x² - 12x + 27? what is the factored form of this polynomial ​

Answer:

a. probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed

Step-by-step explanation:

In Statistics, a p-value also known as the probability value is the probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed.

The p-values can be calculated by using spreadsheets, statistical software and p-value tables and is widely used in research fields such as economics, physics, sociology, accounting etc.

The p-value can be mathematically expressed as a function of the null hypothesis, H and the random variable, X.

Answer:

In that day 1300 children and 700 adults were admitted.

Step-by-step explanation:

Since the people who enter the park are either adults or children, the sum of these two types of people must be equal to the total amount that entered the park. So we have:

children + adults = 2000

The total amount collected must be the sum of the people that entered the park multiplied by the ticket fee for each type. We have:

1.5*children + 4*adults = 4750

We now have two equations and two variables so we can solve the system.

children + adults = 2000                                             equation 1

1.5*children + 4*adults = 4750                                     equation 2

We can multiply the equation 1 by -1.5 and sum it with the equation 2 to solve for adults, we have:

-1.5*children - 1.5*adults = -3500

1.5*children + 4*adults = 4750

2.5*adults = 1750

adults = 1750/2.5 = 700

To solve for children we apply the found value for adults on the equation 1.

children + 700 = 2000

children = 2000 - 700 = 1300

In that day 1300 children and 700 adults were admitted.

Answer:

700 adults and 1300 children

Step-by-step explanation:

Let 'C' represent number of children

'A' represent number of adults

->If  2,000 people entered the park, the equation will be

C+A=2000

C=2000-A ->eq(1)

->$1.50 for children and $4.00 for adults.

$1.50C+$4.00A=$4,750

Substituting for C from above.

$1.50(2000-A)+$4.00A= $4,750

$3000-$1.50A+$4.00A=$4,750

$2.50A = $4,750 - $3000

$2.50A=$1750

A= 700

and for children:

eq(1)=>

C=2000-700

C= 1300

Thus, 700 adults and 1300 children were admitted.

Answer:

a) [tex]n=\frac{0.58(1-0.58)}{(\frac{0.05}{2.58})^2}=648.600[/tex]  

And rounded up we have that n=649

b) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.58})^2}=665.64[/tex]  

And rounded up we have that n=666

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]

Part a

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.58(1-0.58)}{(\frac{0.05}{2.58})^2}=648.600[/tex]  

And rounded up we have that n=649

Part b

For this case we can use an estimator for p as [tex]\hat p=0.5[/tex]

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.58})^2}=665.64[/tex]  

And rounded up we have that n=666

Answer:

y = x + 2

Step-by-step explanation:

It looks like its adding 2 everytime.

y = x + 2

Answer:

If you're asking about which graph would be better, you can show it by a histogram best.

Step-by-step explanation:

Sorry if this is not your question if not I misunderstood, but a line graph is to measure the changes between data, while histograms measure a single measurement for each subject matter. So the best graph to display this info would be through a histogram

Answer:

1 μ = M μ ≠ M 2

2 μ > M μ < M 1

3 μ < M μ > M 1

If we use a 5% significance level, the p-value of 0.165 is not less than α = 0.05 so we would not

reject H0 : pf = pm. T

Answer:

1,177.5cm^3 of candle wax will be required.

Step-by-step explanation:

The attached files contain further information so please check them.

Answer:

Step-by-step explanation:

Given

Volume of Cylinder (V)= 480 cm

height (h) = 30 cm

radius (r) = ?

WE KNOW THAT WE HAVE FORMULA

Volume (V) = [tex]\pi r^{2} h[/tex]

           480 = 3.14 * r^2 *30

            480 = 94.2 r^2

             480/94.2 = r^2

               r^2 = 5.1

                 r =[tex]\sqrt{5.1}[/tex]

Therefore r = 2.3 cm

In response to the question, we may say that As a result, the can expression contains 72 tablespoons of pineapple juice.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To begin, we must convert the provided measurements to the same unit.

2 tablespoons = 1 fluid ounce

3 teaspoons = 1 tablespoon

Thus, 12 fluid ounces of canned pineapple juice equals:

12 fluid ounces divided by 2 tablespoons per fluid ounce is 24 tablespoons

And because we need to know how much juice is in teaspoons, we can convert tablespoons to teaspoons by:

72 teaspoons = 24 tablespoons × 3 teaspoons/tablespoon

As a result, the can contains 72 tablespoons of pineapple juice.

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Answer:

The correct option is;

d. 24.2 to 25.6

Step-by-step explanation:

Here we have a sample with unknown population standard deviation, we therefore apply the student t distribution at 64 - 1 degrees of freedom

Therefore, we have

[tex]CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex]

Where:

[tex]\bar x[/tex] = Mean = 25

σ = Standard deviation = 2

n = Sample size = 64

t = T value at 98% = [tex]\pm 2.387[/tex]

Which gives

[tex]CI=25\pm t_{63}\frac{2}{\sqrt{64}}[/tex]

That is the value is from

24.40325 to 25.59675 which gives,by rounding to one decimal place, is

24.4 to 25.6.

The 98% confidence interval for the true average age of all students at the university, given a sample mean age of 25, standard deviation of 2, and a sample size of 64, is approximately option (d) 24.4 to 25.6 years.

The 98% confidence interval for the true average age of all students in the university can be calculated using the sample mean, the sample standard deviation, and the size of the sample. Since the population standard deviation is unknown and the sample size is less than 30, we use the t-distribution to find the critical value (t).

First, we find the t-score corresponding to a 98% confidence level with 63 degrees of freedom (n-1 = 64-1). Using a t-distribution table or calculator, the t-score is approximately 2.390.

Next, we calculate the margin of error (ME) using the formula:
ME = t * (s/√n)
where s is the sample standard deviation and n is the sample size. Plugging in our numbers:
ME = 2.390 * (2/√64) = 0.5975

Finally, we add and subtract this margin of error from the sample mean to find the confidence interval:
CI = mean ± ME
CI = 25 ± 0.5975
CI = (25 - 0.5975, 25 + 0.5975)
CI = (24.4025, 25.5975)

Therefore, the 98% confidence interval for the true average age is approximately 24.4 to 25.6 years.

Final answer:

The shortest side of the new similar triangle, where the longest side is 9 inches, is found to be 4.8 inches. This is determined by using the scale factor 3/5, obtained from the original triangle with sides 15 inches, 8 inches, and 10 inches.

Explanation:

The student asks for the length of the shortest side of a new triangle similar to the one given, with the length of the longest side being 9 inches. To find this, we need to use the concept of similar triangles. Similar triangles have proportional corresponding sides.

The original triangle has sides of lengths 15 inches (longest side), 8 inches (shortest side), and 10 inches. Given that the longest side of the new triangle is 9 inches, we can find the scale factor by dividing the new longest side by the original longest side: 9 inches / 15 inches = 3/5.

Now, we use this scale factor to find the length of the shortest side in the new triangle: 8 inches (original shortest side) x 3/5 (scale factor) = 4.8 inches.

Therefore, the length of the shortest side of the new triangle is 4.8 inches.

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Final answer:

Maura saves $14.10 by purchasing 30 daffodil bulbs in the more economical 3-bulb packages instead of the 2-bulb packages.

Explanation:

To determine how much Maura saves by buying 30 daffodil bulbs at the better price, we first need to calculate the price per bulb for each package option and then find the total cost for 30 bulbs. Let's compare the two package options:

The package of 3 bulbs has a better price per bulb than the package of 2 bulbs. To buy 30 bulbs at the better price, Maura would need 10 packages of 3 bulbs, which will cost:

10 packages × $5.37 per package = $53.70

Now let's calculate how much it would cost if she bought the 2-bulb packages:

Since 30 is an odd number, Maura would need to buy 15 packages of 2 bulbs to get 30 bulbs. This will cost:

15 packages × $4.52 per package = $67.80

Maura saves by purchasing the 30 bulbs in 3-bulb packages:

$67.80 - $53.70 = $14.10

Therefore, Maura saves $14.10 by purchasing the 30 bulbs in the more economical 3-bulb packages.

Answer:

Number of seconds to reach maximum height = 3 seconds

Maximum height = 144 ft

Step-by-step explanation:

We are given that;

s(t) = -16t² + 96t

Now, s(t) is a function whose graph is an upside-down parabola, so the maximum s value occurs at the vertex.

Thus, the applicable formula for coordinate of vertex is t = -b/(2a) where a is the coefficient -16 and b is 96

Thus,t = -96/(2 x - 16)

t = 96/32

t = 3

Thus maximum height will be at 3 seconds.

Thus;

Max height = s(3) = -16(3)² + 96(3)

Max height = -144 + 288 = 144 ft

The object will reach its maximum height of 144 feet in 3 seconds.

Given information:

An object is projected upward from ground level with an initial velocity of 96 ft per​ sec.

The height in feet after t seconds is given by [tex]s(t)=-16t^2+96t[/tex].

Now, it is required to find the time at which the object will reach its maximum height.

The object will reach maximum height when velocity of the object becomes zero.

So, the velocity of the object can be written as,

[tex]s(t)=-16t^2+96t\\v(t)=\dfrac{d(s(t))}{dt}=-32t+96[/tex]

So, the time at maximum height can be calculated as,

[tex]v(t)=-32t+96=0\\t=3[/tex]

So, after 3 seconds the object will reach its maximum height.

Now, the maximum height of the object will be,

[tex]s(t)=-16t^2+96t\\s(3)=-16\times 3^2+96\times 3\\s(3)=144\rm \; ft[/tex]

Therefore, the object will reach its maximum height of 144 feet in 3 seconds.

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Answer:

Step-by-step explanation:LOOK IN PG 1 OF PDF 3 QUESTION.

HOPES THIS WAS HELPFUL

The required probability is 9/23

According to the problem,

Number of students with experience and a degree = ( 140 - 10 ) = 130

Number of students with only degree = (220 - 130) = 90

Probability that a new hire has a college degree but no experience              = 90/230 = 9/23

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Final answer:

To find the total daily water usage of the family, divide the amount of water they use for cleaning, 68.9 gallons, by the percentage of their total usage that goes to cleaning, which is 26.5%. The result is that the family uses about 260 gallons of water every day.

Explanation:

To calculate how many gallons of water the family uses every day, we need to establish the total daily water usage based on the percentage used for cleaning.

Since we know that 26.5% of their total water usage is allocated for cleaning, and they use 68.9 gallons for this purpose, we can find the total daily usage with a simple division:

Total daily water usage = Water used for cleaning / Percentage used for cleaning Total daily water usage = 68.9 gallons / 0.265 Total daily water usage = 260 gallons (rounded to the nearest whole number)

Thus, the family uses approximately 260 gallons of water per day for all their needs, including cooking, cleaning, and drinking.

Final answer:

To find out how many gallons a family uses every day, set up a proportion to find the total amount of water used for cleaning and solve for x. The family uses approximately 259.62 gallons of water every day.

Explanation:

To find out how many gallons a family uses every day, we need to determine the total amount of water used for cleaning. The question states that 26.5% of the water used each day is for cleaning, and the family uses 68.9 gallons for cleaning. We can set up a proportion to find the total amount of water used:

26.5% / 100% = 68.9 / x

Now we can solve for x by cross multiplying:

26.5x = 68.9 * 100

Dividing both sides of the equation by 26.5, we find that x is approximately 259.62.

Therefore, the family uses approximately 259.62 gallons of water every day.

