When Mason commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 38 minutes and a standard deviation of 3 minutes Out of the 283 days that Mason commutes to work per year, how many times would his commute be longer than 41 minutes , to the nearest whole number?

Answer:

30,000

Step-by-step explanation:

hope this helps!!!

Answer:6^21

Step-by-step explanation:

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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easy the answer would be  2.2

The probability that this adult used non-prescription antidepressants is 0.78.

Based on the information given, the following can be deduced:

Let A = event where adults visit therapist.

Let B = event where adults used non prescription antidepressants.

P(A) = 0.27

P(B) = 0.46

P(A n B) = 0.21

The probability that a randomly selected adult who visited the therapist used non-prescription antidepressants will be:

= 0.21/0.27

= 0.78

The probability that an adult visited a therapist during the past year, given that he or she used non-prescription antidepressants will be:

= 0.21/0.46

= 0.46

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Answer:

Approximately 40,069 days

Answer:

area of a trapezoidal base  of each prism with heights  6 and 8 units are 4 square units and 3 square units respectively

Step-by-step explanation:

Let us first be aware of formula of volume for any regular geometrical figure.

Fundamental formula for  volume for any regular geometrical figure is.

volume = area of cross section of object*  height of object (A)

In the problem stated area of cross section of object will be  area of a trapezoidal base.

Given in the question is

Volume of both the trapezoidal prisms = 24 cubic units

*************************************************************************************

For prism with height 6 unit

Substituting the value of height and volume in formula for trapezoidal prisms

24 = 6 * area of a trapezoidal base

=> area of a trapezoidal base = 24/6 = 4 square units

*************************************************************************************

For prism with height 8 unit

Substituting the value of height and volume in formula for trapezoidal prisms

24 = 8 * area of a trapezoidal base

=> area of a trapezoidal base = 24/8 = 3 square units

*************************************************************************************

Therefore area of a trapezoidal base  of each prism with heights  6 and 8 units are 4 square units and 3 square units respectively.

Answer:

C)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The guy above me is correct

Answer:

(317-7)/6≈52

Step-by-step explanation:

There was approximately 52 kids in each bus

Total number of kids = 317

Total number of buses = 6

Number of kids sick = 7

Therefore, the number of kids on each bus will be:

= (317 - 7) / 6

= 310/6

= 51 2/3

= 52 kids approximately

In conclusion, there was approximately 52 kids in each bus.

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If angle BOC in circle is 68° then the measure of angle BAC is 34°.

Given that angle BOC in the circle is 68°.

We have to find the angle BAC.

We have that m∠BOC=arc BC ------by central angle.

we have m∠BOC=68°.

therefore arc BC=68°.

We know that the inscribed angle is half that of the arc it comprises so m∠BAC=1/2 *(arc BC)-----1

In geometry one of the theorem states states that angle at the center of a circle is twice angle at the circumference.

We have that arc BC=68°

substitute arc BC in equation 1 to get the measurement of ∠BAC.

m∠BAC=\(68/2\)

=34°

Hence if angle BOC in circle is 68° then the measure of angle BAC is 34°.

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Answer:

Jayden: 9t+3s=420

Carson: 1t+6s=296

Step-by-step explanation:

I hope that helps =)

so I guess is getting the area of both sectors, hmmm, ok, well, one sector is 101° and the other must be 259°, both have a radius of 2.

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=2\\ \theta =101 \end{cases}\implies A=\cfrac{(101)\pi (2)^2}{360}\implies A\approx 3.53~m^2 \\\\[-0.35em] ~\dotfill\)

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=2\\ \theta =259 \end{cases}\implies A=\cfrac{(259)\pi (2)^2}{360}\implies A\approx 9.04~m^2\)

Answer:

Add all the digits of the number, then check if that sum is divisible by 9. If yes, we know the number is divisible by 9.

Here is the correct format for the question

At 2:00 PM a car's speedometer reads 30 mi/h. At 2:15 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:15 the acceleration is exactly 80 mi/h².Let v(f) be the velocity of the car t hours after 2:00 PM.Then \(\dfrac{v(1/4)-v(0)}{1/4 -0} = \Box\). By the Mean Value Theorem, there is a number c such that 0 < c < \(\Box\)  with v'(c) = \(\Box\). Since v'(t)  is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly 80 mi/h^2.

