6.53 x 10^7 is more than, the same as, less than 65300000?

Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)

Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:

The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).

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The answers are a) (f+g)x = 4x+15, b) 39 and c) the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) is called a function.

Given that, the function f(x) = 3x + 10 represents the number of animals adopted at one shelter, and the function g(x) = x + 5 represents the number of animals adopted at another shelter, where x is the number of months.

a) (f+g)x = f(x) + g(x)

= 3x+10 + x+5

= 4x+15

∴ (f+g)x = 4x+15

b) (f + g)(6)

Put x = 6 in (f+g)x = 4x+15

∴ (f + g)(6) = 4(6)+15

= 24+15

= 39

c) It means, the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.

Hence, the answers are a) (f+g)x = 4x+15, b) 39 and c) the animals adopted in 6 months are 24 and there were already 15 animal at the shelter.

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Answer:

Step-by-step explanation:

Part A: (f + g)(x) = 4x + 15.

My work for Part A:

Step 1: Write the functions without the parentheses: x + 5 + 3x + 10 .

Step 2: Rewrite the function so like terms are next to each other: x + 3x + 5 + 10.

Step 3: Combine like terms: x + 3x = 4x, and 5 + 10 = 15.

Step 4: Write the final function in standard form: (f + g)(x) = 4x + 15.

Part B: (f + g)(6) = 39.

My work for Part B:

Step 1: Write the first function substituting x for 4: f(6) = 6 + 5.

Step 2: Solve the function: f(6) = 6 + 5 = 11.

Step 3: Write the final answer for the first function: f(6) = 11.

Step 4: Write the second function substituting x for 4: g(4) = 3 x 6 + 10.

Step 5: Solve the function: g(4) = 3 x 6 = 18, and 18 + 10 = 28.

Write the final answer for the second function: g(4) = 28.

Step 6: Add the output answers together: 11 + 28 = 39.

Step 7: Write the final output answer for both functions: (f + g)(4) = 39.

Part C: 39 represents the total number of animals adopted at two shelters in 6 months.

The available values for each variable in the formula are h= 43.12 and r=8.75. and the volume is 10,366.3 \(in^3\).

A cylinder's volume can be calculated using the following formula:

V = \(\pi r^2h\)

where pi is a mathematical constant, h is the height of the cylinder, and r is the radius of the base.

Substituting the given values, we get:

V = \(3.14(8.75)^2(43.12)\)

\(V= 3.14*76.56*43.12\)

Simplifying the equation, we get:

V ≈ 10366.3 cubic units

Therefore, the volume of the cylinder with a height of 43.12 units and a radius of 8.75 units, using pi as approximately 3.14, is approximately 10,366.3 cubic units.

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Answer:

Step-by-step explanation:

It is given that length and width of a rectangle is 11 cm and 10 cm.

We know the formula of Perimeter of rectangle

\(:\implies \: \) Perimeter = 2(L + B)

Where 'L' denote the length of the rectangle and 'B' denotes the breadth of the Rectangle.

Now Let's substitute the value of Length= 11 cm and Breadth = 10 cm in the above formula .

\(:\implies \: \) 2(11 + 10)

\(:\implies \: \) 2 × 21

\(:\implies \: \) 42 cm

Henceforth The perimeter of the rectangle is 42 cm

The perimeter of a rectangle is calculated by multiplying by 2 the sum of its length and width. So, in this case, the rectangle's perimeter is 42 cm.

The subject of this question is on calculating the perimeter of a rectangle. The formula for finding the perimeter of a rectangle is 2*(length + width). Applying the values given, that is length = 11 cm and width = 10 cm.

So, the perimeter of a rectangle = 2*(11 + 10) cm = 2*21 cm = 42 cm

Therefore, the correct option is OC. 42 cm.

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Answer:

\(\displaystyle \int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x}-\frac{1}{25}e^{5x}+C\)

Step-by-step explanation:

Given Problem

\(\displaystyle \int {xe^{5x}} \, dx\)

Make substitutions for IBP

Let \(u=x,\,du=dx\) and \(v=\frac{1}{5}e^{5x},\,dv=e^{5x}dx\)

Perform IBP

\(\displaystyle \int {u} \,dv=uv-\int {v} \, du\\\\\int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x} -\int {\frac{1}{5}e^{5x}} \, dx\\\\\displaystyle \int {xe^{5x}} \, dx=\frac{1}{5}xe^{5x}-\frac{1}{25}e^{5x}+C\)

By finding all the four slopes, we can see that the word is ECHA.

We know that the general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

s = (y₂ - y₁)/(x₂ - x₁)

With that formula we can get the slopes.

1) Using the points (0, 3) and (2, 4).

m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.

2)Using (-1, -12) and (1, -8)

m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.

