To comply with their general computer or Internet policy while allowing Bobby to access the internet for a specific task, the bank can implement several measures to monitor and restrict Bobby's Internet usage for personal and official use.
First, the bank can establish a separate, secured network for employees who need internet access for work purposes. This network should be isolated from the internal network to protect sensitive information.Second, the bank can implement strict access controls and authentication measures, such as providing a unique username and password for Bobby to access the internet. Third, the bank can install a firewall and web filtering system that blocks access to non-work-related websites and content. This will prevent personal use of the internet while still allowing access to the necessary websites for Bobby's work.
Fourth, the bank can regularly monitor and audit Bobby's internet usage, including the websites visited, the amount of time spent online, and any data transmitted or received. Finally, the bank should provide training and guidelines to Bobby regarding the acceptable use of the internet for work purposes, emphasizing the importance of confidentiality and adherence to the bank's security policies.
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This table shows dogs’ weights at a competition.
Dogs' Weights (pounds)
35, 22, 31, 23, 35, 22, 30, 35, 40
One 42-pound dog could not make it to the competition. ++++Select all++++ the ways the measures of center of the data set change if she had entered the competition.
A. The median increases
B. The mode increases
C. The mean increases
D. The median decreases
E. The mode decreases
F. The mean decreases
The measures of central tendencies changed as mode remained the same, the median increased and the mean increased.
How will the data set change if she had entered the competition?To determine how the data set would've changed if she entered the competition, we simply need to work on the mean, median and mode of the data.
Given data;
35, 22, 31, 23, 35, 22, 30, 35, 40
Rearranging this data;
22, 22, 23, 30, 31, 35, 35, 35, 40
The mean of this data will be
mean = 30.3
The mode = 35
The median = 31
When her weight is added, the measures of central tendencies change to;
mean = 31.5
median = 33
mode = 35
The median decreases, the mode remains the same and the mean increases
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You earn $130.00 for each subscription of magazines you sell plus a salary of $90.00 per week. How many subscriptions of magazines do you need to sell in order to make at least $1000.00 each week?
The subscriptions of magazines you need to sell is at least 7
How many subscriptions of magazines do you need to sell?From the question, we have the following parameters that can be used in our computation:
Earn $130.00 for each subscription of magazines You sell plus a salary of $90.00 per weekUsing the above as a guide, we have the following:
f(x) = 130x + 90
In order to make at least $1000.00 each week, we have
130x + 90 = 1000
So, we have
130x = 910
Divide by 130
x = 7
Hence, the number of orders is 7
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You pick a card at random. Without putting the first card back, you pick a second card at random
What is the probability of picking an odd number and then picking an even number?
The probability of picking an odd number and then picking an even number 5/18
The probability of picking an odd number on the first card is 1/2 since there are 5 odd cards out of 10 total cards. After picking an odd card, there are now 4 odd cards and 5 even cards left out of a total of 9 cards. So the probability of picking an even card on the second draw is 5/9.
To find the probability of both events happening, we multiply the probabilities:
P(odd and even) = P(odd) * P(even | odd)
= (1/2) * (5/9)
= 5/18
Therefore, the probability of picking an odd number and then picking an even number is 5/18.
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Menlo Company distributes a single product. The company's sales and expenses for last month follow:
Per Unit
$ 40
28
$ 12
Sales
Variable expenses
Contribution margin
Fixed expenses
Net operating income
Total
$ 600,000
420,000
180,000
Required:
1. What is the monthly break-even point in unit sales and in dollar sales?
2. Without resorting to computations, what is the total contribution margin at the break-even point?
3-a. How many units would have to be sold each month to attain a target profit of $70,800?
3-b. Verify your answer by preparing a contribution format income statement at the target sales level.
146,400
$ 33,600
4. Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms.
5. What is the company's CM ratio? If the company can sell more units thereby increasing sales by $69,000 per month and there is no
change in fixed expenses, by how much would you expect monthly net operating income to increase?
Complete this question by entering your answers in the tabs below.
Req 1
Margin of safety
Req 3A
Req 3B
Req 2
Req 5
Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms. (Round your
percentage answer to 2 decimal places (i.e. 0.1234 should be entered as 12.34).)
Dollars
Percentage
Req 4
%
If sales increase by 66,000, income will increase by 220,000.00
Net operating income 37,200.00
The margin of safety is 14.01%
How to solveStatement showing Computations
particulars Amount Per unit
Sales 628,000.00 40.00
Variable Expenses 439,600.00 28.00
Contribution Margin 188,400.00 $ 12.00
Fixed Expenses 151,200.00
Net operating income 37,200.00
'
1) BEP in unit sales = 151,200/12 12,600.00
.BEP in sales $ = 12,600 * 40 504,000.00
2) Total Contribution margin at BEP = Fixed costs 151,200.00
3)a Target Profit $ 64,800.00
Fixed Expenses 151,200.00
Desired Contribution 216,000.00
3b. No of units to be sold = 216,000/12 18,000.00
Sales 720,000.00
Variable Expenses 504,000.00
Contribution Margin 216,000.00
Fixed Expenses 151,200.00
Net operating income 64,800.00
4) Margin of safety = 628,000.00-540,000.00 88,000.00
MOS in % = 88,000/6280001 14.01%
5)CM Ratio = 188,400/628,000 0.3
If sales increase by 66,000, income will increase by 220,000.00
66,000/0.3
=220,000.
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Consider the diagram shown. The sphere and cylinder have the same diameter. The height of the
cylinder is equal to the diameter of the sphere.
Find the approximate volume of the sphere by using 3.14 for 7. Round to the nearest tenth
of a cubic unit.
8.4
8.4
Answer:
310.2 cubic units
Step-by-step explanation:
since we know the diameter of the sphere (8.4), the radius is [tex]8.4/2 = 4.2[/tex]
The volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex]
Plugging in 3.14 as [tex]\pi[/tex] and 4.2 as r, we get 310.2
Mike can mop McDonald's in three hours. Nancy can mop the same store in 4 hours. If they worked together how long would it take them?
The combined time if Mike and Nancy worked together is approximately 1.71 hours.
To answer your question, we can use the concept of work rates. Mike can mop McDonald's in 3 hours and Nancy can do it in 4 hours. To find the combined work rate, we can use the formula:
1/Mike's rate + 1/Nancy's rate = 1/combined rate
1/3 + 1/4 = 1/combined rate
To solve for the combined rate, we can find a common denominator for the fractions:
(4 + 3) / (3 × 4) = 1/combined rate
7/12 = 1/combined rate
Now we can find the combined time by inverting the combined rate:
Combined time = 12/7
So, if Mike and Nancy worked together, they would mop McDonald's in 12/7 hours, which is approximately 1.71 hours.
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Main answer:
Working together, Mike and Nancy can mop the McDonald's in 12/7 hours or approximately 1.71 hours (rounded to two decimal places).
Explanation:
To solve the problem, we can use the following formula:
time = work / rate
where time is the time it takes to complete the job, work is the amount of work to be done (which in this case is mopping the McDonald's), and rate is the rate of work, or the amount of work done per unit of time.
Let's let x be the time it takes for Mike and Nancy to mop the McDonald's together. Then, we can set up two equations based on the given information:
x = work / (Mike's rate of work)
x = work / (Nancy's rate of work)
To solve for x, we can use the fact that the amount of work to be done is the same in both equations. So we can set the two equations equal to each other:
work / (Mike's rate of work) = work / (Nancy's rate of work)
Simplifying this equation by multiplying both sides by (Mike's rate of work)*(Nancy's rate of work), we get:
work * (Nancy's rate of work) = work * (Mike's rate of work)
We can cancel out the work on both sides, and then solve for x:
x = 1 / [(1/Mike's rate of work) + (1/Nancy's rate of work)]
Substituting in the given rates of work, we get:
x = 1 / [(1/3) + (1/4)] = 12/7
Therefore, it takes Mike and Nancy 12/7 hours, or approximately 1.71 hours (rounded to two decimal places), to mop the McDonald's together.
To solve 6÷1/4, james thinks about how the distance from his home to the store is 1/4 mile and he wonders how many times he would have to walk that distance to walk 6 miles. what is the quotient of 6 and 1/4? enter your answer in the box.
The quotient of 6 and 1/4 is 24.
We have applied division operation to this question. Firstly, we will understand the meaning of a proper fraction. A fraction in which the numerator is less than the denominator is called a proper fraction. This means that the denominators will always be bigger than the numerators for appropriate fractions.
We can represent this condition in either of the two ways.
Denominator < Numerator
(Or)
Numerator > Denominator
We are given a numerical expression which is 6÷ 1/4 and we have to solve this.
To convert this division sign into a multiplication sign, we will take the reciprocal of 1/4.
The reciprocal of 1/4 is 4.
Therefore,
6÷ 1/4
= 6 × 4
= 24
Therefore, the quotient of 6 and 1/4 is 24.
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(1 point) Use Lagrange multipliers to find the minimum value of the function f(x,y) = 2 + y subject to the constraint xy=5 Minimum:
function f(x,y) = 2 + y
The minimum value are f(√5, √5) = 2 + √5.
Lagrange multipliers:To find the minimum value of the function f(x,y) = 2 + y subject to the constraint xy=5 using Lagrange multipliers,
we first set up the Lagrangian function:
L(x,y,λ) = f(x,y) - λ(xy - 5)
Taking partial derivatives with respect to x, y, and λ, we get:
∂L/∂x = 0 = -λy
∂L/∂y = 1 - λx
∂L/∂λ = xy - 5
Solving for λ from the first equation and substituting into the second equation, we get:
x/y = 0/λ
1 - λx = 0
xy - 5 = 0
From the first equation, we see that either x = 0 or y = 0. But since xy = 5, neither x nor y can be zero.
Therefore, we have:
λ = 0
1 - λx = 0
xy - 5 = 0
Solving for x and y from the last two equations, we get:
x = 5/y
y = ±√5
We take the positive root for y since we are looking for a minimum value of the function.
Substituting y = √5 into x = 5/y, we get x = √5.
Therefore, the minimum value of f(x,y) = 2 + y subject to the constraint xy=5 is:
f(√5, √5) = 2 + √5.
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Calculate the truth value for each compound proposition, using the given truth values for the simple statement letters. Type T or F beneath each letter and operator. Also, identify the main operator of each statement by typing a lowercase x in the box beneath it. Use the provided dropdown menu to indicate whether the compound statement is true or false, given the assigned truth values.
Given Truth Values
True False
K Q
L R
M S
Statement 1: (M ~ R { v ~ S L)
T or F:
Main Operator:
Assuming the given truth values, Statement 1 is____.
Statement 2: (~ S = M ). (L ~ K )
T or F:
Main Operator:
Assuming the given truth values, Statement 2 is____.
Statement 3: ~(R V ~ L) (~ S S)
T or F:
Main Operator:
Assuming the given truth values, Statement 3 is____.
Statement 4: ~ [(Q V ~ S). ~ (R = ~ S)]
T or F:
Main Operator:
Assuming the given truth values, Statement 4 is____.
Statement 5: (S = Q) = [(K ~ M) V ~ (R. ~ L)]
T or F:
Main Operator:
Assuming the given truth values, Statement 5 is_____
Statement 5 is True
Statement 1: (M ∧ ~R) ∨ (~S ∧ L)
T or F: T
Main Operator: ∨
Assuming the given truth values, Statement 1 is True.
Statement 2: (~S ↔ M) ∧ (L ∧ ~K)
T or F: F
Main Operator: ∧
Assuming the given truth values, Statement 2 is False.
Statement 3: ~(R ∨ ~L) ∧ (~S ∨ S)
T or F: F
Main Operator: ∧
Assuming the given truth values, Statement 3 is False.
Statement 4: ~ [(Q ∨ ~S) ∧ ~(R ↔ ~S)]
T or F: T
Main Operator: ~
Assuming the given truth values, Statement 4 is True.
Statement 5: (S ↔ Q) ↔ [(K ∧ ~M) ∨ ~(R ∧ ~L)]
T or F: T
Main Operator: ↔
Assuming the given truth values, Statement 5 is True.
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What is the scale factor for the similar figures below?
The value of the scale factor for the similar figures is 1/4
What is the scale factor for the similar figures?From the question, we have the following parameters that can be used in our computation:
The similar figures
The corresponsing sides of the similar figures are
Original = 8
New = 2
Using the above as a guide, we have the following:
Scale factor = New /Original
substitute the known values in the above equation, so, we have the following representation
Scale factor = 2/8
Evaluate
Scale factor = 1/4
Hence, the scale factor for the similar figures is 1/4
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If we roll a regular, 6-sided die 5 times. What is the probability that at least one value is observed more than once
The probability that at least one value is observed more than once when rolling a regular 6-sided die 5 times is approximately 0.598.
The total number of possible outcomes when rolling a die 5 times is 6⁵ = 7776 (since there are 6 possible outcomes for each roll and there are 5 rolls). To calculate the number of outcomes where no value is repeated, we can use the permutation formula: P(6,5) = 6! / (6-5)! = 6! / 1! = 720, since there are 6 possible outcomes for the first roll, 5 for the second roll (since one outcome has been used), and so on.
So, the probability of not observing any repeated values is P(no repeats) = 720 / 7776 ≈ 0.0926. Therefore, the probability of observing at least one repeated value is P(at least one repeat) = 1 - P(no repeats) ≈ 0.9074.
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write 1/r^2 in terms of spherical bessel functions
The function 1/[tex]r^2[/tex] can be expressed in terms of the spherical Bessel functions of the first kind, which are a family of solutions to the spherical Bessel differential equation.
The expansion involves a combination of the delta function and the first two spherical Bessel functions, j_0(r) and j_1(r). Specifically, the expansion can be written as (1/2)*[pi * delta(r) + (1/r)*d/d(r)(r * j_0(r)) + (1/[tex]r^2[/tex])*d/d(r)[[tex]r^2[/tex] * j_1(r)]]. This expansion is valid for all values of r except for r=0, where the first term dominates. The spherical Bessel functions are commonly used in physics, particularly in the context of scattering problems and wave propagation.
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Question 13
"s
the measure of one of the small angles of a right triangle is 30 less than 7 times
small angle. find the measure of both angles.
smallest angle:
other non-right angle:
add work
> next question
The smallest angle measures 15 degrees and the other non-right angle measures 75 degrees.
To find the measure of both angles in a right triangle with the given conditions, we will use the information provided:
Let x be the measure of the smallest angle. The problem states that the measure of one of the small angles is 30 less than 7 times the smallest angle, which can be written as:
Other non-right angle = 7x - 30
Since this is a right triangle, the sum of the two small angles must be 90 degrees (because the other angle is 90 degrees, and the sum of angles in a triangle is 180 degrees). So, we can set up the following equation:
x + (7x - 30) = 90
Now, solve for x:
8x - 30 = 90
8x = 120
x = 15
So, the smallest angle is 15 degrees. Now, we can find the measure of the other non-right angle:
Other non-right angle = 7x - 30 = 7(15) - 30 = 105 - 30 = 75 degrees
In summary, the smallest angle measures 15 degrees and the other non-right angle measures 75 degrees.
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Select the equation that most accurately depicts the word problem. The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches. 68 = 9(L + 2) 68 = 2L + 2(9) 68 = 2(L - 9) 68 = 9L + 2 68 = 2/L + 2/9 68 = L/2 + 2(9)
The equation which most accurately represents the word problem, is (b) 68 = 2L + 2(9).
The word problem states that the perimeter of a rectangle is 68 inches, and the perimeter equals twice the length (L) plus twice the width (9). We can represent this relationship by using the equation as :
We know that, the perimeter of rectangle is : 2(length + width),
Substituting the value,
We get,
⇒ 68 = 2(L + 9);
⇒ 68 = 2L + 2(9); and this statement is represented by Option(b).
Therefore, the correct equation is (b) 68 = 2L + 2(9).
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The given question is incomplete, the complete question is
Select the equation that most accurately depicts the word problem.
"The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches".
(a) 68 = 9(L + 2)
(b) 68 = 2L + 2(9)
(c) 68 = 2(L - 9)
(d) 68 = 9L + 2
(e) 68 = 2/L + 2/9
(f) 68 = L/2 + 2(9)
CI is tangent to circle O at point c. If arc CUH=244*, find m
The value of angle HCI is determined as 244⁰.
What is the value of angle HCI?The value of angle HCI is calculated by applying intersecting chord theorem as follows;
The intersecting chord theorem, also known as the secant-secant theorem, states that when two chords intersect inside a circle, the products of the segments of one chord are equal to the products of the segments of the other chord.
From the diagram, the value arc CUH is equal to the value of angle HCI.
