Answer:
P [ X < 67 ] = 0,66,81 or 66,81 %
Step-by-step explanation:
We assume Normal Distribution N ( μ ; σ ) N ( 76 ; 6 )
z score for 67 is :
z(s) = ( X - μ ) /σ
z(s) = ( 67 - 76 ) / 6
z(s) = - 9 / 6
z(s) = - 1,5
with 1,5 we fnd n z-table area undr the curve α = 0,6681
Then P [ X < 67 ] = 0,66,81 or 66,81 %
If the solutions for a quadratic equation are -2 and 5 what is the equation
Answer:
f(x) = x^2 - 3x -10
Step-by-step explanation:
If the solutions are {-2, 5}, the factors of the quadratic are (x + 2) and (x - 5).
The equation is f(x) = (x + 2)(x - 5) = x^2 - 3x -10
Write 8x8x88888 as power
Answer:
8[2]×88888
Step-by-step explanation:
[8×8]=8[2]×88888
The temperature dropped 15 degrees in an hour. If the starting temperature was 10 degrees, What was the final temperature?
Answer:
Step-by-step explanation:
15-10=5 degrees
If f(x)=2x-6and g(x)=3x+9 find (f+g)(x)
Answer:
(f+g)(x) = 5x + 3
Step-by-step explanation:
(f+g)(x) is the sum (term by term) of f(x) and g(x):
(f+g)(x) = 2x - 6 + 3x + 9
Combining like terms, we get
(f+g)(x) = 5x + 3
Answer:
(f+g)(x)= 5x+3
Step-by-step explanation:
The question asks us to find (f+g)(x). In other words, the sum of f(x) and g(x).
f(x) + g(x)
We know that f(x)= 2x-6 and g(x)=3x+9. Therefore, we can substitute the expressions in.
(2x-6) + (3x+9)
Now, simplify by combining like terms. Add the terms with variables, then the terms without variables.
(2x+3x) + (-6+9)
Add 2x and 3x.
5x + (-6 + 9)
Add -6 and 9.
5x + 3
If f(x)=2x-6and g(x)=3x+9, then (f+g)(x) is 5x+3
What is the equation of the line in the following graph?
Answer:
2 . y=-1
Step-by-step explanation:
m=0 (it is a straight line)
use (-6,-1) in y=mx+b
-1=0(-6)+b
-1=b
equation is now
y=0(x)-1
y=-1
Will give brainliest answer
What is the range of possible sizes for side z?
Pro
Pro
Tea
2
4.1
1.3
Stuck? Watch a video or use a hint.
Reportage
Answer:
2.8 < x < 5.4
Step-by-step explanation:
Given the triangle with two known sides, 4.1 and 1.3, the range of possible values of the third side, x, can be ascertained by considering the triangle inequality theorem.
According to the theorem, when you add any two of the angles in a triangle, it should give you a value greater than the third side.
If a, b, and c are 3 sides of a triangle, the theorem implies that:
a + b > c.
Therefore, a - b < c < a + b
We can use this logic to find the possibly values of x in the given triangle above.
Thus,
4.1 - 1.3 < x < 4.1 + 1.3
2.8 < x < 5.4
Range of possible sizes of x is 2.8 < x < 5.4
Put these numbers in order from greatest to least.
8
-2-
25
2.45
-0.84
Answer:
25, 2.45, 8, -0.84, -2
Step-by-step explanation:
negative is a least number
positive is a greater number
Positive number-8, 25, 2.45
Negative number-(-2), -0.84
ordering number from greatest to least:
25, 2.45, 8, -0.84, -2
-2 is smallest then -0.84 because 2 is bigger then 0.84. It is opposite with the positive number.
The bigger the positive number the biggest it is. While the bigger the negative number the smallest it is.
Answer:
Step-by-step explanation:
The numbers are:
● 8
● -2
● 25
● 2.45
● -0.84
To make it easy classify the positive numbers apart and the negatives ones alone
● 2.45<8< 25
● -2 < -0.84
25 is the greatest and -2 is the least
● 25 > 8 > 2.45 > -0.84 > -2
Question 2: Jamie has a jar of coins containing the same number of nickels, dimes and quarters. The total value of the coins in the jar is 13.20. How many nickels does Jamie have?
Answer:
?
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
Let "x" be the number of nickels, of dimes, and of quarters.
The value of the nickels is 5x cents.
The value of the dimes is 10x cents
The value of the quarters is 25x cents.
Equation:
Value of nickels + Value of dimes + Value of quarters =1320 cents
5x + 10x + 25x = 1320
Sove for "x". Then you will know the number of each coin.
According to the local union president, the mean gross income of plumbers in the Salt Lake City area follows a normal distribution with a mean of $48,000 and a population standard deviation of $2,000. A recent investigative reporter for KYAK TV found, for a sample of 49 plumbers, the mean gross income was $47,600. At the 0.05 significance level, is it reasonable to conclude that the mean income is not equal to $47,600? Determine the p value. State the Null and Alternate hypothesis: State the test statistic: State the Decision Rule: Show the calculation: What is the interpretation of the sample data? Show the P value
Answer:
Step-by-step explanation:
Given that:
population mean [tex]\mu[/tex] = 47600
population standard deviation [tex]\sigma[/tex] = 2000
sample size n = 49
Sample mean [tex]\over\ x[/tex] = 48000
Level of significance = 0.05
The null and the alternative hypothesis can be computed as follows;
[tex]H_0 : \mu = 47600 \\ \\ H_1 : \mu \neq 47600[/tex]
Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.
The test statistics can be calculated by using the formula:
[tex]z= \dfrac{\overline X - \mu }{\dfrac{\sigma}{ \sqrt{n}}}[/tex]
[tex]z= \dfrac{ 48000-47600 }{\dfrac{2000}{ \sqrt{49}}}[/tex]
[tex]z= \dfrac{400 }{\dfrac{2000}{ 7}}[/tex]
[tex]z= 1.4[/tex]
Conclusion:
Since 1.4 is lesser than 1.96 , we fail to reject the null hypothesis and that there is insufficient information to conclude that the mean gross income is not equal to $47600
The P-value is being calculate as follows:
P -value = 2P(Z>1.4)
P -value = 2 (1 - P(Z< 1.4)
P-value = 2 ( 1 - 0.91924)
P -value = 2 (0.08076 )
P -value = 0.16152
What is numbers 1-30 added all together
Answer:
465
Step-by-step explanation:
The sum of consecutive numbers has a formula, and it's
[tex]\frac{n(n+1)}{2}[/tex].
Where n is the amount of numbers.
From 1-30, it's 30 numbers, so:
[tex]\frac{30(30+1)}{2} \\\\\frac{30(31)}{2} \\\\\frac{930)}{2} \\\\\\465[/tex]
Hope this helped!
If x to the 2nd power equal 60, What is the value of x
Answer:
7.745
Step-by-step explanation:
Square root of 60 equals X.
A model rocket is launched with an initial velocity of 240 ft/s. The height, h, in feet, of the rocket t seconds after the launch is given by
h = −16t2 + 240t.
How many seconds after launch will the rocket be 390 ft above the ground? Round to the nearest hundredth of a second.
s (smaller value)
s (larger value)
Answer:
About 1.85 seconds and 13.15 seconds.
Step-by-step explanation:
The height (in feet) of the rocket t seconds after launch is given by the equation:
[tex]h = -16t^2 + 240 t[/tex]
And we want to determine how many seconds after launch will be rocket be 390 feet above the ground.
Thus, let h = 390 and solve for t:
[tex]390 = -16t^2 +240t[/tex]
Isolate:
[tex]-16t^2 + 240 t - 390 = 0[/tex]
Simplify:
[tex]8t^2 - 120t + 195 = 0[/tex]
We can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}[/tex]
In this case, a = 8, b = -120, and c = 195. Hence:
[tex]\displaystyle t = \frac{-(-120)\pm \sqrt{(-120)^2 - 4(8)(195)}}{2(8)}[/tex]
Evaluate:
[tex]\displaystyle t = \frac{120\pm\sqrt{8160}}{16}[/tex]
Simplify:
[tex]\displaystyle t = \frac{120\pm4\sqrt{510}}{16} = \frac{30\pm\sqrt{510}}{4}[/tex]
Thus, our two solutions are:
[tex]\displaystyle t = \frac{30+ \sqrt{510}}{4} \approx 13.15 \text{ or } t = \frac{30-\sqrt{510}}{4} \approx 1.85[/tex]
Hence, the rocket will be 390 feet above the ground after about 1.85 seconds and again after about 13.15 seconds.
Given a sample of 35, what is the sample standard deviation of a pair of jeans if the 90% confidence interval is [37.14, 42.86]
Answer:
10.295Step-by-step explanation:
Using the value for calculating the confidence interval as given;
CI = xbar + Z*σ/√n
xbar is the mean = 37.14+42.86/2
xbar= 80/2
xbar = 40
Z is the z-score at the 90% confidence = 1.645
σ is the standard deviation
n is the sample size = 35
Given the confidence interval CI as [37.14, 42.86]
Using the maximum value of the confidence interval to get the value of the standard deviation, we will have;
42.86 = xbar + Z*σ/√n
42.86 = 40 + 1.645* σ/√35
42.86-40 = 1.645*σ/√35
2.86 = 1.645*σ/√35
2.86/1.645 = σ/√35
1.739 = σ/√35
1.739 = σ/5.92
σ= 1.739*5.92
σ = 10.295
Hence, the sample standard deviation of a pair of jeans is 10.295
If 75% of a number 60, what is the number?
Answer:
80
Step-by-step explanation:
75 60
------ = ------
100 x
100 x 60 = 6000
75x = 6000
x = 80
Halla x si:
a) 4√5 b) √5 c) 4√3 d) 4 e) 4√2
Answer:
Option A. 4√5
Step-by-step explanation:
To obtain the value of x, we must first obtain the value of y as shown in the attached photo.
The value of y can be obtained by using the pythagoras theory as illustrated below:
In this case y is the longest side i.e the Hypothenus.
y² = 4² + [4√3]²
y² = 4² + [4² × (√3)²]
y² = 4² + [4² × 3]
y² = 16 + [16 × 3]
y² = 16 + 48
y² = 64
Take the square root of both side
y = √64
y = 8
Finally, we shall determine the value of x by using the pythagoras theory as illustrated below.
Note: x is the longest side i.e the Hypothenus in this case.
x² = 4² + 8²
x² = 16 + 64
x² = 80
Take the square root of both side
x = √80
x = √(16 × 5)
x = √16 × √5
x = 4√5
Therefore, the value of x is 4√5.
15. The height and yolume of a cylinder are 4cm and 616cm respectively. Calculate the diameter of the base. (take t = 27 쪽 A. 7cm B. 154cm C. 14cm D. 64cm
Step-by-step explanation:
Given that,
Height of cylinder = 4 cmVolume of cylinder = 616 cm³To find,
Diameter of the base = ?Firstly we'll find the base radius of the cylinder.
[tex]\longmapsto\rm{V_{(Cylinder)} = \pi r^2h}\\[/tex]
According to the question,
[tex]\longmapsto\rm{616= \dfrac{22}{7} \times r^2 \times 4}\\[/tex]
[tex]\longmapsto\rm{616 \times 7 = 22 \times r^2 \times 4}\\[/tex]
[tex]\longmapsto\rm{4312 = 88 \times r^2 }\\[/tex]
[tex]\longmapsto\rm{\cancel{\dfrac{4312}{88}} = r^2 }\\[/tex]
[tex]\longmapsto\rm{49 = r^2 }\\[/tex]
[tex]\longmapsto\rm{\sqrt{49} = r }\\[/tex]
[tex]\longmapsto\rm{7 \; cm = r }\\[/tex]
Now,
[tex]\longmapsto\rm{Diameter = 2r }\\[/tex]
[tex]\longmapsto\rm{Diameter = 2(7 \; cm) }\\[/tex]
[tex]\longmapsto\bf{Diameter = 14 \; cm}\\[/tex]
The required answer is 14 cm.
George buys a pizza he eats 3-8 of pizza for lunch and 1-4 of pizza for dinner what fraction of pizza has George eaten
Answer:
George has eaten 5/8 of the pizza
Step-by-step explanation:
Step 1: Multiple 1/4 by 2 so it shares a common denominator with 3/8
1.4 x 2 = 2/8
Step 2: Because they share a denominator you can add the numerator together
2/8 + 3/8 = 5/8
Therefore George has eaten 5/8(Five Eigths) of the pizza
George has eaten 5 by 8 of the pizza
The calculation is as follows:
Here we have to Multiple 1 by 4 with 2 so it shares a common denominator with 3 by 8
[tex]1.4 \times 2 = 2\div 8[/tex]
Now
since they share a denominator you can add the numerator together
So, [tex]\frac{2}{8} + \frac{3}{8} = \frac{5}{8}[/tex]
Learn more: https://brainly.com/question/17429689?referrer=searchResults
A television screen has a length to width ratio of 8 to 5 and a perimeter of 117 inches. What is the diagonal measure of the screen (to the nearest tenth of an inch)?
Answer:
[tex]D = 42.5\ inch[/tex]
Step-by-step explanation:
Given
[tex]L = Length[/tex] and [tex]W = Width[/tex]
[tex]L:W = 8: 5[/tex]
[tex]Perimeter = 117[/tex]
Required
Determine the Diagonal
First, the dimension of the screen has to be calculated;
Recall that; [tex]L:W = 8: 5[/tex]
Convert to division
[tex]\frac{L}{W} = \frac{8}{5}[/tex]
Multiply both sides by W
[tex]W * \frac{L}{W} = \frac{8}{5} * W[/tex]
[tex]L = \frac{8W}{5}[/tex]
The perimeter of a rectangle:
[tex]Perimeter = 2(L+W)[/tex]
Substitute [tex]L = \frac{8W}{5}[/tex]
[tex]Perimeter = 2(\frac{8W}{5}+W)[/tex]
Take LCM
[tex]Perimeter = 2(\frac{8W + 5W}{5})[/tex]
[tex]Perimeter = 2(\frac{13W}{5})[/tex]
Substitute 117 for Perimeter
[tex]117 = 2(\frac{13W}{5})[/tex]
[tex]117 = \frac{26W}{5}[/tex]
Multiply both sides by [tex]\frac{5}{26}[/tex]
[tex]\frac{5}{26} * 117 = \frac{26W}{5} * \frac{5}{26}[/tex]
[tex]\frac{5 * 117}{26} = W[/tex]
[tex]\frac{585}{26} = W[/tex]
[tex]22.5 = W[/tex]
[tex]W = 22.5[/tex]
Recall that
[tex]L = \frac{8W}{5}[/tex]
[tex]L = \frac{8 * 22.5}{5}[/tex]
[tex]L = \frac{180}{5}[/tex]
[tex]L = 36[/tex]
The diagonal of a rectangle is calculated using Pythagoras theorem as thus;
[tex]D = \sqrt{L^2 + W^2}[/tex]
Substitute values for L and W
[tex]D = \sqrt{36^2 + 22.5^2}[/tex]
[tex]D = \sqrt{1296 + 506.25}[/tex]
[tex]D = \sqrt{1802.25}[/tex]
[tex]D = \sqrt{1802.25}[/tex]
[tex]D = 42.4529150943[/tex]
[tex]D = 42.5\ inch[/tex] (Approximated)
Factor the trinomial below. x^2 + 5x – 24 A. (x – 8)(x + 3) B. (x – 4)(x + 6) C. (x – 3)(x + 8) D. (x – 6)(x + 4)
Answer:
The answer is option CStep-by-step explanation:
x² + 5x - 24
To factorize first write 5x as a difference so that when subtracted will give you 5 and when multiplied will give you - 24
That's
x² + 8x - 3x - 24
Factorize x out
That's
x( x + 8) - 3(x + 8)
Factor x + 8 out
We have the final answer as
(x + 8)(x - 3)Hope this helps you
Answer:(x-3)(x+8)
Step-by-step explanation:
What’s the next number is this series 31,29,24,22,17,
Answer:
15
Step-by-step explanation:
Just find out the pattern. It is decreasing, so let's find out how much it is decreasing by.
31-29= -2
29-24= -5
24-22= -2
22-17= -5
The pattern is -2, -5, -2, -5... So the next one should be -2 again! 17-2=15.
Remember, a pattern doesn't always have to be subtracting, adding, dividing, or multiplying at a constant number! It can switch between two, like this problem!
44,587 plus what equals 65,000
Let the missing number be x.
=> x + 44587 = 65000
=> x = 65000 - 44587
= 20413
Ans.= The missing number will be 20413.
Hope this answer helps you..
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Select it as the BRAINLIEST..
Identifying the Property of Equality
Quick
Check
Identify the correct property of equality to solve each equation.
3+x= 27
X/6 = 5
Answer:
a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication
Step-by-step explanation:
a) This expression can be solved by using the Compatibility of Equality with Addition, that is:
1) [tex]3+x = 27[/tex] Given
2) [tex]x+3 = 27[/tex] Commutative property
3) [tex](x + 3)+(-3) = 27 +(-3)[/tex] Compatibility of Equality with Addition
4) [tex]x + [3+(-3)] = 27+(-3)[/tex] Associative property
5) [tex]x + 0 = 27-3[/tex] Existence of Additive Inverse/Definition of subtraction
6) [tex]x=24[/tex] Modulative property/Subtraction/Result.
b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:
1) [tex]\frac{x}{6} = 5[/tex] Given
2) [tex](6)^{-1}\cdot x = 5[/tex] Definition of division
3) [tex]6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6[/tex] Compatibility of Equality with Multiplication
4) [tex][6\cdot (6)^{-1}]\cdot x = 30[/tex] Associative property
5) [tex]1\cdot x = 30[/tex] Existence of multiplicative inverse
6) [tex]x = 30[/tex] Modulative property/Result
Answer:
3 + x = 27
✔ subtraction property of equality with 3
x over 6 = 5
✔ multiplication property of equality with 6
On Halloween, a man presents a child with a bowl containing eight different pieces of candy. He tells her that she may have three pieces. How many choices does she have
Answer:
[tex]56[/tex] choices
Step-by-step explanation:
We know that we'll have to solve this problem with a permutation or a combination, but which one do we use? The answer is a combination because the order in which the child picks the candy does not matter.
To further demonstrate this, imagine I have 4 pieces of candy labeled A, B, C, and D. I could choose A, then C, then B or I could choose C, then B, then A, but in the end, I still have the same pieces, regardless of what order I pick them in. I hope that helps to understand why this problem will be solved with a combination.
Anyways, back to the solving! Remember that the combination formula is
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex], where n is the number of objects in the sample (the number of objects you choose from) and r is the number of objects that are to be chosen.
In this case, [tex]n=8[/tex] and [tex]r=3[/tex]. Substituting these values into the formula gives us:
[tex]_8C_3=\frac{8!}{3!5!}[/tex]
[tex]= \frac{8*7*6*5*4*3*2*1}{3*2*1*5*4*3*2*1}[/tex] (Expand the factorials)
[tex]=\frac{8*7*6}{3*2*1}[/tex] (Cancel out [tex]5*4*3*2*1[/tex])
[tex]=\frac{8*7*6}{6}[/tex] (Evaluate denominator)
[tex]=8*7[/tex] (Cancel out [tex]6[/tex])
[tex]=56[/tex]
Therefore, the child has [tex]\bf56[/tex] different ways to pick the candies. Hope this helps!
What is the factored form of the binomial expansion x3 + 9x2 + 27x + 27?
(x + 3)3
(x - 3)3
(x + 9)3
(X - 9)3
Answer:
A
Step-by-step explanation:
the factored form of the binomial expansion x^3 + 9x^2 + 27x + 27 is (x+3)^3
solve for x please help! (show work)
Answer:
x = 3/2
Step-by-step explanation:
4/3 ( 3x+9) -2x= 15
Distribute 4/3
4x+12 -2x =15
Combine like terms
2x+12 = 15
Subtract 12 from each side
2x+12-12 =15-12
2x = 3
Divide by 2
2x/2 = 3/2
x = 3/2
Answer:
4/3(3x+9)-2x=15
4x+12+9-2x=15
2x+21=15
2x=-6
x=-3
Let me know if this helps!
I need help please, show work
Answer:
24 and 32 ft or 32 and 24 ft
Step-by-step explanation:
Perimeter of rectangle(p)=2(l+b)
or, 112/2=l+b
Therefore, l+b=56
Now,
diagonal(d)=40
By pythogoras theorem,
h^2=p^2+b^2 (d=h here)
40^2=l^2+b^2
Now,
Square l+b=56
(l+b)^2=56^2
l^2+2lb+b^2=3136
2lb=3136-1600
lb=1536/2
Therefore, lb=768
b=768/l
Now,
Perimeter of rectangle(p)=2(l+b)
l+b=56
l+768/l=56
l^2+768=56l
l^2+768-56l=0
Factoring,
(l - 32) (l - 24) = 0
Either l= 32 or l = 24
When l=32,
l+b=56
32+b=56
b=24
When l=24
l+b=56
24+b=56
b=32
So the dimensions of the dance floor are 24 and 32 ft or 32 and 24 ft.
Answer:
24 ft x 32 ft
Step-by-step explanation:
[tex]2x+2y=112[/tex]
[tex]\sqrt{x^{2}+y^{2} } =40[/tex]
Graph the equations
Find the point where they intersect
Answer is 24 ft and 32 ft
3-(-4) answer the question
Answer:
7Step-by-step explanation:
[tex]3-(-4) \\-\times - = +\\3+4 \\=7[/tex]
Answer:
7
Step-by-step explanation:
because you when multiply -1 by -4 u get positive 4 then 3 + 4 equals 7
BRAINLEST Find the sum of the first 6 terms of the infinite series: 1 - 2 + 4 - 8+...
Answer:
-21
Step-by-step explanation:
1-2+4-8+16-32
=-21
Answer:
The sum of the first 6 terms of the infinite series will be - 21.
Step-by-step explanation:
In this case, the infinite geometric series 1 - 2 + 4 - 8 + ... is represented by the following summation,
[tex]\sum _{{k=0}}^{{n}}(-2)^{k}[/tex]
Therefore if we continue this pattern, the first 6 terms will be 1 - 2 + 4 - 8 + 16 - 32. Adding these terms,
1 - 2 + 4 - 8 + 16 - 32
= - 1 + 4 - 8 + 16 - 32
= 3 - 8 + 16 - 32 = - 5 + 16 - 32
= 11 - 32 = Solution : - 21
Need Assitance
*Show Work*
Answer:
66 2/3 %
Step-by-step explanation:
First find the students not in the 8th grade
24 - 8 = 16
16 students are not in the 8th grade
Take the fraction of the students not in the 8th grade over the total
16/24 = 2/3
Change to a decimal
.66666666666
Multiply by 100 to change to a percent
66.666666%
66 2/3 %
Answer:
66.67% of students are not in eighth grade
Step-by-step explanation:
8/24=1/3
1/3=0.33333333333
1-0.33333333333=0.66666666667
0.66666666667=66.67%