Solve: x^2 + 16x = 0

Answer:

(0,-5)

(2,1)

5,3

Step-by-step explanation:

In this experimental research, the independent variable is the type or intensity of the aerobic exercise program assigned to the sedentary older adults.

In the given scenario of sedentary older adults randomly assigned to aerobic exercise programs, the independent variable would be the type or intensity of the aerobic exercise program. The independent variable is the factor or condition that is manipulated or controlled by the researcher to observe its effect on the dependent variable.

In this case, the researchers are interested in studying the impact of aerobic exercise on cognitive decline in sedentary older adults.

To investigate this, they would have different groups of participants randomly assigned to different aerobic exercise programs. These programs could vary in terms of intensity, duration, frequency, or specific exercises included.

By manipulating the independent variable (the type or intensity of the aerobic exercise program), the researchers aim to observe its influence on the dependent variable, which in this case would be the occurrence or risk of significant cognitive decline.

The dependent variable is the outcome or behavior that is being measured or observed to determine the effect of the independent variable.

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Answer: Positive correlation

Step-by-step explanation:

As you go up and along the graph the values go up.

Both have to be increasing basically.

Answer:

$105

Divide 85 by 17 which equals 5 so each sandwich cost $5. Then multiply 21 by 5 which is 105.

Answer:

Step-by-step explanation:

According to given table, we can see each line has relationship:

Convert this into equation of the line:

Correct choice is D

Answer:

5/8 of a mile

Step-by-step explanation:

Let the distance from Post Office to Friend's house =D

7/8 + 5/6 + D =miles - Total distance from Georgia's house to a Friend's house.

42 minutes / 18 minutes per mile =2 1/3 miles - total distance from her house to a friend's house. So, we have:

7/8 + 5/6 + D = 2 1/3, solve for D

[21 + 20] / 24 + D = 2 1/3

41/24 + D = 2 1/3                     subtract 41/24 from both sides

D =2 1/3 - 41/24

D =7/3 - 41/24

D =[56 -41] / 24

D = 15 / 24

D = 5/8 of a mile - the distance between the School and her Friend's house.

Answer:

a=15, b=14

Step-by-step explanation:

We know all angles must add up to 360, so lets add all angles and set them equal to 360.

\(7a+33+3b+10a-12+6b-42=360\\17a+9b-21=360\)

We also know that any angle opposite another is equal. Lets take 6b-42 and 3b and set them equal.

\(3b=6b-42\)

Now solve for b in both equations

\(3b=6b-42\\-3b=-42\\b=14\)

\(17a+9b-21=360\\9b-21=360-17a\\9b=381-17a\\b=\frac{381-17a}{9}\)

Now we set the two equations equal to each other to solve for a:

\(14=\frac{381-17a}{9} \\126=381-17a\\-255=-17a\\15=a\)

This gives a=15, b=14.

Answer:

You would need about 13 eggs.

Step-by-step explanation:

216 cookies would be taking the original recipe and making 4 and a half batches. So we multiply 3 by 4.5 to get 13.5.

The value of c that makes the limit of f(x) exist as x approaches 5 for the function f(x) = x² - 7 is c = 18.

To determine the value of c, we need to find the value that makes the left-hand limit (LHL) equal to the right-hand limit (RHL) as x approaches 5. The left-hand limit is obtained by evaluating the function for values of x approaching 5 from the left side, while the right-hand limit is obtained by evaluating the function for values of x approaching 5 from the right side.

For x < 5, the function f(x) = x² - 7 becomes f(x) = (x - 5)(x + 5). Therefore, the left-hand limit is given by LHL = lim(x→5-) (x - 5)(x + 5). By direct substitution, LHL = (5 - 5)(5 + 5) = 0.

For x > 5, the function f(x) = x² - 7 remains the same. Therefore, the right-hand limit is given by RHL = lim(x→5+) (x² - 7). By direct substitution, RHL = (5)² - 7 = 18.

For the limit of f(x) to exist as x approaches 5, the LHL and RHL must be equal. In this case, 0 = 18. Since this equation is not true for any value of c, it implies that the limit of f(x) does not exist as x approaches 5 for the given function.

