Answers
9514 1404 393
Answer:
1. 5 seconds
2. 4.5 seconds
Step-by-step explanation:
Both of these questions can be solved the same way. Each quadratic gives height as a function of time. You're interested in the time at which the height is zero. Factor the quadratic and find the positive value of x that makes the relevant factor be zero.
__
1) y = -15x(x -5)
x = 5 makes the second factor zero
The golf ball is in the air 5 seconds.
__
2) y = -12x(x -4.5)
x = 4.5 makes the second factor zero
The football is in the air for 4.5 seconds.
_____
Additional comment
The "zero product rule" tells you a product will be zero if and only if one or more of the factors is zero. When a factored quadratic (or any other polynomial) is zero, one of the factors must be zero. If the factor is of the form (ax+b), then the corresponding solution is ...
ax+b = 0 ⇒ ax = -b ⇒ x = -b/a
That is, once you have the factored form, you can write the solutions "by inspection."
Related Questions
Determine which data are qualitative and which data are quantitative. Explain your reasoning
a. The yearlysalaries of the employees at aschool district.(2pts)
b. The employeenumbers of the employees at an accounting firm.(2pts)
c. The areacodes of a sample of 350 residents of nursing homes.(2pts)
d. The ages of a sample of 350 residents of nursing home. (2pts)
e. The answers to a survey of 5000 people about how likely is it that the US will enter a 1930s-like depression. The answers are: Very likely, somewhat likely, not very likely, not at all likely. (2pts)
f. The IQ index of the students in a statistics class.(2pts)
Answers
Answer:
a. Quantitative
b. Qualitative
c. Qualitative
d. Quantitative
e. Qualitative
f. Quantitative
Step-by-step explanation:
Qualitative measures:
Answers are labels, that is, yes/no, good/bad, or numbers in which comparisons or operations cannot be made.
Quantitative measures:
Answers are numbers in which comparisons are made, or possible operations.
a. The yearly salaries of the employees at a school district.(2pts)
Salaries are numbers, in which comparisons can be made(more or less), so quantitative.
b. The employee numbers of the employees at an accounting firm.(2pts)
Number, but comparisons aren't made with these numbers, so qualitative.
c. The area codes of a sample of 350 residents of nursing homes.(2pts)
Number, but comparisons aren't made with these numbers, so also qualitative.
d. The ages of a sample of 350 residents of nursing home. (2pts)
Number, comparisons made, you can rank by age for example, so quantitative.
e. The answers to a survey of 5000 people about how likely is it that the US will enter a 1930s-like depression. The answers are: Very likely, somewhat likely, not very likely, not at all likely. (2pts)
Labels, so qualitative.
f. The IQ index of the students in a statistics class.(2pts)
Students can be ranked by IQ, so quantitative.
use the following picture to classify the following statements as true or false
Answers
BC ≈ EF
BAC ≈ EDF
ABC ≈ DEF by ASA
AC ≈ DF
Not True:
ABC ≈ FDE
ABC ≈ DEF by AAS
A data set lists weights (lb) of plastic discarded by households. The highest weight is 5.31 lb, the mean of all of the weights is x=2.088 lb, and the standard deviation of the weights is s=1.968 lb. a. What is the difference between the weight of 5.31 lb and the mean of the weights? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the weight of 5.31 lb to a z score. d. If we consider weights that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the weight of 5.31 lb significant?
Answers
Answer:
a) The difference is of 3.222 lbs.
b) 1.64 standard deviations.
c) Z = 1.64
d) Not significant, as the z-score of 1.64 is between -2 and 2.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean of all of the weights is x=2.088 lb, and the standard deviation of the weights is s=1.968 lb.
This means that [tex]\mu = 2.088, \sigma = 1.968[/tex]
a. What is the difference between the weight of 5.31 lb and the mean of the weights?
This is [tex]X - \mu = 5.31 - 2.088 = 3.222[/tex]
The difference is of 3.222 lbs.
b. How many standard deviations is that [the difference found in part (a)]?
This is the z-score. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5.31 - 2.088}{1.968}[/tex]
[tex]Z = 1.64[/tex]
1.64 standard deviations.
c. Convert the weight of 5.31 lb to a z score.
Z = 1.64, as found above.
d. If we consider weights that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the weight of 5.31 lb significant?
Not significant, as the z-score of 1.64 is between -2 and 2.
How many-foot pieces of wood
can you cut from a board that is
6 feet long?
Answers
Answer:
6
Step-by-step explanation:
Foot long = 1 foot
6 / 1 = 6 foot pieces
If the entire board is 6 feet long and you wanted to cut it into 1 foot intervals, you would do 6/1 and get 6
Actividad N°2: Marque la alternativa correcta en la siguiente pregunta.
Sea una función tal que () = 7 − 3 cuyo dominio es el conjunto () =
{−1, 0, 1, 2, 3}, entonces el () es:
5 PUNTOS
A) () = {−2, 1, 4, 7, 10}
B) () = {−1, 0, 1, 2, 3}
C) () = {4, 7, 10, 13, 16}
D) () = {1, 2, 3, 4, 5}
E) () = {−16, −13, −10, −7, −4}
Answers
Answer:
Hola busco amigos
Perdí mi otra cuenta
Ayúdame y te ayudo con tus tareas
¿ si?
Step-by-step explanation:
3.
Use the concept of a series to sum up 0.315+0.000315+0.000000315+.... Give your final answer
in reduced fraction form. Note: There are several methods to prove this fact. I am specifically asking
you to use a series.
Answers
Dividing each term in the given series by 0.315 reveals a simple geometric sum,
0.315 (1 + 1/1,000 + 1/1,000,000 + …)
or
0.315 (1 + 1/10³ + 1/10⁶ + …)
or
[tex]\displaystyle 0.315 \sum_{n=0}^\infty \frac1{10^{3n}} = 0.315 \sum_{n=0}^\infty \frac1{1000^n}[/tex]
i.e. a geometric sum with a common ratio of 1/1,000. I'm not sure what your instructor expects exactly, but you may already know that
[tex]\displaystyle a\sum_{n=0}^\infty r^n = \frac a{1-r}[/tex]
if |r | < 1. This is the case here, so
0.315 (1 + 1/1,000 + 1/1,000,000 + …) = 0.315 / (1 - 1/1,000)
… = (315/1000) / (999/1000)
… = 315/999
… = 35/111
Which inequality represents all numbers x on a number line that are farther from −8 than from −4?
Answers
Answer:
x - 8>-4-x
Step-by-step explanation:
Looking at x - 8>-4-x
Collect the like terms;
x+x > -4 + 8
2x < 4
x > 4/2
x < 2
Since the values of x are greater than 2,this shows that they are positive values and will be farther from -8 than -4
Can you figure out what the area of this shape is?
Answers
Answer:
22 units
Step-by-step explanation:
split it into 3 sections, there are two sections of 2x3 and one of 1x10, together they make 22 units
What is the common ratio for the geometric sequence below, written as a fraction?
768, 480, 300, 187.5, …
/
Answers
9514 1404 393
Answer:
5/8
Step-by-step explanation:
Since the ratio is common, it can be found from the ratio of any pair of adjacent terms.
r = 480/768 = (5·96)/(8·96) = 5/8
The common ratio is 5/8.
When draining her hot tub, the height of the water in Brittany’s hot tub decreases at a rate of 2 inches per minute. After 9 minutes there are 11 inches of water in the tub. Assume that the height is decreasing at a constant rate.
a. Write an equation for the height of water left in the tub (h) as a function of the number of the minutes (t) that have elapsed.
b. What values of the domain, t, make sense? Why?
c. What values of the range, h, make sense? Why?
Answers
Step-by-step explanation:
a.
Let's give the starting amount of water as s. Every minute, 2 inches of water are lost, meaning that given the starting amount, s, we subtract 2 inches from s every minute, so s - 2 every minute = height of water left, so s - 2t (t representing minutes) = h
To figure out s, we simply plug our known value -- 9 minutes in and 11 inches left. s - 2(9) = 11, s-18=11, s= 29
29 - 2t = h
b. We know that we cannot have negative minutes, so the minimum amount of time that makes sense is 0. To figure out the maximum, we stop counting how much time has occurred when there is no water left, so we have to figure out when h = 0
29-2t = h = 0
t=14.5
Therefore, anything between 0 and 14.5 minutes makes sense
c. Anything between 0 and 29 makes sense because the height of water cannot be negative and we cannot get higher than the starting amount
A coin is flipped 8 times. Find the probability of the event:
exactly 6 heads
Answers
Answer:
P(E)=56256=732. Step-by-step explanation:
Thus, the probability of getting exactly 3 heads when a coin is flipped 8 times in a row
Which pair of expressions below are equivalent?
a. 7(2n) and 9
b. 3n + 5n and 15n
c. 4(2n-6) and 8n - 24
d. 7(2n) and 72n
Answers
Answer:
The answer is C
Hope this helped!
An angle measures 104° more than the measure of its supplementary angle. What is the measure of each angle?
___° and ___°
thank you <3 best answer will get brainliest.
Answers
Mark Brainliest please
Answer:
38 degrees
Step-by-step explanation:
Let the angle be x
Supplement:: 180-x
Equation:
x = 180-x + 104
2x = 284
x = 142 degrees
therefore , 180-x = 180-142= 38 degrees
What’s the value of X????
Answers
137
Step-by-step explanation:
Sum of opposite angles in a quadrilateral embedded in a circle=180
43+x=180
X=180-43
X=137
ABCD is a quadrilateral such that the measures of three of its interior angles are given as B=122 degrees, C= 75 degrees, D= 51 degrees, find m=A
please help me with explanation
Answers
Answer:
angle A is 112 degree.