Given:

In the given triangle,

With respect to y, Perpendicular = 10 cm and Base = 8 cm

To find the value of y.

Formula

By Trigonometric Ratio we get,

[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]

Now,

Putting the values of perpendicular and base we get,

[tex]tan\theta = \frac{10}{8}[/tex]

or, [tex]\theta = tan^{-1} (\frac{10}{8})[/tex]

or, [tex]\theta = 51.34 ^\circ[/tex]

Rounding off to the nearest tenth, we have;

[tex]\theta = 51.3 ^\circ[/tex]

Hence,

The value of y is 51.3°.

Answer:

The correct options are 1, 3, and 5

Step-by-step explanation:

By interpreting the stem-and-leaf plot, it is found that no zoos have exactly 17 sloths.

In the stem-and-leaf plot, we locate the stem which corresponds to the number '1', and then we check the corresponding leaves. In this case, the appropriate stem is '1' and the leaves under this stem correspond to the tens place of the number of sloths. So, now we check the leaf '7' under stem '1'. Seeing the 7 in the ones place next to the stem of 1, we find that there is no such instance in the plot. Therefore, we can conclude that no zoos have exactly 17 sloths.

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Stem-and-leaf plots represent numerical data in statistics. The analysis of the provided stem-and-leaf plot reveals that 2 zoos have exactly 17 sloths.

Stem-and-leaf plots are used in statistics to represent numerical data. Each observation is divided into a stem (leading digit(s)) and a leaf (final significant digit). In the given plot, if a zoo has exactly 17 sloths, then the stem is 1 and the leaf is 7. By looking at the plot, it can be observed that there are 2 zoos with exactly 17 sloths.

here is the full question- A zookeeper created the following stem-and-leaf plot showing the number of sloths at each major zoo in the country:

0 3

1 6 7 7

2 0 4

3 0 1 1 2 4 7 9 9

4 1 2 3 5 7

Key: 4|1=41 sloths How many zoos have exactly 17 sloths? x=frac =frac (-)²(-)² 2005.

Answer:

Hence the function only :

Secx and Cosx functions are symmetric about y-axis

And remaining functions are not symmetric about y-axis.

Step-by-step explanation:

Given:

Six circular function as :

y= sinx ,y=cosx , y=tanx,  y= cotx ,y=secx  y=cosecx

To Find:

Which functions are symmetric about the y-axis

Solution:

The function is said to be symmetric about the y-axis is given by

f(x)=f(-x)

Now

1)For y=sinx  i.e. f(x)=sinx

So put x=-x

f(-x)=sin(-x)

=-sinx

Hence f(x)≠f(-x)

This function is not symmetric about y-axis

2)For y=cosx ,i.e. f(x)=cosx

put  x=-x

f(-x)=cos(-x)...............(as value for x and -x cos value remain the same )

=cosx

hence f(x)=f(-x)

This function is symmetric to the y-axis

3)For y=tanx     i.e   f(x)=tanx

put  x=-x

f(-x)=tan(-x)

=-tanx

Hence f(x)≠f(-x)

This function is not symmetric about y-axis

4)For y=cotx  i.e.  f(x)=cotx

Using above observation,

f(x)≠f(-x)

This is not symmetric about y-axis

5)For y=secx  i.e f(x)=secx

f(x)=f(-x)

This function is symmetric about y-axis.

6) for y=cosecx

f(x)≠f(-x)

This function is not symmetric about y-axis

Answer:

The answer is 5, 10, 15, 20 or any positive multiples of 5

Step-by-step explanation:

Since the ratio of green grapes to the total number of grapes is 9:14 and there are only purple and green grapes on the shelf. It implies the total number of purple grapes to overall grapes is 5:14.

Since this ratio is already at it's lowest form, it implies the possible number of purple grapes are 5, 10, 15, 20 or any positive multiple of 5.

Hi there! Hopefully this helps!

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Answer: The population is 1,625.

So the equation is:

p = 35t + 1,450.

t = the number of years since 2015.

2020 - 2015 = 5.

So now we are in 2020, which is 5 years ahead from 2015.

So: t = 5.

Now we need to rewrite the equation, then evaluate.

35(5) + 1,450 =

175 + 1,450 =

Answer:

(-∞,∞)

B) x cannot equal -4, 2

Step-by-step Explanation:

The function, y = x + 2, has a domain of (-∞,∞) because the equation will remain true no matter number you plug for x.

For the second question, x would be equal to -2 and 4.  You can find this by factoring the equation.  x² + 2x - 8 = (x - 2)(x + 4)  Your answer should be B

Answer:

B) x cannot equal −4, 2

Step-by-step explanation:

x² + 2x - 8 = 0

When x = -4, 2

When the denominator becomes zero, function becomes undefined

Answer: 280

Step-by-step explanation:

??/500=7/100

7x500/100

35/500=7/100

35x8=280

I think this is the answer.

Answer:

$859.09

Step-by-step explanation:

Answer:

The distance from the ground to the top of the ladder the building is touched is 16 feet.

Step-by-step explanation:

Given:

A ladder that is 20 feet tall is leaning against a building.Samuel measures that the base of the ladder touches the ground 12 feet from the base of the building.

Now, to find the distance from base of the building to the top of the ladder where building is touched.

Here, to understand the situation below is the figure attached:

Now, to get the distance from the ground to the top of the ladder where the building is touched we use pythagorean theorem:

[tex]AB^2+BC^2=AC^2\\\\AB^2+12^2=20^2\\\\AB^2+144=400\\\\Subtracting\ both\ sides\ by\ 144\ we\ get:\\\\AB^2=256\\\\Using\ square\ root\ on\ both\ sides\ we\ get:\\\\AB=16\ feet.[/tex]

Therefore, the distance from the ground to the top of the ladder the building is touched is 16 feet.

Answer:

-6 and 4

Step-by-step explanation:

the explanation is in the picture

please like and Mark as brainliest

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Given:

Skylar has 1/2 of her sub left from lunch she wants to cut it into thirds

Question asked:

Find the length of each piece ?

Solution:

Sub left from lunch = [tex]\frac{1}{2}[/tex]

As she want to cut into third, we will divide [tex]\frac{1}{2}[/tex] into [tex]\frac{1}{3}[/tex]

[tex]=\frac{1}{2}\div\frac{1}{3}\\ \\ =\frac{1}{2}\times\frac{3}{1} \\ \\ =\frac{3}{2}[/tex]

Thus, length of each piece will be [tex]\frac{3}{2}[/tex]

Answer:

It's correct answer is A.

Answer:

A represents the connector of X and Y.

Step-by-step explanation:

Answer:

The x-intercepts would be where the line hits the x-axis, so the x-intercepts would be:

-3, 2, and 5.

Step-by-step explanation:

Answer:

q4 is -3,2,5

and for q3 is the start point

Answer:

$38.92

Step-by-step explanation:

In this question, we are calculating the amount it would cost purchasing a turkey wing after giving some rebate.

Firstly, we calculate the cost of purchasing 22 pounds turkey

That would be 22 * $1.79 = $39.38

Now we subtract the cost of the rebate ;

That would be $39.38 -$1 = $38.38

Now, we add the envelope cost and the stamp cost

That would be $38.38 + $0.39 + $0.15 = $38.92

The final cost of the 22-pound turkey after accounting for the price per pound, mail-in rebate, and the costs of an envelope and stamp is $38.92.

The cost of a 22-pound turkey at $1.79 per pound is calculated first, then subtract the $1 mail-in rebate, and finally add the costs of the envelope and the stamp required for the rebate.

First, find the total cost of the turkey without the rebate:

Next, add the cost of the envelope and stamp:

After receiving the rebate of $1, the final cost is calculated:

Therefore, the final cost of the turkey after the rebate is $38.92.