Brainliest giving to who gets this CORRECT first. Check all that apply.

Answer:

h'(x) = (-x² ln x + x² + 1) / (x (x² + 1)^(³/₂))

Step-by-step explanation:

h(x) = ln x / √(x² + 1)

You can either use quotient rule, or you can rewrite using negative exponents and use product rule.

h(x) = (ln x) (x² + 1)^(-½)

h'(x) = (ln x) (-½) (x² + 1)^(-³/₂) (2x) + (1/x) (x² + 1)^(-½)

h'(x) = (-x ln x) (x² + 1)^(-³/₂) + (1/x) (x² + 1)^(-½)

h'(x) = (x² + 1)^(-³/₂) (-x ln x + (1/x) (x² + 1))

h'(x) = (1/x) (x² + 1)^(-³/₂) (-x² ln x + x² + 1)

h'(x) = (-x² ln x + x² + 1) / (x (x² + 1)^(³/₂))

Solution:

h(x) = ln(x)/√x^2+1

h(x) = ln(x) * (x^2 + 1)^-1/2

h(x) = ln(x) * (-1/2) * (x^2 + 1)^-3/2 * 2x + 1/x * (x^2 + 1)^-1/2

h(x) = -x ln(x) * (x^2 + 1)^-3/2 + 1/x * (x^2 + 1)^-1/2

h(x) = (x^2 + 1)^-3/2 * (-x ln(x) + 1/x * (x^2 + 1))

h(x) = -x^2ln(x)+x^2+1/(x(x^2+1)^3/2)

Best of Luck!

Answer:

[tex]c = \frac{2}{0.42} [/tex]

Step-by-step explanation:

AB = c

[tex] \frac{a}{sin \: A} = \frac{c}{sin \: C} \\ \frac{2}{sin \: 25} = \frac{c}{sin \: 90} \\ \frac{2}{0.42} = \frac{c}{1} \\ 0.42 \: c = 2 \\ c = \frac{2}{0.42} [/tex]

Answer:

4.73

Step-by-step explanation:

​

​

Answer: this is the right answer Graph A represents j(x). The y-intercepts for f(x) and g(x) can be 1 and 3. And The rate of change of the sum of f(x) and g(x) is greater than that of either function. your welcome

Step-by-step explanation:

The rate of change of the sum of f(x) and g(x) is greater than that of either function.

From the question, we have the following parameters:

The graphs of the functions are not given;

However, if all the functions are linear functions, then the slopes of the sum of functions f(x) and g(x) could be greater than the slopes of h(x) and j(x)

Hence, the true statement (by observation) is (c)

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Answer:

  d(t) = -20t -260

Step-by-step explanation:

We are given two points ...

  (t, d) = (3, -320) and (8, -420)

The 2-point form of the equation of a line can be useful when 2 points are given.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Substituting the given points, we have ...

  d(t) = (-420 -(-320))/(8 -3)(t -3) -320

  d(t) = -20(t -3) -320

  d(t) = -20t -260

Answer:

Your answer will be [tex]12[/tex] cups of popcorn.

Step-by-step explanation:

To find out how much the new bags hold, you need to find out the discount.

[tex]\frac{20}{100 } = .2[/tex]

[tex]15 * .2 = 3[/tex]

We know that the discount is [tex]3[/tex].

To figure out how much the new bags hold, subtract by the old bags.

[tex]15 - 3 = 12[/tex]

The new bags hold 12 cups of popcorn.

Answer:

16 people

Step-by-step explanation:

First subtract the cost of the rental from the amount of money:

$400-$150 = $250

Therefore Tia has $250 to spend for additional people. Then if each person is $15, divide the remaining amount of money by the amount of money per person:

$250/$15 = 16.67

Since you can't have 0.67 of a person she can have 16 people go with her.

