

length = 6 ft

height =  4 ft

width =  5/2 ft

Volume of container = length × height × width

             =  6 ×  4 ×   5/2

             =   60 ft³

1 ft³ = 60 pounds

60 ft³  = 60 × 60 pounds

           =  3600 pounds

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The pair of figures are similar because:• Both figures are parallelograms

• All sides are congruents and • Scale factor 1: 2.5

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The pair of figures are similar because:

• Both figures are parallelograms

• All sides are congruents

• Angles W and Y are congruent with angles P and R

• Angles X and Z are congruent with angles S and Q

• Scale factor 1: 2.5

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The net torque about the axle is zero, as no external forces are acting on the disk.  Since there are no external forces acting on the disk, the sum of all the torques must be zero. Therefore, the net torque about the axle is zero.

The net torque about the axle is calculated by summing up all the torques about the axle due to external forces. Since there are no external forces acting on the disk, the sum of all the torques must be zero. Therefore, the net torque about the axle is zero.

The net torque about the axle of the 16-cm diameter disk in is zero, since there are no external forces acting on the disk. To calculate the net torque about the axle, we need to take the sum of all the torques about the axle due to external forces. Since there are no external forces, this sum must be zero. This means that the net torque about the axle is zero. This is because there is no force causing the disk to rotate and therefore, the net torque about the axle must also be zero. This result is consistent with the law of conservation of angular momentum, which states that when no external forces are acting on an object, the total angular momentum of the system must remain constant. Thus, the net torque about the axle of the 16-cm diameter disk in is zero.

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Answer:

In factored form: [tex]y=\sqrt{-\frac{1}{25}(2x-10)(2x+10)}[/tex]

In standard form: [tex]y=\sqrt{-\frac{4}{25}x^2+4}[/tex]

Step-by-step explanation:

Generally for these type of equations we want to get the term with "y" by it self (ignoring coefficients and any operations such as square root, etc...) so we want to get rid of the [tex]4x^2[/tex] from the left side which we can do by subtracting this from both sides to maintain equality and get rid of it on the left side.

[tex]25y^2=-4x^2+100[/tex]

One thing I want to note here is we can actually factor the right side which we generally want to do, we can rewrite it as: [tex]-(4x^2-100)[/tex] and from here we have a difference of squares: [tex]a^2-b^2=(a-b)(a+b)[/tex] so we can rewrite this as: [tex]-(2x-10)(2x+10)[/tex]

[tex]25y^2=-(2x-10)(2x+10)[/tex]

From here we divide both sides by 25:

[tex]y^2=-\frac{1}{25}(2x-10)(2x+10)[/tex]

Now from here to get rid of that square we do the inverse which is taking the square root:

[tex]y=\sqrt{-\frac{1}{25}(2x-10)(2x+10)}[/tex]

The reason factoring is useful in this case is we can now easily determine the domain of the function since inside the square root we have a quadratic which is opening down meaning it's only not negative between the zeroes (including the zeroes since they're... zero not negative) and this would be the domain of the graph. But if we wanted it to not be in factored form we would just put back what we had so we would have:

[tex]y=\sqrt{-\frac{1}{25}(4x^2-100)}[/tex]

then distribute the -1/25 to get:

[tex]y=\sqrt{-\frac{4}{25}x^2+4}[/tex]

By using divisibility rule, the possible factors of number are-

For the stated number:

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The correlation coefficient for the data in the table is given as follows:

r = 0.724.

The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.

The input and output variables are given as follows:

Hence the points that compose the data-set are given as follows:

(48, 34), (70, 46), (81, 38), (81,49), (86,49).

Inserting these points into a calculator, the correlation coefficient for the data is given as follows:

r = 0.724.

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This is a answer of graph format. (1 - x) • (2x + 5)  = 0

what is graph?

Pull out like factors : [tex]-2x^{2} - 3x + 5 = -1 • (2x^{2} + 3x - 5)[/tex]

Factoring  [tex]2x^{2}[/tex] + 3x - 5

The first term is,  [tex]2x^{2}[/tex]  its coefficient is  2 .

The middle term is,  +3x  its coefficient is  3 .

The last term, "the constant", is  -5

Multiply the coefficient of the first term by the constant   2 • -5 = -10

Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   3 .

       -10    +    1    =    -9

     -5    +    2    =    -3

     -2    +    5    =    3    That's it

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  5

                    [tex]2x^{2} - 2x + 5x - 5[/tex]

Add up the first 2 terms, pulling out like factors :

                   2x • (x-1)

             Add up the last 2 terms, pulling out common factors :

                   5 • (x-1)

Add up the four terms of step 4 :

                   (2x+5)  •  (x-1)

            Which is the desired factorization.

Equation :

 (1 - x) • (2x + 5)  = 0

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The mean of the random variable w is 15, and the standard deviation is 3.46.

