Jon's bathtub exists rectangular and its base exists 18 ft². The water level rising if Jon is filling the tub at a rate of 0.2 ft³/min is 0.011 ft/min.
What is meant by differential equation?A differential equation in mathematics exists an equation that links the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.
If we take a look at a rectangular bathtub, the volume of the bathtub can be expressed as:
Volume (V) = length × breadth × height
where; base = length × breadth = 18ft²
The volume of the rectangular bathtub = 18h ......... (1)
Using differentiation to differentiate 18h with respect to t implicitly, then:
[tex]$\frac{\mathrm{dV}}{\mathrm{dt}}=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]
When the rate of rising of the volume is 0.2 ft² / min
[tex]$0.2=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]
substitute the values in the above equation, we get
[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=\frac{1}{18} \times(0.2)$$[/tex]
[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=0.011 \mathrm{ft} / \mathrm{min}$$[/tex]
Therefore, we can conclude that the rate at which the water level rises if Jon is filling the tub at 0.2 ft³/min exists 0.011 ft/ min.
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A person has lost a card game and is counting the points left in his hand. He announces that he has five fours and five sevens. Write this statement as a number expression.
The statement as number expression is given by the total number of points are 55.
What is Mathematical expression?
An expression is a finite combination of symbol and numbers depending on the context
We are given that A person has lost a card game and he is counting the points left in his hand.
His cards were five fours and five sevens
And we have to write this statement as number expression
Now there are five fours that is [tex]5*4=20 points[/tex]
And five sevens that is [tex]5*7=35 points[/tex]
Hence the total number of points are 20+35=55 points.
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Kamal invest $6130 at a rate of r% per year compound interest the value of his investment at the end of 5 years is $6669
The rate which the investment is compounded annually is 1.7%
Compound InterestCompound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
The formula to calculate compound interest is given as
[tex]A = p(1 + \frac{r}{n})^n^t[/tex]
A = final amountp = principalr = rate n = number of times compoundedt = timesubstituting the values into the equation and solve for rate at which the investment is compounded
[tex]A = p(1 + \frac{r}{n})^n^t\\6669 = 6130(1+ \frac{r}{1})^1^*^5\\ r = 1.7[/tex]
The rate of the investment is 1.7%
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according to multiple studies, including those by the american association of university women and the pew research center, on average, women are paid approximately which percent of what men are paid? select one: a. 80 b. 100 c. 90 d. 70
Women are paid approximately 80 percent of what men are paid.
Multiple studies have been carried out to discuss the income inequality prevailing in United States. Pay inequity has been found as a corollary of the income inequality.
The women and men has different pay levels for the same work at certain work places. Income inequality is considered as an injustice and to put forward this issue may organizations are trying.
Hence according to multiple studies, including those by the American association of university women and the pew research center, on average, women are paid approximately 80 percent of what men are paid.
We can see the appreciable difference in the pay levels of women and men prevailing.
As a result several laws has been passed recently to have a solution for this injustice.
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Find the area. Pls help with 12-13
12. A = [tex]3x^3-21x[/tex]
A = lw
A = 3x * (-7x * x^2)
(distribute the 3x
A = -21x * x^3
A = [tex]3x^3-21x[/tex]
13. A = [tex]4x^3 -4x[/tex]
A = lw
A = 4x * (x^2 * -7x + 6)
(distribute the 4x)
A = 4x^3 * -28x +24x
A = [tex]4x^3 -4x[/tex]
what are the appropriate measures of central location for interval data? mean and median median and mode mean, median, and mode what are the appropriate measures of variability for interval data? range, interquartile range, variance, standard deviation, and coefficient of variation variance coefficient of variation what are the appropriate measures of relative standing for interval data? interquartile range percentiles and quartiles none
The appropriate measures of central location for interval data are Mode, median, and average
The measure of a data set's most valuable position is its core location. Basically, they are mean, median, and mode.
Mean: The mean is the data set's average value. It is the total number of data divided by the sum of the data set.
The data point in the middle of the data collection is known as the median.
It can be obtained by halving the data set, which will show where the median is located.
Simply put, mode refers to the data that occurs most frequently.
