a manufacturer must test that his bolts are 4.00cm long when they come off the assembly line. he must recalibrate his machines if the bolts are too long or too short. after sampling 196 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.14cm. he knows that the population standard deviation is 0.83cm. assuming a level of significance of 0.05, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?

The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet

Let x represent the length of the fence and y represent the width of the fence.

Since the area is 3750, hence:

Area = length * width = x * y

3750 = xy

y = 3750/x

A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:

Amount of fencing needed (P) = x + x + y + y  + y = 2x + 3y

Amount of fencing needed (P) = 2x + 3(3750/x) = 2x + 1800/x

To minimize the amount of fencing needed, dP/dx = 0, hence:

dP/dx = 2 - 1800/x²

2 - 1800/x² = 0

2 = 1800/x²

2x² = 1800

x² = 900

x = 30 feet

y = 600/x = 600/30 = 20 feet

Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet

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Answer: -3/7

Step-by-step explanation:

So the fomula for slope is m=x2-x1/y2-y1

if (6,6) is our first coordinate and (3,13) is our second that means 6 is x1 and 3 is x2. 6 will be y1 and 13 will be y2. now we plug in the numbers

m=3-6/13-6

m= -3/7

The converse, inverse and contrapositive statements for the given conditional statement are :

Converse: if I sleep well, then I go to be early

Inverse: if I don't go to be early, then I don't sleep well

Contrapositive: if I don't sleep well, then I don't go to be early.

A conditional statement is a part of mathematical reasoning which is a critical skill that enables students to analyze a given hypothesis without any reference to a particular context or meaning.

Given is a conditional statement, "If I go to be early, then I sleep well", we need to form its converse, inverse and contrapositive statements,

The rules for the given conditional statement are ;

Let p and q be the parts of the statement,

1) Converse statement = if p then q, converse = if q then p.

Therefore,

Converse: if I sleep well, then I go to be early.

2) Inverse statement = if p then q, inverse = if not p then not q.

Therefore,

Inverse: if I don't go to be early, then I don't sleep well.

3) Contrapositive statement = if p then q, Contrapositive = if not q then not p.

Therefore,

Contrapositive: if I don't sleep well, then I don't go to be early.

Hence, the converse, inverse and contrapositive statements for the given conditional statement are :

Converse: if I sleep well, then I go to be early

Inverse: if I don't go to be early, then I don't sleep well

Contrapositive: if I don't sleep well, then I don't go to be early.

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With the help of unitary method , we can say that ,To create a batch of 15%-pigment paint, he needs to mix 98.57 liters of the 27%-pigment paint with the 12%-pigment paint.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

Paint volume times pigment concentration equals pigment amount.

or

V × c = P

If the three options are referred to as 1, 2, and 3, then

P₁ + P₂ = P₃

V1c1 = V2c2 + V3c3

Let x equal the paint's 11% volume.

Then

230 × 21 % + x × 11 % = (230 +x) × 18 %

Add 4830 plus 11x to get 4140 plus 18x, then take 4140 away from each side.

690 + 11x = 18x Take 11 times off of each side.

Divide each side of 690 by 7 to get the answer.

x = 98.57 L

The worker needs to add 98.57 L of the paint with a 21% pigment.

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Answer: 3

Step-by-step explanation:

Answer:

length of base = 9 feet

Step-by-step explanation:

b= base   A= area   h= height

[tex]b=2*\frac{A}{h} = 2*\frac{29.25}{6.5} = 9[/tex]

The mean median mode of the data 9,10,9,9,11,9,10,9,9,10 is

Mean =9.5

Median = 11 or 9

Mode is 9

Given that,

The data is 9,10,9,9,11,9,10,9,9,10

The data's mean, median, and mode must be determined.

We know that,

The arithmetic mean of the provided data is another name for mean. If the data are grouped and sorted in ascending order, the median is the value that falls in the middle of the set of grouped data. The value that dominates the data is known as the mode. The Mean, Median, and Mode formulas are described independently for the group of data in the sections that follow.

