Answer:
The amount the school pays is £32.40
Step-by-step explanation:
The cost of each pen = 15 pence
The cost of each ruler = 20 pence
The number of pens bought by the school = 150
The number of rulers bought by the school = 90
The cost reduction (discount) on the items bought = 1/5
Therefore, we have;
The total cost of the pens bought by the school = 150 × 15 = 2250 = £22.50
The total cost of the rulers bought by the school = 90 × 20 = 1800 = £18.00
The total cost of the writing materials (rulers and pens) bought by the school = £22.50 + £18.00 = £40.50
The discount = 1/5 total cost reduction = 1/5×£40.50 = $8.10
The amount the school pays = The total cost of the writing materials - The discount
The amount the school pays = £40.50 - $8.10 = £32.40
The amount the school pays = £32.40.
HELPP ASAP NEEDED MATH
There are $20n$ members in the Trumpington marching band, and when they line up in rows of 26, there are 4 band members left over. If $n$ is an integer and there are fewer than 1000 band members, what is the maximum number of people that could be in the Trumpington marching band?
Answer:
992
Step-by-step explanation:
Divide 1000 by 26.
The answer is 38 and some left over. We don't care what the leftover is because it is nearly 0.5 and that means 13 people were left over.
Take the integer value (38) and multiply it by 26. You get 988.
You want there to be 4 left over. 4 + 988 = 992. That's one way of doing the problem.
Answer: 940 people is the maximum
==========================================
Explanation:
n = 1 means 20n = 20*1 = 20 members total, which is 4 short of making a row of 26 (so the remainder is 20)
n = 2 means 20n = 20*2 = 40 members. 40/26 = 1 remainder 14. We could make one full row with 14 members left over.
20n < 1000 solves to n < 50 after dividing both sides by 20. This means n is smaller than 50. It has to be larger than 0 or else 20n would be 0 or negative. We can write 0 < n < 50 to specify the range for n.
Since n < 50, this means the largest n can get is n = 49.
--------------------
If n = 49, then 20n = 20*49 = 980
980/26 = 37 remainder 18, which isn't the remainder we want (of 4).
If n = 48, then 20n = 20*48 = 960
960/26 = 36 remainder 24, again not the remainder we want
If n = 47, then 20n = 20*47 = 940
940/26 = 36 remainder 4
If we have 940 members, then we can form 36 rows (26 in each row). So 26*36 = 936 people so far. Then we have 940-936 = 4 people left over.
There are other solutions as well such as n = 34, n = 21, and n = 8. Though n = 47 is the largest n possible to fit all the conditions required.
Find the solution for this system of equations. 2x - 3y = 2 x= 6y -5
Answer:
Step-by-step explanation:
2(6y - 5) = 2
12y - 10 = 2
12y = 12
y = 1
x = 6(1) - 5
x = 6 - 5 = 1
(1,1)
Answer: (1,1)
Step-by-step explanation: 2(6y - 5) = 2
12y - 10 = 2
12y = 12
y = 1
x = 6(1) - 5
x = 6 - 5 = 1
(1,1)
the product of 5 and z
Answer:
5z
Step-by-step explanation:
As product = multiplication =>
5 x z --> 5(z)
[tex]\text{Find the product of 5 and z}\\\\\text{The key term in this questions is product, and in math it translates to}\\\text{the answer when multiplled}\\\\\text{In this case, you would multiply them together to get your "product"}\\\\\text{Solve:}\\\\5\cdot z\\\\\boxed{5z}[/tex]
Lilli jogs 12 mile in 110 hour. What is Lilli's rate in miles per hour?
Answer:
.109090909 miles per hour
Step-by-step explanation:
To find miles per hour, take the miles and divide by the hours
12 miles/110 hours
.109090909 miles per hour
Answer:
0.11
Step-by-step explanation:
Hello!
To find how many miles Lilli jogs per hour we divide the distance by the time it took
12/110 = 0.109
The answer is 0.11
Hope this helps!
Which function has only one x-intercept at (-6, 0)?
Of(x) = x(x-6)
O f(x) = (x - 6)(x - 6)
f(x) = (x + 6)(x - 6)
Of(x) = (x + 6)(x + 6)
Answer:
f(x) = (x + 6)(x + 6)
f(x)=0
x+6=0 ⇒ x=-6
Set (x+6)(x+6) equal to zero and solve each equation for x. We really only have one equation and it would be x+6 = 0 which solves to x = -6.
Plug x = -6 into f(x) and you would get f(x) = 0.
Suppose that $9500 is placed in an account that pays 9% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
so
(b) Find the amount in the account at the end of 2 years.
$
?
Answer:
$11286.95 second year
$10335 first year
Step-by-step explanation:
9% of 9500 is 855, 9500 plus 855 = 10335. (first year)
9% of 10335 is 931.95, and 10335+931.95 is 11286.95. (second year)
The amount in the account at the end of 1 year $10335 (first year)
The amount in the account at the end of 2 years $11286.95.
What is the compound interest?Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Formula:
A = P(1 + {r}/{n})^{n.t}
here, we have,
$9500 is placed in an account that pays 9% interest compounded each year.
so, we get,
9% of 9500 is 855,
9500 plus 855 = 10335. (first year)
again,
9% of 10335 is 931.95,
and 10335+931.95 is 11286.95. (second year)
Hence, The amount in the account at the end of 1 year $10335 (first year)
The amount in the account at the end of 2 years $11286.95.
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Briefly explain how you would graph an equation such as y=7x-2
Answer:
put a mark at negative 2 on the graph then you would go up seven rigght one until you cant then you would go back to -2 and go down seven left one until you cant
Step-by-step explanation:
If 8(x) = -2 and g(x) = 2x2 + x = 3, find ( +g)(x).
A. 2x2 + 2x-5
B. x - 6
C. 2x - 3+1
D. 2x2 + x +1
[tex](f+g)(f)=f(x)+g(x)\\\\\\f(x)=\dfrac{x}{2}-2\\g(x)=2x^2+x-3\\\\(f+g)(x)=\dfrac{x}{2}-2+2x^2+x-3\\(f+g)(x)=2x^2+\dfrac{x}{2}+\dfrac{2x}{2}-5\\(f+g)(x)=2x^2+\dfrac{3x}{2}-5\\(f+g)(x)=2x^2+\dfrac{3}{2}x-5[/tex]
Which number is equal to 10^-3?
-1,000
-30
0.001
0.003
Work Shown:
10^(-3) = 1/( 10^3 ) = 1/1000 = 0.001
The rule used here is x^(-k) = 1/( x^k )
Answer:
C. O.001
Step-by-step explanation:
10^-3 = (1)/(10^3)
move the negative exponent to the denominator
(1)/(1000)
simplify 10^3 in the denominator
(1)/(1000) = 0.001
What are the vertical asymptotes of the function above?
1) x= -1 and x = -2
2) x= -1 and x = 2
3) x= 1 and x = -2
4) x = 1 and x = 2
Answer:
third option
Step-by-step explanation:
Given
f(x) = [tex]\frac{5x+5}{x^2+x-2}[/tex]
The denominator cannot be zero as this would make f(x) undefined.
Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.
solve x² + x - 2 = 0 ← in standard form
(x + 2)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 1 = 0 ⇒ x = 1
The vertical asymptotes are x = 1 and x = - 2
Write the equation of the line which passes
through the points (4,2) and (-3, 1)
Answer:
y = 1/3x + 4/7
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Formula: y = mx + b
Step 1: Find slope m
m = (1 - 2)/(-3 - 4)
m = -1/-7
m = 1/7
y = 1/7x + b
Step 2: Find y-intercept b
1 = 1/7(3) + b
1 = 3/7 + b
b = 4/7
Step 3: Write linear equation
y = 1/3x + 4/7
it’s a 425 mile drive from San Jose to Los Angeles.
it’s about 320 mile Drive from San Jose to Santa Barbara.
write an equation showing that the distance traveled on the first day plus the distance traveled on the second is equal to 425 miles
Answer:
The answer is below
Step-by-step explanation:
The distance traveled the first day = Distance from San Jose to Santa Barbara = 320 mile.
The distance traveled the second day = Distance from Santa Barbara to Los Angeles.