Step-by-step explanation:
quadilateral have 4 angles .
sum of the interior angles of a quadilateral is 360 degree
Here,
angle A = be x
angle B = 122
angle C = 75
angle D = 51
Now,
angle A + angle B + angle C + angle D =360 degree
x + 122 + 75 + 51 = 360
x + 248 = 360
x = 360 - 248
x = 112
[tex]4 \sqrt{(3x}^{3} [/tex]
write in exponential form
Answers
Answer:
[tex]4(3x)^{\frac{3}{2} }[/tex]
Step-by-step explanation:
hope that helps
seven more than the quotient of a number and 2 is equal to 3 equation
Answers
Answer:
Step-by-step explanation:
seven more than the quotient of a number and 2 is 10
7+n/2=10 n=6 check 7+3=10 ok
Which of the following is a point-slope equation of a line with the point (-6,2)
and a slope of ? 1/2
Answers
Answer:
Choose (D)
y-y1=m(x-x1)
y-2=1/2(x+6)
What is the gradient of the blue line
Answers
Answer:
Up 2 to the right 1
Step-by-step explanation:
that would be i think
Find the vertex of the graphed function.
16= \x - 4 +3
2
The vertex is at
Answers
Answer:
16=/-4+3+2
16=/-1jhcdf why
hyee852iok
Which points are on the graph of the function rule f(x) = 10 - 4x
Answers
Explanation:
WILL GIVE BRAINLIEST
4
3
2x + 4
x+7
Answers
Answer:
x = 8
Step-by-step explanation:
[tex]\frac{x+7}{3} =\frac{2x+4}{4}[/tex]
do cross multiplication
[tex]3(2x+4) = 4(x+7)\\6x + 12 = 4x + 28\\6x - 4x = 12 - 16\\2x = 16\\x = 16/2\\x = 8[/tex]
Balu had a collection of coins1/2 of the coins were from Asian countries,1/3
of them from European countries and the remaining 36 from America.
How many coins were from ASIAN countries?
A)18
B)30
C)108
D)216 step by step explanation please
Answers
Step-by-step explanation:
[tex] \frac{1}{2} = asian \\ \frac{1}{3} = european \\ 36 = american \\ \frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6} = \frac{5}{6} \\ \frac{6}{6} - \frac{5}{6} = \frac{1}{6} = 36 \\ \frac{1}{6} = 36 \: so \\ \frac{6}{6} =6 \times 36 = 216 \\ \frac{1}{2} \times 216 = asian \\ \frac{1}{2} \times 216 = 108asian \\ please \: mark \: brainliest[/tex]
There are total 108 coins belonging to Asian countries.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Balu had a collection of coins 1/2 of the coins were from Asian countries, 1/3 of them from European countries and the remaining 36 from America.
Let the total number of coins be x,
Establishing the equation, we get,
x/3+x/2+36 = x
Multiplying the equation by 6, we get,
2x+3x+216 = 6x
6x-5x = 216
x = 216
Therefore, the total numbers of coins are 216,
Since, there are 1/2 of total coins are Asian coins,
Therefore, number of Asian coins = 216 / 2 = 108
Hence, There are total 108 coins belonging to Asian countries.
For more references on equations, click;
https://brainly.com/question/29657983
#SPJ2
determine the missing angle.
Answers
Explanation: 180-50=130
The area of a square is64. Cm
What is the length of its side
Answers
Answer:
The length is 8 cm. Since its a square, so the length of both its sides are equal.
l^2=64
where l=length of side
square root both sides
then, l=8
Answer:
8cm is the length of its side.
Step-by-step explanation:
Match each three dimensional figure to its volume based on the given dimensions.
Answers
please attach a diagram
Laura, David, and Carlos served a total of 115 orders Monday at the school cafeteria. David served 3 times as many orders as Carlos. Laura served 10 more orders than Carlos. How many orders did they each serve?
Answers
Answer:
Step-by-step explanation: ts 6 11 19 56
Laura, David, and Carlos served a total of 115 orders
David served 3 times as many orders as Carlos. David = 3x
Laura served 10 more orders than Carlos. let Carlos = x
How many orders did they each serve? Laura = x + 10
Carlos + David + Laura = 115
x + 3x + x+10 = 115
5x + 10 = 115
5x = 115 - 10
5x = 105
x = 21 Carlos
63 Davide
31 Laura
add then up 115 Total
pls help me out in this assignment PLSSSSS anyone plss
Answers
Answer:
what number?
number three or number two
Assume that Y is normally distributed with mean μ and standard deviation σ. After observing a value of Y, a mathematician will construct a rectangle with length L = |Y|and width W = 3 |Y|. Let A denote the area of the resulting rectangle. What is E(A)?
Answers
Please help me with this as quickly as possible!
Answers
Answer:
1:2
is your answer
Step-by-step explanation:
