Ms. Hawkinson is planning to take more pictures of her students. She bought 8 rolls of film and 2 camera batteries for $23.00. The next day, she went back and bought 6 more rolls of film and 2 batteries for $18.00. How much did each roll of film and battery cost?
Answers
Answer:
1 Roll = $2.50
1 Battery = $1.50
Step-by-step explanation:
From the question we know that,
8 Rolls + 2 Batteries = $23, and
6 Rolls + 2 Batteries = $18
We can subtract the two equations to obtain a third equation,
(8 Rolls + 2 Batteries) - (6 Rolls + 2 Batteries) = $23 - $18
(8 - 6) Rolls + (2 - 2) Batteries = $23 - $18
2 Rolls = $5
Divide RHS and LHS by 2, to obtain the cost of a roll,
2 Rolls / 2 = $5 / 2
1 Roll = $2.50
If one roll costs $2.50 then 6 rolls cost $15,
6 x $2.50 = $15
We plug in this value into the second equation,
$15 + 2 Batteries = $18
Subtract both sides by $15,
$15 + 2 Batteries - $15 = $18 - $15
2 Batteries = $3
Divide RHS and LHS by 2 to obtain the final answer,
2 Batteries / 2 = $3 / 2
1 Battery = $1.50
Related Questions
What fraction of the class has the number of pets that occurs most often? Express your answer as a percent, too. *
Answers
Answer:
i dont think you have included all the info of the question so if you do that i might be able to help you :)
Step-by-step explanation:
Three boys step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. What is the minimum distance each should cover so that all can cover the distance in complete steps?
Answers
Answer:
Step measure of 1
st
Boy=63cm
Step measure of 2
nd
Boy=70cm
Step measure of 3
rd
Boy=77cm
LCM of 63,70,77
LCM=2×3×3×5×7×11=6930
Hence, the minimum distance each should cover so that all can cover the distance in complete steps is 6930 cm.
2 ∣
63,70,77
3 ∣
63,35,77
3 ∣
21,35,77
5 ∣
7,35,77
7 ∣
7,7,77
11 ∣
1,1,11
1,1,1
Step-by-step explanation:
P.S- like my comment and more thanks
Answer:
6930 cm
Step-by-step explanation:
To find the minimum distance that all three boys can cover in complete steps, we need to find the least common multiple (LCM) of their step lengths.
The least common multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the given numbers without leaving a remainder.
The step lengths of the three boys are 63 cm, 70 cm, and 77 cm.
To find the LCM of 63, 70 and 77, first find the prime factorization of each number.
Prime factorization is the process of expressing a positive integer as a product of its prime factors.
Prime factorization of 63: 3 × 3 × 7 = 3² × 7
Prime factorization of 70: 2 × 5 × 7
Prime factorization of 77: 7 × 11
To find the LCM, take the highest power of each prime factor that appears in any of the numbers and multiply them together:
\(\begin{aligned} \implies \sf LCM &= 2 \times 3^2 \times 5 \times7 \times11 \\&= 2 \times 9 \times 5 \times 7 \times11 \\&= 18 \times 5 \times 7 \times11 \\&= 90 \times 7 \times11 \\&= 630 \times11 \\&=6930\end{aligned}\)
Therefore, the minimum distance each boy should cover so that all can cover the distance in complete steps is 6930 cm.
1) Mrs. Pinkard is wrapping a present in a box. What is the total amount of wrapping paper he will need if the dimensions of the box are 4 inches in height, 8 inches in width, and 12 inches in length? *
Answers
Answer:
2,304
Step-by-step explanation:
4x8x12
4x8=32
32x12=384
384x6=2,304
True or False: Determine whether each statement is true or false, and briefly explain your answer by citg a Theorem, providing a counterexample, or a convincing argument. A. If A is a 7 x 4 matrix, then A can have rank 5 b. If A is a 4 x 7 matrix, then A can have nullity 5 c. If A is a 7 x 4 matrix, then A can have nullity 5d. If A is a 7 × 4 matrix, then rank(A) + nullity(A) = 7 e. If A is a 6 x 8 full rank matrix, then nullity(A)2 f. If A is a 5 x8 full-rank trix, then A16] is always consistent for any beR g. IfA is a 5 × 8 full-rank matrix, then | Alb | always has a unique solution for any b E R
Answers
The following are the statements with explanation whether the statement is true or false, using rank-nullity theorem and invertible matrix theorem.
a. False. According to the rank-nullity theorem, the rank of a matrix plus its nullity equals the number of columns. As a result, a 7 x 4 matrix can only have a rank of 4, because the nullity cannot be negative.
b. False. According to the rank-nullity theorem, the nullity of a matrix plus its rank equals the number of columns. As a result, because the rank cannot be negative, a 4 x 7 matrix can have a maximum nullity of 3.
c. True. According to the rank-nullity theorem, the nullity of a matrix plus its rank equals the number of columns. As a result, a 7 x 4 matrix has a maximum nullity of 3, implying that it can have a nullity 5.
d. True. According to the rank-nullity theorem, the rank of a matrix plus its nullity equals the number of columns. As a result, if A is a 7 x 4 matrix, rank(A) + nullity(A)= 4 + nullity(A) = 7. When we solve for nullity(A), we get nullity(A) = 3, therefore rank(A) + nullity(A) = 4 + 3 = 7.
e. False. According to the rank-nullity theorem, the nullity of a matrix plus its rank equals the number of columns. As a result, if A is a 6 x 8 full-rank matrix, its nullity is 8 - 6 = 2, rather than nullity(A) = 2² = 4.
f. True. According to the invertible matrix theorem, a full-rank matrix has a unique solution for any non-zero right-hand side vector b. As a result, the system Ax = b is always consistent for every non-zero b.
g. True. According to the invertible matrix theorem, a full-rank matrix has a unique solution for each right-hand side vector b. As a result, the system Ax = b will always have a distinct solution for any b.
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can someone help please and thank you
Answers
Answer:
1.125
Step-by-step explanation:
d/0.25=4.5
•0.25 •0.25
d= 1.125
If PQ = 6cm, QR = 55cm and RP = 55cm, What type of triangle can be constructed?
Answers
Answer:
isosceles triangle
Step-by-step explanation:
In an isosceles triangle 2sides are equal
Profit, P(x), is the difference between revenue, R(x), and cost, C(x), so P(x) = R(x) - CC). Which
expression represents P(x), if R(I) = 224 – 3x3 + 2x – 1 and C(x) = 24 – + 22 + 3?
3.14 - 31" - 22 + 4x + 2
** _ 3.7? _ 22 +42 + 2
I _ 313 + x² - 4
208_32
I NEED HELP ASAP
Answers
Answer:
Step-by-step explanation:
Profit, P(x), is the difference between revenue, R(x), and cost, C(x)
R(x) = 2x^4 - 3x^3 + 2x - 1
C(x) = x^4 -x^2 + 2x + 3
Substituting into the equation
P(x) = R(x) - C(x)
= (2x^4 - 3x^3 + 2x - 1) - (x^4 -x^2 + 2x + 3)
= x^4 - 3x^3 + x^2 - 4
The answer is the lower left option.
Answer:
\(P(x)=x^4-3x^3+x^2-4\)
(This is the option found in the lower-left corner)
Step-by-step explanation:
When given the following functions,
\(R(x)=2x^4-3x^3+2x-1\)
\(C(x)=x^4-x^2+2x+3\)
The problem asks one to find (\(P(x)\)), moreover, one is given the following information,
\((P(x))=(R(x))-(C(x))\)
Substitute,
\(P(x)=(2x^4-3x^3+2x-1)-(x^4-x^2+2x+3)\)
Simplify, multiply everything in the second parenthesis by the negative sign outside of it,
\(P(x)=2x^4-3x^3+2x-1-x^4+x^2-2x-3\)
Combine like terms, only operations between coefficients of the same variable with the same degree (exponent) can be performed,
\(P(x)=x^4-3x^3+x^2-4\)
if you decide to have four officers, a president, a vice president, a secretary and a treasurer, how many possible choices for officers are there?
Answers
giving you a total of 4 x 3 x 2 x 1 = 24 possible combinations.
If you decide to have four officers, a president, a vice president, a secretary, and a treasurer, there are 24 possible choices for officers. This is because you can choose any of the four positions for the president, then any of the remaining three positions for the vice president, any of the remaining two positions for the secretary, and the last position for the treasurer, giving you a total of 4 x 3 x 2 x 1 = 24 possible combinations.
A permutation is an act of arranging objects or numbers in order.
Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
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Beth Mack and her dog Trouble are exploring in the woods east of Birnam Woods Road, which runs north-south. They begin walking in a zigzag pattern: 1 km south, 1 km west, 1 km south, 2 km west, 1 km south, 3 km west, and so on. They walk at the rate of 4 km/h. If they started 15 km east of Birnam Woods Road at 3:00 p.m., and the sun sets at 7:30 p.m., will they reach Birnam Woods Road before sunset? Explain.
Answers
We need to find whether the people and the dog will reach the road before sunset.
The people and their dog will not reach the road by 7:30 pm.
The path of the people is 1 km south and a subsequent increase of 1 km distance towards the west direction.
So, the path will be
1 km South, 1 km West
1 km South, 2 km West
1 km South, 3 km West
1 km South, 4 km West
1 km South, 5 km West
In order to reach the road the total 15 km west has to be walked.
So, now the total distance walked west is
\(1+2+3+4+5=15\ \text{km}\)
Time to walk = 4 hours and 30 minutes = 4.5 hours
Speed of walking = 4 km/h
Total distance walked = \(1+2+3+4+5+1+1+1+1+1=20\ \text{km}\)
Time is given by
\(\dfrac{20}{4}=5\ \text{hours}\)
So, Beth, Mack and her dog would not reach the road before sunset.
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67 = 4u — 9, simplify your answer as much as possible
Answers
Answer:
u=19
Step-by-step explanation:
4u-9=67 1. add 9 on both sides
4u = 76 divide 4 on both sides
4u/4 = 76/4
u = 19
67=4u-9
-4=-9-67
-4u=-76
u=-76/-4
u=19
Lydia invests $1000 in an account that pays
5.25% compounded daily. Gabrielle invests the
same amount of money in an account that pays
5.25% compounded semi-annually instead.
Lydia makes more money in 3 years, but how
much more does she make?
Answers
Lydia earns $52.5 more than Gabrielle after 3 years.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
we can use the formula for compound interest:
\(A = P(1 + r/n)^n^t\)
where A is the final amount,
P is the principal (initial investment),
r is the annual interest rate (as a decimal),
n is the number of times the interest is compounded per year, and
t is the number of years.
For Lydia (n=365)
A=1000(1+0.0525/365)¹⁰⁹⁵
A=1115.7
For Gabrille, we use the same formula but with n = 2 (compounded semi-annually):
A = 1000(1 + 0.0525/2)⁶
A = 1000(1.0265625)⁶
A = 1168.2
To find the difference in the amounts earned, we subtract Gabrielle's amount from Lydia's:
1168.2- 1115.7 = 52.5
Hence, Lydia earns $52.5 more than Gabrielle after 3 years.
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Doordash and Uber Eats motivate their drivers to take jobs by offering more money as more time passes. The following information shows how much each company offers depending on
how many minutes have passed after the customer's request.
DoorDash(table):
minutes: 0 ,5,10,15, 20, 25, (greater then or equal to sign) 30
money offered: $2.50 , $2.75 , $3.00, $5.00,$8.00, $12.00,$30.00
a) State the y-intercepts of each function and state what each one represents in this real-world context (Show your work)
b) State the maximum of each function and state what each one represents in this real-world context. (Show your work)
c) At what point do both companies pay the same amount? If you had to choose one company to work for, which one would you choose and why? (Show your work. Use evidence from above)
Answers
The functions of DoorDash and UberEats are linear functions and piecewise functions
The y-intercepts are $2.50 and $5, respectivelyThe maximum of the functions are $12.00 and $8.00, respectively.The point where the salaries are the same is (25, 12.00)The y-intercept of the functions?This is the point where the input value is 0 i.e. x = 0.
From the table, we have:
(x,y)= (0,2.50)
From the graph, we have:
(x,y)= (0,5)
Hence, the y-intercepts are $2.50 and $5, respectively
The maximum of the functionsThis is the point where the output value is at the highest
From the table, we have:
(x,y)= (25,12.00)
From the graph, we have:
(x,y)= (20,8.00)
Hence, the maximum of the functions are $12.00 and $8.00, respectively.
This also represents the maximum salaries of working in both companies
When the salary is the sameThis is the point where the values of both functions are equal
From the table and the graph, we have:
(x,y)= (25,12.00)
Hence, the point where the salaries are the same is (25, 12.00)
DoorDash has a higher maximum salary; so I would choose to work at DoorDash
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1. Differentiate the function f(x) = ln (81 sin^2 (x)) f’(x) 2. Differentiate the function P(t) = in ( √t2 + 9) p' (t) 3. if x2 + y2 + z2 = 9, dx/dt = B, and dy/dt = 4, find dz/dt when (x,y,z) = (2,2,1)
dz/dt =
Answers
First you will get 4dz
Find the area of the composite figure below.
Answers
Answer:
96m
Step-by-step explanation:
The sum of squares due to regression (SSR) is a. 1434 b. 505.98 c. 50.598 d. 928.02
Answers
The correct answer is option d. 928.02. This can be answered by the concept of sum of squares.
The sum of squares due to regression (SSR) is a statistical term that measures the total amount of variation in the dependent variable that can be explained by the regression model. It is also known as the explained sum of squares. SSR is an important component of the analysis of variance (ANOVA) used in regression analysis to assess the goodness of fit of the regression model.
In the given options, option d. 928.02 is the correct answer as it represents the sum of squares due to regression (SSR). Option a. 1434, option b. 505.98, and option c. 50.598 are not correct as they do not represent the sum of squares due to regression (SSR).
Therefore, the correct answer is d. 928.02.
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please help if you can!
Answers
Answer:
m' (-2, 4)
n' (-2, 1)
o' (3, 1)
p' (3, 4)
Step-by-step explanation:
As an estimation we are told £3 is €4.
Convert £28.20 to euros.
Give your answer rounded to 2 D
Answers
Answer:
21
Step-by-step explanation:
In the figure below, DBE is the result of a dilation of ABC with point B as the center of dilation. Which statement best uses this information to explain why the AA criterion can be used to prove ABC ~ DBE ?
Answers
Answer: the 4
Step-by-step explanation:
Answer: Its B
Step-by-step explanation:
select all the correct answers. which three pairs of side lengths are possible measurements for the triangle?
Answers
The three pairs are (AB = 6, BC = 6) (AB = 4, AC = 4√2) and (BC = 2√2, AC = 4). So, First option, Option 5. and Option 6 are correct answers.
Since we know that,
Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
The formula for a 30-60-90 triangle is this:
1) Side opposite to 30 will be value a.
2) Side opposite to 60 will be value a√3
3) Hypotenuse will be 2a.
AB is opposite of the angle with 30 degree measurement.
BC is opposite of the angle with 60 degree measurement.
The sides of an isosceles right triangle are in the ratio,
1:1:√2
where √2 is the hypotenuse.
For the example, BC = 2√2, then AC = 2√2 x √2 = 4.
Therefore, the three pairs are;
1. (AB = 6, BC = 6)
5. (AB = 4, AC = 4√2)
6.(BC = 2√2, AC = 4).
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The complete question is attached below:
Which data set could be represented by the box plot shown below?
Choose 1 answer:
A 2,3,5,5, 7, 7, 8, 10, 11
B 2,3,5,5,6,7,8,8,11
C 2,3,5,5, 6, 7, 8, 10, 11
D 3,3,5,5, 6, 7, 8, 9, 11
Answers
A data set which could be represented by the box plot shown above include the following: B. 2, 3, 5, 5, 6, 7, 8, 8, 11.
What is a box plot?In Mathematics, a box plot is sometimes referred to as a box-and-whisker plot and it can be defined as a type of chart that is used for the graphical or visual representation of the five-number summary of a data set with respect to locality, skewness, and spread.
By using the box-and-whisker plot (box plot) shown in the image attached above, the five-number summary for the given data set include the following:
Minimum = 2.First quartile = 4.Median = 6.Third quartile = 8.Maximum = 11.By critically observing the box-and-whisker plots (see attachment), we can logically deduce that it represents all of the five-number summary for 2, 3, 5, 5, 6, 7, 8, 8, and 11.
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what is the best game that you think of
Answers
Answer:
The best game I can think of is the game of life
Step-by-step explanation:
Simply because its fun to have different experiences each time you play and can chose whatever
Answer:
Mobile- Animal crossing pocket camp
Step-by-step explanation:
I love this game :3
It's really relaxing and a fun way to pass a few minutes. -Crispin
I just need the answer ASAP Image transcription textThink of each segment in the diagram as part of a line. All the angles are right angles. Which plane(s) contain(s) point B and appear to be parallel to
plane CDH?
B
D
A
NO
FISHING
G
F
H
E
plane ABC
plane AEH
O plane ABF
O plane BCF
O plane ADE
Scald... Show more
Answers
The planes that contain point B and appear to be parallel to plane CDH are plane ABC and plane ADE.
In the given diagram, we can observe that point B lies on both plane ABC and plane ADE. To determine if these planes are parallel to plane CDH, we need to examine the angles formed. Since all the angles in the diagram are right angles, we can conclude that plane ABC and plane ADE are perpendicular to plane CDH. Therefore, they appear to be parallel to plane CDH.
Based on the information provided, we can state that plane ABC and plane ADE contain point B and appear to be parallel to plane CDH.
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Determine the equation of the circle with center (0, -4) containing the point
(√44,-5).
Answers
The equation of the circle with center (0, -4) containing the point (√44,-5) is \(x^2 + (y + 4)^2 = 45.\)
The center of the circle is given as (0, -4). Let the radius of the circle be denoted by r. Then the equation of the circle can be written as:
\((x - 0)^2 + (y + 4)^2 = r^2\)
where (x, y) represents any point on the circle.
Now we need to find the value of r. We know that the circle passes through the point (√44,-5). Substituting these values in the equation above, we get:
(√44 - \(0)^2 + (-5 + 4)^2 = r^2\)
Simplifying this, we get:
\(44 + 1 = r^2\)
Thus\(, r^2 = 45.\)
Substituting this value of\(r^2\)in the equation of the circle, we get:
\(x^2 + (y + 4)^2 = 45\)
Therefore, the equation of the circle with center (0, -4) containing the point (√44,-5) is:
\(x^2 + (y + 4)^2 = 45.\)
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Work out m and c for the line:
y=x-8
never mind i got it
Answers
Answer:
m = 1 c = -8
Step-by-step explanation:
40 points!! Two questions (a) and (b)!!
Answers
Answer:
(a) Kaylee earns $19.50 per hour.
(b) Kaylee earns more per hour.
Step-by-step explanation:
a)
\(m\) = $ per hour
\(y = mx\)
\((39) = m(2)\)
\((39 = m(2)) = 19.50 = m\)
b) Kaylee earns more per hour
Kaylee earns $19.50 per hour and Joey earns $16.50 per hour.
Suppose we want to choose 3 letters, without replacement. from the 5 letters A, B, C, D, and E. How many ways can this be done, if the order of choices does not matter? Answer: [a]
Answers
The number of different combinations of 3 letters is 10 (if order does not matter)
In how many ways can this be done?Remember that if we have a set of N elements, and we want to select K from these, the number of different combinations is given by:
\(C(N,K) = \frac{N!}{(N - K)!*K!}\)
In this case we know that:
N = 5 (the number of letters)
K = 3 (the ones that we select)
Replacing that we will get:
\(V(5, 3) = \frac{5!}{(5 - 3)!*3!} = \frac{5*4}{2} = 10\)
It can be done in 10 different ways.
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. Sofia learned 10 recipes to create party dishes. She learned these recipes in two weeks. How many recipes can Sofia learn in 5 weeks?
Answers
Answer:
Sofia can learn 25 recipes in 5 weeks.
Step-by-step explanation:
First, to find the unit rate, we have to do 10/2 which = 5.
If the unit rate is 5 recipes per week, than she can learn 25 recipes in 5 weeks because 5 x 5 = 25
Hope this helps!
Answer:
She can learn 25 recipies
Step-by-step explanation:
A number is equal to 3 times a smaller number. Also, the sum of the smaller number and 4 is the larger number. The
situation is graphed on the coordinate plane below, where x represents the smaller number and y represents the
larger number.
Which two equations represent the situation?
A. y = 1/3x and y = x - 4
B. y = 1/3x and y = x + 4
C. y = 3x and y = x + 4
D. y = 3x and y = x - 4
Answers
Explanation: just trust me
Find the radius of a circle with the equation:x^2+y^2-18x-14y+124=0
Answers
Answer:
23
Step-by-step explanation:
hope this helps
Step-by-step explanation:
Center = (-1/2 Coefficient of x, -1/2 Coefficient of y)
or, Center = {-1/2*(-18), -1/2*(-14)}
or, Center = (18/2, -14/2)
Ans: (9, 7)
plz help answer will mark brainiest
Answers
Answer:
4/3 litres of water is enough to water 2/5 of the plants
Assuming the number of plants in the house is an unknown variable, take the value as x.
Thus, 4/3 litres is enough to water 2x plants in the house.
x = 4/3 ÷ 2
= 2/3 litres
Amount of water for all the plants = 5x = 5 × 2/3
= 10/3 litres
Thus, 10/3 litres of water is necessary to water all the plants in the house.