This can also be modeled by this inequality:

[tex]150 + 15x \leqslant 400[/tex]

Answer:

[tex]45\pi$ square inches[/tex]

Step-by-step explanation:

The radius, r of the expanding circle of oil is modeled by the function:

[tex]r=3\sqrt{s}[/tex] , where s is time in seconds.

When s=5

Radius [tex]r(5)=3\sqrt{5}$ inches[/tex]

Area of a circle [tex]=\pi r^2[/tex]

Therefore, the area of the oil spill when s=5 seconds

[tex]=\pi* (3\sqrt{5})^2\\=45\pi$ square inches[/tex]

The area of the spill when s=5 seconds is 45pi square inches.

Answer:

D

Step-by-step explanation:

since sam invest the least, let a be the amount invested by sam

sam = a

paul = a + 5000

bob = a + 5000 + 4000

3a + 14000 = 50000

3a = 36000

a = 12000

thus sam is 12000, paul is 17000 and Bob is 21000

therefore the ratio of B:P:S is 21:17:12

profit by paula is 17/50 x 70000 = 23800

The profit by Paula is 17/50 x 70000 = 23800.

We have given that Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000

Since sam invest the least, let a be the amount invested by sam

Therefore we get,

sam = a

The investment of Paul = a + 5000

Bob = a + 5000 + 4000

3a + 14000 = 50000

3a = 36000

divide both sides by 3 so we get,

a=36000/3

a = 12000

Therefore, sam is 12000,

paul =5000+12000=17000 and

Bob =12000+9000= 21000

Therefore the ratio of B:P:S is 21:17:12

The profit by Paula is 17/50 x 70000 = 23800.

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Answer:

(0.12,∞)

Step-by-step explanation:

The inequality x>0.12 means "all numbers greater than 0.12." There is no upper end to the solution to this inequality. In interval notation, we express x>0.12 as (0.12,∞). Notice that the parenthesis symbol shows that the endpoint of the inequality, 0.12, is not included.

The inequality x ≤ - 0.12 is written in interval notation as,

⇒ x ∈ (- ∞, - 0.12 ]

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ x ≤ - 0.12

Now, We can write the inequality in interval notation as;

⇒ x ≤ - 0.12

⇒ x ∈ (- ∞, - 0.12 ]

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Answer:

4.24

Step-by-step explanation:

To solve this, use the Pythagorean therom. A^2 + b^2 = C^2

in this case a = 3  and b = 3

so 9 + 9 =  sqrt 18  

4.24

Answer:3√(2)

Step-by-step explanation:

DF=3

EF=3

DE=√(3^2 + 3^2)

DE=√(3x3 + 3x3)

DE=√(9+9)

DE=√(18)

DE=√(2 x 9)

DE=√(2) x √(9)

DE=√(2) x 3

DE=3√(2)

Answer:

x=12

Step-by-step explanation:

4x+5 (5x-39) = 153

4x + 25x - 195 = 153

29x - 195 = 153

29x =  348

x = 12

Answer:

80% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases ([tex]\mu_1-\mu_2[/tex]) is [-9.132 , 23.332].

Step-by-step explanation:

We are given that a random sample of 7 sales receipts for mail-order sales results in a mean sale amount of $81.70 with a standard deviation of $18.75.

A random sample of 11 sales receipts for internet sales results in a mean sale amount of $74.60 with a standard deviation of $28.25.

Firstly, the Pivotal quantity for 80% confidence interval for the difference between population means is given by;

                            P.Q. =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex]  ~ [tex]t__n__1-_n__2-2[/tex]

where, [tex]\bar X_1[/tex] = sample mean sales receipts for mail-order sales = $81.70

[tex]\bar X_2[/tex] = sample mean sales receipts for internet sales = $74.60

[tex]s_1[/tex] = sample standard deviation for mail-order sales = $18.75

[tex]s_2[/tex] = sample standard deviation for internet sales = $28.25

[tex]n_1[/tex] = size of sales receipts for mail-order sales = 7

[tex]n_2[/tex] = size of sales receipts for internet sales = 11

Also, [tex]s_p=\sqrt{\frac{(n_1-1)s_1^{2} +(n_2-1)s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(7-1)\times 18.75^{2} +(11-1)\times 28.25^{2} }{7+11-2} }[/tex] = 25.11

Here for constructing 80% confidence interval we have used Two-sample t test statistics as we don't know about population standard deviations.

So, 80% confidence interval for the difference between population means, ([tex]\mu_1-\mu_2[/tex]) is ;

P(-1.337 < [tex]t_1_6[/tex] < 1.337) = 0.80  {As the critical value of t at 16 degree

                                         of freedom are -1.337 & 1.337 with P = 10%}  

P(-1.337 < [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] < 1.337) = 0.80

P( [tex]-1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] < [tex]{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}[/tex] < [tex]1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] ) = 0.80

P( [tex](\bar X_1-\bar X_2)-1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] < ([tex]\mu_1-\mu_2[/tex]) < [tex](\bar X_1-\bar X_2)+1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] ) = 0.80

80% confidence interval for ([tex]\mu_1-\mu_2[/tex]) =

[ [tex](\bar X_1-\bar X_2)-1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] , [tex](\bar X_1-\bar X_2)+1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] ]

= [ [tex](81.70-74.60)-1.337 \times {25.11 \times \sqrt{\frac{1}{7} +\frac{1}{11} } }[/tex] , [tex](81.70-74.60)+1.337 \times {25.11 \times \sqrt{\frac{1}{7} +\frac{1}{11} } }[/tex] ]

= [-9.132 , 23.332]

Therefore, 80% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases ([tex]\mu_1-\mu_2[/tex]) is [-9.132 , 23.332].

Answer:

-7x⁹

Step-by-step explanation:

[tex]\sqrt{49x^{18}} = \sqrt{(7^2)(x^9)^2} =\sqrt{(7x^{9})^2} = |7x^9|[/tex]

Since  x < 0 ,then |7x⁹| = -7x⁹

Answer:69°43'

Step-by-step explanation:

Complementary angles add up to 90

Let them complement be y

y+20°17`=90°

Collect like terms

y=90-20°17' 20°17'=1217/60

y=90-1217/60

y=(60x90 -1 x 1217)/60

y=(5400-1217)/60

y=4183/60

y=69°43'

Answer:

64

Step-by-step explanation:

x^2 +16x+c

Take the coefficient of x

16

Divide by 2

16/2 =8

Square it

8^2 = 64

This is c

Answer:

c = 64

Step-by-step explanation:

The value for c is A. 64.  That comes from the process of completing the square where you take half the linear term, square it, and add it in.  Our linear term is 16.  Half of 16 is 8, and 8 squared is 64. 

Answer:

2.33 units

Step-by-step explanation:

[tex]\tan 25\degree =\frac{AC}{5}\\\\0.46630 = \frac{AC}{5}\\\\AC = 0.46630 \times 5\\AC =2.3315\\AC = 2.33 \: units[/tex]

Answer:

[tex]8.182X10^8 $pounds[/tex]

a=8.182 and b=8

Step-by-step explanation:

Weight of the Empire State Building =[tex]7.3X 10^8[/tex] pounds.

Weight of the One World Trade Center building= 88,200,000 pounds.

=[tex]8.82 X 10^7[/tex]

The addition of the two:

[tex]=7.3X 10^8+8.82 X 10^7\\$To make it easier to add, express both as powers of 8\\=7.3X 10^8+0.882 X 10^8\\=(7.3+0.882)X10^8\\=8.182X10^8 $ pounds[/tex]

Comparing with the form: [tex]aX10^b[/tex]

a=8.182 and b=8

Answer:

Let's denote:

x: number of ticket 28$

y: number of ticket 40$

Then, we have:

x + y =5000

28x + 40y = 153200

=> 28(5000 - y) + 40y = 153200

=> 12y = 153200 - 140000

=> 12y =13200

=> y = 1100 (ticket 40$)

=> x = 5000 - 1100 = 3900 (ticket 28$)

Answer:

3

Step-by-step explanation:

Amplitude is the number in front of the sin or the number multiplied by the whole equation.  In this case its 3

Answer:

The correct test statistic for the hypothesis test is [tex]t = -1.87[/tex]

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} = 16[/tex]

The alternate hypotesis is:

[tex]H_{1} < 16[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

In this question:

[tex]X = 15.6, \mu = 16, s = 0.8, n = 14[/tex]

So

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{15.6 - 16}{\frac{0.8}{\sqrt{14}}}[/tex]

[tex]t = -1.87[/tex]

The correct test statistic for the hypothesis test is [tex]t = -1.87[/tex]

Hypothesis test used to check the results of the experiments gives true for the meaningful results.. The correct test statistic for the hypothesis test is -1.871.

Given information-

The mean battery life of the laptop is 16 hours claimed by the company.

The random sample for the test is 14.

Average life of the batteries found out as 15.6 hours.

The deviation for this result is 0.8 hours.

Hypothesis test used to check the results of the experiments gives true for the meaningful results.

As the mean battery life of the laptop is 16 hours claimed by the company.The null hypothesis for the given problem is,

[tex]H_o\mu=16[/tex]

As average life of the batteries found out as 15.6 hours. Thus the alternate hypothesis for the given problem is,

[tex]H_1\mu<16[/tex]

One sample t test can be found using the below formula,

[tex]t=\dfrac{\overline x -\mu_o}{\dfrac{s}{\sqrt{n} } }[/tex]

Here, [tex]\overline x[/tex] is mean value, [tex]n[/tex] is the number of random sample and [tex]s[/tex] is the deviation.

Put the values,

[tex]t=\dfrac{15.6 -16}{\dfrac{0.8}{\sqrt{14} } }\\t=-1.871[/tex]

Thus the correct test statistic for the hypothesis test is -1.871.

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Answer:

Half way

Step-by-step explanation:

Half way, because the dog can run all the way through the woods, but only half of the time he is going in, the rest of the time he is going out.

Answer:

Assuming this is a 45 - 45 - 90 right triangle, The answer would be B) Two sides have the same length, which is less than the length of the third side

Hence statements stated true false along with reason

A triangle is a three-sided polygon with three edges and three vertices in geometry. The sum of a triangle's interior angles equals 180 degrees is the most significant feature of a triangle.

Triangle of Isosceles: Triangle with Obtuse Angle

Triangle Inequality in the Scalene Triangle

Triangle Surface Area: Triangle with Sharp Angle

Triangle with Right Angles: Triangle Form of Pascal...

Given a triangle and statements related to it let's check

Each side has a different length.

-This statement can't always be true as in equilateral triangle all sides are equal

Two sides have the same length, which is less than the

length of the third side.

-this statement is correct but when it is a right angles triangle where other two anges are 45degrees each then this can't be true.

The three sides have the same length.

-this statement is true for equilateral triangle

D. The sum of the lengths of two sides is equal to the

length of the third side.-

-This statement is true when we talk of only right angled triangle

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Answer:

72x^2-96x+37

Step-by-step explanation:

Answer:

1320 feet

Step-by-step explanation:

All we have to do is multiply the rate of change of altitude by the time it took the altitude to change.

The altitude of an airplane is decreasing at a rate of 44 feet per second. After 30 seconds, the change is altitude is:

44 * 30 = 1320 feet

The altitude of the airplane has changed by 1320 feet.

