maths enlargements calculations of lines in shapes help pls

Answer: The probability of 60% or less scared speechless out of a group of 50 customers (i.e. 30 customers) is 0.0932% or 0.000932.

Step-by-step explanation: Given problem meets all criteria for application of a binomial distribution with the probability of success; p=0.8 or 80% (which makes probability of failure; q=0.2 or 20%) and the total number of trials; n=50.

Let probability of 30 or less people scared (30 is 60% of 50 people) be P(x≤30), where x≤30 encapsulates all possibilities from 0 to 30 people scared speechless.

Then, by binomial distribution,

P(x≤30) =r=030nCr*pr*q(n-r)

Now we can substitute given values and find the desired probability,

P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)(50-r)

P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)-r*(0.2)50

P(x≤30) =(0.2)50*r=03050!(50-r)!r!*(0.8)r*(0.2)-r

P(x≤30) =(0.2)50*r=03050!(50-r)!r!*4r

The first value on the right hand side of equation is a very small number while the summation factor on second is a relatively larger number.

P(x≤30) = 0.000932

Thus, there is a 0.09% chance of 30 or less people scared speechless out of a group of 50.

Learn more about binomial distribution probability here https://brainly.com/question/24756209

#SPJ4

36×(35)-1000=1260-1000=260

The solution for x in the equation given as 3/2 (4x – 1) – 3x = 54 –(x + 2) is 13.375

From the question, the algebraic expression is given as

3/2 (4x – 1) – 3x = 54 –(x + 2)

There is no constant to multiply or divide in the expression

3/2 (4x – 1) – 3x = 54 –(x + 2)

Open the brackets

So, we have

6x – 3/2 - 3x = 54  - x - 2

Collect the like term in the above equation

This gives

6x - 3x + x = 54 - 2 + 3/2

Evaluate the like term in the above equation

So, we have the following representation

4x = 53.5

Divide through by 4

x = 13.375

The above equation cannot be solved further

Hence, the solution is x = 13.375

Read more about equations at

https://brainly.com/question/2476251

#SPJ1

Answer:

0.000065 km

Step-by-step explanation:

To get from cm to km you need to divide 6.5 by 0.000001 which equals 0.000065km

Betsie should buy the 250 envelopes from the shop Letter2go.

As, 250 envelopes will cost £31.9 in Shop Letter2go whereas will cost £33.17 in Shop Value World.

Given, that Betsie is going to buy 250 envelopes.

the cost of envelopes in two shops:

Value World:

Pack of 10 envelopes for £1.99

Buy 2 packs get 1 pack free

Letters2go:

Pack of 25 envelopes for £3.19

Now, if we see the cost of envelopes in shop 1 i.e. Value World

Cost of Pack of 10 envelopes = £1.99

Also, 1 pack is free for 2 packs

1 pack = £1.99

2 packs = 2×£1.99 = £3.98

Also, with 2 packs Betsie get 1 pack free

so, Betsie gets 3 packs for £3.98.

1 pack = 10 envelopes

3 packs = 30 envelopes.

Hence, In shop Value World:

30 envelopes = £3.98

1 envelope = £3.98/30

250 envelopes = (3.98/30)×250

So, 250 envelopes will cost £33.17 in Shop Value World.

And in shop Letter2go:

25 envelopes = £3.19

1 envelope = £3.19/25

250 envelopes = (3.19/25)×250

So, 250 envelopes will cost £31.9 in Shop Letter2go.

Hence, 250 envelopes will cost £33.17 in Shop Value World and £31.9 in Shop Letter2go.

So, Betsie should buy the 250 envelopes from the shop Letter2go.

Learn more about Unitary Method here https://brainly.com/question/23423168

#SPJ1

The equation of the line that is parallel to the line y = -x + 10 is y = -x - 13.

Given table:

x            y

0           10

4           6

8           2

12         -2

slope m = 6 - 10 / 4 - 0

= -4/4

m = -1

substitute in y=mx+c

y = -x+c passes through (0,10)

10 = -0 + c

c = 10.

y = -x + 10.

here m = -1 and passes through (-3,-10)

y = mx +c

-10 = -1(-3)+c

-10 = 3 + c

c = -13

y = -x + (-13)

y = -x - 13.

Therefore the equation of the line that is parallel to the line y = -x + 10 is y = -x - 13.

Learn more about the equation of the line here:

https://brainly.com/question/21511618

#SPJ1

Answers:

1st box:  0

2nd box:  67

===============================================

Explanation:

The y intercept always occurs when x = 0. This is when the function curve either crosses or touches the vertical y axis. Therefore, the y intercept is when the student studies 0 hours

Plug x = 0 into the equation

y = 2.7x + 67

y = 2.7*0 + 67

y = 67

Or you can note that the equation is of the form y = mx+b

The y-intercept of 67 tells us that the person studying for 0 hours is estimated to get a score of 67

Step-by-step explanation:

so basically, because Painting C costs £368 and Painting B is half that cost, Painting B costs £184. And Painting A is three times that amount Painting A costs £552.

You're Welcome ♡.

Answer:

74 square yards

Step-by-step explanation:

Area of rectangular garden:

                 l = 20 yds

                 w = 15 yds

     Area of the rectangular garden = l *w

                                                          = 20 * 15

                                                          = 300 square yards.

Area of the outer rectangle (rectangular garden and the sidewalk):

             length = 20 + 1 + 1 = 22 yds

            width   = 15 + 1 + 1  = 17 yds

       Area of outer rectangle = 22 * 17

                                               = 374 square yards

To find the area of the sidewalk, subtract the area of rectangular garden from the outer rectangle.

Area of the sidewalk = area of outer rectangle - area of sidewalk

                                  = 374 - 300

                                  = 74 square yards

The solution of the equation given as -13x + x = 8x - 20x is infinite many solutions

From the question, the equation is given as

-13x + x = 8x - 20x

To start with, we need to rewrite the expression

So, we have the following representation

x - 13x = 8x - 20x

Solving further, we need to evaluate the like terms

So, we have the following equation

-12x = 8x - 20x

Evaluate the like terms again

So, the equation becomes

-12x = -12x

Both sides of the above equation are the same

i.e. -12x is on both sides of the equation

When we have a solution that all sides of the equation have the same value, then the solution is that the equation has infinite many solutions

Hence, -13x + x = 8x - 20x has infinite solutions

Read more about equations at

https://brainly.com/question/2476251

#SPJ1

Answer:

Vertex: (2, -1)

Axis of Symmetry: x=2

Parabola: Downwards

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

48 = x + 8 + 2x + x

    48 = 4x + 8

   -8           -8

40 = 4x

divide both sides by 4

10 = x or x =10

The value of PQ is 43.

What is an isosceles triangle?

A triangle with at least two equal-length sides is known as an isosceles triangle in geometry.

From the figure,

PQ=3x+10, QR=5x-12

Given that, PQ=QR

So, 3x+10=5x-12

Find x:

3x+10=5x-12

Separate variable terms and constants

5x-3x=10+12

2x=22

x=22/2=11

we have PQ=3x+10=3(11)+10=33+10=43

So, PQ=43

To learn more about the isosceles triangle from the given link

https://brainly.com/question/28226565

#SPJ1

The order of the rational numbers from the least to greatest is   [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 <  [tex]7\frac{3}{4}[/tex]  .

in the question ,

it is given that the rational numbers are -7.3, [tex]7\frac{3}{4}[/tex], 7.23, [tex]-7\frac{2}{3}[/tex] .

we have to arrange the rational numbers in order from least to greatest .

For arrangement we first convert all the rational numbers in decimal form .

the decimal form of the given rational numbers are as follows .

(i) -7.3 is already given in decimal form .

(ii) [tex]7\frac{3}{4}[/tex] = (7*4+3)/4 = (28+3)/4 = 31/4 = 7.75

(iii) 7.23 is already in decimal form .

(iv) [tex]-7\frac{2}{3}[/tex] = -(7*3+2)/3 = -23/3 = -7.666

the order is -7.666 < -7.3 < 7.23 < 7.75

which is   [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 <  [tex]7\frac{3}{4}[/tex]

Therefore , The order of the rational numbers from the least to greatest is    [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 <  [tex]7\frac{3}{4}[/tex] .

The given question is incomplete , the complete question is

Order the following rational numbers from least to greatest.

-7.3, [tex]7\frac{3}{4}[/tex], 7.23, [tex]-7\frac{2}{3}[/tex]   .

Learn more about Order here

https://brainly.com/question/28820570

#SPJ1

The minimum amount of fence needed to enclose the lots is 120ft.

Adding areas of both fields, the combined area comes about to be 600sq ft.

The dimensions of the new plot are x length and y breadth. According to the question, there is a fence in the middle with y breadth.

g(x, y, z) = xy - 600

g(x, y, z) = 2x + 3y

∇g = ∇ (xy - 600) = (y, x)

∇f = ∇(2x + 3y) = (2, 3)

Now from the Lagrange method,

∇f = λ∇g

2 = λy

3 = λx

Now to get the value of lambda,

(2/y) = (3/x) = λ

x = 1.5y

Solving now we get,

1.5y² = 600

y = 20

x = 1.5 × 20 = 30

Thus after getting (x,y) we can put the value in the function to get the answer as 120ft.

To learn more about Lagrange multipliers,

https://brainly.com/question/4609414

#SPJ4

The correct statements are,

(1) The equation 2n = p should be 2p = n.

(2) The actual cost of the onions is $3.00 per pound.

(3) Potatoes cost $1.50 per pound.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Mr. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as much as potatoes.

The equation will be formed as,

6p + 3n = 18

n = 2p

Substitute the value of n = 2p in the equation,

6p + 3(2p) = 18

6p + 6p = 18

12p = 18

p = $1.5

The cost of an onion is,

n = 2p

n = 1.5 x 2

n = $3

To know more about an expression follow

https://brainly.com/question/11884798

#SPJ1

Answer:

s is the price of each laptop that gives maximum profit

p is the maximum total profit that can be made.

Step-by-step explanation:

See the attached worksheet for additional explanation.  The question asks for the meaning of s (selling price) and p (total profits) at the vertex of the curve.  s is in units of price/laptop, while p is in units of total profits.  Implicit in this graph is a demand curve (not shown) that illustrates how demand for laptops changes as the price changes.  Also not shown, but assumed, is that if the laptops are sold at a low price,  the declining profit margins resuce the overall total profits.  This graph incorporates the cost and demand imformation in a manner that provides a condensed view of the more important variable:  total profits.

Answer:

8

Step-by-step explanation:

Put the numbers in order from lowest to highest. Add all the numbers together. We will ignore a for this step. You should get 34 when adding it all together. Then if you were to add 8 to that 34 you'd get 42. Divide 42 by the amount of numbers you have which is 7. Your answer is 6. Now to make sure 8 is our value. We want to make sure the median is also 6. to find the median you need to have the numbers in order for lowest to highest and find the number in the middle. Don't forget to add your new number 8 into that order. You should get 6 as the median. Therefore our answer is 8

Answer:

d

Step-by-step explanation:

Because answer would be 4/10 or 5/10

The 3 in the equation is the starting point

Function given:

h(t) = −4.5t2 + 19.6t + 3

At t =0 we get h(0) = 3. This is called the y-intercept

It is the start point indicating the disc was thrown at 3 feet of height.

Using the common convention in geometry the horizontal axis in a graph in represented by the x-axis and the vertical axis in a graph is represented by the y-axis. The intercepts are the points on the graph at which the graph crosses the two axes. The point where the graph is drawn crosses the horizontal axis is called the x-intercept or the x-axis, and when the graph crosses the vertical axis is called as the y-intercept or the y-axis.

I hope this answer helps.

To learn more about intercepts,

https://brainly.com/question/14180189

There is a 1/3 chance that random variable will have a value higher than 5.

For the variable t, which follows uniform probability distribution.

0 ≤ t ≤ 8

Total variables = 9.

For the probability of value greater than 5 for the random variable.

P(t > 5) = P(t = 6) + P(t = 7) + P(t = 8)

P(t > 5) = 1/9 + 1/9 + 1/9

P(t > 5) = 3/9

P(t > 5) = 1/3

Thus, there is a 1/3 chance that random variable will have a value higher than 5.

To know more about the random variable, here

https://brainly.com/question/18119965

#SPJ4

Answer:

113

Step-by-step explanation:

Finding a remainder seems like you should be dividing. Remember everything is a shortcut for something else in math. So first you learn Long Division, but that's too much writing, so then you learn Synthetic Division, but there's an even shorter shortcut. It is called Remainder Theorem. If you just substitute 3 (because x-3 in the question) into the function, and you calculate it, you get the remainder.

f(x) = 4x^3 + 5

f(3) = 4(3)^3 + 5

f(3) = 4(27) + 5

= 108 + 5

= 113

See image.

Step-by-step explanation:

we switch the like terms across the equation and when we do that we change the signs

Answer:

[tex] \frac{1}{6} {x}^{3} y + \frac{5}{6} x {y}^{2} \\ \frac{1}{6} xy( {x}^{2} + 5y)[/tex]

option 3 is correct

The value of a=2 and b= 4.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

a + 1 / b-1 = 5/1 and a-1/ b+ 1 = 1/1

So, a + 1 / b-1 = 5/1

now, cross multiplying

a+ 1 = 5b - 5

a- 5b = -6............(1)

Also, a-1/ b+ 1 = 1/1

a-1 = b + 1

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

solving Equation (1) and (2) , we get

2+ b - 5b= -6

-4b = -8

b= 2

and, a = 2 + 2 = 4

Learn more about Equation here:

https://brainly.com/question/10413253

#SPJ1

The population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

All these elements are taken into account when formulating the population growth formula.

r = [(b + i) - (d + e)]/1000

Put the values in the formula.

r =  [(2,000 + 100) - (500 + 200)]/1000

r = 2100 - 700/ 1000

r = 1.4

Thus, the population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

To know more about the population growth rate, here

https://brainly.com/question/14174002

#SPJ4

Answer:I am not fully going to do it for you, but here is the best way i can explain, it if not i am sorry.

Step-by-step explanation: Simply take the sales price minus the unit cost, and divide that number by the unit cost. Then, multiply by 100 to determine the markup percentage. For example, if your product costs $50 to make and the selling price is $75, then the markup percentage would be 50%: ( $75 – $50) / $50 = . 50 x 100 = 50%.

Answer:

10) 6

11) 18

12) 7.1

13) 1.3

Step-by-step explanation:

all you have to do is substitute

10 - 4 = 6

12 + 6 = 18

1.9 + 5.2 = 7.1

3.4 - 2.1 = 1.3

The polynomial function which has a leading coefficient 1 is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))

Given that a polynomial function has leading coefficient 1 and roots (7+i) and (5-i) with multiplicity 1.

We want to find the polynomial function.

As we know that the complex conjugate properties of the roots of a polynomial states that if a+bi is a root of a polynomial then their complex conjugate a-bi is also a root.

So, according to this property (7-i) and (5+i) with multiplicity 1 is also a root of polynomial.

Thus, all the roots are x=7+i, x=7-i, x=5+i and x=5-i

So, the polynomial is f(x)=(x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i))

Hence, the polynomial function which has a leading coefficient 1 and roots (7+i) and (5-i) is (x-(7+i))(x-(5-i))(x-(7-i))(x-(5+i)).

Learn more about the polynomial function from here brainly.com/question/12701202

#SPJ9