The difference between the greatest and least areas is 72 square inches.
What is perimeter of a rectangle?
Let L be the length and w be the width of the rectangle.
Perimeter = 2l + 2w = 48
Since each side is a whole number, list pairs of whole numbers that satisfy the equation.
Potential pairs (length, width) are:
(23, 1)
(22, 2)
(21, 3)
(20, 4)
(19, 5)
Let's calculate the areas for the pairs mentioned:
Area = l*w
(23, 1)) A = 23* 1 = 23
(22, 2) A = 22 *2 = 44
(21, 3) A = 21 *3 = 63
(20, 4) A = 20 *4 = 80
(19, 5) A = 19 *5 = 95
The greatest area is 95 square inches, and the least area is 23 square inches.
The difference between the greatest and least areas is 95 - 23 = 72 square inches. Therefore, the answer is 72.
If one line has a slope of 2/3, then the slope of a line parallel to it would be?
-3/2
perpendicular slopes are those that are opposite sign and reciprocal of the original given slope
What are the tangent ratios for Y and Z? The triangle is not drawn to scale. Please help I selected an answer but I’m sure it’s wrong
Answer:
[tex]tanY = \frac{4}{5}[/tex] and [tex]tanZ=\frac{5}{4}[/tex]
Explanation:
The tan of an angle in a triangle is equal to [tex]\frac{opposite}{adjacent}[/tex] for the side lengths. Opposite side is the one found directly across the triangle and the adjacent is the side touching the angle that is not the hypotenuse. This means the tan for Y is 4 over 5 and the tan for Z is 5 over 4.
The tangent ratios are:
tan(Y) = 5/4
tan(Z) = √41/4
In a right triangle with sides labeled X, Y, and Z, and angles labeled x, y, and z, you can use the trigonometric ratios to find the tangent ratios for angles Y and Z.
The tangent ratio is defined as:
For angle Y (opposite to side XY): tan(Y) = opposite / adjacent = XY / ZX
For angle Z (opposite to side ZY): tan(Z) = opposite / adjacent = ZY / XZ
Given the following values:
ZX = 4
XY = 5
ZY = √41
Let's calculate the tangent ratios:
For angle Y (opposite to XY):
tan(Y) = XY / ZX = 5 / 4
For angle Z (opposite to ZY):
tan(Z) = ZY / XZ = √41 / 4
So, the tangent ratios are:
tan(Y) = 5/4
tan(Z) = √41/4
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Determine the quotient of 2 over 5 divided by 3 over 4. 8 over 15 6 over 20 5 over 9 1 and 7 over 8
Answer:
1. Is 8/15
Step-by-step explanation:
Use the figure below to find the Measure of Angle BEH
Explain/Show how you got your answer please
Answer:
The measure of angle BEH is 55°
Step-by-step explanation:
we know that
m<DEB=45° -----> by corresponding angles
m<GEH=80° -----> by corresponding angles
m<DEB+m<BEH+m<GEH=180° ------> line DG
substitute the values and solve for m<BEH
45°+m<BEH+80°=180°
m<BEH=180°-125°=55°
Solve. Please HELP ASAP
change 7 5/6 to an improper fraction
= 47/6
change 6 1/2 to an improper fraction
13/2
rewrite
Q - 47/6 = 13/2
add 47/6 on both sides
Q = 13/2 + 47/6
times 13/2 by 3 to get a common denominator of 6
Q = 39/6 + 47/6
Q = 86/6
change to mixed number
14 2/6
simplify
= 14 1/3
Name the different forms of linear equations you learned. If (1, 2) and
(3, 4) lie on the same line, give the slope-intercept equation of the line.
2
Explain how to find the inverse of f(x) = (x-1)/4
2
What is average rate of change? How do you calculate it? What can you tell about the average rate of change for linear functions? Compare the slopes of horizontal and vertical lines.
3/4
Compare the processes of graphing linear equations and inequalities with examples of your own.
3/4
Create a real-life scenario in which you show how you interpret key features of functions and graphs such as slope and y-intercept?
Module 2
1
What is the definition of “i”? What do we use it for? Demonstrate with an example of your own.
2
Why are radicals simplified before adding and subtracting? Explain your reasoning by adding sqrt8 and sqrt32. Compare the process to multiplying and dividing.
2
Give an example of an expression with a rational exponent and explain how to convert it into radical form.
3/4
A good practice in mathematics is to always check your work. Explain why it is very important to do so when you are solving equations that involve radical expressions?
Where in real life do you work with radical expressions and functions? Give an example of your own.
Module 3
Webbs DOK
Discussion Prompt
1
How many different ways can you solve a quadratic equation? List them.
2
Create a trinomial that can be factored and write it in standard form.
2
Factor x^2 – 7x + 10, 4x^2 – 81 and p(x)=3x^3-12x
3/4
What key features of a quadratic graph can be identified and how are the graphs affected when constants or coefficients are added to the parent quadratic equations? Compare the translations to the graph of linear function. Create examples of your own to explain the differences and similarities.
3/4
A ball is kicked into the air and follows the path described by
h(t)= -4.9t^2+6t+0.6, where t is the time in seconds and h is the height in meters above the ground. Find the maximum height of the ball. What value would you have to change in the equation if the maximum height of the ball is more than 2.4 meters?
The solution to this exercise has been attached below. The problem has been solved in this way:
________________
1. Different forms of linear equations. Point slope-intercept equation of the line that passes through two points.2. Inverse Function. 3. Average Rate of Change.4. Comparison of linear equations and inequalities5. Real-life problems6. Imaginary Number7. Radicals8. Rational exponent and radical form9. Radical expressions10. Quadratic equation11. Trinomial12. Factoring expressions13. Quadratic and linear graph14. A problem of heightAnswer:
Everything he said was correct!
Step-by-step explanation:
I hope this helps!
- sincerelynini
what quadrilateral always has 4 congruent angles and opposite sides that are congruent and parallel?
Answer:
See below.
Step-by-step explanation:
A rectangle has 4 * 90 degree angles and opposite sides are congruent and parallel. A square also fits the bill.
A car of the same type and make is 3 1/2 years old. Estimate the value of the car.
The values in the scatter diagram indicate;
a) The graph of the data showing the location of the car that costs £2600 and is 4 years of age created with MS Excel is attached
b) The value of the cars decreases as the age increases
c) £3687.9
To address the question, plot the new car data on a scatter diagram, describe the trend of decreasing value with increasing age, and estimate the value of a car based on its age by interpolating between data points.
The question requests steps on how to represent data on a scatter diagram as well as how to interpret and estimate values from it.
a. Add the new point to the scatter diagram for a car that's 4 years old and valued at £2600. This point (4, £2600) should be plotted on the graph along with the other data points.
b. Describe the relationship by observing how the value tends to change as the age of the cars increases. Generally, as cars age, their value decreases, which suggests a negative relationship between the age and the value of the cars.
c. For estimating the value of a car that is 3.5 years old can be found as follows; The equation of the trend line for the scatter diagram obtained usinfg MS Excel is; y = -1290.2·x + 8203.6, indicates that when x = 4, we get;
y = -1290.2 × 3.5 + 8203.6
-1290.2 × 3.5 + 8203.6 =
The estimated price of the car is £3687.9
The complete question found through search is presented as follows;
The scatter diagram shows information about 10 cars.
The 10 cars are of the same type and make
Another car is 4 years old and has been valued at £2,600
a) Show this information on the graph
b) Describe the relationship between the age and the values of the cars
A car of the same type and age is 3¹/₂ years old
c) Estimate the value of the car
Find the area of the trapezoid. leave your answer in simplest radical form.
Answer:
Area[tex]=70in^2[/tex]
Step-by-step explanation:
The given diagram is a tra-pezoid.
The area of a tra-pezoid is calculated using the formula;
Area[tex]=\frac{1}{2} (Sum\:of\:parallel\:sides)\times height[/tex]
This implies that;
Area[tex]=\frac{1}{2} (8+12)\times 7[/tex]
Area[tex]=\frac{1}{2} (20)\times 7[/tex]
Area[tex]=(10)\times 7[/tex]
Area[tex]=70in^2[/tex]
The last choice is correct.
The probability assigned to each experimental outcome must be
Answer:
Between 0 and 1
Step-by-step explanation:
The probability for each outcome in experimental probability must be a value between 0 and 1. A probability of 0 means the event did not happen; the probability of 1 means it is certain. We cannot have probabilities smaller than 0 or greater than 1.
All of the probabilities in an experiment must sum to 1 whole.
The probability assigned to each experimental outcome must be greater than 0 or less than 1 or lies in between 0 and 1.
The probability of extremely certain event is 1 and the probability of extremely uncertain event is 0. The sum of all the probabilities in an experiment is always equals to 1.
Hence the probability assigned to each experimental outcome must be greater than 0 or less than 1 or lies in between 0 and 1.
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FIND ST OF THIS CIRCLE.
[tex]\bigtriangleup RSP \cong\bigtriangleup RQT\Rightarrow \frac{RS}{RQ}=\frac{RP}{RT}\Leftrightarrow RS=3 \\ \Rightarrow ST=RT-RS=5[/tex]
What is 0.36 expressed as a fraction in simplest form? Enter your answer in the box. Repeating 36
Answer: 9/25
Step-by-step explanation: .36 equals 36/100 in decimal form.
Reducing it into its simplest form:
Both numbers are divisible by 4-
36/100 = 9/25 - which is the simplest form.
When you multiply expressions with the same base, you ______ the exponents. Add multiply
Answer:
... you add the exponents
Step-by-step explanation:
An exponent is a way of showing repeated multiplication. For example, ...
x^2 means x·x
and
x^3 means x·x·x
If we multiply these two expressions together, we get ...
(x^2)·(x^3) = (x·x)·(x·x·x) = x·x·x·x·x
This is a product in which x appears as a factor 5 times, so we can write it using an exponent as ...
x·x·x·x·x = x^5
___
That is, when we multiply the expressions, we add the numbers of times the factor appears in the product:
2 + 3 = 5
x^2 · x^3 = x^(2+3) = x^5
Answer: Add
Step-by-step explanation: When you multiply expression with the same base you ADD the exponents. The exponent tells you how many times you multiply the base by itself. This means the exponent corresponds to the amount of base replications. If you add the exponents you are adding the replications of the base.
use words and symbols to describe the value of each term as a function of its position
Fortnite Yee yee boi get them toes
Question 2(Multiple Choice Worth 4 points) (08.02)A pair of equations is shown below. x + y = 5 y = one halfx + 2 If the two equations are graphed, at what point do the lines representing the two equations intersect? (2, 5) (5, 2) (2, 3) (3, 2)
Answer:
[tex](2,3)[/tex]
Step-by-step explanation:
The first equation is [tex]x+y=5[/tex]
The second equation is [tex]y=\frac{1}{2}x+2[/tex]
When we graph these two equations, they will meet at a point which represent the solution of the two equations.
We can solve the two equations simultaneously to determine their point of intersection.
Let us substitute the second equation into the first equation to get;
[tex]x+\frac{1}{2}x+2=5[/tex]
Multiply through by 2 to get;
[tex]2x+x+4=10[/tex]
Group similar terms to obtain;
[tex]2x+x=10-4[/tex]
Simplify;
[tex]3x=6[/tex]
Divide both sides by 3;
[tex]\Rightarrow x=2[/tex]
Put [tex]x=2[/tex] into the second equation;
[tex]y=\frac{1}{2}(2)+2[/tex]
[tex]\Rightarrow y=1+2[/tex]
[tex]\Rightarrow y=3[/tex]
Therefore the graphs of the two functions intersect at (2,3)
See graph in attachment.
The standard IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of all adults. We wish to find the sample size necessary to estimate the mean IQ score of all people who have successfully passed a college statistics course. We want to create a confidence interval that is no wider than 8 IQ points. The standard deviation for this sub-population is certainly less than 15 as it should be a less variable population. Therefore by using σσ = 15 we will obtain a conservative sample size, meaning it will be sufficient large enough. How large a sample should we utilize for a 95% confidence interval? (use the z-score 1.95996 )
Answer:
55 people is the minimum sample size
Step-by-step explanation:
The formula for minimum sample size is for µ is: n = [(z*σ)/E]²
We are given z = 1.95996, σ = 15 and E = 4
E is 4 because they said they want the interval no wider than 8, so that means 4 lower and 4 higher than the mean, so E is 4
Calculate: n = [(1.95996*15)/4]² = 54.02, we always round up when talking about people. Since 54.02 is the score, we need more than 54 people, since we can't have parts of a person, we need to round up to 55
To estimate the mean IQ score of all people who have successfully passed a college statistics course with a 95% confidence interval and a total width not exceeding 8 points, we require a sample size of 137, using the given standard deviation.
Explanation:In mathematics, specifically in statistics, the required sample size to estimate a population mean with a given level of confidence and margin of error can be obtained by using many formulas, but when we have an estimate of the population standard deviation (σ), the formula to calculate the sample size (n) is: n = ((Z × σ) / E)^2, where E is the desired margin of error, Z is the z-score related to the desired level of confidence.
Here, we are given the standard deviation (σ) as 15 (even though we believe the true standard deviation for the subpopulation in question is probably less), the desired margin of error (E) as 4 (since we want the total width of the confidence interval to be 8, the margin of error will be half of this), and the z-score (Z) for a 95% confidence interval is approximately 1.96 (as given in the question).
Plugging these values into the formula, we get: n = ((1.96 × 15) / 4)^2 which is approximately 136.09. As we can't have a fraction of a person, we round this up to the nearest whole number, so the required sample size is 137.
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Please help Asap 50 points
Use the distance formula to find the length of each side.
AB = √((5+1)^2 + (-1-1)^2) = √(6^2+-2^2) = √40 = 2√10 = 6.3
BC = √((0+1)^2 +(-3-1)^2) = √(1^2 + -4^2) = √17 = 4.1
AC = √((0-5)^2 +(-3+1)^2) = √(5^2 + -2^2) = √29 = 5.4
Perimeter = 6.3 + 4.1 + 5.4 = 15.8
6.3 + 4.1 + 5.4 = 15.8 is your answer.
Josh took out a payday loan for $1300 that charged a $75 fee. If the loan matures in 2 weeks, what is the approximate effective interest rate of the loan?
A. 430%
B. 33%
C. 43%
D. 330%
(Apex)
The approximate effective interest rate of the loan is 330%.
What is Interest?The cost of borrowing money or the fee you charge to lend it is known as interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
Given:
The amount owed increases by $75 in two weeks.
n= 52/2 = 26 periods
If the loan applied with same interest rate, then the total amount owed
=[tex](1375/1300)^{26}[/tex] x $1300
Now, If we subtract the original principle $1300, then the compounding interest as a percentage of that principle is
= [[tex](1375/1300)^{26}[/tex] x $1300 - $1300] / $1300
= 5,493.8 - 1300 / 1300
= 330%
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Final answer:
To find the effective interest rate of Josh's payday loan, you divide the interest ($75) by the principal ($1300) and multiply by 100 to get a two-week rate. Then you annualize it by multiplying by the number of two-week periods in a year (26), resulting in an approximate annual interest rate of 150%. The options provided in the question appear to be incorrect considering this calculation.
Explanation:
To calculate the effective interest rate of Josh's payday loan, we first need to determine the interest he's paying compared to the principal. The fee associated with the loan can be considered the interest, which in this case is $75. Since the loan is for $1300, we can calculate the interest rate for the two-week period by dividing the interest by the principal and then multiplying by 100 to get a percentage:
Interest Rate for 2 Weeks = ($75 ÷ $1300) × 100
Then, to annualize this rate, since there are 26 two-week periods in a year, we multiply the result by 26:
Annualized Interest Rate = Interest Rate for 2 Weeks × 26
Performing the calculations gives us:
Interest Rate for 2 Weeks = (75 ÷ 1300) × 100 ≈ 5.769%
Annualized Interest Rate = 5.769% × 26 ≈ 150%
However, the options given in the question do not match this calculation. It seems there might be a mistake with the options provided. The effective interest rate calculated here is approximately 150%, which is much lower than the options given. It is crucial to double-check the information or the methodology if this seems inconsistent with expected results. Note that payday loans typically have extremely high-interest rates, so a very high annual percentage rate (APR) is possible, but it may be calculated in a different manner.
The figures below are similar. Compare the larger figure to the smaller. which of the following is the ratio of the areas of the figures?
Answer:
4:3
Step-by-step explanation:
The ratio is 8:6, which simplifies to 4:3.
Answer:
16:9
Step-by-step explanation:
Given the following sets, which of the following is false? A={4, 6, 8} B={-2, 0, 2, 4} C={13, 23, 33, 43}
Answer:
gfjhgfterjrjtryuyrt
Step-by-step explanation:
hgfdjjrfdsfdjuytitdfgfdsuygeryauvfudsgygwerauyerwaguyfdsguyagsuydzgfuygewsabfuyguyeravcuyeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraerajhbfcds
Solve the equation by using tu basic properties of logarithms log(2x)=3 (Picture provided)
Answer:
Option b
Step-by-step explanation:
According to the property of sum of logarithms we know that
[tex]log(ab) = log(a) + log(b)[/tex].
In this case we have the equation:
[tex]log(2x) = 3[/tex]
Using the property of sum of logarithms:
[tex]log(2) + log(x) = 3[/tex]
[tex]log(x) = 3 - log(2)[/tex]
We also know that:
[tex]10 ^{(logx)} = x[/tex] -------- Inverse logarithm
So:
[tex]x = 10 ^{3-log(2)}[/tex]
[tex]x = 500[/tex]
Another easiest way to solve it is the following:
Make [tex]w = 2x[/tex].
Then:
[tex]log(2x) = log(w)[/tex]
[tex]log(w) = 3[/tex]
[tex]w = 10^3[/tex] -------- Inverse logarithm property
[tex]w = 1000[/tex]
but [tex]w= 2x[/tex]. Then:
[tex]2x = 1000\\\\x = 500[/tex]
Lines p and q are perpendicullllar if the slope of line p is 2 what is the slope of line q
q= -1/2
perpendicular slopes are those that are opposite sign and reciprocal of the original given slope
One part of a circle is shaded 1/3 and another is shaded 1/2. How much of the circle is shaded? Write your answer as a fraction in simplest form.
Answer:
5/6
Step-by-step explanation:
1/3 + 1/2 = 5/6
At school 95% of students arrive on time.If there are 200 students how many are expected to be late
Answer:
10 students (late)Step-by-step explanation:
total students = 200
95% of students arrived on time
5% of students were late.
95% x 200 = 190 students (on time)
5% x 200 = 10 students (late)
-------------------------------------
200 students
The number of nails of a given length is normally distributed with a mean length of 5.00 in. and a standard deviation of 0.03 in. Find the number of nails in a bag of 120 that are between 4.97 and 5.03 in. Long.
4.97 is 1 standard deviation below the mean, since 5.00 - 0.03 = 4.97. Similarly, 5.03 is 1 standard deviation above the mean. The 68-95-99.7 rule (sometimes called "empirical rule") says that approximately 68% of any normally distributed population lies within 1 standard deviation of the mean, so
[tex]P(4.97<X<5.03)\approx0.68[/tex]
So out of 120 nails, we can expect [tex]0.68\cdot120=81.6\approx82[/tex] nails to be within the prescribed length.
The number of nails in a bag of 120 that are between 4.97 and 5.03 in. Long will be 82.
