help please
The average distance from Earth to the sun is 149,598,000 kilometers. How do you write this measurement in scientific notation?

149,598 x 10−8 kilometers
149,598 x 10−8 kilometers149,598 x 10−8 kilometers

149,598 x 103 kilometers
149,598 x 103 kilometers149,598 x 103 kilometers

149.598 x 106 kilometers
149.598 x 106 kilometers149.598 x 106 kilometers

1.49598 x 108 kilometers
1.49598 x 108 kilometers

Answer:

40.4

Step-by-step explanation:

I used a calculator

The correct answer is:

b. Test statistic: t = -1.841

Critical value = ±2.045

Do not reject H0

To conduct the hypothesis test using the pooled t-test, we compare the calculated test statistic to the critical value at a significance level of α = 0.05.

Given the following statistics for two independent samples:

Sample 1: x1 = 11.1, s1 = 4.5, n1 = 14

Sample 2: x2 = 17.2, s2 = 4.9, n2 = 17

The pooled t-test assumes that the population variances are equal. We calculate the pooled standard deviation (sp) using the formula:

sp = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2) / (n1 + n2 - 2))

Next, we calculate the test statistic (t) using the formula:

t = (x1 - x2) / (sp * sqrt(1/n1 + 1/n2))

For the given data, the calculated test statistic is t = -3.577.

To determine whether to reject or fail to reject the null hypothesis (H0), we compare the absolute value of the test statistic to the critical value from the t-distribution at a significance level of α = 0.05. In this case, the critical value is ±1.699.

Since the absolute value of the test statistic (-3.577) is greater than the critical value (1.699), we do not reject the null hypothesis (H0). Therefore, the correct answer is c. Test statistic: t = -3.577, Critical value = ±1.699, Do not reject H0.

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Among the four given functions, function IV, f(x) = 25x¹⁰(4-x¹), is an even function. An even function is a function that satisfies the property f(x) = f(-x) for all x in its domain.

In other words, the function is symmetric with respect to the y-axis. To determine if a function is even, we need to check if f(x) is equal to f(-x) for all values of x in the domain of the function. Examining the given functions, we find that function IV, f(x) = 25x¹⁰(4-x¹), satisfies the property of an even function. By substituting -x into the function, we have f(-x) = 25(-x)¹⁰(4-(-x)¹) = 25(-x)¹⁰(4+x¹). Simplifying further, we get f(-x) = 25(-x¹⁰)(4+x¹). Comparing f(x) and f(-x), we observe that they are identical. Therefore, function IV, f(x) = 25x¹⁰(4-x¹), is an even function as it satisfies f(x) = f(-x) for all values of x in its domain.

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9514 1404 393

Answer:

  (c)  162 cm

Step-by-step explanation:

The centroid divides a median into parts with the ratio 1:2, so RL:LD = 1:2. Then RL:RD = 1:(1+2), and RD = 3RL.

  RD = 3·54 cm

  RD = 162 cm

Answer:

- 6

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [ - 1, 4 ] , then

f(b) = f(4) = 4³ - 6(4)² - 4 = 64 - 96 - 4 = - 36

f(a) = f(- 1) = (- 1)³ - 6(- 1)² - (- 1) = - 1 - 6 + 1 = - 6 , then

average rate of change = \(\frac{-36-(-6)}{4-(-1)}\) = \(\frac{-36+6}{4+1}\) = \(\frac{-30}{5}\) = - 6

Answer:

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

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

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Answer:

Eighth half-hour

Step-by-step explanation:

Given pattern:

Calculate the differences between the number of bows used:

\(12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16\)

Therefore, the pattern for the bows used is:

If the pattern continues:

\(12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16\underbrace{}_{-3}13\underbrace{}_{+5}18\underbrace{}_{-3}15\underbrace{}_{+5}20\)

Create a table with the given and found data, and add a cumulative total column:

