The height of the right-angle triangle which is the base of the triangular prism will be 10 cm.
What is the volume of the prism?A prism is a polyhedron composed of an n-sided polygon basis, an extra base that is a translated duplicate from the first, and n additional faces, most of which must be parallelograms, connecting matching sides of the two grounds. All parallel cross-sections to the foundations are translations of the grounds.
The volume is given as,
V = AH
The cross part of the crystal is a right-calculated triangle the foundation of the triangle has a length of 6 cm. the crystal has a length of 20 cm the crystal has a volume of 600 cm³.
Then the base area is given as,
600 = A x 20
A = 30
1/2 x 6 x h = 30
h = 10 cm
The height of the right-angle triangle which is the base of the triangular prism will be 10 cm.
More about the volume of the prism link is given below.
https://brainly.com/question/1578538
#SPJ1
Brainliest if you do all questions showing your work.
The solution to each of the given algebraic expressions are;
1) 2n - 2 = 10
2) 12n - 1 = 17
3) 4 * 9 = 36
4) 23 - 8 = 15
5) (3 * 7) + 1 = 22
6) ¹/₆ * 42 = 7
7) 3n - 6 = 70
8) y - 2 = 9
9) x = 5 * 12
10) -48 = -4 * 12
11) -32/-8 = 4.
12) (15 - 3)n = 2
13) (5 + 8)n = 42
14) (12 + 6)/2 = 9
15) -4 = -2(5 - 3)
16) x + (x + 1) = 25
17) (x) + (x + 1) = -3
18) 11 - x = -1
How to solve algebra word problems?1) Two less than twice a number is equal to 10 is expressed as;
2n - 2 = 10
2) 17 is one more than twice a number;
2n - 1 = 17
3) Four times 9 is 36;
4 * 9 = 36
4) Eight less than 23 is fifteen;
23 - 8 = 15
5) One more than 3 times 7 is 22;
(3 * 7) + 1 = 22
6) One sixth of forty two is seven;
¹/₆ * 42 = 7
7) Six less than 3 times a number is equal to seventy;
3n - 6 = 70
8) Two dollars off the regular price of a calculator is $9;
y - 2 = 9
9) A number is equal to five times 12;
x = 5 * 12
10) Negative 4 is a product of the opposite of four and 12;
-48 = -4 * 12
11) Four is the quotient of -32 and -8;
-32/-8 = 4.
12) When 15 minus 3 is multiplied by a number, the product is 2;
(15 - 3)n = 2
13) A number times the sum of five and 8 is 42;
(5 + 8)n = 42
14) 9 is the quotient when 12 + 6 is divided by 2;
(12 + 6)/2 = 9
15) -4 = -2(5 - 3)
16) x + (x + 1) = 25
17) (x) + (x + 1) = -3
18) 11 - x = -1
Read more about algebraic expressions at; https://brainly.com/question/4344214
#SPJ1
The following tree heights were recorded on a school campus:
61, 72, 84, 88, 77, 67, 76, 79, 63, 79, 69, 70, 86, 78, 82, 82, 80, 73, 87, 90, 73, 76, 79, 71, 75, 79, 76, 83, 84, 87, 72, 81, 89, 74, 77, 78, 81, 84
A science teacher wants to choose a data display that will highlight every height. Which display will present the information in this way?
Box plot
Circle graph
Histogram
Line plot
A line plot would be the best data display to highlight every height.
A line plot, also known as a dot plot, is a type of graph that displays data as a series of dots on a number line. Each dot represents a single data point, and the dots are placed above the corresponding value on the number line.
Line plots are useful for displaying small data sets because they provide a simple visual representation of the data. They can quickly show the range of values in the data set, as well as any outliers or clusters of data points. Line plots are commonly used in elementary and middle school classrooms to teach basic data analysis and graphing skills. They are also used in scientific research and statistical analysis to visualize small data sets and identify patterns in the data.
A line plot, also known as a dot plot, displays the data as points on a number line. Each data point is represented by a dot, making it easy to see every height in the data set. Here is an example of a line plot for the given data:
A display that will highlight every height would be a line plot, which would show each individual height as a dot along a number line.
To know more about dot plot or a strip plot visit:
brainly.com/question/13298277
#SPJ1
Find the partial fraction decomposition of the rational expression with repeated factors.
The partial fraction decomposition of the expression with repeated factors is given as follows:
[tex]\frac{1}{x} - \frac{2}{x + 4} - \frac{1}{(x + 4)^2}[/tex]
How to obtain the partial fraction decomposition of the function?The function in this problem is defined as follows:
(-x² - x - 16)/(x³ + 8x² + 16x).
The decomposition is made considering the factors of the denominator, which are obtained as follows:
x³ + 8x² + 16x = 0.
x(x² + 8x + 16) = 9
x(x + 4)² = 0.
Hence the denominators are as follows:
x.x + 4.(x + 4)².Then the decomposition is of:
A/x + B/(x + 4) + C/(x + 4)²
Then the expression will be given as follows:
[tex]\frac{A(x + 4)^2 + Bx(x + 4) + Cx}{x^3 + 8x^2 + 16x} = \frac{-x^2-x+16}{x^3 + 8x^2 + 16x}[/tex]
Then the system of equations, equaling the numerators, is given as follows:
A + B = -1. -> terms with x².8A + 4B + C = -1 -> terms with x.16A = 16 -> independent term.Hence:
16A = 16
A = 1.
B = -1 - A
B = -2.
C = -1 - 8A - 4B
C = -1.
Meaning that the third option is correct.
More can be learned about partial fraction decomposition at brainly.com/question/18958301
#SPJ1
dollar general sends out a $5 off coupon to its email subscribers. what percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon?
The classification model is used to define the percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon.
Percentage:
In math, number or ratio that can be expressed as a fraction of 100 refers the percentage.
Given,
Here we have a dollar general sends out a $5 off coupon to its email subscribers.
And we need to find the percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon.
Then the model used to define the this type of situation is refers as the classification model, because in this model, we have classify the given group of people based on the constraint.
To know more about Percentage here.
https://brainly.com/question/13729841
#SPJ4
Help me solve it please
((2*2)²)²
Answer:
256
Step-by-step explanation:
((2*2)²)²
(((4)²)²)
(16)²
256
Popular wisdom is that eating presweetened cereal tends to increase the number of dental caries (cavities) in children A sample of children was (with parental consent) entered into a study and followed for several years. Each child was classified as a sweetened-cereal lover or a unsweetened cereal lover. At the end of the study, the amount of tooth damage was measured. Here are the summary data: 10 15 Mean 6.41 5.20 Std Dev 5.0 15.0 225 Sweetened Unsweetened Assuming the necessary conditions for inference are met, which of the following an approximate 95% confidence interval for the difference in the mean tooth damage?
O (6.41 -5.20) + 2.145 3+
O (6.41 - 6:20) +1.96 Vi+
O (6.41 -- 5.20) +1,96/13 + 38
O (6.41 -5.20) +2.202/33+
O (6.41 - 5:20): 2.2821+13 228 X
An approximate 95% confidence interval for the difference in the mean tooth damage is (6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]
For sweetened samples
The value of n = 10
The mean of the samples = 6.14
The standard deviation of the sample = 5.0
For unsweetened samples
The value of n = 15
The mean of the sample = 5.20
The standard deviation of the sample = 15.0
We have to assume that necessary conditions for inference are met
The confidence interval = 95%
The equation will be
(6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]
Therefore, the difference in the mean tooth damage is (6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]
Learn more about standard deviation here
brainly.com/question/23907081
#SPJ4
The question is at the top
1. Describe the different ways of solving a system of nonlinear equations.
2. Explain the process of finding the composition of two functions f (g(x)) and g(f (x)).
3. How can you determine if a function is invertible and how do you find its inverse?
4. Explain the difference quotient and how to calculate it.
Answer:
Look below
Step-by-step explanation:
There are several methods for solving a system of nonlinear equations, which are a set of equations that cannot be solved using linear methods. Some of these methods include:
Graphical methods: These involve plotting the equations on a graph and finding the points where they intersect, which represent the solutions to the system.
Substitution method: This involves solving one of the equations for one variable in terms of the other, and substituting this expression into the other equation. The resulting equation is then solved for the remaining variable.
Elimination method: This involves adding or subtracting the equations in such a way as to eliminate one of the variables. The resulting equation is then solved for the remaining variable.
Newton's method: This is an iterative method that involves starting with an initial guess for the solution and then using an iterative process to improve the guess until it converges to the true solution.
Broyden's method: This is a variant of Newton's method that involves using a Jacobian matrix to calculate the updates to the solution at each iteration.
To find the composition of two functions f(g(x)) and g(f(x)), you need to apply the outer function to the result of the inner function. For example, if f(x) = x^2 and g(x) = x + 1, then the composition f(g(x)) would be equal to f(x+1) = (x+1)^2, and the composition g(f(x)) would be equal to g(x^2) = x^2 + 1.
To determine if a function is invertible, you need to check if it is one-to-one. A function is one-to-one if every element in the range corresponds to exactly one element in the domain. If a function is one-to-one, it has an inverse function, which is denoted by f^(-1)(x). To find the inverse function, you can solve the original function for the variable in the range and express the variable in the domain in terms of the range. For example, if f(x) = x^2 + 1, then f^(-1)(x) would be the inverse function, which can be found by solving f(x) for x to get x = sqrt(x-1).
The difference quotient is a mathematical concept that is used to approximate the slope of a curve at a particular point. It is defined as the difference between the y-values of two points on the curve, divided by the difference between the x-values of those points. The difference quotient can be written as:
(f(x + h) - f(x))/h
where f is the function, x is the x-value of the point at which the slope is being approximated, and h is a small value that is used to calculate the approximation. To calculate the difference quotient, you can plug the values of f, x, and h into the formula and perform the calculations.
Solve log 2x + log 5 = 1. Round to the nearest thousandth if necessary.
Answer: x=1
Step-by-step explanation:
Assume that "log" is the base-10 logarithm
log (2x)+log (5)=1
log 10{10}(2x)+log (5)=1
Assume that "log" is the base-10 logarithm
\log 10{10}(2x)+\log (5)=1
\log 10{10}(2x)+\log10{10}(5)=1
Apply the logarithm product identity
\log 10{10}(2x)+\log 10{10}(5)=1
log 10{10}(2x x 5)}=1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Make a list of all the patterns you notice in the number arrangement above. If we were to continue this number arrangement, what would be the middle number on the 50th row? What about the nth row?
Answer:
chronological
or +1 each number up
Step-by-step explanation:
The middle number on the 50th row is 891.5.
The nth row is 18n - 17.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
We see that there are 18 numbers in each row.
The numbers are consecutive natural numbers.
Now,
We can see that,
The first number of each row is 1.
The first number of the second row is 19.
The first number of the third row is 37.
The first number in each row can form a series.
1, 19, 37,....
This series is an arithmetic sequence.
First term = 1
Common difference = 18
The nth term is a + (n - 1)d.
50th term.
= 1 + (50 - 1)18
= 1 + 49 x 18
= 1 + 882
= 883
This means,
The 50th row will have the following series.
883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900.
The middle number is the midpoint of 891 and 892.
= 891.5
The nth row.
= 1 + (n - 1)18
= 1 + 18n - 18
= 18n - 17
Thus,
The middle number on the 50th row is 891.5.
The nth row is 18n - 17.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
enter the letters of the points that are below the graph of $y = -\frac 1 3 x.$
The letters of points below the graph of y = - 1/3x are B, C, F, H, J.
What is a graph?A diagram or pictorial representation of facts or values that is arranged might be referred to as a graph in mathematics.Graph points frequently show the relationship between two or more things. A relation is a particular instance of a graph of a function. A function is truly equal to its graph in the modern mathematical foundations and typically in set theory. However, it is frequently helpful to think of functions as mappings, which include not just the relationship between input and output but also the sets that constitute the domain and codomain. Both print and electronic media frequently employ graphs. Because a graph can show a trend or comparison, data can be presented more clearly by a graph than by a table.Here, the points that are below the graph of y = - 1/3x are B, C, F, H, J. (Refer images for graphs of the points and the line .)To learn more about graph , refer:
https://brainly.com/question/19040584
#SPJ4
ray il bisects angle hij. if m∠hil = (6x − 7)° and m∠jil = (5x 4)°, what is m∠jil? 118° 59° 44° 11°
The measure of angle JIL is 59°.
We are given that;
Ray IL bisects angle HIJ, we know that the measure of angle HIL is equal to the measure of angle JIL.
Using the given expressions for these angles, we can write:
m∠HIL = m∠JIL
(6x − 7)° = (5x + 4)°
To solve for x, we can subtract 5x from both sides and add 7 to both sides:
x − 7 = 4
x = 11
Now that we have the value of x, we can plug it into the expression for m∠JIL and simplify:
m∠JIL = (5x + 4)°
m∠JIL = (5 × 11 + 4)°
m∠JIL = (55 + 4)°
m∠JIL = 59°
Therefore, by the angle the answer will be 59°.
Learn more about angle;
https://brainly.com/question/14164971
#SPJ12
YOO need help with a short word problem :)
Using a system of linear equations the number of quarter and dime present are 1 and 8 respectively
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.
Let:
q = quarterd = dime1 quarter = $0.25
1 dime = $0.1
A) An equation for the number of coins
q + d = 9 ...eq(i)
B) The amount of money can be represented as;
0.25q + 0.1d = 1.05 ..eq(ii)
C) The number of dimes; solving equation (i) and (ii)
q + d = 9 ..eq(i)
0.25q + 0.1d = 1.05 ...eq(ii)
q = 1, d = 8
There are 8 dimes
D) There is 1 quarter in the money
Learn more on system of linear equation here;
https://brainly.com/question/13729904
#SPJ1
3
6
1
2
8
7
Press "Deal" to receive your cards.
Drag cards from your hand to the red and blue areas.
GOAL: Create two groups of cards with the SAME SUM
using as many cards as possible.
Submit
Answer:
I'm sorry I don't know
Step-by-step explanation:
........
which best describes the reason we use summary statistics to describe our data? group of answer choices summary statistics provide evidence of associations we may not have considered. even for relatively small datasets, it is difficult or impossible to analyze data simply by looking at it. summary statistics prove whether our public health interventions are having an impact. our goal in biostatistics is to conduct complex and sophisticated analyses.
The information about your sample data is summarized and provided by summary statistics.It provides information regarding the values in your data set.This covers the distribution of the mean and the skewness of your data.
What are the components of summary statistics? The essence of the information about the sample data is summarized and provided by summary statistics, a subset of descriptive statistics.By identifying a measure of location or central tendency, such as the arithmetic mean, statisticians frequently attempt to define and classify the observations.The technique of inferring statistically from a sample or subset of data is known as statistical inference.Most of the time, it is not feasible to collect all the measurements from a population.Quick summaries of data are provided by summary statistics, which are especially helpful when comparing one project to another or before and after.Measures of dispersion and central tendency are the two primary categories of summary statistics used in appraisal.To learn more about summary statistics refer
https://brainly.com/question/14004024
#SPJ4
A 9-inch candle burns down in 6 hours. How far has it burned after 5 1/2 hours? Use the dropdown menu to state your answer as a decimal, mixed number, or improper fraction.
The amount of candle burn after 6 hours is 4.95 inches.
What is the total amount?
Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total.
Here, we have
Given that the 9-inch candle burns in 6 hours.
We know that we first have to calculate how 1 hour how much candles will burn.
Candle burn in 1 hour is :
= 9 / 10
= 0.9 inch
Now,
To find out how far the candle burnt after 6 hours we need to multiply the part of the candle burned by one hour by 11/2 hours.
= 11/2 × 0.9
= 4.95 inches
Hence, the amount of candle burn after 6 hours is 4.95 inches.
To learn more about the total amount from the given link
https://brainly.com/question/26670496
#SPJ1
Match each system of equations with the number of solutions the system has. 1. No solutions 2. One solution 3. Infinitely many solutions A. y=-4/3x+4 y=-4/3x-1 B. y=4x-5 y=-2x+7 C. 2x+3y=8 4x+6y=17 D. y=5x-15 y=5(x-3)
A. y = - (4/3)x + 4.
y = - (4/3)x - 1.
No solution.
B. y = 4x - 5.
y = - 2x + 7.
one solution.
C. 2x + 3y = 8
4x + 6y = 17.
No solution.
D. y = 5x - 15.
y = 5(x - 3).
Infinitely many solutions.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
We'll graph each system of equations, If they intersect at one point they have one solution, if they are parallel to each other they have no solution and if they are coinciding with each other they have infinitely many solutions.
y = - (4/3)x + 4.
y = - (4/3)x - 1.
These are parallel lines no solution.
y = 4x - 5.
y = - 2x + 7.
These lines intersect at (2, 3) one solution.
2x + 3y = 8
4x + 6y = 17.
They are parallel to each other.
y = 5x - 15.
y = 5(x - 3).
These are coinciding lines if we distribute the terms hence infinitely many solutions.
learn more about the system of equations here :
https://brainly.com/question/24065247
#SPJ1
What theorem would this one be?
Answer:
C. Yes, SAS
Step-by-step explanation:
You want to know the congruence theorem that lets you say ∆ACD≅∆CAB, given that AB=CD and AB║CD.
Congruent trianglesThe triangles are congruent if an angle or side can be shown congruent, in addition to at least one angle and at least one side.
Here, the sides AB and CD are shown congruent. The side AC is congruent to itself, so we only need the angle(s) between them to show the triangles are congruent.
The Alternate Interior Angles theorem tells you that transversal AC creates congruent angles CAB and ACD with respect to the parallel lines AB and CD.
Hence we can show triangle ACD and CAB are congruent by the SAS congruence theorem.
Yes, The triangle is congruent by Angle - Side - Angle congruence theorem.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
⇒ AB || CD
Now,
In figure,
⇒ AB || CD
So, In triangle ACD and triangle CAB;
⇒ AB || CD
So, By definition of alternate angles,
⇒ ∠ BAC = ∠ DCA
And, ∠ DAC = ∠ ACB
Here, Line AC is common in both tringle.
Hence, By Angle - Side - Angle congruence theorem,
⇒ Δ ACD ≅ Δ CAB
Thus, The triangle is congruent by Angle - Side - Angle congruence theorem.
Learn more about the triangle visit:
https://brainly.com/question/13984402
#SPJ1
1. What is the value of x?
2. Determine mzYJO.
(x-40)
(X-80)
Answer:
The value of x should be x = 40.
Step-by-step explanation:
Which proportion could be used to prove that HJ is parallels to KL? multiple choice
Answer:
fourth option
Step-by-step explanation:
to prove that HJ is parallel to KL , then KL divides the sides HG and JG proportionally , that is
[tex]\frac{GK}{HK}[/tex] = [tex]\frac{GL}{LJ}[/tex]
express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 2 π , 4 π ]
The limit as a definite integral on the interval [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π , 4π] is [tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex].
What is meant by definite integral?
A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.
Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.
If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.
Let the equation be
[tex]$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$[/tex]
substitute the values in the above equation, we get
= [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π, 4π],
simplifying the above equation
[tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex]
To learn more about definite integral refer to:
https://brainly.com/question/24353968
#SPJ4
how many eight-digit numbers contain the digit 2 exactly once, the digit 3 exactly twice, and the digit 4 exactly thrice?
There are 1260 eight-digit numbers that have 2 once, 3 twice, and 4 thrice.
There are 10 digits in the number system from 0 to 9.
Let the 8-digit number be represented by
_ _ _ _ _ _ _ _
Here the numbers will have a single 2, a doublet of 3, and a triplet of 4 hence we get
2 3 3 4 4 4 _ _
Now for the last 2 numbers, we have 0, 1, 5, 6, 7, 8, 9. Therefore the last 2 digits can be chosen in ⁷C₂ ways.
= 7!/(2 X 5!)
= 21 ways
There are 6 fixed numbers which can e arranged in 6! ways. Since there are numbers repeated twice and thrice, we can arrange them in
6!/(2! X 3!)
= 6 X 5 X 2
= 60 ways.
Therefore we get
60 X 21 numbers
= 1260 numbers.
To learn more about Permutation and combination visit
https://brainly.com/question/4318885
#SPJ4
Valeria has an action figure collection of 500 action figures. She keeps 235 of
the action figures on her wall. What percentage of Valeria's action figure
collection does she keep on her wall?
The percentage of Valeria's action figure collection is 47% which she keeps on her wall.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
To find the percentage of Valeria's action figure collection that she keeps on her wall, we need to divide the number of action figures she keeps on her wall by the total number of action figures in her collection and then multiply by 100%.
Since Valeria has a collection of 500 action figures and she keeps 235 of them on her wall, the percentage of her collection that she keeps on her wall is :
⇒ 235 / 500 × 100% = 47%.
Thus, the percentage of Valeria's action figure collection is 47%
Learn more about the percentages here:
brainly.com/question/24159063
#SPJ1
A company has a monthly time series that regularly shows sales being higher in the summer months. This is an example of which component? O A. Random O B. Seasonal O C. Trend O D. Cyclical Click to select your answer O Type here to search
A company has a monthly time series that regularly shows sales being higher in the summer months, this is an example of Seasonal Component
A seasonal variation is a calendar-related and systematic effect. One example is an increase in water consumption during the summer due to warmer weather.
Other seasonal effects include trading day effects (the number of working or trading days in a given month varies from year to year, affecting the level of activity in that month) and moving holiday effects (the timing of holidays such as Easter varies, so the effects of the holiday will be experienced in different periods each year).
In the given question,
A company has a monthly time series that regularly shows sales being higher in the summer months,
This is an example of Seasonal variation in times series
As the Sales increases in every summer seasons
To know more about Seasonal variation here
https://brainly.com/question/28502067
#SPJ4
If triangle DOG is similar to triangle CAT then find the measure of each of the following:
m
m
Therefore, the above sides and angles will be the corresponding angles and sides of a similar triangle.
What is congruence?Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have an identical appearance.
Here,
In the event that "CAT"
As per SSS guideline, we receive
CA=DO
AT=OG
CT=DG
The congruent triangles' corresponding angles will also be:
∠CAT = ∠DOG
∠ATC = ∠OGD
∠ACT = ∠ODG
Two triangles are similar if they are congruent with one another.
if ∆CAT≅∆DOG
Next,∆CAT~∆DOG
As a result, the angles and sides of the triangle with the same sides as those above will be the same.
To know more about congruence , visit
https://brainly.com/question/7888063
#SPJ1
An investor invested a total of $2,300 in two mutual funds. One fund earned a 6% profit while the other earned a 4% profit. If the investor's total profit was $102, how much was invested in each mutual fund?
The amounts in each mutual fund are $500 and $1800. By using a system of equations, the required values are evaluated.
What is a system of equations?The system of equations is a set of one or more equations that intersects at locations called solutions of the system.The system of equations is solved for solutions in three different methods. They are the Elimination method, Substitution method, and Graphing method.Calculation:It is given that, an investor invested $2300 in two mutual funds.
Consider the amount invested in two mutual funds as fund1 = x and fund2 = y.
So, we can write the equation for the total investment is
x + y = 2300 ...(1)
The percentage of profit earned from the fund1 = 6% = 0.06
The percentage of profit earned from the fund2 = 4% = 0.04
The total profit for the investor = $102
Then, the equation from this statement is
0.06x + 0.04y = 102 ...(2)
Then the system of equations is
x + y = 2300 ...(1)
0.06x + 0.04y = 102 ...(2)
Applying the substitution method to solve the obtained system of equations.
So, from (1), we can write x = 2300 - y
Then, equation (2) becomes
0.06(2300 - y) + 0.04y = 102
⇒ 6(2300 - y) + 4y = 10200
⇒ 13800 - 6y + 4y = 10200
⇒ 13800 - 2y = 10200
⇒ 2y = 13800 - 10200 = 3600
∴ y = 3600/2 = $1800
So, the value of x is x = 2300 - 1800 = $500
Thus, the amount of investment in two mutual funds is $500 and $1800.
Learn more about the system of equations here:
brainly.com/question/13729904
#SPJ1
1. Business is major
The sampling distribution of p
PROBLEM:
According to the National Center for Education Statistics, 20% of students who
recently earned bachelor's degrees were business majors. Imagine taking an SRS of
300 students who recently earned bachelor's degrees and calculating p = the
proportion of students in the sample who majored in business.
(a) Identify the mean of the sampling distribution of p.
(b) Calculate and interpret the standard deviation of the sampling distribution of p.
Verify that the 10% condition is met.
(c) Describe the shape of the sampling distribution of p. Justify your answer.
a) The mean of the sampling distribution of p is of 0.2.
b) The standard deviation of the sampling distribution of p is of: 0.0231, which is the amount that the sample proportions may differ from 0.2.
c) The shape of the sampling distribution of p is approximately normal.
How to define the sampling distribution of p?The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has:
Approximately normal shape.Mean equals to p.Standard deviation equals to [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]The parameters for this problem are given as follows:
p = 0.2, n = 300.
The 10% condition is given as follows:
np = 300 x 0.2 = 60 > 10.n(1 - p) = 300 x 0.8 = 240 > 10.Then the standard error of the sampling distribution of p is calculated as follows:
[tex]s = \sqrt{\frac{0.2(0.8)}{300}} = 0.0231[/tex]
More can be learned about the Central Limit Theorem at https://brainly.com/question/25800303
#SPJ1
2. The sum of eight squared and the quantity four times eleven
Answer:
Step-by-step explanation:
8^2 = 64
+
4*11 = 44
-> 64 + 44 = 108
in herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to what?
In Herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to behaviour.
THE MATCHING LAW
Herrnstein's Experiment Herrnstein (1961) conducted an experiment with pigeons in a room with two response buttons, red and white. Each key was assigned its own VI gain schedule. For example, under one condition, the left button pick was boosted on a VI 135 second schedule, and the right button pick was boosted on a VI 270 second schedule.
After the birds have learned as much as possible about this electoral situation, how do they distribute their responses? We trained them for days and then measured their reactions. As is often the case with VI schedules, birds returned many responses for each reinforcer received. Most interesting, however, is that in this condition, where two-thirds of the reinforcers came from the left button, the birds performed about two-thirds of the responses with the left button. That is, the proportion of left button responses equaled or matched the proportion of reinforcers delivered by the left button. In another condition, two birds received only about 15% of reinforcers from the left key and responded about 15% to that key.
Based on these results, Herrnstein proposed the following general principle for individual behavior when presented with alternative sequences. So, what you think makes sense rather than other options available at that particular moment.
To learn more about Matching law, refer:
https://brainly.com/question/15875828
#SPJ4
i want the answer
fast
Answer:
original fraction = [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
let the denominator of the fraction be x then the numerator is x - 1 , so
original fraction is
[tex]\frac{x-1}{x}[/tex]
if 1 is added to the numerator and 5 to the denominator , then fraction is
[tex]\frac{-1+1}{x+5}[/tex] = [tex]\frac{x}{x+5}[/tex]
equate this to [tex]\frac{1}{2}[/tex]
[tex]\frac{x}{x+5}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = x + 5 ( subtract x from both sides )
x = 5
then original fraction is
[tex]\frac{x-1}{x}[/tex] = [tex]\frac{5-1}{5}[/tex] = [tex]\frac{4}{5}[/tex]
Answer:
Below
Step-by-step explanation:
Original fraction (x-1) / x <====given (use in final step below)
Altered fraction (x-1 +1) / (x+5) = 1/2 <====solve this for 'x'
x / (x+5) = 1/2 cross multiply
2x = x+5
x = 5
So original fraction was 4/5
