a normal distribution with a mean of 15 and standard deviation 0f 5.95% its area is within ?

QUESTION 1

We can use the cosine rule to find the missing side length.

Recall that the cosine rule for a triangle with sides a,b,c and an included angle A is

[tex]a^2=b^2+c^2-2bc\cos A[/tex]

Let the missing side length in the triangle with sides 6, 9 and the included angle of [tex]37\degree[/tex] be [tex]a[/tex] units.

We then substitute the values into the cosine rule to obtain;

[tex]a^2=6^2+9^2-2(6)(9)\cos 37\degree[/tex]

[tex]a^2=36+81-108\cos 37\degree[/tex]

[tex]a^2=30.747[/tex]

[tex]\Rightarrow a=\sqrt{30.747}[/tex]

[tex]\Rightarrow a=\sqrt{30.747}[/tex]

[tex]\Rightarrow a=5.5[/tex] units to the nearest tenth.

QUESTION 2

We again use the cosine rule: [tex]a^2=b^2+c^2-2bc\cos A[/tex]

We substitute the given values to obtain;

[tex]a^2=11^2+13^2-2(11)(13)\cos 108\degree[/tex]

[tex]a^2=121+169-286\cos 108\degree[/tex]

[tex]a^2=378.379[/tex]

[tex]\Rightarrow a=\sqrt{378.379}[/tex]

[tex]\Rightarrow a=19.5[/tex] to the nearest tenth

QUESTION 3

We again use the cosine rule :

[tex]|BA|^2=(\frac{1}{2})^2+(\frac{1}{3})^2-2(\frac{1}{2})(\frac{1}{3})\cos 100\degree[/tex]

[tex]|BA|^2=0.418899[/tex]

[tex]|BA|=\sqrt{0.418899}[/tex]

[tex]|BA|=0.65[/tex] to the nearest hundredth

Answer:

Step-by-step explanation:

You would do this question like this.

4 meats * 2 cheeses * x breads = 24 different kinds of  sandwiches.

8x = 24

8x/8 = 24/8

x = 3

There are 3 different kinds of breads.

So the ratio are 1:2:3:4 and all these add up to 10

Now we divide 360 by 10 resulting to 36

A=(36)

B=(72)

C=(108)

D=(144)

All these add up to 360 and has been divided equally according to the ration provided

Final answer:

To find the measures of the angles in quadrilateral ABCD with ratios 1:2:3:4, we set the angles as x, 2x, 3x, and 4x, and use the fact that their sum equals 360 degrees. Solving for x, we find x to be 36 degrees, which gives us the individual angles as 36 degrees, 72 degrees, 108 degrees, and 144 degrees respectively.

Explanation:

Calculating the Measures of the Angles in a Quadrilateral

Given that the measures of the angles A, B, C, and D in quadrilateral ABCD are in the ratio of 1:2:3:4 respectively, we first need to understand that the sum of the interior angles in a quadrilateral is always 360 degrees. To find the measure of each angle, we should express the ratio in terms of x, which would give us the angles as x, 2x, 3x, and 4x. Summing these and setting them equal to 360 degrees, we get the equation x + 2x + 3x + 4x = 360. Simplifying, we have 10x = 360, which when solved for x yields x = 36 degrees. Therefore, the measures of the angles are:

Angle A = 1x = 36 degrees

Angle B = 2x = 72 degrees

Angle C = 3x = 108 degrees

Angle D = 4x = 144 degrees

Hence, each angle's measure has been found using the given ratio and the property of the sum of interior angles in a quadrilateral.

Answer:

B) 1.

Step-by-step explanation:

x^2 - 8x + 7 = 0

(x - 1)(x - 7) = 0

x= 1, 7.

Answer:

x = 1

Step-by-step explanation:

Please express exponentiation using the symbol  " ^ "  :  x^2 - 8x + 7 = 0

Let's solve this equations using "completing the square:"

x^2 - 8x + 7 = 0

1) Identify the coefficient of the x term.  Here it's -8.

2) take half of that and square it:  we get (-4)² = 16

3) insert " +16 - 16 " between the 8x and the 7:

        x^2 - 8x +  16 - 16  +7 = 0

4)  Rewrite this perfect square:

          (x - 4)² - 16 + 7 = 0  ->   (x - 4)^2 = 9

5)  Solve for (x -4) by taking the square root of both sides:

           x - 4 ± sqrt(9)    ->  x - 4 ± 3

6)  Solve for x:  x = 4  ± 3, or x = 7 and x = 1.  

7)  Take the lesser root of 7 and 1.  That would be x = 1.  Answer B is correct.

Answer:

A) μ = 590.45 mm; B) σ² = 0.053 mm

Step-by-step explanation:

To find the mean, we add together all of the values and divide by the number of data values:

590.1+590.2+590.3+590.4+590.5+590.6+590.7+590.8 = 4723.6

There are 8 data values; this gives us

4723.6/8 = 590.45

To find the variance, we subtract each of the data values from the mean.  We then square this difference, and find the mean of the squares:

590.1-590.45 = -0.35; (-0.35)² = 0.1225

590.2-590.45 = -0.25; (-0.25)² = 0.0625

590.3-590.45 = -0.15; (-0.15)² = 0.0225

590.4-590.45 = -0.05; (-0.05)² = 0.0025

590.5-590.45 = 0.05; (0.05)² = 0.0025

590.6-590.45 = 0.15; (0.15)² = 0.0225

590.7-590.45 = 0.25; (0.25)² = 0.0625

590.8-590.45 = 0.35; (0.35)² = 0.1225

(0.1225+0.0625+0.0225+0.0025+0.0025+0.0225+0.0625+0.1225)/8

= 0.42/8 = 0.0525 ≈ 0.053

(a) The mean of the glass parts rounded to nearest tenths of millimeters

= 590.45 and (b) Variance in tenths of millimeters is = 0.053 mm.

In a given set of data one which repeats most frequently is called the mode of the given data set.

To obtain the mean we add together all of the values and divide by the number of data values.

590.1+590.2+590.3+590.4+590.5+590.6+590.7+590.8 = 4723.6

There are 8 data values; this gives us

4723.6/8 = 590.45

To find the variance, we subtract each of the data values from the mean and we square this difference to find the mean of the squares.

590.1-590.45 = -0.35; (-0.35)² = 0.1225

590.2-590.45 = -0.25; (-0.25)² = 0.0625

590.3-590.45 = -0.15; (-0.15)² = 0.0225

590.4-590.45 = -0.05; (-0.05)² = 0.0025

590.5-590.45 = 0.05; (0.05)² = 0.0025

590.6-590.45 = 0.15; (0.15)² = 0.0225

590.7-590.45 = 0.25; (0.25)² = 0.0625

590.8-590.45 = 0.35; (0.35)² = 0.1225

(0.1225+0.0625+0.0225+0.0025+0.0025+0.0225+0.0625+0.1225)/8

= 0.42/8 = 0.0525 and rounded to tenths of millimeters is 0.053

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Answer:

$16.50

Step-by-step explanation:

If Jason spends $3.75 and Maya spends three times that amount, Maya spends 3.75(3) or $11.25. If Tia spends $5.25 more than Maya, Tia spends 11.25 + 5.25 or $16.50.

Check the picture below.

notice, we use the 30-60-90 rule to get the length of RT, and then the 45-45-90 rule to get "x".

Answer:

Step-by-step explanation:

Remark

x is going to be the same thing as the hypotenuse of ΔRST.  Find that and you have x.

Givens

<STR = 60°

RT = 2√3

Solution

Sin(60°) = opposite / hypotenuse

Sin(60°) = √3 / 2

Sin (60°)= 2 √3 / hypotenuse

hypotenuse = 2√3 // sin(60°)

hypoteneuse = 2√3 /√3/2

[tex]\text{hypotenuse = }\dfrac{2\sqrt{3}}{\dfrac{\sqrt{3} }{2}} = 2*2[/tex]

The √3's cancel. The answer is 4

========================

ΔRTQ is a right angle isosceles triangle

∴RT = RQ

X = 4

Answer:

8 < 6x

Step-by-step explanation:

Just write what you see by the letters

Answer:4.375 Maybe?

Step-by-step explanation:

Answer: 100%

Step-by-step explanation:

We are given a Box- plot, in which the minimum value is described by the left whisker is 3 and the maximum value is described by the right whisker is 24.

Since the range of all data values in a data is given from minimum value to the maximum value.

⇒ The percentage of the data values falls between the values of 3 and 24 in the data set shown = 100%

if we distribute 2(2x+5), we'll end up with 4x + 10, so in short, the right-hand-side, is really the left-hand-side in disguise.

and since  4x + 10 = 4x + 10, both equations are equal, meaning in short, the system has an infinite number of solutions.

Answer: [tex]x=-\frac{3}{5}[/tex]

Step-by-step explanation:

By the negative exponent rule, you have that:

[tex](\frac{1}{a})^n=a^{-n}[/tex]

By the exponents properties, you know that:

[tex](m^n)^l=m^{(nl)}[/tex]

You can rewrite 16 and 9 as following:

16=4²

9=3²

Therefore, you can rewrite the left side of the equation has following:

[tex](\frac{4^2}{3^2})^{(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3^2}{4^2})^{-(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3}{4})^{-2(2x+5)}=(\frac{3}{4})^{(x-7)}[/tex]

 As the base are equal, then:

[tex]-2(2x+5)=x-7[/tex]

Solve for x:

[tex]-2(2x+5)=x-7\\-4x-10=x-7\\-4x-x=-7+10\\-5x=3\\x=-\frac{3}{5}[/tex]

Answer:

[tex]log_{3}(x . y^\frac{1}{3} / z^5 )[/tex]

Step-by-step explanation:

Given in the question an expression

[tex]log_{3} x+\frac{1}{3}log_{3} y-5log_{3} z[/tex]

To Condense this log into a single log we will use logarithm rules

logb(x^y) = y ∙ logb(x)

[tex]\frac{1}3}log_{3} y = log_{3}y^\frac{1}{3}[/tex]

[tex]5log_{3} z = log_{3} z^5[/tex]

logb(x ∙ y) = logb(x) + logb(y)

[tex]log_{3} x + log_{3}y^\frac{1}{3} = log_{3}(x . y^\frac{1}{3} )[/tex]

[tex]logb(x / y) = logb(x) - logb(y)\\log_{3}(x . y^\frac{1}{3} )- log_{3} z^5[/tex]

= [tex]log_{3}(x . y^\frac{1}{3} / z^5 )[/tex]

The number [tex] \pi [/tex] is defined as the ratio between the circumference and the diameter of a circle. In other words, for every circle, we have

[tex]\pi=\dfrac{C}{d}=\dfrac{C}{2r}[/tex]

Since the diameter is twice the radius.

Solving for the circumference, we have

[tex]C=2\pi r[/tex]

So, in your case, the answer is

[tex]C=16\pi[/tex]

Answer:

50.24

Step-by-step explanation:

The possible coordinates for point B that are 10 units away from point A at (2,-3) could be (12, -3), (2, 7), (-8, -3), or (2, -13), moving directly horizontal or vertical.

If point A is located at (2,-3), and there are 10 points between A and B, we're likely looking at points equidistant from A, forming a sort of 'circle' with A at the centre. However, in a Cartesian plane, if the distance between two points is equal to 10 units, there are various possibilities depending on the orientation of the line connecting the two points.

For a point B to be 10 units away from point A at (2, -3), it can move horizontally to the right or left, or vertically up or down. Thus, the possible coordinates for point B would change by 10 units either in the x-coordinate (horizontally) or the y-coordinate (vertically).

Possible Coordinates for Point B

Horizontally to the right: (2+10, -3) = (12, -3)

Vertically up: (2, -3+10) = (2, 7)

Horizontally to the left: (2-10, -3) = (-8, -3)

Vertically down: (2, -3-10) = (2, -13)

Other options like (12, -6), (2, -7), (12, 3), or (-8, 3) do not adhere to being 10 units away from point A directly horizontally or vertically.

The complete question is:

If point A is located at (2,-3) , and there are 10 points between A and B, what * 1 could be the possible coordinates for point B? Choose all that apply. (12,-3) (2,7) (12,-6) (-8,-3) (2,-7) (-8,3) (2,-13) (12,3)

Answer:

38°

Step-by-step explanation:

The triangle solver app on your calculator, phone, or tablet can solve this for you readily. There are on-line triangle solvers, too.

___

For solution "by hand", the Law of Cosines is useful. It tells you ...

a^2 = b^2 + c^2 -2ab·cos(A)

Then the angle A can be found as ...

cos(A) = (b^2 +c^2 -a^2)/(2ab) = (3^2 +7^2 -5^2)/(2·3·7) = 33/42 = 11/14

A = arccos(11/14) ≈ 38°

_____

In formulas like the Law of Cosines or the Law of Sines, the uppercase letters stand for the measures of angles, and the lowercase letters stand for their opposite side lengths.

Each friend should get 1/5 of a bag of trail mix. Since there are three bags of trail mix, you would add those into it. Hope this helps!

Answer:

D) 8

Step-by-step explanation:

Given function for height =  f(x) = 80(0.5)^x

It shows that the height of ball after any bounce can be calculated by putting bounce number in place of x in this equation.

so, height after first bounce f(1) is calculated by placing 1 in place of x

f(1) = 80(0.5)^1

f(1) = 80(0.5)

f(1) = 40

Similarly, the height after 4th bounce f(4)

f(4) = 80(0.5)^4

f(4) = 80(0.0625)

f(4) = 5  

Therefore, the height of 1st bounce is 40/5 = 8 times higher than the fourth bounce. So, option D is correct.

The first bounce is 8 times higher than the fourth bounce. Option D (8) is correct.

The height of the bouncing ball is given by the function f(x) = 80(0.5)^x, where x represents the number of bounces. To find how many times higher the first bounce is than the fourth bounce, we'll calculate the heights for f(1) and f(4) and then compare them.

Therefore, the first bounce is 8 times higher than the fourth bounce, corresponding to option D (8).

Answer:

(u)^{2}+7(u)-8=0

Step-by-step explanation:

Answer:

The equivalent quadratic equation corresponding to (3x + 2)² + 7(3x + 2) – 8 = 0 is y² + 7y – 8 = 0  

Step-by-step explanation:

Here given (3x + 2)² + 7(3x + 2) – 8 = 0

Substitute 3x + 2 as y

Solving

          y² + 7y – 8 = 0  

The equivalent quadratic equation corresponding to (3x + 2)² + 7(3x + 2) – 8 = 0 is y² + 7y – 8 = 0  

Answer:

B.

Step-by-step explanation:

Because the graph shown is not constant, if you look at when it hits a whole unit. It is increasing because it is moving right.

The true statement is:

B.  

The function indicates that the number of members is increasing at a rate that is not constant.

We could write the data points as is given on the graph as follows:

  x       y

  0      40

  1       50

  2      60

  3      80

  4      100

  5      120

  6      150

  7      190

  8      240

  9      300

  10     370

Hence, the rate of change from x=0 to x=1 is:

[tex]Rate=\dfrac{50-40}{1-0}\\\\\\Rate=\dfrac{10}{1}\\\\\\Rate=10[/tex]

Rate of change from x=3 to x=5 is:

[tex]Rate=\dfrac{120-80}{5-3}\\\\\\Rate=\dfrac{40}{2}\\\\\\Rate=20[/tex]

Hence, the rate is not constant.

Also we could see that with the increasing value of x the y-value also increases.

                  Hence, option: B is the correct answer.

Final answer:

The dimensions of the price tag are 9 cm by 4 cm, which are found by solving two equations derived from the given area and perimeter.

Explanation:

The student is asking for the dimensions of a rectangular price tag that has an area of 36 square centimeters and a perimeter of 26 centimeters. To solve this, we need to use two formulas: one for area (A = length × width) and one for perimeter (P = 2 × (length + width)).

First, let's denote the length of the rectangle by l and the width by w. The given area, 36 cm2, implies that l × w = 36.

Second, we know the perimeter is 26 cm, which gives us the equation 2 × (l + w) = 26. Dividing both sides by 2, we get l + w = 13.

This system of equations can be solved using substitution or elimination. If we rearrange the perimeter equation to express one variable in terms of the other (for instance, w = 13 - l), we can then substitute this expression into the area equation. Solving for l and w afterwards will give us the required dimensions.

Through solving, we find that the dimensions of the rectangle are 9 cm by 4 cm, since 9 × 4 = 36 and 2(9 + 4) = 26.

Answer:

The length of the arc is [tex]27\pi \ cm[/tex]

Step-by-step explanation:

step 1

Find the circumference

we know that

The length of a complete circle is equal to the circumference of the circle

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=18\ cm[/tex]

substitute

[tex]C=2\pi (18)[/tex]

[tex]C=36\pi\ cm[/tex]

step 2

we know that

A central angle of  [tex]2\pi[/tex] radians subtends the circumference of [tex]36\pi\ cm[/tex]

so

by proportion

Find the length of the arc by a central angle of [tex]\frac{3\pi }{2}[/tex] radians

[tex]\frac{36\pi }{2\pi}\frac{cm}{radians}=\frac{x}{(3\pi/2)}\frac{cm}{radians} \\ \\x=18*(3\pi/2)\\ \\x=27\pi \ cm[/tex]

The cosine of the angle formed by the line whose equation is y=2x and the positive x axis cos =63.435 to the nearest thousandth

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Final answer:

To find the cosine of the angle formed by the line y=2x and the positive x-axis, we calculate the arctangent of the slope (2), which gives us an angle of approximately 63.435 degrees. The cosine of this angle is then approximately 0.447 to the nearest thousandth.

Explanation:

The question is asking for the cosine of the angle formed between the line y = 2x and the positive x-axis. To find this, we first need to determine the angle that the line makes with the x-axis. The slope of the line, given by m, is 2, which also represents the tangent of the angle the line forms with the x-axis (tan(θ) = m). We can calculate the angle using the arctangent function (tan⁻¹).

θ = tan⁻¹(2) = Approx. 63.435 degrees

The cosine of this angle can be found using the cosine function:

cos(θ) = cos(63.435 degrees) = Approx. 0.447

To the nearest thousandth, the cosine of the angle is 0.447.

The sides could be 10.2 inches or 15.7 inches.

See the attached picture for the equations:

Answer:

The baby would be 160 ounces.

Step-by-step explanation:

The baby who weighted 10 pounds, weighs 160 ounces.

Given that at a doctor's appointment, a baby weighed 10 pounds.

From the conversion table, we know that 1 pound is equal to 16 ounces.

Thus 10 pounds is equal to 160 ounces.

Therefore, the baby weighted 160 ounces.  

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Answer:

See below

Step-by-step explanation:

The score increase was 35 points. They claimed an increase of at least 50 points.  For a significance level of 5%, the z-score for the situation needs to be at smaller than -1.645.  For a significance level of 1%, the z-score needs to be smaller than -2.325

The z score for our situation:  z = (385 - 350)/50 = 0.7

The average score of 385 of Tutor O-Rama scores is not significantly different from the average of the other students SAT scores.  The evidence doesn't support their claim of being effective tutoring.

Answer:

The answer is

D.16

Step-by-step explanation:

She can buy 20 1$ items, or 10 $2 items, at most

Answer:

f(x) = 70 + 2x

Step-by-step explanation:

In this problem, we first need to consider how much we get per day.

$70 is our constant.

$2 will be dependent on the number of books sold.

Here 'x' will represent the number of books sold.

f(x) = 70 + 2x

Now let's try it out.

Let's say we sold 0 books

f(0) = 70 + 2(0) = 70

This shows us that we only get our constant pay.

Now let's try for 1 or more books.

f(1) = 70 + 2(1) = 72

f(2) = 70 + 2(2) = 74

So the recursive formula f(x) = 70 + 2x is a good formula to model the situation.

Answer:

a1 = 70

an = an–1 + 2

Step-by-step explanation: