27. Stuart wants to play a trick on his friend by hiding his pencil in the box of tissues shown below. If
his friend's pencil is 9 inches in length, will it fit diagonally in the box of tissues? Explain.

Given :

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%.

Its current value is $2,000.

To Find :

Age of car.

Solution :

Price of car after 1 year :

\(P_1=P_o(1-0.35)\)

Price of car after 2 year :

\(P_2=P_1(1-0.35)\\\\P_2=[P_o(1-0.35)](1-0.35)\\\\P_2=P_o(1-0.35)^2\)

So, price of car after n years.

\(P_n=P_o(1-0.35)^n\)

\(2000=16000(1-0.35)^n\\\\0.65^n=0.125\\\\n\times log(0.56)=log(0.125)\\\\n=\dfrac{log(0.125)}{log(0.56)}\\\\n=3.58\)

Therefore, age of car in nearest whole number is 4 years.

Hence, this is the required solution.

\( = - 8 + (- 8(6n)) (- 8(1)) \\ = - 8 - 48n - 8 \\ = - 16 - 48n\)

Answer:

Step-by-step explanation:

The volume is the product of three dimensions

Given:

w = x + 1, l = x + 2 and V(x) = x³ + x² - 4x - 4

1) Let's find the height:

2) x = 4 m

Volume is:

3) x = 4 m

Dimensions are:

Full surface area is:

Answer:

njj

Step-by-step explanation:

Answer:

19 = 7z - 2z

19 = 5z

z = 19/5

Hope this helps!

Answer:

z = 3.8

Step-by-step explanation:

19 = 7z - 2z

19 = 5z

19/5 = z

3.8 = z

The complete factorization of the polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

A polynomial is an expression consisting of coefficients and variables forming an equation.

Given the polynomial:

x³ + 2x² -x - 2

Factorizing:

= (x + 2)(x² - 1)

= (x + 2)(x + 1)(x - 1)

The polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

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Answer:

A

Step-by-step explanation:

Since the shaded region on the right is greater than or equal to 3, and the shaded region on the left is less than -4 (since numbers decrease as the arrow moves towards the left on the number line).

Answer:

-1/2

Step-by-step explanation:

\(-\frac{1}{6}\) ÷ \(\frac{2}{6}= -\frac{1}{6}\) x \(\frac{6}{2} \\\) = \(\frac{-6}{-12} =- \frac{1}{2}\)

Answer:

2^12=2*2*2*2*2*2*2*2*2*2*2*2=4*4*4*4*4*4=16*16*16=256*16=4096

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

7x-11=-19+3x

7x-3x=-19+11

4x=-8

4x/4=-8/4

x=-2

Answer:

b=− 3/4 =−1.333

b= 2/3=1.500

explanation

middle term, which is   -1 .  

     -72    +    1    =    -71

     -36    +    2    =    -34

     -24    +    3    =    -21

     -18    +    4    =    -14

     -12    +    6    =    -6

     -9    +    8    =    -1    That's it

Two real solutions:

b =(1+√289)/12=(1+17)/12= 1.500

or:

b =(1-√289)/12=(1-17)/12= -1.333

Step-by-step explanation:

T : S

5 : 95

1 : 19

Tu : S

6. : 48

1. : 8

10 : 80

There are 19 students per teacher.

There are 8 students per teacher.

The school will need 10 tutors if there is 80 students.

Answer:

1 1/2 miles per hour

Step-by-step explanation:

3/4 + 3/4 = 6/4 = 1 2/4 = 1 1/2 miles per hour

Answer:

I think it 4.5

Step-by-step explanation:

The required answer to the subtraction problem 83,456 - 728.88 is, 82,727.12

Subtraction is mathematical terminology that helps and elaborates the decrease in the original value by some value.

Here,
To perform the subtraction, you line up the decimal points and subtract the digits in each place value starting from the right. In this case, you subtract 8 from 6, which requires borrowing 1 from the digit to the left, giving you 16 - 8 = 8 in the one's place. You then subtract 2 from 5, giving you 3 in the tenth place. Continuing this process, you get the result of 82,727.12.

Thus, the answer to the subtraction problem 83,456 - 728.88 is, 82,727.12

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Therefore , the required probability is therefore 1/151200, which is the answer to the probability problem.

The probability that a happening will happen or that the proposition is true is determined by a field of mathematics known as probability theory. A probability is a number between 0 and 1, where 1 represents certainty and 0 roughly represents the likelihood that an event will occur. A probability is a numerical expression of a certain event's likelihood or chance of happening. The percentages 0% - 100% and 0 to 1 can also be used to express probabilities. the percentage of times in an ideal collection of equally likely alternatives that an event occurs compared to all possible outcomes.

Here,

The six numbers can only be chosen in one way if the order chosen must match my phone number.

In 10P6 methods, six random digits from a possible total of ten can be chosen.

So the necessary probability is equal to 1/P. (10,6).

Alternative: Probability = 1/151200

The required probability is therefore 1/151200, which is the answer to the probability problem.

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Answer:

Step-by-step explanation:

To calculate the probability of obtaining x = 116 or fewer individuals with the characteristic, we need to use the normal distribution. We can use the sample proportion p-hat and the population proportion p to find the mean and standard deviation of the sampling distribution of p-hat.

