Solve the Quadratics:

1) m^2+5m+6=0
2) 5p^2-125=0
3) 2x^2-4x-30=0
4) 6n^2-10n-16=3
5) 5v^2-2-v=-v

Answer: the 3rd one

Step-by-step explanation: you can type it into a graphing calculator and get the answer

Answer:

Step-by-step explanation: Im pretty sure they are asking you for the slope so it would be y = 0.5x

Answer:

0.5

Step-by-step explanation:

The unit rate is the number of units obtained in the "y" variable per unit obtained in the "x" variable. This behavior is observed in proportional relationships. For example: imagine that we know that the price for 5 pencils is $2.5. Since this is a proportional relationship, the unit rate will be the price of 1 single pencil, that is obtained by dividing 2.5 / 5 = 0.5.

In this case we also know that the graph passes through the point (1, 0.5), so the unit rate is given in that point.  :)

Answer:

A regression coefficient is the same thing as the slope of the line of the regression equation.

Step-by-step explanation:

The equation for the regression coefficient that you'll find on the AP Statistics test is: B1 = b1 = Σ [ (xi – x)(yi – y) ] / Σ [ (xi – x)2].

To find a regression equation, you plot the data on a scatter plot, draw an approximate line of best fit, calculate its slope and y-intercept, and then write the equation. Alternatively, you can use statistical software or a calculator's regression function to find the most accurate equation.

To find a regression equation, one can follow these steps:

An example regression equation from sample data might look like this: ŷ = 173.51 + 4.83x, where x is the independent variable and ŷ is the predicted value of the dependent variable, y.

It is crucial to remember that regression equations predict outcomes for the variables within the given data set, but they should not be extrapolated beyond the scope of the available data. Variability in real data means that different samples might yield different regression equations, which is why it is important to consider the goodness of fit, such as the correlation coefficient or the coefficient of determination (r2).

Answer:

3 hours

Step-by-step explanation:

275+55 t=440

55 t=440-275

or 55 t=165

t=165/55=3

Answer:

  $607.75

Step-by-step explanation:

As a first approximation, compound interest will be slightly higher than simple interest for a relatively short time period. Here simple interest at 5% for 4 years will add 4×5% = 20% to the value, adding about $100 to the initial $500 value. That is, we expect the value in 4 years to be slightly more than $600.

The appropriate answer choice is $607.75.

_____

The actual amount can be calculated using the multiplier 1.05 for each of the 4 years, or 1.05^4 ≈ 1.21550625 for the entire period. Then the predicted item value is ...

  $500 × 1.21550625 = $607.753125 ≈ $607.75

Answer:

Answer: $607.75

Step-by-step explanation:

Answer:

 $607.75

Step-by-step explanation:

As a first approximation, compound interest will be slightly higher than simple interest for a relatively short time period. Here simple interest at 5% for 4 years will add 4×5% = 20% to the value, adding about $100 to the initial $500 value. That is, we expect the value in 4 years to be slightly more than $600.

The appropriate answer choice is $607.75.

_____

The actual amount can be calculated using the multiplier 1.05 for each of the 4 years, or 1.05^4 ≈ 1.21550625 for the entire period. Then the predicted item value is ...

 $500 × 1.21550625 = $607.753125 ≈ $607.75

Answer: Ok, let's think our dependent variable like the position of a car with velocity of 50km/h, and our independent variable the time.

so, you can choose any time you want, and for each time, the car will be in a different position, so the position is a variable dependent of the time.

let's suppose you don't know the velocity of the car.

first you see the position at a time t₁ and the position is r₁.

then you see the position at time t₂, and the result is r₂.

here you changed the independent variable and observed how the dependent variable changed. And in this case, with the 4 numbers you observed you can obtain the velocity of the car.

So yes, you can call it an experiment.

Answer:

  5 1/2

Step-by-step explanation:

Your calculator can give you the correct answer.

___

[tex]\sqrt[3]{343}+\dfrac{3}{4}\sqrt[3]{-8}=7+\dfrac{3}{4}(-2)=7-\dfrac{3}{2}=5\frac{1}{2}[/tex]

Answer:

b) $455,500

Step-by-step explanation:

We have been given that Blossom Company began the year with retained earnings of $390000. During the year, the company recorded revenues of $489000, expenses of $379000, and paid dividends of $44500.

