It takes almost 18 days to reach the population of bacteria in 3000 million.
What is the growth of bacteria?
With the passage of time, the number of bacterial populations increases as bacteria grow.
Why does growth of bacteria count is necessary?
The development of bacterial populace happens dramatically with time. In the food business it is compulsory to count the bacterial populace so food varieties are sold and devoured with flawless timing.
According to the given question:
Given, population of bacteria in millions after t days of packing= 3000
The number of bacteria is given by the equation, f(t) = 500 e∧0.1t
where t is the time in day.
we need to calculate the time taken to grow 3000 million bacteria
f(t) =3000
from the above equation, 3000 = 500e∧0.1t
3000/500 = e∧ 0.1t
6 = e∧0.1t
㏑6 = ㏑(e∧0.1t) [take ln on both side]
1.7918 = 0.1t
time, t= 17.92 days or 18 days
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Write a compound inequality for the graph shown below.
Use x for your variable.
The interval is [4, 6], and the compound inequality equals 4 ≤ x < 6 as indicated on the number line.
Given,
The number line;
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
Here,
The blue line runs from 1 to 4 and then to 6.
The solid dot at position 4 denotes inclusion, whereas the hollow dot at position 6 denotes exclusion.
Then,
x ≥ 4 and x < 6
Combindlly 4 ≤ x < 6
Hence "The interval is [4, 6], and the compound inequality on the number line is 4 ≤ x < 6 ."
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Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
Answer:
Step-by-step explanation:
Since the domain of the function h is -3 ≤ x ≤ 11 and the range is 1 ≤ h(x) ≤ 25, the possible values of h(x) for a given value of x in the domain will be within the range of 1 to 25. Additionally, we are given that h(8) = 19 and h(-2) = 2, so for the values x = 8 and x = -2, the corresponding values of h(x) are 19 and 2, respectively.
Given this information, the statement that could be true for the function h is: "For every value of x in the domain of h, the corresponding value of h(x) is within the range of 1 to 25." This statement is true because the domain and range of h are such that the possible values of h(x) for any value of x in the domain will be within the range of 1 to 25.
in a simple linear regression analysis, the p-value associated with a test of the slope coefficient was equal to .028, which would lead us to do what at the 3% level of significance? group of answer choices accept the null hypothesis. not enough information is given to answer this question. conclude that the true slope for the population is equal to zero. conclude that a linear relationship exists between the two variables.
Out of the given choices, we choose 'not enough information given to answer this question' and concluded that the true slope for the population is equal to zero.
Since, we are given a p-value associated with a test of the slope coefficient equal to 0.028 which leads to 3% level of significance, it means that there is 3% chance of finding difference which is larger than the one given in our study given that the null hypothesis is true. Since, it is less than 5% level of significance, the null hypothesis is rejected and accept an alternative hypothesis. As this hypothesis is not given, we conclude that there is not enough information to give an answer to the question.
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Find the value of the test statistic for testing whether there is a linear relationship between the and the estimated number. Round your answer to two decimal places, if necessary.
the value of the test statistic for testing whether there is a linear relationship between the and the estimated number is 0.3506905
Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127
The test statistic :
T = r² / √(1 - r²) / (n - 2)
Sample size, n = 10
Hence,
T = 0.127² / √(1 - 0.127²) / (10 - 2)
T = (0.016129 / 0.3506905)
T = 0.3506905
The value of the test statistic to 2 decimal places is 0.35
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To celebrate the holiday season this year, the Gaylord Texan has created an extreme eight-lane, tubing hill
with real snow called the "Kung Fu Panda Awesome SNOW Tubing Ride." The cost of each ticket for one day
is $21. This can be modeled by the function f(x) = 21x. The number of tickets purchased by groups is given
by the domain (4, 6, 103. which would be a reasonable range for the total cost of the tickets the groups
would pay?
The reasonable range for the total cost of the tickets the groups
would pay is {84, 126, 2163}.
What is Domain and Range?The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation.
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.
Given:
The Function modeled for the situation is
f(x) = 21 x where x is the number of tickets sold.
So, For x= 4 Tickets
Fare, F(x) = 21 x 4= $84
and, For x= 6 Tickets
Fare, F(x) = 21 x 6 = $126
and, For x= 103 Tickets
Fare, F(x) = 21 x 103 = $2163.
Hence, the range is {84, 126, 2163}.
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A rocket motor is manufactured by bonding together two types of propellants, an igniter and a sustainer. The shear strength of the bond (y) is thought to be a linear function of the age of the propellant (X) when the motor is cast. Twenty observations are shown in the following table.
A) find the least squares estimated of the slope and intercept in the linear regression model
B) find the estimate of (?^2)
C) estimate the mean shear strength of a motor made from propellant that is 20 weeks old
A- The fitted line or the fitted linear regression model is:[tex]y=2625.385462-36.96179663*x[/tex]
B- [tex]s^{2} = 9811.21237[/tex]
C- [tex]y_{20} = 1886.14953[/tex]
A fundamental and widely used form of predictive analysis is linear regression. Regression analysis' main goal is to look at two things: (1) Is it possible to accurately forecast an outcome (dependent) variable using a set of predictor variables? (2) Which individual variables—as shown by the size and sign of the beta estimates—are highly important predictors of the outcome variable, and how do they affect the outcome variable? The link between one dependent variable and one or more independent variables is explained using these regression estimations.
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What is the value of x in the figure shown below?
x =
C
xo
32°
3.2
A
115°
4
4
D
3.2
B
A cube of 9cm wan filled with 405cubic centimeters of water what is the height of water in the cube
Answer:
The answer 700 centimeters cubic.
There are 4 consecutive even integers that add up to 100. What is the least of the 4 integers?
The least among all 4 integers such that they sum up to 100 will be 22.
What is an integer?An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.
Integer; ....-2 , -1 , 0 , 1 , 2 , .....
Integers are non-decimal numbers and all integers are rational numbers.
Suppose the first integer is x.
The next three digits will be, x + 2, x + 4, and x + 6 correspondings.
Sum x + x + 2 + x + 4 + x + 6 = 100
(x + x + x + x) + (2 + 4 + 6) = 100
4x + 12 = 100
4x = 88
x = 22
Hence"The smallest of the four integers that add up to 100 is 22".
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solve the system by using elementary row operations on the equations. follow the systematic elimination procedure. x1 3x2
On solving, the given system reduces to x1 = 12, & x2 = —7 which is the required solution.
What is matrix?Linear algebra is a subfield of mathematics that mostly uses matrices. When you start solving linear equation systems, linear algebra first starts to seem good. You may concentrate on the figures and greatly simplify the procedure by condensing all the information into a single large chart and leaving out the rest.
Which 4 types of matrices are there?Almost as their name implies, square, symmetric, triangular, and diagonal matrices. All-zero identity matrices except along the major diagonal, where the values are
T he augmented matrix of the given system is B =
[tex][AB] = \left[\begin{array}{ccc}2&4&-4\\5&7&11\\\end{array}\right] \\on solving we get \\ [AB] = \left[\begin{array}{ccc}1&0&12\\0&1&-7\\\end{array}\right] \\[/tex]
Hence the given system reduces to x1 = 12 x2 = -7
Hence the given system reduces to
x1 = 12, & x2 = —7
which is the required solution.
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A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 14 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area.
The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder.
The total volume of the solid is 10 cubic centimeters.
The volume of a cylinder is given by:
V = πr²h
The total volume of the two hemispheres is given by:
V = 2 x 2/3 πr³
Now, the total volume of the solid is given by:
V total = πr²h + 2 x 2/3πr³
Now, substitute the value of the total volume in the above expression and then solve for h.
10 = πr²h + 4/3πr³
h = 10/πr² + 4r/3
Now, the surface area of the curved surface is given by:
A = 2πrh
Now, the surface area of the two hemispheres is given by:
A' = 2 x 2πr²
A' = 4πr²
Now, the total area is given by:
A total = 2πrh + 4πr²
Now, substitute the value of 'h' in the above expression.
A total = 2πr(h = 10/πr² + 4r/3) + 4πr²
Simplify the above expression.
dA = -20/r + 4πr²/3
Now, differentiate the total area with respect to 'r'.
dA/dr = 20/r + 8πr/3
Now, equate the above expression to zero.
0 = -20/r² + 8πr/3
Simplify the above expression in order to determine the value of 'r'.
8πr³ = 60
r = 1.34 cm
Therefore, the radius of the cylinder that produces the minimum surface area is 1.34cm
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if the 90 percent confidence interval for u is from 34 to 50 then there is a 10 percent chance that this interval does not contain u
AS per the given confidence interval, the z score is 0.54
The term confidence interval refers a parameter will fall between a pair of values around the mean.
Here we have given that if the 90 percent confidence interval for u is from 34 to 50 then there is a 10 percent
And we need to find the z value.
While we looking into the given situation, we have identified the following values,
Confidence interval = 95%
Interval = 34 - 50
Mean = 10
Through the given interval we have identified the that sample size was calculated as,
=> 50 - 34
=> 16
Then the z score is
=> z = 10/√16
=> z = 10/4
=> z = 2.5
Then according to the confidence interval, the value from the z table is obtained as.
=> z = 1.96
Then the difference is
=> 2.5 - 1.96
=> 0.54
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Select all the true statements.
The angle bisectors of a triangle intersect at the circumcenter.
A circle is circumscribed about a
• triangle if the triangle's vertices are on the circle.
A circle is inscribed in a triangle if
• the sides of the triangle are tangential to the circle.
The perpendicular bisectors of the
• sides of a triangle intersect at the circumcenter.
All statements that are true from the options are:
The angle bisectors of a triangle intersect at the circumcenter.A circle is circumscribed about a triangle if the triangle's vertices are on the circle.A circle is inscribed in a triangle if the sides of the triangle are tangential to the circle.The perpendicular bisectors of the sides of a triangle intersect at the circumcenter.i. To circumscribe a given shape implies drawing a circle outside the a given shape. While to inscribe a given shape means to draw a circle within the boundaries of the shape.
ii. A tangent is a straight line which intersect the the circumference of a circle at a point externally.
iii. A perpendicular bisector is a straight line that divides a given line into two equal halves. And it is at right angle to the given line.
iv. The circumcenter of a triangle is the middle point/ center of the triangle.
Therefore, the statements that are true are:
The angle bisectors of a triangle intersect at the circumcenter.A circle is circumscribed about a triangle if the triangle's vertices are on the circle.A circle is inscribed in a triangle if the sides of the triangle are tangential to the circle.The perpendicular bisectors of the sides of a triangle intersect at the circumcenter.Thus all the given statements are true.
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A skier skis along a circular ski trail that has a radius of 1.7 km. The skier starts at the East side of the ski trail and travels in the CCW direction. Let θ represent the radian measure of the angle the skier has swept out.
a) Write an expression (in terms of θ) to represent the skier's distance to the East of the center of the ski trail (in km).
b) Write an expression (in terms of θ) to represent the skier's distance to the North of the center of the ski trail (in km).
The skier's distance to the east of the center of the ski trail is
x = 1.25cosθ
The skier's distance to the north of the center of the ski trail is
y = 1.25sinθ
When radius 'r' and the angle θ are given, the coordinates (x,y) as shown
x = east direction
y = north direction
In this case we get,
x = r cosθ
y = r sinθ
Given r = 1.25 km
We get,
x = 1.25 cosθ in east direction
y = 1.25 sinθ in north direction
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The temperature of a liquid in an experiment starts at 0 degrees Celsius. The experiment calls for the temperature of the liquid to change at a rate of –0.6 degree Celsius per minute.
How long will it take for the liquid to reach –10.5 degrees Celsius? pls answer quick
Answer:
17.5 or 17 minutes and 30 seconds
Step-by-step explanation:
consider the modified keynesian model with a change in the way that taxes are incorporated:
a) The Keynesian cross graphs an economy's planned expenditure function,
[tex]$\mathrm{E}=\mathrm{C}(\mathrm{Y}-\mathrm{T})+\mathrm{I}+\mathrm{G}$[/tex],
and the equilibrium condition that actual expenditure equals planned expenditure.
How do you find the expenditure function?
To derive the expenditure function we can either (i) invert V(·) and solve for M, or (ii) set up the dual of the consumer's choice problem, solve for Hicksian demand functions and substitute them into the objective (i.e., expenditure) function.
The amount by which[tex]$\mathrm{Y}$[/tex]falls is given by the product of the tax multiplier and the increase in taxes
[tex]: $\Delta \mathrm{Y}=[-\mathrm{MPC} /(1-\mathrm{MPC})] \Delta \mathrm{T}$.[/tex]
c) We can calculate the effect of an equal increase in government expenditure and taxes by adding the two multiplier effects that we used in parts a and b :
[tex]\Delta \mathrm{Y}=\left[(1 /(1-\mathrm{MPC}))^* \Delta \mathrm{G}\right]-[(\mathrm{MPC} /(1-\mathrm{MPC}))]^* \Delta \mathrm{T}[/tex]
Because government purchases and taxes increase by the same amount, we know that [tex]\Delta \mathrm{G}=\Delta \mathrm{T}$. Therefore we can rewrite the equation as:$$\Delta \mathrm{Y}=[(1 /(1-\mathrm{MPC}))-(\mathrm{MPC} /(1-\mathrm{MPC}))]^* \Delta \mathrm{G}=\Delta \mathrm{G}[/tex]
This expression tells us that an equal increase in government purchases and taxes increases [tex]$\mathrm{Y}$[/tex] by the amount that [tex]$\mathrm{G}$[/tex] increases. That is, the balanced-budget multiplier is exactly 1 .
Complete question: Consider the Keynesian model with a change in the way that taxes are incorporated: (1) PAE = C + IP + G + NX Definition of Planned Aggregate Expenditure (2) C = C+ mpc (1-1) .y Consumption Function (3) PAE = Y Short-run Equilibrium Condition In this case, taxes paid are proportional to income, i.e. taxes paid are t - Y, where t is the tax rate and 0<t< 1. Disposable income is the part of income after taxes, i.e., (1-t). Y. Solve for the PAE spending line with PAE as a function of Y. What is the slope?
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There are 40 school days in a 2-month
period. How many times can a boy be
expected to take attendance?
A. 16
B. 20
C. 24
D. 28
If there are 40 school days in a 2-month period. The number of times can a boy be expected to take attendance is: B. 20.
How to find the number of attendance times?Given data:
Number of school days = 40
Number of month = 2
Now let find the number of attendance times
Number of attendance times = Number of school days/ Number of month
Number of attendance times = 40/2
Number of attendance times = 20
Therefore the correct option is B.
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The following data come from a study designed to investigate drinking problems among college students. In 2013, a group of students were asked whether they had ever driven an automobile while drinking. In 2017, after the legal drinking age was raised, a different group of college students were asked the same question. Drove While Year Drinking 2013 2017 Total Yes 1236 1008 2244 No 1405 1657 3062 Total 2641 2665 5306 (a) Use the chi-square test to evaluate the null hypothesis that the population propor- tions of students who drove while drinking are the same in the two calendar years. (b) What do you conclude about the behavior of college students? (c) Again test the null hypothesis that the proportions of students who drove while drinking are identical for the two calendar years. This time use the method based on the normal approximation to the binomial distribution (refer to slides 25 to 31 of Unit 12). Do you reach the same conclusion? (d) Construct a 95% confidence interval for the true difference in population propor- tions. (e) Does the 95% confidence interval contain the value of 0? Would you have expected that it would?.
the 95% confidence interval contains the value of 0. This is expected since the result from the chi-square test and the result from the normal approximation test were both significant.
a) The chi-square test statistic is 15.95 and is significant at the 0.005 level. This indicates that the population proportions of students who drove while drinking are not the same in the two calendar years.
b) The behavior of college students regarding driving while drinking changed between 2013 and 2017.
c) The test based on the normal approximation to the binomial distribution also yields a significant result (p-value = 0.0045), indicating that the population proportions of students who drove while drinking are not the same in the two calendar years.
d) The 95% confidence interval for the true difference in population proportions is [-0.072, -0.023].
e) Yes, the 95% confidence interval contains the value of 0. This is expected since the result from the chi-square test and the result from the normal approximation test were both significant.
Chi-square test statistic:
X2 = 15.95
Normal approximation test statistic:
P-value = 0.0045
95% confidence interval:
[-0.072, -0.023]
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if a linear function is increasing, explain mathematically why the reciprocal function must be decreasing
If a linear function is increasing, the reciprocal function must be decreasing, mathematically because the reciprocal function is the inverse of the linear function
The reciprocal function of a linear function is given by the formula:
f(x) = 1/x
If a linear function is increasing, then its slope (m) is positive. This means that the slope of the reciprocal function must be negative. The slope of the inverse of a linear function is the negative reciprocal of the slope of the linear function, meaning that the slope of the reciprocal function must be negative for the linear function to be increasing.
To illustrate this, we can consider a simple example of a linear function, f(x) = 2x. This linear function has a positive slope (2), so its reciprocal function, f(x) = 1/x, must have a negative slope (-1). This means that the reciprocal function is decreasing.
In general, if a linear function is increasing, then its reciprocal function must be decreasing, as the slope of the reciprocal function must be the negative reciprocal of the slope of the linear function.
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The sum of the interior angles of a triangle is sometimes, but not always, 180º.
True
False
The sum of the interior angles of a triangle is sometimes, but not always, 180º is false.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
There are three angles in a triangle.
The sum is always 180 degrees.
Thus,
The sum of the interior angles of a triangle is always 180°.
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c) For the high jump, each competitor receives multiple opportunities to clear the bar at
each height. On average, Shane completes 3 out of 3 jumps on the lowest bar, 5 out of
6 jumps on the middle bar, and 3 out of 4 jumps on the highest bar. What is
Shane’s overall average number of jumps completed? (2 points)
d) If Shane’s average number of jumps completed is greater than one-half, then the eighth
graders earn 50 points. Which grade should be awarded 50 points**? (1 point)
PLEASE QUICK!
c) Shane’s overall average number of jumps completed is of 2.458275.
d) As Shane's overall average number is greater than one half, then the eight graders will be awarded the 50 points.
How to obtain the average number of jumps completed?The jumps that Shane takes are given as follows:
Lowest bar: 100% probability of completed, as 3/3 = 100.Middle bar: 0.8333 = 83.33% probability, as 5/6 = 0.8333.Highest bar: 0.75 = 75% probability, as 3/4 = 0.75.Then the probabilities for each number are given as follows:
One jump -> only the lowest: 1 x (1 - 0.8333) = 0.1667.Two jumps -> lowest and middle: 1 x 0.8333 x (1 - 0.75) = 0.208325.Three jumps -> all -> 1 x 0.8333 x 0.75 = 0.624975.Then the distribution of the number of jumps completed is given as follows:
P(X = 1) = 0.1667.P(X = 2) = 0.208325.P(X = 3) = 0.624975.The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability, hence:
E(X) = 1 x 0.1667 + 2 x 0.208325 + 3 x 0.624975 = 2.458275.
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Write the equation of the line in fully simplified slope-intercept form.
The equation of the line in fully simplified slope-intercept form is y = -x/3 -1
The slope-intercept form of a straight line is used to find a line's equation. We need to know the slope of the line and the intercept where the line crosses the y-axis in order to use the slope-intercept formula.
Consider a straight line with y-intercept b and slope m. For a straight line with slope "m" and y-intercept "b,"
The slope intercept form equation is: y = mx + b.
According to the question,
The line is passing through (3,-2) and (-3 ,0)
Slope of any line passing through two points = y2-y1 / x2-x1
Slope of required line: m = 0 - (-2) / -3 - 3
=> m = -2/6
=> m = -1/3
Equation of line => y = -1/3 x + b -----(1)
As we know this line is passing through (-3,0)
Substituting the value in equation(1)
=> 0 = 1 + b
=> b = -1
Hence , The equation of line is y = -1/3 x -1
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tell me the answer to pls 40 divided by m
The expression of the statement 40 divided by m is 40/m
How to determine the expressionFrom the question, we have the following parameters that can be used in our computation:
40 divided by m
The above statement is a mathematical statement
The mathematical statement can be expressed as an expression
Recall that, we have
40 divided by m
The term "divided by" means a quotient expression
To divide is represented as / i.e. quotient
So, the expression that represents 40 divided by m is 40/m
Hence, the complete expression is 40/m
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How many solutions does 9x+7=8x+7
Answer:
One
Step-by-step explanation:
The equation 9x+7=8x+7 has only one solution. This can be seen by setting the two sides of the equation equal to each other and then solving for x.
First, we set the two sides equal to each other by canceling out the 7 on the right side of the equation:
9x+7 = 8x+7
Then, we move all of the terms that have an x on the same side of the equation, and all of the constant terms on the other side:
9x - 8x = 7 - 7
Next, we combine like terms on the left side of the equation:
x = 0
Finally, we solve for x to find the value of x that makes the equation true:
x = 0
Therefore, the only solution to the equation 9x+7=8x+7 is x=0.
3. Solve the equation. Show your work. Express your answer as both a simplified mixed number and as a decimal.
Answer:
the sum of a number, 1/6 of that number, and 7 is 121/2 find the number
Answer:
The number is:
321/7
Step-by-step explanation:
a + a/6 + 7 = 121/2
6a/6 + a/6 + 42/6 = 363/6
6a + a + 42 = 363
7a = 363 - 42
7a = 321
a = 321/7
Check:
321/7 + (321/7)/6 + 7 = 121/2
321/7 + 321/42 + 7 = 121/2
1926/42 + 321/42 + 294/42 = 2541/42
1926 + 321 + 294 = 2541
how many eight digit numbers contain the digit 2 once, the digit 3 twice, and the digit 4 thrice. leading 0s are allowed. (
0.0405 is the number that contains the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.
based on data gathered from the sources
Suppose the information as shown by
How many eight-digit numbers have more 5s than 3s and contain the digits 2 exactly once, 3 exactly twice, and 4 precisely three times
Let there be more 5s than 3s and more 8-digit numbers with the digits 2 once, 3 twice, 4 three times, and 5s than 3.
2,3,3,4,4,4
after that:
= 8!/2!3!3!4!4!4!
= 8.7.6.5.4!/2×6×6×24×24×4!
= 35/864
Now, 0.405, followed by a digit 2 and 3 make up the eight-digit number.
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24. Name a point on ∠MNO
Only point Q is on the ∠MNO because when we connect the point M and O then point R lies outside the ∠MNO. Only point Q remains inside.
In the given question we have to name a point on ∠MNO.
As we know that;
Evaluating the number of points in the curve of the triangle's vertices that are close to the location in question is the easiest method for determining whether a point is inside a triangle. The point on the curve is inside the triangle if it has three points; if it has four, it is outside the triangle.
When we check in the graph then only point Q is on the ∠MNO because when we connect the point M and O then point R lies outside the ∠MNO. Only point Q remains inside.
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#9.
The table represents some points on the graph of linear function f.
Which function represents f ?
f(x)=32(3 x-1)
f(x)=-32(x-3)
f(x)=-2(32 x-3)
f(x)=16(2 x-1)
The option a is giving the same value according the table. So the option a is correct answer.
In the given question, the table represents some points on the graph of linear function f.
We have to find which function represents f.
(a) f(x)= 32(3x-1)
(b) f(x)= -32(x-3)
(c) f(x)= -2(32x-3)
(d) f(x)= 16(2x-1)
We find the pattern we firstly observe the given table closely.
So from the given table;
f(-2) = -224, f(1) = 64, f(5) = 448, f(10) = 928
To check which option is giving the value of f(x) right according to table, we put the value in each option.
Firstly taking the option a.
f(x)= 32(3x-1)
Now checking the option 1.
Putting x=-2, if the value of f(-2) = -224, then the option is correct.
f(-2)= 32(3(-2)-1)
f(-2)= 32(-6-1)
f(-2)= 32*(-7)
f(-2)= -224 (True)
Now putting x=1 in the same option to cross check, if the value of f(1) = 64, then the option is correct.
f(1)= 32(3(1)-1)
f(1)= 32(3-1)
f(1)= 32(2)
f(1)= 64
Now the option a is giving the same value according the table. So the option a is correct answer.
We find the right answer so we don't check the further option. To check next option you can use the same way.
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Use interval notation to express the set of real numbers x that satisfies the inequality -2 <= x < 5.
To express the set of real numbers x that satisfies the inequality -2 ≤ x < 5, we used the Interval notation method and got the solution set as [-2,5).
Interval Notation Method :Interval notation is a way of representing intervals on the number line. That is, how to write a subset of the real number line. Intervals include numbers between two specific numbers. We can use this notation to express inequalities.
Generally, we read about the three types of intervals :
Open intervals : This type of interval does not contain the endpoints of the inequality. For example, for set {x | -a< x < b}, the open interval notation is (-a, b).Closed Intervals: This type of interval contains the endpoints of the inequalities. For example, for set {x | -a≤ x ≤ b} the closed interval notation is [-3,1].Half-Open Interval: This type of interval contains only one endpoint of the inequality. For example, for set {x| -a ≤ x < b} the half-open interval notation is [-3,1).We have given an inequality as -2 ≤ x < 5
We have to express the set of real numbers x that satisfies the given inequality.
Let's started, The first thing we'll want to ask ourselves is if we're going to use parentheses or brackets when we write this.
y = { x | -2 ≤ x < 5 }
We see that the lower value of x is -2 or greater than -2 and higher value of x is less than 5. We're just going to write it down. Using the interval notation, the lower side x is greater than and equal to -2 so, we use closed bracket here and the upper side x is less than 5 that is we use parentheses or open bracket here.
Thus, in interval notation y = x , x∈[-2, 5)
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