√(112) - √(80) / √(20) - √(28) = ?​

Answer: 70 days

Step-by-step explanation:

The coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25)

The coordinates of point A = (-5, -4),

The coordinates of the point B = (-3, 3)

Let the point at the distance 3/4 from A to B = P

The coordinates of point 3/4 from A to B = P

At the x-coordinate, the distance from B to A is =  -3-(-5) = 2 units.

At the y-coordinate, the distance from B to A is = 3-(-4) = 7 units.

Hence, the coordinates of P = (-5 + (3/4×(x-coordinate), -4 + 3/4×(y-coordinate)

                                            P = (-5 + (3/4×(2), -4 + 3/4×(7))

                                            P = (-3.5, 1.25)

Hence, the coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25).

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The complete question is -

What are the coordinates of the point 3/4 of the way from A to B?

Answer: 2.12 seconds

Step-by-step explanation:

From the question, we are informed that Josie ran a lap in 45.23 seconds while Erica ran a lap in 43.11 seconds.

To calculate the extra amount of time it took Josie to complete the lap, we subtract Erica's time from Josie's time. This will be:

= 45.23 seconds - 43.11 seconds

= 2.12 seconds

a. 95% confidence Interval of the True Mean Reading Score for All Fifth Graders: (76.85, 87.15)

b. 95% Confidence Interval of the Mean Reading Scores of All Fifth Graders: (77.03, 86.97)

c. 99% Confidence Interval of the Mean Reading Scores of Fifth Graders:(75.85, 88.15)

s. The 99% confidence interval is wider than the 95% confidence intervals because a higher confidence level requires a larger margin of error and a wider interval to capture the true mean with a higher degree of certainty.

To find the confidence intervals, we'll use the formula:

Confidence Interval = Mean ± (Critical Value × Standard Error)

Where:

Mean is the sample mean

Critical Value is the value corresponding to the desired confidence level and degrees of freedom

Standard Error is the standard deviation of the sample divided by the square root of the sample size

a. 95% Confidence Interval of the True Mean Reading Score for All Fifth Graders:

Since the sample size is 35, the degrees of freedom (df) will be 35 - 1 = 34.

The critical value for a 95% confidence level and 34 degrees of freedom is approximately 2.032.

Standard Error (SE) = Standard Deviation (SD) / √n

SE = 15 / √35 = 2.533

= 82 ± 5.15

= (76.85, 87.15)

b. 95% Confidence Interval of the Mean Reading Scores of All Fifth Graders:

We consider the standard error as the standard deviation of the population divided by the square root of the sample size.

Confidence Interval = 82 ± (2.032 × (15 / √35))

= 82 ± 4.97

= (77.03, 86.97)

c. 99% Confidence Interval of the Mean Reading Scores of Fifth Graders:

The critical value for a 99% confidence level and 34 degrees of freedom is approximately 2.728.

Confidence Interval = 82 ± (2.728 × (15 / √35))

=82 ± 6.15

= (75.85, 88.15)

s. Comparing the Intervals:

The 99% confidence interval is larger than the 95% confidence intervals (both for the true mean reading score and the mean reading scores of all fifth graders).

Because a higher confidence level requires a wider interval to capture the true mean with a higher degree of certainty.

As the confidence level increases, the critical value increases, resulting in a larger margin of error and a wider confidence interval.

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Based on the coordinates of the vertices of the parallelogram ORST, the coordinates of S can be found to be (a + b, d).

As this is a parallelogram, the horizontal distance between O and R would be the same as the horizontal distance between S and T.

The horizontal distance between O and R is represented by "b".

The horizontal distance between T and S would therefore be:

= a + b

The fact that R and S are on the same plane would mean that the y-value of S is the same as that of R which is d.

The coordinates of S is:

( a + b, d).

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Answer:

D is the correct answer.

Step-by-step explanation:

\(3 {x}^{2} + 7x - {(x + 4})^{2} - 9 \)

\(3 {x}^{2} + 7x - ( {x}^{2} + 8x + 16) - 9\)

\(3 {x}^{2} + 7x - {x}^{2} - 8x - 16 - 9\)

\(2 {x}^{2} - x - 25\)

The greatest weight the ant can carry is 44 pounds, expressed in standard form as 4.4 x 10^1 pounds.

The ant can carry objects up to 5,000 times greater than its own body weight. Given that the ant weighs 8.8 x 10^(-6) pounds, we can calculate the maximum weight it can carry by multiplying its own weight by 5,000.

This gives us (8.8 x 10^(-6)) x 5,000 = 44 x 10^(-6) pounds. Simplifying this in standard form, we express it as 4.4 x 10^(1) pounds or simply 44 pounds. Therefore, the ant can carry a maximum weight of 44 pounds.

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F(x) = 4x & g(x) = 3x are the two functions which the (f o g)(x) was equal to "12x".

Legislation, a regulation, or a declaration that demonstrates the relationships between the independent and relationship between the factors (the dependent variable). Functions may be found everywhere in mathematics, and they are essential for building physical connections in the sciences.

The functions f(x) & g(x) are given, and the task is to determine (f o g) (x).

For the following two functions, (f o g)(x) was identical to "12x":

f(x) = 4x and g(x) = 3x.

Proof :

g(x) = 3x

(f o g)(x) = f(x = 3x) = 4(3x) = 12x

(f o g)(x) = 12x

Hence, f(x) = 4x or g(x) = 3x are the 2 type which the (f o g)(x) was equal to 12x.

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The sine function becomes, \(y = 4sin(\frac{\pi }{2}x) + 1\).

What is sine function?

The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others.

The general sine function is

\(y = Asin(b(x+c)+D\)

Where

Amplitude = A

Period = \(\frac{2\pi }{B}\)

Phase shift = c

Vertical shift = D

Given:

A = 4 (amplitude)

\(\frac{2\pi }{B} = 4\)  (period)

\(B = \frac{\pi }{2}\)

Since midline: y = 1

And we know that graph of \(4sin(\frac{\pi }{2}x)\), midline to be y = 1.

It must have vertical shift D = 1.

Since, y - intercept (0, 1)

⇒ x = 0, y = 1

⇒ It has no phase shift  ⇒ c = 0

Since it satisfy \(y = 4sin(\frac{\pi }{2}(x+c))+D\)

The graph of the sine function is attached below.

Hence, the sine function becomes, \(y = 4sin(\frac{\pi }{2}x) + 1\).

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Answer:

\(y=2-2\cos(x)\)

Step-by-step explanation:

We have the differential:

\(y^\prime=2\sin(x)\)

With the general solution:

\(y=C-2\cos(x)\)

And we want to find the particular solution such that it satisfies the initial condition:

\(\displaystyle y\Big(\frac{\pi}{3}\Big)=1\)

So, we have:

\(y=C-2\cos(x)\)

Substituting π/3 for x and 1 for y yields:

\(\displaystyle 1=C-2\cos\Big( \frac{\pi}{3} \Big)\)

Solve for C. Evaluate:

\(\displaystyle 1=C-2(\frac{1}{2})\)

Simplify:

\(1=C-1\)

Hence:

\(C=2\)

Therefore, our particular solution will be:

\(y=2-2\cos(x)\)

Hence, our answer is C

f(-a) is the remainder when f(x) is divided by (x+a). This can be obtained by remainder theorem for polynomials.

Given that f(x) is divided by (x+a) and leaves a reminder

Using the remainder theorem for polynomials we get,

f(x) = (x+a)·g(x) + r, where g(x) is the quotient and r is the remainder.

Put x = -a, then

f(-a) = (-a+a)·g(-a) + r

f(-a) = (0)·g(x) + r

f(-a) = r

f(-a) is the remainder.

Hence f(-a) is the remainder when f(x) is divided by (x+a).

