Nate rides his bike to school every day. From his home he rides 2.5 miles north, and then six miles west. If a straight line is drawn from Nate's house to the school, find the distance between these two locations.

Answers

Answer 1

use Pythagorean Theorem

2.5^2 + 6^2 = x^2

6.25 +36 = 42.25

x= sqrt(42.25) = 6.5 miles

Answer 2

By the Pythagorean Theorem, the length of the hypotenuse of a right triangle is equal to the sum of the side lengths squared, mathematically:

h^2=x^2+y^2

h^2=6^2+2.5^2

h^2=36+6.25

h^2=42.25

h=√(42.25) miles

h=6.5 miles

Related Questions

Calculating the return on investment using financial leverage. suppose Dave invested only 20,000 of his own money and borrowed 180,000 interest-free from his rich father. what was his return on investment?

Answers

His return on investment (ROI) is based solely on money from his pocket.
If the profit is x dollars, the ROI is x/20000. Here Dave levered 10:1 with the help of his father.
If he had invested totally with his own money, the ROI would be x/200000, a much less impressive number even though the profit is the same.

Write an appropriate inverse variation equation if y = 9 when x = 3.

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \begin{cases} y=9\\ x=3 \end{cases}\implies 9=k3\implies \cfrac{9}{3}=k\implies \boxed{3=k} \\\\\\ thus\qquad y=3x[/tex]

IHELP ME OUT WITH THIS MATH QUESTION
f DE is a mid segment of the triangle, then the measure of AC:

7.5
15.
30.
None of the choices are correct.

Answers

The mid segment of the triangle is always // to the base and is equal to half this base, then

DE = (AC)/2

15 = (AC/2) → AC = 30 (3rd answer)

A cone shaped funnel has a radius of 3 inches and a height of 7 inches.

Betty closes the nozzle of the funnel and fills it completely with a liquid. She then opens the nozzle. If the liquid drips at the rate of 14 cubic inches per minute, how long will it take for all the liquid in the funnel to pass through the nozzle? (Use π = 3.14.)

A) 4.71 minutes

B) 3.14 minutes

C) 14.13 minutes

D) 9.42 minutes

Answers

V=Pi*r^2*h
= Pi(3*3)*7/3 = 4.71
Answer A

Answer:

Hence, it will take 4.71 minutes for all the liquid in the funnel to pass through the nozzle.

Step-by-step explanation:

A cone shaped funnel has a radius(r) of 3 inches and a height(h) of 7 inches.

Now, the volume(V) of the cone is given as:

[tex]V=\dfrac{1}{3}\times (\pi r^2h)[/tex]

Hence, on putting the value of r and h in the formula of volume we obtain the volume of cone funnel as:

[tex]V=\dfrac{1}{3}\times (3.14\times (3)^2\times 7)\\\\\\V=\dfrac{1}{3}\times (197.82)\\\\V=65.94 \ in^3[/tex]

If the liquid drips at the rate of 14 cubic inches per minute.

i.e. for 14 cubic inches it takes 1 minutes.

Now for 1 cubic inches it will take:

[tex]\dfrac{1}{14} \ min.[/tex]

Hence, for all the liquid ( i.e. 65.94 cubic inches) to pass the nozzle is the time taken is:

[tex]\dfrac{65.94}{14}\ min.\\\\=4.71\ min.[/tex]

Hence, it will take 4.71 minutes for all the liquid in the funnel to pass through the nozzle.

If a squared + b -c÷m, if a=6 ,b = 8, c=5 and m =3

Answers

6^2+8-5/3
Pemdas dictates that exponents go first.
36+8-5/3
Then evaluate the division.
36+8-(5/3)
Then add and subtract going from left to right.
36+8=44
44-(5/3)= 42 1/3

Henry Devine bought a new dishwasher for$320 he paid $20 down and made 10 monthly payments of $34 what actually yearly rate did Henry pay

Answers

First we need to find the amount financed, total payments and total interest

Amount financed
320-20=300

Total payments
34×10=340

Total interest=total payments-amount financed
Total interest=340-300=40

Now to find the yearly interest rate use the formula of
I=(2yc)÷(m×(n+1))
I ?
Y number of months in a year 12
C total interest 40
M amount financed 300
N number of payments 10
I=(2×12×40)÷(300×(10+1))
I=0.2909×100=29.09%

What is 16.35 written as a fraction

Answers

16.35 as a fraction16 7⁄20

Improper fraction:
327⁄20

hello here isa solution :
16.35 = 1635/100

"what is the binary equivalent of the decimal value 97?"

Answers

01100001 = 97 64+32+1=97 (if the leading bit is 0 it's usually not shown)
very easy
8 bits
Bit 1 Value 128
Bit 2 value 64
Bit 3 value 32
Bit 4 value 16
Bit 5 value 8
Bit 6 value 4
Bit 7 value 2
Bit 8 value 1

Final answer:

To find the binary equivalent of the decimal number 97, one divides it by 2 repeatedly and records the remainders in reverse order, resulting in the binary number 1100001.

Explanation:

The binary equivalent of the decimal value 97 can be found using a process of dividing by 2 and keeping track of the remainders. Firstly, divide 97 by 2, which gives a quotient of 48 and a remainder of 1. We write down the remainder. Continuing this process:

48 divided by 2 equals 24 with 0 remainder.24 divided by 2 equals 12 with 0 remainder.12 divided by 2 equals 6 with 0 remainder.6 divided by 2 equals 3 with 0 remainder.3 divided by 2 equals 1 with 1 remainder.1 divided by 2 equals 0 with 1 remainder (as we have now reached a value less than 2).

After collecting all the remainders in reverse order, the binary equivalent of decimal 97 is 1100001.

You are dealt one card from a standard 52-card deck find the probability of being dealt an ace or an 8

Answers

there are 4 Aces and 4 8's for a total of 8 cards

52 cards in a deck

so probability of picking an Ace or 8 = 8/52

Final answer:

The probability of being dealt an ace or an 8 from a standard 52-card deck is 2/13, which is approximately 15.38%.

Explanation:

The question asks for the probability of being dealt an ace or an 8 from a standard 52-card deck. There are 4 aces and 4 eights in a 52-card deck. To calculate the probability of getting either an ace or an 8, we add the probability of getting an ace to the probability of getting an 8. The probability of drawing an ace (P(Ace)) is 4/52 and the probability of drawing an 8 (P(8)) is also 4/52. Since these are mutually exclusive events (you cannot draw an ace and an 8 simultaneously with one card), we can simply add these probabilities together:

P(Ace or 8) = P(Ace) + P(8)
= (4/52) + (4/52)
= 8/52
= 2/13

Therefore, the probability of being dealt an ace or an 8 is 2/13, which is approximately 0.1538 or 15.38%.

Jeremiah is asked to write the equation of an ellipse. He is given one vertex along the major axis and the location of the center. He realizes he does not have enough information to write the equation. He asks his teacher for one additional piece of information. What information could Jeremiah ask for to help him write the equation? Check all that apply.
-the location of the focus nearest the given vertex
-the location of the focus nearest the other vertex
-the location of the other vertex along the major axis
-the location of one covertex along the minor axis
-the location of the directrix nearest the given vertex
-the location of the directrix nearest the other vertex
-the length of the minor axis

Answers

Jeremiah needs additional information such as the location of the foci, the other vertex on the major axis, a covertex along the minor axis, or the length of the minor axis to write the equation of the ellipse that is options A, B, C, D and G are correct.

Jeremiah is asked to write the equation of an ellipse given one vertex along the major axis and the location of the center.

He realizes he does not have enough information. He could ask for the following additional pieces of information to help him write the equation:

The location of the focus nearest the given vertexThe location of the focus nearest the other vertexThe location of the other vertex along the major axisThe location of one covertex along the minor axisThe length of the minor axis

With any of these pieces of information, he could determine the necessary parameters to complete the equation of the ellipse.

Jeremiah could ask for the other information that is the location of the other vertex along the major axis, the location of one covertex along the minor axis, the length of the minor axis and the location of the focus nearest the given vertex.

