Which graph represents an exponential function? On a coordinate plane, a line curves upwards gradually. On a coordinate plane, a curve decreases, changes directions, and then decreases again. On a coordinate plane, a line is level and then curves upwards rapidly. On a coordinate plane, 2 curves mirror each other in quadrants 1 and 3.
Answers
The options are not clear but we can describe exponential function as follows
Exponential function are of the form
[tex]y = b^x \; where\; b >0 = Exponentially\; Growing\\b<0 \; Exponentially\; Decaying \\\\x = Exponent[/tex]
The exponential functions are curved upwards gradually (figure attached )
Figure 1 (graph attached ) Shows the graph of function
[tex]y = 2^x[/tex]
We can conclude that exponential function is a monotonous function and
depending upon the value of b the exponential function is either continuously increasing or continuously decreasing
[tex]y = -3^x[/tex]
as shown by Figure 2 (figure attached )
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Answer:
It's D
Hopefully this helps someone :D
Related Questions
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?
Answers
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".
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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) .
Answers
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.
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
Answers
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:(0.333 + 0.555) / 2 = 0.444.
= p with caretCalculate the margin of error:
(0.555 - 0.333) / 2 = 0.111.
= Upper E
The confidence interval can be written as 0.444 plus or minus 0.111.
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
Answers
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 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.
Answers
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.
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?
Answers
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.
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
Answers
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.
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?
Answers
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:
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
Answers
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]
Based on counting the number of galaxies in a small patch of the sky and multiplying by the number of such patches needed to cover the entire sky, the total number of galaxies in the observable universe is estimated to be approximately
A) 100 million.
B) 100 billion.
C) 1 billion.
D) 1 trillion.
E) 10 billion.
Answers
Answer:
100 billion
Step-by-step explanation:
Some astronauts reveals that there are 100 billion galaxies in the universe.
The distance from the centroid of a triangle to its vertices are 16cm, 17cm, and 18cm. What is the length of the shortest median
Answers
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]
If 40% of a number is 32, what is 25% of that number?
Answers
Answer:
I think that the answer is 24
Answer:
The number is 80. 25% of that number is = 20.
Step-by-step explanation:
The radius of a circle is increased from 8.008.00 to 8.038.03 m. Estimate the resulting change in area, and then express the estimate as a percentage of the circle's original area. The estimated change in area is nothing msquared2.
Answers
Answer:
Step-by-step explanation:
The area of a circle is expressed as
Area = πr^2
Where r = radius of the circle
π = constant = 3.14
The radius of a circle is increased from 8.00800 to 8.03803 m. This means that the original radius of the circle is 8.00800 and the new radius of the circle is 8.03803
Area of original circle =
3.14 × 8.00800^2 = 201.36212096
Area of new circle =
3.14 × 8.03803^2 = 202.87516852203
Increase in area = 202.87516852203 - 201.36212096
= 1.51304756203
Expressing the change as a percentage, it becomes
1.51304756203/201.36212096 ×100
Percentage change = 0.75 %
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
Answers
Answer:
Step-by-step explanation: See annex
The figures are in feet
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?
Answers
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.
The monthly output P of a light bulb factory is given by the formula P = 450LK, where L is the amount invested in labor and K the amount invested in equipment (in thousands of dollars). If the company needs to produce 4,000 units per month, how should the investment be divided among labor and equipment to minimize the cost of production? The cost of production is L + K. (Round your answers to the nearest cent.)investment in labor _______ $investment in equipment ________$
Answers
Answer:
C(p) = 4,96 (in thousands of dollars)
l = 2980 $ invest in labor
k = 2980 $ invest in equipment
Step-by-step explanation:
Information we have:
Monthly output P = 450*l*k ⇒ k = P/450*l
But the production need to be 4000
Then k = 4000/450*l
Cost of production = l * k (in thousands of dollars)
C(l) = l + 4000/450*l
Taking derivatives (both members of the equation)
C´(l) = 1 - 400 /45*l² ⇒ C´(l) = 0 ⇒ 1 - 400/45l² = 0
45*l² - 400 = 0 ⇒ l² = 400/45
l = 2.98 (in thousands of dollars)
l = 2980 $ And
k = 400/45*l ⇒ k 400/45*2.98
k = 2.98 (in thousands of dollars)
C(p) = l + k
C(p) = 2980 + 2980
C(p) = 5960 $
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?
Answers
\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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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
Answers
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:
Please help!!
What is the equation of the line that represents the initial climb?
Answers
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
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
Answers
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
Please please help me with this
Answers
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.
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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
Answers
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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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.
Answers
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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4^1/2 equals 2. Why? Show steps and explain
Answers
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
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.
Answers
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.
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?
Answers
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
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
Answers
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.
Serious answers only. Do not answer if you dont know please!How does the graph of the circle described by x^2 + (y-7)^2 = 49 change when its equation is changed to (x +5)^2 + (y-4)^2 =64. Select each correct answer. The circles radious increases, The circle moves up, The circle moves left, The circles radious decreases, The circle moves down, The circle movea right.
Answers
Answer:
The circles radious increases The circles moves left The circles moves downStep-by-step explanation:
The equation of a circle can be written as [tex](x-a)^2+(y-b)^2=r^2[/tex], where "r" is the radious, and (a,b) are the coordenates in the axis x and b respectively.Then, in the first circle the coordenates are (0,7), which means that the circle will be center there, and the radious is 7 ([tex]\sqrt{49}[/tex]).The second circle have different coordenates: (-5,4), which means that the circle has moved left (from 0 to -7 in the x axis) and down (from 7 to 4 in the y axis). Additionally, its radious has increased from 7 ([tex]\sqrt{49}[/tex], from 8 ([tex]\sqrt{64}[/tex]).See the attached figure please.Then, the correct answers are:The circles radious increases (from r=7 to r=8)The circles moves left (from x=0 to x=-5)The circles moves down (from y=7 to y=4)helppppppppppppppppppp
Answers
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!
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.
Answers
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