**ANSWER :**

The answer is **5/33 or 0.15**

**EXPLANATION :**

From the problem, we have a total of 5 number of species.

Using the given Biodiversity Index formula :

[tex]\frac{\text{ total number of species}}{\text{ total number of individuals}}=\frac{5}{14+2+9+1+7}=\frac{5}{33}\quad or\quad0.1515[/tex]In a sample of 30000 first borne babies, 6 were found to have Down syndrome. Find the empirical probability thay a famili’s first child will be born with this sydrome

The **probability** that a family’s first child will be born with down syndrome **is** 1/5000

Number of **first borne** babies = 30000

Number of first borne babies having **Down syndrome** = 6

Probability is defined as the ratio of number of favorable outcomes to the total outcome.

Probability = (number of favorable outcomes)/(total outcome)

We have to find the probability that a family’s first child will be born with down syndrome. So, Number of first borne babies having Down syndrome is equal to the total number of** favorable outcomes **and Number of first borne babies will also be equal to **total outcome**. Hence we can write,

Probability = (number of favorable outcomes)/(total outcome)

Probability = 6/30000

Probability = 1/5000

So, the required **probability** is 1/5000.

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what function is represented in the table ?- y = 3 (4x )- y = 2 ( .25x )- y = 4 ( .25 ) x - y = 4 ( 3x )

[tex]y=4(0.25)^{x}[/tex]

**1) ** To determine which is the function from the table we need to attentively look for a constant factor in the y-column.

**2) **As we can see from this table, the factor we can tell that goes from 64 to 16 and then 4 is **1/4**. Or in decimal form **0.25**. So, we can tell the factor "b" is going to be 1/4 considering this model:

**3) **Let's pick one point (0,4) and plug it to find the other elements:

And finally, we can tell the function is:

[tex]undefined[/tex]A box of chocolates contains five milk chocolates and five dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. What is the probability that both pieces are milk chocolate?

**SOLUTION**

This is a probability question that has to do with the *"without replacement" *scenario, because every chocolate eaten *leaves the box and never returns*

*The probability that both pieces are milk chocolate is calculated thus:*

Number of milk chocolates = 5

NUmber of dark chocolates = 5

Total number of chocolates in the box = 5+5 =10

*The probability that both pieces are milk chocolate is:*

**The probability that both pieces are milk chocolate is: **

Use the slope formula to find the slope of the line through the points (−8,−6) and (0,−7).

**Answer:**

Slope formula is given as (y2-y1) ÷ (x2-x1) or (y1-y2) ÷ (x1-x2), where x and y are the coordinates of the points.

Slope = (-7-(-6)) ÷ (0-(-8))

= (-7+6) ÷ (0+8)

= -1/8

Write an equation of function g(x) and describe the effects on the graph of the parent function f(x)=x^2. g(x)=f(x)+d where d=2

Given:

a.) f(x) = x²

b.) g(x) = f(x) + d

c.) d = 2

To be able to complete the equation of function g(x), let's substitute the function of f(x) and d.

We get,

g(x) = f(x) + d

g(x) = x² + 2

Therefore, **g(x) = x² + 2**.

Which of the following is the correct mathematical expression for:

The difference between three times a number and 4

Answer:

3x - 4

Step-by-step explanation:

"Difference" is a clue word that tells you to use subtraction. The other clue word is "times" but that means times, or multiplication and is pretty straight forward.

"Three times a number" means to multiply a number, but we don't know the number, so we use a variable (a letter). I put x but you could use n or c or almost any letter for the variable.

"the difference of ___ and ___" means to subtract those two things.

So we get 3x - 4

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Question

On Friday, there were 6 snowboarders for every 2 skiers at a local ski resort. Or

Saturday, the ratio of the number of snowboarders to the number of skiers

was 5:3. There were 144 snowboarders at the ski resort on Friday. There were

same number of people at the ski resort on Saturday as there were on Friday

How many more skiers were there than snowboarders at the ski resort on

Saturday?

As calculated by the given **ratios**, 36 more skiers were there than snowboarders at the local resort on Saturday.

**What is ratio?**

A **ratio **illustrates how two or more values differ in terms of size.

**Ratios **can be displayed in a variety of ways, including as decimals (after dividing one value by the whole), percentages (after dividing one value by the entire), and using the ":" or "/" to separate values.

As given in the question,

Ratio of Snowboarders to Skiers

On Friday: ratio is 6:2

On Saturday: 5:3

Population = 144

Now, lets calculate the number of snowboarders and skiers at Saturday:

Given **ratio**: 5:3

total = 5+3

total = 8

No. of skiers is:

= (3/8)(144)

= 54

No. of snowboarders is:

= (5/8)(144)

= 90

Now lets calculate the difference between no. of snowboarders and skiers:

= 90-54

= 36

Hence, there are 36 more snowboarders than skiers.

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3/5 × 2/9 and 5/6 × 4/7 and 3/10 × 5/6 and 6/7 × 7/15

1

Step

Multiple both numerator and both denominator

[tex]\frac{3}{5}\text{ x }\frac{2}{9}\text{ = }\frac{3\text{ x 2}}{5\text{ x 9}}\text{ = }\frac{6}{45}\text{ = }\frac{2}{15}[/tex]2

[tex]\frac{5}{6}\text{ x }\frac{4}{7}\text{ = }\frac{5\text{ x 4}}{6\text{ x 7}}\text{ = }\frac{20}{42}\text{ = }\frac{10}{27}[/tex]3

[tex]\frac{3}{10}\text{ x }\frac{5}{6}\text{ = }\frac{3\text{ x 5}}{10\text{ x 6}}\text{ = }\frac{15}{60\text{ }}\text{ = }\frac{1}{4}[/tex]4

[tex]\frac{6}{7}\text{ x }\frac{7}{15}\text{ = }\frac{6\text{ x 7}}{7\text{ x 15}}\text{ = }\frac{42}{105}\text{ = }\frac{2}{5}[/tex]tod has 20 books he donated 2/5 how many books did he donate?

Given:

Total number of books is, *N* = 20.

Number of books donated is, *d = *2/5 of books.

The objective is to find the number of books donated.

Consider the number of books donated as *x*.

**Hence, the number of books donated is 8.**

PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!

YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!

1) [tex]VX=ZX, \angle XVY=\angle XZW[/tex] (given)

2) [tex]\angle X=\angle X[/tex] (reflexive property)

3) [tex]\triangle VXY \equiv \triangle ZXW[/tex] (ASA)

The hypotenuse of a right triangle is four times the length of one of the legs. The length of the other leg is sqrt(240) feet. Find the lengths of the leg and hypotenuse

**ANSWER**

**Hypotenuse: 16 ft**

**Leg: 4 ft**

**EXPLANATION**

**Given:**

A right angle triangle with only one leg = sqrt(240) feet

**Desired Outcomes:**

Lengths of the leg and hypotenuse

**Declaration of variables**

Let **x **represent the length of leg

Hypotenuse = 4 times the length of leg = **4x**

**Apply Pythagorean theorem**

Hypotenuse = 4x = 4 (4) = **16 ft**

**Hence, the Lengths of the leg and hypotenuse are 4 ft and 16 ft respectively.**

3.Justify each step of the solution by stating the name of the property that was used to get to each step.Given: Step 1: 1.________________________________Step 2: 2. _______________________________Step 3: 17x = 403. _______________________________Step 4: 4. _______________________________Answer:

We are given the following equation:

[tex]2(10-13x)+9x=-34x+60[/tex]In the first step we will use the distributive property on the left side:

[tex]20-26x+9x=-34x+60[/tex]In step 2, we will add like terms on the left side using associative properties of addition and subtraction and we will subtract 20 from both sides, we get:

[tex](20-20)+(-26x+9x)=-34x+(60-20)[/tex]Solving the operations we get:

[tex]-17x=-34x+40[/tex]In step 3 we will add 34x to both sides, this is the inverse additive inverse:

[tex](-17x+34x)=(-34x+34x)+40[/tex]Solving the operations:

[tex]17x=40[/tex]In step 4, we divide both sides by 17, this is the division property of equality:

[tex](\frac{17x}{17})=\frac{40}{17}[/tex]Solving the operations:

[tex]x=\frac{40}{17}[/tex]A number with an absolute value of 42 was divided by a number with an absolute value of 7 The quotient -6. Write two posibble numeric equations

**Answer: **

**-42/7 and 42/-7**

**Explanation:**

The absolute value of a number is represented by:

[tex]|x|[/tex]The lines represent absolute value of a number x, and what it does is that it **makes everything into a positive number.**

For example |-5|=5 and |5|=5, so we always have two options with an absolute value: that it comes from a negative number or that it comes from a positive number.

In this case we have that a number with an absolute value of 42 (it could be |-42|=42 or |42|=42) divided by a number with an absolute value of 7 (it could be |-7|=7 or |7|=7) the quotient is -6.

One possible numberic equation is:

[tex]\frac{-42}{7}=-6[/tex]Since this meets all the above conditions

Another possible numeric equation is:

[tex]\frac{42}{-7}=-6[/tex]Since this too meets all the above conditions.

A 20-foot ladder is leaning against the side of a house so that the bottom of the ladder is 12 feet from the base of the house. Will the ladder reach a window that is 14.5 feet above the ground?

Yes, because the ladder will reach 32 feet high

Yes, because the ladder will reach 16 feet high

No, because the ladder will only reach 16 feet high

No, because the ladder will only reach 12 feet high

Yes, because the **ladder **will **reach **16 feet high

The relationship between the **three sides **of a right-angled triangle is explained by the **Pythagoras theorem**, commonly known as the Pythagorean theorem.

According to the Pythagoras theorem, the **square **of the **hypotenuse **of a triangle, which has a straight angle of 90 degrees, **equals **the **sum **of the **squares **of the other **two sides**.

Given:

**Hypotenuse**= 20 feet

**base**= 12 feet

Using **Pythagoras theorem**

H²= P² + B²

20² =12² +P²

P²= 400-144

P²= 256

P= 16 FEET.

Hence, Yes, because the **ladder **will **reach **16 feet high

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helllpppppppppppppp.

**Answer:**

See below

**Step-by-step explanation:**

⦁ A room 12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square. Answer the following questions. Assume there is no waste in materials, and round off your answer to the next largest unit. Show both exact and rounded figures in the blanks provided.

The amount of **wall surface **in **square feet **is there to paint is: 364 square ft. While the **floor area **is 169.58sq ft. See the calculations below:

The **square foot **is an imperial measure of area and a customary unit of area in most countries. It is defined as the **area** of a square with **one**-**foot sides.**

The **calculation **for the above **solution **is given as:

**Step I** - Recall the Given Stats:

**Dimensions **of the room are:

12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square.

Let Lenght (l) = 13'9" = 13(9/12) ft = 13(3/4) = 55/4 ft.

Let Width(w) = 12'4" = 12(4/12) ft = 12(1/3)ft = 37/3 ft

Let Height h = 8'0" = 8ft.

Recall that we have a door with **dimensions **3' x 7' and two windows 4'x4'

**Step II ** - A) Surface area of the wall to be painted is:

Area of 4 walls less (area of door plus area of window)

Surface Area = 2LH + 2WH - ((3 x7) + 2(4x4))

= 2(l +w)h - (21 + 32)

= 2 ((55/4) + (37/3))8 -53

= 220 + 592/3 - 53

= 167 + 592

= (501+ 592)/3

= 1093/3

Hence,

The **Surface Area **to be **painted **is = **364.33 Sq ft.**

**Step III** - B) The **Area of the Floor **= Lx W

= (55/4) x (37/3)

= 2035/12

= 169.583333333

Hence,

**Area of the Floor is approximately = 169.58**

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**Full Question:**

A room 12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square.

Answer the following questions. Assume there is no waste in materials, and round off your answer to the next largest unit. Show both exact and rounded figures in the blanks provided.

A. How much wall surface in square feet is there to paint?

B. What is the floor area?

Enter the ratio as a fraction in lowest terms6 ft to 78 in.

To answer this question, we need to remember that a ratio is a comparison of two or more units. We can also need to have into account that these units must be in the same units.

We have one of the quantities is 6ft, the other is equal to 78 inches. We can convert 6ft to its equivalent in inches, or 78 inches into its equivalent in feet. Then, we have:

[tex]6ft\cdot\frac{12in}{1ft}=72in[/tex]Then, we can conclude that the ratio of 6feet (72 inches) to 78 inches is equivalent to:

[tex]\text{Ratio}=\frac{72in}{78in}=\frac{12}{13}\Rightarrow Ratio=\frac{12}{13}[/tex]Use fundamental identities to find the value. Step by step can u explain.

To answer this question, we will use the following diagram as reference:

To determine the tangent of θ, we have to find the value of x.

To find x, we use the Pythagorean theorem and get:

[tex]4^2=3^2+x^2.[/tex]Therefore:

[tex]x=\sqrt{4^2-3^2}=\sqrt[]{7}.[/tex]Therefore:

[tex]\tan \theta=\frac{3}{\sqrt[]{7}}.[/tex]**Answer:**

Maria is to weld a support for a 23-m conveyor so that it will operate at a 20 degree angle. What is the length of the support?

The **length** of the support when **Maria** is to weld a support for a 23-m conveyor is 7.87 m.

From the information, **Maria** is to weld a support for a 23-m conveyor so that it will operate at a **20 degree** angle.

Let AB = 23m

Let x = 20°

We can then use the sine rule to find the **length**. This will be illustrated thus:

Sin x = AC / AB

Sin 20° = AC / 23

AC = 23 × sin 20°

AC = 7.87

The **length** is 7.87m

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4-[x]=1 absolute value equation

**Answer: x=-3, x=3**

**Step-by-step explanation:**

**Answer:**

4-[x]=1

-4. -4

-[x]=-3

x=3

There are 36 students in s2a some of them usually bring their own lunch and the other buy lunch.if 1/5 of the students who usually bring their own lunch buy their lunch today , the ratio of the number of students bringing their own lunch to number of students buying lunch becomes 1:2. how many students are there who usually bring thier own lunch ?

The **no**. of students who usually **bring **their own **lunch **is 15.

The ratio is a **comparison **between two or more quantities in simplest form.

Given there are 36 **students **in an s2a class some of them **bring **their own lunch and the others **buy **their lunch.

Assuming **x **students bring their own lunch hence (**36 - x**) students buy their lunch.

(1/5)th of the student who brings their own lunch is (1/5)×x = (x/5).

∴ x - (x/5) : (36 - x) + (x/5) = 1 : 2. (The **reduced **students are **added **to the

other category).

4x/5 : 36 - 4x/5 = 1 : 2.

4x/5 : (180 - 4x)/5 = 1 : 2.

(4x/5)÷(180 - 4x)/5 = 1/2.

(4x/5)×5/(180 - 4x) = 1/2.

4x/(180 - 4x) = 1/2.

4x = (180 - 4x)/2.

8x = 180 - 4x.

12x = 180.

x = 15.

∴ 15 **students **usually bring their own lunch.

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A worker's salary increased from $750 to $900 per month. Which equation shows the increase of the worker's salary to the nearest percent?