Answer:

Step-by-step explanation:

From the information given :

At  2:00 PM ;

a car's speedometer v(0) = 30 mi/h

At 2:15 PM;

a car's speedometer v(1/4) = 50 mi/h

Given that:

v(f) should be the velocity of the car t hours after 2:00 PM

Then \(\dfrac{v(1/4)-v(0)}{1/4 -0} = \Box\) will be:

\(= \dfrac{50-30}{1/4 -0}\)

\(= \dfrac{20}{1/4 }\)

= 20 × 4/1

= 80 mi/h²

By the Mean value theorem; there is a number c such that :

\(\mathbf{0 < c< \dfrac{1}{4}}\)     with \(\mathbf{v'(c) = \dfrac{v(1/4)-v(0)}{1/4 -0}} \mathbf{ = 80 \ mi/h^2}\)

By the mean value, theorem a number \(C\) is \(0 < C < \frac{1}{4}\).

The velocity of the car is \(80 \ mi/h^{2}\).

Speed is defined as The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

Given that,

at 2:00 pm \(v(0)=30 \ mi/h\)

at 2:15 pm \(v(1/4)=50 \ mi/h\)

Then,

\(=\frac{v(1/4)-v(0)}{1/4-0} \\=\frac{50-30}{1/4} \\=20\times4\\=80 \ mi/h^{2}\)

By the mean value theorem a number \(C\) such that express as,

\(0 < C < \frac{1}{4}\).

Now with,

\({v}'(c)=\frac{v\left ( \frac{1}{4} \right )-v\left ( 0 \right )}{\frac{1}{4}-0} \\ =80 \ mi/h^{2}\)

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Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

Answer:

3 . 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3 7 5 1 0 5 8 2 0 9 7 4 9 4 4 5 9 2 3 0 7 8 1 6 4 0 6 2 8 6 2 0 8 9 9 8 6 2 8 0 3 4 8 2 5 3 4 2 1 1 7 0 6 7 9 8 2 1 4 8 0 8 6 5 1 3 2 8 2 3 0 6 6 4 7 0 9 3 8 4 4 6 0 9 5 5 0 5 8 2 2 3 1 7 2 5 3 5 9 4 0 8 1 2 8 4 8 1 1 1 7 4 5 0 2 8 4 1 0 2 7 0 1 9 3 8 5 2 1 1 0 5 5 5 9 6 4 4 6 2 2 9 4 8 9 5 4 9 3 0 3 8 1 9 6 4 4 2 8 8 1 0 9 7 5 6 6 5 9 3 3 4 4 6 1 2 8 4 7 5 6 4 8 2 3 3 7 8 6 7 8 3 1 6 5 2 7 1 2 0 1 9 0 9 1 4 5 6 4 8 5 6 6 9 2 3 4 6 0 3 4 8 6 1 0 4 5 4 3 2 6 6 4 8 2 1 3 3 9 3 6 0 7 2 6 0 2 4 9 1 4 1 2 7 3 7 2 4 5 8 7 0 0 6 6 0 6 3 1 5 5 8 8 1 7 4 8 8 1 5 2 0 9 2 0 9 6 2 8 2 9 2 5 4 0 9 1 7 1 5 3 6 4 3 6 7 8 9 2 5 9 0 3 6 0 0 1 1 3 3 0 5 3 0 5 4 8 8 2 0 4 6 6 5 2 1 3 8 4 1 4 6 9 5 1 9 4 1 5 1 1 6 0 9 4 3 3 0 5 7 2 7 0 3 6 5 7 5 9 5 9 1 9 5 3 0 9 2 1 8 6 1 1 7 3 8 1 9 3 2 6 1 1 7 9 3 1 0 5 1 1 8 5 4 8 0 7 4 4 6 2 3 7 9 9 6 2 7 4 9 5 6 7 3 5 1 8 8 5 7 5 2 7 2 4 8 9 1 2 2 7 9 3 8 1 8 3 0 1 1 9 4 9 1 2 9 8 3 3 6 7 3 3 6 2 4 4 0 6 5 6 6 4 3 0 8 6 0 2 1 3 9 4 9 4 6 3 9 5 2 2 4 7 3 7 1 9 0 7 0 2 1 7 9 8 6 0 9 4 3 7 0 2 7 7 0 5 3 9 2 1 7 1 7 6 2 9 3 1 7 6 7 5 2 3 8 4 6 7 4 8 1 8 4 6 7 6 6 9 4 0 5 1 3 2 0 0 0 5 6 8 1 2 7 1 4 5 2 6 3 5 6 0 8 2 7 7 8 5 7 7 1 3 4 2 7 5 7 7 8 9 6 0 9 1 7 3 6 3 7 1 7 8 7 2 1 4 6 8 4 4 0 9 0 1 2 2 4 9 5 3 4 3 0 1 4 6 5 4 9 5 8 5 3 7 1 0 5 0 7 9 2 2 7 9 6 8 9 2 5 8 9 2 3 5 4 2 0 1 9 9 5 6 1 1 2 1 2 9 0 2 1 9 6 0 8 6 4 0 3 4 4 1 8 1 5 9 8 1 3 6 2 9 7 7 4 7 7 1 3 0 9 9 6 0 5 1 8 7 0 7 2 1 1 3 4 9 9 9 9 9 9 8 3 7 2 9 7 8 0 4 9 9 5 1 0 5 9 7 3 1 7 3 2 8 1 6 0 9 6 3 1 8 5 9 5 0 2 4 4 5 9 4 5 5 3 4 6 9 0 8 3 0 2 6 4 2 5 2 2 3 0 8 2 5 3 3 4 4 6 8 5 0 3 5 2 6 1 9 3 1 1 8 8 1 7 1 0 1 0 0 0 3 1 3 7 8 3 8 7 5 2 8 8 6 5 8 7 5 3 3 2 0 8 3 8 1 4 2 0 6 1 7 1 7 7 6 6 9 1 4 7 3 0 3 5 9 8 2 5 3 4 9 0 4 2 8 7 5 5 4 6 8 7 3 1 1 5 9 5 6 2 8 6 3 8 8 2 3 5 3 7 8 7 5 9 3 7 5 1 9 5 7 7 8 1 8 5 7 7 8 0 5 3 2 1 7 1 2 2 6 8 0 6 6 1 3 0 0 1 9 2 7 8 7 6 6 1 1 1 9 5 9 0 9 2 1 6 4 2 0 1 9 8 9 3 8 0 9 5 2 5 7 2 0 1 0 6 5 4 8 5 8 6 3 2 7 8 8 6 5 9 3 6 1 5 3 3 8 1 8 2 7 9 6 8 2 3 0 3 0 1 9 5 2 0 3 5 3 0 1 8 5 2 9 6 8 9 9 5 7 7 3 6 2 2 5 9 9 4 1 3 8 9 1 2 4 9 7 2 1 7 7 5 2 8 3 4 7 9 1 3 1 5 1 5 5 7 4 8 5 7 2 4 2 4 5 4 1 5 0 6 9 5 9 5 0 8 2 9 5 3 3 1 1 6 8 6 1 7 2 7 8 5 5 8 8 9 0 7 5 0 9 8 3 8 1 7 5 4 6 3 7 4 6 4 9 3 9 3 1 9 2 5 5 0 6 0 4 0 0 9 2 7 7 0 1 6 7 1 1 3 9 0 0 9 8 4 8 8 2 4 0 1 2 8 5 8 3 6 1 6 0 3 5 6 3 7 0 7 6 6 0 1 0 4 7 1 0 1 8 1 9 4 2 9 5 5 5 9 6 1 9 8 9 4 6 7 6 7 8 3 7 4 4 9 4 4 8 2 5 5 3 7 9 7 7 4 7 2 6 8 4 7 1 0 4 0 4 7 5 3 4 6 4 6 2 0 8 0 4 6 6 8 4 2 5 9 0 6 9 4 9 1 2 9 3 3 1 3 6 7 7 0 2 8 9 8 9 1 5 2 1 0 4 7 5 2 1 6 2 0 5 6 9 6 6 0 2 4 0 5 8 0 3 8 1 5 0 1 9 3 5 1 1 2 5 3 3 8 2 4 3 0 0 3 5 5 8 7 6 4 0 2 4 7 4 9 6 4 7 3 2 6 3 9 1 4 1 9 9 2 7 2 6 0 4 2 6 9 9 2 2 7 9 6 7 8 2 3 5 4 7 8 1 6 3 6 0 0 9 3 4 1 7 2 1 6 4 1 2 1 9 9 2 4 5 8 6 3 1 5 0 3 0 2 8 6 1 8 2 9 7 4 5 5 5 7 0 6 7 4 9 8 3 8 5 0 5 4 9 4 5 8 8 5 8 6 9 2 6 9 9 5 6 9 0 9 2 7 2 1 0 7 9 7 5 0 9 3 0 2 9 5 5

Step-by-step explanation:

Answer:

a) -2+6

b) -2 + (-6)

Step-by-step explanation:

do like previous man

Answer:

-2+6

Step-by-step explanation:

False

The median car price is the one right in the middle of the price list. To find the median, we first need to rank the prices from lowest to highest.

The ordered price list looks like this:

$3,999; $4,500; $4,999; $5,000; The median price is $4,999, which is the median price. The average price is not $4,799.60.

Median is a measure of the central tendency of a dataset. The value that separates the top and bottom halves of the record. To find the median, we need to enter the values ​​in the dataset in order from lowest to highest. If the dataset has an odd number of values, the median is the mean.

For example, given the following five values: For 3, 5, 7, 9, 11, the median is the median, so the median is 7. If the dataset has an even number of values, the median is the average of the two middle values. For example, given the following 6 values:

For 3, 5, 7, 9, 11, 13, the median is (7 + 9)/2 = 8. In this case, there are 5 values, which are odd, so the median is the median. , which is $4,999.

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The answers are -0.5, 2.2, 3.8, and 9.0

We need to evaluate the expression 3.8 + 0 + y for the given values of y.

Let x = 3.8 + 0 + y

The values of y are -4.3, -1.6, 0, and 5.2

Let's substitute the value of y in the expression and calculate the values of x.

Refer to the attached image for the values of the expression corresponding to the values of y.

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Answer:

-0.5, 2.2, 3.8, and 9.0

Step-by-step explanation:

Hello!

0.85b-0.2b

0.65b

0.65b=0.65b

So these expressions are equivalent.

Hope it helps!

~Just a determined gal

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\(MysteriousNature\)

Check the picture below.

Make sure your calculator is in Degree mode.

Answer:

x = 49°, and y = 63°

Step-by-step explanation:

Starting with x, you can see that it is in a corner where two lines cross each other.  That means that x is equal to the angle on the other side of that intersection, which we are given.  x then, is equal to 49°

And with y, You'll notice that is formed with two lines, a horizontal one and and a diagonal one.  At he bottom of the shape you can see another horizontal one intersecting with the same diagonal one.  Notice also that the two lines use the ">" symbol, noting that the lines are parallel.  Because those lines are parallel, the angles between each of those and the diagonal one are the same.  This tells us that y is equal to 63°

The equation log(x²+6) = 1 + log(x-1) has two solutions: x = 2 and x = 8.

To solve the equation log(x²+6) = 1 + log(x-1), we can use C properties to simplify and solve for x.

First, we can combine the logarithms on the right side of the equation using the property log(a) + log(b) = log(ab). Applying this property, we have:

log(x²+6) = log(x-1) + log(10)

Since the logarithms are equal, we can remove them, and the equation becomes:

x² + 6 = (x-1) * 10

Expanding the right side of the equation, we have:

x² + 6 = 10x - 10

Rearranging the equation, we get:

x² - 10x + 16 = 0

Now, we can factor the quadratic equation:

(x - 2)(x - 8) = 0

Setting each factor equal to zero, we have two possible solutions:

x - 2 = 0, which gives x = 2

x - 8 = 0, which gives x = 8

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Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{Let\ the\ age\ of\ Sophia\ be\ }x\mathrm{\ and\ age\ of\ Mohal\ be\ }x+2.\\\mathrm{Given,}\\\mathrm{Product\ of\ their\ ages = 15}\\\mathrm{or,\ }x(x+2)=15\\\mathrm{or,\ }x^2+2x=15\\\mathrm{or,\ }x^2+2x-15=0\\\mathrm{or,\ }x^2+5x-3x-15=0\\\mathrm{or,\ }x(x+5)-3(x+5)=0\\\mathrm{or,\ }(x+5)(x-3)=0\\\mathrm{i.e.}\ x=-5\ \mathrm{or}\ 3.\)

\(x=-5\ \mathrm{is\ disgarded\ because\ age\ cannot\ be\ negative.}\\\mathrm{So\ the\ age\ of\ Shopia,\ }x=3\)

The  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

Given the equation;

8x - 9y = 15

First, we find the x-intercepts by simply substituting 0 for y and solve for x.

8x - 9y = 15

8x - 9(0) = 15

8x = 15

Divide both sides by 8

8x/8 = 15/8

x = 15/8

Next, we find the y-intercept by substituting 0 for x and solve for y.

8x - 9y = 15

8(0) - 9y = 15

- 9y = 15

Divide both sides by -9

- 9y/(-9) = 15/(-9)

y = -15/9

y = -5/3

We list the intercepts;

x-intercept: ( 15/8, 0 )

y-intercept: ( 0, -5/3 )

Therefore, the  x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.

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Answer:

2

Step-by-step explanation:

PEMDAS says to do the equations in parentheses first

(14-4) = 10

PEMDAS then says to do multiplication or division, whichever comes first in the equation, which is multiplication in this case

(10)2 = 20

20 ÷ 10 = 2

Answer:

Step-by-step explanation:

34

Answer:

34

Step-by-step explanation: