The five number from the box plot is presented as follows:
Minimum value: 42.First quartile: 44.Median: 50.Third quartile: 54.Maximum value: 56.What does a box-and-whisker plot shows?A box and whisker plot shows five things of a distribution, listed as follows:
The data set's lowest value.The value that 75% of the measures are larger than is found in the first quartile, which is the median of the data set's lowest 50% of measurements.
50% of the data set is less than the median and 50% is more than the median, which is the midpoint value of the data set.The third quartile, which is the median of the data set's top 50% of measurements, is the value that 75% of the measures fall below.The data set's maximum value.
These numbers, which make up the five number summary, are the values highlighted on the box plot from left to right, from the minimum value to the greatest value, passing through the first quartile, the median, and the third quartile.
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HELP.
This item has two parts: Part A and Part B. Use the function to complete Part A and Part B.
f(x) = (x – 5)(x + 3)(x – 1)2
Which of the following statements CORRECTLY identifies the degree and number of unique zeros of the function?
degree: 3; number of unique zeros: 4
degree: 4; number of unique zeros: 3
degree: 4; number of unique zeros: 4
degree: 3; number of unique zeros: 3
Part B
What is the end behavior of the function?
as x → –∞, f(x) → ∞ and as x → ∞, f(x) → –∞
as x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞
as x → –∞, f(x) → –∞ and as x → ∞, f(x) → ∞
as x → –∞, f(x) → –∞ and as x → ∞, f(x) → –∞
The degree and number of unique zeros of f(x) = (x – 5)(x + 3)(x – 1)² is:
Degree: 4; number of unique zeros: 3.
The end behavior of the polynomial is:
As x → –∞, f(x) → ∞ and as x → ∞, f(x) → ∞.
How to obtain the degree of the function?The degree of the polynomial function is given by the sum of the multiplicities of the roots.
These roots are given as follows:
x = 5 with a multiplicity of 1.x = -3 with a multiplicity of 1.x = 1 with a multiplicity of 2.Hence the degree is:
1 + 1 + 2 = 4.
The unique zeros are the roots, hence there are three unique zeros, which is the same number of linear factors of the function.
What is the end behavior of the function?The end behavior is the limit of the function as x goes to negative infinity and to positive infinite, hence:
lim x -> -∞ f(x) = lim x -> -∞ x^4 = (-∞)^4 = ∞.lim x -> ∞ f(x) = lim x -> ∞ x^4 = (∞)^4 = ∞.Learn more about the end behavior of a function at brainly.com/question/1365136
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solve for x. "-8+x/4=-4" simplify your answer as much as possible
Answer:
48
Step-by-step explanation:
multiply by 4 to make x whole number
-32+x=16
+32 to isolate x
x=16+32
add for answer
x=48
b. Kadisha claims that the distance she has walked and the distance she has left to walk has a ratio of 5:7. How many miles has Kadisha walked?
Based on the figures that we are provided, we can see that Kadisha has walked 10 miles already and is yet to walk 14 miles.
How can the total distance walked by Kadish be obtained?The total distance Kadisha has to walk is 24 miles
The distance she has walked is represented in the ratio as 5
The distance she has left to work is 7
5x + 7x = 24
12x = 24
x = 2
Therefore, the distance that Kadisha has walked is
5 × 2 = 10 miles
The distance she is yet to walk is
7 × 2 =14 miles
When represented as a ratio, 10/14 is the same as 5/7, so the answer is proven to be correct.
Complete Question:
A hiking trail is 24 miles from start to finish. There are two rest areas located along the trail. a. The first rest area is located such that the ratio of the distance from the start of the trail to the rest area and the distance from the rest area to the end of the trail is 2:9. To the nearest hundredth of a mile, how far is the first rest area from the starting point of the trail? b. Kadisha claims that the distance she has walked and the distance she has left to walk has a ratio of 5:7. How many miles has Kadisha walked?
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Please help me simplify
Answer: [tex]\frac{4\sqrt{x} }{t^2}[/tex]
Step-by-step explanation:
You can start by either applying the exponent to both the numerator and denominator (exponent rule), or make things simpler by dividing first. Doing the latter allows me to show both properties. Since the terms in the fraction are being multiplied, we can divide common terms which will leave us with [tex]\frac{16x}{t^4}[/tex] on the inside. Now that it is simplified, we can apply the exponent. We will end up with 4x^1/2 in the numerator and t^2 in the denominator. If the exponent seems daunting, it is also helpful to know that raising something to the exponent of 1/2 is basically taking the square root of it.
Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 76 hours over the last two weeks and had a total of $1,790 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
A.
$953
B.
$371
C.
$684
D.
$269
A rectangular patio has a length of 9 2/5 feet and an area of 81 3/8 square feet. What is the width of the patio?
Step-by-step explanation:
81 3/8 ÷ 9 2/5
81*8+3 = 651
651/8
9 2/5 = 9*5+2=47
47/5
651/8 ÷ 47/5 =
651/8 * 5/47 = 3255/376 =
8.65691489362
the mean absolute deviation of Mr. Zimmerman's class is 0.46 What does this mean
Mean absolute deviation is the variation in a data set and is the average distance between each value and mean.
It is calculated by finding the difference between each data value and mean and then finding average of that.
So, let data set be x1,x2,x3,x4...xN.
mean of the data set is [tex]\bar{x}[/tex].
then mean absolute deviation will be
[tex]M.A.D=\sum\limits^N_{n=0}\frac{ {x_n-\bar{x}}}{N}[/tex]
Thus, mean absolute deviation shows how much the data vary in the data set.
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i need help answering this question
Answer:
Step-by-step explanation:
there is no question?
The velocity function of a car is given by v(t) = -3t2 + 18t + 9 m/s. Find the acceleration of the car three seconds before it comes to a stop.
A.
a = -6.46 m/s²
B.
a = -2.76 m/s²
C.
a = -0.46 m/s²
D.
a = 2.76 m/s²
Answer: In photo below
You're Welcome :)
The acceleration of the car three seconds before it comes to a stop is -2.76 m/s² (Letter B).
Derivative
Derivative indicates the rate of change of a function with respect to a variable. Thus, when you derivate the position function, you find the velocity function. And, when you derivate the velocity function, you find the acceleration function.
In other words, the velocity function represents the first derivative of the position, meanwhile, the acceleration function represents the second derivative of the position.
For derivating an equation, you should apply the rule: [tex](\frac{d}{dx} ) (x^n ) = nx^{n-1}[/tex]. Example: x²= 2x
The car stops when the velocity is equal to zero. Thus, v(t) = -3t² + 18t + 9 =0. Therefore, you should solve this quadratic function:
Δ=b²-4ac=[tex]18^2-4\left(-3\right)\cdot \:9=324+12*9=324+108=432[/tex]
[tex]t_{1,\:2}=\frac{-18\pm \sqrt{432}}{2\left(-3\right)}\\ \\ t_{1,\:2}=\frac{-18\pm \sqrt{432}}{-6}[/tex]
[tex]t_1=\frac{-18+12\sqrt{3}}{-6}=3-2\sqrt{3}[/tex]
[tex]t_2=\frac{-18-12\sqrt{3}}{-6}=3+2\sqrt{3}[/tex]
Like t is a positive number, you should use [tex]t_2[/tex]. Thus, the value of t that you should apply to find the acceleration of the car three seconds before it comes to a stop is [tex]2\sqrt{3}[/tex].
The acceleration can be found from the derivative of the velocity function. See below.
a(t)= -6t+18 , for t=[tex]2\sqrt{3}[/tex]
a(t)= -6*[tex]2\sqrt{3}[/tex]t+18
a(t)= [tex]-12\sqrt{3}[/tex]t+18
a(t)=-2.76
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What is the size of angle x?
Write a justification for your answer.
The angle x will be 34°.
From the properties of circles we get to know that the angle at the center and the angle between two tangents are always supplementary.
Supplementary angles are those which always sum to to 180°.
For example ∠HJK is supplementary to ∠HIK the their sum will come out to be 180°.
similarly ∠ROP + ∠RQP = 180°
∠RQP = 180° - ∠ROP
∠ROP is given to us 146°
After putting it in the equation above we get ∠RQP = 34°
Therefore x comes out to be 34°.
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Solve the system of equations by the substitution method.
x+y=8
y=-3x
Using the substitution method, the solution to the system of equations is: x = -4 and y = 12.
How to Solve a System of Equations by Substitution?To solve a system of equations using the substitution method, find the value of one of the variables in one equation, then substitute it in the second equation and solve to find the value of the second variable.
Given the equations:
x + y = 8 --> eqn. 1
y = -3x --> eqn. 2
Substitute -3x for y into equation 1:
x + (-3x) = 8
x - 3x = 8
-2x = 8
-2x/-2 = 8/-2
x = -4
Substitute x = -4 into equation 2:
y = -3(-4)
y = 12
The solution is, x = -4 and y = 12.
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A basketball player in a game makes x free throws worth 1 point and y 2-point baskets. The player needs to score at least 28 points to win the scoring title. What inequality represents the number and type of shots the player needs to win the title?
The inequality that represents the number and type of shots the player needs to win the title is -
x + 2y ≥ 28
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have A basketball player in a game who makes [x] free throws worth 1 point and [y] free throws worth 2 point baskets. The player needs to score at least 28 points to win the scoring title.
The inequality that represents the number and type of shots the player needs to win the title is -
x + 2y ≥ 28
Therefore, the inequality that represents the number and type of shots the player needs to win the title is -
x + 2y ≥ 28
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Could you please help with this.
Answer:
[tex] \sqrt[2]{15} = 7.5[/tex]
Last year, Dan had $ 10,000 into invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $730 in interest. How much did he invest in each account?
The amount invested in the account that yields 10% simple interest is $1,000.
The amount invested in the account that yields 7% simple interest is $9,000.
How much was invested in each account?The first step is to form a system of equations using the information provided in the question:
a + b = $10,000 equation 1
0.1a + 0.07b = 730 equation 2
Where:
a = amount invested in the account that yields 10% simple interest
b = amount invested in the account that yields 7% simple interest
The elimination method would be used to solve the equations
Multiply equation 1 by 0.1
0.1a + 0.1b = 1000 equation 3
Subtract equation 2 from equation 3
0.03b = $270
Divide both sides of the equation by 0.03
b = $270 / 0.03
b = 9,000
Substitute for b in equation 1
a + 9,000 = 10,000
a = 10,000 - 9,000
a = 1000
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The velocity function of a car is given by v(t) = -3t^2 + 18t + 9 m/s. Find the acceleration of the car three seconds before it comes to a stop. A. a = -6.46 m/s² B. a = -2.76 m/s² C. a = -0.46 m/s² D. a = 2.76 m/s²
The acceleration when the car comes to a full stop is 20.76 meters per square second.
How to find the acceleration?Here we have the velocity function:
v(t) = -3t^2 + 18t + 9
To find the acceleration we need to differentiate with respect to the variable t, so we will get the acceleration:
a(t) = 2*(-3)*t + 1*18
a(t) = - 6*t + 18
Now, the car will come to a stop when the velocity is equal to zero, so we need to solve:
-3t^2 + 18t + 9 = 0
Dividing all by -3 we get:
(-3t^2 + 18t + 9)/-3 = 0
t^2 - 6t - 3 = 0
The solutions are:
[tex]t = \frac{6 \pm \sqrt{(-6)^2 - 4*1*-3} }{2*1} \\\\t = \frac{6 \pm 6.92}{2}[/tex]
We only care for the positive solution:
t = (6 + 6.92)/2 = 6.46
The acceleration at that time is:
a(6.46) = - 6*6.46 + 18 = -20.76
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2x−4y=6
Step 2 of 2 : Determine the missing coordinate in the ordered pair (?,5) so that it will satisfy the given equation.
I need help with solving problem.
Answer:
x=-1,x=3/5
Step-by-step explanation:
Those are the two values of x
Consider the equation and the following ordered pairs: (1,y) and (x,−3).
6x+3y=15
You roll a fair six-sided die twice. Find the probability of rolling a 3 the first time and a number greater than 4 the second time.
The probability of rolling a 3 first time and a number greater than 4 thre second time is 1/18
What is probability?Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain. An example of a certain event is tomorrow being Friday if today is Thursday. This is definitely going to happen.
The possible outcomes of a fair die are : 1, 2, 3, 4, 5, 6. which is 6 in all
the required outcome for obtaining a 3 = 3 which is 1 outcome
the required outcome for obtaining a number greater than 4 : 5, 6. which is 2 outcomes.
probability of getting 3 first time = 1/6
probability of getting a number greater than 4 = 2/6 ( lowest term = 1/3)
Probability of rolling a 3 first time and a number greater than 4 second time is = 1/6 x 1/3 = 1/18
In conclusion, probability of obtaining a 3 and a number greater than 4 is 1/18.
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in 2017 , sharjah unfurled the worlds largest flag measuring 70m in length and 35m in width.the flag broke the guiinness world record for the largest flag hoisted on a fixed flagpole . there are 4 colours that occupy almost the same area in the flag . based on the above information , how much area will the black part occupy
Answer:
612.5
Step-by-step explanation:
Area is the length times the width
a = 70x35
a = 2450 Divide this number by 4
612.5
what is the solution of the linear-quadratic system of equations y=x^2+2x-3 y=2x+1
Answer:
(x, y) = {(-2, -3), (2, 5)}
Step-by-step explanation:
You want to solve the system of equations y=x²+2x-3 and y=2x+1.
SolutionThe two expressions for y can be equated, and the resulting equation put in standard form.
x² +2x -3 = 2x +1
x² -4 = 0 . . . . . . . . . . subtract (2x+1)
(x -2)(x +2) = 0 . . . . . factor
Values of x that make the factors zero are 2 and -2.
Corresponding values of y are ...
y = 2x +1 = 2(2) +1 = 5
y = 2(-2) +1 = -3
Solutions are ...
(x, y) = (2, 5)(x, y) = (-2, -3)Please help with this table. Not sure why this is difficult
Solve the Inequality and graph the solution set.
-8-8(2x-4)>-5(4x-5)-21
Answer:
x > -5
Make a number line. Put a circle on the number line at -5 and then darken an arrow on the number line going to the right of -5
Step-by-step explanation:
-8-8(2x-4) > -5(4x -5) -21 Distribute the -8 and -5
-8 - 16x + 32 > -20x +25 -21 Combine like terms
-16x + 24 > -20x +4 Add 20x to both sides
4x + 24 > 4 Subtract 24 from both sides
4x > -20 Divide both sides by 4
x > -5
Graph y > -
5x + 5.
4
(I suggest using desmos graphing calculator for the future.)
(0,5) and (4,0) or the one in the left upper corner. Hope this helps.
Gotta answer this quick this is timed please
Answer:
Step 1:subtract 5 from both sides
step 2: divide both sides by two
final answer: c= p-5/2
Answer:
Step 1: Subtract 5 from both sides.
Step 2: Divide 2 from both sides.
Final answer: C= p-5 / 2
Step-by-step explanation:
7v-7-4v-10=v+7-4v help now pleas
Answer:
v = 4
Step-by-step explanation:
[tex]collect \: like \: terms \: \\ 7v - 4v - v + 4v = 7 + 7 + 10\\ 3v - v + 4v = 14 + 10\\ \\ 2v + 4v = 24 \\ 6v = 24 \\ v = 4[/tex]
cos(θ)=−2√5 / 5
If (θ) is an angle in quadrant ll what is the value of sin (θ)
The exact value of sin(θ) given that cos(θ) = -2√5/5 is √5/5
How to determine the value of sin(θ):The given trigonometry ratio is
cos(θ) = -2√5/5
By the trigonometry ratio, we have
sin²(θ) + cos²(θ) = 1
Substitute cos(θ) = -2√5/5 into the above equation
So, we have the following representation
sin²(θ) + (-2√5/5)² = 1
Evaluate the exponent
sin²(θ) + 4/5 = 1
Subtract 4/5 from both sides
This gives
sin²(θ) = 1/5
Take the square root of both sides
√sin²(θ) = √1/5
Evaluate the square root
sin(θ) = ±1/√5
Sin is positive in quadrant II
So, we have
sin(θ) = 1/√5
Rationalize
sin(θ) = 1/√5 * √5/√5
This gives
sin(θ) = √5/5
This gives the value of sin(θ)
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Find the average rate of change.
The average rate of change = 1.59 ≈ 2
The average rate of change can be calculated by
1) The first one = [tex]\frac{3 + 0}{2}[/tex] = 1.5
2 ) the second can also be solved by ; 8 + 2/ 2 = 5
3 ) the third one will be 20 + 6 / 2 = 13
4) 8.5
5) 12.5
To calculate the average rate of change
we will first add all the distance
Adding all the distance we will get the sum = 3 + 8 + 20 + 10 + 10 = 51
The total time = 2 + 6 + 9 +15 = 32
Thus the average rate of change = 51 / 32 = 1.59
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A cube has a volume of 125 cubic inches. What us the length of each adge? Enter your answer in the box
5 inches
I just randomly guessed
4. Daryll rides a bike 8 miles in 40 minutes. Isabella rides a bike 5 miles in 30
minutes. If they continue to ride at those speeds, who will bike the farthest
in 2 hours? How much father? Show your work.
5 A student sells 5 ears of corn for $2.00 how much will 9 ears cost show your work
6 A market sells 4 oranges for 2.45 how much will 8 oranges cost ? 12 oranges show your work
