Sofia has a rectangle poster that is 42 inches long and 30 inches wide. The area of the poster is 1260 square inches.
The area of a rectangle depends on its sides. Basically, the area formula is equal to the product of the length and width of a rectangle. When we talk about the perimeter of a rectangle, it is equal to the sum of its four sides. Therefore, we can say that the area bounded by the perimeter of a rectangle is its area. But in the case of a square, since all sides are equal, the area of the square will be equal to the square of its length.
area of rectangle = length x width
We know that :
Area of rectangle = Length × Breadth
= 42 × 30 inches
= 1260 square inches.
Therefore, the area of a rectangle is 1260 square inches.
Complete Question:
Sofia has a rectangular poster that is 42 inches long and 30 inches wide. What is the area of the poster in square inches? Do not round your answer. Be sure to include the correct unit in your answer.
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kathy needs money for her trip to europe. if she has us dollars in the bank but wants to withdraw half of it in british pounds and half of it in euros, how many more euros than pounds will she have? assume pound is equal to usd and euro is equal to usd, and round to the nearest whole number.
The difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero.
Kathy needs to exchange half of her US dollars into British pounds and half of her US dollars into euros. Since it is given that pound is equal to USD and euro is also equal to USD, when she withdraws half of her US dollars as British pounds and half of it as euros, she will have the same amount of pounds and euros. Thus, the difference between the amount of money she will have in Euros and the amount she will have in British pounds will be zero. Therefore, she will have the same amount of money in both currencies, and the answer to the question is 0 (rounded to the nearest whole number).
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As part of a manufacturing process for widgets, an quality controller at ACME Corporation randomly samples 856 widgets during a day of production to test the current rate of defective widgets. The controller finds 34 defective widgets.The historical rate of defective widgets produced by ACME Corporation was 7%. Approximately, how many standard deviations is the point estimate from 7%?
The historical rate of defective widgets produced by ACME Corporation was 7%. Approximately, 91.2 is the standard deviations is the point estimate from 7%.
In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values. A low standard deviation indicates that the values tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values are spread over a wider range.
The standard deviation can be abbreviated SD, and is most commonly used in mathematical texts and equations with the lowercase Greek letter σ (sigma) for the population standard deviation, or the Latin letter s for the standard deviation of the sample.
The standard deviation of a random variable, sample, population, data set, or probability distribution is the square root of its variance. It is algebraically simpler than the mean absolute deviation, although less robust in practice. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data.
According to the Question:
Given that:
Defective widgets produced by ACME corporation was 7%
Total sample was 856 widgets.
Therefore, the Standard Deviation estimates from 7% is:
856 of 7% = 91.2
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you have 2 buckets, one which can hold 1 gallon of liquid and the other hold a half of gallon liquid. you must use these two buckets to fill up your gas tank with exactly 5 and 1/2 gallons of gas. what type of problem is this?
Answer:
The problem is the answer to your equation
Step-by-step explanation:
Im sorry to disappoint but these questions don't really have a name.
factor completely 3x^2+9x-3
Answer:
3(x^2+3x-1)
Step-by-step explanation:
3x^2+9x-3
3(x^2+3x-1)
christina molded a triangular prism from clay. she then took piana wire and sliced through the prism, as shown by the dotted lines. what is the shape of the cross section
The shape of the cross section is a triangle.
To find the shape of the cross section after slicing through the triangular prism with piano wire, follow these :
Determine the original shape of the triangular prism.
Consider the orientation of the dotted lines indicating where the piano wire sliced through the prism.
Analyze the resulting shape after the cut is made.
In this case, Christina has a triangular prism, and she sliced it with piano wire.
Based on your description, the cross section would be a triangle since the wire cut through the triangular sides of the
prism.
an emotional relationship involving a couple and a third person with whom one of them is also involved.
Therefore, the shape of the cross section is a triangle.
a plane figure with three straight sides and three angles
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Orpheus needs a new cat lounge. The pet store has one in stock that Orpheus likes for $33. The local sales tax rate is 4.25% where Orpheus lives. The store is running a clearance event on cat furniture with discounts of forty percent off.
Answer:
$20.64
Step-by-step explanation:
When you take 40% of 33, you are left with 19.8. You then translate the sales tax into 84 cents and add it to 19.8. That will give you $20.64 as the after tax price.
circumference
Calculate the
of a pie that has a 12 inch
diameter.
Answer:
12pi
Step-by-step explanation:
circumfrence : 2*pi*r
the radius is found by dividing the diameter in half so, 12/2 or 6
now multiply 6 with 2 and pi and you get 12pi
~lmk if you got Qs
Similar triangles ABE and BCD are shown on the coordinate plane
The slope of the line AB is 1.5 and the ratio of the sides is 2
How to find the slope of line ABThe slope, m of line AB is solved using the formula
m = y2 - y1 / x2 - x1
using points 'A (-9, -5) and B (3, 3)
m = -9 - 3 / -5 - 3
m = -12 / -8
m = 1.5
For a similar triangle the ratio of side lengths are equal
AB / BC = AE / BD = BE / CD
The length of AB and BC is solved as follows
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points we want to find the distance between.
For AB:
x1 = -9, y1 = -5 (coordinates of A)
x2 = 3, y2 = 3 (coordinates of B)
distance_AB = sqrt((3 - (-9))^2 + (3 - (-5))^2)
distance_AB = sqrt(144 + 64)
distance_AB = sqrt(208)
distance_AB ≈ 14.42
For BC:
x1 = 3, y1 = 3 (coordinates of B)
x2 = 9, y2 = 7 (coordinates of C)
distance_BC = sqrt((9 - 3)^2 + (7 - 3)^2)
distance_BC = sqrt(36 + 16)
distance_BC = sqrt(52)
distance_BC ≈ 7.21
From the graph,
AE = 12
BD = 6
BE = 8
CD = 4
AB / BC = 14.42 / 7.21 = 2
AE / BD = 12 / 6 = 2
BE / CD = 8 / 4 = 2
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find the equation of the circle below
Answer:
x² + y² = 16
Step-by-step explanation:
the circle has its centre at the origin (0, 0 )
the equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
the radius r of the circle is 4 , then
x² + y² = 4² , that is
x² + y² = 16
Jacob has some ingredients to make apple chutney. 2 large apples
1 red onion
125g sultanas
80ml vinegar
40 g sugar
Jacob has 100g of sugar. Using all of this sugar, what weighs of sultanas will he need to make this recipe
Answer:
312.5
Step-by-step explanation:
125g sultans for every 40g sugar
40 times 2 is 80, 125 times two is 250, then divide 125 by two to get how many for 20g of sugar
250+62.5=312.5
Find the difference.
(k^3-7k+2)-(k^2-12)=
The difference between the two expressions is:
(k³-7k+2)-(k²-12) = k³ - k² - 7k + 14
What is an expression?
We can begin by simplifying the left side of the equation:
(k³ - 7k + 2) - (k² - 12)
= k³ - 7k + 2 - k² + 12 // Distribution of the negative sign
= k³ - k² - 7k + 14 // Combining like terms
So the difference between the two expressions is:
k³ - k² - 7k + 14
An expression is a combination of one or more values, variables, and operators that can be evaluated to produce a result. Expressions can be as simple as a single number or variable, or they can be complex, combining multiple operators and functions.
What are variables?
A variable is a symbol or a named memory location that can hold a value. It is used to store and manipulate data during the execution of a program. Variables can be assigned different types of values, such as numbers, text, or Boolean (true/false) values. The value of a variable can change during the execution of a program, and it can be used in expressions and statements to perform calculations, make decisions, or control the flow of the program.
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Complete question is: (k³-7k+2)-(k²-12) = k³ - k² - 7k + 14
If anyone could help that would help so much!
1. The center of circle is (5, -10)
2. The new center of circle is (4, -12)
3. Equation is [tex](x-4)^2+(y+12)^2 = 64[/tex]
Define the term Circle identities?The Circle identities defines a set of fundamental identities in trigonometry that depends on the six trigonometric functions of an angle in a right-angled triangle.
Given circle equation is [tex](x-5)^2+(y+10)^2 = 64[/tex]
after translated 1 left and 2 down, by simply add 1 in x and add 2 in y axis, So, the new circle equation will be,
[tex](x-4)^2+(y+12)^2 = 64[/tex]
1. The center of the given circle [tex](x-5)^2+(y+10)^2 = 64[/tex]
Generally the equation of circle is [tex](x-h)^2 +(y-k)^2 =r^2[/tex]
where, (h, k)is center of circle and r is radius.
by comparing the given equation, we get, h = 5, k = -10
So, the center of circle is (5, -10)
2. New center after translation
equation is [tex](x-4)^2+(y+12)^2 = 64[/tex]
comparing the given equation, we get, h = 4, k = -12
So, the new center of circle is (4, -12)
3. Equation of the resulting circle is [tex](x-4)^2+(y+12)^2 = 64[/tex]
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what is the measurement of the unknown angle?
