Describe a transformation that would make quadrilateral ABCD into a square
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Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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Answer:

StSin 135° = 0.7071

Cos 135° = - 0.7071.

Tan 135 = 1

Step-by-step explanation:

We are given that;

θ = 3π/4 rads

Now, 3π/4 in radius means that θ = 135°

Thus;

Sin 135° = 0.7071

Cos 135° = - 0.7071.

Tan 135 = sin 135/cos 134 = 1

Without additional details, we cannot determine the number of two-dozen tulip arrangements the florist should expect to sell with the anticipated 4,600 more customers.

To determine the number of two-dozen tulip arrangements the florist should expect to sell if they anticipate 4,600 more customers, we need to examine the given results and make a reasonable assumption based on the available information.

Unfortunately, the given results or information regarding the number of tulip arrangements sold or the relationship between customers and sales are not provided. Without this data, it is not possible to accurately estimate the number of arrangements that will be sold with an additional 4,600 customers.

To make an accurate prediction, we would need more information such as the average number of tulip arrangements sold per customer or any patterns or trends observed in the sales data.

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The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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The probability that less than 75% of the sample students have iPhones is approximately 0.2478.

What is probability?

This is a binomial probability problem, where each student either has an iPhone or does not have an iPhone, and the probability of success (having an iPhone) is 0.789.

Let X be the number of students in the sample who have an iPhone. We want to find P(X < 0.75 * 50) = P(X < 37.5)

Using the binomial probability formula, we have:

P(X < 37.5) = Σ P(X = k), for k = 0, 1, 2, ..., 37

However, this is a tedious calculation. Instead, we can use a normal approximation to the binomial distribution, since n * p = 50 * 0.789 = 39.45 > 10 and n * (1 - p) = 50 * 0.211 = 10.55 > 10.

Using the normal approximation, we can standardize the random variable X:

Z = (X - μ) / σ

where μ = n * p = 39.45 and σ = √(n * p * (1 - p)) = √(50 * 0.789 * 0.211) = 2.88.

Then, we have:

P(X < 37.5) = P(Z < (37.5 - 39.45) / 2.88) = P(Z < -0.68)

Using a standard normal table or calculator, we find that P(Z < -0.68) is approximately 0.2478.

Therefore, the probability that less than 75% of the sample students have iPhones is approximately 0.2478.

Binomial probability is a type of probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure. It assumes that the probability of success in each trial is constant, and the trials are independent of each other. The binomial distribution is characterized by two parameters: the number of trials and the probability of success in each trial.

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The value of x, y and z in the system equation is (1, 2, 3).

The solution of the equation can be determined by using Cramer's rule as follows;

[-5    -6      0] = [ -17]

[-3     -5     5]    [2   ]

[-6    -5      1]     [-13 ]

The determinant of the matrix is calculate as;

Δ = -5 (-5 + 25) + 6(-3 + 30) + 0(15 + 30)

Δ = 62

The x-determinant of the matrix is calculated as follows;

Δx = -17(-5 + 25) + 6(2 + 65) + 0

Δx = 62

The y-determinant of the matrix is calculated as follows;

Δy = -5(2 + 65) + 17(-3 + 30) + 0

Δy = 124

The z-determinant of the matrix is calculated as follows;

Δz = -5(65 + 10) + 6 (39 + 12) - 17(15 - 30)

Δz =  186

The value of x, y and z is calculated as follows;

x = Δx/Δ = 62/62 = 1

y = Δy/Δ = 124/62 = 2

z = Δz/Δ = 186/62 = 3

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Solution:

Markup refers to the difference between the selling price of a good or service and its cost. It is expressed as a percentage above the cost.

Given:

Mark up is given by;

Mark up percent is;

Therefore, the percentage mark up on the boat is 11.76%

The polar coordinates for each point are given as follows:

a. \((r, \theta) = \left(2\sqrt{5}, \frac{7\pi}{4}\right)\)

b. \((r, \theta) = \left(6, \frac{\pi}{3}\right)\)

Suppose we have a point with Cartesian coordinates given as follows:

(x,y).

The polar coordinates will be found as follows:

For item a), the Cartesian coordinates are as follows:

(-4, 4).

Hence the polar coordinates will be given as follows:

For item a), the Cartesian coordinates are as follows:

(3, 3sqrt(3)).

Hence the polar coordinates will be given as follows:

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Answer:

The rate is 5 dollars per student.

Step-by-step explanation:

The rate per student can be found with \(\frac{dollars}{student}\):

\(\frac{150dollars}{30student}=5\frac{dollars}{student}\\\\\frac{350dollars}{70student}=5\frac{dollars}{student}\)

The rate is 5 dollars per student.

Answer:

One Apple.

Step-by-step explanation:

This is a basic subtraction and addition problem. She began with one apple and gave one to her friend. How many apples is Elysia holding now? 2-1= 1

One apple.

Elysia will have one apple, as one apple is being subtracted because she gave it to her friend.

In math, to subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less.

Given that, Elysia has 2 apples she gives 1 to her friend,

To find the number of apples Elysia left with, we will subtract the number of apples she gave to her friend to the number of apples she had,

Number of apples Elysia left with = 2-1 = 1

Hence, Elysia will have one apple.

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Based on the information, there is a t, 2≤ t ≤ 4. using the Mean value theorem and t=2

The given parameters are

t: 2≤t≤4

t is a continuous function between 2≤t≤4

We should equally know that the amount of coffee at the cup at a time y=C

Using the formula  for t

t=C(4) -C(2)/4-2

Inputting the values of t at the extremes values

t=C(4) -C(2)/4-2  = (12.8-8.8)/4-2

Simplifying this to get

4/2

=2

⇒ C(2) is continuous on the coordinates (2,4) and this can be differentiated in the coordinates (2,4)

If we apply the intermediate value theorem, the is t in (2,4)

Therefore, C(t) = [C(4)- C(2)]/ 4-2

This implies that C(t) = 2

In conclusion, based on the information, there is a t, 2≤ t ≤ 4. using the Mean value theorem. and t=2

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The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Answer:

4 degrees Celsius

Step-by-step explanation:

Since the mean is (total/amount), we can remake this to get That mean*amount=total. For the first 7 days, 4*7=28 for our total, and add that to the 8th day to get 32 for our total. 32/8=4 for our mean for the first 8 days of january

Answer:

Answer:

4 degrees Celsius

Step-by-step explanation:

Since the mean is (total/amount), we can remake this to get That mean*amount=total. For the first 7 days, 4*7=28 for our total, and add that to the 8th day to get 32 for our total. 32/8=4 for our mean for the first 8 days of january

The size of the angle between AH and the plane ABCD is approximately 74.4°, rounded to one decimal place.

To find the size of the angle between AH and the plane ABCD in the given cuboid, we can use the concept of three-dimensional geometry.

First, let's consider the right triangle BCA. The given angle BCA is 48°, and we know that the length of AB is 7.3 cm. Using trigonometric functions, we can find the length of BC:

BC = AB * sin(BCA)

BC = 7.3 * sin(48°)

BC ≈ 5.429 cm

Now, let's look at the right triangle BAH. The length of AH is given as 8.1 cm. We can find the length of BH by subtracting BC from AB:

BH = AB - BC

BH ≈ 7.3 - 5.429

BH ≈ 1.871 cm

Next, let's consider the right triangle ABH. We want to find the angle BAH, which is the complement of the angle between AH and the plane ABCD. We can use the cosine function to find the angle BAH:

cos(BAH) = BH / AH

cos(BAH) ≈ 1.871 / 8.1

BAH ≈ arccos(1.871 / 8.1)

BAH ≈ 74.4°

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Answer:$31,500

Step-by-step explanation:

To calculate the total amount Mario will pay, including the loan amount and interest, for the loan from First Bank of Trust, we need to calculate the interest and add it to the loan amount.

The formula to calculate simple interest is:

Interest = (Loan Amount) x (Interest Rate) x (Loan Length)

Let's plug in the values given:

Loan Amount = $25,000

Interest Rate = 6.5% (or 0.065 as a decimal)

Loan Length = 4 years

Interest = $25,000 x 0.065 x 4 = $6,500

Now, let's calculate the total amount Mario will pay:

Total Amount = Loan Amount + Interest = $25,000 + $6,500 = $31,500

Therefore, the total amount Mario will pay, including the loan amount and interest, for the First Bank of Trust loan is $31,500.

Answer:

We need to add 400 ml of pure water to obtain the solution at 55%

Step-by-step explanation:

Concentration

The concentration of a solution measures the amount of solute that has been dissolved in a given amount of solution. The question states the alcohol is the solute and water is the solvent to produce the mix or solution.

The concentration can be calculated with the formula:

\(\displaystyle c=\frac{solute}{solute+solvent}*100\%\)

Originally, the mixture was 95% concentrated.

Substituting in the formula:

\(\displaystyle 95\%=\frac{solute}{solute+solvent}*100\%\)

We know there were 550 ml of solution (solute+solvent), thus

\(solution*0.95=solute=522.5\ ml\)

Now we know there were 522.5 ml of alcohol.

We now need to add x ml of water to have a 55% concentrated solution. Recall that water is solvent, the solute keeps its original value, thus:

\(\displaystyle 55\%=\frac{solute}{550+x}*100\%\)

Operating:

\(0.55(550+x)=522.5\)

Dividing by 0.55

\(550+x=950\)

Thus \(x=950-550=400\)

We need to add 400 ml of pure water to obtain the solution at 55%

Answer: here

Step-by-step explanation: id say about 322 cuase of the decimal

Answer:

y = -2/3x + 5

Step-by-step explanation:

lmk if you want an explanation

Answer:

The first box : -4  the second one : 6

Step-by-step explanation:

subtract 7 from 3 for the first box, then add 10 to -4 for the second one.

Answer:

charged with providing of three types of clients

Answer:

Umm are you going to repost and actually ask the question and give the right amount of points?

Step-by-step explanation:

Answer:

119400

Step-by-step explanation:

The approximate population of the city was 119400

The number of Jim's model car is 48

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

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

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

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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Answer:

Step-by-step explanation:

lets have one side =a

P=3a+a+(17+a)=52

P=5a+17=52

5a=52-17

5a=35

a=7

second side=21

third side=24

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Step-by-step explanation:

the mean is always the sum of all data divided by the number of data points.

we have 5 data points.

their sum is

12 + 9 + 4 + 10 + 15 = 50

the mean is

50/5 = 10

The distance between (4, 2) and (8, 5) is 5 units.

The distance between two given points can be calculated using the following formula :

Distance, D =  [ ( x2 - x1 )^2 + ( y2 - y1 )^2 ]^1/2

Coordinates of point A = (4,2)

Coordinates of point B = (8,5)

For the above mentioned formula, we get

x1 = 4

x2 = 8

y1 = 2

y2 = 5

Substituting these values in the distance formula, we get

D = [ ( 8 - 4 )^2 + ( 5 - 2 )^2 ]^1/2

=> D = [ ( 4 )^2 + ( 3 )^2 ]^1/2

=> D = [ 16 + 9 ]^1/2

=> D = [25]^1/2

=> D = 5

Therefore, using the distance formula, we get the distance between (4, 2) and (8, 5) as 5 units.

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Answer:

number 2 - x=50, y =69

Step-by-step explanation:

Angles in a polygon of a pentagon add up to 540

so 180 +125+98+98 = 429

540 - 429 = 111

now you do x = 50 so

2 times 50 which is 100

then plus 11 which is 111