Romeo is 171.5 feet away from Juliet when she saw her at an angle of depression of 5 degrees.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, Juliet is standing atop a 15-‐foot balcony when she spots Romeo at an angle of depression of 5°.
Here height is 15 feet and by interior alternate angles theorem angles is 5°
we have to determine the length of the adjacent side or base.
tan5° = 15/base.
base = 15/0.087.
base = 171.5 feet.
learn more about trig ratios here :
https://brainly.com/question/14977354
#SPJ1
If you put aside $25 each month for 12 months in a CD, how much will you have saved?
Two angles are complementary to each other. one angle measures 18°, and the other angle measures (8x − 28)°. determine the value of x. 12.5 20 44.5 16
The value of x in complementary angle is 12.5⁰.
We need to know about complementary angles to solve this problem. The complementary angle is the angle that can make another angle has a value of 90⁰. It can be written as
A + B = 90⁰
where A and B are the complementary angles.
From the question above, the given parameters are
A = 18⁰
B = (8x - 28)⁰
By substituting the given parameters, we can calculate the x value
A + B = 90⁰
18⁰ + (8x - 28)⁰ = 90⁰
8x = 90 - 18 + 28
8x = 100
x = 12.5⁰
Find more on complementary angle at: https://brainly.com/question/20428380
#SPJ4
Answer: 12.5
Step-by-step explanation:
18+8x-28=90
18-18
90-18
8x-28=72
28+28
72+28
8x=100
8x/8
100/8
x=12.5
Cassie volunteers at an animal shelter. She needs a totsl of 40 hours of volunteers time for a class. So far, she has volunteered for 18.5 hours. How many more hours does she need to volunteer.
Answer: 21.5 hrs
Step-by-step explanation:
40 - 18.5 = 21.5 hours left
Answer:
21.5
Step-by-step explanation:
hope it helps
the united company had 15 applications for funding this year. if 8 of these applications can be funded, how many different lists of successful applications are there
A company received 15 funding applications and want to select 8 of them to be funded. The number of different lists of successful applications is 6,435
Suppose we have n objects in total and we want to select r objects among total objects, the number of ways they can be selected is given by the combination formula:
ⁿCr = n! / [r! (n-r)!]
Data from the problem:
n = total applications = 15
r = number of selected applications = 8
Hence, the number of different lists of successful applications is:
¹⁵C₈ = 15! / [8! (15-8)!]
= 15! / [8! 7!]
= 6,435
Thus, the number of different lists can be selected is 6,435
Learn more about combination here:
https://brainly.com/question/17139330
#SPJ4
when sample size increases, everything else remaining the same, the width of a confidence interval for a population parameter will:
when sample size increases, everything else remaining the same, the width of a confidence interval decreases.
The sample size is defined as the the number of observations or participants included in a study.
The confidence interval is defined as the mean of the estimate plus and minus the variation in that estimate. That means when you do the test multiple times, then the value may be vary from the estimated value. The confidence interval is the range of those values.
So when the sample size increases the width of the confidence interval decreases
Hence, when sample size increases, everything else remaining the same, the width of a confidence interval decreases.
Learn more about confidence interval here
brainly.com/question/24131141
#SPJ4
Suppose that you use a pair of chopsticks
and apply a force of 1 are
N over a distance of 0.01 m. How much
work do you do? If the output force of the
chopsticks is only 0.5 N, how far do the tips
of the chopsticks move?
0.01 N of work is to be done to move the chopsticks to a distance of 0.01 m
0.02m far the tips of the chopsticks move.
What is work done?
Every time a force pushes something over a distance, work is done. By multiplying the force by the distance moved in the force's direction, you may determine the energy transferred, or work done. Energy transmitted equals work done, which is force times the distance travelled in the force's direction.
1. WD = F×d
= 1×0.01
= 0.01 N
2. d = WD/F
= 0.01/(0⋅5)
= 0.02m
0.02m far the tips of the chopsticks move.
Learn more about Work done from the link below
https://brainly.com/question/22015026
#SPJ1
G is the centroid of triangle abc. what is the value of x? what is the length of segment dg? units what is the length of segment ag? units what is the length of segment ad? units
According to the Centroid Ratio Theorem , we have:
x = 37 , DG = 22,
AG = 44 and AD = 66
Centroid Ratio Theorem:
The Centroid ratio theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid point of the side.
according to the centroid ratio theorem, we have,
AG = 2/3 (AD) ----------------------------- (1)
AG = x + 7
DG = x - 15
AD = x + 7 + x- 15 = 2x - 8
Putting the values in equation (1)
x + 7 = 2/3 (2x - 8)
⇒ 3(x + 7) = 2( 2x - 8)
⇒3x + 21 = 4x - 16
⇒ -x = -37
⇒ x = 37
Putting the value of x= 37
DG = 37 - 15 = 22
AG = 37 +7 = 44
AD= 2×37 - 8 = 66
Learn more about Centroid ratio of theorem :
https://brainly.com/question/20627009
#SPJ4
sorry for the bad picture but help needed asap! points!!!
Jessica bought 5 yards of fabric, plus 20% extra fabric. Derek bought 3 yards of fabric, plus 25% extra. Who bought more fabric? How much more? SHOW WORK PLEASE AND THANK U !!! <3
A. Jessica bought 1/4 yard more than derek.
B. Jessica bought 2 and 1/4 yards more than derek.
C. Derek bought 1/4 yards more than jessica.
D. Derek bought 2 and 1/4 more than jessica.
Jessica bought [tex]2\frac{1}{4}[/tex] yards of fabric more than Derek.
According to the question,
We have the following information:
Jessica bought 5 yards of fabric, plus 20% extra fabric. Derek bought 3 yards of fabric, plus 25% extra.
Now, we will find first the extra fabric they both bought:
For Jessica, we have:
20% of 5
20*5/100
1 yard
Now, the total fabric Jessica has:
5+1
6 yards
For Derek, we have:
25% of 3
25*3/100
3/4 yards
Now, the total fabric Derek has:
3 + 3/4
Taking 4 as the least common factor and adding the fractions:
15/4 yards
Now, we will subtract the fabric Derek has from the fabric Jessica has:
6 - 15/4
(24-15)/4
9/4
Converting this into mixed fraction:
[tex]2\frac{1}{4}[/tex] yards
Hence, the correct option is B.
To know more about Jessica bought here
https://brainly.com/question/2551588
#SPJ1
Write the equation of a line that passes through the points (4,6) and (−8,3)
Answer:
y= 1/4x+5
Step-by-step explanation:
y=mx+c
to calculate gradient: change in y/change in x
-3/-12 = 0.25
y = 1/4x+c
4 * 1/4 = 1
6-1 = 5
c= 5
Totally:
y= 1/4x+5
Lydia buy 5 pound of apple and 3 pound of banana for a total cot of $8. 50. Ari buy 3 pound of apple and 2 pound of banana for a total cot of $5. 25. Thi ytem of equation repreent the ituation, where x i the cot per pound of apple, and y i the cot per pound of banana
We need to multiply equation 2 with 3 and result is x = 1.25. The cost of one apple and one banana is $1.25 and $0.75 respectively.
Forming the equation using given variables x and y. Firstly writing the equation based on Lydia's items.
5x + 3y = 8.50 : Equation 1
Now writing the equation based on Ari's items.
3x + 2y = 5.25 : Equation 2
Now we need to equate one variable to find the other variable. So, multiplying equation 1 with 2 and equation 2 with 3.
10x + 6y = 17 : Equation 3
9x + 6y = 15.75 : Equation 4
Subtracting equation 4 from equation 3. We get the result -
x = 1.25
Keep the value of x in equation 1 to find the value of y
5×1.25 + 3y = 8.50
6.25 + 3y = 8.50
3y = 8.50 - 6.25
3y = 2.25
y = 2.25/3
y = 0.75
Thus, the cost of one apple is $1.25 and cost of one banana is $0.75.
