The polynomial passes through the point (1, 10), and having the roots 2, -3, and 4 is a cubic polynomial.
What is a polynomial?A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
The polynomial having the highest power of 3 is called the cubic polynomial.
Given that the roots 2, -3, and 4 that has to pass through the point (1, 10).
The polynomial will be written as,
Y = (x-2)(x+3)(x-4)
Y = x³+x²-6x-4x²-4x=24
Y = x³-3x²-10x+24
Therefore, the polynomial passes through the point (1, 10), and having the roots 2, -3, and 4 is a cubic polynomial.
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a random sample of 1000 people was taken. four hundred fifty of the people in the sample favored candidate a. what is the upper limit for a 95% confidence interval for the true proportion of people who favored candidate a? round your answer to three decimal places.
The 95% confidence interval for the true proportion of people who favored candidate a is 0.419, 0.481
How to calculate confidence interval?
First, calculate sample proportion by divide number people who favored candidate by number of sample. So:
[tex]\pi[/tex] = 450 / 1,000 = 0.45
Then we use the formula for confidence interval
[tex]\pi[/tex] ± [tex]z\sqrt{\frac{\pi (1-\pi )}{n}}[/tex]
In which z is z score that has a p value of [tex]1 - \frac{\alpha }{2}[/tex]
For 95% confidence interval z is the value of Z that has a p value of [tex]1 - \frac{0.05}{2}[/tex] = 0.975, so z = 1.96
After we have [tex]\pi[/tex] value and z value then put it in the formula. So:
= 0.45 ± [tex]1.96\sqrt{\frac{0.45(1-0.45)}{1000} }[/tex]
= 0.45 ± 0.0308
= 0.419, 0.481
Thus, the 95% confidence interval for the true proportion of people who favored candidate a is 0.419, 0.481
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Hallar centro, radio y longitud de los siguientes intervalos
a) [3, 8]
b) [-5,2]
c) [0, 12]
d) [-9,0]
A continuación, se resume el centro, el radio y la longitud de cada intervalo:
Caso A: Centro: 5.5, Radio: 2.5, Longitud: 5
Caso B: Centro: - 1.5, Radio: 3.5, Longitud: 7
Caso C: Centro: 6, Radio: 6, Longitud: 12
Caso D: Centro: - 4.5, Radio: 4.5, Longitud: 9
¿Cómo hallar el centro, el radio y la longitud de un intervalo?
En este problema tenemos cuatro casos de intervalos de números reales sobre una recta numérica. Los números reales representan un conjunto continuo, no discreto, lo cual significa que existe un número infinito de puntos dentro de la distribución lineal.
El centro es igual al punto medio del intervalo, el radio es la distancia entre el punto medio y cualesquiera de los extremos y la longitud es el doble del radio del intervalo.
Centro:
C = 0.5 · (m + M)
Radio
R = C - m
Longitud
L = 2 · R
Donde:
m - Límite inferior del intervalo.M - Límite superior del intervalo.A continuación, determinamos el centro, el radio y la longitud de cada intervalo:
Caso A
C = 0.5 · (3 + 8) = 0.5 · 11 = 5.5
R = 5.5 - 3 = 2.5
L = 2 · 2.5 = 5
Caso B
C = 0.5 · [(- 5) + 2] = 0.5 · (- 3) = - 1.5
R = - 1.5 - (- 5) = - 1.5 + 5 = 3.5
L = 2 · 3.5 = 7
Caso C
C = 0.5 · (0 + 12) = 6
R = 6 - 0 = 6
L = 2 · 6 = 12
Caso D
C = 0.5 · [(- 9) + 0] = - 4.5
R = - 4.5 - (- 9) = 4.5
L = 2 · 4.5 = 9
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What is the formula for Circumcentre?
There is no definite formula for calculation of circumcenter of a triangle but a process for calculation of circumcenter has been described here.
What is circumcenter of a triangle?
Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.
Let the coordinate of A, B, C [tex]\Delta[/tex] ABC be ([tex]x_1, y_1[/tex]), [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] respectively and let the coordinate of circumcenter of [tex]\Delta ABC[/tex] is (x, y)
We need to find the length of AB, BC and AC
The length will be obtained in terms of x and y
On solving the equations, we will obtain the value of x and y
The value of x and y is the required coordinate of the circumcenter.
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what is the answer to this
-1 39/45
that is the answer
Describe the relationship between <1 and <5
Angles 1 and 5 constitutes one of the pairs
Step-by-step explanation:
need help for this question dhsjwiqibdbsns
Answer:
130°
Step-by-step explanation:
Triangle JKL is an isosceles triangle and leg angles are equal :
m<J = m<L
The sum of interior angles in a triangle is equal to 180.
m<J + m<L + m<K = 180
25 + 25 + m<K = 180
50 + m<K = 180 subtract 50 from both sides
m<K = 130°
Austin is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 2 people, and large rooms that can hold 3 people. Austin booked a total of 22 rooms which can accommodate 53 guests altogether. Determine the number of small rooms reserved and the number of large rooms reserved.
Answer:
There are 13 small rooms and 9 large rooms reserved.
Step-by-step explanation:
First, we can make a system of equations. We can use s to represent the number of small rooms and l to represent the number of large rooms.
2 guests per small room added to 3 guests per large room equals 53 guests total, so 2s + 3l = 53.
The number of small rooms (s) plus the number of large rooms (l) equals the total number of rooms, so s + l = 22 or s = 22 - l.
We can substitute the first second equation into the first equation.
2 (22 - l) + 3l = 53
44 - 2l + 3l = 53
l = 9
So, the number of large rooms is 9. Then, to find the number of small rooms, we can substitute l into the second equation.
s = 22 - 9
s = 13
So, the number of small rooms is 13.
Please help I’m really confused on this. Thanks!
Answer:
[tex]y=\frac{1}{2}x-8[/tex]
Step-by-step explanation:
Perpendicular lines have the same slope. So, the slope of the line we need to find is 1/2.
Thus, the equation is
[tex]y+5=\frac{1}{2}(x-6) \\ \\ y+5=\frac{1}{2}x-3 \\ \\ y=\frac{1}{2}x-8[/tex]
each side of a square is increasing at a rate of 8 cm/s. at what rate (in cm2/s) is the area of the square increasing when the area of the square is 16 cm2? incorrect: your answer is incorrect. cm2/s
The rate of the square increasing when the area is 16 cm² is 64 cm²/s. The result is obtained by using basic derivative rules.
How to count the rate of a square increasing?The rate of a square increasing can be counted by the derivative of the area of the square as a function of time.
dA/dt = 2s ds/dt
Where s is side length.
If each side of a square is increasing at a rate of 8 cm/s, what is the rate of the square increasing when the area is 16 cm²?
We have the side of the square as the function of time.
ds/dt = 8 cm/s
When the area is 16 cm², the side length is
A = s²
16 = s²
s = √16
s = 4 cm
The rate of the square increasing is
dA/dt = 2s ds/dt
dA/dt = 2 × 4 × 8
dA/dt = 64 cm²/s
Hence, the rate of the square increasing when the area is 16 cm² is 64 cm²/s.
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what is 1 divided by [tex]\frac{1}{2}[/tex]?
ANSWER ASAP 8TH GRADE MATH EASY
Answer:
It is the first option
Step-by-step explanation:
Is it possible that creating a Boxplot could show outliers but z-scores show no outlier?
No, Is it not possible that creating a Boxplot could show outliers but z-scores show no outlier. This is because Any z-score that is either higher than +3 or lower than -3 is viewed as an issue.
When there isn't an anomaly, what does that mean?When you declare a data point to be an outlier and reject it, you are indicating that even if you have already observed the point, it is unlikely to happen again.
Z scores make it easier to determine whether a data value is larger or less than the mean and how far from the mean it is. The Z score precisely indicates the number of standard deviations a data point deviates from the mean.
So, Outliers can be highlighted using scatterplots, histograms, and boxplots. Asterisks or other symbols are displayed on the graph in boxplots to plainly show the presence of outliers in a dataset.
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v - 10 + k³ when v = -2 and k = -3
-2 - 10 + (-3)^3
= -12 - 27
= -39
Answer:
-39
Step-by-step explanation:
Substitute v and k
v - 10 + k³
-2 - 10 -3³
Multiply the 3 and the power of thirds together
-2 -10 + 27
Combine like terms
100 points if you answer this correctly
Since triangle P'Q'R' is the result of a transformation of triangle PQR, an algebraic representation which best describes this transformation is: C. (x, y) → (5x/2, 5y/2).
