what is the probability that a senator is under 70 years old given that he or she is at least 50 years old?

Answer:

a= -2

Step-by-step explanation:

Answer: a = -2

Step-by-step explanation: Provided in the attachment.

Answer:

Step-by-step explanation:

a). \(\text{cos}^4(\frac{\theta}{6})-\text{sin}^4(\frac{\theta}{6})=\text{cos}\frac{\theta}{3}\)

   By solving left hand side of the equation,

   = \([\text{cos}^2(\frac{\theta}{6})-\text{sin}^2(\frac{\theta}{6})][\text{cos}^2(\frac{\theta}{6})+\text{sin}^2(\frac{\theta}{6})]\)

   = \([\text{cos}^2(\frac{\theta}{6})-\text{sin}^2(\frac{\theta}{6})](1)\) [Since, cos²a + sin²a = 1]

   = \(\text{cos}\frac{\theta}{3}\) [Identity used → cos²a - sin²a = cos(2a)]

Hence, left hand side of the given equation = Left hand side of the equation.

Answer:

The answer to your problem is, C. \(-\frac{4}{3}\)

Step-by-step explanation:

Given that, the green line has a slope of \(\frac{3}{4}\)

We would need to find the slope of the red line.

The formula for the slope of perpendicular lines is m1.m2 = -1. The productof the slopes of perpendicular lines is equal to -1.

Since, m1=\(\frac{3}{4}\)

Now, \(\frac{3}{4}\). M2 = -1

⇒m2 = \(-\frac{4}{3}\)

Thus the answer to your problem is, \(C. -\frac{4}{3}\)

The loop will be written in Matlab.

Simply setting the years' range will allow the for loop to run its course and complete the task. To allow the loop to iterate from 1 to the number of years, we add the expression 1:number years.

function savingsBalance = CalculateBalance(numberYears,savingsBalance)

% numberYears: Number of years that interest is applied to savings

% savingsBalance: Initial savings in dollars

interestRate = 0.025;  

% 2.5 percent annual interest rate

% Complete the for loop to iterate from 1 to numberYears (inclusive)

for n = 1:numberYears

savingsBalance = savingsBalance + (savingsBalance * interestRate);

end

end

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Answer:

16

Step-by-step explanation:

You're doing a subtraction problem between (x+5) and (2x+3)

(x+5) - (2x+3) =

**You need to solve for x first then plug it in to find the answer.***

(I had to break the parentheses because that is the only way to solve)

-x +8

x= -8

-8 + 5 - (-16+3)

-3 + 16 + 3

13 + 3 = 16

Answer:

-x+2

Step-by-step explanation:

(x+5)-(2x+3)
distribute
x+5-2x-3
combine like terms
x-2x+5-3
-x+2

Answer:

10000000.9

Step-by-step explanation:

The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.

In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.

In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.

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Rounding to the nearest minute, the athlete's trip will take approximately 96 minutes.

Let's start by drawing a diagram to better visualize the situation:

        A     x     D         C

        o-----x------------x

              |            |

              |            |

              |            |

              |            |

              |            |

              |            |

              B            |

              o------------o

Here, point A is where the athlete starts, point B is where she comes ashore due to the current, point C is her intended destination on the shoreline, and point D is the point where she switches from rowing to running.

From the diagram, we can see that the distance AB is 3 miles, and the distance AC is 3 + 1/2 = 3.5 miles.

We can use the Pythagorean theorem to find the distance BC:

\(BC^2 = AB^2 + AC^2\)

\(BC^2 = 3^2 + 3.5^2\)

\(BC^2 = 12.25\)

BC = sqrt(12.25)

BC = 3.5

So the distance the athlete needs to travel on foot is 3.5 miles.

Let's first calculate the time it takes for her to row to point D:

Time to row to D = Distance / Speed

Time to row to D = 1/2 / 2

Time to row to D = 1/4 hours

Next, let's calculate the time it takes for her to run from D to C:

Time to run to C = Distance / Speed

Time to run to C = 3.5 / 4

Time to run to C = 7/8 hours

Now, we need to find the time it takes her to travel from B to C.

We can use the law of sines to find the angle between AB and BC:

sin(28) / 3 = sin(\(\theta\)) / 3.5

sin(theta) = 3.5 * sin(28) / 3

sin(theta) = 0.5407

theta = arc sin(0.5407)

theta = 33.15 degrees

Therefore, the angle between AB and BC is approximately 33.15 degrees.

We can use this angle and the distance BC to find the distance the athlete actually traveled from B to C:

Distance traveled from B to C = BC * sin(\(\theta\))

Distance traveled from B to C = 3.5 * sin(33.15)

Distance traveled from B to C = 1.925 miles

Finally, we can calculate the total time of the trip:

Total time = Time to row to D + Time to run to C + Time to travel from B to C

Total time = 1/4 + 7/8 + (1.925 / 4)

Total time = 0.25 + 0.875 + 0.48125

Total time = 1.60625 hours

To convert this to minutes, we can multiply by 60:

Total time = 1.60625 * 60

Total time = 96.375 minutes.

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Answer:

1232

Step-by-step explanation:

1232 6th grades went on the trip because 160p multiplied by .77, the amount of chaired covered by 6th graders, is equal to 1232.

The probability of getting the color yellow when spinning a spinner with three equal sections colored red, white, and blue is 0%. Therefore, the correct answer is d) 0%.

Since the spinner has three equal sections colored red, white, and blue, and there is no section labeled yellow, it is not possible to obtain the color yellow when spinning the spinner. Each section has an equal chance of being landed on, but none of them represent the color yellow. Therefore, the probability of getting the color yellow is 0%. It's important to note that probability represents the likelihood of an event occurring, and in this case, the event of landing on the color yellow is not possible given the given information about the spinner. Therefore, the probability is 0%.

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Answer:

Step-by-step explanation:

3x = f

2x = e

x is how many batches you want to make.

Answer:

14 more nurses.

Step-by-step explanation:

So, there are 3 shifts a day that need 7 nurses each.

To find out how many nurses the hospital needs to employ, they would need to multiply the number of shifts by the amount of nurses needed. '

In this situation it would look like this:

3 shifts x 7 nurses = 21 total nurses

The hospital would need to employ 14 more nurses if they don't want the nurses' shifts to overlap.

Hope this helps!!

Answer:

67

Step-by-step explanation:

Multi-Inscribed Quadrilateral: 15

Bananas: 4

Clock: 3

Therefore, we can substitute for the last equation the values, so it would become:

3 + 4 + 4 x 15 = ?

First, we solve the multiplication according to PEMDAS.

4 x 15 = 60

Then, we can add from left to right.

3 + 4 + 60 = ?

3 + 4  = 7

7 + 60 = 67

Therefore, our answer would be 67.

Answer:

\(15 + 15 + 15 = 45 \\ 4 + 4 + 15 \: \: \: \: = 23 \\ 4 + 3 + 3 = 10 \\ 3 + 4 + 4 \times 11 = 51\)(according to BODMAS)

Step-by-step explanation:

First divide 45 by three

\(45 \div 3 = 15\)

then subtract 15 from 23 and divide that answer by 2

\(23 - 15 = 8 \\ 8 \div 2 = 4\)

Now subtract 4 from 10 and then divide that answer by 2

\(10 - 4 = 6 \\ 6 \div 2 = 3\)

Now add 3+4+4*11 you will get the answer for ?

\(3 + 4 + 4 \times 11\)

3 + 4 + 44

7 + 44

= 51

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

There are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe

WHAT IS COMBINATION ?

Combination refers to a mathematical concept used to count the number of ways in which a specific number of objects can be selected from a larger set, without considering their order. In other words, it is a way to calculate the number of possible combinations that can be formed from a given set of objects, where the order in which the objects are chosen does not matter. Combinations are denoted by the symbol "nCr" or "C(n,r)" and can be calculated using the formula: nCr = n!/r!(n-r)!, where n represents the total number of objects, and r represents the number of objects being chosen.

To solve this problem, we can use the combination formula. The number of ways to select k items from a set of n items is given by:

C(n, k) = n! / (k! * (n - k)!)

where n! means n factorial (i.e. n multiplied by all the positive integers less than n).

In this case, we want to select 10 employees for the dayshift and 4 employees for the night shift, out of a total of 14 employees. So the number of ways to make this assignment is:

C(14, 10) * C(4, 4) = (14! / (10! * 4!)) * (4! / (4! * 0!))

Simplifying this expression, we get:

C(14, 10) * C(4, 4) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1) * 1

C(14, 10) * C(4, 4) = 1001 * 1

C(14, 10) * C(4, 4) = 1001

So there are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe

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Answer:

perimeter=1/2*2πr

Step-by-step explanation:

1/2*2*3.142*10

=31.42

Given:

A line passes through the points (-6, 8) and (-16, 33).

To find:

The slope of the line.

Solution:

If a line passes through two points, then the slope of the line is

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

The line passes through the points (-6, 8) and (-16, 33). Using the above formula, the slope of the line is

\(m=\dfrac{33-8}{-16-(-6)}\)

\(m=\dfrac{25}{-16+6}\)

\(m=\dfrac{25}{-10}\)

\(m=-2.5\)

Therefore, the slope of the line is -2.5.

Slope of the line passing through the points ( -6,8)  and (-16,33) will be -2.5.

Given information:

The line passes through the points ( -6,8)  and (-16,33).

It is required to find the slope of the line.

Slope of the line passing from two points  \((x_1,y_1) \; and\; (x_2, y_2)\) can be written as

\(m= \dfrac{y_2-y_1}{x_2- x_1}\)

So, the slope of the given line can be calculated as,

\(m= \dfrac{33-8}{-16- (-6)}\\m = \dfrac{25 }{-10} \\m = -2.5\)

Therefore the slope of given line will be -2.5.

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Answer:

106 degrees

Step-by-step explanation:

Answer:

106

Step-by-step explanation:

The actual weight is 0.0042 pounds lighter than the labeled weight.

The actual weight of the chocolates is 0.3798 pounds, while the label on the bag states it should weigh 0.384 pounds. To determine how much lighter the actual weight is, we can calculate the difference between the two weights.

Subtracting the actual weight from the labeled weight, we get:

0.384 pounds - 0.3798 pounds = 0.0042 pounds.

Therefore, the actual weight is 0.0042 pounds lighter than the labeled weight.

It's important to note that this difference may seem small, but it can be significant depending on the context. Accuracy in labeling is crucial for various reasons, such as complying with regulations, providing precise information to consumers, and ensuring fair trade practices. Even minor discrepancies can impact trust and customer satisfaction.

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The Total Monetary amount amassed in song downloads was 1,080,190 dollars.

The following question can easily be solved by simply multiplying the song downloads with the amount received per download:

991,000×1.09= 1,080,190 dollars

Also, total sales in videos:

550,000x9= 4,950,000 dollars

So, total amount received by selling videos and song downloads= 1,080,190+4,950,000= 6,030,190 dollars

Donny West's share is about 15% of the total amount= \(\frac{15}{100}\) × 6,030,190= 904,529 dollars.

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Answer:

\(h=16inches\)

Step-by-step explanation:

From the question we are told that:

Base of  flag \(l_b=8inch\)

Area of flag \(A=64 inch^2\)

Generally the equation for a triangle is mathematically given by

 \(Area=\frac{1}{2}l_b*h\)

Therefore

 \(h=\frac{2A}{l_b}\\h=\frac{2*64}{8}\)

 \(h=16inches\)

Therefore the hieght of the ship is  mathematically given as

 \(h=16inches\)

Answer:

18.01 units to 2 dec. places.

Step-by-step explanation:

Calculate the length of the 3 lines of the triangle

AB = √ [(5 --1)^2 + ( 0 - -4)^2]

= √(36 + 16)

= √52

= 7.211.

BC = √ [(-1-3)^2 + (-4- -6)^2]

= √(16 + 4)

= √20

= 4.472.

CA = √ [(3-5)^2 + (-6-0)^2]

= √(4 + 36)

= √40

= 6.325.

So the perimeter = 7.211 + 4.472 + 6.325

= 18.008

Answer:

the answer to your question is 24

Step-by-step explanation:

hope this helps

Answer:

Option 1

Step-by-step explanation:

Solve each piece individually first.

4 ^(1/2) = 2

The 4th root of 16 is 2 so 2/2 = 1

So we have:

2 * 1 - 10 ÷ 2

Order of operations.

2 * 1 = 2        10 ÷ 2 = 5

2 - 5 = -3

The answer is the first option.

Answer:

the 3rd one

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

The first number is 40 and decreases by 4 in each factor, and the second number is -10 and increases by 1 in each factor.

The first number is positive and decreases by 10% its value in each factor, and the second number is negative and increases by 10% its absolute value in each factor. That means we will have a factor where both numbers are 0 (in the 11th value, we will have the first number 40 - 4*10 = 0 and the second number -10 + 1*10 = 0), so the factor will be 0 + 0 = 0, and then whole product will be zero.

The correct option is B) Not valid. Consider the statement “Since some shoes are sneakers, some non-sneakers are non-shoes.”

We know that all sneakers are shoes, but all shoes are not sneakers.  Hence, some shoes are sneakers. But, this statement does not imply that “some non-sneakers are non-shoes.” This inference cannot be drawn by contraposition. So, it is not valid.Inferences cannot be drawn in contraposition all the time. Contraposition is a type of logical statement that involves reversing and negating the terms of an original proposition. It is a logical relationship between a proposition and its converse. If a proposition is true, the contrapositive is always true.An example of contraposition can be shown as follows:“If a person is a human, then they are mortal.”We can write the contrapositive of this statement as:“If a person is not mortal, then they are not human.”

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