By using the formula, days = (original number of people / new number of people) * original number of days, the same food would last for 20 days.
What is number?A number is a mathematical concept that refers to a quantity or value that can be represented by a symbol. Numbers can be used to represent quantities in various contexts, such as counting, measuring, and quantifying.
What is irrational numbers?Irrational numbers are numbers that cannot be expressed as the ratio of two integers (e.g. pi, the square root of 2).
days = (original number of people / new number of people) * original number of days
In this case, we can plug in the values as follows:
days = (80 / (80 + 40)) * 30
days = (80 / 120) * 30
days = 2/3 * 30
days = 20
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show that if a, b, c, and d are integers, where a = 0, such that a | c and b | d, then ab | cd.
If a, b, c, and d are integers, where a = 0, such that a | c and b | d, then ab | cd.
In this question we need to prove if a, b, c, and d are integers, where a = 0, such that a | c and b | d, then ab | cd.
We know that the definition of divisibility i.e., m divides n if there exists an integer p such that n = mp
If a | c and b | d, then there exist integers x and y such that c = ax and d = by.
Consider a multiplication c * d
= (ax) * (by)
= axby
= (ab)xy
= ab(xy)
Let k be equal to the integer xy
So, cd = ab(k)
Using the definition of divisibility, cd is divisible by ab.
Therefore, if a | c and b | d, then ab | cd.
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6th grade math IXL program
Answer:
1.5 groups.
Step-by-step explanation:
1 divided by 8/12 is 1.5
Answer:
1 1/2
Step-by-step explanation:
The figure shows a large rectangle that is divided into 12 parts of equal size.
Think of the entire rectangle as 1.
Each small rectangle is 1/12 of 1.
Now count 8 small rectangles starting at the left.
When you divide 1 by 8/12, you can fit 1 full 8/12 (8 small rectangles) and another half of 8/12 (another 4 small rectangles.
Since you can fit 1 1/2 groups of 8 small rectangles,the result is 1 1/2.
Answer: 1 ÷ 8/12 = 1 1/2
tom and addison made plans to meet up in the state park to spend some time hiking together. tom arrived early and started wandering up the trail, snapping some photos along the way. his speed was 4 kilometers per hour. addison arrived later, when tom was already 6 kilometers ahead, and started hiking up the trail at 10 kilometers per hour to catch up. how much time did it take addison to catch up to tom?
Answer:
Math Expert Answer
Step-by-step explanation:
So toms equation is y= 4x + 6 and addisons equation is y=10x so they will meet eachother in 1 hour. You can use a desmos calculator to input the equations for the answer
Answer:
1 hour
Step-by-step explanation:
Let's set up an equation for Tom's and Addison's distances: T(x) = 4x + 6, A(x) = 10x, where x is the amount of time since Addison started (in hours).
We solve for A(x) = T(x) and get:
10x = 4x + 6 → subtract 4x from both sides
6x = 6 → divide both sides by 6
x = 1
Therefore, it took Addison 1 hour to catch up with Tom
Find the value of x. A B D E C i an irregular pentagon with parallel ide A B and C E. Angle A B D meaure 104 degree. Angle C E D meaure 28 degree. Angle B D E meaure x degree
Angle B D E measure 228 degrees in the irregular pentagon A B D E C.
Polygons that lack equal sides and angles are referred to as irregular polygons. Polygons that are irregular are not regular, in other words. Closed two-dimensional shapes known as polygons are created by connecting three or more line segments. Regular and irregular polygons are two different forms of polygons.
As we know, the Sum of the interior angles of an irregular polygon =
(n − 2) × 180°
{ 'n' = the number of sides of a polygon.}
As given, A B D E C is a pentagon, so
n= 5
The sum of interior angles=
3 X \180= 540
As AB and CE are parallel to each other:
angle BAC=y
angleECA= 180-y
=>the sum of interior angles:
104+x+28+180-y+y= 540
104+x+28+180=540
x+312=540
=> x=228
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Calculate the magnitude of y. trapezium
K = 123°
L = 71°
M = 39°
N = y
Explanation:
A trapezium has four sides, so it is a quadrilateral.
Any quadrilateral has all four interior angles add to 360 degrees.
K+L+M+N = 360
123+71+39+y = 360
233+y = 360
y = 360-233
y = 127
Figure A ha an area of 18 quare feet. Figure B ha an area of 98 quare feet and one of the ide length i 14 feet. Find the miing correponding ide length if figure A i imilar to Figure B
The side length of Figure A can be determined using the ratio of areas and the known side length of Figure B. The area of Figure A is 18 square feet and the area of Figure B is 98 square feet. The side length of Figure B is 14 feet. Using these values, the corresponding side length of Figure A can be calculated to be 7 feet.
The missing corresponding side length of Figure A can be determined using the ratio of areas and the known side length of Figure B. If two shapes are similar, then their corresponding sides are in the same ratio as their areas. Since the area of Figure A is 18 square feet and the area of Figure B is 98 square feet, the ratio of their areas is 18/98. Since the side length of Figure B is 14 feet, the corresponding side length of Figure A can be calculated by multiplying 14 feet by the ratio of 18/98, which is 0.1837. This value can be rounded to 7 feet. Therefore, the missing corresponding side length of Figure A is 7 feet. This result can be verified by calculating the area of Figure A using the known side length and the missing side length. If the two side lengths are multiplied together, the product should be equal to the area of Figure A, which is 18 square feet.
7 feet x 11 feet = 77 feet^2
77 feet^2 = 18 feet^2 (Area of Figure A)
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natalie is the creator of better brain, a new mindfulness app for teens. the app currently has 1,262 downloads, and natalie has set a goal of doubling the downloads every month. write an exponential equation in the form y
Answer:
1262(2)^x
Step-by-step explanation:
Write y+4=2(x-7) in standard form
[tex] \Large{\boxed{\sf 2x - y = 18}} [/tex]
[tex] \\ [/tex]
Explanation:We will try to write the given linear equation in standard form.
[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Standard \ Form \ of \ a \ linear \ equation \text{:}} \\ ~ \\ \tt Ax + By = C \end{array} \right] } [/tex]
Where:
A is a positive integer. (A ≠ 0)B and C are integers. (B ≠ 0)[tex] \\ [/tex]
Given linear equation:
[tex] \sf y + 4 = 2(x - 7) [/tex]
[tex] \\ [/tex]
First, expand the right side of the equation:
[tex] \sf y + 4 = 2 \cdot x + 2 \cdot (-7) \\ \\ \sf y + 4 = 2x - 14 [/tex]
[tex] \\ [/tex]
Subtract 2x from both sides of the equation:
[tex] \sf y + 4 - 2x = 2x - 14 - 2x \\ \\ \sf -2x + y + 4 = -14 [/tex]
[tex] \\ [/tex]
Subtract 4 from both sides of the equation:
[tex] \sf -2x + y + 4 - 4 = -14 - 4 \\ \\ \sf -2x + y = -18 [/tex]
[tex] \\ [/tex]
Since the coefficient of x (-2) has to be positive, multiply both sides of the equation by -1:
[tex] \sf -1 \cdot (-2x + y) = -1 \cdot (-18) \\ \\ \sf -1 \cdot (-2x) + (-1) \cdot y = 18 \\ \\ \boxed{\boxed{\sf 2x - y = 18 }} [/tex]
[tex] \\ [/tex]
[tex] \hrulefill [/tex]
[tex] \\ [/tex]
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Please help me respond these two questions!!
The score of the 60th percentile on the test is 84.
What is a percentile?The definition of percentile is the percentage that a certain percentage falls beneath. Ben is the fourth-tallest child in a group of 20 kids, whereas 80% of the kids are shorter than you.
Given:
58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96
Calculate the percentile of score 71 as shown below,
[tex]Percentile = n / N \times 100[/tex]
Here, n is the number of scores below the score of 60th percentile and N is the total number of scores,
60 = n / 15 × 100
n / 15 = 60 / 100
n = 0.6 × 15
n = 9
Thus, the 9th term = 84 is the score of the 60th percentile,
Therefore, the score of the 60th percentile on the test is 84.
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sum of two numbers is -11/12 ,one of them is 9/2, find the other
pls answer fasttttttt!!!!
plssssssssssssssssssssssssssssss.
step by step
Answer:
- [tex]\frac{65}{12}[/tex]
Step-by-step explanation:
let the number to be found be n , then
n + [tex]\frac{9}{2}[/tex] = - [tex]\frac{11}{12}[/tex]
multiply through by 12 ( the LCM of 2 and 12 ) to clear rhe fractions
12n + 54 = - 11 ( subtract 54 from both sides )
12n = - 65 ( divide both sides by 12 )
n = - [tex]\frac{65}{12}[/tex]
This equation has one solution. 5(x – 1) 3x = 7(x 1) what is the solution?
Answer:
send the complete question . there are some missing signs .
Which are irrational numbers?
Answer:
A is the only irrational number present.
Step-by-step explanation:
The bottom two numbers can be simplified into 7 and 5. Meanwhile, B is a repeating number. A is a non-repeating and non terminating number.
Answer:
A.
Step-by-step explanation:
An irrational number is any real number that cannot be equally divided by 2 integers. (It's not a perfect square.)
No whole number multiplied by itself equals 27.
f(x)=x^4+8x^3+11x^2-9x+28=0
The roots of the quartic polynomial f(x) = x⁴ + 8x³ + 11x² - 9x + 28 are ±1, ±2, ±3, ±4, ±7, ±14, ±28
Roots of a PolynomialIn the given problem, we have to find the roots of the fourth degree polynomial and factorize the given polynomial equation first in order to obtain three equations which are linear and quadratic equation. We can easily determine the zeros of the fourth degree polynomial.
Generally, polynomials of fourth degrees are called quartic polynomials.
f(x) = x⁴ + 8x³ + 11x² - 9x + 28
When we factorize this, we wouldn't get a lower value because this quartic polynomial cannot be factorized.
However, we can still find the roots which are the solution to the polynomial and are
x = ±1, ±2, ±3, ±4, ±7, ±14, ±28
These values are the solution to the polynomial.
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complete question : What are the roots of f(x)=x^4+8x^3+11x^2-9x+28
Find u•v where theta is the angle between u and v
Answer:
88√2 = 124.5 (nearest tenth)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Dot Product of two vectors}\\\\$a \cdot b=|a||b| \cos \theta$\\\\where:\\ \phantom{ww}$\bullet$ $|a|$ is the magnitude of vector a. \\ \phantom{ww}$\bullet$ $|b|$ is the magnitude of vector b. \\ \phantom{ww}$\bullet$ $\theta$ is the angle between $a$ and $b$. \\ \end{minipage}}[/tex]
Given:
[tex]|u| = 8[/tex][tex]|v| = 22[/tex][tex]\theta =\dfrac{\pi}{4}[/tex]Substitute the given values into the dot product formula:
[tex]\begin{aligned}\implies u \cdot v &=|u||v| \cos \theta\\\\&=8 \cdot 22 \cdot \cos \left(\dfrac{\pi}{4}\right)\\\\&=176 \cdot \dfrac{\sqrt{2}}{2}\right)\\\\&=88\sqrt{2}\\\\&=124.5\; \sf (nearest\;tenth)\end{aligned}[/tex]
the figure(figure 1) shows the acceleration graph for a particle that starts from rest at t = 0s.
a) The velocity of particle at t=2s is 5m/s
b) The velocity of particle at t=4s is 20m/s
To obtain the function of velocity from the graph we need to find the equation of accleration- time graph
so the equation of accleration is :
a= [tex]\frac{10-0}{4-0}[/tex]t
a= 5/2t
and we know that :
a= [tex]\frac{dv}{dt}[/tex]
=> dv= adt
=> dv= [tex]\frac{5}{2}[/tex] t dt
integrating both side we get:
v= [tex]\frac{5}{4}[/tex][tex]t^2[/tex] +c
where c is constant
it is given that at t=0s it starts from rest so
v=0 at t=0
=> 0 = 0+c
=>c=0
so v=[tex]\frac{5}{4}t^2[/tex] ---- (i)
a) as we have got the equation of velocity with respect to time
we have to find velocity at t=2s
putting t=2s we get
v = 5/4 *4
so velocity of particle at t=2s is 5m/s
b) as we have got the equation of velocity with respect to time
we have to find velocity at t=4s
putting t=4s we get
v = 5/4 *16
so velocity of particle at t=2s is 20m/s
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equation of simple straight line
Complete question:
the figure shows the acceleration graph for a particle given that particle starts from rest at t=0.
determine the velocity of partice at
a)2s
b)4s
What is 10 percent of 75
Answer:
7.5
Step-by-step explanation:
100% = 75
100% divided by 10 is 10%
75 divided by 10 is 7.5
What is the domain of this function?
f(x) = ²x - 3| + 1 ?
Answer: A.
Step-by-step explanation:
Most of the function f(x) has a domain (- infinity, positive infinity), and the function in the picture is the same. So, the answer is A
Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 33 cards, which was 10% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
Answer:330
Step-by-step explanation:
Set up cross multiplication:
33/x 10/100
Cross multiply
10*x 100*33
Divide sums
3,300/10x
Answer:
330 total cards
At her health clubs, Lauren uses a treadmill every 2 days and the weight machines every 8 days. She used a treadmill on march 2 and will use the weight machines on march 8. Lauren says that the first time she will use both a treadmill and the weight machines in march is march 16 because the lcm of 2 and 8 is 16. Does Lauren’s reasoning make sense? Use an example or a counterexample to explain your analysis
Lauren's reasoning does not make sense because the LCM of 2 and 8 is not 16, the LCM will be equal to 8.
What is LCM?The Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least frequent multiple (LCM) for two numbers.
It can also be computed for several different numbers.
As per the given information in the question,
Lauren says that the LCM of 2 and 8 is 16.
Now, let's check whether it is correct or not.
Let's make a factor of both numbers,
2 = 2 × 1
8 = 2 × 2 × 2
So, the LCM will be: 2 × 2 × 2 = 8
It means that the LCM of 2 and 8 is not 16, the LCM is 8.
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Jayden’s family has completed 90% percent of the trip. They have traveled 75 miles. How far is the trip?
Answer:
[tex]83\frac{1}{3} miles[/tex]
Step-by-step explanation:
90/100=75/x
90x=100(75)
90x=7500
/90. /90
x=83 1/3 miles
Hopes this helps
a rectangular storage container without a lid is to have a volume of 10 m3. the length of its base is twice the width. material for the base costs $15 per square meter. material for the sides costs $9 per square meter. let w denote the width of the base.
The total cost is $245.31.
Given,
Volume = 10[tex]m^{3}[/tex]
Width = w
Length = 2w
Base area = Length x Width = [tex]2w^{2}[/tex]
Cost of base = $15
Cost of sides = $9
Since the volume is 10[tex]m^{3}[/tex],
Volume = Base Area x Height
Height = [tex]\frac{10}{2w^{2} }[/tex] = [tex]\frac{5}{w^{2} }[/tex]
Cost of making such a container:
Cost of base = [tex]2w^{2}[/tex] x 15 = $[tex]30w^{2}[/tex]
Cost of sides = [(2 x 2w x [tex]\frac{5}{w^{2} }[/tex]) + (2 x w x [tex]\frac{5}{w^{2} }[/tex])] x $9 = $[tex]\frac{270}{w}[/tex]
Overall Cost = Cost of Base + Cost of Sides
f(x) = [tex]30w^{2} + \frac{270}{w}[/tex] = [tex]30(w^{2} + \frac{9}{w})[/tex]
To get the minimum cost, we will have to find the derivative of f(x) and equate it to zero.
d(f(x))/dx = 0
[tex]2w - \frac{9}{w^{2} } = 0\\w^{3} = 4.5 \\w = 1.651m[/tex]
Putting the value of w in f(x),
f(x) = $245.31 (after calculations)
Therefore, the final answer is $245.31.
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Pls helppp i dont get it at all
Answer:
Law of Sines
Step-by-step explanation:
Chocolate bars cost $2.50 each.
The more chocolate bars Terri buys, the more
money she will have to pay.
Identify the dependent variable.
Answer:
The dependent variable is the cost
Step-by-step explanation:
The dependent variable is the variable that depends on the independent variable to either increase or decrease.
In this case, the dependent variable is the cost, and the independent variable is the number of chocolate bars.
5(x-9)=55
What would you do to both ide firt?
A. Subtract 5
B. Divide by 5
C. Add 9
D. Subtract 55
Answer:
b
Step-by-step explanation:
we first make
1.Subtraction/Adding
2.Mutiply/Division
please help will give brainliest
The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.
Given that, the polygon IJKL if IJ≅KL, JK≅LI, IJ⊥JK, JK⊥KL, KL⊥LI and LI⊥IJ.
What is a rectangle?A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
Here, the opposite sides IJ and KL are equal and the opposite sides JK and LI are equal.
Since, all the sides are perpendicular to each other makes an angle 90°
The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.
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Statistics tree diagram word problem, select the correct tree diagram.
Each day mr brightside chooses one digit number from a random number table to decide if he will walk to work or drive that day. the numbers 0 through 3 indicate he will drive, 4 through 8 mean he will walk. if he drives, he has a probability of 0.1 of being late. if he walks, his probability of being late rises to 0.25. let 2=walk, d= drive, l=late, and nl= not late. which of the following tree diagrams summarizes these probabilities?
The tree diagram that summarizes these probabilities is Option (D).
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Here, N(S) = 10, The numbers from 0 - 9.
The probability of going to work by driving is (4/10) = 0.4.
If he drives, he has a probability of 0.1 of being late so P(NL) = 1 - 0.1 = 0.9.
The probability of going to work by walking is = 6/10 = 0.6.
if he walks, his probability of late rising to 0.25 so, P(NL) = 1 - 0.25 = 0.75.
Now we'll connect this information to the given options.
From the given options, Option (D) satisfies the given information.
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all the sides of a triangle are integers, and the perimeter is 12. how many different possible triangles are there
3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).
Given that,
The perimeter of a triangle 12cm.if the lengths of the three sides are all integers (in cm).
We have to find how many such difference triangle are possible.
We know that,
Perimeter of the triangle is 12cm.
p=12
a+b+c=12
a+b≥c
b+c≥a
So,
a+b+c≥2c
12≥2c
c≤6
So,
a≤6,b≤6,c≤6
We get,
a=6,b=3,c=3
a=5,b=4,c=3
a=4,b=4,c=4
Therefore, 3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).
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Jana purchase a jewelry making kit to make gifts for her friends.The kit includes Material to make 72 bracelets.Write and solve an equation to show how many more bracelets she can make from the kit.
WILL GIVE BRAINLIEST
Answer:
72 = b + 24
Step-by-step explanation:
b = 48 bracelets
for conducting a two-tailed hypothesis test with a certain data set, using the smaller of n11 and n21 for the degrees of freedom results in df11, and the corresponding critical values are t2.201. using the formula for the exact degrees of freedom results in df19.063, and the corresponding critical values are t2.093. how is using the critical values of t2.201 more conservative than using the critical values of 2.093?
Using the critical values of t=+/-2.201 is less likely to lead to rejection of the null hypothesis than using the critical values of +/-2.093.
Critical Value Definition -
Critical value can be defined as a value that is compared to a test statistic in hypothesis testing to determine whether the null hypothesis is to be rejected or not.
If the value of the test statistic is less extreme than the critical value, then the null hypothesis cannot be rejected.
Critical values are essentially cut-off values that define regions where the test statistic is unlikely to lie; for example, a region where the critical value is exceeded with probability \alpha if the null hypothesis is true.
Using the critical values of t=±2.201 is more "conservative" than using the critical value of ±2.093 because it is more likely to reject the null hypothesis using the greater value i-e t=±2.201.
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In the figure to the right, AE + DC = 1 1/5 cm, AB = 1 3/4 cm, DE = 1 1/4 cm, and BC = 1 3/10 cm. Find the perimeter of the figure.
active attachment
The perimeter of the given composite figure is; 5¹/₂ cm
How to find the perimeter of the composite figure?
To get the perimeter of the given composite figure, what we will do is to dd up the given segment side lengths and we are given the following;
AE + DC = 1¹/₅ cm
AB = 1 ³/₄ cm
DE = 1 ¹/₄ cm
BC = 1 ³/₁₀ cm.
Thus, we can say that the Perimeter is;
Perimeter = AE + DE + DC + BC + AB
Perimeter = (AE + DC) + DE + BC + AB
= 1¹/₅ + 1 ¹/₄ + 1 ³/₁₀ + 1 ³/₄
= (1²/₁₀ + 1³/₁₀) +(1¹/₄ + 1³/₄)
= 2⁵/₁₀ + 3
= 5¹/₂ cm
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