The length and width of the rectangle are equal to: 7 ft and 5 ft, respectively
QuadrilateralsThere are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2L+2W.
For this question, the length is 2ft longer than the width - L=2+W. Thus,
24=2*(2+W)+2W
24=4+2W+2W
24-4=4W
20=4W
W=5 ft
If W=5, L will be 2+5=7 ft.
Read more about the perimeter here:
https://brainly.com/question/24571594
$SPJ1
Which absolute value function defines this graph?
The vertex of the graph is at (-2, 3).
This means the equation is of the form [tex]f(x)=a|x+2|+3[/tex].
Substituting in the coordinates of one of the other points on the graph that is not the vertex, such as (-1, -1),
[tex]-1=a|-1+2|+3\\\\-1=a+3\\\\a=-4[/tex]
So, the equation is [tex]\boxed{f(x)=-4|x+2|+3}[/tex]
A 3-gallon bucket of paint costs $108.60. What is the price per quart?
Answer:
9.05
Step-by-step explanation:
make gallons into quarts
quar prefix in many languages means 4
1 gallon is 4 quarts
3 gallons is 4 times 3 -> 12 quarts
just by seeing 108 and 12 the answer will be around 9
108.90 ÷ 12 = 9.05
The sum of 9 consecutive integers is 369. The middle integer is:
A. 38
B.35
C.41
D.10
PLEASE ANSWER QUICKKKk
We have an odd number of consecutive integers, therefore the middle one is equal to the average of all of them. And since the average is equal to the sum of the numbers divided by their number, the middle integer in this problem is equal to 369 divided by 9, which is equal to 41.
Kubin Company's relevant range of production is 29,000 to 33,000 units. When it produces and sells 31,000 units, its average costs per unit are as follows:
Direct materials $8.90
Direct labor $5.90
Variable manufacturing overhead $3.40
Fixed manufacturing overhead $6.90
Fixed selling expense $5.40
Fixed administrative expense $4.40
Sales commissions $2.90
Variable administrative expense $2.40
1. If 29,000 units are produced and sold , what is the variable cost per unit produced and sold ?
2. If 33,000 units are produced and sold , what is the variable cost per unit produced and sold ?
3. If 29,000 units are produced and sold , what is the total amount of variable cost related to the units produced and sold ?
4. If 33,000 units are produced and sold , what is the total amount of variable cost related to the units produced and sold ?
5. If 29,000 units are produced , what is the average fixed manufacturing cost per unit produced ?
6. If 33,000 units are produced , what is the average fixed manufacturing cost per unit produced ?
7. If 29,000 units are produced , what is the total amount of fixed manufacturing overhead incurred to support this level of production ?
8. If 33,000 units are produced , what is the total amount of fixed manufacturing overhead incurred to support this level of production ?
Which of the following is a geometric sequence?
• A. 6, 18, 54, 162
O B. 1, 4, 5, 9, 14
O C. 3, 6, 9, 12, 15
O D. 3, 5, 8, 13, 21
Answer: A. 6, 18, 54, 162
Step-by-step explanation:
Each term is 3 times the last, meaning the common ratio is 3.
Daniel plays a shooting game in a funfair. He needs 48 points to get a skateboard. Each shot that hits the target will be given 6 points while 4 points will be deducted for every failed attempt. Daniel has already failed in three attempts. how many shots that are needed to hit the target for him to win the skateboard
The vehicle preference of police officers and firefighters is given in the table.
Police Officers Firefighters
Cars 12
Trucks 9
SUVS 15
3
4
2
Based on the information in the table, which of the following is an example of independent events.
An example of independent events is P(Police Officers and choose cars).
Which pair of events are called independent events?When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.
Symbolically, we have:
Two events A and B are said to be independent if we have:
P(A ∩ B) = P(A)P(B)
Police Officers Firefighters
Cars 12 3
Trucks 9 4
SUVs 15 2
Let P(A) = Firefighters choose cars
P(B) = Firefighters choose Trucks
P(A ∩ B) = Police Officers choose cars
Thus,
P(A ∩ B) = P(A)P(B)
12 = (4) ( 3)
Hence, an example of independent events is P(Police Officers and choose cars).
Learn more about independent events;
https://brainly.com/question/12619550
#SPJ1
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe
the population proportion is approximately p 37%. You would like to be 99.5% confident that your
esimate is within 2.5% of the true population proportion. How large of a sample size is required?
H
n=
The sample size required is 2938.645
What is Probability ?Probability is the likeliness of an event to happen.
It is given that
p = .37
∈ = 0.025
∝ = 1 - 0.995 = 0.005
∝[tex]\rm z_{\alpha/2} = z_{0.005/2} = 2.807[/tex] (From z table)
Sample size n is given by
[tex]\rm n = (\dfrac{z_{\alpha/2}}{\epsilon})^2 p (1-p)\\\\n = (\dfrac{2.807}{.025})^2 *0.37*(1-0.37)\\\\n = 2938.645\\[/tex]
Therefore the sample size required is 2938.645
To know more about Probability
https://brainly.com/question/11234923
#SPJ1
Suppose that x and y vary inversely. Write a function that models each inverse
variation.
x = -13 when y = 100
EE ⁹⁹ 흐흐흐≡
Q√ C
Since the product of variables in inverse proportion is constant, the equation is [tex]\boxed{xy=-1300}[/tex]
St^2 e^-10t dt
Evaluate the intergral
It looks like you're talking about the indefinite integral
[tex]\displaystyle \int t^2 e^{-10t} \, dt[/tex]
Integrate by parts:
[tex]\displaystyle u\,dv = uv - \int v\,du[/tex]
Let
[tex]u = t^2 \implies du = 2t \, dt[/tex]
[tex]dv = e^{-10t} \, dt \implies v = -\dfrac1{10} e^{-10t}[/tex]
Then
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \int t e^{-10t} \, dt[/tex]
Integrate by parts again, this time with
[tex]u = t \implies du = dt[/tex]
[tex]dv = e^{-10t} \, dt \implies v = -\dfrac1{10} e^{-10t}[/tex]
Then
[tex]\displaystyle \int t e^{-10t} \, dt = -\frac1{10} t e^{-10t} + \frac1{10} \int e^{-10t} \, dt[/tex]
Putting everything together, we get
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \int t e^{-10t} \, dt[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \left(-\frac1{10} t e^{-10t} + \frac1{10} \int e^{-10t} \, dt\right)[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} + \frac1{50} \int e^{-10t} \, dt[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} + \frac1{50} \left(-\frac1{10} e^{-10t}\right) + C[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} - \frac1{500} e^{-10t} + C[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = \boxed{-\frac{e^{-10t}}{500} \left(50t^2 + 10t + 1\right) + C}[/tex]
What is the density of the oak board
Step-by-step explanation:
easy how thick it is we need a picture
Given ZW=20. Answer the questions please.
a) Corresponding angles of similar figures are congruent, so [tex]\angle B \cong \boxed{\angle Z}[/tex]
b) Scale factor = (image)/(preimage). Since we are looking for ABCD to WZYX, this means that WZYX is the image and ABCD is the preimage. Thus, the scale factor is [tex]\frac{25}{10}=\boxed{5/2}[/tex]
c) Since the scale factor is 5/2,
[tex]\frac{20}{t}=\frac{5}[2}\\\\40=5t\\ \\ t=\boxed{8}[/tex]
50 children had a choice of beans,plantain and rice.21 of them took beans,24 took plantain and 18 took rice.3 took beans only and 2 took rice only and 9 took plantain only. 5 took all the three items of food required. A.Draw a venn diagram to illustrate this information. B.Use your diagram to find the number of children who took ,1.plantain and beans only. 2.Rice and beans only.3.none of the three items of food.
The Venn diagram to illustrate this information is given in the image attached.
What is the Venn diagram about?The number of children who took plantain and beans only are:
Let beans = a
Rice = b
Plantain = P
So: a + b = 24 - 9 - 5 = 10
Note that 24 children took plantain.
9 children took only Plantain.
5 took the 3 food items.
So:
b + c = 18 -2 - 5 = 11
a + c = 21 - 3 - 5 = 13
P∩B = a + 5
= 6 + 5 = 11
R ∩ B = C + 5
=7 + 5 = 12
None of the three items of food =
50 - (3 + 2 + 9 + 6 + 4 + 7 + 5)
= 50 - 36
=14
Learn more about Venn diagram from
https://brainly.com/question/2099071
#SPJ1
Find slope:
(3,7) & (6,-1)
Answer:
-8/3
Step-by-step explanation:
Slope = (-1-7)/(6-3) = -8/3
Answer:
-8/3
Step-by-step explanation:
You can use the slope formula which is (y2 - y1) / (x2 - x1). So using these values we get
(-1 - 7) / (6 - 3) = -8/3
12, 3.1.52
If f(x) = x and g(x) = 2x³, find f[g(x)], and g[f(x)]
Given that [tex]f(x) = x[/tex] and [tex]g(x) = 2x^3[/tex], we have
[tex]f(g(x)) = f(2x^3) = 2x^3[/tex]
and
[tex]g(f(x)) = g(x) = 2x^3[/tex]
algebra 2 help needed image below urgent !!!
Answer:
Domain = x ≥ 0
Range = y ≥ 20
Step-by-step explanation:
The equation in slope-intercept form would look like this:
y = 4x + 20
The slope is $4 because that is the money that can be made depending on the week. Because he received a random $20 at the beginning, this is just an additional income.
---------------------------------------------------------------------------
In this scenario, the domain (x-values) represent the number of weeks. The range (y-values) represent the total money made.
So the domain is asking, what is the lowest/highest amount of weeks he can save for? We know the number of weeks cannot be negative because he can't save for negative weeks. However, he could save for zero weeks. He can be saving for theoretically infinite weeks. Therefore, the domain is x ≥ 0.
The range is asking, how much money can he save? Since he starts out with a baseline of $20, this is the lowest amount of money he can have. If he were to save for an infinite amount of weeks, he could make an infinite amount of money. Therefore the range is y ≥ 20.
solve for x -
[tex]\bold{x {}^{2} - 4 = 0}[/tex]
ty! ~
Answer:
x² - 4 = 0
x² = 4
x =± √4
x = +2 or x = -2.
Answer:
2 and -2 (±2)
Step-by-step explanation:
Step 1: Move -4 to the other side of the equal sign; we get x² = 4.
Step 2: A lot of people miss the negative answer! The square root of 4 is equal to both positive 2 and negative 2.
Hope this helped! Please mark me as Brainliest b/c I really need it!!!If a-4b=18,what is 3a/81b
Answer:
You cannot solve this problem with only one given equation
Step-by-step explanation:
You need at least 2 equations to solve for two variables.
Instructions: Match each equations with correct type of event.
P(A) · P(BA)
P(A) + P(B)
PA and B)
P(A)
P(A) · P(B)
P(A) + P(B) - P(A and B)
The question is incomplete. Below you will find the missing contents.
The correct match of events with order are,
P(A)P(B|A) - Dependent event P(A)+P(B) - Mutually exclusive events P(A and B)/P(A) - Conditional events P(A) . P(B) - Independent Events P(A)+P(B) -P(A and B) - not Mutually exclusive events.When two events A and B are independent then,
P(A and B)=P(A).P(B)
when A and B are dependent events then,
P(A and B) = P(A) . P(B|A)
When two events A and B are mutually exclusive events then,
P(A and B)=0
So, P(A or B) = P(A) + P(B) - P(A and B) = P(A) + P(B)
P(A) + P(B) = P(A or B)
When events are not mutually exclusive then the general relation is,
P(A or B) = P(A) + P(B) - P(A and B)
If the probability of the event B conditioned by A is given by,
[tex]\mathrm{P(B|A)=\frac{P(A~and~B)}{P(A)}}[/tex]
Hence the correct match are -
[tex]\mathrm{P(A)P(B|A)\rightarrow}[/tex] Dependent event [tex]\mathrm{P(A)+P(B)}\rightarrow[/tex] Mutually exclusive events [tex]\mathrm{\frac{P(A ~and ~B)}{P(A)}\rightarrow}[/tex] Conditional events [tex]\mathrm{P(A) . P(B)\rightarrow}[/tex] Independent Events [tex]\mathrm{P(A)+P(B) -P(A ~and ~B)\rightarrow}[/tex] not Mutually exclusive events.Learn more about Probability of Events here -
https://brainly.com/question/79654680
#SPJ10
One person ran 4 miles in 24 minutes. At this rate, how long would it take to run 26 miles?
Which expression could help you find the distance
between (10, 4) and (-6, 4)?
O [10] +1-41
O 1101 +141
O 1-61 +141
O |10| +-61
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
Correct Expression :
[tex]\qquad \tt \rightarrow \: |10| + | - 6| [/tex]
[tex]\qquad \tt \rightarrow \: distance = 16\:\: units\degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{Using distance formula -} [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{( - 6 - 10) {}^{2} + (4 - 4) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{( - 16) {}^{2} + 0} [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{256} [/tex]
[tex]\qquad \tt \rightarrow \: 16 \: \: units[/tex]
For short it can be expressed as :
[tex]\qquad \tt \rightarrow \: |10| + | - 6| = 10 + 6 = 16[/tex]
[ y - coordinate of both the points are same ]
Correct option - D
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Given the exponential growth function f ( x ) = 75 ( 1.02 ) x f ( x ) = 75 ( 1.02 ) x What is the initial value of the function? What is the growth factor, or growth rate of the function (as a percent)? %
Answer:
Step-by-step explanation:
The initial vale is when x = 0
- That is 75,
The growth factor is 2%.
HELPPPPPPPPPPPP plssss -. A bag of cookies cost the cookie company $.50 to make, but the local grocery store sells the same bag of cookies for $4.50. How much does the local grocery store mark up the price of the bag of cookies?
Answer:
$4
Step-by-step explanation:
Company $0.50
Store. $ 4.50
Price up $ X
4.50
- 0.50
------------
4.00
X= $4.00
The shadow of a tree is 10m longer when the angle of elevation of the sun is 45° than when it is 60°, find the height of the tree.
The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The length of the tree is 23.66 meters.
What is Tangent (Tanθ)?The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
Let the height of the tree be represented by x.
The length of the shadow when the angle of elevation is 45°.
Length of shadow = x/ Tan(45°)
The length of the shadow when the angle of elevation is 60°.
Length of shadow = x/ Tan(60°)
Now, since the difference between shadows is 10 meters. Therefore, we can write,
x/ Tan(45°) - x/ Tan(60°) = 10m
x[1/ Tan(45°) - 1/ Tan(60°) ] = 10 m
x (0.42265) = 10 m
x = 23.66 m
Hence, the length of the tree is 23.66 meters.
Learn more about Tangent (Tanθ):
https://brainly.com/question/10623976
#SPJ1
Please help! Which choice belongs in space number 3?
Answer:
The Answer is [B]
Step-by-step explanation:
i actually dont have one
Answer:
∠MOP ≅ ∠NOQ
Step-by-step explanation:
Vertical Angle Theorem
When two straight lines intersect, they form two pairs of angles. The vertically opposite (non-adjacent) angles are congruent.
Therefore:
∠MON ≅ POQ and ∠MOP ≅ ∠NOQ
What is the units digit of the sum 1! + 2! + 3! + 4! + 5! + ... + 1000!?
please help if you can
Which pair of equations below represents two lines that are not parallel?
Select one:
a.
y = 2x + 8 and y = 2x + 8
b.
y = ( 1 / 6 ) x + 1 /2 and y = (1 / 6 ) x + 2
c.
y = ( 1 / 6 ) x + 8 and y = 6x + 4
d.
y = ( 1 / 2 ) x + 9 and y = ( 1 / 2) x + 4
The pair of equations (c) y = (1 / 6) x + 8 and y = 6x + 4 are not parallel
How to determine the pair of equations?A linear equation is represented as:
y = mx + b
Where m is the slope of the line
Two lines are said to be parallel if their slopes are the same
i.e. y = mx + b and y = mx + c
Using the above as a guide, the option (c) represents lines that are not parallel, because they do not have the same slope
Hence, y = (1 / 6) x + 8 and y = 6x + 4 are not parallel
Read more about linear equations at:
https://brainly.com/question/14323743
#SPJ1
1.
Which of the following is the given function's
average rate of change on the interval
-3
Answer: -2
Step-by-step explanation:
[tex]g(-3)=0\\\\g(-2)=-2\\\\\frac{g(-3)-g(-2)}{-3-(-2)}=\frac{0-(-2)}{-1}=\boxed{-2}[/tex]
5. Dan is making the perfect shade of purple paint for his Nana. The perfect shade of purple mixes red and blue paint at a
ratio of 4 to 5. Accidently Dan mixed five cups of red and four cups of blue, using up all his red paint. How much blue must
he add to fix his mistake?
Answer:
2 and 1/4 cups
Step-by-step explanation:
4 cups-5 cups
5 cups-?
(5×5)÷4=6 cups and 1/4
6 and 1/4-4=2 cups and 1/4
If 462 subjects were studied and 99 of them expressed a preference for Brand Y, what percentage
expressed a preference for Brand Y? Round to the nearest tenth percentage. Enter the numerical value
only. For example, if your answer is 12.2%, enter 12.2 in the blank.
Answer:
20
Step-by-step explanation:
492/99x100=21.43
nearest tenth percentage is 20
