Can a triangle be formed with side lengths 4, 8, 11? Explain. No, because 11 − 8 < 4 Yes, because 11 − 4 < 8 No, because 4 + 8 > 11 Yes, because 4 + 8 > 11

Answer: He would have $1,500 alone from making $150 each year, and the total would be $3,500.

Step-by-step explanation: To find how much money he makes in 10 years (not including the $2,000) we would multiply 150 by 10 to get 1500.

Now, we need to add 2000 + 1500, and we get 3,500.

I hope this helps!

If n is an integer and n3 is divisible by 24, The largest number that must be a factor of n is 8.

N3 is a number that is divisible by 24, meaning it can be expressed as 24k, where k is an integer.

This can further be expressed as 8(3k), meaning that 8 is the largest number that is a factor of 24, and therefore must also be a factor of n3. Consequently, the largest number that must be a factor of n3 is 8.

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Answer: 1 1/8

Step-by-step explanation:

1/4 in half is equivalent to 1/8

Answer:

73u/ - 11

Step-by-step explanation:

Answer:

-5.05. U -6

Step-by-step explanation:

Distribute the Negative Sign:=3.65u−11+−1(−5+8.7u)=3.65u+−11+(−1)(−5)+−1(8.7u)=3.65u+−11+5+−8.7uCombine Like Terms:=3.65u+−11+5+−8.7u=(3.65u+−8.7u)+(−11+5)=−5.05u+−6

Yes, The quotient of two polynomial expressions is a rational expression. so the statement is true

Polynomial Expression

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

Rational expression

A rational expression is the quotient of two polynomial expressions where the denominator is not equal to zero.

Consider two polynomial p(x) & q(x)

and q(x) [tex]\neq[/tex] 0

then the quotient is a rational expression

so the statement is true.

Yes, The quotient of two polynomial expressions is a rational expression. so the statement is true

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The probability that he will serve exactly four aces out of seven serves is 5.7 %.

Given :

if the probability that a certain tennis player will serve an ace is 1 / 4 .

If we let p stand for the probability of a succes, then p = 1/4, and ( 1 - p ) = 3/4.  (1-p) is the probability that he will NOT serve an ace.

Formula  for probability:

P (m successes in n trials) = ( nCm ) * p^m * ( 1 - p )^( n - m ).

= 7C4 * ( 1/4 )^4 * ( 3/4 )^( 7 - 4 )

= 7! / ( 7 - 4 )! 4! * 1/256 * 27/64

= 7 * 6 * 5 / 3 * 2 * 1 / 256 * 27/64

= 35/256 * 27/64

= 945/16384

= 0.057

= 0.057 * 100 %

= 5.7 %

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Answer:

Step-by-step explanation:

find x

7x+10=2x+40+3x

2x=30

x=15

ABD = 7(15)+10 = 115

ABD + ABC =180

115+ABC=180

ABC=65

95.1% of the proportion of observed variation in hardness can be explained by the simple linear regression model relationship between hardness and elapsed time.

Linear regression model:

In statistics, linear regression model defined the relationship between a dependent variable, y, and one or more independent variables, X.

Given,

Here we need to find the percentage of observed variation in hardness can be explained by the linear relationship between hardness and elapsed time.

In order to find the percentage we must know the definition of observed variation which means  the combined variation that is derived from all sources.

In order to solve this let us consider that the linear regression model is used by statisticians to predict the value of the response variable for given values of the predictor variables.

So, if there are two variables involved in the regression analysis, then the model is called a bivariate one.

Where as If there are more than two independent variables, then the regression model is known as the multiple regression model.

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The number of different sets of officers possible is 1716 sets.

The number of sets of officers possible is the number of ways people can be chosen for the given posts.

Since there are 13 people available for the post of president,

The choice can be made in

13 ways.

For the post of the Vice-President, there are 12 likely candidates. Hence, the choice can be made in

12 ways

Similarly for the post of treasurer, there are 11 likely candidates available. Hence, the choice can be made in 11 different ways.

