Answer:
D. 99.9936%.
Step-by-step explanation:
We have been given that the length of a screw produced by a machine is normally distributed with a mean of 0.65 inches and a standard deviation of 0.01 inches.
To find the percent of screws that are between 0.61 and 0.69 inches, first of we will find z-score for our given raw scores using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z=\text{z-score}[/tex],
[tex]x=\text{Raw-score}[/tex],
[tex]\mu=\text{Mean}[/tex],
[tex]\sigma=\text{Standard deviation}[/tex].
Now let us find z-score corresponding to our given raw scores.
[tex]z=\frac{0.61-0.65}{0.01}[/tex]
[tex]z=\frac{-0.04}{0.01}[/tex]
[tex]z=-4[/tex]
Now let us find z-score for raw score 0.69.
[tex]z=\frac{0.69-0.65}{0.01}[/tex]
[tex]z=\frac{0.04}{0.01}[/tex]
[tex]z=4[/tex]
Now we will use formula to find the probability between two z-score as:
[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]
Upon substituting our given values in above formula we will get,
[tex]P(-4<z<4)=P(z<4)-P(z<-4)[/tex]
Using normal distribution table we will get,
[tex]P(-4<z<4)=0.99997-0.00003[/tex]
[tex]P(-4<z<4)=0.99994[/tex]
Now let us convert our answer into percent by multiplying 0.99994 by 100.
[tex]0.99994\times 100=99.994\%[/tex]
Therefore, 99.994% of screws are between 0.61 and 0.69 inches and option D is the correct choice.
The length of a rectangle is eight times it's width. If the length was decreased by 10 meters and the width decreased by 2 meters the area would be decreased by 162 m. Find the original dimensions.
This prism has a volume of 112 cm3. What would the volume of the prism be if each dimension was doubled?
(Scale factor is 2)
224 cm3
896 cm3
448 cm3
336 cm3
If each dimension was doubled, the volume of the prism would be: B. 896 cm³.
What is a scale factor?In Geometry and Mathematics, a scale factor simply refers to the ratio of two corresponding side lengths in two similar geometric figures such as pentagons, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
In Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:
Scale factor of volume = (Scale factor of dimensions)³
Scale factor of volume = (2)³
Scale factor of volume = 8
Therefore, the new volume is given by;
New volume of prism = 112 × 8
New volume of prism = 896 cm³.
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Find 93 • 87 using mental math.
To estimate 93 × 87 using mental math, round 87 to 90, multiply by 93 to get 8370, and subtract 3 × 93 (279) for an estimate of 8091.
To find 93 × 87 using mental math, we can employ a strategy that simplifies the multiplication process. One way is to round one of the numbers to the nearest multiple of ten, perform the multiplication, and then adjust the result accordingly. Here, we can round 87 up to 90 and multiply 93 by 90. This is easier because 90 is a multiple of 10.
93 × 90 = (93 × 9) × 10 = 837 × 10 = 8370
Since we rounded 87 to 90, we overestimated by 3 per unit of 93. Hence, we need to subtract 3 times 93 from 8370.
3 × 93 = 279
Thus, 8370 - 279 = 8091.
Select the additive inverse of 51
Whats the perimeter of a rectangle with length 12 m and width 5m
Neptune has 8 known moons. This is 2 more than 1/3 of the number of known moons on Saturn. How many moons is Saturn known to have?
Through setting up and solving the equation 1/3 * x + 2 = 8, where x represents the number of Saturn's moons, it was determined that Saturn is known to have 18 moons.
Explanation:The student's question pertains to a comparison of the moons of Neptune and Saturn, using mathematical operations to deduce the number of known moons of Saturn. First, we're told that Neptune has 8 known moons, which is said to be 2 more than 1/3 of the number of known moons on Saturn. We are seeking to solve for the number of moons that Saturn has.
To find out, we set up an equation where 1/3 of the number of moons of Saturn plus 2 equals the number of Neptune's moons: 1/3 * x + 2 = 8, where x represents the number of Saturn's moons. Solving for x, we subtract 2 from both sides to get 1/3 * x = 6. We then multiply both sides by 3 to isolate x and find that x = 18.
Therefore, Saturn is known to have 18 moons according to the given information.
A house is 50.0 ft long and 26 ft wide and has 8.0-ft-high ceilings. what is the volume of the interior of the house in cubic meters and in cubic centimeters? 290
What is
5.63×
10
−6
in decimal form?
a. 0.00000563
b. 0.000000563
c.5,630,000
d. 56,300,000
the leg of a right triangle is 5 units and the hypotenuse is 8 units.what is the length in units of the other leg of the triangle
The square of the hypotenuse is equal to the sum of the square of other two sides. The length in units of the other leg of the triangle is 6.2 units
What is Pythagoras theorem?The square of the hypotenuse is equal to the sum of the square of the other two sides.
Mathematically;
l^2 = a^2 + b^2
Given
l = 8 units
a = 5 units
Substitute
8^2 = 5^2 + b^2
64 - 25 = b^2
b^2 = 6.2units
Hence the length in units of the other leg of the triangle is 6.2 units
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Please help! Given b = 4 and h = 1, what is the equation of the graph if the parent function is y = sqrt x?
A. y = sqrt (4x - 4)
B. y = sqrt (4x + 4)
C. y = - sqrt (4x - 4)
D. y = - sqrt (4x + 4)
To solve this problem, we make use of the formula:
y = a sqrt (b (x – h)) + k ---> 1
Since we are given the parent function:
y = sqrt (x) ---> 2
Then this automatically means that:
a = 1 and k = 0
So going back to equation 1 at a = 1 and k = 0:
y = 1 sqrt (b (x – h))
Since it is given that, b = 4 and h = 1, therefore:
y = sqrt (4 (x – 1))
y = sqrt (4 x – 4)
Answer:
A. y = sqrt (4 x – 4)
How do you write 56% as a fraction in simplest form?
We can write 56% as a fraction to the simplest form as [tex]\mathbf{= \dfrac{14}{25} }[/tex]
A fraction is a numeric value divided into two parts, the upper part(numerator) and the lower part(denominator) which are separated by a division line.
From the given information:
56% can be written in fraction as [tex]\mathbf{\dfrac{56}{100}}[/tex]
Now, to its simplest form means to divide the numerator and the denominator to their lowest term. By doing so, we have:
[tex]\mathbf{\dfrac{56}{100}}[/tex]
Divided by (2)
[tex]\mathbf{= \dfrac{28}{50} }[/tex]
Divided by (2)
[tex]\mathbf{= \dfrac{14}{25} }[/tex]
Therefore, we can conclude that 56% as a fraction to the simplest form is [tex]\mathbf{= \dfrac{14}{25} }[/tex] since no other number can go in both the numerator and the denominator.
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find the value of x if f(x) equals 7 f(x) equals 4x minus 1
PQRS is an isosceles trapezoid and m angle Q=127. Find M angle P.
Answer:
[tex]m<P=127\°[/tex]
Step-by-step explanation:
we know that
If the trapezoid PQRS is an isosceles trapezoid
then
[tex]PS=QR[/tex] ----> congruent sides
[tex]m<P=m<Q[/tex] -----> congruent angles
In this problem we have
[tex]m<Q=127\°[/tex]
therefore
[tex]m<P=127\°[/tex]
Mr. James has cylindrical beakers that measure 4 inches in diameter and are 9 inches high. What is the volume contained within the beakers? Use 3.14 for pi. Round your answer to the nearest hundredth. 56.52 cubic inches 100.34 cubic inches 113.04 cubic inches 226.08 cubic inches
The answer is C, or 113.04 cubic inches.
if a metal tool chest has the shape of a prism with a pentagonal base of 6194in squared in area, calculate the volume of the metal chest and pick where length c = 6 inches and length m = 19 inches
The volume of the metal tool chest is 37,164 cubic inches. To calculate the volume of the metal tool chest, we use the formula for the volume of a prism: Volume = Base area × Height
Given that the pentagonal base has an area of 6194 square inches, and the length c (which represents the height) is 6 inches, we can calculate the volume as follows:
Volume = 6194 in² × 6 in
Volume = 37,164 cubic inches
So, the volume of the metal tool chest is 37,164 cubic inches.
As for the lengths provided:
c = 6 inches (height)
m = 19 inches (unknown side length of the pentagon)
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Which of the following types of functions cannot have "all real numbers" as either its domain or its range? Exponential function Quadratic function Linear function Inverse Variation function
Use the horizontal line test to identify the relation whose inverse is not a function.
The graph 3 whose inverse is not a function.
What is an inverse of a function?The inverse function agrees with the resultant, operates and reaches back to the original function. If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x.
Horizontal Line Test :-
Let f be a function. If any horizontal line intersects the graph of f more than once, then f does not have an inverse. If no horizontal line intersects the graph of f more than once, then f does have an inverse.
So, according to the definition, the only graph which follows the rule of horizontal lines test is the graph 3.
Hence, the graph 3 whose inverse is not a function.
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By using the horizontal line test, a relation whose inverse is not a function is: D. relation D.
In Mathematics and Euclidean Geometry, the horizontal line test states that if the graph of a function (f) is intersected by any horizontal line more than once, then, the function (f) does not have an inverse.
Conversely, if the graph of a function (f) isn't intersected by any horizontal line more than once, then, the function (f) has an inverse.
By critically observing the graph of the given relation shown in the image attached below, we can logically deduce that it does not have an inverse because it didn't pass the horizontal line test.
Sue took a taxi from her home to her friends house. It cost $3.58 per mile and she gave the driver a $5 tip. If she paid $87.34, how many miles does she live from her friend?
87.34-5 = 82.34
82.34/3.58 = 23
she lives 23 miles away
Geometry Question Please Help!!!!
where is the best place to learn spanish for free and become fluent on line
Answer:
DUOLINGOOOO
Step-by-step explanation:
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What is 5.928301 to 2 decimal places?
Final answer:
To round 5.928301 to 2 decimal places, we observe the third decimal place. It's 8, so we round up, making the answer 5.93.
Explanation:
When rounding the number 5.928301 to 2 decimal places, we need to look at the third decimal digit to decide whether to round up or down. Since the third decimal digit (8) is greater than 5, we round up. Therefore, the number 5.928301 rounded to 2 decimal places is 5.93.
Rounding a number to two decimal places involves examining the third decimal digit to determine whether to round up or down. In the case of 5.928301, the third digit is 8, which is greater than 5. Consequently, rounding up is necessary. Thus, the rounded value of 5.928301 to two decimal places is 5.93, emphasizing the role of the third digit in the rounding decision.
Trey's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Trey $4.80 per pound, and type B coffee costs $5.85 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $603.45 . How many pounds of type A coffee were used?
Let x = the number of pounds of Type A coffee.
We know that this month's blend used 3 times as many pounds of type B coffee as type A coffee.
Total pounds of coffee = x + 3x
The total cost is:
(cost for Type A)(x) + (cost for Type B)(3x) = $603.45
$4.80x + $5.85(3x) = $603.45
$4.80x + $17.55x = $603.45
$22.35x = $603.45
x = 603.45/22.35 = 27 pounds
Which of the following sets is not finite?
A basketball is thrown with an initial upward velocity of 25 feet per second from a height of 8 feet above the ground. The equation h=−16 t 2 +25t+8 h=−16t2+25t+8 models the height in feet t seconds after it is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?
Determine whether the sequence shown are arithmetic or geometric 1,8,15,22,29
The area of a rectangular wall of a barn is 75 75 square feet. its length is 10 10 feet longer than the width. find the length and width of the wall of the barn.
First, represent the unknown width as 'x'. Then, because the length is 10 feet more than the width, represent the length as 'x + 10'. Since the area is 75 square feet, set up and solve the equation x*(x + 10) = 75 for 'x'. This will give the width and the length will be this width plus 10 feet.
Explanation:This problem can be solved using algebra. First, let's denote the width of the wall as x in feet. If the length of the wall is 10 feet longer than the width, then we can express the length as x + 10. We're told that the area of the rectangle formed by the wall is 75 square feet. The area of a rectangle is calculated by multiplying its length by its width. Therefore:
x*(x + 10) = 75
You can solve this quadratic equation for x. The positive solution will be the width of the wall and the length will be that value plus 10 feet.
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The parabola has a vertex of (1,-16) and y intercept of (0,-15) that crosses the x axis in two places. one x intercept is (5,0) what is the other x intercept
a bag contains 5 red marbles, 3 yellow marbles, and 2 blue marbles. Once a marble is drawn, it is not replaced.what is the probability of drawing a blue on the first draw and a second blue marble on the next draw ?
Find the value of x for which abcd must be a parallelogram 5x-1 2x+5
The growth of a new strain of bacteria is represented by 7=79.31(1.48)^x,where x represents the number of days and y represents the number of bacteria. which is the best prediction for the number of bacteria on day 6
A.833
B.117
C.704
D.647
Answer:
A. 833
Step-by-step explanation:
Given:
The growth of a new strain of bacteria is represented by [tex]y = 79.31(1.48)^x[/tex], where "x" represents the number of days and "y" represents the number of bacteria.
We need to find the number of bacteria on day 6.
So, here x = 6, we need to plug in x = 6 in the given function and find the answer.
[tex]y = 79.31(1.48)^6[tex]
Simplify the above expression, we get
y = 833.49
The bacteria cannot be in decimal form, let's round off the answer to nearest whole number.
y = 833
Therefore, answer is A. 833