3. One morning, the elevator in Emilio's apartment building was out of order. When he walked down the stairs from
his apartment to the ground floor, he counted 252 steps. Emilio lives on the 14th floor. How many steps are
between each floor?
A 10
C 22
B 18
D 32

Answer:

(a) At 21.46 psi, the TPMS trigger a warning for this car.

(b) The probability that the TPMS will trigger a warning is 0.0001.

(c) The probability that the tire’s inflation is within the recommended range is 0.6826.

Step-by-step explanation:

We are given that tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch).

(a) It is stated that TPMS warns the driver when the tire pressure of the vehicle is 26% below the target pressure.

So, the TPMS trigger a warning for this car when;

Pressure = 29 psi - 26% of 29 psi

               = [tex]29-(0.26 \times 29)[/tex]  = 21.46 psi

At 21.46 psi, the TPMS trigger a warning for this car.

(b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi.

Let X = The pressure at which TPMS will trigger a warning

So, X ~ Normal([tex]\mu=29, \sigma^{2} =2^{2}[/tex])

Now, the probability that the TPMS will trigger a warning is given by = P(X [tex]\leq[/tex] 21.46)

        P(X [tex]\leq[/tex] 21.46) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{21.46-29}{2}[/tex] ) = P(Z [tex]\leq[/tex] -3.77) = 1 - P(Z < 3.77)

                                                              = 1 - 0.9999 = 0.0001

The above probability is calculated by looking at the value of x = 3.77 in the z table which has an area of 0.9999.

(c) The manufacturer’s recommended correct inflation range is 27 psi to 31 psi.

So, the probability that the tire’s inflation is within the recommended range is given by = P(27 psi < X < 31 psi)

     P(27 psi < X < 31 psi) = P(X < 31 psi) - P(X [tex]\leq[/tex]27 psi)

     P(X < 31 psi) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{31-29}{2}[/tex] ) = P(Z < 1) = 0.8413

     P(X [tex]\leq[/tex] 27 psi) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{27-29}{2}[/tex] ) = P(Z [tex]\leq[/tex] -1) = 1 - P(Z < 1)

                                                        = 1 - 0.8413 = 0.1587

Therefore, P(27 psi < X < 31 psi) = 0.8413 - 0.1587 = 0.6826.

At 21.46 psi, the TPMS trigger a warning for this car.

The probability that the TPMS will trigger a warning is 0.0001.

The probability that the tire’s inflation is within the recommended range is 0.6826.

Given that,

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure.

Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch).

We have to determine,

At what psi will the TPMS trigger a warning for this car.

What is the probability that the TPMS will trigger a warning.

What is the probability that the tire’s inflation is within the recommended range.

According to the question,

So, the TPMS trigger a warning for this car when;

Pressure = 29 psi - 26% of 29 psi

[tex]Pressure = 29- (0.26 \times 29) = 21.46psi[/tex]

At 21.46 psi, the TPMS trigger a warning for this car.

Let X = The pressure at which TPMS will trigger a warning

So, X ~ Normal [tex]\mu = 29, \sigma^2 = 2^2\\[/tex]

Now, the probability that the TPMS will trigger a warning is given by = P(X≤  21.46).

[tex]P(X\leq 21.46) = P (\dfrac{X-\mu}{\sigma}\leq \dfrac{21.46-29}{2}) = P(Z\leq -3.77) = 1-P(Z<3.77) \\\\= 1-0.9999 = 0.0001[/tex]

The above probability is calculated by looking at the value of x = 3.77 in the z table which has an area of 0.9999.

So, the probability that the tire’s inflation is within the recommended range is given by = P(27 psi < X < 31 psi)

[tex]P(27psi<X<31psi) = P(X<31psi)-P(X\leq psi)\\\\P(X<31psi) = P(\dfrac{x-\mu}{\sigma}\leq \dfrac{31-29}{2}) = P(Z<1) = 0.8413\\\\P(X<27psi) = P(\dfrac{x-\mu}{\sigma}\leq \dfrac{27-29}{2}) = P(Z\leq -1) = 1-P(Z<1) = 0.8413\\[/tex]

Therefore, , P(27 psi < X < 31 psi) = 0.8413 - 0.1587 = 0.6826.

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Answer:

See below :)

Step-by-step explanation:

Given ordered pairs :

( 2 , 3 ) , ( - 2 , 4 ) , ( 4 , 8 ) , ( - 2 , 5 )

Domain is the set of all x -coordinates in the set of ordered pairs.

( 2 , 3 ) , ( -2 , 4 ) , ( 4 , 8 ) , ( -2 , 5 )

List them :

Domain = { - 2 , 2 , 4 )

Range is the set of all y - coordinates in the set of ordered pairs.

( 2 , 3 ) , ( - 2 , 4 ) , ( 4 , 8 ) , ( - 2 , 5 )

List them :

Range = { 3 , 4 , 5 , 8 }

Hope I helped !

Best regards!!

Answer:

Total number of people in the concert

= 186

Step-by-step explanation:

There are 80 people in level 2

Then in level one

The dimensions of the room are 62 feet by 31 feet.

15 people fit in a 3 feet by 6 feet space.

Area of the room= 62*31= 1922 feet²

area of 15 people space= 3*6= 18 feet²

To know how many 15 people we get in the 2nd level

=Area of room/area of 15 people space

= 1922/18

= 106.77

= 106 (we round down because this is human being.)

Total number of people in the concert

= 106+80

= 186

Answer:

  a) 30 kangaroos in 2030

  b) decreasing 8% per year

  c) large t results in fractional kangaroos: P(100) ≈ 1/55 kangaroo

Step-by-step explanation:

We assume your equation is supposed to be ...

  P(t) = 76(0.92^t)

__

a) P(10) = 76(0.92^10) = 76(0.4344) = 30.01 ≈ 30

In the year 2030, the population of kangaroos in the province is modeled to be 30.

__

b) The population is decreasing. The base 0.92 of the exponent t is the cause. The population is changing by 0.92 -1 = -0.08 = -8% each year.

The population is decreasing by 8% each year.

__

c) The model loses its value once the population drops below 1/2 kangaroo. For large values of t, it predicts only fractional kangaroos, hence is not realistic.

  P(100) = 75(0.92^100) = 76(0.0002392)

  P(100) ≈ 0.0182, about 1/55th of a kangaroo

Answer:

|w - v| or |v - w|

Step-by-step explanation:

The answer is the absolute value of the difference of the two numbers written in either order.

|w - v| or |v - w|

Answer:

B |w-v|

Step-by-step explanation:

khan academy

Answer:

= 0.1 miles per minute

Step-by-step explanation:

= 1.5 miles / 15 min.

= 0.1 miles per minute

First thing to do is distribute the [tex]-3[/tex]:

[tex]-3(x+n)=x\\-3x+-3n=x[/tex]

Now we're gonna solve for [tex]x[/tex]:

[tex]-3x-3n=x\\-4x=3n\\x=-\frac{3n}{4}[/tex]

To solve for [tex]n[/tex]:

[tex]-3x-3n=x\\-3n=4x\\n=-\frac{4x}{3}[/tex]

Answer:

0.5

Step-by-step explanation:

Plug in -1 as x into the function:

f(-1) = -1 + 3/2

f(-1) = 0.5

[tex]\bf \underline{ \underline{Given : }}[/tex]

f(x) =x + 3/2

[tex]\bf \underline{ \underline{To \: be \: calculated : }}[/tex]

what is the value of f(-1) ?

[tex] \bf \underline{ \underline{Solution : }}[/tex]

[tex] \sf{f(x) = x + \dfrac{3}{2} }[/tex]

[tex] \rightarrow \sf {f( - 1) = ( - 1) + \dfrac{3}{2} }[/tex]

[tex] \rightarrow \sf{f( - 1) = \dfrac{ - 2 + 3}{2} }[/tex]

[tex] \rightarrow \sf{f( - 1) = \dfrac{ 1}{2} }[/tex]

[tex] \rightarrow \sf {f( - 1) = 0.5}[/tex]

Answer:

The surface area is 7600

I would really appreciate brainliest!

Step-by-step explanation:

L=Ph

L=(40x2 50x2) 20

L=3600

S= L+2B

S=3600 +2(40x50)

S= 3600+4000

S= 7600

Answer: Hi!

There are three different rectangles that make up this closed box. We need to calculate the area of them to find the surface area of this shape. Here are the measurements:

Rectangle 1: 40 * 20

Rectangle 2: 50 * 20

Rectangle 3: 50 * 40

Note that there are two of each type of rectangle, so when we are done calculating the area of each rectangle we will multiply each by 2.

Rectangle 1: 40 * 20 = 800(2) = 1600

Rectangle 2: 50 * 20 = 1000(2) = 2000

Rectangle 3: 50 * 40 = 2000(2) - 4000

Now, we add the areas together: 1600 + 2000 + 4000 = 7600

The surface area of this closed box is 7600cm squared.

Hope this helps!

Hello, to find the sign of the product we use the following rules.

- by + is -

"The enemy of my friend is an enemy."

+ by - is -

"The friend of my enemy is an enemy."

- by - is +

"The enemy of my enemy is a friend."

+ by + is +

"The friend of my friend is a friend."

We can build the following array.

[tex]f(x)=(x+1)(x-3)(x-7)(x+6)[/tex]

[tex]\begin{array}{|c|ccccccccc}x &-\infty & -6 & & -1 & & 3 & & 7 & +\infty\\---&---&---&---&---&---&---&---&---&---\\(x+1)&-&-5&-&0&+&4&+&8&+\\(x-3)&-&-9&-&-4&-&0&+&5&+\\(x-7)&-&-13&-&-8&-&-4&-&0&+\\(x+6)&-&0&+&5&+&9&+&13&+\\---&---&---&---&---&---&---&---&---&---\\f(x)&+&0&-&0&+&0&-&0&+\\\end{array}[/tex]

So f(x) > 0 <=> x < -6 or -1 < x < 3 or x > 7

Thank you

Answer:

According to the graph, there are 6 pumpkins with the mass of 9kg to 12kg and 4 pumpkins with the mass of 0kg to 3kg.

In order to find how many pumpkins more, you have to subtract it so it will be 6 pumpkins - 4 pumpkins = 2 pumpkins.

Therefore, there are 2 more pumpkins with the mass of 9 to 12kg compared to the pumpkins with the mass of 0 to 3kg.

Answer:

2

Step-by-step explanation:

Answer:

x = (-5 ± 2√10) / 3

Step-by-step explanation:

5 − 10x − 3x² = 0

Write in standard form:

-3x² − 10x + 5 = 0

Solve with quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ -(-10) ± √((-10)² − 4(-3)(5)) ] / 2(-3)

x = [ 10 ± √(100 + 60) ] / -6

x = (10 ± 4√10) / -6

x = (-5 ± 2√10) / 3

Step-by-step explanation:

[tex]5 - 10x - 3 \times 2 = 0[/tex]

[tex]multiply \: the \: numbers \\ \\ 5 - 10 x- 6 = 0[/tex]

[tex]collect \: like \: terms \\ \\ 5 - 6 - 10x[/tex]

[tex] - 1 - 10x = 0[/tex]

[tex] - 10x = 1[/tex]

[tex]divide \: both \: sides \: of \: the \: equation \: by \: - 10[/tex]

[tex]x = - \ \frac{1}{10} [/tex]

[tex]alt \: form \: = \\ \\ = 0.1 \\ x = - 10 {}^{ - 1} [/tex]

Hope this helps. :)

Answer:

Technically neither, but Mia is correct.

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Since our slope m is equal to 6, it is a positive number. That means that the slope/line will be positive, so the line should be going up, not down. That means the blue line would be correct. Therefore, Mia is correct.

Technicality:

Since the blue line is dotted, the equation should be a inequality and not a linear equation. No solutions on the line would technically work. If the equation was y < 6x + 4 or something with an inequality sign, then it would be correct.

Answer:

3n^(2) - 18

Step-by-step explanation:

Answer:

The inverse represents the temperature F corresponding to a temperature C.

The domain of the inverse function is all real numbers.

194°F

Step-by-step explanation:

Let C= y

y= 5/9 (F - 32),

F= 9/5y + 32

But y= C, hence;

F= 9/5 C +32

The inverse represents the temperature F corresponding to a temperature C.

Given;

F= 9/5 C +32

The domain of the inverse function is all real numbers.

Given C= 90°

F= 9/5 C +32

F= 9/5 (90°) +32

F= 194°F

Answer:

13.75

Step-by-step explanation:

The expected value of the hourly wage is the sum of the probabilities (percentage of time spent on each job) multiplied by the payoff (money earned) from each possible occurrence (job): 0.6 × 11 + 0.25 × 19 + 0.15 × 16 = $13.75.

The average hourly wage will be equal to 13.75 hours.

An average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that work at a convenience store 60% of your time, and earn $11.00 an hour. Referee games at your city park 25% of your time, and earn $19.00 an hour. Do your elderly neighbor’s housework 15% of your time, and earn $16.00 an hour.

The expected value of the hourly wage will be calculated as below:-

The expected value of the hourly wage is the sum of the probabilities (percentage of time spent on each job) multiplied by the payoff (money earned) from each possible occurrence (job):

0.6 × 11 + 0.25 × 19 + 0.15 × 16 = $13.75.

Therefore, the average hourly wage will be equal to 13.75 hours.

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Answer & Step-by-step explanation:

Slope-intercept form:

[tex]y=mx+b[/tex]

m is the slope and b is the y-intercept. Insert the given slope:

[tex]y=-5x+b[/tex]

To find the y-intercept, take the given coordinate point and insert:

[tex](-9_{x},-5_{y})\\\\-5=-5(-9)+b[/tex]

Solve for b:

Simplify multiplication:

[tex]-5=45+b[/tex]

Subtract 45 from both sides:

[tex]-50=b\\\\b=-50[/tex]

The y-intercept is -50. Insert:

[tex]y=-5x-50[/tex]

[tex]m=-5\\b=-50[/tex]

Use the slope formula for when you have two points:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]

The slope is the change in the y-axis over the change in the x-axis, or rise over run. Insert the points:

[tex](2_{x1},4_{y1})\\(10_{x2},2_{y2})[/tex]

[tex]\frac{2-4}{10-2}=\frac{-2}{8}=-\frac{2}{8}=-\frac{1}{4}[/tex]

The slope is [tex]-\frac{1}{4}[/tex] . Insert:

[tex]y=-\frac{1}{4}x+b[/tex]

Now follow the steps from the last problem to find the y-intercept. Choose a point and insert into the equation:

[tex](2_{x},4_{y})\\\\4=-\frac{1}{4}(2)+b[/tex]

Solve for b:

Simplify multiplication:

[tex]-\frac{1}{4}*\frac{2}{1}=-\frac{2}{4}=-\frac{1}{2}[/tex]

Re-insert:

[tex]4=-\frac{1}{2} +b[/tex]

Subtract b from both sides:

[tex]4-b=-\frac{1}{2} +b-b\\\\4-b=-\frac{1}{2}[/tex]

Subtract 4 from both sides:

[tex]4-4-b=-\frac{1}{2}-4\\\\-b=-\frac{1}{2}-4[/tex]

Simplify subtraction:

[tex]-\frac{1}{2}-4=-\frac{1}{2} -\frac{4}{1} =-\frac{1}{2} -\frac{8}{2} \\\\-\frac{1}{2} -\frac{8}{2}=-\frac{9}{2}[/tex]

Re-insert:

[tex]-b=-\frac{9}{2}[/tex]

Divide both sides by -1 to make the variable positive (can be seen as -1b):

[tex]b=\frac{9}{2}[/tex]

The y-intercept is [tex]\frac{9}{2}[/tex] .

Write the equation:

[tex]y=-\frac{1}{4}x+\frac{9}{2}[/tex]

:Done

Answer:

third answer

point Y, ray YZ, angle XYZ

Step-by-step explanation:

These can all be found on the figure are; point Y, ray YZ, angle XYZ. Hence, option C is correct.

An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.

The point of their joint is called vertex of that angle.

Those two line segments forming it are called arms of that angle.

The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on...

These can all be found on the figure are; point Y, ray YZ, angle XYZ.

Hence, option C is correct.

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Answer:

2x + 5 = 61

Step-by-step explanation:

Let x be equal to the temperature in Boise.

Since the temperature in San Diego is 5 degrees warmer than twice the temperature in Boise, we must double the temperature in Boise and then add 5 degrees. To do this we put a 2 in front of the x and then add 5 to that.

2x + 5

Since we know the temperature in San Diego is 61 we can make the equation equal to 61.

2x + 5 = 61

Answer:

The entire floor can contain approximately 4178 fans

Step-by-step explanation:

The first step is to calculate the area of the basketball floor.

we can do this by multiplying the length by the breadth as such 94 X 50 = 4700 square feet.

The second step is to calculate the area occupied by 8 of the fans. We can do this by multiplying 3 ft by 3ft = 9 square feet.

From this, it will be easier to estimate the area occupied by only one fan. This can be got by dividing 9 square feet by 8.  

This is = 1.125 square feet.

To get the number of students it can occupy, we divide the total area of the court by the area occupied by one student.

4700/ 1.125 =4177.8 [tex]\approx[/tex] 4178 fans

The correct answer is A. 12y + 11

Explanation:

In mathematics, the word "product" is mainly used to refer to multiplication. For example, the product of 5 and 2 is 10 as 5 x 2 = 10. This means, the section "the product of 12 and y" means 12 needs to be multiplied by y, which can be expressed as 12y. Additionally, the word "increased" refers to addition, which means 11 needs to be added to 12y. This means the final expression is 12y + 11, and therefore the correct answer is the first one or option A.

Answer: the answer is 12y + 11

Step-by-step explanation:

i too the test and got a 100

Answer:

There are multiple ways this can be said :

Answer:

1280 sq inches

Step-by-step explanation:

A = LW

A = 40 in. * 32 in.

A = 1280 sq inches

Answer:

Step-by-step explanation:

Since the TV screen is a rectangle

Area of a rectangle = l × w

where

l is the length / height

w is the width

From the question

height = 32 inches

width = 40 inches

Substitute the values into the above formula

That's

Area of TV screen = 32 × 40

We have the answer as

Hope this helps you

Answer:

Se requiere 12 cajas con 4 manzanas y 3 duraznos cada una.

Step-by-step explanation:

Se requiere el menor número posible de manzanas y duraznos para obtener el mayor número de cajas. Puesto que no se considera cortar fruta alguna en porciones y sabiendo que hay más manzanas que duraznos, se determina la razón mínima de manzanas por duraznos:

[tex]x = \frac{48\,manzanas}{36\,duraznos}[/tex]

[tex]x = \frac{4 manzanas}{3\,duraznos}[/tex]

Se requiere 4 manzanas por cada 3 duraznos. Entonces, cada caja debe contener 3 duraznos y 4 manzanas. El número máximo de cajas es:

[tex]n = \frac{48\,manzanas}{4\,\frac{manzanas}{caja} } = \frac{36\,duraznos}{3\,\frac{duraznos}{caja} }[/tex]

[tex]n = 12\,cajas[/tex]

Se requiere 12 cajas con 4 manzanas y 3 duraznos cada una.

Answer:

2 and 4 6/7

Step-by-step explanation:

1. First equation

2. Second equation

Answer:

y+6 = 3/5(x-4)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y --6 = 3/5( x-4)

y+6 = 3/5(x-4)

Answer:  The number has to be less than 27.

Step-by-step explanation:

81 + n > 4n  

      -n    -n

81  > 3n

n<27