Thus, angle HCI = 244⁰
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How is the product of a complex number and a real number represented on the complex plane?
Consider the product of 2−4i and 3.
Drag a value or phrase into each box to correctly complete the statements
The product of 2-4i and 3 is represented on the complex plane as a vector with magnitude 6√5 and angle -63.43 degrees, starting from the origin.
To represent the product of a complex number and a real number on the complex plane:
We multiply the real part and the imaginary part of the complex number by the real number.
The magnitude (or length) of the resulting complex number is multiplied by the absolute value of the real number.
The angle (or argument) of the resulting complex number is the same as the angle of the original complex number.
For the product of 2−4i and 3:
We multiply the real part (2) and the imaginary part (-4i) of the complex number by the real number (3), to get:
3(2) + 3(-4i) = 6 - 12i
The magnitude of the resulting complex number is:
|6 - 12i| = √(6² + (-12)²) = √180 = 6√5
The angle of the resulting complex number is the same as the angle of the original complex number (2-4i), which can be found using the inverse tangent function:
tanθ = (imaginary part) / (real part) = (-4) / 2 = -2
θ = atan(-2) ≈ -1.107 radians or ≈ -63.43 degrees
Therefore, the product of 2-4i and 3 is represented on the complex plane as a vector with magnitude 6√5 and angle -63.43 degrees, starting from the origin.
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The original selling price of a jacket was
s
s dollars. The selling price was then changed on two occasions by the store owner. Its price is now represented by
0. 85
(
1. 4
s
)
0. 85(1. 4s). Which expression could explain what happened to the price of the jacket?
The expression that explains what happened to the price of the jacket is 0.85(1.4s), which represents a 40% increase in price followed by a 15% discount.
The expression 0.85(1.4s) represents the current selling price of the jacket, which includes two price changes.
To explain what happened to the price of the jacket, we can break down the expression into two steps:
1. The first change was an increase by 40%, which can be represented as multiplying the original price "s" by 1.4 (100% + 40% = 140% or 1.4). So, the price after the first change is 1.4s.
2. The second change was a discount of 15%, which can be represented as multiplying the price after the first change by 0.85 (100% - 15% = 85% or 0.85). So, the price after both changes is 0.85(1.4s).
So, the expression that explains what happened to the price of the jacket is 0.85(1.4s), which represents a 40% increase in price followed by a 15% discount.
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Help I don't know what I did wrong.
[tex]4\sqrt{125} -2\sqrt{243} -3\sqrt{20}+5\sqrt{27}[/tex]
Suppose the surface area for a can having a particular volume is minimized when the height of the can is equal to 22 cm. If the surface area has been minimized, what would you expect the radius of the can to be? (Round your answer to the nearest tenth if
necessary. You do not need to include the unit.)
If the surface area of a can with a particular volume is minimized when the height of the can is 22 cm, we would expect the radius of the can to be the same as the height, given that a cylinder has the smallest surface area when its height and radius are equal.
The surface area of a can with height h and radius r can be given by the formula:
A = 2πr² + 2πrh
The volume of the can is given by:
V = πr²h
If we differentiate the surface area with respect to r and equate it to zero to find the critical point, we get:
dA/dr = 4πr + 2πh(dr/dr) = 0
Simplifying this expression, we get:
2r + h = 0
Since we know that the height of the can is 22 cm, we can substitute h = 22 in the equation to get:
2r + 22 = 0
Solving for r, we get:
r = -11
Since the radius of the can cannot be negative, we discard this solution. Therefore, the radius of the can should be equal to its height, which is 22 cm.
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Water flows into an empty reservoir at a rate of 3200+ 5t gal/hour. What is the quantity of water in the reservoir after 11 hours? Answer:_____ gallons.
To find the quantity of water in the reservoir after 11 hours, we need to integrate the rate of flow with respect to time from 0 to 11. The quantity of water in the reservoir after 11 hours is 38,225 gallons.
∫(3200 + 5t) dt from 0 to 11
= [(3200 * 11) + (5/2 * 11^2)] - [(3200 * 0) + (5/2 * 0^2)]
= 35,200 + 302.5
= 35,502.5 gallons
Therefore, the quantity of water in the reservoir after 11 hours is 35,502.5 gallons.
To find the quantity of water in the reservoir after 11 hours with the rate of 3200 + 5t gal/hour, we need to first find the total amount of water that flows into the reservoir within that time.
Step 1: Identify the given rate of flow: 3200 + 5t gal/hour.
Step 2: Integrate the flow rate function with respect to time (t) to find the total quantity of water. The integral of the function will give us the quantity of water in gallons:
∫(3200 + 5t) dt = 3200t + (5/2)t^2 + C, where C is the constant of integration.
Since the reservoir is initially empty, the constant C will be 0.
Step 3: Substitute t=11 hours into the integrated function to find the total quantity of water:
Q(11) = 3200(11) + (5/2)(11)^2
Q(11) = 35200 + 3025
Step 4: Add the values to find the total quantity of water in gallons:
Q(11) = 38225 gallons
The quantity of water in the reservoir after 11 hours is 38,225 gallons.
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John is planning an end of the school year party for his friends he has $155 to spend on soda and pizza he knows he has to buy 10 2 L bottles of soda choose the any quality and calculate the greatest number of pizzas he can buy
If John has to buy 10 "2-Liter" bottles of soda, then the inequality representing this situation is "10(1.50) + 7.50p ≤ 150" and greatest number of pizzas he can buy is 18, Correct option is (d).
Let "p" denote the number of "large-pizzas" that John can buy.
One "2-liter" bottle of soda cost is = $1.50,
So, the cost of the 10 bottles of soda is : 10 × $1.50 = $15,
one "large-pizza's cost is = $7.50,
So, the cost of p large pizzas is : $p × $7.50 = $7.50p,
The "total-cost" of the soda and pizza must be less than or equal to $150, so we can write the inequality as :
10(1.50) + 7.50p ≤ 150
Simplifying the left-hand side of the inequality,
We get,
15 + 7.50p ≤ 150
7.50p ≤ 135
p ≤ 18
Therefore, John can buy at most 18 large pizzas with his remaining budget, the correct option is (d).
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The given question is incomplete, the complete question is
John is planning an end of the school year party for his friends he has $150 to spend on soda and pizza.
Soda (2-liter) costs $1.50;
large pizza cost $7.50;
He knows he has to buy 10 "2-Liter" bottles of soda.
Choose the inequality and calculate the greatest number of pizzas he can buy.
(a) 10(1.50) + 7.50p ≥ 150; 54 pizzas
(b) 10(7.50) + 1.50p ≤ 150; 53 pizzas
(c) 10(7.50) + 1.50p ≥ 150; 19 pizzas
(d) 10(1.50) + 7.50p ≤ 150; 18 pizzas
Please help me im struggling sm
The measurements are x = 7 and ∠NJK = 51°
Given is a rectangle, we need to find the asked measurement,
So,
Since we know that the diagonals of a rectangle bisect each other,
So,
JN + JN = JL
4x+4+4x+4 = 5x+29
8x+8 = 5x+29
3x = 21
x = 7
And,
The vertex angle is 90° so,
∠NMJ + ∠NML = 90°
∠NML = 51°
Also,
∠NML = ∠NJK because they are alternate angles,
So, ∠NJK = 51°
Hence x = 7 and ∠NJK = 51°
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Victor opened a savings account that earns 4.5% simple
interest. He deposited $5,725 into the account. What will be
Victor's account balance after five years? Round to the nearest
cent.
7.1
Answer:
(5,725)1.045^5
Step-by-step explanation:
(5,725)1.045^5
5,725 is the original amt of $
1.045 is the % of interest
5 is the # of years
Solve this and round the nearest
cent.
Determine whether each statement regarding surface area is true, Select True or False for each
statement
1. The surface area of a cone is the sum of the areas of a circle and sector of a circle.
2. The surface area of a sphere is greater than a cube's with s=r.
3. A composite figure's surface area is the sum of each individual figure's surface area.
The first statement about the surface area in the question are false, the second statement about surface area is false and the third statement about surface area is true respectively.
1. False. The surface area of a cone is the sum of the areas of the circular base and the curved lateral surface.
2. False. The surface area of a sphere is given by 4πr^2, while the surface area of a cube with side length s=r is 6r^2. Since 4πr^2 is less than 6r^2 for any value of r, the surface area of a sphere is actually less than the surface area of such a cube.
3. True. The surface area of a composite figure is the sum of the surface areas of each individual figure that make up the composite figure.
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How much money did Susan earn per hour
Answer:
$9.50
Step-by-step explanation:
Divide the total earnings by total hours.
Admission Charge for Movies The average admission charge for a movie is $5. 81. If the distribution of movie admission charges is approximately normal with a standard deviation of $0. 81, what is the probability that a randomly selected admission charge is less than $3. 50
The probability that a randomly selected admission charge is less than $3. 50 is 0.23% or 0.0023.
To find the probability that a randomly selected admission charge is less than $3.50, we will use the z-score formula and a standard normal table. The z-score formula is:
Z = (X - μ) / σ
Where X is the value we are interested in ($3.50), μ is the average admission charge ($5.81), and σ is the standard deviation ($0.81).
Z = (3.50 - 5.81) / 0.81 ≈ -2.84
Now, look up the z-score (-2.84) in a standard normal table, which gives us the probability of 0.0023. Therefore, the probability that a randomly selected admission charge is less than $3.50 is approximately 0.23% or 0.0023.
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write any ten ordered pairs in which the first elements is country the second element is its capital
Answer:
Sure, here are ten ordered pairs with the country as the first element and the capital as the second element:
1. (France, Paris)
2. (United States, Washington D.C.)
3. (China, Beijing)
4. (Mexico, Mexico City)
5. (Brazil, Brasília)
6. (Japan, Tokyo)
7. (Canada, Ottawa)
8. (Germany, Berlin)
9. (Australia, Canberra)
10. (India, New Delhi)
Need this really fast !
consider the function whose criterion is f(x) = = ax + b si x 3 The required values for a and t for the function to be continuous at X=3
The function will be continuous at x = 3 for any values of a and b.
How to determine the values for the function?f(x) = ax + b to be continuous at x = 3
A function is continuous at a point x = c if:
1. f(c) is defined
2. The limit of f(x) as x approaches c exists
3. The limit of f(x) as x approaches c is equal to f(c)
For f(x) = ax + b to be continuous at x = 3:
1. f(3) is defined:
f(3) = a(3) + b
2. The limit of f(x) as x approaches 3 exists.
3. The limit of f(x):
lim (x->3) (ax + b) = a(3) + b
There are no specific values for a and b that must be satisfied. The function will be continuous at x = 3 for any values of a and b.
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please help with the question in the image !!
Answer:
image dosent load
Step-by-step explanation:
Answer:
a = 80°, b = 100°, c = 80°, d = 100°
Step-by-step explanation:
You know a + b + c + d = 360°.
Plugging b + c + d = 280° into the formula above:
a + 280° = 360°.
a = 80°.
You know a + d = 180° because of angles on a straight line. Solve for d:
80° + d = 180°.
d = 100°.
For the same reason, you know a + b = 180°. b must be equal to d, which is 100°.
Lastly, c + d = 180° because they make up the second line. Solve for c:
c + 100° = 180°.
c = 80°.
a = 80°, b = 100°, c = 80°, d = 100°.
in the absence of predators the natural growth rate of rabbits is 4% per year. a population begins with 100 rabbits. the function f(x) = 100(1.04) ^x gives the population of rabbits in x years. how long will it take the population of rabbits to double? how long will it take the population of rabbits to reach 1000?
a) It will take approximately 16.85 years for the rabbit population to double.
b) It will take approximately 37.28 years for the rabbit population to reach 1000.
The formula for calculating the population of rabbits in x years, starting with 100 rabbits and a natural growth rate of 4% per year, is given by:
f(x) = 100(1.04)ˣ
(a) To find out how long it will take for the rabbit population to double, we need to solve the following equation:
100(1.04)ˣ = 200
Dividing both sides by 100, we get:
(1.04)ˣ = 2
Taking the logarithm of both sides with base 1.04, we get:
x = log₁.₀₄ 2
Using a calculator, we get:
x ≈ 16.85
(b) To find out how long it will take for the rabbit population to reach 1000, we need to solve the following equation:
100(1.04)ˣ = 1000
Dividing both sides by 100, we get:
(1.04)ˣ = 10
Taking the logarithm of both sides with base 1.04, we get:
x = log₁.₀₄ 10
Using a calculator, we get:
x ≈ 37.28
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