given the functiom y=x^4 -8x^2+16. on which intervals is the function increasing​

Answer:

[tex]\large\boxed{4\pi\ cm\approx12.56\ cm}[/tex]

Step-by-step explanation:

The formula of a length of an arc:

[tex]\dfrac{\pi\alpha r}{180^o}[/tex]

We have

[tex]\alpha=120^o\\\\r=6\ cm[/tex]

Substitute:

[tex][tex]\hat{MN}=\dfrac{\pi(120)(6)}{180}=4\pi\ cm\approx4(3.14)=12.56\ cm[/tex]

ANSWER

See below

EXPLANATION

The given function is

[tex]f(x)= {x}^{2} + 2x - 3[/tex]

We complete the square to rewrite this function in the vertex form.

[tex]f(x)= {x}^{2} + 2x + 1 - 1- 3[/tex]

[tex]f(x)= {(x + 1)}^{2} - 4[/tex]

The vertex is (-1,-4).

The axis of symmetry is x=-1

To find x-intercepts , put f(x)=0.

[tex]{(x + 1)}^{2} = 4[/tex]

[tex]x + 1 = \pm \sqrt{4} [/tex]

[tex]x = - 1\pm2[/tex]

[tex]x = - 3 \: or \: x = 1[/tex]

The x-intercepts are (-3,0), (1,0)

To find y-intercept , put x=0.

[tex]f(x)= {0}^{2} + 2(0) - 3 = - 3[/tex]

The graph is shown in the attachment.

Answer:

C [tex]4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8)[/tex]

Step-by-step explanation:

First use the property of logarithms

[tex]\log _ab-\log_ac=\log_a\dfrac{b}{c}.[/tex]

For the given expression you get

[tex]\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}[/tex]

Now use property of logarithms

[tex]\log_ab^k=k\log_ab.[/tex]

For your simplified expression, you get

[tex]\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).[/tex]

Answer: C

Step-by-step explanation:

Answer:

the answer is the second one (6, 9)

Answer: The answers are (9, -1) and (6, 1)

Step-by-step explanation:

Answer:

864 sq.in.

Step-by-step explanation:

Given:

Prism with each leg of length 12

hence given prism is cube

Formula for Area of cubic prism= 6a^2

where a is length of a side

Area=6(12)^2

        =6(144)

         =864 !

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-2)}{1-3}\implies \cfrac{4+2}{1-3}\implies \cfrac{6}{-2}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-2)=-3(x-3) \\\\\\ y+2=-3x+9\implies y=-3x+7[/tex]

Hello There!

First let me say this. I did not like how this question was worded I am a tutor in math and I had to read this problem over and over 5 times. It was confusing but I managed to figure it out. The answer is 61%

My work is shown on paper

Final answer:

Diego's method may introduce bias by not representing all student subgroups, suggesting that a random, stratified random, or systematic sampling method would better reflect student satisfaction with cafeteria food.

Explanation:

The question asks if selecting the first 25 students who purchase a lunch at the cafeteria is a good way for Diego to sample students to determine satisfaction with the cafeteria food. This sampling method may lead to bias because it does not represent all subgroups within the school population equally. For instance, it may only capture the opinions of students who already have a preference for cafeteria food, thus overlooking those who avoid it due to dissatisfaction. A better approach would be a random sampling method, where every student has an equal chance of being selected, ensuring a more accurate reflection of the entire student body’s opinion.

To improve the survey, Diego could consider using a stratified random sample, where the school population is divided into strata, such as grade levels or lunch periods, and then a random sample is taken from each stratum. This approach helps ensure that all segments of the student population are represented. Alternatively, a systematic sampling method, where every nth person is selected from a list or a line, could provide a more structured yet still random selection process compared to Diego's original plan.

Diego's approach is convenient but prone to bias. Random sampling across various days would improve representativeness and accuracy.

Diego's approach to surveying the students about cafeteria satisfaction has both strengths and weaknesses. Let's break down the pros and cons step by step:

1. **Convenience**: Approaching students during lunchtime in the cafeteria is convenient because it allows Diego to access a large number of students in one place and at a time when they are likely to be available.

2. **Sampling Bias**: However, selecting only the first 25 students who purchase lunch on a Monday might introduce sampling bias. For example, if there is a rush in the cafeteria during that time, Diego might end up surveying students who are in a hurry and may not accurately represent the entire student population.

3. **Limited Sample Size**: The sample size of 25 students is relatively small. While a larger sample size is not always necessary for accurate results, a larger sample size generally leads to more reliable findings. With only 25 students surveyed, there's a risk of the results being skewed by chance variations.

