The Probability that Robert randomly pulls out a black sock is 1/5 .
In the question ,
it is given that
Total number of socks in sock drawer = 30 socks
number of white socks in the drawer = 16 socks
number of black socks in the drawer = 6 socks
number of red socks in the drawer = 2 socks
number of yellow socks in the drawer = 6 socks
So , the probability that he randomly pulls out a black sock = (number of black socks in the drawer) / ( total number of socks in the drawer )
= 6 / 30
= 1/5
Therefore , The Probability that Robert randomly pulls out a black sock is 1/5 .
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find the trig graph equation
Step-by-step explanation:
I assume, based on what I see, that the solid line is just cos(x), right ?
and we need to find the equation that draws the dotted line, correct ?
the notation is strange, as it seems we need to find a multiplication factor for x in the cos function.
but there is no multiplication factor that moves the cosine wave by pi to the left or to the right (so that the max. happens, where originally the minimum happens, and vice versa).
so, we need to add (or subtract) pi in the cosine function.
the rest is clear :
the normal distance between min. and max. of the cosine function is 2 (between +1 and -1). the target is 4. so we need to multiply by 2.
and since the values of that function have to be between -4 and 0 (instead of -2 and +2), we have to subtract overall 2.
giving us the function :
y = 2×cos(pi + x) + -2
PLEASE HELP
Question
A function f(x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
f(x)=
The graphed function in the slope-intercept form can be written as:
y = -4*x - 2
How to get the linear function?
A general linear function in the slope-intercept form is written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
On the graph, we can see that our line intercepts the y-axis at y = -2, so the y-intercept is b = -2, replacing that we get:
y = m*x - 2
We also can see that the line passes through (-1, 2), replacing these values on the linear equation we get:
2 = m*(-1) - 2
m = -2 - 2
m = -4
Thus, the linear function in the graph is:
y = -4*x - 2
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10 miles per hour equal feet per second
Let's recalll that:
• 1 mile per hour = 1.46667 feet per second
Therefore:
• 10 miles per hour = 1.46667 * 10 feet per second
,• 10 miles per hour = 14.6667 feet per second, Khalil!
At a high school, the cafeteria staff provides optional comment cards to students eating in the cafeteria. Students who wish to make a comment can obtain and fill out a comment card and return it to a drop box in the front office. At the end of the semester, the staff analyzes the responses and finds that 72% of the students who filled out a comment card recommend major changes to the food selection. What conclusions can the cafeteria staff draw from these responses?.
Based on the described sampling approach, it should be concluded that the responses were from a voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions. (Option D).
Voluntary response sample refers to a response sample in which the researcher puts out a request for population members to join the sample, and the decision of whether or not to be in the sample resides with the people. As it is a sample comprising of voluntarily participants, people who chose to participate usually do so as they have a strong opinion on the subject of the survey. Typically, voluntary response samples oversample members with strong opinions and under sample members with little to no opinion on the subject of the survey. Hence, inferences from a voluntary response sample are not as reliable as conclusions based on a random sample of the entire population under consideration.
Note: Question is incomplete. The options were missing which are a. Since all of the students had an opportunity to respond, this is evidence that a majority of all the students supports major changes. b. The cafeteria staff should not use the results to draw any conclusions since some students may not have filled out a comment card, which is nonresponse. c. If the students recorded their grade level with their response, the staff could make the original sample a stratified sample and use the responses to learn what proportion of each grade recommends major changes to food selection. d. The responses were from a voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions. e. The opportunity to fill out comment cards should be offered to students at all high schools in the school district to get a larger sample size, which will make the results more reliable
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Part A: Given the function g(x) = |x + 3|, describe the graph of the function, including the vertex, domain, and range.
explanation is ideal but not essential :)
Considering the absolute value function, it is found that:
The vertex is at (-3,0).The domain is all real values.The range is [0, ∞).Absolute value functionThe absolute value function of vertex at point (h,k) is defined according to the following rule:
f(x) = |x - h| + k.
In the context of this problem, the function is given as follows:
g(x) = |x + 3|.
Hence the coefficients are:
h = -3, k = 0.
Meaning that the coordinates of the vertex are given by:
(-3,0).
The domain is the input values of the function, and since the absolute value function has no restriction, it is composed by all real values.
The range of the function is the set containing the output values of the function, and since the function has no vertical shift, it is the non-negative numbers.
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Estimate 71.47 + 54.357 by first rounding each number to the nearest whole number.
Answer:
125
Step-by-step explanation:
71.47 rounded to the nearest whole number would be 71.
54.357 rounded to the nearest whole number would be 54.
Now, when we add 71 and 54, we get:
71+54=
125
The total would be 125
How tall is a building that casts a 71-ft shadow when the angle of elevation of the sun is 29 degrees.Round to the nearest foot
Solution
We will draw a diagram to illustrate the information
Using the concept of SOHCAHTOA
We are given adjacent and we want to find opposite
[tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ tan29=\frac{H}{71} \\ cross\text{ multiply} \\ H=71tan29 \\ H=39.35594265 \\ H=39ft \end{gathered}[/tex]Therefore, the answer is
[tex]undefined[/tex]How do I find the slope and Y-intercept of the line x+2y=-2
slope = -1/2
y-intercept = (0, -1)
Explanation:Given:
[tex]x\text{ + 2y = - 2}[/tex]To find:
the slope and the y-intercept
To determine the slope we will use the linear function formula:
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}[/tex]We need to rewrite the given equation in the form above so as to get the slope
[tex]\begin{gathered} x\text{ + 2y = -2} \\ 2y\text{ = -x - 2} \\ y\text{ = -}\frac{x}{2}\text{ - }\frac{2}{2} \\ y\text{ = }\frac{-x}{2}-1 \end{gathered}[/tex]From the above, m = -1/2
Hence, the slope is -1/2
The y-intercept is the value of y when x = 0
To get the y-intercept, we will substitute x with 0:
[tex]\begin{gathered} y\text{ = }\frac{-0}{2}\text{ - 1} \\ y\text{ = 0 - 1} \\ y\text{ = -1} \\ \\ The\text{ y-intercept in ordered pair \lparen x, y\rparen:} \\ when\text{ x = 0, y = -1} \\ y-\text{ intercept = \lparen0, -1\rparen} \end{gathered}[/tex]suppose that you need to build as many chairs as possible. each chair requires one seat, one back, and four legs. if you have 12 seats, 15 backs, and 44 legs, which of the chair components limits the number of chairs you can make? legs seats backs how many chairs can you make with the 12 seats, 15 backs, and 44 legs? what chair components will be leftover after making as many chairs as possible? seats and backs legs and backs seats and legs
The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.
What is meant by probability?The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.
The maximum number of chairs that can be made will be the minimum of the number of parts divided by the number of parts required for each chair, as calculated across the various types of parts required.
seats: 12 available, used 1 per chair: 12/1 = 12 chairs possible
backs: 15 available, used 1 per chair: 15/1 = 15 chairs possible
legs: 44 available, used 4 per chair: 44/4 = 11 chairs possible
The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.
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Mrs. Harris has 5 blue, 8 red, 3 green, and 7 yellow candies in a bag. If Mrs. Harrisrandomly selects a candy, what is the probability she will select a yellow or blue candy?
Blue = 5
Red = 8
Green= 3
Yellow= 7
Total candles = 5+8+3+7 = 23
Yellow and blue candles = 7+5 = 12
To find the probability divide the number of blue and yellow candles (12) by the total number of candles.
