1.68 km from the skydiving center did Stella land .
What is trigonometric ratio?Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.
The basic trigonometric ratios formulas are given below,
sin θ = Perpendicular/Hypotenusecos θ = Base/Hypotenusetan θ = Perpendicular/Basesec θ = Hypotenuse/Basecosec θ = Hypotenuse/Perpendicularcot θ = Base/PerpendicularAccording to the question
Stella's friends got her a skydiving lesson .
Her helicopter took off from the skydiving center, ascending in an angle of 37 degree .
i.e angle of elevation = 37°
then traveled a distance of 2.1 kilometers , 1 kilometers before she fell in a straight line perpendicular to the ground.
i,e
Her helicopter is making a right angled triangle with respect to ground
in which
Hypotenuse of triangle = 2.1 km
Perpendicular of triangle = 1 km
with angle of elevation = 37°
now,
the distance from the skydiving center did Stella land
According to the Trigonometric ratios
cos θ = Base/Hypotenuse
substituting the value in formula
cos 37° = [tex]\frac{Base}{2.1}[/tex]
0.7986 * 2.1 = Base
Base = 1.68
Hence, 1.68 km from the skydiving center did Stella land .
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Simplify the expression. Show each step.
–5 × 1 × 11 × 4.
Is 100 a reasonable estimate 915.25 divided by 88.22
The reasonable estimate is 10.
We can approximate 915.25 to 900.
We can approximate 88.22 to 90.
Then we divide them: [tex]\frac{915.25}{88.22}\approx\frac{900}{90}=10[/tex].
So the reasonable estimate is 10.
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100 is not a reasonable estimate for the operation 915.25 divided by 88.22, as the actual answer is approximately 10.37. While estimates don't provide exact numbers, the difference here is too great for 100 to be considered reasonable, depending on the level of accuracy needed.
Explanation:In mathematics, estimation is commonly used when you do not need the exact answer, but rather a ballpark number close to the actual value. The student's question revolves around whether 100 is a reasonable estimate for the operation 915.25 divided by 88.22. We can check this by performing the actual division: 915.25 / 88.22 equals approximately 10.37. Although this is not exactly 100, it is within an order of magnitude which might make the estimate reasonable depending on the context. Therefore, as a quick estimate, 100 might not be suitable for high-precision contexts.
It's important to understand how estimates work. Their value is not in providing exact numbers, but in giving a quick understanding of a situation, especially when the exact numbers are complex or cumbersome. Here, however, the difference between the actual result (10.37) and the estimate (100) is quite significant, which suggests that 100 might not be a reasonable estimate in this case, depending on the level of accuracy needed.
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if the least value the variable k can be is 12,which of the following inequalities best shows all the possible values of k
Answer:
Its K ≥ 12
Step-by-step explanation:
Hope this helps! Have a good day!:) and happy St. Patrick's day lol
The store is 7⁄8 of a mile away from your house. You walked 1⁄5 of a mile towards the store before getting on the bus. If the bus went directly to the store, how many miles long was the bus ride?
27/40 miles long was the bus ride.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
The store is 7⁄8 of a mile away from your house.
Distance covered by Walking = 1/5
and, the rest is covered by Bus.
So, the distance covered by Bus
= 7/8- 1/5
= 35/ 40- 8/40
= 27/40
Hence, 27/40 miles covered by Bus.
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Betty is participating in a walk a thon. For every .25 miles she walks, she earns a donation. Betty walks 2.50 miles. How many donations did she earn?
Deb has of a brownie. She wants to divide it up into 's of a brownie so she can have it throughout the day. How many 's will she have?
She can enjoy her original 3/4 brownie divided into six equal parts, each constituting 1/8 of the delectable treat.
Deb possesses 3/4 of a brownie and intends to partition it into smaller portions, each equivalent to 1/8 of a brownie, allowing her to savor it throughout the day.
To determine the number of 1/8 portions she'll obtain, we can perform a simple division.
By dividing 3/4 by 1/8, we essentially multiply the numerator of 3/4 by the reciprocal of 1/8, which is 8/1.
This multiplication yields (3 * 8) / (4 * 1) = 24/4.
Simplifying further, we find that Deb will have 6 portions of 1/8 of a brownie.
Consequently, she can enjoy her original 3/4 brownie divided into six equal parts, each constituting 1/8 of the delectable treat.
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Question
Deb has 3/4 of a brownie. She wants to divide it up into 1/8 of a brownie so she can have it throughout the day. How many 1/8s will she have's will she have?
Walt received a package that is 2 1/3 inches long, 6 3/4 inches high, and 8 1/2 inches wide. What is the surface area of the package?
Answer : The surface area of the package is, [tex]185.9inch^3[/tex]
Step-by-step explanation :
The given package is in cuboid shape. Now we have to calculate the surface area of the package by using volume of cuboid.
Formula used for volume of cuboid is:
[tex]V=2(lb+bh+hl)[/tex]
where,
V = volume of package
l = length of package = [tex]2\frac{1}{3}inch=\frac{7}{3}inch[/tex]
b = width of package = [tex]8\frac{1}{2}inch=\frac{17}{2}inch[/tex]
h = height of package = [tex]6\frac{3}{4}inch=\frac{27}{4}inch[/tex]
Now put all the given values in the above formula, we get:
[tex]V=2\times [(\frac{7}{3}\times \frac{17}{2})+(\frac{17}{2}\times \frac{27}{4})+(\frac{27}{4}\times \frac{7}{3})][/tex]
[tex]V=2\times [\frac{119}{6}+\frac{459}{8}+\frac{63}{4}][/tex]
[tex]V=185.9inch^3[/tex]
Therefore, the surface area of the package is, [tex]185.9inch^3[/tex]
A window washer cleaned 38 windows in 2 hours. At this rate, how many windows did he clean in 7 hours?
Simplify the expression. 5x + 1 - 18
I'm confused about this question, can someone help me
Amir is operating a machine that adds sand to a concrete mixture. The machine adds 110 ton of sand to the mixture in 45 minute. Enter a number in each box to complete the statements. Write the ratio that compares 110 ton of sand to 45 minute. The ratio in ton(s) per minute(s) is $$ .
A new car is purchased for 20300 dollars. The value of the car depreciates at 8.75% per year. What will the value of the car be, to the nearest cent, after 12 years?
Answer:
$6,765.35.Step-by-step explanation:
Here we have to use the rate of depreciation, the initial value and the total time to find the final value with this formula
[tex]A=A_{0}(1-r)^{t}[/tex]
Where [tex]A[/tex] is the final value, [tex]A_{0}[/tex] is the initial value, [tex]r[/tex] is the rate of depreciation and [tex]t[/tex] is the time.
Replacing all values, we have
[tex]A=20300(1-0.0875)^{12}[/tex]
[tex]A=6765.35[/tex]
Therefore, after 12 years the car will value $6,765.35.
If James can swim 10 laps in 23 minutes, what would be his expected time for 15 laps?
Kim paycheck was 257.20. She put 1/4 of her paycheck into a savings account and used 1/3 of what was left to pay bills.How much money does she have remaining from her paycheck
What scale factor was applied to the first rectangle to get the result image?
Answer:
Step-by-step explanation: Add pic so ppl can help
help!!!!!!!! plz I need your help
sally purchased a rectangular table for her drawing room. The sides of the table are 24 inches and 18 inches. What is the diagonal length of the table?
HELP FOR BRAINLIEST
Choose the correct simplification of the expression a^7b^8/a^4b^4
A: a^11b^12
B: a^3b^4
C: 1/a^3b^4
D: 1/a^3b^2
A vendor pays a rock band 1/3 of the total profit from T-shirts and sweatshirts sold at every concert. The vendor paid the rock band $726 after the last concert. If the profit from T-shirts sales was $1,632, what was the profit from sweatshirt sales?
Ms.Gibson made an initial deposit of $500 when opening a bank account. After the initial deposit, she deposited the same amount of money each month. The table below shows the total amount of money, a, she deposited into the account after a certain number of months, t, since opening it. Write an equation to model the relationshipbetween t and a.
To model the relationship between the number of months, t, since opening the bank account and the total amount of money, a, deposited into the account, we can use the equation a = 500 + 500t.
Explanation:To model the relationship between the number of months, t, since opening the bank account and the total amount of money, a, deposited into the account, we need to find the pattern. According to the information given, Ms. Gibson made an initial deposit of $500 and then deposited the same amount each month. This means that the total amount of money, a, deposited after a certain number of months, t, can be represented by the equation:
a = 500 + 500t
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A recipe for cookies calls for 3 1/4 cups of sugar. Amy already put in 3 1/9 cups. How many more cups does she need to put in
Cereal is packaged in a box shaped like a rectangular prism with a base 7.5 inches by 2 inches and a height of 10 inches. Manufacturing each box requires 10% more cardboard than the box's surface area. How much cardboard is needed to make each box?
Answer: 1032
Step-by-step explanation: you welcome
Given that 2x - 3y = 8 and 4x + 3y = -2, what is the product of x and y?
Please answer I give out Brainliest, I thank, and I give out stars!
Jeremy is making a cube using blocks. The cube is solid and has no holes. How many cubes did Jeremy use? A. 125 B. 75 C. 25 D. 15
Brett has a $30 online gift voucher. He plans to buy as many books as he can. The cost of each book is s4. There is also a single shipping charge of $2. How many books can he afford without spending more than his gift voucher amount?
General Idea:
When we are working with word problems, we need to follow the below steps:
Step 1: Assign variable for the unknown that we need to find.
Step 2: Write a meaningful mathematical equation using the sentence given
Step 3: Solve the equation by Performing reverse operation by Undoing whatever is done to the variable. Solving means find the value of the variable which will make the equation TRUE.
Applying the concept:
Step 1: Let x be the number of books that Brett can afford without spending more than his gift voucher amount.
Step 2: Writing mathematical equation based on the given sentence "Brett has a $30 online gift voucher. He plans to buy as many books as he can. The cost of each book is $4. There is also a single shipping charge of $2"
[tex] Online \; Gift \; Voucher=Number \; of \; books \; \times \; Cost\;per \; Book \; + \; Single \; shipping \; charge [/tex]
[tex] 30=4x+2 [/tex]
Step 3: Solving equation
[tex] 4x+2=30\\ Subtract \; 2 \; on \; both \; sides\\ \\ 4x+2-2=30-2\\ Combine \; like \; terms\\ \\ 4x=28\\ Divide \; 4 \; on \; both \; sides\\ \\ \frac{4x}{4}= \frac{28}{4} \\ Simplifying \; fraction \; on \; both \; sides\\ \\ x=7 [/tex]
Conclusion:
The number of books that Brett can afford without spending more than his gift voucher amount is 7 !!
What is the solution set?
3.3x−11.6>18.1
Enter your answer in the box.
Please answer fast thanks!
The solution set is (9, ∞).
To solve the inequality 3.3x-11.6>18.1, we need to isolate the variable x.
First, we can add 11.6 to both sides of the inequality to get 3.3x>29.7.
Then, we can divide both sides by 3.3 to solve for x: x>9.
We can express the solution set using interval notation as (9, ∞).
Therefore, The solution set is (9, ∞).
The solution set for the inequality 3.3x - 11.6 > 18.1 is x > 9, meaning x is greater than 9.
To solve the inequality 3.3x - 11.6 > 18.1, you can follow these steps:
1. Add 11.6 to both sides to isolate the term with x:
3.3x - 11.6 + 11.6 > 18.1 + 11.6
3.3x > 29.7
2. Now, divide both sides by 3.3. Remember, when you divide by a positive number, the inequality sign remains the same:
[tex]\[ \frac{3.3x}{3.3} > \frac{29.7}{3.3} \][/tex]
[tex]\[ x > \frac{29.7}{3.3} \][/tex]
x > 9
So, the solution set for the inequality 3.3x - 11.6 > 18.1 is x > 9.
Can u guys help me with the visual question please
simplify the radical expression square root of 64y^10h^5/16y^12h^5
After the simplification of the given radial expression [tex]\sqrt{\frac{64}{16}(\frac{y^{10} }{y^{12} } )\frac{h^{5} }{h^{5} } }[/tex] we get [tex]\frac{2}{y}[/tex].
What is radical expression?
A radical expression is defined as any expression containing a radical ([tex]\sqrt{}[/tex]) symbol.
The term underneath the radical symbol is called the radicand.
How to solve radical expression?To solve a radical expression, simply take the the square root of the radicand.
According to the given question, we have a radical expression
[tex]\sqrt{\frac{64y^{10}h^{5} }{16y^{12} h^{5} } }[/tex]
=[tex]\sqrt{\frac{64}{16}(\frac{y^{10} }{y^{12} } )\frac{h^{5} }{h^{5} } }[/tex] ([tex]\frac{x^{m} }{x^{n} } =x^{m-n}[/tex])
= [tex]\sqrt{4(\frac{1}{y^{2} })(1) }[/tex]
= [tex]\sqrt{\frac{4}{y^{2} } }[/tex]
= [tex]\frac{2}{y}[/tex]
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PLEASE HELP ME SOLVE WILL MARK AS BRAINLIEST IF ANSWERED CORRECTLY AMND SERIOUSLY
k/2+1-1k=-2k
Choose the correct simplification of the expression g to the power of 5 times h to the power of 4 all over g to the second power times h to the third power.
A g7h
B g3h
C g7h7
D g to the third power over h to the seventh power
Answer:
g3h
Step-by-step explanation:
I got it right