PLEASE HELP!!

Howard has been asked to draw a map of the Federalist Triangle in Washington, D.C. (pictured below) The actual
Federalist Triangle has a base of 3000 ft. and a height of 1200ft. On Howard's map the base of the triangle is 10
inches. What should the height of the triangle be?

A. 2 inches
B. 4 inches
C. 6 inches
D. 8 inches
E. There is not enough information to determine​

9514 1404 393

Answer:

  528

Step-by-step explanation:

The sum can be decomposed into parts that may be easier to figure.

  \(\displaystyle\sum_{n=1}^{24}(2n-3)=2\sum_{n=1}^{24}(n)-3\sum_{n=1}^{24}(1)=2\dfrac{24\cdot25}{2}-3\cdot24\\\\=600-72=\boxed{528}\)

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Answer:

answer is 28

Step-by-step explanation:

3x=84

x=84/3= 28

Answer:

d. m<R = 128, m<S = 52, m<T = 128, m<U = 52

Step-by-step explanation:

The sum of interior angles in this rectangle is equal to 360°

6x - 4 + 2x + 8 + 2x + 8 + 6x -4 = 360° add like terms

16x + 8 = 360 subtract 8 from the both sides

16x = 352 divide both sides by 16

x = 22 now to find the value of each angle replace x with 22

The required answer is  sec θ = -√2.

Explanation:-

Part 1: Given cosine of theta is equal to radical 3 over 2 on the domain [0,[infinity]).

To determine three possible angles θ,  the cosine inverse function which is a cos and since cosine function is positive in the first and second quadrant. Therefore  conclude that, cosine function of θ = radical 3 over 2 implies that θ could be 30 degrees or 330 degrees or 390 degrees. So, θ = {30, 330, 390}.Part 2:To convert 495° to radians, multiply by π/180°.495° * π/180° = 11π/4To find sec θ, we use the reciprocal of the cosine function which is sec.

Therefore, sec θ = 1/cos θ.To find cos 11π/4,  the reference angle, which is 3π/4. Cosine is negative in the third quadrant so the final result is sec θ = -√2.

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Answer:

y=8

Step-by-step explanation:

Slope-intercept form

y=mx+b

Plug in values

y=0x+b

8=0(-4)+b

b=8

substitute

y=8

Answer:

11.3 feet

Step-by-step explanation:

let x= answer

x²+4²=12²

x²=128

x=11.3137085

which rounds to

11.3

Answer:

≈ 11.3 ft.

Step-by-step explanation:

In order to solve this, we must use some trigonometry, in this case, SOH-CAH-TOA. If you don't know what it is, here's a quick explanation:

- SOH: Sin(θ) = Opposite / Hypotenuse

- CAH: Cos(θ) = Adjacent / Hypotenuse

- TOA: Tan(θ) = Opposite / Adjacent

(Remember, SOH-CAH-TOA can ONLY be used for right triangles. If the problem does not clearly show a right triangle, meaning that there's no box in the corner, you cannot use it)

When using SOH-CAH-TOA, we first must choose an angle, either the top one or the bottom one. We can't use the right angle as, well, you just can't :). First, we have to find the bottom angle, so circle it. Literally, just circle the angle, you'll thank me later. I'll explain why we don't solve the top angle later on.

After that, we just do some labeling on the sides of the triangle. First, label the shortest side that forms the circled angle, which is the floor (4 ft), as the Adjacent side. Then label the longest side of the triangle, which is the ladder (12 ft), as the Hypotenuse. Finally, label the side that doesn't form the circled angle as the Opposite side. This is why the circling comes in handy :)

Then, out of SOH, CAH, and TOA, we choose the one that has the sides that forms the circled angle. In this case, it's CAH, or cosine, as the adjacent and hypotenuse form the circled angle.

Next, we write out the formula and solve:

Cos(m∠Circled Angle) = Adjacent/Hypotenuse

Cos(m∠Circled Angle) = 4/12

Cos(m∠Circled Angle) x Cos^-1 = 1/3 x Cos^-1

m∠Circled Angle ≈ 70.5288 (Rounding to the nearest ten-thousandth)

Note: Pay attention to the 3rd line. 'Cos^-1' is basically the equivalent of '÷ Cos'.

The reason why we did the bottom angle first is because you cannot have two unknown variables when solving for one of them. That would've been the case if we did choose the top angle as we wouldn't know the measure of the wall nor the angle. Now that we have solved the bottom angle, we can move onto solving the length of the wall.

Looking at SOH-CAH-TOA, we can either use sine or tangent as we have the measures for both the adjacent and hypotenuse. I'll use sine cause why not? Anyways, let's move on!

Just like last time, we write out the formula and solve:

Sin(m∠Circled Angle) = Opposite/Hypotenuse

Sin(70.5288) = Opposite/12

0.9428 = Opposite/12

0.9428 x 12 = Opposite/12 x 12

11.3137 ≈ Opposite (Wall)

Wall ≈ 11.3 ft. (Rounding to the nearest tenth, as asked to do so by the problem)

Note: Be careful with SOH-CAH-TOA because I've messed up multiple times with my calculator while typing out my explanation, so just make sure you go over it several times before submitting your answer when solving trig problems :). But I'm confident with my answer, so just submit it without hesitation as I've already double-checked my work.

To calculate the amount of mechlorethamine hydrochloride that should be administered to a 132-lb. patient, we first need to convert their weight to kilograms. Therefore, the patient should be administered 0.6 ml of the injection.

132 lbs. is approximately 60 kg.
The dose of mechlorethamine hydrochloride is 0.1 mg/kg, which means that for every kilogram of the patient's weight, they should receive 0.1 mg of the drug.
Therefore, for a 60 kg patient, the dose would be:
0.1 mg/kg x 60 kg = 6 mg
Now we need to figure out how much of the 1:10 trituration of mechlorethamine hydrochloride to administer to achieve a dose of 6 mg.
The trituration is diluted to 10 ml with water for injection, which means that 100 mg of the drug is present in 10 ml of solution.
To calculate how much of the solution we need to administer to achieve a 6 mg dose, we can use the following proportion:
100 mg/10 ml = 6 mg/x ml
Solving for x, we get:
x = 0.6 ml
Therefore, 0.6 ml of the injection should be administered to the patient to achieve a dose of 6 mg of mechlorethamine hydrochloride.
The patient should be administered 0.6 ml of the injection. This is calculated by converting the weight of the patient to kilograms and determining the appropriate dose based on the patient's weight. The trituration is diluted to 10 ml with water for injection, which means that 100 mg of the drug is present in 10 ml of solution. Using a proportion, we can calculate that 0.6 ml of the injection is required to administer a dose of 6 mg of mechlorethamine hydrochloride.

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Answer: y = 4/9 x - 1/3

Step-by-step explanation:

standard form means y = mx + c

so,

4x-8=9y-5

4x-8+5=9y

(4x-3)/9=y

y = (4/9)x - (1/3)

Assuming that we are starting with a pool of 8 people, we can form the committee in 8 different ways. This is because the committee must contain exactly 3 Ravenclaws, 1 Gryffindor, and 4 people from other houses.

First, we will choose 3 Ravenclaws from the 8 people. This can be done in 8 combinations. Then, we will choose 1 Gryffindor from the remaining 5 people. This can be done in 5 combinations. Lastly, we will choose 4 people from the remaining 4 people, which can be done in 4 combinations.

By multiplying the number of combinations, we get for each step, we can conclude that the total number of ways to form an 8-person committee with the requirement is 8 x 5 x 4 = 160. However, since the order of the people in the committee does not matter, this total number is reduced to 8. In conclusion, we can form the 8 person committee with the given requirement in 8 different ways.

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3x-4y=16

add 4y to both sides

3x=4y+16

divide both sides by 3

x=(4y+16)/3

The smallest possible value of x is 8.

Given:

LCM of x and 60 = 240

240 = 2*2*2*2*3*5

= \(2^{4} *3*5\)

60 = 2*2*5*3

= \(2^2*5*3\)

so x must have the same primes as 240.

x = \(2^i*3^j*5^k\)

i<=4 and j,k <= 1

so,

x = \(2^4\)

x = 8.

Therefore the smallest possible value of x is 8.

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Answer:

B.  y ≤ 1/2x + 3

Step-by-step explanation:

Well we can start by finding the y-intercept which is the point on the line that touches the y-axis in this case it’s 3.

And by looking at the shade it is facing down and the line is solid so the inequality starts with y ≤,

So we can cross out answer choices C. and D.

And the slope is 1/2 because that’s how far away each points are from each other.

So the inequality is y ≤ 1/2x + 3

Look at the image below.

The probability of rain given lightning is 2/15. To find the probability of rain given lightning, we can use Bayes' theorem.

It states that P(A|B) = P(B|A) * P(A) / P(B), where A and B are events. Let's assign the events as follows: A: Rain; B: Lightning. We are given: P(A) = 1/2 (probability of rain); P(B) = 3/10 (probability of lightning); P(B|A) = 2/5 (probability of lightning given rain).

Using Bayes' theorem, we can calculate P(A|B): P(A|B) = P(B|A) * P(A) / P(B) = (2/5) * (1/2) / (3/10) = (2/5) * (1/2) * (10/3) = 20/150 = 2/15. Therefore, the probability of rain given lightning is 2/15.

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Answer:

Step-by-step explanation:

Answer:

for every 2  girls, there is one boy so 1/2 which i 50%

Step-by-step explanation:

Answer

try

Step-by-step explanation:

Both rates and ratios are a comparison of two numbers. ... The difference is that a rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit. For example, in a room full of students, there are 10 boys and 5 girls. This means the ratio of boys to girls is 10:5.

Answer:

y = \(\frac{3}{2}\)x-3 ; Graph C

2x + 6y = -6 ; Graph A

y = \(\frac{1}{2}\)x + 2; Graph B

If for her party, Carla bought a 5-pound bag of candy to give as party treats. She invited 15 people. The amount of candy that each of the 15 people get is: A) 15 ÷ 5 = 15/5 = 3 pounds.

Given data:

Candy bought = 5

Number of people invited = 15

Now let find the amount of candy to gives as party treats

Number of candy = Number of people invited / Candy bought

Number of candy = 15/5

Number of candy = 3 pounds

Therefore we can conclude that the correct option is A.

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Answer:

"sequence"

Step-by-step explanation:

That'd be a "sequence."

The commonest sequences are 1) arithmetic and 2) geometric.

Answer:

pattern

Step-by-step explana

usatest prep

The type of data collected by the postal worker counting the number of complaint letters received by the United States Postal Service in a given day is quantitative discrete data.

Quantitative data refers to numerical data that can be measured or counted. In this case, the postal worker is counting the number of complaint letters, which is a numerical value.

Discrete data refers to values that can only take on specific whole numbers, in this case, the count of complaint letters. Since the number of complaint letters is a countable value and does not take on fractional or continuous values, it falls under the category of discrete data.

The data collected by the postal worker represents the quantity of complaint letters received and can be used for further analysis and statistical interpretation.

Therefore, the data collected by the postal worker, which counts the number of complaint letters received by the United States Postal Service in a day, is categorized as discrete quantitative data.

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Answer:

yes

Step-by-step explanation:

you can use the vertical line test- for every line going up and down there should only be one point. if there is one and only one, it's a function. if there are more than one per line, then it is not a function.

Answer:

lim_( 3\/(-5 + x) = 0

Step-by-step explanation:

h(x) = 1\/(x - 5)×3

{x element R : x!=5}

{h element R : h!=0}

d\/dx(3\/(x - 5)) = -3\/(x - 5)^2

integral 3\/(x - 5) dx = 3 log(x - 5) +

I think it's 28 units²

The answer is C, 6.6 miles.

Answer:

B

Step-by-step explanation:

I've done these type of questions before, pretty easy you can even figure it out without paper, just pure logic.

Answer:

b ≤ -200

( - ∞, -200]

Explanation:

We have to solve

for b.

Multiplying both sides by -10 reverses the direction of the inequality and gives

which simplifies to give

We plot the above on the number line.

The above plot tells us that all values of b less than or equal to -200 satisfies the inequality.

Using the interval notation, we write the interval as

Where parenthesis tells us that ∞ itself is not included in the interval, the bracket '[' tells us that -200 is included in the interval.

Answer:

Percentage of computers working equals:

90%

Step-by-step explanation:

Three of the thirty computers are out of service.

Number of computers working=30-3=27

Total computers=30

Percentage of working computers=

                                                       =  

                                                       = 90%

Hence, Percentage of computers working is:

90%

Answer :

90%

Step-by-step explanation:

3/30 = 10% and the remaining percent is 90%

0 J. When the child carries the box at a constant speed, the net force on the box is zero because there is no acceleration. Therefore, the work done by the child on the box is zero. So, the correct option is 0 J.

To determine the amount of work done by the child while walking across the floor at a constant speed, we need to consider the following terms: work, force, and displacement.

Work is the amount of energy transferred when a force is applied over a certain distance. It is calculated as:

Work = Force x Distance x cos(θ)

where Force is the applied force, Distance is the displacement, and θ is the angle between the force and displacement vectors.

When the child carries the box with a constant speed across the room, the force applied is equal to the gravitational force acting on the box (i.e., the weight of the box). However, since the force and displacement are in different directions (the force is acting vertically, while the displacement is horizontal), the angle between the force and displacement is 90 degrees.

Now, we know that cos(90°) = 0. Thus,

Work = Force x Distance x cos(90°) = Force x Distance x 0 = 0 J

So, the work done by the child on the box while walking across the floor at constant speed is 0 J.

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The statements that are true about the given algorithms are: I. Algorithm 1 does not work on lists where the smallest value is at the start of the list or the largest value is at the end of the list.  II. Algorithm 2 does not work on lists that contain all negative numbers or all numbers over 1000.

Algorithm 1's reliance on initializing minVal to the first value and maxVal to the last value can lead to incorrect results if the smallest or largest value is not properly updated during the iteration. Similarly, Algorithm 2's fixed initial values for minVal and maxVal can result in incorrect differences when dealing with lists containing all negative numbers or all numbers over 1000.

It is important to consider these limitations and potential failure cases when choosing and implementing an algorithm for calculating the difference between the smallest and largest values in a list.

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The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

You should perform x trials until you observe a success.

We have given that,

There are exactly two possible outcomes success and failure.

We have to determine the following is NOT a common characteristic of a binomial distribution.

By process of elimination:-

A binomial experiment is a statistical experiment that must meet certain requirements

All trials are independent.

There are a fixed number of n trials.

The probability of success, p, is the same for each trial.

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