Answers
If its an equilateral all angles are equal
Related Questions
Two boxes contained 155 lb of flour. If you take 20 lb from the first and add it to the second, the first box will contain 12/19 of what is now in the second. What amount of flour was originally in each box?
Answers
The first equation describes the original weight in each box.
x+y=155
The second equation describes the weight after the 20 pounds is removed from the first box and added to the second:
[tex]x-20=\frac{12}{19}(y+20)[/tex], because 20 pounds is taken from the first box, x, and added to the second box, y; and that makes the first box equal to 12/19 of the second one.
We now have this system of equations:
[tex] \left \{ {{x+y=155} \atop {x-20=\frac{12}{19}(y+20)}} \right. [/tex]
We will simplify the bottom equation first by multiplying both sides by 19 to cancel the fraction:
[tex]19(x-20)=19(\frac{12}{19})(y+20)[/tex]
We use the distributive property on the left, and cancel the 19 on the right:
[tex]19*x-19*20=12(y+20) \\19x-380=12*y+12*20 \\19x-380=12y+240[/tex]
We will move the 12y to the left side of the equation by subtracting:
19x-380-12y=12y+240-12y
19x-12y-380=240
Now we will cancel the 380 by adding:
19x-12y-380+380=240+380
19x-12y=620
Now our system looks like this:
[tex] \left \{ {{x+y=155} \atop {19x-12y=620}} \right. [/tex]
To eliminate a variable, we want the coefficients to be the same. We will multiply the top equation by 19 to achieve this:
[tex] \left \{ {{19(x+y=155)} \atop {19x-12y=620}} \right. \\ \\ \left \{ {{19x+19y=2945} \atop {19x-12y=620}} \right. [/tex]
Now we will subtract the bottom equation to cancel x:
[tex] \left \{ {{19x+19y=2945} \atop {-(19x-12y=620)}} \right. \\ \\19y--12y=2945-620 \\19y+12y=2325 \\31y=2325[/tex]
Divide both sides by 31:
31y/31=2325/31
y=75
Substituting this back into our original first equation:
x+75=155
Subtract both sides by 75:
x+75-75=155-75
x=80
Answer:
it is 80 and 75
Step-by-step explanation:
I go to RSM and when I answered this answer it said that it was correct
What is the probability of flipping a coin six times in a row and getting three heads and three tails?
Answers
Final answer:
The probability of flipping a coin six times and getting exactly three heads and three tails is calculated using the binomial formula and is found to be 31.25%.
Explanation:
The probability of flipping a coin six times and getting exactly three heads and three tails can be calculated using the binomial probability formula, which is P(x; n, p) = (n choose x) * p^x * (1-p)^(n-x), where 'n' is the number of trials, 'x' is the number of successes, and 'p' is the probability of success on any given trial.
In this instance, since we are flipping a fair coin, the probability 'p' of getting heads (success) on any single flip is 0.5. We want to find the likelihood of getting 'x' = 3 heads out of 'n' = 6 flips. Therefore, the equation becomes:
P(3; 6, 0.5) = (6 choose 3) * 0.5^3 * 0.5^(6-3)
The combination (6 choose 3) calculates the number of ways to choose 3 successes (heads) from 6 trials, which is 20. Plugging these values into the equation gives:
P(3; 6, 0.5) = 20 * (0.5^3) * (0.5^3) = 20 * (0.125) * (0.125) = 20 * 0.015625
This results in a probability of 0.3125, or 31.25%.
Therefore, the chance of flipping a coin six times and getting three heads and three tails is 31.25%.
Find the annual interest rate.
I = $54, P = $900, t = 18 months
Answers
I=P(i)t
54=900(i)(18/12)
i=54/900*(12/18)=4% annually
We have been given that
[tex]I = $54, P = $900, t = 18 \text{ months
}[/tex]
We know the formula,
[tex]I=Prt[/tex]
On substituting the given values, we get
[tex]54=900\cdot r\cdot \frac{18}{12}\\\\r=\frac{54\cdot 12}{900\cdot 18}\\\\r=\frac{1}{25}\\\\r=0.04\\\\r=4\%[/tex]
The annual rate interest is 4%
In a multiple regression analysis what would likely be the culprit of a dramatic increase in the P-value of one of the variables?
Answers
This is called multicollinearity.
If there is a high correlation between your independent variables can lead to problems.
It can lead to increased variance of the coefficient estimates and make the estimates very sensitive to minor changes in the model.
im having trouble with this word problem. A train travels 160 km in the same time that a plane covers 720 km. if the speed of the plane is 20 km per hour less than 5 times the speed of the train, find both speeds. Not sure how to solve.
Answers
The speed of the train is 40 km/h, and the speed of the plane is 180 km/h.
To solve the word problem regarding the speeds of a train and a plane, we first let the speed of the train be x km/h. According to the problem, the plane's speed is 20 km/h less than 5 times the speed of the train, which can be expressed as 5x - 20 km/h. Since they both travel the same amount of time, we can set up an equation based on their speeds and distances traveled:
Time taken by the train = Distance / Speed of the train = 160 / x
Time taken by the plane = Distance / Speed of the plane = 720 / (5x - 20)
Since the time is the same for both:
160 / x = 720 / (5x - 20)
Cross-multiply to solve for x:
160(5x - 20) = 720x
800x - 3200 = 720x
80x = 3200
x = 40
a juice can is shaped like a cylinder ]. it is 12 centimeters wide and 16 centimeters tall. find its volume to the nearest whole number . use 3.14
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To find the volume of the cylinder-shaped juice can, calculate using the formula V = π r² h with the radius being half of the can's width and the given height. The volume is found to be approximately 1804 cm³ when rounded to the nearest whole number.
Calculating the Volume of a Cylinder:
To calculate the volume of a cylinder, you should use the formula V = π r² h. First, we need to determine the radius of the juice can. Since it is given that the can is 12 centimeters wide, that means the diameter is 12 centimeters, and therefore, the radius (r) is half of that, which is 6 centimeters. We also have the height (h) of the can, which is 16 centimeters. Plugging these values into the formula gives us:
V = 3.14 × 6² × 16
Now, we calculate:
V = 3.14 × 36 × 16
V = 3.14 × 576
V = 1803.84 centimeters cubed (cm³)
When we round this to the nearest whole number, the volume of the juice can is approximately 1804 cm³.
What is the solution to this equation? -4x + 2 = 26 A. x = 7 B. x = 6 C. x = -7 D. x = -6
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A. -4*7 +2 = -26 ≠ 26 . . . . not a solution
B. -4*6 +2 = -22 ≠ 26 . . . . not a solution
C. -4*-7 +2 = 30 ≠ 26 . . . . not a solution
D. -4*-6 +2 = 26 = 26 . . . . this is your solution
_____
Of course, you can also solve the equation.
.. -4x +2 = 26
.. -4x = 24 . . . . . . subtract 2 (the term that doesn't contain x)
.. x = -6 . . . . . . . . .divide by -4 (the coefficient of x)
The volume v of a right circular cone of radius r and height h is given by v = 1/3 pi r^2 h. suppose that the height decreases from 20 in to 19.95 in and the radius increases from 4 in to 4.05 in. compare the change in volume of the cone with an approximation of this change using a total differential.
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dV = (π/3)*(2r*h*dr +r^2*dh)
The approximate change in volume is
.. ∆V ≈ (π/3)*(2*4*20*0.05 +4^2*(-.05))
.. = (π/3)*(8 - 0.8) = 7.2(π/3) . . . . . in^3
The actual change in volume is
.. (π/3)*(4.05^2*19.95 -4^2*20) = 7.229875(π/3) . . . . . in^3
The actual change in volume is slightly more than the linear approximation would suggest.
In mathematics, central tendency is the tendency of data values to cluster around some central value. What does a measure of variability tell you about the central tendency of a set of data? Explain.
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Create a pattern with the rule n x 2 + 1
Answers
The pattern that can be created with the rule n x 2 + 1 is 1, 3, 5, 7, 9, 11
Given:
n × 2 + 1
= 2n + 1
where
n = number of terms
when n = 0
2(0) + 1
0 + 1
= 1
when n = 1
2(1) + 1
= 2 + 1
= 3
when n = 2
2(2) + 1
4 + 1
= 5
when n = 3
2(3) + 1
6 + 1
= 7
when n = 4
2(4) + 1
8 + 1
= 9
Therefore, the pattern that can be created with the rule n x 2 + 1 is 1, 3, 5, 7, 9, 11
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The circumference of a circle is 10π cm. What is the Radius of the circle? A) 4 cm B) 5 cm C) 10 cm D) 20 cm
ASAP
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C=2pieR
if C=10pie
then you have to devide 10 by 2
I need help !! This packet is due tomorrow and I have no idea what I’m doing .
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Given: angle M congruent to angle X; angle N congruent to angle Y; YO congruent to NZ.
1. YZ=YO+OZ; reason: segment addition postulate (YZ is made up of YO and OZ).
2. ON=NZ+OZ; reason: segment addition postulate (ON is made up of NZ and OZ).
3. YO=NZ; reason: given.
4. ON=YO+OZ; reason: substitution (since NZ is congruent to YO, we substitute YO for NZ).
5. ON=YZ; reason: substitution (since YZ=YO+OZ, we substitute YZ for YO+OZ).
6. MNO is congruent to XYZ; reason: AAS (we have 2 sides and a non-included angle in each triangle congruent, which is the angle-angle-side theorem).
Answer:
Given is :
∠M≅∠X
∠N≅∠Y
YO≅NZ
We have to prove that ΔMNO≅ΔXYZ
Using segment addition postulate we get YZ=YO+OZ and ON=NZ+OZ and YO=NZ is already given. Using substitution of YO for NZ; we get ON=YO+OZ
Now substituting YZ for YO+OZ we get ON=YZ and also YZ=YO+OZ.
Now applying AAS we get ΔMNO is congruent to ΔXYZ because of angle-angle-side theorem as we have already proved that two sides are congruent and a non-included angle in each triangle is congruent.
Angle D is a vertical angle to F. The measure of D is 53° . What is the measure of F?
Answers
Angle F will have the same measure as angle D, which is 53°, because they are vertical angles and thus congruent.
Explanation:The question asks about the measure of angle F given that it is a vertical angle to angle D, which measures 53°. In geometry, vertical angles (also known as opposite angles) are pairs of non-adjacent angles formed when two lines intersect. Vertical angles are congruent, which means they have the same measure. Therefore, since angle D is 53°, angle F, being its vertical angle, will also have a measure of 53°.
Angle D and angle F are vertical angles, which means they are congruent. If angle D measures 53°, then angle F will also measure 53°. This is because vertical angles are equal in measure.
what is domain of g(x)= square root plus one
Answers
1. if the given function is
[tex]g(x)= \sqrt{x+1} [/tex]
then
2. domain is x+1≥0; ⇒ x≥-1 or x∈[-1;+oo).
answer: [-1;+oo)
What is the area of a figure 36m×21×10×9×8×23×4×7×
Answers
use multiplication to create an equivalent fraction 6/5
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To get an equivalent fraction for 6/5, we must multiply the numerator and the denominator by the SAME number.
Let's multiply by 2.
6 × 2 = 12
5 × 2 = 10
Giving us 12/10.
So, 12/10 is equivalent to 6/5.
You can get more equivalent fractions by multiplying. 18/15, 24/20, 30/25 are all equivalent to 6/5.
Party favors are on sale for $2.40 each. You have $380 to spend on the decorations and gifts, and you have already spent $270 on decorating. Write and solve an inequality to find the number of party favors you can buy.
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Hence, the number of party favors you can buy is $[tex]45[/tex].
What is inequality?
An inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Here given that,
Party favors are on sale for $[tex]2.40[/tex] each. You have $[tex]380[/tex] to spend on the decorations and gifts, and you have already spent $[tex]270[/tex] on decorating.
So,
[tex]380-270=[/tex] $[tex]110[/tex]
To find the number of party favors you can buy, we divide $[tex]110[/tex] by the favors that are on sale for $[tex]2.40[/tex] is
[tex]\frac{110}{2.40}[/tex] = $[tex]45[/tex]
Hence, the number of party favors we can buy is $[tex]45[/tex].
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Elias purchases a home for $38,900. The value of the home, in thousands of dollars, since his purchase is shown in the table. Find an exponential function that models the data. Round numerical values to the nearest hundredth. Let x be the number of years since the purchase. The function f(x) =()x models the data. Use the model to predict the home’s value. After 12 years, the home’s value will be about $thousand. After 35 years, the home’s value will be about $thousand.
Answers
Answer:
f(x)=39.59
(1.09)
After 12 years: 111
After 35 years: 808
The exponential function models the data would be f(x) = 39.59 (1.09). After 12 years, the home’s value will be about $111 thousand and After 35 years, it will be about $808 thousand.
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
Elias purchases a home for $38,900.
Let x be the number of years since the purchase. The function f(x) =()x models the data.
f(x) = 39.59 (1.09)
by using the model to predict the home’s value.
After 12 years, the home’s value will be about $
111 thousand.
After 35 years, the home’s value will be about $
808 thousand.
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if f(x) = 2x+1/x-4, what is the value of f^-1 (3)?
Answers
=> xy - 4y = 2x + 1
=> xy - 2x = 4y + 1
=> x(y - 2) = 4y + 1
=> x = (4y + 1) / (y - 2)
=> f-1(x) = (4x + 1) / (x - 2)
subtitute x = 3
=> f-1(3) = 13
As per the inverse of a function, the value of [tex]f^{-1}(3)[/tex] is 13.
What is the inverse of a function?"An inverse function is defined as a function, which can reverse into another function."
The given function is
[tex]f(x) = \frac{2x+1}{x-4}[/tex]
⇒ [tex]y = f(x) = \frac{2x+1}{x-4}[/tex]
⇒ [tex]xy - 4y = 2x + 1[/tex]
⇒ [tex]xy - 2x = 4y + 1[/tex]
⇒ [tex]x(y - 2)= 4y + 1[/tex]
⇒ [tex]x = \frac{4y+1}{y-2}[/tex]
⇒ [tex]f^{-1}(x) = \frac{4y+1}{y-2}[/tex]
Now, [tex]f^{-1}(3) = \frac{4(3)+1}{3-2} = (12+1) = 13[/tex]
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what is the coefficient of the term 13a in the expression 13a+6b
Answers
The factorization of x2 + 3x – 4 is modeled with algebra tiles.What are the factors of x2 + 3x – 4?
Answers
The factors of x^2 + 3x – 4 are (x + 4) and (x - 1), found by determining the factors of -4 that add up to 3.
Explanation:The factors of x2 + 3x – 4 can be found using the method of factoring quadratics. To factor this quadratic expression, we look for two numbers that multiply to give the constant term (-4) and add to give the coefficient of the middle term (3). Those numbers are 4 and -1, as 4 × -1 = -4 and 4 + (-1) = 3. Therefore, the expression can be factored into (x + 4)(x - 1).
Visualizing with algebra tiles or drawing on the concepts of geometric representation of polynomials, we can understand that this factoring corresponds to breaking down the area of a rectangle (represented by x2 + 3x – 4) into two smaller rectangles whose dimensions give the factors (x + 4) and (x - 1).
What is the fractional notation for 0.097
Answers
[tex]\bf 0.\underline{097}\implies \cfrac{0097}{1\underline{000}}\implies \cfrac{97}{1000}[/tex]
Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. It is found that 10% of the members in that city prefer swimming on weekends and are female, while 55% of the members in that city prefer swimming on weekdays and are female. The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is . NextReset
Answers
.. = 10%/25%
.. = 2/5 = 0.4
Answer: There is a probability that a club member picked randomly is female, given that the person prefers swimming on weekends is 40%.
Step-by-step explanation:
Let E₁ be the event that members prefer swimming on weekends.
Let E₂ be the event that members prefer swimming on weekdays.
Let A be the event that the members are female.
Probability that members prefer swimming on weekends P(E₁) = 25%
Probability that members prefer swimming on weekdays P(E₂)= 75%
Probability that members prefer swimming on weekends and are female PA∩E₁)= 10%
Probability that members prefer swimming on weekdays and are female P(A∩E₂) = 55%
Using Conditional theorem, we will find the probability that a member is female given that the the person prefers swimming on weekends.
[tex]P(A\mid E_1)=\dfrac{P(A\cap E_1)}{P(E_1)}\\\\P(A\mid E_1)=\dfrac{10}{25}\\\\P(A\mid E_1)=0.4\\\\P(A\mid E_1)=0.4\times 100\%=40\%[/tex]
Hence, there is a probability that a club member picked randomly is female, given that the person prefers swimming on weekends is 40%.
Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year, Merle deposits an additional $20,000 that's also compounded semiannually at 10%. At the end of six years, what's the balance in Merle's account?
Answers
For the P=$40,000 deposit,
i=10%/2=5% (semi-annual)
number of periods (6 months), n = 6*2 = 12
Future value (at end of year 6),
F = P(1+i)^n = 40,000(1+0.05)^12 = $71834.253
For the P=20000, deposited at the START of the fourth year, which is the same as the end of the third year.
i=5% (semi-annual
n=2*(6-3), n = 6
Future value (at end of year 6)
F=P(1+i)^n = 20000(1+0.05)^6 = 26801.913
Total amount after 6 years
= 71834.253 + 26801.913
=98636.17 (to the nearest cent.)
Answer:
93,600.16
Step-by-step explanation:
Mrs. Hicks has 35 students in her chemistry class. The ratio of girls to boys is 3:4. How many girls does she have in her class? Let both antecedents represent girls and let both consequence represent total students.
Answers
35/7 = 5
5 * 3 = 15
there are 15 girls
It is 20 minutes after 8:00 what is the correct way to write the time.
Answers
5x+13≥−37. Find the solution set of the inequality.
Answers
The answer is: x≥-10
The solution of the inequality 5x + 13 ≥ − 37 will be greater than or equal to negative 10.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
5x + 13 ≥ − 37
Simplify the inequality for 'x', then we have
5x + 13 ≥ − 37
5x ≥ − 50
x ≥ − 10
The solution of the inequality 5x + 13 ≥ − 37 will be greater than or equal to negative 10.
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complete the steps to solve the polynomial equation x3-21x=-20 according to the rational root theorem, which number is a potential root of the polynomial?
Answers
potential roots are factors of 20 eg 1, 2 ,4 ,5, 10, 20 and the negative values of these
1 looks like a rots . Try it:-
f(1) = 1 - 21 + 20 = -20+20 = 0
Yes 1 is a solution.
2 is not.
Try 4:-
4^3 - 21*4 + 20 = 64 - 84 + 20 = 0
Try 5 No
Try 10 - N0
20 no.
Try -4 - No
-5:-
Yes
Roots are 1, 4 and -5
George has $23 to spend on art supplies he wants to buy markers papers and glue if the total cost of markers and papers is more than $14 which inequality represents the dollar amount P George can spend on glue
Answers
i think that is the correct answer
Factor.x ^2 + 17x + 72
Answers
since we have 1x^2, a and c=1
so factor into (x+b)(x+d)
if we expand, we get
[tex](x+b)(x+d)=x^2+(b+d)x+bd[/tex]
so we need 2 numbers that add to get the middle number and multiply to get the last number
I would factor the last number and see which ones add to the middle one
what 2 numbers multily to get 72 and add to get 17?
hmm, list factor of 72 and add them
1+72=73, nope
2+36=38, nope
3+24=27, nope
4+13=17, yep
so it facotrs to (x+4)(x+13)
Find factors of x^2 and 72, that, when combined, will give you 17x
x ^2 + 17x + 72
x 9
x 8
(x + 9)(x + 8) is your factor.
hope this helps