In ΔWXY, W Y ‾ WY is extended through point Y to point Z, m ∠ Y W X = ( 2 x + 12 ) ∘ m∠YWX=(2x+12) ∘ , m ∠ W X Y = ( 2 x + 5 ) ∘ m∠WXY=(2x+5) ∘ , and m ∠ X Y Z = ( 7 x − 1 ) ∘ m∠XYZ=(7x−1) ∘ . What is the value of x ? x?
Applying the exterior angle theorem, the value of x in the given triangle is: x = 6.
How to Apply the Exterior Angle Theorem?The exterior angle theorem states the relationship between the two remote angles in a triangle and the angle measure of the external angle formed by an extended side outside the triangle.
According to the exterior angle theorem:
The measure of the exterior angle = sum of the measures of the two remote angles in a triangle.
Given the following:
Measure of angle YWX = (2x + 12)°
Measure of angle WXY = (2x + 5)°
Measure of angle XYZ = (7x - 1)°
Therefore:
m∠XYZ = m∠YWX + m∠WXY [exterior angle theorem]
Substitute
(7x - 1)° = (2x + 12)° + (2x + 5)°
Solve for x
7x - 1 = 2x + 12 + 2x + 5
Combine like terms
7x - 1 = 4x + 17
7x - 1 + 1 = 4x + 17 + 1 [addition property of equality]
7x = 4x + 18
7x - 4x = 4x + 18 - 4x [subtraction property of equality]
3x = 18
3x/3 = 18/3 [division property of equality]
x = 6
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can you form a triangle with side lengths of 3/8, 1 1/6 and 3/4?
Answer:
No
Step-by-step explanation:
for the sides to form a triangle then the sum of any 2 must be greater than the third.
[tex]\frac{3}{8}[/tex] , 1 [tex]\frac{1}{6}[/tex] , [tex]\frac{3}{4}[/tex] ( change 1 [tex]\frac{1}{6}[/tex] into an imprioper fraction )
[tex]\frac{3}{8}[/tex] , [tex]\frac{7}{6}[/tex] , [tex]\frac{3}{4}[/tex]
rewrite each fraction with a denominator of 24 ( the LCM of 8,6,4 )
This will allow the fractions to be compared more easily.
[tex]\frac{9}{24}[/tex] , [tex]\frac{28}{24}[/tex] , [tex]\frac{18}{24}[/tex]
[tex]\frac{9}{24}[/tex] + [tex]\frac{28}{24}[/tex] = [tex]\frac{37}{24}[/tex] > [tex]\frac{18}{24}[/tex]
[tex]\frac{28}{24}[/tex] + [tex]\frac{18}{24}[/tex] = [tex]\frac{46}{24}[/tex] > [tex]\frac{9}{24}[/tex]
[tex]\frac{9}{24}[/tex] + [tex]\frac{18}{24}[/tex] = [tex]\frac{27}{24}[/tex] < [tex]\frac{28}{24}[/tex]
the condition is not met for the 3 sides , so they do not form a triangle.
Martin Office Supplies paid a $6 dividend last year. The dividend is expected to grow at a constant rate of 7 percent over the
next four years. The required rate of return is 20 percent (this will also serve as the discount rate in this problem). Use Appendix
B for an approximate answer but calculate your final answer using the formula and financial calculator methods.
a. Compute the anticipated value of the dividends for the next four years.
Anticipated Value
D1
D2
D3
D4
The anticipated value of the dividend in:
Year 1 is $45.86
Year 2 is $49.07.
Year 3 is $52.50.
Year 4 is $56.18.
What is the anticipated value of the dividend?The formula that can be used to determine the value of the dividend is:
Value = dividend paid last year x (1 + growth rate^number of years) / (required return - growth rate)
D1 = ($6 x 1.07) / (20% - 7%) = $45.86
D2 = ($6 x 1.07²) / (20% - 7%) = $49.07
D3 = ($6 x 1.07³) / (20% - 7%) = $52.50
D4 = ($6 x 1.07^4) / (20% - 7%) = $56.18
Which shape has only one pair of parallel sides?
Answer:
The answer is C.
Step-by-step explanation:
This is because that shape only has the top and bottom lines which are parallel. The sides are not vertical and leaning outwards, which are not parallel. Leaving that shape to only have one pair of parallel sides.
Answer:
C.
Step-by-step explanation:
A & B both have 2 pairs of parallel lines, so they're not a choice. D has three sides, making it a triangle. Meaning it has no pairs of parallel lines. That leaves us with C. The reason why C is the answer is because, we can see that both top and bottom lines are parallel to each other. However, the left and right lines are not.
I hope this helped!
The figure below is made of 2 rectangular prisms.
What is the volume of this figure?
Answer:
1800.Step-by-step explanation:
First: split the figure into 2:
(5 * 9 * 2)*(5 * 4)Then, solve the first:
5 * 9 * 2= (5 * 9) * 2= 45 * 2= 90Next, solve the second part:
5 * 4= 20Finally, multiply both parts:
90 * 20= 1800.Answer is 1800.
Find the missing angle y. (Image attached)!!
Answer:
111°
Step-by-step explanation:
first to find y we know that y+69=180.1. Which of the following points is the reflection of (8.-5) in the y-axis? A. (8,5) c. (-8,5) B. (-5, 8) D. (-8,-5)
Answer: d. (-8,-5)
1nonly(((((((((((:<3
what is 9.789 in word form?
Answer:
nine and seven hundred eighty-nine thousandths
Step-by-step explanation:
....
Answer:
nine and seven hundred eighty-nine thousandths
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)
Question
Use a two-dimensional representation of the prism, if necessary, to find the area of the entire surface of the prism.
The surface area of the prism is
square units.
Question
Find the area of the figure.
Answer:
162 units^2
Step-by-step explanation:
add all of the areas of the sides
2 ( 3 x 7) + 2 ( 3 x 6) + 2 ( 6 x 7 ) = 162 units^2
If 3 is subtracted from 5 times a number, the result is the same as 9 added to the number. Find the number.
A.)4
B.)-4
C.)3
D.)-3
Answer:
c).3
Step-by-step explanation:
let the number be x
5x-3=x+9
collect like terms
5x-x=9+3
4x= 12
divide both sides by 4
x=3
the number is 3
What is 9 x (8 + 5) - 3?
Also please read the comments, please.
Answer:
114
Step-by-step explanation:
following order of operations, we have to do parenthesis first
9 x (8+5) - 3=
9 x 13 - 3
since we have no exponents, we multiply next
117-3
finally, we subtract and get our answer
114
Answer:
The answer is 114
Step-by-step explanation:
search up "Calculator" and type in this problem, and thats how you get 114
lol basically I used a calculator so that's how ik its correct
can some one tell me answer
Answer:
d = 3.4
Step-by-step explanation:
d × 5 = 17
Divide by 5 from both sides,
[tex]\frac{d(5)}{5}=\frac{17}{5}[/tex]
d = 3.4
Change. 2.75km to metres
Answer:
2,750 meters
Step-by-step explanation:
1000 meters = 1 kilometer
M = 2.75 km (M = variable for unknown amount of meters)
Cross multiply: 1000 * 2.75 km = 1 * M
2.75 km * 1000 m = 2750 meters
A fan with a resistance of 20 Ω is connected to a power supply. The current flowing through the circuit is 2.5 A.
What is the voltage of the power supply?
(1 point)
8.0 V
8.0 V
22.5 V
22.5 V
17.5 V
17.5 V
50.0 V
Answer: 50V
Step-by-step explanation:
Use Ohm's Law, which states that the voltage is proprtional to the current. The proprtionality constant is the resistance:
[tex]V=IR[/tex]
We are given the resistance in Ohms, and the current in Amps. Therefore:
[tex]V=(2.5)(20)=50V[/tex]
NO LINKS!! Please help with this problem
Answer:
EI = 30
GH = 30
RS = 10
Step-by-step explanation:
Given: PQRST ~ HGFEI
From inspection of the diagram, the corresponding sides are:
RS ~ FE
ST ~ EI
TP ~ IH
QP ~ GH
QR ~ GF
The only pair of sides that both have side lengths are QR and FG. Therefore, we can use these to work out the scale factor of dilation.
QR = 8 and GF = 20
⇒ GF/QR = 20/8 = 2.5
Therefore, HGFEI is an enlargement of PQRST by a scale factor of 2.5
If ST = 12,
⇒ EI = 12 x 2.5 = 30
If QP = 12,
⇒ GH = 12 x 2.5 = 30
If EF = 25,
⇒ RS = 25 / 2.5 = 10
If IH = 15,
⇒ TP = 15 / 2.5 = 6
Answer:
See below ~
Step-by-step explanation:
As they are similar, find the scale factor.
QR ~ GF8 : 202 : 5Finding EI
ST ~ EIST : EI = 2 : 5EI = 5 x 12 / 2 EI = 30Finding GH
QP : GH = 2 : 5GH = 5 x 12 / 2GH = 30Finding RS
RS : FE = 2 : 5RS = 2 x 25 / 5RS = 101. what are "odds for" stopping on a 2, 3, 7, 10?
2. What are the "odds against" stopping on a number less than 5.
NO LINKS!!
Answer:
1) 1/2, 2) 2Step-by-step explanation:
#1Number of total outcomes is 12 (numbers 1 through 12)Favorable outcomes are 2, 3, 7, 10, total number is 4Unfavorable outcomes are the rest of numbers, total number is 8The 'odds' is
Odds for (2, 3, 7, 10) = 4/8 = 1/2#2Number of total outcomes is 12 Number of favorable outcomes is 4 (numbers less than 5)Number of unfovorable outcomes is 8 (the rest of numbers)The 'odds against' is
Odds against (< 5) = 8/4 = 2/1 or 2Answer:
Question 1"Odds for" - Number of successes : Number of failures
Number of success = 2, 3, 7 or 10
Number of failures = 1, 4, 5, 6, 8, 9, 11, 12
⇒ odds for stopping on 2, 3, 7 or 10 = 4/8 = 1/2
Question 2"Odds against" - Number of failures : Number of successes
Number of success = 1, 2, 3, 4
Number of failures = 5, 6, 7, 8, 9, 10, 11, 12
⇒ odds against stopping on 1, 2, 3 or 4 = 8/4 = 2
The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8.9 cm.
a. Find the probability that an individual distance is greater than 212.50 cm
b. Find the probability that the mean for 25 randomly selected distances is greater than 201.00 cm
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
a. The probability is
(Round to four decimal places as needed)
b. The probability is I
(Round to four decimal places as needed.)
c. Choose the correct answer below.
O A The normal distribution can be used because the mean is large.
B. The normal distribution can be used because the finite population correction factor is small.
OC. The normal distribution can be used because the probability is less than 0.5
OD. The normal distribution can be used because the original population has a normal distribution
Answer:
I am not sure if you're accustomed to using a z-score and table of probabilities or technology, so I will answer using both!
a) Since you're choosing one person from the population, you will use the mean and standard deviation from the population. z= (210.9-197.5)/8.6 = 1.56 Using a table of normal probabilities,
P(x>210.9)= 1-P(z<1.56)= 1- 0.9406=0.0594
Using technology: normalcdf(210.9, 1E99, 197.5, 8.6)=0.0596
b) Since you're calculating the population for a sample to occur, you need to get a mean of the sampling distribution and standard deviation of the sampling distribution.
Meanpop=Meansampling dist.=197.5
St. Devsampling dist.= Stdpopulation/√n = 8.6/√15 = 2.22
Using technology, P(X>196.20)= normalcdf( 196.20, 1E99, 197.5, 2.22) = 0.7209
c) You only have to worry about the sample size in a sampling distribution if you either do not know the shape of the distribution of the population or if the distribution of the population is not normally distributed. Since this population is normally distributed (as stated in the given information), then your sample size does not have to be greater than 30.
Step-by-step explanation:
At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 26 minutes and a standard deviation of 4 minutes. Using the empirical rule, determine the interval of minutes that the middle 95% of customers have to wait.
The middle 95% of customers have to wait for 18 to 34 minutes at the resturant.
What is the empirical rule?The empirical rule states that for a normal distribution. 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean
Given a mean of 26 minutes and a standard deviation of 4 minutes. Hence:
95% are within 2 standard deviations = 26 ± 2(4) = (18, 34)
The middle 95% of customers have to wait for 18 to 34 minutes at the resturant.
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what is the digit 9 in this number 195,487
Answer:
90,000 (ninty thousand)
Step-by-step explanation:
hope this helps:)
Answer:
The number that is in the ten thousands is 9, whose value is 90,000
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Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
Which statements are correct? Check all the apply.
Variable d is the independent variable.
Variable h is the independent variable.
The number of hours worked causes a change in the number of dollars earned.
Variable d is the dependent.
The number of dollars earned causes a change in the number of hours worked.
Variable h is the dependent variable.
The more hours are worked, the fewer dollars that are earned.
Answer:
Step-by-step explanation:
1) wrong
2) Right
3) Right
4) Right
5) Wrong
6) Wrong
7) Wrong
Susan is six years older than
Beth. In four years, Susan will
be twice as old as Beth. How
old is Susan now?
Answer:Susan is eight years now
Step-by-step explanation:
Asappp!!!!! What is the measure of line segment AC
Which exponential function has a growth factor of 5?
f(x) = 2(5x)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It goes through (negative 1, 2) and crosses the y-axis at (0, 0.5).
f(x) = 0.5(2x)
A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries one-eighth, one-fourth, one-half, 1, 2.
An exponential function can represent growth or decay, and the function that has a growth factor of 5 is f(x) =2(5^x)
How to determine the exponential function?An exponential function is represented as:
f(x) = ab^x
Where b represents the growth factor
From the list of options, we have:
f(x) = 2(5^x) and f(x) = 0.5(2^x)
This means that:
b = 5 for f(x) = 2(5^x)
And b = 0.2 for f(x) = 0.5(2^x)
Hence, the function that has a growth factor of 5 is f(x) =2(5^x)
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Answer:
A.
f(x) = 2(5x)
Step-by-step explanation:
Hey umm i just need help thx if u do
Answer:
900in goes in 25 yd
3960ft goes in 0.75 mi
360in goes in 30 ft
10yd goes in 30 ft
75ft goes in 25 yd
1320yd goes in 0.75 mi
Step-by-step explanation:
[tex]\frac{1yd}{36in} =900in[/tex]
900 · 1 = 900
900/36 = 25 yd
______________
[tex]\frac{1mi}{5280ft} =3690ft[/tex]
3690 · 1 = 3690
3690/5280 = 0.75 mi
______________
[tex]\frac{1ft}{12in} =360in[/tex]
360 · 1 = 360
360/12 = 30 ft
______________
[tex]\frac{3ft}{1yd} =10yd[/tex]
3 · 10 = 30
30/1 = 30 ft
______________
[tex]\frac{1yd}{3ft} =75ft[/tex]
75 · 1 = 75
75/3 = 25 yd
______________
[tex]\frac{3ft}{1yd} =1320yd[/tex]
3 · 1320 = 3960
3960/1 = 3960ft
[tex]\frac{1mi}{5280ft} =3960ft[/tex]
3960 · 1 = 3960
3960/5280 = 0.75 mi
______________
hope this helps!
Write an expression to represent the area of each figure
Answer:
A = 4x² + 3x - 1
Step-by-step explanation:
Area of trapezoid = (a + b)(h)/2
a = 5x - 4b = 3x + 2h = x + 1A = [((5x - 4) + (3x + 2)) · (x + 1)] ÷ 2
A = [(8x - 2) · (x + 1)] ÷ 2
A = (8x² + 8x - 2x - 2) ÷ 2
A = 4x² + 4x - x - 1
A = 4x² + 3x - 1
Hope this helps and God bless!
To setup an equation for the area of the figure:
⇒ must know the formula for the area of a trapezoid
[tex]\frac{1}{2}*(base1+base2)*height[/tex]
base 1 --> 5x - 4base 2 --> 3x + 2height --> x + 1Now's lets set up the equation:
[tex]Area =\frac{1}{2}(5x-4+3x+2)(x+1) =\frac{1}{2}(8x-2)(x+1)=\frac{1}{2}*(8x^2+8x-2x-2)\\Area = \frac{1}{2} *(8x^2+6x-2)\\Area = 4x^2+3x-1[/tex]
Thus the equation is [tex]4x^2+3x-1[/tex]
Answer: [tex]4x^2+3x-1[/tex]
Hope that helps!
Log(x^2)+log(x^3)/log(70x)=4
Answer:
x=24010000
Step-by-step explanation:
Log(x^2)+log(x^3)=log(70^4x^4)
Log(x^2x^3)=log(70^4x^4)
x^2x^3=70^4x^4
x^5=70^4x^4
x=70^4=24010000
Question 4 on math!
Please help me 15 points
Answer:
A, B, C, or D.
Step-by-step explanation:
Use the quadratic formula to find both solutions to the quadratic equation given below.
x^2 + 6x = 27
A. x = -9
B. x = -6+√27/2
C. x = -6-√27/2
D. x = 3
E. x = -1
F. x = 3-√-7/2
A. x = -9
__________
D. x = 3
__________
The ratio of the circumferences of two circles is 2:3. If the large circle has a radius of 39cm what is the radius of the small circle
Mrs. Galicia is creating a bunny farm. The farm starts with 820 bunnies and is growing at a rate of 20.75% per month. How many months will it take for the farm to triple in size? **Must solve using log/ln method**
The number of months it would take the bunny farm to triple in size is 5.3 months.
When would the bunny farm be triple its size?The formula that can be used to determine the number of months it would take Mrs. Galicia's bunnies to triple in size is:
Number of years = (In FV / PV) / r
FV = future population of the bunniesPV = present population of the bunniesr = rate of growthFV / PV = 3IN(3) / 0.2075 = 5.3 months
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