Answer:
625
Step-by-step explanation:
here we are in an inverse proportion situation :
As the number of days increases
when the number of students decreases and vice versa.
__________________
Say n is the original number of students.
___________________________________________
After 15 days, the rest of food is enough for n students for 45 days,
or enough for n+500 students for 25 days.
Then
45n = 25×(n + 500)
Then
45n = 25n + 25×500
Then
45n - 25n = 25×500
Then
20n = 12500
Then
n = 12500÷20
= 625
and thus , there were 625 students in the hostel.
Suppose there is a big drop in interest rates in Mexico and a small drop in U.S. interest rates. Everything else equal, what is likely to happen to value of the MXN?
If we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.
The foreign exchange market works according to the principles of firms, households, and investors:
These three constituent factors of the foreign exchange market determine the demand and supply patterns in the market. Demand for a foreign currency might increase in the foreign exchange market is linked to the expectation of an increase in the value of a foreign currency. Supply of a foreign currency in the foreign exchange market is linked to an inverse principle, where the expectation of a decrease in the value of foreign currency pushes supply upwards. If we are to suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A., then the value of the MXN will decrease, with everything being equal. A higher interest rate leads to the appreciation of a foreign currency relative to other currencies in the foreign exchange market. A lower interest rate leads to the depreciation of a foreign currency relative to other currencies in the foreign exchange market.Therefore, if we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.
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Tickets for a soccer game cost $5 for students and $8 for adults. the number of students was 7 less than 11 times the numbers of adults. the amount of the money from tickets was 3682 how many of each tickets were sold?tichets
The number of students will be 642 and the number of the adults will be 59.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
Tickets for a soccer game cost $5 for students and $8 for adults.
The number of students was 7 less than 11 times the numbers of adults.
The amount of the money from tickets was 3682.
Let x be the number of students and y be the number of the adults.
Then the equation will be
x = 11y – 7 …1
5x + 8y = 3682 …2
From equation 1 and 2, we have
5(11y – 7) + 8y = 3682
55y + 8y – 35 = 3682
63y = 3717
y = 59
Then the value of x will be
x = 11 × 59 – 7
x = 642
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find the distance around one-fifth of a circle with diameter of 14 inches
To solve this problem, you will need to know the formula to find the circumference of a circle given the diameter of a circle. After calculating the circumference, you will then divide this result by 5 to obtain the final answer needed for this problem.
Find the CircumferenceThe circumference of a circle is found using the formula C = 2πr.
[tex]C = 2\pi r[/tex]
We are given the diameter. The radius can be found using r = D/2.
[tex]\displaystyle r=\frac{D}{2}[/tex]
[tex]\displaystyle r=\frac{14}{2}[/tex]
[tex]r=7[/tex]
Plug in the radius to the formula for a circle's circumference: C = 2πr.
[tex]C = 2 \pi (7)[/tex]
Rearrange the equation to distribute the 7 into the 2π.
[tex]C = 7(2\pi)[/tex]
Distribute the 7.
[tex]C=14\pi[/tex]
Find One-Fifth of the DistanceTo find one-fifth of the distance (formally termed the circumference) around the circle, divide the circumference by 5.
[tex]\displaystyle \frac{14\pi}{5}[/tex]
If you are looking for a simplified answer in terms of π, this will suffice. If you need an exact answer that does not reference π, continue reading.
For a solution not in terms of π, first, multiply 14 by π.
[tex]14\times\pi = 43.98229715[/tex]
Divide this value by 5.
[tex]\displaystyle \frac{43.98229715}{5} = 8.7964594[/tex]
To make this easier to present, round to the hundredths place.
[tex]8.7964594 \approx 8.80[/tex]
The final answer, dependent on the value you are asked to provide, is:
[tex]{\boxed{\displaystyle \frac{14\pi}{5} \ \text{inches}}[/tex]
[tex]\boxed{\text{approximately} \ 8.8 \ \text{inches}}[/tex]
What is the domain of the function represented by the list of ordered pairs?
(0, 2), (-3, 6), (4, 8), (2, 5), (-2, 4)
Answer:
D: (-3,4).
Step-by-step explanation:
There is really no need to solve it. Plot those points onto a graph and draw lines. I have done it on desmos. Looking at the x-axis to find the domain. From the left to right x-axis we can see that the domain should be D: (-3,4).
The equation for free fall at the surface of some planet (s in meters, t in seconds) is s=2.86t^2. How long does it take a rock falling from rest to reach a velocity of 25.1 m/s on this planet?
The time taken by the rock will be 8.77 seconds.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
Given that:-
The equation for free fall at the surface of some planet (s in meters, t in seconds) is s = 2.86t²
The time will be calculated by using the speed formula.
Speed = Distance \ Time
25.1 = 2.86t² \ t
t = 25.1 / 2.86
t = 8.77 seconds
Therefore the time taken by the rock will be 8.77 seconds.
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On Monday, the water was shut off 3 times for ¼ hours, 2/3 hours, and 1-3/4 hours, respectively. What was the total number of hours the water was off?
Answer:
2-2/3 hours
Step-by-step explanation:
1/4 + 2/3 + 1-3/4 = 1/4 + 2/3 + 7/4. Use common is 12, so we get 3+8+21/12 = 32/12. Simplify equal 8/3 or 2-2/3 hours!
A student has a test scores of 87, 89, 94 points. What must he score on the fourth exam to have an average of at least 92 points?
Answer: He must have atleast 98 points on the next exam in order to get an average of 92 points.
Step-by-step explanation: To calculate average, you need to add all the numbers given, and divide the sum by how many numbers there are. 87 + 89 + 94 + 98 (equals 368), and divide 368 by 4. You will get the average of 92 as its result.
PLS HELP!!
The tables show functions representing the growth of two types of bacteria on certain days within an experiment that lasted a total of 10 days.
How do the functions in the table compare?
Since x-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
O Since y-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
O Since the maximum value in the table for bacteria A
is greater than the maximum value in the table for
bacteria B, bacteria A has a faster growth rate than
bacteria B.
O Since the minimum value in the table for bacteria A
is less than the minimum value in the table for
bacteria B, bacteria A has a slower growth rate than
bacteria B
The correct answer are as follows:
A. False
B. True
C. False
D. False
What is Function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
A. Since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
False, it is the y-intercept of the function that indicates the amount at the start of the experiment.
B. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
True, the y-intercept is given when x = 0, indicating the initial value of the function.
C. Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.
False, because the maximum value of each table is given in different times, and also the initial value of each table is different.
D. Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.
False, the growth rate is not given by the initial value. If we model both tables with an exponential function, the count of bacteria A quadruped in two days, and the count of bacteria B doubled in one day, so they have the same growth rate.
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When completing the square on the equation c^2 + 11c = 12, the resulting solution is
Answer:
Attached file is the solutions
Step-by-step explanation:
Which linear function represents the line given by the point-slope equationy-2=4x-3)?
O fx)=6x-1
Of(x)=8x-6
Of(x)=4x-14
Of(x)=4x-10
3a =2b + -6 (solve for a)
Answer:
shown below
Step-by-step explanation:
3a = 2b - 6
a = (2b - 6) / 3 or 2b / 3 - 2
Answer:
a = (2b-6)/3
Step-by-step explanation:
3a = 2b + -6
lets make a the subject of the formula
divide both sides of the equation by 3
3a/3 = a = (2b-6)/3
a = (2b-6)/3
Find the perimeter of the following polygon. Be sure to include the correct unit in your answer. 19 cm 15 cm 14 cm 9 cm
How do you find the median and standard deviation for 3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,10,10,11,11, 11,11,11
Answer:
Median is 6
standard deviation is 2.39
Step-by-step explanation:
the median is the mid number in the data set
The median formula is {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number.
There are 51 data points in this set (n = 51)
so 51 / 2 = 25.5, the. number in the 25th slot is our median
3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11
the standard deviation is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
If f(x) = 4x² + 1 and g(x)=x²-5, find (f+ g)(x). ( x ) = 4x² + 1 and g ( x ) = x² - 5 , find ( f + g ) ( x ) .
Answer: [tex]5x^{2}-4[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)=4x^{2}+1+x^{2}-5=\boxed{5x^{2}-4}[/tex]
Input 1,2,3,4,5, n output 2,-1,-4,-7, ?please help me find the linear function!
Answer:
f(x) = -3x + 5
Step-by-step explanation:
The slope of the function is -3 as the outputs decrease by three for each iteration.
The constant is 5 and can be determined if you plug in 1 as an x value and solve for c in an equation like this: -3(1) + c = 2
Toyota manufactures most of the vehicles it sells in the United Kingdom in Japan. The base platform for the Toyota Tundra truck line is ¥1,650,000. The spot rate of the Japanese yen against the British pound has recently moved from ¥197/£ to ¥190/£. How does this change the price of the Tundra to Toyota's British subsidiary in British pounds? Explain.
When the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.
Prices = 1,650,000
Exchange rates = ¥197/£
Change in exchange rate = ¥190/£
So, here Original price of the Toyota tundra is
= 1,650,000 ÷ 197
= 8375.63
New import price is = 1,650,000 ÷ 190
= 8,684.21
Percentage change in the price of the imported trucks should be
= ( New price - Old price) / old price *100 = (8,684.21 - 8375.63) ÷ 8375.63 = 3.68%
Hence , when the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.
(This is the percentage change in the Japanese yen as the price of the truck remains unchanged).
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Find the area of the rectangle.
A rectangle is shown. The left side is labeled with the expression 8 x. The top side is labeled with the expression 7 x plus 1. (1 point)
15x + 1
56x2 + 8x
56x + 8
15x2 + 9x
Answer:
B
Step-by-step explanation:
= (7x+1) • (8x)
= 56x^2 + 8x
Find DG.
DE
2x+17
EF
8
FG
2
x + 20
The value of DG is 4x + 45
Determine the length of a line segmentFrom the question, we are to determine the value of DG
From the given information,
DE = 2x + 17
EF = 8
FG = 2x + 20
Then,
DG = DE + EF + FG
DG = 2x + 17 + 8 + 2x + 20
DG = 4x + 45
Hence, the value of DG is 4x + 45
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Consider the line 4x-8y= -6.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line
Answer:
Perpendicular slope = -2Parallel slope = 1/2======================================================
Explanation:
Let's solve for y to get the equation into y = mx+b form, aka slope intercept form.
4x-8y= -6
-8y= -6-4x
y = (-6-4x)/(-8)
y = -6/(-8) + (-4x)/(-8)
y = 3/4 + (1/2)x
y = (1/2)x + 3/4
This is now in y = mx+b form
m = 1/2 = slope
b = 3/4 = y intercept
We'll ignore the y intercept and focus on the slope only.
-----------------
Rule: If the slope of a line is a/b, then the perpendicular slope is -b/a
Flip the fraction and flip the sign.
In this case, the original slope 1/2 has a perpendicular slope of -2/1 or simply -2.
The original slope multiplied with the perpendicular slope yields -1. So (1/2)*(-2/1) = -1
-----------------
Another rule: Two parallel lines always have equal slopes, but different y intercepts.
The original slope is 1/2, so the parallel slope is also 1/2.
Problem
Suppose that J is between H and K. If HJ=2x+4, JK=3x+3, and KH=22, find the lengths of HJ and JK. Remember to always draw an image first and to pay attention to what the question is asking for!
Solution
Find the Segment Addition Postulate
Use the Segment Addition Postulate and then substitute what we know. Do not use any spaces in your answers.
HJ+JK= Answer
( Answer
)+( Answer
)= Answer
Find x
Once we combine our like terms we get:
Answer
x+ Answer
= Answer
x= Answer
Find HJ and JK
Our questions asked us for the lengths of HJ and JK so we must plug in the value of x to solve for those values. We were given HJ=2x+4 and JK=3x+3.
HJ=2x+4
HJ=2( Answer
)+4
HJ= Answer
And
JK=3x+3
JK=3( Answer
)+3
JK= Answer
3x-4
Check Work
View checked work
Answer:
The lengths of HJ and JK are 50 and 72 respectively.
Given:
J is between H and K.
HJ=2x+4
JK=3x+3
HK=22
Step-by-step explanation:
The total length is given as:
HJ+JK=HK
⇒ (2x+4)+(3x+3)=22
⇒ 5x+7=22
⇒ 5x=22-7
⇒ 5x=15
⇒ x=3
Thus, the length of HJ is (2x+4)=(2*3+4)=10
And the length of JK is (3x+3)=(3*3+3)=12
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The lengths of HJ and JK are 50 and 72 respectively.
Given: J is between H and K. the length of HJ=2x+4, JK=3x+3, and HK=22.
The line HJ and JK are collinear then the total length is given as: HJ+JK=HK
substitute values
⇒ (2x+4)+(3x+3)=22
⇒ 5x+7=22
⇒ 5x=22-7
⇒ 5x=15
⇒ x=3
Thus, the length of HJ is (2x+4)=(2*3+4)=10
And the length of JK is (3x+3)=(3*3+3)=12
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Consider the following data concerning the demand (y) and price (x) of a consumer product the least squares line is found to be y= 306,619-27.71.x
A) Interpret b1
B) find a point prediction of the demand corresponding to be price 2.10
C) Find %95 confidence interval for b1 and interpret it
The value of B1 shows a fall in demand as price rises by a unit. The point prediction is given as y = 306,560.8
How to solve the question using the interceptThe regression equation shows that y= 306,619-27.71.x
b1 = -27.71
The interpretation for b1 is that if the price of this good is increased by 1, then the demand for the good would fall by about 27.71.
The point prediction for demandThe regression line equation is given as
y= 306,619-27.71.x
when x which is price is = 2.10
Then the value of y would be:
y = 306,619 - 27.71*2.10
y = 306,560.8
c. a 95% C1 for B1 is given as:
1.96 * 27.71.
= 54.31
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What is the function that defines the following sequence? 10, 12, 14, 16, 18…
The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).
How to define the function behind a sequence
Sequences are sets of elements characterized by at least a rule. In this case, the sequence shown is characterized by a function that generates even numbers equal or greater than 10. The function behind the sequence is shown below:
s = 10 + 2 · (n - 1) (1)
Where n is the element index.
The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).
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list 4 factors of 24. list 4 multiples of 24.
Answer:
Factors of 24: 1, 2, 3, 4, 6 etc.
Multiples of 24: 48, 72, 96, 120
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
Factors of 24:24 can be written as:
= 1 × 24
= 2 × 12
= 3 × 8
= 4 × 6
So, 1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24.
Multiples of 24 are:1 × 24 = 24
2 × 24 = 48
3 × 24 = 72
4 × 24 = 96
and so on...
So, the first 4 multiples of 24 are 24, 48, 72 and 96.
[tex]\rule[225]{225}{2}[/tex]
what is the measure of 4?
Answer:
∠ 4 = 80°
Step-by-step explanation:
∠ 5 and 100° are vertical angles and are congruent , so
∠ 5 = 100°
∠ 4 and ∠ 5 are same- side interior angles and sum to 180° , that is
∠ 4 + ∠ 5 = 180°
∠ 4 + 100° = 180° ( subtract 100° from both sides )
∠ 4 = 80°
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
3x-4y-5z=-27
5x+2y-2z=11
5x-4y+4z=-7
a. (1,5,51)
b. ( 10, 5, 51)
c. (10, 51, 23)
d. ( 1, 5, 2)
The value of x, y and z will be 1, 5 and 2 respectively
An augmented matrix in linear algebra is a matrix created by joining the columns of two supplied matrices, often so that the same basic row operations may be applied to each of the given matrices individually.
Lets write the augmented matrix by writing the coefficients of all the variables:
3 -4 -5 -27 Row 1
5 2 -2 11 Row 2
5 -4 4 -7 Row 3
We need to get
1 0 0
0 1 0
0 0 1
then the values of x, y, and z will be in the last column.
The row operation (R1=R1/3) is used to get the identity matrix.
1 -4/3 -5/3 -9 Row 1
5 2 -2 11 Row 2
5 -4 4 -7 Row 3
Add row 2 to row 1 and multiply by 5 (R2=R2(5)R1).
1 -4/3 -5/3 -9 Row 1
0 26/3 19/3 56 Row 2
5 -4 4 -7 Row 3
Add row 3 to row 1 and multiply by 5 (R3=R3(5)R1).
1 -4/3 -5/3 -9 Row 1
0 26/3 19/3 56 Row 2
0 8/3 37/3 38 Row 3
Multiply row 2 by 326 (R2=(3/26)R2)
1 -4/3 -5/3 -9 Row 1
0 1 19/26 84/13 Row 2
0 8/3 37/3 38 Row 3
Add row 2 multiplied by 4/3 to row 1 (R1=R1+(4/3)R2)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 8/3 37/3 38 Row 3
Add row 3 to row 2 and multiply the result by 8/3 (R3=R3(8/3)R2).
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 0 135/13 270/13 Row 3
Multiply row 3 by 13/135 (R3=(13/135)R3)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 0 1 2 Row 3
Add row 3 multiplied by 9/13 to row 1 (R1=R1+(9/13)R3)
1 0 0 1 Row 1
0 1 19/26 84/13 Row 2
0 0 1 2 Row 3
Row 2 is reduced by row 3 multiplied by 19/26 (R2=R2(19/26)R3).
1 0 0 1 Row 1
0 1 0 5 Row 2
0 0 1 2 Row 3
Hence the value of x, y and z will be 1, 5 and 2 respectively
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What is the surface area of the cylinder below?
Answer:
Surface Area = 378.25
Step-by-step explanation:
Comment
It's not clear whether the figure has 0 1 or 2 lids. Since it is a cylinder, I will assume 2 lids like a can of soup.
Area lids
diameter = 11.4
radius = d/2
radius = 11.4/2
radius = 5.7
Area = pi * r^2
Area = (3.14 * 5.7^2) * 2 There are 2 lids.
Area = 102.01 yd^2
Area body
This is found by finding the circumference of the lid and multiplying by the height
Circumference
C = 2*pi*r
2*r = the diameter
2*r = 11.4
C = 3.14*11.4
C = 35.80
Area body
Area body = C* h
h = 7.8
Area body = 35.80 * 7.8
Area body = 279.24
Total Area = 102.01 + 279.24 = 378.25
True or False? A corollary is a statement that can be easily proved by using theorem.
simplify (4+i)(3-2i)
Answer: 14 - 5i
Step-by-step explanation:
Answer:
-10i+15 or 15-10i
Step-by-step explanation:
Use the cross multiply method
(4+1)(3-2i)
4x3=12
4x-2i=-8i
1x3=3
1x(-2i)=-2i
now we sum our similarities.
-10i+15
An electrician charges a $40 fee to make a house call plus an hourly rate for labor. If the total bill that takes 2 hours comes to $99 what is the electrician hourly labor rate?
A business student is interested in estimating the 95% confidence interval for the proportion of students who bring laptops to campus.
He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within five percentage points
of the population proportion. What is the minimum sample size required by this student, given that no prior estimate of the population
proportion is available?
(You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places
and "2" value to 3 decimal places. Round up your answer to the nearest whole number.)
Using the z-distribution, the minimum sample size required by this student is of 385.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
We want a margin of error of M = 0.05, with no prior estimate, hence [tex]\pi = 0.5[/tex], then we have to solve for n to find the minimum sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96(0.5)[/tex]
[tex]\sqrt{n} = 1.96 \times 10[/tex]
[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]
n = 384.16
Rounding up, the minimum sample size is of 385.
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