please help compare these integers by typing the symbol that would make the statement true
12 ________ - 18
Urgent!! Need an answer ASAP!
Professor Scott has 84 students in his college mathematics lecture class. The scores on the midterm exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9. How many students in the class can be expected to receive a score between 63.4 and 81.2? Express the answer to the nearest student.
Answer: 57
=====================================================
Explanation:
Convert each raw score to a z score
If x = 63.4, then
z = (x-mu)/sigma
z = (63.4-72.3)/8.9
z = -1
if x = 81.2, then
z = (x-mu)/sigma
z = (81.2-72.3)/8.9
z = 1
So P(63.4 < x < 81.2) is the same as P(-1 < z < 1)
Through the empirical rule (aka the 68-95-99.7 rule), we know that roughly 68% of the data values are within one standard deviation of the mean. In other words
P(-1 < z < 1) = 0.68 approximately (see note below)
Multiply 0.68 by the total 84 to get
0.68*84 = 57.12
which rounds to 57 people
Note: we can use a calculator to get a more accurate result of 0.68268949; a data table works as well but it won't be as accurate. For the purposes of this problem, the value 0.68 is good enough
What is the surface area of a square pyramid with a height of 12 mm and a base that measures 10 mm on each side? Round to the nearest tenth if necessary.
The surface area of the square pyramid is [tex]\(360 \, \text{mm}^2\)[/tex]
To calculate the surface area of a square pyramid, we need to find the area of its base and the area of its four triangular faces. Given the following:
The base side length [tex](\(s\))[/tex] is [tex]10\ mm[/tex].
The height of the pyramid [tex](\(h\))[/tex] is [tex]12 \ mm[/tex]
Step-by-Step Calculation:
1. Area of the base:
The base is a square with side length [tex]\(s = 10\) mm.[/tex]
[tex]\[\text{Area of the base} = s^2 = 10^2 = 100 \, \text{mm}^2\][/tex]
2. Slant height of the pyramid:
To find the slant height [tex](\(l\))[/tex], we need to use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle where one leg is half the side length of the base [tex](\(\frac{s}{2} = \frac{10}{2} = 5\) mm)[/tex] and the other leg is the height of the pyramid [tex](\(h = 12\) mm)[/tex].
[tex]\[l = \sqrt{\left(\frac{s}{2}\right)^2 + h^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \, \text{mm}\][/tex]
3 Area of the four triangular faces:
Each triangular face has a base of [tex]10\ mm[/tex] and a slant height of [tex]13 \ mm[/tex].
[tex]\[\text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 10 \times 13 = 65 \, \text{mm}^2\][/tex]
Since there are four triangular faces:
[tex]\[\text{Total area of the four triangular faces} = 4 \times 65 = 260 \, \text{mm}^2\][/tex]
4. Total surface area:
The total surface area of the square pyramid is the sum of the area of the base and the area of the four triangular faces:
[tex]\[\text{Total surface area} = \text{Area of the base} + \text{Total area of the four triangular faces} = 100 + 260 = 360 \, \text{mm}^2\][/tex]
At sea, the distance to the horizon is directly proportional to the square root of the elevation of the observer. if a person who is 36 feet above the water can see 7.4 miles, find how far a person 64 feet above the water can see.
The person 64 feet above the water can see 9.84 miles.
It is given in the question that the distance to the horizon is directly proportional to the square root of the elevation of the observer.
if the elevation of the observer be h and distance to the horizon be x then:
[tex]x=k\sqrt{h}[/tex] where k is the constant of proportionality
from the given data:
[tex]7.4= k\sqrt{36}\\\\7.4=6k\\\\k=1.23[/tex]
So, if h = 64 feet then,
[tex]x=k\sqrt{h}\\\\x=1.23\sqrt{64}\\\\x=9.84 miles[/tex] is how far the person 64 feet above the water can see.
Learn more:
https://brainly.com/question/16998607
What is the greatest common factor of 60x4y7, 45x5y5and 75x3y?
Answer:
15x^3·y
Step-by-step explanation:
The numbers 60, 45, 75 are all multiples of 15, so 15 is their greatest common factor.
The least power of the factor x is 3; the least power of the factor y is 1, so the GCF is ...
GCF = 15·x^3·y
The perimeter of a rectangle is 32 cm. The difference between the length and the width is 4cm. find the width
simplify: 10(6y+x)=4
How is the interquartile range calculated? HELP WITH APEX PLEASE!
By definition the interquartile range or IQR is obtained when the 25th percentile or [tex] Q_{1} [/tex] is subtracted from the 75th percentile or [tex] Q_{3} [/tex].
Thus, from the above definition, the formula for IQR is:
[tex] IQR=Q_{3}-Q_{1} [/tex]
As we can see from the provided options that the definition of IQR matches the expression provided in Option A and thus, Option A is the correct answer.
Quartile 3 (Q3) minus quartile 1 (Q1) is right for apex.
write a polynomial function of nth degree that has the given zeros
A polynomial function of nth degree with given zeros, use the form f(x) = a (x - x1)(x - x2)...(x - xn), which is [tex]f(x) = x^3 - 2x2 - 5x + 6[/tex]
To write a polynomial function of the nth degree with given zeros, you can use the fact that a polynomial function f(x) with zeros at x1, x2, ..., xn can be expressed as:
f(x) = a (x - x1)(x - x2)...(x - xn)
Where 'a' is the leading coefficient, which can be any non-zero real or complex number, and (x - xi) are factors for each zero of the polynomial. If the polynomial is supposed to have a specific coefficient for the highest power term, then 'a' is that coefficient; otherwise, 'a' can be chosen freely to define the polynomial.
To illustrate with an example, if we had a polynomial of degree 3 with zeros at 1, -2, and 3, and we want the leading coefficient to be 1, our polynomial would be:
f(x) = (x - 1)(x + 2)(x - 3)
Expanding this product, we would get:
[tex]f(x) = x^3 - 2x2 - 5x + 6[/tex]
This polynomial of third degree has the specified zeros and a leading coefficient of 1.
A circle has a circumference of 10. It has an arc of length 9/2
The ratio between the volumes of two cubes is 125 to 216. what is the ratio between their respective surface areas?
PLEASE HELP will give brainiest if correct
An ice chest contains 88 cans of apple juice, 44 cans of grape juice, 55 cans of orange juice, and 66 cans of mango juice. suppose that you reach into the container and randomly select three cans in succession. find the probability of selecting three cans of appleapple juice.
If Michael and imani add an 18% tip to the bill,what does their lunch cost in total
Answer:
X + (0.18 * X)
where X is the price of the bill without the tip
Step-by-step explanation:
The first thing you have to do is convert the percentage to a decimal value. For example, if it is 30%, its decimal value is 0.30. As simple as dividing that 300 by 100. Repeat the previous step with all the percentages you have to add.
In this case it is 18% therefore the decimal value will be 0.18. As we do not have the value of the account, we will call this value X .
Therefore the total price of the account, that is, with the addition of the tip is as follows:
X + 18% de X =
X + (0.18 + X)
Which quadratic equation is equivalent to (x+2)2+5(x+2)-6=0
Which group of values makes the expression 3x2y−2z UNDEFINED? A) x = –1; y = 0; z = 3 B) x = –1; y = 3; z = 0 C) x = 0; y = −1; z = 3 D) x = 0; y = 3; z = −1 E) x = –1; y = 2; z = 1
Answer:
The answer is A
Step-by-step explanation:
sadly i dont have the work of it just by looking it up you can get the answer tho. Answer is A
Which shapes have rotational symmetry that occurs at 180°?
Check all that apply.
regular octagon regular pentagon regular hexagon square right isosceles triangle
It should be regular octagon, regular hexagon, and square
The volume of a solid gold statue can be approximated as 1000 cm3. If the density of gold is about 20/cm3, what is the mass of the statue?
The density of water is 1000 kilograms per cubic meter and the density of ice is about 916 kilograms per cubic meter of 700 kilograms of water and 450 kilograms of ice is combined in a container what is the volume of the water
The volume of water can be calculated by dividing the mass of water by the density of water.
Explanation:The question asks for the volume of water when 700 kilograms of water and 450 kilograms of ice are combined in a container. To find the volume of water, we need to subtract the volume of ice from the total volume. The density of water is 1000 kg/m³, so the volume of water can be calculated by dividing the mass of water (700 kg) by the density of water (1000 kg/m³).
Volume of water = Mass of water / Density of water
Volume of water = 700 kg / 1000 kg/m³
Volume of water = 0.7 m³
Learn more about density of water here:https://brainly.com/question/14373997
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the line y=2x-4 is dilated bt a scale factor of 3/2 and centered at the origin. Write an equation that represent that image of the line after dilation
The equation that represent that image of the line after dilation is
[tex]y = 2x-6[/tex]
Given :
The line [tex]y=2x-4[/tex] is dilated by a scale factor of [tex]3\div2[/tex] and centered at the origin.
Solution :
The given line has slope 2 and y intercept -4.
As dilation conserves the parallelism, the dilated line will have the same slope = 2 and the y intercept of the dilated line is
[tex]= -4\times \dfrac{3}{2}=-6[/tex]
Therefore the equation that represent that image of the line after dilation is
[tex]y = 2x-6[/tex]
For more information, refer the link given below
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PLEASE HELP!!!Which pair of angles are corresponding? Two horizontal lines cut by a diagonal transversal. Angles 1, 3, 5, and 7 are located on the left-hand side of the transversal starting from the top. Angles 2, 4, 6 and 8 are located on the right-hand side of the transversal starting at the top. Question 2 options: 1 and 3 1 and 4 4 and 8 1 and 8
Answer:
According to the description of the case, the angles should be named after this picture.
The congruents angles among each other are:
Blue: 1,4,5,8
Purple: 2,3,6,7
Therefore the three possibilities are:
a. 1 and 4
b. 4 and 8
c. 1 and 8
Step-by-step explanation:
A woman can bicycle 27 miles in the same time it takes her to walk 9 miles. she can ride 10 mph faster than she can walk. how fast can she walk
Describe the locus that the figure represents.
Question 13 options:
all points equidistant from line l
all points equidistant from point A and point B
none of these
all points 1 cm from line l
Jane is choosing a 3 -letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?
How do you write an equation for a circle with center (2,4) and passes through point (5, 9)?
The length of a rectangle is 10 feet longer than it is wide. if each side is increased 10 feet, then the area is multiplied by 4. what was the size of the original rectangle?
Final answer:
The original rectangle had a width of 20 feet and a length of 30 feet (20 feet + 10 feet). After solving a quadratic equation, we determined the original dimensions by setting up an equation that represented the area before and after the increase.
Explanation:
The original rectangle has a length that is 10 feet longer than its width. Let the width be represented by w feet. Therefore, the length would be w + 10 feet. After increasing each side by 10 feet, the new width is w + 10 and the new length is w + 20. The area of the new rectangle is 4 times larger than the original rectangle's area.
The area of the original rectangle is given by w(w + 10). The area of the larger rectangle is given by (w + 10)(w + 20). By multiplying the larger area, we get 4 times the original area, so (w + 10)(w + 20) = 4w(w + 10). We can simplify this equation to solve for w.
Step-by-step solution:
Set up the equation: (w + 10)(w + 20) = 4w(w + 10).Expand and simplify to: w² + 30w + 200 = 4w² + 40w.Rearrange to: 3w² + 10w - 200 = 0.Factor the quadratic equation: (3w - 20)(w + 10) = 0.Solve for w: w = 20 or w = -10 (we discard the negative solution).Thus, the original width is 20 feet and the original length is 30 feet (20 + 10).
Would someone Please answer this question please will be thanked and also will pick brainly!! (please be honest)
A bag of uninflated balloons contains 10 red, 12 blue, 15 yellow and 8 green balloons. A balloon is drawn at random, what is the probability of drawing a red balloon?
We have been given that a bag of uninflated balloons contains 10 red, 12 blue, 15 yellow and 8 green balloons.
We need to find the probability of drawing a red balloon.
We know that probability is given by
[tex]\\ \text{Probability =} \frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Since we know that there are 10 red balloons. Therefore, our number of favorable outcomes is 10.
In order to find the total number of outcomes, we will add balloons of all colors.
Therefore, total outcomes are = [tex]10+12+15+8 = 45[/tex]
We can now substitute the values of favorable outcomes and total outcomes in order to find the required probability.
[tex]\\ \text{Probability =} \frac{\text{10}}{\text{45}} = \frac{2}{9}[/tex]
Determine if the following data set follows a linear, quadratic, or exponential model. (0, 1), (1,3), (2, 9), (3, 19), (4, 33)
show your work
PLEASE SOMEONE HELP!
I think that it would be a linear model.
Answer:
Step-by-step explanation:
quadratic C
Given that b=8,a=3,and b=65,find the measure of
A. 19.9 or 160.1
B.19.9
C160.1
D not a triangle
Answer: B. 19.9
Step-by-step explanation: Set up an equation where sin and the degree angle is in the numerator, and the side length is in the denominator.
Sin65/8 = Sinx/3
Plug Sin65 into your calculator and you will get 0.9063. Divide this number by 8.
0.9063/8 = 0.1133
Your equation is now 0.1133 = sinx/3
Multiply by 3 on each side.
0.3399 = sinx
Put sin on the left side. It will look like:
Sin^-1(0.3399) = x
Press enter on your calculator. You will get
X = 19.9.