In ΔXYZ, x = 5.2 inches, y = 9.8 inches and z=7.1 inches. Find the measure of ∠Z to the nearest degree.

Answer: y = 2 and x = 2

Step-by-step explanation:

\(9x^2+4(y-2)^2=36\\x^2=2y\)

First, get the entire thing in terms of y, because you cant solve for two variables at the same time. They gave us the fact that x^2 = 2y

\(9(2y)+4(y-2)^2=36\\18y+4(y^2-4y+4)=36\\18y+4y^2-16y+16=36\\4y^2+2y-20=0\)

What two numbers multiply to equal -80 but add to equal 2? That is +10 and -8.

\(4y^2+2y-20=0\\(4y^2-8y)+(10y-20)=0\\4y(y-2)+10(y-2=0)\\(4y+10)(y-2)=0\\y=-5/2\\y=2\)

Now solve for x by plugging in y to the easier equation

\(x^2=2(-5/2)\\x\neq \sqrt{-5}\)

If I didn't make a mistake, this should be the only answer. In the case of y = -5/2, you would get an imaginary x-value. Therefore y cannot equal -5/2

\(x^2=2(2)\\x=2\)

The solution of the expression are,

x = 2.28 , y = 2.62

Or, x = 3.9i , y = - 7.62

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equations are,

9x² + 4 (y - 2)² = 36  .. (i)

x² = 2y  .. (ii)

Substitute the value of x² from (ii) in (i);

9x² + 4 (y - 2)² = 36

9 × 2y + 4 (y - 2)² = 36

18y + 4 (y - 2)² = 36

9y + 2 (y - 2)² = 18

9y + 2 (y² + 4 - 2y) = 18

9y + 2y² + 8 - 4y = 18

2y² + 5y + 8 - 18 = 0

2y² + 5y - 10 = 0

y = - 5 ± √5² - 4×2×- 10 / 2×2

y = - 5 ± √ 25 + 80 / 2

y = - 5 ± √ 105 / 2

y = - 5 ± 10.24 / 2

y = - 5 + 10.24 / 2

y = 5.24/2

y = 2.62

y = - 5 - 10.24 / 2

y = - 15.24 / 2

y = - 7.62

From (ii);

x² = 2y

x² = 2 × 2.62

x² = 5.24

x = 2.28

x² = 2y

x² = 2 × - 7.62

x² = - 15.24

x = 3.9i

Thus, The solution of the expression are,

x = 2.28 , y = 2.62

Or, x = 3.9i , y = - 7.62

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Answer:

  f(x) = 20(5^x) +3   (read the comment)

Step-by-step explanation:

You want an exponential function f(x) that models the data (x, f(x)) = (0, 23), (1, 103), (2, 503), (3, 2503).

Except for the apparently added value of 3 with every term, the terms have a common ratio of 5. After subtracting 3, the first term (for x=0) has a value of 20. This is the multiplier.

The exponential function is ...

  f(x) = 20(5^x) +3

__

Additional comment

We see numerous questions on Brainly where the exponent (or denominator) of a number appears to be an appended digit. The "3" at the end of each of the numbers here suggests it might not actually be the least significant digit of the number, but might represent something else.

If the sequence of f(x) values is supposed to be 2/3, 10/3, 50/3, ..., then the exponential function will be ...

  f(x) = 2/3(5^x)

This makes more sense in terms of the kinds of exponential functions we usually see in algebra problems. However, there is nothing in this problem statement to support that interpretation.

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Statement Problem: The sum of two numbers is 7. Five times the larger number plus four times the smaller number is 48. Find the numbers.

Solution:

Let x be the larger number and y be the smaller number such that;

From equation 1, we have;

Substitute equation3 in equation2, we have;

Then, substitute the value of y in equation3;

Thus, the larger number is 20 and the smaller number is -13

Answer:

x= 2.5

Step-by-step explanation:

-7.5 (x-3) = 3.75

(divide both sides of the equation by -7.5)

x-3 = -0.5

(move the constant to the righthand side and change the sign)

x = -0.5+3

(calculate the sum)

x = 2.5

Answer:

\(\frac{10}{7}\)

Step-by-step explanation:

\(\sqrt{100}\) = 10

\(\sqrt{49\\\) = 7

there should be a button on your calculator "root".

Answer : \(\frac{10}{7}\)

if the terminal point determined by t is in quadrant I, then tan(t) = sin(t)/sqrt(1 - sin^2(t)).

If the terminal point determined by t is in quadrant I, then both sine and tangent are positive. We can use the identity:

tan(t) = sin(t)/cos(t)

to express tangent in terms of sine. Since the terminal point is in quadrant I, cosine is positive, so we can use the Pythagorean identity:

sin^2(t) + cos^2(t) = 1

to solve for cosine:

cos(t) = sqrt(1 - sin^2(t))

Substituting this expression for cosine in the formula for tangent, we get:

tan(t) = sin(t)/cos(t) = sin(t)/sqrt(1 - sin^2(t))

what is quadrant?

A quadrant is one of the four regions that a coordinate plane is divided into by the x-axis and the y-axis. The x-axis is a horizontal line that runs left and right through the plane, and the y-axis is a vertical line that runs up and down through the plane. The point where the x-axis and the y-axis intersect is called the origin.

Each quadrant is labeled with a Roman numeral (I, II, III, or IV) to distinguish it from the others. Quadrant I is the region in the upper-right corner of the plane, where both the x and y coordinates are positive. Quadrant II is the region in the upper-left corner of the plane, where the x-coordinate is negative and the y-coordinate is positive.

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An appropriate hypothesis test to determine whether scores of depression are different pre- and post-treatment would be the paired t-test.

The paired t-test is suitable in this scenario because it compares the mean scores of depression before and after the treatment within the same group of participants.

This test takes into account the paired nature of the data, where each participant is measured twice (pre- and post-treatment).

By conducting a paired t-test, the researchers can assess whether there is a statistically significant difference in depression scores before and after the treatment. This will help determine the effectiveness of the new treatment for depression.

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Based on the number of names of winners that can be drawn, and the number of names in the basket, the number of different ways they can be drawn is 190 different ways

There are 20 names that you can draw from, in the raffle. There are however, only 2 names that can be picked for the same prize. This means that this is a combination problem.

The number of ways to pick the two winners can be modelled as:

= ₂₀C₂

= 20! / ( 2 ! ( 20 - 2) ! )

= 190 different ways

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Answer: 12.5

Step-by-step explanation:

12.5 is the length of BC.

Here, we have,

given that,

In the diagram shown below, AC is tangent to circle o at A and to circle Pat C, OP intersects AC at B, OA = 5, AB = 5, and PC = 10.

now, we know that,

∠OAB and  ∠BCP are right angles, because of the tangents.

and, ∠OBA ≅ ∠CBP (vertical angles)

thus, we get,

ΔAOB ≅ ΔCBP, by AA rule.

so, we can set up the proportion:

10/4 = x/5

or, x = 12.5

Hence, 12.5 is the length of BC.

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The Blu-ray movie will cost approximately $36.42 in 5 years with an inflation rate of 12% and continuous compounding.

To calculate the future cost of the Blu-ray movie in 5 years with an inflation rate of 12% and continuous compounding, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:

A = Future value

P = Present value

e = Euler's number (approximately 2.71828)

r = Annual interest rate (in decimal form)

t = Time period in years

In this case, the present value (P) is $19.99, the inflation rate (r) is 12% or 0.12, and the time period (t) is 5 years. Substituting these values into the formula, we get:

A = 19.99 * e^(0.12 * 5)

Calculating the exponent first:

0.12 * 5 = 0.6

Then:

e^0.6 ≈ 1.82212

Finally:

A = 19.99 * 1.82212 ≈ 36.42

Using the formula for continuous compound interest, we calculated that a Blu-ray movie that costs $19.99 today will cost approximately $36.42 in 5 years, assuming an inflation rate of 12% and continuous compounding.

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Answer:

(a)The solution set is: \(x \in [6, \infty) \forall x \in R\)

(c) \(6 \leq x\)

Step-by-step explanation:

Given the inequality: \(12+\dfrac{11}{6}x\leq 5+3x\)

We solve by collecting like terms

\(12+\dfrac{11}{6}x\leq 5+3x\\12-5\leq 3x-\dfrac{11}{6}x\\7\leq \dfrac{18x-11x}{6}\\42 \leq 7x\\$Divide both sides by 7\\6 \leq x\\$We can re-write this as:\\x\geq 6\)

The solution set is therefore: \(x \in [6, \infty) \forall x \in R\)

The line drawn from the midpoint of the one side of a triangle, parallel to the second side bisects the third side.

Given : In △ABC ,D is the mid point of AB and DE is drawn parallel to BC

To prove AE=EC :

Draw CF parallel to BA to meet DE produced to F

DE∣∣BC (given)

CF∣∣BA (by construction)

Now BCFD is a parallelogram

BD=CF

BD=AD (as D is the mid point of AB)

AD=CF

In △ADE and △CFE

AD=CF

∠ADE=∠CFE (alternate angles)

∠ADE=∠CEF (vertically opposite angle)

∴△ADE≅△CFE (by AAS criterion)

AE=EC (Corresponding sides of congruent triangles are equal.)

Therefore, E is the mid point of AC.

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The cost of constructing the box will be = $81.77

Since the question gives us information about the rectangle,

so the area of the rectangle is shown by,

Area = 2 x (length + width)

So we have the area as,

Area = 2(lh + wh) +lw

(since the area per square meter is also given so we added l x w)

Since the cost of the base is = $5 per square meter and the cost of the sides is = $3 per square meter, so area in terms of the cost function,

⇒ C = 3 x 2(lh + wh) + 5 x l x w

⇒ C = 6(lh + wh) +5lw ---------equation 1

According to the question, the length of the rectangular container is twice that of the width of the container,

⇒ l = 2w

Substituting the new value of l in equation 1,

⇒ C = 6(2wh + wh) + 10 \(w^{2}\)

⇒ C = 18wh + 10 \(w^{2}\) ---------- equation 2

To calculate the volume of the rectangle,

V = length x width x height ( lwh )

substituting v = 10 and 2w = l,

2\(w^{2}\)h = 10

h = \(\frac{5}{w^{2} }\)

Substitute the value of h in equation 2,

⇒ C = 18w x \(\frac{5}{w^{2} }\) + 10\(w^{2}\)

⇒ C = \(\frac{90}{w}\) + 10\(w^{2}\) --------- equation 3

Differentiating the above equation we get,

⇒ C* = - \(\frac{90}{w^{2} }\) + 20w

⇒ 20w = \(\frac{90}{w^{2} }\)

Multiply both sides by \(w^{3}\)

⇒ \(20w^{3}\) = 90

⇒ \(w^{3}\) = 4.5

w = 1.65

Put the value of w in equation 3,

⇒ C = \(\frac{90}{1.65}\) + 10 x \(1.65^{2}\)

⇒ C = 81.77

Therefore, The cost of constructing the box will be = $81.77

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Answer:

^7√(-4)^2 or 1.48 I hope it helps

\((-4)^{2/7}\) in radical form is \(\sqrt[7]{-4^{2} }\)

An expression is combination of variables, numbers and operators.

We have to write \((-4)^{2/7}\) in radical form

The radicals is the name of the sign we use in roots. The numerator is the power of the exponential, and the denominator is the power of the root.

So we take the radical:

\(\sqrt[7]{-4^{2} }\)

\((-4)^{2/7}\) in radical form is \(\sqrt[7]{-4^{2} }\)

Hence,  \((-4)^{2/7}\) in radical form is \(\sqrt[7]{-4^{2} }\)

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The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The length of QS can lie between 3 < QS < 13.

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

As per the given law of triangle inequality, the sum of the two sides of the triangle is greater than the third side.

x + 8 > 5

x > -3

x + 5 > 8

x > 3

8 + 5 > x

13 > x

Hence, the length of QS can lie between 3 < QS < 13.

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To encode the message word (1,0,1,1) using the Hamming (7,4) code, we first add three parity bits to the message word. The parity bits are calculated as follows: Parity bit 1 = XOR of bits 1, 2, and 3, Parity bit 2 = XOR of bits 2, 3, and 4, Parity bit 3 = XOR of bits 3, 4, and 5. The resulting code word is (1,0,0,1,0,0,1).

The Hamming (7,4) code is a linear error-correcting code that can correct single-bit errors. The code works by adding three parity bits to a four-bit message word. The parity bits are calculated as follows: Parity bit 1 = XOR of bits 1, 2, and 3.Parity bit 2 = XOR of bits 2, 3, and 4.Parity bit 3 = XOR of bits 3, 4, and 5. The resulting code word is seven bits long. If a single-bit error occurs during transmission, the decoder can use the parity bits to determine which bit was in error and correct it. The words (1,0,0,1,0,0,1) and (0,1,1,0,0,1,1) are both valid code words because they have the correct number of bits and the parity bits are correct. The word (0,0,0,0,0,0,0) is not a valid code word because it does not have enough bits.

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Answer The answer is biased.

Hospital sites provide a variety of learning opportunities for students to apply their knowledge, skills, and theories to practice.

Students can work directly with patients to provide care and treatment. This provides them with the opportunity to learn about the different aspects of patient care, such as physical assessment, medication administration, and patient education.

Students can observe experienced clinicians as they provide care to patients. This allows them to learn about the different techniques and approaches that can be used in patient care.

Students can attend conferences and workshops to learn about new developments in their field. These events can also provide them with the opportunity to network with other professionals and to learn about different career options.

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First part of the question is:

Field Experience Site Details- Hospital site

Let X be the number of fixed points of a random permutation of n elements. A fixed point is an element that remains in the same position after the permutation. Thus, the probability that an element is fixed is 1/n, and the probability that it is not fixed is (n-1)/n.

Using the linearity of the expected value, we can calculate the expected value of X as:

E(X) = E(X1 + X2 + ... + Xn) = E(X1) + E(X2) + ... + E(Xn)

where Xi is the indicator random variable that is equal to 1 if the i-th element is fixed and 0 otherwise. Since the probability of an element being fixed is 1/n, we have E(Xi) = 1/n. Therefore,

E(X) = n * (1/n) = 1

To find the variance of X, we need to compute E(X^2) - E(X)^2. We can use the fact that X^2 = X1 + X2 + ... + Xn, where Xi is the indicator random variable that is equal to 1 if the i-th and j-th elements are both fixed and 0 otherwise. Then,

E(X^2) = E(X1 + X2 + ... + Xn)^2 = E(X1^2 + X2^2 + ... + Xn^2) + 2 E(X1X2 + X1X3 + ... + X(n-1)n)

Since there is only one way to fix two elements out of n, we have E(XiXj) = 1/(n(n-1)). Therefore,

E(X^2) = n * (1/n) + n(n-1) * (1/(n(n-1))) = 1 + 1/n

Finally, the variance of X is

Var(X) = E(X^2) - E(X)^2 = 1 + 1/n - 1^2 = 1/n

Therefore, the variance of the number of fixed elements of a randomly selected permutation of n elements is 1/n.

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Answer:

Step-by-step explanation:

C = 3.14 * 2 * r

44 = 3.14 * 2 * r

44 = 6.28 *r

r is approximately 7

diameter = 2 * r

diameter = 2*7

diameter = 14

Approximately means that you round your answer.

the placebo effect means in this specific situation that The benefit is due to the fact that the co-workers are given a "treatment" (coffee, although decaffeinated) and not an effect of the "active ingredient" (caffeine).

Therefore, it appears that Janae is serving decapitated coffee to its customers, who have said that it has given them more energy. We want to examine the placebo effect, and when we think of the placebo effect, we imagine that a guy should publish. The best response you have provided is to recognize that they are receiving treatment, even though it is not caffeine, and causing them to believe that they are experiencing an increase in energy and that it is not the result of an active ingredient. As a result, they are receiving treatment and are having an impact by which. They aren't actually being impacted by the caffeine, though. You will typically feel more energized as a result of that.

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Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

Answer:

2(2x - 3)(x^2 -4)

Step-by-step explanation:

the second one

Answer:

2352

Step-by-step explanation:

You just multiply them

Distribution C has the most variability about its mean as it has the highest standard deviation compared to the other distributions.

The distribution with the most variability about its mean is the one with the widest spread of data points. This distribution will have the highest standard deviation.

To determine which distribution has the most variability, we can compare the standard deviations of the three distributions. The standard deviation is a measure of how spread out the data is from the mean.

A high standard deviation indicates that the data is spread out over a wide range, while a low standard deviation indicates that the data is clustered close to the mean.

The following table shows the standard deviations of the three distributions:

Distribution Standard Deviation

Distribution A        10

Distribution B   5

Distribution C         2

As you can see, Distribution C has the highest standard deviation, which means that it has the most variability about its mean.

Here is a visual representation of the three distributions

Distribution A:

* Mean = 22

* Standard deviation = 10

* Data points are spread out over a wide range.

Distribution B:

* Mean = 22

* Standard deviation = 5

* Data points are clustered closer to the mean.

Distribution C:

* Mean = 22

* Standard deviation = 2

* Data points are very close to the mean.

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If of 400 randomly selected people in the city of lyon, france, 60 people had the first name hugo . The statement that does not represent inferential statistics is: c. 15% of the people surveyed have the first name hugo.

Using this formula

Inferential statistics=Number of people with first name hugo/Random selected people×100

Let plug in the formula

Inferential statistics=60/400×100

Inferential statistics=15%

The statement that represent the  inferential statistics are:

Therefore  the statement that does not represent inferential statistics is: c. 15% of the people surveyed have the first name hugo.

The complete question is:

Of 400 randomly selected people in the city of lyon, france, 60 people had the first name hugo. which of these does not represent inferential statistics?

a. 15% of the people who live in france have the first name hugo.

b. 15% of the people who live in europe have the first name hugo.

c. 15% of the people surveyed have the first name hugo.

d. 15% of the people who live in lyon have the first name hugo.

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Answer:

she messed up on the part where u need to cube root the solution she should of gotten 6 from the 4.

A node or event with a duration of 0 days is a b. milestone

A milestone refers to an important event in a project that has a duration of zero days. It signifies the completion of a significant phase or task within the project. Milestones are numbers placed on roads, such as roads, railroads, canals, or borders. They can show distances to cities, towns, and other places or regions; or they can set their work on track with respect to a reference point.

They are found on the road, often by the roadside or in a warehouse area. They are also called mile markers (sometimes abbreviated MM), milestones, or mileposts (sometimes abbreviated MP). "mile point" is the term used for the medical field where distance is usually measured in kilometers rather than miles. "Distance marking" is a general term that has nothing to do with units.

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Answer:

Step-by-step explanation:

Put the data in the ascending order:

Sum the 3 lowest numbers:

Sum the 3 highest numbers:

Subtract the sums: