the given triangle A 45-45-90 triangle is a right triangle having interior angles measuring 45°, 45°, and 90° in degrees.
A 45-45-90 triangle is also an isosceles triangle, which means that its two legs are equal in length.
All 45-45-90 triangles are similar to each other.
Line segments DE and FG are perpendicular to side AB of the 45-45-90 triangle, ABC. Triangles ADE and AFG are also 45-45-90 triangles now, △ABC~△ADE~△AFG.
The ratio of the side lengths of a 45-45-90 triangle is:
ratio= 1:1: √2
The legs of opposite the 45° angles (the shorter sides) are √2÷2of the length of the hypotenuse (the side opposite the 90° angle)
The hypotenuse is √2 times the length of either leg.
Since a 45-45-90 triangle is also an isosceles triangle, then, the two legs are equal on measuring. Assuming x is the length of the leg and b is the length of the hypotenuse and using the Pythagorean Theorem:
x^2 + x^2= b^2
Thus, the ratio of the side lengths of a 45-45-90 triangle are x:x:√2 or 1:1: √2 respectively.
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How do you find the mean and standard deviation of a simple random sample?
The steps of finding mean and standard deviation of a simple random sample are given below.
What is standard deviation and mean?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.
The steps of finding mean and standard deviation of a simple random sample are:
Divide the population standard deviation (σX) by the square root of the sample size (n) to get the standard deviation of the sample mean (σX): = σ/n.
How to determine sample means
Add up the examples' components. You must first count the number of sample items in each data set and then add up all of the sample items. ...
Sum divided by the quantity of samples.
The outcome is the mean.
To determine the variance, use the mean.
To determine the standard deviation, use the variance.
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which number is a composite
11, 5 , 9, or 2
(i need an answer asap
Answer:
2
Step-by-step explanation:
What is the discriminant of the quadratic equation 3x^2+8x+4=0
7. A stock is worth $21. Its value is increasing at a rate of $0. 25 per week a.
Write an equation for the value y (in dollars) of the stock after x weeks.
b. If this trend would continue, what would be the value of the stock after 20 weeks?
The Equation for the value y is a. y = 21 + 0.25x (where x represents the number of weeks)
b. The value of the stock after 20 weeks would be 21 + (0.25 * 20) = $26.
This equation represents the linear relationship between the value of the stock (y) and the number of weeks (x). The value of the stock is initially $21, and it increases by $0.25 every week. This is represented by the coefficient of x (0.25) in the equation. By plugging in x=20 into the equation, we can find that after 20 weeks, the value of the stock would be $26. This is assuming that the rate of increase remains constant over time.
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There are 3 boys for every 5 girls in a kindergarten class. How many total students are there if there are 6 boys?
Answer:
16 students
Step-by-step explanation:
It is a 3 to 5 ratio, so if there are six boys, there are 10 girls. Six plus ten is 16 students.
In an inverse variation, y = 3 when x = 8. Write an inverse variation equation that shows
the relationship between x and y.
Write the equation using a decimal or an integer.
How do I find this?
Answer:
y = 24/xStep-by-step explanation:
An inverse variation equation is:
y = k/xWe have y = 3 when x = 8, find the coefficient k:
3 = k/8k = 3*8k = 24The equation is:
y = 24/xIf θ is an angle in standard position and its terminal side passes through the point (-3,4), find the exact value of tanθ in simplest radical form.
Answer:
so x = 20 , y = -21 , which is in quad IV
r^2= 400+441 = 841
r = √841 = 29
then cos Ø = 20/29
sec Ø = 29/20 = 1.45
Step-by-step explanation:
please give brainliest
A quadrilateral has vertices (-5,1) (-2,5) (2,2) (-1,-2). Determine if it is a square by using the distance formula to calculate the length of the diagonals, and the slope formula to determine if the diagonals are perpendicular
Length of diagonals are :
[tex]D_1 = \sqrt{ (-5-(-1))^2 + (1-(-2))^2 }\\\\D_1 = 5\ units[/tex]
[tex]D_2 = \sqrt{(-2 -2 )^2 + (5-2)^2}\\\\D_2 = 5 \ units[/tex]
Now, Slope of both the diagonal is :
[tex]m_1 =\dfrac{1-(-2)}{-5-(-1)} \\\\m_1 = -\dfrac{3}{4}\\\\m_2 = \dfrac{5-2}{-2-2}\\\\m_2 = -\dfrac{3}{4}[/tex]
Now, product of slopes are :
[tex]m_1 \times m_2 = \dfrac{-3}{4} \times \dfrac{-3}{4}\\\\m_1 \times m_2 = \dfrac{9}{16}[/tex]
Since, the product of slope is not equal to -1 . It means that the slopes are not perpendicular.
Therefore, this quadrilateral is not square.
You have a cup with 17 coins inside. The total inside the cup is $5. 50. Determine how many half dollars and quarters are inside the cup. Use a system of equations. Be sure to define the variables and show all work
There are 8 half dollars and 9 quarters inside the cup.
We can set up a system of equations to represent the number of half dollars (h) and quarters (q) in the cup and the total value of the coins.
Let h be the number of half dollars and q be the number of quarters.
The first equation represents the total number of coins in the cup:
h + q = 17The second equation represents the total value of the coins:
0.5h + 0.25q = 5.50To solve for h and q, we can use either the substitution or elimination method.
By substitution, we can solve for one variable in terms of the other in one of the equations and substitute it into the other equation.
So, q = 17 - h
then substitute it into the second equation:
0.5h + 0.25(17 - h) = 5.50
By solving for h, we get h = 8, then we can substitute it back into the first equation to get q = 9
So, there are 8 half dollars and 9 quarters inside the cup.
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Using traditional methods it takes 8.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 21 students and observed that they had a mean of 8.8 hours with a variance of 1.21. Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Assume the population distribution is approximately normal. Step 1 of 5 : State the null and alternative hypotheses
There is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
What are the hypothesis tested?At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:
[tex]H_0: \mu = 8.5[/tex]
At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:
[tex]H_1: \mu \neq 8.5[/tex]
We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:
|z| = 1.96.
(p-value of 1 - (0.05/2)).
Hence the decision rule is given as follows:
|z| < 1.96 -> do not reject the null hypothesis -> not enough evidence.|z| > 1.96 -> reject the null hypothesis -> enough evidence.What is the test statistic?The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.
The equation is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]
Hence the test statistic is of:
[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}[/tex]
z = 1.24.
|z| < 1.96, hence there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
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PLEASE HELP!!! I WILL MARK BRAINLEST. please help me guys
Wyatt is joining the Shorewood Sharks swim team. He has been taking swimming lessons for several years at the community pool. The community pool is shaped like a rectangular prism and holds 480,000 liters, or 480 cubic meters, of water. It is 12 meters wide and 2 meters deep. The Shorewood Sharks practice in the pool at Shorewood High School. The high school's pool is also shaped like a rectangular prism. It is 15 meters wide, 2.5 meters deep, and holds 937,500 liters, or 937.5 cubic meters, of water. How much longer is the high school's pool than the community pool? Write your answer as a whole number or decimal. Do not round.
Answer:
11.25 m
Step-by-step explanation:
Since the volume of a rectangular prism, V = lwh where l = length, w = width and h = depth,
So, l = V/wh
Now, for the length of the community pool, its volume, V = 480 m³, h = 2 m and w = 12 m
So, l = V/wh
= 480 m³/(12 m × 2 m)
= 480 m³/24 m²
= 20 m
Also, for the length, l' of the Shorewood High School pool, its volume, V' = 937.5 m³, its depth, h' = 2.5 m and its width, w' = 15 m
So, l' = V'/w'h'
= 937.5 m³/(15 m × 2 m)
= 937.5 m³/30 m²
= 31.25 m
So, the difference in length of the pools is l' - l = 31.25 m - 20 m = 11.25 m
So, the high school's pool is 11.25 m longer than the community pool.
Given P(A) = 0.32, P(B) = 0.2 and P(AU B) = 0.366, find the value of
P(An B), rounding to the nearest thousandth, if necessary.
By using formula, P(A n B) = 0.346. Rounded to the nearest thousandth, P(A n B) = 0.346
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In between 0 and 1, the closer the probability is to 1, the more likely the event is to occur. The probability of an event is usually represented by the letter P, followed by the event in parentheses.
What is rounding off?Rounding off is a mathematical operation that is used to reduce the number of digits in a number while maintaining its value within a certain degree of accuracy. When we round off a number, we look at the digit that is immediately to the right of the last digit that we want to keep. If the number is less than 5, we keep the last digit as it is, but if the number is greater than or equal to 5, we add 1 to the last digit.
We can use the formula of conditional probability to find the value of P(A n B).
P(A n B) = P(A U B) - P(A) - P(B) + P(An B)
We know that:
P(A U B) = P(A) + P(B) - P(A n B)
So we can substitute this in the first equation:
P(A n B) = P(A U B) - P(A) - P(B) + P(An B)
P(An B) = P(A U B) - P(A) - P(B) + P(An B)
Now we can substitute the given values:
P(An B) = 0.366 - 0.32 - 0.2 + P(An B)
P(An B) = 0.346 + P(An B)
To find P(An B) we can subtract 0.346 from both sides of the equation:
P(An B) = P(An B) - 0.346
P(An B) = P(An B) - 0.346
So, P(An B) = 0.346
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If the length of the American flag is 1.8 yards, find the hight
Peggy completed 5/6 of the math homework and Al completed 4/5 of the homework. Did Peggy or Al complete more hoof the math homework?
Peggy completed more of the math homework than Al
What does division of fractions mean?
A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.
we know that
In order to be able to compare fractions more easily it is recommended that both have the same denominator
Peggy
5/6 x 5 = 25/30
Al
4/5 x 6 = 24/30
Peggy completed more of the math homework
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A car moving on a road with velocity 30 m/ ,
when brake are applied it velocity decreae at a rate
of 6 meter per econd. Find the ditance it will cover before coming to ret
the distance it will cover before coming to rest is 75m. Solved using the concept of velocity.
What is velocity?Simply said, velocity is the rate of movement in a certain direction. such as the speed of a car driving north on a highway or the pace at which a rocket takes off.
Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. Since acceleration is only the rate at which velocity changes, acceleration is likewise a vector quantity.
Given that,
initial velocity (u) = 30 m/s
acceleration (a) = - 6 m/s²
As we know,
v² = u² + 2as
or, 0 = (30)² + 2 × (-6) × s
or, s = 75 m
Hence, the distance it will cover before coming to rest is 75m
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35 POINTS Complete the sentence.
Statistics is the result of __________ data.
Answer:
analysis (i got to put a bunch of random stuff here cs the limit)
what is the slope and y-intercept for y=1/2+4x
Answer:
- 1/4 slope
y-intercept: 2
pls mark me brainless if im right.
How do you make a truth table?
If we want to create a truth table , for say expression (P ∨ Q)∧(~P⇒Q) , then we will create different columns having the column head as , P , Q , ~P , P ∨ Q,~P⇒Q and (P ∨ Q)∧(~P⇒Q) and then perform the logical operation on them.
Truth table is a medium used to perform logical operations on expressions. These operations consists of Boolean algebra or Boolean functions expressions.
On performing these logical operation we get to know whether the propositional expression is correct or incorrect, based on the input values. This entire process is based on Boolean algebra and the table is made up of rows and columns for one or more input values.
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Nathan had 58 pieces of gum that he wants to make last six days how much can he chew each day so that the gum last him six days between what two whole numbers does your answer lie
Natha can chew between 9 to 10 chewing gum each day so that it could last for 6 days.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Nathan had 58 pieces of gum that he wants to make last six days.
Therefore, The number of chewing gums he can chew is the total number of chewing gums he has divided by the total number of days which is,
= (58/6).
= 9.66 chewing gums but it should be a whole number.
So, Nathan can chew between 9 to 10 chewing gums each day.
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Slope = -7; (4, -30) step by step
Answer:
the equation of the line is y = -7x - 2.
Step-by-step explanation:
To find the equation of the line with slope -7 that passes through the point (4, -30), we can use the point-slope form of a line.
The point-slope form of a line is:
y - y1 = m(x - x1)
where:
(x1, y1) is a point on the line
m is the slope of the line
Substituting the given values, we get:
y - (-30) = (-7)(x - 4)
Expanding the right side, we get:
y + 30 = -7x + 28
Combining like terms, we get:
y = -7x - 2
So the equation of the line is y = -7x - 2.
What is the perimeter of kite KLMN? StartRoot 2 EndRoot + StartRoot 5 EndRoot units StartRoot 14 EndRoot units 2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units 4 StartRoot 5 EndRoot units
HELP PLEEEEAASEEE
Answer:
C. 2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units
Step-by-step explanation:
Answer:
The Answer is C.
Step-by-step explanation:
2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units
The weights of 2-pound bags of Best Dog Food are approximately normally distributed with a given mean ul and
standard deviation o. According to the Empirical Rule, what percentage of the bags will have weights within 3 standard deviations of the mean?
Answer: 99.7%
Step-by-step explanation:
Edg 2020
pls help with this its due today
Using PEMDAS to solve the algebraic expression, the value is 2
What is Mathematical OperationMathematical operations are operations that involve the manipulation of numbers, variables, and/or equations. Examples of mathematical operations include addition, subtraction, multiplication, division, exponentiation, and root extraction.
In this problem, we can use PEMDAS to solve this algebraic expression.
[(3/5 + 0.425 - 0.005) ÷ 0.1] / [30.5 + 1/6 + 3 (1/3)] + [6(3/4) + 5(1/2)] / 26 ÷ 3(5/7)] - 0.05
This will become;
[10.2 / 34] + [12.25 / 7] - 0.05
Dividing and adding the numbers will give us;
(0.3 + 1.75) - 0.05 = 2
The value is 2
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What is a mark up in math?
What is the relationship between multiplying and factoring?
You multiply numbers or expressions to produce a
[Select]
numbers or [Select]
produce it.
✓. You factor a product into the
✓that were multiplied to
Polynomial factoring is the opposite of polynomial multiplication. A polynomial's leftover will be 0 if it is divided by its factors after factoring.
What do "multiply" and "factor" mean?A multiple is a number that is the result of multiplying the provided number by other numbers, as opposed to a factor, which divides the given number perfectly without leaving a remainder.
What connection exists between the factor theorem and the division of polynomials?When a polynomial f(x) is divided by (x - c), and (x - c) is a factor of the polynomial f(x), the remainder of the division is simply equal to 0. Therefore, if the remainder of a division like the ones mentioned above equals zero.
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Which expression is the factored form of X^3 2x^2 5x 6?
The factors of the given equation x³ - 2x² - 5x + 6 is (x - 1)(x + 2)(x - 3) with the help of synthetic division.
Let f(x) = x³ - 2x² - 5x + 6
Substitute x = 1
f(1) = (1)³ - 2(1)² - 5(1) + 6
⇒ f(1) = 1 - 2 - 5 + 6
⇒ f(1) = -1 + 1
⇒ f(1) = 0
As x = 1 is the root of the given equation therefore one of the factor of the given equation is (x-1)
Now use long division method, we get (x² - x - 6) as another factor.
⇒ f(x) = (x - 1)(x² - x - 6)
⇒ f(x) = (x - 1)(x² - 3x + 2x - 6)
⇒ f(x) = (x - 1)(x(x-3) + 2(x-3))
⇒ f(x) = (x - 1)(x - 3)(x + 2)
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Finding the slope ?identify the slope
the slope of the given straight line will be -3
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
Slope is = y2-y1/x2-x1
=9-0/0-3
=-3
Hence the slope of the given straight line will be -3
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1.) Select all shapes that are quadrilaterals. A D C С B H E G F
whats the answer for this question i need help
The answer for it is r = -4 :))