Nicole, Miguel, and Samuel served a total of 115 orders Monday at the school cafeteria. Miguel served 3 times as many orders as Samuel. Nicole served 10 more orders than Samuel. How many orders did they each serve?
Answer:
Samuel = 21 orders
Nicole = 31 orders
Miguel = 63 orders
Step-by-step explanation:
Let N represent Nicole's orders, M represents Miguel's orders, and S represent Samuel's orders.
We know that the sum of their tree orders equals 115 as
N + M + S = 115
Since Miguel served 3 times as many orders as Samuel, we know that
M = 3S.
Since Nicole served 10 more orders than Samuel, we know that
N = S + 10
Samuel's Orders:
Now we can plug in 3S for M and S + 10 for N to find S, the number of Samuel's orders:
S + 10 + 3S + S = 115
5S + 10 = 115
5S = 105
S = 21
Thus, Samuel served 21 orders.
Nicole's Orders:
Now we can plug in 21 for S in N = S + 10 to determine how many orders Nicole served:
N = 21 + 10
N = 31
Thus, Nicole served 31 orders.
Miguel's Orders:
Now we plug in 19 for S in M = 3S to determine how many orders Miguel served:
M = 3(21)
M = 63
Thus, Miguel served 63 orders.
what is question 4????
Answer:
2.2
Step-by-step explanation:
(1.85 x 2) - 1.50
...............
Mr. Marshal spent his salary of $8 400 in the following manner: Rental .....1/5 Food.......1/10 Bank ......1/4 Miscellaneous ......... the remainder. what fraction of the money was spent on miscellaneous. how much did he spend on rental. if marshal spent 4/9 of miscellaneous on a trip what fraction of his entire salary was spent on the trip ?
Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.
To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.
Rental: 1/5
Food: 1/10
Bank: 1/4
To find the fraction spent on miscellaneous:
Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)
Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40
Fraction spent on miscellaneous = 1 - 17/40 = 23/40
So, Mr. Marshal spent 23/40 of his salary on miscellaneous.
To find the amount spent on rental, we multiply the fraction spent on rental by his salary:
Amount spent on rental = (1/5) [tex]\times[/tex] $8,400 = $1,680
Therefore, Mr. Marshal spent $1,680 on rental.
If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.
Fraction spent on the trip = (4/9) [tex]\times[/tex] (23/40) = 92/360 = 23/90
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Which set of numbers are integers but not whole numbers or natural numbers?
Step-by-step explanation:
C
se logarithms to solve the problem.
The rule of 70 is a rule of thumb for estimating the doubling time of a quantity (e.g., investment, GDP, population) experiencing growth that is compounded continuously. The rule states that if the growth rate is r% per year, then the time it takes for the quantity to double is approximately 70/r years.
(a)
Use the rule of 70 to estimate the time it takes for an investment to double in value if it grows at the rate of 5% per year compounded continuously.
yr
(b)
What is the exact time it will take for the investment in part (a) to double in value? (Round your answer to two decimal places.)
yr
a. The investment to double in value take about 14 years for the funding to double in value.
b. The genuine time it will take for the funding to double in fee is about 13.86 years.
(a) To estimate the time it takes for an funding to double in cost the use of the rule of 70, we want to decide the increase rate. In this case, the increase price is given as 5% per 12 months compounded continuously.
Using the rule of 70, we can calculate the estimated doubling time:
Time to double ≈ 70 / boom rate
Time to double ≈ 70 / 5
Simplifying, we have:
Time to double ≈ 14 years
Therefore, it would take about 14 years for the funding to double in value.
(b) To decide the genuine time it will take for the funding to double in value, we can use the formulation for non-stop compounding:
Doubling time (exact) = ln(2) / (ln(1 + r))
where r is the increase fee as a decimal.
In this case, the increase charge is 5% per year, or 0.05 as a decimal.
Doubling time (exact) = ln(2) / (ln(1 + 0.05))
Doubling time (exact) ≈ 13.86 years (rounded to two decimal places)
Therefore, the genuine time it will take for the funding to double in fee is about 13.86 years.
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-Ready
Algebraic Expressions with Exponents-Instruction-Level F
Amelia is building 3 square garden beds that are all the same size. She arranges them side-
by-side to separate certain plants. Amelia wants to know the total area of the garden beds.
length (ft) of one side of a garden bed
Write an expression to show the total
area of the garden beds.
