Step-by-step explanation:
For this question, what we have to do is to rewrite and form some of these statements with their contrapositives
here is the reordering;
1. if Object is at the left of the tree, then it is blue
2. If the object is blue then it smells good.
3. If thus thing smells good then it tastes good.
4. If it tastes good then it is expensive
∴ every object to the left of the tree is expensive
1. Calculate the variance of the set of data to two decimal places.
{ 1,2,4,4,5,6,6}
a. 22
b. 4
c.3.14
d. 1/7
e.2
============================================================
Explanation:
First we need the arithmetic mean
Add up the values to get 1+2+4+4+5+6+6 = 28
Divide this over the number of values (n = 7) to get 28/n = 28/7 = 4
The mean is 4.
Next, we subtract the mean from each data value and square the difference
(1-4)^2 = 9(2-4)^2 = 4(4-4)^2 = 0(4-4)^2 = 0(5-4)^2 = 1(6-4)^2 = 4(6-4)^2 = 4Add up those results: 9+4+0+0+1+4+4 = 22
Lastly, we divide over the number of items (n = 7) to get the population variance: 22/n = 22/7 = 3.14 approximately
----------
Side note:
If you wanted the sample variance, then you divide over n-1 = 7-1 = 6
22/(n-1) = 22/6 = 3.67 is the approximate sample variance
An animal shelter has enough pens for x small dogs and y large dogs, and can hold up to 36 dogs at a time. It costs the shelter $12 a week to keep a large dog and $7 a week to keep a small dog. The shelter must keep its weekly costs under $350. Which system of inequalities can be used to represent this situation?
Answer:
7x+12y<350
Step-by-step explanation:
7 times each small dog (x) plus 12 times each large dog (y) needs to be less than (<) 350
Mathema
8. Leg XY of the right triangle shown in the
diagram below is twice as long as
leg YZ.
Z
Y
х
If the area of the triangle is 36 cm?, what
is the length, in cm, of leg XY?
(1)
6
(2)
9
(3)
12
(4)
18
(5)
24
9514 1404 393
Answer:
(3) 12
Step-by-step explanation:
Let x represent the length of leg XY. Then the length of YZ is x/2 and the area of the right triangle is ...
A = 1/2bh
A = 1/2(x)(x/2) = x²/4
36 = x²/4 . . . . . use the given value for area
144 = x² . . . . . . multiply by 4
√144 = 12 = x . . . . . take the square root
The length of leg XY is 12 cm.
in a system of equations why is the intersection the solution
9514 1404 393
Answer:
It satisfies both equations.
Step-by-step explanation:
The points on the graph of an equation are the values of the variables that satisfy the equation (make it true).
In a system of equations, you're generally looking for values of the variables that satisfy all of the equations in the system. That is, the solution will be a point on the graph of every equation in the system.
For a point to be on more than one graph, it must lie at a point of intersection of the graphs. If all of the graphs of a system go through the point of intersection, that point satisfies all of the equations, so is a solution of the system of equations.
In how many ways can the letters in the word 'Oklahoma' be arranged?
Answer:
720
Hope that this helps!
Find the perimeter of this problem
Answer:
below
Step-by-step explanation:
perimeter of a semicircle
½ * 2πr
=πr
= 3.142*27
=84.78cm
Know how to rearrange formulae Question 1: Make y the subject of each of the following
(a) y + w = c
(b) y- p = m
C) m + y = s
(d) y - 2g = n
(e) 3y = c
(f) ay = w
(g) y/c =w
(h) y/a= 2c
(i) a = y + p
Someone please help me.
Answer:
y=c - w
y=m+p
y=n+2g
y=c/3
y=w/a
y=w×c
y=2c×a
y=a-p
Step-by-step explanation:
crossing the equality sign
- = +
+ = -
× = ÷
÷ = ×
hope this would help
$6300 is invested, part of it at 11% and part of it at 6%. For a certain year, the total yield is $533.00. How much was invested at each rate?
$___ was invested at 11%
Answer:
Invested at 11% : 3100
Invested at 6% : 3200
Step-by-step explanation:
let x= amount invested at 11%
let y= amount invested at 6%
we can write
Equation 1: x+y=6300
Equation2: .11x+.06y=533
Divide equation 2 by .06 to get
1.8333333x+y=8883.33333333
Subtract equation 2 from equation 1
.8333333x= 2583.33333333
x= 3100
Plug in x= 3100 into equation 1
3100+y= 6300
y= 3200
Reeba is baking cookies for the bake sale. She bakes 3 ¾ dozen chocolate chip cookies to sell . If Reeba sells ⅔ of the cookies, how many cookies did she sell?
Answer:
30 cookies
Step-by-step explanation:
Reeba sells [tex]\frac{2}{3}[/tex] of [tex]3\frac{3}{4}[/tex] of 12 chocolate chip cookies.
Let us start by finding [tex]3\frac{3}{4}[/tex] of 12. We simply have to multiply the two numbers. However, it would be much easier if we had an improper fraction than a mixed number. Let us make [tex]3\frac{3}{4}[/tex] an improper fraction first.
[tex]3\frac{3}{4} =\frac{15}{4}[/tex]
Ok! Let's multiply.
[tex]\frac{15}{4} *\frac{12}{1} =\\15*3\\=45[/tex]
Ok, Reeba baked 45 cookies in total. We know that she sells [tex]\frac{2}{3}[/tex] of her baked cookies, so we can again multiply the two numbers.
[tex]\frac{2}{3} *\frac{45}{1} =\\2*15=\\30[/tex]
Therefore, Reeba sold 30 cookies.
I hope this helps! Let me know if you have any questions :)
simplify (25-4)3^ times 5
Answer:
46305
Step-by-step explanation:
Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent.
Answer:
ASA
Step-by-step explanation:
The two small angles which are the base angles of the small triangle in the middle are marked as equal.
The two large angles of the two triangles are also marked as conguent.
The base of the small triangle in the middle is common to both the larger triangles by the reflexive property (a line is always equal to itself). The line is between two sets of congruent angles. Therefore the two large triangles are congruent by ASA
Explanation:
It might help to peel the triangles apart as I have done so below.
We have two pairs of congruent angles, as shown by the distinct angle markers. Between the congruent angles, we have a pair of congruent sides.
The side (S) is between the angles (A), which is why we use ASA.
Note: SAA is slightly different where the congruent sides are not between the congruent angles.
The yearbook staff receive 75 submissions for yearbook articles. Paul will acceptſ of all submissions. Currently, Paul plans for the yearbook to have 156
pages.
How many more pages will Paul need to add to the yearbook to have 2 articles on every 13 pages? Show your work and explain your thinking.
Answer:
The correct answer is - 332 pages.
Step-by-step explanation:
Given:
number of articles submissions - 75
number of pages in the yearbook on current plan = 156
pages required for two articles = 13 pages.
The number of pages to add = ?
Solution:
1 article takes pages in the yearbook = 13/2
= 6.5
the number of pages required for 75 articles = 75*6.5
= 487.5
The number of pages to add in the yearbook = 487.5 - 156
= 331.5 or 332.
Thus, the correct answer is - 332 pages.
Write the point-slope form of the equation for a line that passes through (-1, 4) with a slope of 2.
The value of xt is
The value of yn is
The point-slope form of the equation is
Answer:
67 f
Step-by-step explanation:
- ⅘ x = 8.....................
im actually in middle school btw dunno why it says college
Answer:
-10
Step-by-step explanation:
See image below:)
Answer:
x = -10
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
-4/5x = 8
Step 2: Solve for x
[Division Property of Equality] Divide -4/5 on both sides: x = 8 / -4/5Divide: x = -10Dave Bowers collects U.S. gold coins. He has a collection of 49 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $690, how many of each denomination does he have?
How many $10 coins does he have?
How many $20 coins does he have?
The demand function of a product is q = 7,000 - 50p, where p is the price.
The cost function is given by C = 2,000 + 259. At what price is the break-even
Production attend?
Answer: 139.65 or 25.34.
Step-by-step explanation:
The revenue function will be:
= Price × Quantity
= P × (7,000 - 50p)
= 7000p - 50p²
The coat function is given as:
C = 2,000 + 25q
C = 2000 + 25(7000 - 50p)
C = 2000 + 175000 - 1250p
C = 177000 - 1250p
Then, we'll equate the revenue function to the cost function. This will be:
7000p - 50p² = 177000 - 1250p
-50p² + 7000p + 1250p - 177000 = 0
-50p² + 8250p - 177000 = 0
Divide through by -50
p² - 165 + 3540 = 0
Solving to get the value of P will then give us 139.65 or 25.34.
Someone help me please
whats the square root of 9 over 16
Answer:
± [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{\frac{9}{16} }[/tex] = [tex]\frac{\sqrt{9} }{\sqrt{16} }[/tex] = ± [tex]\frac{3}{4}[/tex] ← note plus or minus
Answer:
3/4
Step-by-step explanation:
The square root of 9 is 3 and the square root of 16 is 4 so you get an answer of 3/4.
Hope it helps
im in need of help for this problem (listing BRAINLIST and giving points) :)
I hope this is help full to you
Please help!
Suppose that a population parameter is 0.1 and many samples are taken from the population. If the size of each sample is 90, what is the standard error of the distribution of sample proportions? O A. 0.032 . B. 0.072 O C. 0.095 O D. 0.055 SUBMIT
Answer:
[tex]\text{A. 0.032}[/tex]
Step-by-step explanation:
Let [tex]\sigma_p[/tex] be the standard error of the distribution of sample proportions.
Formula:
[tex]\sigma_p=\sqrt{\frac{P(1-P)}{n}}[/tex], where [tex]P[/tex] is the population parameter and [tex]n[/tex] is sample size.
What we're given:
[tex]P[/tex] of 0.1[tex]n[/tex] of 90Substituting given values, we get:
[tex]\sigma_p=\sqrt{\frac{0.1(1-0.1}{90}},\\\sigma_p=\sqrt{\frac{0.1\cdot 0.9}{90}},\\\sigma_p=\sqrt{0.001}\approx\boxed{\text{A. 0.032}}[/tex]
If X + Y means X is the brother of Y, X - Y means X is the sister of Y, and X * Y means X is the father of Y, then which of the following means that C is the son of M?
(1) M-N * C + F
(2) F-C + N * M
(3) N +M-F * C
(4) M * N-C + F
(5) M-N+F * C
Answer:
4
Step-by-step explanation:
Based on this question, addition means the first number is the brother of the other, subtract means the first number is the sister of the other and multiplying means the first number is the father of the other.
We see 4 is literally multiplying M by N-C, meaning N is the sister of C and M is the father of N and C.
A cone-shaped paper drinking cup is to be made to hold 24 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Round your answers to two decimal places.)
Answer:
I. Radius, r = 2.90 cm
II. Height, h = 4.10 cm
Step-by-step explanation:
Given the following data;
Volume of cone = 24 cm³
To find the height and radius of the cup that will use the smallest amount of paper;
Mathematically, the volume of a cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex] ......equation 1
Where;
V is the volume of the cone.
r is the radius of the base of the cone.
h is the height of the cone.
Substituting into the formula, we have;
[tex] 36 = \frac{1}{3} \pi r^{2}h[/tex]
Multiplying both sides by 3, we have;
[tex] 108 = \pi r^{2}h[/tex]
Making radius, r the subject of formula, we have;
[tex] r^{2} = \frac {108}{ \pi h} [/tex]
Taking the square root of both sides, we have;
[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]
Mathematically, the lateral surface area of a cone is given by the formula;
[tex] LSA = \pi rl [/tex] ......equation 2
Where;
r is the radius of a cone
l is the slant height of a cone.
To find the slant height, we would apply the Pythagorean' theorem;
[tex] l = \sqrt {r^{2} + h^{2}} [/tex]
Substituting r into the above equation, we have;
[tex] l = \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]
Substituting the values of r and l into eqn 2, we have;
[tex] LSA = \pi * \sqrt { \frac {108}{ \pi h}} * \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]
Simplifying further, we have;
[tex] LSA = \sqrt {108} * \sqrt { \frac {\pi h^{3} + 108}{\pi h}} [/tex]
[tex] LSA = \sqrt {108} * \sqrt { \frac {108}{ h^{2}} + \pi h}} [/tex]
Next, to find the value of h, we differentiate the above mathematical equation with respect to h;
[tex] \frac {dS}{dh} = \sqrt {108} * (\pi - \frac {216}{h^{3}}) * (\pi h + \frac {108}{h^{2}}) [/tex]
Limiting [tex] \frac {dS}{dh} [/tex] w.r.t 0;
[tex] \frac {dS}{dh} = 0 [/tex]
[tex] (\pi - \frac {216}{h^{3}}) = 0 [/tex]
Rearranging the equation, we have;
[tex] \pi = \frac {216}{h^{3}} [/tex]
We know that π = 3.142
[tex] 3.142 = \frac {216}{h^{3}} [/tex]
Cross-multiplying, we have;
[tex] 3.142h^{3} = 216 [/tex]
[tex] h^{3} = \frac {216}{3.142} [/tex]
[tex] h^{3} = 68.75 [/tex]
Taking the cube root of both sides, we have;
Height, h = 4.10 cm
Lastly, we find the value of r;
[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]
[tex] r = \sqrt { \frac {108}{3.142 * 4.10}} [/tex]
[tex] r = \sqrt { \frac {108}{12.88}} [/tex]
[tex] r = \sqrt {8.39} [/tex]
Radius, r = 2.90 cm
The height and radius of the cup that will use the smallest amount of paper is;
Radius = 2.52 cm
Radius = 2.52 cmHeight = 3.58 cm
Let us first state some relevant formulas;
Volume of a cone is;
V = ⅓πr²h
Surface area of a cone is;
S = πrL
Where L is Slant height and has a formula;
L = √(h² + r²)
We are told that the cone is to hold 24 cm³. Thus; V = 24 cm³
24 = ⅓πr²h
πr²h = 72
r = √(72/πh)
Putting √(72/πh) for r in the Slant height equation gives;
L = √(h² + (72/πh))
Thus;
S = π × √(72/πh) × √(h² + (72/πh))
Differentiating with respect to h gives;
dS/dh = √72 × (π - 144/h³) × 1/√(πh + 72/h²)
At dS/dh = 0,we will have;
(π - 144/h³) = 0
Thus;
h³ = 144/π
h = 3.58 cm
Thus, from r = √(72/πh);
r = √(72/(π × 3.58))
r = 2.52 cm
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At Bill’s Burger Barn, every time you buy a burger there is a one in eight chance of winning a free burger. Nicholas bought a hamburger every day for five days. What is the probability that Nicholas wins 1 free hamburger this week?
Answer:
im not sure about this one but my answer is 0.025.
Step-by-step explanation:
if there is a 1 out of 8 chance of getting a free burger, convert that into 1/8. divide that by 5 and you get 0.025.
PLSSSS HELP ASAP !!! PLSSS WILL MARK BRAINLIEST TO WHOEVER GETS IT RIGHT
Answer:
See below.
Step-by-step explanation:
Angle 7 and Angle 4Angle 1 and Angle 5Answer:4000000
Step-by-step explanation:783
Help ASAP 100 PTS!!!!
Describe how to determine the average rate of change between x = 1 and x = 3 for the function f(x) = 3x3 + 1. Include the average rate of change in your answer. Please show all work and explain it thourougly.
Answer:
39
Step-by-step explanation:
Find the value of f(x) at both points
f(3) = 3(3)³ + 1 = 82
f(1) = 3(1)³ + 1 = 4
---------------------------
Average Rate of Change is just like slope
Divide the change in f(x) by the change in x
r = (82 - 4) / (3 - 1)
r = 78/2
r = 39
what is the measure and type of zy
9514 1404 393
Answer:
angle zoy is 70°, an acute angle
Step-by-step explanation:
Each of the 18 spaces around the 180° semicircle identifies 10° of arc. There are 7 spaces between rays z and y, so the angle zoy is 70°. It is less than 90°, so it is an acute angle.
please help! (listing BRAINLIST and giving points)
You used (formula in screenshot) when calculating variance and standard deviation. An alternative formula for the standard deviation that is sometimes convenient for hand calculations is shown below. You can find the sample variance by dividing the sum of squares by n-1, and the sample standard deviation by finding the square root of the sample variance. Complete parts (a) and (b) below.