What is a transformation?In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.
From the information provided above, we can logically deduce the following coordinates:
Point P = (-1, 1)Point Q = (2, 0)Point R = (-1, -2)Point P' = (-5/2, 5/2)Point Q' = (5, 0)Point R' = (--5/2, -5)Therefore, the transformation rule is given by:
P (x, y) → P' (x, y)
Point P = (-1, 1) → Point P' = ((5/2 × -1), (5/2 × 1)) = Point P' = (-5/2, 5/2).
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what is 0.675 as a percent
Answer:
67.5
Step-by-step explanation:
Answer:67.5
Step-by-step explanation:0.675*100=67.5
Which is a solution set for |x + 3| = 6?
{-3, 3}
{-9,3}
{-6, 9}
The values of x in the given equation are x = -9 and x = 3. The solution set is [-9, 3]
Solving for the values of x in an equationFrom the question, we are to determine the value of x in the given equation.
The given equation is
|x + 3|= 6
Then, we can write that
x + 3 = 6 and -(x + 3) = 6
Solving the first equation
x + 3 = 6
Subtract 3 from both sides of the equation
x + 3 - 3 = 6 - 3
x = 3
Solving the second equation
-(x + 3) = 6
-x - 3 = 6
Add 3 to both sides of the equation
-x - 3 + 3 = 6 + 3
-x = 9
Multiply both sides of the equation by -1
-1 × -x = -1 × 9
x = -9
Hence, the solutions are x = -9 and x = 3
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Please help me, please
Answer:
m∠1 = 88°
m∠2 = 42°
m∠3 = 113°
Step-by-step explanation:
All of the angles in a triangle add up to 180°. This knowledge can be used to find angle 3, which I will rename c to make writing an equation easier.
[tex]180=25+42+c\\180=67+c\\113=c[/tex]
Angle 3 is 113°
Two angles on either side of the intersection of two straight lines are equal, therefore angle 2, or b:
[tex]b=42[/tex]
Angle 2 is 42°
Now that two angles are known in the leftmost triangle, we can solve for the last one: Angle 1, or a:
[tex]180=50+42+a\\180=92+a\\88=a[/tex]
Angle 1 is 88°
Alyssa works 6.4-hour shifts at the donut shop each day. Last week she earned $480 for working 32 hours. Describe the unit rate in this problem.
The unit rate for this problem is how much Alyssa earns per hour
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Alyssa works 6.4-hour shifts at the donut shop each day.
Last week she earned $480 for working 32 hours.
Now, To determine her earnings per hour we have to divide her total earnings by the total no. of hours she worked which is,
= $(480/32).
= $15 per hour.
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I need help please please
In order to combine exponents with the multiplication or division properties, the terms must have the same?
Answer:
To multiply terms containing exponents, the terms must have the same base and/or the same power. To multiply terms with the same base, keep the same base and add the powers together. To multiply terms with different bases but the same power, raise the product of the bases to the power.
Step-by-step explanation:
a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 400 gram setting. based on a 25 bag sample where the mean is 399 grams and the variance is 400, is there sufficient evidence at the 0.025 level that the bags are underfilled? assume the population distribution is approximately normal. find the value of the test statistic. round your answer to three decimal places.
Using the t test statistic, the value of the test statistic is 1.25.
In the given question we have to find the value of the test statistic.
A manufacturer of chocolate potato chips would like to know whether its bag filling machine works correctly at the 400 gram setting.
= 400
A 25 bag sample had a mean of 399 grams and the variance is 400.
There is sufficient evidence at the 0.025 level that the bags are underfilled.
