solve with clear steps pleaseQuestion 5 Evaluate the integral. 2x² 3+x dx Solution:

Using a 35-bag sample with a mean of 406.0 grams, a known standard deviation of 25.0 grams, and a level of significance of 0.05, you can perform a one-tailed Z-test to determine whether to reject or fail to reject the null hypothesis.

To test if the potato chip manufacturer's bag filling machine is working correctly at the 411.0-gram setting, we will state the hypotheses using the given terms.

Null Hypothesis (H0): The machine fills bags correctly, with a mean weight of 411.0 grams (µ = 411.0 grams)
Alternative Hypothesis (H1): The machine is underfilling bags, with a mean weight less than 411.0 grams (µ < 411.0 grams)

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Answer:

y = 2x - 10

Step-by-step explanation:

y2 - y1/ x2 - x1

0 - 2 / 5 - 6

= 2

y = 2x + b

2 = 2(6) +b

2 = 12 + b

-10 = b

The equation is y = 2x - 10

Answer:

10

Step-by-step explanation:

A perfect square of \((a-b)^2\) should be in the form \(a^2-2ab+b^2\). In this case, \(a^2=1\), and \(b^2 =25\), so a=1 and b=5. Now, we need to find 2ab, so we do

2(1)(5)=10, so 10 goes in the blank.

Never. Correlation coefficients are used to measure the strength of a linear relationship between two variables, not to prove cause and effect. To determine causation, it is necessary to conduct an experiment or study in which the independent variable is manipulated and the dependent variable is measured.

Correlation coefficients are used to measure the strength of a linear relationship between two variables. They can measure the degree to which variables move together, but they cannot be used to prove cause and effect. To determine causation, it is necessary to perform an experiment or study in which one variable is manipulated and the other is measured. This allows researchers to control for confounding variables and to determine if the manipulation of the independent variable had a direct effect on the dependent variable. Therefore, correlation coefficients cannot be used to support a claim of cause and effect.

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Answer:

add it + 2

Step-by-step explanation:

If there is orange with a volume of 113.1 cm3, the area of the cross-section when the orange is cut in half is approximately 34.9 sq cm.

If we assume that the orange is a sphere and has a volume of 113.1 cm3, we can use the formula for the volume of a sphere to find the radius of the orange. The formula for the volume of a sphere is V = (4/3) * pi * r^3, where r is the radius of the sphere.

Substituting the given volume of 113.1 cm3 and solving for the radius r, we find that r = (3V / (4 * pi))^(1/3) = (3 * 113.1 / (4 * pi))^(1/3) approximately 3.3 cm.

Next, we can use the formula for the surface area of a sphere to find the area of the cross-section when the orange is cut in half. The formula for the surface area of a sphere is A = 4 * pi * r^2, where r is the radius of the sphere. Substituting the value of the radius that we calculated above, we find that the area of the cross-section is A = 4 * pi * (3.3 cm)^2 approximately 34.9 sq cm.

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Answer:

Step-by-step explanation:

A function does not have any repeating domains (x-coordinates).

Hope it helps!

Answer:

\(y=0.400x+-0.800\)

Step-by-step explanation:

Given the following question:

point A = (-3, -2)
point B = (2, 0)

To write the equation of the line that passes through two points we have to write the points in slope intercept form.

Formula for slope intercept:

\(y=mx+b\)

M is equal to the slope of the two points, so first we need to fine the slope of the two points.

\((-3,-2)=(x1,y1)\)
\((2,0)=(x2,y2)\)

\(m=\frac{y2-y1}{x2-x1}\)
\(m=\frac{0--2}{2--3} =\frac{2}{5}\)
\(m=\frac{2}{5} =0.400\)

\(y=mx+b\)
\(y=-2\)
\(m=0.400\)
\(x=-3\)
\(-2=0.400(-3)+b\)
\(0.400\times-3=-1.20\)
\(-2+1.2=-0.800\)
\(b=-0.800\)

\(y=0.400x+-0.800\)

Hope this helps.

Answer:

8 gallons

Step-by-step explanation:

Already a question from another person.

Answer:

5 gallons

Step-by-step explanation:

Answer:

He traveled 520 miles

Step-by-step explanation:

8 x 65 = 520

Answer: 520 miles

Step-by-step explanation:

Data: Juan drove 8 hours

Drove at an average Speed of 65 mph

Miles driven=x

Only step: Multiply 65 by 8 which is 520

Explanation: Since Juan drove at an average speed of 65 miles per hour, that means he drove 65 mile for every hour he drove. So since he drove for 8 hours, you multiply 8 hours by 65 miles so that you get get the total amount of hours driven by him.

Don't forget to add "Miles" to the end of your answer because most math teachers tend to want that in an answer like this.

I hope this helps(Mark brainiest if you want to, thanks)

Answer:

help with what? you can tell me and I would be glad to answer.

Step-by-step explanation:

For the given figure, where m and nare relatively prime positive integers. The value of m+n is 32.

The law of cosines, also known as the law of cosines, relates all three sides of a triangle to one angle of the triangle. Most useful for searching for missing information in triangles. For example, if you know all three sides of a triangle, you can use the law of cosines to find the measure of the angle. Similarly, if you know two sides and the angle between them, you can find the length of the third side by the law of cosines.

Let X be the intersection of the circles with centers B and E, and Y be the intersection of the circles with centers C and E.

Since the radius of B is 3, AX = 4.

Assume AE = p.

Then EX and EY are radii of circle E and have length 4 + p.

AC = 8, and ∠CAE = 60° because we are given that triangle T is equilateral.

Using the Law of Cosines on Δ CAE, we obtain

(6+p)² =p² + 64 - 2(8)(p) cos 60

The 2 and the cos 60 terms cancel out:

p² + 12p + 36 = p² + 64 - 8p

12p+ 36 = 64 - 8p

p = 28/20

= 7/5

The radius of circle E is 4 + (7/5)

= 27/5,

So, the answer is 27 + 5 = 32

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Answer:

B.) 4,096 feet

Step-by-step explanation:

You were given a time, and time in the equation is represented by "t". To find the height, represented by "h", you just need to plug the given value in for "t" and simplify to find "h".

t = (1/4)√x                                         <--- Original equation

16 = (1/4)√x                                      <--- Plug 16 in "t"

64 = √x                                            <--- Divide both sides by (1/4)

4,096 ft = x                                    <--- Square both sides

The object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.

The equation is t=1/4 √x , where t is time in seconds and x is height in feet. To determine the height  x at which an object should be dropped to reach the ground in 16 seconds, you can plug in the value of t=16 into the equation:

16 = 1/4 √x

Simplify the equation by multiplying both sides by 4:

4⋅16= √x

64= √x

Now, square both sides to isolate x:

64²=x

4096 = x

Therefore, to have the object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.

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If Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.

Number of cups of blue paint for each art station = 2 cups

Given that,

One cup = 8 ounce

1 gallon = 128 ounce

2 cups of blue paint = 2 × 8

= 16 ounce of blue paint

1 gallon of blue paint = 128 ounce of blue paint

Number of jars that he can fill with 1 gallon of blue paint =  1 gallon of blue paint / 2 cups of blue paint

Here we have to use division

= 128/16

= 8 jars

Hence, if Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.

The complete question is:

Mr. dyer pours 2 cups of blue paint into a jar for each art station. how many jars can he fill with 1 gallon of blue paint? One cup = 8 ounce and 1 gallon = 128 ounce

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The sum of all angles in a triangle = 180 degree

So :

Angle x + Angle 5x + 72 = 180

x + 5x + 72 = 180

6x = 180 - 72

6x = 108

Divide both side by 6 :

6x/6 = 108/6

x = 18

x = 18

since all the angles are less than 90 degree so the triangle is an acute triangle,

as 5x = 90 thus one angle is of 90 degree

Thus triangle is Acute Right angle triangle

Answer : x = 18, acute right angle triangle

Answer:

Step-by-step explanation:

Volume of the figure = Base area * height

Base area:

