Melissa sees a lighthouse from her sailboat. She knows the height of the lighthouse is 154 feet. She uses a measuring device and determines that the angle to the top of the lighthouse from her boat is 35°. How far is the sailboat from the base of the lighthouse?

Answer:

32

Step-by-step explanation:

Alicia needs 32 square feet of carpet to cover the space.

Area of triangular space is 1/2 * length * height.

Given, space has base length of 10 ft. and a height of 6.4 ft.

Using the formula,

Area of triangular space is 1/2 * length * height = 1/2 * 10 * 6.4

                                                                               = 32 square feet

Hence , Alicia needs 32 square feet of carpet to cover the space.

To learn more about the triangular spaces ;

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Answer:

t = 20.3 years

Step-by-step explanation:

I am assuming that this amount of money invested is compounding annually, so I am going to use the formula that goes along with that assumption:

[tex]A(t)=P(1+r)^t[/tex]

where A(t) is the amount at the end of compounding, P is the initial investment, r is the interest rate in decimal form, and t is the time in years.  We are solving for t.  Right now it is the exponent, but we have to get it down from that position in order to solve for it.  The only way we can do that is to eventually take the natural log of both sides.  But let's write the equation first and then do some simplifying to make things a bit easier mathematically:

[tex]19,700=5,500(1+.065)^t[/tex] and

[tex]19,700=5,500(1.065)^t[/tex]

We will divide both sides by 5,500:

[tex]3.58181818=(1.065)^t[/tex]

Taking the natural log of both sides gives us:

[tex]ln(3.58181818)=ln(1.065)^t[/tex]

The power rule for logs (both common and natural) tells us that once we take the log or ln of a base, the exponent comes down out front:

ln(3.58181818) = t ln(1.065)

Now we can divide both sides by ln(1.065) and do the math on our calculators to find that

t = 20.2600 or, to the tenth of a year,

t = 20.3 years

It will take for $5500 to grow to $19700 at a 6.5% interest rate, approximately 19.7 years for the account to reach.

The question involves calculating the amount of time it takes for an investment to grow to a certain value given a fixed annual interest rate. This is a common problem in personal finance and uses the concept of compound interest. To find the time needed for an initial investment of $5500 to grow to $19700 at an annual interest rate of 6.5%, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time in years.

In this case, interest is compounded annually so n = 1. We rearrange the formula to solve for t:

t = log(A/P) / (n*log(1 + r/n))

Where log is the logarithm function. We substitute our known values:

t = log(19700/5500) / (1*log(1 + 0.065/1))

Calculating this gives:

t ≈ log(3.5818) / log(1.065)

t ≈ 19.7

Answer with step-by-step explanation:

A. WX is perpendicular to XY - TRUE:

(since X is adjacent to X and Y and all angles are 90 degrees in a square, therefore WX is perpendicular to XY)

B. ∠W is congruent to ∠X - TRUE:

(all angles in a square are equal to each other)

C. ∠W is supplementary to ∠X - TRUE:

(∠W and ∠X both are right angles which add up to 180 degrees so they are supplementary angles)

D. WXYZ is a rhombus - TRUE:

(a rhombus has all sides equal in length and so has a square so it is a rhombus)

E. WXYZ is a trapezoid - FALSE:

(a trapezoid has only one pair of parallel sides while a square has two pairs of parallel sides)

F. WX is parallel to YZ - TRUE:

(WX and YZ are parallel to each other)

[tex]2\sqrt4=2\cdot2=4[/tex]

Answer:

4

Step-by-step explanation:

2√4 = 2√(2^2) = 2·2 = 4

__

Or, any calculator can help you with this. The Google search box serves as input to that calculator.

Answer:

i think it is 5:17

Step-by-step explanation:

length=50

perimeter=170

the highest factor of 50 and 170 is 10 so the answer will be 5:17

hopefully this made sense

Answer:

Step-by-step explanation:

outcome

Answer:

  A = 1000·1.04^5

Step-by-step explanation:

When 4% of the amount in the account is added to the amount in the account, the result is that amount is multiplied by 1.04:

  amount + 0.04×amount = amount×(1 + .04) = 1.04×amount

The account is multiplied this way for each of 5 years. An exponent is used to signify repeated multiplication, so we can write the account balance as ...

  A = ((((1000×1.04)×1.04)×1.04)×1.04)×1.04 = 1000×1.04^5

The exponential equation that represents the value of the account, ( A ), after five years is [tex]\[ A = 1000 \times (1.04)^5 \][/tex]

To determine the value of Maria's savings account after five years with annual compounding interest, we use the formula for compound interest:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

Given:

( P = 1000 ) dollars (initial investment)

( r = 0.04 ) (4% interest rate per year)

( n = 1 ) (compounded annually)

( t = 5 ) years

Now, substitute these values into the formula:

[tex]\[ A = 1000 \left(1 + \frac{0.04}{1}\right)^{1 \cdot 5} \][/tex]

[tex]\[ A = 1000 \left(1 + 0.04\right)^5 \][/tex]

[tex]\[ A = 1000 \times (1.04)^5 \][/tex]

Calculate [tex]\( (1.04)^5 \)[/tex]:

[tex]\[ (1.04)^5 \approx 1.21665 \][/tex]

Now multiply by 1000:

[tex]\[ A \approx 1000 \times 1.21665 \][/tex]

[tex]\[ A \approx 1216.65 \][/tex]

Therefore, the value of Maria's savings account at the end of five years, with annual compounding interest at 4%, is approximately [tex]\( \$1216.65 \)[/tex].

To summarize, the exponential equation that represents the value of the account, ( A ), after five years is:

[tex]\[ A = 1000 \times (1.04)^5 \][/tex]

Answer:

(9,5)

Step-by-step explanation:

Linear combination (also known as elimination) is trying to somehow combine the equations together so that it eliminates one variable in order to solve for the other one.

So you have

-4x+9y=9

  x-3y =-6

In elimination, you want the equations to be in the same form which they are here in this case.  You want one of the columns to contain opposites or sames.

If opposites, you add the equations.

If sames, you subtract the equations.

We have neither opposites or sames in either of the first two variable columns which is where we want one of these columns to be.

So I'm going to multiply the bottom equation by 3.  This is not the only way. This is the way I'm going to do it. You could decide to multiply the bottom equation by 4 or -4 or -3 instead.  

So anyways multiply bottom equation by 3. This is what my system looks like now:

 -4x+9y=9

  3x-9y=-18

  ----------------Now we get to add this equations because the 2nd column,

                     the y column, we have opposites.

------------------------adding now

 -1x+0y=-9                  -4+3=1 and -9+9=0  and 9+-18=0      

  -x      =-9                    -1x=-1*x=-x     and 0y=0*y=0

   x      =9                       Take opposite of both sides

Now once we find one variable we must obtain the other variable by replacing x with 9 and solving for y in one of the equations (don't use both-just choose one- doesn't matter which)

x-3y=-6 was the second equation before manipulation

Plug in 9 for x

9-3y=-6

Subtract 9 on both sides

 -3y=-6-9

  -3y=-15  

Divide both sides by -3

    y=5

So the solution is (x,y)=(9,5)

Answer:

  y = -1/4

Step-by-step explanation:

  y/5 +3/10 = (y+2)/7

The LCD is 10·7 = 70. Multiplying the equation by 70 gives ...

  14y +21 = 10(y +2)

  14y +21 = 10y +20 . . . . eliminate parentheses

  4y + 21 = 20 . . . . subtract 10y

  4y = -1 . . . . . . . . . subtract 21

  y = -1/4 . . . . . . . . .divide by 4

_____

Check

  (-1/4)/5 +3/10 = (-1/4 +2)/7 . . . . . substitute for y

  -1/20 +6/20 = (7/4)/7 . . . simplify a bit, rewrite 3/10

  5/20 = 1/4 . . . . . . . . . . true

Answer: 64 fluid ounces

Step-by-step explanation:

See paper attached. (:

Let h = number of hours the Sun was up today.

There are 24 hours in one day.

So, we are looking at the fraction h/24.

Answer: The fraction of the time the Sun was up today.

The function that multiplies the number of hours the Sun was up (h) by 60 represents the number of minutes the Sun was up today.

If h represents the number of hours the Sun was up today, to calculate the number of minutes the Sun was up, we would multiply h by 60, since there are 60 minutes in an hour. Therefore, the function that multiplies h by 60 will give us the number of minutes the Sun was up today. On the contrary, to find the number of hours the Sun was down today, we would typically take the total number of hours in a day, which is 24, and subtract h from it. To represent the fraction of the time the Sun was up today, we would use the ratio of h to 24, since there are 24 hours in a whole day. Thus, the correct quantity represented by the function when h is multiplied by 60 is the number of minutes the Sun was up today.

For this case we have that the area of the kite is formed by the ara of two triangles with the same base of[tex]9 + 9 = 18[/tex] meters and one with height 9 meters and another with height 6 meters.

So:

[tex]A = \frac {1} {2} b * h + \frac {1} {2} b * h\\A = \frac {1} {2} 18 * 9 + \frac {1} {2} 18 * 6\\A = \frac {1} {2} 162+ \frac {1} {2} 108\\A = 81 + 54\\A = 135 \ m ^ 2[/tex]

ANswer:

Option B

Answer:

135 m^2

Step-by-step explanation:

Gradpoint approved, good luck guys.

Final answer:

To determine how many miles Marcus biked, we can write the equation 2m - 3 = 4, where 'm' represents the number of miles Marcus biked. Solving this equation, we find that Marcus biked 3.5 miles.

Explanation:

To write an equation to determine how many miles Marcus biked, we can use the given information. Let's assume that the number of miles Marcus biked is represented by the variable 'm'. According to the problem, Jenny biked 3 miles less than twice the number of miles Marcus biked. So, we can write the equation as: 2m - 3 = 4.

To solve this equation, we need to isolate the variable 'm'. Adding 3 to both sides of the equation, we get: 2m = 7. Finally, dividing both sides by 2, we find that Marcus biked 3.5 miles.

Answer:

D. 25%

Step-by-step explanation:

f(x) = 2 * (1.25)^x

This is in the form

y = a b^x

where b is 1 plus the growth rate

b = 1.25 = 1+growth rate

1.25 = 1 + growth rate

.25 = growth rate

25% = growth rate

The answer is D) 25%

Answer:

3

Step-by-step explanation:

2/3 =2/9  m

2/3 =2m/9                         note: 2/9 m is the same as 2/9 *m/1=2m/9

cross multiply

18=6m

so m=3

[tex]\text{Hey there!}[/tex]

[tex]\text{In order for you to solve for the value of m you have to flip the equation around!}[/tex]

[tex]\text{Here is what I meant}\downarrow[/tex]

[tex]\bf{\frac{2}{9}m=\frac{2}{3}}[/tex]

[tex]\text{Then for your second step, you have to MULTIPLY by\ }\frac{9}{2}\text{\ on your sides}[/tex]

[tex]\text{Here's what I meant}\downarrow[/tex]

[tex]\bf{\frac{9}{2}(\frac{2}{9})m=\frac{9}{2}(\frac{2}{3})}[/tex]

[tex]\text{Cancel out:}\frac{9}{2}(\frac{2}{9}m)\text{\ because it equals to 1}[/tex]

[tex]\text{Keep: \ }\frac{9}{2}(\frac{2}{3})\text{\ because it helps us solve for the value of m}[/tex]

[tex]\text{If you solved the kept one correctly, you have your answer}[/tex]

[tex]\boxed{\boxed{\text{Answer: C. 3}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

  52

Step-by-step explanation:

Put the numbers in the expression and do the arithmetic.

  (-8)² - |-12| = 64 -12 = 52

Answer:

  175 hot dogs

Step-by-step explanation:

The new price will be $3.85 + 0.55 = $4.40. Since the price has increased by a factor of 4.40/3.85 = 8/7, the number of hot dogs sold, which is inversely proportional, will be ...

  (7/8)·200 = 175 . . . hot dogs sold at the higher price

The vendor can expect to sell approximately 233 hot dogs if the price is increased by 55 cents.

To determine how many hot dogs the vendor can expect to sell if the price is increased by 55 cents, we can use the inverse proportionality relationship between the number of hot dogs sold and the price charged.

First, let's set up a proportion with the initial price and number of hot dogs sold:

$3.85 / 200 = (new price + $0.55) / x

Next, we can cross multiply and solve for x:

x = (200 * ($3.85 + $0.55)) / $3.85

Calculating this expression gives us a value of x ≈ 233.77.

Since the number of hot dogs sold must be a whole number, we round down to the nearest whole number, giving us an estimated value of 233 hot dogs.

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Answer:

When a number is halfway between two multiples of one thousand, round to "the larger multiple."

For example: If you have 852, the nearest thousand is 1000. So it should be round to 1000.

Answer:

rounded to the larger multiple.

For this case we have that by definition, the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

A: It is the radius of the circle

We have as data that the diameter is 10 feet, then the radius is half, that is, 5 feet.

Substituting:

[tex]A = \pi * (5) ^ 2\\A = 25 \pi\\A = 78.5[/tex]

Rounding out we have that the circle area is[tex]79 \ ft ^ 2[/tex]

Answer:

Option A

Answer:

A. 79 ft²

Step-by-step explanation:

Area of a circle is given by the formulae

[tex]A=\pi *r^2[/tex]

where r is the radius of the circle

Given diameter= 10 ft

Radius of a circle is one half the diameter of a circle.

Radius = [tex]r=\frac{10}{2} =5ft[/tex]

Area=[tex]\pi *5^2=3.14*5^2=78.5ft^2\\\\=79ft^2[/tex]

Answer: 2 friends/1 pair

Step-by-step explanation:

Mainly because if you do the math, a pair of friends is 2. Knowing that there is 2 short straws (Which if those are the ones that are chosen you get to go), and 4 long straws. Only 2 friends are going to draw the short straws.

Hope this helped :)

Answer:

15 possible pairs of friends could be chosen in this way.

Step-by-step explanation:

Given : You have 6 friends who want to go to a concert with you, but you only have room in your car for 2 of them. To avoid accusations of favoritism, you have your friends draw straws: There are 4 long and 2 short straws, and the short straws win.

To find : How many possible pairs of friends could be chosen in this way?  

Solution :

Total number of friends = 6

The space in the car is for 2 person.

Since, the order doesn't matter we have to choose 2 people out of 6 so we apply combination.

As There are 4 long and 2 short straws, and the short straws win.

i.e. that 2 friends were chosen.

So, Possible ways to find the pairs of friends is [tex]^6C_2[/tex]

Solving,

[tex]^6C_2=\frac{6!}{2!(6-2)!}[/tex]

[tex]^6C_2=\frac{6\times 5\times 4!}{2\times 1\times 4!}[/tex]

[tex]^6C_2=3\times 5[/tex]

[tex]^6C_2=15[/tex]

Therefore, 15 possible pairs of friends could be chosen in this way.

Answer:

56

Step-by-step explanation:

from observing the graph between x=-3 and x = 1.5, we can see that the highest most point of the graph (i.e the maximum) value occurs at x=-1.6, y = 56

Hence the maximum y-locatoin is 56

Answer:

B) 56

Step-by-step explanation:

Answer:

P/7x dollars.

Step-by-step explanation:

If the raffle prize is P dollars, then each person will receive  P/7x dollars.

Answer with explanation:

Let total Prize money = $ P

Number of people into which this money is divided =7 x People

Amount of money that each person will Receive

          [tex]=\frac{\text{Total Prize Money}}{\text{Number of people into which this money is divided}}\\\\=\frac{P\text{Dollars}}{7x}[/tex]        

[tex]\sqrt{(x2 - x1)^{2}  + (y2 - y1)^{2} }= \\ \\\sqrt{(-4 - (-1))^{2}  + (-1 - 4)^{2} }= \\\\\sqrt{-3^{2}  + -5^{2} }= \\\\\sqrt{9  + 25 }=\\\sqrt{34 }=\\5.83[/tex]

Distance between each pair of points is: 5.83

The distance formula, derived from the Pythagorean theorem, is used to find the distance between two points. You subtract and square the x-coordinates, do the same with the y-coordinates, sum those results, and take the square root of the sum to get the distance.

The distance formula in mathematics is used to determine the distance between two points in a coordinate plane. The formula is derived from the Pythagorean theorem and is represented as D = √[(x2-x1)² + (y2-y1)²]. Let's say we have two points A1(x1, y1) and A2(x2, y2).

The final result gives you the distance between the two points in the cartesian plane.

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Answer: second option.

Step-by-step explanation:

When two parallel lines are intersected by a third line (which is called "Transversal"), the angles that are of the same side of the transversal (but one located in interior and the other one located in the exterior), are known as "Corresponding angles".

Corresponding angles are congruent.

You can observe that the angle 2 and the angle 6 are Corresponding angles. Therefore, the missing justification is: "Corresponding angles formed by a transversal on parallel lines are congruent."

Answer:

Corresponding angles formed by a transversal on parallel lines are congruent.

Answer:

Step-by-step explanation:

The equation for the y-axis is x = 0. Your shading is to the left of that, so the inequality will be x ≤ 0.

The blue line has a rise of 3 for a run of 4, so its slope is 3/4. It intercepts the y-axis at y=-5, so the slope-intercept equation for that line is y = 3/4x -5. Since the shading is below that solid line, the inequality is ...

  y ≤ 3/4x -5

bearing in mind that a whole is simply same/same or just 1.

3 dozen, there are 3 dozens in 3 dozen, obviously

dozen dozen dozen.

in 2 dozens, there are 2 of course

dozen dozen.

if 3 dozens is three thirds namely 3/3 = 1 = whole, then 2 dozens is just two of those dozens, namely two thirds, 2/3.

so if we use that many ingredients to make a whole three thirds, how much will it be to make only two thirds of it?  well, is simply their product, so we'll simply multiply each ingredient amount by 2/3.

[tex]\bf \stackrel{flour}{3\cdot \frac{2}{3}}\qquad \stackrel{sugar}{1\cdot \frac{2}{3}}\qquad \stackrel{chips}{2\cdot \frac{2}{3}}\qquad \implies \qquad \stackrel{flour}{2}\qquad \stackrel{sugar}{\frac{2}{3}}\qquad \stackrel{chips}{\frac{4}{3}}[/tex]

Answer:

-7 > v OR vice-versa [v < -7]

Step-by-step explanation:

Combine like-terms [-5v > 35], then divide by -5.

NOTE: Since you are dividing by a negative, reverse the sign.

Answer:

[tex]{\huge \boxed{V<-7}}[/tex]

Step-by-step explanation:

Add similar into elements. Add the numbers from left to right.

-3v-2v=-5v

Simplify.

-5v>35

Multiply by -1 from both sides of equation.

(-5v)(-1)<35(-1)

Simplify.

35(-1)=-35

5v<-35

Divide by 5 from both sides of equation.

5v/5<-35/5

Simplify, to find the answer.

-35/5=-7

v<-7 is the correct answer.

I hope this helps you, and have a wonderful day!

the answer to this is

x=9,-15

Answer:

x={9,-15}

Step-by-step explanation:

|x+3|=12 means

x+3 could be 12 or -12 since |12|=12 and |-12|=12 are true

x+3=12                              x+3=-12

x=12-3                               x=-12-3

x=9                                    x=-15

Answer:

[tex]P=\frac{11}{40}+\frac{1}{4}-\frac{1}{20}[/tex]

Step-by-step explanation:

Given,

Students of,

Consumer education, n(C) = 22,

French, n(F) = 20,

Both, n(C∩F) = 4,

Total students, n(S) = 80

Thus, the number of students from Consumer Education, French, or both,

n(C∪F) = n(C) + n(F) - n(C∩F)

= 22 + 20 - 4

[tex]\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}[/tex]

Hence, probability of a student from Consumer Education, French, or both,

[tex]P=\frac{n(C\cup F)}{n(S)}[/tex]

[tex]=\frac{22+20-4}{80}[/tex]

[tex]=\frac{22}{80}+\frac{20}{80}-\frac{4}{80}[/tex]

[tex]=\frac{11}{40}+\frac{1}{4}-\frac{1}{20}[/tex]

LAST option is correct.

The equation of probability, P, that represents a randomly selected student from this class takes Consumer Education, French, or both are: [tex]\rm Probability = \dfrac{1}{4} + \dfrac{11}{40} -\dfrac{ 1}{20}[/tex] .

Given :

In a freshman high school class of 80 students, 22 students take Consumer Education, 20 students take French, and 4 students take both.

Given that students take Consumer Education: n(C) = 22

The students that take French: n(F) = 20

The students that take both: [tex]\rm n(C\cap F) = 4[/tex]

Total Students: n(S) = 80

Students that take Consumer, French, or both:

[tex]\rm n(C\cup F) = n(F) + n(C) - n(C\cap F)[/tex]

[tex]\rm n(C\cup F) = 20 + 22 - 4[/tex]

[tex]\rm Probability = \dfrac{Favourable \;Outcomes}{Total \; Outcomes}[/tex]

[tex]\rm Probability = \dfrac{n(C\cup F)}{n(S)}[/tex]

[tex]\rm Probability = \dfrac{20 + 22 - 4}{80}[/tex]

[tex]\rm Probability = \dfrac{20}{80} + \dfrac{22}{80} -\dfrac{ 4}{80}[/tex]

[tex]\rm Probability = \dfrac{1}{4} + \dfrac{11}{40} -\dfrac{ 1}{20}[/tex]

Therefore, the correct option is D).

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Answer:

Step-by-step explanation:

The reference angle is π/6, and the angle is in the 4th quadrant. So, sine and tangent will be negative while cosine is positive. You have memorized the values of trig functions for π/6, so you know ...

Adjusting the signs to match those required for a 4-th quadrant angle, you have ...