The ratio of Student Ambassadors to total Students in Mr. Thompson's class is 1:4.
Ratios and proportions are two fundamental concepts in mathematics that are used to compare quantities and express relationships between them.
A ratio is a comparison of two quantities that are expressed in the same units. Ratios are typically written in the form of "a:b" or "a to b", where a and b are two quantities being compared. For example, the ratio of the number of boys to the number of girls in a class of 20 students might be 3:2, indicating that there are 3 boys for every 2 girls.
A proportion is a statement that two ratios are equal. Proportions are used to solve problems involving ratios by setting up an equation that equates two ratios.
The total number of students in Mr. Thompson's class is 6 + 18 = 24.
The ratio of Student Ambassadors to total Students is 6:24, which can be simplified by dividing both the numerator and denominator by 6 to get 1:4.
Therefore, the ratio of Student ambassadors to total Students in Mr. Thompson's class is 1:4.
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A line of best fit predicts that when x equals 33, y will equal 31.65, but y
actually equals 31. What is the residual in this case?
A. -0.65
B. 1.35
C. 0.65
D. 2
Round your answer to the nearest hundredth.
Answer:
∠ A ≈ 75.96°
Step-by-step explanation:
using the tangent ratio in the right triangle
tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{8}{2}[/tex] = 4 , then
∠ A = [tex]tan^{-1}[/tex] ( 4 ) ≈ 75.96° ( to the nearest hundredth )
Brainliest and 20 points to whoever shows work the best
Using Pythagorean's theorem we can see that the variables are:
t = 13.86
w = 12.81
How to find the values of the variables?Remember that for any right triangle, Pythagorean's theorem says that the sum of the squares of the legs is equal to the square of the hypotenuse, where the hypotenuse is the side opposite to the 90° angle.
Then for the first triangle we can write:
t² + 8² = 16²
Solving for t:
t = √(16² - 8²) = 13.86
For the second triangle we have:
10² + 8² = w²
Solving for w:
w = √(10² + 8²)
w = 12.81
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Two households are saving money each month to go towards the shared costs of a vacation trip. One household has $700 saved and will continue saving $400 each month. The other household has $1,000 saved and will continue saving $300 each month.
Use the system of equations, where y represents total saved and x represents number of months, to answer the question.
y = 400x + 700
y = 300x + 1,000
At what point would the two lines intersect if graphed?
The two lines will intersect after 3 months.
How to explain the equationWe can set the two expressions for y equal to each other:
400x + 700 = 300x + 1,000
100x + 700 = 1,000
100x = 300
x = 3
So the two lines will intersect after 3 months. In this case, to find the corresponding value of y, we can substitute x = 3 into either of the equations:
y = 400x + 700
y = 400(3) + 700
y = 1,500
Therefore, the two lines will intersect after 3 months, at a point with coordinates (3, 1,500).
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if P = (4,2), Find: Rx=3 (P). Pls help!!
The coordinates of the reflected point P' will be (4, -3).
When a point is reflected over the x-axis, its y-coordinate changes sign.
In this case, the point P has coordinates (4,3).
To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.
So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.
Therefore, the coordinates of the reflected point P will be (4, -3).
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Answer:
Step-by-step explanation:
draw a rectangular array with 3 rows and ___ columns
The rectangular shaped array with 3 rows and 4 columns is drawn
X X X X
X X X X
X X X X
Given data ,
Let the number of rows for the rectangle be r = 3
Let the number of columns for the rectangle be c = 4
So , when r = 3 and c = 4
X X X X
X X X X
X X X X
Hence , the rectangle shaped array is solved
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Layla works at a trampoline park. Last month, she earned $1,568 in gross income. Her net income was $1,338.79.
The amount of tax and deductions from the income is $229.21
Calculating the amount of tax and deductionsFrom the question, we have the following parameters that can be used in our computation:
Gross income = $1,568
Net income = 1,338.79
Using the above as a guide, we have the following:
Deductions = Gross income - net income
Substitute the known values in the above equation, so, we have the following representation
Deductions = $1,568 - 1,338.79
Evaluate the expression
So, we have
Deductions = $229.21
Hence, the amount of tax and deductions from the income is $229.21
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The height, h, in centimeters of a species of mammal that is t years old can be modeled by the equation below.
h = 37.8 (2.07+)³ + 78.6
What is the best interpretation of f (2.07€) ³2
A. the product of 2.07, the age of the mammal, and one-third
B. the product of the cube root of 2.07 and the age of the mammal
C. the product of 2.07 and the cube root of the age of the mammal
D. the cube root of the product of 2.07 and the age of the mammal
The best interpretation is the product of the cube root of 2.07 and the age of the mammal
How to interptete the equationh = 37.8 (2.07t)³ + 78.6
Now, let's analyze the term (2.07t)³:
2.07t: This term represents the product of 2.07 and the age of the mammal (t).(2.07t)³: This term cubes the product of 2.07 and the age of the mammal (t).Based on this analysis, the best interpretation of (2.07t)³ is:
B. the product of the cube root of 2.07 and the age of the mammal
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Find the sum of the first 6 terms of the following sequence. Round to the
nearest hundredth if necessary,
12,
4,
4
3
Sum of a finite geometric series:
Sn
-
1-r
Тhе sum оf thе first 6 tеrms оf thе given sеquеncе is аpproximаtely 14.56.
Determining the sum of the first 6 termsFirst detеrmine thе common rаtio (r) аnd thе first tеrm (а1).
Eаch tеrm is obtаined by multiрlying thе prеvious tеrm by 1/3. Тherefоre, thе common rаtio is r = 1/3.
Тhe first tеrm is а1 = 12.
Now wе cаn use thе fоrmulа fоr thе sum оf а finite geоmetric series:
Sn = а1(1 - r^n) / (1 - r)
whеrе n is thе number оf tеrms.
Plugging in thе vаlues, wе gеt:
Sn = 12(1 - (1/3)^6) / (1 - 1/3) ≈ 14.55
Rounding to thе neаrest hundredth, wе gеt:
Sn ≈ 14.55 ≈ 14.56
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help me please i don’t understand
Answer:
Step-by-step explanation:
Quadratic form:
ax²+bx+c
>We are going to work backwards from getting an equation and then solving for the x's.
>From a graph, you are given your x's.
>Put those x's (x-intercepts) into factored form.
Red:
x = -7 >add 7 to both sides
x+7 = 0
x = -5 >add 5 to both sides
x+5=0
x+5 and x+7 are your factors
y= (x+5)(x+7) >FOIL
y=x²+7x+5x+35
y=x²+12x+35 for RED
Blue: follow same pattern as RED
x= -4 and x=-2
(x+4)=0 (x+2)=0
-(x+4)(x+2) There is a negative in front because this one is facing
down
-(x²+6x+8) FOILED and simplified, now distribut negative
y= -x²-6x-8 BLUE
Green:
x=-1 x=1
y=(x+1)(x-1) FOIL and simplify
y=x²-1 GREEN
Orange:
x= 2 x=4
-(x-2)(x-4)
-(x²-6x+8)
y= -x²+6x-8 ORANGE
Purple:
x=5 x=7
(x-5)(x-7)
y=x²-12x+35 PURPLE
Help its urgent i need to get these done
The planes that are parallel in the cube shown would be C. NOR and LMP.
What are parallel planes ?Two planes that are located on a cube and are always opposite and never intersect; they remain continuously at the same distance from each other. A cube consists of three pairs of parallel planes in correspondence with its triplet of opposing faces.
From the given options, the only parallel planes would be NOR and LMP. One of the reasons for this, is that these planes have no point of intersection unlike the planes in the other options.
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Find the volume of the composite solid
6 cm.
14 cm.
120 cm*
460 cm³
1462 cm³
980.2 cm³
The volume of the composite solid is 980.2 cm³.
What is a composite solid?
A composite solid is a solid made of two or more well-defined solid objects.
To calculate the volume of the composite solid, we use the formula below
Formula:
V = (πr²h/3)+(2πr³/3)...................... Equation 1Where:
V = Volume of the composite solidr = Radius of the cone and the hemisphereh = Height of the coneFrom the question,
Given:
r = 6 cmh = 14 cmπ = 22/7Substitute these values into equation 1
V = (6²×14×22/7)/3+(2×6³×22/7)/3V = 528+452.2V = 980.2 cm³Learn more about composite shape here: https://brainly.com/question/8370446
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Out of 100 people sampled, 12 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.
Give your answers as decimals, to three places
< p
The true population proportion of people with kids is between 0.0565 and 0.1835.
We are given that;
Number of people= 100
Percent= 95%
Now,
To construct a 95% confidence interval for the true population proportion of people with kids. Here are the steps to do so:
Find the sample proportion p. This is the ratio of the number of successes (people with kids) to the sample size. In this case, p = 12 / 100 = 0.12.
Find the z-value that corresponds to the 95% confidence level. You can use a table or a calculator to find this value. The z-value for a 95% confidence level is 1.96.
Find the standard error of the sample proportion. This is the standard deviation of the sampling distribution of p. You can use the formula √p (1-p) / n to find this value. In this case, the standard error is √0.12 (1-0.12) / 100 = 0.0324.
Plug these values into the formula for the confidence interval and simplify. You get:
Confidence interval = 0.12 +/- 1.96*0.0324 Confidence interval = 0.12 +/- 0.0635 Confidence interval = [0.0565, 0.1835]
Therefore, by proportions the answer will be 0.0565 and 0.1835.
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please help I am bad at maths
a) The principal of the account is given as follows: 1238.27 euros.
b) The interest rate of the account is given as follows: 4.3%.
How to obtain the balance using simple interest?The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are listed and explained as follows:
A(t) is the final balance.P is the value of the initial deposit.r is the interest rate, as a decimal.t is the time in years.We can take the ratio between the balances two consecutive years to obtain the interest rate as follows:
r = 1569.4/1504.5 - 1
r = 1.0431 - 1
r = 0.043
r = 4.3%.
After 5 years, the balance was of 1504.50, hence the principal is obtained as follows:
1504.5 = P(1 + 0.043 x 5)
P = 1504.5/(1 + 0.043 x 5)
P = 1238.27 euros.
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Fast will give Brainliest.
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over y = −2.
N′(−3, 2), M′(0, 1), O′(−5, 3)
N′(−5, 0), M′(−2, −1), O′(−3, 1)
N′(−5, 1), M′(−2, 0), O′(−3, 2)
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Answer:
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Step-by-step explanation:
To reflect a point over a line, we can use the following steps:
Find the distance between the point and the line.
Construct a perpendicular line from the point to the given line.
Extend this perpendicular line to the same distance on the other side of the given line.
The intersection of the extended perpendicular line with the given line is the reflected point.
Alternatively, we can use the fact that reflecting a point over a line is equivalent to reflecting the coordinates of the point across the line. In this case, we are reflecting over the line y = -2, so we can simply negate the y-coordinate of each point to find its reflection.
Using this method, the reflected vertices are:
N'(-5, -4)
M'(-2, -3)
O'(-3, -1)
′(Therefore, the correct answer is option D: N−5, −6), M′(−2, −5), O′(−3,-7)
In the coordinate plane, the point A (-2, -4) is translated to the point A' (-3, -1). Under the same translation, the points B (0, -7) and C (-5, -8) are translated to B' and C', respectively. What are the coordinates of B' and C'?
Answer:
B' ( -1,-4)
C' (-6,-5)
Step-by-step explanation:
Take each point and move it one unit left and then 3 units up.
Helping in the name of Jesus.
Find the value of x in the isosceles triangle shown below
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{8}\\ a=\stackrel{adjacent}{2}\\ o=\stackrel{opposite}{x} \end{cases} \\\\\\ x=\sqrt{ 8^2 - 2^2}\implies x=\sqrt{ 64 - 4 } \implies x=\sqrt{ 60 }[/tex]
What is - 8/9 divided by 2/3
Answer:
-4/3
Step-by-step explanation:
-1.33333333333 or -1 1/3
A company wants to open a new store in a mall. They have a choice of three different locations. To decide which location would have the greatest number of people passing by, they select 20 different hours at random from all hours the mall is open during one week and count the number of people who pass by each location. Which of these best explains the validity of the sampling procedure used by the company?
A.
It is valid because the company applied the same procedure to all three locations and used random sampling to select the times to collect data.
B.
It is not valid because the company applied the same procedure to all three locations and used random sampling to select the times to collect data.
C.
It is valid because the company applied the same procedure to all three locations and used a method that is convenient for the survey takers.
D.
It is not valid because the company applied the same procedure to all three locations and used a method that is convenient for the survey takers.
The statement that explains the validity of the sampling procedure used by the company is the company applied the same procedure to all three locations and used random sampling to select the times to collect data. The Option A is correct.
Why is the sampling procedure used by the company valid?The procedure used is valid because they applied the same procedure to all three locations and used random sampling to select the times to collect data.
By using the random sampling, they ensured that they were selecting a representative sample of the entire population of mall visitors.
Also, by applying same procedure to all three locations, they ensured that they were collecting comparable data and this helps to increase the generalizability of their findings and make their decision-making process more reliable.
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10 points!
pls give explanation how you reached your answer!! question in the image
Answer: A
Step-by-step explanation: complementary is 180 that’s the angle is A. Supplementary is 90 so that’s incorrect.
Which comparison is true? (Homework)
A) 8 x 2 5/6 < 8
B) 2 x 1 2/5 > 2
C) 5 x 1 1/3 < 5
D) 7 x 3/7 > 7
B.
B, is the true comparison
HELP ASAP PLEASE 10 points
A). spinning a spinner that has 5 equal sections marked 1 through 5 and landing on an even number
B). picking a diamond from a standard deck of playing cards which has 13 cards in each of four suits: spades, hearts, diamonds and clubs
(Information for the problem in the photo)
The probability of spinning an even number on the spinner is 40%.
The probability of picking a diamond from a standard deck of playing cards is 25%.
How to calculate the probabilityP(even) = number of even sections / total number of sections
= 2/5
= 0.4
= 40%
Therefore, the probability of spinning an even number on the spinner is 40%.
P(diamond) = number of diamonds / total number of cards
= 13/52
= 1/4
= 0.25
= 25%
Therefore, the probability of picking a diamond from a standard deck of playing cards is 25%.
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If you were to graph 9x + 5y > 1 , where would you shade according to the slope of the line? The shading would occur above the solid line of the slope The shading would occur below the solid line of the slope. The shading would occur below the dashed line of the slope. The shading would occur above the dashed line of the slope.
The requried shading would appear above the solid line of the slope.
To graph the inequality 9x + 5y > 1, we first require to graph the equation 9x + 5y = 1, which is the equation of the line that separates the two regions determined by the inequality.
To graph this line, we can solve for y in terms of x:
9x + 5y = 1
y = (-9/5)x + 1/5
Although the slope of the line is negative, the shading should occur above the line, which means the correct answer is, the shading would occur above the solid line of the slope.
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A building supply store is selling tiles with an area of 790 cm square Find the length of each side of the tile correct to 3 significant figures.
The length of each side of the tile with an area of 790 cm² correct to 3 significant figures is 28.1 cm.
What are significant figures?Significant figures are the digits in a number that give a reliable accuracy of the quantity of a measurement.
The significant figures do not include the zeros immediately after the decimal place but those that occur between other numbers are regarded as significant.
The area of a square tile = Length x Length
= 790 cm²
The length of each side = √790 = 28.1069
= 28.1 cm
Thus, we can conclude that the length of each side of the square tile is 28.1 cm.
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How many meters is in 270 centimeters
Answer:2.7
Step-by-step explanation:
Formula, divide the value in centimeters by 100 so 1 meter equals 100 centimeters
So 270 centimeters = 270/100 = 2.7
HELP ASAP PLEASE 20 POINTS!!!!!!
Answer:I’m not so sure but I’m pretty sure it’s the 4th one?
Step-by-step explanation:
Answer:
Option b
Step-by-step explanation:
For x=1, y=-0.5
For x=0, y=2
For x=1, y=-7/2
Graphing the equation on the coordinate plane we get the second graph.
4. Marcy makes $19 an hour working as a librarian. She gets a 5% raise.
Which of the following statements are true about Marcy's new rate of pay? Select the 3 correct answers.
A Marcy will make an additional 1/20 of her salary an hour.
B Marcy will make an additional $0.95 an hour.
C Marcy’s new hourly rate is $19.50 an hour.
D After working 10 hours at the new rate, Marcy will make $195.
E After working 15 hours at the new rate, Marcy willmake $299.25.
For the system shown below, what are the coordinates of the solution that lies in quadrant I?
Write your answer in the form (a,b) without using spaces.
The coordinates of the solution that lies in quadrant I are
How to graphically solve this system of equations?In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
x² + 4y² = 100 ......equation 1.
4y - x² = -20 ......equation 2.
In this exercise, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.
Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (6, 4).
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A store is having a sale. Each item is on sale for 1/4 off the regular price, m. Which pair of equivalent expressions represent the sale price for any one item?
A. 0.75m and m-1/4
B. m-0.25 and m-1/4
C. 0.75m and m-1/4m
D. 0.75-m and m-1/4m
The pair of equivalent expressions that represent the sale price for any one item is 0.75m and m-1/4m. Option C
How to determine the pair of equivalent expressions that represent the sale price for any one itemThe sale price of an item is the regular price minus 1/4 of the regular price. This can be represented as:
sale price = regular price - (1/4)regular price
Simplifying this expression, we get:
sale price = (3/4)regular price
Therefore, the sale price for any one item can be represented as 0.75m, which is equivalent to option C.
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VAN
Susan practices the piano for 30 minutes per day. Write an equation that represents the total number of minute
m, she practices the piano for t days.
The expression to represent the given situation is M =30t.
Let's use the variable M to represent Susan's overall piano practice time over the course of t days.
Given that Susan practices the piano for 30 minutes every day, the sum of her practice time over the course of t days is:
M = 30t
As a result, M = 30t is the equation that describes the total amount of time Susan spends practicing the piano over the course of t days.
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