Hence, the total number of sets of officers possible are

13 X 12 X 11

= 1716 sets.

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Answer:

Kayla Calculated the Mean instead of the median.

Step-by-step explanation:

If Kayla's work is the sum of all the numbers, she is calculating the mean.

Answer:

Sandwich = 2

Cookie = 1

Step-by-step explanation:

Let

This would mean :

3x + 2y = 8  and 7x + 2y = 16

Because we have two similar terms in the equations, (2y) we can subtract the two equations from each other cancelling out the terms resulting in us having one term that we can solve for. This is known as the elimination method

  7x + 2y = 16

-  3x + 2y  = 8

-----------------------

4x   +   0y   = 8

==> 4x = 8

==> x = 2

We can now plug in the value of x into one of the equations and solve for y

==> 7x + 2y = 16

==> 7(2) + 2y = 16

==> 14 + 2y = 16

==> 2y = 2

==> y = 1

We can conclude that the cost of a sandwich is 2 and the cost of a cookie is 1

A system of linear equations has one solution when the graphs intersect at a point.

A system of linear equations has no solution when the graphs are parallel.

A system of linear equations has infinite solutions when the graphs are on the exact same line.

The graphs attached below show the linear equations that have one solution, multiple solutions, and no solutions.

A linear equation in two variables of the form axe + by + c = 0, where a, b, c R, a 0, and b 0. By comparing the coefficients of the equations while taking the system of linear equations into consideration, we may determine how many solutions there are. Additionally, we can use a graphical way to determine whether the equation system has a single solution or an infinite number of solutions.

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Answer:

# of adult tickets = 10

# of child tickets = 4

Step-by-step explanation:

a = # of adult tickets

c = # of child tickets

a + c = 14

a = 14-c

9a + 5c = 110

9(14-c) + 5c =110

126 - 9c + 5c = 110

-4c = 110-126 = -16

c = -16/-4 = 4

a = 14-4 = 10

Answer:

128 4/7

Step-by-step explanation:

100%-30%=70%

90=.7X

900=7X

128 4/7=X

The value of p in the equation is as follows:

The subject of a formula is the variable which is expressed in terms of the other variables.

In other words, the subject of the formula is the variable which is on the left hand side of the formula.

Therefore, let's make p the subject of the formula in the equation xp - rx = ah.

xp - rx = ah

add rx to both sides of the equation

xp - rx = ah

xp - rx  + rx = ah + rx

xp = ah + rx

divide both sides by x

xp = ah + rx

xp / x = ah / x + rx / x

Therefore, the value of p = ah / x + r

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Answer:

Step-by-step explanation:

Step 1

1 of 5

Graph the three points and connect them to create the mid segments of the triangle:

Use midsegments of triangles in the coordinate plane.

Use the Triangle Midsegment Theorem to fi nd distances.

Using the Midsegment of a Triangle

A midsegment of a triangle is a segment that connects the

midpoints of two sides of the triangle. Every triangle has

three midsegments, which form the midsegment triangle.

The midsegments of △ABC at the right are MP —, MN —,

and NP —. The midsegment triangle is △MNP.

Using Midsegments in the Coordinate Plane

In △JKL, show that midsegment MN — is parallel to JL —

and that MN =

1

—2 JL.

SOLUTION

Step 1 Find the coordinates of M and N by fi nding

the midpoints of JK — and KL —.

M (—

−6 + (−2)

2

, —

1 + 5

2

) = M ( −8 —

2

, 6

—

2

) = M(−4, 3)

N (—

−2 + 2

2

, —

5 + (−1)

2

) = N ( 0

—

2

, 4

—

2

) = N(0, 2)

Step 2 Find and compare the slopes of MN — and JL —.

slope of MN —= —

2 − 3

0 − (−4) = −

1

—

4

slope of JL — = —

−1 − 1

2 − (−6) = −

2

—

8

= −

1

—

4

Because the slopes are the same, MN — is parallel to JL —.

Step 3 Find and compare the lengths of MN — and JL —.

MN = √——

[0 − (−4)]2 + (2 − 3)2 = √—

16 + 1 = √—

17

JL = √———

[2 − (−6)]2 + (−1 − 1)2 = √—

64 + 4 = √—

68 = 2 √—

17

JL = √———

[2 − (−6)]2 + (−1 − 1)2 = √—

64 + 4 = √—

68 = 2 √—

17

Because √—

17 =

1

—2

(2 √—

17 ) , MN =

1

—2 JL.

Monitoring Progress onitoring Progress Help in English and Spanish at BigIdeasMath.com

Use the graph of △ABC.

1. In △ABC, show that midsegment DE — is parallel

to AC — and that DE =

1

—2 AC.

2. Find the coordinates of the endpoints of

midsegment EF —, which is opposite AB —. Show

that EF — is parallel to AB — and that EF =

1

—2 AB.

READING

In the fi gure for Example 1,

midsegment MN — can be

called “the midsegment

opposite JL —.”

midsegment of a triangle,

p. 330

Previous

midpoint

parallel

slope

coordinate proof

Core Vocabulary Core Vocabulary

A C

P

N

M

B

x

y

4

6

−2

−6 −4 −2

M

N

K(−2, 5)

J(−6, 1)

L(2, −1)

x

y

−4

−6

−2 2 4 6

D

E

C(5, 0)

B(−1, 4)

A(

2327 is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.

Given that,

TV viewers frequently doubt the validity of particular advertising. In an attempt to counter their critics, a large advertiser wants to determine the true proportion of consumers who believe what is depicted in ads. About 40% of individuals examined, according to preliminary studies, seem to believe what is depicted in advertisements.

We have to find what is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.

We know that,

Let

Population proportion (p)= 0.40

Margin of error = 2% = 0.02

Confidence level = 95% = 0.95

α = 1- 0.95 = 0.05

α/2 = 0.025

Let's find out the Z critical value using excel for the 95% confidence level,

Use the following excel command.

= ABS(NORMSINV(α/2))

= ABS(NORMSINV(0.025))

We will get, Z critical value = 2.17009

Sample size (n) = p(1-p)×(Zα/2)/E

n = 0.40(1-0.40)({2.17009}÷{0.05})²

Sample size (n) = 2327

Therefore, 2327 is the minimal number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the genuine population proportion.

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Answer:

No solution

Step-by-step explanation:

-6x - 9y = 0

-24x -36y = 0

Multiply the top equation by -4 and add that to the second equation

24x + 36y = -4

-24x - 36y = 0

0 + 0 = -4

0 ≠ -4  Since this is a false statement, the answer is no solution.

The evaluation of 12P7 through permutation is 3991680.

This is a question of permutations . The capital letter P is a symbol for permutations. A permutation is a word that describes the number of ways things can be ordered or arranged. In other words , a permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

The formula for permutation is P(n,r)=n! (n−r)!

Hence , 12P7 = 12!/(12-7)!

⇒ 12!/5!

⇒ 12×11×10×9×8×7×6×5!/5!

Now , cancelling 5! from both denominator and numerator, we get
⇒ 12×11×10×9×8×7×6

⇒ 3991680

Therefore , the answer is 3991680.

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Answer:

Chemical energy is changed to heat energy.

Step-by-step explanation:

The exact value of tanθ is  -1/2  

What is the trigonometric ratio?

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Given:

θ is an angle in standard position and its terminal side passes through the point (2,-1).

To find:

The exact value of tanθ in simplest radical form.

If θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of tanθ is:

tanθ = y/x

It is given that, θ is an angle in standard position and its terminal side passes through the point  (2,-1),. So, t he exact value of tanθ is:

tanθ = -1/2

Therefore, the required value is  tanθ = -1/2  

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Answer:

5

Step-by-step explanation:

x=-1 doesn't fit in the range -1<x<2 since x>-1, not x=-1.

Hence, x=-1 fits in the range x<=-1 since (x<-1 or x=-1) which is true.

Hence, the expression -x+4 should be used

g(-1) =

-x + 4 =

-(-1) + 4 =  ==> plugin -1 for x

1 + 4 = 5  ==> Negating a negative number is equal to taking a positive

                       number

The smallest degree of rotation that will map a regular 16-agon onto itself is 22.5 degrees.

What is a degree?

A degree is a unit of measurement used to express angles. It is defined as 1/360th of a full rotation, or 1/2π radians.

To see this, note that a regular 16-agon has 16 sides, and each angle between sides measures 180(16-2)/16 = 135 degrees. Therefore, to rotate the 16-agon so that it maps onto itself, we must rotate it an integer multiple of 135 degrees.

However, we want the smallest such angle, so we must find the smallest integer multiple of 135 degrees that is greater than or equal to 360 degrees (since a full rotation maps the figure onto itself). The smallest such multiple is 2, which is equal to 270 degrees.

The smallest degree of rotation that will map the 16-agon onto itself is 270 degrees / 2 = 135 degrees / 2 = 22.5 degrees.

Hence, The smallest degree of rotation that will map a regular 16-agon onto itself is 22.5 degrees.

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The standard deviation is 4.95.

The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each value lies from the mean.

A high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean. The standard deviation and the mean together can tell you where most of the values in your frequency distribution lie if they follow a normal distribution.

Dataset: 1,2,4,7,8

So, n = 5 (because the sample size is 5)

We calculate the mean X by taking the average of the data values, which is dividing the sum of the data values by the number of data values:

X = 1+2+4+7+8/5

X=22/5 = 4.4

So, the average is 4.4

For standard deviation calculation,

$ = [tex]{\sqrt{(x-X)^2/n-1} }[/tex]

Thus, the standard deviation is 4.95.

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The pumpkin hangs between the two scales and weighs 58.77 N.

The given data is-

The result of the 2 scale readings is equal to the weight of a pumpkin swinging from the two scales.

The two forces combine to create resultant force;

R² = a² + b² - 2abcos(θ)

R² = 44² + 46² - 2(44)(46)cos(72)

R² = 3454.97

R = 58.77

Consequently, the pumpkin's weight on the two scales is 58.77 N.

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Luianne earns $4340 weekly by working as waitress at a local emerald Monday restaurant.

As per the known fact, one week comprises of seven days. Concerning this, the formula to be used for calculation is -

Regular weekly pay = Numbers of hours of work × number of days in a week × pay per hour

Keep the values in formula to find the regular weekly pay

Regular weekly pay = 40 × 7 × 15.50

Performing multiplication on Right Hand Side of the equation

Regular weekly pay = 4340

Hence, she earns $4340 weekly.

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36 is  the number of possible pairs of outcomes by probability.

What is a probability answer?

Mathematics' branch of probability, where probability is the likelihood that any event will occur, deals with the occurrence of random events.      

                                                 The probability value is given as a number between 0 and 1. Probabilities are always between 0 and 1. The basic probability formula is: Probability = Number of Favorable Outcomes / Total Number of Outcomes.

We have two dice in this question. A die is known to be make up of 6 faces.

Therefore the number of faces for two dice = 6*6 = 36

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The statements that are true for functions g(x) = x² and h(x) = -x² are given as follows:

The functions for this problem are defined as follows:

The function h(x) is given by the multiplication of the function g(x) by -1, meaning that it is the reflection over the x-axis of the function g(x).

The two quadratic functions share the same vertex at the origin, meaning that it cannot be affirmed that one function will always be greater than the other for all values of x.

However, considering that the x² function is non-negative in all it's domain, the reflected function -x² will be non-positive at all it's domain, they are equal only at the origin, which is the vertex, all for all remaining non-zero values, g(x) is greater than h(x).

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