The data is 9,10,9,9,11,9,10,9,9,10

Mean = 9+10+9+9+11+9+10+9+9+10/10 =95/10=9.5

Median = 11 or 9

Mode is 9

Therefore, The mean median mode of the data 9,10,9,9,11,9,10,9,9,10 is

Mean =9.5

Median = 11 or 9

Mode is 9

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Answer: $38.50 per month

Step-by-step explanation: We have to find 10% of 35 and add it to 35. This is because 10% of 35 is the amount that will increase so adding that to the original 35 will be her new premium. 10% of 35 is $3.50 and $3.50 + $35 is $38.50. This means her new premium is $38.50 per month.

Answer:

p represents the original per pound price

3p represents the cost of three pounds

3p + 3(0.75) = 5.88           multiply

3p + 2.25 = 5.88               subtract 2.55 from both sides

3p = 3.63                          divide both sidesby 3

p = 1.21

The original price was $1.21 per pound.

1.21 = 0.75

1.96

3(1.96)

5.88

The percentage of water in the milk cup and the percentage of milk in the water cup are same.

What is milk?

A white liquid meal called milk is generated by mammals' mammary glands. Before they can digest solid food, it is the main source of nutrition for young mammals. Milk immunity is influenced by immune components and immune-modulating elements.

Given:

There are a cup of milk and a cup of water.

Take one teaspoon of milk, put into the water cup; mix well.

Take one teaspoon of the mixture in the water cup and put into the milk cup then mix well.

Suppose the percentage of water cup are 'p' and the percentage of milk cup are 'q'.

When we add one teaspoon of milk and put into water cup then the percentage of water cup are 'p + 1'.

And the percentage of milk cup are 'q - 1'.

Again one teaspoon of mixture in the water cup put into the milk cup.

So, the percentage of milk cup are, q - 1 + 1 = q.

And the percentage of water cup are p + 1 - 1 = p.

The percentage will be same for both milk cup and water cup.

Hence, the percentage of water in the milk cup and the percentage of milk in the water cup are same.

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What grade is that?

Step-by-step explanation:

The FALSE condition for the given inequality 3(n−6)<2(n+12) is (D) S:{42}.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

So, we have the inequality: 3(n − 6) < 2(n + 12)

Now, verify the false inequality as follows:

(A) S:{−5}

3(n − 6) < 2(n + 12)

3(-5 − 6) < 2(-5 + 12)

3(-11) < 2(7)

-33 < 14: TRUE

(B) S:{3}

3(n − 6) < 2(n + 12)

3(3 − 6) < 2(3 + 12)

3(-3) < 2(15)

-9 < 30: TRUE

(C) S:{12}

3(n − 6) < 2(n + 12)

3(12 − 6) < 2(12 + 12)

3(6) < 2(24)

18 < 48: TRUE

(D) S:{42}

3(n − 6) < 2(n + 12)

3(42 − 6) < 2(42 + 12)

3(36) < 2(54)

108 + 108: FALSE

Therefore, the FALSE condition for the given inequality 3(n−6)<2(n+12) is (D) S:{42}.

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Correct question:

Given the inequality 3(n − 6) < 2(n + 12), determine which integer makes the inequality false.

a. S:{−5}

b. S:{3}

c. S:{12}

d. S:{42}

The confidence interval for a proportion should be constructed since the variable of interest is a person's opinion, which is a qualitative variable.

A trait that cannot be quantified is referred to as a categorical variable (also known as a qualitative variable).

Nominal or ordinal categorical variables are also acceptable.

Since the variable of interest is a person's opinion, which is a qualitative variable, the confidence interval for a proportion should be built.

Statistical Variables Qualitative variables also referred to as categorical variables are variables without a built-in sense of hierarchy.

As a result, they are quantified using a nominal scale.

For instance, a qualitative variable is a name as well as hair color (Black, Brown, Gray, Red, Yellow).

Therefore, the confidence interval for a proportion should be constructed since the variable of interest is a person's opinion, which is a qualitative variable.

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Answer:

3. 70 degrees

4. 110 degrees

Step-by-step explanation:

3. The angles are mirrored on both sides

4. A straight line is equal to 180 degrees so if <AED is 70 degrees then you would do 180-70 to get 110 degrees

Answer:

I would be C

Step-by-step explanation:

lookup here

For the two lines to be parallel, the value of n must be 3

When two straight lines are plotted on the coordinate plane, we can tell if they are parallel from the slope, of each line. If the slopes are the same then the lines are parallel.

The slope of each line is calculated as (y2-y1)/x2-x1

for line AB, the slope = (6n-n)/10-4 = 5n/6

for line CD, the slope= 8n-(-6)/9-(-3)=( 8n+6)/12

for AB and CD to be parallel,

5n/6 = (8n+6)/12

multiply both sides by 12

10n= 8n+6

collect like terms

10n-8n= 6

2n= 6

n= 6/2= 3

therefore for the value of n= 3 line CD and AB are parallel.

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The required solution to the trigonometry equation is x = π/4 + π n.

The equation of trigonometry functions is given in the question as

secx - cscx = 0

We have to determine the solution to the given equation

As per the question, we have

⇒ secx - cscx = 0

⇒ 1/cosx - 1/sinx = 0

⇒ (-cosx + sinx)/cosxsinx = 0

Using property : f(x)/g(x) = 0 ⇒ f(x) = 0

⇒ -cosx + sinx = 0

Divided by cosx into the equation,

⇒ -1 + tanx = 0

⇒ tanx  = 1

The general solution for tan tanx  = 1 is

⇒ x = π/4 + π n

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Answer:

5r

Step-by-step explanation:

r+r+r+r+r=5r

Answer:

Yes, the point (-7, 5) satisfies the inequality y > -3/7x + 2

Step-by-step explanation:

Plug in the values to the inequality and verify if it is true:

x = -7, y = 5

5 > (-3/7*-7) + 2

5 > (-3/-49) + 2

5 > 3/49 + 2

5 > 101/49

The inequality above is true (5 is greater than 101/49 [101/49 is about 2.06]), so the point (-7, 5) satisfies y > -3/7x + 2

The radius of the circle  with arc length of 2.4 and subtended angle at the center, 7.1 radians is 0.3

The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.

length of arc = 2.4

if 7.1 rad is the angle subtended by the intercepts of the arc

But [tex]\pi[/tex] rad = 180°

so 7.1 rad in degree = [tex]\frac{7.1}{\pi }[/tex] x 180  which is [tex](\frac{1278}{\pi } )^{} }[/tex] degree which is [tex]\alpha[/tex]

Length of an arc = [tex]\frac{\alpha }{360} * 2\pi r[/tex]

2.4 =  [tex](\frac{1278}{\pi } )^{} }[/tex] x [tex]\frac{1}{360}[/tex] x 2 x [tex]\pi[/tex] x r

The equation reduces to

2.4 = 7.1r

r = 2.4 ÷ 7.1

r = 0.334 which is 0.3

In conclusion the radius of the circle is 0.3

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Answer:

Show that the ratios UV/XY and WV/ZY are equivalent, and ∠V ≅ ∠Y.

The probability that one of the first five customers agrees to take the survey is 71%

Here we have to use binomial distribution.

What is binomial distribution?

A common probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It provides a summary of the number of trials when each trial has an equal chance of producing a particular result.

A binomial distribution with the following formula could be used to represent the proportion of clients who agree to participate in the survey out of 5:

X ~ Bin (n = 5, p = 0.22)

Thus the probability is computed as:

P(X >= 1) = 1 - P(X = 0) = [tex]1 - (1-0.22)^5[/tex]

= 0.71

The required probability in this case is therefore 71%.

