The solution of the system of linear equations determines if the system has no solution, one solution, or an infinite number of solutions
2·x - 3·y = 3 and -4·x + 6·y = 6
3·x - 2·y = 3 and x + 2·y = 5
-8·x + 12·y = -12 and 2·x - 3·y = 3
y = -x + 2 and y = 3·x - 2
What is a system of equations?A system of equations is a set of two or more equations that are formed by the same variable.
Each of the equations are solved as follows to determine whether it has no solution, one solution, or an infinite number of solutions
1. 2·x - 3·y = 3 and -4·x + 6·y = 6
Multiplying the first equation by 2, we get; 4·x - 6·y = 6.
Adding the above equation to the second equation,we get;
4·x - 6·y + (-4·x + 6·y) = 6 + 6 = 12
0 = 12 (False)
Therefore, the system has no solution
2. 3·x - 2·y = 3 and x + 2·y = 5
Adding the two equations, we get;
3·x - 2·y + (x + 2·y) = 3 + 5 = 8
4·x = 8
x = 8/4 = 2
Substituting x = 2 into the second equation, we get;
x + 2·y = 5
2 + 2·y = 5
2·y = 5 - 2 = 3
y = 3/2 = 1.5
y = 1.5
Therefore, the system has one solution
3. -8·x + 12·y = -12 and 2·x - 3·y = 3
Multiplying the second equation by 4, we get; 8·x - 12·y = 12
Adding the product of the second equation and 4 to the first equation we get;
8·x - 12·y + (-8·x + 12·y) = 12 + (-12) = 0
0 = 0
Therefore, the system has infinite number of solutions
4. y = -x + 2 and y = 3·x - 2
Substituting y = -x + 2 into the second equation, we get;
-x + 2 = 3·x - 2
3·x - 2 = -x + 2
3·x + x = 2 + 2 = 4
4·x = 4
x = 4/4 = 1
x = 1
y = -x + 2
y = -1 + 2 = 1
y = 1
Therefore, the system has one solution.
Therefore, the first system has no solution, the second system has one solution, the third system has an infinite number of solutions, and the fourth system has one solution.
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20 points!!! Pleaseee help
T3=R1
T4=R2}==>TUR=TSR
RT=RT
so: S=U
can someone please help me:(
The equation, (x - 10)² + (y - 5)² = 144, represents a circle with center (10, 5) and radius 12.
Determining the center and radius of a circleFrom the question, we are to determine the center and radius of the circle represented by the given equation
From the given information, the given equation is
(x - 10)² + (y - 5)²= 144
To determine the center and the radius of the circle we will compare the given equation to the standard form of the equation of a circle:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
The equation
(x - 10)² + (y - 5)²= 144
can be written as
(x - 10)² + (y - 5)²= 12²
By comparison,
h = 10, k = 5 and r = 12
Hence, the center of the circle is (10, 5) and the radius is 12
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What's the area of a regular triangle with a side length of 15? (Explanations step-by-step are appreciated!)
the area of the equilateral triangle with a side length of 15 is approximately 97.4279 square units.
A regular triangle is also known as an equilateral triangle, which means all of its sides are equal in length. To find the area of an equilateral triangle with a side length of 15, we can use the following formula:
Area = (√(3) / 4) × side²
where "side" is the length of one side of the triangle.
Let's plug in the given value of side length, which is 15, into the formula:
Area = (√(3) / 4) × 15²
Area = (√(3) / 4) × 225
Area = 97.4279 (rounded to 4 decimal places)
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A study found that 4 out of every 5 driver use seatbelts two cars are randomly stopped at a seat belt check what is the probability both drivers are wearing their seatbelt
I think we need to (4 divided by 5)+2
4 divided by 5= 0.8
0.8+2
=2.8
answer: 2.8
the probability that both drivers are wearing their seatbelts is 0.64, or 64%.
what is multiplication rule for independent events?P(A and B) = P(A) x P(B|A)
The probability of both drivers wearing seatbelts can be calculated as follows, assuming that one driver's use of a seatbelt has no effect on the other driver's use of a seatbelt and that the probability of a driver wearing a seatbelt is independent of the other driver:
Let P(S) be the probability that a driver wears a seatbelt, then P(not S) is the probability that a driver does not wear a seatbelt.