But From San Jose to Los Angeles = 425 mile. Therefore:
Distance From San Jose to Los Angeles = Distance from San Jose to Santa Barbara + Distance from Santa Barbara to Los Angeles
425 = 320 + Distance from Santa Barbara to Los Angeles.
Distance from Santa Barbara to Los Angeles = 425 - 320 = 105 mile
The distance traveled the second day = Distance from Santa Barbara to Los Angeles = 105 miles
The distance traveled the first day + The distance traveled the second day = Distance from San Jose to Santa Barbara + Distance from Santa Barbara to Los Angeles = 320 + 105 = 425 miles
The distance traveled the first day + The distance traveled the second day = 425 miles
For a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r=0.989. Using alph=0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Correlation Coefficient (r) = 0.989
alph=0.05
Number of observations (n) = 8
determine if there is a linear correlation between chest size and weight.
Yes, there exists a linear relationship between chest size and weight as the value of the correlation Coefficient exceeds the critical value.
What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?
To determine the the proportion of variation in weight that can be explained by the linear regression line between weight and chest size, we need to obtain the Coefficient of determination(r^2) of the model.
r^2 = square of the correlation Coefficient
r^2 = 0.989^2 = 0.978121
Hence, about 0.978 (97.8%) of the variation in weight can be explained by the linear relationship between weight and chest size.
In the expression 7³ - 4 · 3 +8, the first operation is? A. An Exponent B. Subtraction C. Multiplication D. Addition
Answer:
An exponent
Step-by-step explanation:
look at PEM/DA/S
Parenthesis
EXPONENTS
and then you can stop the first operation is 7^3
this is an exponent
(also brainliest if this helped please!)
The first operation according to the PEM/DA/S rule to evaluate the 7³ - 4 · 3 +8 expression is an exponent.
What is PEM/DA/S rule?It is the order or sequence of evaluating a math expression. We can remember the order using PEM/DA/S: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In the given expression, using PEM/DA/S rule (Sometimes called BODMAS; the synonym of PEM/DA/S):
evaluate 7³ - 4 · 3 +8
The first operation is an exponent term, i.e.,
[tex]7^{3}[/tex]
Hence our first operation in the sequence of evaluating the given expression value is an exponent.
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The distance between two schools A and B is 2km.A market is situated 3/4 of the distance from A to B.How far is the market from B?
Answer:
0.5 km
Step-by-step explanation:
the schools are 2km apart, so we are trying to find 3/4 of 2km, which is 1.5. So, the market is 1.5km from school A, which means that it is .5km from school b since they are 2km apart
. Find the sum of the geometric sequence. (1 point) 1, one divided by four, one divided by sixteen, one divided by sixty four, one divided by two hundred and fifty six
Answer:
0.332
Step-by-step explanation:
given series
1/4, 1/16,1/64.1/256
this is geometric series
where common ratio r is given by
nth term/ (n-1)th term
let the second term is nth term and first term is (n-1)th term
r = 1/16 / (1/4) = 1/4
___________________________________________
sum of series is given by
a (1-r^n)/1-r
where a is first term
n is the number of terms
r is the common ration
___________________________________________
in the given series
1/4, 1/16,1/64.1/256
a = 1/4
r = 1/4
n = 4
thus ,
sum = 1/4(1-(1/4)^4)/ (1-1/4)
sum = 1/4(1-(1/256)/(4-1)/4
sum = 1/4((256-1)/256 / 3/4
1/4 in numerator and denominator gets cancelled
sum =( 255/256*3) = 255/768 = 0.332
Thus, sum of series is 0.332.
Answer:
341/256
Step-by-step explanation:
I took the test and got the answer right
You just give all the fractions a common denominator of 256 and then change and add up the numerators and you get 341
Write a formula that will give the area of the shaded region in the figure below .
Answer:
a=(29-2)*(12-3)
Step-by-step explanation:
a=LW
a=(L-2)*(W-3)
a=(29-2)*(12-3)
a=27*9
a=243ft²
Answer:
[tex]\Large \boxed{A = (29 - 2) \times (12 - 3)}[/tex]
Step-by-step explanation:
The length of the whole rectangle is 29 feet.
The width of the whole rectangle is 12 feet.
The length of the shaded region is 2 feet less than the length of the whole rectangle.
The width of the shaded region is 3 feet less than the width of the whole rectangle.
The area of a rectangle is length × width.
So we can create a formula to solve for the area of the shaded region:
A = (29 - 2) × (12 - 3)
Solving for the area.
A = 27 × 9
A = 243
The area of the shaded region is 243 feet².
When three is added to four times a number, the result is 15
(a) Write an equation to represent the above information.
Answer
(b) Solve your equation in (a)
Answer:
A. 4y + 3 = 15
B. y = 3
Step-by-step explanation:
Three is added to four times a number, the result is 15
A. Equation to represent the above information:
Let the unknown number= y
4 * y + 3 = 15
4y + 3 = 15
B. Solve your equation in (a)
4y + 3 = 15
Collect like terms
4y = 15 - 3
4y = 12
Divide both sides by 4
4y / 4 = 12 /4
y = 3
Therefore, the unknown number is 3
Question is in the pic I really suck at this stuff can I get some help plssssss
Answer:
see below
Step-by-step explanation:
The hypotheses is the if part of the statement ( after the if)
hypotheses: it is January
The conclusion is the then part of the statement ( after the then)
conclusion there is snow
The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?
Answer:
[tex] 9.3 + b = 14.5 [/tex]
Step-by-step explanation:
Longest side of ∆ = 2a = 6.2 cm
If the shortest side is, a, and we are told that the longest side is twice the shortest side, therefore, length of shortest side is
The sum of the 3 sides = perimeter = 14.5 cm
Thus,
[tex] a + 2a + b = 14.5 cm [/tex]
Plug in the values of a and b
[tex] 3.1 + 6.2 + b = 14.5 [/tex]
The equation that can be used to find the side lengths is [tex] 9.3 + b = 14.5 [/tex]
(x-y)²-(x+y)² a)0 b)2y² c)-2y² d)-4xy e)-2(x+y)²
Answer:
D
Step-by-step explanation:
-4xy
will be your answer after factoring
Answer:
d
Step-by-step explanation:
Given
(x - y)² - (x + y)² ← expand both factors using FOIL
= x² - 2xy + y² - (x² + 2xy + y²) ← distribute by - 1
= x² - 2xy + y² - x² - 2xy - y² ← collect like terms
= - 4xy → d
john is 15 years old. john's mom takes him and his younger soster to a football game. tickets are $22 for adults and $16 for children (18 and under). what is the total cost of thr tickets?
Answer:
$38
Step-by-step explanation:
cost of ticket for adult = $22
cost of ticket for youngster = $16
______________________________
cost of ticket for John's mom = $22 as she is adult
cost of ticket for john = $16 as he is young , his age is less than 18 years
Total cost of ticket for John and his mother = $22 + $16 = $38
for 0°<θ<-180° which of the primary trigonometric functions may have positive values?
sine and cosecant.
you can see the graph or on unit circle, as the for these ratios, (which depend on y coordinate) 1st and 2nd quadrant have positive y coordinate
The scale on a map of Virginia shows that 1 inch represents 20 miles the actual distance from Richmond Virginia to Washington DC is 110 miles on the map how many inches are between the two cities
Answer:
5.5 inches
Step-by-step explanation:
Proportions:
1 inch ⇔ 20 miles
W inch ⇔ 110 miles
W = 110*1/20
W = 5,5 inch
root 64 divided by root 3 64
Answer:
4
Step-by-step explanation:
4x4x4=64
Answer:
0.4193
Step-by-step explanation:
Root 64=8
Root 364=19.08...in 4 s.f
8÷19.08=0.4193...in 4 significant figures (4s.f)
Two buildings are 12m apart on the same horizontal level. From the top of the taller building, the angle of depression of the bottom of the shorter building is 48degrees and from the bottom, the angle of of elevation of the top of the shorter building is 36 degrees. Calculate the difference in the heights of the buildings
Answer:
2.08 meters
Step-by-step explanation:
From the diagram attached :
We can calculate the height of the shorter building using trigonometry :
s = Height of shorter building
t = height of taller building
Tanθ = opposite / Adjacent
θ = 36°
Adjacent = 12, opposite = s
Tan36° = s / 12
0.7265425 × 12 = s
s = 8.72 meters
s = height of shorter building 8.72 meters ( 2 decimal places)
Height of taller building :
Tanθ = opposite / Adjacent
θ = 48°
Adjacent = t ; opposite = 12
Tan48° = 12 / t
1.1106125 = 12 / t
1.1106125 × t = 12
t = 12 / 1.1106125
t = 10.80 meters ( 2 decimal places)
Height of Taller building = 10.80 meters
Difference in height :
(10.80m - 8.72m) = 2.08 meters
Which of the following is an example of the difference of two squares?
A x2−9
B x3−9
C (x+9)2
D (x−9)2
I know the answer is either A or B i might be wrong tho pls help im not sure.
Answer:
1) What does it mean when a polynomial equation is in standard form?
All terms are on one side of the equation, and zero is on the other side.
2) When factoring 6x2−7x−20 by grouping, how should the middle term be rewritten?
It should be written as 8x−15x.
3) Is the given equation a quadratic equation? Explain.
x(x−6)=−5
The equation is a quadratic equation because there is an x2-term.
4) Which of the following factored forms given below represent the correct factorization of the trinomial x2+10x+16?
(2+x)(8+x)
5) Which of the following is an example of the difference of two squares?
x2−9
Step-by-step explanation:
I hope this helps you out ☺
A binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:
A. [tex]x^2 - 9[/tex]
Recall:
Difference of two squares is when you have a binomial that is expressed as [tex]x^2 - y^2[/tex].The first and second term of the binomial will have an exponential of 2 wile the subtraction sign will be in the middle.Thus, from the options given, option A: [tex]x^2 - 9[/tex] is an example of a binomial that is the difference of two squares.
This is why:9 can be expressed as [tex]3^2[/tex].
In summary, a binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:
A. [tex]x^2 - 9[/tex]
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1. Over the next two days, Clinton Employment Agency is interviewing clients who wish to find jobs. On the first day, the agency plans to interview clients in groups of 2. On the second day, the agency will interview clients in groups of 4. If the employment agency will interview the same number of clients on each day, what is the smallest number of clients that could be interviewed each day? 1
Answer:
the smallest number of clients that could be interviewed each day is 2
Step-by-step explanation:
From the information given, we are being told that:
Over the next two days, Clinton Employment Agency is interviewing clients who wish to find jobs.
On the first day, the agency plans to interview clients in groups of 2.
This implies that , a single group contains 2 clients
On the second day, the agency will interview clients in groups of 4.
This implies that, a single group contains 4 clients
If the employment agency will interview the same number of clients on each day,
the objective is to determine the smallest number of clients that could be interviewed each day.
We we are meant to find out here is the Lowest Common Multiple i.e the L.C.M of the group of clients.
So,
the factors of 2 = 1 , 2
the factors of 4 = 1, 2 and 4
The lowest common multiple from the above factors is 2
Therefore, the smallest number of clients that could be interviewed each day is 2
All of Ralph's ranch land was divided equally among his six children whose daughter land portion of the ranch land was divided among her four children how much of Roslyn was in Inherited by 1 of Lynn's children
Complete question:
All of Ralph's ranch land was divided equally among his 6 children. His daughter Lynn's portion of the ranch land was divided equally among her 4 children. How much of Ralph's ranch land was inherited by 1 of Lynn's children?
Answer:
1 / 24
Step-by-step explanation:
Number of Ralph's children = 6
Number of Lynn's children = 4
If Ralph's land were divided equally among his six children, the fraction each child gets equals
Proportion of land / number of children
= 1 / 6
Therefore, Lynn who is also Ralph's daughter gets 1/6 portion.
If 1/6 is shared equally between her four children, then ;
Her portion ÷ 4
(1/6) ÷ 4
(1/6) × (4/1)
= 1/ 24
Each of Lynn's children gets 1 / 24
which of the following shows maximum rise in temperature?
a} 23 to 32
b} [ -10] to 1
c} [-18] to [-11]
d} [-5] to 5
Answer:
b) (-10) to 1Step-by-step explanation:
it shows the maximum rise in temperature.
Answer:
b answer, will show the rise in temperature
