Answer:
Average waiting time = 4 minutes
Step-by-step explanation:
From this question, we are told that the sky train is supposed to arrive every 8 minutes.
Thus, the waiting time of the passengers for the train = 8 minutes.
Then, the average waiting time is simply the mean or 50th percentile of the total waiting time.
So, average waiting time = 50% × 8
Average waiting time = 4 minutes
1/x=1/2 / 4/5
Solve for x.
X =
Answer:
1/x = 1/2÷4/5
1/x=1/2 x 5/4
1/x=5/8
5x=8
x=1.6
Find the SURFACE AREA of this composite solid.
FINDING THE SURFACE AREA OF A COMPOSITE SOLID
About "Finding the surface area of a composite solid"
Finding the surface area of a composite solid :
A composite solid is made up of two or more solid figures.
To find the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.
Finding the surface area of a composite solid - Examples
Example 1 :
Daniel built the birdhouse shown below. What was the surface area of the birdhouse before the hole was drilled ?
Solution :
Step 1 :
Identify the important information.
• The top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.
• The bottom is a rectangular prism with h = 18 cm. The base is a 30 cm by 24 cm rectangle.
• One face of each prism is not on the surface of the figure.
Step 2 :
Find the surface area of each prism.
Add the areas. Subtract the areas of the parts not on the surface.
Step 3 :
Find the area of the triangular prism.
Perimeter = 17 + 17 + 30 = 64 cm
Base area = (1/2)(30)(8) = 120 sq.cm
Surface area = Ph + 2B
Surface area = 64(24) + 2(120)
Surface area = 1,776 sq.cm
Step 4 :
Find the area of the rectangular prism.
Perimeter = 2(30) + 2(24) = 108 cm
Base area = 30(24) = 720 sq.cm
Surface area = Ph + 2B
Surface area = 108(18) + 2(720)
Surface area = 3,384 sq.cm
Step 5 :
Add. Then subtract twice the areas of the parts not on the surface.
Surface area = 1,776 + 3,384 - 2(720) = 3,720 sq.cm
The surface area before the hole was drilled was 3,720 sq.cm.
The surface area before the hole was drilled was; 3,720 sq.cm.
What is composite solid?A composite solid is made up of two or more solid figures.
To determine the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.
Given that the top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.
The bottom is a rectangular prism with h = 18 cm.
The base is a 30 cm x 24 cm rectangle.
One face of each prism is not on the surface of the figure.
Then the surface area of each prism.
Add the areas. Subtract the areas of the parts not on the surface.
The area of the triangular prism.
Perimeter = 17 + 17 + 30 = 64 cm
Base area = (1/2)(30)(8) = 120 sq.cm
Surface area = Ph + 2B
Surface area = 64(24) + 2(120)
Surface area = 1,776 sq.cm
Now the area of the rectangular prism.
Perimeter = 2(30) + 2(24) = 108 cm
Base area = 30(24) = 720 sq.cm
Surface area = Ph + 2B
Surface area = 108(18) + 2(720)
Surface area = 3,384 sq.cm
Now,
Surface area = 1,776 + 3,384 - 2(720) = 3,720 sq.cm
Learn more about the area;
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Find the circumference of each circle, use 3.14 for . Include units and round to the nearest tenth. Show work
7. The circumference of a circle is 34.54 cm. What is the diameter and radius of the circle? (Show work)
8. What is the circumference of a circle in terms of , if it has a radius of 3.5 in?
(in terms of means do not substitute 3.14 for pi, leave the symbol in the final answer)
Answer:
Answer:-
a) The circumference of the circle C = 21.98 m
b) The circumference of the circle C = 37.68 ft
c) The circumference of the circle C = 40.82 km
d) The radius of the circle = r = 11 c.m
The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m
e) The circumference of the circle = 21.98 inches
Step-by-step explanation:
a) In First diagram
Given radius of the circle 'r' = 7.1 m
The circumference of the circle C = 2πr
C = 2 (3.14) (7.1)
C = 21.98 m
The circumference of the circle C = 21.98 m
b) In second diagram
Given diameter of the circle 'd' = 12 ft
The circumference of the circle C = 2πr
C = π(2 r)
Diameter = 2 X radius
d = 2 r
The circumference of the circle C = πd
C = 3.14 ×12
The circumference of the circle C = 37.68 ft
c)
Given diameter of the circle 'd' = 13 km
The circumference of the circle C = 2πr
C = π(2 r)
Diameter = 2 X radius
d = 2 r
The circumference of the circle C = πd
C = 3.14 ×13
The circumference of the circle C = 40.82 km
7) The circumference of the circle C = 2πr
Given The circumference of a circle is 34.54 cm
Now 2πr = 34.54
2(3.14) r = 34.54
[tex]r = \frac{34.54}{3.14} = 11[/tex]
The radius of the circle = r = 11 c.m
The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m
8) Given radius of the circle 'r' = 3.5 inches
The circumference of the circle C = 2πr
C = 2 (3.14) (3.5)
C = 21.98
The circumference of the circle = 21.98 inches
−2.73(m+4)=−6m−4.38.
Answer:
m=2
Step-by-step explanation:
-2.73m-10.92=-6m-4.38
3.27m=6.54
m=2
The vector ~v represents the displacement vector from Portland, Oregon to Houston, Texas. The vector w~ represents the displacement vector from Houston, Texas to Akron, Ohio. Use the vectors ~v and w~ to answer the following questions:
a. What is the displacement vector Of a plane which flies from Akron, Ohio to Houston, Texas?
b. In order to fly home from Portland to Akron I have a layover in Houston. Find a vector which describes my total displacement over the whole trip.
c. It is approximately 3000 km from Portland to Houston. It is approximately 5500 km from Anchorage, Alaska to Houston. A plane flies in a straight line from Houston to Anchorage and during the flight it passes directly over Portland. Find a vector which describes the displacement of the plane.
Answer:
a
the displacement of the plane is [tex]- \= w[/tex]
b
The displacement of plane from Portland to Akron with layover at Houston is
[tex]\= v + \= w[/tex]
c
the vector which defines this displacement is [tex]\= v + \= w =- 2500 \ km[/tex]
Step-by-step explanation:
From the question we are the
The displacement from Portland, Oregon to Houston, Texas. is [tex]\= v[/tex]
The displacement from Houston, Texas to Akron, Ohio. is [tex]\= w[/tex]a
a
The motion of the plane in question a is in the opposite direction to vector [tex]\= w[/tex]
So the displacement of the plane is [tex]- \= w[/tex]
b
The motion of Portland to Houston to Akron is in the direction of both vector [tex]\= v[/tex] and [tex]\= w[/tex] so
The displacement of plane from Portland to Akron with layover at Houston is
[tex]d = \= v + \= w[/tex]
c
From the question we are told that the plane flies over Portland to get to Anchorage, Alaska which implies that it is moving in opposite direction to the vector [tex]\= v[/tex]
Give that distance from Portland to Houston is [tex]\= v = 3000 km[/tex]
and the distance from Portland to Anchorage is [tex]\= w = - 5500[/tex]km
Then the vector which defines this displacement is mathematically represented as
[tex]\= v + \= w = 3000 -5500[/tex]
[tex]\= v + \= w =- 2500 \ km[/tex]
What is the value of x?
Answer:
x = 22
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the interior angles
6x+1 = 79+ 2x+10
Combine like terms
6x+1 = 2x+89
Subtract 2x from each side
4x+1 = 89
Subtract 1 from each side
4x = 88
Divide by 4
4x/4 = 88/4
x = 22
Answer:
The answer is
Step-by-step explanation:
We can cross out A. So it has to be either B, C, or D.
n a random sample of 10 residents of the state of Florida, the mean waste recycled per person per day was 2.8 pounds with a standard deviation of 0.64 pounds. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Florida. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places
Answer:
The critical value is T = 2.2622.
