A rectangle has a perimeter of 48 inches. If twice the length decreased by three is equal to three times the width, then find the length and width.
1. Write a system of equations that will solve the problem
2. Define your variables
3. Solve the problems SHOW YOUR WORK
4. Sketch a graph of your solution
Answers
1) The system of equations to solve the given problem are:
2l-3=3b
2(l+ b)=48
2) The variables l and w stands for length and width, respectively.
3) Length l=15 and Width w=9
4) The graph of the solution is shown below:
What is meant by perimeter?A perimeter is a closed path that covers, surrounds, or outlines a two-dimensional shape or a one-dimensional length.
The perimeter calculation has various practical uses. A calculated perimeter is the length of fencing required to encircle a yard or garden. The circumference of a wheel/circle specifies how far it will roll in one revolution. Similarly, the amount of string coiled around a spool is proportional to the spool's perimeter; if the length of the string were precise, it would equal the perimeter.
1) The system of equations to solve the given problem are:
2l-3=3b
2(l+ b)=48
2) Here the variables are l, w
The variables l and w stands for length and width, respectively.
3) Given, perimeter of the triangle=48 inches
2l-3=3b
l=(3(b+1))/2
So, 2(l+ b)=48
3b+3+2b=48
5b=45
b=9
l=(3(10))/2
l=15
Therefore, length l=15 and width w=9
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Related Questions
Use cylindrical coordinates.Evaluatex2 dV,iiintegral.gifEwhere E is the solid that lies within the cylinderx2 + y2 = 4,above the planez = 0,and below the conez2 = 16x2 + 16y2.
Answers
The value of the integral ∫x²dV using cylindrical coordinates is 512π / 3 .
In this case, the solid is positioned between the cylinder x² + y² = 4 and will be evaluated by using the cone z²= 16x² + 16y² .
Cylindric coordinates will be used to calculate this integral [tex]\int\limits_e {x^2} \, dx[/tex].
The distance from the origin to the point (x, y, 0) and the angle the point (x, y, 0) makes with the x-axis, respectively, are provided by the formulas.
x = r cos θ
y= r sin θ
With these coordinates, we shall characterize the solid E.
The boundary is then x² + y² = r²
The boundary also becomes r² = 4 or ( 0 ≤ θ ≤ r² )
Again z = 16r²
The original integral must now be translated into terms of these new coordinates. It is necessary to multiply the function by the Jacobian of the change in coordinates in order to ensure that the result remains the same. The value for the cylindric coordinates is r. Then
[tex]\int_ex^2 dx = \int\limits^{2\pi}_0\int\limits^2_0\int\limits^{16r^2}_0 r(r^2cos^2\theta)dzdrd\theta[/tex]
[tex]=\int _0^{2\pi }\int _0^216r^5\cos ^2\theta drd\theta[/tex]
[tex]=\int _0^{2\pi }\frac{512}{3}\cos ^2\theta d\theta[/tex]
= 512/3 π
Hence the volume of the solid that is enclosed by the integral is given by 512/3 π .
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for the given scenario, determine the type of error that was made, if any. (hint: begin by determining the null and alternative hypotheses.) a new whitening toothpaste advertises four shades as the mean number of shades the toothpaste whitens your teeth. one user claims that the mean number of shades the toothpaste whitens your teeth is less than four shades. the user conducts a hypothesis test and fails to reject the null hypothesis. assume that in reality, the mean number of shades the toothpaste whitens your teeth is three shades. was an error made? if so, what type?
Answers
Yes there was an error made and it is a type II error
What is type i and ii error in Hypotheses testing?
A Type I mistake in statistics is a false positive finding, whereas a Type II error is a false negative finding.
The possibility of making these mistakes is inherent in hypothesis testing since making a statistical choice always entails some level of uncertainty.
The significance level, or alpha (), determines the likelihood of a Type I mistake, whereas beta () determines the likelihood of a Type II error. These dangers can be reduced by carefully designing the layout of your study.
Comparison of Type I and Type II errors
Considering your minor symptoms, you decide to get checked for COVID-19. There are two mistakes that could happen:
False positives of type I are when a test indicates you have a coronavirus when you don't.
False negative type II errors occur when the test results indicate that you don't have coronavirus but in fact you have.
The null and alternate hypotheses are provided below for the scenario:
H0: The average amount of tooth whitening achieved by toothpaste is four shades.
Ha: The average amount of colors your teeth lighten after using toothpaste is less than four.
H0: µ = 4
Ha: µ < 4
While we reject the null hypothesis when it is true, we made a type I error, according to the definition.
The failure to reject the null hypothesis when the null hypothesis is false is what is referred to as a type II error .
In the hypothetical situation, it is said that the average number of shades that toothpaste whitens teeth is three. This implies,
There are less than four hues. This proves that the null hypothesis is untrue.
