What is the sum of the first five positive integers?​

Answer:

1/823543

Step-by-step explanation:

7^-5/7^2

so basically add them because its a neg. exponent.

7^-3

that equals 1/7^3

mark me brianliest please!

Answer:

is a

Step-by-step explanation:

got it right on the asighnment

The total volume of the interior of the house after adding a second floor is 43,100 cubic feet, calculated by summing the volume of the original one-story (29,600 cubic feet) and the second floor (13,500 cubic feet).

To calculate the total volume of the interior of the house after the addition of a second floor, we need to find the volume of both floors and add them together. The original one-story house covers an area of 3,700 square feet with ceilings 8 feet high. To find the volume, we multiply the area by the height of the ceilings:

Volume of first floor = Length * Width * Height = 3,700 ft^2 * 8 ft = 29,600 ft^3

The second floor is a bit smaller than the first floor, with dimensions of 50 feet by 30 feet and ceilings that are 9 feet high. So, the volume of the second floor is:

Volume of second floor = Length *Width*Height = 50 ft*30 ft *9 ft = 13,500 ft^3

Adding the two volumes together gives us the total volume of the house:

Total Volume = Volume of first floor + Volume of second floor = 29,600 ft^3 + 13,500 ft^3 = 43,100 ft^3

The triangle STV is not a right angled triangle.

Explanation:

Given that STV is a triangle with side lengths of 7, 11 and 14 units

We need to determine that STV is a right angled triangle.

Using Pythagorean theorem, we have,

[tex]c^2=a^2+b^2[/tex]

where [tex]c=14, a=7[/tex] and [tex]b=11[/tex]

Substituting the values in the above formula, we have,

[tex]14^2=7^2+11^2[/tex]

Squaring the terms, we get,

[tex]196=49+121[/tex]

[tex]196=170[/tex]

Since, both sides of the equation are not equal, then the triangle STV is not a right angled triangle.

Final answer:

To determine if triangle STV is a right triangle, apply the Pythagorean theorem. The theorem shows that STV is not a right triangle because the squares of the two shorter sides do not add up to the square of the longest side.

Explanation:

To determine whether triangle STV with side lengths of 7, 11, and 14 units is a right triangle, we can use the Pythagorean theorem. Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, if c represents the length of the hypotenuse and a and b represent the lengths of the other two sides, then the triangle is right if and only if c² = a² + b².

For triangle STV, let's assign the longest side, which is 14 units, as the hypotenuse c, and the other two sides as a and b. So:

a = 7 units

b = 11 units

c = 14 units

Now, we check:

c² = 14² = 196
a² + b² = 7² + 11² = 49 + 121 = 170

Since 196 does not equal 170, we conclude that triangle STV is not a right triangle.

Answer: The height of the pole is 26 ft

Step-by-step explanation: Please refer to the attached diagram for details.

The diagram shows a right angled triangle labeled PEG. The point P is the top of the flagpole, the point E is the eye level of the observer, while point G is the point where the flagpole touches the ground. However, we must not forget that the observer’s eye is 5 ft from the ground. This means the height of the flagpole in the triangle has an extra 5 ft that would be added after our calculation. So, we have an opposite, which is the unknown and an adjacent, which is the side that lies between the reference angle and the right angle (that is, 30). Also we have the reference angle as 35.

Using the trigonometric ratios,

TanE = opposite/adjacent

Tan35 = PG/30

By cross multiplication we now have

Tan35 x 30 = PG

0.7002 x30 = PG

21.006 = PG

The height of the pole is approximately 21 ft.

However, we remember that the eye of the observer is 5 ft away from the ground. That means the pole actually goes an additional 5ft when it touches the ground. Hence the actual length of the pole is 21 + 5 = 26

Height of pole = 26 ft

Answer: A rhombus with 4 right angles make a square

The expression which is equivalent to 2⁵ is, 2×2×2×2×2

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The given expression is  2⁵

Equivalent expression = ?

Given expression can be write in the factors of  2⁵

⇒ 2⁵ = 2×2×2×2×2

Hence, The equivalent expression is 2×2×2×2×2

To know more about Expressions check:

brainly.com/question/16804733

#SPJ2

Answer:

1/2

Step-by-step explanation:

The slope of Y = 1/2x + 1 is 1/2.

In a typical equation, there are 4 parts: Y, M, X, and B (since an equation in standard form is Y = MX + B. Y and X are typically variables, unless you fill them in with coordinate points to solve for B. B is the Y intercept, or where the line crosses the Y axis, and M is the slope of the line.

Thus meaning 1/2 is the slope for the equation given.

I hope this helps!

The choices are missing, but we can solve the problem from the given information

Answer:

The equation which represents the circle is (x - 2)² + (y + 1)² = 16

Step-by-step explanation:

The form of the equation of a circle is (x - h)² + (y - k)² = r², where

∵ The coordinates of the center of the circle are (2 , -1)

∴ h = 2 and k = -1

The radius of the circle is the segment whose join the center of the circle and any point on the edge of the circle

∵ The circle passes through point (-2 , -1)

∴ The radius of the circle is the distance from the center (2 , -1)

    and the point (-2 , -1)

The y-coordinates of the two points are equal that means the radius is a horizontal segment and its length is the difference between their x-coordinates

∵ r = 2 - (-2)

∴ r = 4

Now let us substitute h, k, and r in the form of the equation of the circle

∵ (x - 2)² + (y - -1)² = (4)²

∴ (x - 2)² + (y + 1)² = 16

The equation which represents the circle is  (x - 2)² + (y + 1)² = 16

Answer:

21,000

Step-by-step explanation:

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

Answer:

I'm pretty sure it's 2,100

Step-by-step explanation:

Divide 70,000 by 1,000 to get 70

The cash value for a policy on its fifth anniversary is 30.00

multiply 70*30 to get 2,100

That's it :)

The flag is 31.6 feet from the bottom of the sailboat.

Step-by-step explanation:

Step 1:

In the given triangle, the angle is 58°. Assume the opposite side has a length of x feet and the adjacent side has a length of 16 feet.

To determine the length of the opposite side of the triangle, we use the tan of the given angle.

[tex]tan \theta = \frac{oppositeside}{adjacent side} .[/tex]

Step 2:

In the given triangle,

The length of the opposite side = x feet,

The length of the adjacent side = 16 feet,

The angle of the triangle = 58°.

[tex]tan \theta = \frac{oppositeside}{adjacent side} , tan 58 = \frac{x}{16}, tan 58 = 1.6000.[/tex]

[tex]1.6 = \frac{x}{16} , x = (1.6)(16) = 25.6.[/tex]

Since Shianne's eyes are 6 feet from the bottom of the sailboat, the distance between the flag and the bottom of the sailboat [tex]= 25.6 + 6 = 31.6.[/tex]

So the flag is 31.6 feet from the bottom of the sailboat.

16 gallons will be burned

Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{8}{5}=\frac{16}{z}\\\\ 8*z=16*5\\\\z=\frac{16*5}{8}\\\\z=2*5\\\\z=10[/tex]

Answer:

42

Step-by-step explanation:

3 * (18 - 4) = 3 * 14 = 42

Answer:

42

Step-by-step explanation:

18-4=14. 14*3=42

Answer:

36

Step-by-step explanation:

[tex]4 \times {t}^{2} = 4 \times {3}^{2} \\ = 4 \times 9 \\ = 36[/tex]

Answer:

c. -11

Step-by-step explanation:

Answer: Hello, the answer is C. -11 glad to help have a great day and im here for any more questions you might have!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ok, so when it says "3x, x[tex]\leq[/tex]2," it means that when the x value is less than or equal to 3, you graph 3x. You would have the following points on the line: (-3,-9), (-2,-6), (-1,-3), (0,0), (1,3), and (2,6). The endpoint of the ray on the left side (the points I just said) would be (2,6)

When it says, "1/2 x +5, 2[tex]\leq[/tex]x," it means that when the value of x is greater than or equal to 2, the y value is .5x + 5. You would graph the following points: (2,6), (4,7), (6,8), and (8,9). The endpoint of th ray on the right (the points I just said) would be (2,6).

Keep in mind that though the graph is continuous, it isn't one line, but 2 rays (which you probably already know).

Answer

a) Linear because there is a constant slope

b) Linear: y=x

Non-linear: y=1/x

Step-by-step explanation:

First we find the slope using the formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

For the points (0,2) and (1,3), we have

[tex]m = \frac{4-3}{1-0} = \frac{1}{1} = 1[/tex]

For the points (0,2) and (2,4), we have

[tex]m = \frac{4 - 2}{2 - 0} = \frac{2}{2} = 1[/tex]

For (1,3) (2,4), we have;

[tex]m = \frac{4 - 3}{2 - 1} = 1[/tex]

Since there is a constant rate of change the graph represents a linear function.

b) For a linear function, the highest degree is 1.

An example of a linear function is y=2x

For a non-linear function the degree of the variable is not equal to 1.

[tex]y = \frac{1}{x} [/tex]

Answer:

1/5

Step-by-step explanation:

y2 -y1/x2 - x1

5 - 6/ -2 - 3

-1/-5

1/5

Answer:

[tex]6\dfrac{23}{30} s[/tex]

Step-by-step explanation:

The first step in simplying

[tex]$4s+\frac{1}{6}s +2\frac{3}{5}s $[/tex]

is to bring the mixed number [tex]2\frac{3}{5}s[/tex] into the form of an improper fraction:

[tex]$2\dfrac{3}{5}s = (2+\frac{3}{5})s =(\frac{10}{5} +\frac{3}{5})s = \frac{13}{5}s $[/tex]

Therefore, the expression now becomes

[tex]$4s+\frac{1}{6}s +\frac{13}{5}s $[/tex]

and to simplify further we find the common denominator of the fractions which is

[tex]6*5 =30[/tex],

therefore,

[tex]$4s+\frac{5}{30}s +\frac{78}{30}s $[/tex]

[tex]$\frac{120}{30} s+\frac{5}{30}s +\frac{78}{30}s $[/tex]

add the numerator and get:

[tex]\dfrac{203}{30} s[/tex]

as a mixed number this is

[tex]6\dfrac{23}{30} s[/tex]

Thus,

[tex]$\boxed{4s+\frac{1}{6}s +2\frac{3}{5}s = 6\dfrac{23}{30} s} $[/tex]

Answer:

[tex]19x+36[/tex]

Step-by-step explanation:

Answer: The coordinates of point B are (19 , 20).

Step-by-step explanation:

The mid point (x,y) of line joining (a,b) and (c,d) is given by :-

[tex](x,y)=(\dfrac{a+c}{2},\dfrac{b+d}{2})[/tex]                        (1)

Given : Point A is located at (3,6). The midpoint of line segment AB is point C(11,13).

Let the coordinates of point B are (a,b) m, the according to (1) , we have

[tex](\dfrac{3+a}{2},\dfrac{6+b}{2})=(11,13)\\\\\Rightarrow\ \dfrac{3+a}{2}=11\ \ ,\ \ \dfrac{6+b}{2}=13\\\\\Rightarrow\ 3+a=22\ \ ,\ \ \ 6+b=26\\\\\Rightarrow\ a=19,\ \ b= 20[/tex]

Hence, the coordinates of point B are (19 , 20).

Answer: x= 5-y/2

y= 5-2x

Step-by-step explanation:

2x + y= 5

4x + 2y=10

Addition of the two equations gives:

6x + 3y = 15

6x= 15- 3y

x= 15-3y/6 or simplified to x = 5-y/2

3y= 15- 6x

y= 15-6×/3 or simplified to y= 5-2x

Answer:

$4.38

Step-by-step explanation:

Lets recap the information we are told in the problem:

There are 4 students in total

Their total profit is $17.52

The total profit needs to be split equally between them

Now we can focus on solving. To do so we can set up an equation like this:

(Total profit) ÷ (Number of students) = (Amount each student gets)

Lets insert our numbers into this equation:

$17.52 ÷ 4 = $4.38

So each student gets $4.38 each when the profit is split equally.

Out of the entire profit of $17.52, each one of the students will be able to take home a profit of $4.38.

These four students were able to sell enough lemonade that they made $17.52.

They will need to divide the profit amongst themselves and when they do so, each one of them will get:

= Profit made / Number of students

= 17.52 / 4

= $4.38

In conclusion, each one of the students will get $4.38.

Find out more at https://brainly.com/question/21391192.

Answer:

Step-by-step explanation:

-2p-4=2

Collect like terms

-2p=2+4

-2p=6

p=6/-2=-3

Answer:

p=-3

Step-by-step explanation:

-2p-4=2

add 4 to both sides then get -2p =6

divide both sides by -2 and get p=-3

Hope this helped

Answer:

The number is 12

Step-by-step explanation:

Step 1:  Convert words into an expression

Twelve less than a product of a number and 6 is 60

(n * 6) - 12 = 60

Step 2:  Solve for n

(n * 6) - 12 + 12 = 60 + 12

n * 6 / 6 = 72 / 6

n = 12

Answer:  The number is 12

Answer:

B) A one-sample t-test for population mean would be used.

Step-by-step explanation:

The complete question is shown in the image below.

The marketing executive is interested in comparing the mean number of sales of this year to that of previous year.

The marketing executive already has the value of mean from previous year and uses a sample to calculate the mean and standard deviation of sales for the current year.

Since, data is being collected for one sample only this limits us to chose between one sample test for mean. So now the possible options are one sample t-test for population mean and one sample t-test for population mean.

If we read the statement we can see that we have the value of sample mean and sample standard deviation. Value of population standard deviation is unknown. In cases where value of population standard deviation is not known and sample standard deviation is given, t-test is used.

Therefore, we can conclude that A one-sample t-test for population mean would be used.

T test is the test is a statistical test that is used to compare the means of two groups. The option B is correct option because a one sample t test for a population mean is the appropriate test for the executive's investigation for the given problem.

Given-

The options for the given question are-

T test is the test is a statistical test that is used to compare the means of two groups.

In the given problem the marketing executive wants to compare the annual sales mean number for the this year to the past year.

The mean value of the past year is known to the marketing executive.

The mean value of this year has to be calculated by the marketing executive.

For this the executive collects a random sample of 100 customer orders from a large population of orders and calculates the sample mean and sample standard deviation.

As t test is used to determine a significant difference between the means of the two groups which may be related in certain features. Thus this test is best suitable for the given problem.

Hence the option B is correct option because a one sample t test for a population mean is the appropriate test for the executive's investigation for the given problem.

For more about the t test, follow the link below-

https://brainly.com/question/1189751