A bag has 2 yellow marbles and 16 red marbles. Half of the red marbles are made of plastic. A marble is selected at random from the ball What is the probability that it is a red, plastic marble? Write your answer as a fraction in simplest form.
Answer:
4/9
Step-by-step explanation:
2+16 = 18 total marbles
16 ÷ 2= 8 plastic marbles
Since there are 18 total marbles and 8 plastic red marbles we can say that there is a probability of 8/18.
8/18 in simplest form is 4/9.
Hope this helps! Brainliest?
Find the equation of a sphere if one of its diameters has endpoints: (-14. -3, -6) and (-4, 7, 4) Note that you must move everything to the left hand side of the equation and that we desire the coefficients of the quadratic terms to be 1.
Answer:
[tex]x^2+y^2+z^2-18x-4y+2z-21=0[/tex]
Step-by-step explanation:
From the question we are told that:
Diameters has endpoints: [tex](-14. -3, -6) & (-4, 7, 4)[/tex]
Generally the equation for Center of The sphere is mathematically given by
[tex]C=(\frac{-14+(-4)}{2},\frac{-3+(7)}{2},\frac{-6+(4)}{2})[/tex]
[tex]C=(9,2,-1)[/tex]
Generally the equation for Radius of the sphere is mathematically given by
[tex]R=\sqrt{(9-2)^2+(2-9)^2+(-1-2)^2}[/tex]
[tex]R=\sqrt{107}[/tex]
Therefore the Equation of the Sphere is
[tex](x-9)^2+(y-2)^2+(z+1)^2=107[/tex]
[tex](x^2-18x+81)+(y^2-4y+4+(z^2+2z+1))=107[/tex]
[tex]x^2+y^2+z^2-18x-4y+2z-21=0[/tex]
What is the surface area and volume of the sphere shown below?
Your response should show all necessary calculations and diagrams.
Answer:
ur mom
Step-by-step explanation:
doin doin
name an outcome that has a probability between 0.5 and 1
Answer:
a coin flip
Step-by-step explanation:
The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero.
a rope of length 18 m is used to form a sector of a circle of radius 3.5 m on a school field. What is the size of the angle of the sector?
Answer:
Perimeter of the sector = 2r + length of arc= 2(3.5)+11= 7+11=18 meters exactly the length of the rope.
Step-by-step explanation:
The perimeter of the sector is equivalent to the length of the rope which is 18 meters
Perimeter of the sector= 2 x radius + length of the arc
But length of arc= radius x central angle in radian
18= 2(3.5)+ 3.5(central angle in radians)
18=7+3.5 (central angle in radians)
18–7=3.5(central angle)
11=3.5(central angle)
central angle =11/3.5=3.14 radians or pi radians
Angle in degrees =pi radians x 360 degrees/2pi radians =pi radians x 180 degrees/pi radians = 180 degrees
Therefore the central angle = 180 degrees because pi radians is half of 2pi radians which is half of 360 degrees
Notes: This sector shape is a semicircle because the central angle is 180 degrees
Check: Length of Arc for semicircle =3.5(pi radians)=11 meters
Perimeter of the sector = 2r + length of arc= 2(3.5)+11= 7+11=18 meters exactly the length of the rope.
The following hypothetical data represent a sample of the annual numbers of home fires started by candles for the past several years.
5640, 5090, 6590, 6380, 7165, 8440, 9980
The population has a standard deviation equal to 1210. Assuming that the data is from a distribution that is approximately normal, construct a 90 % confidence interval for the mean number of home fires started by candles each year
Answer:
(6290.678 ; 7790.742)
Step-by-step explanation:
Given the data :
5640, 5090, 6590, 6380, 7165, 8440, 9980
The sample mean, xbar = Σx / n = 49285 / 7 = 7040.71
The 90% confidence interval :
Xbar ± Margin of error
Margin of Error = Zcritical * σ/√n
Since the σ is known, we use the z- distribution
Zcritical at 90% confidence = 1.64
Hence,
Margin of Error = 1.64 * 1210/√7
Margin of Error = 750.032
90% confidence interval is :
7040.71 ± 750.032
Lower boundary = 7040.71 - 750.032 = 6290.678
Upper boundary = 7040.71 + 750.032 = 7790.742
(6290.678 ; 7790.742)
one half plus one third
Answer:
0.83333333333
Step-by-step explanation:
One-half plus one-third equals 5/6 or 0.8333.
Given that:
Expression: 1/2 + 1/3
To add one-half (1/2) and one-third (1/3), to find a common denominator and then add the fractions together.
The least common denominator (LCD) of 2 and 3 is 6. To convert the fractions to have a common denominator of 6, multiply the numerator and denominator of 1/2 by 3, and the numerator and denominator of 1/3 by 2:
1/2 × 3/3 = 3/6
1/3 × 2/2 = 2/6
Now that the fractions have a common denominator of 6, add them:
3/6 + 2/6 = 5/6
3/6 + 2/6 = 0.8333
Therefore, one-half plus one-third equals 5/6 or 0.8333.
Learn more about Divisor here:
https://brainly.com/question/30925934
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The probability that he or she is a female given that the person is married
Answer:
3 /4
Step-by-step explanation:
The probability that selected person is a female Given she is married :
This is a conditional probability in the form ; A given B
P(A|B) = P(AnB) / P(B)
Let, Female = F ; Married = M
P(F|M) = P(FnM) / P(M) = 150 / 200 = 3 / 4
Charlie (c) has 75 more pencils than Kate (k). Together, they have 135 pencils. How many pencils does Kate have? *
Answer:
60
Step-by-step explanation:
135-75 = 60
HOPE IT HELPS
Help, please
no links
9514 1404 393
Answer:
4/10 and 10/25
Step-by-step explanation:
If each of the ratios reduces to the same lowest terms, then they are a proportion. All are in lowest terms except the first pair. Reducing those gives ...
4/10 = 10/25 = 2/5
4/10 and 10/25 form a proportion
__
All of the other pairs are pairs of different ratios, so do not form a proportion.
Find the perimeter of the figure.
Answer:
below
Step-by-step explanation:
p = 2( a + b)
p = 2(24 +16)
p =80 in
p semicircle
=πr
= 3.142 *8
= 25.136
p of figure
p =80 +25.136
p=105.136 in
Find the area of the figure.
1 in
1 in
5 in
3 in
3 in
PLEASE HELP ITS URGENT ITS DUE BY 8
Answer:
It is 4
Step-by-step explanation:
1 times 1 for square
3 times 3 then divide by 2 = 3
add together
4
Answer:
a = 5.5 in²
Step-by-step explanation:
square
a = lw
a = 1 * 1
a = 1
Triangle
a = (1/2)bh
a = (1/2) * 3 * 3
a = 4.5
combined figure
a = 1 + 4.5
a = 5.5 in²
What is the answer to this
Answer:
x = 25
Step-by-step explanation:
3x-15 = 2x+10
x-15 = 10
x = 25
Answer:
x = 25 degree
Step-by-step explanation:
3x - 15 = 2x + 10 (their relation will be alternate interior angles if they [tex]l_{1}[/tex] and [tex]l_{2}[/tex] are parallel)
3x - 2x = 10 + 15
x = 25 degree
Please help!
Geometry
10 points!
Which number line represents the solution set for the inequality -4(x + 3) S-2 – 2x?
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
4 5 6 7
+
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2:-1 0 1
2.
+
6
+
7
3 4
01
5
02
Answer:
the answer is the alphabet A at the picture
The circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A
Inequality expressionGiven the inequality expression
-4(x+3) <= -2-2x
Expand the inequality
-4x - 12 <= -2-2x
Collect the like terms
-4x + 2x <= -2+12
-2x <= 10
Divide both sides by -2
-2x/-2 >= 10/-2
x >= -5
For the number line, the circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A.
Learn more on inequality expression: https://brainly.com/question/24372553
Find the complement of the set given that
U = {x | x is in I and −3 ≤ x ≤ 7}.
(Enter your answers as a comma-separated list.)
{−1, 1, 3, 5, 7}
2. How many miles the trucks will have to drive for the costs of the trucks to be equal?
Step-by-step explanation:
kayo na po bahala mag calculate
In the accompanying diagram, ABC is isosceles, BC is extended to D. AB = AC. and M
Answer:
m∠ACD = 130
Step-by-step explanation:
If ABC is an isosceles, AB = AC and m∠A = 80°, then m∠B and m∠C is equal to 50°.
This is because angles in a triangle adds up to 180°.
180° - 80° = 100°/2 = 50°
∴ m∠ACD = 130°, this is because the interior opposite angles in a triangle is supplementary to the opposite exterior angle:
50° + 80° = 130°
Or
Angles on a straight line adds up to 180°.
180° - 50° = 130°
What is the answer to this?
Evaluate the function.
f(x) = 2x2
Find f(-3)
Can anybody answer this?
Answer:
18
Step-by-step explanation:
f(x) = 2x^2
Let x = -3
f(-3) = 2 * (-3)^2
Exponents first
f(-3)=2 *9
f(3) = 18
Answer:
f ( - 3 ) = 18
Step-by-step explanation:
f ( x ) = 2x²
Find f ( - 3)
let , x = - 3
lf ( - 3 ) = 2 ( -3 )²
f ( - 3 ) = 2 × ( - 3 )²
Evaluate the power
f ( -3) = 2 × 9
multiply the numbers
f ( - 3 ) = 18
If you leave Louisville Ky at 8:15 am and arrive in Chicago at 2:25 pm how long did you travel ?
Answer: 6 hours and 10 minutes
Step-by-step explanation:
Three lines intersect at point P, as shown in the diagram below. Find the measure of
Answer:
VPQ = 83°
Step-by-step explanation:
You can draw a circle around the point P, and a circle have 360°, so it means that the sum off all the angles have ro be 360°. Some of these angles have the same measure, because they're formed by the same lines segments, they are:
SPR = UPV; TPU = RPQ; TPS = VPQ
360 - SPR - UPV - RPQ - TPU = VPQ + TPS
As some of they are equal, we can just multiply they by 2:
360 - 2×SPR - 2×RPQ = 2× VPQ
360 - 2×35 - 2×62 = 2×VPQ
360 - 70 - 124 = 2×VPQ
2 VPQ = 166
VPQ = 166/2
VPQ = 83°
Get brainiest if right!!!
10points if right!!
Answer:
the next three terms, 0.075,0.0375,0.01875 (common ratio 0.5)
the formula is 0.3*0.5^n-1
the formula for finding the nth term of a geometric sequence preset would be
a*r^n-1
a is first term
r is common ratio
Step-by-step explanation:
4. What is the product of (3x - 1)(x + 4)?
HELP PLEASE RIGHT NOT SHOW YOURE WORK!!!!!
[tex]3 {x}^{2} + 11x - 4[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex](3x - 1)(x + 4) \\ \\ = 3x(x + 4) - 1(x + 4) \\ \\ = 3 {x}^{2} + 12x - x - 4 \\ \\ = 3 {x}^{2} + 11x - 4[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
How far does a train travel in 12 hours at 115 miles per hour?
1,509 mi
1,265 mi
1,380 mi
Answer:1380
Step-by-step explanation: 12x115
Answer:
1,380
Step-by-step explanation: 12 times 115 gives you the product of 1,380. :)
Hope this is helpful
PLEASSSSSSSSSSSEEEEEEEE HELPPP IM BEGGING SOMEONE PLEASEEEEEEEE PLEASEEEEEEEEEEE HELPPPP
Answer:
20 degree
Step-by-step explanation:
x + x + 70 = 110 degree (sum of two opposite interior angle equal to the exterior angle formed)
2x = 110 - 70
x = 40/2
x = 20 degree
What is the production matrix?
Answer:
[tex]\left[\begin{array}{ccc}3\\3.8\end{array}\right][/tex]
Step-by-step explanation:
Here we want to compute the product of two matrices, one 2x2, and other 2x1.
[tex]\left[\begin{array}{ccc}0.3&0.3\\0.35&0.4\end{array}\right]*\left[\begin{array}{ccc}4\\6\end{array}\right][/tex]
Remember that in the product, we multiply the rows of the first one by the columns of the second one, then the product is just:
[tex]\left[\begin{array}{ccc}0.3&0.3\\0.35&0.4\end{array}\right]*\left[\begin{array}{ccc}4\\6\end{array}\right] = \left[\begin{array}{ccc}0.3*4 + 0.3*6\\0.35*4 + 0.4*6\end{array}\right] = \left[\begin{array}{ccc}3\\3.8\end{array}\right][/tex]
City A had a population of 10000 in the year 1990. City A’s population grows at a constant rate of 3% per year. City B has a population that is growing exponentially. In the year 2000, there were half as many people in B as in A. In the year 2010, the population of A was 20% more than the population of B.
When will the populations be equal? Give your answer in years after 1990.
Answer:
City A and city B will have equal population 25years after 1990
Step-by-step explanation:
Given
Let
[tex]t \to[/tex] years after 1990
[tex]A_t \to[/tex] population function of city A
[tex]B_t \to[/tex] population function of city B
City A
[tex]A_0 = 10000[/tex] ---- initial population (1990)
[tex]r_A =3\%[/tex] --- rate
City B
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex] ----- t = 10 in 2000
[tex]A_{20} = B_{20} * (1 + 20\%)[/tex] ---- t = 20 in 2010
Required
When they will have the same population
Both functions follow exponential function.
So, we have:
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
Calculate the population of city A in 2000 (t = 10)
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_{10} = 10000 * (1 + 3\%)^{10}[/tex]
[tex]A_{10} = 10000 * (1 + 0.03)^{10}[/tex]
[tex]A_{10} = 10000 * (1.03)^{10}[/tex]
[tex]A_{10} = 13439.16[/tex]
Calculate the population of city A in 2010 (t = 20)
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_{20} = 10000 * (1 + 3\%)^{20}[/tex]
[tex]A_{20} = 10000 * (1 + 0.03)^{20}[/tex]
[tex]A_{20} = 10000 * (1.03)^{20}[/tex]
[tex]A_{20} = 18061.11[/tex]
From the question, we have:
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex] and [tex]A_{20} = B_{20} * (1 + 20\%)[/tex]
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex]
[tex]B_{10} = \frac{1}{2} * 13439.16[/tex]
[tex]B_{10} = 6719.58[/tex]
[tex]A_{20} = B_{20} * (1 + 20\%)[/tex]
[tex]18061.11 = B_{20} * (1 + 20\%)[/tex]
[tex]18061.11 = B_{20} * (1 + 0.20)[/tex]
[tex]18061.11 = B_{20} * (1.20)[/tex]
Solve for B20
[tex]B_{20} = \frac{18061.11}{1.20}[/tex]
[tex]B_{20} = 15050.93[/tex]
[tex]B_{10} = 6719.58[/tex] and [tex]B_{20} = 15050.93[/tex] can be used to determine the function of city B
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
For: [tex]B_{10} = 6719.58[/tex]
We have:
[tex]B_{10} = B_0 * (1 + r_B)^{10}[/tex]
[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
For: [tex]B_{20} = 15050.93[/tex]
We have:
[tex]B_{20} = B_0 * (1 + r_B)^{20}[/tex]
[tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex]
Divide [tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex] by [tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
[tex]\frac{B_0 * (1 + r_B)^{20}}{B_0 * (1 + r_B)^{10}} = \frac{15050.93}{6719.58}[/tex]
[tex]\frac{(1 + r_B)^{20}}{(1 + r_B)^{10}} = 2.2399[/tex]
Apply law of indices
[tex](1 + r_B)^{20-10} = 2.2399[/tex]
[tex](1 + r_B)^{10} = 2.2399[/tex] --- (1)
Take 10th root of both sides
[tex]1 + r_B = \sqrt[10]{2.2399}[/tex]
[tex]1 + r_B = 1.08[/tex]
Subtract 1 from both sides
[tex]r_B = 0.08[/tex]
To calculate [tex]B_0[/tex], we have:
[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
Recall that: [tex](1 + r_B)^{10} = 2.2399[/tex]
So:
[tex]B_0 * 2.2399 = 6719.58[/tex]
[tex]B_0 = \frac{6719.58}{2.2399}[/tex]
[tex]B_0 = 3000[/tex]
Hence:
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
[tex]B_t = 3000 * (1 + 0.08)^t[/tex]
[tex]B_t = 3000 * (1.08)^t[/tex]
The question requires that we solve for t when:
[tex]A_t = B_t[/tex]
Where:
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_t = 10000 * (1 + 3\%)^t[/tex]
[tex]A_t = 10000 * (1 + 0.03)^t[/tex]
[tex]A_t = 10000 * (1.03)^t[/tex]
and
[tex]B_t = 3000 * (1.08)^t[/tex]
[tex]A_t = B_t[/tex] becomes
[tex]10000 * (1.03)^t = 3000 * (1.08)^t[/tex]
Divide both sides by 10000
[tex](1.03)^t = 0.3 * (1.08)^t[/tex]
Divide both sides by [tex](1.08)^t[/tex]
[tex](\frac{1.03}{1.08})^t = 0.3[/tex]
[tex](0.9537)^t = 0.3[/tex]
Take natural logarithm of both sides
[tex]\ln(0.9537)^t = \ln(0.3)[/tex]
Rewrite as:
[tex]t\cdot\ln(0.9537) = \ln(0.3)[/tex]
Solve for t
[tex]t = \frac{\ln(0.3)}{ln(0.9537)}[/tex]
[tex]t = 25.397[/tex]
Approximate
[tex]t = 25[/tex]
The party planning committee has to determine the number of tables needed for an upcoming event. If a square table can fit 8 people and a round table can fit 6 people, the equation 150 = 8x + 6y represents the number of each type of table needed for 150 people.
The variable x represents the number of
Answer:
Square tables used
Step-by-step explanation:
x represents the number of square tables used since it is being multiplied times 8 which is the number of people a square table can fit
Answer:
answer in pictures
Step-by-step explanation:
Help!!!!!!!!!!! Photo attached
Answer:
option A : 25
Step-by-step explanation:
Given :
P = (- 6, 7) , Q = ( 2 , 1 ) , R = ( -1 , -3)
Find the length of PQ ,QR , PR.
Using distance formula to find the lengths.
[tex]distance = \sqrt{(x_2 - x_1 )^2 + (y_ 2- y_1)^2[/tex]
[tex]PQ = \sqrt{(2 -- 6)^2 + (1-7)^2} = \sqrt{8^2 + 6^2 } = \sqrt{64 + 36 } =\sqrt{100} = 10\\\\QR = \sqrt{(2 --1)^2 + (-3-1)^2}= \sqrt{3^2 + 4^2} =\sqrt{9+ 16} =\sqrt{25} = 5\\\\PR = \sqrt{(-1--6)^2 + (-3 -7)^2} = \sqrt{5^2 + 10^2} = \sqrt{25 + 100} = \sqrt{125}[/tex]
Clearly , the triangle satisfies Pythagoras theorem :
Square of larger side = Sum of squares of other sides.
Therefore , PQR is a right triangle,
with base = 5, height 10 and slant height(hypotenuse) = [tex]\sqrt{125}[/tex] .
[tex]Area = \frac{1}{2} \times base \times height[/tex]
[tex]=\frac{1}{2} \times 5\times 10\\\\= 5 \times 5 \\\\= 25 \ square\ units[/tex]