if 15% of adults in a certain country work from home, what is the probability that fewer than 60 out of a random sample of 500 adults will work from home?

The solutions to the given simultaneous equations as required in the task content are; (1.4, 9.2) and (-0.9, 2.3).

It follows from the task content that the solution to the simultaneous equations as given in the task content is to be determined.

Given: y = 3x + 5 and y = 4x² + x.

Therefore, since y = y; it follows that the equation which holds true is;

3x + 5 = 4x² + x

4x² - 2x - 5 = 0.

Therefore, the quadratic equation above can be solved for the values of x so that by approximation, we have;

x = 1.4 OR x = -0.9.

Therefore, the corresponding values of y are;

y = 3(1.4) + 5 = 9.2

OR

y = 3(-0.9) + 5 = 2.3

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Answer:

I do not see the original triangle, but you would take the original and move it one unit to the left and 5 units up.

Step-by-step explanation:

For example, if the three vertices (corners) of the triangle were points:

(0,0), (1,5) and (-2,3).

Point (0,0) would move to (-1, 5)  0-1 and 0+5

Point (1,5) would move to (0, 10)

Point (-2,3) would move to (-3, 8)

Answer:

To graph the image of the triangle after the transformation, we first need to have the coordinates of the vertices of the original triangle. Once we have those coordinates, we can apply the transformation to each vertex to obtain the coordinates of the corresponding vertex in the transformed image. Then, we can plot the three transformed vertices to obtain the image of the triangle.

Let's say the original triangle has vertices A, B, and C with coordinates A(x1, y1), B(x2, y2), and C(x3, y3), respectively.

To obtain the transformed coordinates of A, we apply the transformation rule (x, y) → (x - 1, y + 5) to the coordinates of A:

A' = (x1 - 1, y1 + 5)

Similarly, we can obtain the transformed coordinates of B and C:

B' = (x2 - 1, y2 + 5)

C' = (x3 - 1, y3 + 5)

Now that we have the transformed coordinates of the three vertices, we can plot them to obtain the image of the triangle.

Here's an example:

Suppose the original triangle has vertices A(2, 4), B(5, 6), and C(7, 3). Applying the transformation rule (x, y) → (x - 1, y + 5) to each vertex gives us:

A' = (2 - 1, 4 + 5) = (1, 9)

B' = (5 - 1, 6 + 5) = (4, 11)

C' = (7 - 1, 3 + 5) = (6, 8)

Plotting these three points gives us the image of the triangle after the transformation:

Before transformation:

B (5, 6)

/ \

/ \

A (2, 4) C (7, 3)

After transformation:

B' (4, 11)

/ \

/ \

A' (1, 9) C' (6, 8)

Here's what the image of the transformed triangle would look like on a graph:

|

|

C' | B'

|

---------|--------

|

A' |

|

The cost for 14 boxed lunches is $107.10.

From the information, the company orders 11 boxed lunches from a deli for $84.15. Therefore, we need to calculate the unit price and this will be:

= Total amount / Number of orders

= $84.15 / 11

= $7.65

Therefore, the value for 14 boxes will be:

= Unit price × Number of orders

= $7.65 × 14

= $107.1

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Answer:

1. 10

Step-by-step explanation:

1. 20% of 50

[tex] \frac{20}{100} \: \: \: \times \: \: \: 50 \\[/tex]

=

[tex] \frac{1000}{100} [/tex]

= 10

The number of months till Dan and Sydney would have paid the same amount for the high-speed Internet service is 6.12 months

Assuming the number of months is denoted as x, the total cost equation for Dan's provider would be:

= Installation cost + internet charge per month x number of months

= 60 + 42.95x

The total cost equation for Sydney's provider is:

= Installation cost + internet charge per month x number of months

= 0 + 52.75x

= 52.75x

To find the number of months till Dan and Sydney pay the same amount, equate the equations:
60 + 42.95x = 52.75x

52.75x - 42.95x = 60

9.8x = 60

x = 60 / 9.8

x = 6.12 months

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Answer:

11.725

Step-by-step explanation:

Add all the numbers together and divide it by how many numbers are in the set

The equation for the quadratic graphed is [tex]2x^{2}+4x+2[/tex].

Let the quadratic equation be [tex]y =a x^{2}+bx+c[/tex]

Points given in graph,

A(-1,0), B(-2,2), C(0,2)

Put the values in quadratic equation

For C(0,2)

[tex]2 =a(0)^{2}+b(0)+c[/tex]

[tex]2 = 0+0+c[/tex]

c = 2

For A(-1,0)

[tex]0 =a(-1)^{2}+b(-1)+2[/tex]

[tex]a-b+2 = 0[/tex]

a - b = -2              ...........(i)

For B(-2,2)

[tex]2 =a(-2)^{2}+b(-2)+2[/tex]

[tex]4a-2b+2=2[/tex]

2a - b = 0            ............(ii)

Solving eq (i) and (ii)

a = 2

b = 4

Putting the value of a, b and c in quadratic equation,

[tex]y =2x^{2}+4x+2[/tex]

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The window width in the blueprint is 1.5 in.

