The coordinates of the resulting point, g' is :
(-1,1)
Given:
The coordinate plane allows for the translation of any object both horizontally (left/right) and vertically (up/down).
Rules are:
Replace x with x - k when the form is moved k units to the left.Replace x with x + k when the form is moved k units to the right.Replace y with y + k when the form is raised by k units.Change y to y - k when the form is shifted down by k units.The point g(2,1) is translated 3 units left.
we are asked to find the coordinates of the resulting point, g'.
By translating 2 units left, it means the x-axis value is made more negative by 2 units
So we are going to subtract two from the x-coordinate
So we have;
(2-3,1)
= (-1,1)
Hence we get the required coordinates.
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Write the point-slope form of the equation of the line that goes through the points (-5, -5) and (1, -3).
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}} \implies \cfrac{-3 +5}{1 +5} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{1 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{1 }{ 3 }}(x-\stackrel{x_1}{(-5)}) \implies y +5 = \cfrac{1 }{ 3 } ( x +5)[/tex]
Please help me with this question with solution ??
The measure of the value of [x] is x = √5/2
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a triangle as shown in the image.
We can write -
sin(30) = x/(√5)
x = √5 sin (30)
x = √5/2
Therefore, the measure of the value of [x] is x = √5/2.
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help I need my grade raised
I NEED HELP PLEASE WITH THIS PROBLEM
Answer:
48
Step-by-step explanation:
the ratio of blue cards to yellow cards can be expressed with
4:3.
the total amount of blue and yellow cards can be interpreted as 4x+3x=7x
then you can find the value of x by dividing 84/7, which is 12
since the value of blue cards is 4x, 4(12) = 48
a vertical cylinder is leaking water at a rate of ft3/sec. if the cylinder has a height of ft and a radius of ft, at what rate is the height of the water changing when the height is ft?
The rate in the height of water changing for the given cylinder is equal to 0.318m/s.
As given in the question,
Change in volume represent the decrease in rate of change of water height in the cylinder in time t
dV/dt = 4m³/sec.
Decrease in volume represent the change in the height of the water
Let 'h' be the height
h = 10m
radius 'r' = 2m
V = πr²h
Rate of change of leaking water only change the height radius remain constant.
⇒V = (3.14)(2²) h
Differentiate both the side with respect to 't' to get the rate of change
dV/dt = (3.14)(4)dh/dt
⇒4 =(3.14)(4)dh/dt
⇒dh/dt = 4/ (3.14)(4)
⇒dh/dt = 0.318 m/s
Therefore, the rate of change of height is equal to 0.318m/s.
The complete question is:
A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate is the height of the water changing when the height is 3m?
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Find the roots of each equation x^2 - 7x + 12 = 0
Answer:
x=3,x=4
Step-by-step explanation:
(x-3)(x-4)=0
x=3, 4
Answer:
x = 3
x = 4
Step-by-step explanation:
"find the roots" means to find the solutions to the equation.
Roots are solutions are zeros are x-intercepts.
You are being asked to solve the equation.
First, factor the quadratic.
x^2 -7x + 12 = 0
(x - 3)(x - 4) = 0
This works because -3 × -4 is 12 and
-3 + -4 is -7
You see the 12 in the equation is the constant and the -7 is the middle term, the x-term in the trinomial.
So we have
(x - 3)(x - 4) = 0
Separate the two factors into two separate tiny, one-step equations.
x - 3 = 0 , x - 4 = 0
Solve.
x = 3 , x = 4
These are the roots (solutions, zeros and x-intercepts)
a population of protozoa develops with a constant relative growth rate of 0.6685 per member per day. on day zero the population consists of two members. find the population size after seven days. (round your answer to the nearest whole number.)
When the population of a protozoa develops with a constant relative growth rate of 0.6685 per member per day, and there are two members on the day zero, the population after will consist of 7 at the end of seven days period.
The total population of the protozoa at the end of the seven days can be computed using the calculations given below,
Total Population = Growth Rate x Number of Days + Day zero Population
Total Population = (0.6685 x 7) + 2
Total Population = 6.667, or ~ 7.
Therefore, there will be 7 protozoa at the end of seven days.
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In the diagram below, mZCIH = 100° and mZBGD = 42°. Find m/FHG.
Step
1
2
try
Angle
m/CIH 100°
m/BGD = 42°
mz
B.
42% G
Select a Reason
Reason
Given
Given
F
H
E
100°
A
C
A triangle is a plane figure that consists of three sides and three internal angles. Thus m<FHG is [tex]122^{o}[/tex].
How to illustrate the triangleA triangle is a family of polygon which is bounded by three straight sides, thus forming three internal angles. The sum of the internal angles of a trigon is [tex]180^{o}[/tex]. While exterior angles are angles which are outside the edges of a triangle.
From the given question;<IGH = <BGD = 42° (vertically opposite angles)<HIG = 180 - <CIH = 180 - 100<GIH = [tex]80^{o}[/tex]
Thus, we can conclude that;<IGH + <GIH + <GHI = [tex]180^{o}[/tex]42 + 80 + <GHI = [tex]180^{o}[/tex]<GHI = [tex]180^{o}[/tex] - 122 = 58<GHI = [tex]58^{o}[/tex]So that;m<FHG
= [tex]180^{o}[/tex] - M<GHI = [tex]180^{o}[/tex] - 58
= [tex]122^{o}[/tex]m<FHG
= [tex]122^{o}[/tex]
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a standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 1313 cards (ace, two through ten, jack, queen, and king) for a total of 5252 cards in all. 1) how many cards in the deck are either a jack or a heart?
The number of cards in the deck are either a jack or a heart are 17.
What is card deck?
A playing card is a specially made piece of card stock, heavy paper, thin cardboard, paper coated with plastic, cotton-paper blend, or thin plastic that is imprinted with distinctive motifs. To make handling easier, each card frequently has a finish on the front and back.
Given:
A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all.
We have to find the number of cards in the deck are either a jack or a heart.
Since, there are four Jack in a 52 card deck.
So, one jack can be chosen by 4C1 ways.
Also there are 13 cards of hearts in a 52 card deck.
So, one heart can be chosen by 13C1 ways.
The number of ways = 4C1 + 13C1 = 4 + 13 = 17.
Hence, the number of cards in the deck are either a jack or a heart are 17.
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A juice company introduces a new recipe which
contains less sugar. A bottle of juice made using the
new recipe is shown below.
If the bottle of juice now contains 8.19 g of sugar,
how many grams (g) of sugar did it contain before
the new recipe was introduced?
Answer: x = 18
Step-by-step explanation:
1) 100% - 54.5% = 45.5%.
2) 45.5/100 = 0.455.
3) 0.455 * X = 8.19g.
4) x = 8.19/0.455.
5) x = 18.
a researcher found that a cigarette smoker smokes on average 31 cigarettes a day. she feels that this average is too high. she selected a random sample of 8 smokers and found that the mean number of cigarettes they smoked per day was 28. the sample standard deviation was 2.9. at
At 0.01 significance level the hypothesis is rejected.
Null Hypothesis (H₀): The sample data occurs purely from chance.
Alternative Hypothesis (H₁): The sample data is influenced by some non-random cause.
If the p-value of the hypothesis test is less than some significance level (e.g. α = .01), then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.
Given that,
x = 28
s = 2.9
μ = 31
n = 8
α = 0.01
Then, the Null Hypothesis : H₀ = 31
The Alternate Hypothesis : H₁ < 31
The average number of cigeratte smoker per day is less than 31.
Test Statistics:
t = x -μ / s√n
= 28 - 31/ 2.9√8
= -3/ 8.41
= -0.356
Since the p-value of 0.0046 is less than the significance level of 0.01, the auditor rejects the null hypothesis.
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Jenny says the when you multiply any whole number by a fraction, the product is always less than the whole number. Do agree with Jenny Why or Why not? if no, provide an example
Answer: When multiplying a whole number by a PROPER fraction (always less then 1), the product is always less than a whole number. So yes, i agree with jenny when using proper fractions.
the speed of a car, measured in miles per hour, was determined 10 times at random. the results are 22, 43, 35, 32, 41, 28, 29, 30, 37, and 43 miles per hour. construct a 95% confidence interval for the mean speed of this vehicle.
28.9641 ≤ x-bar(t) ≤ 39.0359.
Step-by-step explanation:1. Determine the size of the sample (n).Knowing that we have 10 different values of speed, the size of the sample is 10; n=10. Therefore, this sample is considered statistically small because n < 30.
2. Calculate the arithmetic mean of the sample.Arithmetic mean= (Sum of all values) / (Amount of values)
x-bar= (340) / (10)
x-bar= 34.0000.
x-bar= arithmetic mean.
3. Calculate the standard deviation using the formula for samples.We're going to use the Microsoft Excel tool for the standard deviation for samples (check attached image 1).
Standard deviation for samples (s)= 7.0396.
4. Calculate σ(x-bar).Check attached image 2.
σ(x-bar)= 2.2261.
5. Calculate α/2.α is the error that the confidence interval will have. Given a 95% confidence level, we know that the error is 5%; Error= 1 - Confidence.
α/2= 5%/2= 0.05/2= 0.025.
6. Find the absolute t-student value for α/2.You can either use the probability tables or the Microsoft Excel tools to find the inverse of a t-student distribution for this α/2 value (check attached image 3).
In this case we use the t-student distribution instead of the normal distribution because the sample size is small and the standard deviation of the population is unknown.
T-student value= -2.2622
Absolute t value= 2.2622.
7. Calculate the intervals.Check attached image 4 to see the formulas.
Lower limit = (34) - (2.2622*2.2261) = 28.9641
Upper limit = (34) + (2.2622*2.2261) = 39.0359
28.9641 ≤ x-bar(t) ≤ 39.0359
8. Conclude.This result means that the value of speed could be any value between 28.9641 and 39.0359, including, with a 95% confidence level. There's a 5% chance that a newly measured value of speed is outside this interval.
in a recent poll, 330 people were asked if they liked dogs, and 73% said they did. find the margin of error of this poll, at the 95% confidence level.
The confidence interval for the one-way analysis of variance experiment be, (138.94 , 181.06) and the margin of error of the poll be,
±31.06.
On Subtracting 1 from your sample size, we get
330 – 1 = 229.
On Subtracting confidence level from 1, and then divide by two.
(1 – .95) / 2 = 0.025
Now, df = 229 and α = 0.025
from the table at df = 999 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
150 / √(330) = 1.37
Now, 2.262 × 1.37 = 31.06
So, the confidence interval be,
(150 - 31.06 , 150 + 31.06) = (138.94 , 181.06)
Hence, the confidence interval for the one-way analysis of variance experiment be, (138.94 , 181.06) and the margin of error of the poll be,
±31.06.
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Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
An Endure chosen randomly the likelihood of any battery lasting longer than 550 hours is 10.56%.
What does z score mean?An indicator of how nearly a value relates to the mean of either a set of values is called a Z-score.Z-score is quantified using standard deviations relative to the mean.The data point's entire score is equal to the mean score when the Z-score is 0.The amount that the raw score departs first from mean is determined using the Z score.These steps are used to determine the Z score:
z = (x - μ)/σ
As mentioned in question-
x > 550 and μ = 500, σ = 40:
z = 550 - 500 / 40
z = 1.25
Obtain the p-value from normal distribution chart,
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Thus, an Endure chosen at random the likelihood of any battery lasting longer than 550 hours is 10.56%.
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im almost done with this
Answer:
[tex]1\frac{1}{2}[/tex]
Step-by-step explanation:
we multiply the fractions
1/8 x 12/1
12/8
1 4/8
1 1/2
Hopes this helps please mark brainliest
on average, a banana will last 6.5 days from the time it is purchased in the store to the time it is too rotten to eat. is the mean time to spoil greater if the banana is hung from the ceiling? the data show results of an experiment with 15 bananas that are hung from the ceiling. assume that that distribution of the population is normal.
No, the mean time to spoil is not necessarily greater if the banana is hung from the ceiling.
This can only be determined by analyzing the data from the experiment with 15 bananas. If the sample mean is greater than 6.5 days, then the mean time to spoil is greater when the banana is hung from the ceiling. If the sample mean is less than or equal to 6.5 days, then the mean time to spoil is not necessarily greater when the banana is hung from the ceiling.
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Mr. Jones bought 6 and 2/7 lb. of salmon. He cooked 1/5 of it for lunch. How much salmon did he have for lunch?
The amount of the salmon left after Mr Jones used some part is
5 and 1/35 lbHow to find the amount leftTotal amount of salmon bought is 6 and 2/7 lb = 6 2/7 lb
The amount used is 1/5 of the amount Mr Jones bought
= 1/5 * 6 2/7
= 44 / 35
= 1 9/35
= 1.257
The amount left is calculated by subtraction
= 6 2/7 - 1 9/35
= 176 / 35
= 5 1/35
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Keiko is using metric units of capacity to find an equivalent measure for 3 gallons. She records the liquid volume using milliliters and deciliters. Which unit will give a more precise measure? Explain.
If she records the liquid volume using milliliter and deciliter, then the deciliter gives more precise measure
The total capacity = 3 gallon
Convert the gallon to milliliter
We know
1 gallon = 3.785 ml
The total capacity in milliliter = The total capacity × 3.785
Substitute the values in the equation
= 3 × 3.785
= 11.355 milliliter
Convert the gallon to deciliter
We know,
1 gallon = 37.854 deciliter
Total capacity in deciliter = The total capacity × 37.854
Substitute the values in the equation
= 3 × 37.854
= 113.562 deciliter
Here deciliter is much smaller than millimeter
Therefore, deciliter gives more precise measure
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Solve for each variable. Show your work and explain in paragraph form how you solved each problem.
Base Angles Theorem
Converse to Base Angles Theorem
Corollary
Converse to the corollary
Sum of Interior Angles
Exterior angles
Answer:
can u see when i do this????
Step-by-step explanation:
A cylindrical container with capacity 355cc is to be produced. The bottom and side of the container are to be made of material that costs 0. 02 cents per cm2 , while the top of the container is made of material costing 0. 03 cents per cm2. Find the dimensions that will minimize the cost of the container. Provide a convincing argument that your results give the least expensive cost
The dimension of the cylindrical container that will minimize the cost of the container is a radius of 4.371 and a height of 25.85
since we know that the volume of a cylinder is :
355=πr²h, where r is the radius of the base and h is the height
So, we can say h=355/πr², here we have two circular components with the areas 2A=2πr² , for the cost of 0. 02 cents per cm² and a rectangular component of area A=2πrh , with cost of 0. 03 cents per cm².So the cost function will be :
C=0.02(2πr²)+0.03(2πrh)
C=0.04(πr²)+0.06(πrh), substuting the vale of h
C=0.04(πr²)+0.06(πr(350/πr²))
C=0.04(πr²)+(21/r), differentiating both sides we get .
C'=0
=>0.08(πr)-(21/r²)= 0, simplifying the equation we get
=>r= 3√525/2π =4.371
so for h, it will be: 355/π(3√(525/2π)) = 355/π(3√(83.55)) =350/π( 4.371) =25.85
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gregory has a coupon for $1 off the purchase of 3 boxes of munchie brand cereal. the store has 5 different varieties of munchie brand cereal. how many ways can gregory choose 3 boxes of cereal?
Gregory has 10 ways to choose 3 boxes of cereal.
What do you mean by purchase?
A corporation or organization uses the purchasing process to buy products or services in order to achieve its objectives. Although many organizations make an effort to establish standards for the purchasing process, procedures can differ significantly between organizations.
According to data in the given question,
We have :
The purchase of 3 boxes and the store has 5 different varieties of munchie brand cereal.
The order in which the boxes of cereal are chosen is not important as Gregory can randomly choose any 3 different varieties. So, this is a combination problem.
Use the combination formula:
[tex]_nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Putting n=5 (5 different varieties) and r=3 (3 different varieties). So, the number of ways Gregory choose 3 boxes of cereal is:
[tex]_{5}C_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!2!}= \frac{5.4.3.2.1}{3.2.1.2.1} _{5}C_3=\dfrac{5\cdot 4}{2\cdot 1}=10[/tex]
Therefore, the required answer is 10 ways.
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1 how fast must a ball be rolled along a 70-cm-high table so that when it rolls off the edge it will strike the floor at this same distance (70 cm) from the point directly below the table edge?
A ball must be fast rolled is 185.2cm/sec, according to the question.
What do you mean by distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
According to the given question,
We have the given information:
Table height = h = 70cm
Distance = s = 70cm
g = 9.8[tex]ms^{-1}[/tex]
Now, we have to find the time of falling,
[tex]t=\sqrt{\frac{2h}{g} }=0.378c[/tex]
Horizontal velocity,
[tex]v=\frac{s}{t}=\frac{70cm}{0.378s}=185.2cm/s[/tex]
Therefore, the required answer is 185.2cm/sec.
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Given the following piecewise function,
The value of f(0) is f(0) = 3 and the value of f(-4) is f(-4) = 1
Determining the value of a functionFrom the question, we are to determine the value of the given functions
The functions are
f(0) and f(-4)
First, we will determine the value of f(0)
Since 0 ≥ -2, we will use the function
f(x) = x² + 2x + 3
Thus,
f(0) = (0)² + 2(0) + 3
f(0) = 0 + 0 + 3
f(0) = 3
Now, we will determine the value of f(-4)
Since -4 < -2, we will use the function
f(x) = x + 5
Thus,
f(-4) = -4 + 5
f(-4) = 1
Hence, f(0) = 3 and f(-4) = 1
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Please HELPPPP
Quadrilateral ABCD is a square and the length of AC is 20 cm. What is the length of DE and DC?
What is
m ADE ?
For the square on the diagram, we can see that:
DE = 10cmDC = 14.14cmmADE = 45°What is the length of DE and DC?
Remember that all the sides of a square have the same length.
Here we know that AC, the diagonal of the square, has a measure of 20 cm.
Then the length of DE, which is half of the diagonal of the square, is half of that, then:
20cm/2 = 10cm
DE = 10cm
DC is one of the sides of the square. Remember that for a square of sidelength S, the diagonal is:
D = √2*S
Then the sidelength is:
S = D/√2
Here we know that the diagonal measures 20 cm, then:
DC = S = 20cm/√2 = 14.14 cm
DC = 14.14cm
Finally, mADE refers to the measure located at the vertex D on the triangle on the angle ADE.
Remember that all the angles of a square measure 90°, and here the ray DE divides that angle in two halves, then mADE = 90°/2 = 45°
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a car is driving at 100 kilometers per hour. how far, in meters, does it travel in 2 seconds? meters
A car travels 500/3 meters in 2 seconds.
What is speed?
The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.
Here, we have
Speed of car = 100 KM/ hour
1 km= 1000m
1 hour = 3600 seconds
Let's find the speed of the car in Meters/second
Speed of car in m/sec = 100*1000 m/3600 second
Here we have taken 1000 for km and 3600 for an hour
Speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second
Speed of car in m/sec = 250/9 m per sec
We know that
Distance = speed*time
Speed = 250/9 m per sec
Time = 2 second
Distance = 250/9 * 2 meters = 500/3 meters
Hence, a car travels 500/3 meters in 2 seconds.
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a piece of solid aluminum is in the shape of a cube. if the temperature of the cube is increased so that the length of each side increases by a factor of 0.001 (that is, by 0.10%), by what factor does the volume of the cube increase?
The factor by which the volume of cube increased is 0.0030
What is a cube ?
A cube is a three-dimensional solid object in geometry that is surrounded by six square faces, facets, or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.
The fundamental distinction between a cube and a square is that the former has three dimensions—length, breadth, and height—while the latter only has two. A cube is composed of squares, which are a type of 2-dimensional (2D) shape (such as a circle, square, triangle, etc.).
let l be the side of a cube
the new length of cube is l' = 1.001l
Initial volume (v1) = l³
final volume (v2) = (1.001)³l³
The factor by which the volume increased is = v1 / v2
= ((1.001)³l³ - l³)/l³
= 0.003003
= 3 x 0.001
≅ 0.0030
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Evaluate each expression.
Answer:
0.2
Step-by-step explanation:
First part yields 0.008 if you take sqrt((1/25)^3).
Then the cuberoot of 0.008 is 0.2.
Answer:
Look at the attachment! :D
Hope this helps!
Step-by-step explanation:
When contructing 95% confidence interval for the mean when the parent population i right kewed and the ample ize i mall, the proportion of interval that include the population mean approache
So when parent population is right-skewed and the sample size is small, the percentage of intervals that include population mean is (above, below, equal to) 0.95 when building 95% confidence intervals for said mean.
Explain the term confidence interval?A confidence level of both the CI refers to the likelihood that its confidence interval contains the actual population mean value.
Any confidence level can be used to determine a CI, although 95% is the most typical value.A 95% confidence interval, strictly speaking, means that if we generate a 95% confidence interval each of 100 independent samples, then about 95 of a 100 confidence intervals include the true mean value (μ).Thus, when parent population is right-skewed and the sample size is small, the percentage of intervals that include population mean is (above, below, equal to) 0.95 when building 95% confidence intervals for said mean.
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First Ave.
70°
300 ft
Main St.
Canal St.
Part A:
What is the distance, in feet, on Main Street between First Avenue and Canal Street? Round your answer to the nearest hundredth.
The distance, in feet, on Main Street between First Avenue and Canal Street, using relations in a right triangle, is of:
319.25 ft.
How to obtain the distance?The situation is represented by a right triangle, hence the three trigonometric measures are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Sine of angle = length of opposite side divided by the length of the opposite side.From the image given at the end of the answer, the parameters are given as follows:
Missing Information: Hypotenuse.The side length opposite to the angle of 70º is of 300 ft.Hence the distance of the Main Street is found using the sine of the angle of 70º, as follows:
sin(70º) = 300/x
x = 300/sin(70º)
x = 319.25 ft.
Missing InformationThe right triangle is given by the image shown at the end of the answer.
More can be learned about the relations in a right triangle at https://brainly.com/question/16437014
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