Each of these provides positional information on the data, as can be seen from the definition.
The one value that other values in the data center around is given by the mean.
Therefore, the correct options are Mode, median, and average
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Write an equation in slope-intercept form of the line that passes through the given points.
The equation of the line is y = -2.5x - 1
How to determine the line equation?The table represents the given parameter
On the table, we have the following points
Point, (x, y) = (0, -1) and (2, -6)
So, we start by calculating the slope of the line using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are defined above
So, we have
Slope = (-6 + 1)/(2 - 0)
Evaluate
Slope = -2.5
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
Slope, m = -2.5
(x₁, y₁) = (0, -1)
So, we have
y = -2.5(x + 0) - 1
Open the brackets and evaluate
y = -2.5x - 1
Hence, the line has an equation of y = -2.5x - 1
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Claire scheduled a taxi to pick her up at her house. The taxi service says it will take 15 minutes to get to her house based on normal traffic routines. However, due to either no traffic or more traffic than normal, the time could vary by as much as 4 minutes. Which inequality and solution show the range of possible minutes, t, it will take for the taxi to get to Claire's house?
The inequality would be 15 ≤ t ≤ 19 showing the range of possible minutes it will take for the taxi to get to Claire's house.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The time could vary by as much as 4 minutes.
Let t be the range of possible minutes
The taxi service says it will take 15 minutes to get to her house based on normal traffic routines.
So the inequality as 15 ≤ t
The time could vary by as much as 4 minutes.
So the inequality as 15 ≤ t ≤ 15 + 4
⇒ 15 ≤ t ≤ 19
Therefore, the inequality would be 15 ≤ t ≤ 19 showing the range of possible minutes.
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Only 20 percent of the spectators left the contest discontented. If 6000 spectators left the contest contented,
how many left discontented?
There are 24000 spectators left the contest discontented.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that Only 20 percent of the spectators left the contest discontented.
If 6000 spectators left the contest contented, then the contest left discontented are;
The spectators left the contest contented = 6000
20/ 100 x D = 6000
D = 6000 x 100/20
D = 30000
Now the contest left discontented are;
80 percent = 80/100 x 30000
= 24000
Hence, 24000 spectators left the contest discontented.
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Find the area of the figure. Use 3.14 for pi.
assuming that the population size is 1,000 people, the prevalence of smoking in epiland is 60% and the percentage of people drinking water with a high concentration of heavy metals is 30%, calculate the total number of cases of cancer x that could be prevented if each one of the exposures were eliminated. what would be your suggestion to the public health agencies if they asked you which one of the exposures would have a greater impact on reducing the prevalence of the disease if it was eliminated?
1. The total number of cases of cancer x that could be prevented if each one of the exposures were eliminated is 900.
2. The suggestion to the public health agencies if they requested the one exposure that would have a greater impact on reducing the prevalence of cancer x if eliminated is smoking.
What is the prevalence rate?The prevalence rate refers to the proportion of the population who have a particular disease or attribute or can be exposed to risks at a specified time or over a specified period.
The assumed population size in Epiland = 1,000
Prevalence of smoking in Epiland = 60%
The number of Epiland smokers = 600 persons (1,000 x 60%)
Percentage of people drinking water with a high concentration of heavy metals = 30%
The number of people drinking the water = 300 (1,000 x 30%)
The total number of people exposed to cancer x = 900 (600 + 300).
Thus, 90% of the population in Epiland is exposed to cancer x based on the prevalence rate of smoking and the high concentration of heavy metals in their drinking water.
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-6 = -2/9w solve for w and simplify your answer as much as possible
Answer:
w = 27
Step-by-step explanation:
Solve for w: -6 = -2/9w
-6 = -2/9w
divide both sides by -2/9:
-6/(-2/9) = -2/9w/(-2/9)
27 = w
Do the interior angles of a quadrilteral always add up to the same thing? Explain why you think so.
A car, initially traveling east with a speed of 15 meters per second , is accelerated uniformly at 4 meters per second 2 east for 10 seconds along a straight line. what is the total distance the car travels during this 10 second interval?
