At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before the customer adds the toppings. After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces. Which of the following graphs represents the acceptable weights for the frozen yogurt options?
Answers
So the answer will be the 3rd graph
Answer: Third graph represents the acceptable weights for the frozen yogurt options.
Step-by-step explanation:
Since we have given that
Number of ounces of frozen yogurt a machine fills cups with before the customer adds the toppings = 4
After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces.
So, it means the weight should be lie between 4 ounces and 7 ounces.
So, it can be written as [4,7].
4≤ x ≤7, here, x is the weight of frozen yogurt.
So, third graph represents the acceptable weights for the frozen yogurt options.
Related Questions
Complete parts (a) and (b) using the probability distribution below.
The number of overtime hours worked in one week per employee
Overtime hours
0 1 2 3 4 5 6
Probability
0.026 0.072 0.154 0.303 0.215 0.164 0.066
(a) Find the mean, variance, and standard deviation of the probability distribution.
Find the mean of the probability distribution.
μ = 3.4
σ2 = 2.0
σ = 1.4
Choose the correct answer below.
A.
An employee works an average of 2.0 overtime hours per week with a standard deviation of approximately 1.4 hours.
B.
An employee works an average 3.4 of overtime hours per week with a standard deviation of approximately 4 hours.
C.
An employee works an average of 1.4 overtime hours per week with a standard deviation of approximately 3.4 hours.
D.
An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.
Answers
μ = 0 + 0.072 + 0.304 + 0.909 + 0.86 + 0.82 + 0.396
μ = 3.361 ≈ 3.4
We need the value of ∑X² to work out the variance
∑X² = (0²×0.026) + (1²×0.072) + (2²×0.152) + (3²×0.303) + (4²×0.215) + (5²×0.164) + (6²×0.066)
∑X² = 0+0.072+0.608+2.727+3.44+4.1+2.376
∑X² = 13.323
Variance = ∑X² - μ²
Variance = 13.323 - (3.4)² = 1.763 ≈ 2
Standard Deviation = √Variance = √1.8 = 1.3416... ≈ 1.4
The correct answer related to the value of mean and standard deviation is the option D
An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.
The mean number of overtime hours worked is 3.4 with a standard deviation of approximately 1.4 hours, which corresponds to option D.
Explanation:The correct answer for the given probability distribution of overtime hours worked per employee in one week is D. An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.
To find the mean (μ) of the probability distribution, we multiply each possible value by its corresponding probability and then sum all these products. The mean of this distribution is given as 3.4, which is found by summing up the product of each value of overtime hours and its corresponding probability:
μ = (0 * 0.026) + (1 * 0.072) + (2 * 0.154) + (3 * 0.303) + (4 * 0.215) + (5 * 0.164) + (6 * 0.066) = 3.4
The variance (σ2) is calculated by taking each value's deviation from the mean, squaring it, multiplying by the probability, and summing all these values. The variance for this distribution is given as 2.0:
σ2 = Σ [(x - μ)2 * P(x)] = 2.0
And the standard deviation (σ) is simply the square root of the variance:
σ = √σ2 = 1.4
P(1+r)t Using the expression above, choose the correct answers for the new balance and the amount of interest earned in the following compound interest problem. $950 at 7% for 8 years, compounded annually. Total Amount = $ Interest Amount = $
Answers
Future value = accumulated amount, F = P(1+r)^t
P=principal
r=annual interest rate [compounded annually]
t=number of years of loan
Given:
P=950
r=0.07
t=8
F=950(1.07)^8
= 1632.28 (total amount)
Interest = total amount - principal
=1632.28 - 950
=682.28
Final answer:
The new balance after 8 years with an initial $950 at a 7% annual interest rate compounded annually is $1632.77, and the amount of interest earned is $682.77.
Explanation:
The compounded interest formula is P(1+r)^t, where P is the principal amount, r is the annual interest rate (in decimal form), and t is the time in years. To find the new balance and amount of interest earned for $950 at 7% for 8 years, compounded annually, we use the formula with P = $950, r = 0.07 (7% as a decimal), and t = 8.
First, we calculate the new balance:
Total Amount = $950(1 + 0.07)^8
Total Amount = $950(1.07)^8
Total Amount = $950 * 1.718186
Total Amount = $1632.77 (rounded to two decimal places)
Subsequently, to find the amount of interest earned, we subtract the original principal from the total amount:
Interest Amount = Total Amount - Original Principal
Interest Amount = $1632.77 - $950
Interest Amount = $682.77
Therefore, the new balance after 8 years is $1632.77, and the interest earned is $682.77.
Sam used his calculator to find the answer and wrote down cos 1.75 = 0.999. Does this seem like a reasonable answer to you? What might he have done wrong on his calculator?
Answers
Since pi is equivalent to 3.14 and means 180°, therefore 1.75 which is about half of pi should be at almost 90°. The cos of a 90° angle which is located on the y axis should be zero, therefore cos 1.75 must be near zero. However in this case it is near one, clearly his calculator is in degree mode that is why he got an erroneous answer.
What Sam can do to get the correct answer would be to convert his calculator into radian mode or convert the given 1.75 rad into degrees:
θ = 1.75 rad (180° / π rad)
θ = 100.2676
cos 100.2676 = -0.1782 which is now correct since it is nearer to zero
Use the position equation
s = −16t^2 + v0t + s0
as the model for the problem.
A cargo plane flying at 6000 feet over level terrain drops a 700-pound supply package.
(a) How long will it take the package to strike the ground? (Round your answer to two decimal places.)
(b) The plane is flying at 600 miles per hour. How far will the package travel horizontally during its descent? (Round your answer to two decimal places.)
Answers
A. To solve for the time it takes for the package to strike the ground, all we have to do is to plug in the given values in to the position equation:
s = −16 t^2 + v0 t + s0
Where,
s = distance of the plane from the ground = - 6000 ft (negative since the package moves from top to bottom)
t = time for it to strike the ground = unknown
v0 = 0 since the package starts from rest
s0 = 0 since we take the plane as the reference point
Substituting the given values:
- 6000 = -16 t^2 + 0 * t + 0
16 t^2 = 6000
t^2 = 375
t = 19.36 s
B. s = v * t
where v = 600 miles / hr = 0.17 miles / s
s = (0.17 miles / s) * 19.36 s
s = 3.23 miles = 17,054 ft
there is a cafe at the park it is 13 meters long and 8 meters wide. what is the area of the cafe
Answers
The answer should be 104 meters cubed
how to prove a polygon is a rectangle?
Answers
Rewrite the expression x^2-12x as a(x-h)^2+k
Answers
BE is the midsegment of triangle ACD. The value of x is:
5.
20.
35.
40.
Answers
solve, explain why the algorithm works
3892
-2567
Answers
If I assume that you want to subtract 2567 from 3892, I'd write the problem in a slightly different manner:
3892
-2567
--------
Now subtract. Borrow 1 from 9 to obtain a 12, and then subtract 7 from 12, obtaining 5. Result: 1825. Is this correct? You could check by adding 1825 to 2567. You are correct if their sum is 3892.
Which number produces an irrational number when multiplied by 0.4?
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arman needs 4 1/2 inches of cable to make A,3 3/4 inches to make B, and 5 1/8 inches to make C. He used a 12 inch piece of cable to make A and B.
Answers
He used 12 inches of cable...
12 - 8 1/4 = 11 4/4 - 8 1/4 = 3 3/4....length left after A and B are made
he doesn't have enough to make the last one...
5 1/8 - 3 3/4 = 41/8 - 15/4 = 41/8 - 30/8 = 11/8 = 1 3/8....he is short by 1 3/8 inches
Answer:
8 1/4
Step-by-step explanation:
Graph y=3x^2 -5 and it's inverse
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=3x^{2}-5[/tex] -----> quadratic equation of a vertical parabola open upward
Find the inverse function
Exchange variables x for y and y for x
[tex]x=3y^{2}-5[/tex]
Isolate the variable y
[tex]3y^{2}=x+5[/tex] -----> inverse function (horizontal parabola open to the right)
or
[tex]y=(+/-)\sqrt{\frac{x+5}{3}}[/tex]
using a graphing tool
see the attached figure
The graph of function and it's inverse of the graph is shown in image.
We have to given that,
To graph the function y = 3x² - 5 and it's inverse.
Here, The equation is,
y = 3x² - 5
So, We can find it's inverse as,
y = 3x² - 5
y + 5 = 3x²
(y + 5) / 3 = x²
x² = (y + 5)/3
x = √(y + 5)/3
Hence, the inverse of function is,
f ⁻¹ (x) = √ (x + 5)/3
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Convert 85°to radians
Answers
1 degree = 0.0174533 radians
85* 0.0174533 = 1.4835305 radians
Round answer as needed
Answer:
17pi/36 (PLATO answer)
Step-by-step explanation:
Verify that the divergence theorem is true for the vector field f on the region
e. give the flux. f(x, y, z) = 3xi + xyj + 4xzk, e is the cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3.
Answers
[tex]\implies\nabla\cdot\mathbf f(x,y,z)=3+x+4x=3+5x[/tex]
[tex]\displaystyle\iint_{\partial E}\mathbf f(x,y,z)\,\mathrm dS=\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV[/tex]
[tex]=\displaystyle\int_{z=0}^{z=3}\int_{y=0}^{y=3}\int_{x=0}^{x=3}(3+5x)\,\mathrm dx\,\mathrm dy\,\mathrm dz[/tex]
[tex]=\displaystyle9\int_0^3(3+5x)\,\mathrm dx[/tex]
[tex]=\dfrac{567}2[/tex]
To verify the divergence theorem, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.
Explanation:To verify the divergence theorem for the given vector field f(x, y, z) = 3xi + xyj + 4xzk on the region e, which is a cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.
The flux, Ƭ, can be calculated using the surface integral of the vector field over each face of the cube. According to the divergence theorem, this should be equal to the volume integral of the divergence of the vector field over the entire volume of the cube.
By calculating both sides of the equation, we can verify that the divergence theorem holds true for the given vector field on the specified region.
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3y^2-16y+16
could someone help me walk through this?
Answers
3y^2-16y+16
Multiply a by c value and replace as shown below
y^2-16y+48
Factor normally
(y-12)(y-4)
Divide both numbers by the previous a value
(y-12/3)(y-4/3)
(y-4)(y-4/3)
Because -4/3 does not become a whole number change the three to become the coefficient of y
(y-4)(3y-4)
Check by foiling
Final answer: (3y-4)(y-4)
Ocean currents influence all of the following except
temperature
climate
radiation from the sun
weather
Answers
If one calendar year had two consecutive months with Friday the thirteenth, which months would they be?
Answers
In a leap year, no 2 months in a row would have that.
Write and solve an equation to answer the question.
What number a is 24% of 25?
Answers
the number 6 is 24% 0f 25.
Just write 24% as a decimal .24 or 0.24
Final answer:
To find the number that is 24% of 25, you multiply 0.24 by 25, which equals 6.
Explanation:
To find what number a is 24% of 25, we can set up an equation using the concept that a percent is a way of expressing a fractional amount of something.
We know that 24% means 24 out of 100, which can be written as the fraction 24/100 or 0.24 in decimal form.
To translate the question into an equation, we write:
a = 0.24 × 25
Next, we calculate the value of a by multiplying 0.24 (the decimal form of 24%) by 25. This gives us:
a = 6
Therefore, the number a, i.e., 24% of 25 is 6.
..Simplify √x^100y^16
Answers
√(x^50*x^50*y^8*y^8)
x^50*y^8 (third one down :P)
In triangle FE = 5 and angle D=43 . Find DE to the nearest tenth
Answers
Answer:
5.4? I don't really know I'm just going off other answers but clearing it up,,,hope it help :')
Step-by-step explanation:
If CD is the perpendicular bisector of AB, then the value of x is:
10.
5.
22.
11.
Answers
CD = CD [ Common side ]
AD = BD [ CD is the perpendicular "bisector" of AB ]
∠CDA = ∠CDB [ CD is the "perpendicular" bisector of AB ]
Thus, ΔCAD and ΔCBD are congruent triangles. [ SAS congruency ]
If these triangles are congruent, then AC = BC.
2x = 3x -10
x = 10.
brainliest + thanks if were safe:)))))
Explain how to use the standard normal table to find the probability associated with the shaded area under the curve.
Answers
Answer:
The standard normal table gives areas under the curve to the left of z-scores.
Find the probability in the standard normal table that a value is to the left of 1.9.
Find the probability in the standard normal table that a value is to the left of 0.4.
Subtract the probability of a value being to the left of 0.4 from the probability of a value being to the left of 1.9.
Step-by-step explanation:
edge2020
In order to find the probability associated with the shaded area under the curve using the standard normal table, you should subtract the probability of a value left of 0.4 from the probability of a value left of 1.9.
How do you find the probability associated with the shaded area?We are trying to find the probability of the area between 1.9 and 0.4 so the first thing to do is to find the probability that a value is to the left of 1.9 from the Standard normal table.
After this is done, you then find the probability that the value is left of 0.4.
To find the probability of the middle area, subtract the value to the left of 0.4 from that of the value left of 1.9
Find out more on the standard normal table at https://brainly.com/question/7001627.
EASY 5 POINTS!!! Choose the equation that correctly uses the Pythagorean Theorem for the given right triangle.
Answers
^2 = squared
Answer:
Option C
Step-by-step explanation:
In the given right angle triangle
Hypotenuse = 4.5 cm
Height = 2.5 cm
and base = g cm.
