ANSWER:
Therefore, Stephanie cannot pass the exam even if she gets full marks in Paper 2.
Step-by-step explanation:
Pass mark = 65 + 75 = 140
Stephanie got 80% of the marks for Paper 1, which is:
0.8 x 65 = 52
To pass the exam, Stephanie must get a total of 140 marks, and she already has 52 from Paper 1. Therefore, she needs to get the remaining marks from Paper 2:
140 - 52 = 88
So, Stephanie must get at least 88 marks out of 75 in Paper 2 to pass the exam. However, this is not possible as the maximum marks for Paper 2 are 75.
Lisa drew a line through points E(6,5) and F(2,-3). She drew a different line through points G(2,-1) and H(4,-5)
Answer:
Step-by-step explanation:
survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.
Grocery Options
Store Online
Women
32 9
Men
28 8
What percent of the people surveyed shop at a local grocery store? Round your answer to the nearest whole number percent.
Thus, 78% of the people surveyed, shopped at a local grocery store.
Explain about the percent:In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Grocery Options:
Store Online Total
Women 32 9 41
Men 28 8 36
Total 60 17 77
Total people = 77
Total people who shop at a local grocery store = 60
Thus,
Percentage = 60/77 *100 = 77.92% = 78%
Thus, 78% of the people surveyed, shopped at a local grocery store.
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A theater sets up its chairs in equal rows. Alison had a seat which was third from the front and 18th from the back. Naida could see 8 chairs to her left and 11 chairs to her right. How can chairs are in the theater?
Answer:
Let's call the total number of chairs in the theater "x". Since Alison's seat is 3rd from the front, there are 2 chairs in front of her. Similarly, since her seat is 18th from the back, there are 17 chairs behind her. Therefore, the number of chairs between the 2 chairs that Alison and Naida are sitting on is: x - (2 + 17) = x - 19 Now, if Naida can see 8 chairs to her left and 11 chairs to her right, that means there are 8 + 1 + 11 = 20 chairs between her and Alison. So we can set up an equation: (x - 19) - 20 = Alison's seat number Simplifying this equation: x - 39 = Alison's seat number We
The volume of a large tank is 525 . It is 16 2/3
wide and 2 4/5
high. What is the length of the tank
?
Answer:
The answer to your problem is, 11.25
Step-by-step explanation:
Formula used:
v = height x width x length
length = v / (width x height)
The volume equals 525, width 16 2/3 (16.67) and height 2 4/5 (2.8), replacing, length = 525 / (16.67 * 2.8)
Therefore the length being 11.25
Thus the answer to your problem is, 11.25
the volume of a cubic ice cube is decreasing at a rate of1.5cm3/sec. at what rate is a side of the ice cube decreasing when the side is6cm?
When the side of the ice cube is 6 cm, it is decreasing at a rate of approximately -0.0139 cm/sec.
To find the rate at which a side of the cubic ice cube is decreasing when the side is 6 cm, we need to use the chain
rule from calculus.
Let V be the volume of the cube and s be the side length. We know that [tex]V = s^3.[/tex]
Differentiate both sides of the equation with respect to time (t). This gives us [tex]dV/dt = 3s^2 × ds/dt.[/tex]
Plug in the given values. We know that dV/dt = -1.5 cm³/sec (since the volume is decreasing) and s = 6 cm.
Solve for ds/dt, which represents the rate at which a side of the ice cube is decreasing.
[tex]-1.5 = 3(6^2) × ds/dt[/tex]
Now, divide both sides by [tex]3(6^2)[/tex]:
ds/dt = -1.5 / (3 × 36)
ds/dt = -1.5 / 108
ds/dt ≈ -0.0139 cm/sec
So, when the side of the ice cube is 6 cm, it is decreasing at a rate of approximately -0.0139 cm/sec.
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Which expression is equivalent to 5(h+9)?
45h
14h
5h+9
5h+45
Answer:
D) 5h+45
Brainly asked me to put at least 20 words so I'm adding this here.
Answer: The expression equivalent to 5(h+9) is 5h+45, so the answer is option 4.
OPEN ENDED QUESTION
Why in finding the Volume of a 3-D shape, do you
cube the measurement?
Answer:
Great question! When we find the volume of a 3D shape, we need to calculate the amount of space occupied by the object. This space is measured in cubic units, which is why we need to cube one dimension or multiply three dimensions together to find the volume of a 3D shape. For example, if we want to find the volume of a cube with side length "s", we would cube that value by raising it to the power of 3. This is because we need to multiply the length "s" by the width "s" and the height "s" to get the total space occupied by the cube, which is s^3. Similarly, if we want to find the volume of a rectangular prism with dimensions "l", "w", and "h", we would multiply these three values together to get the total volume. This is because the space
explain the difference between the reciprocal of a function and the inverse of a function. why must the domains of the sine, cosine, and tangent functions be restricted in order to define their inverse functions? be specific. provide examples and graphs to support your answers.3
The main difference between the reciprocal and inverse of a function is their definition and properties. The reciprocal of a function f(x) is defined as 1/f(x), while the inverse of a function f(x) is a function f^(-1)(x) such that [tex]f(f^(-1)(x))=x and f^(-1)(f(x))=x[/tex] for all x in their respective domains.
The domains of sine, cosine, and tangent functions need to be restricted to define their inverse functions because they are not one-to-one functions. In order to have an inverse, a function must be both one-to-one (each output has only one input) and onto (each output value is mapped by at least one input value).
For example:
- sine: restricted domain to [-π/2, π/2] to define its inverse, arcsin (sin^(-1))
- cosine: restricted domain to [0, π] to define its inverse, arccos (cos^(-1))
- tangent: restricted domain to (-π/2, π/2) to define its inverse, arctan (tan^(-1))
These restrictions ensure that the functions become one-to-one and onto, making it possible to define their inverses uniquely.
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A fish tank is a rectangular prism that is 30 inches long, 24 inches deep, and 18 inches high. How much water will it hold in cubic inches
The fish tank will hold 12,960 cubic inches of water.
What is volume ?
Volume is a physical quantity that refers to the amount of space occupied by an object or a substance. In mathematical terms, volume can be defined as the measure of the three-dimensional space enclosed by a closed surface or shape. It is usually expressed in cubic units such as cubic meters, cubic feet, or cubic centimeters, depending on the system of measurement being used.
The volume of a rectangular prism can be calculated by multiplying its length, width, and height. Therefore, the volume of the fish tank is:
30 inches (length) x 24 inches (depth) x 18 inches (height) = 12,960 cubic inches
Therefore, the fish tank will hold 12,960 cubic inches of water.
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A community has an empty field ready for development and plans to place a playground in the center. A model of the plan for the project is shown.
A large rectangle with dimensions of 28 feet by 48 feet. Inside it is a smaller rectangle with dimensions of 20 feet by 16 feet.
How much area is left for development in the field outside the playground?
320 ft2
512 ft2
1,024 ft2
1,344 ft2
The area left for development in the field outside the playground is C)1024[tex]ft^2[/tex].
What is area?The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
We know that area of rectangle formula is,
Area = [tex]length\times breadth[/tex] square unit
The total area of the field is the area of the large rectangle, which is:
=> [tex]28 \times48 = 1,344 ft^2[/tex]
The area of the playground is the area of the smaller rectangle, which is:
=> [tex]20 \times 16 = 320 ft^2[/tex]
Therefore, the area left for development outside the playground is:
=> [tex]1,344 ft^2 - 320 ft^2 = 1,024 ft^2[/tex]
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The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10,16,20, and 28. There are two dots above 8 and 14. There are three dots above18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 47, with an IQR of 8
Bus 14, with an IQR of 6
Bus 47, with a range of 8
Bus 14, with a range of 6
Answer:
Answer below :)
Step-by-step explanation:
To determine which bus is the most consistent, we need to look at the measures of variability for each bus. The two measures of variability that are commonly used are the range and the interquartile range (IQR).
The range is the difference between the maximum and minimum values in a dataset. It gives an idea of how spread out the data is but can be affected by extreme values or outliers. The IQR is a better measure of variability as it is not affected by extreme values and is a more robust measure of variability.
Looking at the given data, Bus 47 has a range of 8 and an IQR of 8, while Bus 14 has a range of 6 and an IQR of 6. This indicates that Bus 14 has less variability in its travel times than Bus 47.
Therefore, we can conclude that Bus 14 is the most consistent in terms of travel times.
Please help me toppers
Step-by-step explanation:
Factor out 3 a^2 b from the numerator to get :
3a^2b ( 2a-4a^2+5ab- b ) / 3a^2b then the 3a^2b 'cancels out'
and you are left with
2a -4a^2 + 5ab - b <====this is the answer
but it can be further factored to:
2a (1-4a) + b(5a-1) if you want this form
Answer:
2a -4a^2 + 5ab - b
Step-by-step explanation:
I did the test
Hope this help :)
Jasmine has 5 books that she wants to read she wants to read the nonfiction book first and the mystery book last in how many different orders can she read the books
Answer:
Step-by-step explanation:
Jasmine has 5 books that she wants to read. She wants to read the nonfiction book first and the mystery book last. Therefore, there are 3 remaining books that can be read in any order.The nonfiction book can be chosen in 1 way, and the mystery book can be chosen in 1 way. The remaining 3 books can be arranged in 3! (or 6) ways.Therefore, the total number of different orders in which Jasmine can read the books is:1 × 3! × 1 = 6 × 1 = 6So, there are 6 different orders in which Jasmine can read the books.
a sample of 45 pieces of laminate used in the manufacture of circuit boards was selected and the amount of warpage (in.) under particular conditions was determined for each piece, resulting in a sample mean warpage of 0.0631 and a sample standard deviation of 0.0072. a) construct and interpret in context a 99% confidence interval for the average amount of warpage in all such pieces of laminate. b) construct and interpret in context a 90% confidence interval for the average amount of warpage in all such pieces of laminate. c) which interval is wider? why?
The true average amount of warpage in all such pieces of laminate lies between 0.0609 and 0.0653 inches with 99% confidence.
a) To construct a 99% confidence interval for the average amount of warpage in all such pieces of laminate, we can use the formula:
CI = X ± Z × (s / √n)
where X is the sample mean warpage, Z is the Z-value from the table below, s is the sample standard deviation and n is the number of observations.
The Z-value for a 99% confidence interval is 2.576. (refer the image)
Plugging in the values we get:
0.0631 ± 2.576 × (0.0072 / √45)
= [0.0609, 0.0653]
b) To construct a 90% confidence interval for the average amount of warpage in all such pieces of laminate, we can use the same formula as above but with a different Z-value.
The Z-value for a 90% confidence interval is 1.645.
Plugging in the values we get:
0.0631 ± 1.645 × (0.0072 / √45)
= [0.0618, 0.0644].
c) Because we need to be more positive that our interval contains the genuine population mean as our confidence level rises, the interval for a 99% confidence level is greater than that for a 90% confidence level. This suggests that in order to account for all possible values of the population mean, we must widen our interval.
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Use the Triangle Angle Sum Theorem to find the measure of the angle on point C.
(1 point)
Therefore , the solution of the given problem of triangle comes out to be curve C has a measure of 70 degrees.
What precisely is a triangle?If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.
Here,
Sum of Triangle Angles According to a theorem, a triangle's internal angles always add up to 180 degrees.
We are aware that angle B in the trapezoid is 50 degrees and angle A is 60 degrees. As a result, we can apply the Triangle Angle Sum Theorem to determine the size of angle C:
Angle A +Angles B + C = 180 degrees.
With the known numbers substituted, we obtain:
Angle C: 60° + 50°+60° = 180°
By condensing the left half, we obtain:
Angle C = 180-110 degrees
By taking away 110 degrees from each side, we arrive at:
C = 70-degree slope.
As a result, curve C has a measure of 70 degrees.
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Consider the perceptron in two dimensions: h(x) sign(vyTx) where w-[w0, w1, w2" and x = [1M, 2]". Technically, x has three coordinates, but we call this perceptron two-dimensional because the first coordinate is fixed at 1. (a) Show that the regions on the plane where h(x) = +1 and h(x) =-1 are separated by a line. If we express this line by the equation x2 = azi +b, what are the slope a and intercept b in terms of wo, wi, w2?
we get a = -w1/w2b = -w0/w2
Therefore, the slope a is -w1/w2 and the intercept b is -w0/w2.
What are the slope a and intercept b in terms of wo, wi, w2?In this case, the relevant terms are "perceptron," "dimensions," and "equation."
A perceptron is a single layer neural network that processes information through a linear filter. It can be used for classification tasks and is especially useful in binary classification. The perceptron in two dimensions is given by the equation:
h(x) = sign(vyTx)where w = [w0, w1, w2] and x = [1, M, 2].
Technically, x has three coordinates, but we call this perceptron two-dimensional because the first coordinate is fixed at 1.We need to show that the regions on the plane where
h(x) = +1 and h(x) = -1 are separated by a line. To do this, we can set h(x) = 0 and solve for x. We get:
v(w0 + w1M + w22) = 0x2 = (-w0/w2) - (w1/w2)M
This is the equation of a line. The regions where h(x) = +1 and h(x) = -1 are separated by this line. We can express this line by the equation x2 = az + b,
where a and b are the slope and intercept of the line, respectively. To find a and b in terms of w0, w1, and w2, we substitute the equation of the line we found earlier into the equation for x2:(-w0/w2) - (w1/w2)M = az + bb = (-w0/w2)
Simplifying, we get:a = -w1/w2b = -w0/w2
Therefore, the slope a is -w1/w2 and the intercept b is -w0/w2.
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when analyzing survey results from a two-way table, the main distinction between a test for independence and a test for homogeneity is the number of columns in the two-way table. the number of rows in the two-way table. how the expected counts are calculated. the number of samples obtained. how the degrees of freedom are calculated.
Expected counts are calculated by the test of independence and also by using Homogeneity.
The main difference between a test of independence and a test of uniformity when analyzing voting results from a two-page table is how the expected count is calculated.
The test of independence calculates expected frequencies assuming no relationship between the two variables analyzed and is based on the marginal totals of the two-way table.
Independence tests are used to know whether there is a significant association between two variables or not.
Homogeneity tests, on the other hand, compute expected frequencies assuming that the two groups being compared have the same distribution for the variable being analyzed, based on the row sums of a two-way table.
Homogeneity tests are used to know whether there is a difference in the distribution of a categorical variable between groups.
The number of columns and rows in the two-way table and the number of samples obtained are important factors to consider when performing both tests.
However, how the expected count is calculated is the main difference between the two tests. The degrees of freedom are also calculated differently for the two tests, but this is secondary.
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Aloysius finds that the price of his favourite pecan pie has gone up 225% in one year if the pie now costs $26 what did it cost one year ago 
If the price of Aloysius' favorite pecan pie has gone up 225% in one year and the pie now costs $26, the cost one year ago was $11.55.
How is the cost determined?The old price of the pie can be determined by proportions.
Proportion refers to the equation of two ratios.
The current price of the pecan pie (in percentage terms) = 225%
The current price or cost of the pie = $26
Proportionately, 225% = $26, and the old price a year ago = 100%.
The old price a year ago of the pie = $11.55 ($26 × 100 ÷ 225)
Thus, if Aloysius bought his favorite pecan pie last year, the cost would have been $11.55.
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Using the substitution method, find the solution to this system of equations. Be sure to show your work!
-2x+2y=7
-x+y=4\
PLEASE HELP MEEEE
The two equations represent two lines in the plane that are parallel and never intersect, so there is no point that satisfies both equations simultaneously. No solution equations.
Describe Equation?In mathematics, an equation is a statement that two expressions are equal. It consists of two sides separated by an equal sign (=). The expression on the left side of the equal sign is usually called the left-hand side (LHS), while the expression on the right side is called the right-hand side (RHS).
Equations can take many different forms and can involve various types of functions and operators, such as addition, subtraction, multiplication, division, exponentiation, logarithms, trigonometric functions, and more. They can also involve one or more variables, which can be solved for to obtain a specific value or range of values that make the equation true. Equations are used extensively in mathematics, science, engineering, economics, and many other fields.
We can solve this system of equations using the substitution method by solving one of the equations for one variable in terms of the other, and then substituting that expression into the other equation.
Let's solve the second equation for y in terms of x:
-x + y = 4
y = x + 4
Now we substitute this expression for y into the first equation and solve for x:
-2x + 2y = 7
-2x + 2(x + 4) = 7
-2x + 2x + 8 = 7
8 = 7
This last equation is a contradiction, which means that there is no solution to the system of equations. Geometrically, the two equations represent two lines in the plane that are parallel and never intersect, so there is no point that satisfies both equations simultaneously.
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solve [tex]\sqrt{8x=6}[/tex]
[tex] \: \: [/tex]
I believe the equation you meant to write is:
√(8x) = 6
To solve for x, we need to isolate x on one side of the equation. We can do this by squaring both sides:
(√(8x))^2 = 6^2
Simplifying the left side, we get:
8x = 36
Dividing both sides by 8, we get:
x = 4.5
Therefore, the solution to the equation √(8x) = 6 is x = 4.5.
if f(x) = 2x^3+x^2+3 then what is the remainder when f(x) is divided by x-1
The remainder when f(x) is divided by x-1 can be calculated using the division theorem.
The remainder when f(x) is divided by x-1 is 6.
remainder is 6 and divisor is x-1.
What is the division theorem?According to the division theorem, when a polynomial function is divided by another polynomial function, the remainder is equal to the function evaluated at the point where the divisor of the division equation is equal to zero.
In this case, the divisor is x-1, and when x-1 is equal to zero, then x = 1.
Therefore, the remainder when f(x) is divided by x-1 can be calculated by evaluating the function f(x) at x = 1:
[tex]f(1) = 2(1)^3 + (1)^2 + 3[/tex]
= 2 + 1 + 3
= 6
f(1) = 2(1)³ + (1)² + 3 = 6
Therefore, the remainder when f(x) is divided by x-1 is 6.
remainder is 6 and divisor is x-1.
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The tower of terror ride in disney world, florida is 199 feet tall. If josh is standing 125 feet from the base of the ride, what is the angle of elevation from the point where Josh is standing to the top of the tower?
The angle of elevation from the point where Josh is standing to the top of the tower is approximately 58.7 degrees.
How to calculate angle of elevation?
We can use trigonometry to calculate the angle of elevation:
tan(angle) = opposite/adjacent
In this case, the opposite is the height of the tower (199 feet) and the adjacent is the distance from Josh to the base of the tower (125 feet). So:
tan(angle) = 199/125
We can solve for the angle by taking the inverse tangent (tan^-1) of both sides:
angle = tan^-1(199/125)
Using a calculator, we find that:
angle ≈ 58.7 degrees
Therefore, the angle of elevation from the point where Josh is standing to the top of the tower is approximately 58.7 degrees.
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Which two expressions are equivalent to 7(t + 5)?
Two expressions that are equivalent to 7(t + 5) are: 7t + 35 and 7t + (5 * 7)
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
When we have an expression of the form a(b + c), we can simplify it using the distributive property of multiplication over addition. This property allows us to distribute the multiplication of a across the terms of the sum (b + c), and then add the resulting products.
In the case of 7(t + 5), we can use the distributive property to distribute the multiplication of 7 across t and 5, resulting in the expression 7t + 7(5). We can then simplify 7(5) to 35, giving us the equivalent expression 7t + 35.
Alternatively, we can simplify 7(t + 5) by first multiplying 7 and 5 to get 35, and then adding it to 7t, resulting in the expression 7t + 35.
Therefore, two expressions that are equivalent to 7(t + 5) are:
7t + 35
7t + (5 * 7)
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Answer question 4 and 8 plss thank u
2. The farthest distance that a student rode during Friday's ride is 35 miles.
3. The longest time that a student rode during Friday's ride is 120 minutes.
6. 15 minutes.
7. 4 miles.
What is cluster?A cluster in a scatter plot is a group of points that are close to each other. Clusters helps to visualize the spread of data.
2. The farthest distance that a student rode during Friday's ride is 35 miles.
3. The longest time that a student rode during Friday's ride is 120 minutes.
4. The first cluster consists of points with lower values for t and higher values for s. This cluster is composed of riders who trained on mountain roads, as the lower values for t indicate that it took longer for them to cover the same distance as the other group.
The second cluster consists of points with higher values for t and lower values for s. This cluster is composed of riders who trained on flat roads, as the higher values for t indicate that it took them less time to cover the same distance as the other group.
6. The shortest time that a family member rode during Friday's ride was 15 minutes.
7. The longest distance that a family member rode during Friday's ride was 4 miles.
8. The data on the scatter plot is broken into two clusters because there are two distinct groups of data points.
The first cluster consists of points (15,2), (20,2), and (25,2), which indicate that a family member rode for 15, 20, and 25 minutes, respectively, and traveled a distance of 2 miles each time.
The second cluster consists of points (40,4), (50,4), and (60,4), which indicate that a family member rode for 40, 50, and 60 minutes, respectively, and traveled a distance of 4 miles each time.
This could be explained by the fact that a family member rode for a longer period of time and traveled a longer distance on Friday than the other family members.
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Find x please and show work I don’t know how to solve problems like these have a blessed day
Answer:
Step-by-step explanation:
These questions all use Pythagorean Theorem to solve for x.
The hypotenuse is the side across from the right angle.
It is always c in the equation.
10) a² + b² = c²
x² + 9² = 15²
x² + 81 = 225
x² + 81 - 81 = 225 - 81
x² = 144
√x² = √144
x = 12
11. a² + b² = c²
x² + 2² = 5²
x² + 4 = 25
x² + 4 - 4 = 25 - 4
x² = 21
√x² = √21
x = 4.58
13. a² + b² = c²
(1/5)² + (3/5)² = c²
1/25 + 9/25 = c²
10/25 = c²
√10/25 = √c²
√10/√25 = √c²
√10/5 = c
14. a² + b² = c²
a² + (4/9)² = (8/9)²
a² + 16/81 = 64/81
a² + 16/81 - 16/81 = 64/81 -16/81
a² = 48/81
√a² = √48/81
a = √48/√81
a = 4√3/9
please guys it's dew tomorrow
Step-by-step explanation:
3 is the Gulf of Mexico
1 is the Caribbean Sea
Answer:
The answer is C.
Step-by-step explanation:
The Gulf of Mexico is located in between America and Cuba.
pls help me find the answer
The correct inequality that can be used to determine g, the maximum number of gigabytes Rahul can use while staying within his budget is:
95 > 4g + 36
What is an inequality?
Rahul pays a flat cost of $36 per month and $4 per gigabyte. So, his monthly bill can be expressed as:
Bill = 4g + 36
where g is the number of gigabytes used in the month.
We want to find the maximum number of gigabytes Rahul can use while staying within his budget of $95 per month. This means we need to find the value of g that satisfies the inequality:
Bill ≤ 95
Substituting the expression for Bill, we get:
4g + 36 ≤ 95
Subtracting 36 from both sides, we get:
4g ≤ 59
Dividing both sides by 4, we get:
g ≤ 14.75
Since the number of gigabytes used cannot be a fraction, we can conclude that the maximum number of gigabytes Rahul can use while staying within his budget is 14. Therefore, the correct inequality is:
95 > 4g + 36
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Trapezoid QRST is dilated by a scale factor of 3.4 to create trapezoid Q'R'S'T'. The area of trapezoid QRST is y square units.
What is the area in square units of trapezoid Q'R'S'T'?
Responses
A 2(3.4 + y) square units2(3.4 + y ) square units
B 3.4y square units3.4 y square units
C (3.4y)2 square units(3.4 y ) 2 square units
D (3.4)2y square units
Using dilation, we can find the area of the new trapezoid to be 3.4y unit². So, the correct option is Option B.
Define scale factor?The dimensions of the new shape are scale factor. It can be calculated using the original shape's dimension as the fundamental formula. The formula is scale factor = larger figure dimensions. Reduced figure dimensions if the original figure is expanded.
Area of the trapezoid QRST is = y unit².
Scale factor by which QRST is dilated = 3.4
Now area of new trapezoid Q'R'S'T'
= old area × scale factor.
= y × 3.4
= 3.4y unit²
Therefore, area of the new trapezoid will be = 3.4y unit².
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Lauren wants to buy a printer for $75 dollars. Her weekly allowance is $20. If she saves $15 each week toward the cost of the printer, how many weeks will it take Lauren to save enough to buy it?
Answer: it would take 5 weeks
Students' scores on the YAST test (Yet Another Standardized Test) are approximately normally distributed with mean 319 and standard deviation 94.
a. Bill's score on the YAST was 432. Approximately what percent of the scores were lower than Bill's?
%
b. How high must a score be to be in the top 11%?
The score must be at least
c. In any distribution 1/4 of the values lie below the first quartile Q1 and 3/4 of the values lie below the third quartile. What are the first and third quartiles of the YAST scores?
Q1 = . Q3=
d. Reports on students' scores often give a percentile rank. A student's percentile tells what percent of all the test scores lie below the student's score. For example if 43% of all the test scores lie below your score then your percentile is 43.
i. Jane's score on the YAST is 464. What is Jane's percentile?
ii. Ann will receive a scholarship if her score is at the 66rd percentile or above. What score must Ann receive on the YAST test to get the scholarship?
Approximately 88.5% of the scores were lower than Bill's. The score must be at least 432.6 to be in top 11%. Q1 ≈ 251.3, Q3 ≈ 386.7.Jane's percentile is approximately 93.3%. Ann will receive a score of 357.4.
What does invNorm mean?The invNorm is a mathematical function that calculates the inverse of the cumulative normal distribution. It is used to find the value of a standard normal variable for a given probability. The standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one. The function takes a probability value as an input and returns the corresponding z-score, which represents the number of standard deviations from the mean. The invNorm function is commonly used in statistics and probability theory to find critical values for hypothesis testing, confidence intervals, and other statistical calculations.
a. To find the percentage of scores lower than Bill's score of x = 432, we need to find the area under the normal curve to the left of 432. Using the mean of m = 319 and the standard deviation of s = 94, we can standardize Bill's score as follows:
z = [tex]\frac{(x - m)}{s}[/tex] = [tex]\frac{(432 - 319)}{94}[/tex] = 1.2
Using a standard normal distribution table, we can find that the area to the left of z = 1.2 is approximately 88.5%. Therefore, approximately 88.5% of the scores were lower than Bill's.
b. To find the score that corresponds to the top 11%, we need to find the z-score that has an area of 0.11 to its right. Using a standard normal distribution table or calculator, we can find that the z-score that corresponds to an area of 0.11 to the right is approximately 1.22. Therefore, we can solve for the score as follows:
z = [tex]\frac{(x - m)}{s}[/tex]
1.22 = (x - 319) / 94
x - 319 = 1.22 × 94
x = 319 + 1.22 × 94
x ≈ 432.6
Therefore, a score of at least 432.6 is required to be in the top 11%.
c. We know that the first quartile (Q1) corresponds to the 25th percentile, and the third quartile (Q3) corresponds to the 75th percentile. Using the mean of 319 and the standard deviation of 94, we can find the z-scores that correspond to these percentiles using a standard normal distribution table or calculator.
For Q1:
z = invNorm(0.25) ≈ -0.6745
x = m + zs = 319 + (-0.6745) × 94 ≈ 251.3
Q1 ≈ 251.3
For Q3:
z = invNorm(0.75) ≈ 0.6745
x = m + zs = 319 + (0.6745) × 94 ≈ 386.7
Q3 ≈ 386.7
Therefore, Q1 ≈ 251.3 and Q3 ≈ 386.7.
d. (i) To find Jane's percentile, we need to find the area under the normal curve to the left of her score of 464. Using the mean of 319 and the standard deviation of 94, we can standardize Jane's score as follows:
z = [tex]\frac{(x - m)}{s}[/tex] = (464 - 319) / 94 ≈ 1.55
Using a standard normal distribution table, we can find that the area to the left of z = 1.55 is approximately 93.3%. Therefore, Jane's percentile is approximately 93.3%.
(ii) To find the score that corresponds to the 66th percentile, we need to find the z-score that has an area of 0.66 to its left. Using a standard normal distribution table, we can find that the z-score that corresponds to an area of 0.66 to the left is approximately 0.44. Therefore, we can solve for the score as follows:
z = [tex]\frac{(x - m)}{s}[/tex]
0.44 = (x - 319) / 94
x - 319 = 0.44 * 94
x = 319 + 0.44 * 94
x ≈ 357.4
Therefore, Ann will receive a score of approximately 357.4.
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