5(x + 3) – 12 = 43 solve

Answer:

70

Step-by-step explanation:

You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.

Answer:

It is the first graph

Step-by-step explanation:

Just got it right on the test review :)

Inequalities help us to compare two unequal expressions. The graph shows that all the values of x that satisfies the given inequality are x>7. Thus, the correct option is A.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given inequality can be solved as,

[tex]\dfrac29(x+3) > 4(\dfrac59)\\\\\dfrac{2x+6}{9} > \dfrac{20}{9}\\\\2x + 6 > 20\\\\2x > 20 - 6\\\\x > \dfrac{14}{2}\\\\x > 7[/tex]

Hence, the graph shows that all the values of x that satisfies the given inequality are x>7. Thus, the correct option is A.

Learn more about Inequality:

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Answer:

Step-by-step explanation:

Given that:

If C(x) =  the cost of producing x units of a commodity

Then;

then the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

We are to consider a given function:

[tex]C(x) = 54,000 + 130x + 4x^{3/2}[/tex]

And the objectives are to determine the following:

a) the total cost at a production level of 1000 units.

So;

If C(1000) = the cost of producing 1000 units of a commodity

[tex]C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}[/tex]

[tex]C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )[/tex]

[tex]C(1000) = 54,000 + 130000 + 4(31622.7766)[/tex]

[tex]C(1000) = 54,000 + 130000 + 126491.1064[/tex]

[tex]C(1000) = $310491.1064[/tex]

[tex]\mathbf{C(1000) \approx $310491.11 }[/tex]

(b) Find the average cost at a production level of 1000 units.

Recall that :

the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

SO;

[tex]c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}[/tex]

Using the law of indices

[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]

[tex]c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}[/tex]

c(1000) =$ 310.49 per unit

(c) Find the marginal cost at a production level of 1000 units.

The marginal cost  is C'(x)

Differentiating  C(x) = 54,000 + 130x + 4x^{3/2} to get  C'(x) ; we Have:

[tex]C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}[/tex]

[tex]C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}[/tex]

[tex]C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}[/tex]

[tex]C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}[/tex]

[tex]C'(1000) = 319.7366596[/tex]

[tex]\mathbf{C'(1000) = \$319.74 \ per \ unit}[/tex]

(d)  Find the production level that will minimize the average cost.

the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]

the production level that will minimize the average cost is c'(x)

differentiating [tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex] to get c'(x); we have

[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }[/tex]

[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }[/tex]

Also

[tex]c''(x)= \dfrac{108000}{x^3} -x^{-3/2}[/tex]

[tex]c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0[/tex]

[tex]x^2 = 27000\sqrt{x}[/tex]

[tex]\sqrt{x} (x^{3/2} - 27000) =0[/tex]

x= 0;  or  [tex]x= (27000)^{2/3}[/tex] = [tex]\sqrt[3]{27000^2}[/tex] = 30² = 900

Since  production cost can never be zero; then the production cost = 900 units

(e) What is the minimum average cost?

the minimum average cost of c(900) is

[tex]c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}[/tex]

c(900) = 60 + 130 + 4(30)

c(900) = 60 +130 + 120

c(900) = $310 per unit

Answer:

Null hypothesis :

[tex]H_o:p_1-p_2 = 0[/tex]

Alternative hypothesis:

[tex]H_1:p_1-p_2 \neq 0[/tex]

Decision Rule:

To reject the null hypothesis if  z < -1.65 and z > 1.65

Conclusion:

Failed to reject null hypothesis if z > -1.65 or z < 1.65

z -value = 0.33022

P-value = 0.7414

Decision Rule:

Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1

Conclusion:  we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode

Step-by-step explanation:

From the summary of the given statistical data sets.