Answer:
[tex]Varianve = 3.842[/tex]
[tex]SD = 1.960[/tex]
Step-by-step explanation:
Given
See attachment for data
First, calculate [tex]\sum x^2[/tex]
[tex]\sum x^2 = 18^2 + 17^2 +20^2 + 19^2 + 20^2 + 16^2 + 16^2 + 15^2 + 18^2+14^2 +19^2 + 19^2+18^2+17^2 + 16^2+20^2+16^2+18^2+14^2+20^2[/tex]
[tex]\sum x^2 = 6198[/tex]
Calculate [tex]\sum x[/tex]
[tex]\sum x = 18 + 17 +20 + 19 + 20 + 16 + 16 + 15 + 18+14 +19 + 19+18+17 + 16+20+16+18+14+20[/tex]
[tex]\sum x = 350[/tex]
So, we have:
[tex]SS_x = \sum x^2 -\frac{(\sum x)^2}{n}[/tex]
[tex]SS_x = 6198 -\frac{350^2}{20}[/tex]
[tex]SS_x = 6198 -\frac{122500}{20}[/tex]
[tex]SS_x = 6198 -6125[/tex]
[tex]SS_x = 73[/tex]
Solving (a): The variance
[tex]Varianve = \frac{SS_x}{n-1}[/tex]
[tex]Varianve = \frac{73}{20-1}[/tex]
[tex]Varianve = \frac{73}{19}[/tex]
[tex]Varianve = 3.842[/tex]
Solving (b): The standard deviation
[tex]SD = \sqrt{Variance}[/tex]
[tex]SD = \sqrt{3.842}[/tex]
[tex]SD = 1.960[/tex]
A cardiologist is interested in the average recovery period for her patients who have had heart attacks. Match the vocabulary word with its corresponding example.
-
The average recovery time for all heart attack patients that the cardiologist has or will treat
-
All heart attack patients that the cardiologist has cared for or will care for in the future
-
The average recovery time for the 32 heart attack patients
-
The 32 heart attack patients who were observed by the cardiologist
-
The list of all 32 heart attack patients' recovery times
-
The recovery time for a heart attack patient
Answer: See explanation
Step-by-step explanation:
1. The average recovery time for all heart attack patients that the cardiologist has or will treat. = Parameter
2. All heart attack patients that the cardiologist has cared for or will care for in the future = Population.
3. The average recovery time for the 32 heart attack patients = Statistics
4. The 32 heart attack patients who were observed by the cardiologist = Sample
5. The list of all 32 heart attack patients' recovery times = Data
6. The recovery time for a heart attack patient. = Variable
A taxi service charges $1.50 plus $0.60 per mile for a trip to the airport. The total charge is $13.50.
Which equation can be used to determine the number of miles, m, to the airport?
Answer:
13.50=1.50+.6x
Step-by-step explanation:
13.50=1.50+ .6x
12=.6x
20=x
The value of the equation is 13.50 = 1.50 + 0.6m , where y is the total cost and x is the number of miles traveled and m = 20 miles
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the total cost of the taxi be represented as y
Let the number of miles traveled be represented as m
Now , the total cost = $ 13.50
The number of miles = m miles
The initial cost of taxi = $ 1.50
The cost per mile = $ 0.60
So , the equation is 13.50 = 1.50 + 0.6m
Subtracting 1.50 , we get
12 = 0.6m
Divide by 0.6 , we get
m = 20 miles
Hence , the number of miles is 20 miles
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At the playground, the new sandbox was 10 meters wide and had an area of 60 square meters. How long is the sandbox?
Answer:
6 meters
Step-by-step explanation:
Area is length times width. If the width is 10 and the area is 60, then you would find 10 times ??? equals 60. Or 60 divided by 10. which is 6