4. **Day of the Week Bias**: Monday might not be the best day to conduct the survey. Students' satisfaction with cafeteria food might vary depending on the day of the week due to factors like menu rotation or weekend leftovers. Therefore, surveying only on Mondays might not provide a comprehensive picture of overall satisfaction.

5. **Response Bias**: There's also the potential for response bias. Students who are particularly satisfied or dissatisfied with the food might be more likely to respond to Diego's survey, leading to results that don't accurately reflect the general sentiment of all students.

6. **Alternatives**: A better approach might be to conduct the survey at different times and days of the week to capture a more diverse range of student experiences. Additionally, Diego could use random sampling techniques to ensure that every student has an equal chance of being surveyed, reducing the risk of bias.

In summary, while Diego's approach is convenient, it may not yield the most accurate or representative results due to potential sampling bias, limited sample size, and other factors. To improve the validity of the survey findings, Diego should consider adjusting his sampling method and survey timing.

f(5) means to replace x in the equation with 5 then solve.

f(x) = x^2 +2x

f(5) = 5^2 + 2(5)

f(5) = 25 +10

f(5) = 35

The answer is D)35

Answer:

4x=6

Step-by-step explanation:

The value of the equation is 4x = 6.

The two equations in the system are added or subtracted to produce a new equation with just one variable when using the addition/subtraction method. The other variable must cancel out for the new equation to have just one variable.

Given

eq 1 :8x+3y=14

eq 2 :4x+3y=8

eq1 - eq 2

(8x+3y=14) - (4x+3y=8)

=> (8x-4x) + ( 3y-3y) = (14-8)

=> 4x + 0 = 6

4x = 6.

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Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=5(2)^{x}[/tex]  

This is a exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]  

where

a is the initial value

b is the base

In this problem

a=5

b=2

using a graphing tool

see the attached figure

Answer:

A

Step-by-step explanation:

Edge

Answer:

B

Step-by-step explanation:

volume = length x width x height

For the top half i use the formula for the area of a triangle (area = base x height ÷ 2), which results in 45. times it 10 and you have 450³ which is the volume of the top part.

For the bottom half it is just 10 x 10 x 10 = 1000³

450³+1000³=1450³

The Volume of the frozen figure is C. 1,000 cm³.

To calculate the volume of the frozen figure, we need to determine the shape of the mold first. Assuming the mold is a rectangular prism, we can use the volume formula for a rectangular prism:

Volume = length × width × height

Given that the dimensions of the mold are:

Now, let's calculate the volume:

Volume = 10 cm × 9 cm × 10 cm = 900 cubic centimeters (cm³)

The correct answer to the question C. 1,000 cm³

Answer:

Step-by-step explanation:

11.5 + 12.5 - 10 - 75*x  = 0

               4  

multiply both sides by 4

11.5 + 12.5 - 10 - 75x = 0     Combine the first 2 terms.

24 - 10 - 75x = 0                 Subtract 10    

14 - 75x = 0                         Subtract 14 from both sides

-75x = - 14                           Divide by - 75

-75x/-75 = -14/75                Do the division

x = 0.187

The answer would be A

Answer:

Lets first subtract 35 from 22 since 35 is his total and the answer would be 13.

Step-by-step explanation:

I guess it would be 13 dollars left.

IF IT'S RIGHT PLZZ MARK BRAINLIST PLZZZ

Answer:

The factors are: (3a+2b +ab-6)(3a+2b -ab+6)

Step-by-step explanation:

[tex](a^2-4)(9-b^2)+24ab[/tex]

We need to solve the above expression using factorization.

Multiplying (a^2-4)(9-b^2)

9(a^2-4)-b^2(a^2-4) + 24ab

9a^2 -36 -a^2b^2+4b^2 + 24ab

Rearranging:

9a^2 + 4b^2 +24ab -36 -a^2b^2

We try to make perfect square of the form a^2+2ab-b^2

We have 24ab that can be written as 12ab + 12ab

Now, we can arrange the above equation:

9a^2 +12ab+ 4b^2 -(a^2b^2-12ab +36)

(3a)^2 +2(3a)(2b) + (2b)^2 -((ab)^2 -2(ab)(6)+(6)^2)

The perfect square will be:

(3a+2b)^2 - (ab-6)^2

Now We know a^2 - b^2 = (a+b)(a-b)

Here a = 3a+2b , b=ab-6

So,

(3a+2b +(ab-6))(3a+2b - (ab-6))

(3a+2b +ab-6)(3a+2b -ab+6)

So, the factors are: (3a+2b +ab-6)(3a+2b -ab+6)

Answer:

y=6(x+1)^(2)-16

Step-by-step explanation:

Use the formula x=-b/2a

Plug it in for x to get y. That will give you the vertex. Plug the numbers in where they go. There will be one number left that hasn't been filled out. The first number in the equation id 6, so it goes out front.