As per the given question-

A window in the room measures 2. 5 feet in width.

The given scale is-

Blue print (inches) : original (feet)

3 in : 5 ft

Divide both side by 2

1.5 in : 2.5 ft

Window's width in Blue print (inches) = 1.5 in.

As a result, the window width in the blueprint is 1.5 in.

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for an ordered pair (x comma y )in a relation, the x element represents the horizontal axis.

125° is the  angle of CBD

An angle pair that forms a straight line is referred to as a straight angle pair. This pair's sum of any two or more angles is always equal to 180°.

A straight angle has a 180° angle.

The two angles are from a straight line, and they sum to 180 degrees.

A + B + C = 180

8x -41+ 9x+17 = 180

Conjoin similar terms

17x -24 = 180

24 more on each side

17x -24+24 = 180 +24

17x = 204

multiply by 17

17x/17 = 204/17

x =12

We desire CBD angled.

CBD = 9x+17

= 9*12+17=108+17

= 125

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The converse statement is:

"If next month ends in the letter r, then this month is September."

And a counterexample of this is the month of September.

A conditional statement is of the form:

If P, then Q.

And a converse statement of the above one will be:

if Q, then P.

Here our conditional statement is:

"If this month is September, then next month ends in the letter r."

So we have:

P = this month is September.

Q = The next month ends in the letter r.

Replacing that in the converse statement formula we get:

"If next month ends in the letter r, then this month is September."

A counterexample is September, it ends with an r, and the month after it is not September.

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Answer:

If next month ends in the letter r, then this month is September. The converse is invalid; a counterexample is December.

Assume the account pays a nominal annual interest of r% compounded quarterly, the value of the interest rate (r) is equal to 7.87%.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r/n)^{nt}

Where:

Substituting the given parameters into the formula, we have;

1.6(3,818) = 3,818(1 + r/8)^{8 × 6}

1.6 = (1 + r/8)^{48}

Taking the 48th root of both sides of the equation, we have:

[tex]\sqrt[48]{1.6} = \sqrt[48]{(1 + \frac{r}{8} )^{48} }[/tex]

1.00983983823726 = 1 + 0.125r

0.125r = 1.00983983823726 - 1

0.125r = 0.00983983823726

Interest rate, r = 0.00983983823726/0.125

Interest rate, r = 0.0787

Interest rate, r = 7.87%

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Answer:

It would take them 13.5 days to raise enough money.

Step-by-step explanation:

In order to find the answer, you just have to take the amount of money they want to raise, which is $162, and divide it by the amount of money they save each day, or $12. In this case that would be dividing 162/12 giving you an answer of 13.5 days.

You started with a total of 28 muffins

From the question, the given parameters are:

Proportion carried away = 16 of the total muffins

Proportion carried away = 4/7 of the total muffins

The above parameters implies that

4/7 of the total muffins = 16

Represent the amount you started with x

So, we have the following representation

4/7 of x = 16

Express as products

4/7x = 16

Make x the subject

x = 7 * 16/4

Evaluate

x = 28

Hence, the total number of muffins is 28

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The overall budget the Mr Hollis has is $12800.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, Mr.Hollis determines that he gives away 800 each month and the fraction is 1/6 of his budget.

The value of the overall budget will be illustrated as x.

Therefore 1/16 × x = 800

x / 16 = 800

x = 16 × 800

x = 12800

Hollis has $12800 as budget.

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The value of function is positive so the function have maximum value 30 at x=3.

In the given question we have to find the maximum or the minimum value of a function.

The given function is

f(x) = -3x^2+18x+3

To find the maximum or minimum value we firstly find the value of f'(x).

f'(x) = -6x+18

Now put f'(x)=0

-6x+18=0

Subtract 18 on both side we get

-6x=-18

Divide by -6 on both side we get

x = 3

Now finding the value of function at x=3

f(3)= -3*(3)^2+18*3+3

f(3)= -3*9+54+3

f(3)= -27+54+3

f(3)= 30

Since the value of function is positive so the function have maximum value 30 at x=3.

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a) 90° counterclockwise about the origin

How can a rectangle be rotated?

A shape with rotational symmetry is a rectangle, for instance. When a rectangle is rotated around its center, the shape and placement remain unchanged. The placement of the specified points is the only distinction. Rectangles are of order 2 because they have half-turn symmetry.

When rectangle ABCD is rotated 90° counterclockwise about the origin , the vertex of 'A' in rectangle ABCD is (2,1) becomes (-1,2) in rectangle A'B'C'D'.

Therefore when rectangle ABCD is rotated we get rectangle A'B'C'D'.

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Answer:

       7 [tex]\frac{7}{8}[/tex]

Step-by-step explanation:

Multiply 3 1/2 by 2 1/4

Convert to improper fraction to make it simpler:

7/2 times 9/4 = 7 7/8 square millimeters.

