A wire 18cm long is cut into 2 pieces. the longer piece is 2 cm longer than the shorter piece. Find the lenght of the shorter piece

Answer:

Use the Rational Zero Theorem to list all possible rational zeros of the function. Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial. Repeat step two using the quotient found with synthetic division.

Step-by-step explanation:

One of the methods to finding zeros and factors of higher degree polynomial functions is using the Remainder theorem.

The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.

The methods to finding zeros and factors of higher degree polynomial functions

Hence, one of the methods to finding zeros and factors of higher degree polynomial functions is using the Remainder theorem.

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Answer:

$18,750

Step-by-step explanation:

Take the earnings per week times the number of weeks

50 * 375

18,750

Answer:

$18,750

Step-by-step explanation:

If we want to find the nurse's aide's earnings for the year, we have to multiply her weekly salary by the number of weeks she worked.

weekly salary * number of weeks

She earns $375 per week and she worked for 50 weeks.

$375*50 weeks

375*50

Multiply the 2 numbers

18,750

Her total earnings for the year are $18,750

Answer:

Area of rectangle = [tex]196\,m^2[/tex]

Length of rectangle = 14 m

Width of rectangle = 14 m

Step-by-step explanation:

Given:

Perimeter of rectangle is 56 m

To find: the maximized area of a rectangle and the length and width

Solution:

A function [tex]y=f(x)[/tex] has a point of maxima at [tex]x=x_0[/tex] if [tex]f''(x_0)<0[/tex]

Let x, y denotes length and width of the rectangle.

Perimeter of rectangle = 2( length + width )

[tex]=2(x+y)[/tex]

Also, perimeter of rectangle is equal to 56 m.

So,

[tex]56=2(x+y)\\x+y=28\\y=28-x[/tex]

Let A denotes area of rectangle.

A = length × width

[tex]A=xy\\=x(28-x)\\=28x-x^2[/tex]

Differentiate with respect to x

[tex]\frac{dA}{dx}=28-2x[/tex]

Put [tex]\frac{dA}{dx}=0[/tex]

[tex]28-2x=0\\2x=28\\x=14[/tex]

Also,

[tex]\frac{d^2A}{dx^2}=-2<0[/tex]

At x = 14, [tex]\frac{d^2A}{dx^2}=-2<0[/tex]

So, x = 14 is a point of maxima

So,

[tex]y=28-x=28-14=14[/tex]

Area of rectangle:

[tex]A=xy=14(14)=196\,m^2[/tex]

Length of rectangle = 14 m

Width of rectangle = 14 m

Answer:

1680 is the answer.

Step-by-step explanation:

Here, we have 11 letters in the word MISSISSIPPI.

Repetition of letters:

M - 1 time

I - 4 times

S - 4 times

P - 2 times

As per question statement, we need a substring MISS in the resultant strings.

So, we need to treat MISS as one unit so that MISS always comes together in all the strings.

The resultant strings will look like:

xxxxMISSxxx

xxMISSxxxxx

and so on.

After we treat MISS as one unit, total letters = 8

Repetition of letters:

MISS - 1 time

I - 3 times

S - 2 times

P - 2 times

The formula for combination of letters with total of n letters:

[tex]\dfrac{n!}{p!q!r!}[/tex]

where p, q and r are the number of times other letters are getting repeated.

p = 3

q = 2

r = 2

So, required number of strings that contain MISS as substring:

[tex]\dfrac{8!}{3!2!2!}\\\Rightarrow \dfrac{40320}{6\times 2 \times 2}\\\Rightarrow 1680[/tex]

So, 1680 is the answer.

The solution to the system of equations is (-1, 2, 4), which is equal to choice (c) (-1, 2, 4).

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

To solve the system of equations, we can represent it in an augmented matrix and use row operations to find its reduced row-echelon form.

The augmented matrix for the system is:

[ 2  1  4 | 16 ]

[ 5 -2  2 | -1 ]

[ 1  2 -3 | -9 ]

We want to get the matrix in reduced row-echelon form.

