caleb and emily are standing 100 yards from each other. caleb looks up at a 45 degree angle to see a hot air balloon. Emily looks yup at a 60 degree angle to see the same hot air ballon. approximate how far is the hot air ballon off the ground?
Answers
thus then
[tex]\bf \begin{cases} y=100-a\\ y=a\sqrt{3} \end{cases}\implies 100-a=a\sqrt{3}\implies 100=a+a\sqrt{3} \\\\\\ 100=a(1+\sqrt{3})\implies \boxed{\cfrac{100}{1+\sqrt{3}}=a} \\\\\\ \textit{what is the altitude \underline{y} then?}\qquad y=100-a \\\\\\ y=100-\cfrac{100}{1+\sqrt{3}}\implies y\approx 63.39745962156~yards[/tex]
The height of the air balloon is 63.4 yards.
What is a trignometry?Trigonometry is a branch of mathematics that uses variables to determine heights and distances. It is the study of the properties of right angled triangles and trigonometric functions and of their applications.
For the given situation,
The diagram below shows the situation described above.
The distance between Caleb and Emily = 100 yards
Let the distance from Caleb to the air balloon be 'x'
Let the distance from Emily to the air balloon be 'y'
Let height of the air balloon be 'h'
⇒ [tex]x+y=100[/tex]
⇒ [tex]x=100-y[/tex]
We know that, [tex]tan[/tex] θ = [tex]\frac{perpendicular }{base}[/tex]
Now consider the triangle with angle 45°,
[tex]tan 45[/tex]° = [tex]\frac{h}{x}[/tex]
We know that tan 45° = 1 and substitute x = 100-y,
⇒ [tex]1 = \frac{h}{100-y}[/tex]
⇒ [tex]h=100-y[/tex]
This is equation 1.
Now consider the triangle with angle 60°,
[tex]tan60[/tex]° = [tex]\frac{h}{y}[/tex]
We know that, tan 60° = √3
⇒ [tex]\sqrt{3} = \frac{h}{y}\\[/tex]
⇒ [tex]h=y\sqrt{3}[/tex]
This is the equation 2.
On equating equation 1 and 2,
⇒ [tex]100-y=y\sqrt{3}[/tex]
⇒ [tex]y+y\sqrt{3}=100[/tex]
⇒ [tex]y(\sqrt{3}+1 )=100[/tex]
⇒ [tex]y=\frac{100}{\sqrt{3}+1 }[/tex]
Thus height, [tex]h=y\sqrt{3}[/tex]
Substitute the value of y in h,
⇒ [tex]h=\sqrt{3}(\frac{100}{\sqrt{3} +1} )[/tex]
⇒ [tex]h=\frac{100\sqrt{3} }{\sqrt{3}+1 }[/tex]
⇒ [tex]h=\frac{173.205}{2.732}[/tex]
⇒ [tex]h=63.397[/tex]
⇒ [tex]h=63.4[/tex]
Hence we can conclude that the height of the air balloon is 63.4 yards.
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Related Questions
I really need explanation for this Mean Value Theorem. Thanks
Answers
the mean value theorem states, that the function for such value to exist, must be continuous and differentiable, graph wise, that means the graph of the function between those bounds, must be "a smooth line", without any abrupt jumps or changes like a spike or a sharp sink.
so, rewording the material some, the piece-wise function has 3 subfunctions, and within the interval of [0, 2], those 3 must meet seamlessly at the junction points, namely 0 and 1, so the "4" part must seamlessly blend in with the ax + b part at 0, and the ax + b part must meet seamlessly with the x²+5x+c.
that said, we could simply freely pick a "c" value for the third subfunction, and from there, make the second subfunction to meet it at that point, so let's do so.
let's say, we pick c = 3, so the 3rd subfunction is x² + 5x + 3.
now, what's f(x) for that parabola at x = 1?, well, is 1²+5(1)+3, or 9, so it lands on the ( 1, 9 ) point then.
now, the "4" subfunction is just a horizontal line, well, at x = 0, is really just a dot, so, ax + b must meet that dot and also must meet the parabola at (1, 9), given that c = 3.
so, now, what's the equation of a line that passes through (0, 4) and (1, 9)?
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ 4}})\quad % (c,d) &({{ 1}}\quad ,&{{ 9}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{9-4}{1-0}\implies 5 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=5(x-0)\implies \boxed{y=5x+4}[/tex]
so, that'd be the 2nd subfunction, meeting "4" and x² + 5x + 3, and surely you can see what "a" and "b" are.
check the picture below.
and since they meet seamlessly, they meet the mean value theorem at [0, 2].
