The ratio of the height of shape A to the height of shape C is [tex]\frac{3}{10}[/tex]
Calculations and Parameters:First step:Recall that similar figures have the same scale factor squared due to the ratio of its surface area.
Hence,
We would make:
z-----> the scale factorx----> surface area shape Ay----> surface area shape B[tex]z^2 = x/y\\z= 2/5[/tex]
Therefore, the ratio of the height of shape A to the height of shape B is = [tex]\frac{hA}{hB} = \frac{2}{5}[/tex]
Next step:To find the ratio of the height of shape B to the height of shape C, we would perform a similar operation which is:
[tex]z^3 = 27/64\\z= 3/4[/tex]
The ratio is:
[tex]\frac{hB}{hC} = \frac{3}{4}[/tex]
Final step:To find the ratio of the height of shape A to the height of shape C would be:
[tex](\frac{hA}{hB}) (\frac{hB}{hC} )= \frac{hA}{hC}[/tex]
= 6/20
= 3/10
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Sally has 10 pounds she wants to buy 28 cans of soda which cost 28p each does she have enough money
Answer:
Yes, Sally has enough money to buy 28 cans of soda.
Step-by-step explanation:
Yes, because £10 = 1000p
1000p / 28p = 35 cans
35 cans < 28 cans
So Sally has enough money for 28 cans.
what is the value of x makes the equation 3/ 4(x+8) =9 true
if population function x has mean M(x)=2 and M(x²)=8, find its standard deviation
The standard deviation of the population function is 2
How to determine the standard deviation?The given parameters are:
M(x) = 2
M(x²)=8
The standard deviation is calculated using:
[tex]\sigma = \sqrt{M(x^2) - (M(x))^2[/tex]
Substitute known values
[tex]\sigma = \sqrt{8 - 2^2[/tex]
Evaluate the expression
[tex]\sigma = 2[/tex]
Hence, the standard deviation of the population function is 2
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I need this answered quickly!
1. Trig Function
2. Coordinate value (x, y)
3. Value in terms of sinθ and/or cosθ
sinθ = _________________
cosθ = _________________
secθ = _________________
cscθ = _________________
tanθ = _________________
cotθ = _________________
The value of the trigonometry functions will be:
sinθ = opposite / hypothenuse
cosθ = adjacent / hypothenuse
secθ = 1 / cosθ
cscθ = 1 / sinθ
tanθ = opposite / adjacent
cotθ = 1 / tanθ
What is trigonometry?It should be noted that trigonometry is the branch of mathematics that's is concerned with angles and their application.
When a triangle is drawn, the longest side is the hypothenuse, the side facing the angle is the opposite and the last side is the adjacent.
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At a football game, the quarterback threw the football and the receiver caught it for a 12-yard gain. What integer represents the yards gained?
1/12
12
-12
6
James has organised a game to raise money for charity at a local fair. He rolls a fair six sided dice and flips a fair coin. If the coin lands on heads, the number on the dice is squared. If the coin lands on tails, the number on the dice is cubed. Each person pays 50p to play. If they score above 30, they win £1 The game is played 450 times. How much money does James raise for charity?
The total amount that was raised for charity is £75.
What is the total amount raised?Here is the sample space
1 2 3 4 5 6
Heads 1 4 9 16 25 36
Tails 1 8 27 64 125 216
Probability of getting a number greater than 30 = 4/12 = 1/3
1/3 x 450 = 150
Total value of people getting more than 30 : 150 x £1 = £150
Total amount paid = 50 x 450 = £225
Amount raised = £225 - 150 = £75
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5 oranges are shared equally by 2 people.
About how many oranges does each person get
Answer:
2.5
Step-by-step explanation:
5 divided by 2 is 2.5
Answer:
Each person would get around 2.5 oranges.
Step-by-step explanation:
There are five oranges to split between two people- this can set up the equation 5 divided by 2 equals x. The answer to 5 divided by 2 is 2.5, meaning that each person would get around 2.5 oranges. I hope this helps! :)
Which expression is equivalent to the given expression?
(First one is question, the rest are possible answers)
Answer:
[tex](2x + 1)(x - 6)[/tex]
Step-by-step explanation:
[tex]2 {x}^{2} - 11x - 6[/tex]
[tex]2 {x}^{2} + x - 12x - 6[/tex]
[tex]x(2x + 1) - 6(2x + 1)[/tex]
[tex](2x + 1)(x - 6)[/tex]
hi I need help answering this question please worth 20 points
question is : how many people went on the fishing trip ?
A set of equations is given below: Equation C: y = 6x + 9 Equation D: y = 6x + 2 How many solutions are there to the given set of equations? (1 point) a One solution b No solution c Two solutions d Infinitely many solutions
Since the values on both sides are different, hence the set of equations has no solution
System of equationsSystem of equation are made of two equations with unknown variables. Given the following equations
y = 6x + 9
y = 6x + 2
Equate
6x + 9 = 6x + 2
Collect the like terms
6x - 6x = 2 - 9
0x = -7
Since the values on both sides are different, hence the set of equations has no solution
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Anyone know how to do this?
To solve this, we need to use our trignometric functions;
⇒ look at the diagram attached
Let's examine what the problem wants:
hypotenuse (longest side) of the triangleLet's examine what the problem gives us:
side adjacent to the 45-degree angleangle that has measure of 45-degreesLet's solve:
[tex]sin(45)=\frac{5}{x} \\5=x*sin(45)\\x = \frac{5}{sin(45)} \\x=7.07[/tex]
Answer: 7.1 (rounded to nearest tenth)
Hope that helps!
Answer:
[tex]5\sqrt2[/tex]
Step-by-step explanation:
This is a 45-45-90 triangle so we can find all the side lengths easily.
The ratio between the base and the hypotenuse of a 45-45-90 triangle is [tex]1:\sqrt2[/tex], which means for this triangle it would be [tex]5:5\sqrt2[/tex]. This means the length of the hypotenuse is [tex]5\sqrt2\\[/tex], which is [tex]x[/tex], which is the answer.
Write the slope-intercept form of the equation for the line.
y = -10/3x + 1/2
y = -3/10x + 1/2
y = 1/2x +3/10
y = 3/10x +1/2
Answer:
y=-3/10x+1/2
use the coordinates to find the gradient (m)then substitute it in this formula y=mx+c
find c by substituting one of the coordinate
What is the value of x? x = 2.25 x = 11.25 x = 13 x = 22
Answer:
x = 2.25 x = 11.25 x = 13 x = 22
Step-by-step explanation:
Write the equation of the following line in slope-intercept form. X
Answer:
[tex]y=-\frac{1}{2}x+2[/tex]
Step-by-step explanation:
The equation for slope-intercept form is [tex]y=mx+b[/tex].
First, we find b by looking at where the line passes through where [tex]x=0[/tex]. We can see that it is 2, so in our equation for slope-intercept form [tex]b=2[/tex].
Next, we find the slope or m. Find the slope by taking two points and plugging them into this expression [tex]\frac{x_{1}-x_{2}}{y_{1}-y_{2}}[/tex]. To demonstrate, I will choose points (0,2) and (2,1), however, any pair of points will give you the same answer. When we plug in these points, we should get the expression [tex]\frac{0-2}{2-1}[/tex]. By solving this, we get -1/2. Therefore, in our equation for slope-intercept form, [tex]m=-\frac{1}{2}[/tex].
By putting the information we have about m and b together, we get the equation [tex]y=-\frac{1}{2}x+2[/tex].
You design a bean bag toss board using a coordinate plate. You plot vertices of the board at C (3,2) D (3,6) E (5,2) F (5,6). What is the perimeter of the bean bag toss board?
The perimeter of the bean bag toss board is 12 units
What is the perimeter of the bean bag toss board?The points are given as:
C (3,2) D (3,6) E (5,2) F (5,6)
Calculate the distance between adjacent points using:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
So, we have:
[tex]CD = \sqrt{(3 - 3)^2 + (2 - 6)^2} = 4[/tex]
[tex]DF = \sqrt{(3 - 5)^2 + (6 - 6)^2} = 2[/tex]
[tex]FE = \sqrt{(5 - 5)^2 + (2 - 6)^2} = 4[/tex]
[tex]CE = \sqrt{(3 - 5)^2 + (2 - 2)^2} = 2[/tex]
The perimeter is then calculated as:
P = CD + DF + FE + CE
This gives
P = 4 + 2 + 4 + 2
Evaluate
P =12
Hence, the perimeter of the bean bag toss board is 12 units
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Quadrilateral a'b'c'd' is the result of dilating quadrilateral abcd about point p by a scale factor of
5/2
The two statements about the dilated quadrilateral a'b'c'd' are false.
bc and bc' are on the same line ( False)
The length of the cd and c'd' are the same. (False)
The complete question is attached with the answer below.
What is dilation?Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
Here the quadrilateral abcd is dilated by the scale factor 5 / 2.So the new quadrilateral is a'b'c'd'.
The given two statements are false:-
bc and bc' are on the same line ( False)
The length of the cd and c'd' are the same. (False)
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I need help with question two please, it’s due tomorrow first thing so kinda need to get it done
A 7th grade teacher at a local middle school wants to know which
of two candidates for class president is more popular among the
7th grade students in the school. Which group of people should
make up a sample that will best answer her question?
OA) other 7th grade teachers in her
school
OB) parents of 7th graders in her school
OC) 7th graders in her school
OD) 7th graders in her homeroom
The answer is Option C) 7th graders in her school.
In order to ascertain the suitability of a candidate for any popular position, his popularity can be assessed by taking a survey of the concerned sample.
Answer:
She should ask the 7th graders in the school
Step-by-step explanation:
Because their opinion is important in electing the president.
Graph the composite function g(f(x)).
f(x)= -2x - 5
g(x) = x - 1
The equation of the composite function is g(f(x)) = -2x - 6
How to graph the composite function g(f(x))?The functions are given as:
f(x)= -2x - 5
g(x) = x - 1
In function g(x), we have:
g(x) = x - 1
Substitute f(x) for x
g(f(x)) = f(x) - 1
Substitute f(x)= -2x - 5
g(f(x)) = -2x - 5 - 1
Evaluate the difference
g(f(x)) = -2x - 6
This means that the equation of the composite function is g(f(x)) = -2x - 6
See attachment for the graph
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a triangle has sides lenghts of 6.8cm, 28.5cm and 29.3cm. is this a right angled triangle
Answer:
Yes it is a right angled triangle
Step-by-step explanation:
If its a right triangle it would satisfy the Pythagoras theorem.
29.3^2 = 858.49
28.5^2 = 812.25
6.8^2 = 46.24
Adding the last 2 values:
812.25 + 46.24
= 858.49
So YES.
The average vehicle releases 1.39 grams of nox per mile driven. if a vehicle is driven 22,000 miles per year for 15 years, how much nox does that vehicle release
In 15 years, the average car releases 458.7 kilograms of nox.
How much nox does that vehicle release?
We know that the average vehicle releases 1.39 grams per mile driven.
And, in average, that car drives 22,000 miles per year.
So in a year, a car releases:
M = (22,000)*1.39 g = 30,580 g = 30.58 kg
In one year, the average car releases around 30.58 kilograms of nox.
Then in 15 years, the car releases 15 times that amount, then we have the product:
T = 15*30.58 kg = 458.7 kg
In 15 years, the average car releases 458.7 kilograms of nox.
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5. you work at a t-shirt printing business. 175 of 3,500 t-shirts shipped are printed improperly. what is the experimental probability that a t-shirt is printed improperly?
a: 6%
b: 1.75%
c: 5%
d: 35%
Answer:
C: 5%
Step-by-step explanation:
175 out of 3500 = 175/3500
175/3500 = 1/20
1/20 = 0.05
0.05 = 5%
Answer:
C 5%
Step-by-step explanation:
I am smart so trust me
Find f(-3) for f(x)=4•(2)^x
A. 1/2
B. -32
C. -24
D. 1/8
2. Determine if the set of ordered pairs is a relation or a function.
{(-3,0), (-1,3), (1,0), (3,3)}
O relation
O function
O both
Function
According to defination
A relation is called to be a function if every domain of the relation has an unique range .
Or
f(x)=yHere
f(-3)=0f(-1)=3f(1)=0f(3)=3Every domain has unique range
Hence it's a function
Answer:
Function
Step-by-step explanation:
The point is a function because it passes the vertical line test
It is not a relationship because each input have only 1 out put
that’s the question
Answer:
all real numbers
ez clappp
Draw and label a net to find the surface area of the original juice box. it costs
supreme packaging $0.02 per square inch to create one juice box. the company
groups eight juice boxes together as one package. how much does it cost to
create one package?
Based on the area of the juicebox and the cost per square inch, the cost to create one package is $7.20.
What is the cost of one package?First, find the area of the juice box. The formula is:
= 2lh + 2lw + 2hw
= (2 x 3 x 4) + (2 x 3 x 1.5) + (2 x 4 x 1.5)
= 45 inch²
The Cost is $0.02 per square inch and the number per package is 8 juice boxes. The total cost is:
= 45 x 0.02 x 8 boxes
= $7.20
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Car 2 passes car 1. To a stationary observer, car 1 has a velocity of 28 m/s to the east and car 2 has a velocity of 33 m/s to the east. How much time will pass before car 2 is 14 m ahead of car 1?
Answer:
2.8 s
Step-by-step explanation:
33x = 28x + 14(m)
5x = 14(m)
x = 2.8(s)
Find the number of palindromes between 10,000 and 99,999 that are divisible by 25
20 palindromes exist that qualify this criteria rigorously
Examples:
52025, 52125, 52225, 52325, 52425, 52525, 52625, 52725, 52825, 57975 etc.
What should your units on your base area calculations be, and why? how is this different from the units on your volume calculations? explain in two to three sentences.
The units used for area are squared length units, where the length units are: meter, inch, feet, etc.
Which units are used for surface areas?
The units used for surface areas are length units (meters, inches, feet, etc) squared.
Why we use those? Because area is defined as the product between the two dimensions (two sides of rectangle, for example) of a figure. And these dimensions are given in length units. So if we take the product of two of these, we will get squared length units.
The difference with volume units, is that for volume we need 3 dimensions, then we will have cubed length units.
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Fiona asked her team to suggest ways of surveying the population of their middle school to find out how many students use bottled water.
Which student has the method that is most representative of the school’s population?
Raina suggested that she ask everyone in her math class on Friday.
Miya suggested that she ask students sitting in the first row of her classes on Friday.
Ryo suggested that he ask the basketball players at his practice on Friday.
Amir suggested that he ask every tenth student as he or she walks into school in the morning.
The students who has the method that is most representative of the school’s population is Amir.
What is a population?Population refers to the group of people being studied in an experiment or the group from which a sample is drawn.
Amir has the method that is most representative of the school’s population because the method includes all students in the school studying different subjects but picked at random (every tenth students)
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