To find the retained earnings, we will use following formula.

[tex]\text{Retained earnings}=\text{Retained earnings (Previous)+Revenue}-\text{Expenses}-\text{Dividends}[/tex]

Upon substituting our given values, we will get:

[tex]\text{Retained earnings}=\$390,000+\$489,000-\$379,000-\$44,500[/tex]

[tex]\text{Retained earnings}=\$879000-\$423,500[/tex]

[tex]\text{Retained earnings}=\$455,500[/tex]

Therefore, the retained earnings at the end of the year was $455,500.

Answer:

  21

Step-by-step explanation:

Let n represent the number we're looking for. Then ...

  n × (proteus length) = 3 × (palustris length)

  n × 0.7 mm = 3 × 4.9 mm

  n = (3 × 4.9 mm)/(0.7 mm) = 3 × 49/7 = 3 × 7

  n = 21

You would have to line up 21 amoeba proteus to equal the length of three pelomyxa palustris.

Answer:

21

Step-by-step explanation:

1.  49    

  x  3   1

  14.7.

            21                              _=period move

2. 0.7./14.7.

          -14

             07

              -7

               0

check your answer:

  21

x0.7.   1

14.7.

Step-by-step explanation:

a) Compute the probability that 2 or fewer will withdraw

First we need to determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:

[tex](0.3)^2(0.7)^{18}[/tex].

Then, we must multiply this quantity by

[tex]{20\choose2}=\frac{20!}{18!2!}=\frac{20\times19}{2}=190,[/tex]

which is the number of ways to choose 2 students from the total of 20. Therefore:

Following an analogous process we can determine that:

Finally, the probability that 2 or fewer students will withdraw is

[tex]190(0.3)^2(0.7)^{18}+20(0.3)(0.7)^{19}+(0.7)^{20}=(0.7)^{18}(190(0.3)^2+20(0.3)(0.7)+(0.7)^2)\approx0.0355[/tex]

b) Compute the probability that exactly 4 will withdraw.

Following the process explained in a), the probability that 4 student withdraw is given by

[tex]{20\choose4}(0.3)^4(0.7)^{16}=\frac{20\times19\times18\times17}{4\times3\times2} (0.3)^4(0.7)^{16}=4845(0.3)^4(0.7)^{16}\approx 0.1304.[/tex]

c) Compute the probability that more than 3 will withdraw

First we will compute the probability that exactly 3 students withdraw, which is given by

[tex]{20\choose3}(0.3)^3(0.7)^{17}=\frac{20\times19\times18}{3\times2} (0.3)^3(0.7)^{17}=1140(0.3)^3(0.7)^{17}\approx 0.0716.[/tex]

Then, using a) we have that the probability that 3 or fewer students withdraw is 0.0355+0.0716=0.1071. Therefore the probability that more than 3 will withdraw is 1-0.1071=0.8929

d) Compute the expected number of withdrawals.

As stated in the problem, 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.

This problem involves using the binomial distribution to compute probabilities of student withdrawal and the expected number of withdrawals. Probability values are computed using the binomial probability formula and the expected number of students withdrawing from the course is given by n*p.

To solve the probability and expected value questions, we need to use the binomial distribution since the event (a student withdraws or not) is independent and repeated a fixed number of times.

1. The probability that 2 or fewer will withdraw is [tex]P(X < =2) = P(0)+P(1)+P(2) where P(x) = C(n, x) * (p^x) * (q^(n-x)). For n=20, p=0.3, q=0.7.[/tex]

2. The probability that exactly 4 withdraw is given by the binomial probability formula P(X=4). Again, use the same values of n, p, and q.

3. The probability that more than 3 will withdraw is P(X > 3) which is 1 - P(X<= 3). Compute P(X<=3) similar to the first situation and subtract it from 1.

4. The expected number of withdrawals, or the expectation of a binomial distribution, is given by n*p.

Calculations using these formulas will give you the desired probabilities to the accuracy you require.

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Answer:

[tex]A' = (-4,-2)\\B'=(-1,-1)\\C'=(-2, 2)[/tex]

Step-by-step explanation:

Given:

[tex]A = (1,1)\\B=(4,2)\\C=(3,5)[/tex]

A translation upward or downward affects the [tex]y[/tex] value of a coordinate while a translation left or right affects the [tex]x[/tex] value of a coordinate.

We are translating the whole triangle down three units, so we subtract all the[tex]y[/tex] values by 3.

We are also translating the whole triangle to left left five units, so we will subtract all the [tex]x[/tex] values by 5.

[tex]A = (1-5,1-3)\\B=(4-5,2-3)\\C=(3-5,5-3)[/tex]

New Coordinates:

[tex]A' = (-4,-2)\\B'=(-1,-1)\\C'=(-2, 2)[/tex]

Answer:

I've actually know the answer, its easy it's simple it's completely easy like it's so easy like its extremely easy. Okay the answer to this written question will be 78

Step-by-step xplanation:

because

Answer:

24

Step-by-step explanation:

The air pressure in tire should be 32.135 pounds per square inch. Hence, Rounding of to nearest tenths, we get 32.1 pounds per square inch.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

The air pressure in the tire should be  pounds per square inch. This pressure is in the form of a mixed fraction. It is required to convert this pressure into a decimal form. We can convert it as follows;

The air pressure in tire  =32 27/200

It is given in the form of a mixed fraction.

32 27/200 = ( 32 x 200) 27/200

First we, convert this mixed fraction into unlike fraction and then convert it into a decimal number;

32 27/200 = ( 32 x 200) 27/200

= 6427 /200

= 32.135

Therefore, the air pressure in tire should be 32.135 pounds per square inch.

Hence, Rounding of to nearest tenths, we get 32.1 pounds per square inch.

Learn more about the unitary method;

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Answer: 11

Step-by-step explanation:

We know that the degree of freedom for a t-distribution is given by :-

[tex]df=n-1[/tex], where n is the sample size.

Given : A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10.

Then, the number of  individuals participated in each study = [tex]df+1=10+1=11[/tex]

Hence, the number of  individuals participated in each study =11.

Answer:

  p(at most one space between) = (4n-6)/(n(n-1))

Step-by-step explanation:

There are n-1 ways the cars can be parked next to each other, and n-2 ways they can be parked with one empty space between. So, the total number of ways the cars can be parked with at most one empty space is ...

  (n -1) +(n -2) = 2n-3

The number of ways that 2 cars can be parked in n spaces is ...

  (n)(n -1)/2

So, the probability is ...

  (2n-3)/((n(n-1)/2) = (4n -6)/(n(n -1))

___

If the cars are considered distinguishable and order matters, then the number of ways they can be parked will double. The factor of 2 cancels in the final probability ratio, so the answer remains the same.

__

Check

For n=2 or 3, p=1 as you expect.

For n=4, p=5/6, since there is only one of the 6 ways the cars can be parked that has 2 spaces between.

The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.

We have,

To find the probability that there is at most one empty parking space between Mary and Tom's cars, we need to consider two scenarios:

Mary and Tom park their cars in adjacent spaces.

Mary and Tom park their cars in spaces with one empty space in between them.

Scenario 1: Mary and Tom park their cars in adjacent spaces.

In this case, there are (n - 1) ways for them to pick adjacent spaces out of the n spaces. Since there are n spaces to choose from initially, the probability for this scenario is (n - 1) / n.

Scenario 2: Mary and Tom park their cars with one empty space between them.

In this case, there are (n - 2) ways to pick two parking spaces with one empty space in between them. Again, since there are n spaces to choose from initially, the probability for this scenario is (n - 2) / n.

Now, we add up the probabilities of both scenarios because they are mutually exclusive:

Total Probability = Probability of Scenario 1 + Probability of Scenario 2

Total Probability = [(n - 1) / n] + [(n - 2) / n]

To make these fractions have a common denominator, we can rewrite them as:

Total Probability = [(n - 1) + (n - 2)] / n

Total Probability = [2n - 3] / n

Thus,

The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.