38²
What is the total area if each garden
bed has a length of 4 feet?
ft²
A = $²
7 8 9
6
3
4
51
1
1 2
X
1
t
X
The correct answer is each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.
To find the total area of the garden beds, we can use the expression:
Total area = (length of one side)^2 * number of garden beds
Given that each garden bed has a length of 4 feet, we substitute 4 for the length of one side in the expression:
Total area = (4)^2 * 3
Simplifying:
Total area = 16 * 3
Total area = 48 square feet
Therefore, if each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.
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4) AD is a common internal tangent to circles B and C. Find the length of the radius
of circle B. Round to the nearest hundredth. (Hint: Prove that the two triangles
are similar and use proportions to find missing lengths.) (10 points)
I
B
E
6
D
Both triangles in the image are similar based on the AAA similarity theorem. The radius of the circle B is therefore calculated as: AB = 12.
What are similar triangles?Similar triangles are geometric figures that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are in proportion to each other.
Since AD serves as a common tangent, angle BAE is equal to 90 degrees, which is also equal to angle CDE due to being opposite angles.
By the Angle-Angle-Angle (AAA) similarity criterion, triangles ABE and DCE are similar.
Therefore:
AB/EA = DC/ED
Substitute:
AB/18 = 4/6
Cross multiply:
AB = 18 * 4/6
AB = 12
Therefore, the radius of the circle B is: 12.
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HELP ASAP!!!!!! LOOK AT THIS:
Alice, Raul, and Maria are baking cookies together. They need 3/4 cup of flour and 1/3 cup of butter to make a dozen cookies. They each brought the ingredients they had at home . Alice brought 2 cups of flour and 1/4 cup of butter, and Maria brought 1and1/4 cups of flour and 3/4 cup of butter. If the students have plenty of the other ingredients they need (sugar, salt, baking soda, etc.), how many whole batches of a dozen cookies can they make ?
,Alice, Raul, and Maria can make 1 whole batch of a dozen cookies together using the ingredients they brought.
To determine how many whole batches of a dozen cookies they can make, we need to compare the amount of flour and butter they have with the required amounts for each batch of cookies.
Let's calculate the total amount of flour and butter each student brought:
Alice:
Flour: 2 cups
Butter: 1/4 cup
Maria:
Flour: 1 1/4 cups
Butter: 3/4 cup
Now let's compare the amounts with the required ingredients for a batch of cookies:
Required amount per batch:
Flour: 3/4 cup
Butter: 1/3 cup
First, let's see how many batches of cookies Alice can make:
Flour: Alice has 2 cups, and each batch requires 3/4 cup. So she can make 2 cups / (3/4 cup) = 8/3 = 2 and 2/3 batches of cookies.
Butter: Alice has 1/4 cup, and each batch requires 1/3 cup. Since she doesn't have enough butter for a full batch, she can't make any batches of cookies with the butter she brought.
Next, let's see how many batches of cookies Maria can make:
Flour: Maria has 1 1/4 cups, and each batch requires 3/4 cup. So she canmake (5/4 cups) / (3/4 cup) = 5/3 = 1 and 2/3 batches of cookies.
Butter: Maria has 3/4 cup, and each batch requires 1/3 cup. So she can make (3/4 cup) / (1/3 cup) = 9/4 = 2 and 1/4 batches of cookies.
Now, to find the maximum number of whole batches they can make together, we take the minimum of the number of batches each student can make:
Alice: 2 and 2/3 batches
Maria: 1 and 2/3 batches
Raul: Not mentioned, so we assume he brought the required ingredients.
The minimum value is 1 and 2/3 batches, which means they can make 1 whole batch of a dozen cookies together.
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The diagram shows a cuboid. 8 cm 15 cm 20 cm What is the volume of the cuboid?
Answer:
The answer is 2400 cm^3
Step-by-step explanation:
You just need to multiply the dimensions
Answer:
2400 cm³
Step-by-step explanation:
Volume of cuboid = length × width × height
Volume = 8 cm × 15 cm × 20 cm
Volume = 2400 cm³
So, the volume of the cuboid is 2400 cm³
A bakery is making cupcakes using a cylindrical mold. The cupcake mold has a diameter of 8.5 centimeters and is 6 centimeters tall. Which of the following shows a correct method to calculate the amount of cupcake batter needed to fill the mold all the way to the top? Use 3.14 for π.
V = (3.14)(8.5)2(6)
V = (3.14)(6)2(8.5)
V = (3.14)(4.25)2(6)
V = (3.14)(6)2(4.25)
Answer:
V = (3.14)(4.25)²(6)
Step-by-step explanation:
Find the linear function
The linear function for this case is:
f(x) = 5,000*x + 7,000
How to find the linear function?The general linear function is written as:
f(x) = a*x + b
Where a is the slope and b is the y-intercept.
Here we want a linear function for the given scenario, we know that the initial population is 7,000, then we can write:
f(x)= a*x + 7,000
Then we know that the population increases by 5,000 per year for 5 years, so the slope is 5,000, then we can write the function as:
f(x) = 5,000*x + 7,000
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The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base.
O False
O True
Answer: True
Step-by-step explanation:
The lateral faces are the triangular faces that connect the apex of the pyramid to the edges of the base. The area of each lateral face can be calculated using the formula for the area of a triangle, which is [tex]\frac{1}{2} \times b \times h[/tex]. The area of the base is simply the area of the polygon that forms the base of the pyramid.
__________________________________________________________
The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. (True or False)
Answer:The correct answer is True.
Explanation:The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. This can be represented by the formula:
[tex]\qquad\qquad\Large\boxed{\rm{\:SA = B + LA\:}}[/tex]
The lateral faces are the faces that are not the base, so their areas are calculated using the formula for the area of a triangle. The area of the base is calculated using the appropriate formula depending on the shape of the base.
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Select the correct answer from each drop-down menu.
Given: Line segment WU is the perpendicular bisector of line TV.
Prove: Line TU ≠ Line VU
WU is the perpendicular bisector of TV and W is the midpoint of TV.
Statements:
WU is the perpendicular bisector of TV.
W is the midpoint of TV.
TW = VW.
∠ZTWU and ∠ZVWU are right angles.
∠ZTWU ≅ ∠LVWU.
WU = WU.
∠ATWU ≅ ∠AVWU.
TU = VU.
Reasons:
Given.
Definition of the perpendicular bisector: It divides a segment into two congruent parts, and W is the midpoint of TV.
Definition of midpoint: The segment TW is congruent to VW because W is the midpoint of TV.
Given that WU is the perpendicular bisector, it means that ∠ZTWU and ∠ZVWU are right angles.
All right angles are congruent.
Reflexive property of congruence: Any segment or angle is congruent to itself.
Corresponding parts of congruent triangles are congruent (CPCTC): Since ∠ATWU and ∠AVWU are corresponding parts of congruent triangles, they are congruent.
Corresponding parts of congruent triangles are congruent (CPCTC): Since TU and VU are corresponding parts of congruent triangles, they are congruent.
Therefore, the correct statements and reasons are:
Statements:
WU is the perpendicular bisector of TV.
W is the midpoint of TV.
TW = VW.
∠ZTWU and ∠ZVWU are right angles.
∠ZTWU ≅ ∠LVWU.
WU = WU.
∠ATWU ≅ ∠AVWU.
TU = VU.
Reasons:
Given.
Definition of the perpendicular bisector.
Definition of midpoint.
Given.
All right angles are congruent.
Reflexive property of congruence.
CPCTC.
CPCTC.
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answer a) and b) please
a : 10<x<=20
b: 20<x<=30
find g[h(-2)] from f(x)=x^(2),g(x)=5x , h(x)=x+4
Explanation:
Plug x = -2 into h(x)
h(x) = x+4
h(-2) = -2+4
h(-2) = 2
This means g[ h(-2) ] = g(2) after replacing h(-2) with 2.
g(x) = 5x
g(2) = 5*2
g(2) = 10
Therefore, g[ h(-2) ] = 10
Results from a marijuana drug test study showed 143 subjects with positive test results including 24 false positive results. There were 157 negative results, including 3 false negative results. What is the probability that a randomly selected subject did not use marijuana? Round to three decimal places as needed.
Part 1
A. 0.533
B. 0.593
C. 0.523
D. 0.477
Answer:
B. 0.593
Step-by-step explanation:
Type the correct answer in each box. Round your answers to the nearest thousandth.
A company has 200 machines. Each machine has 12% probability of not working.
If you were to pick 40 machines randomly, the probability that 5 would not be working is
and the probability that at least one machine would be working is
the probability that all would be working is
1) The probability that 5 will be working is: 0.187
2) The probability that at least one machine would be working is: 0.006
3) The probability that all would be working is : 1
How to find the probability of working?We are given the parameters as:
Total number of machines = 200
Probability that a Machine is working = 12% = 0.12
1) Now, you want to pick 40 machines and want to find the probability that 5 will be working.
This probability is given by the expression:
P(5 working) = C(40,5) * 0.12⁵·0.88³⁵ ≈ 0.187
where C(n, k) = n!/(k!(n-k)!)
2) The probability that at least one machine would be working is:
0.88⁴⁰ ≈ 0.006
3) The probability that all would be working is the complement of the probability that all have failed. Thus:
P(all working) = 1 - 0.12⁴⁰ ≈ 1
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A file that is 268 megabytes is being downloaded if the download is 14.3% complete how many megabytes have been downloaded
Find the equation of the line in slope-intercept form, perpendicular to a line with a slope of
1
13 and passing through (-1,3).
The equation of the line perpendicular to a line with a slope of -- and passing through (-1,3) is.
(Simplify your answer. Type your answer in slope-intercept form.)
The equation of the line perpendicular to the line with a slope of 1/13 and passing through the point (-1, 3) is y = -13x - 10.
To find the equation of a line perpendicular to a line with a slope of 1/13 and passing through the point (-1, 3), we need to determine the slope of the perpendicular line.
The slope of a line perpendicular to another line can be found by taking the negative reciprocal of the given slope. The negative reciprocal of 1/13 is -13/1, or simply -13.
Now that we have the slope (-13) and a point (-1, 3) that the line passes through, we can use the point-slope form of a linear equation to find the equation of the perpendicular line.
The point-slope form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
Substituting the values (-1, 3) and -13 into the point-slope form, we get:
y - 3 = -13(x - (-1))
Simplifying:
y - 3 = -13(x + 1)
Expanding the equation:
y - 3 = -13x - 13
To convert the equation to slope-intercept form (y = mx + b), we can isolate y:
y = -13x - 13 + 3
y = -13x - 10
Therefore, the equation of the line perpendicular to the line with a slope of 1/13 and passing through the point (-1, 3) is y = -13x - 10.
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if you borrow $1,000 for 4 years at an annual interest rate of 8% what is the total amount of money you will pay back
The table below represents the function, and the following graph represents the function g.
4 -3 -2 -1 0 1
X-6 -5
f(x) 8-2
-8 -10 -8 -2 8 22
Complete the following statements.
The functions f and g have
The y-intercept of fis
the y-intercept of g.
Over the interval [-6, -31, the average rate of change of fis
m. All rights reserved.
9
-6 -4
-2
6
4
2
4-
N
6
2
4 6
the average rate of change of g
The correct options to the questions posed are :
The functions f and g have the same axis of symmetry.The y-intercept of f is greater than the y-intercept of g.Over the interval [-6, -3], the average rate of change of f is less than the average rate of change of g.Axis of symmetryFrom the given table of f(x) and x, from which we have;
The minimum point for f(x) as it's vertex as (-3, -10) = -3
For the function g(x). represented by the graph, the axis of symmetry is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3
InterceptThe y-intercept, is the point on the graph where the line intersects the y-axis or where x = 0. Here , the point is (0,8) = 8
Over the interval [-6, -3]
The average rate of change of f(x) is
(-10 - 8)/(-3 -(-6)) = -6
Using the graph g(x)From the graph of g(x), we have;
The axis of symmetry is the line x = -3
The y-intercept = (0, -2) = -2
Over the interval [-6, -3]
The average rate of change = (6 - (-2))/(-3 -(-6)) = 8/3 = 2.67
Hence,
The functions f and g have the same axis of symmetry.
The y-intercept of f is greater than the y-intercept of g.
Over the interval [-6, -3], the average rate of change of f is less than the average rate of change of g.
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0.059 and 0.01 which is greater?
In 1995, wolves were introduced into Yellowstone Park.
The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.
By what percent does the number of wolves change each year?
In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.
Percent calculation.
To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.
The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.
To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:
Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.
In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.
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Study these equations:
f(x) = 2x – 4
g(x) = 3x + 1
What is h(x) = f(x)g(x)?
h(x) = 6x2 – 10x – 4
h(x) = 6x2 – 12x – 4
h(x) = 6x2 + 2x – 4
h(x) = 6x2 + 14x + 4
Answer:
6x2-10x-4
Step-by-step explanation:
hx=(2x-4)(3x+1)
hx=2x(3x+1)-4(3x+1)
hx=6x2+2x-12x-4
hx=6x2-10x-4
PLSSSS HELPPP I WILL FIVE BRAINLY!!!!
Answer:
The first box : -4 the second one : 6
Step-by-step explanation:
subtract 7 from 3 for the first box, then add 10 to -4 for the second one.
What is the volume of the triangular prism?
3 in.
15 in.
13 in.
I only need help with the f(0)= the equation is above all the rest is filled in thank you
f(0) = -3
I believe, since the graph has a closed circle/point at (0,-3), f(0) should equal -3. Also, the graph 3x-3 has a domain of x>=0.
However, in terms of limits, the limit approaching x-->0 does not exist since the left and right limits do not equal one another.
Hope this helps.
a. Find the open intervals on which the function is increasing and those on which it is decreasing.
b. Identify the function's local extreme values, if any, saying where they occur.
a. The open interval on which the function is increasing is [-2/3, 0].
The open intervals on which the function is decreasing are [-∞, -2/3] and [0, -∞].
b. The function's has a local maximum at (0, 0) and a local minimum at (-2/3, -4/27).
What is a decreasing function?For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.
By critically observing the graph of the given function, we can reasonably infer and logically deduce that it is decreasing over the following open intervals:
increasing = [-2/3, 0].
decreasing = [-∞, -2/3] and [0, -∞].
Part b.
The local minimum of a graph is the point on the graph of a function where it changes from a decreasing function to an increasing function, which is given by this ordered pair (-2/3, -4/27);
h(x) = -x³ - x²
h'(x) = -3x² - 2x
0 = -3x² - 2x
3x² = -2x
3x = -2
x = -2/3
h(-2/3) = -(-2/3)³ - (-2/3)²
h(-2/3) = -4/27.
For the local maximum, we have:
(0, 0)
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The Hernandez family orders 3 large pizzas. They cut the pizzas so that each pizza has the same number of slices, giving them a total of 24 slices.
The Wilson family also orders several large pizzas from the same pizza restaurant. They also cut the pizzas so that all their pizzas have the same number of slices. For the Wilson family, the equation y = 10x represents the relationship, where x represents the number of pizzas and y represents the number of total slices.
Which statements best describe the pizzas bought by the Hernandez and Wilson families? Select two options.
Suppose a random sample of size 44 is selected from a population with =8 . Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).
the size is n=500
the size is 5,000
the size is 50,000
Case 1: SE = s / √500
Case 2: SE = s / √5,000
Case 3: SE = s / √50,000
To find the standard error of the mean in each of the given cases, we can use the formula:
Standard Error (SE) = population standard deviation / square root of sample size
However, since the population standard deviation is not provided, we'll need to use an estimated value. We'll assume the population standard deviation is unknown and use the sample standard deviation as an estimate.
Given that the sample size is 44 and the population mean (μ) is 8, we'll calculate the standard deviation for each case:
Case 1: Sample size (n) = 500
The sample size (500) is larger than 5% of the population (44), so we can assume it's a large enough sample. In this case, we'll use the standard formula for the standard error of the mean without the finite population correction factor:
SE = sample standard deviation / square root of sample size
= s / √n
Case 2: Sample size (n) = 5,000
Similar to Case 1, the sample size (5,000) is larger than 5% of the population (44), so we'll use the standard formula without the finite population correction factor:
SE = s / √n
Case 3: Sample size (n) = 50,000
In this case, the sample size (50,000) is much larger than the population size (44), which means we have a large enough sample. Therefore, we'll also use the standard formula without the finite population correction factor:
SE = s / √n
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