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The percentage of racers that  did not complete the marathon is 12.9 %

What is arithmetic?

Arithmetic is an elementary a part of mathematics that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots

Main Body:

Total racers = 240

racers that completed race = 209

so racers that did not complete the marathon = 240 - 209

 = 31

percentage of racers that  did not complete the marathon = (31/240)*100

                                                                           = 12.9 %

Hence percentage of racers that  did not complete the marathon is 12.9%

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The number of tickets that they give away to employees is 33.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenarios.

Let the number of employees be x

Therefore, number of listener = 5x

Total number of people = 198

Therefore, this will be illustrated thus:

x + 5x = 198

6x = 198

Divide

x = 198/6

x = 33

Therefore 33 tickets are given to employees.

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The maximum volume of this cylinder = 256π  cubic inches

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

Let h be the height and r be the radius.

Then, h+r = 12

=> h=12-r

Volume of the cylinder (V):

V=πr²h

=> h= πr² ( 12-r )

=> h=  π ( 12r² - r³ )

Differentiate with respect to r , we get

dv/dr = 24 πr - 3πr²

Find r by taking dv/dr=0

24 πr - 3πr²  = 0

3π ( 8r - r² ) = 0

8r = r²

r=8

Again differentiating, we get

d²V/dr² = 24π - 6 π r

When r=8, 24π - 48 π  <0

So, V is maximum at r= 8 inches

And h= 12-8= 4 inches

Hence, the required volume of the cylinder = π8²*4 = 256π  cubic inches

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Answer:

Step-by-step explanation:

fx+35+lovebased2=94

The slope and y-intercept of the given equations of line are shown below.

When any equation is represented in the y = mx +c form, it is called the slope intercept from of the equation.

Here m is slope and c is constant.

(1)

y = 3x + 3

Slope m = 3

y intercept, at x =0,

y = 3

(2)

y = 3x - 3

Slope m = 3

y intercept, at x =0,

y = - 3

(3)

y = (1/3)x + 3

Slope m = 1/3

y intercept, at x =0,

y = 3

(4)

y = -(1/3)x + 3

Slope m = -1/3

y intercept, at x =0,

y = 3

(5)

y = (1/3)x - 3

Slope m = 1/3

y intercept, at x =0,

y = -3

(6)

y = -(1/3)x - 3

Slope m = -1/3

y intercept, at x =0,

y = -3

(7)

y = -3x + 3

Slope m = -3

y intercept, at x =0,

y = 3

(8)

y = -3x - 3

Slope m = -3

y intercept, at x =0,

y = - 3

The slope and y-intercept are shown above.

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Answer:To help read it step by step until you understand trust me you will get it!

Step-by-step explanation:

The total volume of the ice cream in and on top of the cone is (16/3)πd³.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3 πr²h.

We have,

Volume of the hemisphere = 4 in³

The volume of ice cream.

= Volume of the hemisphere + Volume of the cone

= 4 + (1/3)π(d/2)²h

[ height = diameter ]

= 4 + (1/3) x π x d²/4 x d

= 4 + (1/3) x π x d³/4

= 4 + (4/3)πd³

= (16/3)πd³

Thus,

The volume of the ice cream is (16/3)πd³.

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Avea received 28 stickers when brianna, and carson in the ratio 1:3:4 and  brianna received 21 stickers.

The ratio is defined as the comparison of two or more quantities of the same units, which shows how much bigger one quantity is than another.

Given,The ratio of the distribution of stickers among Avea, Brianna and Carson is 1:3:4

The number of stickers Briana received is 21

Let us consider x as the common factor of the given ratio then, The number of stickers received by the girls are

Avea = xBriana = 3x

Carson = 4x

As we know 3x = 21 x

 = 21/3

= 7

then,4x

= 4×7

= 28

The number of stickers that Avea received is 28. Hence, the answer is 28

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