Suppose the following facts to be true: $\bullet$ The probability of a random kindergartener having chicken pox at any given time is $2\%$. $\bullet$ Among kindergarteners who have chicken pox, $75\%$ have red spots. $\bullet$ Among kindergarteners who do not have chicken pox, $1\%$ have red spots. Given that Sanjay, a kindergartener, has red spots, what is the probability that Sanjay has chicken pox? Enter your answer as a fraction in simplified form.

Answer:

4.625

Step-by-step explanation:

5/8 = 0.625

To find 5/8, simply divide it.

So 4 and 5/8

= 4.625

Answer:

[tex]x = 10[/tex]. In other words, there number of girls is [tex]10[/tex].

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

[tex]\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}[/tex].

Rewrite to obtain:

[tex]\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}[/tex].

For this question:

[tex]\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}[/tex].

[tex]\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}[/tex].

Therefore:

[tex]\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}[/tex].

On the other hand, there are [tex](15 + x)[/tex] boys and girls in total. Using the formula for average:

[tex]\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}[/tex].

From the question, this average should be equal to [tex]123[/tex]. In other words:

[tex]\displaystyle \frac{1875 + 120\, x}{15 + x} = 123[/tex].

Solve this equation for [tex]x[/tex] to obtain:

[tex]1875 + 120\, x= 123\, (15 + x)[/tex].

[tex](123 - 120)\, x = 1875 - 123 \times 15[/tex].

[tex]x = 10[/tex].

In other words, the number of girls here is [tex]10[/tex].

Answer:

[tex]\Huge \boxed{m=0}[/tex]

Step-by-step explanation:

[tex]m +5=-m-2-5m+7[/tex]

Adding m and 5m to both sides of the equation.

[tex]m +5+m+5m= -m-2-5m+7+m+5m[/tex]

Subtracting 5 from both sides of the equation.

[tex]m +5+m+5m-5=-2+7-5[/tex]

Combining like terms and simplifying.

[tex]7m=0[/tex]

Dividing both sides of the equation by 7.

[tex]m=0[/tex]

Answer:

m = 0

Step-by-step explanation:

m + 5 = - m - 2 -5m + 7

m + 5 = -m - 5m - 2 + 7

m + 5 = -6m + 5  (combine like terms)

m = 0

Answer:

  see below

Step-by-step explanation:

The four major arcs that include B will be the remainder of the circle after each minor arc is excluded.

Excluding minor arc AB, we have major arc BCA.

Excluding minor arc BC, we have major arc CDB.

Excluding minor arc CD, we have major arc DAC.

Excluding minor arc DA, we have major arc ABD.

Answer:

C.

Step-by-step explanation:

The sum of two sides have to be greater than than the third (Triangle Inequality Theorem). 24 is equal to 24, not greater.

Answer:

C. 24m cannot be the length of the third side

Step-by-step explanation:

the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

a = 12,  b = 12

c < a + b

c < 24

therefore based on the choices...

C. 24m cannot be the length of the third side.

Answer:

A

Step-by-step explanation:

X times x is x squared then x times - 2 is - 2x but 4 times x is 4x. So 4x plus - 2x is 2x. Then 4 times - 2 is - 8 put that all together you'll get x^+ 2+2x-8

Answer:

There are two simple rules to remember: When you multiply a negative number by a positive number then the product is always negative.

Step-by-step explanation:

Answer:

x = -5

Step-by-step explanation:

x + 4 = -1  (subtract -4 on each side)

(x + 4) + (-4) = -1 + (-4)

therefore,

x = -5

Answer:

B?

Step-by-step explanation:

2 are colored left to right, and 5 down

2/3 of the chart is taken up

Answer:

Hey there!

The correct answer would be C (Third one from the left).

The width is 2/5 (two out of five) and the length is 2/3 (two out of three)

Let me know if this helps :)

Answer:

Step-by-step explanation:

[tex]a^{m}*a^{n}= a^{m+n}\\\\\\(-3)^{5}*(-3)^{2}=(-3)^{5+2}=(-3)^{7}[/tex]

Answer:

[tex]\Huge \boxed{\mathrm{(-3)^7}}[/tex]

Step-by-step explanation:

[tex](-3)^5 \times (-3)^2[/tex]

When bases are same for exponents in multiplication, the exponents are added.

[tex]a^b \times a^c=a^{b+c}[/tex]

[tex](-3)^{5+2}[/tex]

Add the exponents.

[tex](-3)^7[/tex]

Answer:

-6

Step-by-step explanation:

We use PEMDAS to solve this,

so P stands for parentheses, so that's where we start.

We first, square the innermost parentheses with the exponent which is the E in PEMDAS, then then the outer parentheses

-12/3*(-8+16-6)+2

-12/3*(2)+2

Now we divide as in Division in PEMDAS.

-4*2+2

Now we multiply as in Multiplication in PEMDAS.

-8+2

Now we add as in A for Addition

-6

In PEMDAS, Multiplication doesn't always come before division, and same for addition and subtraction.

Answer:

P=25 q= -31

Step-by-step explanati

The value of p and q​ are 32 and 24. The relationship will be as p/q = 8/6.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The cost of an electrical gadget and the cost of a plumbing material were in the ratio 8:6 last year ,this year each cost was reduced by GHÇ 4.00 and their ratio changed to 7:5.

Make p the subject

p = 8q/6 ........equation 1

The year the price was reduced by 4

p - 4/q - 4 = 7/5

Cross multiplication;

5(p-4) = 7(q-4)

5p-20 = 7q-28

5p - 7q = -8 .......equation 2

Subtract 8q/6 for p in equation 1

5(8q/6) - 7q = -8

Multiply through by 6

40q - 42q = -48

-2q = -48

q = 24

Subtract 24 for q in equation 1

p = 8(24)/6

p = 192/6

p = 32

Therefore, the value of p and q​ are 32 and 24. The relationship will be as p/q = 8/6.

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Answer:

3q + 5

Step-by-step explanation:

Three times a number q is 3q, and 5 more than that is 3q + 5.

Answer:

A (0, 0).

Step-by-step explanation:

y = x

y = -x

Therefore x = -x.

x + x = 0

x = 0

and y = x = 0.

Answer:

Which ordered pair is a solution to the following linear system?

y = x

y = –x

(1, 1)

(0, 1)

(1, 0)

Correct Answer

(0, 0)

Step-by-step explanation:

just did this on a test.

Answer:

The age of brothers are 4 years and 2 years respectively.

Step-by-step explanation:

We are given that the ages of two brothers have a ratio of 2 to 1. When 4 years have passed, the ratio of their ages will be 8 to 6.

Let the age of the first brother be 'x years' and the age of the second brother be 'y years'.

So, according to the question;

                                      [tex]\frac{x}{y} =\frac{2}{1}[/tex]  

                                      [tex]x=2y[/tex]  -------------- [equation 1]

                                       [tex]\frac{x+4}{y+4}=\frac{8}{6}[/tex]

                               [tex]6({x+4})=8}(y+4)[/tex]

                               [tex]6x+24=8y+32[/tex]

                               [tex]6(2y)+24=8y+32[/tex]

                               [tex]12y-8y=32-24[/tex]

                                    [tex]4y=8[/tex]

                                     [tex]y=\frac{8}{4}[/tex] = 2 years

Putting the value of y in equation 1 we get;

                                     x = 2y

                                      x = [tex]2 \times 2[/tex] = 4 years

Hence, the age of brothers are 4 years and 2 years respectively.

Answer:

[tex]\huge\boxed{x=0}[/tex]

Step-by-step explanation:

[tex]x+1=1\\\\x+1-1=1-1\\\\\boxed{x=0}[/tex]

Answer:

156

Step-by-step explanation:

n times the constant of proportionality = a

so n will always 156 times greater

Answer:

Rs 253.13

Step-by-step explanation:

The item cost him x.

Selling at a profit of 20% means he sold it for 1.2x.

Selling at a loss of 12% means that he sold it for 0.88x.