Answer:

(SA - π r^2)/πr = s

Step-by-step explanation:

SA = πrs + π r^2

Subtract  π r^2 from each side

SA - π r^2 = πrs + π r^2-π r^2

SA - π r^2 = πrs

Divide each side by  πr

(SA - π r^2)/πr = πrs/πr

(SA - π r^2)/πr = s

Answer:

D

Step-by-step explanation:

SA = πrs + πr²

SA - πr² = πrs

s = (SA - πr²)/πr

Answer:

a) [tex] z= \frac{34-34}{2.5}= 0[/tex]

[tex] z= \frac{39-34}{2.5}= 2[/tex]

And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %

b) [tex] P(X<31.5) [/tex]

[tex] z= \frac{31.5-34}{2.5}= -1[/tex]

So one deviation below the mean we have: (100-68)/2 = 16%

c) [tex] z= \frac{29-34}{2.5}= -2[/tex]

[tex] z= \frac{36.5-34}{2.5}= 1[/tex]

For this case below 2 deviation from the mean we have 2.5% and above 1 deviation from the mean we got 16% and then the percentage between -2 and 1 deviation above the mean we got: (100-16-2.5)% = 81.5%

Step-by-step explanation:

For this case we have a random variable with the following parameters:

[tex] X \sim N(\mu = 34, \sigma=2.5)[/tex]

From the empirical rule we know that within one deviation from the mean we have 68% of the values, within two deviations we have 95% and within 3 deviations we have 99.7% of the data.

We want to find the following probability:

[tex] P(34 < X<39)[/tex]

We can find the number of deviation from the mean with the z score formula:

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

And replacing we got

[tex] z= \frac{34-34}{2.5}= 0[/tex]

[tex] z= \frac{39-34}{2.5}= 2[/tex]

And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %

For the second case:

[tex] P(X<31.5) [/tex]

[tex] z= \frac{31.5-34}{2.5}= -1[/tex]

So one deviation below the mean we have: (100-68)/2 = 16%

For the third case:

[tex] P(29 < X<36.5)[/tex]

And replacing we got:

[tex] z= \frac{29-34}{2.5}= -2[/tex]

[tex] z= \frac{36.5-34}{2.5}= 1[/tex]

For this case below 2 deviation from the mean we have 2.5% and above 1 deviation from the mean we got 16% and then the percentage between -2 and 1 deviation above the mean we got: (100-16-2.5)% = 81.5%

Answer:

(49 - 29) + 1 =(50 - 29)

Step-by-step explanation:

The 20 comes from the subtraction of 29 in both sides of the previous step equality. In the following, I transcript the complete procedure and I add the step that you need to understand why 20 appears (in bold numbers):

29+20=49

49+1=50

(49 - 29) + 1 =(50 - 29)

20+1=21

50-29=21

hence, it was only nesseraty to subtract 29

Answer:

D

Step-by-step explanation:

I'm really sry if it's wrong!

Answer:33/9

Step-by-step explanation:

Log10(x+3)-Log10(x-3)=1

Log10((x+3)/(x-3))=1

(x+3)/(x-3)=10^1

(x+3)/(x-3)=10

Cross multiply

x+3=10(x-3)

Open brackets

x+3=10x-30

Collect like terms

10x-x=30+3

9x=33

Divide both sides by 9

9x/9=33/9

x=33/9

Answer:

[tex] y = 300 (2)^x[/tex]

Where x represent the number of period of times of 22 minutes. If we want to know the value of the population after 66 minutes we need to find the value of x on this way:

[tex] x = 66 minutes *\frac{1period}{22 minutes}= 3[/tex]

So then we need to replace the value of x =3 and we got:

[tex] y= 300 (2)^3 = 2400[/tex]

Step-by-step explanation:

For this case we have the following function:

[tex] y = 300 (2)^x[/tex]

Where x represent the number of period of times of 22 minutes. If we want to know the value of the population after 66 minutes we need to find the value of x on this way:

[tex] x = 66 minutes *\frac{1period}{22 minutes}= 3[/tex]

So then we need to replace the value of x =3 and we got:

[tex] y= 300 (2)^3 = 2400[/tex]