\(\begin{array}{c|c|c}\vphantom{\dfrac12} \textsf{Half Hour} & \textsf{Bows used per half hour} & \sf Cumulative\; total\\\cline{1-3} \vphantom{\dfrac12} \sf 1st & 12 & 12\\\vphantom{\dfrac12} \sf 2nd &9 &21 \\\vphantom{\dfrac12} \sf 3rd & 14&35 \\\vphantom{\dfrac12} \sf 4th & 11& 46\\\vphantom{\dfrac12} \sf 5th & 16& 62\\\vphantom{\dfrac12} \sf 6th & 13& 75\\\vphantom{\dfrac12} \sf 7th &18 & 93\\\vphantom{\dfrac12} \sf 8th & 15& 108\\\vphantom{\dfrac12} \sf 9th & 20& 128\\\end{array}\)

If Clifford has a total of 100 bows, he will run out of bows during the eighth half-hour.

Answer:

21 Oreos

Step-by-step explanation:

2 × 3 = 6

7 × 3 = 21

hope this helps

The exponential function that goes through the points (0,7) and (2,112) is y = 7 × 4ˣ.

To write an exponential function that goes through the points (0,7) and (2,112), we can use the general form of an exponential function:

y = abˣ

where a is the initial value, b is the base, and x is the independent variable (usually time).

Using the two points given to find the values of a and b.

Let's start with the point (0, 7):

y = a × bˣ

Plug in x = 0 and y = 7

7 = a ×  b⁰

7 = a × 1

a = 7

Next, let's use the point (2, 112):

y = a × bˣ

Plug in x = 2, y = 112 and a = 7

112 = 7 × b²

7b² = 112

Dvide both sides by 7

b² = 16

b = ±√16

b = ±4

We can eliminate the negative solution since we are looking for a function that is growing, so:

b = 4

Now, plug these values into y = a × bˣ

y = 7 × 4ˣ

Therefore, the exponential function y = 7 × 4ˣ

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The simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x  + 3

The side lengths are given as:

2x^2 + 5x + 3, 2 + 2x and 3x - 2

Add these lengths to determine the perimeter (P)

P = 2x^2 + 5x + 3 + 2 + 2x + 3x - 2

Collect like terms

P = 2x^2 + 5x + 2x + 3x  + 3 + 2 - 2

Evaluate the like terms

P = 2x^2 + 10x  + 3

Hence, the simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x  + 3

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Answer:

There are no solutions. Hope this helps! :)

The highest common factor of 60 and 96 is 12.

The given numbers are 60 and 96.

Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself.

A factor tree is a technique that identifies the prime factors of any number. The list of prime numbers or prime factors that you would multiply together to produce a particular number is known as the prime factorization of that number.

The factors of 60 and 96 are

60 = 2×2×3×5

96 = 2×2×2×2×2×3

So, the common factors are 2×2×3

= 12

Therefore, the highest common factor of 60 and 96 is 12.

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Answer:

36pi-113.04

Step-by-step explanation:

C=dpi

so C=36 pi or 113.04

Answer:

I think its B)

Step-by-step explanation:

The harder you hit a baseball, the further the ball travels.

This is newton's first law of motion.

Option A is the correct answer.

It states that every object will remain in its state unless an external force acts on it.

Example:

Moving forward for a person sitting inside a moving car when it suddenly stops.

We have,

The harder you hit a baseball, the further the ball travels.

This is newton's first law of motion.

If it was about the fastest the ball travels it will be newtons second law of motion.

Thus,

The harder you hit a baseball, the further the ball travels is an example of Newton's first law of motion.

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The obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

(x-3)² + 9 = 0

(x-3)²= -9

(x-3)=√-9

(x-3)=√9×√-1

(x-3)=±3i

x=3±3i

Thus, the obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

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Answer:

2.667

Step-by-step explanation:

I have learned how to do this. I hope it is right! (;

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Answer:

(4)

Step-by-step explanation:

one 'x' value maps to more than one 'y' value

Answer: The answer is 3.60 dollars.

Step-by-step explanation:

1 bottle = 10 cents

12 bottles = 120 cents

100 cents = 1 dollar

1 cent = 1/100

120 = 1/100 * 120 = 1.2 dollars

now

1 aluminium can = 5 cents

48 cans = 5*48 = 240 cents

240 cents = 1/100 * 240 = 2.4 dollars

so total = (1.2+2.4) dollars

= 3.6 dollars

On a scatter plot, the line that runs through the center of the dots is called a "trendline" or "line of best fit."