1.2x - 81 = 0.88x

1.2x - 0.88x = 81

0.32x = 81

x = 253.13

Answer:

Step-by-step explanation:

Using the sine rule

Airplane A has

6 / sin 44 =

6 / 0.6947 =

8.64

Airplane B has.

6 / sin 40 =

6 / 0.6428 =

9.33

therefore, the answer is airplane B, because it was 9.33 miles away

Answer:

A. 39

Step-by-step explanation:

( 2 + 6 ) / 4 + 12 × 3 + 1

first solve the bracket .

8 / 4 + 12 × 3 + 1

then do the division or multiplication.

2 + 36 + 1

finally do the addition or subtraction.

39

The order

{

1. B - Bracket

2. O - Or

3. D - Division

M - Multiplication

4. A - Addition

S - Subtraction }

Answer:

Hello, thank you for your word problem. However, your word problem doesn't have a question to it. Please double check your answer. Thank you!

Step-by-step explanation:

Answer:

F' = (-6,3)

Distance = 12 units

Step-by-step explanation:

F is currently at (6,3).

Reflected over the y-axis, it would be at (-6,3).

That puts them 12 units apart.

Answer to the 1st part: [tex]6x^2+12xh+6h^2-2x-2h+1[/tex]

Answer to the 2nd part: [tex]12x+6h-2[/tex]

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

Work Shown:

Replace every x with (x+h). Expand and simplify

[tex]f(x) = 6x^2-2x+1\\\\f(x+h) = 6(x+h)^2-2(x+h)+1\\\\f(x+h) = 6(x^2+2xh+h^2)-2(x+h)+1\\\\f(x+h) = 6x^2+12xh+6h^2-2x-2h+1\\\\[/tex]

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

Subtract off f(x), then divide everything over h. Simplify.

[tex]f(x+h) = 6x^2+12xh+6h^2-2x-2h+1\\\\f(x+h)-f(x) = 6x^2+12xh+6h^2-2x-2h+1-(6x^2-2x+1)\\\\f(x+h)-f(x) = 6x^2+12xh+6h^2-2x-2h+1-6x^2+2x-1\\\\f(x+h)-f(x) = 12xh+6h^2-2h\\\\\frac{f(x+h)-f(x)}{h} = \frac{12xh+6h^2-2h}{h}\\\\\frac{f(x+h)-f(x)}{h} = \frac{h(12x+6h-2)}{h}\\\\\frac{f(x+h)-f(x)}{h} = 12x+6h-2\\\\[/tex]

The value of Function,  [tex]f (x + h) = 6x^2 + 6 h^2 + 12 x h - 2x -2h + 1[/tex]

And, The value of  [tex]\frac{f (x + h)- f(x)}{h} = 12 x + 6h -2[/tex].

Here, the function is given as,

[tex]f (x) = 6x^{2} -2x + 1[/tex]

What is function?

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

Now,

Replace every x with (x + h) and expand it,

   [tex]f (x) = 6x^{2} -2x + 1\\f (x+h) = 6(x+h)^{2} -2(x+h) + 1\\f (x+h) = 6 (x^{2} +h^{2} + 2xh) - 2x -2h +1\\f (x+h) = 6x^{2} +6h^{2} +12xh -2x-2h+1\\[/tex]

And,

[tex]f (x+h) - f(x) = ( 6x^{2} +6h^{2} +12xh -2x-2h+1) - (6x^{2} -2x+1)\\\frac{f (x+h) -f (x)}{h} =\frac{ ( 6x^{2} +6h^{2} +12xh -2x-2h+1) - (6x^{2} -2x+1)\\}{h} \\\frac{f (x+h) -f (x)}{h} =\frac{ 6x^{2} +6h^{2} +12xh -2x-2h+1 -6x^{2} +2x-1\\}{h} \\\\\frac{f (x+h) -f (x)}{h} =\frac{12xh +6h^{2}-2h }{h} \\\frac{f (x+h) -f (x)}{h} = 12x + 6h -2[/tex]

Hence,

The value of function [tex]f (x + h) = 6x^2 + 6 h^2 + 12 x h - 2x -2h + 1[/tex]

And, The value of  [tex]\frac{f (x + h)- f(x)}{h} = 12 x + 6h -2[/tex].

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Answer:

Step-by-step explanation:

What's missing from the original condition.

1000

1001

1002

=====

3003

So the answer is y - 3003

Answer:

0.19 = 19/100

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator

0.19=0.191

Multiply to remove 2 decimal placesy 102 = 100

0.19/1 × 100/100 = 19100

Conclusion

0.19=19100

Answer:

7

Step-by-step explanation:

5×0.4 = 2

2 + 5 = 7

The number a would be 7 which is 40% more than five more than a number a.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given the number that is 40% more than five more than a number a.

We need to find the unknown number a.

So, 40 % = 0.4

Let find the first part that is; "the number that is 40% more than five"

5 × 0.4 = 2

Now, five more than a number a.

2 + 5 = a

a = 7

Therefore, the number a would be 7 which is 40% more than five more than a number a.

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Answer:

Volume of a rectangular prism = x^3 - 4x^2

Step-by-step explanation:

V = L*W*H

Where,

V= Volume of a rectangular prism

L= Length

W= Width

H= height

Volume of a rectangular prism= Length × Width × Height

Let

length of the box = x

width = length

Width = x

Height= x - 4

Volume of a rectangular prism= Length × Width × Height

= x * x * (x - 4)

= x^2 * (x - 4)

= x^3 - 4x^2

Volume of a rectangular prism = x^3 - 4x^2

Answer:

A) 2 miles

Step-by-step explanation:

2)   In the figure the solid path indicates the usual path of a taxi cab. Unfortunately, there was construction and the taxi cab had to take the dotted route. If each tick mark represents one mile, how much longer was the detour than the regular route?  

A) 2 miles  

B) 3 miles  

C) 5 miles  

D) 11 miles  

Answer:

Step-by-step explanation:

the product of 3 and n in mathematics is 3n or 3 times n The product of a number and three" should be  3n

where n is the number.

IN the answer of the question you would have to explain something like this:

Let n be the number. The product then is  3n

The reason for this is that you could also let n stand for the number, in which case the answer would be 3n

.                                                                        

Answer:

See below.

Step-by-step explanation:

1)

So we have the equation:

[tex]2x+3y=1470[/tex]

To change into the slope-intercept form, we need to isolate the y-variable. Thus, subtract 2x from both sides:

[tex](2x+3y)-2x=(1470)-2x[/tex]

The left side cancels:

[tex]3y=1470-2x[/tex]

Now, divide both sides by 3. The left side cancels:

[tex](3y)/3=(-2x+1470)/3\\y=-\frac{2}{3} x+490[/tex]

The slope-intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

Thus, the slope is -2/3 and the y-intercept is 490.

2)

So, since we already know the y-intercept is 490, plot a point at (0,490).

The slope is too small to use. Thus, multiply the fraction by 100. It is now (-200/300). This means that we move down 200 for every 300 (recall that the slope means rise over run. Thus, we move down 200 for every 300 to the right). Thus, another possible point would be (0+300,490-200) or (300,290). Plot that. Then, connect them.

3)

To write in in function notation, simply substitute the y-variable for the function notation. Our independent variable here is x so we'll use that.

[tex]y=-\frac{2}{3}x+490\\ f(x)=-\frac{2}{3}x+490[/tex]

This means that for every x sandwiches made, there is f(x) wraps made for the total sum to be $1,470.

For example, if 105 sandwiches were made, then f(105)=-2/3(105)+490=420 wraps were made for the total profit to be $1,470.

4)

Please refer to the attached graph.

5)

First, since the total profit has now increased, the graph above and to the right of the old graph. This is because Sal needs to sell more sandwiches and wraps. Likewise, because of this, the x- and y-intercepts will also be different. Nevertheless, if converted into the slope-intercept equation, the slope will remain the same.

Answer:

Hey mate,these answers has been excluded from the NCERT syllabus.

Thank you

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