Heart rates. A trainer records the maximum heart rates of 9 random cyclists over the course of a workout. The numbers are displayed below, and heart rate is known to be normally distributed. Construct a 95% confidence interval for the average maximum heart rate.


150 155 162 163 166 172 178 189 192


(a) The confidence interval is: (Round to one decimal place)

( ) , ( )
,

Step-by-step explanation:

please make me brainalist and keep smiling dude

as a fraction

the first is 6, then 1, then 4

There are 1620 ways of selecting the committees

Combination is a way of selecting items from a collection where the order of selection does not matter.

How to determine this

Faculty member can be selected in 3 ways

Male students in 6 ways

Female students in 6 ways

Parents in 5 ways

School board member in 3 ways

So, to get the total number of ways,

= 3 * 6 * 6 * 5 * 3

= 1620 ways

Therefore, the committee can be selected in 1620 ways

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Answer: how many students are on the team??

Step-by-step explanation:

add this!!!

0.3 is the lowest possible value

Answer:

Step-by-step explanation:

The dependent variable (y) is the total cost for renting the paddleboat.

The independent variable (x) is the number of hours that the paddleboat is rented for.

The equation that shows the relationship between x and y is:

y = 5x + 10

This equation represents a linear relationship where the slope (or rate of change) is $5 per hour, and the y-intercept is $10 (the cost for renting the boat for 0 hours). The term "5x" represents the additional cost for each hour rented, and the constant term "10" represents the initial cost of renting the paddleboat. To find the total cost of renting the boat for a specific number of hours (x), we can substitute that value of x into the equation and solve for y.

Answer:

(30.1, 185.6)

Step-by-step explanation:

p = -4q + 306

P = 6q +5

from here, all we need to do is solve the system. Since the value of p is already isolated for us, we can just plug this into the first equation

(6q + 5) = -4q + 306

Add like terms

10 q + 5 = 306

Subtract:

10 q = 301

Q = 30.1

We can them plug this into the second equation:

P = 6(30.1) + 5

P = 180.6 + 5

P = 185.6

So together, we have (30.1, 185.6)

thanks, and please give brainliest!

Answer:

(185.6, 30.1)

Step-by-step explanation:

Set the equations equal to each other and solve for q

-4q + 306 = 6q + 5  add 4q to both sides

4q - 4q + 306 = 6q + 4q + 5

306 = 10q + 5  Subtract 5 from both sides

306 - 5  = 10q + 5 - 5

301 = 10q  Divide both sides by 10

30.1 =  q

Substitute 30.1 for q in either of the two original equations.  It does not matter which one, they will both work to solve for p.

p = 6q + 5

p = 6(30.1) + 5

p = 180.6 + 5

p = 185.6

Helping in the name of Jesus.

Answer: 125.66

Step-by-step explanation: C=2πr=2·π·20≈125.66371

The values of a and b are 7 and 2 respectively.

Let's represent Kyle's equation as:

3a + 2b = 25

And Tess's equation as:

5a + 4b = 43

We can solve this system of equations by elimination. Let's multiply the first equation by 4 and the second equation by -2, and then add them together:

12a + 8b = 100

-10a - 8b = -86

2a = 14

Therefore, a = 7. We can substitute this value into either equation to find b. Let's use Kyle's equation:

3a + 2b = 25

3(7) + 2b = 25

21 + 2b = 25

2b = 4

b = 2

So, the values of a and b are a = 7 and b = 2.

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Answer: %82

Step-by-step explanation: First you want to subtract 200-36 because you need the final price to help you get the percentage. Next, you times 200 by different percentages to try to get to 164 which is the final price. I assumed it was %80 first, so I did 200 times .80, but that was 160, so then I proceeded to times it by .82 or %82 and that was the answer. Hope this helps!

Answer:

I believe the answer is D. c + 0.95

Step-by-step explanation:

Answer:

Step-by-step explanation:

ΔABC is an isosceles triangle, which is indicated by the marks on the two sides.

Isosceles triangles are triangles that have two equal side lengths and angles. So here, ∠A and ∠C have the same angle measures.

Additionally, the sum of the three angles of any triangle sums up to 180°.

..................................................................................................................................................

Given: m∠A = 8x, m∠B = 44x, and m∠C = 8x

Step 1: Set the measure of the angles to equal 180.

[tex]\implies 8x+44x+8x=180[/tex]

[tex]\implies 60x=180[/tex]

Step 2: Divide both sides by 60.

[tex]\implies \dfrac{60x}{60}=\dfrac{180}{60}[/tex]

[tex]\implies x=3[/tex]

Step 3: To find the measure of each angle, substitute 3 for x.

[tex]\implies m \angle A = 8(3) = 24^\circ[/tex]

[tex]\implies m \angle B = 44(3) = 132^\circ[/tex]

[tex]\implies m \angle C = 8(3) = 24^\circ[/tex]

The measures of ∠A, ∠B, and ∠C all sum up to 180°.

The required three angles of the triangle are 15 degrees, 75 degrees, and 90 degrees.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here

Let's denote the measure of the smallest angle as x.

According to the problem, one of the angles is five times as large as x and the other angle is six times as large as x.

So, the measures of the three angles can be written as: x, 5x, and 6x.
We know that the sum of the angles of a triangle is 180 degrees. Therefore, we can write:

x + 5x + 6x = 180

12x = 180

x = 15

Substituting x = 15 in the expressions for the angles, we get:

Smallest angle = x = 15 degrees

Second angle = 5x = 75 degrees

Third angle = 6x = 90 degrees

Therefore, the three angles of the triangle are 15 degrees, 75 degrees, and 90 degrees.

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In the straight line slope -2/3 and y-intercept will be 4.

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The equation of the y = -2/3x +4

So here the slope is -2/3

The y-intercept will be 4.

Hence In the straight line slope -2/3 and y-intercept will be 4.

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The total cost if you buy 2 bottles of liquid soap and 3 sponges is $6.79.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+6. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=5 and b=6.

First, you should convert the given text into an equation. See below.

From previous equations (1) and (2), you can find the unit cost. See below.

If 6b=9.12, you have:

    b=9.12/6

    b=$1.52

If 4s=5.00, you have:

    s=5.00/4

    s=$1.25

Since you know the unit cost for the bottles of soap and the sponges, you can find the total cost if you buy 2 bottles of liquid soap and 3 sponges.

2b + 3s =?

2*1.52+3*1.25

3.04+3.75=6.79

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The given triangles are similar by the AA similarity property.This property states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar

There are three similarity properties of triangles:

First, AA similarity property: AA stands for "angle-angle." This property states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the corresponding sides of the triangles are proportional in length. This property is also known as the "angle-angle-angle" (AAA) similarity property.

Second, SAS similarity property: SAS stands for "side-angle-side." This property states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar. This means that the corresponding angles of the triangles are congruent, and the remaining side of each triangle is ." This proportional in length.

Third, SSS similarity property: SSS stands for "side-side-side." This property states that if the corresponding sides of two triangles are proportional, then the triangles are similar. This means that the corresponding angles of the triangles are congruent and the remaining side of each triangle is proportional in length.

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The value of x in the trapezium is 3 .

A midsegment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid. Therefore, the midpoint is equal distance from both ends of the lines of the legs.

Hence,

12.5 = 1 / 2 (3x + 1 + 15)

12.5 = 1 / 2 (3x + 16)

12.5 = 3 / 2 x + 8

12.5 - 8 = 1.5x

4.5 = 1.5x

divide both sides by 1.5

x = 4.5 / 1.5

x = 3

Therefore,

x = 3

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Answer:

The solutions are

S

=

{

1

2

π

,

3

2

π

,

1

6

π

,

5

6

π

}

Step-by-step explanation:

We need

sin

2

x

=

2

sin

x

cos

x

Therefore,

sin

2

x

=

cos

x

sin

2

x

−

cos

x

=

0

2

sin

x

cos

x

−

cos

x

=

0

cos

x

(

2

sin

x

−

1

)

=

0

So,

{

cos

x

=

0

2

sin

x

−

1

=

0

⇔

,

{

cos

x

=

0

sin

x

=

1

2

⇔

,

{

x

=

π

2

3

2

π

x

=

1

6

π

5

6

π

∀

x

∈

[

0

,

2

π

]

The solutions are

S

=

{

1

2

π

,

3

2

π

,

1

6

π

,

5

6

π

}

graph{sin(2x)-cosx [-1.622, 9.475, -2.51, 3.04]}

The transformations that preserve congruence in a triangle are:

A reflection of the triangle across a line of reflection (e.g., x-axis, y-axis, a given line) and a rigid motion (combination of translation, rotation, and reflection) are required.

Based on the information, the other transformations mentioned, (x, y) → (-x, ax) and (x, y) → (3x, 3y), are not rigid motions and do not preserve the shape of the triangle. The transformation (x, y) → (x +7, y-8) is a translation, which is a rigid motion, but it does not preserve congruence since it changes the size and orientation of the triangle.

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The weak, moderate, strong and very strong Positive linear correlation is discussed below.

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data

Given is that there is a positive linear correlation between the x–value (years since 2000) and y–value (student enrollment).

Positive linear correlation means that the correlation coefficient value is between 0 and 1.

Now we can further write -

{a}. Weak correlation : The value is between {0} and {0.3}.

{b}. Moderate correlation : The value is between {0.3} and {0.7}.

{a}. Strong correlation : The value is between {0.7} and {0.85}.

{a}. Very strong correlation : The value is between {0.85} and {1}.

Therefore, the weak, moderate, strong and very strong Positive linear correlation is discussed above.

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Answer:

4.8

Step-by-step explanation:

The item is 80 dollars. Sales tax is 6% or .06

80*.06 would be your answer.

It is equal to 4.8.

The required equation is y = (-A/B)x + (C/B) in point-slope form.

To write the equation in point-slope form, we also need to have a point on the line. Let's use the point (x₁, y₁). Then, the point-slope form of the equation is:

y - y₁ = (-A/B)(x - x₁)

To write the equation Ax + By = C in point-slope form, we first need to solve for y:

Ax + By = C

By = -Ax + C

y = (-A/B)x + (C/B)

Now, we can see that the slope of this line is -A/B.

Thus, the required equation is y = (-A/B)x + (C/B) in point-slope form.

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"mph" stands for "miles per hour" and this simply means "the number of miles divided by the number of hours."

28 miles ÷ 7 hours = 4 miles per hour or 4 mph.

Answer:

a. 4 mph

Step-by-step explanation:

The maximum volume of the silvered solids is when the sphere and cube have the same surface area coverage.

Surface is the outermost layer of an object or environment. In the physical world, surface can refer to the physical features of a place, such as the topography of land, the texture of a material, or the shape of an object. In the physical sciences, surface refers to the interface between two different phases, such as a liquid and a gas, or a solid and a liquid. Surfaces can be studied in terms of their properties, such as friction, porosity, adhesion, and viscosity.
In this case, they will have the same volume. Since 4 square meters of surface area is available, each solid will have 2 square meters of surface area.
For the sphere, the radius can be determined by the surface area formula 4πr2 = 2, which can be solved for r to get r = 0.5m.
For the cube, the side length can be determined by the surface area formula 6s2 = 2, which can be solved for s to get s = 0.6m.
The minimum volume of the silvered solids is when one of the solids has all the area coverage while the other has none. In this case,
the sphere will have all 4 square meters of coverage and the cube will have none.
For the sphere, the radius can be determined by the surface area formula 4πr2 = 4, which can be solved for r to get r = 1m.
For the cube, the side length can be determined by the surface area formula 6s2 = 0, which can be solved for s to get s = 0m.

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Answer:

Step-by-step explanation:

(a) Step 1

Distance ran by Finn = 3.2

Distance ran by Jake = 3.9

Total Distance of team A = 7.1

   Step 2

Distance ran by team B = 7.2

Hence team B ran further

(b) Difference in distances ran by team A and B = 7.2 -7.1

                                                                                   = 0.1 km

Hence team B ran 0.1 km more than team A

A. The data is a random sample from the population of interest.

C. Individual observations can be considered independent.

B. The sampling distribution of is approximately normal.

What is the sampling distributions?

In statistics, the sampling distribution refers to the probability distribution of a statistic based on a random sample from a population. The sampling distribution is a theoretical concept that describes the distribution of values that the statistic would take across all possible samples of the same size from the population.

A and C are the conditions that have been met:

A. The data is a random sample from the population of interest.

C. Individual observations can be considered independent.

The condition that has not been met is:

B. The sampling distribution of is approximately normal.

Since the distribution of page lengths is skewed to the right with high outliers, the assumption of normality is not satisfied. Therefore, a t interval may not be appropriate for constructing a confidence interval for the mean page length. Alternative methods, such as a bootstrap or a nonparametric interval, may be more appropriate in this case.

Hence,

A. The data is a random sample from the population of interest.

C. Individual observations can be considered independent.

B. The sampling distribution of is approximately normal.

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The slope of a line perpendicular to the line whose equation is 2x + 3y = 24 is 1/3.

In Mathematics and Geometry, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles).

From the information provided above, the slope for the equation of the line can be calculated as follows:

2x + 3y = 24

y = -2x/3 + 24/3

y = -2x/3 + 8

Therefore, slope (m) = -2/3

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-2/3 × m₂ = -1

-2m₂ = -3

Slope, m₂ = -3/-2.

Slope, m₂ = 3/2.

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Step-by-step explanation:

Let x be the amount invested at 9% interest.

Then the amount invested at 7% interest is:

27,000

The total amount invested is the sum of these two amounts:

x + 27,000

The total interest earned is given as $2,110. We can set up an equation using the interest earned from each investment:

0.07(27,000) + 0.09x = 2,110

Simplifying and solving for x:

1,890 + 0.09x = 2,110

0.09x = 220

x = 2,444.44 (rounded to two decimal places)

Therefore, the woman invested $27,000 at 7% interest and $2,444.44 at 9% interest.

Answer:

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

According to definition of a function, each input value should have exactly one corresponding output value.

Verify the data sets:

The factored form of the expression yx - 24y + 3y² - 8x is ( x + 3y )( y - 8 ).

Given the expression in the question;

yx - 24y + 3y² - 8x

To factor the expression yx - 24y + 3y² - 8x, we can first group the terms with common factors:

yx - 24y + 3y² - 8x

yx - 8x + 3y² - 24y

Next, we can factor the first two terms by factoring out the greatest common factor, which is x:

x(y - 8) + 3y² - 24y

We can then factor the last two terms by factoring out the greatest common factor, which is 3y:

x(y - 8) + 3y(y - 8)

Notice that we now have a common factor of (y - 8) in both terms, so we can factor it out:

(x + 3y)(y - 8)

Therefore, the factored form is ( x + 3y )( y - 8 ).

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