The frequency table shows the results of a survey about favorite exhibits. Find the relative frequency that a randomly selected student's favourite exhibit was either dinosaurs, or planets, express your answer as a decimal.


Butterfly: 12

Dinosaurs: 25

Planets: 17

Trains: 6

Answers

Answer 1

The relative frequency that a randomly selected student's favorite exhibit was either dinosaurs, or planets is 0.7.

How do we find the relative frequency?

To find the relative frequency, we will divide the number of students who chose dinosaurs or planets by the total number of students surveyed.

The total number of students surveyed is 12 + 25 + 17 + 6 = 60.

The number of students who chose dinosaurs or planets is 25 + 17 = 42.

Therefore, the relative frequency will then be 42 / 60 = 0.7.

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Related Questions

The Maths GCSE test scores of 240 students are shown in the histogram below.

Answers

The required median is 110- 120 and the upper quartile of the scores is 110-120.

Given that, the data from the histogram is

CI                 |             f

80-90          |            5

90-100,        |            3

100-110,        |            4

110-120,        |            4

120-130,       |             3

130-140,       |             3

140-150,       |             2

150-160        |             2

To find the median and upper quartile of the given scores, make the cumulative frequency table.

The cumulative frequency table is given below.

CI                 |             f               |             cf            

80-90          |            5               |             5

90-100,        |            3               |             8

100-110,        |            4               |            12

110-120,        |            4               |             16

120-130,       |             3               |             19

130-140,       |             3               |             22

140-150,       |             2               |             24

150-160        |             2               |             26

N = 26.

The median is the N/2 th score when N is even.

Median  = 13th score = 110-120 scores

To find the upper quartile, the product of (3/4 and N )th score gives the upper quartile.

Upper quartile = (3/4 x 26)th score.

Upper quartile = 19.5th  score.

The upper quartile score range is 110 - 120.

Therefore,the required median is 110- 120 and the upper quartile of the scores is 110-120.

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Evaluate your data. Has there been an increase in the number of certain individuals of this
population of bacteria? Please explain how you think this might lead to the emergence of a
superbug over time, or the extinction of certain strains of this bacteria.

Answers

The increase in certain individuals leads to:

Selective pressure.Emergence of antibiotic-.Extinction .Genetic variations.Difficulty in treating infections.Competition for resources leading to disadvantage for other strains.

An increase in certain individuals within a bacterial population can lead to:

Selective pressure favoring individuals with advantageous traitsEmergence of antibiotic-resistant strains or "superbugs"Extinction of less competitive strainsGenetic variations being passed on to future generationsDifficulty in treating infections caused by resistant bacteriaCompetition for resources leading to disadvantage for other strainsOutcome depends on selective pressure, genetic diversity, resource availability, and adaptability.

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Need this asap will give brainliest

Answers

Answer:

measure of angle 7 + measure of angle 8 = 180°.

Does anyone know how to solve this?

Answers

Let's call the number of pencils in each package "p".

Kayana used 4 packages of pencils, so she used 4p pencils in total for the first semester.

After that, she used 10 more pencils, so the total number of pencils she used is:

4p + 10

Therefore, the expression to represent the total number of pencils Kayana used is 4p + 10.

50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answers

Answer:

B). No two lines are parallel

Step-by-step explanation:

In spherical geometry, there are no parallel lines. This is because any two lines on a sphere will eventually intersect.

Please actually help me I really need it

Answers

Area of shape 1:

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 6 × 8

Area of triangle = 24 cm²

Area of shape 2:

Area of Semicircle = πr²/2

Radius of Semicircle = Diameter / 2

Radius of Semicircle = 3 cm

Then,

Area of semicircle = π(3)²

Area of semicircle = 9π cm²

Total Area = Area of semicircle + Area of triangle

Total Area  = (24 + 9π) cm²

Total Area = 52.27 cm² .

Hence Total area of the figure combining triangle and semicircle is 52.27 cm².

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Solve 5(2x – 3) = x – 15 + 9x for x. Question 7 options: A) Infinitely many solutions B) –18∕5 C) 0 D) –12∕5

Answers

Step-by-step explanation:

5(2x – 3) = x – 15 + 9x

10x - 15 = x - 15 + 9x

10x - 9x - x = -15 + 15

0 = 0

Answer = A) Infinity many solutions

Can u help me please fill in the square

Answers

The equation of the circle is (x + 4)² + (y - 1)² = 81

Given is an equation of a circle we need to convert it in standard form,

x² + y² + 8x - 2y = 64,

To convert the equation of a circle to standard form, you need to complete the square for both the x and y variables.