Learn more about probability here:

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5:

C = 5/9(F - 32)

C = 5/9(F) - 17.777

-5/9(F) + C = -17.777

-5/9(F) = -C - 17.777

F = 5/9(C) + 32.0306

Answer:

[tex]5.\, F=\frac{9C}{5}+32\\6.\,y=\frac{c-ax}{b}\\7.\,p=\frac{mq}{n}\\8.\,t=\frac{A-P}{Pr}\\9.\,y=\frac{12-6x}{5}\\10.\,y=\frac{9x-6}{3}\\12. x=\frac{9+5y}{6}\\13.\,\pi=\frac{c}{d}\\14.\,A=\frac{s^2}{R}\\15.\,w=\frac{P-2l}{2}\\16.\,y=\frac{3x-2}{5}\\17.,x=\frac{6-3by}{2a}\\18.\,w=\frac{V}{lh}[/tex]

Step-by-step explanation:

We need to solve following equations in terms of indicated variable:

[tex]5.C=\frac{5}{9}\left ( F-32 \right ):F\\6.ax+by=c;y\\7.\frac{m}{n}=\frac{p}{q};p\\8.A=P+Prt;t\\9.6x+5y=12;y\\10.3y+2=9x-4;y\\12.6x-5y=9;x\\13.C=\pi d\\14.R=\frac{s^2}{A};A\\15.P=2l+2w;w\\16.3x-5y=2;y\\17.2ax+3by=6;x\\18.V=lwh;w[/tex]

Solution:

[tex]5.\, F=\frac{9C}{5}+32\\6.\,y=\frac{c-ax}{b}\\7.\,p=\frac{mq}{n}\\8.\,t=\frac{A-P}{Pr}\\9.\,y=\frac{12-6x}{5}\\10.\,y=\frac{9x-6}{3}\\12. x=\frac{9+5y}{6}\\13.\,\pi=\frac{c}{d}\\14.\,A=\frac{s^2}{R}\\15.\,w=\frac{P-2l}{2}\\16.\,y=\frac{3x-2}{5}\\17.,x=\frac{6-3by}{2a}\\18.\,w=\frac{V}{lh}[/tex]

Answer:

The answer to your question is: Perimeter = 108 in

Step-by-step explanation:

Data

Length (l) = 5 width (w)

A = 405 in²

Perimeter = ?

Formula

Area = l x w

Perimeter = 2w + 2l

Process

                      405 = 5w x w

                       405 = 5w²

                     405/5 = w²

                       w = √81

                       w = 9 in

                       l = 5(9) = 45 in

Perimeter = 2(9) + 2(45)

                 = 18 + 90

                 = 108 in

Answer:

eventually the gender ratio of population in this society will be 50% male and 50% female.

Step-by-step explanation:

For practical purposes we will think that every couple is healthy enough to give birth as much children needed until giving birth a girl.

As the problem states, "each couple continue to have more children until they get a girl and once they have a girl they will stop having more children". Then, every couple will have one and only one girl.

We will denote for P(Bₙ) the probability of a couple to have exactly n boys.

Observe that statement 1 implies that:

[tex]P(B_{n-1})=(0.5)^{n}[/tex].

Then, the average number of boys per couple is given by

[tex]\sum^{\infty}_{n=1}(n-1)P(B_{n-1})=\sum^{\infty}_{n=1}(n-1)(\frac{1}{2} )^n=\sum^{\infty}_{n=2}n(\frac{1}{2} )^n=\\\\=\sum^{\infty}_{m=2}\sum^{\infty}_{n=m}(\frac{1}{2} )^n=\sum^{\infty}_{m=2}(\frac{1}{2} )^{m-1}=\sum^{\infty}_{m=1}(\frac{1}{2} )^{m}=1.\\[/tex]

This means that in average every couple has a boy and a girl. Then eventually the gender ratio of population in this society will be 50% male and 50% female.

Answer:

The answer to your question is: d) 50°F

Step-by-step explanation:

Data

n = 52 chirps/min

Formula

F = n/4 + 37

Substitution

F = 52/4 + 37

F = 13 + 37         simplifying

F = 50 °F        result

Answer:

Your travel time will be 32.71 secs.

