The smallest positive integer n will be 10 .
To find : the smallest positive integer n such that the rightmost digits of n ! and ( n + 1 ) ! are same .
Since ,
putting n = 10 gives
n ! = 10 ! = 3628800
and ( n + 1 ) ! = 39916800
Last three digits ( rightmost digits ) ie. 800 are same .
Hence , n = 10 is the required answer ,
Therefore , the smallest positive integer is n = 10 such that the rightmost digits of n ! and ( n + 1 ) ! are same .
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Determine the value of any unknown GIVE REASONS
The value of angle b is 60 degrees. The reason is angle b is a supplementary angle to angle 120 degrees
angle b is equal to angle c the reason id that they form alternate internal angles
What are linear pairs?A linear pair is a situation where two adjacent angles are on a straight line, hence their sum is 180 degrees.
Linear pair is special cases of supplementary angles involving only two angles that are adjacent
How to solve for angle b
b + 120 = 180
b = 180 -120
b = 60
c = b (alternate internal angles)a = 80 degrees vertical anglesLearn more about linear pair here
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Find the length of side AC. Give your answer to 1 decimal place.
The length of AC is 17.3 cm
What is rectangle?We also refer to a rectangle as an equiangular quadrilateral since all of its angles are equal.A closed 4-sided shape is called a quadrilateral.A rectangle can also be referred to as a right-angled parallelogram because its sides are parallel.A quadrilateral with equal and parallel opposite sides is referred to as a parallelogram.Paralleograms are a specific instance of rectangles.acc to our question,
AC is the perpendicularAB is the base and θ = 68°So,tan 68° = or, AC = tan 68°×AB 17.3 (approx)Hence,The length of AC is 17.3 cm
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A rectangle has an area of 50 square
centimeters. The width is 5 more than 1 times
the length. Find the length and width, in
centimeters, of the rectangle.
Show your work here
The measurements of the rectangle are 10 cm and 5cm.
What is rectangle?
A rectangle could be a quadrilateral with four right angles in geometer geometry. It may be outlined as an angulate quadrilateral as a result of all of its angles square measure equal; or a quadrangle with a right angle.
Main Body:
Let the width be x.
According to question :
width is 5 more than 1 times the length(l), so
length (l) = width -5
Area if rectangle = 50 cm²
Formula for area of rectangle = length * width
⇒50 = x*(x-5)
⇒50 = x² - 5x
⇒x² - 5x - 50 =0
splitting the middle term
⇒x²- 10x +5x -50 = 0
⇒x(x-10) +5(x-10)
⇒(x-10)(x+5)
Hence the value for x = 10 or -5 .
but length can never be -ve so x= 10.
Width = 10 cm
length = width -5
length = 10 -5
l = 5cm
Hence Measurements of rectangle are 10cm and 5cm.
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mike has 40 coins consisting of dimes and quarters. if the dimes were quarters and the quarters dimes he would have 90 cents more. how many quarters does he have?
In the word problem, if mike has 40 coins consisting of dimes and quarters and if the dimes were quarters and the quarters dimes, he would have 90 cents more, he has 17 quarters.
A word problem refers to a mathematical exercise where significant information on the problem is given in ordinary language and not mathematical notation. Let x be the number of dimes (10 cents) and y be the number of quarters (25 cents). Hence, the total number of coins is:
x + y = 40
The amount of the total coins would be 0.1x + 0.25y.
If the dimes were quarters and quarters were dimes, he would have 90 cents more than the amount he has now.
Hence,
0.25x + 0.10y = 0.1x + 0.25y + 0.9
Solving,
0.25x – 0.1x = 0.25y – 0.1y +0.9
0.15x = 0.15y + 0.9
As x + y = 40, x = 40 – y
Substituting,
0.15 (40 – y) = 0.15y + 0.9
6 - 0.15 y = 0.15y + 0.9
0.15y + 0.15y = 6 – 0.9
0.3y = 5.1
y = 5.1/0.3 = 17
Hence, the number of quarters are 17.
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3. Suppose that your calculator does not have a square root key. How could you still use your calculator to determine √144?
Answer
12
Step-by-step explanation:
click on square root
click on 144
then your answer will pop out below your equation
a line with slope 2 intersects a line with slope 6 at the point (40, 30). what is the distance between the x-intercepts of these two line
The distance between the x-intercepts of these two line is 10 units.
Given that,
These two lines' x-intercepts are separated by 10 units.
Equation of the line with slope 2 is
y-30/x-40 = 2
For x intercept put y = 0,
then
-30/x-40 =2
x =25
Equation of the line with slope 6 is
y-30/x-40 =6
For x intercept put y = 0,
then
-30/x-40 =6
x =35
Distance between x-intercepts of these two lines is difference of the two intercepts i.e,
D = 35-25 = 10.
Thus, the distance between the x-intercepts of these two line is 10 units.
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his table shows the ratio of the number of people to the number of pizzas needed. A 2-column table has 4 rows. Column 1 is labeled People with entries 5, 10, 15, 20. Column 2 is labeled Pizzas with entries 2, 4, 6, 8. Complete the statement about the equivalent ratios shown in this table. When the number of people is multiplied by 4, the number of pizzas is multiplied by .
When the number of people is multiplied by 4, the number of pizzas is multiplied by 4.
What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Mathematically, a proportional relationship can be modeled by the following mathematical expression:
y = kx
Where:
x represents the number of people.y represents the number of pizzas needed.k represents the constant of proportionality.If the x-value is multiplied by 4, we have:
x = 5 × 4
x = 20
From the corresponding y-value for 20 is equal to 8 and as such the number of pizzas needed should be multiplied by 4, in order to produce an equivalent ratio.
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Convert the following. Round to 1 decimal.
0. 57 miles2 converted into feet2
0.57 mi² = 15,890,688 ft² after converting square miles in square foot.
Define the meaning of unit conversion?A unit conversion is the expression of the same feature in an another unit of measurement. Time, for example, can be stated in minutes rather than hours, and distance can be translated from miles into kilometers, feet, or indeed any length measurement. Measurements are frequently stated in one set of units, including feet, but require different units, such like chains. A conversion factor seems to be a numerical equation that allows for the equal exchange of feet and chains.The given conversion in question is-
0.57 mi² = __ ft²
We know that
1 mi² = 27,878,400 ft²
Then, multiply both sides by 0.57
1 x 0.57 mi² = 27,878,400 x 0.57 ft²
0.57 mi² = 15,890,688 ft²
Thus, the conversion of 0.57 mi² = 15,890,688 ft².
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The following sets of ordered pairs represent relations from the set X to the set Y. Which one is a function?
A (3, 4), (3, 5), (3, 6), (3, 7)
B (2, 5), (2, 8), (3, 7), (3, 9)
C (1, -1), (0, 0), (1, 1), (4, 2)
D (0, 0), (1, 1), (4, 2), (9, 3)
The set of ordered pairs that is a function is (d) (0, 0), (1, 1), (4, 2), (9, 3)
How to determine the ordered pair that is a function?The list of options represents the given parameter
As a general rule, for an ordered pair to be a function;
The y values on the ordered pair must point to different x values
In (a) the y values 4, 5, 6 and 7 have the same x value of 3
So, it is not a function
In (b) the y values 5 and 8 have the same x value of 2
So, it is not a function
In (c) the y values -1 and 1 have the same x value of 1
So, it is not a function
In (d) all the y values have different x values
So, it is a function
Hence, the ordered pair that is a function is (d)
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Dominic needs a new bike mirror. His old mirror was a square with a side length of 9 cm. He wants the new mirror to have an area as close as possible to his old bike mirror.
