A parachutist falls 11 seconds before the parachute opens, so 1936 ft far the parachutist fall during this time.
We have to find how far does the parachutist fall during this time.
The formula for estimating the time in seconds it will take an object to fall d feet is given below.
t = [tex]\sqrt{\frac{d}{16}}[/tex]
We merely need to enter the specified time t into the formula to find the distance answer.
11 = [tex]\sqrt{\frac{d}{16}}[/tex]
taking square on both side, we get
121 = d/16
Multiply by 16 on both side, we get
d = 1936 ft
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The complete question is:
The approximate time t in seconds that it takes an object to fall a distance of d feet is given by
t = [tex]\sqrt{\frac{d}{16}}[/tex]
Suppose a parachutist falls 11 seconds before the parachute opens. How far does the parachutist fall during this time?
I. Jill is training for a marathon
and runs 2 ⅓ miles three times
a week. How far will she run in
six weeks?
Answer:42 miles
Step-by-step explanation: She runs 3 times a week so 2 1/3 times 3 is equal to 7.
7x6=42
the population of algae in an experiment increases by %5 each day. if there were 50 algae at the beginning, predict the number of algae after 7 days.
The number of algae after 7 days is approximately 70.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Given that,
Initial population of algae = 50
Percentage increase = 5%
To calculate the number of algae at any day, we need to find a formula.
Initial population = 50
After 1 day, population = 50 + (5% × 50) = 50 + (0.05 × 50) = 50 (1 + 0.05)
After 2 days, population = 50 (1 + 0.05)²
So, population after n days = 50 (1 + 0.05)ⁿ
Population of algae after 7 days = 50 (1 + 0.05)⁷
= 50 (1.05)⁷
= 70.355 ≈ 70
Hence there will be approximately 70 algae after 7 days.
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solve. 10) what are the dimensions of a right triangle with a 5 inch hypotenuse and an area of 6 square inches?
Answer:
The dimensions are 3, 4 and 5 inches.
Step-by-step explanation:
Area = 1/2 * height * base
6 = 1/2 * h * b
h * b = 12.
As the hypotenuse is 5 inches long
H^2 + B^2 = 5^2
From the third line: h = 12/b, so we have
(12/b)^2 + b^2 = 25
144/b^2 + b^2 = 25
144 + b^4 = 25b^2
b^4 - 25b^2 + 144 = 0
Let B = b^2, so
B^2 - 25B + 144 = 0
(B - 16)(B - 9) = 0
B = 16, 9
So, b = 4, 3
h = 12/b
= 3 , 4.
Amadou i going to invet $11,000 and leave it in an account for 9 year. Auming the interet i compounded continuouly, what interet rate, to the nearet tenth of a percent, would be required in order for Amadou to end up with $14,000?
The required interest rate would be 6.9% to the nearest tenth of a percent.
We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.
In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.
Plugging these values into the percent formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.
We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.
In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.
Plugging these values into the formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.
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1 A line passes through (8, -2) and has a slope of ¼.
a. Write an equation for the line in point-slope form.
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{8}) \implies {\large \begin{array}{llll} y +2= \cfrac{1}{4} (x -8) \end{array}}[/tex]
Alg Fndins 1 A
Order of Operations
Evaluate each expression.
(Help me please)
Jacob is a construction worker who earns a yearly Income given by the expression 2000x + 3000, where X is the number of
hours he works each week. Carlos works with Jacob and earns a yearly Income given by the expression 3800x - 39000.A
manager predicts that if Carlos and Jacob each work 42 hours, they will earn the same amount of money.
Answer:20
Step-by-step explanation:
you do it
the area of trapezoid $abcd$ is $80$. one base is $12$ units longer than the other, and the height of the trapezoid is $5$. find the length of the median of the trapezoid.
The trapezoid abcd median is 16 lengths long.
Regarding the query,
Considering that,
The trapezoid's area is equal to 80,
The trapezoid abcd is 5 inches tall.
Let a be the base of the trapezoid abcd.
So, b = a + 12 ,
In the formula Area of the trapezoid = A =(a+b)h/2, the value is substituted.
(a + a + 12)5/2 = 80
(2a + 12)5 = 160
2a + 12 = 160/5
2a + 12 = 32
2a =32 - 12
2a = 20
a = 20/2
a = 10 units
additional base is 10 + 12 = 22 units.
Therefore, the median's length will be equal to (10 + 22)/2.
= 32/2 = 16 units
As a result, the median's length is 16.
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Can I get help on this question ?
The solution of the expression is 3m-5.
How to simplify the equation?Basic Guidelines and Procedures for Condensing Any Algebraic Expression
By multiplying factors, remove the parentheses and brackets.If the terms have exponents, you should eliminate grouping using the exponent rule.Add or subtract coefficients to combine similar terms.Incorporate the constants.step1:
(6m² -13m+5)/(2m-1): 3m-5
6m² -13m+5/2m-1
factor 6m² -13m+5 : (2m-1) (3m-5)
=(2m-1) (3m-5)/2m-1
step2:
cancel the common factor 2m-1
=3m-5
The solution of the expression is 3m-5
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Which of the following represents "36 is 18 times as many as 2"?
Answer:
36 = 2 x 18
Step-by-step explanation:
Simplify fully.
[tex]3\cdot \log_{\frac{4}{9}}(\sqrt[4]{\dfrac{27}{8}})[/tex]
I know how to get the fourth root fraction inside the log to [tex](\dfrac{3}{2})^{3/4}[/tex] but don't understand how to advance from there
Answer:
-9/8
Step-by-step explanation:
You want a full simplification of ...
[tex]3\cdot\log_{\frac{4}{9}}{\sqrt[4]{\dfrac{27}{8}}}[/tex]
Rules of logarithmsThe relevant rules of logarithms are ...
log(ab) = log(a) +log(b)
log(a/b) = log(a) -log(b)
log(a^b) = b·log(a)
logₐ(b) = log(b)/log(a)
Application[tex]3\cdot\log_{\frac{4}{9}}{\sqrt[4]{\dfrac{27}{8}}}=\dfrac{3}{4}\log_{\frac{4}{9}}\left(\dfrac{27}{8}\right)=\dfrac{3}{4}\cdot\dfrac{\log\dfrac{27}{8}}{\log\dfrac{4}{9}}\\\\\\=\dfrac{3(\log(3^3)-\log(2^3))}{4(\log(2^2)-\log(3^2))}=\dfrac{3(3\cdot\log(3)-3\cdot\log(2))}{4(2\cdot\log(2)-2\cdot\log(3))}\\\\\\=\dfrac{9(\log(3)-\log(2))}{8(\log(2)-\log(3))}=\boxed{-\dfrac{9}{8}}[/tex]
__
Additional comment
We have reduced everything to the difference of the logs of 2 and 3. You could stop the reduction to smallest parts at any point where you recognize things that will cancel. You could write numerator and denominator in terms of powers of (3/2), for example.
Please answer these questions step-by-step
Jose has scored 320 points on his math tests so far this semester. To get an A for the semester, he must
score at least 389 points.
Part 1 out of 2
Enter an inequality to find the minimum number of points he must score on the remaining tests in order to
get an A. Let n represent the number of points Jose needs to score on the remaining tests.
The inequality is
+ n (select)
HELP ME WAAKAIAKAKAKAK
The inequality that represents the minimum number of points he must score on the remaining tests in order to get an A is 320 + n ≥ 389, n ≥ 69, where n is the number of points.
When we use ≥ symbol, as at least means greater than or equal to.
320 + n ≥ 389
Subtracting 320 on both the sides,
n ≥ 69,
n represents the score he must receive on the remaining tests. Then n + 320 represents his total score for the semester.
Thus, the required inequality is n ≥ 69, which means that n is the minimum scored points to get A.
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the back of dante's property is a creek. dante would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. if there is 200 feet of fencing available, what is the maximum possible area of the corral?
If there is 200 feet of fencing available, the maximum possible area of the corral is 5000 Feet.
In the question, if there is 200 feet of fencing available, then we have to find the maximum possible area of the corral.
The formula of area of rectangle is:
A = L × B, where L is the length of the rectangle and B is the breadth of the rectangle.
The A = 200 feet and rectangular area is enclosed using the creek as one side and fencing for the other three sides, to create a corral.
So, L + 2B = 200
Subtract L on both side, we get
2B = 200 - L
Divide by 2 on both side, we get
B = 100 - L/2
A = f(L)
A = L·(100 - L/2)
A = 100L - [tex]L^2[/tex]/2
Now finding the derivative.
A' = [tex]\frac{df(L)}{dL}[/tex]
A' = -L + 100
Let A' = 0
-L + 100 = 0
Subtract 100 on both side, we get
-L = -100
L = 100 feet
Now putting the value of L in B = 100 - L/2.
B = 100 - 100/2
B = 100 - 50
B = 50 feet
The maximum possible area of the corral = 100 × 50
The maximum possible area of the corral = 5000 Feet
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HELPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!
YALL AMAZING :)
Answer:
11 and 12
Step-by-step explanation:
Solving this would be the case of finding that square root of 131, then rounding both up and down.
First, to solve
The square root of 131 is 11.45
Now we take that 11.45 and round both up and down
Rounding down is 11 and rounding up is 12.
11 and 12 are next to each other, making them consecutive.
Answer:
I think its 11 and 12
Step-by-step explanation:
two side lengths of a triangle are 11 and 17. what is the longest possible integer length of the third side of the triangle?
Therefore, the potential length of a triangle's third side is 17-11<x<17+11 is equals to 6 < x< 28.
A triangle's third side must always have a length that falls between (but not exactly equal to) the sum and difference of the other two sides. Consider the examples 2, 6, and 7 as an example. The third side length must therefore be larger than 4 and less than 8.
According to the Triangle Inequality Theorem, any two triangle sides must add up to more than the third side's length. To find the potential length of a triangle, multiply the sum of the two sides by the difference of the two sides.
Therefore, the potential length of a triangle's third side is 17-11<x<17+11.
= 6 < x< 28
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As a result, the third side of a triangle may be equal to 17-11<x<17+11 is equals to 6 < x< 28.
The third side of a triangle must always have a length that is between the sum and difference of the other two sides, but is not exactly equal to either. As an illustration, think about cases 2, 6, and 7. Therefore, the third side length must be more than 4 and lower than 8.
The Triangle Inequality Theorem states that any two triangle sides must add up to greater than the length of the third side. Multiply the sum of the two sides by the difference of the two sides to determine the potential length of a triangle.
Consequently, 17-11<x<17+11.= 6 < x< 28 is the possible length of the third side of a triangle.
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The_____area includes all surfaces.The______area does not include bases
1st blank (lateral surface or total surface)
2nd blank (lateral surface or total surface)
Your savings account increased by 3% in the last year. Write an expression as a product to represent the amount of money in your savings account(s) now.
Sammy wants to know what percent of students at her high school have a driver’s license. She surveys all students in her statistics class and finds that 68% of the students in her sample have a driver’s license.
What type of sample did Sammy obtain?
Explain why this sampling method is biased. Is 68% likely to be greater than or less than the percent of all students at her high school who have a driver’s license?
Explain how Sammy could avoid the bias described in part (b)
Sammy obtained a convenient sample.
The sampling method is biased because the students in the statistics class are not representative of the entire high school population. The sample only includes the students in one particular class and does not account for the experiences or characteristics of other students in the school.
68% is likely to be greater than the percent of all students at the high school who have a driver's license.
To avoid the bias, Sammy could use a more representative sample, such as a simple random sample or a stratified sample, to ensure that the sample includes a diverse group of students from various backgrounds, classes, and demographics. This would give a more accurate representation of the experiences and characteristics of the entire high school population.
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Solve the equation with the quadratic
formula. Enter the smallest solution
first and round to the nearest tenth.
2x² - 4x - 48 = 0
x = [?], [?]
For the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.
What is quadratic equation?
The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients. Here, the variable "X" is unknowable.
ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
We have a quadratic equation;
2x² - 4x - 48 = 0
To find the value of x we have to follow these steps ;
(2x^2 - 4x) - 48 = 0
Pull out like factors :
2x^2 - 4x - 48 = 2 • (x^2 - 2x - 24)
x2 multiplied by 2x and 24
x^2 is the initial term, and it has a coefficient of 1.
The coefficient of the middle term, which is -2x, is 2.
"The constant," the final term, is -24.
⇒ x^2 - 6x + 4x - 24
⇒ (x+4) • (x-6)
⇒ 2 • (x + 4) • (x - 6) = 0
therefore x+4 = 0
x = -4
and x-6 = 0
Add 6 to both sides of the equation :
x = 6
Hence, for the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.
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I need help understanding how to do this
Answer:
113.04
Step-by-step explanation:
see attached
Gilowing 50 Hz. A, B, C and D are points on the wave A Direction of wave motion 10 m B 3 m Calculate the time that the wave takes to travel the distance AB. Calcuplate the wavelength of this wave. Calculate the amplitude of this wave. Are points A and B on the wave in phase? Explain your answer
The time it takes for the wave to travel from point A to point B is 0.0086 seconds.
How to find the time of wave to travel from point A to point B?Assuming the question is referring to a sinusoidal wave with a frequency of 50 Hz, we can use the wave speed formula to calculate the time it takes for the wave to travel from point A to point B.
Wave speed (v) = frequency (f) x wavelength (λ)
Since the frequency is given as 50 Hz, we need to determine the wavelength to find the wave speed.
To calculate the wavelength, we can use the distance between two consecutive points on the wave that is in phase, such as points A and D or B and C. From the given information, we know that the distance between A and D or B and C is one wavelength. Therefore, we can calculate the wavelength as follows:
wavelength (λ) = distance between A and D or B and C = 10 m - 3 m = 7 m
Using the wave speed formula and the calculated wavelength, we can find the wave speed:
v = f x λ = 50 Hz x 7 m = 350 m/s
Now we can use the wave speed formula to find the time it takes for the wave to travel from point A to point B:
v = d / t
where d is the distance between A and B (which is 3 m) and t is the time it takes for the wave to travel that distance.
Rearranging the formula, we get:
t = d / v = 3 m / 350 m/s = 0.0086 s
Therefore, the time it takes for the wave to travel from point A to point B is 0.0086 seconds.
To find the amplitude of the wave, we would need additional information, as the amplitude is the maximum displacement of the wave from its equilibrium position.
As for whether points A and B are in phase, we need to compare the phase difference between the two points to the wave period. The period of a wave is the time it takes for one complete oscillation, and it is given by:
period (T) = 1 / frequency (f) = 1 / 50 Hz = 0.02 s
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Determine the intercepts of the line.
Do not round your answers.
y=-3x+12
y-intercept:
x-intercept:
Answer:
y- intercept = 12, x- intercept = 4
Step-by-step explanation:
to find the y- intercept, the point where the line crosses the y- axis.
let x = 0 in the equation and solve for y
y = - 3(0) + 12 = 0 + 12 = 12
then y- intercept = 12
to find the x- intercept, where the line crosses the x- axis.
let y = 0 in the equation and solve for x
0 = - 3x + 12 ( subtract 12 from both sides )
- 12 = - 3x ( divide both sides by - 3 )
4 = x
then x- intercept = 4
I just need the answer to UV
Answer:
In a rhombus, all sides are equal. Therefore, you can set WV (s+12) and UV (3s) equal to each other.
s+12 = 3s
Subtract s from both sides, so the variables are all on one side.
12 = 2s
Divide both sides by 2 to isolate the variable.
6 = s
UV = 3s
UV = 3(6)
UV = 18
Find the area of shaded region?
Please help me!!!!
The are of shade part of semi-circle is 75.36 cm^2.
What is a circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.
The equation of circle in the plane is given as:
(x-h)^2 + (y-k)^2 = r^2
where (x, y) are the coordinate points
(h, k) is the coordinate of the center of a circle
and r is the radius of a circle.
and Area of circle = πr²
Now,
Area of the shaded region=area of large semicircle-2*area of small semicircles
radius for large semicircle=7cm
radius for small semicircle=3.5cm
Therefore,
Area of the shaded region=πR^2-2*πr^2
=3.14(7^2-2*3.5^2)
=3.14*(49-25)
=3.14*24
Area of the shaded region =75.36 cm^2
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stressed out, part ii. in a study evaluating the relationship between stress and muscle cramps, half the subjects are randomly assigned to be exposed to increased stress by being placed into an elevator that falls rapidly and stops abruptly and the other half are left at no or baseline stress. can this study be used to conclude a causal relationship between increased stress and muscle cramps?
The following type of study can be concluded as an observational study.
An observational study is a type of study that is used to gather data on the characteristics and behaviors of a particular group of people or subjects without actively manipulating or interfering with the subjects.
This study can be used to suggest a causal relationship between increased stress and muscle cramps, but it cannot conclusively prove causality.
There are several reasons why this study design cannot be used to conclude a causal relationship. First, the study is a non-randomized, uncontrolled experiment, which means that there may be other factors that could be influencing the results.
For example, the subjects in the stress group may have other characteristics or preexisting conditions that are related to muscle cramps. Additionally, the study does not have a control group for comparison, so it is not possible to determine if the muscle cramps are caused by stress or by some other factor.
Second, the study design is a single-blind study, which means that only the subjects are not aware of their group assignment, but the experimenter knows which group the subjects are in. This can lead to bias in data collection, analysis, or interpretation.
Therefore, The following type of study can be concluded as an observational study.
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Quadrilateral U is a scaled copy of quadrilateral T.
What scale factor takes quadrilateral T to quadrilateral U?
The scale factor that takes quadrilateral T to quadrilateral U would be = 1.6
What is a scale factor?A scale factor is defined as the factor that is used to creat a similar shape of an object with a different dimension.
The formula that is used for the new object = original object × scale factor
The original object = quadrilateral T
The new object = quadrilateral U.
The scale factor the was used to form U using the length of the quadrilateral as 16;
16 = 10 * Scale factor
This gives
Scale factor = 16/10
Scale factor = 1.6
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Half of this two digit number is 3 times half of 28 this number is ?
Answer:
84
Step-by-step explanation:
x/2=3*28/2=3*14 = 42
x=84
1+1=??????
Help me I am stuck
For the translation below, give the vertices of ABC
Answer:
see explanation
Step-by-step explanation:
a translation [tex]T_{(-5,-4)}[/tex]
means subtract 5 from the original x- coordinate and subtract 4 from the original y- coordinate.
A (2, - 1 ) → A' (2 - 5, - 1 - 4 ) → A' (- 3, - 5 )
B (- 4, - 2 ) → B' (- 4 - 5, - 2 - 4 ) → B' (- 9, - 6 )
C (3, 2 ) → C' (3 - 5, 2 - 4 ) → C' (- 2, - 2 )