The probability that it is likely that a randomly selected cookie from the batch will be a chocolate chip cookie.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
If P(chocolate chip) = 0.50, it means that the probability of randomly selecting a chocolate chip cookie from the batch is 0.50 or 50%.
Interpreting this probability, we can say that it is likely that a randomly selected cookie from the batch will be a chocolate chip cookie since the probability is relatively high.
Therefore, the correct answer would be an option (B) Likely.
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Ethan is planning for his retirement. He has narrowed it down to two investment options. The first is an IRA where monthly payments are made, in the amount of $416.66, for 30 years. The second is a Roth IRA where annual payments are made, in the amount of $5000, for 30 years. If both compound interest at a rate of 2.5%, determine which account will yield the largest future value for Ethan, and how much greater that value will be than that of the other account. Round your final answer to the nearest cent.
The account that will yield the greatest future value is the first IRA. The difference in value would be $3,403.07.
Which account will yield the greatest IRA?The formula for calculating future value = annuity factor x monthly payments
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest raten = number of periodsFuture value with monthly compounding: $416.66 x [{1.00208^360] - 1 }/0.00208] = $222,916.59
r = monthly interest rate = annual interest rate / 12 = 2.5% /12 = 0.208%n = number of periods = number of years x rate of compounding = 30 x 12 = 360Future value with annual compounding: 5000 x [{1.025^30) - 1} / 0.0205] = $219,513.52
Difference in values = $222,916.59 - $219,513.52 = $3,403.07
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Adult men have heights with a mean of 69. 0 inches and a standard deviation of 2. 8 inches. Find the z-score of a man 63. 4 inches tall. (to 2 decimal places)
If the adult men have a height with mean as 69 inches , standard deviation as 2.8 inches , then the z-score for 63.4 inches tall man is .
To find the z-score of a man 63.4 inches tall, we use the formula: z = (x - μ)/σ ;
where x is = the individual height, μ is = the mean height, and σ is = the standard deviation.
Substituting the values, we get ;
⇒ z = (63.4 - 69.0)/2.8 ;
Simplifying, we get:
⇒ z = -5.6/2.8 = -2 .
⇒ z = -2 .
Therefore, the z-score of a man 63.4 inches tall is -2 which means that the man's height is 2 standard deviations below the mean height of adult men.
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hugh poured 100 kilograms of water into 10 kg of salt. He made ...... kilograms of ......% salt solution
Hugh poured 100 kilograms of water into 10 kg of salt. He made 110 kilograms of 9.09 % salt solution.
Finding the concentration of a solution:To find the mass of the solution add the mass of salt and the mass of the solution. To find the concentration of the solution divide the salt mass by the total mass of the solution and multiply by 100.
Here we have
Hugh poured 100 kilograms of water into 10 kg of salt.
After adding 100 kilograms of water to 10 kg of salt.
The total mass of the solution = 100 + 10 = 110 kg
The concentration of salt
= [ Mass of salt/ Mass of solution] × 100
= [ 10/110] × 100 = 9.09%
Therefore,
Hugh poured 100 kilograms of water into 10 kg of salt. He made 110 kilograms of 9.09 % salt solution.
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please help with this
Answer:
The monthly fee is [tex]\boxed{\$\;3.00}[/tex] and the yearly fee is [tex]\boxed{\$\;12.00}[/tex]
Step-by-step explanation:
The graph is a straight line whose equation can be represented in general terms as
y = mx + b
m = slope which is the rate of change of y with respect to x
b = y-intercept which is the value of y when x = 0; also the y-value where the line crosses the y-axis
To find m:
Take any two points on the line
To find b:
So the equation of the line is
y = 3x + 12
In this context 3 represents the monthly fee since for 1 month, the cost goes up by $3
The constant 12 represents the yearly cost of membership which is the amount incurred regardless of how long you are with the music group
Answers
Monthly fee: $3
Yearly fee = $12
Question 2 (2 points)
About what percent of the data falls after 34?
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
_________டப
25%
50%
75%
100%
From the given data points, about 50% of the data points are above the point 34.
What does a Percentage define?Percentage defines the parts of a number per fraction of 100 or a part per 100. It is usually denoted by the symbol '%'.
Percentage of a number is calculated by dividing the number with the whole and then multiply with 100.
Given are a set of data points.
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
The numbers are in ascending order.
Total number of data points = 16
Data points above 34 are,
36 38 40 42 44 46 48 50
Number of data points which are above 34 = 8
Percent of numbers above 34 = (8 / 16) × 100 = 50%
Hence the percent of the data falls after 34 are 50%.
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A map of a highway has a scale of 2 inches = 33 miles. The length of the highway on the map is 6 inches. There are 11 rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of 1 inch = 30 miles. How far apart are the rest stops on the new map?
Thus, the required rest stops are approximately 4.09 miles apart on the new map.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
The total length of the highway in miles can be found by using the scale of the original map. Since 2 inches on the map represent 33 miles in reality, 6 inches on the map represent:
= 6 inches × (33 miles/2 inches) = 99 miles
Since there are 11 equally spaced rest stops along the highway,
= (99 miles)/(11 intervals) = 9 miles per interval
To create the new map with a scale of 1 inch = 30 miles, we need to use a scale factor of (1/2) × (30/33) = 15/33.
Therefore, the distance between each rest stop on the new map can be found by multiplying the distance between rest stops on the old map by the scale factor,
= (9 miles per interval) × (15/33) = 4.09 miles per interval
So, the required rest stops are approximately 4.09 miles apart on the new map.
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Find the zeros of g(x) = 2x² + 32.
The zeros of g are x =
and x =
Mckenna spends 7/4 hours mopping the floors and 27/8 hours mowing and weeding the yard how many hours does she needs to spend on her chors
The total amount of time McKenna spends on her chores is 41/8 hours, or approximately 5.125 hours.
To find the total amount of time McKenna spends on her chores, we need to add up the time she spends mopping the floors and mowing and weeding the yard.
First, let's convert both the time spent mopping the floors and mowing and weeding the yard to a common denominator. The least common multiple of 4 and 8 is 8, so we can convert 7/4 hours to
7/4 * 2/2 = 7/2 hours.
Next, we can add the time spent on each chore:
7/2 hours + 27/8 hours = (14 + 27)/8 hours = 41/8 hours.
So, the total amount of time McKenna spends on her chores is 41/8 hours, or approximately 5.125 hours.
It is important to note that this calculation assumes that the time spent on each chore is a continuous amount of time, rather than broken up into smaller increments throughout the day.
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Someone please explain how to solve this.
Just multiply each side by side
Step-by-step explanation:1.Times one side by another
2. Times your answer by the third side
The graph of f(x) = ce^x crosses the y -axis at (0, c) where c is some constant: Where does the graph of g (x) = f(x)- d cross the y -axis? The graph of g (x) = f(x) -d crosses the Y ~axis
The graph of g(x)=f(x)-d crosses the y-axis at (0,c-d).
What does y-intercept mean?
The point on a line where it crosses the y-axis is known as the y-intercept. To put it another way, it is the value of y when x is equal to 0.
It is given that graph [tex]f(x)=ce^{x}[/tex] crosses the y-axis at (0,c).
Because at x=0,
[tex]f(0)=ce^{0}\\f(0)=c[/tex].
So, if g(x)=f(x)-d
[tex]g(x)=ce^{x}-d[/tex]
when x=0:
[tex]g(0)=ce^{0}-d\\g(0)=c-d[/tex]
So the graph of g(x)=f(x)-c touches the y-axis at (0,c-d).
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The amount of $100 is divided into 2 first prizes of equal value and 3 second prizes of equal value. Each prize is a whole number of dollars and first prize is at least 4 times the second prize. If the second prize is more than $6, find the amount of each prize.
The amount for first prize is $36 and second prize is $9.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the amount for Second price be x.
Then, amount of first Prize is 4x.
So, x+ x +x + 4x + 4x = 100
11x= 100
x= $9
So, the first prize would be (9 x 4)= $36
and, the second prize is $9 each.
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A plane is flying at a speed of 175 miles per hour.
The pilot plans on flying at this speed for the next
250 miles, plus or minus 25 miles. Find
the minimum and maximum number of hours th
plane will travel at that speed.
The maximum number of hours is 1.6 hours and the minimum number of hours is 1.6 hours.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, a plane is flying at a speed of 175 miles per hour.
The distance covered by the pilot, d = 250 ± 25 miles
We know that, speed = Distance/Time
The equation for the maximum number of hours is given as;
175 =(250+25)/t
t=275/175
t=1.6 hours
The equation for the minimum number of hours is given as;
175 =(250-25)/t
175=225/t
t=225/175
t=1.3 hours
Therefore, the maximum number of hours is 1.6 hours and the minimum number of hours is 1.6 hours.
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Ken bought a bike that was priced at $450. He was offered a 25% discount what was the discount on the bike
If discount offered is 25% then the discount on the bike is $112.50 by multiply the rate by the original price.
What is discount price?
Discount pricing is a type of promotional pricing strategy where the original price for a product or service is reduced with the aim of increasing traffic, moving inventory, and driving sales.
According to the question:
Ken bought a bike that was priced at $450
Discount percentage offered to him is 25%
To find the discount price, first the rate is usually given as a percent.
To find the discount, multiply the rate by the original price.
Discount = [tex]450 \times \frac{25}{100}[/tex]
Therefore the discount on the bike is $112.50
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Shape A is reflected in the line with equation x = 2 to give Shape B
In mathematical terms, each point (x, y) on Shape A is mapped to a point (2 + (2 - x), y) on Shape B as reflected line equation and explained as
When a shape is reflected in a line, it means that each point on the original shape is mapped to a corresponding point on the reflected shape that is symmetrical with respect to the reflecting line.
The line of reflection can be any straight line, and in this case, the line of reflection is given by the equation x = 2. To understand how the reflection works, imagine holding a mirror along the line x = 2 and placing Shape A on the mirror. The reflected shape, Shape B, would be the image that you see in the mirror. In mathematical terms, each point (x, y) on Shape A is mapped to a point (2 + (2 - x), y) on Shape B. This means that for each point on Shape A, we take its x-coordinate, subtract it from 2 to find the distance from the line of reflection, and then add that distance to 2 to find the x-coordinate of the corresponding point on Shape B. The y-coordinate remains the same.
The line of reflection acts as a dividing line between Shape A and Shape B, and the points on Shape B are exactly the same distance from the line of reflection as the points on Shape A, but on the opposite side. This means that Shape B is a perfect mirror image of Shape A, reflected across the line x = 2.
In summary, the reflection of Shape A in the line x = 2 maps each point on Shape A to a corresponding point on Shape B that is symmetrical with respect to the line of reflection. The result is a perfect mirror image of the original shape, reflected across the line.
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help i dont understand this fully
910x+45=28.3
can you please help me i have been on this question forever
Answer:
x = -0.01835
Step-by-step explanation:
1) Isolate the term with the variable, 910x, by subtracting 45 on both sides:
910x + 45 = 28.3910x + 45 - 45 = 28.3 - 45910x = -16.72) Divide both sides by 910 to solve for x
If all of the diagonals are drawn from a vertex of an n-gon, how many triangles are formed?A) n - 2B) n - 1C) nD) n + 1
The correct answer to the given question about all of the diagonals drawn from a vertex of an n-gon is option b) n-1
If all of the diagonals are drawn from a vertex of an n-gon, the number of triangles formed is equal to the number of non-diagonal sides of the n-gon. To see why, imagine selecting a vertex of the n-gon and drawing all of the diagonals from that vertex. Each diagonal connects that vertex to a non-adjacent vertex of the n-gon, which splits the n-gon into a series of triangles. The total number of triangles formed is equal to the number of non-diagonal sides of the n-gon, because each non-diagonal side forms one triangle with the selected vertex and one of its adjacent vertices. An n-gon has n sides, so the number of non-diagonal sides is equal to n - 3. This is because each vertex is connected to two adjacent vertices, so there are n - 2 diagonal sides emanating from the selected vertex, and the remaining n - 2 sides are non-diagonal. In addition, there are three sides at the selected vertex that are not counted as non-diagonal sides, so we subtract 3 from n - 2 to get n - 3. Therefore, the answer is (B) n - 1.
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Find the value of each trigonometric ratio. Express your answer as a fraction in lowest terms.
The value of the trigonometric ratios are
1. sin C = 21/29
2. sin C = 3/5
3. cos C = 12/13
4. cos C = 8/17
5. tan A = 12/35
6. tan X = 4/3
How to find the trigonometric ratiosThe trigonometry problem in a triangle is worked using an acronym SOH CAH TOA, this acronym means:
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
1. sin C
sin C = opposite / hypotenuse = 21/29
3. cos C = 12/13
cos C = adjacent / hypotenuse = 36/39 = 12/13 to the lowest term
6. tan X = 4/3
tan X = opposite / adjacent = 36/27 = 4/3 to the lowest term
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A rectangle flower garden is 9 2/5 feet long and 6 1/2 feet wide.What is the area of the flower garden?
Answer: 61 1/10
Step-by-step explanation:
9 2/5 x 6 1/2
The data in the table was produced by a researcher studying the
number of vegetables people ate for one week. Group A and Group B,
each with 20 people, recorded the vegetables that they ate. If a person
is chosen at random from those who ate at least 7 vegetables, what is
the probability that the person belonged to Group A?
The probability that the person belonged to Group A is given as follows:
Probability = number of people in Group A that ate at least 7 vegetables / total number of people that ate at least 7 vegetables.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The outcomes for this problem are given as follows:
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PLEASE HELP DUE TOMORROW:
Instructions: Fill in each matching colored box with same solution that makes each equation true. For example, if one red box was 3 then all the other red boxes must be 3. (JUST AN EXAMPLE)
Answer:
red=7
pink=4
purple=15
dark pink=22
gray=18
solve for v -62=8v-12v-18
Answer:
v=11
Step-by-step explanation:
Combined like terms and then divide at the end
Answer: V=11
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
If 30% of a number is 42 and 70% of the same number is 98, find 40% of that number.
Answer:
56 is 40% of the original number
Step-by-step explanation:
Let [tex]n[/tex] represent the original number
We are given that
30% of number is 42
70% of the same number is 98
Lets convert the precents to decimals
30% as a decimal is [tex]0.3[/tex]
70% as a decimal is [tex]0.7[/tex]
We can create an equation for each scenario
[tex]0.3n=42\\0.7n=98[/tex]
We can choose either one to evaluate [tex]n[/tex].
[tex]0.3n=42[/tex]
Lets solve for [tex]n[/tex].
Divide both sides by [tex]0.3[/tex].
[tex]n=\frac{42}{0.3}[/tex]
Evaluate [tex]\frac{42}{0.3}[/tex].
[tex]n=140[/tex]
Now that we know what the original number is we can calculate what 40% of the number is.
40% as a decimal is [tex]0.4[/tex].
[tex]140*0.4=56[/tex]
3b + 6 identify the first term of the algebraic expression. Indicate whether the term is a variable term or a constant term. For a variable term, identify the variable and the coefficient of the term
Variable and Coefficient of the given algebraic expression 3b + 6 is b and 3 respectively.
A variable is a symbol or letter that represents a value that can change or vary in a given context. Variables are often used to represent unknown or changing quantities in equations,
A coefficient is a numerical factor that is multiplied by a variable or variables in an algebraic expression. In other words, it is the number that appears in front of a variable.
3b + 6 identify the first term of the algebraic expression. Indicate whether the term is a variable term or a constant term. For a variable term, identify the variable and the coefficient of the term:
The first term of the algebraic expression 3b + 6 is 3b.
This is a variable term because it contains the variable "b".
The variable is "b" and the coefficient of the term is 3.
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<
Lesson 6-2
Question 7 of 15
Question 7
>
A is the incenter of A POR. Find m.ARU.
Need help with this question?
(3x + 2)°
20
(4x-9)º
40 R
Sav
The value off ARU based on the information will be 35°.
How to calculate the valueWe know, the incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle.
A)By property, AR is angle bisector of angle KRU.
Therefore m(<ARU) = m(<ARK) = 40°
m<ARU= 40°
B) The angle bisectors in a triangle are always concurrent and the point of intersection is known as the incenter of the triangle.
AU = AT = 20
Therefore,
AU = 20
C) AP is angle bisector of <QPR,
By definition of angle bisector
m<QPA = m<APR
3x+2 = 4x-9
4x-3x = 9+2
x =11
m<QPA = 3(11) +2 = 35°
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Factorise 3y²+12y ‼️‼️‼️
Answer:
3y(y + 4)
Explanation:
[tex]3y^{2} + 12y\\3(y^{2} + 4y)\\3y(y + 4)\\[/tex]
During a sale, a store offered a 35% discount on a tablet computer that originally sold for $340. After the sale, the discounted price of the tablet computer was marked up by 35%. What was the price of the tablet computer after the markup? Round to the nearest cent.
The marked-up price of the discounted tablet computer is $298.35.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, During a sale, a store offered a 35% discount.
So, The discounted price of the computer tablet is,
= [(100 - 35)/100]×340.
= (65/100)×340.
= $221.
Now, The price is marked up by 35% which is,
= [(100 = 35)/100]×221.
= (135/100)×221.
= $298.35.
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the mayor of a town believes that above 72% of the residents favor annexation of an adjoining community. is there sufficient evidence at the 0.05 level to support the mayor's claim? state the null and alternative hypotheses for the above scenario.
Null hypothesis: Proportion of residents favoring annexation <= 72%. Alternative hypothesis: Proportion of residents favoring annexation > 72%
The null hypothesis is that the proportion of residents who favor annexation is equal to or less than 72%. The alternative hypothesis is that the proportion of residents who favor annexation is greater than 72%.
To determine if there is sufficient evidence to support the mayor's claim, a hypothesis test should be performed. A common approach is to use a one-sample proportion test. This test compares the proportion of residents who favor annexation in a sample to the hypothesized proportion of 0.72.
Assuming a significance level of 0.05, if the p-value is less than 0.05, then there is sufficient evidence to reject the null hypothesis and conclude that the proportion of residents who favor annexation is greater than 72%.
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What is the sum of 9.72 × 108 and 1.93 × 107?
Answer:
The solution is 9,913 × 10⁸
Step-by-step explanation:
9,72 × 10⁸ and 1,93 × 10⁷
9,72 × 10⁸ + 1,93 × 10⁷
Factor the shape
= 10⁷ (9,72 × 10 + 1,93)
= 10⁷ (97,2 + 1,93)
= 10⁷ × 99,13
= 9,913 × 10⁸
Consider Juan Soto's wins above replacement statistics for the four seasons in the table. In which season did he have the greatest value to his team?
Answer: 2021
Step-by-step explanation:
