Answer:
P( fraction) = 1/2
P ( percent) = 50%
P ( decimal) = .5
Step-by-step explanation:
The possible outcomes on a six sided cube are 1,2,3,4,5,6
Multiples of 2 are 2,4,6
P( multiple of 2) = number of multiples of 2 / total outcomes
= 3/6 = 1/2
P( fraction) = 1/2
P ( percent) = 50%
P ( decimal) = .5
Tell whether the following two triangles can be proven congruent through SAS.
A.Yes, the two triangles are congruent because they’re both right triangles.
B.Yes, the two triangles are congruent because two sides and their included angle are congruent in both triangles.
C.No, the two triangles can only be proven congruent through SSS.
D.No, the two triangles can only be proven congruent through AAA.
Answer:
C.No, the two triangles can only be proven congruent through SSS.
-09
2 1 point
The amount of a radioactive substance y that remains after t years is given by the equation y = a (e)^kt, where a is the initial
amount present and k is the decay constant for the radioactive substance. If a = 100, y = 50, and k = -0.035, find t.
Answer:
19.80
Step-by-step explanation:
Given the equation :
y = a (e)^kt
If a = 100, y = 50, and k = -0.035, find t.
50 = 100(e)^(-0.035t)
50/100 = e^(-0.035t)
0.5 = e^-0.035t
Take the In
In(0.5) = - 0.035t
-0.693147 = - 0.035t
-0.693147 / - 0.035 = t
19.8042 = t
Hence, t = 19.80
Hannah ran 12 laps for 8 days. How many laps did she run in total if she take a break of 1 complete day and 1 half day.
Answer:
The correct answer would be - 9.75 laps (if runs 12 laps in 8 days) or 78 laps (if 12 laps each day for 8 days)
Step-by-step explanation:
Given:
a) Laps covered in 8 days = 12
interval = 1 and half day
total laps = ?
Solution:
To know the total laps with intervals we need to calculate the laps run each day :
= 12/8 laps per day
= 3/2 laps per day
Now multiply the daily run with days
= (3/2)*6.5 (due to 8 - 1.5 = 6,5 days)
= 9.75 laps
B) Given:
Laps covered in 8 days = 12*8 =96
interval = 1 and half day
total laps = ?
Solution:
To know the total laps with intervals we need to calculate the laps run each day :
= 96/8 laps per day
= 12laps per day
Now multiply the daily run with days
= 12*6.5 (due to 8 - 1.5 = 6,5 days)
= 78 laps
The value of y varies with x and z, and y=8, when x=4 and z=10. What is the value of y when x=5 and z=11
How many boxes could you stack safely on a pallet if the pallet is 5 feet deep, five feet across, every box. is 1 x 1 and the maximum safe stacking height is 5 boxes? *
Answer:
25 boxes could be stacked safely on the pallet.
Step-by-step explanation:
To determine how many boxes could you stack safely on a pallet if the pallet is 5 feet deep, five feet across, every box is 1 x 1 and the maximum safe stacking height is 5 boxes, the following calculation should be performed:
Pallet = 5 x 5 = 25 square feet
Box = 1 x 1 = 1 square foot
25/1 = 25
Therefore, 25 boxes could be stacked safely on the pallet.
On a coordinate plane, 2 triangles are shown. The first triangle has points A (negative 1, negative 2), B (negative 4, negative 2), C (negative 1, negative 4). The second triangle has points A prime (1, 2), B prime (4, 2), C prime (1, 4). What rule describes the rotation about the origin? (x, y) → How many degrees was the figure rotated about the origin?
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Answer:
(x, y) ⇒ (-x, -y)180°Step-by-step explanation:
Each image point has its signs reversed from the pre-image point.
(x, y) ⇒ (-x, -y) . . . . describes the rotation
Rotation from the third quadrant (A) to the first quadrant (A') is a rotation of 180°.
Answer:
3rd and 2nd option
Step-by-step explanation:
Parallel lines
What is the segment
Answer:
Step-by-step explanation:
if the smaller side of a rectangle was increased by 7 cm, it would be exactly 55% of the 110 cm longer side. Find the area of the rectangle
Answer:
5886 cm
Step-by-step explanation:
start by finding 55% of 110 which is 60.5. then subtract by 7 and then you get 53.5
then multiply 53.5 by 110 = 5885 cm
Which number produce a rational number when multiples by 1/5
Answer:
-2/3
Step-by-step explanation:
A rational number is a number that can be expressed by a fraction so when y add to fractions it’s a rational number.
HELP ASAP I WILL GIVE BRAINLIST
If sin ∅ = -sqrt{3} OVER 2 and π < ∅ < 3π OVER 2, what are the values of cos ∅ and tan ∅? What is ∅ in degrees and radians? Be sure to show and explain all work.
