Combining like terms gives
9x−30=180. Adding 30 to both sides yields
9x=210. Dividing by 9, we find x=23.3333.
To solve the equation
4x+5x−30=180, we first combine like terms:
4x+5x=9x
So the equation becomes:
9x−30=180
Next, we isolate the variable
x by adding 30 to both sides:
9x=180+30
9x=210
Finally, we divide both sides by 9 to solve for
Find the proportion of heights that are within 1 standard deviation of the sample mean and also the proportion that are within 2 standard deviations of the sample mean. use the unrounded values for the mean and standard deviation when doing this calculation. give your answers as decimals to 2 decimal places.
68% of heights that are within 1 standard deviation of the sample mean and 95% are within 2 standard deviations of the sample mean.
Empirical ruleEmpirical rule states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean, 99.7% of the values are within three standard deviation from the mean
Using empirical rule:
68% of heights that are within 1 standard deviation of the sample mean and 95% are within 2 standard deviations of the sample mean.
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Final answer:
The Empirical Rule indicates approximately 68% of data lies within 1 standard deviation of the mean, and about 95% lies within 2 standard deviations for a normally distributed set.
Explanation:
To find the proportion of heights within 1 and 2 standard deviations of the sample mean, we use the Empirical Rule or the 68-95-99.7 rule for a bell-shaped distribution. This rule states that about 68% of the data will fall within 1 standard deviation of the mean, and about 95% will fall within 2 standard deviations of the mean.
This means that for a given set of data, if you calculate the mean and standard deviation, you can expect approximately 68% of your values to lie within 1 standard deviation (either side of the mean) and about 95% to lie within 2 standard deviations.
To perform this calculation, you first need to calculate the unrounded mean and standard deviation of your data set. Once calculated, you can then state, based on the Empirical Rule, that approximately 0.68 or 68% of the data is within 1 standard deviation of the mean and 0.95 or 95% is within 2 standard deviations, given the data is normally distributed.
Mia has two whole bananas and one-fifth of another banana. Write a mixed number that represents the amount of bananas she has.
The Gades Foundation and HBM Corporation are eager to donate generously to their favorite charities. The Gades Foundation donated $250 in the first month, and each month afterward their cumulative donation total increases by $100. The HBM Corporation donated $64 in the first month, and each month afterward their cumulative donation total increases by 75 %. In which month will the HBM Corporation's cumulative donation total first exceed the Gades Foundations' cumulative donation total?
Answer:
month 6
Step-by-step explanation:
khan academy
The perimeter of a rectangle is 12 inches. If the length and width are whole numbers, what are the least and greatest possible areas?
Answer:
5in and 9in
Step-by-step explanation:
help!!! 10pts!!
The coordinates of the vertices of triangles are listed in the options below. Which is a right triangle?
D(2, −3), E(−5, 7), F(6, −9)
A(−3, 2), B(−3, −9), C(2, −4)
P(−6, 2), Q(1, 0), R(−3, −2)
X(3, 1), Y(−4, −3), Z(−1, 8)
Pierce wishes to purchase a municipal bond with a par value of $500 from Arapahoe County, and he is trying to decide which broker he should employ to purchase the bond. Broker A charges a 3.1% commission on the market value of each bond sold. Broker B charges a flat $24 for each bond sold. If the bond has a market rate of 88.754, which broker will give Pierce the better deal, and by how much?
Answer:
Since the given problem statement and data is
Manicipal bond with par value=$500
commission rate =3.1%
charges of broker B=$24
bond market rate=$88.754
hence from the given data Broker A charges a 3.1% commission on the market value of each bond sold is a better deal.
amelia has 2.15 in coins. all of her coins are either quarters or nickels and she has 15 coins in her pile. how many of each coin does she have?
Let us say Amelia has y number of quarters and x number of nickel coins.
So total she has 15 coins.
[tex] x+y=15 [/tex]
[tex] x=15-y [/tex].................(1)
Now she has total amount = $2.15
1 dollar = 20 nickels and 1 dollar = 4 quarters
1 nickel = 0.05 dollar and 1 quarter = 0.25 dollar
so we can say that in terms of dollars,
[tex] 0.05x + 0.25y =2.15 [/tex].................. (2)
Plugging x from (1) in (2)
[tex] 0.05(15-y) + 0.25y =2.15 [/tex]
On solving we get ,
y=7
x=15-y =15-7 = 8
Answer: There are 8 nickels and 7 quarters.
Amelia has 7 quarters and 8 nickels, totaling $2.15 with 15 coins in total.
Let's solve it step by step.
Let's denote:
- [tex]\( Q \)[/tex] as the number of quarters.
- [tex]\( N \)[/tex] as the number of nickels.
Given that Amelia has a total of 15 coins, we can write the equation:
[tex]\[ Q + N = 15 \][/tex]
We're also given that the total value of her coins is $2.15. Since each quarter is worth $0.25 and each nickel is worth $0.05, we can write another equation for the total value:
[tex]\[ 0.25Q + 0.05N = 2.15 \][/tex]
Now, we can use these two equations to solve for [tex]\( Q \)[/tex] and [tex]\( N \)[/tex].
Step 1: Solve the first equation for [tex]\( Q \)[/tex]:
[tex]\[ Q = 15 - N \][/tex]
Step 2: Substitute this expression for [tex]\( Q \)[/tex] into the second equation:
[tex]\[ 0.25(15 - N) + 0.05N = 2.15 \][/tex]
Step 3: Distribute and solve for [tex]\( N \)[/tex]:
[tex]\[ 3.75 - 0.25N + 0.05N = 2.15 \][/tex]
[tex]\[ 3.75 - 0.20N = 2.15 \][/tex]
[tex]\[ -0.20N = 2.15 - 3.75 \][/tex]
[tex]\[ -0.20N = -1.60 \][/tex]
Step 4: Divide both sides by -0.20 to solve for [tex]\( N \)[/tex]:
[tex]\[ N = \frac{-1.60}{-0.20} \][/tex]
[tex]\[ N = 8 \][/tex]
Now that we know Amelia has 8 nickels, we can substitute this value back into one of the original equations to solve for [tex]\( Q \).[/tex]
Step 5: Use the first equation to solve for [tex]\( Q \)[/tex]:
[tex]\[ Q = 15 - 8 \][/tex]
[tex]\[ Q = 7 \][/tex]
So, Amelia has 7 quarters and 8 nickels.
the diagram shows an artificial lake. When Amanda jogged twice around the lake she jogged a distance of 2,700 meters. Find the value of x
Assuming that the attached file is the lake which you are mentioning in the question.
The perimeter is the distance around the lake, we need to set up an equation based on the statement "When Amanda jogged twice around the lake she jogged a distance of 2,700 meters" as below:
[tex] 2(Perimeter \; of\; the\; lake) =2700\\ \\ 2(x+140+x+x+250+x+x+3x)=2700\\ Group \; Like\; Terms\\ \\ 2(x+x+x+x+x+3x+140+250)=2700\\ Combine \; Like\; Terms\\ \\ 2(8x+390)=2700\\ Distribute\; 2\; in\; left\; side\; of\; the\; equation\\ \\ 16x+780=2700\\ Subtract \; 780\; on\; both\; sides\\ \\ 16x+780-780=2700-780\\ Combine \; like\; terms\\\\16x=1920 \\ Divide\; 16 \; on\; both\; sides\\ \\ \frac{16x}{16}=\frac{1920}{16}\\ Simplify\; fraction\; on\; both\; sides\\ \\ x=120 [/tex]
Conclusion:
The value of x is 120 meters
kevin said that if you triple his age, the result will be 1 less than his mother's age
During a rainstorm Willow received 7/16 inch of rain, Summerset received 1/2 inch of rain, Clarkdale received 3/4inch of rain, and Riverton received 5/8 inch of rain. Which community received the most rain?
there are 5.816x10 to the power of 4 spectators in a stadium watching a football game.in a theatre there are 1,150 people watching a concert. which venue has more people? by how many people?
Some species of hummingbirds appear to hover in mid-air by flapping their tiny wings 80 times per second. How many times per minute do hummingbirds flap their wings?
Final answer:
To calculate the number of times a hummingbird flaps its wings per minute, you multiply the number of flaps per second by 60. In this case, hummingbirds flap their wings approximately 4800 times per minute.
Explanation:
To calculate how many times a hummingbird flaps its wings per minute, you can start by determining how many times it flaps its wings per second. Given that some species of hummingbirds flap their wings 80 times per second, you can simply multiply this by 60 to find the number of times per minute:
80 flaps/second x 60 seconds/minute = 4800 flaps/minute
Therefore, hummingbirds flap their wings approximately 4800 times per minute.
What percent is 6 out of 7?
PLEASE HELP!!!!
Which is the following best describes the graph below?
A. it is many-to-one function
B. it is a function but it is not one to one.
C. it is a one to one function
D. it is not a function
Solution:
we are given with a graph and we have been asked to find Which of the given options best describes the graph ?
As we know from the vertical line test of a function that a curve reprsents a function , if we draw a vertical line and that line intersect that curve only once.
If that vertical line interscet the given curve more than once it mean that curve does not represent a function.
Here for the given curve if we will draw any vertical line, that line will intersect it more than once.
Hence the given curve does not represent a fimction.
Hence the correct option is D.
Jim Lee received his bank statement from Bayne Bank indicating a balance of $7,980. Lee's checkbook showed a balance of $6,800. Jim noticed that checks outstanding were $1,330. The bank statement also revealed an NSF check for $120 and a service charge of $30. The reconciled balance is:
The reconciled balance is calculated by starting with the checkbook balance, subtracting outstanding checks and any bank charges or errors. In Jim Lee's case, the reconciled balance is $4,320.
Explanation:The reconciled balance for Jim Lee's bank account involves adjusting Jim's checkbook balance by accounting for any outstanding checks and any bank charges or errors. To calculate the reconciled balance, you follow these steps:
Start with the checkbook balance: $6,800.Subtract the total outstanding checks: $1,330.Subtract any bank charges or errors, in this case, an NSF (Non-Sufficient Funds) check for $120 and a service charge of $30.Add any deposits in transit or errors in the bank's favor, in this question, there are none mentioned.So, the reconciled balance would be: $6,800 (checkbook balance) - $1,330 (outstanding checks) - $120 (NSF check) - $30 (service charge) = $4,320.
Lily swims a 100meter race she swims the first half 27.8 she swims the second half in 30.12 seconds how much longer does it take her to swim the second half on the race than the first half
Answer: 2.32 seconds.
Step-by-step explanation:
Knowing that:
Lily swims the first half of the 100 meters race in 27.8 seconds. Lily swims the second half of the 100 meters race in 30.12 seconds.You can calculate how much longer it takes to her to swim the second half than the first half, by subtracting 30.12 seconds and 27.8 seconds.
Then:
[tex]30.12\ seconds-27.8\ seconds=2.32\ seconds[/tex]
Therefore, it took her 2.32 seconds longer to swim the second half on the race than the first half.
Answer:
2.32 seconds.
Step-by-step explanation:
We have been given that Lily swims a 100 meter race. She swims the first half 27.8 seconds and she swims the second half in 30.12 seconds.
To find how much longer it took Lily to swim the second half on the race than the first half, we need to subtract the time taken by Lily on first half from the time taken by Lily on second half.
[tex]\text{Difference of time}=30.12\text{ seconds}-\text{27.8 seconds}[/tex]
[tex]\text{Difference of time}=2.32\text{ seconds}[/tex]
Therefore, it took Lily 2.32 seconds more to swim the second half on the race than the first half.
Multiple choice questions will mark brainlist answer asap
The solution for the inequalities x² < 144 is the set of numbers that are greater than -12 and less than 12. Therefore, the solutions from the given options are 11, 7, -8, and -20.
The solution for the given inequality, x² < 144, is the set of all real numbers x for which x² is less than 144.
First, take the square root on both sides of the inequality to get -12 < x < 12.
This means x can be any number greater than -12 and less than 12.
The following numbers amongst the options given satisfy these conditions: -20, -8, 7, and 11.
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What is the remainder of x3 + 3x2 − 10x + k divided by (x + 4)?
Which type of function best models the data shown on the scatterplot?
To solve the problem we must know about quadratic equations.
The type of function best models the data shown on the scatterplot is a quadratic function.
Graph of a Parabolic functionThe graph of a quadratic function is a curve that is in the shape of a parabola. the highest point or the lowest point of the curve is known as the vertex of the parabola.The leading coefficient decides the opening of the parabola therefore if the leading coefficient is positive the parabola will open upside while downside if the leading coefficient is negative.The example of a quadratic equation is given below in the image.
Data showed of the scatterplotAs we can see the data on the scatter plot is also a parabolic shape with vertex at x = 4, and opening downwards, therefore the leading coefficient of the function is negative.Hence, the type of function best models the data shown on the scatterplot is a quadratic function.
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Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8. Simplify [Q - R] + [S - T].
Answer: [tex][Q - R] + [S - T]=10m+7n-14[/tex]
Step-by-step explanation:
Given : [tex]Q = 7m + 3n[/tex],
[tex]R = 11 -2m[/tex],
[tex]S = n + 5[/tex], and
[tex]T = -m - 3n + 8[/tex]
Now , [tex]Q-R= 7m + 3n-(11 - 2m)[/tex]
[tex]Q-R= 7m +3n-11+2m[/tex] [ ∵ (-)(+)=(-) and (-)(-)=(+)]
[Note : when -1 is outside the parenthesis it indicates that -1 should be multiplied with each of the terms present inside the parenthesis .]
[tex]Q-R= 9m +3n-11[/tex] [Combine like terms.]
[tex]S-T=n + 5-(-m - 3n + 8)[/tex]
[tex]S-T=n + 5+m+3n-8[/tex] [ ∵ (-)(+)=(-) and (-)(-)=(+)]
[tex]S-T=4n +m-3[/tex] [Combine like terms.]
Now, [tex][Q - R] + [S - T]=[9m +3n-11]+[4n +m-3][/tex]
[tex]=9m +3n-11+4n+m-3[/tex]
[tex]=10m+7n-14[/tex] [combine like terms]
Hence, [tex][Q - R] + [S - T]=10m+7n-14[/tex]
How do you write the equation of Mary has 10 roses John has 2 less
Determine the intercepts of the line. -6x+3y=-7
For the equation -6x+3y = -7, x intercept is at (7/6, 0) and y-intercept is at (0, -7/3).
To determine the intercepts of the line described by the equation -6x+3y=-7, we will find both the x-intercept and the y-intercept. The x-intercept is found by setting y=0, and solving the equation for x, while the y-intercept is found by setting x=0 and solving for y.
For the x-intercept:
Set y=0 in the equation: -6x+3(0) = -7.Simplify and solve for x: -6x = -7.Divide by -6: x = 7/6 or approximately 1.167.For the y-intercept:
Set x=0 in the equation: -6(0)+3y = -7.Simplify and solve for y: 3y = -7.Divide by 3: y = -7/3 or approximately -2.333.So the x-intercept is at (7/6, 0) and the y-intercept is at (0, -7/3).
What is the probability that a card randomly drawn from a standard deck of 52 cards is NOT a king?
Answer : The probability for not a king is, [tex]\frac{12}{13}[/tex]
Step-by-step explanation :
Probability : It is defined as the extent to which an event is likely to occur. That means, it is measured by the ratio of the favorable outcomes to the total number of possible outcomes.
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of favorable outcomes}}[/tex]
Favorable outcomes are, 52
Now we have to calculate the probability for not a king.
Total number of king in a deck of 52 cards = 4 (spade, heart, diamond and club)
Favorable outcomes for NOT a king = 52 - 4 = 48
Total number of outcomes = 52
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes for a multiple of 3}}{\text{Total number of favorable outcomes}}[/tex]
[tex]\text{Probability}=\frac{48}{52}[/tex]
[tex]\text{Probability}=\frac{12}{13}[/tex]
Therefore, the probability for not a king is, [tex]\frac{12}{13}[/tex]
The radius of a sphere is increasing at a rate of 5 mm/s. how fast is the volume increasing when the diameter is 60 mm? evaluate your answer numerically. (round the answer to the nearest whole number.)
The rate of change of volume of the sphere is [tex]56520\;\rm{mm/sec}[/tex].
According to the question, the radius of a sphere is increasing at a rate of [tex]5 mm/s[/tex] and the diameter is [tex]60 mm[/tex].
The volume of the sphere is, [tex]V=\dfrac{4}{3}\pi r^3[/tex] where, [tex]r[/tex] is the radius of the sphere.
Differentiate the volume of the sphere both sides with respect to [tex]t[/tex] as-
[tex]\dfrac{dV}{dt}=\dfrac{4\pi}{3}\dfrac{dr^3}{dt}\\\dfrac{dV}{dt}=\dfrac{4\pi}{3}\times 3r^2\dfrac{dr}{dt}\\\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}[/tex]
The radius of the sphere is-
[tex]r=\dfrac{60}{2}\\r=30mm[/tex]
Substitute the value of the parameter as-
[tex]\dfrac{dV}{dt}=4\pi\times (30)^2\times 5\\\dfrac{dV}{dt}=62.8\times 900\\\dfrac{dV}{dt}=56520\;\rm{mm/sec}[/tex]
Hence, the rate of change of volume of the sphere is [tex]56520\;\rm{mm/sec}[/tex].
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Suppose 60% of a graduating class in a certain high school goes on to college. if 240 stuare going on to college, how many students are in the graduating class?
solve the systems of linear equations by graphing y=-5/2x-7 x+2y=4 what is the solution to the system of linear equations A. (-4.5,4.25) B. (-1.7,-2.8) C. (0,-7) D. (3,0.5)
we have
[tex]y=-\frac{5}{2}x-7[/tex] ------> equation A
[tex]x+2y=4[/tex] ------> equation B
we know that
The intersection point both graphs is the solution of the system of linear equations
Using a graphing tool
see the attached figure
The solution is the point [tex](-4.5,4.25)[/tex]
therefore
the answer is the option A
[tex](-4.5,4.25)[/tex]
3 full and distinct reasons for 100%.
WYR
See teachers armed with guns in the classroom.
OR
See things like bullet-proof vests and other safety measures in the classroom.
OPEN
(3 reasons for full credit)
Giving 99 pionts!
Answer:
i will say bullet proof vest there are my reason
1. your teacher is suppose to keep you safe
2.bullet proof vest would keep you safe from gun shootings
3. school guards should check everyone's pockets before interning the school building
i hope this helps you -pandamathhelper
On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine burns out. The rocket's height, h, in feet above the surface of the lake, is given by the equation, h = -16t^2 + 64t + 80, where t is time in seconds. The maximum height of the rocket is _______ feet
Select each equation that has NO real solution!
To determine equations with no real solutions, assess for a negative discriminant or no x-intercepts in quadratic equations. Steps include identifying unknowns, choosing appropriate equations, simplifying terms, and checking for reasonableness.
Explanation:To select each equation that has NO real solution, we must assess the equations provided, looking for specific characteristics that indicate the absence of real solutions. One of the hallmarks of such equations is when they represent a quadratic equation with no x-intercepts or the discriminant (b^2 - 4ac) in the quadratic formula is negative, which means the roots are complex numbers.
When working on problems like these, it's crucial to go through several steps: Identify the unknown, identify the knowns, choose an equation, eliminate terms to simplify the algebra, and then check the answer to see if it is reasonable.
Let's use an example equation: x^2 + 4 = 0. To determine if this has real solutions, we can identify the unknown (x), the knowns (coefficients of x), solve the equation or calculate the discriminant (4^2 - 4*1*-4 = 16 +16 = 32, which is positive), and confirm whether the solutions are real or not. In this case, because the discriminant is positive, this equation does have real solutions, and therefore would not be included in a list of equations with no real solutions.
The equations 2x² - 4x + 5 = -3, x² - 12x + 60 = 12, and x² + 3x + 6 = 0 have no real solutions, based on their negative discriminants.
We need to determine the discriminant (b² - 4ac) of each equation to check for real solutions. A negative discriminant indicates no real solutions.
Equations Analysis
2x² + 2x = 2: Rewrite as 2x² + 2x - 2 = 0. Here, a = 2, b = 2, c = -2. The discriminant is 2² - 4(2)(-2) = 4 + 16 = 20 (positive, so there are real solutions).2x² - 4x + 5 = -3: Rewrite as 2x² - 4x + 8 = 0. Here, a = 2, b = -4, c = 8. The discriminant is (-4)² - 4(2)(8) = 16 - 64 = -48 (negative, so there are no real solutions).x² - 12x + 60 = 12: Rewrite as x² - 12x + 48 = 0. Here, a = 1, b = -12, c = 48. The discriminant is (-12)² - 4(1)(48) = 144 - 192 = -48 (negative, so there are no real solutions).x² - 4 = 0: This is already in quadratic form with a = 1, b = 0, c = -4. The discriminant is 0² - 4(1)(-4) = 16 (positive, so there are real solutions).x² + 3x + 6 = 0: Here, a = 1, b = 3, c = 6. The discriminant is 3² - 4(1)(6) = 9 - 24 = -15 (negative, so there are no real solutions).Equations with No Real Solutions
2x² - 4x + 5 = -3x² - 12x + 60 = 12x² + 3x + 6 = 0Complete Question - Select each equation that has no real solution.
2x² + 2x = 22x² - 4x + 5 = -3 x² - 12x + 60 = 12 x² - 4 = 0 x² + 3x + 6 = 0Please help me with questions 23, 24, and 25