Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. 2 4 6 8 10 amount of sugar (mg) 180 182 184 186 188 190 192 194 Frequency What is the sample size for this data set?

Answer:

156.75 tons

Step-by-step explanation:

627/4 = 156.75

Answer:

156(3/4)

Step-by-step explanation:

with this your divide.

627/4=156.75

as a mixed numer it would 156(3/4). It is 3/4 because the number ends in .75

Answer:

16

Step-by-step explanation:

(-8)^4/3

-(8^1/3)⁴

-(∛8)⁴

-(2)⁴

-2⁴

= 16

Answer: the ^^^^ right I check it

Step-by-step explanation:

Answer: 14 cans

Step-by-step explanation:

Given, Total area to paint = 400 square meters

approximately 3.28 feet in a meter.

So, 400 square meters = 400 x (3.28)² square feet

i.e. Total area to paint  = 4303.36 square feet

One gallon of paint requires for every 300 square feet.

One liter contains approximately 0.264 gallons

Then, One gallon = [tex]\dfrac{1}{0.264}\approx3.78\text{ liters}[/tex]

So, 3.78 liters paint requires for every 300 square feet.

Paint requires for each square feet = (3.78)÷(300) liters

Total paint required  = (Total area to paint ) x (Paint requires for each square feet)

= (4303.36)x (3.78)÷(300)

≈54.22 liters

Each can contains 4 liters of paint.

Smallest number of cans required = (Total paint required )÷ 4

=(54.22 ) ÷ 4

= 13.55≈ 14

Hence, 14 cans are required .

Answer:

See below

Step by step explanation

[tex] \tan( \frac{\pi}{4} + A) \tan( \frac{3\pi}{4} + A) = - 1 [/tex]

L.H.S

[tex] \tan( \frac{\pi}{4} + A) \tan( \frac{3\pi}{4} + A ) [/tex]

We know that ,

[tex] \tan(A + B) = \frac{tan \: A + tan \: B}{1 - \tan \: A \: \tan \: B } [/tex]

[tex]( \frac{ \tan( \frac{\pi}{4} + \tan \: A ) }{1 - \tan \frac{\pi}{4} \tan \: A} ) \: (\frac{ \tan \frac{3\pi}{4} + \tan \: A}{1 - \tan \frac{3\pi}{4} \tan( \: A) } )[/tex]

[tex]( \frac{1 + \tan \: A }{1 - \tan\: A} )( \frac{ \tan( x - \frac{x}{4} + \tan \: A ) }{1 - \tan(\pi - \frac{\pi}{4} ) \: \tan \: A }) [/tex] (tan π / 4 = 1 )

[tex]( \frac{1 + \tan \: A}{ -1 - \: \tan \: A } )( \frac{ - \tan( \frac{\pi}{4} + \tan \: A ) }{1 - ( - \tan \: \frac{\pi}{4}) \: \tan \: A } )[/tex] [ tan ( π - B ) = - tan∅ ]

[tex]( \frac{1 + tan \: A}{1 - tan \: B} )( \frac{ - 1 + \tan\: A }{1 + \tan \: A } )[/tex]

[tex] = \frac{ - (1 - \tan\: A)}{(1 - \tan \: A) } [/tex]

[tex] = - 1[/tex]

Hope this helps..

Best regards!!

Answer:

Maybe D-DE

Step-by-step explanation:

Because D has been decrease to E

Answer:

they represent the same line

Step-by-step explanation:

i went to desmos graphing calculator and put x+3y=5 in the first spot then i put 4x+12y=20 below that and it showed me what the lines looked like

Both the equation represent the same line

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

x + 3y = 5

4x + 12y = 20

Now , the equation 4x + 12y = 20 can be simplified as

4x + 12y = 20

Divide by 4 on both sides ,

x + 3y = 5

Therefore , x + 3y = 5 is the same equation

Hence , both the equation represent the same line

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Answer: options 2,3and 6

Answer:

option

2-Twelve students answered Mr. Chiu’s question.

3-Three people studied for two hours.

6-Four people studied for four or more hours.

Step-by-step explanation:

hope this helps:)

Answer:

here,

A=2×22÷7×17/2×21

A=22×17×3

A=1122 sq.cm

Answer:

[tex]\boxed{x = 15}[/tex]

Step-by-step explanation:

Let the number be x

Condition:

[tex]2x - \frac{2}{3} x = 20[/tex]

Multiplying 3 to both sides

=> 3(2x) - 2x = 3(20)

=> 6x - 2x = 60

=> 4x = 60

Dividing both sides by 4

=> x = 15

Answer:

15

Step-by-step explanation:

Let x be that number.

2/3 of x subtracted from twice of x is 20.

2x - 2/3x = 20

Solve for x.

Combine like terms.

4/3x = 20

Multiply both sides by 3/4

x = 60/4

x = 15

The number is 15.

Answer:

Option (1)

Step-by-step explanation:

Congruent complements theorem;

"If two angles are complementary to the same angle, then these angles are congruent to each other."

It's given that ∠4 and ∠5 are the complements and ∠1 and ∠5 are compliments.

Which shows ∠1 and ∠4 are complimentary to the same angle ∠5.

Therefore, ∠1 and ∠4 will be congruent.

Option (1) will be the answer.

Answer:

1

Step-by-step explanation:

Answer:

Step-by-step explanation:

29 is 6 more than K

Let's create an equation

[tex]29 = 6 + k[/tex]

Move variable to L.H.S and change its sign

Similarly, move constant to R.H.S and change its sign

[tex] - k = 6 - 29[/tex]

Calculate

[tex] - k = - 23[/tex]

Change the sign on both sides of the equation

[tex]k = 23[/tex]

Hope this helps..

Best regards!!

The equation for the statement 29 is 6 more than K is solved and K = 23

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists  mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by the statement below

29 is 6 more than K

On simplifying , we get

29 = 6 + K

Subtracting 6 on both sides , we get

K = 29 - 6

K = 23

Therefore , the value of K is 23

Hence , the equation is K = 23

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Answer:

12 / 253

Step-by-step explanation:

There are a total of 4 + 4 + 9 + 6 = 23 cookies in the bag, therefore, there are 23 * 22 = 506 ways to pick one cookie, eat it, and then pick another cookie. There are 6 ways to choose the first cookie (because there are 6 oatmeal cookies) and 4 ways to choose the second cookie (because there are 4 chocolate chip cookies) so there are 6 * 4 = 24 successful ways. The probability is thus 24 / 506 = 12 / 253.

Answer:

t = kp, i think

Answer:

21 feet 4 inches

Step-by-step explanation:

Ellie bought two planks of wood that were each 4ft 3in long

Total length of these two planks = 4ft 3in + 4ft 3in = 8 feet 6 inches

she also bought  two planks of wood that were each 6 ft 5in long

Total length of these two  6 ft 5in planks =  6 ft 5in +  6 ft 5in = 12 feet10 inches

Thus, total length of all the woods purchased = Total length of 4ft 3in two planks  + Total length of the two  6 ft 5in planks

= 8 feet 6 inches + 12 feet 10 inches

adding feet with feet and inches with inches term

= 20 feet 16 inches

we know that 12 inches is equal to 1 feet

thus, 16 inches can be written as 1 feet 4 inches

thus,

20 feet 16 inches will be same as 21 feet 4 inches

The total length of the wood Ellie purchased is 21 feet 4 inches.

Answer:

56

Step-by-step explanation:

The range is the right line value minus the left line value

140 - 84

56

Step-by-step explanation:

Q8.  

Step 1.

35.4 - 31 = 4.4

Step 2.

4.4 ÷ 31 = 0.1419....

Step 3.

0.1419.... x 100 = 14.19...

Step 4.

To one decimal place = 14.2% increase

Q9.

Step 1.

£10 ÷ 40 articles = £0.25 = 25p (this is the answer to part a)

Step 2.

32p x 40 articles = £0.32 x 40 articles = £12.80 (this is the answer to part b)

Step 3.

£12.80 - £10 = £2.80 (this is the answer to part c)

Step 4.

£2.80 ÷ £10 = 0.28

Step 5.

0.28 x 100 = 28% (this is the answer to part d)

Hope this was what you were looking for :)

(Also, hi to a fellow Brit - there aren't that many of us around here)

Bluey :)

Answer:

Continous distributions:

- A probability distribution showing the average number of days mothers spent in the hospital.

- A probability distribution showing the weights of newborns.

Step-by-step explanation:

A probability distribution showing the number of vaccines given to babies during their first year of life will have a discrete distribution as only a natural number can represent the number of vaccines (0, 1, 2 vaccines and so on).

A probability distribution showing the average number of days mothers spent in the hospital can be described as continous because we are averaging days and this average can be fractional, so it is not discrete.

A probability distribution showing the weights of newborns is continous, as the weights are a continous variable (physical measurement), not discrete.

A probability distribution showing the amount of births in a hospital in a month is a discrete distribution, as the number of births can only be represented by natural numbers.

The option that describes a continuous distribution include:

A continuous distribution simply means the probabilities of the values of a continuous random variable.

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Answer:  1) [tex]\pm \sqrt{x+4}[/tex]

               2) see graph

               3) Choose one color from the graph

               4) D: x ≥ -4

                   R: y ≥ 0 for [tex]\sqrt{x+4}[/tex]     or      y ≤ 0   for [tex]-\sqrt{x+4}[/tex]

Step-by-step explanation:

1) To find the inverse, swap the x's and y's and solve for y:

Given: y = x² - 4

Swap: x = y² - 4

    x + 4 = y²

  [tex]\pm \sqrt{x+4}=y[/tex]

2) see attachment. Red and Blue combined creates the graph of the inverse.

3) Choose either the positive (red graph) or the negative (blue graph).

red graph: [tex]y= \sqrt{x+4}[/tex]

blue graph: [tex]y= -\sqrt{x+4}[/tex]

4) Domain reflects the x-values of the function.  The x-values for the red graph is the same as the blue graph so the answer will be the same regardless of which equation you choose.

Domain: x ≥ 0

Range reflects the y-values of the function.  The y-values differ between the positive and negative inverse functions. Positive is above the x-axis. Negative is below the x-axis.

Range (red graph): y ≥ 0 for  [tex]y= \sqrt{x+4}[/tex]

Range (blue graph):  y ≤ 0 for [tex]y= -\sqrt{x+4}[/tex]

Answer:

Step-by-step explanation:

From the give information: A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 275 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                           53                    17                      70

Not Vaccinated                    62                    143                   205

Total                                     115                     160                  275

In this study, we have two variables   ( Vaccination and diseases status ) The null and the alternative hypothesis can be stated as follows:

Null hypothesis: The two variables   ( Vaccination and diseases status ) are independent

Alternative hypothesis : The two variables   ( Vaccination and diseases status ) are dependent

The Chi-square test statistics can be computed as:

The Expected Values for the table can be calculated by using the formula:

[tex]E_i=\dfrac{row \ total \times column \ total}{grand \ total}[/tex]

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                       29.273                 40.727              70

Not Vaccinated                85.727                 119.273             205

Total                                     115                     160                  275

[tex]Chi - Square \ X^2 = \dfrac{(O_i-E_i)^2}{E_i}[/tex]

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                       19.232                13.823              33.055

Not Vaccinated                6.564                 45.573              52.137

Total                                  25.796               59.396             85.192

Therefore;

the Chi-Square Test Statistics = 85.192

For this study; we two rows and two columns

Therefore, the degree of freedom = (rows-1) × (columns-1)

the degree of freedom = (2 - 1) × (2 - 1)

the degree of freedom =  1 × 1

the degree of freedom =  1

Using the level of significance of ∝ = 0.05 and degree of freedom = 1 for the chi-square test

The p-value for the test statistics  = 0.00001

Decision rule: Since the P-value is lesser than the level of significance , therefore we reject the null hypothesis at the level of significance of 0.05

Conclusion:

We accept the alternative hypothesis and  conclude that the two variables

(Vaccination and diseases status ) are dependent  i.e the  vaccination and disease status are related

Answer:

Step-by-step explanation:

The standard equation of an ellipse centered at the point (h,k) is

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1[/tex]

where a is the distance from the center to one of the vertex. We have the relation [tex]c= \sqrt[]{a^2-b^2}[/tex] where c is the distance from one of the focus to the center.

The distance between one vertex and the center is 5. So a=5. The distance from one focue to the center is 3. Then c =3. So we have that [tex]b^2 = a^2-c^2 = 16[/tex]

so the equation is

[tex]\frac{(x-2)^2}{25}+\frac{(y-2)^2}{16} = 1[/tex]

Given Information:

Starting population = P₀ = 47,597

rate of growth = 1.8%

Required Information:

Equation that defines the population t years = ?

Answer:

The following equation defines the population t years after 2010.

[tex]$ P(t) = 47,597e^{0.018t} $[/tex]

Step-by-step explanation:

The population growth can be modeled as an exponential function,

[tex]$ P(t) = P_0e^{rt} $[/tex]  

Where P₀ is the starting population in 2010, r is the rate of growth of the population and t is the time in years after 2010.

We are given that the starting population is 47,597 and rate of growth is 1.8%

So the population function becomes

[tex]$ P(t) = 47,597e^{0.018t} $[/tex]

Therefore, the above function may be used to estimate the population for t   years after 2010.

For example:

What is the population after 10 years?

For the given case,

t = 10

[tex]$ P(10) = 47,597e^{0.018(10)} $[/tex]

[tex]$ P(10) = 47,597e^{0.18}$[/tex]

[tex]$ P(10) = 47,597(1.1972)$[/tex]

[tex]$ P(10) = 56,984[/tex]

Answer:

A.50,000 units

B.62,500 units

C.Process A with a profit of $700,000 to maximize profit

Step-by-step explanation:

A.Calculation for the breakeven volume for Process A

Using this formula

Breakeven volume for Process A= Fixed cost/(Sales per units-Variable cost per units)

Let plug in the formula

Breakeven volume for Process A=500,000/(35-25)

Breakeven volume for Process A=500,000/10

Breakeven volume for Process A=50,000 units

B.Calculation for the breakeven volume for Process B

Using this formula

Breakeven volume for Process B= Fixed cost/(Sales per units-Variable cost per units)

Let plug in the formula

Breakeven volume for Process B=750,000/(35-23)

Breakeven volume for Process B=750,000/12

Breakeven volume for Process B=62,500 units

C. Calculation for what the company should do if the total demand (volume) is 120,000 units

Using this formula

Profit=(Total demand*(Sales per units-Variable cost per units for Process A)- Process A fixed cost

Let plug in the formula

Profit =120,000*($35-$25)-$500,000

Profit=120,000*10-$500,000

Profit=1,200,000-$500,000

Profit= $700,000

Therefore If total demand (volume) is 120,000 units, then the company should select Process A with a profit of $700,000 to maximize profit.

Greetings from Brasil...

See the attached figure. The smaller the θ angle, the smaller the AB side will be. If the angle θ = 90º, then AB = 25. As θ < 90, then AB < 25

5X - 10 < 25

5X < 25 + 10

X < 35/5

X < 7

The AB side can be neither zero nor negative. So

5X - 10 > 0

5X > 10

X > 10/5

X > 2

Answer:

Cosx is the answer.

Step-by-step explanation:

We have to simplify the trigonometric fraction given in this question.

[tex]\frac{\text{Cotx}}{\text{Cscx}}[/tex]

Further we can rewrite this ratio in the simplified form.

Since, Cot x = [tex]\frac{\text{Cosx}}{\text{Sinx}}[/tex] and Cosec(x) = [tex]\frac{1}{\text{Sinx}}[/tex]

Now substitute these simplified forms of Cotx and Cscx in the given fraction.

[tex]\frac{\text{Cotx}}{\text{Cscx}}[/tex] = [tex]\frac{\frac{\text{Cosx}}{\text{Sinx}}}{\frac{1}{\text{Sinx}}}[/tex]

      = [tex]\frac{\text{Cosx}}{\text{Sinx}}\times \text{Sinx}[/tex]

      = Cosx

Therefore, Cosx will be the answer.

Answer:

387

Step-by-step explanation:

The required sum of the arithmetic series 19+25+31+37+… Where n=9 is 387.

An arithmetic series is given,19+25+31+37+… sum of this series is to be determined where n=9.

Arithmetic progression is the series of numbers that have a common difference between adjacent values.

Here,
The Sum of an arithmetic series is given as
[tex]Sn=n/2(2a+(n-1)d)[/tex]
Where n (total terms) =9
            a  (first term) = 19
             d (common difference) = 6
Now,
[tex]S_9=9/2(2*19+(9-8)6)\\ S_9=9/2(38+64)\\S_9=9/2*86\\S_9=387[/tex]

Thus, the required sum of the arithmetic series 19+25+31+37+… Where n=9 is 387.

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Answer: 3 hours

Step-by-step explanation:

Here is the correct question:

Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 6 hours to paint a house alone. How long does it take karen to paint a house working alone?

Since Betty takes 6 hours to paint a house alone, that means she can paint 1/6 of the house in 1 hour.

Karen can also paint 1/x in 1 hour

Both of them will paint the house in 3/2 hours.

We then add them together which gives:

1/6 + 1/x = 3/2x

The lowest common multiple is 6x

1x/6x + 6/6x = 9/6x

We then leave out the denominators

1x + 6 = 9

x = 9 - 6

x = 3

Karen working alone will paint a house in 3 hours.

For any isosceles right triangle (aka 45-45-90 triangle), the hypotenuse is always equal to sqrt(2) times the leg. If x is the leg and y is the hypotenuse, then

[tex]y = x*\sqrt{2}[/tex]

which solves to

[tex]x = \frac{y}{\sqrt{2}}[/tex]

from here we plug in the given hypotenuse y = 10 to get the final answer. Optionally we could rationalize the denominator, but your teacher has chosen not to.

Answer:b

On edge

Step-by-step explanation:

Answer:

C. With 99% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

Step-by-step explanation:

A confidence interval let us make an inference about a population parameter from a sample statistic. In this case, a sample proportion let us infere aout the population proportion with a certain degree of confidence.

With this confidence interval, we are 99% confident that the polpulation proportion falls within this interval. This means that there is 99% chances of having the population proportion within this interval.

To estimate the population proportion of adults who do not believe in UFO's we should have to construct another confidence interval with the proportion (1-p), but this parameter can not be estimated from the confidence interval for p.

Answer:

5sqrt(2)

Step-by-step explanation:

you can split 50 into sqrt(25×2)

and the sqrt(25) is 5, so than your left with just the 2 in the sqrt.

Answer:

(a) 25 degrees

(b) -11 degrees

(c) 38 degrees

Step-by-step explanation:

The temperature function is:

[tex]T(t) = -t^2+4t+34[/tex]

(a) The average value for a temperature is:

[tex]M=\frac{1}{b-a}* \int\limits^b_a {f(x)} \, dx[/tex]

In this particular case, the average temperature is:

[tex]M=\frac{1}{9-0}* \int\limits^9_0 {T(t)} \, dt \\M=\frac{1}{9}* \int\limits^9_0 {(-t^2+4t+34)} \, dt \\M=\frac{1}{9}* {(-\frac{t^3}{3}+2t^2+34t)}|_0^9\\M=\frac{1}{9}*( {(-\frac{9^3}{3}+2*(9^2)+34*9)-0)[/tex]

[tex]M=25[/tex]

The average temperature is 25 degrees.

(b) The expression is a parabola that is concave down, therefore there are no local minimums, which means that the minimum temperature will be at one of the extremities of the interval:

[tex]T(0) = -0^2+4*0+34=34\\T(9) = -9^2+9*4+34=-11[/tex]

The minimum temperature is -11 degrees.

(c) The maximum temperature will occur at the point for which the derivate of the temperature function is zero:

[tex]T(t) = -t^2+4t+34\\T'(t)=-2t+4=0\\2t=4\\t=2[/tex]

At t = 2, the temperature is:

[tex]T(2) = -2^2+4*2+34=38[/tex]

The maximum temperature is 38 degrees.