Step-by-step explanation:
sin ∅ = -(√3)/2
Note that
cos²∅ + sin²∅ = 1
cos²∅ = 1 - sin²∅
= 1 - (-√3 / 2)²
= 1 - (-√3)²/ 2²
= 1 - 3/4
= 1/4
cos²∅ = 1/4
Taking square root of both sides
cos∅ = 1/2
Note that tan∅ = sin∅/cos∅
therefore, tan∅ = -(√3)/2 ÷ 1/2
= -(√3)/2 × 2/1
= -√3
tan∅ = -√3
Since sin∅ = -√3 /2
Then ∅ = -60⁰
The value of ∅ for the given range (third quadrant) is 240⁰.
NB: sin∅ = sin(180-∅)
Also, since 180⁰ is π radians, then ∅ = 4π/3
I believe the answer is 7% but it says round to the nearest tenth of a percent so I am not sure if it is a decimal answer or not. Can someone help me out please?
Answer: 6.1% decrease
Note: It appears that your teacher doesn't want you to type in the percent sign, as that's already covered for you.
=========================================================
Explanation:
The salary decreased by 51500-48355 = 3145
Divide this over the initial salary to get 3145/51500 = 0.0611 which is approximate.
This converts to the percentage 6.11% and that rounds to 6.1%
----------------
As an alternative, you can use the formula method below
A = old value = 51500
B = new value = 48355
C = percent change when going from A to B
C = [ (B-A)/A ] * 100%
C = [ (48355-51500)/51500 ] * 100%
C = (-3145/51500)*100%
C = -0.0611*100%
C = -6.11%
C = -6.1%
The negative C value indicates a percent decrease.
Determine the domain and range of the function
Answer:
Domain: -4 ≤ x ≤ -1
Range: -1 ≤ y ≤ 3
Step-by-step explanation:
Hi there!
The domain is the possible x-values of a function.
The lowest x-value the function contains is -4, and the greatest is -1.
Therefore, the domain is -4 ≤ x ≤ -1.
The range is the possible y-values of a function.
The lowest y-value the function contains is -1, and the greatest is 3.
Therefore the range is -1 ≤ y ≤ 3.
I hope this helps!
Which equation can be simplified to find the inverse of
Answer:
x=y²-7hope it helps.
stay safe healthy and happy...The sum of -4 and the difference of 3 and 1
4b^2+300=0 this is a quadratic equation that I am trying to solve including any solutions with imaginary numbers I will include a picture
Answer:
b= 5i square root of 3
b = -5i square root of 3
Step-by-step explanation:
4b^2+300=0
4b^2 = -300
b^2 = -75
b = square root of -75
b = -75^1/2
^1/2 means square root
b = 25^1/2 * 3^1/2 * i
b= 5i square root of 3
b = -5i square root of 3
the slope of line is
Answer:
there is no file attached
Step-by-step explanation:
The coordinator of the vertices of the triangle are (-8,8),(-8,-4), and
Answer with Step-by-step explanation:
Complete question:
The coordinates of the vertices of the triangle are (-8,8),(-8,-4), and. Consider QR the base of the triangle. The measure of the base is b = 18 units, and the measure of the height is h = units. The area of triangle PQR is square units.
Let
P=(-8,8)
Q=(-8,-4)
QR=b=18 units
Height of triangle, h=Length of PQ
Distance formula
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the formula
Height of triangle, h=[tex]\sqrt{(-8+8)^2+(-4-8)^2}=12units[/tex]
Area of triangle PQR=[tex]\frac{1}{2}\times base\times height[/tex]
Area of triangle PQR=[tex]\frac{1}{2}\times 18\times 12[/tex]
Area of triangle PQR=108 square units
Length of QR=18units
Let the coordinates of R(x,y)
[tex]\sqrt{(x+8)^2+(y+4)^2}=18[/tex]
[tex](x+8)^2+(y+4)^2=324[/tex]
[tex]x^2+64+16x+y^2+8y+16=324[/tex]
[tex]x^2+y^2+16x+8y=324-64-16[/tex]
[tex]x^2+y^2+16x+8y=244[/tex] ......(1)
Using Pythagoras theorem
[tex]H=\sqrt{P^2+B^2}[/tex]
[tex]H=\sqrt{(18)^2+(12)^2}[/tex]
[tex]H=6\sqrt{13}[/tex]units
[tex](6\sqrt{13})^2=(x+8)^2+(y-8)^2[/tex]
[tex]x^2+64+16x+y^2+64-16y=468[/tex]
[tex]x^2+y^2+16x-16y=468-64-64=340[/tex]
[tex]x^2+y^2+16x-16y=340[/tex] .....(2)
Subtract equation (2) from (1) we get
[tex]24y=-96[/tex]
[tex]y=-96/24=-4[/tex]
Using the value of y in equation (1)
[tex]x^2+16x+16-32=244[/tex]
[tex]x^2+16x=244-16+32[/tex]
[tex]x^2+16x=260[/tex]
[tex]x^2+16x-260=0[/tex]
[tex]x^2+26x-10x-260=0[/tex]
[tex]x(x+26)-10(x+26)=0[/tex]
[tex](x+26)(x-10)=0[/tex]
[tex]x=-26, x=10[/tex]
Hence, the coordinate of R (10,-4) or (-26,-4).
class 7th chapter: Simple Equation
The solution of the equation p-1 =20 is -------- *
a) 19
b) 20
c) 21
Answer:
C
Step-by-step explanation:
p=20+1
5. In 2015, Texas led the nation in the percentage of people who lacked health insurance (21.6% of the population). It is known that, nationally, 5% of patients account for 50% of the costs of healthcare. These are the “high cost” patients Assume* that: Being a high cost patient and being uninsured are independent characteristics Insured and uninsured people become “patients” at the same rate The uninsured and high cost patients in Texas are evenly distributed across the state, and that high cost patients are evenly distributed across insured and uninsured patient populations a. What is the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured?
Answer: 0.108
Step-by-step explanation:
Since the probability of the uninsured is 21.6% of the population, then the probability of insured will be:
= 1 - 21.6%
= 78.4%
The probability of high cost patients is 5%. Therefore, the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured will be:
= 5% × 21.6%
= 0.05 × 0.216
= 0.108
7. Draw an equilateral triangle of side 6.5 cm and after locating its circumcentre. Draw its circumcircle. send it with image
Answer:
Step-by-step explanation:
A circumcircle can be referred to as a circumscribed circle to a triangle. The steps to follow is stated below:
i. Since the triangle is equilateral, draw the triangle with sides 6.5 cm
ii. Bisect any of its two sides. The two bisecting lines would intersect at center, O, of the triangle.
iii. With the center and either radius OA, OB or OC, draw a circumscribed circle to the triangle.
The construction is attached to this answer for clarifications.
log2(6x) – log2 (x)-2
Answer:
xlog(64)−xlog(2)−2
Step-by-step explanation:
Simplify 6log(2) by moving 6 inside the logarithm.
log(2^6)x − log(2)x − 2
Raise 2 to the power of 6.
log(64)x − log(2)x − 2
Reorder factors in log(64)x − log(2)x −2.
How long will it take her to travel 72 miles? use the unit ratio to solve the following problem.
Answer:
It will take Noshwa 3 hours and 36 minutes to travel 72 miles.
Step-by-step explanation:
Since Noshwa is completing the bike portion of a triathlon, assuming that she travels 40 miles in 2.5 hours, to determine how long will it take her to travel 72 miles, the following calculation must be performed:
40 = 2.5
72 = X
72 x 2.5 / 50 = X
180/50 = X
3.6 = X
1 = 60
0.6 = X
0.6 x 60 = X
36 = X
Therefore, it will take Noshwa 3 hours and 36 minutes to travel 72 miles.
Calculate the difference and enter it below.
-5 - (-10)
Answer: Simply the expression = 5
Step-by-step explanation:
Simplify = 5
Step-by-step explanation:
-5-(-10) = -5+10 = 5
Therefore the answer of your question is 5.
Mark me as the brainliest answer.
ES
What is the mZACB?
А.
10°
B
O 50°
(4x)
O 90°
O 180°
(7x-20)
С
Done
Intro
Answer:
B
O 50° is the mZACB out of the options
PLEASEEEE HELPP MEEEE I NEED HELPPPPPPP PLELASEEEEEE I REALLY DONT GET THIS AT ALL I JUST WANNA PAST THE 6th grade
suppose △abc≅△xyz. what is the corresponding congruent part for each segment or angle?
Answer:
See below
Step-by-step explanation:
Hi there!
We're given that ΔABC≅ΔXYZ
When two triangles are congruent, their corresponding parts are congruent
Because of that, it means vertex A in ΔABC is congruent to vertex X in ΔXYZ, vertex B is congruent to vertex Y, and vertex C is congruent to vertex Z
Since we don't have a picture of the triangles given, we can use the names of the triangles to find the corresponding parts
so, to find the corresponding congruent angle to <BCA:
B is the first letter in the angle, and the corresponding letter in ΔXYZ is Y.
C is the second letter in the angle, and the corresponding letter is Z.
A is the last letter in the angle, and the corresponding letter is X
so that means <YZX is congruent to <BCA
now let's do the same for <ZYX
Z is the first letter in the angle, and the corresponding letter that's in the same place in ΔABC is C
Y is the second letter in the angle, and the corresponding letter is B
X is the last letter in the angle, and the corresponding letter is A
So that means <CBA is congruent to <ZYX
Now to find corresponding sides:
We can still use the names of the triangles, ΔABC and ΔXYZ
so to find the corresponding side to AB,
in ΔABC, AB makes up the first and second letter of the name of the triangle
The corresponding side must also make up the first and second letter of the name of the triangle
in ΔXYZ, the letters X and Y make up the first and second letter
so that means XY must be corresponding to AB
finally,
we need to find the segment congruent to YZ
in ΔXYZ, YZ makes up the second and third letter of the name of the triangle
the corresponding side must also make up the second and third letter of the name of the triangle
in ΔABC, the letters B and C make up the second and third letter in the triangle
So that means BC must be congruent to YZ
Hope this helps!
A small college has 1200 students and 80 professors. The college is planning to increase enrollment to 1450 students next year. How many new professors should be hired to keep the ratio of students to professors the same
The number of new professors needed to hire to keep the ratio of students and professors the same is 16.66 professors.
Given,
A small college has 1200 students and 80 professors.
The college is planning to increase enrollment to 1450 students next year.
We need to find how many new professors should be hired to keep the
ratio of students to professors the same.
What is meant by proportion?If the two ratios are the same then we called it that they are in proportion.
Example:
4/6 = 10/15
2/3 = 2/3
Find the ratio between the students and professors before the increase in enrollment.
= Number of students / Number of professors
= 1200 / 80
Dividing by 8
= 150 / 10
= 15 / 1
This means one professor for 15 students.
Find the number of students after the increase in enrollment.
= 1450
Find the number of new students enrolled.
= 1450 - 1200
= 250
Since the ratio between the students and professor is 15 students for one professor.
For 250 new students, the number of new professors we need is:
= 250 ÷ 15
= 16.66
This means we need around 16.66 new professors.
Thus the number of new professors needed to hire to keep the ratio of students and professors the same is 16.66 professors.
Learn more about finding the number of students in a college with students and professors relation is given here:
https://brainly.com/question/4773301
#SPJ2
In the diagram, point D is the center of the medium-sized circle that passes through C and E, and it is also the center of the largest circle that passes through A and G. Each of the diameters of the small circles with centers B and F equals the radius of the medium-sized circle with center D. The shaded area is what fraction of the largest circle?Single choice.
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Answer:
5/8
Step-by-step explanation:
The area of the smaller circles is proportional to the square of the ratio of their diameters. The two smallest circles have diameters equal to 1/4 the diameter of the largest circle. Hence their areas are (1/4)^2 = 1/16 of that of the largest circle.
Similarly, the medium circle has a diameter half that of the largest circle, so its area is (1/2)^2 = 1/4 of the are of the largest circle.
The smaller circles subtract 2×1/16 +1/4 = 3/8 of the area of the largest circle. Then the shading is 1-3/8 = 5/8 of the area of the largest circle.
24
4
3+
2+
2
1
-3
-
-1
1
1
2
3
4
-1+
-2 +
-3+
4
What is the slope of the line?
Answer:
1.5/2
Step-by-step explanation:
slope formula = y2-y1/ x2 - x1
point one (2,0)
point 2 (0, 1.5)
you dont really need to subtract anything because the intercepts, so the slope is 1.5/2
(slope or m = 1.5 - 0 / 2 - 0 )
x intercept = value of x when y is 0
y intercept = value of y when x is 0
You have $1000 to invest in two different accounts. To save the money you need for college, you need to average 5.7 percent interest. If the two accounts pay 4 percent and 6 percent interest, how much should you invest in each account?
$550 in 4%, $450 in 6%
$300 in 4%, $700 in 6%
$700 in 4%, $300 in 6%
$150 in 4%, $850 in 6%
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Answer:
$150 in 4%, $850 in 6%
Step-by-step explanation:
The fraction that must earn the highest rate is ...
(5.7 -4.0)/(6.0 -4.0) = 1.7/2 = 0.85
That is 0.85 × $1000 = $850 must be invested at 6%. Matches the last choice.
_____
If you let x represent the amount that must earn 6%, then the total interest earned must be ...
x·6% +(1000 -x)·4% = 1000·5.7%
x(6 -4) = 1000(5.7 -4) . . . . . . multiply by 100, subtract 4·1000
x = 1000·(5.7 -4)/(6 -4) = 850 . . . . as above