Step-by-step explanation:

Let the total distance be x feet.

Speed while walking = [tex]\frac{x}{54}[/tex] feet per second

Speed on the sidewalk = [tex]\frac{x}{83}[/tex] feet per second

Therefore, total speed while walking on moving sidewalk =

[tex]\frac{x}{54} +\frac{x}{83y}[/tex]

= [tex]\frac{83x+54x}{54\times83}[/tex]

= [tex]\frac{137x}{4482}[/tex]

= [tex]\frac{x}{32.71}[/tex]

Hence, your travel time will be 32.71 secs.

Answer:

970m^{2}

Step-by-step explanation:

This polygon can be divided in two figures: one is a triangle, an the other one is a square.

We'll begin calculating the triangle's area, using the following formula:

[tex]At= \frac{b.h}{2}[/tex]

Where:

[tex]H= height = 30 m[/tex]

[tex]B = 9 m + 9 m + 20 m = 38 m[/tex]

As you can see, I added both sides of the triangle that measure 9 m and also the lenght of the square that measures 20 m! This added up is what the base of the triangle measures on total.

[tex]At= \frac{38 m .30 m}{2}[/tex]

[tex]At= \frac{1140 m^{2} }{2}[/tex]

[tex]At= 570 m^{2} [/tex]

Now we are going to calculate the square's area, that is much more simple:

[tex]As= L^{2} [/tex]

Where:

[tex]L=20 m [/tex]

[tex]As= (20 m)^{2} = 400m^{2} [/tex]

To know the whole figure's area, we add up both areas:

[tex]A = At+As = 570m^{2} +400m^{2}=970m^{2} [/tex]

Answer:

Karen has been a member of Girl Scouts for 22 months

Step-by-step explanation:

Let

x -----> the time in months

we know that

The total number of patches must be equal to the number of months multiplied by 3 patches each month plus 4 patches

so

[tex]70=3x+4[/tex]

Solve for x

Subtract 4 both sides

[tex]70-4=3x\\66=3x[/tex]

Divide by 3 both sides

[tex]22=x[/tex]

Rewrite

[tex]x=22\ months[/tex]

therefore

Karen has been a member of Girl Scouts for 22 months

Karen has been a member of the Girl Scouts for 22 months.

To determine the number of months Karen has been a member of the Girl Scouts, we can set up an equation using the information given.

Let's assume that Karen has been a member for x months.

Since she earns 3 patches each month, the total number of patches she has earned is 3x.

Adding the initial 4 patches she received upon joining, we have the equation 3x + 4 = 70.

To solve for x, we can subtract 4 from both sides of the equation: 3x + 4 - 4 = 70 - 4, which simplifies to 3x = 66.

Finally, we can divide both sides of the equation by 3 to solve for x: x = 66 ÷ 3 = 22.

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Answer:

The number of batteries sold was 240 and the number of small boxes of pens sold was 48

Step-by-step explanation:

Let

x -----> the number of batteries sold

y ----> the number of small boxes of pens sold

we know that

[tex]3x+5y=960[/tex] -----> equation A

[tex]x=5y[/tex] ----> equation B

substitute equation B in equation A

[tex]3(5y)+5y=960\\15y+5y=960\\20y=960\\y=48\ boxes\ of \ pens[/tex]

Find the value of x

[tex]x=5(48)=240\ batteries[/tex]

therefore

The number of batteries sold was 240 and the number of small boxes of pens sold was 48

Answer:

width = 11 feet

Step-by-step explanation:

The perimeter of a rectangle is 2 times length + width.

He already decided that the perimeter is at most 60 feet and the length is 19 feet. Then replacing in the formula for perimeter you have:

60 = 2 ( 19 + width)

30 = 19 + width

11 = width

Therefore the maximum width is 11 feet

Answer:

Complete the square on x by adding​ 49 to both sides.

Complete the square on y by adding​ 81 to both sides.

Step-by-step explanation:

We have been given an equation [tex](x^2+14x)+(y^2+18y)=5[/tex]. We are asked to complete the squares for both x and y.

We know to complete a square, we add the half the square of coefficient of x or y term.

Upon looking at our given equation, we can see that coefficient of x is 14 and coefficient of y is 18.

[tex](\frac{14}{2})^2=7^2=49[/tex]

[tex](\frac{18}{2})^2=9^2=81[/tex]

Now, we will add 49 to complete the x term square and 81 to complete y term square on both sides of our given equation as:

[tex](x^2+14x+49)+(y^2+18y+81)=5+49+81[/tex]

Applying the perfect square formula [tex]a^2+2ab+b^2=(a+b)^2[/tex], we will get:

[tex](x+7)^2+(y+9)^2=135[/tex]

Therefore, We can complete the square on x by adding​ 49 to both sides and the square on y by adding​ 81 to both sides.

Answer:

If the mean of the sample standard deviations is equal to the population standard​ deviation, then the sample standard deviations target the population standard deviation and are called an unbiased estimator.  

If the mean of the sample standard deviations is not equal to the population standard​ deviation, then the sample standard deviations target the population standard deviation and are called a biased estimator.

A biased estimator regularly underestimates or overestimates the parameter.  

Final answer:

Sample standard deviations do not target the population standard deviation but serve as estimators. The accuracy of the estimation depends on the sample size.

Explanation:

The sample standard deviations do not target the exact value of the population standard deviation. Instead, they serve as estimators of the population standard deviation. In general, sample standard deviations can be good estimators of population standard deviations, but the accuracy of the estimation depends on the sample size. When the sample size is large, the sample standard deviation tends to be close to the population standard deviation. However, when the sample size is small, the sample standard deviation may not accurately estimate the population standard deviation.

Answer:

18, 72

Step-by-step explanation:

Two angles are complementary if they sum up to 90°. Call them [tex] x, (90-x) [/tex]. From the second part,

[tex]

3 x = 90-x+18 \\

4x = 72 \\

x= 18 [/tex]

The second angle is [tex] 90-18 = 72 [/tex]

Answer:

[tex]\frac{dF}{F}=4\frac{dR}{R}[/tex]

So a 5% relative increase in R would mean a 20% relative increase in F

Step-by-step explanation:

First we need to remind the definition of relative increase of a variable.

For a variable A its relative increase is given by [tex]\frac{dA}{A}[/tex].

Using this, the relative increase in F is [tex]\frac{dF}{F}[/tex] and similarly the relative increase in R is given by [tex]\frac{dR}{R}[/tex].

Let's then start by deriving F with respect to R:

[tex]\frac{dF}{dR}=4kR^3[/tex]

thus

[tex]dF=4kR^3dR[/tex]

[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{F}[/tex]

[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{kR^4}[/tex]

[tex]\implies \frac{dF}{F}=4\frac{dR}{R}[/tex].

If we plug the value 5% [tex]\left( \frac{5}{100}\right)[/tex] in [tex]\frac{dR}{R}[/tex] we get

[tex]\frac{dF}{F}=4\times5\%=20\%[/tex]

According to Poiseuille's Law, the flux of blood through a blood vessel is proportional to the fourth power of the vessel's radius. By differentiating both sides of the equation, it can be shown that a small relative change in radius corresponds to four times that change in flux. Therefore, a 5% increase in radius results in a 20% increase in blood flow.

Poiseuille’s Law states that the flux (F), which is the volume of blood flowing per unit time through a given point in a blood vessel, is proportional to the fourth power of the blood vessel's radius, R. In terms of an equation, F = kR4, where k is a constant of proportionality.

To show that the relative change in F is approximately four times the relative change in R, consider a small change in R (expressed as ΔR), and the corresponding change in F (ΔF). The relative change in F is ΔF/F and the relative change in R is ΔR/R.

By differentiating both sides of the equation, you get ΔF/ΔR = 4kR3. Therefore, ΔF/F = 4(ΔR/R), proving the statement. A 5% increase in the radius would therefore result in a 20% increase in the flux, or the blood flow rate.

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Answer:

Step-by-step explanation:

B or C is your answer