the sum of three consecutive even numbers is 114 what's the smallest of these numbers​

Answers

Answer 1

Answer:

36

Step-by-step explanation:

consecutive even numbers are 2,4, 6...

Let the smallest of the 3 numbers be x.

2nd number= x+2

3rd number

=x+2+2

= x+4

sum of the 3 numbers= x +x+2 +x+4

114= 3x+6

3x= 114 -6 (-3 on both sides)

3x= 108 (simplify)

x= 108 ÷3

x= 36

Thus, the smallest number is 36.

Let's check!

36+38+40= 114 ✓


Related Questions

True or False: The height is always twice the length of tue base edge of any triangular pyramid.

Answers

Answer:

true

Step-by-step explanation:

3n3n3p0mdo98rueu33

Pls help with this one I will give brainliest thank you!

Answers

Answer:

B. 10 in.

Step-by-step explanation:

When you do length times width times height 10*10*10 equals 1000

10*10=100 and 100*10=1000

Answer:10 feet

Step-by-step explanation:

edge=[tex]\sqrt[3]{1000}[/tex]= 10 so the answer is B

Simon knows that 25% of the people at a movie theater are seeing a romantic comedy. How many people are at the movie theater if 55 people are seeing a romantic comedy?

Answers

Answer:

220

Step-by-step explanation:

Number of people in theater = x

25% * x = 55

x = 55 / 25% = 55 / 25 * 100 = 55 * 4 = 220

HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.

Answers

Answer:

In this case, you should check the x-intercept (y = 0).

=> (x-3)(x+4) = 0

=> Two x-intercept at x = 3 and x = -4

C, D are  not right, because there is no two x-intercepts.

A is not correct, because both of x-intercepts are less than 0.

=> Option B is correct.

Hope this helps!

:)

:
What is 475.189 rounded to the nearest hundredth?

Answers

Answer:

It is:475.19.

HOPE THIS HELPED

Answer:

475.19.

Step-by-step explanation:

The hundredths place is two places to the right of the decimal, or (0.01).

In the number given, the number to the right of the hundredths place is larger than 5, meaning we will round up giving us:

475.189 --> 475.19.

Tommy purchased a new vacuum for $1,150 at the Best Buy. He has a 15% coupon. How much will he save?

Answers

Answer:

$172.50

Step-by-step explanation:

1150 * 0.15 = 172.5

Answer:

the answer is 172.50

Step-by-step explanation:

So is the price for the the vacuum 1.150 and the coupon is 15% then u multiply them and get 172.50 which is your answer

Step-by-step explanation

1150 * 0.15 = 172.5

If it was helpful can u mark me brainliest pls!!!!!!!!!!!

Graphs of what functions are shown below?

Answers

Answer:

 y = -√(x -5) +2

Step-by-step explanation:

This looks like a square root function reflected vertically, and translated up 2 and right 5.

 y = -√(x -5) +2

_____

g(x) = a·f(x -h) +k   represents a translation of f(x) by (h, k) and a vertical scaling by a factor of "a". If "a" is negative, the function is reflected across the x-axis.

اذا كانت س زاويه حاده و كان جاس= ٣/٥ فان ظا س=؟؟​

Answers

Alright idk y u said that here but ok

What is the length of AC?

Answers

Answer:

2.96

Step-by-step explanation:

The cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse. In this case:

[tex]\cos 65=\dfrac{x}{7}[/tex]

[tex]x=7\cdot \cos 65\approx 2.96[/tex]

Hope this helps!

I keep gettin it wrong please help!!!

Answers

Answer:

-5≤ x ≤5 or [-5,5]

Step-by-step explanation:

domain is related to independent variable x

black dots means that number is included in the domain

in this case function is from -5,5 included or -5≤ x ≤5 or [-5,5]

what is the result of 3×3/5×(-8×1/3)

Answers

Answer:

-4.8

Step-by-step explanation:

Answer:

−24/5

Step-by-step explanation:

3x3/5x(-8x1/3)

Use the order of operations method, PEMDAS, in order to solve this expression.

U
14 poi
At the college football game there were 48,000 people. If 77% of the
people at the game were supporters for the home team, how many
people were supporting the home team? *

Answers

Answer:

36960 people

Step-by-step explanation:

Answer:

36,960 people

Step-by-step explanation:

[tex]\frac{is}{of}=\frac{percent}{100}[/tex] is the formula to solve for this equation, here plugging in all our numbers gives us [tex]\frac{x}{480,000} = \frac{77}{100}[/tex].

We do not know our "is" so we replace it for x and solve → [tex]x=(480,000)(\frac{77}{100} )[/tex] = 36,960 people

Factor the expression. d2 + 12d+ 36

Answers

Answer:

the factored expression is

(d+6)(d+6) or (d+6)^2

Step-by-step explanation:

Ten cards numbered from 1 to 10 inclusive are placed in a hat Irene takes a card out of the hat without looking what is the probability that she takes out:
A] the number 10
B] an odd number
C] a number greater than 4
D] a prime number
E] a number between 5 and 9?

Answers

A] 1/10
B] 5/10
C] 6/10
D] 4/10
E] 3/10

five more than the quotient of y and 2 is -3

Answers

Answer:

y/2 + 5 = -3

y/2 = -8

y = -16

Step-by-step explanation:

Write the slope-intercept form of the equation of the line through (-1,4) and parallel to x=5

Answers

Answer:

x = -1

Step-by-step explanation:

When lines are parallel, they have the same slope

x = 5 means the line is a vertical line going through x=5

The new line is a vertical line

We have a point (-1,4)

It will need to go through the x point of -1 and be a vertical line ( which is in the form x=  )

x=-1

A circle has a circumference that is greater than 8 meters. The inequality 3.14 d greater-than 8 can be used to determine the possible lengths of the diameter of the circle. What are the possible values of d, the length of the diameter in meters?
d less-than 25.1
d greater-than 25.1
d less-than 2.5
d greater-than 2.5

Answers

Answer:

It is the last one

Step-by-step explanation:

Answer:

it is d

Step-by-step explanation:

Two datasets arranged in descending order are; {8, x, 4,1} and {9, y, 5,2}. If the medians of
the two given datasets are equal, what is the value of (y − x)
2
?

Answers

Answer:

1

Step-by-step explanation:

A data arranged in descending order is a data arranged from the biggest to the smallest. The medisn of the data sets is the value at the middle of the dataset after rearrangment.

For the dataset {8, x, 4,1}, the median will be x and 4. Since we have two median values, we will take their average as shown

Median(1) = [tex]\frac{x+4}{2}[/tex]... 1

Simialrly for dataset {9, y, 5,2}, the median will be y and 5.

Median(2) = [tex]\frac{y+5}{2}[/tex] ...2

Since the medians of  the two given datasets are equal, we will equate equation 1 and 2 and calculate for y-x as shown;

[tex]\frac{x+4}{2} = \frac{y+5}{2}[/tex]

[tex]x+4 = y+5\\x-y = 5-4\\x-y = 1\\y-x = -1[/tex]

Therefore y-x = -1

(y-x)² = (-1)²

= 1

A 95​% confidence interval of 17.6 months to 49.2 months has been found for the mean duration of​ imprisonment, mu​, of political prisoners of a certain country with chronic PTSD. a. Determine the margin of​ error, E. b. Explain the meaning of E in this context in terms of the accuracy of the estimate. c. Find the sample size required to have a margin of error of 11 months and a 99​% confidence level.​ (Use sigmaequals45 ​months.) d. Find a 99​% confidence interval for the mean duration of​ imprisonment, mu​, if a sample of the size determined in part​ (c) has a mean of 36.5 months.

Answers

Answer:

a) [tex] E = \frac{49.2-17.6}{2}= 15.8[/tex]

b) For this case we have 95% of confidence that the true mean would be between [tex]\pm 15.8[/tex] units respect the true mean.

c) [tex]n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112[/tex]

So the answer for this case would be n=112

d) [tex]36.5-2.58\frac{45}{\sqrt{112}}=25.53[/tex]    

[tex]36.5+2.58\frac{45}{\sqrt{112}}=47.47[/tex]

Step-by-step explanation:

Part a

For this case we know that the cinfidence interval for the true mean is given by:

[tex] \bar X \pm E[/tex]

Where E represent the margin of error. For this case we have the confidence interval at 95% of confidence and we can estimate the margin of error like this:

[tex] E = \frac{49.2-17.6}{2}= 15.8[/tex]

Part b

For this case we have 95% of confidence that the true mean would be between [tex]\pm 15.8[/tex] units respect the true mean.

Part c

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =11 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The critical value would be [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112[/tex]

So the answer for this case would be n=112

Part d

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

Replcaing the info given we got:

[tex]36.5-2.58\frac{45}{\sqrt{112}}=25.53[/tex]    

[tex]36.5+2.58\frac{45}{\sqrt{112}}=47.47[/tex]

given h(x)=-2x+5, find h(-6)

Answers

This question is easy! it's simply asking to plug in -6 instead of the variable x.

h(-6)=-2(-6)+5

       =12+5

       =17

17 is your final answer.

Fernanda is filling a cylindrical pot with cans of vegetable soup. The pot has a diameter of 15 in. and a height of 10 in. The soup can has a diameter of 4 in. and a height of 5 in. How many cans of soup will it take to fill up the pot?

Answers

Answer:

28.125 cans

Step-by-step explanation:

Step 1: Determine the Volume of the Pot

Diameter= 15 inches, therefore Radius=15/2=7.5 Inches

Height =10 Inch

Volume of a cylinder =[tex]\pi r^2h[/tex]

Volume of the Pot [tex]=\pi*7.5^2*10=562.5\pi[/tex] cubic inches.

Step 2: Determine the Volume of each can

Diameter= 4 inch, therefore Radius=4/2=2 Inches

Height =5 In.

Volume of a cylinder =[tex]\pi r^2h[/tex]

Volume of one can [tex]=\pi*2^2*5=20\pi[/tex] cubic inches.

Step 3: Divide the Volume of the Pot by the Volume of the can

To obtain the number of cans that will fill the pot, we divide the Volume of the Pot by the Volume of the can.

Volume of the Pot÷Volume of one can

[tex]=562.5\pi \div 20\pi\\=28.125 \:cans[/tex]

Therefore, we conclude that it takes 28.125 cans to fill up the cylindrical pot of soup.

Audrey collected 4⁄5 pint of blueberries. Addison collected 12 times as many pints of blueberries as Audrey. How many pints of blueberries did Addison collect?

Answers

Answer:

48/5≈ 9 3/5

Step-by-step explanation:

12 is the same thing as 12/1

so your multiply fractions

4/5 times 12/1

numerator=top

denominator=bottom

so to multiply a fraction you multiply the numerator times the numerator

so in that case your multiplying 4 times 12

=48

to find the bottom half you multiply the denominator times the denominator

in that case is 5 times 1

=5

numerator/denominator

48/5

if you want to simplify it further simply divide 48/5

5 goes into 48 about 9 times

and were left with 3/5

so 9 and 3/5

pls mark me brainliest

Math Help!!! Can someone solve this?? I will give you Brainliest!!!!!!

Answers

Answer:first one is false, second is true and third is true

Step-by-step explanation:

Not sure on how to do these questions

Answers

Answer:f(8)=g(8)

Step-by-step explanation:

So in these problems f(8) means that you look at the f(x) function (function 1) and plug in 8 for x.  Then since it says g(8), you look at the g(x) function and substitute x for 8.  If we do that, f(x)=2(8)-3 which is 13.  g(x)=3/2x+1=13.  The two of them are equal when x=8.  So the answer is the third choice

Answer:

f(8)=g(8)

Step-by-step explanation:

Just put the values of given functions in the equation

word problem of addition or subtraction

Answers

Answer:

subtraction

Step-by-step explanation:

In order to find out how many more flowers you need, you need to subtract both of the numbers to get the difference.

Answer:19

Step-by-step explanation:subtract 27 from 8.

Pete's checking account showed a balance at the beginning of the month of $180. After 3 days the checking account showed a balance of $160. Write a linear equations to represent the total in the checking account f(x) according to the day x.

Answers

Answer:

180 - 172 =$8 8/3=2.56

Which equation describes a line of symmetry for a square ABCD?

Answers

Answer:

y=x

Step-by-step explanation:

The equation of the line is line DB

From y=mx + c

From the graph y = 0 when x =0

This means y=x;

The graph cuts through the origin.

Meaning the y -intercept C=0

. The pet store salesman told Evan to feed his dog 8 ounces of food per day. The food is sold in pounds. How many pounds does Evan need to buy for 2 weeks of feeding his dog? (16 ounces = 1 pound)?

Answers

It’s 7 pounds. 8 ounces per day then multiply that by 7 days which is 56 ounces then multiply 56 by 2 which makes 112, then multiply 112 by 16 which stands for ounces and you get 7.

An elementary ntimesn scaling matrix with k on the diagonal is the same as the ntimesn identity matrix with _______ exactly one at least one all of the ______ 0's 1's replaced with some number k. This means it is _______ an invertible matrix, a zero matrix, a singular matrix, a triangular matrix, an identity matrix, and so its determinant is the _______ sum product of its diagonal entries.​ Thus, the determinant of an elementary scaling matrix with k on the diagonal is nothing.

Answers

Answer:

exactly one, 0's, triangular matrix, product and 1.

Step-by-step explanation:

So, let us first fill in the gap in the question below. Note that the capitalized words are the words to be filled in the gap and the ones in brackets too.

"An elementary ntimesn scaling matrix with k on the diagonal is the same as the ntimesn identity matrix with EXACTLY ONE of the (0's) replaced with some number k. This means it is TRIANGULAR MATRIX, and so its determinant is the PRODUCT of its diagonal entries.​ Thus, the determinant of an elementary scaling matrix with k on the diagonal is (1).

Here, one of the zeros in the identity matrix will surely be replaced by one. That is to say, the determinants = 1 × 1 × 1 => 1. Thus, it is a a triangular matrix.

help help help please

Answers

Answer:

to add to the table, continue the arithmetic sequence in each columnto use the table, extend the third column to 45, or multiply the first row by 9

Step-by-step explanation:

The numbers in the first column are an arithmetic sequence with a common difference of 2. The next few numbers will be 6, 8, 10, ...

The numbers in the second column are an arithmetic sequence with a common difference of 3. The next few numbers will be 9, 12, 15, ...

The numbers in the third column are an arithmetic sequence with a common difference of 5. The next few numbers will be 15, 20, 25, ...

To use the table, Mark can extend each sequence until he has a row with 45 in the third column, or he can multiply or add rows to give a result of 45 in the third column. For example, multiplying the first row by 9 gives 18:27:45 meaning that Mark needs 18 liters of blue and 27 liters of yellow to make 45 liters of green paint.

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