Solve for x. 4(x+113)=923 Enter your answer as a mixed number in simplest form in the box.
Answers
Answer:
\(4(x + 113) = 923 \\ 4x + 452 = 923 \\ 4x = 471 \\ x = \frac{471}{4} \\ x = 117 \frac{3}{4} \)
Related Questions
Write an equation of the line passing through point P(-8, 0) that is perpendicular to the line 3x - 5y = 6.
y =
Answers
Answer:
y = -5/3x - 6/5
Step-by-step explanation:
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let f=(y z)i (z x)j (x y)k. find line integral of f over the path c: r(t)=ti t^2j t^4k, 0
Answers
To find the line integral of vector field F = (yz)i + (zx)j + (xy)k over the path C: r(t) = ti + t^2j + t^4k, where t ranges from 0 to 1, we need to compute the integral of the dot product between F and the derivative of r(t) with respect to t, dr/dt.
Let's start by calculating the derivative of r(t):
dr/dt = (d/dt)(ti) + (d/dt)(t^2j) + (d/dt)(t^4k)
= i + 2tj + 4t^3k
Now, we can compute the line integral by evaluating the dot product F · (dr/dt) and integrating over the given interval [0, 1]:
∫[C] F · dr = ∫[0,1] (F · (dr/dt)) dt
Substituting the values of F and dr/dt:
∫[0,1] ((yz)i + (zx)j + (xy)k) · (i + 2tj + 4t^3k) dt
Expanding the dot product:
∫[0,1] (yz + 2tzx + 4t^3xy) dt
Now, we can integrate each component separately:
∫[0,1] yz dt + ∫[0,1] 2tzx dt + ∫[0,1] 4t^3xy dt
For the first integral:
∫[0,1] yz dt = yz ∫[0,1] dt = yz[t]₀¹ = yz
For the second integral:
∫[0,1] 2tzx dt = 2zx ∫[0,1] t dt = 2zx [t^2/2]₀¹ = zx
For the third integral:
∫[0,1] 4t^3xy dt = 4xy ∫[0,1] t^3 dt = 4xy [t^4/4]₀¹ = xy
Putting it all together:
∫[C] F · dr = yz + zx + xy = yz + 2zx + 4xy
Therefore, the line integral of F over the path C is yz + 2zx + 4xy
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a teacher is interested in whether learning while listening to classical music improves performance in math. one week during the semester, the students learn some select basic math skills while listening to soft classical music. during another week of the semester, the students learn a new set of basic math skills without listening to music. at the end of each of the weeks, students complete a quiz to measure their math performance (higher scores indicate better performance). a dependent means (i.e. paired samples) t-test is conducted. the output from the analysis is below. (note: output from jamovi.)
Paired Samples T-Test Music playing No music playing student'st Statistic : -4.60
df : 180 p : < 001
Mean difference : -2.42
SE difference : 0.526
Decriptives
N Mean Median SD SE
Musix playing 19 15.5 16 1.65 0.377
No music playing 19 17.9 18 2.05 0.41
4a.) In words, briefly state the null hypothesis.
4b.) In words, briefly state the research/alternative hypothesis based on the researcher's hypothesis. 4c.) Based on the output for the analysis, report the following: The mean math performance when music played: The mean math performance when no music played: The calculated t statistic: The p-value associated with the test statistic: 4d.) Is the p-value (probability value) associated with this result greater than or less than .05? [Remember: when we have output like this, we no longer have to worry about critical values. We can look at the reported p-value and observe whether it is greater or less than .05. 4e.) Based on the p-value, do we retain or reject the null hypothesis? 4f.) Is the result statistically significant? 4g.) Based on this information, is it safe to conclude that students perform better when listening to music while learning? [Hint: You need to look at more than the p-value to answer this accurately]
Answers
4a) The null hypothesis is that there is no difference in math performance between learning while listening to classical music and learning without music.
4b) The research/alternative hypothesis based on the researcher's hypothesis is that learning while listening to classical music improves math performance.