12/23 = 0.52
the difference of t and five multiplied by six is four
The expression of the mathematical statement given as the difference of t and five multiplied by six is four is 6(t - 5) = 4
How to express the mathematical statement as an expression?From the question, the mathematical statement is given as
the difference of t and five multiplied by six is four
The difference of numbers means that we subtract the numbers
i.e. difference means subtraction
So, we have
the difference of t and five multiplied by six is four ⇒ (t - five) multiplied by six is four
The multiplication of numbers means that we take the product of the numbers
i.e. multiply means product
So, we have
the difference of t and five multiplied by six is four ⇒ (t - five) x six is four
Lastly, we have
(t - five) x six = four
Express as numbers
(t - 5) x 6 = 4
This becomes
6(t - 5) = 4
Hence, the expression represented by the statement is 6(t - 5) = 4
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PLEASE HELP! This is due tomorrow!
Determine whether the equation represents a linear or nonlinear function. Explain.
I just need help with these, I have a busy day today :(
The categories of the functions are:
Linear functions: (16) y = 7 - x (17) y = ∛8 - x (19) 2 + y = x + 4 (21) x -y = |-54|Nonlinear functions: (15) y = x² + 13 (18) y = x . x . x (20) 7 - y = 2ˣ (22) |x| + 12 = yHow to categorize the functions?The category of the functions are given as
Linear functionsNonlinear functionsAs a general rule, linear functions can take any of the following forms
y = a x = by = xy = mxy = mx + cy - y1 = m(x - x1)Ax + Bx = CWhere the variables a, A, m, b, B, c and C are real numbers
Any equation that do not have the above form is considered a nonlinear function
Using the above forms as a guide, we have the linear equations to be
(16) y = 7 - x (17) y = ∛8 - x (19) 2 + y = x + 4 (21) x -y = |-54|
All other equations are nonlinear equations
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Harry invests £6000 in a savings account.
The account pays 3.4% compound interest per year.
Work out the value of his investment after 3
Give your answer to the nearest penny.
years.
Answer:
$6633.04
Step-by-step explanation:
6000x1.034^3=6633.04
The value of his investment after 3 years will be $6633.04.
What is compound interest?In finance and economics, interest is the payment of an amount above the repayment of the principal sum by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by a borrower or depositor. It differs from a fee that the borrower may pay to the lender or a third party.
Compound interest is the interest added to the principal amount of a loan or deposit, also known as interest on interest plus interest.
Given that Harry invests £6000 in a savings account. The account pays 3.4% compound interest per year.
The compound interest will be calculated as,
[tex]A = P( 1 + \dfrac{r}{100})^{nt[/tex]
Substitute the values in the equation above and solve,
A = 6000 x 1.034³
A = $6633.04
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Please explain how you get the answer
The measure of the angle is calculated using the attached figure.
What is an angle?
An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. This measurement is the length of a circular arc divided by its radius. The arc is centered at the vertex in the case of a geometric angle.
From figure,
angle x = 180° - 110° = 70° (linear pair)
angle y = 37° (alternate interior angles)
Measure of angle 1 = 70° + 37° (exterior angle in a triangle is equal to the sum of opposite interior angles)
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what is 3b= 39 can you pleasee help me
Answer: b=13
Step-by-step explanation:
b=39/3
b=13
Answer: its 13
Step-by-step explanation
As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____ distribution.
As the sample size becomes larger, the sampling distribution of the sample mean approaches a normal distribution.
In the theory of probability, the central limit theorem states that the distribution of a sample mean approximates a normal distribution as the size of the sample increases. For the central limit theorem to hold, it is necessary that the sample size at least cross a margin of 30. Having a sufficiently larger sample size can predict the characteristics of the sample more accurately. The central limit theorem is applicable when we are analyzing large data sets.
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f(x)=-2x-3 find f(6)
Sailman A gets paid $300 a month plus $8 for every sale he makes. Salesman B gets paid $1500 a mont. Write and equation and solve to see how many salesman a must make in order to make the same amount of salesman b
the number of sales by b must be 150 to make the same amount of salesman B.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
given that :
Salesman A gets paid $300 a month plus $8 for every sale he makes :
let the no. of sales A made be : x
then, in order to make the same amount of salesman b we equate btoth the amount :
300 + 8x = 1500
8x = 1500-300
8x = 1200
x = 1200/8
x = 150
Therefore, the number of sales by A must be 150 to make the same amount of salesman b.
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help please thank you !
Consider the sequence 9, 16, 25, 36, 49, ...
(1) Write down the next two terms of
the sequence.
i) Find, in terms of n, a formula for the n term
of the sequence.
i) Hence, find the 25th term.
Answer:
1) 64 and 81
2) a(n) = (n + 2)^2, where n = 1, 2, 3, ...
3) a(25) = (25 + 2)^2 = 27^2 = 729
Sydney has a quarters and y dimes, having no less than 18 coins worth a maximum of $3.60 combined. A minimum of 4 of the coins are quarters and at least 16 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
HELP ME ASAP PLEASE!!!
Step-by-step explanation:
x + y = 18 We have at least 4 quarters
0.25x + 0.1y = 3.6
If we graph both equations, the point of intersection will give us our answer.
In this case, the lines intersect at the point (12, 6) which means I have 12 quarters and 6 dimes. This solution is correct as it also satisfies the condition of having at least 4 quarters.
(got this from another website, maybe it's wrong..
Wishing you the best!! )
In Exercises 1-3, graph AABC and its image after a reflection in the given line.
1. A(0, 2), B(1, -3), C(2, 4); x-axis
1.
2. A(-2,-4), B(6,2), C(3. – 5); y-axis
3. A(4, -1), B(3, 8), C(-1, 1); y = -2
The figures after each reflection are given at the end of the answer.
Reflection over the x-axis
The rule for the reflection over the x-axis is:
(x,y) -> (x, -y)
Hence the signal of the y-coordinate is changed.
Then the coordinates of the image of triangle ABC are given as follows:
A'(0,-2), B'(1,3) and C(2,-4)
Reflection over the y-axis
The rule for the reflection over the x-axis is:
(x,y) -> (-x, y)
Hence the signal of the x-coordinate is changed.
Then the coordinates of the image of triangle ABC are given as follows:
A'(2,-4), B'(-6,2) and C'(-3,-5)
Reflection over y = -2The rule for the reflection over the line y = -2 is:
(x,y) -> (x, y +/- constant)
The constants for each point are given as follows:
A': -3, hence point (4,-3), as -1 is one unit above y = -2, hence the reflected coordinate will be one unit below.B': -12, hence point (3,-12), as 8 is 10 units above y = -2, hence the reflected coordinate will be ten units below.C': -5, hence point (-1, -5), as 1 is 3 units above y = -2, hence the reflected coordinate will be three units below at y = -5.More can be learned about reflections at https://brainly.com/question/27224272
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Yasmin is making some pancakes. Her recipe makes 6 pancakes.
Flour
Eggs
Milk
100g
2
250ml
Yasmin wants to make 15 pancakes.
Complete the table to show how much she will need of each ingredient.
Answer:
tbh times them all by 15 and u should get the answers
Please help i need an explanation i have no idea how to do this.
Answer:
f(2)=3
f(1)=2
f(-1)=0
f(0)=1
Step-by-step explanation:
f(x)=y
when finding what f(x)=? you would see whats in the () and find that number on the x-axis. Find where the line hits on the x-axis and find the number on the y-axis that correlates with it. The y-axis number is what goes the the ().
when finding whats in the () you find what number it equal to on the y-axis and what is in the () would be the number that the line is on on the x-axis
What is the average speed of a walker who walks 600hm in 20 seconds
Answer:
30 km/s
Explanation:
Formula for average speed = Total distance/total time
From the question,
Total distance = 600 km, Total time = 20 seconds
∴ Average speed = 600 km/20 seconds
Average speed = 30 km/s
I need this answered please
Answer:
76 child tickets were sold
Step-by-step explanation:
let a represent number of adults and c number of child tickets sold, then
a + c = 165 → (1)
5.8a + 8.9c = 1192.6 → (2)
multiplying (1) by - 5.8 and adding to (2) will eliminate a
- 5.8a - 5.8c = - 957 → (3)
add (2) and (3) term by term to eliminate a
0 + 3.1c = 235.6
3.1c = 235.6 ( divide both sides by 3.1 )
c = 76
that is 76 child tickets were sold that day
Shawn and his bike have a total mass of
48.1 kg. Shawn rides his bike 1.5 km in
12.5 min at a constant velocity.
The acceleration of gravity is 9.8 m/s
2
.
What is Shawn’s kinetic energy?
Answer in units of J.
If the velocity is 2 meters per second. Then the kinetic energy of the Shawn will be 96.2 Joules.
What is kinetic energy?The energy an item has as a result of motion is known as kinetic energy in mechanics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its propulsion until its speed changes.
The kinetic energy is given as,
KE = (mv²)/2
Where m is the mass and v is the velocity.
Shawn and his bike have a total mass of 48.1 kg. Shawn rides his bike 1.5 km in 12.5 min at a constant velocity.
The velocity is given as,
v = 1.5/12.5
v = 0.12 km/min
v = 0.12 x 1000 / 60
v = 2 m/s
Then the kinetic energy of Shawn will be given as,
KE = (48.1 x 2²) / 2
KE = 48.1 x 2
KE = 96.2 J
If the velocity is 2 meters per second. Then the kinetic energy of the Shawn will be 96.2 Joules.
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Graph the following. y=3-4x
Here Ya Go! :D
Hope this helps! If so, please lmk. Thanks and good luck!
Apply the laws of exponents to evaluate the expression.
(0.5) (0.5) 4
(0.5)²
After evaluation using the exponential laws, the expression "(0.5)∧(0.5)∧4 + (0.5)²" is evaluated as 2(0.5)².
What are exponents?Exponentiation is a mathematical operation that involves the base b and the exponent or power n. It is written as bn and is pronounced as "b to the n." There are four different types of exponents: positive, negative, zero, and rational/fractional. By interpreting the exponent as the total number of times the base number must be multiplied by the same base, one can determine the value of the number. Exponents laws: Keep the base constant when multiplying like bases and add the exponents. Keep the base constant and multiply the exponents when raising a base with power to another power. When dividing with like bases, keep the base constant and deduct the exponents of the numerator and denominator.So, evaluate "(0.5)∧(0.5)∧4 + (0.5)²" using laws of exponents:
Then,
(0.5)∧(0.5)∧4 + (0.5)By law: Power of power rule
(0.5)∧(0.5)×4 + (0.5)(0.5)²+ (0.5)²2(0.5)²Therefore, after evaluation using the exponential laws, the expression "(0.5)∧(0.5)∧4 + (0.5)²" is evaluated as 2(0.5)².
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The correct question is given below:
Apply the laws of exponents to evaluate the expression.
(0.5)∧(0.5)∧4 + (0.5)²
In ∆ STU, the measure of < U=90°, UT=12, SU=35, and TS=37. What ratio reprecents the secant of < T?
By definition, a Right triangle is a triangle that has an angle whose measure is 90 degrees (which is also called "Right angle").
You can identify that the triangle STU is a Right triangle, because:
[tex]\angle U=90\degree[/tex]The following is one of the Trigonometric ratios. It's called "Secant":
[tex]\sec \alpha=\frac{hypotenuse}{adjacent}[/tex]In this case you can identify that:
[tex]\begin{gathered} \alpha=\angle T \\ hypotenuse=TS=37 \\ adjacent=UT=12 \end{gathered}[/tex]Then, substituting values, you get that the answer is:
[tex]\sec \angle T=\frac{37}{12}[/tex]