if a line is perpendicular to a line segment what angle do they form at their intersection
A. 180°
B. 0°
C. 90°
D. 45°

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

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Considerando la definición de mínimo común múltiplo, el mínimo común múltiplo entre 10, 18 y 36 es 180.

Un número es múltiplo de otro cuando lo contiene n veces de forma exacta. Es decir, los múltiplos de un número son aquellos que obtienes cuando multiplicas un número por otros.

El mínimo común múltiplo (mcm) es la cifra más pequeña que satisface la condición de ser múltiplo de todos los elementos de un conjunto de números. En otras palabras, el mínimo común múltiplo (mcm) es el número positivo más pequeño que es múltiplo de dos o más números.

Una forma de calcular el mcm es descomponiendo los números en sus divisores (número que está contenido en otro de forma exacta una cantidad n de veces) y que estos sean números primos (que solo pueden dividirse entre ellos mismos y el 1 para obtener un número entero). Es decir, se debe descomponer en factores primos cada número.

Luego, se debe seleccionar los factores primos comunes y no comunes con mayor exponente para finalmente multiplicar los factores primos seleccionados.

En primer lugar, se descomponen los números:

Los factores primos comunes y no comunes con mayor exponente:

Entonces, el mínimo común múltiplo entre 10, 18 y 36 es calculada como:

M.C.M(10,18,36)= 2²×3²×5= 2×2×3×3×5= 180

Finalmente, el mínimo común múltiplo entre 10, 18 y 36 es 180.

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Answer:

A-△MNK ≅ △RTP

B- TR≅NM

C- X=7

Step-by-step explanation:

I did the assignment loves.

The given statements to be completed are completed as follows;

A) △MNK ≅ △RTP

B) TR ≅ NM

C) x = 7

We are given that;

△NMK ≅ △TRP

This means that Triangle NMK is congruent to Triangle TRP.

A) The naming of △NMK is now △MNK. Thus, we have to now re-name Triangle TRP to match the naming of △MNK. Thus;

△MNK ≅ △RTP

B) From the 2 given triangles, we can see that TR and NM are the same length and also perpendicular lines.

Thus they are congruent to each other and as such;

TR ≅ NM

C) Since TR and NM are congruent to each other. Then;

TR = NM

Thus;

3x - 1 = 20

3x = 20 + 1

3x = 21

x = 21/3

x = 7

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Answer:

B.$68 + d < $96

Step-by-step explanation:

Ellis is going on a tour that costs $68 while on vacation. He brought less than $96 to pay for the cost of the tour and dinner.

$68 + d less than $96

$68 + d < $96

Note:

< = Less Than

> = Greater Than

≤ = Less Than or Equal to

≥  Greater Than or Equal to

Answer:

6x + 154

Step-by-step explanation:

4(x + 40) +2(x -3) =

4x + 160 + 2x - 6 =

6x + 154

Answer:

2(3x + 77)

Step-by-step explanation:

4(x+40)+2(x-3)

4x+160+2x-6

6x+154

=2(3x+77)

The value of the given summation is:

\(\sum (29a_i - 13b_i) ]= -30\)

Here we know that the sums are:

\(\sum a_i = -10\\\\\sum b_i = -20\)

And we want to find the value of the sum:

\(\sum (29a_i - 13b_i)\)

First we can distribute the sum to get:

\(\sum 29a_i + \sum - 13b_i\)

And take the coefficients out of the sum:

\(29\sum a_i -13\sum b_i\)

Now replace the known values:

\(29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30\)

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The triangles are congruent by SAS theorem

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be represented as ΔRST

Let the second triangle be represented as ΔXYZ

Now , the measure of side RS = measure of side XY

And , the measure of side ST = measure of side YZ

The measure of angle ∠S = measure of angle ∠Y

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

Therefore , the triangles ΔRST and ΔXYZ are congruent triangles by the SAS theorem

Hence , they are congruent

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The expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

We break up a number according to its place value and expand it to show the value of each digit.

Given that to write expanded form of 706.039

Expanded Factors Form:

706.039 = 7 × 100  + 0 × 10 + 6 × 1  + 0 × 0.1 + 3 × 0.01 + 9 × 0.001

Expanded Notation Form:

706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

Hence, the expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

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Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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The value for x is 125. The solution has been obtained by using linear equation.

What is a linear equation?

The equation with the biggest degree of one is known as the linear equation. The lack of variables in a linear equation with an exponent larger than one is demonstrated by this. A straight line is produced by such an equation on the graph.

We are given an equation as

⇒2x + 6x = 1,000

On adding the like terms, we get

⇒8x = 1,000

On dividing both sides by 8, we get

⇒x = 125

Hence, the value for x is 125.

