Step-by-step explanation:
If the interest is not compounded, it means that Mabel will earn a simple interest of 11% per year on her principal amount of $30,000.
The formula for calculating simple interest is:
Interest = (Principal x Rate x Time)
Where:
Principal = $30,000
Rate = 11% = 0.11 (as a decimal)
Time = 2 years
So, substituting the values in the formula, we get:
Interest = (30,000 x 0.11 x 2) = $6,600
Therefore, Mabel will earn $6,600 in interest over a period of 2 years.
Answer this ASAP, I will give the brainliest answer.
Given that y = 4 cm and θ = 38°, work out x rounded to 1 DP.
The diagram is not drawn accurately.
from S^OH
sinθ=opp/hyp
sin38°=x/4
cross multiply and make x the subject of the formulax=4sin38°
x=4×(0.61566147533)
x=(2.4626459013)
to 1dp
x=2.5cm
the sheet is a series of arcs of radius 10cm,each arc subtending 120° at it's centre. if there are 14 such arcs in one sheet, how wide would the sheet be if flattened out
The sheet would be approximately 93.13 cm wide if flattened out.
Describe Arc?The length of an arc is determined by the degree measure of the central angle that subtends the arc. For example, if a circle has a radius of 5 units and an arc has a central angle of 90 degrees, the length of the arc can be found using the formula:
arc length = (central angle / 360) x 2πr
where r is the radius of the circle. In this case, the length of the arc would be:
arc length = (90/360) x 2π(5) = 1.25π units
The length of each arc can be found using the formula:
length = (angle / 360) x 2πr
where angle is the central angle of the arc in degrees, r is the radius of the arc, and π is pi (approximately equal to 3.14).
In this case, the radius is 10 cm and the central angle is 120 degrees, so the length of each arc is:
length = (120/360) x 2π(10) = (1/3) x 20π = (20/3)π cm
There are 14 such arcs in one sheet, so the total length of the sheet when flattened out is:
total length = 14 x (20/3)π = (280/3)π cm
This is approximately equal to 93.13 cm if we use the approximation π ≈ 3.14.
Therefore, the sheet would be approximately 93.13 cm wide if flattened out.
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Quadrilateral MNOP has vertices M(-2,4) N(-2,1) O(3,1) and P(3,4). what are the coordinates of the image of point P after a reflection across the X-axis??
After just a reflection along the [tex]X-axis[/tex], a quadrilateral [tex]MNOP[/tex] of position [tex]P[/tex] is [tex](3, -4)[/tex].
Describe the quadrilateral form.Four closed sides are making up a quadrilateral. Quadrilaterals are the following figures: Designed by Raphael. a four-sided figure. There is just one pair of parallel sides to the form, and there are no right angles.
With an example, define a quadrilateral.A closed form known as a quadrilateral is known to be have sides with various widths and lengths. It is a closed polygon in two dimensions with four vertices, four angles, and four sides. Some examples of a quadrilateral are a cohesion and coherence, parallelogram, rectangle, rhombus, square, and kite.
When a point is reflected across the [tex]X-axis[/tex], the [tex]X-[/tex]coordinate stays the same, but the [tex]Y-[/tex]coordinate is multiplied by [tex]-1[/tex].
So to find the image of point [tex]P[/tex] after a reflection across the [tex]X-axis[/tex], we keep the [tex]X-[/tex]coordinate of [tex]P[/tex] the same (which is 3) and multiply the [tex]Y-[/tex]coordinate by [tex]-1[/tex]
New [tex]Y-[/tex]coordinate of [tex]P = -1 * 4 = -4[/tex]
Therefore, the image of point [tex]P[/tex] after a reflection across the [tex]X-axis[/tex] is [tex](3, -4)[/tex].
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 find the difference between the perimeters of two circular planets if one has a radius of 16.8 CM and the other has a diameter of 16.8 CM 
Answer:
16.8π cm or 52.78 cm
Step-by-step explanation:
We are given the radius of one planet and the diameter of the other.
So, we have perimeter (circumference) of a circle is:
C = 2πr
where C is the circumference and r is the radius of the circle.
For the first planet with a radius of 16.8 cm, we can calculate its circumference as:
C1 = 2π(16.8) = 33.6π cm
For the second planet with a diameter of 16.8 cm, we can calculate its radius as half of the diameter:
r2 = d/2 = 16.8/2 = 8.4 cm
And then, we can calculate its circumference as:
C2 = 2π(8.4) = 16.8π cm
The difference between the perimeters of the two planets is:
C1 - C2 = (33.6π - 16.8π) cm
C1 - C2 = 16.8π cm
Therefore, the difference between the perimeters of the two planets is approximately 52.78cm, rounded to two decimal places.
Consider the expression 1/2 parentheses to a + 1 a + 3 complete the two description of parts of an expression the entire explosion is the product of blank on its own parentheses to a + 1/8
The expression 1/2(2a + 1)(a + 3) can be described as the product of two expressions as 1/2 and (2a + 1)(a + 3).
The entire expression is the product of two smaller expressions, namely 1/2 and (2a + 1)(a + 3).
The second expression, (2a + 1)(a + 3), is a product of two binomials. Each binomial contains two terms separated by a plus sign.
The first binomial, 2a + 1, has a coefficient of 2 in front of the variable a and a constant term of 1. The second binomial, a + 3, has a coefficient of 1 in front of the variable a and a constant term of 3.
To simplify the expression 1/2(2a + 1)(a + 3), we can distribute the 1/2 to both terms inside the parentheses, resulting in the expression (a+1/2)(a+3).
The expression can be further simplified by multiplying the two binomials together, resulting in the quadratic expression a² + 7/2a + 3/2.
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Complete Question:
Consider the expression 1/2(2a + 1)(a + 3)
Complete 2 descriptions of the parts of the expression.
What is 3 divided by the difference of 4 and a numb
er
The result of 3 divided by the difference of 4 and 2 is 1.5.
Formula:
3 / (4 - x)
Let's take the number x to be equal to 2.
Therefore, the calculation is 3 divided by the difference of 4 and 2, which is 3 / (4 - 2) or 3 / 2.
The answer is 1.5.
To explain further, when we divide the number 3 by the difference of 4 and 2, we are essentially dividing the number 3 by the result of subtracting 2 from 4. The result of subtracting 2 from 4 is 2. When we divide 3 by 2, the answer is 1.5.
Therefore, 3 divided by the difference of 4 and a number is equal to 1.5 when the number is equal to 2.
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Complete question:
What is 3 divided by the difference of 4 and a number?
Consider the following time series data. Using the naive method (most recent value) as the forecast for the next week, compu (a) mean absolute error
MAE=
(b) mean squared error
MSE =
(c) mean absolute percentage error (Round your answer to two decimal places.) ।
×
(d) What is the forecast for week 7 ?
The forecast for week 7 is 309
Given time series data for the problem is; Week 1Week 2Week 3Week 4Week 5Week 6Week 7Observed value220254280276297309Naive forecast220254280276297309Where, the forecast for the next week is the most recent value. It means that the forecast for week 7 is 309.The formula to calculate mean absolute error (MAE) is;$$\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}|y_i-\hat{y}_i|$$Where, $n$ is the total number of observations, $y_i$ is the $i$th observed value, and $\hat{y}_i$ is the $i$th forecasted value by the naive method.MAE = $(1/7) \times (38+26+4+17+12+4+0)$ = 13.57Mean squared error (MSE) is given by;$$\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat{y}_i)^2$$MSE = $(1/7) \times (38^2+26^2+4^2+17^2+12^2+4^2+0^2)$ = 3004.29Mean absolute percentage error (MAPE) is given by;$$\text{MAPE}=\frac{1}{n}\sum_{i=1}^{n}\left(\frac{|y_i-\hat{y}_i|}{y_i}\right)\times 100$$MAPE = $(1/7) \times [(38/220) + (26/254) + (4/280) + (17/276) + (12/297) + (4/309) + (0/309)] \times 100$MAPE = 5.17%Thus, (a) mean absolute error (MAE) is 13.57, (b) mean squared error (MSE) is 3004.29, (c) mean absolute percentage error (MAPE) is 5.17% and (d) the forecast for week 7 is 309.
