A 2010 study of 240 randomly-selected residents of a subtropical resort city with 82,000 residents found that 5.4% of them had been exposed to the mosquito-borne virus that causes Dengue fever. Suppose the actual percentage of people in the city who have been exposed to the virus is 3%. Let p^= the proportion of residents who have been exposed in a random sample of 240.
The standard deviation of p^ is approximately...

Answer:

sum of the interior angles=900°

Answer:

900°

Step-by-step explanation:

To find any shape sum of interior angles ,

we use the formula,

(n-2)180°, where n is the number of sides

So for heptagon,

n=7

using formula,

(7-2)180°

=> 5(180)

=> 900°

This is a case of Compound Interest.

It takes around 3.22 years for investment to grow to 1500$ from 1000$.

The interest charged on a loan or deposit is known as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

Annual amount, A=P(1+\(\frac{r}{n}\))∧nt

Given,

P=1000$

A=1500$

r=13%=0.13

A=P(1+\(\frac{r}{n}\))∧nt

n=2(Compounded semi-annually)

⇒1500=1000(1+\(\frac{0.13}{2}\))^2t

⇒\(\frac{1500}{1000}\)=(1.065)^2t

⇒1.5=(1.065)^2t

Taking log on both sides

㏒(1.5)=2t㏒(0.625)

⇒t=\(\frac{log(1.5)}{2log(0.625)}\)

⇒t=3.219years≈3.22years

This is a case of Compound Interest.

It takes around 3.22 years for investment to grow to 1500$ from 1000$.

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Answer:

\(length = l\\width = 5 + l\\Diagonal = 36\\diagonal^2 = (5+l)^2 + l^2\\36^2 = 25 + l^2 +10l + l^2\\1296 = 2l^2 +10l +25 \\2l^2 +10l=1271\\\\l_1=\frac{-10+2\sqrt{2567}}{2\cdot \:2},\:l_2=\frac{-10-2\sqrt{2567}}{2\cdot \:2}\)

\(l_1=\frac{-5+\sqrt{2567}}{2},\:l_2=\frac{-5-\sqrt{2567}}{2}\)

clearly,

      \(l_{2} \ is \ a \ negative\ number\)

So we consider

\(l_{1} =\frac{-5+\sqrt{2567}}{2} = 22.83\)

Therefore height = 22.8inches

Answer:

difference between 4 1/5 and 2 2/5 is 9/5 in simplest form.

Step-by-step explanation:

To find the difference between 4 1/5 and 2 2/5, we need to first convert the mixed numbers to fractions with a common denominator.

4 1/5 can be written as: 4 + 1/5 = (4 x 5 + 1) / 5 = 20/5 + 1/5 = 21/5

2 2/5 can be written as: 2 + 2/5 = (2 x 5 + 2) / 5 = 10/5 + 2/5 = 12/5

Now we can subtract: 21/5 - 12/5 = 9/5

So the difference between 4 1/5 and 2 2/5 is 9/5 in simplest form.

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The correct question is Find the difference between 4 1/5 - 2 2/5 and represent your answer in simplest form

Answer:

100+10n

Step-by-step explanation: a(10)

100+10(10)

100+100 = 200

Answer:

She will pay $13.20 altogether.

Step-by-step explanation:

1. 40% of 20 is 8.

Write 40% as 40/100.

40/100 of 20 = 40/100 × 20.

2. Sale Price = $12. This means the cost of the dress to Molly is $12. She will pay $12 for a dress with an original price of $20 when discounted 40%.

3. The 10% tax will be $1.20. When a store-issued coupon is redeemed, the sales tax is based on the discounted price (the cost of the item after the coupon is applied). So multiply 12 x 0.10 and you will get 1.20.

4. After tax is added to the sale price, she will pay $13.20.

12.00 + 1.20 = 13.20.

a) The linear function used to find the equipment rental fee is of: y = 9x + 20.

b) The cost for 6 hours of training is of: $74.

The linear function is defined considering it's slope-intercept format, given as follows:

y = mx + b.

The coefficients of the function are given as follows:

A soccer training camp charges $9.50 per hour for training, hence the slope is of:

m = 9.

The total fee for 12 hours of training was $128, hence the intercept b is obtained as follows:

128 = 9(12) + b

b = 128 - 108

b = 20.

Hence the function is defined as follows:

y = 9x + 20.

The cost for six hours of training is obtained as follows:

y = 9(6) + 20 = $54.

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1)

\((-2+\sqrt{-5})^2\implies (-2+\sqrt{-1\cdot 5})^2\implies (-2+\sqrt{-1}\sqrt{5})^2\implies (-2+i\sqrt{5})^2 \\\\\\ (-2+i\sqrt{5})(-2+i\sqrt{5})\implies +4-2i\sqrt{5}-2i\sqrt{5}+(i\sqrt{5})^2 \\\\\\ 4-4i\sqrt{5}+[i^2(\sqrt{5})^2]\implies 4-4i\sqrt{5}+[-1\cdot 5] \\\\\\ 4-4i\sqrt{5}-5\implies -1-4i\sqrt{5}\)

3)

let's recall that the conjugate of any pair a + b is simply the same pair with a different sign, namely a - b and the reverse is also true, let's also recall that i² = -1.

\(\cfrac{6-7i}{1-2i}\implies \stackrel{\textit{multiplying both sides by the denominator's conjugate}}{\cfrac{6-7i}{1-2i}\cdot \cfrac{1+2i}{1+2i}\implies \cfrac{(6-7i)(1+2i)}{\underset{\textit{difference of squares}}{(1-2i)(1+2i)}}} \\\\\\ \cfrac{(6-7i)(1+2i)}{1^2-(2i)^2}\implies \cfrac{6-12i-7i-14i^2}{1-(2^2i^2)}\implies \cfrac{6-19i-14(-1)}{1-[4(-1)]} \\\\\\ \cfrac{6-19i+14}{1-(-4)}\implies \cfrac{20-19i}{1+4}\implies \cfrac{20-19i}{5}\implies \cfrac{20}{5}-\cfrac{19i}{5}\implies 4-\cfrac{19i}{5}\)

Answer:

1) -1-4√(5)*i

2)(8/41)+(10/41)i

3)4+i

4)x=(1/3)±[√(23)/3]i OR x=(1/3)+[√(23)/3]i and x=(1/3)-[√(23)/3]i

Step-by-step explanation:

1) remember the special product:

(a+b)²=a²+2ab+b²

in this situation, a=-2 and b=√(-5)

(-2+√(-5))²=(-2)²+2(-2)(√(-5))+(√(-5))²

                =4-4*√(-5)+(-5)

                =-1-4√(-5)

√(-5)=-√(5)*i, so the final answer is: -1-4√(5)*i

2) remember the special product:

(a+b)(a-b)=a²-b²

multiply by the conjugate of the denominator (so multiply the numerator and denominator by 4+5i to remove i from the denominator, I'll demonstrate)

  2/(4-5i) * (4+5i)/(4+5i)

=2(4+5i)/[(4-5i)(4+5i)]

use the special product; in this situation, a=4 and b=5i

=(8+10i)/[16-(5i)²]

simplify: (5i)²=5²*(√(-1))²=25*-1=-25

(8+10i)/[16-(5i)²]=(8+10i)/[16-(-25)]

                        =(8+10i)/41

and finally, divide to get the answer in the correct form:

                        =(8/41)+(10/41)i

you can use a calculator to write 8/41 and 10/41 as decimals instead.

3) again, multiply by the conjugate of the denominator to both the top and the bottom:

 (6-7i)/(1-2i) * (1+2i)/(1+2i)

=(6-7i)(1+2i)/[(1-2i)(1+2i)]

now for the multiplication of the numerator:

(6-7i)(1+2i)=6(1+2i)-7i(1+2i)=(6+12i)-(7i+14i²)

i²=-1, so 14i²=-14

(6+12i)-(7i+14i²)=6+12i-7i-(-14)=6+5i+14=20+5i

as for the denominator, do what we did in 2) and use the special product to get:

(1-2i)(1+2i)=1-(2i)²=1-(-4)=5

so the answer is (20+5i)/5

now divide to convert the answer to the proper form/simplify

(20/5)+(5/5)i=4+i

4) use the quadratic formula, this is how you solve second-degree equations that aren't very easy to factor.

the formula: for ax^2+bx+c=0, x=[-b±√(b²-4ac)]/2a

in this case, a=4.5, b=-3, and c=12

plug in the values (± means that there are two solutions, one is when you add, and one is when you subtract.)

x=[-(-3)±√((-3)²-4*4.5*12)]/(2*4.5)

 =[3±√(9-216)]/9

 =[3±√(-207)]/9

√(-207)=√(207)*√(-1)=√(207)*i

√(207) can be simplified to 3√(23):

√(207)=√(9*23)=√(9)*√(23)=3√(23)

so now:

x=[3±3√(23)*i]/9

divide by 9 to get the answer in the correct form:

x=(3/9)±[(3√(23))/9]i

x=(1/3)±[√(23)/3]i

you can also rewrite this as x=(1/3)+[√(23)/3]i and x=(1/3)-[√(23)/3]i (just make sure to include both answers)

hopefully that helped! more practice will make these kinds of problems much easier :)

The possible perimeters are 140 feet, 148 feet and 160 feet.