Sample size(n) = 25
sample Mean = 399
Sample Variance = 400
Standard Deviation = √Sample Variance
Standard Deviation = √400
Standard Deviation = 20
Population Mean = 400
So , the null and alternative hypothesis are
H0 : μ = 400
Ha : μ < 400
Using the sample t test statistic
t = (Population Mean - Sample Mean)/(Standard Deviation/Sample size)
t = (400 - 399)/(20/25)
t = 1*25/20
t = 1.25
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i need help pls
PLEASE GIVE ME THE CORRECT ANSWERS FOR ALL 3 PROBLEMS IM BEGGING
The values of the function when x = 3 are -10. -1 and -3, respectively
The values of the functionFunction 1
The equation of the function is given as
y = -4x + 2
We have the value of x to be 3
So, we have
y = -4 x 3 + 2
Evaluate
y = -10
Function 2
The graph represents the notation of the function
On the graph, we have the value of y to be -1, when x = 3
This means that
y = -1
Function 3
The table represents the notation of the function
On the table, we have the value of y to be -3, when x = 3
This means that
y = -3
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Select the correct answer.
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
A. y = 3x + 4
B. y = 3x − 14
C. y = 3x − 4
D. y = 3x + 12
(It is not y = 3x - 4 OR C)
It takes 5 minutes for your printer to print 40 papers
How long does it take for your printer to print 12 papers?
It will take 1.5 minutes for printer to print 12 papers.
Given,
Time taken to print 40 papers=5 minutes
then,
Time taken to print 1 paper =[tex]\frac{5}{40}=\frac{1}{8}[/tex] minutes
then to find time taken to print 12 papers, multiply 12
Time taken to print 12 paper,
[tex]Time=\frac{1}{8}*12\\\\Time=1.5\ minutes[/tex]
Thus, it will take 1.5 minutes for printer to print 12 papers.
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Ms. Fraser’s total monthly cell phone bill this month was
$56.70. Her phone company charges $45.60 for unlimited
minutes and $0.10 for every text message sent.
Answer:
She sent 111 texts that month
Step-by-step explanation:
a manager of a clothing store always orders 2 small T-shirts and 3 large t-shirts for every 4 medium T-shirts.The manager plans to order 24 medium T-shirts. How many small T-shirts and large T-shirts should the manager order? show your work.
Answer: 12 small t-shirts and 18 large t-shirts
Step-by-step explanation:
24÷4=6
2×6=12 small t-shirts
3×6=18 large t-shirts
a) Work out (5 × 10³) × (9 × 10')
Give your answer in standard form.
b) Work out (7 × 105) + (2 × 10²)
Give your answer in standard form.
Find x, y and z. ILL GIVE BRAINLIEST
Answer:
x = 30
y = 15
z = 150
Step-by-step explanation:
90°, 2x°, and x and supplementary.
Using this knowledge, we can form the equation:
2x° + 90° + x° = 180°
and solve for x.
3x°+ 90° = 180°
3x° = 90°
x° = 30°
x = 30
x and z are same side interior angles. Therefore, they are supplementary.
Using this knowledge, we can form the equation:
x° + z° = 180°
30° + z° = 180°
z° = 150°
z = 150
z° and 2y° are supplementary.
Using this knowledge, we can form the equation:
z° + 2y° = 180°
150° + 2y° = 180°
2y° = 30°
y° = 15°
y = 15
Answer:
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Assume that louisa carried an average balance of $1,000 from her credit card purchases over the past year. The a. P. R. On her credit card for the past year was 19. 99%. Approximately how much interest would louisa have paid over the course of the year?.
It would have cost Louisa $200 in interest charges.
The simple interest amount is calculated as follows;
SI = P*I*t
That is where we have
The balance is P.
The interest rate is I.
The time is t.
Regarding this issue;
Balance of $1,000, 19.99% APR, and 1 year.
She will pay the following sum;
SI = 1000 *0.199*1
SI = 199.9
SI ≅ 200
Louisa would have had to pay $200 in interest fees.
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At the penalty apr rate of 28. 99% and a balance of about $1800, approximately how much interest would you owe in one month?.
The interest rate for one month is 2.42% and the interest amount is $40 approximately.
Given,
The penalty APR rate = 28.99%
Balance amount = $1800
We have to find the interest for one month;
Here,
The APR of 28.99% is the yearly interest. To find the monthly rate:
= Rate / 12 months
= 28.99% / 12
= 2.42%
The amount owed is therefore;
= 1,800 x 2.42%
= $43.56
= $40.00 approximately
That is,
The interest rate for one month is 2.42% and the interest amount is $40 approximately.
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