Answer:
7.5%
Step-by-step explanation:
Approximate distance = 180 miles
Actual distance = 167.5 miles
Percent error = { (approximate value - actual value) / actual value } × 100
= { (180 - 167.5) / 167.5 } × 100
= (12.5 / 167.5) × 100
= 0.075 × 100
= 7.5%
Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places. x2 = 19
Answer:
[tex] x = \pm \sqrt{19} [/tex]
[tex] x = \pm 4.36 [/tex]
Step-by-step explanation:
[tex] x^2 = 19 [/tex]
[tex] x = \pm \sqrt{19} [/tex]
[tex] x = \pm 4.36 [/tex]
The exact solution is 4.36.
What is square root?Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value. Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.
Given:
x² = 19
On taking root on both side
√x² = √19
x= √19
x = 4.3588
Hence, the exact solution and its approximation rounded to two decimal places is 4.36.
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Izzy is buying a car that costs $12,764. She must pay $2,000 the day she buys the car and then $299 every month until the car is paid off. How many months will it take for Izzy to pay for the car?
Answer:
Step-by-step explanation:
50
Apply distributive property to create an equivalent expression 6(5r-3)=
Answer:
30r-18
Step-by-step explanation:
6*5=30
6*3=18
Answer:
30r-18
Step-by-step explanation:
Find the indicated side of the
right triangle.
Answer:
?=9
Step-by-step explanation:
We have a special right triangle, the 45-45-90 triangle.
In a 45-45-90 triangle, the side lengths are x, and the hypotenuse is x√2.
Since we know that the side length is 9, this means that:
[tex]x=9\\\text{Hypotenuse}=x\sqrt2\\\text{Hypotenuse}=9\sqrt2[/tex]
The ? is 9.
Answer: 9
Step-by-step explanation:
There are 16 sixth graders and 20 seventh graders in the Robotics Club. For the first project, the club sponsor wants to organize the club members into equal-size groups. Each group will have only sixth graders or only seventh graders. How many students will be in each group if each group has the greatest possible number of club members?
g The false positive rate, P(+|N), for a test is given as 0.04. What is the specificity for this test?
Answer:
Step-by-step explanation:
Let us consider a data of prevalent diseases.
If the false positive rate is P(Test + | N) = 0.04
Therefore, sensitivity is defined as the probability of a positive test result given the presence of the disease. This can be written as: P (positive test | disease present).
Specificity is defined as the probability of a negative test result given absence of disease, that is, P (negativetest | diseaseabsent). PPV is defined as the probability of the presence of disease given a positive test result, ie, P (disease present | positivetest).
One integer is 7 more than another. Their product is 98. Find the integers,
Answer:
- 14, - 7 or 7, 14
Step-by-step explanation:
Let the the two integers be x and (x + 7)
[tex] \therefore \: x(x + 7) = 98 \\ {x}^{2} + 7x - 98 = 0 \\ {x}^{2} + 14x - 7x - 98 = 0 \\ x(x + 14) - 7(x + 14) = 0 \\ (x + 14)(x - 7) = 0 \\ (x + 14) = 0 \: or \: (x - 7) = 0 \\ x = - 14 \: or \: x = 7 \\ \\ when \: x = - 14 \\ x + 7 = - 14 + 7 = - 7 \\ \\ when \: x = 7 \\ x + 7 = 7 + 7 = 14 \\ [/tex]
Hence the required integers are - 14, - 7 or 7, 14
Use De Morgan’s law for quantified statements and the laws of propositional logic to
show the following equivalences:________
a) ¬ x(P (x) ¬Q(x)) x(¬P (x) Q(x))∀∧≡∃∨
b) ¬ x(¬P (x) = Q(x)) x(¬P (x) ¬Q(x))∀⇒≡∃∧
c) ¬ x(¬P (x) (Q(x) ¬R(x))) x(P (x) (¬Q(x) R(x)))
Answer:
A) ¬(¬q) ≡ q
B) ≡ ( эx) (¬p(x) ∧ ¬q(x)
C) ≡ ( зx ) (p(x) ∧ (¬ q(x) ∨ r(x)) )
Step-by-step explanation:
using De Morgan's law for quantified statements and the laws of propositional logic to show the equivalent of the following
from De -Morgan law
¬(A ∨ B ) = ¬ A ∧¬ B
ATTACHED BELOW IS THE COMPLETE SOLUTION
The product of two whole numbers is 936 and the sum is 62. What are the two numbers
Answer:
26 and 36.
Step-by-step explanation:
Let the two whole numbers be a and b. Thus, the product of them is 936 while their sum is 62. In equations, this is:
[tex]ab=936\\a+b=62[/tex]
This is a system of equations. To solve, subtract either a or b from the second equation and substitute it into the first.
For instance, subtract b from both sides in the second equation:
[tex]a+b=62\\a=62-b[/tex]
Substitute this into the first equation:
[tex](62-b)(b)=936[/tex]
Distribute:
[tex]62b-b^2=936[/tex]
Rearrange:
[tex]-b^2+62b=936[/tex]
Divide everything by -1 to make the leading coefficient positive:
[tex]b^2-62b=-936[/tex]
Add 936 to both sides:
[tex]b^2-62b+936=0[/tex]
This is now a quadratic. Solve for b.
To do so, we can factor.
After a bit of testing, we can see that -36 and -26 are possible. Thus:
[tex](b-26)(b-36)=0[/tex]
For for b:
[tex]b=26\text{ or } b=36[/tex]
Thus, b is 26 or 36.
Now, plug these back into the isolated equation to solve for a:
[tex]a=62-b\\a=62-(26) \text{ or } a=62-(36)\\a=36\text{ or } a=26[/tex]
It doesn't really matter which one we choose since they're the same.
Thus, the answer is 26 and 36.
What is the value of 3.5 (11) + 1.9 (11) + 1.6 (11)?What is the value of 20 + 3 (7 + 4) + 5 + 2 (7 + 9)?
Answer:
1)77 2)90
Step-by-step explanation:
1)take 11 common
therefore, 11(3.5+1.9+1.6)
=11(7)
=77 (multiply 11 with 7)
2)First solve the numbers in bracket
20 +( 3×11 )+ 5 +( 2×16)
=20+33+5+32
=90
calculate the area of area of a rectangular with a base of 10cm and a height of 6cm
Answer:
[tex]\Huge \boxed{\mathrm{60 \ cm^2 }}[/tex]
Step-by-step explanation:
Area of a rectangle is length × width.
The length of the rectangle is 10 cm.
The width of the rectangle is 6 cm.
[tex]\Rightarrow 10 \cdot 6 \\\\\\ \Rightarrow 60[/tex]
The area of the rectangle is 60 cm².
Answer:
60cm is the answer
Step-by-step explanation:
Area of a rectangle is length × width.
so..... The length of the rectangle is 10 cm.
And the width of the rectangle is 6 cm.
so... 10x6=60 cm
10-(2x-3)
A. 7-2x
B. 13+2x
C. 15x
D. 13-2x
Answer:
D.13-2x
Step-by-step explanation:
[tex]10-\left(2x-3\right)\\\\-\left(2x-3\right):\quad -2x+3\\=10-2x+3\\\\\mathrm{Simplify}\:10-2x+3:\\\quad -2x+13[/tex]
Answer:
13 -2x
Step-by-step explanation:
10-(2x-3)
Distribute the minus sign
10 -2x +3
Combine like terms
13 -2x
A distribution is negatively skewed. Which is the most probable order for the three measures of central tendency
Options :
a mean - 40, median - 50, mode - 60
b. mean-60, median - 50, mode - 40
c. mean - 40, median-60, mode - 50
d. mean - 50, median - 50, mode - 50
Answer: mean - 40, median - 50, mode - 60
Step-by-step explanation: A negatively skewed distribution is characterized by it long tail being positioned to the left(negative direction) with its peak positioned to the right (positive direction) of the distribution. On a general note, the mean is always positioned towards the left or negative side if the peak, with the median coming next and usually positioned to the right of the mean and the mode positioned to the right side of the median.
Hence, for a negatively skewed distribution, the mean has the least value followed by the median, with the mode boasting the highest.
That is : mean < median < mode
List the new coordinate of point J' when the figure is reflected over the y-axis.
Answer: (-4, -3)
Step-by-step explanation:
The original coordinate of J is (4, -3)
Since it is reflex over y-axis, the y value remains.
For the x value, it is originally 4 units away from the y-axis positively, thus, after reflexing, it will be 4 units away from the y-axis negatively.
The new coordinate of J' is (-4, -3)
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3.21 x 10^4 in standard notation
Answer:
32100
Step-by-step explanation:
hope this helps
sorry if its wrong
the table represents a function what is f(5)?
Answer:
U should delete the q btw
Use 5 as the value of x
Step-by-step explanation:
Answer: it’s A. -8
Step-by-step explanation: just took the test on edge
Stefen earns $88 in 8 hours. At this rate, how many dollars will he warn in 40 hours
Answer:
$440
Step-by-step explanation:
You need to find the unit rate by dividing how much he earned (88)by how many hours he worked (8) which equals $11 per hour.Then you take the unit rate (11) and multiply it by 40 which equals $440.
