Answer:
2.375 inches
Step-by-step explanation:
Main Steps
1. Identifying important parts of the question
2. Solving the problem
Step 1. - Identifying important parts of the question
In the question, there is some extraneous information. For instance, the question introduces the terms "diameter" and "loaded in shear" and "with a safety factor of 1.5". However, given the information in the problem, and the question asked, it isn't necessary to know that it is "loaded in shear" means, or to know what a diameter is (since everything stays with diameters, and doesn't involve another dimension), and the problem gives the result that will satisfy "a safety factor of 1.5".
Sifting through the problem/question, these are the important parts:
- "to the nearest 1/8 inch" (meaning round to the nearest 1/8th of a unit)
- with "units of inches to 3 decimal places"
- The number to round is "2.4183 inches
Step 2. - Solving the Problem
To round to the nearest 1/8 inch, we can divide the number 2.4183 by 1/8.
[tex]2.4183 \div(1/8)[/tex]
Recall that dividing by a fraction is the same as multiplying by the reciprocal
[tex]2.4183 * 8[/tex]
19.3464
So, there are approximately 19, one-eighth-inches in the measurement. (Note that 19.3464 is closer to 19 than it is to 20). To find the final rounded measurement, multiply 19 by 1/8
[tex]19 * (1/8)[/tex]
2.375 inches
So, the diameter of the bolt that should be used (if rounded to the nearest 1/8 inch, to allow for a factor of safety of 1.5) is 2.375 inches
Albert has y stickers.
Latika has more stickers than Albert.
John has times as many stickers as Latika.
Write down an expression, in terms of y , for the number of stickers John has.
The algebraic expression, in terms of y , for the number of stickers John has is given by 4(y + 2)
How to write algebraic expression?Algebra refers to the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
Number of stickers Albert has = yNumber of stickers Latika has = y + 2Number of stickers John has = 4(y + 2)The expression for the number of stickers John has = 4(y + 2)
For instance, if y = 3
Number of stickers Latika has = y + 2
= 2 + 2
= 4 stickers
Number of stickers John has = 4(y + 4?2)
= 4(3 + 2)
= 4(5)
= 20 stickers
Therefore, the expression which can be used to represent the number of stickers John has is 4(y + 2)
Complete question:
Albert has y stickers.
Latika has 2 more stickers than Albert.
John has 4 times as many stickers as Latika.
Write down an expression, in terms of y , for the number of stickers John has.
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Find the domain and solve. screenshot included
The domain of the expression [tex]{\frac{1}{4} }^{\frac{2-x}{x} } > 64^{2}[/tex] is
-∞ < x < 0; 0 < x < ∞The solution of the equations is
x < -2/5How to find the domainThe domain of a function is all possible input values of the function
for a fraction the denominator should not be zero. therefore
In the function given: (2 - x) / x in this case x ≠ 0
The domain is then all numbers excluding 0, (-∞, 0) U (0, ∞)
The equation is solved as follows
[tex]{\frac{1}{4} }^{\frac{2-x}{x} } > 64^{2}[/tex]
solving to have a common base
[tex]4^{-1\frac{2-x}{x} } > (4^{2}) ^{3}[/tex]
[tex]4^{-\frac{2-x}{x} } > 4^{6}[/tex]
equating the bases
[tex]{-\frac{2-x}{x} } > 6[/tex]
-2 + x > 6x
-2 > 6x - x
-2 > 5x
-2/5 > x
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Two buildings are 18.5 meters apart. The angles of elevation from the top of one building to the top of the other is 18 degrees. If the taller building is 15 meters tall, how tall is the shorter building?
A mill uses 4 times as much power as a lathe. If the total power used by a mill and 3 lathes is 1540 kilowatts, find the power used by a single lathe.
Answer:
Step-by-step explanation
Answer:
220 kW
Step-by-step explanation:
You want the power used by a single lathe when a mill uses 4 times as much, and a mill plus 3 lathes uses 1540 kW.
SetupLet p represent the power used by a single lathe. Then a mill uses 4p, and the given total is ...
(4p) +3p = 1540
Solution7p = 1540 . . . . . . collect terms
p = 220 . . . . . . . divide by 7
A single lathe uses 220 kW.
Find the missing length indicated.
Answer:
14 unitsStep-by-step explanation:
Let the missing part be x.
According to triangle proportionality theorem we have:
x/28 = 6 /(18 - 6)x = 28*6/12x = 14The missing length will be 14 units.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown is figure.
Now,
Let the missing length = x
So, By the definition of triangle proportionality theorem, we get;
⇒ x/28 = 6 /(18 - 6)
Solve for x as;
⇒ x/28 = 6 /(18 - 6)
⇒ x/28 = 6 / 12
⇒ x/28 = 1 / 2
⇒ x = 28/2
⇒ x = 14
Thus, The missing length will be 14 units.
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NOW DUE AT 2:00PM !!!!!!!
Solve.
34.2 = 13.4 + 9.6x
Enter your answer as a mixed number in simplest form in the box.
Answer:
21 and 167/1000
"/" represents a fraction, so 167 over 1,000
Step-by-step explanation:
Hard to explain.
Answer: 2 1/6
Step-by-step explanation:
34.2 = 13.4 + 9.6x
34.2-13.4=9.6x
20.8=9.6x
20.8 divided by 9.6= 2.166666666
2 1/6
Evaluate:
Tan(cos^-1(x/4))
The trigonometric function tan(cos⁻¹(x/4)) evaluates to √(16 - x²) / x
To evaluate a trigonometric function?
Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles
Given the trigonometric function tan(cos⁻¹(x/4)) to evaluate:
tan(cos⁻¹(x/4))
Let θ = cos⁻¹(x/4)
Thus, cos θ = (x/4) (remember: cos θ = adjacent/hypotenuse)
We can use this information to draw a right-angled triangle as shown (image attached). Considering the triangle:
4² = x² + y²
y² = 16 - x²
y = √(16 - x²)
That means, the opposite is y = √(16 - x²)
tan θ = y/x = √(16 - x²) / x (Since tan θ = opposite/adjacent)
tan(cos⁻¹(x/4)) = √(16 - x²) / x
Therefore, tan(cos⁻¹(x/4)) evaluates to √(16 - x²) / x
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A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining 30 squares, how many grains of wheat should be placed on square ? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)
The number of grains on square 13 will be 4096 grains.
How to calculate the number of grain?No. of grains on the first square = 1 = 2^0
No. of grains on the second square = 2 = 1*2 = 2¹
No. of grains on the third square = 4 = 2*2 = 2²
No. of grains on the fourth square = 8 = 2*4 = 2³
From the pattern it could be seen that amount of wheat is doubled for every next square
So, the number of grains in the nth square = 2^n-1
Therefore, No. of grains on 13th square
= 2^13 -1
= 4096
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Alyssa has saved 4700 cents from selling lemonade.
How many dollars does Alyssa have?
Answer: 47 dollars
Step-by-step explanation: 100 cents makes a dollar 4700/100= 47
Jacob is a long-distance runner. His race is 10,000m. How far is the distance in miles?
Answer:
10000 meters = 6.214 miles
About 6 miles
Step-by-step explanation:
Soultion: How many meters are in a mile?
1600 meters: roughly 1 mile or 4 laps around the track.
Answer: 6.214
Calvin states that it is not possible to find the equation of a line
parallel to y=2 and passing through the point (5,-1) using the
point-slope form because the equation of the line does not have
an x-term. Explain the error in Calvin's reasoning.
The equation of a line y = 2 in point-slope form can be written as
(y + 1) = 0(x - 5).
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, An equation of a line y = 2 which is a line parallel to the x-axis at
y = 2.
As it is parallel to the x-axis the slope of the line is zero passing through points (5, - 1).
The equation of a line in point-slope form is (y - y₁) = m(x - x₁).
∴ (y + 1) = 0(x - 5).
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NEED HELP ASAP!!
Translate the image using the rule down below
By translating the pre-image triangle CRT with this translation rule (x, y) → (x + 2, y - 4), the coordinates of the image triangle C'R'T' are: C' (-2, -2), R' (-3, -5), and T' (3, -3).
What is a translation?In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or parent function.
Note: Each interval on this graph represents 1 unit.
Next, we would transform triangle CRT by using this translation rule (x, y) → (x + 2, y - 4) to create the vertices of triangle C'R'T' as follows:
(x, y) → (x + 2, y - 4)
Point C (-4, 2) → Point C' = (-4 + 2, 2 - 4) = (-2, -2)
Point R (-5, -1) → Point R' = (-5 + 2, -1 - 4) = (-3, -5)
Point T (1, 1) → Point T' = (1 + 2, 1 - 4) = (3, -3)
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a solid cube of side length 11 is removed from each corner of a solid cube of side length 33. how many edges does the remaining solid have?
Answer:
After taking cubes from each corner,no edge will
Kim drives 156 miles from Rotherham to London.
She drives at an average speed of 60 miles per hour.
She leaves Rotherham at 7:30 am.
Does she arrive in London before 10:00 am?
You must show your working.
Find the x-intercept of the line 8x+8y=–
1
Answer:
x-intercept is [tex]\frac{-1}{8}[/tex]
Step-by-step explanation:
The x-intercept is the Value of x when y = 0
So for our Equation , 8x + 8y = -1
At y = 0 , 8x + 0 = -1
Then 8x = -1
Then x = -1/8
A forest ranger wants to do a survey to check the general health of the trees in their care. These are:
Oak 50
Beech 40
Walnut 10
Pine 80
Spruce 20
They have enough time to survey 40 trees, and they want to do a stratified survey. How many trees are there? How many oaks should they survey? How many pines should they survey?
There are a total of 200 trees in the forest ranges and there are 50 oak trees while there are 80 pine trees.
What is a frequency table?A frequency table lists a group of values along with how frequently each one occurs. The frequency of a given data value in your dataset is the number of times it appears. These tables assist you in determining which data values are typical and which are uncommon.
It is given that the data in the table,
Oak 50
Beech 40
Walnut 10
Pine 80
Spruce 20
Thus, there are a total of 200 trees in the forest ranges and there are 50 oak trees while there are 80 pine trees.
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What is the area of a rectangles with the side lengths 5/2 inches and 4/3 inches?
HELPPP 60 pointssssss MATH
Answer:
-8
Step-by-step explanation:
y=mx+c
m=y2-y1/x2-x1
-8-0/-7-+1
-8/-8
m=1. c=-1
y=1x+-1
y=x-1
since f(-7)
y=-7-1
y=-8
Please help me thank u very much
Answer:
y=-6
Step-by-step explanation:
this is because y equal to 7 is flat so for it to be parallel the other line also has to be flat so the line will be passing through the same y value for the entire time which is -6
Hopes this helps pleae mark brainliest
A horse trainer records the distance a horse travels during three different trials. What is the horse's average speed in kilometers per minute?.
A horse trainer records the distance a horse travels during three different trials.
The horse's average speed = 0.3 kilometers per minute.
Given the following data:
Time 1 = 15 minutes
Time 2 = 30 minutes
Time 3 = 45 minutes
Distance 1 = 4.5 kilometers
Distance 2 = 9.0 kilometers
Distance 3 = 13.5 kilometers
To determine the horse's average speed in kilometers per minute:
First of all, we would find the total time and total distance covered:
For total time:
Total Time = 15+30+45
Total time = 90 minutes
For total distance:
Total Time = 4.5+9.0+13.5
Total time = 27 kilometers.
Mathematically, average speed is given by the formula:
[tex]Average speed = \frac{Total Distance}{Total Time}[/tex]
[tex]Average Speed = \frac{27}{90}[/tex]
Hence, the answer is the horse's average speed = 0.3 kilometers per minute.
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Quick pls In the triangle below, with right angle G, suppose that mZF-(3x-14)° and mZH=(5x-16).
Find the degree measure of each angle in the triangle.
The degree measure of each angle in the triangle are:
F = 31°
G = 90°
H = 59°
How to calculate the angles?It is important to note the following in the triangle:
Sum of all angle in a triangle = 180°
A right angle = 90°
Therefore, since G is a right angle, it's 90°.
H = 5x - 16
F = 3x - 14
The value of x will be found thus:
F + G + H = 180°
3x - 14 + 90° + 5x - 16 = 180
Collect like terms
3x + 5x = 180 + 14 - 90 + 16
8x = 120
Divide
x = 120 / 8
x = 15°
Therefore,
H = 5x - 16
H = 5(15) - 16
H = 75 - 16
H = 59°
F = 3x - 14
F = 3(15) - 14
F = 45 - 14
F = 31°
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if 2=394.76366368379232
then how much would
938738393x2+8732893673-8238339x2=
Answer:
Following is a very common example of calculating Sales Commission based on levels of Reven…
•=IF(C9>15000,20%,IF(C9>12500,17.5%,IF(C9>10000,15%,IF(C9>7500,12.5%,IF(C9>5000,10%,0))…
This formula says IF(C9 is Greater Than 15,000 then return 20%, IF(C9 is Greater Than 12,500 th…
While it’s remarkably similar to the earlier Grades example, this formula is a great example of how difficult it can be to maintain large IF statements – what would you need to do if your organization decided to add new compensation levels and possibly even change the existing dollar or percent
Step-by-step explanation:
How do I solve a 1 2bh?.
To solve 1/2bh, you can put up the values in the formula and find the area of the triangle.
What is the area of the triangle?
In a two-dimensional plane, the area of a triangle is the region enclosed by it. As we all know, a triangle is a closed shape with three sides and three vertices. Thus, the area of a triangle is the total space occupied by the triangle's three sides. The general formula for calculating a triangle's area is half the product of its base and height.
The given formula is 1/2bh
so this is the formula for finding out the area of the triangle where 'B' is the base of the triangle and H is the height of the triangle.
To solve 1/2bh, you can put up the values in the formula and find the area of the triangle.
Hence, to solve 1/2bh, you can put up the values in the formula and find the area of the triangle.
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On a map of texas, the cities of midland, lubbock, and odessa form a triangle. Midland is 20 miles from odessa, and lubbock is 113 miles from midland. What is the farthest, in miles, odessa could possibly be from lubbock?.
The shortest possible distance in miles between Odessa and Lubbock is 114.75 miles
Given information;
The cities of Midland, Lubbock, and Odessa make a triangle on a Texas map. Odessa is 20 miles away from Midland, and Lubbock is 113 miles away.
What is the shortest possible distance in miles between Odessa and Lubbock?
It states that a triangle is formed and the required distance is the farthest one.
So, for a triangle applying the hypotenuse theorem can solve the case,
The theorem states that the sum of the squares of the two sides is equal to the square of the other side.
D² = 20² + 113²
D² = 400 + 12769
D² = 13169
D = √13169
D = 114.75
Therefore, Odessa could be 114.75 miles from Lubbock.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Using compound interest formula, the the amount after 5 years is $15,095.39
How to find the total amount the student have in her/his saving?The total amount a college student has in a saving account if 13000 dollars was invested and earned 3% compounded quarterly for 5 years can be calculated as follows:
Therefore,
[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]
where
p = principalr = rate t = timen = number of time compoundedTherefore,
p = 13000 dollars
t = 5 years
n = 4
r = 3% = 0.03
Therefore,
[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]
[tex]A = 13000(1+ \frac{0.03}{4} )^{(4)(5)}[/tex]
A = 13,000.00(1 + 0.0075)²⁰
A = $15,095.39
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which statement is not true about nonresponse issues in sampling? increasing the response rate may not reduce nonresponse bias. response rates themselves do not indicate whether the respondents are representative of the original sample. nonresponse error is one of the most significant problems in survey research. for a given study, if the nonrespondents differ from the respondents on the characteristics of interests, the sample estimates will only be mildly biased.
Non-response bias can occur when subjects who refuse to take part in a study, or who drop out before the study can be completed, are systematically different from those who participate.
What is sampling?A statistical technique called sampling uses a small portion of a larger population to represent the entire population. Sampling is a topic that takes into account the many approaches that might be used to survey a segment of the population and looks for a sample that is most representative of the entire population. The ability of a particular subset of a population's members to be generalized to the entire population is referred to as a sample's "generalizability," or "representativeness." For a highly generalizable outcome,Sampling is a key tool in the scientific method, allowing researchers to provide evidence that generalizable theories are true simply from a sample of specific facts.Hence,Non-response bias can occur when subjects who refuse to take part in a study, or who drop out before the study can be completed, are systematically different from those who participate.
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Write each fraction or mixed number as a decimal.
Use bar notation if the decimal is a repeating
decimal.
1. 3/11
2. -7 3/5
Answer:
1. 0.27 (with bar notation)
2. -7.6
Step-by-step explanation:
The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 1,536 cm2, find the dimensions (in cm) of the poster with the smallest area.
The dimensions of the poster with the smallest area are = 64cm X 56cm where Width of the poster is 64 and Height of the poster is 56.
In order to establish a condition equation that represents the printed area's width (w) in terms of its height (h), we must first use what we know about the printed area.
Ap(w,h)=wh [Printed area]
Ap(w,h)=wh [ Substitute Ap(w,h)=1536]
1536=wh
w=1536h [width ''w'' in terms of height ''h'' ]
The smallest surface area must be determined. We need to find out the area as a function of the variable h using the condition equation.
W=w+16 [ Width of the rectangular poster ]
H=h+24 [ Height of the rectangular poster ]
Ar(w,h)=(w+16)(h+24) [Area of the rectangular poster ]
Ar(w,h)=(w+16)(h+24)
Put the value of W in terms of ‘h’ that we got above.
Ar(w)=(1536h+16)(h+24)
Ar(w)=36864h+16h+1920
Ar(w)=36864/w+16w+1920 (objective function)
Determine the domain of objective function
D={w∈R:w>0} [Domain of the Objective area function]
Ar(w)=36864/w+16w+1920
A′r(w)=−36864w2+16 [First derivative of the Objective area function]
A′r(w)=0 [critical point condition]
−36864/w2+16=0
16=36864/w2
w2=36864/16
w2=2304
w=±48
w=−48 [w=−48∉D]
w=48 [w=48∈D]
w=48 [Critical point of the Objective area function ]
Applying sufficient condition for extremes (Second derivative test)
A′r(w)=−36864/w2+16
A′′r(w)=73728/w3[Second derivative of the Objective area function]
A′′r(48)=0.6 [A′′r(48)>0]
w=48 [Minimum point of the Objective area function ]
Calculate the dimensions of the rectangular poster with minimum area
w=48 Width of the print area
h=1536/48=32 (Height of the print area)
W=48+16=64 (Width of the rectangular poster)
H=32+24=56 (Height of the rectangular poster)
The dimensions of the poster with the smallest area are: ⟹64cm×56cm
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(100 POINTS AND BRAINLIEST)
An electric toothbrush costs $69, including a 50% price markup. What was the cost for the store to purchase the electric toothbrush?
Answer:
The cost of the electric toothbrush is the $34.
Step-by-step explanation:
We have to find that the cost for the store to purchase the electric toothbrush.
cost of the electric toothbrush = $69 - 50% of $69
cost of the electric toothbrush = $69 - 50/100* 69
cost of the electric toothbrush = $69 - 34.5
cost of the electric toothbrush = 34.5.
8) The line segment YZ is a midsegment,
VW = 5x + 5, and YZ = 3x, find the length
of YZ.
Answer:
I'm going to assume that YZ is half of VW.
VW = (YZ)2
5x + 5 = (3x)2
5x + 5 = 6x
[subtract 5x from both sides]
5 = x
YZ = 3x, and x = 5, so YZ = 3(5).
YZ = 15.