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The numbers in the order of least to greatest is :

₋1.8 , ₋1/4 , 1/2 , 1.41 , 7.2 , 9.1 , 121

Given, the numbers are in decimal and fraction form.

1/2 , -1/4 , 7.2 , 121 , 1.41 , -1.8 , 9.1

we need to convert the fractions and then arrange the numbers in the ascending order.

Writing the numbers in an ordered list according to their values means arranging them from least to greatest. The smallest number should be put on the left, followed by the next smallest number, which should be written directly to its right.

for 1/2:

1/2 = 0.5

for ₋1/4:

₋1/4 = 0.25

now arrange the numbers according to the least to greatest form.

we have numbers:

0.5 , 0.25 , 7.2 , 121 , 1.41 , ₋1.8 , 9.1

least to greatest form:

₋1.8 , 0.25 , 0.5 , 1.41 , 9.1 , 121

i.e , ₋1.8 , 1/4 , 1/2 , 1.41 , 9.1 , 121

Hence we get the required form.

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A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(\sigma)= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) \(=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\)

So n \(=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

Te given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(\(\sigma\))= 2×1.55

Standard deviation of resistance(\(\sigma\))= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5\()^2\)

n=(15.996\()^2\)

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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If we have a population that doesn't follow the normal distribution, we must choose a minimum sample size of 30 to ensure an approximately normal (symmetric) distribution.

        According to the Central Limit Theorem (CLT), a minimum sample size of 30 is required to ensure a normal distribution, regardless of the shape of the population distribution.

       In this case, a minimum sample size of 30 will suffice for a normal distribution, regardless of the population's shape, as long as the sample is random and the population's standard deviation is known or greater than 30.

      Therefore the minimum sample size of 30 we should select in order to have an approximately normal distribution (symmetric).

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Answer:

y= -1/2x -1

Step-by-step explanation:

y= mx +b where the y-intercept is B and the slope is m.

Hope i helped!

Answer: 525

Step-by-step explanation:

if your looking for 150 percent of 350, the answer is 525 because....

150 x 350/ 100 =525

The two positive integers that maximize the sum of their squares while satisfying the constraint x + y = 10 are x = y = 5.

To set up the optimization problem, let x and y be the two positive integers we are trying to find. Then, we want to minimize and maximize the sum of their squares, which can be expressed as:

Minimize: \(f(x, y) = x^2 + y^2\)

Subject to: x + y = 10 and x, y > 0

Maximize: \(g(x, y) = x^2 + y^2\)

Subject to: x + y = 10 and x, y > 0

Note that the constraint x, y > 0 means that we are looking for positive integers, and the constraint x + y = 10 means that their sum must be 10.

To solve the minimization problem, we can use the method of Lagrange multipliers. The Lagrangian function is:

L(x, y, λ) = \(x^2 + y^2 + λ(10 - x - y)\)

Taking the partial derivatives with respect to x, y, and λ, we get:

∂L/∂x = 2x - λ = 0

∂L/∂y = 2y - λ = 0

∂L/∂λ = 10 - x - y = 0

Solving these equations simultaneously, we get:

x = y = 5

λ = 10

Therefore, the two positive integers that minimize the sum of their squares while satisfying the constraint x + y = 10 are x = y = 5. The minimum value of the sum of their squares is:

\(f(5, 5) = 5^2 + 5^2 = 50\)

To solve the maximization problem, note that the function x^2 + y^2 is a continuous and increasing function of x and y. Since x and y must sum to 10 and be positive integers, the maximum value of their sum of squares occurs when one of them is as large as possible, which is 5. Thus, the maximum value of the sum of their squares is:

\(g(5, 5) = 5^2 + 5^2 = 50\)

Therefore, the two positive integers that maximize the sum of their squares while satisfying the constraint x + y = 10 are x = y = 5.

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The storm rainfall flux is 0.00127 m2/hr, 1.27 kg liquid water/m2hr, 2.8 lb liquid water/m2hr, 1.27 liters liquid water/m2hr, and 0.335 gallons liquid water/m2hr. The amount of liquid water fell on the garden is 80.6 L, 21.3 gallons.

Dimensions of outdoor vegetable garden = 2 m × 2 m

Storm rainfall = 0.8 inches of rain

Time of storm = 1 hr(

a) The rainfall flux is the amount of rainfall per unit area and unit time. It is given as:

Rainfall flux = (Amount of rainfall) / (Area × Time)

Given the area of the garden is 2 m × 2 m, and the time is 1 hr, the rainfall flux is:

Rainfall flux = (0.8 inches of rain) / (2 m × 2 m × 1 hr)

Converting inches to meters, we get:

1 inch = 0.0254 m

Therefore,

Rainfall flux = (0.8 × 0.0254 m) / (2 m × 2 m × 1 hr) = 0.00127 m/hr

Converting the rainfall flux to other units:

In kg/hr:

1 kg of water = 1000 g of water

Density of water = 1000 kg/m3

So, 1 m3 of water = 1000 kg of water

So, 1 m2 of water of depth 1 m = 1000 kg of water

Therefore, 1 m2 of water of depth 1 mm = 1 kg of water

Therefore, the rainfall flux in kg/hr = (0.00127 m/hr) × (1000 kg/m3) = 1.27 kg/m2hr

In lbs/hr:

1 lb of water = 453.592 g of water

So, the rainfall flux in lbs/hr = (0.00127 m/hr) × (1000 kg/m3) × (2.20462 lb/kg) = 2.8 lbs/m2hr

In liters/hr:

1 m3 of water = 1000 L of water

So, 1 m2 of water of depth 1 mm = 1 L of water

Therefore, the rainfall flux in L/hr = (0.00127 m/hr) × (1000 L/m3) = 1.27 L/m2hr

In gallons/hr:

1 gallon = 3.78541 L

So, the rainfall flux in gallons/hr = (0.00127 m/hr) × (1000 L/m3) × (1 gallon/3.78541 L) = 0.335 gallons/m2hr

(b) To calculate the amount of water that fell on the garden, we need to calculate the volume of water.

Volume = Area × Depth.

The area of the garden is 2 m × 2 m.

We need to convert the rainfall amount to meters.

1 inch = 0.0254 m

Therefore, 0.8 inches of rain = 0.8 × 0.0254 m = 0.02032 m

Volume of water = Area × Depth = (2 m × 2 m) × 0.02032 m = 0.0806 m3

Converting the volume to other units:

In liters:

1 m3 of water = 1000 L of water

Therefore, the volume of water in liters = 0.0806 m3 × 1000 L/m3 = 80.6 L

In gallons:

1 gallon = 3.78541 L

Therefore, the volume of water in gallons = 80.6 L / 3.78541 L/gallon = 21.3 gallons.

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Answer:

b.) y=3x+2

Step-by-step explanation: The linear equation is y= mx + b

m is the slope and b is the y-intercept

Answer b is the linear equation!

The shortest routes between each pair of nodes are:
- Fruit - Hay: Fruit - Shade - Grass - Hay or Fruit - Shade - Barn - Hay (tied for shortest route)
- Grass - Pond: direct route with a distance of 190

To determine the shortest route between a pair of nodes, we need to consider all possible routes and compare their distances.

In this case, we have five pairs of nodes to consider: Fruit - Hay, Grass - Pond, Fruit - Shade, Barn - Pond, and Fruit - Pond.

Starting with Fruit-Hay, we don't have any direct distance given between these two nodes. However, we can find a route that connects them by going through other nodes.

One possible route is Fruit - Shade - Grass - Hay, which has a total distance of 165 + 95 + 60 = 320.

Another possible route is Fruit - Shade - Barn - Hay, which has a total distance of 165 + 35 + 120 = 320.

Therefore, both routes have the same distance and are tied for the shortest route between Fruit and Hay.

Moving on to Grass-Pond, we have a direct distance of 190 between these two nodes.

Therefore, this is the shortest route between them.

For Fruit-Shade, we already considered one possible route when looking at Fruit-Hay.

However, there is also another route that connects Fruit and Shade directly, which has a distance of 165.

Therefore, this is the shortest route between Fruit and Shade.

Looking at Barn-Pond, we don't have a direct distance given. We can find a route that connects them by going through other nodes.

One possible route is Barn - Hay - Grass - Pond, which has a total distance of 120 + 60 + 190 = 370. Another possible route is Barn - Shade - Fruit - Pond, which has a total distance of 35 + 165 + 300 = 500.

Therefore, the shortest route between Barn and Pond is Barn - Hay - Grass - Pond.

Finally, we already considered Fruit-Pond when looking at other pairs of nodes. The shortest route between them is direct, with a distance of 300.

In summary, the shortest routes between each pair of nodes are:

- Fruit - Hay: Fruit - Shade - Grass - Hay or Fruit - Shade - Barn - Hay (tied for shortest route)
- Grass - Pond: direct route with a distance of 190
- Fruit - Shade: direct route with a distance of 165
- Barn - Pond: Barn - Hay - Grass - Pond
- Fruit - Pond: direct route with a distance of 300

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Answer:

2880 tiles

Step-by-step explanation:

A rectangular path has dimensions 60 m and 3 m.

Area of a rectangular path = length × breadth = 60 × 3 = 180 \(m^2\)

Use \(1\,m^2=10000\,cm^2\)

So,

Area of a rectangular path = 180(10000) = 18,00,000 \(cm^2\)

Side of a square tile = 25 cm

Area of a square tile = side × side = 25(25) = 625 \(cm^2\)

Number of square tiles = Area of a rectangular path ÷ Area of a square tile

= \(\frac{1800000}{625} =2880\) tiles

The solution is, the boundaries of the indicated value,

4 feet is 16 ft.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

the length = 4 ft.

so, boundary = perimeter of the square

i.e. 4+4+4+4

=4*4

=16

Hence, The solution is, the boundaries of the indicated value,

4 feet is 16 ft.

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Answer:

the coefficient of 0 indicates that there is no relationship between the two values

How much does it cost to buy 10 computer mice (not the living thing :) ) that are $24.75 each.

10(24.75)=247.5

It will cost $247.5

It would be $247.50

Step-by-step explanation:

24.75 x 10

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following division

Now we carry out the operation and we have:

We divide the quotients of the higher degree terms of the numerator and the divisor

Then we multiply this quotient by the denominator

Now, we subtract this value from the numerator and we have

Therefore the final result would be

Step-by-step explanation:

We can solve this kind of trigonometric problem

easily by the followings method :

Given :

cos^4a + cos^2a = 1

or, cos4^a = 1 - cos^2a

Therefore; cos^4a = sin^2a

Again,

To prove: cot^4a - cot^2a = 1

L.H.S = Cot^4a - cot^2a

= Cos^4a÷ sin^4a - Cos^2a ÷ sin^2a

= Sin^2a ÷ Sin^4a - cos^2a ÷ Sin^2a

= 1 ÷ Sin^2a - cos^2a ÷ Sin^2a

= 1 - cos^2a ÷ Sin^2a

= Sin^2a ÷ Sin^2a

= 1 = R.H.S proved.

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Answer: the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Step-by-step explanation:

Let's assume the price of one senior citizen ticket is 's' dollars and the price of one student ticket is 't' dollars.

According to the given information, on the first day, the school sold 7 senior citizen tickets and 11 student tickets, totaling $125. This can be expressed as the equation:

7s + 11t = 125 ---(1)

On the second day, the school sold 14 senior citizen tickets and 8 student tickets, totaling $180. This can be expressed as the equation:

14s + 8t = 180 ---(2)

We now have a system of two equations with two variables. We can solve this system to find the values of 's' and 't'.

Multiplying equation (1) by 8 and equation (2) by 11, we get:

56s + 88t = 1000 ---(3)

154s + 88t = 1980 ---(4)

Subtracting equation (3) from equation (4) eliminates 't':

(154s + 88t) - (56s + 88t) = 1980 - 1000

98s = 980

s = 980 / 98

s = 10

Substituting the value of 's' back into equation (1), we can solve for 't':

7s + 11t = 125

7(10) + 11t = 125

70 + 11t = 125

11t = 125 - 70

11t = 55

t = 55 / 11

t = 5

Therefore, the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Answer:

The volume of the spherical grain is of 1.13*10^-7 cubic centimeters.

Step-by-step explanation:

The volume of a sphere with radius r is given by the following formula:

In this question:

The spherical grain has volume of 5*10^-3 centimeters = 0.005. So r = 0.005. Then

The volume of the spherical grain is of 1.13*10^-7 cubic centimeters.