You own 24 CDs. You want to randomly arrange 7 of them in a CD rack. What is the probability that the rack ends up in alphabetical order
Answer:
the probability that the rack ends up in alphabetical order is 0.0001984
Step-by-step explanation:
Given that:
You own 24 CDs. You want to randomly arrange 7 of them in a CD rack.
Th probability that the rack ends up in alphabetical order can be determined by taking note of the permutations and combinations.
From above; all possible permutations of size 7 we can derive from 24 is
24P7
Similarly,we are meant to estimate all the possible ways a unique set of 7 things can be gotten from a total of 24
i.e
24 C7
∴
The probability = [tex]\dfrac{^{24}{C}_7}{^{24}{P}_7}[/tex]
= [tex]\dfrac{\dfrac{24!}{7!(24-7)!} }{ \dfrac{24!}{(24-7)!} }[/tex]
=[tex]\dfrac{\dfrac{24!}{7!(17)!} }{ \dfrac{24!}{(17)!} }[/tex]
= [tex]\dfrac{346104}{ 1.74436416 \times 10^9}[/tex]
= 0.0001984
the probability that the rack ends up in alphabetical order is 0.0001984
The probability that the rack ends up in alphabetical order is 0.0001984
The total number of CD is given as:
[tex]\mathbf{n = 24}[/tex]
The number of CDs to select is given as:
[tex]\mathbf{r = 7}[/tex]
The number of arrangement of 7CDs in 24 is represented as 24P7
So, we have:
[tex]\mathbf{^{24}P_7 = \frac{24!}{(24 - 7)!}}[/tex]
[tex]\mathbf{^{24}P_7 = \frac{24!}{17!}}[/tex]
Simplify
[tex]\mathbf{^{24}P_7 =1744364160}[/tex]
The number of selecting 7 CDs from 24 is represented as 24C7
So, we have:
[tex]\mathbf{^{24}C_7 = \frac{24!}{(24 - 7)!7!}}[/tex]
[tex]\mathbf{^{24}C_7 = \frac{24!}{17!!7}}[/tex]
Simplify
[tex]\mathbf{^{24}C_7 =346104}[/tex]
So, the probability is:
[tex]\mathbf{Pr = \frac{346104}{1744364160}}[/tex]
Divide
[tex]\mathbf{Pr = 0.0001984}[/tex]
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Vincent earns $546 on Monday and he earns $352 on Tuesday. How much total money does Vincent earn?
Answer:
$898
Step-by-step explanation:
Easy, 546 + 352 =
898
What is the scientific notation of 0.0038
Answer: 3.8 * 10^-3 (10 to the negative third power)
Step-by-step explanation:
First, you would find the leading digit which is 3. Then, include the following digits after the decimal. The following digit is 8 so you have 3.8. After that, you count how many places the decimal point would move until it's after three. (3 places) And since the number is smaller than 1, the exponent is negative.
the number of points by a basketball player in the first eight games of a season are shown before. 15,35,18,30,25,21,32,16
Answer:
24
Step-by-step explanation:
Assuming you want to find a mean, the answer is: 24 (sum of all values/number of values)
Range is largest-smallest
Median is middle value
There are 10,000 mutual fund managers. 22 claim that they are the best, since their fund beat the relevant index every year for 7 years. However, you think that markets are efficient and that the average fund manager is as likely to deliver a better performance than the index as to underperform the index, before fees.
Part 1 | Attempt 1/10 for 10 pts. What is the probability that the average single fund managers beats the index 7 years in a row (before fees)? 4+ decimals
Part 2 | Attempt 1/10 for 10 pts. How many fund managers would you expect to beat the index 7 years in a row if only luck and no skill was involved? No decimals
Answer:
Part A:
Probability that average single manager beat the index= [tex](0.5)^7=0.0078125=0.0078 (4\ decimals)[/tex]
Part B:
Fund Managers to beat index 7 years=78.125≅78 managers.
Step-by-step explanation:
Part A:
Given data:
Since there are equal chances for delivering equal better performance and of under performance so
Probability of better performance =0.5
Required:
Probability that the average single fund managers beats the index 7 years in a row (before fees)=?
Solution:
Since there is 7 year index:
Probability that average single manager beat the index= [tex](0.5)^7=0.0078125=0.0078 (4\ decimals)[/tex]
Part B:
Given Data:
Number of mutual fund managers=10,000
Probability that average single manager beat the index= 0.0078125 (Calculated in part A)
Required:
How many fund managers would you expect to beat the index 7 years in a row if only luck and no skill was involved?
Solution:
Fund Managers to beat index 7 years=Total number of managers*probability average single member beat the index
Fund Managers to beat index 7 years=10,000*0.0078125
Fund Managers to beat index 7 years=78.125≅78 managers.
Seventy-two percent of the shareholders in a service corporation are women. If the corporation is
owned by 47800 people, how many of the shareholders are women?
Answer:
34416
Step-by-step explanation:
.72(percentage) × 47800(people)
34416
If there are 17.5 grams of sugar in 225 grams of an aqueous sugar solution, the percent-mass sugar is ______ and the percent-mass water is ______ . Express both answers to the correct number of significant figures.
Answer:
7.77%(m/m) ; 92.22%(m/m)
Step-by-step explanation:
Given that:
17.5 grams of sugar in 225 grams of an aqueous sugar solution
Percentage by mass of A in a solution (mass percent) = (mass of A / total mass of solution) × 100
Hence,
Percentage by mass of sugar:
= (mass of sugar / total mass of solution) * 100
= (17.5 / 225) × 100
= 0.0777777 × 100 = 7.77%(m/m)
Mass of water(solvent) = (225 - 17.5)g = 207.5g
= (207.5 / 225) × 100
= 0.922222 × 100 = 92.22%(m/m)
(60b ÷ 5) + c when b= 1/2 and c= 11
Answer:
17
Step-by-step explanation:
(60b divided by 5) + c
(60(1/2) divided by 5) + 11
(30 divided by 5) + 11
6 + 11
17
PLZ HURRY Yummy donuts gave 2 dozen chocolate donuts and 6 donut jelly donuts to the school.how many donuts did they give?
Answer:
they gave 18 donuts to the school.
Answer:
2 dozen= 24 + 6 = 30 donut.
Type the standard form of three hundred thousand two hundred one
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Standard form is numbers only.
Examples of standard numbers are 4, 225, or 9,002
A thousands number has 4 digits.
A hundreds number has 3 digits.
A tens number has 2 digits.
A regular number has 1 digit (itself).
Three hundred means 300.
Three hundred thousand, would be 300 times 1,000 (one thousand), or adding 3 zeros.
Two hundred is 200.
One is 1.
300 times 1,000 is 300,000.
300,000 and 200 is 300,200.
If the ones digit has a 1, then the number is 300,201.
Three hundred thousand, two hundred one written in standard form is 300,201.
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Three hundred thousand, two hundred one written in standard form is 300,201.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
A thousand number has 4 digits.
A hundred number has 3 digits.
A tens number has 2 digits.
A regular number has 1 digit (itself).
Three hundred means 300.
Three hundred thousand would be 300 times 1,000 (one thousand), or adding 3 zeros.
Two hundred is 200.
One is 1.
300 times 1,000 is 300,000.
300,000 and 200 is 300,200.
If the one digit has a 1, then the number is 300,201.
Three hundred thousand, two hundred one written in standard form is 300,201.
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A storage pod has a rectangular floor that measures 21 feet by 9 feet and a flat ceiling that is 7 feet above the floor. Find the area of the floor and the volume of the pod.
Answer:
area: 189 ft²volume: 1323 ft³Step-by-step explanation:
The area of the rectangular floor is the product of its length and width:
A = LW = (21 ft)(9 ft) = 189 ft²
The volume of the pod is the product of that floor area and the height:
V = Bh = (189 ft²)(7 ft) = 1323 ft³
The area of the floor is 189 ft²; the volume of the pod is 1323 ft³.
One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years’ time, I will be twice as old as my brother.” How old are they each now?
Answer:
One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years’ time, I will be twice as old as my brother.” How old are they each now?
Step-by-step explanation:
Let us suppose two years ago my brother's age was x years
Then, my age was 3x
Three years from now, my brother's age will be (x +2+3) = (x+5) years
And my age will be (3x+2+3) = (3x+5) years
But it is given that i will be twice as old as my brother.
So, 2(x+5)= (3x+5)
or, x= 5 years
So my brother's present age is 5+2= 7 years
And my age is 5*3+2= 17 years
The age of the older brother is 13 and the age of the younger brother is 5.
Two simultaneous equations can be determined from this question:
y = 3x - 2 equation 1
y = 2x + 3 equation 2
Where:
y = older brother's age
x = younger brother's age
Equate equation 1 and equation 2
3x - 2 = 2x + 3
Combine similar terms
3x - 2x = 3 + 2
x = 5
Substitute for x in equation 1
3(5) - 2
15 - 2
y =13
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Which is the correct answer choice?
Answer:
i think b is answer. i think this is useful to you