In order to determine the width that would be used to determine the possible perimeters, the formula for the area would have to be rewritten.

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals that bisect each other at right angles.

Area of a rectangle = length x width

Width = area / length

1200 / 40 = 30 feet

1200 / 50 = 24 feet

1200 / 60 = 20 feet

Perimeter of a rectangle = 2 x (length + width)

Perimeter when width is 30 feet : 2(40 + 30) = 140 feet

Perimeter when width is 24 feet : 2(24 + 50) = 148 feet

Perimeter when width is 20 feet : 2 (20 + 60) = 160 feet

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Interest is a fee charged by a lender to a borrower for the use of money or credit, usually expressed as a percentage of the amount borrowed or invested over a period of time. Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.  The total interest earned after one year is $229

How much was in each account?

Let x be the amount invested in the first account that pays 3% interest, and let y be the amount invested in the second account that pays 8% interest. Since the total amount invested is $5800, we have:

\(x + y = 5800\)

The amount of interest earned on the first account is 0.03x, and the amount of interest earned on the second account is 0.08y. Since the total interest earned after one year is $229, we have:

\(0.03x + 0.08y = 229\)

We now have two equations with two unknowns:

\(x + y = 5800\)

\(0.03x + 0.08y = 229\)

We can solve for x and y by using elimination or substitution method. Here, we will use the substitution method.

Solve the first equation for x:

\(x = 5800 - y\)

Substitute this expression for x into the second equation and solve for y:

\(0.03(5800 - y) + 0.08y = 229\)

\(174 - 0.03y + 0.08y = 229\)

\(0.05y = 55\)

\(y = 1100\)

Now substitute this value of y into either equation to solve for x:

\(x + 1100 = 5800\)

\(x = 4700\)

Therefore, Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.

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The equation for w(width of rectangle) is: W = (P - 2L)/2

The correct answer is an option (c)

We know that the formula for the perimeter of the rectangle is:

P = 2L + 2W

where P is the perimeter of the rectangle,

L is the length of the rectangle,

and W is the width of the rectangle.

We need to rearrange this equation for w.

Consider equation,

P = 2L + 2W

P - 2L = 2L + 2W - 2L      ......(subtract 2L from each side of equation)

P - 2L = 2W

(P - 2L)/2 = 2W/2             .....(divide each side by 2)

W = (P - 2L)/2

Therefore, the correct answer is  W equals the quantity P minus 2 times L all over 2

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The complete question is:

Makayla is taking a math course and is working with the perimeter of rectangles. She knows the perimeter and length of her rectangle but wants to solve for the width. Rearrange the following equation for W, where P is the perimeter, L is the length, and W is the width of the rectangle. P = 2L + 2W.

a) W = 2P − 2L

b) W = P/ 2-2 times L

c) W equals the quantity P minus 2 times L all over 2

d) W = 2P + 2L

Answer:

c) W equals the quantity P minus 2 times L all over 2

Step-by-step explanation:i just took the test

The composite functions are given as;

(.f . g)(x) =  -x³ - x + 1  

(g . f)(x) =  -x³ - x - 1

A function can simply be described as a law, equation or rule that tends to express the relationship between variables in an expression

These variables are known as;

From the information given, we have that;

To determine the composite function (f . g)(x), substitute the value of x as g(x) in the function f(x)

(f . g)(x) = (-x)³ + (-x) + 1

expand the bracket

(f . g)(x) = -x³ - x + 1

To determine the composite function  (g . f)(x), we have;

(g . f)(x) = -  (x ³+ x +1 )

expand the bracket

(g . f)(x) = -x³ - x - 1

Hence, the functions are  -x³ - x + 1 and -x³ - x - 1

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For this problem we can use the definition of euclidean distance given by:

We have these coordinates:

And replacing we got:

And when we simplify we got:

And if we simplify we got:

The midpoint can be calculated with this formula:

And replacing we got:

Answer:

Option 2 or B

Step-by-step explanation:

B, if you look at the data table, you can notice that x and y are decreasing (therefore going down). I hope this helps?

