A survey found that 3 out of 4 students bring lunch from home. Based
on the survey, predict the number of students in a class of 100 who bring
Lunch from home.

Answer:

[tex]4\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\sqrt{80}=\sqrt{16*5} =\sqrt{16}*\sqrt{5}=4\sqrt{5}[/tex]

It's not entirely clear what the full instructions are, and I wish your teacher posted a diagram of figures A and B. However, I think I know what your teacher is after.

I'm assuming this is pertaining to similar polygons.

The larger figure has a side length of 88 ft and corresponds to the smaller side length of 11 ft. This is a scale factor of 11/88 = 1/8 = 0.125

What it means is that we multiply each larger side length by 1/8 or 0.125 to get the smaller corresponding side length. In other words, 88*(1/8) = 11

Square this linear scale factor to get the area scale factor

(1/8)^2 = (0.125)^2 = 0.015625

This value of 0.015625 is the area scale factor. We multiply this by the area of figure A to get

4928*0.015625 = 77

This is how your teacher got 77 as the final answer for figure B.

------------------------------------------------------

Admittedly this concept is a bit confusing at first.

Let's do another example.

Consider a 2 by 3 rectangle of area 2*3 = 6 square units.

Now apply a linear scale factor of 4 to quadruple each side. We get a 8 by 12 rectangle of area 8*12 = 96.

Notice the jump from 6 to 96 is "times 16" (since 96/6 = 16) and it's no coincidence that 16 is 4^2, i.e. the result of squaring the linear scale factor.

new area = (area scale factor)*(old area)

new area = 16*(old area)

new area = 16*6

new area = 96

This shows that 16 is the area scale factor.

Answer:

Option A

Step-by-step explanation:

Given expression:

Option A

⇒ (x - 4)(3x + 2)

⇒ (x × 3x) + (2 × x) + (-4 × 3x) + (-4 × 2)

⇒ (3x²) + (2x) + (-12x) + (-8)

⇒ 3x² + 2x - 12x - 8

⇒ 3x² - 10x - 8

3x² - 10x - 8 = 3x² - 10x - 8 (Yes!)

Option B

⇒ (3x - 4)(x - 2)

⇒ (3x × x) + (3x × -2) + (-4 × x) + (-4 × -2)

⇒ (3x²) + (-6x) + (-4x) + (8)

⇒ 3x² - 6x - 4x + (8)

⇒ 3x² - 10x + 8

3x² - 10x - 8 = 3x² - 10x + 8 (No!)

Option C

⇒ (3x - 4)(x + 2)

⇒ (3x × x) + (3x × 2) + (-4 × x) + (-4 × 2)

⇒ (3x²) + (6x) + (-4x) + (-8)

⇒ 3x² + 6x - 4x - 8

⇒ 3x² + 2x - 8

3x² - 10x - 8 = 3x² + 2x - 8 (No!)

Option D

⇒ (3x - 2)(x - 4)

⇒ (3x × x) + (3x × -4) + (-2 × x) + (-2 × -4)

⇒ (3x²) + (-12x) + (-2x) + (8)

⇒ 3x² - 12x - 2x + 8

⇒ 3x² - 14x + 8

3x² - 10x - 8 = 3x² - 14x + 8 (No!)

Since the expression of option A has the same value as the given expression, option A is correct.

Answer:

Hi! Let's find which expression is equivalent to [tex]3x^{2} - 10x - 8[/tex]. First, remember that expressions are equivalent when they have identical solutions or roots. That means we have to do three things:

- solve [tex]3x^{2} - 10x - 8[/tex]

- review the listed expressions

- determine which solution is equivalent to the solution of [tex]3x^{2} - 10x - 8[/tex]

First, let's solve [tex]3x^{2} - 10x - 8[/tex].

Use the sum-product pattern -

3x^2 - 10x - 8

3x^2 + 2x - 12x - 8

Common factor from the two pairs -

3x^2 + 2x - 12x - 8

x(3x + 2) - 4(3x + 2)

Rewrite in factored form -

x(3x + 2) - 4(3x + 2)

(x - 4)(3x + 2)

Now, let's review the listed expressions. We have:

A. (x - 4)(3x + 2)

B. (3x - 4)(x - 2)

C. (3x - 4)(x + 2)

D. (3x - 2)(x + 4)

We're looking for one of these expressions to be equivalent to the solution of [tex]3x^{2} - 10x - 8[/tex], which we know is (x - 4)(3x + 2). The first choice, A. (x - 4)(3x + 2), would be our answer!

I hope this helps you. Have a wonderful day and let me know if I can help you with anything else! =)

Answer:

104

Step-by-step explanation:

Simple addition:

Add the units place first:

2+2 = 4

Now add the tens together:

60+40= 100

Now add the 2 numbers together to give you 104.

Answer:

18x⁴ - 30x³ + 66x² - 40x + 56

Step-by-step explanation:

1) Distribute

2) Distribute

3) Distribute

4) Combine like terms

Expression

Example: 2 + 2 = 4

Combination

Answer:

The product would be 18x^4 - 30x^3 + 66x^2 - 40x + 56

Step-by-step explanation:

Answer:

A' = (-4, -2.5)

B' = (1.5, 2.5)

C' = (-1, 5)

Step-by-step explanation:

Dilation using the origin as a center means that we multiply each coordinate by 0.5:

[tex]A = (-8, -5)\\ \\B = (3, 5)\\ \\C = (-2, 10)[/tex]

[tex]A' = (-4, -2.5)\\ \\B' = (1.5, 2.5)\\ \\C' = (-1, 5)[/tex]

The equation that can be used to find the value of x is (2.5x+1.5)4=36, and the value of x is 3.

The area of a rectangle is the product of its length and breadth. It is given by the formula,

Area of rectangle  =  Length × width

Given the length of the rectangle is 2.5x+1.5, while the width is 4. Also, it is mentioned in the question that the area of the rectangle is 36 square units. Therefore, we can write the area of the rectangle as,

[tex](2.5 x+1.5) \times 4 = 36\\\\(2.5 x \times 4) +(1.5\times 4) = 36\\\\10x + 6=36\\\\x = \dfrac{36-6}{10}\\\\x = 3[/tex]

Hence, the equation that can be used to find the value of x is (2.5x+1.5)4=36, and the value of x is 3.

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Answer:

720

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

6! = 6*5*4*3*2*1 = 720

Answer:

68

Step-by-step explanation:

As the date in the box plot ends at 68. it is the maximum value

Answer:

JK = 18

Step-by-step explanation:

LK = x - 1

KJ = x + 11

LJ = LK + KJ = x - 1 + x + 11

-> LJ = 2x + 10

LM = 12

By tangent secant segment theorem:

[tex]LK \times LJ = JM^2 \\ \\ \implies \: (x - 1)(2x + 10) = {(12)}^{2} \\ \\ \implies \: x (2x + 10) - 1(2x + 10) = 144\\ \\ \implies \: 2x^{2} + 10x - 2x - 10 - 144 = 0\\ \\ \implies \: 2x^{2} + 8x - 154 = 0\\ \\ \implies \: 2(x^{2} + 4x - 77) = 0\\ \\ \implies \: x^{2} + 4x - 77 = 0\\ \\ \implies \: x^{2} + 11x - 7x- 77 = 0\\ \\ \implies \: x(x + 11) - 7(x + 11) = 0\\ \\ \implies \: (x + 11) (x - 7) = 0 \\ \\ \implies \: (x + 11) = 0 \: \: or \: \: (x - 7) = 0 \\ \\ \implies \: x = - 11 \: \: or \: \: x = 7 \\ \\ x \: can \: not \: be \: negative \\ \implies \: x \neq \: - 11 \\ \\ \implies \: x = 7 \\ \\ \implies \: JK = x + 11 = 7 + 11 \\ \\ \implies \: \huge \: { \orange{JK =18}}[/tex]

Hope it helps you in your learning process.

Have a great day ahead.

Answer:

Question 3:

f(3) = (3,-8) this is because -2*-2=4*-2=-8.

Questions 4:

D. (1,7)

Answer:

Mean = 75

Median = 73.5

Mode = 95

Range = 36

Step-by-step explanation:

Given:

Sort:

To find:

Mean:

[tex]\displaystyle \large{\dfrac{1}{n}\sum_{i =1}^n x_i = \dfrac{x_1+x_2+x_3+...+x_n}{n}}[/tex]

Sum of all data divides by amount.

