A rectangular prism made of wood has a length of 10 centimeters, a width of 8 centimeters, and a height of 12 centimeters. A rectangular hole
with a length of 2 centimeters and a width of 3 centimeters is cut through the prism as shown. What is the volume of the resulting figure?
3 cm
2 cm
12 cm
8 cm
10 cm

Answer:

x = 28.01t,

y = 10.26t - 4.9t^2 + 2

Step-by-step explanation:

If we are given that an object is thrown with an initial velocity of say, v1 m / s at a height of h meters, at an angle of theta ( θ ), these parametric equations would be in the following format -

x = ( 30 cos 20° )( time ),

y = - 4.9t^2 + ( 30 cos 20° )( time ) + 2

To determine " ( 30 cos 20° )( time ) " you would do the following calculations -

( x = 30 * 0.93... = ( About ) 28.01t

This represents our horizontal distance, respectively the vertical distance should be the following -

y = 30 * 0.34 - 4.9t^2,

( y = ( About ) 10.26t - 4.9t^2 + 2

In other words, our solution should be,

x = 28.01t,

y = 10.26t - 4.9t^2 + 2

These are are parametric equations

Answer:

D.  4

Step-by-step explanation:

If he leaves the science assignments for the next day, he will spend zero hours on science assignments.  This means that y is equal to 0.  Plug this into the given equation and solve for x.

2x + y = 8

2x + 0 = 8

2x = 8

x = 4

Gerald can complete 4 math assignments.

Answer:

  √17

Step-by-step explanation:

The Pythagorean theorem can be used for the purpose.

  hypotenuse² = base² +height²

  (√26)² = 3² +height²

  26 -9 = height²

  height = √17

The length of the other leg is √17.

Answer:

a) 77.3-73/10.7= 0.40187

b) 62.9-66.8/10.8= -0.36111

c) Kylie did relatively better

Step-by-step explanation:

Answer:

x = 0,00375 mm

Step-by-step explanation:

a) El factor de ampliación es 400/1   es decir el tamaño real se verá ampliado 400 veces mediante el uso del microscopio

b) De acuerdo a lo establecido en la respuesta a la pregunta referida en a (anterior) podemos establecer una regla de tres, según:

Si al microscopio el tamaño de la célula es 1,5 mm, cual será el tamaño verdadero ( que es reducido 400 en relación al que veo en el microscopio)

Es decir     1,5 mm      ⇒    400

                    x (mm)    ⇒       1 (tamaño real de la célula)

Entonces

x  =  1,5 /400

x = 0,00375 mm

Answer:

Following are the description of the given course code:

Step-by-step explanation:

The given course code is Pre-Algebra, which is just an introduction arithmetic course programs to train high school in the Algebra 1. This course aims to strengthen required problem solving skills, datatypes, equations, as well as graphing.

Answer:

A

Step-by-step explanation:

Answer:

A. The mean mileage per gallon is _____ 28.99__

A. The median mileage per gallon is _____27.905_____

B. The mode does not exist.

Step-by-step explanation:

Mean= Sum of values/ No of Values

            Mean =  24.2 + 22.2+  37.8+ 22.7 + 35.4 +31.61/ 6

           Mean = 173.91/6= 28.985 ≅ 28.99

The median is the middle value of an ordered data which divides the data into two equal halves. For an even data the median is  the average of n/2 and n+1/2 value where n is the number of values.

Rearranging the above data

22.2 , 22.7 , 24.2 , 31.61 , 35.4, 37.8

Third and fourth values are =24.2 + 31.61 = 55.81

Average of third and fourth values is = 55.81/2= 27.905

Mode is the values which is occurs repeatedly.

In this data there is no mode.

Answer:

1.5

Step-by-step explanation:

6 to the log base of 6 will be one (they essentially cancel each other out, log is the opposite of exponents) and we are left with 1.5.

Answer:

Question 2

Step-by-step explanation:

2) The time when she woke up was -  3° C

During nature walk, temperature got 3° C warmer than when she woke up.

So, temperature during nature walk = - 3 + 3 = 0° C

Answer:

Hey there!

15/k, when k=3

15/3=5

Answer:

5

Step-by-step explanation:

its a simple as 15/3 = 5

have fun

Answer:

(a)$67

(b)You are expected to win 56 Times

(c)You are expected to lose 44 Times

Step-by-step explanation:

The sample space for the event of rolling two dice is presented below

[tex](1,1), (2,1), (3,1), (4,1), (5,1), (6,1)\\(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)\\(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)\\(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)[/tex]

Total number of outcomes =36

The event of rolling a 5 or a 6 are:

[tex](5,1), (6,1)\\ (5,2), (6,2)\\( (5,3), (6,3)\\ (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)[/tex]

Number of outcomes =20

Therefore:

P(rolling a 5 or a 6)  [tex]=\dfrac{20}{36}[/tex]

The probability distribution of this event is given as follows.

[tex]\left|\begin{array}{c|c|c}$Amount Won(x)&-\$1&\$2\\&\\P(x)&\dfrac{16}{36}&\dfrac{20}{36}\end{array}\right|[/tex]

First, we determine the expected Value of this event.

Expected Value

[tex]=(-\$1\times \frac{16}{36})+ (\$2\times \frac{20}{36})\\=\$0.67[/tex]

Therefore, if the game is played 100 times,

Expected Profit =$0.67 X 100 =$67

If you play the game 100 times, you can expect to win $67.

(b)

Probability of Winning  [tex]=\dfrac{20}{36}[/tex]

If the game is played 100 times

Number of times expected to win

[tex]=\dfrac{20}{36} \times 100\\=56$ times[/tex]

Therefore, number of times expected to loose

= 100-56

=44 times

Answer:

1, 2.2, 5.5, 10.2.

Step-by-step explanation: these are simplified to the nearest tenth

Answer:

Step-by-step explanation:

A graphing calculator can perform logarithmic regression, as can a spreadsheet. The least-squares best fit log curve is about ...

  y ≈ 33.7·ln(x) -45.9

The value of x estimated to make y = 5.2 is about 4.6.

Answer:

B. g(x) = (x-2)^2 +1

Step-by-step explanation:

When you see this type of equation your get the variables H and K in a quadratic equation. In this case the (x-2)^2 +1  is your H. The (x-2)^2 +1 is your K.

For the H you always do the opposite so in this case instead of going to the left 2 times you go to the right 2 times (affects your x)

For the K you go up or down which in this case you go up one (affects your y)

And that's how you got your (2,1) as the center of the parabola

-Hope this helps :)

Answer:

55.11% probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 5, \sigma = 1, n = 9, s = \frac{1}{\sqrt{9}} = 0.3333[/tex]

Find the probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.

This is the pvalue of Z when X = 5.1 subtracted by the pvalue of Z when X = 4.5. So

X = 5.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{5.1 - 5}{0.3333}[/tex]

[tex]Z = 0.3[/tex]

[tex]Z = 0.3[/tex] has a pvalue of 0.6179

X = 4.5

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{4.5 - 5}{0.3333}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

0.6179 - 0.0668 = 0.5511

55.11% probability that the mean life a random sample of 9 such blenders falls between 4.5 and 5.1 years.

Answer:

[tex] \mu = 23.33, \sigma =6.13[/tex]

And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:

[tex] z=\frac{X -\mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]

We know that the proportion of area beyond the Z score associated with this age is  .05 so then the percentile would be: 95

Step-by-step explanation:

For this case we have the following parameters:

[tex] \mu = 23.33, \sigma =6.13[/tex]

And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:

[tex] z=\frac{X -\mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]

We know that the proportion of area beyond the Z score associated with this age is  .05 so then the percentile would be: 95

Answer:

Length = 29 m

Width = 29 m

Step-by-step explanation:

Let x and y be the length and width of the rectangle, respectively.

The area and perimeter are given by:

[tex]A=xy\\p=116=2x+2y\\y=58-x[/tex]

Rewriting the area as a function of x:

[tex]A(x) = x(58-x)\\A(x) = 58x-x^2[/tex]

The value of x for which the derivate of the area function is zero, is the length that maximizes the area:

[tex]A(x) = 58x-x^2\\\frac{dA}{dx}=0=58-2x\\ x=29\ m[/tex]

The value of y is:

[tex]y = 58-29\\y=29\ m[/tex]

Length = 29 m

Width = 29 m

Answer: probability =  0.506

Step-by-step explanation:

The data we have is:

Total people: 205 + 160 + 40 = 405

prefer cats: 205

prefer dogs: 160

neither: 40

The probability that a person chosen at random prefers cats is equal to the number of people that prefer cats divided the total number of people:

p = 205/405 = 0.506

in percent form, this is 50.6%

Answer:

x = y = 26 cm; z = 13 cm

Step-by-step explanation:

We can calculate the dimensions of the square base as

∛(2·8788) = 26 cm

the height of the box will be half of 26/2 which is 13 cm.

x = y = 26 cm; z = 13 cm

then the minimum area for the given volume can be calculated using what we call Lagrange multipliers, this makes it easier

area = xy +2(xz +yz)

But we were given the volume as 8788

Now we will make the partial derivatives of L to be in respect to the cordinates x, y, z, as well as λ to be equal to zero, then

L = xy +2(xz +yz) +λ(xyz -8788)

For x: we have

y+2z +λyz=0

For y we have

y: x +2z +λxz=0

For z we have 2x+2y +λxy=0............eqn(*)

For we have xyz -8788=0

If we simplify the partial derivative equation of y and x above then we have

λ = (y +2z)/(yz).

= 1/z +2/y............eqn(1)

λ = (x +2z)/(xz)

= 1/z +2/x.............eqn(2)

Set eqn(1 and 2) to equate we have

1/z +2/y = 1/z +2/x

x = y

From eqn(*) we can get z

λ = (2x +2y)/(xy) = 2/y +2/x

If we simplify we have

1/z +2y = 2/x +2/y

Then z = x/2

26/2 =13

Therefore,

x = y = 2z = ∛(2·8788)

X= 26

y = 26 cm

z = 13 cm

Answer:

a) Mean = 0.125 inch

Standard deviation = 0.13975 inch

b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25) = 0.18673

c) Probability that the door does not fit in the casing = P(X < 0) = 0.18673

Step-by-step explanation:

Let the distribution of the width of the casing be X₁ (μ₁, σ₁²)

Let the distribution of the width of the door be X₂ (μ₂, σ₂²)

The distribution of the difference between the width of the casing and the width of the door = X = X₁ - X₂

when two independent normal distributions are combined in any manner, the resulting distribution is also a normal distribution with

Mean = Σλᵢμᵢ

λᵢ = coefficient of each disteibution in the manner that they are combined

μᵢ = Mean of each distribution

Combined variance = σ² = Σλᵢ²σᵢ²

λ₁ = 1, λ₂ = -1

μ₁ = 24 inches

μ₂ = 23 7/8 inches = 23.875 inches

σ₁² = (1/8)² = (1/64) = 0.015625

σ₂ ² = (1/16)² = (1/256) = 0.00390625

Combined mean = μ = 24 - 23.875 = 0.125 inch

Combined variance = σ² = (1² × 0.015625) + [(-1)² × 0.00390625] = 0.01953125

Standard deviation = √(Variance) = √(0.01953125) = 0.1397542486 = 0.13975 inch

b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25)

This is a normal distribution problem

Mean = μ = 0.125 inch

Standard deviation = σ = 0.13975 inch

We first normalize/standardize 0.25 inch

The standardized score of any value is that value minus the mean divided by the standard deviation.

z = (x - μ)/σ = (0.25 - 0.125)/0.13975 = 0.89

P(X > 0.25) = P(z > 0.89)

Checking the tables

P(x > 0.25) = P(z > 0.89) = 1 - P(z ≤ 0.89) = 1 - 0.81327 = 0.18673

c) Probability that the door does not fit in the casing

If X₂ > X₁, X < 0

P(X < 0)

We first normalize/standardize 0 inch

z = (x - μ)/σ = (0 - 0.125)/0.13975 = -0.89

P(X < 0) = P(z < -0.89)

Checking the tables

P(X < 0) = P(z < -0.89) = 0.18673

Hope this Helps!!!

Answer:

One solution

Step-by-step explanation:

99% of the time, linear equations (equations that have the first degree) have only one solution. However, it's always good to check.

6 - 3x = 12 - 6x

6 = 12 - 3x

-3x = -6

x = 2

As you can see, only one solution. Hope this helps!

Answer:

The frequency table is shown below.

Step-by-step explanation:

The data set arranged ascending order is:

S = {33 , 34 , 39 , 48 , 49 , 50 , 53 , 54 , 55 , 56 , 58 , 58,  60 , 63 , 64 , 65 , 70 , 71 , 74 , 84}

It is asked to use the minimum value from the data set as the lower class limit for the first row.

So, the lower class limit for the first class interval is 33.

To determine the class width compute the range as follows:

[tex]\text{Range}=\text{Maximum}-\text{Minimum}[/tex]

          [tex]=84-33\\=51[/tex]

The number of classes requires is 5.

The class width is:

[tex]\text{Class width}=\frac{Range}{5}=\frac{51}{2}=10.2\approx 10[/tex]

So, the class width is 10.

The classes are:

33 - 42

43 - 52

53 - 62

63 - 72

73 - 82

83 - 92

Compute the frequencies of each class as follows:

Class Interval                  Values                        Frequency

   33 - 42                      33 , 34 , 39                             3

   43 - 52                      48 , 49 , 50                            3

   53 - 62          53 , 54 , 55 , 56 , 58 , 58,  60              7

   63 - 72                 63 , 64 , 65 , 70 , 71                      5

   73 - 82                              74                                  1

   83 - 92                             84                                   1

   TOTAL                                                                   20

Compute the relative frequencies as follows:

Class Interval          Frequency        Relative Frequency

   33 - 42                        3                   [tex]\frac{3}{20}\times 100\%=15\%[/tex]

   43 - 52                        3                   [tex]\frac{3}{20}\times 100\%=15\%[/tex]

   53 - 62                        7                   [tex]\frac{7}{20}\times 100\%=35\%[/tex]

   63 - 72                        5                   [tex]\frac{5}{20}\times 100\%=25\%[/tex]

   73 - 82                         1                   [tex]\frac{1}{20}\times 100\%=5\%[/tex]

   83 - 92                         1                   [tex]\frac{1}{20}\times 100\%=5\%[/tex]

   TOTAL                        20                          100%

Answer:

The answer is "Option A"

Step-by-step explanation:

The valid linear programming language equation can be defined as follows:

Equation:

[tex]\Rightarrow \ Min\ 4x + 3y + (\frac{2}{3})z[/tex]

The description of a linear equation can be defined as follows:

It is an algebraic expression whereby each term contains a single exponent, and a single direction consists in the linear interpolation of the equation.

Formula:

[tex]\to \boxed{y= mx+c}[/tex]

Answer:

Option C.

Step-by-step explanation:

This is a function because all of the numbers have a partner, and none of them have more than one.

                                    Example of Not a Function

Function                                Not a Function

-4 to 5                                       -4 to 5                             <

9 to 7                                       -4 to 3                              <

13 to 3                                       13 to 3                              ^

-7 to 5                                        9 to 7                               ^

                                                 -7 to 5                               ^

                                           Not a Function because of this

Answer:

Correct!

Step-by-step explanation:

-5(x+8)=-25

x+8=5

x=-3

Answer:

here, -5(x+8)=-25

or, -5x +(-40)= -25

or, -5x=-25+40

or, x= 15/-5

therefore the value of x is -3....ans..

hope u understood..

Answer:

Monthly: $4,821

Weekly: $1112.54

Step-by-step explanation:

Monthly

A monthly salary can be found by dividing the yearly salary by the number of months.

salary / months

His salary is $57,852 and there are 12 months in a year.

$57,852/ 12 months

Divide

$4,821 / month

Jeremy makes $4,821 per month.

Weekly

To find the weekly salary, divide the yearly salary by the number of weeks.

salary / weeks

He makes $57,852 each year and there are 52 weeks in one year.

$57,852 / 52 weeks

Divide

$1112.53846 / week

Round to the nearest cent. The 8 in the thousandth place tells use to round the 3 up to a 4 in the hundredth place.

$1112.54 / week

Jeremy makes $1112.54 per week

Answer:

a) P(x=3)=0.089

b) P(x≥3)=0.938

c) 1.5 arrivals

Step-by-step explanation:

Let t be the time (in hours), then random variable X is the number of people arriving for treatment at an emergency room.

The variable X is modeled by a Poisson process with a rate parameter of λ=6.

The probability of exactly k arrivals in a particular hour can be written as:

[tex]P(x=k)=\lambda^{k} \cdot e^{-\lambda}/k!\\\\P(x=k)=6^k\cdot e^{-6}/k![/tex]

a) The probability that exactly 3 arrivals occur during a particular hour is:

[tex]P(x=3)=6^{3} \cdot e^{-6}/3!=216*0.0025/6=0.089\\\\[/tex]

b) The probability that at least 3 people arrive during a particular hour is:

[tex]P(x\geq3)=1-[P(x=0)+P(x=1)+P(x=2)]\\\\\\P(0)=6^{0} \cdot e^{-6}/0!=1*0.0025/1=0.002\\\\P(1)=6^{1} \cdot e^{-6}/1!=6*0.0025/1=0.015\\\\P(2)=6^{2} \cdot e^{-6}/2!=36*0.0025/2=0.045\\\\\\P(x\geq3)=1-[0.002+0.015+0.045]=1-0.062=0.938[/tex]

c) In this case, t=0.25, so we recalculate the parameter as:

[tex]\lambda =r\cdot t=6\;h^{-1}\cdot 0.25 h=1.5[/tex]

The expected value for a Poisson distribution is equal to its parameter λ, so in this case we expect 1.5 arrivals in a period of 15 minutes.

[tex]E(x)=\lambda=1.5[/tex]

Circumference = πd

~substitute → (π)(6 cm)

~simplify → 6π cm.

So the circumference of the circle shown here is 6π cm.

Answer:

18.85 cm

Step-by-step explanation:

The circumference of a circle has a formula.

Circumference = π × diameter

The diameter is 6 centimeters.

Circumference = π × 6

Circumference ≈ 18.85

The circumference of the circle is 18.85 centimeters.