Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
1) List out all distances singly, before rounding off.
i) From London to Paris → 517Km
ii) From Paris to Munich → 837Km
iii) From Munich to Vienna → 399Km
iv) From Vienna to Moscow → 2,088Km
2) Estimating the distances singly on the basis of rounding off to the nearest 100.
i) 517Km ≈ 500Km to the nearest 100
ii) 837Km ≈ 800Km to the nearest 100
iii) 399Km ≈ 400Km to the nearest 100
iv) 2,088Km ≈ 2,100Km to the nearest 100
3) Summing all estimated distances.
500 + 800 + 400 + 2100
= 3,800Km.
NB: when a number is equal or above 50, you are to round it off as 100; when the number is below 50, you are to round off as zero (0).
If ABCD is a parallelogram, AD = 14, EC = 11, mZABC = 64°, mZDAC = 71°, and mZBDC = 25,
find each measure.
А
a) BC =
d) mZABD =
B
b) AC =
e) m ACD =
E
D
С
c) m DAB
f) mZADB =
Find attached to this answer the diagram of the Quadrilateral
Question:
If ABCD is a parallelogram, AD = 14, EC = 11, m∠ABC = 64°, m∠DAC = 71°, and m∠BDC = 25, find each measure.
a) BC =
b) AC =
c) m∠DAB =
d) m∠ABD =
e) m∠ACD =
f) m∠ADB =
Answer:
a) BC = 11
b) AC = 22
c) m∠DAB = 116°
d) m∠ABD = 39°
e) m∠ACD = 45°
f) m∠ADB = 25°
Step-by-step explanation:
a) BC
In the question above, EC = 11
We can see that EC and BC are equal sides of a diagonal line that has been divided into two equal parts in a Quadrilateral.
Hence, In a quadrilateral ABCD,
EC = BC
Hence BC = 11
b) AC
AC is one of the diagonal lines that divided parallelogram ABCD
AC = BC + EC
AC = 11 + 11
AC = 22
c) m∠DAB
m∠ABC = 64°
m∠ADC = 64°
For the two angles above, a diagonal bisects through those angles.
Also the sum of angles in a triangle = 180°
Hence,
180° = 1/2m∠ABC + 1/2m∠ADC +
m∠DAB
m∠DAB = 180° - ( 1/2 (64) + 1/2(64))
m∠DAB = 180 ° - 64°
m∠DAB = 116°
d) m∠ABD
Since,
m∠ABC = 64° and m∠BDC = 25
m∠ABC = m∠BDC + m∠ABD
64 = 25+ m∠ABD
m∠ABD = 64° - 25°
m∠ABD = 39°
e) m∠ACD
In the above question,
m∠ABC = 64°,
m∠ADC = m∠ABC, this is because, opposite angles in a quadrilateral are congruent and equal to each other.
Hence, m∠ADC = 64°
m∠DAC = 71°,
In a triangle , all the angles in a triangle = 180°
Hence,
180° = m∠DAC + m∠ADC + m∠ACD
180° = 71° + 64 ° + m∠ACD
m∠ACD = 180° -(71 + 64)°
m∠ACD = 180° - 135°
m∠ACD = 45°
f) m∠ADB
Since
m∠DAB = 116°
m∠ABD = 39°
The sum of angles in a triangle = 180°
180° = m∠ABD + m∠DAB + m∠ADB
180° = 39 ° + 116° + m∠ADB
m∠ADB = 180° - ( 116 + 39)°
m∠ADB = 25 °
a) BC = 11
b) AC = 22
c) m∠DAB = 116°
d) m∠ABD = 39°
e) m∠ACD = 45°
f) m∠ADB = 25°
Given : AD=14 , EC=11, m∠ABC= 64°, m∠DAC=71° and m∠BDC=25°
To find: BC =? , AC =? , m∠DAB =?, m∠ABD =? ,m∠ACD =? ,m∠ADB =?
Consider the figure given below ABCD is a parallelogram
To find a) BC
Given, EC = 11
As seen in figure that EC and BC are equal sides of a diagonal line that has been divided into two equal parts in a Parallelogram.
Hence, In a Parallelogram ABCD,
EC = BC
Hence BC = 11
To find b) AC
AC is one of the diagonal lines that divided parallelogram ABCD
AC = BC + EC
AC = 11 + 11
AC = 22
To find c) m∠DAB
Given, m∠ABC = 64°
m∠ADC = 64°
(For the two angles above, a diagonal bisects through those angles)
Also From Angle sum property;
Hence,
180° = 1/2m∠ABC + 1/2m∠ADC + m∠DAB
m∠DAB = 180° - ( 1/2 (64) + 1/2(64))
m∠DAB = 180 ° - 64°
m∠DAB = 116°
To find d) m∠ABD
Since,
m∠ABC = 64° and m∠BDC = 25
m∠ABC = m∠BDC + m∠ABD
64 = 25+ m∠ABD
m∠ABD = 64° - 25°
m∠ABD = 39°
To find e) m∠ACD
Given, m∠ABC = 64°;
m∠ADC = m∠ABC, this is because, opposite angles in a quadrilateral (here parallelogram) are congruent and equal to each other
Hence, m∠ADC = 64°
m∠DAC = 71°,
In a triangle , all the angles in a triangle = 180°(Angle sum property)
Hence,
180° = m∠DAC + m∠ADC + m∠ACD
180° = 71° + 64 ° + m∠ACD
m∠ACD = 180° - (71 + 64)°
m∠ACD = 180° - 135°
m∠ACD = 45°
To find f) m∠ADB
Since ,m∠DAB = 116° and m∠ABD = 39°
From Angle sum property;
180° = m∠ABD + m∠DAB + m∠ADB
180° = 39 ° + 116° + m∠ADB
m∠ADB = 180° - ( 116 + 39)°
m∠ADB = 25 °
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A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer. It costs $4 to store one can of paint for one year and $500 to set up the plan for production of the primer. Let x be the number of cans of paint produced during each production run, and let y be the number of production runs. Then the setup cost is 500y and the storage cost is 2.c, so the total storage and setup cost is C = 500y +2.c. Furthermore, .cy = 16,000 to account for the annual demand. How many times a year should the company produce this primer in order to minimize the total storage and setup costs?
A. The company should have 6 production runs each year.
B. The company should have 8 production runs each year.
C. The company should have 10 production runs each year.
D. The company should have 11 production runs each year.
Answer:
B. The company should have 8 production runs each year.
Step-by-step explanation:
From the given information:
A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer
It costs $4 to store one can of paint for one year
$500 to set up the plan for production of the primer
Let x be the number of cans of paint produced during each production run
Let y be the number of production runs.
If the total storage and setup cost is C = 500y + 2c
and cy = 16000
Then c = 16000/y
From;
C = 500y + 2c
Replacing c with 16000/y, we have;
C = 500y + 2(16000/y)
C = 500y + 32000/y
in order to minimize the total storage and setup costs [tex]C_{min} = C[/tex]
Therefore [tex]\dfrac{dc}{dy}=0[/tex]
⇒ 500 - 32000/y² =0
y² = 32000/500
y² = 320/5
y² = 64
y = (√64)
y = 8
Therefore; The company should have 8 production runs each year in order to minimize the total storage and setup costs
ian invested an amount of money at 3% per annum compound interest. At the end of 2 years the value of the investment was £2652.25 Work out the amount of money Ian invested.
Answer:
the amount of money Ian invested is P = £2,500
Step-by-step explanation:
The standard formula for compound interest is given as;
[tex]A = P(1+r/n)^{nt} \\P = \frac{A}{(1+r/n)^{nt}} ...........1\\[/tex]
Where;
A = final amount/value
P = initial amount/value (principal)
r = rate yearly
n = number of times compounded yearly.
t = time of investment in years
For this case, Given that;
A = £2652.25
t = 2 years
n = 1 (semiannually)
r = 3% = 0.03
substituting the given values into equation 1;
[tex]P = \frac{A}{(1+r/n)^{nt}} ...........1\\P = \frac{2652.25}{(1+0.03)^{2}} \\P = \frac{2652.25}{(1.03)^{2}} \\[/tex]
P = £2,500
the amount of money Ian invested is P = £2,500
What is the area of the shaded region? 21 mm2 24 mm2 42 mm2 48 mm2
Answer:
B or 24 mm2
Step-by-step explanation:
Just did the test :)
The area of the shaded region is 24mm^2
What is the area of triangle?Let b be the base and h be the height of the triangle. The area of the triangle is given by bh/2 square units.Step 1: Find area of the larger triangle
Here base b = 5 mm
Height h = 12 mm
Area of the larger triangle = (5*12)/2 = 60/2 = 30mm^2
Step 2: Find area of the smaller triangle
Here base b = 3 mm
Height h = 4 mm
Area of the smaller triangle = (3*4)/2 = 12/2 = 6 mm^2
Step 3: Find area of the required shaded region
Area of the required shaded region = Area of larger triangle - Area of smaller triangle
= 30 mm^2 - 6 mm^2
=24 mm^2
Hence, the area of the shaded region is 24mm^2
Learn more about area of triangle here:
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#SPJ2
(6/22 + 5/77) ^2 equalviant to in fraction form
Answer:
676/5929
Step-by-step explanation:
Solve x is less than or equal to 0 and x is greater than or equal to -4
Answer:
x = {-3, -2, -1, 0}
Step-by-step explanation:
x ≤ 0
x > -4
then
x {-3, -2, -1, 0}
Given: AB=BC,AM=MC BM ⊥AC , EF⊥BC Prove: EC/AB = FC/MA
Answer:
90 degree EFC. and. BMC
across fc/ma
across ec/ab
Help please!!!!!!! Thxxxxx
Answer:
x= 155°
straight line equals 180°
since you have a side that equals to 25°
you subtract
180°-25° = 155°
baby weights: a study was conducted to determin the average birth weight (in ounces) of babies born in hospitals in a five county area of a given state. A Simple Random Sample of Recent birth records at the local hospitals were selected and the confidence interval was calulated to be (117.89 ounces, 124.91), at a 95% level of confidence. Which statistic is appropriate for this confidences interval?
Answer: Sample mean [tex](\overline{x})[/tex]
Step-by-step explanation:
Given: A study was conducted to determine the average birth weight (in ounces) of babies born in hospitals in a five county area of a given state.
i.e. The parameter of the study is [tex]\mu[/tex] . (Population mean).
A Simple Random Sample of Recent birth records at the local hospitals were selected and the confidence interval was calculated to be (117.89 ounces, 124.91), at a 95% level of confidence.
Since a measure of sample is a statistic , and this case statistic is sample mean denoted by [tex]\overline{x}[/tex].
Hence, the statistic is appropriate for this confidences interval : [tex]\overline{x}[/tex]
trang can test message about 38 words per minute. if she types at this rate for 20 minutes about how many words will she type?
Answer:
760 words for 20 minutes.
Step-by-step explanation:
38 words = 1 minute
1 x 20 = 20
38 x 20 = 760 words
Solve for x: ( 1/2 )^(x−1)=2^(3x−4)
Answer:
[tex]\huge\boxed{x=\dfrac{5}{4}}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{1}{2}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\\left(2^{-1}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{(-1)(x-1)}=2^{3x-4}\qquad\text{use the distributive property}:\ a(b+c)=ab+ac\\\\2^{(-1)(x)+(-1)(-1)}=2^{3x-4}\\\\2^{-x+1}=2^{3x-4}\iff-x+1=3x-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=3x-4-1\\\\-x=3x-5\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-x-3x=3x-3x-5\\\\-4x=-5\qquad\text{divide both sides by (-4)}[/tex]
[tex]\dfrac{-4x}{-4}=\dfrac{-5}{-4}\\\\x=\dfrac{5}{4}[/tex]
Write the Verbal phrases as an equation or an inequality? Use "x" as the variable?
Step-by-step explanation:
8.x×8-12=50
8x-12=50
9.1/2x>or=100
10.2 whole number5/9-x=31
Daniel's mom deposits $80 into his savings account for the year. Daniel decides to upgrade his game account which costs $7 per month. How many months will Daniel be able to pay for his game account if his mom doesn't deposit any more money into his savings account?
Answer:
11.43
Step-by-step explanation:
80÷7= 11.428571428571428571428571428571
i hope this helps
9 less than twice a number is 13. What is the number?
Answer:
11
Step-by-step explanation:
Answer:
x = 11.
Step-by-step explanation:
9 less than twice a number is the same thing as twice a number minus 9. Let's say that the number is x.
2x - 9 = 13
2x = 22
x = 11
Hope this helps!
Cell phone bills for residents of have a mean of $47/line with a standard deviation of $9/line. Find the probability that the average cost/line for the Math
A fair die is rolled two times. What is the probability that both rolls are 6?
Answer:
1/36
Step-by-step explanation:
the fair die has 6 equal parts which means its the total
the probability of rolling a 6 is 1/6
the probability of rolling another 6 is 1/6
so u multiply 1/6 times 1/6 which is 1/36
hope this helps
Hey there
To make it perfectly clear, consider the sample space for rolling a die twice. There are 36 equally likely possible outcomes, 6 of which define the event "rolling the same number two times in a row". Then, the probability of this event occurring is 636, which is equal to 16.Hope this hopeIf (5^4)m=5^12 What is the value of M
Answer:
Step-by-step explanation:
Easy way to solve
5^4 = 625.
5^12=244140625.
Thus, 625m=244140625.
Divide both sides by 625/
m=390625, or 5^8.
Better way to solve
When dividing by exponents [tex]x^{4}/x^{2} =x^{4-2}=x^2[/tex]
Thus, simply do 12-4=8 to know that m=5^8.
Hope it helps <3
Answer:
5⁸Step-by-step explanation:
(5⁴)m = 5¹²
Divide both sides by 5⁴
((5⁴)m)/5⁴ = 5¹²/5⁴
m = 5⁸
What is the equation of the line that passes through the point (3,6) and has a slope of 4/3
Answer:
y = 4/3x+2
Step-by-step explanation:
We can use the slope intercept form of the equation
y = mx+b
Where m is the slope and b is the y intercept
y= 4/3 x +b
Substitute the point into the equation
6 = 4/3(3) +b
6 = 4 +b
Subtract 4 from each side
2 = b
y = 4/3x+2
write the statement for 4p = 8
Answer:
See below
Step-by-step explanation:
The statement that can be written for 4p = 8 is:
=> Four times a certain number equals eight.
Share £1200 in the ratio 3:5.
so you have the amount.
amount: 1200
then you have the ratio
ratio: 3:5
you have the count.
count: 2
and then you have the shares
shares: 8
and the amount per share is 150.00
so the total amount of shares is the sum of each person's ratio so,
so 1:5:2:3:9 = 1 + 5 + 2 + 3 +9 = 20 shares. hope that helps you..
6th grade math , help me please :)
Answer:
a. 4.5 grams per cup
b. 3.2 ounces per week
c. 19.2 grams per cubic centimeters
d. $3.29 per gallon
Step-by-step explanation:
The unit rate is simply a ratio comparing 2 given quantities, whereby the denominator is 1.
The unit rate of the above given problems can be determined as shown below:
a. 18 grams of salt per 4 cups, to find the unit rate, calculate how many grams of salt you'd get in 1 cup by dividing 18 by 4
[tex] \frac{18}{4} = 4.5 [/tex]
Unit rate = 4.5 grams per cup
b. 19.2 ounces is gained by the baby in 6 weeks.
Unit rate is the amount of ounces gained in 1 week
Unit rate = [tex] \frac{19.2}{6} = 3.2 [/tex]
Unit rate = 3.2 ounces per week
c. Unit rate = [tex] \frac{76.8}{4} = 19.2 [/tex]
Unit rate = 19.2 grams per cubic centimeters
d. Unit rate = [tex] \frac{23.03}{7} = 3.23 [/tex]
Unit rate = $3.29 per gallon
Em uma prova de conhecimentos gerais, Fernando errou 3/8 do total de 72 questões. Quantas são as questões que Fernando ACERTOU?
Vamos lá.....
Duas maneiras praticas:
1 - Multiplicar a fraçao pelo total, vai informar quanto a fracao representa (o que é questionado na questao)
2 - Regra de 3.
1:
72 × (3/8)
216/8
27
Ele acertou 27 questoes
(pergunta mais que interessante: qntas questoes havia na prova??? 72)
solve the inquality 1/2*<10
Answer:
[tex]\boxed{x<20}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2} x<10[/tex]
Multiply both sides by 2.
[tex]x<20[/tex]
Write the equation in slope intercept form for the line that passes through the point (0,-3) with slope -1/2.
Answer:
y = -1/2x - 3
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Determine known variables
Slope = -1/2 (m = -1/2)
y-intercept - (0, -3), so b = -3
Step 2: Write in known variables
y = -1/2x - 3
Answer:
y = -1/2 - 3
Step-by-step explanation:
Well slope intercept is y = ax + b
ax is the slope which is given,
b is the y intercept which is -3 because the point (0,-3)
doesn’t have a x coordinate meaning if the line goes through that point it touches the y intercept at -3.
Thus,
the equation in slope-intercept is y = -1/2 - 3.
Hope this helps :)
Which system of equations represents the matrix shown below?
Answer:
c
Step-by-step explanation:
im not too sure
N
5. Use AABC to find the value of sin B.
A 7
B
25
B 24
C
24
А
C7
25
D 24
*see the attachment below for the missing figure
Answer:
[tex] sin B = \frac{24}{25} [/tex]
Step-by-step explanation:
Given a right angled triangle, ∆ABC
AB = 25
BC = 7
AC = 24
<ACB = 90°
Required:
Value of Sin B
Solution:
Using trigonometric ratio formula,
[tex] sin B = \frac{opposite}{hypotenuse} [/tex]
Opposite = AC = 24 (the side opposite to <B)
Hypotenuse = AB = 25 (the longest side facing the right angle)
[tex] sin B = \frac{24}{25} [/tex]
The Sugar Sweet Company is going to transport its sugar to market. It will cost $3500 to rent trucks, and it will cost an additional $150 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this equation to find the total cost to transport 17 tons of sugar.
Answer:
C = 150S + 3,500.
$6,050.
Step-by-step explanation:
It costs $3,500 to rent the trucks, so your constant/y-intercept will be $3,500.
It will cost $150 for every ton of sugar, so your slope will be $150.
You then have your equation:
C = 150S + 3,500.
If you were to transport 17 tons of sugar...
C = 150 * 17 + 3,500
C = 2,550 + 3,500
C = $6,050.
Hope this helps!
Answer:
C = $6050
Equation:
To write the equation, we have to remember that C is the total cost, so that means the equation should end in "= C". S is the amount of sugar, so the equation would look something like this:
[tex]3500+150(S)=C[/tex]
3500 is at the beginning since that is the cost for the trucks, and each ton of sugar costs $150, and that would get multiplied by S amount of sugar, to get the total cost, C.
Solving the equation
To solve the equation when S = 17, we simply have to plug in S as 17 into our equation we wrote above.
[tex]3500+150(17)=C[/tex]
150 * 17 is 2550, and 3500 + 2550 is 6050, which is C.
C = $6050
g The equation for the change of position of a train starting at x = 0 m is given by The dimensions of b are Select one: a. L-1T-1 b. LT-1 c. T-3 d. LT-2 e. LT-3
Answer:
B. LT⁻¹Step-by-step explanation:
The question is incomplete. Here is the complete question,
The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__
from the equation of motion given, the constant b is the velocity of the body. For us to get the dimension of b, we have to find the dimension of the velocity .
Since velocity is the rate of change of displacement of a body, then;
VELOCITY = DISPLACEMENT/TIME
displacement is measured in metres while time in seconds.
expressing the formula in terms of its fundamental unit,
v = metre/secs
Since the fundamental quantity of the metre is length (L) and that of seconds is the time (T); the dimensions is expressed as;
V = L/T
V = L * 1/T
V = L * T⁻¹
V = LT⁻¹
Hence the dimension of b is LT⁻¹.
Note that the dimension of a body is written in terms of its fundamental quantities.
The dimensions of b from the given equation are; B: LT⁻¹
Dimensional Analysis
The complete question is;
The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__
Now, in that equation above, b represents the velocity of the motion. Now, the formula for velocity is;
Velocity = Distance/Time
Now, distance is also called Length and represented by L in basic parameters units while Time is represented by T.
Thus, the dimensions of b are; L/T or expressed as LT⁻¹
Read more on dimensional analysis at; https://brainly.com/question/1528136
Compute the mean and variance of the following probability distribution. (Round your answers to 2 decimal places.) x P(x) 6 0.10 12 0.35 18 0.25 24 0.30
Answer:
Mean = 16.5
Variance = 35.55
Step-by-step explanation:
x P(x) x. P(x) x² x². P(x)
6 0.10 0.6 36 3.6
12 0.35 4.2 144 50.4
18 0.25 4.5 324 81
24 0.30 7.2 576 172.8
∑x P (x) 16.5 ∑x² P (x) 307.8
The expected value of x E[X] gives the mean where X is the discrete random variable with the given probabilities.
Mean is given by E(X)= ∑x P (x) = 16.5
Similarly the variance is also calculated using the expected value of X and X².
Variance is given= E(X)²- [E(X)]²= 307.8- (16.5)²= 307.8-272.25 = 35.55
Please answer this without making mistakes
Answer:
14.16 miles further.
Step-by-step explanation:
Campbell to Summerfield
9.52mi + 4.62 mi + 10.08 mi = 24.24 mi
Princeton to summerfield
is 10.08 mi
Therefore difference is 24.24mi - 10.08mi = 14.16 mi
Hope this helps.