The time in seconds, t, it takes for a specific object being dropped from a particular height in feet above sea level, h, to reach the ground can be found by the radical function t equals one fourth times radical h period At what height should you drop an object in order for it to reach the ground in 12 seconds?
9 feet
36 feet
96 feet
2,304 feet
Answers
The height that you should drop an object in order for it to reach the ground in 12 seconds is; 2304 feet
How to solve projectile motion?We are told that time in the equation is represented by "t".
Now, for us to find the height, represented by "h", we will just plug in the given value in for t and simplify to find h.
Thus;
t = (1/4)√x
Plug in 12 for t to get;
12 = (1/4)√x
Multiply both sides by 4 to get;
48 = √x
Square both sides to get;
x = 2304 ft
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Related Questions
Can someone tell me why the answer for this absolute value equation is all real numbers?
Answers
Answer:
yo its not that hard it just means that it can be any number
58 children go into the hall for a concert. There are six seats in a row. How many rows are needed to seat everyone?
Answers
To seat all 58 children in the hall for the concert, 10 rows are needed.
1. Determine the number of children per row: Since there are 6 seats in a row, each row can accommodate 6 children.
2. Divide the total number of children by the number of children per row: Divide 58 (the total number of children) by 6 (the number of children per row).
58 ÷ 6 = 9 with a remainder of 4
This means that 9 full rows can be formed, and there will be 4 children left after the last full row.
3. Check if there are any remaining children: Since there are 4 children remaining, they cannot form a complete row by themselves.
4. Calculate the number of rows needed: Add 1 to the number of full rows to account for the remaining children.
9 full rows + 1 row for the remaining children = 10 rows in total.
Therefore, to seat all 58 children in the hall for the concert, 10 rows are needed.
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You are taking samples from a normally distributed population with mean 138 and standard deviation 14. Your batch size is 16. Let X-bar be the average of all 16 of your samples. What is the variance of X-bar?
Answers
The variance of X-bar is 12.25.
To find the variance of the sample mean (X-bar) for a normally distributed population, we can use the formula:
Variance of X-bar = (Population Variance) / (Sample Size)
In this case, the population mean (μ) is 138 and the standard deviation (σ) is 14. The population variance (σ^2) can be calculated as the square of the standard deviation, which gives us 14^2 = 196.
Since we are sampling with a batch size of 16, the sample size is also 16.
Now we can substitute these values into the formula:
Variance of X-bar = 196 / 16 = 12.25
Therefore, the variance of X-bar is 12.25.
It's important to note that the sample mean (X-bar) is an unbiased estimator of the population mean (μ). The smaller the sample size, the greater the variability of X-bar around the population mean.
As the sample size increases, the variance of X-bar decreases, indicating a more precise estimate of the population mean.
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PLSSS HELP!! Ty whoever helped me! :) Question: Select the statement that is true about the two-dimensional figure.
A quadrilateral with the vertices labeled L, M, N and O. Angles M L O and L M N are greater than 90 degrees, and angles L O N and M N O are less than 90 degrees.
∠LMN is an acute angle.
∠LMN is an obtuse angle.
∠MNO is an obtuse angle.
∠MNO is a right angle.
Answers
∠LMN is an obtuse angle.
==========================================
Explanation
Let's go through the answer choices to see which are true, and which are false.
A. This is false. It is stated that "LMN is greater than 90 degrees", so this angle is obtuse. Acute angles are less than 90 degrees.B. This is true. See choice A above.C. This is false. We're told that "angle MNO is less than 90 degrees". That makes the angle acute. D. This is false. See choice C above. Right angles are 90 degrees exactly. Often a small square marker is used to denote a 90 degree angle.Bananas cost $2 a bunch and apples cost $0.75 each. If “b” represents the number of bunches of bananas and “a” represents the number of apples, which of the following expressions represents the total cost?
2.75ab
2b + 0.75a
2.75b + a
2.75(b + a)
Answers
Answer: 2b + 0.75a
Step-by-step explanation:
Answer:
This answer was correct: 2b + 0.75a
Step-by-step explanation:
these statements are the congruence statements for right triangles: ha, ll, la, and hl. you will need to use them for congruence statements. match the abbreviation to its description. for right triangles: 1. a hypotenuse and a leg define congruence. hl 2. a hypotenuse and an acute angle define congruence. la 3. a leg and an acute angle define congruence. ll 4. two legs define congruence. ha
Answers
hl: a hypotenuse and a leg define congruence
la: a hypotenuse and an acute angle define congruence
ll: a leg and an acute angle define congruence
ha: two legs define congruence
These abbreviations are used in congruence statements for right triangles, which are statements that describe when two right triangles are congruent (i.e., have the same shape and size). In a right triangle, the sides are labeled with the letters "a," "b," and "c," where "a" and "b" are the legs of the triangle and "c" is the hypotenuse.
The congruence statements for right triangles use these labels to describe when two triangles are congruent. For example, the statement "ha" means that two right triangles are congruent if their legs (labeled "a" and "b") are of equal length. The statement "ll" means that two right triangles are congruent if one of their legs (labeled "a" or "b") and one of their acute angles (labeled "A" or "B") are of equal length and measure, respectively.
Similarly, the statement "la" means that two right triangles are congruent if their hypotenuses (labeled "c") and one of their acute angles (labeled "A" or "B") are of equal length and measure, respectively. And the statement "hl" means that two right triangles are congruent if their hypotenuses (labeled "c") and one of their legs (labeled "a" or "b") are of equal length.
The distribution of monthly charges for cellphone plans in the United States is approximately normal with a mean of $62 and a standard deviation of $18. What percentage of plans have charges that are less than $83.60?
Answers
About 88.49% of cellphone plans have charges that are less than $83.60.
How to determine the percentage of plans have charges that are less than $83.60?To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.
z = (x – μ) / σ
where x = 83.60, mean, μ = 62 and standard deviation, σ = 18
Thus, the z-score of $83.60 is:
z = (83.60 - 62) / 18 = 1.2
Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).
Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.
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I need help solving this problem.
Answers
9514 1404 393
Answer:
8/7
Step-by-step explanation:
\(\displaystyle\left(\frac{g}{f}\right)(-2)=\frac{g(-2)}{f(-2)}=\frac{7(-2)-2}{-2(-2)^2+3(-2)}\\\\=\frac{-16}{-8-6}=\boxed{\frac{8}{7}}\)
Answer:
the answer is 8/7
Step-by-step explanation:
:)))))
2007 Federal Income Tax Table
Single:
Over But not over The tax is
$0 $7,825 10% of the amount over $0
$7,825 $31,850 $788 + 15% of the amount over $7,825
$31,850 $77,100 $4,386 + 25% of the amount over $31,850
$77,100 $160,850 $15,699 + 28% of the amount over $77,100
$160,850 $349,700 $39,149 + 33% of the amount over $160,850
$349,700 And Over $101,469 + 35% of the amount over $349,700
Mary Hernandez earned $43,000 in taxable income. She figured her tax from the single taxpayer table above.
1. Find her earned income level.
2. Entered the base amount. = $
3. Found the amount over $
= $
4. Multiplied line 3 by 25% = $
5. Added Lines 2 and 4 = $
Answers
Earned income is supposed to be $35,000. The federal income tax is the biggest wellspring of income for the U.S. government.
The base tax amount at that level is $4386.
The amount more than $31850 is $35000-31850 = $3150
Line 3 is duplicated by 25%: $3150×0.25 = $787.50
The amount of lines 2 and 4 is $4386 +787.50 = $5173.50
This amount divided by 12 is ... $5173.50/12 ≈ $431.13
The federal income tax is the biggest wellspring of income for the U.S. government.
Federal income tax is utilized for different costs going from building and fixing the country's foundation to further developing instruction and public transportation and giving calamity alleviation.
Federal income taxes are based on your income and documentation status; taxes apply to everybody, paying little mind to where they live or work.
Federal income tax liability can be diminished by tax allowances and tax credits, a regulation that gives advantages to explicit sorts of taxpayers.
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BRAINLEST , If y varies inversely with the square of x, and y = 26 when x = 4, find y when x = 2.
Answers
Answer:
Question 18: B. 104
Question 19: \( x = \frac{3}{2} \)
Step-by-step Explanation:
Question 18:
Step 1: express the inverse relationship with an equation
\( y = \frac{k}{x^2} \) ,
where k is constant
y = 26 when x = 4,
Constant, k, = \( y*x^2 = k \)
\( k = 26*4^2 = 416 \)
The equation would be \( y*x^2 = 416 \)
Step 2: use the equation to find y when X = 2.
\( y*x^2 = 416 \)
\( y*2^2 = 416 \)
\( y*4 = 416 \)
Divide both sides by 4
\( \frac{y*4}{4} = \frac{416}{4} \)
\( y = 104 \)
Question 19:
\( \frac{x}{3} = \frac{x + 2}{7} \)
Cross multiply
\( x(7) = 3(x + 2) \)
\( 7x = 3x + 6 \)
Subtract 3x from both sides
\( 7x - 3x = 3x + 6 - 3x \)
\( 4x = 6 \)
Divide both sides by 4
\( \frac{4x}{4} = \frac{6}{4} \)
\( x = \frac{3}{2} \)
Answer: D.) 52
Explanation: I guessed and got it right lol
Select all of the following tables which represent y as a function of and are one-to-
one.
Answers
Answer:
Option 3
Step-by-step explanation:
Each value of x maps onto one value of y and vice versa.
The basketball team raised a total of $154,694 in September and $29,987 more in October than in September. How much money did they raise in October?
Answers
Answer:
$184,681
Step-by-step explanation:
154,694+29,987= 184,681
Just add the two numbers up. Hope this helps
A region consists of 2,545 thousand acres of farm land. If 32% of this land is privately owned, find how may acres are not privately owned
Answers
Answer:
1730.6
Step-by-step explanation:
First you have to substract 100 - 32 to find the percentage of land (acres) that is not privately owned
You get 68 percent, then you need to multiply the percentage to the 2,545 thousand acres of farmland the region consists
So, 2,545 x .68
=1730.6
Freemont run club surveyed a random sample of 30 of their members about their running habits
Answers
The reasonable estimate would be 25
How to solve for the estimateWe have to solve this using the rule of 3
9 out of 30 members said that they run more than 5 days a week.
We will form the equations
when 9 ran = 30 menbers
when n ran = 84 members
we will then cross multiply
84 x 9 = 30 x n
n = 25.2
When we round this, the reasonable estimate would be 25
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Complete question
Freemont Run Club surveyed a random sample of 30 of their members about their running habits. Of the members surveyed, 9 said that they run more than 5 days a week.
There are 84 Freemont Run Club members.
Based on the data, what is the most reasonable estimate for the number of Freemont Run Club members who run more than 5 days a week?
what type of scale is used on the map?
Answers
The type of scale commonly used on maps is a graphic scale, which uses a line or bar to represent distances accurately.
The type of scale used on a map is known as a map scale. It is a graphical representation that shows the relationship between distances on the map and their corresponding measurements in the real world. A map scale allows us to understand the size and proportion of features depicted on the map.
There are three main types of map scales: verbal scales, graphic scales, and representative fraction scales.
Verbal Scale: A verbal scale uses words to describe the relationship between distances on the map and real-world measurements. For example, a verbal scale might state "1 inch represents 1 mile" or "1 centimeter represents 10 kilometers." Verbal scales are commonly used on small-scale maps, where the level of detail is not as important.
Graphic Scale: A graphic scale, also known as a bar scale or linear scale, uses a line or a bar marked with specific distances. This line is divided into equal segments that represent units of measurement. By comparing the length of the line on the map to the corresponding distance in the real world, you can determine distances accurately. Graphic scales are often found on the margin or the legend of a map and are commonly used on medium- to large-scale maps.
Representative Fraction (RF) Scale: A representative fraction scale expresses the relationship between map distances and real-world distances using a ratio. For example, a representative fraction of 1:100,000 means that one unit of measurement on the map represents 100,000 of the same units in the real world. This type of scale is useful because it allows for precise calculations and conversions between map distances and real-world distances. Representative fraction scales are commonly used on topographic maps and engineering plans.
It's important to note that a map may include multiple scales to accommodate different levels of detail. For instance, a large-scale map of a city may have a more detailed scale than a small-scale map of an entire country.
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I'LL MARK THE BRAINLIEST
The diameter of a circle is 10 3/4 inches.
What is the radius, r, of the circle?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
Answer: The radius of the circle is 5 3/8 inches.
Step-by-step explanation:
The radius of the circle is half of the diameter. We can start by converting the mixed number diameter to an improper fraction:
10 3/4 = (10 × 4 + 3)/4 = 43/4
So, the diameter of the circle is 43/4 inches. The radius is half of this, which we can find by dividing by 2:
r = (43/4) ÷ 2 = 43/8
To simplify the fraction, we can divide the numerator and denominator by their greatest common factor (GCF), which is 1:
r = 43/8 = 5 3/8
Therefore, the radius of the circle is 5 3/8 inches.
Answer:5 3/4
Step-by-step explanation:
10 3/4 * 1/2
1/2 * 43/4 = 43/8
8/43=5 3/4
Determine if the following ratios form a proportion
a) 45 g to 60 g and 36 kg to 48 kg
b) 450 m to 3 km and 75 cm to 7 m
Answers
Answer:
a was ture
b was wrong
Step-by-step explanation:
a)
\(\frac{45}{60} =\frac{3}{4}\)
\(\frac{36}{48} =\frac{3}{4}\)
b)
\(\frac{450m}{3km} =\frac{450}{3000} =\frac{3}{20} \\\)
\(\frac{75cm}{7m}=\frac{75}{700} =\frac{15}{140}\)\(=\frac{1}{7}\)
Answer:
1. 45:60 = 36:48
(45:60)/15 = (36:48)/12 (divide by their GCF)
3:4 = 3:4
PROPORTION2. 4500:3 = 75:700
(4500:3)/3 = (75:700)/25
1500:1 = 3:28
NOT PROPORTIONStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Complete the table. Then
identify the y-intercept
and the coordinate
where x = 1.
Consider the following
exponential equation.
Sketch the graph of the
exponential function.
y = 16(4x+1)
у
х
-2
-1
o
1
2
3
As x increases (x ).
у
As x decreases (x-co),
у
Answers
Answer:
y x
-2 1/4
-1 1/2
0 1
1 2
2 4
Step-by-step explanation:
its easy algbra
doing it rn to
(-6,1) after a translation of (x-2y)
Answers
Answer:
(-8,1)
Step-by-step explanation:
Imma assume you meant (x-2, y)
x coordinate becomes -6-2=-8
y coordinate stays the same
so the image is (-8,1)
the density of machine oil is .05 grams per cubic millimeter. what is the volume of a bottle that will hold 250 grams of the machine oil?
Answers
Answer:
Step-by-step explanation:
cuanto es 2 mas 2 mas 82 menos 72?
Answers
Answer:
14
Step-by-step explanation:
2+2+82-72
86 - 72 = 14
Solve by Factoring:
2x^2 - x - 3 = 0
Answers
Answer:
x = 3/2 or x = -1
Step-by-step explanation:
2x² - x - 3 = 0
2*(-3) = -6
Factors of -6:
(-1, 6), (1, -6), (-2, 3), (2, -3)
We need to find a pair that adds up to the co-eff of x which is (-1)
Factors :(2,-3)
2 - 3 = -1
so, 2x² - x - 3 = 0 can be written as:
2x² + 2x - 3x - 3 = 0
⇒ 2x(x + 1) -3(x + 1) = 0
⇒ (2x - 3)(x + 1) = 0
⇒ 2x - 3 = 0 or
x + 1 = 0
⇒ 2x = 3 or x = -1
⇒ x = 3/2 or x = -1
Change 3Y - 2X = -6 to the slope-intercept form of the equation of a line.
Answers
Answer:
y = 2/3x -2
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
3y -2x = -6
Solve for y
Add 2x to each side
3y = 2x-6
Divide by 3
3y/3 = 2x/3 -6/3
y = 2/3x -2
1.
Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 3000/3 π, in^3?. One day, his sink
clogged. He has to use one of two cylindrical cups to scoop the water out of the sink. The sink is completely
full when Anthony begins scooping.
(a) One cup has a diameter of 5 in, and a height of 6 in. How many cups of water must Anthony scoop
out of the sink with this cup to empty it? Round the number of scoops to the nearest whole
number. Show all your work.
(b) One cup has a diameter of 6 in, and a height of 6 in. How many cups of water must he scoop out of
the sink with this cup to empty it? Round the number of scoops to the nearest whole number.Show all your work
Answers
Answer:
a) 27
b) 19
Step-by-step explanation:
a) Calculate the volume of the the cup using volume of cylinder equation: \(V = \pi r^{2} h\)
Where V = Volume, r=radius, and h=height. Your answer should be in cubic inches (\(in^3\)).
You're given diameter, so use equation \(d/2 = r\) to find radius.
Substituting these equations will give you: \(V = \pi (d/2)^2 h\)
However, the given volume of the sink is 3000/3\(\pi\) or 1000\(\pi\), meaning that you should modify your results to match this value. Do not substitute \(\pi\) for 3.14..., leave it as a symbolic value. Your final V of the cup should = 37.5 \(\pi\)
Divide the volume of the sink by the volume of the cup. This number will be the amount of cups needed to empty it. In equation form:
\(Vsink / V cup =\) # of cups.
Note the the \(\pi\) will cancel each other out, so there's not need to factor that in.
b) Repeat the steps above with the new d (diameter) value.
which graph represents the parabola with the equation y^2=-1/3x
Answers
Step-by-step explanation:
The graphs are not give but the graph looks like the above picture.
Liam will spin the pointer one time. What is the probability that the pointer will land on red?
Answers
Answer:
Step-by-step explanation:
What are the other colors?
if there are two colors ( red and another color ) then the probability of the pointer landing on red will be 1/2
similarly if there are 3 colors ( red and two other colors) then the probability of the pointer landing on red will be 1/3 ....
depends on how many colors are there
How many pairs of intersecting line segments are shown ?
Answers
Answer:
16
Step-by-step explanation:
Example:
Consider A vertex. A is connected with two other vertices C and B.
Thus 3 line segments are formed. At A, two pair of intersecting lines are formed, AC & AE ; AE and AB
Each vertex form two pair of intersecting line segments. Totally , there are 8 verteces. So, 8*2 = 16 pair of intersecting lines
During July in Jacksonville florida
Answers
Answer:
yo i live in florida
Step-by-step explanation:
NO LINKS!! Please help me with these problems. Exponential.
Answers
Answer:
f(x) = 10400·(1/4)^x; table values: x = -1, f(x) = 162.5g(x) = 1.8·2.4^xIncorrect for b < 1.Step-by-step explanation:
You want to write exponential functions through the given points.
1. TableThe exponential function ...
f(x) = a·b^x
will have the values ...
f(0) = af(1) = ab ⇒ b = f(1)/f(0)Using these relations we can write the function from the table values:
f(x) = 10400·(2600/10400)^x
f(x) = 10400·(1/4)^x
Then your table is ...
\(\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7}\vphantom{\dfrac{b}{g}}x&-1&0&1&3&4&6\\\cline{1-7}\vphantom{\dfrac{b}{g}}f(x)&41600&10400&2600&162.5&40.625&2.5390625\\\cline{1-7}\end{array}\)
2. PointsUsing the given points in the exponential function form, we have ...
4.32 = a·b^1
59.71968 = a·b^4
Dividing the second equation by the first, we find ...
59.71968/4.32 = b^3 ⇒ b = 2.4
Using this in the first equation, we get ...
4.32 = a·2.4 ⇒ a = 1.8
The equation of the function is ...
g(x) = 1.8·2.4^x
3. IncreasingThe exponential function ...
y = a·b^x . . . . . . a > 0, b > 0
will be increasing when the growth factor (b) is greater than 1. When 'b' is less than 1, the function will be decreasing.
Sarah's belief is incorrect.
Answer:
\(\textsf{1.} \quad f(x)=10400(0.25)^x\)
(-1, 41600) and (3, 162.5)
\(\textsf{2.} \quad g(x)=1.8(2.4)^x\)
3. Sarah is incorrect.
Step-by-step explanation:
\(\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}\)
Question 1The y-intercept is when x = 0.
Therefore, from inspection of the given table, the y-intercept is 10400:
\(\implies a=10400\)
Substitute point (1, 2600) and a = 10400 into the exponential function and solve for b:
\(\implies 2600=10400b^1\)
\(\implies 2600=10400b\)
\(\implies b=\dfrac{2600}{10400}\)
\(\implies b=0.25\)
Therefore, the equation of the function is:
\(\boxed{f(x)=10400(0.25)^x}\)
Find the value of x when f(x) = 41600:
\(\begin{aligned} f(x)&=41600\\\implies 10400(0.25)^x&=41600\\(0.25)^x &=\dfrac{41600}{10400}\\(0.25)^x &=4\\\ln (0.25)^x &=\ln 4\\x \ln (0.25)&=\ln 4\\x&=\dfrac{\ln 4}{\ln (0.25)}\\x&=-1\end{aligned}\)
Find the value of f(x) when x = 3:
\(\begin{aligned}x=3 \implies f(3) & =10400(0.25)^3\\& =10400(0.015625)\\& = 162.5\end{aligned}\)
Therefore, the completed table is:
\(\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} \vphantom{\dfrac12}x & -1 & 0 & 1 & 3 & 4 & 6\\\cline{1-7} \vphantom{\dfrac12}f(x) &41600 &10400 &2600 &162.5 &40.625 & 2.5390625\\\cline{1-7} \end{array}\)
Question 2Given points:
(1, 4.32)(4, 59.71968)Substitute the given points into the exponential formula g(x) = abˣ
\(\implies ab=4.32\)
\(\implies ab^4=59.71968\)
To find b, divide the equations:
\(\implies \dfrac{ab^4}{ab}=\dfrac{59.71968}{4.32}\)
\(\implies b^3=13.824\)
\(\implies b=\sqrt[3]{13.824}\)
\(\implies b=2.4\)
Substitute one of the points and the found value of b into the equation and solve for a:
\(\implies 2.4a=4.32\)
\(\implies a=\dfrac{4.32}{2.4}\)
\(\implies a=1.8\)
Therefore, the equation of the function is:
\(\boxed{g(x)=1.8(2.4)^x}\)
Question 3Sarah is incorrect. For an exponential function in the form a · bˣ:
If a > 0 and b > 1 then it is an increasing function.If a > 0 and 0 < b < 1 then it is a decreasing function.Use a geometric mean theorem or set up similar triangles to solve for the variable or find the indicated side length.All answers should be in simplified radical form:Please enter a square root as follows:2v2 as 2sqrt2 OR V2 as sqrt2
Answers
The figure for the triangle is,
Consider the triangle ABD and triangle ABC.
\(\begin{gathered} \angle ABD\cong\angle ABC\text{ (Common angle)} \\ \angle BAC=\angle BDA\text{ (Each right angle)} \\ \Delta ABD\approx\Delta CBA\text{ (By AA similarity)} \end{gathered}\)So triangle ABD is similar to triangle CBA. So ratio of sides of triangle are equal.
\(\frac{AD}{AC}=\frac{AB}{CB}=\frac{BD}{AB}\)Determine the length of AB by using the ratio of sides.
\(\begin{gathered} \frac{AB}{14}=\frac{6}{AB} \\ (AB)^2=84 \end{gathered}\)Consider the triangle ABD.
Determine the value of x by using the pythagoras theorem
\(\begin{gathered} (AB)^2=x^2+(6)^2 \\ 84=x^2+36 \\ x=\sqrt[]{84-36} \\ =\sqrt[]{48} \\ =4\sqrt[]{3} \end{gathered}\)So value of x is,
\(4\sqrt[]{3}\)