[tex]A+\frac{x}{100}A=B[/tex]

where A is the first value, B the second value and x the percent

we can solve x

[tex]\begin{gathered} \frac{x}{100}A=B-A \\ x=\frac{100\times(B-A)}{A} \end{gathered}[/tex]this is the equation

and this is the percent:

[tex]\begin{gathered} x=\frac{100\times(900-750)}{750} \\ \\ x=20 \end{gathered}[/tex]the percent is 20%

Consider the function whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree. Is this a one-to-one function? Explain why or why not.

No, a **function** whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree is not a **one-to-one function**.

A **one-to-one function **is also referred to as an injective **function** and it can be defined as special type of **function** in which every element of the range is mapped to exactly a single element of its domain. This ultimately implies that, the output values (y-values) of a **one-to-one function **never repeat themselves.

Additionally, a **one-to-one function** maps distinct elements of its domain (y-values) to distinct elements of the range (x-values) and as such, it connotes the mapping of two (2) sets.

In this context, we can reasonably and logically deduce that this **function **is not a **one-to-one function **because it fails the horizontal line test as there could be the same temperature at different times of the day.

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Put the following equation of a line into slope-intercept form, simplifying all fractions.

4x-20y=-160

The **equation** of the **line **4x-20y = -160 in the **slope intercept **form is y = x/5 + 8 .

The equation of the line in **slope intercept** form is written as

y = mx + c ,

where m is the slope of the line , and c is the y intercept .

In the question ,

the equation of the line is given

**equation of line** is given as 4x-20y = -160

to convert the equation in **slope intercept** form , we rewrite it as

20y = 4x+160

dividing both sides by 20 ,

we get

20y/20 = 4x/20 + 160/20

y = x/5 + 8

hence ,the **slope intercept** form is y = x/5 + 8 , where 8 is the y intercept and 1/5 is the slope .

Therefore , the **equation** of the **line** 4x-20y = -160 in the **slope intercept** form is y = x/5 + 8 .

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Thomas invested $1498 at

6% Sumple interest per annum.

Calculate.

1) The interest, in dollars,

earned after six months

well, keeping in mind that a year has 12 months, that means 6 months is 6/12 of a year, so

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1498\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases} \\\\\\ I = (1498)(0.06)(\frac{1}{2}) \implies I = 44.94[/tex]

El área de un sector circular de un círculo con radio igual a 8cm y ángulo central igual a 56° es aproximadamente

The sectorial **area** of the circle is equal 31.3cm^2

The formula for the b of the **sector** of a circle is /360o (r2) where r is the radius of the circle and is the angle of the sector.

Area of a Sector of Circle = (θ/360º) × πr^2, where, θ is the sector angle subtended by the arc at the center, in degrees, and 'r' is the radius of the circle.

Data;

Radius - 8cmangle = 56 degreesThe area of the sector can be calculated using the formula given

[tex]A = \frac{\theta }{360} * \pi r^2[/tex]

Substituting the values into the formula;

[tex]A = \frac{\theta }{360} * \pi r^2\\A = \frac{56}{360}* \pi * 8^2\\A = 31.27cm\\A = 31.3cm^2[/tex]

The area is equal 31.3cm^2

Translation:

The area of a circular sector of a circle with radius equal to 8cm and central angle equal to 56 degrees.

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Name the segments in the figure below.Q R S ISelect all that apply.

**Answer**

**Options A, F, G, N**

**The line segments include**

**QR**

**QS**

**QT**

**RS**

**RT**

**ST**

**Note that the segments only have a dash on top of them and not an arrow.**

**Explanation**

A line segment is a region of a line bounded by two different endpoints and contains all the points on the line that are between the two endpoints.

From the attached image, we can see that there is a line with infinite length (the arrows at the two endpoints indicate that this line continues till infinity), has points **Q, R, S **and **T.**

**So, the line segments will be any space from one endpoint to another. They'll include**

**QR**

**QS**

**QT**

**RS**

**RT**

**ST**

**Note that the segments only have a dash on top of them and not an arrow.**

**Hope this Helps!!!**

The area of the floor of a square play pen is 6 square meters. What is the perimeter of the play pen? Approximate your answer by rounding to the nearest integer.

Help must be done in less than 10 minutes

**Answer:**

10 m

**Step-by-step explanation:**

Area of a square

[tex]A=s^2[/tex]

where s is the side length.

If the **area **of the floor is 6 m²:

[tex]\begin{aligned}A&=s^2\\\implies 6&=s^2\\\sqrt{6}&=\sqrt{s^2}\\s&=\sqrt{6}\end{aligned}[/tex]

Therefore, the **side length **of the **square **is √6 m.

Perimeter of a square

[tex]P=4s[/tex]

where s is the side length.

Substitute the found value for s into the **formula **to find the **perimeter**:

[tex]\begin{aligned}P&=4s\\\implies P&=4 \cdot \sqrt{6}\\P&=4 \sqrt{6}\\P&=9.79795897...\\ P&=10 \sf \;m\;(nearest\:integer)\end{aligned}[/tex]

Therefore, the **perimeter **is **10 m **to the nearest integer.

An anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. The results were as follows: 855 drankalcohol regularly, 657 smoked cigarettes, 192 used illegal drugs, 418 drank alcohol regularly and smoked cigarettes, 109 drank alcohol regularly and used illegal drugs,116 smoked cigarettes and used illegal drugs, 88 engaged in all three behaviors, and 251 engaged in none of these behaviors.Answer parts a, b, c, d, e, f, g for this question.

To solve the question, we will be using a Venn Diagram. Let's list down what's given first:

855 drank alcohol

657 smoked cigarettes

192 used illegal drugs

418 both drank alcohol and smoked cigarettes

109 drank alcohol and used illegal drugs

116 smoked cigarettes and used illegal drugs

88 engaged in all three

and 251 engaged in none of these

We will draw a Venn Diagram with 3 circles, one for each vice. Then we will start with the intersection of all three and the area outside of the circles (for those who do not engage in vices).

Because we know how many engaged in all 3 vices, we can deduct that number from those who belong to the intersection of 2 vices since they have already been counted in that too.

418 - 88 = 330 drank and smoked, but not used drugs

109 - 88 = 21 drank and used drugs, but not smoked

116 - 88 = 28 smoked and used drugs but not drank

Then, we subtract the numbers in each circle from the total for each vice.

855 - (330 + 88 + 21) = 416 drank only

657 - (330 + 88 + 28) = 211 smoked only

192 - (88 + 21 + 28) = 55 used drugs only

To find the total number of surveyed students, we just need to add all the numbers in the Venn Diagram.

416 + 330 + 88 + 21 + 211 + 28 + 55 + 251 = 1,400

Therefore, there were **1,400 students who were surveyed.**

May I please get help with this for I am confused and have tried many times to re-create the reflection of the triangle

We have to reflect the triangle across the y-axis.

If we have a point P = (x,y) and we reflect it across the y-axis, we will change the x-coordinate to its opposite value and and the y-coordinate is kept the same.

The image point then is P' = (-x,y).

Then, to reflect the triangle, we have to reflect the three vertices and then join the vertices.

We can then reflect the vertices as:

the tuition at a certain college was $29,694 last year and increased 5.6% from last year to the current year. how much is this year's tuition?
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Question 1 (1 point)Write the equation in slope intercept form13x 11y = 12Dont forget to transpose
a firewall can do which of the following? (choose all that apply.) a. screen traffic for viruses. b. determine what user is sending transmissions. c. filter traffic based on rules. d. provide a layer of protection for the network.
You are hiking a trail over multiple days. At the start of your hike, you decide that you need to hike at least 22 miles in the first 3 days, but can't hike more than 34 miles, as you'll pass into swampy terrain where camping won't be possible. You want to hike the same distance each day. Let x represent the number of miles you hike each day.