We are asked to identify which of the given inequalities represent the given graph.
Notice that the graph is showing the area below the intersection of inequalities.
This means that the inequalities must be "less than"
Also, notice that the lines are solid (not dashed) so the inequalities must be "equal to or less than"
Therefore, the correct inequalities are
\(y\le\frac{3}{4}x+10\; and\; y\le-\frac{1}{2}x-3\)Option A is the correct answer.
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
a triangle has one side length of 9cm and another side of .12cm what are 3 possible answers for the third side
If a triangle has one side length of 9cm and another side of .12cm . The 3 possible answers for the third side are: 17, 20, and 21.
What are the possible lengths for the third side?To determine the possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
Using this theorem, the possible lengths for the third side can be found by checking which of the following inequalities hold:
9 + 12 > x
9 + x > 12
12 + x > 9
Simplifying these inequalities, we get:
x > -3 (always true)
x > -9 (always true)
x > -3 (always true)
Therefore, the possible lengths for the third side of the triangle must satisfy x > -9, which eliminates the answer 3 (which is less than 9 - 12 = -3).
The possible lengths for the third side are:
9 + 12 > x, so x < 21
9 + x > 12, so x > -3
12 + x > 9, so x > -3
Therefore, the possible lengths for the third side of the triangle are:
17 (9 + 12 = 21, which is greater than 17)
20 (9 + 12 = 21, which is greater than 20)
21 (9 + 12 = 21, which is equal to 21)
So, the three possible lengths for the third side of the triangle are 17, 20, and 21.
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The complete question is:
A triangle has one side length of 9
centimeters (cm) and another side length of 12
cm.
Which answers are possible lengths for the third side?
Select three that apply
17
22
9
21
20
3
Question 2 The current report quantitatively analyzes three variables - load factors, revenue passenger mile, and available seat miles for American Airlines. The data retrieved for the analysis was extracted from the Bureau of Transportation Statistics, focusing on domestic flights from January 2006 to December 2012. The quantitative analysis focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. Table 2: Summary Statistics of American Airlines (Domestic) Revenue Passenger Miles Mean 6,624,897 Median 6,522,230 Mode NONE Minimum 5,208,159 Maximum 8,277,155 Standard Dev 720,158.571 Variance 518,628,367,282.42 Load Factors Mean 82.934 Median 83.355 Mode 84.56 Minimum 74.91 Maximum 89.94 Standard Dev 3.972 Variance 15.762 Revenue Passenger Miles 9000000 8000000 7000000 6000000 5000000 4000000 3000000 2000000 1000000 0 0 10 American Airlines (Domestic) Performance 20 30 ● Revenue Passenger Miles 40 50 Load Factors Available Seat Miles 60 Mean 7,984,735 Median 7,753,372 Mode NONE Minimum 6,734,620 Maximum 9,424,489 Standard Dev 744,469.8849 Variance 554,235,409,510.06 70 80 Linear (Revenue Passenger Miles) 90 100 Figure 1: American Airlines (Domestic) Performance Write a report based on the given data. Please include additional tests such as hypothesis testing, skewness, z statistic, level of significance, and other necessary tests, as well as a discussion of the results obtained.
The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.
The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.
Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).
The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.
The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.
The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).
Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
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The set of ordered pairs (1, 7), (3, 8), (3, 6), (6, 5), (2, 11), (1, 4) represents a relation. Is the relation a function?
Answer:
Step-by-step explanation:
This relation is not a function because the x value repeats. (3,8) and (3,6)
If you plot these points, they won't past the vertical line test
No, the given set of ordered pair do not represent a relation.
What is function?A function is defined as a relation between a set of inputs having one output each.
Given is a set of ordered pairs, (1, 7), (3, 8), (3, 6), (6, 5), (2, 11), (1, 4)
We see, in points (3, 8) and (3, 6), the value of x corresponds to two values of y, i.e. 8 and 6, which contradicts the definition of relation function.
Hence, we can say that given ordered pair do not show a relation.
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Determine whether the following inequalities satisfy the number line shown below.
The inequalities which satisfy the number line shown is x>2 and x>=2.
We are given that;
The number line showing inequality
Now,
x>2 satisfies the equation by the given number line
x>=2 satisfies the equation by the given number line
x<=-3 does not satisfies the equation by the given number line
x<=-3 does not satisfies the equation by the given number line
Therefore, by the number line the answer will be x>2 and x>=2 .
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NO LINKS!!
Consider the following equation.
y = x^3 + 5
Test for symmetry. (select all that apply)
1. x-axis symmetry
2. y-axis symmetry
3. origin symmetry
4. no origin symmetry
Graph the equation.
Answer:
4. no origin symmetry-----------------------------
Given function:
y = x³ + 5Graph it first (see attached).
Test the graph for symmetry.
We know the odd degree parent function y = x³ has an origin symmetry, whilst even degree functions may have axis symmetry.
The given function is a translation of cubic function 5 units up so the center of symmetry has translated as well. Therefore correct answer is 4.
Answer:
4. no origin symmetry
Step-by-step explanation:
Functions are symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, −b) on the graph:
f(x, y) = f(x, −y)To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.
\(\begin{aligned}&\textsf{Given}: \quad &y &= x^3 + 5\\&\textsf{Replace $y$ for $(-y)$}: \quad &-y &= x^3 + 5\\&\textsf{Simplify}: \quad &y &= -x^3 - 5\end{aligned}\)
Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the x-axis.
--------------------------------------------------------------------------------------------------
Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:
f(x, y) = f(-x, y)To determine if a graph is symmetric with respect to the x-axis, replace all the x's with (−x). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.
\(\begin{aligned}&\textsf{Given}: \quad &y&=x^3+5\\&\textsf{Replace $x$ for $(-x)$}: \quad &y&=(-x)^3+5\\&\textsf{Simplify}: \quad &y&=-x^3+5\end{aligned}\)
Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the y-axis.
--------------------------------------------------------------------------------------------------
Functions are symmetric with respect to the origin if for every point (a, b) on the graph, there is also a point (-a, -b) on the graph:
f(x, y) = f(-x, -y)To determine if a graph is symmetric with respect to the origin, replace all the x's with (−x) and all the y's with (-y). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the origin.
\(\begin{aligned}&\textsf{Given}: \quad &y&=x^3+5\\&\textsf{Replace $x$ for $(-x)$ and $y$ for $(-y)$}: \quad &(-y)&=(-x)^3+5\\&\textsf{Simplify}: \quad &-y&=-x^3+5\\&&y&=x^3-5\end{aligned}\)
Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the origin.
Select the correct answer from each drop-down menu.
A coordinate grid is placed on top of a city map, showing the following characteristics:
• Washington Avenue is represented by the line x = 3.
.
Lincoln Avenue passes through the point (5,2).
Lincoln Avenue and Washington Avenue are parallel.
line
Lincoln Avenue is represented by the line
Answer:
Lincoln Avenue is represented by the line \( x = 5 \), which is a VERTICAL LINE.
Step-by-step explanation:
The equation of the line of Washington Avenue, x = 3, suggests that the line is a vertical line, since a vertical line takes the form of x = k, where k is the value x would always take and also it is the x-intercept.
Given that Lincoln Avenue passes through the point (5, 2), and its line is parallel to that of Washington Avenue, it means that the line do not intercept each other, and Lincoln Avenue is also a vertical line.
Therefore, if Lincoln Avenue passes through (5, 2), its line can be represented also in the form, x = k. Where, k is the value that x would always take, and also, it is the x-intercept. x would always be 5 even when y changes.
Therefore, the equation of the line that represents Lincoln Avenue would be:
✅ \( x = 5 \)
✅This is also a Vertical line.
simplify using the rules of rational exponents
The subtraction problem 4/5 - 2/7 can be rewritten as the addition problem _[blank].
Enter your answer as the expression that correctly fills in the blank.
Enter fractions formatted like this: 3/14
It can be written as 13/35.
how do we rewrite a fraction.
Divide the numerator by the denominator
Write down the whole number result
Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.
A number that will divide evenly into both the numerator and denominator so it can be reduced, or
The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number
4/5-3/7
⇒4×7-3×5/ 35 ( 5 and 7 have no common divisor).
⇒ 28- 15/35
⇒13/35
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Please help!! I know 37x25=925, but I need the blank part I can’t figure it out.
37
26
___
925
I WILL GIVE BRAINLY. The couch in the living room of Angela's dollhouse is 6 centimeters long. The couch in Angela's real living room is 8 feet long What is the unit rate that compares the length of the couch in the living room to the length of the couch in the dollhouse? Enter your answer, as a mixed number in simplest form, by filling in the boxes.
We have :
\( \frac{8}{6} = \frac{6 + 2}{6} = \frac{6}{6} + \frac{2}{6} = 1 + \frac{1}{3} = 1 \frac{1}{3} \)
Ok done. Thank to me :>
The unit rate that compares the length of the couch in the living room to the length of the couch in the dollhouse is 1.33 ft/cm
A unit rate describes the ratio of two different units for the quantity of one. It has one in the denominator.
The unit rate that compares the length of the couch in the living room to the length of the couch in the dollhouse is gotten by:
Ratio of the length of the couch in the living room to the length of the couch in the dollhouseHence:
Unit rate = 8 feet / 6 cm
Unit rate = 1.33 ft/cm
The unit rate that compares the length of the couch in the living room to the length of the couch in the dollhouse is 1.33 ft/cm
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Find the second differences
The second difference of the given number table is: Option A: -2
How to find the second differences?The second difference method can be used to determine a quadratic model. In order for us to calculate the second difference, we will select 3 consecutive y-values, and then subtract the first y-value from the second and the second y-value form the third. Then we will find the difference of these two resulting values. That difference is what we refer to as the second difference.
Thus, Applying the second difference concept to our problem, we have:
First difference:
-4 - (-9) = 5
-1 - (-4) = 3
Thus, second difference is:
3 - 5 = -2
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2) Key components of financial planning include all of the following except:
A) Write out a detailed plan for accomplishing your goals
B) Replace money myths with money truths
C) Allow your financial planner to make all of your major money decisions
D) Regularly monitor and reassess your financial plan
Answer:
b
Step-by-step explanation:
i took the test pls mark me the brainliast
Please anyone that can help me
Answer:
\(|\frac{x}{y} |\)
Step-by-step explanation:
Pre-SolvingWe are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.
We want to simplify it.
To do that, we can first simplify what is under the radical, then take the square root of what is left.
Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.
SolvingTo simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).
So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .
Under the radical, we now have:
\(\sqrt{x^2y^{-2}}\)
Now, we take the square root of both exponents to get:
\(|xy^{-1}|\)
The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.
However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.
Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).
So, by using that,
\(|x * \frac{1}{y} |\)
This can be simplified to:
\(|\frac{x}{y} |\)
Which table represents y as a function of x?
Answer:
The first one
Step-by-step explanation:
Let f(x) = x^2-4 what is the range
Answer:
Range: [−4,∞)
Step-by-step explanation:
Hope it helps:)
Answer:
Range: [-4, ∞), {y|y ≥ -4}
Step-by-step explanation:
It helps if you graph the function to better understand what the range is.
In interval and set-builder notation, the range is:
[-4, ∞), {y|y ≥ -4}
This is knowing that the Domain is:
(-∞, ∞), {x|x ∈ R}
which of the following is most likely the next step in the series
Answer:
A.
Step-by-step explanation:
Let's think of this as a clock. We can see that the 2 lines start in the same place, around 3 o'clock. Next, one of the line segments shifts down to around 6 o'clock. Next, it shifts to about 9 o'clock. Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.
We can also just use a regular circle, with one of the line segments moving 90 degrees each time.
Hope this helps! :)
Use the following table to find the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Students on the Student Government Board
On-Campus Housing Off-Campus Housing
Freshman 2 2
Sophomore 2 4
Junior 0 3
Senior 4 2
Graduate Student 2 0
The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).
1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:
Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19
2. Calculate the total number of graduate students on the Student Government Board:
Total Graduate Students = 2 + 0 = 2
3. Calculate the total number of students living in on-campus housing:
Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10
4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:
Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19
5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:
Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19
6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:
Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19
7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.
8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).
9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.
Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).
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In each of the following scenarios, select the appropriate scale of measurement. a. A meteorologist records the amount of monthly rainfall over the past year.
A. Nominal B. Ordinal C. Interval D. Ratio b. A ski resort records the dally temperature daring the month of Januiry. A. Nominal B. Ordinal C. Interval D. Ratio
c. A restaurant surveys its customers about the qualty of lts waiting staff pin a scale of 1 to 4 where 1 is poor and 4 is excelient. A. Nominat B. Ordinal C. interval D. Ratio
In each of the following scenarios, the appropriate scale of measurement is given below.
What is ratio?
The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
Nominal - naming or labeling
Ordinal - a rating of sorts
Interval - the ability to organize data into intervals
Ratio - Zero is the strongest level of measurement and is significant.
A meteorologist records the amount of monthly rainfall over the past year = Ratio.
A ski resort records the daily temperature during the month of January = Interval.
A restaurant surveys its customers about the quality of its waiting staff on a scale of 1 to 4, where 1 is poor and 4 is excellent = Ordinal
Therefore, all the appropriate measurements are given above.
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48. Line h passes through the point (4, 12) and is parallel to line k.
Line k passes through the points (-12, -3) and (4,9).
Which of the following is the equation for line h?
Answer: y = 3/4 x + 8
Step-by-step explanation: First you must find the slope of line k.
y2 - y1
m = ----------- The slope is 3/4
x2 - x1
Since the two lines are paralell you know that line h has the same slope.
Next you must find the y-intercept by replacing x and y with the values given by the point.
y = 3/4x + ? -----> 12 = 3/4(4) + ?
12 = 3 + 8
The y-intercept is 8
Your equation for line h is y = 3/4 x +8
Hope this was helpful!
In the equation (x-3)²+(y-2)2=16, the radius of the circle is...
16
3
32
4
Step-by-step explanation:
This is of the form
(x-h)^2 + ( y-k)^2 = r^2 so r^2 = 16 means r = 4 units
If given that :-
\( {\quad \leadsto \quad \bf f(\phi) = {\phi}^{2} - \phi - \displaystyle \bf \int_{\bf 0}^{1} f(\phi) d \phi }\)
Then find :-
\( { \quad \leadsto \quad \displaystyle \bf \int_{0}^{2} f(\phi) d \phi }\)
Integrate by parts with
\(u = f(\phi) \implies du = f'(\phi) \, d\phi = (2\phi - 1) \, d\phi\)
\(dv = d\phi \implies v = \phi\)
to evaluate the integral in the definition of \(f\).
\(\displaystyle \int_0^1 f(\phi) \, d\phi = \phi\,f(\phi) \bigg|_0^1 - \int_0^1 \phi(2\phi-1) \, d\phi = f(1) - \frac16\)
Now if \(\phi=1\), we have
\(f(1) = 1^2 - 1 - \left(f(1) - \dfrac16\right) \implies 2f(1) = \dfrac16 \implies f(1) = \dfrac1{12}\)
and so
\(\displaystyle \frac1{12} = 1^2 - 1 - \int_0^1 f(\phi) \, d\phi \implies \int_0^1 f(\phi) \, d\phi = -\frac1{12}\)
It follows that
\(\displaystyle \int_0^2 f(\phi) \, d\phi = \int_0^2 \left(\phi^2 - \phi + \frac1{12}\right) \, d\phi \\\\ ~~~~~~~~~~~~~~~ = \left(\frac{\phi^3}3 - \frac{\phi^2}2 + \frac\phi{12}\right) \bigg|_0^2 \\\\ ~~~~~~~~~~~~~~~ = \frac{2^3}3 - \frac{2^2}2 + \frac2{12} \\\\ ~~~~~~~~~~~~~~~ = \boxed{\frac56}\)
Determine the probability p(1 or fewer) for a binomial experiment with trials and the success probability . Then find the mean, variance, and standard deviation.
Complete Question
Determine the probability P(1 or fewer) for a binomial experiment with n = 16 trials and the success probability p = 0.2. Then find the mean, variance, and standard deviation
Answer:
The probability is \(P(X \le 1 ) = 0.0484\)
The mean is \(\mu = 3.2\)
The variance is \(\sigma ^2 =2.56\)
The standard deviation is \(\sigma =1.6\)
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.2
The sample size is n = 16
Generally this experiment follows a binomial distribution
i.e
\(X \~ \ \ \ B(n , p)\)
and the probability distribution function for binomial distribution is
\(P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}\)
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the the probability P(1 or fewer) is mathematically represented as
\(P(X \le 1 ) = P(X = 0 ) + P(X = 1 )\)
=> \(P(X \le 1 ) = [^{15}C_0 * (0.2)^0 * (1- 0.2)^{15-0}] + [^{15}C_1 * (0.20)^1 * (1- 0.20)^{15-1} ]\)
=> \(P(X \le 1 ) = [1 * 1* 0.0352 ] + [15 * 0.20 * 0.0439]\)
=> \(P(X \le 1 ) = 0.0484\)
Generally the mean for this experiment is mathematically represented as
\(\mu = n * p\)
=> \(\mu = 16 * 0.2\)
=> \(\mu = 3.2\)
Generally the variance is mathematically represented as
\(\sigma ^2 = n * p * (1- p )\)
=> \(\sigma ^2 = 16 * 0.2 * (1- 0.2)\)
=> \(\sigma ^2 =2.56\)
Generally the standard deviation is mathematically represented as
\(\sigma = \sqrt{\sigma ^2 }\)
=> \(\sigma =1.6\)
jose spent 6 hours in school. each school period is 3/4 hour long. how many period did jose spend in school?
Answer:
why are you asking me ask jose
what the mean of 1,3,5,5, 1, 3, 0, 0, 5
1+3+5+5+1+3+5+0+0
4+5+5+1+3+5
9+5+1+3+5
14+1+3+5
15+3+5
18+5
23
23/9
the mean is 2 and 5/9
Helppppppppppppppppppppppppppp
Answer:
hola como esta bb te extraño cuando vienes a casa para el favor
Answer:
I may be wrong! But, I think it is 76 degrees
Step-by-step explanation:
if you draw a straight line between the left line to the point of W you get a right triangle on the left. Now you know two angles 41+90= 131. A right triangle=180 degrees.
take 180-131= 49 degrees. This is the angle next to W on the left
Then, do the same thing to the right. Draw a right triangle, take 35+90=125, 180-125=55.
55 is the angle to the left of W.
Now add those two numbers, 55+49= 104
A straight line=180 so do 180-104=76, check 76+55+49=180
76 should be W
For P(x) = 2x^4 – 5x^3+x-10, use synthetic substitution to evaluate P(-2). P(1), and P(2).
Answer:
P(-2) = 2(-2^4) - 5(-2^3) + (-2) -10
= 2(16) - 5(-8) + (-2) - 10
= 32+40-2-10
= 60
P(1) = 2(1^4) - 4(1^3) + (1) - 10
= 2 - 4 + 1 - 10
= -11
P(2). = 2(2^4) - 5(2^3) + (2) - 10
= 2(16) - 5(8) + 2 - 20
= 32-40+2-10
= -20
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
9,16,23,...
Find the 46th term.
The 46th term of the sequence is 324.
We have,
To find the 46th term of the sequence, we need to determine the pattern or rule that generates the terms.
Since the difference between consecutive terms is a constant value of 7, we know that this is an arithmetic sequence with a common difference
of 7.
To find the 46th term, we can use the formula for the nth term of an arithmetic sequence:
a(n) = a(1) + (n - 1) d
where a(1) is the first term, d is the common difference, and n is the term number we want to find.
Using the given information, we have:
a(1) = 9
d = 7
n = 46
Plugging these values into the formula, we get:
a (46) = 9 + (46 - 1)7
a (46) = 9 + 45 (7)
a(46) = 9 + 315
a(46) = 324
Therefore,
The 46th term of the sequence is 324.
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Mary has 7 cups of flour. It takes 5/6 cup of flour to make one cake. How many cakes can Mary make?
Mary can bake 8 cakes the with 7 cups of flour she possesses because we are unable to create a quarter of a cake.
What is the flour recipe?Starch, a polymer, is one of the ingredients in all-purpose flour, which has the chemical formula (C6H5O10)n (C 6 H 5 O 10) n.
We need to divide Mary's total flour supply by the quantity of flour required for creating one cake in order to determine how many cakes she can produce.
First, we must divide 5 by 6 to get the fraction 5/6 in decimal form:
5 ÷ 6 = 0.8333...
Hence, 0.8333 cups of flour are required to produce one cake.
We're able to divide Mary's entire flour supply by the quantity of flour needed to produce one cake:
7 cups of flour ÷ 0.8333 cups of flour per cake = 8.4 cakes
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Rationalize the denominator.
Hello and Good Morning/Afternoon!
Let's take this problem step-by-step:
What the problem asks for:
⇒ to rationalize the denominator
⇒ rationalize means that you multiply the numerator and
demonimator by the denominator
Let's put that into action:
\(\frac{\sqrt{a +1}-2 }{\sqrt{a+1}+2 } * \frac{\sqrt{a +1}+2 }{\sqrt{a+1}+2 }\\=\frac{a +1-4 }{a+1+4\sqrt{a+1}+4 } \\=\frac{a-3}{a+4\sqrt{a+1}+5 }\)<== Answer
Hopefully that helps!