In order to increase the likelihood that a blue marble would be drawn at random to 3/4, we must thus add 32 more blue marbles.
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. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.
Here,
Let the number of blue marbles added be x,
Probability=3/4
Total marbles=20
Number of blue marbles=7
(7+x)/(20+x)=3/4
4(7+x)=3(20+x)
28+4x=60+3x
x=60-28
x=32
So, we need to add 32 more blue marbles to make the probability of randomly drawing a blue marble be 3/4.
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For linear function f.f(2)= 0 and f(4)=-6.
Write function f in slope-intercept
How do you find the slope of the line when you have 2 points?
Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].
What is the slope of line?
The slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be easily determined by finding the difference between the coordinates of the points.
The slope is usually represented by the letter [tex]m[/tex].
Here given that,
The linear function [tex]f(2)= 0[/tex] and [tex]f(4)=-6[/tex].
Let the linear function is
[tex]y=mx+b[/tex]
[tex]x=2,y=0[/tex]
Then
[tex]0=m(2)+b\\\\2m+b=0[/tex] .......[tex](1)[/tex]
And for
[tex]f(4)=-6\\x=4,y=-6[/tex]
[tex]-6=m(4)+b\\\\4m+b=-6[/tex] ......[tex](2)[/tex]
Solving equation [tex](1)[/tex] and [tex](2)[/tex], we get
In equation [tex](1)[/tex]
[tex]b=-2m[/tex] ........[tex](*)[/tex]
Substitute [tex]b=-2m[/tex] in equation [tex](2)[/tex]
[tex]4m-2m=-6\\\\2m=-6\\\\m==\frac{6}{2}\\\\m=-3[/tex]
Put [tex]m=-3[/tex] in [tex](*)[/tex] equation
[tex]b=2m\\\\b=-2(-3)\\\\b=6[/tex]
Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].
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Fred deposits $6,500 in a saving account that pays 0.5% interest, compounded quarterly. Round each answer to the nearest cent.
a. Find the first quarter's interest.
b. Find the first quarter's ending balance.
c. Find the second quarter's interest.
d. Find the second quarter's ending balance.
e. Find the third quarter's interest.
f. Find the third quarter's ending balance.
g. Find the fourth quarter's interest.
h. What is the balance at the end of one year?
i. How much interest does the account earn in the first year?
The amount of interest earned quarterly at 0.5% interest rate compounded quarterly are;
a. Interest for the first quarter = $8.125
b. First quarter ending balance = $6,508.125
c. Interest for the second quarter = $8.13515625
d. Second quarter ending balance = $6,516.26015625
e. Interest for the third quarter = $8.1432520325
f. Third quarter closing balance = $6,524.40548145
g. Interest for the fourth quarter = $8.15550685975
h. The amount of interest earned in a year is about $32.56
What is an interest earned on an amount?
An interest is the amount a borrower pays to a lenders as to make use of the lender's funds.
The amount Fred deposited, P = $6,500
The interest paid by the account, r = 0.5% compounded quarterly
a. The first quarter interest can be found by the formula;
C.I. = P[tex](1+ r/4)^{4 . 1/4}[/tex] - P
Therefore
C.I. = 6500 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6500 = 8.125
b. The first quarter ending balance is therefore;
A = P + C.I.
A = $6,500 + $8.125 = $6,508.125
c. The second quarter's interest can be found from the formula;
C.I. = 6508.125 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6508.125 = 8.13515625
The second quarter's interest is $8.13515625
d. The second quarter ending balance is therefore;
A = $6,508.125 + $8.13515625 = $6,516.26015625
The second quarter ending balance is $6,516.26015625
e. The third quarters interest is therefore;
C.I. = 6516.26015625 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6516.26015625 = 8.1432520325
The third quarter's interest is about $8.1433
f. The third quarter's ending balance is therefore;
A ≈ $6516.26015625 + $8.1432520325 = $6,524.40548145
The third quarter's ending balance is $6,524.40548145
g. The fourth quarter's interest can be found as follows;
C.I. = 6524.40548145 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6524.40548145 = 8.15550685975
The fourth quarter's interest is; $8.15550685975
h. The balance at the end of one year is therefore;
Balance = C.I. fourth quarter + Principal for the fourth quarter
Therefore;
Balance = $6,524.40548145 + $8.15550685975 = $6,532.56098831
i. The interest the account earns in a year is therefore;
$6,532.56098831 - $6,500 = $32.5609883
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Verify the trig identity and show all expanded steps
We have proved that tanθ.cosθ + cotθ.sinθ = sinθ + cosθ.
What are trigonometric identities?
Trigonometric Identities are the equalities that involve trigonometry functions and hold true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.
tan∅ = sin∅/cos∅
cot∅ = cos∅/sin∅
Given:
tanθ.cosθ + cotθ.sinθ = sinθ + cosθ
Now LHS = tanθ.cosθ + cotθ.sinθ
= (sinθ/cosθ)cosθ + (cosθ/sinθ)sinθ
= sinθ + cosθ
LHS = RHS
Hence, we have proved that tanθ.cosθ + cotθ.sinθ = sinθ + cosθ.
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1) In the figure below Zy Zz and segment
AB I CD.
What is the length of AE?
F. 18
G. 20
H. 24
J. 30
Answer:
F
Step-by-step explanation:
15/10 = x+12/12
180=10x+120
x=6
x+12=18=AE
Evaluate the expression for a = 3, b = 2, and c = 4.
2a - b + c
Answer:
The expression is 2 * 3 - 2 + 4 = 8.
Step-by-step explanation:
In this expression, the variables a, b, and c are given specific values. Substituting these values into the expression, we have 2 * 3 - 2 + 4, which simplifies to 8.To evaluate an expression, we substitute the given values for the variables and carry out the operations according to the order of operations (i.e. parentheses, exponents, multiplication and division, addition and subtraction). In this case, the expression is already fully simplified, so we don't need to do any further calculations.
Mrs. Smith is planning a field trip for all of the fourth grade students. There are 7 classes of
Fourth graders with 20 students in each class. If 30 students fit on a bus, how many buses will
Mrs. Smith need to reserve for the trip?
Answer:
5 buses
Step-by-step explanation:
Mrs. Smith will need to reserve buses for 7 classes of Fourth graders, with 20 students in each class, for a total of
7 * 20 = <<7*20=140>>140 students.
Since 30 students fit on a bus, Mrs. Smith will need to reserve
140 / 30 = <<140/30=4.67>>4.67 buses.
Since Mrs. Smith can't reserve a partial bus, she will need to reserve 5 buses for the trip.
Answer: 5 busses, you have to multiple the number of students by the amount of classes (7 x 20) to get a product of 140 students. If only 30 can fit on to each bus you have to divide 140 by 30 and you get 4.6666667 so you need to round up to get an answer of 5 busses
Step-by-step explanation:
What is the vertex of this question
The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = x² - 16x + 24
Convert the equation into vertex form, then we have
y = x² - 16x + 24
y = x² - 2·8·x + 8² - 8² + 24
y = (x - 8)² - 64 + 24
y = (x - 8)² - 40
The vertex of the parabola y = x² - 16x + 24 will be at (8, -40). Then the correct option is D.
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a new dictionary in the shape of a rectangular prism will have a thickness of 333 inches (\text{in})(in)(, start text, i, n, end text, ). the volume of the dictionary will be 216\,\text{in}^3216in 3 216, start text, i, n, end text, cubed. what must be the area of the front cover, a face perpendicular to the thickness, in square inches?
The area of the front cover a face perpendicular to the thickness is 72in²
What is a rectangular prism?
Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom, and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.
Here, we have
Given:
A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches.
The volume of the dictionary will be 216in².
Volume = W×L×H
Surface = volume/ height
= 216/3
= 72in²
Hence, the area of the front cover of a face perpendicular to the thickness is 72in².
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find using distributive property.{[7]\frac{x}{y}[/5]×([-3]\frac{x}{y}[/12])}±{[7]\frac{x}{y}[/5]×[5]\frac{x}{y}[/12]
The value of expression will be;
⇒ 7 / 30
⇒ - 14/15
What is Distributive property?
By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.
Given that;
The expression is,
⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]
Now,
Since, The expression is,
⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]
Solve the expression by using distributive property as;
⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]
⇒ [ 7/5 ] × [ - 3/12 ± 5/12 ]
It gives two solution as;
⇒ 7/5 × [ - 3/12 + 5/12 }
⇒ 7/5 × 2/12
⇒ 7/5 × 1/6
⇒ 7 / 30
And, 7/5 × [ - 3/12 - 5/12 }
⇒ 7/5 × - 8/12
⇒ 7/5 × - 2/3
⇒ - 14 / 15
Thus, The value of expression will be;
⇒ 7 / 30
⇒ - 14/15
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For the volume of soap in bottle, ryan determined the margin of error as 354. 85 mL to 354. 95 mL. What was the volume of soap the he measured
If the margin error of the volume of the soap is 354.85 ml to 354.95 ml, then the volume of the soap that he measured is 354.9 ml
The margin of error = 354.85 ml to 354.95 ml
The margin error is defined as the difference between the actual and projected results in a random survey sample. If the actual measurement is x, there is a chance of error in the measurement because of numerous reasons.
The margin of error in the measurement is 354.85 ml to 354.95 ml
In the given options the correct value is 354.9 ml, because it is the middle value of the given margin or error 354.85 ml to 354.95 ml
Therefore, the volume of soap that he measured is 354.9 ml
I have solved the question in general, as the given question is incomplete
The complete question is:
For the volume of soap in a bottle, Ryan determined the margin of error as 354.85 mL to 354.95 ml. What was the volume of soap that he measured? a) 354.8 mL b) 354.85 mL c) 354.9 mL d) 354.95 mL
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A group of 10 students took tests in math, English, and chemistry.
The scatter plots compare the students’ scores on the tests
Complete the sentences to describe the data.
The math and English scores show
a positive correlation
a negative correlation
no correlation
The math and chemistry scores show
a positive correlation
a negative correlation
no correlation
The correlation of the scatterplots are defined as;
The math and English scores show; A positive correlation.
The math and chemistry scores show; A negative correlation
What is the correlation of the scatterplot?In correlation in statistics, it could either be positive correlation, negative correlation or no correlation at all.
A positive correlation is defined as a relationship between two variables that tend to move in the same direction. Thus, a positive correlation exists in the event that one variable tends to decrease while the other variable decreases, or one variable tends to increase while the other variable increases.
A negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.
No correlation means there is no relationship between the two variables.
Now, for scatterplot of the math and English scores shown, we see that majority of the english scores increase as the maths scores increase and as sch it is a positive correlation.
Meanwhile, for the math and chemistry scores shown, majority of the maths score decreases with an increase in the chemistry score and as such this is a negative correlation.
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Reduce 45/99 to the standard form
Answer:
= 4.54545 × 10^-1
Step-by-step explanation:
[tex] \frac{45}{99} = \frac{5}{11} [/tex]
= 0.45454545
= 4.54545 × 10^-1
I hope this helped
if a blood stain has a length of 3.0cm and a width of 1.5cm what is the angle of impact
If a blood stain has a length of 3.0cm and a width of 1.5cm, the angle of impact is 30 degrees
The length of the blood stain = 3 cm
The width of the blood stain = 1.5 cm
The equation for measuring the angle of impact is
sin (angle of impact) = The width of the blood stain / The length of the blood stain
Angle of impact = sin^-1 (The width of the blood stain / The length of the blood stain)
Substitute the values in the equation
Angle of impact = sin^-1(1.5 / 3)
= sin^-1(0.5)
= 30 degrees
Therefore, the angle of impact is 30 degrees
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Evan drew 8 pictures. Alexa drew p fewer pictures than Evan. Write an expression that shows how many pictures Alexa drew?
An expression or equation that shows how many pictures Alexa drew is 8-p.
What is an equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
Given, Evan drew 8 pictures.
Alexa drew p fewer pictures than Evan.
then, Alexa = 8-p
Hence, an expression or equation that shows how many pictures Alexa drew is 8-p.
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The starting salary for a new employee is 25,000. The salary for this employee increases by 8% per year. what is the salary after 1 year?
Answer: $27,000
Step-by-step explanation:
f(x) = 3x³ + 4x² - 2x + 8 and g(x) = 2x³+3x²+5x+2. Find f(x) + g(x)
The value of f(x)+g(x) is 5x³+7x²+3x+10
Given that,
f(x)=3x³+4x²-2x+8
g(x)=2x³+3x²+5x+2
f(x)+g(x)=3x³+4x²-2x+8+2x³+3x²+5x+2
=3x³+2x³+4x²+3x²+5x-2x+8+2
=5x³+7x²+3x+10
Step-by-step explanation:
This question is a type of quadratic equation. To solve this type of question first, we have to put the values of f(x) and g(x). Then we have to put similar terms(which have similar coefficients with similar power)together. Then we add the similar term of f(x) with the similar term of g(x) like 3x³+2x³=5x³, 4x²+3x²=7x², 5x-2x=3x and 8+2=10
Therefore the value of f(x)+g(x) is 5x³+7x²+3x+10
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If 9, 12, 15 is a Pythagorean Triple, which of the following could also be a Pythagorean Triple?
a) 5,7,9
b) 17, 20, 23
c) 36, 48, 60
d) 19, 22, 25
Answer:
c) 36, 48, 60
Step-by-step explanation:
A Pythagorean Triple is a set of positive integers (a, b, c) that follows the rule:
[tex]\boxed{a^2+b^2=c^2}[/tex]
where a < c and b < c.
It always consists of:
all even numbers, ortwo odd numbers and an even number.When a and b are both even, c is even.
When one of a and b is odd and the other is even, c is odd.
(5, 7, 9) cannot be a Pythagorean Triple since it consists of all odd numbers.
(17, 20, 23) is not a Pythagorean Triple since:
[tex]\implies 17^2+20^2=23^2[/tex]
[tex]\implies 289+400=529[/tex]
[tex]\implies 689 \neq 529[/tex]
(36, 48, 60) is a Pythagorean Triple since:
[tex]\implies 36^2+48^2=60^2[/tex]
[tex]\implies 1296+2304=3600[/tex]
[tex]\implies 3600=3600[/tex]
(19, 22, 25) is not a Pythagorean Triple since:
[tex]\implies 19^2+22^2=25^2[/tex]
[tex]\implies 361+484=625[/tex]
[tex]\implies 845\neq 625[/tex]
Compare the function f(x)=3x-1/2 to the function shown in the graph. Which statements are correct?
Answer: B
Step-by-step explanation:
For [tex]f(x)=3x-\frac{1}{2}[/tex], comparing it with slope-intercept form yields that the slope is [tex]3[/tex] and the [tex]y[/tex]-intercept is [tex]-1/2[/tex].
For the graphed function, the slope is [tex]\frac{-4-0}{-2-6}=\frac{1}{2}[/tex] and the [tex]y[/tex]-intercept is about [tex]-3[/tex].
Since the absolute value of the slope of the graphed function is less than that of [tex]f(x)[/tex], option B is correct.
the salaries of pharmacy techs are normally distributed with a mean of $32,000 and a standard deviation of $3,000. if 25 pharmacy techs are selected at random, what is the probability their average salary is less than $33,200? the answer should be typed as a decimal with 4 decimal places.
The probability their average salary is less than $33,200 is = 0.6554
Given that,
Mean = $32,000
Standard deviation = $3,000
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.
Standard deviation (SD) is a widely used measurement of variability used in statistics. It shows how much variation there is from the average (mean). A low SD indicates that the data points tend to be close to the mean, whereas a high SD indicates that the data are spread out over a large range of values.
The Z score is used to calculate how many standard deviations above or below the mean the raw score is. It comes from,
z = (x- μ) / σ (Equation-1)
Where,
x=raw score,
μ=mean,
σ=standard deviation
μ=32,000,
σ=3,000
Average salary is less than $33,200
x < 33,200
We can substitute values in Equation-1,
z = (33,200-32,000)/3000
z = 1200/3000
z = 0.4
Using the normal distribution table as a guide,
P(x < 33,200) = P(z < 0.4)
P(x < 33,200) = 1-P(z>0.4)
P(x < 33,200) = 0.6554
Therefore,
The probability their average salary is less than $33,200 is = 0.6554
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Roanne earned $5 for 1/2 of an hour of babyitting. How much would Roanne make in 1 hour
Using simple mathematical operations, we can conclude that Roanne will earn $10 in 1 hour.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.
The order of operations refers to the rules that govern how to solve an expression with several operations.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).
So, we know that:
Roanne earns $5 for 1/2 hour.
Roanne will earn in 1/2 * 2 = 1 hour:
5 * 2 = $10
Therefore, using simple mathematical operations, we can conclude that Roanne will earn $10 in 1 hour.
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Select the correct answer.
Which expression is equivalent to this polynomial expression?
(82²y9z³y+9y) - (6x³y - zy² + 4y)
OA. 8-3x²y - zy² + 13y
OB.
82² 15z²y + zy² + 5y
O C. -7z²y - zy² + 13y
OD.
-72²y + zy² + 5y
Answer:
B. Just Minus expression with same one
pls help!
select the row of Pascal's triangle that is used to expand the binomial expression (2x^3+3y^2)^7
Row one: 1
Row two: 1 1
Row three: 1 2 1
Row four: 1 3 3 1
Row five: 1 4 6 4 1
Row six: 1 5 10 10 5 1
Row seven: 1 6 15 20 15 6 1
Row eight: 1 7 21 35 35 21 7 1
Row nine: 1 8 28 56 70 56 28 8 1
The row of Pascal's triangle that is used to expand the binomial expression (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.
What is a binomial expression?A binomial expression is an expression that contains only two terms.
What is Pascal's triangle?Pascal's triangle is an algorithm for finding the coefficients of a binomial expansion.
How to find the row that is used to expand the binomial expression (2x³ +3y³)⁷?Since we require the expansion of the binomial expression (2x³ +3y³)⁷ using Pascal's triangle, we note that, the power of the binomial expression is always equal to the second and second to the last coefficient of the terms in the Pascal's triangle.
So, we see that the Row eight: 1 7 21 35 35 21 7 1, satisfies this condition.
So, the row of Pascal's triangle that is used to expand the binomial expression (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.
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Angles x and y are supplementary. angle x measures 132.54°, and angle y measures (m − 15)°. find m∠y. 47.46° 62.46° 85.08° 117.54°
The value of the angle y will be equal to 47.46. The correct option is A.
What is a supplementary angle?Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles because the sum of 130° and 50° equals 180°.
The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Given that the angle x is equal to 132.54°. The value of the angle y will be calculated as,
x + y = 180
132.54 + y = 180
y = 180 - 132.54
y = 47.46
Therefore, the value of the angle y will be equal to 47.46. The correct option is A.
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It costs £80.50 to buy 7 skirts. How much does it
cost to buy 10 skirts? Give your answer in pounds
(£).
Answer:
£115
Step-by-step explanation:
simplify the expression 6²+4x3-18 divided by 6
Answer: The answer to this solution is 5.
Are x and y proportional?
Answer:
No
Step-by-step explanation:
If you look at the first numbers, 1 and 3, we can see that 1 is being multiplied by 3 to get 3.
But if you look at the second numbers, 2 and 4, then you can see that 2 is not being multiplied by 3 to get 4.
Therefore, it is not proportional.
If your school uses Desmos pls respond
20 points
Answer:
I use desmos; what do you need help with?
Answer:zegari6636 is king of brainlist
Step-by-step explanation:
My algebra teacher use Desmos and also thanks for the points have a good day do you need help
Dennis Anderson purchased four gallons of milk for $11.67. Find the unit price per gallon rounded to the nearest cent.
Answer:
$2.92
Step-by-step explanation:
Divde $11.67 by the 4 gallons that Dennis bought.
11.67/4=2.9175
round to the nearst cent (or hundreths place)
since 7 is greater than 5, it rounds up
$2.92
What is the length of segment AC?
By using the property of congruency, it can be calculated that
Length of line segment AC is 26 units
What are congruent triangles?
Two triangles are said to be congruent if their corrosponding sides are equal and the corrosponding angles are equal.
There are six axioms of congruency. They are
AAS axiom, SAS axiom, ASA axiom, SSS axiom, RHS axiom
In [tex]\Delta[/tex] ABC and [tex]\Delta[/tex] XYZ,
[tex]\angle[/tex]B = [tex]\angle[/tex]Y [Given]
[tex]\angle[/tex]C = [tex]\angle[/tex]Z [Given]
BC = YZ [Given]
[tex]\Delta[/tex] ABC [tex]\cong[/tex] [tex]\Delta[/tex] XYZ [ASA axiom]
AC = XZ [Corrosponding parts of congruent triangles are congruent]
AC = 26 units
Length of line segment AC is 26 units
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What is the value of b?
Enter your answer in the box.