Answer:
The vertex is ( -1/2, 3/4)
Step-by-step explanation:
f(x)=x^2+x+1
The vertex form is
y = a( x-h) ^2 +k where (h,k) is the vertex
Rewriting the function by completing the square
Taking the coefficient of x and dividing by 2 and squaring it
(1/2) ^2 = 1/4
Adding it and subtracting it
f(x) = x^2 + x + 1/4 -1/4 +1
= ( x^2+ x +1/4) + 3/4
= ( x+ 1/2) ^2 + 3/4
= ( x- -1/2) ^2 + 3/4
The vertex is ( -1/2, 3/4)
pls help me pls pls
Answer:
B
Step-by-step explanation:
the slope of parallel lines are equal
A sample of 120 creative artists is used to test whether creative artists are equally likely to have been born under any of the twelve astrological signs. Assuming that the twelve astrological signs each contain an equal number of calendar days, the expected frequency for each category equalsa) 5
b) 10
c) 12
d) 120
Answer:
b) 10
Step-by-step explanation:
In this case the frequency would be equal to the quotient between the sample that creative artists tell us (that is to say 120 people) and the amount of sastrological signs that there are (that is to say 12 signs), therefore it would be:
F = 120/12 = 10
Which means that the expected frequency for each category equal to 10.
So the answer is b) 10
Here is the feasible region.
28
А
52 + 8y 120
B
y 5
What are the coordinates of vertex A?
Enter your answer in the boxes
Answer:
A(8, 10)
Step-by-step explanation:
Vertex A is on the vertical line x=8, so we can find the y-coordinate by solving the boundary equation ...
5x +8y = 120
5(8) +8y = 120 . . . use the x-value of the vertical line
5 + y = 15 . . . . . . . divide by 8
y = 10 . . . . . . . . . . subtract 5
Point A is (8, 10).
Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and passes through the point (2, 18).
By "slope" I assume you mean slope of the tangent line to the parabola.
For any given value of x, the slope of the tangent to the parabola is equal to the derivative of y :
[tex]y=ax^2+bx+c\implies y'=2ax+b[/tex]
The slope at x = 1 is 5:
[tex]2a+b=5[/tex]
The slope at x = -1 is -11:
[tex]-2a+b=-11[/tex]
We can already solve for a and b :
[tex]\begin{cases}2a+b=5\\-2a+b=-11\end{cases}\implies 2b=-6\implies b=-3[/tex]
[tex]2a-3=5\implies 2a=8\implies a=4[/tex]
Finally, the parabola passes through the point (2, 18); that is, the quadratic takes on a value of 18 when x = 2:
[tex]4a+2b+c=18\implies2(2a+b)+c=10+c=18\implies c=8[/tex]
So the parabola has equation
[tex]\boxed{y=4x^2-3x+8}[/tex]
Using function concepts, it is found that the parabola is: [tex]y = 4x^2 - 3x + 14[/tex]
----------------------------
The parabola is given by:
[tex]y = ax^2 + bx + c[/tex]
----------------------------
Slope 5 at x = 1 means that [tex]y^{\prime}(1) = 5[/tex], thus:
[tex]y^{\prime}(x) = 2ax + b[/tex]
[tex]y^{\prime}(1) = 2a + b[/tex]
[tex]2a + b = 5[/tex]
----------------------------
Slope -11 at x = -1 means that [tex]y^{\prime}(-1) = -11[/tex], thus:
[tex]-2a + b = -11[/tex]
Adding the two equations:
[tex]2a - 2a + b + b = 5 - 11[/tex]
[tex]2b = -6[/tex]
[tex]b = -\frac{6}{2}[/tex]
[tex]b = -3[/tex]
And
[tex]2a - 3 = 5[/tex]
[tex]2a = 8[/tex]
[tex]a = \frac{8}{2}[/tex]
[tex]a = 4[/tex]
Thus, the parabola is:
[tex]y = 4x^2 - 3x + c[/tex]
----------------------------
It passes through the point (2, 18), which meas that when [tex]x = 2, y = 18[/tex], and we use it to find c.
[tex]y = 4x^2 - 3x + c[/tex]
[tex]18 = 4(2)^2 - 3(4) + c[/tex]
[tex]c + 4 = 18[/tex]
[tex]c = 14[/tex]
Thus:
[tex]y = 4x^2 - 3x + 14[/tex]
A similar problem is given at https://brainly.com/question/22426360
3. Your friend is solving a system of linear equations and finds the following solution:
0=5
What is the solution of the system? Explain your reasoning.
Answer:
No solution.
Step-by-step explanation:
Because the equations are combined but the final answers are not equal, the equations have no solution. This is because "no matter what value is plugged in for the variable, you will ALWAYS get a contradiction".
Hope this helps!
If a,b,and 2a in ap show that 3ab/2(b-a)
Answer:
[tex]S_n = \frac{3ab}{2 (b-a)}[/tex]
Step-by-step explanation:
The correct question is: If the first, second and last term of an AP are a,b and 2a respectively, then show that the sum of all terms of an AP is 3ab/2(b-a).
Firstly, as we know that the nth term of an A.P. is given by the following formula;
[tex]a_n=a+(n-1)d[/tex] , where a = first term of AP, d = common difference, n = number of terms in an AP and [tex]a_n[/tex] = last term
Since it is given that the first, second and last term of an AP are a,b and 2a respectively, that means;
first term = a
d = second term - first term = b - a
[tex]a_n[/tex] = 2a
So, [tex]a_n=a+(n-1)d[/tex]
[tex]2a=a+(n-1)(b-a)[/tex]
[tex]2a-a=(n-1)(b-a)[/tex]
[tex]a=(n-1)(b-a)[/tex]
[tex]\frac{a}{b-a} = n - 1[/tex]
[tex]\frac{a}{b-a} +1= n[/tex]
[tex]\frac{a+(b-a)}{b-a} = n[/tex]
[tex]n=\frac{b}{b-a}[/tex] ------------- [equation 1]
Now, the formula for the sum to n terms of an AP when the last term is given to us is;
[tex]S_n = \frac{n}{2}[\text{first term} + \text{last term}][/tex]
[tex]S_n = \frac{b}{2\times (b-a)}[a +2a][/tex] {using equation 1}
[tex]S_n = \frac{b}{2 (b-a)}[3a][/tex]
[tex]S_n = \frac{3ab}{2 (b-a)}[/tex]
Hence proved.
What is the solution of log (2 t + 4) = log (14 minus 3 t)? –18
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Logarithms,
so we get as,
t = 2
In a survey at a shoe store, 200 customers were asked whether they have
running shoes or basketball shoes. The results are in the relative frequency
table
Total
Have running shoes
0.16
No running shoes
0.26
Have basketball shoes
No basketball shoes
Total
0.24
0.34
What percentage of the people surveyed have basketball shoes?
Answer:the answer would be 0.42
Step-by-step explanation: The reason is you basically have to add both 0.16 and 0.26 and you get the percentage!
The percentage of the people surveyed who have basketball shoes is 42%.
What is Relative Frequency?Relative frequency of a data set is defined as the ratio of the number of outcomes that occured by the total number of trials.
Given a relative frequency table which shows the relative frequency of each of the sections have running shoes, have basketball shoes, and does not have any one of them or both.
Given that,
Total number of people surveyed = 200
Relative frequency of people who have basketball shoes = 0.16 + 0.26 = 0.42
So percentage = 0.42 × 100 = 42%
Hence the percentage of people who have basketball shoes is 42%.
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In 2 years, my sister will be twice as old as she was 2 years ago, and in 3 years my brother will be three times older than he was 3 years ago. Which sibling is older?
Answer:
Sister
Step-by-step explanation:
Let the sister’s age be x.
Let the brother’s age be y.
2 + x = 2x - 2
3 + y = 3y - 3
Solve the first equation.
x - 2x = - 2 - 2
-x = -4
x = 4
Solve the second equation.
y - 3y = -3 - 3
-2y = -6
y = 3
The sister is 4 years old.
The brother is 3 years old.
The sister is older than the brother.
Which equation should be used to find the volume of the figure?
V=1/3(10)(6)(12)
V=1/2(10)(6)(12)
V=1/3(10)(6)(13)
V=1/2(10)(6)(13)
Answer:
The answer is option 1.
Step-by-step explanation:
Given that the volume of pyramid formula is:
[tex]v = \frac{1}{3} \times base \: area \times height[/tex]
The base area for this pyramid:
[tex]base \: area = area \: of \: rectangle[/tex]
[tex]base \: area = 10 \times 6[/tex]
Then you have to substitute the following values into the formula:
[tex]let \: base \: area = 10 \times 6 \\ let \: height = 12[/tex]
[tex]v = \frac{1}{3} \times 10 \times 6 \times 12[/tex]
Answer:
A. V = 1/3 (10)(6)(12)
Step-by-step explanation:
Just took the test and got it right
A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 100 models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 10 to year 20.
Answer:
The farmer should expect to LOSE 10 pounds of soybeans per acre per year
Step-by-step explanation:
f(x)=-x^2 + 20x + 100
just find how many soybeans his land will yield (per acre) after 10 and 20 years:
After 10: 200 pounds of soybeans/acre
After 20: 100 pounds of soybeans/acre
Because 10 years have passed and they lost 100 pounds of soybean production per acre, the farmer should expect to lose 10 pounds of soybeans per acre per year (-10 pounds of soybeans per acre/year)
The steps to prove the Law of Sines with reference to ∆ABC are given. Arrange the steps in the correct order.
1). Draw a perpendicular from point A to side BC. Let AD = h
2). sin A = h/c and sin C = h/a
3). h = c Sin A, h = a sin C
4). c Sin A =a sin C
5). Divide both side by Sin A * Sin C
6). c Sin A/(Sin A * Sin C) =a sin C/(Sin A * Sin C)
7). c/sin C = a/Sin A
8). Similarly prove that, c/sin C = b/Sin B
9). c/sin C = b/Sin B = a/Sin A
correct on plato
You want to study how the number of popped kernels in a microwave popcorn bag is affected by brand, microwave power, and time in microwave. You manipulate three different factors: brand, power, and time. There are three brands, two power settings, and three different microwave times. a. How many unique treatment combinations are there
Answer:
Number of unique treatment combinations = 8
Step-by-step explanation:
Given:
Number of brands = 3
Number of power settings = 2
Number of microwave times = 3
Find:
Number of unique treatment combinations.
Computation:
Number of unique treatment combinations = Number of brands + Number of power settings + Number of microwave times
Number of unique treatment combinations = 3 + 2 + 3
Number of unique treatment combinations = 8
Write the following equation into logarithmic form. 5=3x
Answer:
[tex]log_35=x[/tex]
Step-by-step explanation:
I am going to assume you meant [tex]5=3^x[/tex]
When converting exponential equations into logarithmic form, remember this: [tex]y = log_bx[/tex] is equivalent to [tex]x = b^y[/tex]
Choose the equation of the horizontal line that passes through the point (−5, 9). y = −5 y = 9 x = −5 x = 9
Answer:
y = 9
Step-by-step explanation:
Since we are trying to find a horizontal line, our line would have to be y = [a number]. That takes our x = -5 and x = 9 out as answer choices. We are left with y = -5 and y = 9. y = 9 is correct because the horizontal line is the y-values, and since in (-5, 9), our y-value is 9, our line is y = 9.
You weigh six packages and find the weights to be 19, 15, 35, 17, 33, and 31 ounces. If you include a package that weighs 39 ounces, which will increase more, the median or the mean?
Answer:
Step-by-step explanation:
Mean & median of 6 packages:
15, 17, 19, 31, 33 , 35
Median = [tex]\frac{19+31}{2}[/tex]
= [tex]\frac{50}{2}[/tex]
= 25
[tex]Mean = \frac{15+17+19+31+33+35}{6}\\\\=\frac{150}{6}\\=25[/tex]
Mean & median of 7 packages:
15,17,19,31,33,35,39
Median = 31
[tex]Mean=\frac{19+15+35+17+33+31+39}{7}\\\\=\frac{189}{7}\\\\=27[/tex]
After including 39 ounce package, Median will increase more
a bridge in the shape of a parabolic arch is modelled by this function (see pic).
Answer:
(C) 25,35 and 175,35
8716 no es divisible por 4
Answer:
False
Step-by-step explanation:
No esta verdad.
8716/4 = 2179 (divisible por 4)
Together two ferries can transport a day's cargo in 7 hours. The larger ferry can transport cargo three times faster than the smaller ferry. How long does it take the larger ferry to transport a day's cargo working alone?
Answer:
9 hours, 20 minutes
Step-by-step explanation:
When two ferries work together, they transport a day's cargo in 7 hours
The speed proportion or ratio of larger ferry to smaller ferry is given as 3 : 1
The sum of the ratio = 4 (3 + 1)
This means that it will take the smaller ferry = 7 x 4 hours to work alone = 28 hours, since the larger ferry is faster by 3.
Therefore, when larger ferry works alone, it will take it (7 x 4)/3 = 9.33 hours.
9.33 hours = 9 hours, 20 minutes.
Find x. Round your answer to the nearest tenth of a degree.
Answer:
x = 64.1 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj/ hypotenuse
cos x = 7/16
Take the inverse cos of each side
cos ^-1 cos x = cos ^-1 ( 7/16)
x = cos ^-1 ( 7/16)
x =64.05552023
To the nearest tenth
x = 64.1 degrees
calcula la fracción generatriz de 0,245 y da como respuesta su numerador
Answer: 49/200, numerador= 49
Step-by-step explanation:
How to find the scale factor, ratio of area, & ratio of volume?
Step-by-step explanation:
If the scale factor of two similar solids is a: b:. then
(1) the ratio of corresponding perimeters is a:b
(2) the ratio of the base areas, of the lateral areas, and of the total areas is [tex]a^2: b^2[/tex]
(3) the ratio of the volumes is [tex]a^3:b^3[/tex]
Dylan wants to determine a 90 percent confidence interval for the true proportion of high school students in the area who attend their home basketball games. How large of a sample must he have to get a margin of error less than 0.03
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.64})^2}=747.11[/tex]
And rounded up we have that n=748
Step-by-step explanation:
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
The best estimatr for the proportionis 0.5 since we don't have any other info provided. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.64})^2}=747.11[/tex]
And rounded up we have that n=748
Sequence of numbers 1.5,2.25,3.0,3.75 in a recursive formula?
Answer:
f(n + 1) = f(n) + 0.75
Step-by-step explanation:
Please PLease PLEASE HELP ME!!!!!!!!!!!!!! Consider what would happen if you were to slice a face at a vertex (cut a corner) of a particular polyhedron. You would see a new polygonal face where the old vertex used to be. What type of polygon would a slice of a hexahedron at a vertex create? Explain how you know. What type of polygon would a slice of an icosahedron at a vertex create? Explain how you know.
Answer:
A triangle
Step-by-step explanation:
The plane which cuts a corner intersects the polyhedron in n faces that depend on the specific polyhedron as seen in the attachment
And here's a cube, and three faces intersect. Because the intersection of two planes is a line, and that there are three planes with which to intersect, the polygon has three sides.
Therefore in the given situation, the polygon is a triangle
It was reported that in a survey of 4764 American youngsters aged 6 to 19, 12% were seriously overweight (a body mass index of at least 30; this index is a measure of weight relative to height). Calculate a confidence interval using a 99% confidence level for the proportion of all American youngsters who are seriously overweight. (Round your answers to three decimal places.)
Answer:
Step-by-step explanation:
confidence level for the proportion of all American youngsters who are seriously overweight is (0.137, 0.163)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue
Read
The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3639 3639 miles, with a variance of 145,161 145,161 . If he is correct, what is the probability that the mean of a sample of 41 41 cars would differ from the population mean by less than 126 126 miles
Answer:
96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
A reminder is that the standard deviation is the square root of the variance.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5[/tex]
Probability that the mean of the sample would differ from the population mean by less than 126 miles
This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So
X = 3765
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3765 - 3639}{59.5}[/tex]
[tex]Z = 2.12[/tex]
[tex]Z = 2.12[/tex] has a pvalue of 0.983
X = 3513
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3513 - 3639}{59.5}[/tex]
[tex]Z = -2.12[/tex]
[tex]Z = -2.12[/tex] has a pvalue of 0.017
0.983 - 0.017 = 0.966
96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles
A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test millimeters versus millimeters, using the results of n samples. Find the boundary of the critical region if the type I error probability is and
Complete question:
A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test H0: u=175 millimeters versus Ha:u>175 millimeters, using the results of n samples. Find the boundary of the critical region if the type I error probability is [tex] \alpha = 0.01 [/tex] and n = 16
Answer:
186.63
Step-by-step explanation:
Given:
[tex] \alpha = 0.01 [/tex]
Using the standard normal deviate table:
NORMSINV(0.01) = 2.326
Thus, the Z score = 2.326
To find the critical value if the mean, use the formula:
[tex]\frac{X' - u_0}{\sigma/\sqrt{n}} = Z[/tex]
Since we are to find X', Make X' subject of the formula:
[tex] X' = u_0 + (Z * \frac{\sigma}{\sqrt{n}}) [/tex]
[tex] X' = 175 + (2.326 * \frac{20}{\sqrt{16}}) [/tex]
[tex] X' = 175 + (2.326 * 5) [/tex]
[tex] X' = 175 + 11.63 [/tex]
[tex] X' =186.63 [/tex]
The boundary of the critical region is 186.63
The cost c in $ of producing x items is in the equation c=x/7+1 which of the following choices will find the cost c if x is 35
Answer:
care of it and I will get back to you with a new one for me and support you in whatever way
Step-by-step explanation:
try to get the morning and then we can go from there to the meeting tonight but I can tomorrow
The value of the cost when x is 35 given the equation c=x/7+1 is $6.
How to calculate the cost?From the information given, the cost c in $ of producing x items is in the equation c=x/7+1.
Therefore, the value of the cost when x is 35 will be;
c = x/7 + 1
c = 35/7 + 1
c = 5 + 1
c = 6
Therefore, the cost is $6.
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plz answer question in screen shot
Answer:
first one 5/[tex]\sqrt{39}[/tex]
Step-by-step explanation:
We must calculate cosθ first :
cos²θ+sin²θ =1⇒ cos²θ= 1-sin²θ=1-(25/8)= 39/64⇒cosθ= √39/8
tanθ = sinθ/cosθtanθ= (5/8)/(√39/8)=5/8*8/√39 = 5/√39