Which of the following best describes the square root property of equality
Answers
if they have two quantities that are equal to the same things, then they would be equal to each others.
When more than one function has the same name they are called ________ functions?
Answers
When more than one function has the same name they are called overloaded functions.
Hope This Helps You!
Good Luck :)
- Hannah ❤
A pail holds
4 1/4
gallons of water. How much is this in cups?
Answers
1) 4 gallons x 16 cups= ?
2) 1/4 of 16 cups is 4 cups.
Take the sum from each problem and add them together, you've got your answer.
how do you find all possible combinations to pay for 65 cent lemonade. you have 3 quarters, 5 dimes, and 5 nickels
Answers
How to find? You can multiply or add them up until you get 65.But here’s some ways. You have 3 quarters, 5 dimes, and 5 nickels.5 x 5 = 25 10 x 5 = 5025 x 3 = 75One way, Two quarters, a dime, and a nickel.Another way, one quarter, and 4 dimes.I'm pretty sure there's more ways but I don't have time. hope it helped though! :)
In how many ways can the letters BEACH be rearranged
Answers
Alex wants to start an IRA that will have $1,250,675 in it when he retires in 30 years. How much should he invest semiannually in his IRA to do this if the interest is 4.5% compounded semiannually? Assume an Annuity Due. Round to the nearest cent.
Answers
Fv=pmt [(1+r/k)^(kn)-1)÷(r/k)]×(1+r/k)
Fv future value 1250675
PMT semiannual payment?
R interest rate 0.045
K compounded semiannual 2
N time 30 years
Solve the formula for PMT
PMT=Fv÷ [(1+r/k)^(kn)-1)÷(r/k)]×(1+r/k) Plug in the formula
PMT=1,250,675÷((((1+0.045
÷2)^(2×30)−1)÷(0.045÷2))×(1+0.045÷2))
=9,828.44...Answer
Hope it helps!
Answer:
$9828.44
Step-by-step explanation:
The semi annual payment is such that the future value of the annuity due is equal to the desired amount when he retires.
The formula to calculate future value of an annuity due periodic payment of M for time period T for given periodic return r,
A=[tex]\frac{M(1+r)^{T+1}-(1+r)}{r}[/tex]
in this question there are 30*2= 60 payments and the semi annual rate= 4.5/2= 2.25%
putting values we get
1250675= [tex]\frac{M(1+2.25%)^{60+1}-(1+2.25%)}{2.25%}[/tex]
on solving we get M= $9828.44
Alex needs to invest $9828.44 semiannually in his IRA
Maricella plots two ordered pairs on the grid below.
Answers
Answer: (0,-10)
Step-by-step explanation:
The equation of a line (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
From the given graph , the line is passing through (6,2) and (8,6) is given by :_
[tex](y-6)=\dfrac{6-2}{8-6}(x-8)\\\\\Rightarrow\ y-6=\dfrca{4}{2}(x-8)\\\\\Rightarrow\ y-6=2(x-8)\\\\\Rightarrow\ y=2(x-8)+6[/tex]
To find the y intercept put x =0 , we get
[tex]y=2(0-8)+6=-16+6=-10[/tex]
Hence, the y-intercept of the graph : (0,-10)
If a flower is 6.5 cm wide, its width expressed in millimeters is x mm, where x is
Answers
A unit of measure is the actual unit in which the associated values are measured. If a flower is 6.5 cm wide, its width expressed in millimeters is 65 mm,
What is Unit of Measurement?A Unit of measure is the actual unit in which the associated values are measured.
Unit of Measurement is used as a standard for measurement of the same kind of quantity. The weight is measured in kilograms, grams. The kilogram is unit of mass. litres is the unit of measuring liquids and length is measured in different units, feet, inches, meters, kilometers, centimeters.
We know that 1 centimeter = 10 milli meters.
So if a flower is 6.5 cm wide, its width expressed in millimeters is x mm
We need to find the value of x.
6.5 cm = 6.5×10
=65
So 6.5 cm in millimeters is 65 mm.
Hence if a flower is 6.5 cm wide, its width expressed in millimeters is 65mm.
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153 inches to 19 feet
Answers
153 inches 1 foot 153 51 3
--------------- = --------------------------- = ----------- = -------- = --------- (answer)
19 feet [12 inches ] 1428 476 28
Note that this is a ratio and has no units of measurement.
What is the percent increase from 250 to 900?
1. Write the percent change formula for an increase.
Percent Increase =
Amount of Increase
Original Amount
2. Substitute the known quantities for the amount of the increase and the original amount.
Percent Increase =
900 − 250
250
3. Subtract.
Percent Increase =
650
250
4. Express the ratio as a percent:
%
Answers
650 / 250 = 13 / 3 = 2.6 = 260%
Answer:
260 %
Step-by-step explanation:
1) Since, the percentage formula is,
[tex]\text{Percent Increase}=\frac{\text{Amount of Increase}}{\text{Original Amount}}[/tex]
2) Given,
Original amount = 250,
New amount = 900
So, the amount of increase = New amount - Original amount = 900 - 250 = 650
By substituting the values,
[tex]\text{Percentage increase}=\frac{650}{250}[/tex]
3) Now, for expressing the ratio into percentage we need to multiply by 100,
[tex]\frac{650}{250}\times 100=\frac{65000}{250}= 260\%[/tex]
Find the probability of getting exactly 6 girls in 8 births.
Answers
The probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is [tex]\boxed{\bf 0.10937}[/tex].
Further explanation:
Concept used:
The probability of an event [tex]E[/tex] is calculated as follows:
[tex]\boxed{P(E)=\dfrac{n(E)}{n(S)}}[/tex]
Here, [tex]n(E)[/tex] is the number of favorable outcomes in an event [tex]E[/tex] and [tex]n(S)[/tex] is the number of element in sample space [tex]S[/tex].
The probability of exactly [tex]r[/tex] success in [tex]n[/tex] trial is expressed as follows:
[tex]\boxed{P(F)=^{n}C_{r}p^{r}q^{n-r}}[/tex]
Here, [tex]r[/tex] is the probability of success in an event and [tex]q[/tex] is the probability of failure.
Calculation:
Consider [tex]A[/tex] as an event of having a girl in first birth and [tex]P(A)[/tex] as the probability of event [tex]A[/tex].
The probability of having a girl is [tex]P(A)=\frac{1}{2}[/tex].
Assume that [tex]A'[/tex] is the complement event of an event [tex]A[/tex] and [tex]P(A')[/tex] is the probability of complementary event [tex]A'[/tex].
The event is the event of not having a girl in the first birth.
The probability of event [tex]A'[/tex] is calculated as follows:
[tex]\boxed{P(A')=1-P(A)}[/tex] …… (1)
Substitute [tex]P(A)=\frac{1}{2}[/tex] in the equation (1) to obtain the probability of event [tex]A'[/tex].
[tex]\begin{aligned}P(A')&=1-\dfrac{1}{2}\\&=\dfrac{1}{2}\end{aligned}[/tex]
The probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is calculated as follows:
[tex]\begin{aligned}P(F&)=^{8}C_{6}\left(\dfrac{1}{2}\right)^{6}\left(\dfrac{1}{2}\right)^{8-6}\\&=\dfrac{8!}{6!\cdot 2!}\cdot (0.5)^{6}\cdot (0.5)^{2}\\&=28(0.5)^{8}\\&=0.10937\end{aligned}[/tex]
Thus, the probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is [tex]\boxed{\bf 0.10937}[/tex].
Learn more:
1. Learn more about problem on numbers: https://brainly.com/question/1852063
2. Learn more about problem on function https://brainly.com/question/3225044
Answer details:
Grade: Senior school
Subject: Mathematics
Chapter: Probability
Keywords: Probability, exact event, sample space, number of element, complement event, success, failure, favorable, trial, P(E)=n(E)/n(S), P(A')=1-P(A).
Final answer:
To find the probability of getting exactly 6 girls in 8 births, we use the binomial probability formula. In this case, the probability is approximately 0.01.
Explanation:
To find the probability of getting exactly 6 girls in 8 births, we can use the binomial probability formula:
P(x = 6) = C(n, x) * pˣ * (1-p)(n-x)
Where:
C(n, x) is the binomial coefficient, which represents the number of ways to choose x objects from a set of n objects.p is the probability of success (in this case, the probability of having a girl) in a single trial. n is the number of trials (in this case, the number of births).x is the desired number of successes (in this case, the desired number of girls).In this particular case, P(x = 6) = C(8, 6) * (0.5)⁶ * (0.5)(8-6) = 28 * 0.015625 * 0.015625 = 0.009765625, or approximately 0.01.
If ying zyiyu covered the first 200 miles of a trip going at 50 mph and the last hundred miles going at 40 mph, what was his average speed for the entire trip? Teacher told me it is not 45
Answers
To find the total time we need to do some division.
Time for 200 miles=200/50=4 hours.
Time for 100=100/40=5/2 hours.
Total time=13/2 hours. Total distance=200+100=300 miles.
Av speed=300/(13/2)=300×2/13=600/13=46.15 mph approx.
The average speed of ying zyiyu is [tex]46.15\;\rm{mph}[/tex]
Average speed is the ratio of the total distance traveled by a body to the total time taken by the body to cover the total distance.
Here, ying zyiyu covered the first [tex]200\;\rm miles[/tex] of the trip at [tex]50\;\rm mph[/tex] so,
Total time taken by ying zyiyu to cover [tex]200\;\rm miles[/tex] is calculated as-
[tex]t_1=\dfrac{200}{50}\\t_1=4\;\rm hour[/tex]
Similarly, ying zyiyu covered the first [tex]100\;\rm miles[/tex] of the trip at [tex]40\;\rm mph[/tex] so,
Total time taken by ying zyiyu to cover [tex]100\;\rm miles[/tex] is calculated as-
[tex]t_2=\dfrac{100}{40}\\t_2=2.5\;\rm hour[/tex]
So, the total time taken by ying zyiyu to travel [tex]300\;\rm miles[/tex] is [tex]4+2.5=6.5\;\rm hours[/tex]
Now, the average spped is calculated as-
[tex]\rm{Average\;Speed}=\dfrac{Total\;Distance}{Total\;Time}\\\rm{Average\;Speed}=\dfrac{300}{6.5}\\\rm{Average\;Speed}=46.15\;\rm mph[/tex]
Hence, the average speed of ying zyiyu is [tex]46.15\;\rm{mph}[/tex].
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The school is 3.65 miles from Tonya’s house and 1.28 miles from Jamall‘s house. How much farther from school is Tonyas house than Jamall‘s house? Explain how you can use a quick picture to solve the problem.
Answers
The answer is 2.37 miles. The possible explanation for this is I can illustrate 3.65 using 3 squares for ones, 6 lines for tenths, and 5 circles for hundredths. I would now then reform 1 tenth as 10 hundredths. Then, I would subtract 8 hundredths from 15 hundredths. Then, I would take away 2 tenths from 5 tenths. Last, I would deduct 1 from 3.
What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?
y = x + 4
y = x +
y = –5x + 4
y = –5x +
Answers
we know that
If two lines are parallel, then their slopes are the same
Step 1
Find the slope of the given line
we know that
the formula to calculate the slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
in this problem we have
[tex](x1,y1)=(-5,-4)\\(x2,y2)=(0,-3)[/tex]
substitute in the formula
[tex]m=\frac{(-3+4)}{(0+5)}[/tex]
[tex]m=\frac{(1)}{(5)}[/tex]
[tex]m=\frac{1}{5}[/tex]
Step 2
Find the equation of the line
we know that
the equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{1}{5}[/tex]
[tex](x1,y1)=(-2,2)[/tex]
substitute
[tex]y-2=\frac{1}{5}(x+2)[/tex]
[tex]y=\frac{1}{5}x+\frac{2}{5}+2[/tex]
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
therefore
the answer is
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
Action movies make up 85% of Devon’s movie collection. If he has 20 movies, how many action movies are in Devon’s collection ? Explain your reasoning to classmate
Answers
Multiply 20 and .85.
20 x .85 = 17
17 action movies are in Devon's collection.
85% of 20....turn ur percent to a decimal..." of " means multiply
0.85(20) = 17.....so Devon has 17 action movies <=
Find the exact circumference of a circle with an area equal to 36 sq. in.
1) 12
2) 18
3) 324
Answers
Answer:
The answer would be option 1) 12
Answer:
The circumference is [tex]C=12\sqrt{\pi }\:in[/tex].
Step-by-step explanation:
The area of a circle when we know the circumference is
[tex]A=\frac{C^2}{4\pi }[/tex]
We know the area [tex]A=36 \:{in^2}[/tex], we plug this value into the above equation and we solve for C the circumference.
[tex]36=\frac{C^2}{4\pi }\\\frac{C^2}{4\pi }=36\\\frac{C^2\cdot \:4\pi }{4\pi }=36\cdot \:4\pi \\\\C^2=144\pi \\C=\sqrt{144\pi }\\C=12\sqrt{\pi }[/tex]
The circumference is [tex]C=12\sqrt{\pi }\:in[/tex].
Solve the exponential equation. 2x = 1/2
Options: -1
-1/2
1
Answers
2x = 1/2 is an entirely different problem; its solution is x = 1/4.
You are to solve 2^x = 1/2.
1 1
Note that 1/2 = --------, so 1/2 = -------- = 2^x
2^1 2^1
Multiplying both sides by 2, we get 1 = 2(2^x) = (2^1)(2^x) = 2^(x+1)
Take the log to the base 2 of both sides of 1 = 2^(x+1). The result is
0 = (x+1)(1), or 0 = x+1
Then x = -1.
check: subst. -1 for x in 2^x = 1/2. Is the equation then true?
2^(-1) = 1/2 ?
1
-- = 1/2? Yes. So, x=-1 has been verified.
2
The exponential equation, 2ˣ = 1/2, has a value of -1.
What is an exponential equation?Exponential equations are equations in which variables occur as exponents.
Given is an exponential equation, 2ˣ = 1/2, we need to solve it,
2ˣ = 1/2
Taking ㏒ both the side,
㏒ 2ˣ = ㏒ 1/2
x ㏒ 2 = ㏒ 0.5
x = -0.301029996 / 0.301029996
x = -1
Hence, the exponential equation, 2ˣ = 1/2, has a value of -1.
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Convert the following temperatures from K to °C.
100 K = °C
273 K = °C
6 K = °C
143°C = K
573°C = K
Answers
273K=-0.15C
6K=-267.15C
143C=416.15
573C=846.15K
Formula for C to K
K = °C + 273.15
Formula for K to C
° C = K - 273.15
we know that
The formula to convert K to C is equal to
[tex]\° C =\°K - 273.15\°[/tex] --------> equation [tex]1[/tex]
and
The formula to convert C to K is equal to
[tex]\° K =\°C +273.15\°[/tex] --------> equation [tex]2[/tex]
case a) [tex]100\° K[/tex]
convert to C
substitute in the equation [tex]1[/tex]
[tex]\° C =100\°- 273.15\°=-173.15\°[/tex]
therefore
the answer Part a) is
[tex]\° C =-173.15\°[/tex]
case b) [tex]273\° K[/tex]
convert to C
substitute in the equation [tex]1[/tex]
[tex]\° C =273\°- 273.15\°=-0.15\°[/tex]
therefore
the answer Part b) is
[tex]\° C =-0.15\°[/tex]
case c) [tex]6\° K[/tex]
convert to C
substitute in the equation [tex]1[/tex]
[tex]\° C =6\°- 273.15\°=-267.15\°[/tex]
therefore
the answer Part c) is
[tex]\° C =-267.15\°[/tex]
case d) [tex]143\° C[/tex]
convert to K
substitute in the equation [tex]2[/tex]
[tex]\° K =143\°+ 273.15\°=416.15\°[/tex]
therefore
the answer Part d) is
[tex]\° K =416.15\°[/tex]
case e) [tex]573\° C[/tex]
convert to K
substitute in the equation [tex]2[/tex]
[tex]\° K =573\°+ 273.15\°=846.15\°[/tex]
therefore
the answer Part e) is
[tex]\° K =846.15\°[/tex]
Maricella plots two ordered pairs on the grid below.
Answers
Answer:
B. [tex](0,-10)[/tex]
Step-by-step explanation:
We have been given an image of a line segment on coordinate plane. We are asked to find the y-intercept of line, is the line segment is extended to cross both the axes.
We will find the equation of line in slope-intercept form: [tex]y=mx+b[/tex], where,
m = Slope of line,
b = The y-intercept.
We will find slope of our given line using the coordinates of our given points (6,2) and (8,6).
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{6-2}{8-6}[/tex]
[tex]m=\frac{4}{2}[/tex]
[tex]m=2[/tex]
Now, we will substitute [tex]m=2[/tex] and coordinates of point (8,6) in slope-intercept form of equation.
[tex]6=2*8+b[/tex]
[tex]6=16+b[/tex]
[tex]6-16=16-16+b[/tex]
[tex]-10=b[/tex]
Since y-intercept of our given line is [tex]-10[/tex], which is at [tex]x=0[/tex], therefore, option B is the correct choice.
You make $0.75 for every newspaper you sell. How many newspapers do you have to sell to buy soccer cleats? (soccer cleats are $36.00)
Write an equation then solve
Answers
0.75x = 36.00
x is the amount of newspapers you sell. We put it as x because we dont know how much we need to sell to buy soccer cleats, which are $36.00. To solve, we will use inverse operations:
0.75x = 36.00
0.75x / 0.75 = 36.00 / 0.75
x = 48
You will have to sell 48 newspapers to get the soccer cleats.
As part of a traffic safety campaign a speed detector was used to record speed in the entrance driveway to the Jefferson High School parking lot. The box and whisker plot shows the results.
HELP ME PLEASE ASAP
Answers
A student solved the problem below by first dividing 20 by 10. What mistake did the student make? A baseball team has won 20 games and lost 10 games. What percent of the games did the team win?
Answers
Answer:
Step-by-step explanation: The student divided the number of wins by the number of losses.
The student should have divided the number of wins by the total number of games.
The student should have first added 20 and 10 to find that there were a total of 30 games.
Answer:
SAMPLE RESPONSE: The student divided the number of wins by the number of losses, instead of dividing the number of wins by the total number of games. The student should have divided 20 by 30.
Step-by-step explanation:
other answer: The student divided the number of wins by the number of losses.
The student should have divided the number of wins by the total number of games.
The student should have first added 20 and 10 to find that there were a total of 30 games.
A chicken soup recipe calls for 15 cups of chicken stock. How much is this in quarts?
Answers
Write the decimal 2.06 as a mixed number.
Answers
6 2 3
--- / --- = ------
100 2 50
Answer: 2 3/50
I hope this helps :)
Marianna martinez sells copy paper to local schools. SHE EARNS A 13 PERCENT STRAIGHT COMMISSION ON ALL SALES. IN NOVEMBER HER SALES TOTALED $28,540. WHAT WAS HER COMMISSION?
Answers
We can do this by multiplying 28,540 by .13 .
This give you the answer of a $3,710.20 commission.
Hope this helps.
Joaquin has $1,300 in the bank and has investments worth $4,000. He also has $7,000 worth of credit card debt. What is Joaquin's net worth? Select the best answer from the choices provided. $1,300 -$7,000 $5,300 -$1,700
Answers
In this question, we can separate the account into positive/debit and negative/credit value. The positive/debit value should be:
Joaquin has $1,300 in the bank
He has $4,000 worth of investment
Total positive value = $1300 + $4000= $5300
The negative value should be
$7,000 worth of credit card debt
Total positive value =$7000
Then the net worth should be: $5300 - $7000= -$1700
A rectangular box with a volume of 784 ft3 is to be constructed with a square base and top. the cost per square foot for the bottom is 15¢, for the top is 10¢, and for the sides is 1.5¢. what dimensions will minimize the cost
Answers
The Soup Shack usually makes tomato soup with 9 tomatoes for every 12 cups of soup. Today, they made 8 cups of soup with 6 tomatoes. How does today's soup compare to the usual recipe?
Answers
Answer: We compare today's soup to the usual recipe by using "Unitary Method".
Step-by-step explanation:
Since we have given that
The Soup Shack makes tomato soup with 9 tomatoes for every 12 cups of soup.
For every 12 cups of soup , 9 tomatoes is needed
For every 1 cup of soup , the number of tomato is needed is given by
[tex]\frac{9}{12}=\frac{3}{4}[/tex]
Today, they made 8 cups of soup with 6 tomatoes ,
For 8 cups, 6 tomatoes are used .
For 1 cup, number of tomato is used is given by
[tex]\frac{6}{8}=\frac{3}{4}[/tex]
So, we can see that both the soup has same quantity .
∴ We compare today's soup to the usual recipe by using "Unitary Method".
Rectangles ABCD and EFGH are similar. The perimeter of rectangle ABCD is 5 times greater than the perimeter of rectangle EFGH. What is the relationship between the areas of the rectangles?
A. The area of rectangle EFGH is 25 times greater than the area of rectangle ABCD.
B. The area of rectangle EFGH is 5 times greater than the area of rectangle ABCD.
C. The area of rectangle ABCD is 25 times greater than the area of rectangle EFGH.
D. The area of rectangle ABCD is 5 times greater than the area of rectangle EFGH.
Answers
If the length is 5 times bigger and the width is 5 times bigger, than the area is 25 times bigger
Answer:
Step-by-step explanation:
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