The patient has an order for oxytocin (Pitocin) to infuse at 7 mu/minute. Available is oxytocin 10 units/1000 mL 0.9% NaCl. At what rate will the nurse set the infusion? ___ mL/hr (If needed, round to the nearest whole number.)

Answer:

  T(x, y) = T(0, -8)

Step-by-step explanation:

The first reflection can be represented as ...

  (x, y) ⇒ (-x, y)

__

The rotation about the origin is the transformation ...

  (x, y) ⇒ (-x, -y)

so the net effect of the first two transforms is ...

  (x, y) ⇒ (x, -y)

__

Then the reflection across y=4 alters the y-coordinate:

  (x, y) ⇒ (x, 8-y)

so the net effect of the three transforms is ...

  (x, y) ⇒ (x, 8+y)

__

In order to bring the figure back to place, we must translate it down 8 units using ...

  (x, y) ⇒ (x, y-8) . . . . net effect: (x, y) ⇒ (x, (8+y)-8) = (x, y)

The translation is by 0 units in the x-direction and -8 units in the y-direction.

[tex] \\ \binom{2\pi}{ b} [/tex]the period will be

[tex]\pi[/tex]

amplitude is none. Domain x is not equal to

[tex] \frac{\pi}{4} + \frac{n\pi}{2} [/tex]

range

[tex](- \infty , -1) U [1 \infty )[/tex]

vertical asymptotes

[tex]x = \frac{n\pi}{2} [/tex]

where n is integer

Answer:

Domain is [tex]D=\bold R-(n+1)\dfrac{\pi}{2}[/tex]

Range is [tex]R=\bold R-(-1,1)[/tex]

Other details are included in the explanation part.

Step-by-step explanation:

The given function is [tex]f(x) = \rm {sec }\;2\mathit x[/tex].

The function is a secant function which is the reciprocal of cosine function.

The graph of the function is is attached as an image.

The domain of the function is the range of x where it is defined. The domain of the function will be,

[tex]D=\bold R-(n+1)\dfrac{\pi}{2}[/tex] here, R is the real number.

The range of the function is the range of value of function for every value of  x which is,

[tex]R=\bold R-(-1,1)[/tex]

it means that the range is real numbers excluding the range of (-1,+1).

The vertical asymptotes will form where the curve tends to parallel to the y-axis. So, the vertical asymptotes are at [tex](n+1)\dfrac{\pi}{2}[/tex].

The period of the function is [tex]2\pi[/tex] as the function repeats itself after that period.

The function goes to infinity and hence, it doesn't has any amplitude.

For more details, refer the link:

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Hey there!:

The number of students in the sample who have experienced math anxiety is a binomial distribution  

Bin (n , p) where n = 10 and p = 0.2  

The mean of a binomial distribution is np = 2  

The variance is np (1- p) = 1.6 so the standard deviation is √ 1.6 = 1.265  

mean=2; standard deviation= 1.265

Hope this helps!

The standard deviation of the of the number of students with anxiety in the sample which is the square root of the variance is 1.265

Probability of those who have experienced anxiety :

The standard deviation can be defined thus :

Therefore, the standard deviation of the number of sampled students with anxiety is 1.265

Learn more : https://brainly.com/question/18153040

Answer:

The equation of the vertical line through (-6, -9) is 1x+0y=-6.

Step-by-step explanation:

The standard form of a line is

[tex]ax+by=c[/tex]

where a, b, and c are integers with no factor common to all three, and a>0.

If a vertical line passes through the point (a,b), then the equation of vertical line is x=a.

It is given that the vertical line passes through the point (-6,-9). Here a=-6 and b=-9, so the equation of the vertical line through (-6, -9) is

[tex]x=-6[/tex]

[tex]1x+0y=-6[/tex]

The standard form of the line is 1x+0y=-6. where the value of a,b c are 1, 0, -6 respectively.

Therefore the equation of the vertical line through (-6, -9) is 1x+0y=-6.

Answer:

  (0, -1), (1, 0), (2, 1)

Step-by-step explanation:

I find this easier to do after multiplying the equation by -1:

  y = x - 1

Pick any value for x, then subtract 1 from it to find the corresponding value of y.

Answer:

2/13

Step-by-step explanation:

there are 4 jacks and 4 threes in a standard poker deck.

4+4 is 8

8/52=2/13

The probability of drawing either a Jack or a three from a standard deck of 52 cards is 2/13, because there are 8 such cards in a deck and the total number of cards in the deck is 52.

The question asks for the probability of drawing either a Jack or a three from a standard deck of 52 cards. To solve this, we need to count how many Jacks and threes there are in a deck. Since each suit (hearts, diamonds, clubs, and spades) includes one Jack and one three, there are 4 Jacks and 4 threes in a standard deck. Therefore, there are 8 cards that satisfy the condition (either a Jack or a three).

Since the total number of cards in the deck is 52, the probability of drawing either a Jack or a three is calculated as the number of favorable outcomes (drawing a Jack or a three) divided by the total number of outcomes (drawing any card from the 52-card deck). Thus, the probability is:

Probability = (Number of Jacks + Number of threes) / Total number of cards = (4 + 4) / 52 = 8 / 52 = 2 / 13

Therefore, the probability of drawing either a Jack or a three from a standard deck of 52 cards is 2/13.

Well, 27 = 9*3, and mod 26 leaves a remainder of 1, so [tex]n=3[/tex] is a solution.

Answer:237 days

Step-by-step explanation:

Interest=[tex]\$ [/tex]1341

Principal[tex]\left ( P\right )=\$ 51,700[/tex]

rate of interest[tex]\left ( t\right )=4%=0.04[/tex]

We know

Simple Interest=[tex]\frac{P\times r\times t}{365}[/tex]

[tex]time\left ( t\right )[/tex]=[tex]\frac{I\times 365}{P\times r}[/tex]

[tex]time\left ( t\right )[/tex]=[tex]\frac{1341\times 365}{51700\times 0.04}[/tex]

[tex]time\left ( t\right )[/tex]=[tex]236.68 days\approx 237 days[/tex]

Answer:

Tim has 2 apples, Jerry has no apple.

Step-by-step explanation:

Given that Tim has 1 apple.

Jerry has 1 apple as well.

After Jerry gives Tim one apple,

Tim has 1 + 1 = 2 apples, and  Jerry has 1 - 1 = 0

Tim has 2 apples, Jerry has no apple.

Answer: A x B = {(x,1), (x,2), (y,1), (y,2)}

Step-by-step explanation:

The Cartesian product of any two sets M and N is the set of all possible ordered pairs such that the elements of M are first values and the elements of N are the second values.

The Cartesian product of sets M and N is denoted by M × N.

For Example : M = {x,y} and N={a,b}

Then , M × N ={(x,a), (x,b), (y,a), (y,b)}

Given : Let A = {x, y}, B = {1,2}

Then , the Cartesian products of A and B will be :

A x B = {(x,1), (x,2), (y,1), (y,2)}

Hence, the Cartesian products of A and B = A x B = {(x,1), (x,2), (y,1), (y,2)}

Answer:   0.1563

Step-by-step explanation:

The Poisson distribution probability formula is given by :-

[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex], where [tex]\lambda[/tex] is the mean of the distribution and x is the number of success

Given : Cars enter a car wash at a mean rate of 2 cars per half an hour.

In an hour, the number of cars enters in car wash = [tex]\lambda=2\times2=4[/tex]

Now, the probability that, in any hour, exactly 5 cars will enter the car wash is given by :-

[tex]P(X=5)=\dfrac{e^{-4}4^5}{5!}=0.156293451851\approx0.1563[/tex]

Therefore, the required probability = 0.1563

Answer:

Option b Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]A(-4,-2)\\B(-7,-7)[/tex]

step 1

substitute the values in the formula

[tex]d=\sqrt{(-7-(-2))^{2}+(-7-(-4))^{2}}[/tex]

step 2

Simplify

[tex]d=\sqrt{(-7+2)^{2}+(-7+4)^{2}}[/tex]

step 3

[tex]d=\sqrt{(-5)^{2}+(-3)^{2}}[/tex]

step 4

[tex]d=\sqrt{25+9}[/tex]

step 5

[tex]d=\sqrt{34}[/tex]

therefore

Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.

She would offer to split the cookies evenly, so they each get 4.

If she offered Max less than 4, he would not accept and their dad would eat half, so each person would only get 2 cookies each.

If she offered Max more than 4, then she doesn't maximize the amount she would get.

Answer:

(A+B)(A+B)=A.A+B.A+A.B+B.B

Step-by-step explanation:

Given that matrices A and B are nxn matrices

We need to find (A+B)(A+B)

For understanding the multiplication of matrices let'take A is mxn and B is pxq matrices,we can multiple only when n=p,so our Ab matrices will be mxq.

We know that that in matrices AB is not equal to BA.

Now find  

(A+B)(A+B)=A.A+B.A+A.B+B.B

So from we can say that (A+B)(A+B) is not equal to A.A+2B.A+B.B because AB is not equal to BA in matrices.

So (A+B)(A+B)=A.A+B.A+A.B+B.B

Answer:

(a) 0.2721

(b) 0.7279

(c) 0.2415

Step-by-step explanation:

(a) If we choose only one student, the probability of being a math major is [tex]\frac{5}{18}[/tex] (because there are 5 math majors in a class of 18 students). So, the probability of not being a math major is [tex]\frac{18}{18} - \frac{5}{18} = \frac{13}{18}[/tex] (we subtract the math majors of the total of students).

But there are 4 students in the group and we need them all to be not math majors. The probability for each one of not being a math major is [tex]\frac{13}{18}[/tex] and we have to multiply them because it happens all at the same time.

P (no math majors in the group) = [tex]\frac{13}{18} *\frac{13}{18}*\frac{13}{18}*\frac{13}{18} = (\frac{13}{18}) ^4[/tex] = 0.2721

(b) If the group has at least one math major, it has one, two, three or four. That's the complement (exactly the opposite) of having no math majors in the group. That means 1 = P (at least one math major) + P (no math major). We calculated this last probability in (a).

So, P (at least one math major) = 1 - P(no math major) = 1 - 0.2721 = 0.7279  

(c) In the group of 4, we need exactly 2 math majors and 2 not math majors. As we saw in (a), the probability of having a math major in the group is 5/18 and having a not math major is [tex]\frac{13}{18}[/tex]. We need two of both, that's [tex]\frac{5}{18}*\frac{5}{18}*\frac{13}{18}*\frac{13}{18}[/tex]. But we also need to multiply this by the combinations of getting 2 of 4, that is given by the binomial coefficient [tex]\binom{4}{2}[/tex].

So, P (exactly 2 math majors) = [tex]\binom{4}{2}*(\frac{5}{18} )^2*(\frac{13}{18})^2[/tex] = [tex]\frac{4!}{2!2!}*\frac{25}{324}*\frac{169}{324}[/tex] = 0.2415

Answer:

The number of watches must he repair to have the lowest cost is 54.

Step-by-step explanation:

The cost of operating Bob's shop is given by

[tex]C(x)=2x^2-216x+11243[/tex]

Differentiate the given function with respect to x.

[tex]C'(x)=2(2x)-216(1)+(0)[/tex]

[tex]C'(x)=4x-216[/tex]             ... (1)

Equate C'(x) equal to 0, to find the critical point.

[tex]0=4x-216[/tex]

[tex]216=4x[/tex]

Divide both sides by 4.

[tex]\frac{216}{4}=x[/tex]

[tex]54=x[/tex]

Differentiate C'(x) with respect to x.

[tex]C''(x)=4[/tex]

C''(x)>0, it means the cost of operating is minimum at x=54.

Therefore the number of watches must he repair to have the lowest cost is 54.

Answer:

42.05 m

Step-by-step explanation:

(see attached)

Answer:

t is 2.106284 hours

Step-by-step explanation:

Given data

office maintained temperature (T) = 21°C

body temperature ( t) = 29°C

time = 1 hr

died body temperature (Td) = 37°C

chief's body  temperature (Tc) = 31°C

to find out

show coroner was killed 2 hours and 7 minutes before his body was found

solution

we use here Newton's law of cooling that is

dT/dt = -k (t - T )

now solve this equation and we get value of k i,e

-k (t ) = ln (t-T) / (Tc - T)

we know in 1 hour body temperature change 31°C to the 29°C

so now put value of t and T , Tc to find value of k

-k(1) = ln (29-21) / (31-21)

so -k =  ln (8)/(10)

and k = ln 10/8

and when temp change 37°C to 31°C we will find out time so that is

-kt = ln (31-21) / (37-21)

-ln 10/8 × t = ln (10) / (16)

so -t = ( ln 10/16) / ( ln 10/8 )

-t = −2.106284 approx  two hours and seven minutes

so it is -t = −2.106284 approx  two hou about two hours and seven minutes before his body was found

(a)

The probability is :  1/2

(b)

The probability is :  1/2

The numbers​ 1, 2,​ 3, 4, and 5 are written on slips of​ paper, and 2 slips are drawn at random one at a time without replacement.

The total combinations that are possible are:

(1,2)   (1,3)    (1,4)    (1,5)

(2,1)   (2,3)   (2,4)   (2,5)

(3,1)   (3,2)   (3,4)   (3,5)

(4,1)   (4,2)   (4,3)   (4,5)

(5,1)   (5,2)   (5,3)   (5,4)

i.e. the total outcomes are : 20

(a)

Let A denote the event that the first number is 4.

and B denote the event that the sum is: 9.

Let P denote the probability of an event.

We are asked to find:

               P(A|B)

We know that it could be calculated by using the formula:

[tex]P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}[/tex]

Hence, based on the data we have:

[tex]P(A\bigcap B)=\dfrac{1}{20}[/tex]

( Since, out of a total of 20 outcomes there is just one outcome which comes in A∩B and it is:  (4,5) )

and

[tex]P(B)=\dfrac{2}{20}[/tex]

( since, there are just two outcomes such that the sum is: 9

(4,5) and (5,4) )

Hence, we have:

[tex]P(A|B)=\dfrac{\dfrac{1}{20}}{\dfrac{2}{20}}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}[/tex]

(b)

Let A denote the event that the first number is 3.

and B denote the event that the sum is: 8.

Let P denote the probability of an event.

We are asked to find:

               P(A|B)

Hence, based on the data we have:

[tex]P(A\bigcap B)=\dfrac{1}{20}[/tex]

( since, the only outcome out of 20 outcomes is:  (3,5) )

and

[tex]P(B)=\dfrac{2}{20}[/tex]

( since, there are just two outcomes such that the sum is: 8

(3,5) and (5,3) )

Hence, we have:

[tex]P(A|B)=\dfrac{\dfrac{1}{20}}{\dfrac{2}{20}}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}[/tex]

Using the probability concept, it is found that:

a) 0.5 = 50% probability that the first number is 4​, given that the sum is 9.

b) 0.5 = 50% probability that the first number is 3​, given that the sum is 8.

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

The possible outcomes are:

(1,2), (1,3), (1,4), (1,5) .

(2,1), (2,3), (2,4), (2,5).

(3,1), (3,2), (3,4), (3,5).

(4,1), (4,2), (4,3), (4,5).

(5,1), (5,2), (5,3), (5,4).

Item a:

Then:

[tex]p = \frac{1}{2} = 0.5[/tex]

0.5 = 50% probability that the first number is 4​, given that the sum is 9.

Item b:

Then:

[tex]p = \frac{1}{2} = 0.5[/tex]

0.5 = 50% probability that the first number is 3​, given that the sum is 8.

A similar problem is given at https://brainly.com/question/24262336

Answer:

  (a)  P = 5.664e^(0.024t)

  (b)  7.74 million

Step-by-step explanation:

(a) We are given the population for t=7, so we can write the equation as ...

  P = 6.7·e^(0.024(t -7))

This can be put in the desired form by factoring out 6.7e^(-0.024·7):

  P = 6.7e^(-0.024·7)e^(0.024t)

  P = 5.664e^(0.024t)

__

(b) Evaluated for t=13, this is ...

  P = 5.664e^(0.024·13) ≈ 7.74 . . . million

The exponential growth model of the population in Paraguay is P = 6.7e0.024*7 = 8.07 (approx). Using this model, we can predict that the population in 2013 will be around 9.34 million.

The subject of the question is related to the mathematical concept of exponential growth. Here, we are given that the population of Paraguay in 2007 was 6.7 million and the continuous annual rate of change 'k' of the population was 0.024.

To find the exponential growth model P = Cekt, where t=0 corresponds to 2000, we use the given data. Here, 'P' is the final population, 'C' is the initial population, 'k' is the rate of growth, and 't' is the time in years. Hence;

P = 6.7e0.024*7 = 8.07 (approx)

We used 7 for 't' as 2007 is 7 years ahead of 2000. Also, we expressed 'k' in percentages and hence k=0.024.

To predict the population of the country in 2013, we put t=13 in the equation (as 2013 is 13 years ahead of 2000).

P = 6.7e0.024*13 = 9.34 (approx)

Therefore, the population of Paraguay is estimated to be around 9.34 million in 2013.

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Answer:

x=2, y=4.

2 thousand of A panels and 4 of B.

Step-by-step explanation:

First, the profit is determined by the revenue minus the cost, so built a profit equation with that information.

[tex]P(x,y)=R(x,y)-C(x,y)\\ P(x,y)=6x+8y-x^{2}+3xy-8y^{2} -14x+50y+4\\ P(x,y)=-8x+58y-x^{2} -8y^{2} +3xy+4[/tex]

Then, use the partial derivative criteria to determine which is the maximum.

The partial derivative criteria says that in the local maximum or minimum, the partial derivatives are equal to zero, so:

[tex]P_{x}=-8-2x+3y=0\\  P_{y} =58-16y+3x=0[/tex]

So, let's solve the equation system:

First, isolate x:

Eq. 1 [tex]2x=3y-8[/tex]

Eq. 2[tex]3x=16y-58[/tex]

Multiply equation 1 by (-3) and equation 2 by 2:

[tex]-6x=-9y+24\\ 6x=32y-116[/tex]

Sum the equations:

[tex]0=23y-92\\ y=\frac{92}{23}=4[/tex]

Find x with eq. 1 or 2:

[tex]x=\frac{3y-8}{2}= \frac{3*4-8}{2}=2[/tex]

To maximize profit, we need to find the values of x and y that satisfy the equations for R(x,y) and C(x,y), then substitute them into the profit equation. The maximum profit is achieved at x = 8, y = 3.

To maximize profit, we need to find the values of x and y that maximize the equation P(x,y) = R(x,y) - C(x,y), where P(x,y) represents the profit.

Substitute the equations for R(x,y) and C(x,y) into the profit equation and simplify. We will get: P(x,y) = -x^2 + 9xy - 6y^2 + 6x + 58y + 4.

To find the maximum value of P(x,y), we need to find the critical points. Use partial derivatives to find the critical points and check which ones give the maximum value for profit. The critical point that gives the maximum profit is x = 8, y = 3.

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Answer:

The dimensions of swimming pool are:

Length = 26.2 feet

Width = 16.3 feet

Height = 5 feet

During a few hot weeks during the summer, some water evaporates from the pool, and Jill needs to add 8 inches of water to the depth of the pool.

We will convert 8 inches o feet.

1 inch = 1/12 feet

So, 8 inch = [tex]8/12=0.66[/tex] feet

Now we have to tell how much water will be there in 0.66 feet depth.

So, volume = [tex]16.3\times26.2\times0.66=281.86[/tex] cubic feet.

1 cubic feet has 7.480 gallons

So, 281.86 cubic feet will have [tex]281.86\times7.480=2108.31[/tex] gallons of water.

The volume is the product of the area of the top of the pool and the

height of water added which is approximately 8,062 liters.

Response:

The given dimensions of the pool are;

Width of the pool = 16.3 feet

Length of the pool = 26.2 feet

Height of water to be added = 8 inches

Required:

The volume of water to be added in liters

Solution:

First part

1 feet = 12 inches

Therefore;

[tex]8 \ inches = \dfrac{8}{12} \ feet = \mathbf{ \dfrac{2}{3} \ feet}[/tex]

Therefore;

Volume of water added is therefore;

Volume, V = Length × Width × Depth

[tex]V = 16.3 \times 26.2 \times \dfrac{2}{3} = \mathbf{284\frac{53}{75}}[/tex]

Therefore;

The volume added, V = [tex]\mathbf{284\frac{53}{75}}[/tex] ft.³

1 ft.³ = 28.31685 L

Therefore;

[tex]284\frac{53}{75} \, ft.^3 = 284\frac{53}{75} \times 28.31685 \ L \approx \mathbf{8062 \, L}[/tex]

Second part

1 L = 0.264172 gallons

8062 L = 8062 × 0.264172 gallons ≈ 2129.8 gallons

Learn more about calculating the volume of solids here:

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Answer:

The minimum score that an applicant must make on the test to be​ accepted is 360.

Step-by-step explanation:

Given : A highly selective boarding school will only admit students who place at least 2.5 standard deviations above the mean on a standardized test that has a mean of 300 and a standard deviation of 24.

To find : What is the minimum score that an applicant must make on the test to be​ accepted?

Solution :

We apply the z formula,

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Where, z value= 2.5

[tex]\mu=300[/tex] is the mean of the population

[tex]\sigma=24[/tex] is the standard deviation

x is the sample mean.

Substituting the values in the formula,

[tex]2.5=\frac{x-300}{24}[/tex]

[tex]2.5\times24=x-300[/tex]

[tex]60=x-300[/tex]

[tex]x=60+300[/tex]

[tex]x=360[/tex]

Therefore, The minimum score that an applicant must make on the test to be​ accepted is 360.

The minimum score that an applicant must make on the test to be​ accepted is 360 and this can be determined by using the z formula.

Given :

A highly selective boarding school will only admit students who place at least 2.5 standard deviations above the mean on a standardized test that has a mean of 300 and a standard deviation of 24.

The formula of z can be used in order to determine the minimum score that an applicant must make on the test to be​ accepted. The z formula is given by:

[tex]\rm z = \dfrac{x - \mu}{\sigma}[/tex]

Now, substitute the values of the known terms in the above formula.

[tex]2.5=\dfrac{x - 300}{24}[/tex]

Cross multiply in the above equation.

[tex]2.5\times 24 = x - 300[/tex]

60 = x - 300

x = 360

So, the minimum score that an applicant must make on the test to be​ accepted is 360.

For more information, refer to the link given below:

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Answer:

The mean is 5.309.

Step-by-step explanation:

Given group of data,

4.1, 8.9, 3.2, 1.9, 7.3, 6.3, 6.7, 8.6, 3.2, 2.3, 5.9,

Sum = 4.1+ 8.9 + 3.2 + 1.9 + 7.3 + 6.3 + 6.7 + 8.6 + 3.2 + 2.3 + 5.9 = 58.4,

Also, number of observations in the data = 11,

We know that,

[tex]Mean=\frac{\text{Sum of all observation}}{\text{Total observations}}[/tex]

Hence, the mean of given data = [tex]\frac{58.4}{11}=5.30909\approx 5.309[/tex]

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

[tex]f(x)=4x-6\\[/tex]

We need to find the double derivative i.e. f''(x).

So, we first derivate the f(x) w.r.t. x:

[tex]f(x)=4x-6\\\\f'(x)=4[/tex]

Now, we again derivative the f'(x) w.r.t x :

[tex]f''(x)=0[/tex]

(Because f'(x) has no term with variable x)

Hence, Option 'D' is correct.

Answer:

Option 1: triangle HFG is congruent to triangle KIJ

Step-by-step explanation:

F and I are same as they are on 90 degrees.

In figure 1, from I to K is the height of the triangle.

In figure 2, from F to H is the height of the triangle.

Therefore, IK is congruent to FH

In figure 1, I to J is the base of the triangle from 90 degrees.

In figure 2, F to G is the base of the triangle from 90 degrees.

Therefore, IJ is congruent to FG

Therefore, triangle HFG is congruent to triangle KIJ.

The first option is correct.

!!

Answer:

96x+28

Step-by-step explanation:

Given function,

[tex]y=(6x+5)(8x-2)[/tex]

Differentiating with respect to x,

[tex]\frac{dy}{dx}=\frac{d}{dx}[(6x+5)(8x-2)][/tex]

By the product rule of derivatives,

[tex]\frac{dy}{dx}=\frac{d}{dx}(6x+5).(8x-2)+(6x+5).\frac{d}{dx}(8x-2)[/tex]

[tex]\frac{dy}{dx}=6(8x-2)+(6x+5)8[/tex]

[tex]\frac{dy}{dx}=48x-12+48x+40[/tex]

[tex]\frac{dy}{dx}=96x+28[/tex]

Hence, the derivative of the given function is 96x+28.

Answer:

502.4 ± 30.14 in^3

Step-by-step explanation:

r = 4 in, h = 10 in

error = ± 0.1 inch

Volume of a cylinder, V = π r² h

Take log on both the sides

log V = log π + 2 log r + log h

Differentiate both sides

dV/V = 0 + 2 dr/r + dh /h

dV/V = 2 (± 0.1) / 4 + (± 0.1) / 10

dV/V = ± 0.05 ± 0.01 = ± 0.06 .... (1)

Now, V = 3.14 x 4 x 4 x 10 = 502.4 in^3

Put in equation (1)

dV = ± 0.06 x 502.4 = ± 30.144

So, V ± dV = 502.4 ± 30.14 in^3

[tex]A\cup B=\{a,b,c,d,f,g\}\\A\cap B=\{b,c\}\\A\setminus B=\{d,f,g\}\\B\setminus A=\{a\}[/tex]

Answer:

x=333.33%

Step-by-step explanation:

hello

you can resolve this by using the rule of 3,let´s see

75 oranges =100%

250 oranges = x%?

75 oranges* x%=250 oranges *100%

[tex]x=\frac{250*100}{75}[/tex]

x=333.33%

Have a great day.