A waterfall has a hit of 1500 ft. A pebble is thrown upward at the velocity of 24ft per second. The hot, h, of the pebble after t seconds is given by the equation h=-16t+24t+1500. How long after the pebble is thrown will it hit the ground.
Answer:
A waterfall has a height of 1500 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 24 feet per second. The height, h, of the pebble after t seconds is given by the equation h =−16t^2+24t+1500. How long after the pebble is thrown will it hit the ground?
Pebble will hit the ground after 10.46 seconds.
Step-by-step explanation:
Given:
The height, "h" of the pebble after t seconds, "h" = −16t^2+24t+1500
We have to find the time it will take to hit the ground.
For this we have to put h = 0 and solve the quadratic.
Quadratic formula:
⇒ Standard equation : [tex]ax^2+bx+c=0[/tex]
⇒ [tex]x =\frac{-b\pm \sqrt{(b)^2-4ac} }{2a}[/tex]
Now,
Solving the above equation with quadratic formula after comparing its values with the standard equation.
⇒ [tex]a=-16,\ b=24,\ c=1500[/tex]
⇒ [tex]t =\frac{-b\pm \sqrt{(b)^2-4ac} }{2a}[/tex]
⇒ [tex]t =\frac{-24\pm \sqrt{(24)^2-4(-16)(1500)} }{2(-16)}[/tex]
⇒ [tex]t =\frac{-24\pm \sqrt{576+96,000} }{-32}[/tex]
⇒ [tex]t =\frac{-24\pm(310.76)}{-32}[/tex]
⇒ [tex]t =\frac{-24+(310.76)}{-32}[/tex] ⇒ [tex]t =\frac{-24-(310.76)}{-32}[/tex]
⇒ [tex]t =-\frac{286.76}{32}[/tex] ⇒ [tex]t =\frac{334.76}{32}[/tex]
⇒ [tex]t=-8.96\ sec[/tex] ⇒ [tex]t=10.46\ sec[/tex]
Discarding the negative values.
The pebble will hit the ground after 10.46 seconds.
Quart cartons of milk should contain at least 32 ounces. A sample of 22 cartons was taken and amount of milk in ounces was recorded. We would like to determine if there is sufficient evidence exist to conclude the mean amount of milk in cartons is less than 32 ounces?
If the sample mean is close to 32 ounces or the sample standard deviation is large, it is less likely that we will reject the null hypothesis.
To determine if there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces, we would conduct a hypothesis test. The null hypothesis (H0) would state that the mean amount of milk in cartons is at least 32 ounces, while the alternative hypothesis (Ha) would state that the mean amount is less than 32 ounces.
The null hypothesis: [tex]\( H_0: \mu \geq 32 \)[/tex]
The alternative hypothesis: [tex]\( H_a: \mu < 32 \)[/tex]
Here is the step-by-step process to conduct the hypothesis test:
1. **Identify the sample mean [tex](\( \bar{x} \))[/tex] and the sample standard deviation (s).** These values would be calculated from the sample of 22 cartons.
2. **Calculate the test statistic (t-score).** The formula for the t-score in a one-sample t-test is:
[tex]\[ t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}} \][/tex]
where [tex]\( \mu_0 \)[/tex] is the hypothesized mean (32 ounces in this case), [tex]\( \bar{x} \)[/tex] is the sample mean, [tex]\( s \)[/tex] is the sample standard deviation, and [tex]\( n \)[/tex] is the sample size.
3. **Determine the degrees of freedom (df).** For a one-sample t-test, the degrees of freedom are [tex]\( n - 1 \)[/tex], where [tex]\( n \)[/tex] is the sample size. In this case, [tex]\( df = 22 - 1 = 21 \)[/tex].
4. **Find the critical t-value or p-value.** Using the degrees of freedom, we can find the critical t-value from a t-distribution table or calculate the p-value. The significance level (α) is typically set at 0.05 for such tests.
5. **Make a decision.** If the test statistic is less than the critical t-value or if the p-value is less than α, we reject the null hypothesis in favor of the alternative hypothesis. This would mean there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces.
6. **Calculate the p-value.** The p-value is the probability of observing a sample mean at least as extreme as the one observed, assuming the null hypothesis is true. It can be calculated using statistical software or a t-distribution table.
7. **Report the results.** If the p-value is less than α, we report that there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces. If the p-value is greater than α, we report that there is not enough evidence to conclude that the mean amount is less than 32 ounces.
Without the actual sample data (sample mean and sample standard deviation), we cannot perform the calculations or make a conclusion. However, if the sample mean is substantially less than 32 ounces and the sample standard deviation is small, it is more likely that we will reject the null hypothesis. Conversely, if the sample mean is close to 32 ounces or the sample standard deviation is large, it is less likely that we will reject the null hypothesis.
A small accounting firm has 4 accountants who each earn a different salary between 50,000 and 60,000 and a 5th accountant who works part-time for tax season and earns 10,000
The firm decides to get rid of the part-time accountant and keep the other 4 salaries the same
How will getting rid of the part-time accountant affect the mean and median
Answer: B
Step-by-step explanation:
Both the mean and the median will decrease, but the mean will decrease by more than the median.
Answer:
Both the mean and the median will decrease, but the mean will decrease by more than the median.
Step-by-step explanation:
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Which equation can be used to find the unknown length, a, in this triangle?
A right triangle has a side with length 15 meters and hypotenuse with length 17 meters. The other side is labeled a.
A. a squared + 15 squared = 17 squared
B. 15 squared + 17 squared = a squared
C. a squared + 15 = 17 squared
D. a + 15 squared = 17 squared
Answer:
It is A.
Look at the attachment down below:
Step-by-step explanation:
The equation is used to find the unknown length (a) will be 17² =15² + a². Then the correct option is A.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
A right triangle has a side with length 15 meters and a hypotenuse with length 17 meters.
The other side is labeled a.
17² =15² + a²
Then the correct option is A.
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Complete the equation describing how x and y are related
Answer:
? = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Take two points in this case, (-2,4) and (0,5)
Use rise over run for slope to find ?
5-4/0+2 = 1/2
To find the other blank, enter one of the two points into the existing equation.
y = 1/2x + b
5 = 0 + b
b = 5
The equation is y = 1/2x + 5
Which statements best describe displacement? Check all that apply.
Displacement is measured along the path an object travels.
Displacement is a measurement that includes direction.
Displacement is the difference between a starting point and an ending point.
Displacement is how far an object travels from starting point to ending point.
Displacement is measured as a straight line between a starting point and an ending point.
Answer: displacement is a measure that includes direction
Displacement is the difference between a starting point and a ending point
Displacement is measured as a straight line between a starting point and an ending point
Step-by-step explanation:
A rectangular prism with a height of 20 cm, length of 70 cm, and width of 29 cm is filled completely with water. The water is then poured into a large cylindrical container with a radius of 31 cm. What is the depth of the water in the container, to the nearest centimeter?
Answer:
13 cm
Step-by-step explanation:
Volumes should be equal
20 × 70 × 29 = 3.14 × 31² × h
h = 13.4546683723 cm
What the area of a trapezoid
Answer:
A =176 cm^2
Step-by-step explanation:
The area of a trapezoid is found by
A =1/2 (b1+b2) *h
where b1 and b2 are the lengths of the bases
A =1/2(12+10) *16
A = 1/2(22)*16
A =176 cm^2
starting in the year 1800 the population of the untied states recored until the year 2000
Final answer:
The population of the United States grew from around 5 million in 1800 to approximately 281 million in 2000, with growth rates declining over time due to lower birth rates and increasing reliance on immigration.
Explanation:
The population growth of the United States from 1800 to 2000 showcases remarkable changes over two centuries. Starting with the beginning of the 19th century, the US population was around 5 million and by the year 2000, it had grown to approximately 281 million according to the decennial census data. This substantial increase can be attributed to various factors including immigration, natural growth, and economic prosperity.
During the early 1800s, the population saw a significant surge, increasing by 38% between 1800 and 1810. However, as time progressed, the growth rate began to slow down. Between 1900 and 1910, the growth rate was at 21%, and it further reduced to 10% between 2000 and 2010. The declining growth rates in the later years are linked to a decrease in the total fertility rate (TFR), which at 1.9, is below the replacement rate of 2.1. The nation's population started to rely more on immigration for its growth as the birth rates declined.
In terms of economic impact, the period between 1850 and 1860 is noted for its astounding economic growth despite political tensions, where the nation's wealth and various economic indicators such as farm value and product manufacturing saw increases surpassing 100%.
Which inequality represents an acute angle?
A. 0
B. 90
C. 180
D. 270
The material used to make a storage box costs $1.25 per square foot. The boxes have the same volume, so how much does a company save by choosing to make 50 of Box 2 instead of Box 1?
Answer:
$41.685
Step-by-step explanation:
Given:-
- The material cost per square foot, C = $1.25
- The two boxes have the dimensions:
Box 1 : ( 9 x 9 x 10 ) in
Box 2: ( 11 x 7 x 10 ) in
Find:-
so how much does a company save by choosing to make 50 of Box 2 instead of Box 1?
Solution:-
- We will first determine the surface areas of the two boxes Box 1 ( A1 ) & Box 2 (A2).
A1 : 2*( 9*9) + 4*( 9*10) = 522 in^2 = 43.5 ft^2
A2 : 2*(11*7) + 2*(11*10) + 2*(7*10) = 514 in^2 = 42.833 ft^2
- Determine the cost for each box:
Cost of box 1 = A1*C = 43.5*$1.25 = $54.375
Cost of box 2 = A2*C = 42.833*$1.25 = $53.5413
- The amount saved by the company by choosing to make 50 Box 2 as compared to 50 Box 1:
Amount saved = 50*(Cost of box 1 - Cost of box 2)
= 50*( 54.375 - 53.5413 )
= $41.685
Angle x is coterminal with angle y. If the measure of angle x is greater than the measure of angle y, which statement is true
regarding the values of x and y?
©
X = y - 180n for any positive integer n
X-y-360n for any integer n
X = y + 360n for any positive integer n
x = y + 180n for any integern
The statement which is true regarding the values of x and y is option C; x=y+360n , for any positive integer n.
What are Coterminal angles?The algebraic sum of Coterminal angles at a point is 360°.
From the given information;
Angle x is coterminal with angle y.
If the measure of angle x is greater than the measure of angle y.
Then, the statement which is correct is will be as;
x = y + 360n , for any positive integer n.
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An aquarium tank can hold liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in minutes. The second pipe can fill the tank in minutes by itself. When both pipes are working together, how long does it take them to fill the tank
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An aquarium tank can hold 6600 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 55 minutes. The second pipe can fill the tank in 66 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?
Given Information:
Time to fill tank by first pipe = 55 minutes
Time to fill tank by first pipe = 66 minutes
Total capacity of tank = 6600 liters
Required Information:
Time required to fill tank when both pipes are working together = ?
Answer:
Time required to fill tank when both pipes are working together = 30 mins
Step-by-step explanation:
The rate of filling the tank of the first pipe is,
first pipe = [tex]\frac{6600}{55} = 120[/tex] [tex]L/m[/tex]
The rate of filling the tank of the second pipe is,
second pipe = [tex]\frac{6600}{66}= 100[/tex] [tex]L/m[/tex]
Let x is the time to fill the tank when both pipes are used so the equation becomes,
[tex]120 + 100 = \frac{6600}{x}[/tex]
[tex]120x + 100x = 6600[/tex]
[tex]220x = 6600[/tex]
[tex]x = \frac{6600}{220}[/tex]
[tex]x = 30[/tex] [tex]mins[/tex]
Therefore, it would take 30 minutes to fill the entire tank when both pipes are used to fill the tank.
Find the area of the shape below
Answer:
A =32 units^2
Step-by-step explanation:
This figure is a trapezoid
We can find the area from
A = 1/2(b1+b2)h where b1 and b2 are the base length and h is the height
A = 1/2(4+12) *4
A = 1/2 (16)*4
A =32 units^2
a regular pentagon has a perimeter of 60 cm what is the measure of angle CBD
The measure of angle CBD in a regular pentagon with perimeter 60 cm is 108°. This conclusion assumes that CBD refers to an internal angle of the pentagon and is based on the formula for internal angles of a regular polygon.
Explanation:The subject of the question is related to a regular pentagon which is a polygon with 5 equal sides and equal angles. If the perimeter of the regular pentagon is 60 cm, it means each side measures 60/5 = 12 cm.
The question is asking for the measure of angle CBD. In a regular pentagon, angles are not directly named but it's likely referring to an internal angle of the pentagon. Based on this assumption, we can calculate the measure of an internal angle of a regular polygon using the formula: (n-2) x 180° / n where 'n' is the number of sides. Substituting '5' in place of 'n' because a pentagon has 5 sides, we get (5-2) x 180° / 5, which results in 108°. Therefore, if CBD is an internal angle then it measures 108 degrees.
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What is the exact volume of the cylinder V=Bh
. V =324πin.3
Answer:
324
Step-by-step explanation
the answer is c. i do online work, yw!
A leaf blower runs on a mixture of gas and oil. The ratio of ounces of gas to ounces of oil is 40 to 1. How many ounces of gas does the leaf blower need for 3 ounces of oil?
Answer:
120
Step-by-step explanation:
Each time you add 40 to gas(oz)
Answer: 120 ounces of gas
Step-by-step explanation: Given: 40 ounces of gas to 1 ounce of oil
We need to find: __ ounces of gas to 3 ounces of oil
What we know:
1 × 40 = 40 ounces of gas
2 × 40 = 80 ounces of gas
3 × 40 = 120 ounces of gas
So, all you needed to do was multiply 3 times 40 to get 120 ounces of gas.
Conclusion: The answer is 120 ounces of gas.
The price of a liter of milk increased 10% compared with last year . If the new price is $1.21 per liter , what was last years price?
Answer:
$1.1
Step-by-step explanation:
First take if 110% is equals to $1.21 what about 100%
1.21×100=121÷110= $1.1
Alex, a manager at Symbic Inc., plotted the company's total energy costs of 1 billion dollars over the past 10 years on a chart. The chart suggested that the energy costs appear to be increasing in a fairly predictable linear fashion and that the energy costs are related to time by a linear function Y t =3+5t, where Y trepresents the estimate of the energy cost in year t. Given the equation, which of the following is the value of the intercept of the straight line that best fits the time series?
A. 1
B. 3
C. 5
D. 10
A cereal box's length is 25 cm, height is 30 cm and width is 10 cm.
The surface area of the cereal box is 2600 square centimeters. Volume of the cereal box is 7500 cubic centimeters.
The surface area of the cereal box in the image is 2600 square centimeters. The volume of the cereal box is 7500 cubic centimeters.
To calculate the surface area, we need to find the area of each of the six faces of the box and add them all up. The two largest faces have dimensions 25 cm by 30 cm, so their area is 25 * 30 = 750 square centimeters each. The two next-largest faces have dimensions 10 cm by 30 cm, so their area is 10 * 30 = 300 square centimeters each. The two smallest faces have dimensions 25 cm by 10 cm, so their area is 25 * 10 = 250 square centimeters each. Therefore, the total surface area of the box is 750 + 750 + 300 + 300 + 250 + 250 = 2600 square centimeters.
To calculate the volume, we simply multiply the length, width, and height of the box together. The length is 25 cm, the width is 10 cm, and the height is 30 cm, so the volume is 25 * 10 * 30 = 7500 cubic centimeters.
Here is a table summarizing the surface area and volume of the cereal box:
| Property | Value |
|--------------------|--------------------------------------|
| Surface area | 2600 square centimeters|
| Volume | 7500 cubic centimeters |
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Select all the expressions equivalent to 2(x + 3). Explain your reasoning. A 2 ⋅ (x + 3) B (x + 3)2 C 2 ⋅ x + 2 ⋅ 3 D 2 ⋅ x + 3 E (2 ⋅ x) + 3 F (2 + x)3
Answer: B and A
Step-by-step explanation:
(X+3)2 = 2×x + 2×3
= 2x + 6
Likewise
2(x+3) = 2×x +. 2×3
= 2x + 6
Hence they are both same
2.(X +3) still equivalent to 2x +6
Answer:
A and B
Step-by-step explanation:
In this question, we are asked to pick the options which have the same value as the expression in the question.
Firstly, let’s expand the main expression in the question.
Mathematically, expanding this, we have 2x + 6
now let’s consider the options one after the other.
Options A and B are correct as they mean the same thing and would refer to the expression in the question.
Option c is wrong. Expanding option c would yield 2x + 4
option d is wrong as the multiplication is only between 2 and x and does not cover 3. This makes the expression as 2x + 3
option E is is also wrong as it is same as D but expressed in another fashion
option F is is wrong also as expanding would give 6 + 3x which is different from 2x + 6
Find the length if the darkened arc. Leave your answer in terms of pi.
Answer:
6π in
Step-by-step explanation:
Length of arc
[tex] = 2\pi \: r \frac{120}{360} [/tex]
[tex] = 2\pi \times 9 \times \frac{1}{3} [/tex]
[tex] = 6\pi[/tex] in
7s=245 what does s equal?
Answer:
35
Step-by-step explanation:
You would have to get rid of the 7. To do that you would divide each side by 7 to get s=35
TIME REMAINING
50:03
Which factors can be multiplied together to make the
trinomial 5x2 + 8x - 4? Select two options
0 (x+1)
(2x + 1)
(x+2)
(5x + 1)
(5x-2)
Answer:
(5x−2) and (x+2)
Step-by-step explanation:
Answer:
(5x-2)(x+2)
If you want to check your answer mulitply (5x-2)(x+2) and you get the same
trinomial 5x2 + 8x - 4.
SLOVE BY ELIMIMATION METHOD
X+Y=6
X-Y=10
Step-by-step explanation:
x + y = 6 ...................equation 1
x - y = 10 ..................equation 2
Solving equation 1 and 2
x + y = 6
x - y = 10
2x = 16
x = 16 /2
Therefore x = 8
Now
putting x = 8 in equation 1
8 + y = 6
y = 6 -8
y = -2
hope it was helpful :)
Answer:
x=8 and y= -2
Step-by-step explanation:
x+y=6
x-y=10 + ( add them together)
-----------------
2x=16 ( substitute/ plug x back in )
x=8
8+y=6
8-y=10
y=-2
a music company offers a loan to buy a drum set for 1500 dollars. what is the monthly payment. 11.8 simple interest equal monthly payment for 2 years
Answer:
I = Prt
I = 1500(.118)(2) = 354
Total amount to pay = $1854
Monthly payment = $77.25
Step-by-step explanation:
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Which of the following are Pythagorean Triples?
Answer:
6, 8, 10
8, 15, 17
3, 4, 5
5, 12, 13
are the right answers
Step-by-step explanation:
What is the center of the circle with the equation: X2 + y2 +18x + 14y + 105 = 0
Answer:
(9, -7)
Step-by-step explanation:
[tex]x^2+y^2+18x+14y+105=0\\[/tex]
Rearrange like x and y terms next to each other, then complete the square on both.
[tex](x-9)^2-361 + (y+7)^2 - 49 + 105 = 0[/tex]
The negative of the # numbers instead the brackets give you the centre of the circle.
The given equation does not represent a circle because the radius is an imaginary number.
Explanation:The given equation represents a circle in the Cartesian coordinate plane. The general form of a circle equation is (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r is the radius. By rearranging the equation, we can find the centre by completing the square for both x and y.
For the given equation, x² + y² + 18x + 14y + 105 = 0, we complete the square for x by adding (18/2)² = 81 to both sides of the equation and for y by adding (14/2)² = 49 to both sides of the equation. This gives us:
(x² + 18x + 81) + (y² + 14y + 49) + 105 - 81 - 49 = 0
(x + 9)² + (y + 7)² = -175
The equation (x + 9)² + (y + 7)² = -175 does not represent a circle because the radius, which is the square root of -175, is an imaginary number. Therefore, the given equation does not have a real centre or radius.
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There are 18 blueberries in a bowl there are 3 times as many blueberries as strawberries in the bowl how many strawberries are in the bowl
Final answer:
There are 6 strawberries in the bowl.
Explanation:
To find the number of strawberries in the bowl, we can set up an equation based on the given information. Let's assume the number of strawberries is S.
The problem states that there are 3 times as many blueberries as strawberries, so we can write this as:
18 = 3S.
To solve for S (the number of strawberries), we can divide both sides of the equation by 3:
S = 6.
Therefore, there are 6 strawberries in the bowl.