Scatter Plot: A scatter plot is a graphical representation of data points in a Cartesian coordinate system, where each point represents the values of two variables.

Data Points: Each data point on the scatter plot represents the values of the two variables being plotted. The position of each point is determined by the respective values of the variables.

Trendline: A trendline is a line that attempts to represent the general pattern or trend in the data. It is often drawn through the center of the dots to provide a visual indication of the relationship between the variables.

Line of Best Fit: The trendline is also known as the "line of best fit" because it is the line that minimizes the overall distance between the line and the data points. It represents the best approximation of the overall trend in the data.

Therefore, the trendline or line of best fit on a scatter plot is the line that runs through the center of the dots and represents the general pattern or trend in the data.

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Answer:

8

Step-by-step explanation:

When you add it together, you get 8.

It would take approximately 19 years for the value of the account to reach $2,590.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

First, convert R as a percent to r as a decimal

r = R/100

r = 2.2/100

r = 0.022 per year.

Plug the given values into the above formula and solve for time t.

A = P( 1 + r/n )^( n × t )

t = In(A/P) / n[ In( 1 + r/n ) ]

t = In( $2,590/$1,700 ) / ( 12[ In( 1 + 0.022/12 ) ] )

t = 19.155 years

t = 19 years

Therefore, the time taken is approximately 19 years.

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The measurement 779,000 mi has three significant digits and they are: 7, 7, and 9.

To determine the number of significant digits in a measurement, we follow these rules:

1. Non-zero digits are always significant. In this case, the digits 7, 7, and 9 are non-zero, so they are all significant.

2. Zeros between non-zero digits are also significant. There are no zeros between the non-zero digits in this measurement.

3. Leading zeros, or zeros to the left of the first non-zero digit, are not significant. In this case, there are no leading zeros.

4. Trailing zeros, or zeros to the right of the last non-zero digit, may or may not be significant.

In this measurement, the zeros at the end are not significant because they only serve to indicate the magnitude of the number.

Therefore, the measurement 779,000 mi has three significant digits: 7, 7, and 9.

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(2,2)

Step-by-step explanation:

You have to add them together and minus the negatives

Step-by-step explanation:

the slope-intercept form is

y = ax + b

"a" is the slope (the slope is in all forms the factor of x). and "b" is the y-intercept (the y value when x = 0).

so the first equation is

y = -5x + b

b we get by using the point coordinates :

-22 = -5×5 + b = -25 + b

b = 3

so, the full equation is

y = -5x + 3

for the second equation we need to calculate the slope first. remember, it is the ratio "y coordinate change / x coordinate change" :

x changes by +1 (from -4 to -3).

y changes by +7 (from -2 to 5).

the slope is +7/+1 = 7/1 = 7.

the equation looks like

y = 7x + b

again, we use the coordinates of a point to get b. I picked (-4, -2) :

-2 = 7×-4 + b = -28 + b

b = 26

and the full equation is

y = 7x + 26

Answer:

The answer is

Step-by-step explanation:

principal = 100× I/R×T

=100×350/7/2×3

Answer:

We will need 4 pitchers to fill with water the new cylinder.

Step-by-step explanation:

The volume of the first cylinder is:

\(V_{1}=\pi r^{2}h\)  (1)

Where:

Using the values of the problem we have:

\(V_{1}=\pi 4^{2}9\)

\(V_{1}=452.4\: in^{3}\)

We know that it can fill a certain pitcher, so the volume of the pitcher is 452.4 in³.

Let's find the new volume of the second cylinder to find how many of these pitchers can this cylinder.

We know that the cylinder has the same height and the radius is 2 times the older one.

\(V_{2}=\pi (2r)^{2}h\)

\(V_{2}=\pi (2*4)^{2}9\)

\(V_{2}=1809.6\: in^{3}\)

Now, we just need to divide V(2) by V(1) to find the number of pitchers (np).

\(np=\frac{1809.6}{452.4}=4\)

Therefore, we will need 4 pitchers to fill with water the new cylinder.

I hope it helps you!