4c) The mean math performance when music played was 15.5, and when no music played was 17.9. The calculated t statistic was -4.60, and the p-value associated with the test statistic was < .001.
4d) The p-value associated with this result is less than .05.
4e) Based on the p-value, we reject the null hypothesis.
4f) The result is statistically significant.
4g) Based on this information alone, it is not safe to conclude that students perform better when listening to music while learning. Other factors could have influenced the results, such as individual differences in the students or other environmental factors. Further research would be necessary to make a definitive conclusion.
4a.) The null hypothesis states that there is no significant difference in math performance between the two conditions (learning with classical music and learning without music).
4b.) The research/alternative hypothesis states that learning while listening to classical music improves performance in math compared to learning without music.
4c.)
- Mean math performance when music played: 15.5
- Mean math performance when no music played: 17.9
- Calculated t statistic: -4.60
- P-value associated with the test statistic: < 0.001
4d.) The p-value associated with this result is less than 0.05.
4e.) Based on the p-value, we reject the null hypothesis.
4f.) The result is statistically significant.
4g.) While the result is statistically significant, it actually shows that students performed better when not listening to music while learning. This contradicts the researcher's initial hypothesis, so it is not safe to conclude that students perform better when listening to music while learning.
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For the following LP, x2 and s1 are basic variables in the optimal tableau. Use the formulas of section 6.2 from your text book to determine the optimal tableau. max z = -X1 + X2 s.t. 2x1 + x2 = 4 x1 + x2 = 2 x1,x220
Answers
The optimal solution to the LP is x1 = 0, x2 = 2, with an optimal objective function value of 2.
To use the formulas from section 6.2 of the textbook to find the optimal tableau, we need to start with the initial feasible tableau, which has the following form:
Basis x1 x2 s1 s2 RHS
s1 2 1 1 0 4
s2 1 1 0 1 2
z -1 1 0 0 0
The first step is to identify the pivot element, which is the smallest positive ratio of the right-hand side (RHS) to the coefficient of the basic variable in each row. In this case, the ratios are:
s1: 4/2 = 2
s2: 2/1 = 2
Since both ratios are equal, we choose the variable with the smallest coefficient in the objective function as the entering variable. In this case, that is x1.
The second step is to perform the pivot operation, which involves dividing the pivot row by the pivot element and subtracting a suitable multiple of the pivot row from each of the other rows to eliminate the x1 variable from them. The result is a new tableau:
Basis x1 x2 s1 s2 RHS
s1 1 0 1/2 -1 2
x1 1 1 0 1 2
z 0 2 1 1 2
The new tableau shows that x2 and s1 are the basic variables in the optimal solution, with values of 2 and 2, respectively. The optimal value of the objective function is also shown in the tableau, which is 2.
Therefore, the optimal solution to the LP is x1 = 0, x2 = 2, with an optimal objective function value of 2.
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the equations with the equal method value
Answers
Answer:
a. x=2 y=8
Step-by-step explanation:
6x-4=-3x+14 y=6x2-4 12-4=8
9x-4=14
9x=18
x=2
the answer is yes or no ?
Answers
one pound is around 2.5 dollars
Answer:
No!!
Step-by-step explanation:
For every 1 pound it costs $2⁵⁰
For every 2 pounds it costs $5⁰⁰
For every 3 pounds it costs $7⁵⁰
and so on going by 2.50 each pound.
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 11, with tick marks every one unit up to 25. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 20 on the number line. A line in the box is at 19. The lines outside the box end at 12 and 24.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 12.
The IQR is the best measure of variability, and it equals 12.
The range is the best measure of variability, and it equals 3.
Answers
Therefore , the solution of the given problem of range comes out to be IQR is the most accurate gauge of dispersion, and its value is 3.
What is range?By multiplying the highest value observed value by the lowest observed value, a variable range is determined. (minimum). Two possible range or central disparity limits are varying steel prices and various designs. An indication of the maximum or expected spread that a weapon's missile can be found in the dimension or extent of a procedure or action. A list's or subgroup's range is the number between its minimum and maximum.
Here,
The Interquartile Range (IQR), which is the range of the middle 50% of the data, is the proper measure of variability for the data displayed by the box plot.
It is computed as the gap between the first and third quartiles (Q1 and Q3). (Q1).
We can see from the box diagram that Q1 is 17 and Q3 is 20. Consequently, the IQR is:
=> IQR = Q3 - Q1 = 20 - 17 = 3
The IQR is the most accurate gauge of dispersion, and its value is 3.
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Graph h(x) = -|x- 6| + 3.
Answers
Answer: Shift the graph to the right by 6, and up by 3.
Step-by-step explanation: If a number is in parentheses or absolute value lines, use the inverse sign. If it’s outside of the parentheses, move it like normal.
To graph the function h(x) = -|x - 6| + 3, we can follow a step-by-step approach:
Step 1: Determine the key points:
Identify the vertex: The vertex of the absolute value function y = |x| is at (0, 0). In this case, since we have y = -|x - 6| + 3, the vertex is obtained by shifting the vertex (0, 0) horizontally by 6 units to the right and vertically up by 3 units. Therefore, the vertex is at (6, 3).
Find additional points: Choose some x-values on both sides of the vertex to determine corresponding y-values. Let's choose x = 0, 3, 6, and 9.
Step 2: Calculate the y-values:
For x = 0: h(0) = -|0 - 6| + 3 = -|-6| + 3 = -6 + 3 = -3.
For x = 3: h(3) = -|3 - 6| + 3 = -|-3| + 3 = -3 + 3 = 0.
For x = 6: h(6) = -|6 - 6| + 3 = -|0| + 3 = -0 + 3 = 3.
For x = 9: h(9) = -|9 - 6| + 3 = -|3| + 3 = -3 + 3 = 0.
Step 3: Plot the points:
Plot the points (0, -3), (3, 0), (6, 3), and (9, 0) on a coordinate plane.
Step 4: Draw the graph:
Connect the plotted points smoothly. Since we have an absolute value function with a negative sign, the graph will be an upside-down V-shape, opening downwards, with the vertex at (6, 3).
Here's a visual representation of the graph of h(x) = -|x - 6| + 3:
Please note that the graph above is a rough representation and may not be perfectly to scale.
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Jodie wanted to match  Mandys obstacle course record of 68.2 seconds. She had already spent 40 1/4 seconds on rock climbing and 12.84 seconds on the ropes how much time did she have left to match the record
Answers
The time Jodie have left to match the record of Mandy is 15.11 seconds
TimeMandy's obstacle course = 68.2 secondsJodie:
Time spent climbing rock = 40 1/4 seconds= 40.25 seconds
Time spent on the rope = 12.84 seconds
Total time spent = 40.25 seconds + 12.84 seconds
= 53.09 seconds
Total time she have left to match the record = Mandy's obstacle course - Total time spent
= 68.2 seconds - 53.09 seconds
= 15.11 seconds
Therefore, the time Jodie have left to match the record of Mandy is 15.11 seconds
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To divide 572 Stanley estimated to place the first digit of the quotient in which place is the first digit of the quotient?
Answers
Answer:
its about estimation, so we don't need to divide.
so let's round up the number to see it more
clearly:
572 can be rounded up to 600, let's leave 4 as it
is, since it's just one digit.
we see that 6 is bigger than 4, so the result will
look like this 1xx
so we see,
it will be at leasta 100, and the first
digit will be in the hundred's place that's the
Correct answer!
There are currently 3000 in the state of Colorado their population is increasing at a rate of 2% per year how many years will it be before there are 6000 moose in the state of Colorado. Round your answer to the nearest year
Answers
Answer:
50 years
Step-by-step explanation:
the answer is 50 years bc 2% of 3000 is 60 and to get to 300 from 60 you would multiply by 50 to get 3000 added to the populationg colorado has now you get 6000.
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Order from least to greatest 4/7,5/8,0.7,72%
Answers
Answer:
\(\huge\boxed{\dfrac{4}{7};\ \dfrac{5}{8};\ 0.7;\ 72\%}\)
Step-by-step explanation:
Two ways.
1. Convert to the decimal:
\(\dfrac{4}{7}=4:7=0.\overline{571428}\\\\\dfrac{5}{8}=5:8=0.625\\\\0.7=0.7\\\\72\%=\dfrac{72}{100}=0.72\)
therefore
\(0.\overline{571428}<0.625<0.7<0.72}\)
\(\dfrac{4}{7};\ \dfrac{5}{8};\ 0.7;\ 72\%\)
2. Convert to the fractions with common denominator.
\(\dfrac{4}{7};\ \dfrac{5}{8}\\\\0.7=\dfrac{7}{10}\\\\72\%=\dfrac{72}{100}=\dfrac{18}{25}\)
\(LCD=7\cdot8\cdot5\cdot5=1400\\\\\dfrac{4}{7}=\dfrac{4\cdot200}{7\cdot200}=\dfrac{800}{1400}\\\\\dfrac{5}{8}=\dfrac{5\cdot175}{8\cdot175}=\dfrac{875}{1400}\\\\0.7=\dfrac{7}{10}=\dfrac{7\cdot140}{10\cdot140}=\dfrac{980}{1400}\\\\72\%=\dfrac{72}{100}=\dfrac{72\cdot14}{100\cdot14}=\dfrac{1008}{1400}\\\\\dfrac{800}{1400}<\dfrac{875}{1400}<\dfrac{980}{1400}<\dfrac{1008}{1400}\)
therefore
\(\dfrac{4}{7};\ \dfrac{5}{8};\ 0.7;\ 72\%\)
yo i need some help this determines weather i pass or fail
Answers
To make 4 dozen cookies she would need
→ 3/2 cup peanut butter
→ 3 cup of vegetable shortening
→ 1 1/2 cups of firmly packed light brown sugar
→ 6 tablespoons of milk
→ 2 3/2 tablespoons of vanilla extract
→ 2 cups of flour
→ 3/2 teaspoon of baking soda
→ 1/2 teaspoon salt
To make 4 dozen cookies
she will need double the items which are mentioned in the list
thus the required list will look like this
3/4 × 2 = 3/2 cup peanut butter
3/2 cup of vegetable shortening = 3/2 × 2 = 3 cup of vegetable shortening
1 1/4 cups of firmly packed light brown sugar = 1 1/4 × 2 = 1 1/2 cups of firmly packed light brown sugar
3 tablespoons of milk = 3 × 2 = 6 tablespoons of milk
2 3/4 tablespoons of vanilla extract = 2 3/2 tablespoons of vanilla extract
1 large egg = 1× 2 = 2 large eggs
1 1/2 cups flour = 1 1/2×2 = 1 + 1 = 2 cups of flour
3/4 teaspoon baking soda = 3/2 teaspoon of baking soda
1/4 teaspoon salt = 1/4 × 2 = 1/2 teaspoon salt
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__________ typically are used to display continuous measures.
Answers
Histograms typically are used to display continuous measures.
The histograms typically are used to display continuous measures.
Charts TypesThere are different types of charts: histogram, line chart, pie chart, and others.
The histogram is a type of chart used as a tool that provides a way to assess the distribution of data. From this type of chart, a set of data are previously tabulated and divided into classes. In the other words, the histogram is applied to summarize discrete or continuous measures, so it becomes more easily the understand the used data. There are many websites and software that allow the plot of this type of chart.
From the explanation, it is possible to identify the histograms typically are used to display continuous measures.
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Whats the distance (7,0) and (-8,45)
Answers
Answer:
\(d = 15\sqrt{10}\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra II
Distance Formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)Step-by-step explanation:
Step 1: Define
Point (7, 0)
Point (-8, 45)
Step 2: Find distance d
Substitute: \(d = \sqrt{(-8-7)^2+(45-0)^2}\)Subtract: \(d = \sqrt{(-15)^2+(45)^2}\)Exponents: \(d = \sqrt{225+2025}\)Add: \(d = \sqrt{2250}\)Simplify: \(d = 15\sqrt{10}\)Write an equation of the line in slope-intercept form.
f(3)=-2, f(0)=1
Answers
Answer:
The equation of the line in slope-intercept form is y = -x + 1
Step-by-step explanation:
The slope-intercept form of the linear equation is y = m x + b, where
m is the slope of the lineb is the y-intercept ⇒ value y at x = 0The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where
(x1, y1) and (x2, y2) are two points on the line∵ f(x) = y ⇒ is the function of the set of ordered pairs (x, y)
∴ f(3) = -2 is the point (3, -2)
∴ f(0) = 1 is the point (0, 1)
∴ x1 = 3 and y1 = -2
∴ x2 = 0 and y2 = 1
→ Substitute them in the rule of the slope to find it
∵ m = \(\frac{1--2}{0-3}\) = \(\frac{1+2}{-3}\) = \(\frac{3}{-3}\)
∴ m = -1
→ Substitute it in the form of the equation above
∵ y = -1(x) + b
∴ y = -x + b
∵ b is the value of y at x = 0
∵ at x = 0, y = 1
∴ b = 1
∴ y = -x + 1
∴ The equation of the line in slope-intercept form is y = -x + 1
A company currently pays a dividend of $2.2 per share (D
0
=$2.2). It is estimated that the company's dividend will grow at a rate of 24% per year for the next 2 years, and then at a constant rate of 5% thereafter. The company's stock has a beta of 1.3, the risk-free rate is 9%, and the market risk premium is 4.5\%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.
Answers
The estimated current price of the stock is $57.83.
To calculate the stock's current price, we can use the dividend discount model (DDM). The DDM states that the price of a stock is equal to the present value of its future dividends.
In this case, the dividend is expected to grow at a rate of 24% per year for the next 2 years and then at a constant rate of 5% thereafter. We can calculate the dividends for the next two years as follows:
D1 = D0 * (1 + growth rate) = $2.2 * (1 + 0.24) = $2.728
D2 = D1 * (1 + growth rate) = $2.728 * (1 + 0.24) = $3.386
To find the price of the stock at the end of year 2 (P2), we can use the Gordon growth model:
P2 = D2 / (r - g) = $3.386 / (0.09 - 0.05) = $84.65
Next, we need to discount the future price of the stock at the end of year 2 to its present value using the required rate of return. The required rate of return is the risk-free rate plus the product of the stock's beta and the market risk premium:
r = risk-free rate + (beta * market risk premium) = 0.09 + (1.3 * 0.045) = 0.1565
Now, we can calculate the present value of the future price:
P0 = P2 / (1 + r)^2 = $84.65 / (1 + 0.1565)^2 = $57.83
Therefore, based on the given information and calculations, the estimated current price of the stock is $57.83.
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Find the width of a cuboid given that it has a length of 7 cm, height of 10 cm and volume of 490 cm3
Answers
The width of a cuboid is 7 cm
In geometry, a cuboid is a solid shape or a three-dimensional shape. A convex polyhedron that is bounded by six rectangular faces with eight vertices and twelve edges is called a cuboid. A cuboid is also called a rectangular prism. A cuboid with six square faces is called a cube. An example of a cuboid in real life is a rectangular box.
volume = l * b * h = 490
7 * b *10 = 490
b = 7 cm
In Maths, we can observe other shapes which are exactly the same as cuboid, they are rectangular cuboid, rectangular box, right rectangular prism, right cuboid, rectangular parallelepiped, and rectangular hexahedron
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A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 8% are pennies and 36% are dimes. There are 9 more nickels than pennies. How much money does the bag contain?
Answers
during the two days after a blizzard, 77% of the snow had melted. If the snow is currently 30 inches deep, how much snow fell during the snow?
Answers
By answering the above question, we may infer that Hence, during the equation blizzard, snowfall totaled about 100.43 inches.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
To begin, let's calculate the amount of snow that evaporated. If 77% of the snow melted, the quantity of snow that is left is 100% - 77%, or 23%, of what was originally there.
This can be represented as:
Snow remaining equals 0.23x.
Assume that x inches of snow were present at the start. Thus, we may construct the equation shown below:
0.23y = 30
By finding y, we obtain:
y = 30 / 0.23 ≈ 130.43
Hence, the initial snowfall measured about 130.43 inches.
We may use the difference between the present depth of snow and the original depth of snow to calculate how much snow fell during the blizzard:
130.43 - 30 = 100.43
Hence, during the blizzard, snowfall totaled about 100.43 inches.
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A line passes through the point (8,4) and is parallel to 9x + 3y=12 . What is the equation of the line?
Answers
To find the slope of the original line and use the point slope formula y-y^1 =m(x-x^1) to find the parallel to 9x +3y=12
What is an equation of the line that passes through the point
(−3,−5) and is parallel to the line
2x+3y=15
Answers
Therefore, the equation of the line passing through (-3, -5) and parallel to the line 2x + 3y = 15, in slope-intercept form, is y = (-2/3)x - 7.
What is the Equation of Parallel Lines?To find the equation of a line parallel to the line 2x + 3y = 15 and passing through the point (-3, -5), we need to determine the slope of the given line and use it to construct the equation in slope-intercept form (y = mx + b).
The given line is in the form Ax + By = C, where A = 2, B = 3, and C = 15. To find the slope of this line, we can rearrange the equation to isolate y:
2x + 3y = 15
3y = -2x + 15
y = (-2/3)x + 5
The slope of the given line is -2/3.
Since the line we want to find is parallel to this line, it will have the same slope. Therefore, the slope of the line passing through (-3, -5) will also be -2/3.
Now, we can use the point-slope form of a linear equation to write the equation of the line:
y - y1 = m(x - x1)
Substituting the values of (-3, -5) and -2/3 for (x1, y1) and m, respectively:
y - (-5) = (-2/3)(x - (-3))
y + 5 = (-2/3)(x + 3)
To convert this equation into slope-intercept form, we can simplify and rearrange:
y + 5 = (-2/3)x - 2
y = (-2/3)x - 2 - 5
y = (-2/3)x - 7
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18x + 27 divided by 9
Answers
18x + 3
1. We are combining like terms / using PEMDAS order by dividing before adding
18x + 3 is the most simplified equation you could get as you can’t add 18x and 3 as they aren’t like terms and there’s no possible answer that it gives us to solve it as a two-step equation.
18x + 3
Answer:
that is the answer
Step-by-step explanation:
I hope it's help
Antonio randomly surveyed 20 people at a bus stop on Friday morning and in Saturday morning. He asked how old each person was. The table shows the means, median, and mode for the date Antonio collected on Friday and Saturday.
Friday morning:
Mean: 22.5
Median: 18
Mode: 16
Saturday morning
Mean: 28.8
Median: 22.5
Mode: 18
What conclusion could Antonio make about the ages of people that ride the bus?
A.) Every person that rides the bus is older than the age of 16.
B.) Every person that rides the bus is younger than the age of 29.
C.) Most people that ride the bus are older than the age of 25.
D.) Most people that ride the bus are younger than the age of 25.
Answers
Answer:
D.
Step-by-step explanation:
hope it's helppp
hopefully you
Find the missing terms in each geometric sequence.
1. 3, 12, 48 __, __
2. __, __, 32, 64, 128, ...
3. 120, 60, 30, __, __
4. 5, __, 20, 40, __, __
5. __, 4, 12, 36, __, __
Answers
2. 8, 16 (it was adding the number together 8+8)
3. 15, 7.5 ( it was half of the number)
4. 10, 80, 160 ( times 2 )
5. .75, 108, 324 ( times 4 )
Hope this helped! Lmk if you need more help!
the numerical coefficient of x2 in 3x2-3x
Answers
Answer:
Step-by-step explanation:
the numerical coefficient of x2 here is 3.
What are the 5 ways of factoring?
Answers
There are several methods for factoring expressions, including factoring out the greatest common factor (GCF), by grouping, using the difference of squares or sum/difference of cubes, using the FOIL method or the reverse FOIL method or using special cases such as perfect square trinomials or difference of squares.
Factoring out the GCF: This method involves finding the greatest common factor of all the terms in an expression and then dividing it out of each term. For example, if we have the expression 12x^2 + 8x^2, the GCF is 4x^2, so we can factor it out and write the expression as 4x^2(3 + 2).
Factoring by grouping: This method involves grouping the terms of an expression into pairs and factoring out a common factor. For example, if we have the expression x^2 + 3x + 2x + 6, we can group the first two terms and the last two terms and factor out a common factor of x from the first group and 2 from the second group. This gives us x(x + 3) + 2(x + 3)
Factoring quadratics: There are a few methods to factor quadratics, such as factoring a difference of squares, or factoring a sum or difference of cubes. For example, if we have the expression x^2 - y^2, we can factor it as (x-y)(x+y) using difference of squares.
Factoring trinomials: There are a few methods to factor trinomials, such as FOIL method or reverse FOIL method. The FOIL method is a mnemonic acronym for first, outer, inner, and last, which is used to multiply two binomials. Reverse FOIL is used to factor a trinomial that is the product of two binomials. For example, if we have the expression x^2 + 5x + 6, we can factor it as (x+2)(x+3) using reverse FOIL method.
Factoring special cases: There are some special cases of factoring that have specific methods. For example, factoring perfect square trinomials such as x^2 + 2x + 1 is factored as (x+1)^2 and factoring difference of squares such as x^2 - y^2 is factored as (x-y)(x+y)
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You draw one card from a 52-card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing a diamond each time.
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Solution:
Given:
A 52-card deck
There are four suits in a standard deck of cards, Clubs, Hearts, Spades, and Diamonds.
There are 13 diamond cards.
Hence,
\(\begin{gathered} \text{Diamond cards = 13} \\ \text{Total cards = 52} \end{gathered}\)Probability is calculated by;
\(\text{Probability}=\frac{n\text{ umber of required outcomes}}{n\text{ umber of total or possible outcomes}}\)Thus, the probability of drawing a diamond on the first draw is;
\(\begin{gathered} \text{Probability of drawing a diamond}=\frac{n\text{ umber of diamond cards}}{\text{total number of cards}} \\ \text{Probability of drawing a diamond}=\frac{13}{52} \\ \text{Probability of drawing a diamond}=\frac{1}{4} \\ P(D_1)=\frac{1}{4} \end{gathered}\)Since two draws are made with replacement, the cards are completed back again before the next draw.
Hence, the probability of drawing a diamond on the second draw is;
\(\begin{gathered} \text{Probability of drawing a diamond}=\frac{n\text{ umber of diamond cards}}{\text{total number of cards}} \\ \text{Probability of drawing a diamond}=\frac{13}{52} \\ \text{Probability of drawing a diamond}=\frac{1}{4} \\ P(D_2)=\frac{1}{4} \end{gathered}\)Therefore, the probability of drawing a diamond each time;
\(\begin{gathered} P(D_1D_2)=\frac{1}{4}\times\frac{1}{4} \\ P(D_1D_2)=\frac{1}{16} \end{gathered}\)please show your work !!!!!!!!!!!!
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Answer:
\((3.4)\)
Step-by-step explanation:
Our equation is \(f(x)=-2(x-3)^2+4\) Now there are 2 ways you can do this, I'll show you the shortcutIf you have an equation like this, just take the value in parenthesis and equate it to zero\(x-3=0.x=3\) is the x of the vertexPut this back into the equation\(f(x)=-2(x-3)^2+4\\x=3\\f(3)=-2(3-3)^2+4\\f(3)=-2(0)^2+4=4\) this is the yWhat does congruent mean in geometry?
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Answer:
The equivalency between there shapes and sizes