Answer:
1: A=1
2: -3
3: C
Step-by-step explanation:
1: If 3x+4 is a factor, then -4/3 is equal to x. Substitute it in for x and solve for a. This gives us A=1.
For the commenter not understanding how I got -4/3: 3x+4 being a factor means that it equals 0. It might help you understand this if you remember that after factoring, like I did for 38 in my photo, we take expressions like x-4 and set them equal to 0 to get x=4, a solution. So, subtract 4 from both sides to get 3x=-4, then divide both sides by 3 to get x alone. Thus, x=-4/3.
2: To find the sum, we first need to find the two solutions. We can factor to get (x+7)(x-4). This gives us x=-7 and x=+4. The solution of these two would be (-7)+4 is -3.
3: B is a close answer, but the signs are wrong on the bottom. Factoring the question would give us 2(x-2) / 2(x^2-x-2). Factoring that equation is 2(x-2) / 2(x+1)(x-2). Simplifying this gives us 1 / x+1.
Sorry for the bad penmanship, I wanted to make it a little clearer for you! I really hope I helped! :)
The angles in a triangle are 89, 1, and 90 degrees. Classify the triangle by its angles and sides.
A. Right isosceles
B. Right Scalene
C. Obtuse scalene
D. Acute isosceles
E. Acute scalene
F. Obtuse isosceles
Answer: B. Right Scalene
Step-by-step explanation: Right because one of the degrees is 90 and scalene because no of the sides of the triangle are the same length.
Answer:
b
Step-by-step explanation:
A sign on the gas pumps of a chain of gasoline stations encourages customers to have their oil checked with the claim that one out of four cars needs to have oil added. If this is true, what is the probability of the following events?
a. One out of the next four cars needs oil.
b. Two out of the next eight cars needs oil.
c.Three out of the next 12 cars need oil.
Answer:
a) 0.4219 = 42.19% probability that one out of the next four cars needs oil.
b) 0.3115 = 31.15% probability that two out of the next eight cars needs oil.
c) 0.2581 = 25.81% probability that three out of the next 12 cars need oil.
Step-by-step explanation:
For each car, there are only two possible outcomes. Either they need oil, or they do not need it. The probability of a car needing oil is independent of any other car, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One out of four cars needs to have oil added.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
a. One out of the next four cars needs oil.
This is P(X = 1) when n = 4. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}.(0.25)^{1}.(0.75)^{3} = 0.4219[/tex]
0.4219 = 42.19% probability that one out of the next four cars needs oil.
b. Two out of the next eight cars needs oil.
This is P(X = 2) when n = 8. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.25)^{2}.(0.75)^{6} = 0.3115[/tex]
0.3115 = 31.15% probability that two out of the next eight cars needs oil.
c.Three out of the next 12 cars need oil.
This is P(X = 3) when n = 12. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{12,3}.(0.25)^{3}.(0.75)^{9} = 0.2581[/tex]
0.2581 = 25.81% probability that three out of the next 12 cars need oil.
At the beginning of an experiment, a scientist has 120 grams of radioactive goo. After 135 minutes, her sample has decayed to 3.75 grams. Find an exponential formula for G ( t ) G(t) , the amount of goo remaining at time t t .
Answer:
[tex]G(t) = 120e^{-0.0257t}[/tex]
Step-by-step explanation:
Amount of substance:
The amount of the substance after t minutes is given by:
[tex]G(t) = G(0)e^{-kt}[/tex]
In which G(0) is the initial amount and k is the decay rate.
At the beginning of an experiment, a scientist has 120 grams of radioactive goo.
This means that [tex]G(0) = 120[/tex], so:
[tex]G(t) = G(0)e^{-kt}[/tex]
[tex]G(t) = 120e^{-kt}[/tex]
After 135 minutes, her sample has decayed to 3.75 grams.
This means that [tex]G(135) = 3.75[/tex].
We use this to find k. So
[tex]G(t) = 120e^{-kt}[/tex]
[tex]3.75 = 120e^{-135k}[/tex]
[tex]e^{-135k} = \frac{3.75}{120}[/tex]
[tex]\ln{e^{-135k}} = \ln{\frac{3.75}{120}}[/tex]
[tex]-135k = \ln{\frac{3.75}{120}}[/tex]
[tex]k = -\frac{\ln{\frac{3.75}{120}}}{135}[/tex]
[tex]k = 0.0257[/tex]
So
[tex]G(t) = 120e^{-0.0257t}[/tex]
What is the slope formula?
