Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range:

La altura del triangulo está dada por el polinomio:

p(x) = a + 4

Recordar que para un triangulo de base B y altura H, el area es

A = B*H/2

En este caso, sabemos que la base es B = (4*a^2 + 6)

Y el area es A = 2a^3 + 8a^2 +3a +12

Entoces la altura será un polinomio tal que:

P(a)*(4*a^2 + 6)/2 = 2a^3 + 8a^2 +3a +12

P(a)*(4*a^2 + 6) = 2*(2a^3 + 8a^2 +3a +12) = 4a^3 + 16a^2 + 6a + 24

Podemos ver que p(a) va a ser un polinomio de grado 1, entonces:

p(a) = (c*a + b)

Reemplazando eso:

(c*a + b)*(4*a^2 + 6) = 4a^3 + 16a^2 + 6a + 24

Expandiendo:

(4c)*a^3 + (6c)*a + (4b)*a^2 + 6*b = 4a^3 + 16a^2 + 6a + 24

Comparando terminos del mismo exponente, podemos ver que:

(4c) = 4

6c = 6

4b = 16

6b = 24

Resolviendo esas ecuaciones para c y b, podemos ver que:

b = 16/4 = 4

c = 4/4 = 1

Entonces la altura del triangulo está dada por el polinomio:

p(x) = a + 4

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Answer:

C. 109x

Step-by-step explanation:

We know that there are 109 students in the fourth grade, who each have x cupcakes. In order to find the total amount of cupcakes, we could add all of the cupcakes together to get:

x + x + x + x + .... x

109 times because there are 109 students.

This can be simplified to become 109x.  

Answer:

Step-by-step explanation:

y=-1/2x+6

Answer:

6cm,20cm,80cm,1m,1m,1.15m,132cm

Step-by-step explanation:

Hence,1 m=100 cm

The equation of the line is b = am + c

Linear equations are equations that have a constant slope, average rate of change or gradients

The point is given as

(x, y) = (a, b)

The slope is given as

Slope = m

A linear equation is represented as

y = mx + c

Where me represents the slope

Substitute (x, y) = (a, b)

b = am + c

Hence, the equation of the line is b = am + c

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Answer:

C

Step-by-step explanation:

y > 2x² - 6x - 36 is the inequality in standard form represents the region greater than the quadratic function with zeros –3 and 6 and includes the point (–2, –16) on the boundary line. This can be obtained by finding zeroes of each inequality to check whether the zeroes are –3 and 6 and then substituting (–2, –16) in the inequality.

To find the zeroes of the inequality we use the formula,

x = (-b ± √b² - 4ac)/ 2a, where a, b and c are the coefficients of x², x and constant respectively.

Find the zeroes,

x = (3/2 ± √9/4 + 18)

x = 3/2 ± 9/2

⇒ x = 12/2 = 6, x = -6/2 = - 3

Putting x = –2 in the inequality we get,

1/2 x² - 3/2x - 9 = 1/2 (-2)² - 3/2(-2) - 9

                         = 2 + 3 - 9 = - 4 ≠ -16

Therefore option 1 is incorrect

Find the zeroes,  

x = (-6 ± √36 + 288) / 4

x = (-6 ± 18) / 4

⇒ x = 12/4 = 3, x = -24/4 = - 6

Therefore option 2 is incorrect

Find the zeroes,  

x = (6 ± √36 + 288) / 4

x = (6 ± 18) / 4

⇒ x = 24/4 = 6, x = -12/4 = - 3

Also , Putting x = –2 in the inequality we get,

2 x² - 6x - 36 = 2 (-2)² - 6(-2) - 36

                     = 8 + 12 -36

                     = - 16

The inequality includes the point (–2, –16) on the boundary line.

Hence y > 2x² - 6x - 36 is the inequality in standard form represents the region greater than the quadratic function with zeros –3 and 6 and includes the point (–2, –16) on the boundary line.

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Which inequality in standard form represents the region greater than the quadratic function with zeros –3 and 6 and includes the point   (–2, –16) on the boundary line?

a) y > 1/2 x² - 3/2x - 9

b) y > 2 x² - 6x - 36

c) y > 2 x² - 6x - 36

d) y > 1/2 x² + 3/2x - 9

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Answer:

4/3

Step-by-step explanation:

The slope is the change in y over the change in x.  

Your y's from the point given is -2, and 2.

