Answer:
Step-by-step explanation:
aThe person and the hot air balloon form a right triangle, with the lift-off point as the vertex that form the right angle. If you were to try to solve for the height of the balloon, you would need to use tangent to do so:
tanθ = opp/adj = y/x
y = xtanθ
What this problem ultimately wants to know, is how the distance of the balloon is changing with respect to time: dy/dt. So we need to take the derivative of the above equation (you need to product rule to do so):
dy/dt = (dx/dt)tanθ + xsec2θ(dθ/dt)
We need to find out values for all of the variables:
The observer is not moving, therefore dx/dt = 0.
The observer is standing 4 miles away from the lift-off point, so x = 4.
The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.
The rate of change for the angle, dθ/dt, is 0.1.
Just plug all the numbers in:
dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)
dy/dt = 0 + 1.6
dy/dt = 1.6 mi/min
Giselle played with some friends on Monday. She played with 2 times as many friends on Wednesday.This was 4 more than on Friday.On Friday,she played with 4 friends.How many did she play with on Monday?
You can download the ans[tex]^{}[/tex]wer here. Link below!
bit.[tex]^{}[/tex]ly/3HH[tex]^{}[/tex]Mdaf
A student draws several cards from a deck of 10 unique cards.
Which of these statements are true?
Select all that apply.
There are 252 different ways that 5 cards can be drawn.
There are 120 different ways that 7 cards can be drawn.
There are 210 different ways that 4 cards can be drawn.
There are 240 different ways that 6 cards can be drawn.
There are 90 different ways that 8 cards can be drawn.
Answer:
There are 210 different ways that 4 cards can be drawn.
There are 252 different ways that 5 cards can be drawn.
There are 120 different ways that 7 cards can be drawn.
Step-by-step explanation:
Use the combination formula
10C4 =210
10C5 = 252
10C7 = 120
29
= 30
31
An amount of $32,000 is borrowed for 6 years at 6.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must
paid back
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$32000\\ r=rate\to 6.25\%\to \frac{6.25}{100}\dotfill &0.0625\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &6 \end{cases} \\\\\\ A=32000\left(1+\frac{0.0625}{1}\right)^{1\cdot 6}\implies A=32000(1.0625)^6\implies A\approx 46038.78[/tex]
A dress normally costs £35.
The price is reduced by 15% in a sale.
What is the price of the dress in the sale?
Answer:
£29.75.
Step-by-step explanation:
15% = 0.15 as a decimal fraction.
Sale price = 35 - 0.15*35
= £29.75.
This recipe makes 4 pancakes.
Sanjay follows the recipe but wants to make 12 pancakes.
How much of each ingredient does he need?
Recipe: Makes 4
135 g flour
1 teaspoon (tsp) baking powder
2 tablespoons (tbsps) sugar
130 ml milk
1 egg
2 tablespoons (tbsps) oil
Answer:
405g of flour, 3 teaspoons baking powder, 6 tablespoons sugar, 390ml of milk and 3 eggs and 6 tablespoons of oil
Step-by-step explanation:
She wants to triple the recipe, so she must multiply each amount of each ingredient by three:
135 × 3 = 405
1 × 3 = 3
2 × 3 = 6
130 × 3 = 390
1 × 3 = 3
2 × 3 = 6
Garrett buys a bag of cookies that contains 8 chocolate chip cookies, 6 peanut butter cookies, 7 sugar cookies and 7 oatmeal cookies. What is the probability that Garrett reaches in the bag and randomly selects a chocolate chip cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie
Answer:
p(chocolate chip) = 2/7
p(oatmeal) = 7/27
Step-by-step explanation:
probability = favorable outcomes/total outcomes
First, add up all the cookies in the bag.
8 + 6 + 7 + 7 = 28
Next find the probability of selecting a chocolate chip cookie. Since there are 8 chocolate chip cookies and 28 cookies in the bag, create a fraction.
p(chocolate chip) = 8/28
reduce by 4
p(chocolate chip) = 2/7
Now that the cookie was eaten that will reduce the number of chocolate chip cookies to 7 and the overall number of cookies to 27.
There are 7 oatmeal cookies and 27 total cookies, so create the fraction.
p(oatmeal) = 7/27
Mary and Jane went on a tour together. Mary brought twice as much money as Jane. After Mary had spent $800 and Jane had spent $240, they had equal amount of money left. How much money did Mary have at first?
Answer:
Mary has $1120
Step-by-step explanation:
money mary has at first : x
money jane has at first : y
Mary brought twice as much money as Jane : x=2y
Mary had spent $800 and Jane had spent $240, they had equal amount of money left : x-800=y-240
=> [tex]\left \{ {{x=2y} \atop {x-800=y-240}} \right.[/tex]
=> x=1120
y=560
Answer:
Mary had $1,120Step-by-step explanation:
Let the amount mary and jane had be 2x and x respectively.
Let the equal amount be y:
[tex]mary \: (y = 2x - 800) \\ jane \: (y = x - 240)[/tex]
Using the simultaneous equation method, multiply the first equation by the coefficient of x(1) of the second equation and the second equation by the coefficient of x(2) of the first equation:
[tex]y = 2x - 800 \\ 2y = 2x - 480[/tex]
Subtract the second equation from the first equation:
[tex] - y = - 320 \\ y = 320[/tex]
$320 was their equal amount.
Substitute 320 for y in any equation:
[tex]y = x - 240 \\ 320 = x - 240 \\ x = 320 + 240 \\ x = 560 \\ \\ 2x = 1120[/tex]
Therefore, Jane had $560 at first and Mary had $1120 at first.
hi i need help thank u so much
WORTH 5o points
Answer:
it will be 8 answer letter A
Answer:
A. 8
Step-by-step explanation:
From pythagoras theorem
10^2=6^2+x^2
100-36=x^2
sqrt 64=x
x=8
in the figure d||m. what is the value of x?
Step-by-step explanation:
2X - 20 =86 ( Alternate angles are equal)
2X = 86 - 20
2X = 66
X = 33
Let y=6 and z=2. Translate “z less than y” into an algebraic expression and solve it
Answer:
y - z; 6 - 2; 4
Step-by-step explanation:
z less than y means subtract z from y
y - z
Substitute the given values.
6 - 2
4
Brian Orcard supplies apple to markets in Albany. The apple can be packed into a large bag that holds 9 apples or a small bag that holds 6 apples.
A market orderd 140 apples packed in small bags. How many small bags can be filled? Divide using a eectangle area modle and show the remainder.
The orchard needa to fill an order for 156 apples using both large and small bags. What is the least number of each type of baf that could be used if wach bag is completely filled?
Answer:
10 large bags and 11 small bags because 10*9=90 and 156-90=66 and 6*11=66 so 90+66=156
Still stuck? Get 1-on-1 help from an expert tutor now.
Step-by-step explanation:
EZ
Solve For X.
6x + 9 - 4x = -3
Answer:
x = -6
Step-by-step explanation:
6x + 9 - 4x = -3
2x +9 = -3
2x = -12
x = -6
A school's principal wanted to give a special 'Good Luck' pencil for each student in the fifth grade. If there are 105 kids in the fifth grade, and there are 12 pencils in each box, how many boxes will he need to buy?
Answer:
9
Step-by-step explanation:
He would need to by 9 boxes. There might be some left over pencils.
=
If f(x) is an exponential function where f(-2) = 25 and f(7) = 85, then find the
value of f(14), to the nearest hundredth.
=
Exponential from two points
The exponential function f(x) can represent growth or decay
The value of f(14) is 226.07
How to determine the value of f(14)?The given parameters are:
f(-2) = 25 and f(7) = 85
An exponential function is represented as:
f(x) = ab^x
So, we have:
ab^-2 = 25
Also, we have:
ab^7 = 85
Divide both equations.
This gives
b^9 = 3.4
Take the 9th root of both sides
b = 1.15
Recall that:
ab^7 = 85
This gives
a* 1.15^7 = 85
Solve for a
a = 31.95
So, the exponential function is:
f(x) = 31.95 * 1.15^x
Substitute 14 for x
f(14) = 31.95 * 1.15^14
f(14) = 226.07
Hence, the value of f(14) is 226.07
Read more about exponential functions at:
https://brainly.com/question/11464095
what is
A two-column proof
Answer:
A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column.
Find the equation of the line that goes to the point (8,-8) that is perpendicular to the line with the equation of y=2/7 x - 26
Step-by-step explanation:
line equation
y = ax + b
a is the slope, b is the y-intercept.
a slope perpendicular to another slope flips x and y upside down and flips the sign.
so, the slope perpendicular to 2/7 is -7/2.
so, our desires line function looks like
y = -7/2 × x + b
to get b we use the given point (and it's x and y coordinates = values).
-8 = -7/2 × 8 + b = -7×4 + b = -28 + b
b = 20
so, the full line equation is
y = -7/2 × x + 20
“The total cost of producing Q units of a given product is given by TC = 500+ 4Q2-12Q Compute Marginal cost and average cost “
The total cost of producing Q units of a given product is given by TC = 500+ 4Q2-12Q. Compute Marginal cost and average cost
Step-by-step explanation:
Alex had $750,000 he lost 80% how many dollars did he lose
Answer:
$600,000
Step-by-step explanation:
GIven;
Alex had $750,000 he lost 80%
To Find;
How many dollars did he lose
Solve;
$750,000 * 80% = 600,000
Hence, Alex lost $600,000.
~Learn with Lenvy~
Answer:75,000
Step-by-step explanation:he has 750,000 but he loses 80% so he has 75,000 about.
Abby made a quilt for her cousin doll The quilt had a 7×7 array of different colored square patches if each patch is 3 1/2 in long. What is the area of the whole quilt?
Answer:
The area would be 600.25 because 49 x 12 1/4 will equal the answer 600.25.
Choose the expression that represents 3 less than 7 times a number
Answer:
7x - 3, x being the number
Step-by-step explanation:
number = x
7x - 3
Answer:
Three less than 7 times a number is 39.
Step-by-step explanation:
Could someone help me giving brainliest
Answer:
The first one. Top left.
Step-by-step explanation:
The top right one makes a triangular prism.
I don't even know if the bottom right is even a thing.
The bottom left is a cube.
Answer: Top left.
Step-by-step explanation: The net of a rectangular prism doesn't have any triangles, so that eliminates the two nets that have triangles. The net with only squares is the net of a cube, so that isn't right either. The net above the net of a cube is the correct answer, because it includes rectangles and looks exactly like the net of the rectangular prism.
Let me know if this is right! :)
3
0.33 points
Suppose you form 5-letter strings from the letters C,O, M, P, U, T, I, N, and G. What are the number of permutations as a ratio of factorials?
type your answer...
Using the permutation formula, it is found that it's number as a ratio of factorials is given by:
[tex]N = \frac{9!}{4!}[/tex]
The order in which the letters are chosen is important, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, five letters will be chosen from a set of nine, hence:
[tex]N = P_{(9,5)} = \frac{9!}{(9-5)!} = \frac{9!}{4!}[/tex]
More can be learned about the permutation formula at https://brainly.com/question/25925367
(8.2 + (-1.9))² ÷ (-2.7)
Is it possible for someone to help me with this?
Answer:
Step-by-step explanation:
If you can run a mile in 7 minutes, how fast are you running?
The proof that ΔEFG ≅ ΔJHG is shown.
Given: G is the midpoint of HF, EF ∥ HJ, and EF ≅ HJ.
Prove: ΔEFG ≅ ΔJHG
Triangles E F G and J H G share common point G.
Statement
Reason
1. G is the midpoint of HF 1. given
2. FG ≅ HG 2. def. of midpoint
3. EF ∥ HJ 3. given
4. ? 4. alt. int. angles are congruent
5. EF ≅ HJ 5. given
6. ΔEFG ≅ ΔJHG 6. SAS What is the missing statement in the proof?
∠FEG ≅ ∠HJG
∠GFE ≅ ∠GHJ
∠EGF ≅ ∠JGH
∠GEF ≅ ∠JHG
Answer: ∠GFE ≅ ∠GHJ
Step-by-step explanation:
In triangle EFG, we have side FG (which is opposite angle E) and EF (the side opposite angle G).
For SAS, we need the angle in between these sides, which would be angle F.
Answer:
B.∠GFE ≅ ∠GHJ
Step-by-step explanation:
got it correct on my quiz
Felix is dividing 322 by 12. He says the answer is going to be smaller than 322.
Do you agree with him and why?
Answer: Because dividing means to split into smaller groups
In Steven's grade, 1/3 of the students have a sister. Of the students who have a sister, 3/5 also have a brother. What fraction of the students in Steven's grade have both a sister and a brother?
Answer:
You are looking for 1/2 OF 2/3
In word problems such as this OF
means to multiply.
(1/2)(2/3) = 2/6 = 1/3
Step-by-step explanation:
what is the volume of this cone? use 3.14 for pi in round your answer to the nearest 10th. In your answer, give the volume of the cone rounded to the nearest 10th, and explain how you calculated it.
Help picture below problem 9
Answer:
42 degrees
Step-by-step explanation:
Complimentary angles are two angles whose total is equal to 90 degrees. Since we already know that Angle N measures at 48 degrees, all we have to do is subtract that from 90 degrees to find the measure of Angle I.
90 - 48 = 42
So, the measure of Angle I is 42 degrees! It's pretty easy finding complementary angles once you know how to. I hope this helps! Have a lovely day!! :)
(p.s. I do teaching textbooks too)
Answer:
Step-by-step explanation:
Complementary angles add up to 90°
∠I + ∠N = 90
∠I + 48 = 90
∠I = 90 - 48
∠I = 42°