The standard form of a circle equation is:

(x - h)² + (y - k)² = r²

where (h, k) represents the center of the circle, and r represents the radius.

Let's convert the given equation to standard form step by step:

x² + y² + 8x - 2y = 64

Rearrange the equation to group the x-terms and y-terms:

x² + 8x + y² - 2y = 64

Now, complete the square for the x-terms.

Take half of the coefficient of x (which is 8 in this case), square it, and add it to both sides of the equation:

x² + 8x + 16 + y² - 2y = 64 + 16

Simplify:

(x + 4)² + y² - 2y = 80

Complete the square for the y-terms.

Take half of the coefficient of y (which is -2 in this case), square it, and add it to both sides of the equation:

(x + 4)² + y² - 2y + 1 = 80 + 1

Simplify:

(x + 4)² + (y - 1)² = 81

Now, the equation is in standard form, with the center at (-4, 1) and a radius of √81 = 9.

Hence the equation of the circle is (x + 4)² + (y - 1)² = 81

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Which of the following options represents the phrase "eight less than the quotient of 24 and 12"?

Answers

Hello!:

24/12 - 8

= 2 - 8

= -6

hat amount did she get back? (h) Ujeli had 11 pencils. She kept 3 pencils for herself and divided the remaining pencil equal among 4 of her friends. How many pencils did she give to each of them? ​

Answers

Answer:

2

Step-by-step explanation:

Ujeli had 11 pencils and she kept 3 so 11-3 = 8

so that means that the remaining pencil were dived by 4 (8÷2) = 2

b) 9 mm 6 mm 7 mm surface area for this question

Answers

The surface area of the rectangular prism is 318 square mm

What is the surface area of the rectangular prism?

From the question, we have the following parameters that can be used in our computation:

9 mm by 6 mm by 7 mm

The surface area of the rectangular prism is calculated as

Surface area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * (9 * 6 + 9 * 7 + 6 *7)

Evaluate

Area = 318

Hence, the area is 318 square mm

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Question

The net of a rectangular prism and its dimensions are given as 9 mm 6 mm 7 mm. What is the total surface area of the rectangular prism in square inches?

A girl is on a bridge 38.9 m high. She throws a rock straight down at -12.5 m/s. How long does it the rock to hit the ground

Answers

Answer:

3.14 seconds

Step-by-step explanation:

According to the synthetic division below, which of the following statements are true? -4/3 7 20

Answers

According to the synthetic division below, the true statements are as follows:

B. The number 4 is a root of F(x) = 3x2-13x+4.

D. (3x2 - 13x+4) - (x - 4) = (3x - 1)

F. (x-4) is a factor of 3x2.13x+ 4.​

How to determine the true statements

Synthetic divisions are the manual ways of bypassing long divisions while performing the Euclidean dividion of polynomials. For the given expressions, we can determine the true statements in this way:

1. F(x) = 3x² - 13x +4.

(x-4) (3x-1)

So, x = 4 or 1/3

4 is an actual root of the function.

2. (3x² - 13x + 4) ÷ (x - 4) = (3x - 1)

3. 3x² - 13x + 4 = (x-4) (3x-1)

So, since all these expressions are true, they meet the requirements for the synthetic division.

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Complete Question:

According to the synthetic division below, which of the following statements are true? Check all that apply. 4 4)3 -13 12 3 0 O A. The number -4 is a root of F(x) = 3x2.13x + 4. B. The number 4 is a root of F(x) = 3x2-13x+4. O C. (3x2 - 13x + 4) - (x + 4) = (3x - 1) D. (3x2 - 13x+4) - (x - 4) = (3x - 1) O E. (x + 4) is a factor of 3x2 - 13x + 4. IF (x-4) is a factor of 3x2.13x+ 4.​

A statue that is 25 feet tall casts a shadow that is 16 feet long. A cement pose next to the statue is 4 feet tall. find the length of the cement post’s statue.

Answers

The length of the cement post's statue is 6.25 feet.

How to calculate the length of the cement post's statue?

We shall use Mathematical operators to compute the length of the cement post's statue.

(Height of the statue) / (Length of the shadow) = (Height of the cement post's statue) / (Height of the cement post)

Given:

Height of the statue = 25 feet

Length of the shadow = 16 feet

Height of the cement post = 4 feet

Let x =  length of the cement post's statue

25 feet / 16 feet = x / 4 feet

To find x, we cross-multiply:

25 * 4 = 16 * x

100 = 16 * x

To isolate x, we divide both sides of the equation by 16 feet:

100 / 16 = x

x ≈ 6.25 feet

Therefore, the length of the cement post's statue is 6.25 feet.

