Step-by-step explanation:
x = number of quarters.
y = number of dimes.
z = number of pennies.
0.25x + 0.1y + 0.01× = 1.05
but it is not possible to find a combination of a subset of the coins to create exactly 1 (= the change for $1).
like to have only 3 quarters and 3 dimes (and no pennies). that makes $1.05, and no combination can create exactly $1.
as a consequence
x < 4 (because 4 quarters is $1, and more than 4 quarters is already more than $1.05).
z < 5 (because with 5 or more pennies, since the total sum is $1.05, if I simply remove 5 pennies, I get $1 with the other coins, no matter what combination they are).
with 1 or 2 or 3 or 4 pennies I cannot build a total sum of $1.05, as the other coins will can only build a sum that ends in 0 or in 5.
so, the sum of these other coins and 1, 2, 3, 4 pennies can never end in 5.
that means, we have 0 pennies.
that rules out to have 0 or 2 quarters, because then together with the dimes the sum can only end in 0 (and actually also give change for $1).
so, we can have only 1 or 3 quarters.
that means the solutions are
1 quarters and 8 dimes
or
3 quarters and 3 dimes.
1 quarter and 8 dimes (and 0 pennies) is the desired solution, because it contains more coins.
for the maximum amount of money built by coins not providing change for $1 we need to remember :
4 quarters are $1 (and would provide change for $1). so, we always need less than 4 quarters. but also at least 1 quarter to keep the sum from ending with a 0 (which would allow again to build $1).
10 dimes are $1 (and provide change for $1). we always need less than 10 dimes.
5 or more pennies would always allow to take away or fill up to create a sum that ends in 0 and therefore build $1. so, we always need less than 5 pennies.
that means again
1 or 3 quarters
max. 9 dimes
4 pennies.
if the the maximum possible sum would be higher than 1.19, then we could only increase in steps of 0.10 (dimes) : 1.29, 1.39, ...
if the sum is 1.29, I could remove 1 quarter and 4 pennies to make $1.
if it is 1.39, I could remove 1 quarter, 1 dime and 4 pennies to make $1.
and so on.
any sum >= 1 created incl. 4 or more quarters or 10 or more dimes or 5 and more pennies can always be reduced to a full $1.
$1.19 can only be built by 1 quarter and 9 dimes and 4 pennies, so that we cannot build $1 out of a subset, or by 3 quarters, 4 dimes and 4 pennies.
and 1 quarter, 9 dimes and 4 pennies has more coins.
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
24 yd
30 yd
18 yd
The area is 108yd2(square yards).
In the given triangle a base
24yd and the corresponding height of 6 yds are given, so to calculate the area we can use:
A=12×b×h
If we substitute the given numbers we get:
A=\(\frac{1}{2}\)×24×18
=12×9
=108
The units of base and height are the same (yards), so the calculated area is in yd2
The area is the quantity that expresses the extent of a region on the plane or on a curved surface. the world of a plane region or plane area refers to the area of a shape or planar lamina, while area refers to the area of an open surface or the boundary of a three-dimensional object. The area is often understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the quantity of paint necessary to cover the surface with a single coat. it's the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).
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Please me with this. I got it wrong. I will give extra points and a Brainly.
Answer:
24
Step-by-step explanation:
First, we know the total number of students: 135
Then we can see that 22+31+28 students like two flavours: 81
Then we can see how many students like all three flavours: 15
Because the students who like two flavours are counted twice, we need to subtract them once.
Because the students who like three flavours are counted three times, we need to subtract them twice.
So we get 135-81-15*2
135-81-30
24
24 students do not like any of the given flavours
if this was helpful pls give me brainliest <3
Answer: 24 students dislike any of the flavors
Step-by-step explanation:
Soo since you have the diagram without any error it the other question soo at the start of the question they have told that in total there are 135 students.
so at the all the number of students with the different types of flavors then you will get the total amount of students who like 2 kinds of flavors and all three flavors.
31+22+28+15+15= 111 students (since the students who like three flavors are counted three times, we need to subtract them twice, I add it here to make it easier *15+15*)
so next you should subtract that amount from the total amount of students who likes multiple flavors in order to get the number of students who dislikes and of the flavors.
135-111= 24 students dislike any of the flavors
I hope this helped you I tried my best... I hope this is understandable and good luck!
Write the explicit formula for the arithmetic sequence below. 14, 9, 4, -1, ...
Step-by-step explanation:
To find the next term or number, we'll need to keep subtracting 5. So the formula is: n-5
Does Anyone know how to do this It’s very difficult for me
Answer: D
Step-by-step explanation: y int is when x=0, thus when there are no chirps.
Y=(1/6)x + 50
put in 0
Y=(1/6)*0 + 50
Y=50
Slope is the rate at which x changes, in this case, 1/6
Perform the following mathematical operation, and report the answer to the appropriate number of significant figures.
1204.2 + 4.72613 = [?]
The answer is not 1208.92613
The result of the addition operation of 1204.2 + 4.72613 is approximately 1208.93.
What is an addition operation?An addition operation involves two addends added together to result in a number called the sum.
The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.
Mathematical operations combine numbers, variables, and values with mathematical operands to solve mathematical questions.
1204.2 + 4.72613
= 1208.92613
= 1208.93
Thus, the addition of 1204 and 4.72613 yields a total of 1208.93 approximately.
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Find the perimeter of a
hexagon with each side
measuring 184 ft.?
Answer:
P = 1104
a - Side
Step-by-step explanation:
P = 1104
a - Side
Answer:
P=1140
Step-by-step explanation:
P=1140 BANANA SORRY THE ANSWER I DONT HAVE IT BUT HAVE A GOOD DAY
How many terms are in the following:
19x - 4y - 2?
Answer:
3
Step-by-step explanation:
Just count how many terms are there in the expression
2. Two cars leave the same point at the same time traveling in opposite directions. One car travels west at 20 mph and the other travels east at 60 mph. In how many hours will they be 280 miles apart?
Answer:4 and 1/2 hours
Step-by-step explanation:
Both cars will be 280 meters apart from one another after 3.5 hrs of their start.
What is time in Kinematics?Time is used to define the distance covered per unit speed. Mathematically-
t = D/S
where -
D is distance covered
S is speed
Given are two cars which leave the same point at the same time such that One car travels west at 20 mph and the other travels east at 60 mph.
Speed of car going to west = S[W] = 20 mph.
Speed of car going to east = S[E] = 60 mph.
Since both the cars are moving in opposite direction, their relative speed will be -
V[R] = S[W] + S[E]
V[R] = 20 + 60
V[R] = 80 mph
Now, distance between the cars [D] should be 280 miles. Assume that at time 't', the distance between the cars is 28o miles. Then -
t = [D]/[V]
t = 280/80
t = 3.5 hrs
Therefore, both cars will be 280 meters apart from one another after 3.5 hrs of their start.
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Which two points could be removed to make this relation a function?
A. Points R and S
B. Points Q and T
C. Points P and Q
D. Points Q and R
Option (D) D. Points Q and R is used to removed to make this relation a function.
To determine which two points could be removed to make the relation a function, we need to check if there are any repeated x-values (inputs) in the given set of points. In a function, each input should have a unique output.
Let's analyze the given options:
A. Points R and S: (R, 3), (S, 5)
B. Points Q and T: (Q, 2), (T, 5)
C. Points P and Q: (P, 1), (Q, 2)
D. Points Q and R: (Q, 2), (R, 3)
In this case, if we remove points Q and R, we eliminate the repeated x-value of 2, which ensures that each input has a unique output. Therefore, the answer is:
D. Points Q and R.
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In ΔIJK, the measure of ∠K=90°, KI = 3.8 feet, and JK = 6.7 feet. Find the measure of ∠I to the nearest degree.
Answer:
60
Step-by-step explanation:tanI=
adjacent
opposite
=
3.8
6.7
\tan I = \frac{6.7}{3.8}
tanI=
3.8
6.7
I=\tan^{-1}(\frac{6.7}{3.8})
I=tan
−1
(
3.8
6.7
)
I=60.44\approx 60^{\circ}
I=60.44≈60
∘
help will mark Brainliest!!
Answer:
1/20
Step-by-step explanation:
1/4 = 0.25
0.25 / 5 = 0.05
0.05 as a fraction = 5/100
simplified
5 / 5 = 1
100 / 5 = 20
1/20
The perimeter of a rectangular picture frame is 62 inches. The length of the 1
frame is one more than twice its width. What are the length and the width
of the frame?
Answer- each width = 10, each length = 21
Explanation: from the question we know that L=2w + 1 and we also know that a rectangle has the perimeter of 62 when we plug it in the equation we will get 62= 2(2w+1+w) we will multiply the 2 now and we will get 62=4w+2+2w we will combine like terms and we will minus two from both sides ending up with 60=6w we will divide six from both sides and we will get w=10 then we will use l=2w+1 to find the length and it will be 21
Translate the given quadrilateral to the left 6 units and down 5 units. please show work
Answer:
A wouldn now be at -4, -1
B would be at -1, -1
C would be placed at -1, -5
D would be located at -2, -2
Step-by-step explanation:
Hope it helps!
Answer:
5
Step-by-step explanation:
Factor- 5
\(Domain: x - R\)
\(Range : y - R\)
\(Zeros - 0\)
\(Y - intercept \: \: y = 5\)
\(Horizontal \: asmptotes \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 5, x > + \infty \)
\(Parity : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: The \: function \: is \: even\)
\(Monotonicity : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( - \infty , \: \infty \: \: ) constant\)
.
.
An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of the residents of a state if you want to be 95% confident that the sample mean is within 4 IQ points of the true mean.
What is the required sample size?
Answer:
55
Step-by-step explanation:
\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)
Make sure to always round up the required sample size to the nearest integer!
Solve the problem.
Find m so that x + 4 is a factor of 5x3+ 18x² + mx + 16
The value of m such that x +4 is a factor of 5x³ + 18x² + mx + 16 is; -4.
What is the value of m for which x +4 is a factor of 5x³ + 18x² + mx + 16?It follows from the task content that the value of m for which x +4 is a factor of 5x³ + 18x² + mx + 16 is to be determined.
Hence, if x + 4 is a factor, it follows that x = -4 is a zero of the expression.
Therefore; 5(-4)³ + 18(-4)² + m(-4) + 16 = 0.
-320 + 288 - 4m + 16 = 0.
-16 - 4m = 0
4m = -16
m = -16/4
m = -4.
Ultimately, the value of m for which x+4 is a factor of 5x³ + 18x² + mx + 16 is; -4.
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What does 10.98+4.06
Answer:
15.01
Step-by-step explanation:
10.95+4.06
Answer:
15.01
Hope that helps :-)
What is the mesure of 5
Answer:
69
Step-by-step explanation:
PLEASE HELP ME IN ONE MINUTE WILL MARK BRAINLIST
I think I did this already it should be c
An arrow is shot from 3 ft above the top of a hill with a vertical upward velocity of 108 ft/s. If it strikes the plain below after 9.5 s, how high is the hill?
If the arrow is launched at t0, then write an equation describing velocity as a function of time?
The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),
To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:
h = h0 + v0t + 1/2at^2
where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).
In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.
At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:
v = v0 + at
we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:
0 = 108 - 32.2t
t = 108/32.2 ≈ 3.35 s
Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.
Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:
h_hill = h0 + v0t + 1/2at^2 - h_top
where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:
h_top = h0 + v0^2/2a
Plugging in the given values, we get:
h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft
Plugging this into the first equation, we get:
h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78
h_hill ≈ 25.73 ft
If the arrow is launched at t0, the equation describing velocity as a function of time would be:
v(t) = v0 - gt
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3. Margaret has a tax liability of $3400. She cannot pay on time. The penalty is $150 per
month. The interest rate for late tax payments is 30% annually, compounded monthly. If
Margaret does not pay her tax bill for 5 months, what is her total tax liability?
Margaret's total tax liability after 5 months is $4,185.6.
What is her total tax liability?The penalty charges of Margaret is calculated as follows;
The penalty for not paying on time is $150 per month, so over 5 months, is calculated as;
$150 x 5 = $750
The interest charges is calculated as;
30% / 12 = 2.5% per month
\(A = P(1 + \frac{r}{n} )^{nt}\)
Where;
A = the total amount owedP = the principal (the original tax liability)r = the interest rate per period (2.5% per month)n = the number of times the interest is compounded per year (12)t = the time in years (5/12)\(A = 3400(1 + \frac{0.025}{12} )^{12 \times (5/12)}\)
A = 3400(1.0020833)⁵
A = 3400(1.011028)
A = $3,435.6
The total amount owed after 5 months is calculated as;
= $3,400 + $750 + $35.6
= $4,185.6
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it’s a -10 btw and a positive 9
Answer: -1 and -9
Step-by-step explanation:
(- 1) + (-9) = -10
(-1) * (-9) = +9
hope this helps!
HELP
what is the equation of the lines in slope - intercept form
Answer:
y=7x
Step-by-step explanation:
slope intercept form is y=mx+b.
m is the slope (rise over run) and b is your y- intercept. you leave y as it is. if the line is going down, you have a negative slope. hope this helped :)
Teresa started to run on a treadmill after setting its timer for 78 minutes. The display says that she has finished 57% of her run. How many minutes have gone by? Round your answer to the nearest tenth
The nearest tenth, 44.5 minutes have gοne by.
What is time?Time is the οngοing prοgressiοn οf existence and events that take place in what appears tο be an irreversible οrder frοm the past thrοugh the present tο the future. It is οne οf the quantities that make up variοus measurements that are used tο cοmpare the lengths οf events οr the gaps between them, tο cοmpare hοw lοng they last, tο οrder events, and tο measure hοw quickly certain quantities in the physical wοrld οr in cοnsciοus experience change. The fοurth dimensiοn, in additiοn tο the three spatial dimensiοns, is frequently referred tο as time.
If Teresa has finished 57% οf her run, then she has 43% left tο cοmplete.
Let x be the number οf minutes that have gοne by.
Since 57% οf the run is cοmpleted in 78 minutes, we can set up the fοllοwing prοpοrtiοn:
57/100 = x/78
Sοlving fοr x, we get:
x = (57/100) * 78
x = 44.46
Therefοre, tο the nearest tenth, 44.5 minutes have gοne by.
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A bank charges 12% Simple interest p.a on cash loans to its clients.tito has asked for R10000loan amount and has promised to repay the the loan over 4years
Calculate the interest which Tito has to pay on loan ?
Determine the total amount to be paid back
Determine the monthly repayment amount
If Tito took a loan of $10000 from a bank to be repaid within 4 years, at 12% Simple interest per annum, then, he will have to pay overall $4800 as interest to the bank over 4 years and a total payment of $14800 at the end of the 4th year to repay and close off the loan.
As per the question statement, a bank charges 12% Simple interest per annum on cash loans to its clients and Tito took a loan of $10000 from the same bank to be repaid within 4 years.
We are required to calculate the overall interest Tito has to pay to bank if he repays and closes the loan at the end of 4th year, and also to calculate the total payment required to repay and close off the loan at the end of the 4th year.
To solve this question, we need to know the formula to calculate the interest amount in case of simple interest which goes as
Interest (I) \(=(\frac{P*R*T}{100} )\)
where, "P" = Principle amount of Loan,
"R" = Rate of simple interest charged on the principle per annum, and
"T" = Time period within which, the loan is to be repaid.
Here, (P = 10000), (R = 12%) and (T = 4). Then, the overall interest Tito will have to pay at the end of 4th year = \((\frac{10000*12*4}{100}) = (100*12*4)=(48*100)=4800\)
And total amount to be paid to repay and close of the loan at the end of 4th year will be = $[4800 + 10000] = $14800.
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The distance around the outside of an apartment is 0.3 mile. Keira ran 0.1 of the distance during her lunch. How far did she run?
Answer:
0.1
Step-by-step explanation:
if f(x)=3x-3 and g(x)=-x2+4,then f(2)-g(-2)=
Answer:
3
Step-by-step explanation:
f(x)=3x-3
g(x)=-x^2+4,
f(2) = 3(2) -3 = 6-3 =3
g(-2) = -(-2)^2+4 = -4+4 = 0
f(2)-g(-2)= = 3-0 = 3
¿Qué es y cómo se forman un enlace químico?
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 19 subjects had a mean wake time of 104.0 min. After treatment, the 19 subjects had a mean wake time of 94.9 min and a standard deviation of 24.3 min. Assume that the 19 sample values appear to be from a normally distributed population and construct a 99% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 104.0 min before the treatment? Does the drug appear to be effective?
Construct the 99% confidence interval estimate of the mean wake time for a population with the treatment.
The answer of the given question based on the confidence interval is , it suggests that the drug treatment has significantly reduced the mean wake time , the drug appears to be effective in treating insomnia in the older subjects.
What is Mean?Mean is a statistical measure of central tendency that represents the average of a set of numerical values. It is also referred to as the arithmetic mean or simply "the average." To calculate the mean, we add up all the values in the set and divide the sum by the number of values.
To construct the 99% confidence interval estimate of the mean wake time for a population with the treatment, we can use the following formula:
CI = x⁻ ± tα/2 (s/√n)
where x⁻ is the sample mean (94.9 min), s is the sample standard deviation (24.3 min), n is the sample size (19), and tα/2 is the critical t-value with α = 0.01/2 and degrees of freedom (d f) = n - 1.
The degrees of freedom for this sample is d f = 19 - 1 = 18. Using a t-table or a t-distribution calculator, we find that t0.005,18 = 2.878, where 0.005 is the tail probability for a 99% confidence interval (α/2 = 0.005).
Plugging in the values, we get:
CI = 94.9 ± 2.878 * (24.3/√19) = (80.36, 109.44)
Therefore, we can say with 99% confidence that the mean wake time for a population with the drug treatment falls between 80.36 and 109.44 minutes.
Regarding the mean wake time of 104.0 min before the treatment, we can compare it with the lower bound of the confidence interval (80.36 min). Since the lower bound is much lower than 104.0 min, it suggests that the drug treatment has significantly reduced the mean wake time.
Therefore, based on the confidence interval estimate, the drug appears to be effective in treating insomnia in older subjects.
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A computer generates 90 integers from 1 to 8 at random. The results are recorded in this table. Outcome 1 2 3 4 5 6 7 8 Number of times outcome occurred 26 8 10 12 8 6 9 11 What is the experimental probability of the computer generating a 3 or a 5? Responses 9% 9% 20% 20% 18% 18% 40%
The solution is, the experimental probability of the computer generating a 1 is D. 40 %.
Here, we have,
At first, we will add the outcomes to get the total number of times the integers were generated ;
= 36 + 11 + 13 + 12 + 18
= 90
The number of times 1 was generated was 36.
The experimental probability is therefore;
= number of times 1 was generated / total number of outcomes
= 36 / 90
= 0. 4
= 40 %
Therefore, the experimental probability of the computer generating a 1 is 40 %.
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complete question:
A computer generates 90 integers from 1 to 5 at random. The results are recorded in the table.
What is the experimental probability of the computer generating a 1?
Responses:
10%
20%
30%
40%
I took the test and the other fool who answered decided to change the numbers you provided him with so yea here it is:
suppose we have 13 real numbers with the following property: if we remove any one of the numbers, the remaining 12 can be split into two sets of 6 numbers each with equal sum. prove: all the 13 numbers are equal. (hint: first assume all the numbers are integers.)
All the 13 numbers must be equal.
Let the 13 numbers be x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, and x13.
Assuming the 13 numbers are all integers, the sum of all the 13 numbers is equal to S = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12 + x13.
By the given property, when any one of the numbers is removed, the sum S of the remaining 12 numbers can be split into two groups of 6 numbers with equal sum.
Therefore, S/2 = x1 + x2 + x3 + x4 + x5 + x6 = x7 + x8 + x9 + x10 + x11 + x12 + x13.
This implies that x1 + x2 + x3 + x4 + x5 + x6 – x7 – x8 – x9 – x10 – x11 – x12 – x13 = 0.
By rearranging the equation, we have x13 = x1 = x2 = x3 = x4 = x5 = x6 = x7 = x8 = x9 = x10 = x11 = x12.
Thus all the 13 numbers are equal.
Therefore, all the 13 numbers must be equal.
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