Base area = area of trpezium + area of triangle

Trapezium:

a, b area the length of parallel sides and h is the height of trapezium.

a = 8 m ; b =  5 m & h = 3 m

\(\boxed{ \text{ Area of trapezium = $\dfrac{(a +b)*h}{2} $}}\)

                               \(=\dfrac{(8+5)*3}{2}\\\\\\=\dfrac{13*3}{2}\\\\\\= \dfrac{39}{2}\\\\\\= 19.5 \ m^{2}\)

Triangle:

height = 4 m & base = 8 m

\(\boxed{\text{Area of triangle =$\dfrac{1}{2}*base*height$}}\)

                           \(=\dfrac{1}{2}*8*4\\\\\\= 4*4\\\\= 16 \ m^{2}\)

Base area = 19.5 + 16

                 = 35.5 m²

Volume of the figure = Base area * height

                                     = 35.5 * 14

                                      = 497 m³

Answer:

DE/AB= DC/AC , 12/AB= 6/11 , AB= 12×11/6=2×11=22 , Sory i can't explain , i bad know english language. or so ABC~CDE because DE||AB=> DE/AB=DC/AC

The given company has two major departments: Development and Marketing. A total of twelve employees are selected randomly from each of the department and their ages are recorded. It is also mentioned that both of the departments have an employee who is of age 56 years. It is equally unusual to have a 56-year-old employee in both the departments.

To solve this problem, we need to determine the spread of the ages in each department. The spread of the ages in each department can be determined by calculating the range. The range is the difference between the maximum age and the minimum age in each department. We will then compare the range in both departments. The department with the greater range will be considered to be more unusual to have a 56-year-old employee.

The following are the ages of the employees in the Development and Marketing departments respectively: Development Department: 43, 24, 38, 56, 29, 22, 45, 47, 40, 33, 28, 30Marketing Department: 41, 56, 35, 23, 26, 49, 42, 50, 38, 29, 55, 46The range of the Development department can be calculated as: Range = Maximum Age - Minimum Age= 56 - 22= 34The range of the Marketing department can be calculated as: Range = Maximum Age - Minimum Age= 56 - 23= 33As we can see, the range in both departments is close. The range of the Development department is 34 and the range of the Marketing department is 33.

Therefore, it is difficult to determine which department is more unusual to have a 56-year-old employee. Hence, the answer is that it is equally unusual to have a 56-year-old employee in both the departments.

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This question's answer is 2 pizzas in total

Answer:

first and third

Step-by-step explanation:

the equation representing direct proportion is

y = kx ← k is the constant of proportion

y = - 4x is in this form with k = - 4

y = 7x is in this form with k = 7

The required missing values are $2.5 when the cup of milk is 1, $8.75 when the cup of milk is 3.5, and $6.25 when the cup of milk is 2.5.

The table is given in the question as :

Tea (cups) $3.75

Milk (cups) $1.5  $1   $3.5   $2.5

Let the missing value cup of tea would be x when the cup of milk is 1,

The missing value cup of tea would be y when the cup of milk is 3.5,

And the missing value cup of tea would be z when the cup of milk is 2.5,

According to the given question, we can write the ratio as:

$3.75 Tea (cups) : $1.5 Milk (cups) = x Tea (cups) : $1 Milk (cups)

⇒ 3.75 / 1.5 = x / 1

⇒ x = 3.75 / 1.5

⇒ x = $2.5

$3.75 Tea (cups) : $1.5 Milk (cups) = y Tea (cups) : $3.5 Milk (cups)

⇒ 3.75 / 1.5 = y / 3.5

⇒ y = (3.75 / 1.5) × 3.5  

⇒ y = 2.5 × 3.5  

Apply the multiplication operation,

⇒ y = $8.75

$3.75 Tea (cups) : $1.5 Milk (cups) = z Tea (cups) : $2.5 Milk (cups)

⇒ 3.75 / 1.5 = y / 2.5

⇒ z = (3.75 / 1.5) × 2.5  

⇒ z = 2.5 × 2.5  

Apply the multiplication operation,

⇒ z = $6.25

Thus, the required missing values are $2.5 when the cup of milk is 1, $8.75 when the cup of milk is 3.5, and $6.25 when the cup of milk is 2.5.

