The Aerobics instructor teaches 7 classes each Saturday.
what is Algebraic expression?
An Algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.
To find the number of classes the Aerobics instructor teaches on Saturdays, we need to divide the total hours she teaches by the length of each class:
Total hours taught = 5 1/4 hours
Length of each class = 3/4 hour
Number of classes = (Total hours taught) / (Length of each class)
Number of classes = (5 1/4) / (3/4)
We need to convert the mixed number to an improper fraction first:
5 1/4 = (4 x 5 + 1) / 4 = 21/4
Now we can substitute the values:
Number of classes = (21/4) / (3/4)
fractions mean multiplying the first fraction by the reciprocal of the second fraction:
Number of classes = (21/4) * (4/3)
The 4 in the numerator and denominator cancel out, leaving us with:
Number of classes = 21/3
Dividing 21 by 3, we get:
Number of classes = 7
Therefore, To find the number of classes the Aerobics instructor teaches on Saturdays, we need to divide the total hours she teaches by the length of each class:
Total hours taught = 5 1/4 hours
Length of each class = 3/4 hour
Number of classes = (Total hours taught) / (Length of each class)
Number of classes = (5 1/4) / (3/4)
We need to convert the mixed number to an improper fraction first:
5 1/4 = (4 x 5 + 1) / 4 = 21/4
Now we can substitute the values:
Number of classes = (21/4) / (3/4)
Dividing fractions means multiplying the first fraction by the reciprocal of the second fraction:
Number of classes = (21/4) * (4/3)
The 4 in the numerator and denominator cancel out, leaving us with:
Number of classes = 21/3
Dividing 21 by 3, we get:
Number of classes = 7
Therefore, the Aerobics instructor teaches 7 classes each Saturday.
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what is 4x-3 i need a 6th grade explanation
Answer:
-12?
Step-by-step explanation:
PLEASEEEE HELP ASPPPPP
Answer:
R is (-10,4) S is (-1,7) T is (-1,-2) U is (-10,-2)
4: 7 and 12 : whats the ratio
8 The trinomial 4x^(2)-20x+25 is factorable. Which of these is the correct factorization? F (2x+5)(2x-5) G (2x-5)^(2) H (2x+5)^(2) J (x-5)(4x-5)
The trinomial 4x²-20x+25 is factorable. The correct factorization of the trinomial 4x²-20x+25 is H (2x+5)².
To factor a trinomial, we need to find two numbers that multiply to give the constant term (25) and add to give the coefficient of the middle term (-20). In this case, the two numbers are -5 and -5. We can then write the trinomial as (4x²-10x-10x+25), and factor by grouping:
4x²-10x-10x+25 = (4x^(2)-10x) + (-10x+25) = 2x(2x-5) - 5(2x-5) = (2x-5)(2x-5) = (2x+5)²
Therefore, the correct factorization of the trinomial is H (2x+5)²
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Alex has a pile of two pence coins. She swapped exactly half of them for the same number of 10p coins. Now she has £4.20. How much money did Alex have initially?"
Alex initially had 60 two pence coins.
What is Algebra?Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It is used to solve problems and represent mathematical relationships and formulas. In algebra, letters and other symbols are used to represent numbers and quantities, allowing us to express mathematical relationships and patterns in a more general and abstract way.
What is Simplification?In mathematics, simplification refers to the process of reducing an expression or equation to a simpler form. This is typically done by applying mathematical operations or rules to the expression or equation to eliminate unnecessary terms, factors, or operations.
For example, if we have the expression (x^2 + 4x + 4)/(x + 2), we can simplify it by factoring the numerator and canceling out the common factor with the denominator. This gives us (x + 2), which is a simplified form of the original expression.
In the given question,
Let's start by using some algebra to solve the problem.
Let's say that Alex initially had x two pence coins. After swapping half of them for 10p coins, she would have x/2 ten pence coins. We can use this information to set up an equation relating the value of her coins to the total amount of money she ended up with:
0.02x + 0.10(x/2) = 4.20
Simplifying this equation, we get:
0.02x + 0.05x = 4.20
0.07x = 4.20
x = 60
So Alex initially had 60 two pence coins. Checking our answer, we can see that she swapped half of them for 30 ten pence coins. The value of her 60 two pence coins is 0.02 x 60 = £1.20, and the value of her 30 ten pence coins is 0.10 x 30 = £3.00. Together, these add up to £4.20, as required.
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A rectangle has a length of 6 centimeters and a width of x + 10 centimeters. Write an expression to represent the rectangle’s: area (square centimeters
A 51-foot building casts a shadow 48 feet long. What is the angle of elevation of the sun? (Please use the exact ratio to calculate the angle and round your answer to the nearest tenth).
The angle of elevation of the sun is 19. 75 degrees
How to determine the valueIt is crucial to know there are six trigonometric identities.
These identities are;
secantcosecanttangentcotangentcosinesineFrom the information given, we have that;
The angle of elevation = θ
The opposite side = The height of the building
The adjacent side = shadow of the building
Using cosine identity, we have;
cos θ = 48/51
divide the values
cos θ = 0. 9412
Take the cosine inverse
θ = 19. 75 degrees
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Can someone help me find angle E,angle D,angle A and angle F and explain how you got it
The measure of the angles e, d, a, and f will be 26°, 122°, 102°, and 58°, respectively.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
By the supplementary property, the equation is given as,
f + 78° + 44° = 180°
f = 58°
By the complementary property, the equation is given as,
e + 64° = 90°
e = 26°
By the corresponding angles property, the equation is given as,
c = f
c = 58°
By the supplementary property, the equation is given as,
c + d = 180°
58° + d = 180°
d = 122°
By the corresponding angles property, the equation is given as,
b = 78°
By the supplementary property, the equation is given as,
a + b = 180°
a + 78° = 180°
a = 102°
The diagram is given below.
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Nathan caught 8, 10, 6, 5 and 14 ladybugs over the last 5 days. If he adds the 8 ladybugs he caught today to his data set, what will happen?
Nathan will therefore have captured a total of 51 ladybirds over the previous 6 days after including the 8 that he collected today in his data set.
what is set ?A set is a group of unique objects, known as elements, that are treated as a singular entity in mathematics. Anything, including letters, numerals, and even other sets, can be the objects. The components of sets are typically listed between curly braces and separated by commas. Sets are typically represented by capital letters. The set of even numbers, for instance, can be represented as 2, 4, 6, 8,..., where the dots signify that the pattern is infinite. Several operations, including union, intersection, and complement, can be used to modify sets. The set of all components that are members of either set A or set B or both is the union of the two sets A and B, denoted as A B.
given
Nathan's overall catch over the previous 6 days will rise if he includes the 8 ladybirds he caught today in his data set. The new data collection will be specifically:
8, 10, 6, 5, 14, 8
We merely add up all the figures in the data set to determine the new total number of ladybirds Nathan has captured:
8 + 10 + 6 + 5 + 14 + 8 = 51
Nathan will therefore have captured a total of 51 ladybirds over the previous 6 days after including the 8 that he collected today in his data set.
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A cat weighs 814 pounds.How many ounces does the cat weigh?
Answer: 13,024
Step-by-step explanation:
used a converter
Answer:
Step-by-step explanation:
16 ounces is equal to 1 pound so to convert ounces to pounds just multiply by 16. 814 times 16 is equal to 13,024 or thirteen thousand and twenty-four.
what would happen if you put your hand on the stove and got burnt, but put your hand back on 5 more times just to make sure it's actually hot?
If you put your hand on a hot stove and got burnt, it is a natural response to remove your hand from the stove to prevent further injury. However, if you choose to repeatedly put your hand back on the stove even after being burnt, you will continue to experience pain and potentially cause further damage to your skin and tissues.
Repeatedly exposing yourself to the source of the burn will not change the fact that it is hot and causing damage to your skin. In fact, each time you touch the hot surface, you are likely to make the burn worse, as the heat will continue to damage your skin and tissues.
Additionally, repeated exposure to the hot stove may lead to nerve damage, which can result in a loss of sensation in your hand, making it harder to recognize when you are in danger of burning yourself in the future.
It is important to listen to your body's natural responses to pain and remove yourself from harmful situations. In the case of a burn, it is best to seek immediate medical attention and follow proper first aid procedures to minimize damage and promote healing.
A major league baseball directly from home plate to second base (the diagonal of the square )?
The distance between home plate and second base in a Major League Baseball field is approximately 127.28 feet.
The distance from home plate to second base in a major league baseball field is 127 feet and 3⅜ inches, or approximately 127.28 feet. This is because the distance between each base (from home to first, first to second, etc.) is 90 feet, and the diagonal of a square is found by using the Pythagorean theorem: a² + b² = c². In this case, a and b are both 90 feet, so the equation becomes 90² + 90² = c². Simplifying and solving for c gives us c = 127.28 feet. Therefore, the distance from home plate to second base is 127.28 feet.
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Project Option 1-Individually 1 Change the equation to slope intercept form identify the slope and y-intercept of the equation. Be sure to show all your work 2 Describe how you would graph this line using the slope intercept method Be sure to write using complete sentences 4 Graph the function On the graph make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan 5 Suppose Saf's total profit on lunch specials for the next month is $1.503. The profit amounts are the same $2 for each sandwich and S graphs of the functions for the two months are similar and how they are different 02.03 Key Features of Linear Functions-Option 1 Rubric Requirements Student changes equation to slope-intercept form Student shows all work and identifies the slope and y-intercept of the equation Student writes a description which is clear precise, and correct, of how to graph the line using the slope-intercapt method Student changes equation to function notation Student explains clearly what the graph of the equation represents Student graphs the equation and labels the intercepts correctly Student writes at least three sentences explaining how the graphs of the two equations are the same and how they are different
The profits exist the same (slope) but the y-intercept is more increased than the actual diagram.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
The slope-intercept form of a linear equation is where one side includes only "y"
2x+ 3y= 1470
y= -2/3 x + 490
Hence, the y-intercept exists at 490 and the slope is -2/3x.
As, 2x + 3y = 1593
3y = -2x +1593
y = -2/3x +531
The profits exist the same (slope) but the y-intercept is more increased than the actual diagram.
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Fill in each blank with a number or expression such that each row and column adds up to the same total.
The blanks are filled by the following
8-3x 3x-6 4x-5 -2x+5
2x-3 3 2-x x
1-2x 4x-1 3x-2 -3x+4
5x-4 6-5x -4x+7 6x-7
How to fill the blanksThe blanks are filled by adding the complete row, this will be used for comparison and solve for other missing spaces.
let the missing value in each case be y
Adding the complete row gives
2x - 3 + 3 + 2 - x + x = 2x + 2
Column 1
8 - 3x + 2x - 3 + 1 - 2x + y = 2x + 2
6 - 3x + y = 2x + 2
y = 5x - 4
Column 2
y + 3 + 4x - 1 + 6 - 5x = 2x + 2
y + 8 - x = 2x + 2
y = 3x - 6
Row 4
5x - 4 + 6 - 5x + y + 6x - 7 = 2x + 2
6x - 5 + y = 2x + 2
y = -4x + 7
Column 3
y + 2 - x + 3x - 2 - 4x + 7 = 2x + 2
y + 7 - 2x = 2x + 2
y = 4x - 5
Row 1
8 - 3x + 3x - 6 + 4x - 5 + y = 2x + 2
-3 + 4x + y = 2x + 2
y = -2x + 5
Row 3
1 - 2x + 4x - 1 + 3x - 2 + y = 2x + 2
5x - 2 + y = 2x + 2
y = -3x + 4
check
This should be equal to Row 1 which is y = -2x + 5
Column 4
y + x - 3x + 4 + 6x - 7 = 2x + 2
y + 4x - 3 = 2x + 2
y = -2x + 5
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Heather runs 3 miles in 28 minutes. At the same rate, how many miles would she run in 42 minutes?
Heather runs 3 miles in 28 minutes, so at the same rate, she would run 4.494 miles in 42 minutes.
To find out how many miles Heather would run in 42 minutes at the same rate, we use the concept of unit rate. Unit rate is a comparison of two different quantities when they are combined together. In this case, we need to find the unit rate of Heather's running speed in miles per minute.
Step 1: Find the unit rate of Heather's running speed in miles per minute.
To do this, we divide the distance she ran by the time she took to run it:
3 miles ÷ 28 minutes = 0.107 miles per minute
Step 2: Use the unit rate to find out how many miles Heather would run in 42 minutes.
To do this, we multiply the unit rate by the time she runs:
0.107 miles per minute × 42 minutes = 4.494 miles
Therefore, Heather would run 4.494 miles in 42 minutes at the same rate.
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.
Leona has a jar containing some sweets, of which 90 are pear drops. She takes a random sample of 70 sweets from the jar and finds that 22 of these are pear drops. She then puts the 70 sweets back into the jar. Work out an estimate for the total number of sweets in the jar. Give your answer to the nearest integer.
Answer:
We can use the concept of proportion to estimate the total number of sweets in the jar.
Let's represent the total number of sweets in the jar by "x". We know that 90 of these are pear drops. So the proportion of pear drops in the jar is 90/x.
Leona takes a random sample of 70 sweets from the jar and finds that 22 of these are pear drops. So the proportion of pear drops in the sample is 22/70.
We can assume that the proportion of pear drops in the sample is roughly equal to the proportion of pear drops in the jar. Therefore, we can set up a proportion and solve for "x":
90/x = 22/70
Cross-multiplying, we get:
22x = 90 * 70
Dividing both sides by 22, we get:
x = 90 * 70 / 22
Using a calculator, we get:
x ≈ 287
Therefore, an estimate for the total number of sweets in the jar is 287, rounded to the nearest integer.
Answer:
We can use the concept of proportion to estimate the total number of sweets in the jar.
Let's represent the total number of sweets in the jar by "x". We know that 90 of these are pear drops. So the proportion of pear drops in the jar is 90/x.
Leona takes a random sample of 70 sweets from the jar and finds that 22 of these are pear drops. So the proportion of pear drops in the sample is 22/70.
We can assume that the proportion of pear drops in the sample is roughly equal to the proportion of pear drops in the jar. Therefore, we can set up a proportion and solve for "x":
90/x = 22/70
Cross-multiplying, we get:
22x = 90 * 70
Dividing both sides by 22, we get:
x = 90 * 70 / 22
Using a calculator, we get:
x ≈ 287
Therefore, an estimate for the total number of sweets in the jar is 287, rounded to the nearest integer.
Step-by-step explanation:
The marked price of an article is Rs, 2,500. If 40% discount is allowed and the 13% VAT is Charged, Find the selling price of the article with VAT?
Answer:
The answer to your problem is, 1130
Step-by-step explanation:
Calculation of work:
discount=40% of 2500
=40/100 x 2500
=1000
discount price=1000
VAT = 13% of 1000
How to find /\:
Percetage graph:
=13/100*1000
=130
price=1000+130
=1130.
Thus, the answer to your problem is, 1130.
3x-y=3 graph each linear equation
Answer:
y = 3x + 3
Step-by-step explanation:
The equation of the line is in standard form, which means we need to convert it into slope intercept form [tex]y=mx+b[/tex], where m is the slope and b is the y intercept.
[tex]3x-y=3[/tex]
Add 3x to both sides
[tex]y=3x+3[/tex]
Now we need to graph it:
The y intercept is 3, so we start at 3. Our slope is [tex]\frac{3}{1}[/tex] or 3, so we go down 3 and 1 to the left.
tell whether each equation has no solution or infinitely many solution. 3(x+2)=x+2x+2
Because 6 cannot equal 2, this statement is false. As a result, this equation cannot be solved.
What is an equation, exactly?By fusing two expressions, the equation generates a mathematical expression, similar to an expression. A common equation would have been 3x - 5 = 16. The solution to this equation reveals that the variable x has a value of 7.
First, we employ the distributive property to simplify the left side of the equation:
3(x + 2) = 3x + 6
The right side of the calculation is then made simpler by grouping related terms together:
x+2x+2 = 3x+2
The initial equation is now:
3x + 6 = 3x + 2
3x both from sides are subtracted, giving us:
6 = 2
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10. There are 60 people in a group. Males make up 40% of the group. If 25% of the males wear hats, how many males wear hats?
Answer:
6
Step-by-step explanation:
Step 1: How many males are there?
40% of 60 = 0.4 × 60 = 24
There are 24 males.
Step 2: Of the 24 males, how many wear a hat?
25% of 24 = 0.25 × 24 = 6
Answer: 6
Does anyone knows this Central Angle
The value of x is
x=-5
What is The value of x?
Generally, An angle is a figure formed by two rays (or line segments) that share a common endpoint. Angles are usually measured in degrees, with a full angle measuring 360 degrees.
Considering that the angle on a point is 630 , we have that the missing angle is
y=360-(148+92)
y=120
Therefore
y=x+125
Hence
x=y-125
x=120-125
x=-5
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Divide the monomials. Is the result of division a monomial? If yes, write the monomial in standard form. -0.26a^(3)b^(6)-:(4(1)/(3)a^(3)b^(2))
The result of the division is a monomial, and it is in standard form: [tex]-0.195b^4[/tex]
The result of the division of the monomials is a monomial. To find the result, we need to divide the coefficients and subtract the exponents of the same variables.
The steps are as follows:
Divide the coefficients: -0.26 ÷ (4(1)/(3)) = -0.26 ÷ (4/3) = -0.26 × (3/4) = -0.195
Subtract the exponents of the same variables: a^(3-3) = a^0 = 1, b^(6-2) = b^4
Multiply the result of step 1 and step 2: -0.195 × 1 × b^4 = -0.195b^4
Therefore, the result of the division is a monomial, and it is in standard form: -0.195b^4.
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(a) if tan∅ = 8/15, find the value of
sin∅ + cos∅(1- cos∅) (b)The angle of elevation of the top of a radio mask from a point due east of it and 96m away from its base is 30degrees. From another point, due west of the mask, the angle of elevation of the top is 60degrees. Calculate the distance of the second point from the base of the mast.
Answer:
Below in bold.
Step-by-step explanation:
The right triangle of which ∅ is a part has
Hypotenuse = sqrt(8^2 + 15^2)
= sqrt289
= 17,
So, sin ∅ = 8/17 and cos ∅ = 15/17
and
sin∅ + cos∅(1- cos∅)
= 8/17 + 15/17(1 - 15/17)
= 8/17 + 15/17 - 225/289
= 166/289.
(b) tan 30 = h/96 where h is height of the mast
h = 96 tan 30.
= 55.4256
tan 60 = 55.4256/d where d is the required distance
d = 55.4256/ tAN60
= 32 M
For the given word problem, write a system of equations, clearly define any variables, and show work for full credit.
A photographer is mixing 5% acetic acid solution with a 10% acetic acid solution to get two liters of a 7% solution.
How many liters of each solution should he add?
Answer:
Let x be the amount (in liters) of the 5% acetic acid solution to be added.
Let y be the amount (in liters) of the 10% acetic acid solution to be added.
The system of equations is:
x + y = 2 (the total amount of solution is 2 liters)
0.05x + 0.10y = 0.07(2) (the amount of pure acetic acid in the final solution is 7% of 2 liters)
Simplifying the second equation:
0.05x + 0.10y = 0.14
5x + 10y = 14 (multiplying both sides by 100)
We now have a system of two equations with two variables. We can solve it by substitution or elimination. Here, we'll use substitution:
x + y = 2 => x = 2 - y (subtracting y from both sides)
Substituting x in the second equation:
5(2 - y) + 10y = 14 (replacing x by 2 - y)
10 - 5y + 10y = 14
5y = 4
y = 0.8
So the photographer should add 0.8 liters of the 10% acetic acid solution and 2 - 0.8 = 1.2 liters of the 5% acetic acid solution. We can check that this solution satisfies both equations:
0.05(1.2) + 0.10(0.8) = 0.06 + 0.08 = 0.14
1.2 + 0.8 = 2
Therefore, the answer is:
The photographer should add 0.8 liters of the 10% acetic acid solution and 1.2 liters of the 5% acetic acid solution.
A sandwich shop makes home deliveries. The average amount of time from when an order is placed until when it is delivered can be modeled by the equation y = 2.5x + 5, where x is the number of miles between the shop and the delivery location and y is the time in minutes. Which of these statements are correct according to the model? Select two that apply.
The correct statements according to the model are: if the delivery location is 0 miles away, the order will take 5 minutes to be delivered, and if the delivery location is 10 miles away, the order will take 30 minutes to be delivered.
What is statements ?
A statement is a sentence that expresses a complete thought and can be either true or false. In mathematics, statements are often used to make claims or propositions that can be proven or disproven using logical reasoning and evidence.
The equation y = 2.5x + 5 models the average amount of time from when an order is placed until when it is delivered for a sandwich shop that makes home deliveries, where x is the number of miles between the shop and the delivery location, and y is the time in minutes.
To answer the question, we need to look at the statements and see which ones are correct according to the model:
If the delivery location is 0 miles away, the order will take 5 minutes to be delivered.
This statement is true because if x=0, then y=2.5(0)+5=5, which means the order will take 5 minutes to be delivered.
If the delivery location is 10 miles away, the order will take 30 minutes to be delivered.
This statement is true because if x=10, then y=2.5(10)+5=30, which means the order will take 30 minutes to be delivered.
If the delivery location is 1 mile away, the order will take 2.5 minutes to be delivered.
This statement is false because if x=1, then y=2.5(1)+5=7.5, which means the order will take 7.5 minutes to be delivered, not 2.5 minutes.
If the delivery location is 5 miles away, the order will take 20 minutes to be delivered.
This statement is false because if x=5, then y=2.5(5)+5=17.5, which means the order will take 17.5 minutes to be delivered, not 20 minutes.
Therefore, the correct statements according to the model are: if the delivery location is 0 miles away, the order will take 5 minutes to be delivered, and if the delivery location is 10 miles away, the order will take 30 minutes to be delivered.
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Find the minimum and maximum values of z=7x+3y , if possible, for the following set of constraints.
4x + 6y ≥ 24
x + 6y ≥ 12
x ≥ 0, y ≥ 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The minimum value is (Round to the nearest tenth as needed.) B. There is no minimum value.
The minimum value is 24
To find the minimum value of z=7x+3y, we must use the given constraints to determine the values of x and y.
First, solve 4x + 6y ≥ 24. Rearrange the equation to solve for x: x ≥ (24 - 6y) / 4.
Next, solve x + 6y ≥ 12. Rearrange the equation to solve for y: y ≥ (12 - x) / 6.
Using the two equations, determine the possible values of x and y:
If y = 0, then x = 6
If x = 0, then y = 2
Substitute the possible values of x and y into the equation z = 7x + 3y and find the minimum value:
z = 7(6) + 3(0) = 42
z = 7(0) + 3(2) = 24
Therefore, the minimum value of z is 24.
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Quadrilateral ABCD is inscribed in a circle.
What is the measure of angle A?
Enter your answer in the box.
m/A=
The measure of ∠A is 77 degrees.
What is Circle?A round-shaped figure that has no corners or edges is called as Circle.
ABCD is the quadrilateral which is inscribed in the circle.
We have to find angle A measure.
The opposite angles of a cyclic quadrilateral are supplementary so we apply to find the measure.
Therefore, angle A + angle C = 180 degrees
2x+9+3x+1=180
5x+10=180
Subtract 10 from both sides
5x=170
Divide both sides by 5
x=34
Now plug in x value in angle A, 2x+9.
∠A=2x+9
=2(34)+9
=68+9
=77 degrees.
Hence, the measure of ∠A is 77 degrees.
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A local county has an unemployment rate of 6.5%. A random sample of 20 employable people are picked at random from the county and are asked if they are employed. The distribution is a binomial. Round answers to 4 decimal places. a) Find the probability that exactly 3 in the sample are unemployed. b) Find the probability that there are fewer than 3 in the sample are unemployed. c) Find the probability that there are more than 2 in the sample are unemployed. d) Find the probability that there are at most 3 in the sample are unemployed.
The distribution is binomial.
a) The probability that exactly 3 in the sample are unemployed is 0.0311, b) The probability that there are fewer than 3 in the sample are unemployed is 0.5354, c) The probability that there are more than 2 in the sample are unemployed is 0.4646, d) The probability that there are at most 3 in the sample are unemployed is 0.5665.
The binomial distribution formula is P(x) = (nCx)(p^x)(q^(n-x)), where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.
a) To find the probability that exactly 3 in the sample are unemployed, we plug in the values: n = 20, x = 3, p = 0.065, and q = 0.935.
P(3) = (20C3)(0.065^3)(0.935^17) = 1140(0.000274625)(0.099961375) = 0.0311
b) To find the probability that there are fewer than 3 in the sample are unemployed, we need to find the probability that 0, 1, or 2 are unemployed and add them together.
P(0) = (20C0)(0.065^0)(0.935^20) = 1(1)(0.1645) = 0.1645
P(1) = (20C1)(0.065^1)(0.935^19) = 20(0.065)(0.1725) = 0.2249
P(2) = (20C2)(0.065^2)(0.935^18) = 190(0.004225)(0.1812) = 0.1460
P(<3) = P(0) + P(1) + P(2) = 0.1645 + 0.2249 + 0.1460 = 0.5354
c) To find the probability that there are more than 2 in the sample are unemployed, we can subtract the probability that there are fewer than 3 from 1.
P(>2) = 1 - P(<3) = 1 - 0.5354 = 0.4646
d) To find the probability that there are at most 3 in the sample are unemployed, we can add the probabilities that there are 0, 1, 2, or 3 unemployed.
P(≤3) = P(0) + P(1) + P(2) + P(3) = 0.1645 + 0.2249 + 0.1460 + 0.0311 = 0.5665
Therefore, the answers are:
a) 0.0311
b) 0.5354
c) 0.4646
d) 0.5665
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Rick saved $400. On Rick's birthday, his brother Jon gave him
1/8 of savings. Including the gift, Rick has $475. Write and solve
an equation to determine Jon's savings before he gave Rick the
gift.
Jon's savings before he gave Rick the gift was $600. An equation to represent this situation: 400 + (1/8)x = 475
To determine Jon's savings before he gave Rick the gift, we can use an equation. Let's represent Jon's savings with the variable x.
According to the problem, Jon gave Rick 1/8 of his savings, which is equal to (1/8)x. We also know that Rick originally had $400 and after receiving the gift, he had $475. So we can write an equation to represent this situation:
400 + (1/8)x = 475
Now, we can solve for x to find out Jon's savings before he gave Rick the gift. First, let's isolate the variable on one side of the equation:
(1/8)x = 475 - 400
(1/8)x = 75
Next, we can multiply both sides of the equation by 8 to get rid of the fraction:
x = 75 * 8
x = 600
So, Jon's savings before he gave Rick the gift was $600.
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Gloin is pretty smart and thinks about the future. We currently has $300,000 set aside for the future. We knows he should invest this capital so it gains interest but is also unsure. His advisor suggests that he split the money up in three investments: a. A high yield savings account that yields 9% per year, compounded quarterly for 5 years. b. A municipal bond that yields 6.78% per year, compounded twice a year for 10 years. If the first investment yields $200,000 at maturity and the second investment yields $100,000 at maturity then how much money does he have left over today?
The amount left over is $120,499.85.
What is the amount left over?The present value of the amount invested in the municipal bond and the high yield savings account has to be determined.
Present value = FV ÷ (1 + r)^(nm)
Where:
r = interest rate
m = number of compounding
FV = future value
Present value of the future value in the high yield savings account:
r = 9/4 = 2.25%
m = 4
200,000 ÷ ( 1 + 0.0225)^(4 x 5)
200,000 ÷ (1.0225^20)
= 128,163.29
Present value of the future value of the municipal bond: r = 6.78 / 2 = 3.39%
m = 2
100,000 ÷ (1 + 0.0339)^(2 x 10)
100,000 ÷ (1.0339^20) = $51,336.86
Amount left over = $300,000 - $51,336.86 - 128,163.29 = $120,499.85
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