3) We have (2, -6) and (-4, -3) so:

m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H

4)we can use the points (0, 3) and (1, 1), so:

m = (1 - 3)/(1 - 0) = -2, so the letter is A

Then the word is ECHA

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The difference between the observed and expected number of late departures is statistically significant, we need to perform a binomial test by calculating the probability of observing 16 or more late departures out of 300 flights assuming the null hypothesis is true. If the resulting p-value is less than 0.05, we can conclude that the difference is statistically significant.

Based on the given information, an airline with a 95% on-time departure rate has 16 out of 300 flights with late departures. The question asks whether the difference between what occurred (16 late departures) and what you would expect by chance is statistically significant.
To determine if the difference is statistically significant, we need to conduct a hypothesis test. In this case, we can use a binomial test since we are dealing with two possible outcomes: on-time departure or late departure.
The null hypothesis (H0) assumes that the observed number of late departures is equal to what would be expected by chance. The alternative hypothesis (Ha) assumes that there is a significant difference between the observed and expected values.
In this case, the expected number of late departures can be calculated by multiplying the total number of flights (300) by the expected on-time departure rate (95%). This gives us an expected value of 300 * 0.05 = 15.
To perform the binomial test, we can calculate the probability of observing 16 or more late departures out of 300 flights, assuming the null hypothesis is true. This probability can be calculated using the binomial probability formula or by using statistical software.
If the resulting probability (also known as the p-value) is less than the significance level (usually 0.05), we can reject the null hypothesis and conclude that the difference between what occurred and what would be expected by chance is statistically significant. Otherwise, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the difference is not statistically significant.
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Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

The answer would be

50-22.50=d

Answer:

a) 26/12=13/6

b) 95/15=19/3

c) 63/27=7/3

d) 17/19=85/95

Graph (a) represent the equation x+2y=4, and it is a function.

A function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.

To determine the function, solve with the help of option,

(A) The graph define the equation of line x+2y = 4

For any value of x, y gives a unique value,

This satisfies the definition of function,

Therefore, graph (A) is a function.

(B)

The graph defines the function x = |y-2|

For one value of x, y has two values,

Thus, values of y are not unique.

(C)

The graph defines the equation of circle x²+y² = 1

For one value of x, y has two values,

Thus, values of y are not unique.

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Answer:

44

Step-by-step explanation:

Answer:

use the pythagorean theorem to solve for the sides and the degree for both triangles so your using cos sin or tan im not sure which one

Step-by-step explanation:

i really hope this helps the question is really vague im sorry if this wasnt a help

sin(θ) = Opposite / Hypotenuse

cos(θ) = Adjacent / Hypotenuse

tan(θ) = Opposite / Adjacent

Answer:

the value of x must be 71°

Step-by-step explanation:

180° - (38° + 33°) = 109°

x = 180° - 109°

x = 71°

Answer:

x = 71

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 38 + 33 = 71

Answer:

Amadi: 20 years old

Chima : 4 years old

Answer:

option B is correct answer.

Step-by-step explanation:

(200-75)/2 = 62.5 miles per hour.

a. According to the range, the two distributions have the same variability.

b. According to the standard deviation, the second distribution has greater variability than the first distribution.

a. To compute the range, we will subtract the lowest score from the highest score.

For the first set of scores: Range = 12 - 0 = 12

Similarly, for the second set of scores: Range = 12 - 0 = 12

Therefore, both sets of scores have the same range.

b. Now, to compute the standard deviation, we will first calculate the mean of the scores.

For the first set of scores: Mean = (0 + 6 + 6 + 12) / 4 = 6

Next, we calculate the deviation of each score from the mean:

0 - 6 = -6

6 - 6 = 0

6 - 6 = 0

12 - 6 = 6

Then, we square each deviation:

\((-6)^2\) = 36

\(0^2\) = 0

\(0^2\) = 0

\(6^2\) = 36

Taking the average of these squared deviations:

(36 + 0 + 0 + 36) / 4 = 18

Finally, we take the square root of this average to get the standard deviation:

SD = \(\sqrt{18}\) = 4.24 (rounded to two decimal places)

Similarly, we can find the mean calculate the standard deviation for the second set of scores which will come out to be -

Mean = (0 + 0 + 12 + 12) / 4 = 6

Standard deviation = \(\sqrt{36}\) = 6

Therefore, for the second set of scores, the standard deviation is larger, indicating greater variability.

Hence we can conclude that -

According to the range, the two distributions have the same variability and according to the standard deviation, the second distribution has greater variability than the first distribution.

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Step-by-step explanation:

put sides into Pythagorean theorem

do algebra

find solution

Answer:

A = 228 tickets

Step-by-step explanation:

We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.

Because the number of adult and student tickets together equals 506, we have A + S = 506.

Because there are 56 more student tickets than adult tickets we have A + 56 = S

And the way the system is already set up allows us to use substitution.

Thus, we have:

\(A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S\)

The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.

You graph >7 with an open dot to the right.

The inequalities ≤ and ≥ would have a closed dot on the number line.

a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".

s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".

t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".

Inequality signs are mathematical symbols used to indicate that one quantity is greater than, less than, or equal to another quantity. These inequality signs includes:

These symbols are used in mathematical expressions and equations to compare values and express relationships between them.

Therefore, with a good understanding of inequality signs we conclude that:

On a graph, > 7 is with an open dot to the right.

Only the inequalities ≤ and ≥ would have a closed dot on the number line.

a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".

s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".

t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".

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Answer:

None of the above.

Step-by-step explanation:

The box plot given has an asterisk which represents an outlier in the data set plotted. This outlier is an extreme data set value which is obviously the maximum value in the data set.

The question mark can be regarded as the highest observation that doesn't take the outlier observation into consideration.

Therefore, none of the options given is the correct label for the point on the box plot represented by the question mark.

Answer:

Workdone = 4900joules

Step-by-step explanation:

Work-done = force x distance

Force = mass x acceleration

If we suppose that the aquarium is at height 0 at the top and height 1 at the bottom (since it's 1m deep), then we need to lift the slide at height x by x metres.

Mass = Density x Volume, therefore force needed to lift the slice is given is

F = density*volume*∆x*acceleration

Since we the mass changes as we take out water then there will be a change in height, for this reason we have ∆x.

Acceleration is due to gravity, therefore g=9.8m/s²

Density = 1000kg/m³

Volume = 4*1*1 = 4m³

F = 1000*4*∆x*9.8 = 39200∆x

Since our distance from the top of the aquarium to the bottom is x metres, then

Work-done = 39200x∆x

To find the total workdone, we find the integral of 39200xdx and the limit will be from 0 to 0.5 since we are to pump halfway of the aquarium. Integrating that we have

19600*x² limit from 0 to 0.5

19600(0.5² – 0²) = 19600(0.25 – 0) = 19600(0.25) = 4900joules

The program is an illustration of loops.

Loops are used to perform iterative and repetitive operations.

The program where comments are used to explain each line is as follows:

public class MyProgram extends ConsoleProgram {

   public void run()     {

//This prompts the user for the number of times to repeat the message

       echo("Anybody home?", readInt("Times to repeat: "));

   }

    private void echo(String lineOne, String lineTwo, int numTimes)     {

//The following iteration is repeated numTimes times

       for (int i = 0; i < numTimes; i++){

//This prints lineOne

       System.out.println(lineOne);

//This prints lineTwo

       System.out.println(lineTwo);

       }

   }

}

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Answer:

2196 fish

Step-by-step explanation:

:)

Answer:

2196 fish

Step-by-step explanation:

your welcome

Answer:

P- value =  0.0069

Step-by-step explanation:

Given that :

sample size n = 1600

The sample proportion  \(\hat p\) = 0.42

The population proportion p = 0.39

The null hypothesis and the alternative hypothesis can be expressed as:

\(H_o : p =0. 39\)

\(H_1 : p >0.39\)

The  test statistics can be computed as follows:

\(Z = \dfrac{\hat p - p }{\sqrt{\dfrac{p(1-p)}{n}}}\)

\(Z = \dfrac{0.42 - 0.39 }{\sqrt{\dfrac{0.39(1-0.39)}{1600}}}\)

\(Z = \dfrac{0.03 }{\sqrt{\dfrac{0.2379}{1600}}}\)

\(Z = \dfrac{0.03 }{\sqrt{1.486875 \times 10^{-4}}}\)

\(Z = \dfrac{0.03 }{0.0121937484}\)

\(Z = 2.4603\)

Z \(\simeq\) 2.46

Determine the P-value of the test statistic.

The P- value = P(Z > \(Z_o\) )

P- value = 1 - P( Z ≤ 2.46)

Using the Excel Function ( = NORMSDIST (2.46))

P- value = 1 - 0.993053

P- value = 0.006947

P- value =  0.0069    to four decimal places

The value of x in the triangle is determined as 45.

The value of x in the triangle is calculated by applying the following formula,.

The measure of angle ABD = 0.2x + 52

The measure of angle CBD = 0.2x + 42

From the diagram, we can set-up the following equations;

x + 16 = 0.2x + 52

Simplify the equation above, by collecting similar terms;

x - 0.2x = 52 - 16

0.8x = 36

Divide both sides of the equation by " 0.8 "

0.8x / 0.8 = 36/0.8

x = 45

Thus, the value of x in the triangle is calculated by equating the appropriate values to each other.

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Answer:

1/7 or 0.14

Step-by-step explanation:

Answer:

0.14

Step-by-step explanation:

All I did was plug it into my calculator. If you don't have one, you can use your phone or computer. Both devices have calculators programmed in. This answer is not the exact answer; it is just the first two decimals.

Please let me know if you need more help. Hope this helps!

Answer:

0.6, 1.2, 1.8, _, _, _

1. 2.4

2. 3.0

3. 3.6

Step-by-step explanation:

You increase the number by .6 each time.