The equation is y = 6x2 + 12x – 10 rewritten in vertex form is y=6(x+1)²-16

By using the formula   x=-b/2a

simplify

y = 6x2 + 12x – 10

as y=6(x+1)²-16

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Answer:

the Bision is 10 miles / hour faster if he could keep it up

Step-by-step explanation:

There are 60 minutes in an hour.

Therefore the bison can run [3520 feet / min] * [60 min ] =211288 feet in an hour.

Now you have to convert 212200 to miles. Do this by dividing by 5280

212200/5280 = 40 miles.

Kind of hard to believe isn't it. 40 miles is a long way when you are running it.

The bison is faster by 10 miles / hour.

This can be done all in 1 step if you know how to do dimensional analysis

3520 feet / minute * [ 60 min/ hour ] * [ 1 mile / 5280 feet] = 40 miles

Answer:

A bison is 10 miles per hour faster than a deer.

Your answer will be 13,331 because you add up all the asset and subtract all the liabilities

Answer:

Option D.

Step-by-step explanation:

To calculate the net worth we subtract the liabilities from the assets.

Total assets

Checking and savings   $6432

Automobile                     $8345

Apartment contents       $5242

Valuables                        $867

                               -------------------------

                Total               $20886

Total Liabilities

Auto loan                       $2820

Credit card                     $1181

Other loans                    $3554

                              ---------------------------

                 Total              $7555

Net worth = Assets - liabilities

                = $20886 - $7556

                = $13331

Option D is the answer.  

Answer:

Answer: There are 21 eggs left.

Step-by-step explanation:

One carton has 12 eggs.

2 cartons are two times one carton, so two cartons have 2 times 12 eggs.

2 * 12 = 24

There are 24 eggs in two cartons.

Margot uses 3 eggs. We subtract 3 eggs from 24 eggs.

24 - 3 = 21

Answer: There are 21 eggs left.

There are 21 eggs are left if each carton 12 eggs. There are 2 full cartons in the refrigerator. Margot uses 3 eggs to make a quiche.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

Each carton contains = 12 eggs

Number of carton = 2

Number of total eggs = 12×2 = 24

Margot uses 3 eggs to make a quiche.

Remaining eggs = 24 - 3 = 21

Thus, there are 21 eggs are left if each carton 12 eggs. There are 2 full cartons in the refrigerator. Margot uses 3 eggs to make a quiche.

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Examples of Quadratic Equation. A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.

Final answer:

A real-life example of a quadratic model is a ball's trajectory when thrown upwards, described by the quadratic equation h(t) = -4.9t^2 + v0t + h0, with -4.9 representing the acceleration due to gravity.

Explanation:

A common example of a quadratic model in real life is the path of a projectile. For instance, when you throw a ball, its trajectory can be described by a quadratic equation. Let's say a person throws a ball upwards with an initial velocity, and we want to model the ball's height above the ground over time.

The quadratic equation for the ball's height h at time t can be written as: h(t) = -4.9t2 + v0t + h0, where -4.9 is the acceleration due to gravity (in meters per second squared), v0 is the initial velocity (in meters per second), and h0 is the initial height (in meters).

For example, if the initial velocity is 14.3 m/s and the ball is thrown from the ground (initial height is 0), the equation becomes h(t) = -4.9t2 + 14.3t. To find when the ball hits the ground, we solve for t when h(t) = 0 using the quadratic formula.

Answer:

[tex]\large\boxed{(F\circ F)(n)=4n+6}[/tex]

Step-by-step explanation:

[tex]F(n)=2n+2\\\\(F\circ F)(n)\to\text{Replace n with 2n + 2 in F(n)}:\\\\(F\circ F)(n)=2(2n+2)+2\qquad\text{use the distributive property}\\\\(F\circ F)(n)=(2)(2n)+(2)(2)+2=4n+4+2=4n+6[/tex]

Answer:

Width = [tex]1\frac{1}{3}[/tex] ft

Step-by-step explanation:

The tank holds 150 gallons of water.

7.5 gallons holds 1 ft³ of water.

