Find the slope of the line graphed above. Question 2 options: A) –6 B) –10 C) –8 D) –5

Answer:

Step-by-step explanation:

The sum of the measures of the angles in a triangle is 180°.

  X + Y + Z = 180°

  84° +(r +59)° +(r +51)° = 180°

  2r +194 = 180 . . . . . . . . . divide by ° and simplify

  2r = -14 . . . . . . . . . .  subtract 194

  r = -7

Then the measure of Y is ...

  Y = (r +59)° = (-7 +59)°

  Y = 52°

__

Additional comment

Z = 44°

Gillian earned  $42.75 last week.

Arithmetic operators are used to perform mathematical operations like addition, subtraction, multiplication and division.

...

There are 7 arithmetic operators in Python :

Addition.

Subtraction.

Multiplication.

Division.

Modulus.

Exponentiation.

Floor division.

Gillian work

2.2 hours+3.5 hours= 5.7 hours

5.7 hours× $7.50 =  $42.75

Therefore Gillian earned $42.75

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The solution is , 225 mg remain in Aldi bloodstream.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

150mg of amoxicillin was given daily for 10 days equals 1,500

of the 1500-40% =600mg

so, we get,

600mg divided by  4 days

= 225mg still in blood stream

Hence, The solution is , 225 mg remain in Aldi bloodstream.

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Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Answer:

  15 litres

Step-by-step explanation:

  (1/2 litre/day)(30 days) = 15 litres

__

Multiply rate by time to get quantity.

Answer:

2x+9y=18

Step-by-step explanation:

Answer:

sophie receives £210

Step-by-step explanation:

120÷4=30

30x7=210

Jan, this is the solution to the problem:

Inequality to find the number of muffins a bakery makes everyday:

3x + 11 ≤ 260

Let's solve for x, this way:

3x ≤ 260 - 11

3x ≤ 249

Dividing by 3 at both sides:

3x/3 ≤ 249/3

x ≤ 83

The most accurate phrase that describes the number of muffins the bakery makes each day is:

at most 83 muffins

Answer:

3x + 1/2x

Step-by-step explanation:

Just replace "a number" with x

"Three times x added to half x"

The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.

To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    \(5x^3 + 2x^2 - 4x + 4\)

_______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              \(5x^3(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- (\(5x^3 + 5x^2)\)

This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

-\((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- \((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

-\((2x^2 + 2x)\)

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

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Answer:

125

Step-by-step explanation:

All the work is in picture attat

Answer: 20

Step-by-step explanation:

Answer:

The 90% confidence interval for the proportion of all letters mailed in the United States that were delivered the day after they were mailed is (0.7426, 0.8374). The lower limit is 0.7426 while the upper limit is of 0.8374.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

Suppose that 158 out of a random sample of 200 letters mailed in the United States were delivered the day after they were mailed.

This means that \(n = 200, \pi = \frac{158}{200} = 0.79\)

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a p-value of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.79 - 1.645\sqrt{\frac{0.79*0.21}{200}} = 0.7426\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.79 + 1.645\sqrt{\frac{0.79*0.21}{200}} = 0.8374\)

The 90% confidence interval for the proportion of all letters mailed in the United States that were delivered the day after they were mailed is (0.7426, 0.8374). The lower limit is 0.7426 while the upper limit is of 0.8374.

Answer:

3,000

Step-by-step explanation:

Answer:

I got 3,000

Step-by-step explanation:

Answer:

a) Hence the endpoints of a t-distribution with 5% beyond them in each tail if the sample has size n=12 is ± 1.796.

b) Hence the endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20 is ± 2.539.

Step-by-step explanation:

Here the answer is given as follows,

Answer:

Volume = 100 cm³

​Surface area of the square pyramid = 145 cm²

Step-by-step explanation:

Given:

Perpendicular height = 12cm

Square length = 5cm

Find:

Volume

​Surface area of the square pyramid

Computation:

Area of base = side²

Area of base = 5²

Area of base = 25 cm²

Volume = (1/3)(A)(h)

Volume = (1/3)(25)(12)

Volume = 100 cm³

​Surface area of the square pyramid = A + 1/2(P)(h)

Perimeter square pyramid = 4(s)

Perimeter square pyramid = 4(5)

Perimeter square pyramid = 20 cm

​Surface area of the square pyramid = 25 + 1/2(20)(12)

​Surface area of the square pyramid = 145 cm²

The linear equation written in the slope-intercept form is:

y = (-3/5)*x

The correct option is C.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we can see that the line crosses through the poin (0, 0), so the y-intercept is 0.

b = 0

y = a*x + 0

y = a*x

To find the value of a, we can use another point on the graph.

We can see that the linear equation passes through (5, - 3), replacing these values:

-3 = a*5

-3/5 = a

Then the linear equation is just:

y = (-3/5)*x

The correct option is C.

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An orthonormal set is a set of orthogonal unit vectors.

Normalization is the process of making unit vectors.

A set of vectors in which each vector is orthogonal to every other vector in the set is called an orthogonal set of vectors.

Two vectors are orthogonal when their dot product equals zero.

An orthonormal set is one in which each vector has length 1 and is orthogonal.

The process of creating a vector of length 1 in the same direction of the original vector is called "normalization".

An orthonormal set of vectors that is a basis of a vector space is quite useful. We can use the Gram-Schmidt process to transform a basis of a vector space (which may not be orthogonal) into an orthonormal basis.

To normalize vectors to produce an orthonormal set of vectors, we calculate the length of the vector and divide the vector by its length, to obtain a unit vector.

Since the question asked about "how to normalize vectors to produce an orthonormal set" that implies that the vectors already form an orthogonal set.

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The given question is incomplete,

So , I take another question, The question is:

How to normalize vectors to produce an orthonormal set?

Answer:

P=0.071429

Step-by-step explanation:

1) if the first member of team needed is already choosen and this is a girl, then the rest members are 4 boys and 4 girls. The rest 3 positions should be choosen from that 8 persons;

2) according to the condition 3 boys should be choosen from the rest team members, but there are 4 boys+4girls. The required probability can be written as

\(P=\frac{C^3_4}{C^3_8};\)

3) finally,

\(P=\frac{C^3_4}{C_8^3}=\frac{4*3!*5!}{8!}=\frac{1}{14}=0.07142857142857142857142857142857;\)

⇔ P=0.071429.

P.S. if it is possible, check the suggested solution in other sources.

The solution by substituting 15 for b in the Original equation. The answer is true.

The steps needed to solve the equation b + 6 = 21 are:

Subtract 6 from both sides of the equation: b + 6 - 6 = 21 - 6, which simplifies to b = 15.

Check the solution by substituting 15 for b in the original equation: 15 + 6 = 21, which is true.

Therefore, the correct steps to solve the equation are:

Subtract 6 from both sides of the equation. The answer is b = 15

the solution by substituting 15 for b in the original equation. The answer is true.

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Correct question:

An urn contains 3 red and 7 black balls. Players A and B withdraw balls from the urn consecutively until a red ball is selected. Find the probability that A selects the red ball. (A draws the first ball, then B, and so on. There is no replacement of the balls drawn).

Answer:

The probability that A selects the red ball is 58.33 %

Step-by-step explanation:

A selects the red ball if the first red ball is drawn 1st, 3rd, 5th or 7th

1st selection: 9C2

3rd selection: 7C2

5th selection: 5C2

7th selection: 3C2

9C2 = (9!) / (7!2!) = 36

7C2 = (7!) / (5!2!) = 21

5C2 = (5!) / (3!2!) = 10

3C2 = (3!) / (2!) = 3

sum of all the possible events = 36 + 21 + 10 + 3 = 70

Total possible outcome of selecting the red ball = 10C3

10C3 = (10!) / (7!3!)

         = 120

The probability that A selects the red ball is sum of all the possible events divided by the total possible outcome.

P( A selects the red ball) = 70 / 120

                                         = 0.5833

                                         = 58.33 %

Answer:

x + 3y = -15

Step-by-step explanation:

There are 2 ways to find this equation:

The first way:  We have: y = ax + b (this is the line, right?)

The line is through the point (-6, -3) so we have:

-3 = (-6)a + b      (1)

The line is also through the point (-9, -2) so we have:

-2 = (-9)a + b.       (2)

From (1) and (2) we get a equals -1/3, b equals -5. Then:

\(y=-\frac{1}{3} x - 5\)

<=> \(x + 3y=-15\)

The second way:

Let A(-6, -3) and B(-9, -2), then AB = (-3, 1).

=> The normal vector of this line is n = (1, 3).

The line that is through the points A(-6, -3) and B(-9, -2), and has the normal vector n=(1, 3) has the equation:

\(1(x+6) +3(y+3)=0\\x+3y +15=0\\x+3y=-15\)

Answer:

1 /2

Step-by-step explanation:

3×1 = 3

So it is 3 /6 = 1/2

3/6 ÷2 = 1/2

Step-by-step explanation:

law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a,b,c being the sides of the triangle, A, B, C are the corresponding opposite angles in the triangle.

the angle of depression is the external angle of the triangle vertex at the balloon. that means the internal angle is 60°, as both together must be 90° (the angle between the height of the balloon and the horizontal line at the balloon).

the angles at the ground at the fire are mirrored : the internal angle there is 30°, the external angle is 60°.

and so,

height/sin(30) = 150/0.5 = distance/sin(60)

distance = sin(60)×150/0.5 = sin(60)×300 =

= 259.8076211... ft ≈ 260 ft

Check the picture below.

The length of the hypotenuse (x) in the given right triangle is approximately 10 units.

Hence the correct option is B.

Given is right triangle with perpendicular side having measurement of 5 units,

The acute angle between the base and the hypotenuse = 30°

The acute angle between the perpendicular and the hypotenuse = 60°

We need to find the length of the hypotenuse (x).

We can use the trigonometric ratio for sine (sin) to relate the lengths of the sides.

In this case, we'll use the sine of the 30° angle:

sin(30°) = opposite/hypotenuse

sin(30°) = 5/x

To solve for x, we can rearrange the equation:

xsin(30°) = 5

x = 5 / sin(30°)

Now, we can calculate the value of x using this equation:

x = 5 / sin(30°)

x ≈ 10 units

Therefore, the length of the hypotenuse (x) in the given right triangle is approximately 10 units.

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Answer:

The 95% confidence interval   \( 81.852  <  \mu <  280.098 \)

Step-by-step explanation:

From the question we are told that

   The  sample mean is  \(\= x  =  180.975\)

   The standard deviation is  \(\sigma  =  143.042\)

   The sample size is n = 8

Given that the confidence level is  95%  then the level of significance is  

    \(\alpha =( 100- 95) \%\)

=>  \(\alpha =0.05\)    

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>  \(E = 1.96 *  \frac{ 143.042 }{\sqrt{8} }\)

=>  \(E = 99.123 \)

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  \mu <  \=x  +E\)

=>    \(180.975 -99.123 <  p <  180.975 +99.123\)

=>    \( 81.852  <  \mu <  280.098 \)

Using the t-distribution, it is found that the 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).

The information given is:

We have the standard deviation for the sample, hence, the t-distribution is used.

The interval is given by:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The critical value for a two-tailed 95% confidence interval with 8 - 1 = 7 df is t = 2.3646.

Then:

\(\overline{x} - t\frac{s}{\sqrt{n}} = 180.975 - 2.3646\frac{143.042}{\sqrt{8}} = 61.39\)

\(\overline{x} + t\frac{s}{\sqrt{n}} = 180.975 + 2.3646\frac{143.042}{\sqrt{8}} = 300.56\)

The 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).

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Answer:

I think it b

Step-by-step explanation:

I had the same question

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1