The ratio of the number of children to the number of adults in this group is 2 : 3
How to determine the ratio?The admission is given as:
Children=4
Adult = 6
Express as ratio
Ratio = Children : Adult
This gives
Children : Adult = 4 : 6
Simplify
Children : Adult = 2 : 3
Hence, the ratio of the number of children to the number of adults in this group is 2 : 3
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In the monthly rate payment formula M= Pr(1+r)^n/(1+r)^n-1, what value do you give r if the interest rate is 7.3%?
Answer:
r = 0.073/12 ≈ 0.0060833...
Step-by-step explanation:
In the given amortization formula, the interest rate (r) is the rate for one payment period.
Period interest rateThe given 7.3% interest rate is presumed to be a nominal annual interest rate. Since there are 12 months in a year, the corresponding monthly interest rate is ...
7.3%/12 = 0.073/12 ≈ 0.00608333...(repeating)
The value of r that goes in this formula is 0.0608333...(repeating).
Answer:
0.61
Step-by-step explanation:
one day, duncan and his friends had lunch while sitting at tables of 6. another day, they had lunch at tables of 5. what is the smallest number of people that could be in the group?
Answer:
the smallest number of people that could be in his group with the possibility of it being less than five people, will be three people.
Please help ill appreciate it best answer gets the brainliest answer!
Answer:
Linear
Step-by-step explanation:
Notice that x values increase by 1 each row and that the y values increase by 5 each row. By definition, in linear functions, x and y values both increase by constant values. Going down each row, the y value increases by 5 as the x value increases by 1, so we know that the graph must be a linear function.
Function Type: linear
Equation: y = 5x + 7
Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has already picked 1
1
2
bushels, and she picks at a rate of
5
Solve the equation for x.
2
3
x −1
9
x + 5 = 20
x =
The number of hours it will take Brigid to fill 5 bushels of strawberries is; 5³/₅ hours
How to simplify algebraic equations?
We are told that the scenario that Brigid represents is;
⁵/₈x + 1¹/₂ = 5
where x is is the number of hours she picks
Now, let us solve for x by converting the mixed fraction to improper fraction to get;
⁵/₈x + ³/₂ = 5
Multiply through by 8 to get;
5x + 12 = 40
Subtract 12 from both sides to get;
5x = 28
x = 28/5
x = 5³/₅ hours
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(-3x2 + x + 5) − (4x2 − 2x)
Answer:
-7x^2 + 3x + 5
Step-by-step explanation:
-3x^2 + x + 5 - 4x^2 + 2x
An encryption machine uses a formula to encrypt words, by taking each letter and changing it to the letter that is just before it in the alphabet. If the letter is ‘a’, it changes it to ‘z’. If you put the word STAR into the machine, what would the output be?
A) TARS
B) RSZQ
C) TUBS
D) RSTA
The output of the word STAR is RSZQ
How to determine the output?The encryption rule is given as:
Change a letter to the previous letter
This means that:
S -> R
T -> S
A -> Z
R -> Q
So, we have:
STAR -> RSZQ
Hence, the output of the word STAR is RSZQ
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PLEASE HELP ASAP!!! Two weeks in a row, the golf course hosts a group of golfers. The second week had 10 more golfers than the first week. Use the dot plots to choose the true statement.
dot plot titled Number of Golfers for Week 1 with number line labeled Age of Golfer, 1 dot at 62, 3 dots at 68, 1 dot at 69, 2 dots at 70, 3 dots at 72, 2 dots at 75, 1 dot at 76, 2 dots at 78, 3 dots at 80, and 2 dots at 89
dot plot titled Number of Golfers for Week 2 with number line labeled Age of Golfer, 3 dots at 62, 4 dots at 63, 2 dots at 64, 1 dot at 66, 1 dot at 67, 3 dots at 68, 1 dot at 69, 2 dots at 70, 3 dots at 72, 2 dots at 75, 1 dot at 76, 2 dots at 78, 3 dots at 80, and 2 dots at 89
A) The range for Week 1 equals the range for Week 2.
B) The range for Week 1 is greater than the range for Week 2.
C) The median for Week 1 is less than the median for Week 2.
D) The mean for Week 1 is greater than the mean for Week 2.
The true statement is the range for Week 1 equals the range for Week 2.
What is the true statement?A dot plot is a graph that is used to show the frequency of a data set using dots. Range is the difference between the highest and lowest values of a set of observations
Range = highest value - lowest value
Range of the first dot plot : 89 - 62 = 27
Range of the second dot plot : 89 - 62 = 27
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Which question is a biased question?
(1) How old are you?
(2) What is your favorite color out of red, blue, and green?
(3) Do you prefer a beautiful sunny day or a depressing rainy day?
(4) How many siblings do you have?
Answer:
3!
Explanation:
By calling a sunny weather "beautiful" and rainy weather "depressing", you're inserting your own opinion into the question- which makes it biased!
On a coordinate plane, polygons A B C D and A prime B prime C prime D prime are shown. The points of A B C D are (2, negative 2), (4, negative 2), (3, negative 4), and (1, negative 4). The points of A prime B prime C prime D prime are (3, negative 3), (6, negative 3), (4.5, negative 6), (1.5, negative 6).
Given the pre-image ABCD and the image after a dilation, A'B'C'D', what is true about the polygons? Check all that apply.
The length AB is 2.
The length A'B' is 3.
The image is smaller than the pre-image.
The scale factor is Three-halves.
The scale factor is Two-thirds.
Polygon ABCD was dilated by a scale factor of 3/2 to form polygon A'B'C'D'. The scale factor used was 3/2. The length AB is 2 and the length A'B' is 3.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
[tex]AB=\sqrt{(4-2)^2+(-2-(-2))^2}=2\ units[/tex]
Polygon ABCD was dilated by a scale factor of 3/2 to form polygon A'B'C'D'. The scale factor used was 3/2. The length AB is 2 and the length A'B' is 3.
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Answer:
A, B, and D
Step-by-step explanation:
yw enjoy summer
Researchers hypothesize that the first self-replicating molecule may have been ____. This is known as the ______world hypothesis.
Researchers hypothesize that the first self-replicating molecule may have been RNA. This is known as the RNA world hypothesis.
Life likely evolved between 3.53.53, point 5 and 3.93.93, point 9 billion years ago, when the Earth formed around 4.54.54, point 5 billion years ago.
According to the Oparin-Haldane hypothesis, "building blocks" like amino acids initially formed and then came together to form complex polymers as life gradually evolved from inorganic molecules.
The first proof that organic molecules required for life might be created from inorganic elements was supplied by the Miller-Urey experiment.
The RNA world hypothesis, which contends that RNA was the primordial form of life, is backed by certain scientists. Others support the concept that metabolic networks come before DNA or RNA.
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Suppose babies born in a large hospital have a mean weight of 3685 grams, and a variance of 330,625. If 113 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would be less than 3631 grams
The probability that the mean weight of the sample babies would be less than 3631 grams is 0.1591 or 15.91%.
The mean weight of the babies (μ) = 3685 grams.
The variance (σ²) = 330625.
Therefore, the standard deviation (σ) = √330625 = 575.
The sample size (n) = 113.
The sample mean = μ - 3685 grams.
The sample standard deviation (s) = σ/√n = 575/√113 = 54.09145.
We are asked to find the probability that the mean weight of the sample babies is less than 3631 grams, that is,
P(X < 3631) = P(Z < {(3631 - 3685)/54.09145})
Using the formula: Z = (x - μ)/s,
or, P(Z < -0.9983) = 0.1591 or 15.91%.
From the table of area under the z-score.
P(X < 3631) can also be calculated using calculator function:
Normalcdf(-100000000,3631,3685,54.0195), which gives the value 0.1591 or 15.91%.
Thus, the probability that the mean weight of the sample babies would be less than 3631 grams is 0.1591 or 15.91%.
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Show you work for full credit Use the SUBSITUTION method or ELIMINATION method to solve this system of equations. y = 4x and 8x + y = 18
Answer:
A. (3/2, 6)
Step-by-step explanation:
Use the substitution method:
8x + y = 18 and y = 4x
8x +4x = 18
12x = 18
x = 18/12 = 3/2
y = 4x
= 4(3/2)
= 12/2
= 6
Suppose you are given a triangle with hypotenuse of length 2 and legs of length x+1 and x-1 . Find the numerical length of both sides.
Answer:
Step-by-step explanation:
[tex](2)^2=(x+1)^2+(x-1)^2\\[/tex]
By solving this equation we can get:
[tex]x=1 \\x=-1 (Impossible)[/tex]
∴
The value of the x will be equal to 1.
What is the Pythagorean theorem?The section of the zoo is a right triangle. The new path is in front of the right angle, therefore it is the hypotenuse. To find the length of the hypotenuse we use the Pythagorean theorem:
H² = P² + B²
Given that the hypotenuse is of length 2 and legs of length x+1 and x-1. The value of x will be calculated as:-
H² = P² + B²
2² = ( x + 1 )² + ( x - 1 )²
4 = ( x² + 2x + 1 ) + ( x² - 2x + 1 )
4 = 2x² + 0 + 2
4 - 2 = 2x²
x = √1 = ±1
x = 1 and x = -1 ignore negative value.
Therefore, the value of the x will be equal to 1.
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15. Robin ordered pizza and opted for delivery.
She prepaid $48.95 over the phone using
her credit card and plans to give an 18%
cash tip upon delivery. If she has $7, will this
be enough to cover the tip?
Answer: No she'll need atlease 9 dollars
Step-by-step explanation:
48.95 x 18% is 8.811 which is greater than
I Need Help Quickly Please And Thank You
Answer:
Step 2: it should be P - 2x, not P + 2x.
Step-by-step explanation:
A regular hexagon is truncated to form a regular dodecagon (12-gon) by removing identical isosceles triangles from its six corners. What percent of the area of the original hexagon was removed
7.2 percent of the area of the original hexagon was removed
The area of hexagon is the region that lies within the sides of the hexagon. A hexagon is a two-dimensional shape that has 6 sides, 6 angles, and, 9 diagonals, and the sum of its interior angles is 720°
Area of the hexagon = (3√3 s2)/2, where 's' is the length of the side of the hexagon.
Her, We have
[tex]\(1-2s=s\sqrt3, 1=2s+s\sqrt3, 1=s(2+\sqrt3), s=\frac{1}{2+\sqrt3}\)[/tex]
Rationalize the denominator to get [tex]\(s=2-\sqrt3\)[/tex]
The area of the hexagon is [tex]\(\frac{3\sqrt3}{2}\)[/tex] and the dodecagon is [tex]\(\frac{3s^2\sqrt3}{2}\).[/tex]
The deleted area is [tex]\(s^2=0.072=7.2%\)[/tex] percent
Formula used:
Area = (3√3 s2)/2
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A standard number cube was rolled multiple times, and the results were recorded in the table above. What can be said
about the experimental probability of rolling a two versus the theoretical probability of rolling a two?
Answer:
Experimental Probability = 1/3
Theoretical Probability = 1/6
========================================================
Explanation:
Count how many times the number "2" shows up in the "Result" column. There are 4 instances of this value. This is out of 12 trials total.
Divide the two numbers to get 4/12 = 1/3 as the experimental probability
-------------
In contrast, the theoretical probability is 1/6 because there's 1 side labeled "2" out of 6 sides total.
The decimal form of each fraction is:
1/3 = 0.333 approximately
1/6 = 0.167 approximately
Consider the following system of equations given in slope-intercept form.
y = −1
3
x + 17,
y = 5x - 23
Use the graphing calculator to determine the best window range to find the point of intersection.
–10 Less-than-or-equal-to x Less-than-or-equal-to 10, –10 Less-than-or-equal-to y Less-than-or-equal-to 10
–20 Less-than-or-equal-to x Less-than-or-equal-to 0, –20 Less-than-or-equal-to y Less-than-or-equal-to 0
0 Less-than-or-equal-to x Less-than-or-equal-to 20, 0 Less-than-or-equal-to y Less-than-or-equal-to 20
20 Less-than-or-equal-to x Less-than-or-equal-to 40, 20 Less-than-or-equal-to y Less-than-or-equal-to 40
answer: c.0 Less-than-or-equal-to x Less-than-or-equal-to 20, 0 Less-than-or-equal-to y Less-than-or-equal-to 20
Option c. The range of window for the data is given as 0 Less-than-or-equal-to x Less-than-or-equal-to 20, 0 Less-than-or-equal-to y Less-than-or-equal-to 20
How to solve for the range of the dataWe have the equation to be
y = −3x + 17,
and y = 5x - 23
We have to make the two equations to be equal
This would then give us
−3x + 17 = 5x - 23
The next step is to take the like terms
3x - 5x = -23-17
-2x = -40
From you we have to divide by -2
x = 20
The range would be written as
0 ≤ x ≤ 20, 0 ≤ y ≤ 20
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asap! find the length of the arc
Answer:
8π ft
Step-by-step explanation:
Arc length = 2πr ( θ / 360 )
Here,
θ = 90
r = 90 ft
Arc length = 2πr ( θ / 360 )
Arc length = ( 2π * 16 ) ( 90 / 360 )
= ( 2π * 16 ) ( 1 / 4 )
= ( 2π * 16 )/4
= 2π * 4
Arc length = 8π ft
Answer:
B
Step-by-step explanation:
the arc length is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{90}{360}[/tex]
= 2π × 16 × [tex]\frac{1}{4}[/tex]
= 2π × 16 × [tex]\frac{1}{4}[/tex]
= 32π × [tex]\frac{1}{4}[/tex]
= 8π ft
What is DF? Help me please :)
The value of DF = 20.
What is similarity?Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
Given:
Using theorem
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
ΔSDF/Δ RTY = (SD/RT)= (DF/TY)= (FS/ YR)
ar ΔSDF² / ar ΔRTY² = 16/81
SD/ RT = 4/9
SD = 4x, RT= 9x
SD= 8
4x = 8
x = 2
So,
RT= 9*2 = 18
SF = RT -2
SF = 16
(SD/RT)= (FS/ YR)
8 / 18 = 16/ YR
YR= 36
TY= 9 +RY = 45
(DF/TY)= (FS/ YR)
DF / 45= 16/ 36
DF=20
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What is 3+(−5 2/3)? Write the answer as a mixed number in simplest form.
Answer:
-2 2/3
Step-by-step explanation:
3+(-5 and 2/3)=3-5 2/3= -5 2/3+3=-2 2/3
The sum of two numbers is [tex]-2\frac{2}{3}[/tex] .
What is addition of two fractions?To add fractions there are three simple steps:
Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator.
Step 3: Simplify the fraction (if possible)
Given that, 3+([tex]-5\frac{2}{3}[/tex])
= 3-17/3
= (9-17)/3
= -8/3
= [tex]-2\frac{2}{3}[/tex]
Therefore, the sum of two numbers is [tex]-2\frac{2}{3}[/tex] .
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Figure A Figure B 3 ft 10 ft 2 ft 4 ft V= 120 cu ft Find the volume of Figure B.
The volume of the small figure is v = 120/8 cubic ft or v = 1.5 cubic ft if the volume of the larger cube is 120.
What is a scale factor?The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.
As we have given the volume of the larger cube is 120
Let v is the volume of the small shape.
[tex]\rm \dfrac{120}{v} =\left( \dfrac{4}{2} \right)^3[/tex]
After simplifying:
v = 120/8 cubic ft
or
v = 1.5 cubic ft
Thus, the volume of the small figure is v = 120/8 cubic ft or v = 1.5 cubic ft if the volume of the larger cube is 120.
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x+y=5
x×y=6
Solve simultaneously with steps
Answer:
(3, 2), (2, 3)
Step-by-step explanation:
x + y = 5
xy = 6
Solve the first equation for x.
x = 5 - y
Substitute 5 - y for x in the second equation.
xy = 6
(5 - y)y = 6
5y - y² = 6
y² - 5y + 6 = 0
Factor.
(y - 2)(y - 3) = 0
y - 2 = 0 or y - 3 = 0
y = 2 or y = 3
Now substitute 2 for y in the first equation and solve for x.
x + y = 5
x + 2 = 5
x = 3
One solution is x = 3; y = 2, or (3, 2).
Now substitute 3 for y in the first equation and solve for x.
x + y = 5
x + 3 = 5
x = 2
Another solution is x = 2; y = 3, or (3, 2).
Answer: (3, 2), (2, 3)
The graph represents the heights of two climbers on a climbing wall over a 12-minute time period.
A graph titled The Climbing Wall where the horizontal axis shows time (minutes), numbered 1 to 12, and the vertical axis shows height (feet) numbered 2 to 24. The line labeled Brynn's climb begins at 0 feet in 0 minutes, to 15 feet from 5 to 7 minutes, to 0 feet in 10 minutes. The line labeled Abby's climb begins at 4 feet in 0 minutes, to 14 feet from 4 to 6 minutes, to 22 feet in 8 minutes, to 0 feet in 12 minutes.
Which statement is true about the climbers’ heights?
Brynn was resting at a constant climbing height when Abby’s climbing height was decreasing.
Abby’s climbing height was decreasing when Brynn’s climbing height was increasing.
The heights of both climbers increased, then decreased, with no rest at a constant height.
Both climbers rested on the wall at a constant height for 2 minutes.
Both climbers rested on the wall at a constant height for 2 minutes.
How to determine the true statement?The complete question is added as an attachment
From the attached graph, we have the following highlights
Abby's movement stopped from 4 minutes to 6 minutes i.e. 2 minutesBrynn's movement stopped from 5 minutes to 7 minutes i.e. 2 minutesThe above means that both climbers stopped for 2 minutes
Hence, the true statement about the climber's height is that (d) Both climbers rested on the wall at a constant height for 2 minutes.
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Answer: D: Both climbers rested on the wall at a constant height for 2 minutes.
Step-by-step explanation: i did the quiz edge 2022
[tex]\sqrt(1-2)+\sqrt(1+2)\\[/tex]
An opinion poll survey based on a sample of ____________________ people is likely to provide the most accurate results.
An opinion poll survey based on a sample of a small section of people is likely to provide the most accurate results.
What is an opinion poll?An opinion poll, often known as a poll or survey, is a human research survey of the general public from a specific sample. By asking a series of questions and extending generalizations into ratios or confidence intervals, opinion polls are often created to represent the opinions of a population. A person who conducts polls is referred to as a pollster.
An opinion poll is a survey that samples a tiny portion of the population in an effort to forecast election outcomes or gauge popular sentiment toward various concerns.
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Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 145 millimeters, and a standard deviation of 6 millimeters. If a random sample of 39 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by less than 0.5 millimeters
The probability that the sample mean would differ from the population mean by less than 0.5 millimeters is 0.3970.
Given mean diameter of 145 millimeters, standard deviation of 6 millimeters.
We have to find out the probability that the sample mean would differ from the population mean by less than 0.5 millimeters.
μ=145 and ,σ=60 ,n=39 then
s=60/[tex]\sqrt{39}[/tex]=0.96
By finding the probability that the sample mean would differ by less than 0.5 mm equal to p value of Z when X=145+0.5=145.5 mm subtracted by the p value of Z when X==145-0.5=144.5 mm.
When X=145.5 mm
Z=(X-μ)/σ
By central limit theorem
Z=(145.5-145)/5
=0.5/0.96
=0.52
p value of 0.52=0.6985.
When X=144.5
Z=(144.5-145)/0.96
=-0.5/0.96
=-0.52
p value of -0.52=0.5-0.1985=0.3015
Required probability=0.6985-0.3015=0.3970.
Hence the probability that the sample mean would differ from the population mean by less than 0.5 mm is 0.3970.
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4. Write the trinomial represented by each rectangle of algebra tiles. Then, determine the
dimensions of each rectangle.
Answer:
Trinomial: [tex]\boldsymbol{\text{x}^2 + 3\text{x} - 4}[/tex]
Dimensions: [tex]\boldsymbol{\text{x}+4} \text{ by } \boldsymbol{\text{x}-1}[/tex]
=======================================================
Explanation:
The big green square is x units by x units. Its area is [tex]\text{x} * \text{x} = \text{x}^2[/tex] which represents x squared.
The long vertical green rectangles are x units tall and 1 unit across. The area of one such rectangle is x times 1 = x. Since we have four of these green rectangles, so far we have x+x+x+x = 4x in additional area.
So far the area is [tex]\text{x}^2+4\text{x}[/tex]
---------------
All of the green areas mentioned so far are positive areas so to speak.
In contrast, the red areas are negative areas. They take away from the positive. You can think of it like a bank balance.
If a single green rectangle is x square units in area, then a red rectangle is negative x or -x
So we go from 4x to 4x-x = 3x
Then we subtract off 4 due to the 4 small squares
This gives a total area of [tex]\text{x}^2 + 3\text{x} - 4[/tex] and this represents the standard form of the polynomial area. It is a trinomial since it has 3 terms.
---------------
Now onto the dimensions.
Check out the diagram below. The overall figure is x+4 units across the horizontal dimension, and x-1 units tall along the vertical dimension.
If you were to use the FOIL rule, then you would find that [tex](\text{x}+4)(\text{x}-1) = \text{x}^2 + 3\text{x} - 4[/tex] which helps show how the two forms connect to one another.
This also helps show that area = length*width which is what we'd expect from any rectangular area.
1.You realize a short time into the carnival that you don’t have enough prizes to last the entire event. You call your teacher, and she suggests that you change the winning number so that a participant will win only 25% of the time. What number will that be? Support your answer.
2. Participants achieving a winning score of 36 or higher in four consecutive attempts will receive a large prize! What is the probability of this occurring?
3.After changing the game rules, participants and the crowd are disappointed when the first five games yield scores of 12, 18, 30, 28, and 24. What statement can you recommend the teacher posts to reassure everyone that the game is fair?
SHOW ALL WORK!!!!
When you win 25% of the time based on the probability, this illustrates that the number of products picked will be 7 products.
How to illustrate the probability?Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.
Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:
= 24 + 4 = 28
The frequency table will be such that 28 or more have a relative frequency of 9. Therefore, the probability that a person wins the game will be:
= 9/28 = 32.1%
When you win 25% of the time, this illustrates that the number of products picked will be:
= 25% × 28
= 7 products.
The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:
= 1/6⁴
= 1/1296
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Please help with this geometry question.
The exercise below is one that requires the proof that of certain dimensions using the rules of congruence. of triangles.
What does it mean for two angles to be congruent?
It simply means that both angles are similar in measure.
What is the required proof of the given problem?It is given that ∠BAD=∠EAC
∠BAD+∠DAC=∠EAC+∠DAC [add ∠DAC on both sides]
Therefore ∠BAC=∠DAE
In △BAC and △DAE
AB=AD (Given)
∠BAC=∠DAE (Proved above)
AC=AE (Given)
Therefore △BAC≅△DAE (By SAS congruence rule)
Therefore BC=DE because Corresponding Parts of Congruent Triangles CPCT are congruent.
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