Which equation correctly shows the multiplication of the means and extremes in the proportion 7.2 ∕ 9.6 = 21.6 ∕ 28.8?
a. 7.2 ⋅ 9.6 = 21.6 ⋅ 28.8
b. 9.6 ⋅ 21.6 = 28.8 ⋅ 7.2
c. 7.2 ⋅ 21.6 = 28.8 ⋅ 9.6
d. 7.2 ⋅ 28.8 = 21.6 ⋅ 28.8
Answer:
b. 9.6 ⋅ 21.6 = 28.8 ⋅ 7.2
Step-by-step explanation:
When a proportion say a/b = c/d is given, the outer terms are called the extremes while the inner/middle terms are called the means.
In the case of a / b = c / d,
the outer terms are a and d
the inner terms are b and c
Often times, we find the cross products of the proportion to test whether the two ratios in the proportion are equal. To do that, we find the product of the extremes and equate it to the product of the means.
In the case of a / b = c / d,
the cross products are a x d and b x c
So if a x d = b x c, then a/b = c/d is a true proportion.
Now to the question;
Given proportion: 7.2 / 9.6 = 21.6 / 28.8
Extremes = 7.2 and 28.8
Means = 9.6 and 21.6
The correct multiplication of the means and extremes is therefore
9.6 x 21.6 = 7.2 x 28.8
or
9.6 · 21.6 = 7.2 · 28.8
Find the length of the hypotenuse , c, using the Pythagorean theorem (a^2+b^2=c^2) round the nearest tenth if necessary
Answer:
19.4 units
Step-by-step explanation:
The hypotenuse length (c) of the given right triangle, ∆ABC, can be calculated using the Pythagorean Theorem, [tex] a^2 + b^2 = c^2 [/tex],
Where,
c is the longest/hypotenuse, a and b are the length of the other two legs.
Therefore,
[tex] c^2 = (16)^2 + (11)^2 [/tex]
[tex] c^2 = 256 + 121 = 377 [/tex]
[tex] c = \sqrt{377} = 19.4 [/tex] (nearest tenth)
Area of the figure with steps
Answer:
2400
Step-by-step explanation:
length times width times height
Answer:
350
Step-by-step explanation:
Area of rectangle = Length * width
Area = 25 * 8
Area = 200
Area of a triangle = [tex]\frac{h_{b}*b}{2}[/tex]
Area = 150
Area = triangle area + rectangle
Area = 350
Find the distance between the given points (2,8) and (7,7)
Answer:
[tex]d=\sqrt{26}\approx5.0990[/tex]
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula.
The distance formula is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let (2,8) be x₁ and y₁ and let (7,7) be x₂ and y₂. Thus:
[tex]d=\sqrt{(7-2)^2+(7-8)^2}[/tex]
Simplify:
[tex]d=\sqrt{5^2+(-1)^2}[/tex]
Square:
[tex]d=\sqrt{25+1}[/tex]
Add:
[tex]d=\sqrt{26}\approx5.0990[/tex]
And that's our answer :)
Find the slope of the line passing through the pair of points. (0, 21), (9, 0)
Answer:
m =-7/3
Step-by-step explanation:
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(0,\:21\right),\:\left(x_2,\:y_2\right)=\left(9,\:0\right)\\\\m=\frac{0-21}{9-0}\\\\m = \frac{-21}{9} \\\\Use\:3\:to\:divide\:through \\m=-\frac{7}{3}[/tex]
A local church has 225 students in 15 sunday school classes.what is the average number of students in each class? Please help.
Answer:
Average of 15 students in each Sunday school class.
Step-by-step explanation:
The average (or arithmetic mean) number of students per class, is the total number of students divided by the number of classes. In this case:
225/15 = 15
average of 15 students per Sunday school class.
Simplify 8√63x^14y^9
Answer:
See step by step
Step-by-step explanation:
add. 4x² – 5xy + 3y?, 8x + 7xy - 6y?, -2x? - 9xy + 13y
Answer:
0x²-7xy+10y²
Step-by-step explanation:
4x²-5xy+3y² + 8x²+7xy-6y²
4x²+8x²-5xy+7xy+3y²-6y²
=12x²+2xy-3y²
12x²-5xy+3y² + -2x²-9xy+13y²
12x²-5xy+3y² - 2x²-9xy+13y²
12x²-2x²-5xy-9xy+3y²+13y²
= 10x²-7xy+10y²
Hoped I helped
If log.. (125) = 3, then x =
solve for p -5(p + 3/5) = 4
Answer:
p =-7/5Step-by-step explanation:
[tex]-5\left(p+\frac{3}{5}\right)=4\\\\\mathrm{Divide\:both\:sides\:by\:}-5\\\frac{-5\left(p+\frac{3}{5}\right)}{-5}=\frac{4}{-5}\\\\Simplify\\p+\frac{3}{5}=-\frac{4}{5}\\\\\mathrm{Subtract\:}\frac{3}{5}\mathrm{\:from\:both\:sides}\\p+\frac{3}{5}-\frac{3}{5}=-\frac{4}{5}-\frac{3}{5}\\\\Simplify\\p=-\frac{7}{5}\\\\p=-\frac{7}{5}[/tex]
At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
Answer:
What is the cost of a chicken shawarma wrap?
$10.99
What is the cost of one order of spiced potatoes?
$4.99
If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
3x + 2y = $42.95..........Eq 1
5x + 4y = $74.91..........Eq 2
Step-by-step explanation:
Cost of a chicken sharwarma wrap = a
Cost of an order of spiced potatoes = b
Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.
3x + 2y = $42.95 .............Equation 1
Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.
5x + 4y = $74.91 ................Equation 2
So we have:
3x + 2y = $42.95..........Eq 1
5x + 4y = $74.91..........Eq 2
We use Elimination method
Multiply Equation 1 by coefficient of y in Equation 2
Equation 2 by coefficient of y in Equation 1
3x + 2t= $42.95 .............Equation 1 × 4
5x + 4y = $74.91 ................Equation 2 × 2
12x + 8y = 171.80..............Equation 3
10x + 8y = 149.82..............Equation 4
Subtract Equation 3 from Equation 4
2x = 21.98
x = 21.98/2
x = 10.99
Therefore, x = Cost of Chicken sharwarma wrap = $10.99
Subtitute 10.99 for 9in Equation 1
3x + 2y = $42.95 .............Equation 1
3(10.99) + 2y = 42.95
32.97 + 2y = 42.95
2y = 42.95 - 32.97
2y = 9.98
y = 9.98/2
y = 4.99
y = Cost of an order of spiced potatoes = $4.99
Hence,
The cost of a chicken sharwarma wrap = $10.99
The cost of an order of spiced potatoes = $4.99
1. 4y-9=15 2 6x+7=-5 3 -9t+2=56
Answer:
1. y=6
2. x=-2
3. t=-6
Step-by-step explanation:
1.
[tex]4y-9=15\\4y-9+9=15+9\\4y=24\\\frac{4y}{4}=\frac{24}{4}\\y=6[/tex]
2.
[tex]6x+7=-5\\6x+7-7=-5-7\\6x=-12\\\frac{6x}{6}=\frac{-12}{6}\\x=-2[/tex]
3.
[tex]-9t+2=56\\-9t+2-2=56-2\\-9t=54\\\frac{-9t}{-9}=\frac{54}{-9}\\t=-6[/tex]
Identify the correlation you would expect to see between the average amount of snowfall (inches) and the number of school closings.
Answer:
Simple Linear Regression Correlation
Step-by-step explanation:
When it snows normally the schools continue .But constant snowing affects the schools continuity. As more and more snow falls more schools are closed.
There may be a situation where all the schools are closed at a certain temperature.
So it is a simple linear regression correlation because in it there are two variables and one variable is dependent on the other. In this example the schools are dependent on the average snowfall.
If there's a snow blizzard or extreme weather all the schools are definitely closed .
It can be represented by a graph.
Please help dood pls
Answer:
[tex]\Large \boxed{\mathrm{\bold{B.} } \ x=7, \ y = 4\sqrt{2} }[/tex]
Step-by-step explanation:
We can split the shape into a right triangle and a rectangle.
tan θ = opp/adj
Let c be the missing base for the right triangle.
tan45 = 4/c
c = 4/tan45
c = 4
x = 3 + 4
x = 7
sin θ = opp/hyp
sin45 = 4/y
y = 4/sin45
y = [tex]4\sqrt{2}[/tex]
What is the slope of the line? y + 5=2(x+1)
Answer:
The slope of the line given by the equation is two.
Step-by-step explanation:
We are given the equation:
[tex]y+5=2(x+1)[/tex]
Notice that the equation is written in point-slope form. That is:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope.
From our given equation, we can see that m = 2.
Therefore, the slope of the given line is 2.
Answer:
2
Step-by-step explanation:
Put the line into slope intercept form:
y + 5 = 2(x+1)
Distribute the 2
y + 5 = 2x + 2
Isolate y to put into y = mx + b form
y = 2x - 3
So, the slope is 2 because it is the coefficient to x.
4
*
The moon is 250,000 miles away. How many inches is it away from earth?
Answer:
about 15 billion
Step-by-step explanation:
what is the 2 step equation -1=(5+x)6
Which of the following factors influences a consumer when deciding to buy a
product?
A. Opinion factor
B. Multiple factor
C. Stock market
D. External factor
The factor that influences a consumer when deciding to buy a product is D. External factor.
Who is a consumer?A consumer is a person or group who intends to order or uses purchased goods, products, or services primarily for personal, social, family, or household needs and is not directly involved in entrepreneurial or business activities.
Consumers consider a variety of factors, including the product's characteristics, the price charged, the product's availability at the required location, and much more. Personal factors include the consumer's age, occupation, lifestyle, social and economic status, and gender.
External factors such as the market economy, culture, social values, fashion, and corporate policies for consumers all have a large impact on consumer perceptions, attitudes, and behavior.
External factors may include family and friend expectations, cultural or gender stereotypes, and family responsibilities. These factors can have an impact on decision-making, either positively or negatively.
Therefore, based on the information illustrated, the correct option is D.
Learn more about consumers on:
https://brainly.com/question/380037
#SPJ1
Express (1+i)²-3(2-i)³ in the from of a+ib
[tex](1+i)^2-3(2-i)^3=1+2i-1-3(8-12i-6+i)=2i-6+33i=\boxed{-6+35i}[/tex].
Hope this helps.
PLEASE HELP! If the altitude is √7, find the volume. 36√7 cu. units 18√7 cu. units 12√7 cu. units
Answer:
Step-by-step explanation:
volume=1/3×area of base×height=1/3×6×6×√7=12√7 cubic units
value of tan(90 - cot^-1(1/3))
Answer:
0.36
Step-by-step explanation:
We need to solve the first bracket first and then the others,
Value of Cos^ - 1(1/3) =70.53°
Then, 90 - the value of cosine
=19.47°
Then, put the new in the calculator:
Tan (19.47°)
and the answer comes 0.3535294237
then I use the nearest formula and got the answer = 0.36
!!important!!
equation: —2(bx — 5) = 16
question: the value of x when b is 3 is ...
Answer:
x =-1
Step-by-step explanation:
[tex]-2(bx - 5) = 16\\b = 3\\x = ?\\-2(3x -5)=16\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(3x-5\right)}{-2}=\frac{16}{-2}\\\\Simplify\\3x-5=-8\\\\\mathrm{Add\:}5\mathrm{\:to\:both\:sides}\\3x-5+5=-8+5\\\\Simplify\\3x=-3\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\frac{3x}{3}=\frac{-3}{3}\\\\Simplify\\x =-1[/tex]
Simplify. (-2xy4)^4
Step-by-step explanation:
[tex] {( - 2x {y}^{4} })^{4} [/tex]
[tex] = {( - 2)}^{4} \times {x}^{4} \times { {y}^{4} }^{4} [/tex]
[tex] = 16 {x}^{4} {y}^{16} [/tex]
Why is 1 a factor of every number
Answer:
because 1 is the smallest factor of a multiple and greatest factor of a multiple is the multiple itself
Step-by-step explanation:
hope that help and u can understand it :\
“Simplify the following expression by combining like terms. 5x-y-3x+10+x+2y
Answer:
3x+10+y
Step-by-step explanation:
5x-y-3x+10+x+2y
5x-3x+x+10-y+2y
3x+10+y
Answer:
3x+y+10
Step-by-step explanation:
Since we are trying to combine like terms, we must rearrange the terms, and group the terms with an x, together, a y together, and the constants. Doing that, we get
(5x+x-3x)+(2y-y)+10
Now we start with the x terms, and we add 5x+x=6x and then 6x-3x= 3x, so you have 3x, and now for the y terms
we have 2y-y=y and lastly we have a ten, so adding them together, we get
3x+y+10
(3/5) divided by 4
please help !!!
Answer:
3/20
Step-by-step explanation:
3/5 ÷ 4
Copy dot flip
3/5 * 1/4
3/20
Need to also show work but confused
Answer:
S = 2
Step-by-step explanation:
1st step: Simplify both sides of the equation
4/5 s - 3/4 s = 1/10
4/5 s + -3/4 s = 1/10
(4/5 s + -3/4 s) = 1/10 (combine like terms)
1/20 s = 1/10
1/20 s = 1/10
step 2: multiply both sides by 20
20 * (1/20 s) = 20 * (1/10)
s = 2
Hope this helped!
Please help e it’s from my math class
Answer:
a - 1/2
Step-by-step explanation:
there are 3 even and 3 odd numbers so the probability is half of them
HELP ME QUICK!!! this has to be turned in in 46 min
Answer:
the answer is most likely A
Step-by-step explanation:
What is 5x times (3x2 - 5)?
3x2 + 5x -5
A
B 15x2-5
с
15x3 - 5
15x3 - 25x
Answer:
15x3-25x
Step-by-step explanation:
5x(3x2 -5)
step1: distribute 5x to both sides
Step 2: 3x2 would change into 15x3 (because you're multiplying by 5x)
Step3: -5 would turn into -25x (because you are multiplying by 5x also)
Step4: put both answers together and your end product would be (15x3 - 25x)
Answer:
15x3-25x
Step-by-step explanation:
Spencer sampled 50 students of a private school who were questioned about their scores in Mathematics. Spencer wants to test the hypothesis that the private school students score better than the general public which has an average of 62 marks with a population standard deviation of 7 marks. Z= If the sample mean is 65 marks, what is the z-score? Answers are rounded to the hundredths place.
a.) -3.84
b.) 1.56
c.) 3.03
d.) -2.56
Answer:
C) 3.03
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 50
The Mean of the population (μ) = 62
The standard deviation of the Population (σ) = 7
Mean of the sample(x⁻) = 65
Z-score
[tex]Z= \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
Step(ii):-
[tex]Z= \frac{65 -62}{\frac{7}{\sqrt{50} } }[/tex]
Z = 3.03
Final answer:-
The Z-score = 3.03