Answer:
a. 250
b. 70
c. 3
Step-by-step explanation:
w = weeks
70 + 3w = 250
3w = 250 - 70
w = (250 - 70) / 3
Step-by-step explanation:
got u bro
airpods=250
her saving=70
30 per week=30x6=180
180+70=250
so she have 6 weeks till she buys the airpods pro
<1 and <2 form a linear pair. The measure of <2 is six more than twice the measure of <1. Find m<2.
Answer:
∠ 2 = 122°
Step-by-step explanation:
given ∠ 2 = 2 ∠ 1 + 6
a linear pair of angles sum to 180° , then
∠ 1 + ∠ 2 = 180° , that is
∠ 1 + 2∠ 1 + 6 = 180° ( subtract 6 from both sides )
3∠ 1 = 174° ( divide both sides by 3 )
∠ 1 = 58° , then
∠ 2 = 180° - 58° = 122°
Estimate the value of 50.75 x 0.18
Answer:
10
Step-by-step explanation:
50.75 = 50
0.18 = 0.2
50x 0.2 = 50/5
50/5 = 10
Let [tex]\beta[/tex] be a real number. Consider the matrix [tex] \rm A = \begin{bmatrix} \beta &0&1 \\ 2 &1& - 2 \\ 3&1& - 2\end{bmatrix}[/tex] . If [tex] \rm A^7 - ( \beta - 1) {A}^{6} - \beta {A}^5[/tex] is a singular matrix, then the value of [tex]9\beta [/tex] is
Compute the characteristic polynomial of [tex]A[/tex].
[tex]p(\lambda) = \det(A - \lambda I) \\\\ ~~~~~~~~ = \begin{vmatrix} \beta - \lambda & 0 & 1 \\ 2 & 1 - \lambda & -2 \\ 3 & 1 & -2-\lambda \end{vmatrix} \\\\ ~~~~~~~~ = (\beta-\lambda)\begin{vmatrix}1-\lambda&-2\\1&-2-\lambda\end{vmatrix} + \begin{vmatrix}2&1-\lambda \\ 3 & 1 \end{vmatrix} \\\\ ~~~~~~~~ = -\lambda^3 + (\beta-1) \lambda^2 + (\beta + 3) \lambda - 1[/tex]
By the Cayley-Hamilton theorem,
[tex]p(A) = -A^3 + (\beta - 1) A^2 + (\beta + 3) A - I = 0[/tex]
Note that
[tex]A^7 - (\beta - 1) A^6 - \beta A^5 \\\\ ~~~~~~~~ = -(-A^3 + (\beta - 1) A^2 + \beta A) A^4 \\\\ ~~~~~~~~ = -(\underbrace{-A^3 + (\beta - 1) A^2 + (\beta + 3) A - I}_{p(A)=0} - 3A + I) A^4 \\\\ ~~~~~~~~ = (3A - I) A^4[/tex]
Recall that [tex]\det(AB) = \det(A) \det(B)[/tex]. Note that [tex]A[/tex] is not singular, and hence [tex]A^n[/tex] is not singular for any natural [tex]n[/tex].
[tex]\det(A) = \begin{vmatrix} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 & -2 \end{vmatrix} \\\\ ~~~~~~~~ = \beta \begin{vmatrix}1&-2\\1&-2\end{vmatrix} + \begin{vmatrix}2&1\\3&1\end{vmatrix} \\\\ ~~~~~~~~ = -1 \neq 0[/tex]
Then [tex]3A-I[/tex] must be singular. So
[tex]\det(3A-I) = \begin{vmatrix} 3\beta - 1 & 0 & 3 \\ 6 & 2 & -6 \\ 9 & 3 & -7 \end{vmatrix} \\\\ ~~~~~~~~ = (3\beta-1) \begin{vmatrix}2&-6\\3&-7\end{vmatrix} + 3 \begin{vmatrix}6&2\\9&3\end{vmatrix} \\\\ ~~~~~~~~ = 4 (3\beta-1)[/tex]
[tex]4(3\beta-1) = 0 \implies \beta = \dfrac13 \implies 9\beta = \boxed{3}[/tex]
A random experiment has sample space Ω = {a, b, c} and probabilities pa = 1/7, pb = 2/7 and pc = 4/7. Describe an urn experiment that can be used to simulate this random experiment.
To find the probability of an outcome the steps are as follows:
Find the total number of outcomes of the random experiment. Find the number of favorable outcomes. Divide step 2 by step 3 to determine the probability.The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive .Urn -some objects of real interest are represented as colored balls .
Given data
space Ω = {a, b, c}
p(a )= 1/7,
p(b) = 2/7 and
p(c) = 4/7.
p(E) = p(a) + p(b) +p(c).
where p(E) = random experiment i. e. union
p(E) = 1/7 + 2/7 + 4/7
p(E) = 7/7
p(E) =1
An outcome is a result of a random experiment. The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set. Here are some examples of random experiments and their sample spaces:
Random experiment: toss a coin; sample space: S={heads,tails} or as we usually write it, {H,T}.
Random experiment: roll a die; sample space: S={1,2,3,4,5,6}.
Random experiment: observe the number of iPhones sold by an Apple store in Boston in 2015; sample space: S={0,1,2,3,⋯}.
Random experiment: observe the number of goals in a soccer match; sample space: S={0,1,2,3,⋯}.
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Find the expected value E(X) of the following data. Round your answer to one decimal place. x −5 −4 −3 −2 −1 P(X=x) 0.1 0.3 0.1 0.2 0.3
Based on the values in the table of values, the expected value of the data is -3.3
How to determine the expected value of the data?The dataset is given as
x −5 −4 −3 −2 −1
P(X=x) 0.1 0.3 0.1 0.2 0.3
The expected value of the dataset is calculated as
E(x) = ∑x * P(x)
Substitute the known values in the above equation
So, we have
E(x) = (-5 * 0.1) + (-4 * 0.3) + (-3 * 0.3) + (-2 * 0.2) +(-1 * 0.3)
Evaluate the products in the above equation
So, we have
E(x) = -0.5 - 1.2 - 0.9 - 0.4 - 0.3
Evaluate the difference in the above equation
So, we have
E(x) = -3.3
Hence, the expected value of the data is -3.3
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The cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up, write an equation to represent the new function
The equation of the function is h(x) = ∛[(1/4)x - 5] + 3 if the cube root parent function is horizontally stretched by a factor of 4.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up.
The parent function is:
f(x) = ∛x
Horizontally stretched by a factor of 4:
g(x) = ∛[(1/4)x]
Translated 5 units right:
G(x) = ∛[(1/4)x - 5]
Translated 3 units up:
h(x) = ∛[(1/4)x - 5] + 3
Thus, the equation of the function is h(x) = ∛[(1/4)x - 5] + 3 if the cube root parent function is horizontally stretched by a factor of 4.
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The sum of a three-digit number and one-digit number is 731. The product of the numbers is 2,908. What are the numbers?
Solving a system of equations we can see that the two numbers are 727 and 4
How to find the two numbers?Let's define x as the 3-digit number and y as the one-digit number.
Then we know that the sum is equal to 731:
x + y = 731
And the product is equal to 2,908, then:
x*y = 2,908
So we have a system of equations:
x + y = 731
x*y = 2,908
Isolating x on the first equation gives:
x = 731 - y
Now we can replace that in the other equation to get:
(731 - y)*y = 2,908
Now we can solve this quadratic equation to find the value of y.
731*y - y^2 = 2,908
-y^2 + 731*y - 2,908 = 0
The solutions are:
y = (-731 ± √( 731^2 - 4*(-2,908)*(-1))/(-2)
y = (-731 ± 723)/-2
Now, y is an one digit number, then:
y = (-731 + 723)/-2 = 4
And x will be the 3 digit number:
x = 731 - x = 731 - 4 = 727
So the two numbers are 727 and 4
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6.2
2.
Graph the image of the figure using the transformation given.
LAST 3 PICS ARE THE OPTIONS
The image of the translation is shape WYX is shown by option 2.
What is defined as the translation about the x axis?The process of substituting the axes inside a Cartesian coordinate system with such a new set of axes parallel to the first, which is used to write equations for curves that are not centered about the origin.
Horizontal translation of a graph is equivalent to changing the base diagram left or right in the x-axis direction. A graph is horizontally translated k units by relocating each point just on graph k units horizontally.The principle for reflecting over X axis is to invalidate the value of each point's y-coordinate while keeping the x-value constant.As, from the rule of translation along x axis;
The coordinates of the x axis are not changed and y are changed.
Thus, for the given figure XWY the image after translation about the x axis is shown by the option 2 graph.
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1. In the last few months, local news channels have featured stories about price increases in
Cincinnati. The monthly cost of cable TV for some families increased from $75 to
(a) $ 79.15. The average cost of a dozen eggs increased from (b) $ 1.70 to
$2.37.
(a) Calculate the absolute change in the monthly cost of
cable TV. Round to the nearest cent.
(3)
(b) Calculate the relative change in the monthly cost of
cable TV. Round to one decimal place.
(4)
(c) Calculate the absolute change in the cost of a dozen (d) Calculate the relative change in the cost of a dozen
eggs. Round to the nearest cent.
eggs. Round to one decimal place.
(3)
(4)
(e) A cable customer feels that the monthly cost of cable TV increased the most arog
Using the concept of absolute and relative change, it is found that:
a) The absolute change in the monthly cost of cable TV is of $4.15.
b) The relative change in the monthly cost of cable TV is of 5.53%.
c) The absolute change in the monthly cost of eggs is of $0.67.
d) The relative change in the monthly cost of eggs is of 39.41%.
e) Due to the higher relative change, the cost of the eggs increased the most.
What is absolute and relative change?Between two amounts, the absolute change is given by the difference between the two amounts.The relative change is given by the absolute change divided by the initial value.Hence the absolute changes are given as follows:
Cable TV: 79.15 - 75 = $4.15.Eggs: 2.37 - 1.70 = $0.67.The relative changes are given as follows:
4.15/75 = 0.0553 = 5.53%.0.67/1.70 = 0.3941 = 39.41%.Hence, for item e:
Due to the higher relative change, the cost of the eggs increased the most.
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6. The amount of carbon-14 left / years after the death of an organism is given by
2(1) = Que-0.0001221
where Qo is the amount left at the time of death. For this problem, assume Qo=
6.0 x 1010 carbon-14 atoms.
(a) How much is left after 50,000 years? What fraction of the original amount is this?
(b) How much is left after 100,000 years? What fraction of the original amount is
this?
(c) What is the half-life of carbon-14?
(d) About how many half-lives will occur in 50,000 years? Roughly what fraction will
be left? How does this compare to your answer in part (a)?
The half-life of carbon-14 is 5,730 years. Assuming you start with 100% of carbon-14, what is the expression for the percent, P(t), of carbon-14 that remains in an organism that is t years old and what is the percent of carbon-14 remaining (rounded to the nearest whole percent) in an organism estimated to be 20,000 years old
Carbon-14, C-14, 14
C or radiocarbon, is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method pioneered by Willard Libby and colleagues (1949) to date archaeological, geological and hydrogeological samples. Carbon-14 was discovered on February 27, 1940, by Martin Kamen and Sam Ruben at the University of California Radiation Laboratory in Berkeley, California. Its existence had been suggested by Franz Kurie in 1934.[2]
There are also trace amounts of the unstable radioisotope carbon-14 (14C) on Earth. Carbon-14 has a relatively short half-life of 5,730 years, meaning that the fraction of carbfon-14 in a sample is halved over the course of 5,730 years due to radioactive decay to nitrogen-14.
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Betty can mow a lawn in 90 minutes. Melissa can mow the same lawn in 60 minutes. How long does it take for both Betty and Melissa to mow the lawn if they are working together? Express your answer as a reduced fraction.
____________ minutes
Answer:
36 min
Step-by-step explanation:
rate b = 1 / 90
rate m = 1/60
now add the rates together for 1 lawn
1 lawn / (1/60 + 1/90) = 36 min
Solve the equation.
3|10x - 4| = 78
Answer:
x(down 1)=-11/5, x(down 2) =3
Step-by-step explanation:
Someone help me on this math paper
The measure of the angles 1,2 and 3 are 75, 42 and 138 respectively.
The value of ∠1 = 180- 105 [supplementary angles]
∠1 = 75°
∠1 + ∠2 + 63° = 180 [angle - sum property]
75 + ∠2 + 63 = 180
∠2 = 180 - (75 + 63)
∠2 = 42°
∠2 + ∠3 = 180 [supplementary angles]
42 + ∠3 = 180
∠3 = 180 - 42
∠3 = 138°
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Rotate trapezoid ABCD 90° clockwise around the origin. What are the coordinates of D’?
Responses
A (-4, 2)(-4, 2)
B (4, -2)(4, -2)
C (4, 0)(4, 0)
D (0, 4)(0, 4)
IF U ANSWER THE WRONG QUESTION THAT IS OFF TOPIC OR IF IT IS SPAM I WILL REPORT YOU IMMEDIATLEY AND DELETE YOUR ACCOUNT but to whoever does it correct will have brainliest and 100 points pls and thank you and WARNING TO SPAM!!!!! AND PLEASE HELP ME FAST THIS IS DUE TODAY PLS HELP FAST!!!!
