How many solutions does the following equation have? −5(z+1)=−2z+10

Answer:

0.8 < x < 16.8

Step-by-step explanation:

8.0 + 8.8 = 16.8

The range of possible sizes for the side x are 0.8 < x < 16.8.

A triangle is a geometrical shape in two dimensional geometry which has three sides, three vertices and three angles.

The sum of all the three angles inside the triangle is supplementary.

This implies that if a, b and c are the three interior angles of a triangle, then, a + b + c = 180°.

If two sides of a triangle are given, then the third side of the triangle will always be in between the difference of the length of the other two sides and the sum of the length of the other two sides.

Here two lengths are given as 8.0 and 8.8.

Difference of the lengths = 8.8 - 8.0 = 0.8

Sum of the lengths = 8.8 + 8.0 = 16.8

So the x lies between 0.8 and 16.8.

Hence the range of the possible length of the given triangle is 0.8 < x < 16.8.

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Answer:

Step-by-step explanation:

In double angle, sin2x = sin(x+x) = sinxcosx+cosxsinx

sin2x = 2sinxcosx ... 1

Applying this formula to prove that sin(4x) = 4 sinx cosx(1 − 2sin2x is shown below;

sin(4x) = sin(2x+2x)

= sin2xcos2x+cox2xsin2x

sin4x = 2sin2xcos2x ..2

also cos2x = cos(x+x) = cosxcox-sinxsinx

cos 2x = cos²x - sin²x ...3

Substituting equation 1 and 3 into 2, we will have;

sin4x = 2(2sinxcosx(cos²x - sin²x ))

sin4x = 4sinxcosx(cos²x - sin²x )

From sin²x+cos²x =1; cos²x = 1-sin²x

Substituting the expression into the resulting equation will give;

sin4x = 4sinxcosx(1-sin²x - sin²x )

sin4x = 4sinxcosx(1-2sin²x) Verified!  

Answer:

The maximum one-day percentage loss = -1.15%

Step-by-step explanation:

Let assume that with the  normal distribution, 95% of observations are smaller than 1.65 standard deviations above the mean.

Given that:

Cerra estimates the standard deviation of daily percentage changes of the euro to be 1 percent over the last 100 days.

if the expected percentage change of the euro tomorrow is 0.5 percent

and that Z value at 95% C.I level = 1.65

∵ The maximum one-day percentage loss = (expected percentage change -   Z-Value) × standard deviation

The maximum one-day percentage loss =  (0.5 - 1.65) ×  1

The maximum one-day percentage loss = -1.15  ×  1

The maximum one-day percentage loss = -1.15%

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:

161/184 or 0.875

Step-by-step explanation:

Total number of cans = 24 cans

Total number of diet soda = 3 cans

Total number of regular soda = 21 cans

We are asked to find the probability that:that at least one contain regular soda if two cans are selected randomly

We have two ways for this happening

a) two of the cans are regular soda

b) one of the cans is regular , while one is diet

Hence,

Probability (that at least one contain regular soda) = Probability(that two of the cans are regular soda) + Probability ( one of the cans is regular , while one is diet)

Probability(that two of the cans are regular soda) = 21/24 × 20/23

= 35/46

Probability ( one of the cans is regular , while one is diet) = 21/24 × 3/23

= 21/184

Probability (that at least one contain regular soda) = 35/46 + 21/184

We find the Lowest common multiple of the denominators = 184

= 35/46 + 21/184

= (35 × 4) + (21 × 1)/184

= 140 + 21/184

= 161/184

= 0.875

Therefore, the probability that at least one can contains regular soda = 161/184 or 0.875

Answer:

t= 1.89736659

Step-by-step explanation:

Answer:8

Step-by-step explanation:

The smallest prime is 2

cube of 2 is equal to 8

2*2*2=8

Answer:

729

Step-by-step explanation:

The second smallest prime number is 3 (preceded by 2). We have (3^2)^3=3^6=729.

