Answer:
-2
Step-by-step explanation:
x^2 + x=2
Subtract 2 from each side
x^2 + x-2=2-2
x^2 + x-2=0
Factor
What 2 numbers multiply to -2 and add to 1
2*-1 = -2
2+-1 =1
(x-1)(x+2)=0
Using the zero product property
x-1 = 0 x+2 = 0
x=1 x = -2
Product of the roots
1*-2 = -2
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The
outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.
Outcomes Probability
HHT HHH THH HTH HTT TTT TTH THT
Event A: Alternating tail and head (with either coming first)
Event B: No tails on the first two tosses
Event C: A tail on both the first and the last tosses
Answer:
Step-by-step explanation:
In this question, the sample space contains 8 elements and has been given as;
HHT HHH THH HTH HTT TTT TTH THT
1. For event A:
Outcomes of alternating tail and head = THH HTH HTT THT
= 4 outcomes
Pr(alternating tail and head (with either coming first)) = [tex]\frac{4}{8}[/tex]
= [tex]\frac{1}{2}[/tex]
2. For event B:
Outcomes of no tails on the first two tosses = HHT HHH
= 2 outcomes
Pr (No tails on the first two tosses) = [tex]\frac{2}{8}[/tex]
= [tex]\frac{1}{4}[/tex]
For event C:
Outcomes of a tail on both the first and the last tosses = THT TTT
= 2 outcomes
Pr(A tail on both the first and last tosses) = [tex]\frac{2}{8}[/tex]
= [tex]\frac{1}{4}[/tex]
âClaim: Most adults would erase all of their personal information online if they could. A software firm survey of 551 randomly selected adults showed that 50.4â% of them would erase all of their personal information online if they could. Make a subjective estimate to decide whether the results are significantly low or significantlyâ high, then state a conclusion about the original claim.
Look at the file, it has every bit of the answer
Write an algebraic expression for each person’s share, if P people share 16 slices of pizza equally.
Answer:
P /16
Step-by-step explanation:
Take the total amount, P and divide by the number of people sharing, 16
P /16
If it takes 247.2 yards of yarn to knit 2.5 baby bibs, how many yards of yarn would it take to knit 4 baby bibs? SHOW ALL WORK! ONLY ANSWER IF YOU KNOW THE ANSWER!
Answer:
395.52
Step-by-step explanation:
247.2/2.5=98.88(1 bib)
98.88x4=395.52(4 bibs)
Help? Please!?
ASAP if you can
Answer:
tan A = 1.375
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan A = CB/ AC
tan A = 11/8
tan A = 1.375
It costs a clothing company $463.45 to make 169 T-shirts.
What is the unit price for 1 T-shirt?
Answer:
The unit price for 1 T-shirt is about $2.74.
Step-by-step explanation:
Set up an equation:
Variable x = unit price for 1 T-shirt
169x = 463.45
Divide both sides by 169:
x = 2.742307...
Round to the nearest cent:
x = 2.74
I need help ASAP thank you guys
Answer:
The fraction is undefined when x=-2
Step-by-step explanation:
The fraction will be undefined when the denominator is zero
x+2 = 0
x+2-2 = 0-2
x = -2
The fraction is undefined when x=-2
Answer:
as to me 5
Step-by-step explanation:
ask someone else to say that I am not sure if you have any questions or need any further information please contact me at the end of the world
You have 576 feet of fencing to enclose a rectangular plot of land. Find the dimensions of the rectangular plot that would maximize the area. List the smaller number first.
Answer:
The dimension that maximizes area is 144ft by 144ft
Step-by-step explanation:
Given
[tex]P = 576[/tex] -- perimeter
Required
The dimension that gives maximum area
Perimeter is calculated as:
[tex]P= 2 * (L + W)[/tex]
So, we have:
[tex]2 * (L + W) = 576[/tex]
Divide through by 2
[tex]L + W = 288[/tex]
Make L the subject
[tex]L = 288 -W[/tex]
Area is calculated as:
[tex]A = L * W[/tex]
Substitute [tex]L = 288 -W[/tex]
[tex]A = (288 - W) * W[/tex]
Open bracket
[tex]A = 288W - W^2[/tex]
Differentiate A with respect to W
[tex]A' = 288 - 2W[/tex]
Set to 0 to calculate W
[tex]288 - 2W = 0[/tex]
Collect like terms
[tex]2W = 288[/tex]
Divide by 2
[tex]W = 144[/tex]
Recall that:
[tex]L = 288 -W[/tex]
[tex]L = 288 - 144[/tex]
[tex]L = 144[/tex]
100 divided by 200-3+1000=
Answer:
997.5 is the answer to your question..
What is the expected value of the two investments? Type the correct answer in each box. Round your answers to the nearest whole dollar value. The expected value of the Computer Co. stock is $ 5,040 0], and the expected value of the US Treasury bond is $ 5,085
THE AWNSER IS IN THE QUESTION
Answer: $5,040 & $5,085
Step-by-step explanation:
The expected value of the Computer Co. stock is $5,040, and the expected value of the US Treasury bond is $5,085
The expected value of both the stocks Computer Co. and US Treasury bond is $5,062.5.
What is the weighted average?When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.
To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.
The expected value is the weighted average also known as the mean.
Given, The expected value of the Computer Co. stock is $ 5,040, and the expected value of the US Treasury bond is $ 5,085.
Therefore the expected value of both stocks is,
= (5040 + 5085)/2.
= $5,062.5
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Rebecca buys a new couch for $1,200. She plans on making a monthly payment of $75 on the balance, starting the month
after she buys the couch. Which recursive function models the amount of money Rebecca still has to pay for the couch?
The recursive function is A(t + 1) = A(t) - 75
Where;
A(t) = 1,200 - 75×t
The known parameter are;
The amount Rebecca buys the new couch = $1,200
The amount she plans to make as monthly payment = $75
The time she plans to start paying = The month after she buys the couch
Strategy;
Define a recursive function that models the amount of money Rebecca still has to pay
Definition
A recursive function is one which has its own process as an input in the process of its implementation
A recursive function that models the amount of money Rebecca still has to pay for the couch is found as follows;
The amount left for her to pay in the present month = The amount left to pay in the previous month - $75
Let A(t + 1) represent the amount left for her to pay in the present month and let A(t) represent the amount left to pay in the previous month, we get;
A(t) = 1,200 - 75×t
A(t + 1) = 1,200 - 75×t - 75 = A(t) - 75
The recursive function is A(t + 1) = A(t) - 75
The function is recursive because, the function, A(t), is called in as an input to the execution of the function
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Answer:
f(1) = 1,200
f(n) = f(n-1) -75 for n > 2
Step-by-step explanation:
Since the initial loan amount is $1,200, f(1) =1200.
And since $75 is deducted from the balance each month starting with n >2 , the common difference, d, is -75 .
Use the general recursive function for an arithmetic sequence,f(n)= f (n - 1 ) +d , for n > 2 to write the recursive function models Rebecca’s situation:
the polygons in each pair are similar find the scale factor smaller figure to the larger
Answer:
smaller figure/larger figure = ½
Step-by-step explanation:
The scale factor = any of the side length of the smaller figure / the corresponding side length of the larger figure
Side length of smaller figure = 3
Corresponding sides length of larger figure = 6
Scale factor = smaller figure/larger figure = 3/6
Simplify
Scale factor = smaller figure/larger figure = ½
The diameters of ball bearings are distributed normally. The mean diameter is 7373 millimeters and the variance is 44. Find the probability that the diameter of a selected bearing is less than 7676 millimeters. Round your answer to four decimal places.
Answer:
0.9332
Step-by-step explanation:
We are given that
Mean diameter, [tex]\mu=73[/tex]
Variance, [tex]\sigma^2=4[/tex]
We have to find the probability that the diameter of a selected bearing is less than 76.
Standard deviation, [tex]\sigma=\sqrt{variance}=\sqrt{4}=2[/tex]
[tex]P(x<76)=P(\frac{x-\mu}{\sigma}<\frac{76-73}{2})[/tex]
[tex]P(x<76)=P(Z<\frac{3}{2})[/tex]
Where [tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]P(x<76)=P(Z<1.5)[/tex]
[tex]P(x<76)=0.9332[/tex]
Hence, the probability that the diameter of a selected bearing is less than 76=0.9332
Alejandro wants to determine how much money he made in the last month after taxes, social security, and Medicare were taken out of his paycheck. What number should he look at on his paystub? O a) Federal tax amount b) Net pay O c) Gross pay O d) Deductions
Answer:
absolutely B
Step-by-step explanation:
A is one type of tax
C) gross pay includes taxes, social security and something else
D) deductions are the type of fee
and B is the amount of money that he received
Alejandro should look at Net pay on his paystubs the answer is Net pay option (b) is correct.
What is the income tax rate?It is defined as the tax rate applied on the solely earned money by a single entity.
It is given that:
Alejandro wants to determine how much money he made in the last month after taxes, social security, and Medicare were taken out of his paycheck.
The options are:
A) Federal tax amount
The Federal tax amount is one type of tax.
C) Gross pay
The gross pay includes taxes, social security, and other charges
D) Deductions
The deductions are the type of fee or negative amounts.
Alejandro should look at Net pay on his paystubs.
Thus, Alejandro should look at Net pay on his paystubs the answer is Net pay option (b) is correct.
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With one alarm clock, we have a 0.875 probability of being awakened. What is the probability of being awakened if we are using two alarm clocks?(
The probability will be the same for both clocks.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
With one alarm clock, we have a 0.875 probability of being awakened.
The probability for the two clocks will be the same because both the clocks will ring at the same time.
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help me please !
4,5 and 6
9514 1404 393
Answer:
4a. ∠V≅∠Y
4b. TU ≅ WX
5. No; no applicable postulate
6. see below
Step-by-step explanation:
4.a. When you use the ASA postulate, you are claiming you have shown two angles and the side between them to be congruent. Here, you're given side TV and angle T are congruent to their counterparts, sides WY and angle W. The angle at the other end of segment TV is angle V. Its counterpart is the other end of segment WY from angle W. In order to use ASA, we must show ...
∠V≅∠Y
__
b. When you use the SAS postulate, you are claiming you have shown two sides and the angle between them are congruent. The angle T is between sides TV and TU. The angle congruent to that, ∠W, is between sides WY and WX. Then the missing congruence that must be shown is ...
TU ≅ WX
__
5.The marked congruences are for two sides and a non-included angle. There is no SSA postulate for proving congruence. (In fact, there are two different possible triangles that have the given dimensions. This can be seen in the fact that the given angle is opposite the shortest of the given sides.)
"No, we cannot prove they are congruent because none of the five postulates or theorems can be used."
__
6.The first statement/reason is always the list of "given" statements.
1. ∠A≅∠D, AC≅DC . . . . given
2. . . . . vertical angles are congruent
3. . . . . ASA postulate
4. . . . . CPCTC
Help with 5b please . thank you.
Answer:
See explanation
Step-by-step explanation:
We are given f(x)=ln(1+x)-x+(1/2)x^2.
We are first ask to differentiate this.
We will need chain rule for first term and power rule for all three terms.
f'(x)=(1+x)'/(1+x)-(1)+(1/2)×2x
f'(x)=(0+1)/(1+x)-(1)+x
f'(x)=1/(1+x)-(1)+x
We are then ask to prove if x is positive then f is positive.
I'm thinking they want us to use the derivative part in our answer.
Let's look at the critical numbers.
f' is undefined at x=-1 and it also makes f undefined.
Let's see if we can find when expression is 0.
1/(1+x)-(1)+x=0
Find common denominator:
1/(1+x)-(1+x)/(1+x)+x(1+x)/(1+x)=0
(1-1-x+x+x^2)/(1+x)=0
A fraction can only be zero when it's numerator is.
Simplify numerator equal 0:
x^2=0
This happens at x=0.
This means the expression,f, is increasing or decreasing after x=0. Let's found out what's happening there. f'(1)=1/(1+1)-(1)+1=1/2 which means after x=0, f is increasing since f'>0 after x=0.
So we should see increasing values of f when we up the value for x after 0.
Plugging in 0 gives: f(0)=ln(1+0)-0+(1/2)0^2=0.
So any value f, after this x=0, should be higher than 0 since f(0)=0 and f' told us f in increasing after x equals 0.
(A) The weight of cans of vegetables is normally distributed with a mean of 1380 grams and a standard deviation of 80 grams. What is the probability that the sample mean of weight for 15 randomly selected cans is more than 1410
Answer:
7.35%
Step-by-step explanation:
μ = 1380
σ = 80
n = 15
P(x>1410)
= (1410-1380)/((80)/(sqrt(15)))
= 1.4524
P(z>1.4524) = 0.4265 (from the graph)
P(z>1.4524) = 0.5 - 0.4265 = 0.0735
Find f(2) given f(x) = -3x^2 + 2x+11
Answer:
Answer:f(2)=-3(2)^2+2*2+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11 =3
hence, f(2)=3
Find length of AC? Help please
Answer:
D
Step-by-step explanation:
cos(theta) = B/H
cos(51)= AC/58
AC=36.5
Answer:
36.5 = AC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj side/ hypotenuse
cos A = AC / AB
cos 51 = AC /58
58 cos 51 = AC
36.50058 = AC
Rounding to the nearest tenth
36.5 = AC
HELP PLEASE ASAPPPP!!
Answer:
12
Step-by-step explanation:
(10/y + 13) -3
Let y=5
(10/5 + 13) -3
PEMDAS says parentheses first
(2 +13) -3
15 -3
12
Answer anyone ? Tyia :)
Find the center and radius of the circle. Write the standard form of the equation.
(1,6) (10,6)
Answer:
Centre, ((1+10)/2,(6+6)/2)
or, (11/2,12/6)
or, (5.5,6)
Radius,
[√{(10-1)²+(6-6)²}]/2
= (√81)/2
= 9/2 = 4.5
(x-11/2)²+(y-6)²=20.25
The segments shown below could form a triangle.
A
C
7
9
12
B
А
a
A. True
B. False
Answer:
TRUE
Step-by-step explanation:
I SEEN SOME ONE ELSE WIT 5 STARS SAY SO(:
The given segment can form triangle. Therefore, the given statement is true.
What is triangle?A polygon has three edges as well as three vertices is called a triangle. It's one of the fundamental geometric shapes. In Euclidean geometry, each and every three points that are not collinear produce a distinct triangle and a distinct plane. In other words, every triangle was contained in a plane, and there is only single plane that encompasses that triangle.
All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Unless when otherwise specified, this article discusses triangles within Euclidean geometry, namely the Euclidean plane. The given segment can form triangle.
Therefore, the given statement is true.
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Angelica’s bouquet of dozen roses contains 5 white roses. The rest of the roses. What fraction of the bouquet is pink? There are 12 roses in a dozen
Answer:
7/12
Step-by-step explanation:
total: 12 roses
white roses: 5
pink roses: 7
fraction of pink roses = 7/12
Solve for x in the diagram
Answer:
x = 20°
Step-by-step explanation:
x + 2x + (x+10) =90° {being a right angle triangle}
3x + x + 10 = 90°
or, 4x = 90° - 10°
or, 4x = 80°
or, x = 80°/4
so, x = 20°
An article in the Journal of Composite Materials describes the effect of delamination on thenatural frequency of beams made from composite laminates. Five such delaminated beams were subjected to loads, and the resulting frequencies were as follows (in Hz):
230.66, 233.05, 232.58, 229.48, 232.58
(a) Find a 90% two-sided CI on mean natural frequency. Round your answers to 2 decimal places.
(b) Do the results of your calculations support the claim that mean natural frequency is 235 Hz?
(A). _____________<= U<= _______________
(B). YES OR NO ?
Answer:
(230.21 ; 233.13)
Step-by-step explanation:
Given the data :
230.66, 233.05, 232.58, 229.48, 232.58
To calculate the 90% CI
WE obtain the mean and standard deviation of the sample data :
Mean of sample, ΣX /n = 1158.35/5 = 231.67
The standard deviation of the sample, s = 1.531 (Using calculator).
(The 90% Tcritical value, 2 sided, df = 4) = 2.132
The confidence interval, CI :
Mean ± Tcritical * s/√n
C.I = 231.67 ± (2.132 * (1.531/√5)
C. I = 231.67 ± 1.4597
(231.67 - 1.4597) ; (231.67 + 1.4597)
(230.21 ; 233.13)
Round 254 212 610 to the nearest million
Answer:
254,000,00
I hope this helps
I’m new to this app and I need help with those two questions please help!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
y=-4x²-8x+1
а<0 so we will be looking for maximum
х=-b/2a=8/-8=-1
у=4+8+1=13
Maximum point (-1;13)
Use order of operations to solve. PEMDAS
7 + 8(32-2)
Answer:
247
Step-by-step explanation:
7 + 8(32-2)
Parentheses first
7 + 8(30)
Then multiply
7+240
Then add
247
Answer:
247
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
7 + 8(32 - 2)
Step 2: Evaluate
(Parenthesis) Subtract: 7 + 8(30)Multiply: 7 + 240Add: 247