Answer: 12 minutes
Step-by-step explanation:
This is a standard Work Formula question (2 or more 'entities' that work on a task together). When there are just 2 entities and there are no 'twists' to the question, we can use the Work Formula to get to the correct answer.
Work = (A)(B)/(A+B) where A and B are the individual times needed to complete the task.
We're told that two hoses take 20 minutes and 30 minutes, respectively, to fill a pool. We're asked how long it takes the two hoses, working together, to fill the pool.
(20)(30)/(20+30) = 600/50 = 12 minutes to fill the pool.
FortyForty people purchase raffle tickets. Three winning tickets are selected at random. If first prize is $50005000, second prize is $45004500, and third prize is $500500, in how many different ways can the prizes be awarded?
To determine the number of different ways the prizes can be awarded, we need to use the concept of combinations.
Explanation:To determine the number of different ways the prizes can be awarded, we need to use the concept of combinations. Since there are 40 people purchasing raffle tickets, and 3 winning tickets are selected at random, we can find the number of ways the prizes can be awarded using the formula for combinations:
C(n, r) = n! / ((n-r)! * r!)
Where n is the total number of items and r is the number of items chosen at a time. In this case, n = 40 and r = 3:
C(40, 3) = 40! / ((40-3)! * 3!)
= 40! / (37! * 3!)
= (40 * 39 * 38) / (3 * 2 * 1)
= 9880
Therefore, there are 9,880 different ways the prizes can be awarded.
4^1/2 equals 2. Why? Show steps and explain
raising some base to the power of 1/2 is the same as square root
Answer:
Step-by-step explanation:
4 to the first power is 4
then divide by 2
What is the original message encrypted using the RSA system with n = 43 · 59 and e = 13 if the encrypted message is 0667 1947 0671? (To decrypt, first find the decryption exponent d which is the inverse of e = 13 modulo 42 · 58.)
Answer:
Ik sorry but you can
Step-by-step explanation:
search in internet
The student needs to find the decryption exponent 'd' for the RSA algorithm by computing the modular multiplicative inverse of e modulo φ(n), and then use that to decrypt the message.
Explanation:The student is asking how to decrypt a message that was encrypted using the RSA algorithm. The given public key consists of n = 43 · 59 and e = 13, and the encrypted message is 0667 1947 0671. To decrypt the message, we need to find the private key, which includes the decryption exponent d. The decryption exponent is the modular multiplicative inverse of e modulo φ(n), where φ(n) is the Euler's totient function of n. Since n is the product of two primes, 43 and 59, φ(n) is (43-1)(59-1) which equals 42 · 58. Now, we need to find d such that it satisfies the congruence ed ≡ 1 (mod φ(n)), which will be d = 13⁻¹ mod 42 · 58. Once d is computed, we can decrypt each part of the message using the formula M = C^d mod n, where M is the original message and C is each part of the encrypted message.
Miguel earns 2,456.75 every month he also earns an extra 4.75 every time he sells a new gym membership last month Miguel sold 32 new gym membership how much money did Miguel earn last month
Answer: Total amount of money earned last month = $2608.75
Step-by-step explanation:
Miguel earns 2,456.75 every month. This is his constant pay for the month. He also earns an extra 4.75 every time he sells a new gym membership.
Last month, Miguel sold 32 new gym membership. This means that the extra money that he earned for last month will be the number of new gym membership sold times the amount her earns per new gym membership sold. It becomes
32 × 4.75 = 152
Total amount of money earned last month will be sum of his monthly salary + the extra earned. It becomes
2456.75 + 152 = $2608.75
The late fee for library books is $2.00 plus 15 cents each day for a book that is late.If Maria's fee for a late book was $3.20,write and solve a linear equation to find many days late the book was.
First we will subtract $2 from $3.2 since that is late fee to get $1.2.
Now we divide $1.2 by $0.15 to get number of cents hence 8 days.
The answer is Maria is 8 days too late to hand over the book.
Hope this helps.
The linear equation is 3.20 = 2.00 + 0.15*x. Hence, Maria's book was 8 days late.
To find out how many days Maria's book was late, we need to set up a linear equation using the given information.
The total late fee equation is given by:
Late Fee = 2.00 + 0.15*x
Where $2.00 is the base fee, and 0.15 dollars is the additional late fee per day. Since Maria's total fee was $3.20, we can set up the equation as follows:
3.20 = 2.00 + 0.15*x
Now, solve for x, which represents the number of days the book was late:
Subtract $2.00 from both sides:
3.20 - 2.00 = 0.15*x
Simplify the equation:
1.20 = 0.15*x
Divide both sides by 0.15 to isolate x:
x = 1.20 / 0.15
Calculate the result:
x = 8
So, Maria's book was 8 days late.
A rectangle has length x and width x – 3. The area of the rectangle is 10 square meters. Complete the work to find the dimensions of the rectangle. x(x – 3) = 10 x2 – 3x = 10 x2 – 3x – 10 = 10 – 10 (x + 2)(x – 5) = 0 What are the width and length of the rectangle?
Answer:
Step-by-step explanation:
Area of rectangle = Length × Width
The given rectangle has a length if x meters
The width of the triangle is (x-3) meters
The area of the rectangle is given as 10 square meters.
Area if rectangle = x(x-3) = 10
Multiplying each term in the parentheses,
x^2 -3x = 10
x^2 -3x -10 = 0
This is a quadratic equation
We will look for two numbers such that when they are multiplied, it will give us -10x^2 and when they are added, it will give -3x. It becomes
x^2 + 2x - 5x -10 = 0
x(x+2)-5(x+2) =0
( x + 2)(x-5) = 0
x = -2 or x = 5
The length of the rectangle cannot be negative so the length is 5 meters
Widith = x+3 = 5-3 = 2 meters
Final answer:
The dimensions of the rectangle are found by solving the quadratic equation derived from the area. The length is 5 meters, and the width is 2 meters, as negative dimensions are not possible.
Explanation:
To find the dimensions of the rectangle with an area of 10 square meters and the sides defined as x and x
- 3, we have derived a quadratic equation x^2 - 3x - 10 = 0 which factors down to (x + 2)(x - 5) = 0. This gives us two possible solutions for x: either x + 2 = 0 or x - 5 = 0. Solving these equations, we find x = -2 or x = 5. Since a rectangle cannot have a negative dimension, we disregard x = -2. Therefore, the length of the rectangle is x = 5 meters and the width is x - 3 = 2 meters.
Suppose you pay $1.00 to play the following game. A card is drawn from a standard deck. If it is an ace, you recieve $5.00, if it is a king, queen, or jack, you receive $3.00. Otherwise you recieve no money. Find the expected value of your net winning. Use decimal notation for your answer.
Answer:
0.08
Step-by-step explanation:
A standard deck contains 52 cards. There are 4 aces and 12 kings/queens/jacks. This means that there is a 4/52 (or 1/13) chance of you winning 5$, and a 12/52 (or 3/13) chance of you winning 3$. To find the expected value, we can simply find the average amount of winnings. This can be done by adding the possible winning values for each card.. Since there is a 1/13 chance that you win 5$, we can add 5*1=5 to the sum. For the kings/jacks/queens, we can add 3*3=9 to the sum. Then, since we win nothing for anything else, we can find the expected value to be 14/13 = 1.08 (approximately). Subtracting the 1$ pay, the expected net winning is 0.08, or 8 cents.
The previous triangular prism had a surface area of 288 square units. What happens to the surface area of your prism when you double all four measurements?
If all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.
Solution:Given that
Surface area of a triangular prism = 288 square unit
Need to evaluate new surface area if all four measurement of triangular prism is double.
Relation between surface area and the four dimensions of the triangular prism is given by following formula
Surface Area of triangular prism = bh + 2ls + lb
Where h is height of the prism , b is length of base of the prim , l is length of the prism and s is side length of the prism.
Given that Area of triangular prism = 288 square unit
=> bh + 2ls +lb = 288
Doubling the four dimensions means replace b by 2b, l by 2l , s by 2s and h by 2h in formula of Surface area of triangular prism.
[tex]\text { We get Surface area of new triangular prism }=2 b \times 2 h+2 \times 2 l \times 2 s+2 l \times 2 b[/tex]
[tex]\begin{array}{l}{=4 \times b h+4 \times 2 l s+4 \times l b} \\\\ {=4(b h+2 l s+l b)}\end{array}[/tex]
=> Surface area of new triangular prism = 4 (bh + 2ls +lb)
=> Surface area of new triangular prism = 4 x 288 = 1152 square unit.
Hence we can conclude that if all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.
Answer: C, the surface area increases by 4 times
Step-by-step explanation:
six-foot person walks from the base of a streetlight directly toward the tip of the shadow cast by the streetlight. When the person is 11 feet from the streetlight and 5 feet from the tip of the streetlight's shadow, the person's shadow starts to appear beyond the streetlight's shadow. (a) Draw a right triangle that gives a visual representation of the problem. Show the known quantities and us
Answer:
Step-by-step explanation: See annex
The figures are in feet
A baseball player strikes out three times for every two hits he gets if the player strikes out 15 times how many hits does he get if the player gets 46 hit how many times does he strike out
The player will get 10 hits for 15 times strikes out.
The player will strike out 69 times for 46 hits.
Step-by-step explanation:
Given,
Ratio of strike out to hits = 3:2
Condition 1: If the player gets 15 strikes out;
Let,
x be the hits for 15 times strikes out.
Using proportion;
Strike out : hit :: strike out : hit
[tex]3:2::15:x[/tex]
Product of mean = Product of extreme
[tex]15*2=3*x\\3x=30[/tex]
Dividing both sides by 3;
[tex]\frac{3x}{3}=\frac{30}{3}\\x=10[/tex]
The player will get 10 hits for 15 times strikes out.
Condition 2: if the player gets 46 hits
Let,
y be the strikes out.
Using proportion,
Strike out : hit :: strike out : hit
[tex]3:2::y:46[/tex]
Product of mean = Product of extreme
[tex]2*y=46*3\\2y=138[/tex]
Dividing both sides by 2;
[tex]\frac{2y}{2}=\frac{138}{2}\\y=69[/tex]
The player will strike out 69 times for 46 hits.
Keywords: Ratio, proportion
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Answer:The player will get 10 hits for 15 times strikes out.
The player will strike out 69 times for 46 hits.
Step-by-step explanation:
Given,
Ratio of strike out to hits = 3:2
Condition 1: If the player gets 15 strikes out;
Let,
x be the hits for 15 times strikes out.
Using proportion;
Strike out : hit :: strike out : hit
Product of mean = Product of extreme
Dividing both sides by 3;
The player will get 10 hits for 15 times strikes out.
Condition 2: if the player gets 46 hits
Let,
y be the strikes out.
Using proportion,
Strike out : hit :: strike out : hit
Product of mean = Product of extreme
Dividing both sides by 2;
The player will strike out 69 times for 46 hits.
Keywords: Ratio, proportion
Step-by-step explanation:
A quality control technician checked a sample of 30 bulbs. Two of the bulbs were defective. If the sample was representative, find the number of bulbs expected to be defective in a case of 450.
36
45
30
24
Answer:
if sample of 30 bulbs has 2 defective bulbs so,
there is one defective bulb every
[tex] \frac{30}{2} = 15[/tex]
bulbs.
total defective bulbs in 450 bulbs =
[tex] \frac{450}{15} = 30[/tex]
The mathematical theory behind linear programming states that an optimal solution to any problem will lie at a(n) ________ of the feasible region.
a) interior point or center
b) maximum point or minimum point
c) corner point or extreme point
d) interior point or extreme point
e) None of these
Answer:
Option C) corner point or extreme point
Step-by-step explanation:
Linear Programming:
Linear programming is an optimization(maximization or minimization) technique for a system of linear equations and a linear objective function. The objective function defines the quantity to be minimized or maximized.The goal of linear programming is to find the values of the variables that maximize or minimize the objective function.Corner Point Theorem:
The corner point theorem states that the optimum value of the feasible region occurs at the corner point of the feasible region, thus the minimum or maximum value will occur at the corner point or the extreme point.Thus,
The mathematical theory behind linear programming states that an optimal solution to any problem will lie at corner point or extreme point of the feasible region
4x^3+26x^2-15x-74x3+26x 2 −15x−7 is divided by x+7x+7? If there is a remainder, express the result in the form q(x)+\frac{r(x)}{b(x)}q(x)+ b(x) r(x) .
Answer:
4x^2 -2x -1
Step-by-step explanation:
Synthetic division works well for dividing by a linear binomial. See the attached for the working and the interpretation of the result.
Please please help me with this
Answer:
Step-by-step explanation:
First find the equations of the lines, then fill in the proper inequality sign. The upper line has a y-intercept of 1 and a slope of 1/2, so the equation, in slope-intercept form is
[tex]y=\frac{1}{2}x+1[/tex]
Since the shading is below the line, the inequality sign is less than or equal to. The inequality, then, is
[tex]y\leq \frac{1}{2}x+1[/tex]
But the solutions are in standard form, so let's do that:
[tex]-\frac{1}{2}x+y\leq 1[/tex]
AND they do not like to lead with negatives, apparently, so let's change the signs and the way the inequality is facing, as well:
[tex]\frac{1}{2}x-y\geq -1[/tex]
Let's do the sae with the lower line. The equation, in slope-intercept form is
[tex]y=\frac{3}{2}x-3[/tex] since the slope is 3/2 and the y-intercept is -3. Now, since the shading is above the line, the inequality is greater than or equal to:
[tex]y\geq \frac{3}{2}x-3[/tex]
In standard form:
[tex]-\frac{3}{2}x+y\geq -3[/tex] and not leading with a negative gives us
[tex]\frac{3}{2}x-y\leq 3[/tex]
Those 2 solutions are in choice B, I do believe.
Triangle $ABC$ has sides of $6$ units, $8$ units, and $10$ units. The width of a rectangle, whose area is equal to the area of the triangle, is $4$ units. What is the perimeter of this rectangle, in units
Answer:
20
Step-by-step explanation:
Given that the area of the rectangle is equal to that of the triangle
Area of triangle $ABC$
= 1/2 (bh)
Given that the sides of the triangle are $6$ units, $8$ units, and $10$ units,
The base and the heights are $6$ units and $8$ units. The $10$ units is the hypotenuse
From Pythagoras theorem,
6^2 + 8^2 = 10^2
Therefore, area of triangle
=1/2 (6 × 8)
= $24$ units^2
Area of rectangle = L × W
Where L = Length, W = Width
Area of the rectangle = area of triangle
L × 4 = 24
L= 24/4
L = $6$ Units
Perimeter of rectangle
=2 (L + B)
= 2(6 + 4)
= $20$ Units
Answer:
20
Step-by-step explanation:
We use the Pythagorean Theorem to verify that triangle $ABC$ is a right triangle, or we recognize that $(6,8,10)$ is a multiple of the Pythagorean triple $(3,4,5)$. The area of a right triangle is $\frac{1}{2}bh$ where $b$ and $h$ are the lengths of the two legs, so the area of triangle $ABC$ is $\frac{1}{2}(6)(8)=24$. If the area of the rectangle is $24$ square units and the width is $4$ units, then the length is $\frac{24}{4}=6$ units. That makes the perimeter $6+6+4+4=\boxed{20}$ units.