This indicates that when the null hypothesis is false, we are unable to reject it.
It is a type II error as a result.
Yes, a type II error.
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Write the slope-intercept form of the line
Answers
y=2x/3-2 is the required slope-intercept form of the line
The coordinate of points where the line intersects at the x-axis is (-3,0) and at the y-axis is (0,-2) now from there two points we can find slope if line that is
slope=y₂-y₁/x₂-x₁=(-2-0)/(0-(-3))
slope =-2/3
with one point (0,-2) and slope we can find the slope-intercept form that is y=mx+c
where m is slope and c is intercept on the y-axis
y=2x/3-2 this is the slope-intercept form and by simplifying it we get
3y=2x-6
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Given the equation, y=3x, complete the table of values
x (input)
y (output)
-2
-1
0
1
2
Answers
Answer:
To find the answers you just need to multiply each value by 3. This is as we are given the information that y is equal to 3x. If we know this and we know the values of x we can easily work out the output (y)!!
-2 = 3 x -2 = -6-1 = 3 x -1 = -30 = 3 x 0 = 01 = 3 x 1 = 32 = 3 x 2 = 6We can also see a pattern of +3 going upwards!!
Hope this helps, have a great day!
What’s the difference between factoring x4+9x2+8 and factoring x2+9x+8?
Answers
Answer:
The difference between factoring x4+9x2+8 and factoring x2+9x+8 is that the first equation is a fourth degree polynomial, while the second equation is a second degree polynomial. The first equation can be factored into (x2 + 3)(x2 + 8), while the second equation can be factored into (x + 8)(x + 1).
If Jasmine roller skates 280 miles in 7 weeks and skates the same distance each week, how many miles does she skate each week?
Answers
Answer:
40
Step-by-step explanation:
280 divided by 7
The following data values represent the daily amount spent by a family during a 7 day summer vacation. Find the sample standard deviation of this dataset: $96, $125, $80,$110, $75, $100,8121 Round the final answer to one decimal place. . Provide your answer below std
Answers
The sample standard deviation of the following dataset is dev = $22.4 : $96, $125, $80,$110, $75, $100,8121.
The square root of the variance of a random variable, sample, mean ,statistical population, data set, or probability distribution is that variable's standard deviation. Although less robust in practice, it is algebraically simpler than the average absolute deviation.The fact that the standard deviation is expressed in the same unit as the data, as opposed to the variance, is a useful characteristic of the statistic.
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what is 14 = h/5 ive tried and tried...its still incorrect
Answers
Answer: h = 70
Step-by-step explanation: We just need to take 14 timed 5 and we will get h.
14 = h/5 because it is divided so to get rid of it we multiply by 5
70=h
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Find an equation in standard form for the ellipse graphed below.
Answers
The equation of the ellipse in the graph, with center at (0, 0), and semi major and minor axis of 3 and 2 can be presented as follows;
[tex]\dfrac{x^2}{2^2} +\dfrac{y^2}{3^2 } = 1[/tex]
What is the locus of an ellipse?An ellipse is the locus of a point that moves such that the sum of the distance from two points is constant.
The standard form of the equation of an ellipse can be presented as follows;
[tex]\dfrac{(x - h)^2}{b^2} + \dfrac{(y - k)^2}{a^2} = 1[/tex]
Where;
(h, k) = The coordinates of the center of the ellipse
a = The semi major axis
b = The semi minor axis
From the attached graph the coordinates of the center of the ellipse is; (0, 0)
The semi major axis, a = 3
The semi minor axis, b = 2
Therefore;
[tex]\dfrac{(x - 0)^2}{2^2} + \dfrac{(y - 0)^2}{3^2} = 1[/tex]
The equation of the ellipse in standard form is therefore;
[tex]\dfrac{x^2}{2^2} + \dfrac{y ^2}{3^2} = 1[/tex]
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from a population with a standard deviation of 35, a sample of 150 items is selected. at 95% confidence, what is the margin of error for the population mean? round your answer to three decimal places.
Answers
The margin of error for the population mean is 5.601
What does the term "margin of error" mean?
Your results will deviate by how many percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.
Given c = 0.95
The significance level is obtained as follows:
alpha = 1 - c
alpha = 1 - 0.95
alpha = 0.05
Also, it is given that n = 150 and sigma = 35 .
The critical value of Z distribution at 0.05 level of significance can be computed in MS Excel using + NORMS INV (alpha/2) function as follows:
Thus, [tex]Z_{0.005/2}=1.96[/tex]
Now, the margin of error can be computed as follows: ME = Critical Value x Standard Error
[tex]Z_{0.005/2}*\frac{sigma}{\sqrt{n} } \\= 1.96 * \frac{35}{\sqrt{150} } \\= 5.601[/tex]
Thus, the margin of error for the population mean is 5.601
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wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. based on this information, what is a possible amount of time, in hours, that it could take wyatt to husk 72 dozen ears of cor
Answers
The possible amount of time that it could take Wyatt to husk 72 dozen ears of corn is 4 to 6 hours.
What are time and work?
Time is the span of any action or work that occurs or is ongoing. Work is a task or series of activities carried out to accomplish a specific goal.
Given, Wyatt can husk anywhere from 12 to 18 dozen ears of corn per hour.
Thus, to find the time taken to husk 72 dozen ears of corn,
the maximum time = 72/12 =6 hours
And, the minimum time = 72/18 =4 hours
Thus, depending on his speed, Wyatt takes anywhere from 4 to 6 hours to husk 72 dozen ears of corn.
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Mihir has 14,203 beads. He uses 36 beads to
make one necklace. How many necklaces can
he make?
Answers
Answer:
394
Step-by-step explanation:
because 14,203 divided by 36 is 394.527777778 but the complete number of necklaces he can make is 394.
Choose the correct answer below
Answers
Answer: B. Angle Bisector
Why: the line from D to be is intersecting or bisecting the 90 degree angle
help me solve this one! please.
thank u.
Answers
The required are of shaded region for the given question is 20.7 cm^2.
Explain sector of circle.A circle is partitioned into two areas, specifically the significant area, and the minor area. A bigger piece of the circle involved by the radii and the significant circular segment is supposed to be a significant area. A more modest part involved by two radii and a minor circular segment is known as the minor area.
According to question:We have,
∠BOC = 2π/5, radius = 6 cm, OA = 2 cm, DC = 2 cm
OD = 6 - 2 = 4 cm,
We know that
Area of triangle = OA×OD×sin(2π/5)/2
A = 2×4×0.475/2 = 1.9 sq. cm
And
Area of sector = (π/5)/2π ×πr^2
Area of sector = π(6)^2/5
Area of sector = 22.6 sq. cm
Area of shaded region = 22.6 - 1.9 = 20.7 sq. cm
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Mr. Brown is making a total of n wooden frames. If he has made two-thirds of them so far, what would be an expression to represent the number of frames he has left to make?
Answers
An expression that would represent the number of frames he has left for him to make would be = X = n - ⅔.
What is a fraction?A fraction is an expression that is used to represent the part of a whole structure or an object such as the wooden frame.
The total number of wooden frames to be made= n.
The number of frames that Mr. Brown has made= ⅔
The number that is left to be made = X
But, n = ⅔ + X
To find X, make X the subject of formula;
X = n - ⅔.
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Give an example of a function that is a dilation and a reflection of the parent function.
Answers
Answer: f(x) = -1/2(x+3)
Example: g(x) = -1/2(-x-3)
This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.
PLEASE HELPPPPP
Also that’s a 14 and 17
Answers
A hypothesis test was used to test the hypothesis that people with a significant other are happier on average than people without. The P-value was 0.07 and the level of significance used was 0.1. Then there is sufficient evidence to conclude that, on average, people witha significant other are happier than single people. Hint Textbook Pages True False
Answers
True, A P-value of 0.07 is less than that significance requirement of 0.1, suggesting that there is sufficient evidence to conclude that people who have a significant other are happier than single people.
The hypothesis being examined was that those who have a significant other are happier on average than those who do not. To test this hypothesis, data from a sample size of persons were collected and evaluated to compute the P-value.
The P-value of 0.07 was determined to be less than the level of significance established at 0.1, implying that there is sufficient evidence to support the hypothesis that persons with a significant other are happier on average than solitary people.
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a university charges students $2,300 less for tuition each year to encourage them to stay in school. the tuition for freshman year is $34,000. write a regression equation for this formula, with y
Answers
The regression equation of the formula regarding tuition will be given as y = 34000 - 2300x.
Regression method of writing an equation is used to show relation between two variables. The two variables include an independent variable and a dependent variable. The dependent variable is related to the independent variable and their relation and changes can be shown with the help of regression model. According to the question
the charge for tuition = $32000
Charge deduced from tuition per year = $2300
So we assume the tuition cost as y and the number of years as x.
The regression equation will be
y = 34000 - 2300x
where y is the tuition cost and x is the number of years in school and y is dependent variable and x is independent variable.
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Determine whether the pair of lines appear to be parallel or perpendicular.
1. The lines are perpendicular because they are always the same distance apart and never intersect.
2. The lines are parallel because they intersect at a right angle.
3. The lines are parallel because they are always the same distance apart and never intersect.
4. The lines are perpendicular because they intersect at a right angle.
Answers
7-radical 7 over10+radical 3
Answers
The simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].
What is an algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
The given statement is "7-radical 7 over10+radical 3".
Write the statement in mathematical form and simplify:
[tex]\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\\\\\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\times\frac{10 - \sqrt{3}}{10 -\sqrt{3}}\\\\\frac{(7 - \sqrt{7})(10-\sqrt{3})}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex]
Hence, the simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].
