Given
While sailing a boat offshore, Bobby sees a lighthouse and calculates that
the angle of elevation to the top of the lighthouse is 3°.
When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.
To find:
How tall, to the nearest tenth of a meter, is the lighthouse?
Explanation:
It is given that,
While sailing a boat offshore, Bobby sees a lighthouse and calculates that
the angle of elevation to the top of the lighthouse is 3°.
When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.
That implies,
[tex]\tan3\degree=\frac{y}{x+700}[/tex]Also,
[tex]\begin{gathered} \tan5\degree=\frac{y}{x} \\ y=x\tan5\degree \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \tan3\degree=\frac{x\tan5\degree}{x+700} \\ (x+700)\tan3\degree=x\tan5\degree \\ x\tan3\degree+700\tan3\degree=x\tan5\degree \\ (\tan5\degree-\tan3\degree)x=700\tan3\degree \\ 0.0351x=36.6854 \\ x=1045.7m \end{gathered}[/tex]Then,
[tex]\begin{gathered} \tan5\degree=\frac{y}{1045.7} \\ y=1045.7\tan5\degree \\ y=91.5m \end{gathered}[/tex]Hence, the height of the light house is, 91.5m.
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Which inequality correctly compares 118%, 0.34, and two and one fifth?
0.34 < 118% < two and one fifth
118% < 0.34 < two and one fifth
0.34 < two and one fifth < 118%
two and one fifth < 0.34 < 118%
Which inequality correctly compares 118%, 0.34, and two and one fifth?
0.34 < 118% < two and one fifth
118% < 0.34 < two and one fifth
0.34 < two and one fifth < 118%
two and one fifth < 0.34 < 118%
118% = 118%
0.34 = 34%
2 and 1/5 = 200.2%
34% < 118% < 200.2%
Line k is shown below.Vai4 321 (2, 1)x-5 -4 -3 -2I NON0 1 2 3 4 5k(-4,-2) 3-5Which ratio represents the slope of a line parallelto line k??221O-221
hello
to solve this problem, we have to use the formula of slope of a line
[tex]\begin{gathered} \text{slope(m)}=\frac{y_2-y_1}{x_2-x_1} \\ y_2=1 \\ x_2=2 \\ y_1=-2 \\ x_1=-4 \end{gathered}[/tex]substitute the values into the equation (formula)
[tex]m=\frac{1-(-2)}{2-(-4)}=\frac{1+3}{2+4}=\frac{4}{6}=\frac{2}{3}[/tex]from the calculations above, the slope of the line is equal to 2/3
What ordered lair is closest to a local minimum of the function, f(x)?A. (-1, -3)B. (0, -2)C. (1, 4)D. (2, 1)
We have the following function given:
x f(y)
-2 -8
-1 -3
0 -2
1 4
2 1
3 3
And we can see that the minimum of the function is for the lowest f(y) value on this case -8
And the closest pair to this local minimum is:
A. (-1,3)
In the figure, ABCD and DEFG are squares.AC:FD=7:5, find CE
Given:
The ratio of the diagonals of the squares ABCD and DEFG is:
[tex]AC:FD=7:5[/tex]Required-the value of CE.
Explanation:
Given that the ratio of the diagonals of the squares ABCD and DEFG is:
[tex]AC:FD=7:5[/tex]So, the sides will be in the same ratio.
[tex]AD:GD=7:5[/tex]Let the sides of the two triangles ABCD and DEFG be 7x and 5x.
Given that
[tex]AG=3cm[/tex]So, we can write AG as:
[tex]\begin{gathered} AG=AD-GD \\ 3=7x-5x \\ \\ 2x=3....(1) \end{gathered}[/tex]Now, we have to find CE, so we can write CE as:
[tex]\begin{gathered} CE=CD+DE \\ \\ CE=7x+5x \\ \\ CE=12x \\ \\ CE=6(2x) \\ \\ CE=6\times3 \\ \\ CE=18cm \end{gathered}[/tex]Final answer: The value of CE is 18 cm.
