A ratio of two numbers a/b, where b is no zero
[tex]{ \large{ \red{{\green{✮}} \: \: \sf{A \: \: number \: \: in \: \: the \: \: form \: \: of \: \:{\pink{ \frac{a}{b} \: \: where \: \: b≠0 }}\: \:{\orange{ is \: \: called \: \: a }}\: \: { \blue{ \underline{ \underline{ \tt{Rational \: \: Number}.}}}}}}}}[/tex]
a wall that is 4 ft. 3 in. tall is next to a tree. the figure shows the shadows that they cast. what is the height of the tree in feet and inches?
Answer:
[tex]Tree = 17ft[/tex]
Step-by-step explanation:
Given
[tex]Wall = 4ft\ 3in[/tex]
[tex]Wall\ Shadow = 6ft[/tex]
[tex]Tree\ Shadow = 24ft[/tex]
Required:
Determine the height of the tree
To do this, we make use of the following equivalent ratios
Wall : Wall Shadow = Tree : Tree shadow
Substitute values for Wall, Wall Shadow and Tree Shadow
[tex]4ft\ 3in : 6ft = Tree : 24ft[/tex]
Convert all units to ft
[tex]4ft+ 0.25ft : 6ft = Tree : 24ft[/tex]
[tex]4.25ft : 6ft = Tree : 24ft[/tex]
Convert to fractions
[tex]\frac{4.25ft}{6ft} = \frac{Tree }{ 24ft}[/tex]
Cross Multiply
[tex]Tree * 6ft = 4.25ft * 24ft[/tex]
[tex]Tree * 6ft = 102ft^2[/tex]
Make Tree the subject
[tex]Tree = \frac{102ft^2}{6ft}[/tex]
[tex]Tree = \frac{102ft}{6}[/tex]
[tex]Tree = 17ft[/tex]
Hence, the tree is 17ft tall
SUMO Some people believe that the N(555, 101)lbs distribution is not the correct model for sumo wrestlers’ weights. Their opinion is that the N(326, 80)lbs distribution is a better model. Manny Yarbrough, a former American sumo wrestling champion, weighed roughly 700 lbs.
If we use the N(555, 101)lbs model, would Manny’s weight be considered typical or unusually high?
i. There is a certain number that you would calculate and then use to answer the above question. Which of the following options is it?
a. (700-555)/sqrt(101) = 14.43
b. (555-700)/sqrt(101) = -14.43
c. 700/sqrt(101) = 69.65
d. (555-700)/101 = -1.44
e. (700-555)/101 = 1.44
f. 700-(3*101) = 397
g. 555-(3*101) = 252
Answer:
The answer is "Option e"
Step-by-step explanation:
use formula:
[tex]N(\mu\ , \ \sigma)= N(555,101)\\\\ \frac{N}{\mu}= 326\\\\\sigma=80\\\\\text{manny has weight}=700 \ lbs\\\\\to z-score= \frac{x-\mu}{\sigma}[/tex]
[tex]=\frac{(700-555)}{101} \\\\ = \frac{(145)}{101} \\\\ = 1.44[/tex]
Find the 8th term of the geometric sequence 3, 12, 48, ....
Answer:
The eighth term of the geometric sequence 3, 12, 48 ... is 49,152. You just multiply every number by 4 :)
So, the required 8th term is 49152.
Geometric Series:The Geometric series formula or the geometric sequence formula gives the sum of a finite geometric sequence.
The sequence will be of the form [tex]\{a, ar, ar^2, ar^3, ..\}[/tex]
And the formula for the nth term is [tex]t_n=ar^{n-1}[/tex]
The given series is,
3, 12, 48, ....
First term=3
The common ratio is,
[tex]\frac{12}{3}=4\\ \frac{48}{12}=4[/tex]
So, the given series is geometric series so the 8th term by the above formula is,
[tex]t_8=3\times (4)^{8-1}\\t_8=49152[/tex]
Learn more about the topic Geometric Series:
https://brainly.com/question/26042879
Compare the wins-to-losses ratios for the teams.
Team Records
Team
Wins
Losses
Cougars
12
10
Bobcats
20
10
Bulldogs
8
5
Tigers
3
5
Which team has the greatest ratio of wins-to-losses?
Cougars
Bobcats
Bulldogs
Tigers
Answer:
Bobcats (i am assuming you need the team with the higest ratio of wins to losses)
Step-by-step explanation:
As a decimal cougars is 1.2 Bulldogs is 1.6 tgers is 0.6 and the largest is bobcats which os 2.0 so the answer is bobcats.
Answer:
B
Step-by-step explanation:
Can someone help me with this problem?
Answer:
Step-by-step explanation:
The dashed vertical line indicates that -3 is not included so x is greater than -3. The diagonal line is solid indicating that it is included so y is greater than or equal to -4x/5 -2. So it is second answer.
Draw the proble. give me steps. Please
Answer:
I cant draw 4 u sry
Answer:
A. c = 3.5h + 15
Step-by-step explanation:
I can't exactly draw the problem BUT I can still help.
C represents the cost altogether but we do not know how much the total cost would be.
So we're paying $15 as a fee, no more from that.
Next, there's another fee that costs $3.50 per hour but since we wouldn't know how long we would use the kayak, hours would represent h.
Now, c = 3.5h + 15.
(In other words, the cost to rent a kayak would be $3.5 PLUS the additonal 15 one time cost.)
1/3 divided by 4 3/4
Answer:
0.07017543859
Step-by-step explanation:
I hope this helps have a nice day!
How can you use ratios to convert metric units of measure?
Answer:
We can convert any measuring unit to another by multiplying it by a very special ratio (or ratios) that equals ONE. We can form these special ratios from the conversion factors. For example, 1 ft = 12 in is a conversion factor, and we can write from it the ratios 1 ft/12 in and 12 in/1 ft, which both equal 1.
Answer: You can convert any measuring unit to another by multiplying it by ratios that equals one.
Step-by-step explanation:
Name the segment that is parallel to the
given segment.
9. AB
10. BC
11. EF
12. CA
13. GE
14. FG
Answer:
13 is the answer (GE) i hope this helped
Help with geometry please
9514 1404 393
Answer:
27/36
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the tangent relation is ...
Tan = Opposite/Adjacent
tan C = AB/CB
tan C = 27/36
Find the distance d(P1, P2) between the points P1 and P2.
P1 = (4,-5); P2 = (3,3)
d(P1,P2) =
(Simplify your answer. Type an exact answer, using radicals as needed.)
Answer:
[tex]\displaystyle d = \sqrt{65}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
P1 (4, -5) → x₁ = 4, y₁ = -5
P2 (3, 3) → x₂ = 3, y₂ = 3
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(3-4)^2+(3--5)^2}[/tex][Distance] [√Radical] (Parenthesis) Simplify: [tex]\displaystyle d = \sqrt{(3-4)^2+(3+5)^2}[/tex][Distance] [√Radical] (Parenthesis) Subtract/Add: [tex]\displaystyle d = \sqrt{(-1)^2+(8)^2}[/tex][Distance] [√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{1+64}[/tex][Distance] [√Radical] Add: [tex]\displaystyle d = \sqrt{65}[/tex]A line passes through the point (8,-8) and has a slope of 3/4. Write an equation in slope-intercept form for this line.
Answer:
Step-by-step explanation:
y + 8 = 3/4(x - 8)
y + 8 = 3/4x - 6
y = 3/4x - 14
4. The length of a rectangle is eight more
than twice its width. The perimeter is 96
feet. Find the dimensions of the rectangle.
Variable:
Equation:
Solution:
Answer:
L = length
W = width
L = 2(2W + 8)
W = 2W
Perimeter: 96 = 4W + 16 + 2W
96 = 6W + 16
80 = 6W
13.33 = W
Plug this into the equation:
2(13.33) + 8
26.67 + 8 or 34.67 = L
Step-by-step explanation:
The difference between x and 2 is less than 9
Answer:
difference between x and 2
Step-by-step explanation:
x-2< 9
x< 11
Arrange the following numbers in ascending order. (a) 5812214,
Answer:
1, 1, 2, 2, 4, 5, 8
Step-by-step explanation:
Hope this helps :)
Maybe brainliest?
3. What is the value of (4/3)^3
Answer:
64/27 = 2.37037037
Step-by-step explanation:
(4/3)^3
Calculate 4/3 to the power of 3 and get 64 /27
64/27
According to Open Data Network, in 2016 there were approximately 3,737 people per square mile in Houston, Texas. If Houston, Texas is 600 square miles, approximately how many people lived in Houston, Texas in 2016?
Answer:
Number of people lived in Texas = 2,242,200
Step-by-step explanation:
Given:
People per square mile = 3,737
Area of Texas = 600 square mile
Find:
Number of people lived in Texas
Computation:
Number of people lived in Texas = People per square mile x Area of Texas
Number of people lived in Texas = 3,737 x 600
Number of people lived in Texas = 2,242,200
The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. The article "Nutrient Intakes and Dietary Patterns of Older Americans: A National Study" (J. of Gerontology, 1992: M145–150) reports the following summary data on intake for a sample of males age 65–74 years: n=115, barx =11.3, and s=6.43. Does this data indicate that average daily zinc intake in the population of all males ageing 65–74 falls below the recommended allowance?
A. State the null and alternative hypotheses.
B. Calculate the test statistic
C. Define the rejection region at ?=0.05.
D. Make a decision about the test and interpret.
E. Find the p-value corresponding to the test and based on which make a decision about the test. (The decision should be the same with D.)
Answer:
H0 : μ = 15
H1 : μ < 15
−6.170774
Step-by-step explanation:
Given :
n=115, barx =11.3, and s=6.43
H0 : μ = 15
H1 : μ < 15
−0.053658 ;
The test statistic :
(xbar - μ) ÷ s/sqrt(n)
(11.3 - 15) ÷ (6.43/sqrt(115))
Test statistic = −6.170774
Rejection region :
Reject Null ; if
Tstatistic < Zcritical
The P value is 0.00001 ; using the p value from Z calculator
Since,
P value < α
0.00001 < 0.05
Reject the null
The medical practice you are working at has seen an average of 22.4 patients a day for the past 3 months. 3/4ths of those patients have insurance in one form or another.
Is 16:14 equivalent to 64:60
Answer:
no
Step-by-step explanation:
64/16 = 4
60/14 = 4.28...
Please help!! Timed!! Brainliest for correct, multiple choice !
Answer:
its d)x=3.
Step-by-step explanation:
If we're finding the extrema using the vertex then its x=3
compare fractions
HELP, GIVING BRAINLIEST
Answer:
a) 5/6
b) 7/8
c) 3/4
Step-by-step explanation:
Draw models for the fractions provided and compare.
Hope this helps.
Answer:
5/6<6/7 3/4<5/6>7/8 2/3>3/4>7/12
Find the x- and y-intercepts of the graph of the equation.
x - 2y = 2
A line passes through the point (10,-8) and has a slope of -1/2. Write an equation in slope-intercept form for this line
Combine these radicals.
- 12V12-23
O -503
0-2275
O -263
0 -10/12
Answer
its the 3rd answer 26V3
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Question 1 of 6
Use the guess and check method to solve this problem.
Blue cassettes hold 45 minutes of music. Green cassettes hold 55 minutes
of music. If Niko has 14 cassettes containing 710 minutes of music, how
many are blue, and how many are green?
O
A. 6 blue cassettes and 8 green cassettes
B. 3 blue cassettes and 11 green cassettes
O O O
C. 5 blue cassettes and 9 green cassettes
O D. 4 blue cassettes and 10 green cassettes
Loo
Answer:
A
Step-by-step explanation:
6 blue cassettes × 45 min = 270 min
8 green cassettes × 55 min = 440 min
270 min + 440 min = 710 min
In the text box, write the next 3 terms in the sequence and describe the pattern. In the checkbox, identify if the sequence is arithmetic, geometric or neither and identify if the sequence has a common ratio, a common difference or neither.
-4, -2, 0, 2, ____, ____, ____,
Arithmetic
Geometric
Neither
Common difference
Common ratio
Answer:
d = 2
Next 3 terms = 4, 6 and 8
Step-by-step explanation:
Given the sequence
-4, -2, 0, 2, ____, ____, ____,
common difference = -2-(-4) = 0-(-2) = 2
Since they have the same common difference, hence it is an arithmetoc progression
Tn = a +(n-1)d
a is the first term = -4
n is the number of terms
d is the common difference = 2
Get the fifth term
T5 = -4+(5-1)2
T5 = -4+(4)(2)
T5 = -4 + 8
T5 = 4
T6 = -4+(6-1)2
T6 = -4+(5)(2)
T6 = -4 + 10
T6 = 6
T7 = -4+(7-1)2
T7 = -4+(6)(2)
T7 = -4 + 12
T8 = 8
Hence the next 3 terms are 4, 6 and 8
11. Harvey the wonder hamster can run 3 1/4 km in 1/2 hour. If Harvey runs at a constant rate, how fast can he run in 1 hour. (Write your answer as a decimal.) *
Answer:
He runs 6.5 km in one hour.
Step-by-step explanation:
3 ¼ km per half hour = 6.5 km per hour.
Answer:
12 2/3
Step-by-step explanation:
there are 4 quarters to 1 hour
3 1/6 x 4 =
19/6 * 4 = 76/6 = 12 4/6, reduces to 12 2/3 km per hour
pls mark brainliest
Sam ate 2/7 of a pizza. Jules ate 2/5 of the same pizza, not the portion of it left by Sam. How much was left. Write a fraction.