Hope this helps :)

Answer:

Step-by-step explanation:

3.5 x 2.25 = 7.875 or 7 and 7/8

Answer:

it is d

Step-by-step explanation:

Answer: Down Below ↓

Step-by-step explanation: Here's an easy tip for measuring the angles of triangles. Every triangle has a sum (total) of 180 degrees. Take the two angles that are already shown, add them together, then subtract them from 180.

I cannot read the numbers on the paper, so I hope this answer somewhat helps.

Edit: Oh my lord, it's a coloring page too? I remember those, they suck. :')

Answer:

1/6

Step-by-step explanation:

y = -6x + 8

Perpendicular line would be the reciprocal of the slope

In 286 ways are there to distribute seven identical apples and six identical pears to three distinct people.

There are 7 identical apples and 6 identical pears.

So total number of fruits here = 7+6 = 13 identical fruits

The number of ways to distribute 13 fruits in three distinct people is given by [tex]=^{13}C_3=286[/tex] ways.

Hence the number of ways is 286.

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There is no graph in your question

Answer:

Step-by-step explanation:

You have two revenue relations and want the price of each adult and child ticket. 150 adult and 100 child tickets sold for $3087.50; 200 adult and 150 child tickets sold for $4287.50.

Each of the revenue relations can be formulated as an equation. If x and y represent the price of each adult and child ticket, respectively, then ...

  150x +100y = 3087.50

  200x +150y = 4287.50

The solution can be found many ways. A graphing calculator (first attachment) shows the solution to be ...

The calculator function that reduces a matrix to row-echelon form can be used on the augmented matrix of coefficients. That, too, gives the solution about as quickly as you can enter the coefficients. This is shown in the second attachment.

Subtracting twice the second equation from 3 times the first will eliminate the y-variable:

  3(150x +100y) -2(200x +150y) = 3(3087.50) -2(4287.50)

  50x = 687.50

  x = 13.75 . . . . . . divide by 50

From the second equation, ...

  y = (4287.50 -200(13.75))/150 = 1537.50/150

  y = 10.25

Answer:

64822

Step-by-step explanation:

Half-life model:

            [tex]P=P_o* \left(\frac{1}{2}\right)^{\frac{t}{D}}[/tex]

[tex]P_o[/tex] is the initial value, D is the time taken for the quantity to reduce half-life and t is the given time period.

       [tex]\sf P_o = 259,288 \ grams\\\\D = 1 \ hour\\\\t = 2 \ hours[/tex]

            [tex]P = 259,288*(\frac{1}{2})^\frac{2}{1}\\\\P = 259,288*(\frac{1}{2})^2\\\\P = 259,288*\frac{1}{4}\\\\P = 64822[/tex]

The graph has no vertex

The transformations from the parent function are

The graph represents the given parameter

As a general rule, the maximum or the minimum of a graph is the vertex

However, the graph has no maximum or minimum

This means that there is absence of a vertex in the graph

Here, we have:

This transformation can be represented as (x - 4, y - 2)

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The total number of students at library using part part whole model is 13.

What is part part whole model ?

  The idea that numbers may be divided into parts, often known as the part-whole model or part-part-whole reasoning, is one that can be used to the study of mathematics. The relationship between the entire number and its component components will be clear to children utilising this model, which will aid learners in connecting addition and subtraction.

Here Number of student who leave library = 6

Number of students who stay at library = 7

Here we have to take  Number of student who leave library as one part and Number of students who stay at library as another part . Then

Total number of students at library at start = 6+7 = 13.

The part part whole model like,

=>        Total = 13

Part=6              Part=7

Hence the Total number of students is 13.

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The probability that the next spin will land on red or green or purple is 75%

Given , A spinner is divided into five colored sections that are not of equal size

Color      Frequency

Red            18

Blue            11

Green          8

Yellow         4

Purple          19

Total spin recorded = 18+11+8+4+19

=60

Let "A" be the event when spinner land on Red , "B" be the event when spinner land on Green and "C" be the event when spinner land on Purple

P(A) = 18/60 = 0.3

P(B) = 8/60 = 0.134

P(C) = 19/60 = 0.32

Probability that the next spin will land on red or green or purple will be P(A∪BC) = P(A) + P(B) + P(C)

P(A∪BC)  = 0.3 + 0.134 + 0.32 =0.754

= 0.754 × 100 = 75%

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Step-by-step explanation:

2x - 27 + 3x + 27 = 180

5x = 180

x = 36

When the number of people is multiplied by 4, the number of pizzas is multiplied by 4.

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a proportional relationship can be modeled by the following mathematical expression:

y = kx

Where:

If the x-value is multiplied by 4, we have:

x = 5 × 4

x = 20

From the corresponding y-value for 20 is equal to 8 and as such the number of pizzas needed should be multiplied by 4, in order to produce an equivalent ratio.

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