Written Assignment #5
3.) Your stats test has five multiple choice questions, each having four possible answers with one correct
answer per question. If you completely guess (which you would never do), what is the probability (in
decimal form) that each of the following will happen? Show your work.
a.) get all of the questions correct
b.) get none of the questions correct
c.) get at least one of the questions incorrect
d.) get the first three questions correct and the last two incorrect
The probability of doing all questions correct is 1/3.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.So, the probability to get all questions correct:
Probability formula: P(E) = Favourable outcomes/Total outcomes
The number of questions is 5.The options for each question are 4. Possible answers are 1.Then,
Favourable events = 1 × 5 = 5Total events = 3 × 5 = 15Now, find the probability by putting the values as follows:
P(E) = Favourable outcomes/Total outcomesP(E) = 5/15P(E) = 1/3Therefore, the probability of doing all questions correct is 1/3.
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The correct question is given below:
Your stats test has five multiple-choice questions, each having four possible answers with one correct answer per question. If you completely guess (which you would never do), what is the probability (in decimal form) that each of the following will happen? Show your work.
A) Get all of the questions correct
which of the following are not an example of a rigid transformation
When we talk of rigid transformation, we refer to transformation that occurs, and the size of the shape is not affected. Of the three options, dilation is the only sort of transformation that affects the size of the object.
DILATION
Write the following comparison as a ratio reduced to lowest terms 2 nickels to 27 dimes
The ratio of 2 nickels to 27 dimes is 27.
What is ratio?A ratio in mathematics demonstrates how many times one number is contained in another. For instance, the ratio of oranges to lemons in a dish of fruit is eight to six if there are eight oranges and six lemons present. Similarly, the ratio of oranges to the total amount of fruit is 8:14 while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b, expressed as a / b, where b is not equal to 0. A percentage is an equation in which two ratios are made equal to one another. For instance, you could express the ratio as 1: 3 (one boy to three females), meaning that one in four of the population is male.
Nickel is equivalent to 0.05 dollars.
2 nickels are equivalent to (0.05 × 2) = 0.01 dollars.
1 dime is equal to 0.1 dollars.
27 dimes are equivalent to (27 × 0.01) = 0.27dollars.
Therefore, to compare 27 nickels to 2 dimes as a ratio reduced to lowest term will be 0.27 : 0.01
= 27
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Expressions: Tutorial
Simplify this expression:
4(126) + 76 - 10.
Type the correct answer in the box.
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sin
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CSC sec cot
The simplified form of expression 4(126) + 76 - 10 is 6 (100 - 5).
What is a expressions?A mathematical expression is a sentence that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions.
A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6. Complex puzzles can be solved using mathematical expressions.
We have been asked to simply the expression
4(126) + 76 - 10
= 4(60 + 66) + 66
= 4(60) + 4(66) + 66
= 4(60) + 5(66)
= 4(60) + 5( 60 + 6)
= 4(60) + 5(60) +5(6)
= 60(4+5) + 6(5)
= 60(9) + 6(5)
= 6(90 + 5)
= 6(95)
= 6 (100 - 5) simplified form
= 600 - 30
= 570
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Write the equation of the line with the given information. Through (-1, -1) parallel to h(x)=-1+10
The equation of a line that passes through (-1, -1) and parallel to h(x) = -1x + 10 is y = -x -2
How to find equation of a line?The line passes through (-1, -1) and it is parallel to h(x) = -1x + 10
When lines are parallel, the slopes are the same.
Therefore, the equation of a line that passes through (-1, -1) and parallel to h(x) = -1x + 10 can be calculated as follows:
Hence,
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the y-intercept using (-1, -1)
y = -x + b
-1 = -(-1) + b
b = -1 - 1
b = -2
Therefore, the equation of the lines is y = -x -2
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Solve the following quadratic equation by the square root method. If needed, write your answer as a fraction reduced to lowest term
Solution
Solve the following quadratic equation by the square root method.