Which circular bike mirror should Dominic buy? Answer Choices: 8 cm , 7 cm , and 6 cm Answer ASAP FOR Brainlist.
Answer:
6 cm
Step-by-step explanation:
The circular mirror Dominic should buy is the mirror with a side length of
8 cm.
Option A is the correct answer.
What is a square?A Square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side².
We have,
Old mirror.
Side = 9 cm
Area = 9 x 9 = 81 cm²
New mirror.
Side = 8 cm
Area = 64 cm²
Side = 7 cm
Area = 7 x 7 = 49 cm²
Side = 6 cm
Area = 6 x 6 = 36 cm²
64 cm² is closer to 81 cm².
Thus,
A circular mirror with a side length of 8 cm should be bought.
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p x 3,700=4,070
There was a % percent increase in the number of visitors.
There was 110% percent increase in the number of visitors.
Percent:
Basically, percentage refers the number or ratio that can be expressed as a fraction of 100.
Given,
p x 3,700=4,070
There was a % percent increase in the number of visitors.
Here we need to find the increase in the percentage.
While we looking into the given question we have identified that,
The Old population = 3700
And the new population = 4070
So, the value of P is calculated as,
=> p = 4070/3700
=> p = 1.1
When we convert this into percent then we get 110% as increase.
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Marie has $180 in a savings account in week 1. She plans to deposit $12 each following week. Assuming that she does not withdraw any money from her account, what will her balance be in week 20?
The balance in Marie saving account in week 20 will be $408 .
In the question ,
it is given that
the amount in Marie's saving account in week 1 is $180 .
amount of money deposited every week is = $12 .
to find the balance in week 20 means , she deposited money for 19 weeks .
the amount deposited in 19 weeks = 19 × 12 = $228
the equation to represent the balance after w weeks = 180 + 12*w
putting w = 19 in the equation , we get
the balance in saving account in week 20 = 180 + 12*19
the balance in week 20 = 180 + 228
= $408
Therefore , The balance in Marie saving account in week 20 will be $408 .
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Each page of a top-secret report on aliens requires 2 \text{ KB}2 KB2, start text, space, K, B, end text of space in digital format.
What is the maximum number of pages the report can have so that it can be completely stored on a USB drive that holds 4 \cdot 10^6 \text{ KB}4⋅10
6
KB4, dot, 10, start superscript, 6, end superscript, start text, space, K, B, end text?
Write your answer in scientific notation, and round to one decimal place.
The maximum number of pages the report can have, using scientific notation, is of:
2 x 10^6.
What is scientific notation?A number in scientific notation is written as follows:
[tex]a \times 10^b[/tex]
With the base symbolized [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.
For this problem, the maximum number of pages that the report can have is given by the following division:
Maximum number of pages = Total capacity/Size of page.
These variables, from the text, are given as follows:
Total capacity: 4 x 10^6 KB.Size of a page: 2 KB / page.Hence the number of pages is obtained as follows:
Maximum number of pages = 4 x 10^6 KB / (2 KB/ page) = 2 x 10^6 pages.
When two numbers are divided in scientific notation, the bases are divided(4/2 = 2), while the exponents are subtracted (6 - 0 = 6).
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Please help me!!!!!!!!
the radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing (in mm3/s) when the diameter is 80 mm? (round your answer to two decimal places.)
Increase in volume is 802424.77 cubic mm/s when the diameter is 80 mm.
Let the radius of the sphere be R.
So, the volume of the sphere is given by,
V = [tex]\frac{4}{3}\pi r^3[/tex]
Differentiating the above relation with respect to time 't' we get,
dV/dt = 4[tex]\pi r^2[/tex]. dr/dt
Given that, the change of radius (dr/dt) = 4 mm/s
When the diameter is 80 mm, then the radius = 80/2 = 40 mm
So the volume change when the diameter is 80 mm is given by,
dV/dt [tex]=4\pi\times40^2\times4\approx 802424.77[/tex] cubic mm/s
Hence the volume increase in 802424.77 cubic mm/s.
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15x+12=13x-15
…….?????
Answer:
x_6x=21_15_3x/. x+6x=21+15+3x
Step-by-step explanation:
Pls help due tomorrow!!!!!!!
We have : (a+b)^2 = a^2 + 2ab + b^2.
So, we can see here : the first term (3x) is a, the second term (a) is b.
For it to be expanded as such, the second term in the bracket must be equal to a^2 when it is squared.
Therefore, the missing term is a.
Recheck : (3x + a)^2 = (3x)^2 + 2.3x.a + a^2 = 9x^2 + 6ax + a^2.
Solve the following equation for y. 3y - 7(y + 5) = y - 35 Also Show your work Describe and show each step taken.
A. y = 0
B. y = 1
C. y = 2
D. All real values for y are correct solutions.
The equation is,
→ 3y - 7(y + 5) = y - 35
Now the value of y will be,
→ 3y - 7(y + 5) = y - 35
→ 3y - 7y - 35 = y - 35
→ -4y - y = -35 + 35
→ -5y = 0
→ y = 0/-5
→ [ y = 0 ]
Hence, option (a) is correct.
you are a contestant in a quiz show, answering a series of questions. you answer correctly with probability p, or incorrectly with proabaility q; you get $1 for every correct answer, and you are eliminated when you first give two consecutive wrong answers. the questions are indepdent. find the expecred number of questions you attempt, and your expecred total prize moeny
The expected total prize money is $2p/q.
Given that,
You participate as a participant in a game show and respond to questions. You receive $1 for each correct response, and you are disqualified if you first provide two consecutive inaccurate answers. You can answer properly with probability p or wrongly with probability q. Each question stands alone.
Let,
The probability of correctly answering a question is = p
The probability of incorrectly answering a question is = q
The number of failures after which you are eliminated is = 2
Let r = 2 = No. of failures and
Let q = The probability of failure in a single question
Now, the number of questions that you will attempt will follow a negative binomial distribution whose parameters are r and q.
The expected value of a negative binomial distribution is given by
E[X] = r/q
So, the expected number of questions that you will attempt is = r/q = 2/q
Out of 2/q questions, the expected number of correct questions is = 2p/q
So, the expected total prize money is $2p/q.
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Given mn, find the value of x.
+
(8x-4)°
(6x-12)°
Answer:
The value of the equation will be 14
How to solve and answer for IXLs
Answer: r = 77.3 degrees
Step-by-step explanation:
-Add both numbers together.
- 46.2
+ 31.1
= 77.3
-That is the value of "r".
Use function notation to write the rule for each function
f{(0,1) (1,3) (2,5) (3,7) (4,9)}
Answer: y=2x+1
Hope this helps
The table shows the side
lengths and perimeters of
regular hexagons. Is the
relationship between the
perimeter and the side
length of the hexagons
proportional? Explain.
The relationship between the perimeter and the side length of the hexagons is proportional.
What is a proportional relationship?A proportional relationship is one that illustrates the constant between the data that are given.
In this case, when the side length is 2, the perimeter is 12. The constant is:
= Perimeter / Length
= 12 / 2
= 6
Also, when the length is 3, the perimeter is 18. The constant will be:
= 18 / 3
= 6
Since they have 6 as constant, it's a proportional relationship.
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what is the probability that a positive integer not exceeding 100 selected at random is divisible by 5 or 7
Answer:
So, the probability of selecting a number from 1 to 100 that is divisible by 5 or 7 is 0.32.
Hope this helped!
A football team loses 4 yards on each of 9 consecutive plays. Find the total change in yards from where the team started.
The total change in yards where the team started is 36 yards
How to determine the total change in yards?The given parameters in the question are:
Yards per play = 4 yards
Number of plays = 9 consecutive plays
The total change in yards is the amount of yard per play multiplied by the number of plays
This is represented as
Total change = Yards per play * Number of plays
Substitute the known values in the above equation So, we have the following equation
Total change = 4 * 9
Evaluate
Total change = 36
Hence, the total change is 36 yards
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TWO FRIENDS EARNED MORE THAN
$400 SELLING T-SHIRTS. THEY
PAID THEIR PARENTS $55 FOR
SUPPLIES AND DIVIDED THE REST
OF THE MONEY EQUALLY. WRITE AN
INEQUALITY TO FIND POSSIBLE
AMOUNTS EACH FRIEND EARNED.
A pediatrician prescribes 5 milliliters (ml) of a pain reliever for every 25 pounds of a child's weight. How many milliliters of
medicine will the doctor prescribe for a child who weighs 60 pounds?
If the child's weight is 60 pounds , then the doctor will prescribe 12 milliliter of medicine .
In the question, '
it is given that
the for every 25 pounds of weight 5 milliliter of pain reliever is required .
we need to find the amount of medicine for the child weighing 60 pounds
So , for 25 pounds = 5 milliliter is needed
for 1 pound = 5/25 ml is needed
hence for 60 pound = 60*(5/25) ml will be prescribed .
on simplifying further ,
we get
= 60*(5/25)
= 60*(1/5)
= 12 ml
Therefore , the doctor will prescribe 12 ml of medicines .
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what is 56/80 as a percentage
Answer:
To do percentages with fractions,
divide the numerator by denominator to get a decimal,
so for example, your question 56/80.
56/80 is 0.7 decimal, and then to make it percent,
we multiply by 100,
how does that work?
you move two places to the right because 100 has two zeros
so 0.7 would be 70,
therefore the percent of 56/80 would be 70%
Good day ml! <3
I need to find the equation for y=
For the format f(x)=|x|.
Answer:
[tex]f(x)=-|2x|[/tex]
Step-by-step explanation:
First, find the slope of the right side of the graph. It is -2. But because an absolute value always makes the value inside positive, we put the negative sign outside the absolute value.
The rule of thumb for absolute value graphs is: if it opens upwards, the absolute value is positive; if it opens downwards, the absolute value is negative.
So, the equation we can construct from this information is:
[tex]f(x)=-|2x|[/tex]
Reflect the figure over the line y=1/3x+1
Answer:
see the attachment
Step-by-step explanation:
You want a graph of the given figure reflected over the line y = 1/3x +1.
Line of reflectionThe given line of reflection can be written in general form as ...
y = 1/3x +1
3y = x +3 . . . . . . multiply by 3
x -3y +3 = 0 . . . . subtract 3y
This is in the general form ...
ax +by +c = 0
where a=1, b=-3, c=3.
The line of reflection is the perpendicular bisector of the segment joining a point (x, y) with its reflection (x', y').
Reflected pointUsing the formula in the second attachment, we find the reflection
(x1, y1) ⇒ (x, y)
satisfies ...
(x -x1)/a = (y -y1)/b = -2(ax1 +by1 +c)/(a² +b²)
or ...
x = -2a/(a²+b²)·(ax1 +by1 +c) +x1
y = -2b/(a²+b²)·(ax1 +by1 +c) +y1
Using the known values for a, b, c, we have ...
x = -2(1)/(1² +(-3)²)·(x1 -3y1 +3) +x1 = (1/5)(4x1 +3y1 -3)
y = -2(-3)/10·(x1 -3y1 +3) +y1 = (1/5)(3x1 -4y1 +9)
Rewriting the mapping in more conventional terms, we have ...
(x, y) ⇒ ((4x +3y -3)/5, (3x -4y +9)/5)
It is convenient to let a spreadsheet do the repetitive tedious math. The third attachment shows the application of this mapping to the coordinates of the figure's vertices (clockwise from bottom).
__
Additional comment
The figure showing the reflected polygon was created by a geometry program using its "reflect over a line" feature.
