SOLUTION
TO DETERMINE
84 as a product of primes.
Use index notation to write the number
EVALUATION
Here the given number is 84
We prime factorise the given number
84 = 2 × 2 × 3 × 7
Number of 2's = 2
Number of 3's = 1
Number of 7's = 1
Rewriting the given number in index form we get
━━━━━━━━━━━━━━━━
Learn more from Brainly :-
The difference between face value and place value of 5 in 2,10,519
brainly.in/question/22495648
2. if one bee drinks 1ml honey then how much honey 1000 bees will drink??
Which side is adjacent to Angle Q?
48
14
50
Answer: 48
Step-by-step explanation: 50 is the hypotenuse
14 is the opposite side - its opposite of angle Q
The distribution of the number of words in text messages between employees at a large company is skewed right
with a mean of 8.6 words and a standard deviation of 4.3 words. If a random sample of 39 messages is selected,
what is the probability the sample mean is more than 10 words?
0.0210
0.2454
0.3724
0.9790
The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The z score is given by:
z = (raw score - mean) / (standard deviation / √sample size)
Given mean of 8.6 words and a standard deviation of 4.3 words. If a random sample of 39 messages, hence, for x > 10:
z = (10 - 8.6) / (4.3 / √39) = 2.03
P(x > 10) = P(z > 2.03) = 1 - P(z < 2.03) = 1 - 0.9788 = 0.0212
The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%
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Answer:
A. .0210
Step-by-step explanation:
I'm taking the test... could be wrong though...
Solve the following system of equations algebraically.
x+y=27
y=x+3
*first person to get it right gets brainliest :)
Answer:
(x, y) = (12, 15)
Step-by-step explanation:
The given expression for y suggests that using substitution would be a good choice for the method of solution.
__
x +(x +3) = 27 . . . . substitute for y using the second equation
2x = 24 . . . . . . . subtract 3
x = 12 . . . . . . . divide by 2
y = 12 +3 = 15 . . . . use the second equation to find y
The solution is (x, y) = (12, 15).
Find the median and mean of the data set below:
2,26,29,38,22,27
Answer: The mean is 24, and the median is 26.5 .
Step-by-step explanation: To find the mean, one must add all the numbers in a set of data and divide it by the amount of numbers added. To find the median, one must line the numbers in a set of data from biggest to smallest. The number in the middle is the median. If the amount of numbers in the set are even, resulting in no middle, the two numbers closest to the middle are added and then divided by two. The resulting number is the median. In this case I had to add and divide.
The sum of terms of an A.P. is 136, the common difference 4, and the last term 31, find n
Step-by-step explanation:
[tex]\huge{\color{black}{\fbox{\color{pink}{\colorbox{pink}{\color{red}{Answer ✨☑️}}}}}}[/tex]
The number of terms are 8. Step-by-step explanation: Given : The sum n terms of an A.P is 136 the common difference is 4 and last term is 31.
Answer:
Sn=2n{2a+(n−1)d}
a+(n−1)d=31⇒a=31−4(n−1)
∴136=2n{2[31−4(n−1)]+(n−1)d}
n[70−8n+4n−4]=272
n(66−4n)=272
4n2−66n+272=0
2n2−33n+136=0
2n(n−8)−17(n−8)=0
(2n−17)(n−8)=0
∴n=8
The Small Business Administration guarantees some loans. The fee for this can range up to 3.75%. On a $1M business loan, how high could the fee be?
Answer:
$37,500
Step-by-step explanation:
The amount of the fee is the product of the fee rate and the amount to which that rate is applied.
__
3.75% × $1,000,000 = 0.0375 × $1,000,000 = 37.5 × $1000
= $37,500
The fee on a $1M loan could range up to $37,500.
_____
Additional comment
If you're computing this by hand, it can be easier to (a) use scientific notation, or (b) adjust the decimal points as we have shown here. In this case, we multiplied the percentage by 1000 and divided the loan amount by 1000. The product remains the same, but the numbers are easier to deal with.
In scientific notation, this is 3.75E-2 × 1E6 = 3.75E4 = 37.5E3 = 37,500, where the "E" notation would be that used by a calculator or spreadsheet.
Answer with steps pls
Answer:
A) 2¹²
Step-by-step explanation:
Given :
3x - y = 12Equate the equation to y :
3x - y + y = 12 + y12 + y = 3x12 + y - 12 = 3x - 12y = 3x - 12Substituting in the expression :
[tex]\frac{8^{x} }{2^{y} }[/tex][tex]\frac{2^{3x} }{2^{3x-12} }[/tex][tex]{2^{3x-3x+12}}[/tex]2¹²Use three different values of n to demonstrate that 2 n + 3 n is equivalent to 5 n .
Answer:
2n + 3n equals to 5n in the end, so just set n equal to literally any number :)
Step-by-step explanation:
Example:
Let n = 1000
2(1000) + 3(1000) = 5(1000)
5000 = 500
Basically, plug in the number and solve on both sides each time. You will know you've demonstrated it if it's equal on both sides
Answer:
2n + 3n equals to 5n in the end, so just set n equal to literally any number
Step-by-step explanation:
Example:
Let n = 1000
2(1000) + 3(1000) = 5(1000)
5000 = 500
Basically, plug in the number and solve on both sides each time. You will know you've demonstrated it if it's equal on both sides
Solve for the exact values of x and y.
x =
y =
Answer:
Here is the solution...hope it helps:)
Can a regular polygon have an interior angles of 160
Answer:
Step-by-step explanation: interior angle of a regular polygon is 160 degrees, then the exterior angle is 20 degrees. The sum of all exterior angles is 360 degrees so there must be 360/20 sides = 18 sides.
yes it can have 160 degree as interior angel
A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.
Enter the correlation coefficient. Round your answer to the nearest hundredth.
The correlation coefficient is 0.92
What is Correlation Coefficient ?
A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.
In other words, it reflects how similar the measurements of two or more variables are across a dataset.
When one variable changes, the other variables change in the same direction or opposite direction.
Perfect positive correlation :When one variable changes, the other variables change in the same direction.
Perfect negative correlation :When one variable changes, the other variables change in the opposite direction.
[tex]\rm r = \dfrac{\sum (x_{i}-x')(y_{i}-y')}{\sqrt {\sum (x_{i}-x')^{2} \sum (y_{i}-y')^{2}}}[/tex]
After calculation we get
r = 0.92
Therefore it is a Perfect positive correlation
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need help asap pls pls
Answer:
I think no solution I'm not sure sorry if I'm wrong
If a sprinkler rotated 90˚, paused and then rotated another 90˚, how many degrees
did it rotate altogether
Answer:180 or halfwayStep-by-step explanation:90 is 1/4 and 360 is a full rotation so it rotated halfway all together.
PLEASE HELP!! ILL MARK U AS BRAINLIEST!!!
The answer would be [tex]\frac{1}{2}[/tex].
The probability of getting a 5 is [tex]\frac{1}{100}[/tex] and the probability of getting a number larger than 50 is [tex]\frac{49}{100}[/tex] (the 50 doesn't count). Add those up and you get [tex]\frac{50}{100}[/tex] and can be simplified to [tex]\frac{1}{2}[/tex].
Answer:
51/100
Step-by-step explanation:
The probability is the ratio of the number of outcomes of interest to the total number of possible outcomes.
__
There is one number 5. There are 50 numbers in the range 1–100 that are greater than 50. So, the total number of outcomes of interest is 1+50 = 51.
The possible outcomes are any of the numbers 1–100, so there are 100 of them.
The probability of interest is ...
P(n=5||n>50) = 51/100
a student was asked to multiply a number by 3/2. instead he divided the number by 3/2 and obtained a number smaller by 2/3, the number is:
Answer:
[tex]\boxed{\bf \sf number : \ \frac{4}{5} }[/tex]
Explanation:
Let the number be n
According to students Condition:
[tex]\rightarrow \sf \dfrac{3}{2} \ x \ n \quad = \quad \dfrac{3n}{2}[/tex]
What He actually Did:
[tex]\rightarrow \sf n \div \dfrac{3}{2} \quad = \quad n \ x \ \dfrac{2}{3} \quad = \quad \dfrac{2n}{3}[/tex]
He got a smaller number by 2/3, so:
[tex]\rightarrow \sf \dfrac{3n}{2} - \dfrac{2n}{3} = \dfrac{2}{3}[/tex]
make the denominator's same
[tex]\rightarrow \sf \dfrac{3(3n)}{6} - \dfrac{2(2n)}{6} = \dfrac{2}{3}[/tex]
multiply the integers
[tex]\rightarrow \sf \dfrac{9n}{6} - \dfrac{4n}{6} = \dfrac{2}{3}[/tex]
Join the fractions
[tex]\rightarrow \sf \dfrac{9n-4n}{6} = \dfrac{2}{3}[/tex]
Subtract integers
[tex]\rightarrow \sf \dfrac{5n}{6} = \dfrac{2}{3}[/tex]
Cross multiply
[tex]\rightarrow \sf n = \dfrac{6 \ * \ 2}{5 \ * \ 3} \quad = \quad \dfrac{4}{5}[/tex]
Lets see
the number be x
The expression is
3x/2-2x/3=2/39x-4x)6=2/35x)6=2/315x=12x=12/15=4/5enlarge (2,-2) (4,-2) (2,-4) (4,-4) by scale factor 3.5 with centre of enlargement (4, -6)
The image of dilating the points by a scale factor 3.5 with centre of enlargement (4, -6) is (-7, 14), (0, 14), (-7,7) and (0, 7)
How to dilate the points?The coordinates are given as:
(2,-2) (4,-2) (2,-4) (4,-4)
The scale factor is given as:
k = 3.5
The center of enlargement is given as:
(a,b) = (4, -6)
The image of dilation is calculated using:
[tex](x,y) \to (k(x -a), k(y -b))[/tex]
So, we have:
A = (3.5(2 -4), 3.5(-2 +6))
A = (-7, 14)
B = (3.5(4 -4), 3.5(-2 +6))
B = (0, 14)
C = (3.5(2 -4), 3.5(-4 +6))
C = (-7,7)
D = (3.5(4 -4), 3.5(-4 +6))
D = (0, 7)
Hence, the image of dilating the points is (-7, 14), (0, 14), (-7,7) and (0, 7)
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Kegan thought that the solution to this equation might be around 10.
Does that make sense to you?
4x − 20 = 2x + 8
Answer:
x=14
Step-by-step explanation:
collect like terms, like so
Answer:4(x−2)−8=4+2x
Use the distributive property to multiply 4 by x−2.
4x−8−8=4+2x
Subtract 8 from −8 to get −16.
4x−16=4+2x
Subtract 2x from both sides.
4x−16−2x=4
Combine 4x and −2x to get 2x.
2x−16=4
Add 16 to both sides.
2x=4+16
Add 4 and 16 to get 20.
2x=20
Divide both sides by 2.
x=
2
20
Divide 20 by 2 to get 10.
x=10
Step-by-step explanation:
What is 5log3+log4 as a single logarithm?
[tex]~~~5 \log 3 + \log4 \\\\=\log 3^5 + \log 4~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=\log(3^5 \cdot 4)~~~~~~~~~~~~~~~~~~~~~~;[\log_b(mn) = \log_b m + \log_b n]\\\\=\log(972)[/tex]
I need the numbers please con y’all help me
Answer:
y=2/3x+4
Step-by-step explanation:
4 is y-intercept
2/3 is the slope (rise/run)
Answer: y = [tex]\frac{2}{3}[/tex]x + 4
Step-by-step explanation:
This is in slope-intercept form. We are missing the m and the b value. See attached for more information.
[m aka the slope]
Starting from point (-6, 0), counting up 2 units, then right 3 units to point (-3, 2), gives us a slope of [tex]\frac{2}{3}[/tex] via rise-over-run
[b aka the y-intercept]
The line intersects the y-axis at positive 4.
-> This value is "4"
I'm having difficulties with this haha please help :(
If the function is h(t) = - 4.9t² + 39.2t + 5. Then the maximum height will be 83.4 meters.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The function is given as
h(t) = - 4.9t² + 39.2t + 5
Then the differentiation of the function will be
h'(t) = - 9.8t + 39.2
For the maximum height, put h'(t) equals zero. Then we have
h'(t) = 0
- 9.8t + 39.2 = 0
t = 4
Then the maximum height will be
h(t) = - 4.9(4)² + 39.2 x 4 + 5
h(t) = - 4.9 x 16 + 39.2 x 4 + 5
h(t) = - 78.4 + 156.8 + 5
h(t) = 83.4 meters
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A model stature is 5 in wide. If it was built with a scale of 1 in: 2 ft, then how wide is the real statue?
(Pls awnser quickly)
Answer:
10 ft.
Step-by-step explanation:
Scale ⇒ 1 in. : 2 ft.
1 in. : 2ft. = 5 in. : x ft. [x is the width of the real statue]1/2 = 5/xx = 5 × 2x = 10 ft.Scale factor
1in=2ftWidth of model=5in
Width of structure
5(2)10ftcan you pleas help this is a math question
Answer:
10.5 baskets
Step-by-step explanation:
The median is the middle value, but for this one just add the two in the middle and divide by 2.
4+3 = 7
Each ball is 3 baskets
7×3 = 21
21/2 = 10.5
Please help fast. Need soon!
What fraction is 3 hours of 30 minutes
Answer:
7/2
Step-by-step explanation:
3 hours and 30 minutes = 7/2 in improper fraction
1 hour = 60 minutes
30 minutes = 30 minutes * 1 hour/60 minutes =30/60 = 1/2 hour
3 hours and 30 minutes:
= 3 hours + 1/2 hour
= 3 1/2 hours
= [(2 * 3)+1]/2
= [6+1]/2
= 7/2
Perimeter and Area Geometry homework! {Jim Thompson}
Part A
The yard is a quadrilateral with the following corner points
(0,0)(0,40)(40,50)(50,0)I'll label those points A through D in the order presented above.
From A to B is 40 feet since 40-0 = 40. We can subtract the y coordinates because the x coordinates are the same.
In short: side AB is 40 feet long.
The length of side BC is not as simple. We'll need the distance formula.
[tex]B = (x_1,y_1) = (0,40) \text{ and } C = (x_2, y_2) = (40,50)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-40)^2 + (40-50)^2}\\\\d = \sqrt{(-40)^2 + (-10)^2}\\\\d = \sqrt{1600 + 100}\\\\d = \sqrt{1700}\\\\d = \sqrt{100*17}\\\\d = \sqrt{100}*\sqrt{17}\\\\d = 10\sqrt{17}\\\\d \approx 41.2311\\\\[/tex]
Segment BC is exactly [tex]10\sqrt{17}[/tex] feet long, which is about 41.2311 feet.
Use the distance formula again to find the distance from point C(40,50) to D(50,0)
[tex]C = (x_1,y_1) = (40,50) \text{ and } D = (x_2, y_2) = (50,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(40-50)^2 + (50-0)^2}\\\\d = \sqrt{(-10)^2 + (50)^2}\\\\d = \sqrt{100 + 2500}\\\\d = \sqrt{2600}\\\\d = \sqrt{100*26}\\\\d = \sqrt{100}*\sqrt{26}\\\\d = 10\sqrt{26}\\\\d \approx 50.9902\\\\[/tex]
Lastly, the side AD is exactly 50 feet because 50-0 = 50. We can subtract x coordinates because the y coordinates are the same. Use of the distance formula from A to D should show a result of 50 exactly.
We have these side lengths:
AB = 40
BC = 41.2311 (approximate)
CD = 50.9902 (approximate)
AD = 50
Add up those four sides and we'll get the perimeter of the quadrilateral.
AB+BC+CD+AD = 40+41.2311+50.9902+50 = 182.2213
Answer: About 182.2213 feet===================================================
Part B
The garden is a rectangle that is 15 feet across horizontally (since subtracting x coordinates gives us 25-10 = 15) and 20 feet vertically (since subtracting y coordinates gives us 35-15 = 20).
This 15 by 20 rectangle has an area of 15*20 = 300 square feet.
The deck is a trapezoid with the parallel bases of 20 feet up top and 35 feet down below. Like before, we subtract x coordinates to find the horizontal distance (since the y coordinates are the same). The height of this trapezoid is 15 feet. Subtract the y coordinates to find the height.
The area of the trapezoid is
A = h*(b1+b2)/2
A = 15*(20+35)/2
A = 412.5
That decimal value is exact.
Add it onto the area of the rectangle
412.5+300 = 712.5
Answer: 712.5 square feet exactly.The figure below includes a semicircle and
trapezoid. Find the area of the figure.
Answer:
244.93
Step-by-step explanation:
area formula for trapezoid:1/2*(b1+b2)*h
area formula for semi circles: (3.14*r^2)/2
so then we cut the figure to make a semi cirlce and trapazoid
semicircle- 14 is the full diameter, divide by 2 to make 7, 7×3.14×7)/2=76.93
trapezoid: base one is 18. base 2 is 14. 18+14=32 then times that by 10.5 which is 336 and divide that by 2 is 168
add both and you get 244.93
1. Jessica drove 345 miles on
Friday. To the nearest 100,
about how many miles did she
drive?
Answer:
To the nearest 100 miles, Jessica drove about 300 miles since we haven't reached 350 miles. If we have a number that is greater than 350 miles than we would've rounded it up to 400 but since ours is less than that we round down to the nearest hundred which is 300 miles.
The triangles are similar. Find the missing measure.
Step-by-step explanation:
Triangle MŇO is congruent to Triangle UŤS
NO=4
MN=4
MO=5.6( Which is 140% bigger than 4)
UT=10
TS=10(Therefore this also should be 10)
US=14(Which is 140% bigger than 10)
I think this is the solution but I am not 100% sure
Answer:
x=14
Step-by-step explanation:
Find the distance between the points (2, 8) and (-1, 9).
1.√10
2. √2
3.2√3
Answer:
1.
Step-by-step explanation:
distance = √(X2 - X1)^2 + (Y2 - Y1)^2
= √(-1 - 2)^2 + (9 - 8)^2
= √(-3)^2 + (1)^2
= √ 9 + 1
= √10
Answer:The distance is √10
Step-by-step explanation:
Soup A has 8 grams of sodium in 10 cups. Soup B has 7 grams of sodium in 14 cups. Which soup has more sodium per cup?
Answer:
Soup A
Step-by-step explanation:
For this we need to find the number of sodium per cup. To do this, we divide the ratios by the number of cups. 8:10 would be 10/10 (1 cup) and 8/10 (.8 g per cup). 7:14 would be 14/14 (1 cup) and 7/14 (.5 g per cup). So, soup A has .8 g of sodium per cup and soup B has .5 g of sodium per cup. .8>.5, so soup A has more sodium.
Hope this helps!