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PLEASE HELP!!! Solve 5sin(π/3x)=3 for the four smallest positive solutions

Answers

Let's solve ~

This one's a special case of a right angled triangle with sides (3, 4, and 5 units)

Back to the problem :

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5 \sin \bigg( \frac{ \pi}{3} x \bigg) = 3[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \frac{3}{5} [/tex]

Now, check the triangle, sin 37° = 3/5

therefore,

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin(37 \degree) [/tex]

[ convert degrees on right side to radians ]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin \bigg(37 \degree \times \frac{ \pi}{180 \degree} \bigg ) [/tex]

There are three more possible values as :

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin( \theta) = \sin(\pi - \theta) [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( { 2\pi}{} + \theta \bigg) [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( \frac{ 3\pi}{} - \theta\bigg) [/tex]

Equating both, we get :

First value :

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 37 \times \frac{ \cancel \pi}{180} \times \frac{3}{ \cancel \pi} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = \frac{37}{60} [/tex]

or in decimals :

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 0.616666... = 0.6167[/tex]

[ 6 repeats at third place after decimal, till four decimal places it would be 0.6167 after rounding off ]

similarly,

Second value :

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(1 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 1 - \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 1[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 0.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 2.385[/tex]

Third value :

[tex]\qquad\displaystyle \tt \dashrightarrow \: 2\pi + \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(2 + \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 2 + \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.205 - 2[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = - 1.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times -1 .795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = -5.385[/tex]

Fourth value :

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3 \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(3 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3 - \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 3[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 2.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 2.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 8.385[/tex]

" x can have infinite number of values here with the same result, here are the four values as you requested "

I hope it was helpful ~

Write a system of linear equations for the graph below. really need lots of help with this!

i also need the y's ​

Answers

Answer:

friend with this information you cannot know the answer you have to say everything says about that mathematical problem

A pair of equations is shown below:

y = 3x − 5
y = 6x − 8

Part A: Show all of your steps of how you will use substitution to determine the values for x and y. (4 points)

Part B: What is the solution, or ordered pair, for the two equations?

Answers

Part A: equate the expressions 6x - 8 = 3x - 5

collect the like terms 6x -3x = -5 + 8

Divide by the coefficient x = 1

Part B: The values are (1, -3)

How to determine the values

To determine the value of the variables,  we need to consider the equations.

From the information given, we have the equations given as;

y = 3x − 5

y = 6x − 8

Now, equate the expressions, we get;

6x - 8 = 3x - 5

collect the like terms, we have;

6x - 3x = -5 + 8

add or subtract the like terms

3x = 3

Divide by the coefficient

x = 1

Substitute the value

y= 6(1) - 9

expand the bracket

y = 6 - 9 = -3

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77th term of the sequence 16,19,22,25

Answers

The 77th term of the given Sequence is 244.

The given sequence is an arithmetic progression with a common difference of 3. To find the 77th term of the sequence, we can use the formula for the nth term of an arithmetic progression.

The formula for the nth term of an arithmetic progression is:

_ = _1 + ( − 1),

where _ is the nth term, _1 is the first term, is the position of the term in the sequence, and is the common difference.

In this case, _1 = 16 and = 3. Plugging in these values into the formula, we get:

_77 = 16 + (77 − 1) × 3.

_77 = 16 + 76 × 3.

_77 = 16 + 228.

_77 = 244.

Therefore, the 77th term of the given sequence is 244.

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Which of the following is the appropriate notation when calculating conditional probabilities

Answers

The notation which is the most appropriate notation when calculating conditional probabilities is option B.

What is the notation for conditional probabilities?

The appropriate notation for calculating conditional probabilities is often denoted using the vertical bar symbol "|". This symbol represents "given" or "conditional on."

In a mathematical expression, the conditional probability of event A given event B is written as P(A | B), where "P" stands for probability. This notation indicates that the probability of event A occurring is being calculated assuming that event B has already occurred.

Thus option B is correct.

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Please help me

The stem-and-leaf plot shows the numbers of confirmed cases of a virus in 15 countries.

A stem and leaf plot. A vertical line separates each stem from its first leaf. The first row has a stem of 4 and leaves 1, 1, 3, 3, and 5. The second row has a stem of 5 and leaves 0, 2, 3, and 4. The third row has a stem of 6 and leaves 2, 3, 3, and 7. The fourth row has a stem of 7 and leaf 5. The fifth row has a stem of 8 and no leaves. The sixth row has a stem of 9 and leaf 7. The key shows 5 vertical bar 0 is equal to 50 cases.

How many of the countries have more than 60 confirmed cases

Answers

Answer:

There are 6 countries with more than 60 confirmed cases

Step-by-step explanation:

- Draw your stem and leaf plot

-There is a stem without a leaf (There are no values in this class)

-Count the values in the stem and leaf plot and ensure they are 15. Each value represents the number of confirmed case in a county.

There are six numbers greater than 60 which are 62,63,63,67,65 and 97

Hence, there are 6 countries which have more than 60 confirmed cases

Geometry
Show work and number

Answers

Using the trigonometric ratios:

(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule:

(2). x = √116

(3). x = 90

What is trigonometric ratios?

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

(1). sinA = 5/13 {opposite/hypotenuse}

cosA = 12/13 {adjacent/hypotenuse}

tanA = 5/13 {opposite/adjacent}

By Pythagoras rule

(2). x = √(4² + 10²)

x = √(16 + 100)

x = √116

(3). 106² = x² + 56²

x² = 106² - 56²

x = √(11236 - 3136)

x = √8100

x = 90

Therefore, using trigonometric ratios:

(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule;

(2). x = √116

(3). x = 90

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Which of the following exponential regression equations best fits the data shown below?
(-4,0.05), (-3, 0.20), (-2, 0.75)

Answers

The exponential regression equation is y = 11.37 * 3.87ˣ

How to determine the exponential regression equation

From the question, we have the following parameters that can be used in our computation:

(-4,0.05), (-3, 0.20), (-2, 0.75)

To calculate the exponential regression equation that best fits the data shown, we use a graphing tool

An exponential function is represented as

y = abˣ

From the graphing tool, we have

a = 11.37

b = 3.87

substitute the known values in the above equation, so, we have the following representation

y = 11.37 * 3.87ˣ

Hence, the exponential regression equation is y = 11.37 * 3.87ˣ

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An artist made a cone of stainless steel, then sliced it into three pieces. what is the volume of the largest piece? PLEASE SHOW WORK AND EXPLAIN HOW YOU GOT YOUR ANSWER I WILL MARK YOU BRAINLIEST!!!

Answers

The volume of the largest piece is 10, 597. 5 cm³

How to determine the volume

The largest part of the cone takes the shape of a cylinder.

Now, the formula for calculating the volume of a cylinder is expressed as;

V = πr²h

The parameters of the formula are enumerated as;

V is the volume of the cylinder.r is the radius of the cylinder.h is the height of the cylinder.

Now, substitute the values, we get;

Diameter = 2 radius

Radius = 30/2

Radius = 15cm

Height = 15cm

Now, substitute the values, we get;

Volume = 3.14 × 15² ×15

Find the square value and substitute, we have;

Volume = 10, 597. 5 cm³

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find the invoice total, the amount should be paid after cash discount, the total amount due including shipping and insurance.​

Answers

The total invoice is $788.80, we find this by find the cost of each item.

To find the invoice total, we need to calculate the total cost of each item.

For the tablecloth:

Quantity: 16

Unit Price: $35.00

Total Cost = Quantity × Unit Price = 16 × $35.00 = $560.00

For the rings:

Quantity: 8

Unit Price: $6.50

Total Cost = Quantity × Unit Price = 8 × $6.50 = $52.00

For the cups (cases):

Quantity: 4 cases

Unit Price: $25.30

Total Cost = Quantity × Unit Price = 4 × $25.30 = $101.20

For the bowls:

Quantity: 12

Unit Price: $6.30

Total Cost = Quantity × Unit Price = 12 × $6.30 = $75.60

Now, let's calculate the invoice total by adding up the total costs of each item:

Invoice Total = $560.00 + $52.00 + $101.20 + $75.60

= $788.80

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MP4 Model with Math Write an
expression for the volume of the bar magnet.
0.5 in. N
2.25 in.
S
0.25 in.

Answers

The volume of the bar magnet with dimensions 0.5 in. (length), 2.25 in. (width), and 0.25 in. (thickness) is 0.28125 cubic inches.

The expression for the volume of a bar magnet can be calculated by multiplying its length, width, and thickness.

In this case, the dimensions provided are:

Length = 0.5 in.

Width = 2.25 in.

Thickness = 0.25 in.

To find the volume, we multiply these dimensions together:

Volume = Length × Width × Thickness

= 0.5 in. × 2.25 in. × 0.25 in.

Simplifying this expression, we get:

Volume = 0.28125 in³

Therefore, the volume of the bar magnet with dimensions 0.5 in. (length), 2.25 in. (width), and 0.25 in. (thickness) is 0.28125 cubic inches.

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In the figure below, S is the center of the circle. Suppose that JK = 20, LM = 3x + 2, SN = 12, and SP = 12. Find the
following.

Answers

Answer:

x = 6
JN = 10

Step-by-step explanation:

if the values of SN and SP are the same, so are the corresponding sides next to the right angles.
which means:
if SP = SN, then JK = LM.
Use the reverse version of the function for calculating LM (3x + 2).
-2 * 1/3
Now apply that function to 20.
(20-2)/3
= 18/3
= 6.
x = 6
Now JK is a chord.
and Radius SQ intersects JK at a perpendicular right angle (at point N).
So JN would be half the length of JK.
20/2 = 10.
JN = 10

does anyone have answers to Practice: Unit Rates for Ratios with Fractions Level G iready and the quiz? I will give a lot of points and brainliest answer

Answers

What is the rate in cups of flour per cup of water that Sophie uses?
6 c of flour per c of water


Which fraction represents Raul's speed in miles per hour?

What is Raul's speed in miles per hour?
8 over 4/5

10


What is the rate in cups of corn starch per cup of water?
3/8


What is the price per pound of the dried apricots?
$6


What is Ellie's speed in miles per minute?
1/12 mi/min


At that rate, what is the price of 2 tons of gravel?
128


Final answer:

While direct answers to iReady tasks are not provided, guidance for tackling problems involving unit rates and ratios with fractions was presented. The concept to calculate the unit rate involves dividing the first quantity by the second quantity. One should work towards solving these problems independently to reinforce the learning.

Explanation:

I'm sorry, but I cannot provide direct answers to your iReady task; it would not be fair or beneficial to your learning. However, I can guide you in how to tackle problems involving unit rates and ratios with fractions. With a unit rate, you're finding a ratio that compares a quantity to one unit of another quantity. The method typically involves dividing the first quantity by the second one.

For example, if you have a problem that says '6 cookies cost $1.50, what is the unit rate?', you would solve it by dividing 1.50 (the cost) by 6 (the number of cookies) to find the unit cost of a single cookie. This gives you a unit rate of $0.25 per cookie. If your questions on iReady involve complex fractions or operations, follow the same concept but use the relevant operation (multiplication, division, etc.). Practice moving toward solving these problems independently to improve your understanding of the concept.

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find the surface area​

Answers

Answer:

The surface area of the hexagonal pyramid is 313.13 square inches.

Step-by-step explanation:

Hexagonal pyramid,

Surface Area = Area of hexagon base + areas of six triangles

b = 6

h = 12.2 (height of the triangle)

A = [tex]\frac{3\sqrt{3} }{2}b + 6(\frac{1}{2} bh)[/tex]

A = [tex]\frac{3\sqrt{3} }{2}b +3bh[/tex]

A = [tex]\frac{3\sqrt{3} }{2}6 +3*6*12.2\[/tex]

A = 93.53 + 219.6

A = 313.13 square inches

9. PUGS is a parallelogram. The equation of line PU is y = 4x-2. What is the slope of GS?​

Answers

If PUGS is a parallelogram, then the opposite sides of the parallelogram are parallel.

The equation of line PU is given as y = 4x - 2. This equation is in slope-intercept form (y = mx + b), where the coefficient of x represents the slope of the line.

In this case, the slope of line PU is 4.

Since the opposite sides of a parallelogram are parallel, the slope of GS will also be 4.

Therefore, the slope of GS is 4.

what is greatest common factor of -x^2+6x-19

Answers

The greatest common factor of -x^2 + 6x - 19 is 1.

To find the greatest common factor (GCF) of the polynomial [tex]-x^2 + 6x - 19,[/tex] we need to factorize the polynomial and identify the common factors among its terms.

First, let's examine the polynomial and see if we can factor it further:

[tex]-x^2 + 6x - 19[/tex]

The polynomial does not appear to have any common factors among its terms.

It cannot be factored using simple integer factors.

In this case, we can say that the GCF of the given polynomial is 1.

It is important to note that the GCF represents the highest degree of common factors that can be factored out from all terms of a polynomial. In this particular case, the polynomial does not possess any common factors that can be factored out.

It's worth mentioning that this polynomial is already in its simplest form and cannot be factored further.

However, if the polynomial had common factors that could be factored out, such as common binomial factors or other mathematical patterns, the GCF would differ from 1.

But in this case, the polynomial does not exhibit any common factors beyond 1.

For similar question on greatest common factor.  

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