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Please help on this question
Answers
Answer:yes
Step-by-step explanation: 2/8=4
4/1=4 since both of them equal 4 they are equivalent
a firm in a purely competitive industry is currently producing 1,000 units per day at a total cost of $700. if the firm produced 800 units per day, its total cost would be $450, and if it produced 500 units per day, its total cost would be $425.
Answers
a firm in a purely competitive industry is currently producing 1,000 units per day at a total cost of $700 then average total cost is $ 0.61
The average total cost is calculated as the total cost divided by the number of outputs. The firm's ATC at these three levels of production will be:
1. 1,000 units per day at a total cost of $700.
ATC = Total cost/output
ATC = $700/1000
ATC = $0.58
2. If the firm produced 500 units per day, its total cost would be $450.
ATC = Total cost/output
ATC = $450/500
ATC = $0.45
3. If it produced 700 units per day, its total cost would be $425.
ATC = Total cost/output
ATC = $425/700
ATC = $0.61
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PLSSS HURRYYYY!!! 30 POINTS!
The slopes of the sides of quadrilateral JKLM are: 3,-3,, and -3.
Answers
Why you lie you say 30 but give a 15
true or false? when the direction of the bias is toward the null, it means that the error causes the true measure of association to be overestimated.
Answers
it is false that that when the direction of bias is towards love it means that the error causes the true measure of association to be overestimated
A Measurement process is biased if it systematically overstates or understates the true value of the measurement
Systematic error due to difference in accuracy or completeness of recall to memory of past or experience is the most associated with recall bias.
Positive association is biased toward the null null value it means that the error causes the true value of association to be underestimated
but in the given given question the statement states that when the direction of the bias is toward the null it means that the error causes the true measure of association to be overestimated which is false
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Joan's nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for the planting of a medium-sized tree. Actual times from a sample of 10 plantings during the past month follow (times in hours).
Answers
The average sample of 10 plantings tree-planting time is two hours- P-value = 0.251453
The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project-P-value = 0.251453
We are unable to reject the null hypothesis and accept it because the p value is higher than the significance level.
As a result, we draw the conclusion that the average tree-planting time is two hours.
Hypothesis:
In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.
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How many times can 24 go into 528
Answers
Answer:
22
Step-by-step explanation:
4.
Raquel scored an
80% on her science
test. If she got 20
questions correct,
how many
questions were on
the test?
5.
Answers
Answer:
25
Step-by-step explanation:
knowing that 80 is 4/5 of 100, we need to find the number that is 5/4 of 20. That number is 25. This can be proven by calculating that 20/25 and 80/100 both can be simplified to 4/5.
shelby was asked to determine the number of packages that can be wrapped with 12 feet of ribbon if it takes a half of a foot to wrap one package.
Answers
The number of packages that can be wrapped with 12 feet of ribbon is 24.
Explain the term unitary method?The unitary approach is a strategy for problem-solving that involves first obtaining the value of a specific unit, then multiplying that value to determine the required value.The unitary approach includes determining the value of a single unit, from which we can calculate the values of the appropriate number of units.For the stated question.
Total length of the ribbon = 12 feet.
Ribbon required to wrap a one box = 1/2 foot.
Number of boxes = Total length / required ribbon for one box
Number of boxes = 12/ (1/2)
Number of boxes = 12 x 2
Number of boxes = 24
Thus, the number of packages that can be wrapped with 12 feet of ribbon is 24.
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The population of a bee hive is growing with a monthly percentage rate compounded continuously. the population doubles in 3 months. find the monthly percentage rate according to the exponential growth function. leave your answer in terms of ln. note: when entering natural log in your answer, enter lowercase ln as "ln". there is no "natural log" button on the alta keyboard.
Answers
The exponential growth function's estimate of the monthly percentage rate is; log 3/ 3.
Explain the term exponential growth function?A function called exponential growth depicts an expansion within a population than happens at the same pace across time. If a population doubles or triples in size, you can assume that the data grows exponentially. Exponential decay is the inverse of exponential growth, in which data contracts rather than expands.We will employ the exponential function, as indicated, to determine the monthly percentage rate;
P(t) = P(0)e∧(rt)
The initial population is P0 for the bee hive.The end population will be 3P0 if the beginning population doubles in three months.Enter the following parameters into the calculation to obtain the rate "r".
P(t) = P(0)e∧(rt)
3P(0) = P(0)e∧(rt)
3 = e∧(rt)
Taking log both sides.
log 3 = (rt)
r = log 3 / 3
r = 0.366
r = 36.6%
Consequently, the exponential growth function's estimate of the monthly percentage rate compounded continuously is; log 3/ 3.
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Answer: the answer is ln(2)/3
Step-by-step explanation: