Answer:
504
Step-by-step explanation:
40%=.40
360*.40=144
original number + increase = x
360+144=504
A principal of a large high school wants to estimate the true proportion of high school students who use the community's public library. To do so, he selects a random sample of 50 students and asks them if they use the community's public library. The 95% confidence interval for the true proportion of all students who use the community's public library is 0.25 to 0.34. If the principal had used a sample size of 200 students rather than 50 students, how would the length of the second interval compare to the original interval?
O It would be half as wide.
O It would be twice as wide.
O It would be one-fourth as wide.
O It would be four times as wide
ws
Considering the margin of error of a confidence interval, it is found that the correct option is:
It would be half as wide.
What is the margin of error of a confidence interval?It is modeled by:
[tex]M = z\frac{s}{\sqrt{n}}[/tex]
In which:
z is the critical value.s is the standard deviation.n is the sample size.From this, we get that the margin of error is inversely proportional to the square root of the sample size. Then, multiplying the sample size by 4, when it changes from 50 to 200, cuts the margin of error in half, making the interval half as wide.
More can be learned about the margin of error of a confidence interval at https://brainly.com/question/25890103
Answer: It would be half as wide
Step-by-step explanation:
If the principal had used a sample size of 200 students rather than 50 students, the length of the second interval would be half as wide compared to the original interval.
The width of a confidence interval is inversely proportional to the square root of the sample size. In this case, the sample size is multiplied by 4 (from 50 to 200), so the square root of the sample size is doubled. As a result, the width of the confidence interval is divided by 2, making it half as wide.
Therefore, the correct answer is: It would be half as wide.
If v is the circumcenter of pqr ,pr =46 ,tv=15,and vr=25 find each measure
Answer:
1. a) SR = 23
b) QV = 25
c) QT = 20
d) PQ = 40
e) VS = 4·√6
2. a) LH = 16
b) EL = 2·√185
c) JG = 30
d) EK = 22
e) KG = 30
3. a) XT = 37
b) TZ = 34
c) ZW = 17
d) XZ = 21
e) SY = 69
Step-by-step explanation:
The circumcenter ΔPQR is the center of the circle that circumscribes ΔPQR
The length of the radius of the circle ≡ VR = VP = QV = 25
a) Given that VR ≅ VP - Radius of circumcircle
VS ≅ VS Reflective property
∠VPS ≅ ∠VRS - Base angles of an isosceles triangle
Right triangle VPS ≅ Right triangle VRS -Hypotenuse and one Leg HL congruency
Therefore, SR ≅ PS -Corresponding parts of congruent triangles are congruent CPCTC
SR + PS = PR = 46
SR + PS = SR + SR = 2·SR = 46
∴ SR = 46/2 = 23
b) QV = VR = 25 = Radius of circumcircle of ΔPQR -Given V = center and Q = vertices of the triangle circumscribed by the circle referred to in the question
c) QT = √(QV² - TV²) = √(25² - 15²) = √400 = 20
d) TV ≅ TV - Reflexive property of congruency
ΔTQV ≅ ΔTVP - Hypotenuse and one Leg (HL) congruency
QT ≅ TP -Corresponding parts of congruent triangles are congruent CPCTC
PQ = QT + TP Given
∴ PQ = QT + QT since QT = TP
PQ = 2·QT = 2 × 20 = 40
e) VS = √(VR² - SR²) = √(25² - 23²) = √96 = 4·√6
2. The incenter is the center of the incircle of ΔEFG
a) LH = LK = JL = 16 -Radius of incircle of ΔEFG
b) EL = Hypotenuse of right triangle LHE = √(LH² + EH²) = √(16² + 22²) = √740 = 2·√185
c) JG = Leg length of right triangle JGL = √(LG² - JL²) = √(34² - 16²) = √900 = 30
d) EK = Leg length of right triangle LKE = √(EL² - LK²) = √(740 - 256) = 22
e) KG = Leg length of right triangle LKG = √(LG² - LK²) = √(34²- 16²) = √900 = 30
3. Point Z id the centroid of ΔRST
a) XT = XS - point X on ST bisected by median line RX
ST = XT + XS = XT + XT = 2.XT = 74
XT = 74/2 = 37
b) TZ = 2/3×TW - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
TZ = 2/3×51 = 34
c) TZ + ZW = TW
∴ ZW = TW - TZ = 51 - 34 = 17
d) RZ = 42 = 2/3×RX - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
∴ RX = 3/2×42 = 63
RZ + XZ = RX - Given
XZ = RX - RZ = 63 - 42 = 21
e) SZ = 2/3×SY - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
SZ + ZY = SY
∴ ZY = SY - SZ = SY - 2/3×SY = 1/3×SY = 23
Which gives;
SY = 3 × 23 = 69.
Help fast please and thank you!
Answer: 1/4 .!
Step-by-step explanation: hope this helped :).
HELP PLEASE FOR NUMER 3 and 4 PLEAESE ASAP ANI WILL GIVE BRANILESS FOR THE FIRST PERSON
Wheres the ? n answers at for #3 n #4
A figure is made up of three triangles. Each triangle has a base of 5 feet and a height of 4.5 feet. What is the total area of the figure?
Group of answer choices
33.75 ft²
43.75 ft²
67.5 ft²
22.5 ft²
Answer:
Step-by-step explanation:
3 * 1/2 * 5 * 4.5
= 33.75 fT^2.
 find the equation of the line that is parallel to the line Y equals 3X -6 and passes through the points (1 -8). Write the equation in point slope form
=====================================================
Parallel lines have the same slope.
So if the given line has a slope of 3, then the line parallel to it has the same slope (3)
Now, let's write the equation of the line in Point-Slope Form.
Remember, point-slope form looks like so:-
[tex]\bigstar{\underline{\boxed{\pmb{y-y1=m(x-x1)}}}[/tex]
Where
y₁ is the y-coordinate of the point that the line passes through
m is the slope
x₁ is the x-coordinate of the point that the line passes through
In this case,
y₁ is equal to -8
m is equal to 3
x₁ is equal to 1
Plug in the values:
[tex]\longrightarrow\sf{y-(-8)=3(x-1)}[/tex]
Simplify:
[tex]\longrightarrow\sf{y+8=3(x-1)}[/tex]
and we're done!
=========================================================
note:-Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
it is 3 kilometers from Linda's house to the nearest mailbox. How far is it in meters? Be sure to include the correct unit in your answer.
Answer:
1km=1000m... thats basically the answer so the nearest mail box is 3000M
3
14) There are seven million, eight hundred and fifty-four thousand,
three hundred and eight people in a country. i lleda
Round this number to the nearest ten thousand people.
Answer:
7,854,000
because the 308 people would have to be at least 500 to round up to 7,855,000
U is the midpoint of TV and S is the midpoint of RT.
If RV=w and SU=w–30, what is RV?
Answer:
60
Step-by-step explanation:
By the triangle midsegment theorem, 2(SU)=RV.
2(w-30)=w, meaning w=60.
So, RV=60 as well
Pamela is 6 years younger than Jiri. The sum of their ages is 78 . What is Jiri's age?
What is the volume of a sphere with a diameter of 7.5 cm, rounded to the nearest tenth of a cubic centimeter?
Answer:
V≈220.89cm³
Step-by-step explanation:
Answer: 220.9
4/3 π(3.75)^3=220.9
What is the median age of a group of employees
whose ages are 32, 37, 30, 43, 29 and 31?
Rounding please help! Math
it is just still 5 I believe :P hope this helps
A quantity with an initial value of 200 grows continuously at a rate of 4% per second.
What is the value of the quantity after 1.55 minutes, to the nearest hundredth?
The growth of the quantity is an illustration of an exponential function
The value of the quantity after 1.55 minutes is 76759.22
How to determine the amount of the quantity?The given parameters are:
Initial value, a = 2000
Rate, r = 4%
An exponential growth function is represented as:
y = a(1 + r)^x
Substitute the value in the equation
y = 2000(1 + 4%)^x
After 1.55 minuted, x = 1.55 * 60
So, we have:
y = 2000(1 + 4%)^(1.55 * 60)
Evaluate the expression
y = 76759.22
Hence, the value of the quantity after 1.55 minutes is 76759.22
Read more about exponential functions at:
brainly.com/question/24077767
Answer:
Step-by-step explanation:
9398.61
Please help me I will mark brainliest to whoever answers
Step-by-step explanation:
All Natural Number (1,2,3,4,5...) are integers
All Whole numbers (0,1,2,3,4...) are not natural numbers (1,2,3,4...)
All integers are rational numbers
All real numbers are not irrational numbers as real nimber contain both rational and irrational numbers hence it is false.
Hence statement 1 and statement 3 are true
Answer:
The answeris D
Step-by-step explanation:
All whole numbers are natural numbers; natural numbers are numbers we use for counting 1, 2, 3....and so on, so that makes them whole because thay have no fraction, or decimils.
Bo needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged him $63 for parts. The total was $551.75. What was the cost of labor, per hour?
Lucy bought 4 pairs of pants for $21.79 each. She paid the cashier using as few $20 bills as necessary. How much change did she receive?
The amount of change Lucy receives if she paid with few $20 bills is $12.84
How to find amount of change to receiveCost of each pair of pants = $21.79Number of pairs of pants = 4Total cost of pants = $21.79 × 4
= $87.16
Amount paid to the cashier = few $20 billsIf the total cost of the pants exceeds $80, then she paid with 5 $20 bills
5 $20 bills = $100
Her change = $100 - $87.16
= $12.84
Learn more about cost:
https://brainly.com/question/2021001
PLS HELP I WILL GIVE BRAINLESt TO THE PERSON WHO SOLVES ALL OF THE CORRECTLY
Answer:
m^4 - 225c^10 = (m^2 - 15c^5 )(15c^5 + m^2)
4.8xy + 36y^2 + 0.16x^2 = (6y + 0.4x)^2
The solid below is dilated by a scale factor of 3. Find the volume of the solid created
upon
dilation.
The volume of the solid created upon dilation bythe scale factor of 3 is 5832 units³.
What is the volume of the dilated solid?An image is dilated if the dimensions of the image is resized in a way that does not change the shape of the image. When an image is dilated, it is made larger.
Dimensions of the dilataed solid = 6 x 3 = 18
Volume = 18³ = 5832 units³
To learn more about dilation, please check: brainly.com/question/3457976
1. Find the Area of the Sector:
2. Find the length of the missing side:
Answer:
1) 14.137 2)10
Step-by-step explanation:
area of sector is central angle / 360 times (pi)(r^2)
45/360 x pi (6^2)
1/8 x 36pi
14.137
3-4-5- right triangle. Or Pythagorean Theorem.
6^2 + 8^2 = c^2
c= 10
please help me answer the question in the photo
Step-by-step explanation:
please mark me as brainlest
ans
[tex] \frac{3x}{x + 4} [/tex]
need some help with these questions in the image
a. answer:_77
2_ (7 * 9) _ 16
2_ (63) _16
_61_16
_77
How do you do this problem:
1- 3 (4 - 3) + (27- 2 x 3)
Answer:
19
Step-by-step explanation:
Do what is in parenthesis first.
(4 - 3) = 1
(27 - 2 * 3) = (27 - 6) = 21
Now the equation looks like this:
1 - 3 (1) + (21) =
1 - 3 + 21 =
19
Please help me with 20 through 22 please I really appreciate it! Thank you very much!
Answer:
20. 2x+y
21. 4
22. x+y
Step-by-step explanation:
20. 9x+2y - x-2y find your LCM
4 4
=(9x+2y)-(x-2y) clear bracket
4
=9x+2y-x+2y collect terms
4
=9x-x+2y+2y
4
=8x+4y factorize
4
=4(2x+y)
4
=2x+y
with this, you will understand the following
21. 4x + 8y
x+2y x+2y
=4x+8y
x+2y
=4(x+2y)
x+2y
=4
22. 2x-y + 2x+5y
4 4
=2x-y+2x+5y
4
=4x+4y
4
=4(x+y)
4
=x+y
Erin wants to fill the jewelry box with beads. One package of beads is 120 cubic inches. How many packages of beads should Erin purchase to fill the jewelry box completely?
Answer:
9 packages of beads
Step-by-step explanation:
volume of cuboid = area of base × height
⇒ volume of jewelry box = (15 × 12) × 6
= 180 × 6
= 1080 in³
Given:
1 package of beads = 120 in³Number of packages of beads = volume of box ÷ volume of 1 package of beads
⇒ Number of packages of beads = 1080 ÷ 120
= 9
Are the base angles of an isosceles triangle always congruent?
Answer: Yes
Step-by-step explanation:
If you draw the altitude of an isosceles triangle from the vertex angle, then the two triangles formed are congruent, meaning the base angles are congruent by CPCTC.
Yes, the base angles of an isosceles triangle are congruent because in n isosceles triangle two of its sides are always congruent, and also angles opposite to congruent sides are congruent.
What is the isosceles triangle?An isosceles triangle is a triangle that has at least two sides of equal length.
When an altitude is drawn to the base of the isosceles triangle, it bisects the vertex angle. As it bisects the base, the two congruent triangles are created.
An isosceles triangle with only two congruent sides, the congruent sides are called legs. The third side is called the base. The angle opposite the base is called the vertex angle, and the angles opposite the legs are called base angles.Hence, Yes, the base angles of an isosceles triangle are congruent because in n isosceles triangle two of its sides are always congruent, and also angles opposite to congruent sides are congruent.
To learn more about the isosceles triangle click the link given below.
https://brainly.com/question/27177888
#SPJ4
Which ordered pair would form a proportional relationship with the point graphed below?
(–40, 20)
(–10, –20)
(15, –30)
(5, –15)
Answer:
(c) (15, -30)
Step-by-step explanation:
A proportional relationship has the equation ...
y = kx
The value of the constant of proportionality is the ratio of y to x:
k = y/x = 40/-20 = -2
__
The point that is on the line y = -2x is the point (15, -30).
Really need help, I’m trying to catch up in my math and get my marks back up before mid term..
Answer:
a) 12x + 22 b) 17[tex]x^{2}[/tex] - x
Step-by-step explanation:
Perimeter is the sum of the each side length.
The first example is a rectangle so the (4x+8) and the (2x+3) are doubled.
(4x+8) x 2 = 8x+16
(2x+3) x 2 = 4x + 6
12x+22
(6[tex]x^{2}[/tex] - 12x) + (2[tex]x^{2}[/tex] + x) + (9[tex]x^{2}[/tex] + 10x)
combine like-terms.
17[tex]x^{2}[/tex] - x
Answer:
12x + 22 for the rectangle, 17x^2 - x for the triangle
Step-by-step explanation:
The perimeter of a square/rectangle is equal to 2*width + 2*length
So for the rectangle, it would be 2*(4x + 8) + 2*(2x + 3)
This can be further simplified as 8x + 16 + 4x + 6
Which can be further simplified as 12x + 22
The perimeter of a triangle is equal to length if side one + length of side two + length of base
That would be (6x^2 - 12x) + (2x^2 + x) + (9x^2 + 10x)
Which becomes 8x^2 - 11x + (9x^2 + 10x)
17x^2 - x
Write the quadratic equation whose roots are 1 and −5, and whose leading coefficient is 4.
Answer:
Standard Form: y = 4(x-1)(x+5)
Step-by-step explanation:
4 is the leading coefficient, so it should go in front. When making a standard quadratic equation, you must do the opposite for each of the roots (negative to positive, positive to negative.)
if you’re asking for a general form quadratic equation, then sorry, I am unable to help you with that :(
18x3 + 6x2y - 9x2 - 3xy
factor completely
Answer:
[tex]\sf 3x(3x+y)(2x-1)[/tex]
Step-by-step explanation:
Given expression:
[tex]\sf 18x^3 + 6x^2y - 9x^2 - 3xy[/tex]
Factor out common term [tex]\sf 3x[/tex]:
[tex]\sf \implies 3x(6x^2 + 2xy - 3x - y)[/tex]
Factor [tex]\sf (6x^2 + 2xy - 3x - y)[/tex]
Rearrange:
[tex]\sf \implies 6x^2 - 3x+ 2xy - y[/tex]
Factor pairs of terms:
[tex]\sf \implies 3x(2x-1)+ y(2x - 1)[/tex]
Factor out common term (2x - 1):
[tex]\sf \implies (3x+y)(2x-1)[/tex]
Final solution:
[tex]\sf \implies 3x(3x+y)(2x-1)[/tex]
Answer:
6x2y(3xy2 − 1)
Step-by-step explanation:
i got it right on my quiz :D