The 90% CI for the mean tension μ of all the screens produced on this day = (292.32, 320.32).
Describe Confidence Interval?A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence. It is calculated from a sample of data, and provides a measure of the precision and uncertainty of the estimate.
a. Objective: To construct a 90% confidence interval for the mean tension μ of all the screens produced on this day
STATE: State the parameter you want to estimate and the confidence level.
Parameter: In the given problem we are asked to estimate the mean tension μ of all the screens produced on this day, by listing a range of plausible values. Hence, the parameter of interest is the true mean tension of the population (μ).
Confidence level: As mentioned in the problem, we need to estimate the range of plausible values that the true mean tension (μ) can take with 90% confidence. Hence,
Confidence level = 90%
PLAN: Identify the appropriate inference method and check conditions.
Name of procedure: Statistical inference by Confidence interval approach - Since the population standard deviation is unknown, the underlying distribution would be assumed to follow a t distribution with n - 1 degrees of freedom.
Check conditions:
- The data is normally distributed; although the sample size is small.
From the summary statistics and dot plot, the data does appear to be symmetric and approximately normally distributed.
- The observations are randomly selected and are independent of one another
This is ensured the data collection
The population variance is unknown
Since the conditions are met, we may construct the 90% CI as folllows:
General Formula:
Sample Mean ± Margin of Error
= Sample Mean ± [tex]t_{n-1}[/tex]SE
Specific Formula:
A 100(1-a)% CI for population mean for unknown population standard deviation can be constructed using the formula:,
[tex]\bar x \± t_{a,n-1}\frac{s}{\sqrt{n} }[/tex]
where [tex]\bar x[/tex], s, n denote the mean, standard deviation and size of the sample and the t denotes the critical value for n - 1 degrees of freedom at a % level of significance.
Work:
From t table, the critical value of t for 20 - 1 = 19 df at 10% level of significance can be obtained as:
Table is mentioned below
Substituting the descriptive and the critical value in the CI formula:
306.32 ± (1.729) [tex](\frac{36.209}{\sqrt{20} } )[/tex]
306.32 ± (1.729)(8.097)
≈ 306.32 ± 14
≈ (292.32,320.32)
The 90% CI for the mean tension μ of all the screens produced on this day = (292.32, 320.32)
CONCLUDE:
We are 90% confident that the true mean tension μ of all the screens produced on this day would lie in the interval (292.32, 320.32).
b. Given:
The manufacturer’s goal is to produce screens with an average tension of 300 mV. Here, we need to test:
[tex]H_{0}[/tex] : μ= 300 Vs [tex]H_{a}[/tex] : μ ≠ 300
Using the Confidence Interval approach for testing the hypothesis,
Since, a Confidence Interval (CI) consists of all plausible values for true mean μ; it consists of all the values for which the null would not be rejected; if the 90% CI contains the null value '300', it would imply that '300' is also one of the plausible values the true mean μ can take; i.e. there would be a pretty good chance that μ is indeed equal to '300'; hence, we would fail to reject H0 based on such a CI.
Here, we find that the 90% CI for μ (292.32, 320.32) does contain the null value '300'. And hence, we fail to reject Họ: = H=300 at 10% level of significance. Hence, based on the interval, we may state that there is not enough convincing evidence that the screens produced this day don’t meet the manufacturer’s goal.
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The complete question is:
1/2x + 2y, when x = 7 and y=8 help me please
Answer:
39/2 or 19.5
Step-by-step explanation:
To evaluate the expression 1/2x + 2y when x = 7 and y = 8, we can substitute the values of x and y into the expression and perform the necessary calculations.
Given:
x = 7
y = 8
Plugging these values into the expression, we get:
1/2(7) + 2(8)
Now, we can follow the order of operations (PEMDAS/BODMAS) to simplify the expression:
1/2(7) + 2(8)
= 1/2 * 7 + 2 * 8 (Multiplication has higher precedence than addition)
= 7/2 + 16 (Performing the multiplications)
= 7/2 + 32/2 (Finding the common denominator for addition)
= (7 + 32)/2 (Adding the numerators)
= 39/2 (Simplifying the fraction)
So, the value of the expression 1/2x + 2y when x = 7 and y = 8 is 39/2 or 19.5.
Someone tell me of number 16 is correct please.
The volume of the composite figure that comprises two cuboids is calculated as: 150 ft³.
How to Find the Volume of a Cuboid?The volume of a cuboid is given by the formula:
V = l × w × h
where V is the volume, l is the length, w is the width, and h is the height of the cuboid.
The shape in number 16 comprises two cuboids. Find each and add together.
Volume of smaller cuboid = l × w × h = 5 × 3 × 2
= 30 ft³
Volume of larger cuboid = l × w × h = 10 × 6 × 2
= 120 ft³
The total volume = 150 ft³
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can anyone explain how to solve this
Mortgage (monthly)
Amount
$985.64
Cell phone (monthly)
$58.30
Groceries (twice a month
$154.00
Clothing (monthly with 25% job-related) $180.00
Water & electric (monthly)
S128.40
Weekly dinner & movie
$55.00
Property taxes (6 months)
$684.80
Car insurance (guarterly)
$330.00
Your realized income is $2.943.20/month. How much are your fixed expenses each month? How much could you save per month if you take 25% of your discretionary monies and put it in a savings account?
Answer:
To calculate the fixed expenses each month, we need to add up all the monthly expenses:
Mortgage: $985.64
Cell phone: $58.30
Groceries: $154.00 x 2 = $308.00
Clothing (with 25% job-related): $180.00
Water & electric: $128.40
Weekly dinner & movie: $55.00 x 4 = $220.00
Total monthly fixed expenses: $1,880.34
To calculate how much could be saved per month, we need to first calculate the discretionary income:
Realized income: $2,943.20
Fixed expenses: $1,880.34
Discretionary income: $2,943.20 - $1,880.34 = $1,062.86
25% of discretionary income: 0.25 x $1,062.86 = $265.72
Therefore, the amount that could be saved per month by putting 25% of the discretionary income in a savings account is $265.72.
Help please i need this asap!! I'll give 100 points
The range is expressed in interval notation as (-1, ∞)
How to find the function (f+g)(x)?To find the linear function f(x), let us use the table given.
A linear function with the following equation that passes through the points (a, g(a)) and (b, g(b)):
[tex]g(x) - g(a) = \frac{g(b)-g(a)}{b-a} (x-a)[/tex]
Because the g(x) line crosses through points (-6, 14) and (-3, 8), we have:
a = -6, g(a) = 16, b = -3 and, g(b) = 10
Therefore g(x)
[tex]g(x) - (16) = \frac{10-16}{-3-(-6)} (x--(6))\\g(x) - 16 = \frac{10-16}{-3+6} (x+6)\\g(x) - 16 = \frac{-6}{3} (x+6)\\g(x) - 16 = -2(x +6)\\g(x) = -2x -12+16\\g(x) = -2x+4[/tex]
now find the (f+g)(x).
[tex](f+g)(x) = f(x) + g(x) = x^{2} + 2x -5 -2x + 4\\(f+g)(x) = f(x) + g(x) = x^{2} - 1\\[/tex]
(f+g)(x) = (x-1)(x+1), therefore we get the values x = 1 and x = -1
The parabola's vertice has x-coordinate 0 (the midway between the roots). At x = 0, we get:
[tex](f +g)(x) = 0^{2} - 1 = -1[/tex]
Furthermore, because the coefficient of [tex]x^{2}[/tex] is 1, which is positive, this function indicates a parabola that has been opened upwards.
As a result, the function's minimal value is y = -1. As a result, the function's range includes all real numbers equal to or greater than -1.
The range is expressed in interval notation as (-1, ∞)
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the tables show the cost of bagels at four different bakeries. choose two bakeries with the same unit cost.
Answer:The diagram shows the market demand and supply curves for the bread market. You know that there are 250 identical bakeries operating in the market
Step-by-step explanation:
Solve on the interval [0,2pi):
1 - cos theta = 2-√3/2
Thus, the solution of the given cosine function is obtained for the angles- θ = 30º and θ = 330º between the intervals of [0,2pi).
Explain about the cosine function:The ratio of the triangle's side next to the angle to the hypotenuse is known as the cosine function. Thus, the cosine function does have a period of 2π, we can say.
Normally, radians rather than degrees are used when examining the cosine function in this manner. The common unit of measurement for angles in mathematics is the radian. 360° is equivalent to two radians, or one full circle.
Given data:
Function: 1 - cosθ = (2-√3)/2Interval - [0,2pi)1-cosθ = (2-√3)/2
cosθ = 1-(2-√3)/2
isolating the cosθ function:
cosθ = 1-(1-[√3/2])
cosθ = 1-1+√3/2
cosθ = √3/2
Now,
cos is √3/2 for ∏/6 = 30º and for 11∏/6 = 330º (Interval - [0,2pi))
Thus, the solution of the given cosine function is obtained for the angles-
θ = 30º and θ = 330º between the intervals of [0,2pi).
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Determine whether the following statements are TRUE or FALSE (do not write down the statements
just state TRUE or FALSE). [7 marks]
a. () ≥ 1 for any event .
b. () = 1 where is the Sample space.
c. If {} is any finite or infinite sequence of disjoint events, then (⋃
=1 ) = ∑ ()
=1 .
d. If ⊆ where and are two events in a sample space, then () ≤ ().
e. If and are two events in a sample space, then ( ∪ ) = () − () + ( ∩ ).
f. If and are two independent events in a sample space, then ( ⁄ ) = (∩)
() .
g. Mutually exclusive events are not independent
a. TRUE, b. TRUE, c. TRUE, d. TRUE, e. TRUE, f. FALSE, g. TRUE
How to determine whether the following statements are TRUE or FALSEa. TRUE: The probability of an event can never be negative, and can at most be equal to 1, which represents certainty.
b. TRUE: The sample space is the set of all possible outcomes of an experiment, and the probability of the sample space is always equal to 1, since one of the outcomes must occur.
c. TRUE: If the events in a sequence are disjoint, then they have no outcomes in common, so the probability of the union of the events is the sum of the probabilities of the individual events.
d. TRUE: If one event is a subset of another event, then the probability of the subset is less than or equal to the probability of the superset. This follows from the fact that the subset contains fewer outcomes than the superset.
e. TRUE: The probability of the union of two events is the probability of the first event plus the probability of the second event, minus the probability of the intersection of the events, which is the probability of both events occurring together. This is known as the inclusion-exclusion principle.
f. FALSE: The formula (P(A ∩ B) = P(A)P(B)) only applies to independent events, but not all independent events are mutually exclusive. For example, if A is the event of rolling a 4 on a die, and B is the event of rolling an even number, then A and B are independent, but not mutually exclusive.
g. TRUE: If two events are mutually exclusive, then they have no outcomes in common, so the occurrence of one event tells us that the other event cannot occur. This dependence means that the events are not independent.
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Hiya, I need help on a few questions URGENTLY
Boris has a coin collection that contains US, Euro and British coins.If the ratio of US to Euro coins is 5 to 2 and the ratio of Euro to British coins is 5 to 1. What is the ratio of US to British coins?
Amanda works at the local cafe and gets paid £10 per hour (h) and a fixed sum of £50 for a month. Write a formula for the money (m) that she will receive in a month?
A holiday package costs £190, plus £50 a day. What. formula shows the cost of the holiday, C for d days?
The ratio of US to British coins is 25 to 4.
The second term, £50, is a fixed sum she receives regardless of the number of hours worked.
The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.
How to solve the Problem?1. The ratio of US to Euro coins is 5 to 2, and the ratio of Euro to British coins is 5 to 1. To find the ratio of US to British coins, we can combine these ratios.
First, we need to make sure that the ratios have a common term. We can do this by multiplying the first ratio (US to Euro) by 5, which gives us a ratio of 25 to 10.
Next, we can use the second ratio (Euro to British) to convert Euro coins to British coins. Since the ratio is 5 to 1, for every 5 Euro coins, there is 1 British coin. So for every 10 Euro coins, there are 2 British coins.
Finally, we can combine the US to Euro ratio (25 to 10) with the Euro to British ratio (10 to 2) to get the ratio of US to British coins.
25 : 10 :: 10 : 2
Multiplying both sides by 2, we get:
50 : 20 :: 10 : 2
Simplifying, we get:
The ratio of US to British coins is 25 to 4.
2. To calculate Amanda's monthly pay, we can use the formula:
m = 10h + 50
where m is the total money Amanda receives in a month, and h is the number of hours she works.
The first term, 10h, represents her pay for the number of hours she works, which is £10 per hour. The second term, £50, is a fixed sum she receives regardless of the number of hours worked.
3. To calculate the cost of the holiday package for d days, we can use the formula:
C = 190 + 50d
where C is the cost of the holiday package, and d is the number of days.
The first term, £190, represents the fixed cost of the holiday package. The second term, £50d, represents the additional cost per day, which is £50 multiplied by the number of days.
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tigate
b) The construction of a tangent to a circle given a point outside the circle can be justified using the
second corollary to the inscribed angle theorem. An alternative proof of this construction is shown
below. Complete the proof. (5 points)
Given: Circle C is constructed so that CD = DE = AD; CA is a radius of circle C.
Prove: AE is tangent to circle C.
1.
2.
3.
4.
5.
C
A
Statements
CD=DE
D
Circle C is constructed so that CD = DE = AD;
CA is a radius of circle C.
CD DE LAD
AACD is an isosceles triangle;
AADE is an isosceles triangle.
m/CAD+mzDCA+mzADC = 180º;
mzDAE+mzAED+mZEDA=
180°
E
1.
2.
3.
4.
Given
Reasons
Definition of congruence
Isosceles triangle
Substitution property
5. Isosceles triangle theorem
The proof that AE is tangent to circle C is given below:
What is the angle addition postulate?The angle addition postulate is a fundamental concept in geometry that states that the measure of an angle formed by two adjacent angles can be obtained by adding the measures of the two angles.
More specifically, given two adjacent angles with measures A and B, the measure of the angle formed by the two adjacent angles (denoted as AOB) can be found by adding the measures of the two angles:
A + B = AOB
This postulate is often used in geometric proofs and can be applied to any adjacent angles, including those formed by intersecting lines, parallel lines, or polygons.
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A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 56.923 miles.
Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)
Part B: What is the equation for Sn? Show all necessary math work. (3 points)
Part C: If this pattern continues, what is the total number of miles the hiker will travel in 14 days? Round your answer to the hundredths place and show all necessary math work. (3 points)
Let x be the distance traveled on the first day. Then, the distance traveled on the second day is 1.1x, on the third day is 1.1(1.1x) = 1.21x, and so on. After 7 days, the total distance traveled is:
x + 1.1x + 1.21x + ... + (1.1)^6 x = 56.923
Using the formula for the sum of a geometric series, we have:
x(1 - (1.1)^7)/(1 - 1.1) = 56.923
x(1 - 1.1^7)/(-0.1) = 56.923
x = 56.923(-0.1)/(1 - 1.1^7) ≈ 4 miles
Therefore, the hiker traveled approximately 4 miles on the first day.
The equation for Sn, the sum of the first n terms of the sequence, is:Sn = x(1 - r^n)/(1 - r)
where x is the first term, r is the common ratio (in this case, 1.1), and n is the number of terms.
Using the equation for Sn from Part B, we can find the total number of miles the hiker will travel in 14 days:S14 = x(1 - 1.1^14)/(1 - 1.1)
S14 ≈ 167.63
Therefore, the hiker will travel approximately 167.63 miles in 14 days.
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Explain what the constant of proportionality means in the equation 1 over 2 x + y
In the equation 1 over 2 x + y=c, the constant proportionality is defined as c. It displays the line's y-intercept and slope.
What is constant of proportionality?If the ratio of one statistic to the other is constant, then there is a proportional relationship between the two variables.
The ratio of y to x is the constant of proportionality if x and y have a proportional connection. At times, we can also say that x is to y.
The proportionality constant, or c, in the equation 1 over 2 x + y = c serves as a gauge for how quickly two variables change. The proportionality constant's value doesn't change when the value of one of the variables does.
A linear equation with two variables, x and y, is 1 over 2x + y = c. In the x-y plane, it symbolises a straight line.
If x = 0
Then,
1/2(0) + y = c
y = c
The proportionality constant, c, can be seen in the equation
1 over 2 x + y = c.
This number, which is unrelated to the actual values of the variables, shows the relationship between the two variables x and y.
The slope of the line connecting the two variables is another name for the constant of proportionality.
Two variables, x and y, are included in the equation 1 over 2 x + y = c in addition to the proportionality constant. The two quantities that
are being compared are represented by these variables.
In the equation 1 over 2 x + y=c, the proportionality constant is defined as c. It displays the line's y-intercept and slope.
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The Complete questions as follows-
Explain what the constant of proportionality means in the equation 1 over 2 x + y = c
Please help I’m confused
The value of c in cubic and quadratic function is -6
What is the value of cWhen x = -1, the equation of the line becomes:
y = 3(-1) + 4 = 1
We can substitute this value of y into the equation of the curve:
1 = -2(-1)³ - 3(-1)² + 8(-1) + c
Simplifying and solving for c, we get:
1 = 2 - 3 + 8 + c
c = -6
Therefore, the value of c is -6.
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if i have 45 days left of school and need to do 69 lessons how many lessons a day would i need to do?
I just picked a random subject so....
500 points if answered correctly
Step-by-step explanation:
Simply divide lessons by days
69 lessons / 45 days = 1 8/15 = 1.53 lessons per day
If P = 3x² - x + 2 and Q = x² + 5x - 6, then P+ Q =
Answer:
Step-by-step explanation:
If P = 3x² - x + 2 and Q = x² + 5x - 6, then P+ Q = 3x² - x + 2 + x² + 5x - 6 =
4x^2 +4x - 4
D = 16 + 64 = 80
x12 = [tex]\frac{-4+-\sqrt{80} }{8}[/tex]
Flying against the wind, an airplane travels 2370 kilometers in 3 hours. Flying with the wind, the same plane travels 10160 kilometers in 8 hours. What is the rate of the plane in still air and what is the rate of the wind?
In still air, the jet's speed is 1030 mph, while the wind's speed 240 miles per hour.
What is velocity?It is the rate of change of an object's position with regard to time and a frame of reference. Although it may appear difficult, velocity is essentially speeding in a particular direction. Due to the fact that it is a vector quantity, velocity must be defined in terms of both magnitude (speed) and direction. It has a metre per second SI unit (ms-1).
What is speed?The distance travelled in relation to the time it took to travel that distance is how speed is defined. As speed simply has a direction and no magnitude, it is a scalar quantity.
Jet's velocity against wind is 2370/3=790 mile per hour and flying with wind it is 10160/8= 1270 miles per hour.
According to question,
Let the velocity of jet in still air be x miles per hour and velocity of wind be y miles per hour.
As such its velocity against wind is x−y and with wind is x+y and therefore
x−y=790 and x+y=1270
Adding the two 2x= 2060 and x=1030
and y=240
Hence velocity of jet in still air is 1030 miles per hour and velocity of wind is 240 miles per hour.
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The law of
applies during online sales
of shoes that is when consumers rush to buy products at 50% discounts.
The law of
The law of demand applies during online sales of shoes; that is when consumers rush to buy products at 50% discount.
What is the law of demand?In Mathematics and Economics, the law of demand can be defined as an economic theory which states that there exist a negative relationship between the price of a product (good) and the quantity of the product (good) that is being demanded by consumers.
This ultimately implies that, holding all the other factors constant, there would be a significant decrease (fall or decline) in the demand for a product (good) and service when the price of a product (good) and service in the market increases (rises), and vice-versa in accordance with the law of demand.
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Complete Question:
The law of ___________applies during online sales of shoes; that is when consumers rush to buy products at 50% discount
Find the area of the trapezoid 11 yd 11 yd 7 yd
Answer:
Step-by-step explanation:
A=1/2(b1+b2)h
=1/2 (11yd+11yd)(7yd)
=1/2(22yd)(7yd)
=(11yd)(7yd)
=77yd
Use the graph to answer the questions
WILL MARK BRAINLIEST!!
The diagram of the Gateway Arch on the coordinate plane, analyzed using quadratic equations indicates;
1. The vertex point is (50, 630)
2. The solution point are; (20, 0), and (80, 0)
3. Vertex form; f(x) = -0.7·(x - 50)² + 630
4. Factored form; f(x) = -0.7·(x - 20)·(x - 80)
What is a quadratic equation?A quadratic equation is an equation of the form f(x) = a·x² + b·x + c
1. The vertex obtained from the graphical diagram of the Gateway Arch indicates that the point corresponding to the vertex point is; (50, 9 × 70 = 630)
The vertex point is; (50, 630)
2. The solution are the points the curve of the Gateway intersects the x-axis, which are points where the y-axis values are zero, therefore;
The solutions are; (20, 0), and (80, 0)
3. The vertex form of a quadratic equation is; f(x) = a·(x - h)² + k
Where;
(h, k) = The coordinates of the vertex
Therefore;
(h, k) = (50, 630)
f(20) = 0 = a·(20 - 50)² + 630
a·(20 - 50)² = -630
a = -630/((20 - 50)²) = -630/900 = -7/10
a = -7/10 = -0.7
The vertex form quadratic equation is therefore; f(x) = -0.7·(x - 50)² + 630
4. The factored form of a quadratic equation is; f(x) = a·(x - r₁)·(x - r₂)
r₁ = 20, and r₂ = 80, a obtained from the vertex is; a = -0.7
The factored form is therefore; f(x) = -0.7·(x - 20)·(x - 80)
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Let's get this party started!
Warm Up Time!
Graph a relationship in which the value of y is 5 less than half the value of x.
Select two points on the coordinate grid. A line will connect the points.
2
3
Step 1: Write the equation (Translate from
words to a number sentence)
Step 2: Graph using Slope Intercept Form
What is the Y-intercept? Plot this point first!
What is the slope? Use the slope to plot a 2nd point
The slope of the equation is 1/2 and the y-intercept is -5.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
Step 1:
The relationship between x and y can be expressed as:
y = (1/2)x - 5
This equation says that y is equal to half of x, with 5 subtracted from that value.
Step 2:
To graph this equation using the slope-intercept form (y = mx + b), we can identify the slope and y-intercept.
The slope of the equation is 1/2, which means that for every increase of 1 unit in x, y increases by 1/2 unit.
The y-intercept is -5, which is the point where the line crosses the y-axis.
To graph the equation, we can start by plotting the y-intercept, which is the point (0, -5).
Next, we can use the slope to find another point on the line. Since the slope is 1/2, we can move up 1 unit and right 2 units (since the slope is rise over run, or change in y over change in x). This gives us the point (2, -4).
We can now draw a line that connects these two points, which represents the relationship between x and y.
The two points are:
(0, -5)
(2, -4)
The graph of the equation is in the attached image.
Hence, The slope of the equation is 1/2 and the y-intercept is -5.
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Consider the line shown on the graph.
Enter the equation of the line in the form v = mx + b
where m is the slope and b is the y-intercept.
An equation of this line in slope-intercept form is equal to y = 2x + 7.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (7 + 1)/(0 + 4)
Slope (m) = 8/4
Slope (m) = 2
At data point (0, 7) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 7 = 2(x - 0)
y - 7 = 2x
y = 2x + 7
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In a lab experiment, the decay of a radioactive isotope is being observed. At the
beginning of the first day of the experiment the mass of the substance was 1500
grams and mass was decreasing by 10% per day. Determine the mass of the
radioactive sample at the beginning of the 10th day of the experiment. Round to the
nearest tenth (if necessary).
The radioactive isotope has a final mass of 523 grams.
How to predict the mass of a radioactive isotope in time
Herein we find the case of a radioactive isotope, whose mass is decreasing exponentially in time. Whose expression is described below:
m(x) = a · (1 - r / 100)ˣ
Where:
a - Initial mass of the radioactive isotope, in grams.r - Decrease rate, in percentage.x - Time, in daysIf we know that a = 1500, r = 10 and x = 10, then the mass of the radioactive isotope is:
m(10) = 1500 · 0.90¹⁰
m(10) = 523.018
The final mass of the radioactive isotope is equal to 523 grams.
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Need help asap!!
Find the value of X
The answer is X + 5 = 10
X = 5
Please answer all the steps and what the question states for each question in the image I need this and you’ll get 55 points and mark Brainiest!
1. The new volume will be 60 cubic feet. 2. Molly will earn $31.25 if she sells all of the dog beds after subtracting the cost of the fabric.
Describe Volume?In general, volume refers to the amount of space occupied by an object or substance, measured in three dimensions: length, width, and height. It is a physical quantity that is typically expressed in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).
1. The volume of the cuboid is calculated as follows:
Volume = length x width x height
Volume = 5 ft x 3 ft x 2 ft
Volume = 30 cubic feet
If we double the height, the new height will be 2 x 2 ft = 4 ft. The new volume can be calculated as:
New Volume = length x width x new height
New Volume = 5 ft x 3 ft x 4 ft
New Volume = 60 cubic feet
Therefore, the new volume will be 60 cubic feet.
2. Step 1: Determine how many dog beds Molly can make with the fabric she bought.
Molly bought 12.5 yards of fabric, and she uses 2.5 yards of fabric for each dog bed. We can use division to find how many dog beds she can make:
12.5 yards / 2.5 yards per dog bed = 5 dog beds
Therefore, Molly can make 5 dog beds with the fabric she bought.
Step 2: Calculate the cost of the fabric for each dog bed.
Molly bought the fabric for $4.50 per yard, and she uses 2.5 yards of fabric for each dog bed. Therefore, the cost of the fabric for each dog bed is:
$4.50 per yard x 2.5 yards per dog bed = $11.25 per dog bed
Step 3: Calculate the revenue from selling one dog bed.
Molly sells each dog bed for $17.50.
Step 4: Calculate the profit from selling one dog bed.
Profit = revenue - cost
Profit = $17.50 - $11.25
Profit = $6.25
Step 5: Calculate the total revenue from selling all of the dog beds.
Molly can make 5 dog beds, and each dog bed sells for $17.50. Therefore, the total revenue is:
5 dog beds x $17.50 per dog bed = $87.50
Step 6: Calculate the total cost of the fabric for all of the dog beds.
Molly uses 2.5 yards of fabric for each dog bed, and she can make 5 dog beds. Therefore, the total cost of the fabric is:
2.5 yards per dog bed x 5 dog beds = 12.5 yards
$4.50 per yard x 12.5 yards = $56.25
Step 7: Calculate the total profit from selling all of the dog beds.
Profit = revenue - cost
Profit = $87.50 - $56.25
Profit = $31.25
Therefore, Molly will earn $31.25 if she sells all of the dog beds after subtracting the cost of the fabric.
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An actuarial study finds that in a sample of 2000 18-year-old drivers, 124 are involved in an accident.
cost of such an accident to the insurance company is $15 000. If the company wants to make a 20% profit on policies, what should they charge 18-year-old drivers?
Answer: Let's start by calculating the probability that an 18-year-old driver is involved in an accident:
P(accident) = 124/2000 = 0.062
Let's assume that the insurance company pays the full cost of the accident, which is $15,000. Then the expected cost of covering one 18-year-old driver is:
Expected cost = P(accident) x Cost of accident = 0.062 x $15,000 = $930
If the insurance company wants to make a 20% profit on policies, they need to charge a premium that covers their expected cost plus their desired profit. The premium, denoted by P, can be calculated as follows:
P = (Expected cost + Desired profit) / (1 - Profit margin)
where Profit margin is the percentage of the premium that represents the profit. In this case, Profit margin is 20%, or 0.20.
Substituting the values we have calculated, we get:
P = ($930 + 0.20 x $930) / (1 - 0.20)
= $1,236.00
Therefore, the insurance company should charge 18-year-old drivers a premium of $1,236.00 to make a 20% profit on policies.
Step-by-step explanation:
I need help with this please
Answer:
thats 4th grade math... 0_0 but the answer is 414 ft².
Step-by-step explanation:
So you need to do 23x18 which equals 414. Listen to your teacher in class please kid. But you do you boo
The distribution of scores on a standardized test is approximately normal with
a standard deviation of 40. Suppose a sample of 100 students had a mean
score of 180.23.
Find the margin of error for a 90% confidence interval for the mean score of all
students on this test. Round your answer to two decimal places.
Answer: The margin of error (ME) for a 90% confidence interval using a normal distribution with a known population standard deviation is given by:
ME = z* (σ/√n)
where z* is the z-score corresponding to the desired confidence level (in this case, 90% confidence), σ is the population standard deviation, and n is the sample size.
Using a z-score table or calculator, we find that the z-score corresponding to a 90% confidence level is 1.645.
Substituting the given values, we have:
ME = 1.645 * (40 / √100) = 6.58
Therefore, the margin of error for a 90% confidence interval for the mean score of all students on this test is 6.58. We can report the 90% confidence interval as:
180.23 ± 6.58 or (173.65, 186.81)
Step-by-step explanation:
In a 30°-60°-90° triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
3.) Which is greater: xº or 0x? Justify your answer
For the given expression - xº is greater than 0x as, xº = 1 and 0x = 0.
Explain about the exponents:The power or exponent of a number tells us how many times that number must be multiplied by itself in order to utilise it in a multiplication. Any integer, fraction, or decimal can serve as the basis in this situation. Moreover, the exponent might have either a positive or negative value.
a product's lawAccording to the law, we must add the exponents to obtain the product of exponential statements that have the same base.
quotient lawAccording to the law, we must subtract the exponents in order to divide two exponential expressions with the same base.
Given expression:
xº = 1 (any number raised to power 0 is always 1)
0x = 0 (any value multiplied with 0 becomes 0).
Thus, xº is greater than 0x as, xº = 1 and 0x = 0.
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Work out sheet below please
Answer:
-4 + 8 = 4
-2 + 6 = 4
-1 + 5 = 4
So the three pairs are -4 and 8; -2 and 6; and -1 and 5.
5. A type of bacteria doubles in number every 25 minutes. Find the constant k
for this type of bacteria, then write the equation for modeling this exponential
growth.
To find the constant k for this type of bacteria, we can use the formula for exponential growth:
N(t) = N0 * e^(kt)
where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, e is Euler's number (approximately 2.71828), and k is the constant we're looking for.
We know that the bacteria doubles in number every 25 minutes, which means that after 25 minutes, the number of bacteria will be 2 times the initial number (N0). Therefore, we can write:
N(25) = 2 * N0
Substituting this into the formula, we get:
2 * N0 = N0 * e^(k*25)
Dividing both sides by N0 and simplifying, we get:
2 = e^(25k)
Taking the natural logarithm of both sides, we get:
ln(2) = 25k
Solving for k, we get:
k = ln(2)/25 ≈ 0.0278
Therefore, the equation for modeling the exponential growth of this type of bacteria is:
N(t) = N0 * e^(0.0278t)
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