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wait times of between 0 and 20 minutes at a local restaurant follow a uniform distribution. sketch the distribution use the distribution that a randomly selected diner waits between 2 and 7.5 minutes for a table find the probability a randomly selected diner waits less than 8 minutes for a table find the probability a randomly selected diner waits more than 1.5 minutes
a) The probability of a randomly selected diner waits less than 8 minutes for a table is 0.4
b) The probability of a randomly selected diner waits more than 1.5 minutes is 0.925
Given, wait times of between 0 and 20 minutes at a local restaurant follow a uniform distribution.
The probability density function of a uniform distribution is given by
f(x) = {1/(b-a)} where a ≤ x ≤ b
where a = 0 and b = 20
Therefore, the probability density function of f(x) = 1/20 for 0 ≤ x ≤ 20
For the probability that a randomly selected diner waits between 2 and 7.5 minutes for a table, we need to find the area under the curve from x = 2 to x = 7.5
∴ P(2 ≤ x ≤ 7.5) = ∫₂⁷.⁵(1/20) dx
= 5.5/20 ⇒ 0.275
a) We need to find the area under the curve from x = 0 to x = 8
∴ P(x < 8) = ∫₀⁸(1/20) dx
= 8/20 ⇒ 0.4
b) We need to find the area under the curve from x = 1.5 to x = 20
∴ P(x > 1.5) = ∫₁.₅²⁰(1/20) dx
= 18.5/20 ⇒ 0.925
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Using the nth term formula a + (n-1)d,
(i) Find the nth term of this arithmetic sequence 8, 11, 14, 17,20,...
(ii) Find the 50th term ?
Answer:
i) here a=8 d=3 nth term= 8+(n-1)3
ii)50th term= 8+49×3=155
Step-by-step explanation:
i hope you find it helpful
Step-by-step explanation:
hope you understood the answer
You get brainilest if the answer is right.Do what the picture says!!!!
Answer:
67.12
Step-by-step explanation:
Area of 1/2 circle = 1/2πr^2 = 1/2(3.14)(4^2) = 1/2(3.14)(16) = 25.12
Area of top rectangle = 8 x 3 = 24
Area of bottom rectangle = 3 x 6 = 18
Total area : 25.12 + 24 + 18 = 67.12
Answer:Hello how are you
Step-by-step explanation:
need help with multiple questions (and if you can, show your work, thanks):
1: Measure 8 tbsp. chocolate sauce and add 2 1/2 cups of milk.
2: Start with 1 3/4 cups of milk and add 2 1/2 tbsp. chocolate sauce.
3: Add 3 1/3 tbsp. chocolate sauce to 1 1/4 cups milk.
4: For every 1 cup of milk add 2 1/2 tbsp. of chocolate sauce.
5: Stir 1 tbsp. chocolate sauce into 2/3 cup milk.
With this query, no effort is necessary. measure the tbsp. of all items.
Is milk consumption healthy?A great source of both phosphorus and calcium, which are essential for the growth and upkeep of strong, strong teeth and bones, is milk. They lower the chance of developing osteoporosis and suffering broken bones later in life. Milk encourages strong bones.
1. Measure [tex]8[/tex] tbsp. chocolate sauce and add [tex]2\frac{1}{2}[/tex] cups of milk.
No work is required for this question. It is a simple instruction to measure out 8 tbsp. of chocolate sauce and add it to [tex]2\frac{1}{2}[/tex] cups of milk.
2. Start with [tex]1\frac{3}{4}[/tex] cups of milk and add [tex]2\frac{1}{2}[/tex] tbsp. chocolate sauce.
No work is required for this question. It is a simple instruction to start with [tex]1\frac{3}{4}[/tex] cups of milk and add [tex]2\frac{1}{2}[/tex] tbsp. of chocolate sauce.
3. Add [tex]3\frac{1}{3}[/tex] tbsp. chocolate sauce to [tex]1\frac{1}{4}[/tex] cups milk.
No work is required for this question. It is a simple instruction to add [tex]3\frac{1}{3}[/tex]tbsp. of chocolate sauce to [tex]1\frac{1}{4}[/tex] cups of milk.
4. For every 1 cup of milk add [tex]2\frac{1}{2}[/tex] tbsp. of chocolate sauce.
No work is required for this question. It is a simple instruction to add [tex]2\frac{1}{2}[/tex] tbsp. of chocolate sauce for every [tex]1[/tex] cup of milk.
5. Stir [tex]1[/tex] tbsp. chocolate sauce into [tex]\frac{2}{3}[/tex] cup milk.
No work is required for this question. It is a simple instruction to stir 1 tbsp. of chocolate sauce into [tex]\frac{2}{3}[/tex] cup of milk.
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Use the place-value charts to round each decimal to the nearest
whole number, nearest tenth, and nearest hundredth. 67.822
Nearest whole number:
Nearest tenth:
Nearest hundredth:
Answer:
------------
Step-by-step explanation:
Thanks...........
the diagram Shows a sector of a circle radius 10cm and angle 135 degrees find out perimeter
Answer: 22.4 cm
Step-by-step explanation:
Perimeter of sector is: P = 2r + 2πr(θ/360) P = 2*10 + 2(3.14) (135/360) = 22.4 cm (rounded)
A softball coach has ordered softballs for two different leagues. The Junior League uses an 11-inch softball priced at $2.50 each. The Senior League uses a 12-inch softball priced at $3.50 each. The softball coach ordered a total of 120 softballs for $350.
The first step to solving a system of linear equations by substitution is to solve one of the equations for one of its variables. Solve the first equation in the system of equations that you selected above. Write the equation with an isolated variable as your response below.
The number of 11-inch softballs ordered is 70 and the number of 12-inch softballs ordered is 50.
How many of each size of softball was ordered?a + b = 120 equation 1
2.50a + 3.50b = 350 equation 2
Where:
a = number of 11-inch softballs ordered b = number of 12-inch softballs orderedThe substitution method would be used to determine the number of each size of softball ordered.
Make a the subject of the formula in equation 1:
a = 120 - b
Substitute for a in equation 2:
2.50(120 - b) + 3.50b = 350
300 - 2.5b + 3.50b = 350
Combine and add similar terms:
3.5b - 2.5b = 350 - 300
b = 50
Substitute for b in equation 1
a + 50 = 120
a = 120 - 50
a = 70
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How can the area of this triangle be determined by forming a
rectangle?
Select from the drop-down menus to correctly complete the
statements
Copy and rotate the triangle and place it next to the existing
triangle to form a rectangle. The length of the rectangle is
Choose.
units. The width of the rectangle is
Choose.
units. The area of the rectangle IS
N
Choose..
square units
The area of the triangle is half the area of the rectangle, so the
area of the triangle is Choose.
square units.
The area of triangle will be 1/2*area of rectangle.
what exactly is a triangle?
A triangle is a geometric shape that consists of three line segments or sides, and three angles. Triangles are among the simplest and most fundamental shapes in geometry, and they are used in many fields of mathematics, science, engineering, and art.
The sum of the three interior angles of a triangle is always 180 degrees. The length of each side of the triangle is related to the size of the angles opposite to it, and to the length of the other sides, through various trigonometric functions.
Now,
The area of given triangle can be found by making a whole rectangle by making equal and parallel lines base and perpendicular.
let 1 box represent 1 unit if length
then area of rectangle=L*B
=5*4
=20 unit²
then, area of triangle=1/2*area of rectangle
=20/2
=10 unit²
hence,
The area of triangle will be 1/2*area of rectangle.
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PLEASE HELP ME IM STRUGGLING AHHH
The total cost after tax to repair Deborah’s computer is represented by 0.08(73h) + 73h, where h represents the number of hours it takes to repair Deborah’s computer. What part of the expression represents the amount of dollars Deborah has to pay in tax? Explain.
Answer:
0.073(73h)
Step-by-step explanation:
[tex]0.08(73h)+73h[/tex]
[tex]=\dfrac{73}{100}(73h)+73h[/tex]
[tex]=73\%(73h)+73h[/tex]
Since, it took 50h to repair the computer so, 0.073(73h) represents the amount of tax Deborah has to pay. Which is 73% of 73h.
Nine less than four times a nunber equals fithteen
The required number for given expression is a = -3/2
What are expression?Mathematical expressions consist of at least two numbers or variables, at least one math procedure, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical procedure. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
According to question:We given that
Nine less than four times a number equals fithteen;'
Let the number is a.
So,
9 - 4a = 15
-4a = 6
a = 6/-4
a = -3/2
Thus, required number is a = -3/2
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A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling
10
1010 tickets, they were still at a net loss of
$
800
$800dollar sign, 800 (due to the production costs). They sold each ticket for
$
70
$70dollar sign, 70. Let
�
yy represent the net profit (in dollars) when they have sold
�
xx tickets. Complete the equation for the relationship between the net profit and number of tickets sold
The equatiοn fοr the relatiοnship between the net prοfit and the number οf tickets sοld is y = 70x - 1500.
What is an Equatiοn?In mathematics, an equatiοn is a statement that shοws the equality between twο expressiοns. The equatiοns can cοntain variables, cοnstants, and mathematical οperatiοns such as additiοn, subtractiοn, etc. In wοrd prοblems, the variables represent the unknοwn quantity οr unknοwn number
Here we have
A charity οrganizatiοn had tο sell a few tickets tο their fundraiser tο cοver necessary prοductiοn cοsts.
Cοst οf each ticket =$70
Number οf tickets sοld = 10
Tοtal cοst οf 10 tickets = $ 70 × 10 = $ 700
Lοss after selling 10 tickets = $800
Hence, tοtal cοst οf prοductiοn = $ 700 + $ 800 = $ 1500
Let's assume that they sοld 'x' tickets and gοt 'y' prοfit
=> Tοtal revenue gained by selling tickets = $ 70x
Prοfit y = Tοtal revenue - Prοduct cοst
=> y = 70x - 1500
Therefοre,
The equatiοn fοr the relatiοnship between the net prοfit and the number οf tickets sοld is y = 70x - 1500.
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Complete Question:
A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling 10 tickets, they were still at a net loss of $800 (due to the production costs). They sold each ticket for $70. Let y represent the net profit in dollars) when they have sold tickets. Complete the equation for the relationship between the net profit and the number of tickets sold.
What is a mixed number with the same denominator for 3 7/8
The improper fraction that is equivalent to 3 7/8 is 31/8.
A mixed number consists of a whole number and a proper fraction. In the case of 3 7/8, the whole number is 3 and the proper fraction is 7/8.
To convert a mixed number to an improper fraction, you need to first convert the whole number to a fraction by multiplying it by the denominator of the fraction in the mixed number. In this case, the denominator of the fraction is 8, so we multiply 3 by 8 to get 24.
Next, you add the numerator of the fraction to the result of the multiplication. In this case, the numerator is 7, so we add it to 24 to get 31.
3 7/8 = (3 x 8 + 7) / 8
= (24 + 7) / 8
= 31/8
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The given question is incomplete, the complete question is:
What is 3 7/8 as an improper fraction?
The figure below is a net for a right rectangular prism.
What is the surface area of the right rectangular prism, in square inches?
schoology
will give branliest if answer IS RIGHT
Answer:
586 square inches
Step-by-step explanation:
[tex]2((11(7) + 12(7) + 12(11))[/tex]
[tex]2(77 + 84 + 132)[/tex]
[tex]2(293) = 586[/tex]
which equation represents a tangent function with a domain of all real numbers such that where n is an integer?
The tangent function is defined as the ratio of the sine function to the cosine function. It is periodic with a period of pi and has vertical asymptotes at odd multiples of pi/2. An equation for a tangent function with a domain of all real numbers and n as an integer is given by the following equation:
y = tan(x + n(pi))
The tangent function is defined as the ratio of the sine function to the cosine function, and it is periodic with a period of pi. It has vertical asymptotes at odd multiples of pi/2.
The tangent function can be represented by the following equation:
y = tan(x)
Where x is the angle measured in radians.
If we want to shift the graph of the tangent function by a certain amount, n, in the horizontal direction, we can use the following equation:
y = tan(x + n(pi))
Where n is an integer.
For example, if n = 2, then the graph of the tangent function would be shifted 2pi units to the left, and the equation would be:
y = tan(x - 2pi)
If n = 3, then the graph of the tangent function would be shifted 3pi units to the left, and the equation would be:
y = tan(x - 3pi)
And so on for any integer value of n.
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Deondra has $420 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys a new bicycle for $236. 31. She buys 2 bicycle reflectors for $3. 07 each and a pair of bike gloves for $34. 75. She plans to spend some or all of the money she has left to buy new biking outfits for $59. 50 each. Write and solve an inequality which can be used to determine oo, the number of outfits Deondra can purchase while staying within her budget
Deondra can purchase 2 amount outfits for $59.50 each within her budget of $420.
$420 - ($236.31 + $3.07 + $3.07 + $34.75) ≥ $59.50oo
$147.00 ≥ $59.50oo
$147.00 ÷ $59.50 ≥ oo
2.46 ≥ oo
Deondra can purchase 2 outfits.
Deondra has $420 to spend at a bicycle store for some new gear and biking outfits. She first buys a new bicycle for $236.31, then she buys two bicycle reflectors for $3.07 each and a pair of bike gloves for $34.75. In order to determine how many outfits she can purchase while staying within her budget, an inequality can be written and solved. The inequality is $420 - ($236.31 + $3.07 + $3.07 + $34.75) ≥ $59.50oo. This can be simplified to $147.00 ≥ $59.50oo. Dividing both sides of the inequality by $59.50, we get $147.00 ÷ $59.50 ≥ oo. After solving, this simplifies to 2.46 ≥ oo. Since Deondra can only purchase a whole outfit, the answer becomes 2 outfits. Therefore, Deondra can purchase 2 outfits while staying within her budget.
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Specify the number of ways to perform the task described. Give your answers using P(n, r) or C (n, r) notation. Eleven magazines are competing for six identical awards for excellence in journalism. No magazine can receive more than one award. The number of ways to perform the task is ________.(Do not evaluate.)
The number of ways to perform the task is 462.
Combinations:In mathematics, a combination is a way of selecting items from a larger set in which the order of selection does not matter.
For example, if you are selecting a team of 3 people from a group of 10 people, the order in which you select the team members does not matter.
Here we have
Number of magazines = 11
Number of awards = 6
Using the combination formula,
No of ways to select 6 magazines out of 11 = C(11, 6)
= 11! / (6! × (11-6)!) = 11! / (6! × 5!) = 462
Therefore,
The number of ways to perform the task is 462.
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A global research study found that the majority of today's working women would prefer a better 'work-life balance' to an increased salary. One of the most important contributors to 'work-life balance' identified by the survey was 'flexibility' with 46% of women saying that having a flexible work schedule is either very important or extremely important to their career success. Suppose you select a sample of 100 working women. (Round answers to four decimal places.) a) What is the probability that, in the sample, fewer than 50% say that having a flexible work schedule is either very important or extremely important to their career success? b) What is the probability that, in the sample, more than 43% say that having a flexible work schedule is either very important or extremely important to their career success?
z = (x - np) / σ
z = (43 - 100(0.50)) / 0.05
z = -1.4
P(z > -1.4) = 0.9192
a) The number of working women in the sample is 100. The majority of women prefer a better 'work-life balance' to a higher salary, according to a global research study. The majority in percentage is 50% or greater, which implies that 50% of 100 working women or more prefer a better work-life balance to an increased salary. If we assume that the null hypothesis is correct and the number of women who say having a flexible work schedule is important is exactly 50, the standard error for the sample can be calculated as follows:
σ = sqrt(p(1-p)/n)
σ = sqrt(0.50(1-0.50)/100)
σ = 0.05
P(x<50) can be calculated as follows:
z = (x - np) / σ
z = (50 - 100(0.50)) / 0.05
z = -20
P(z < -20) = 0
Therefore, the probability that fewer than 50% of the sample say that having a flexible work schedule is either very important or extremely important to their career success is 0.
b) The proportion of women who said having a flexible work schedule is very important or extremely important to their career success is more than 43%. That implies the number of women in the sample who say having a flexible work schedule is important is greater than 43.
P(x > 43) can be calculated as follows:
z = (x - np) / σ
z = (43 - 100(0.50)) / 0.05
z = -1.4
P(z > -1.4) = 0.9192
Therefore, the probability that more than 43% of the sample says having a flexible work schedule is very important or extremely important to their career success is 0.9192.
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Given m∠LON\qquad m \angle LON m∠LON m, angle, L, O, N is a straight angle. M∠LOM=4x+30∘\qquad m \angle LOM = 4x + 30^\circ m∠LOM=4x+30 ∘ m, angle, L, O, M, equals, 4, x, plus, 30, degrees m∠MON=8x+90∘\qquad m \angle MON = 8x + 90^\circ m∠MON=8x+90 ∘ m, angle, M, O, N, equals, 8, x, plus, 90, degrees Find m∠MONm\angle MON m∠MON m, angle, M, O, N : OO O LL L NN N MM M ∘{}^{\circ} ∘ degrees Show Calculator Stuck?Watch a video or use a hint. Report a problem
Using the definition of a straight angle, the measure of angle MON is calculated as: 130°.
What is a Straight Angle?A straight angle is an angle that measures exactly 180 degrees. It is a flat angle, which means it has no curvature and looks like a straight line.
Therefore, we have:
m∠LOM + m∠MON = 180 [straight angle is equal to 180 degrees]
Substitute:
4x + 30 + 8x + 90 = 180
Solve for x:
12x + 120 = 180
12x = 180 - 120
12x = 60
x = 60/12
x = 5
m∠MON = 8x + 90° = 8(5) + 90
m∠MON = 130°
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Complete Question:
Given
m∠LON is a straight angle.
m∠LOM = 4x + 30°
m∠MON = 8x + 90°
Find m∠MON
Problem 2 Suppose you observe a single realization of a binomial random variable,
X∼Bin(n,p), and you want to test the hypothesis H0 :p=0.5 against H1:p=0.8
. (a) Derive the likelihood ratio, assuming the realization of X equalsx. (b) Give a full description of the most powerful test between H0 and H1 at the significance level α=0.1. (c) Suppose n=20
and x=15. Does your test from part (b) at the significance level α=0.1 reject H0?
α = 0.1
Answer: (a) Suppose X ∼ Bin(n, p). The likelihood function isL(p) = [n!/x!(n − x)!] px (n−p)−x.Then, we get the likelihood ratio asLR = [L(p1)] / [L(p0)]=[p1^x * (1−p1)^(n−x)] / [p0^x * (1−p0)^(n−x)]Let X be a binomial random variable. We can write the likelihood function as L(p) = [nCx px(1−p)n−x] . (b) Most powerful test: To derive the most powerful test, we need to find the likelihood ratio as LR = (p1/p0)x(1−p1/1−p0)n−x. Accept H0 if LR < c and reject H0 if LR ≥ c for some constant c.LRc= (0.8/0.5)^15*(0.2/0.5)^5 / (0.8/0.5)^15*(0.2/0.5)^5= (8/5)^15 = 34.99We reject H0 if the LR ≥ 34.99. Accept H0 if the LR < 34.99. (c) Reject H0 if the LR ≥ 34.99.LR = (0.8/0.5)15*(0.2/0.5)5 = 20.96Since 20.96 < 34.99, we accept H0. Therefore, at α = 0.1, we do not reject H0.
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In which number does the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728?
A. 137,982
B. 142,398
C. 292,389
D. 392,097
In number 292,389 the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728.
What is a number?
A number is a mathematical value used for counting or measuring or labelling objects. Numbers are used to performing arithmetic calculations.
The value of a digit depends on its place value in a number. For example, the digit 3 in the number 143,728 has a value of 3 x 1,000 = 3,000 because it is in the thousands place.
Let's call the number we are looking for "x". We want to find a number where the value of the digit 3 is 10 times as great as the value of the digit 3 in 143,728.
The value of the digit 3 in x is 10 times the value of the digit 3 in 143,728, so we can set up the equation:
3 x place value of 3 in x = 10 x 3,000
Simplifying this equation, we get:
3 x place value of 3 in x = 30,000
Dividing both sides by 3, we get:
place value of 3 in x = 10,000
So the digit 3 in x must be in the ten thousands place. Now we can eliminate choices A and B, because they do not have a digit 3 in the ten thousands place.
Checking the remaining choices, we find that only choice C has a digit 3 in the ten thousands place, with a value of 3 x 10,000 = 30,000. Therefore, the answer is:
C. 292,389
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WILL MARK BRAINLEIST!!!!
The last three problems in this set involve the Mean Value Theorem.
Let [a, b] = [0, 1] and let f(x) = x³. Find a number c = _______ such that
f(b) - f(a) = f'(c)(b − a).
Answer:
We have:
a = 0
b = 1
f(x) = x³
f'(x) = 3x²
Using the Mean Value Theorem, we have:
f(b) - f(a) = f'(c)(b - a)
Substituting the given values:
f(1) - f(0) = f'(c)(1 - 0)
Simplifying the left side of the equation:
1³ - 0³ = 1
Simplifying the right side of the equation:
f'(c) = 3c²
Therefore:
3c² = 1
Solving for c:
c² = 1/3
c = ±√(1/3)
Since c must be between 0 and 1, we have:
c = √(1/3)
Therefore, c = √(1/3).
I hope this helps!
irst, find the terms of the missing factor. 25 Now, write 125x-50y in factored form.
Answer:
25(5x - 2y)
Step-by-step explanation:
25 is the common factor for the equation. so the answer will be 25( 5x - 2y )
Which equation has x = 8 as its only solution?
O 3(2x + 1) + 5 = 4x + 2x + 8
O 2(x+3) = (6x - 4)
-
○ −3x+8 = x − 3x+6−½(2x − 4)
-
-
-
○ − (6x + 4) = 2x − 4
The equation −6x + 4 = -4 has x = 8 as its only solution, which can be verified using the substitution property of equality.
The equation that has x = 8 as its only solution is − (6x + 4) = 2x − 4. To solve this equation, we first need to move all the terms with x to one side and all the constants to the other side. To do this, we can first subtract 2x from both sides, giving us −6x − 4 = −4. We then need to subtract 4 from both sides, giving us −6x = −8. Finally, we need to divide both sides by −6 to get x = 8.
To check if this is the only solution, we can use the substitution property of equality. This property states that if two expressions are equal, then replacing one with the other should still make the equation equal. Therefore, if we substitute x = 8 into the original equation, we should get 0 = 0. To do this, we plug 8 into the equation and get − (6(8) + 4) = 2(8) − 4, which simplifies to −52 = 8 − 4, which is equal to 0 = 0. Since the equation still holds true, x = 8 is the only solution.
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