Hope this helped! :)

Answer:

F'(-3) = 18

Step-by-step explanation:

Let g(x) = u and apply the chain rule

[tex]F(x)=f(g(x))=f(u)\\F'(x)=\frac{df(u)}{du}[/tex]

[tex]\frac{du}{dx}=g'(x)[/tex]

[tex]\frac{df(u)}{du}*\frac{du}{dx} = \frac{df(u)}{dx}\\F'(x)= \frac{df(u)}{du}*g'(x)\\F'(x)= f'(u)*g'(x)\\F'(x)= f'(g(x))*g'(x)[/tex]

We now have all of the necessary definite values to solve the expression for x= -3:

[tex]F'(-3)= f'(g(-3))*g'(-3)\\F'(-3)= f'(-4)*6\\F'(-3)= 3*6\\F'(-3)= 18[/tex]

Finally, we have that F'(-3)= 18.

Answer:

23 dimes, 32 nickels

Step-by-step explanation:

Let n equal the number of nickels and d be the number of dimes. We can use the information given to create a system of equations, as follows:

The total number of coins (the number of nickels plus the number of dimes) is 55, giving us the equation n + d = 55.

The total amount is $3.90. Since each nickel is worth $0.05 and each dime is worth $0.10, we get the equation 0.05n + 0.10d = 3.90.

Multiplying the second equation by 20, we get n + 2d = 78. We can subtract the first equation to get d = 23. Substituting this into the first equation, we get that n = 32.

Therefore, there are 23 dimes and 32 nickels.

Answer: 100 penny 2 qtrs 50 noclke

Step-by-step explanation:

Answer:

What I would tell Charli is that his prediction is somewhat right because there is a 50/50 chance of landing the coin on each side because 325 is half of 650.

Step-by-step explanation:

Answer:

[tex]\boxed{ \sf 41.81}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trigonometric functions.

[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]\sf sin(?)=\frac{2}{3}[/tex]

[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]

[tex]\sf ?= 41.81031489...[/tex]

Answer:

[tex]\boxed{41.81}[/tex]

Step-by-step explanation:

∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.

The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).

However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.

Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.

Answer:

The volumes of the cubes are 6³ = 216, 8³ = 512, 10³ = 1,000 and 12³ = 1,728 for a combined volume of 216 + 512 + 1,000 + 1,728 = 3456 which means that each side of the scale must have a combined volume of 3456 / 2 = 1728. This means that in order for the scale to be balanced we need to put the 12 cm cube on one side and the other 3 cubes on the other side.

Complete question:

The line graph relating to the question was not attached. However, the line graph has can be found in the attachment below.

Answer:

17,209

Step-by-step explanation:

The line graph provides information about alcohol-related highway fatalities between year 2001 to 2010.

Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.

The average number of alcohol related fatalities between 2001 - 2006 can be calculated thus :

From the graph:

Year - - - - - - - - - - Number of fatalities

2001 - - - - - - - - - - 17401

2002 - - - - - - - - -  17525

2003 - - - - - - - - -  17013

2004 - - - - - - - - - 16694

2005 - - - - - - - - - 16885

2006 - - - - - - - - - 17738

To get the average :

Sum of fatalities / number of years

(17401 + 17525 + 17013 + 16694 + 16885 + 17738) / 6

= 103256 / 6

= 17209.333

Average number of alcohol related fatalities is 17,209 (to the nearest whole number)

Answer:

[0, infinity)

Step-by-step explanation:

clarence, I believe you meant y = |3x + 1|.  The absolute value of 3x + 1 is never less than 0, so the range of the given function (above) is [0, infinity).

Answer:

87.92 ft³

Step-by-step explanation:

The formula for the volume of a cylinder is πr² · h

1. Set up the equation

π2² · 7

2. Solve

(3.14)(4)(7) = 87.92

The volume of a cylindrical water tank with a diameter of 4 feet  and a height of 7 feet is 87.92 cubic feet.

Given that, a cylindrical water tank with a diameter of 4 feet and a height of 7 feet.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

We know that, the volume of a cylinder πr²h

Here, radius =4/2 = 2 feet

The volume of a cylinder = 3.14×2²×7

= 3.14×4×7

= 87.92 cubic feet

Therefore, the volume of a cylindrical water tank with a diameter of 4 feet  and a height of 7 feet is 87.92 cubic feet.

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Answer:

slope = 4

The line is increasing

Step-by-step explanation:

slope can be found through the equation [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]. So, if we plug these points in, we get [tex]\frac{7-3}{8-7}[/tex], which simplifies to 4. So, the slope is 4.

Since the slope is positive, the line is increasing.

Answer: B) 22

Step-by-step explanation:

y coordinate of line = 3

y coordinate of point = -19

On a number line, distance between 3 & -19 = 22

Answer:

30 cm

Step-by-step explanation:

1 inch is 2.54 centimeters, and 2.54 times 12 is 30.48, which would be the closest.

The following metric units of measure is 30 cm

The correct option is (A)

Measurement” is the act of determining a target's size, length, weight, capacity, or other aspect.

Step 1: Write the conversion as a fraction.

Step 2: Multiply or divide, as required.

Step 3: Cancel the units (same units from top and bottom)

Step 4: Write the simplified answer with its correct unit.

Now, as we know that

1 inch = 2.54 cm

So, we can write

12 inch = 2.54 * 12

12 inch= 30.48 cm

Hence, the closest unit is  30 cm in the given metric system.

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3*5 ≡ 15 ≡ 3 (mod 12)

3*7 ≡ 21 ≡ 9 (mod 12)

3*9 ≡ 27 ≡ 3 (mod 12)

5*7 ≡ 35 ≡ 11 (mod 12)

5*9 ≡ 45 ≡ 9 (mod 12)

7*9 ≡ 63 ≡ 3 (mod 12)

Your table should look like the attached.

It's unclear what you're supposed to evaluate for part (b)...

Answer:

1) [tex](a+ib)(a-ib)[/tex]

2) [tex]a^2+i^2b[/tex]

Step-by-step explanation:

1) [tex]a^2+b^2[/tex]

=> [tex]a^2 - (-1)b^2[/tex]      (We know that -1 = [tex]i^2[/tex] )

=> [tex]a^2-i^2b^2[/tex]

=> [tex](a)^2-(ib)^2[/tex]

Using Formula [tex]a^2 -b^2 = (a+b)(a-b)[/tex]

=> [tex](a+ib)(a-ib)[/tex]

2) [tex]a^2-b[/tex]

=> [tex]a^2+(-1)b[/tex]      (We know that -1 = [tex]i^2[/tex] )

=> [tex]a^2+i^2b[/tex]  (It cannot be simplified further)

Answer:

[tex]\boxed{(a+ib)(a-ib)}[/tex]

[tex]\boxed{a^2+i^2b}[/tex]

Step-by-step explanation:

[tex]a^2 + b^2[/tex]

Rewrite expression.

[tex]a^2- (-1)b^2[/tex]

Use identity :  [tex]-1=i^2[/tex]

[tex]a^2- i^2 b^2[/tex]

Factor out square.

[tex]a^2-(ib)^2[/tex]

Apply difference of two squares formula : [tex]a^2-b^2 =(a+b)(a-b)[/tex]

[tex](a+ib)(a-ib)[/tex]

[tex]a^2-b[/tex]

Rewrite expression.

[tex]a^2+(-1)b[/tex]

Use identity :  [tex]-1=i^2[/tex]

[tex]a^2+i^2b[/tex]

Answer:

None,

they are all correct.

Step-by-step explanation:

A)

3/4 - 75%

4/5 - 80%

3/4 < 4/5

B)

5 ÷ 6 = .83333333333

5/6 > .83

C)

2 ÷ 3 = .666666666

2/3 > .66

D)

1 ÷ 3 = .33333333333

1/3 > .3

Thus,

all of the given statements are correct.

Hope this helps :)

Answer:

B

Step-by-step explanation:

Answer:  i) θ = 30°, 60°, 210°, & 240°

              ii) θ = 20° &  200°

Step-by-step explanation:

i) sin (2θ) = cos 30°

[tex]\sin(2\theta)=\dfrac{\sqrt3}{2}\\\\.\quad 2\theta=\sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\\\\.\quad 2\theta=60^o\qquad 2\theta=120^o\\\\.\quad \theta=30^o\qquad \theta=60^o[/tex]

To include all of the solutions for one rotation, add 360/2 = 180 to the solutions above.   θ = 30°, 60°, 210°, 240°

If you need ALL of the solutions (more than one rotation), add 180n to the solutions.   θ = 30° + 180n   &   60° + 180n

*********************************************************************************************

ii) cos α = sin (50 + α)

Use the Identity: cos α = sin (90 - α)

Use Transitive Property to get:   sin (50° + α) = sin (90° - α)

50° + α = 90° - α

50° + 2α = 90°

        2α = 40°

          α = 20°

To find all solutions for one rotation, add 360/2 = 180 to the solution above.

α = 20°, 200°

If you need ALL of the solutions (more than one rotation), add 180n to the solution. α = 20° + 180n

Answer:

Step-by-step explanation:

3(−2a - 4)+3a

=-6a - 12 +3a

A: -6a - 12 +3a

[tex]hope \: this \: helps[/tex]

Answer:

the answer is A

Step-by-step explanation:

you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a

Answer:

this is all i got for the second question.

Step-by-step explanation:

That is, the average rate of change of from 3 to 0 is 1. That is, over the interval [0,3], for every 1 unit change in x, there is a 1 unit change in the value of the function. Here is a graph of the function, the two points used, and the line connecting those two points.

hope this kinda helps

-lvr

Answer:

a:b:c

1a) 14:16:7

b) 2:1:5

c) 2:1:48

d) 15:24:32

2) 56:12:3

Step-by-step explanation:

Untuk membentuk nisbah tiga kuantiti, pertama-tama kita menukar masing-masing menjadi unit yang sama.

a) 2 minggu hingga 16 hari hingga 1 minggu

Menukar semuanya menjadi bilangan hari, kerana ia sangat setanding.

2 minggu = 14 hari

16 hari = 16 hari

1 minggu = 7 hari

2 minggu hingga 16 hari hingga 1 minggu = 14 hari hingga 16 hari hingga 7 hari

14: 16: 7

b) 0.1 kg hingga 50 g hingga 0.25 kg

Menukar semua menjadi gram

= 100 g hingga 50 g hingga 250 g

= 100: 50: 250

Bahagikan dengan 50

= 2 : 1 : 5

c) 4 minit hingga 120 saat hingga 1.6 jam

Menukar semua menjadi beberapa saat

= 240 saat hingga 120 saat hingga (1.6 × 60 × 60) saat

= 240 saat hingga 120 saat hingga 5,760 saat

= 2: 1: 48

d) 3 m hingga 480 cm hingga 6 400 mm

Menukar semua ini menjadi mm

= 3000 mm hingga 4800 mm hingga 6400 mm

Membahagi hingga 200 mm

= 15:24:32

2) RM5.60 hingga RM1.20 hingga 30 sen

Menukar semuanya kepada sen

= 560 sen hingga 120 sen hingga 30 sen

Membahagi hingga 10

= 56: 12: 3

Semoga ini Membantu !!!

English Translation

Solution

0.02 m: 3 cm: 4.6 cm = 2 cm: 3 cm: 4.6 cm = 2: 3: 4.6

20:30:46

10:15:23

Self Training 4.1a

1. Represent the relationship between the following three quantities in the form a: b: c.

(a) 2 weeks to 16 days to 1 week

(b) 0.1 kg to 50 g to 0.25 kg

(c) 4 minutes to 120 seconds to 1.6 hours

(d) 3 m to 480 cm to 6 400 mm

2. Tahir pays RM5.60 for a plate of beriani rice, RM1.20 for a glass of tea and 30 cents for a piece of cake.

Represent the price relationship for beriani rice, tea and cake in the form of a: b: c.

Solution

To form a ratio of three quantities, we first convert each of them to the same units.

a) 2 weeks to 16 days to 1 week

Converting all of it to number of days, as itnis very comparable.

2 weeks = 14 days

16 days = 16 days

1 week = 7 days

2 weeks to 16 days to 1 week

= 14 days to 16 days to 7 days

14 : 16 : 7

b) 0.1 kg to 50 g to 0.25 kg

Converting all into grams

= 100 g to 50 g to 250 g

= 100 : 50 : 250

Divide through by 50

= 2 : 1 : 5

(c) 4 minutes to 120 seconds to 1.6 hours

Converting all into seconds

= 240 seconds to 120 seconds to (1.6×60×60) seconds

= 240 seconds to 120 seconds to 5,760 seconds

= 2:1:48

(d) 3 m to 480 cm to 6 400 mm

Converting all of this to mm

= 3000 mm to 4800 mm to 6400 mm

Dividing through by 200 mm

= 15:24:32

2) RM5.60 to RM1.20 to 30 cents

Converting it all to cents

= 560 cents to 120 cents to 30 cents

Dividing through by 10

= 56:12:3

Hope this Helps!!!

Answer:

An apple a day keeps the doctor away

Step-by-step explanation:

Type in the answer

Its gonna be right

Answer: (a) No, the data suggests it is possible to reject the hypothesis which states that the 2 methods provide same mean value.

(b) (-10.957,-0.063)

Step-by-step explanation:

(a) Hypotheses for this data are:

[tex]H_{0}[/tex]: [tex]\mu_{1} = \mu_{2}[/tex]

[tex]H_{a}: \mu_{1} \neq \mu_{2}[/tex]

First find the differences in values:

1 => -0.31

2 => -0.63

3 => -2.85

4 => -3.46

5 => -6.43

6 => -7.52

7 => -17.39

Now, find the mean and standard deviation of the differences:

mean = [tex]\frac{-0.31+(-0.63)+...+(-17.39)}{7}[/tex] = - 5.51

sd = [tex]\sqrt{\frac{(-0.31-(-5.51))^{2}+...+(-17.39-(-5.51))^{2}}{7-1} }[/tex] = 5.89

The value of test statistics is:

t = [tex]\frac{mean}{\frac{s}{\sqrt{n} } }[/tex] = [tex]\frac{-5.51}{\frac{5.89}{\sqrt{7} } }[/tex] = - 2.4750

Analysing Student's T distribution, at a df = 7-1 = 6:

p-value = 0.025*2 = 0.05

To reject the null hypothesis, p-value must be less or equal than α. Since they are equal, reject the null hypothesis, i.e., reject the claim suggesting the 2 methods provide the same mean value for natural vibration frequency.

(b) For a CI = 95%:

t-score for α = 0.025 and df = 6 is 2.447.

mean ± [tex]t.\frac{s}{\sqrt{n} }[/tex]

-5.51 ± 2.447.[tex]\frac{5.89}{\sqrt{7} }[/tex]

-5.51 ± 5.4471

lower limit: -5.51 - 5.4471 = - 10.957

upper limit: -5.51 + 5.4471 = - 0.063

The interval on the mean difference is (-10.957,-0.063)

Answer:

-3a

Step-by-step explanation:

3(-a)

Expand brackets.

3 × -1a

-3a