Let consider to [tex]p_1[/tex] represent percentage of the first group ; &

[tex]p_2[/tex] represent percentage of the second group

The null and the alternative hypothesis can be stated s follows:

Null hypothesis :

[tex]H_o:p_1-p_2 = 0[/tex]

Alternative hypothesis:

[tex]H_1:p_1-p_2 \neq 0[/tex]

At the level of significance ∝ = 0.1; the two tailed critical value from the z-table

[tex]z_{\alpha/2} = 1.65[/tex]

Decision Rule:

To reject the null hypothesis if  z < -1.65 and z > 1.65

Conclusion:

Failed to reject null hypothesis if z > -1.65 or z < 1.65

However; from the question:

There are 55 people in the first group and this group will be administered the new drug.

There are 45 people in the second group and this group will be administered a placebo.

After one year, 11% of the first group has a second episode and 9% of the second group has a second episode.

The test statistic for the for the first group who suffered from the second episode can be denoted as :

[tex]\hat p_1 = \dfrac{\overline x_1}{n_1}=0.11[/tex]

The test statistic for the for the second group who suffered from the second episode can be denoted as :

[tex]\hat p_2 = \dfrac{\overline x_2}{n_2}=0.09[/tex]

where;

[tex]n_1[/tex] = sample size of group 1 = 55

[tex]n_2[/tex] = sample size of group 2 = 45

The total probability of both group is :

[tex]\hat p = \dfrac{n_1 \hat p_1 + n_2 \hat p_2}{n_1 + n_2}[/tex]

[tex]\hat p = \dfrac{55*0.11+ 45 * 0.09}{55+45}[/tex]

[tex]\hat p = \dfrac{6.05+ 4.05}{100}[/tex]

[tex]\hat p = \dfrac{10.1}{100}[/tex]

[tex]\hat p = 0.101[/tex]

The standard error of the statistic [tex]\hat p_1 - \hat p_2[/tex] an be computed as follows:

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{ p_1 (1 - \hat p)( \dfrac{1}{n_1}+\dfrac{1}{n_2})}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101 (1 - 0.101)( \dfrac{1}{55}+\dfrac{1}{45})}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101(0.899)(0.0404)}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.0036682796}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)=0.060566[/tex]

Now; The test statistics is determined to be :

[tex]z = \dfrac{(\hat p_1 - \hat p_2 ) - (p_1-p_2)}{SE(\hat p_1 - \hat p_2)}[/tex]

[tex]z = \dfrac{(0.11-0.09) - 0}{0.060566}[/tex]

z = 0.33022

Hence; the value for the test statistics =  0.33022

the value for the test statistics =  0.33

From the z value; The P-value for the test statistics can be computed as:

P-value = 2P(Z ≥ |z|)

P-value = 2P(Z ≥  0.33022)

P-value = 2 × P (Z ≤ - 0.33022)

From the z table Z ≤ - 0.33022 = 0.3707

P-value = 2 × 0.3707

P-value = 0.7414

Decision Rule:

Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1

Conclusion:  we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode

Answer:

x > 29

Step-by-step explanation:

−x<−29

Divide each side by -1, remembering to flip the inequality

x > 29

Answer:

Step-by-step explanation:

-x < -29   change the signs

x > 29

To clear the fractions we multiply both sides by the least common multiple of all the denominators.

1/2  x + 2/3 = 4

Denominators 2 and 3, so multiply both sides by [Answer]: 6

3/4 x + 1 = 5/6

Denoms 4 and 6, LCM=12  Answer: 12

6/7 x - 2/3 = 5/21

LCM(7,3,21)=21 Answer: 21

3/5 + x/2 = 9

LCM(5,2)  Answer: 10

25/4 = 6 + 1/2 x

LCM(4,2)  Answer: 4

We have a known hypotenuse, but unknown opposite side. Use the sine ratio to tie the two together to be able to solve for x.

sin(angle) = opposite/hypotenuse

sin(50) = x/6.5

6.5*sin(50) = x

x = 6.5*sin(50)

x = 4.97928888027336 make sure your calculator is in degree mode

x = 4.98

Answer is choice B

Answer:

b

Step-by-step explanation:

Answer:

Second choice is correct.

Step-by-step explanation:

Simple interest = $12600

Compounded interest = $14656

Best Regards!

Answer:

The hypothesis test is a two-tail test

Step-by-step explanation:

The test hypothesis:

Null hypothesis                  H₀       p = 0,39         or   p  =  p₀

Where p₀ is a nominal proportion (established proportion) and

Alternate hypothesis         Hₐ       p  ≠  0,39        or  p ≠  p₀

Is a two-tail test, (≠) means different, we have to understand that different implies bigger and smaller than something.

For a test to be one tail-test, it is necessary an evaluation only in one sense in relation to the pattern ( in this case the proportion )

Answer:

I did my best with the information! The Man died at around 11:20 am.

Step-by-step explanation:

So due to the algus mortis process, after death, a body can stay at its regulated temperature for up to 2 to 3 hours postmortem. But after that, the body soon drops at about 1 degrees celsius each hour. 1 degrees celsius is about -33 . So he was found at 42 degrees fahrenheit, which means he died somewhere around 11 o-clock. We do not know how long the postmortem process had his temperature delayed, so it would be roughly I say around 11: 20 am.

Answer: 54 mL

Step-by-step explanation:

Simply do 9(number of containers)*6(Syrup per container) to get 54 mL of syrup.

Hope it helps <3

Answer:

d - 12.50 = 17

add 12.50 to both sides to get d alone.

d = 12.50 + 17

Answer:

It's B d= 17 + 12.50

Step-by-step explanation:

Got it right on edg

When the wavelength of a diffraction grating is decreased,  the distance between lines decreases.

The diffraction grating is used to carry out interference experiments. It consists of a  number of small lines that are constructed to be close to each other and produce an interference pattern.

The outcome of decreasing the wavelength of incident light on a diffraction grating is that the distance between lines decreases.

Learn more about diffraction grating:https://brainly.com/question/13902808

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Answer:

-3

Step-by-step explanation:

2x + 3 +7x = -24

Add the X together

9x +3 = -24

Bring over the +3. [when you bring over change the sign]

9x = -24 -3

9x = -27

-27 divide by 9 to find X

therefore answer is

x= -3.

Hope this helps

Answer:

x = -3

Step-by-step explanation:

question is

2x + 3 + 7x = -24

First you combine the like terms

2x and 7x you can add them so it will be 9x

so it will then it will be like this:

9x + 3 = -24

now you take the 3 and send it to the other side, and right now the 3 is positive so when it goes to the other side it will turn into -3

so

9x = -24 -3

again now you combine the like terms

-24 -3 = - 27

now you have

9x = -27

now just divide each side by 9

x = -27/9

x = -3

Sorry if this doesnt help

Answer:

5 meters : 1 gallon

fuel efficiency of Car is 7 meters per gallons

Step-by-step explanation:

Given Tanya car goes 45 meters on 7 gallons.

In terms of ratio  of distance traveled and fuel consumed

45 meters : 7 gallons

since both 45 and 7 are multiple of 7 dividing both side by 7

45/7 meters : 7/7 gallons

5 meters : 1 gallon

Thus, fuel efficiency of Car is 7 meters per gallons.

Answer: A, (0, -3)

Step-by-step explanation:

Inequalities, once graphed, take the form of the image you attached:

Linear inequalities are straight lines, sometimes dotted and sometimes solid, with shading on one side of the line.

Any point in the shading is a correct solution to the inequality.

In this case, the line is solid, so any point on the line is a solution to the inequality.

Looking at answer choice A: (0, -3), it lies on the line as the y-intercept.

The correct choice is A.

Answer:

8 and 9

Step-by-step explanation:

If x is the smaller integer, and x + 1 is the larger integer, then:

(x + 1)² + 3x = 105

x² + 2x + 1 + 3x = 105

x² + 5x − 104 = 0

(x + 13) (x − 8) = 0

x = -13 or 8

Since x is positive, x = 8.  So the two integers are 8 and 9.

Answer:

[tex]P(\overline X < 2.3) = 0.9999[/tex]

Step-by-step explanation:

Given that:

mean = 2

standard deviation = 0.5

sample size = 50

The probability that the sample mean is less than 2.3 hours is :

[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{2.3 - 2.0}{\dfrac{0.5}{\sqrt{50}}})[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq \dfrac{0.3}{0.07071})[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq 4.24268)[/tex]

[tex]P(\overline X < 2.3) = P(Z \leq 4.24)[/tex]

From z tables;

[tex]P(\overline X < 2.3) = 0.9999[/tex]

Answer:

x = -8 and x= 7

Step-by-step explanation:

recall that for a rational expression, the vertical asymptotes occur at x-values that causes the expression to become undefined. These occur when the denominator becomes zero.

Hence the asymptototes will occur in x-locations where the denominator , i.e

(x+8)(x-7) = 0

solving this, we get

(x+8) = 0 ----> x = -8

or

(x-7) = 0 ------> x = 7

hence the asymptotes occur x = -8 and x= 7

Answer:

x = -8 and x = 7.

Step-by-step explanation:

The vertical asymptotes are lines that the function will never touch.

Since no number can be divided by 0, the function will not touch points where the denominator of the function is equal to 0.

[tex]\frac{x - 6}{(x + 8)(x - 7)}[/tex], so the vertical asymptotes will be where (x + 8) = 0 and (x - 7) = 0.

x + 8 = 0

x = -8

x - 7 = 0

x = 7

The vertical asymptotes are at x = -8 and x = 7.

Hope this helps!

Answer:

18+18 as point XYZ is in centroid of Q

Step-by-step explanation:

so it's equal.

36.which is option A.

Answer:

see explanation

Step-by-step explanation:

The median is the middle value of the data set in ascending order. If there is no exact middle then the median is the average of the values either side of the middle.

Given

3   8   14   19   22   29   33   37   43   49

                            ↑ middle is between 22 and 29

median = [tex]\frac{22+29}{2}[/tex] = [tex]\frac{51}{2}[/tex] = 25.5

The upper quartile [tex]Q_{3}[/tex] is the middle value of the data to the right of the median.

29   33   37   43   49

               ↑

[tex]Q_{3}[/tex] = 37

The lower quartile [tex]Q_{1}[/tex] is the middle value of the data to the left of the median.

3   8   14   19   22

           ↑

[tex]Q_{1}[/tex] = 14

The min is the smallest value in the data set, that is 3

The max is the largest value in the data set, that is 49

The 5 number summary is

3,  14,  25.5,  37,  49

Answer:

x < -( 8-2b) /a  a > 0

Step-by-step explanation:

−ax + 2b > 8

Subtract 2b from each side

−ax + 2b-2b > 8-2b

-ax > 8 -2b

Divide each side by -a, remembering to flip the inequality ( assuming a>0)

-ax/-a < ( 8-2b) /-a

x < -( 8-2b) /a  a > 0

Answer: [tex]x<\frac{-8+2b}{a}[/tex]

                  [tex]a>0[/tex]

Step-by-step explanation:

[tex]-ax+2b>8[/tex]

[tex]\mathrm{Subtract\:}2b\mathrm{\:from\:both\:sides}[/tex]

[tex]-ax>8-2b[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]

[tex]\left(-ax\right)\left(-1\right)<8\left(-1\right)-2b\left(-1\right)[/tex]

[tex]ax<-8+2b[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}a[/tex]

[tex]\frac{ax}{a}<-\frac{8}{a}+\frac{2b}{a};\quad \:a>0[/tex]

[tex]x<\frac{-8+2b}{a};\quad \:a>0[/tex]

Answer:

3/11

Step-by-step explanation:

There are eleven equal parts.

So the denominator is 11.

He copies 8 parts on Sunday.

11-8=3.

He copied 3 parts on Saturday.

Hope this helps ;) ❤❤❤

Answer:

[tex]\boxed{V=lwh}[/tex]

Step-by-step explanation:

The formula for volume of a cuboid is:

[tex]V=lwh[/tex]

[tex]volume = length \times width \times height[/tex]

Answer:

V = l w h

Step-by-step explanation:

Volume of a Cuboid = Length × Width × Height

Where l = length, w = width and h = height

Answer:

(3) x ≥ -3

(4) 2.5 gallons

(4) -12x + 36

Step-by-step explanation:

Hey there!

1)

Well its a solid dot meaning it will be equal to.

So we can cross out 1 and 2.

And it's going to the right meaning x is greater than or equal to -3.

(3) x ≥ -3

2)

Well if each milk container has 1 quart then there is 10 quarts.

And there is 4 quarts in a gallon, meaning there is 2.5 gallons of milk.

(4) 2.5 gallons

4)

16 - 4(3x - 5)

16 - 12x + 20

-12x + 36

(4) -12x + 36

Hope this helps :)

Answer:

[tex]x = -5[/tex]

Step-by-step explanation:

We can simplify this equation down until x is isolated.

[tex]2x - 3 + 3x = -28[/tex]

We can combine the like terms of x.

[tex]5x - 3 = -28[/tex]

Add 3 to both sides.

[tex]5x = -25[/tex]

Now we can divide both sides by 5.

[tex]x = -5[/tex].

So x = -5.

Hope this helped!

Answer:

x=-5

Step-by-step explanation:

first combine like terms

5x-3=-28

add on both sides

5x=-25

divide

x==-5

Answer:

Option (D)

Step-by-step explanation:

In the picture attached,

An obtuse angle triangle ABC has been given.

By applying Sine rule in the triangle,

[tex]\frac{\text{SinB}}{b}=\frac{\text{SinA}}{a}=\frac{\text{SinC}}{c}[/tex]

Since, m∠A + m∠B + m∠C = 180°

45° + 110° + m∠C = 180°

m∠C = 180°- 155° = 25°

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=\frac{\text{Sin25}}{7}[/tex]

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=0.060374[/tex]

[tex]\frac{\text{Sin110}}{b}=0.060374[/tex]

b = [tex]\frac{\text{Sin110}}{0.060374}[/tex]

b = 15.56

b ≈ 15.56

[tex]\frac{\text{Sin45}}{a}=0.060374[/tex]

a = [tex]\frac{\text{Sin45}}{0.060374}[/tex]

a = 11.712

a = 11.71

Therefore, Option (D) will be the answer.

Answer: 0.5

Step-by-step explanation:

If the probability of the time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. Therefore, the probability that a flight is between 125 and 140 minutes is 0.5

Answer:

The third answer (C).

Step-by-step explanation:

This graph starts at 10. So it needs the +10 at the end.

Also the slope is -1/2 because the graph goes down one, right two. Rise/run.

Answer:

y= -1/2x+10

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.

For the the given graph, the y-intercept is 10. The slope can be determined by finding the rate of change between any two points on the graph, such as (2,9) and (8,6).

you can imagine this as a venn diagram. the "or" event would consist of everything in both sides and the middle of the venn diagram because you can choose form either event x or event y.

the "and" event would consist of everything in the middle of the venn diagram because you choice must be a part of both event x and event y.

the complement of an event is just everything that is not included in the event. for example, in a coin flip, the complement of heads is tails. in a dice roll, the complement of {1,2} is {3,4,5,6}

so if you come across these just think "either or" or "both and." and remember that the complement is everything excluding what is listed.

i apologize if this does not help, im not that great at explaining things