Given that 4 out of every 5 drivers wear seatbelts, we have P(S) = 4/5 = 0.8 and P(not S) = 1 - P(S) = 1 - 0.8 = 0.2.
Let A be the event that the first driver wears a seatbelt, and B be the event that the second driver wears a seatbelt. We need to find the probability of both A and B occurring, which is denoted as P(A and B).
he probability of the first driver wearing a seatbelt is P(A) = P(S) = 0.8,
and the probability of the second driver wearing a seatbelt given that the first driver is wearing a seatbelt is P(B|A) = P(S) = 0.8 because the two drivers are stopped at random.
Using the multiplication rule for independent events, we have:
P(A and B) = P(A) x P(B|A)
= 0.8 x 0.8
= 0.64
Therefore, the probability that both drivers are wearing their seatbelts is 0.64, or 64%.
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A new player joins the team and raises the mean to 22
A. The mean age of the team rounded to 1 decimal place is 20.9 years
B. The age of the new player is 23.1 years
A. How do i determine the mean age of the team?The mean age of the team can be obtained as illustrated below:
Age (x) = 19, 20, 21, 22, 23, Frequency (f) = 2, 3, 1, 4, 1Mean age =?Mean age = ∑fx / ∑f
Mean age = [(19 × 2) + (20 × 3) + (21 × 1) + (22 × 4) + (23 × 1)] / (2 + 3 + 1 + 4 + 1)
Mean age = 230 / 11
Mean age = 20.9 years
Thus, the mean age of the team is 20.9 years
B. How do i determine the age of the new player?The age of the new player can be obtained as follow:
Mean of previous player = 20.9 yearsNew mean = 22Age of new player =?New mean = (mean of previous + age of new player) / 2
22 = (20.9 + age of new player) / 2
Cross multiply
22 × 2 = 20.9 + age of new player
44 = 20.9 + age of new player
Collect like terms
44 - 20.9 = Age of new player
Age of new player = 23.1 years
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Complete question:
Pleas attached photo
I got through with part A but not part B, it's really confusing.
Therefore, the coordinates of A are (1, 3) and (2, 4). Therefore, the area of the shaded region is (1/2) square units.
What is area?In mathematics, area is the measure of the amount of surface enclosed by a two-dimensional shape or object. It is the size of a surface, and is typically measured in square units such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²).
Here,
First, we need to find the coordinates of the point where the line and the curve meet (point A).
Substituting y = x(4 – x) into y + 2x = 5, we get:
x(4 – x) + 2x = 5
Simplifying and rearranging, we get:
x² – 3x + 2 = 0
Factoring, we get:
(x – 1)(x – 2) = 0
Therefore, x = 1 or x = 2.
When x = 1, y = 3, and when x = 2, y = 4. Therefore, the coordinates of A are (1, 3) and (2, 4).
To find the area of the shaded region, we need to find the integral of the curve y = x(4 – x) between x = 1 and x = 2, and subtract the area under the line y + 2x = 5 between the same limits.
The equation y + 2x = 5 can be rewritten as y = -2x + 5.
Integrating y = x(4 – x) between x = 1 and x = 2, we get:
∫(1 to 2) x(4 – x) dx = (8/3) – (2/3)
= 2
Integrating y = -2x + 5 between x = 1 and x = 2, we get:
∫(1 to 2) (-2x + 5) dx = (3/2)
Therefore, the area of the shaded region is:
=2 - (3/2)
= (1/2) square units
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Last month I used 2205 kWh of electricity. If the rate was $.09884, my bill would be $
Answer:
$217.99
Step-by-step explanation:
To calculate your electricity bill, you need to multiply the number of kilowatt-hours (kWh) used by the rate per kWh.
Using the given information:
Number of kWh used = 2205
Rate per kWh = $0.09884
To calculate the bill:
Bill = Number of kWh used x Rate per kWh
= 2205 kWh x $0.09884/kWh
= $217.99
Therefore, your electricity bill would be $217.99 if you used 2205 kWh at a rate of $0.09884 per kWh.
Answer:
To calculate your bill for using 2205 kWh of electricity at a rate of $.09884 per kWh, you can use the following formula:
Bill = kWh used x Rate per kWh
Plugging in the values given, we get:
Bill = 2205 x 0.09884
Simplifying the calculation, we get:
Bill = 217.5354
Rounding to two decimal places, the bill would be $217.54.
Hope This Helps!
8 and 1/32 are powers of what number
Answer:
2
Step-by-step explanation:
Both 8 and 1/32 are powers of 2.
2³ is 8, since 2*2*2=8.
2^-5 is 1/32.
2^5 is 2*2*2*2*2, and the negative sign in front of the 5 flips the answer to be 1/32
which congruency theorem can be used to prove that △abd ≅ △dca?
a. SAS
b. Not enough information
c. SSS
d. AAS
the correct answer is a. SAS congruency theorem can be used to prove that ABD =DCA.
In this question we accept two angles is given that is:
two triangles ∠ABD and
In this, an angle is common that is,
AD = AD
AB = CD
∠A is equal = ∠A (which is given)
That is the reason the SAS rule is right.
SSS is a geometric term that stands for "side-side-side." It refers to a congruence condition in which three sides of one triangle are equal to three corresponding sides of another triangle, making the two triangles congruent. Congruent triangles have the same size and shape, so if two triangles are congruent, all corresponding angles and sides are equal.
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the complete question is:
Which congruency theorem can be used to prove
that ABD =DCA?
a. SAS
b. Not enough information
c. SSS
d. AAS
help pls with explanation maybe?
The domain of this function can be expressed as (-∞,0) U (0,∞).
The interval on which the function is decreasing is
(-∞,0) U (0,∞).
The interval on which the function is increasing is none.
The interval on which the function is constant is (0,0).
What is domain?The domain of a function is the set of all acceptable inputs for the function. In other words, it is the set of all values for which the function is defined.
The domain of the given function is all real numbers, excluding 0.
This can be seen by observing that the denominator in the fraction is the absolute value of t, which is always positive.
Therefore, the domain of the function is all real numbers except 0, which can be expressed as (-∞,0) U (0,∞).
The function is decreasing over all intervals in its domain since the negative sign preceding the fraction indicates that the value of the function is always negative.
Therefore, the interval on which the function is decreasing is
(-∞,0) U (0,∞).
The function is constant over the interval (0,0) since the absolute value of 0 is 0 and thus, the denominator in the fraction is equal to 0.
Therefore, the interval on which the function is constant is (0,0).
Finally, the function is not increasing over any interval in its domain since the negative sign preceding the fraction indicates that the value of the function is always negative.
Therefore, the interval on which the function is increasing is none.
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Help don’t understand
Thank you geometry 10tg grade
The surface area of a cylinder is given by the formula:
A = 2πrh + 2π[tex]r^{2}[/tex]= 2*3.14*4.8*19.1= 575.504 square ft.
What is surface area?Surface area is the measure of the total area that the surface of an object occupies. It is the sum of all the areas of the individual faces or surfaces of the object. For example, if you have a cube, the surface area would be the sum of the areas of all six faces of the cube. The surface area is usually measured in square units, such as square meters, square centimeters, or square feet, depending on the system of measurement used. Surface area is an important concept in many fields of study, including mathematics, physics, chemistry, and engineering.
by the question.
The surfaces area of a cylinder is given by the formula:
[tex]A = 2πrh + 2πr^2[/tex]
where r is the radius of the circular base of the cylinder, and h is the height of the cylinder.
If a=9.6ft and b=19.1ft, we need to determine the values of r and h before we can calculate the surface area.
Since the cylinder has a circular base, we know that the diameter of the base is equal to b, or 19.1ft. Therefore, the radius of the base is half the diameter, or:
r = b/2 = 19.1/2 = 9.55ft
we know that the radius of the cylinder is = diameter/2
= 9.6/2
= 4.8
The surfaces area of a cylinder= [tex]A = 2πrh + 2πr^2[/tex]
A = 2πrh + 2π[tex]r^{2}[/tex]= 2*3.14*4.8*19.1= 575.504 square ft.
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tell whether the ratios form a proportion 4:14 and 12:40
Answer:
NO
Step-by-step explanation:
First, we should simplify both fractions to the most simple form.
4/14=2/7
12/40=6/20=3/10
A proportion means that it is equal. 2/7 does not equal 3/10, so the answer is no.
Ms. Maynard grates 23/30 of a block of cheese. Mr. Connor then eats another 3/30 of the cheese. What fraction of the cheese is left over?
Ms. Maynard grates 23/30 of a block of cheese, leaving the fraction of 7/30 of the cheese. Mr. Connor then eats 3/30 of the cheese, leaving the fraction of 4/30 of the cheese remaining.
Let us suppose the total block of cheese as 1.
If Ms. Maynard grates 23/30 of a block of cheese, then the fraction of cheese left is:
Remaining cheese = 1 - 23/30 = 7/30
After Mr. Connor eats 3/30 of the cheese, the fraction of cheese left is:
Remaining cheese = 7/30 - 3/30 = 4/30
Therefore, 4/30 of the cheese is left over after grating by Ms. Maynard and Mr. Connor respectively.
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A big box store decreased the price of a computer from $399 to $349. What is the approximate percentage that the price of the computer was reduced?
Responses
12.5%
14.3%
25%
35%
The approximate percentage that the price of the computer was reduced is 12.5%.
what is a percentage?A number can be expressed as a fraction of 100 using a percentage. The letter "%" stands for it. We may compare numbers of various sizes quickly and efficiently using percentages to compare a quantity to its entire or total.
To find the approximate percentage that the price of the computer was reduced, we can use the following formula:
percentage decrease = (original price - new price) / original price x 100%
Substituting the given values, we get:
percentage decrease = (399 - 349) / 399 x 100%
percentage decrease = 50 / 399 x 100%
percentage decrease ≈ 12.5%
Therefore, the approximate percentage that the price of the computer was reduced is 12.5%.
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The table shows the numbers of losses yo gomer has x weeks after getting a new
video game.
Cotter Plot DESMOS GRAPHING CALCULATOR ONLY
Perion
1 Plot the points on the groph
2 Draw the line of best fit
3. Insert data into DESMOS table to:
Determine the slope.
a
b.
Determine the y-intercept
c. Write the equation of the line.
4. What is the correlation coefficient?
Week, x
1
3 A S
Losses, y 15 12 10 7
NUMBER OF LOSSES
S2
5. Use the equation to predict the weeks if
the number losses is 20.
6. Use the equation to predict the losses if
the week is 15.
6
6
VIDEO GAME LOWES
3
4 R
3.a. The slope of the line is -2.
b. The y-intercept of the line is 17.
c. The equation of the line is y=-2x+17.
4. The correlation coefficient is -2.
5. When the number of losses is 20, the week is 6.
6. When the week is 15, the number of losses is -13.
What is slope?It is calculated by dividing the vertical change (rise) between two points by the horizontal change (run) between the same two points.
3.a. The slope of the line is -2.
This can be determined by calculating the change in the y-values
(15-12=3,
12-10=2,
10-7=3,
7-6=1,
6-3=3,
and 3-1=2)
and dividing by the change in the x-values
(1-2=-1,
2-3=-1,
3-4=-1,
4-5=-1,
5-6=-1,
and 6-7=-1),
which gives us (3+2+3+1+3+2)/-6=-2.33=-2
b. The y-intercept of the line is 17.
This can be determined by finding the y-value when x=0.
Since there is no x=0 value in the table, we can use the equation of the line to calculate the y-value when x=0.
When x=0, y=17.
c. The equation of the line is y=-2x+17.
4. The coefficient of correlation is -2.
This can be determined by using the slope of the line, which is -2.
The coefficient of correlation is equal to the slope of the line, which is -2.
5. When the number of losses is 20, the week is 6.
This can be determined by using the equation of the line and solving for x when y=20.
When y=20,
-2x+17=20,
so 2x=3 and x=3/2, which is 6 weeks.
6. When the week is 15, the number of losses is -13.
This can be determined by using the equation of the line and solving for y when x=15.
When x=15,
y=-2(15)+17
=-13.
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Eric rents a bounce house for his son's birthday. There is a rental fee of $85 and a fee of $8 per hour. Eric only has $125 to spend on the bounce house. Write an equation to find the number of h, hours, that Eric can rent the bounce house.
please help, I need an answer and fast!
Answer:
[tex]85 + 8h = 125[/tex]
Hi I don’t understand help
The exact value of x is 12.97.
Describe Bisector?In geometry, a bisector refers to a line or plane that divides a geometric figure into two equal parts. Specifically, a bisector divides an angle into two equal angles, a line segment into two equal parts, or a plane figure into two equal areas.
There are two types of bisectors:
Angle bisector: A line or ray that divides an angle into two equal angles is called an angle bisector. The point where the bisector intersects the angle is known as the vertex of the angle.
Segment bisector: A line, ray, or line segment that divides a line segment into two equal parts is called a segment bisector. The point where the bisector intersects the line segment is known as the midpoint of the line segment.
We can use the angle bisector theorem to find the value of x. According to the angle bisector theorem, the length of the segment bisecting an angle in a triangle is proportional to the lengths of the two sides adjacent to that angle.
Let's call the point where ST intersects QS point U. Then, by the angle bisector theorem, we have:
QU / QR = SU / SR
Substituting the given values, we get:
QU / 20 = x / 16
Multiplying both sides by 20, we get:
QU = (20x) / 16 = (5x) / 4
Similarly, we have:
SU / QS = TU / TR
Substituting the given values and simplifying, we get:
SU / 12 = x / 20
Multiplying both sides by 12, we get:
SU = (12x) / 20 = (3x) / 5
Now, we can use the fact that QRS is a triangle to find the remaining side length:
QR + RS = QS
20 + 16 = 12 + SU + QU
36 = 12 + (3x/5) + (5x/4)
Multiplying both sides by 20, we get:
720 = 240 + 12x + 25x
720 = 37x + 240
37x = 480
x = 480/37
So the value of x is approximately 12.97 (rounded to the nearest hundredth).
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!!!TIMED!!! !!!Please help as fast as possible!!!
Find the value of a.
In right triangle LMN, angles L and M are complementary.
Find the mesure of angle L.
The work, W (in joules), done when lifting an object is jointly proportional to the product of the mass, m (in kilograms), of the object and the height, h (in meters), that the object is lifted. The work done when a 100-kilogram object is lifted 1.5 meters above the ground is 2116.8 joules.
Answer:
The constant of variation in the given problem is 9.8
GIVEN
w = 2,116.8
m = 120
h = 1.8
SOLUTION
w=kmh
2116.8 = k(120)(1.8)
2116.8=216k
9.8=k
Use a trigonometric ratio to solve for y. Round to two decimals places as necessary giving brainliest to whoever gets the correct answer. Image is below
Check the picture below.
[tex]\sin(43^o )=\cfrac{\stackrel{opposite}{y}}{\underset{hypotenuse}{18}}\implies 18\sin(43^o )=y\implies 12.28\approx y[/tex]
Make sure your calculator is in Degree mode.
Write the equation in standard form for the circle with center (3,0) and radius 5.
The equatiοn οf the circle will be [tex]x^{2}+y^{2} -6x-16=0[/tex]
What is circle?A clοsed rοund shaped figure which cοntains nο cοrners is called circle. It has center called (h, k) and radius r. Rοund clοck, car tire, wheels are the examples οf circle.
If the center and radius is given then the equatiοn οf circle is:
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex] ------------- (1) where (h, k) centre and r radius.
Here center οf the circle is (3,0) and radius οf the circle is 5
putting h= 3 , y=0 and r=5 in equatiοn (1) we get
[tex](x-3)^{2} + (y-0)^{2} =5^{2}[/tex]
⇒ (x²- 6x+9) +y²=25
⇒ x²+y²-6x+9-25=0
⇒x²+y²-6x-16=0
Hence the equatiοn οf circle is x²+y²-6x-16=0.
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the amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 22 minutes and a standard deviation of 6 minutes. find the probability that a randomly selected athlete uses a stairclimber for (a) less than 18 minutes, (b) between 22 and 31 minutes, and (c) more than 30 minutes.
The probability that a randomly selected athlete uses a stair climber for,
(a) P(X < 18) = 0.2514
(b) P(22 < X < 31) = 0.4332
(c) P(X > 30) = 0.0918
Let X be the amount of time an athlete uses a stair climber. Then, X ~ N(22, 6^2) represents a normal distribution with mean 22 and standard deviation 6.
(a) To find the probability that a randomly selected athlete uses a stair climber for less than 18 minutes, we need to calculate P(X < 18).
Z-score for 18 minutes = (18 - 22) / 6 = -0.67
Using a standard normal table or calculator, we find that P(Z < -0.67) = 0.2514.
Therefore, P(X < 18) = P(Z < -0.67) = 0.2514.
(b) To find the probability that a randomly selected athlete uses a stair climber for between 22 and 31 minutes, we need to calculate P(22 < X < 31).
Z-score for 22 minutes = (22 - 22) / 6 = 0
Z-score for 31 minutes = (31 - 22) / 6 = 1.5
Using a standard normal table or calculator, we find that P(0 < Z < 1.5) = 0.4332.
Therefore, P(22 < X < 31) = P(0 < Z < 1.5) = 0.4332.
(c) To find the probability that a randomly selected athlete uses a stair climber for more than 30 minutes, we need to calculate P(X > 30).
Z-score for 30 minutes = (30 - 22) / 6 = 1.33
Using a standard normal table or calculator, we find that P(Z > 1.33) = 0.0918.
Therefore, P(X > 30) = P(Z > 1.33) = 0.0918.
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Whom does Atticus ask to go with him to tell Helen Robinson about the death of her husband?
Scout
Calpernia
Jem
No one
Atticus asks Calpurnia to go with him to tell Helen Robinson about the death of her husband. Option B is the correct answer.
Helen Robinson was Tom Robinson's widow in To Ki-ll a Mockingbird, a novel by Harper Lee. Despite the fact that she is not a major character in the story, she plays a significant role in the novel's plot. When Bob Ewell accuses Tom Robinson of ra-pe, Atticus Finch is hired to defend him, and Helen Robinson appears in the story.
When Tom Robinson, a black man, was accused of rapi-ng a white woman, Mayella Ewell, he was arrested and imprisoned in the local jail. He was sentenced to death, but he attempted to flee and was subsequently sh-ot and kill-ed by a group of guards. When the news of his death reaches Atticus, he goes to tell Helen Robinson that her husband had died. Atticus, recognizing that it will be difficult for her to receive such news, offers to accompany her and asks Calpurnia to come along with him.
Calpurnia was the Finch family's black housekeeper in the novel To K-ill a Mockingbird. She is one of the few African American characters in the book who has a speaking role, and she serves as a motherly figure to Scout and Jem. Throughout the novel, she serves as a bridge between the white and black communities, and she plays a crucial role in the story's resolution.
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A town with a population of 80,250 people has 500 city blocks. Each block is one-tenth mile long by one-tenth mile wide. Find the population density of the town in the people per square mile.
Answer:
First, we need to find the area of one block:
Area of one block = length x width = (1/10) mile x (1/10) mile = 1/100 square mile
Since there are 500 blocks in the town, the total area of the town is:
Total area of town = 500 blocks x (1/100) square mile/block = 5 square miles
To find the population density, we divide the population by the total area:
Population density = population / total area
Population density = 80,250 / 5 = 16,050 people per square mile
Therefore, the population density of the town is 16,050 people per square mile.
What is the axis of symmetry of h(x) = 6x2 − 60x + 147?a. x=−5b. x=−3c. x=3d. x=5
The axis of symmetry of the function h(x) is x = 5. So, option D is correct.
The axis of symmetry of a quadratic function is a vertical line that divides the parabola into two symmetric parts. The axis of symmetry is always a vertical line passing through the vertex of the parabola.
In algebraic terms, the axis of symmetry of a quadratic function of the form [tex]f(x) = ax^2 + bx + c[/tex] is given by the equation:
[tex]x = -\frac{b}{2a}[/tex]
Where a and b are the coefficients of the quadratic expression.
Let's consider the given question:
To find the axis of symmetry of the quadratic function [tex]h(x) = 6x^2 - 60x + 147[/tex], we can use the formula [tex]x = -\frac{b}{2a}[/tex], where a and b are the coefficients of the quadratic expression.
In this case, a = 6 and b = -60, so the axis of symmetry is:
[tex]x = -\frac{(-60)}{2*(6)}[/tex]
[tex]x = 5[/tex].
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fizzfizz soda comes in two flavors, regular and diet. if a researcher has 7 boxes of each, how many ways can he select 4 boxes, consisting of 2 boxes of regular and 2 boxes of diet, for a quality control test?
Number of ways that the researcher can select 4 boxes, consisting of 2 boxes of regular and 2 boxes of diet, for a quality control test is 441
To select 4 boxes consisting of 2 regular and 2 diet from 7 boxes of each, we need to use combinations.
The number of ways to select 2 regular boxes out of 7 is
C(7,2) = 21
Similarly, the number of ways to select 2 diet boxes out of 7 is also 21.
Now we need to choose 2 regular boxes out of 2 and 2 diet boxes out of 2, which can only be done in one way.
So the total number of ways to select 4 boxes consisting of 2 regular and 2 diet is
21 x 21 x 1 x 1 = 441
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Find the output, fff, when the input, ttt, is 777.
f = 2t - 3f=2t−3
Answer:
The value of the function f at t = 7, will be 11.
Step-by-step explanation:
What is a function?
A statement, principle, or policy that creates the link between two variables is known as a function.
The function is given as,
f = 2t – 3
Then the value of the function f at t = 7, will be
f = 2 x 7 – 3
f = 14 – 3
f = 11
Answer:
f = 11
Step-by-step explanation:
i got it right on khan academy lol
Jim has only 5p coins and 10p coins.The ratio of the number of 5p coins to the number of 10p coins 2:3 work out the ratio of total value of the 5p coin : the total value of the 10p coin give your answer in its simplest form
Answer: required ratio is 1;3
Step-by-step explanation:
Since we have given that
Ratio of the number of 5 p coins to the number of 10 p coins = 2:3
So, the number of 5p coins be '2x'
Let the number of 10p coins be '3x'.
Value of 5p coins = 5p x 2x =10px
Value of 10p coins = = 10p x 3px=30px
So, the ratio of value of 5p coins to the value of 10p coins is given by
10px:30px
1:3
to bake a cake , raffy needs 3 cups of sugar for 5 cups of flour. if he uses 35 cups of flour, how much sugar doe he need and how many cakes will he bake
Answer: 21 cups of sugar, 7 cakes
Solve the following proportion:
3/5=x/35
Cross multiply:
5x=35(3)
5x=105
x=21 cups of sugar
3 cups of sugar= 1 cake
21 cups of sugar= x cakes
Cross multiply:
3x=21
21/3
7 cakes
. Principal $400
Rate 5%
Time 1 year