The 95% confidence interval for the mean waste recycled per person per day for the population of Florida is between 1.352 pounds and 4.248 pounds.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 10 - 1 = 9
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622, which is the critical value.
The margin of error is:
M = T*s = 2.2622*0.64 = 1.448
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 1.448 = 1.352 pounds
The upper end of the interval is the sample mean added to M. So it is 2.8 + 1.448 = 4.248 pounds
The 95% confidence interval for the mean waste recycled per person per day for the population of Florida is between 1.352 pounds and 4.248 pounds.
Solve the inequality.
-3(x-1) > -3x - 2
Answer:
all real x
Step-by-step explanation:
-3(x-1) > -3x - 2
Distribute
-3x +3> -3x -2
Add 3x to each side
-3x +3 +3x > -3x+3x - 2
3 > -2
This is always true so the inequality is true for all x
Which expression is equivalent to 4+2(1+3x)
Answer:
I'm glad you asked!
Step-by-step explanation:
OK,let's simplify the number for a equivalent expression.
[tex]4+2(1+3x)[/tex]
Distribute:
[tex]=4+(2)(1)+(2)(3x)[/tex]
[tex]= 4+2+6x[/tex]
Combine Like Terms:
[tex]=4+2+6x[/tex]
[tex]=(6x)+(4+2)[/tex]
[tex]=6x+6[/tex]
The Final Answer is : [tex]6x+6[/tex]
The expression that is equivalent to 4+2(1+3x) is 6x+6.
What is an Algebraic expression?Mathematical expressions that are made up of constants, variables, and coefficients that are combined using algebraic operations such as multiplication, addition, subtraction, and division are called Algebraic expressions.
How do simplify the algebraic expression?Given, 4+2(1+3x)
Firstly distribute 2(1+3x) to get 2+6x then,
4+2(1+3x)
=4+2+6x
=6x+6
Thus, 4+2(1+3x)=6x+6
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Please answer this correctly I have to finish this today as this is my deadline
Answer:
r = 1.499619733762 m There is no such thing a quarter radius!
C = 9.4223886775301 m
A = 7.065 m^2
Step-by-step explanation:
Calculate r and C | Given A
Given the area of a circle calculate the radius and circumference
r = √(A / π)
C = 2πr
Agenda:
r = radius
C = circumference
A = area
π = pi = 3.1415926535898
√ = square root
Help??!!??!?!!??anyone
Answer:
A. 32.25
Step-by-step explanation:
Because of the first row, we know that to find the cost, we are multipling the gallons by 2.15.
so [tex]15*2.15=32.25[/tex]
So the answer is A.
Hope this helps!
Plx give brainliest
1.
On hand: Magnesium sulfate 30 grams is mixed in 500 ml Lactated Ringers. Order: infuse a
maintenance dose of magnesium sulfate at 4 grams/hour. At what rate should the nurse set the
pump:
Answer:
The IV will run [tex]66.67 \ ml /hr[/tex]
Step-by-step explanation:
From the question we are told that
The mass of Magnesium sulfate is [tex]m_g = 30 \ g[/tex]
The volume of the Magnesium sulfate [tex]V_R = 500ml[/tex]
The rate at which the dose of the solution (Magnesium sulfate + Lactated Ringers. ) is infused is [tex]R = 4g/hr[/tex]
The concentration of Magnesium sulfate in Lactated Ringers is mathematically evaluated as
[tex]C_m = \frac{m_g}{V_R}[/tex]
substituting values
[tex]C_m = \frac{30}{500}[/tex]
[tex]C_m = 0.06\ g/ ml[/tex]
This implies that
0.06 g of Magnesium sulfate is in every 1 ml of Lactated Ringers
So 4 g of Magnesium sulfate is in x ml of Lactated Ringers
So
[tex]x = \frac{4}{0.06}[/tex]
[tex]x = 66.67 \ ml[/tex]
So the amount of the solution in ml that is been infused in 1 hour is
[tex]66.67 \ ml /hr[/tex]
Triangle JKL was dilated using the rule D Subscript M, one-third. The image, triangle J'K'L', is the result of the dilation. Point M is the center of dilation. Triangle J K L is dilated to form smaller triangle J prime K prime L prime. The length of M L prime is 2.5. What is L'L? 5 units 7.5 units 10 units 12.5 units
Answer: the answer is A 5 units
The length of L'L in the dilated figure is 5 units.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Dilation is the increase or decrease in size of a figure.
Triangle JKL was dilated by 1/3 with M as the center of dilation to form J'K'L'.
Given that ML' = 2.5 units, hence:
L'L = (2.5 * 3) - 2.5 = 5 units
The length of L'L in the dilated figure is 5 units.
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Solve the inequality 2(4x-3)>-3(3x)+5
Answer:
48x>+2
Step-by-step explanation:
A rectangle has a length of 60 in and a width of 8 in. Given a scale factor of 4in:5ft. What is the area of the rectangle?
Answer:
750ft²
Step-by-step explanation:
Area of rectangle = L*B
Before we find the area of the given rectangle, we need to convert the dimensions using the given scale.
Thus, dimensions of the given rectangle using the scale factor of 4in:5ft would be:
==> Length = 60in = (60*5)/4 = 75ft
Breadth or Width = 8in = (8*5)/4 = 10ft
Therefore, area of rectangle = L * B
= 75ft * 10ft
= 750 ft²
Area of rectangle = 750ft²
Find the constant of variation for the relation and use it to write and solve the equation.
if y varies directly as x and as the square of z, and y=25/9 when x=5 and z=1, find y when x=1 and z=4
Answer:
When x = 1 and z = 4, [tex]y=\frac{80}{9}[/tex]
Step-by-step explanation:
The variation described in the problem can be written using a constant of proportionality "b" as:
[tex]y=b\,\,x\,\,z^2[/tex]
The other piece of information is that when x = 5 and z = 1, then y gives 25/9. So we use this info to find the constant "b":
[tex]y=b\,\,x\,\,z^2\\\frac{25}{9} =b\,\,(5)\,\,(1)^2\\\frac{25}{9} =b\,\,(5)\\b=\frac{5}{9}[/tex]
Knowing this constant, we can find the value of y when x=1 and z=4 as:
[tex]y=b\,\,x\,\,z^2\\y=\frac{5}{9} \,\,x\,\,z^2\\y=\frac{5}{9} \,\,(1)\,\,(4)^2\\y=\frac{5*16}{9}\\y=\frac{80}{9}[/tex]
Which rule represents the translation from he pre-image, ABCD, to the image, A’B’C’D’?
Answer:
Option (4)
Step-by-step explanation:
From the figure attached,
Quadrilateral ABCD has been translated to form an image A'B'C'D' by shifting 'a' units right and 'b' units up.
Let the rule for translation is,
(x, y) → (x + a, y + b)
Coordinates of point A is (-4, 4) and the coordinates of the image A' are (-2, 5).
So, (-4, 4) → [(-4 + 2), (4 + 1)]
Therefore, the translation can be represented by [tex]T_{2, 1}(x, y)[/tex] (shifted 2 units right and 1 unit up).
Option (4) will be the answer.
Answer:
T2,1(x,y)
Step-by-step explanation:
A tree diagram is simply a way of representing a sequence of events. True or False.
Answer:
True.
Step-by-step explanation:
A tree diagram is a diagram used in general mathematics, statistics, and probability to show a sequence of events. This tool is used to calculate the number of possibilities of an event to occur. Commonly, the tool of a tree diagram is used to find the possibility of outcome while flipping a coin. It is a diagram in which connections between the events is shown using the strucure of branching connecting lines.
So, the given statement is true, that is a simple way of showing events in a sequence.
Write the equation of the line parallel to y+4= 1/4(x+5) and passing through the point (8, 20). Write in the format y = mx + b
Answer:
[tex]y=0.25x+18[/tex]
Step-by-step explanation:
So first we take the equation we are given and write it in slope-intercept form (y = mx + b):
[tex]y+4= \frac{1}{4} (x+5)\\\\y+4=0.25x +1.25\\\\y=0.25x-2.75[/tex]
Now we know parallel lines have the same slope, so the line we are looking for has a slope of 0.25.
so we can start to set up our equation:
[tex]y=0.25x+b[/tex]
and then substitue in the point (8,20) to find the y-intercept.
[tex]20=0.25(8)+b\\20=2+b\\b=18[/tex]
So now we have our equation:
[tex]y=0.25x+18[/tex]
Hope this helps!
25
Which expression represents half the sum of n and 7 ?
Answer:
1/2(n+7)
the sum of n and 7 is (n+7). to half it just put 1/2 in front of the parentheses. :)
Arsha predicted that she would sell 225 magnets. She actually sold 240 magnets. What are the values of a and b in the table below? Percent Error Item Approximate value Exact value Error Absolute error Ratio Percent error Magnets 225 240 a b a = Negative StartFraction 15 over 225 EndFraction; b = negative 6.7 percent a = Negative StartFraction 15 over 240 EndFraction; b = negative 6.25 percent a = StartFraction 15 over 240 EndFraction; b = 6.25 percent a = StartFraction 15 over 225 EndFraction; b = 6.7 percent
Answer:
c
Step-by-step explanation:
Lily paints 3 trees for a wall mural. The middle tree is 2 1/2 ft tall. The tree on the left is 3/4 as tall as the middle tree. The tree on the right is 1 3/4 times as tall as the middle tree. How tall is each tree?
Answer:
middle is 2.5 ft
right is 4375 ft
left is 1875 ft
Step-by-step explanation:
work out the weekly mean number of 50 kg bags of flour used in these 5 weeks
Kim is a baker, she buys flour in 50kg bags.
weeks 1 2 3 4
NO of bags of flour 7 14 8 13
Kim will make 2400 loaves in week 5
Each of these loaves will need 250g of lour
Kim works out weekly mean number of 50kg bags of flour used in these 5 weeks.
she will use the figure for future orders.
Answer:
Weekly Mean Number of 50-kg bags =10.8 bags
Step-by-step explanation:
In Week 1, Kim uses 7 50kg bags of flour
In Week 2, Kim uses 14 50kg bags of flour
In Week 3, Kim uses 8 X 50kg bags of flour
In Week 4, Kim uses 13 X 50kg bags of flour
In Week 5, Kim will make 2400 loaves.
Each of these loaves will need 250g of flour.
Total Mass of flour that will be used =2400 X 250=600,000 grams
[tex]600,000$ grams=600,000 \div 1000$ kg =600kg\\Number of 50-kg bags =600 \div$ 50 =12 bags[/tex]
In Week 5, Kim will use 12 bags.
Therefore:
Weekly Mean number of 50kg bags of flour used in these 5 weeks.
[tex]=\dfrac{7+14+8+13+12}{5}\\\\ =\dfrac{54}{5}\\\\=10.8 \\ \approx 11$ bags[/tex]
The sales price of a single family house in Charlotte is normally distributed with mean $210,000 and standard deviation $35,000. 1. A random sample of 49 single-family houses in Charlotte is selected. Let X ¯ be the mean sales price of the sample. What is the mean of X ¯?
Answer:
E(X ¯)=210,000.
Step-by-step explanation:
A sampling distribution for samples of size n=49 from a population with means μ=210,000 and standard deviation σ=35,000, has the following means anda standard deviation:
[tex]\mu_s=\mu=210,000\\\\\sigma_s=\sigma/\sqrt{n}=35,000/\sqrt{49}=35,000/7=5,000[/tex]
If X ¯ is the mean sales price of the sample, it will have a mean value of E(X ¯)=210,000.
Which graph represents the solution set for
-X2 + 8x - 12 > 0?
Answer:
B
Step-by-step explanation:
What is the value of x to the nearest tenth? gradpoint
Answer:
5
Step-by-step explanation:
(12 /`15) ÷ (25/ 16) =
Answer:
[tex]\frac{64}{125}[/tex]
Step-by-step explanation:
[tex]\frac{12}{15} \div \frac{25}{16}[/tex]
[tex]\frac{12}{15} \times \frac{16}{25}[/tex]
[tex]\frac{12 \times 16}{15 \times 25}[/tex]
[tex]\frac{192}{375}[/tex]
[tex]\frac{64}{125}=0.512[/tex]
Answer:
[tex]\frac{64}{125}[/tex]
Step-by-step explanation:
=> [tex]\frac{12}{15} / \frac{25}{16}[/tex]
Changing the division sign into multiplication and inverting the term after the sign.
=> [tex]\frac{12}{15} * \frac{16}{25}[/tex]
=> [tex]\frac{12*16}{15*25}[/tex]
=> [tex]\frac{192}{375}[/tex]
=> [tex]\frac{64}{125}[/tex]
This is the required form.
Some scientists believe there is a limit to how long humans can live. One supporting argument is that during the past century, life expectancy from age 65 has increased more slowly than life expectancy from birth, so eventually these two will be equal, at which point, according to these scientists, life expectancy should increase no further. In 1900, life expectancy at birth was 45 years, and life expectancy at age 65 was 75 yr. In 2010, these figures had risen to 78.7 and 84.5, respectively. In both cases, the increase in life expectancy has been linear. Using these assumptions and the data given, find the maximum life expectancy for humans.
Answer:
The maximum life expectancy for humans is approximately 87 years.
Step-by-step explanation:
We have to calculate the point in which both linear functions (Life expectancy from birth and Life expectancy from age 65) intersect, as this is the point in which is estimated to be the maximum life expectancy for humans.
NOTE: to simplify we will consider t=0 to the year 1900, so year 2010 becames t=(2010-1900)=110.
The linear function for Life expectancy from birth can be calculated as:
[tex]t=0\rightarrow y=45\\\\t=110\rightarrow y=78.7\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{78.7-45}{110-0}=\dfrac{33.7}{110}=0.3064\\\\\\y=0.3064t+45[/tex]
The linear function for Life expectancy from age 65 can be calculated as:
[tex]t=0\rightarrow y=75\\\\t=110\rightarrow y=84.5\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{84.5-75}{110-0}=\dfrac{9.5}{110}=0.0864\\\\\\y=0.0864t+75[/tex]
Then, the time t where both functions intersect is:
[tex]0.3064t+45=0.0864t+75\\\\(0.3064-0.0864)t=75-45\\\\0.22t=30\\\\t=30/0.22\\\\t=136.36[/tex]
The time t=136.36 corresponds to the year 1900+136.36=2036.36.
Now, we can calculate with any of both functions the maximum life expectancy:
[tex]y=0.0864(136.36)+75\\\\y=11.78+75\\\\y=86.78\approx87[/tex]
The maximum life expectancy for humans is approximately 87 years.
What is the difference written in scientific notation?
Answer:
6.2 × 10⁵
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10.
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Help meee please 15 points!!
Answer:
B.
Step-by-step explanation:
B.
- 9 ≤ - 3x - 6 ≤ 6
1 part.
- 9 +6 ≤ - 3x - 6 +6
- 3/(- 3) ≤ - 3x/(- 3)
1 ≥ x
2d part
- 3x - 6 +6≤ 6 + 6
- 3x ≤ 12
- 3x/(-3) ≥ 12/(-3)
x ≥ - 4
x ≥ - 4 and x≤ 1