The two side lengths are congruent, and their opposite angles are congruent, and the hypotenuse is the length of either leg times the square root of two, √2.
A 45° 45° 90° triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.
properties of 45°-45°-90°:
It's the only possible right triangle that is also an isosceles triangle, and it has the smallest ratio of the hypotenuse to the sum of the legs.It has the greatest ratio of the altitude from the hypotenuse to the sum of the legs.To know more about 45° 45° 90° triangle:
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find the measure indicated in each parallelogram
Answer:
Step-by-step explanation:
WX≅VY
VY = 7
CD≅BE
BE = 13
A manufactor makes integrated circuits that each have a resistance layer with a target thickness of 200 units. A circuit won't work well if this thickness varies too much from the target value. These thickness measurements are approximately normally distributed with a mean of 200 units and a standard deviation of 12 units. A random sample of 17 measurements is selected for a quality inspection. We can assume that the measurements in the sample are independent. What is the probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value?Choose 1 answer:A) 0.16B) 0.32C) 0.40D) 0.80E) We cannot calculate this probability because the sampling distribution is not normal.
The probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.
What is the Central Limit Theorem?
The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
We can use the Central Limit Theorem to determine that the sampling distribution of the mean thickness of a random sample of size 17 from a population with a mean of 200 units and a standard deviation of 12 units will be approximately normal with a mean of 200 units and a standard deviation of (12 units)/√17 = 2.8 units.
Given that the mean thickness in these 17 measurements x is farther than 3 units away from the target value, we can use the standard normal table to find the probability.
Let's call X = mean thickness,
if X > 203, we have P(X>203) = P(Z> (203-200)/2.8) = P(Z>1.071) = 0.15
if X < 197, we have P(X<197) = P(Z< (197-200)/2.8) = P(Z<-1.071) = 0.15
Hence, the probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.
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A submarine must descend at an average rate of at least 12 feet per minute for 5 minutes. The table shows how many feet the submarine descends
in the first 4 minutes. How many feet must the submarine descend in the fifth minute?
Submarine must descend 17 feet in the 5th minute.
What is the average of the data?
Only numerical variables, whether continuous or discrete, can be used to calculate the mean. It is calculated by merely dividing the total number of values in a data set by the sum of all the values in the data set. A frequency table of data or raw data can both be used for the calculation.
Let the distance descended by submarine in 5th minute = x feet
Average distance descended by the submarine
= (Total distance distended/ Duration or time)
= (6 + 8 + 14 + 15 + x) / 5
= (43 + x) / 5
Statement given in the question → "Submarine must descend at an average rate of at least 12 feet per minute"
So the inequality for the statement will be,
(43 + x) / 5 ≥ 12
43 + x ≥ 60
x ≥ 17
Therefore, submarine must descend 17 feet in the 5th minute.
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What is the formula for a isosceles triangle?
The formula for an isosceles triangle is A = (1/2) * b * h, where b is the base, h is the height, and A is the area.
The formula for an isosceles triangle is A = (1/2) * b * h. This formula is used to calculate the area of an isosceles triangle. To use the formula, you need to know the base, b, and the height, h, of the triangle. The base is the length of any one of the two equal sides of the isosceles triangle, and the height is the distance from the base to the opposite vertex. Once you have these measurements, you can plug them into the formula to calculate the area of the triangle. The formula multiplies the base, b, by the height, h, and then divides the product by two. This will give you the area of the triangle, A.
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Abby works in the sales department. This month the company is offering a 3-week paid vacation to every employee who sells 230% of the amount sold last month. If Abby sold $480 products last month, how much does she need to sell this month to earn the vacation
well, what's 230% of $480?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{230\% of 480}}{\left( \cfrac{230}{100} \right)480}\implies \text{\LARGE 1104}[/tex]
What are the coefficients of the equation 3x 6y 13 *?
In the equation [tex]3x-6y=-13[/tex] , the coefficient of equation are , coefficient of [tex]x[/tex] is [tex]3[/tex] and the coefficient of [tex]y[/tex] is [tex]-6[/tex] .
What are Coefficients ?
The Coefficients are defined as a number that is placed with a variable. It is a integer that is multiplied by the variable and written next to it.
In simpler words, we can say that ; a coefficient is a multiplicative factor in the terms of a polynomial, a series, or any expression.
The variables that do not have a number written with them are assumed to have 1 as their coefficient.
For example, in the expression [tex]3x[/tex] , the coefficient of [tex]x[/tex] is [tex]3[/tex] , but in the expression [tex]x^{2} +3[/tex], [tex]1[/tex] is the coefficient of [tex]x^{2}[/tex].
The equation to find the coefficient is given as [tex]3x-6y=-13[/tex] ,
we see that , the numerical part with [tex]x[/tex] is [tex]3[/tex] and with [tex]y[/tex] is [tex]-6[/tex] ;
Therefore , the coefficient of [tex]x[/tex] is [tex]3[/tex] and [tex]y[/tex] is [tex]-6[/tex] .
The given question is incomplete , the complete question is
What are the coefficients of the equation 3x -6y = - 13 ?
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i) a butcher has some hamburger that is 80% lean and some that is 88% lean. he wishes to make 800 ponds of a burger mix that is 83% lean. how much of each type should he use?
by splanation, in be clearly what he taking about. the hamburger, usually. is 1/4 p.1/2 p. in triple hamburger on 4 by 4
The number of used hamburgers that is 80% lean is = 500
and the number of used hamburgers that is 88% lean is = 300.
Let the number of hamburger that is 80% lean be = x.
So the number of hamburger that is 88% lean is = 800 - x
According to question after the mixing all these the total percentage of lean in 800 ponds of burgers is 83%.
So, the suitable mathematical equation is,
80% of x + 88% of (800 - x) = 83% of 800
(80/100) x + (88/100) * (800 - x) = (83/100) * 800
80x + 88 (800 - x) = 83 * 800 [Multiplying 1000 with both sides]
80x + 88 * 800 - 88x = 83 * 800
88x - 80x = 88 * 800 - 83 * 800 = 800 (88 - 83) = 5 * 800
8x = 800 * 5
x = (800 * 5)/8 = 100 * 5 = 500
Hence the number of hamburger with 80% lean is 500 and the number of hamburger with 88% lean is = (800 - 500) = 300.
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can someone please help with this question i’ve been stuck on it for an hour thanks
Answer:
110° and 215°
Step-by-step explanation:
to measure the bearing from one point to another
the bearing is measured clockwise from a north line.
(a)
clockwise from the north line N at C to D is 110°
(b)
clockwise from the north line N at C to D is 215°
At what ordered pair will the function
f ( x ) = √ x + 2 - 2
begin on the coordinate plane?
( ? , ?)
Answer:(-2,-2)
Step-by-step explanation:
The radical has a value of 0 when x = -2. At that point, the function value is ...
f(-2) = √(-(-2)-2) -2 = √(0) -2
f(-2) = -2
What is the length of the hypotenuse of a 45 45 90 triangle if the length of the leg is 5?
The length of the hypotenuse will be 5√2 = 7.07
The triangle specified in the question is right-angled, one angle is mentioned to be 90°. It is also an isosceles triangle since both other angles are equal. if both angles are equal, both sides will also be equal.
So the length of both equal sides = 5 cm
Pythagoras' theorem tells us about the relationship between the three sides of a right-angled triangle. It states that the square of the hypotenuse of the right-angled triangle will be equal to the sum of squares of the other two sides. If a, b, and c are the sides
c² = a²+ b²
c = √(a²+b²)
According to Pythagoras' theorem, Hypotenuse = √base²+ alt²
Hypotenuse = √5²+5²
= 5√2
= 7.07 cm
So the length of the hypotenuse is 5√2 = 7.07 cm.
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Last year there
were 620 7th grade
students. This year
enrollment has
increased by 105%.
How many 7th
grade students are
there this year?
Answer: 1271
Step-by-step explanation:
620 + (105% × 620) =
620 + 105% × 620 =
(1 + 105%) × 620 =
(100% + 105%) × 620 =
205% × 620 =
205 ÷ 100 × 620 =
205 × 620 ÷ 100 =
127,100 ÷ 100 =
1,271
Mike has $21 to spend at the mall. He spends all of his money on bracelets for his sisters. Bracelets cost $3 each. How many bracelets dose he buy?
Answer:
7
Step-by-step explanation:
What is a real solution example?
Solutions refers to the answer to the problem, The example of real solution can be the solution for the value of 'x' in a equation.
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
example:
x+2=0
x=-2
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At what point does the graph of the linear equation 2x 3y =- 15?
The graph of the linear equation 2x - 3y = -15 is a line that passes through the point (-5, 5), and has a slope of 2/3.
The linear equation
2x - 3y = -15
can be written in the form
y = mx + b,
where m is the slope and b is the y-intercept. To find the slope of this equation, we can rearrange the equation to be in the form y = mx + b, which gives us
y = (2/3)x - 5.
This means that the slope of the line is 2/3. To find the y-intercept, we can plug in 0 for x and solve for y. This gives us
y = -5.
Therefore, the graph of this equation is a line that passes through the point (-5, 5) and has a slope of 2/3.
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Jackson is trying to find the density, in g/cm", of a block of wood.
The block of wood is in the shape of a cuboid.
He measures
the length as 13. 2 cm, correct to the nearest mm
the width as 16. 0 cm, correct to the nearest mm
the height as 21. 7 cm, correct to the nearest mm
He measures the mass as 1970 g, correct to the nearest 5 g.
By considering bounds, work out the density of the wood.
Give your answer to a suitable degree of accuracy.
You must show all your working and give a reason for your final answer.
The density of the wood is between 0.35 g/cm^3
The density of a substance can be calculated using the formula:
density = mass / volume
To calculate the volume of the cuboid, we can use the formula:
volume = length x width x height
So, using the measurements provided:
volume = 13.2 cm x 16.0 cm x 21.7 cm = 5541.44 cm^3
To calculate the density of the wood, we divide the mass by the volume:
density = 1970 g / 5541.44 cm^3
We can convert cm^3 to g/cm^3 by converting the volume to g
1cm^3 = 1g/cm^3
density = 1970 g / 5541.44 g/cm^3
density = 0.3555 g/cm^3
However, as the measurements provided have a degree of uncertainty, we should consider bounds to find the range of possible densities.
The lower bound for the length is 13.2 cm - 0.1 cm = 13.1 cm
The upper bound for the length is 13.2 cm + 0.1 cm = 13.3 cm
The lower bound for the width is 16.0 cm - 0.1 cm = 15.9 cm
The upper bound for the width is 16.0 cm + 0.1 cm = 16.1 cm
The lower bound for the height is 21.7 cm - 0.1 cm = 21.6 cm
The upper bound for the height is 21.7 cm + 0.1 cm = 21.8 cm
The lower bound for the mass is 1970 g - 5 g = 1965 g
The upper bound for the mass is 1970 g + 5 g = 1975 g
We can now use these bounds to calculate the range of possible densities:
Density lower bound = 1965 g / (13.3 cm x 16.1 cm x 21.8 cm) = 0.350 g/cm^3
Density upper bound = 1975 g / (13.1 cm x 15.9 cm x 21.6 cm) = 0.360 g/cm^3
So the density of the wood is between 0.35 and 0.36 g/cm^3 to one decimal place.
So the density is 0.35 g/cm^3 with an uncertainty of 0.01 g/cm^3
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Find the measure of MN
Answer:
The measure of arcMN is 60°
Step-by-step explanation:
All the way around the circle is 360°. Two marked arcs are 100° and 140°. AngleMON and AngleNOP are marked equal, which means that ArcMN and ArcNP are also equal. So we can write an equation:
100+140 + x+x =360
combine like terms.
240 + 2x = 360
subtract 240.
2x = 120
divide by 2
x = 60
ArcMN is 60°
How do you calculate F G and G of f?
You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).
What is function ?
A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.
Have given ,
Two functions , f(x) and g(x)
The composition of two functions g and f is the new function we get by performing f first, and then performing g. For example, if we let f be the function given by f(x) = x2 and let g be the function given by g(x) = x + 3, then the composition of g with f is called gf and is worked out as gf(x) = g(f(x)) .
So , You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).
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The sun of a number, x, and 1/2 is equal to 4. What set of equations correctly repaints x
The set of equations correctly representing x are as follows:
(x + 1/2) and (x = 7/2).
What exactly is a set or group of equations?A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is one that has two equations as well as two variables. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.
What is the name of an equation system?Systems of equations in mathematics are a collection of relationships between different unknown variables that can be stated in terms of algebraic expressions. They are also known as simultaneous equations. Graphing, substitution, as well as elimination by addition, are methods that can be used to find the solutions to a basic system of equations.
According to the given information:Sum means addition (+).
Given that sum of a number, x and 1/2 is 4.
This means the adding two numbers
x+1/2=4
Now make x the subject of formula,
x=4-1/2
Finding the L.C.M = 8-1/2
x=7/2
∴ x=3 1/2
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How do you draw a logarithmic graph?
Choose the range of values for the x-axis and the y-axis , Plot the points on the graph, using the logarithmic formula , Connect the points with a smooth curve and Label the axes and add any other details you want to include.
1. Choose the range of values for the x-axis and the y-axis. Select the minimum and maximum values for both the x-axis and the y-axis.
2. Plot the points on the graph, using the logarithmic formula. Use the formula log(x) = y to calculate the points that should be plotted on the graph. For example, if the x-axis range is from 1 to 10, and the y-axis range is from 0 to 10, then the first point would be (1,0).
3. Connect the points with a smooth curve. Once all the points have been plotted, use a ruler or a graphing calculator to connect them with a smooth curve.
4. Label the axes and add any other details you want to include. Use a ruler or a graphing calculator to label the axes and add any other details you want to include, such as a title, a legend, or a grid.
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How do you solve systems by substitution step by step?
Answer:
1.Solve one of the equations for either variable.
2.Substitute the expression from Step 1 into the other equation.
3.Solve the resulting equation.
4.Substitute the solution in Step 3 into one of the original equations to find the other variable.
5.Write the solution as an ordered pair.
6.Check that the ordered pair is a solution to both original equations.
Step-by-step explanation:
somebody help please
Answer:
Step-by-step explanation:
because HA⊥HR, HR⊥DR, so HA ║ DR, then we know ∠DHR=∠ARH,
we konw, AR=HD, They have a common segment HR, as well as the same angle，so HRA≅RHD
Wenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:
# of movies Frequency
0 4
1 9
2 5
3 6
4 1
a) Find the sample standard deviation, s. (Round your answer to two decimal places. )
b) Find the sample mean x^-
Answer: 35
Step-by-step explanation:
: i took this quiz before :)
32(43x−23) is equivalent to
Answer:
1376x-736
Step-by-step explanation:
Take 32 and multiply it by 43. By multiplying vertically, distribute the multiplication of 3 (from 43) times both the 2 and 3 of 32 (right to left)
3 x 2=6; 3 x 3=9:
32
x
43
--------
96
Then, distribute the multiplication of 4 (from 43) times both the 2 and 3 of 32 (right to left) and leave a zero under the last number of your previous answer while moving the distribution of numbers forward.
4 x 2=8; 4 x 3=12
32
x
43
--------
96
+
1280 <----(this is the zero you must leave under your previous set)
After distributing each number of 43 to each number of 32 while multiplying, add your answers together vertically from right to left and bring down the x:
96
+
1280
----------
1376x
Now do the same for 32 x -23 after learning vertical multiplication to get -736
Your final answer put together is 1376x-736
Can you help me with this
Answer:
slope = 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line
m = [tex]\frac{4-0}{1-(-1)}[/tex] = [tex]\frac{4}{1+1}[/tex] = [tex]\frac{4}{2}[/tex] = 2
Answer: The slope is 2.
Step-by-step explanation: To find the slope of a line, we first need to pick two points on a line. To solve this, I picked points (-2, -2) and (1, 4). The slope is rise over run, so you need to find the rise and run and divide.
We need to go 6 spaces up from (-2, -2) to get to (1, 4). This is our rise. Then, we go 3 spaces to the right. That is our run. 6 / 3 is 2, so that's your slope. Notice that if you cannot divide the rise and run into a whole number, keep it as a fraction instead.
Let me know if this is right! :)
How many terms are there in the expression 2p 3 3p 2 4p 7 *?
The total number of terms which are in the polynomial expression –2p³ – 3p² + 4p + 7 is 4 terms.
A polynomial expression is made up of multiple terms joined either by addition , subtraction or multiplication or division.
The given expression is
–2p³ – 3p² + 4p + 7
If we will break them down in simpler terms we will get ,
–2p³, – 3p², + 4p, + 7
Therefore, number of terms are found to be 4
The terms of an algebraic expression are referred to as the the components of that expression . An algebraic expression can have one or more terms.
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. If a population of college student ages is skewed right, then this indicates: a. there are a greater number of older students b. the modal age is greater than the median age c. as the age of a student increases, the frequency of the student ages increases. d. there are more younger students within the population e. not enough information
The correct answer is c. as the age of a student increases, the frequency of the student's ages increases.
A skewed right population means that the data is distributed in such a way that the majority of the values are on the right side of the data set. In the case of a population of college students, this would mean that there is a greater frequency of older students (those in their late twenties or older) than younger students. As the age of a student increases, the frequency of the student's ages increases.
Option a. there are a greater number of older students is also correct, but it is not complete.
Option b. the modal age is greater than the median age is not correct, as the modal age is the most common age in the population and the median age is the middle value of the population, and there is no relationship between them.
Option d. there are more younger students within the population is not correct as a skewed right population indicates the opposite.
Option e. not enough information is not correct as the question is providing enough information to make a conclusion.
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Can someone please help me on this & I’ll reward you afterwards
Answer: 4y (4y^2-2y-5)
Step-by-step explanation:
Chose the best 3 options
The beat three options are: The slope of the line is 1/5, (2) The possible equation if the line is y=1/5x, (3) The slope and the y intercept are the same
What is slope of a line?Lope is the rate of change of y with respect to x. slope is also the increase in y over increase in x vice versa
Slope is denoted by rise/run
The Possible solutions from the graph are:
The slope and y-intercept are the sameThe possible equation of the line is y=1/5xThe slope of the line is 1/5Taking any two points on the graph : (4, 1) and -4, -1,)
We can find the slope as (1--1)/4--4
Therefore, the Slope = 2/3≡1/5
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What is equal function with example?
The given two functions are said to be equal functions if and only if both it's domain and range are equal.
In mathematics we use functions to show the relation between two objects.
They are used in various aspects of real life. The domain of a function is known as all the possible input values which can be given to the function.
The range of the function is the set of all the possible outputs which can be obtained from a function. We also have co-domain of a function which can be defined as the set of outputs for a relation or function , it can be equal to the range.
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Which system of equations is represented by the graph?
one parabola opening upwards and one parabola opening downwards intersecting at points (3, 9) and (-3, 9)
y = x2 + 3x
y = –x2 + x + 18
y = x2
y = –x2 +18
y = x2
y = x2 + 18
y = x2
y = –x2 – x – 18
Answer:
Blue: y = x²
Red: y = -x² + 18
Step-by-step explanation:
The blue parabola opens upwards, therefore the term in x² is positive.
The red parabola opens downwards, therefore the term in x² is negative.
The x-value of the vertices of both parabolas is x = 0.
Therefore, the equations of both parabolas will not have a term in x.
The y-intercept of the blue parabola is also the y-value its vertex: y = 0.
The y-intercept of the red parabola is also the y-value its vertex: y = 18.
Therefore, the equation for each parabola is:
Blue: y = x²Red: y = -x² + 18To check, substitute x = ±3 into both equations:
Blue
[tex]x=3 \implies y=(3)^2=9[/tex]
[tex]x=-3 \implies y=(-3)^2=9[/tex]
Red
[tex]x=3 \implies y=-(3)^2+18=9[/tex]
[tex]x=-3 \implies y=-(-3)^2+18=9[/tex]
Answer:
y = x2
y = –x2 +18
Step-by-step explanation:
I got it right on the test.