So 150 gallons will hold;

[tex]\frac{150}{7.5}[/tex] × 1 ft³ = 20 ft³

The volume of the tank = Length(l) × Width(w) × Height(h) = 20 ft³

i.e 5 ft × w × 3 ft = 20 ft³

15w ft² = 20 ft³

w = [tex]\frac{20 ft^3}{15 ft^2}[/tex] =  [tex]1\frac{1}{3}[/tex] ft

Answer:

The probability that a student buys a drink  is 0.47

Step-by-step explanation:

The probability that a student buys a drink will be given by;

( the number of students who bought a drink)/(the total number of students)

We are told that;

Of the 100 students who came to the movie, 62 bought popcorn and 47 bought a drink. Therefore, the required probability is;

47/100= 0.47

Answer:

B

Step-by-step explanation:

The volume (V) of a triangular prism is

V = area of triangular end × length

area of Δ = [tex]\frac{1}{2}[/tex] bh

where b is the base and h the perpendicular height

here b = 8 and h = 5, so

area = 0.5 × 8 × 5 = 20 units²

the length of the prism is 10, hence

V = 20 × 10 = 200 units³

The Volume of the Triangular prism is 200 units³

The correct option is (B)

The volume of a triangular prism is the space inside it or the space occupied by it.

Volume (V) of a triangular prism,

V = base area × length

area of Δ =  bh

where b =base and h =perpendicular height

Given that,  b = 8 and h = 5, so

Area = 0.5 × 8 × 5

= 20 units²

The length of the prism is 10. So,

V = 20 × 10

  = 200 units³

volume of the triangular prism 200 units³

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Answer:

Step-by-step explanation:

pyramids have 5 surfaces and a point. a cube has 6 surfaces and is a square

Answer:  [tex]Range:[/tex]{[tex]1,3,4,7[/tex]}

Step-by-step explanation:

We know that, by definition, the Domain is the set of all the x-coordinates of the ordered pairs  and the Range is the set of all the y-coordinates of the ordered pairs.

Therefore, given [tex]f=(2,3),(5,7),(5,4),(9,1)[/tex], you can observe that the set of all second elements of ordered pairs (the values of "y") is the following:

{[tex]3,7,4,1[/tex]}

 Therefore, we can conclude that if [tex]f=(2,3),(5,7),(5,4),(9,1)[/tex] , then the range is:

 [tex]Range:[/tex]{[tex]1,3,4,7[/tex]}

Answer:

The range of f is {1 , 3 , 4 , 7}

Step-by-step explanation:

* Lets revise the relation

- f is a relation between x and y

- x is the input of the relation

- y is the output of the relation

- x is called the domain of the relation

- y is called the range of the relation

- The range is the corresponding value to x

* Now lets solve the problem

∵ f = {(2 , 3) , (5 , 7) , (5 , 4) , (9 , 1)

∵ x = {2 , 5 , 9}

∴ The domain of f is {2 , 5 , 9}

∵ y = {1 , 3 , 4 , 7}

∴ The range of f is {1 , 3 , 4 , 7}

Answer:

80% markup

Step-by-step explanation:

You first subtract the original amount from the final to get:

54-20 = 24

Then you divide it by the original:

24/30 = .80

You multiple this by 100% to get 80%

Answer:

The markup is 80%

Answer:

The difference of the original two-digit number and the number with reversed digits is 98 - 89 = 9

Step-by-step explanation:

Let the digit at unit(one's) place = y

Let the digit at ten's place =  x

So, the two-digit number will be: 10x +y

According to given condition:

Five times the sum of the digits of a two-digit number is 13 less than the original number. This statement can be written as:

5(x +y) = (10x +y) - 13

If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number.

if digits are reserved the two digit will be 10y + x

4(x + y) = (10y + x) -21

So, we have 2 equations, solving these 2 equations we can find the 2 digit number.

5(x +y) = (10x +y) - 13

5x + 5y = 10x +y -13

Rearranging:

5x -10x +5y -y = -13

-5x + 4y = -13 (eq1)

4(x + y) = (10y + x) -21

4x +4y = 10y +x =-21

4x -x +4y -10y = -21

3x -6y = -21 (eq2)

Solving:

Multiply eq 1 with 3 and eq 2 with 2

-15x + 12 y = -39

6x - 12y = -42

_______________

-9x = -81

x = -81/-9

x = 9

Putting in eq(1)

-5x + 4y = -13

-5(9) +4y = -13

-45 + 4y = -13

4y = -13 + 45

4y = 32

y = 32/4

y = 8

So, y =8 and x = 9

The 2 digit number is:

10x + y = 10(9) + 8 = 90+8 = 98

The reversed 2 digit number is:

10y + x = 10(8) + 9 = 80+9 = 89

The difference of the original two-digit number and the number with reversed digits is 98 - 89 = 9

The answer is:

There are 17.6 ounces in 0.5 kilograms.

To calculate how many ounces are in 0.5 kilograms, we need to use the following factor:

[tex]1Kg=35.274ounces[/tex]

So, converting we have:

[tex]0.5Kilogram*\frac{35.274ounces}{1Kilogram}=17.637ounces=17.6ounces[/tex]

Have a nice day!