Answer:
12.4 miles
Step-by-step explanation:
It would be 1km / 0.62mi as this gives us a direct relationship between kilometers and miles. It's essentially telling us each kilometer is equal to 0.62 miles. Since we have 20 kilometers and we want to convert this to miles, we just multiply by 20 by 0.62 miles which gives us 12.4 miles
If you spent $20,750 for goods, service and housing in 2000, what would the same purchase have cost in 1984?
Answer:
$20584
Step-by-step explanation:
using of proportion
if $20,750 = 2000
than ? = 1984
=1984/2000 × 20750
=4116,8000/2000
=$20584
look at the image letter a is 5/8 and 2/3 letter b is 1/6 and 2/9 letter c is 7/12 and 5/8
The fractions are 15/24 < 16/24, 6/36 < 8/36, and 14/24 < 20/24. This can be found using LCM.
What is LCM?Finding the smallest common multiple between any two or more integers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple.
The given fractions are:
A:
5/8 and 2/3
Using the least common multiple take a common denominator:
Here LCM = (8)(3) =24
5/8 multiply the numerator and denominator by 3.
5/8 = 15/24
Similarly, 2/3 multiply the numerator and denominator by 8.
2/3 = 16/24
15/24 < 16/24
B: Using LCM:
1/6 and 2/9
6/36 and 8/26
6/36 < 8/36
C: 7/12 and 5/8
Using LCM:
14/24 < 20/24
Hence, the fractions are 15/24 < 16/24, 6/36 < 8/36, and 14/24 < 20/24. This can be found using LCM.
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Tennis great Roger Federer made 63% of his first serves in a recent season. When Federer made his first serve, he won 78% of the points. When Federer missed his first serve and had to serve again, he won only 57% of the points. Suppose you randomly choose a point on which Federer served. You get distracted before seeing his first serve but look up in time to see Federer win the point.
What’s the probability that he missed his first serve given he won the point?
answer choices
0.3000
0.37
0.63
If we randomly choose a point on which Federer served and get distracted before seeing his first serve but look up in time to see Federer win the point , then the probability that he missed his first serve given he won the point is (a) 0.3000
To calculate the probability that Federer missed his first serve given that he won the point, we Let , event A is = Federer missed his first serve and
event B is = Federer won the point.
So, probability of Federer missing his first serve = (100-63)% = 37% = 0.37,
probability of Federer winning point given he missed his first serve= 57%.
⇒the probability he first serve and misses point = (0.37)(0.57) = 0.2109 .
The probability of Federer winning the point, regardless of whether he made his first serve or not, can be calculated as
⇒ (0.63)(0.78) + (0.37)(0.57) = 0.7023 .
So , the probability of Federer missing his first serve given that he won the point is 0.2109/0.7023 = 0.300 .
The given question is incomplete , the complete question is
Tennis great Roger Federer made 63% of his first serves in a recent season. When Federer made his first serve, he won 78% of the points. When Federer missed his first serve and had to serve again, he won only 57% of the points. Suppose you randomly choose a point on which Federer served. You get distracted before seeing his first serve but look up in time to see Federer win the point.
What is the probability that he missed his first serve given he won the point?
(a) 0.3000
(b) 0.37
(c) 0.63
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John restaurant on 150 Main Street has 120 tables, but 30 percent of these tables are reserved. Therefore how many tables are available.
Answer:
84 tables are available
Step-by-step explanation:
30% = 30 ÷ 100
120 x (30 ÷ 100) = 36
36 tables are reserved hence
120-36 = 84
84 tables are available
Which matrix represents the system of equations shown below?
The matrix of the system is [tex]\left[\begin{array}{cc}11&3\\1&-2\end{array}\right] \left[\begin{array}{c}20&5\end{array}\right][/tex]
How to determine the matrix of the systemThe complete question is added as an attachment
From the question, we have the following system of equations that can be used in our computation:
11x + 3y = 20
x - 2y = 5
Remove the variables
So, we have the following representation
x y
11 3 20
1 -2 5
Next, we input the numbers in a matrix
This gives
[tex]\left[\begin{array}{cc}11&3\\1&-2\end{array}\right] \left[\begin{array}{c}20&5\end{array}\right][/tex]
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(4x-5)=(-2x+9) what is the aswner to this
Answer:
x = 7/3
Step-by-step explanation:
Given equation,
→ 4x - 5 = -2x + 9
Now the value of x will be,
→ 4x - 5 = -2x + 9
→ 4x + 2x = 9 + 5
→ 6x = 14
→ x = 14/6
→ [ x = 7/3 ]
Hence, value of x is 7/3.
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.9 years with a standard deviation of 0.8 years. Step 1 of 2 : If a sampling distribution is created using samples of the ages at which 68 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.
Mean of the sampling distribution of sample means is 5.9 years.
What is Normal Distribution?A normal distribution in statistics is defined as the type of continuous probability distribution where the data are arranged in a symmetrical bell shaped graph.
Population mean, μ = 5.9 years
Population standard deviation, σ = 0.8 years
If the sample size is at least 30, we can use the normal approximation of sampling distribution of sample means.
Here, sample size for the sampling distribution, n = 68 > 30.
For a sample which is drawn from a normally distributed population, mean of the sampling distribution of sample means is equal to the population mean and standard deviation = σ / √n.
Mean of the sampling distribution of sample means = μ = 5.9 years.
Hence mean is same as the population mean.
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This circle is centered at the point (3,2), and the length of its radius is 5. What is the equation of the circle
Answer:
C
Step-by-step explanation:
The standard form of a circle is
(x-a)^2 + (y-b)^2 = r^2
Where (a, b) is the centre and r is the radius
3 Coffee 5.85
1 Diet Bev. – lg. 3.38
1 Sparkling Water 2.50
3 Ranch Chicken Sandwich 44.97
1 Classic Burger 12.95
1 Thai Stir-fry Special 11.50
2 Club Sandwich 22.98
Subtotal 104.13
Tax (13%) 13.54
Total 117.67
2. Calculate the cost of each ranch chicken sandwich before tax.
The cost of each ranch chicken sandwich before tax is, $14.99
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
Given that,
3 Coffee 5.85
1 Diet Bev. – lg. 3.38
1 Sparkling Water 2.50
3 Ranch Chicken Sandwich 44.97
1 Classic Burger 12.95
1 Thai Stir-fry Special 11.50
2 Club Sandwich 22.98
Subtotal 104.13
Tax (13%) 13.54
Total 117.67
The cost of each ranch chicken sandwich before tax.= ?
Total Amount = 44.97
⇒ For 1 ranch chicken sandwich = 44.97/3 = 14.99
Therefore, the cost for 1 ranch chicken sandwich is $44.97/3
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Among employees of a certain company, 60% know C/C++, 50% know R, 30% know both languages, and 20% know neither language. Assume independence of events. Let A = knows C/C++ and B = knows R. Show work including the use of complement, union, and intersection notations and the computations.
(a) What is the probability that an employee does not know C/C++?
(b) What is the probability that an employee knows either C/C++ or R?
(c) What is the probability that an employee knows R and does not know C/C++?
(d) What is the probability that an employee knows at least one of the languages?
a) The probability that an employee does not know C/C++ = 0.4
(b) The probability that an employee knows either C/C++ or R = 0.8
(c) The probability that an employee knows R and does not know C/C++ = 0.2
(d) The probability that an employee knows at least one of the languages = 0.8
Let us assume that an event A: employee knows C/C++ languages
here, 60% know C/C++
So, P(A) = 0.6
event B: employee knows R
here, 50% know R
This means, P(B) = 0.5
30% know both languages
This means, P(A ∩ B) = 0.3
Also, 20% know neither language.
⇒ P(A ∪ B)c = 0.2
a. the probability that an employee does not know C/C++ would be,
1 - P(A)
= 1 - 0.6
= 0.4
b. the probability that an employee knows either C/C++ or R
We know that the formula, P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 0.6 + 0.5 - 0.3
P(A∪B) = 0.8
c. the probability that an employee knows R and does not know C/C++
P(B) - P(A∩B)
= 0.5 - 0.3
= 0.2
d. the probability that an employee knows at least one of the languages
1 - P(A ∪ B)c
= 1 - 0.2
= 0.8
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find a quadratic equation in X whose roots are -2 and 3/4
Answer:
4x² + 5x - 6 = 0
Step-by-step explanation:
Quadratic equation:
[tex]\boxed{x^2-(sum \ of \ roots)x+product \ of \ roots=0}[/tex]
[tex]Sum \ of \ roots = -2 + \dfrac{3}{4}[/tex]
[tex]= \dfrac{-2*4}{1*4}+\dfrac{3}{4}\\\\=\dfrac{-8}{4}+\dfrac{3}{4}\\\\=\dfrac{-5}{4}\\\\[/tex]
[tex]\sf product \ of \ roots =-2 *\dfrac{3}{4}[/tex]
[tex]=\dfrac{-6}{4}[/tex]
Quadratic equation:
[tex]x^2 - \left(\dfrac{-5}{4}\right)x+\left(\dfrac{-6}{4}\right)=0[/tex]
Multiply the entire equation by 4,
4x² - (-5)x + (-6) = 0
4x² + 5x - 6 = 0
6666652222-12 what can you do if the number is 2 times 6 times 8 times 9 and / 78
Multiplication's characteristics. Commutative and associative properties of multiplication, respectively.
Which four ways of multiplying are there?Multiplication's characteristics. Commutative and associative properties of multiplication, respectively.
Multiplication's "Distributive Property"
Multiplication's identity property.
The Japanese technique of multiplication is only a graphic representation of the four stages. Two integers are multiplied by each of the four smaller products represented by each cluster of intersections.
6666652222 - 12
6666652210 * 2 / 78 = 175438216.05
6666652210 * 6 / 78 = 512819400.76
6666652210 * 8 /78 = 701752864.21
6666652210 * 9 / 78 = 789471972.23
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whitch expression is equivalent to /147?
A7/3 C3/7
B49/3 D21/7
Answer:
B 49/3
Explanation:
I did the work, unlike your lazy ahh! :)
Find the amount that results from the given investment.
$500 invested at 12% compounded quarterly after a period of 3 years
the amount that results from the given investment $500 invested at 12% compounded quarterly after a period of 3 years is: $711.66. This can be solved using the concept of compound interest.
What is compound interest?When calculating compound interest, the starting principle amount is multiplied by one together with the yearly interest rate raised to the number of compound periods minus one. The resultant value is then reduced by the whole initial loan amount. When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. Compound interest accelerates the growth of your money since it calculates interest on both your original principle and the interest that has accrued over time. The initial investments and the revenue generated by those investments increase simultaneously as a result of compounding, which can have a snowball effect.
Principal amount (P) = $500
interest rate (r) = 12%
time (t) = 3 years
period (n) = 3
Final amount = A
As we know, A = P ( 1 + r/n) ^{nt}
or, A = 500 (1 + 0.12 / 3)^{3*3}
or, A = $711.66
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A real estate office manages an apartment complex with 40 units. When the rent is $780 per month, all 40 units are occupied. However, when the rent is $852, the average number of occupied units drops to 36. Assume that the relationship between the monthly rent p and the demand x is linear. (Note: the term demand refers to the number of occupied units.)
(a) Write a linear equation giving the demand x in terms of the rent p.
Answer:
The linear equation giving the demand x in terms of the rent p can be written as x = 40 - 0.042p, where x is the number of occupied units and p is the monthly rent.
The length of a leg of a right triangle is two times the length of the other, and the hypotenuse is 25.What is the length of the longer leg?
In a right triangle, the length of the hypotenuse is the square root of the sum of the squares of the other two legs. Therefore, we can use the Pythagorean theorem to find the length of the legs of a right triangle given the length of the hypotenuse.
Pythagorean theorem: c^2 = a^2 + b^2
where c is the hypotenuse and a and b are the legs of the right triangle.
If the length of the longer leg is x, then the length of the other leg is 2x.
Using the Pythagorean theorem:
25^2 = x^2 + (2x)^2
625 = x^2 + 4x^2
625 = 5x^2
x = √(625/5) = √125 = 5
So, the length of the longer leg is 5 units.
Three draws are made at random with replacement from a box with 10 tickets numbered 1 through 10. The chance the 3rd number is bigger than twice the first is:
A. None of these choices
B. 1
C. 3
D. 2
The chance that the third number is bigger than twice the first number is equal to the number of combinations where the first number is between 1 and 5 (inclusive) and the third number is between 2 * first number + 1 and 10 (inclusive).
