Answer: 12 Tbsp
Step-by-step explanation:
Note: 1 Tbsp = 3 tsp
2 tsp x 21 = 42 tsp
42 tsp ÷ 3 = 12 Tbsp
The owner of a music store gathered data from several schools about the number of students in their concert and marching bands. The scatter plot shows the data she gathered and the line of best fit. The equation of the line of best fit is y = 0.677x + 1.77. Based on the line of best fit, approximately how many students are predicted to be in the marching band at a school with 35 students in the concert band?
Answer:
25 students
Step-by-step explanation:
Given the equation of the best line of fit, [tex] y = 0.677x + 1.77 [/tex] , the number of students predicted to be in the matching band, if we have 35 students in the concert band, can be approximated by plugging in 35 as "x" in the equation of the best line of fit, and solve for "y". y would give us the predicted number of students to expect in the marching band.
[tex] y = 0.677(35) + 1.77 [/tex]
[tex] y = 23.695 + 1.77 [/tex]
[tex] y = 25.465 [/tex]
The approximated number of to be in the marching band, with 35 students in the concert band is roughly 25 students.
Answer:25 students
Step-by-step explanation:
Intelligence quotients (IQs) measured on the Stanford Revision of the Binet Simon Intelligence Scale are normally distributed with a mean of 100 and a standard deviation of 16. Determine the percentage of people who have an IQ between 115 and 140.
Answer:
the percentage of people who have an IQ between 115 and 140 is 16.79%
Step-by-step explanation:
From the information given:
We are to determine the percentage of people who have an IQ between 115 and 140.
i.e
P(115 < X < 140) = P( X ≤ 140) - P( X ≤ 115)
[tex]P(115 < X < 140) = P( \dfrac{X-100}{\sigma}\leq \dfrac{140-100}{16})-P( \dfrac{X-100}{\sigma}\leq \dfrac{115-100}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq \dfrac{140-100}{16})-P( Z\leq \dfrac{115-100}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq \dfrac{40}{16})-P( Z\leq \dfrac{15}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.9375)[/tex]
[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.938)[/tex]
From Z tables :
[tex]P(115 < X < 140) = 0.9938-0.8259[/tex]
[tex]P(115 < X < 140) = 0.1679[/tex]
Thus; we can conclude that the percentage of people who have an IQ between 115 and 140 is 16.79%
Using the normal distribution, it is found that 82.02% of people who have an IQ between 115 and 140.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of [tex]\mu = 100[/tex].The standard deviation is of [tex]\sigma = 15[/tex].The proportion of people who have an IQ between 115 and 140 is the p-value of Z when X = 140 subtracted by the p-value of Z when X = 115, hence:
X = 140:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 100}{16}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a p-value of 0.9938.
X = 115:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{115 - 100}{16}[/tex]
[tex]Z = -0.94[/tex]
[tex]Z = -0.94[/tex] has a p-value of 0.1736.
0.9938 - 0.1736 = 0.8202.
0.8202 = 82.02% of people who have an IQ between 115 and 140.
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An appliance company determines that in order to sell x dishwashers, the price per dishwasher must be p = 420 - 0.3x. It also determines that the total cost of producing x dishwashers is given by C(x) = 5000 + 0.3x2. How many dishwashers must the company produce and sell in order to maximize profit? g
The company must produce and sell 350 dishwashers in order to maximize profit.
How to determine the number of dishwashersTo determine the number of dishwashers the company must produce and sell in order to maximize profit, we need to find the value of x that corresponds to the maximum point of the profit function.
The profit (P) is given by the equation:
P(x) = Revenue - Cost
The revenue is calculated by multiplying the price per dishwasher (p) by the number of dishwashers sold (x):
Revenue = p * x
The cost is given by the function C(x):
Cost = C(x)
Therefore, the profit function can be expressed as:
P(x) = p * x - C(x)
Substituting the given expressions for p and C(x):
P(x) = (420 - 0.3x) * x - (5000 + 0.3x²)
Expanding and simplifying the equation:
P(x) = 420x - 0.3x² - 5000 - 0.3x²
Combining like terms:
P(x) = -0.6x² + 420x - 5000
To find the value of x that maximizes profit, we need to find the vertex of the quadratic function. The x-coordinate of the vertex can be determined using the formula:
x = -b / (2a)
In our case, a = -0.6 and b = 420:
x = -420 / (2 * -0.6)
x = -420 / (-1.2)
x = 350
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350 dishwashers must the company produce and sell in order to maximize profit.
Maxima means a point at which the function attains the maximum value.
Given the following information:
Price per dishwasher, p = 420 - 0.3x
Total cost of producing x dishwashers, C(x) = 5000 + 0.3x2
Profit= Total Selling price- Total Cost Price
Total Selling price of x dishwasher, S.P= xp
S.P=x(420 - 0.3x)
S.P=420x - 0.3x²
Profit= 420x - 0.3x² - ( 5000 + 0.3x²)
Profit= 420x - 0.3x² - 5000 - 0.3x²
Profit= -0.6x²+420x-5000
So, profit, f(x)=-0.6x²+420x-5000
To determine the value of x so that maximum profit is possible:
1. Calculate the first derivative of profit function and calculate the value of x by equating it to zero.
2. Select that value of x for which the profit function attains the maximum value, to check the maxima calculate 2nd derivative, if it gives a negative value for the value of x. Then, x is the point of maxima for the given function.
[tex]f(x)=-0.6x^2+420x-5000\\f\prime(x)=-1.2x+420\\f\prime(x)=0\\-1.2x+420=0[/tex]
Calculating the value of x by transposing,
x=420/1.2
x=350
To check maxima, calculating second derivative.
[tex]f\prime(x)=-1.2x+420=0\\f\prime\prime(x)=-1.2[/tex]
2nd derivative is negative, it means that x=350 is the point of maxima.
Thus, a company must produce and sell 350 dishwashers in order to maximize profit.
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A special tool manufacturer has 50 customer orders to fulfill. Each order requires one special part that is purchased from a supplier. However, typically there are 2% defective parts. The components can be assumed to be independent. If the manufacturer stocks 52 parts, what is the probability that all orders can be filled without reordering parts
Answer:
0.65463
Step-by-step explanation:
From the given question:
It is stated that 2% of the parts are defective (D) out of 50 parts
Therefore the probability of the defectives;
i.e p(defectives) = [tex]\dfrac{N(D)}{N(S)}[/tex]
p(defectives) = [tex]\dfrac{2}{50}[/tex]
p(defectives) = 0.04
The probability of the failure is the P(Non-defectives)
p(Non-defectives) = 1 - P(defectives)
p(Non-defectives) = 1 - 0.04
p(Non-defectives) = 0.96
Also , Let Y be the number of non -defective out of the 52 stock parts.
and we need Y ≥ 50
P( Y ≥ 50) , n = 52 , p = 0.96
P( Y ≥ 50) = P(50 ≤ Y ≤ 52) = P(Y = 50, 51, 52)
= P(Y = 50) + P(Y =51) + P(Y=52) (disjoint events)
P(Y = 50) = [tex](^{52}_{50}) ( 0.96)^{50}(1-0.96)^2[/tex]
[tex]P(Y = 50) = 1326 (0.96)^{50}(0.04)^2[/tex]
P(Y = 50) = 0.27557
P(Y = 51) =[tex](^{52}_{51}) ( 0.96)^{51}(1-0.96)^1[/tex]
[tex]P(Y = 51) = 52(0.96)^{51}(0.04)^1[/tex]
P(Y = 51) = 0.25936
(Y = 52) =[tex](^{52}_{52}) ( 0.96)^{52}(1-0.96)^0[/tex]
[tex]P(Y = 52) = 1*(0.96)^{52}(0.04)^0[/tex]
P(Y = 52) = 0.1197
∴
P(Y = 50) + P(Y =51) + P(Y=52) = 0.27557 + 0.25936 + 0.1197
P(Y = 50) + P(Y =51) + P(Y=52) = 0.65463
What additional information do you need to prove △ABC ≅ △DEF by the SSS Postulate? A. BC = EF B. AB = DE C. AC = DF
Answer:
AC = DF
Step-by-step explanation:
The SSS Postulate occurs when all three corresponding pairs of sides are congruent, therefore, the only missing pair is AC = DF.
Find f o g if f(x) = 3x^2 - 12 and g(x) = 5x + 3. f(g(x)) = Choices: a. 35x2 - 70 b. 15x2 - 30x + 9 c. 75x2 + 45x - 10 d. 75x2 + 90x + 15
Answer:
d.
Step-by-step explanation:
[tex]f(g(x))=3(g(x))^2-12=3(5x+3)^2-12=3(25x^2+30x+9)-12=75x^2+90x+27-12=75x^2+90x+15[/tex]
ANZ Corporation manufactures a product available in two models: ABC, and PQR. Despite the growing popularity of the PQR model, company profits have been declining steadily, and management is beginning to think there might be a problem with their costing system. Material and Labour costs are given below:
ABC PQR
Sales demand 30000 15000
Direct material cost/unit $45 $60
Direct labour cost/unit $30 $40
Production overheads are $600,000 each month.
These are absorbed on a sales demand basis.
Calculate the full production costs for ABC and PQR, using traditional costing method
Answer:
The full production costs are:
ABC = $22,900,000
PQR = $1,700,000
Step-by-step explanation:
Traditional costing method is a costing method that allocates or applies overhead based on a particular metric determined by a company. It therefore add both direct cost of production and production overheads absorbed to obtain the full cost of production.
Since production overheads in this question is absorbed on demand sales basis, the full production costs for ABC and PQR can be computed as follows:
ANZ Corporation
Computation of Full Production Costs
Particulars ABC PQR
Sales demand 30,000 15,000
Cost $ $
Direct cost:
Direct materials cost (w.1) 1,350,000 900,000
Direct labor cost (w.2) 900,000 600,000
Total direct cost 22,500,000 1,500,000
Indirect cost:
Production overhead (w.3) 400,000 200,000
Full production cost 22,900,000 1,700,000
Workings:
w.1: Computation of direct material cost
Direct material cost = Direct material cost per unit * Sales demand
Therefore;
ABC Direct material cost = $45 * 30,000 = $1,350,000
PQR Direct material cost = $60 * 15,000 = $900,000
w.2: Computation of direct labor cost
Direct labor cost = Direct labor cost per unit * Sales demand
Therefore;
ABC Direct material cost = $30 * 30,000 = $900,000
PQR Direct material cost = $40 * 15,000 = $600,000
w.3: Allocation of production overhead
Production overheads allocated to a model = Production overheads * (Model's Sales Demand / Total Sales demand)
Total Sales demand = 30,000 + 15,000 = 45,000
Therefore, we have:
Production overhead allocated to ABC = $600,000 * (30,000 / 45,000) = $400,000
Production overhead allocated to PQR = $600,000 * (15,000 / 45,000) = $200,000
01:
Which expression can be used to model the phrase the sum of three and a number?
Answer:
3+x
Step-by-step explanation:
sum= addition
a number= a number
Answer:
3+x
eplanation
easy khan academy math. please answer asap
Answer:
[tex]\boxed{\sf B \ and \ C}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions to solve.
[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(60)=\frac{5.2}{KL}[/tex]
[tex]\sf KL=\frac{5.2}{sin(60)}[/tex]
[tex]\sf sin(90-60)=\frac{3}{KL}[/tex]
[tex]\sf KL=\frac{3}{sin(90-60)}[/tex]
Determine whether the outcome of the following hypothesis test was a correct decision, a type I error, or a type II error. Claim: "Less than 40% of college students graduate with student loan debt." A hypothesis test of this claim resulted in the decision to reject H0. The actual percentage of college graduates with student loan debt is 45%.
Answer:
Step-by-step explanation:
The claim: "Less than 40% of college students graduate with student loan debt."
The null hypothesis: more than 40% of college students graduate with student loan debt." p >= 40%
If the actual percentage of college graduates with student loan debt is 45%. The researcher was supposed to fail to reject the null but since he rejected it when it was actually true, it is a type I error.
A type I error occurs when the research rejects the null when it is actually true.
express 11011 in base two
Answer:
27
Step-by-step explanation:
Hello,
11011 in base 2 is
1 * 16 + 1 * 8 + 0 * 4 + 1 * 2 + 1 in base 10
which is 16 +8+2+1=27
Do not hesitate if you have any question
4x + 12 = 20y Solve for x.
Answer:
x=5y-3
Step-by-step explanation:
[tex]4x+12=20y\\4x=20y-12\\x=\frac{20y-12}{4} \\x=\frac{20y}{4}- \frac{12}{4} \\x=5y-3[/tex]
write the equation for taking away 5 from x gives 10
Answer:
[tex]\boxed{\sf x - 5 = 10}[/tex]
Step-by-step explanation:
Taking away 5 from x ⇒ subtracting 5 from x
[tex]\large {\sf x - 5[/tex]
Gives 10 ⇒ result is 10
[tex]\large {\sf x - 5 = 10[/tex]
easy math please help!
Answer:
[tex]\boxed{ \sf 41.81}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions.
[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(?)=\frac{2}{3}[/tex]
[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]
[tex]\sf ?= 41.81031489...[/tex]
Answer:
[tex]\boxed{41.81}[/tex]
Step-by-step explanation:
∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.
The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).
However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.
Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.
What expression be used to add 3/4 + 1/6
Answer:
11 / 12 or 0.9167
Step-by-step explanation:
Given:
3/4 + 1/6
Find:
Value with expression
Computation:
"3/4 added to number 1/6"
3/4 + 1/6
By taking LCM
[9 + 2] / 12
11 / 12 or 0.9167
The equation to the graph is y = -1/2 x - 3
Answer:
Hope it helps <3
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▹ Answer
Use a graphing calculator. Attached is an image.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
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What scenario depicts two independent events
Step-by-step explanation:
A t
eacher is calling on students to present their reports. He calls on Mario first and then chooses the next presenter from the remaining students. The girls’ basketball team is playing against the boys’ basketball team. The coach chooses a captain for the girls’ team and then chooses a captain for the boys’ team. Yasmin is picking flowers from a garden to create a bouquet. She picks a flower, keeps it for the bouquet, and then she picks another. Felipe is making a dentist appointment. First he chooses the day for his appointment, and then he chooses the time from the available openings.
Answer:
A.The school play opens tonight and it is raining.
B.Neva is hungry and she buys a snack from the concession stand.
C. Ari chooses a partner for a group project and then Ezekial chooses a partner from the remaining classmates.
D.Luka paints during school and he stains his shirt.
Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (5 points)
Answer:
4x² + 30x - 2 = 0
Step-by-step explanation:
Given:
Area = 58 square feet
Width = 7 feet
Length = 8 feet
Since the area is 58, writing the equation, we have:
(8 + 2x)(7 + 2x) = 58
Now expand the equation:
56 + 16x + 14x + 4x² = 58
56 + 30x + 4x² = 58
Collect like terms:
30x + 4x² + 56 - 58 = 0
30x + 4x² - 2 = 0
Rearrange the equation to a proper quadratic equation:
4x² + 30x - 2 = 0
The quadratic equation that can be used to determine the thickness of the frame, x is 4x² + 30x - 2 = 0
Help ASAP!!!!
Solve for X. Round to the nearest hundredth if necessary.
Answer:
11.47Step-by-step explanation:
Given : A right triangle
To do : Solve for x
Solution,
[tex]cos \: 55 = \frac{x}{20} [/tex] ( by definition of cos function, adjacent / hypotenuse )
[tex]0.5736 = \frac{x}{20} [/tex]
multiply both sides of the equation by 20
[tex](0.5736) \times 20 = x[/tex]
Calculate the product
[tex]11.471 = x[/tex]
Swipe both sides of the equation
[tex]x = 11.471[/tex]
Round answer to nearest hundredth
[tex]x = 11.47[/tex]
Hope this helps...
Best regards!!
HEREEEEEEEEEEEEEElollll
Answer:
Hey there!
Your answer would be 4/50. The total times she drawed a purple tile was 4, and she drawed 50 times.
Hope this helps :)
Shawn has 25 coins, all nickels and dimes. The total value is $2.00. How many of each coin does he have ?
Answer:
[tex]\boxed{15 \ dime \ and \ 10 \ nickel \ coins}[/tex]
Step-by-step explanation:
1 dime = 10 cents
1 nickel = 5 cents
So,
If there are 15 dimes
=> 15 dimes = 15*10 cents
=> 15 dimes = 150 cents
=> 15 dimes = $1.5
Rest is $0.5
So, for $0.5 we have 10 nickels coins
=> 10 nickels = 10*5
=> 10 nickels = 50 cents
=> 10 nickel coins = $0.5
Together it makes $2.00
The line passing through points
(4,0) and (-2, 1) has a slope of?
A. -6
B. -1/6
C. 1/2
D. 2
E. 1/6
Answer:
b. -1/6
Step-by-step explanation:
slope = (difference in y)/(difference in x)
slope = (1 - 0)/(-2 - 4) = 1/(-6) = -1/6
Answer:
m = -1/6 = B
Step-by-step explanation:
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\ x_1=4\\ y_1=0\\ x_2=-2\\y_2=1.\\m = \frac{1-0}{-2-4} \\m = \frac{1}{-6}[/tex]
I NEED HELP ASAP choose one of the multiple choice
Answer:
B. Square both sides of the equation.
Step-by-step explanation:
You cannot do anything to the equation unless you square both sides to eliminate the square root on the left (squaring each individual term of the equation does not help; you need to square the entire square root to eliminate it).
Hope this helps!
You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a tail AND an even number on the die AND a card less than 5 (assume the ace is equal to 1) from the deck?
[tex]|\Omega|=2\cdot6\cdot52=624\\|A|=1\cdot3\cdot16=48\\\\P(A)=\dfrac{48}{624}=\dfrac{1}{13}[/tex]
Answer:
1/13
Step-by-step explanation:
help i will give you brailenst
Plz help this is an evil question
Answer:
18.9 units of fencing
Step-by-step explanation:
First find the perimeter
P = 2(l+w)
P = 2( 2.5+1.28)
P = 2( 3.78)
P =7.56m
We need 2.5 units of fencing for each meter
Multiply by 2.5
7.56*2.5
18.9 units of fencing
Answer:
Julio needs to purchase 18.9 units of fencing.
Step-by-step explanation:
I meter of the perimeter accounts for 2.5 units of fencing. Respectively 2 meters account for 2 times as much, and 3 meters account for 3 times as much of 2.5 units. Therefore, if we determine the perimeter of this rectangular garden, then we can determine the units of fencing by multiplying by 2.5.
As you can see this is a 2.5 by 1.28 garden. The perimeter would be two times the supposed length, added to two times the width.
2.5 x 2 + 1.28 x 2 = 5 + 2.56 = 7.56 - this is the perimeter. The units of fencing should thus be 7.56 x 2.5 = 18.9 units, or option d.
Please answer this correctly without making mistakes Please simplify the correct answer
Answer:
1/5 are towboats
Step-by-step explanation:
In order to find the answer, we need to find the total number of flag vessels. We can find this by adding all the categories together
30k + 10k + 10k= 50k
In total there are 50,000 flag vessels
Of those 50,000, 10,000 of them are tow boats
10,000/50,000 can be simplified to 1/5
1/5 are towboats
Answer:
1/5
Step-by-step explanation:
Well to find the fraction we first need to know the total amount of Flag Vessels.
30,000 + 10,000 + 10,000 = 50,000
If there are 10,000 towboats we can make the following fraction.
10,000/50,000
Simplified
1/5
Thus,
the answer is 1/5.
Hope this helps :)
A casino offers a game wherein a player can roll one six sided die. If the player rolls a 1or 2, they
win. If the player rolls a 3, 4, 5, or 6, they lose. If a player bets $2.00 and wins, they will be paid out
an additional $3.00. If they lose, they lose their initial $2.00. Find the expected value of the $2.00
bet.
Enter your answer rounded to the nearest cent and don't forget, expected values can be negative!
Answer:
Expected Value of $2:
Expected Value of $2:
Win, 0.3333 x $3 = $1
Plus
Loss, 0.6667 x -$2 = -$1.33
Expected value = ($0.33)
Step-by-step explanation:
Probability of a win = 2/6 = 0.3333
Probability of a loss = 4/6 = 0.6667
Expected Value of $2:
Win, 0.3333 x $3 = $1
Plus
Loss, 0.6667 x -$2 = -$1.33
Expected value = ($0.33)
The casino game player's expected value is computed by multiplying each of the possible outcomes by the likelihood (probability) of each outcome and then adding up the values. The sum of the values is the expected value, which amounts to a loss of $0.33.
f(x)=2x+1 and g(x)=3x2+4, find (f∘g)(−2) and (g∘f)(−2).
Answer:
Step-by-step explanation:
Fog=2(g)+1
2(3x+2+4)+1
2{3x+6)+1
6x+12+1
=6x+13
Fog(-2)=6(-2)+13
-12+13
=1
Gof=3(f)+2+4
=3(2x+1)+6
6x+3+6
=6x+9
Gof(-2)=6(-2)+9
-12+9
=-3
The height of a cylinder is 9.5 cm. The diameter is 1.5 cm longer than the height. Which is closest to the volume of the cylinder?
Answer:
853.8cm^3
Step-by-step explanation:
[tex]h = 9.5cm\\d = 1.5cm + 9.5 = 10.7\\r =d/2=10.7/2=5.35\\\\V = \pi r^2 h\\V = 3.14 \times (5.35)^2 \times 9.5\\\\V =853.8 cm^3[/tex]