Answer:
D is your answer
Step-by-step explanation:
Answer:
Here the slope formula m = ( y 2 − y 1 )/( x 2 -x 1 ) = Δy/Δx
Step-by-step explanation:
Which graph represents the function f (x) = StartFraction 5 minus 5 x squared Over x squared EndFraction? On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.
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Answer:
2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3
Step-by-step explanation:
Technically, the curve is not a hyperbola. A hyperbola is of the form 1/x; this one is of the form 1/x².
The function can be simplified to ...
f(x) = 5/x² -5
which is a "hyperbola" with a vertical asymptote at x=0 and a vertical translation of -5 units to bring parts of it into the 3rd and 4th quadrants.
Avi uses 11 toothpicks to form a row of 5 attached triangles, as shown. Suppose he continues this pattern, using 89 toothpicks in all. What is the total number of triangles formed? (sorry the picture wasn't uplodaing)
Answer:
44
Step-by-step explanation:
Given that Avi used 11 toothpicks to form a row of 5 attached triangles.
Total number of toothpicks used = 89
Let the total number of triangles formed be represented by x, so that:
11 toothpicks = 5 triangles
It would be observed that only the first triangle starting the pattern has 3 toothpicks. So that;
the average number of toothpicks for 1 triangle = [tex]\frac{11}{5}[/tex]
= 2.2
The number of toothpicks per triangle = 2.0
Thus,
x = [tex]\frac{89}{2.0}[/tex]
= 44.5
x = 44
The total number of triangles formed is 44.
Didi invested a total of $16125 in two accounts paying 8.5% and 4% simple interest. If her total return at the end of 2 years was 1740 , how much did she invest in each account?
Answer:
5000 ;
11125
Step-by-step explanation:
Given :
Total principal = 16125
Rates = 8.5% and 4%
Period, t = 2 years
Total interest = 1740
Let :
Principal amount invested at 8.5% = x
Principal amount invested at 4% = 16125 - x
Interest formula :
Interest = principal * rate * time
Hence, mathematically ;
(x * 8.5% * 2) + [(16125 - x) * 4% * 2] = 1740
(0.17x + 1290 - 0.08x ) = 1740
0.09x + 1290 = 1740
0.09x = 1740 - 1290
0.09x = 450
x = 450 / 0.09
x = 5000
Amount invested at 4% :
16125 - 5000 = 11125
Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 28. A pollster draws a sample of 92
people to interview.
Answer:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes 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.
Mean of 41, standard deviation of 28:
This means that [tex]\mu = 41, \sigma = 28[/tex]
Sample of 92:
This means that [tex]n = 92, s = \frac{28}{\sqrt{92}} = 2.92[/tex]
Distribution of the sample means:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
What is the domain of the relation described by the set of ordered pairs (-2,8), (-1,1) (0,0) (3,5), (4,-2)?
Step-by-step explanation:
(-2,-1,0,3,4) are the domain
(x,y)=(domain,range)
simply x components are the domain whereas y components are the range
The longest leg is Select one:
a. 5√3
b. 10√3
c. 5
d. 20
Answer:
D:20
sqrt(3) is less than 2 thus 10*sqrt(3) is less than 20
Step-by-step explanation:
ms.+sanchez+bought+3+pounds+of+turkey+to+make+sandwiches+for+her+family+.+She+uses+.25+of+a+pound+for+each+sandwich+.+How+many+sandwiches+can+she+make+?
Answer:
she can make 12 sandwiches
Step-by-step explanation:
3/.25 is the solution
find the exact value of tan -75
How do you know if a radical can be simplified? Explain.
Answer:
An expression is considered simplified only if there is no radical sign in the denominator. If we do have a radical sign, we have to rationalize the denominator . This is achieved by multiplying both the numerator and denominator by the radical in the denominator.
The diameter of a circle is inches what is the area?
Answer:
Pie( r ^2)
Step-by-step explanation:
Here value of r is in inches
Answer quick please.
Answer
The Answer is A C D
Step-by-step explanation:
You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 2x - 3y = 12
-x + 2y = 13
O A. Multiply the left side of equation 2 by 2. Then subtract the result from equation 1.
O B. Multiply equation 1 by 2 and equation 2 by 3. Then add the new equations.
C. Multiply equation 2 by-2. Then add the result to equation 1.
Answer:
A.
