Answer:
10 square units.
Step-by-step explanation:
Area of Polygon C = 40 square units.
Scale factor used in obtaining polygon D = [tex]\dfrac12[/tex]
To obtain the area of the new polygon, we multiply the area of the polygon from which it was derived by the square of the scale factor.
Therefore:
Area of Polygon D
[tex]=40 \times (\frac12)^2\\\\=40 \times \frac14\\\\=10$ square units[/tex]
The area of polygon D is 10 square units.
Helppp!!!! please!!!
Answer:
...........................
NEED HELP ASAP!!!! I will reward you as the most brainliest!
Step-by-step explanation:
v = 1/3πr²h
1/3×314/100×4×4×7
11,722.666round off
11722.67
formula =v= 3.14×radius×radius ×height ×3
Step-by-step explanation:
pie×radius×squared ×7×3
=117.29
when we round it to the nearest hundredth
its=117.29m squared
Paul is 12 years older than Colin. Caroline is 3 years younger than Colin. If the total of their ages is 87, how old is the youngest of them?
Answer:
23
Step-by-step explanation:
87=x+(x+12)+(x-3)
87=3x+9
3x=78
x=26
This is Colin's age. Caroline is 3 years younger than Colin, so she is the youngest, and we need to find her age. Subtract 3 from 26, and you get your final answer, 23.
A Christian needs to have answers to questions about his faith so that: answer: he may lose his faith, he will become confident in his faith, he may change his faith.
Answer:
become more confident in his faith
Answer:
he will become confident in his faith
Explanation:
the Bible is very open to interpretation and does not always have definite answers. if you are able to form your own ideas and interpretation of the Bible then you'll have a stronger connection to it which will make you more confident in your faith.
Which of the following represents a rotation of triangle XYZ, which has vertices (-4,7), Y(6,2), and Z (3,-8) about the origin by 90 degrees? HELP PLS options: A: X (-7,-4) Y(6,-2) Z(-8,3) B: X(7,-4) Y(-2,6) Z (3,-8) C: X (-7,-4) Y(-2,6) Z (8,3) D: X(7,-4) Y (-2,6) Z (-3,8)
Answer:
The best option is B: X' = (-7,-4), Y' = (-2,6), Z'=(8, 3).
Step-by-step explanation:
Each vertex can be represented as a vector with regard to origin.
[tex]\vec X = -4\cdot i + 7\cdot j[/tex], [tex]\vec Y = 6\cdot i + 2\cdot j[/tex] and [tex]\vec Z = 3\cdot i -8\cdot j[/tex].
The magnitudes and directions of each vector are, respectively:
X:
[tex]\|\vec X\| = \sqrt{(-4)^{2}+7^{2}}[/tex]
[tex]\|\vec X\| \approx 8.063[/tex]
[tex]\theta_{X} = \tan^{-1}\left(\frac{7}{-4} \right)[/tex]
[tex]\theta_{X} \approx 119.744^{\circ}[/tex]
Y:
[tex]\|\vec Y\| = \sqrt{6^{2}+2^{2}}[/tex]
[tex]\|\vec Y\| \approx 6.325[/tex]
[tex]\theta_{Y} = \tan^{-1}\left(\frac{2}{6} \right)[/tex]
[tex]\theta_{Y} \approx 18.435^{\circ}[/tex]
Z:
[tex]\|\vec Z\| = \sqrt{3^{2}+(-8)^{2}}[/tex]
[tex]\|\vec Z\| \approx 8.544[/tex]
[tex]\theta_{Z} = \tan^{-1}\left(\frac{-8}{3} \right)[/tex]
[tex]\theta_{Z} \approx 290.556^{\circ}[/tex]
Now, the rotation consist is changing the direction of each vector in [tex]\pm 90^{\circ}[/tex], which means the existence of two solutions. That is:
[tex]\vec p = r \cdot [\cos (\theta \pm 90^{\circ})\cdot i + \sin (\theta \pm 90^{\circ})\cdot j][/tex]
Where [tex]r[/tex] and [tex]\theta[/tex] are the magnitude and the original angle of the vector.
Solution I ([tex]+90^{\circ}[/tex])
[tex]\vec p_{X} = 8.063\cdot [\cos (119.744^{\circ}+90^{\circ})\cdot i + \sin (119.744^{\circ}+90^{\circ})\cdot j][/tex]
[tex]\vec p_{X} = -7\cdot i -4\cdot j[/tex]
[tex]\vec p_{Y} = 6.325\cdot [\cos(18.435^{\circ}+90^{\circ})\cdot i+\sin(18.435^{\circ}+90^{\circ})\cdot j][/tex]
[tex]\vec p_{Y} = -2\cdot i +6\cdot j[/tex]
[tex]\vec p_{Z} = 8.544\cdot [\cos(290^{\circ}+90^{\circ})\cdot i +\sin(290^{\circ}+90^{\circ})\cdot j][/tex]
[tex]\vec p_{Z} = 8.029\cdot i +2.922\cdot j[/tex]
Solution II ([tex]-90^{\circ}[/tex])
[tex]\vec p_{X} = 8.063\cdot [\cos (119.744^{\circ}-90^{\circ})\cdot i + \sin (119.744^{\circ}-90^{\circ})\cdot j][/tex]
[tex]\vec p_{X} = 7\cdot i +4\cdot j[/tex]
[tex]\vec p_{Y} = 6.325\cdot [\cos(18.435^{\circ}-90^{\circ})\cdot i+\sin(18.435^{\circ}-90^{\circ})\cdot j][/tex]
[tex]\vec p_{Y} = 2\cdot i -6\cdot j[/tex]
[tex]\vec p_{Z} = 8.544\cdot [\cos(290^{\circ}-90^{\circ})\cdot i +\sin(290^{\circ}-90^{\circ})\cdot j][/tex]
[tex]\vec p_{Z} = -8.029\cdot i -2.922\cdot j[/tex]
The rotated vertices are: i) X' = (-7,-4), Y' = (-2,6), Z'=(8.029, 2.922) or ii) X' = (7,4), Y' = (2,-6), Z' = (-8.029, -2.922). The best option is B: X' = (-7,-4), Y' = (-2,6), Z'=(8, 3).
6. Trail Bike Rentals charges a $16 fixed fee plus $8 per hour for renting a bike. Matt paid $72
to rent a bike. How many hours did Matt use the bike? Write an equation to represent this
scenario and solve for the variable. (2 marks)
Answer:
[tex]C =8t+16\\7\ hours[/tex]
Step-by-step explanation:
Given that, Fixed charge = $16
Per hour charge for renting the bike = $8/hour
To find:
If Matt paid $72 to rent a bike, for how many hours did he rent the bike?
Solution:
Let 't' be the time for which Matt rents the bike.
1 hour charge for the bike rent = $8
't' hour charge for the bike rent = $8 [tex]\times t[/tex]
Total Charge for the bike = Charge for renting the bike for t hours + fixed charge
Let 'C' be the total charge, so the equation becomes:
[tex]C = 8t + 16[/tex]
Given that C is $72, we need to find t:
[tex]72 = 8t+16\\\Rightarrow 8t=72-16\\\Rightarrow 8t=56\\\Rightarrow t = 7\ hours[/tex]
So, he rented the bike for 7 hours.
The equation is: [tex]C = 8t + 16[/tex]
The graph below shows a line of best fit for data collected on the number of toys sold at a toy store since the opening of the store. Based on the line of best fit, how many toys were sold 13 days after the store opened?
A.) 195
B.) 260
C.) 325
D.) 130
The answer that line of best fit, how many toys were sold 13 days after the store opened is A.) 195
Answer this question
Answer: a.) (3x +1)(2x +3)
Step-by-step explanation:
The factors that work to get the middle term, 11x, are 3×3x = 9x and 1×2x=2x. 2x +9x = 11x
Is ΔABC ~ ΔLMN? If so, name which similarity postulate or theorem applies.
Step-by-step explanation:
sss similarity theorem
–3x + 1 + 10x = x + 4
Answer: x=2
Step-by-step explanation:
7x+1=x+4
7x=x+3
6x=3
x=2
hope it correct :D
The world record for the largest collection of bookmarks is 71 235 bookmarks. Find the closest benchmark for each: a) in thousands _______________ b) in hundreds _______________ c) in tens _______________
Answer:
A: 71,235,000
B: 71,235,00
C: 71,240
Step-by-step explanation: Round by thousands, hundreds and tens.
How do you do this? please help me
Answer:
f = 10, g = 4.8 cm
Step-by-step explanation:
Area of ABCE = 60 cm²
Area of ABCD = 48 cm²
So,
Area of ADE = 60-48
=> 12 cm²
Area of ADE = [tex]\frac{1}{2} (Base)(Height)[/tex]
Where Area = 12 cm², Base = 4 cm
12 = [tex]\frac{1}{2}(4)(Height)[/tex]
Height = 12-2
Height = 10 cm
Where Height is AD
So, AD = 10 cm
Also, AD is parallel and equal to BC[tex](f)[/tex]
So,
f = 10 cm
Now, Finding g
Area of ABCD = [tex]Base * Height[/tex]
Where Area = 48 cm², Base = 10 cm
48 = 10 * Height
Height = 48/10
Height = 4.8 cm
Whereas, Height is g
So, g = 4.8 cm
the area of a rectangular sandbox can be expressed as 72xy + 18x the width of the sandbox is 9x what is the perimeter of the sandbox
Answer:
18x +16y +4
Step-by-step explanation:
The area is the product of length and width, so the length is ...
A = LW
L = A/W = (72xy +18x)/(9x) = 8y +2
The perimeter is double the sum of length and width:
P = 2(L +W) = 2(8y +2 +9x)
P = 18x +16y +4 . . . . the perimeter of the sandbox
Please help i will mark brainliest
Answer:
y=-6x+1
Step-by-step explanation:
Divide 5 3/4 divided by 1 1/2
Answer:
[tex] 3\frac{5}{6} [/tex]
solution,
[tex]5 \frac{3}{4} \div 1 \frac{1}{2} \\ = \frac{5 \times 4 + 3}{4} \div \frac{2 \times 1 + 1}{2} \\ = \frac{20 + 3}{4} \div \frac{2 + 1}{2} \\ = \frac{23}{4} \div \frac{3}{2} \\ = \frac{23}{4} \times \frac{2}{3} \\ = \frac{23}{6} \\ = 3 \frac{5}{6} [/tex]
hope this helps...
Good luck on your assignment..
Answer:
23/6=3 5/6
Step-by-step explanation:
5 3/4=(4*5+3)/4=23/4
1 1/2=(2*1+1)/2=3/2
23/4:3/2=23/4*2/3=23*2/4*3=23/2*3=23/6
Please help!! Rhombus LMNO is shown with its diagonals. The length of LN is 30 centimeters. What is the length of LP?
A.) 14
B.) 15
C.) 20
D.) 30
Answer:
The correct answer to the following question will be Option B (15).
Step-by-step explanation:
The given values is:
LN = 30 cm
Although the diagonals of that same rhombus bisects or bend one another, this implies that P seems to be the midpoint of both the LN.
So that,
⇒ [tex]LP=\frac{1}{2}\times LN[/tex]
On putting the estimated value, we get
⇒ [tex]=\frac{1}{2}\times 30[/tex]
⇒ [tex]=15[/tex]
Therefore, Option B seems to be the appropriate one.
find the values of a and b such that x^2+2x+2=(x-a)^2+b
Answer:
a = -1
b = 1
Step-by-step explanation:
Step 1: Isolate x's
x² + 2x = -2
Step 2: Complete the Square
x² + 2x + 1 = -2 + 1
(x + 1)² = -1
Step 3: Move everything to 1 side
(x + 1)² + 1 = 0
And we have our answer.
Answer:
A=1 and b=1
Step-by-step explanation:
Rachel is a lunch room supervisor at west school the children eat lunch at 15 long tables when all tables are used 240 children can eat at one time how many seats are there at each table?
Answer:
16
Step-by-step explanation:
15x = 240 x stands for number of students at 1 table
To solve this we divide by 15 both sides for the "x" to remain alone on one side of the equality sign.
(15/15) x = 240/15
So, x = 16.
Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $120 and a sample of 23 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100. Let 4 year old automobiles be represented by population 1.State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $120 and a sample of 23 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100. Let 4 year old automobiles be represented by population 1.
State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles.
At a 0.01 level of significance, what is your conclusion? What is the p-value?
Answer:
Null hypotheses = H₀ = σ₁² ≤ σ₂²
Alternative hypotheses = Ha = σ₁² > σ₂²
Test statistic = 1.44
p-value = 0.1954
0.1954 > 0.01
Since the p-value is greater than the given significance level therefore, we cannot reject the null hypothesis.
We can conclude that there is no sufficient evidence to support the claim that the variance in annual repair costs is larger for older automobiles.
Step-by-step explanation:
Let σ₁² denotes the variance of 4 years old automobiles
Let σ₂² denotes the variance of 2 years old automobiles
State the null and alternative hypotheses:
The null hypothesis assumes that the variance in annual repair costs is smaller for older automobiles.
Null hypotheses = H₀ = σ₁² ≤ σ₂²
The alternate hypothesis assumes that the variance in annual repair costs is larger for older automobiles.
Alternative hypotheses = Ha = σ₁² > σ₂²
Test statistic:
The test statistic is given by
Test statistic = σ₁²/σ₂²
Test statistic = 120²/100²
Test statistic = 1.44
p-value:
The degree of freedom corresponding to 4 years old automobiles is given by
df₁ = n - 1
df₁ = 26 - 1
df₁ = 25
The degree of freedom corresponding to 2 years old automobiles is given by
df₂ = n - 1
df₂ = 23 - 1
df₂ = 22
Using Excel to find out the p-value,
p-value = FDIST(F-value, df₁, df₂)
p-value = FDIST(1.44, 25, 22)
p-value = 0.1954
Conclusion:
When the p-value is less than the significance level then we reject the Null hypotheses
p-value < α (reject H₀)
But for the given case,
p-value > α
0.1954 > 0.01
Since the p-value is greater than the given significance level therefore, we cannot reject the null hypothesis.
We can conclude that there is no sufficient evidence to support the claim that the variance in annual repair costs is larger for older automobiles.
SI LOS ELEMENTOS DE UN CONJUNTO PERTENECEN TODOS A OTRO CONJUNTO SE LLAMAN: a) Iguales b) Subconjunto c) Cardinalidad
Answer:
B; Subconjunto
Step-by-step explanation:
Aquí, se nos pide que seleccionemos el término que define un conjunto con sus elementos que pertenecen a un conjunto más grande.
La respuesta correcta es que el conjunto más pequeño es un subconjunto del conjunto más grande.
Esto significa que el conjunto más pequeño es parte del conjunto más grande, lo que lo convierte en una subdivisión del conjunto más grande
11 POINTS !!GEOMETRY!! find the radius and area to the nearest hundredth given the circumference is 8.61. show work.
Step-by-step explanation:
C=2×pi×r
8.61=2pi*×r
8.61÷2pi=13.52 radius
A=pi×r^2
pi×13.52^2=574.25 area
Which expression is equivalent to 28 + 12? (1 point) 4(7 + 3) 4(24 + 8) 7(4 + 12) 7(21 + 5)
Answer:
4(7+3)
Step-by-step explanation:
28 and 12 are both divisible by 4.
28 ÷ 4 = 7
12 ÷ 4 = 3
Answer:
4(7+3)
Step-by-step explanation:
4(7) = 28
4(3)= 12
28+12=28+12
Hope this helps!
arcs and circles formula? can someone help me find the answer?
Answer:
9.2 cmHere,
The length of an arc of a sector with theta nag radius'r' is:
[tex] \frac{theta}{360} 2\pi \: r[/tex]
CD=?
Radius=7.9 cm
theta=66.4
Length of CD
[tex] \frac{66.4}{360} \times 2 \times \pi \times 7.9 \\ = \frac{66.4}{360} \times 2 \times 3.14 \times 7.9 \\ = 9.1506 \\ = 9.2 \: cm[/tex]
Hope this helps...
Good luck on your assignment..
Point Z is equidistant from the sides of ΔRST. Point Z is equidistant from the sides of triangle R S T. Lines are drawn from the point of the triangle to point Z. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. Which must be true? Line segment S Z is-congruent-to line segment T Z Line segment R Z is-congruent-to line segment B Z AngleCTZ Is-congruent-to AngleASZ AngleASZ Is-congruent-to AngleZSB
Answer:
AngleASZ Is-congruent-to AngleZSB
Step-by-step explanation:
The incenter of a triangle is a point inside a triangle that is equidistant from all the sides of a triangle. The incenter is the point formed by the intersection of all the three angles of the triangle bisected. The lines drawn from the incenter to the sides of the triangle forming right angles to the sides are congruent.
If Point Z is equidistant from the sides of ΔRST, point Z is the incenter of triangle RST. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. This lines are therefore congruent to each other, i.e. ZA = ZB = ZC.. Since the angles of the sides of the triangles are bisected to form the incenter, therefore:
AngleASZ Is-congruent-to AngleZSB
Answer:
AngleASZ Is-congruent-to AngleZSB
Step-by-step explanation:
D is the correct answer
Which expression is equivalent to the given expression?
(-4abc)
A-12a3bc
B-64a3883
C-64a3883
D-12a3883
Answer:
A
Step-by-step explanation:
If you see - 12a3bc, - 12a divided by 3 will give you - 4a then just put the rest beside them. So the answer will be A.
The probability of event A is 0.48, the probability of event A and B is 0.21, and the probability of events A or B is 0.89. What is the probability of event B?
Answer:
[tex] P(A)= 0.48, P(B)= ?, P(A \cap B)= 0.21, P(A \cup B) =0.89[/tex]
And for this case we can use the total rule of probability given by:
[tex] P(A \cup B) = P(A) +P(B) -P(A\cap B)[/tex]
And if we solve for [tex] P(B) [/tex] we got:
[tex] P(B)= P(A \cup B) -P(A) +P(A \cap B)[/tex]
And replacing we got:
[tex] P(B) = 0.89 -0.48 +0.21= 0.62[/tex]
Step-by-step explanation:
We have the following probabilities given:
[tex] P(A)= 0.48, P(B)= ?, P(A \cap B)= 0.21, P(A \cup B) =0.89[/tex]
And for this case we can use the total rule of probability given by:
[tex] P(A \cup B) = P(A) +P(B) -P(A\cap B)[/tex]
And if we solve for [tex] P(B) [/tex] we got:
[tex] P(B)= P(A \cup B) -P(A) +P(A \cap B)[/tex]
And replacing we got:
[tex] P(B) = 0.89 -0.48 +0.21= 0.62[/tex]
Answer:
0.62
Step-by-step explanation:
A shopkeeper had some watches for sale. He sold a total of 342 watches
in January and February. In March he sold 25% of the remainder and was
left with 18% of the watches he had at first. How many watches did he
have at first?
Answer: 450 watches
Step-by-step explanation:
Given the following :
Let Initial number of watches = n
Total number sold in January and February = 342
Total sold in march = 25% of (n - 342) = 0.25(n - 342) = 0.25n - 85.5
Total watches left = 18% of n = 0.18n
Therefore,
Initial number of watches = (watches left + total watches sold)
n = 0.18n + (0.25n - 85.5) + 342
n = 0.18n + 0.25n - 85.5 + 342
n = 0.43n + 256.5
n - 0.43n = 256.5
0.57n = 256.5
n = 256.5 / 0.57
n = 450
n = Initial number of watches = 450
노
+
Il
what is the circumference of a circle
with a radius of 14.7cm
C xd
7 car and so
22/7
3/7 x
Answer:
Circumference
(22÷7)×14.7×2 = 92.4cm
If weight is an explanatory variable and cost is the corresponding response variable which of these would be represented by the y-axis on a scatterplot A. Weight B. Neither weight nor cost C. Both weight and cost D. Cost
Answer:
D. Cost
Step-by-step explanation:
In a scatter diagram we have that the x axis corresponds to the explanatory variable or also called the independent variable, since it is the value that is entered in the equation and does not depend on another.
While the y-axis corresponds to the response variable or also called the dependent variable since it is the value of the result of the equation
In this case, the explanatory variable is weight, that is, on the x-axis the weight would go and the cost is the response variable and would go on the y-axis, therefore, the answer is D. Cost
HELP MEEEEE PLEASEEEEE SOMEONE!!
Answer:
A
Step-by-step explanation:
the triangles share one angle and they have two equal sides