Answer is 64.05% probability that if we chose a student at random
To find the probability that a randomly chosen student would not like the school lunches, we need to find the complement of the probability that they do like the school lunches.
The proportion of 9th graders in the sample is 45%, so the proportion of 10th graders is 100% - 45% = 55%.
Of the 9th graders, 31% said they liked the school lunches, so the proportion that did not like them is 100% - 31% = 69%.
Of the 10th graders, 42% said they liked the school lunches, so the proportion that did not like them is 100% - 42% = 58%.
So, the probability that a randomly chosen student would not like the school lunches is:
(0.45 * 0.69) + (0.55 * 0.58) = 0.6405 or 64.05% (rounded to two decimal places).
Therefore, there is a 64.05% probability that if we chose a student at random, they would not like the school lunches.
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Math
learning
area of circles - item 34972
the diameter of a quarter is about 1 in.
you trace around the edge of the quarter on a sheet of paper.
what is the area of the circle on the paper?
use 3. 14 as an approximation for a round your answer to the nearest tenth,
the area of the circle on the paper is approximately 0.8 square inches.
To find the area of the circle traced on the paper, we'll use the formula for the area of a circle, which is A = πr², where A is the area, π is approximately 3.14, and r is the radius.
The diameter of the quarter is about 1 inch, so the radius is half of that, which is 0.5 inches. Now, plug the radius into the formula:
A = 3.14 × (0.5)²
A = 3.14 × 0.25
A ≈ 0.785
Therefore, the area of the circle on the paper is approximately 0.8 square inches when rounded to the nearest tenth.
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Verify that MQ:QN = 2:3 by finding the lengths of MQ and QN
The length of MQ and QN is 10 and 15 respectively and verify that MQ: QN = 2:3
The coordinate of M = (-12,-5)
The coordinate of N = (8,10)
n = 2 , m = 3
By using the section formula coordinate of Q =( [tex]\frac{mx_{1} + nx_{2} }{m+n }[/tex] , [tex]\frac{my_{1} + ny_{2} }{m+n}[/tex])
Coordinate of Q = ([tex]\frac{(-12)3 + 8(2)}{3+2}[/tex] , [tex]\frac{10(2) + 3(-5)}{2+3}[/tex])
Coordinate of Q = ( -4, 1)
Now using the distance formula
MQ = [tex]\sqrt{ (x_{2}- x_{1} )^{2} +(y_{2} -y_{1} )^{2}[/tex]
MQ = [tex]\sqrt{(-4+12)^{2}+(1+5)^{2} }[/tex]
MQ = √100
MQ = 10
Similarly,
QN = [tex]\sqrt{(8+4)^{2}+(10-1)^{2} }[/tex]
QN = [tex]\sqrt{225}[/tex]
QN = 15
MQ:QN = 10:15
MA :QN = 2:3
Hence it is verified that MQ: QN = 2:3
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The graph shows the height of a scratch on the edge of a circular gear.
Which function is the best model for the height of the scratch?
a. h(t) = 3.5 sin (π t) + 1.5
b. g(t) = 1.5 sin (π t) +3.5
c. h(t) = 1.5 sin (2 π t) + 3.5
d. h(t) = 1.5 sin (π/2 t) + 3.5
Answer:
b. g(t) = 1.5 sin (π t) +3.5
Step-by-step explanation:
You want to choose the function that has the given graph.
Test pointsAt t = 0, the graph shows a value of 3.5. The sine of 0 is 0, so this eliminates choice A.
At t = 1/2, the graph shows a value of 5. The values given by the different formulas are ...
b. g(1/2) = 1.5·sin(π/2) +3.5 = 5 . . . . . matches the graph
c. h(1/2) = 1.5·sin(π) + 3.5 = 3.5 . . . . no match
d. h(1/2) = 1.5·sin(π/4) +3.5 = 0.75√2 +3.5 . . . . no match
__
Additional comment
The horizontal distance for one period of the graph (from peak to peak, for example) is T = 2 seconds. If the sine function is sin(ωt), then the value of ω is ...
ω = 2π/T = 2π/2 = π
This tells you the function g(t) = 1.5·sin(πt)+3.5 is the correct choice.
if a researcher finds a small difference in average test scores between a large sample (over 700) of experimental participants and a large sample (same size) of control participants, it is very likely that the difference is
The null and alternative hypotheses are H₀: μ₁ - μ₂ = 0 and H₁: μ₁- μ₂ ≠ 0 and the test statistic value is equal to 0.45.
The null hypothesis (H₀) states,
That there is no significant difference between the population means of the experimental group and the control group.
The alternative hypothesis (H₁) states that there is a significant difference between the two means.
State the hypotheses as,
H₀: μ₁ - μ₂ = 0 (there is no difference in means)
H₁: μ₁- μ₂ ≠ 0 (there is a difference in means)
where μ₁ is the population mean of the experimental group
And μ₂ is the population mean of the control group.
The test statistic,
Use the t-test formula,
t = (x - μ) / (s / sqrt(n))
where x is the sample mean = 102
μ is the hypothesized population mean = 100
s is the sample standard deviation =88
n is the sample size= 10
Plugging in the values, we get,
t = (102 - 100) / (88 / sqrt(10))
= 0.45
Therefore, the null and the alternative hypotheses states that H₀: μ₁ - μ₂ = 0 there is no difference in means and H₁: μ₁- μ₂ ≠ 0 there is a difference in means and the test statistic for a sample mean of 102 is 0.45.
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The given question is incomplete, I answer the question in general according to my knowledge:
If a researcher finds a small difference in average test scores between a large sample of 700 experimental participants with a standard deviation of 88, a mean of 100, and with a sample size of 10.
a. State the null and the alternative hypotheses.
b. Compute the test statistic for sample mean 102.
Please help with these Please explain if possibile
By using Pythagoras' theorem, triangle 3 and 4 is a right triangle, and others are not.
What is the triangle?
A triangle is a three-sided polygon with three vertices. The angle produced within the triangle is 180 degrees.
What is right-angled triangle?
A right-angled triangle is one with one of its interior angles equal to 90 degrees, or any angle is a right angle.
According to the given information:
The Pythagorean theorem states that " In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides"
Let's check fig (3)
[tex]15^{2} =12^{2} +9^{2}[/tex]
225 = 144 + 81
225 = 225
both sides are equal, Therefore it is a right-angled triangle.
Let's check fig (4)
[tex]48.5^{2}=39^{2}+32.5^{2}[/tex]
2352.25 = 1521 + 1056.25
2352.25 ≠ 2577.25
Both sides are not equal, Therefore it is not a right-angled triangle.
Let's check fig (5)
[tex]11^{2}=9^{2}+\sqrt{115} ^{2}[/tex]
121 = 81 + 115
121 ≠ 196
Both sides are not equal, Therefore it is not a right-angled triangle.
Let's check fig (6)
[tex]16^{2} = 10^{2} + (2\sqrt{39}) ^{2}[/tex]
256 = 100 + 156
256 = 256
both sides are equal, Therefore it is a right-angled triangle.
Hence figure 3 and 6 is right angle triangle, others are not.
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Let y = tan(5x + 5). Find the differential dy when x = 3 and dx = 0.4 Find the differential dy when x = 3 and dx = 0.8
When x = 3 and dx = 0.4, the differential dy is approximately 4.056, and when x = 3 and dx = 0.8, the differential dy is approximately 8.113.
Differential,
To find the differential dy, we use the formula:
dy = f'(x) * dx
where f'(x) is the derivative of the function y = tan(5x + 5) with respect to x.
Taking the derivative, we get: f'(x) = sec^2(5x + 5) * 5 Plugging in x = 3, we get: f'(3) = sec^2(20) * 5
Now we can find the differential dy for dx = 0.4 and dx = 0.8:
When dx = 0.4: dy = f'(3) * dx dy = sec^2(20) * 5 * 0.4 dy ≈ 4.056
When dx = 0.8: dy = f'(3) * dx dy = sec^2(20) * 5 * 0.8 dy ≈ 8.113
Therefore, when x = 3 and dx = 0.4, the differential dy is approximately 4.056, and when x = 3 and dx = 0.8, the differential dy is approximately 8.113.
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Projectile motion. the height, y metres, of a ball after it has been hit can be modelled by the equation y = -1/8x²+x+c, where x is the horizontal distance travelled by the object in metres and c is a constant. (i) given that the maximum height attained by the ball is 2.4 metres, find the value of c and the corresponding horizontal distance travelled by the ball.
The value of c is 0.4 and the corresponding horizontal distance travelled by the ball is 4 meters.
How to solve projectile equations?
We are given the projectile equation:
y = -1/8x² + x + c
To find the value of c, we can use the fact that the maximum height attained by the ball is 2.4 meters. The maximum height occurs at the vertex of the parabola, which is given by:
x = -b/2a
where a = -1/8 and b = 1.
Therefore,
x = -(1)/(2*(-1/8)) = 4
So, the corresponding horizontal distance travelled by the ball is 4 meters.
Now, we can use the maximum height attained by the ball to solve for c.
y = -1/8x² + x + c
Substituting x = 4 and y = 2.4, we get:
2.4 = -1/8(4)² + 4 + c
2.4 = -1/8(16) + 4 + c
2.4 = -2 + 4 + c
c = 0.4
Therefore, the value of c is 0.4.
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In the diagram shown, segments AE and CF are both perpendicular to DB.
DE=FB, AE=CF. Prove that ABCD is a parallelogram.
Answer:
Step-by-step explanation:
Given:- ABCD is a parallelogram, and AE and CF bisect ∠A and ∠C respectively. To prove:- AE∥CF Proof:- Since in a parallelogram, opposite angles are equal.
Charlie collects dimes in a jar. The total mass of the dimes is 1. 265 x 10 grams. The mass of each dime is 2. 3 grams. How many dimes
are in the jar?
A 5. 5 x 103 dimes
B. 5. 5 x 102 dimes
C 2. 9 x 103 dimes
D2. 9 x 102 dimes
There are approximately 5500 dimes in the jar. A) 5.5 x 103 dimes.
How we find the dimes?To determine the number of dimes in the jar, we can divide the total mass of the dimes by the mass of each dime.
Total mass of dimes = 1.265 x 10 grams
Mass of each dime = 2.3 grams
Let "x" be the number of dimes in the jar. Then, we can set up the following equation:
x(2.3 grams) = 1.265 x 10 grams
Simplifying this equation, we get:
x = 1.265 x 10 / 2.3
x ≈ 5500
It is important to that this calculation assumes that all dimes have the same mass, and that there are no other objects in the jar.
the actual number of dimes may vary slightly due to measurement error or variability in the mass of each dime.
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Many types of bias exist when it comes to surveys, including nonresponse bias, undercoverage, and poorly worded survey questions. think about a survey you’ve been asked to participate in. maybe it was printed on a fast-food receipt or a store directed you to an online survey after you made a purchase. what influenced you to participate in the survey or to opt out of participating?
Analysis whether the biases were present in the survey or not .
The different types of biases are:
Nonresponse bias
Under coverage
Poorly worded
Given,
Biases in survey .
When it comes to surveys, there are several factors that can influence a person's decision to participate, such as the timing and location of the survey, the perceived relevance of the questions and incentives offered for participation. In some cases, people may opt-out of participating in a survey due to privacy concerns, lack of interest or distrust of the organization conducting the survey.
In terms of biases, survey designers should be careful of different types of biases that can affect the results, such as sampling bias, selection bias and response bias.
For example, if a survey is only given to certain demographics, the results may not be representative of the target audience.
Similarly, if the survey questions are worded in a leading or biased way, it can influence a person's response and skew the results.
It is important for survey designers to be aware of these biases and take steps to minimize their impact. This can include using random sampling techniques to ensure a representative sample, testing survey questions with focus groups to ensure they are clear and unbiased, and providing clear and transparent information about the purpose and use of the survey data. By taking these steps, survey designers can create surveys that produce accurate and reliable results.
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AABC DEF. What sequence of transformations will move AABC onto ADEF?
A. A dilation by a scale factor of 2, centered at the origin, followed by
a reflection over the y-axis
B. The translation (x, y) - (x + 7, y), followed by a dilation by a scale
factor of 2 centered at the origin
C. A dilation by a scale factor of 2, centered at the origin, followed by
the translation
(x,y) → (x+7, y)
D. A dilation by a scale factor of 2, centered at the origin, followed by
the translation (x, y) - (x+7, y)
Therefore, the correct sequence of transformations is:
Dilation by a scale factor of 2, centered at the origin.
Translation of 7 units to the left.
This is equivalent to option D.
To move AABC onto ADEF, we need to perform a sequence of transformations that will map each point of AABC onto the corresponding point of ADEF. Let's first label the vertices of AABC and ADEF as shown:
We can see that A and D have the same coordinates, so we only need to map B, C, and A' to E, F, and D', respectively.
Option A suggests a dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis. This transformation will map B to E, but it will also map C to C' which is not the same as F. Moreover, A' will be mapped to a point that is reflected over the y-axis and does not coincide with D. Therefore, option A is not the correct answer.
Option B suggests a translation of 7 units to the right, followed by a dilation by a scale factor of 2 centered at the origin. This transformation will not map B to E, but it will map A' to D', and C to a point that is 7 units to the right of F. Therefore, option B is not the correct answer either.
Option C suggests a dilation by a scale factor of 2, centered at the origin, followed by a translation of 7 units to the right. This transformation will map A' to D', and B to a point that is 7 units to the right of E. However, it will also map C to a point that is 7 units to the right of F, which is not the same as F. Therefore, option C is not the correct answer.
Option D suggests a dilation by a scale factor of 2, centered at the origin, followed by a translation of 7 units to the left. This transformation will map B to E, and A' to D', but it will also map C to a point that is 7 units to the left of F. However, if we reflect the resulting figure over the y-axis, we obtain the desired result.
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In a certain high school, a survey revealed the mean amount of bottled water consumed by students each day
was 153 bottles with a standard deviation of 22 bottles. Assuming the survey represented a normal distribution,
what is the range of the number of bottled waters that approximately 68. 2% of the students drink?
The range of the number of bottled waters that approximately 68. 2% of the students drink is between 131 and 175 bottled waters per day.
The range of the number of bottled waters that approximately 68.2% of the students drink can be calculated using the empirical rule, also known as the 68-95-99.7 rule.
According to this rule, for a normal distribution:
Approximately 68.2% of the data falls within one standard deviation of the mean
Approximately 95.4% of the data falls within two standard deviations of the mean
Approximately 99.7% of the data falls within three standard deviations of the mean
falls within a certain number of standard deviations from the mean
Since we are interested in the range of values that approximately 68.2% of the students drink, we can start by calculating one standard deviation from the mean:
One standard deviation = mean ± standard deviation
= 153 ± 22
= 131 to 175
This answer is based on the empirical rule, which is a useful tool for understanding the spread of data in a normal distribution. It tells us that for a normal distribution, a certain percentage of the data
Therefore, approximately 68.2% of the students drink between 131 and 175 bottled waters per day.
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rewrite each equation using the properties of exponents
1. ([tex](\frac{4}{64\frac{5}{6} })^{\frac{1}{2} }[/tex]
2. [tex]3m\frac{1}{4} (mn\frac{1}{3} ) ^{\frac{3}{2} }[/tex]
3.[tex]2a\frac{1}{2} (5a\frac{1}{2} b\frac{1}{4} )^{2}[/tex]
The properties of exponents
1. [tex](64)^{1/2}[/tex] = √(64) = 8
2. [tex]3m(mn)^(3/2)[/tex] = [tex]3m(m^{3/2}n^{3/2})[/tex]
3. 2a(5ab)² = [tex]2a(25a^2b^2) = 50a^3b^2[/tex]
The properties of exponents can be used to simplify and rewrite expressions involving powers and roots. The most common properties are:
Product of powers: [tex]a^m[/tex] * aⁿ = [tex]a^{m+n}[/tex]
Quotient of powers: [tex]a^m[/tex]/ aⁿ = [tex]a^{m-n}[/tex]
Power of a power: [tex](a^m)^n[/tex] = [tex]a^{mn}[/tex]
Power of a product: [tex](ab)^m[/tex] = [tex]a^m[/tex] * [tex]b^m[/tex]
Power of a quotient: [tex](a/b)^m[/tex] = [tex]a^m[/tex]/ [tex]b^m[/tex]
Using these properties, we can rewrite the given equations as follows:
1. [tex](64)^{1/2}[/tex] = √(64) = 8
The square root of 64 is 8. The power of 1/2 represents the square root.
2. [tex]3m(mn)^(3/2)[/tex] = [tex]3m(m^{3/2}n^{3/2})[/tex]
The power of 3/2 represents the square root of the square. We can use the product of powers property to combine the m and n terms under the same square root.
3. 2a(5ab)² = [tex]2a(25a^2b^2) = 50a^3b^2[/tex]
We can use the power of a product property to square the 5ab term, and then simplify by combining the like terms.
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A) What internal goods does mathematics offer? Discuss how these goods multiply when you share them with others. B) Discuss creative power and coercive power that you have witnessed in mathematical settings. C) How can teachers affirm their students' dignity as creative human beings in the ways they do mathematics?
A) Internal goods in mathematics include problem-solving skills, logical thinking, analytical reasoning, and a deep understanding of mathematical concepts.
B) Coercive power, on the other hand, might manifest when individuals impose their methods or beliefs on others, potentially stifling creativity and discouraging alternative perspectives.
C) Teachers affirm their students' dignity as creative human beings in the ways they do mathematics by creating a safe space, encourage exploration and expression, value the learning process, celebrate creativity and originality in problem-solving
A) When you share these goods with others, they multiply in the sense that others also develop these skills, fostering collaboration, and generating new ideas, ultimately contributing to the overall progress in the field of mathematics.
B) Creative power in mathematical settings can be seen when individuals or teams come up with innovative solutions to problems, develop new theories, or find unique ways to apply mathematics to real-world situations.
C) Teachers can affirm their students' dignity as creative human beings in the ways they do mathematics by:
1. Encouraging students to explore multiple solution methods and strategies, allowing them to find the approach that best suits their thinking style.
2. Valuing each student's input, ideas, and questions, creating a safe and supportive environment for them to express their thoughts.
3. Challenging students with open-ended problems that require creativity and critical thinking, emphasizing the importance of understanding concepts over rote memorization.
4. Recognizing and celebrating each student's unique strengths and contributions to the learning process, promoting a growth mindset and a sense of accomplishment.
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Natalie earns $85 for 4 hours of work. If she makes a constant hourly wage, which table represents the relationship between the number of hours she works and her total earnings?
Her total earnings increase by $21.25 for every hour she works, since her hourly wage is constant.
The relationship between Natalie's earnings and the number of hours she works can be represented by a linear equation in the form y = mx + b, where y is her total earnings, x is the number of hours she works, m is her hourly wage, and b is her initial earnings (or y-intercept).
To find the hourly wage, we can divide her total earnings by the number of hours she works:
hourly wage (m) = total earnings / number of hours worked
m = 85 / 4 = 21.25
So, Natalie's hourly wage is $21.25.
Now, we can use this information to create a table that shows the relationship between the number of hours she works and her total earnings:
| Hours worked (x) | Total earnings (y) |
|------------------|-------------------|
| 1 | 21.25 |
| 2 | 42.50 |
| 3 | 63.75 |
| 4 | 85.00 |
As you can see, her total earnings increase by $21.25 for every hour she works, since her hourly wage is constant. Therefore, the correct table that represents the relationship between the number of hours she works and her total earnings is the one shown above.
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1) What do you think this graph is suggesting regarding skill levels for future employment, give two suggestions..
2) What occupational group will people with a skill level 5 be able to join?
Answer:
1) I think the graph is suggesting that a higher level of skill, or degree, will ultimately help you get a better job easier and faster.
2) With a skill level of five, you can become a sales worker or labourer. It is a low percentage of people with a skill level five to become community and personal service workers.
Thanks for reading! Always work toward your dreams! :)
The diagram represents a model of a ramp the skateboard club wants to create at the neighborhood skate park. If one pint of paint covers 200 square inches, how many pints of paint will the club need to purchase? Paint is only sold in whole pints.
The number of pints of paint that the club will need is given as follows:
2 pints of paint.
How to obtain the amount of paint?Before obtaining the amount of paint, we must obtain the surface area of the figure.
The figure in this problem is composed as follows:
One rectangle of dimensions 19 in and 8 in.One rectangle of dimensions 6 in and 19 in.Two right triangles of sides 6 in and 8 in.Hence the surface area is given as follows:
S = 19 x 8 + 19 x 6 + 2 x 0.5 x 6 x 8
S = 314 in².
If one pint of paint covers 200 square inches, hence the number of pints is given as follows:
314/200 = 2 -> rounded up, as there is not a decimal amount of pints, and one pint is not enough.
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multiply 5/12 by the reciprocal of 17/-6
Answer:
[tex]\frac{-5}{34}[/tex]
Step-by-step explanation:
[tex]\frac{5}{12} * \frac{-6}{17}[/tex] = [tex]\frac{-30}{204}[/tex]
We can simplify.
[tex]\frac{-15}{102}[/tex] ⇒ Divided both by 2
[tex]\frac{-5}{34}[/tex] ⇒ Divided both by 3
[tex]\frac{-5}{34}[/tex] is the final answer
If you could draw a number line that shows the relationship between tons and pounds what would it look like complete the explanation since one ton is 2000 pounds one the number line would show tick marks for every whole number from 0 to [blank].each tick mark from 0 to [blank] would represent [blank]pound(s). the tick mark at the end would represent [blank] ton(s).
Drawing a number line is a useful way to visualize the relationship between tons and pounds and can help make conversions easier to understand.
If we were to draw a number line that shows the relationship between tons and pounds, we would start with the fact that one ton is equivalent to 2000 pounds. We would then draw tick marks on the number line for every whole number from 0 to 10, with each tick mark representing 100 pounds. So, the tick mark at 0 would represent 0 pounds, the tick mark at 1 would represent 100 pounds, the tick mark at 2 would represent 200 pounds, and so on. The tick mark at 20 would represent 2000 pounds, or one ton.
We could then continue the number line past 20 to show larger quantities of tons and pounds, with each additional tick mark representing another ton (2000 pounds). For example, the tick mark at 30 would represent 3000 pounds, or 1.5 tons, the tick mark at 40 would represent 4000 pounds, or 2 tons, and so on.
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The cylinder below has a height of 6 centimeters and a radius of r1. The volume of the cylinder is 302 cubic centimeters.
Find the radius of the cylinder. Round to the nearest whole centimeter.
___ centimeters
Answer:
There is a cylinder with a height of 6 centimeters and a radius of r1, which has a volume of 302 cubic centimeters. It's fascinating to see how the volume of different shapes can vary based on their dimensions.
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Suki has $2 coins, $1 coins, and quarters in
her wallet. She owes her brother $2. 50. Use
an organized list to show all the possible
combinations of coins that she could use to
get exactly $2. 50
There are 4 possible combinations of coins that Suki could use to get exactly $2.50.
How to get the possible combinationsLet's denote the number of $2 coins as x, the number of $1 coins as y, and the number of quarters as z.
We need to find all the possible combinations of x, y, and z that satisfy the equation:
2x + y + 0.25z = 2.50
Here's the corrected organized list of combinations:
(1, 0, 2) → $2 + $1 + $0 = $2.50
(0, 2, 2) → $0 + $2 + $0.50 = $2.50
(0, 1, 6) → $0 + $1 + $1.50 = $2.50
(0, 0, 10) → $0 + $0 + $2.50 = $2.50
There are 4 possible combinations of coins that Suki could use to get exactly $2.50.
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please help................
Answer:
31
Step-by-step explanation:
1. Replace the variables with numbers
8(5)-(9)
2.Conduct order of operations
8(5)-9 --> 40-9 ---> 31
Answer:
31
Explanation:
Trust
I need to find the equation?
To determine the person who made the best kick, you could use an equation that relates distance, speed, and height: distance = speed × time.
How to determine the person with the best kickTo determine the person with the best kick, it is vital that a correlation be drawn between the distance and height. In the absence of information about time, the person with the farthest distance and longest height can be determined as the person with the best kick.
So, to get the result without having the complete data, you can compare the height to determine the individual with the farthest distance and highest kick.
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if y=x^2+2x-5 for -3<=x<=3 then which of the following sets is the range of y
The range of the equation y = x² + 2x -5 where -3 ≤ x ≤ 3 is [-3,10]
The function is y = x² + 2x -5
Domain of x is [-3,3]
By putting the value of x = -3
y = (-3)² + 2(-3) - 5
y = 9 - 6 -5
y = -2
Minimum possible value is -2
And by putting the value of x = 3
y = 3² + 2(3) -5
y = 9 + 6 -5
y = 10
Maximum possible value is 10
The value of y ranges between -2 ≤ y ≤ 10
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The question is incomplete the complete question is :
If y = = x² + 2x -5 for -3 ≤ x ≤ 3 then what will be the range of y ?
In my class, everyone studies French or German, but not both languages.
One third of the girls and the same number of boys study German.
Twice as many boys as girls study French.
Which of these could be the total number of boys and girls in my class?
The possible total number of boys and girls in the class is 21, and
the answer is b).
Let's denote the number of girls in the class as 'g' and the number of
boys as 'b'.
We know that all students in the class study either French or German,
but not both.
Therefore, the total number of students in the class is equal to the sum
of the number of students who study French and the number of students
who study German
From the given information, we can write the following equations:
g + b = total number of students(1/3)g = (1/3)b (one third of the girls and the same number of boysstudy German
2(1/3)g = b (twice as many boys as girls study French)We can simplify the second equation by multiplying both sides by 3:g = bSubstituting this into the first equation, we get:
2g = total number of studentsSubstituting the second equation into the third equation, we get:2g = b (twice as many boys as girls study French)Substituting this into the first equation, we get:
3g = total number of studentsTherefore, the total number of students in the class must be a multiple
of 3.
Let's try the answer choices:
a) 15 students (total number of students is not a multiple of 3)
b) 21 students (total number of students is a multiple of 3 and the
number of girls is a multiple of 3, so this is a possible solution)
c) 24 students (total number of students is a multiple of 3 and the
number of girls is not a multiple of 3)
d) 30 students (total number of students is a multiple of 3 but the
number of girls is not a multiple of 3)
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A globe company currently manufactures a globe that is 18 inches in diameter if the dimensions of the globe are reduced by half what would the volume be 
The volume of the new globe would be 381.51 cubic inches, which is half the volume of the original globe.
The volume of a sphere is given by the formula:
V = (4/3)πr³
where r is the radius of the sphere.
If the diameter of the globe is reduced by half, then the new diameter would be 9 inches, and the new radius would be half of that, or 4.5 inches.
The new volume would be:
V' = (4/3)π(4.5)³
= (4/3)×3.14×(91.125)
= 381.51 cubic inches
Therefore, the volume of the new globe would be 381.51 cubic inches, which is half the volume of the original globe.
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NEED ANSWERS ASAP
Peter creates a square pyramid
model for History class. The
base of the pyramid has an
area of 20 square inches. Each
triangle has an area of 10
square inches. If Peter wants to
cover the entire pyramid with
gold paper, how much paper
will he need?
WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
Peter will need 60 square inches of gold paper to cover the entire square pyramid for his History class.
You need to find the total surface area of the square pyramid that Peter creates for his History class to determine how much gold paper he will need. This can be done as follows.
1: Identify the given information.
Base area: 20 square inches
Triangle area: 10 square inches
2: Determine the number of triangles in a square pyramid.
A square pyramid has 4 triangular faces.
3: Calculate the total area of the triangular faces.
Multiply the area of one triangle by the number of triangles: 10 square inches x 4 = 40 square inches.
4: Calculate the total surface area of the pyramid.
Add the base area and the total area of the triangular faces: 20 square inches (base) + 40 square inches (triangles) = 60 square inches.
Hence, the gold paper to cover the entire square pyramid is 60 square inches.
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moving company is using a large shipping container to pack up several smaller boxes. The smaller boxes are cubes with each side length measuring
The larger container will hold 20 smaller boxes along its width, 40 boxes along its length, and 20 boxes along its height.
e this information to fill in the blanks below.
please look at the photo:(
The volume of one smaller box is 1 cubic foot.
Solution to Shipping Container ProblemThe volume of one smaller box is calculated by raising the length of its sides to the power of 3, so the volume of one smaller box is:
Volume (smaller box) = (1 foot)³ = 1 cubic foot
The number of smaller boxes that fit into a shipping container is obtained by multiplying the number of boxes that fit along each dimension, so the number of smaller boxes that fit into a shipping container is:
Number of smaller boxes = 20 boxes (width) × 40 boxes (length) × 20 boxes (height) = 16,000 boxes
To calculate the volume of the large shipping container, we need to multiply the length, width, and height of the container. Since each dimension is given in terms of the number of boxes it can hold, we need to multiply each dimension by the length of one smaller box (1 foot) to obtain the dimensions in feet. Therefore, the volume of the large shipping container is:
Volume of the large shipping container = 20 boxes (width) × 1 foot (length of one smaller box) × 40 boxes (length) × 1 foot (length of one smaller box) × 20 boxes (height) × 1 foot (length of one smaller box) = 16,000 cubic feet
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This is my math hw someone help pls ?
Astha had $5,700 in her savings account when Henry opened a savings account with zero dollars.
Astha deposited $100 into her account each week for x weeks.
Henry deposited $75 into his account each week for x weeks.
The accounts did not earn interest.
Which inequality represents this situation when the amount of money in Astha's account was greater than the amount of money in Henry's account?
Answer choices:
100x < 5,700 + 75x
75x > 5,700 + 100x
100x > 5,700 + 75x
75x < 5,700 + 100x
Astha's account was greater than the amount of money in Henry's account is:
5700 + 100x > 75x
Why Astha's account was greater?Let's start by finding the total amount of money deposited by Astha and Henry after x weeks.
Astha deposited $100 into her account each week for x weeks, so the total amount she deposited is 100x.
Similarly, Henry deposited $75 into his account each week for x weeks, so the total amount he deposited is 75x.
To find the inequality that represents the situation when the amount of money in Astha's account was greater than the amount of money in Henry's account, we need to compare the total amount of money each of them deposited.
Astha started with $5,700 and deposited $100 each week for x weeks, so the total amount of money in her account after x weeks is:
5700 + 100x
Henry started with zero dollars and deposited $75 each week for x weeks, so the total amount of money in his account after x weeks is
75x
Therefore, the inequality that represents the situation when the amount of money in Astha's account was greater than the amount of money in Henry's account is:
5700 + 100x > 75x
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