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The box plot shows the number of jumping jacks completed in a workout class by the class members.

A box plot uses a number line from 14 to 54, with tick marks every one unit. The box extends from 27 to 45 on the number line. A line in the box is at 37. The lines outside the box end at 16 and 52. The graph is Jumping Jacks Completed, and the line is labeled Number of Jumping Jacks.

Which of the following lists the range and IQR for this data?

The range is 18, and the IQR is 36.
The range is 36, and the IQR is 37.
The range is 36, and the IQR is 18.
The range is 18, and the IQR is 37.

It would take 116.18 seconds for the space stations that are 7100 km apart at speed of 110000 km to meet

An equation is an expression that shows the relationship between two or more numbers.

The speed of an object is the ratio of the total distance travelled to the total time taken. It is given by:

Speed = distance / time

Distance = Speed * time

The spaceships are moving at 110000 km/h

The distance covered by each in x hours is:

Distance = 110000 * x = 110000x

Since they are 7100 km apart, hence:

110000x + 110000x = 7100

220000x = 7100

x = 0.03227 hours = 116.18 seconds

It would take 116.18 seconds for the spaceships to meet.

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By using linear equation, it can be calculated that

Number of calls in the first evening = 8

Number of calls in the second evening = 4(8 + 9) =68

Number of calls in the third evening = 8 + 9 = 17

What is linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Let the number of calls Maya receives in the first evening be x

Number of calls she receives in third evening = x + 9

Number of calls she receives in the second evening = 4(x + 9)

Total number of phone calls = x + 4(x + 9) + x + 9

By the problem,

The linear equation is

x + 4(x + 9) + x + 9 = 93

x + 5(x + 9) = 93

x + 5x + 45 = 93

6x = 93 - 45

6x = 48

x = \(\frac{48}{6}\)

x = 8

Number of calls in the first evening = 8

Number of calls in the second evening = 4(8 + 9) =68

Number of calls in the third evening = 8 + 9 = 17

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The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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The surface area of the square pyramid is: 451 cm²

The lateral surface area of the square pyramid = 330 cm²

Surface area = a² + 2al, where a is the base edge and l is the slant height.

Lateral Surface Area =  2al.

Given the following:

Surface area = a² + 2al = 11² + 2(11)(15)

Surface area = 451 cm²

Lateral Surface Area =  2al = 2(11)(15)

Lateral Surface Area = 330 cm²

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The lateral and surface area of a square base pyramid with side length of 11 cm and slant height of 15 cm are 330 cm² and 451 cm².

surface area = A + 1 / 2 ps

where

Therefore,

surface area = 11² + 1 / 2 × (11 × 4) × 15

surface area = 121 + 1 / 2 × 44 × 15

surface area = 121 + 330

surface area = 451 cm²

lateral area = 1 / 2 ps

lateral area = 1 / 2 × 44 × 15

lateral area = 330 cm²

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Answer: The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Step-by-step explanation: irst, we calculate the amount of discount that is applied to the original price:

30% of $1199 = 0.3 x 1199 = $359.70

So, the discounted price is:

$1199 - $359.70 = $839.30

Next, we apply the additional 10% off coupon to this discounted price:

10% of $839.30 = 0.1 x $839.30 = $83.93

The final price after the coupon is applied is:

$839.30 - $83.93 = $755.37

Finally, we calculate the sales tax on this final price:

7% of $755.37 = 0.07 x $755.37 = $52.88

The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Step-by-step explanation:

Log(x²+8)=log 10+ log x

Log(x²+8)=log(10×x)

x²+8=10x

x² - 10x + 8=0

x is approximately to - 1 and - 8✅

The solutions to the given equation are x = -1 and x = 8.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

Using logarithmic properties, we can simplify the given equation:

logs(x² + 8) = 1 + log g(x)

logs(x² + 8) - log g(x) = 1

log[(x² + 8)/g(x)] = 1

(x² + 8)/g(x) = 10

x² + 8 = 10g(x)

Now we can solve for x by substituting the given answer options and solving for g(x):

For x = -2 and x = -4:

x = -2:

(-2)² + 8 = 12, which is not equal to 10 g(x) for any value of g(x).

So x = -2 is not a solution.

x = -4:

(-4)² + 8 = 24, which is also not equal to 10g(x) for any value of g(x).

So x = -4 is not a solution.

For x = -1 and x = 8:

x = -1:

(-1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = -1 is a solution.

x = 8:

(8)² + 8 = 72, which is equal to 10g(x) when g(x) = 7.2.

So x = 8 is a solution.

For x = 1 and x = -8:

x = 1:

(1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = 1 is a solution.

x = -8:

(-8)² + 8 = 56, which is not equal to 10g(x) for any value of g(x).

So x = -8 is not a solution.

Therefore,

The solutions to the given equation are x = -1 and x = 8.

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Answer:

55

Step-by-step explanation:

a triangle adds up to 180°

25+30+x= 180

55+x=180

x=180-55

x=125

x and y is a straight line so it adds up to 180°

x=125 y=?

x+y=180

125+y=180

y=180-125

y=55°

y= 55°

The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

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The total area of clothes used is 12627m².

It is important to note that a football is in the shape of a sphere. Therefore, the area of a ball will be:

= 4πr²

In this case, the radius which is represented by r is given as 9.15m.

The area will be:

= 4πr²

= 4 × 3.142 × 9.15²

= 1052.22

Therefore, since there are 12 pitches, the area will be:

= 1052.22m² × 12

= 12627m²

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Answer: The ratio of the number of scoops Marsha ate to the number Liz ate is 200 : 180

Hope this helps :)

Step-by-step explanation:

Answer:

Answer: The ratio of the number of scoops Marsha ate to the number Liz ate is 200 : 180

It is right trust me try it

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = \(\frac{EF}{BC}\) = \(\frac{11}{66}\) = \(\frac{1}{6}\)

Answer:

Drugs are substances that change a person’s mental or physical state. They may have an impact on how your brain functions, how you feel and behave, as well as your perception and senses. This makes them unpredictable and dangerous, especially to children and teenagers. The effects of drugs vary depending on the person and the medication. I'm don't think anyone would want to maintain reproductive health, unless there in a good state of mind.

Step-by-step explanation:

Answer:

Julio's number is 40.

Step-by-step explanation:

Solve:

(x - 19) * (-7) = -147

-7x + 133 = -147

-7x = -280

x = 40

Check:

40 - 19 = 21

21 * (-7) = -147

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

The value of the expression 4 1/5 ÷ 2 1/4 will be -28/15. Then the correct option is E.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The mixed fraction numbers are given below.

- 4 1/5 and 2 1/4

The mixed fraction number is converted into a fraction number.

-4 1/5 = -21/5

2 1/4 = 9/4

Then the division of the fraction numbers will be

⇒ -(21/5) ÷ (9/4)

⇒ -(21/5) · (4/9)

⇒ -28/15

Then the value of the expression 4 1/5 ÷ 2 1/4 will be -28/15.

Then the correct option is E.

The missing option will be negative 28 over 20.

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Answer:

10*10*10

This is answer

Answer:

10^3=10*10*10

Step-by-step explanation:

Exponents is just saying how many there are basicly. so if it is 10 to the 3. It is just 10 *10*10

Answer:

1/12

Step-by-step explanation:

Let A represent point (3,8) and B represent point (-5,5)

To find the distance between Points A and B you have to calculate the difference between the x-coordinates and the difference between the y-coordinates of both points:

In the diagram I uploaded I marked the distance over the x and y axis with blue lines and determined a triangle. The distance over the x-axis represents the base of the triangle "a"

Base:

The base of the triangle is a=8

The distance over the y-axis is the height of the triangle "b", you have to calculate as the difference between both y-coordinates:

Height:

The height of the triangle is b=3

Finally the distance between both points (black line) is the hypothenuse of the triangle. To calculate this distance you have to apply Pythagoras theorem, this theorem states that the square of the hypothenuse is equal to the sum of the squares of the base and height of the triangle:

Replace it using the calculated values a=8 and b=3

Answer:

a) the probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly is 0.4013

b) the probability that at least one of 40 successive points indicates a problem when in fact the process is operating correctly is 0.8715

Step-by-step explanation:

following how the independence multiplication rule works,

i.e finding p(A)' which is 1 - p(No problem) because what we need is an intersection not a union so;

a) 10 successive points

probability (problem) = 0.05

probability (No problem) = 0.95

required probability = 1 - [probability (No problem)]^10

= 1 - (0.95)^10

= 1 - 0.5987

= 0.4013

the probability that at least one of 10 successive points indicates a problem when in fact the process is operating correctly is 0.4013

b) 40 successive points

probability (problem) = 0.05

probability (No problem) = 0.95

required probability = 1 - [probability (No problem)]^40

= 1 - (0.95)^40

= 1 - 0.1285

= 0.8715

the probability that at least one of 40 successive points indicates a problem when in fact the process is operating correctly is 0.8715

Answer:

Step-by-step explanation:

This expressions equals \(\sqrt{(x-2)^{2}\)

You can simplify to absolute value of x-2 when x is less than 2

The percentage error in the density of metal will be 3.4%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.

The percentage error will be calculated as:-

Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100

Percentage = 0.034x 100

Percentage = 3.4%

Hence, the percentage error will be 3.4% for the densities.

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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a. The teacher can expect the batteries to last at least 92.09 days  on minimum average.

b. The teacher will need to spend at most $49.92 on batteries for calculators over the year.

What is minimum average day?

a. The margin of error of ‡9% means that we can be 95% confident that the true average number of days the batteries will last is within 9% of the sample average. To find the minimum average number of days a teacher can expect to have the batteries last in her classroom, we subtract the margin of error from the sample average:

Minimum average = 101 - (0.09)(101) = 92.09 days (rounded to two decimal places)

Therefore, the teacher can expect the batteries to last at least 92.09 days on average.

What is spend ?

b. The total number of batteries required for the 24 TI-84 calculators is:

24 calculators x 4 batteries per calculator = 96 batteries

The total cost of the batteries will be:

96 batteries x $0.52 per battery = $49.92 (rounded to two decimal places)

Therefore, the teacher will need to spend at most $49.92 on batteries for calculators over the year, assuming all batteries need to be replaced.

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SOLUTION

We want to factor the polynomial

This means we are to factorise it. This becomes

Hence, the answer is

Answer:

243212

Step-by-step explanation:

Substitute the given value of t into the given formula. To find t, subtract 1997 from 2020.

2020−1997=23

Now substitute 23 into the equation for t and calculate.

N(t)N(23)==≈410(1.32)t410(1.32)23243,212

The number of unique visitors to the college website in the year 2020 was approximately 243,212.

The mass of the cubic cuboid is 1.479 kilograms.

Dimensionally speaking, density (ρ), in kilograms per cubic meter, is mass (m), in kilograms, per unit volume (V), in cubic meters. By the assumption of uniform density within the copper cuboid, the mass of the solid is equal to:

m = ρ · V

Where V is the volume of cuboid, in cubic meters.

And the volume of cuboid is:

V = w · h · l

Where:

Please notice that a kilogram equals 1000 grams and a meter equals 100 centimeters.

First, calculate the volume of the cuboid:

V = (0.05 m) · (0.03 m) · (0.10 m)

V = 1.5 × 10⁻⁴ m³

Second, determine the mass of the cuboid:

m = (9.86 g / cm³) · (1 kg / 1000 g) · (1000000 cm³ / m³) · (1.5 × 10⁻⁴ m³)

m = 1.479 kg

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Answer:

22 hamburgers

Step-by-step explanation:

number of well-done hamburgers = total hamburgers sold x percent of well-done hamburgers

40 x 0.55 = 22

The factorial expression 26! has a value of 4.032914600e+26

The expression is given as

26!

The above expression is a factorial expression

And the factorial of a number n where n >= 0 and n is not a decimal number is calculated using

n! = n x (n - 1) x (n - 2) x ..... x 1

This means that

n = 26

So, we have

26! = 26 x 25 x 24 x  23 x ..... x 1

Evaluate the products

26! = 4.0329146e+26

Approximate

26! = 4.032914600e+26

Hence, the value of the expression is 4.032914600e+26

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