A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.

A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 7 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 4 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 6 centimeters.

What is the area of the tile shown?

58 cm2
44 cm2
74 cm2
70 cm2

An integral in calculus is a mathematical concept that can be used to represent an area or an expanded version of an area. The basic components of calculus are integrals and derivatives is\(-1/2*(t^2/2+18ln(t)-81/(2t^2))+C\\\).

The terms antiderivative and primal are additional terms for integral. Something that is essential is crucial or required. If you are an essential member of the team, it signifies that you are necessary for the team to work. To complete the whole, an essential component is required. The term "essential" is almost a synonym in this context.

The set of functions (the antiderivative) whose derivative is the integrand is represented by the integral, which is referred to as an indefinite integral. Calculus' fundamental theorem connects the assessment of definite integrals to that of indefinite integrals.

From 1 to 3:

\(sqrt(x^2+9)=t+x\\x=(9-t^2)/(2*t)\\anddx=-(t^2+9)/(2t^2)dt\\= 1/2int (t^2+9)^2/t^3dt\\= -1/2int (t+18/t+81/t^3)dt\\= -1/2*(t^2/2+18ln(t)-81/(2t^2))+C\\\)

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Answer:

12

Step-by-step explanation:

cross multiply. 5*x=(x+3)4 5x=4x+12, therefore x=12

Answer:

2x²+3x-54

Step-by-step explanation:

(2x-9)(x+6)

=x(2x-9)+6(2x-9)

=2x²-9x+12x-54

=2x²+3x-54

The coordinates of the unit vector, having positive first coordinate and orthogonal to the plane through a given point P(3, -4, 4) = \((\frac{\sqrt{2} }{2}, \frac{-\sqrt{2} }{2},0)\)

Let the coordinates of Q be (6 , -1 , 7) and R be (6, -1 ,9).

Then coordinates of vector(PQ) = < 6 - 3, -1 - (-4), 7 - 4 > = (3, 3, 3)

And coordinates of vector(PR) = < 6 - 3, -1 - (-4), 9 - 4 > = (3, 3, 5)

Thus, vector (n) = vector (PQ) x vector (PR)

=> vector (n) =  \(\left[\begin{array}{ccc}3&3&3\\3&3&5\end{array}\right]\)

Solving for the determinant, we get the coordinates of vector (n)

= (6, -6, 0).

Magnitude of vector (n) = \(\sqrt{6^{2}+{(-6)^{2}+{0^{2} }\) = \(6\sqrt{2}\)

Thus, the unit vector (n) = \(\frac{Coordinates Of Vector (n)}{Magnitude Of Vector(n)}\)

=> Unit vector (n) = \(\frac{(6,-6,0)}{6\sqrt{2} }\) = \((\frac{\sqrt{2} }{2},\frac{-\sqrt{2} }{2},0)\)

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COMPLETE QUESTION:

Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P (3,-4,4).

Answer:

P = 156 units

Step-by-step explanation:

the perimeter (P) is the sum of the 3 sides of the triangle.

tangents from an external point to the circle are congruent , that is

HK = HJ ( substitute values )

13x - 8 = 7x + 4 ( subtract 7x from both sides )

6x - 8 = 4 ( add 8 to both sides )

6x = 12 ( divide both sides by 2 )

x = 2

Then

HK = HJ = 7x + 4 = 7(2) + 4 = 14 + 4 = 18

and

KI = IL = 21

then

GL = GJ = 60 - 21 = 39

Thus

P = HK + KI + IG + GJ + JH = 18 + 21 + 60 + 39 + 18 = 156 units

Answer:

3.0625 seconds

Step-by-step explanation:

From the question,

✓She slides at a rate of 8 m/s downward

✓after 3 seconds is 5 m off of the ground

We can calculate the the number of seconds she will use to get to the ground by

Velocity= distance/time

Time= distance/ velocity

=5/8 seconds

=0.625seconds

To know how many seconds it will take her to slide to the ground from the top can be calculated as

( 3seconds + 0.625 seconds)

= 3.0625 seconds

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Answer:

i guess you are trying to find out what the "some blue seats are". Lets show this as x.  So you are trying to find x. Now 88 seats in the theater divided by the 4 identical sections. that would give you 22. Now like you said 14 of the seats are red..That means that we have to find out what the blue is or x. 22-14 is 8. That means that there are 8 seats left that are not red...That means that 8 seats in the theater are blue.

Given :

\(\begin{lgathered}\bullet\:\:\textsf{Perimeter of reactangle = \textbf{32 cm}}\\\bullet\:\:\textsf{Width = \textbf{7 cm}}\end{lgathered}\)

\(\rule{130}1\)

Solution :

\(:\implies\sf Perimeter\:of\: rectangle = 2 (Length + Breadth) \\\\\\:\implies\sf 32 = 2 (l + 7)\\\\\\:\implies\sf 32 = 2l + 14\\\\\\:\implies\sf 32 - 14 = 2l\\\\\\:\implies\sf 2l = 18\\\\\\:\implies\underline{\boxed{\sf Length = 9\:cm}} \)

\(\rule{170}2\)

\(\dashrightarrow\sf\:\:Area\:of\: rectangle = Length \times Breadth\\\\\\\dashrightarrow\sf\:\: Area\:of\: rectangle = 7\:cm \times 9\:cm\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Area\:of\: rectangle = 63\:cm^2}}\)

⠀

\(\therefore\:\underline{\textsf{The area of reactangle is \textbf{63}}\:\sf{cm^2}}.\)

Answer:

Area of the rectangle is 63 cm².

Step-by-step explanation:

Given :-

To find :-

Solution :-

Consider,

width = 7 cm

Formula used :-

\({\boxed{\sf{Perimeter of rectangle=2(Length+breadth)}}}\)

According to the question ,

2(x+7) = 32

→ x+7 = 32/2

→ x +7 = 16

→ x = 16-7

→ x = 9

★ Length = 9 cm

Area of the rectangle ,

= length × Breadth

= 9 × 7 cm²

= 63 cm²

Therefore, the area of the rectangle is 63 cm².

Using unit conversions the total height change from the top of mount Everest to the bottom of the Mariana trench is 12.3 miles

We know that 1 km = 0.62136 miles and 1 foot = 0.000189 miles

Depth of Mariana Trench (d) = 11 km = 11 × 0.62136

                                                          = 6.835 miles

Height of Mount Everest (h) = 29000 ft = 29000 × 0.000189

                                                              = 5.492 miles

Therefore the total height difference top of Mount Everest and to bottom of the Mariana Trench is given by

H = Depth of Mariana Trench + Height of Mount Everest

H = d + h

H = 6.835 miles + 5.492 miles

H = 12.327 miles

H = 12.3 miles

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The probability of getting a subject who is not diabetic, given that the test result is negative, is approximately 0.1786.

To find the probability of getting a subject who is not diabetic, given that the test result is negative, we can use the data provided in the table. From the table, we can see that out of the total subjects tested, 5 are not diabetic and have a negative test result. The total number of subjects with a negative test result is 28.

To calculate the probability, we divide the number of subjects who are not diabetic and have a negative test result (5) by the total number of subjects with a negative test result (28).

Probability = Number of subjects who are not diabetic and have a negative test result / Total number of subjects with a negative test result

Probability = 5 / 28

Simplifying this fraction, we get:

Probability ≈ 0.1786

Therefore, the probability of getting a subject who is not diabetic, given that the test result is negative, is approximately 0.1786.

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Answer:

f(-2) = -11

f(0) = -1

f(x+1)= f (x+1)=5x+4

Step-by-step explanation:

answer : 0.375 of pint

hope this helps !

Answer:

5 => 2

6 => 3

7 => 4

8 => 5

9 => 6

Answer:

2,3,4,5,6

Step-by-step explanation:

y = 5 - 3 = 2

y = 6 - 3 = 3

y = 7 - 3 = 4

y = 8 - 3 = 5

y = 9 - 3 = 6

Answer:

C not like terms

Step-by-step explanation:

Answer:

the answer is LIKE TERMS because 10 doesnt have a variable of y

Step-by-step explanation: Brainliest please.

Hey there!

a = 5 ; b = 2

Option A.

a + b

= 5 + 2

= 7

Option B.

a - b

= 5 - 2

= 3

Option C.

2a + 3b

= 2(5) + 3(2)

= 10 + 6

= 16

Option D.

5a - b

= 5(5) - 2

= 25 - 2

= 23

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

118

Step-by-step explanation:

AB and CD are parallel lines

∠ ABC + ∠DCB = 180   {Co- interior angles are supplementary}

3n - 47 + n + 7 = 180

3n + n - 47 + 7 = 180 {Combine like terms}

4n - 40 = 180

Add 40 to both sides

4n = 180 + 40

4n = 220

Divide both sides by 4

n = 220/4

n = 55

∠ABC = 3n - 47 = 3*55 - 47

         = 165 - 47

∠ABC = 118

Check the picture below.

since the one on the left is a cube, all its sides are equal, and we know the cube and cuboid both have the same volume, so

\(\stackrel{ \textit{\LARGE volumes} }{\stackrel{ cube }{(8)(8)(8)}~~ = ~~\stackrel{ cuboid }{(x)(4)(8)}}\implies 512=32x\implies \cfrac{512}{32}=x\implies 16=x\)

Answer:

\( \sf 9,802 \frac{1}{3} \)

Step-by-step explanation:

\( \sf = \frac{588,140}{60} \)

\( \sf = \frac{58,814}{6} \)

\( \sf = 9,802 \frac{2}{6} \)

\( \sf = 9,802 \frac{1}{3} \)

Answer:

With a car worth $9,200, the approximate interest rate is 6.25% and you'd have to pay it off in 4 years.

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Answer:

\(\huge\boxed{slope=\dfrac{3}{5}=0.6}\)

Step-by-step explanation:

The formula of a slope:

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

We have the points (1, -1) and (6, 2).

Substitute:

\(m=\dfrac{2-(-1)}{6-1}=\dfrac{2+1}{5}=\dfrac{3}{5}=0.6\)

The first 50 names in the telephone directory may or may not be a random sample. It depends on how the telephone directory is compiled.

The first 50 names in the telephone directory may or may not be a random sample, depending on the context and purpose of the study.

To determine if it is a random sample, we need to consider how the telephone directory is compiled.

If the telephone directory is compiled randomly, where each name has an equal chance of being included, then the first 50 names would be a random sample.

This is because each name would have the same probability of being selected.

However, if the telephone directory is compiled based on a specific criterion, such as alphabetical order, geographic location, or any other non-random method, then the first 50 names would not be a random sample.

This is because the selection process would introduce bias and would not represent the entire population.

To further clarify, let's consider an example. If the telephone directory is compiled alphabetically, the first 50 names would represent the individuals with names that come first alphabetically.

This sample would not be representative of the entire population, as it would exclude individuals with names that come later in the alphabet.

In conclusion, the first 50 names in the telephone directory may or may not be a random sample. It depends on how the telephone directory is compiled.

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The probability that the chosen student is of sociology is P(sociology) = 0.25

Probability is the measure of the chances of an event happening.

Probability of an event is calculated by dividing the number of favorable outcomes of the given event divided by the total number of given outcome

Let E be an event , Probability of the event  E,

P(E) = outcomes favorable to E/ total outcomes

Given that there are  five anthropology students, three sociology students and four psychology students.

Number of anthropology students = 5

Number of Sociology students = 3

Number of Psychology students = 4

Total number of students = 5+3+4 = 12

If one name is selected at random to assist in the professor's new study,

Then the Probability that the chosen student is of sociology.

P(sociology)= Number of sociology students  / total students  =  3/12

= 1/4 = 0.25

Therefore , the probability  that the chosen student is of sociology is P(sociology) = 0.25

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Therefore, the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll is approximately 0.038.

Since the arrival of cars at a tollbooth follows a Poisson process with a rate of 5 cars every 10 minutes, the time between arrivals of cars follows an exponential distribution with a mean of 2 minutes (10 minutes / 5 cars). Let X be the time between arrivals of cars. Then, X ~ Exp(1/2) since the mean of an exponential distribution is equal to the reciprocal of the rate.

To find the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll, we need to find the probability that the sum of the waiting times for the first seven cars is less than 26.30 minutes and the waiting time for the eighth car is greater than the remaining time.

Let Y be the waiting time for the eighth car. Then, Y ~ Exp(1/2) since the waiting time for each car is independent and identically distributed. Therefore, the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll can be calculated as follows:

P(Y > 26.30 - T), where T is the sum of waiting times for the first seven cars.

Since the waiting times for each car are independent, the sum of the waiting times for the first seven cars follows a gamma distribution with parameters k = 7 and θ = 1/2. Therefore, we have:

T ~ Gamma(7, 1/2)

Now, we can calculate the desired probability as follows:

\(P(Y > 26.30 - T) = ∫∫\int\limits^a_b { (e^(-t/2) * (1/2)^{7})/6! } \, dx\)

= 0.038

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Answer:

\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)

Answer:

c.-18

Step-by-step explanation:

follow me and -GOOD LUCK-

Answer:

1/2

Explanation:

If you take a sample of 1 drawn from the 8, you will have 8 possible options and 4 of them didn't contain defects. So, the probability can be calculated as:

Therefore, the answer is 1/2

The probability that a sample of 1 of the 8 computers will not contain a defective computer is 1/2.

The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.

Given a shipment of 8 computers contain 4 with defects.

That means 8 -4 = 4 computers have no defect.

To find the probability;

we have 8 possible computers and 4 computers have no defect.

The probability;

= 4 /8

= 1/2

= 0.5

Therefore, the probability that a sample of 1 of the 8 computers will not contain a defective computer is 1/2.

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