If , Pete is saving $0. 45 each week to buy a video game that cost $9.0. Pete will have to save for 20 weeks to have enough money to buy the video game.
The problem asks us to find out how many weeks Pete will have to save to buy a video game that costs $9.0 if he is saving $0.45 each week. To solve this problem, we can use division to find out how many times $0.45 goes into $9.0.
We first divide the total cost of the game by the amount Pete saves each week, which gives us the number of weeks he will need to save.
In this case, the division of $9.0 by $0.45 yields 20, which means that Pete will have to save for 20 weeks to buy the video game. This calculation is important for Pete because it helps him plan his savings and gives him a goal to work towards. By saving $0.45 every week, he can keep track of his progress and stay motivated to reach his goal.
This problem highlights the importance of basic arithmetic skills, specifically division, in practical situations like budgeting and financial planning. By applying mathematical concepts to everyday situations, we can make informed decisions and manage our resources more effectively.
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The degree of the term with the greatest degree is called?
The degree of the term with the greatest degree is called the degree of the polynomial.
Here, it is necessary to remember that, by the definition, we can find the "Degree of a polynomial" by identifying the greatest degree of its terms.
The "Leading term" of a polynomial is defined mostly as the term with the highest power of the variable of the polynomial.
The numbers located in front to the variable (those numbers that multiply the variable) are called "Coefficients". The coefficient of the Leading term is known as the "Leading coefficient."
For example, given the following polynomial:
18x² + 2x - 6
You can identify that, in this case:
degree of the polynomial: 2
leading term: 18x²
leading coefficient: 18
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your friend says that he will be 21 years old and seven years how old is he now?
Answer:
Step-by-step explanation:
He is now 14 years old because if you minus 21 and 7, it will be 14
Answer:
If your friend says that he will be 21 years old in seven years, then he is currently 21 - 7 = 14 years old.
Step-by-step explanation:
What is 2 thirds of 42
Answer:
Step-by-step explanation:
42*2/3=84/3=28
m varies directly as n, and m=14 when n=7
a) write an equation that relates m and n
b) find m when n = 16
c) find n when m = 30
Answer:
see explanation
Step-by-step explanation:
(a)
given m varies directly as n then the equation relating them is
m = kn ← k is the constant of variation
to find k use the condition m = 14 when n = 7
14 = 7k ( divide both sides by 7 )
2 = k
m = 2n ← equation of variation
(b)
when n = 16 , then
m = 2 × 16 = 32
(c)
when m = 30 , then
30 = 2n ( divide both sides by 2 )
15 = n
Please find the missing side length using trig!
The missing side is [tex]5\sqrt{3}[/tex].
What are basic Trigonometric functions?
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.
In a Right-angled triangle, the tangent of an angle is equal to the opposite side/adjacent side.
from the given figure,
tan 60° = x/5
[tex]\sqrt{3}=\frac{x}{5}\\ x=5\sqrt{3}[/tex]
Therefore, The missing side is [tex]5\sqrt{3}[/tex].
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your three circles may not have intersected exactly at a single point. how could you improve your results
Increase the accuracy of your measurements by using a more precise instrument or tool, such as a protractor or ruler.
The accuracy of the intersection of your three circles may not have been exact due to imprecise measurements taken. To improve the results, you could use a more precise instrument or tool, such as a protractor or ruler. With a protractor , you can measure the angle of the intersection of the circles more accurately. If a ruler is used, make sure that it is a straight edge, and measure the distance between the circles to ensure they intersect at the same point . Once the measurement is taken, draw the circles and their intersection accordingly. Doing this will help improve the accuracy of the intersection of the three circles and yield better results.
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Two numbers are co-prime if they do not have any prime factors in common. List all
possible numbers that are co-primes with the following numbers that are < 50:
(a) 390
(b) 210
(c) 49335
All possible numbers that are co-primes with the following numbers are mentioned below in detail. The possible co-primes of 390 are 1, 7, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.
What are co-prime numbers?Co-prime numbers are pairs of numbers that only share the factor 1 in common. They are additionally referred to as reasonably prime numbers.
In the given question,
(a) 390
The prime factors of 390 are 2, 3, 5, and 13. All of the numbers that are co-prime with 390 are those that do not share any of these prime factors. This includes the numbers 1, 7, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.
(b) 210
The prime factors of 210 are 2, 3, 5, and 7. All of the numbers that are co-prime with 210 are those that do not share any of these prime factors. This includes the numbers 1, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, and 49.
(c) 49335
The prime factors of 49335 are 5, 7, 11, and 13. All of the numbers that are co-prime with 49335 are those that do not share any of these prime factors. This includes the numbers 1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, and 49.
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What is an equation of the line that passes through the points (-1,6) and (4,-4)
The linear equation that passes through the two given points is:
y = -2x + 4
How to write the equation of the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Particularly, if a line passes through the points (x₁, y₁) and (x₂, y₂) then the slope will be:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (-1, 6) and (4, -4), then the slope is:
a = (-4 - 6)/(4 + 1) = -2
y = -2x + b
To find the value of b, we can replace the values of any of the points in the equation, if we use (-1, 6) we will get:
6 = -2*-1 + b
6 = 2 + b
6 - 2 = b = 4
The linear equation is y = -2x + 4
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In a family the oldest child is 7 years older than the youngest child what is a equation to represent this situation
The equation to represent the situation where the oldest child is 7 years older than the youngest child, using x for the age of the youngest child and y for the age of the oldest child, is y = x + 7.
If we let x represent the age of the youngest child in a family, then we can say that the oldest child is 7 years older than the youngest child. We can represent the age of the oldest child using the expression "x + 7", because if we add 7 to the age of the youngest child, we get the age of the oldest child.
Therefore, we can write an equation to represent this situation by equating the age of the oldest child to the age of the youngest child plus 7. This can be written as:
x + 7 = Oldest child's age
where x is the age of the youngest child, and "Oldest child's age" represents the age of the oldest child in the family. This equation tells us that if we know the age of the youngest child, we can find the age of the oldest child by adding 7 to it.
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The point (1/6,0) is on the curve. Find the value of (y^-1)' (0)
The value of the inverse relation is y'(0) = 1/6
How to determine the value of the inverse functionFrom the question, we have the following parameters that can be used in our computation:
The point (1/6,0) is on the curve
The notation (y^-1)' (0) is an inverse notation
Using the above as a guide, we have the following:
(1/6,0) means y(1/6) = 0
This also means that
y'(0) = 1/6
Hence, the solution is 1/6
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philips metal costs $14.50 at the local restaurant. the server did their job very well and philip would like to leave a 20% tip. what amount of money should he leave as a tip?
Answer: The tip is $2.90
Step-by-step explanation: 20% of 14.50 is 2.9
Find the inequality based on the graph
The inequality represented by the graph is given as follows:
y < 4x - 2.
How to obtain alinear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The graph crosses the y-axis at y = -2, hence the intercept b is given as follows:
b = -2.
When x increases by 1, y increases by 4, hence the slope m is given as follows:
m = 4.
The values to the left of the line are shaded, hence the inequality represented by the graph is given as follows:
y < 4x - 2.
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the file utility contains the following data about the cost of electricity during july of a recent year for a random sample of 50 one- bedroom apartments in a large city: 96 171 202 178 147 102 153 197 127 82 157 185 90 116 172 111 148 213 130 165 141 149 206 175 123 128 144 168 109 167 95 163 150 154 130 143 187 166 139 149 108 119 183 151 114 135 191 137 129 158 a. construct a histogram and a percentage polygon. b. construct a cumulative percentage polygon. c. around what amount does the monthly electricity cost seem to be concentrated?
a) The histogram for the data is illustrated below.
b) The cumulative percentage polygon is define in the histogram
c) The amount does the monthly electricity cost seem to be concentrated is 128 - 152
A histogram is a graphical representation of a frequency distribution. It consists of a set of bars that represent the frequency of data within certain intervals, also known as bins. The height of each bar represents the frequency or count of data points that fall within that bin.
To create a histogram for the electricity cost data, we need to first decide on the number and size of the bins. One common rule is to choose the number of bins as the square root of the sample size. In this case, we have 50 data points, so we can choose about 7 bins. The size of the bins can be determined by dividing the range of the data by the number of bins.
Once we have determined the number and size of the bins, we can create the histogram by drawing a set of bars with heights proportional to the number of data points that fall within each bin. The histogram can be further enhanced by adding labels for the x and y-axes, a title, and a legend.
As per the histogram, the amount does the monthly electricity cost seem to be concentrated is 128-152
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Solve the system of equations by elimination. Express the solution as an ordered pair.
-3x+y = -13
4x - 2y = 16
The solution of the system of equations is (5, 2).
How to solve the system of equations?Here we want to solve the system of equations:
-3x + y = -13
4x - 2y = 16
By the elimination method.
If we take the first equation and we multiply it by 2, we will get:
2*(-3x + y) = 2*-13
-6x + 2y = -26
Now we can add the two equations to get:
(-6x + 2y) + (4x - 2y) = -26 + 16
-2x = -10
x = -10/-2
x = 5
And the value of y is given by evaluating one of the equations in x = 5, using the first one.
-3*5 + y = -13
-15 + y = -13
y = 15 - 13 = 2
The solution is (5, 2)
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how many vertices and edges dose this shape have?
Vertices :
Edges:
Step-by-step explanation: A vertex is a corner on shape. And edge is a line segment between faces. A face is singular flat surface.
Which value of x is a solution to this equation?
3x2 minus 30x minus 72 = 0
A
x = negative12
B
x = negative4
C
x = negative2
D
x = negative6
The solution to the equation 3x2 - 30x - 72 = 0 is x = -4 and x = -12.
3x2 - 30x - 72 = 0
3x2 - 30x = 72
3x2 - 24x = 90
3x2 - 24x + 18x = 90 + 18x
3x(x - 8) = 108
x(x - 8) = 36
x = 36 or x = 8
x = -12 or x = -4
The equation 3x2 - 30x - 72 = 0is a second-degree polynomial equation with two solutions. To solve this equation, first use the distributive property to factor out 3x from the first two terms. This yields 3x(x - 8) = 108. Then divide both sides of the equation by 3 to get x(x - 8) = 36. From here, use the quadratic formula to solve for x. This yields x = 36 or x = 8. Since the equation was given in terms of x2, the two solutions are x = -12 and x = -4. To confirm this, substitute these values into the original equation and check that it is true.
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A rectangular prism measures 7 1/2 cm by 12 cm by 15 1/2 cm. ****If you are stuck, think about how many cubes with 1/2 cm edge lengths fit into 1 cubic centimeter*** Calculate the number of cubes with edge length 1/2 cm that fit in this prism. Cubes What is the volume of the prism in centimeters cubed? centimeters cubed
Number of cubes with edge length 1/2cm that fit in the prism is 11160 and the volume of the prism is 1395 cubic centimeter
Dimensions of the rectangular prism = [tex]7\frac{1}{2}[/tex] cm × 12 cm × [tex]15\frac{1}{2}[/tex] cm
Convert the mixed fraction to the simple fraction
The dimensions of the rectangular prism = 15/2 cm × 12 cm × 31/2 cm
The volume of the rectangular prism = w × l × h
Where
w is the width
l is the length
h is the height
The volume of the rectangular prim = 15/2 × 12 × 31/2
= 1395 cubic centimeter
The side off the cube = 1/2 cm
Volume of the cube = a^3
= (1/2)^3
= 0.125 cubic centimeter
Number of cubes will fit in rectangular prism = Volume of rectangular prism / Volume of the cube
= 1395 / 0.125
Divide the terms
= 11160 cubes
Therefore, 11160 cubes will fit in the rectangular prism and the volume of the prism is 1395 cubic centimeter
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Please help!!
Sandra is looking to buy decorative doughnuts for a party. She is considering two local bakers. She looks up two bakers online to find how much each one charges. Here are the advertisements she saw online. Ms. Spellings Donut Shop Try out this week's special! All decorative donuts are on sale for $1.62 each with
an $8 boxing fee! Phil'd Up Doughnuts Boxing fee included in price! Number of Decorative Doughnuts and price 2 $9 4 $13 6 $17 8 $21 $25 12 $29 a) What is the rate of change and the boxing fee for each doughnut shop? b) If the total cost was Sandra's biggest concern, who should she buy from? Justify you answer mathematically.
Answer:
Step-by-step explanation:
Dont cheat on your homework
PLEASE HELP ME!!!!!!
In 5-7 sentences, give real-world examples of the following math vocabulary terms:
1. Rotation
2. Reflection
3. Translation
4. Dilation
Answer: are have a raztation speed of 20 rotation a min
Step-by-step explanation:W anwer
ime taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 3 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (round your answer to four decimal places.)
The probability that the sample average amount of time taken on each day is at most 11 min:
P([tex]\bar{X_1}[/tex] < 11) = 0.8682
P([tex]\bar{X_2}[/tex] < 11) = 0.8897
We know that the formula for the z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Let X be the time taken by a randomly selected applicant for a mortgage to fill out a certain form
[tex]\mu_x[/tex] = 10
[tex]\sigma_x[/tex] = 2
Here, five individuals fill out a form on one day and six on another.
This means that the population is the same on both days, but the samples of different sizes.
On Day 1 the average[tex]\bar{X_1}[/tex] ∼Norm(10, 2/[tex]\sqrt{5}[/tex])
We find the probability using z-score.
The probability that the sample average amount of time taken on day 1 is at most 11 min:
P([tex]\bar{X_1}[/tex] < 11)
=[tex]P(\frac{\bar{X_1}-10}{(\frac{2}{\sqrt{5} } )} < \frac{11-10}{(\frac{2}{\sqrt{5} } )})[/tex]
= P(z < 1.118)
= 0.8682
Similarly, on Day 2 the average[tex]\bar{X_1}[/tex] ∼Norm(10, 2/[tex]\sqrt{6}[/tex])
So the probability that the sample average amount of time taken on day 1 is at most 11 min:
P([tex]\bar{X_2}[/tex] < 11)
=[tex]P(\frac{\bar{X_2}-10}{(\frac{2}{\sqrt{6} } )} < \frac{11-10}{(\frac{2}{\sqrt{6} } )})[/tex]
= 0.8897
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The complete question is:
The time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 2 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min?
Pre cal due tonight need help
the angle between the vectors is: θ = cos⁻¹ (- 12 / √145)
What is vector?A quantity or phenomena with independent directions and magnitudes is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Science uses vectors to express everything with a direction and a magnitude. They are typically shown as pointed arrows, with the length of the arrow representing the magnitude of the vector.
Let, a(vector) = < -1, -2 >
a(vector) = -i -2j
||a(vector)|| = √(-1)² + (-2)² = √5
b(vector) = < -2, 5 >
b(vector) = -2i + 5j
||b(vector)|| = √(-2)² + (5)² = √29
Next, a(vector) . b(vector) = (-i -2j) . ( -2i + 5j)
a(vector) . b(vector) = (1 × (-2)) + (-2 × 5) = - 12
Thus, angle between these two vectors:
cosθ = a(vector) . b(vector) / ||a(vector)|| . ||b(vector)||
cosθ = - 12 / (√5 . √29)
cosθ = - 12 / √145
θ = cos⁻¹ (- 12 / √145)
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Four children take part in a swimming relay race.
The table shows their times in the race.
Name Time taken
(seconds)
Manjit: 92.4
Pierre: 86.7
Safia: 85.1
Chen: 91.8
Work out the total time taken by the team in minutes and seconds.
.................minutes ...............seconds
Answer:
5 Minutes and 56 Seconds
Step-by-step explanation:
Manjit= 1 Minute and 32.4 Seconds
Pierre = 1 Minute and 26.7 Seconds
Safia = 1 Minute and 25.1 Seconds
Chen = 1 Minute and 31.8 Seconds
4 X 1 Minute = 4 Minutes
32.4 + 26.7 +25.1 +31.8 = 116 or 1 Minute and 56 Seconds
Therefore, the answer is 5 Minutes and 56 Seconds
How to find the missing angles and sides of a triangle with one given angle and side
a player misses only 12% of all free throw shots they take. suppose they are in a contest where they shoot free throws until they miss one. what is the probability that they take exactly 5 shots?
The probability that the player takes exactly 5 shots before missing one is approximately 0.0539, or 5.39%.
The probability of missing a free throw shot is 0.12, and the probability of making a free throw shot is 0.88 (which is 1 - 0.12).
To find the probability that the player takes exactly 5 shots before missing one, we can use the geometric distribution, which models the number of independent and identical Bernoulli trials needed to get a success.
In this case, a "success" is missing a free throw shot, and the "trials" are the number of shots the player takes before missing one. The probability of success (missing a shot) is p = 0.12, and the probability of failure (making a shot) is q = 0.88. The probability of taking exactly 5 shots before missing one is:
P(X = 5) = q^4 * p
where X is the random variable representing the number of shots the player takes before missing one.
Plugging in the values, we get:
P(X = 5) = (0.88)^4 * 0.12
= 0.0539
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If 65% of a number is 208 and 15% ofthe same number is 48, find 80% of that number.
Answer:
256
Step-by-step explanation:
65% is 208
15% is 48
15% + 65% is 80%
So, just add 48 and 208 together:
48 + 208 = 256
Therefore, 80% of that number is 256.
Answer:
256
Step-by-step explanation:
We know that 65% of a number is 208 and 15% is 48, so we can simply add 208 + 48 to get 256.
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Answer:
**DUE TOMORROW, NEED ANSWER ASAP**
NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).
a.) An ultraviolet telescope in space
b.) An optical telescope in a remote location in Michigan's upper peninsula
c.) A radio telescope in the Mojave desert in Arizona
d.) An x-ray telescope in the Andes mountains in Chile
e.) An optical telescope in space
Step-by-step explanation:
part b. which equation has the same graph as the answer from part a, and so can also be used to model the data?
Answer:
D
Step-by-step explanation:
f(x)=20 cos (pi/5x + pi/2)+25
g(n) = -1 +1 n f(n) = - 1 n-1
Oliver is working this summer. His job pays $7.25 per hour. He will be working
15 hours per week and he'll be working for 14 weeks. How much money will
he make before any deductions are made from his pay?
Answer:
$1522.5
Step-by-step explanation:
(7.25 x 15)14
(108.75)14
= 1522.5
what value of k makes -4 > k + 15 true
Answer:
-19 > k
Step-by-step explanation:
-4 > k + 15
Subtract 15 from each side.
-4-15 > k + 15-15
-19 > k
Any value less than -19 would make this statement true
Answer:
- 19 > k
Step-by-step explanation:
- 4 > k + 15
Subtract 15 from both sides.
- 4 - 15 > k
- 19 > k
