Answers
Answer:
z = 110
Step-by-step explanation:
The measure of an angle created by the intersection of two secants outside a circle is half the difference of the angles it intercepts. In this it would be:
2x + 15 = 1/2 * (10x + 20 - 80)
We can now solve:
4x + 30 = 10x - 60
30 = 6x - 60
6x = 90
x = 15
This means the values of 10x + 20 is 10(15) + 20, which is 170.
Now, we can add up all the arcs in a circle, which sum to 360 degrees:
360 = z + 170 + 80
360 = z + 250
z = 110
Answer:
[tex]A)\ \ z = 110[/tex]
Step-by-step explanation:
One is given a circle with two secants. Please note that a secant is a line that intersects a circle in two places. The secant exterior angle theorem states that when two secants intersect each other outside of a circle, the measure of the angle formed is half the of the positive difference of the intersecting arcs. One can apply this theorem here by stating the following:
[tex]2x+15=\frac{(10x+20)-(80)}{2}[/tex]
Simplify,
[tex]2x+15=\frac{(10x+20)-(80)}{2}[/tex]
[tex]2x+15=\frac{10x-60}{2}[/tex]
[tex]2x+15=5x-30[/tex]
Inverse operations,
[tex]2x+15=5x-30[/tex]
[tex]15=3x-30[/tex]
[tex]45=3x[/tex]
[tex]15=x[/tex]
Substitute this value into the equation for one of the intersecting arcs to find the numerical value of that intersecting arc:
[tex]10x+20\\x = 15\\\\10(15) + 20\\= 150 + 20\\= 170[/tex]
The sum of all arc measures in a circle is (360) degrees. One can apply this here by stating the following:
[tex]80 + 170 + z = 360[/tex]
Simplify,
[tex]80 + 170 + z = 360[/tex]
[tex]250 + z = 360[/tex]
Inverse operations,
[tex]250 + z = 360[/tex]
[tex]z = 110[/tex]
Related Questions
Elena drank 3 liters of water yesterday. Jada drank 3/4 times as much water as elena. Link drank twice as much as Jada. Did jada drink more or less then elena? Explain how you know
Answers
Answer:
Step-by-step explanation:
3\4 bc on a nuberline it would be 3 3\4
I--I----(etc)
so yeah hope i helped
In a particular year, a total of 46,601 students studied in two of the most popular host countries when traveling abroad. If 8483 more students studied in the most popular host country than in the second most popular host country, find how many students studied abroad in each country. There were ____ students who studied abroad in the most popular host country.
Answers
Answer:
31,783.5
Step-by-step explanation:
Half of 46601 = 23300.5
23300.5 + 8483 =31783.5
1. Đường kính của một loại trục máy là một đại lượng ngẫu nhiên có phân phối chuẩn N (μ = 250mm, σ2 = 25mm2). Trục máy được gọi là hợp quy cách nếu đường kính từ 245mm đến 255mm. Cho máy sản xuất 100 trục. Tính xác suất để:
a. Có 50 trục hợp quy cách.
b. Có không quá 80 trục hợp quy cách
Answers
Answer:
please ask in English
Step-by-step explanation:
then I can help
In 10 words or fewer, what is the square root of -9?
Type answer here...
What is the square root of -9
Answers
Answer:
no solution
Step-by-step explanation:
a negative number cannot be square rooted
Answer:
"not possible". no such thing as a negative squared number
Find the lengths of AD, EF, and BC in the trapezoid below.
Answers
We know that,
[tex]EF=\dfrac{AD+BC}{2}[/tex]
which is
[tex]x=\dfrac{x-5+2x-4}{2}[/tex]
Now solve for x,
[tex]x=\dfrac{3x-9}{2}[/tex]
[tex]2x=3x-9[/tex]
[tex]x=9[/tex]
Since x is 9, the lengths are,
[tex]AD=x-5=9-5=\boxed{4}[/tex]
[tex]EF=x=\boxed{9}[/tex]
[tex]BC=2x-4=18-4=\boxed{14}[/tex]
Hope this helps :)
At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 1997, a simple random sample of 100 entering freshmen found that only 10 finished in the bottom third of their high school class. Let p 1 and p 2 be the proportions of all entering freshmen in 1993 and 1997, respectively, who graduated in the bottom third of their high school class. What is a 90% plus four confidence interval for p 1 – p 2?
Answers
Answer:
The 90% confidence interval for the difference of proportions is (0.01775,0.18225).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
p1 -> 1993
20 out of 100, so:
[tex]p_1 = \frac{20}{100} = 0.2[/tex]
[tex]s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
p2 -> 1997
10 out of 100, so:
[tex]p_2 = \frac{10}{100} = 0.1[/tex]
[tex]s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
Distribution of p1 – p2:
[tex]p = p_1 - p_2 = 0.2 - 0.1 = 0.1[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05[/tex]
Confidence interval:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.1 - 1.645*0.05 = 0.01775 [/tex]
The upper bound of the interval is:
[tex]p + zs = 0.1 + 1.645*0.05 = 0.18225 [/tex]
The 90% confidence interval for the difference of proportions is (0.01775,0.18225).
Please help on my hw
Answers
Answer:
Base is 3 centimeter and hight is 12 cent.
Is it true that every whole number is a solution of x > 0? Use complete sentences to explain your reasoning.
Answers
Whole numbers are natural numbers, and natural numbers do not include negatives, decimals, fractions, or roots, so all whole numbers can indeed satisfy the inequality.
Tom and Jerry had a race. Tom started at 0200 running at 4.5km per hour. Jerry started
later at 6:30am running at 6.5km per hour. After five hours, who was ahead, and by how
much (answer in kilometres)
Answers
Answer:
Tom, 10.25
Step-by-step explanation:
Distance covered by Tom=4.5*(4 1/2+5)=81/4=42.75km
Distance covered by Jerry=6.5*(5)=32.5km
Tom is ahead from Jerry by 10.25km
What number x gives maximum value for c(12,x)?
Answers
Answer:
i will say methods try yourself:
How to Determine Maximum Value
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...-x2 + 4x - 2.
How to Determine Maximum ValueIf your equation is in the form ax2 + bx + c, you can find the maximum by using the equation:max = c - (b2 / 4a).The first step is to determine whether your equation gives a maximum or minimum. ...-x2 + 4x - 2.Since the term with the x2 is negative, you know there will be a maximum point.
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plzz follow and make brainlist
To make sky blue Sam uses two drops of blue paint for every eight drops of white paint. He wants to
make a large amount of sky blue paint. If he uses sixteen drops of blue, how many drops of white will he
need?
Answers
Answer:
64
Step-by-step explanation:
The Ratio of Blue to White drops is 2:8
16*4=64,... 16:64 Have a nice day!
in triangle JKL, angle JKL is a right angle, line KM is an altitude, JL=20, ML=4. Find KM
Answers
9514 1404 393
Answer:
KM = 8
Step-by-step explanation:
The ratio of long side to short side is the same for all of the triangles in this geometry:
KM/ML = JM/KM
KM² = ML·JM = 4(20-4) = 64
KM = √64 = 8
The length of KM is 8 units.
Which graph represents the function h(x) = |x – 3|?
On a coordinate plane, an absolute value graph has a vertex at (0, 3).
On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).
On a coordinate plane, an absolute value graph has a vertex at (3, 0).
On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
Answers
Answer:
option 3
Step-by-step explanation:
i know because i got it right.
Solve the formula for the given variable.
-2x - 6 = 4x
Please helppp
Answers
Answer:
s snsnnssjsjjsnsnsjs
es 17 es
What is the slope of the line that passes through the points (-7, -4) and
(-11, -2)? Write your answer in simplest form.
Answers
Answer:
-1/2
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -2 - -4)/( -11 - -7)
=( -2+4)/( -11+7)
= 2 / -4
= -1/2
Please help me with this on the picture
Answers
Answer:
1. 748
2. 901
3. 27
4. 672
Step-by-step explanation:
1. 1011-263=748
2. 653+248=901
3. 1161÷43=27
4. 48×14=672
Third one-43x27
Let a submarine be at a constant depth of 5 km. It is headed in the direction of a lighthouse. If the distance between the submarine and the base of the lighthouse is decreasing at a rate of 24 km/h when the sub is 13 km away from the base, then what is the speed of the submarine
Answers
Answer:
24 km/h
Step-by-step explanation:
Given:
Constant speed of submarine = 24 km/h
Depth under sea = 5 km
Distance of submarine from lighthouse = 13 km
Find:
Speed of the submarine
Computation:
At steady speed, the distance between both the submarine and the lighthouse base decreases at a rate of 24 km/hr.
So, when it is 13 kilometres from its starting point, the speed remains constant at 24 kilometres per hour.
Find the value of x.
X 9 9 7 x = [?]
Answers
The king and queen spent $1500 on decorations for the ball +8 dollars per guest for party favors. The king and queen are charging each guest $12 to enter the dance. How many guests must come to the ball for the king and queen to break even? (you must write an equation and then solve)
Answers
Answer:
375 guests
Step-by-step explanation:
costs: 1500 + 8g
income: 12g
They must be equal
1500+8g = 12g
Subtract 8g from each side
1500 +8g-8g =12g-8g
1500= 4g
Divide by 4
1500/4 = 4g/4
375 = g
write the equation of the graph, y=? SOMEBODY PLEASE HELP
Answers
Answer:
[tex]y=\left(6\right)^{x}\ -3[/tex]
Step-by-step explanation:
A vehicle purchased for $20700 depreciates at a constant rate of 6%.
Determine the approximate value of the vehicle 14 years after purchase.
Round to the nearest whole number.
Question Help: Viden M Message instructor
n Post to forum
Answers
Answer:
$22,000
Step-by-step explanation:
Find the distance between the points (-4, -2) and (-8, 6)
Answers
Answer:
distance=√[(x2-x1)²+(y2-y1)²]
√[{6-(-2)}²+ (-8-(-4))²]
√(64+16)
√[100]
10
Points given
(-4,-2)(-8,-6)Distance:-
[tex]\\ \sf \longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{(-8+4)^2+(6+2)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{(-4)^2+(8)^2}[/tex]
[tex]\\ \sf \longmapsto \sqrt{64+16}[/tex]
[tex]\\ \sf \longmapsto \sqrt{80}[/tex]
[tex]\\ \sf \longmapsto 8.4[/tex]
What are the coordinates of point K?
A (-2,4)
B (-2,-4)
C (2,-4)
D (2, 4)
Answers
Answer:
A
Step-by-step explanation:
I guess that is the answer
Bob wants to replace a glass window in his restaurant. The window is in the shape of a square. Its side lengths are 6 feet. Suppose glass costs $7 for each square foot. How much will the glass cost to replace the window?
Answers
ANSWER: The glass window will cost $252.00 for window replacement.
EXPLANATION:
The area of a square is given by the formula:
s^2
where s is the side length.
If we were to replace the glass window, and it will cost $7.00 per square foot, the total price will be:
FIND AREA OF THE GLASS WINDOW:
6^2 = 36 square feet
$7 per square foot so:
36 x 7 = 252
Therefore it will cost $252.00 to replace the glass window.
what is the simple definition of realnumbers
Answers
Answer:
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion).
22. The ratio in which (4, 5) divides the join of (2, 3)
and (7, 8) is :
(a) 4 : 3
(c) 3 : 2
(b) 5:2
(d) 2:3
Answers
Let the ratio be m:n
(x,y)=(4,5)Points be (x1,y1)=(2,3)(x2,y2)=(7,8)We know
[tex]\boxed{\sf (x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]
[tex]\\ \sf\longmapsto (4,5)=\left(\dfrac{7m+2n}{m+n},\dfrac{8m+3n}{m+n}\right)[/tex]
Now
.[tex]\\ \sf\longmapsto \dfrac{7m+2n}{m+n}=4\dots(1)[/tex]
[tex]\\ \sf\longmapsto \dfrac{8m+3n}{m+n}=5\dots(2)[/tex]
Adding both
[tex]\\ \sf\longmapsto \dfrac{7m+2n+8m+3n}{m+n}=4+5[/tex]
[tex]\\ \sf\longmapsto \dfrac{7m+8m+2n+3n}{m+n}=9[/tex]
[tex]\\ \sf\longmapsto \dfrac{15m+5n}{m+n}=9[/tex]
[tex]\\ \sf\longmapsto 15m+5n=9(m+n)[/tex]
[tex]\\ \sf\longmapsto 15m+5n=9m+9n[/tex]
[tex]\\ \sf\longmapsto 15m-9m=9n-5n[/tex]
[tex]\\ \sf\longmapsto 6m=4n[/tex]
[tex]\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{6}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{3}{2}[/tex]
[tex]\\ \sf\longmapsto m:n=3:2[/tex]
Option B is correct
Find the radius of the circle containing 18
degree arc of a circle whose length is 15 Pi meters
Answers
9514 1404 393
Answer:
150 m
Step-by-step explanation:
The relationship between arc length (s), radius (r), and central angle (θ) is ...
s = rθ
Dividing by θ gives the formula for r:
r = s/θ = (15π m)/(18°(π/180°))
r = 150 m . . . . the radius of the circle
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of
$750. What was the rate charged per hour by each mechanic if the sum of the two rates was $105 per hour?
Answers
Step-by-step explanation:
let's convert the statement into equation..
let the charge of 1st mechanic be x and second be y..
by the question..
10x+5y=750...(i)
x+y=105..(ii)
from eqn(ii)..
x+y=105
or, x=105-y...(iii)
substituting the value of x in eqn (i)..
10x+5y=750
or, 10(105-y)+5y=750
or, 1050-10y+5y=750
or, 1050-750=5y
or, y=300/5
•°• y=60
substituting the value of y in eqn(iii).
x=105-y
or, x=105-60
•°• x= 45..
the rate charged by two mechanics per hour was 60$ and 45$
Find the degree of each polynomial and indicate whether the
polynomial is a monomial, binomial, trinomial, or none of these.
Answers
Answer:
1. Degree = 1, monomial
2. Degree = 2, monomial
3. degree = 2, trinomial
4. Degree = 2, binomial
5. Degree = 2, binomial
Step-by-step explanation:
State two similarities and one difference between the graphs of f(x)= 3^x and g (x)= (1/3) ^x
