Answer:
[tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]
Step-by-step explanation:
First, convert this into a quadratic, [tex]x^{2}+7x+8=0[/tex]. We can use the quadratic formula for this, [tex](-7[/tex]±[tex]\sqrt{7^{2}-4(1)(8)})[/tex][tex]/2(1)[/tex]. This becomes [tex](-7[/tex]±[tex]\sqrt{49-32})/2[/tex]. This is [tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]. This is your answer
Okey please help me out
Rewrite the second expression as
[tex]\dfrac1{1+x^m + x^{-n}} = \dfrac{x^{\ell+n}}{x^{\ell+n} + x^{\ell+m+n}+x^\ell} = \dfrac{x^{-m}}{x^{-m} + 1 + x^\ell}[/tex]
and the third expression as
[tex]\dfrac1{1 + x^n + x^{-\ell}} = \dfrac{x^\ell}{x^\ell + x^{\ell+n} + 1} = \dfrac{x^\ell}{x^\ell + x^{-m} + 1}[/tex]
so the fractions all have the same denominator.
Then combining the fractions gives the desired result,
[tex]\dfrac1{1+x^\ell+x^{-m}} + \dfrac1{1+x^m+x^{-n}} + \dfrac1{1+x^n+x^{-\ell}} = \dfrac{1+ x^\ell + x^{-m}}{1+x^\ell+x^{-m}} = \boxed{1}[/tex]
The two dot plots below compare the forearm lengths of two groups of schoolchildren: Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group X and the title for the bottom plot is Forearm Length, Group Y. Below the line for each dot plot is written Length in inches. There are markings from 10 to 13 on each line at intervals of one. For the top line there are 4 dots above the first mark, 4 dots above the second mark, and 2 dots above the third mark. For the bottom line there are 2 dots above the second mark, 2 dots above the third mark, and 6 dots above the fourth mark. Based on the visual inspection of the dot plots, which group appears to have the longer average forearm length? Group X, because no child in the group has a forearm length longer than 12 inches. Group X, because four children in the group have the least forearm length of 10 inches. Group Y, because a child in the group has the least forearm length of 10 inches. Group Y, because six children have a forearm length longer than 12 inches.
The group that have the longer average forearm length is group Y, because six children have a forearm length longer than 12 inches.
Which group has a longer forearm length?
A dot plot is a graph that shows the frequency of a number using dots. The greater the number of dots above a number, the greater its frequency.
In group X, the highest arm length is 12 while in group Y, it is 13. This means that group Y would have longer arm lengths.
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Find Q2 of the following data set 3, 9, 12, 4, 6, 40, 25, 14, 10
Answer:
Q₂ = 10
Step-by-step explanation:
Given data set: 3, 9, 12, 4, 6, 40, 25, 14, 10
Q₂ is the median (the middle value) of the given data set when the data set is ordered from smallest to largest.
Order the values in the data set:
3, 4, 6, 9, 10, 12, 14, 25, 40
As the number of values is odd, the middle value is the 5th value.
Therefore, the median (Q₂) of the given data set is 10.
If the number of data values is even, and therefore there are two middle values, the median is halfway between them.
A teacher wants to know whether their course helps students on the SAT. The hypothesized population mean for SAT scores is 500. The standard deviation of the population is 77. The sample size is 100. The sample mean for students who took the course is 533. What is the z-score
The z-score is -0.428
What is a z-score?A z-score, also known as a standard score, provides information on how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.
You can plot a z-score on a normal distribution curve.
You must be aware of the mean and population standard deviation to use a z-score.
Z-scores allow results to be compared to a "normal" population.
According to the question,
x=500
μ=533
σ=77
z-score=(x-μ)/σ
On substituting the values,
z-score=(500-533)/77
= -0.428
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At the store, there were 6 bags of chips for every 8 cookie boxes. If there were 104 cookie boxes, how many bags of chips were there?
Answer: There were 78 bags of chips.
How to represent 5 rational numbers on line. the numbers should be of form p/q where p or q should be a taxicab number. the fraction can be then reduced to its standard form. write about the taxicab numbers in brief.
The five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1 and the numbers should be of form p/q where p or q should be a taxicab number.
According to the question,
To represent 5 rational numbers on line, the numbers should be of form p/q where p or q should be a taxicab number.
A taxicab number is a smallest integer can be expressed as a sum of two positive integer cube.
The most famous taxicab number is 1729. Thus,
1729 = 1³ + 12³
1729 = 9³+ 10³
Now, 2 = 1³ + 1³ so, 2 is the first taxicab number. Therefore, five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1.
In 1/1729 -> 1729 is taxicab number
In 1/2 -> 2 is taxicab number
In 3/2 -> 2 is taxicab number
In 1/1729 -> 2 is taxicab number
In 1729/1 -> 1729 is taxicab number
Hence, five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1 and the numbers should be of form p/q where p or q should be a taxicab number.
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Which answer represents the following conditional statement in shorthand?
if megan is swimming, then it is warm outside.
The expression which represents the given conditional statement in shorthand is: S → W.
What is a conditional statement?A conditional statement can be defined as a statement that can be written to contain both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."
Where:
P and Q represent sentences.
If Megan is swimming = S
It is warm outside = W
Therefore, if Megan is swimming, then it is warm outside is represented by S → W.
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If point (4, 5) is on the graph of a function, which equation must be true?
f(5)=4
f(5,4)=9
f(4)=5
f(5,4)=1
Answer:
f(4) = 5
Step-by-step explanation:
Think about it this way
a point with an x value of 4,
this x value is put into the function,
then the function outputted a y value (or value) of 5.
So, we can name this function f(x)
Then, we let x = 4,
then the output for f(4) = 5
Answer: f(4) = 5
Step-by-step explanation:
If the point (4, 5) is on the graph of a function, this means that when you input 4 you get an output of 5.
Inputs are usually shown with the x-coordinate, and outputs are usually shown with the y-coordinate.
This means that (4, 5) is an input of 4 for an output of 5.
What is the -value in the solution to this system of linear equations?y
4 + 5 = −12xy
-2 + 3 = −16xy
The xy-value in the solution to the given system of linear equation shows that x = 2 and y = -4.
What is a system of linear equations?Whenever two or more linear equations operate simultaneously, we create a System of Linear Equations. These equations must contain one or more similar variables in order to operate together.
When solving a system of linear equations, our objective is to simplify two equations having two variables to a single equation having one variable. Because each equation in the system includes two variables, substituting an expression for a variable is one technique to minimize the number of variables in an equation.
From the given information:
4x + 5y = -12 --- (1)
-2x + 3y = -16 ----- (2)
From equation (1)
4x+5y+(−5y) = −12 + (−5y) (Add -5y to both sides)
4x = −5y − 12
Divide both sides by 4
[tex]\mathbf{\dfrac{4x}{4}= \dfrac{-5y-12}{4}}[/tex]
[tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]
Replacing the value of x in [tex]\mathbf{ \dfrac{-5}{4}y-3}[/tex] into equation (2); we have:
[tex]=\mathbf{-2(\dfrac{-5}{4}y-3)+3y=-16}[/tex]
[tex]\mathbf{\dfrac{11}{2}y+6 =-16}[/tex]
Simplifying both sides of the equation, we have:
[tex]\mathbf{\dfrac{11}{2}y+6-6 =-16-6}[/tex]
[tex]\mathbf{\dfrac{11}{2}y=-22}[/tex]
Cross multiply
11y = -44
y = -4
Replace the value of y = -4 into [tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]
[tex]\mathbf{x= \dfrac{-5}{4}(-4)-3}[/tex]
x = 2
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Based on the polynomial remainder theorem, what is the value of the function when x=−5?
f(x)=x^4+12x^3+30x^2−12x+70
Answer:
5.
Step-by-step explanation:
f(x)=x^4+12x^3+30x^2−12x+70
The remainder theorem says that f(a) is the value of f(x) when f(x) is divided by (x - a).
So when a = -5 f(a) will be 5.
Answer is 5.
When drawing a context diagram, standardized names should be used within each set of symbols. a. True b. False
The statement is False that When drawing a context diagram, standardized names should be used within each set of symbols.
According to the statement
we have given the statement and we have to show that the statement is a true or false after analyzing.
So, to analyse the statement
Context diagrams show the interactions between a system and other actors (external factors) with which the system is designed to interface. System context diagrams can be helpful in understanding the context .
But we know that the standardized names is not used within each set of symbols. so, this is used in a randomly sets.
that's why the given statement is not true in the case of the standardized names.
So, The statement is False that When drawing a context diagram, standardized names should be used within each set of symbols.
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The following table shows the weights of nine subjects before and after following a particular diet for two months. Test the claim that the diet is effective in helping people lose weight Subject A B DEFGHI Before 168 180 157 132 202 124 190 210 171 After 162 178 145 125 171 126 180 195 163
Using the t-distribution, it is found that there is not enough evidence that the diet is helping people lose weight.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean hasn't decreased, that is:
[tex]H_0: \mu_B \leq \mu_A[/tex]
[tex]H_0: \mu_B - \mu_A \leq 0[qtex]
At the alternative hypothesis, it is tested if the mean has decreased, that is:
[tex]H_1: \mu_B - \mu_A > 0[qtex]
What are the mean and the standard error for the distribution of differences?For each sample, they are given as follows:
[tex]\mu_B = 170.44, s_B = \frac{29.275}{\sqrt{9}} = 9.7583[/tex].[tex]\mu_A = 160.56, s_A = \frac{24.203}{\sqrt{9}} = 8.067[/tex].Hence, for the distribution of differences, they are:
[tex]\overline{x} = \mu_B - \mu_A = 170.44 - 160.56 = 9.88[/tex].[tex]s = \sqrt{s_B^2 + s_A^2} = \sqrt{9.7583^2 + 8.067^2} = 11.66[/tex]What is the test statistic and the decision?
The test statistic is:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{9.88 - 0}{11.66}[/tex]
t = 0.85.
Considering a right-tailed test with 9 + 9 - 2 = 16 df, with a standard significance level of 0.05, the critical value is t = 1.7459. Since t = 0.85 < 0.85, there is not enough evidence that the diet is helping people lose weight.
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Which points lie on the graph of f(x) = -√-x?
□(-9,3)
□(-4,-2)
□ (-1, 1)
□(0,0)
□ (1,1)
□(2,-4)
□(9,3)
Answer:
(-4, -2).
(0, 0).
Step-by-step explanation:
Both coordinates will be negative or (0.0).
It's these followings:
□(-4,-2)
□(0,0)
Hope this helps!
A parachute speed free fall reaches 45 meters per second what is this speed in feet per second at this speed how many feet will the parachutist fall during 5 seconds of free fall in your computations assume that 1 meter is equal to 3.3 feet. Don’t round your answers
The speed is:
S = 742.5ft
The distance that the parachutist falls in 5 seconds is:
D = 742.5ft
How to get the speed in feet per second?
We know that the speed in free fall is:
S = 45 m/s.
We know that:
1 m = 3.3ft
Then we can rewrite the speed as:
S = 45 m/s = 45 *(3.28ft)/s = 148.5 ft/s
Then, the distance that the parachutist falls during 5 seconds is:
D = S*5s = (148.5 ft/s)*5s = 742.5ft
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Chemotherapy in adult highgrade glioma: a systematic review and metaanalysis of individual patient data from 12 randomized trials
Systemic chemotherapy's impact on survival and recurrence in people with high-grade glioma has not been conclusively studied.
What is Systemic chemotherapy?Patients undergoing systemic chemotherapy can get their chemotherapy drugs intravenously or orally. The medication may be injected into the body intravenously, or through an IV, or intramuscular, into a muscle (IM).
Some Key features of systemic chemotherapy are-
Background: In order to evaluate the effects of such treatment on survival and recurrence, we conducted a systematic review and meta-analysis.Methods: From 12 randomised controlled studies, information on 3004 patients was incorporated (11 published and one unpublished).Findings: Overall, the findings indicated a significant survival extension associated with chemotherapy, with a hazard ratio of 0.85 (95 percent confidence interval [CI] 0.78–0.91, p0.0001) or a relative reduction in mortality risk of 15%. There was no proof that a patient's age, gender, histology, performance status, or degree of resection affected how chemotherapy worked in any particular way.Interpretation: Further research into pharmacological treatment for malignant tumors is encouraged by this modest but noticeable improvement in survival from chemotherapy.To know more about Chemotherapy, here
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If u are 13, and ur birthday is 21 of october, how old will you be in 2050?
Answer:
41 years old
Step-by-step explanation:
2050-2022=28 years
13years old +28years = 41 years old (sorry if wrong)
Answer: Based on today's date of 7/19/2022, you will be 41 until October 21, 2050. On October 21, 2050 you will turn 42. You were born in 2008
Step-by-step explanation:
calculate the volume of the composite shape
please please help giving brainliest!!
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
There are two hemispheres in there with radius 3 cm, so we can consider it as a whole one. and the other shape in between is Cylinder with radius 3 cm and height 4 cm.
