Answer:
The square root property should have been applied to both complete sides of the equation instead of to select
variables.
Helpi
Identify the domain of the function shown in the graph.
Answer:
D = all reals (or -7 to 7)
Step-by-step explanation:
If the line continues on for infinity, then the domain is all reals, or negative infinity to positive infinity. If the line ends on the graph that we can see, though, the domain would be [-7 , 7]
What is the equation of a parabola with its vertex at the origin and its focus at (–2, 0)?
Step-by-step explanation:
this is the answerI hope it helps
I need help solving this problem .
Step-by-step explanation:
here is the answer to your question
Jill has 32 crayons. She loses 4 of the crayons. How many are left?
Answer:
the answer here is d
the answer is d
Answer:
28
Step-by-step explanation:
Total number of crayons = 32
Number of crayons lost = 4
Therefore, number of crayons she is left with is : 32 - 4 = 28
Working :
[tex]32\\04 - \\\overline{28}[/tex]
Evaluate the given expression for x=7.
8x +9
The answer is ---
Answer:
The answer is 65
Step-by-step explanation:
Evaluate:
8x + 9
When x = 7
Use PEMDAS order of operations:
8x + 9
= 8(7) + 9
= 56 + 9
= 65
Hope this helps
Find the length of CE
Answer:
C. 37.8 units
Step-by-step explanation:
ED = 17/ cos(38°) = 17 / 0.7880 = 21.6 units
DF = 17× tan (38°) = 17× 0.7813 = 13.3 units
CD = 10/13.3 × 21.6 = 16.2 units
so, the length of CE = 21.6+16.2 = 37.8 units
Levi makes the minimum salary for actuary. Andres maybe the median salary for cpa. Who makes more money
Answer:
Andres
why?
Because he is median salary for cpa
Yess again pls help!
Tyyy
Exactly how many planes contain points J, K, and N?
a - 0
b - 1
c - 2
d - 3
Pls could someone help me with this
Answer:
- Bar Gaps should be the same
Y-axis up in units of 5 would help out
Step-by-step explanation:
The light from a lamp creates a shadow on a wall with a hyperbolic border. Find the equation of the border if the distance between the vertices is inches and the foci are inches from the vertices. Assume the center of the hyperbola is at the origin.
The equation of the hyperbola is,
(x/12)² - 4y²/(527) = 1
The standard equation of the hyperbola is
(x/a)² - (y/b)² = 1
Here (a, 0) and (-a, 0) are vertices and asymptotes y = ± √(b/a)x
Foci are (c, 0) & (-c, 0)
Then a² + b² = c²
Here we have to give that.,
2a = 24
a = 12
And 2c = 7
c = 7/2
Therefore a = 12 and c = 3.5
Substituting a and c in Pythagorean identity;
b² = 527/4
Then, the equation of the hyperbola is
(x/12)² - 4y²/(527) = 1
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We have b = 0, which implies that the foci coincide with the vertices, making the hyperbola a degenerate case. In this scenario, the equation of the border would be a vertical line passing through the vertices/foci, given by the equation x = ±a.
To find the equation of the hyperbolic border created by the shadow on the wall, we can start by understanding the properties of a hyperbola. A hyperbola is defined as the set of all points such that the difference of the distances from any point on the hyperbola to two fixed points, called the foci, is constant.
Let's label the vertices of the hyperbola as A and B, and the foci as F1 and F2. The distance between the vertices is given as 2a inches, and the foci are located at a distance c inches from the vertices.
Using the given information, we can find the value of a and c. Since the center of the hyperbola is at the origin, the coordinates of the vertices are (±a, 0), and the coordinates of the foci are (±c, 0).
The distance between the foci is given by the equation:
c = √(a^2 + b^2)
We know that the distance between the foci is given as 2c inches, so:
2c = 2√(a^2 + b^2)
Since c is given as a distance from the vertices, we can substitute c = a - b to simplify the equation:
2(a - b) = 2√(a^2 + b^2)
Squaring both sides to eliminate the square root:
4(a - b)^2 = 4(a^2 + b^2)
Expanding the equation:
4(a^2 - 2ab + b^2) = 4a^2 + 4b^2
Simplifying the equation:
4a^2 - 8ab + 4b^2 = 4a^2 + 4b^2
Canceling out the common terms:
-8ab = 0
Dividing by -8:
ab = 0
This implies that either a = 0 or b = 0. However, since a represents the distance between the vertices and b represents the distance between the foci and vertices, we can rule out a = 0 as it would result in a degenerate hyperbola.
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A loan of £1000 has a compound interest rate of 2.7% charged monthly. Express the original loan as a percentage of the total amount awed after 2 months if no payment are made
Answer:
£1054.729
Step-by-step explanation:
To find compound interest you need to use the equation 1000(1.027)^x.
To find the interest rate (1.027):
100 + 2.7 = 102.7
102.7 / 100 = 1.027
The value of x is the amount of months if no payment is made in this situation, so 2 would be the x value for this problem.
Hope this helps!
Suppose a large telephone manufacturer has a problem with excessive customer complaints and consequent returns of the phones for repair or replacement. The manufacturer wants to estimate the magnitude of the problem in order to design a quality control program. How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence
Answer:
80 telephones should be sampled
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 z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
89% confidence level
So [tex]\alpha = 0.11[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.11}{2} = 0.945[/tex], so [tex]Z = 1.6[/tex].
How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence?
n telephones should be sampled, an n is found when M = 0.09. We have no estimate for the proportion, thus we use [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.09 = 1.6\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.09\sqrt{n} = 1.6*0.5[/tex]
[tex]\sqrt{n} = \frac{1.6*0.5}{0.09}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.6*0.5}{0.09})^2[/tex]
[tex]n = 79.01[/tex]
Rounding up(as 79 gives a margin of error slightly above the desired value).
80 telephones should be sampled
Help and explain !!!!!!
Answer:
x = -4 or x = 5
Step-by-step explanation:
To solve the absolute value equation
|X| = k
where X is an expression in x, and k is a non-negative number,
solve the compound equation
X = k or X = -k
Here we have |2 - 4x| = 18
In this problem, the expression, X, is 2 - 4x, and the number, k, is 18.
We set the expression equal to the number, 2 - 4x = 18, and we set the expression equal to the negative of the number, 2 - 4x = -18. Then we solve both equations.
2 - 4x = 18 or 2 - 4x = -18
-4x = 16 or -4x = -20
x = -4 or x = 5
Answer:
x = -5 . x= 4
Step-by-step explanation:
because |4| = 4 and |-4| = 4
you can see that TWO inputs can get an output of (lets say) 4
The absolute value function can be seen as a function that ignores negative signs
so to get an OUTPUT of "18" using the absolute value function
there are really two ways of getting there
"2-4x = 18" AND "2-4x = -18"
if you solve both of those you will find that -5 and 4 will
produce the 18 and -18
Cole biked at 5 mph for 1 hours. Which of the following choices show how far he biked?
A=5.5 miles
B=6.5 miles
C=7.5 miles
D=10 miles
Answer:
Most Likely A, 5.5 Miles
Step-by-step explanation:
However the question doesn't make sense as the logical answer is simply 5 miles, but the safest choice is 5.5
Four times a number is 88 less than 6 times the number. Find the number.
Answer:
44
Step-by-step explanation:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
The number is 44.
To find the number.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers. Arithmetic is the basics of the abstract science of numbers and operations on them. The formula for any arithmetic sequence is this: an = a1 + d (n - 1).
Given that:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
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Please kindly help
According to a newspaper article 15% more home remodeling was done in 1985 than in 1984. Professionals performed 75% of all remodeling. If $80.4 billion was spent on residential remodeling in 1985 what was the value of the work done by professionals in 1985?
(1) $ 8.4 billion
(2) $12.06 billion
(3) $20.1 billion
(4) $60 billion
(5) $60.3 billion
Answer:
(3) $20.1 billion
Step-by-step explanation:
hope it help
Answer:
(5) $60.3 billion
Step-by-step explanation:
Find the value of x.
Answer:
x = 3
Step-by-step explanation:
A midsegment in a trapezoid is formed when one connects the midpoints of the two legs (non-parallel sides) in a trapezoid. The midsegment theorem states that the length of the midsegment is equal to the average of the two bases (that is the parallel sides).
One can apply the midsegment theorem here by stating the following;
[tex]\frac{(YZ)+(TM)}{2}=PW[/tex]
Substitute,
[tex]\frac{23+11x+2}{2}=29[/tex]
Simplify,
[tex]\frac{25+11x}{2}=29[/tex]
Inverse operations,
[tex]\frac{25+11x}{2}=29[/tex]
[tex]25+11x=58\\\\11x = 33\\\\x = 3[/tex]
1. Suppose half of all newborns are girls and half are boys. Hospital A, a large city hospital, records an average of 50 births a day. Hospital B, a small, rural hospital, records an average of 10 births a day. On a particular day, which hospital is less likely to record 80% or more female births?
Answer:
5%
Step-by-step explanation:
Hospital A (with 50 births a day), because the more births you see, the closer the proportions will be to 0.5.
Hospital B (with 10 births a day), because with fewer births there will be less variability.
The two hospitals are equally likely to record such an event, because the probability of a boy does not depend on the number of births
Two hospitals have an equal chance of recording such an event.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given
Hospital A (with 50 births per day), as the proportions will be closer to 0.5 the more births you see.
Hospital B (with 10 births per day), thus there will be less unpredictability with fewer births.
Due to the fact that the likelihood of a boy does not rely on the number of births, the two hospitals have an equal chance of recording such an event.
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A cyclist completes a journey of 500 m in 22 seconds, part of the way at 10 m/s and the remainder at 50 m/s. How far does she travel at each speed. solve by forming simultaneous equation
Answer:
150 m at 10 m/s
350 m at 50 m/s
Step-by-step explanation:
x + y = 500
x/10 + y/50 = 22
~~~~~~~~~~~~~~~~~
x + y = 500
5x + y = 1100
~~~~~~~~~~~~~~~~
x + y = 500
-5x - y = -1100
-4x = -600
x = 150
y = 350
Write an equation that expresses the following relationship.
d varies directly with w and inversely with p.
In your equation, use k as the constant of proportionality.
9514 1404 393
Answer:
d = kw/p
Step-by-step explanation:
When d varies directly with w, the equation is ...
d = kw
When d varies inversely with p, the equation is ...
d = k/p
When d does both, the equation is ...
d = kw/p
1. You measure 24 textbooks' weights, and find they have a mean weight of 75 ounces. Assume the population standard deviation is 3.3 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.
2. You measure 37 backpacks' weights, and find they have a mean weight of 45 ounces. Assume the population standard deviation is 10.1 ounces. Based on this, construct a 95% confidence interval for the true population mean backpack weight.
3. You measure 30 watermelons' weights, and find they have a mean weight of 37 ounces. Assume the population standard deviation is 4.1 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight.
4. A student was asked to find a 99% confidence interval for widget width using data from a random sample of size n = 16. Which of the following is a correct interpretation of the interval 11.8 < μ < 20.4?
A. There is a 99% chance that the mean of a sample of 16 widgets will be between 11.8 and 20.4.
B. The mean width of all widgets is between 11.8 and 20.4, 99% of the time. We know this is true because the mean of our sample is between 11.8 and 20.4.
C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4.
D. With 99% confidence, the mean width of a randomly selected widget will be between 11.8 and 20.4.
E. There is a 99% chance that the mean of the population is between 11.8 and 20.4.
5. For a confidence level of 90% with a sample size of 23, find the critical t value.
Answer:
(73.845 ; 76.155) ;
(41.633 ; 48.367) ;
1.273 ;
C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4. ;
1.717
Step-by-step explanation:
1.)
Given :
Mean, xbar = 75
Sample size, n = 24
Sample standard deviation, s = 3.3
α = 90%
Confidence interval = mean ± margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 90% ; df = 24 - 1 = 23
Tcritical = 1.714
Margin of Error = 1.714 * 3.3/√24 = 1.155
Confidence interval = 75 ± 1.155
Confidence interval = (73.845 ; 76.155)
2.)
Given :
Mean, xbar = 45
Sample size, n = 37
Sample standard deviation, s = 10.1
α = 95%
Confidence interval = mean ± margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 95% ; df = 37 - 1 = 36
Tcritical = 2.028
Margin of Error = 2.028 * 10.1/√37 = 3.367
Confidence interval = 45 ± 3.367
Confidence interval = (41.633 ; 48.367)
3.)
Given :
Mean, xbar = 37
Sample size, n = 30
Sample standard deviation, s = 4.1
α = 90%
Margin of Error = Tcritical * s/√n
Tcritical at 90% ; df = 30 - 1 = 29
Tcritical = 1.700
Margin of Error = 1.700 * 4.1/√30 = 1.273
5.)
Sample size, n = 23
Confidence level, = 90%
df = n - 1 ; 23 - 1 = 22
Tcritical(0.05, 22) = 1.717
The ocean surface is at 0 ft elevation. A diver is underwater at a depth of 138 ft. In this area, the ocean floor has a depth of 247 ft. A rock formation rises to a peak 171 ft above the ocean floor. How many feet below the top of the rock formation is the diver?
Answer:
The ocean surface is at 0 ft elevation. A diver is underwater at a depth of 138 ft. In this area, the ocean floor has a depth of 247 ft.
Step-by-step explanation:
19. Divide 6/13 by 6/12.
A. 12/13
B. 13/12
c. 1/12
D.9/16
Answer:
12/13 is the answer
Step-by-step explanation:
By recognizing the series as a Taylor series evaluated at a particular value of x, find the sum of each of the following convergent series
1 + 3 + 9/2! + 27/3! + 81/4! + .....
Answer:
the answer should be e^3
Step-by-step explanation:
i hope it helps you
Is a linear model or a quadratic model a better fit? Quadratic model graph quadratic model linear model
You and a friend were invited to a
party. You both were asked to bring
pizzas and chips. Your friend brought
three pizzas and four bags of chips
and spent $48.05. You brought five
pizzas and two bags of chips and
spent $67.25. What is the cost of
each? Answer should be in (Pizza, Chips)
Answer:
Pizza = 12.35
Chips = 2.75
Step-by-step explanation:
Let :
Pizza = x
chips = y
3x + 4y = 48.05 - - - (1)
5x + 2y = 67.25 - - - (2)
Multiply (1) by 5 and (2) by 3
15x + 20y = 240.25
15x + 6y = 201.75
Subtract :
20y - 6y = 240.25 - 201.75
14y = 38.50
y = 38.50/ 14
y = 2.75
Put y = 2.75 in (1)
3x + 4(2.75) = 48.05
3x + 11 = 48.05
3x = 48.05 - 11
3x = 37.05
x = 37.05 / 3
x = 12.35
Pizza = 12.35
Chips = 2.75
A multiple regression model is ^Y = 8.114 + 2.005X1 + 0.774X2. Which of the following values is the estimate for the intercept parameter?
a. 0.774.
b. 8.114.
c. 1.000.
d. 2.005.
Answer:
B. 8.114
Step-by-step explanation:
The intercept parameter is the zero-grade component of the multilinear equation, that is, the component independent from [tex]x_{1}[/tex] and [tex]x_{2}[/tex]. Hence, the intercept parameter of the multilinear regression is 8.114. (Correct answer: B)
TZ is a midsegment, which of the following statements CANNOT be true
Answer:
Option C: QT < TR
Step-by-step explanation:
From the triangle, we can see that UX bisects RS into two equal parts and so it is a perpendicular bisector.
TZ Is a mid segment and it means that T bisects QR into 2 equal parts as well as QS into 2 equal parts.
Thus;
QT = QR
And QZ = SZ
So Option C is not correct because QT = QR
The thickness X of aluminum sheets is distributed according to the probability density function f(x) = 450 (x2 - x) if 6 < x < 12 0 otherwise 5-1 Derive the cumulative distribution function F(x) for 6 < x < 12. The answer is a function of x and is NOT 1! Show the antiderivative in your solution. 5-2 What is E(X) = {the mean of all sheet thicknesses)? Show the antiderivative in your solution.
Solution :
Given :
[tex]f(x) = \left\{\begin{matrix}\frac{1}{450}(x^2-x) & \text{if } 6 < x < 12 \\ 0 & \text{otherwise}\end{matrix}\right.[/tex]
1. Cumulative distribution function
[tex]$P(X \leq x) = \int_{- \infty}^x f(x) \ dx$[/tex]
[tex]$=\int_{- \infty}^6 f(x) dx + \int_{6}^x f(x) dx $[/tex]
[tex]$=0+\int_6^x \frac{1}{450}(x^2-x) \ dx$[/tex]
[tex]$=\frac{1}{450} \int_6^x (x^2-x) \ dx$[/tex]
[tex]$=\frac{1}{450}\left[\frac{x^3}{3}-\frac{x^2}{2}\right]_6^x$[/tex]
[tex]$=\frac{1}{450}\left[ \left( \frac{x^3}{3} - \frac{x^2}{2}\left) - \left( \frac{6^3}{3} - \frac{6^2}{2} \right) \right] $[/tex]
[tex]$=\frac{1}{450}\left[\frac{x^3}{3} - \frac{x^2}{2} - 54 \right]$[/tex]
2. Mean [tex]$E(x) = \int_{- \infty}^{\infty} \ x \ f(x) \ dx$[/tex]
[tex]$=\int_{6}^{12}x . \left( \frac{1}{450} \ (x^2-x)\right)\ dx$[/tex]
[tex]$=\frac{1}{450} \int_6^{12} \ (x^3 - x^2) \ dx$[/tex]
[tex]$=\frac{1}{450} \left[\frac{x^4}{4} - \frac{x^3}{3} \right]_6^{12} \ dx$[/tex]
[tex]$=\frac{1}{450} \left[ \left(\frac{(12)^4}{4} - \frac{(12)^3}{3} \right) - \left(\frac{(6)^4}{4} - \frac{(6)^3}{3} \right) $[/tex]
[tex]$=\frac{1}{450} [4608 - 252]$[/tex]
= 17.2857
