Answer:
C
Step-by-step explanation:
+) L = 3W + 6
+) L×W = (3W + 6)×W = 3W² + 6W ≤ 250
Find any solution(s) (refer to attachment) of and select the correct statement.
A. The equation has no solution.
B. The equation has two solutions.
C. The equation has one solution.
D. The equation has one solution and one extraneous solution.
Charlie invests $325 in an account that pays 8% simple interest for 15 years.
Use the simple interest formula, I = P ∙ r ∙ t, to answer the following questions.
How much interest will Charlie’s initial investment earn over the 15-year period?
How much money does Charlie have after the 15 years?
Answer: To answer these questions using the simple interest formula, we need to know the values of P (the principal or initial investment), r (the interest rate), and t (the time period in years).
In this case, P = $325, r = 0.08 (8% expressed as a decimal), and t = 15.
Using the simple interest formula, I = P ∙ r ∙ t, we can calculate:
I = $325 ∙ 0.08 ∙ 15 = $390
Therefore, Charlie's initial investment will earn $390 in interest over the 15-year period.
To calculate how much money Charlie will have after the 15 years, we need to add the interest earned to the initial investment.
The total amount of money that Charlie will have after the 15 years is:
Total amount = Initial investment + Interest earned
Total amount = $325 + $390
Total amount = $715
Therefore, Charlie will have $715 after 15 years.
Step-by-step explanation:
A partial table of nutrients and Daily Values (DVS)
based on a 2000-calorie diet is provided. The Sodium row and the Vitamin D row are completed, and each % of the DV is calculated.
Compare each amount with the amount on the given nutrition label. Now use the amount of
saturated fat on the nutrition label to calculate its
% of DV, X. Use the saturated fat amount on the nutrition label
to calculate the %DV for saturated fat.
Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.
What is the explanation for the above response?To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.
From the label, we see that the serving size contains 3.5g of saturated fat.
To calculate the %DV for saturated fat, we use the equation:
%DV = (amount of nutrient per serving / DV) x 100%
Plugging in the values for saturated fat, we get:
%DV = (3.5g / 19g) x 100%
%DV = 0.1842 x 100%
%DV ≈ 18%
Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.
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Naya has a pitcher that contains 3 cups of salted lassi, a yogurt drink with sait and sites. She pours 6 fluid ounces of lassi into each glass. If she uses all of the lassi, how many glasses does Naya use?
A. 2
B. 4
C. 16
D. 18
After 6 fluid ounces , Naya uses 4 glasses as a result.
Define ounces?A unit of weight is an ounce. There are various kinds of ounces, including avoirdupois, troy, and fluid ounces. One sixteenth of a pound is equivalent to one avoirdupois ounce . A troy ounce, often known as an apothecaries' measure, is equivalent to 480 grains or one-twelfth of a pound. A volume unit is a fluid ounce. 1/8 of a cup, 2 tablespoons, or 6 teaspoons make to one fluid ounce
In Naya's pitcher, there are three glasses of salted lassi.
She fills each glass with six fluid ounces of lassi.
By translating cups to fluid ounces and dividing the entire amount of lassi by the amount put into each glass, we can determine how many glasses Naya uses if she consumes all of the lassi.
8 fluid ounces make constitute a cup.
Consequently, 3 cups equal 24 fluid ounces (3 x 8).
24 divided by 6 results in:
4 glasses are equal to 24/6.
Naya uses four glasses as a result.
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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
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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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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please help me fill these boxes
The measurements for area of Jacobs yard are;
Part A = 6m x 3m = 18m
Part B = 4.5m x 3m = 13 m
Part C = 1/2 x 3m x 3m = 4.5 m²
Total area = 18m² + 13.5m² + 4.5m² = 36m²
How do you identify sections that would help in calculating area?To identify sections that would help in calculating area, you need to look for shapes or figures that can be divided into simpler geometric shapes, such as squares, rectangles, triangles, and circles.
Once you have identified the simpler shapes, you can use their formulas to calculate their areas and then add them together to find the total area of the larger shape or figure.
For example, a rectangle can be divided into two triangles or two smaller rectangles, and a circle can be divided into a sector or a ring. Breaking down a larger shape into smaller, simpler shapes can make it easier to calculate their areas accurately.
Jacob is putting tiles on the section of his yard labeled A, B, C. What is the area of the parts that need tiles?
Part A = .............. x ........... = ...........m
Part B = + .............. x ............. = ............ m
Part C = 1/2 x ................. x ............ = ............... m²
Total area = ................... + ..................... + .................. = ..............m
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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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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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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
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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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
Determine the effective tax rate for a taxable income of $115,500. Round theginal answer to the nearest hundredth
A) 18.71%
B) 17.20%
C) 24.10%
D) 24.75%
The effective tax rate for a taxable income of $115,500 is A) 18.71%
How to calculate the taxThe introductory $10,275 is subjected to a 10% tax burden, with the converted dollar amount representing $1,027.50 in taxes. The additional taxable sum of $30,900 ($41,175 - $10,275) is accessed at a 12% charge and aggregates to $3,708 worth of duties. An extra levy of 22% is imposed on the total $47,900 that lies between the two stipulated ranges ($89,075 - $41,175). The final evaluation stands at 24%, which provides an identical tax rate for the remaining $25,350 ($115,500 - $89,075). ).
Effective Tax Rate = (Total Tax Paid / Taxable Income) x 100%; which further articulates to ($21,357.50 / $115,500) x 100%,
= 18%
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how to solve 3(x+6) = x + 8 + x
the solution to the equation is x = -10.use the distributive property of multiplication over addition to simplify the left-hand side of the equation
what is distributive property ?
The distributive property is a mathematical property that is used to simplify expressions that involve multiplication and addition or subtraction. It states that when you multiply a number (or variable) by a sum or difference,
In the given question,
To solve the equation 3(x+6) = x + 8 + x, you can use the distributive property of multiplication over addition to simplify the left-hand side of the equation, and then combine like terms on both sides of the equation.
Here are the steps:
Distribute the 3 on the left-hand side of the equation:
3(x+6) = 3x + 18
Combine the two x terms on the right-hand side of the equation:
3x + 18 = 2x + 8
Subtract 2x from both sides of the equation:
3x - 2x + 18 = 2x - 2x + 8
Simplifying this expression gives:
x + 18 = 8
Finally, subtract 18 from both sides of the equation:
x + 18 - 18 = 8 - 18
Simplifying this expression gives:
x = -10
Therefore, the solution to the equation 3(x+6) = x + 8 + x is x = -10.
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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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In 2012, the population of a city was 5.51 million. The exponential growth rate was 3.82% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 10 million?
d) Find the doubling time.
helppppppp
Answer:
a) To find the exponential growth function, we can use the formula:
P(t) = P0 * e^(rt)
Where:
P(t) = the population at time t
P0 = the initial population (in this case, 5.51 million)
e = the mathematical constant e (approximately 2.71828)
r = the annual growth rate (in decimal form)
t = the number of years
Substituting the given values, we have:
P(t) = 5.51 * e^(0.0382t)
b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:
P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million
Therefore, the estimated population of the city in 2018 is approximately 6.93 million.
c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:
10 = 5.51 * e^(0.0382t)
e^(0.0382t) = 10/5.51
0.0382t = ln(10/5.51)
t ≈ 11.7 years
Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.
d) To find the doubling time, we can use the formula:
T = ln(2) / r
Where:
T = the doubling time
ln = the natural logarithm
2 = the factor by which the population grows (i.e., doubling)
r = the annual growth rate (in decimal form)
Substituting the given value of r, we have:
T = ln(2) / 0.0382 ≈ 18.1 years
Therefore, the doubling time for the population of the city is approximately 18.1 years.
how did slugger mcfist get a black eye
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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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)
*IG:whis.sama_ent
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
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.
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:
The most important of the Shinto gods is the sun goddess who gave light to the world, named ______.
Amaterasu
Susanoo
Tsukyomi
Izanagi
Answer: Amaterasu
Step-by-step explanation: The sun goddess Amaterasu is considered the most important of the Shinto gods because she is believed to be the ancestor of the Japanese imperial family, and therefore the protector of the Japanese people. She is also associated with agriculture, which was a vital part of Japanese society.
Use the box plot showing the ages of those who watch the television show 'The Code" to answer the question that follows.
Which value is the best approximation for the range in ages for the middle 50% of viewers?
A) 10
B) 15
C) 20
D) 45
The range in ages for the middle 50% of viewers is the interquartile range (IQR), which is the height of the box in the box plot. The best approximation is C) 20.
What is interqurtile range?The interquartile range (IQR) is a measure of statistical dispersion that represents the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset. It is a useful measure of spread because it is not influenced by outliers.
What is Range?Range is a statistical measure that represents the difference between the highest and lowest values in a set of data. It provides a simple indication of the spread or variability of the data.
According to the given information:
A box plot is a graphical representation of the distribution of a dataset. The box in the plot represents the middle 50% of the data, with the lower end of the box representing the 25th percentile (Q1) and the upper end of the box representing the 75th percentile (Q3). The distance between Q1 and Q3, which is represented by the height of the box, is called the interquartile range (IQR).
To answer the question, we need to find the best approximation for the range in ages for the middle 50% of viewers. From the box plot, we can see that the height of the box is approximately 20 units, which is the IQR. Therefore, the best approximation for the range in ages for the middle 50% of viewers is option C) 20. This means that 50% of viewers are between Q1-10 to Q3+10, where Q1 is the 25th percentile and Q3 is the 75th percentile.
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In a 30°-60°-90° triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
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
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:
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.