A personal trainer determines that an individual will get the most benefit from a workout if they keep their heart rate at an average of 150 beats per minute during workouts. To determine if the individual is doing so successfully, a random sample of 30 workouts is selected from their fitness watch. A 95% confidence interval for these workouts reveals that the true mean heart rate while working out is between 158 and 167 beats per minute. Based upon this interval, what conclusion should be made about the hypotheses: H Subscript 0 Baseline: mu = 150 versus H Subscript alpha Baseline: mu not-equals150 where μ = this individual’s true mean heart rate during working out at α = 0.05?

Reject H0. There is convincing evidence that the mean heart rate from these 30 workouts differs from 150.
Reject H0. There is convincing evidence that this individual’s true mean heart rate while working out differs from 150.
Fail to reject H0. There is not convincing evidence that the mean heart rate from these 30 workouts differs from 150.
Fail to reject H0. There is not convincing evidence that this individual’s true mean heart rate while working out differs from 150.

Answer:

a = 6

Step-by-step explanation:

Given information:

Slope = 6

Coordinates: (-9, 0) and (-8, a)

Slope formula = y2 - y1 / x2 - x1

Substitute the given values into the formula.

6 = a - 0 / -8 - (-9)

6 = a - 0 / 1

6 = a - 0

a = 6

hope this helps!! p.s. i really need brainliest :)

Answer:

C) 75.36 cubic feet

Step-by-step explanation:

Volume of a cone: ⅓hπr²

Given:

Substitute the given values to find the volume:

V = (⅓)(8)(3.14)(3)²

V = (⅓)(8)(3.14)(9)

V = (⅓)(226.08)

V = 75.4 ft³ (nearest tenth)

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The terms a1, a2 and a3 do not have a common difference, and the value of a1 in the geometric sequence is 10/9

The arithmetic sequence is given as:

a₁, a₂ and a₃

The geometric sequence is given as:

a₄, a₇ and a₁₂

The common ratio of a geometric sequence is:

[tex]r = \frac{T_2}{T_1}[/tex]

So,we have:

[tex]\frac{a_7}{a_4} = \frac{a_{12}}{a_7}[/tex]

Cross multiply

[tex]a_{12} * a_4 = a_7 * a_7[/tex]

Given that a7 = 30, the equation becomes

[tex]a_{12} * a_4 = 30 * 30[/tex]

Evaluate the product

[tex]a_{12} * a_4 = 900[/tex]

Rewrite as:

[tex]a_{4} * a_{12} = 900[/tex]

Express 900 as 10 * 90

[tex]a_{4} * a_{12} = 10 * 90[/tex]

By comparison, we have:

a₄ = 10 and a₁₂ = 90

This means that the geometric sequence is:

10, 30, 90 ---- it has a common ratio of 3

The nth term of a geometric sequence is:

[tex]a_n = ar^{n-1}[/tex]

So, we have:

[tex]a_7 = ar^6[/tex]

[tex]a_4 = ar^3[/tex]

Substitute values for a7 and 14

[tex]ar^6 = 30[/tex]

[tex]ar^4 = 10[/tex]

Divide both equations

[tex]r^2 = 3[/tex]

Take the cube of both sides

[tex]r^6 = 27[/tex]

Substitute [tex]r^6 = 27[/tex] in [tex]ar^6 = 30[/tex]

[tex]a * 27 = 30[/tex]

Divide both sides by 27

[tex]a = \frac{10}{9}[/tex]

Hence, the value of a1 in the geometric sequence is 10/9

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Answer:

The answer is 5/36.

Step-by-step explanation:

Test approved.

The probability that she rolls a 1 on the first cube and a number greater than 1 on the second cube is 5/36.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

Given that Stef rolls two six-sided number cubes.

Based on the diagram of the sample space.

Therefore, the probability that she rolls a 1 on the first cube and a number greater than 1 on the second cube

=  5/36.

Hencce, the correct option is B.

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Answer:

6

Step-by-step explanation:

b+4=10

  -4 .-4

b=6

Answer:

b= 6

Step-by-step explanation:

subtract the answer (10) by the remaining 4, (so 10-4) which equals 6

Step-by-step explanation:

well don't breath just collect like terms and booom

To multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32

To answer the question, we need to know what logarithm of a number is

The logarithm of a number x is the power to base 10 of that number.

So, logarithm of x to base 10 is written as ㏒x.

Since we want to multiply 64 × 83.2, we convert this to logarithmic equation using the addition rule of logarithm.

㏒ab = ㏒a + ㏒b

So, 64 × 8.32 to logarithm is ㏒(64 × 8.32) = ㏒64 + ㏒8.32

So, to multiply 64 × 8.32 use the logarithm equation 2)㏒64 + ㏒8.32

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The product and the sum of the functions will be 3x² - 6x - 24 and 4x + 2. The value of the function (f - g) at x = 4 is negative 18.

In mathematics, functions are everywhere and are necessary for constructing physical connections. A function is a statement, rule, or law that establishes the connection between two variables.

The functions are given below.

f(x) = x - 4

g(x) = 3x + 6

Then the product of the functions will be

(f × g)(x) = (x - 4)(3x + 6)

(f × g)(x) = 3x² -12x + 6x - 24

(f × g)(x) = 3x² - 6x - 24

Then the sum of the functions will be

(f + g)(x) = x - 4 + 3x + 6

(f + g)(x) = 4x + 2

Then the difference in the functions at x = 4 will be

(f - g)(4) = (x - 4) - (3x + 6)

(f - g)(4) = x - 4 - 3x - 6

(f - g)(4) = -2x - 10

(f - g)(4) = -2 (4) - 10

(f - g)(4) = -8 -10

(f - g)(4) = -18

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Answer:

6.15 × 10⁵

Step-by-step explanation:

When converting a number of scientific notation, we need to move the decimal point until the number is greater than 1 and less than 10, then multiply this by 10 to the power of the number of places we moved the decimal point (negative when moving it forwards, positive when moving it backwards).

Therefore, 615000 = 6.15 × 10⁵

Answer:

−x^2+10x−21

Step-by-step explanation:

Hope this helped you! If this is wrong, please tell me and have a good day!

Original: y = 3^x

---To find the inverse, switch the x and y, then solve for y.

Inverse: x = 3^y

---Take the log base 3 of both sides to get y by itself

Answer: [tex]log_{3}(x) = y[/tex]

[tex]y = log_{3}(x)[/tex]

Hope this helps!

Your answer is B.

Vertical goes straight up and down.

Horizontal lines go side to side

A diagonal line is slanted.

Answer:

  4.23 square units

Step-by-step explanation:

The area of the triangle is given by the formula ...

  K = 1/2ab·sin(C)

__

Filling in the given values, we find the area to be ...

  K = 1/2(4)(5)sin(25°) = 4.23 . . . . square units

Answer:

2 outliers

Step-by-step explanation:

(1,9) and (10,7) both are outliers.

There are 2 outliers in the given scatter plot. Therefore, option B is the correct answer.

An outlier is a data point that does not fit the rest of the data. It lies outside of a cluster and does not follow the same pattern. Scatter plots can have many outliers, just one outlier, or no outliers.

From the given graph, we can see that coordinates (1, 9) and (10, 7) are not in the cluster.

These two points lies out side the cluster, so these points are outliers.

Therefore, option B is the correct answer.

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Answer:

4 bulbs

Step-by-step explanation:

Answer:

35 square feet

Step-by-step explanation:

Area of the rug :

Because this is a right triangle, we can use a trigonometric function to solve for the missing side.

Remember: SOH-CAH-TOA

We are given an angle, as well as the adjacent side and hypotenuse. Therefore, we should use the cosine function to solve for x.

cos(67) = x / 15

x = cos(67) * 15

x = 5.9

Answer: 5.9

Hope this helps!

Answer:

2513 miles

Explanation:

[tex]\sf Length \ of \ arc = \dfrac{\theta}{360} * 2\pi r[/tex]

Here given:

∅ = 36°

radius = 4000 miles

Insert following:

[tex]\sf \rightarrow \dfrac{36}{360} * 2\pi (4000)[/tex]

[tex]\sf \rightarrow 800\pi \ \ \ (in \ terms \ of \ \pi )[/tex]

[tex]\sf \rightarrow 2513.3 \ \ (rounded \ to \ nearest \ tenth)[/tex]

[tex]\sf \rightarrow 2513 \ \ (rounded \ to \ nearest \ mile)[/tex]

Answer:

Daniel =Were you thinking of perpendicular lines?

Oris= It seems like you've got the basic idea, but your definition could be more precise.

Kaoris= Yes well done...

Answer:

im not really sure what that means im so sorry

Step-by-step explanation:

Let the price of an adult ticket is x and a child ticket is y .

from the question ,

[tex]6x + 2y = 124 \: \: ...(i) \\ \\ 3x + 5y = 100 \: \: ...(ii)[/tex]

Multiply 2 in eq (ii)

[tex]6x + 10y = 200 \: \: ...(iii)[/tex]

On adding eq (iii) and (i)

[tex]6x + 10y = 200 \\ \\ 6x + 2y = 124[/tex]

we get ,

[tex]8y = 76 \\ \\ y = \frac{76}{8} \\ \\ y = 9.5[/tex]

putting y in eq (i)

[tex]6x + 2y = 124 \\ \\ 6x + 2 \times 9.5 = 124 \\ \\ 6x + 19 = 124 \\ \\ 6x = 124 - 19 \\ \\ 6x = 105 \\ \\ x = \frac{105}{6} \\ \\ x = 17.5[/tex]

The value of x = 17.5 and y = 9.5

The area of the composite figure is 1152 square meters

A rectangular prism and 2 triangular prisms. The rectangular prism has a length of 20 meters, width of 6 meters, and height of 8 meters. The triangular prisms each have 2 triangular sides with a base of 6 meters and height of 8 meters. The rectangular sides are 20 meters by 6 meters, 20 meters by 10 meters, and 20 meters by 8 meters.

The composite figure shown is made up of 2 triangular prisms and one rectangular prism. If the area of each triangle base of the triangular prisms has an area of 24 m2, what is the total surface area of the composite figure?

The given parameters are:

Rectangular prism :

Length = 20 meters; Width = 6 meters; Height = 8 meters

Triangular prism :

The area of the rectangular prism is:

Area = 2 * (Length * Width + Length * Height + Width * Height)

So, we have:

Area = 2 * (20 * 6 + 20 * 8 + 6 * 8)

Area = 656

The area of the triangular prism is:

Area = 2 * Base Area + Areas of Rectangular sides

So, we have:

Area = 2 * 24 + (20 * 6 + 20 * 10 + 20 * 8)

Area = 528

The common area between the prisms is:

Common area = 8 * 4

Common area = 32

Subtract the common area from the sum of the areas of the triangular prism and the rectangular prism to get the area of the composite figure

Composite figure = 656 + 528 - 32

Evaluate the sum

Composite figure = 1152

Hence, the area of the composite figure is 1152 square meters

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Answer: D, 1152 m2

Step-by-step explanation: I got it correct

Answer:

Your answer is A.

Step-by-step explanation:

Absolute values of any number are positive.

|4| = 2

|-2| = 2

2 = 2 and 4 > -2

C and D can be true, but they are not since less than or greater than doesn't apply if they were less than/greater than or equal, then yes.

Answer:

Picture Below :)

Step-by-step explanation:

*ta da*

- Have a great day -

Answer:

$8,051.62

Step-by-step explanation:

Compound interest formula

[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]

where:

Given:

Substituting given values into the formula:

[tex]\implies \sf A=5000(1+\frac{0.06}{4})^{4 \times 8}[/tex]

[tex]\implies \sf A=5000(1.015)^{32}[/tex]

[tex]\implies \sf A=8051.62\:(nearest\:hundredth)[/tex]

Rate of interest

So

Compound ineterest formula to be used

Answer:

Ib = $16 per lb

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

21 = 3 x 7

35 = 7 x 5

70 = 2 x 5 x 7

The greatest common factor of 21, 35 and 70 is 7.

Note : -

The greatest common factor ( GCF ) of a set of numbers is the largest factor that all the numbers share.

Correct option is A)

Consider the given equation,

3

2x

+10.3

x

−9=0

Let ,y=3

x

Now ,

y

2

−10y+9=0

y

2

−9y−y+9=0

y(y−9)−1(y−9)=0

(y−9)(y−1)=0

When,

x−9=0

x=9

Now ,

9=3

x

3

2

=3

x

x=2

When,

y−1=0

y=1

3

x

=1

3

x

=3

0

x=0

x=0,x=2

This is the answer

Using proportions, it is found that the dimensions of the reception area of of 12 feet by 20 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the scale factor is of 1 inch = 4 feet, meaning that each inch on the drawing represents a dimension of 4 feet.

The drawing is of 3 inches by 5 inches, hence the real dimensions are given by;

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