Volume of whole ahape = volume of Cylinder + volume of sphere ~
Volume of sphere :
[tex]\qquad \sf \dashrightarrow \: \cfrac{4}{3} \pi {r}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{4}{3} \sdot3.14 \sdot {(3)}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: (4 )\sdot(3.14) \sdot(9)[/tex]
[tex]\qquad \sf \dashrightarrow \: 113.04 \: \: cm {}^{3} [/tex]
Volume of Cylinder :
[tex]\qquad \sf \dashrightarrow \: \pi {r}^{2} h[/tex]
[tex]\qquad \sf \dashrightarrow \: 3.14 \cdot(3) {}^{2} \sdot4[/tex]
[tex]\qquad \sf \dashrightarrow \: 3.14 \sdot(9) \sdot(4)[/tex]
[tex]\qquad \sf \dashrightarrow \: 113.04 \: \: cm {}^{3} [/tex]
Volume of whole shape :
[tex]\qquad \sf \dashrightarrow \: 113.04 + 113.04 = 226.08 \: \: cm {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 226.08 \: \: cm {}^{3}[/tex]
find x please (look at the image)
Answer:
55
Step-by-step explanation:
Draw a line through the center (horizontally).
Then draw a vertical line through the vertex of the right angle.
You'll get 2 triangles
I'll let you figure this out, it pretty easy
Remember a straight angle add up to 180 degrees, a triangle adds up to 180 degrees.
What are the ratios for sin A and cos A? The diagram is not drawn to scale.
Answer:
C
Step-by-step explanation:
Sin represents opposite/hypotenuse. Thus, when A is the reference angle, 21 is the measure of the opposite side (CB) and 29 is the measure of the hypotenuse (AB).
Cos represents adjacent/hypotenuse. Therefore, when A is the reference angle, 20 is the measure of the adjacent side (AC) and 29 is the measure of the hypotenuse (AB).
What is the equation of the line parallel to the given line with an x-intercept of 4? y = x
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2022, tysm for the help!
Answer:
d: y=5x
Step-by-step explanation:
Since we know a few points: (2,10), (3,15), (4,20), we can use two of them to first find the slope. The equation for the slope is (Increase in y)/(increase in x).
1. Slope between (2,10) and (3,15) is 5/1 which is 5. So the slope will be 5.
2. With the slope, we know that our equation will be: y=5x+b. To find b, we can replace x and y with another point. 20 = 5(4)+b. --> 20 = 20 +b. Now we know that b equals 0.
Our final equation will be y = 5x.
RECHECKING!
I'll recheck whether my answer is right or not using Desmos (A online graphing calculator).
I added an image down below, and I drew the points in blue. This shows that since the graph crosses all three points, it is correct.
WHY y=1/5x IS NOT CORRECT (based on your comments)
If you look at the points, the relationship between x and y is not 1/5. If you multiply something from x, it should become 10.
--> 2 times __ = 10
--> 3 times __ = 15
--> 4 times __ = 20
And clearly, __ will be 5. If it becomes 1/5, we won't get the right number of y.
This is why y=1/5 is not correct.
Hope this helps!
8. Find (f+g)(x) if f(x) = 4x² - 5x and g(x) = 3x² + 6x - 4.
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: (f + g)(x)[/tex]
[tex]\qquad \sf \dashrightarrow \: f(x) + g(x)[/tex]
[tex]\qquad \sf \dashrightarrow \: (4 {x}^{2} - 5x) + (3 {x}^{2} + 6x - 4)[/tex]
[tex]\qquad \sf \dashrightarrow \: 7 {x}^{2} + x - 4[/tex]
The Drury Lane Theater has 10 seats in the first row and 38 rows in all. Each successive row contains one additional seat. How many seats are in the theater?
Anyone is here
Answer:
1083 seats
Step-by-step explanation:
this is an arithmetic sequence :
an = an-1 + c
in our case
a1 = 10 (10 seats in the first row)
a2 = a1 + 1 = 10 + 1 = 11
a3 = a2 + 1 = a1 + 1 + 1 = 10 + 1 + 1 = 12
an = an-1 + 1 = a1 + (n-1)×1 = a1 + n - 1 = 10 + n - 1 = 9 + n
a38 = a1 + 37 = 10 + 37 = 47 seats.
altogether this means the sum of the arithmetic sequence of a1 to a38.
the general sum of an arithmetic sequence from a1 to an is
n×(a1 + an)/2
in our case
38×(10 + 47)/2 = 19×57 = 1083 seats
ILL GIVE BRAINLIEST
1 x/3 - 3/4= 5/12
solve for x
You’re taking a 33 question multiple choice test. Each question has 4 choices. Clueless on 1 question, you decide to guess. What’s the chance you’ll get it right?
give the volume of the triangular prism shown
A-440in^3
B-528in^3
C-880in^3
D-264in^3
Answer:
D. 264 in³
Step-by-step explanation:
The missing edge dimension can be found using the Pythagorean theorem. Then the volume can be found using the appropriate formula.
Edge dimensionThe missing dimension and the two given for the top triangle will satisfy the Pythagorean theorem. If the missing dimension is represented by 'a', then we have ...
a² +8² = 10²
a = √(100 -64) = 6 . . . . inches
VolumeThe area of the top triangle is ...
A = 1/2bh . . . . where b and h are the base and height dimensions
A = 1/2(6 in)(8 in) = 24 in²
The volume of the triangular prism is ...
A = Bh . . . . . where B is the area of the triangular base, and h is the prism height
A = (24 in²)(11 in) = 264 in³
The volume of the triangular prism shown is 264 in³.
Tommy has created a new tomato soup recipe. Before he cans and sells his soup, he must gather information about how much soup cans of different sizes will hold.
The better way to calculate the amount of substance is Volume.
According to the statement
we have to find the all information about the soup cans.
So we know that if we put a liquid in the container then in that case surface area is not important but a volume is more important for this purpose.
So, That's why The weight in the case of soup is not important when evaluating a package to be able to sell the product. A container is usually specified according to its volume, especially those containing liquids. Because the weight can vary concerning the concentration of the product, the best way to calculate the amount of substance to be packaged is the volume.
So, The better way to calculate the amount of substance is Volume.
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HELP ASAP PLEASE
Kaydence is saving for an RR$P. She saved $100 the first year, $200 the second year, $300 the third year, and so on. If she put $100 away on January 1, 2014. $200 away on January 1, 2015, and continued to put money away on the first of each year, how much money would Kaydence have saved by the end of the day on January 1, 2050?
Based on the information given, the total money that is expected Kaydance save is $70300
How much money will Kaydance save every year?It is known she started saving $100 and each year she saves $100 more than the previous year. Also she will save a total of 36 years. This will be equal to:
100+200+300+400+500+600+700+800+900+1000+1100+1200+1300+1400+1500+1600+1700+1800+1900+2000+2100+2200+2300+2400+2500+2600+2700+2800+2900+3000+3100+3200+3300+3400+3500+3600+3700
How much money will she save in total?100+200+300... = $70300
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The mean number of goals a netball team scores
per match in the first 9 matches of a competition
is 4.
a) How many goals does the team score in total in
the first 9 matches of the competition?
b) If the team scores 3 goals in their next match,
what would their mean number of goals after 10
matches be?
The goals does the team score in total in the first 9 matches of the competition is 36 and their mean number of goals after 10 matches is 3.9.
What is the total goals scored by the team in 9 matches ?Given that the mean number of goals a netball team scores per match in the first 9 matches of a competition is 4.
Thus the average of the goals in 9 matches is 4.
Total number of goals is = 9*4 = 36 goals .
What is the mean number of goals after 10 matches ?Given that the team scores 3 goals in their next match .
Thus the total number of goals scored in 10 matches is 36 + 3 = 39 goals,
Required mean = Total goals / 10 matches .
∴ Required mean = 39/10 = 3.9 .
Therefore, the goals does the team score in total in the first 9 matches of the competition is 36 and their mean number of goals after 10 matches is 3.9.
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Complete the double number line to show the other values of fat and protein.
The double number line which shows the other values of fat and protein is: option B.
What is a number line?A number line is a type of graph with a graduated straight line which contain numerical values that are placed at equal intervals along its length.
For the fat component, we have:
Fat = 2n = 0, 2, 4, 6, 8.
For the protein component, we have:
Protein = 11n = 0, 11, 22, 33, 44.
Note: n represent integers such as 0, 1, 2, 3 and 4.
In conclusion, the double number line which represent the other values of fat and protein is shown in the image attached below.
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Complete Question:
One serving of beef je-rky contains 2 grams of fat and 11 grams of protein. Complete the double number line to show the other values of fat and protein.