To write an equation for the cubic polynomial function with zeroes at 2, 3, and 5, we can use the factored form of a polynomial.
The factored form is given by (x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots.
So, for this problem, the equation would be (x - 2)(x - 3)(x - 5).
Regarding the multiplicity of the roots, in this case, none of the roots have multiplicity. Each root appears once in the equation.
To find a function with these roots, you can use the factored form of the polynomial and substitute different values for the coefficients to get different functions.
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Find the missing side. 31° Z z = [?] Round to the nearest tenth. Remember: SOHCAHTOA 21
A²+B²= C²
31²+ 21²= z²
961+441 = z²
1402= z²
z= 37.443290454
divide the polynomials x^2-10,000/x-100
Answer:
x+100
Step-by-step explanation:
x^2-10,000/x-100
x^2-10000 is a difference in squares and can be factored.
x^2-10000 = (x+100)(×-100).
(x+100)(x-100)/(x-100)
(x-100) cancel each other.
x+100 remains.
Find the area of a composite figure.
The area of the composite figure is 800m²
What is area of a figure?The area of a figure is the number of unit squares that cover the surface of a closed figure.
Composite geometric figures are made from two or more geometric figures.
The figure consist of a rectangle , a semi circle and a triangle.
Area of the semicircle = 1/2 πr²
= 1/2 × 3.14 × 10²
= 314/2 = 157 m²
Area of the rectangle = l × w
= 25 × 20
= 500m²
area of the triangle = 1/2bh
= 1/2 × 10 × 25
= 25 × 5
= 125 m²
Therefore the area of the composite figure
= 125 + 500 + 175
= 800m²
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Determine the measure of the third angle in a triangle when the other two angles total 165 degrees.
Answer:
15
Step-by-step explanation:
180-15
Hello!
the sum of the angles in the triangle = 180°
so the 3rd angle = 180° - 165° = 15°
The answer is 15°If a dozen eggs cost R18, how much would 1 egg cost?
Answer:
1.50 rand
Step-by-step explanation:
divide 18 by 12
= 1.5
therefore each egg costs 1 rand 50
Answer:
2/3
Step-by-step explanation:
if a dozen of eggs costs 18 rupees, what is the cost of each egg?
to get this we have to divide the cost of 12 eggs to 18 rupees
12/18
2/3 that's all
One interior angle and one exterior angle are marked on the 7-sided shape
below.
Calculate the size of the exterior angle x.
Т
134°
The size of the exterior angle in the given 7-sided shape, as shown in the image attached below is: x = 46°.
How to Calculate the Size of the Exterior Angle of a Polygon?To calculate the size of the exterior angle in a polygon when the interior angle is known, we can use the following relationship:
Interior angle + Exterior angle = 180°
Given that the interior angle measures 134°, as shown in the image below, we can substitute it into the equation:
134° + Exterior angle = 180°
To isolate the exterior angle, we subtract 134° from both sides of the equation:
Exterior angle = 180° - 134°
Simplifying further:
Exterior angle = 46°
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In a controlled laboratory experiment, scientists at the University of Minnesota discovered that
25% of a certain strain of rats subjected to a 20% coffee
bean diet and then force-fed a powerful cancer-causing
chemical later developed cancerous tumors. Would we
have reason to believe that the proportion of rats developing tumors when subjected to this diet has increased
if the experiment were repeated and 16 of 48 rats developed tumors? Use a 0.05 level of significance.
Yes, we would have reason to believe that the proportion of rats developing tumors when subjected to this diet has increased if the experiment were repeated and 16 of 48 rats developed tumors.
To determine whether there is an increase in the proportion of rats developing tumors when subjected to a coffee bean diet, we can conduct a hypothesis test using the 0.05 level of significance.
1. State the hypotheses:
- Null hypothesis (H0): The proportion of rats developing tumors remains the same.
- Alternative hypothesis (Ha): The proportion of rats developing tumors has increased.
2. Identify the test statistic:
We will use a z-test to compare the observed proportion of rats developing tumors with the expected proportion.
3. Set the significance level:
The significance level (α) is given as 0.05.
4. Collect data:
In the original experiment, 25% of rats developed tumors. In the repeated experiment, 16 out of 48 rats developed tumors.
5. Compute the test statistic:
The test statistic formula for comparing proportions is:
z = (p - P) / sqrt(P(1-P)/n)
where p is the observed proportion, P is the hypothesized proportion, and n is the sample size.
Using the observed proportion (16/48 = 0.333), the hypothesized proportion (0.25), and the sample size (48), we can calculate the test statistic.
6. Determine the critical value:
Since we are using a 0.05 level of significance and conducting a one-tailed test (Ha: >), we can find the critical value from the standard normal distribution table. The critical value for a 0.05 significance level is 1.645.
7. Make a decision:
If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the proportion of rats developing tumors has increased.
8. Calculate the test statistic:
Plugging in the values into the formula, we calculate the test statistic:
z = (0.333 - 0.25) / sqrt(0.25 * 0.75 / 48) = 1.404
9. Compare the test statistic and critical value:
The test statistic (1.404) is less than the critical value (1.645).
10. Make a decision:
Since the test statistic is not greater than the critical value, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the proportion of rats developing tumors has increased when subjected to this diet.
In summary, based on the given data and conducting a hypothesis test, we do not have reason to believe that the proportion of rats developing tumors has increased if the experiment were repeated and 16 of 48 rats developed tumors.
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The July bank statement sent by the bank to ABC company shows a balance of cash on deposit at July 31 of Br.4,964.47 Assume that on July 31, assume the on July 31, ABCs ledger shows a bank balance of Br. 4 173. 83. 1. A deposit of Br 410. 90 made after banking hours and doesnt appear in the bank statement2. A check drawn for Br. 79 had been erroneously charged by the bank Br.973. For checks issued in July have not yet been paid by the bank (outstanding checks). : Theses checks are;- Check No date amount 801 June 15 ---Br.100,00 888 July 24 ----Br. 10.25 890 July 27--- Br. 294.50 891 July 30 ---Br. 205.004. A check written for birr 210 had been incorrectly charged by the bank as birr 120 5. Proceeds from collection of a interest bearing note receivable from David. ABC Company had left this note with the banks collection department. The face amount of the note was birr 500 6. Br. 24.75 interest earned on average account balance during July7. A check for Br. 10 returned with the statement had been recorded in the check register as Br. 100. The check was for the payment of an obligation to Davis Equipment Company for the purchase of office supplies on account 8. Br. 5,00 fee charged by bank for handling collection of note receivable 9. Br. 50.25 check from customer John deposited by ABC company charged bank as Non sufficient fund (NSF) 10. Br. 12.70 service charged by bank for the month of July. 11. Check number 875 was issued July 20 in the amount of Br 85 but was erroneously recorded in the cash payment Journal as Br 58 for payment of telephone expense
Based on the given information and adjustments, the adjusted bank balance for ABC Company on July 31 would be Br. 5,169.42.
Based on the provided information, let's analyze the various transactions and their impact on the bank reconciliation for ABC Company:
1. The deposit of Br. 410.90 made after banking hours: This deposit does not appear in the bank statement, so it should be added to the bank balance. After including this deposit, the adjusted bank balance would be Br. 5,375.37 (Br. 4,964.47 + Br. 410.90).
2. The erroneously charged check of Br. 79: This check should be deducted from the bank balance as it was charged in error by the bank. After deducting this amount, the adjusted bank balance would be Br. 5,296.37 (Br. 5,375.37 - Br. 79).
3. Outstanding checks: The outstanding checks that haven't been paid by the bank need to be deducted from the adjusted bank balance. The total amount of outstanding checks is Br. 610.75 (Br. 100 + Br. 10.25 + Br. 294.50 + Br. 205). After deducting this amount, the adjusted bank balance would be Br. 4,685.62 (Br. 5,296.37 - Br. 610.75).
4. Incorrectly charged check of Br. 210 as Br. 120: This error made by the bank needs to be corrected. The bank balance should be increased by the difference, which is Br. 90. Therefore, the adjusted bank balance would be Br. 4,775.62 (Br. 4,685.62 + Br. 90).
5. Proceeds from collection of an interest-bearing note receivable: The face amount of the note was Br. 500. Since the note was left with the bank's collection department, the amount collected should be added to the bank balance. Therefore, the adjusted bank balance would be Br. 5,275.62 (Br. 4,775.62 + Br. 500).
6. Interest earned on the average account balance: The interest earned of Br. 24.75 should be added to the bank balance. After including this amount, the adjusted bank balance would be Br. 5,300.37 (Br. 5,275.62 + Br. 24.75).
7. The returned check of Br. 10: This check was recorded in the check register as Br. 100 but was returned for Br. 10. The difference of Br. 90 should be deducted from the bank balance. Therefore, the adjusted bank balance would be Br. 5,210.37 (Br. 5,300.37 - Br. 90).
8. Fee charged by the bank for handling the collection of the note receivable: The fee of Br. 5.00 should be deducted from the bank balance. After deducting this fee, the adjusted bank balance would be Br. 5,205.37 (Br. 5,210.37 - Br. 5.00).
9. Check from customer John charged as Non-sufficient funds (NSF): The check of Br. 50.25 should be deducted from the bank balance. After deducting this amount, the adjusted bank balance would be Br. 5,155.12 (Br. 5,205.37 - Br. 50.25).
10. Service charge by the bank for the month of July: The service charge of Br. 12.70 should be deducted from the bank balance. After deducting this charge, the adjusted bank balance would be Br. 5,142.42 (Br. 5,155.12 - Br. 12.70).
11. Erroneously recorded check of Br. 85 as Br. 58: This error in the cash payment journal needs to be corrected. The bank balance should be increased by the difference, which is Br. 27. Therefore, the adjusted bank balance would be Br. 5,169.42 (Br. 5,142.42 + Br. 27).
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A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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What is the constant in 12r + r/2-19
Answer:
constant is - 19
Step-by-step explanation:
the constant is the term in an expression with no variable attached to it.
12r + [tex]\frac{r}{2}[/tex] - 19
the only term without the variable r attached to it is - 19
then the constant term is - 19
ABC is a right angle. The ratio of the measures of and is 3 to 2. Find mABD and mDBC . Investigate all possible cases related to a location of the point D. Do a sketch of both cases in GeoGebra. Type your solution in the space provided below. Insert a screenshot of your GeoGebra sketches.
To find the measures of angles ABD and DBC in the right triangle ABC, we considered two cases: when point D lies on segment AB and when point D lies on segment BC. In both cases, the measures of the angles were determined based on the given ratio of 3:2.
In the given problem, we have a right triangle ABC, and we need to find the measures of angle ABD (mABD) and angle DBC (mDBC) based on the ratio of the measures of angle A and angle B.
Let's consider the different cases for the location of point D:
Case 1: Point D lies on segment AB.
In this case, angle ABD and angle DBC will be acute angles. Let's assume that angle ABD has a measure of 3x and angle DBC has a measure of 2x. Since angle ABD and angle DBC are acute angles, the sum of their measures should be less than 90 degrees.
Therefore, we have the inequality: 3x + 2x < 90. Solving this inequality, we get 5x < 90, which gives x < 18. So, the measure of angle ABD (mABD) will be 3x, and the measure of angle DBC (mDBC) will be 2x.
Case 2: Point D lies on segment BC.
In this case, angle ABD and angle DBC will be obtuse angles. Let's assume that angle ABD has a measure of 3x and angle DBC has a measure of 2x. Since angle ABD and angle DBC are obtuse angles, the sum of their measures should be greater than 90 degrees.
Therefore, we have the inequality: 3x + 2x > 90. Solving this inequality, we get 5x > 90, which gives x > 18. So, the measure of angle ABD (mABD) will be 3x, and the measure of angle DBC (mDBC) will be 2x.
By investigating these two cases, we can find the measures of angle ABD (mABD) and angle DBC (mDBC) based on the given ratio of 3:2. The specific values of mABD and mDBC will depend on the exact location of point D within the triangle ABC.
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¿De qué número 64 es el 80%?
how many ft makes a height of 1.66m.
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters
Given: Angle1 and Angle2 are supplements, and Angle3 and Angle2 are supplements.
Prove: Angle1 Is-congruent-to Angle3
Three separate angles are shown. They are labeled 1, 2, 3 from left to right.
Complete the missing parts of the paragraph proof.
By the definition of
angles, the sum of the measures of angles 1 and 2 is 180 degrees. Likewise, the sum of the measures of angles
is 180 degrees. By the
property, mAngle1 + mAngle2 = mAngle3 + mAngle2. Subtract the measure of angle
from each side. You get mAngle1 = mAngle3, or Angle1 Is-congruent-to Angle3, by the definition of congruence.
The missing parts of the proof of supplementary angles are:
Supplementary; ∠2 and ∠3; substitution; 2.
How to Identify the supplementary angles?Supplementary angles are defined as angles whose measures sum to 180°. Thus this is the first answer.
Since we are told that ∠2 and ∠3 are supplementary, their measures sum to 180° and they are the second answer.