The solution for the equation -2(2x + 5) - 3 = -3(x - 1) is x = - 16 which can be solved by the use the distributive property.

Distributive Property that when we multiply a number by a group of numbers that are added together, we can multiply each value in the group separately, then add the products of the multiplications.

-2(2x + 5) - 3 = -3(x - 1)

To solve this equation, we need to first use the distributive property to expand the left side of the equation.

We have:

-4x-10-3 = -3(x - 1)

-4x-13 = -3(x - 1)

Now, we can group the like terms on the left side and the right side of the equation.

On the left side, we have -4x - 13 and on the right side, we have -3x + 3.

-4x-13 = -3x + 3

To solve for x, we can add 3x to left side of the equation and add 13 to the right side.

This results in the equation:

-4x+ 3x  = 13 + 3

Now, we can add 3x with -4x of the equation to isolate the x-term.

We have:

-x = 16

x = - 16

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Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

We are given:                                                                                                        

Density of glass in g/cm³ = 2.5

Finding the density in kg/m³:                                                                              

In converting 2.5 g/cm³ to kg/m³, we will first convert the g to kg

Converting the g to kg:

2.5 g/cm³ * 1

Since 1kg = 1000g, 1kg/1000g = 1

2.5 g/cm³ * 1kg / 1000g

the g in the numerator and the denominator will cancel out and we will get:

2.5 kg / 1000 cm³

Converting the cm³ to m³:

We know that 1 m³ = 10⁶ cm³

So, 10⁶ cm³ / 1 m³ = 1

Multiplying the density by 1

2.5 kg / 10³ cm³   *   1

2.5 kg / 10³ cm³   *   10⁶ cm³ / 1 m³

the cm³ in the numerator and the denominator will cancel out

2.5 * 10⁶ kg / 10³ m³

2.5 * 10³ * 10³ kg / 10³ m³

2.5 * 10³ kg / m³

2500 kg/m³

Answer:

-2/12, -0.1, 1/9

Step-by-step explanation:

Answer:

Least to greatest: -2/12 , -0.1 , 1/9

Greatest to least: 1/9, -0.1, -2/12

Step-by-step explanation:

Change all of the numbers so that they are either fractions or decimals. Usually it is easier to change all the numbers to decimal.

Divide:

1/9 = ~0.111 (rounded)

-0.1 = -0.1

-2/12 = - ~0.167 (rounded)

Put the numbers in number order:

-~0.167 , -0.1 , ~0.111

-2/12 , -0.1 , 1/9

~

Answer:

Step-by-step explanation:

The answer is there are 450 chocolate bars in the large box because the small box has 25 chocolate bars and it is 18 small boxes in a large box so you will have the problem of 18 x 25= 450

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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Answer:

2

Step-by-step explanation:

1+1=2

Answer:

The volume of a right cylinder is equal to the 3 times of the volume of a right circular cone.

Step-by-step explanation:

Given that,

The volume of a right circular cone is 300 cubic inches

We need to find the volume of a  right cylinder that  has the same base and height as the cone.

Volume of a cone is given by :

\(V=\dfrac{1}{3}\pi r^2h\)

And volume of a cylinder is given by :

\(V'=\pi r'^2 h'\)

If the base and height of cone and cylinder are same, r=r' and h=h'

\(\dfrac{V}{V'}=\dfrac{1/3\pi r^2 h}{\pi r'^2h'}\\\\=\dfrac{1/3\pi r^2 h}{\pi r^2h}\\\\\dfrac{V}{V'}=\dfrac{1}{3}\\\\V'=3V\)

So, the volume of a right cylinder is equal to the 3 times of the volume of a right circular cone.

Answer:

b

Step-by-step explanation:

b is  correct.

The value of a triangular piece of land is, 1500 dollars.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We know that;

Area of triangular piece of land = 1/2 x  length x height

Here, Length = 20m

Height = 10m

Hence, We get;

Area = 1/2 x 20 x 10

       = 100 cm²

Since, The land is 15 dollar per square meter.

Hence, The total value is,

Value = 15dollars x 100

         = 1,500 dollars

Thus, The value of a triangular piece of land is, 1500 dollars.

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