5. A banner in the gym is in the shape of a right triangle.
It has a height of 4 ft and a base of 9 ft. What is the
area of the banner?

The correct answer is A. 600 nautical miles is not the distance you will cover when traveling south along the 180° longitude from 5°N to 5°S. The correct distance is 0 nautical miles since the points are on the same line of longitude.

The distance traveled along a line of longitude can be calculated using the formula:

Distance = (Latitude 1 - Latitude 2) * (111.32 km per degree of latitude) / (1.852 km per nautical mile)

Given:

Latitude 1 = 5°N

Latitude 2 = 5°S

Substituting the values into the formula:

Distance = (5°N - 5°S) * (111.32 km/°) / (1.852 km/nm)

Converting the difference in latitude from degrees to minutes (1° = 60 minutes):

Distance = (0 minutes) * (111.32 km/°) / (1.852 km/nm)

Simplifying the equation:

Distance = 0 * 60 * (111.32 km/°) / (1.852 km/nm)

Distance = 0 nm

Therefore, traveling south along the 180° longitude from 5°N to 5°S, you will cover approximately 0 nautical miles.

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To prove the properties of the projection matrix, we'll assume that p is the projection matrix corresponding to a subspace S of \(R^{m}\).

(a) p² = p

To show that p² = p, we need to demonstrate that applying the projection matrix p twice is equivalent to applying it once.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, if we apply the projection matrix p again to p(x), we have:

p(p(x)) = projection of p(x) onto S

Since p(x) is already the projection of x onto S, applying the projection matrix p once more won't change the result. Hence, we can write:

p(p(x)) = p(x)

This equation holds for any vector x in \(R^{m}\), meaning that p² = p.

(b) \(p^{T}\) = p

To prove that \(p^{T}\) = p, we need to show that the transpose of the projection matrix p is equal to p.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, let's compute the transpose of p(x):

\((p(x))^{T}\) = \((projection of x onto S)^T\)

The transpose of a projection onto a subspace doesn't change the result because it only affects the column vectors of the projection matrix. The transpose of p(x) is still the projection of x onto S. Hence, we can write:

\((p(x))^T\) = p(x)

Since this equation holds for any vector x in \(R^{m}\), we can conclude that \(p^T\) = p.

Therefore, we have shown that (a) p² = p and (b) \(p^T\) = p, proving the properties of the projection matrix corresponding to a subspace S of \(R^{m}\).

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When there is 580 feet of fencing available to complete the job, the largest possible total area of the 5 pens is 7008.33 feet.

The quantity area expresses the extent of a region on a plane or curved surface.

STEP 1: We know that,

A=x y

The perimeter equals 580feet.

The equation is,

580=6x+2y

Step 2: Solving y terns with x,

y=-3x+290

This information will assist us in obtaining our Area equation in terms of a single variable (just in terms of x).

Step 3: Using the x-y relationship discovered in Step 2, write your Area equation in terms of x only. You should obtain

A=x y

A=x(-3x+290)

A=-3x²+290x

Step 4: Derive the area equation,  A' = -6x+290

Step 5: Set A' = 0

-6x+290=0

x=290/6

x=48.33

Step 6: Find y by substituting 48.33 in x in the perimeter equation then,

y=-3(48.33)+290

y=145.01

Step 7:  A=x y

A=(48.33)(145.01)

A=7008.33 feet

The largest possible total area of the 5 pens is 7008.33 feet

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Answer:

The answer is C

Step-by-step explanation:

Answer:

C.) 7, 8, 9, 1, 3, 7, 2, 4

Step-by-step explanation:

A paired-test can be used to check if the two blood pressure taken from 2 groups,one group having normal blood pressure another having white coat hypertension differ or not.

A paired t-test is used to determine whether two sample means are equal or not. White coat hypertension occurs when a person's blood pressure rises when they are in a medical setting.

To assess whether the two blood pressure measurements differ, a paired t-test should be used. The paired t-test is used to compare two dependent samples that are connected in some manner. A random sample of 50 patients should be taken to see if the two blood pressures differ. Here are the steps for conducting a paired t-test:

- State the null and alternative hypotheses.
- Calculate the difference between the two groups of data.
- Calculate the sample mean, sample standard deviation, and sample size.
- Use the t-distribution to determine the critical value.
- Compute the test statistic.
- Determine the p-value.
- Make a decision.

It is worth noting that in order to use the paired t-test, the data must be normally distributed. Additionally, this test can be performed on a one-tailed or two-tailed basis, depending on the hypothesis test. F-distribution is not used in a paired t-test.

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b.4+3cos²x is the simplification of the given trigonometric identity

Explanation:
Using the identity sin²x + cos²x = 1, we can simplify the expression:

4-4sin²x/(cot²x) + 7cos²x
= 4 (1-sin²x)/(cot²x) + 7cos²x
= 4 cos²x/cot²x + 7cos²x
= 4sin²x + 7cos²x

= 4sin²x + 4cos²x + 3cos²x

=4+3cos²x

Hence, the answer is b. 4 + 3cos²x

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Answer:

B) $1.25/ 4

Step-by-step explanation:

if Anna had $5.00 to start with and after buying 4 pencils she had $3.75 left that would mean each pencil was around $1.25.

$5.00 subtract $3.75 equals $1.25

hope this helps :D

The statement "Consistent system of equations has at least one solution, and an inconsistent system has no solution" is true.

In the context of systems of linear equations, a consistent system refers to a system where there exists at least one solution that satisfies all the equations in the system. This means that the equations can be simultaneously satisfied by a set of values for the variables.

On the other hand, an inconsistent system refers to a system of equations that has no solution. This occurs when the equations are contradictory or cannot be satisfied simultaneously by any values for the variables.

Therefore, a consistent system guarantees the existence of at least one solution, while an inconsistent system does not have any solution.

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Answer:

third option: 103.62cm

Step-by-step explanation:

Circumference of circle

= π × d

= 3.14 × 33

= 103.62cm

Answer:

6 feet per hour

Step-by-step explanation:

36 / 6 = 6

Answer: to wirte and solve for a missing side length of a rectangle, do your perimeter equation backwards, hope this helps

Step-by-step explanation:

(a) The angle measurement of first unknown angle is c = 80 degrees

(b) The angle measurement of second unknown angle is y = 110 degrees

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees

The angle measurement of first unknown angle will be:

a + b + c = 180  (sum of angles in a triangle is 180 degrees)

c = 180 - a - b

c = 180 - 30 - 70

c = 80 degrees

(b) The angle measurement of second unknown angle will be:

y = 180 - b  (sum of angles on a straight line is 180 degrees)

y = 180 - 70

y = 110 degrees

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Answer:

Step-by-step explanation:

Given :

Using cosine rule :

c² = a² + b² - 2abCosC

c² = 45² + 25² - 2(45)(25) - cos70

c² = 2650 - 2250 * - 0.3420201

c² = 2650 + 769.54532

c² = 3419.5453

c = sqrt(3419.5453)

c = 58.476

c = 58.5 feets

The area of the right triangular puppy pen found using the formula 1/2(b.h²) is 4900.90 feet².

What is a triangle?

A polygon with three edges and three vertices is called a triangle. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. A right triangle is a specific kind of triangle that has one angle that is exactly 90 degrees.

Given,

 The length of OY = 12 feet

The length of DY = 31 feet

m∠OYD = 65°

Since SDOG is a rectangle, m∠DOY = 90°.

So the ΔDOY is a right triangle.

Area of right triangle = 1/2 * b * h²

where b = base length

          h = height

From the given figure,

b = OY = 12

h = OD

h can be found using Pythagoras' theorem.

DY² = OD² + OY²

OD² = DY² - OY² = 31² - 12²  = 817

OD = √817 = 28.58 feet = h

Therefore the area of the right triangle ΔDOY is

area =  1/2 * b * h² = 0.5 * 12 *28.58² = 4900.90 feet².  

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Answer:

Last one

A student‘s test score is likely to increase about 20 points for each hour of studying

Step-by-step explanation:

We can see that the indepedent value is hours spent studying and dependent value is test scores.

As the hours of studying get greater, so does the test scores. So it has to be either the second to last or last one.

If you pay attention to the numbers, you’d see that the last one would be the answer.

Answer:

last one

Step-by-step explanation:

each hour spent studying increases the by around 20 points. the slope of the line is 20.

btw there's nothing on the intercept in the question

The probability that the next person will pay with a debit card is:

P =  0.63

We want to find he probability that the next customer will pay with a debit card.

That probability can be estimated as the quotient between the number of customers that paid with debit card and the total number of customers.

We know that:

15 paid in cash.

50 paid with debit card.

15 paid with credit card.

For a total of 15 + 50 + 15 = 80

Then the probability is:

P = 50/80 = 0.63

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Answer: 90

Step-by-step explanation: Divide 20 by 4 and Multiply the 18

Let:

Therefore:

Answer:

y=x2 -10

Step-by-step explanation:

it is because x is squared

Answer:

the question is probably wrong

Step-by-step explanation:

10 - -6 = 16

-6 - -6 = 0

16/0= undefined?

It is important to carefully evaluate the results of any study before drawing conclusions about the effectiveness of a treatment.

Yes, the result of a study can indicate whether the treatment is effective. However, without knowing the specific study and treatment being referred to, it is impossible to provide a confidence interval. A confidence interval is a range of values that we can be reasonably confident contains the true population parameter based on the data collected from a sample.

It is typically expressed as a range of values with a certain level of confidence, such as 95% or 99%.To determine if a treatment is effective, researchers will typically conduct a study with a treatment group and a control group.

The treatment group receives the treatment being tested, while the control group receives a placebo or another standard treatment.

The researchers then compare the outcomes of the two groups to determine if there is a significant difference that can be attributed to the treatment being tested.

If the results show a significant difference, then the treatment is considered effective.

However, it is important to note that there are many factors that can affect the outcome of a study, such as sample size, study design, and the characteristics of the participants.

Therefore, it is important to carefully evaluate the results of any study before drawing conclusions about the effectiveness of a treatment.

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The tangents of the acute angles in the right triangle are;

tan D = 7/24 = 0. 2917

tan F = 24/7 =3.4286

Trigonometric identities are mostly defined as those equalities of a trigonometric functions that shows certainty of all the values of the equation.

In mathematics, there are different trigonometric identities, such as;

From the information given, we have that;

Using the tangent identity, we have;

tan D = opposite/ adjacent

Substitute the values

tan D = 7/24 = 0. 2917

For the tangent of F, we have

tan F = 24/7 =3.4286

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well, clearly is 4 :).

now, if we take 25 to be the 100%, what is 4 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 25 & 100\\ 4& x \end{array} \implies \cfrac{25}{4}~~=~~\cfrac{100}{x} \implies 25x=400\implies x=\cfrac{400}{25}\implies x=16\)

The function whose graph is given below is y = tan (x).

Therefore, for x = 0, y = 0 for the given function

Now, at x = 0,

y = sec (0) = 1

y = tan (0) = 0

y = cosec (0) = Not defined

y = cot (0) = Not defined

Now, it is clear that, the function y = tan (x) represents the given graph.

The complete question is:

Choose the function whose graph is given below.

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Answer:

A. Obtuse

Step-by-step explanation:

Angle R is greater than 90°.

Answer:

Obtuse

Step-by-step explanation:

We know this because the angle is larger than 90 degrees which is also known as an obtuse :)

Let us designate the box's width as x inches. According to the information provided, the length is three inches longer than the width, hence the length is (x + 3) inches. The height is specified as ten inches.

We multiply the length, width, and height of the box to determine its volume. So far, we have:

540 = (x + 3) x 10 Volume = Length Width Height

Extending this equation yields:

540 = 10x^2 + 30x

The equation is now rearranged to become a quadratic equation:

10x^2 + 30x - 540 = 0

This equation may be simplified by dividing all of the terms by ten:

x^2 + 3x - 54 = 0

We may get the potential values for x by factoring or using the quadratic formula. Because width cannot be negative, we eliminate -9, leaving us with the box's width of 6 inches.

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Answer: Using the multiple angle formula for cosine, we have:

cos 4x = 2cos^2 2x - 1

Now we need to rewrite cos 2x in terms of cos x. Again, using the multiple angle formula for cosine, we have:

cos 2x = 2cos^2 x - 1

Substituting this expression into the previous equation, we get:

cos 4x = 2(cos^2 x)^2 - 1

Simplifying the expression further, we have:

cos 4x = 2(cos^4 x) - 1

Therefore, cos 4x can be written in terms of cos x as 2(cos^4 x) - 1.

Step-by-step explanation:

Answer:

84in

Step-by-step explanation:

10 times 5 = 50 (top half)

7 times 4 = 28 (bottom half)

3 times 4 = 12 / 2= 6 (triagle)