Answer:
12.5% probability that when a couple has three children, there are exactly 0 girls.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Possible outcomes:
b for boy, g for girl
g - g - g
g - g - b
g - b - g
g - b - b
b - g - g
b - g - b
b - b - g
b - b - b
8 outcomes, one of which (b - b - b) with exactly 0 girls.
So
1/8 = 0.125
12.5% probability that when a couple has three children, there are exactly 0 girls.
The probability that when a couple has three children, there are exactly 0 girls is 12.5%
Calculation of the probability:Here we assume b for boy, g for girl
Now the probability conditions are
g - g - g
g - g - b
g - b - g
g - b - b
b - g - g
b - g - b
b - b - g
b - b - b
There are 8 outcomes, one of which (b - b - b) with exactly 0 girls.
So
[tex]= 1\div 8[/tex]
= 0.125
Learn more about probability here: https://brainly.com/question/24613748
What time did they arrive at the airport?
Answer:
32
Step-by-step explanation:
Which best compares the slope and y-intercepts of the linear functions f and g where f= 1/3 x + 3 and g is shown in the table? X =0,1,2,3 and g(x) =3,6,9,12
Answer:
different slope same intercept
Step-by-step explanation:
g(x)= 3x+3
this means they both intercept the y axis at 3 but the incline of g is much greater then f since the slope is much larger.Hope this is what you were looking for
What are the x-intercepts of the graph of the function below?
y = x^2 – 3x - 28
A. (-7,0) and (-4,0)
B. (7,0) and (-4,0)
C. (7,0) and (4,0)
D. (-7,0) and (4.0)
Answer:
The x intercepts are (7,0) and (-4,0)
Step-by-step explanation:
y = x^2 – 3x - 28
Set y=0
0 = x^2 – 3x - 28
Factor. What 2 numbers multiply to -28 and add to -3
-7*4 = -28
-7+4 = -3
0 = (x-7)(x+4)
Using the zero product property
0 = (x-7) 0 = x+4
x=7 x = -4
The x intercepts are (7,0) and (-4,0)
The number of hits on a certain website during a one-minute interval follows a Poisson distribution with a mean rate of four hits per minute. What is the probability that there is at least one hit in a 30-second period (that is the probability of one or more hits)
Answer:
86.47% probability that there is at least one hit in a 30-second period
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Mean rate of four hits per minute.
This means that [tex]\mu = 4n[/tex], in which n is the number of minutes.
What is the probability that there is at least one hit in a 30-second period
30 seconds is 0.5 minutes, so [tex]\mu = 4*0.5 = 2[/tex]
Either the site doesn't get a hit during this period, or it does. The sum of the probabilities of these events is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1353 = 0.8647[/tex]
86.47% probability that there is at least one hit in a 30-second period
Find the original price of a pair of shoes if the sale price is $144 after a 25% discount.
Answer:
$192
Step-by-step explanation:
1: Subtract the discount from 100% then divide the sale price by this number (100%-25%=75%, $144/75%=$192)
hope this helped
Answer:
$192
Step-by-step explanation:
144 is actually 75% from the original price x:
0.75 x=144
x=144/0.75= $192
check : 192*0.25= $ 48 discount
192-48= $ 144 price of the shoe
what is the recursiveformula for this geometric sequence? 4,-12,36,108
Answer:
a[1] = 4
a[n] = -3·a[n-1]
Step-by-step explanation:
The sequence given is not a geometric sequence, since the ratios of terms are -3, -3, 3 -- not a constant.
If we assume that the last given term is supposed to be -108, then the common ratio is -3 and each term is -3 times the previous one. That is expressed in a recursive formula as ...
a[1] = 4 . . . . . . . . . . . first term is 4
a[n] = -3·a[n-1] . . . . . each successive term is -3 times the previous one
One solution to the problem below is 10. what is the other solution?
b^2-100=0
Answer:
the same
Step-by-step explanation:
Answer:
The two solutions can be +10 and -10
Step-by-step explanation:
b^2 - 100 = 0
b^2 = 100
Take the root of both sides
b = +- 10
b = +10 , b = -10
If the legs of a right triangle are 10 and 24, then the
hypotenuse is
26.
Step-by-step explanation:
To figure out the missing side of a right triangle, we will use the Pythagorean theorem. This is...
[tex]a^2+b^2=c^2[/tex]
With this Pythagorean theorem, a and b will always be the legs and the c will always be the hypotenuse, no matter what. Now knowing this, we can plug the legs into the equation.