3 friends share the cost of a gift. The gift costs $70, but the store manager takes $10 off the market price. What amount should they each pay? What is the answer
Answer:
Amount each friend pays for the gift = $20
Step-by-step explanation:
Market price of a gift = $70
The store manager takes $10 off the market price.
Marked down amount = $10
New cost price = Marked price - Marked down amount [tex]=\$70-\$10=\$60[/tex]
The cost of the gift is divided among three friends.
This means that the cost of gift which is $60 is divided by three to get each one's contribution in the gift.
∴ Amount each friend pays for the gift [tex]=\frac{60}{3}=\$20[/tex]
The bacterial strain Acinetobacter has been tested for its adhesion properties, which is believed to follow a normal distribution. A sample of five measurements gave readings of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm. Assume that the standard deviation is known to be 0.7 dyne-cm_2 and that the scientists are interested in high adhesion (at least 2.66 dyne-cm^2)(a) Should the alternative hypothesis be one-sided or two-sided? Write down the null and alternative hypotheses.(b) Based on your answer to part (a), test the hypothesis to see if the mean adhesion is at least 2.66 dyne-cm_2 (Use the p-value approach) What can be concluded?
Answer:
a) Alternative hypothesis should be one sided. Because Null and Alternative hypotheses are:
[tex]H_{0}[/tex]: μ=2.66 dyne-cm.
[tex]H_{a}[/tex]: μ<2.66 dyne-cm.
b) the hypothesis that mean adhesion is at least 2.66 dyne-cm is true
Step-by-step explanation:
Let μ be the mean adhesion in dyne-cm.
a)
Null and alternative hypotheses are:
[tex]H_{0}[/tex]: μ=2.66 dyne-cm.
[tex]H_{a}[/tex]: μ<2.66 dyne-cm.
b)
First we need to calculate test statistic and then the p-value of it.
test statistic of sample mean can be calculated as follows:
t=[tex]\frac{X-M}{\frac{s}{\sqrt{N} } }[/tex] where
X is the sample mean M is the mean adhesion assumed under null hypothesis (2.66 dyne-cm) s is the standard deviation known (0.7 dyne-cm_2)N is the sample size(5)Sample mean is the average of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm, that is [tex]\frac{2.69+5.76+2.67+1.62+4.12}{5}[/tex] ≈ 3.37
using the numbers we get
t=[tex]\frac{3.37-2.66}{\frac{0.7}{\sqrt{5} } }[/tex] ≈ 2.27
The p-value is ≈ 0.043. Taking significance level as 0.05, we can conlude that sample proportion is significantly higher than 2.66 dyne-cm.
Thus, according to the sample the hypothesis that mean adhesion is at least 2.66 dyne-cm is true
PLEASE HELP!!!! WILL GIVE BRAINLIEST!!!!!!!
Matthew picks flowers and sells them to tourists. The function s(t) approximates how many flowers Matthew picks per hour. The function W(h) represents how hours per week Matthew spends picking flowers. What are the units of measurement for the composite function s(W(h))?
a. flowers/hour
b. hours/week
c. flowers/week
d. weeks/flower
Answer:
c Flower/ Week
Step-by-step explanation:
think about it like this
hours (flowers)
____. x. _______
Weeks hours
Both of the hours cancel out similar to unit conversions in chemistry and you are left with flowers per week. since the value of flowers you get per hour you work, and x is dependant on the amount of hours you work in a week. These two functions work in conjuction to give flowers per week picked, this crossing off happens diagonally from left down to the right.
The units of measurement for the composite function s(W(h)) is Option(C) flowers/week.
What is the given unit of the composite function ?Given that the function s(t) approximates how many flowers Matthew picks per hour.
Unit of function s(t) is flowers/hours.
Also given that the function W(h) represents how many hours per week Matthew spends picking flowers.
Unit of W(h) = hours/week .
The composite function s(W(h)) will have unit -
= Flowers/hours * hours/week
= Flowers/week
The units of measurement for the composite function s(W(h)) is Option(C) flowers/week.
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Julia makes friendship bracelets. She was recently given nine bracelets from different people. At Christmas, she plans to give away ome third of her bracelets. She will be left with 23. With how many did she start?
Answer:
The number of bracelets with she start are 48.
Step-by-step explanation:
Given:
Julia was recently given 9 bracelets. She plans to give 1/3 of her bracelets. She will be left with 23.
Now, we need to find with how many did she start.
Let the bracelets with she start be [tex]x[/tex].
She plans to give [tex]\frac{1}{3}ofx[/tex] = [tex]\frac{x}{3}[/tex].
According to question:
[tex]x-9-\frac{x}{3}=23[/tex]
On solving the equation:
[tex]\frac{3x-27-x}{3} =23[/tex]
Multiplying both sides by 3 we get:
[tex]3x-27-x=69[/tex]
[tex]2x-27=69[/tex]
Adding both sides by 27 and then dividing by 2 we get:
[tex]x=48[/tex]
Therefore, the number of bracelets with she start are 48.
Please help!!
What is the equation of the line that represents the initial climb?
Answer:
y = (5/2)x
Step-by-step explanation:
The rise is 5 squares and the run is 2 squares between the two marked points. That means the slope is 5/2. The line starts at (0, 0), so the equation is ...
y = (5/2)x
Which of the following is NOT a requirement to conduct a goodness-of-fit test? Question 1 options: a) For each category, the observed frequency is at least 5. b) The sample data consist of frequency counts for each of the different categories c) The sample is simple random sample. d) For each category, the expected frequency is at least 5.
The statement that is NOT a requirement to conduct a goodness-of-fit test is (a) For each category, the observed frequency is at least 5
How to determine the false statement?To conduct a goodness-of-fit test, only the expected frequency must be at least 5.
This means that it is false that the observed frequency is at least 5
Hence, the statement that is NOT a requirement to conduct a goodness-of-fit test is (a)
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Miguel took a taxi to the beach 23 miles from his hotel. After his day at the beach, he took a bus back for 11 miles. Then a friend pick him up and drove another 12 miles towards the hotel. How many more miles does Magill need to go until he is back at his hotel
Answer:
0 additional miles
Step-by-step explanation:
Miguel travelled from his hotel to the beach by taxi. Total distance travelled by Miguel during the journey is 23 miles.
During the return journey, he travelled by a bus for 11 miles to an intermediate location.
From this point his friend picked him up and drove him towards the hotel for 12 miles.
So the total distance travelled by Miguel during the return journey = 11 + 12 = 23 miles
But this is the same distance as the onward journey. So at the end, Miguel is back at the hotel and there are 0 additional miles that he needs to cover.
Answer: 0 miles
Step-by-step explanation:
Miguel took a taxi to the beach 23 miles from his hotel. After his day at the beach, he took a bus back for 11 miles. This means at this point, his distance from his hotel is 23 - 11 = 12 miles. Then a friend pick him up and drove another 12 miles towards the hotel. This means that they covered the remaining 12 miles from the hotel. Therefore
Miguel needs to go 12 - 12 = 0 miles until he is back at his hotel.
A high school drama club is selling tickets to their show. There is a maximum of 400 tickets. The tickets cost $10 (if bought before day of show) and $15 (if bought day of show). Let x represent the number of tickets sold before the day of the show and y represents the number of tickets sold the day of the show. To meet the expenses of the show, the club must sell at least $3500 worth of tickets. The club sells 300 tickets before the day of the show. Is it possible to sell enough additional tickets on the day of the show to meet the expenses of the show? Justify your answer.
Answer:
yes
Step-by-step explanation:
The club can sell 100 more tickets before they reach their maximum. If they sell those at the "day-of" price, they will have additional revenue of ...
100 × $15 = $1500
Then their total revenue would be ...
300 × $10 + $1500 = $4500 . . . . more than enough to meet expenses.
_____
To make up the additional $500 they need, the drama club only needs to sell ...
ceiling($500/$15) = 34 . . . tickets at the "day-of" price.
helppppppppppppppppppp
Answer:
Option D: 2 . cos(90 + x) = -2a
Step-by-step explanation:
Given that:
sin x = a --------- eq1
As we know that trignometry says:
cos(90 + x) = -sinx-------- eq2
In option two we are given that:
cos(90 + x) = -2a ---------- eq3
So by equating both sides of eq2 and eq3:
-2a = -2sinx
By cancelling -2 from both sides we get:
sinx = a
That is given in eq1
hence proved
i hope it will help you!
PLEASE HELP URGENT!!! 90 POINTS
One zero of the polynomial function f(x) = x3 − x2 − 20x is x = 0. What are the zeros of the polynomial function?
\Given :
x^{3} +x^{2} -20x
Solution:
x^{3} +x^{2} -20x
taking x common from the given polynomial
⇒x(x^{2} +x-20)=0
⇒x(x(x+5)-4(x+5))=0
⇒x(x+5)(x-4)=0
⇒ x=0 , x+5=0 , x-4=0
⇒x = 0 , x = -5 , x = 4
The zeros of the polynomial function f(x) = x³ - x² - 20x are x = 0, x = 5, and x = -4.
To find the remaining zeros, we can use polynomial division or factoring techniques. Since the given polynomial is already in its factored form, we can use the zero-product property to find the other zeros.
The given polynomial f(x) = x³ - x² - 20x can be factored as
f(x) = x(x² - x - 20).
Now, we have two factors: x and (x² - x - 20).
To find the zeros of the second factor, we can set it equal to zero and solve for x. So, we have
x² - x - 20 = 0.
We can factor this quadratic equation by splitting the middle term:
x² - x - 20 = (x - 5)(x + 4).
Now, we have three factors: x, (x - 5), and (x + 4). To find the zeros, we set each factor equal to zero and solve for x:
x = 0 (given) x - 5 = 0 => x = 5 x + 4 = 0 => x = -4
Therefore, the zeros of the polynomial function
f(x) = x³ - x² - 20x are x = 0, x = 5, and x = -4.
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The distance from the centroid of a triangle to its vertices are 16cm, 17cm, and 18cm. What is the length of the shortest median
Answer:
[tex]24[/tex] [tex]\text{cm}[/tex]
Step-by-step explanation:
Given: The distance from the centroid of a triangle to its vertices are [tex]16\text{cm}[/tex], [tex]17\text{cm}[/tex], and [tex]18\text{cm}[/tex].
To Find: Length of shortest median.
Solution:
Consider the figure attached
A centroid is an intersection point of medians of a triangle.
Also,
A centroid divides a median in a ratio of 2:1.
Let G be the centroid, and vertices are A,B and C.
length of [tex]\text{AG}[/tex] [tex]=16\text{cm}[/tex]
length of [tex]\text{BG}[/tex] [tex]=17\text{cm}[/tex]
length of [tex]\text{CG}[/tex] [tex]=18\text{cm}[/tex]
as centrod divides median in ratio of [tex]2:1[/tex]
length of [tex]\text{AD}[/tex] [tex]=\frac{3}{2}\text{AG}[/tex]
[tex]=\frac{3}{2}\times16[/tex]
[tex]=24\text{cm}[/tex]
length of [tex]\text{BE}[/tex] [tex]=\frac{3}{2}\text{BG}[/tex]
[tex]=\frac{3}{2}\times17[/tex]
[tex]=\frac{51}{2}\text{cm}[/tex]
length of [tex]\text{CF}[/tex] [tex]=\frac{3}{2}\text{CG}[/tex]
[tex]=\frac{3}{2}\times18[/tex]
[tex]=27\text{cm}[/tex]
Hence the shortest median is [tex]\text{AD}[/tex] of length [tex]24\text{cm}[/tex]
Tim is looking at two websites that allow customers to print their own designs on T-shirts. One website charges $24 per T-shirt plus $8 shipping. The other website uses the equation C = 22 n + 12 C=22n+12 to find the total cost, C C, of printing on T-shirts. What is the difference in the cost of each website if Tim orders 10 T-shirts?
Answer: The difference is $16
Step-by-step explanation:
n will equal the amount of t-shirts bought
Website 1's Costs: c = 24n + 8
Website 2's cost: c = 22n + 12
Then, we substitute 10 for n
c = 24(10) + 8
c = 240 + 8
c = 248
c = 22(10) + 12
c = 220 + 12
c = 232
248 - 232 = 16
The difference between the total cost of the first website and that of the second based on the given function will be $16.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given,
On the first website,
Cost to buy 10 T-shirts.
C = 24(10) + 8
C = 240 + 8
C = $248
The second website
The total cost to buy 10 T-shirts
C = 22(10) + 12
C= 220 + 12
C= $232
The differnce $248 - $232 = $16
Hence "The difference between the total cost of the first website and that of the second based on the given function will be $16".
For more about the function,
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Express the confidence interval 0.333 less than p less than 0.555 in the form Modifying Above p with caret plus or minus Upper E. Modifying Above p with caret plus or minus Upper E equals nothing plus or minus nothing
Answer: = [tex]0.444\pm 0.111[/tex]
Step-by-step explanation:
The confidence interval for population proportion(p) is given by :-
[tex]\hat{p}-E<p<\hat{p}+E[/tex] (1)
It is also written as : [tex]\hat{p}\pm E[/tex] (*)
The given confidence interval for population proportion :
[tex]0.333<p<0.555[/tex] (2)
Comparing (1) and (2) , we get
Lower limit = [tex]\hat{p}-E=0.333[/tex] (3)
Upper limit = [tex]\hat{p}+E=0.555[/tex] (4)
Adding (3) and (4) , we get
[tex]2\hat{p}=0.888\\\Rightarrow\ \hat{p}=\dfrac{0.888}{2}=0.444[/tex]
Put value of [tex]\hat{p}=0.444[/tex] in (2) , we get
[tex]0.444+E=0.555\\\\\Rightarrow\ E=0.555-0.444=0.111[/tex]
Put values of [tex]\hat{p}=0.444[/tex] and E= 0.111 in (*) , we get
Required form = [tex]0.444\pm 0.111[/tex]
The confidence interval 0.333 to 0.555 can be written in the form 0.444 +/- 0.111 This helps to clearly represent the sample proportion and its margin of error.
The confidence interval 0.333 less than p less than 0.555 can be expressed in the form Modifying Above p with caret plus or minus Upper E. To do this, we need to find the middle point of the interval, which represents the sample proportion and the margin of error (E").
Find the midpoint:The confidence interval can be written as 0.444 plus or minus 0.111.
The mean score of a placement exam for entrance into a math class is 80, with a standard deviation of 10. Use the empirical rule to find the percentage of scores that lie between 60 and 80. (Assume the data set has a bell-shaped distribution.)
Answer:
47.5%
Step-by-step explanation:
In his suitcase, Jack has 3 shirts, 4 pants, 2 socks (pairs of socks), and 2 shoes (pairs of shoes). How many unique ways can Jack get fully dressed? Show your work and explain.
Answer:
48
Step-by-step explanation:
the number of shirts are 3, number of pants 4, number of socks pairs 2 and 2 pairs of shoes.
first lets start with shirts and pants, number of unique combinations are,
(for each shirt there are 4 different pant combinations) = [tex](3)(4)[/tex]
=12
similiarly for each shirt pant pair there are 2 shoes and 2 socks pairs.
thus, total number of combinations are=
[tex](12)(2)(2)[/tex]
= 48