Learn more about equation -
https://brainly.com/question/21405634
#SPJ4
The complete question is -
lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. this system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas. 5x 3y = 8.5 3x 2y = 5.25 if you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination? complete the multiplication and add the equations. what is the result? what is the price per pound of apples? what is the price per pound of bananas?
in a survey of 2480 golfers, 15% said they were left-handed. the survey's margin of error was 3%. construct a confidence interval for the proportion of left-handed golfers.
The confidence interval for the proportion of left-handed golfers is of:
(0.12, 0.18).
How to obtain a confidence interval?A confidence interval is calculated as the sample mean plus/minus the margin of error, hence the bounds of the confidence interval are given as follows:
Lower bound: sample mean - margin of error.Upper bound: sample mean + margin of error.In the context of this problem, these parameters are given as follows:
Sample mean: 15% as a percentage, 0.15 as a proportion.Margin of error: 3% as a percentage, 0.03 as a proportion.Hence the lower bound of the confidence interval for the proportion of left-handed golfers is:
0.15 - 0.03 = 0.12.
The upper bound of the confidence interval for the proportion of left-handed golfers is:
0.15 + 0.03 = 0.18.
Then the interval is:
(0.12, 0.18).
More can be learned about confidence intervals at https://brainly.com/question/25890103
#SPJ1
The jenkins family drinks 3/4 of a gallon of orange juice every 3 days. How many orange juice do they drink per day?
Answer:
1/4
Step-by-step explanation:
3/4 divided by 3=1/4
pls send the correct answer and show work!
Answer: x = 140°
Step-by-step explanation:
The sum of all interior angles in a pentagon is 540°.
Since you have every other angle except for one, you can subtract them from the total:
540°-120°-118°-89°-73° = 140°
Therefore the x angle is equal to 140°.
What is the solution to this system of linear equations 2x y 1 3x y 6 1 3?.
The solution to the linear equation is (-1, 3).
What is a linear equation ?
Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.
2x + y = 1 …… (1)
3x - y = -6 …… (2)
To solve the linear equations in two variables
By adding both the equations
5x = -5
x = -1
Substitute the value of x in equation (1)
2 (-1) + y = 1
-2 + y = 1
y = 1 + 2 = 3
y = 3
Therefore, the solution to the linear equation is (-1, 3).
Learn mlore about linear equation here;
https://brainly.com/question/25858757
#SPJ4
three letters are written to three different people and three envelopes are appropriately addressed. if each letter is placed into a randomly selected envelope so that each envelope contains exactly one letter, what is the probability that at least one person will receive the correct letter?
The probability that at least one person will receive the correct letter is 2/3.
Given data,
Let's say that the letter matching to the envelope is A, B, and C.
Each envelope has exactly one letter inside it once the letters are randomly placed inside.
Aa, Bb, Cc, Aa, Bc, Cb, Ab, Ba, Cc, Ab, Bc, Ca, Ac, Bb, Ca, Ac, Ba, Cb, are all possible combinations.
Thus, the total number of scenarios is 6 (n(S)).
A=(Aa, Bb, Cc), (Aa, Bc, Cb), (Ac, Bb, Ca), (Ab, Ba, Cc), n(A)=4
let A be an event that at least one letter is in its right envelope.
So,
The probability that at least one letter is in the right envelope P(A) = n(S) / n(A) = 4 / 6
= 2 / 3
To learn more about probability click here:
brainly.com/question/11234923
#SPJ4
THE VALUE OF JOHN'S
BASEBALL CARD
INCREASED BY $5. IT IS
NOW WORTH
$158.
(percent change)
The percent change of the worth is 3.26%.
Apples were for sale from a fruit vendor. He has 420 apples and sells 40% of them. How many apples did he have in total when he first started?
Solution: Assume a fruit vendor had x apples in stock.
According to the query,
(100 – 40%) of x = 420
60% of x = 420
60/100 x = 420
X = 700
The fruit vendor, therefore, had 700 apples in all.
