The amount of rainfall in January in a certain city is normally distributed with a mean of 4.2 inches and a standard deviation of 0.5 inches. Find the value of the quartile Q1

Answers

Answer 1
Q1 = the exact amount 

Related Questions

An obtuse triangle with area 12 has two sides of lengths 4 and 10. Find the length of the third side. (There are two answers.) (Use law of cosines) ...?

Answers

Final answer:

Using the Law of Cosines, the length of the third side of the obtuse triangle is x = sqrt(52) or x = 2sqrt(13).

Explanation:

To find the length of the third side of an obtuse triangle with sides of lengths 4 and 10 and an area of 12, you can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the equation c^2 = a^2 + b^2 - 2ab * cos(C) can be used to find the length of side c.

In this case, let's assume that the third side of the triangle has length x. We can set up the equation as x^2 = 4^2 + 10^2 - 2*4*10 * cos(C), where C is the angle opposite side x.

Simplifying the equation, we get x^2 = 116 - 80*cos(C).

Since we know that the area of the triangle is 12, we can use the formula Area = 0.5 * a * b * sin(C) to find the value of sin(C). Plugging in the given values, we get 12 = 0.5 * 4 * 10 * sin(C). Solving for sin(C), we find sin(C) = 0.6.

Using this value of sin(C), we can then find the value of cos(C) by using the trigonometric identity sin^2(C) + cos^2(C) = 1. Substituting sin(C) = 0.6, we get 0.6^2 + cos^2(C) = 1. Solving for cos(C), we find cos(C) = 0.8.

Now, we can substitute the value of cos(C) into the equation x^2 = 116 - 80*cos(C), giving us x^2 = 116 - 80*0.8. Simplifying further, we get x^2 = 52, which means that the length of the third side is either x = sqrt(52) or x = -sqrt(52).

However, since we are dealing with the length of a side, it cannot be negative. Therefore, the length of the third side is x = sqrt(52), which simplifies to x = 2sqrt(13).

rewrite 6 3/4 as an decimal number

Answers

6 3/4 as a decimal number is 6.75

Shape 1 and shape 2 are plotted on a coordinate plane. Which statement about the shapes is true?

Shape 1 is congruent to shape 2, which can be shown using a sequence of dilations and translations.

Shape 1 is not congruent to shape 2 because the shapes do not have the same absolute coordinates.

Shape 1 is congruent to shape 2, which can be shown using a translation.

Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 onto shape 2."

Answers

We can see that shape 2 has longer "stick" sorta say. we can see that stick on shape 1 is 2 units high (from 4 to 6) while stick on shape 2 is nearly 4 units high.

The "bulb" part of both shapes are congruent but because of their extensions they arent. Shapes dont have to be in same spot to be congruent. which is why second option isn't correct

Answer is last option

Solution:

As, you can see that shape 1 and shape 2 are not congruent nor the shape 1 is dilated by any factor to get the shape 2.

Both the shapes are concave polygon.

The base length of two shapes are equal .

→2 ×  AB  =  P Q  →(approx)

→BC=QR

→2 × CD= RS→→→(approx)

If translation has taken place, all the vertices has been translated by same amount.

So, option (4) is true,which is Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 onto shape 2."

The condition ∑ Fi = 0 is sufficient to assure that a rigid body is in equilibrium.
True
False ...?

Answers

It is false that the condition ∑ Fi = 0 is sufficient to assure that a rigid body is in equilibrium.
It is false because torque has to be zero as well as force. 
Answer:

The given statement:

The condition ∑ Fi = 0 is sufficient to assure that a rigid body is in equilibrium is a

TRUE statement.

Step-by-step explanation:

According to the condition for the equilibrium of a rigid body, the vector sum of all the forces acting on the body must be zero.

The first condition of equilibrium for a rigid body is as follows:

                             ∑ Fi = 0

where the expression  ∑ Fi are the sum of all the forces acting on the body.

Hence, the given statement is a TRUE statement.

Express the number in scientific notation.

0.042

Answers

In scientific notation, it would be: 4.2 * 10⁻²

The formula for the area of a square is A = s2, where s is the length of one side. Rearrange the formula to solve for s and select the correct option below.

s = square root of A
s = A2
s = 2A
s = A over 2

Answers

The answer is s = square root of A



Since x² = y    is         x = √y, then:
A = s²
s² = √A
√A is  square root of A.


if y=15 when x=3/4, find x when y=25

Answers

If y=15 when x=3/4, then y=5 when x=1/4 because 15 and 3/4 are both divisible by 3. We have to find x when y=25, and 25 is divisible by 5, so to find x you have to multiply y=5 and x=1 by 5 for y to equal 25. 5 times 5 equals 25, and 1 times 5 equals 5, so when y=25, x=5. 

The value of the x is 5/4 when y=25 if y=15 when x=3/4 the answer would be 5/4

What is a proportional relationship?

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

x and y are in a proportional relationship if y=15 when x=3/4,

y ∝ x

y = kx

15 = k(3/4)

k = 20

y = 20x

Plug y = 25

25 = 20x

x = 25/20

x = 5/4

Thus, the value of the x is 5/4 when y=25 if y=15 when x=3/4 the answer would be 5/4

The complete question is:

x and y are in a proportional relationship if y=15 when x=3/4, find x when y=25.

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WHAT IS THE BENEFIT OF A "SPACE CUSHION" AROUND YOUR VEHICLE?

Answers

A space cushion is a certain amount of distance you keep between u and the car in front of u that allows u to easily maneuver in any condition. The benefit would be : if another driver makes a mistake, ur space cushion gives u time to react.
Final answer:

A 'space cushion' increases safety by providing more time to react and decreasing the force of impact in a collision, akin to how airbags and crumple zones function in a vehicle.

Explanation:

The concept of a "space cushion" around your vehicle pertains to having a safe distance between your vehicle and others on the road. This increases the time you have to react to unexpected events and minimizes the force of impact during a collision, related to the physics principle of impulse. A larger space cushion effectively reduces the net force on your vehicle and its occupants by allowing more time for the vehicle to come to a stop or slow down. Features like airbags and crumple zones in cars serve a similar purpose by increasing the time over which a collision occurs, thereby reducing the impact force. This is crucial because the severity of injuries incurred during a vehicle accident is often directly related to the force exerted on the occupants.

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A fair coin is tossed n times. What is the probability that no two consecutive heads appear? A fair coin is tossed n times. What is the probability that no two consecutive heads appear?

Answers

If a coin is tossed, for example, 10 times:

There are 2^10 = 1024 total possible outcomes of 10 tosses. 

Now we count the number of possible outcomes with no two consecutive heads. Let x_n be this number for n tosses - we wish to find x_10. For n > 2, the string of tosses must fall into one of two disjoint categories: 

(i) tosses ending with a tail 

(ii) tosses ending with a tail then a head 

(i.e. tosses ending with a head then a head is impossible) 

Given that the first n-1 or n-2 tosses must also have no two consecutive heads, we sum the number of possibilities of case (i) and (ii) and find 
x_n = x_{n-1} + x_{n-2}. 

We also easily see that x_1 = 2, x_2 = 3. From the above recurrence we can compute x_n as terms of the Fibonacci sequence until x_10 = 144. 

Since the coin is unbiased all these possibilities are equally likely and the answer is 144/1024 = 9/64.

A system of equations has no solution. If y = 8x + 7 is one of the equations, which could be the other equation?

y = 8x + 7
y = 8x – 7
y = –8x + 7
y = –8x – 7

Answers

y=8x-7 is the answer. hope this helps!

Answer:

Option B. y = 8x - 7

Step-by-step explanation:

Parallel lines don't have the common points or the points of intersection.

In a system of equations has no solutions out of which one equation is y = 8x + 7

So a line parallel to this line will have no solutions.

For parallel lines slope will be same as 8, so the equation will be

y = 8x - 7

Option B. y = 8x - 7 will be the answer.

Which description represents the expression 3x+4 ? A.4 less than 3 times a number B.4 divided by the product of 3 and a number C. 4 added to 3 plus a number D.the sum of 3 times a number and 4

Answers

3x + 4

the sum of 3 times a number and 4


The answer is D since it's 3x which is three times a number and plus for

How do I simply this, thanks!

Answers

(-a^3b^2*-a^-2b^-3)^-2/2a^2b^-3 = a^4b^9/2a^8b^4 =b^5/2a^4 so your answer is b^5/2a^4

You buy a bicycle helmet for $22.26, which includes 6% sales tax. The helmet is discounted 30% off the selling price. What is the original price?

Answers

6% de 22,26 = 
6*22,26/100 = 
1,3356
22,26 - 1,3356 = 20,9244
70% de 20,9244 = 
70*20,9244/100 = 
14,64708 ~ 14,64
Final cost/1.06 = sale price

[tex] \frac{22.26}{1.06} = 21.06[/tex]

The sales price is $21.06

Sales price/.70 (70% of the original price) = original price

[tex] \frac{21.06}{.70} = 30.09[/tex]

The original price of the helmet was $30.09

In a linear equation, the independent variable increases at a constant rate while the dependent variable decreases at a constant rate. The slope of this line is
A. zero
B. negative
C. positive
D. undefined
...?

Answers

The best and most correct answer among the choices provided by your question is the second choice or letter B.

The slope of this line is NEGATIVE.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Answer: B. negative

Step-by-step explanation:

Given: In a linear equation, the independent variable increases at a constant rate while the dependent variable decreases at a constant rate.

We know that the slope of a line is given by :-

[tex]k=\dfrac{\text{change in y}}{\text{change in x}}[/tex]

According to the given information, if independent variable increases at a constant rate while the dependent variable decreases at a constant rate, then the slope of line will be :-

[tex]k=\dfrac{\text{Negative}}{\text{Positive}}=\text{Negative}[/tex]

Hence, the slope of line = Negative.

Ria is an Indian student who was admitted to a US university. Her annual tuition is $42,000. She has to pay her tuition fees in US dollars. She needs to calculate how many Indian rupees she will need to buy one dollar. The dollar to rupee exchange rate is 63.76 and rupee to dollar exchange rate is 0.015. How many Indian rupees will Ria need to buy one dollar?
50.00 rupees
56.00 rupees
63.76 rupees
76.63 rupees

Answers

Answer:

C:63.76

Hope this helps

Final answer:

Ria will need 63.76 Indian rupees to buy one US dollar according to the given exchange rate.

Explanation:

The student is asking how many Indian rupees are needed to buy one US dollar based on the given exchange rates. According to the given information, the exchange rate from dollars to rupees is 63.76. This means that one US dollar is equivalent to 63.76 Indian rupees. The other exchange rate provided, which is the value of a rupee in terms of dollars (0.015), is not directly relevant to the question being asked. Therefore, Ria will need 63.76 Indian rupees to buy one US dollar.

Tim wants to model a dollhouse from a real house that measures 60 feet in length by 28 feet in width. He decides to use a scale in which 1/4 inch equals 1 foot. What will the dimensions of his model be?

Length= __________ inches
Width= ___________ inches

Answers

There are two ways you can use to answer this question, I'll put both so you can decide which makes sense to you:
1. You could say that for every foot, you go 0.25 inches (because 0.25 is 1/4) and therefore if you do 0.25 × 60, you get the length as 15 inches, and 0.25 × 7, you get the width as 7 inches.
2. You could think of it a different way, and say that if 0.25 inches is 1 foot, then 1 inch must be 4 feet. Using this logic, you can then divide 60 by 4 to get 15, and divide 28 by 4 to get 7.

Either way you use, you get the length as 15 inches, and the width as 7 inches. Hope this helps!

Answer:

15

7

Just to simplify the answer above.

Step-by-step explanation:

When Katie was born her mother invested $5000 in an account for her college savings. The interest rate is 3.5% compounded annually. To represent this, we can use the formula V = 5000(1 + r)t where r represents the interest rate and t represents the time in years. How much will Katie have in her account when she turns 18? A) $5,175 B) $7,127 C) $9,287 D) $12,472

Answers

Final answer:

After performing the calculations based on the provided formula and values, Katie will have approximately $9127 in her college savings account when she turns 18. The closest option given in the question would be C) $9287.

Explanation:

To solve this problem, you would input the given values into the formula V = P(1 + r)t where P is the principal amount (in this case $5000), r is the annual interest rate (3.5% or 0.035 when expressed as a decimal), and t is the number of years (18).

When you substitute these values in, the equation becomes V = 5000(1 + 0.035)18.

Using a calculator, you'll find that V equates to approximately $9127. Therefore, Katie will have approximately $9127 in her account when she turns 18. The correct answer among the given options is thus closest to option C) $9287.

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Joshua used two wood beams, PC and QA, to support the roof of a model house. The beams intersect each other to form two similar triangles QRP and ARC as shown in the figure below. The length of segment PR is 4.8 inches and the length of segment CR is 7.2 inches. The distance between A and C is 9.6 inches.



What is the distance between the endpoints of the beams P and Q?

7.2 inches

3.6 inches

6.4 inches

12.0 inches

Answers

we will use Thalès theorem
since triangle PRQ and ARC are similar
PR  =  QR =   PQ
AR      CR       AC 
so we can use
PR  =  PQ
AR      AC      
but AR = CR   finally, PQ = AC x PR  / CR 

PQ = 9.6  x  4.8  / 7.2  = 6.4

 the true answer is 6.4 inches

Answer:

The answer is C, 6.4 inches

Step-by-step explanation:

What is the volume of a cube where the length of each side is 6 centimeters?

Answers

Answer:

The answer is A

Step-by-step explanation:

Knowing that you use 275 KWH from 7am-7pm and 265 KWH 7pm-7am, answer the question.

How much have you paid on the NightTImer plan?
NightTimer Plan: If more than 50% of usage is outside of 7pm-7am, then you have to pay the DayTimer rate for all power used between 7am-7pm. $0.06445/KWH

DayTimer: As long as most power used if from 7am-7pm, then you receive a 20% discount on power usage between 7pm-7am.
$0.06831/KWH

Answers

Answer: 35.86

Step-by-step explanation:

Final answer:

By applying the DayTimer and NightTimer plans' rules and doing the necessary calculations, the total payment on the NightTimer plan would be $33.26747.

Explanation:

The total power used from 7am-7pm is 275 KWH and from 7pm-7am is 265 KWH. In this case, you have used more power during the 7am-7pm period. As such, you qualify for the DayTimer plan's rate. Therefore, you pay $0.06831/KWH for the power used between 7am-7pm, which results in 275 KWH * $0.06831/KWH = $18.78575. However, since most of your power usage is from 7am-7pm, you receive a 20% discount on your night usage. The night rate, therefore, is 20% less than the DayTimer rate, which is $0.06831 * (1 - 20/100) = $0.054648/KWH. Hence, you will pay 265 KWH * $0.054648/KWH = $14.48172 for power used between 7pm-7am. By adding these two amounts together, your total payment on the NightTimer plan would be $18.78575 + $14.48172 = $33.26747.

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What is the most precise name for quadrilateral ABCD with vertices A(-4, -4), B(-4, -2), C(-1, -2), and D(-1, -4)?

A) quadrilateral

B) parallelogram

C) rhombus

D) rectangle

Answers

D a rectangle because it has four sides easy for abcd

Answer:

Option D.

Step-by-step explanation:

The given vertices of quadrilateral ABCD are A(-4, -4), B(-4, -2), C(-1, -2), and D(-1, -4).

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, we get

[tex]AB=\sqrt{\left(-4-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{0^2+(2)^2}=\sqrt{4}=2[/tex]

Similarly,

[tex]BC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-2\right)\right)^2}=3[/tex]

[tex]CD=\sqrt{\left(-1-\left(-1\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=2[/tex]

[tex]AD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-4\right)\right)^2}=3[/tex]

[tex]AB = CD[/tex]

[tex]BC = AD[/tex]

Measure of diagonals:

[tex]AC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{13}[/tex]

[tex]BD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=\sqrt{13}[/tex]

[tex]AC = BD[/tex]

Since measure of opposite sides are equal and measure of diagonals are equal, therefore the given quadrilateral ABCD is a rectangle.

Hence, the correct option is D.

Which speed is the fastest? A 18 feet in 20 minutes B 90 feet in 2.5 hours C 20 yards in 1.5 hours D 3 2/3 yards in 15 minutes

Answers

''90 feet in 2.5 hours'' have fastest speed.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

There are some distances and time.

Now,

For Option A;

⇒  18 feet in 20 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 18/20

               = 0.9 feet per minutes

For Option B;

⇒  90 feet in 2.5 hours

⇒ 90 feet in 150 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 90/150

               = 0.6 feet per minutes

For Option C;

⇒  20 yards in 1.5 hours

Since, 1 yards = 3 feet

⇒ 60 feet in 90 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 60/90

               = 0.67 feet per minutes

For Option D;

⇒  3 2/3 yards in 15 minutes

Since, 1 yards = 3 feet

⇒ 11 feet in 15 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 11/15

               = 0.73 feet per minutes

Hence, Clearly ''90 feet in 2.5 hours'' have fastest speed.

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Final answer:

After converting each option to the same unit of speed, it's clear that Option A with a speed of 0.9 feet per minute is the fastest.

Explanation:

To determine which speed is the fastest, we need to convert each option into the same unit of speed, typically feet per minute or meters per second for consistency. Here, we'll choose feet per minute for simplicity.

Option A: 18 feet in 20 minutes = 0.9 feet/minute

Option B: 90 feet in 2.5 hours (150 minutes) = 0.6 feet/minute

Option C: 20 yards (60 feet) in 1.5 hours (90 minutes) = 0.67 feet/minute

Option D: 3 2/3 yards (11 feet) in 15 minutes = 0.73 feet/minute

Comparing these speeds, Option A is the fastest with 0.9 feet per minute.

Which phrase describes the end behavior of the graph of ƒ(x) = –x5 – 4x4 + 7x2 – 2?

Answers

well for end behavior, you simply look at the highest exponent (in this case 5) and look for 2 things:
Is it even or odd? Odd
Is it positive or negative? Negative

Using this we can determine that it is up to the left, and down to the right

Or, for more advanced terms, as x approaches -∞, y approaches ∞, and as x approaches ∞, y approaches -∞

The ordered pairs (1, 81), (2, 100), (3, 121), (4, 144), and (5, 169) represent a function. What is a rule that represents this function?

y = x^8

y = 8^x

y = (x + 8)^2

y = 8x ...?

Answers

Answer:

[tex]y=(x+8)^{2}[/tex]

Step-by-step explanation:

we have that

The ordered pairs [tex](1, 81), (2, 100), (3, 121), (4, 144)[/tex], and [tex](5, 169)[/tex] represent a function

The rule that that represent this function is equal to

[tex]y=(x+8)^{2}[/tex]

Verify

For [tex]x=1[/tex] -----> Find the value of y in the equation

[tex]y=(1+8)^{2}=81[/tex] -----> is correct

For [tex]x=2[/tex] -----> Find the value of y in the equation

[tex]y=(2+8)^{2}=100[/tex] -----> is correct

For [tex]x=3[/tex] -----> Find the value of y in the equation

[tex]y=(3+8)^{2}=121[/tex] -----> is correct

For [tex]x=4[/tex] -----> Find the value of y in the equation

[tex]y=(4+8)^{2}=144[/tex] -----> is correct

For [tex]x=5[/tex] -----> Find the value of y in the equation

[tex]y=(5+8)^{2}=169[/tex] -----> is correct


y = 1/2 x + 2

x = 8

y = __

Answers

you have to replace x with 8 in the first ecuation
y=(1/2)*8+2=8/2+2=4+2=6
y=x/2+2

x=8

y=8/2 + 2

y = 4 + 2
 
y = 6

If sec 2A = 1/sin 13A, determine the angle A in degrees.
a. 5°
b. 6°
c. 3°
d. 7°

Answers

sec 2 A = 1 / cos 2 A
1 / cos 2 A = 1 / sin 13 A
cos 2 A = sin 13 A
2 A = 90° - 13 A
2 A + 13 A = 90°
15 A = 90°
A = 90° : 15
Answer:
B ) A = 6°

on a grid, what is the distance between two points located at (2,1) and (14,6)

A.) 5
B.) 13
C.) 12
D.) 17.46

Answers

√(y2-y1)²+(x2-x1))

Simple Pythagorean Theorem.....

√(12)²+(5²))
√(169)
B.) 13
the awser is b trust in me

what is the squar root of 21

Answers

The square root of 21 is 4.5826


Tomas wrote the equation y = 3x +3/4. When Sandra wrote her equation, they discovered that her equation had all the same solutions as Tomas’s equation. Which equation could be Sandra’s?

–6x + y = 3/2
6x + y = 3/2
–6x + 2y = 3/2
6x + 2y = 3/2

Answers

–6x + 2y = 3/2

or, 2y= 6x + 3/2
or, y= (6x + 3/2)/2
or, y = 6x/2 + 3/4
or, y = 3x + 3/4

Therefore, –6x + 2y = 3/2 is Sandra's equation.  


In order for Sandra's equation to have all the same solutions as Tomas's equation they need to lie on each other or in other words to be exactly the same.

So now we need to transform options in tomas equation form and compare.

First option:
y = 6x + 3/2    not the same

Second option:
y = -6x + 3/2   not the same

Third option:
-6x + 2y = 3/2   when -6x goes on other side it changes its sign and will become:
2y = 6x + 3/2
when we divide by 2 we get
y = 3x + 3/4 which marks with Tomas's equation

Answer is third option.

If a line segment has endpoints A(3x + 5, 3y) and B(x − 1, −y), what are the coordinates of the midpoint of AB ?

(x + 3, 2y)
(2x + 3, y)
(2x + 2, y)
(4x + 4, 2y) ...?

Answers

You need to use the midpoint formula of (x1+x2)/2,(y1+y2)/2

put in the actual points will look like this. (3x+5+x-1)/2,(3y-y)/2

now solve to get (4x+4)/2,(2y)/2

finish (2x+2,y)

Final answer:

The coordinates of the midpoint of the line segment with endpoints A(3x + 5, 3y) and B(x - 1, -y) are (2x + 2, y), using the midpoint formula.

Explanation:

To find the coordinates of the midpoint of a line segment with endpoints A and B, you can use the midpoint formula, which is ((x₁ + x₂)/2, (y₁ + y₂)/2). For the given endpoints A(3x + 5, 3y) and B(x - 1, -y), substituting the coordinates into the formula gives us the midpoint coordinates as follows:

x-coordinate of the midpoint = (3x + 5 + x - 1)/2 = (4x + 4)/2 = 2x + 2y-coordinate of the midpoint = (3y - y)/2 = 2y/2 = y

Hence, the coordinates of the midpoint of AB are (2x + 2, y).

Other Questions
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