Answer:
the sum is 3m-12
Step-by-step explanation:
The nunbers are:
[tex]m-2\\m-4\\m-6\\the~sum~is:\\sum=(m-2)+(m-4)+(m-6)\\sum=m-2+m-4+m-6=m+m+m-2-4-6\\sum=3m-12[/tex]
The sum of three odd consecutive integers is 3m - 12
What are odd integers?"These are the integers which are not divisible by 2."
For given question,
We need to find the sum of three consecutive odd integers.
Let x, x + 2, x + 4 be three consecutive odd integers.
We have been given the last one is m - 2
This means x + 4 = m - 2
So, the second odd integer would be,
x + 2 = m - 4
and the first odd integer would be,
x = m - 6
, we find the sum of the three odd consecutive integers.
⇒ (m - 6) + (m - 4) + (m - 2)
= m + m + m - 6 - 4 - 2
= 3m - (6 + 4 + 2)
= 3m - 12
Therefore, the sum of three odd consecutive integers is 3m - 12
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what's the answer to this
Answer:
the volume = 1152cm^2
Step-by-step explanation:
> The volume of cylinder =4 spheres
> Volume of sphere = v= 4/3πr³
> radius =6cm
volume of 4 spheres =
[tex]v \: = 4 \times \frac{4}{3} \times \pi \times {6}^{3} \\ \\ v = 1152cm {2} [/tex]
Answer:
the unused volume is 18095,57cm cubed
the sum of the first ten terms of an arithmetic progression consisting of positive integers is equal to the sum of the 20th, 21st and 22nd term. If the first term is less than 20, find how many terms are required to give a sum of 960
Answer:
The correct answer is = 15.
Step-by-step explanation:
Formula:
The sum of the first n terms of an arithmetic progression with first term a and constant difference d is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d[/tex]
using this formula in this problem
Solution:
The sum of the first ten terms is
[tex]S_{10}=\dfrac{10}{2}[2a+(10-1)d[/tex]
[tex]S_{10}=5(2a+9d)[/tex]
The sum of the 20th, 21st, and 22nd terms is three times the 21st term:
[tex]3a_{21}=3(a+(21-1)d)[/tex]
[tex]3a_{21}=3(a+20d)[/tex]
[tex]3a_{21}=3a+60d[/tex]
The problem then tells us
[tex]S_{10}=3a_{21}[/tex]
[tex]10a+45d=3a+60d[/tex]
[tex]7a=15d[/tex]
there are only positive integers and the first term a is less than 20 as given. Since 7 and 15 have no common factor, the only explanation of the requirements is a = 15 and d = 7. So the progression is
then, 15, 22, 29, 36, ...
The problem says to find the number of terms n for which the sum is 960:
putting value in the formula
[tex]30n+7n^{2}-7n=1920\\7n^{2}+23n-1920=0[/tex]
solving quadratic will give n = 15
thus, the correct answer is 15.
3. university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 4 hours. How large a sample must be selected if he wants to be 96% confident of finding whether the true mean differs from the sample mean by 2 hours
Answer:
A sample of 17 must be selected.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.96}{2} = 0.02[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.02 = 0.98[/tex], so Z = 2.054.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The standard deviation from a previous study is 4 hours.
This means that [tex]\sigma = 4[/tex]
How large a sample must be selected if he wants to be 96% confident of finding whether the true mean differs from the sample mean by 2 hours?
A sample of n is required.
n is found for M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 2.054\frac{4}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 2.054*4[/tex]
Simplifying both sides by 2:
[tex]\sqrt{n} = 2.054*2[/tex]
[tex](\sqrt{n})^2 = (2.054*2)^2[/tex]
[tex]n = 16.88[/tex]
Rounding up:
A sample of 17 must be selected.
The following table shows the distribution of people in a tennis tournament, and one
person is to be selected at random.
Find the probability that the selected person is a female.
Express your answer as a decimal, rounded to the nearest hundredth.
Under Age 35
Male 8 Female 18
35 years and older
Male 11 Female18
Answer:
36/55
Step-by-step explanation:
Total 55 persons, total females 36.
The probability that the selected person is a female from the given table is gotten as; 0.65
What is the Probability?
From the given table we see that;
Males under 35 years = 8
Females under 35 years = 18
Males 35 years and older = 11
Females 35 years and older = 18
Thus;
Total number of people = 8 + 18 + 11 + 18
Total people = 55
Thus, probability that the selected person is a female is;
P(female) = (18 + 18)/55
P(female) = 36/55
P(female) = 0.65
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what is the solution to the system of equations below 2x - y = 10 and y=1/2 x+5
Answer:
(10, 10 )
Step-by-step explanation:
Given the 2 equations
2x - y = 10 → (1)
y = [tex]\frac{1}{2}[/tex] x + 5 → (2)
Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)
2x - ([tex]\frac{1}{2}[/tex] x + 5) = 10 ← distribute parenthesis on left side by - 1
2x - [tex]\frac{1}{2}[/tex] x - 5 = 10
[tex]\frac{3}{2}[/tex] x - 5 = 10 ( add 5 to both sides )
[tex]\frac{3}{2}[/tex] x = 15 ( multiply both sides by 2 to clear the fraction )
3x = 30 ( divide both sides by 3 )
x = 10
Substitute x = 10 into (2) and evaluate for y
y = [tex]\frac{1}{2}[/tex] (10) + 5 = 5 + 5 = 10
solution is (10, 10 )
Say you buy halibut at $19 per pound . One portion of seared halibut requires 6 ounces of halibut . How much does the halibut for one portion cost ? Round to the nearest cent .
Answer:
$7.13
Step-by-step explanation:
Given data
Cost of halibut per pound= $19
Let us convert pound to ounces first
1 pound = 16 ounces
Hence 16 ounces will cost $19
6 ounces will cost x
cross multiply we have
x= 19*6/16
x=114/16
x=$7.13
Hence 6 ounces will cost $7.13
Help!! Picture included
Answer:
The answer is the last option- the fourth root of 16x^4.
Step-by-step explanation:
(16x^4)^(1/4) = 2*abs(x).
Whenever you are dealing with a square root of a variable, if you have an even root and get out an odd power, you're going to need to always include an absolute value.
Is [0,2) is compact in R?
Answer:
no it is not compact in R
A circle has a circumference of 2cm. Which statement about the circumference and area is true?
A comparison of the area and circumference is not possible since the area cannot be determinec
The numerical values of the circumference and area of the circle are equal.
The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
ОО
Answer:
The numerical values of the circumference and area of the circle are equal.
15. The area of a triangle is 72 in the base is 12 in. Find the height.
Answer:
[tex]hright =12[/tex]
Step-by-step explanation:
----------------------------------------
The formula to find the area of a triangle is [tex]A=\frac{1}{2}bh[/tex] where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.
But we already know the area and the base. So to find the height, let's substitute 72 for [tex]A[/tex] and 12 for [tex]b[/tex], and solve.
[tex]72=\frac{1}{2}(12)(h)[/tex]
[tex]72=6h[/tex]
Here, divide both sides by 6
[tex]12=h[/tex]
--------------------
Hope this is helpful.
Answer:
height = 12
Step-by-step explanation:
.............
Yess again pls help!
Tyyy
Drag the label to the correct location on the image
9514 1404 393
Answer:
-∞ < y ≤ 12
Step-by-step explanation:
The range is the vertical extent of the graph of the function. Here the function values range from -∞ to a maximum of about 12. An appropriate description is ...
-∞ < y ≤ 12
pls help with all the questions
Answer:
Step-by-step explanation:
Since, CD is an altitude, ∠CDB will be a right angle.
m∠CDB = m∠CDA = 90°
By applying triangle sum theorem in ΔABC,
m∠CAB + m∠CBA + m∠ACB = 180°
20° + m∠CBA + 90° = 180°
m∠CBA = 180° - 110°
= 70°
Therefore, m∠CBD = 70°
By applying triangle sum theorem in ΔBCD,
m∠BCD + m∠CDB + m∠DBC = 180°
m∠BCD + 90° + 70° = 180°
m∠BCD + 160° = 180°
m∠BCD = 20°
m∠CAD = m∠A = 20°
m∠ACD = 90° - m∠BCD
= 90° - 20°
m∠ACD = 70°
i’ll give brainliest to the right answer
Answer:
First one , 0.0000805
Step-by-step explanation:
With negative exponents the decimal is moved to the left the amount of the exponent. The spaces are filled with zeros.
With positive exponents the opposite occurs. The decimal moves to the right.
7/3a - 8/5 +4/15a
Simplified
Answer:
13/5a - 8/5
Step-by-step explanation:
= 35/15a + 4/15a - 8/5
= 39/15a - 8/5
= 13/5a - 8/5
The simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that the expression is,7/3a - 8/5 +4/15a.
We have to simplify the expression.
We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
=7/3a - 8/5 +4/15a
= 35/15a + 4/15a - 8/5
= 39/15a - 8/5
= 13/5a - 8/5
Thus, the simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.
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PLEASE HELP SOON Find the value of x. Round to the nearest tenth. 27° х 34° 11 X = ? [?] 9 Law of Sines: sin A sin C sin B b a Enter
The picture of the problem has been attached below :
Answer:
13.5
Step-by-step explanation:
Applying the sine rule to solve for x
SinA /a = SinB / b = SinC/ c
Sin 34 / x = Sin 27/11
Cross multiply :
11 * sin34 = x * sin 27
6.1511219 = 0.4539904x
Divide both sides by 0.4539904
6.1511219/0.4539904 = x
13.549 = x
x = 13.5
No more than one state of nature can occur at a given time for a chance event. This indicates that the states of nature are defined such that they are
a. conservative events.
b. mutually exclusive.
c. independent outcomes.
d. collectively exhaustive.
Answer:
b. mutually exclusive.
Step-by-step explanation:
The given description is an illustration of mutually exclusive events.
Take for instance, when you roll a die;
It is impossible to have an outcome of 2 and 6 at the same time; these means that 2 and 6 are mutually exclusive.
In a nutshell, when two or more sates of events/states of nature can not happen at the same time; such events/states of nature are mutually exclusive.
Need help putting the answer in
Step-by-step explanation:
We can rewrite the given equation as
[tex]x^2 + \frac{1}{5}x - \frac{12}{25} = (x + \frac{4}{5})(x - \frac{3}{5})[/tex]
As a check, let's multiply out the factors:
[tex](x + \frac{4}{5})(x - \frac{3}{5}) = x^2 - \frac{3}{5}x + \frac{4}{5}x - \frac{12}{25}[/tex]
[tex]= x^2 + \frac{1}{5}x - \frac{12}{25}[/tex]
and this is our original equation.
what is the approximate value of x in the diagram below?
Answer:
Where is the diagram though..
Step-by-step explanation:
Let v=-9i+j and w=-i-6j find 8v-6w
Answer:
78i+52j
Step-by-step explanation:
8(9i+2j)-6(-i-6j)
72i+16j+6i+36j
=78i+52j
The graph shows the distance Liam traveled from school in miles (y) as a function of time in seconds (x). The graph is divided into four segments labeled P, Q, R, and S, respectively.
Graph shows 4 segments. Segment P is a horizontal straight line. Segment Q is a slanting straight line going up. Segment R is a slanting line going up. Segment S is a slanting straight line going down that touches the x-axis.
Which segment shows Liam waiting for a cab? (5 points)
Select one:
a. P
b. Q
c. R
d. S
Answer:
P
Step-by-step explanation:
Since we are looking at an f(x) graph where x is time and y is distance. Any time a graph is sloping we are either moving closer or further from the school. When there is a horizontal line, this means that there is no change in distance, thus Liam is waiting/standing still.
Answer:
a. P
Step-by-step explanation:
i took the test :)
if f(x)=-5^x-4 and g(x)=-3x-2,find (f+g) (x)
Answer: (f-g)(x) = - 5^x + 3x - 2
Step-by-step explanation:
if f(x) = -5^x - 4 and g(x)= - 3x - 2,find (f-g)(x)
(f-g)(x) = -5^x - 4 - (-3x - 2)
(f-g)(x) = -5^x - 4 + 3x + 2
(f-g)(x) = - 5^x + 3x - 2
how do you find the slope of -2
4. The average salary for public school teachers for a specific year was reported to be $39,385. A random sample of 50 public school teachers in a particular state had a mean of $41,680, and the population standard deviation is $5975. Is there sufficient evidence at the a _ 0.05 level to conclude that the mean salary differs from $39,385
Answer:
The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385
Step-by-step explanation:
The average salary for public school teachers for a specific year was reported to be $39,385. Test if the mean salary differs from $39,385
At the null hypothesis, we test if the mean is of $39,385, that is:
[tex]H_0: \mu = 39385[/tex]
At the alternative hypothesis, we test if the mean differs from this, that is:
[tex]H_1: \mu \neq 39385[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
39385 is tested at the null hypothesis:
This means that [tex]\mu = 39385[/tex]
A random sample of 50 public school teachers in a particular state had a mean of $41,680, and the population standard deviation is $5975.
This means that [tex]n = 50, X = 41680, \sigma = 5975[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{41680 - 39385}{\frac{5975}{\sqrt{50}}}[/tex]
[tex]z = 2.72[/tex]
P-value of the test and decision:
The p-value of the test is the probability that the sample mean differs from 39385 by at least 2295, which is P(|Z| > 2.72), which is 2 multiplied by the p-value of Z = -2.72.
Looking at the z-table, Z = -2.72 has a p-value of 0.0033
2*0.0033 = 0.0066
The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385
Can someone please help me
Answer:
sorry I can't help you sorry
Answer:
c
Step-by-step explanation:
A reflection in the x- axis of the parent function is - [tex]\sqrt{x}[/tex]
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here the shift is 3 units up , then
g(x) = - [tex]\sqrt{x}[/tex] + 3
A teacher is paid an annual salary of $37.165. What is her gross monthly salary.
Answer:
3.01
Step-by-step explanation:
To Find :-
Monthly salary .SOLUTION :-
=> Monthly salary = $ 37.165/12= $ 3.01
Private nonprofit four-year colleges charge, on average, $26,208 per year in tuition and fees. The standard deviation is $7,040. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(
26208
Correct,
7040
Correct)
b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 22,924 per year.
c. Find the 60th percentile for this distribution. $
(Round to the nearest dollar.)
Answer:
#########
Step-by-step explanation:
Round your answer to the nearest hundredth.
3
А
с
?
8
B
HELP!!!
Answer:
Step-by-step explanation:
This appears to be an SSA application of solving the triangle
We have 2 sides, so we will use the law of cosines
The law of cosines defines for a triangle ABC with side a/b/c with corresponding angles A/B/C
a^2 = b^2+c^2 - 2*b*c * (cos A)
this applies to the other 2 sides
first using the pythagorean theorem we find that BC = sqrt(55)
then we substitute all 3 sides into our equation to find angle A
55 = 64 + 9 - 2*8*3* (cos A)
18 = 2*8*3(cos A)
3/8 = (cos A)
and angle A is approximately 68 degrees
Please check if I'm correct
Answer:
67.98°
Step-by-step explanation:
Given 2 sides, you can find the missing angle of a right triangle using basic trig functions.
Since Cos∅=adjacent/ hypotenuse, we can use the adjacent side to the angle, 3 and they hypotenuse, 8 in the ratio by doing 3/8. This is 0.375. Then we use the inverse cosine function to find the angle. This gives 67.98°
Or
Cos∅=0.375
Cos^-1= 67.98
A cylinder with radius 3 meters and height 7 meters has its radius tripled. How many times greater is the volume of the larger cylinder than the smaller cylinder?
How many times greater is the volume of the larger cylinder than the smaller cylinder?
Please help :)
Answer:
9x
Step-by-step explanation:
Quick maths, I dont really have an explaination pls give me brainliest ;-;.
The 2010 GSS provides the following statistics for the average years of education for lower-, working-, middle-, and upper-class respondents and their associated standard deviations. Assume that years of education are normally distributed in the population. Mean Standard Deviation N Lower-class 11.61 2.67 123 Working-class 12.80 2.85 697 Middle-class 14.45 3.08 626 Upper-class 15.45 2.98 38 How many years of education correspond to a Z score of +1.2 for upper-class respondents?
Answer:
The answer is "18.087 years".
Step-by-step explanation:
For upper class:
[tex]\mu=15.45 \ years\\\\\alpha=2.98 \ years\\\\[/tex]
[tex]P(Z \leq 1.2)[/tex] from the standard normal distribution on the table:
[tex]P(Z \leq 1.2) =0.8849\\\\x=z_{\alpha}+\mu\\\\[/tex]
[tex]=0.8849 \times 2.98 +15.45\\\\ = 2.637002+15.45 \\\\=18.087 \ \ years\\[/tex]