equation is y = 8x
=============================================
Explanation:
Divide each x and y pair like so: y/x
If we get the same result each time, then we have a direct proportion.
y/x = 32/4 = 8
y/x = 56/7 = 8
y/x = 96/12 = 8
Each time we get the same result 8, which is the constant of proportionality. The table does show a direct proportional relationship. The equation is y = 8x which is in the form y = kx. The k value is the constant of proportionality. So k = y/x.
What is the decision regarding the differences between the observed and expected frequencies if the critical value of the chi-square is 9.488 and the computed chi-square value is 6.079 g
Answer:
Accept the null hypothesis if it is two tailed test.
Step-by-step explanation:
The null hypotheses can only be accepted if it is a two tailed test and calculated chi square must be less than the critical value of chi square.
Then the difference between the the observed and expected frequencies will be zero.
where
H0 : σ²-σ²= 0 Ha: σ²-σ²≠0
For this the critical region would be greater than the calculated value of chi square. If so we will accept the null hypothesis and reject the alternative hypothesis.
FUNNY ONE ANSWER ! !!!!!!!!!
Answer: trapezoid
Step-by-step explanation: A trapezoid is a quadrilateral
with exactly one pair of parallel sides.
Also, quadrilaterals are two-dimensional shapes.
So it's impossible that's its 3-d.
Answer:
A. trapezoid
Step-by-step explanation:
The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
Car Age (years) Selling Price ($000)
1 9 11.1
2 5 9.5
3 13 4.4
4 17 4.4
5 7 8.0 6
6 12.0 7
7 10.6
8 14 8.1
9 12 8.1
10 17 4.8
11 4 12.5
12 4 10.7
a. Determine the regression equation. Use the rounded slope value to compute the y-intercept. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
a = ___
b = ___
b. Estimate the selling price (in dollars) of a 7-year-old car. (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)
$____
c. Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)
For each additional year, the car decreases $ ___ in value.
(Scroll Down for Answer!)
Answer:
b= - 1.26317
a = 17.237
b. The selling price (in dollars) of a 7-year-old car
y = 8394.81 dollars
C. For each additional year, the car decreases $ ___ in value.
1263.17 $ decreases per year
Step-by-step explanation:
Let y be the selling price in thousands and x be the age in years
Car Age Selling Price
(years) ($000) XY X²
X Y
1 9 11.1 99.9 81
2 5 9.5 47.5 25
3 13 4.4 57.2 169
4 17 4.4 74.8 289
5 7 8.06 56.42 49
6 1 2.07 2.07 1
7 1 0.6 0.6 1
8 14 8.1 113.4 196
9 12 8.1 97.2 144
10 17 4.8 81.6 289
11 4 12.5 50 16
12 4 10.7 42.8 16
∑ 97 84.33 723.49 1276
The estimated regression line of Y on X is
Y= a +bX
and the two normal equations are
∑ y= na + b∑X
∑XY= a∑X + b∑X²
Now
X`= ∑X/n = 97/12= 8.083
b= n∑XY - (∑X)(∑Y)/ n∑ X²- (∑X)²
b= 723.49 - (97)(84.33)/ 12(1276) - (97)²
b= -7456.52/ 5903
b= - 1.26317
a= Y`- b X`
a= 7.0275 - (-- 1.26317)8.083
a = 17.237
Y = 17.237 - 1.26317 X
y= - 1.26317 X + 17.237
b. The selling price (in dollars) of a 7-year-old car
y = - 1.26317 (7) + 17.237
y= 8.39481
y = 8394.81 dollars
C. For each additional year, the car decreases $ ___ in value.
1.26317 *1000= 1263.17 $ decreases per year
Pleaase help with both questions ! PLease explain if you can!
Answer:
See below for answers to both questions.
Step-by-step explanation:
Question 13)
We know that the perimeter is the sum of all of the side lengths of the square, and we know that a square has 4 sides that are all the same length. This lets us set up the following equation:
4(10x + 6) = 74
To solve this equation, we should first distribute the 4 through the parentheses using the distributive property.
40x + 24 = 74
Next, we should subtract 24 from both sides of the equation.
40x = 50
Finally, we should divide both sides by 40.
x = 50/40 = 1.25
Therefore, the answer to question 13 is x = 1.25.
Question 14)
If we know the rectangle and triangle have the same perimeter, we can set up the following equation:
2(4x-1) + 2(x-1) = (4x + 1) + (3x + 5) + (x + 1)
We should begin by simplifying the left side of the equation using the distributive property, as we did above.
8x - 2 + 2x -2 = 4x + 1 + 3x + 5 + x + 1
Next, we can combine like terms on both sides of the equation. This means adding together the constant terms (numbers) and also combining the variable terms (x's). This is modeled below:
(8x + 2x) + (-2 + -2) = (4x + 3x + x) + (1 + 5 + 1)
10x - 4 = 8x + 7
Next, we should subtract 8x from both sides.
10x - 8x - 4 = 8x - 8x + 7
2x - 4 = 7
Next, we should add 4 to both sides.
2x - 4 + 4 = 7 +4
2x = 11
Finally, we should divide both sides by 2.
x = 11/2 = 5.5
The question asks us to find the perimeter, so we can use the perimeter of the rectangle:
10x - 4 = 10(5.5) - 4 = 51
Therefore, the answer is 51 units.
Hope this helps!
You please help me with this problem I’ll give you brainless
Answer:
C
Step-by-step explanation:
-27 -(-38)
when you subtract a negative it turns into addition
-27+38
Answer:
c) -27 +38
Step-by-step explanation:
the reason is because when a number is in parentheses, especially if they are negatives, they become the opposite which in this case is + so -(-38) can be the same as saying -1 × -38 and since they are both negatives, the sign becomes positive and it's just 38 while the 27 isn't affected because there's nothing in front of it I hope I helped.
The temperature at the point (x, y, z) in a substance with conductivity K = 4.5 is u(x, y, z) = 5y2 + 5z2. Find the rate of heat flow inward across the cylindrical surface y2 + z2 = 7, 0 ≤ x ≤ 2.
Answer:
The rate of the heat flow = 1260 π
Step-by-step explanation:
From the information given :
k = 4.5
u(x,y,z) = 5y² + 5z²
Surface cylinder:
y² +z² = 5, 0 ≤ x ≤ 2
[tex]\mathtt{\overline F = \bigtriangledown u = -k(0,10y, 10z )}[/tex]
[tex]\mathtt{\overline F = -4.5(0,10y, 10z )}[/tex]
[tex]\mathtt{\overline F = (0,-45y, -45z ) \ --- (1)}[/tex]
Now parameterizing the surface by :
x = u , y = [tex]\mathtt{\sqrt{7} \ cos \ t}[/tex] , z = [tex]\mathtt{\sqrt{7} \ sin \ t}[/tex]
0 ≤ x ≤ 2 , 0 ≤ t ≤ 2π
[tex]\mathtt{{ \left. \begin{array}{1} \overline{r_y} = (1,0,0) } \\ \\ \overline{r_t} = (0, \ - \sqrt{7}\ sin \ t, \sqrt{7} \ cos \ t) \end{array} \right\} = r_u \times r_t}[/tex]
[tex]\mathtt{\overline r_u \times \overline r_t = ( -0, - \sqrt{7} \ cos \ t , - \sqrt{7} \ sin \ t) --- (2)}[/tex]
Taking integral of both equations; we have:
[tex]\mathtt{= \int ^{2}_0 \int ^{2 \pi}_{0} (0, -45y, -45 z) (0, - \sqrt{7} \ cos \ t, - \sqrt{7} \ sin \ t) \ dtdu}[/tex]
[tex]\mathtt{= \int ^{2}_0 \int ^{2 \pi}_{0} ( 45\sqrt{7} \ y\ cos \ t+ 45 \sqrt{7} \ z \ sin \ t) \ dtdu}[/tex]
[tex]\mathtt{= 45\sqrt{7}\ \int ^{2}_0 \int ^{2 \pi}_{0} (( \sqrt{7} \ cos \ t)cos \ t + (\sqrt{7} \ \ sin \ t) sin \ t) \ dtdu}[/tex]
[tex]\mathtt{= 45\times {7}\ \int ^{2}_0 \int ^{2 \pi}_{0} (1) \ dtdu}[/tex]
= 315 × (2) × (2π)
= 1260 π
Laura orders 50 m² of concrete paving slabs. The slabs cost £16.75 per m². How much do the slabs cost in total
Answer:
£837.5
Step-by-step explanation:
Cost of slabs = £16.75 / m²
Ordered amount = 50 m²
Total cost:
£16.75*50 = £837.5Total cost of slabs is £837.5
Solve m +9 = 2.
Please and thank you.
Answer:
the answer is -7
Step-by-step explanation:
m+9=2-9
-9
m=. -7
.If you dye 1/3 of it blue, ¼ pink and 2/5 black, how much of your original hair colour is left?
Answer:
You have 1/60 of the original hair color left
Step-by-step explanation:
Add up the fractions
1/3 + 1/4 + 2/5
Get a common denominator of 60
1/3 * 20/20 + 1/4 * 15/15 + 2/5 * 12/12
20/60 + 15/60 + 24/60
59/60
The total is 1 or 60/60
60/60 - 59/60
1/60
You have 1/60 of the original hair color left
Debbie needs to fill juice cups for her little brother's birthday party. There are 20 juice cups and each juice cup holds 10 fluid ounces. The juice comes in 1-gallon bottles. How many 1-gallon bottles of juice will Debbie need to purchase?
Answer:
Debbie would need to purchase 2 1-gallon bottles of juice.
Step-by-step explanation:
So we have 20 cups and each cup holds 10 fluid ounces. 20 times 10 equals 200 fluid ounces. We need to see how many fluid ounces are in 1 gallon. There are 128 fluid ounces in 1 gallon. 200 divided by 128 equals to 1.56 gallons. Debbie needs more than 1 gallon. Since we have a decimal and 1 is on the left of the decimal, Debbie would need to purchase 2 1-gallon bottles of juice.
In the healthy handwashing survey conducted by Bradley Corporation, a study was found that 64% of adult Americans operate the flusher of toilets in public restrooms with their foot. Suppose a random sample of n=20 adult Americans is obtained, and the number x who flush public toilets with their feet is recorded.
A) Explain why this is a binomial experiment.
B) Find and interpret the probability that exactly 12 flush public toilets with their foot.
C) Find and interpret the probability that at least 16 flush public toilets with their foot.
D) Would it be unusual to find more than 17 who flush public toilets with their foot? Why?
Answer:
A) It fulfills the condition of binomial experiment
B) P (x=12) =0.1678
C)P ( x ≥16)= 0.1011
d) P (x>17) =0.0096 < 0.5
Step-by-step explanation:
A. The binomial probability distribution has the following four properties
1. the outcomes of each trial maybe classified into success and failure.
2) the probability of success p remains constant for all trials.
3) the successive trials are all independent.
4) the experiment is repeated a fixed number of times ,n.
These all conditions are fulfilled by the given question so it is a binomial experiment.
B) P (x=12) = 20C12 (0.64)^12 * (1-0.64)^8= 0.1678
C) P ( x ≥16) = P (x=16) + P (x=17) + P (x=18) + P (x=19)+ P (x=20)
where
P (x=16)= 20C16 (0.64)^16 * (1-0.64)^4= 0.0645
P (x=17)= 20C17 (0.64)^17 * (1-0.64)^3= 0.0270
P (x=18)= 20C18 (0.64)^18 * (1-0.64)^2= 0.0080
P (x=19)=20C19 (0.64)^10 * (1-0.64)^1= 0.0015
P (x=20)= 20C20 (0.64)^20 * (1-0.64)^0= 0.0001
so
P ( x ≥16)= 0.0645+ 0.0270 +0.0080+ 0.0015+0.0001= 0.1011
d) P (x>17)= P (x=17) + P (x=18) + P (x=19)+ P (x=20)
=0.0270 +0.0080+ 0.0015+0.0001
=0.0096
From this we see that the probability of more than 17 people who flush public toilets with their foot is unusual because it is far away from the mean which is supposed to be somewhere 0.5 in a given distribution.
Determine the measure of the central angle for a regular
7-sided polygon, round answers to one decimal place.
Select one:
a. 25.7°
b. 51.4°
c. 61.4°
d. 62.2°
Answer:
B
Step-by-step explanation:
If the figure is regular, then everyone of the central angles are equal. They add up to 360 degrees.
x + x + x + x + x + x + x = 360 Combine
7x = 360 Divide by 7
x = 360/7
x = 51.43
an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec. Find the rate of change of the water depth when the water depth is 10 ft.
Answer:
the rate of change of the water depth when the water depth is 10 ft is; [tex]\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}[/tex]
Step-by-step explanation:
Given that:
the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.
We are meant to find the rate of change of the water depth when the water depth is 10 ft.
The diagrammatic expression below clearly interprets the question.
From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t
Then the similar triangles ΔOCD and ΔOAB is as follows:
[tex]\dfrac{h}{r}= \dfrac{20}{8}[/tex] ( similar triangle property)
[tex]\dfrac{h}{r}= \dfrac{5}{2}[/tex]
[tex]\dfrac{h}{r}= 2.5[/tex]
h = 2.5r
[tex]r = \dfrac{h}{2.5}[/tex]
The volume of the water in the tank is represented by the equation:
[tex]V = \dfrac{1}{3} \pi r^2 h[/tex]
[tex]V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h[/tex]
[tex]V = \dfrac{1}{18.75} \pi \ h^3[/tex]
The rate of change of the water depth is :
[tex]\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}[/tex]
Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec
Then,
[tex]\dfrac{dv}{dt}= - 4 \ ft^3/sec[/tex]
Therefore,
[tex]-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}[/tex]
the rate of change of the water at depth h = 10 ft is:
[tex]-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}[/tex]
[tex]100 \pi \dfrac{dh}{dt} = -4 \times 6.25[/tex]
[tex]100 \pi \dfrac{dh}{dt} = -25[/tex]
[tex]\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}[/tex]
Thus, the rate of change of the water depth when the water depth is 10 ft is; [tex]\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}[/tex]
Answer:
the rate of change of the water depth when the water depth is 10 ft is;
Step-by-step explanation:
Given that:
the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.
We are meant to find the rate of change of the water depth when the water depth is 10 ft.
The diagrammatic expression below clearly interprets the question.
From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t
Then the similar triangles ΔOCD and ΔOAB is as follows:
( similar triangle property)
h = 2.5r
The volume of the water in the tank is represented by the equation:
The rate of change of the water depth is :
Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec
Then,
Therefore,
the rate of change of the water at depth h = 10 ft is:
Thus, the rate of change of the water depth when the water depth is 10 ft is;
Step-by-step explanation:
what complex number has an absolute value of 5 ?
Answer:
the absolute value of -5 is 5, and the absolute value of 5 is also 5. ∣ a + b i ∣ = a 2 + b 2 . |a+bi| = \sqrt{a^2 +b^2}
please give me heart
Express the alternative hypothesis in symbolic form
An automobile technician claims that the mean amount of time (in hours) per domestic car repair is more than that of foreign cars. Assume that two samples are independent. Let the domestic car repair times be the first population and the foreign car repair times be the second population.
A. H: mu1< mu2
B. H1: mu1 = mu2
C. H: mu1>mu2
D. H: mu not= mu2
Answer:
A. H: mu1< mu2
Step-by-step explanation:
Given that :
Mean amount of time per domestic cars = mu1
Mean amount of time per foreign cars = mu2
Automobile technicians claim :
The mean amount of time (in hours) per domestic car repair is more than that of foreign cars. This will be the Null hypothesis.
Null hypothesis : mu1 > mu2
The alternative hypothesis will negate the Null hypothesis and will hence be the opposite. This can this be expressed as :
Alternative hypothesis : mu1 < mu2
Which of the following represents a closer relationship between two variables?a) r =.00.b) r = .50.c) r = -30. d) r = -65.
Answer:
d) r = -65.
Step-by-step explanation:
The absolute value of r represents the relationship strength and the sign represents the relationship direction
Also if the relationship is nearest to 1 then it would be termed as positive correlated and if the relationship is nearest to -1 then it would be termed as negative correlated
Therefore based on the given options, the last option is correct
What is the ratio 18 to 27 written as a fraction and lowest terms
Step-by-step explanation:
18:27
=18/27
=2/3 or 2:3
PLEASE HELP ME, I DON'T UNDERSTAND THIS! :(
Answer Choice 1
Take it step by step!
First find what sqrt(x-7) is like. Compare it to sqrt(x).
You can see that in sqrt(x), when x = 0, y = 0. However, in sqrt(x-7), when x = 7, y = 0. When y = 0, sqrt(x-7) is 7 more, which means it is shifted 7 units to the right.
Similarly, +8 means that whatever sqrt(x-7) is, you add 8 more to y. Adding on extra for y is just moving it up by 8 units.
Hope that helped,
-sirswagger21
Use the diagram to find the angle measures of the triangle. Recall that the sum of the angle measures of a triangle is 180°. (2+4) 3 (x + 4) =
Answer: 45 45 90
Step-by-step explanation:
If it’s 11:50 amwhat timewillitbetwohoursfromnow
Answer:
It will be 1:50
Step-by-step explanation:
Answer:
11:50 + 2 hr. = 1:50 or 13:50 Military/European time
Step-by-step explanation:
HELP ME PLEASE
(The problem is in the picture)
Answer:
Hey there!
In this expression, 5k and -6 are terms, not factors.
In this expression, 5 and k are factors, so the last option is correct.
Let me know if this helps :)
Answer:
5 and k are factors.
Step-by-step explanation:
A factor would be a value or variable which is multiplied by something else. It is 'a part' of the product.
In [tex]5k-6[/tex], 5 and k are being multiplied by each other. This would mean that 5 and k are factors.
Option E should be the correct answer.
Multiply.
(y- 4z) (4y - 7)
Simplify your answer
Answer:
4y²-7y+16yz+28z
Step-by-step explanation:
4y²-7y+16yz+28z
Statistical Quality Control Stat class
1) For a single-sampling plan for attributes, what do the following symbols represent?
a. N
b. n
c. c
d. d
2) For a double-sampling plan for attributes, what do the following symbols represent?
a. n1
b. n2
c. c1
d. c2
e. d1
f. d2
Answer:
Step-by-step explanation:
In a single - sampling plan, when a decision on acceptance / rejection of the lot is made on the basis of only one sample, Then , the acceptance plan is said to be a single sampling plan. The single sampling plan is known as the most common and easiest sampling plan
The following symbol representation can be written as follows:
a. N → Lot size from which the sample is drawn
b. n → sample size
c. c → acceptance number
d. d → number of defectives in the sample
For example:
if we take a randomized sample of size 'n' from the Lot size.
The next step will be to inspect all items in the sample to find the defectives 'd'
The decision rule is that:
If the number of defectives is less than or equal to acceptance number, then answer is YES i.e d ≤ c, Then , we accept the Lot
If the number of defectives is not less than or equal to acceptance number, then the answer is NO . Then , we reject the Lot.
So if we reject, we either do 100% inspection or return the lot to the supplier.
In a double sampling plan , the decision on acceptance/rejection of the Lot is based on two samples.
The following symbol representation can be written as follows:
a. n1 → number of size of sample 1
b. n2 → number of size of sample 2
c. c1 → acceptance number for sample 1
d. c2 → acceptance number for sample 2
e. d1 → number of defectives in sample 1
f. d2 → number of defectives in sample 2
Was it evaluated correct?
explain your reasoning
Answer:
Yes
Step-by-step explanation:
Yes. They did exponents and grouping symbols first, then multiplication and division left to right. Addition came before multiplication and division because it was inside a grouping symbol.
An online retailer is offering a 30% savings on your total order. You decide to purchase a pair of pants for $82, two shirts for $53 each, and a pair of shoes for $120. A sales tax of 8.25% will be added to your order. What is the final price including all discounts and taxes for the clothing? Round your answer to the nearest cent
Answer:
$233.39
Step-by-step explanation:
Pants = $82, 2 Shirts = $53 * 2, Shoes = $120
Add all these values up to find the total cost of your order excluding tax.
82 + 53(2) + 120 = 308
Next find the price w/ tax. Multiply 308 by 8.25%, or 0.0825.
308 * 0.0825 = 25.41
Now you add the tax to the total value.
308 + 25.41 = 333.41
The total value including tax is $333.41. The online retailer is offering a 30% savings (discount), so multiply the total price including tax by 30% (0.30).
333.41 * 0.30 = 100.023
Now you subtract the discount from the total price.
333.41 - 100.023 = 233.38700
The question say the answer rounded to the nearest cent or hundredths, so your final answer is 233.39.
The final price of the clothing including all discounts and taxes is $233.39.
What is the remainder when f(x) = x^2 + 14x − 8 is divided by (x − 5)? 103 88 87 72
Answer:
The remainder is 87.
Step-by-step explanation:
By definition of remainder theorem, whenever a polynomial f(x) is divided by (x-b) the remainder will be: f(b)
Following the Remainder Theorem, in this question the remainder will be f(5).
In this case we were given f(x) as
f(x) = x^2 + 14x − 8
We're are to find the remainder when it is divided by (x-5)
Then(x-5)= 0
X=5
If we substitute x=5 into equation of f(x), we will have the remainder of
f(x) = x^2 + 14x − 8
f(4)= (5)^2 +14(5)-8
f(4)=25+70-8
f(4)=87
Hence, The remainder is 87.
Answer:
87
Step-by-step explanation:
A bowl holds the pieces of fruit shown below. The image shows 8 apples and 7 oranges. If Jasmine correctly writes the fraction of fruit that are apples, which of the following would be the numerator of the fraction?
Answer:
8+7=15 therefore 8
5
Step-by-step explanation:
The numerator from the fraction of apple fruits to total fruits is 8
How to find fraction of apples to total fruits?
Number of apples = 8Number of oranges = 7Total fruits = apples + oranges
= 8 + 7
= 15
Fraction of apple fruits to total fruits = Number of apples / Total fruits
= 8/15
Therefore, the numerator from the fraction of apple fruits to total fruits is 8
Learn more about fraction:
https://brainly.com/question/1622425
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which property is represented by 5+8(-8)=-8+5?
indentity, associative, commutative, distributive
Answer:
The Commutative property is represented by 5 + (-8) = -8 + 5.
Step-by-step explanation:
We are the following the following expression below;
5 + (-8) = -8 + 5
Identity property;This property says that is any number is added to 0, then the result is the number itself, i.e.;
2 + 0 = 2 or (-7) + 0 = -7.
Associative property;Suppose there are three numbers; a, b and c.
So, this property hold the condition that; a + (b + c) = (a + b) + c
If we add the second and third numbers and then add the first number to it or if we add the first and second numbers and then add the third number to it, the result will be the same.
Commutative property;Suppose there are two numbers 6 and 8.
This property states that if we add 6 + 8 or 8 + 6, both are equal, i,e;
6 + 8 = 8 + 6
14 = 14.
Distributive property;This property states the following condition;
a [tex]\times[/tex] (b + c) = (a [tex]\times[/tex] b) + (a [tex]\times[/tex] c)
So, 5 + (-8) = -8 + 5 is represented by the commutative property.
Determine if the two triangles shown are similar. If so, write the similarity statement. options:
A) ΔWUV ∼ ΔFGH
B) ΔUVW ∼ ΔFGH
C) Impossible to determine.
D) The triangles are not similar.
Answer:
B
Step-by-step explanation:
∠ U = ∠ F = 76° thus are congruent
Consider the ratios of corresponding sides
[tex]\frac{UW}{FH}[/tex] = [tex]\frac{9}{21}[/tex] = [tex]\frac{3}{7}[/tex]
[tex]\frac{UV}{FG}[/tex] = [tex]\frac{18}{42}[/tex] = [tex]\frac{3}{7}[/tex]
Thus Δ UVW ~ Δ FGH by the SAS postulate
Yes the given two triangles are similar.
The similarity statement is B) ΔUVW ∼ ΔFGH
What do we mean by similar triangles ?
The triangles that have similar shape but the sizes of the triangles may be different, are called similar triangles.
Are the given triangles similar or not ?Here, in the given triangles,
∠U = ∠F = 76°
Therefore they are congruent.
The ratio of corresponding sides, [tex]\frac{UW}{FH} =\frac{9}{21} = \frac{3}{7}[/tex]
Again the ratio of corresponding sides, [tex]\frac{UV}{FG}=\frac{18}{42}=\frac{3}{7}[/tex]
Thus, ΔUVW ∼ ΔFGH by SAS rule of similarity.
Learn more about Similarity of triangle here :
https://brainly.com/question/14285697
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A chef orders carrots and celery in bulk. The chef orders 2.2 lb more carrots than celery. The two orders weigh 10.8 lb
combined.
What is the weight of the carrots?
Answer:
Y= 7.9 lb
X= 10.1 lb
Step-by-step explanation:
The chef orders 2.2 lb more carrots than celery. The two orders weigh 10.8 lb combined.
Let carrot= x
Let celery= y
X+y = 18...... equation one
X= 2.2 +y.... equation two
Substituting the value of x into equation one
2.2 +y +y =18
2y= 18-2.2
2y= 15.8
Y= 7.9 lb
Substituting the value of yinto equation 2
X= 2.2 +y
X= 2.2 + 7.9
X= 10.1 lb