Answer:
p = 0.3125
Step-by-step explanation:
given data
watching the video = 16 students
noticed the gorilla = 5
to find out
Calculate p
solution
so we get here proportion p that is express as
p = noticed the gorilla ÷ watching the video .....................1
put here value and we get
p = [tex]\frac{5}{16}[/tex]
p = 0.3125
5.
Peggy wants to build a solid cube with a side length of 5 units. Peggy has 45 unit cubes. How many
more unit cubes does she need?
Answer:
80
Step-by-step explanation:
V = s^3
V = 5^3 = 125
125 - 45 = 80
She needs 80 more unit cubes.
A client would like a logo printed onto a canvas that is at least 70 inches tall. The original logo is 4.5 inches wide by 3.6 inches tall. Which dimensions will keep the logo in proportion and large enough to meet the client's requirements?
Answer:
to find the dimension I would get 3.6/4.5=x/70 amd u get 3.6*70=4.5x and u get 252=4.5x and x=56
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let the width of logo printed on canvas = x inches
Dimensions are in proportion
[tex]\frac{70}{x}=\frac{3.6}{4.5}\\[/tex]
Cross multiply
70 * 4.5 = x * 3.6
x * 3.6 = 315
[tex]x=\frac{315}{3.6}\\\\=\frac{3150}{36}\\\\x=87.5inches[/tex]
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean 1261 and a standard deviation of 118. (a) Determine the 30th percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle 98% of bags. (c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Answer:
(A) 1199.168
(B) 1503.372
(C) 159.17728
Step-by-step explanation:
(A) To determine the 30th percentile for the number of chocolate chips in the bag, we find the z-score for the 30th percentile.
Found using a z-table or z-calculator, the z-score for the 30th percentile is -0.524
The formula for finding X (the number of items in a given percentile) is:
X = M + Z(S.D.)
Where M is the mean, Z is the specific z-score of the sought percentile and S.D. is the standard deviation.
So for the 30th percentile,
X = 1261 + (-0.524)(118)
X = 1261 - 61.832 = 1199.168
(B) The number of chocolate chips that make up the middle 98% of chips in the bag is
X = 1261 + (2.054)(118)
X = 1261 + 242.372 = 1503.372
(C) For normal distributions, Interquartile range is Q3 - Q1, that is; 3rd quartile minus 1st quartile.
This is within 1.34896 standard deviations of the mean.
IQR = (1.34896)(118)
IQR = 159.17728
Which of these graphs represents a function? Please help
Answer:
Top Right Graph is the only function.
Step-by-step explanation:
Imagine a vertical line moving from left to right over the entire width of the graph. If at any position, the line intersects more than one point on the graph, the graph is not a function. This is called the vertical line test.
The only graph that passes the vertical line test is the top right graph. All other graphs fail the vertical line test because a vertical line intersects more than one point at some position.
Using the function concept, it is found that graph x represents a function.
----------------------------
A function is only represented if each value of the input only has one respective value of output.In a graph, for one value of x(horizontal axis), there can only be one respective value of y(horizontal axis).This can be verified applying the vertical line test. It is a function if the line crosses the function only once.In the appended image, it can be see that on graphs w, y, and z, the line crosses the function more than once, thus, they are not functions.Then, graph x is a function, as there are no points aligned vertically.A similar problem is given at https://brainly.com/question/12463448
4) A large number of people were polled and asked which of four different animals were their
favorite. 13% said Penguin, 21% said Iguana, 22% said Parrot, and 44% said Turtle. Suppose you
decide to carry out a simulation given these percentages. You decide to select two digits at a
time. Which would be a proper assignment of digits for these teams?
a) 01-13 = Penguin, 01-21 = Iguana, 01-22 = Parrot, 01-44 = Turtle
b) 00-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 = Turtle
c) 01-13 = Penguin, 14-35 = Iguana, 36-58 = Parrot, 59-99 & 00 = Turtle
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
e) None of these
Answer:
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
Step-by-step explanation:
13 − 01 + 1 = 13
34 − 14 + 1 = 21
56 − 35 + 1 = 22
99 − 57 + 1 + 1 = 44
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
Answer:
52.78% probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X greater than x is given by the following formula.
[tex]P(X > x) = \frac{b-x}{b-a}[/tex]
Uniformly distributed between 0 and 9 minutes.
This means that [tex]a = 0, b = 9[/tex]
Find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
[tex]P(X > 4.25) = \frac{9 - 4.25}{9 - 0} = 0.5278[/tex]
52.78% probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s) the degree of the function f(x) = -(x+1)^2(2x-3)(x+2)^2 is _ , and its y-intercept is ( _ , _ )
Answer:
Degree of the function = 5
y-intercept = (0, 12)
Step-by-step explanation:
Degree of a polynomial function is determined by the degree of the term having highest degree.
In the given function,
f(x) = -(x + 1)²(2x - 3)(x + 2)²
(x + 1)² → highest degree term = x²
(2x - 3) → highest degree term = x
(x + 2)² → highest degree term = x²
When we multiply these terms,
(x + 1)²(2x - 3)(x + 2)² highest degree term of the function will be,
[tex]x^{2} \times x \times x^{2} = x^{5}[/tex]
Therefore, degree of the function = 5
For y-intercept,
f(0) = -(0 + 1)²(0 - 3)(0 + 2)² = 12
Therefore, y-intercept of the function is (0, 12)
There is a bag filled with 4 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting at least 1 red?
Answer:
[tex]\dfrac{65}{81}[/tex] or 80.25%
Step-by-step explanation:
Number of blue Marbles = 4
Number of Red Marbles = 5
Total Number of marbles =4+5=9
[tex]P(B)=\dfrac49\\\\P(R)=\dfrac59[/tex]
In the experiment, two marbles are chosen one after the other with replacement.
The possible outcomes are: BB, BR, RB and RR
The probability of getting at least 1 red
=P(BR or RB or RR)
=P(BR)+P(RB)+P(RR)
[tex]=\left(\dfrac49\times\dfrac59\right) + \left(\dfrac59\times\dfrac49\right)+\left(\dfrac59\times\dfrac59\right)\\\\=\dfrac{20}{81}+\dfrac{20}{81}+\dfrac{25}{81}\\\\=\dfrac{65}{81}[/tex]
Expressed as a percentage, we have:
[tex]\dfrac{65}{81}\times100=80.25\%[/tex]
The probability of getting at least 1 red is 80.25%.
Which is greater 36÷(4×3) or 54-48-(16÷4
Step-by-step explanation:
36 ÷ (4 x 3)
36 ÷ 12
= 3
54 - 48 - (16 ÷ 4)
54 - 48 - 4
= 2
So first one is greater
Determine f(-1) (3). Use the following table of values
Answer:
-5
Step-by-step explanation:
The value of x that gives f(x) = 3 is -5.
[tex]f^{-1}(3)=-5[/tex]
Makayla is teaching Rodney how to construct a square inscribed in a circle.
I need help ...... Makayla says Rodney should draw diameter AB, and then use a compass and a straightedge to find chord CD that bisects diameter AB. Makayla also tells Rodney he should use a straightedge to draw the four chords that make up the square: chords AC, AD, BC, and BD.
What error, if any, is Makayla making in her instructions to Rodney?
Answer:
A.) Chord CD must not only bisect but must also be perpendicular to diameter AB.
Step-by-step explanation:
The error, Makayla is making in her instructions to Rodney is that the chords that make up the square are chords AB, BC, CD, and DA.
What is Geometric construction?Geometric construction is method todraw any sketch lines, angles, and other geometric forms and figures only using a compass and a straightedge. It generally is done without employing precise measurements of length, angle, etc.
Now the steps taken by Makayle are,
→draw diameter AB
→use a compass and a straightedge to find chord CD that bisects diameter AB.
→use a straightedge to draw the four chords that make up the square: chords AC, AD, BC, and BD.
Now here the error she is making is that the required chords will be AB, BC, CD, and DA, not AC, AD, BC, and BD.
Hence,the error, Makayla is making in her instructions to Rodney is that the chords that make up the square are chords AB, BC, CD, and DA.
To learn more about Geometry:
https://brainly.com/question/7558603
#SPJ2
Suppose that 3 is a factor of a, a is a divisor of 12, and a is positive. What is the number of possible values of a?
Answer:
3
Step-by-step explanation:
12 is divisible by: 1, 2, 3, 4, 6, 12
Because 3 is a factor of a, that means 3 multiplied by another number equals a. Additionally, a is a divisor of 12, meaning a multiplied by another number equals 12.
Out of the numbers, 12 is divisible by, only 3 are also divisible by 3: 3, 6, 12 This gives three possible values of a.
A is any nonnegative real number and b is a square root of that number. Is a a function of b, b a function of a, both, or neither?
Answer:
B is a function of A
Step-by-step explanation:
If you do something to another thing, it is a function of that.
If a polynomial function f(x) has roots 3+root5 and -6, what must be a factor of f(x)? (X+(3-root5) (x-(3-root5)) (x+(5+root3)) (x-(5-root3))
Answer:
[tex](x-(3+\sqrt5))[/tex] or [tex](x-3-\sqrt5)[/tex] is a factor of the given polynomial.
Step-by-step explanation:
Let us learn the concept with an example first.
Let the polynomial be a quadratic function [tex]g(x)[/tex].
[tex]g(x) = x^{2} -5x+6[/tex]
The roots of [tex]g(x)[/tex] are 2 and 3.
Putting [tex]x= 2\ in \ g(x)[/tex]
[tex]2^2-5\times 2+6 = 4-10+6 =0[/tex]
Putting [tex]x= 3\ in \ g(x)[/tex]
[tex]3^2-5\times 3+6 = 9-15+6 =0[/tex]
Putting x = 2 or x = 3, g(x) = 0 [tex]\therefore[/tex] The roots of equation g(x) are 2 and 3.
Now, let us try to factorize g(x):
[tex]x^{2} -2x-3x+6\\\Rightarrow x(x -2)-3(x-2)\\\Rightarrow (x-3)(x-2)[/tex]
so, the equation can be written as:
[tex]g(x) = x^{2} -5x+6=(x-3)(x-2)[/tex] where 3 and 2 are the roots of equation.
The factors are (x-3) and (x-2).
[tex]\therefore[/tex] for the polynomial f(x) which has roots [tex]3+\sqrt5\ and\ -6[/tex] will have a factor:
[tex](x-(3+\sqrt5))[/tex] or [tex](x-3-\sqrt5)[/tex]
The radius of a sphere is 3 inches. Which represents the volume of the sphere? 12π cubic inches 36π cubic inches 64π cubic inches 81π cubic inches
Answer:
36pi
Step-by-step explanation:
Answer:
36pi
Step-by-step explanation:
i got it right on my test
Factor completely 2x⁴y³-12x³y²-8x²y
The lines shown below are perpendicular. If the green line has a slope of a
what is the slope of the red line?
O A 22
OB.
Answer:
-4/3
Step-by-step explanation:
since the both lines are perpendicular the product of their slopes equals -1 let m be the slope of the red line m*a = -1 m = -1/a a = (8-5)/(0-(-4)) = 3/4 so m = -4/3Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.
Coefficients Standard Error
Constant 12.924 4.425
x1 -3.682 2.630
x2 45.216 12.560
Analysis of Variance
Source of Degrees of Sum of Mean
Variation Freedom Squares Square F
Regression 4853 2426.5
Error 485.3
We want to test whether the variable x1 is significant. The critical value obtained from ttable at the 1% level is:_______.
1. ±2.650.
2. ±2.921.
3. ± 2.977.
4. ± 3.012.
Answer:
4. ± 3.012
Step-by-step explanation:
Hello!
Assuming that for both variables X₁ and X₂ n₁= n₂ = 16
You need to test at 1% if the variable is significant, this means, if the slope for X₁ is different from zero (β₁≠0) using the t-statistic and the critical value approach.
The hypotheses are:
H₀: β₁= 0
H₁: β₁≠ 0
α: 0.01
[tex]t= \frac{b_1-\beta_1}{Sb_1} ~t_{n_1-3}[/tex]
The degrees of freedom "n₁-3" are determined by the number of parameters that you estimate for the multiple regression, in this case there are three "β₁" "β₂" and "δ²e"
The rejection region for this test is two-tailed, the critical values are:
±[tex]t_{n-3;1-\alpha /2}= t_{13;0.995}= 3.012[/tex]
I hope this helps!
If y = x2 + 2x , find the value of y when x = 3
and
If y = x3 - 3 , find the value of y when x = 2 plsss help me
Answer:
y=15; y=5
Step-by-step explanation:
y=x2+2x
plug in x as 3:
y=3 2+ 2*3
y=9+6
y=15
Next problem:
y=x3-3
plug in x as 2:
y=2 3-3
y=8-3
y=5
y = 0.8x+ 7.2
20x + 32y = 48
Step-by-step explanation:
y = 0.8x+ 7.2 ..........(1)
20x + 32y = 48 .........(2)
Substitute (1) in (2)
20x +32*(0.8x+7.2) = 48 expand
20x + 25.6x+230.4 = 48 add
45.6x+230.4 = 48 transpose and simplify
45.6x = 48-230.4 = -182.4
x = -182.4 / 45.6
x = -4
Answer:
x=-4, Y=4
Step-by-step explanation:
20x+32(0.8x+7.2)=48
45.6x =48-230.4
x=-4
substitute x=-4 in y eqn
y=-3.2+7.2
y=4
Two ships leave a port at the same time.
Ship A sails 12 knots on a bearing of 035°
Ship B sails 16 knots on a bearing of 270°
Calculate the distance between the ships after 2 hours
(1 knot = 1 nautical mile per hour)
Answer: 49.8 nautical miles
Step-by-step explanation:
Angle between routes = 125⁰
after 2 hours :-
d² = 24² + 32² - 2 x 24 x 32 cos 125⁰
d = 49•8 nautical miles
A, B, and C are collinear, and point B lies in between point A and point C. Point D is a point not on the line. Given that measure of angle ABD = (8x - 2) degrees and measure of angle CBD = (5x) degrees, find measure of angle CBD.
Answer:
The measure of angle CBD is 70 degrees.
Step-by-step explanation:
Given that A, B, and C are collinear (on a straight line) and B is in between A and C.
For a point D not on the line:
[tex]\angle ABD+\angle CBD=180^\circ $ (By the Linear Postulate)\\(8x-2)^\circ+5x^\circ=180^\circ\\8x+5x=180^\circ+2^\circ\\13x=182^\circ\\$Divide both sides by 13\\x=14^\circ[/tex]
Therefore, the measure of angle CBD
= 5 X 14
[tex]=70^\circ[/tex]
The measure of angle CBD is 70 degrees.
20 pts! If Quadrilateral J K L M is congruent to quadrilateral C B D A, which pair of sides must be congruent? Segment J K and Segment A B Segment J K and Segment C B Segment J M and Segment A D Segment J M and Segment B C
Answer:
segment I'm and segment ad
Answer:
The answer is B
Step-by-step explanation:
Can you help pls ty. :)
Answer:
bi) A
bii) -1.5
biii) -1.2, 3.2
Step-by-step explanation:
bi)
In order to find the curve that is represented by the equation, we need to factorise so we are able to see the real roots - we can then compare them to the roots on the curves drawn.
[tex]y=x^2-2x-3\\y=(x-3)(x+1)[/tex]
We can see that the factors of -3 are either -3 and 1 or -1 and 3. We know that these factors must add up to equal the middle term, which in this case is -2. So our factors must be -3 and 1.
Now we need to remember that our intercepts are the negative of our roots.
As we have -3 and +1, our intercepts will be -(-3) and -1. Or 3 and -1.
Curve A is the only curve that intercepts these points.
bii)
For the next part we can either read the values off the graph, or use our equation to determine more precise values. As we are just estimating - we will use the first method.
When x = 2.5, y = -1.5
iii) As the question refers to the word "values" instead of value, we know there is more than one answer. Using the same reasoning for the past question.
When y = 1, x = -1.2, y=3.2
how many are 4 x 4 ?
which regression equation best fits these data
Answer:
D. y = 2.13x² +0.13x +6.39
Step-by-step explanation:
The quadratic regression function of a spreadsheet or graphing calculator will tell you the best choice is D.
Given the sequence rn defined recursively below, find r3. r1rn=2=−rn−1+n−2
Answer:
[tex]r_3=3[/tex]
Step-by-step explanation:
Given:
[tex]r_1=2\\r_n=-r_{n-1}+n-2[/tex]
We want to find the value of [tex]r_3[/tex] .
[tex]\\r_2=-r_{2-1}+2-2\\r_2=-r_1\\r_2=-2\\\\r_3=-r_{3-1}+3-2\\r_3=-r_{2}+1\\r_3=-(-2)+1\\r_3=2+1\\r_3=3[/tex]
The relation R is shown below as a list of ordered
pairs.
R={(1, 4), (1, 3), (-1,3), (2, 15)}
Which ordered pairs prevent this relation from
being a function?
0 (1, 4) and (1,3), because they have the same
X-value
(1, 3) and (-1, 3), because they have the
same y-value
Answer:
(1, 4) and (1,3), because they have the same x-value
Step-by-step explanation:
For a relation to be regarded as a function, there should be no two y-values assigned to an x-value. However, two different x-values can have the same y-values.
In the relation given in the equation, the ordered pairs (1,4) and (1,3), prevent the relation from being a function because, two y-values were assigned to the same x-value. x = 1, is having y = 4, and 3 respectively.
Therefore, the relation is not a function anymore if both ordered pairs are included.
The ordered pairs which make the relation not to be a function are: "(1, 4) and (1,3), because they have the same x-value".
Find the distance from R to S on the graph. Round to the nearest tenth.
Answer:
7.2
Step-by-step explanation
plug the values in in the distance formula
the points are -3,3 and 1, -3
sqrt((-3-1)^2+(3-(-3))^2)
sqrt(16)+(36)
sqrt(52)
approximately 7.2
1/9 − y2 when factored is:
Answer:
Step-by-step explanation:
hello
[tex]\dfrac{1}{9}-y^2=(\dfrac{1}{3})^2-y^2=(\dfrac{1}{3}-y)(\dfrac{1}{3}+y)=\dfrac{(1-3y)(1+3y)}{9}[/tex]
hope this helps