We know that m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°. We can substitute "m∠2 + m∠3" for 180° in the first equation; this is the substitution property.
To isolate m∠1 on the right, we will subtract m∠2 from each side, and get that m∠1 = m∠3 and the angles are congruent.
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Lily measured the lengths of 16 fish.
Use the graph below to estimate the lower and upper quartiles of the fish
Answer:
The lower quartile of the fish lengths is 15 inches
The upper quartile of the fish lengths is 30 inches
Step-by-step explanation:
(the cumulative frequency gives how much of the observations/measurements are under a certain value e.g, in our case, for lengths of 40 inches, all 16 of the fish have length in that range (less than or equal to 40) so, the cumulative frequency is 16 and so on)
We need to find the lower and upper quartiles of the fish lengths,
Now, the lower quartile contains 25% (or 1/4) of the values
in our case, since there are 16 fish,
25% of 16 is 4
So, for the lower quartile, the cumulative frequency should be 4.
For which the length is 15 inches,
So, the lower quartile of the fish lengths is 15 inches
The upper quartile contains 75% (or 3/4) of the values,
Now, 3/4 of 16 is 12.
So, for the upper quartile, the cumulative frequency should be 12.
For which the length is 30 inches
So, the upper quartile of the fish lengths is 30 inches
Mira la siguiente recta numérica.
1
0
?
1
→
Identifica el punto en la recta numérica y
escríbelo como fracción y como decimal.
According to the information, the number of the image would be 17/100 or 0.17
How to express this number in fraction and decimal?To express this number in fraction and decimal we must take into account different aspects. First of all we must consider the reference numbers that are on the number line.
On the other hand, we must count how many segments each unit of the line is divided into. In this case it is in 10. So to identify the number we can add a 0 to the denominator and take the numerator as an integer that would be 17. Then the fraction would remain:
17 / 100In the case of the decimal we only have to carry out the division and we will obtain the decimal.
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Nadia wants to find out if students in her year like the school lunches. She
decides to ask her class to complete a survey.
Which of the statements below describes:
ack to task
a) the population?
b) the sample?
All the students in the school
All the students in Nadia's class
All the students in Nadia's year
All the students not in Nadia's class
All the students not in Nadia's year
Answer:
a) All the students in Nadia's year are the population
b) All the students in Nadia's class are the sample
Step-by-step explanation:
She wants to find out if students in her year like the school lunches.
So, this is the population.
i.e All the students in Nadia's year
She asks her class to complete a survey,
So, this is the sample of the population (Her classmates are in the same year as her and so on)
i.e All the students in Nadia's class
Given the diagram below, what is
cos(45*)?
8 √2
450
Triangle not drawn to scale
O A. 1/√2
O B. 2 √2
O C. 4 √2
O D. √2
The value of cos(45°) is √2/2. The correct answer choice is D. √2.
In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.
Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.
Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:
cos(45°) = x/(x√2) = 1/√2
Simplifying further, we rationalize the denominator:
cos(45°) = 1/√2 * √2/√2 = √2/2
Therefore, the value of cos(45°) is √2/2.
The correct answer choice is D. √2.
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it costs 50p for posting a parcel that weighs 20g. how much does it cost altogether to post 1 parcel weighing 170g and 2 parcels weighing 320g each?
It would cost 2025p to send one parcel weighing 170g and two parcels weighing 320g each.
In order to find out how much it will cost to send one parcel weighing 170g and two parcels weighing 320g each, we can use the information given to us in the question: it costs 50p to post a parcel that weighs 20g. Using this information, we can create a proportion. We know that 50p is the cost to send a parcel weighing 20g, so if we multiply the weight of the parcel by 2.5, we can find out how much it would cost to send that parcel.
For example, a parcel weighing 50g would cost 125p (50 x 2.5 = 125). To find out how much it would cost to send a parcel weighing 170g, we can use this porpotion: 50p/20g = x/170g
Multiplying both sides by 170g, we get:
x = (50p/20g) * 170gx = 425p
So, it would cost 425p to send a parcel weighing 170g.To find out how much it would cost to send two parcels weighing 320g each, we can use the same proportion:
50p/20g = x/320g
Multiplying both sides by 320g, we get:
x = (50p/20g) * 320gx = 800p
So, it would cost 800p to send two parcels weighing 320g each.
To find out the total cost to send all three parcels, we simply add up the costs:
425p + 800p + 800p = 2025p.
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