Answer:
Step-by-step explanation:
This is a binomial problem where the basketball player has a probability of success of 0.725 (making a free throw) and is attempting 60 shots. The number of successful shots is a binomial random variable X ~ Bin(60, 0.725). We need to find the probability that she makes at least 15 of her next 60 shots, which is P(X ≥ 15). This can be computed using the binomial cumulative distribution function (CDF) as follows:
P(X ≥ 15) = 1 - P(X < 15) = 1 - binom.cdf(14, 60, 0.725) ≈ 0.998
Therefore, the probability that she makes at least 15 of her next 60 shots is approximately 0.998.
This is also a binomial problem where the probability of success is 0.14 (a smartphone requiring servicing) and the number of trials is 100 (smartphones in a shipment). We need to find the probability that no more than 10 smartphones in the shipment will require servicing, which is P(X ≤ 10). This can be computed using the binomial CDF as follows:
P(X ≤ 10) = binom.cdf(10, 100, 0.14) ≈ 0.289
Therefore, the probability that no more than 10 smartphones in the shipment will require servicing is approximately 0.289.
This is also a binomial problem where the probability of success is 0.06 (a scratch-off lottery ticket having a prize of a free ticket) and the number of trials is 200 (tickets at the local convenience store). We need to find the probability that this prize is on 15 or more of the tickets, which is P(X ≥ 15). This can be computed using the binomial CDF as follows:
P(X ≥ 15) = 1 - P(X < 15) = 1 - binom.cdf(14, 200, 0.06) ≈ 0.021
Therefore, the probability that the prize is on 15 or more of the 200 tickets at the local convenience store is approximately 0.021.
Shirley says that the product (x - 15) (x + 15) is not a difference of two squares because the product is not in the form (a + b) (a - b). Explain to Shirley why she is incorrect
Shirley is incorrect because regardless of how the expressions are grouped they would produce the same output or result.
What is a difference of two (2) squares?In Mathematics and Geometry, the standard form for a difference of two (2) squares is modeled or represented by this mathematical equation:
a² - b² = (a + b)(a - b) or a² - b² = (a - b)(a + b).
Where:
a and b represent numerical values (numbers or numerals).
Based on the information provided, we have the following mathematical equation:
(x - 15)(x + 15) = x² + 15x - 15x - 225
(x - 15)(x + 15) = x² - 225
By rewriting the product, we have the following;
(x + 15)(x - 15) = x² - 15x + 15x - 225
(x + 15)(x - 15) = x² - 225
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Please help me with the question
Your store sales average $150,000 per month. Your triple net lease has the following
monthly terms: rent is 4% of sales, insurance is $200, maintenance is $125, utilities total
$375, and taxes are $90. You expect next year's sales to increase 6%, but your lease terms
will remain the same. Calculate next year's annual lease payment.
Next year's annual lease payment is $85,800 we get it by multiplying monthly lease payment by 12
To calculate next year's annual lease payment, we need to first calculate next year's monthly sales.
Since sales are expected to increase by 6%, next year's monthly sales will be:
$150,000 + (6% x $150,000) = $159,000
Now calculate the monthly lease payment by adding up all the monthly lease expenses:
Rent: 4% x $159,000 = $6,360
Insurance: $200
Maintenance: $125
Utilities: $375
Taxes: $90
Total monthly lease payment = $6,360 + $200 + $125 + $375 + $90
= $7,150
Finally, we can calculate next year's annual lease payment by multiplying the monthly lease payment by 12:
Annual lease payment = $7,150 x 12
= $85,800
Therefore, next year's annual lease payment is $85,800.
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The Ferris Wheel at the amusement park is 74 feet from the bottom of the wheel to the top. What is the distance around the ride?
Answer:
C = 74π feet = about 232.48 feet
A baking company has developed two new cookie recipes, however, they only have the resources to add one item to their product line. They decide to randomly sample three groups of 100 people to determine which cookie recipe, A or B, is preferred. The results are shown in the following table.
Recipe A Recipe B
Sample #1 29 71
Sample #2 38 62
Sample #3 24 76
A. Based on the collected data, which recipe should the baking company add to their product line? How confident should the company be in their decision? Explain your reasoning using complete sentences.
B. Using the mean of the data for Recipe A, approximately what percentage of people would you expect to prefer Recipe A over Recipe B?
A)
There is a significant difference between the two recipes.
B)
We would expect approximately 30% of people to prefer recipe A over recipe B.
We have,
A.
To determine which recipe the baking company should add to its product line, we can perform a hypothesis test.
The null hypothesis would be that there is no difference between the two recipes (i.e., the proportion of people who prefer recipe A is the same as the proportion who prefer recipe B), and the alternative hypothesis would be that there is a difference between the two recipes.
We can use a two-sample proportion test to test the hypothesis.
Using the given data, the proportion of people who preferred recipe A in sample 1 is 0.29, in sample 2 is 0.38, and in sample 3 is 0.24.
The overall proportion of people who preferred recipe A is the average of these proportions, which is (0.29 + 0.38 + 0.24)/3 = 0.30.
Similarly, the overall proportion of people who preferred recipe B is 1 - 0.30 = 0.70.
To perform the hypothesis test, we calculate the test statistic z as:
[tex](P_1 - P_2)/\sqrt{\hat{P}(1/n_1 + 1/n_2)[/tex]
where p1 and p2 are the proportions of people who preferred recipe A in the two groups being compared, n1 and n2 are the sample sizes, and [tex]\hat{P}[/tex] is the overall proportion of people who preferred recipe A.
The calculated z-value is -4.07, which corresponds to a p-value of less than 0.0001.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is a significant difference between the two recipes.
Based on the results of the hypothesis test, the baking company should add recipe B to their product line, as it was preferred by a higher proportion of people overall.
However, the company should be somewhat cautious in its decision, as there is a small chance (less than 0.05) that the difference in preference between the two recipes could have occurred by chance alone.
B.
The mean of the data for recipe A is the average proportion of people who preferred recipe A across the three samples, which we calculated to be 0.30.
This means that we would expect approximately 30% of people to prefer recipe A over recipe B.
Thus,
There is a significant difference between the two recipes.
We would expect approximately 30% of people to prefer recipe A over recipe B.
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The solution is : 200 people were in the sample.
We have,
given data:
In a sample 76 people or 38% voted the mayor to be prosecuted.
solution:
how many people were in that sample
if 38% = 76 people
therefore;
let
p = total number of people
76/p = 38/100
cross multiply both sides
38p = 7600
divide both sides by 38
38p /38 = 7600 /38
p = 200
the number of people in the sample original was 200.
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complete question:
In a sample, 76 people or 38% of the people in the sample said that the mayor should be prosecuted for misconduct. How many people were in the sample
The vertices of a triangle are A (6, 0), B(-6, -3), and
C(0,6). Draw the image after a dilation with a scale factor of
1/3
The image of the triangle after the dilation are A' (2, 0), B' (-2, -1), and C' (0, 2)
Drawing the image of the triangle after the dilationFrom the question, we have the following parameters that can be used in our computation:
The vertices of a triangle are A (6, 0), B(-6, -3), and C(0,6).
This means that
A (6, 0), B(-6, -3), and C(0,6).
The scale factor is given as 1/3
So, we have
Image = 1/3 * Point
Substitute the known values in the above equation, so, we have the following representation
Image = 1/3 * A (6, 0), B(-6, -3), and C(0,6).
This gives
A' (2, 0), B' (-2, -1), and C' (0, 2)
Hence, the image are A' (2, 0), B' (-2, -1), and C' (0, 2)
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How do you write the standard number 1,649,000 in scientific notation?
A.
1.649 × 106
B.
16.49 × 106
C.
1.649 × 107
D.
16.49 × 105
Scientific notation is a way of writing very large or very small numbers using powers of 10. In scientific notation, a number is expressed as the product of a coefficient and a power of 10.
1,649,000 in scientific notation is written as
1,649,000 = 1.649 x [tex]10^{6}[/tex]
Hence, the correct option is A.
To write the standard number 1,649,000 in scientific notation, we first need to move the decimal point so that there is only one non-zero digit to the left of the decimal point.
In this case, we can move the decimal point six places to the left to get 1.649. Next, we need to express the remaining digits as a power of 10, Since we moved the decimal point six places to the left, we can express this as [tex]10^{6}[/tex].
Putting this together, we get
1,649,000 = 1.649 x [tex]10^{6}[/tex]
Hence, the correct option is A.
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On a piece of paper, graph f(x) = { 2 ifz > ²
x < 2
.
2
answer choice matches the graph you drew.
O A.
-5
52
y
-53
Click here for long description
Then determine which
A graph that matches the answer choice is shown in the image attached below.
What is a piecewise-defined function?In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is constant over the interval x ≥ 2 and increasing over the interval x < 2.
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solve for x and show your work!
*Round to nearest tenth.
Answer : So the value of x is 5
Step-by-step explanation:
As we know it is a right angled triangle which means that the angle from the origin(0,0) is 90 degree, so the angle right to it has a value of 37 degree and the angle above it has a value of 53 degree, and the value of sin37 degree is 3/5, So by applying Pythagoras theorem we get to know that the value of sin is actually Perpendicular by Hypotenuse, so we get to know that the value of x is actually 5 derived from it.
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A student mows lawns on the weekends. It takes him 110 minutes to mow 2 lawns. What prediction can you make about the time he will spend this weekend if he has 12 lawns to mow?
It will take him 10 hours to mow 12 lawns.
It will take him 11 hours to mow 12 lawns.
It will take him 17 hours to mow 12 lawns.
It will take him 48 hours to mow 12 lawns.
The prediction for the weekend is it will take him 11 hours to mow 12 lawns
Given data ,
A student mows lawns on the weekends
It takes him 110 minutes to mow 2 lawns
Now , the time taken for mowing 12 lawns is given by the proportion ,
where 110 / 2 = A / 12
Multiply by 12 on both sides , we get
A = 6 x 110
On further simplification, we get:
A = 660 minutes
On converting 660 minutes to hours
1 hour = 60 minutes
So , 660 minutes = 11 hours
A = 11 hours
Hence , the time taken is 11 hours
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If a nonlinear system of equations contains one linear function that touches the quadratic function at its minimum, then the system has:_________
If a nonlinear system of equations contains one linear function that touches the quadratic function at its minimum, then the system has exactly one solution.
This is because the linear function intersects the quadratic function at its minimum point, where there is only one value of x that satisfies both equations.
If a nonlinear system of equations contains one linear function that touches the quadratic function at its minimum, then the system has one unique solution.
Here's a step-by-step explanation:
1. A nonlinear system is a set of equations where at least one of the equations is not linear.
2. In this case, the nonlinear system contains one linear function and one quadratic function.
3. The quadratic function has a minimum point, which is the lowest point of its parabolic graph.
4. The linear function touches the quadratic function at its minimum, which means they intersect at exactly that point.
5. Since the two functions intersect at one point, the system has one unique solution, which corresponds to the coordinates of that intersection point.
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the areas of two similar quadrilaterals are 36 m^2 and 64 m^2. what is the scale factor and perimeter ratio?
The ratio of the perimeters is 4/3.
If two quadrilaterals are similar, then their corresponding sides are proportional, meaning that there is a constant ratio between the lengths of corresponding sides. The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.
Let's call the scale factor between the two similar quadrilaterals "k". Then, we can write:
k^2 = 64 m^2 / 36 m^2
Simplifying the right side of the equation, we get:
k^2 = (8/6)^2
k^2 = (4/3)^2
Taking the square root of both sides, we get:
k = 4/3
Therefore, the scale factor between the two similar quadrilaterals is 4/3.
To find the ratio of their perimeters, we can use the same scale factor. Since the sides of the two quadrilaterals are proportional, we can multiply each side of the smaller quadrilateral by the scale factor to get the corresponding side of the larger quadrilateral.
Let's call the perimeter of the smaller quadrilateral "P1" and the perimeter of the larger quadrilateral "P2". Then, we can write:
P2 = k * P1
Substituting the scale factor k = 4/3, we get:
P2 = (4/3) * P1
Therefore, the ratio of the perimeters is:
P2/P1 = (4/3) * P1 / P1
P2/P1 = 4/3
So, the ratio of the perimeters is 4/3.
The scale factor is approximately 1.333. Since the quadrilaterals are similar, their perimeters are proportional to their corresponding sides. Therefore, the perimeter ratio is the same as the scale factor, which is approximately 1.333.
To find the scale factor, we need to take the square root of the ratio of the areas:
sqrt(64/36) = 4/3
So the scale factor is 4/3. This means that corresponding sides of the two quadrilaterals are in a ratio of 4:3.
To find the perimeter ratio, we can use the same ratio:
Perimeter of larger quadrilateral: 4x + 4y
Perimeter of smaller quadrilateral: 3x + 3y
We know that the areas are in a ratio of 64/36 = 4/3, so we can set up the following equation:
3x * 4y = 4x * 3y
Simplifying this gives:
12xy = 12xy
So the perimeters are equal! This means that the perimeter ratio is 1:1.
The areas of the two similar quadrilaterals are 36 m^2 and 64 m^2. To find the scale factor, you need to take the square root of the ratio of the areas:
Scale factor = √(Area2 / Area1) = √(64 m^2 / 36 m^2) = √(1.7777) ≈ 1.333
The scale factor is approximately 1.333. Since the quadrilaterals are similar, their perimeters are proportional to their corresponding sides. Therefore, the perimeter ratio is the same as the scale factor, which is approximately 1.333.
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If f(x)=6x^2-4 what is f(-1)
The function value of f(-1) from f(x) = 6x^2 - 4 is 2
Evaluating the function valueFrom the question, we have the following parameters that can be used in our computation:
f(x) = 6x^2 - 4
In f(-1), we have
x = -1
Substitute the known values in the above equation, so, we have the following representation
f(-1) = 6(-1)^2 - 4
Evaluate
f(-1) = 2
Hence, the solution is \f(-1) = 2
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a theater has n rows of seats, and each row has d more seats than the row in front of it. there are x seats in the last (nth) row and a total of y seats in the entire theater. how many seats are in the front row of the theater? write your answer in terms of n, x, and y.
The number of seats in the front row of the theater is a = [2y/(n(n-1)) - x/(n-1)]/2
Let's call the number of seats in the first row "a". We can use the information given in the problem to set up an equation in terms of "n", "d", "x", and "y"
y = a + (a + d) + (a + 2d) + ... + (a + (n-1)d) (1)
We can simplify this equation by using the formula for the sum of an arithmetic series
y = [n/2][2a + (n-1)d] (2)
We can solve this equation for "a" in terms of "n", "d", and "x"
2a = (2y/n) - (n-1)d - 2xd
a = [(2y/n) - (n-1)d - 2xd]/2
Since we know that the number of seats in the last row is "x", we can substitute that into the equation
x = a + (n-1)d
x = [(2y/n) - (n-1)d - 2xd]/2 + (n-1)d
Simplifying this equation gives us
2x = (2y/n) + (n-1)d
2d = (2x - (2y/n))/(n-1)
Now we can substitute this value of "d" into the equation we found for "a"
a = [(2y/n) - (n-1)d - 2xd]/2
a = [(2y/n) - x - (2x - (2y/n))/(n-1)]/2
a = [2y/(n(n-1)) - x/(n-1)]/2
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10. If the coefficient of x*4 is equal to that of x*6 in (1+x² + ax³)*4 what is the value of a
Answer: We can expand the given expression using the binomial theorem:
(1 + x² + ax³)^4 =
C(4,0) + C(4,1)x² + C(4,2)(ax³)^2 + C(4,3)x^6 + C(4,4)(ax³)^4
where C(n,k) denotes the binomial coefficient "n choose k", which is equal to n! / (k!(n-k)!).
The coefficient of x^4 is the coefficient of the second term, which is C(4,1) = 4. The coefficient of x^6 is the coefficient of the fourth term, which is C(4,3) = 4.
Since the coefficient of x^4 is equal to that of x^6, we have:
4 = C(4,1) = 4a C(4,3) = 4a
Solving for a, we get:
a = 1/4
Therefore, the value of a is 1/4.
Step-by-step explanation:
to allow the compost to be mixed, the manufacturer recommends that it not be filled more than 23 full. what is the maximum recommended amount of compost that can be added to the bin, to the nearest cubic inch?a.2,771 in3b.27,143 in3c.10,179 in3d.6,786 in3
For a garden composite bin is cylindrical shape with height 40 inch and diameter 18 inch, the maximum recommended amount of composite added to bin is 6786 in³. So, option(d) is right one.
We have a garden compost bin on store. The shape of bin is cylindrical with the
Height of cylinder = 40 inch
diameter of cylinder = 18 inch
radius of cylinder= d/2 = 9 inch
We have to determine the maximum amount of compost added to bin. Manufacturer recommends that it not be filled more than 2/3. That is Volume of composit < 2/3 of volume of bin --(1)
As we know, Volume of cylinder is written as V = πr² h
where, h--> height of cylinder
r--> radius of cylinder
here, h = 40 inch, r = 9 inch
So, volume V = π× 9² × 40 in³= 10173.6 in³.
Now, from equation (1), the maximum amount of compost that can be added to the bin = [tex]10,173.6× \frac{2}{3}[/tex]
= 6785.50~ 6786 in³
Hence, required value is 6786 in³.
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Complete question:
A garden compost bin on sale at the hardware store is shaped like a cylinder with a 40 inch height and 18 inch diameter. To allow the compost to be mixed, the manufacturer recommends that it not be filled more than 2/3 full. What is the maximum recommended amount of compost that can be added to the bin, to the nearest ? Use for and round to the nearest
a) 2771 in³
b) 2374 in3
c) 10719 in³
d) 6786 in³
A second story window is 20feet about the ground and the ladder is at a 70° angle. How long must the ladder be?
The ladder must be 21.26 feet long.
We can use trigonometry to solve this problem. Let's call the length of the ladder "L". We can use the sine function, which relates the opposite side of a right triangle to its hypotenuse, to find the length of the ladder:
sin(70°) = opposite / hypotenuse
sin(70°) = 20 / L
To solve for L, we can rearrange the equation:
L = 20 / sin(70°)
Using a calculator, we can find that sin(70°) is approximately 0.9397. Plugging this value into the equation, we get:
L = 20 / 0.9397
L = 21.26 feet (rounded to two decimal places)
Therefore, the ladder must be about 21.26 feet long to reach the second story window that is 20 feet above the ground at a 70° angle.
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What are the zeroes of the function g\left(x\right)=x^{2}+8x+16g(x)=x 2 +8x+16 written as a coordinate point?
g\left(x\right)=x^{2}+8x+16g(x)=x 2 +8x+16 is g(x) = x^2 + 8x + 16
The zeroes of function [tex]g(x) = x^2 + 8x + 16[/tex] or [tex]g(x) = (x+4)^2[/tex] is at x = -4.
We need to solve for x when g(x) equals zero in order to find the zeros of the function [tex]g(x) = x^2 + 8x + 16[/tex]. In simple words, we have to find the value of x that make the equation [tex]x^2 + 8x + 16 = 0[/tex] true.
By using the identity, [tex]a^{2} + 2ab + b^{2}= (a+b)^{2}[/tex]
[tex]x^2 + 8x + 16 = 0[/tex] can be easily factored as:
[tex](x + 4)^2[/tex] [tex]=0[/tex]
Using the zero-product property, each factor is equal to zero: x + 4 = 0. Solving for x, we get x = -4.
Therefore, there is only one zero of the function [tex]g(x) = x^2 + 8x + 16[/tex] is x = -4. This indicates that the function's parabola intersects the x-axis at x = -4.
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I need help with this problem
Answer: 5024
Step-by-step explanation:
multiply 3.14 and 1600
A random sample of 100 customers at a local ice cream shop were asked what their favorite topping was. The following data was collected from the customers.
Topping Sprinkles Nuts Hot Fudge Chocolate Chips
Number of Customers 17 12 27 44
Which of the following graphs correctly displays the data?
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27 ,and the fourth bar labeled chocolate chips going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
A graph that correctly displays the data include the following: C. a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27 ,and the fourth bar labeled chocolate chips going to a value of 44.
What is a histogram?In Mathematics and Geometry, a histogram can be defined as a type of chart that is used to graphically represent a group of data points (statistical information) into user-specified ranges through the use of rectangles or rectangular bars.
Based on the information provided about the random sample of 100 customers at a local ice cream shop that were asked what their favorite topping, we can reasonably infer and logically deduce that a graph that correctly displays the data is a histogram.
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A group of physical education majors was discussing the heights of female runners and whether female runners tended to be tall, on the average. They decided to estimate the mean height of female runners. A sample of 12 runners showed a sample mean height of 65.80 inches and a sample standard deviation of 1.95 inches. Assume the population is approximately normal. Construct a 90% confidence interval for the mean of the population of female runners from which the 12 runners were selected.a. What is the left boundary of the confidence interval? Round answer to two decimal places.b. Regarding the sample in question 8, what is the right boundary of the 90% confidence interval? Round answer to two decimal places.
Therefore, we can say with 90% confidence that the true population mean height of female runners is between 64.874 inches and 66.726 inches.
To construct a 90% confidence interval for the mean height of female runners, we can use the formula:
CI = x ± z*(σ/√n)
where x is the sample mean (65.80 inches), σ is the population standard deviation (unknown), n is the sample size (12), and z is the z-score corresponding to the desired level of confidence (90%).
Using a z-table or calculator, we find that the z-score for a 90% confidence interval is 1.645.
We are given the sample standard deviation (s = 1.95 inches), but we need to estimate the population standard deviation using the formula:
s/√n = σ/√n
1.95/√12 ≈ 0.562
So, our 90% confidence interval is:
CI = 65.80 ± 1.645*(0.562)
a. The left boundary of the confidence interval is:
65.80 - 0.926 = 64.874 (rounded to two decimal places)
b. The right boundary of the confidence interval is:
65.80 + 0.926 = 66.726 (rounded to two decimal places)
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true or false: when comparing normal distribution curves, the distribution with the largest standard will have the highest peak.
False. The peak of a normal distribution curve is determined by its mean, not its standard deviation.
The standard deviation measures the spread or variability of the distribution, with larger values indicating a wider distribution. However, the peak of the curve remains the same as long as the mean remains constant.
Therefore, when comparing normal distribution curves, the one with the highest mean will have the highest peak, regardless of the standard deviation. Additionally, it's important to remember that in a normal distribution, the peak occurs at the mean value and the curve is symmetric.
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Please help, I will give you brainliest.
Answer:
Roots: 1/2 , -3/2
Vertex: (-1/2, -4)
AOS: x = - 1/2
Min/Max: (-1/2, -4)
Step-by-step explanation:
x y
-2 7
-1.5 1
-1 -1
-0.5 -3.5
0 -3
0.5 -1
1 1
Gilles and aleena are arranging an academic and sports award banquet they know how many guest are going to be seated in different tables arrangement
The number of guests that can sit in each arrangement, given the diagram would be:
1 table - 6 guests2 tables - 10 guests3 tables - 14 guestsHow to find the number of guests ?To find the number of guests that are able to sit in each arrangement, you can look at the number of dots around each table arrangement on the diagram.
What we see is that for 1 table, six guests are able to sit around the table. When there are 2 tables, around 10 guests can sit around the table. This number increases by 4 to fourteen when there are 3 tables put together as shown in the diagram.
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mary has $2.30 in her change purse. if she has 11 coins, which coins does she have?
Answer:
She has 8 quarters and 3 dimes.
Step-by-step explanation:
8 times .25 is equal to 2. If you add .1 times 3 to this sum you get $2.30.
Karma invests Nu 125,000 in T-Bank shares with a face value of Nu 100 but they are being sold at a premium of 25%. How many shares can he buy?
question #1
Which vector translates Quadrilateral ABCD to Quadrilateral A'B'C'D' given the coordinates listed below?
(-5,4), B(-2,5), C (-3,2), D(-6, 1);A' (-6, 6), B' (-3,7), C’ (-4,4),D' (-7,3)
A = (-2,1)
v = (-1,2)
B
C = (1, -2)
v
D
=(2, -1)
The translation vector that translates Quadrilateral ABCD to Quadrilateral A'B'C'D' is (-4, 5).
A mathematical vector called a translation vector expresses how far one point or object is moved away from another in a specific direction. To put it another way, it is a vector that shows how far and in which direction an item or point is moved from one position to another.
Subtract the corresponding vertices of the two quadrilaterals to determine the vector that converts Quadrilateral ABCD to Quadrilateral A'B'C'D'.
Let's consider vertex A:
Translation vector = A' - A
= (-6, 6) - (-2, 1)
= (-6+2, 6-1)
= (-4, 5)
Therefore, the translation vector that translates Quadrilateral ABCD to Quadrilateral A'B'C'D' is (-4, 5).
Similarly, we can find the translation vectors for vertices B, C, and D:
For vertex B: Translation vector = B' - B = (-3, 7) - (-2, 5) = (-1, 2)
For vertex C: Translation vector = C' - C = (-4, 4) - (-3, 2) = (-1, 2)
For vertex D: Translation vector = D' - D = (-7, 3) - (-6, 1) = (-1, 2)
All the translation vectors have the same value (-1, 2), which means that the two quadrilaterals are translated by the same amount in the x and y directions.
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What is the value of 3¹. 34
The value of the expression is 243
What are index forms?Index forms are simply described as mathematical forms that are used or the representation of numbers that are too large or in small sizes in more convenient forms.
These index forms are also termed;
Scientific notationsStandard formsExamples of index forms are;
a³, b², c²
From the information given, we have that;
3¹. 3⁴
Now, since they are of the same bases, add their exponent values
3⁵
Find the values, we get;
243
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The letters in the word mathematics are arranged randomly. write your answers in decimal form. round to the nearest thousandth as needed. what is the probability that the first letter is e?
There are 11 letters in the word mathematics. The probability of selecting the letter "e" first is 1/11, which is approximately 0.091 in decimal form when rounded to the nearest thousandth.
This is because there is only one "e" in the word mathematics, and we are selecting one letter out of the 11 total letters.
To find the probability that the first letter is "e" in the word "mathematics," follow these steps:
1. Count the total number of letters in the word: There are 11 letters in "mathematics."
2. Count the occurrences of the letter "e": There is 1 "e" in "mathematics."
3. Calculate the probability: Divide the occurrences of "e" by the total number of letters.
Probability = (Occurrences of "e") / (Total number of letters) = 1 / 11
In decimal form and rounded to the nearest thousandth, the probability that the first letter is "e" in the word "mathematics" when arranged randomly is approximately 0.091.
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Which will be smoother, a 50-day or a 200-day moving average?50-day 200-day
Due to its larger time frame and less sensitivity to transient variations in the data, the 200-day moving average is often smoother than the 50-day moving average.
The 200-day moving average is typically smoother than the 50-day moving average because it covers a longer period of time and is therefore less reactive to short-term fluctuations in the data. However, the choice between using a 50-day or a 200-day moving average ultimately depends on the specific data being analyzed and the desired level of sensitivity to changes in the data.
A 200-day moving average will be smoother than a 50-day moving average. The 200-day moving average considers a longer period of time, which reduces the impact of short-term fluctuations and provides a clearer overall trend. The 50-day moving average is more sensitive to recent price changes and will appear more volatile in comparison.
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