Using the slope concept, it is found that the distances from the shore at each moment are given by:
a) 2664 feet.
b) 976 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
Item a:
The vertical distance is of 280 feet, with an angle of 6º. The distance from the shore is the horizontal distance of x. Hence:
[tex]\tan{6^\circ} = \frac{280}{x}[/tex]
[tex]x = \frac{280}{\tan{6^\circ}}[/tex]
x = 2664.
Item b:
The vertical distance is of 280 feet, with an angle of 16º. The distance from the shore is the horizontal distance of x. Hence:
[tex]\tan{16^\circ} = \frac{280}{x}[/tex]
[tex]x = \frac{280}{\tan{16^\circ}}[/tex]
x = 976.
More can be learned about the slope concept at https://brainly.com/question/18090623
Choose all of the symbols that make the following sentence true.
4 ^0 ___ 5 ^-1
=
<
≥
≤
≠
>
Answer:
≠ and >
Step-by-step explanation:
_________________
1. Jeremy has $12000 cash to invest in the bank compounded at 4% interest annually.
a.
What equation will calculate the value in x years? y =
Answer:
[tex]A(x) = 12000(1.04)^x[/tex]
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
$12000 cash
This means that [tex]P = 12000[/tex]
Compounded at 4% interest annually.
This means that [tex]r = 0.04, n = 1[/tex]
What equation will calculate the value in x years?
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(x) = P(1 + \frac{r}{n})^{nx}[/tex]
[tex]A(x) = 12000(1 + 0.04)^x[/tex]
[tex]A(x) = 12000(1.04)^x[/tex]
using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equation 10.0y-4.55x=581. where x is the number of years after 2000 what is projected population in 2026?
Answer:
The projected population in 2026 is of 699.3 million.
Step-by-step explanation:
Population:
The population, in x years after 2000, is given by the follwing equation:
[tex]y - 4.55x = 581[/tex]
That is:
[tex]y(x) = 4.55x + 581[/tex]
What is projected population in 2026?
2026 - 2000 = 26, so this is y(26).
[tex]y(26) = 4.55(26) + 581 = 699.3[/tex]
The projected population in 2026 is of 699.3 million.
Out of 350 applicants for a job, 158 are female and 66 are female and have a graduate degree. Step 2 of 2 : If 110 of the applicants have graduate degrees, what is the probability that a randomly chosen applicant is female, given that the applicant has a graduate degree
Answer:
33/55
Step-by-step explanation:
Total applicants, n(T) = 350
Female applicants, n(F) = 158
Female and Graduate applicants, n(FnG) = 66
Graduates, n(G) = 110
Probability of female Given that applicant has graduate degree; this is a conditional probability problem;
Recall :
P(A given B) = P(A|B) = P(AnB) / P(B)
Therefore ;
P(F|G) = P(FnG) / P(G) = 66 / 110 = 33/55
What is the result of subtracting the second equation from the first
I didn’t undertand the question... mayb ur attachment isnt added! Plz check!
QUESTION 14 · 1 POINT
Translate the English phrase into an algebraic expression: 6x less than 81xsquared
Answer:
Step-by-step explanation:
81x² - 6x
Answer:
81x² - 6x
Step-by-step explanation:
81x² - 6x
Which expression is equivalent to:1/m6
Answer:
A
Step-by-step explanation:
6 is a power. So both C and D are wrong because 6 is being treated as an ordinary integer.
So the answer must be either A or B.
B is not correct because to move an expression from the denominator to the numerator changes the sign in the base (which is m in this question).
A is correct. the power is changed from 6 in the denominator to -6 in the numerator. m is shifted to the numerator as well.
14+6×(9-6)
please answer
Answer:
32
Step-by-step explanation:
14+6(9-6)
[9-6=3]
14+6x3
[6x3=18]
14+18
32
---
hope it helps
Answer:
14+6×(9-6)=32
Which of these random samples represents a representative sample of the number of students who enjoy science class?
A. 30 students in the lunchroom.
B. 30 students who failed science class last year.
C. 30 students who received high grades in their science class last semester.
D. 30 students who participated in the science fair.
Answer: A. 30 students in the lunchroom.
Step-by-step explanation:
A representative sample simply refers to the sample that has same characteristics just like the population.
A random-based selection is regarded as a representative of the population. In this case, the random sample that represents a representative sample of the number of students who enjoy science class is "30 students in the lunchroom".
When the students in the lunchroom are chosen, then it's a representation of the entire students in the school. This is the best option when compared to other options as they don't represent the students entirely.
Answer:
30 students in the lunchroom
Step-by-step explanation:
Got it right on the test.
write an equation of the line below
Calculating area of rectangle
Your measurments Another student's measurements
Length (cm) 20.70 20.74
Width (cm) 10.44 10.46
Area (cm2)
Required:
Why might two students have different calculated areas when measuring the same rectangle?
Answer:
[tex]Area = 216.108cm^2[/tex] --- You
[tex]Area = 216.940cm^2[/tex] --- Another student
Reason: Because there is a variation in the given dimensions
Step-by-step explanation:
Given
Your measurement
[tex]Length = 20.70cm; Width =10.44cm[/tex]
Another students'
[tex]Length = 20.74cm; Width =10.46cm[/tex]
Solving (a): The area
Area is calculated as:
[tex]Area = Length * Width[/tex]
For you
[tex]Area = 20.70cm * 10.44cm[/tex]
[tex]Area = 216.108cm^2[/tex]
For the other student
[tex]Area = 20.74cm * 10.46cm[/tex]
[tex]Area = 216.940cm^2[/tex]
Solving (b): Reason for the variation in the areas
The given measurements are estimates of the dimensions of the rectangle.
Since there is a variation in the estimates, there will be some level of variation in the calculated area.
pls help for both 12 and 13!!
Answer:
The answer to 12 is 40 cubic units
Step-by-step explanation:
A recipe calls for 24 ounces of oil and 8 ounces of vinegar. Kim is making dressing with 12 ounces
of vinegar using the same ratio of oil to vinegar
How much oil should kin use?Complete the Table
Answer:
36 ounces.
Step-by-step explanation:
The ratio being 24:8 can be simplified to 3:1
Multiply the one (the vinegar) by a factor of 12
What happens to one side has to happen to the other
12(3:1)
36 ounces.
Answer:36
Step-by-step explanation:
Which is the graph of an even monomial function?
Answer:
The graph of an even function is symmetric about the y-axis. The graph of an odd function is symmetric about the x-axis. It is possible that the use of these two words originated with the observation that the graph of a polynomial function in which all variables are to an even power is symmetric about the y -axis.
Which ones are correct?
Answer:
Th answer is D
Step-by-step explanation:
Two and three fifths plus one and three fifths
Answer:
2 3 + 1 3 = 3/5 + 3/5 = 1 1/5 + 2+1 = 3 + 1 !/5 = 4 1/5
5 5
Step-by-step explanation: The Slashes mean The number bellow
Please make this answer Brainlist...
Meg makes a dot plot for the data 9, 9, 4, 5, 5, 3,
4,5, 3, 8, 8, 5. Where does a gap occur?
The gap consists of the values 6 and 7.
Check out the dot plot below to see what I mean. We have one cluster on the left from 3 to 5. Then another cluster on the right from 8 to 9.
Answer:
The gap is present around 6 & 7
Step-by-step explanation:
Since there is no evidence of dots above 6 & 7, there must have been a freeze in data around then, called a gap.
if jane give £2 pounds to charlotte they will have equal amount of money. instead
charlotte give £4 to jane the ratio of jane's money to charlotte will be 2:1. how much
do jane and charlotte each have to start with
4/8 =?/2 please answer
Answer:
? = 1
Step-by-step explanation:
4/8 = ?/2
Change the ? into a variable so it's easier to calculate:
Variable x = ?
4/8 = x/2
Cross multiply:
4 × 2 = 8 × x
8 = 8x
Divide both sides by 8 to isolate the variable:
1 = x
Check your work:
4/8 = 1/2
4 × 2 = 8 × 1
8 = 8
Correct!
Find the size of the of angle x.
Answer:
80 degrees
Step-by-step explanation:
Since a triangle is 180 degrees
you then add to 2 degrees given and subtract it from 180
65+35=100
180-100=80 degrees
How to solve the inequality 8x + 10 ≤ 60
Answer:
x ≤ 6.25
Step-by-step explanation:
8x + 10 ≤ 60
Subtract 10 from both sides
8x ≤ 50
Divide both side by 8
x ≤ 6.25
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
How to solve this?!?!? (5x+24)(9x+12) + (3x+9)(8x+6)(2x+7)
Answer and Step-by-step explanation:
First, multiply the parentheses, then add everything together.
-- (5x + 24)(9x + 12)
-- 45[tex]x^2\\[/tex] + 60x + 216x + 288 (Simplify)
-- 45[tex]x^2\\[/tex] + 276x + 288
--- (3x + 9)(8x + 6)
--- 24[tex]x^2\\[/tex] + 18x + 72x + 54 (Simplify)
--- 24[tex]x^2\\[/tex] + 90x + 54
---- (2x + 7)(24[tex]x^2\\[/tex] + 90x + 54)
---- 48[tex]x^{3}[/tex] + 180[tex]x^2\\[/tex] + 108x + 168[tex]x^2\\[/tex] + 630x + 378 (Simplify)
---- 48[tex]x^{3}[/tex] + 348[tex]x^2\\[/tex] + 738x + 378
----- 45[tex]x^2\\[/tex] + 276x + 288 + 48[tex]x^{3}[/tex] + 348[tex]x^2\\[/tex] + 738x + 378
----- 48[tex]x^{3}[/tex] + 393[tex]x^2\\[/tex] + 1014x + 666
48[tex]x^{3}[/tex] + 393[tex]x^2\\[/tex] + 1014x + 666 is the final answer.
#teamtrees #PAW (Plant And Water)
Answer:
[tex] \rm \displaystyle {48x}^{3} + 393 {x}^{2} +1014x + 660[/tex]
Step-by-step explanation:
we would like to simplify the following:
[tex] \rm \displaystyle (5x + 24)(9x + 12) + (3x + 9)(8x + 6)(2x + 7)[/tex]
there're two parts the multiplication the whole part to solve the multiplication part we can consider FOIL and for the whole, PEMDAS which can be represented as
[tex] \rm\displaystyle \rm \displaystyle \underbrace{\underbrace{(5x + 24)(9x + 12) } _{ \text{FOIL - 1}}+ \underbrace{ (3x + 9)(8x + 6)(2x + 7)} _{ \text{FOIL - 2}}} _{ \text{PEMDAS}}[/tex]
let's figure out FOIL-1 part
By FOIL we obtain:
[tex] \displaystyle {45x}^{2} + 60x + 216x + 288[/tex]
simplify addition:
[tex] \displaystyle {45x}^{2} + 276x+ 288[/tex]
let's figure out FOIL-2:
By FOIL and PEMDAS we acquire:
[tex] \rm \displaystyle {48x}^{3 } + {348x}^{2} + 738x + 378[/tex]
finally the whole part
[tex] \rm \displaystyle {45x}^{2} + 60x + 216x + 288+ {48x}^{3 } + {348x}^{2} + 738x + 378[/tex]
combine like terms:
[tex] \rm \displaystyle {48x}^{3} + 393 {x}^{2} +1014x + 660[/tex]
and we are done!
Find C.
Round to the nearest tenth.
20 ft)
22 ft
B
18 ft
А
Triangle D E F is shown. Angle E F D is a right angle. The length of E F is 24 and the length of D F is 7.
Which trigonometric ratios are correct for triangle DEF? Select three options.
sin(D) = StartFraction 24 Over 25 EndFraction
cos(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 24 Over 7 EndFraction
sin(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 7 Over 24 EndFraction
Answer:
Sin(E) = 7/25
Sin(D) = 24/25
Tan(D)= 24/7
Step-by-step explanation:
Sin=opp/hyp
Tan=opp/adj
Cos=adj/hyp
The trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
How to determine the trigonometric ratios?The given parameters are:
EF = 24
DF = 7
Start by calculating the length DE using:
DE²= EF² + DF²
So, we have:
DE²= 24² + 7²
Take the square root of both sides
DE= 25
The sine of the angles is calculated using:
sin(Ф) = opp/hyp
So, we have:
sin(E) = 7/25
sin(D) = 24/25
The tangent of the angles is calculated using:
tan(Ф) = opp/adj
So, we have:
tan(D)= 24/7
Hence, the trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
Read more about trigonometric ratios at:
https://brainly.com/question/11967894
Please help it’s a riddle can you find the correct answer
the product of 2 numbers, p and q, decreased by 3 times their sum. (as an algebraic expression)
Answer:
3 - (p*q) im not sure lol
Step-by-step explanation:
0.87 written as a fraction
Answer:
[tex] \frac{87}{100} [/tex]Step-by-step explanation:
Convert to a mixed number by placing the numbers to the right of the decimal over 100. Reduce the fraction.
Hope it is helpful...Answer:
87/100
Step-by-step explanation:
Help me out plsssssss
Answer:
125
Step-by-step explanation:
the bearing of b to a is equal to 85+45
What is the value of X
A. x=20
B. x=15
C. x=10
D. x=5
Tamara uses a coupon to save 20% off her purchase at the bookstore. The original cost of Tamara's purchase is d dollars.
Which expressions represent the cost, in dollars, of Tamara's purchase after using the coupon? Choose all that apply.
Answer:
The equation would be d - (d×0.2)