We can start by using row operations to get a 1 in the upper left corner:

R(1/2) -> R1:

[ 1 1/2  2 |  8 ]

[ 5 -2  2 | -1 ]

[ 1  2 -3 | -9 ]

Now we want to get zeros in the first column below the pivot element (1). We can do this by subtracting 5 times the first row from the second row, and subtracting the first row from the third row:

-5R1 + R2 -> R2:

-R1 + R3 -> R3:

[ 1  1/2   2  |  8 ]

[ 0 -9/2  -8  | -41 ]

[ 0  3/2 -5  | -17 ]

R2 + R3 -> R3:

[ 1  1/2   2  |  8 ]

[ 0 -9/2  -8  | -41 ]

[ 0  -3    -13 | -58 ]

We can continue with row operations to get a 1 in the second row, second column:

(-2/9)R2 -> R2:

[ 1  1/2   2    |  8 ]

[ 0   1   16/9  |  82/9 ]

[ 0  -3    -13 | -58 ]

3R2 + R3 -> R3:

[ 1  1/2   2    |  8 ]

[ 0   1   16/9  |  82/9 ]

[ 0  0    -23/3 | -92/3 ]

Finally, we can get a 1 in the third row, third column:

(-3/23)R3 -> R3:

[ 1  1/2   2    |  8 ]

[ 0   1   16/9  |  82/9 ]

[ 0  0    1 | 4 ]

Now the matrix is in reduced row-echelon form.

We can read the solution directly from the last column:

x = 8 - (1 + 8) = -1

y = 82/9 - (16/9)(4) = 2

z = 4

Therefore, the solution to the system of equations is (-1, 2, 4).

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Answer:

The population density is 618.93 per square mile.

Step-by-step explanation:

It is given that,

No. of people, N = 70,000

The radius of a city's town hall, r = 6 miles

We need to find the population density. It can be calculated by the formula i.e. number of people divided by area of land such that,

[tex]P=\dfrac{N}{A}\\\\P=\dfrac{N}{\pi r^2}\\\\P=\dfrac{70000}{\pi (6)^2}\\\\P=618.93\ \text{per square mile}[/tex]

So, the population density is 618.93 per square mile.

Answer:

The probability of observing between 9 and 15 (inclusive) swarms is 0.6639.

Step-by-step explanation:

The random variable X can be defined as the number of swarms of honeybees seen each spring.

The average value of the random variable X is, λ = 13.

A random variable representing the occurrence of events in a fixed interval of time is known as Poisson random variables.

For example, the number of customers visiting the bank in an hour or the number of typographical error is a book every 10 pages.

So, the random variable X follows a Poisson distribution with parameter λ = 13.

The probability mass function of X is as follows:

[tex]P(X=x)=\frac{e^{-\lambda}\ \lambda^{x}}{x!}; x=0,1,2,3...[/tex]

Compute the  the probability of observing between 9 and 15 (inclusive) swarms as follows:

P (9 ≤ X ≤ 15) = P (X = 9) + P (X = 10) + P (X = 11) + ... + P (X = 15)

                      [tex]=\sum\limits^{15}_{x=9}{\frac{e^{-\lambda}\ \lambda^{x}}{x!}}\\\\=0.06605+0.08587+0.10148+0.10994\\+0.10994+0.10209+0.08848\\\\=0.66385\\\\\approx 0.6639[/tex]

Thus, the probability of observing between 9 and 15 (inclusive) swarms is 0.6639.

Answer:

Step-by-step explanation:

Hello!

Distribution in attachment.

The variable of interest is:

X: Number of successes after flipping a coin 5 times.

If you check the binomial criteria:

The number of trials is fixed: n=5

There are only two possible outcomes "success" or "failure"

Each flip of the coin is independent of the others.

The probability of success in the same from one trial to another, in this case, if we consider the coin to be balanced, the probability of success is p=0.5

The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis)

Statements:

1) The bar for any number k represents the probability of getting k successes in 5 flips. Correct. The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis). Each bar represents the probability of success for each possible value.

2) The number of successes, k, can range from 0 (no success) to 5 (all successes). Correct. The variable count the number of successes after flipping a coin 5 times. It can happen that you flip it and all the flips turn to be failures (X=0), that you flip it 5 times and only one turns out to be a success and the other 4 are failures (X=1), and so on until you flip it 5 times and all flips are successes (X=5)

3) Each coin flip is independent; it is not affected by any other coin flip. Correct, if not, this variable wouldn't have a binomial distribution as specified in the text.

4) For 5 coin flips, P(2 heads) = P(3 heads). Correct

Looking at the histogram, the bars for "2 successes" and "3 successes" have the same height, a little above 0.3, this means that both values have the same probability of occurrence.

5) The sum of the probabilities shown in the binomial distribution is p.

Incorrect.

For the binomial distribution "p" represents the probability of success for each trial, in this case, flipping the coin once.

For this distribution, as well as for other probability distribution, the sum of all probabilities is always 1, if not, then it is not a probability distribution.

I hope this helps!

Answer:

Lets make this easier for you guys. The correct answers are 1 through 4.

The bar for any number k represents the probability of getting k successes in 5 flips.

The number of successes, k, can range from 0 (no success) to 5 (all successes).

Each coin flip is independent; it is not affected by any other coin flip.

For 5 coin flips, P(2 heads) = P(3 heads

Step-by-step explanation:

Correct on edge :))

Answer:

Yes- these answers are equivalent.

Step-by-step explanation:

In the expression 7(2d+3), the 7 is outside the parentheses, meaning everything inside the parentheses is multiplied by 7.

2d X 7 = 14 d

3 X 7 = 21

7(2d+3) = 14d + 21

Yes, the expressions are equivalent.

By combining numbers, variables, functions in mathematics we get an expression.

Example : 4p+2, 3x-4y etc

Given expressions are 14d+21 and 7(2d+3)

Here, simplifying the expression 7(2d+3) we get,

7(2d+3) = (7×2d)+(7×3) = 14d+21

Therefore, the given two expressions are equal to each other, i.e same.

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Answer: 35

Step-by-step explanation:

The number of combinations of r things selected out of n things is given by

[tex]^nC_r= \dfrac{n!}{r!(n-r)!}[/tex]

Given , the total number of types of toppings available = 7

The number of toppings needed to be selected = 4

Then, the number of ways to do this would be

[tex]^7C_4=\dfrac{7!}{4!(7-4)!}\\\\=\dfrac{7\times6\times5\times4!}{4!3!}\\\\=\dfrac{7\times5}{1}=35[/tex]

Hence, the number of combinations of 5 scoops of ice cream and 4 toppings are possible = 35.

Answer:

A)  [tex]B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}[/tex]

B) [tex]M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right][/tex]

Step-by-step explanation:

Let [tex]A = \left[\begin{array}{ccc}a&b\\c&d \end{array}\right][/tex] where a, b, c and d are real numbers

Since A is said to be a half magic square matrix, a = d, b = c.

The matrix A therefore becomes  [tex]A = \left[\begin{array}{ccc}a&b\\b&a \end{array}\right][/tex] where [tex]a,b \epsilon R[/tex]

A can therefore be manipulated as:

[tex]A = a \left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]

The matrices [tex]\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right][/tex] and [tex]\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex] are apparently linearly independent and therefore form a basis B for V

[tex]B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}[/tex]

B) Find the coordinate vector [M]_B of M [-2 -7, -7 -2]

 [tex]M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right][/tex]

[tex]M[/tex] can be written in the form [tex]M = a\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]

[tex]M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right] = -2\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] -7\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]

The coordinate vector is therefore, [tex]M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right][/tex]

Answer:

26 feet

Step-by-step explanation:

Let the length of the required wire =l

The height of the tree =24 cm

We want the tree to fall to the ground 10 feet away from the base.

Ths problem forms a right triangle which I have drawn and attached below.

To determine the length of the wire l required, we use Pythagoras theorem to solve for the hypotenuse of the right triangle.

[tex]B$y Pythagoras theorem: Hypotenuse^2=Opposite^2+Adjacent^2\\$Therefore:\\l^2=24^2+10^2\\l^2=676\\$Take the square root of both sides\\l=\sqrt{676}\\ l=26$ feet[/tex]

Thw wire must be 26 feet long to reach the ground.

Answer:−2x=−8

4sin2(x)−1=0

2x+3=3

Step-by-step explanation:

Answer:

1600

please see the attached picture for full solution

Hope it helps...

Answer:

Solve   -x2+11xandg+6x-6  = 0

Step-by-step explanation:

Answer:

rectangular prism

Step-by-step explanation:

A rectangular prism has 6 sides that are rectangles.

Answer:

Chemical rocks form when minerals dissolve in a solution and crystalize.

Answer:

Chemical rocks don't form from solidification from a melt

Step-by-step explanation:

Answer:

The number of pencils in the box A is 70

The number of pencils in the box B is 42

Step-by-step explanation:

The number of pencils in the box A is a

The number of pencils in the box B is b

We have:

a + b = 112

a - (1/5)a = b + (1/5)a

or

a + b = 112

a - (2/5)a = b

or

a + b = 112

(3/5)a = b

or

a + (3/5)a = 112

or

(8/5)a = 112

or

a = 112*(5/8)

or

a = 70

=> b = 112 - 70 = 42

Hope this helps!

Answer:

A= (0,0) and B = (6,3)

We can find the length AB with the following formula:

[tex] d = \sqrt{(x_B -x_A)^2 +(y_B -y_A)^2}[/tex]

And replacing we got:

[tex] d = \sqrt{(6-0)^2 +(3-0)^2} = \sqrt{45}= 3\sqrt{5}[/tex]

So then the length AB would be [tex] 3\sqrt{5}[/tex]

Step-by-step explanation:

For this case we have the following two points:

A= (0,0) and B = (6,3)

We can find the length AB with the following formula:

[tex] d = \sqrt{(x_B -x_A)^2 +(y_B -y_A)^2}[/tex]

And replacing we got:

[tex] d = \sqrt{(6-0)^2 +(3-0)^2} = \sqrt{45}= 3\sqrt{5}[/tex]

So then the length AB would be [tex] 3\sqrt{5}[/tex]

Answer:6.71

Step-by-step explanation: awesomeness

Answer:

B) Mia Hamm helped her soccer team at the University of North Carolina at Chapel Hill win four NCAA titels.

Step-by-step explanation:

The first option is an opinion, not a fact.

Answer:

The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 6

Standard deviation = 0.5

Middle 95% of weights:

By the Empirical Rule, within 2 standard deviations of the mean.

6 - 2*0.5 = 5

6 + 2*0.5 = 7

The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

The interval representing the weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

The Empirical Rule states that for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

The empirical rule says that, in a standard data set, virtually every piece of data will fall within three standard deviations of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 6

Standard deviation = 0.5

Middle 95% of weights

By the Empirical Rule, within 2 standard deviations of the mean.

6 - 2*0.5 = 5

6 + 2*0.5 = 7

The interval representing the weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

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Answer: They are not parallel, they are coincident

Step-by-step explanation:

If two lines have the same slope but a different y-intercept, the lines are parallel. If two lines have the same slope and the same y-intercept, the lines are coincident.

We can rewrite 5x−y=−5 adding -5x to both sides and multiplying by -1:

5x - y =-5

5x - y -5x = -5 - 5x (adding -5x to both sides)

-y = -5 - 5x

Multiplying by -1

y = 5x + 5

Both equations look the same so they are coincident. They have the same intercept y=5 and the same slope m=5.

Answer:

47.50

Step-by-step explanation:

According to the question above Salid bought 30 feet of window at a hardware trim store

The trim cost of each window is $1.75 per foot with an inclusion of sales tax added to this amount

= $1.75×30

= 52.5

Since Salid paid for the trim service with a cash of $100.00, his change is calculated as follows

=$100-52.5

= $47.50

Hence Salid change is $47.50

Answer:

Step-by-step explanation:

Midline is the horizontal line that passes exactly in the middle between the graph's maximum and minimum points.

Amplitude is the vertical distance between the midline and one of the extremum points.

Period is the distance between two consecutive maximum points, or two consecutive minimum points (these distances must be equal).

To find the formula for [tex]g(x)[/tex]. First, let's use the given information to determine the function's amplitude, midline, and period.

The midline of a sinusoidal function passes exactly in the middle of its extreme values. So we can find the midline by finding the average of the maximum and minimum values.

The midline passes exactly between the minimum value 1, and the maximum value 11, so the midline equation is

[tex]midline=y=\frac{11+1}{2} =6[/tex]

The extremum points are 5 units above or below the midline, so the amplitude is 5.

The maximum point is 0.5 units to the right of the minimum point, so the period is [tex]2\cdot 0.5 =1[/tex]. We multiply by 2 because the distance between consecutive minimum and maximum points is always [tex]\frac{1}{2}[/tex] of the period.

The general sinusoidal equation [tex]y=a\cos(bx)+d[/tex] is the result of horizontal and vertical shifts, reflections, and stretches of the parent equation [tex]y=\cos(x)[/tex] where

The amplitude is 5, so [tex]|a|=a=5[/tex].

The midline is y = 6, so d = 6.

The period is 1, so b = [tex]\frac{2\pi }{1}=2\pi[/tex].

The formula for [tex]g(x)=5\cos(2\pi x)+6[/tex].

Answer:

Step-by-step explanation:

The smaller/closer the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct concluding that the data fits that particular distribution given.

Answer:

260

20

Step-by-step explanation:

speed of plane= p

speed of wind =w

and

added up the 2 equations we get:

then

Answer:

[tex]z=\frac{0.231 -0.2}{\sqrt{\frac{0.2(1-0.2)}{221}}}=1.152[/tex]  

The p avlue for this case is given by:

[tex]p_v =P(z>1.152)=0.125[/tex]  

The p value for this case is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is higher than 0.2 or 20%

Step-by-step explanation:

Information provided

n=221 represent the random sample taken

X=51 represent the people with nausea

[tex]\hat p=\frac{51}{221}=0.231[/tex] estimated proportion of people with nausea

[tex]p_o=0.21[/tex] is the value to test

[tex]\alpha=0.1[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to verify

We want to check if the true population is higher than 0.20, the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.2[/tex]  

Alternative hypothesis:[tex]p > 0.2[/tex]  

The statistic is given:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.231 -0.2}{\sqrt{\frac{0.2(1-0.2)}{221}}}=1.152[/tex]  

The p avlue for this case is given by:

[tex]p_v =P(z>1.152)=0.125[/tex]  

The p value for this case is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is higher than 0.2 or 20%

Answer:

alternative hypothesis : H₁ :

Recent  Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average

Alternative Hypothesis : H₁: μ < $1.298 a gallon

Step-by-step explanation:

Explanation:-

Given A recent gasoline survey said that the national average price of gasoline was $1.298 a gallon

Population average μ= $1.298 a gallon

sample size 'n' = 37

Sample mean (x⁻) = $1.192 a gallon

Sample standard deviation 'S' = $0.0436

Null hypothesis :H₀ : μ =  $1.298 a gallon

Alternative Hypothesis : μ < $1.298 a gallon

Degrees of freedom : ν = n-1= 37-1=36

t₀.₀₂₅ = 1.688

Test statistic

                       [tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]

                       [tex]t = \frac{1.192-1.298 }{\frac{0.0436}{\sqrt{37} } }[/tex]

                     t =  -14.8044

|t| = |-14.8044| > 1.688

Null hypothesis is rejected

Alternative hypothesis is accepted

Recent  Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average