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Given :

Three trolley tours leave from the same stop at 9:00 am.

Tour A returns to the stop every 75 minutes, Tour B returns every 60 minutes, and Tour C returns every 40 minutes.

To Find :

In how many hours will all three tours return to the stop at the same time.

Solution :

We know, they will return to the stop at the same time is the L.C.M of three i.e 75, 60 and 40 minutes.

So, their L.C.M is :

L.C.M = 600 minutes.

Now, 600 minutes = 600÷60 hours = 10 hours.

Therefore, they will all meet at stop in 10 hours.

Hence, this is the required solution.

Answer:

150

Step-by-step explanation:

30+60n=30+120=150

Answer to 1:

\(\frac{x^3}{2y^25}\)

First thing you want to do is combine like terms on the bottom. Since it's multiplication, all you have to do is add the exponents. So for x you'd get x raised to the -9 power and for y you'd get 2y raised to the power of 7

Second thing is the numerator of the fraction. Since this is raising what is inside the paranthesis to a power, you must multiply this power by the powers of x and y, respectively. You should get x raised to the power of -6 and y raised to the power of -18

Here's where it gets complicated. to rationalize the problem, you must add parts from the numerator and denominator or vice versa. You cannot have any negative exponents anywhere in the fraction.  So that means for x you have to add 9 to the x on the top to cancel out the -6 and rationalize the remaining x's. You should end up with x^3.

For y, you work the opposite way. Since the negatives are only on the top, you simply add 18 to the bottom y's and it remains rationalized.

If done correctly this should come out to x^3/2y^25

Answer to 2:

(x^20y^12)/256

First thing you can do on this one is to cancel out the x^0s. Anything to the power of 0 equals one so only the coefficients will remain. Multiply those together and you'll get 4.

Next you will rationalize the ys. Add the bottom 3 to the top to cancel out the denominator and you're left with y^-3. Leave it like this for now.

Now is the difficult part. You must take everything that is inside the parenthesis to the power of -4. That includes the coefficients and the exponents. 4^-4 = 1/256. This means that you now must move the coefficients to the bottom. You should currently have y^-3/(256x^5).

Now take the exponents to the power using the same rules as question 1. -3*-4 = 12 and 5*-4 = -20. You should now have y^12/(256x^-20)

Lastly, we must rationalize the denominator. To do so, move the x^-20 to the numerator and make the exponent positive. After doing this, you have the answer: (x^20y^12)/256

Answer:

Step-by-step explanation:

Per ASCE 7, the Mean Roof Height (h) is defined as the average of the roof eave height and the height to the highest point on the roof surface, except that, for roof angles of less than or equal to 10°, the mean roof height is permitted to be taken as the roof eave height

i hope it helps

The correct conclusion is the P-value 0.028 is not significant and so does not strongly suggest that μ > 17.4

From the information given, we have that;

Population mean,  μ = 17.4,

sample mean = 18.641

Standard deviation (s = 1.905)

Sample size , n = 11

Using the the formula is given as;

t =  (x - μ) / (s / √n)

Substitute the values, we have;

t =  (18.641 - 17.4) / (1.905 / √11

t = 1.241/0.5743

Divide the values

t ≈ 2.161

Now, we have the degree of freedom as;

degree of freedom = 11 - 1 = 10

Using the t-distribution table or a statistical calculator, we have P-value as

P(0. 2151) = 0.028.

Then, we have to reject the hypothesis.

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The area of a shape is the amount of space it occupies

The area of the rectangle is \(6\frac 3{16}\) inches square

The dimensions are given as:

\(Length= 2\frac 14\)

\(Width= 2\frac 34\)

The area is then calculated as:

\(Area = Length * Width\)

So, we have:

\(Area = 2\frac14 * 2\frac 34\)

This gives

\(Area = 6\frac 3{16}\)

Hence, the area of the rectangle is \(6\frac 3{16}\) inches square

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Answer:

3

Step-by-step explanation: