Answer:
-2151
Step-by-step explanation:
f(x) = –15x^2+9.
Let x = 12
f(12) = -15 ( 12)^2 +9
= -15 (144) +9
= -2151
Answer:
-2151
Step-by-step explanation:
F(x) = -15x^2 + 9
F(12) = -15 (12)^ 2 + 9
= -15 * 144 + 9
= -2160 + 9
= -2151
Graph a parabola whose intercepts are x=-3 and x=5 and whose minimum value is y =-4
Answer:
[tex]y = 4(x^{2} + 8x + 15) = 4x^{2} + 32x + 60[/tex]
Step-by-step explanation:
A parabola has the following format:
[tex]y = f(x) = ax^{2} + bx + c[/tex]
If a is positive, it's minium value is:
[tex]y_{M} = -\frac{\bigtriangleup}{4a}[/tex]
In which
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
Factoring:
[tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], in which [tex]x_{1} and x_{2}[/tex] are the intercepts.
In this question:
[tex]x_{1} = -5, x_{2} = -3[/tex]
So
[tex]a(x - x_{1})*(x - x_{2}) = a*(x - (-5))*(x - (-3)) = a*(x+5)*(x+3) = a*(x^{2} + 8x + 15)[/tex]
Suppose a = 1, we have:
[tex]x^{2} + 8x + 15[/tex]
[tex]\bigtriangleup = 8^{2} - 4*1*15 = 4[/tex]
The minimum value will be:
[tex]y_{M} = -\frac{4}{4} = -1[/tex]
We want this minimum value to be -4, which is 4 times the current minimum value, so we need to multiply a by 4. Then
[tex]a = 4[/tex]
And the parabola is:
[tex]y = 4(x^{2} + 8x + 15) = 4x^{2} + 32x + 60[/tex]
Two different samples will be taken from the same population of test scores where the population mean and standard deviation are unknown. The first sample will have 25 data values, and the second sample will have 64 data values. A 95% confidence interval will be constructed for each sample to estimate the population mean. Which number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean? The answer is the sample with data values.
Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - α)% confidence interval for population mean μ is:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}[/tex]
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (n).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
n₁ = 25
n₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\ [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Width for n = 64:[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\ [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Thus, the sample consisting of 64 data values would give a greater precision.
The number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean is 64 and this can be determined by using the formula of width.
Given :
The first sample will have 25 data values.The second sample will have 64 data values. 95% confidence interval.The following steps can be used in order to determine the number of data values would you expect to give a greater precision for estimating the population mean:
Step 1 - The below formula of width is used in order to determine the number of data values.
Step 2 - The formula of width is given below:
[tex]w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{n} }[/tex]
where [tex]z_{\alpha /2}[/tex] is the z-score, [tex]\sigma[/tex] is the standard deviation, and 'n' is the sample size.
Step 3 - Now, at n = 25 the formula of 'w' becomes:
[tex]w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{25} }[/tex]
[tex]w = \dfrac{1}{5}\left(2\times z_{\alpha /2}\times\sigma }\right)[/tex]
Step 4 - Now, at n = 64 the formula of 'w' becomes:
[tex]w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{64} }[/tex]
[tex]w = \dfrac{1}{8}\left(2\times z_{\alpha /2}\times\sigma }\right)[/tex]
The number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean is 64.
For more information, refer to the link given below:
https://brainly.com/question/12402189
I’ve been stuck on this one for a while can anyone help me?
Answer:
It would be Unlikely
Step-by-step explanation:
find the value of log 3 base 81.
Exact value
Decimal form
0.47712125
Answer:
[tex]log_{81} 3 = \frac{1}{4}[/tex]
Step-by-step explanation:
[tex]Let \; log_{81} 3 = x \\\therefore 3 = {81}^x ..(by\: changing\: in \: exponential\: form)\\\therefore 3^1 = {3}^{4x}\\\therefore 1 = 4x.\\(\because bases \: are \: equal,\: hence \: exponents\: will\: also\: be \: equal)\\\therefore x = \frac{1}{4}\\\\\huge\purple{\boxed{\therefore log_{81} 3 = \frac{1}{4}}}[/tex]
Imagine that you are an engineer for a soda company, and you are tasked with finding the most economical shape for its aluminum cans You are given a set of constraints: the can must hold a volume of liquid and be a cylindrical shape of height hand radius r, and you need to minimize the cost of the metal required to make the can
Look at a variety of aluminum cans of different sizes from the supermarket. Which models from problems a–c best approximate the shapes of the cans? Are the cans actually perfect cylinders? Are there other assumptions about the manufacture of the cans that we should take into account? Do a little bit of research, and write a one-page response to answer some of these questions by comparing our models to the actual dimensions used.
Answer:
The answer to that depends on the company
Step-by-step explanation:
Please help !!!!ASAP!!!!
Please answer the Picture below.
Answer:
Part A) shorter base = 6 yd longer base = 8 yd
Part B) C. 42 yds²
Step-by-step explanation:
Part A) The width and the length of the shorter side are the same, at 6 yds each. The longer base is 8 yds because there is a spot of 1 yd on both sides of the shorter side, making the longer side.
Part B) Find the area of the square first.
A = L x W
A = 6 x 6
A = 36 yds²
Next, find the area of a triangle and multiply the answer by 2 because there are two triangles.
A = 1/2bh
A = 1/2(1)(6)
A = 1/2(6)
A = 3(2)
A = 6 yds²
Add together all of the area measurements to find the area of the entire figure
36 + 6 = 42 yds²
Find the volume of a pyramid with a square base, where the side length of the base is
16.6
m
16.6 m and the height of the pyramid is
10.1
m
10.1 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
Volume of the pyramid = 927.72 m² (Approx)
Step-by-step explanation:
Given:
Length of base = 16.6 m
Height of the pyramid = 10.1 m
Find:
Volume of the pyramid = ?
Computation:
Area of the square base = Side²
Area of the square base = (16.6)²
Area of the square base = 275.56 m²
[tex]Volume\ of\ the\ pyramid = \frac{1}{3}(Area\ of\ base)(Height)\\\\Volume\ of\ the\ pyramid = \frac{1}{3}(275.56)(10.1)\\\\Volume\ of\ the\ pyramid = 927.7186[/tex]
Volume of the pyramid = 927.72 m² (Approx)
What’s the correct answer for this?
Answer:
c) √137
Step-by-step explanation:
Explanation:-
The distance between two points formula
[tex]\sqrt{(x_{2}-x_{1} )^{2} + (y_{2} -y_{1} )^{2} }[/tex]
Given points are R (3,7) and S(-1,-4)
[tex]RS = \sqrt{(-1- (3 )^{2} + (-4 -7 )^{2} }[/tex]
[tex]RS = \sqrt{(-4 )^{2} + (-11 )^{2} }[/tex]
[tex]RS = \sqrt{16 + 121 }[/tex]
RS = √137
The distance between the two points are RS = √137
30 POINTS!!!!! URGENT!
Step-by-step explanation:
Average daily balance: Add all balances up and divide by the number of days.
157.63*9+239.98*1+239.98*4+180.38*1+180.38*9+190.57*1+190.57*6 gives us our total of 5756.36, and there were 9+1+4+1+9+1+6=31 days, so 5756.36/31 gives us our average of 185.69, or the fourth option
Daily interest rate: 24.99/365, as a percent, which is the first option
Finance charge: This is the cost of borrowing, and does not seem to be given, so we can take it to be the lowest amount, or the third value
New account balance: Again, this does not seem to be given, but the only option remaining is the second one
Answer:
Average daily balance: Add all balances up and divide by the number of days.
157.63*9+239.98*1+239.98*4+180.38*1+180.38*9+190.57*1+190.57*6 gives us our total of 5756.36, and there were 9+1+4+1+9+1+6=31 days, so 5756.36/31 gives us our average of 185.69, or the fourth option
Daily interest rate: 24.99/365, as a percent, which is the first option
Finance charge: This is the cost of borrowing, and does not seem to be given, so we can take it to be the lowest amount, or the third value
New account balance: Again, this does not seem to be given, but the only option remaining is the second one
m
Step-by-step explanation:
which of the following is equivalent to -7/-12?
7/-12
7/12
12/7
Step-by-step explanation:
7/ 12 is equivalent to - 7/-12
express in the form n:1 give n as a fully simplified fraction 6:10
Answer:
n = 3/5
Step-by-step explanation:
We are given the ratio 6 : 10.
We see that we want to get a number n to 1 ratio; n : 1
In order to get one, we must divide 10 by 10, and so we would divide the entire ratio by 10 and simplify:
6/10 : 10/10
3/5 : 1 or 0.6 : 1
What’s the area of this figure?
Answer:
C. 155.5 cm2
Step-by-step explanation:
area = 5*15 + (15+8)*7/2 = 75 + 80.5 = 155.5 cm2
Why is this a parallelogram?
Answer:
b both pairs of opposite sides are parallel
Answer:
B or the second choice from the top
Step-by-step explanation:
The definition of a parallelogram, in my own words, is a quadrilateral with two pairs of opposite parallel sides (hence the name). Therefore, the second choice from the top is correct. Hope this helps!
Which is the equation of a parabola with vertex (0,0) and focus (0,2)?
Answer:
The equation of the parabola is y=(1/8)x^2
[tex]y=\dfrac{1}{8}x^2[/tex]
Step-by-step explanation:
We know the vertex (0,0) and the focus (0,2) of the parabola.
The equation in vertex form is written as:
[tex]y=a(x-h)^2+k\\\\\text{vertex}=(h,k)[/tex]
Then, in this case, we have the equation:
[tex]y=a(x-0)^2+0=ax^2[/tex]
As the focus is (0,2), it is at a distance of 2 units from the vertex (0,0).
For the focus, we have the following equation:
[tex]4p(y-k)=(x-h)^2[/tex]
where p is the distance from the focus to the vertex (in this case, p=2).
h and k are the vertex coordinates, both 0.
So we have:
[tex]4p(y-k)=(x-h)^2\\\\4(2)(y-0)=(x-0)^2\\\\8y=x^2\\\\y=\dfrac{1}{8}x^2[/tex]
a sector with a area of 11 over 2 pi cm squared has a radius of 3 cm
Answer:
Step-by-step explanation:
Step-by-step explanation:
Area of sector = angle/360 * pi * r^2
5.5pi = angle/360 * pi * 9
5.5 = angle/360 * 9
angle = (5.5 * 360)/9 = 40 * 5.5 = 220
What’s the correct answer for this?
Answer:
As shown in picture, if MC is median of triangle ABC, M is midpoint of AB.
Denote the coordinate of A, B and M are (Ax, Ay), (Bx, By) and (Mx, My) respectively.
The formula relating coordinate of A, B and M is:
Ax + Bx = 2Mx
Ay + By = 2My
In detail,
-1 + Bx = 2 x 4 => -1 + Bx = 8 => Bx = 9
11 + By = 2 x 11 = > 11 + By = 22 => By = 11
=> Option D is correct
Hope this helps!
:)
One approach to active learning is a "flipped classroom." This commonly involves students watching video lectures outside of class and working on problem solving activities in class. Research has primarily focused on comparing teaching approaches using end-of-class outcomes, such as final grades. In a recent project, researchers compared the lasting benefits of a flipped classroom by comparing grades received in the subsequent course of the series. Here are the results:
Groups n I s
Flipped 166 2.45 1.09
Traditional 129 1.59 1.20
Assume the population variances are equal.
Do the average grades received differ across the two delivery styles of the previous course? Use a=0.01.
Answer:
Yes, they differ across the two delivery styles of the previous course.
Step-by-step explanation:
So, we are given the following data or information or parameters from the question above;
Flipped(group) => 166(n) 2.45(l) 1.09(s).
Traditional(group) => 129(n) 1.59(l) 1.20(s).
Therefore, the hypothesis is given below as; Jo : b1 = b2, Jx : b1 ≠ b2.
Recall that we are given; 166 = (n1), 2.45 = (l1), 1.09 = (s1) and 129 = (n2) , 1.59 = (l2), 1.20 = (s2).
Therefore, we will be using the following mathematical representation or formula to solve this question;
s = √(s1^2/ n1 + s2^2/n2).
When we slot it the values accordingly and solve for s, we will have a value of;
s = 0.1354.
Thus , for our t*, we can calculate that by using the formula below:
t*= l1 - l2/ s.= (2.45 - 1.59)/ 0.1354= 6.35.
Thus: p value = 2P(V> 6.35) = 2.1 × 10^-10.
Since we are given that a=0.01, thus, p value is less than 0.01 we can reject Jo.
I dont understand anything, plz help
Bob has been hired by Global Domination Inc. to examine the mass of widgets being produced by two
different factories. The data he gatheredare in the following tables:
Factory 1:
234 234 237 239 245 248 250 256 257 260
262 262 262 266 267 268 274 275 277 279
Factory 2:
146 247 249 250 251 253 253 254 255 257
257 257 258 259 261 266 267 267 269 274
Construct two box-and-whisker plots, one for each factory, and arrange them side-by-side using the
same scale.
Using the following data, calculate the mean absolute deviation:
10 7 1 6 7 9 8 10 2 5
What is the mean absolute deviation for these data? (60 points)
a) 2
b) 2.4
c) 6.5
d) 7
Answer:
2.4
Step-by-step explanation:
First we need to find the mean
Add up all the number
(10+ 7+ 1+ 6+ 7+ 9+ 8+ 10+ 2+ 5)/10
65/10 = 6.5
Then find the absolute difference from each point and the mean and sum them together and divide by the number of points
((10-6.5) + (7-6.5) +(6.5- 1) +(6.5-6) + (7-6.5)+( 9-6.5)+( 8-6.5)+ (10-6.5)+(6.5- 2)+(6.5- 5)) /10
24/10
2.4
Answer:
b) 2.4
Step-by-step explanation:
Mean = (10+7+1+6+7+9+8+10+2+5)/10
= 65/10 = 6.5
Sum|x-mean| = 3.5+0.5+5.5+0.5+0.5+2.5+1.5+3.5+4.5+1.5 = 24
MAD = 24/10 = 2.4
If 3x−y=12, what is the value of 8x/2y?
Answer:
17.2
Step-by-step explanation:
3x=12+y
x=12+y/3
[tex]8( \frac{12 + y}{3}) \div 2y[/tex]
[tex] \frac{96 + 8y}{3} \times \frac{1}{2y} [/tex]
[tex] \frac{96 + 8y}{6y} [/tex]
(y is divided by y so it no longer exists)
[tex] \frac{96 + 8}{6} [/tex]
[tex] \frac{104}{6} [/tex]
[tex]17.2[/tex]
Plz help I need this in soon and I don't know the answer
Answer:
.13
Step-by-step explanation:
We need to find the areas of the regions
Area of the shaded region
A =pi r^2
pi (5)^2
25pi
The area of the total region
A = pi r^2
A = pi 14^2
= 196 pi
P(shaded) = shaded/ total
= 25 pi/196 pi
25/196
.12755102
To the nearest hundredth
.13
Answer:
0.13
Step-by-step explanation:
Total area:
Pi × 14²
3.14 × 196
615.44
Shaded area:
3.14 × 5²
78.5
Probability: 78.5/615.44
0.12755102
please help me w this question — pls show work
Answer:
B. 129.7°
Step-by-step explanation:
The law of sines tells you ...
sin(C)/c = sin(A)/a
sin(C) = (c/a)sin(A)
C = arcsin((c/a)sin(A)) = arcsin(117/57·sin(22°)) = 50.3°
The value shown is the result of using the arcsin function, but we know that the supplement of this angle has the same sine value. Then, we could have ...
C = 180° -50.3° = 129.7°
The figure shows C as an obtuse angle, so we choose this latter value as the appropriate answer to this question.
C = 129.7° . . . . . matches choice B
_____
Comment on the answer
We note that choice C (50.3°) matches the result of straightforward use of the law of sines. This triangle actually has two solutions for angle C, as we have noted above. Often, figures are "not to scale," so the appearance of angle C as an obtuse angle cannot always be taken at face value. Here, because both choices for angle C are offered, we use the appearance of the figure to help decide the right one.
Evelyn says that ⅗ is equivalent to 9/15. Anna says that ⅗ is equivalent to 15/25. Who is correct? How do you know?
Answer:
Both are correct
Step-by-step explanation:
3. ×3. 9
5. ×3. 15
3. ×5. 15
5. ×5. 25
If the function m(x) has the point (5, 2) on its graph name a point that would be on the function m(5x).
(1, 2)
(10, 2)
(5, 10)
(25, 2)
Answer:
21
Step-by-step explanation:
help plz I need big help someone plz help me with this question!
Answer:
Step-by-step explanation to be honest probably 12 if not i’m so sorry
Matthew has 3.5 pounds of clay to make ceramic objects.
he needs 1/2 of a pond of clay to make one bowl.
A.how many bowls can Matthew make with his clay
B. Matthew can make two mugs with the same amount of clay he uses to make one ceramic bowl. How much clay does he need to make with all of his clay
Step-by-step explanation:
Step 1: Answer part a
He has 3.5 pounds of clay and each bowl is 0.5 pounds of clay. Therefore, 3.5 / 0.5 will give us the amount of bowls he can make.
3.5 / 0.5
7
Answer: He can make 7 bowls
Step 2: Answer part b
I don't really understand what the questions asking about how much clay does he need to make with all of his clay. If you explain what that means I can answer it.
If you meant how much mugs he is able to make → 14
If you meant how much clay he needs to have for each mug → 0.25
Answer & Explanation:
Part A
It gives us 2 numbers to determined how much bowls he can make.
He need 0.5 of clay to make 1 bowl and he has 3.5 pounds of clay.
[tex]3.5[/tex] ÷ [tex]0.5[/tex]
= [tex]7[/tex]
He can make 7 bowls out of the 3.5 pounds of clay that he has.
Part B
This question is very confusing...
He can make 1 mug with 0.25 pounds of clay.
[tex]3.5[/tex] ÷ [tex]0.25[/tex]
= [tex]14[/tex]
He can make 14 mugs if he uses all of his clay.
hope this helps
give brainliest if you please
Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to In.
A. Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nxn identity matrix, In
B. Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in A must be on the main diagonal. Hence A is the nxn identity matrix, In.
C. Suppose A is n x n and the equation Ax=0 has only the trivial solution. Then there are n free variables in this equation, thus A has n pivot columns. Since A is square and then pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nxn identity matrix, In.
Answer:
i think that the answer is like hhhhhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
Which table represents the statement “A giraffe runs at a rate of 32 miles per hour”? A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled Distance with entries 32, 64, 96. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled Distance with entries 16, 32, 48. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled Distance with entries 8, 16, 24. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled Distance with entries 32, 33, 34.
Answer:
The answer is A.
Step-by-step explanation:
Answer:
Step-by-step explanation:
A
The CPI for "personal computers and peripheral equipment" in June 2006 was 10.7 (1982-1984 = 100). Interpret this index.
A. There was no significant increase in the price of "personal computers and peripheral equipment"
B. The price of "personal computers and peripheral equipment" increased 10.7%.
C. The price of "personal computers and peripheral equipment" decreased 89.3%.
D. If the average price of a computer in 1982-1984 was $3000.00, the CPI for "personal computers and peripheral equipment" would predict that the price of a computer in June 2006 would be $893.
Answer:
C. The price of "personal computers and peripheral equipment" decreased 89.3%.
Step-by-step explanation:
Consumer Price Index (CPI) measures change in price level, of weighted average market basket of consumer goods & services produced by households.
CPI calculated change in current year price level with regards to base year price level, base year price = 100. CPI > 100 implies that inflation (price rise) has occurred in current year from base year. CPI < 100 implies that deflation (price fall) has occurred in current year from base year.
CPI for 'personal computers & equipment' = 10.7 implies that prices of 'personal computers & equipment' have fallen or deflated. As per base year price = 100, prices have fallen by 100 - 10.7 = 89.3%
Answer:
The answer is "Option B"
Step-by-step explanation:
[tex]CPI = 10.7 \ in \ (\ june, \ 2006) \\\\CPI_{2006}= \frac{\ cost \ of \ basket \ of \ year \ 2006}{\ cost \ of \ basket \ of \ year \ 1982 \ to \ 84} \times 100\\\\\frac{10.7}{100} =\frac{\ cost \ of \ basket \ of \ year \ 2006}{\ cost \ of \ basket \ of \ year \ 1982 \ to \ 84}\\\\[/tex]
The cost of basket [tex]_{1982 \ to 1984} \times 0.107= \ cost \ of \ basket_{2006} \\\\[/tex]
[tex]\ cost \ of \ basket_{1982 \ to 1984} \ is \ given \ as \ 100\\\therefore \ \ cost \ of \ basket_{2006} = 100 \times 0.107\\\\[/tex]
[tex]\ = 10.7\\\\[/tex]
So, the answer is 10.7 % .
Throughout his photography career, Paul has photographed 200 adult elephants in the wild. If each elephant weighed approximately 1.4 x 104 pounds, find the combined weight of all 200 elephants expressed in scientific notation.
Answer:
[tex] (200*1.4) *10^4[/tex]
And we got:
[tex] 280 x10^4[/tex]
And if we move the decimal point two units to the left we got:
[tex] 2.8 x10^6[/tex]
Step-by-step explanation:
We know that each elefeant weight about [tex]1.4 x10^4[/tex]
And we have a total of 200 elephants so then we can find the total weights for the elephants with this formula:
[tex] 200 *1.4*10^4[/tex]
Using the properties of multiplication we can do this:
[tex] (200*1.4) *10^4[/tex]
And we got:
[tex] 280 x10^4[/tex]
And if we move the decimal point two units to the left we got:
[tex] 2.8 x10^6[/tex]