[tex]10^2+24^2=c^2[/tex]
[tex]100+576=c^2[/tex]
Add the legs together.
[tex]676=c^2[/tex]
Now, since c is squared we will have to find the square root of 676.
[tex]\sqrt{676}[/tex]
= 26
The average amount of water in randomly selected 16-ounce bottles of water is 16.15 ounces with a standard deviation of 0.45 ounces. If a random sample of thirty-five 16-ounce bottles of water are selected, what is the probability that the mean of this sample is less than 15.99 ounces of water? Answer: (round to 4 decimal places)
Answer:
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 16.15, \sigma = 0.45, n = 35, s = \frac{0.45}{\sqrt{35}} = 0.0761[/tex]
What is the probability that the mean of this sample is less than 15.99 ounces of water?
This is the pvalue of Z when X = 15.99. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15.99 - 16.15}{0.0761}[/tex]
[tex]Z = -2.1[/tex]
[tex]Z = -2.1[/tex] has a pvalue of 0.0179
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
Please help me with this problem, I can't figure it out
Answer: 44
Step-by-step explanation:
This is a confusing problem to look at, so use PEMDAS(parenthesis, exponents, multiplication, division, addition, subtraction).
5 * (-4) + (1 - (-3)^2)^2 simplify inside the parenthesis
5 * (-4) + (1 - 9)^2
5 * (-4) + (-8)^2 simplify exponents
5 * (-4) + 64 multiply
-20 + 64 finally, addition
44
Error Analysis A problem on a test says that 70% of people enjoy the beach. The students are
asked to use the simulation numbers below to estimate the probability that exactly one person says
he or she enjoys the beach. Let the numbers 0-6 represent a person who enjoys going to the beach
and let 7-9 represent a person who does not. One student says that the probability is about 100%.
Estimate the probability that exactly one person enjoys the beach. What error might the student have
made?
(5,8) (2,7) (0,9) (0,2) (9,0) (1,9) (4,7) (0,3) (6,7) (7,5)
Use the simulation to estimate the experimental probability that exactly one person enjoys the beach
is 40%
Enter your answer in the answer box and then click Check Answer
pan
rema
Answer:
Probability that exactly one person says he or she enjoys the beach = 80%
Check Explanation for how to get this and which error the studemt that made the 100% claim must have made.
Step-by-step explanation:
The simulation presented is that for a series of two people sample.
Numbers 0 to 6 represents that the beach-goer enjoys going to the beach and numbers 7 to 9 represents that the beach-goer doesn't enjoy going to the beach.
So, the simulation is then obtained to be
(5,8) (2,7) (0,9) (0,2) (9,0) (1,9) (4,7) (0,3) (6,7) (7,5)
Using the simulation, estimate the probability that exactly one person says he or she enjoys the beach
From the simulation, the ones with exactly one of the two numbers ranging from 0 to 6 to indicate enjoying going to the beach include
(5,8) (2,7) (0,9) (9,0) (1,9) (4,7) (6,7) (7,5)
The probability of an event is defined and expressed as the number of elements in that event divided by the total number of elements in the sample space.
Probabilty that exactly one person says he or she enjoys the beach = (8/10) = 0.80 = 80%
The student claims that this probability is 100%, but the other two simulations that did not satisfy the condition of exactly one person saying that he or she enjoys the beach include
(0,2) and (0,3), which show that in the two cases, the two participants both expressed enjoying going to the beach.
The student's error must have been in counting these two simulations as part of 'exactly one person saying he or she enjoys the beach' which is indeed an error.
Hope this Helps!!!
The Environmental Protection Agency must visit nine factories for complaints of air pollution. In how many ways can a representative visit five of these to investigate this week? Since the representative's travel to visit the factories includes air travel, rental cars, etc., then the order of the visits will make a difference to the travel costs.
Answer:
The number of ways is [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
Step-by-step explanation:
From the question we are told that
The number of factories visited is [tex]n = 9[/tex]
The number of factories to be visited by a representative r = 5
The number of way to visit the 5 factories is mathematically represented as
[tex]\left 9}\atop } \right. P _5 = \frac{9!}{(9-5)!}[/tex]
Where P represents permutation
=> [tex]\left 9}\atop } \right. P _5 = \frac{9 \ !}{4\ !}[/tex]
=> [tex]\left 9}\atop } \right. P _5 = \frac{9 *8*7 * 6 * 5 * 4!}{4\ !}[/tex]
=> [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
Please answer this correctly
Answer:
The mode would not change
Step-by-step explanation:
Mode is the frequency of 1 number. In this case, the mode is 3. If we add 8, the frequency of 3 would not change; there would still be 4 3's, and 3 would still have the most of itself.
