The dependent variable, y from the given situation is 15
Solve for the dependent variableThe number of groups = 3Number of exercises each group practice on = 3The total number of exercises the individual needs, y = 3x/3
Where,
y = independent variable x = dependent variable = 15So,
y = 3x/3
substitute the value of x into the equation
y = 3(15) / 3
open parenthesis
y = 45 /3
y = 15
In conclusion, the value of the dependent variable is 15
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k h S Which of the following is a true proportion of the figure based on the triangle proportionality theorem?
The true proportion of the figure based on the triangle proportionality theorem is Option (A).
What is the basic proportionality theorem?
According to the Basic Proportionality Theorem (BPT), if a line is parallel to a triangle's side that divides the other sides into two separate points, the line will divide those sides proportionately.
Given that TU is parallel to QR, by the proportionality theorem, we get
[tex]\frac{ST}{TQ} = \frac{SU}{UR}[/tex]
or, [tex]\frac{k}{j} = \frac{h}{i}[/tex]
or, [tex]\frac{i}{j} = \frac{h}{k}[/tex]
Ans: [tex]\frac{i}{j} = \frac{h}{k}[/tex]
Hence, a true proportion of the figure based on the triangle proportionality theorem is (A) [tex]\frac{i}{j} = \frac{h}{k}[/tex]
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Which lists all the real zeros of the polynomial p(x)=x(x2−9)
The zero's of the polynomial p(x) = x(x² - 9) are -3, 0 and 3.
How to find zero's of a polynomial?The zero's of a polynomial p(x) are all the x-values that make the polynomial equal to zero.
In other words, zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.
Therefore, let's find the zero's of the polynomial .
p(x) = x(x² - 9)
p(x) = x³ - 9x
0 = x³ - 9x
x³ = 9x
x² = 9
x = √9
Therefore, x = -3 or 3
x = 0
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Nancy's pack of pens had 80% red pens. If
there were 55 pens total in the pack, how
many were red?
Answer:
44
Step-by-step explanation:
80*55/100 = 44
Answer:78
Step-by-step explanation:
The force “F” (in pounds) needed on a wrench handle to loosen a certain bolt varies inversely with the length “L” (in inches) of the handle. A force of 35 pounds is needed when the handle is 6 inches long. If a person needs 25 pounds of force to loosen the bolt, estimate the length of the wrench handle. Round answer to two decimal places if necessary.
______ inches.
The length of the wrench handle 8.4 inches.
What is length?
Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units.
f = k/l
35 = k/6
k = 210
f = 210/l
25 =210/l
l = 8.4 inches
The length "L" (in inches) of a wrench handle has an inverse relationship with the force "F" (in pounds) required to remove a certain bolt. In the case of a handle that is 6 inches long, 35 pounds of power is required. The length of the wrench handle if the bolt needs to be loosened with 25 pounds of force is 8.4 .
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5) Is the point (2,4) a solution to the system of inequalities in the graph shown below? Explain. (Yes or No 1 point) (Explain 1 point)
y<2 x+3
y≥ -4 x+1
Yes, the point (2,4) is a solution to the system of inequalities in the graph.
How to solve inequalities?
By definition, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
The given parameters include
Points (4,2)
y<2x+3
y≥-4x+1
Solving these inequalities
y<2x+3
Let y<0
0<2x+3
-3<2x
x<-3/2
(-3/2,0)
when x<0
y<2(0)+3
y<3
(0,3)
From equation 2
y≥-4x+1
x≥0
y≥0+1
y≥1
(0,1)
y≥0
0≥-4x+1
x≥-1/4
(-1/4,0)
Using the coordinates to draw the graphs the lines cut each other at points where (4,2)
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. 3F furniture dealer has always sold its merchandise through 4 company-operated stores. Last year sales were birr 1million and net profit was 8% of sales. Fixed costs were birr 170,000. As a result of shifting population and increased competition, the four locations have become less desirable. 3F is considering eliminating its retail stores in favor of door-to-door selling. It is estimated that sales would increase by 25% and net profit by birr 30,000. Fixed costs would increase by birr 30,000 because operations would be moved to a low-rent warehouse. Required a) What was the break-even point under the old situation? b) What will be the break-even point under the proposed situation? c) What birr sales volume must be obtained under the proposed plan to make as much profit as last year?
a) The break-even point under the old situation is 680000.
b) The break-even point under the proposed situation is 806451.
c) Birr sales volume must be obtained under the proposed plan to make as much profit as last year is 1129032.
a) The break-even point under the old situation:
100000 * a - 170000 = 1000000 * 8%
a = 25% (Profit rate)
x.a = 170000
x = 680000
b) The break-even point under the proposed situation:
1250000 * b - 170000 -30000 = 80000 + 30000
b = 24.8%
x.b = 20000
x = 806451
c) Birr sales volume must be obtained under the proposed plan to make as much profit as last year :
x.b - 200000 = 80000
x.b = 28000
x = 1129032
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Help Please!!
Line q has an equation of y+7=9(x+4). Line r is perpendicular to line q and passes through (9,–10). What is the equation of line r?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answer:
Y= -1/9x-9 that's the answer, you're welcome
The equation of line which is perpendicular to the line q is given by
y = ( -1/9 )x - 9
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
The point is P ( 9 , -10 )
Let the equation of line q be y + 7 = 9 ( x + 4 )
Now , on simplifying the equation , we get
y + 7 = 9x + 36
Subtracting 7 on both sides of the equation , we get
y = 9x + 29
Now , the slope of the equation q is m₁ = 9
Now , since the line r is perpendicular to line q
The product of the slope is -1
So , m₁ x m₂ = -1
Substituting the values in the equation , we get
9 x m₂ = -1
Divide by 9 on both sides of the equation , we get
m₂ = -1/9
So , the slope of the line r m₂ = -1/9
The equation of line is given by y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - ( -10 ) = -1/9 ( x - 9 )
On simplifying the equation , we get
y + 10 = -1/9 ( x - 9 )
y + 10 = ( -1/9 )x + 1
Subtracting 10 on both sides of the equation , we get
y = ( -1/9 )x - 9
Therefore , the value of A is y = ( -1/9 )x - 9
Hence , the equation of line r is y = ( -1/9 )x - 9
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As part of the training for the cross-country team, you must run a total of 20 miles per week. You ran 5.6 miles in the first two days of the week. If you run the same amount each day for the remaining five days, how many miles must you run per day to complete the 20 miles?
Write and solve an equation to determine the number of miles, m, you must run per day.
5m + 2(5.6) = 20; m = 1.76
5m + 5.6 = 20; m = 2.88
5m − 5.6 = 20; m = 5.12
m + 5(5.6) = 20; m = 8
pls help
The equation to determine the number of miles, m, you must run per day is B. 5m + 5.6 = 20; m = 2.88
How to illustrate the equation?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. An equation is not the same as a mathematical expression. The equal (=) operator is always used to join two mathematical expressions in an equation.
In mathematics, an equation is a relationship between two expressions that is expressed as an equality on either side of the equal to sign. An equation would be 3y = 16, for instance. Equations can be categorized into one of the following three categories depending on their degree:
linear formulaquadratic formulaCubic problemIn this scenario, the person must run a total of 20 miles per week and ran 5.6 miles in the first two days of the week.
Let the number of miles for the remaining 5 days be m.
This will be:
5m + 5.6 = 20;
Solving for m = will give 2.88.
In conclusion, the correct option is B.
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The area of the Sea of Japan is 1.007 × 106 km2. The area of the Southern Ocean is 2.0327 × 107 km2. Find the total area. Write the final answer in scientific notation with the correct number of significant digits.
2.1334 × 107 km2
3.0397 × 1013 km2
2.133 × 107 km2
3.040 × 1013 km2
The total area of the Sea of Japan and the Southern Ocean is 2.1334 × 10⁷ km². The correct option is the first option 2.1334 × 10⁷ km²
Calculating the total area of the Sea and OceanFrom the question, we are to calculate the total area of the sea and ocean
From the given information,
"The area of the Sea of Japan is 1.007 × 106 km²"
and
"The area of the Southern Ocean is 2.0327 × 107 km²"
Thus,
The total area of the sea and ocean = 1.007 × 10⁶ km² + 2.0327 × 10⁷ km²
The total area of the sea and ocean = 0.1007 × 10⁷ km² + 2.0327 × 10⁷ km²
The total area of the sea and ocean = 2.1334 × 10⁷ km²
Hence, the total area is 2.1334 × 10⁷ km²
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In the last ten games, Jamal made 7/9 of his free throws and Brian made 5/8of his free throws. Which player has the better record? Explain.
By using the concept of fraction, it can be calculated that
Jamal has the better record
What is a fraction?
Suppose there is a collection of objects and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.
This is a word problem on fraction
Portion of free throws Jamal made in the last ten games = [tex]\frac{7}{9}[/tex]
Portion of free throws Brian made in the last ten games = [tex]\frac{5}{8}[/tex]
To compare between [tex]\frac{7}{9}[/tex] and [tex]\frac{5}{8}[/tex]
LCM of 9 and 8 = 72
[tex]\frac{7}{9} = \frac{7 \times 8}{9 \times 8} = \frac{63}{72}[/tex]
[tex]\frac{5}{8} = \frac{5 \times 9}{8 \times 9} = \frac{45}{72}[/tex]
As [tex]\frac{63}{72} > \frac{45}{72},[/tex]
So [tex]\frac{7}{9} > \frac{5}{8}[/tex]
So, Jamal has the better record
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Suppose that you have 4 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards without replacement.
The probability that two cards will be drawn at random, without replacement, is 13/18.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
According to our answer-
P(at least 1 green) = 1 - P(no green)
P(no green) = draw yellow on both draws
= P(draw yellow on 1st draw) * P( draw yellow on 2nd draw, given draw yellow on 1st draw)
= 5/9 * 4/8 = 20/72 = 5/18
P(at least 1 green) = 1 - 5/18
= 13/18
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Aiman has 6 pizzas to share at a party. If each person will eat 3 8 of a pizza, how many people can share the pizzas?
HINT: Use division!
Answer: 16
Step-by-step explanation: 16 people can share the pizzas.
The law of large numbers and the central limit theorem tell us how standard deviations behave as medians increase.
a. true
b. false
The law for all large numbers with the central limit-theorem will tell us about how standard deviations doesn't as increase with medians. So b). false is correct.
The Law for all Large Number states that once pattern length has a tendency to infinity, the pattern imply equals to populace imply. The statements aren't contradictory. The Central Limit Theorem inform us that because the pattern length has a tendency to infinity, the of the distribution of pattern method methods the ordinary distribution.
The regulation of huge numbers has a completely vital position in possibility and statistics. It states that in case you repeat an test independently a huge variety of instances and common the result, what you got must be near the predicted value.
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Use the commutative property to write an expression 8c-1.5
Answer:
Step-by-step explanation:
i need help on that too
What is the slope of a line parallel to the line whose equation is 3x-2y=14
Answer: 3/2
Step-by-step explanation:
3x - 2y = 14
-2y = 14-3x
y = 3/2x-7 divide both sides by -2
There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. How many are left in
the box?
The number of sweets left in the box after giving 35% is 325.
How to find the sweet left in the box?There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. The number of sweets left in the box can be calculated as follows:
Therefore, the number of sweet left in the box = 500 - 35% of 500
number of sweet left in the box = 500 - 35 / 100 × 500
number of sweet left in the box = 500 - 17500 / 100
number of sweets left in the box = 500 - 175
= 325
Therefore, the number of sweets left in the box will be 325
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Gualberto has a barrel that collects rainwater. As the rainwater evaporates,
the height of the rainwater changes from 24.83 in. to 18.08 in. over a period of
5 2/5 days. What is the average change in the height of the rainwater each day?
The average change in the height of the rainwater is 1.25 inches per day
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
The initial height of the rainwater measured = y₁
The value of y₁ = 24.83 inches
The final height of the rainwater measured = y₂
The value of y₂ = 12.08
The change in height = y₁ - y₂
Substituting the values in the equation , we get
The change in height = 6.75
The number of days = 5 2/5 days
The number of days = 27/5 days = 5.4 days
So , the equation will be
The average change in the height of the rainwater = change in height / number of days
Substituting the values in the equation , we get
The average change in the height of the rainwater = 6.75 / 5.4
The average change in the height of the rainwater = 1.25 inches per day
Hence , the average change is 1.25 inches per day
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To fill an order, the factory dyed 21 yards of silk indigo and 75 yards teal. How many yards of silk did it dye for that order?
Answer:
96
Step-by-step explanation:
21+75
A garden table and a bench cost $703 combined. The garden table costs $47 less than the bench. What is the cost of the bench?
Answer:
375
Step-by-step explanation:
let a garben table cost x
a bench cost x+47
x+x+47=703
2x=703-47
2x=656
x=656÷2=328
bench: 328+47=375
Dominique throws a softball from the outfield. After 1 second, the ball is 15 feet high. After 4 seconds, the ball reaches its maximum height of 42 feet. After 7 seconds, it returns to a height of 15 feet. What is the equation of the quadratic function that models the height of the ball h(t) at time t? h(t) = −2(t − 4)2 + 42 h(t) = 2(t + 4)2 + 42 h(t) = −3(t − 4)2 + 42 h(t) = 3(t + 4)2 + 42
The equation of the quadratic function that models the height of the ball h(t) at time t is h(t) = −3(t − 4)² + 42
How to determine the equation of the height function?From the question, we have the following parameters that can be used in our computation:
Height after 1 second = 15 feetHeight after 7 seconds = 15 feetMaximum height = 42 feetThe above parameters mean that
h(1) = 15
h(7) = 15
h max = 42
This also means that the leading coefficient of the function is negative
So, the possible equations from the options are
h(t) = −2(t − 4)² + 42
h(t) = −3(t − 4)² + 42
Calculate h(1) and h(7)
h(t) = −2(t − 4)² + 42
h(1) = −2(1 − 4)² + 42 = 24
h(7) = −2(7 − 4)² + 42 = 24
h(t) = −3(t − 4)² + 42
h(1) = −3(1 − 4)² + 42 = 15
h(7) = −3(7 − 4)² + 42 = 15
Hence, the function is h(t) = −3(t − 4)² + 42
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Answer: Answer is C
Step-by-step explanation:
I took the test and it gave me credit for this question
If f(x)=ex and the 4th degree Taylor polynomial of f(x) centered at 2, what is T4(2.4)?
Round your answer to four decimals.
The fourth degree Taylor polynomial of f(x) centered at 2 the [tex]T_4(2.4) = 11.0225[/tex].
What is Taylor polynomial?
The Taylor series or Taylor expansion of a function in mathematics is the infinite sum of terms expressed in terms of the function's derivatives at one particular point. The function and the sum of its Taylor series are roughly equal for the majority of common functions at this point.
Given:
[tex]f(x) = e^x[/tex] centered at 2.
[tex]f(2) = e^2[/tex]
[tex]f'(x) = \frac{d}{dx}e^x = e^x , f'(2) = e^2\\f"(x) = \frac{d^2}{dx}(e^x) = e^x, f"(2) = e^2\\ f^3(x) = \frac{d^3}{dx}(e^x) = e^x, f^3(2) = e^2\\ f^4(x) = \frac{d^4}{dx}(e^x) = e^x, f^4(2) = e^2[/tex]
Therefore,
[tex]T_4(x) = f(2) + \frac{f'(2)(x-2)}{1!} + \frac{f"(2)(x-2)^2}{2!} + \frac{f^3(2)(x-2)^3}{3!} + \frac{f^4(2)(x-2)^4}{4!} \\T_4(x) = e^2 [1 + (x - 2) + \frac{(x-2)^2}{2}+\frac{(x-2)^3}{6}+ \frac{(x-2)^4}{24} \\ T_4(2.4) = e^2[1 + (2.4-2) + \frac{(2.4-2)^2}{2}+ \frac{(2.4-2)^3}{6}+\frac{(2.4-2)^4}{24}]\\ T_4(2.4) = 11.0225[/tex]
Hence, the fourth degree Taylor polynomial of f(x) centered at 2 the [tex]T_4(2.4) = 11.0225[/tex].
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On monday, a museum had 150 visitors. On tuesday, it had 260 visitors. Estimate the percent change in the number of visitors to the museum.
The percentage change in the number of visitors = 42.30%.
Percentage change:The prior value's increase or reduction is indicated by the percentage change. The percentage increase may be used to calculate how much it has increased if the present value exceeds the previous value.
The percentage decline may be used to calculate how much it has reduced if the current value is smaller than the prior value.
The formula for Percentage change in case of increase is given by
Percentage Increase = ( Increase/Original Number) × 100
Here we have
On Monday a museum had 150 visitors
On Tuesday it had 260 visitors
The number of visitors increased from Monday to Tuesday
= 260 - 150 = 110
By the given formula percentage of change can be calculated as given below
Percentage Increase = (110/260) × 100
= 42.30%
Therefore,
The percentage change in the number of visitors = 42.30%.
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Gaspar writes the algebraic expression 5b +3.79.
It represents the total cost, in dollars, of buying 5 bagels
and a container of cream cheese. Identify any variables,
coefficients, and terms in the expression. Tell what
each represents.
Answer:
B is a variable it is a letter
5 is a coefficient because it's in front of the variable
3.79 is a term because it is just numbers by itself
Step-by-step explanation:
in a certain hyperbola, the center is at $(-2,0),$ one focus is at $(-2 \sqrt{34},0),$ and one vertex is at $(-5,0).$ the equation of this hyperbola can be written as\[\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2}
The equation of certain hyperbola with center ( -2,0) is (x+ 2)²/25 - (y)²/ 9 = 1
According to the question,
Equation of hyperbola is given : (x-h)²/a² - (y-k)²/b² = 1
Center of hyperbola = (-2,0)
Focus = (-2√34 , 0)
vertex = (-5,0)
This hyperbola is from left to right
As center is (-2,0) means h = -2 and k = 0
Hyperbola are symmetric ,
Second focus = (-2√34 , 0)
Second vertex = ( 5,0)
Vertex are (a,b) => a = 5
Foci of general hyperbola are ( h ± ck)
=> ( h ± c, k) = (-2√34 , 0)
=> -2 ± c = -2√34
=> c = ± √34
Also , c^2 = a^2 + b^2
=> 34 = 25 + b^2
=> b^2 = 9
=> b = 3
Substituting all the values ,
Equation of Hyperbola is (x+ 2)²/25 - (y)²/ 9 = 1
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there is a line that includes the point (11,5) and has a slope of 8/11. what is its equation in slope intercept form?
Answer:
[tex]y=\frac{8}{11} x-3[/tex]
Step-by-step explanation:
Plug in the slope and point into the equation y=mx+b to solve for the y-value of the y-intercept. Plug in the x value for x, the y value for y, and the slope for m.
[tex]5=\frac{8}{11} (11)+b[/tex]
[tex]5=8+b[/tex]
[tex]-3=b[/tex]
After solving that, you can plug the slope and y-intercept back into the equation to solve for y.
[tex]y=\frac{8}{11} x+(-3)[/tex]
[tex]y=\frac{8}{11} x-3[/tex]
Answer:
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept. We have all the information we need except for the y-intercept, so we can plug in our point to solve for the y-intercept.
------------------------------------Solving for y-intercept------------------------------------
Plugging in the point gives us [tex]5=8/11*11+b[/tex]. Simplifying this equation results in [tex]5=8+b[/tex]. To solve for b, we subtract 8 from both sides, giving us that [tex]b=-3[/tex]. We now have both the slope and the y-intercept, so our equation is y = 8/11x -3.
Feel free to contact me with any questions about my answer. I hope this helps!
In March, Delphine's house had 40\%40%40, percent more snowfall than in February. Delphine's house had fff centimeters of snowfall in February.
Which of the following expressions could represent how much snowfall Delphine had at her house in March?
Choose 2 answers:
The expressions that could represent how much snowfall Delphine had at her house in March will be:
1.4f
f + 0.4f
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Since Delphine's house had 40 percent more snowfall than in February. Delphine's house had f centimeters of snowfall in February.
The expression will be:
f + (40% × f)
f + 0.4f
= 1.4f
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Which statement is true about the diagram?
B
4
Ο Δ ABD =Δ ACB by SSS
Ο Δ ABC =Δ ABD by SAS
O A CAB DAB by SSS
O No triangles are congruent
The statement "Δ ABD = Δ ACB by SSS" is true about the diagram.
The statement "Δ ABD = Δ ACB by SSS" is true about the diagram. SSS stands for Side-Side-Side, which is a congruence postulate stating that if three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent. In the given diagram, Δ ABD and Δ ACB are congruent because their corresponding sides AB, BD, and AC are equal in length.
This means that the triangles have the same shape and size, but they may be oriented differently. The SSS congruence allows us to conclude that all corresponding angles and other corresponding sides of the two triangles are also congruent. Therefore, we can say that Δ ABD is congruent to Δ ACB based on the Side-Side-Side congruence.
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Solve the equation: x^2-13/2 x+15/2=0
Answer:
Step-by-step explanation:
199/4
How do i simplify
4+-2=2&1/4
what do you mean by &?
if its multiplication than
2 × 1/4 = 0.50 or 1/2
4+ (-2) = 2
so the answer is:
2 = 1/2
false
suppose that we have collected information on how much a sample of households spend on clothing per year. if we are 90% confident that the true population mean will lie between $1,500 and $2,100, the chance that the population mean will either be less than $1,500 or above $2,100 is %.
10% of the time, the population mean will go below $1,500 or exceed $2,100.
Given that,
Assume that we have data on the annual spending on apparel of a sample of families. The probability that the population mean will fall below $1,500 or rise over $2,100 is ________% if we are 90% positive that the genuine population mean will be between $1,500 and $2,100.
We have to fill the blank.
We know that,
90% of the time, the real population mean will fall in the range of $1,500 and $2,100.
The genuine population mean will therefore most likely fall between $1,500 and $2,100, with a 90% probability.
So, the probability that it will fall outside of this range (i.e., be either less than $1,500 or beyond $2,100) is 100-90, or 10%.
Therefore, 10% of the time, the population mean will go below $1,500 or exceed $2,100.
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