To write the equation of an ellipse, Jeremiah needs more information. Given the center and one vertex along the major axis, he can ask for:

The location of the other vertex along the major axis: This will help determine the length of the major axis.The location of one covertex along the minor axis: This will help find the length of the minor axis.The length of the minor axis: Directly needed to formulate the equation.The location of the focus nearest the given vertex: This helps identify the distance from the center to the foci, which is necessary for finding the equation.

With any of this additional information, Jeremiah can confidently determine the parameters required to write the equation of the ellipse.

Let r(t)=⟨t2,1−t,4t⟩. calculate the derivative of r(t)⋅a(t) at t=5, assuming that a(5)=⟨−4,4,−5⟩ and a′(5)=⟨−5,9,3⟩

Answers

[tex]\mathbf r(t)=\langle t^2,1-t,4t\rangle[/tex]
[tex]\implies\mathbf r'(t)=\langle 2t,-1,4\rangle[/tex]

[tex]\dfrac{\mathrm d(\mathbf r(t)\cdot\mathbf a(t))}{\mathrm dt}\bigg|_{t=5}=\mathbf r'(5)\cdot\mathbf a(5)+\mathbf r(5)\cdot\mathbf a'(5)[/tex]
[tex]=\langle10,-1,4\rangle\cdot\langle-4,4,-5\rangle+\langle25,-4,20\rangle\cdot\langle-5,9,3\rangle[/tex]
[tex]=(-40-4-20)+(-125-36+60)[/tex]
[tex]=-165[/tex]

Convert: 6y + y² = x² from rectangular to polar form.

Answers

[tex]\bf \textit{Double Angle Identities} \\ \quad \\ sin(2\theta)=2sin(\theta)cos(\theta) \\ \quad \\\\ cos(2\theta)= \begin{cases} \boxed{cos^2(\theta)-sin^2(\theta)}\\ 1-2sin^2(\theta)\\ 2cos^2(\theta)-1 \end{cases}\\\\\\ tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\ -------------------------------\\\\[/tex]

[tex]\bf 6y+y^2=x^2\implies \cfrac{6y}{x^2}+\cfrac{y^2}{x^2}=1\implies \cfrac{6rsin(\theta )}{[rcos(\theta )]^2}+\cfrac{[rsin(\theta )]^2}{[rcos(\theta )]^2}=1 \\\\\\ \cfrac{6rsin(\theta )}{r^2cos^2(\theta )}+\cfrac{r^2sin^2(\theta )}{r^2cos^2(\theta )}=1\implies \cfrac{6sin(\theta )}{rcos^2(\theta )}+\cfrac{sin^2(\theta )}{cos^2(\theta )}=1[/tex]

[tex]\bf \cfrac{6sin(\theta )}{rcos^2(\theta )}=1-\cfrac{sin^2(\theta )}{cos^2(\theta )}\implies \cfrac{6sin(\theta )}{1-\frac{sin^2(\theta )}{cos^2(\theta )}}=rcos^2(\theta ) \\\\\\ \cfrac{6sin(\theta )}{cos^2(\theta )\left[ 1-\frac{sin^2(\theta )}{cos^2(\theta )} \right]}=r\implies \cfrac{6sin(\theta )}{cos^2(\theta )-sin^2(\theta )}=r \\\\\\ \cfrac{6sin(\theta )}{cos(2\theta )}=r[/tex]

,,,Help Please.. Question in the file.

Answers

so hmmm there are 5pennies in a nickel, and 10pennies in a dime and 25pennies in a quarter

now, in $6.10, there are 610 pennies

n = amount of nickels coins
d = amount of dime coins
q = amount of quarter coins

so... we know, there are 5*n or 5n pennies in the nickels, and 10*d or 10d pennies in the dimes and 25*q or 25q in the quarter coins, and we know their sum is 610 pennies total, thus

