Write and expression equivalent to 62.7 - 82.4

Step-by-step explanation:

4: Triangle area = b*h/2 = 8*10.5/2 = 42

5: b*h/2 = area

285 = 15*b/2

b = 38

The equation of the sphere that passes through the point (5, 5, −1) and has center (3, 6, 5) is (x-3)^2 + (y-6)^2 + (z-5)^2 = 41.

Sure! To find the equation of the sphere that passes through the point (5, 5, −1) and has center (3, 6, 5), we first need to find the radius of the sphere. This can be done by finding the distance between the center and the given point using the distance formula:

d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

Plugging in the given values, we get:

d = sqrt((5-3)^2 + (5-6)^2 + (-1-5)^2)
d = sqrt(4 + 1 + 36)
d = sqrt(41)

So the radius of the sphere is sqrt(41). Now, we can use the general equation of a sphere to find the specific equation for this sphere:

(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2

where (a ,b , c) is the center of the sphere and r is the radius. Plugging in the values we found, we get:

(x-3)^2 + (y-6)^2 + (z-5)^2 = 41

Therefore, the equation of the sphere that passes through the point (5, 5, −1) and has center (3, 6, 5) is (x-3)^2 + (y-6)^2 + (z-5)^2 = 41.

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Solution 1: Count, which is crazy long so I am going to solution 2.

Solution 2: Calculate.

I am going to split the right part to the left part result two shapes: 8x5 and 6x15

8x5 + 6x15 = 40 + 90 = 130.

Area = 130 units^2

Perimeter: 8x2 + (6x2-5)+ (15x2-5)        (Subtract 5 because the overlap area)

16 + 7 + 25 = 48

Perimeter = 48 units

The probability that exactly 17 households own a DVD player is 0.0124.

Given:

The probability that a house hold in centercity owns a DVD player is = 53%.

So, p = 0.53

The probability that a house hold in centercity does not own a DVD player is = 100% - 53% = 47%

So, q = 0.47

The sample size is 22 households in the city.

So, n = 22

We have to calculate the probability that exactly 17 households own a DVD player.

So, r = 17

The formula to be used in binomial experiment is:

P (r) = \(\frac{n!}{r! (n -r)!}\) × \(p^{r}\) ×\(q^{n-r}\)

The probability that exactly 17 households own a DVD player will be,

= \(\frac{22!}{17! (22 - 17)!}\) × \(0.53^{17}\) ×\(0.43^{22-17}\)

= \(\frac{22!}{17! (5)!}\)× \(0.53^{17}\) ×\(0.43^{5}\)

= 0.0124

Therefore, the probability that exactly 17 households own a DVD player is 0.0124.

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Answer:

3

Step-by-step explanation:

\(3+11t-9u\\\\\rightarrow\boxed{t = 9; u = 11}\\\\3+11(9)-9(11)\\\\3+99-99\\\\102-99\\\\\boxed{3}\)

Hope this helps.

The balance owed is equal to 151 996

The simple interest is the product of principal sum , time and rate. The rate is in percent and the time is usually annually calculated.

The simple interest is used in calculating the interest accrued especially in the business environment. It helps the person taking loan in knowing how much to pay after a certain period. The information will be well suited for decision making.

On the other side it helps the lender know the amount he/she will make when involved in a particular business. Hence we can say that the simple interest can be used by both the lender and the borrower.

Given data

cost of the car = R189 995

75 500 km

deposit of 20 percent

Balance owed = cost of the car - required deposit

solving for the required deposit

= cost of the car * 20 percent

= 189 995 * 20 / 100

= 189 995 * 0.2

= 37 999

Balance owed = cost of the car - required deposit

Balance owed = 189 995 - 37 999

Balance owed = 151 996

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complete question

see attachment

The greatest common factor of polynomial  64xyz−36xy + 24x  is 4x

The greatest common factor of a polynomial is a monomial that divides all terms of the polynomial.

The given polynomial is:

64xyz−36xy + 24x

Notice that there are 3 terms:

64xyz

−36xy

24x

To find the greatest common factor, notice that each terms contain x.

Next, find the gcf of 64, 36, 24.

Using prime factorization:

64 = 2⁶

36 = 2² × 3²

24 = 2³ × 3

Hence the gcf (64, 36, 24) = 2² = 4

Therefore the gcf of  64xyz−36xy + 24x  is 4x

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Answer:

4

Step-by-step explanation:

Answer:x=4

Step-by-step explanation:

Divide 9 by both sides

a. ln(7x) can be expanded as ln(7) + ln(x). b. ln(x + 3) remains as it is, since it cannot be simplified further. c. ln(x^8) can be expanded as 8ln(x). d. 15,000ln(xy^4) can be expanded as ln(x) + 4ln(y) + ln(15,000).

a. To expand the logarithmic expression ln(7x), we can use the property of the natural logarithm that states ln(ab) = ln(a) + ln(b).

Therefore, ln(7x) can be expanded as ln(7) + ln(x).

b. Similarly, the logarithmic expression ln(x + 3) can be expanded using the property ln(ab) = ln(a) + ln(b).

Hence, ln(x + 3) remains as it is since we cannot simplify it further.

c. Expanding the logarithmic expression ln(x^8) can be done using the property ln(a^b) = b * ln(a).

Thus, ln(x^8) becomes 8 * ln(x).

d. Expanding the logarithmic expression 15,000ln(xy^4) can be done by applying the property ln(ab) = ln(a) + ln(b).

Therefore, 15,000ln(xy^4) can be expanded as 15,000[ln(x) + ln(y^4)].

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The required answer are according to the following order,

a) France;

25/60 × 360/1 = 150°

b) Spain;

18/60 × 360/1 = 108°

c) Greece;

15/60 × 360/1 = 90°

d) Other;

2/60 × 360/1 = 12°

What do you mean by sum of angles?

We know that the sum of angles in a triangle is 360°. The question requires us to find the angle that corresponds to each of the given holiday destinations. We shall now proceed as follows:

The angle subtended is obtained from number of people that chose a particular location.

a) France;

25/60 × 360/1 = 150°

b) Spain;

18/60 × 360/1 = 108°

c) Greece;

15/60 × 360/1 = 90°

d) Other;

2/60 × 360/1 = 12°

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Answer:

10

Step-by-step explanation:

First we figure out the area of the triangle!

8 x 6 = 48

48/2 = 24

Now we multiply to figure out the area of the rectangle :)

24 x 5 = 120

Now we divide 120 by 12 to figure out the width!!

120/12 = 10

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

10

Step-by-step explanation:

area of triangle = 1/2 x 8 x 6 = 24

area of rectangle = 5 x 24= 120

area of rectangle = length x width

120 = 12 x w

w = 10

Answer:

25

Step-by-step explanation: i got it right on ed

Answer:

153.6

Step-by-step explanation:

Density is how much matter an object has to its volume. Formula:

Density=Mass x Volume.

12.8 x 12=153.6

Hope this helps :)

Answer:

see below

Step-by-step explanation:

1.

1, H - 2, H - 3, H - 4, H - 5, H

1, T - 2, T - 3, T - 4, T - 5, T

2.

2,H is one out of 10 possible outcomes, so the probability is 1/10

Given the volume of the sphere as 26667 cm³, we calculated the radius to be approximately 17.7 cm using the formula for the volume of a sphere. By multiplying the radius by 2, we found that the diameter of the sphere is approximately 35.4 cm.

To calculate the diameter of a sphere when given its volume, we can use the formula for the volume of a sphere:

V = (4/3) * π * r³

Where V is the volume and r is the radius of the sphere. Since we are given the volume, we can rearrange the formula to solve for the radius:

r = (\(\sqrt[3]{(3V / (4\pi )}\)))

Substituting the given volume V = 26667 cm³ into the formula, we have:

r = (\(\sqrt[3]{(3 * 26667 / (4\pi )))}\)

Calculating this expression, we find:

r ≈ (\(\sqrt[3]{80001 / \pi ))}\) ≈ 17.7 cm

Now that we have the radius, we can calculate the diameter by multiplying the radius by 2:

d = 2 * r ≈ 2 * 17.7 ≈ 35.4 cm

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The pressure exerted is 25 N/m², or 25 Pa.