What is a normal distribution?A normal distribution is a symmetrical continuous probability distribution in which values are usually clustered around the mean.
4.97 is 1 standard deviation below the mean, since 5.00 - 0.03 = 4.97.
Similarly, 5.03 is 1 standard deviation above the mean.
The 68-95-99.7 rule (sometimes called "empirical rule") says that approximately 68% of any normally distributed population lies within 1 standard deviation of the mean, so
P(4.97<X<5.03)068
So out of 120 nails, we can expect 0.68 x120= 81.57=82 nails to be within the prescribed length.
Hence the number of nails in a bag of 120 that are between 4.97 and 5.03 in. Long will be 82.
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What value of k causes the terms 5, 2k, 13 to form an arithmetic sequence?
2
4
9/2
13/4
Answer:
[tex]k=\frac{9}{2}[/tex]
Step-by-step explanation:
The given sequence is
[tex]5,2k,13[/tex]
For the sequence to be arithmetic, then
[tex]2k-5=13-2k[/tex]
We group similar terms to get;
[tex]2k+2k=13+5[/tex]
[tex]4k=18[/tex]
Divide both sides by 4;
[tex]k=\frac{18}{4}[/tex]
Simplify;
[tex]k=\frac{9}{2}[/tex]
Answer:
The correct answer is 3rd option 9/2
Step-by-step explanation:
From the given sequence, 5, 2k, 13
Which are in AP.
We can consider a₁ = 5 , a₂ = 2k and a₃ = 13
To find the value of k
We have,
a₂ = (a₁ + a₃)/2
Here,
2k = (5 + 13)/2 = 18/2 = 9/2
Therefore the correct answer is option 3
9/2
Find the total area of the solid figure.
60 sq. in.
78 sq. in.
90 sq. in.
Answer:
245.04
Step-by-step explanation:
The equation to a cylinder for area is A=2πrh+2πr^2
Fill in and solve.
A=2(3.14)(3)(10)+2(3.14)(3)^2
So using PEMDAS you get the answer 245.04
While taking @Jtakes700's answer and putting it into the form your asking, or putting into one of your options, you would get 78pi sq. in.
There are 45 members on the board of directors for a certain non-profit institution. if they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible?
Answer:
1,221,759.
Step-by-step explanation:
This is the number of combinations of 5 from 45.
This = 45! / 40! 5!
= 1,221,759.
Answer:
1,221,759
Step-by-step explanation:
Angenita drives to work at 50 mph and arrives 1 minute late. she drives to work at 60 mph and arrives 5 minutes early.
Answer:
2 mpm
Step-by-step explanation
Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the squares share one side with the rectangle. The total area of the constructed figure is 120 cm2. What is the perimeter of the rectangle?
Answer:
18 cm
Step-by-step explanation:
Let the width of the rectangle be x cm, then the length of the rectangle is x+5 cm.
The area of the ractangle is
[tex]x\cdot (x+5)\ cm^2.[/tex]
The area of the square with side's length of x cm is
[tex]x^2\ cm^2.[/tex]
The area of the square with side's length of x+5 cm is
[tex](x+5)^2\ cm^2.[/tex]
The area of constructed figure is
[tex]x(x+5)+2x^2+2(x+5)^2\ cm^2.[/tex]
Since the total area of the constructed figure is 120 cm², you have
[tex]x(x+5)+2x^2+2(x+5)^2=120.[/tex]
Solve this equation:
[tex]x^2+5x+2x^2+2x^2+20x+50=120,\\ \\5x^2+25x-70=0,\\ \\x^2+5x-14=0,\\ \\D=5^2-4\cdot (-14)=25+56=81,\\ \\x_{1,2}=\dfrac{-5\pm\sqrt{81}}{2}=-7,\ 2.[/tex]
The width of the rectangle cannot be negative, so x=2 cm and x+5=7 cm and the perimeter of the rectangle is
[tex]2x+2(x+5)=2\cdot 2+2\cdot 7=4+14=18\ cm.[/tex]