No, we cannot perform element by element addition, subtraction, multiplication and division when the matrices are different sizes, because to do this the size of matrices should be same.
The Element-by-element operations, also called element-wise operations, can only be performed when two matrices have the same dimensions, meaning they have the same number of rows and columns.
In this case, the operations are applied to the corresponding elements of each matrix, resulting in a new matrix with the same dimensions as the original matrices.
When the two matrices have different sizes, element-by-element operations are not defined. In some cases, it may be possible to perform other types of operations, such as matrix multiplication or matrix addition (if the matrices have compatible dimensions).
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The given question is incomplete, the complete question is
Can your perform element by element addition, subtraction, multiplication and division when the matrices are different sizes?
Imagine we have a simple linear model, with one X predicting one Y, where R-squared is equal to .81. What was the correlation between X and Y?A) .81 (or maybe -.81)B) There is not enough information to tell.C) .66 (or maybe -.66)D) .90 (or maybe -.90)
The correlation between X and Y can be calculated using the formula r = SQRT(R-squared).The correlation coefficient is a measure of the strength of the linear relationship between two variables and can range from -1 to 1
In this case, the R-squared value is 0.81, so the correlation between X and Y is r = SQRT(0.81) = 0.9 (or -0.9 depending on the direction of the relationship).The correlation between X and Y can be calculated using the formula r = SQRT(R-squared). The correlation coefficient is a measure of the strength of the linear relationship between two variables and can range from -1 to 1, where -1 is a perfectly negative linear relationship, 0 is no linear relationship, and 1 is a perfectly positive linear relationship. In this case, the correlation between X and Y was 0.9, indicating a strong linear relationship between the two variables.
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please find the midpoint of the following line and arc using straightedge-compass-construction method
The midpoint of a line or arc can be found using straight edge-compass-construction method by drawing two perpendicular bisectors. The intersection of these bisectors is the midpoint.
To find the midpoint of a line segment, first draw a straight line passing through both endpoints of the segment using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the line segment. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the line segment. The intersection of these bisectors is the midpoint of the line segment.
To find the midpoint of an arc, first draw a chord that intersects the arc at two points using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the chord. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the chord. The intersection of these bisectors is the center of the circle that the arc belongs to. Draw a line from the center of the circle to the midpoint of the chord. This line will intersect the arc at its midpoint.
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--The question is incomplete, answering to the question below--
"find the midpoint of a line and arc using straight edge-compass-construction method"
What is the average rate of change between
the points (17, 5) and (19, --1)?
The average rate of change between the points (17, 5) and (19, -1) is -3.
What is the average rate of change?If we have a given function y = f(x) with two known points (a, f(a)) and (b, f(b)), then the average rate of change in that interval [a, b] is:
R = ( f(b) - f(a))/(b - a)
Here we have the two points (17, 5) and (19, -1)
So we have:
a = 17 and f(a) = 5
b = 19 and f(b) = -1
Replacing that in the formula for the average rate of change we will get:
R = (-1 - 5)/(19 - 17)
R = -6/2
R = -3
The average rate of change is -3
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Please select the correct answer. Which expression is equivalent to the given expression?
Answer:
[tex]5a^6b[/tex]
Step-by-step explanation:
To simplify this expression, we can divide 20a^8b^2 by 4a^2b.
First, we can simplify the numbers by dividing 20 by 4 to get 5.
Then, we can simplify the variables by subtracting the exponents of the same bases (a and b).
[tex]\frac{20}{4}[/tex] · [tex]\frac{a^8}{a^2}[/tex] · [tex]\frac{b^2}{b}[/tex]
[tex]5[/tex] · [tex]a^6[/tex] · [tex]b[/tex]
This gives us the simplified expression 5a^6b. So the answer would be the third one down, or [tex]5a^6b[/tex].
Michelle bought a new car for $25,000. She paid a 10% down payment and financed the remaining balance for 72 months with an APR of 6.5%. Assuming she makes monthly payments, determine the total interest Michelle pays over of the loan.
Answer:
Michelle paid a 10% down payment, which is:
10% of $25,000 = $2,500
So the amount she financed is:
$25,000 - $2,500 = $22,500
To calculate the monthly payment, we can use the formula for a loan payment:
P = (r * A) / (1 - (1 + r)^(-n))
where P is the monthly payment, r is the monthly interest rate (APR divided by 12), A is the amount financed, and n is the number of payments (72 in this case).
First, we need to calculate the monthly interest rate:
r = 6.5% / 12 = 0.00541667
Plugging in the values, we get:
P = (0.00541667 * $22,500) / (1 - (1 + 0.00541667)^(-72))
P = $363.12
So Michelle will pay $363.12 per month for 72 months.
To calculate the total interest paid over the life of the loan, we can multiply the monthly payment by the number of payments and subtract the amount financed:
Total interest = (P * n) - A
Total interest = ($363.12 * 72) - $22,500
Total interest = $7,111.04
Therefore, Michelle will pay a total of $7,111.04 in interest over the life of the loan
Two cars, one going due east at the rate of 90 km/hr and the other going to south at the rate of 60 km/hr are traveling toward the intersection of two roads. At what rate the two cars approaching each other at the instant when the first car is 0.2 km and the second car is 0.15 km from the intersection ?
The two cars are approaching each other at a rate of 36 km/hr at the given instant.
We can solve this problem by using the Pythagorean theorem and differentiating with respect to time. Let's call the distance of the first car from the intersection "x" and the distance of the second car from the intersection "y". We want to find the rate at which the two cars are approaching each other, which we'll call "r".
At any moment, the distance between the two cars is the hypotenuse of a right triangle with legs x and y, so we can use the Pythagorean theorem
r^2 = x^2 + y^2
To find the rates of change of x and y, we differentiate both sides of this equation with respect to time
2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)
Simplifying and plugging in the given values
dr/dt = (x(dx/dt) + y(dy/dt)) / r
dr/dt = (0.2 x 90 + 0.15 x (-60)) / sqrt((0.2)^2 + (0.15)^2)
dr/dt = (18 - 9) / sqrt(0.04 + 0.0225)
dr/dt = 9 / sqrt(0.0625)
dr/dt ≈ 36 km/hr
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what is the domain of the function {(-1,-1),(0,1),(2,-1)}
a) (-1,1)
b) (-1,0,2)
c) (-1,0,1,2)
d) {(-1,-1),(0,1),(2,-1)}
Answer:
[tex]b) \quad(-1,0,2)[/tex]
Step-by-step explanation:
The domain is the set of all input values for a function. It can be represented as a list of values where it is countable or as a set notation
Here there are only 3 ordered pairs. The first entry in each ordered pair represents the input of the function, the second entry the corresponding output value
Looking at the first entry in all three ordered pairs we get the domain as
[tex](-1, 0 , 2)[/tex]
Given a doubling time of 934 minutes, how long will it take a culture in the exponential growth phase to grow from 15 cells per mL, to 86,059 cells per mL? Explain.
It will take approximately 7.12 days for a culture with a doubling time of 934 minutes to grow from 15 cells/mL to 86,059 cells/mL. This is calculated using the exponential growth equation and logarithms.
If the doubling time is 934 minutes, it means that the number of cells in the culture doubles every 934 minutes. Let t be the time in minutes required to grow from 15 cells/mL to 86,059 cells/mL. We can set up the following equation:
86,059/15 = 2^(t/934)
Taking the logarithm of both sides, we get:
log(86,059/15) = (t/934) log(2)
Solving for t, we get:
t = (log(86,059/15)/log(2)) * 934 ≈ 10,288 minutes ≈ 7.12 days
Therefore, it will take approximately 7.12 days for the culture to grow from 15 cells/mL to 86,059 cells/mL under the given conditions.
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5) What is the probability of picking a vowel, replacing it
and then picking a consonant from the word "SLEEP"?
The probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is approximately 0.096 or 9.6%.
What is probability?Probability is usually expressed as a number between 0 and 1, with 0 meaning that the event is impossible and 1 meaning that the event is certain.
According to question:There are two vowels (E) and three consonants (S, L, P) in the word "SLEEP".
The probability of picking a vowel on the first draw is 2/5, because there are two vowels out of five letters total.
Since we replace the vowel we picked, the probability of picking another vowel on the second draw is also 2/5.
The probability of picking a consonant on the third draw is 3/5, because there are three consonants left out of five letters total.
Therefore, the probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is:
(2/5) x (2/5) x (3/5) = 12/125 or approximately 0.096 or 9.6%.
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convert 457000СМ² to M².
Answer: 45.7
Explanation:
Divide the area value by 10000
do the following statements describe red pulp or white pulp? drag and drop the labels into the corresponding boxes.
After labeling with the corresponding boxes , The statements which describes Red pulp and white pulp are as follow:
1. Red pulp 2. Red Pulp 3. White Pulp 4. Red pulp
5. White Pulp 6. White Pulp 7. Red Pulp.
Red Pulp:
The red pulp of the spleen is made up of connective tissue (also known as Bill Roth's cord) and numerous sinusoids of the spleen which appear red due to excess blood. Its main function is to filter antigens, microorganisms and defective or worn out red blood cells from the blood.
The spleen consists of red and white pulp, separated by the marginal zone; 76-79% of a normal spleen is made up of red pulp. Unlike white pulp, which contains mostly lymphocytes (such as T cells), red pulp is made up of several types of blood cells, including platelets, granulocytes, red blood cells, and plasma.
White Pulp:
White pulp is the histological name for the areas of the spleen (so called because they appear whiter in rough sections than the surrounding red pulp), which make up approximately 25% of the spleen. The white pulp is entirely composed of lymphoid tissue.
Specifically, the white pulp contains several regions with distinct functions:
The periarteriolar lymphatic sheaths (PALS) are usually associated with the arteriolar supply to the spleen; they contain T lymphocytes.
Lymphoid follicles with dividing B lymphocytes located between the PALS and the marginal zone bordering the red pulp. This region produces IgM and IgG2.
These molecules play a role in the opsonization of extracellular organisms, in particular encapsulated bacteria.
The marginal zone exists between the white pulp and the red pulp. It is located away from the central arterioles, close to the red pulp. It contains antigen-presenting cells (APCs), such as dendritic cells and macrophages. Some white pulp macrophages are of a special type called metallolipid macrophages.
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Work out the value of the missing angle
x
.
The diagram is not drawn to scale.
Answer:
No diagram provided here
Two angles of a quadrilateral measure 301° and 10°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?
Answer:
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360°. We know that the measures of two angles are 301° and 10°.
Let x be the measure of the smaller of the other two angles, and let y be the measure of the larger of the two angles.
We know that x:y = 2:5, so we can write y = (5/2)x.
Using the fact that the sum of all four angles is 360°, we can write an equation:
301° + 10° + x + y = 360°
Substituting y = (5/2)x, we get:
301° + 10° + x + (5/2)x = 360°
Combining like terms, we get:
311° + (7/2)x = 360°
Subtracting 311° from both sides, we get:
(7/2)x = 49°
Multiplying both sides by 2/7, we get:
x = 14°
So the smaller of the two angles is 14°.
Using y = (5/2)x, we get:
y = (5/2) × 14° = 35°
Therefore, the measures of the two angles are 14° and 35°.
6th grade math, is this correct?
Answer:
No, it is y = - 3x + 7
( negative 3x not positive )
Hope this helps!
Step-by-step explanation:
1. Subtract both sides by 3x
3x + y - ( 3x ) = 7 - ( 3x )
2. Combine like terms
( 3x - 3x ) + y = 7 - ( 3x )
0 + y = 7 - ( 3x )
y = 7 - ( 3x )
y = -3x + 7
TRUE/FALSE.In a preliminary investigation report, the findings section includes a summary of a project request and a specific recommendation.
In a preliminary investigation report, the findings section includes a summary of a project request and a specific recommendation. - False
The outcomes of the inquiry and any pertinent data or information that was gathered are normally presented in the findings section of a preliminary investigation report. This might contain a synopsis of the problem or topic under investigation, an outline of the research approach taken, and a statement of any findings or recommendations made in light of the data gathered.
On the other hand, the recommendations part often follows the results section and provides detailed ideas or plans for handling the problem or issue at hand. The conclusions of the inquiry, as well as any pertinent research or industry standards, may all be taken into consideration when making the recommendations.
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WILL GIVE BRAINLIEST PLEASE ANSWER FAST!
In each triangle, M, N, and P are the midpoints of the sides. Name a segment parallel to the one given.
Answer: UV
Step-by-step explanation:
Both descriptive statistics (mean, median, mode, and range) and probability (the likelihood that something will happen) can be useful in our academic, professional, and personal lives. • Determine which of the two (descriptive statistics or probability) you find to be the most useful in your life and explain why using two (2) specific examples.
Descriptive statistics are the most useful in life. Descriptive statistics provide information about a data set and can help to summarize and interpret data. Specifically, I find the mean and median to be the most useful.
What does Descriptive statistics mean?Descriptive statistics involves the use of measures such as the mean, median, mode, and range, as well as graphical representations of the data, such as histograms, box plots, and scatter plots.
The mean is the average of a set of data and is useful for summarizing and interpreting data. For example, when I am studying for a test, I often use the mean of my practice test scores to understand my overall performance.
The median is the middle value of a set of data and is useful for understanding the spread of the data. For example, when I am tracking my monthly expenses, I often use the median to understand how much I am spending each month. By taking the median of my monthly expenses, I can get an idea of which expenses are taking up the most of my budget.
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What is the difference between the longest and
shortest pieces of scrap wood
The variation in length between the longest and shortest scraps of wood is 0.875.
Explain about the mixed fractions?The sum of both an entire number and a legal fraction is contained in a mixed fraction or number.
We translate an improper fraction into such a mixed fraction and use the basic arithmetical operations. An incorrect fraction is one in which the numerator exceeds the denominator.
Longest value ; 5
Shortest value; 4 1/8 (mixed fraction)
Convert mixed fraction in to proper fraction.
4 1/8 = ( 4*8 + 1 )/8
4 1/8 = 33/8
difference = longest pieces of scrap wood - shortest pieces of scrap wood
difference = 5 - 33/8
difference = 0.875
Thus, the difference in length between the longest and shortest scraps of wood is 0.875.
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the given point is on the graph of y=f(x). Find a point on the graph of y=g(x).
g(x)=f(x−1)+3; (6,15)
The point (6, 15) on the graph of y = f(x) corresponds to the point (6, 18) on the graph of y = g(x).
What is graph?A graph is a visual representation of data, usually depicted as a set of points or lines plotted on a coordinate plane or a series of bars or other shapes displayed in a bar chart or pie chart. Graphs are used to show relationships between variables, trends over time, or comparisons between different data sets.
According to question:The problem asks us to find a point on the graph of y = g(x) given that (6, 15) is a point on the graph of y = f(x), and g(x) = f(x - 1) + 3.
To find a point on the graph of y = g(x), we need to substitute the given value of x = 6 into the formula for g(x):
g(6) = f(6 - 1) + 3
Simplifying the expression on the right-hand side, we have:
g(6) = f(5) + 3
Since (6, 15) is a point on the graph of y = f(x), we know that f(6) = 15.
g(6) = f(5) + 3
g(6) = 15 + 3
g(6) = 18
Therefore, the point (6, 15) on the graph of y = f(x) corresponds to the point (6, 18) on the graph of y = g(x).
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Let A and B be events with P(A) = 0.3, P(B) = 0.6, and P(A and B) = 0.03. Are A and B mutually exclusive? Explain why or why not.
Answer:
A and B are not mutually exclusive
Step-by-step explanation:
A and B are not mutually exclusive because P(A and B) > 0. If A and B were mutually exclusive, then they would have no outcomes in common and the probability of their intersection would be zero. However, in this case, they do share some outcomes, since P(A and B) is greater than zero.
The diagram shows 3 identical circles inside a rectangle.
each circle touches the other 2 circles and the side of the rectangle, as shown in the diagram.
Radius of each circle is 28mm.
work out the area of the rectangle.
Give your answer correct to three significant figures
The area of the rectangle is 6272 mm² (to three significant figures).
What is area?Area is a physical quantity that refers to the amount of space within a two-dimensional shape or surface. It is typically measured in square units such as square meters, square centimeters, or square feet.
What is radius?Radius is a measure of the distance from the center of a circle to any point on its circumference. It is often denoted by the letter "r" and is usually expressed in units of length, such as meters or millimeters.
In the given question,
We can start by drawing lines connecting the centers of the circles and the rectangle.
Let's call the width of the rectangle "w" and the height of the rectangle "h".
Since each circle touches the side of the rectangle, we know that the diameter of each circle is equal to the width of the rectangle, so:
diameter of each circle = radius of each circle = 28 mm
Therefore, we can write:
2 x 28 mm + w + w = h
Simplifying, we get:
w + 56 mm = h/22w + 56 mm = h
Now we can find the area of the rectangle by multiplying its width and height:
Area of rectangle = w x h
Substituting for "h", we get:
Area of rectangle = w x (2w + 56 mm)
Expanding and simplifying, we get:
Area of rectangle = 2w² + 56w mm²
To find the value of "w", we can use the fact that the radius of each circle is 28 mm and the circles touch each other, so:
w + 2 x 28 mm + w = 3 x diameter of each circle
Simplifying, we get:
2w + 56 mm = 3 x 2 x 28 mm
2w + 56 mm = 168 mm
2w = 112 mmw = 56 mm
Now we can substitute this value of "w" into the formula for the area of the rectangle:
Area of rectangle = 2w² + 56w mm²
Area of rectangle = 2 x (56 mm)² + 56 mm x 56 mm
Area of rectangle = 6272 mm²
Therefore, the area of the rectangle is 6272 mm² (to three significant figures).
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Consider relation Ron set A, where R = {(a,b) a divides b), and A is the set of positive Integers. Which of the following properties does the relation have? Check all that apply. Antisymmetric Transitive Reflexive Symmetric
Consider relation Ron set A, where R = {(a, b)| a divides b), and A is the set of positive Integers. The relation have antisymmetric. So the option A is correct.
A relation is antisymmetric if and only if it is not symmetric and for all elements a and b in the set, if (a,b) is in the relation, then (b,a) is not in the relation. In other words, if a is related to b and b is related to a, then a must be equal to b.
A relation is antisymmetric if for all elements (a,b) in the relation, if a divides b and b divides a then a=b. In this case, if a divides b and b divides a, then a and b must both be the same number since a positive integer cannot divide itself. Therefore, Ron set A is antisymmetric. So the option A is correct.
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The complete question is:
Consider relation Ron set A, where R = {(a, b)| a divides b), and A is the set of positive Integers. Which of the following properties does the relation have? Check all that apply.
A. Antisymmetric
B. Transitive
C. Reflexive
D. Symmetric
Consider points A(1,3) , B(4,-2) , and C(5,2). Let D be the midpoint of AB. How can you prove that C lies on the perpendicular bisector of AB? Complete each statement.
The coordinates of D are: B. (2.5, 0.5).
The product of the slopes of CD and AB is: C. -1.
This shows that AB is perpendicular to CD. Therefore, C lies on the perpendicular bisector of AB.
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Substituting the given parameters into the midpoint of a line segment formula, the midpoint of line AB is given by;
Midpoint AB = [(4 + 1)/2, (-2 + 3)/2]
Midpoint AB = [5/2, 1/2]
Midpoint AB = (2.5, 0.5).
5, 2
Next, we would determine the slopes of line segment CD and AB:
Slope (m) of CD = (0.5 - 2)/(2.5 - 5)
Slope (m) of CD = -1.5/-2.5 = 3/5
Slope (m) of AB = (-2 - 3)/(4 - 1)
Slope (m) of AB = -5/3 = 0.6
Product of the slopes = 3/5 × -5/3 = -3/3 = -1.
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Just need help on 7,8, and 9
According to the given information, the missing values in the ratio table are:
7. 6:1/3, 12:2, 6:1, 24:4
8. 1/4:3, 2:6, 1:12, 5/4:15
9. 1/3:8/3, 2/3:2/3, 1:1, 4/3:1.04
What is ratio?
A ratio is a mathematical comparison of two or more quantities. Ratios express the proportional relationship between the quantities being compared. Ratios are often written using a colon (:) or as a fraction, such as "1:2" or "1/2".
7.
We can simplify the ratio of feet to seconds by converting 1/3 to its equivalent fraction with a denominator of 3:
Ratio of feet to seconds = 6 : 1/3 = 6 : (1/3) = 6 : (1/3) x (3/3) = 6 : 1
So, the ratio of feet to seconds is 6 : 1.
Using this ratio and the other ratios given, we can create equations to solve for the missing values:
6 : 1 = 12 : x
Cross-multiplying, we get: 6x = 12
Solving for x, we get: x = 2
y : 1 = 6 : 1
Cross-multiplying, we get: y = 6
6 : 1 = 24 : z
Cross-multiplying, we get: 6z = 24
Solving for z, we get: z = 4
Therefore, the missing values are:
x = 2, y = 6, z = 4
8.
We can set up equations based on the given ratios and solve for the missing values.
1/4 : x = blue ribbon : red ribbon
y : 6 = blue ribbon : red ribbon
1 : z = blue ribbon : red ribbon
5/4 : 15 = blue ribbon : red ribbon
To find x:
1/4 : x = 1 : z (since blue ribbon : red ribbon = 1 : z)
Cross-multiplying, we get:
1z = 4x
z = 4x
To find y:
y : 6 = 1/4 : x (since blue ribbon : red ribbon = 1/4 : x)
Cross-multiplying, we get:
y * x = 6 * 1/4
y * x = 3/2
y = (3/2) / x
To find z:
1 : z = 5/4 : 15 (since blue ribbon : red ribbon = 1 : z)
Cross-multiplying, we get:
1 * 15 = 5/4 * z
z = (1 * 15 * 4) / 5
z = 12
Therefore, the values of x, y, and z are x = 3, y = 2, and z = 12.
9.
To find the values of x, y, and z, we need to first simplify the ratios given.
The ratio between orange fabrics and yellow fabric is:
1/3 : 8/3
We can simplify this ratio by multiplying both sides by 3 to get:
1 : 8
The ratio between 2/3 and x is:
2/3 : x
The ratio between 1 and y is:
1 : y
The ratio between 4/3 and z is:
4/3 : z
We can simplify this ratio by multiplying both sides by 3/4 to get:
1 : (4/3)z or 1 : 1.33z (rounded to two decimal places)
Now we have the following ratios:
Orange : Yellow = 1 : 8
2/3 : x = 2/3 : x
1 : y = 1 : y
1 : (4/3)z = 1 : 1.33z
To solve for x, y, and z, we can use cross-multiplication.
Orange : Yellow = 1 : 8
1/8 = (Orange / Yellow)
8/1 = (Yellow / Orange)
2/3 : x = 2/3 : x
This ratio is already in its simplest form, so x = 2/3.
1 : y = 1 : y
This ratio is already in its simplest form, so y = 1.
1 : (4/3)z = 1 : 1.33z
1 = (4/3)z / 1.33z
1 = 0.96z
z = 1.04
Therefore, the values of x, y, and z are:
x = 2/3, y = 1, z = 1.04
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I need help with this
In the figure below, YE bisects ZFYD. Use the figure to answer are mZEYF.
What is figure?Figure is a page in a book, magazine, website, or other printed material that contains a graphical representation of data, such as a chart, diagram, drawing, or photograph. Figures are often used to help explain complex concepts or to present data in an easily digestible way. Figures can also be used to highlight important information or to make an argument more visually appealing.
The angle YEZ is an inscribed angle, and it bisects the central angle ZFYD. Therefore, the measure of angle YEZ is equal to one-half the measure of angle ZFYD, which is mZYEF. Thus, mZEYF = mZYEF.
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Intersect Combining these two facts, we get mZCFR + mZRFY = 2mZEYF, which simplifies to m2FYD.
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We can use the fact that when two lines intersect, the opposite angles formed are equal. Therefore, we can say that mZCFR = mZRFY.
In addition, since YE bisects ZFYD, we can say that mZFYD = 2mZEYF.
Combining these two facts, we get mZCFR + mZRFY = 2mZEYF, which simplifies to m2FYD.
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A sample of 128g of an unknown substance has a half-life of 1,250
years. Approximately how long will it take for 37 grams of the substance
to remain (to the nearest year)?
The radioactive decay will take approximately 3,051 years for 37 grams of the substance to remain.
What is radioactive decay ?
Radioactive decay is the process by which an unstable atomic nucleus loses energy (in terms of mass in its rest frame) by emitting ionizing particles or radiation such as alpha particles, beta particles, gamma rays, or positrons. As a result of this decay, the nucleus may transform into a different nuclide or isotope with a different number of protons or neutrons or into a different energy state. The rate of decay of a radioactive substance is measured by its half-life, which is the amount of time it takes for half of the original amount of the substance to decay.
According to the question:
The half-life formula for radioactive decay is:
[tex]N = N0 (1/2)^{t/h}[/tex]
where N is the amount of substance remaining after time t, N0 is the initial amount of substance, h is the half-life, and t is the time elapsed.
We can use this formula to find the time it takes for 37 grams of the substance to remain. Let N0 be the initial amount of substance, which is 128 g, and N be the amount of substance remaining, which is 37 g. We know the half-life is 1,250 years. Let's plug in these values and solve for t:
[tex]37 = 128 (1/2)^{t/1250}[/tex]
Dividing both sides by 128, we get:
[tex](1/2)^{t/1250} = 37/128[/tex]
Taking the logarithm of both sides with base 1/2, we get:
t/1250 = log(37/128) / log(1/2)
Simplifying, we get:
t = 1250 log(128/37) / log(1/2)
t ≈ 3,051 years
Therefore, it will take approximately 3,051 years for 37 grams of the substance to remain.
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The weight of a goat increased by 12 pounds is 38 pounds. Write an equation to represent the situation.
The answer would be g+12=38
Answer:
x+12=38
Step-by-step explanation:
we do not know the starting weight of the goat so we can use x to represent it and then is increased by twelve so we can add that and we know the current weight is 36 pounds so x+12 with equal 36
Find the area of the region that is bounded by the given curve and lies in the specified sector.
r = e^ θ/2
π/6 = θ = 7π/6
The area of the region that is bounded by the given curve and lies in the specified sector is A = 2(e^(7π/12) - e^(π/12))
The polar curve r = e^(θ/2) represents a spiral that starts from the origin and gets farther away as it unwinds. We want to find the area of the region that lies inside this spiral and inside the sector defined by the angles θ = π/6 and θ = 7π/6.
To solve the problem, we need to find the points where the curve intersects the sector, which are given by plugging in the values of θ:
r(π/6) = e^(π/12)
r(7π/6) = e^(7π/12)
Then we can set up the integral for the area inside the sector:
A = 1/2 ∫[π/6, 7π/6] (r(θ))^2 dθ
Substituting the equation for r:
A = 1/2 ∫[π/6, 7π/6] e^θ/2 dθ
Using the power rule for integration:
A = 2(e^(7π/12) - e^(π/12))
This is the exact value of the area inside the sector and inside the spiral. If we want a decimal approximation, we can use a calculator or computer software to evaluate it.
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what is 7 in x 3 in x 6 in x 4 in x 15 in=
Answer:
7,560 inches.
Step-by-step explanation:
Given: 7 in x 3 in x 6 in x 4 in x 15 in = ?
First, multiply 7 and 3:
21 in x 6 in x 4 in x 15 in
Then multiply 21 and 6:
126 in x 4 in x 15 in
Then multiply 4 and 15:
126 in x 60 in
Finally, multiply 126 and 60:
= 7,560 inches.
Gilberto opened a savings account for his daughter and deposited $1500 on the day she was born. Each year on her birthday, he deposited another $1500. If the account pays 9% interest, compounded annually, how much is in the account at the end of the day on her 11th birthday?
Using compound interest, the amount in the account at the end of the day on her 11th birthday is $240,019.25.
To solve this problem, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^{(nt)}[/tex]
where A is the amount of money in the account at the end of the 11th year, P is the principal amount (initial deposit), r is the annual interest rate (9%), n is the number of times interest is compounded per year (once annually), and t is the number of years (11).
First, we need to calculate the total amount of money that Gilberto deposited into the account over the 11 years:
1500 + 1500 × 10 = $16,500
Next, we can plug the values into the formula and solve for A:
A = 1500[tex](1 + 0.09/1)^{(1 * 11)}[/tex] + 1500[tex](1 + 0.09/1)^{(2 * 11)}[/tex] + ... + 1500[tex](1 + 0.09/1)^{(11 * 11)}[/tex]
A = 1500 × [[tex](1.09)^{11}[/tex] + [tex](1.09)^{22}[/tex] + ... + [tex](1.09)^{121}[/tex]]
A = 1500 × [[tex](1.09^{11}[/tex] - 1)/(1.09 - 1)]
A = 1500 × [(1.315 - 1)/(0.09)]
A = $240,019.25
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