[tex]\begin{gathered} y^2-10y+25=-49 \\ y^2-10y+25+49=0 \\ y^2-10y+74=0 \end{gathered}[/tex]Therefore the correct answer for y are
[tex]y=5+7i,\text{ 5-7i}[/tex]Seven less than n is 11
MATHEMATICALLY THIS CAN BE WRITTEN AS:
[tex]n - 7 = 11 \\ n = 11 + 7 \\ n = 18[/tex]
THAT NUMBER n IS 18
HOPE THIS HELPS
Which statement does NOT represent an expression? A (8 + x) - 7 B 4 + x = 12 C x2 = 24 D 5
Answer
The statement that does not represent an expression are 4 + x = 12 and x^2 = 24 which are option B and C respectively
Explanation:
An expression is a set of term combined using the operators +, - /
From the option given
8+ x - 7 this can be further expressed as
8 + x - 7
x + 8 - 7
x - 1
The only expression in the option are x - 1, and 5
4 + X = 12 is an equation. This is because it is a combination of two expressions that are equal to each other
x^2 = 24 is also an equation
Therefore, the statement that does not represent an expression are 4 + x = 12 and x^2 = 24 which are option B and C respectively
what is written on the back of a deposit slip?
Some banks merely need one to write "for deposit only" on the back of your check along with the account number, routing information, and sort code.
Some banks will need one to enclose a deposit slip with the check.
What is a Deposit Slip?A deposit slip is a form that a bank gives a depositor to complete and is intended to list the things involved in the deposit transaction in categories. The categories include the item's nature and, if it's a check, the source, such as a state if the bank is out of town. Along with the deposit (cash and checks), the teller retains the deposit slip and issues a receipt to the depositor. It is quite convenient to pay for them because they are filled out in a store rather than a bank. They serve as a vehicle for moving money as well.To learn more about Deposit slip, refer to:
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The following data set represents the ACT scores for students in Mrs. Smith's collegescience class.18 32 16 2319 21 28 2922 30 19 21What is the range for the ACT scores for the class?
The range is the difference between the greatest and the smallest number, so it is 32 - 16 = 16.
Choose the equation of a circle with radius 9 and center (3,-4).
Choose the correct answer below.
○ A. (x+3)² + (y− 4)² = 81
○ B. (x − 3)² + (y+4)² = 81
○ C. (x+3)² + (y−4)² = 9
OD. (x-3)²+(y+4)² =
Answer:
B. (x − 3)² + (y+4)² = 81
Step-by-step explanation:
If a circle has center located at (a, b) and radius of r, the equation of this circle is
(x - a)² + (y-b)² = r²
We have a = 3, b = -4 and r = 9
So equation is
(x - 3)² + y - (-4))² = 9²
==> (x − 3)² + (y+4)² = 81
A ticket to see your favorite baseball team costs $30.86. That price decreases by $0.35 for every game lost during the regular season. What equation could you use to find the cost C of a ticket after L losses? Represent the total change in the cost of a ticket after the team loses 31 games. What is the price of a ticket after the team loses 31 games?
Answer:20.01
Step-by-step explanation:
0.35x31=10.85
30.86-10.85=20.01
a jewelry company loses $450 as a result of a delivery delay.The 9 owners of the company must share the loss equally. Which integer was represents the change in profit for each owner A. $-50 B. $-35 C. $5 D. $50
We know that they lots of $450.
If they want to share the loss equally, we just have to divide the amount by 9 owners.
[tex]\frac{450}{9}=50[/tex]Therefore, the loss per owner is A. $-50.Remember that losses are represented by negative numbers.
Write a function rule for the table. X f(x) 3 5 9 101
Based on the data of the table, you can notice that the following function f(x):
f(x) = x + 4
represents the relation in between the values of the columns of the table.
For instance, you have:
f(3) = 3 + 4 = 7
f(4) = 4 + 4 = 8
f(5) = 5 + 4 = 9
f(6) = 6 + 4 = 10
Which expression is equivalent to -4(2 - 6x) - 2.5x ?
Rewriting the expression, we have:
[tex]\begin{gathered} -4\mleft(2-6x\mright)-2.5x \\ =-8+24x-2.5x \\ =21.5x-8 \end{gathered}[/tex]So an equivalent expression is 21.5x - 8.
7. Write the equation of the line in slope-intercept form given the following:Point (-5, -3), slope =3/5
start by writing in the form
[tex]y=mx+b[/tex]where you already have the slope and you must find b, which is the y-intercept
[tex]y=\frac{3}{5}x+b[/tex]use the point given (-5,-3) to find b
[tex]\begin{gathered} -3=\frac{3}{5}(-5)+b \\ -3=-3+b \\ -3+3=b \\ b=0 \end{gathered}[/tex]Hello, I need some assistance with this precalculus homework question, please?HW Q2
Answer:
A. The solution set is {4096}.
Explanation:
Given the logarithmic equation:
[tex]\frac{1}{2} \log _{6} x=3 \log _{6} 4[/tex]Multiply both sides of the equation by 2:
[tex]\begin{gathered} \frac{1}{2}\times2\log_6x=3\times2\log_64 \\ \log_6x=6\log_64 \end{gathered}[/tex]Next, apply the power law of logarithms to the right side of the equation.
[tex]\begin{gathered} \log_6x=\log_64^6 \\ \implies\operatorname{\log}_6x=\operatorname{\log}_64096 \end{gathered}[/tex]Since the bases are the same, equate the numbers:
[tex]x=4096[/tex]The solution set is {4096}.
Ravi built a large wooden storage box. The box was in the shape of a rectangular prism, as shown below. He covered all the sides of the box with special wallpaper that cost a total of $856. How much did the wallpaper cost per square foot?
The area, A, of a rectangle with dimensions l and b is given by:
A = l times b
Therefore the total area of the two opposite and congruent rectangular sides with
the dimension 6 by 5 is:
[tex]2\times6\times5=60ft^2[/tex]The total area of the two opposite and congruent rectangular sides with
the dimension 6 by 7 is:
[tex]\begin{gathered} 2\times6\times7=84ft^2 \\ The\text{ total area of the two opposite and congruent rectangular sides with the dimension} \\ 5\text{ by 7 is:} \\ 2\times5\times7=70ft^2 \\ \\ \text{Hence the total surface area = 60+84+70=214 square ft} \\ \\ \text{Therefore the cost per square foot = }\frac{856}{214}=4dollars\text{ per square foot} \end{gathered}[/tex]Write a quadratic equation in standard form with the given root(s) -7,3/4 and can you explain how you did it? i need it ASAP please and thank you
The equation of the quadratic equation is P(x) = x² + 23/4x - 21/4
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the quadratic equation?The given parameters are
Zeros = -7 and 3/4
The sum of multiplicities of the quadratic equation must be equal to the degree.
This means that the multiplicity of the zeros -7 and 3/4 is 1
The equation of the quadratic equation is then calculated as
P(x) = (x - zero)^ multiplicity
So, we have
P(x) = (x + 7)(x -3/4)
Expand
P(x) = x² + 7x - 3/4x - 21/4
This gives
P(x) = x² + 23/4x - 21/4
Hence, the equation is P(x) = x² + 23/4x - 21/4
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Make sure to show your work when answering the question. The insurance company pays the full cost of 3,900 prescriptions claims out of 4,500 prescriptions claims submitted. What is the rate of the claims paid expressed as a percent? Round to two decimal places.
The rate of the claims paid expressed as a percent is 86.67%.
Out of the 4,500 prescription claim submissions, it has been stated that the insurance company covers 3,900 prescription claims in full.
We must determine what percentage of 4,500 is 3,900 in order to solve the presented problem.
Percent of the claims paid = 3,900 / 4,500 x 100
Percent of the claims paid = 0.8666666 × 100
Percent of the claims paid 86.66666%
Percent of the claims paid = 86.67%
As a result, 86.67% would be the rate of claims paid represented as a percentage.
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a survey survey asked 200 students to name their favorite fruit the table shows the results of a survey
Part A
Fraction of peach 2/5
Total = 200
number of students that pick peach as their favorite fruits
[tex]\begin{gathered} =\text{ }\frac{2}{5}\text{ x 200} \\ =\text{ }\frac{2\text{ x 200}}{5} \\ =\text{ }\frac{400}{5} \\ =\text{ 80 students} \end{gathered}[/tex]Part B
number of students that pick orange as their favorite fruits
[tex]\begin{gathered} =\frac{3}{8}\times200^{} \\ =\text{ }\frac{3\text{ x 200}}{8} \\ =\text{ }\frac{600}{8} \\ =\text{ 75} \end{gathered}[/tex]number of students that pick plum as their favorite fruits
[tex]\begin{gathered} =\text{ }\frac{1}{10}\text{ x 200} \\ =\text{ }\frac{200}{10} \\ =\text{ 20} \end{gathered}[/tex]There are 55 more students that chose orange rather than plum.
Find the distance between the points (0,–1) and (0,–11).Question 4 options:1191012
We are given the following points:
[tex](0,-1);(0,-11)[/tex]We can use the formula for the euclidean distance:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where:
[tex]\begin{gathered} (x_1,y_1)=(0,-1) \\ (x_2,y_2)=(0,-11) \end{gathered}[/tex]Replacing the values:
[tex]d=\sqrt[]{(0-0)^2+(-11-(-1))^2}[/tex]Solving we get:
[tex]d=\sqrt[]{(-11+1)^2}[/tex]Solving the square root
[tex]d=-11+1=10[/tex]Therefore, the distance is 10.
O GRAPHS AND FUNCTIONSFinding a difference quotient for a linear or quadratic function
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given difference quotient formula
[tex]\frac{f(x+h)-f(x)}{h}[/tex]STEP 2: Write the given function f(x)
[tex]f(x)=-2x^2-4x+7[/tex]STEP 3: Get f(x+h)
[tex]\begin{gathered} f(x)=-2x^2-4x+7,\text{ we n}eed\text{ to get }f(x+h) \\ f(x+h)=-2(x+h)^2-4(x+h)+7 \\ -2(x+h)^2-4(x+h)+7=-2(x^2+2xh+h^2)-4x-4h+7 \\ \Rightarrow-2x^2-4xh-2h^2-4x-4h+7 \\ \Rightarrow-2x^2-2h^2-4xh-4x-4h+7 \end{gathered}[/tex]STEP 4: Rewrite the expression by substitution
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}\Rightarrow\frac{-2x^2-2h^2-4xh-4x-4h+7-(-2x^2-4x+7)}{h} \\ \Rightarrow\frac{-2x^2-2h^2-4xh-4x-4h+7+2x^2+4x-7_{}}{h} \\ Re-\text{arrange the expression} \\ \frac{-2x^2+2x^2-2h^2-4xh-4x+4x-4h+7-7}{h} \\ \Rightarrow\frac{-2h^2-4xh-4h}{h} \\ \Rightarrow\frac{-h(2h)}{h}-\frac{(4x)h}{h}-\frac{h(4)}{h} \\ \Rightarrow-2h-4x-4 \end{gathered}[/tex]Hence, the result of the simplification is:
[tex]-2h-4x-4[/tex]water stations will be placed every 400 metets of a 5 kilometer racehow many water staions are neeedded
13 water stations will be placed every 400 meters of a 5 kilometer.
Given: Water stations will be placed ; every 400 meters
Also the total distance = 5 km = 5000 meters
Thus if a water station is supposed to be kept at every 400 meter distance then that means we can find out this distance by using unitary method
this means by using unitary method we get;
Number of water stations needed is = 5000 divided by 400
12.5 = 13 water stations would be required.
Thus 13 water stations will be placed every 400 meters of a 5 kilometer.
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sarah knows how important it is to budget her monthly expenses she earns 3,120 every month and her monthly expenses total $2,130. Determine how much money Sarah spends on her monthly Rent. Rent=49%, School Loan=23%, Car Insurance=3%, Car=20%, Phone=5%?
The rent represents 49% of her expenses.
Her total expenses are $2130, then she spends $2130*49% = $1043.7 on her rent.
If A={h,y,d,r,o,p,l,a,n,e,s} and U={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}, find A′
Answer:
A' = { b,c,f,g,i,j,k,m,q,t,u,v,w,x,z }
Step-by-step explanation: