WY = a = 4
ZY = b = 3
As WYZ is forming a right angle triangle, therefore, we can use pythagorean theorem to find the value of c
a2+b2=c2 (4)2+(3)2=C2 16+9=C2 C2=25
Taking square root on both sides
√c2= √25 c=5
The value of c is 5 units.
The value of c is 5 units
The complete question is an illustration of a right-triangle, where the equation to calculate the value of c is:
c^2 = a^2 + b^2
The equation becomes
c^2 = 3^2 + 4^2
Evaluate the exponents
c^2 = 9 + 16
Evaluate the sum
c^2 = 25
Take the square root of both sides
c =5
Hence, the value of c is 5 units
Read more about right-triangles at:
https://brainly.com/question/2437195
help please this is important
Answer:
i think is e or b
Step-by-step explanation:
[tex]7(b-2)[/tex] Can be interpreted as letter E.
Bill and Ben each have three cards numbered 4,5,6 they each take one of their own cards then they add the two numbers on the cards what is the probability that their answer is an odd number. What is the probability that their answer is a number less than 11.
Answer:
P(odd) = 4/9P(<11) = 2/3Step-by-step explanation:
There are 9 possible outcomes for (Bill, Ben)'s cards:
(4, 4) total 8; (4, 5) total 9; (4, 6) total 10;
(5, 4) total 9; (5, 5) total 10; (5, 6) total 11;
(6, 4) total 10; (6, 5) total 11; (6, 6) total 12.
Of these 9 outcomes, 4 have an odd total; 6 are less than 11.
P(odd) = 4/9
P(sum < 11) = 2/3
The graph of f(x) = x2 is shifted 3 units to the left to obtain the graph of g(x). Which of the following equations best describes g(x)?
g(x) = (x + 3)2
g(x) = x2 − 3
g(x) = x2 + 3
g(x) = (x − 3)2
Answer:
g(x) = (x + 3)^2
Step-by-step explanation:
When a function is shifted to the left or right we can think of a change of units, like a new independent variable is used.
If we have a quadratic function
[tex]f(x)=x^2[/tex]
and the graph is shifted 3 units to the left, then we can think of a new unit u that is:
[tex]g(x)=u^2[/tex]
The vertix of this parabola, that happens for u=0, happens for x=-3, as the graph is shifted 3 units to the left.
Then, the relation between u and x is:
[tex]u-x=0-(-3)=3\\\\u=x+3[/tex]
We can use this relation in the new graph and replace u as:
[tex]g(x)=(x+3)^2[/tex]
Answer:
g(x) = (x + 3)^2
Step-by-step explanation:
I took the practice test as well.
Lisa drew three circles to form a figure. The areas of the circles were in the
ratio 1:4:16. She then shaded some parts of the figure as shown.
What fraction of the figure was shaded?
Answer:
Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]
Step-by-step explanation:
Ratio of the areas of the given circles are 1 : 4 : 16
Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]
= 1 : 2 : 4
If the radius of the smallest circle = x units
Then the radius of the middle circle = 2x units
and the radius of the largest circle = 4x units
Area of the smallest circle = πx²
Area of the middle circle = π(2x)² = 4πx²
Area of the largest circle = π(4x)²= 16πx²
Area of the region which is not shaded in the middle circle = πx²(4 - 1)
= 3πx²
Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded
= 16πx² - 3πx²
= 13πx²
Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]
= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]
= [tex]\frac{13}{16}[/tex]
Using the unit circle, determine the value of cos(-150°).
Explanation:
The identity we'll use is cos(-x) = cos(x) for any value of x.
So cos(-150) = cos(150).
Then locate the angle 150 on the unit circle. The terminal point is [tex]\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)[/tex]
The x coordinate of this terminal point is the value of cos(150).
Answer:
Cos(-150°)=-√3/2
Step-by-step explanation:
-150° is found at the third quadrant so the cost value at third quadrant is negative
Cos(-150°)= -cos(30)=-cos(210)
Cos(-150°)=- (√3/2)
Cos(-150°)=-√3/2
Hope it helps
What is the APPROXIMATE circumference of a circle with a radius of 9 inches? Use 3.14 for π. 28.3 in. 56.5 in. 254.34 in. 113.0 in.
Answer:
56.52 in
Step-by-step explanation:
Circumference Formula: C = 2πr
Since we are given radius r = 9, simply plug it into the formula:
C = 2π(9)
C = 18π
C = 56.5487
Answer:
56.5
Step-by-step explanation:
The circumference is the product of the diameter and PI
P = (9+9)*π = 18*3.14=56.52
8÷2 2/9 −2 11/15 I need help and this is a whole equation I need this ASAP
Answer: (1 and 22/45)
Step-by-step explanation:
I guess that we are working with mixed numbers here, and we have the equation:
(8÷2 2/9) − (2 11/15)
first we solve: 8÷2 = 4.
Now, we can write this as:
(4 + 2/9) - (2 + 11/15)
(4 - 2) + (2/9 - 11/15)
now, 9*5 = 45
15*3 = 45
then we can write the right side as: 2/9 - 11/5 = 10/45 - 33/45 = -23/45
2 - 23/45
But in mixed numbers we also need to work with a positive rational, then we have:
2 - 23/45 = 1 + 1 -23/45 = 1 + 45/45 - 23/45 = 1 + 22/45
then the solution is:
(1 and 22/45)
0.3y+ z y 0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5z, equals, 5.
Answer:
5
Step-by-step explanation:
Substitute the given values and do the arithmetic.
[tex]0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}[/tex]
Factor the expression x2 − 5x − 24. A. (x − 4)(x + 6) B. (x − 3)(x + 8) C. (x + 3)(x − 8) D. (x + 4)(x − 6)
Answer:
C. (x + 3)(x − 8)
Step-by-step explanation:
We need two numbers that add to -5 and multiply to -24.
They are -8 and 3 since -8 + 3 = -5, and -8 * 3 = -24.
x^2 - 5x - 24 = (x - 8)(x + 3)
When would you need to arrange polynomials
How can Ari simplify the following expression? StartFraction 5 Over a minus 3 EndFraction minus 4 divided by 2 + StartFraction 1 Over a minus 3 EndFraction
Answer:
[tex]-\frac{8}{3}[/tex]
Step-by-step explanation:
Given
[tex]\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}[/tex]
Required
Simpify
The very first step is to take LCM of the given expression
[tex]\frac{-10 -4 - 2}{6}[/tex]
Perform arithmetic operations o the numerator
[tex]-\frac{16}{6}[/tex]
Divide the numerator and denominator by 2
[tex]-\frac{16/2}{6/2}[/tex]
[tex]-\frac{8}{3}[/tex]
The expression can't be further simplified;
Hence, [tex]\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}[/tex] = [tex]-\frac{8}{3}[/tex]
The price of a gallon of unleaded gas has dropped to 2.82 today. yesterday's price was 2.89. find the percentage decrease. round to the nearest tenth
Answer :
percentage decrease = {(2.89-2.82)/2.89}x100 = 2.42%
what is the Lcd of fra tions 1_3 and 11 _15
it's 15, since it is divisible by both 15 (15 x 1) and 3 (3 x 5)
Answer:
15
Step-by-step explanation:
Well to find the least common denominator of [tex]\frac{1}{3}[/tex] and [tex]\frac{11}{15}[/tex].
We have to see if 11/15 can be reduced, and by looking at the fraction it can’t be reduced.
So we just have to make 1/3 fraction have the same demimitator as 11/15.
So we just multiply it by 3 to get 15 go the LCD is 15.
Find the length of AB. Leave
your answer in terms of 7.
A
20° AB = [ ? ]
27
1B
Enter
Answer:
AB = 3π
Step-by-step explanation:
See attachment for correct format of question.
Given
From the attachment, we have that
θ = 20°
Radius, r = 27
Required
Find length of AB
AB is an arc and it's length can be calculated using arc length formula.
[tex]Length = \frac{\theta}{360} * 2\pi r[/tex]
Substitute 20 for θ and 27 for r
[tex]Length = \frac{20}{360} * 2\pi *27[/tex]
[tex]Length = \frac{20 * 2\pi * 27}{360}[/tex]
[tex]Length = \frac{1080 \pi}{360}[/tex]
[tex]Length = 3\pi[/tex]
Hence, the length of arc AB is terms of π is 3π
Which point is a reflection of T(-6.5, 1) across the x-axis and the y-axis? A. point U B. point V C. point W D. point X
Hey there! :)
Answer:
Point V.
Step-by-step explanation:
Given the coordinates of T at (-6.5, 1), U represents T before any reflections. (Helps to visualize this better)
Reflecting across the x-axis results in the sign of the y-coordinate changed. Point T after this reflection becomes (-6.5, -1).
Finally, reflecting across the y-axis will change the sign for the x-coordinate.
(-6.5, -1) becomes (6.5, 1). This is represented by point V.
Use synthetic division to solve What is the quotient?
Answer:
[tex]3{x}^{3} + 2x + 5[/tex]
Step-by-step explanation:
Sorry if my notes weren't very clear.
Answer:B
Step-by-step explanation: got it right
In 1994 the city of Anoka had a population of 18,000 people. Since then the population has grown by 5.2% each year. In 1994 the city of Minneapolis had a population of 390,000 and has been decreasing by 2.3% each year. How many more people will be living in Minneapolis compared to Anoka after 25 years?
Answer:
After 25 years, Minneapolis will have 154,062 more residents than Anoka.
Step-by-step explanation:
First, let's write a function for each case.
For Anoka, the initial population is 18,000. The population grows 5.2% or 0.052 each year. Thus:
[tex]A(x)=18000(1.052)^x[/tex], where x represents the amount of years after 1994.
Inversely, for Minneapolis, the population decreases by 2.3% or 0.023. Another way to write this is that it in changes by 1-0.023 or .977 or 97.7%. Thus:
[tex]M(x)=390000(0.977)^x[/tex].
To find how many more people are living in Minneapolis than Anoka after 25 years, simply plug 25 into the functions and then subtract.
In Anoka, after 25 years, there will be:
[tex]A(25)=18000(1.052)^{25}\approx 63924[/tex] residents.
In Minneapolis, after 25 years, there will be:
[tex]M(25)=390000(.977)^{25}\approx217986[/tex] residents.
217986-63924=154,062 residents.
Evaluate the expression x to the power of 2 ⋅x to the power of 1 for x =9 = what
Answer:
729
Step-by-step explanation:
Replace x with 9. [tex]9^{2}[/tex] which is 9*9=81 than [tex]9^{1}[/tex] which is 9*1=9. Simplify 81*9=729.
Questlon 3 of 10
2 Points
The volume of a cube depends on the length of its sides. This can be written
in function notation as (s). What is the best interpretation of (4) = 64?
O A. 4 sides of the cube have a total length of 64 feet.
B. A cube with side lengths of 4 feet has a volume of 64 cubic feet.
C. A cube with a volume of 4 cubic feet has side lengths of 64 feet.
O D. 4 of these cubes will have a total volume of 64 cubic feet.
SUBMIT
Answer:
b)A cube with side lengths of 4 feet has a volume of 64cubic feet
Step-by-step explanation:
volume=length×width×height
=4×4×4
=64feet³
11. What's the approximate area of a segment of a circle with a height 6 m and the length of the chord is 20 m? round to the nearest whole number.
O A. 746 67 m2
O B. 74 6 m2
O C.85 4 m2
O D. 8 54 m2
Answer:
85.4
Step-by-step explanation:
first you have to find the radius before you find the area. so given the height, the radius is 11.3 meters. then, you need to find the area behind the arc, which is 85.4 meters/
Which list orders the numbers from least to greatest
Answer:
3rd option
Step-by-step explanation:
-5 is smaller than -2.
-2 is smaller than 1
1 is smaller than 3
Answer:
the 3 one
Step-by-step explanation:
the larger the negative number,the higher up the number line it goes
so -5 is the greatest negative number,-2 the next, the 1 and 3
ASAP will give brainliest Which of the following formulas would find the surface area of a right cylinder where h is the height, r is the radius, LA is the lateral area, and BA is the base area?
Answer:
A. BA + 2πrh
C. 2πr² + 2πrh
Step-by-step explanation:
height of cylinder = h
Radius of cylinder = r
=>Lateral area of cylinder = LA (THis is the area of the cylinder excluding the area of its circular bases)
L.A of a cylinder = 2πrh
=>Base area = BA (this is the area of both circular bases of the cylinder)
Area of circle = πr²
Area of the 2 circular bases of the cylinder (BA) = 2(πr²) = 2πr²
=>Surface area of a right cylinder = B.A + L.A
= 2πr² + 2πrh
The formulas that can be used to find surface area of a right cylinder from the given options are:
A. BA + 2πrh (note: BA = 2πr², LA = 2πrh)
C. 2πr² + 2πrh
For f(x) = 4x +1 and g(x) = x2 - 5, find (f-8)(x).
Answer:
(f-g)(x) = -x² +4x +6
Step-by-step explanation:
We assume you want to find (f -g)(x).
[tex](f-g)(x)=f(x)-g(x)=(4x+1)-(x^2-5)\\\\\boxed{(f-g)(x)=-x^2+4x+6}[/tex]
Given the following diagram, are OC and OE opposite rays ?
Answer:
No
Step-by-step explanation:
If they were opposite, they would be equal.
But they are not, (on one of the spaces in between them is smaller and one is larger.)
Hope I have helped you, since it seems I haven't helped "other people" the last time :/
Answer:
No
Step-by-step explanation:
find the value of the geometric series
1000 + 1000(1.03) + 1000(1.03)2 + . . . + 1000(1.03)9
Answer:
[tex]\boxed{\sf \ \ \ 11,464 \ \ \ }[/tex]
Step-by-step explanation:
hello
we need to compute the following
[tex]\sum\limits^9_{i=0} {1000(1.03)^i}=1000\dfrac{1.03^{10}-1}{1.03-1}=11463.879...[/tex]
hope this helps
Question
Shelly has 50 shortsin her closet. Shawnie her
Sister borrowed Some of
her shorts. Now shelly has
44 Shosts. How many
Shorts did Shawnie borrow.
A. 50-n = 44
B. 50 t n = 44
c. 50 n = 44
D.44 n =50
Answer:
A.50-n=44, 6 shorts borrowed
Step-by-step explanation:
If her sister borrowed n shorts, that means Shelly now has n less shorts. Since her amount of shorts is 50, then 50-n must equal how many shorts she has now, meaning 50-n=44. Solving the equation we get n=6. This means that her sister borrowed 6 shorts.
Answer:
A
Step-by-step explanation:
50 minus the shorts Shawnie borrowed (n) equal to 44
Need help with question
Answer:
x-6+x
2x-6=14
2x=20
x=10
Answer:
x-6+x
2x-6=14
2x=20
x=10
Step-by-step explanation:
I tried hard... I really hope this helps!
Is the answer correct in this question
Answer:
Yeah, you got the answer right.
Step-by-step explanation:
make h the subject of the formula A=(1/2)ah-(1/2)bh
Answer:
h = A ÷ ½(a - b)
Step-by-step explanation:
A = ½ah - ½bh
A = ½h( a - b)
Divide both sides by the coefficients of h
A ÷ ½(a - b) = h
Dr. Pagels is a mammalogist who studies meadow and common voles. He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices. So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Indicate which of the following is the null hypothesis, and which is the alternate hypothesis.
There food preferences among vole species are independent of one another. _____
There is a relationship between voles and food preference. ______
To test for independence, we need to calculate the Chi-square statistic.
These are the data that Dr. Pagels collected:
meadow voles common voles
apple slices 26 32
peanut butter-oatmeal 35 25
When transferring your answers, make sure you carry them out to AT LEAST SIX SIGNIFICANT FIGURES unless otherwise stated.
_____= expected meadow vole/apple slices
_____= expected common vole/apple slices
_____= expected meadow vole/peanut butter-oatmeal
_____= expected common vole/peanut butter-oatmeal
_____= chi-square value
_____= degrees of freedom (whole number only)
_____= using Statistical Table A (pg 704 of your textbook), what is the chi-square critical value with significance level of alpha=0.05?
_____= will you reject or fail to reject the null hypothesis? (answer either reject or fail to reject)
Answer:
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 28.983051
Chi-square value = χ² = 2.154239
Degree of freedom = 1
Critical value = 3.841
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.
Step-by-step explanation:
He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.
So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Data collected by Dr. Pagels:
meadow voles common voles Row Total
apple slices 26 32 58
peanut butter-oatmeal 35 25 60
Column Total 61 57 118
Where 118 is the grand total.
The expected number is given by
Expected = (row total)×(column total)/grand total
Expected meadow vole/apple slices = 58×61/118
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 58×57/118
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 60×61/118
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 60×57/118
Expected common vole/peanut butter-oatmeal = 28.983051
The chi-square statistic value is given by
χ² = Σ(Observed - Expected)²/Expected
χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051
χ² = 2.154239
The degrees of freedom is given by
DoF = (row - 1)×(col - 1)
For the given case, we have 2 rows and 2 columns
DoF = (2 - 1)×(2 - 1)
DoF = 1
The given level of significance = 0.05
The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be
Critical value = 3.841
Conclusion:
Reject H₀ If χ² > Critical value
We reject the Null hypothesis If the calculated chi-square value is more than the critical value.
For the given case,
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.