Answer:
346.78
Step-by-step explanation:
Rounding a number to hundredth means approximating or making the number after the second position of the decimal to either a 10 or zero.
Thanks for the number after the second is greater or equal to 5, it is rounded up to ten where the 1 is added to the second position if not it turns 0.
So 346.7812 to hundredth
= 346.78
What is the ratio between 10 lions and14 tigers
Answer:
10:14
Step-by-step explanation:
10lions:14tigers
Answer:
5:7
Step-by-step explanation:
Lions:tigers = 10:14 = 5:7A pond has been created in a remembrance garden. It has an approximate diameter of 10 metres. A person walks around the
pond four times a day. How far have they travelled per day to the nearest metre?
(Circumference of a circle is 2T or C=Td, where te=3.14)
Answer:
126 meters
Step-by-step explanation:
First, let's find the circumference of the pond. We know that C = πd, π = 3.14 and d = 10 so the circumference is 3.14 * 10 = 31.4 meters. However, the person walks around the pond 4 times so the answer is 31.4 * 4 = 125.6 meters which rounds to about 126 meters.
Answer the question below for brainliest
Answer:
(BD/DA) = (CE/EA)
slope is calculated using rise over run, and the ratios represent the rise over the run
10 to 7 power equals
Answer: 10,000,000
Step-by-step explanation: when anything rasied to the power you take what ever the Exponaten is and take how everything was there for example 10⁷ 10x10x10x10x10x10x10. And you multiply that.
Answer:
The answer is: 10,000,000
You would do 10 x 10 x 10 x 10 x 10 x 10 x 10
Round 3.642 to the nearest hundredth
Answer:
3.64
Step-by-step explanation:
Identify the hundredth:
3.642
Check the value of the thousandth:
3.642
If the number is greater than or equal to 5, then we round up.If the number is less than of equal to 4, we round down.
2 is less than four, therefore, we will round down.
3.642 ≈ 3.64
What is the solution of x⁴– 3x³ + x²+ 3x – 2 < 0
Hello, let's note
[tex]f(x)=x^4-3x^3+x^2+3x-2\\\\f(1)=1-3+1+3-2=0[/tex]
So we can put (x-1) in factor. We are looking for a and b such that
[tex]f(x)=(x-1)(x^3+ax^2+bx+2)=x^4+(a-1)x^3+(b-a)x^2+(2-b)x-2[/tex]
We identify the like terms, it comes
a-1=-3 <=> a = -2
b-a=1 <=> b = 1 + a = -1
2-b=3
So it comes.
[tex]f(x)=(x-1)(x^3-2x^2-x+2)[/tex]
And we can go further using the same method to find that
[tex]x^3-2x^2-x+2=(x-1)(x^2-x-2)[/tex]
The sum of the zeroes is 1=2-1 and the product is -2=(-1)*2, so, we can factorise.
[tex]\boxed{f(x)=(x-1)^2(x+1)(x-2)}[/tex]
The sign of f(x) is the same as the sign of (x+1)(x-2) as a square is always positive.
To find the sign of a product, we can apply the following.
"- multiplied by - gives +"
"+ multiplied by + gives +"
"- multiplied by + gives -"
"+ multiplied by - gives -"
This is this what we are doing below.
[tex]\begin{array}{|c|ccccccc}x&-\infty&&-1&&2&&+\infty\\---&---&---&---&---&---&---&---\\x+1&-&-&0&+&3&+&+\\---&---&---&---&---&---&---&---\\x-2&-&-&-3&-&0&+&+\\---&---&---&---&---&---&---&---\\f(x)&+&+&0&-&0&+&+\\\end{array}[/tex]
So, to answer the question
[tex]\Large \boxed{\sf \bf \ f(x) < 0 <=> -1 < x < 2 \ }[/tex]
Thank you.
Simple math but I can't seem to understand it: x+y=2 becomes y=2-x, in order to find slope and y intercept y=mx+b The result becomes slope = -1, y intercept = 2. Though I'm not sure how to get these.
Answer:
See below.
Step-by-step explanation:
We are given the equation:
[tex]x+y=2[/tex]
And we subtracted x from both sides to acquire:
[tex]y=2-x[/tex]
Notice that this is the slope-intercept form:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
If we rearrange our equation, we acquire:
[tex]y = -(1)x+(2)[/tex]
Therefore, m = -1 and b = 2.
In other words, the slope is -1 and the y-intercept is 2.
Answer:
[tex]\Large \boxed{{m=-1, \ b=2}}[/tex]
Step-by-step explanation:
x + y = 2
We need the equation in the form y = mx + b.
m = slope
b = y-intercept
Solve for y by subtracting x from each side.
y = 2 - x
The -x can be written as -1x.
y = 2 - 1x
Rearrange the expression.
y = -1x + 2
The equation is in form y = mx + b.
The slope is -1.
The y-intercept is 2.
HELP ASAP ROCKY!!! will get branliest.
Answer:
-4Step-by-step explanation:
The equation is y = slope + or - y-intercept
Slope = mx
So the slope is -4
The slope can be found also by having 2 points and doing (y2 - y1)/(x2 - x1). Also, you can do rise over run. These are options for if you have a graph.
Hope this helped,
Kavitha
Answer:
-4
Step-by-step explanation:
y= -4x + 9
y= mx + C
comparing
m= -4
How do we do pemdas? What do each letter stand for?
PEMDAS is the order of operation, and is what you follow to solve a expression/equation.
PEMDAS =
Parenthesis
Exponents: This step also includes solving for any roots.
Multiplication
Division
Addition
Subtraction
Answer:
the answer is
Step-by-step explanation:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Someone please help me!!
Answer: B
Step-by-step explanation:
Answer:
Solution : Option B
Step-by-step explanation:
Taking a look at the graph, we can see that the parabola has the following features.
Vertex : (3, - 4)
y - intercept : (0, 5)
x - intercept : (1, 0) and (5, 0)
axis of symmetry : x = 3
The vertex, y - intercept, and x - intercept can all be determined through the intersection of the graph at a certain point. However the axis of symmetry is the line with which splits this parabola into two " similar " parts.
Your solution is option b.
Simplify 8h + 9h -2h + 7 + 9 when h=4
Answer:
60h +16 is the answer. If you wanna simpifiy it and the rule still applies then 60 times 4 =240 plus 16 which is 256. 256 is the Simplest anwser.
Step-by-step explanation:
I am only in my first year of 12th grade.
What is the equation of the given line? A. x=−3 B. y=−3 C. x = 1 D. y = 1
Answer:
x=1
Step-by-step explanation:
the line is one unit up from the x axis
Simplify 9y+2y-5y please answer
Answer:
[tex]9y+2y-5y=6y[/tex]
Step-by-step explanation:
So we have the expression:
[tex]9y+2y-5y[/tex]
To simplify, simply combine the like terms. Therefore:
[tex]9y+2y-5y\\=11y-5y\\=6y[/tex]
Further notes:
To understand why we can combine like terms in the first place, we just need to use the distributive property. So we have the expression:
[tex]9y+2y-5y[/tex]
Now, factor out a y from the three terms:
[tex]=y(9+2-5)[/tex]
Do all the operations inside the parenthesis:
[tex]y(9+2-5)\\=y(11-5)\\=y(6)=6y[/tex]
And we moved the y back to the front!
This is the same result as before. When combining like terms, this is what we're essentially doing but without doing the distributive property manually. I hope you understand a bit better on how and why we can combine like terms!
Answer:
6y
Step-by-step explanation:
We are given the expression:
9y+2y-5y
and asked to simplify.
Each term in the expression has the same variable, a "y". Therefore, all three terms are like terms. We can combine the like terms in the expression.
First, factor out a y from each term.
9y+2y-5y
(9+2-5)*y
Solve inside the parentheses first. Add 9 and 2.
(11-5)*y
Subtract 5 from 11.
(6)*y
6y
The expression 9y+2y-5y simplified is 6y.
SupposeX1andX2are independent with Γ(α,1) and Γ(α+12,1) distributions. LetY= 2√X1X2.FindEYandvar(Y).
Answer:
E(Y) = √a + √(a+12)
Step-by-step explanation:
X1 and X2 are independent variables while Y is the dependent variable, such that
Y = f(X1, X2)
Meaning Y is a function of X1 and X2
In this case,
Y = 2√X1X2
When (X1, X2) = (a, 1) ; Y = 2√a
When (X1, X2) = (a+12, 1) ; Y = 2√a+12
The expected value of Y is
[2√a + 2√a+12] ÷ 2 = √a + √a+12
Please Halp 0.3x+18=−27
Answer: x=-150
Step-by-step explanation:
To solve for x, we would need to use our order of operations.
0.3x+18=-27 [subtract both sides by 18]
0.3x=-45 [divide both sides by 0.3]
x=-150
BRAINLIEST An artist has a book of clay in the shape of a cube. The edges of the cube measure 3 inches. The artist will use the clay to make models of
pine trees. Each tree will be a solid cone with a base diameter of 1.5 inches and a height of 2 inches.
Part 8
The artist plans to decorate each clay pine tree with pieces of yam that will extend directly from the top of the tree to the base of the tree.
write an equation that can be used to determine the length, x, in inches, of each piece of yam that the artist will need. Explain your
equation
Answer:
a) 22 pine trees
b) x² = 2² + 0.75²
Step-by-step explanation:
a) The volume of a cube is given as:
Volume of cube = length³
The length of the cube = length of the edges = 3 inches, hence:
Volume of cube = (3 inches)³ = 27 in³
The pine tree is the shape of a cone with diameter of 1.5 inches and a height (h) of 2 inches. The radius (r) = diameter / 2 = 1.5 inches / 2 = 0.75 inches.
The volume of the cone = πr²(h/3) = π × (0.75)² × (2/3) = 1.178 in³
The number of pine trees that the artist can make = Volume of cube / Volume of cone = 27 / 1.178 = 22.9
The number of pine trees that can be made = 22
b) The yam length need to extend from the top of the tree to the base is the same as the slant height of the cone.
Let the yam length be x, therefore:
x² = height² + radius²
x² = 2² + 0.75²
x² = 4 + 0.5625 = 4.5625
x = √4.5625 = 2.136 in
The yam length is 2,136 in
Please help: A recipe for a pizza that serves 12 people calls for 2 cups of shredded cheese. If each bag of shredded cheese contains 3 cups, what is the minimum
number of bags required to make pizza for 48 people?
Answer: 3
Step-by-step explanation:
Given: A recipe for a pizza that serves 12 people calls for 2 cups of shredded cheese.
12 people = 2 cups of shredded cheese.
Multiply 4 on both sides , we get
48 people = 8 cups of shredded cheese.
So we require 8 cups of shredded cheese to make pizza for 48 people.
Since, each bag of shredded cheese contains 3 cups.
Then minimum number of bags required = [tex]\dfrac{8}{3}=2.67\approx3[/tex]
Hence, minimum 3 bags required to make pizza for 48 people.
What is the difference between plotting (2, 3) and (3, 2) on a coordinate plane? Explain
Answer:
see below (I hope this makes sense and I hope it helps!)
Step-by-step explanation:
Points are found in the form (x, y) where x represents the x - value which is basically how far you move from the origin on the x-axis, and the same goes for y except it represents how far you move from the origin on the y-axis. A positive x means you move right, a negative x means you move left, a positive y means you move up and a negative y means you move down. Following these rules, to plot (2, 3), you move 2 units right and 3 units up from the origin and to plot (3, 2), you move 3 units right and 2 units up from the origin. The difference between plotting the two points is that first of all, they are different points so they are in different locations and second, their coordinates are "flipped"; what I mean by that is the x-coordinate of the first point is the y-coordinate of the second point and vice versa. Therefore, you move the same amount but in different directions.
These points are similar.
They both lie in quadrant 1.
However, the x coordinate is different in each ordered pair.
So (3, 2) moves farther from the origin than (2 , 3).
However, (2, 3) moved farther up than (3, 2).
Take a look below.
Susan is buying supplies for a party. Spoons only come in bags of 6 and forks only come in bags of 22.
What is the least number of spoons and the least number of forks she can buy so that she has the same
number of each?
The least number of spoons and the least number of forks she can buy, so that she has the same number
of each, is forks and spoons.
Answer:
11 bags of spoons and 3 bags of forks
Step-by-step explanation:
figure out what common number that multiples of 6 and multiples of 22 share
that number is 66
6x11 = 66 spoons total
22x3= 66 forks total
the ages of some lecturers are 42 54 50 54 50 42 46 46 48 and 48
find the mean age
Answer:
48
Step-by-step explanation:
add the values of the ages of the lecturers which should give you 434 then divide by the number of lecturers in question
=480/10
=48
Answer:
48.
Step-by-step explanation:
There are a total of 10 lecturers in the list
You find the mean by dividing the sum of all the ages by 10.
The mean age = 480/10 = 48.
A company is criticized because only 16 of 50 in executive-level positions are women. The company argues that the representation of women among their executive ranks could be better but statistically it’s at least as high as the national average of 35%. Do an appropriate hypothesis test to determine if the company’s claim is false at a significance level of 0.1.
Answer:
We can conclude that there is sufficient evidence to state that the companies claim is not false
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.35[/tex]
The level of significance is [tex]\alpha = 0.10[/tex]
The sample size is n = 50
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{16}{50 }[/tex]
[tex]\r p = 0.32[/tex]
The null hypothesis is [tex]H_o : p\ge 0.35[/tex]
The alternative hypothesis is [tex]H_a : p< 0.35[/tex]
Generally the standard error is evaluated as
[tex]SE = \sqrt{ \frac{0.35 (1- 0.35 )}{ \sqrt{50 } } }[/tex]
[tex]SE = 0.067[/tex]
So
The test statistics is evaluated as
[tex]t = \frac{\r p - p }{ SE }[/tex]
=> [tex]t = \frac{0.32 - 0.35 }{ 0.067 }[/tex]
=> [tex]t = -0.45[/tex]
The p-value is obtained from the z-table , the values is
[tex]P( Z < -0.45) = 0.32636[/tex]
From the calculation we see that
[tex]p-value > \alpha[/tex] so we fail to reject the null hypothesis
Hence we can conclude that there is sufficient evidence to state that the companies claim is not false
In a regular triangle ABC with side 1, two squares MNKL, RKPT are drawn such that points M, L, R are on the side AC (the order of the points on that side is as follows: A, M, L, R, C). Points P, T are on the side BC (the order of the points on that side is as follows: B, P, T, C). And the point N is on the side AB. Find the lengths of the sides of the two squares.
Answer:
MN = (21 -6√3)/37 ≈ 0.286694RK = (14√3 -12)/37 ≈ 0.331046Step-by-step explanation:
In the attached figure, we have defined LM to be length x. Then the other lengths on side AC are ...
AM = LR = x/√3
RC = (2/√3)RK = (2/√3)(2/√3)x = 4/3x
Then the sum of lengths along AC is ...
AC = AM +ML +LR +RC
1 = x(1/√3 +1 +1/√3 +4/3) = x(7/3 +2/√3) = x(7√3 +6)/(3√3)
Then the value of x is ...
[tex]x=\dfrac{3\sqrt{3}}{7\sqrt{3}+6}=\dfrac{3\sqrt{3}(7\sqrt{3}-6)}{(7\sqrt{3})^2-6^2}=\dfrac{3(21-6\sqrt{3})}{3(49-12)}\\\\\boxed{MN=\dfrac{21-6\sqrt{3}}{37}}\\\\RK=\dfrac{2\sqrt{3}}{3}MN\\\\\boxed{RK=\dfrac{14\sqrt{3}-12}{37}}[/tex]
a recreation park measurers 560m long and 700m wide. A 250m and 150m area of the park is used for soccer and baseball filed .How much of the area remains.
Answer: 354500m²
Step-by-step explanation:
Area of the recreation park = 560m x 700m
= 392000m²
Area used for soccer and baseball = 250m x 150m
= ¹⁵⁰⁰⁰⁰/₄
= 37500m².
Area of the remaining park = 392000 - 37500
= 354500m²
Of the 200 graduate students who were interviewed for a par time position at a call center, 110 had a bicycle, 25 had a master card and 130 had a mobile phone. 50 of them had both, a bicycle and a master card, 30 had both, a master card and a mobile phone and 60 had both, a bicycle and mobile phone and 10 had all three. How many candidates had none of the three?
S = Total students
B = number that had bikes
M = number that had a master card
P = number that had a phone
S = 200
B = 110
M = 25
P = 130
BM = 50
MP = 30
BP = 60
BMP = 10
B + M + P = 110 + 25 + 130 = 265
BM + MP + BP - BMP = 50 + 30 + 60 -10 = 130
265 - 130 = 135
Students that had none of the three = 200 - 135 = 65
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 3 small boxes has a total weight of 120 kilograms. A delivery of 7 large boxes and 9 small boxes has a total weight of 234 kilograms. How much does each type of box weigh?
Answer:
one large box equals 15.75kg
one small box equals 13.75kg
Step-by-step explanation:
First, identify your variables:
Let "l" represent the weight of one large box.
Let"s" represent the weight of one small box.
Then, stack the two equations on top of each other:
[tex]5l+3s=120\\7l+9s=234[/tex]
Next, multiply the first equation by 3 so we can use elimination of the "s" variable to find the "l" variable first:
[tex]3(5l+3s=120)\\7l+9s=234\\\\15l+9s=360\\7l+9s=234[/tex]
Now, subtract the two equations to cancel out the s-variable and find the l-variable:
[tex]15l+9s=360\\-(7l+9s=234)\\8l=126\\\frac{8l}{8}=\frac{126}{8}\\l=15.75[/tex]
Then, substitute your l-variable in the original first equation to find the s-variable:
[tex]5l+3s=120\\5(15.75)+3s=120\\78.75+3s=120\\78.85-78.75+3s=120-78.75\\3s=41.25\\\frac{3s}{3}=\frac{41.25}{3}\\s=13.75[/tex]
With all the information that is collected, you find that one large box weighs 15.75kg and one small box weighs 13.75kg.
The following table shows scores obtained in an examination by B.Ed JHS Specialism students. Use the information to answer the questions that follow: Score 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 Frequency 10 4 10 20 30 15 3 2 1 5.a. Construct a cumulative frequency curve for the data. b. Find the; i. inter-quartile range. ii. 70th percentile class scores. iii. probability that a student scored at most 50 on the examination
Please is urgent .can I get help
Answer:
(a) The cumulative frequency curve for the data is attached below.
(b) (i) The inter-quartile range is 10.08.
(b) (ii) The 70th percentile class scores is 0.
(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.
Step-by-step explanation:
(a)
To make a cumulative frequency curve for the data first convert the class interval into continuous.
The cumulative frequencies are computed by summing the previous frequencies.
The cumulative frequency curve for the data is attached below.
(b)
(i)
The inter-quartile range is the difference between the third and the first quartile.
Compute the values of Q₁ and Q₃ as follows:
Q₁ is at the position:
[tex]\frac{\sum f}{4}=\frac{100}{4}=25[/tex]
The class interval is: 34.5 - 39.5.
The formula of first quartile is:
[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
Here,
l = lower limit of the class consisting value 25 = 34.5
(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 24
f = frequency of the class interval = 20
h = width = 39.5 - 34.5 = 5
Then the value of first quartile is:
[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
[tex]=34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75[/tex]
The value of first quartile is 34.75.
Q₃ is at the position:
[tex]\frac{3\sum f}{4}=\frac{3\times100}{4}=75[/tex]
The class interval is: 44.5 - 49.5.
The formula of third quartile is:
[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
Here,
l = lower limit of the class consisting value 75 = 44.5
(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 74
f = frequency of the class interval = 15
h = width = 49.5 - 44.5 = 5
Then the value of third quartile is:
[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
[tex]=44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83[/tex]
The value of third quartile is 44.83.
Then the inter-quartile range is:
[tex]IQR = Q_{3}-Q_{1}[/tex]
[tex]=44.83-34.75\\=10.08[/tex]
Thus, the inter-quartile range is 10.08.
(ii)
The maximum upper limit of the class intervals is 69.5.
That is the maximum percentile class score is 69.5th percentile.
So, the 70th percentile class scores is 0.
(iii)
Compute the probability that a student scored at most 50 on the examination as follows:
[tex]P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}[/tex]
[tex]=\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89[/tex]
Thus, the probability that a student scored at most 50 on the examination is 0.89.
The number of violent crimes committed in a day possesses a distribution with a mean of 2.3 crimes per day and a standard deviation of 2 crimes per day. A random sample of 100 days was observed, and the mean. number of crimes for the sample was calculated. Describe the sampling distribution of the sample mean.
A) shape unknown with mean-2.3 and standard deviation 2
B) approximately normal with mean 2.3 and standard deviation 2
C) shape unknown with mean 2.3 and standard deviation 0.2
D) approximately normal with mean 2.3 and standard deviation 0.2
Answer:
B) approximately normal with mean 2.3 and standard deviation 2
Step-by-step explanation:
Given the following :
Mean crimes per day = 2.3
Standard deviation = 2
Number of samples = 100
Sampling distribution of the mean:
According to the central limit theorem:
Sample mean = population mean
2.3 = 2.3
The standard deviation of the sample (s) : ratio of the population standard deviation and square root of the sample size.
s = population standard deviation / √sample size
s = 2 / √100
s = 2 / 10
s = 0.2
The central limit theorem also posits that once ths sample size is large enough, the sampling of the sample mean will be approximately normal.
Hence, the distribution is approximately normal, with mean of 2.3 and standard deviation of 0.2
The distance between -7 and 2 on the number line is _____. 5 9 -5 10
there is a room 7 feet x 9 feet you lay a 1-foot wide plank from corner to corner touching all 4 walls how long is the plank
Answer:
Step-by-step explanation:
l^2=[(7-V2)/2]^2+(9-V2/2)^2=
49-7V2+2/4+81-9V2+2/4=
49+81+4/4-16V2=
131-16V2=108.4 ft
so l=V108.4≈10.4ft
Im learning about Recursive and Explicit in Pre-Calc, and it says to use the rule to write the first three terms of each sequence. I have no idea how to figure these out. Only know the first one or two because they give it to you but I have no idea how to figure out for a third one. Someone PLZ HELP!!!!!!!
Hello,
4. you have sequences defined by the first term and a recursive relation.
[tex]a_1=3\\\\a_n=2a_{n-1} \ \ \text{ for n}> 1[/tex]
Take n = 2, it gives
[tex]a_2=2a_1[/tex] , right?
But you know [tex]a_1=3[/tex]
so [tex]a_2=2a_1=2*3=6[/tex]
This is the second term. You are asked to find the first three terms.
Now, let's take n = 3
[tex]a_3=2a_2=2*6=12[/tex]
So the first three terms are 3, 6, 12.
6.
[tex]a_1=12\\\\a_2=\dfrac{1}{2}a_1+1=\dfrac{12}{2}+1=6+1=7 \\ \\a_3=\dfrac{1}{2}a_2+1=\dfrac{7}{2}+1=\dfrac{9}{2}[/tex]
8.
[tex]a_1=10\\ \\a_2=-3a_1=-3*10=-30\\\\a_3=-3a_2=-3*(-30)=90[/tex]
10.
[tex]a_1=2\\\\a_2=-1\\\\a_3=a_2+a_1=-1+2=1\\\\a_4=a_3+a_2=1-1=0[/tex]
Do not hesitate if you have any question.
Thank you