The radius of circle C is 6 units and the measure of central angle ACB is StartFraction pi Over 2 EndFraction radians. What is the approximate area of the entire circle? square units What is the approximate area of the entire sector created by central angle ACB? square units What is the approximate area of the shaded region only? square units
Answer:
Step-by-step explanation:
We khow that the radius of our circle is 6
Let A be the area of our cercle :
A= 6^2*Pi = 36 Pi = 113.09 sq.units
We khow that the mesure of our angle ABC is Pi over 2 wich is 90 degree
So this triangle ABC is a right one .
So I think that we must khow the area of this triangle to be able to khow the area of the sector .
We have a hint : ABC is 90 degree so it is the quarter of our cercle
We need to divide the area of the circle by 4
113.09 ÷4 = 28.27
Answer:
113
28
22
Step-by-step explanation:
The relationship between the number of hours a plumber works and the total work fee she charges is proportional. Her fee for 5 hours of work is $350. Which of the fallowing could be combination of values for the plumbers work hours and total work fee she charges ?
Answer: $70 per hour
Step-by-step explanation:
Hi, to answer this question we have to calculate the hourly fee.
To do this, we simply have to divide the 5 hour fee price (350) by the number of hours worked.(5):
Mathematically speaking:
350/5 = $70 per hour
So, since the work fee is proportional, for x hours, the expression is:
70x
Feel free to ask for more if needed or if you did not understand something.
A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 290 people over the age of 55, 68 dream in black and white and among 288 people under the age of 25, 19 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those underIdentify the test statistic?Identify the p value?Test the claim by constructing an appropriate confidence level?What is the conclusion base on the hypothesis test?What is the conclusion base on the confidence level?
Answer:
he proportion of people over 55 who dream in black and white is greater than the proportion of those under.
The proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).
Step-by-step explanation:
In this case we need to determine if the proportion of people over 55 who dream in black and white is greater than the proportion of those under.
The hypothesis can be defined as follows:
H₀: The proportion of people over 55 who dream in black and white is not greater than the proportion of those under, i.e. p₁ - p₂ ≤ 0.
Hₐ: The proportion of people over 55 who dream in black and white is greater than the proportion of those under, i.e. p₁ - p₂ > 0.
The information provided is:
n₁ = 290
n₂ = 288
X₁ = 68
X₂ = 19
Compute the sample proportions and total proportions as follows:
[tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{68}{290}=0.235\\\\\hat p_{2}=\frac{X_{2}}{n_{1}}=\frac{19}{288}=0.066\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{68+19}{290+288}=0.151[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]
[tex]=\frac{0.235-0.066}{\sqrt{0.151(1-0.151)[\frac{1}{290}+\frac{1}{288}]}}\\\\=5.67[/tex]
The test statistic value is 5.67.
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
Compute the p-value as follows:
[tex]p-value=P(Z>5.67)\\=1-P(Z<5.67)\\=1-\approx1\\=0[/tex]
The p-value of the test is quite small.
The null hypothesis will be rejected at 5% significance level.
Thus, the proportion of people over 55 who dream in black and white is greater than the proportion of those under.
The significance level of the test is 5%.
Then the confidence level will be:
Confidence level = 100% - Significance level
= 100% - 5%
= 95%
Compute the 95% confidence interval for the difference between proportions as follows:
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}[/tex]
The critical value of z for 95% confidence level is z = 1.96.
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}[/tex]
[tex]=(0.235-0.066)\pm1.96\cdot\sqrt{\frac{0.235(1-0.235)}{290}+\frac{0.066(1-0.066)}{288}}\\\\=0.169\pm 0.057\\\\=(0.112, 0.226)[/tex]
The null hypothesis would be rejected if the null value, i.e. (p₁ - p₂) ≤ 0 is not contained in the interval.
The 95% confidence interval consist of values greater than 0.
Thus, the null hypothesis will be rejected.
Concluding that the proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).
Find the area of the following
parallelogram:
1.5 cm
2.5 cm
2.25 cm
A= [?] cm
Answer:
given,
base (b) = 2.25cm
height (h) = 1.5 cm
now,
area (a) = b×h
or, a=2.25cm×1.5cm
therefore the area of parallelogram is 3.375cm^2.
hope it helps..
Answer:3.375 cm²
Step-by-step explanation:
Find the area of the following
parallelogram:
1.5 cm
2.25 cm
Solution:
(1.5×2.25)cm²
= 3.375 cm²
Hope it helps
a fruit drink is made by mixing 60ml of orange juice with 180ml of pineapple juice. what is the ratio of orange juice to pineapple juice in its simplest form?
Answer:
1:3
Step-by-step explanation:
both divide by 60 so do 60 divided by 60 which is one
then 180 divided by 60 which is three
this gives you the answer
Answer:
1:3
Step-by-step explanation:
a ratio is basically the same as a fraction just in a different form. so it would be 60/180 simplified. both 60 and 180 can be divided by 60. so you would divide both numbers by 60 to get 1/3. this cannot be simplified any further. then to put it as a ratio it would just be 1:3
Good morning
Pls I will like you all to pls put full explanation.
I am preparing for my Exam
Thank you
6/5=3/d
d=?
Answer:
5/2 or 2.5
Step-by-step explanation:
6/5=3/d
6*d=3*5
d=3*5/6
d= 5/2 or 2.5
Answer:
D=2.5Solution,
[tex] \frac{6}{5} = \frac{3}{d} \\ or \: 6 \times d = 5 \times 3(cross \: multiplication) \\ or \: 6d = 15 \\ or \: d = \frac{15}{6} \\ d = 2.5[/tex]
hope this helps...
Good luck..
What are the x-and y intercepts for the graph of 5x-2y=20?
Answer: y = (5)(2)x-10
Step-by-step explanation:
Pick all that apply the option answer in two minutes
Answer: PQT and TUV
Step-by-step explanation:
Classify the following triangle. Check all that apply.
Answer:
NO
Step-by-step explanation:
IMAGE
What is the length of XQY?
Answer:
88
Step-by-step explanation:
First you must find the circumference of the entire circle and to do this you use 2πr. The radius in this case is PX=15. This means that the circumference is 30π. Now to find the arc length, we know that the measure of arc XY is 23 degrees, and since there are 360 total degrees in a circle, we must subtract 23 from 360 to get 337° as the measure of arc XQY. Now we have to find what portion of the circumference of the circle is in this arc, and to do this you divide the arc length (337°) by 360° and multiply by the circumference of the circle. Doing this would get you [tex]\frac{337}{360} *30\pi[/tex] which equals ~28. Finally, you have to multiply this by the value of pi and get approximately 88, which is your answer.
What is an equation of the line that is perpendicular to y=−34x+6 and passes through the point (3, 9)?
Answer:
y = 4/3x + 5
Step-by-step explanation:
if the slope is -3/4 then the perpendicular slope is 4/3
y = mx + b
9 = 4/3(3) + b
9 = 4 + b
5 = b
y = 4/3x + 5
A group of 20 people visited Anglesey for a weekend break.
• 10 of the group visited Beaumaris Castle.
• 13 of the group visited South Stack Lighthouse.
• 4 of the group did not visit either of these places.
Complete the Venn diagram below by stating the number of people in each region A,B,C and D to show this information.
The universal set, ε, contains all of the 20 people in the group.
Answer:
A = 4, B = 3, C = 7, D = 6
Step-by-step explanation:
A = 4 because A represents the number of people who didn't visit either place. This means that B + C + D = 20 - 4 = 16. To find C, which is the overlap we can do 10 + 13 - 16 = 7 so C = 7 which means B = 10 - 7 = 3 and D = 13 - 7 = 6.
Answer:
A = 4, B = 3, C = 7, D = 6
Step-by-step explanation:
Someone help me do this? For math
Answer:
1, 4, 5, 7, 8
Step-by-step explanation:
once you plot the points you will see that these coordinates are inside the star
⚠️⚠️⚠️GIVING AWAY HUGE POINTS FOR ANYONE WHO COMPLETES THIS AND GETS THEM RIGHT!!!!!!!⚠️⚠️⚠️
Answer:
The average speed for his journey from York to Blackpool is 61.4 KM/H
Step-by-step explanation:
Please help! For all values of x, F(x)= x-1 And G(x)=2x^2+3 Solve fg(x)= gf(x)
Answer:
[tex]\boxed{\sf \ \ \ x=\dfrac{3}{4} \ \ \ }[/tex]
Step-by-step explanation:
hello,
f(x)=x-1
[tex]g(x)=2x^2+3[/tex]
so
[tex]fog(x)=f(g(x))=f(2x^2+3)=2x^2+3-1=2x^2+2 \ and \\gof(x)=g(f(x))=g(x-1)=2(x-1)^2+3=2x^2-4x+2+3=2x^2-4x+5 \ \ So\\\fog(x)=gof(x) <=>2x^2+2=2x^2-4x+5\\<=>4x=5-2=3\\<=>x=\dfrac{3}{4}[/tex]
hope this helps
[tex]\frac{3}{4}[/tex]
The composition of a function is a process in which two functions [tex]f,g[/tex], are combined to produce a new function, [tex]h[/tex], with the formula [tex]h(x)=g(f(x))[/tex]. It means that the [tex]g[/tex] function is being applied to the [tex]x[/tex] function.
[tex]f(x)=x-1\\g(x)=2x^2+3[/tex]
[tex]f(g(x))=f(2x^2+3)[/tex]
[tex]=2x^2+3-1\\=2x^2+2[/tex]
[tex]g(f(x))=g(x-1)[/tex]
[tex]=2(x-1)^2+3\\=2x^2+2-4x+3\\=2x^2-4x+5[/tex]
[tex]f(g(x))=g(f(x))[/tex]
[tex]2x^2+2=2x^2-4x+5[/tex]
[tex]4x=3[/tex]
[tex]x=\frac{3}{4}[/tex]
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On a coordinate plane, polygon GHIJ translates 8 units to the left to form polygon G'H'I'J'. Which of the following equations is not necessarily true? A. GH = G'H' B. G'G = 8 units C. m∠HIJ = m∠H'I'J' D. m∠HI'J = m∠H'IJ'
Answer:
The answer would be letter B. This is because the problem wants you to find the equation that is not necessarily true. In this case G'G does not equal 8 units.
Find the mid points of the line joining the pairs of points a.(3,4) and (5,2) b.(0,6) and (4,0) c.(4,2) and (4,-4) d.(-1,-5) and (-3,4) e.(-3,2) and (8,-2)
Answer:
a(4,3). b( 2,3). c(4,-1). d(-2,-1/2). e(5/2, 0).
Step-by-step explanation:
Hello , I can help you with that
the mid point is given by
Let
Point 1
[tex](x_{1},y_{1})[/tex]
Point 2
[tex](x_{2},y_{2})[/tex]
the midpoint is(m)
[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )[/tex]
all you have to do is to put those values into the equation
Step 1
P1(3,4) and P2(5,2)
[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{3+5}{2},\frac{4+2}{2} )\\m=(\frac{8}{2},\frac{6}{2} )\\m=(4,3)[/tex]
Step 2
P1(0,6) and P2(4,0)
[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{0+4}{2},\frac{6+0}{2} )\\m=(\frac{4}{2},\frac{6}{2} )\\m=(2,3)[/tex]
Step 3
P1(4,2) and P2(4,-4)
[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{4+4}{2},\frac{2-4}{2} )\\m=(\frac{8}{2},\frac{-2}{2} )\\m=(4,-1)[/tex]
Step 4
P1(-1,-5) and P2(-3,4)
[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{-1-3}{2},\frac{-5+4}{2} )\\m=(\frac{-4}{2},\frac{-1}{2} )\\m=(-2,\frac{-1}{2} )[/tex]
Step 5
P1(-3,2) and P2(8,-2)
[tex]m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} )\\m=(\frac{-3+8}{2},\frac{2-2}{2} )\\m=(\frac{5}{2},\frac{0}{2} )\\m=(\frac{5}{2} ,0)[/tex]
I really hope it helps you, have a nice day
Find the value of x needed to make the equation below true. 1.5(2x-4)=2(4x+2)
Answer:
x= -2
Step-by-step explanation:
1.5(2x-4)=2(4x+2)
3x-6=8x+4
-5x=10
x= -2
Hera are 4 fractions labelled A,B,C and D 3/4 5/6 16/25 9/15 A B C D Write them in order starting from the smallest
Answer: 9/15, 16/25, 3/4 and 5/6.
Step-by-step explanation:
From the question, we have been given four fractions which are 3/4, 5/6, 16/25 and 9/15. We are told to write them in order starting from the smallest. For this to be done, we will have to change the fractions to percentages. This will be:
3/4 = 3/4 × 100 = 75%
5/6 = 5/6 × 100 = 83.3%
16/25 = 16/25 × 100 = 64%
9/15 = 9/15 × 100 = 60%
From the above percentages, arranging the fractions from the smallest will be:
9/15, 16/25, 3/4 and 5/6.
which equation describes this line? A. y-3=2(x-2) B. y-9=2(x-1) C. y-1=2(x-9) D. y-2=2(x-3)
Answer:
y = 2x + 7
Step-by-step explanation:
Step 1: Find slope
m = (9 - 3)/(1 + 2)
m = 2
y = 2x + b
Step 2: Find b
9 = 2(1) + b
9 = 2 + b
7 = b
Step 3: Rewrite equation
y = 2x + 7
Answer:
B) y - 9 = 2(x - 1)
Step-by-step explanation:
(-2, 3) ;(1,9)
[tex]Slope =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{9-3}{1-[-2]}\\\\=\frac{6}{1+2}\\\\=\frac{6}{3}\\\\=2[/tex]
(1, 9 ) ; m = 2
Equation: [tex]y - y_{1}=m(x - x_{1})\\\\[/tex]
y - 9 = 2(x - 1)
y - 9 = 2x -2
y = 2x - 2 + 9
y = 2x + 7
Please help me with this question.
Answer: a) 110√2 meters
b) 2.42 hectares
Step-by-step explanation:
a) Since it is a square, the diagonal cuts the square into two 45-45-90 triangles where the diagonal is the hypotenuse. Therefore, the sides are length x and the diagonal is length x√2.
[tex]x\sqrt2=220\\\\\\x=\dfrac{220}{\sqrt2}\\\\\\x=\dfrac{220}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\x=\large\boxed{110\sqrt2}[/tex]
b) Area of a square is side squared. 10,000 meters² = 1 hectare
[tex]A=(110\sqrt2)^2\\\\.\quad =(110)^2(\sqrt2)^2\\\\.\quad =12100(2)\\\\.\quad =24200\ \text{meters}^2\\\\.\quad =\large\boxed{2.42\ \text{hectares}}[/tex]
A salad bar offers vegetable platters in 4 sizes (small, medium, large, and super-sized) and 6 different vegetables to choose from. Different platters can be created by changing the size and/or the choice of vegetables. If Selena wants to order a platter with exactly 2 different vegetables, how many different platters could she create?
Answer:
The number of different platters Selena can create by selecting two different vegetables is 60 different platters
Step-by-step explanation:
The information given are;
The number of different sizes of salad available = 4
The number of different vegetable to choose from = 6
The number of vegetables Selena ordered = 2
The number of ways Selena can choose 2 vegetables out of 6 = ₆C₂ = 15 ways
The number of different platters (choice of vegetable and size of platter) Selena can create = The number of different sizes of salad available × The number of ways Selena can choose the vegetables
The number of different platters (choice of vegetable and size of platter) Selena can create = 4 × 15 = 60 different platters.
Examine the diagram, and answer the question. The points A(2,7) and B(−4,−3) are located in the coordinate plane as shown. Points A and B are shown in the coordinate plane at the locations indicated. What is the approximate distance between the two points?
Answer:
Option (2)
Step-by-step explanation:
Formula to get the distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
The given points are A(2, 7) and B(-4, -3)
Distance between these points will be,
AB = [tex]\sqrt{(2+4)^2+(7+3)^2[/tex]
= [tex]\sqrt{6^2+10^2}[/tex]
= [tex]\sqrt{136}[/tex]
= 11.66
≈ 11.7 units
Therefore, distance between the points A and B is 11.7 units.
Option (2) will be the answer.
Answer:
For those with the square root answer its 2\sqrt(34)
Step-by-step explanation:
Jo paints some tennis balls and puts them in a bag. She picks a ball at random from the bag and replaces it. She repeats this 60 times, and gets a ball not painted 50 times. Find the experimental probability of getting a painted ball from Jo's bag.
Answer:
1/6
Step-by-step explanation:
An experimental probability is the number of times an event occurred when actually attempted.
So, if Jo does the experiment 60 times and receives 50 unpainted balls, then calculate how many painted balls she got:
60-50 = 10.
So, the probability of picking a painted ball = 10/60 = 1/6
Hope this helps
If f(x) = x + 8 and g(x) = x3, what is (gºf)(-5)?
Answer:
Step-by-step explanation:
f(-5) = -5 + 8 = 3
g(3) = 3^3 = 27
Classify each situation as exponential growth or exponential decay.
Answer:
Step-by-step explanation:
Exponential Growth:
1). The value of a home in a growing community every year.
2). The amount of money in a saving account that earns interest annually.
Exponential decay:
1). The monthly sale of albums of a band whose popularity is declining.
2). The amount of radioactive element remaining in a sample every decade.
3). The temperature of a hot cup of coffee left on the counter every minute.
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Which trigonometric ratio is correct for triangle DEF? (Hint: Use Pythagorean Theorem first) *
Sin(D)= 24/7
Tan(D)= 24/25
Cos(E)= 24/25
Sin(E)= 7/24
Answer:
First find line DE using Pythagoras theorem
That's
DE² = 7² + 24²
DE = √ 49 + 576
DE = 25
The correct trigonometric ratio for triangle DEF is
Cos(E) = 24/25
Hope this helps
Answer:
Cos(E) = 24/25
Step-by-step explanation:
Express 160 as the product of its prime factors.
Write the prime factors in ascending order and
give your answer in index form.
Answer:
Step-by-step explanation:
160 = 2 × 2 × 2 × 2 × 2 × 5
Hope this helps
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The number 160 as a product of prime factors is 160 = 2 × 2 × 2 × 2 × 2 × 5
What are prime factors?A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.
A prime number factor is any prime number that can be multiplied by the original number to get the factor.
The prime factors of the numbers will be:-
160 = 2 × 2 × 2 × 2 × 2 × 5
Therefore, the number 160 as a product of prime factors is 160 = 2 × 2 × 2 × 2 × 2 × 5.
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if x=4 and y=-2, the value of 1/2xy^2 is
a. 32
b. 8
c. -4
d. -8
Answer:
b. 8
Step-by-step explanation:
To solve, we need to plug in the x and y values since we already have the values given to us
1/2(4)(2^2)
We should do the exponents first, 2^2 is 4
Now we are left with 1/2(4)(4)
4 times 4 is 16
16 times 1/2 is the same as 16/2
16/2=8
b. 8
Which of the following compositions of transformations will always produce the same image, regardless of the order in which the transformations are performed?
Answer:
All compositions are affected by the order in which they are performed
Step-by-step explanation:
We have the following transformations:
-translation
-reflection
-rotation
Each of them are affected by the order in which they are performed, for example:
If we rotate we have:
(x, y) -> (y, -x).
After the reflection:
(y, -x) -> (-y, -x).
If we translated by <2, 5> and reflected through the y-axis:
After the translation, (x, y) -> (x + 2, y + 5)
In other words, all compositions are affected by the order in which they are performed