Step-by-step explanation:
The Elimination Method is the method for solving a pair of linear equations which reduces one equation to one that has only a single variable.
If the coefficients of one variable are opposites, you add the equations to eliminate a variable, and then solve.
If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.
When multiplying the equation by a coefficient, we multiply both sides of the equation (multiplying both sides of the equation by some nonzero number does not change the solution).
So, option B is not allowed (it is not allowed to multiply only one part of the equation)
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=tcost, y=tsint, t=π
Step-by-step explanation:
the answer is in the image above
The stopping distance on wet pavement at 20mph is about 60feet. The stopping distance at 30mph is 120feet. What would you estimate the stopping distance is at 40mph? Construct a formula
Answer:
[tex]y = 6x - 60[/tex] --- formula
The stopping distance at 40mph is 180ft
Step-by-step explanation:
Given
[tex](x,y) = (20,60)[/tex]
[tex](x,y) = (30,120)[/tex]
Solving (a): Construct a formula
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{120 - 60}{30-20}[/tex]
[tex]m = \frac{60}{10}[/tex]
[tex]m=6[/tex]
So, the equation is:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 6(x - 20) + 60[/tex]
Open bracket
[tex]y = 6x - 120 + 60[/tex]
[tex]y = 6x - 60[/tex]
Hence, the formula to use is: [tex]y = 6x - 60[/tex]
Solving (b): y, when x = 40
[tex]y = 6x - 60[/tex]
[tex]y = 6 * 40 - 60[/tex]
[tex]y = 180[/tex]
What is the area of a triangle with a base of 9 units and a height of 7 units? O A. 15.75 sq. units O B. 126 sq. units O c. 63 sq. units O D. 31.5 sq. units SUBMIT வன் PREVIOUS
Answer:
D. 31.5 sq. units
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh
A = 1/2 ( 9)(7)
A = 63/2
A = 31.5 units^2
Step-by-step explanation:
For this, we'll use a formula for the area of a triangle.
Area (A) = ( Base (B) * Height (H) ) / 2
[tex]A = (B * H )/2[/tex]
Plug in given values.[tex]A = (9*7)/2[/tex]
Multiply within parentheses.[tex]A = (63)/2[/tex]
Divide by 2.[tex]A = 31.5[/tex]
Answer:
D. 31.5 sq. units
Use differentials to approximate the change in cost corresponding to an increase in sales (or production) of one unit. Then compare this with the actual change in cost.
Function x-Value
C=0.025x^2 + 3x + 4 x=10
dC= ___________
ΔC= __________
Answer:
dC=3.5
DC is between 3.475 and 3.525
Step-by-step explanation:
So let dx=1 since the change there is a change in 1 unit.
Find dC/dx by differentiating the expression named C.
dC/dx=0.05x+3
So dC=(0.05x+3) dx
Plug in x=10 and dx=1:
dC=(0.05×10+3)(1)
dC=(0.5+3)
dC=3.5
Let D be the change in cost-the triangle thing.
Since dx=1 we only want the change in unit to be within 1 in difference.
So this means we want it to be from x=9 to x=1] ot from x=10 to x=11.
Let's do from x=9 to x=10 first:
DC=C(10)-C(9)
DC=[0.025×10^2+3×10+4]-[0.025×9^2+3×9+4]
DC=[2.5+30+4]-[0.025×81+27+4]
DC=[36.5]-[2.025+31]
DC=[36.5]-[33.025]
DC=3.475
Now let's do from x=10 to x=11
DC=[0.025×11^2+3×11+4]-[0.025×10^2+3×10+4]
DC=[0.025×121+33+4]-[36.5]
DC=[3.025+37]-[36.5]
DC=[40.025]-[36.5]
DC=3.525
So DC, the change in cost where the change in unit is 1, is between 3.475 and 3.525.
The product of a negative integer and a positive integer is?
PLEASE ANSWER A, B, C
Answer:
a. negative
b. negative
c. positive
Step-by-step explanation:
a. When a negative and positive integer are being multiplied the product will always be negative. For example, -3*2=-6.
b. Before answering this question it is helpful to realize that it is the exact same as part a. This is because the commutative property states that order does not matter in multiplication. So the answer is also negative, 2*-3=-6.
c. If two negative integers are multiplied then the product will be positive. Whenever two integers of the same sign are multiplied the product is positive. The opposite is true when they have different signs; the product will always be negative. An example of two negative integers would be -3*-2=6.
Which key feature depends on the leading coefficient and the degree of the
function?
A.Axis of symmetry
B.End behavior
C.Intercepts
D.Rate of change
Answer:
B.End behavior
Step-by-step explanation:
Limit as x goes to infinity:
To find the limit as x goes to infinity of a function, we consider only the leading coefficient and the term with the highest degree of the polynomial, and this limits determines the end behavior of a function, and thus, the correct answer is given by option b.
Hii guys plz help me
Answer:
B is the answer
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
you would have to multiply 2000 and the 25 and then divide
Which of the following relations represents a function?
Question 4 options:
{(–1, –1), (0, 0), (2, 2), (5, 5)}
{(0, 3), (0, –3), (–3, 0), (3, 0)}
{(–2, 4), (–1, 0), (–2, 0), (2, 6)}
None of these
Answer:
The first option
Step-by-step explanation:
A function is where one input only has one output, in the other options we can see inputs having different outputs, 0,3 and 0-3 in the second and in the third -2,4 and -2,0.
Chris is reading a book that has nine-hundred seventy-eight pages in it. Every night
Chris reads a number of pages that can be rounded to the nearest hundred. The rst
night Chris reads one-hundred two pages. The second night Chris reads ninety-eight
pages. The third night Chris read one-hundred fty-four pages. The fourth night Chris
reads fty-six pages. The fth night Chris reads two-hundred thirty-four pages. The
sixth night Chris reads forty-eight pages. The seventh night Chris reads one-hundred
seventy pages. On what nights does Chris read a number of pages that can be rounded
to the nearest hundred? Show all your mathematical thinking.
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Answer:
Every night
Step-by-step explanation:
The problem statement tells you ...
"Every night Chris reads a number of pages that can be rounded to the nearest hundred."
Then it asks you ...
"On what nights does Chris read a number of pages that can be rounded to the nearest hundred?"
If we take the problem statement at face value, the answer must be ...
"Every night."
El largo de un terreno es el doble de la medida de su ancho, como se muestra en la imagen. Si el perímetro es de 96 hectómetros, ¿cuáles son las dimensiones del terreno?
Answer:
Step-by-step explanation:
The following configured particulars are states, in accordance by the interrogate:
Perimeter = 96 hectometers.
Assuming the figure is a square, we can assume that,
S = A side length where,
4s = 96, where all side lengths are equivalent.
If so, then s = 24
Thus, that means that w, denoted as width, must be less than or equal to 24.
In addition, likewise, l, denoted as length, must be less than or equal to 24.
Furthermore, the length is acknowledged or stated to be twice that of the width:
Length = 2w
The listed above may be equated to the following:
2w + 2L = 96
2(24) + 2L = 96
2L + 48 = 96
2L = 48
L = 24
Thus, the width of the figure is equivalent to 24. (Length divided by two).
Thus, the length of the figure is equivalent to 24 (twice the width).
*I hope this helps.
If a student (represented by initials) was chosen at random, find P(HHU C).
Answer:
[tex]P(HH\ u\ C) = \frac{13}{16}[/tex]
Step-by-step explanation:
Given
The Venn diagram
Required
[tex]P(HH\ u\ C)[/tex]
This is calculated as:
[tex]P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}[/tex]
Where:
[tex]n(U) = 16[/tex] --- count of students
[tex]n(HH\ u\ C) =13[/tex]
So, we have:
[tex]P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}[/tex]
[tex]P(HH\ u\ C) = \frac{13}{16}[/tex]
Round 61,565 to the
nearest hundred.
Answer:
61600
Step-by-step explanation:
the 3rd digit is the hundreds. because the digit in the 10s is greater 5, we round it up
Answer:
61,600 is your answer please
What are the coordinates of A’ after a 90° counterclockwise rotation about the origin.
Answer:
A' (- 1, - 5 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ), then
A (- 5, 1 ) → A' (- 1, - 5 )
An account manager for a local software firm believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected: Salesperson Number of Contacts Sales (in millions) 1 14 24 2 12 14 3 20 28 What is the dependent variable
Answer:
Amount of sales
Step-by-step explanation:
The dependent variable also called the measured or predicted variable is simply the variable obtained due to inputs in of the independent variable. It is the variable which is being measured in an experiment. Here, the test is that the number of sales depends on the number of contact. Here, the number of contacts will has an influence or determines the amount of sales, hence, the number of contacts is the independent variable while the amount of sales is the dependent variable.
