Answer:
Box=0.95
Orange bag=0.44
Package=0.44
Step-by-step explanation:
Divide the cost by the amount of whatever. For ex. The 3.79/4 because there are 4 boxes.
Final answer:
The unit rate for a box of 4 light bulbs is $0.95 per bulb, for a bag of 5 oranges it's $0.44 per orange, and for a package of 12 bars of soap, the unit rate is $0.44 per bar.
Explanation:
To calculate the unit rate for each item, you divide the total cost by the number of items in the package. This tells you the cost per single item. Let's calculate the unit rates, rounding to the nearest cent.
A box of 4 light bulbs costs $3.79. Unit rate: $3.79 ÷ 4 = $0.95 per light bulb.A bag of 5 oranges costs $2.19. Unit rate: $2.19 ÷ 5 = $0.44 per orange.A package of 12 bars of soap costs $5.25. Unit rate: $5.25 ÷ 12 = $0.44 per bar of soap.Remember, when working with prices, it's standard practice to round to the nearest cent, which represents the smallest unit of currency used in transactions.
BRAINLIEST TO FIRST CORRECT ANSWER ASAP.
Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. When the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. When the tanks are completely fill of air, the submarine reduces its overall mass and floats to the surface. Depending on the density if the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. The volume of the submarine never changes. When the tanks are completely full of water, a submarine with a volume of 7.8 x 10^3 m^3 has a total mass of 8 x 10^6 kg. The density of the seawater is 10^3 kg/m^3. To make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?
A. 8 x 10^6 m^3
B. 2 x 10^2 m^3
C. 8 x 10^3 m^3
D. 2 x 10^5 m^3
Answer:
The volume of the water subtracted from the tanks is 2 × 10² m³ to
make the submarine float nor sink in the ocean ⇒ answer B
Step-by-step explanation:
* Lets talk about the relation between the mass , the volume
and the density
- Mass = Volume × Density
- The unit of the mass is kilogram
- The unit of the volume is cubic meter
- The unit of the density is Kilogram per cubic meter
* Lets find the volume to make the submarine float neutrally
∵ Mass = volume × density
∴ Volume = Mass ÷ density
∵ The mass = 8 × 10^6 kg
∵ The density of the seawater = 10³ kg/m³
∴ The volume = 8 × 10^6 ÷ 10³ = 8 × 10^(6 - 3) ⇒ (to divide numbers
with exponents and have same base, subtract the powers)
∴ The volume = 8 × 10³ m³
- The volume of the submarine never changes
∴ The submarine need to subtract:
8 × 10³ - 7.8 × 10³ = 10³ (8 - 7.8) = 0.2 × 10³ = 2 × 10² m³ from its tanks
* The volume of the water subtracted from the tanks is 2 × 10² m³ to
make the submarine float nor sink in the ocean
Final answer:
To achieve neutral buoyancy, a submarine with a volume of 7.8 x 10³ m³ must expel a volume of water that reduces its mass to that of the water displaced. This amounts to expelling 2 x 10² m³ of water from its ballast tanks.
Explanation:
To make the submarine float neutrally in the seawater, we need to find out how much water the submarine must expel so that its mass equals the mass of the water it displaces. Using Archimedes' principle, the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that is displaced by the object. This is dependent on the volume and density of the fluid.
Since the volume of the submarine is given as 7.8 x 10³ m³ and doesn't change, and the density of the seawater is 10³kg/m³, the mass of the water displaced by the submarine when it is neutrally buoyant must equal the mass of the submarine.
The mass of the water displaced would then be 7.8 x 10³ m³ × 10³ kg/m³ = 7.8 x 10⁶ kg. To achieve neutral buoyancy, the submarine must expel enough water to match this mass. Since we know the total mass of the submarine when fully loaded with water is 8 x 10⁶kg, the volume of water that must be expelled is the difference between the two masses divided by the density of the seawater:
(8 x 10⁶ kg - 7.8 x 10⁶ kg) / (10³ kg/m³) = 0.2 x 10³ m³ or 2 x 10² m³.
Therefore, the correct answer is B. 2 x 10² m³.
A bag contains eleven red marbles, seven blue marbles, nine green marbles, and thirteen yellow marbles. Which of the following statements is not true? The theoretical probability of selecting a red marble from the bag is 27.5%. The odds of selecting a yellow marble from the bag are 13 to 27. The theoretical probability of selecting a blue or green marble from the bag is . The odds of selecting a red or blue marble are .
Answer: In total there are 40 marbles because 11+7+9+13=40
There are 7 Blue marbles, so
P(blue)=7/40
\
Disclaimer: The options were not given correctly so they are added here:
a. The theoretical probability of selecting a red marble from the bag is 27.5%.
b. The odds of selecting a yellow marble from the bag are 13 to 27.
c. The theoretical probability of selecting a blue or green marble from the bag is 2/3.
d. The odds of selecting a red or blue marble are 9/11.
Among the given statements, c. The theoretical probability of selecting a blue or green marble from the bag is 2/3. which is not true.
What is the probability of an event?The probability of an event is the fractional value determining how likely is that event to take place. If the event is denoted by A, the number of outcomes favoring the event A is n and the total number of outcomes is S, then the probability of the event A is given as:
P(A) = n/S.
What are the odds of a given event?When a given event suppose A, has a Probability of occurring = P(A) and Probability of not happening = 1 - P(A).
When we calculate the odds in favor of event A, the value is given by the ratio, P(A):(1 - P(A)).
When we calculate the odds against the event A, the value is given by the ratio, (1 - P(A)):P(A).
How do we solve the given question?We are informed that a bag contains eleven red marbles, seven blue marbles, nine green marbles, and thirteen yellow marbles.
Let the event of selecting a red marble from the bag be R.
Number of outcomes favoring R = 11 (number of red marbles)
Total number of outcomes = 40 (number of marbles in the bag)
∴ The probability of the event R is P(R) = 11/40
1 - P(R) = 1 - 11/40 = 29/40
Let the event of selecting a blue marble from the bag be B.
Number of outcomes favoring B = 7 (number of blue marbles)
Total number of outcomes = 40 (number of marbles in the bag)
∴ The probability of the event B is P(B) = 7/40
1 - P(B) = 1 - 7/40 = 33/40
Let the event of selecting a green marble from the bag be G.
Number of outcomes favoring G = 9 (number of green marbles)
Total number of outcomes = 40 (number of marbles in the bag)
∴ The probability of the event G is P(G) = 9/40
1 - P(G) = 1 - 9/40 = 31/40
Let the event of selecting a yellow marble from the bag be Y.
Number of outcomes favoring Y = 13 (number of yellow marbles)
Total number of outcomes = 40 (number of marbles in the bag)
∴ The probability of the event Y is P(Y) = 13/40
1 - P(y) = 1 - 13/40 = 27/40
Now, we analyze all the options, to check for the ones which are not true.
a. The theoretical probability of selecting a red marble from the bag is 27.5%.
The probability of selecting a red marble P(R) = 11/40 =11/40 * 100% = 27.5%, which is the same we are looking for.
∴ The statement is true.
b. The odds of selecting a yellow marble from the bag are 13 to 27.
The odds of selecting a yellow marble (odds in favor) = P(Y)/(1 - P(Y)) = 13/27 or 13 to 27, which is the value we are looking for.
∴ The statement is true.
c. The theoretical probability of selecting a blue or green marble from the bag is 2/3.
The probability of selecting a blue or green marble from the bag = P(B) + P(G) = 7/40 + 9/40 = 16/40 = 2/5, which is not the value we are looking for.
∴ The statement is not true.
d. The odds of selecting a red or blue marble are 9/11.
The probability of selecting a red or blue marble from the bag
P(R+B) = P(R) + P(B) = 11/40 + 7/40 = 18/40 = 9/20.
1 - P(R+B) = 1 - 9/20 = 11/20
∴ Odds of selecting a red or blue marble (odds in favor)
= P(R+B)/(1 - P(R+B)) = (9/20)/(11/20) = 9/11, which is the value we are looking for.
∴ The statement is true.
So, among the given statements, c. The theoretical probability of selecting a blue or green marble from the bag is 2/3. which is not true.
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An angle with 43 is called
Answer:
Acute
Step-by-step explanation:
Anything with a measure less than 90 degrees is acute
An acute angle. It's less then 90 degrees.
^^^Is that the answer you're looking for?
Is the answer A, B, C or D?
A. this is because when you multiple 280 by 9 you get 2,520 and to get 25% multiple that number by .25 and get 630, add 2520 and 630 to get 3150 ,, subtract 3114 from 3150 to get 36
Answer:
A. He will break the record by 36 yards.
Step-by-step explanation:
Last year:
average yards per game: 280 yards
Increase by 25%:
average yards = 125% of 280 yd = 1.25 * 280 yd = 350 yd
By increasing the yards per game by 25% he will have an average of 350 yd per game this year.
The school record is 3,114 yd, so the average per game for a 9-game season is: 3,114 yd/9 = 346 yd.
He will pass the record by 350 yd - 346 yd = 4 yd per game.
In a 9-game season, he will break the record by 9 * 4 yd = 36 yd.
Answer: A. He will break the record by 36 yards.
The value of Jamie's baseball card collection rose 60% in the last year. It is now worth $192. What was it worth a year ago?
Answer:
The price of baseball card collection last year is $120.
Step-by-step explanation:
In this question we are given the value of Jamie's baseball card collection rose 60% in the last year. It is now worth $192. We need to find the price of baseball card collection last year.
Let x = the price of baseball card collection last year
the value of baseball card collection rose = 0.6x (60% = 60/100 = 0.6)
Current worth = $192
So, we can write
x + 0.6 x = 192
1.6 x = 192
x = 192/1.6
x = 120
So, the price of baseball card collection last year is x = $120
Given that p is an integer, q = -12 and the quotient of p/q is -3, find p.
36, |-12| is 12 and |-3| is 3. Using inverse operations, we multiply and get 36. P=36
Answer:
36
Step-by-step explanation:
36 Because all you do is -12*-3
Select the correct answer.
What is the vertex of the parabola given by y = -(x − 2)2 − 1?
A.
(2, 1)
B.
(2, -1)
C.
(-2, 1)
D.
(-1, 2)
Answer:
Vertex: 2,-1
Step-by-step explanation:
you just gotta graph it
Final answer:
The vertex of the parabola given by the equation y = -(x - 2)² - 1 is (2, -1).
Explanation:
To find the vertex of the parabola given by the equation y = -(x − 2)² − 1, you should recognize that the equation is already in the vertex form, which is y = a(x − h)² + k, where (h, k) is the vertex of the parabola. In this case, h equals 2, and k equals -1, therefore the vertex of the parabola is (2, -1).
In about one hundred words, explain the importance of symbolism to short stories. Use two examples from the short stories in this unit.PLZ HELP
Answer:
portance of symbolism in short stories
Symbolism helps create meaning and emotion in a story. Metaphors and allegory are literary elements that help writers create symbolism in their literary pieces. Colors, objects, seasons, people, situations and words are all types of symbolism that might be used in a literary work.
Step-by-step explanation:
can i have brainlyest
Answer:
The mother's ironing is the main symbol of the story because it reflects on her hopes for Emily. As the mother irons she discusses Emily's life. Through her narration, readers can understand that the mother wanted a smooth life for Emily. But struggles like poverty, unexpected illness, and other negative experiences prevented a normal life for Emily. The iron indicates that the mother wanted to fix Emily. Her sentiments also can be interpreted as regrets that the mother could not help Emily overcome life trials. The ironing can therefore be seen by the readers like the heaviness of a mother's duties towards a child. The continuous action of ironing shows the mother's efforts to address Emily's problems in doing daily tasks. The mother cannot help but reflect upon the reasons Emily developed into a special child. Most importantly, the iron represents that the mother still believes Emily can become a confident person. With the mother's support, Emily may have hope.
The table represents the recommended exercise intensity for the aerobic program based on the number of visits since the beginning program The program recommends a consistent intensity for three visits increase in intensity over three visits then decreasing intensity for three visits before restoring the pattern which set of values could be the intensity of embers exercise during the fourth fifth and six visits check all that apply
A.63%,63%,63%
B.66%,69%,72%
C.66%,62%,58%
D67%,67%,67%
E.63%,65%,67%
F.67%,72%,77%
Final answer:
The correct sets of values for the fourth, fifth, and sixth visits' exercise intensity, according to the described F.I.T.T. pattern of increase after consistent intensity, would be options B (66%, 69%, 72%) and E (63%, 65%, 67%).
Explanation:
The student's question regarding the recommended exercise intensity for the aerobic program is a matter related to health and physical education. Specifically, it involves understanding how to apply the F.I.T.T. principle to plan an aerobic workout regimen. The program described outlines a pattern of consistent intensity, followed by a gradual increase and then a decrease in intensity. When looking for the set of values that could represent the intensity of exercises during the fourth, fifth, and sixth visits, we should look for a pattern that indicates an increase in intensity from the prior three consistent visits.
Given the following options, the correct pattern would be one that shows an increase over three visits:
B. 66%, 69%, 72% - This shows a consistent increase in intensity.
E. 63%, 65%, 67% - This also shows a consistent increase in intensity.
Options A, C, D, and F do not fit the pattern of increasing and then decreasing as described in the student's question. Therefore, the correct set of values for the intensity of exercises on the fourth, fifth, and sixth visits are B and E.
How many triangles can be drawn with one 90° angle ,a 70° angle, and an included side measuring 3 inches?explain
Answer:
1
Step-by-step explanation:
once we know 2 of the angles we can find a third. once we have all 3 angles we only need one side length to tell us how big it is.
Bonus question: How many triangles can be drawn with one 3 inch side ,a 4 inch side, and a 20ºangle?
Only one triangle is formed with an angle 90° , angle 70° and included side with 3 inches.
What is a triangle?
A triangle is a three sided polygon, which has three vertices.
Given that;
Measure of two angles are angle 90° and angle 70°.
Length of side = 3 inches.
Now, Measure of two angles are angle 90° and angle 70°.
Since, Sum of all angles of an triangle are 180°.
Let third angle = x
So, 90° + 70° + x = 180°
160 + x = 180
x = 20°
Thus, We can formed only one triangle.
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Please help me with geometry.
Answer:
m<6 = 50
Step-by-step explanation: Just trust me
Answer:
50 degrees
Step-by-step explanation:
When two parallel lines are cut by a transversal, same side interior angles are supplementary.
In the figure, parallel lines AB and CD are cut by the tranversal shown forming 8 angles. Angles 3 and 6 are same side interior angles, so they are supplementary. That means that their measures have a sum of 180 degrees.
m<3 + m<6 = 180
130 + m<6 = 180
m<6 = 180 - 130
m<6 = 50
Find the unknown side length, x.
√65 = x; using the Pythagorean Theorem, 25 [hypotenuse₁] - 9 [short leg₁] = 16 [long leg₁]. Take the square root of 16 to get 4 [reflexive line where the two triangles meet]. Then, you deal with the larger triangle. You have 16 [short leg₂] + 49 [long leg₂] = 65 [hypotenuse₂]. Finally, take the square root of 65, so long it stays √65. There is no perfect square to find that will simplify that 65 inside that radical.
Answer:
B. √65Step-by-step explanation:
Use the Pythagorean theorem for both triangles.
Let y be the common side of the triangles. Therefore:
y² + 3² = 5²
y² + 9 = 25 subtract 9 from both sides
y² = 16
x² = 7² + y²
x² = 49 + 16
x² = 65 ⇒ x = √65
Find the number of solutions of -x^2 + 5x - 4 = 0.
Answer:
There are 2 solutions for the equation -x^2 + 5x - 4 = 0 i.e x=1 and x=4
Step-by-step explanation:
We can find the number of solutions of the given equation -x^2 + 5x - 4 = 0 by solving the equation using factors method to solve the quadratic equation.
[tex]-x^2 + 5x - 4 = 0\\Taking\,\, - sign\,\, common\\x^2 - 5x + 4 = 0\\making\,\, factors\,\, of\,\, 4x^2\\x^2 -4x -x +4 = 0\\x(x -4) -1 (x - 4) = 0\\(x-1)(x-4)=0\\x-1 = 0 \,\, and \,\, x-4 =0\\x = 1 \,\,and\,\, x = 4\\[/tex]
The values of x are:
x=1 and x=4
So, there are 2 solutions for the given equation -x^2 + 5x - 4 = 0
What is the wavelength for radio waves with frequency 3x10^9
The wavelength of radio waves with a frequency of 3x10^9 Hz can be calculated using the equation c = λf. By substituting the given values and solving for λ, we find that the wavelength is approximately 10 cm.
Explanation:To find the wavelength of radio waves with frequency 3x10^9, first, we need to understand that wave speed, wavelength, and frequency are interconnected. This relation can be written as c = λf, where 'c' is the speed of light, 'λ' is the wavelength and 'f' is the frequency. Given the speed of light, c, is approximately 3.00x10^8 m/s, and the frequency, f, is 3x10^9 Hz, we can substitute these values into the equation and solve for λ (wavelength). This will give us λ = c / f = 3.00x10^8 m/s / 3x10^9 Hz = 0.1 m or 10 cm.
Therefore, the wavelength of the radio waves with a frequency of 3x10^9 Hz is 10 cm.
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To find the wavelength of radio waves with a frequency of 3x10⁹ Hz, use the equation c = fλ, where c is the speed of light (3.00x10^8 m/s). The wavelength is calculated to be 0.1 meters.
Explanation:The question is asking us to calculate the wavelength of radio waves with a given frequency. The formula that connects the speed of light (c), frequency (f), and wavelength (λ) is c = fλ, where c is the speed of light in a vacuum, which is approximately 3.00 × 108 m/s.
To find the wavelength for radio waves with a frequency of 3 × 10⁹ Hz, we can rearrange the formula to λ = c/f. Thus:
λ = (3.00 × 10⁸ m/s) / (3 × 10⁹ Hz)
= 0.1 meters
The wavelength of radio waves with a frequency of 3 × 10⁹ Hz is 0.1 meters.
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What is the sum of 14t/10t^2 + 5t^2+40t/10t^2?
Answer:
(5t^2 + 54t)/ 10t^2
Step-by-step explanation:
since the denominator is the same, you would just add the numerators.
Combine the like terms to create an equivalent expression: −5r+8r+5
Answer:
3r+5
Step-by-step explanation:
Since -5r and 8r both have r in them, we can combine them and the expression looks like:
3r+5
Which is our answer.
Answer:
3r+5
Step-by-step explanation:
Math
Need help for a and b
Answer:
[tex]x = 4.45 \\ y=6[/tex]
Step-by-step explanation:
For part a, we'll be needing to find the vertex.
Convert [tex]y=-x^2+4x+2[/tex] into vertex form by factoring and completing the square.
We'll get...
[tex]y=-(x-2)^2+6[/tex]
So the vertex is [tex](2,6)[/tex]
And therefore, the maximum height will be 6.
Now we can find the zeros to find how far it'll be.
Use the quadratic formula.
[tex]x=\frac{-b±\sqrt{b^2-4ac}}{2a}[/tex]
[tex]a=-1 \\ b=4 \\ c = 2[/tex]
Plug them in.
[tex]x=\frac{-4±\sqrt{(4^2)-4(-1)(2)} }{2(-1)}[/tex]
[tex]x=\frac{-4±\sqrt{16--8}}{-2} \\ \\ x=\frac{-4±\sqrt{24}}{-2} \\ \\ x = 4.45, -0.45[/tex]
Since the x value has to be positive, x ≈ 4.45, so the water will be about 4.45 out when the water reaches pond level.
Equation to find r in terms for V and h
V = πr²h
We want r in terms of V and h, so
[tex]r^2=\frac{V}{h\pi}[/tex]
[tex]r=\sqrt{\frac{V}{h\pi}}[/tex]
A gallon of paint will cover approximately 350 square feet. The family room measures 15x18 feet and has a 8 foot ceilings.How many gallons of paint must be purchased in order to pint the walls
Answer:
2 gallons
Step-by-step explanation:
So first, we need to figure out the total area of the walls,
so 15 x 8 = 120 x 2 = 240
18 x 8 = 144 x 2 = 288
240 + 288 = 384
2 gallons are needed
SUBSTITUTION
p=-4.8 q=3.2
r=3-2p+q^2
R = 3 - 2(-4.8) + 3.2^2
R = 3 + 9.6 + 10.24
R = 22.84
Answer:
r=16.84
Step-by-step explanation:
As we know that [tex]p=-4.8[/tex] and [tex]q=3.2[/tex] we can substitute these values in to the equation in order to find the value of r
[tex]r=-3-2p+q^2\\\\r=-3-2(-4.8)+(3.2)^2\\\\r=-3+9.6+10.24\\\\r=16.84[/tex]
Is the ratio 25 to 16 proportional to 5 to 4.
No because 5:4 time 4 you get 20:16 not 25:16 and if you manage 25 it will be 25:20 so not promotional
Answer:
no
Step-by-step explanation:
because if you divide 25 by 16 you get 1.5625 and if you divide 5 by 4 you 1.25, so they are not proportional. and another way to see if its proportional or not, is to divide the numerators by the same number as you did with the denominators. for example, 25/5 = 5 but 16/5 does not equal 4, so they aren't proportional.
Calculator
158°
120°
126
.
What is the value of x?
Enter your answer in the box
Answer:
is their more to this ?
Step-by-step explanation:
because it could be like X+70=140 what x was there anything like that ?
Answer:
Here it is
Step-by-step explanation:
Use the diagram shown to answer the questions.
If you dropped a vertical line from P to the x-axis to make a right triangle, what is the length of the hypotenuse, r?
Answer:
13
Step-by-step explanation:
First drop the line.
How many units is it from Point r to the x axis?
12.
How many units is it from Point r to the y axis?
5.
Now we can use the Pythagorean Theorem.
[tex]12^2+5^2=c^2 \\ \\ 144+25=c^2 \\ \\ c^2=169 \\ \\ c=13[/tex]
The calculated length of the hypotenuse r has a value of 13 units
How to determine the length of the hypotenuseFrom the question, we have the following parameters that can be used in our computation:
The point P
Where, we have
P = (-5, 12)
This means that
(x, y) = (-5, 12)
The length of the hypotenuse r is calculated as
r = √[x² + y²]
Substitute the known values into the equation
r = √[(-5)² + 12²]
r = √169
When evaluated, we have
r = 13
Hence, the length of the hypotenuse is 13 units
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Costs incurred in detecting poor-quality goods or services are referred to as
A. appraisal costs.
B. internal failure costs.
C. external failure costs.
D. prevention costs.
Answer:
C. external failure costs.
A bag contains 5 red marbles, 6 white marbles, and 5 blue marbles. Find P(red and blue).
Please show work so I can undersand.
The probability of getting blue and red marble is [tex]0.0976[/tex].
What is Probability?
The probability of any event is the ratio of number of favourable outcome and Total number of outcome.
It is given that a bag contains [tex]5[/tex] red marbles, [tex]6[/tex] white marbles and [tex]5[/tex] blue marbles.
We have to find the Probability [tex]\[\text{P}\left( \text{red and blue} \right)\][/tex].
So,
[tex]\[\text{The total number of marbles in the bag}=5+6+5\][/tex]
[tex]= 16[/tex]
Probability of getting red marble [tex]\[\text{P}\left( \text{red} \right)\text{=}\frac{\text{no}\text{.of red marbles}}{\text{total number of marbles}}[/tex]
[tex]\[=\frac{5}{16}\][/tex]
Probability of getting white marble [tex]\[\text{P}\left( \text{white} \right)\text{=}\frac{\text{no}\text{.of white marbles}}{\text{total number of marbles}}[/tex]
[tex]\[=\frac{6}{16}\][/tex]
Probability of getting blue marble [tex]\[\text{P}\left( \text{blue} \right)\text{=}\frac{\text{no}\text{.of blue marbles}}{\text{total number of marbles}}[/tex]
[tex]\[=\frac{5}{16}\][/tex]
Now, we find the probability for [tex]\[\text{P}\left( \text{red and blue} \right)\][/tex],
[tex]\[\text{P}\left( \text{red and blue} \right)\] = $\text{P}\left( \text{red} \right)\text{ }\!\!\times\!\!\text{ P}\left( \text{white} \right)$[/tex]
[tex]$=\frac{5}{16}\cdot \frac{5}{16}$[/tex]
[tex]$=0.0976$[/tex]
Hence, the Probability of [tex]\[\text{P}\left( \text{red and blue} \right)\][/tex] is [tex]0.0976[/tex].
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Final answer:
The probability of drawing a red marble and then a blue marble from a bag containing a mix of marbles is 5/48, calculated by multiplying the probabilities of each individual event occurring in sequence.
Explanation:
The question asks for the probability of drawing a red and then a blue marble from a bag containing 5 red, 6 white, and 5 blue marbles. We begin by calculating the probability of drawing a red marble, which is 5/16 (since there are 5 red marbles out of a total of 16). After drawing a red marble, we do not replace it, so there are now 15 marbles left. The probability of drawing a blue marble next is 5/15 or 1/3, since there are 5 blue marbles left.
To find the combined probability of two independent events, we multiply their individual probabilities. Therefore, the probability of drawing a red then a blue marble without replacement is 5/16 * 1/3, which simplifies to 5/48. So, P(red and blue) is 5/48.
Write the standard form of the line that contains a slope -3/8 and passes through the point (5, -4).
Answer:
y+3/8x=-17/8
Step-by-step explanation:
y=mx+b
y=-3/8x+b
-4=-3/8(5)+b
-4=-15/8+b
-32/8+15/8=b
-17/8=b
y=-3/8x-17/8
change to standard form where x and y are on one side of the equation
y+3/8x=-17/8
if f(x)=x/2-3 and g(x)=3x^2+x-6, find (f+g)(x)
The answer is:
[tex]f(x)+g(x)=3x^{2} +\frac{3x}{2}-9[/tex]
Why?We are working with function addition, to add or subtract two o more functions, we need to follow the following form:
[tex](f+g)=f(x)+g(x)[/tex]
To simplify the expression, we need to work with the like terms, like terms are the terms that share the same variable and the same coefficient, for example:
[tex]x+3x+x^{2}=x^{2} +4x[/tex]
We were able to add only the first two terms since the third term does not share the exponent with the other two.
We are given the functions:
[tex]f(x)=\frac{x}{2}-3\\\\g(x)=3x^{2}+x-6[/tex]
So, solving, we have:
[tex]f(x)+g(x)=(\frac{x}{2} -3)+(3x^{2} +x-6)\\\\f(x)+g(x)=3x^{2}+\frac{x}{2}+x-3-6\\\\f(x)+g(x)=3x^{2}+\frac{x+2x}{2}-9\\\\f(x)+g(x)=3x^{2} +\frac{3x}{2}-9[/tex]
Hence, the answer is:
[tex]f(x)+g(x)=3x^{2} +\frac{3x}{2}-9[/tex]
Have a nice day!
To find (f+g)(x), we need to add the two functions f(x) and g(x). Let's do this step by step:
Given functions:
f(x) = x/2 - 3
g(x) = 3x^2 + x - 6
(f+g)(x) means the sum of f(x) and g(x), so we add the two functions together:
(f+g)(x) = f(x) + g(x)
= (x/2 - 3) + (3x^2 + x - 6)
Now, we combine like terms:
(f+g)(x) = 3x^2 + x/2 + x - 3 - 6
There is a common term x/2 and x, which we can combine by finding a common denominator. The common denominator is 2, so we convert x to 2x/2:
(f+g)(x) = 3x^2 + 2x/2 + x/2 - 3 - 6
= 3x^2 + (2x + x)/2 - 3 - 6
= 3x^2 + 3x/2 - 3 - 6
Now we add or subtract the constants:
(f+g)(x) = 3x^2 + 3x/2 - 9
So, the function (f+g)(x) is equal to:
(f+g)(x) = 3x^2 + 3x/2 - 9
And that is the final expression for the sum of f(x) and g(x).
this is my last question gn guys
pls answer so i can sleep
Answer:
48 cm²
Step-by-step explanation:
Area
= (6 x 2) + (10 - 6) x 9
= 12 + 36
= 48 cm²
Which of these is most likely a pair of independent and dependent variables? A. the selling price of a product and its manufacturing cost B. your pulse rate and your friend’s pulse rate C. the price of a cell phone and the price of a TV D. your calorie intake and your friend’s calorie intake E. the distance of your home from school and your friend’s home from school
Answer:
Dependent Pair of Events: A
Independent pairs of events: B,C,D,E
Step-by-step explanation:
Lets look at each pair one by one..
A. the selling price of a product and its manufacturing cost
We can clearly see that the selling price of a product is always determined on the basis of it's manufacturing cost.
So A is a pair of dependent events.
B. your pulse rate and your friend’s pulse rate
The pulse of rate of one person has nothing to do with the pulse rate of another person.
So B is a pair of independent events.
C. the price of a cell phone and the price of a TV
The price of cell phone and Tv are not related to each other at any level..
So C is a pair of independent events.
D. your calorie intake and your friend’s calorie intake
One person's calorie intake is not related or dependent on any other person's calorie intake.
So D is a pair of independent events.
E. the distance of your home from school and your friend’s home from school
The distances of one person's home from school doesn't affect the distance of another person's home from school.
So E is a pair of independent events..
Determine if direct variation x-2y=0
Answer:
x-2y=0 is a direct variation
Step-by-step explanation:
Direct variation is of the form
y= kx
Can we get the equation in that form
x-2y =0
Add 2y to each side
x-2y+2y =0_2y
x=2y
Divide each side by 2
x/2 = 2y/2
1/2x =y
Flip the sides
y = 1/2x
This is of the form y= kx where k = 1/2
x-2y=0 is a direct variation