Answer:
170 feet per second
Step-by-step explanation:
To answer the question you need to find the unit rate. To find the unit rate divide the denominator with the numerator in a way that the denominator becomes 1.
5,100/30 = 170
The skydiver falls at a rate of 170 feet per second before opening the parachute.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
It takes a skydiver 30 seconds to fall 5,100 feet before opening the parachute.
Hence, Height for this is,
⇒ 5100 / 30
⇒ 170 feet per second
Thus, the skydiver falls at a rate of 170 feet per second before opening the parachute.
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help plsplspls
Find the value of the following expression and round to the nearest integer:
34
Σ 400(0.93)n-2
n=2
The value of the expression is 5193.
How to find the value of the expression?From the question, we have the following parameters that can be used in our computation:
From the notation, we have the following values:
The first term, a = 400
The common ratio, r = 0.93
The number of terms, n = 34 - 1 = 33
The sum of the geometric progression is represented as:
Sum = a(1-rⁿ)/(1-r)
Sum = 400(1-0.93³³)/(1-0.93)
Sum = 5193
Therefore, the value of the expression is 5193
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Hiro painted his room. After 333 hours of painting at a rate of 888 square meters per hour, he had 282828 square meters left to paint.
The solution is, the situation can be modeled as y = 52 - 8x.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.
So, the total area to be painted is (28 + 3 × 8) = 52 square meters.
Let y represent the area (in square meters) left to paint after x hours of painting then the situation can be modeled as
y = 52 - 8x ................ (1) (Answer)
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Help me
Solve this, it's from a worksheet about quadratic equations.
Answer:
Below
Step-by-step explanation:
L X W is area of rectangle ...this figure can be viewed as a rectangle on top of a rectangle
top rectangle is 3x-2 wide and (2x+5) - (3x-2) length
area = (3x-2)( (2x+5) - (3x-2) )
= (3x-2) ( -x + 7) = - 3x^2 + 23x -14 units^2
The bottom is then (3x-2 + 2) * (3x-2)
area = (3x)(3x-2) = 9x^2 - 6x units^2
Add the two areas together (-3x^2+23x-14) + (9x^2 -6x)
6x^2 + 17x -14 and this = 25 cm^2 (given)
6x^2 + 17x -14 = 25
6x^2 + 17x - 39 = 0 Use Quadratic Formula to find x = 1.5
then find the longest side using this value of x
3x-2 + 2 = 4.5 cm
2x+5 = 8 cm <=====longest side
find the quadratic equation whose roots are 5 and -9
The equation of the quadratic equation whose root are 5 and -9 is x² +4x -45
What is quadratic equation?quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The equation of a quadratic is given as :
x²-(alpha+beta)x + alpha×beta = 0
where alpha and beta are the roots of the quadratic equation.
alpha+beta = 5-9 = -4
alpha × beta = -9× 5 = -45
therefore the equation will be;
x²-(-4)x + ( -45) = 0
x² + 4x -45 = 0
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Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days. She also paid $18 for a guided waterfall tour. Tara paid $94 in all. What was the rental cost of each day Tara used the kayak?
Answer:
$19
Step-by-step explanation:
calculate 94-18/4 = 19
Which is the graph of f(x) = 100(0.772)
It is not possible to graph f(x) = 100(0.772) without additional information. A function needs at least two points to graph a line. The expression f(x) = 100(0.772) represents a constant value, not a function of x, so it cannot be graphed on its own.
Answer: knvsvvs
Step-by-step explanation:
a university is conducting research on ways to improve study habits and help students with lower grade point averages. it sends out a questionnaire to undergraduate students asking how they study and what they feel is the most productive way to study. what data collection method is the university using?
As the university is sending out questionnaires, the data collection method the university is using is a survey
The term "survey" describes the method of gathering data on a certain subject generally by employing questionnaires. In order to understand more about a certain topic, a survey is a method of data collection that involves asking a sample of respondents a number of questions. In the given case, the university is using a survey as a tool for gathering data.
Here, the institution is distributing a survey to undergraduate students to learn more about their study habits and what they believe to be the most effective method of studying. In order to efficiently gather data from a large number of participants quickly and effectively, surveys are frequently employed in research investigations.
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Describe the graph of the function at its roots.
f(x) = (x − 2)3(x + 6)2(x + 12)
At x = 2, the graph
the x–axis.
For the graph of given function, At x = 2, the graph crosses x axis At x = - 6, the graph touches x axis, At x = - 12, the graph crosses x axis.
What's an Equation?
The description of an equation in algebra is a fine statement proving the equivalency of two fine expressions.
The two equations 3x 5 and 14 are separated by the" equal" sign in the equation 3x 5 = 14, for illustration.
In mathematics, an equation is a relationship between two expressions that's equal on both sides of the equal to subscribe. An equation is commodity like 3y = 16.
Equation of a function f( x) = ( x − 2) 3( x 6) 2( x 12)
Lets find out the roots and dissect
lets set each factor = 0 and break for x
Exponent in each factor tell us the multifariousness. Using multifariousness we check whether crosses or traces x axis
When multifariousness is odd also graph crosses x axis.
when multifariousness is indeed also graph touches x axis.
f(x) = (x-2)^3(x+6)^6(x+12)
⇒(x-2)^3
⇒x-2 = 0
⇒ x = 2
Root is x = 2 with multifariousness 3. 3 is odd
At x = 2, the graph crosses x axis
⇒ (x+6)^2
⇒ (x+6)=0
⇒ x = -6
At x = - 6, multifariousness is 2 that's indeed.
At x = - 6, the graph touches x axis
x + 12 = 0
x = -12
x = - 12 with multifariousness 1. 1 is odd
At x = - 12, the graph crosses x axis.
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1) The U.S. per capita consumption of beef decreased from 67.8 pounds in 2000 to 55.4 pounds in
2016. Find the relative difference.
Answer:
20.2%
Step-by-step explanation:
he relative difference between two values can be calculated using the formula:
Relative Difference = (|V1 - V2| / ((V1 + V2) / 2)) * 100%
where V1 is the first value and V2 is the second value.
For the U.S. per capita consumption of beef, we have V1 = 67.8 pounds in 2000 and V2 = 55.4 pounds in 2016. Plugging these values into the formula, we get:
Relative Difference = (|67.8 - 55.4| / ((67.8 + 55.4) / 2)) * 100%
Relative Difference = (12.4 / 61.6) * 100%
Relative Difference = 0.202 * 100%
Relative Difference = 20.2%
So the relative difference between the U.S. per capita consumption of beef in 2000 and 2016 is 20.2%.
if you randomly select a mechanical component, what is the probability that it weighs more than 11.5lbf
The probability that randomly selected mechanical component weighs: more than 11.5 lbf is 0.0099, less than 8.7 lbf is 0.3208, less than 5.0 lbf is 0.0228, between 6.2 lbf and 7.0 lbf is 0.1314, between 10.3 lbf and 14.0 lbf is 0.0436, between 6.8 lbf and 8.9 lbf is 0.3464.
We can use the standard normal distribution and z-scores to answer these questions:
P(X > 11.5) = P(Z > (11.5 - 8) / 1.5) = P(Z > 2.33) = 0.0099
Therefore, the probability that a randomly selected mechanical component weighs more than 11.5 lbf is 0.0099, or about 1%.
P(X < 8.7) = P(Z < (8.7 - 8) / 1.5) = P(Z < 0.47) = 0.3208
Therefore, the probability that a randomly selected mechanical component weighs less than 8.7 lbf is 0.3208, or about 32%.
P(X < 5.0) = P(Z < (5 - 8) / 1.5) = P(Z < -2) = 0.0228
Therefore, the probability that a randomly selected mechanical component weighs less than 5.0 lbf is 0.0228, or about 2%.
P(6.2 < X < 7.0) = P((6.2 - 8) / 1.5 < Z < (7 - 8) / 1.5) = P(-1.2 < Z < -0.67) = 0.1314
Therefore, the probability that a randomly selected mechanical component weighs between 6.2 lbf and 7.0 lbf is 0.1314, or about 13%.
P(10.3 < X < 14.0) = P((10.3 - 8) / 1.5 < Z < (14 - 8) / 1.5) = P(1.53 < Z < 2.67) = 0.0436
Therefore, the probability that a randomly selected mechanical component weighs between 10.3 lbf and 14.0 lbf is 0.0436, or about 4%.
P(6.8 < X < 8.9) = P((6.8 - 8) / 1.5 < Z < (8.9 - 8) / 1.5) = P(-0.47 < Z < 0.60) = 0.3464
Therefore, the probability that a randomly selected mechanical component weighs between 6.8 lbf and 8.9 lbf is 0.3464, or about 35%.
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____The given question is incomplete, the complete question is given below:
Suppose that the weight of a mechanical component is normally distributed with mean p = 8.0 Ibf and standard deviation = 1.5 lbf. Answer the following questions: 1. If you randomly select a mechanical component, what is the probability that it weighs more than 11.5 lbf? 2. If you randomly select a mechanical component, what is the probability that it weighs less than 8.7 lbf? 3. If you randomly select a mechanical component, what is the probability that it weighs less than 5.0 lbf? 5. If you randomly select a mechanical component, what is the probability that it weighs between 6.2 lbf and 7.0 lbf? 6. If you randomly select a mechanical component, what is the probability that it weighs between 10.3 lbf and 14.0 lbf? 7. If you randomly select a mechanical component, what is the probability that it weighs between 6.8 lbf and 8.9 lbf?
Frank in going to plant b vegetables in one garden and 2b+1 vegetables seeds in a another how many seed is frank going to plant
Answer: Frank is going to plant "b" vegetables in one garden and "2b + 1" vegetables in another garden. So, the total number of seeds he is going to plant is b + (2b + 1) = 3b + 1.
Step-by-step explanation:
A plumber cut a pipe into 5 equal pieces and had 27 cm of the pipe left. For a second
pipe 15m long, he cut 11 pieces of the same length as that of each piece cut from the
first pipe and had 15 cm of the second pipe left. What was the length, in cm, of each
shorter piece of the second pipe? What was the length of the first pipe originally?
Please input your answer:
Answer:
Step-by-step explanation:
Let's call the length of each shorter piece of the first pipe x. Then the total length of the first pipe would be 5x + 27 cm.
Similarly, the length of each shorter piece of the second pipe would be x and the total length of the second pipe would be 11x + 15 cm.
Since both pipes were cut into the same length pieces, we can set the two equations equal to each other:
5x + 27 = 11x + 15
Solving for x, we can find the length of each shorter piece:
6x = -12
x = -2
This means that each shorter piece of both pipes was -2 cm long, which is not physically possible. So, this solution is not valid. This means that the problem is underdetermined and that we cannot determine the length of each piece.
SOMEONE, PLEASE ANSWER THESE QUESTIONS!!!
Find the y-intercept for both linear functions.
Answer:
Below
Step-by-step explanation:
The y-axis intercept occurs when x = 0
so the first one is y = 21 ( this is the value when x = 0 from table)
the second one shows every 4 increase causes a 3 decrease in y
so every 4 DECREASE in x causes a +3 INCREASE in y
decrease x = 4 to x = 0 increase y = 6 to y = 9
Log_6 x + log_6 3 = log_6 (x+1)
The solution to the equation log_6 x + log_6 3 = log_6 (x+1) is x = 1/2.
Explain:
We can reduce the complexity of the left side of the equation by using the logarithmic identity log a + log b = log (ab):
Log6 x plus Log6 3 equals Log6 (3x)
When we add this to the initial equation, we obtain:
Log6 (3x) equals Log6 (x+1).
Because logarithms have the one-to-one property, we can drop the logarithm on both sides to get the following results:
3x = x + 1
When we simplify this equation, we obtain:
2x = 1
x = 1/2
As a result, x = 1/2 is the answer to the equation log 6 x + log 6 3 = log 6 (x+1).
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Solve -28r = 4r.
r = , r =
Step-by-step explanation:
this is very simple, we only have to divide each side by four to single out our unknown.
[tex]-28=4r[/tex][tex]-14=2r[/tex][tex]-7=r[/tex]
Answer:
the solution to the equation -28r = 4r is r = 0.
Step-by-step explanation:
To solve the equation -28r = 4r, we can isolate the variable "r" on one side of the equation and find its value. To do this, we can start by subtracting 4r from both sides of the equation:
-28r - 4r = 4r - 4r
-32r = 0
Next, we can divide both sides of the equation by -32 to find the value of "r":
(-32r) / -32 = 0 / -32
r = 0
So the solution to the equation -28r = 4r is r = 0.
Find the greatest whole number which divides 372 & 324 without leaving remainder
The greatest whole number that divides both 372 and 324 without a remainder is 4.
To find the greatest whole number that divides both 372 and 324 without a remainder, we can use the concept of the greatest common divisor (GCD).
One method to find the GCD is to factor each number into its prime factors and then find the product of the common prime factors.
372 can be factorized as 2 * 186, and 324 can be factorized as [tex]2^2 * 3^4[/tex]
The greatest common divisor is [tex]2^2[/tex], which is equal to 4.
So, the greatest whole number that divides both 372 and 324 without a remainder is 4. This means that 4 is the largest number that can divide both 372 and 324 evenly, leaving no remainder.
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Please help with this question!!
According to the information, we plan to have cruising speed on for a minimum of 3 hours and a maximum of 4.1 hours.
How to calculate how many hours we are going to have the cruising speed on?To calculate how many hours we are going to have the cruising speed on we must carry out the following process:
To calculate the minimum we must subtract 35 from 215 and then divide by the speed:
215 - 35 = 180180 / 60 = 3So the minimum hours would be 3 hours.
On the other hand, to calculate the maximum we must add 35 to 215 and divide it by the speed:
215 + 35 = 250250 / 60 = 4.1So the maximum time would be 4.1 hours.
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The number of students enrolled at a college 18,000 and grows 5% each year. What is the initial amount
Answer:
900
Step-by-step explanation:
5% of 18,000
A pet toy company performed an experiment to see how
many toys dogs might play with. Each of the 60 dogs
involved was put in a room with its owner and 4 different
toys.
The researchers recorded how many toys each of the 60
dogs used.
Fill in the blanks to complete the probability
distribution.
Do not round your answers.
Toys used
Frequency
Probability .05
0
3
1 2
2
0.25
3
3 4
21 12
9
0.35 0.2 0.15
The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.
What is the probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
To fill in the blanks, we need to use the given information to complete the probability distribution table.
We can see that there were 3 dogs (out of the 60) that did not use any toys, and the probability of a dog not using any toys is 0.05 or 5%. There were 12 dogs (out of the 60) that used 1 toy, and the probability of a dog using 1 toy is 0.2 or 20%. Similarly, there were 15 dogs that used 2 toys, 21 dogs that used 3 toys, and 9 dogs that used all 4 toys. The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.
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amit took part in an cycle race .he started at 1:25 pm and reached the finishing line at 1:50 . what was the duration of the race ?
amit took a part in cycle race .he started at 1:25 and he reached finishing lline at 1:50 pm what was the duration of the race .
Answer:
25 minutes
Step-by-step explanation:
Subtract the two times to find the duration.
If 3 garbage trucks can collect the trash of 24 homes in a day, how many trucks are needed to collect in 72 houses?
Answer:
9
Step-by-step explanation:
72/24 = 3
72 is 3 times 24, so you need 3 times as many garbage trucks.
Answer: 9
LaShonda's Nursery buys crates of firewood to deliver to customers over the winter. Each crate
measures 3 feet long, 2.5 feet wide, and 3 feet high. How much storage space does the nursery
need for the wood if 75 crates are delivered in an order?
OA 675.0 cubic feet
OB 1,687.5 cubic feet
OC 3,937.5 cubic feet
OD 3,375.0 cubic feet
Based on the information provided, the storage space that will be required for 75 is 1,687 cubic feet in total.
How to calculate the storage space for 75 crates?To begin, let's determine the storage space for a single crate and to do this, let's calculate the volume:
Volume: Lenght x height x width
Volume: 3 x 2.5 x 3 = 22.5 cubic feet
Now, let's calculate the space for 75 crates:
volume of one crate x 75 crates
22.5 x 75 = 1,687 cubic feet
Based on this, it can be concluded that 75 crates will occupy 1,687 cubic feet.
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3. Two numbers are in the ratio 2:3. If 3 is added to the numbers, the ratio changes to 3:4. Find the numbers. use linear equation
Using the ratio formula the unknown numbers are found to be 6 and 9.
What is ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.
The original ratio value is 2 : 3.
Three is added to the ratio.
The new ratio value is 3 : 4.
Let the unknown numbers be 2x and 3x.
The equation will be -
2x + 3 / 3x + 3 = 3/4
Solve the equation -
4(2x + 3) = 3(3x + 3)
8x + 12 = 9x + 9
8x - 9x = 9 - 12
-x = -3
x = 3
Substitute the value of x in the unknown numbers -
2x = 2(3) = 6
3x = 3(3) = 9
Therefore, the numbers are 6 and 9.
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What is the area of ∆AOB?
The Area of Rhombus is 97.5 cm².
What is area of Rhombus?The area of a rhombus is equal to half the product of the lengths of the diagonals. The formula to calculate the area of a rhombus using diagonals is given as, Area = (a × b )/2 where, a and b are the diagonals of the rhombus.
Given:
As, diagonals of rhombus bisect perpendicularly.
so, In triangle OAD using Pythagoras theorem
AD² = OD² + OA²
10² = 7.8² + OD²
OD= 6.25 cm
So, length of BD = 2 x 6.25 = 12.5 cm
Now, area of Rhombus = 1/2 x a x b
= 1/2 x 15.6 x 12.5
= 97.5 cm².
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Sasha is bisecting a segment. First, she places the compass on one endpoint, opens it to a width larger tha the compass the same width and places it on the other endpoint. What is her next step?
Swing arcs on both sides to intersect the first two arcs created.
Swing an arc that intersects the segment.
Swing arcs that intersect a point that is not on the segment.
Swing an arc that intersects the opposite endpoint.
When bisecting a segment using a compass, Sasha's next step would be to swing an arc that intersects the segment. Correct option is B.
To bisect a segment, Sasha needs to find the midpoint of the segment. The compass can help her achieve this by creating two arcs with the same radius from each endpoint of the segment. The intersection of these arcs will be the midpoint of the segment.
Sasha's first step is to place the compass on one endpoint of the segment and open it to a width larger than the length of the segment. Then, she places the compass on the other endpoint and draws an arc that intersects the first arc.
The next step is to swing an arc with the same radius from the other endpoint of the segment, again intersecting the first arc. The intersection of these two arcs will give the midpoint of the segment, which can be marked with a straightedge.
Therefore, Sasha's next step in bisecting a segment using a compass is to swing an arc that intersects the segment.
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2 + cscsecx/cscsecx = (sinx+cos)
Answerk bzijnjlngljntgojengojnetgihnrtgkte4wg
A rectangle flower garden is 9 2/5 feet long and 6 1/2 feet wide.What is the area of the flower garden?
Answer: 61 1/10
Step-by-step explanation:
9 2/5 x 6 1/2
PLEASE!!! Someone, please help test tomorrow!! Just explain how to get this please!
The correct value of the expression is,
⇒ (2²)³ - (8 - 4)² × 4 = 0
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ (2²)³ - (8 - 4)² × 4
Now, We can solve as;
⇒ (2²)³ - (8 - 4)² × 4
⇒ (4)³ - (4)² × 4
⇒ 4³ - 4³
⇒ 64 - 64
⇒ 0
Thus, We get;
⇒ (2²)³ - (8 - 4)² × 4 = 0
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A watch salesman earns a commission of 40% of all watch sales made. Yesterday he sold 5 watches for $60 each and 4 watches for $40 each. How much did he earn in commission yesterday?
A. $120
B. $64
C. $40
D. $184
He earns $184 in commission yesterday on sold 5 watches for $60 each and 4 watches for $40 each.
Commission:A sales commission is a sum of money paid to an employee upon completion of a task, usually selling a certain amount of goods or services. Employers sometimes use sales commissions as incentives to increase worker productivity. A commission may be paid in addition to a salary or instead of a salary.
A salesman earns a commission 40%
He sold yesterday 5 watches for $60 each
and, 4 watches for $40 each.
We have to find the how much he earn commission?
Now, According to the question:
Price of 5 watches = 60.00 × 5 = $300
4 watches = $40.00 each
Price of 4 watches = 40.00 × 4 = $160
Total sales made = 300 + 160 = $460
His commission is 40% of the sales = 40% × 460
= 0.40 × 460 = $184
Hence, He earns $184 in commission.
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working alone, Ted can install a new deck in 15 hours. Jimmy can install the same deck in 16 hours. How long would it take them to install the deck if they worked together
The time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.
What is the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value.
Let W be the total work to be done, which is installing a new deck.
Given Ted alone can complete the work W in 15 hours.
Using unitary method,
So in one hour, work done by Ted = W/15
Also given Jimmy alone can complete the work W in 16 hours.
So in one hour, work done by Jimmy = W/16
Using unitary method,
In one hour the work done by Jimmy and Ted together = W/15 + W/16 = 31W/240
ie 31W/240 = 1 hour
So W = 240/31 = 7.7 hours
Therefore the time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.
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