P(both poodle) = (3/10)(3/10) = 9/100
Answer: The probability of choosing the same puppy is 9/100
Singular Savings Bank received an initial deposit of $3000. It kept a percentage of this money in reserve based on the reserve rate and loaned out the rest. The amount it loaned out was eventually all deposited back into the bank. If this cycle continued indefinitely and eventually the $3000 turned into $50,000, what was the reserve rate? And what are the steps to solve?
Tthe reserve rate was approximately 0.9434, or 94.34%.
How to solve for the reserve rateThis is a geometric series with first term 3000r and common ratio (1-r), so we can use the formula for the sum of a geometric series:
sum = a(1 - r^n) / (1 - r)
where a = 3000r is the first term.
As the cycle continues indefinitely, the amount loaned out eventually becomes the final amount of $50,000. Therefore:
3000r/(1-r) = 50,000
Solving for r, we get:
r = (50,000)/(3000 + 50,000) = 0.9434
Therefore, the reserve rate was approximately 0.9434, or 94.34%.
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Enter your answer in the box.
Answer:
- 63
Step-by-step explanation:
When x = 0, x - 1 = -1
f(x - 1) = f(-1) = 21 from the table
-3f(x-1) = -3 (21)
= -63
A recursive rule for a geometric sequence is a1=
4
9
;an=3an−1.
What is the explicit rule for this sequence?
ANSWER:
4
9
(3n−1) just took the test
The explicit rule for the geometric sequence with a recursive rule of a1=4/9 and an=3an-1 is: an = (4/9) * (3)^(n-1)
What is the explicit rule for this sequence?To find the explicit rule for a geometric sequence, we use the formula:
an = a1 * r^(n-1)
where a1 is the first term, r is the common ratio, and n is the term number.
Given the recursive rule for this geometric sequence as a1=4/9 and an=3an-1, we can find the common ratio:
an = 3an-1
an/an-1 = 3/1
r = 3
Now we can use the formula to find the explicit rule:
an = a1 * r^(n-1)
an = (4/9) * (3)^(n-1)
Therefore, the explicit rule is: an = (4/9) * (3)^(n-1)
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Can sum help me with this
Answer:
36°
Step-by-step explanation:
x+27+27+90=180
x=36°
8.6×10 ^7 bacteria are measured to be in a dirt sample that weighs 1 1 gram. Use scientific notation to express the number of bacteria that would be in a sample weighing 19 grams.
scientific notation to express the number of bacteria that would be in a sample weighing 19 grams would be 1.634 ×[tex]10^9[/tex].
what is scientific notationWith scientific notation, one can express extremely big or extremely small values.
When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.
The given number of bacteria in the dirt sample is 8.6 × [tex]10^7[/tex], and the weight of the sample is 1 gram. To find the number of bacteria in a sample weighing 19 grams, we can use the following proportion:
number of bacteria / weight of sample = constant
We can solve for the constant by using the given information:
8.6 ×[tex]10^7[/tex] / 1 gram = constant
constant = 8.6 × [tex]10^7[/tex]
Now we can use this constant to find the number of bacteria in a 19-gram sample:
number of bacteria / 19 grams = 8.6 × [tex]10^7[/tex]
number of bacteria = 8.6 ×[tex]10^7[/tex] × 19 grams
To express the answer in scientific notation, we can multiply the two numbers and adjust the exponent accordingly:
number of bacteria = 1.634 × [tex]10^9[/tex]
Therefore, the number of bacteria in a sample weighing 19 grams would be 1.634 ×[tex]10^9[/tex]
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If the smaller of two numbers is one-half of the larger number and the sum of the two numbers is 63, find the numbers.
Answer:
21 and 42
Step-by-step explanation:
Lets say x and y are our numbers. x is the smaller number, y is the larger.
We can construct the equations:
x = 0.5y
x + y = 63
Substitute 0.5y for x in the second equation.
0.5y + y = 63
1.5y = 63
y = 42.
Plug y into the first equation.
x = 0.5 * 42
x = 21.
Your numbers are 21 and 42.
The percent of US citizens that use the internet on a daily basis is shown on the graph, where the year 2000 corresponds to x=0. Use the concepts of y-intercept and slope of the line to find the equation that best models the given data. Answer in slope intercept form.
An equation of the linear function represented by the graph in slope-intercept form is y = 3x + 60.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (75 - 60)/(5 - 0)
Slope (m) = 15/5
Slope (m) = 3
At data point (0, 60) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 60 = 3(x - 0)
y = 3x + 60
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
For positive acute angles A and B, it is known that tanA= 4/3 and sinB= 53/28 . Find the value of sin(A−B) in simplest form.
The value of sin(A-B) is 2334/6625
What is trigonometric identity?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.