Pressure is defined as the force exerted per unit area.

It is a physical quantity that describes the distribution of force over a given area.

In the International System of Units (SI), pressure is measured in Newtons per square meter (N/m²) is also called Pascal (Pa).

A force of 160 Newtons is applied to an area of 6.4 square meters.

The pressure, we use the formula:

pressure = force / area

Substituting the given values, we get:

pressure = 160 N / 6.4 m²

Simplifying, we get:

pressure = 25 N/m²

The pressure exerted by a force depends on the magnitude of the force and the area over which it is applied.

A force is applied over a smaller area, the pressure exerted is greater. Conversely, when the same force is applied over a larger area, the pressure is lower.

Pressure is an important concept in many fields of science and engineering, including fluid dynamics, aerodynamics and materials science.

It plays a crucial role in understanding the behavior of fluids, gases and solids under different conditions and helps in designing and optimizing various engineering systems.

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A procedure for determining the connections between two variables is referred to as correlation. You discovered that plotting two variables on a "scatter plot" can help you determine whether or not they are generally connected. Correlation is the most widely applied strategy even though there are other measures of association for variables measured at the ordinal or higher level of measurement. The question is asking about the correlation of a set of data after each x value is multiplied by 2.

To find the correlation for the resulting data, you can follow these steps:

1. Multiply each x value by 2.
2. Calculate the correlation coefficient for the new set of x and y values.

Given that the original set of x and y values has a Pearson correlation of r = 0.10, multiplying each x value by 2 does not change the correlation coefficient.

Therefore, the correlation for the resulting data is still r = 0.10.

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Answer:

y = (5/4)x - 11

Step-by-step explanation:

Use y = mx + b as your starting point.  This becomes y = (5/4)x + b.

Substitute 8 for x and -1 for y and solve for b:

-1 = (5/4)(8) + b, or

-1 = 10 + b.

Then b must be -11, and the desired equation is

y = (5/4)x - 11

Answer:

5x + 3y

Step-by-step explanation:

6x − x + 5y − 2y

(6x − x) + (5y − 2y)

5x + 3y

Hope that helps!

Answer:

\(5x+3y\)

Step-by-step explanation:

Given the following question:

\(6x-x+5y-2y\)

In order to find the answer, we combine like terms by adding/subtracting terms with similar variables.

\(6x-x+5y-2y\)
\(6x-x=5x\)
\(5y-2y=3y\)
\(5x+3y\)

Hope this helps.

Answer: 40, -16,-9

Step-by-step explanation:

A. -10+30-20+40

    -30+70

     70-30

      40

b -51+35-0

   35-51

    -16

c. -6+2-8+3

   -14+5

     5-14

      -9

The maximum score in the class is approximately 97. To estimate the maximum score in the class, we can use the concept of the normal distribution and z-scores.

Since the mean and standard deviation are given, we can assume that the scores on the statistics exam are normally distributed.

To estimate the maximum score, we need to determine how many standard deviations above the mean corresponds to the maximum score. In a normal distribution, approximately 99.7% of the data falls within three standard deviations of the mean. We can use this information to estimate the maximum score.

First, we calculate the z-score corresponding to the desired percentile (99.7%). The z-score formula is given by:

z = (X - μ) / σ

Where:

X is the maximum score

μ is the mean score

σ is the standard deviation

Rearranging the formula to solve for X, we have:

X = z * σ + μ

Substituting the values we have:

X = 3 * 9 + 70

X = 27 + 70

X ≈ 97

Therefore, we can estimate that the maximum score in the class is approximately 97.

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The expression 800 - 600i in trigonometric form is approximately 1000 ∠ -36.87°.

To express a complex number in trigonometric form, we need to convert it into polar form with the magnitude (r) and argument (θ). The magnitude (r) is calculated using the formula r = √\((a^2 + b^2)\), where 'a' is the real part and 'b' is the imaginary part. In this case, a = 800 and b = -600.

r = √\((800^2 + (-600)^2)\) ≈ √(640000 + 360000) ≈ √(1000000) ≈ 1000

The argument (θ) can be found using the formula θ = arctan(b/a). Since a = 800 and b = -600, we have:

θ = arctan((-600)/800) ≈ arctan(-0.75) ≈ -36.87°

Therefore, the expression 800 - 600i in trigonometric form is approximately 1000 ∠ -36.87°, where 1000 is the magnitude (r) and -36.87° is the argument (θ).

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Answer:

perimeter = 2*length + 2*width

2x13 + 2x18 = 62ft

hope that answers your question

Step-by-step explanation:

The cost function for the field trip can be represented as C(x) = 100 + 7.50x, where x is the number of students attending. In this case, only 3 students are going, so we can find the total cost by plugging in x = 3:

The cost of going on a field trip for a school club is represented by C(x) where there is a set fee of $100 for the use of the bus and the cost per student is $7.50.

If only 3 students go, we can calculate the total cost as follows: C(3) = $100 + ($7.50 x 3) = $100 + $22.50 = $122.50. Therefore, the range of this event would be { $122.50 }.

This means that the cost of the field trip for 3 students would be anywhere within the range of $122.50. The range is represented by the braces {} and is in dollars as per the problem statement. It is important to note that the range represents the possible values that a function can take, in this case, the cost of the field trip.


Since the cost is directly related to the number of students, and there is only one possibility (3 students), the range will be a single value. Therefore, the range of this event can be written as:

Range = {$122.50}

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Answer:

it has to be whole numbers

Step-by-step explanation:

because all of them are whole number no matter if there negative or positive

Substitute 5 for x in the function f(x) = 2x + 7.

Option C is correct.

Answer:

Step-by-step explanation:

Area of sector = angle/360 * pi * r^2

7.1 = 40/360 * 22/7 * r^2

7.1 = 1/9 * 22/7 * r^2

63.9 = 22r^2/7

r^2 = (7 * 63.9)/22

r^2 = 20.331818181818

r = square root of 20.331818181818

r = 4.51

d = r * 2 = 4.51 * 2 = 9.02

The diameter of circle is \(9.02 inch\)

The area of sector is given as,

                      \(Area=\frac{\theta}{360} *\pi r^{2}\)

Where r is radius of circle and \(\theta\) is angle of sector.

Given that, area is 7.1 and \(\theta=40\)

Substitute values in above relation.

              \(7.1=\frac{40}{360}*3.14*r^{2} \\\\r^{2}=\frac{7.1*360}{40*3.14}=20.35\\ \\ r=\sqrt{20.35}=4.5\)

The diameter of circle is,\(=2r=2*4.51=9.02inch\)

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Answer: See bolded below

Step-by-step explanation:

I am going to label each picture based on it's color.

For the yellow net, it is a rectangular prism. You can tell because when you fold the pieces together, it forms a rectangular prism. Also, all the parts fo teh net are rectangles.

For the green net, it is a square pyramid. For a square pyramid the base is a square. In the picture, the base is a square.

For the purple net, it is a triangular prism. For a triangular prism, it has a ractangle as a base. The purple shows a rectanlge base and triangle sides.

For the blue net, it is a triangular pyramid. A triangular pyramid has a triangle base. The blue has a triangle base.

Answer:

Yes

Step-by-step explanation:

For the given measures of the rectangular prism shape pool 12feet deep , 24 feet long and 18 feet wide the volume of the swimming pool is equal to 147 cubic meters ( nearest cubic meter)

As given in the question,

Shape of the swimming pool is rectangular prism

1 foot = 0.305 meter

Dimensions of the rectangular prism is given by

Height = 12 feet

          = 12 × 0.305

          = 3.66 meters

Length = 24 feet

           = 24 × 0.305

            = 7.32 meters

Width = 18 feet

          = 18 × 0.305

          = 5.49 meters

Volume of the swimming pool = length × width × height

                                              = ( 3.66 × 7.32 × 5.49 ) cubic meters

                                              = 147.083688 cubic meters

                                              =147 cubic meters(nearest cubic meters)

Therefore, for the given measures of the rectangular prism shape pool 12feet deep , 24 feet long and 18 feet wide the volume of the swimming pool is equal to 147 cubic meters ( nearest cubic meter)

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