suppose that the vote on a recent prison reform bill in the us senate had the following results.votes on prison reform billvoted in favorvoted againstrepublican2122democrat447other24if a reporter stops a random senator after the vote, what is the probability that the senator will either be a republican or will have voted against the bill? express your answer as a simplified fraction or a decimal. do not round any intermediate calculations.

the scientific notation is just another mumble jumble way to write the same thing without so many repetitive zeros, so hmmm 780000 has 4 zeros, so what we do is we can say

78 and 4 zeros following it

or we can say

78 * 10⁴, if we get that product, is 780000

in scientific notation, we only leave one digit to the left of the decimal point

so the same thing above can be written as

78 * 10000, can be written as 78.0 * 10000

or as

7.8 * 100000

or as

0.78 * 1000000

check their product

7.8 * 100000, is really just 780000

because we moved the decimal to the left one more slot, it

became 7.8 * 100000

or in

Answer:

780,000 \(=7.8 * 10^5\)

Step-by-step explanation:

Don't worry! I hope you do great on your finals, goodluck<3.

\(a * 10^{b}\)

Variable A represents a number thats absolute value has to be greater than or equal to 1 and less than 10. This is represented below

1 ≤ | a | < 10

Therefore we know that 780,000 will be 7.8, because it is greater than 1 and less than 10 as well can still represent our original number.

\(7.8 * 10^b\)

Assuming you know how powers work, if not I'll go over them very quickly.

For example 8² = 8 * 8, 8³ = 8 * 8 * 8.

what I mean by this is if its in, tenths, hundreths, thousands, 10 thousands..

It's pretty obvious that our number is in the 100 thousands place.

Now if you know you're powers pretty well, this will be easy, although let me try to walk you through it if not.

remember the equation:

\(7.8 * 10^b\)

We are trying to find b.

10 to what power is equal to 100,000

\(10^{1} = 10, 10^{2} = 100, 10^3 = 100, 10^{3} = 1,000, 10^4 = 10,000, 10^5 = 100,000\)

How I like to remember what a power equals is counting the 0's :)

How we know if our answer is correct is plugging it into our equation and solve:

\(7.8 * 10^5\)

We know that 10 to the power of 5 equals 100,000.

\(7.8 * 100,000\)

and using a calculator, or mental math, or doing it the old fashion way, we know that 7.8 * 100,000 is equal to 780,000

Option D. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.

Mean is the average of any data set whereas the median is the middle value we get after arranging the data in ascending order.

So for example, if the salaries of any 5 faculty members are as follows:

$10,000 , $50,000 , $80,000 , $150,000 , $160,000

Mean= (10,000+50,000+80,000+150,000+160,000) / 5

Mean= $90,000

Median= (5+1) / 2

Median= 6/2

Median= 3rd value

As the data is already arranged in ascending order, Median is $80,000

Hence, if the faculty want to give the community the impression that they deserve higher salaries, they should advertise the median of their current salaries.

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The volume common to two spheres, each with radius r, if the distance between their centres is r/2 is V = (11/12)×π×r³.

The attached diagram shows 2 circumferences with radius r and separated centres by r/2.

Let´s call circumferences  1 and 2; by symmetry, rotating area A will produce a volume V₁ identical to a V₂, Obtained by rotating area B ( both around the x-axis), then the whole volume V will be:

V = 2× V₁

V₁ = ∫π×y²×dx         (1)

Now

( x - r/2)²  +  y² = r²       the equation of circumference 1

y² = r² - ( x - r/2)²

Plugging this value in equation (1)

V₁ = ∫π×[  r² - ( x - r/2)²]×dx        with integrations limits    0 ≤ x ≤ r/2

V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx

V₁ = π× [  r²×x - x³/3 + (r/2)²×x - (1/2) × r × x²]    evaluate between 0 and r/2

V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) × r × x²]

V₁ =  π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ -  (1/2) × r × (r/2)²]

V₁ =  π× [ (5/8)×r³ - r³/24 - r³/8]

V₁ =  π× (11/24)×r³

Then

V = 2× V₁

V = 2×π×11/24)×r³

V = (11/12)×π×r³

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Answer:

990×40= 39600

have a nice day <3

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

Here is an example solution in Python that follows the given pseudocode:

# Prompt for and read the first term

first_term = int(input("Enter first term: "))

# Prompt for and read the common difference

common_difference = int(input("Enter common difference: "))

# Prompt for and read the number of terms

number_of_terms = int(input("Enter number of terms: "))

# Calculate the last term

last_term = first_term + (number_of_terms - 1) * common_difference

# Calculate the sum of all the terms

sum_of_terms = number_of_terms * (first_term + last_term) / 2

# Calculate the average of all the terms

average_of_terms = sum_of_terms / number_of_terms

# Display the results

print("The last term is", last_term)

print("The sum of all the terms is", sum_of_terms)

print("The average of all the terms is", average_of_terms)

If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.

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The mean of the given probability distribution is 1.3 (rounded to one decimal place).

To find the mean of a probability distribution, we need to multiply each value by its corresponding probability, and then add up all the products. So, using the given values, we can calculate the mean as:

Mean = (0 x 0.1) + (0.1 x 0.05) + (1 x 0.3) + (2 x 0.55) = 1.25

Therefore, the mean of the given probability distribution is 1.3 (rounded to one decimal place).


To find the mean of a probability distribution, we need to multiply each value by its corresponding probability, and then add up all the products. In this case, the given values are 0, 0.1, 1, 0.05, 2, and 0.3, with their respective probabilities. We can calculate the mean by multiplying each value with its probability and then adding up the products. After the calculation, we get the mean as 1.25. Thus, the mean of the given probability distribution is 1.3 (rounded to one decimal place).


The mean of the probability distribution given as 0, 0.1, 1, 0.05, 2, and 0.3 is 1.3 (rounded to one decimal place). This means that on average, the value of the distribution is around 1.3. The mean is a useful measure of central tendency that helps us understand the characteristics of the probability distribution.

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Answer:

Yes

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 4)

y = 8x - 4

Step 2: Find

yes.

you just have to check like this: 1 is x and 4 is y.

4 = 8(1) - 4

4 = 8 - 4

4 = 4

hope it helps.

Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.

Given:

500.00 kina for the work in 18 hours

To determine the amount of payment for 6 hours of work, we use ratio.

So we let x be the amount of payment if Peter had worked for six hours:

Therefore, Peter would be paid 166.67 Kina if he had worked for six hours.

The function represented in the table changes over equal intervals of 10 for each increase in x. This means that the change in f(x) is constant over these intervals. In other words, the function has a constant rate of change over equal intervals of x.

This tells us that the function is a linear function. Linear functions have a constant rate of change, which means that the change in the output variable (f(x) in this case) is proportional to the change in the input variable (x in this case).

In this specific table, we can see that for every increase in x by 10, f(x) also increases by a constant factor of 5. This indicates that the function is of the form f(x) = 5x + c, where c is a constant.

Overall, the fact that the function changes over equal intervals in a constant manner tells us that it is a linear function, which can be described by a simple equation that relates the input variable (x) to the output variable (f(x)).
Hi! To analyze the function represented in the table, we will look at the changes in the input (x) and output (f(x)) values over equal intervals. By doing so, we can determine the type of function.

Step 1: Identify the interval between the x-values.
In the table, x values are increasing by 10: 14, 24, 34, and 44.

Step 2: Examine the changes in the f(x) values.
For f(x) values, we have: 5, 10, 20, and 40.

Step 3: Analyze the relationship between the changes in x and f(x).
As x increases by 10, the f(x) values double each time:
- From 5 to 10 (10 = 5 * 2)
- From 10 to 20 (20 = 10 * 2)
- From 20 to 40 (40 = 20 * 2)

Step 4: Determine the type of function.
Since the output is doubling for each equal interval of the input, we can conclude that the function is an exponential function.

In summary, the function in the table changes over equal intervals by doubling the output (f(x)) values as the input (x) values increase by 10. This behavior indicates that the function is an exponential function.

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60 ml and 20 ml of each drug is required to make 80 ml of the solution.

What is ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

As two drugs are to be combined in a 3:1 ratio to produce a needed solution.

The ratio is 3:1 so the needed solution are 60 ml/ 20 ml.

Hence, 60 ml and 20 ml of each drug is required to make 80 ml of the solution.

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Answer:

Answer is given below, hope it helps

Step-by-step explanation:

22/4= 11/2

46/8= 23/4

58/10= 29/5

Answer:

Yes one pair of the opposite sides could measure 10 inches , and the other pair could measure 13 inches.

Step-by-step explanation:

A parallelogram have opposite sides parallel and congruent

the given quadrilateral is a parallelogram then

10 = x + 2 Equation A

x + 5 = 2x - 3 Equation B

Solving for Equation A:

x = 10 -2 = 8 inches

Solving for Equation B;

2x - x = 5 + 3

x = 8 inches

Value X are the same equations.

Means that

For x=8 inches opposite side

So Yes one pair of the opposite sides could measure 10 inches , and the other pair could measure 13 inches.

The percentage of people that have a blood glucose level between 100 and 125 is 21.945%

From the question, the given parameters about the distribution are

Mean value of the set of data = 85

Standard deviation value of the set of data = 25

The actual data values = 100 and 125

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

For x = 100, we have:

Substitute the given parameters in the above equation

z = (100 - 85)/25 = 0.6

For x = 125, we have:

Substitute the given parameters in the above equation

z = (125 - 85)/25 = 1.6

The percentage between 100 and 125 is then calculated as:

P(100 < x < 125) = P(z < 1.6) - P(z < 0.6)

From the z table of probabilities, we have;

P(100 < x < 125) = 0.9452 - 0.72575

This gives

P(100 < x < 125) = 0.21945

Express as percentage

P(100 < x < 125) = 21.945%

Hence, the percentage is 21.945%

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The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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The kite will be 61.20 feet above the ground when the string from the kite to her hand is 110 feet long.

A right-angled triangle is a triangle with three sides and three angles, one of which is 90°.

Trigonometric ratios are used to demonstrate the connection between the sides and angles of a right-angled triangle.

Let h denote the perpendicular distance between the top of the kite and her hand. The angle of elevation = 34°. Hence:

sin(34) = h/110

h = 58.20 feet

The distance from the kite to the ground = 58.20 + 3 = 61.20 feet

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The equation of the parabola is y = 2(x - 1)² + 3

From the question, we have the following parameters that can be used in our computation:

Vertex = (1. 3)

Point = (2, 5)

These parameters can be expressed as

(h, k) = (1, 3)

(x, y) = (2. 5)

A parabola can be represented as

y = a(x - h)² + k

Substitute the known values in the above equation, so, we have the following representation

y = a(x - 1)² + 3

Next, we have

5 = a(2 - 1)² + 3

Evaluate the difference and the exponent

5 = a + 3

So, we have

a = 2

Substitute a = 2 in y = a(x - 1)² + 3

y = 2(x - 1)² + 3

Hence, the equation is y = 2(x - 1)² + 3

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The cheapest price for ten (10) rolls would be = £25.50. That is option B.

The wallpapers are those designed paper materials that are used in decoration of a room.

The total number of wall paper that Salima needs to buy= 10 rolls.

A single roll of wallpaper = £9.20

A pack of 3 rolls= £25:50

That is 1 roll = X

make X the subject of formula;

£x = 25.50/3

£x = £8.5

A pack of 5 rolls = £43.05

That is 1 roll = X

make X the subject of formula;

£x = 43.05/3

£x = 14.35

Therefore, the cheapest price that can be used to buy 10 rolls would be = £25.50 because one roll would be = £8.5.

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Answer:

Pack of 3 rolls (total of £85.70

Step-by-step explanation:

25.5+25.5+25.5+9.20= £85.70

If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two

When a categorical variable that has n categories is to be included as an independent variable in a linear regression analysis, it must be converted to n - 1 dummy variables. The reason for this is that including all n categories as dummy variables would cause perfect multicollinearity in the regression analysis, making it impossible to estimate the effect of each variable.In this case, the set of categories {Red, Blue, Green, Yellow} has four categories. As a result, n - 1 = 3 dummy variables are required to represent this variable in a linear regression. This is true since each category is exclusive of the others, and we cannot assume that there is an inherent order to the categories.The dummy variable for the first category is included in the regression model by default, and the remaining n - 1 categories are represented by n - 1 dummy variables. As a result, the number of dummy variables that are required to represent the categorical variable in the regression model is n - 1.

Thus, if a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two .

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Answer:

the answer is d

Step-by-step explanation:

you multiply 35x8=240 then

you divide 240/40=7

Answer:

2,000 square feet

Explanation:

If the kitchen is 300 square feet, we can divide that by the percentage(15%). We get the answer 20, which will be our conversion factor!

Now, we multiply this conversion factor by all the other percentages(without decimals)

5 x 20 = 100

20 x 20 = 400

30 x 20 = 600

15 x 20 = 300

30 x 20 = 600

Now we add up all of these factors and get the answer :D

100 + 400 + 600 + 300 + 600 = 2,000 square feet

Solution:

A point-slope form for a line is given by the following equation:

where (x1,y1) is a point on the line, and m is a slope of this line. In this case, we have that:

(x1,y1)= (-2,3) and m = 2/3

so, the point-slope form for the given line would be:

so that, the correct answer is :

solving for y, this is equivalent to:

applying the distributive property, this is equivalent to:

or

this is equivalent to

that is:

then, the y-intercept is 4.33

and the graph of this line is:

Solution

Answer:

1/8

Step-by-step explanation:

2⁻³ = 1 / 2³ = 1 / (2*2*2) = 1/8

so the minus sign in the exponent means you can put that factor in the denominator without the minus sign.

The total cost of the vegetable seeds is $18.85

We can multiply the cost per package by the number of packets to get the total cost of the vegetable seeds.

There are 13 packages in this case, each costing $1.45 with VAT.

Cost of seeds overall equals Price per packet * Number of packages

Each box costs $1.45.

There are 13 packages total.

$1.45 * 13 is the total cost of the seeds.

We may multiply the price per package ($1.45) by the quantity of packets (13), which will get the total cost:

Total price of seeds: $1.45 multiplied by 13 equals $18.85

It's vital to remember that, as stated in the problem, tax is already included in the pricing per package. Therefore, there is no need to adjust the estimate to account for additional taxes. Given that there are 13 packets and that the price each box is $1.45, we can calculate the total cost by multiplying the number of packages by the price per package.

In order to buy all 13 packages of vegetable seeds, Kevin would need to spend the whole sum shown. In this instance, the overall expense is $18.85.

Include the appropriate unit in your response, which should be "dollars" ($).

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Answer:

The LCM of 4, 5, and 10 is 20, so the smallest perfect square that is divisible by 4, 5, and 10 is 100.

To determine the price the student-athlete should charge for each hot dog to break even, we need to consider the total costs she incurs, including the vendor fee, equipment cost, and the cost per hot dog. By dividing the total costs by the anticipated number of hot dogs sold, we can find the price per hot dog that would allow her to break even.

The total costs for the student-athlete include the vendor fee of $3000 and the equipment cost of $4500, which sums up to $7500 for the season. Additionally, she incurs a cost of $0.35 per hot dog sold. With an anticipation of selling 2000 hot dogs, the total cost for the hot dogs would be 2000 x $0.35 = $700.

To break even, the total revenue from selling the hot dogs should cover the total costs. Therefore, the price per hot dog should be set in such a way that the revenue from selling 2000 hot dogs equals $7500. Dividing the total costs ($7500) by the number of hot dogs (2000), we find that the student-athlete should charge $3.75 per hot dog in order to break even. This price per hot dog would allow her to cover all her expenses and reach the break-even point.

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Using permutation, there are a total of 24 different orders possible.

If there are a total of 4 floats in a parade then the number of possible orders = 4!

If we further calculate it we will get,

               4 x 3 x 2 x 1 = 24

So there are a total of 24 possible orders in which the floats should appear.

The concept used here is the number of arrangements and the technical term used for it in mathematics is a permutation. A permutation is a mathematical calculation that involves finding the number of ways a particular set can be arranged.

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