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Step-by-step explanation:

y int

x=0

y=4(0)-6

y=-6

0;-6

x int

y=0

0=4x-6

6=4x

6/4=x

3/2=x

3/2;0

Answer:

Below in bold.

Step-by-step explanation:

y = 4x - 6

Find y-intercept:

y = 4(0) - 6 = -6

Y intercept is at (0, -6)

x-intercept:

4x - 6 = 0

4x = 6

x = 6/4 =1.5.

x intercept is at (1.5, 0)

Midpoint is at ((0+1.5)/2, (-6 + 0)/2)

= (0.75, -3)

Answer:

\(3x^{3} - 14x^{2} - 5x\)

Step-by-step explanation:

I'm assuming what you're looking for is the expansion, or simplification, of the right side of that equation: x(3x + 1)(x - 5). So, let's go ahead and do that; let me know if you're looking for something else.

First, let's distribute that "x" at the beginning of the expression onto that first parenthetical expression, (3x + 1).

\(x(3x + 1) = x(3x) + x(x) = 3x^{2} + x\)

Now we have something different to simplify, \((3x^{2} + x)(x - 5)\).

\((3x^{2} + x)(x - 5) = \\3x^{2}(x) + 3x^{2}(-5) + x(x) + x(-5) = \\3x^{3} - 15x^{2} + x^{2} - 5x = \\3x^{3} - 14x^{2} - 5x\)

And there's our answer. Hopefully that was helpful - again, if you have any more questions, please let me know. :)

With a speed of 0.013 m/s, the snail would need to traverse 174 km in about 3718 hours.

The term "distance" refers to the length or space across two points as well as objects. It is a tangible quality that can be quantified in a variety of ways, including in metres, kilometres, miles, or feet. The distance formula in mathematics, which is derived first from Pythagorean theorem, can be used to determine the separation in space or in a plane between two points. In a plane, for instance, the distance that separates (x1, y1) and (x2, y2) is represented by: D is equal to sqrt((x2 - x1)2 + (y2 - y1)2) .Sqrt stands for the square root function.

given

We can apply the following formula to resolve this issue:

Time = Speed / Distance

(0.013 m/s) x (3600 s/h) x (1 km/1000 m) = 0.013 m/s

0.013 m/s = 0.0468 km/h

The snail moves at a speed of 0.0468 km/h.

The snail must go 174 km in how many hours, according to the question. The following values can be entered in the formula above:

Distance times speed equals 174 km / 0.0468 km/h, or 3717.94 hours.

To the nearest hour, we round:

duration: 3718 hours

With a speed of 0.013 m/s, the snail would need to traverse 174 km in about 3718 hours.

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Answer:

The answer is the 3rd one, not equivalent. 8x+4y=4(2x+y)

The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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Answer:

(a) 110

Step-by-step explanation:

We can plug in 7 for a and 3 for b.  Then we can simplify

11(a + b)

11(3 + 7)

11(10)

110

Thus, the value of 11(a + b) when a = 7 and b = 3 is 110, or answer a

Answer:

0.

Step-by-step explanation:

Multiplying 3, -2, 5, -1, and 0, we get:

3 x -2 x 5 x -1 x 0 = 0

So, 3(-2)(5)(-1)(0) = 0.

Answer:

Step-by-step explanation:

5x-2=-10x-1=10x3=30x0=0
0 is the very last answer

The measures οf the three angIes are x = 51.43 degrees, y = 92.85 degrees, and z = 118.85 degrees.

A Iinear equatiοn is a mathematicaI equatiοn that describes a straight Iine in a twο-dimensiοnaI pIane.

We can use the infοrmatiοn given in the prοbIem tο fοrm a system οf three equatiοns with three variabIes. Let x, y, and z represent the measures οf the first, secοnd, and third angIes, respectiveIy.

Frοm the first piece οf infοrmatiοn, we knοw that: x + y + z = 180

Frοm the secοnd piece οf infοrmatiοn, we knοw that: y + z = 5x

Frοm the third piece οf infοrmatiοn, we knοw that: z = y + 26

We can substitute the third equatiοn intο the secοnd equatiοn tο eIiminate z:

y + (y + 26) = 5x

2y + 26 = 5x

2y = 5x - 26

y = (5x - 26)/2

We can substitute this expressiοn fοr y intο the first equatiοn tο eIiminate y and z:

x + (5x - 26)/2 + (5x - 26)/2 + 26 = 180

2x + 5x - 26 + 26 = 360

7x = 360

x = 51.43

We can substitute this vaIue οf x back intο the expressiοn fοr y tο find y:

y = (5x - 26)/2

y = (5(51.43) - 26)/2

y = 92.85

FinaIIy, we can use the equatiοn z = y + 26 tο find z:

z = y + 26

z = 92.85 + 26

z = 118.85

Therefοre, the measures οf the three angIes are x = 51.43 degrees, y = 92.85 degrees, and z = 118.85 degrees.

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

1/5

Step-by-step explanation:

Chance is also referred to as probability

probability = Number of event/Total samples space

If there are 6 black socks,8 white socks,2 red socks, and 4 blue socks in a drawer, the total number of socks will be the sample space

Sample space = 6 + 8 + 2 + 4

Sample space = 20socks

Total number of blue socks is the event

Number of event = 4 blue socks

Chance that the socks is blue = n(E)/n(S)

Chance that the socks is blue = 4/20

Chance that the socks is blue = 1/5

Answer:

Images has the answers

Step-by-step explanation:

https://www.wolframalpha.com/input/?i=%28X-1%29%2F%282x%5E2%2Bx-3%29

Answer:

24

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

go to -4 on the x axis, then see which point the line is on, on the y axis.

The sample should be taken to provide a 95% confidence interval is 200.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

Confidence is another name for probability in statistics.

Given the planning value for the population proportion,

probability, p = 0.25

q  = 1 - p = 1 - 0.25

q = 0.75

margin of error = E = 0.06

value of z at 95% confidence interval is 1.96,

the formula for a sample is,

n = (z/E)²pq

n = (1.96/0.06)²*0.25*0.75

n = 200.08

n = 200 approx

Hence sample size is 200.

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The solution is:  the rate of change is 3.

Here, we have,

Since the graph of f(x) is translated 1 unit down, we need to decrease the value of f(x) by 1 to find g(x):

g(x) = f(x) - 1

f(x) = 3|x| – 4

so, we get,

g(x) = 3|x| – 4 - 1

      = 3|x| – 5

Now, to calculate the rate of change over the interval 2 <= x <= 5, we can use the formula below:

rate = g(5) - g(2)/ 5-2

so, we get,

rate = 9/3 = 3

Therefore the rate of change is 3.

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The probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

Let's use the formula for calculating the probability of the intersection of two events: P(A and B) = P(A) × P(B|A), where P(B|A) is the probability of event B occurring given that event A has occurred.

Let A be the event that it is raining, and B be the event that the flight is delayed. We are looking for P(A and B).

We know that:

P(A) = 0.1 (the probability that it will rain)

P(B) = 0.11 (the probability that the flight will be delayed)

P(not A and not B) = 0.88 (the probability that it will not rain and the flight will leave on time)

We can use the complement rule to find P(A or B):

P(A or B) = 1 - P(not A and not B)

P(A or B) = 1 - 0.88

P(A or B) = 0.12

Now we can use the formula for the intersection of two events:

P(A and B) = P(A) × P(B|A)

We know that P(A) = 0.1, and we need to find P(B|A), the probability of the flight being delayed given that it is raining.

We can use Bayes' theorem to find P(B|A):

P(B|A) = P(A and B) / P(A)

P(B|A) = (P(A) × P(B|A)) / P(A)

P(B|A) = P(B and A) / P(A)

We can rearrange this to get:

P(A and B) = P(B|A) × P(A)

Substituting the values we know:

P(B|A) = P(A and B) / P(A)

0.11 = P(A and B) / 0.1

P(A and B) = 0.11 × 0.1

P(A and B) = 0.011

Therefore, the probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

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On solving the provided question, we can say that - the range \(|x + 1| = 0\) \(x + 1 = 0 = > x = -1\) and \(y = 3\)

Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.

The regions where the absolute values are zero are known as the vertex points of an absolute value function.

\(|x + 1| = 0\\x + 1 = 0\\x = -1\)

\(y = |-1 + 1| + 3\\y= 0 + 3\\y = 3\)

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Answer:

The answer is below

Step-by-step explanation:

A function show the relationship between an independent variable and a dependent variable. An independent variable (input) is a variable that does not depend on other variable while a dependent variable (output) is a variable that depends on other variables.

The number of pages read is the dependent variable. Let it be represented as y while the time is the independent variable, let it be represented as x.

Since the  student reads 3 pages of a book every  5 minutes, therefore the function is:

\(y=\frac{3x}{5}\)

Domain is the set of all input (independent variable) while range is the set of all output (dependent variable)

The domain is from 5 minutes to 1 hour, that is 5 minutes to 60 minutes.

Domain = [5, 60]

When x = 60, y = 3(60)/5 = 36

The range = [3, 36]