The measure of the unknown angle is 93°
What is the measurement of the unknown angle?First we should get the interior angles of the triangle in the right side.
The angle in the left side is given by:
x + 127° = 180°
x = 180° - 127°
x = 53°
While the angle in the right side is:
y + 146° = 180°
y = 180° - 146°
y = 34°
Now remember that the sum of the interior angles of a triangle must be 180°, then if the angle at the top is z we can write:
z + 34° + 53° = 180°
z = 180° - 34° - 53°
z = 93°
And this angle is a vertical angle of the one we want to find, so the measure of the unknown angle is also 93°.
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10. advantages and disadvantages of the related-samples design advantages of using a related sample (either one sample of participants with repeated measures or two matched samples) versus using two independent samples include which of the following? check all that apply. a related-samples design reduces or eliminates problems caused by individual differences such as age, iq, gender, or personality. related samples (specifically, one sample of participants with repeated measures) can have an order effect such that a change observed between one measurement and the next might be attributable to the order in which the measurements were taken rather than to a treatment effect. related samples have less sample variance, increasing the likelihood of rejecting the null hypothesis if it is false (that is, increasing power). related samples (specifically, one sample of participants with repeated measures) require fewer participants for the same degree of power.
All the given options applies to the statement. A related-samples design reduces problems due to individual differences; can have an order effect; have less sample variance, increases the likelihood of rejecting the null hypothesis; needs few participants for same degree of power.
1. A related-samples design decreases or eliminates problems that is caused by individual differences such as age, IQ, gender, or personality.
2. Related samples (specifically, one sample of participants with repeated measures) can have an order effect such that a change observed between one measurement and the next might be attributable to the order in which the measurements were taken rather than to a treatment effect.
3. Related samples have less sample variance, which increases the likelihood of dismissing the null hypothesis if it is false (that is, increasing power).
4. Related samples (specifically, one sample of participants with repeated measures) needs very less participants for the same degree of power.
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Annual sales for a fast food restaurant are $649,995 and increasing at a rate of 3.5% per year. Use an exponential function to find the annual sales after 8 years.
After seven years, the yearly sales are 855,355.65.
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
the following parameters
a = 650000
r = 4% = 0.04
t = 7
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I need this soon its due today
The amount of filter paper that you need to line the funnel is given as follows:
125.6 cm³.
How to obtain the volume a cone?The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.
V = πr²h/3.
The parameters for the cone in this problem are given as follows:
Radius of r = 4 cm -> as the diameter is of 8 cm.Height of h = 7.5 cm.Hence the amount of filter paper that you need to line the funnel is given as follows:
V = 3.14 x 4² x 7.5/3
V = 125.6 cm³.
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Classify each number below as an integer or not.
12
55.3
18
2
Integer?
12
17
Yes
O
O
O
No
O
O
-260.43 O O
O
X
Answers:
12 is an integer55.3 is NOT an integer18 is an integer2 is an integer17 is an integer-260.43 is NOT an integerExplanation:
An integer is any positive or negative whole number. Zero is also an integer. Examples include 12, 15, and -27.
Non-integer values are anything with a fractional or decimal part. An example is 2.47; another example is 2/3 (since it turns into roughly 0.667).
Is the formula recursive, explicit, or neither?
NEXT = NOW - 8, starting at 50
The formula NEXT = NOW - 8 is neither recursive or explicit.
What is recursive and explicit formula?In a recursive fοrmula, we can find the value οf a term in the sequence using the value οf the previοus term. Hοwever, in an explicit fοrmula, we can find the value οf a term in the sequence using its pοsitiοn. Hence, this is anοther difference between recursive and explicit.
Recursive formula = [tex]\rm a_{n}=a_{n-1}+ d[/tex]
Explicit formula = [tex]\rm a_n= a_1 + (n - 1) d[/tex]
Here, NEXT = NOW - 8 resembles Recursive formula, but the value of Next isn't given. Even if it starts at 50, The value of n isn't specified.
Therefore, The formula NEXT = NOW - 8 is neither recursive or explicit.
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Complete question:
Is the formula recursive, explicit, or neither?
NEXT = NOW - 8, starting at 50.
recursiveexplicitneitherNEED BY MONDAY PLEASE!!! Select all the true equations:
Find the 8th term of the geometric sequence 2, -10, 50, ...
The 8th term of the given geometric sequence is -156250.
What is geometric sequence?A sequence of numbers is called a geometric sequence if each term, except for the first term, is obtained by multiplying the previous term by a constant factor, which is called the common ratio.
According to given information:The given sequence is a geometric sequence where each term is obtained by multiplying the previous term by -5.
So, the common ratio (r) between any two consecutive terms is -5.
To find the 8th term, we can use the formula for the nth term of a geometric sequence:
[tex]an = a1 * r^{(n-1)[/tex]
where,
an = 8th term
a1 = first term = 2
r = common ratio = -5
n = 8 (since we want to find the 8th term)
Therefore, substituting the values in the formula, we get:
[tex]a8 = 2 * (-5)^{(8-1)}\\\\a8 = 2 * (-5)^7\\\\a8 = 2 * (-78125)\\\\a8 = -156250[/tex]
Hence, the 8th term of the given geometric sequence is -156250.
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what is the answer to: Lines AB and CD are parallel. If 6 measures (4x - 31)°, and 5 measures 111°, what is the value of x?
Lines AB and CD are parallel. If 6 measures (4x - 31)°, and 5 measures 111°, the value of x will be 21 if both angles are supplementary.
If lines AB and CD are parallel, then we can assume that m<5 and m<6 are supplementary that is the sum of both angles is 180 degrees
Therefore we can say that;
then 3x - 31 + 148 = 180
then 3x + 117 = 180
we need to then subtract 117 from both sides
therefore, 3x+117-117 = 180 - 117
then 3x = 180 - 117
then 3x = 63
then x = 63/3
therefore, x = 21
Hence the value of x will be 21 if both angles are supplementary.
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Use the image below to get the value of X, Y and Z
Step-by-step explanation:
For the second triangle, you can find X by subtracting 32+85 from 180, which leaves X as 63.
Next, since Y is the same as X, it means that Z is equal to 180-(45+63)
X=63
Y=63
Z=72
Assume the resting heart rates for a sample of individuals are normally distributed with a mean of 85 and a standard deviation of 20. Use the 68-95-99. 7 rule to find the following quantities
the percentage 68% value is calculated by adding 85 and 20, or 70; the 95% value is calculated by adding 85 and 40, or 115; and the 99.7% value is calculated by adding 85 and 60, or 150.
68%: 70
95%: 115
99.7%: 150
The 68-95-99.7 rule is used to estimate the percentage of a population that falls within a certain range of values when the data is normally distributed. The rule states that 68% of the population falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. To find the percentages, we subtract the mean (85) from the corresponding standard deviation (20, 40, and 60, respectively) and add the result to the mean. Thus, the 68% value is calculated by adding 85 and 20, or 70; the 95% value is calculated by adding 85 and 40, or 115; and the 99.7% value is calculated by adding 85 and 60, or 150.
the complete question is :
Assume the resting heart rates for a sample of individuals are normally distributed with a mean of 85 and a standard deviation of 20. Use the 68-95-99.7 rule to find the following quantities:
1.The percentage of individuals with resting heart rates between 65 and 105.
2.The percentage of individuals with resting heart rates above 125.
3.The range of resting heart rates that includes the middle 95% of the individuals in the sample.
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what proportion of overweight children have left atrial diameters greater than the mean for healthy children? (round your answer to four decimal places.)
The P(Z > 2.90) = 1 - P(Z ≤ 2.90)= 1 - 0.9986= 0.0014Thus, the proportion of overweight children with left atrial diameters greater than the mean of healthy children is 0.0014, rounded to four decimal places.Answer: 0.0014
According to the given question, we have to find what proportion of overweight children have left atrial diameters greater than the mean for healthy children. To calculate the answer, we need to use the z-score of the left atrial diameter. We have to find the z-score value corresponding to the mean of healthy children and the standard deviation of the left atrial diameter of healthy children. Then, we will have to use the z-score formula.
Let’s solve it.Step-by-step explanation:Given that we need to calculate the proportion of overweight children with left atrial diameters greater than the mean of healthy children. Here, we can use the standard normal distribution to solve this problem. To solve this problem, we need to calculate the z-score for the mean of healthy children and the left atrial diameter of healthy children.1. Find the z-score for the mean of healthy children.z = (x - μ) / σz = (0 - 0) / 1z = 0 Thus, the z-score for the mean of healthy children is 0.2.
Find the z-score for the left atrial diameter of healthy children.z = (x - μ) / σz = (3.95 - 2.5) / 0.5z = 2.90Thus, the z-score for the left atrial diameter of healthy children is 2.90.Using the z-score formula, we can find the proportion of overweight children with left atrial diameters greater than the mean of healthy children. Let’s use the formula for it.P(Z > 2.90) = 1 - P(Z ≤ 2.90)From the z-score table, we can find that the value of P(Z ≤ 2.90) is 0.9986.
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f(x) = -2x² - 6x³ + 4x + 1
The function has a local maximum at x = 1/3 and a local minimum at x = -4/3.
What do you mean by Quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x
ax²+bx+c=0
with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots x can be found by completing the square,
ax²+bx+c=0
To analyze the function F(x) = -2x² - 6x³ + 4x + 1, we can begin by finding its derivative:
F'(x) = -4x - 18x² + 4
Then, we can find the critical points of the function by setting F'(x) equal to zero and solving for x:
-4x - 18x² + 4 = 0
Using the quadratic formula, we get:
x = (-(-4) ± ((-4)² - 4(-18)(4))) / (2(-18))
Simplifying, we get:
x = (-(-4) ± (400)²) / (-36)
x = (-(-4) ± 20) / (-36)
x = 1/3 or x = -4/3
So the critical points of the function are x = 1/3 and x = -4/3.
To determine the nature of these critical points, we can use the second derivative test.
F''(x) = -4 - 36x
Plugging in x = 1/3, we get:
F''(1/3) = -4 - 36(1/3) = -16 < 0
So x = 1/3 is a local maximum.
Plugging in x = -4/3, we get:
F''(-4/3) = -4 - 36(-4/3) = 40 > 0
So x = -4/3 is a local minimum.
Therefore, the function has a local maximum at x = 1/3 and a local minimum at x = -4/3.
complete question F(X) = 6x³ - 4x² + 1. Find The Equation Of The Tangent Line To F(X)When X = 2.
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Complete question:
Find the local maximum and minimum of f(x) = -2x² - 6x³ + 4x + 1.
C
M
A
Which set of given
information does not
prove
A CAMA COM?
Answer:
Step-by-step explanation:
Answer: A. You cannot use any theorem along with option A. For B, you can use SAS. For option C, you can use SAS. For option D, you can use SSS. For option D, you can use ASA. So, the answer is A.
Lines ac and rs are coplanar. parallel. perpendicular. skew.
The right choice is Choice D: Lines AC and RS are skew lines. Skew lines are two lines that never cross and are not equal moreover.
A line is characterized as a bunch of focuses that broaden endlessly in one or the other heading. A line is the briefest distance between any two focuses.
What are skew lines?
Skew lines are two lines that never cross and are not equal moreover. Thus we can say that the two lines can not exist in a similar plane.
From the figure obviously
Line AC and RS are in various planes and they are likewise not crossing one another, subsequently, as per the meaning of skew lines, they are skew lines.
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the complete question is:
Lines AC and RS are:
Coplanar
Parallel
Perpendicular
Skew
What is the inequality of -1 1/4 and -1
Answer:
[tex]{ \tt{ - 1 > - 1 \frac{1}{4} }} \\ [/tex]
i need help pls!!!!! question is attached
Therefore, the value of the investment after 3.5 years is $2325.28.
What is percent?Percent is a unit of measurement that represents a fraction of 100. It is often used to express a proportion or rate in relation to a total of 100. For example, if a sales tax is 7%, that means that for every $100 spent, $7 goes towards the tax. The symbol used to represent percent is %.
Here,
The formula for the value of the investment after t years is:
[tex]A = P(1+r/n)^{nt}[/tex]
where:
A is the amount of money after t years
P is the principal investment (initial amount invested)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time in years
Using this formula, we can plug in the values given in the problem:
P = 2000
r = 0.04
n = 12 (monthly compounding)
t = 3.5
A = [tex]2000(1 + 0.04/12)^{12*3.5}[/tex]
A = [tex]2000*(1.003333)^{42}[/tex]
A = 2000(1.162641)
A = $2325.28
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Find 175.7% of 163. Round to the nearest tenth.
Answer: The answer is 286.4! (Not rounded: 286.391)
Step-by-step explanation:
I hope this helped you! <333