Pythagoras theorem says
(hypotenuse)² = (base)² + (height)²
So by putting the values in the formula
(4.5)² + (2.5)² + g²
Option C is the answer.
The value of the given digits in the numbers 7s in 775 823 159
Answers
the circle is centered at the origin and the length of its radius is 4. what is
the circles equation
Answers
Answer: [tex]x^2+y^2=16[/tex]
Step-by-step explanation:
The general equation of a circle having center at (h,k) and radius r is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Given: Radius of the circle : r= 4 units
The center of the circle : (h,k)=(0,0)
Now, the equation of a circle having center at (0,0) and radius 4 units is given by :-
[tex](x-0)^2+(y-0)^2=4^2\\\\\Rightarrow\ x^2+y^2=16[/tex]
Answer:
X²+Y²=16
Step-by-step explanation:
A p e x
Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14?
Answers
Starting at vertex V going until vertex S, we make our calculations.
VR = 14
Rx = x
therefore, xS = VR – Rx
xS = 14 – x ---> 1
Now starting at vertex V going left to vertex S, we make our next set of calculations. Assuming x is on VR but nearer R
VR = 14 - x
at UV = 15 – (14 – x)
at UV = 1 + x
at TU = 7 – (1 + x)
at TU = 6 – x
at ST = 9 – (6 – x)
at ST = 3 + x ---> 2
Equate 1 and 2:
14 – x = 3 + x
2 x = 11
x = 5.5
To find the value of x in the circumscribed pentagon RSTUV with given sides, we set up an equation based on the sum of the lengths of the opposite sides. After solving the equation, we determined that x is 25.
Pentagon RSTUV and the Value of x
Given that pentagon RSTUV is circumscribed about a circle, we need to find the value of x,
where RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14.
For a polygon circumscribed about a circle, the sum of the lengths of the pairs of opposite sides must be equal. Therefore, we can set up the equation:
RS + TU + x = ST + UV + VR
Substituting the given values:
6 + 7 + x = 9 + 15 + 14
Simplifying the right-hand side:
6 + 7 + x = 3813 + x = 38x = 38 - 13x = 25Thus, the value of x is 25.
An employee earned $3,300 working for an employer in the current year. the current rate for fica social security is 6.2% payable on earnings up to $117,000 maximum per year and the rate for fica medicare 1.45%. the employer's total fica payroll tax for this employee is:
Answers
Harland just got his second major credit card, so his credit score rose from 671 to 711. According to the following table for a $150,000 mortgage, how much less per year would Harland have to pay on a $150,000 mortgage with the new credit score?
Answers
Answer:
2004
Step-by-step explanation:
A person in a casino decides to play blackjack until he loses a game, but he will not play more than 3 games. let l denote a loss and w denote a win. what is the sample space for this random experiment
Answers
The sample space for the random experiment of playing blackjack until a loss or a maximum of three games are played is represented by the set {l, wl, ww}.
Explanation:The sample space for this scenario comprises of all possible outcomes of playing "blackjack" until the person loses or has played three games. We represent win and loss by w and l respectively. By these definitions, we get the following possibilities: l (losing on the first game), wl (winning the first game then losing the second), and ww (winning the first two games and decide not to play a third game or it wasn't possible to play a third game). This assumes that the player stops after either losing a game or after playing the third game, even if he won that.
Note that the scenario where the player wins all three games (www) is not included in the sample space because the problem states that the player will stop playing as soon as they lose a game.
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A maintenance man has 12 keys on his key ring. if he tries the keys at random on a storage room door, discarding those that do not work, what is the probability that he will get the door open on his 4th try?
Answers
P(Failure on second try) = 10/11
P(Failure on third try)= 9/10
P(success on fourth try) = 1/9
P(success exactly on fourth try) = 11/12*10/11*9/10*1/9 = 1/12
Final answer:
The probability that the maintenance man will open the storage door on his fourth try with 12 keys is 1/12.
Explanation:
The question asks for the probability that the maintenance man will open a storage room door on his fourth try with 12 unique keys at his disposal. This is a classic probability problem that involves permutations.
To solve this, we consider the scenario as a sequence of independent events. He has 1 out of 12 chances to pick the correct key on the first try, 1 out of 11 on the second try (after discarding the first incorrect key), 1 out of 10 on the third try, and so on. However, we want the first three attempts to be unsuccessful and the fourth to be successful.
Thus, the probability that the first three keys are incorrect is (11/12) * (10/11) * (9/10), and the probability the fourth key is correct is 1/9. The overall probability of the desired outcome is the product of these probabilities, which simplifies to:
(11/12) * (10/11) * (9/10) * (1/9) = 1/12.