5n + 10d + 25q = 610

now, there are 4 more "n" then "d", so whatever "d" is, "n" is 4 more than that
n = d + 4

and twice as many "q" than "n", so, whatever "n" is, then
q = 2n

[tex]\bf 5n+10d+25q=610\implies n+2d+5q=122\qquad \begin{cases} n=d+4\\ q=2n\\ ------\\ q=2(d+4)\\ \qquad 2d+8 \end{cases} \\\\\\ \boxed{d+4}+2d+5\left( \boxed{2d+8} \right)=122[/tex]

solve for "d", to see how many dimes are there

what about the nickels? well, n = d + 4
what about the quarters? well, q = 2d + 8

Expressions 4 tens + 6 tens in standard form

Answers

40+60=100
I hope this helps^^

Explain how the phrase "oh heck another hour of algebra" can help a student recall the trigonometric ratios

Answers

It's suppose to stand for OH AH OA which is for sine, cosine, and tangent. Sine, opposite divide by hypotenuse, cosine adjacent divided by hypotenuse, and tangent, opposite divided by adjacent. I personally like SOHCAHTOA more since it actually has the S,C, and T before what it means

Final answer:

The phrase "oh heck another hour of algebra" can help a student recall the trigonometric ratios by associating key words in the phrase with math concepts. The phrase contains words related to math, such as "algebra" and "hour," as well as a word similar to "angle." By linking these words to the trigonometric ratios, a student can better remember and understand them.

Explanation:

The phrase "oh heck another hour of algebra" can help a student recall the trigonometric ratios by focusing on the key words within the phrase. The phrase contains the words "algebra" and "hour," which are related to math, and the word "heck," which is similar to the word "angle." By associating these words with the phrase, a student can remember the trigonometric ratios, which involve angles and algebraic calculations. For example, the phrase can remind a student that the sine ratio involves the ratio of opposite and hypotenuse sides, similar to finding lengths in algebraic equations.

Learn more about Recalling trigonometric ratios here:

https://brainly.com/question/25122832

#SPJ3

3. A carpenter is framing a window with wood trim where the length of the window is 6 and 2\3 feet. If the width of the window is 7 and3\4 feet, how many feet of the wood is needed to frame the window?

Answers

We can see that window is in shape of rectangle. So the length of the required wood to frame window is equal to the perimeter of rectangle.

SO the length of rectangular window is [tex]= 6 \frac{2}{3} = \frac{20}{3} [/tex] feet.

Width of the rectangular window is = [tex]7 \frac{3}{4} = \frac{31}{4} [/tex] feet.

In general parameter of rectangle is = [tex]2(l+b)[/tex]

So the parameter of window is = [tex]2( \frac{20}{3} + \frac{31}{4}) = 2* \frac{(80+ 93)}{12} = 2* \frac{173}{12} = 28.834 [/tex]

So the required length of wood to frame window is = 28.834 feet

In a literal question what does f and c represent

Answers

If your talking about math, science, or weather f and c will most likely represent fahrenheit and celsius

What is the value of s in the equation 3r=10+5s when r=10

Answers

3*10 = 10+5*s
30 = 10+5s
20 = 5s
s = 4

Answer:

[tex]s=4[/tex].

Step-by-step explanation:

We have been given an equation [tex]3r=10+5s[/tex]. We are asked to find the value of 's', when [tex]r=10[/tex].

To find value of 's', we will substitute [tex]r=10[/tex] in our given equation as shown below:

[tex]3(10)=10+5s[/tex]

[tex]30=10+5s[/tex]

Upon subtracting 10 from both sides of our given equation, we will get:

[tex]30-10=10-10+5s[/tex]

[tex]20=5s[/tex]

Now, we will divide both sides of our equation by 5.

[tex]\frac{20}{5}=\frac{5s}{5}[/tex]

[tex]4=s[/tex]

Therefore, the value of 's' is 4, when [tex]r=10[/tex].

the sum of three numbers is 85. the second number is 5 times more than the first. the third number is 2 time the first. what are the numbers?

Answers

x + y + z = 85
y = x + 5
z = 2x

x + (x + 5) + 2x = 85
4x + 5 = 85
4x = 85 - 5
4x = 80
x = 80/4
x = 20

x + 5 = 20 + 5 = 25
2x = 2(20) = 40

ur numbers are : 20,25,and 40

What is the value 6,035

Answers

6035 theres nothing to take from or add to it

6- thousands
0-hundreds
3-tens
5-ones

Good luck on your assignment!

~MeIsKaitlyn

which of the following is irrational? 7.51•(-4)

Answers

-30.04 is the best i came up with in my head

The irrational number among the options is root 3 + 8.486. option C.

An irrational number is a number that cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal expansion.

Let's examine each option:

A. [tex]$7.51\ldots \times -4$[/tex]

This is a rational number because it's the product of a rational number [tex]($7.51\ldots$) and $-4$,[/tex] which is also rational. So, option A is not irrational.

B. [tex]$\sqrt{16} + \frac{3}{4}$[/tex]

[tex]$\sqrt{16} = 4$[/tex], so this expression simplifies to [tex]$4 + \frac{3}{4}$[/tex], which is a rational number. So, option B is not irrational.

C. [tex]$\sqrt{3} + 8.486$[/tex]

If [tex]$\sqrt{3}$[/tex] is not exactly equal to 8.486 , then this expression is irrational because it's the sum of an irrational number and a rational number. However, if [tex]$\sqrt{3}$[/tex] does happen to be exactly 8.486, then this expression would be rational. To determine if [tex]$\sqrt{3}$[/tex] is exactly 8.486, we need to compute [tex]$\sqrt{3}$.[/tex] Since [tex]$\sqrt{3}$[/tex] is irrational (it's not a perfect square), 8.486 is not [tex]$\sqrt{3}$[/tex], so this expression is irrational. Therefore, option C is the correct answer.

D.[tex]$8 \frac{2}{3} \times 17.75$[/tex]

This is a rational number because it's the product of a rational number [tex]($8 \frac{2}{3}$) and $17.75$,[/tex] which is also rational. So, option D is not irrational.

Complete question: Which of the following is irrational?

A. 7.51... x -4

B. root 16 + 3/4

C. root 3 + 8.486

D. 8 2/3 x 17.75

What is 75% of the area of a circle with a circumference of 10 units? Round the solution to the nearest square unit.

Answers

c=2pir
area=pir^2

so if c=10units
10=2pir
5=pir
5/pi=r

sub for area
area=pir^2
area=pi(5/pi)^2
area=pi(25/pi^2)
area=25/pi

75% or 3/4 of that is
25/pi times 3/4=75/(4pi)
use calculator
5.9683103659460750913331411264693 square units
or rounded
6 square units

Answer: 6 sq. units

Step-by-step explanation:

The formula to find the circumference of a circle is given by :-

[tex]C=2\pi r[/tex], where r is the radius of the circle.

Given : Circumference = 10 units

Then , [tex]10=2\pi r[/tex]

[tex]\\\\\Rightarrow\ r=\dfrac{10}{2\pi}\approx1.59[/tex]

The area of a circle is given by :-

[tex]A=\pi r^2=\pi(1.59)^2=7.9422603875\approx7.94\text{ sq. units}[/tex]

Now, the 75 % of the area is given by :-

[tex]0.75\times7.94=5.955\approx6\text{ sq. units}[/tex]

Hence, 75% of the area of a circle with a circumference of 10 units = 6 sq. units

110 students are surveyed about their pets. The results are shown in the table. Which statement is true?

Answers

Can I see the table?

The only true statement is b. 40% of the boys surveyed have at least one pet.

To determine which statement is true, let's analyze the data provided in the table:

- Total number of boys surveyed: 45

- Total number of girls surveyed: 65

Now, let's break down the information based on the provided table:

1. **At least one pet:**

- Boys: 18

- Girls: 39

- Total: 57

2. **No pets:**

- Boys: 27

- Girls: 26

- Total: 53

Now, let's check each statement:

a. 27% of the boys surveyed have no pets.

- Percentage of boys with no pets = (Number of boys with no pets / Total number of boys surveyed) * 100%

- = (27 / 45) * 100% ≈ 60%

- This statement is false.

b. 40% of the boys surveyed have at least one pet.

- Percentage of boys with at least one pet = (Number of boys with at least one pet / Total number of boys surveyed) * 100%

- = (18 / 45) * 100% = 40%

- This statement is true.

c. 49% of the girls surveyed have no pets.

- Percentage of girls with no pets = (Number of girls with no pets / Total number of girls surveyed) * 100%

- = (26 / 65) * 100% ≈ 40%

- This statement is false.

d. 57% of the students surveyed have at least one pet.

- Percentage of students with at least one pet = (Total number of students with at least one pet / Total number of students surveyed) * 100%

- = (57 / 110) * 100% ≈ 52%

- This statement is false.

So, the only true statement is b. 40% of the boys surveyed have at least one pet.

The probable question may be:

110 students are surveyed about their pets. The results are shown in the table. Which statement is true?

Boys | Girls | Total

At least one pet | 18 | 39 | 57

No pets | 27 | 26 | 53

Total | 45 | 65 | 110

a. 27% of the boys surveyed have no pets.

b. 40% of the boys surveyed have at least one pet.

c. 49% of the girls surveyed have no pets.

d. 57% of the students surveyed have at least one pet.

What is 2/15 in simplest form

Answers

2/15 is already simplified as much as possible, but as a decimal it can be 0.1333...

2/15 is already in simplest form

Hope this helps : )

Simplify: (4a + 2b)(a - b)

A) 4a^2 - 6ab - 2b^2
B) 4a^2 - 2ab - 2b^2
C) 4a^2 - 8ab - 2b^2
D) 4a^2 + 2ab - 2b^2

Answers

The answer would be B.

57% of men consider themselves professional baseball fans. you randomly select 10 men and ask each if he considers himself a professional baseball fan. find the probability that the number who consider themselves baseball fans is (a) exactly five, (b) at least six, and (c) less than four.

Answers

this was my question and I don't need the answer anymore!

(a) [tex]$ P(X = 5) \approx 0.234 $[/tex]

(b) [tex]\[ P(X \geq 6) \approx 0.892 \][/tex]

To solve this problem, we can use the binomial probability formula since each man's response (considering themselves a baseball fan or not) is independent and there are only two possible outcomes (success or failure).

Given:

- Probability of success (considering themselves a baseball fan) [tex]$ p = 0.57 $[/tex]

- Probability of failure (not considering themselves a baseball fan) [tex]$ q = 1 - p = 1 - 0.57 = 0.43 $[/tex]

- Number of trials [tex]$ n = 10 $[/tex]

We'll calculate the probabilities for each case:

(a) To find the probability that exactly five men consider themselves baseball fans:

[tex]\[ P(X = 5) = \binom{10}{5} \times (0.57)^5 \times (0.43)^{10 - 5} \][/tex]

(b) To find the probability that at least six men consider themselves baseball fans, we can find the probability of six, seven, eight, nine, and ten men being baseball fans, and then sum them up.

(c) To find the probability that less than four men consider themselves baseball fans, we need to find the probabilities of zero, one, two, and three men being baseball fans, and then sum them up.

Let's calculate each probability:

(a) [tex]\[ P(X = 5) = \binom{10}{5} \times (0.57)^5 \times (0.43)^{5} \][/tex]

(b) To find the probability of at least six men being baseball fans:

[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]

[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]

We'll use these formulas to find the probabilities for each case. Let me do the calculations.

(a) To find the probability that exactly five men consider themselves baseball fans:

[tex]\[ P(X = 5) = \binom{10}{5} \times (0.57)^5 \times (0.43)^{5} \][/tex]

Using the binomial coefficient formula [tex]$\binom{n}{k} = \frac{n!}{k!(n - k)!}$[/tex], where [tex]$n = 10$[/tex] and [tex]$k = 5$[/tex]:

[tex]\[ \binom{10}{5} = \frac{10!}{5!(10 - 5)!} = \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1} = 252 \][/tex]

Now, we plug in the values:

[tex]\[ P(X = 5) = 252 \times (0.57)^5 \times (0.43)^{5} \][/tex]

[tex]\[ P(X = 5) \approx 0.234 \][/tex]

(b) To find the probability of at least six men being baseball fans:

[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]

For each [tex]$k = 6, 7, 8, 9, 10$[/tex], we calculate [tex]$P(X = k)$[/tex] using the binomial formula and sum them up.

[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]

Similarly, for each [tex]$k = 0, 1, 2, 3$[/tex], we calculate [tex]$P(X = k)$[/tex] using the binomial formula and sum them up. Let me do the calculations.

(a) [tex]$ P(X = 5) \approx 0.234 $[/tex]

(b) To find the probability of at least six men being baseball fans:

[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]

Using the binomial formula for each [tex]$ k = 6, 7, 8, 9, 10 $[/tex] and summing the probabilities:

[tex]\[ P(X \geq 6) \approx 0.892 \][/tex]

[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]

Using the binomial formula for each [tex]$ k = 0, 1, 2, 3 $[/tex] and summing the probabilities:

[tex]\[ P(X < 4) \approx 0.020 \][/tex]

The front of an a frame cabin in a national park is the shape of a triangle, with an area of 189 ft.². If the height is 1 foot less than twice the base, find the base and the height of the front of the cabin.

Answers

check the picture below.

it can't be a negative value, since it's a measurement unit, thus it can't be -27.

so, anyhow, base is "b", and the height is "2b - 1".

Final answer:

The student needs to solve a quadratic equation to find the base and height of a triangle using the area formula and the given relationship between height and base. The solution involves substitution, expansion, and application of the quadratic formula or factoring.

Explanation:

The problem involves finding the base and height of a triangular front of an A-frame cabin based on its given area and a relationship between the height and base. It's a typical quadratic equation problem found in the high school mathematics curriculum when dealing with geometry and algebra.

To find the base (b) and height (h) of the triangle, we first use the area formula of a triangle A = 1/2 × base × height. We know that the area (A) is 189 ft² and that the height (h) is 1 foot less than twice the base, so h = 2b - 1. Substituting h into the area formula, we get 189 = 1/2 × b × (2b - 1). Solving this quadratic equation, we find the values for the base (b) and substitute back to find the height (h).

The process entails expanding the equation, moving all terms to one side to set the equation to zero, and then using the quadratic formula or factoring to find the value of b. Once the base is found, we use the relationship h = 2b - 1 to determine the height.

The sum of the roots of 8x² - 2x = 1 is:
-1/4
1/4
-1/8

Answers

8x^2-2x-1=0

8x^2-4x+2x-1=0

4x(2x-1)+1(2x-1)=0

(4x+1)(2x-1)=0

x=1/2 and -1/4

So the sum is 1/2-1/4=1/4

1/4

8x^2 - 2x = 1
8x^2 - 2x - 1 = 0

(2 +/-√(-2)^2 - 4(8)(-1))/ 2(8)
(2 +/-√4 + 32) / 16
(2 +/-√36) / 16
(2 +/- 6) / 16

2+6/16
1/2

2-6/16
-1/4

now since they want the sum of the roots
1/2 - 1/4

sum = 1/4

Can the sum of two irrational numbers ever be a rational number?

Answers

Irrational numbers are numbers that can not be written as a ratio of two integers. (example: square root of 2). Rational numbers on the other hand can be written as a ratio, as decimal or percentage.
If X is a irrational number, than the number Y=1-X is also irrational and the sum of these two irrational numbers is: X+Y=X+1-X=1 is rational number.
So, the sum of two irrational numbers can be a rational number.

What is 45 ones times 10?

Choices are:
45 hundreds
45 tenths
or 45 tens.

Answers

45 * 10 = 450 or 45 tens

Answer:

Option 3 - 45 tens

Step-by-step explanation:

Given : Expression 45 ones times 10.

To find : What is the expression?

Solution :

We know that,

"one" means " 1

We have 45 ones means multiply 45 by 1.

[tex]45\text{ ones}=45\times 1=45[/tex]

Now, 45 ones times 10 means

[tex]45\times 10=450[/tex]

450 means 45 tens as tens is 10.

So, The correct choice is 45 tens.

Therefore, Option 3 is correct.

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