The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 35 cubic inches when it's base area is 15 square inches and it's height is 7 inches. What is the volume of a pyramid with a base area of 36 square inches and a height of 5 inches?
A ball is thrown from a height of 255 feet with an initial downward velocity of 21/fts . The ball's height h (in feet) after t seconds is given by the following. How long after the ball is thrown does it hit the ground?
The time it takes for a ball thrown downwards at a velocity of 21 ft/s from a height of 255 ft to reach the ground is approximately 4.05 seconds.
Explanation:The physics problem presented is a classic example of a vertically descending projectile. Here, we can use the formula of motion to find the solution. The formula is h = vt + 0.5gt², where v is the initial velocity, g is the acceleration due to gravity, and h is the height.
Since the ball is thrown downwards, the initial velocity will be negative, -21 ft/s. We're also working in feet, so the gravitational acceleration should be in feet/s², which is approximately -32.2 ft/s² (remember it's negative as it's acting downwards).
So, substituting the values into the equation, we have 255 = (-21*t) + 0.5*(-32.2)*t². Simplifying this gives us a quadratic equation: 16.1t² - 21t - 255 = 0.
The roots of this equation represent the times at which the ball will be 255 ft below its starting point. We solve the equation and get t ≈ -3.9s or t ≈ 4.05s. Clearly, time cannot be negative, so the ball hits the ground after approximately 4.05 seconds from being thrown.
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The ball thrown from a height with initial downward velocity hits the ground after 3.79 seconds. This was found by solving the quadratic equation that stems from principles of physical motion (height vs time).
Explanation:The problem can be solved using the principles of kinematics in physics. The height of the ball after t seconds is given by the equation of motion, which is a quadratic equation. If we let h be 0 (height when the ball hits the ground), we can solve the equation for t.
Given: initial height = 255 feet, initial velocity = 21 feet/s, acceleration due to gravity = 32.2 ft/s² (downward); The equation of motion is: h = 255 + 21t - 16t²; We have to find the time when the ball hits the ground i.e when h=0. So, the equation becomes: 0 = 255+21t-16t².
On solving this quadratic equation, we get two roots. Assuming upward direction is positive, the negative time value reflects the time before the ball was launched and the positive value is the time it takes for the ball to hit the ground. The positive root gives us the answer, t = 3.79 s.
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In a school, the probability that a student takes environmental science and geography is 0.72.The probability that a student takes technology is 0.25. What is probability that a student takes geography given that the student is taking environmental science?
Which expression is equivalent to (3b + 2r) + (4b + r)?
Who wanna help me ??
HELP PLEASE???? Jayla has a USB stick that transfers data at 2.4 x 109 bytes per second. Her modem transfers data at 1.2 x 107 bytes per second. Which statement is true?
Answer:
The transfer rate of USB is 200 times the transfer rate of Modem
Step-by-step explanation:
Jayla has a USB stick that transfers data at 2.4 x 10^9 bytes per second. Her modem transfers data at 1.2 x 10^7 bytes per second.
To compare the transfer rate we divide the transfer rate of USB by modem
[tex]\frac{2.4*10^9}{1.2*10^7}[/tex]
2.4 divide by 1.2 is 2
10^9 divide by 10^7 = 10^2
So its 2* 10^2 = 200
The transfer rate of USB is 200 times the transfer rate of Modem
The USB stick transfers data at a rate which is significantly faster than the modem.
Explanation:The statement that is true is that Jayla's USB stick transfers data much faster than her modem. This is because the data transfer rate of the USB stick, which is 2.4 x 109 bytes per second, is greater than the modem's transfer rate of 1.2 x 107 bytes per second. We can compare the two rates directly because they are given in the same units. We can see that the USB's speed is two decimal places further to the right than the modem's speed, meaning it is 100 times faster.
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A telephone pole cast a shadow that is 37 m long find the height of the telephone pole if a statue that is 33 cm tall cast a shadow 83 cm long ?
Answer:
The height of the telephone pole is 14.711 m (Approx) .
Step-by-step explanation:
Let us assume that the height be x .
Let us assume that the shadow be y .
(As the shadow is always proportional to the height .)
Thus
[tex]x\propto y[/tex]
y = kx
Where k is the constant of proportionality .
As given
if a statue that is 33 cm tall cast a shadow 83 cm long .
y = 83 cm
x = 33 cm
Put in the equation y = kx .
83 = 33k
[tex]k = \frac{83}{33}[/tex]
As given
A telephone pole cast a shadow that is 37 m .
Let us assume that the height of the telephone pole be z .
As
1m = 100cm
37m = 3700 cm
y = 3700 cm
x = z
Put in the equation y = kx .
3700 = zk
[tex]k = \frac{3700}{z}[/tex]
Compare the value of k .
[tex]\frac{3700}{z} = \frac{83}{33}[/tex]
[tex]\frac{3700\times 33}{83} =z[/tex]
[tex]\frac{122100}{83} =z[/tex]
z = 1471.1 cm(Approx)
As
[tex]1\ cm = \frac{1}{100}\ m[/tex]
[tex]1471.1\ cm = \frac{1471.1}{100}\ m[/tex]
= 14.711 m (Approx)
Therefore the height of the telephone pole is 14.711 m (Approx) .
Which fraction has a value that's equal to 7/8?
Evaluate ,where e is the solid that lies between the cylinders x^2+y^2=1 and x^2+y^2=16, above the xy-plane, and below the plane z=y+4
To evaluate the solid e which lies between two cylinders and a plane, one would typically set up a triple integral in cylindrical coordinates. This involves translating the given boundaries from rectangular coordinates into cylindrical coordinates to account for the radial, angular, and vertical dimensions of the solid.
Explanation:This question pertains to the evaluation of a solid, denoted as e, that is located between the two cylinders x^2 + y^2 = 1 and x^2 + y^2 = 16. These cylinders are located above the xy-plane and below the plane z = y + 4. The evaluation of such a solid requires the application of integral calculus. Typically, in such cases we would set up a triple integral by converting rectangular coordinates into cylindrical coordinates (r, theta, z).
Given the specifics of the solid, the radial path r would vary between sqrt(1) and sqrt(16), which is between 1 and 4. The angular path theta would cover the full circle, thus varying between 0 and 2π. The z-coordinate would be bounded below by the xy-plane (0) and above by the plane z = y + 4. Please note that you would need to convert the z-boundary into cylindrical coordinates as well.
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The scores of a high school entrance exam are approximately normally distributed with a given mean m = 82.4 and standard deviation = 3.3. What percentage of the scores are between 75.8 and 89?
The percentage of the scores are between 75.8 and 89 can be calculated using z-scores.
The percentage of the scores between 75.8 and 89 is 95%.
Given:
The mean is [tex]m=82.4[/tex].
The standard deviation is [tex]\sigma =3.3[/tex].
Calculate the Z- score for 75.8.
[tex]Z(75.8)=\dfrac{(75.8-82.4)}{3.3} \\Z(75.8) = -2[/tex]
Calculate the Z- score for 89.
[tex]Z(89)=\dfrac{(89-82.4)}{3.3}\\Z(89)=2[/tex]
Calculate the percentage of the scores are between 75.8 and 89.
[tex]P(75.8<X<89)=P(-2<Z<2)\\P(75.8<X<89)=P(Z<2)-P(Z<-2)\\[/tex]
Refer the z-table, put the value,
[tex]P(75.8<X<89)=0.9772-0.0227\\P(75.8<X<89)=0.9545[/tex]
Thus, the percentage of the scores between 75.8 and 89 is 95%.
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Which of the numbers below are whole numbers?Check all that apply. A. 9747.25 B. 0.7832 C. 918 D. 0 E. 46245.7 F. 484.857
Which equation represents the average of the x-intercepts for 4x^2-24x+20
what is the vertex of y=3x^2+6x+5
Holly wants to save money for an emergency. Holly invests $1,100 in an account that pays an interest rate of 8.75%. How many years will it take for the account to reach $6,400
Answer:
20.99 years . plato
Step-by-step explanation:
What's the value of 4 in the number 745
Determine the scale factor of the function f(x)=1/3root x
What is the estimate of 2616
Using the given zero, find one other zero of f(x). Explain the process you used to find your solution. 1-6i is a zero of f(x) = x^2-2x^3+38^2-2x+37
10 raised to negative 3 in standard notation
two similar triangles have areas of 18 and 32 find the ratio of their perimeters
How many centimeters are there in 1.23 x 10-6 kilometers?
Answer:
The correct answer is 0.123 cm.
Step-by-step explanation:
Each kilometer has 1000 meters and each meter has 100 centimeters.
Hence each kilometer has 1000×100=100000=105 centimeters.
Therefore, 1.23×10−6 kilometer will have
1.23×10−6×105=1.23×10−6+5=1.23×10−1 or 0.123 centimeters
Consider the partially completed one-way anova summary table. source sum of squares degrees of freedom mean sum of squares f between 270 within 18 total 810 21 what is the sum of squares within for this anova procedure?
a. 620
b. 390
c. 540
d. 680
The one-way ANOVA or one – way analysis of variance is used to know whether there are statistically substantial dissimilarities among the averages of three or more independent sets. It compares the means between the sets that is being examined whether any of those means are statistically pointedly dissimilar from each other. If it does have a significant result, then the alternative hypothesis can be accepted and that would mean that two sets are pointedly different from each other. The sum of squares within for this ANOVA procedure is 680. The answer is letter D.
Pat writes all the 7-digit numbers in which all the digits are different and each digit is greater than the one to its right (so the tens digit is greater than the units, the hundreds greater than the tens, and so on). For example, 9,865,320 is one of the numbers that Pat writes down.
One of Pat's numbers is chosen at random. What is the probability that the middle (thousands) digit is a 5?
a tree casts a 9 ft shadow at the same time that a person 6 ft tall casts a 4 ft shawdow. what is the height of the tree?
A spinner is divided into 10 equal sections numbered 1 through 10. If the arrow is spun twice, what is the probability the first number will be a 2 and the second number will be a 4?
The probability of spinning 2 then 4: [tex]\( \frac{1}{10} \times \frac{1}{10} = \frac{1}{100} \).[/tex]
To find the probability that the first spin results in a 2 and the second spin results in a 4, we need to determine the probability of each event and then multiply them together because the spins are independent.
1. Probability of spinning a 2 on the first spin:
Since there is 1 section labeled '2' out of 10 sections in total, the probability of spinning a 2 on the first spin is [tex]\( \frac{1}{10} \)[/tex].
2. Probability of spinning a 4 on the second spin:
Similarly, there is 1 section labeled '4' out of 10 sections in total, so the probability of spinning a 4 on the second spin is also [tex]\( \frac{1}{10} \)[/tex].
Now, to find the probability of both events happening (the first spin resulting in a 2 and the second spin resulting in a 4), we multiply the probabilities of each event:
[tex]\[ P(\text{first spin = 2}) \times P(\text{second spin = 4}) \][/tex]
[tex]\[ = \frac{1}{10} \times \frac{1}{10} \][/tex]
[tex]\[ = \frac{1}{100} \][/tex]
So, the probability that the first spin results in a 2 and the second spin results in a 4 is [tex]\( \frac{1}{100} \)[/tex].
It costs $145 for 10 people to attend a concert. How much does it cost a group of 8 people?
Answer:
$145/10 = $14.50
$14.50 * 8 = $116.00
Step-by-step explanation:
459 randomly selected lightbulbs were tested in a laboratory 291 lasted more than 500 hours find a point estimate of the true proportion of all lightbulbs in that last more than 500 hours
Final answer:
The point estimate of the true proportion of all lightbulbs that last more than 500 hours is approximately 0.634, calculated using the sample data of 291 out of 459 lightbulbs lasting more than 500 hours.
Explanation:
To find a point estimate of the true proportion of all lightbulbs that last more than 500 hours, we use the sample data provided. Out of 459 randomly selected lightbulbs, 291 lasted more than 500 hours.
The point estimate is calculated by dividing the number of successes in the sample by the total number of trials. In this case, the point estimate (p-hat) would be 291 divided by 459, which gives us an estimate of the true proportion.
The calculation would be as follows:
Point estimate (p-hat) = Number of successes / Total number of trialsp-hat = 291 / 459p-hat = 0.633987 (rounded to six decimal places)The point estimate for the true proportion of all lightbulbs that last more than 500 hours is approximately 0.634.
Graphs of exponential functions
For both y= 8× and y= (2/7)×, what would be the equation of the horizontal asymptote for those two?
If compact discs cost $15.89 each, how much does one compact disc cost with 6% sales tax?
6% = 0.06
if you want to know the total price including the tax
multiply 15.89 x 1.06 = 16.84
If compact discs cost $15.89 each. Then the cost of each disc after 6% sales tax will be $ 16.84.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
If compact discs cost $15.89 each.
Then the cost of each disc after 6% sales tax will be
→ 1.06 × $ 15.89
→ $ 16.84
If compact discs cost $15.89 each. Then the cost of each disc after 6% sales tax will be $ 16.84.
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Write a real-world situation that can be modeled by y equals 3 to the power of t. post your situation and explain why it is modeled by the equation shown.
a. choose a situation written by another student. do you agree that the student's situation can be modeled by the given equation?
b. explain how you would modify either your situation, or another student's situation, if the equation was changed to y equals 2 open parentheses 3 close parentheses to the power of t.
c. if the equation were rewritten in the form y equals b open parentheses 1 plus r close parentheses to the power of t, what would be the value of r? tell what this value means in relation to either your, or another student's, situation.