Answer: Total Length of ribbon is 99 cm
Step-by-step explanation:
Here ribbon was cut into three parts in the ratio 1:3:5
let x be the common multiple of the above ratio
therefore, the lengths of the three parts of the ribbon is 1x,3x,5x
now, given is that the shortest part i.e 1x is equals to 11cm
i.e 1x=11
x=[tex]\frac{11}{1}[/tex]=11cm
now lengths of the ribbon will be
1x=11cm, 3x=3*11=33cm, 5x=5*11=55cm
now total length of piece of ribbon = 1x+3x+5x=9x=9*11=99cm
Find the value of sin t if tan t = 1 and pi/2 < t < 3pi/2
The value of sin t = sin 135° = 1/√2
What are trigonometric functions?The trigonometric functions are real functions that connect the angle of a right-angled triangle to the ratios of its two side lengths. They are also known as circular functions, angle functions, or goniometric functions[1][2]. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Given; tan t = 1
And the given condition is π/2 < t < 3π/ 2
this mean t lies in the 2nd quadrant because the value of t lies between 90 and 270 degrees.
This means tan t = tan (90 + 45)= cot 45 = 1
thus t = 235 degree
And thus sin t = sin 135 ° = sin (90+ 45) = cos 45 ° = 1/ √2
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cual es la raiz cuadrada de 4096 y 529
The square root of 4096 is 64 and the square root of 529 is 23.
The square root of a number x in mathematics is a number y whose square (the outcome of multiplying the number by itself, or y·y), is equal to x.
For instance, since 4² = (-4)² = 16, 4 and -4 are the square roots of 16.The square root of x is rational if and only if x is a rational integer that can be expressed as the ratio of two perfect squares. (The square root of 2 for proof that this number is illogical; the quadratic irrational for evidence against all non-square natural numbers.) The square root function changes rational numbers into algebraic numbers, which are a superset of rational numbers.The given numbers are 4096 and 529.
Let us find the factors of 4096:
4096 = 2¹²
Therefore the square root of 4096 = √4096 = √(2¹²) = 2⁶ = 64 .
Let us find the factors of 529:
4096 = 23 × 23
Therefore the square root of 529 = √529 = √(23²) = 23 .
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Disclaimer : The question in English is :
What is the square root of 4096 and 529.?
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Given the following: P(A)=0.28, P(B)=0.64, P(B|A)= 0.37, calculate P(A and B)
By definition of conditional probability you know that
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]Now, replace the values that you have and solve for P(A and B)
[tex]\begin{gathered} P(B|A)=\frac{P(A\cap B)}{P(A)} \\ 0.37=\frac{P(A\cap B)}{0.28} \\ \text{ Multiply by 0.28 on both sides of the equation} \\ 0.37\cdot0.28=\frac{P(A\cap B)}{0.28}\cdot0.28 \\ \text{ Therefore,} \\ 0.1036=P(A\cap B) \end{gathered}[/tex]b. Triangle DEF with coordinates D(-2, 2), E (1,5), and F (4, -1) is rotated 90° counterclockwise aboutthe origin
Which are the better statistics to use to compare the team scores
Step 1
We are given two team scores
Required; Which are the better statistics to use to compare the team scores
Step 2
The box plot displays the 5 number summary
-Minimum data value
-Maximum data value
-Median
-First Quartile, and
Third Quartile
The Interquartile Range (IQR) of the data can also be calculated by finding the difference between the First Quartile, and the third Quartile.
The Interquartile Range (IQR) helps us to determine the variability of the data set. The IQR is often seen as a better measure of spread than the range as it is not affected by outliers.
The median that is gotten from the box pot measures the center tendency of the data. The median is the most informative measure of central tendency for skewed distributions or distributions with outliers.
Therefore, the better statistics to use for comparing the scores of the teams are;
Median and IQR.
A family has 6 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 6 girls if it is known the family has at least one girl.
The probability that the family has 6 girls if it is known the family has at least one girl is; 3.125%
What is the Probability?
We are told that each child has the same chance of being a boy or a girl and as such we can say that probability is 1 in 2, or 0.50 or 50%.
Since the family must have at least one girl, if we assume that the first child is a girl, the the probability of the second child being a girl is 50%.
The probability of the other 5 children all being girls is:
(1/2) * (1/2) * (1/2) *(1/2) * (1/2) = 1/32.
This Probability expressed as a decimal or percentage represents a probability that we have as; 1/32 = 0.03125 = 3.125%.
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perfect pizza has 16 Toppings
listed on their menu how many ways can a customer choose a piece of that contains five different toppings
Factorial five. Factorial 16-5. And the response to this question is 4368. There are therefore 4000 368 options for these pizzas with five toppings.
The sum of all positive integers less than or equal to n, indicated by the symbol n!, is the factorial of a non-negative integer n. Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1. The mathematical operation known as a factorial, denoted by the symbol (! ), multiplies a number (n) by each number that comes before it. The factorial function instructs you to multiply all the whole numbers starting at the selected number and going all the way down to one. In further mathematical terms, a number's factorial (n!) equals n (n-1)
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if a varies equal directly with b, and a=8 when b=20 what is the value of a when b= 14.5
Angle JKL is an equilateral triangle jk=13x+5 KL=17x-19 and JL=8x+35
The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
An equilateral triangle is a shape with three sides that have an equal measure of side length.
The 3 sides of triangle JKL are equal to each other, therefore we can equate any of the two sides together to find the unknown variable called x.
So, JK = KL
JK = 13x + 5
KL + 17x - 19
13x + 5 = 17x - 19
Collect like terms;
17x - 13x = 19 + 5
4x = 24
x = 24/4
x = 6
We can now proceed to find the sides;
JK = 13x + 5
13 x 6 + 5
= 78 + 5
= 83
JK = 83
KL = 17x - 19
= 17 x 6 - 19
= 102 - 19
= 83
KL = 83
JL= 8x + 35
= 8 x 6 + 35
= 48 + 35
= 83
JL = 83
Hence, The value of x is 6, then the value of JK is 83, KL is 83 and JL is 83.
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what is the equivalent expression for:
m - (8 -3m)
How do I solve 5/9x+ 6=10?
Due to the inaccuracy of the provided information, we will suppose that the original expression is
[tex]\frac{5x}{9}+6=10[/tex]Solve for x as shown below
[tex]\begin{gathered} \Rightarrow\frac{5x}{9}+6-6=10-6 \\ \Rightarrow\frac{5x}{9}=4 \\ \Rightarrow(9)\frac{5x}{9}=(9)4=36 \\ \Rightarrow5x=36 \\ \Rightarrow(\frac{1}{5})5x=\frac{1}{5}\cdot36 \\ \Rightarrow x=\frac{36}{5} \end{gathered}[/tex]Therefore, the answer is x=36/5
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 17 HCF of water is $32.13 and the cost for using 35 HCF IS 61.83. . What is the cost for using 19 HCF of water?
If the cost for using 35 HCF IS 61.83. . the cost for using 19 HCF of water is :$68.31.
How to find the cost price?Straight line: y=mx+b, m=slope, b=y-intercept
Let y=cost of using 19 HCF water
Let x =amount of water used
m=∆y/∆x =(61.83 - 32.13) / (35-19)
m=∆y/∆x =29.7 /16
m=∆y/∆x = 1.85625
m=∆y/∆x = 1.86 ($/HCF) (approximately)
equation: y=1.86x+b
Solving for b using point (19, 32.13)
32.13 =1.86×19+b
32.13=35.34+b
b=35.34 -32.13
b=3.21
equation:
f(x)=1.86x+3.21
f(25)=1.86×35+ 3.21
= 68.31
Cost of using 35 HCF water= $68.31
Therefore the cost price is $68.31.
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Given P250/75R18 tires, what would be the Circumference in inches of the tire?
Given data:
The given radius of the tire is r=18 in.
Th expression for the circumference is,
C=2πr
Substitute the given values in the above expression.
C=2(3.14)(18)
=113.04 in
Thus, the circumference of the tire is 113.04 inn.
a cylinder shaped popcorn
Answer
Option C is correct.
Volume = 1,413 in³
Explanation
The volume of a cylinder is given as
Volume = πr²h
where
π = pi = 3.14
r = radius of the cylinder = ½ (Diameter) = ½ (10) = 5 inches
h = height of the cylinder = 1.5 feet = 1.5 (12 inches) = 18 inches
The conversion from feet to inches was done using 1 feet = 12 inches
So, we can calculate the volume now
Volume = πr²h
Volume = (3.14) × (5²) × (18)
Volume = 1,413 in³
Hope this Helps!!!
A board 172 inches wide is cut to three-fourths of its original width
Answer: 129 inches
Step-by-step explanation:
172 inches x 3/4 original with = 129 inches
Rudy has $90,000 in a savings account that earns 10% interest per year. The interest is not compounded. How much interest will he earn in 1 year?
The total interest earned by Rudy on the principal is $9000
Amount in Rudy's saving account = $90,000
Interest rate per year = 10%
The formula for simple interest is given:
A loan or deposit's principal amount serves as the foundation for simple interest. Compound interest, on the other hand, is calculated based on both the initial principal and the interest that is added to it each period.
Simple interest = P*R*T/100
where P = principal amount invested
R = rate of interest
T = time in years
Substituting the values in the formula we get:
Simple interest = 90000*10*1/100
= 9000
So, the interest amount is $9000
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Select the table that represents a linear function. (Graph them if necessary.)
OA. x 0 1 2 3
y 2 3 6 11
OB. x 0 1 2 3
y 1 3 9 27
OC. x 0123
y 0149
OD. x 012
3
y 39 15 21
Answer:
The last table represents a linear function.
As x increases by 1 unit, y increases by a constant of 6 units
The equation of the function is
y = 6x + 3
Step-by-step explanation:
A is the point (-6, 5) and B is the point (-2,-3). (a) Find the equation of the straight line, I, that passes through point A and point B. Give your answer in the form y=mx+c.
The linear equation that passes through the point (-6, 5) and B is the point (-2,-3) is:
y = -2x - 7
How to find the linear equation?
A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
s = (y₂ - y₁)/(x₂ - x₁)
In this case, we have the points (-6, 5) and (-2,-3), then the slope is:
s = (-3 - 5)/(-2 + 6) = -8/4 = -2
Then we have:
y = -2*x + c
To find the value of the constant we use one of the points, I will use (-2, -3) to get:
-3 = -2*(-2) + c
-3 = 4 + c
-3 - 4 =c
-7 = c
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There are 151 people in the 6th
grade class. It costs $24 for each
person to go snorkeling. How
much did they pay altogether?
Answer:
Step-by-step explanation:
it cost $3,624
Simplify 3^2 + 3(6 - 2^2) ÷ 6.
Fractions simplification
Apply PEMDAS method. Eliminate parenthesis first.
Then (3^2 + 3•6 - 3•2^2 )/ 6 = (3^2 + 3•6 - 3•2^2 )/ 6
now eliminate exponents
= [3• 3 + 3•6 + 3•4] / 6
= 3•5/6 now multiplicate
3•5= 15
Then
= 15/6 = 2 + 3/6 = 2 + 1/2 = 2.5
what is probability that it is from the 70s is
Given :
the total number of collections = 60 vinyl
There are six from the 70s
So, the probability that is from 70s is :
[tex]\frac{6}{60}=\frac{1}{10}[/tex]Is the following a power function, a polynomial, both, or neither?f(x)=−17x^5
Answer:
Both
Explanation:
Given the function:
[tex]f(x)=-17x^5[/tex]• A power function is a function with a whole number as its exponent.
,• A monomial is a polynomial that has only one term.
The given funtion has 5 as its exponent, thus, it sis a power function. Furthermore, it is a monomial, thus it is also a polynomial.
f(x) is both a power function and a polynomial.
Find the surface area of the prism. 5 m 1 1 4646 om 13 m Not drawn to scale 195 m2 O 48 m2 780 m2 346 m2
Prism surface is formed by
2 rectangles x and 2 rectangles y ,2 rectangles z
then
Area of rectangles for x= 2x13x6 = 156 m2
. For y = 2x5x6= 60 m2
. For z = 2x13x 5 = 130 m2
Then now add all these results
Prism area = 156 + 60 + 130 = 346
Then answer is
OPTION D) 346 m2
The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 4.3% per hour. How many hours does it take for the size of the sample to double? Note this is a continuous exponential growth model. Do not round any intermediate computations, and round your answer to the nearest hundredth.
Answer:
16.12 hours
Explanation:
A continuous exponential growth model is given below:
[tex]P(t)=P_oe^{rt}[/tex]• The growth rate, r = 4.3% = 0.043
,• t = time in hours
,• Po = Initial population
,• P(t) = Present population
We want to find the number of hours it takes the population to double. That is if the initial population, Po = 1
• The present population, P(t) = 1 x 2 = 2.
Substitute these values into the model above to get:
[tex]2=1(e^{0.043t})[/tex]Since natural logarithm(ln) is the inverse of exponential, take the natural logarithm of both sides to remove the exponential operator.
[tex]\begin{gathered} \ln (2)=\ln (e^{0.043t}) \\ \ln (2)=0.043t \end{gathered}[/tex]Divide both sides by 0.043.
[tex]\begin{gathered} \frac{\ln (2)}{0.043}=\frac{0.043t}{0.043} \\ t=\frac{\ln(2)}{0.043} \\ t\approx16.12 \end{gathered}[/tex]It will take 16.12 hours for the size of the sample to double.
I need to check my answer for number 1 I put C.
Given
[tex]f(x)=3(\frac{1}{2})^x[/tex]Find
Plot the graph
Explanation
To plot the graph we need points ,
let
[tex]undefined[/tex]1. Think of a real-life situation, where knowing the percent error would be helpful.2. In a short paragraph, describe the situation and include the percent error. Explain why knowing the percent error is helpful.
SOLUTION:
The percent erroris helpsful in many situations. An example will be when conducting
Find each quotient. All final answers must be in simplest form.9x3y2 + 15x2y - 6x2/ 3x2 = X^2 + 8x - 163xy^2 + 5y + 2 3xy^2 + 5y - 2 3xy^2 - 5y - 2
ok
[tex]\begin{gathered} \frac{9x^3y^2+15x^2y-6x^2}{3x^2}\text{ = }\frac{9x^3y^2}{3x^2}\text{ + }\frac{15x^2y}{3x^2}\text{ - }\frac{6x^2}{3x^2} \\ \text{ = 3xy}^2\text{ + 5y - 2} \end{gathered}[/tex]The answer is on the second row. 3xy^2 + 5y - 2
a different ratio that is equivalent to 3 over 5
Answer:
6 over 10
Step-by-step explanation:
You can use any number, but I used 2. You can multiply both numbers by any whole number, me using 2. I timed 3 by 2 which is 6. And 5 times 2 is 10. So, we have 6 over 10. And we can use 3, 4, 5, 6, and so on, it doesn't matter it is still the same. Just, make sure you multiply both numbers by the same number.
ryan is buying pencil boxes. he wnats to buy the box that will fit the most markers. he can choose between the following 3 options
Answer:
what r the 3 following options??
Step-by-step explanation:
Each relationship below compares the shaded portion the part to the entire figure the whole complete the table 6'60'600'32
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a portion of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Percent refers to one hundred percent.
A decimal is a number divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of full and partially whole quantities.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.
A ratio displays the multiplicity of two numbers. A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations.
Percentage Decimal Fraction Ratio
6% 0.06 6 / 100 6:100
60% 0.6 60 / 100 60:100
600% 6 600 / 100 = 6 / 1 6:1
32% 0.32 32 / 100 32:100
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