Step-by-step explanation:
What other numbers are of this form have exactly four factors?
8 = 2³ has 4 factors 1, 2, 2², 2³
For any prime p, p³ has 4 factors 1, p, p², p³
Do all the perfect cubes have exactly four factors?
If p is not prime, then it is not true anymor
For instance, 8³ has more than 4 factors 1, 2², 2³,:
Is it true that all numbers that have exactly four factors are perfect cubes?
6 has 4 factors : 1, 2, 3, 6 but this is not a perfect cube.
PLEASE HELP MEEE!!! Algebra 2.HELP
Patrick recently bought food for his family reunion. He bought a total of 23 hot dog and hamburger packs. The hot dogs cost $3 each and the hamburgers cost $5 each, he spent a total of $95. How many hot dogs and hamburgers did he buy each?
Write this as a linear equation (_x+_y=_) There should be two of them. PLEASE HELP ME! ITS MY LAST QUESTION ON THISSS
Answer:
3(x)+5(y) = 95
Step-by-step explanation:
I'm pretty sure this is correct, maybe double check, but I hope this helps :)
X is the amount of hotdogs bought, and y is the amount of hamburgers bought.
A cube has an edge of 3 feet. The edge is increasing at the rate of 2 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed. Hint: Remember that the volume of a cube is the cube (third power) of the length of a side. V (m) = 3 feet?
The volume of the cube as a function of m, the number of minutes elapsed, is V(m) = 4m^3 + 18m^2 + 30m + 27.
The volume of a cube with an edge length of 3 feet is given by V = s^3, where s is the length of a side.
Since the edge is increasing at a rate of 2 feet per minute, the length of the side can be expressed as s = 3 + 2m, where m is the number of minutes elapsed.
Substituting this expression for s into the volume formula, we get:
V(m) = (3 + 2m)^3
Expanding this expression, we have:
V(m) = (3 + 2m)(3 + 2m)(3 + 2m)
= (9 + 6m + 6m + 4m^2)(3 + 2m)
= (9 + 12m + 4m^2)(3 + 2m)
= 27 + 18m + 12m + 8m^2 + 6m^2 + 4m^3
= 4m^3 + 18m^2 + 30m + 27
Therefore, the volume of the cube as a function of m, the number of minutes elapsed, is V(m) = 4m^3 + 18m^2 + 30m + 27.
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Which of the following statements is true about the dataset below
4, 2, 0, 3, 2, 1, 9, 6, 4, 5
The mean and the median are equal.
There is only one mode.
The mean is larger than the median.
The median is larger than the mean.
Answer:
Which of the following statements is true about the dataset below?
4, 2, 0, 3, 2, 1, 9, 6, 4, 5
The mean is 3.6
The median is 3.5
The mode is 2 and 4
Thus the statements that are true are:
The mean is larger than the median.
- The mean and the median are equal. This is not true because the mean is 3.6 while the median is 3.5.
- There is only one mode. This is incorrect because there are 2 modes, 2 and 4 both repeat twice.
- The median is larger than the mean. This is also incorrect because 3.5 is not bigger than 3.6.
Step-by-step explanation:
You're welcome.
Which inequality is represented by the graph?(20 POINTS)
Answer:
C. y<5/3x-3
Step-by-step explanation:
First, treat this problem as if you were graphing a normal slope intercept form equation, y=mx+b, where m=slope and b=the y-intercept. To find the slope of the line, find two points on the graph and count the number of units up/down over the number of units right/left. You could also use the slope formula, (y2-y1)/(x2-x1).
Once you have the slope, which, in this equation, is 5/3, find b, the y-intercept. You can find it by seeing where the line intersects with the y-axis (the vertical axis). In this case, b=(-3).
If this was a normal line, the equation would be y=5/3x-3. However, it's an inequality, and we're not quite done yet. We can eliminate answer B.
Look closely at the line. If it's dotted, the symbol is either a less-than/greater-than symbol (< or >). That means the answer can be any number up to that OR any number above that, but not that exact number. If it's a solid line, that means it's either a less-than or equal-to/greater-than or equal-to symbol, which looks like < and >. That means the answer can be that number and any number up to it OR that number and any number above it. This graph shows a dotted line, so we can eliminate answer A.