The formula for the mean of a random variable is μ = E(x), and the formula for the standard deviation of a random variable is σ = sqrt(Var(x)). In this case, the mean of the random variable x is 12, and the standard deviation is 3. We can calculate the mean and standard deviation of the random variable w as follows:

E(w) = E(x) + 3 = 12 + 3 = 15

Var(w) = Var(x) + 9 = 9 + 9 = 18

SD(w) = sqrt(Var(w)) = sqrt(18) = 3.46

Therefore, the mean of the random variable w is 15, and the standard deviation is 3.46.

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The correct answer is Diary.

We acquire a different understanding of participants' experiences than we might from other techniques when participants immediately record their observations or perceptions. Participants may feel more comfortable expressing themselves in a diary than in an interview since sometimes personal reflections are more open. The participant's commitment to following through is, of course, a requirement of diary systems. It can be difficult to anticipate someone's availability to write within the time range set by the researcher. To get over these challenges, contemporary diary researchers employ a range of strategies, including as utilizing apps and technology or combining textual and artistic techniques

Hence, The correct answer is Diary Method.

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The each angle measure of the trigonometric ratios are obtained.

The given values is:

sin x = 0.7547,

Using trigonometric properties,

cos x = √(1 - sin²x)

         = √(1 - 0.7547²)

cos x = 0.6560

Cosec x = 1 / sin x

             = 1 / 0.7547

Cosec x = 1.3250

Now,

1 + cot²x = cosec²x

cot x =  √(cosec²x - 1)

        =  √(1.3250² - 1)

cot x = 0.8692

tan x = 1 / cot x

        =  1 / 0.8692

tan x = 1.1544

Thus, the each angle measure of the trigonometric ratios are obtained.

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The probabilities are given as follows:

The 31% share value is not wrong, as at most one household is not an unlikely outcome, as the probability is higher than 5%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter values for this problem are given as follows:

n = 12, p = 0.31.

The probability of none is given as follows:

P(X = 0) = (0.69)^12 = 0.0116.

The probability of at least one is given as follows:

P(X >= 1) = 1 - 0.0116 = 0.9884.

The probability of at most one is given as follows:

P(X <= 1) = P(X = 0) + P(X = 1)

In which:

P(X = 1) = 12 x 0.31 x 0.69^11

P(X = 1) = 0.0628.

Hence:

P(X <= 1) = P(X = 0) + P(X = 1)

P(X <= 1) = 0.0116 + 0.0628

P(X <= 1) = 0.0744.

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The relative frequency of A, B and C BE 0.5, 0.20 and 0.29.

The proportion between a given event's frequency and all events' frequencies in a statistical experiment.

The ratio of the total number of occurrences occurring in a particular scenario to the frequency of an event can be used to determine relative frequency. Relative frequency is defined as Subgroup frequency divided by Total frequency.

Due to the possibility of interpreting the heights of relative frequency histograms as probabilities, they are significant. These probability histograms offer a graphical representation of a probability distribution that may be used to estimate the probability that specific outcomes will materialize within a given population.

The relative frequency is the ratio of the frequency to the total frequency corresponding to each entry.

The total samples be 60 + 25 + 35 = 10

Also, the frequency corresponding to A is: 60

Corresponding to B is: 25

and corresponding to C is: 35

Hence, the Frequency table is as follows:

Data               Frequency

A                          60  

B                           25

C                           35

The relative frequency table is given by:

Data               Relative Frequency          

A                      60/120 = 0.5

B                       25/120 = 0.20

C                       35/120 = 0.29

Therefore, the relative frequency of A, B and C BE 0.5, 0.20 and 0.29.

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The solution curve for the differential equation dy/dx = (y - y²) / x is plotted in the slope field.

What is a slope field?

The solutions to a scalar function's first-order differential equation are shown graphically by slope fields, also known as direction fields. Functions depicted as solid curves are solutions to a slope field. In order to determine the estimated tangent slope at a point on a curve, where the curve is some solution to the differential equation, one can use a slope field, which displays the slope of a differential equation at specific vertical and horizontal intervals on the x-y plane.

The slope field is a cartesian grid where you draw lines in various directions to represent the slopes of the tangents to the solution. Therefore by drawing a curve through consecutive slope lines, we can find a solution to the differential equation.

The differential equation is dy/dx = (y - y²) / x.

The solution curve is drawn using the solution points (1,2) for the differential equation.

Therefore, the solution curve is obtained.

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The two different quantities to measure which school has higher academic performance are :

• Graduation rate / Budget per student

• SAT average / Budget per student

To specify a number that represents academic achievement. We compare the budget per pupil for each school to a related metric or parameter that measures the academic performance of the students in each school.

The following variables could be used to gauge academic achievement:

• Each school's graduation rate.

• Each school's average SAT score.

Therefore, Graduation rate / Budget per student and SAT average / Budget per student are appropriate in this case.

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The length of the park will be 598 meters.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that two gentlemen are taking their morning walks, beginning from opposite ends of a park. They meet 720 meters away from one of the ends, after which they continue walking. After reaching the end of the park, each turns back. On the way back, they meet at a distance of 400 meters from another end of the park.

The length of the park will be calculated as,

H² = P ² + B²

B² = (720)² - ( 400 )²

B = √ ( 358400 )

B = 598 meters

The length of the park would be 598 meters.

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