There were 481 people that utilized the public swimming pool that day, including 217 children and 264 adults.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.
given
The number of children =X=217
The number of adults=264
Let say the number of children are denoted by X
Then the number of adults are (481-X)
Price for children =1.25X
Price for adults=2.25(481-X)
Price for children +Price for adults=865.25
1.25X+2.25(481-X)=865.25
Solving for X:
1.25X+1082.25-2.25X=865.25
-X=865.25-1082.25
-X=-217
X=217
The number of children =X=217
The number of adults=(481-X)
The number of adults=(481-217)
The number of adults=264
There were 481 people that utilized the public swimming pool that day, including 217 children and 264 adults.
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Slope = -7; (4, -30) step by step
Answer:
the equation of the line is y = -7x - 2.
Step-by-step explanation:
To find the equation of the line with slope -7 that passes through the point (4, -30), we can use the point-slope form of a line.
The point-slope form of a line is:
y - y1 = m(x - x1)
where:
(x1, y1) is a point on the line
m is the slope of the line
Substituting the given values, we get:
y - (-30) = (-7)(x - 4)
Expanding the right side, we get:
y + 30 = -7x + 28
Combining like terms, we get:
y = -7x - 2
So the equation of the line is y = -7x - 2.
Simplify the polynomial.
3x2 – 2x + 4x2 – X+X
Answer:
[tex]7x^{2} - 2x[/tex]
Step-by-step explanation:
combine like terms. not trying to be mean, but that all you have to do.
Answer:
14-2x
Step-by-step explanation:
collect like terms
3×2+4×2-2x-x-x
6+8-2x
=14-2x
whats the answer for this question i need help
The answer for it is r = -4 :))
Tyrese works each day and earns more money per hour the longer he works. Write a function to represent a starting pay of $20 with an increase each hour by 3%. Determine the range of the amount Tyrese makes each hour if he can only work a total of 8 hours.
The range of the amount Tyrese makes each hour if he can only work a total of 8 hours is 20 ≤ x ≤ 24.80
What is a range?The range is the space between the highest and lowest numbers.
Given: Tyrese works every day and gets paid more per hour the more time he puts in. Create a function to represent a starting wage of $20 that rises by 3% each hour.
To find: Establish the range of Tyrese's hourly pay if he can only work a total of 8 hours.
The beginning wage is $20.
Suppose x hours are in a day.
A $20 salary is offered, with a 3% hourly raise.
e.g., increment = (3/100)*20*x = (3/5)x
A function's maximum possible earnings are
y = 20 + (3/5)x
He is only allowed to work a total of 8 hours, per our instructions.
Therefore, the most money she can make in 8 hours is
y = 20 + (3/5)*8
y = 20 + 4.8
y = 24*8
$20 is the first sum.
As a result, if Tyrese can only work a total of 8 hours every day, the range of his hourly wage is .
Therefore, the correct answer is option B) 20 ≤ x ≤ 24.80.
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PLEASE HELP!!! I WILL MARK BRAINLEST. please help me guys
A storage space in a basement is in the shape of a rectangular prism. The height of the storage space is 5 feet. The length is seven times the width. The volume of the storage space is 595 cubic feet. Find the width and length of the storage space.
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same question buts its answered on the link above
Using traditional methods it takes 8.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 21 students and observed that they had a mean of 8.8 hours with a variance of 1.21. Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Assume the population distribution is approximately normal. Step 1 of 5 : State the null and alternative hypotheses
There is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
What are the hypothesis tested?At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:
[tex]H_0: \mu = 8.5[/tex]
At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:
[tex]H_1: \mu \neq 8.5[/tex]
We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:
|z| = 1.96.
(p-value of 1 - (0.05/2)).
Hence the decision rule is given as follows:
|z| < 1.96 -> do not reject the null hypothesis -> not enough evidence.|z| > 1.96 -> reject the null hypothesis -> enough evidence.What is the test statistic?The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.
The equation is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]
Hence the test statistic is of:
[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}[/tex]
z = 1.24.
|z| < 1.96, hence there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
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A quadrilateral has vertices (-5,1) (-2,5) (2,2) (-1,-2). Determine if it is a square by using the distance formula to calculate the length of the diagonals, and the slope formula to determine if the diagonals are perpendicular
Length of diagonals are :
[tex]D_1 = \sqrt{ (-5-(-1))^2 + (1-(-2))^2 }\\\\D_1 = 5\ units[/tex]
[tex]D_2 = \sqrt{(-2 -2 )^2 + (5-2)^2}\\\\D_2 = 5 \ units[/tex]
Now, Slope of both the diagonal is :
[tex]m_1 =\dfrac{1-(-2)}{-5-(-1)} \\\\m_1 = -\dfrac{3}{4}\\\\m_2 = \dfrac{5-2}{-2-2}\\\\m_2 = -\dfrac{3}{4}[/tex]
Now, product of slopes are :
[tex]m_1 \times m_2 = \dfrac{-3}{4} \times \dfrac{-3}{4}\\\\m_1 \times m_2 = \dfrac{9}{16}[/tex]
Since, the product of slope is not equal to -1 . It means that the slopes are not perpendicular.
Therefore, this quadrilateral is not square.
There are 3 boys for every 5 girls in a kindergarten class. How many total students are there if there are 6 boys?
Answer:
16 students
Step-by-step explanation:
It is a 3 to 5 ratio, so if there are six boys, there are 10 girls. Six plus ten is 16 students.
7. A stock is worth $21. Its value is increasing at a rate of $0. 25 per week a.
Write an equation for the value y (in dollars) of the stock after x weeks.
b. If this trend would continue, what would be the value of the stock after 20 weeks?
The Equation for the value y is a. y = 21 + 0.25x (where x represents the number of weeks)
b. The value of the stock after 20 weeks would be 21 + (0.25 * 20) = $26.
This equation represents the linear relationship between the value of the stock (y) and the number of weeks (x). The value of the stock is initially $21, and it increases by $0.25 every week. This is represented by the coefficient of x (0.25) in the equation. By plugging in x=20 into the equation, we can find that after 20 weeks, the value of the stock would be $26. This is assuming that the rate of increase remains constant over time.
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A car moving on a road with velocity 30 m/ ,
when brake are applied it velocity decreae at a rate
of 6 meter per econd. Find the ditance it will cover before coming to ret
the distance it will cover before coming to rest is 75m. Solved using the concept of velocity.
What is velocity?Simply said, velocity is the rate of movement in a certain direction. such as the speed of a car driving north on a highway or the pace at which a rocket takes off.
Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. Since acceleration is only the rate at which velocity changes, acceleration is likewise a vector quantity.
Given that,
initial velocity (u) = 30 m/s
acceleration (a) = - 6 m/s²
As we know,
v² = u² + 2as
or, 0 = (30)² + 2 × (-6) × s
or, s = 75 m
Hence, the distance it will cover before coming to rest is 75m
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Given P(A) = 0.32, P(B) = 0.2 and P(AU B) = 0.366, find the value of
P(An B), rounding to the nearest thousandth, if necessary.
By using formula, P(A n B) = 0.346. Rounded to the nearest thousandth, P(A n B) = 0.346
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In between 0 and 1, the closer the probability is to 1, the more likely the event is to occur. The probability of an event is usually represented by the letter P, followed by the event in parentheses.
What is rounding off?Rounding off is a mathematical operation that is used to reduce the number of digits in a number while maintaining its value within a certain degree of accuracy. When we round off a number, we look at the digit that is immediately to the right of the last digit that we want to keep. If the number is less than 5, we keep the last digit as it is, but if the number is greater than or equal to 5, we add 1 to the last digit.
We can use the formula of conditional probability to find the value of P(A n B).
P(A n B) = P(A U B) - P(A) - P(B) + P(An B)
We know that:
P(A U B) = P(A) + P(B) - P(A n B)
So we can substitute this in the first equation:
P(A n B) = P(A U B) - P(A) - P(B) + P(An B)
P(An B) = P(A U B) - P(A) - P(B) + P(An B)
Now we can substitute the given values:
P(An B) = 0.366 - 0.32 - 0.2 + P(An B)
P(An B) = 0.346 + P(An B)
To find P(An B) we can subtract 0.346 from both sides of the equation:
P(An B) = P(An B) - 0.346
P(An B) = P(An B) - 0.346
So, P(An B) = 0.346
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In an inverse variation, y = 3 when x = 8. Write an inverse variation equation that shows
the relationship between x and y.
Write the equation using a decimal or an integer.
How do I find this?
Answer:
y = 24/xStep-by-step explanation:
An inverse variation equation is:
y = k/xWe have y = 3 when x = 8, find the coefficient k:
3 = k/8k = 3*8k = 24The equation is:
y = 24/x1.) Select all shapes that are quadrilaterals. A D C С B H E G F
Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line. complete the diagram to show smaller and larger batches that would taste the same as lin's favorite blend. please
help it's due tomorrow
Answer:
that is the persons username I got it from
Step-by-step explanation:
3 and 7
6 and 14
9 and 21
12 and 28
15 and 35
Step-by-step explanation:
If the two numbers they give you are 9 and 21, then the cranberry's are 3 ounces and the apples are 7 fliud ounces, then you can divide and multiply them to your will.
You have a cup with 17 coins inside. The total inside the cup is $5. 50. Determine how many half dollars and quarters are inside the cup. Use a system of equations. Be sure to define the variables and show all work
There are 8 half dollars and 9 quarters inside the cup.
We can set up a system of equations to represent the number of half dollars (h) and quarters (q) in the cup and the total value of the coins.
Let h be the number of half dollars and q be the number of quarters.
The first equation represents the total number of coins in the cup:
h + q = 17The second equation represents the total value of the coins:
0.5h + 0.25q = 5.50To solve for h and q, we can use either the substitution or elimination method.
By substitution, we can solve for one variable in terms of the other in one of the equations and substitute it into the other equation.
So, q = 17 - h
then substitute it into the second equation:
0.5h + 0.25(17 - h) = 5.50
By solving for h, we get h = 8, then we can substitute it back into the first equation to get q = 9
So, there are 8 half dollars and 9 quarters inside the cup.
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pls help with this its due today
Using PEMDAS to solve the algebraic expression, the value is 2
What is Mathematical OperationMathematical operations are operations that involve the manipulation of numbers, variables, and/or equations. Examples of mathematical operations include addition, subtraction, multiplication, division, exponentiation, and root extraction.
In this problem, we can use PEMDAS to solve this algebraic expression.
[(3/5 + 0.425 - 0.005) ÷ 0.1] / [30.5 + 1/6 + 3 (1/3)] + [6(3/4) + 5(1/2)] / 26 ÷ 3(5/7)] - 0.05
This will become;
[10.2 / 34] + [12.25 / 7] - 0.05
Dividing and adding the numbers will give us;
(0.3 + 1.75) - 0.05 = 2
The value is 2
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How do you make a truth table?
If we want to create a truth table , for say expression (P ∨ Q)∧(~P⇒Q) , then we will create different columns having the column head as , P , Q , ~P , P ∨ Q,~P⇒Q and (P ∨ Q)∧(~P⇒Q) and then perform the logical operation on them.
Truth table is a medium used to perform logical operations on expressions. These operations consists of Boolean algebra or Boolean functions expressions.
On performing these logical operation we get to know whether the propositional expression is correct or incorrect, based on the input values. This entire process is based on Boolean algebra and the table is made up of rows and columns for one or more input values.
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what is the slope and y-intercept for y=1/2+4x
Answer:
- 1/4 slope
y-intercept: 2
pls mark me brainless if im right.
What is the relationship between multiplying and factoring?
You multiply numbers or expressions to produce a
[Select]
numbers or [Select]
produce it.
✓. You factor a product into the
✓that were multiplied to
Polynomial factoring is the opposite of polynomial multiplication. A polynomial's leftover will be 0 if it is divided by its factors after factoring.
What do "multiply" and "factor" mean?A multiple is a number that is the result of multiplying the provided number by other numbers, as opposed to a factor, which divides the given number perfectly without leaving a remainder.
What connection exists between the factor theorem and the division of polynomials?When a polynomial f(x) is divided by (x - c), and (x - c) is a factor of the polynomial f(x), the remainder of the division is simply equal to 0. Therefore, if the remainder of a division like the ones mentioned above equals zero.
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Nathan had 58 pieces of gum that he wants to make last six days how much can he chew each day so that the gum last him six days between what two whole numbers does your answer lie
Natha can chew between 9 to 10 chewing gum each day so that it could last for 6 days.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Nathan had 58 pieces of gum that he wants to make last six days.
Therefore, The number of chewing gums he can chew is the total number of chewing gums he has divided by the total number of days which is,
= (58/6).
= 9.66 chewing gums but it should be a whole number.
So, Nathan can chew between 9 to 10 chewing gums each day.
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The weights of 2-pound bags of Best Dog Food are approximately normally distributed with a given mean ul and
standard deviation o. According to the Empirical Rule, what percentage of the bags will have weights within 3 standard deviations of the mean?
Answer: 99.7%
Step-by-step explanation:
Edg 2020
Abby works in the sales department. This month the company is offering a 3-week paid vacation to every employee who sells 230% of the amount sold last month. If Abby sold $480 products last month, how much does she need to sell this month to earn the vacation
well, what's 230% of $480?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{230\% of 480}}{\left( \cfrac{230}{100} \right)480}\implies \text{\LARGE 1104}[/tex]
If θ is an angle in standard position and its terminal side passes through the point (-3,4), find the exact value of tanθ in simplest radical form.
Answer:
so x = 20 , y = -21 , which is in quad IV
r^2= 400+441 = 841
r = √841 = 29
then cos Ø = 20/29
sec Ø = 29/20 = 1.45
Step-by-step explanation:
please give brainliest
What is the discriminant of the quadratic equation 3x^2+8x+4=0
Plz help
In 1 week, Kim jogged 5.6 miles. She increased the distance she jogged each week by 3/4 mile. At the end of 5 weeks, how many total miles had Kim jogged?
A. 21.0 miles
B. 29.9 miles
C. 35.5 miles
D. 39.3 miles
Answer: the answer is 19.6
Step-by-step explanation:
just add up by each number, for example 5.6+3 miles is 8.6 miles so just keep adding up the miles to get this answer
How do you find the mean and standard deviation of a simple random sample?
The steps of finding mean and standard deviation of a simple random sample are given below.
What is standard deviation and mean?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.
The steps of finding mean and standard deviation of a simple random sample are:
Divide the population standard deviation (σX) by the square root of the sample size (n) to get the standard deviation of the sample mean (σX): = σ/n.
How to determine sample means
Add up the examples' components. You must first count the number of sample items in each data set and then add up all of the sample items. ...
Sum divided by the quantity of samples.
The outcome is the mean.
To determine the variance, use the mean.
To determine the standard deviation, use the variance.
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Write the simplified expression: 2x + 3(x - 2) - 3(x -6)
Answer:
2x+12
Step-by-step explanation:
2x+3(x−2)−3(x−6)
Distribute:
=2x+(3)(x)+(3)(−2)+(−3)(x)+(−3)(−6)
=2x+3x+−6+−3x+18
Combine Like Terms:
=2x+3x+−6+−3x+18
=(2x+3x+−3x)+(−6+18)
=2x+12
Answer:
=2x+12
Answer:
2x + 12
Step-by-step explanation:
distribute numbers inside parentheses
2x + 3x -6 -3x + 18
add x values together and integers together
2x + 3x -3x = 2x
-6 + 18 = 10
simplified to 2x + 12
What is the perimeter of kite KLMN? StartRoot 2 EndRoot + StartRoot 5 EndRoot units StartRoot 14 EndRoot units 2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units 4 StartRoot 5 EndRoot units
HELP PLEEEEAASEEE
Answer:
C. 2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units
Step-by-step explanation:
Answer:
The Answer is C.
Step-by-step explanation:
2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units
i need help fr fr like my mind honestly went blank
Answer:
894 mi²
Step-by-step explanation:
the area of parallelogram= base x height= 24mi x 37.25mi = 894 mi²