Your x's from the point given is -1, and 2.  Since we want to know how much they have changed, we subtract these numbers to find the change.

Change in y's?  -2 - 2 or -4

Change in x's  -1 - 2 or -3

This gives me a slope of -4/-3  and a negative divided by a positive is a positive.

I could have found the change by going the opposite direction

Change in y's ? 2 - (-2) or 4

Change in x's? 2 - (-1) or 3

This gives me the same slope 4/3

The answer is 112 centimeters.

As this problem represents a right triangle, here we need to apply the Pythagorean Theorem.

The volume of the similar triangular prism is:  1,280 cm³.

Volume of a right triangular prism = 0.5 × b × h × altitude, where:

b is the base length of the triangular base

h is the height of the triangular base

Find the of the first triangular prism

Base length of the triangular base (b) = 4 cm

Height of the triangular base (h) = 4 cm

Altitude of the prism = 20 cm

Volume of the first triangular prism = 0.5 × 4 × 4 × 20 = 160 cm³.

Volume of the first prism/Volume of the second prism = (leg of first prism)³/(leg of second prism)³

160/Volume of the second prism = (4)³/(8)³

160/Volume of the second prism = 64/512

160/Volume of the second prism = 0.125

Volume of the second prism = 1,280 cm³.

Thus, applying the volume formula for a right triangular prism, the volume of the given similar prism is calculated as: 1,280 cm³.

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It takes 1 hour 43 minutes to finish mowing the lawn.

The rate of work done by Gregory and Jennifer finish mowing the lawn in

1 hour 43 minutes.

According to the question

Gregory can mow the family's lawn in 3 hours, she mows at a rate of 1/3 of the lawn per hour(1/3 lawn/hour)

Jennifer can mow it in 4 hours, which means her rate is 1/4 lawn/hour.

Together , their rates are 1/3 + 1/4.

This equals 7/12 lawns/hr.

We want to know how many hours they have to mow in order to mow 1 lawn.

This can be represented by the equation : [tex]\frac{7}{12} \times x = 1[/tex]

To solve for x, we would divide both sides by 7/12.

This leaves us with x = 12/7 which is 1.714.

Convert 1.714 to minutes by multiplying 60.

This gives you a final answer of about 1 hour 43 minutes.

Hence, It takes 1 hour 43 minutes to finish mowing the lawn.

The rate of work done by Gregory and Jennifer finish mowing the lawn in

1 hour 43 minutes.

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The quantity of the radioactive material which would remain 2 years from now is; 4 grams.

Since, it follows from the task content that after two year, the quantity of the radioactive substance decrease by 1 gram. Consequently, it follows from proportion that the quantity remaining in 2 years from now is; 5-1 = 4 grams.

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The linear equation can represent the ages of two sisters that are born one-year apart.

Here we have the linear equation:

y = x + 1

So the value of y is always one more than the value of x, so for example, suppose that two sisters are born one-year appart, then we can use the above linear equation to represent the age of the older sister as a function of the age of of the younger one.

In that case, the slope of 1 means that both of the sisters age at the same ritm.

The y-intercept of 1 means that the older sister is 1 years old when the younger sister was born.

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The inclination to the nearest tenth of a degree exists 0.24146

The given scenario includes a right-angled triangle where the length of the ramp exists hypotenuse and the rise of ramp exists the perpendicular.

Given: H = 4.6 m and P = 1.1 m

We have to use the trigonometric ratios to find the angle. The ratio that has to be used should involve both perpendicular and hypotenuse

Let x be the angle then

sin x = P/H

sin x = 1.1/4.6

sin x = 0.23913

[tex]$$sin^{-1} x[/tex] = 0.24146

The inclination to the nearest tenth of a degree exists 0.24146

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The measure of the angle ∠PQR is 90 degrees

The equation of the line PQ is given as:

3x - y - 2 = 0

The coordinates of the QR are given as:

(0, -2) and (6, -4)

Make y the subject in 3x - y - 2 = 0

y = 3x - 2

The slope of the above line is

m1 = 3

Next, we calculate the slope (m2) of points Q and R.

So, we have:

m2 = (y2- y1)/(x2 - x1)

This gives

m2 = (-4 + 2)/(6 - 0)

Evaluate

m2 = -1/3

The slopes of perpendicular lines are opposite reciprocals.

m1 = 3 and m2 = -1/3 are opposite reciprocals.

This means the lines PQ and QR are perpendicular lines.

The angle at the point of perpendicularity is 90 degrees

Hence, the measure of the angle ∠PQR is 90 degrees

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The value of the given expression is 105.

To find the value of the given expression:

Follow the PEMDAS order of operations:

Multiply and divide (left to right).

Add and subtract (left to right)

Therefore, the value of the given expression is 105.

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The number of days christen’s book is overdue is 22.

The number of days christen’s book is overdue:

According to the graph, the fine levied stops rising after 20 overdue days and then stays at 10 for the remaining days.

Additionally, if Christen's fine was the same as yesterday, her late dates must be longer than 21 days (because the fine on day 20 will be the same).

22 might therefore be the number of days past due based on the options provided.

The number of days christen’s book is overdue is 22.

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[tex]\\ \tt{:}\dashrightarrow \ell=\dfrac{\Theta}{180}\pi r[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180\ell}{\pi r}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180(13)}{5\pi}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=149^{\circ}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=149(60)[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=8940'[/tex]

The angle subtended at the center of a circle of radius 5 cm by a length of 13 cm is 149.1°.

Given that,

The angle is subtended at the center of a circle of radius 5 cm by a length of 13 cm.

Here, Lenght of an arc = 13 cm

The radius of an arc = 5 cm

Used the formula for the angles (θ);

Length of an arc = 2πrθ / 360°

Substitute all the values, we get;

13 = 2 × 3.14 × 5 × θ / 360°

Solve for θ;

13 × 360° = 31.4 × θ

4,680° = 31.4 × θ

θ = 4,680°/31.4

θ = 149.1°

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The probability of pulling a black or red card  = 3/10

Probability that a white card will be drawn, P(white) = 1/25

Probability that a blue card will be dealt, P(black)  = 1/5

Probability that a black card will be dealt, P(red) = 1/10

Probability that a pink card will be revealed, P(pink)  = 1/15

All of these occurrences are distinct from one another and do not relate to one another.

The likelihood that any one of any two events, A and B, with probability P(A) and P(B), will occur is:

                                        P( A ∪ B ) = P(A) + P(B)

Here, event A can be compared to getting a black card, and

incident B is comparable to receiving a red card.

So, P(black or red) = P(black) + P (red)

= (1/5) + (1/10)

= ( 2 + 1 )/10

= 3/10

So, the likelihood that a black or red card will be pulled from the hat:

= 3/10

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Answer:

3:10

10:1

8:1

100:7

Step-by-step explanation:

900:3000

300:1000

3:10

80:8

10:1

2000:750

8:1

100:7

The roots of the resulting polynomial equation are [tex](x_{1} ,y_{1} ) = (-2 , -26), (x_{2} ,y_{2} ) = ( 0.11 , 1.94 )[/tex] and [tex]( x_{3} , y_{3} ) = ( 4.39, - -9.81)[/tex] , respectively.

What is a polynomial easy definition?

A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power (such as a + bx + cx2).

Ariana must graph two polynomic expressions:

[tex]f(x) = x^{3} -5 . x^{2} + 2[/tex] and [tex]g(x) = -x^{3} + 17 . x[/tex]

The roots of the resulting polynomial equation are found by means of this formula-

f(x) - g(x) = 0.........................1

Then, we must look for every point so that  f(x) = g(x)

The roots of the resulting polynomial equation are [tex](x_{1} , y_{1} ) = ( -2,-26) , (x_{2} ,y_{2} ) = ( 0.114 , 1.937 )[/tex] and [tex](x_{3},y_{3} ) = ( 4. 386 , -9. 812)[/tex]  respectively.

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Answer:

D

Step-by-step explanation:

The statement that justifies the relationship is: D. it represents a function because no length has more than one price.

For a relation to be considered a function, any of the following criteria must be met:

In the scenario given:

Length of ribbon = input (x-value)

Price of ribbon = output (y-value).

We can observe that each length of ribbon (input) has its own price (output), therefore, we can conclude that the price of ribbon is a function of the length of the ribbon.

The answer is: D. This relationship represents a function because no length has more than one price.

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3.9 cm is the smallest diameter of pipe that will fit the fiber optic line.

What is diameter?

we know that

The diameter of the circle is equal to BD

Applying the Pythagoras Theorem

BD² = BE² + DE²

substitute the given values

BD² = (3)² + (2.5)²

BD² = 9 + 6.25

BD² = 15.25

BD = √15.25

BD = 3.9 cm

Therefore , 3.9 cm is the smallest diameter of pipe that will fit the fiber optic line.

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Explanation: The 4th one is the distributive property because it shows an     equal sign and the 5th one is the inverse property of addition because it uses more than addition.

Answer: 4th one is distributive property 5th one is inverse property of addition

P.S. I am sure 95% sure that I am correct.

Answer:

11. 333... which can also be written as 11 1/3.

Step-by-step explanation:

Sure.

√(6c - 4) = 8

Squaring both sides:

6c - 4 = 64

6c = 64 + 4 = 68

c = 68/6

  = 11. 333...

Answer:

[tex]c=\dfrac{34}{3}[/tex]

Step-by-step explanation:

Given equation:

[tex]\sqrt{6c-4}=8[/tex]

Square both sides:

[tex]\implies (\sqrt{6c-4})^2=8^2[/tex]

[tex]\implies 6c-4=64[/tex]

Add 4 to both sides:

[tex]\implies 6c-4+4=64+4[/tex]

[tex]\implies 6c=68[/tex]

Divide both sides by 6:

[tex]\implies \dfrac{6c}{6}=\dfrac{68}{6}[/tex]

[tex]\implies c=\dfrac{34}{3}[/tex]

Verify the solution by inputting the found value of c back into the equation:

[tex]\implies \sqrt{6\left(\dfrac{34}{3}\right)-4}[/tex]

[tex]\implies \sqrt{\dfrac{204}{3}-4}[/tex]

[tex]\implies \sqrt{68-4}[/tex]

[tex]\implies \sqrt{64}[/tex]

[tex]\implies \pm 8[/tex]

Therefore, the solution of the found value of c is verified.

When two coins are flipped simultaneously 24 times, on average 12 times we will get a head and a tail.

For given question,

When two coins are tossed simultaneously, the sample space is as follows:

S = { HH, HT, TH, TT} where H denotes Head and T denotes tail.

Using the formula of probability,

P = Number of favorable outcomes/total number of outcomes,

we get,

P(HT) = 1/4

and

P(TH) = 1/4

We know that the occurrence of two mutually exclusive events is the sum of their individual probabilities.

So, P(Head on one and Tail on other)

= P(HT) + P(TH)

= 1/4 + 1/4

= 2/4

= 1/2

= 0.5

So, when two coins flipped simultaneously, the probability of flipping 2 coins and getting a head and a tail is 0.5

In this question, we need to find the number of times getting a head and a tail when two coins are flipped simultaneously 24 times

= 0.5 × 24

= 12

Therefore, When two coins are flipped simultaneously 24 times, on average 12 times we will get a head and a tail.

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The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.

According to the given statement

we have given data set and we have to find the five number summary.

So, For this purpose,

the given data set is:

48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80

Firstly we have to find the upper quartile means median for it.

So, Median = n /2

median = 12/2

median = 6th term.

So, Upper quartile range for this data set is 63.

And

Lower quartile for data set is the lower value of the data set.

So, That's why

Lower quartile range for this data set is 48.

And now, we have to find the Interquartile range

so, Interquartile range means maximum value of data.

So, That's why

Interquartile range of this data is 80.

So, The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.

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Answer:

perimeter = 24

Step-by-step explanation:

formula:

In an equilateral triangle with sides of lengths ‘a’

The height of the triangle is equal to :

[tex]= \frac{\sqrt{3} }{2} a[/tex]

……………………………………………

Calculating ‘a’ :

We have to solve the equation:

[tex]4\sqrt{3} =\frac{\sqrt{3} }{2} a[/tex]

[tex]\Longleftrightarrow 4=\frac{1 }{2} a[/tex]

[tex]\Longleftrightarrow a = 8[/tex]

Calculating the perimeter:

= 3a

= 3 × 8

= 24

the total volume of the chimney is:

V =456 in^3

Remember that the volume of a rectangular prism of dimensions L, W, and H is:

V = L*W*H

If you look at the image of the chimney (bottom right image) you can see that the figure can be viewed as 2 rectangular prisms, one smaller of dimensions:

4in x 12in x 9 in

Then the volume of the larger part is:

V = (4in)*(12in)*(9in) = 432 in^3

The smaller prism has dimensions:

of (6in - 4in) = 2in x 3in x 4in

Then the volume is:

V = (2in)*(3in)*(4in) = 24 in^3

Then the total volume of the chimney is:

V = 432 in^3 +  24 in^3 = 456 in^3

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