Answer:
191.56
Step-by-step explanation:
Given
191.5638
Required
Approximate
Approximating to the nearest hundredth implies that, only to digits after the decimal point is needed
This is:
191._ _
The third digit after the decimal point will approximated using the approximation rule;
Since, the third digit after the decimal point (3) is not up to 5, it'll be approximated to 0 and added to the second digit (6)
So, we have:
191.5 _
The next digit is calculated as 6 + 0 = 6
Hence, the full approximated number is 191.56
2(3w+9z) simplify it please .
Answer:
6w + 18z
Step-by-step explanation:
distribute the 2
2 x 3w = 6w
2 x 9z = 18 z
6w + 18z
Answer:
6w+18z
Step-by-step explanation:
A rectangular tank that is 2048 ft cubed with a square base and open top is to be constructed of sheet steel of a given thickness. Find the dimensions of the tank with minimum weight.
Answer:
The box should have base 16ft by 16ft and height 8ft Therefore,dimensions are 16 ft by 16 ft by 8 ft
Step-by-step explanation:
We were given the volume of the tank as, 2048 cubic feet.
Form minimum weight, the surface area must be minimum.
Let the height be h and the lengths be x
the volume will be: V=x²h then substitute the value of volume, we have
2048=hx²
hence
h=2048/x²
Since the amount of material used is directly proportional to the surface area, then the material needs to be minimized by minimizing the surface area.
The surface area of the box described is
A=x²+4xh
Then substitute h into the Area equation we have
A= x² + 4x(2048/x²)
A= x² + 8192/x
We want to minimize
A
dA/dx = -8192/x² + 2 x= 0 for max or min
when dA/dx=0
dA/dx= 2x-8192/x²=0
2x=8192/x²
Hence
2x³=8192
x³=4096
x=₃√(4096)
X=16ft
Then h=2048/x²
h=2048/16²
h=8ft
The box should have base 16ft by 16ft and height 8ft
Hence the dimensions are 16 ft by 16 ft by 8 ft
5. ACT scores for a group of six students from a local high school is 21, 22, 23, 25, 26, 33. What is the range for this distribution of scores?
Answer:
12
Step-by-step explanation:
The formula for RANGE of a given set if data = Maximum value - Minimum value.
In the above question, we are given a group of ACT scores
21, 22, 23, 25, 26, 33.
Maximum value = 33
Minimum value = 21
Range = 33 - 21
= 12
Therefore, the range for this distribution of scores is 12
Ray runs 30 feet north, 30 feet west, and then 30 feet south. Distance:Displacement:
Answer:
1 MILE
Step-by-step explanation:
Simplify: (x-3) (x-3)
Answer:
x^2 -6x +6
Step-by-step explanation:
Square of a difference (can be found in IM2)
Formula: a^2 -2ab +b^2
x= a; 3= b
(x -3)(x -3)
Plug in to formula.
x^2 -2(x)(3) +3^2
Simplify.
x^2 -6x +6
Answer:
[tex](x - 3)^{2}[/tex]
The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 42°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.There is not sufficient evidence to support the claim that the mean temperature is different from 42 deg There is not sufficient evidence to support the claim that the mean temperature is equal to 42 deg There is sufficient evidence to support the claim that the mean temperature is different from 42 deg There is sufficient evidence to support the claim that the mean temperature is equal to 42deg
Answer:
There is sufficient evidence to support the claim that the mean temperature is different from 42 deg
Step-by-step explanation:
From the given information, we are being told that:
The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 42°F
i. e mean μ = 42
The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.
Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
From above;
The null and the alternative hypothesis can be computed as:
[tex]\mathbf{H_o : \mu = 42} \\ \\ \mathbf {H_1 : \mu \neq 42}[/tex]
Here , the hypothesis test of the claim is the alternative hypothesis.
The conclusion based on the decision rule: is to reject the null hypothesis
∴
The conclusion in non technical terms is that :
There is sufficient evidence to support the claim that the mean temperature is different from 42 deg
A 20-person fraternity is making their weekend plans around 5 different parties in IV. Each brother will attend exactly one of the parties. Fraternity rules state that the fraternity must have a representative at each party. Assume that only the number of brothers that show up at a party is important, i.e. the brothers are indistinguishable. (a) How many different arrangements of plans are possible
Answer:
3876
Step-by-step explanation:
Given the following :
Fraternity members = 20
They are to attend 5 different parties in groups of 4
Meaning a group = 4 persons
Atleast one brother will attend exactly one of the parties. (the brothers are indistinguishable).
Then, exactly one brother at a party (20 - 1) = 19, since they are indistinguishable.
Group members are in 4's
19C4
From: nCr = n! /(n-r)! r!
19C4 = 19! / (19 - 4)! 4!
= 19! / 15! 4!
= (19 * 18 * 17 * 16) / (4 * 3 * 2)
= 93024 / 24
= 3876
A quality control manager is concerned about variability of the net weight of his company’s individual yogurt cups. To check the consistency, he takes a random sample of sixteen 6-ounce yogurt cups and finds the mean of the sampled weights to be 5.85 ounces and the sample standard deviation to be 0.2 ounce.
Requried:
a. Test the hypotheses H0: µ ≥ 6 Ha: µ < 6 at the 5% level of significance. Assume the population of yogurt-cup net weights is approximately normally distributed.
b. Based on the results of the test, will the manager be satisfied that the company is not under-filling its cups?
c. State the decision rule, the test statistic, and the manager’s decision.
Answer:
H₀ should be rejected, yogurt cups are under-filling, the manager has to check the process
Step-by-step explanation:
Normal distribution and n < 30. We must use t-student test.
a) If it is required to test H₀ μ >= 6 Hₐ μ < 6 is a one tail test (left-tail)
At α = 5 % α = 0,05 and n = 16 then degree of freedom is n -1
df = 15 find t(c) = - 1,753
μ = 5,85 and s = 0,2 ( sample mean and standard deviation respectevily)
T compute t(s)
t(s) = ( μ - μ₀ ) / s/√n
t(s) = ( 5,85 - 6 ) /0,2/√16
t(s) = - 0,15*4/0,2
t(s) = - 3
t(s) < t(c) -3 < - 1,753
Then t(s) is in the rejection region we reject H₀. There is enough evidence to claim the yogurt cups are under-filling.
Manager has to check on the process
The larger of two consecutive intergers is 7 greater than twice the smaller.find the intergers
Answer:
Smaller integer = -6
Larger integer = -5
Step-by-step explanation:
Let the two consecutive integers = [tex]x[/tex] and ([tex]x+1[/tex])
As per the given statement,
Larger i.e. ([tex]x+1[/tex]) is 7 greater than twice ([tex]2\times x[/tex]) the smaller integer.
To find:
The value of integers = ?
Solution:
First of all, let us learn about integers.
The integers are of the form (put in increasing order):
[tex]-\infty, ...., -3, -2,-1, 0, 1, 2, 3, ...., \infty[/tex]
and -1 > -2
So the consecutive integers are 1 greater than the smaller.
Therefore, the two integers can be [tex]x, x+1[/tex]
Now, writing the given condition in the form of an equation:
[tex]x+1=2x+7\\\Rightarrow 1-7=2x-x\\\Rightarrow -6=x\\\Rightarrow \bold{x=-6}[/tex]
So, the smaller integer = -6
Larger integer = -6+1 = -5
Help Please!!!!! What is the absolute value of ∣∣2 1/3 ∣∣? Use this number line to determine the absolute value. Enter your answer in the box as a mixed number in simplest form.
Answer:
2 1/3
Step-by-step explanation:
i know because i did the test in k 12
An absolute value of |x| {modulus of x} is the value of a real number x. The absolute value of ||2 1/3|| is 2 1/3.
What is Absolute Value?An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number, for example, |-5| will give 5, and also, |5| will give 5 as well.
The absolute value of ||2 1/3|| is,
||2 1/3||
= |2 1/3|
= 2 1/3
Hence, The absolute value of ||2 1/3|| is 2 1/3.
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Which Greek geometer founded a philosophical society that devoted itself to the study of mathematics?'
Answer:
Pythagoras
Step-by-step explanation:
Pythagoras
What is the slope of the function y= 4x+ 6
Answer:
The answer is 4Step-by-step explanation:
Since the function is a linear function
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question the equation is
y = 4x + 6
Comparing with the general form of equation above the slope of the function is
4Hope this helps you
if 6x is 6, then what is the square root of 4761 x
Answer:
the answer is 69
Step-by-step explanation:
you find the square root of 4761
Answer:
its 69
Step-by-step explanation:
Which equation is true for x = –6 and x = 2?
A.) 2x2 – 16x + 12 = 0
B.) 2x2 + 8x – 24 = 0
C.) 3x2 – 4x – 12 = 0
D.) 3x2 + 12x + 36 = 0
plsssss help its a timed question
Answer:
B.) 2x2 + 8x – 24 = 0
Step-by-step explanation:
For x= 2 and x= -6
Let's determine the equation of the solutions.
(X-2)(x+6)=0
X²+6x -2x -12= 0
X² +4x -12= 0
So the above is the real equation to the solution of x= 2 and x= -6
But in the options, we don't have something like that.
But let's try and multiply the solution will a positive or negative integer.
Lets start with +2
2(X² +4x -12= 0)
2x² + 8x -24 = 0
Yeah, option B is the answer
I will Mark you as brainliest if you show your work
Answer:
16 miles long to work it would be 0 miles shorter
Step-by-step explanation:
8+8 is 16
if the road was just one street it would still be the same distance
I hope this helps. THIS MIGHT BE WRONG though if someone say something else, take a good look at their answer too because the way I did it, seems like it's a little too simple.
Answer: The distance will be about 11 miles . 2) The man's one way-trip will be 5 miles shorter.
Step-by-step explanation:
If the man drove east by 8 miles and North by 8 miles and we want to determine the distance that is directly from east to north then we will use the Pythagorean Theorem solve for that distance.
Now since we are solving for the distance directly from his home to work we will be looking for the hypotenuse in this case.
a^2 + b^2 =c^2 where c is the hypotenuse
8^2 + 8^2 =c^2
64 +64 = c^2
c= [tex]\sqrt{128}[/tex]
c = 11.31
In this case the distance from his home directly to his work will be about 11 miles.
2. To find out how much shorter the man will travel ,add the east and north distance and subtract 11.31 from it.
8 + 8 = 16
16 - 11.31 = 4.69
For a five-year moving average, how many values will be lost at the beginning and end of the time series?
Answer:
2 Values
Step-by-step explanation:
For a five-year moving average, two values will be lost at the beginning and end of the time series.
This is because we add the first five elements and divide it by 5 to get the five year moving average. But the middle value of 5 is 2.5 which is greater than 2 so the result is placed against the third value. In this way the first two and last 2 values are lost.
For understanding let us compute the 5 year moving average as
a1= 1/5( y1+ y2+y3+ y4+y5)
a2= 1/5 ( y2+y3+ y4+y5+ y6)
a3 = 1/5(y3+ y4+y5+ y6+ y7)
a4= 1/5(y4+y5+ y6+ y7+ y8)
a5= 1/5(y5+ y6+ y7+y8+y9)
The average so obtained are placed opposite the middle year of each group.
So the values at the y1,y2 ,at the beginnign and at the end y8 and y9 are lost.
A study of 200 computer service firms revealed these incomes after taxes: Income After Taxes Number of Firms Under $1 million 102 $1 million up to $20 million 61 $20 million or more 37 What is the probability that a particular firm selected has $1 million or more in income after taxes
Answer: 0.49
Step-by-step explanation:
given data:
no of computer services firms =200
no of firms under $1million = 102
no of firms between $1million to $20million = 61
no of firms $20million and above = 37
solution:
probability that a firm selected has 1$million or above.
P ( x ≥ $1million )
= 61/200 + 37/200
= 49/100
= 0.49
the probability of selecting with $1million or more in income taxes is 0.49%
48% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 300 found that 45% of the readers owned a particular make of car. Is there sufficient evidence at the 0.02 level to support the executive's claim?
Answer:
There is no sufficient evidence to support the executive claim
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.48[/tex]
The sample proportion is [tex]\r p = 0.45[/tex]
The sample size is [tex]n = 300[/tex]
The level of significance is [tex]\alpha = 0.02[/tex]
The null hypothesis is [tex]H_o : p= 0.48[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.48[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1 - p )}{n} } }[/tex]
=> [tex]t = \frac{0.45 - 0.48 }{ \sqrt{ \frac{0.48 (1 - 0.48 )}{300} } }[/tex]
=> [tex]t = -1.04[/tex]
The p-value is mathematically represented as
[tex]p-value = 2P(z > |-1.04|)[/tex]
Form the z-table
[tex]P(z > |-1.04|) = 0.15[/tex]
=> [tex]p-value = 2 * 0.15[/tex]
=> [tex]p-value = 0.3[/tex]
Given that [tex]p-value > \alpha[/tex] we fail to reject the null hypothesis
Hence we can conclude that there is no sufficient evidence to support the executive claim
Prove: (AUB) \ (AnB) =(A\B) u (B\A)
Answer:
Prove that (A-B) U (B-A) =(A U B) - (A intersection B). 2. See answers ... izvoru47 and 170 more users found this answer helpful
Are these ratios equivalent 4:5 and 16:20 yes or no
Answer:
yes
Step-by-step explanation:
this is correct because if you multipy them both by 4 you get those answers .
4 x 4 = 16
5 x 4 = 20
The ratios 4:5 and 16:20 are equivalent to each other. Yes, the ratios are equal to 4: 5.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The equivalent is the expression that is in different forms but is equal to the same value.
The two ratios are given below.
4:5 and 16:20
Convert the ratios into their simplified form. Then the ratios are given as,
4:5 and 16:20
4:5 and 4:5
The ratios 4:5 and 16:20 are equivalent to each other. Yes, the ratios are equal to 4: 5.
More about the ratio and the proportion link is given below.
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Which of the following is most likely the next step in the series
Answer:
C
Step-by-step explanation:
In the pattern, there are some similarities with the first three circles.
1. The number is on the blue half.
2. The halves switch spots, red-blue, blue-red, red-blue.
So, the next one should have the number on the blue half and the next pattern should be red-blue, blue-red, red-blue, and blue-red.
Which one has both the number on the blue half and the pattern blue-red?
C
Hoped this helped.
From 12:00 midnight to 6:00am
Answer:
6 hours?
Step-by-step explanation:
12:00 0 hour(s)
1:00 1 hour(s)
2:00 2 hour(s)
3:00 3 hour(s)
4:00 4 hour(s)
5:00 5 hour(s)
6:00 6 hour(s)
What number should be placed in the box to help complete the division calculation? long division setup showing an incomplete calculation. 12 is in the divisor, 8587 is in the dividend, and 7 hundreds and 1 tens is written in the quotient. 8400 is subtracted from 8587 to give 187. An unknown value represented by a box is being subtracted from 187.
Answer:
120
Step-by-step explanation:
Your description is a little different from below picture, but the logic is the same. The 1 in the tens position represents 10x12 = 120, hence 120 should be subtracted and leaves you with 67 to continue.
Answer:
187
Step-by-step explanation:
12 in not the divisor of 8587 in the dividend with 7 hundreds and 1 tens. 8400 you subtracted from 8587 to give 187.
how to solve and answer, pls and thx
Answer:
D
Step-by-step explanation:
first of all we need to solve the inequalities
[tex]3-x\geq 2\\\\3-x+x\geq 2+x\\\\3\geq2+x \\\\3-2\geq 2-2+x\\\\1\geq x\\\\x\leq 1[/tex] (-∞,1] or ]-∞,1]
the second inequality is
[tex]4x+2\geq 10\\\\4x+2-2\geq 10-2\\\\4x\geq 8\\\\\frac{4x}{4}\geq \frac{8}{4} \\\\x\geq 2[/tex] [2,∞) or [2,∞[
so the answer is D
Answer: D
Step-by-step explanation:
To graph the inequalities on the number line, let's first solve them.
3-x≥2 [subtract both sides by 3]
-x≥-1 [divide both sides by -1, remember to flip inequalities]
x≤1
---------------------------------------------------------------------------------------------
4x+2≥10 [subtract both sides by 2]
4x≥8 [divide both sides by 4]
x≥2
---------------------------------------------------------------------------------------------
Now, we have our inequalities, x≤1 and x≥2. Notice that both inequalities are greater/less than or equal to. The "or equal to" part means that x is equal to 1 and 2. Therefore, when graphed, it is a closed circle. This let's us automatically eliminate B and C because they have open circles.
For x≤1, we know that x is going to be 1 and below, meaning it starts at 1 and travels left where it gets smaller and smaller. This tells us that the answer is D, but let's check to be sure.
For x≥2, we know that x is going to be greater than 2. This let's us know that the arrow will be pointing to the right, where the numbers are getting bigger and bigger. Knowing this, we can confirm that D is the correct answer.
cells splits into 2 cells every hour. Write expression to find number of cells in 6 hours
Answer:
12 cells every hour.
Step-by-step explanation:
You would do 2 x 6
(the 2 is the cells per hour, and the 6 is the amount of hours)
Sam missed a question on his Algebra Test. He wrote his work down. Where is his error in solving 3x + 2 = 14?
Answer:
10/3
Step-by-step explanation:
Step 1: Subtract 4 from both sides.
3
x
+
4
−
4
=
14
−
4
3
x
=
10
Step 2: Divide both sides by 3.
3
x
3
=
10
3
1 meter is equivalent to how many feet
Find the value of x that makes AFGH~AJKL.
(Lesson 11.3) (1 point)
X+3.5
20
Answer: The answer is: " x = 2.833333333333...." .
___________________________
or: write as: " 2 [tex]\frac{5}{6}[/tex] " .
___________________________
Step-by-step explanation:
___________________________
Set up a ratio:
Note: Segment FH = (x + 35)
Segment JL = 20 ;
Segment FH ~ Segment JL ;
___________________________
Note: Segment GH = (x - 4) ;
Segment KL = 5 ;
Segment GH ~ Segment KL .
___________________________
So, ( x + 3.5) : 20 :: (x-4) : 5 ;
Write this ratio in fraction format:
___________________________
→ [tex]\frac{(x+3.5) }{20 } = \frac{(x-4) }{5}[/tex] ;
Now; "cross-factor multiply" :
→ [tex]\frac{a}{b} = \frac{c}{d }[/tex] ; → [tex]ad = bc[/tex] ; { [tex]{ a\neq0 ; b\neq0 ; c\neq0 ; d\neq0[/tex] .}.
___________________________
So:
5(x + 3.5) = 20(x - 4) ;
___________________________
→ To simplify, start by divide each side of the equation by "5" ;
___________________________
→ {5(x + 3.5) } / 5 = { 20(x - 4) } / 5 ;
to get:
→ (x + 3.5) = 4(x - 4) ;
___________________________
Now, on the right-hand side of the equation;
let us expand the expression;
___________________________
We have the expression: " 4(x - 4) " ;
To expand:
Note the "distributive property of multiplication:
→ a(b + c) = ab + ac ;
Likewise:
→ 4(x - 4) = 4x - 16 ;
___________________________
Now, we can rewrite our equation:
___________________________
→ " x + 3.5 = 4x - 15 " ;
Now, we can subtract "x" from each side of the question;
& add "15" to each side of the equation; as folllows:
___________________________
→ x + 3.5 = 4x - 15 ;
- x + 15 = - x +15
___________________________
to get: 8.5 = 3x ;
↔ 3x = 8.5 ;
Now, divide each side of the equation by "3" ;
to isolate "x" on one side of the equation;
& to solve for "x" ; as follows:
→ 3x / 3 = 8.5 / 3 ;
to get: x = 8.5 /3
= 2.83333333333 ;
or; write as: " 2 [tex]\frac{5}{6}[/tex] ."
___________________________
Hope this is helpful to you! Best wishes!
___________________________
Solve each equation.
1. 6k – 3 = 2k + 13
Answer:
4k=16
k=4
Step-by-step explanation:
please give 5 star i need it
A ______ is a rule that pairs each element in one set with exactly one element from a second set.
Answer:
function
Step-by-step explanation:
A function is a rule that pairs each element in one set with exactly one element from a second set.
A function is a rule that pairs each element in one set with exactly one element from a second set.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Function is a relation.
Let a set A = {1, 2, 3, ........} and set B = {1, 4, 9, .....}
Let f(x) = x² be the function.
f(1) = 1 , so 1 is mapped to 1
f(2) = 4, so 2 is mapped to 4.
...............
It goes on like this.
No element would map to more than one element.
1 will only map to 1, not to 4, 9, .......
Similarly, 2 will map to 4 only, not any other element.
But more than one element in set A can be mapped to same element in set B.
Suppose A = {......, -2, -1, 0, 1, 2, .......} and B = {1, 4, 9, .....}
We have f(1) = f(-1) = 1
Also, f(2) = f(-2) = 4
But this is a function.
Hence the rule is that pairs each element in one set with exactly one element from a second set.
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