We are given that n = 200 and p-hat = 0.58. The population proportion p is not given, so we will assume it to be 0.5 (which is a common assumption when the population proportion is unknown).

The mean of the sampling distribution of p-hat is:

μp-hat = p = 0.5

The standard deviation of the sampling distribution of p-hat is:

σp-hat = sqrt[p(1-p)/n] = sqrt[(0.5)(0.5)/200] = 0.0354

Now we can standardize the value of x using the formula:

z = (x - μp-hat) / σp-hat

For x = 116, we have:

z = (116 - 100*0.58) / 0.0354 = 1.69

Using a standard normal distribution table or calculator, we can find the probability of obtaining z ≤ 1.69 to be 0.9535. Therefore, the probability of obtaining x = 116 or fewer individuals with the characteristic is approximately 0.9535 (rounded to four decimal places).

The difference between the three variances, Var(x), Var(y), and Var(x + y), can be determined analytically in the context of the bus ridership example.

In the given context, let's consider two variables: x represents the ridership on line l2, and y represents the ridership on line l1. The statement mentions that intuitively, l1 and l2 are not independent, meaning they are related in some way.

To determine the difference between the variances, we need to calculate the variances of x, y, and the sum of x and y, which is x + y.

Var(x): This represents the variance of the ridership on line l2. It quantifies the spread or variability in the data points of x. To calculate Var(x) analytically, you can use the formula: Var(x) = E[(x - μx)^2], where E represents the expectation (mean) operator and μx represents the mean of x.

Var(y): This represents the variance of the ridership on line l1. Similar to Var(x), it quantifies the spread or variability in the data points of y. Var(y) can be calculated using the same formula as Var(x): Var(y) = E[(y - μy)^2], where μy represents the mean of y.

Var(x + y): This represents the variance of the sum of ridership on both lines l1 and l2. It measures the combined variability of the two variables. To calculate Var(x + y), you can use the formula: Var(x + y) = E[(x + y - μ(x + y))^2], where μ(x + y) represents the mean of the sum of x and y.

By analytically calculating the three variances, Var(x), Var(y), and Var(x + y), you can compare them to understand their differences and the relationship between the ridership on line l1 and line l2.

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Answer:

Hello,

Answer m=-1, n=-6,l=2

Step-by-step explanation:

\(A*U=B\\\begin{bmatrix}3&-1&0\\0&1&3\\0&0&2\end{bmatrix}*\begin{bmatrix}m\\n\\l\end{bmatrix}=\begin{bmatrix}3\\0\\4 \end{bmatrix}\\\\\\A^{-1}=\begin{bmatrix}\dfrac{1}{3}&\dfrac{1}{3}&\dfrac{-1}{2}\\\\0&1&\dfrac{-3}{2} \\\\0&0&\frac{1}{2}\end{bmatrix}\\\\\\A^{-1}*A*U=A^{-1}*B\\\)

\(U=\begin{bmatrix}\dfrac{1}{3}&\dfrac{1}{3}&\dfrac{-1}{2}\\\\0&1&\dfrac{-3}{2}\\\\0&0&\dfrac{1}{2}\end{bmatrix}*\begin{bmatrix}3\\0\\4\\\end{bmatrix}=\begin{bmatrix}-1\\-6\\2\end{bmatrix}\\\\\)

Answer:

slope = 3/4

Step-by-step explanation:

rise over run

Using the concepts of probability, we got that  0.063 is the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time

We know very well that probability is defined as the fraction of number of favorable outcomes to the total number of outcomes.

Here, we are rolling a 6-faced dice.

Getting 3 on the top face of dice is same as the any number getting from 1 to 6 on the top face of the dice.

So, every number has equal probability to come on the top face,  therefore the probability of getting 3 on the top face of dice is (1/6)

Now, similarly total number of marbles in the bag=6 blue +3 black+8 orange marble=17 marbles.

Now, picking one marble from 17 marble is can be done in \(^1^7C_1\)  ways, similarly  choosing 1 blue marble from 6 marble can be done in \(^6C_1\) ways.

So, probability of picking 1 blue marble randomly=6/17

Now, the probability of picking 1 blue marble from 17 marbles along with rolling dice probability is given by =(6/17)×(1/6)=(1/17)=0.063

Hence, the probability of picking a blue marble randomly out of a bag of 6 blue marbles, 3 black marbles, and 8 orange marbles while rolling a 3 on a 6-sided dice at the same time is 0.063

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Answer:

poop

Step-by-step explanation:

trust me its b

Answer:

The one in the top right

Step-by-step explanation:

All of the points seem to match the line best, each of the other graphs vary more.

We have that

So the answer is cosA = 0.3846 = 5/13

Answer:

13.2

Step-by-step explanation:

We just divide 79/6 which is equal to 13.1666667 which we can round to 13.2

Answer:

13.166667 best describes the fraction 79/6

Answer:

-10

Step-by-step explanation:

y= kx

or, k= y/x

or, k = 5/4

k = 1.25

y= kx = 1.25 × (-8) = -10