Two solutions of the equation Ax+By = 1 are (2, -1) and (-3,-2). Find A and B.

(4) y = (3 - 2x)³ + 24x

Use the power and chain rules:

dy/dx = 3 (3 - 2x)² d/dx [3 - 2x] + 24

dy/dx = 3 (3 - 2x)² (-2) + 24

dy/dx = -24x ² + 72x - 30

(5) y = 54x - (2x - 7)³

Same basic procedure:

dy/dx = 54 - 3 (2x - 7)² d/dx [2x - 7]

dy/dx = 54 - 3 (2x - 7)² (2)

dy/dx = -24x ² + 168x - 240

Answer:

the percentage increase is 35%

Answer:

10 + 8 + 10 + 10 + 10 + 10 + 8 + 8 + 6 + 6

Answer:  Choice B)  [tex]\sqrt{2}[/tex]

Work Shown:

[tex]\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}\\\\[/tex]

Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.

Answer: 332 cubic inches

Step-by-step explanation:

You can eliminate 69 and 99 as those answers don't make any sense. This leaves you with 703 and 332.

It says the wall of the pipe is 1.25 inches thick so you multiply that by 2 and subtract it by the diameter to get the insider diameter of 5.5

Now you just use the equation V = (3.14)(r^2)(14) where the radius is half of 5.5.

So to finalize the equation you get V = (3.14)(5.5)^2(14) which comes out to 332 cubic inches

The best choice is 332 cubic inches.

69 cubic inches and 99 cubic inches are less and 703 cubic inches is a large approximation.

Diameter = d= 8 inches

Height= Length = l= 14 inches

Thickness= 1.25 inches

Outer Radius= R= diameter/2= 8/2=4 inches

Inner radius = r= Radius - thickness

                            = 4- 1.25= 2.75 inches

Volume of the cylinder = Area × length

                                      = π r²× l

                                       = 22/7 × (2.75)² × 14

                                          = 332. 616 inches cube

So the best answer is 332 cubic inches

https://brainly.com/question/21067083

Answer:

The product of a constant factor of four and a factor with the sum of two terms

Step-by-step explanation:

4(y + 6)

This is two terms, a constant 4 and a term with y+6

We a multiplying so we have a product

Answer:

A

Step-by-step explanation:

I believe A is the best answer because 4 is the constant factor with the sum of y + 6. I just think it best rrepresents the equation! :)

Answer:

Proportions and percent

Answer:

The probability would be 1/8.

Step-by-step explanation:

The probability of the spinner landing on an odd number is 1/2, and the probability of the spinner landing on a number greater than 8 is 1/4. So we multiply those two probabilites to get our answer 1/8.

Answer:

2 = x          -7 = x

Step-by-step explanation:

f(x) = (x - 2)(x + 7)

y  = (x - 2)(x + 7)

Set y = 0

0 = (x - 2)(x + 7)

Using the zero product property

0 = x-2    0 = x+7

2 = x          -7 = x

Answer:

Zeros happen when f(x) = 0. There are two zeros in the given function:

Therefore solve both equations above and you'll get:

Answer:

It took Chau 5 hours, 52 minutes, and 30 seconds to clean both rooms.

Step-by-step explanation:

Given that Chau took 5 3/8 hours to clean the bedroom, and then he took a 1/2 to clean the den, to determine how much total time did he take to clean two rooms the following calculation must be performed:

5 + 3/8 + 1/2 = X

5 + 0.375 + 0.5 = X

5.875 = X

0.875 = 7/8

60/8 x 7 = 52.5

Therefore, it took Chau 5 hours, 52 minutes, and 30 seconds to clean both rooms.

Solution :

Group   Before     After

Mean    693.75    743.75

Sd         155.37     143.92

SEM        54.93     50.88

n              8            8

Null hypothesis : The preparation course not effective.

[tex]$H_0: \mu_d = 0$[/tex]

Alternative hypothesis : The preparation course is effective in improving the exam scores.

[tex]$H_a : \mu_d>0$[/tex]  (after -  before)

Step-by-step explanation:

[tex]a_3 [/tex] = - 4

[tex]a_3 [/tex] = a* + (3- 1) d*

- 4 = a + 2d . . . . . . . . .(i)

[tex]a_8 [/tex] = - 29

[tex]a_8 [/tex] = a + ( 8 - 1) d

- 29 = a + 7d . . . . . . . . (ii)

subtracting equations (i) and (ii)

25 = 5d

d = -5

placing d = -5 in equation (i)

a - 10 = -4

a = 6

For an arithmetic Progtession

[tex]a_n [/tex] = a + (n - 1)d

[tex]a_n [/tex] = 6 + (n- 1)-5

[tex]a_n [/tex] = 6 - 5n + 5

[tex] \underline {a_n = 11 - 5n }[/tex]

[tex]\\[/tex]

*[tex] \boxed{ \mathfrak { a \:stands\: for\: first\: term } } [/tex]

*[tex] \boxed{ \mathfrak { d \:stands\: for\: common \: difference } } [/tex]

Answer:

General rule » -5n+11

Step-by-step explanation:

a3 = a+2d = -4 .......(1)

a8=a+7d = -29..........(2)

(2)-(1) » 5d= -25

d = -25/5

. = -5

substitute d = -5 in ( 1)

» a-2×-5= -4

a-10 = -4

a = -4 +10

= 6

General rule » a +(n-1)d

» 6 +(n-1)×-5

» 6-5n+5

» -5n+11

Answer:

Step-by-step explanation:

Let many universities and colleges have conducted supplemental instruction(SI) programs. In that a student facilitator he meets the students group regularly who are enrolled in the course to promote discussion of course material and enhance subject mastery.

Here the students in a large statistics group are classified into two groups:

1). Control group: This group will not participate in SI and

2). Treatment group: This group will participate in SI.

a)Suppose they are samples from an existing population, Then it would be the population of students who are taking the course in question and who had supplemental instruction. And this would be same as the sample. Here we can guess that this is a conceptual population - The students who might take the class and get SI.

b)Some students might be more motivated, and they might spend the extra time in the SI sessions and do better. Here they have done better anyway because of their motivation. There is other possibility that some students have weak background and know it and take the exam, But still do not do as well as the others. Here we cannot separate out the effect of the SI from a lot of possibilities if you allow students to choose.

The random assignment guarantees ‘Unbiased’ results - good students and bad are just as likely to get the SI or control.

c)There wouldn't be any basis for comparison otherwise.

Answer:

(0 ; 3)

Step-by-step explanation:

hello :

the midpoint of the line segment is : ((-2+2)/2 ;(-2+8)/2 )

(0 ; 3)

Answer:

x = 9.6

x = - 2.6

Step-by-step explanation:

[tex]x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]

Ignore the before the ± it wouldn't let me type it correctly.

x² - 7x - 25 = 0

a = 1

b = - 7

c = - 25

[tex]x=\frac{-(-7)±\sqrt{-7^{2}-4((1)(-25)) } }{2(1)}[/tex]

[tex]x=\frac{7±\sqrt{49-4((1)(-25)) } }{2(1)}[/tex]

[tex]x=\frac{7±\sqrt{49+100 } }{2(1)}[/tex]

[tex]x=\frac{7±\sqrt{149 } }{2}[/tex]

[tex]x=\frac{7±12.2}{2}[/tex]

Two separate equations

[tex]x=\frac{7+12.2}{2}[/tex]

[tex]x=\frac{7-12.2}{2}[/tex]

[tex]x=\frac{7+12.2}{2}[/tex]

[tex]x=\frac{19.2}{2}[/tex]

x = 9.6

[tex]x=\frac{7-12.2}{2}[/tex]

[tex]x=\frac{-5.2}{2}[/tex]

x = - 2.6

For this just use the quadratic formula to find the zeros. In this case, you get 7 +/- square root 149 over 2. Which gives you -2.6 and 9.6.

Answer:

Assessing the association between supplemental vitamin A exposure and mortality and morbidity for measles:

Regarding the relative risk, the correct statement is:

a. Exposure to vitamin A appears to protect against morbidity and mortality for measles.

Step-by-step explanation:

Relative risk for incidence of measles = 0.75

Relative risk for measles mortality = 0.5

Relative risk for mortality and morbidity for measles = 0.375 (0.75 * 0.5)

The combined relative risk is less than 50%

The association is weak because RR is less than 1.

Therefore, there is no association between supplemental vitamin A exposure and mortality and morbidity for measles.

Answer:

Step-by-step explanation:

There are no statements provided, but since it is modeled after the linear function y = mx + b, it is a line. m is the slope or rate of change (which is constant; that's what makes this a line!), and b is the y-intercept (the value of y when x is equal to 0). Its slope is 4 (the function raises 4 units for every 1 unit it moves to the right). Its y-intercept is 8, having the coordinate (0, 8).

Answer:

y = 4x + 8 is a linear function.

Step-by-step explanation:

No statements are given, but here's why:

- It's in slope-intercept form, y = mx + b.

- It has a constant slope.

- A non-linear function does not have a constant slope, and this one does.

Answer:

8

Step-by-step explanation:

Hello!

1) 6/10 × 10/6 × 5/9 = 1/10 × 10 × 5/9 = 1 × 5/9 = 5/9 or 0,5

2) 6/10 × 4/3 × 10/20 = 6 × 4/3 × 1/20 = 2 × 4 × 1/20 = 2 × 1/5 = 2/5 or 0,4

Good luck! :)

Answer:

1) 5/9

2) 2/5

Explanation:

1) 6/10 × 10/6 × 5/9=

Multiply all the denominators and all the numerators then simplify= 300/540 = 5/9

2)  6/10 × 4/3 × 10/20=

Multiply all the denominators and all the numerators then simplify= 240/600 = 2/5

Answer:

   =(s^2 - t^2)/4

Step-by-step explanation:

a + b = s and a - b = t,

Add the two equations together

a + b = s

a - b = t

----------------

2a = s+t

a = (s+t)/2

Subtract the two equations

a + b = s

- a + b = -t

-------------------

2b =(s-t)

b = (s-t)/2

We want to find ab

ab = (s+t)/2 *  (s-t)/2

FOIL

    =(s^2 - t^2)/4

Answer:

3:8

Step-by-step explanation:

i will gadit

that only

Answer:

[tex] {r}^{2} - 4s + {s}^{2} = 8r + 2s = 28 \\ \\ r = \frac{24}{5 } - i \frac{ \sqrt[4]{129} }{5} \\ \: s = \frac{58}{5} + i \frac{ \sqrt[2]{129} }{5 } \\ \\ r = \frac{24}{5} + i \frac{ \sqrt[4]{129} }{5} \\ s = \frac{58}{5} - i \frac{ \sqrt[2]{129} }{5} [/tex]

Answer:

The number of newborns who weighed between 1614 grams and 5182 grams was of 586.

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 mean weight was 3398 grams with a standard deviation of 892 grams.

This means that [tex]\mu = 3398, \sigma = 892[/tex]

Proportion that weighed between 1614 and 5182 grams:

p-value of Z when X = 5182 subtracted by the p-value of Z when X = 1614.

X = 5182

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

[tex]Z = \frac{5182 - 3398}{892}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

X = 1614

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

[tex]Z = \frac{1614 - 3398}{892}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.0228

0.9772 - 0.0228 = 0.9544.

Out of 614 babies:

0.9544*614 = 586

The number of newborns who weighed between 1614 grams and 5182 grams was of 586.

Answer:

-5

2

-125

-3

Step-by-step explanation:

5 + A = 0

Subtract 5 from both sides.

A = -5

-8/4 - B = -4

-2 - B = -4

B + 2 = 4

B = 2

C ÷ 25 = -5

C = -125

D × 13 = -39

D × 13/13 = -39/13

D = -3

Answer:

below

Step-by-step explanation:

A AND C is the right option

congruent angles are angles with exactly the same measure

Answer:

A, B, and E apply

Step-by-step explanation:

One thing we can do is to make everything in the same format, under one square root, with no non-square roots.

First, we can say that 6 is equal to √36 as 6² =36, and 6 ≥ 0. Therefore, 6√3 = √36 * √3 = √108

For A, √3 * √36 = √108, so this applies

For B, √18 * √6 = √108, so this applies

For C, 108² = √something bigger than 108 = √11664, so this does not apply

For D, √54 ≠ √108, so this does not apply

For E, √108 = √108, so this applies

For F, √3 * √6 = √18, so this does not apply

Answer:

555.56

Step-by-step explanation:

Purpose of the study:  To determine if women are better drivers than men.

Survey or Opinion population:  1,000

You are experimenting on 9 out of a thousand opinions.

5 of these opinions are that women are better drivers

4 of these opinions are that women are not better drivers

You want to know the sample (full sample size is 9) proportion for women as better drivers; using the large sample method. This method is also called the asymptotic method.

This involves approximating the desired statistic, with just a small fraction of the population; in this case, 9/1000.

This approximation will get more and more accurate as sample size increases and you know that a larger sample size gives a better representation and interpretation of the population preference!

So using ratio, the sample proportion for women as the better drivers is given by:

5/9 x 1000   = 555.56 opinions

The three modes are 5, 12, and 150 since they occur the most times and they tie one another in being the most frequent (each occurring 3 times).

Only the 7 and 8 occur once each, and aren't modes. Everything else is a mode. It's possible to have more than one mode and often we represent this as a set. So we'd say the mode is {5, 12, 150} where the order doesn't matter.

Answer:

1/425

Step-by-step explanation:

The first card can be any card, so we don’t have to evaluate the probability.

Now we can suppose that the exit card is a two

- For the second card we have 3/51 of possibilities that is a 2 = 1/17

- For the third card we have 2/50 of possibilities that is a 2 = 1/25

1/17 * 1/25 = 1/425