Here's the calculation:
For the first number being 1, the possible third numbers are 3, 4, 5, 6, 7, 8, 9, 10, yielding 8 combinations.For the first number being 2, the possible third numbers are 5, 6, 7, 8, 9, 10, yielding 6 combinations.For the first number being 3, the possible third numbers are 7, 8, 9, 10, yielding 4 combinations.For the first number being 4, the possible third numbers are 9, 10, yielding 2 combinations.For the first number being 5, the possible third number is 10, yielding 1 combination.So in total, there are 8 + 6 + 4 + 2 + 1 = 21 combinations.Therefore, the answer is:
= 21/1000
= 21/10^3
= 0.021
which is closest to choice B, so the answer is B.
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Solve the system of equations below by graphing both equations with a pencil and paper. What is the solution? 4x + 5y = 22 2x + 3y = 12
The value of x is 3 and value of y is 2 in 4x + 5y = 22 and 2x + 3y = 12
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of equations are 4x + 5y = 22 and 2x + 3y = 12
Multiply equation 2 with 2
4x+6y=24
Subtract the above equation from equation 1
4x + 5y -4x-6y= 22-24
-y=-2
y=2
Now plug in y value in equation 2x + 3y = 12
2x+6=12
2x=6
Divide both sides by 2
x=3
Hence, the value of x is 3 and value of y is 2 in 4x + 5y = 22 and 2x + 3y = 12
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Find the perimeter using the area
Answer:
23cm
Step-by-step explanation:
A vertical dam on a large lake is 30 ft tall and 60 ft wide, and the water level is 5 ft below the top of the dam. In the middle of the dam at the very bottom is a gate in the shape of an equilateral triangle 8 ft on a side as shown in the figure below.
(Assume a density of water = 62.4 lb/ft3.)
25 ft8 ft
Find the hydrostatic force (in lb) on the gate. (Round your answer to the nearest integer.)
Rounded to the nearest integer, this is 140165 lb.
We need to find the volume of water that will be pressing against the gate.The height of the water above the gate is 25 ft - 5 ft = 20 ft.
The width of the water perpendicular to the gate is half the width of the dam, or 60 ft / 2 = 30 ft.
The area of the equilateral triangle is (8 ft)^2 * √(3) / 4 = 8 * 8 * √(3) / 4 = 16 * √(3) ft^2.
The volume of the water pressing against the gate is the product of the height, width, and area:
20 ft * 30 ft * 16 * √(3) ft^2 = 2400 ft^3 * √(3).
Finally, the hydrostatic force is the product of the volume, the density of water, and g (acceleration due to gravity):
2400 ft^3 * √(3) * 62.4 lb/ft^3 * 9.8 m/s^2 = approximately 140164.96lb
Therefore, Rounded to the nearest integer is 140165 lb.
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You pay $2000 every month for a total of 15 years on a mortgage with a 4% interest rate.
How much did you pay in interest?
Answer:To calculate the total interest paid on a mortgage, you can use the following formula:
Total Interest = (Interest Rate/12) * (Total Number of Payments) * (Loan Amount)
In this case, the loan amount is the total cost of the mortgage, which is not specified in the question. However, we know that the payments are made for 15 years or 15*12 = 180 months.
We can use the formula above to find the total interest:
Total Interest = (0.04/12) * (2000 * 180) = 53,333.33 dollars
So, you paid $53,333.33 in interest over the life of the mortgage.
Step-by-step explanation:
how is "If a polygon has four congruenet
angles, then it is a rectangle. The converse is not always true." not always true? I thought a sqaure can be a rectangle
If a polygon has four congruent angles then it can be a square and rectangle. Therefore the converse is not always true because square also have this property
What are the properties of a rectangle?The 4 basic property of a rectangle are;
1. A rectangle is a quadrilateral.
2. The opposite sides are parallel and equal to each other.
3. Each interior angle is equal to 90 degrees.
The sum of all the interior angles is equal to 360 degrees.
4.The diagonals bisect each other.
Both the diagonals have the same length.
Some of these properties are also for square. The difference between a square and a rectangle is that the sides of are all equal but only the opposite sides of a rectangle are equal. Both angles in square and rectangle are congruent, they are all 90°.
Therefore the converse of the statement "If a polygon has four congruenet
angles, then it is a rectangle." is not always true because both rectangle and square as these properties
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In quality control, bar charts are used to identify the most important causes of problems.When the bars are arranged in descending order of height from left to right (with the most frequently occurring cause appearing first).Named for its founder, Vilfredo Pareto, an Italian economist.
Yes, that's correct. The Pareto Chart also called bar charts, named after Vilfredo Pareto, is a graphical tool used in quality control and continuous improvement methodologies such as Six Sigma to help identify the most significant causes of problems.
In a Pareto Chart, the bars are arranged in descending order of height, with the most frequently occurring cause appearing first on the left. This allows you to quickly see which issues are the most pressing and require the most attention. By focusing on the most impactful causes, organizations can achieve the greatest improvement in their processes.
A bar chart gives a visual representation of the information.
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The tank for a car holds 16 gallons. The gasoline gauge shows the tank is 5/8 full. How much gas is still in the tank? Give your answer as a whole number or as a mixed fraction reduced to lowest terms.
Answer:
10 gallons is still in the tank.
Step-by-step explanation:
We have to calculate 5/8 of 16.
(5/8)*16 = 10.
(3-i) z³ = -4+8i what are complex solutions for z?
Z = x + yi times its conjugate x – yi is the square of its absolute value |z|²
In complex numbers, how do you solve for Z?A complex number z = x + yi times its conjugate x – yi is simply verified to be the square of its absolute value |z|². As a result, 1/z equals z divided by the square of its absolute value |z|². A complex number z is one that can be represented as x+iy, where x and y are real integers and I is an imaginary unit, i²=1. In this equation, x represents the complex number’s real portion and y represents its imaginary part.
The discriminant, b 2 4 a c, demonstrates the different forms of quadratic equation solutions. If the discriminant is equal to zero, the equation has one genuine solution.
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in exercises 37 and 38, the graph of a function f(x) is given
Answer:
Exercise 37:
In this exercise, the question is to find the x-coordinate of the point of inflection of the graph of the function f(x).
The point of inflection of the graph of the function f(x) is at the x-coordinate of 1.
Connor bought a table on sale for $341, this price was 62% of the original price. What was the original price?
Consider the function in the graph to the right.
The function has a minimum of y = -2 at x = -4
The function is increasing on interval:
(-4 , ∞)
The function is decreasing on interval:
(-∞ , -4)
What is function?A function is a process or a relation that associates each element 'a' of a set A , to a single element 'b' of another set B.
Given function graph,
Function is increasing when, 4 < x < ∞
Function is decreasing when -∞ < x < -4
Function is minimum at (-4 , -2)
Hence,
On interval (-4 , ∞) function increases.
On interval (-∞ , -4) function decreases.
Function has minimum of y = -2 at x = -4.
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2. The area of a rectangular garden is represented by the polynomial shown
below.
x² + 6x + 8
What are the dimensions (length and width) of the rectangular garden?
The statement states that the rectangular garden has the following measurements: length = -4 and width = -2.
Describe polynomials using examples.Sums with terms of something like the form kxn, where k has been any variable & n is a real number, make up polynomials. For instance, the polynomial 3x+2x-5. a description of radicals. The concepts degrees, standard form, monomial, binomial, and trinomial are all covered in this video.
A rectangle's area is represented by the polynomial [tex]x2 + 6x + 8,[/tex] which may be solved in (x + a)(x + b), in which a and b are indeed the rectangle's length and breadth.
So,[tex]x^2 + 6x + 8 = (x + a)(x + b).[/tex]
Solving for a and b, we find that a = -4 and b = -2, so the dimensions of the rectangular garden are length = -4 and width = -2.
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the manager of a furniture factory that operates a morning and evening shift seven days a week wants to forecast the number of chairs its factory workers will produce on a given day and shift. the production manager gathers chair production data from the factory and lists whether the production day was a weekday or a weekend (i.e., saturday or sunday), and whether the shift was in the morning or evening.
This type of data can be analyzed using a two-way analysis of variance (ANOVA) to determine the effect of both the day of the week (weekday or weekend) and the shift (morning or evening) on chair production. The manager can use this information to make predictions about future production based on the day of the week and shift.
The manager can start by creating a table to show the average number of chairs produced on each day of the week and shift. Then, a two-way ANOVA can be performed to determine if there is a significant difference in the mean number of chairs produced between weekdays and weekends, and between morning and evening shifts.
If the results of the ANOVA show that there is a significant effect of the day of the week and/or the shift on chair production, the manager can use this information to make more accurate predictions about future chair production. For example, if the results show that chair production is higher on weekdays compared to weekends, the manager can make predictions based on this information and allocate resources accordingly.
It is important to note that other factors such as the availability of materials, number of workers, and machine downtime can also impact chair production and should be considered when making predictions.
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