Each employee can essemble 28 castles per hour. How many employees worked each hour? (What is the answer to this?)

Consider the given equation [tex]x^2-8x+14=0[/tex]

We will solve this equation by completing the square method.

Consider the coefficient of 'x', divide it by '2'. then adding and subtracting the square of this number in the given equation.

Coefficient of 'x' = -8

By dividing it by '2', we get -4

Taking the square of '-4' = 16

Adding and subtracting '16' from the given equation.

[tex]x^2-8x+14+16-16=0[/tex]

So, [tex]x^2-8x+16 = -14+16[/tex]

This equation shows one of the step used in solving the equation by completing the square method.

Therefore, option 1 is the correct answer.

For Jamal to solve the equation, [tex]x^2 - 8x + 14 = 0[/tex], by completing the square, one of the steps that could be taken is: A. [tex]\mathbf{x^2 - 8x + 16 = - 14 + 16}[/tex]

Jamal was given the equation, [tex]x^2 - 8x + 14 = 0[/tex], to solve by completing the square.

To do this, the first step would be to move the constant, 14 to the other side of the equation by subtracting 14 from both sides of the equation.

[tex]x^2 - 8x + 14 - 14 = 0 -14\\\\x^2 - 8x = -14[/tex]

The next step to take is for Jamal to add the square of half of the coefficient of x to both sides of the equation.

[tex]x^2 - 8x + 16 = - 14 + 16[/tex] (this tallies with the first option given).

Therefore, for Jamal to solve the equation, [tex]x^2 - 8x + 14 = 0[/tex], by completing the square, one of the steps that could be taken is: A. [tex]\mathbf{x^2 - 8x + 16 = - 14 + 16}[/tex]

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Answer:

[tex]x < 17.89[/tex] or [tex]x > 18.61[/tex] , since [tex]\left | x-18.25 \right |>0.36[/tex]

Step-by-step explanation:

According to the question the weight is rejected if it is more than 0.36 oz, the weight should not be beyond 0.36 oz that is from the target weight of 18.25.  

We can say that, the difference between the actual weight and the target weight is greater than 0.36 oz.

Lets say the actual weight is 'x'. So,

[tex]x-18.25>0.36[/tex]

But there can be times when the actual weight 'x' could be less than 0.36, So the order will be changed:

[tex]18.25-x>0.36[/tex]

The absolute value will sum up these two into a single inequality:

[tex]|x-18.25|>0.36[/tex]

Simplifying the inequalities, we get:

[tex]x-18.25>0.36[/tex]

[tex]x>18.61[/tex]   (we have added 18.25 on both sides)

 [tex]18.25-x>0.36[/tex]

Subtracting 18.25 from both the sides we get:

[tex]-x>-17.89[/tex]

After sign change it is:

[tex]x<17.89[/tex]

So we can see that only [tex]x < 17.89[/tex] or [tex]x>18.61[/tex] since [tex]\left | x-18.25 \right |>0.36[/tex] is the one that represents the scenario given above.

Answer:

Hence average rate of change is greater for f(x) in (0,3).

Yes. f(x) is greater than g(x) in the interval (0,3)

Yes. g(3) <f(3)

Step-by-step explanation:

To find average rate of change of f and g in (0,3)

f(3)-f(0)/3 = (9-0)/3 =3

g(3) = -9-18 = -27

g(0) = 0

Rate of change in(0,3) of g(x) = -27/3 =-9

Hence average rate of change is greater for f(x) in (0,3)

---

Both f and g have intercepts of y as 0

Hence both are equal.

3) Yes. f(x) is greater than g(x) in the interval (0,3)

Because g(x) <0 for all x in (0,3) while f(x) >0

4) g(3)= -9-18=-27 <f(3)

Answer:

1).  g(3) ​​ is less than​ f(3).

​2). The average rate of change of f(x) is greater than ​g(x)​ on the interval [0,3] .

Step-by-step explanation:

g(x) = -x^{2} - 6x

so f(3) = 9

let's solve for g(3)

3^{2} = 9

g(3) = - 9 - 18 = -27

so -27 is less than 9

g(3) < f(3)

So our answer is correct: g(3) ​​ is less than​ f(3).

In second option:

put the value from 0 to 3 in function g(x) = - x^{2} - 6x

g(0) = 0

g(1) = -7

g(2) = -16

g(3) = -27

on the other hand values of f(x) are:

f(0) = 0

f(1) = 1

f(2) = 4

f(3) = 9

So average values of f(x) are greater than g(x) so our option is correct.

The average rate of change of f(x) is greater than ​g(x)​ on the interval [0,3] .

i hope you get the idea.

Answer:

Refer answer below

Step-by-step explanation:

Given is a graph in the interval (-infinity, infinity).

From the graph we observe that it is continuous graph.

The curve is decreasing for x <-2 and increases for (-2,1) and again decreases from (1,3) then increases from (3,infinity)

Hence f'(x) >0 for (-2,1) and (3,infinity)

f'(x) <0 for (-infty, -2) and (1,3)

From the above we find that f'(x) =0 for x=-2,1,and 3

Extreme points are -2,1 and 3

Absolute and local minima at x=-2, y=-9.67

Local maxima at (1,6.08) and again

local minima at (3,0.75)

Absolute maxima  lies at infinity

Answer:

 Option 4. overall minimum in (-2.9.67)

Step-by-step explanation:

A global maximum point (x0, f (x0)) is defined as the point at which f (x0) is the maximum value of the function. That is, there is no value in the domain of f (x) other than x0 where f (x) is greater than f (x0)

A global minimum point (x0, f (x0)) is defined as the point at which f (x0) is the smallest value of the function. That is, there is no value in the domain of f (x) other than x0 where f (x) is less than f (x0)

Based on that deficion we must look for the point where f (x) has the lowest value.

That point is (-2.9.67)

Therefore that is the overall minimum of the function.

Although the function has a maximum in (1.6.08), the function keeps growing for x> 4, that means that there is a point where the function is bigger than in x = 1.

Therefore this is not a local maximum.

− x^ 2 + 10 x + 7 so the answer is B.

                                                    hope it helps

Answer:

[tex]-x^2+10x+7[/tex]

Step-by-step explanation:

3x^2+8x+7-(4x^2-2x). find the difference of the polynomials

First remove the parenthesis by multiplying minus inside the parenthesis.

[tex]3x^2+8x+7-4x^2+2x[/tex]

Now we combine like terms. the terms with same variables and same exponents are like terms.

[tex]3x^2-4x^2= -1x^2[/tex]

[tex]8x +2x= 10x[/tex]

[tex]3x^2+8x+7-(4x^2-2x)=-x^2+10x+7[/tex]

There can be 24 unique four-digit numbers formed from the numerals 7, 6, 5, and 3, calculated by the factorial of 4 (4!).

The student asks how many four-digit numbers can be made from the numerals 7, 6, 5, and 3. These numbers can be arranged in a systematic way, and the total number of combinations can be calculated using permutations. The formula to calculate permutations without repetition is n! (n-factorial), where 'n' is the number of numerals to arrange.

In this case, we have 4 numerals, so the calculation would be 4! This equals to 4 × 3 × 2 × 1 = 24. Thus, there are 24 unique combinations when we arrange the numerals 7, 6, 5, and 3 into four-digit numbers without any repetitions.

5.51181 in feet. Hope this helps

The probability that at least one of the three randomly selected internet users is more careful about personal information when using a public wi-fi hotspot is 97.3%.

To find the probability that at least one of the three randomly selected internet users is more careful about personal information when using a public wi-fi hotspot, we can calculate the probability of the complement event, which is the event that none of the users are more careful. Since the probability that an internet user is more careful is 70%, the probability that a user is not more careful is 1 - 70% = 30%. The probability of the complement event for all three users is (0.3)^3 = 0.027. Therefore, the probability that at least one user is more careful is 1 - 0.027 = 0.973, or 97.3%.

Additional information that the survey subjects volunteered to respond does not affect the calculation of the probability. The probability is based solely on the given percentage from the poll, which represents the proportion of internet users who are more careful about personal information when using a public wi-fi hotspot.

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The probability that at least one internet user is more careful about personal information when using a public wi-fi hotspot is 0.973.

To find the probability that at least one person is more careful about personal information when using a public​ wi-fi hotspot, we can use the complement rule. The complement of at least one person being more careful is that no one is more careful. So, the probability that no one is more careful is 0.3 multiplied by 0.3 multiplied by 0.3 (since there are three internet users). Then we subtract this probability from 1 to find the probability that at least one person is more careful. So, the probability that at least one person is more careful is 1 - (0.3 x 0.3 x 0.3) = 0.973.

The additional information that the survey subjects volunteered to respond does not affect the result of the probability calculation. The probabilities are based on the initial survey results, and any additional information would be separate from those probabilities.

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Answer:

SSS Congruence Postulate ​​

Step-by-step explanation:

we know that

The SSS Congruence Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

In this problem

PN≅QR

NQ≅RP

PQ≅QP -----> is the same side

so

Three sides of triangle PNQ are congruent with three sides of triangle QRP

therefore

△PNQ and △QRP are congruent by SSS Congruence Postulate ​​

SSS Congruence Postulate or theorem proves that △PNQ and △QRP are congruent

According to the dictionary, congruent (of figures) is identical in form; coinciding exactly when superimposed. Two figures or objects are congruent if they have the same shape and size.

According to the picture attached, the answer is SSS Congruence Postulate ​​Because I have three pairs of congruent sides such as

PR = NQ is one pair, QR = NP is another pair, then PQ = PQ is the third pair

SSS Congruence Postulate or theorem proves that △PNQ and △QRP are congruent

Which postulate or theorem proves that △PNQ and △QRP are congruent?

.

The other example can be seen in the second attachment of picture. The question is still the same: Determine which postulate or theorem can be used to prove that ABC = DCB!

Then AC = DB

AB = DC

BC = BC, This side is equal to itself

Therefore the three sides of one triangle equal to 3 sides of the other. It means that the triangles are congruent. Therefore the answer is SSS

Hope it helps you to learn more about triangle.

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We could use the standard form of subtraction.

We put 71.120 on top and we put 2.359 at the bottom.

Then, we subtract the thousandths place. It involves a carry-over.

Then, we subtract and the answer is:

68.761

The subtraction of 71.120 and 2.359 equals 68.761.

This question is asking for the subtraction of two decimal numbers, the first being 71.120 and the second being 2.359. To do this, you would stack the numbers on top of each other, aligning the decimal points, and subtract as you would with whole numbers.

So, your subtraction would look like this:

So, 71.120-2.359 equals 68.761.

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Answer:

The cost of one sunflower is $2.25. :psksksksk

Step-by-step explanation:

All you have to do is divide 18 divided by 8. easypeasy. ;psksksksk

Absolute error is defined as the magnitude of the difference between the exact value and the approximation.

Here both the times, the error is 15.

40-25=15 and 75-60=15

No, the percent error is not same because the exact values are different and hence, the percent error is different.

Percent error value in 1st case is :

[tex]40-25=15[/tex]

error percent is= [tex]\frac{15}{40}\times100=37.5[/tex]%

Percent error value in 2nd case:

[tex]75-60=15[/tex]

error percent is=[tex]\frac{15}{75}\times100=20[/tex]%

Answer:

The percent error compares the absolute error

Step-by-step explanation:

4/2=2+1=3x3=9+1=10/2=5+1=6/2=3+1=4/2

That is pretty darn cool.

answer is $560

that is lcm of 70&80

Answer:

To explain the cartoons and the boxes for table tennis balls are like the digits for numbers in base-10 number system

Here we know that, the number of table tennis balls in one box =10 balls

and the number of table tennis balls in boxes in each cartoon = 10 balls

Therefore, The number of table tennis balls in each cartoon =10×10=100 balls

Hence for the number of balls ,the hundreds place tells the number of cartoons and  tens place tells the number of boxes which left as remainder or without cartoon.

For example if the total tennis balls =540 then its hundreds place i.e 5 tells the number of cartoons and its tens place i.e.4 tells the number of boxes which left as remainder or without cartoon.

Answer:

Base 10 Number System = (0,1,2,3,4,5,6,7,8,9)

In a  Carton of table tennis there are  10 boxes.

And Each Box can Hold 10 Balls.and if i mark boxes from 0 to 9, then

then there are 10 boxes , Total number of Balls=100

So if I represent a single Carton by A, then

A[single carton] ={0,1,2,3,4,5,6,7,8,9}= 10 boxes =100 balls

B [2 carton]= 20 boxes=200 balls

C[ 5 cartons + 3 Boxes] = 5× 100+ 3×10 =530 balls

D[ 12 cartons + 8 Boxes]= 12×100+8×10=1280 balls

Now you can see,

Each carton is holding the balls  in decimal number system.

Boxes = Ten's place in number system,

Number of cartons = either Hundred place or thousand place or more than that

In this way we can represent Carton and Box for table tennis balls in decimal number system having base 10 .

The order of their time spent from least to greatest is; Ari, Cindy, Bety

Distance covered by ari = 2³/₄ miles

Speed of ari = 2¹/₂ miles per hour

Formula for time is;

time = distance/speed

Thus;

Time spent by ari = 2³/₄/2¹/₂

Time spent by ari = 1.1 hours

Distance covered by beth = 1³/₄ miles

Speed of beth = 1¹/₄ miles per hour

Formula for time is;

time = distance/speed

Thus;

Time spent by beth = 1³/₄/1¹/₄

Time spent by beth = 1.4 hours

Distance covered by cindy = 1 hour 21 minutes = 1⁷/₂₀ miles

Speed of cindy = 1¹/₈ miles per hour

Formula for time is;

time = distance/speed

Thus;

Time spent by cindy = 1⁷/₂₀/1¹/₈

Time spent by cindy = 1.35 hours

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Answer:

you minus 8 from 20 which will = to 12. Then you divide 12 by 4.99 and it equals to like 2.4 but you can't buy a .4 of a candy bar so have to round it down to 2

Step-by-step explanation:

Janelle can buy 2 snacks with her remaining budget after purchasing a movie ticket. The inequality 20 ">= 8" + 4.99x is satisfied with x=2, where each snack costs $4.99.

Janelle is at the movie theater with a budget of $20 to spend. After purchasing her movie ticket for $8, she wants to buy snacks with the remaining money. Since each snack costs $4.99, we can represent the situation with the following inequality:

20 ≥ 8 + 4.99x

To find out how many snacks, x, Janelle can buy, we subtract the cost of the movie ticket from her total budget:

$20 - $8 = $12

Now, we divide the remaining amount by the cost of one snack:

$12 / $4.99 ≈ 2.4

Since Janelle cannot buy a fraction of a snack, we round down to the nearest whole number. Thus, Janelle can buy 2 snacks with her remaining budget.

Answer:

I would say the Pennington line is steeper because the slope of the purple line is 2 and the other is 3/2 (don't know if they want slope or not) and it represents that it took 2.5 to three hours to travel 240 miles compared to the other one that takes four hours to travel the same distance. Hopefully that's right

Step-by-step explanation:

Answer:

the purple one is steeper

Step-by-step explanation:

bc i said so :) and it shows that it is

[tex]x^2 + 25=\\\\x^2-(-25)=\\\\(x-\sqrt{-25})(x+\sqrt{-25})=\\\\(x-5i)(x+5i)[/tex]

Answer:

A) y - 2 = 3(x+4)

Step-by-step explanation:

Given that the equation is a line with slope =m=3 and

a point on it (x1,y1) = (-4,2)

Any line having slope m and passing through (x1,y1) has equation in point slope form as

y-y1 = m(x-x1)

We are given here x1 =-4, y1 =2 and m =3

y-y1 = y-2 and x-x1 = x-(-4) = x+4

So equation is y-2 = 3(x+4)

Verify:

The line is y = 3x+12+2 = 3x+14

Hence slope =3 is verified

Substitute the point x =-4 and y =2

2 =3(-4)+14 = 2 is true

Thus verified

Answer:

A is correct option. Equation of line: y-2=3(x+4)

Step-by-step explanation:

Slope of line is 3 and passing point (-4,2).

If slope and passing point given then we have an equation of line

[tex]y-y_1=m(x-x_1)[/tex]

where,

[tex](x_1,y_1)\rightarrow (-4,2)[/tex]

Slope (m)=3

Equation of line:

y-2=3(x+4)

This equation match with option A

Thus. option A is correct.

Answer: 40

Step by step explanation

The _______ is asking what 400 ÷ 10 is

400 ÷ 10 = 40

12x + 6y = 24

add -6 to both side

12x + 6y + -6y = 24 + -6y

Combine like terms:

6y + -6y = 0

12x + 0 = 24 + -6y

12x = 24 + -6y

Divide each side by '12'

x = 2 + -0.5y (your answer)

Answer:

2nd, 3rd and 4th equations are correct.

Step-by-step explanation:

[tex]-4x^2(2x^2+5)=-8x^4-20x^2\\\\[/tex]

is right because each term inside is multiplied by -4x square and we find the answer is right.

[tex]-4b^3(5b^2+3)\\\\\\= -4(5)(b^3)(b^2) =-20b^6-12b^3\\[/tex]

Hence correctly done.

[tex]-5a^4(2a^2+4)=  (-5)(2)(a^4)(a^2)+(-5)(4)(a^4\\-10a^6-20a^4\\[/tex]

Correctly done.

[tex]-6^4(4y^2+2)=-24y^8-12y^4\\= -(6)(6)(6)(6) 4y^2 -(6)(6)(6)(6) (2)[/tex]

should be the right answer.

But instead only 6 is multiplied by inner terms. Hence wrong.

I answer is wrong and others are right.

The variable expression represents the phrase '25 decreased by the sum of 6 and a number' is 25-(6+x).

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.

For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and  methods can be used to convert description to mathematical expressions.

We have to find the variable expression represents the phrase '25 decreased by the sum of 6 and a number'

Let the number be x then decrease mean subtract, sum means add

by means parenthesis;

The expression becomes as;

25 - (6 + x)

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Answer: A:1

Step-by-step explanation:

Look at the picture.

It are the examples of a normal distribution.

Answer: B.