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Answer:

x=30+(8d)

x is the money he has or will have and he starts off with 30 and earns 8 dollars per dog he walks, so 8d means he earns 8 times the amount of dogs he walks

Step-by-step explanation:

Answer: Sali gets 6 cakes. Jane gets 3 cakes. Simon in the end keeps 21 cakes.

Step-by-step explanation: 1/5 of 30 is 6 so if Sali gets 1/5 then Sali should get 6 cakes. 10% of 30 is 3 so if Jane gets 10% then she should get 3 cakes. Sali and Jane together get 9 cakes so Simon has 21 cakes left.

Answer:

1539/4 (improper fraction) or 384 3/4 (simplified fraction)

Step-by-step explanation:

To find the improper fraction, write 384.75 as a fraction:

384.75/1

Then, since you have 2 decimal places after the ., multiply the entire fraction by 100:

38475/100

Next, find the GCF, which is 25, and simplify this fraction to find the final improper fraction:

1539/4

To find the simplified fraction, we already have the whole number, 384, so we have to convert 0.75 to a fraction which is 3/4, because 0.75 is 3/4 of 100:

384 3/4

Hope this helps :)

Answer: the net charge will be 0

Step-by-step explanation: Since there are no other charges ij the atom hence the charge will be

10 +(-10)

=0

Neon atom will have 0 as the net charge.

The charge of the atom is dependent on the number of protons and neutrons present in the atomic nucleus. In case of neon it has 10 protons and 10 electrons, which means that protons are with positive charge so, +10 is the charge; whereas 10 electrons means it has -10 as the charge. When added this results in 0 as the net charge because; +10-10 will give 0 . So, the net charge on Neon is zero.

An elevator goes up 10 stories and then goes down 10 stories The option of the elevator includes two quantities in the real world that are additive inverses.

Additive inverse means when both the quantities are added their sum results in zero. Here, when considering an elevator which goes up to 10 stories and then goes down 10 storeys results in the same position from where it started. Therefore, this is the perfect example of the additive inverse.

On the number line when drawn on the positive number line the ' n ' will be on right side in the position of 3 / 4 and the sum will be on the top of zero. For more clear understanding refer the attached picture.

On the number line when we draw from zero towards left the 'h' can be written on -1.4th point on the left side of the number line. Sum can be dragged on zero.

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Answer:

a) x=3

b) x=4.5

Step-by-step explanation:

2(5x – 3) = 24

10x-6=24

10x=30

x=3

5(2x + 1) = 50

10x+5=50

10x=45

x=4.5

The fy(y) is not a valid probability density function for any value of 0.

Given that the probability density function of the random variable Y is:

fy(y) = 3(0² - y²)/203

We need to find the value of the constant, 0 such that fy(y) is a valid probability density function.

To be a valid probability density function, fy(y) must satisfy the following two conditions:

fy(y) ≥ 0 for all y∫fy(y) dy = 1

The condition fy(y) ≥ 0 for all y is satisfied since the numerator, 3(0² - y²) is non-negative for all values of y.

Now, let's evaluate the integral

∫fy(y) dy.∫fy(y) dy

= ∫(3(0² - y²)/203) dy

= (3/203) ∫(0² - y²) dy

= (3/203) [-y³/3]₀0

= -(3/203) (0³ - 0)

= 0

Therefore, the condition ∫fy(y) dy = 1 is not satisfied. In order to satisfy this condition, we must have

∫fy(y) dy = 1.

We know that the integral

∫fy(y) dy

= (3/203) ∫(0² - y²) dy

= (3/203) [-y³/3]₀0

= -(3/203) (0³ - 0)

= 0

Thus, we must have:

∫fy(y) dy

= ∫(3(0² - y²)/203) dy

= ∫3/203 (0² - y²) dy

= 3/203 ∫(0² - y²) dy

= 3/203 [y³/3]₀0

= 3/203 (0³ - 0)

= 0

We can see that this condition is not satisfied for any value of 0.

