The parts of the triangles Ebony needs to compare so as to make sure both triangles are congruent by SAS are;
[tex] \overline{EG} [/tex] and [tex] \overline{OM}[/tex]What are congruent triangles?Two triangles are said to be congruent when the three sides and three interior angles of one triangle have the same measure as the three sides and the three interior angles of the other triangle.
The given triangles are ∆MON and ∆GEF
The segments and angles that Ebony has ensured are congruent are;
[tex] \overline{EF} \cong \overline{ON}[/tex]
[tex] \angle{ MON} \cong \angle{ GEF}[/tex]
The method by which Ebony intends to use to make sure that the two triangles are congruent, SAS, Side–Angle–Side congruency postulate.
The Side–Angle–Side congruency postulate states that two triangles are congruent if two sides and an included angle in one triangle are congruent to the corresponding two sides and included angle in the other triangle.
Given that the sides that form included angles with [tex] \angle{ MON} [/tex] are [tex] \overline{ON}[/tex] and [tex] \overline{OM}[/tex] and the sides that form an included angle with [tex] \angle{ GEF}[/tex] are [tex] \overline{EF} [/tex] and [tex] \overline{EG} [/tex], the other segments Ebony needs to compare are therefore the segments;
[tex] \overline{EG} [/tex] and [tex] \overline{OM}[/tex]
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If the perimeter of the square is 48 m. Find the area of a
circle whose circumference is the same as the square.
The area of the circle is 201 m².
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.So, the area of the circle:
The perimeter of square: 4aCircumference of the circle: 2πrWe know that 4a = 2πr, now calculate r as follows:
4a = 2πr48 = 2πrr = 48/2πr = 48/2(3.14)r = 48/6.28r = 7.64Rounding off: 8m
Area of circle:
πr²3.14(8)²3.14(64)200.96Rounding off: 201 m²
Therefore, the area of the circle is 201 m².
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a certain type of aluminum screen 2 feet in width has, on the average, three flaws in a 100-foot roll. we assume flaws occur randomly so the number of flaws follow some poisson distribution. what is the probability that the first 40 feet in a roll contain no flaws?
The probability of that the first 40 feet in a roll contain no flaws is ≈ .3012
What is probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
CalculationΘ = μ = [tex]\frac{100 foot}{3 flaws}[/tex]
a ) We assume that the length until the first flaw follows an exponential distribution.
Probability density function of exponential distribution:
f(x) = [tex]\frac{1}{Θ} e^{\frac{-x}{Θ} } = \frac{1}{100/3}e^{-x/(100/3)} = \frac{3}{100}e^{-3x/100}[/tex]
The first 40 feet in a roll of 100 feet contain no flaws if the first flaw occurs after 40 feet.
The probability is the integral over the corresponding interval:
the further calculation has been shown in fig. attached
since equation was not possible to write here
b) We assume that the length until the first flaw follows an exponential distribution.
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If I stated 2 * - 3 OR -10/-5 what steps would you follow to find the factor/quotient and its sign? You may use these examples to explain.
If I stated 2 * - 3 OR -10/-5 then the factor/quotient and its sign is given by -6 and 2
What is a quotient in math?
The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient
What is quotient formula?
The quotient formula is given as follows: Dividend ÷ Divisor = Quotient (if the remainder is zero) The general formula for any division problem is given by: Dividend ÷ Divisor = Quotient + Remainder.
2 * -3 = -6 or -10/-5= 2
Thus the quotient is -6 and 2
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The length of a rectangle is eight more than twice it's width. If the length is less than 34,then what is the width?
Answer:
width < 13
Step-by-step explanation:
let width of the rectangle = x
length = 8 + 2x
according to the question,
8+2x < 34
2x < 34-8
2x < 26
x < 13
Which is an equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3?
The value that will be equivalent to the expression will be 5625³.
What is an expression?It should be noted that an expression is simply used in Mathematics to illustrate or show the relationship between the variables.
The equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3 will be illustrated as:
= (3² × 5⁴)³
= (9 × 625)³
= 5625³
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I NEED HELP ASAP
What is the slope-intercept equation for the linear function represented by the
table?
A. y = -x +4
B. y =
-x-4
C. y = x-4
OD. y=x+4
0
x
2 4 6 8
y -4 -1 258
Answer: C : y = 3/2 - 4
Step-by-step explanation:
Find the Slope (Slope Formula)
(4,2) (6,5)
m = (5-2)/(6-4)
m = 3/2
Find "b"
y = mx + b (Slope intercept form)
2 = 3/2(4) + b
2 = 6 + b
-4 = b
explain 8 - 5 * 3 from a 7th grader
Answer:
-7
Step-by-step explanation:
5 * 3 = 15. 15 - 8 = 7; so, 8 - 15 = -7.
Marine biologist studies the population of seals in research area. how many Seals are in the research area?
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
hello..as fast a possible I need the ans pls
Answer:
I think it's because the triangle sides are isometrics so that's why the sides are equal
the denominator of a fraction is two more than the numerator. if both numerator and denominator are increased by ten, the simplified is 9/10. find the original fraction. (Do not simplify).
Give to each part of the fraction a variable (a letter)
Numerator: n
Denominator: d
the denominator of a fraction is two more than the numerator:
[tex]d=n+2[/tex][tex]\frac{n}{d}=\frac{n}{n+2}[/tex]both numerator and denominator are increased by ten, the simplified is 9/10:
[tex]\frac{n+10}{n+2+10}=\frac{9}{10}[/tex]Use the equation above to find the value of n:
[tex]\begin{gathered} 10(n+10)=9(n+12) \\ 10n+100=9n+108 \\ 10n-9n=108-100 \\ n=8 \end{gathered}[/tex]As n is equal to 8 find the value of d:
[tex]\begin{gathered} d=n+2 \\ d=8+2 \\ d=10 \end{gathered}[/tex]The original fraction is:
[tex]\frac{8}{10}[/tex]Write the perimeter of the triangle as a simplified polynomial. Then factor the polynomial.
Answer:
4x² + 29x + 7 = (4x + 1)(x + 7)
Step-by-step explanation:
Simplify the polynomial:Like terms are terms with same variable and same power.
Perimeter = sum of all the sides
= 3x² + 1 + 15x + 6 + x² + 14x
= 3x² + x² + 15x + 14x + 1 + 6
Combine like terms,
= 4x² + 29x + 7
Factorize:
Sum = 29
Product = 4*7 = 28
Factors = 1 , 28 {28 + 1 = 29 & 28*1 = 28}
Rewrite the middle term using the factors,
= 4x² + x + 28x + 7
= x(4x + 1) + 7(4x + 1)
= (4x + 1)(x + 7)
Find the values of x and y.
Answer:
x=71 y=109
Step-by-step explanation:
a couple has four children. neither the father nor the mother is bald; one of the two sons is bald, but neither of the daughters is bald. (a) if one of the daughters marries a nonbald man and they have a son, what is the chance that the son will become bald as an adult? (b) if the couple has a daughter, what is the chance that she will become bald as an adult?
If one of the daughters marries a non-bald man and they have a son, the chance that the son will become bald as an adult is 0%
If the couple has a daughter, the chance that she will become bald as an adult is 0%
In the question, we have been given that the neither the father nor the mother is bald, and out of the four children only one son is bald, but the other son and the two daughters are not bald, now we solve the following:
Part a
A chance that the son will become bald as an adult:
If the daughter has no bald gene (XX), and she marries a non bald man then there is 0% chance that the son will become bald as an adult because neither the mom nor the dad has the baldness gene
Part b
The chance that she will become bald as an adult:
If the daughter having a bald gene ([tex]X^{b} X[/tex]) marries a non bald (XY)man then also there is a 0% chance that the daughter will be bald as an adult. As the baldness is a recessive trait, for the daughter to be bald she needs to have two baldness gene( one from father and one from mother). And since this is not the case the daughter might have baldness gene but the phenotype will be non-bald.
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I NEED HELP FAST
image is the question :)
Garcia's bike rentals, it cost $38 to rent a bike for 9 hours. How many hours of bike use does the customer get per dollar. If necessary, round the answer to the nearest hundredth
From the question, we were told that Garcia's bike rentals cost $38 to rent bike for 9 hours.
We are to find how many hours will a customer use the bike per dollar.
This can also be likened to calculating miles per gallon.
if i can drive 300 miles on 10 gallons of gas then my miles per gallon is 300/10 = 30 mpg.
So, hours per dollar is also a division problem too.
(9 hours)/($38)
= 9/38
= 0.2368
= 0.24 hours per dollar (to the nearest hundredth)
Find the volume of the cylinder (rounded to the nearest tenth).9 in.3 in.
We have the next formula to calculate the volume of the cylinder
[tex]V=\pi r^2h[/tex]where
r is the radius
h is the height
in our problem
r=3in
h=9in
we substitute the values
[tex]V=\pi(3)^2(9)=254.46in^3[/tex]the volume round to the nearest tenth is V=254.5 in ^3
solve each linear equation 7+2x=4x-3
Answer:
Simplifying
7 + 2x = 4x + -3
Reorder the terms:
7 + 2x = -3 + 4x
Solving
7 + 2x = -3 + 4x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4x' to each side of the equation.
7 + 2x + -4x = -3 + 4x + -4x
Combine like terms: 2x + -4x = -2x
7 + -2x = -3 + 4x + -4x
Combine like terms: 4x + -4x = 0
7 + -2x = -3 + 0
7 + -2x = -3
Add '-7' to each side of the equation.
7 + -7 + -2x = -3 + -7
Combine like terms: 7 + -7 = 0
0 + -2x = -3 + -7
-2x = -3 + -7
Combine like terms: -3 + -7 = -10
-2x = -10
Divide each side by '-2'.
x = 5
Simplifying
x = 5
need help again with a question
Answer: x = 58
Step-by-step explanation:
The angles are alternating interior angles. This means that the angles are equal.
So x = 58
scores on the wechsler adult intelligence scale for the 20 to 34 age group are approximately normally distributed with mean 110 and standard deviation 15. how high must a person score to be in the top 5% of all scores? enter your answer as a whole number.
The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
What is defined as the normal distribution?A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder taper off symmetrically toward any extreme.A histogram inside a normal distribution curve is sometimes used to design the curve.The formula for the normal distribution is;
z = (x - μ)/σ
where,
z = z- score, taken fro tableMean μ = 110Standard deviation σ = 15Sample mean x.If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.
In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.
z = 1.7
Put the value in formula ad find x.
1. 7 = (x - 110)/15
x = 25.5 + 110
x = 135.5
x = 136 (whole number)
Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
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2-3x + 4 + x = -2x + 1
Answer:
No solution
Step-by-step explanation:
2- 3x + 4 + x = -2x + 1
2 -3x + 4 + x = -2x + 1
6 -3x + x = -2x + 1
6 -3x + x = -2x + 1
6 -2x = -2x + 1
6 -2x = -2x + 1
move -2x to the right by adding 2x on both sides
6 -2x = -2x + 1
+2x +2x
6 = + 1
is 6 equal to 1?
No, so No solution
How do you write 3 and 6/25 as a decimal
Answer: 1.44
Step-by-step explanation:
The fraction 3 and 6/25 is equal to 1.44 when written as a fraction.
Answer:
3.24
Step-by-step explanation:
6/25 can be read as 6 divided by 25, which is 0.24. Add that to 3 and you get 3.24.
what is the Riemann Hypothesis??
Answer:
lie on a certain vertical straight line
Step-by-step explanation:
In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics.
when an integer is subtracted from 8 times the next consecutive integer, the difference is 71. Find the vale of the greater integer.
The value of the greater integer will be 10.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The algebraic expression is,
'' An integer is subtracted from 8 times the next consecutive integer, the difference is 71.''
Now,
Let a number = x
Then, Its consecutive number = (x + 1)
So, We can formulate;
⇒ 8 (x + 1) - x = 71
Solve for x as;
⇒ 8x + 8 - x = 71
⇒ 7x + 8 = 71
⇒ 7x = 71 - 8
⇒ 7x = 63
⇒ x = 9
Thus, The value of greater number = x + 1
= 9 + 1
= 10
Therefore, The value of the greater integer will be 10.
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Can you simplify 6:4 ?
yes, it is the same than 3:2. And we can not simplify it more
-9^2 x 3
evaluate the experssion!!
Answer:
243
Step-by-step explanation:
-9^2 = -9 * -9 = 81
81 * 3 = 243
A table is made using the following two patterns.
Pattern x: Starting number: 3, Rule: add 3
Pattern y: Starting number: 6, Rule: add 6
Complete the table for the given patterns.
And then it asks to graph the points from 3 points
The rules of the patterns are 3 + 3x and 6 + 6y
How to complete the pattern?The patterns are given as:
Pattern x: Starting number: 3, Rule: add 3Pattern y: Starting number: 6, Rule: add 6For pattern x, we have the following highlights:
Start = 3
Rule = Add 3
This means that the nth term of pattern x is:
Pattern x = 3 + 3x
For pattern y, we have the following highlights:
Start = 6
Rule = Add 6
This means that the nth term of pattern y is:
Pattern y = 6 + 6y
The complete tableFor pattern x, set x = 0, 1, 2 and 3
So, we have
3 + 3x = 3 + 3(0) = 3
3 + 3x = 3 + 3(1) = 6
3 + 3x = 3 + 3(2) = 9
3 + 3x = 3 + 3(3) = 12
For pattern y, set y = 0, 1, 2 and 3
So, we have
6 + 6x = 6 + 6(0) = 6
6 + 6x = 6 + 6(1) = 12
6 + 6x = 6 + 6(2) = 18
6 + 6x = 6 + 6(3) = 24
Next, we plot the graphs of both patterns (see attachment) where the blue line represents pattern 1, and the other represents the second pattern
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Given the frequency table, what percentage of the students that like rap are also in grades 9–10? Round to the nearest whole percent. Show work
A. 16%
B. 38%
C. 40%
The percentage of the students that like rap are also in grades 9–10 is 32%.
Determining the percentage of rap in grades 9-10Given data:
Grade 9-10 for Rap = 40
Row total for grade 9-10 = 125
Now let determine the percentage of rap in grades 9-10 using this formula
Percentage of rap in grades 9-10 = Grade 9-10 for Rap / Row total for grade 9-10
Let plug in the formula
Percentage of rap in grades 9-10 = 40 /125
Percentage of rap in grades 9-10 = 0.32 × 100
Percentage of rap in grades 9-10 = 32%
Therefore we can conclude that 32% is the percentage of rap grade 9-10.
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would you put a closed dot or an open dot on a number line for n > -8?
Answer:
a opened because a closed means that number ond more
Step-by-step explanation:
Wasif spent 1/3 of his income on housing and 2/5 on daily expenditure and save the rest if he save 24600 what was his income altogether
Answer:
61500
Step-by-step explanation:
1/3 = 3/15
2/5 = 6/15
1 - 3/15 - 6/15 = 6/15
6/15 = 24600
24600 ÷ 6 × 15 = 61500
Answer:
92250
Step-by-step explanation:
Forming algebraic equation and solving:
Let the income = x
Amount spent on housing = (1/3) of the income
[tex]\sf = \dfrac{1}{3}x[/tex]
Amount spent of daily expenditure = (2/5) of the income
[tex]\sf =\dfrac{2}{5}x[/tex]
Income = Savings + housing expenditure + daily expenditure
Income - housing expenditure - daily expenditure = savings
[tex]\sf x - \dfrac{1}{3}x-\dfrac{2}{5}x=24600\\\\\\\dfrac{x*15}{1*15}-\dfrac{1*5}{3*5}x-\dfrac{2*3}{5*3}x = 24600\\\\\\[/tex]
[tex]\sf \dfrac{15}{15}x-\dfrac{5}{15}x-\dfrac{6}{15}x = 24600\\\\\\\dfrac{(15 -5 - 6)}{15}x = 24600[/tex]
[tex]\sf \dfrac{4}{15}x = 24600[/tex]
[tex]\sf x = 24600 *\dfrac{15}{4}\\\\ x = 6150*15[/tex]
Income = 92250