Each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
To find the scale factor of the dilation, we can divide the length of each side of the dilated triangle by the length of the corresponding side of the original triangle.
For example, for the side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.
We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.
In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.
This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
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The side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.
We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.
In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.
This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.
According to the 2011 national survey of fishing, hunting, and wildlife-associated recreation, there were over 717171 million wildlife watchers in the us. Of these wildlife watchers, the survey reports that 80\%80%80, percent actively observed mammals. Suppose that one of the census workers repeated the survey with a simple random sample of only 500500500 wildlife watchers that same year.
The survey reports that 80%, percent actively observed mammals = 0.4246
Given that,
The 2011 national survey of fishing, hunting, and wildlife-associated recreation, there were over 71 million wildlife watchers in the us.
The survey reports that 80%, percent actively.
A simple random sample of only 500 wildlife watchers.
Following are the solution to the given question:
By using the approximation of normal for the proportions so, the values:
P ( p⁻ < p ) = P ( Z < ( p⁻ - p ) / [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
So,
P ( 0.79 < p⁻ < 0.81 ) = P ( p⁻ < 0.81 ) - P ( p⁻ < 0.79 )
= P ( Z < (0.81-0.80) / [tex]\sqrt{\frac{0.80(1-0.80)}{500} }[/tex] ) - P ( Z < (0.79-0.80) / [tex]\sqrt{\frac{0.80(1-0.80)}{500} }[/tex] )
= P ( Z < 0.56 ) - P ( Z < -0.56 )
= 0.7123 - 0.2877 (using the Z table )
P ( 0.79 < p⁻ < 0.81 ) = 0.4246
Therefore,
The survey reports that 80%, percent actively observed mammals = 0.4246
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At which root does the graph of f x x 5 3 * x 2 2 touch the X axis?
The root of the graph of f(x) =(x - 5)3(x + 2)2 touches the x-axis at -2,5
(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.
(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.
Given: Function f(x) is (x - 5)3(x + 2)2
If a curve touches the x-axis then f(x) = 0
⇒ (x - 5)3(x + 2)2 = 0.
But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.
⇒ (x - 5)3 = 0 and (x + 2)2 = 0
⇒ (x - 5) = 0 and x + 2 = 0
⇒ x = 5 and x = - 2.
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What is the slope of 5?
A slope of 5 indicates that the corresponding y varies by 5 units for every unit change in x
What is a slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
Given:
The slope of 5.
Think of a slope of 5, which entails climbing 5 steps for each step you take. Much more quickly, you ascend to the top.
The slope is a measurement that indicates how much y shifts when x shifts.
For instance, a slope of 5 indicates that the corresponding y varies by 5 units for every unit change in x.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Therefore, think of a slope of 5, which entails climbing 5 steps for each step you take. Much more quickly, you ascend to the top.
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How to do algebra for beginners?
For solving algebra Determine the issue, Describe your knowledge, Plan beforehand, Execute the plan ,and Check to see whether the response makes sense.
What is Algebra?One of the many different mathematical disciplines is algebra. Algebra, a common thread that runs through nearly all of mathematics, is, roughly speaking, the study of mathematical symbols and the rules for using these symbols in formulae. With the use of mathematical expressions, algebra is the area of mathematics that helps to depict situations or problems. We employ integers that have a fixed or definite value in algebra, such as 2, 7, 0.068, etc. In addition to using numbers, algebra also makes use of variables like x, y, and z.
to do algebra for beginners - Determine the issue, specify your knowledge, Plan, execute, and confirm that the solution makes sense.
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A number is chosen at random from 1 to 25. Find the probability of selecting a number greater than 19.
The probability of selecting a number greater than 19 from 1 to 25 is 6/25 or 0.24.
What is Probability:
The probabilities of an event occurring are defined by probability.
The ratio of favorable outcomes to all possible outcomes of an event is known as probability.
The formula for the Probability of an event is given by
Probability(Event) = Favorable Outcomes/Total Outcomes
Here we have
The set of numbers is from 1 to 25
Total number of numbers from 1 to 25 = 25
In given set of numbers, the number which is greater than 19 are
=> 20, 21, 22, 23, 24, and 25.
The number of favorable outcomes (getting a number, > 19 ) = 6
From the above information,
Probability of selecting a number greater than 19 = 6/25 = 0.24
Therefore,
The probability of selecting a number greater than 19 from 1 to 25 is 6/25 or 0.24
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1. Evaluate each expression. Show your work. (6 points: 2 points for each correct answer with work shown)
B. (9)^1/2 + √25 - 8 ÷ 2 + 3^2
C. 1/2 x 3/5 (2^3 - 6
Please show your work for these 2 expressions.
Answer:
B.) 13
C.) 0.6
Step-by-step explanation:
The order of operations to evaluate these expressions is as follows:
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
So, for B.)
[tex]9^\frac{1}{2}+\sqrt{25}-8\div2+3^2[/tex]
This can be rewritten as
[tex]9^\frac{1}{2}+25^\frac{1}{2}-8\div2+3^2[/tex]
Since there are no parentheses, evaluate the exponents first:
[tex]3+5-8\div2+9[/tex]
Next, there are no multiplication steps, but there is one division:
[tex]3+5-4+9[/tex]
To finish, evaluate from left to right:
[tex]3+5-4+9\\8-4+9\\4+9\\13[/tex]
Follow the same pattern for C.)
[tex](\frac{1}{2})(\frac{3}{5})(2^3-6)[/tex]
This expression can be rewritten as
[tex](1\div2)(3\div5)(2^3-6)[/tex]
First, evaluate the expressions in the individual parentheses, keeping in mind the expression [tex](2^3-6)[/tex] must be evaluated following the same pattern (evaluate the exponent before subtracting six):
[tex](.5)(.6)(8-6)\\(.5)(.6)(2)[/tex]
To finish, evaluate from left to right:
[tex](.3)(2)\\.6[/tex]
Hope that helps!
Which of the following is equivalent to −2(5p − 2q)?
−10p + 4q
−10p − 2q
−7p + 4q
−7p − 4q
Answer:
A,-10p+4q
Step-by-step explanation:
-2(5p-2q)
-2*5p+(-2*-2q)
-10p+4q
Answer:
[tex] - 10p + 4q[/tex]
is the answer. A
PLEASE HELP ME IM STUCK ON IT
The value of c in the given convex polygon is 2°
What is the sum of interior angles of a convex polygon?
If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = (n −2) × 180°
According to the given question:
Number of sides in the given polygon n = 5
Therefore, sum of interior angles of the polygon S = (n -2 ) x 180°
S = (5 -2) x 180°
S = 3 x 180°
S = 540°
Now to find the value of c we can simply add all the interior angles given in the figure and equate it to S
Hence,
136° + 119° + 147° + 48° + 45c = 540°
450° + 45c = 540°
45c = 90°
c = 2°
So the value of c is 2°
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the curved surface area and volume of a cylinder are 880 CM^2 and 3080 cm^3 respectively find its total surface area
The total surface area of a cylinder are 1187.35 cm sq.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
We are given the curved surface area and volume of a cylinder are 880 CM^2 and 3080 cm^3 respectively.
A = 880
V = 3080
Curved surface area of cylinder = 2πrh
880 = 2π x r x h
rh = 880/ 2π
Volume of cylinder = πr x r x h
3080 = πr x r x h
rh = 3080 / πr
Substitue the values;
880/ 2π = 3080 / πr
440/π = 3080 / πr
r = 3080 / 440
r = 7
Now, rh = 880/ 2π
h = 20.01
The total surface area = 2πr(r + h)
= 2π x 7(7 + 20.01)
= 1187.35 cm sq.
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What additional information do you need to know in order to prove the two triangles congruent using HL?
There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.
1. SSS (side, side, side)-If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
2. SAS (side, angle, side) -If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
3. ASA (angle, side, angle)-If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
4. AAS (angle, angle, side)-If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
5. HL (hypotenuse, leg)
This one applies only to right angle triangles
From the figure,
HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs")
It means we have two right-angled triangles with
The same length of hypotenuse andThe same length for one of the other two legs.It doesn't matter which leg since the triangles could be rotated.
For example: From fig(2)
is congruent to fig(3)
If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.
The additional information need to know in order to prove the two triangles congruent using HL is the hypotenuses to be congruent.
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Discuss the difference between r and p. Does r represent population correlation coefficient
Or critical value for the correlation coefficientorsample correlation coefficient.
r stands for the Pearson correlation coefficient, which measures the strength and direction of the linear relationship between two variables. p stands for the critical value for the correlation coefficient, which is used to determine the significance of the correlation coefficient.
The Pearson correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship. The correlation coefficient is a good way to determine the strength of the relationship between two variables.The critical value for the correlation coefficient (p) is used to determine the significance of the correlation. It is determined by the sample size, the number of variables being correlated, and the level of significance. The lower the P value, the more significant the correlation is. If the P value is below the chosen level of significance, then the correlation is considered statistically significant.In conclusion, r is the Pearson correlation coefficient and p is the critical value for the correlation coefficient. R measures the strength and direction of the linear relationship between two variables, while P indicates the significance of the correlation. Both measures are important when assessing the relationship between two variables.
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The quadratic function f(x) has roots of 3 and 7, and it passes through the point (1, 12). What is the vertex form of the equation of f(x)?
f(x) = −(x + 5)2 − 4
f(x) = −(x − 5)2 − 4
f(x) = (x + 5)2 − 4
f(x) = (x − 5)2 − 4
The vertex form of our quadratic equation is:
y = (x - 5)^2 - 4
What is the vertex form of the quadratic?A quadratic equation with a vertex (h, k) and a leading coefficient a is:
y = a*(x - h)^2 + k
We know that the quadratic function has roots of 3 and 7, then if the leading coefficient is a, we can write:
f(x) = a*(x - 3)*(x - 7)
We also know that it passes through the point (1, 12), then:
12 = a*(1 - 3)*(1 - 7)
12 = a*(-2)*(-6)
12 = a*12
12/12 = a
1 = a
Then the quadratic is:
y = (x - 3)*(x - 7)
Expanding that we get:
y = x^2 - 3x - 7x + 21
y = x^2 - 10x + 21
The x-value of the vertex is halfway between the two roots:
x' = (3 + 7)/2 = 5
So evaluating in x = 5 we get:
y = (5)2 - 10*5 + 21
y = 25 - 50 + 21 = -4
The vertex is (5, -4), then the vertex form is:
y = (x - 5)^2 - 4
The correct option is the last one.
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Answer:
f(x) = (x − 5)2 − 4
Step-by-step explanation:
i got it right on my quiz
What is nth formula?
The nth formula of any mathematical expression represents the general formula for the given sequence or series.
nth formula of the given mathematical expression is the way of representing the given sequence or series in standard form.For example nth formula of the arithmetic sequence is given by aₙ= a + ( n - 1 )d.Here aₙ represents the nth term of the sequence.'a' represents the first term of the sequence.'n' represents the number of terms.'d' represents the common difference between the consecutive terms of the sequence.nth term help us to find value of any term without calculating others terms.Therefore, the nth formula is used to represents the mathematical sequence or series in standard form.
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[(5^-1×3^-1)÷6^-1]
how would u do this
Answer:
hi this is so simple you know use
formula to solve
Answer:
[tex] \frac{2}{5} [/tex]
Step-by-step explanation:
[(5^-1×3^-1)÷6^-1]
[tex] = (\frac{1}{5} \times \frac{1}{3}) \div \frac{1}{6} [/tex]
[tex] = \frac{1}{15} \div \frac{1}{6} [/tex]
[tex] = \frac{1}{15} \times 6[/tex]
[tex] = \frac{1}{3 \times 5} \times 3 \times 2[/tex]
[tex] = \frac{3 \times 2}{3 \times 5} [/tex]
[tex] = \frac{2}{5} [/tex]
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you got this five numbers (1, 2, 3, 4). a) if you add a constant number to each, then the mean, the median and the mode changes. b if you add a constant number to each, then the range and the variance remain the same. c) if you multiply each number by a constant, then the mean, the median, the mode, the range change. the standard deviation remain the same. d) if you multiply the mean and the standard deviation by a constant, then both will change by the constant. e) b and c.
The required property that will change with the addition of values in the set will change the mean, median, and mode, While multiplication changes the standard deviation and also the mean by constant.
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Each of the statistic properties will change by adding the number to each number in the set, except properties such as standard deviation and variance. While multiplying the set element with a number each and every property of the statistic corresponding to the set will change.
Thus, Options A, B, and D are correct.
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How many terms are in the expression 4x 5?
There are 2 terms in this mathematical expression. One multiplication sign act as an operator of two numbers.
What is mathematical expression?It is a mathematical statement express the relationship between two or more terms along with mathematical symbols. Terms can be numbers, variables with or without coefficient. symbols can be addition sign, multiplication sign, division and subtraction sign, equal or inequal sign etc. Beside this we have many other operator or symbols to state the mathematical expression.
How many terms we have in the following question?In the above question, we have 2 numbers along with a symbol. We notice that 4 and 5 are two numbers multiplied here as there is a multiplication sign between them.
4 x 5 denotes an expression which state that 4 is multiplied by 5 and the result will be 20.
hence, we have 2 terms and one operator.
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Find the perimeter of the square:
28
Answer:
4×side
Step-by-step explanation:
i hope this helps
Help asap please!!
Find the missing length. The triangles in each pair are similar
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. the missing lengths of HF is 4 and missing length PR =84.
What are Similar Triangles?
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Triangle QRS is similar to triangle FGH.
Let us find the length of unknown side.
By comparing the sides.
SR/QR=HF/HG
8/14 = x/7
Apply cross multiplication
14x = 56
Divide both sides by 14
x = 56/14
x = 4
HF = 4
8)
By properties of triangle we have
QP/BP=PR/PC
56/24= x/36
Apply cross multiplication
24x = 2016
Divide both sides by 24
x = 2016/24
x = 84
PR = 84
Hence the missing lengths of HF is 4 and missing length PR =84.
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A farmer grows only sunflowers and flax on his 240-acre farm.
This year he wants to plant 80 more acres of sunflowers than of flax. How many
acres of each crop does the farmer need to plant?
Answer:
Flax: 80 acres
Sunflowers: 160 acres
Step-by-step explanation:
Let's
x = acres of flax
y = acres of sunflowers
We have the equations:
x + y = 240
y = x + 80
Let's do it in standard form
x + y = 240
x - y = -80
2x = 160
x = 80 acres
Now put 80 back in the equation to find sunflowers
80 + y = 240
y = 160 acres
So, 80 acres of flax and 160 acres of sunflowers!
Can a binomial have degree 3?
Yes , the given statement a binomial can have degree three is true.
As given in the question,
Binomial can have degree three is a true statement explain in a following way:
Binomial is a polynomial which is a combination of two terms combined by '+' addition or '-' subtraction mathematical operation.Binomial may have degree one , two , three , so on.Degree of the polynomial does not effect the definition of binomial.If it is of degree three it is cubic binomial or polynomial.One term represents monomial, three terms represents trinomial and so on.Therefore, binomial may have degree 3 is a true statement.
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Gabby is an editor. She needs to review a textbook with 398 pages. She plans to review 9 pages each day for the next 31 days. She works out that she will have 279 pages left to review after that. Does that sound about right?
Step-by-step explanation:
Gabby is an editor. She needs to review a textbook with 398 pages. She plans to review 9 pages each day for the next 31 days. She works out that she will have 279 pages left to review after that. Does that sound about right?
398 - ( 9 * 31) = 119 pages left
No, because Gabby will only have 119 pages left after reading 9 pages a day for 31 days. 279 pages is an overestimate.
Which number is larger 1.1 10000 or 1000?
Simplification of the given numbers (1.1)^ 10000 or 1000 gives
(1.1)^ 10000 is larger number than 1000.
As given in the question,
Given two numbers are:
(1.1)^ 10000 and 1000
Simplify the numbers to get the larger number we have,
Apply Binomial theorem in the expression (1.1)^ 10000
( a + b )ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +.....+ ⁿCₙa⁰bⁿ
(1.1)¹⁰⁰⁰⁰
= ( 1 + 0.1)¹⁰⁰⁰⁰
Here a = 1, b = 0.1 and n= 10000
( 1 + 0.1)¹⁰⁰⁰⁰
=¹⁰⁰⁰⁰C₀1¹⁰⁰⁰⁰(0.1)⁰ + ¹⁰⁰⁰⁰C₁1¹⁰⁰⁰⁰⁻¹(0.1)¹ + ¹⁰⁰⁰⁰C₂1¹⁰⁰⁰⁰⁻²(0.1)² +..........+ ¹⁰⁰⁰⁰C₁₀₀₀₀1⁰(0.1)¹⁰⁰⁰⁰
= 1 + 1000+......
= 1001+ ....
> 1000
Therefore, from the given numbers (1.1)^ 10000 or 1000 the larger number is (1.1)^ 10000 compare to 1000.
The above question is incomplete , the complete question is :
Which number is larger (1.1)^ 10000 or 1000?
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How do you know if a shape is SAS or SSS?
what is the answer of this?
Answer:
The answer is 5
Step-by-step explanation:
length(Hypotenuse) = 13m
height(opposite) = 12m
ground(adjacent) = ?
using the formula
Hyp² = oppo² + Adj²
13² = 12² + Adj²
Adj² = 13² – 12²
Adj² = 169 – 144
Adj² = 25
Adj = √25
Adj = 5
:- the distance of the foot of the ladder from the bottoms wall is 5
i hope this helps
Alex buys 24 apples from the supermarket. When he gets home, he finds that 6 apples are bad.
What percentage of the apples are bad? Round your answer to the nearest number.
Answer:
To find the percentage of bad apples, we need to divide the number of bad apples by the total number of apples and then multiply by 100%. In this case, there were 24 apples in total and 6 of them were bad, so the percentage of bad apples is 6/24 * 100% = 25%. Rounded to the nearest number, this is equal to 25%.
How can I learn algebra fast?
If you're not motivated, it would take you approximately nine months; however, if you are and can dedicate an hour or two every day to studying, it would only take you about six months.
How quickly can I learn algebra?6 Unknown Methods for Quickly Mastering Algebra
Create your own memory-boosting techniques.One advantage of algebra .math in general, is that the rules never change.Learn shortcuts. familiarise yourself with the calculator. join a study group.get a tutor and encourage your child to ask their teacher for assistance.You may probably self-study Math rather simply as if you were in college with all the free materials available online, including lectures, syllabi, ebooks, and MOOCS. You can go at your own pace, which is the finest part. It's common for algebra to be challenging because we mistakenly think we're learning new material when, in reality, we're just applying language to specific concepts that we already know to be true.
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Multiple choice math graphing
What function describes the graph?
Answer:
D
Step-by-step explanation:
It can't be A or B because those graphs are positive, and our graph is negative.
It can't be C because there is a point at (2,-5), but we don't see that point on this graph!
So, the answer is D
Answer:
d
Step-by-step explanation:
f(x) = \sqrt{x+2} - 5
Sam i uing the number 2,3,5,and 7. She multiplied ome of thee number and got the product of 10. What are all of the product?
The possible product is:
2 * 5 = 10
1 * 10 = 10
In mathematics, multiplication is a process of combining numbers and finding the product. It is denoted by the symbol "x" or "*". There are different ways to perform multiplication, such as using a multiplication table, using a calculator, or using the standard algorithm. The standard algorithm is a systematic method for performing multiplication that involves multiplying the digits in the ones, tens, and so on place value columns, and then carrying and regrouping as necessary.
To find all the possible products that can be obtained by multiplying some combination of the numbers 2, 3, 5, and 7 that result in a product of 10. Here are the two possible products that can be obtained by multiplying these numbers:
2 * 5 = 10
1 * 10 = 10
The possible products that result in a product of 10 are 2 * 5 and 1 * 10.
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The sum of four consecutive integers is -10. What is the largest integer?
The largest number is -1
What is number ?
An arithmetic value known as a number is used to represent a quantity and do calculations. Numbers are represented by written symbols, such as "3," which are referred to as numerals. A number system is a method of writing that uses logically ordered digits or symbols to represent numbers.
An item in mathematics used for measurement, labeling, and counting is a number. The prime numbers 1, 2, 3, 4, and so forth are the original examples. Number words can be used to represent numbers in language.
Let the 4 consecutive integers are
x
x+1
x+2
x+3
x + (x+1) + (x+2) + (x+3) = -10
4x + 6 = -10
4x = -16
x = -4
The 4 consecutive integers are -4 , -3 , -2 , -1
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What is the vertex of 2x² 8x 3?
The vertex of the graph of f(x) = 2x² + 8x - 3 is (-2, -11). It lies in the third quadrant.
Therefore the answer is (-2, -11).
Simplifying the given graph to the form f(x) = a(x - h)² + k
f(x) = 2x² + 8x - 3
f(x) = 2×(x² + 4x) - 3
f(x) = 2×(x² + 4x + 4) - 3 - 2×4
f(x) = 2×(x + 2)² - 11
So f(x) = 2x² + 8x - 3 is symmetrical about the line x = -2. At x = -2, y = -11.
Therefore, the vertex of the graph is (-2, -11).
--The question is incomplete, answering to the question --
"What is the vertex of the graph of f(x) = 2x² + 8x - 3?"
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