The required expression by distributing the w on the right side, we get: A = 5w^2 + 4w
Explain about Rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form.
According to question:Let's call the width of the parking lot "w". According to the problem, the length is 4 yards more than 5 times the width, so we can write the length as 5w + 4.
The formula for the area of a rectangle is A = length × width. Substituting in our values, we get:
A = (5w + 4) × w
Simplifying this expression by distributing the w on the right side, we get:
A = 5w^2 + 4w
This is the formula for the area of the rectangular parking lot in terms of its width. To find the actual area, we need to know the width. Once we have that, we can plug it into the formula and solve for A.
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From the tree diagram find the following.
(a) P(An E)
0
(b) P(A)
(c) P(A|E)
X
0.1
0.9
A A
0.3
0.3
0.4
0.4
0.4
0.2
Answer:
(a) P(A ∩ E) = 0.03
(b) P(A) = 0.39
(c) P(A | E) = 0.1
Step-by-step explanation:
The first level of the tree gives the following probabilities
P(E) = 0.1
P(E') = 1 - P(E) = 0.9
The second level gives conditional probabilities
P(A|E) = 0.3 this is the top most branch from the root
P(A ∩ E) = P(A|E) P(E) = 0.3 x 0.1 = 0.03 Answer(a)
To find P(A) we find all routes that will end in A, compute each probability and add up the individual probabilities
For event E happening, P(A ∩ E) = 0.03 which is computed in A
However A can also happen when the complement event E' happens
P(A ∩ E') = P(A | E') P(E') = 0.4 x 0.9 = 0.36
Add these two together to get 0.03 + 0.36 = 0.39 Answer (b)
P(A|E) is nothing but the probability value when we follow the E branch first followed by the A branch
This is 0.1 answer (c)
A rectangle’s length is three times its width, w. Its area is 243 square units. what would the equation be to find the width of the rectangle?
Answer:
3w² = 243
Step-by-step explanation:
Briana ha $3 in her piggy bank. She has all quarters and dimes. Write and equation in STANDARD FORM to represent this scenario. Use X and Y as your variables (Ax+By=C)
The equation in standard form representing the scenario where Briana has $3 in her piggy bank and has all quarters and dimes, using x for the number of quarters and y for the number of dimes, is [tex]25x + 10y = 300[/tex].
Let x be the number of quarters and y be the number of dimes Briana has in her piggy bank.
The value of each quarter is 25 cents or 0.25 dollars, and the value of each dime is 10 cents or 0.10 dollars. Therefore, the total value of the coins in Briana's piggy bank can be expressed as:
[tex]0.25x + 0.10y[/tex]
Since Briana has $3 in her piggy bank, we can set up the following equation:
[tex]0.25x + 0.10y = 3.00[/tex]
To write this equation in standard form ([tex]Ax + By = C[/tex]), we need to clear the decimals by multiplying both sides of the equation by 100:
[tex]25x + 10y = 300[/tex]
Therefore, the equation in standard form that represents this scenario is:
[tex]25x + 10y = 300[/tex]
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Solve algebraically for y: 4(v-3) ≤ 4(2y + 1)
Answer:
first remove the parentheses on both sides by distributing the multiplication. Then collect all the terms involving
y
on one side (say the left) and the terms without
y
on the right. Finally, divide both sides by the coefficient of
y
. (the number in front of
y
).
It looks like this:
4
(
2
y
−
1
)
=
4
(
y
+
3
)
8
y
−
4
=
4
y
+
12
8
y
−
4
y
=
12
+
4
(subtract
4
y
from both sides and add
4
to both sides)
4
y
=
16
4
y
4
=
16
4
y
=
4
Check your answer.
More thought, looking at the equation:
Instead of distributing the
4
's on both sides, you could start by dividing both sides by
4
(multiplying by
1
4
. This keeps the numbers smaller. It looks like this:
4
(
2
y
−
1
)
=
4
(
y
+
3
)
1
4
[
4
(
2
y
−
1
)
]
=
1
4
[
4
(
y
+
3
]
)
#1/4*4 = [1/4 *4] (y+3)
2
y
−
1
=
y
+
3
2
y
−
y
=
3
+
1
(subtract
y
and add
1
on both sides)
y
=
4
Check your answer.
Answer link
Gió
Mar 25, 2015
First multiply
4
to get rid of the brackets:
8
y
−
4
=
4
y
+
12
Now, isolate the
y
s on one side and numbers on the other of the
=
sign (remembering to change sign in crossing the
=
sign);
8
y
−
4
y
=
+
4
+
12
Notice the change of sign of
4
y
and
−
4
;
now we can add and subtract:
4
y
=
16
The
4
is multiplying the
x
and can go to the right dividing to get:
x
=
16
4
=
4
hope it helps!
what number when divided by 15 20 30 the remainder is always 8
The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The number which is divisible by 15, 20, or 30 will be given as,
LCM of the numbers 15, 20, and 30 will be given as,
2 | 15, 20, 30
2 | 15, 10, 15
3 | 15, 5, 15
5 | 5, 1, 5
1, 1, 1
LCM = 2 x 2 x 3 x 5
LCM = 60
The number whose remainder is always 8 is given as,
⇒ 60 + 8
⇒ 68
The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.
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Neeeeeed hellppppppppll
To draw a centroid for ΔABC, follow the steps below.
Draw the triangle ABC with the line segment CD bisecting it. Line segment CD is called a median and it connects the midpoint of side AB to the opposite vertex, C.Using a protractor, measure the distance between B and C, place the protractor on C and make an arc on both sides of the triangle. Place the protractor on B and repeat the same step. place your ruler such that the ruler is actactly in between the twin arcs on both sides of the triangle, mark the point where the ruler crosses the line segment BC.Call this point long BC point x.repeat this for LIne segment AC.Call the point on line AC y.Draw another line segment from point B to the midpoint of side BC, that is point x and repeat same for point y.The intersection point of line segments CD and XY is the centroid of the ΔABC. Label this point as G.
See the sample attached. Note that this is not constructed to scale.
What is a Centroid?The centroid is the point where the three medians of a triangle intersect.
A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. In this case, line segment CD is one of the medians of triangle ABC because it connects the midpoint of AB (which is also the midpoint of CD) to vertex C. The other two medians connect the midpoints of the other two sides to their opposite vertices.
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Find the value of x
Answer:
x = 20
Step-by-step explanation:
since the 3 sides of the triangle are congruent then it is equilateral with 3 congruent angles, each of 60° , then
3x = 60 ( divide both sides by 3 )
x = 20
Answer:
20
Step-by-step explanation:
We know that sum of corner of a triangle is 180° and if the triangle is equilateral, the corners are same
180:3=3x
60=3x
x=20
Johnson's Farm charges a fee of $26 to enter their orchard, then charges $6 for every pound of cherries you pick. Mood's Farm does not charge customers an entry fee, but cherries picked cost $8 a pound. How many pounds of cherries would you need to pick in order to pay the same amount at each farm?
There are 11/3 pounds of cherries at Johnson's Farm in order to pay the same amount as picking 6 pounds of cherries at Mood's Farm.
In general, the unitary method is a useful tool for solving problems like this where we need to compare the cost of two different scenarios. We can set up equations based on the rates or costs involved, and then use algebra to solve for the unknown variables.
To begin, let's use a unitary method to find the total cost of picking cherries at Johnson's Farm. We know the entry fee is $26, so we can start with that. Then, for each pound of cherries picked, the cost is $6. So, if we let x be the number of pounds of cherries picked, the total cost at Johnson's Farm would be:
Total Cost = $26 + $6x
Now, let's use a unitary method to find the total cost of picking cherries at Mood's Farm. We know that there is no entry fee, so we can start with just the per-pound cost of $8. If we let y be the number of pounds of cherries picked, the total cost at Mood's Farm would be:
Total Cost = $8y
To find how many pounds of cherries you would need to pick at each farm in order to pay the same amount, we need to set these two total costs equal to each other and solve for x:
$26 + $6x = $8y
$6x = $8y - $26
x = (8/6)y - 13/3
x = (4/3)y - 13/3
So, if you picked 6 pounds of cherries at Mood's Farm (y = 6), the equivalent cost at Johnson's Farm would be:
x = (4/3)(6) - 13/3
x = 8 - 13/3
x = 11/3
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given that the electricity for home use is 5 cents per kilowatt-hour (kwh), how much would it cost to operate 5 fluorescent 40w light bulbs for the months of april and may if they are on for 3 hours/day?
The total cost to operate 5 fluorescent 40w light bulbs for the months of April and May if they are on for 3 hours/day is given as follows:
$1,830.
How to obtain the total cost?The total cost is obtained applying the proportions in the context of the problem.
The number of kilowatt hours is given as follows:
200 kw in total per day, as 5 bulbs of 40 kw -> 40 x 5 = 200 kw.Bulbs are on for 30 + 31 = 61 days.Each day, the bulbs are on for 3 hours.Hence:
200 x 61 x 3 = 36,600 kwh.
The cost is of $0.05 per kwh, hence the total cost is given as follows:
0.05 x 36600 = $1,830.
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1. Heights of kindergarteners follow an approximately normal distribution with mean = 40 inches and standard
deviation o-5.2 inches. Let be the sample mean height of 10 randomly selected kindergarteners.
(a) Describe the shape, center, and variability of the sampling distribution of for samples of size 10. Interpret the
standard deviation.
The shape of the sampling distribution will be approximately normal, with a center at 40 inches and a standard deviation of 1.645 inches.
What is the shape, center, and variability of the sampling distribution?The mean of the sampling distribution of the sample mean height for samples of size 10 will also be 40 inches.
The standard deviation of the sampling distribution of the sample mean height can be calculated as:
σ/sqrt(n) = 5.2/sqrt(10) = 1.645
So, the shape of the sampling distribution will be approximately normal, with a center at 40 inches and a standard deviation of 1.645 inches.
The variability of the sampling distribution is smaller than the variability of the population distribution, because the standard error is smaller than the population standard deviation. This means that the sample means are more likely to be closer to the population mean than the individual heights in the population.
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Last year, Becky's dog weighed 55 pounds. One year later, she had gained p pounds. Which expression gives her weight one year later?'
Answer: 55+p
Step-by-step explanation: Since p is in unlike terms as 55, you can just write that as is an the expression to represent the dog's weight.
I need explanations under similar shapes
The two major properties of similar shapes include the following:
They must have the same shape.They can have different sizes.What are the properties of similar geometric shapes?In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied because it would either enlarge (increase) or reduce (decrease) them.
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ainder theorem to find P (-3) for P(x) = -2x³-5x²-3.
give the quotient and the remainder for the associated division and the value of P (-3
= -6x]
8
X
The value of P(-3) is -12, Quotient is (-2x² + x - 3) and Remainder is 6.
What is Remainder theorem?Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that a polynomial P(x) divided by a factor (x - a) is not really an element of the polynomial.
Given:
P(x) = -2x³-5x²-3.
Using the remainder theorem, the value of P(3) is given by:
P(-3)= -2x³-5x²-3.
P(-3) = -2(-3)³-5(-3)²-3
P(-3) = -2(-27) -5(-9) -3
P(-3) = -54 + 45 - 3
P(-3) = -12
As, the divisor of P(x) is (x+3).
so, the division is
(x+3) | -2x³-5x²-3 | -2x² + x - 3
-2x³-6x²
__________
x² - 3
x² + 3x
________
-3x - 3
-3x - 9
_______
6
So, the Quotient is (-2x² + x - 3) and Remainder is 6.
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Help with geometry pls?
The following are the area of the sectors:
6a). π square inches
6b). 24π square centimeters
7a). 9 square centimeters
7b). 16.7 square inches
How to evaluate for the area of the sectors.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
For question 6:
a). (40/360) × π × 3 in × 3 in = π in²
b). (135/360) × π × 8 cm × 8 cm = 24π cm²
For question 7:
a). (90/360) × π × 6 cm × 6 cm = 9 cm²
b). (60/360) × π × 10 in × 10 in = 16.7π in²
Therefore, the following are the area of the sectors:
6a). π square inches
6b). 24π square centimeters
7a). 9 square centimeters
7b). 16.7 square inches
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The rule (x,y)→(y,-x) takes a line to a perpendicular line. Select another rule that takes a line to a perpendicular line
The correct option is E, another rule that takes a line to a perpendicular line (x,y)→(4y,-4x) A B C D OE.
(x,y)→(y,-x)
E:(x,y)→(4y,-4x)→4(y,-x)
So E = (x,y)→(4y,-4x) A B C D OE.
Perpendicular lines play an important role in geometry and trigonometry. They are used to construct right angles, which are essential in measuring angles and finding distances between points. In construction, perpendicular lines are often used to ensure accuracy when building structures, such as walls or flooring.
Perpendicular lines also have real-world applications in navigation, surveying, and astronomy. For instance, in navigation, perpendicular lines are used to calculate a ship's course and location. In surveying, perpendicular lines are used to create precise measurements of land plots, while in astronomy, they are used to calculate distances between celestial objects.The slope of a perpendicular line is the negative reciprocal of the slope of the other line.
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Complete Question: -
The rule (x,y)→(y,-x) takes a line to a perpendicular line. Select all the rules that take a line to a perpendicular line.
A. (x,y)→(2y,-x)
B. (x,y)→(-y,-x)
C. (x,y)→(-y,-x)
D. (x,y)→(0.5y,-2x)
E. (x,y)→(4y,-4x) A B C D OE
next, place point a on the graph to demonstrate how many trips kathy will take if the price is $230 per round-trip ticket. c. if the price of a round-trip ticket is $230, how many trips should kathy take?
Kathy should take 4 trips if the price of a round-trip ticket is 230.
Point A on the graph would be placed at (230, 4). This demonstrates that Kathy should take 4 trips if the price of a round-trip ticket is 230. This can be calculated as follows:
Kathy has a budget of 1,000. Therefore, she can afford 4 round-trip tickets at the price of 230 each. This can be calculated by dividing 1000 by 230, which gives 4. Therefore, Kathy should take 4 trips if the price of a round-trip ticket is 230.
It is important to note that Kathy should also consider other factors such as the cost of other expenses, such as accommodation and food, when deciding how many trips to take. Additionally, Kathy may also want to consider whether the benefits of taking more trips are worth the additional cost.
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QUESTION FOR FOR LIH04
2 2 2 2 = 9 use subtraction addition multiplication addition or parentheses to make the equation true
The numbers 2 2 2 2 can be arranged to make the equation true as follows
(2 + 2/2)² How to arrange the numbers to make the equation trueThe numbers arranged by applying the rule which had acronym of PEMDAS
the full meaning include
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
applying the sequence the problem is solved as follows
= (2 + 2/2)²
solving the parenthesis first we solve the problem inside the parenthesis. Inside the parenthesis we start with division
= (2 + 2/2)²
= (2 + 1)²
Then addition
= (3)²
having completed the parenthesis, we solve for the exponents
= 9
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shawna knows that a correlation between calories of sweeteners consumed and mortality rates among women does not, in itself, mean that drinking more soft drinks will lead to a higher chance of her dying. which of the following would not be a lurking variable in the above scenario? a.) shawna's weight b.) the time of day shawna exercises c.) the number of soft drink brands available for purchase d.) the amount of caffeine available in soft drinks
Answer: Musical preferences
A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely your musical preferences affect mortality or how much sweetener you consume.
The number of soft drink brands available for purchase is not a lurking variable in this scenario. Correct option is C.
The statement is asking which of the given variables is not a lurking variable in the scenario where Shawna is considering the correlation between the calories of sweeteners consumed and the mortality rates among women, and is trying to determine whether drinking more soft drinks will lead to a higher chance of her dying.
A lurking variable is a variable that is not included in the analysis, but has an effect on the relationship between the variables being studied. In this case, the variables being studied are the calories of sweeteners consumed and the mortality rates among women, and the effect of drinking more soft drinks on the chances of dying.
Out of the given variables, the number of soft drink brands available for purchase would not be a lurking variable, as it does not have an effect on the relationship being studied.
Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could all potentially have an effect on the relationship being studied, either as confounding variables or moderators.
For example, Shawna's weight could be a confounding variable, as it is associated with both sweetener consumption and mortality rates. The time of day she exercises could be a moderator, as exercise may affect the metabolism of sweeteners and caffeine, which could in turn affect mortality rates.
The amount of caffeine available in soft drinks could be a confounding variable, as caffeine consumption is associated with both sweetener consumption and mortality rates.
In summary, the number of soft drink brands available for purchase is not a lurking variable in this scenario, while Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could potentially be confounding variables or moderators that need to be accounted for in the analysis.
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3. In the figure below, what is m/2 if m26 = 120°?
A.
60°
B. 90⁰
32
41
5 6
87
C. 120°
D. 150°
The value of m <2 is C. 120°
What is a Corresponding Angle?In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.
In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.
Therefore,
m<2 = m<6
This is because they are corresponding angles
With this in mind, m<6 = 120°
Therefore, m<2 = 120°
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A roller coaster with a potential energy of 235,200 J sits at the top of a 30 m high hill. What is the mass of the roller coaster? (Formula: PE = mgh)
How do i get 800?
The mass of the roller coaster is 800.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
PE = 235,200
Height = h = 30 m
Now,
PE = mhg
We use g = 9.8
So,
Substituting the values.
235,200 = m x 30 x 9.8
m = 235200 / (9.8 x 30)
m = 235200 / 294
m = 800
Thus,
The mass of the roller coaster is 800.
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A square pyramid is shown. What is the surface area?
A square based pyramid, with bases labeled 3.5 centimeters and side length of triangle labeled 7 centimeters.
(4 points)
19.25 cm2
30.625 cm2
49.625 cm2
61.25 cm2
Answer:
61.25
Step-by-step explanation:
brainlest pls and I hope this helped u :)
Solve for x questions in picture
Answer: x = 22
Step-by-step explanation:
Subtract 34 from both sides.
x + 34 - 34 = 56-34 --> x = 22
which function represents an exponential decay function with a y-intercept of -3?
a. f(x) = (0.5)^x - 4
b. f(x) = (0.5)^x - 3
c. f(x) = 2^x - 4
d. f(x) = 2^x - 3
Answer:
A
Step-by-step explanation:
The line has a negative slope, with a y-intercept of (0,-3), and an x-intercept of (-2,0)
Garth was making lemonade for the school carnival. He bought 14 1/4 pounds of sugar to use for the lemonade. When he finished making lemonade, he had 4 3/4 pounds of sugar left over. How much sugar did he use for the lemonade?
A) 19
B) 18 1/2
C) 10 1/2
D) 9 1/2
4 3/4 pounds amount of sugar were left after Garth used 9 1/2 pounds for the lemonade.
9 1/2 pounds of sugar were used from 14 1/4 minus 4 3/4.
Garth needed 14 1/4 pounds of sugar to make lemonade for the school carnival, so he purchased them. He had 4 3/4 pounds of sugar left over when he had done preparing the lemonade. This indicates that he made the lemonade using 9 1/2 pounds of sugar. He took the 14 1/4 pounds of sugar he purchased and subtracted the 4 3/4 pounds that were leftover to get at the amount of sugar he utilised, or 9 1/2 pounds. This indicates that the correct response is D: The lemonade required 9 1/2 pounds of sugar.
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32 children voted for thier favorite ice cream chocolate 3/8 so how may children voted for chocolate explanation
Multiplying the total number of children by the fraction that like chocolate yields [tex]32(3/8)=12[/tex]
What is the answer for -6+3a+4-5a+0
Answer:
-2a-2
Step-by-step explanation:
We can start solving this expression by combining like terms: Constants, or the number values, and Variables(the letters)
We can combine -6, 4, and 0 to get -2.
We can combine 3a and -5a to get -2a.
-2a + (-2) is the expression we are left with.
We can simplify this to
-2a - 2.
It can't be simplified further, so our answer is
-2a-2.
The t-value changes depending on the number of data points collected.
a. True
b. False
The statement that " t-value changes depending on the number of data points collected" is (b) False because t-value is a statistic that is used in hypothesis testing to determine the difference between 2 sample means is significant or not.
The t-value does depend on the sample size (number of data points) as well as the sample mean and standard deviation, but it does not change "depending on" the number of data points in the sense that the same data set will always produce the same t-value for a given statistical test.
So , it is important to note that the t-value is a fixed value for a given set of data, regardless of the number of data points collected.
Therefore, if the same data set is used to perform a t-test multiple times, the resulting t-value will always be the same.
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pls help i dont understand
Answer: C= 24-4t
Step-by-step explanation: Since four were eaten each dat the blue is getting lower, use -4t to represent it. 24 is the total amount gotten by substitution.
I need help with this can someone please help ty
Answer:
Below
Step-by-step explanation:
Go to x = 1 on the x axis number line.....go UP to where the graph crosses x = 1 to find y = 1 <====this is your answer for f(1)
for f(-) go to x = 3 then go UP to the graph crossing at y = 1 <--answer