Let , the worth is $x.
according to the question, $x + $5 =$158
∴ $x= $153
∴ percent change= (5/153)×100
=3.26%
The percent change of the worth is 3.26%.
to learn more about the percentage from the given link,
https://brainly.com/question/24877689
#SPJ13
if the probability that a particular event occurs is 7/10, what are the odds favoring the event not occurring? express your answer in the form a:b.
For the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to
7 : 3.
As given in the question,
Probability of any particular event occurring is equal to 7 /10
Probability of any particular event not occurring is = 1- (7/10)
= (10 -7) /10
= 3/10
Probability of the odds favoring the events which are not occurring
= (7 /10) / (3/10)
= ( 7 × 10) / (3 × 10)
= 7 /3
Odds favoring the events which are not occurring in the form a: b
= 7 : 3
Therefore, for the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to 7 : 3.
Learn more about probability here
brainly.com/question/11234923
#SPJ4
solve for x
3(-7x-3)+4x= -(x-3)
it doesnt accept 3/4 as an answer
thanks in advance
Answer:
[tex]3( - 7x - 3) + 4x = - (x - 3)[/tex]
[tex] - 21x - 9 + 4x = - x + 3[/tex]
[tex] - 21x + 4x + x = 9 + 3[/tex]
[tex] - 16x = 12[/tex]
[tex] - 16 \div ( - 16x = 12)[/tex]
[tex]x = - \frac{3}{4} [/tex]
Step-by-step explanation:
it is negative 3/4 not positive 3/4
A line that includes the point (5, 17) has a slope of 1. What is its equation in slope -intercept form?
Answer:
17 = 5 + b
b = 12
y = x + 12
Chin has $75.00 in a savings account that earns 5% interest,
compounded annually.
What will the balance be after 4 years?
Round to the nearest cent.
75÷100=0.75
0.75×5=3.75
3.75×4=15
75+15=90
Mickey simplified the expression below. He then checked his work by substituting 4 for x. He noticed his two values were not equal. What was Mickey’s error when simplifying?
Expression
Simplified Expression
2 x squared minus 4 x minus 9 minus x squared + 2 x + 3
x squared minus 6 x minus 6
Mickey should have added –4 and 2 when combining the coefficients of the x terms.
Mickey should have added 2 and 1 when combining the x squared terms.
Mickey should have added 9 and 3 when combining the constant terms.
Mickey should have added –4 and –1 when combining the x terms.
The correct option is, Mickey should have added –4 and 2 when combining the coefficients of the x terms.
Given,
The expression; 2x² - 4x - 9 - x² + 2x + 3
We have to simplify the expression;
To group and arrange an expression in such a way that it is easier to understand and solve is to simplify the expression.
We first group and find like terms and then add and cancel out
2x²-x²- 4x+2x - 9+ 3
=x²-2x-6
Mickey did not add the coefficients -4 and +2 for x terms in the expression, instead it looked like he added 4+2 as the coefficients
Therefore the correct option is
Mickey should have added –4 and 2 when combining the coefficients of the x terms.
Learn more about simplifying the expression here;
brainly.com/question/19579628
#SPJ1
Find the simplified product where x20: √5x (√8x²-2√x)
√10x
2x √40x-2x
O 2x10x-2√5x
O2x10x-2x√√5
DONE
The solution of the expression is 2√5x(√2-1).
From the question, we have
√5x ( √8x² - 2√x)
= √5x ( 2√2x - 2√x)
= √5x(√2-1)(2√x)
= 2√5x(√2-1).
The solution of the expression is 2√5x(√2-1).
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
To learn more about multiplication visit: https://brainly.com/question/5992872
#SPJ1
Answer: ITS D
Step-by-step explanation:
2x sqrt 10x - 2x sqrt 5
determine the smallest integer value of x in the solution of the following inequality
4x-9>=17
Step-by-step explanation:
4x - 9 ≥ 17
4x ≥ 17 + 9
4x ≥ 26
4x/4 ≥ 26/4
x ≥ 13/2
x ≥ 6.5
The side lengths of triangle ABC are written in terms of the variable p, where p≥ 3. p+4 4p-1 3p B
Which is correct regarding the angles of the triangle? mm mzB O m/B>m/A> mZC Omze>m/A> m/B Omzc>m/B> m/A
The correct statement that regarding the angles of triangle is option (C) m∠C > m∠A > m∠B
The value of p ≥ 3
Consider the value p = 3
The length of the side AB = 4p - 1
= 4×3 - 1
= 12 - 1
= 11 units
The length of side BC = 3p
= 3×3
= 9 units
The length of the side AC = p + 4
= 3 + 4
= 7 units
Then length of AB > length of BC > length of AC
The angles opposite to the side AB, BC and AC are m∠C , m∠A and m∠B
Then m∠C > m∠A > m∠B
Hence, the correct statement that regarding the angles of triangle is option (C) m∠C > m∠A > m∠B
Learn more about triangle here
brainly.com/question/17738167
#SPJ1
In a positive correlation, __________.
A.
the independent variable is always negative
B.
an increase in the independent variable has a corresponding increase in the dependent variable
C.
the dependent variable is always positive
D.
a decrease in the independent variable has a corresponding increase in the dependent variable.
Answer:
B
Step-by-step explanation:
In a positive correlation, an increase in the independent variable has a corresponding increase in the dependent variable.
What is correlation?
Correlation is a statistical measure that expresses the extent to which two variables are linearly related. We know a positive correlation—when the correlation coefficient is greater than 0 signifies that both variables move in the same direction. Also, A positive correlation exists when one variable decreases as the other variable decreases or one variable increases while the other increases.
I would appreciate it if you mark my answer as brainliest.
The height of a triangle is 5 m longer than the base. If the area is 150 m2 , how long is the base?.
The base of the triangle is 15 meters.
Here, we are given that the height of a triangle is 5 m longer than the base.
Let the height of the triangle be h
Then, the base of the triangle will be = h - 5
Further, we are given that area of the triangle = 150 meter square
We know that area of a triangle = 1/2 × base × height
⇒ 150 = 1/2 × h × (h-5)
150 × 2 = h(h-5)
300 = [tex]h^{2}[/tex] - 5h
[tex]h^{2}[/tex] - 5h - 300 = 0
Now, we solve the above quadratic equation by splitting the middle term.
[tex]h^{2}[/tex] + 15h - 20h - 300 = 0
h( h + 15) - 20( h + 15) = 0
(h - 20) (h + 15) = 0
Thus, h = 20 or -15
But since height cannot be negative, h = 20
⇒ base = h - 5
= 20 - 5
= 15 meters
Thus, the base of the triangle is 15 meters.
Learn more about triangles here-
https://brainly.com/question/1058720
#SPJ4
Please help, for the second variable I couldnt read my own hand writting so im no sure if its f or r, someone please help soon
Answer:
k = [tex]\frac{fr^2}{90}[/tex]
Step-by-step explanation:
f = k [tex]\frac{90}{r^2}[/tex] ( multiply both sides by r² to clear the fraction )
fr² = 90k ( divide both sides by 90 )
[tex]\frac{fr^2}{90}[/tex] = k
Part-Time Job So far this week, you have worked 10 hours at your part-time job.
This is 80% of the number of hours you work each week. How many hours do you
work each week?
Answer:
12.5 hours a week
Step-by-step explanation:
So far this week, you have worked 10 hours at your part-time job. This is 80% of the number of hours you work each week. How many hours do you work each week?
10 hours = 80%
80% = 0.8
10/0.8 = 12.5 hours a week
line has a slope of –1/9 and includes the points (10,6) and (s,7). What is the value of s?
Answer:
s=1
Step-by-step explanation:
Slope formula is
Δy/Δx
Substitute in:
7-6/s-10=-1/9
cross multiply
7-6=-1/9s+10(1/9)
7-6=-1/9s+10/9
1-10/9=-1/9s
-1/9=-1/9s
divide both sides by -1/9
thus:
1=s
s=1
(check by plugging back in)
7-6/1-10=-1/9
