Step-by-step explanation:
Jim has 65 coins in his pocket. All of the coins are nickels and dimes. If the total value of his coins is $5.10, how many nickels or dimes does he have?
nickels = n
dimes = d
We use:
d + n = 65
0.10d + 0.05n = 5.10
solve for d:
d + n = 65
d + n - n = 65 - n
d = 65 - n
substitute in for the second equation: d = 65 - n
0.10(65 - n) + 0.05n = 5.10
6.5 - 0.10n + 0.05n = 5.10
6.5 - 0.05n = 5.10
6.5 - 0.05n - 6.5 = 5.10 - 6.5
- 0.05n= -1.4
n = 28
so there are 28 nickels
Now, solve for d: when n = 28
d + n = 65
d + 28 = 65
d = 37
so there are 37 dimes
Jim has 28 nickels and 37 dimes in his pocket. which is determined by the substitution method.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
Let the number of nickels would be n
Let the number of dimes would be d
As per the given question,
d + n = 65 ....(i)
0.10d + 0.05n = 5.10 ....(ii)
From equation (i),
d + n = 65
d + n - n = 65 - n
d = 65 - n
Substitute in for the equation(ii): d = 65 - n
0.10(65 - n) + 0.05n = 5.10
6.5 - 0.10n + 0.05n = 5.10
6.5 - 0.05n = 5.10
6.5 - 0.05n - 6.5 = 5.10 - 6.5
- 0.05n = -1.4
n = 28
This means there are 28 nickels
Substitute the value of n = 28 in the equation (i),
d + n = 65
d + 28 = 65
d = 37
So there are 37 dimes
Thus, Jim has 28 nickels and 37 dimes in his pocket.
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A biologist wants to estimate how many fish are in a lake. The biologist takes a sample of 10 fish from the lake and tags all 10 fish. The biologist then releases the fish back into the lake. The nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. Using this information, estimate the number of fish in the lake.
If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.
How to find the estimated number?Let x represent the estimated number of fish in the lake
Hence,
x /10 = 7/2
Cross multiply
2x = 10 × 7
2x = 70
Divide both side by 2x
x =70/2
x = 35 fish
Therefore 35 is the number of fish.
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What is the y-intercept of x = -4?
Answer:
DNE
Step-by-step explanation:
You want to know the y-intercept of x = -4.
Y-interceptThe y-intercept is the point where a graph crosses the y-axis.
The line x=-4 is a vertical line parallel to the y-axis, so does not cross the y-axis.
There is no y-intercept. It does not exist (DNE).
factorise fully 8x^2-4x
Answer:
4x(2x−1)
Step-by-step explanation:
[tex] {8x}^{2} - 4x[/tex]
Factor out 4.
[tex]4( {2x}^{2} - x)[/tex]
Consider
[tex] {2x}^{2} - x[/tex]
Factor out x.
x(2x−1)
Rewrite the complete factored expression.
=4x(2x−1)
Question content area top Part 1 What is the constant of proportionality in the equation y=−7.48x?
The constant of proportionality of the equation y =−7.48x is - 7.48.
What is proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent
In other words, two variables have a proportional relationship if the ratios of the variables are equivalent.
Therefore, a proportional relationship is one in which two quantities vary directly with each other.
Hence, in mathematical form,
y ∝ x
y = kx
where
k = constant of proportionalityy varies directly as the variable x.
In the equation,
k = - 7.48
Therefore, the constant of proportionality is - 7.48.
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Max wanted to test a new dishwasher detergent to see if it was less likely to leave residue on his dishes. What would be the null hypothesis in Max’s experiment
Given that Max wanted to test a new dishwasher detergent to see if it was less likely to leave residue on his dishes, the suitable null hypothesis in Max’s experiment will be "the new detergent will leave more residue than the old one".
What is a null hypothesis?In statistics, a null hypothesis means a typical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable between the two sets of observed data and measured phenomena.
Therefore, the Option B is correct.
Missing options' The new detergent will leave less residue than the old one. The new detergent will leave more residue than the old one. O The new detergent is equally likely to leave residue compared to the old detergent. The old detergent will leave more residue than the new detergent."
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Mai has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Congruence Theorem. Since corresponding parts of
congruent triangles are congruent, angle ZWY is congruent to angle XWY and angle ZYW is congruent to angle XYW.
True or False: Mai can now conclude that diagonal WY bisects angles ZWX and ZYX.
True
O False
It is true, Mai can conclude that the diagonal WY bisects the angles ZWX and ZYX
Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:
Diagonal WY bisects angles ZWX and ZYX because:
all corresponding parts of both triangles are congruent. (Option A).
If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.
Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.
If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).
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F(n)= 3n -4 find term 3 of the explicit arithmetic sequence
The third term will be 5 in the explicit arithmetic sequence.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The formula to find the general term of an arithmetic sequence is,
aₙ = a₁ + (n-1)d
The explicit formula of an arithmetic sequence is given in the question as:
F(n) = 3n -4 ....(i)
To determine the term 3.
Substitute the value of n = 3 in equation (i),
T₃ = 3(3) - 4
T₃ = 9 - 4
Apply the subtraction operation,
T₃ = 5
Therefore, the third term will be 5 in the explicit arithmetic sequence.
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Johnny is 5 years younger than twice Bobby's age. If the sum of thier ages is over 66 years.
What is the Johnny's minimum age?
The minimum age of Johnny is 21 as calculated by linear inequality.
Let Johnny 's age be x.
hence bobby's age = (x+5)/2
Now the sum of their ages is over 66 years.
So we will set an inequality to find the minimum age of Johnny.
x + (x+5)/2 > 66
or, 2x + x + 5 > 66
or, 3x > 61
or, x > 20 1/3
Therefore age cannot be fraction hence the minimum age of Johnny is 21 years.
In mathematics, an inequality is a connection that makes an unequal comparison between two numbers and maybe other mathematical expressions. On that number line, size comparisons between two numbers are typically done. Different notations can be used to represent various kinds of inequalities, including:
A is smaller than b, as shown by the symbol a < b.
When the expression a > b is employed, it means that a is greater than b.
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2. Kira has three dogs, Luna, Cooper, and Daisy.
Cooper weighs 25 pounds less than Daisy. Luna
weighs 20 pounds less than three times Cooper.
If their combined weight is 175 pounds, how
much does Luna weigh?
A. 59 pounds
B. 74 pounds
C. 78 pounds
D. 82 pounds
If their combined weight is 175 pounds, The amount of Luna weight is D. 82 pounds.
How to determine the weight?Let x represent the weight of Cooper
Let x +25 represent the weight of Daisy
Let 3x -20 represent the weight of Luna
Hence,
x + (x +25) + (3x -20) = 175
5x +5 =175
Combine like terms
5x = 175 -5
5x =170
Divide both side by 5x
x = 170/5
x =34
Weight of Luna
3x -20 where x= 34
3(32) -20
= 102 -20
= 82 pounds
Therefore the correct option is D.
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A motorboat maintained a constant speed of 14 miles per hour relative to the water in going 33 miles upstream and then
returning. The total time for the trip was 7.0 hours. Use this information to find the speed of the current.
What is speed of the current is miles per hour?
The speed of the current is equal to 8 miles per hour.
How to calculate the speed of the current?Mathematically, speed of any physical object can be calculated by using this formula;
Speed = distance/time
Let the variable c represent the speed of the current in miles per hour. Therefore, the downstream and upstream speed relative to the water would be given by this mathematical expression:
Speed downstream = 14 + c.
Speed upstream = 14 - c.
Additionally, the total time would be given by:
Total time = total distance/speed
Time upstream + time downstream = 6.5 hours
33/(14 - c) + 33/(14 + c) = 7.0
Multiplying both sides of the equation by (14 - c)(14 + c), we have:
33(14 + c) + 33(14 - c) = 7.0(14 - c)(14 + c)
462 + 33c + 462 - 33c = 7.0(196 - c²)
924 = 7.0(196 - c²)
Dividing both sides of the equation by 7.0, we have:
132 = 196 - c²
Speed of the current, c² = 196 - 132
Speed of the current, c² = 64
Speed of the current, c = √64
Speed of the current, c = 8 miles per hour.
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Let's multiply the top equation by -2. What would be our new equation?
2x + 3y = 12
4x - 7y = -54
New equation will be 4x + 6y = 24, if we multiply the equation 2x + 3y = 12 by -2.
Define multiplication.We can rapidly determine the total number of things by multiplying. When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group. A fact involving multiplication is the result of two distinct integers. Additionally, the product is unaffected by the arrangement of the numbers. For instance, 32=6 and 23=6. The distributive, commutative, associative, removes a common factor, and neutral element characteristics of multiplication.
Given,
Equations:
2x + 3y = 12
4x - 7y = -54
Multiplying the top equation by -2:
-2(2x + 3y) = -2(12)
-2(2x) -2(3y) = -24
Product:
-4x - 6y = -24
Taking - common,
-(4x + 6y) = -24
4x + 6y = 24
New equation will be 4x + 6y = 24, if we multiply the equation 2x + 3y = 12 by -2.
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Show, by shading on the grid, the region defined by all three of the inequalities
x ≤ 5 y ≥ 3 y ≤ x
Answer:
See below
Step-by-step explanation:
The area (triangle) marked 'x' in the diagram below
A school is arranging a field trip to the zoo. The school spends 895.28 dollars on passes for 36 students and 2 teachers. The school also spends 321.84 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Need asap! Write the expression as a power and evaluate it. The expression as a power is __. The value is__.
8•2^7 and 16•32
The expression as power is written as 2¹⁰ and 2^9
The values are
2¹⁰= 1024 2^9 = 512How to write expression as a powerpower or exponents as used in mathematics are number written on top of a base number. The power says how many times the base nmber multiplies itself.
8• 2^7
= 2 * 2 * 2 * 2^7
= 2^10
= 1024
16•32
2^5 = 2 * 2 * 2 * 2 * 2
2^4 = 2 * 2 * 2 * 2
16•32 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
= 2^9
= 512
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Question
In 8 years, Estelle's bank account earned $1,270
simple interest at 2.5%. How much had she
deposited in the account?
Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.
According to the question,
We have the following information:
In 8 years, Estelle's bank account earned $1,270 simple interest at 2.5%.
Now, let's take the principal amount to be $x.
We know that the following formula is used to find simple interest:
Simple interest = (principal*rate*time)/100
(x*2.5*8)/100 = 1270
Using the cross multiplication method:
20x = 127000
x = 127000/20
x = $6350
Hence, Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.
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The current on the Little River is 8 mph. Tom's
boat goes 15 mph in still water. How far upstream
can Tom's boat go on the Little River in 1.5 hours?
a) 12 miles
b) 25 miles
c) 10.5 miles
d) 34.5 miles
10.5 miles far upstream can Tom's boat go on the Little River in 1.5 hours.
How to calculate the relative velocity ?The relative velocity formula is written as follows. V is equal to
V → = V A B → + V B C →
Where. VAB is the velocity in relation to A and B, VBC is the velocity in relation to B and C, and VAC is the velocity in relation to A and C.
The current on the Little River is 8 mph.
Tom's boat goes 15 mph in still water.
For Upstream
the Velocity of the boat = 15 mph - 8mph
= 7mph
How far upstream
can Tom's boat go on the Little River in 1.5 hours = 7* 1.5 = 10.5 miles
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According to the questions that are asked in the various Government exams that are held across the nation, the boat and stream concept is one of the most frequently covered subjects.
How to calculate Boat and Stream?The four terms that a candidate has to comprehend in order to grasp the notion of streams are listed below.Stream: A river's flowing water is referred to as a stream.Upstream - A boat is said to be moving upstream if it is moving downstream of the stream. The boat's upstream speed in this situation is its net speed.Downstream - A boat is said to be moving downstream if it is moving in the same direction as the stream. In this instance, the boat's downstream speed is its net speed.Still Water - In this situation, the water is seen as being immobile and has no speed.The main focus of this topic is determining the speed of anything moving through water, whether it is moving with the current or against it.For example : In one hour, a boat goes 13 km/hr in the direction of the stream and 7 km/hr against the direction of the stream. What will be the speed of the boat in still water?Utilizing the formula,Boat speed in still water = 1/2 (downstream speed + upstream speed).
Boat's speed in still water equals 1/2 (13+7) = 1/2 × 20 = 10 km/hr.
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HELP ME PLEASE GRAPH
Answer:
see attached (red)
Step-by-step explanation:
You want the graph of the transformed triangle defined by the lines y=x, x=6, y=-1/3x+4 after rotation 270° and reflection across the y-axis.
TriangleA graph of the lines shows the vertices of the triangle are ...
A(3, 3), B(6, 6), C(6,2)
TransformationsRotation 270° is described by the transformation ...
(x, y) ⇒ (y, -x)
Reflection across the y-axis is described by ...
(x, y) ⇒ (-x, y)
Then the composition of these transformations is ...
(x, y) ⇒ (-y, -x) . . . . . . . . equivalent to reflection over y=-x
ApplicationApplying this composition to the triangle vertices, we find its final location to be ...
A(3, 3) ⇒ A''(-3, -3)
B(6, 6) ⇒ B''(-6, -6)
C(6,2) ⇒ C''(-2, -6)
The triangle with these vertices is shown in red in the attachment.
3) On a large ship, there are 230 mice and rats (combined) each of which either prefers peanut
butter or cheese. Of the 110 mice, 42 prefer peanut butter and 44 rats prefer cheese. What
percent of all rodents on the ship preferred peanut butter? (2 pts) (Mice and rats are both
rodents.)
48.4 % percent of all rodents on the ship preferred peanut butter.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
total number of rodents = 230110 mice in which 42 prefer peanut better,110 * 44= 48.4hence,48.4 % percent of all rodents on the ship preferred peanut butter.
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My sister has three Maltese puppies. Scout weighs 8 1/3 pounds, Kenadi weighs 3 1/8 pounds, and Major weighs 8 1/5 pounds. What is the order of the puppy’s weights from least to greatest?
A.8 1/3,8 1/5 3 1/8
B.8 1/3,3 1/8, 8 1/5
C.3 1/8,8 1/3,8 1/5
D.3 1/8, 8 1/5,8 1/3
Answer: D because 8 1/5 is smaller than 8 1/3
A survey asked 300 students to choose their favorite type of movie.
The results are shown in the following table.
(a) Find the percentage for each type of movie.
Type of movie
Action
Comedy
Drama
Thriller
Number of
students
27
42
120
111
Percentage
1%
%
%
%
X
5
Answer:
300/100%=3%
Step-by-step explanation:
sorry, can't explain.Ihave class tomorrow
Which function is positive for the entire interval [–3, –2]?
Graph 2 represents that the function is positive for the entire interval [-3,-2].
What is a function?Every possible input value results in exactly one output value in a function. "The output is a function of the input," we state. The domain is made up of the input values, while the range is made up of the output values.
Four different graphs for various functions are provided. We must identify the graph that is positive throughout the range [-3,-2].
We make the following observation from the given graphs.
1. The function in graph 1 has a value of 0 at -3 and decreases in value from -3 to -2. As a result, in the provided interval, the function is negative.
2. Graph 2 makes it abundantly evident that the function has a positive value for the entire specified interval.
3. In graph 3, the function shows a negative value entirely in the given interval.
4. In graph 4, the function exhibits both positive and negative values in the given interval and is not positive in the entire interval.
Thus, the function in graph 2 is positive for the entire interval [-3,-2].
The missing image is attached with the answer below,
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Questions
Surds exam questions
Q1. Express √3+√12 in the form a√3 where a is an integer.
Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate the simple interest using I = prt.
$69
$90
$420
$1,080
Answer: The answer to this question is $90.
Step-by-step explanation:
The Simple interest is $90.
What is Simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5.
Given:
P= 1500
R = 12%
T= 6 month = 1/2 year
Using, formula of Simple Interest
I = P x R x T /100
I = 1500 x 12 x 1/ 2x100
I = 18000/200
I = 90
Hence, the interest is $90.
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Pedro has $18 to spend at the grocery store. His mother wants him to use the money to buy fruit. Apples cost $2 a pound and pears cost $3 a pound
Answer:
Pedro can buy 4 pounds of pears and 3 pounds of apples.
Step-by-step explanation:
Pedro has a total of $18, Apples cost $2 a pound, and Pears cost $3 a pound.
$2×3lb + $3×4lb=$18
Five twelfths of the marbles in a bag are blue. What fraction of the marbles are not blue?
Answer:
7/12
Step-by-step explanation:
12/12 - 5/12 = 7/12
please help!!!! 50 points
The number of words per sentence in a certain book is normally distributed with a mean of 21 words and a standard deviation of 4 words.
Approximately what percent of sentences in the book are less than 13 words in length?
A. 2.5%
B. 5%
C. 47.5%
D. 87.5%
The answer will be:
B: 5 percent/ 5%
13 words in length will be 5%
Hope this helped
:)
What is the correct answer
Answer: See coordinate graph below.
Step-by-step explanation: The black point is the original point and the red point is the reflected point.
Ordered pair of the reflected point:
A': (1, -4)
Let me know if this is right! :)
At an arcade, a book of 20 tickets costs $5, a book of 30 tickets costs $7, and a book of 50 tickets costs $10. Would a graph of the relationship between price and number of tickets in a book be a straight line? Explain.
Answer:
yes
Step-by-step explanation:
24.) MULTIPLE FORMS Write the decimal 0.5 in two ways. One with a denominator of 10 and one
with a denominator of 100.
Answer:
A denominator of 10: 5/10
A denominator of 100: 50/100
Two sides are labeled 5,244 feet. The other two sides are labeled 1,495 feet. What is the perimeter to the nearest hundred?
Answer:
Step-by-step explanation:
42feet