Answer:
350m
Step-by-step explanation:
Vi = 15 m/s
A = 4 m/s^2
delta t = 10s
delta x = ?
delta x = (Vi)(delta t) + 1/2(A)(delta t)^2
delta x = (15m/s)(10s) + 1/2(4m/s^2)(10s)^2
delta x = 350 m
Which of the following service providers may use credit reports and/or credit scores to decide whether a person can buy a service and/or what price he or she will pay?Group of answer choicesLandlordMortgage lenderCell phone companyAll of the aboveCredit card issuer
Answer:
All of the above
Explanation:
All the given options make use of credit scores and/or credit reports to decide whether a person can buy a service and/or to decide what price he or she will pay. landlords may use credit scores to decide if they will require a security deposit and, if so, how much it should be. Also, other service providers like Mortgage lender, Cell phone company and Credit card issuer makes use of credit scores and/or credit reports in making certain decisions.
Find the m
bisector.
Answer: [tex]50^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle FDE=25^{\circ}+25^{\circ}=50^{\circ}[/tex]
Find the area of the trapezoid shown above. [?] square inches The measurements are 36in the base. 20in the height. 30 in the top.
The dimensions given are as follows;
Base a = 36
Base b = 30
Height = 20
The area is derived as follows;
[tex]\begin{gathered} A=(\frac{a+b}{2})\times h \\ A=(\frac{36+30}{2})\times20 \\ A=(\frac{66}{2})\times20 \\ A=33\times20 \\ A=660in^2 \end{gathered}[/tex]The area therefore is 660 square inches
A shipment of 8 computers contains 4 with defects. Find the probability that a sample of size 1, drawn from the 8, will not contain a defective computer,What is the probability that a sample of 1 of the 8 computers will not contain a defective computer?(Type an integer or a simplified fraction)Help Me Solve ThisView an ExampleGet More HelpClear All
Answer:
1/2
Explanation:
If you take a sample of 1 drawn from the 8, you will have 8 possible options and 4 of them didn't contain defects. So, the probability can be calculated as:
[tex]\frac{4}{8}=\frac{1}{2}[/tex]Therefore, the answer is 1/2
The probability that a sample of 1 of the 8 computers will not contain a defective computer is 1/2.
What is the probability?The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.
Given a shipment of 8 computers contain 4 with defects.
That means 8 -4 = 4 computers have no defect.
To find the probability;
we have 8 possible computers and 4 computers have no defect.
The probability;
= 4 /8
= 1/2
= 0.5
Therefore, the probability that a sample of 1 of the 8 computers will not contain a defective computer is 1/2.
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A z-score of z = −2.00 indicates a position in a distribution __________.
A- above the mean by a distance equal to 2 standard deviations
B- below the mean by 2 points
C- below the mean by a distance equal to 2 standard deviations
D- above the mean by 2 points
Answer:
C- below the mean by a distance equal to 2 standard deviations
Step-by-step explanation:
The Z-score, or standard score, is the number of standard deviations a given data point lies above or below the mean.The z-score is positive if the value lies above the mean, and negative if it lies below the mean.So, a z-score of z = −2.00 indicates a position in a distribution below the mean by a distance equal to 2 standard deviations.A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she ascended 61.9 feet. How many feet had she been below sea level, if she was 21.6 feet below sea level after she ascended?
The scientist was 83.5 feet below sea level while studying ocean life.
Given that:-
Distance the scientist ascended after studying the ocean life = 61.9 feet
Distance below sea level the scientist is after ascending = 21.6 feet
We have to find the distance by which the scientist was below sea level while studying the ocean life.
We know that,
Distance by which the scientist was below sea level while studying the ocean life = Distance the scientist ascended after studying the ocean life + Distance below sea level the scientist is after ascending
Hence, we can write,
Distance by which the scientist was below sea level while studying the ocean life = 61.9 + 21.6 = 83.5 feet.
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overbooking flights is a common practice of most airlines. a particular airline, believing that 4% of passengers fail to show for flights, overbooks (sells more tickets than there are seats). suppose that for a particular flight involving a jumbo-jet with 267 seats, the airline sells 278 tickets. question 1. what is the expected number of ticket holders that will fail to show for the flight? (use 2 decimal place in your answer.) question 2. what is the probability that the airline will not have enough seats for all the ticket holders who show for the flight? (use 3 decimal places.)
1. 3.2673 is the expected number of ticket holders that will fail to show for the flight.
2. 0.425 is the probability that the airline will not have enough seats for all the ticket holders who show for the flight.
P(airline will not have enough seats for all the ticket holders who show for the flight) = P(more than 267 people show up for the flight)
p = P(will show for flight) = 1 - 0.04 = 0.96
n = 278
µ = n * p = 278 * 0.96 = 266.88
σ = [tex]\sqrt{ n*p* (1 - p)} = \sqrt{278 * 0.96 * 0.04} = 3.2673[/tex]
P(X > 267) = P(X > 267.5)
p(x- µ) / σ > 267.5- µ /σ
= P(Z> 267.5 – 266.88/ 3.2673 )
= P(Z > 0.19)
= 0.425.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. To understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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Yasmin is making some pancakes. Her recipe makes 6 pancakes.
Flour
Eggs
Milk
100g
2
250ml
Yasmin wants to make 15 pancakes.
Complete the table to show how much she will need of each ingredient.
Answer:
tbh times them all by 15 and u should get the answers
Christina is doing an obstacle course in gym class. First, she runs 100 feet and jumps over a hurdle. Then, she crawls through a 20-foot tunnel. Finally, she dribbles a soccer ball 60 feet to the finish line. How many yards long is the obstacle course?
Answer:
60 yards
Step-by-step explanation:
100 feet + 20 feet + 60 feet = 180 feet
180 feet = 60 yards (there are 3 feet in 1 yard)
8. Find the area of the kite.
Answer:
A=16, the formula to find the area of a kite is A=pq/2
Step-by-step explanation:
A=pq/2 = 4×8/2=16
Lexi and Raymond are hosting events that are catered by the same company. Lexi plans to have 63 adults and 59 children attend, so the total projected cost of her meals is $2,582. Raymond has 63 adults and 93 children on her guest list, so he will pay the caterer $3,126. How much does the caterer charge for each meal?
Every adult's meal costs $
, and every child's meal costs $
.
The cost for children meal is $16 and the.cost for adult meal is $26.
How to calculate the value?Let cost of adult meal = a
Let cost of child meal = c
Lexi plans to have 63 adults and 59 children attend, so the total projected cost of her meals is $2,582.This will be:
63a + 59c = 2582 ...... i
Raymond has 63 adults and 93 children on her guest list, so he will pay the caterer $3,126. This will be;
63a + 93c = 3126 ...... ii
Collect both equations
63a + 59c = 2582 ...... i
63a + 93c = 3126 ...... ii
Subtract i from ii
34c = 544
Divide
c = 544 / 34
c = 16
The cost of children meal is $16.
From equation i, 63a + 59c = 2582
63a + 59(16) = 2582
63a + 944 = 2582
Collect like terms
63a = 2582 - 944
63a = 1638
a = 1638/63
a = 26
Adult meals is $26.
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What is the equation of the line that passes through the point (4, 6) and has an
undefined slope?
Answer:
x = 4
Step-by-step explanation:
a line with an undefined slope is a vertical line parallel to the y- axis, with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (4, 6 ) with x- coordinate 4 , then
x = 4 ← equation of line
an engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 140 lbs. and 190lb. the new population of pilots has normally distributed weights with a mean of 158 lbs. and a standard deviation of 27.2 lb. find the probability that a pilot weight is between 140 lbs. and 190 lbs. the probability that the pilot weighs between 140 and 190 pounds is
The probability that the pilot weighs between 140 and 190 pounds is 0.6262.
When provided,
µ = 158
σ = 27.2
We must determine P(140 x 190).
P(140< x < 190) = P(x< 190) - P(x<140)
Locate P(x 190).
Z = (x - µ)/σ
Z = (190 - 158)/27.2
Z = 1.176471
P(Z<1.176471) = P(x<190) = 0.880297
[This probability can be determined using a z-table, Excel, Ti-83/84 calculator, software, etc. Z-table is less accurate than other methods in terms of value.]
Find P(x>140) now.
Z = (x - µ)/σ
Z = (140 - 158)/27.2
Z = -0.66176
P(Z<-0.66176) = P(x<140 ) = 0.254061
P(140< x < 190) = P(x< 190) - P(x<140)
P(140< x < 190) = 0.880297 - 0.254061
P(140< x < 190) = 0.626236
The necessary probability is 0.6262.
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Answer:
Step-by-step explanation:
0.626 is the probability that the pilot weighs between 140 and 190 pounds.
Mean (µ ) = 158
S.D(σ ) = 27.2
P(140 x 190)=?
P(140< x < 190) = P(x< 190) - P(x<140)
Find P(x 190).
Probability determined using Z-table.
Z = (x - µ)/σ
= (190 - 158)/27.2=1.176471
P(Z<1.176471) = P(x<190) = 0.88
Find P(x>140)
Z = (140 - 158)/27.2= -0.66176
P(Z<-0.66176) = P(x<140 ) = 0.254
P(140< x < 190) = 0.88 - 0.254
= 0.626
Therefore probability is 0.626.
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brainly 100!!! Which of the following functions is graphed below?
The function that is represented on the graph is (a) y = x^2 + 4, x < 2 and y = x + 4, x ≥ 2
How to determine the graphed function?The graph represents the given parameter
From the graph, we have the following function types
Whole graph: Piecewise functionQuadratic function to the leftLinear function to the rightUsing the options as a guide, we have the equations to be
Quadratic function: y = x^2 + 4Linear function: y = x + 4Next, we calculate the domain
The quadratic function stops at x = 2 with an open circle
So, the domain is x < 2
The linear function starts at x = 2 with a closed circle
So, the domain is x ≥ 2
Hence, the graphed function is (a)
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If M is between G and T, MG = 2x + 1, MT = 3x + 3, and GT = 19, Then X = ___.MG = ___.MT = __.
We are given the following information
M is between G and T
MG = 2x + 1
MT = 3x + 3
GT = 19
Let us draw a sketch to better understand the problem
As you can see, the sum of MG and MT must be equal to the GT
Mathematically,
[tex]\begin{gathered} GT=MG+MT \\ 19=(2x+1)+(3x+3) \end{gathered}[/tex]Let us solve the above equation or x
[tex]\begin{gathered} 19=2x+1+3x+3 \\ 19=2x+3x+1+3 \\ 19=5x+4 \\ 19-4=5x \\ 15=5x \\ \frac{15}{5}=x \\ 3=x \\ x=3 \end{gathered}[/tex]So, the value of x is 3
[tex]\begin{gathered} MG=2x+1 \\ MG=2(3)+1 \\ MG=6+1 \\ MG=7 \end{gathered}[/tex][tex]\begin{gathered} MT=3x+3 \\ MT=3(3)+3 \\ MT=9+3 \\ MT=12 \end{gathered}[/tex]Therefore, the required values are
x = 3
MG = 7
MT = 12
Karl drove 40 miles in 50 minutes. Teresa drove 35 miles in 42 minutes. Who had a higher average speed?
The person that has the higher average speed is Teresa.
How to calculate average speed?The average speed is the total distance travelled by the object in a particular time interval.
Average speed measures the average rate of speed over the extent of a trip.
Therefore,
average speed = distance / time
Hence, Karl drove 40 miles in 50 minutes.
Therefore,
average speed of Karl = 40 / 50
average speed of Karl = 4 / 5 miles per minute
Teresa drove 35 miles in 42 minutes.
Therefore,
average speed of Teresa = 35 / 42
average speed of Teresa = 5 / 6 miles per minutes
Therefore, Teresa had the higher average speed.
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Ryan Pick 6 1/2 cups of berries from his garden he use 3 3/8 cups of to make fruit salad if he needs 3 cups of berries to make a pie does Ryan have enough very stuff to also make a pie?
We will simply subtract 3 3/8 from 6 1/2
That is;
6 1/2 - 3 3/8
= 3 4-3/8
=3 1/8
The amount of berry left is more than 3 cups, hence Ryan have enough very stuff to also make a pie