Answer:
2
Step-by-step explanation:
For Example, To complete the square when a is greater than 1 or less than 1 but not equal to 0, factor out the value of a from all other terms.
For example, find the solution by completing the square for:
2x2−12x+7=0
a≠1,a=2 so divide through by 2
22x2−122x+72=02
which gives us
x2−6x+72=0
The graph shows the number of y gallons of gasoline remaining in a car x hours after filling the tank.
Answer:
edfghjnsdfghjkm
Step-by-step explanation:
The diagram shows three touching circles.
A is the centre of a circle of radius x centimeters.
B and C are the centers of circles of radius 3.8 centimeters. Angle ABC = 70.
Find the value of x
Answer:
x = 7.31 cm
Step-by-step explanation:
cos 70° = 3.8/AB
0.3420 = 3.8/AB
AB = 11.11 cm
x = 11.11 - 3.8 = 7.31 cm
The value of x which is the radius of circle A is 7.31 cm
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
AB = AC, hence ∠B = ∠C = 70°
∠A + ∠B + ∠C = 180° (angles in a triangle)
∠A + 70 + 70 = 180
∠A = 40°
BC = 3.8 + 3.8 = 7.6
Using sine rule:
BC/sinA = AB / sinB
7.6/sin(40) = AB/sin(70)
AB = 11.11 cm
x = 11.11 - 3.8 = 7.31 cm
The value of x which is the radius of circle A is 7.31 cm
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Help me with my math homework
Please please please help
9514 1404 393
Answer:
a) max height: 210.25 feet
b) time: 7 seconds
Step-by-step explanation:
Since this is about graphing quadratics, it seems appropriate to use a graph produced by a graphing calculator. It shows ...
maximum height: 210.25 feet
time to hit the ground: 7 seconds
(a) Points and are shown on the number line. Part A Find the distances between points and and between points and . Show your work or explain your answers. Refer to the number lint in your explanation. Enter your answers and your work or explanation in the box provided.
Step-by-step explanation:
Im donating points thank you
Answer:
do you have a graph? we can't do it unless you have one.
At what point(s) do these graphs intersect?
y = x^2 + 3x - 5
y = 4x + 1
Seth's solution:
y = x^2 + 3x - 5
y = 4x + 1
x^2 + 3x - 5 = 4x + 1
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0
x = 3 and x = -2
The graphs intersect at.(-20) and (3,0).
Is Seth's solution correct? Explain.
The graphs intersect at the points (3, 13) and (-2, -7).
How to determine the intersection of 2 graphsGiven the following equations:
y₁ = x² + 3x - 5 (quadratic equation)
y₂ = 4x + 1 (linear equation)
To find the intersection point(s) of the two graphs, we need to solve their equations simultaneously. By so doing, we'll set the equations equal to each other:
y₁ = y₂
x² + 3x - 5 = 4x + 1
collect the like terms
x² - x - 6 = 0
Now we'll factor the quadratic expression:
(x - 3)(x + 2) = 0
x - 3 = 0 or x + 2 = 0
x = 3 or x = -2
Now we have the points of intersection on the x-axis.
To get the corresponding values on the y-axis, we'll plug each value of x into either of the original equations.
Let's use the first equation:
y₁ = x² + 3x - 5
When x = 3:
y₁ = 3² + 3(3) - 5 = 13
When x = -2:
y₂ = 4x + 1 = 4(-2) + 1 = -7
So the first intersection point is (3, 13) and the second intersection point is (-2, -7).
Therefore, the graphs intersect at the points (3, 13) and (-2, -7).
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Alex finds a remnant of landscaping fabric at a garden store . The fabric is the standard width , with length 9.7 m . Alex needs twelve 0.85 - m pieces for a garden patio . a ) Will Alex have more fabric than she needs ? If so , how much more ? b ) Will Alex need more fabric ? If so , how much more ?
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Length of remnant fabric = 9.7m
Number of 0.85m length needed for patio = 12
Total length needed = (0.85 * 12) = 10.2m
The length of fabric needed is more than the length of remnant fabric found ;
10.2 m - 9.7m = 0.5m
Hence, Alex will need 0.5m more fabric
The table shows the values (in thousands) of the average salary of NBA players x years after 1990. Write and use an exponential model to find the year
when the average NBA player's salary will be more than $3 million
1
2
Years, X
3
4
5
0
15
30
Salary, y
60
240
480
120
Write an exponential model for this situation
(put parentheses around the "b" value)
What is the projected salary in 9 years?
In what year would the salary be more than $3 million? (round to two decimal places)
Answer:
Step-by-step explanation:
From the given table,
Ratio of each successive term in the row showing salary (y) is,
Ratio = [tex]\frac{30}{15}[/tex] = 2
Therefore, function representing the relation between average salary (y) and years (x) will be the exponential function.
y = a(b)ˣ
For x = 0, y = 15,
15 = a(b)⁰
a = 15
For x = 1, y = 30,
30 = 15(b)¹
b = 2
Therefore, exponential function Or exponential model will be,
y = 15(2)ˣ
Projected salary in 9 years [For x = 9],
y = 15(2)⁹
y = 15 × 512
y = $7680
For the salary more than $3 million [For y = $3000000],
3000000 = 15(2)ˣ
2ˣ = 200000
log(2)ˣ = log(200000)
xlog2 = log(2×10⁵)
xlog2 = log2 + log(10)⁵
(x - 1)log2 = 5
x - 1 = [tex]\frac{5}{\text{log2}}[/tex]
x = 16.609 + 1
x = 17.609
x ≈ 17.61 years
Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 75 manufacturing companies located in the Southwest. The mean expense is $50.93 million and the standard deviation is $10.80 million. Is it reasonable to conclude the sample data are from a population that follows a normal probability distribution? Advertising Expense ($ Million) Number of Companies 25 up to 35 4 35 up to 45 19 45 up to 55 27 55 up to 65 16 65 up to 75 9 Total 75
Answer:
Step-by-step explanation:
The table can be computed as:
Advertising Expenses ($ million) Number of companies
25 up to 35 4
35 up to 45 19
45 up to 55 27
55 up to 65 16
65 up to 75 9
TOTAL 75
Let's find the probabilities first:
[tex]P(25 - 35) = P \Big(\dfrac{25-50.93}{10.80}<z< \dfrac{35-50.93}{10.80}\Big) \\ \\ =P \Big(\dfrac{-25.93}{10.80}<z< \dfrac{-15.93}{10.80}\Big) \\ \\ =P(-2.4009<z<-1.475) \\ \\ =(0.0694 -0.0082) \\ \\ =0.0612[/tex]
For 35 up to 45
[tex]P(35 - 45) = P \Big(\dfrac{35-50.93}{10.80}<z< \dfrac{45-50.93}{10.80}\Big)=P \Big(\dfrac{-15.93}{10.80}<z< \dfrac{-5.93}{10.80}\Big) \\ \\ =P(-1.475<z<-0.5491) \\ \\ =(0.2912 -0.0694) \\ \\ =0.2218[/tex]
For 45 up to 55
[tex]P(45 - 55) = P \Big(\dfrac{45-50.93}{10.80}<z< \dfrac{55-50.93}{10.80}\Big)=P \Big(\dfrac{-5.93}{10.80}<z< \dfrac{4.07}{10.80}\Big) \\ \\ =P(-0.5491<z<0.3769) \\ \\ =(0.6480 -0.2912) \\ \\ =0.3568[/tex]
For 55 up to 65
[tex]P(55 - 65) = P \Big(\dfrac{55-50.93}{10.80}<z< \dfrac{65-50.93}{10.80}\Big)=P \Big(\dfrac{4.07}{10.80}<z< \dfrac{14.07}{10.80}\Big) \\ \\=P(0.3768<z<1.3028) \\ \\ =(0.9032-0.6480) \\ \\ =0.2552[/tex]
For 65 up to 75
[tex]P(65 - 75) = P \Big(\dfrac{65-50.93}{10.80}<z< \dfrac{75-50.93}{10.80}\Big)=P \Big(\dfrac{14.07}{10.80}<z< \dfrac{24.07}{10.80}\Big) \\ \\ =P(1.3028<z<2.2287) \\ \\=(0.9871-0.9032) \\ \\ =0.0839[/tex]
Chi-Square Table can be computed as follows:
Expense No of Probabilities(P) Expe [tex](O-E)^2[/tex] [tex]\dfrac{(O-E)^2}{E}[/tex]
compa cted E (n*p)
nies (O)
25-35 4 0.0612 75*0.0612 = 4.59 0.3481 0.0758
35-45 19 0.2218 75*0.2218 = 16.635 5.5932 0.3362
45-55 27 0.3568 75*0.3568 = 26.76 0.0576 0.021
55-65 16 0.2552 75*0.2552 = 19.14 9.8596 0.5151
65-75 9 0.0839 75*0.0839 = 6.2925 7.331 1.1650
[tex]\sum \dfrac{(O-E)^2}{E}= 2.0492[/tex]
Using the Chi-square formula:
[tex]X^2 = \dfrac{(O-E)^2}{E} \\ \\ Chi-square \ X^2 = 2.0942[/tex]
Null hypothesis:
[tex]H_o: \text{The population of advertising expenses follows a normal distribution}[/tex]
Alternative hypothesis:
[tex]H_a: \text{The population of advertising expenses does not follows a normal distribution}[/tex]
Assume that:
[tex]\alpha = 0.02[/tex]
degree of freedom:
= n-1
= 5 -1
= 4
Critical value from [tex]X^2 = 11.667[/tex]
Decision rule: To reject [tex]H_o \ if \ X^2[/tex] test statistics is greater than [tex]X^2[/tex] tabulated.
Conclusion: Since [tex]X^2 = 2.0942[/tex] is less than critical value 11.667. Then we fail to reject [tex]H_o[/tex]
A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective. Step 2 of 2: Suppose a sample of 1536 floppy disks is drawn. Of these disks, 1383 were not defective. Using the data, construct the 98% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.
Answer:
The 98% confidence interval for the population proportion of disks which are defective is (0.082, 0.118).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Suppose a sample of 1536 floppy disks is drawn. Of these disks, 1383 were not defective.
1536 - 1383 = 153
This means that [tex]n = 1536, \pi = \frac{153}{1536} = 0.1[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1 - 2.327\sqrt{\frac{0.1*0.9}{1536}} = 0.082[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1 + 2.327\sqrt{\frac{0.1*0.9}{1536}} = 0.118[/tex]
The 98% confidence interval for the population proportion of disks which are defective is (0.082, 0.118).
Robert and his friends went to have lunch at a restaurant. The service was great, so they decided to leave a 20% tip. Is the final amount cheaper or more expensive?
Whoever answers correctly will get Brainliest!
Have an amazing day!! :))))
Answer:
More Expensive
Step-by-step explanation:
If they left a tip, that means they would have to pay the full amount of the meal plus 20% fo whatever the full amount was, so they'd pay more.
Find the surface area of a cylinder
whose radius is 5 cm and whose
height is 10 cm.
Round to the nearest whole number.
[?] cm2
Find the surface area of a cylinder
whose radius is 5 cm and whose
height is 10 cm.
Answer:-Given:-[tex] \bullet [/tex] Radius of a cylinder (r) is 5 cm
[tex] \bullet [/tex] Height of a cylinder (h) is 10 cm
To Find:-The surface area of a cylinder
Solution:-We know the formula of surface area of a cylinder is –
[tex] { \boxed{\rm \red {2πr² \: + \: 2πrh}}} [/tex]So, putting the value of r = 5 cm and h = 10 cm we get,
2πr(r + h) = 2 × [tex] \frac{22}{7} [/tex] × 5(5 + 10)
= [tex] \frac{220}{7} [/tex](5 + 10)
= [tex] \frac{220}{7} [/tex] × 15
= [tex] \frac{220 \: × \: 15}{7} [/tex]
= [tex] \frac{3300}{7} [/tex]
= 471.43 cm²
The surface area of a cylinder is 471.43 cm². [Answer]
Distributive Property step by step 3x(x-1) tHxs
Answer:
3x² - 3x
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
3x(x - 1)
Step 2: Expand
Distributive Property: 3x(x) + 3x(-1)Multiply: 3x² - 3xsolve the rational equation
X+3/ 3x -2 - x-3/3x+2=176/9x^2-4
Answer:
8
i hope this will help you
We wish to determine the proportion of small- to medium-sized streams in eastern North Carolina which have runoff from hog farms in order to prepare for issues arising from water quality in the aftermath of hurricanes. A random sample of 174 small- to medium-sized streams is selected and it is found that 100 of them have runoff from hog farms. Which of the following is the value of the parameter of interest in this setting?
a. 0.02322.
b. 0.240.
c. 0.760.
d. the value of the parameter of interest cannot be determined from the given information.
Answer:
The value of the parameter of interest in this setting is 0.5747.
Step-by-step explanation:
The parameter of interest is:
The proportion of small- to medium-sized streams in eastern North Carolina which have runoff from hog farms in order to prepare for issues arising from water quality in the aftermath of hurricanes.
A random sample of 174 small- to medium-sized streams is selected and it is found that 100 of them have runoff from hog farms.
This means that the value of the parameter of interest is:
[tex]p = \frac{100}{174} = 0.5747[/tex]
The value of the parameter of interest in this setting is 0.5747.
3.14*3.14*3.14*x*x*x*x
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
( 3.14 ) ( 3.14 ) ( 3.14 ) * x * x * x * x
=3.14 * 3.14 * 3.14 * x * x * x * x
=30.959144 * x^4
=30.959144x^4
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
30.959144(x^4)
Can anybody help me pls
Answer:
1 and -8
Step-by-step explanation:
I just substituted them until I found the correct one.
Hope this helps ^-^
I need some help with this! I will try to give brainliest!!
Answer:
Left yes
right no
Step-by-step explanation:
that goes for top and bottom
who can help me please
9514 1404 393
Explanation:
Statement .... Reason
( ) .... Given (repeat of the given statements)
ΔACB ≅ ΔDCE .... SAS postulate
BA ≅ ED .... corresponding parts of congruent triangles are congruent
what is 313 3/5 x 65
Answer
20384
Step-by-step explanation:
Can someone please help me with this!
Answer:
It's Positive
Step-by-step explanation:
Find the magnitude of AB.
A(-2, 6), B(1, 10)
O A 2
OB. ✔️15
O C.5
OD ✔️2
Answer:
C. 5
Step-by-step explanation:
Use the Distance Formula.
Substitute the values of x1 , y1 , x2 , and y2 .
|AB|² =|(1--2)²+(10-6)²|
|AB|² = |9+16|
|AB| = √ 25
|AB| =5
Statistic questions
Answer:
a. 1.91
Step-by-step explanation:
because I think I'm lucky today
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
0
10
X
15
Answer:
x ≈ 11.180Steps:
x = √(15²-10²)
x = √(225-100)
x = √125
x ≈ 11.180
HELP DUE ASAP PLEASE!! X.
Y.
10
3 4 5 6 7 8 9
SELECT ALL THAT APPLY for the box plots above.
the first quartile has a greater spread for box plot x than the spread in the first quartile for
box ploty
25% of the data is greater than 7.5 for box plot x and 50% greater for box ploty
the medians have the same value for both box plots
the median for box plot x has the same value as the lower quartile of box ploty
Answer:
D. The median for box plot X is the same as the lower quartile as box plot Y.
Step-by-step explanation:
If you look at box plot X, its median is at 6. Also, the lower quartile for box plot Y is 6 as well. That means that D. is the correct answer. Hope this helps!
Answer:
Below
Step-by-step explanation:
I'm pretty sure it may be B, and D
D because when you look at it X's plot does have the median line up with Y's Lower quartile
And using the rule of crossing out answers that are incorrect I am left with B, because the medians and different and X's lower quartile is smaller than Y's
What is the area of the polygon below in square units?
4 cm
12 cm
18 cm
If log 5 = 0.699 and log 3 = 0.477, find log 45 without using
the log key.
Answer:
1.653
Step-by-step explanation:
Write log45 as a product of its prime factors
log45= log3^2 * log5
Substitute the given logarithms to the respective numbers.
Remember the laws of logaarithms that * changes to +
log 45 = 0.477*2 + 0.699
You will find that log 45 = 1.653
From the given logarithmic values the value of log45 derived as 0.1590.
What are logarithms?In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
Given that, log5=0.699 and log3=0.477.
Here, log45 can be written as log9×log5=log3²×log5
= 0.477²×0.699
= 0.1590
Therefore, the value of log45 is 0.1590.
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The table shows Annabeth’s scores on her math assignments. Find the mean.
Answer:
90.35
Step-by-step explanation:
its on envisions
8-2 quiz
help me answer this question please
9514 1404 393
Answer:
x = ∛4 ≈ 1.587 m
y = (∛4)/2 ≈ 0.794 m
Step-by-step explanation:
Short answer:
An open-top box will use minimum material when it has the shape of half a cube. That is, the x-dimensions will be ...
x = ∛(2·2 m³) = ∛4 m
The y-dimensions will be half that:
y = x/2 = (∛4)/2 m
__
Long answer:
The volume is ...
V = x^2·y
so the y-dimension is ...
y = V/x^2
The area of the sides and bottom will be ...
A = 4xy + x^2
A = 4x(2/x^2) +x^2 = 8/x +x^2
The area is minimized when the derivative of this is zero.
A' = 0 = -8/x^2 +2x
x^3 = 4 . . . . . . . divide by 2 and rearrange
x = ∛4 . . . . . . . . cube root
y = 2/x^2 = 2∛4/4
y = (∛4)/2
___
Additional comment
If you follow the numbers through, you see that the value under the cube-root radical is twice the volume. This is the result we used in the "short answer."
Which Factors would simplify in this expression?
(x-8) 4x(x+6)
——————x————-
8(x+6)(x+10) (x+10)
Answer:
(x+6)
Step-by-step explanation:
because you have ( x+6) on bottom of the first equation and on the top on the second equation