Now, one of the hardest parts, though it's really quite easy. If an equation is less-than or less-than or equal-to, the shaded region (all the possibilities) would be below the line. This is easy to tell with a horizontal line, easy enough to tell with a diagonal line, and a little difficult with a vertical line. With a vertical line, think of a number line with a single point on it. Anything to the left of the point is less than the point, so you would shade to the left of the line. If an equation is greater-than or greater-than or equal-to, the shaded region would be above the line, because it's the opposite of less-than or less-than or equal-to. Because the shaded region is below the line, the symbol to use in this equation is < because the answer is unknown but definitely below that line, but not on the line, because it's not a solid line, which means the answer is included.
The inequality of this line is y<5/3x-3, which is listed as answer C. Hope that helped! Comment if it didn't make sense.
If the density of blood is 1.060 g/ml, what is the mass of 6.56 pints of blood? [1 l = 2.113 pints]
The mass of 6.56 pints of blood is 3.92 grams.
Given
The density of blood = 1.060 g/mL and mass of 6.56 pints
We have 1L = 2.113 pints
The density of a substance can be defined as the ratio of the mass of the substance to the volume of the substance. In chemistry, density is used to measure the concentration of the substance in the solution.
The expression for density = mass/volume
ρ = m/V
m = ρV
Mass = 1.060(1000ml/1L) × 6.56(1L/ 2.113)
= 3290.8 /1000
= 3.29g
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n a survey of 3102 adults, 1443 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results.
A 99% confidence interval for the population proportion is ( ),( ).
(Round to three decimal places as needed.)
Interpret your results. Choose the correct answer below.
A. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
B. The endpoints of the given confidence interval show that adults pay bills online 99% of the time.
C. With 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
With 99% certainty, the population proportion of adults who say they have started paying bills online in the last year is between the given confidence interval's endpoints.
What is confidence interval?We have the following confidence interval of proportions in a sample of n people surveyed with a success probability of π and a confidence level of 1 - α.
Confidence interval = \(\pi\) ± z \(\sqrt{\(\pi (1 - \pi ))/n}\)
z = 1 - α/2
Here given, According to a survey of 3102adults, 1443 have begun paying bills online in the last year.
That is, n = 3102 and x = 1443
p = x / n
= 1443 / 3102
= 0.465
significance level = α
= 1 - confidence
= 1 - 0.99
= 0.01
zα/2 = z0.01 / 2 = 2.58
By substituting in confidence interval formula,
The lower limit is :
0.465 - 2.58\(\sqrt{(0.465 * 0.535) / 3102}\)
= -0.01894056008
The upper limit is:
0.465 + 2.58\(\sqrt{(0.465 * 0.535) / 3102}\)
= 0.02722425658
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The lower limit is 0.456 and upper limit is 0.474
What is confidence interval?
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
As confidence interval (C) = π ± z√[π(1-π)/n]
In the above expression, z = 1 - α/2, where α is the significance level.
Given in the question, n=3102 as the survey was conducted on 3102 adults. Also, x=1443, as 1443 people have started paying bills online in last year.
π = x/n
Substituting the values, we get,
π = 1443/3102
⇒ π = 0.465
Confidence level(α) = 1 - confidence
= 1 - 0.99
= 0.01
Since, z = 1 - α/2
⇒ z = 1 - 0.01/2
⇒ z = 1 - 0.005
⇒ z = 0.995
By substituting in confidence interval formula,
The lower limit is = 0.465 - 0.995√[(0.465*0.535)/3102]
= 0.456
The upper limit is = 0.465 + 0.995√[(0.465*0.535)/3102]
= 0.474
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Help please!!!
12x + 6y= 162
2x + 10y= 126
Solve using system of equations. Show all work
Answer:
(8, 11)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define systems
12x + 6y = 162
2x + 10y = 126
Step 2: Simplify systems
2x + y = 27
x + 5y = 63
Step 3: Rewrite systems
2x + y = 27
x = 63 - 5y
Step 4: Solve for y
Substitute in x: 2(63 - 5y) + y = 27Distribute 2: 126 - 10y + y = 27Combine like terms: 126 - 9y = 27Isolate y term: -9y = -99Isolate y: y = 11Step 5: Solve for x
Define equation: x + 5y = 63Substitute in y: x + 5(11) = 63Multiply: x + 55 = 63Isolate x: x = 8Answer:
x = 8 and y = 11
Step-by-step explanation:
solve for y
12x + 6y = 162
-12x -12x
6y = 162 - 12x
/6 /6
y = 27 - 2x
substitute
2x + 10(y) = 126
2x + 10(27 - 2x) = 126
2x + 270 - 20x = 126
-18x + 270 = 126
-270 -270
-18x = -144
-18 -18
x = 8
substitute again:
y = 27 - 2(x)
y = 27 - 2(8)
y = 27 - 16
y = 11
PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
x = 7
Step-by-step explanation:
\(\frac{3x + 3}{6} = 4\) so we can do multiply by 6 on both sides to get: 3x+3=24
Then we subtract 3: 3x = 21
And divide 3: x= 7
Answer:
x = 7
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, multiply 6 to both sides of the equation:
\(\frac{3x + 3}{6} = 4\\ (\frac{3x + 3}{6}) * 6 = (4 ) * 6\\ 3x + 3 = 4 * 6\\3x + 3 = 24\)
Next, isolate the variable, x. First, subtract 3 from both sides of the equation:
\(3x + 3 = 24\\3x + 3 (-3) = 24 (-3)\\3x = 24 - 3\\3x = 21\)
Then, divide 3 from both sides of the equation:
\(3x = 21\\\frac{3x}{3} = \frac{21}{3} \\x = \frac{21}{3} \\x = 7\)
x = 7 is your answer.
~
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let ~a = 〈1,1,−3〉 and ~b = 〈−1,−3,1〉. find the unit vector in the opposite direction of ~a −~b.
The unit vector in the opposite direction of ~a - ~b can be found by calculating the vector ~v = -(~a - ~b) / |~a - ~b|, where ~v represents the unit vector.
To find the unit vector in the opposite direction of ~a - ~b, we first need to compute the vector ~a - ~b, which is obtained by subtracting the corresponding components of ~a and ~b:
~a - ~b = 〈1, 1, -3〉 - 〈-1, -3, 1〉 = 〈1 - (-1), 1 - (-3), -3 - 1〉 = 〈2, 4, -4〉.
Next, we calculate the magnitude (or length) of ~a - ~b, denoted as |~a - ~b|, using the formula:
|~a - ~b| = sqrt((2^2) + (4^2) + (-4^2)) = sqrt(4 + 16 + 16) = sqrt(36) = 6.
Finally, we can find the unit vector ~v in the opposite direction of ~a - ~b by dividing -(~a - ~b) by |~a - ~b|:
~v = -(~a - ~b) / |~a - ~b| = -(〈2, 4, -4〉) / 6 = 〈-2/6, -4/6, 4/6〉 = 〈-1/3, -2/3, 2/3〉.
Therefore, the unit vector in the opposite direction of ~a - ~b is 〈-1/3, -2/3, 2/3〉.
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What is the slope of the line that passes through the points(7,-4) and (11, –4)? Write your answer in the simplest form.
Solve the following:
4x-3=2x+7
Thanks :)
Answer:
6x+10 i think is right(sorry if its not)
Answer:
5
Step-by-step explanation:
4x-3=2x+7
-2x -2x
2x-3=7
+3 +3
2x=10
2x/2x = x
10/2=5
x=5
A committee of four is formed from five eligible members. Let the eligible members be represented with A, B, C, D, and E. The possible outcomes include S
The correct answer is C and E
A: The first claim is untrue. The total number of options for selecting 4 out of 5 members is stated in the question's body. There are 5 completely unrestricted methods.
B: is untrue. There are four options for creating the committee if A must be on it. B, C, D, and E are each removed from the committee in turn.
C: This is true if members A and C are both on the committee. The three methods are ABCD, ACDE, and ACBE.
D: The solution is the same as the solution for Choice B if E must be on it. This claim is untrue.
E: The query is unclear. How many options are available to you? The answer is correct if you're picking a committee of just four people. I'll go ahead and assume that's what was intended, but the ambiguity can only be resolved by the asker.
What is Probability ?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.To learn more about probability visit:
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Let Z represent a standard normal random variable. P(Z>0) is equal to
0.0
0.5
0.45
0.9
A standard normal random variable (Z) has a mean of 0 and a standard deviation of 1. The probability of Z being greater than 0 is equal to the area under the normal curve to the right of 0, which is exactly half of the total area under the curve (since the curve is symmetric around the mean of 0). Therefore, P(Z>0) is equal to 0.5.
A standard normal random variable, like Z in your question, follows a standard normal distribution, which is a special type of normal distribution with a mean of 0 and a standard deviation of 1. Now, you're asked to find the probability P(Z > 0).
Since the standard normal distribution is symmetrical around the mean (0), the probability of Z being greater than 0 is equal to the probability of Z being less than 0. In other words, half of the distribution is on the right side of the mean, and the other half is on the left side.
Therefore, P(Z > 0) = 0.5, which is your answer.
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In Triangle ABC AB is 6cm,BC is 8cm, AC is 10cm. IS Triangle ABC right Angled triangle?
i know the answer is yes but can somebody send me the process!!! Pls fast tommorrow is my maths exam!!!
Step-by-step explanation:
If triangle ABC is a right angle, it will allign with Pythagoras theorem where a² = b² +c²
A will be the longest side (hypotenuse)
10² = 6² + 8²
100 = 36 + 64
100 = 100
A is square root of 100 on both sides
It is a right angle triangle
help me please.....................
Answer:
HMMMMMMM!
HMMMMMMM
Find the area of the circle. Leave your answer in terms of pie.
Answer:
A= 18.49π m²
Step-by-step explanation:
Given the diameter of 8.6 (which means the radius is half of that number; 4.3
Area = π × r²
Area = π × (4.3)²
Area = 18.49π m²
What single decimal multiplier would you use to decrease by 3% followed by a 3% decrease?
A 3% decrease means you still have 100% - 3% = 97% left
The multiplier here would be 0.97
If you do another 3% decrease, you will use another multiplier of 0.97
Multiply 0.97*0.97 to get 0.9409
So this is a 1-0.9409 = 0.0591 = 5.91% decrease overall
3x2 + x = 2
Solve Real and imaginary solutions
Answer:
3*2+x=2
6+x=2
subtract 6 on both sides
x= -4
Step-by-step explanation:
What is the equation of a parabola that passes through the points (−5, −10), (−3, 2), and (2, −3)?.
The equation of the parabola is y = -x² - 2x + 5
What is a Parabola?
A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k - p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
The equation of the parabola with the points
A ( -5 , -10 ) , B ( -3 , 2 ) and C ( 2 , -3 )
So , from the equation of parabola ,we get
y = ax² + bx + c
Substituting the values of x and y , in the equation of point A , we get
-10 = a ( -5 )² - 5b + c
-10 = 25a - 5b + c be equation (1)
Substituting the values of x and y , in the equation of point B , we get
2 = a ( -3 )² - 3b + c
2 = 9a - 3b + c be equation (2)
Substituting the values of x and y , in the equation of point C , we get
-3 = a ( 2 )² + 2b + c
-3 = 4a + 2b + c be equation (3)
By the method of brute force , we can solve the equations and derive the equation for the parabola
So , the equation for the parabola will be
y = -x² - 2x + 5
Now , substituting the values of x and y from the points , we get
For point A ( -5, -10 )
-10 = - 25 + 10 + 5
-10 = -10
Therefore , the equation is TRUE
Now , substituting the values of x and y from the points , we get
For point B ( -3, 2 )
2 = -9 + 6 + 5
2 = 2
Therefore , the equation is TRUE
Now , substituting the values of x and y from the points , we get
For point C ( 2 , -3 )
-3 = -4 - 4 + 5
-3 = -3
Therefore , the equation is TRUE
Hence , the equation of the parabola is y = -x² - 2x + 5
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A beaker has a mass of 129 g. What is the mass of this beaker in kilograms?
Answer: 0.129 kg
Step-by-step explanation:
A gram to a kilogram can be found by dividing the value of grams by 1000, or multiplying the value by 0.001
Help please i do not know what i am doing
The distributed simplified product is \(2x\sqrt{10x}-2x\sqrt{5}\). So, option 4 is correct.
What is distributive property?The distributive property is given by
a(b + c) = ab + ac or (a + b)c = ac + bc.
This property is used for simplifying large expressions into small ones.
The reverse order we can write as
ab + ac = a(b + c) or ac + bc = (a + b)c.
Calculation:The given expression is \(\sqrt{5x}(\sqrt{8x^2}-2\sqrt{x})\)
On applying distributive property: a(b + c) = ab + ac
\(\sqrt{5x}(\sqrt{8x^2}-2\sqrt{x})\) = \(\sqrt{5x}(\sqrt{8x^2}) - \sqrt{5x}(2\sqrt{x})\)
Applying multiplication of surds,
(multiplication of surds: \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\))
⇒ \(x(\sqrt{5x\times8})-2(\sqrt{5x\times x})\)
⇒ \(x\sqrt{40x}-2\sqrt{5x^2}\)
⇒ \(2x\sqrt{10x}-2x\sqrt{5}\)
Therefore, the simplified product for \(\sqrt{5x}(\sqrt{8x^2}-2\sqrt{x})\) is \(2x\sqrt{10x}-2x\sqrt{5}\).
Thus, option 4 is correct.
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Please I need help with questions 8,9,10 and 13 ASAP is due tomorrow
I HOPE IT WILL HELP YOU.
Thank you.
^ - ^
Sorry if it is wrong.
-81.4+ (-12.7)
What is the answer
Answer:
−94.1
Hope this helped :)
Answer:
\( - 94.1\)
Step-by-step explanation:
\( = > - 81.4 + ( - 12.7) \\ = > - 84.4 - 12.7 \\ = > - 94.1\)
May be useful :)What is the equation of the line ?
50 POINTS
Does the point (1, 3) fall on the graph of the line that goes through (-2, 8) and (3, -1)? Show me how you know without graphing. Show your work algebraically (That is, don't draw me a graph... show me using numbers, variables, and/or symbols).
can someone explain please :)
Step-by-step explanation:
1.First work out the equation of the line.
1.1 work out gradient
\(y = ( \frac{ - 1 - 8}{3 - ( - 2)} )x + c\)
\(y = - \frac{9}{5} x + c\)
1.2 substitute in x and y value of one of the two given point. ill use (3;-1).
\( - 1 = - \frac{9}{5} (3) + c\)
\(c = \frac{22}{5} \)
therefore equation is
\(y = - \frac{9}{5} x + \frac{22}{5} \)
2. Now sub in x value of the point you want to test and see if y value correlates.
\(y = - \frac{9}{5} (1) + \frac{22}{5} \)
\(y = \frac{13}{5} \)
3. We can conclude that point (3;1) does not fall on the graph
pls help me with this...... :).....it's urgent........
Why urgent?
See attachment for math work and answer.
I gave you two different answers for 2b.
The temperature at 9 a.m. is 2 degrees. The temperature rises 3 more degrees by noon. Which expression describes the temperature at noon?
Answer: 2 degrees + 3 degrees = 5 degrees
Step-by-step explanation: Though the times might be confusing, the problem itself is simple addition- if the temperature rises, or goes up, by a certain number, in this case three, you're just going to add that number to the initial number, two.
PLEASSEEEEE HELP ASAPPPPPPP A store owner is tracking inventory based on sales
during the week. The store owner notices that the
number of gallon milk jugs remaining follows a
pattern. The equation N= 50 - 7d represents the
number of gallon milk jugs, N, remaining d days
into the week, at the end of each day.
Which statement is true?
a. The store owner begins the week with 50
gallon milk jugs and adds an average of 7
gallon milk jugs each day,
b. The store owner begins the week with 50
gallon milk jugs and sells an average of 7
gallon milk jugs each day.
c. The store owner begins the week with 57
gallon milk jugs and adds an average of 7
gallon milk jugs each day.
d. The store owner begins the week with 57
gallon milk jugs and sells an average of 7
gallon milk jugs each day.
Answer:
b) The store owner begins the week with 50 gallon milk jugs and sells an average of 7 gallon milk jugs each day.
Another one, thanks in advance!
Marissa's shape is classified as a scalene and obtuse triangle, considering it's concepts presented in this problem.
How to classify the triangle?The triangle has three sides of unequal length, as the opposite angle measures are different, hence it is classified as an scalene triangle.
(it would be equilateral if all had the same length, and isosceles if two sides have the same length).
The triangle has one angle larger than 90º, hence it is classified as an obtuse triangle.
(acute with no angles of 90º or greater, right with one angle of exactly 90º).
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Can someone please help I will add a random question and give 20 extra points :)
Answer:
Step-by-step explanation:
probability ∈[0,1]
or probability ≥0
and ≤1
so a,b,g cannot be the probability of an event.
Answer:
See Explanation
Step-by-step explanation:
The probability of an event ranges from 0 to 1.
So, the options c. 0.6, d. 0.888, e. 0 and f. 0.39 represents the probability of an event.
Probability of an event cannot be negative number or more than 1.
Hence, options a. - 1, b. 4.2, g. - 0.5 does not represent the probability of an event.