Five-thirds divided by one-third =
Answer:
Step-by-step explanation: [tex]\frac{5}{3}[/tex]÷[tex]\frac{1}{3}[/tex] =
(Decimal: 0.555556)
78% of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below.
1. Find the mean of the binomial distribution (Round to the nearest tenth as needed.)
2. Find the variance of the binomial distribution. (Round to the nearest tenth as needed.)
3. Find the standard deviation of the binomial distribution. (Round to the nearest tenth as needed.)
4. Most samples of 6 adults would differ from the mean by no more than nothing. (Type integers or decimals rounded to the nearest tenth as needed.)
Answer:
Step-by-step explanation:
Let x be a random variable representing the number of U.S. adults who think that political correctness is a problem in America today. This is a binomial distribution since the outcomes are two ways. The probability of success, p = 78/100 = 0.78
The probability of failure, q would be 1 - p = 1 - 0.78 = 0.22
n = 6
a) Mean = np = 6 × 0.78 = 4.68
b) Variance = npq = 6 × 0.78 × 0.22 = 1.0
c) Standard deviation = √npq = √(6 × 0.78 × 0.22) = 1.0
d) The standard deviation is used to express the spread of the data from the mean. Therefore, most samples of 6 adults would differ from the mean by no more than 1.0
20 Find the area of the rectangle given that
the perimeter is 50 cm.
3m + 2
m - 5
F 32
G 7
H 46
J 9
Answer: H - 46
Step-by-step explanation:
Primeter = 2(l + w)
50 = 2{(3m+2) + (m-5)}
25 = 3m+2 +m -5
25 = 4m -3
m = 28/4 = 7
l = 3m+2 = 23 cm
w = m-5 = 2 cm
Area = l x b
= 23 x 2 = 46 sq. cm.
Find the work done in emptying a cylindrical tank filled with water. The water is being pumped out from the 6 top. The tank has a diameter of 4 feet and is 6 feet tall. The tank is on ground level. Water is 62.4 lbs/ft
Answer:
908360.67 lb-ft
Step-by-step explanation:
height of tank= 6 ft
diameter of the tank = 4 ft
density of water p = 62.4 lbs/ft
A is the cross sectional area of the tank
A = [tex]\pi r^{2}[/tex]
where r = diameter/2 = 4/2 = 2 ft
A = 3.142 x [tex]2^{2}[/tex] = 12.568 ft^2
work done = force x distance through which force is moved
work = F x d
Force due to the water = pgAh
where g = acceleration due to gravity = 32.174 ft/s^2
Force = 62.4 x 32.174 x 12.568 x 6 = 151393.44 lb
work done = force x distance moved
work = 151393.44 x 6 = 908360.67 lb-ft
8. Suppose Betty saves $200 each month in her 401(k) account. How much less will her monthly take-home pay be? (Assume a combined 20% state and federal income tax rate, as in the example.)
Note: Check the file attached below for the complete question
Answer:
Betty's monthly take home is $20 less
Step-by-step explanation:
Betty's monthly income = $2300
Betty's monthly savings = $200
Amount left after savings = $2300 - $200
Amount left after savings = $2100
Federal and State Income tax rate = 20% = 0.2
Tax amount paid = $420
Monthly take home = $2100 - $420
Monthly take home = $1680
Compared to $150 per month savings, Betty's monthly take home is $20 less
Which linear function has the same y-intercept as the one that is represented by the graph? On a coordinate plane, a line goes through points (3, 4) and (5, 0).
Answer:
A linear equation is an equation with two variables whose graph is a line. The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.If you want to graph a linear equation you have to have at least two points, but it's usually a good idea to use more than two points. When choosing your points try to include both positive and negative values as well as zero
Step-by-step explanation:
Answer:
The answer would be C because the y-intercept is when x is equal to 0
please mark me brainliest
describe this diagram help please
Answer:
U are finding the slope. so the vertical line is ur rise(x value) and the horizontal line is ur y value. Hopefully that helped
Which division sentence is related to the product of a/3 (a/3) when A is not equal to 0?
Answer:
Option 4.
Step-by-step explanation:
Reciprocal of the second fraction turns the product into the division of the two fractions, which equals to 1.
[tex]a/3(a/3)[/tex]
[tex]a/3 \div 3/a=1[/tex]
Two fractions are said to be the reciprocal or multiplicative inverse of each other, if their product is 1.
Answer:
D. a/3 divided by 3/a = 1
Step-by-step explanation:
edge
Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola
Answer:
The probability that a group of 15 randomly selected skiers will overload the gondola = (3.177 × 10⁻⁵¹)
(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)
Step-by-step explanation:
Complete Question
A ski gondola carries skiers to the top of the mountain. If the Total weight of an adult skier and the equipment is normally distributed with mean 200 lb and standard deviation 40 lb.
Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola.
Solution
For 15 people to exceed 5000 lb, each person is expected to exceed (5000/15) per skier.
Each skier is expected to exceed 333.333 lb weight.
Probability of one skier exceeding this limit = P(x > 333.333)
This becomes a normal distribution problem with mean = 200 lb, standard deviation = 40 lb
We first standardize 333.333 lbs
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (333.333 - 200)/40 = 3.33
To determine the required probability
P(x > 333.333) = P(z > 3.33)
We'll use data from the normal distribution table for these probabilities
P(x > 333.333) = P(z > 3.33) = 1 - P(z ≤ 3.33)
= 1 - 0.99957
= 0.00043
So, the probability that 15 people will now all be above this limit = (probability of one person exceeding the limit)¹⁵ = (0.00043)¹⁵
= (3.177 × 10⁻⁵¹)
(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)
Hope this Helps!!!
Angle bisectors $\overline{AX}$ and $\overline{BY}$ of triangle $ABC$ meet at point $I$. Find $\angle C,$ in degrees, if $\angle AIB = 109^\circ$.
Answer:
<C = [tex]38^{o}[/tex]
Step-by-step explanation:
Given that: <AIB = [tex]109^{o}[/tex]
<AIB + <BIX = [tex]180^{o}[/tex] (sum of angles on a straight line)
[tex]109^{o}[/tex] + <BIX = [tex]180^{o}[/tex]
<BIX = [tex]180^{o}[/tex] - [tex]109^{o}[/tex]
<BIX = [tex]71^{o}[/tex]
But,
<AIB = <YIX = [tex]109^{o}[/tex] (opposite angle property)
<XIB = <AIY = [tex]71^{o}[/tex] (opposite angle property)
Therefore,
[tex]\frac{A}{2}[/tex] + [tex]\frac{B}{2}[/tex] = [tex]71^{o}[/tex] (Exterior angle property)
[tex]\frac{A + B}{2}[/tex] = [tex]71^{o}[/tex]
A + B = [tex]142^{o}[/tex]
A + B + C = [tex]180^{o}[/tex] (sum of angles in a triangle)
[tex]142^{o}[/tex] + C = [tex]180^{o}[/tex]
C = [tex]180^{o}[/tex] - [tex]142^{o}[/tex]
C = [tex]38^{o}[/tex]
Thus, angle C is [tex]38^{o}[/tex].
The results of a survey of common allergies was organized into a Venn diagram. Circles D, C, and P overlap. Circle D contains 15. Circle C contains 18. Circle P contains 9. The overlap of circles C and D contains 7. The overlap of circles D and P contains 12. The overlap of C and P contains 10. The overlap of all 3 circles contains 1. Answer the questions about the following sets: D = {x | x is a person allergic to dogs}; C = {x | x is a person allergic to cats}; P = {x | x is a person allergic to pollen} How many people are not allergic to any of the three choices? How many people are allergic to all three choices? How many people are allergic to both dogs and cats but not allergic to pollen? How many people are allergic to cats only?
Answer:
first blank: 22
second blank: 1
third blank: 7
fourth blank: 18
Step-by-step explanation:
edge 2020
Answer: 22, 1, 7, 18
The results of a survey of common allergies was organized into a Venn diagram.
Circles D, C, and P overlap. Circle D contains 15. Circle C contains 18. Circle P contains 9. The overlap of circles C and D contains 7. The overlap of circles D and P contains 12. The overlap of C and P contains 10. The overlap of all 3 circles contains 1.
Answer the questions about the following sets:
D = {x | x is a person allergic to dogs}; C = {x | x is a person allergic to cats}; P = {x | x is a person allergic to pollen}
How many people are not allergic to any of the three choices?
✔ 22
How many people are allergic to all three choices?
✔ 1
How many people are allergic to both dogs and cats but not allergic to pollen?
✔ 7
How many people are allergic to cats only?
✔ 18
Alessandro wrote the quadratic equation -6=x2+4x-1 in standard form. What is the value of c in his new equation? c=-6
Answer:
5
Step-by-step explanation:
To put the equation in standard form, add 6 to both sides.
x^2 +4x -1 +6 = -6 +6
x^2 +4x +5 = 0
The new value of "c" (the constant) is 5.
Answer:
C or 5 for me
Step-by-step explanation:
MY LAST 3 QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
1. Curtis is trying to justify a step in his paragraph proof. What is the property that he should use? AB=BC therefore BC=AB
A) Equality of Congruence Property
B) Reflexive Property of Congruence
C) Symmetric Property of Congruence
D) Transitive Property of Congruence
2. All of the following would make a formal proof incomplete except what?
A) Incomplete sentences
B) Errors in logic
C) A lack of justifications
3. Which step in the proof has a flaw? IMAGE BELOW Given B is the midpoint of AC prove AB=BC
A) Step 2
B) No flaws.
Answer:
1. C
2. A
3. A
Step-by-step explanation:
1. It is the Symmetric Property of Congruence because the definition is literally what it says.
2. Incomplete sentences don't matter as long as you have the right stuff.
3. Step 2 is wrong because it should be Definition of Midpoint.
If Curtis is attempting to defend a step in his proof paragraph. He should apply the symmetric property of congruence so that he can demonstrate that AB=BC and that BC=AB. It's best to choose C.
What is geometry?It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.
A)If Curtis is trying to justify a step in his paragraph proof. Symmetric Property of Congruence that he should use as a result he can show AB=BC therefore BC=AB. Option C is correct.
B)All of the following would make a formal proof incomplete except Incomplete sentences. Option A is correct.
C)Step 2 in the proof has a flaw Because it is not a symmetric property while they show congruency because it must be a midpoint definition. Option A is correct.
Thus, if Curtis is trying to justify a step in his paragraph proof. Symmetric Property of Congruence that he should use as a result he can show AB=BC therefore BC=AB. Option C is correct.
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Prove your work what is 1/12 of a dozen Branliest
Answer:
1/12 of a dozen is 1
Step-by-step explanation:
One dozen means 12. If you ask for 1/12 of 12, you multiply 12 and 1/12. You should get 1 as your answer.
Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be written using
function notation?
Fly) = -
f(x) = - 3x + 4
f(x) =
FCV) = -3y+ 4
Answer:
f(x) = -3x + 4
Step-by-step explanation:
Step 1: Write it in slope-intercept form
9x + 3y = 12
3y = -9x + 12
y = -3x + 4
Step 2: Replace y with f(x)
f(x) = -3x + 4
In math, function f(x) is equal to the variable y.
Compare and contrast the following piecewise
defined functions.
(-x+ 2 x<0
X+2, x<0
f(x) =
x? + 1, x>0 X + 2, x>0
g(x)=
Answer:
Both piecewise functions have a linear portion and a quadratic portion. The y-intercepts of both linear pieces are the same, 2. The quadratics are both open upward, but have different y-intercepts (one at 1, one at 2). The linear portion of the first function is decreasing, while the linear portion of the second function is increasing.
Step-by-step explanation:
Comparing and contrast of the functions are shown in below.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The given piecewise functions are;
⇒ f (x) = { - x + 2 ; x < 0
= { x² + 1 ; x > 0
Now, Comparison and contrast of the above piecewise functions are,
The similarities are;
1) Both piecewise functions are linear when x < 0.
2) Both piecewise functions are quadratic when x > 0.
3) The magnitude the slope of the linear part both function are equal.
4) The leading coefficient of the quadratic function are the same.
5) The y-intercept of the linear function are equal, therefore, the linear functions in f(x) and g(x) intersect on the y-axis.
6) The domain of the linear and quadratic functions are the same.
The contrasts (differences) in the function are;
1) The slope of the linear function of g(x) is positive and the slope of the linear function of f(x) is negative.
2) The y-intercept of the quadratic function in f(x) is +1, while the y-intercept of the quadratic function in g(x) is +2.
3) The quadratic function in f(x) and g(x) have graphs that do not intersect.
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Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer: time = 20 seconds
Step-by-step explanation:
h(t) = -16t² + 316t + 80
The shape of this graph is an upside parabola ∩.
It lands on the ground when height (h) = 0
Set the equation equal to zero, factor, and solve for t.
0 = -16t² + 316t + 80
0 = 4t² - 79t - 20 divided both sides by -4
0 = (4t + 1)(t - 20) factored the equation
t = -1/4 t = 20 Applied Zero Product Property and solved for t
Since we know time cannot be negative, disregard t = -1/4
The only valid solution is: t = 20