[tex]\displaystyle \large{\dfrac{59+60+70+77+89+95}{6}=\dfrac{450}{6}}\\\\\displaystyle \large{\therefore mean=75}[/tex]

Therefore, mean = 75

Median:

If it’s exact middle then that’s the median. However, if two data or values happen to be in middle:

[tex]\displaystyle \large{\dfrac{x_1+x_2}{2}}[/tex]

From 59,60,70,77,89,95, since 70 and 77 are in middle:

[tex]\displaystyle \large{\dfrac{70+77}{2} = \dfrac{147}{2}}\\\displaystyle \large{\therefore median = 73.5}[/tex]

Therefore, median = 73.5

Mode:

The highest value or/and the highest amount of data. Mode can have more than one.

From sorted data, there are no repetitive data nor same data. Consider the highest value:

Therefore, mode = 95

Range:

[tex]\displaystyle \large{x_{max}-x_{min}}[/tex] or highest value - lowest value

Thus:

[tex]\displaystyle \large{95-59 = 36}[/tex]

Therefore, range = 36

Answer:

7

Step-by-step explanation:

(a squared) plus (b squared) equals (c squared)

(6 squared) plus (4 squared) equals (c squared)

36+16=c squared

c equals 7

Answer:

7.21 blks

Step-by-step explanation:

Pythag theorem

a^2  + b^2 = c^2

6^2 + 4^2 = c^2

52 = c^2

c = sqrt 52 = 7.21 blcks

Answer:

(d + 3) would be 10

Step-by-step explanation:

Step 1:  Distribute

[tex]4.5(d + 3) = 45[/tex]

[tex](4.5 * d) + (4.5 * 3) = 45[/tex]

[tex]4.5d + 13.5 = 45[/tex]

Step 2:  Subtract 13.5 from both sides

[tex]4.5d + 13.5 - 13.5 = 45 - 13.5[/tex]

[tex]4.5d = 31.5[/tex]

Step 3:  Divide both sides by 4.5

[tex]\frac{4.5d}{4.5} = \frac{31.5}{4.5}[/tex]

[tex]d = 7[/tex]

Step 4:  Determine what (d+3) is

[tex](d + 3)[/tex]

[tex](7 + 3)[/tex]

[tex]10[/tex]

Answer: (d + 3) would be 10

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\boxed{\mathsf{4.5(d + 3) = 45}}\\\\\large\boxed{\mathsf{\rightarrow 4.5(d) + 4.5(3) = 45}}\\\\\large\boxed{\mathsf{\rightarrow 4.5d + 13.5 = 45}}\\\\\large\boxed{\textbf{SUBTRACT 13.5 to BOTH SIDES}}\\\\\large\boxed{\mathsf{4.5d + 13.5 - 13.5 = 45 - 13.5}}\\\\\large\boxed{\textbf{SIMPLIFY IT!}}\\\\\large\boxed{\mathsf{4.5d = 45 - 13.5}}\\\\\large\boxed{\mathsf{4.5d = 31.5}}\\\\\large\boxed{\textbf{DIVIDE 4.5 to BOTH SIDES}}\\\\\large\boxed{\mathsf{\dfrac{4.5d}{4.5}= \dfrac{31.5}{4.5}}}[/tex]

[tex]\large\boxed{\large\textbf{SIMPLIFY IT!}}\\\\\large\boxed{\mathsf{d = \dfrac{31.5}{4.5}}}\\\\\\\large\boxed{\mathsf{d = 7}}\\\\\\\huge\boxed{\textbf{Therefore, your answer is: \boxed{\mathsf{d = 7}}}}\huge\checkmark[/tex]

[tex]\mathsf{(d + 3)}\\\mathsf{= \bold{7} + 3}\\\mathsf{= 10}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

-13.75

Step-by-step explanation:

[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]

To find :-

More valuable packet of beans

Given :-

500g packet of beans = £114

125g packet of beans = £28

Solution :-

We will find out value of 100g of beans of each packet, then we will compare the value, the less will be the value, the more valuable packet is it.

Packet 1

500g of beans = £114

100g of beans

[tex] = \frac{114}{500} \times 100 \\ = \frac{114}{5} \\ = 22.8[/tex]

The 100g beans of packet 1 will cost £22.8.

Packet 2

125 g of beans = £28

100g of beans

[tex] = \frac{28}{125} \times 100 \\ = \frac{28}{5} \times 4 \\ = 5.6 \times 4 \\ = 22.4[/tex]

The 100g beans of packet 2 will cost £22.4.

Result :-

The packet 2, 125g for £28 is more valuable than packet 1, 500g for £114.

Answer:

the 125 gm packet

Step-by-step explanation:

Find the unit rate of each

1.14 /500 g = .00228  per gram

.28/128 g  = .0021875 per gram   <=====this is the better value  (costs less per gram)

The error which Loren made was C. she should have solved 149 = startfraction 19 over 9 endfraction (10) b for b.

This refers to those miscalculations or misjudgments about a situation or a mathematical solution to give wrong values.

Hence, because Loren is solving an equation of 0 = startfraction 19 over 9 endfraction (149) b for b to find the equation of a trend line that passes through the points (1, 130) and (10, 149), the error she made was option C.

This means that using point (10,149) which takes the form (x,y) the equation will be: 149=19/9(10)+b

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Answer:

C

Step-by-step explanation:

Answer:Nothing further can be done with this topic. Please check the expression.

Step-by-step explanation:

Answer:

The answer is C.

Step-by-step explanation:

3.844 X 10 w/ power of 5= 384400

2 X 10 w/ power of 3= 2000

2000 x 384400= 768800000

7.688 x 10 w/ power of 5 = 768800

Answer:

Jupiter to Sun = 7.688 * 10⁸km

Jupiter to Sun = 2 * 10³ times Earth to Moon

Substitute 3.844 * 10⁵km for Earth to Moon

Jupiter to Sun = 2 * 10³ *  3.844 * 10⁵km

Jupiter to Sun = 2 *  3.844 * 10³ * 10⁵km

Jupiter to Sun = 7.688 * 10³ * 10⁵km

Jupiter to Sun = 7.688 * 10⁸km

Therefore, the answer would be C. 7.688 * 10⁸km

Answer:

110 pages

Step-by-step explanation:

Let number of pages read on 1st day = x

-> No. of pages read on 2nd day = 2x

& No. of pages read on 3rd day = x - 6

Total no of pages read = 458

-> x + 2x + x - 6 = 458

-> 4x - 6 = 458

-> 4x = 458 + 6

-> 4x = 464

-> x = 464/4

-> x = 116

No of pages read on third day = x - 6 = 116 - 6 = 110

The space inside the steps will be 0.04 cubic meter

The space in a three dimensional region occupied by any body is called as volume.

Assume the steps have the dimensions shown in the diagram below.

We can decompose them into two rectangular prisms.

The lower prism has the dimensions 20 in × 16 in × 6 in.

The upper prism has the dimensions 20 in ×   8 in × 6 in.

1. Volume of lower prism

V = lwh = 20 in × 16 in × 6 in = 1920 in³

2. Volume of upper prism

V = lwh = 20 in × 8 in × 6 in = 960 in³

3. Volume of steps

V = 1920 in³ + 960 in³ = 2880 in³

Or the volume in meter will be 2880 cubic inches = 0.04 cubic meters.

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The statement "The slope of the linear regression line can be calculated using any two points in the data." is always true for any two points.

Linear regression shows the relationship between two variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable, and the other is considered to be a dependent variable.

A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable.

Firstly, as per difinition the equation of linear regression line is

y= a + bx, where b is the slope of the line and a is intercept .

The formula to calculate the slope of the line be,

[tex]b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2}) - (\sum x)^2 }[/tex]

here n represent the number of data given in a question, x and y are the two points.

If we look at the formula with point x and y the slope can't be calculated.

Also, the equation of linear regression line , y= a+ bx also contain two points (x, y).

As per the discussion it is not possible to calculate the slope of linear regression line without two points.

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Answer:

B. 0.14

Step-by-step explanation:

Just add the values in the eight row and truck coloum and divide by 200.

Answer:

16

Step-by-step explanation:

6 percent of 15= 0.9

0.9*18≈16

Answer:

Below in bold.

Step-by-step explanation:

588000 is close to 600000

6% of this = 600000 * 0.06

= 36,000 sq. miles.

Answer:

35,280 square miles

Step-by-step explanation:

Step-by-step explanation:

Volume = 1/3 × (10×8) × 6

= 160 in³

The equation he should you use to find the final number of moles of gas in the balloon after the deflation is n1/v1 = n2/v2

The molarity of a solution is the ratio of the mole of the substance to its volume

Since the mole "n" is directy proportional to the volume, hence;

n = kv
k = n/v

Hence the equation he should you use to find the final number of moles of gas in the balloon after the deflation is n1/v1 = n2/v2

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Answer:

answer in picture

Step-by-step explanation: