Answer:
The actual dimensions of the floor are 12,5m by 1,8m.
Step-by-step explanation:
Scale problems are solved by proportions, using a rule of three.
Scale of 1:50
This means that each cm on the cupboard has a real dimension of 50 cm
25 cm on the cupboard:
So the real dimension is:
25*50 = 1250 cm = 12,5m
3.6 cm
The real dimension is:
3.6*50 = 160 cm = 1,8 m
The actual dimensions of the floor are 12,5m by 1,8m.
find the value of the trigonometric ratio. make sure to simplify the fraction if needed
Answer:
Cos C = a/h
= 21/35
Step-by-step explanation:
since cos is equal to adjacent angle over hypotenuse angle, so from the question we conclude Cos C = 21/35
Martina has 240 meters of fencing and wishes to form three sides of a rectangular field. The fourth side borders a river and will not need fencing.
As shown below, one of the sides has length x (in meters).
x
Side along river
(a) Find a function that gives the area Ax of the field (in square meters) in terms of x.
=Ax
(b) What side length x gives the maximum area that the field can have?
Side lengthx:meters
(c) What is the maximum area that the field can have?
Maximum area:square meters
Answer:
Step-by-step explanation:
Answering a comes from simplification, and answering b and c are done all in one step: completing the square on the quadratic that results from a.
(a) If Martina has 240 m of fencing and is only utilizing one side for the length and 2 sides for the width, the perimeter formula is
240 = x + 2w where x is a length and w is the width. Solving this for w in terms of x:
240 - x = 2w so
[tex]w=120-.5x[/tex] The area for a rectangle is L * W, so our area using the lengths we have is
A(x) = x(120 - .5x) and we simplify:
A(x) = 120x - .5x² That's the answer to a.
Now for b and c, we will complete the square on this to get the vertex.
Begin by factoring out the -.5:
[tex]A(x)=-.5(x^2-240x)[/tex] Now we take half the linear term, square it and add it both inside the parenthesis and outside the parenthesis. Our linear term is 240. Half of 240 is 120, and 120 squared is 14400:
[tex]A(x)=-.5(x^2-240x+14400)+7200[/tex] (The 7200 comes from multiplying the 14400 times the -.5; -.5 times 14400 is -7200 so to balance things out, we have to add 7200).
The perfect square binomial that results from this is
A(x) = -.5(x - 120)² + 7200. From this we determine that our vertex is
(120, 7200). The 120 is the value of x, the length we are asked to find in b; the 7200 is the max area we are asked to find in c.
The required solutions are,,
(a) area = 240x - 2x²
(b) the side adjacent to the rivers gives the maximum length of the field.
(c) the maximum area could be 6400-meter square.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
length of the field is x,
The perimeter of the field, = 240
x + x + width = 240
width = 240 - 2x
now,
(a)
area of the field,
= length * width,
= x(240-2x)
= 240x - 2x²
Similarly,
(b) the side adjacent to the rivers gives the maximum area of the field.
(c) the maximum area could be 6400-meter square.
Thus, the required solutions are mentioned above.
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#SPJ2
Cho hình hộp chữ nhật ABCD A B C D
Answer:
A B C D
A×B×C×D
3×3×3×6
162
Help me solve the question in picture
9514 1404 393
Answer:
√5 +√6
Step-by-step explanation:
We know that the square of a binomial is ...
(a +b)^2 = a^2 +2ab +b^2
Then the square root of it is ...
a + b = √(a^2 +b^2 +2ab)
Using a=√x and b=√y, this is ...
√x +√y = √(x + y + 2√(xy))
__
For the given expression, we need to find x and y such that ...
xy = 30 and x+y = 11
Using x=5, y=6, we meet those requirements.
[tex]\displaystyle \sqrt{11+2\sqrt{30}}=\sqrt{5+6+2\sqrt{5\cdot6}}=\boxed{\sqrt{5}+\sqrt{6}}[/tex]
Answer:
√5+√6 ≈ 4.68555772
Step-by-step explanation:
I hope it's correct
Louise has a hard time keeping her workspace clean at her job. She tries, but it just ends up getting messy again. Which of the following is a likely outcome of her consistent messiness? a) She will have fewer safety issues. b) She will feel more productive. c) Customers will think she is very busy. d) She will have a hard time focusing.
A survey of 30-year-old males provided data on the number of auto accidents in the previous 5 years. The sample mean is 1.3 accidents per male. Test the hypothesis that the number of accidents follows a Poisson distribution at the 5% level of significance.
No. of accident No. of males
0 39
1 22
2 14
3 11
>=4 4
Required:
a. What's the Expected probability of finding males with 0 accidents?
b. What's the Expected probability of finding males with 4 or more accidents?
Answer:
0.2725
0.0431
Step-by-step explanation:
The distribution here is a poisson distribution :
λ = 1.3
The poisson distribution :
p(x) = [(e^-λ * λ^x)] ÷ x!
Expected probability of finding male with 0 accident ; x = 0
p(0) = [(e^-1.3 * 1.3^0)] ÷ 0!
p(0) = [0.2725317 * 1] ÷ 1
p(0) = 0.2725317
= 0.2725
2.)
P(x ≥ 4) = 1 - P(x < 4)
P(x < 4) = p(x = 0) + p(x. = 1) + p(x = 2) + p(x = 3)
p(x = 0) = p(0) = [(e^-1.3 * 1.3^0)] ÷ 0! = 0.2725
p(x = 1) = p(1) = [(e^-1.3 * 1.3^1)] ÷ 1! = 0.35429
p(x = 2) = p(2) = [(e^-1.3 * 1.3^2)] ÷ 2! = 0.23029 p(x = 3) = p(3) = [(e^-1.3 * 1.3^3)] ÷ 0! = 0.09979
P(x < 4) = 0.2725 + 0.35429 + 0.23029 + 0.09979 = 0.95687
P(x ≥ 4) = 1 - 0.95687 = 0.0431
Mike wants to buy a scooter worth R10000 but cannot afford so he opts for the hire purchase agreement which requires a 13% deposit and a 24 equal monthly installments at a rate of 15% per annum compounded monthly
A.How much will his deposit be?
B.calculate how much does he still need to pay after the deposit
C.calculate the monthly installment
Answer: I think the answer is A
Step-by-step explanation:
What is the equation of the line that passes through the point (6, -6) and has a slope
of – 5/3?
Answer:
y = -5/3x + 4Step-by-step explanation:
Use the point-slope equation:
y - y₁ = m(x - x₁), where (x₁, y₁) is the given pointThe line is:
y - (-6) = -5/3(x - 6) y + 6 = -5/3x + 10y = -5/3x + 4(b) An economy has an agricultural industry and a textile industry. Each unit of agricultural output requires 0.4 unit of agricultural input and 0.1 unit of textiles input. Each unit of textiles output requires 0.1 unit of agricultural input and 0.2 unit of textiles input.
(i) Write the technology matrix for this economy. [2 marks]
(ii) If surpluses of 5 units of agricultural products and 195 units of textiles are desired, find the gross production of each industry
Leontief input output model (technology matrix) is an economic model that shows the quantitative relationship and sectorial interdependency in a national economy
The responses with regards to the question are;
(i) The technology matrix for the economy is presented as follows;
[tex]\mathbf{ A} =\left[\begin{array}{ccc}Agric&&Textile\\0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] \begin{array}{ccc}\mathbf{Per \ Unit}\\Agriculture\\\\Textile\end{array}\right][/tex]
(ii) The required gross production of each industry to meet the desired surplus are;
50 units of agriculture and 250 units of textile
The reason the above values are correct is as follows:
(i) The given parameters are;
The industries in the economy = Agricultural industry and textile industry
Units of agricultural input required per unit of agricultural output = 0.4
Units of textile input required per unit of agricultural output = 0.1
Units of agricultural input required per unit of textile output = 0.1
Units of textile input required per unit of textile output = 0.2
Let X represent agriculture, and let Y represent textile, we have;
[tex]Agric \ for \ agric = \dfrac{0.4 \ units \ of \ agriculture}{1\ unit \ of \ agric \ produced} \times X \ Agric \ produced= 0.4 \cdot X[/tex]
[tex]Agric \ for \ textile = \dfrac{0.1 \ units \ of \ agriculture}{1\ unit \ of \ textile \ produced} \times Y \ textile \ produced= 0.1 \cdot Y[/tex]
We also have;
Textile for agriculture = 0.1·X
Textile for textile = 0.2·Y
Therefore;
X = 0.4·X + 0.1·Y
Y = 0.1·X + 0.2·Y
Therefore;
The technology matrix for the economy is presented as follows;
[tex]\mathbf{Technology \ matrix, A} =\left[\begin{array}{ccc}Agric&&Textile\\0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] \begin{array}{ccc}\mathbf{Per \ Unit}\\Agriculture\\\\Textile\end{array}\right][/tex]
(ii) Let P represent the production vector, and let d represent the demand vector, we have;
[tex]P = \left[\begin{array}{c}X \\Y\end{array}\right][/tex], [tex]d = \left[\begin{array}{c}5 \\195\end{array}\right][/tex]
P = A·P + d
∴ P - A·P = d
Therefore;
[tex]P = \mathbf{ \dfrac{d}{(I - A)}}[/tex]
Where I = The 2 by 2 identity matrix
We get;
[tex]I - A =\left[\begin{array}{ccc}1&&0\\&&\\0&&1\end{array}\right] - \left[\begin{array}{ccc}0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] = \mathbf{\left[\begin{array}{ccc}0.6&&-0.1\\&&\\-0.1&&0.8\end{array}\right]}[/tex]
With the use of a graphing calculator, we have;
[tex]P =\left[\begin{array}{c}X \\Y\end{array}\right] = \dfrac{\left[\begin{array}{c}5 \\195\end{array}\right]}{\left[\begin{array}{ccc}0.6&&-0.1\\&&\\-0.1&&0.8\end{array}\right]} = \left[\begin{array}{ccc}50\\\\\ 250\end{array}\right][/tex]
The required gross product of agriculture, X = 50 units
The required gross product of textile, Y = 250 units
Learn more about the Leontief input output model here:
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We have that he technology matrix for this economy and the the gross production of each industry are
a) [tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
b) [tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex]
From the Question we have told that
Each unit of agricultural output requires 0.4 unit of agricultural input
Each unit of agricultural output requires 0.1 unit of textiles input.
Each unit of textiles output requires 0.1 unit of agricultural input
Each unit of textiles output requires 0.2 unit of textiles input.
Generally the technology matrix for this economy is given below
With
X =Agricultural industry Gross output
Y= Textile industry Gross Output
Therefore
[tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
b)
From the Question we are told that
Surpluses of 5 units of agricultural products and 195 units of textiles are desired.
Therefore, we have Desired surplus matrix of
[tex]D= \begin{vmatrix}5\\195\end{vmatrix}[/tex]
Generally the Technology equation is mathematically given as
[tex](I-X)\phi=D[/tex]
Where
X =Agricultural industry Gross output
I=A Unit matrix
\phi=Matrix of gross production
Therefore
[tex]\begin{vmatrix}1 & 0\\0 & 1\end{vmatrix}-(\begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}))\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}5\\195\end{vmatrix}[/tex]
[tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex]
In conclusion
The technology matrix for this economy and the the gross production of each industry are
[tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
[tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex] Respectively
In conclusion
https://brainly.com/question/16863924
Ivan caught a total of 7 2/5 pounds of fish one day. Of the fish caught, 4 5/8 pounds were sea bass and the rest were mackerel. He gave away 1 7/8 pounds of mackerel. How many pounds of mackerel did he have left.
Given:
Total fish (Sea bass and mackerel) = [tex]7\dfrac{2}{5}[/tex] pounds
Sea bass = [tex]4\dfrac{5}{8}[/tex] pounds
He gave away [tex]1\dfrac{7}{8}[/tex] pounds of mackerel.
To find:
The remaining mackerel.
Solution:
We know that,
Mackerel = Total fish - Sea bass
[tex]\text{Mackerel}=7\dfrac{2}{5}-4\dfrac{5}{8}[/tex]
[tex]\text{Mackerel}=\dfrac{37}{5}-\dfrac{37}{8}[/tex]
[tex]\text{Mackerel}=\dfrac{296-185}{40}[/tex]
[tex]\text{Mackerel}=\dfrac{111}{40}[/tex]
He gave away [tex]1\dfrac{7}{8}[/tex] pounds of mackerel. So, the remaining mackerel is:
[tex]\text{Remaining Mackerel}=\dfrac{111}{40}-1\dfrac{7}{8}[/tex]
[tex]\text{Remaining Mackerel}=\dfrac{111}{40}-\dfrac{15}{8}[/tex]
[tex]\text{Remaining Mackerel}=\dfrac{111-75}{40}[/tex]
[tex]\text{Remaining Mackerel}=\dfrac{36}{40}[/tex]
[tex]\text{Remaining Mackerel}=\dfrac{9}{10}[/tex]
Therefore, the remaining Mackerel is [tex]\dfrac{9}{10}[/tex] pounds or 0.9 pounds.
Answer:
The amount of Mackerel left is 9/10.
Step-by-step explanation:
total fish = 7 2/5 pounds
sea bass = 4 5/8
The amount of mackerel =
[tex]7\frac{2}{5}-4\frac{5}{8}\\\\=\frac{37}{5}-\frac{37}{8}\\\\=\frac{296-185}{40}\\\\=2 \frac{31}{40}[/tex]
Mackerel left =
[tex]2 \frac{31}{40}-1\frac{7}{8}\\\\= \frac{111}{40}-\frac{15}{8}\\\\=\frac{111-75}{40}\\\\=\frac{36}{40}\\\\=\frac{9}{10}[/tex]
Given a sphere with radius r, the formula 4 r2 gives
O A. the volume
O B. the surface area
O c. the radius
O D. the cross-sectional area
Answer: surface area
Step-by-step explanation:
The term "downers" refers to ..
Manatees can swim in water up to 20 feet deep. Write an expression that represents the depth d, that a manatee can swim
Answer:
0 ≤ d ≤ 20
Step-by-step explanation:
You mention that Manatees can swim in water up to 20 feet deep. So, this means that the largest depth that he can swim is 20 feet, not more than this. Also, keep in mind that the depth can't be negative, so ----> 0 ≤ d ≤ 20 feet
We want to write an expression (an inequality actually) that defines the depth at which a manatee can swim. The inequality is: 0ft ≤ d ≤ 20ft.
We know that the manatees can swim in water up to 20 feet deep. This represents the maximum deep at which manatees can swim, the minimum is trivial, it would be 0ft (when the manatees are on the surface of the water).
Then we can write the inequality:
0ft ≤ d ≤ 20ft.
This gives the range of possible values of d, depth at which the manatee can swim.
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Find the area of the shaded regions
Sector area
Area of whole = 51.313
Area of unshaded = 9.424
Area of shaded = 41.8886
Answer:
40π/3Step-by-step explanation:
Find the area of the bigger circle:
A = πr² = π(4 + 3)² = 49πFind the area of 120° sector AOC:
A = 120°/360°*A = 1/3*49π = 49π/3Find the area of smaller circle:
A = π(3²) = 9πFind the area of 120° sector of DOB:
A = 120°/360°*9π = 3πNow find the shaded area, the difference of areas of sectors:
49π/3 - 3π = 40π/3Find x.
60°
45°
6
—————
Answer:
Step-by-step explanation:
Big sleds must hold 3 children and small sleds must hold 2 children. If 17 children want to go sledding at the same time, how many of each type of sled is needed?
Answer:
5 big sleds and 1 small sled
An F test for the two coefficients of promotional expenditures and district potential is performed. The hypotheses are H0: 1 = 4 = 0 versus Ha: at least one of the j is not 0. The F statistic for this test is 1.482 with 2 and 21 degrees of freedom. What can we say about the P-value for this test?
Answer:
Pvalue > 0.10
Step-by-step explanation:
Given the hypothesis :
H0 : β1 = β4 = 0
H1 : Atleast one of βj is not 0
F statistic = 1.482 ;
Degree of freedom = 2 and 21 ;
DFnumerator = 2
DFdenominator = 21
Using the Pvalue calculator from Fstatistic ;
Pvalue(1.482, 2, 21) = 0.24999 = 0.25
Hence, Pvalue for the test is 0.25
Pvalue > 0.10
I need help with this question!
PLEASE HELP ASAP
Solve the inequality [tex]\sqrt[3]{x+4} \ \textgreater \ \sqrt[2]{-x}[/tex]
A) x < 2
B) x > 2
C) x > –2
D) x < –2
The width of a rectangle is 5 units less than the length. If the area is 150 square units, then find the dimensions of the rectangle
⇛L = W + 5
⇛L × W = 150 sq. units
⇛W (W + 5) = 150
⇛W² + 5W = 150
⇛W² + 5W - 150 = 0
⇛[(W - 10) (W + 15)] = 0
⇛W = -10 , 15 (reject negative width)
☞ Width of rectangle is 10 units
☞ Length of rectangle is 15 units
Solve for f(-7) plz thanks
Answer:
12
Step-by-step explanation:
If f(x) = 5 - x
Then f(-7) = 5 - (-7)
f(-7) = 5 + 7
f(-7) = 12
Can you please help me
Answer: 1/6
Step-by-step explanation:
Given:
4/9 and 11/18
Solve:
STEP ONE: Make the denominators equal by determining the LCM
LCM = Least Common Multiple
First Five multiples of 9 = 9, 18, 27, 36, 45
First FIve multiples of 18 = 18, 36, 54, 72, 90
As we can see from the list above, both 18 and 36 overlap, however, 18 is less than 36. Therefore, 18 is the LCM.
STEP TWO: Compare the size and determine the greater one.
4/9 = (4 × 2) / (9 × 2) = 8/18
11/18 = 11/18
Since 11 > 8, therefore, 11/18 is greater than 8/18
STEP THREE: Find the difference between the two fractions.
11/18 - 4/9
=11/18 - 8/18
=(11 - 8) / 18
= 3 / 18
= 1/6
Hope this helps!! :)
Please let me know if you have any questions
help i’ll give brainliest
Answer:
(0,-4)
Step-by-step explanation:
The plot for x intercept is at -4,0 and the y intercept is at 0,5
type it in as (0,-4), some require the (#,#) format
Zoe earns 22.50 per hour plus 3% commission on sales. last week she worked 34 hours and made sales totalling 15280. Calculate her pay for the week.
Answer: $1,223.40.
Step-by-step explanation:
Since she earns $22.5 per hour, for 34 hours, she would earn:
$22.5 × 34 = $765
She earn 3% of her sales, therefore find 3% of $15,280:
$15280(3%) = $15280(0.03) = $458.4
Add them together:
$765 + $458.4 = $1223.4
9514 1404 393
Answer:
$1,223.40
Step-by-step explanation:
Zoe's total pay is the sum of the products of hours and hourly rate, and sales and commission rate.
Pay = (34 h)($22.50/h) +($15,280)(.03) = $765.00 +458.40
Pay = $1,223.40
Zoe's pay for the week is $1,223.40.
Hey community I thank you guys fir your help
Answer:
A, B, and E.
Step-by-step explanation:
A. 5^x * 5^x
= 5^x+x
=5^(2)(x)
=25^x
B. 5^2x
=5^(2)(x)
=25^x
C. 5*5^2x
=5^1+2x
D. 5*5^x
=5^1+x
E. (5*5)^x
=5^x*5^x
=5^(2)(x)
=25^x
F. 5^2*5^x
=5^2+x
Ellicott City Manufacturers, Inc., has sales of $6,344,210, and a gross profit margin of 67.3 percent. What is the firm's cost of goods sold? Round your final answer to the nearest dollar.
Answer:
$3792116
Step-by-step explanation:
that's the answer above
11. The unit digit in the expression (31 + 132 + 143 + 414 + 515 +156 + 61) i (A) 4 (B) 3 (C) 2 . (D) 1
Answer:
Step-by-step explanation:
[tex]we \ add \ \ only \ \ units \ we \ do \ not \ need \ the \ rest \\\\ \bf (3\underline 1 + 13\underline2 + 14\underline3 + 41\underline4 + 51\underline5 +15\underline6 + 6\underline1)= \\\\ 1+2+3+4+5+6+1=2\underline 2 \\\\ Answer: C) \ 2[/tex]
A scuba diver is practicing
in a marked pool. He
begins 3 feet below the
surface of the water and
then dives down to the 9
foot marker. How far did
he dive?
Answer:
6ft
Step-by-step explanation:
Answer:
6ft
Step-by-step explanation:
Alice wants to estimate the percentage of people who plan
on voting yes for the upcoming school levy. She surveys
380 individuals and finds that 260 plan on voting yes.
Identify the values needed to calculate a confidence interval
at the 90% confidence level. Then find the confidence interval.
zo10 z0.05 zo.025 zo01 z0.005
1.282 1.645 1.960 2.326 2.576
Use the table of common z-scores above.
Answer:
"[tex]0.6450 < p < 0.723[/tex]" is the right solution.
Step-by-step explanation:
Given:
n = 380
x = 260
Point estimate,
[tex]\hat p = \frac{x}{n}[/tex]
[tex]=\frac{260}{380}[/tex]
[tex]=0.6842[/tex]
Critical value,
[tex]Zc = 1.645[/tex]
Standard error will be:
[tex]S.E = \sqrt{\frac{0.6842(1-0.6842)}{380} }[/tex]
[tex]=0.0238[/tex]
Margin of error will be:
[tex]E = Zc\times S.E[/tex]
[tex]=1.645\times 0.0238[/tex]
[tex]=0.0392[/tex]
hence,
Confidence level will be:
= [tex]\hat p \pm E[/tex]
= [tex]0.6842 \pm 0.0392[/tex]
= [tex]0.6450 < p < 0.723[/tex]
Add the first 12 terms of this sequence:
15, 45, 135, 405, 1215, ...
Answer:
Step-by-step explanation:
a₁ = 15
a₂/a₁ = 45/15 = 3
a₃/a₂ = 135/45 = 3
...
It is a geometric sequence with a common ratio r=3.
Sum of first 12 terms = a₁·(1-r¹²)/(1-r)
= 15·(1-3¹²)/(1-3)
= 15·(-531,441)/(-2)
= 3,985,800
