Answer:
the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days
Step-by-step explanation:
Given that :
Mean = 265
standard deviation = 14
The formula for calculating the z score is [tex]z = \dfrac{x -\mu}{\sigma}[/tex]
x = μ + σz
At middle of 50% i.e 0.50
The critical value for [tex]z_{\alpha/2} = z_{0.50/2}[/tex]
From standard normal table
[tex]z_{0.25}=[/tex] + 0.67 or -0.67
So; when z = -0.67
x = μ + σz
x = 265 + 14(-0.67)
x = 265 -9.38
x = 255.62
when z = +0.67
x = μ + σz
x = 265 + 14 (0.67)
x = 265 + 9.38
x = 274.38
the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days
classify the following triangle
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!
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
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
Consider various ways of ordering the letters in the word TENNESSEE. TENENESES, EESSENNET, TNNEESSEE, and so on. (a) How many distinguishable orderings are there
Answer:
3780.
Step-by-step explanation:
To solve this we will start by just considering the number of ways to arrange 9 objects. We can do this in 9! ways.
However since we have 3 reoccurring letters in Tennessee namely n,s and e we need to remove the times these form the same arrangement. Let me give an example to show what this means. Lets say we have the arrangement:
ennetssee
Now what happens if we exchange the places of the letters n for example? Of course we get the same arrangement of letters. We don’t want to count these as 2 different arrangements since for our interests they are the same. We therefore divide 9! by the number of times this type of double counting occurs.
Since the word has the letter n occurring twice we will start by diving by 2! .
The letter s occurs 2 times as well so we will have to divide by 2! again.
Finally the letter e occurs 4 times and so we will have to divide by 4! here.
Now we get the following result:
9/(2 x 2 x 4)=3780.
So in conclusion there are 3780 different ways to arrange the letters in Tennessee.
Find usubscript10 in the sequence -23, -18, -13, -8, -3, ...
Step-by-step explanation:
utilise the formula a+(n-1)d
a is the first number while d is common difference
Answer:
22
Step-by-step explanation:
Using the formular, Un = a + (n - 1)d
Where n = 10; a = -23; d = 5
U10 = -23 + (9)* 5
U10 = -23 + 45 = 22
The graph of g(x) is the result of translating the graph of f(x) = (one-half) Superscript x three units to the left. What is the equation of g(x)?
Answer:
[tex]g(x) = 0.5^{(x+3)}[/tex]
Step-by-step explanation:
Assuming f(x) = [tex]0.5^{x}[/tex] is a correct interpretation of f(x),
the way to translate three units to the left is to change x to x+3. This gives our answer: [tex]g(x) = 0.5^{(x+3)}[/tex]
Answer:
B. g(x) = (1/2)⁽ˣ⁺³⁾
Hope this helps!
Step-by-step explanation:
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%
Can anyone please help me with this ?
Answer:
6.7
Step-by-step explanation:
The formula for volume is V=lwh.
320=(6)(8)x
Solve.
320=48x
Divide both sides by 48.
6.6666666=x
Round to the nearest tenth.
x=6.7
I hope this helps!
pls ❤ and give brainliest pls
Answer:
6.7 =x
Step-by-step explanation:
The volume is given by
V = l*w*h
320 = 8*6*x
320 =48x
Divide each side by 48
320/48 = 48x/48
6.6666666 = x
Rounding to the nearest tenth
6.7 =x
75% increase followed by 50% decrease is it greater than to original
Answer:
Set original amount = xAfter a 75% increase, it would become
x + 75%x = x + 0.75x = x(1 + 0.75) = 1.75x
After a 50% decrease, it would become
1.75x - 50%(1.75x) = 1.75x - 0.5(1.75x) = 1.75x - 0.875x = 0.875x = [tex]\frac{7}{8} x[/tex]
Because [tex]\frac{7}{8} x[/tex] is less than x, the new amount would be less than the original.
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
If 3, 9, 10, x are in proportion find the value of x.
Answer:
[tex]x = 30[/tex]
Step-by-step explanation:
If 3, 9, 10, x are in proportion. Then,
[tex]x \times 3 = 10 \times 9[/tex]
[tex]x \times 3 = 90[/tex]
[tex]x = \frac{90}{3} [/tex][tex]x = 30[/tex]
Hope it is helpful.....Step-by-step explanation:
Given that 3, 9, 10, x are in proportion <br> product of exterms = Product of means <br>
<br>
3x=9×10
X=(9x10)/3
X=90/3
X=30
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..
..
..
Select it as the BRAINLIEST..
After basketball practice, Courtney spent extra time working on free throws. Overall, she made 3 of her 5 shots. What percent of her total shots did she make?
Answer:
I know the answer
Step-by-step explanation:
Courtney made 60% of her shots
Answer:
she made a 60%
Step-by-step explanation:
first you do this 3÷5
that gives you .60
inorder to get a percent multiply by 100
that gives you an end result of 60
add the percent sing and your done 60%
hope i helped
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
How is the next term in this sequence found?
−6, −4, −2, 0, 2
A)
A) Add 2 to the previous term.
B) Add −2 to the previous term.
C) Multiply the previous term by 2.
D) Multiply the previous term by −2.
Answer:
add 2 to every privious term
Step-by-step explanation:
-6+2=-4
-4+2=-2
-2+2=0
0+2=2
What is the value of X
A 15
B 21
C 26
D 105
Answer:
B)21
Step-by-step explanation:
∠KN=∠ML
∠KN=90°+15°
=105°
∠ML=105°
5x°=105°
x°=105÷5
x°=21°
Answer:
[tex]5x=90+15[/tex]
Add, 90 + 15 = 105
[tex]5x=105[/tex]
Divide both sides by 5
[tex]\frac{5x}{5}=\frac{105}{5}[/tex]
[tex]x=21[/tex]°
[tex]\textbf{OAmalOHopeO}[/tex]
What temperature is 10 degrees les then 6 degrees Celsius
Answer:
-4
Step-by-step explanation:
you say 6-10
which is -4
What is the temperature if 10°C less than 6°C
Answer:-10°C less than 6°C is -4°C
Explanation:
So, if we start with 6°C, and we want a temperature 10°C less than that, then we can just subtract 10 from 6.
6-10 = -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
Factor the expression completely. 6×3- 4×2 – 16x A. 0 B. 2x(3×2 – 2x – 8) C. 2x(3x + 4)(x – 2) D. 4x(2x + 1)(x – 4) E. 2x(2×2 + 7x – 4) ill give brainliest
Answer:
The answer is option CStep-by-step explanation:
6x³ - 4x² - 16x
To factorize the expression first factor out the GCF out
The GCF in the expression is 2x
That's
2x( 3x² - 2x - 8)
Next Factorize the terms in the bracket
To factorize write - 2x as a difference
that's
2x( 3x² + 4x - 6x - 8)
Factor out x from the expression
2x [ x( 3x + 4) - 6x - 8 ]
Next factor out - 2 from the expression
2x [ x ( 3x + 4) - 2( 3x + 4) ]
Factor out 3x + 4 from the expression
We have the final answer as
2x( 3x + 4)( x - 2)Hope this helps you
This graph describes which of the expressions given?
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.
Find the area of the triangle.
[? ] ft2
Don't round
Step-by-step explanation:
[tex]Area = \: \frac{bh}{2} \\ : b = 16.9 \: h = 10.4 \\ [/tex]
[tex]Area = \frac{16.9 \times 10.4}{2} = \frac{175.76}{2} = 87.88 {ft}^{2} [/tex]
Base = 16.9
height = 10.4
Area = ½b×h
A = ½(16.9×10.4)
A = ½(175.76)
Area = 175.76/2
A = 87.88ft²
Answer:
[tex]\Large \boxed{\mathrm{87.88 \ ft^2 }}[/tex]
Step-by-step explanation:
[tex]\displaystyle area \ of \ triangle \ = \ \frac{base \times height }{2}[/tex]
[tex]\displaystyle area \ of \ triangle \ = \ \frac{16.9 \times 10.4 }{2}[/tex]
[tex]\displaystyle area \ of \ triangle \ = \ \frac{175.76}{2}[/tex]
[tex]\displaystyle area \ of \ triangle \ = \ 87.88[/tex]
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
1106.666667 to the nearest whole number
Answer:
1106.666667 to the nearest whole number
1107
Answer:
1106.666667 rounds to 1107
Step-by-step explanation:
We look at the whole number, 6
Then look at the tenths place .6
Since 6 is greater than or equal to 5, we round the whole number up one place to 7
1106.666667 rounds to 1107
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!
one third multiplied by the sum of a and b
Answer:
1/3(a+b)
hope it helps :>
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!
A computer is priced at $2,000. If the sales tax rate is 7.5%, find the total cost of the
computer
please help:((
Answer:
it would just be 2000 * 1.075
Step-by-step explanation:
2150
Price = $2000
Sales tax
= 7.5% of Price
= 7.5% of $2000
= (7.5/100) × $2000
= 0.075 × $2000
= $150
Total price
= Price + Sales tax
= $2000 + $150
= $2150
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.