Answer:
hey the answer is d(0,4)
Answer:
It is D
Step-by-step explanation:
I've done this problem before
2
For a given set of data, the standard score,
corresponding to the raw score, 1, is given by ze R
where is the mean of the set and o is the standard
deviation. If, for a set of scores, μ = 78 and o = 6.
which of the following is the raw score. x,
corresponding to z=2?
The raw score x, corresponding to z = 2 is calculated as; 90
How to find the raw score of statistics?
We are given;
Population Mean; μ = 78
Sample mean; x' = ?
Population standard deviation; σ = 6
z-score; z = 2
The formula for z-score is;
z = (x' - μ)/σ
Thus, making x' the sample mean the subject of the formula gives;
x' = zσ + μ
Plugging in the relevant values gives;
x' = (2 * 6) + 78
x' = 12 + 78
x' = 90
Thus, the raw score x, corresponding to z = 2 is 90
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See picture. Sbhdhdjdjddjxhdhdhdh
Solve by substitution.
(x - 4y = 20
2x + 5y = 1
([? ], [ ])
Answer:
x, y =8 -3
Step-by-step explanation:
System of Linear Equations entered :
[1] x - 4y = 20
[2] 2x + 5y = 1
Graphic Representation of the Equations :
-4y + x = 20 5y + 2x = 1
Solve by Substitution :
// Solve equation [1] for the variable x
[1] x = 4y + 20
// Plug this in for variable x in equation [2]
[2] 2•(4y+20) + 5y = 1
[2] 13y = -39
// Solve equation [2] for the variable y
[2] 13y = - 39
[2] y = - 3
// By now we know this much :
x = 4y+20
y = -3
// Use the y value to solve for x
x = 4(-3)+20 = 8
Solution :
{x,y} = {8,-3}
PLEASE HELP! TRIG! THANKS!
The interpretation of the beam on the wall is that when the function is undefined, the light is not shining completely on the wall and and the function rate of changes are 55.236, 68.276, 110.473 and 289.221
How to interpret the beam on the wallThe given parameter is the graph of the beam
From the graph, we can see that the beam does not shine on all parts of the wall.
It shines on some part and doesn't on other parts
This means that the function is undefined
Hence, the interpretation of the beam on the wall is that when the function is undefined, the light is not shining completely on the wall
How to compute the function rate of changesTo do this, we use the following computations:
[d(0.1) - d(0)]/[0.1 - 0] = [5.5236 - 0]/[0.1 - 0] = 55.236
[d(0.2) - d(0.1)]/[0.2 - 0.1] = [12.3512 - 5.5236]/[0.2 - 0.1] = 68.276
[d(0.3) - d(0.2)]/[0.3 - 0.2] = [23.3985 - 12.3512]/[0.3 - 0.2] = 110.473
[d(0.4) - d(0.3)]/[0.4 - 0.3] = [52.3206 - 23.3985]/[0.4 - 0.3] = 289.221
Hence, the function rate of changes are 55.236, 68.276, 110.473 and 289.221
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A chef says to cook a turkey for of an hour for every pound the turkey
weighs. How long should you cook a 19-pound turkey?
Answer:
you should cook it for 19 hours
Simplify y to the negative seventh power over x to the negative third power.
x3y7
1 over quantity x times y to the fourth power end quantity
x cubed over y to the seventh power
(xy)−10
Simplifying the expression y to the negative seventh power over x to the negative third power using law of exponents gives; x³y⁷
How to use laws of exponents?Some of the Laws of Exponents are;
When multiplying similar bases, retain the base as same and add the exponents. When raising a base with a power raised to another one, retain the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.We want to simplify y to the negative seventh power over x to the negative third power. This is expressed as;
y⁷/x⁻³
Now, x⁻³ can also be expressed as 1/x³. Thus, our original equation is now; y⁷/(1/x³) = x³y⁷
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Please answer 1 and 2
The probability of P(A and B) based on the information given will be E. None of the above.
How to calculate the probability?It should be noted that probability is used to illustrate the likelihood that something will occur.
In this case, P(A) = 0.1 and P(B) = 0.4. Therefore, the probability of P(A and B) will be
= P(A) + P(B)
= 0.1 + 0.4
= 0.5
Sine the value of 0.5 isn't given, the correct option is E.
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19/22
How many solutions?
3x+8 = 9+ 3x
Infinitely many solutions
Reason:
Subtract 3x from both sides. They cancel out and go away. The x term is fully eliminated and we're left with the equation 8 = 9, which is a false statement. Therefore, the original equation is always false regardless of what you pick for x. This is why there aren't any solutions.
Visually you can graph y = 3x+8 and y = 3x+9. You'll get parallel lines that never intersect. We need the lines to intersect if we wanted a solution point. Parallel lines have the same slope, but different y intercepts.
Because the system has no solutions, we consider the system inconsistent.
How to simplify the square root of 36
Answer:
6
Step-by-step explanation:
6 times 6 = 36, so 6 is the answer
Hope this helps. Please mark me brainliest!
The answer to the question 36/12=3
Please please please please help me
Answer:
-6 = 1
-4 = 2
0 = 4
2 = 5
8 = 8
How can I solve this without using a Calculator?
Answer:
D
Step-by-step explanation:
[tex]h(x)=2x^5+(a+s)x^4+(b+t)x^3[/tex]
For the polynomial to be divisible by x⁴, the coefficient od the x³ term must be 0, and thus the answer is D.
The distance between the points (-10, -7) and and (-8, 1) round to the nearest tenth is
The distance between two points A (-10, -7) and B(-8,1) will be equal to 8.2 units.
What do you mean by the distance between points ?
Distance between two points is the length of the line segment that connects the two locations in a plane.
It is given that the distance between points A (-10, -7) and B(-8,1) is to be calculated.
We can find out the distance by using the distance formula which is given by :
AB = [tex]\sqrt({x_{2} - x_{1})^2 + (y_{2}- y_{1})^2}[/tex]
AB = √ [( -8 -(-10)]^2 + [ 1 - (-7)]^2}
AB = √ (2² + 8²)
AB = √68
AB = 8.24 units
If we round off it to the nearest tenth then , hundredth place is less than 5 that meant 2 will be at the tenths place.
or
AB = 8.2 units.
Therefore , the distance between two points A (-10, -7) and B(-8,1) will be equal to 8.2 units.
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When hiking down a mountain from her camp, Samantha discovered that the path she was on was 18 yards below the camp. Which value is the opposite of the distance that Sam hiked from her camp?
The value equal to the direct opposite of Samantha's hike from her camp = -18 yards.
What is defined as the inverse?The inverse operation is the inverse of another operation.Subtraction means to take away, and addition means to determine the sum. Subtraction is thus the inverse of addition.As per the given question;
Samantha descends a mountain from her camp.
Samantha discovered that she was 18 yards below the camp on the path she was on.
To locate the value that is the inverse of the distance Samantha hiked from her camp.
Samantha was 18 yards away from the camp.
Samantha hiked for 18 yards underneath the camp (in downwards )
Therefore;
Samantha hiked the opposite distance of 18 yards from the camp.
Samantha hiked for -18 yards.
Thus, the value equal to the inverse of the distance Samantha hiked from her tent = -18 yards
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Answer: 18
Step-by-step explanation:
(X to the second power y to the fifth power)5
Answer:
[tex](x^2y^5)5 = 5x^2y^5[/tex]
Step-by-step explanation:
Remove the parentheses to factor.
[tex]= x^2y^5 \times 5[/tex]
Flip the expression, creating a leading term and simplifying the equation.
[tex]= 5x^2y^5[/tex]
0.09 is 1/10 as much as 0.90
The mathematical statement given as 0.09 is 1/10 as much as 0.90 is true
How to determine the true statement?The mathematical statement is given as:
0.09 is 1/10 as much as 0.90
To determine if the above statement is true, we start by representing the statement as an equation
So, we have
0.09 = 1/10 * 0.90
Express 1/10 as decimal
So, we have
0.09 = 0.10 * 0.90
Evaluate the product
So, we have
0.09 = 0.09
The above equation is true
Hence, the mathematical statement given as 0.09 is 1/10 as much as 0.90 is true
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Possible question
Determine if the following statement is true or false
2. Elisa bought 5 bracelets for a total of $25.95. If the bracelets were the same cost, about how much did each bracelet cost?
$5.19
$125.00
$4.00
$5.00
Answer: A. 5.19$
Step-by-step explanation: divide 25.95 by 5