The width in miles, of the park is equal to 5/6 miles.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width or base of a rectangle.L represents the length or height of a rectangle.Substituting the given points into the area of rectangle formula, we have the following;
25/54 = 5/9 × W
Width, W = 25/54 × 9/5
Width, W = 5/6 miles.
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Complete Question:
The area of a rectangular city park is 25/54 square miles. The length if the park is 5/9 of a mile. What is the width in miles, of the park?
3x^2-9x+2 in standard form
The standard form of 3x² - 9x + 2 is 3x² - 9x + 2.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given:
A quadratic function,
3x² - 9x + 2.
The standard form of the quadratic function is
ax² + bx + c.
The standard form of 3x² - 9x + 2 is 3x² - 9x + 2.
Therefore, 3x² - 9x + 2.
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Pls help me this is very hard
Answer:
Step-by-step explanation:
35tu
(5 and 7 are like terms, and you put the 't' and 'u' in alphabetical order)
Answer:
ut=35
Step-by-step explanation:
5×u×t×7=0
collect like terms
ut=5×7
ut=35
A regulation basketball has a DIAMETER of about 9.2 inches.
What is the volume to the nearest tenths?
Rounding to the nearest tenth, the volume of the basketball is: V ≈ 381.7 cubic inches ≈ 381.8 cubic inches (rounded to the nearest tenth)
What is volume?
Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.
For solid objects, volume refers to the amount of space the object occupies in three-dimensional space.
The diameter of a basketball is 9.2 inches, which means the radius is half of that, or:
r = 9.2 / 2 = 4.6 inches
The formula for the volume of a sphere is:
V = (4/3)πr³
Substituting the radius into the formula, we get:
V = (4/3)π(4.6)³
V ≈ 381.7 cubic inches
Therefore, Rounding to the nearest tenth, the volume of the basketball is: V ≈ 381.7 cubic inches ≈ 381.8 cubic inches (rounded to the nearest tenth)
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$190 is invested in an account earning 7.1% interest (APR), compounded quarterly. Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
Answer:
Value of account after t years is
[tex]A = \boxed{190( 1.0178)^{4t}}[/tex]
Percentage of growth per year
CAGR = [tex]\boxed{7.31\%}[/tex]
Step-by-step explanation:
The generalized equation for the accrued value of an amount P(the principal) deposited at i% annual interest compounded n times a year for t years is
[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]
where r = i/100, the interest rate expressed as a decimal
Given P = $190
i = 7.1% ==> r = 7.1/100 = 0.071
Since the interest is compounded quarterly and there are 4 quarters in a year, the interest is compounded 4 times a year so n = 4
[tex]A = 190 \left(1 + \dfrac{0.071}{4}\right)^{4t}[/tex]
[tex]A = 190\left(1 + 0.01775\right)^{4t}}\\\\A = 190( 1.01775)^{4t}[/tex]\
Rounding the annual growth rate to 4 decimal places gives
[tex]A = P(1.0178)^{4t}[/tex]
In one year, the investment of $190 will grow to
[tex]A = 190(1.0178)^{4}[/tex]
[tex]A = $203.89[/tex]
Compound Annual Growth = = 203.89 - 190 = $13.89
Compound Annual Growth Rage(CAGR) = $13.89/$190 = 0.073105
As a percentage, CAGR Percent = 0.073105 x 100 = 7.3105% or rounded to nearest hundredth it would be 7.31%
At the art store, Maria bought a poster board for $0.65, glitter for $3.29, and glue for $1.99. She told Carl that she paid $5.00 for everything. True or False?
Answer:
False
If we wanted to solve this equation, we can use this expression:
0.65 + 3.29 + 1.99 = 5.93Maria must have spent $5.93, making her statement false.
HELP DUE TONIGHT!!!
The volume of the cone in terms of π is 96π inches³.
How to find the volume of a cone?The cone has a base radius of 6 inches and the height of the cone is 8 inches. Therefore, the volume of cone can be found as follows:
volume of cone = 1 / 3 πr²h
where
r = radius of the coneh = height of the coneTherefore,
r = 6 inches
h = 8 inches
Hence,
volume of cone = 1 / 3 × π × 6² × 8
volume of cone = 1 / 3 × π × 36 × 8
volume of cone = 12 × 8 × π
volume of cone = 96π inches³
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Given sin(-t) = 2/3, find csc (t).
Answer:
csc(t) = -3/2
Step-by-step explanation:
Given sin(-t) = 2/3, we can find the value of csc(t) as follows:
sin(-t) = 2/3
sin(t) = -2/3 (since the sine function is an odd function)
Since csc(t) = 1/sin(t), we have:
csc(t) = 1/sin(t) = 1/(-2/3) = -3/2
Answer:
[tex]\displaystyle \csc(t)=-\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]\displaystyle \sin(-t)=\frac{2}{3}\\\\\sin(t)=-\frac{2}{3}\\ \\\frac{1}{\sin(t)}=\frac{1}{-\frac{2}{3}}\\\\\\\csc(t)=-\frac{3}{2}[/tex]
The second step can be done because sin(-t) is an odd function.
can someone please help me(10 points will give brainliest!!!)
The value of the given function f(4 + h) - f(4) is 5h(x)² + 40h(x)
What is a functionA function is a mathematical concept that maps a set of inputs to a set of outputs with a definite rule. In mathematics, a function is a set of ordered pairs (input, output) where each input is associated with exactly one output. The input is usually referred to as the argument of the function and the output is the value of the function at that argument.
f(x) = 5x²
f(4 + h) - f(4)
f(4 + h(x)) = 5(4 + h(x))²
f(4) = 80
Substituting the values into each other;
5(4+h(x))² - 80
f(4 + h) - f(4) = 5h(x)² + 40h(x)
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Please help I’ll give brainliest
Answer:
Step-by-step explanation:
Given,f(x)=3x^2-x+2
now,f(-4)=3(-4)^2-(-4)+
=3(16)+4+2
=48+4+2
=54
So,f(-4) =
Answer:
The solution is 54
Step-by-step explanation:
f(x) = 3x²-x+2
f(-4) = 3(-4)²-(-4)+2
f(-4) = 48+4+2
f(-4) = 52+2
f(-4) = 54
Leslie and Ben are designing a neighborhood. Drawing their designs out on a grid, they determined that the lot for the community mailboxes would be centered at (0,0). They created the first road to pass through lots centered at (3,1) and at (9,3). They want to make another road that intersects the first road at a 90-degree angle, and they want it to intersect the center of the lot at (3,1). Determine the equation for this second road.
The equation of the second road is y = -3x + 10
The location of the mail box = (0, 0)
The first road passes through the points (3, 1) and (9,3)
The slope of the line is the change in y coordinate with respect to the change in x coordinate
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
m = 3-1 / 9-3
m = 2/6
m = 1/3
The next road is 90 degrees to the first road
Then the slope of the second line will be
m1 = -1/m
= -1/(1/3)
= -3
The second road passing through the point (3, 1)
The equation of line
y = mx + b
Substitute the given values in the equation
1 = -3 × 3 + b
1 = -9 + b
b = 1 +9
b = 10
Therefore, the equation will be y = -3x + 10
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a drawer contains 6 red so cks, 4 green so cks, and 2 black so cks. two so cks are chosen at random. what is the probability that they match?
Answer: 2/12 (1/6 simplified) I think I don’t know I didn’t think much about it
Step-by-step explanation:
Martha has a box of assorted chips. There are 2 bags of Doritos, 4 bags of Cheetos, and 5 bags of plain
potato chips.
a. What is the probabilty that Martha will grab a bag of potato chips? Write your answer as an unreduced
fraction & a percent.
b. If Martha grabs a bag of potato chips and takes them to eat with her lunch, what is the probability that her
friend, Jamie, will grab a bag of potato chips out of the box next? Write your answer as an unreduced fraction
& a percent.
c. Is this an independent or dependent event? EXPLAIN.
Yvette is saving money to buy holiday gifts. She will save the money she makes at her part-time job. However, she borrowed $25 from her sister that she has to pay back before she can start saving.
This relationship can be shown by a linear function. Below is a table showing how many hours Yvette has worked (input), and how much money she's saved (output).
Hours Worked (x) Amount Saved (y)
0 -$25
4 $14
8 $53
12 $92
16 $131
Which of the following statements are true regarding the graph of this linear function? Select all that apply.
Group of answer choices-
The slope of the line, 25, is the amount of money she makes per hour of work.
The slope of the line, 9.75, is the amount of money she starts with having worked 0 hours.
The y-intercept of the line, 0, is the amount of money she starts with, since she's worked 0 hours.
The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.
The slope of the lines, 9.75, is the amount of money she makes per hour of work.
Answer:
Step-by-step explanation:
The statements that are true regarding the graph of this linear function are:
The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.
The slope of the line, 25, is the amount of money she makes per hour of work.
The statement:
The slope of the line, 9.75, is the amount of money she starts with having worked 0 hours. is not true.
And the statement:
The y-intercept of the line, 0, is the amount of money she starts with, since she's worked 0 hours. is not true because the y-intercept is not 0, it's -25, which represents the amount of money she owes to her sister.
In the U.S., shoe sizes are defined differently for men and women, but in Europe, both sexes use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes. What might be the problem with either the mean or the median as a measure of center?
To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them.
The problem with either the mean or the median as a measure of center in this case is that the data is not separated by gender, and the shoe size distributions for men and women are likely to be different. Therefore, computing the mean or median shoe size across all students may not accurately represent the typical shoe size for men or women separately.
For example, if the men in the sample have, on average, larger shoe sizes than the women, then the mean shoe size across all students may be biased towards the larger sizes, even though the majority of the students are women. On the other hand, if there are a few male students with very large shoe sizes, then the median shoe size across all students may be biased towards the larger sizes as well, even if most of the students are women with smaller shoe sizes.
To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them. Alternatively, a better measure of center might be to report the mode, which represents the most common shoe size in the data.
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. A rectangle’s length is twice its width. Its perimeter is 156 meters. What is the rectangle’s length?
Answer:
Step-by-step explanation:
Perimeter is equal to 2 times length and 2 times the width.
This problem says the length is twice the width.
Let's use 2w for the length:
Here's the equation:
2L + 2W = 156
Substitute 2W for the length,
2(2W) + 2W = 156
4W + 2W = 156
6W = 156
6W/6 = 156/6
w = 26
so length is 2 times 26 = 56 Length = 56 m
Talia deposits $100 into her account. If her account balance grows exponentially and she makes no additional deposits or withdrawals, which of these shows her possible balance amounts for the first four years?
The balance of Talia's account will grow exponentially if the interest is compounded annually.
The formula for calculating the balance after n years can be represented as:
[tex]B = P * (1 + r)^n[/tex]
where B is the balance, P is the principal (initial deposit), r is the interest rate as a decimal, and n is the number of years. If Talia deposits $100 into her account and the interest rate is x%, the possible balance amounts for the first four years can be calculated as follows:
Year 1: [tex]B = 100 * (1 + 0.01x)^1[/tex]
Year 2: [tex]B = 100 * (1 + 0.01x)^2[/tex]
Year 3: [tex]B = 100 * (1 + 0.01x)^3[/tex]
Year 4: [tex]B = 100 * (1 + 0.01x)^4[/tex]
It is important to note that the interest rate, x, must be provided in order to calculate the exact balance amounts.
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How many digits do you need to number all 178 buildings on a street?
You need 4 digits to number all 178 buildings on a street.
Explain Digits.In the decimal number system, digits are the symbols used to represent numbers. The 10 digits of the decimal numeral system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. By utilizing them in various combinations and places, these digits are used to represent all possible decimal integers. A digit's value is also affected by its position in a number according to the place value system. For instance, the digits 1 and 2 in the number 123 each stand for one hundred, twenty, and three respectively. Digits are the fundamental components of numbers and are frequently used in daily life for calculations, measurement, and counting.
To find the number of digits in a number, you can take the logarithm of the number with base 10 and add 1. So, using the logarithm function, you can calculate:
log10(178) + 1 = 2.25 + 1 = 3.25
Therefore, you need 4 digits to number all 178 buildings on a street.
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Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship.
your daily calorie intake and your GPA
The correlation between your daily calorie intake and your GPA is not likely to be immediately apparent, and it would require further investigation to determine whether there is a positive or negative correlation, or no linear relationship between the two variables.
It is difficult to predict the correlation between your daily calorie intake and your GPA as they are not obviously related variables. However, it is possible that there may be a weak or indirect relationship between the two variables.
If a person is consuming a well-balanced diet with the right amount of nutrients, vitamins, and minerals, they may have the energy and focus necessary to perform well academically. In this case, there may be a positive correlation between calorie intake and GPA. Alternatively, if a person is consuming an excessive amount of calories from unhealthy foods, they may be more likely to experience health problems that could impact their academic performance. In this case, there may be a negative correlation between calorie intake and GPA.
On the other hand, there may be no direct linear relationship between the two variables, and other factors such as sleep, stress, exercise, and overall health may have a greater impact on academic performance than daily calorie intake.
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the probability that a product will operate properly within an expected time frame is the dimension of quality known as
The probability that a product will operate properly within an expected time frame is the dimension of quality known as reliability
The probability is the ratio of the number of favorable outcomes to the total number of outcomes. The value of the probability is varies from zero to one
Here, the product will operate properly within an expected time frame is the dimension of quality
Reliability is expressed as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions that means the reliability is the complementary to the failure of probability
Therefore, the given statement is know as the reliability
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a standard pair of six-sided dice is rolled. what is the probability of rolling a sum less than or equal to 6 ? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice is 5/18 or approximately 0.2778.
To calculate the probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice, we need to find the number of ways the dice can be rolled to get a sum less than or equal to 6 and divide it by the total number of possible outcomes.
There are 6 x 6 = 36 possible outcomes when rolling a pair of dice, since there are 6 possible outcomes for each die. To get a sum less than or equal to 6, the only possible outcomes are:
1+1 = 2
1+2 = 3
1+3 = 4
1+4 = 5
2+1 = 3
2+2 = 4
2+3 = 5
3+1 = 4
3+2 = 5
4+1 = 5
There are 10 possible outcomes that result in a sum less than or equal to 6. Therefore, the probability of rolling a sum less than or equal to 6 is:
P(sum less than or equal to 6) = number of favorable outcomes / total number of possible outcomes
P(sum less than or equal to 6) = 10 / 36
Simplifying this fraction, we get:
P(sum less than or equal to 6) = 5 / 18
Therefore, the probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice is 5/18 or approximately 0.2778 when rounded to four decimal places.
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Factor completely.
28x³y7z² - 7xy4
Answer: 28xy(7x^2-1)
Step-by-step explanation:
28x^3yx7z^2-7x4xy
196x^3-28xy
help Imao pleaseeeeee
5 minus a number is less than -9: 5 - x < -9.
The product of 2 and a number is a minimum of 34: 2x ≥ 34.
Answer:
2. [tex]2n\geq 34[/tex]
3. [tex]5-n < -9[/tex]
Step-by-step explanation:
The product of 2 numbers is multiplication.
"a minimum of" is greater than or equal to.
A number minus a number is subtraction.
2.
"The product of 2 and a number" can be written as [tex]2n[/tex].
"a minimum of 34" can be written as [tex]\geq 34[/tex]
So all together
[tex]2n\geq 34[/tex]
3.
"5 minus a number" can be written as [tex]5-n[/tex]
"less than -9" can be written as [tex]< -9[/tex]
So all together
[tex]5-n < -9[/tex]
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how many ways can baseball players and basketball players be selected from baseball players and basketball players?
There are many ways that baseball players and basketball players can be selected from a group of athletes who play both sports.
One way is to use a selection process that allows for both players to be chosen based on their individual merits. For example, a team could use a combination of criteria such as previous performance, physical fitness, athleticism, and skill level to select the most suitable players for each sport. This could be done by assigning each player a score based on these criteria and then selecting the highest scoring players for each position.Another way to select players from a group of athletes playing both sports is to use a draft system. This system would allow teams to choose players based on the team's needs, rather than individual merits. This could be done by assigning each player an overall ranking and then allowing teams to select players in order of their ranking. A third way to select players from a group of athletes playing both sports is to have a tryout or combine where players can showcase their skills and abilities. This allows teams to evaluate players in a more comprehensive way and make sure they are selecting the best players for their team. Finally, teams can also use a combination of the above methods to select players. For example, they could use a combination of a draft system, individual merit selection, and a tryout/combine to get a better idea of which players are the best fit for their team. Overall, there are many different ways that teams can select baseball players and basketball players from a group of athletes playing both sports. The method chosen will depend on the team's individual needs and preferences.
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How many different combinations of baseball players and basketball players can be selected from a group of baseball players and basketball players?
Write an expression to display a loss of 42 yards on the football field
Answer:
Step-by-step explanation:
An expression to display a loss of 42 yards on the football field would be: -42 yards.
The negative sign in front of the number 42 indicates a loss or a decrease in the yards, which represents a loss of 42 yards on the football field.
Find the value of x in 3x + 4y = 12 and 9x - 4y = 24.
A.-3
B.3
C.0.75
D.-0.75
Answer:
B. x=3
Step-by-step explanation:
3x+4y=12
9x-4y=24
Add 9x and 3x
Subtract -4y from 4y which will cancel out
Add 12 and 24
12x=36
divide both sides by 12
x=3
after conducting a one-sample z test, you arrived at a value of 0.2 for the z value. what is your conclusion?
The z value of 0.2 indicates the standardized difference between the sample mean and population mean
The z value is a standardized score that tells us how many standard deviations a sample mean is from the population mean. In other words, it helps us determine the likelihood that the difference between the two means is due to chance or some other factor.
Typically, we use a significance level (often denoted by alpha) to determine if the z value is significant or not. If the z value falls within the critical values for the chosen significance level, we reject the null hypothesis and conclude that there is a significant difference between the two means. If the z value falls outside the critical values, we fail to reject the null hypothesis and conclude that there is not a significant difference.
In your case, with a z value of 0.2, it is important to consider what significance level was used in the test. If the chosen significance level was 0.05. Since 0.2 falls within this range, we would fail to reject the null hypothesis and conclude that there is not a significant difference between the sample mean and population mean.
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For lunch, Joan bought a glass of milk for $1. 20, a turkey sandwich for $4. 70, as well as some sherbet for $3. 30. The tax came out to $1. 80, and Joan paid with $19. 0. How much change should Joan receive?
Joan paid with $19.00, she should receive $19.00 - $12.00, which equals $11.30 in change.So Joan should receive 11.30 in change.
Joan should receive $11.30 in change. To calculate this, we must start with the total cost of her items, which comes to $10.20 ($1.20 for the milk, $4.70 for the sandwich, and $3.30 for the sherbet). To this we must add the tax, which was $1.80. This brings the total cost to $12.00. Joan should receive $11.30 in change. To get this answer, we can use the following formula: Change = Total Payment - (Cost of Items + Tax). In this case, the formula would look like this: Change = 19.00 - (1.20 + 4.70 + 3.30 + 1.80). After calculating, the answer is 11.30. So Joan should receive 11.30 in change.
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Solve the system for x and y:
Answer:
x = 6, y = -3
Step-by-step explanation:
[tex]\frac{x}{y + 1} = -3\\\frac{y}{x-3} = -1[/tex]
x = -3(y+1) - Isolate for x or y (I chose x)
x = -3y -3
Plug in x into y
[tex]\frac{y}{x-3} = -1\\\frac{y}{(-3y -3) - 3} = -1\\\frac{y}{-3y -6} = -1\\y = -1(-3y - 6)\\y = 3y + 6\\-2y = 6\\y = -3[/tex]
Plug y back into equation
[tex]\frac{x}{y+ 1} = -3\\\frac{x}{(-3)+ 1} = -3\\\frac{x}{-2} = -3\\x = -3(-2)\\x = 6[/tex]
Jake buys a membership to the YMCA pool. He pays a membership fee of $36 and $2 each visit. Jake has another option to pay $8 each visit and no membership fee. After how many visits will the two plans be equal in cost?
Mr. Powell manages a department store and needs an easy way to look up products on the
computer. He wants to assign each product in his department a unique code that will be the sa
number of letters long and use only the letters A, B, and C in the code. How many letters long
each code need to be so that Mr. Powell can account for all 1, 510 products?
O 12
06
07
O 504
The required number of letters to code for 1510 products is given as 7 letters.
What are permutation and combination?In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets.
Here,
There are 3 possibilities for a letter,
Suppose we need n letters
so 3ⁿ > 1510
Since we need to code for 1510 products that means 3ⁿ must be greater than 1510
So
3⁶ < 1510
3⁷>1510
Thus, the required number of letters to code for 1510 products is given as 7 letters.
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