Example of trigonometric identity include;
cos 2 θ + sin 2 θ = 1 cos 2 θ + sin 2 θ = 1.
1 + cot 2 θ = csc 2 θ 1 + cot 2 θ = csc 2 θ
1 + tan 2 θ = sec 2 θ 1 + tan 2 θ = sec 2 θ
Sin(A-B) = = sin A cos B- cos Asin B
if tan A = 4/3, then 4 is the opp and 3 is the adj,
hyp² = 4²+3²
= 16+9
hyp² = 25
hyp = √25
= 5
cos A = 3/5 and sinA = 4/5
if sinB = 28/53, then opp is 28 is the opp and 53 is the hyp
adj = √ 53²-28²
adj = √ 2809 - 784
adj = √2025
adj = 45
cos B = 45/58
sin(A-B) = 4/5 × 45/58 - 3/5× 28/53
= 18/29 - 84/265
= (4770-2436)/6625
= 2334/6625
therefore the value of sin(A-B) = 2334/6625
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Which of these are statistical questions? Select ALL that Apply Question 1: How many minutes does it usually take each teacher to get from home to work? Question 2: During the past year did you work for more than 50 weeks? Question 3: During the past year how many hours did each teacher usually work each week? Question 4: How many extra hours did each doctor work each week?
The statistical questions are:
Question 1: How many minutes does it usually take each teacher to get from home to work?Question 3: During the past year how many hours did each teacher usually work each week?Question 4: How many extra hours did each doctor work each week?What is a statistical question?
A statistical question is a question that can be answered by collecting and analyzing data. It is a question that expects a variability in the response, meaning different individuals may give different answers. Statistical questions usually ask about a population, a group of individuals or objects that share a common characteristic or feature, and seek to understand a pattern or trend within that population.
In general, a statistical question is open-ended, does not have a single correct answer, and requires data analysis to arrive at a reasonable conclusion.
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Students in a math class recorded the number of text messages they received the previous day. How many students received at least 10 messages? Number of text messages line plot from 0 to 25 by fives. 5 has 2 marks, 10 has 3 marks, 15 has 2 marks, 20 has 4 marks, and 25 has 5 marks. 14 students 11 students 3 students 2 students
Answer:
Step-by-step explanation:
same goes 4 him i though he loved me but 10 =5x2
The amount of money in a saving account increases bu D. 2% every month
Write a function for the amount of money in the accounts, after t months with an initial deposit of tr $ 100
By what' factor does the amount in the account increases ever meant every year?
The exponential function giving the balance of the account after t months is:
[tex]y = 100(1.02)^t[/tex]
The yearly growth factor is given as follows:
26.82%.
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for this problem are given as follows:
a = 100 -> initial deposit.b = 1.02 -> increase of 2% every month -> 1 + 0.02 = 1.02.Hence the function is:
[tex]y = 100(1.02)^t[/tex]
The yearly growth factor can be obtained as follows:
[tex](1.02)^{12} = 1.2682[/tex]
Increase of 26.82% each year, which is composed by 12 months.
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100 POINTS!
Question:
Answer: the answer is f
Step-by-step explanation:
Answer:
answer is f
Step-by-step explanation:
What type of distribution is pictured in this histogram?
Responses
Bimodal
Normal
Skewed
The type of distribution pictured in this histogram is skewed.
What is a skewed distribution?
A skewed distribution is a statistical distribution that is not symmetrical around its mean or median.
In a skewed distribution, the tail of the distribution is pulled in one direction or the other, resulting in a longer tail on one side than the other.
There are two types of skewed distributions: positively skewed and negatively skewed.
The distribution in the image is positively skewed as its is pulled towards the left.
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Average Weekly Earnings in Canada
Occupation 2010 2008
Forestry, logging and support $971 $812
Manufacturing $977 $943
Transportation and warehousing $900 $873
Construction $1071 $1023
Retail trade $501 $486
1. Calculate the mean (average) weekly earnings of workers in the occupations
listed for 2010.
Answer: To calculate the mean weekly earnings for each occupation in 2010, we need to add up the weekly earnings for each occupation and divide by the number of occupations.
For Forestry, logging and support:
Mean weekly earnings = (971) / (1) = $971
For Manufacturing:
Mean weekly earnings = (977) / (1) = $977
For Transportation and warehousing:
Mean weekly earnings = (900) / (1) = $900
For Construction:
Mean weekly earnings = (1071) / (1) = $1071
For Retail trade:
Mean weekly earnings = (501) / (1) = $501
Therefore, the mean weekly earnings for workers in the listed occupations in 2010 are:
Forestry, logging and support: $971
Manufacturing: $977
Transportation and warehousing: $900
Construction: $1071
Retail trade: $501
Step-by-step explanation:
if you divide 781.253 by 100, what will be the place value of 2
Answer:
When you divide 781.253 by 100, you get 7.81253 as the result.
The digit 2 is in the hundredths place in the dividend 781.253. Since we are dividing by 100, which has two decimal places, we move the decimal point two places to the left in the dividend to get the quotient.
Therefore, the digit 2 is in the ten-thousandths place in the quotient 7.81253.
Find the LCD of the given rational equation
The LCD of the rational equation above is 4(x + 7)(x - 7).
What is the explanation for the above response?To find the LCD (Least Common Denominator) of the given rational equation, we need to factor the denominators of each fraction and then take the product of the highest powers of each factor.
The first denominator, x^2 - 49, can be factored using the difference of squares formula:
x^2 - 49 = (x + 7)(x - 7)
The second denominator, 4x + 28, can be factored by factoring out the greatest common factor:
4x + 28 = 4(x + 7)
Therefore, the LCD is the product of the highest powers of each factor, which is:
LCD = 4(x + 7)(x - 7)
So we need to multiply each term in the equation by an appropriate form of 1 so that the denominators of all the fractions become the LCD, 4(x + 7)(x - 7).
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Please help me with this question
Answer:
A
Step-by-step explanation:
based on summation, this is an integral from 1 to 6
answer choice A makes sense since plugging in K value gives appropriate riemann sum
Study the system of equations below.
x + y =-4
x - y = 10 What is the solution to the system of
equations?
A (-4, 10)
B (10, 4)
C(3,-7)
D(7,-3)
Answer:
Option C
Step-by-step explanation:
To solve this system of equations, we can use the method of elimination. Adding the two equations together eliminates the y variable, and we get:
2x = 6
Simplifying, we get:
x = 3
Substituting x = 3 into either of the original equations, we get:
3 + y = -4
Solving for y, we get:
y = -7
Therefore, the solution to the system of equations is (3, -7), which is option C.
Rotate 180 degrees about the origin
The rotation transformation of the quadrilateral IJKL, to obtain the quadrilateral I'J'K'L', are; I'(-2, 3), J'(0, -2), K'(-2, -3), L'(-3, 1)
What is a rotation transformation?A rotation transformation is one in which the coordinates of a geometric figure are rotated about a point.
The coordinates of the vertex points on the figure are;
J(0, 2), K(2, 3), L(3, -1), and I(2, -3)
The coordinates of the point (x, y) following a rotation of 180° about the origin are (-x, -y)
Therefore, the coordinates of the image of the figure J(0, 2), K(2, 3), L(3, -1), and I(2, -3), following a rotation about the origin are;
J(0, 2) ⇒ J'(0, -2)
K(2, 3) ⇒ K'(-2, -3)
L(3, -1) ⇒ L'(-3, 1)
I(2, -3) ⇒ I'(-2, 3)
Therefore, we get;
The coordinates of the image are; I'(-2, 3), J'(0, -2), K'(-2, -3), L'(-3, 1)
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Parametric Functions
Answer:
Step-by-step explanation:
it think it 23 becasue u add
1 divide it by 2
Which of these shapes have rectangular cross sections options. Orectangular prism O triangular prism cylinder D cone ✔cy Osquare pyramid triangular pyramid
The correct options are rectangular prism, square pyramid.
What are the shapes have rectangular cross sections?When a shape has a rectangular cross-section, it means that if the shape is cut perpendicular to its base, the resulting cut will be a rectangle. So, the only shapes that will have a rectangular cross section are those whose base is a rectangle or a shape that can be inscribed within a rectangle.
The shapes that have rectangular cross sections when they are cut perpendicular to the base are:
Rectangular prism
Square pyramid
Therefore, the correct options are rectangular prism, square pyramid.
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Complete question:
Mario is training for a mile-long swim race. In the first week of training, he swims 3/5 three times, 9/10 two times and 23/25 two times . How many total miles did he swim in the first week of training?
To find out how many total miles Mario swam in the first week of training, we need to add up the distances he swam each time:
3/5 + 3/5 + 3/5 + 9/10 + 9/10 + 23/25 + 23/25
To add these fractions, we need to find a common denominator. The smallest common multiple of 5, 10, and 25 is 50.
3/5 = 30/50
9/10 = 45/50
23/25 = 46/50
Now we can add the fractions:
30/50 + 30/50 + 30/50 + 45/50 + 45/50 + 46/50 + 46/50
= (30 + 30 + 30 + 45 + 45 + 46 + 46)/50
= 272/50
= 5.44
Therefore, Mario swam a total of 5.44 miles in the first week of training.
The sum of two numbers is 49. One number is 23 more than the other. Find the numbers.
The larger number is:
The smaller number is:
Answer:
Larger number: 36
Smaller number: 13
Find the graphed inequality below
The inequality represent the given graph is y≤1.4x+2.5.
From the graph, the line passes through (0, 2.5) and (3.5, 0).
Here, slope (m) = (3.5-0)/(2.5-0)
= 3.5/2.5
= 1.4
Substitute m=1.4 and (x, y)=(0, 2.5) in y=mx+c, we get
2.5=1.4(0)+c
c=2.5
So, the equation of a line is y=1.4x+2.5
So, the inequality is y≤1.4x+2.5
Therefore, the inequality represent the given graph is y≤1.4x+2.5.
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James is performing statistical analysis to determine whether the effects of the treatment in his experiment might actually have reflected a chance occurrence; Kendra is performing an analysis to combine the results of a number of experiments to yield an overall conclusion. James is performing a _____, Kendra, a _____.
Hello !
James is performing statistical analysis to determine whether the effects of the treatment in his experiment might actually have reflected a chance occurrence; Kendra is performing an analysis to combine the results of a number of experiments to yield an overall conclusion. James is performing a significance test, Kendra, a meta-analysis.
Please help me with this please
The subtraction of the two matrix is [31 6 12 -14 57 ]
[-19 -27 -18 18 27 ]
[ 47 14 -1 -40 9 ]
[10 12 -19 -15 -58]
[-14 -23 10 4 19]
What is the matrix subtraction?The subtraction of the two matrix is calculated as follows;
The result to 4 multiplied by D is calculated as;
4[D] = [28 -24 12 -32 -36]
[8 -36 -24 24 36]
[32 8 20 -40 -12]
[40 -12 -16 12 - 28]
[4 -8 16 -20 -8 ]
The result to 3 multiplied by B is calculated as;
3[B] = [-3 -30 -24 -18 21]
[27 -9 -6 6 9]
[-15 -6 21 0 -21]
[30 -24 3 27 30]
[18 15 6 -24 -27]
The subtraction of the two matrix is calculated as follows;
4[D] - 3[B] = [31 6 12 -14 57]
[-19 -27 -18 18 27 ]
[ 47 14 -1 -40 9 ]
[10 12 -19 -15 -58]
[-14 -23 10 4 19]
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Please I need some help as soon as possible
Answer:
[tex] {m}^{2} + 7m - 30 = [/tex]
[tex](m - 3)(m + 10)[/tex]
40
Selena is training for a race. Last week, she ran 4 miles each day on 3 different
days. Use the symbol X to make an array that represents the total number of miles
Selena ran last week.
Show your work.
The array that represents the total number of miles is X = 12
Given that;
Selena ran 4 miles per day
And she ran for 3 different days
Let the total miles she ran = X
therefore
X = miles of 1st day + miles of 2nd day + miles of 3rd day
⇒ X = 4 + 4 + 4
⇒ X = 12 miles
Thus the symbolic form of miles Selena ran is,
X = 12.
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PLEASE HURRY
Write the vector v in terms of i and j whose magnitude and direction angle are given ||v|| = 2/3, theta = 116 deg
The vector v can be expressed as v = -0.161 i + 0.618 j, where i and j are the unit vectors
To express a vector v in terms of i and j, we need to find its x and y components. The magnitude ||v|| of a vector is given by:
||v|| = √(v₁² + v₂²)
where v₁ and v₂ are the x and y components of v, respectively.
The direction angle θ of a vector with respect to the positive x-axis is given by:
θ = atan(v₂/v₁)
where atan denotes the arctangent function.
In this problem, we are given that the magnitude ||v|| of the vector v is 2/3, and its direction angle θ with respect to the positive x-axis is 116 degrees. Therefore, we can write:
||v|| = √(v₁² + v₂²) = 2/3
θ = atan(v₂/v₁) = 116°
Solving for the x and y components, we get:
v₁ = ||v|| cos(θ) = (2/3) cos(116°) ≈ -0.161
v₂ = ||v|| sin(θ) = (2/3) sin(116°) ≈ 0.618
Therefore, the vector v can be expressed as:
v = -0.161 i + 0.618 j
where i and j are the unit vectors in the x and y directions, respectively.
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Consider the line y = -8x + 7.
Find the equation of the line that is perpendicular to this line and passes through the point (-5, 3).
Find the equation of the line that is parallel to this line and passes through the point (-5, 3).
The equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.
What is a line?A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature.
Since lines can exist embedded in two, three, or higher dimensions environments, they are one-dimensional objects.
The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
So, the lines with the same slope but a different y-intercept are said to be parallel.
Therefore, we must use the same slope to plug in the point (7, 6) and solve for the y-intercept.
We thus have:
y = 8x + b
6 = 8(7) + b
6 = 56 + b
b + 56 = 6
b + 56 - 56 = 6 - 56
b = -50
The equation is: y = 8x - 50
Therefore, the equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.
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Correct question:
Consider the line y = 8x - 4. Find the equation of the line that is parallel to this line and passes through the point (7, 6).