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Based on the given statement that the population is growing more slowly, we can conclude that the rate of change of the population function, f'(x), is positive but decreasing. This means that the first derivative, of'(x), is greater than zero.

As for the second derivative, f''(x), we can infer that it is negative because the rate of population growth is slowing down. This means that the curve of the population function is concave down.

Therefore, the correct answer is: of'(x) > 0, f''(x) < 0.

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When Chance stops feeding the beanstalk, it loses half its height every day. Chance's beanstalk grows to a height of 20 inches after he stops feeding it= 20.5^t

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares.

The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.

Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.

Hence, When Chance stops feeding the beanstalk, it loses half its height every day. Chance's beanstalk grows to a height of 20 inches after he stops feeding it= 20.5^t

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Answer:

36π

Step-by-step explanation:

2πR= 12π so R=6

S= πR^2=36π

A M function file 'tconvert.m', which can convert coordinates (x, y) into Polar from Cartesian coordinates. is:
"```matlab
function [theta, r] = tconvert(x, y)
```"

To create the M function file 'tconvert.m' that converts Cartesian coordinates (x, y) into Polar coordinates, follow these steps:

1. Open the MATLAB Editor or any text editor and create a new file named 'tconvert.m'.

2. In the file, start with the function declaration line: `function [theta, r] = tconvert(x, y)`.

3. Inside the function, write the conversion code using MATLAB's built-in functions:

  - Calculate the angle theta using `atan2(y, x)`, which returns the angle in radians.

  - Calculate the radius r using `sqrt(x^2 + y^2)`, which gives the distance from the origin.

4. End the function with the `end` keyword.

5. Save the file in a directory accessible by MATLAB.

The function 'tconvert' takes the Cartesian coordinates (x, y) as input and returns the corresponding Polar coordinates (theta, r). The angle theta represents the direction in radians, and the radius r represents the distance from the origin.

The function can be called from the MATLAB command window or from another script or function file.

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Complete question:

Write a M function file 'tconvert.m', which can convert from Cartesian coordinates (x,y) into Polar coordinates.

Answer:

40

Step-by-step explanation:

15 divided by 3 is 5

so each pound is 5 dollars.

now do 5 times 8

that gives you 40

the big bag is 40 dollars

Answer:

251.33, the reason is because the formula for the volume of a cylinder is height x π x (diameter / 2)2, where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is height x π x radius2.

Step-by-step explanation:

hope that makes sense

The required simplified value of x is x > 6 or x ≤ -1.

We have two inequalities here:
5x - 10 > 20 or 5x - 10 ≤ -15

We can start by solving the first inequality:

5x - 10 > 20

5x > 30

x > 6

So x is greater than 6 for the first inequality to hold.

Next, we can solve the second inequality:

5x - 10 ≤ -15

5x ≤ -5

x ≤ -1

So x is less than or equal to -1 for the second inequality to hold.

Putting it all together, the solution to the system of inequalities is:

x > 6 or x ≤ -1

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The final answer for the expression is 3.2 × 10⁻⁴.

We can write the given expression as below:

(4×10−3)÷(5×105)8×10−88×10−70.8×1028×10−9 = (4/5) × (10⁻³ / 10⁵) × (8 / 8) × (10⁻⁸ / 10⁻⁷) × (0.8 × 10¹⁰ / 10⁻⁹)

On solving, we get

(4/5) × (10⁻³ / 10⁵) × (8 / 8) × (10⁻⁸ / 10⁻⁷) × (0.8 × 10¹⁰ / 10⁻⁹) = 0.00032

                                                                                               = 3.2 × 10⁻⁴

Hence, the final answer is 3.2 × 10⁻⁴.

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There are 8 different trips that can be made from City X to City Z, passing through City Y.

To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.

First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.

By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:

Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z

= 2 x 4

= 8

This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.

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Complete question is:

Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?

Answer:

-5.7-4.2=-9.9 is answer

Answer:

D

Step-by-step explanation:

The coordinate plane in option D contains both the points (1 1/2, 4) and (-2, -2 1/2).