A criteria for construction of triangle include the following: B. SAS.
What is a triangle?In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
Generally speaking, the side, angle, side (SAS) criterion is essential for the construction of any triangle such as the following:
Isosceles triangleObtuse triangleEquilateral triangleScalene triangleRight-angled triangleBased on the side, angle, side (SAS) criterion, a statement which is necessary to prove that two (2) triangles are congruent is that one of its side must be equal to another side because their angles are equal in measure or magnitude.
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the traffic flow rate, in cars per hour, past a certain point on a highway is where is in hours and is 8 am. how many cars pass by during the time interval from 8 am to 9 am?
Following integration, we may estimate that between 6 and 8 am, 2080 automobiles will pass through the crossing.
What is integration?In mathematics, an integral assigns numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data.
Integration is the action of locating integrals.
So, the number of automobiles that cross an intersection each hour is:
r(t) = 400 + 800t - 120t²
Integration should be carried out to establish the number of cars traveling through the intersection between 6 am and 8 am.
[tex]\begin{aligned}\int_{t_1}^{t_2} r d t & =\int_0^2 400+800 t-120 t^2 d t \\& =\left[400 t+400 t^2-40 t^3\right]_0^2 \\& =400 \times 2+400 \times 2^2-40 \times 2^3 \\& =800+1600-320 \\& =2080\end{aligned}[/tex]
Therefore, following integration, we may estimate that between 6 and 8 am, 2080 automobiles will pass through the crossing.
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Correct question:
The traffic flow rate (cars per hour) across an intersection is r ( t ) = 400 + 800 t − 120 t 2 , where t is in hours, and t =0 is 6am. How many cars pass through the intersection between 6 am and 8 am?
Given the following exponential function, identify whether the
change represents growth or decay, and determine the
percentage rate of increase or decrease.
y = 3300(0.949)^x
The function simulates exponential decay, and it degrades by 5.1% for every increment in x.
What is exponential growth & exponential decay?Explosive increase and decay are common in situations where quantities change rapidly. It has been suggested that exponential development and decay follow a geometric progression. Quantities that change exponentially rather than continually are referred to be exponentially growing or decaying.
As per the given data in the question,
An exponential function with the formula y = a[tex]r^x[/tex] is the function that is given.
a = 330
r = 0.949
The function indicates exponential growth if the base r is larger than 1. The function shows exponential decline if indeed the base r is far less than 1. In this instance, the function depicts exponential decline because the base r is smaller than 1, or 0.949.
If we want to describe the rate of reduction as a percentage, we can remove the base r by 1 and multiply it by 100.
The rate of reduction as a percentage in this instance is:
1 - 0.949 = 0.051 ×100
= 5.1%.
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What is the additive inverse of the polynomial -6x^3 +4x^2 -4
6x³ -4x² +4 is the additive inverse of polynomial -6x³ +4x² -4
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given polynomial is -6x³ +4x² -4
Polynomial is minus six x cube plus four x square minus four.
Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.
6x³ -4x² +4 is the additive inverse of -6x³ +4x² -4
because -6x³ +4x² -4+6x³ -4x² +4=0
Hence, 6x³ -4x² +4 is the additive inverse of polynomial -6x³ +4x² -4
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Someone please answer this my question is in the picture I will give you brainliest and your getting 50 points no fraud answers.
Step-by-step explanation:
I will help you sir.
Given
Opposite Sides are Congruent
Reflexive
SSS
CPCTC
State the relationship between the congruent angles
For any data set, which measures of central location have only one value? A. Mode and median B. Mode and mean C. Mode and standard deviation D. Mean and median
Any data collection whose metrics of central placement only have the letter A as a value.Mode and median
For any given data set, the mode and median are the two measures of central location that have just one value. The mode is the most commonly occurring value in a given data set, while the median is the middle value in the data set when it is sorted in order from least to greatest. The mean, on the other hand, is an average of all the values in the data set, and the standard deviation is a measure of how much the values in the data set differ from each other. So, the answer is A. Mode and median.
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calculate least squares solution using svd a matrix has the singular value decomposition what is the solution to the least-squares problem that has minimal norm ?
The Least-squares problem that has minimal norm can be given using factorization.
The least squares method is used to find the best fit for a set of data points by minimizing the sum of the offsets from the plotted curve. Singular value decomposition (SVD) is a factorization of a real or complex matrix.
It is a widely used technique to decompose a matrix into several component matrices, exposing many of the useful and interesting properties of the original matrix. The singular value decomposition, guaranteed to exist, is A=UΣV.
When we have the equation system Ax=b, we calculate the SVD of A as A=UΣVT. The matrices U and VT have a very special property. They are unitary matrices. One of the main benefits of having unitary matrices like U and VT is that if we multiply one of these matrices by its transpose (or the other way around), the result equals the identity matrix.
The singular value decomposition (SVD) of matrix A is very useful in the context of least squares problems. It is also very helpful for analyzing the properties of a matrix.
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50 POINTS Giselle wants to buy the newest book in her favorite series. She has some money saved but does not want to
use all her savings on the book. Giselle’s grandma offers to pay some of the cost of the book for every weed she
pulls in her grandma’s garden.
The graph shows the cost to Giselle for the purchase of the book after pulling x weeds in her grandma’s garden.
Select True or False to describe each statement.
(2 points for each correct answer = 10 points)
SELECT True or False
Answer:
true false false true true
Five identical rectangular pieces of cloth of different prints when arranged as shown form a square patch. If the perimeter of each rectangular piece is 48 cm, what is the perimeter of the square patch?
(With explanation)
Answer:
Perimeter of the square patch is 240 cm.
Step-by-step explanation:
If the perimeter of each rectangular piece is 48 cm, then the length of each side of each rectangular piece is 12 cm. When the rectangular pieces are arranged to form a square patch, the patch will have 5 rows and 5 columns of rectangular pieces. Since the rectangular pieces are identical, the length of each side of the square patch will be 5 times the length of one side of a rectangular piece. Therefore, the length of each side of the square patch will be 5 * 12 cm = 60 cm.
The perimeter of the square patch is the sum of the lengths of all four sides of the patch. Since all sides of the patch have the same length, the perimeter of the square patch will be 4 * 60 cm = 240
how many batches of raisin granola bars can inez make if she has 8/3 cups of raisings and each batch requires 2/3 cup of raisins? \frac{1}{4}\enspace batch
If Inez has 8/3 cup of raisings and each batch takes 2/3 cup of raisins, she may create 4 batches of raisin granola bars.
What is fraction?In mathematics, a fraction is used to represent a piece or part of a whole. It symbolizes the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, while the bottom number is known as the denominator. A common fraction is a numeric representation of a rational integer. The same number can be expressed as a decimal, a percentage, or with a negative exponent. Fractions indicate pieces of a whole or group of items. A fraction is made up of two components. The number at the top of the line is referred to as the numerator. It specifies the number of equal sections of the whole or collection that are taken. The figure below the line is denominator.
Here,
8/3÷2/3=4
2/3 • 4 = 8/3
2/3 + 2/3 + 2/3 + 2/3 = 8/3
2/3 = 0.67
0.67 • 4 = 2.67
8/3 = 2.67
4 batches of raisin granola bars can inez make if she has 8/3 cups of raisings and each batch requires 2/3 cup of raisins.
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HELP HURRY ITS TIMED
The length of the side AB represented by x in the triangle ABC is equal to 16 using the trigonometric ratio of sine.
Trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
The triangles ABC and ADB are right-angled triangles, we shall be considering the trigonometric ratio of the sine of angle A which is common to both triangles.
For triangle ABC;
sinA = adjacent/hypotenuse
sinA = x/32
for triangle ADB;
sinA = 8/x
thus we can say that;
x/32 = 8/x {cross multiplication}
x² = 3 × 32
x² = 256
x =√256 {take square root for both sides}
x = 16.
Therefore, 16 is the length of the side AB labelled x, using the trigonometric ratio of sine of the common angle A to the triangles ABC and ADB.
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if we alternately flip a balanced coin and a coin that is loaded so that the probability of getting heads is 0.45, what are the mean and the standard deviation of the number of heads that we obtain in 10 flips of these coins?
Probability of getting head = 0.45
Probability of getting tail = 1- 0.45
= 0.55
No of flip flops = 10
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
-3
Step-by-step explanation:
5 + ( -8 )
-8 - 5 = -3
so final answer: -3 because ( - 8 ) so the ( - ) would go on the answer
Answer: -3
Step-by-step explanation: It would be -3 because since we are adding a negative it would go toward the negative side. Also, it can be modeled as:
5 - 8
This would still = -3.
Austin's final exam in math had two parts. He had a total of 50 minutes to complete the entire exam. He spent 25 minutes on Part one of the exam.write and solve an equation to show how much time he had left to solve part two
The time Austin had left to solve part two will be 25 minutes.
How to illustrate the equation?It is important to note that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Austin's final exam in math had two parts. He had a total of 50 minutes to complete the entire exam.
Since he spent 25 minutes on Part one of the exam, the time he had left to solve part two will be:
t = 50 - 25
t = 25
The time is 25 minutes.
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(06.01 lc) a car traveling in a straight line from its starting position at a speed of 65 miles per hour for 3 hours is represented by the function v(t), where t is the number of hours traveled. what units describe the area under the curve of v(t)?
The required area under the curve of function v(t) is 195 square miles, which depicts the total distance traveled by car during the 3 hours.
The area under the curve of the function v(t) represents the total distance traveled by the car over the given time period.
The function v(t) is defined as the speed of the car (in miles per hour) at any given time t (in hours). Since the speed is constant at 65 miles per hour, the graph of v(t) will be a straight horizontal line at y = 65.
To find the distance traveled, we need to multiply the speed (in miles per hour) by the time (in hours):
Distance = Speed * Time
Following the given case, the speed is 65 miles per hour, and the car traveled for 3 hours:
Distance = 65 miles/hour * 3 hours = 195 miles
So, the area under the curve of v(t) is 195 square miles, which represents the total distance traveled by car during the 3 hours.
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Match the correlation coefficients with the
scatterplots shown below.
The scatterplots shown can be matched to the corresponding correlation coefficients , which are as follows :
Scatterplot A : -0.56
Scatterplot B : -0.96
Scatterplot C : 0.92
Scatterplot D : 0.53
What is correlation coefficient?
Correlation coefficient is a numerical measure of the degree of relationship between two variables. It is used to measure how closely related two variables are, and whether one variable is a good predictor of the other. It is measured on a scale of -1 to 1, with -1 representing a strong negative correlation, 0 representing no correlation, and 1 representing a strong positive correlation. A correlation coefficient of 0 suggests that the two variables are completely unrelated, while a coefficient of 1 suggests that the two variables are strongly related. Correlation coefficients can help to identify patterns in data and can be used to predict future values.
Note the following facts :
Scatterplot that shows a trend that rises from left to your right shows a positive correlation between two variables.
Scatterplot that descends from left to left to right shows a negative correlation between two variables.
The farther away the data points are from each other the greater the value the value of correlation coefficient.
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Many high schools now have drug-testing programs for athletes. The main goal of these programs is to reduce the use of banned substances by students who play sports. It is not practical to test every athlete for drug use regularly. Instead, school administrators give drug tests to randomly selected student athletes at unannounced times during the school year. Students who test positive face serious consequences, including letters to their parents, required counseling, and suspension from athletic participation. Drug test aren't perfect. Sometimes the tests say that athletes took a banned substance when they did not. This is known as a false positive. Other times, drug tests say that athletes are "clean" when they did take a banned substance. This is called a false negative. Suppose that 16% of the high school athletes in a large school district have taken a banned substance. The drug test used by this district has a false positive rate of 5% and a false negative rate of 10%. If a randomly chosen athlete tests positive, what is the chance that the student actually took a banned substance. Use what you have learned in this chapter to help answer the following questions about the district's drug-testing program. A. What is the probability that a randomly chosen athlete tests positive for banned substances? B. If two athletes are randomly selected, what's the probability that at least one of them tests positive? C. What's the probability that a randomly selected athlete did not take a banned substance, given they tested positive? Based on your answer, do you think an athlete who tests positive should be suspended from athletic competition for a year? Why or why not? D. What's the probability that a randomly selected athlete took a banned substance given the student tested negative? Explain why it makes sense for the drug-testing process to be designed so that this probability is less than the one you found in Question 4. E. The district decides to immediately retest and athlete who tests positive. Assume that the results of an athlete's two tests are independent. Find the probability that a student who gets a positive result on both tests actually took a banned substance (hint: took the banned substance given two positive tests). Based on your answer, do you think that an athlete who tests positive twice should be suspended from athletic competition for a year. Why or why not?
Students who test positive face serious consequences, including letters to their parents,
Remata it’s 3 more than 6 times as old as her daughter Isabella. The sumo their ages is 38. What are Renata and Isabella’s ages, respectively.
Answer:
The answer to you question is 18 and 20
18 and 20
Solve using substitution x=-3 -4x-y=10
What is the total area,in square feet,of the shaded sections of the trapezoid below?
Answer:
69.5ft²
Step-by-step explanation:
The shaded area is right triangles,
The formula for area of a right triangle is 1/2 x base x height
Triangle on right
Base: 7.6ft
Height: 10ft
Plug in: 1/2 x base x height = 1/2 x 7.6ft x 10ft = 38
Triangle on left
Base: 6.3ft
Height: 10ft
Plug in: 1/2 x base x height = 1/2 x 6.3ft x 10ft = 31.5
Add both for total shaded area: 31.5 + 38 = 69.5ft²
Are the ratios 3:4 and 11:20 equivalent
Answer:
nah
Step-by-step explanation:
Select the correct answer. What are the solutions of this quadratic equation? x2 + 10 = 0
Answer:x=-5
Step-by-step explanation:
x2+10=0
0-10=-10
x2=-10
-10/2=-5
x=-5
a sample of 50 drills had a mean lifetime of 12.68 holes drilled when drilling a low-carbon steel. assume the population standard deviation is 6.83. what sample size (i.e., how many) would you need to have so that a 95% confidence interval will have a margin of error of 1.0?
Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).
We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:
Sample mean of [tex]x = 12.7[/tex]
Population standard deviation of [tex]\sigma = 6.37[/tex]
Sample size of .n = 50
The margin of error is:
[tex]M = z \frac{\sigma }{\sqrt{n} }[/tex]
In which z is the critical value.
We have to find the critical value, which is z with a p-value of [tex]\frac{1+\alpha }{2}[/tex] , in which [tex]\alpha[/tex] is the confidence level.
In this problem, , thus, z with a p-value of , which means that it is z = 1.96.
Then:
[tex]M= 1.96\frac{6.37}{\sqrt{50} } = 1.77[/tex]
The confidence interval is the sample mean plus/minutes the margin of error, hence:
x- M = 12.17 - 1.77 =10.4
x+M = 12.17 + 1.77 = 13.94
The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).
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if you wander around central park in new york city, you will eventually encounter random large boulders that are made of a type of rock not found in the area. how did these large boulders get to central park?
The random large boulders around central park in new york city got to central park They were carried by glaciers and dropped as glacial erratics.
There have been four kinds of bedrock in Manhattan, including the Manhattan schist and the Hart-land shirts, which are metamorphosed sedimentary rocks found in outcrops. Some of these are made out of igneous rocks that developed billions of years ago. It happened during the period of the Grenville progeny and occurred during the formation of the ancient mega continent.
Various glaciers have covered the region of Central Park in the past, the much more recent being the Wisconsin glacier that developed about around 12,000 years ago.
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suppose that $1,000 is deposited into an account that yields 0.85% interest, compounded annually? how much money will be in that account at the end of 4 years?
The money in the account at the end of the 4 years is $1034
What is compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Now we are given that the initial amount deposited in the account is $1000
This account is giving 0.85% And we have to figure out how much amount will be there
We use compound interest formula to find the amount
[tex]A= P(1+r/n)^{nt}\\\\A= 1000(1+0.0085)^{4}\\A = 1000(1.034)\\A= 1034[/tex]
Hence the amount will be after 4 years is $1034.
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A collection of nickels and dimes is worth $2.85. If there
are 34 coins in the collection and each nickel is replaced
with a quarter, the value of the collection becomes:
O $13.50
O none of the above
O $5.05
O $8.50
In the collection, there are 11 nickels and 23 dimes. If each nickel is replaced with a quarter, the value of the collection becomes $5.05. So, C is correct. By writing them in the system of equations, we get the required value.
Conversion of the given units into dollars:The given units are nickels, dimes, and quarters. Their conversion into dollars is as follows:
1 nickel = $0.05
1 dime = $0.10
1 quarter = $0.25
Calculation:Given a collection of nickels and dimes is worth $2.85.
And there are 34 coins in the collection.
So, consider the number of nickel coins = n and the number of dime coins = d.
Then, the equation for the given collection is
n + d = 34...(1)
0.05n + 0.10d = 2.85...(2)
On simplifying (2), we get
5n + 10d = 2.85 × 100
⇒ 5n + 10d = 285
From (1), n = 34 - d, we get
5(34 - d) + 10d = 285
⇒ 170 - 5d + 10d = 285
⇒ 5d = 285 - 170 = 115
∴ d = 115/5 = 23
Thus, the number of dime coins is 23.
So, from (1), we get n + 23 = 34 ⇒ n = 34 - 23 = 11
∴ n = 11
Thus, the number of nickel coins is 11.
If each nickel coin in the collection is replaced with a quarter, then the value of the collection is
q + d = 34 and 0.25q + 0.10d = Y
Here q = 11; d = 23
So, we get
0.25(11) + 0.10(23) = Y
⇒ 2.75 + 2.3 = Y
⇒ 5.05 = Y
∴ Y = $5.05
The value of the new collection becomes $5.05.
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Angle 9 and angle 10 are corresponding angles formed by two parallel lines cut by transversal. The angles are also complimentary. Find angle 9
The measure of angle 9 is 45 degrees.
What is complementary angles?
Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complementary angles.
Given:
Angle 9 and angle 10 are corresponding angles formed by two parallel lines cut by transversal.
The angles are also complimentary.
We have to find the measure of angle 9.
If <9 and <10 are corresponding, it means they are equal i.e <9 = <10
Since <9 and <10 are also complementary angles, their sum will be 90 degrees
<9+<10 = 90
<9 + <9 = 90
2m<9 = 90
m<2 = 90/2
m<2 = 45 degrees
Hence the measure of angle 9 is 45 degrees.
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if my overall grade is 44 percent and a test is worth 60 percent of my grade and i get 50 percent on a test what would my overall grade be now?
Answer:
Step-by-step explanation:85 percent with equals a b
Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour. How many pages can Shawn type in one hour? A. B. C. D.
Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.
What is typing speed?
How many words a person can correctly type in one minute. He types at a 60 wpm rate.
Given:
Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour.
We have to find how many paged he can type in one hour.
First to convert improper fraction 1 2/7 into a fraction.
⇒ [tex]1\frac{2}{7} = \frac{7*1+2}{7} = \frac{9}{7}[/tex]
So, Shawn can type 9/7 pages in 1/3 of an hours.
i hour = 3/3
So, Shawn can type
9/7 x 3/3 = 27/21 = [tex]1\frac{6}{21}[/tex] pages in one hour.
Hence, Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.
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2) At a concert, 35% of the audience members were teenagers. If the number of audiences at the concert was 1800, what was the number of teenager members?
Answer:
630
Step-by-step explanation:
35% of 1800 = 0.35 × 1800 = 630
