An object sinks into the river at a rate of -2.5 feet per second and reaches the bottom in t seconds. If the equation -2.5= x/t represents this situation, where x is the depth of the river and t = 39 seconds, how deep is the river? pls help me

Answer:

m = 1.08

Step-by-step explanation:

2 - 2.27 = -m/4

-0.27 = -m/4

-0.27 × 4 = -m

-1.08 = -m

1.08 =m

Answer:

m = 1.08

Step-by-step explanation:

Basically, we can start off by finding the difference between 2 and 2.27(which is 0.27). Then we can see that 0.27 is equal to m/4. Since 0.27*4=1.08, we can see that m=1.08.

The camp charge per week = slope = $25 per week.

The slope is also referred to as the unit rate which is given as: m = change in y / change in x.

From the given scenario, let:

x = number of weeks

y = camp charges

We will therefore have these two points:

(6, 190) and (9, 265)

Use the two points to find the slope, which is the swimming camp charge per week:

Camp charge per week (m) = change in y / change in x = 265 - 190 / 9 - 6

= 75/3

= $25 per week.

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A solution of 150 h is administered at a rate of 8 ml / hr.

We express the answer in terms of mg/hr m g / h r

90 mg dopamine / 20 ml = 4.5 mg/ml

4.5 mg/ml * 8 ml/h = 36 mg/h

90 mg * 1 h / 36 mg= 150 h to administer -- using the inverse of 90 mg per 1 hour and cancelling mg in numerator and ml denominator.

Hence, 150 h is administered at a rate of 8 ml / hr.

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Answer:

data given

Universal set 40people

people who can sew 14

people who can knit 12

people who can do both 5

Step-by-step explanation:

•people who can sew only

=14-5

=9

•people who can knit only

=12-9

=7

Union of people who can sew and the one who can knit

=9+7+5

=21

who do neither

=40-21

=19

: .people neither sew or knit are 19

Intersection AND

Union AND, MOSTLY

Disjunction OR

Conjunction AND

For these words, we have:

Intersection, when we and the common results between two sets

So, Intersection A ∩ B A and B

A ={1,2,3} B= {3,4,5} A ∩ B ={3}

Disjunction, OR

When some conditions apply either to one set or to another.

A V B = OR

He is American OR He is British

A OR B

Union, AND, Mostly

When we want all the elements that belong to both Sets

So A ∪ B means A and all the elements from A and all the elements from B, no need no repeat the same element.

A = {1,2,3} B= {3,4,5} A ∪ B ={ 1,2,3,4,5}

Conjunction

A ^ B = AND,

In Logic and Set Theory and we have conjunction, we can use the word

He is a New Yorker AND He is American.

Using trigonometry and the given angles, the length of the bridge, to the nearest whole number, is 378 m.

Let's consider the right triangle formed by the lines of sight from points X and Y to the far end of the bridge, Z. The angles of the triangle are 85.6° and 79.8°.

We can use the tangent function to calculate the length of the bridge. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

Let's denote the length of the bridge as L. Then, we have:

tan(85.6°) = L / (100m - L)

tan(79.8°) = L / (100m)

Now, we can solve these equations to find the length of the bridge L:

Using the first equation:

tan(85.6°) = L / (100m - L)

L = (100m - L) * tan(85.6°)

L = 100m * tan(85.6°) - L * tan(85.6°)

L + L * tan(85.6°) = 100m * tan(85.6°)

L * (1 + tan(85.6°)) = 100m * tan(85.6°)

L = (100m * tan(85.6°)) / (1 + tan(85.6°))

Using the second equation:

tan(79.8°) = L / (100m)

L = 100m * tan(79.8°)

Now, we can substitute the values into the equations to find the length of the bridge L:

L = (100m * tan(85.6°)) / (1 + tan(85.6°))

L = (100m * tan(79.8°))

Calculating these values, we find L ≈ 377.5 m (rounded to one decimal place).

Therefore, the length of the bridge, to the nearest whole number, is 378 m.

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i. Vectors u and w are orthogonal.

ii. The two vectors orthogonal to v = √(2, -3) are u = (3, 2) and w = (-2, 3).

iii. The two unit vectors orthogonal to 7 are u = (1, -1) / √2 and w = (1, 1) / √2.

i. To show that vectors u = (a, b) and w = (-b, a) are orthogonal, we need to demonstrate that their dot product is zero.

The dot product of u and w is given by:

u · w = (a, b) · (-b, a) = a*(-b) + b*a = -ab + ab = 0

ii. To find two vectors orthogonal to vector v = √(2, -3), we can use the result from part i.

Let's denote the two orthogonal vectors as u and w.

We know that u = (a, b) is orthogonal to v, which means:

u · v = (a, b) · (2, -3) = 2a + (-3b) = 0

Simplifying the equation:

2a - 3b = 0

We can choose any values for a and solve for b. For example, let's set a = 3:

2(3) - 3b = 0

6 - 3b = 0

-3b = -6

b = 2

Therefore, one vector orthogonal to v is u = (3, 2).

To find the second orthogonal vector, we can use the result from part i:

w = (-b, a) = (-2, 3)

iii. To find two unit vectors orthogonal to 7, we need to consider the dot product between the vectors and 7, and set it equal to zero.

Let's denote the two orthogonal unit vectors as u and w.

We know that u · 7 = (a, b) · 7 = 7a + 7b = 0

Dividing by 7:

a + b = 0

We can choose any values for a and solve for b. Let's set a = 1:

1 + b = 0

b = -1

Therefore, one unit vector orthogonal to 7 is u = (1, -1) / √2.

To find the second unit vector, we can use the result from part i:

w = (-b, a) = (1, 1) / √2

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Answer:

ur really weird we are not dating you weirdo

Step-by-step explanation:

(a)The median salary of the 20 data's is 48 (b)The mean salary of the 20 data's is 47.65 which is less than the median due to which the histogram is slightly skewed towards right

(c)The first quartile of the 20 salary will be the first 5 datas = (28, 31, 34, 35, 37)

(d) The interquartile range of the 20 salaries will be the lenght of 2nd and 3rd quartile combined = 5 + 5 = 10 from 6th term to 15th term.

The median value of a data set is the value at which 50% of the data points have values lower than it or equal to it and 50% of the points have values higher than it or equal to it. The median is the value that separates the upper from the lower half of a population, a probability distribution, or a sample of data. For a data collection, it may be referred to as "the middle" value.

In mathematics, particularly in statistics, there are a variety of mean types. Each mean aids in the summary of a particular set of data, frequently serving to assess the overall importance of a given data set.

The interquartile range includes the second and third quartiles, or the middle half of your data set (IQR). The range gives the spread of the full data set, whereas the interquartile range gives the range of the middle half of the data set.

The set of salary (data) :

28, 31, 34, 35, 37, 41, 42, 42, 42, 47, 49, 51, 52, 52, 60, 61, 67, 72, 75, 77.

Since there are 20 datas (even) the median will be the average of the 2 centre data = (47+49)/2 = 48

The mean of the data set = (28+ 31+ 34+ 35+ 37+ 41+ 42+ 42+ 42+ 47+ 49+ 51+ 52+ 52+ 60+ 61+ 67+ 72+ 75+ 77)/20 = 953/20 = 47.65

The first quartile of the 20 salary will be the first 5 datas = (28, 31, 34, 35, 37)

The interquartile range of the 20 salaries will be the lenght of 2nd and 3rd quartile combined = 5 + 5 = 10 from 6th term to 15th term.

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The value of df for a test with four categories and a sample of any size is 3.

The degrees of freedom (df) for a chi-square test for goodness of fit is calculated as (number of categories - 1) since one category can be determined from the frequencies of the other categories.

In this case, there are four categories, so the degrees of freedom would be (4 - 1) = 3.

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The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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Answer:

458 (or 459 if you overestimate)

Step-by-step explanation:

Let's work backwards. we know that the 275 students are 60% of the total students enrolled, which we'll denote with x. Therefore:

0.6x = 275

Now divide both sides by 0.6 to get the answer:

x = 458.3

You can't have .3 students, so the answer is either 458 or 459 students, depending on if you want to over or underestimate.

Hope this helps!

The polynomial representing the area of the is 49n² - 25

The formula for area of a square is expressed as;

Area = a²

Where a is the side length

From the image shown, we can see that the side length takes the value (7n - 5)

Substitute the value into the formula

Area = a²

Area = (7n - 5)²

Area = (7n - 5) ( 7n + 5); this is so because of the difference of two squares

Expand the bracket

Area = 49n² + 35n - 35n - 25

collect like terms

Area = 49n² - 25

Thus, the polynomial representing the area of the cube is 49n² - 25

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In a rectangle WXYZ, if the measure of angle 1 is 30 degrees, then the measure of angle 8 can be determined.

A rectangle is a quadrilateral with four right angles. In a rectangle, opposite angles are congruent, meaning they have the same measure. Since angle 1 is given as 30 degrees, angle 3, which is opposite to angle 1, also measures 30 degrees.

In a rectangle, opposite angles are congruent. Since angle 1 and angle 8 are opposite angles in quadrilateral WXYZ, and angle 1 measures 30 degrees, we can conclude that angle 8 also measures 30 degrees. This is because opposite angles in a rectangle are congruent.
Since angle 3 and angle 8 are adjacent angles sharing a side, their measures should add up to 180 degrees, as they form a straight line. Therefore, the measure of angle 8 is 180 degrees minus the measure of angle 3, which is 180 - 30 = 150 degrees.

So, if angle 1 in rectangle WXYZ is 30 degrees, then angle 8 measures 150 degrees.

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Answer: x=910

Step-by-step explanation:

Look at attachment

Answer:

=3.8x108+1.6x107

Step-by-step explanation:

Answer:  5.816 × 10²

581.6 in scientific notation is 5.816 × 10²

Answer:

7:50 am in the morning

Step-by-step explanation:

17:50pm = 5:50pm

first simply this by only adding 12 hours

12 hours later- 5:50 am

Then add 2 hours to get the answer

14 hours- 7:50 am in the morning.

( I think)

...

Assuming that this is a parallelogram, that means the angle opposite each other like Angle L to Angle J and Angle K to Angle M are equal in angle measure.

Thus Angle L is 98 degrees like Angle J

Hope that helps!

Answer:

Step-by-step explanation:

This equation has a vertical asymptote at x = -2 and a horizontal asymptote at y = 1. This is stuff you should know about rational equations as you learn about them. The vertical asymptote serves as the locked gate or really high wall that the graph cannot go through nor can it go around or over or under. The graph will never cross through the VA. The horizontal asymptote is a horizontal line, y = 1, that reveals the graph's end behavior. So picture this:

We have an x/y coordinate plane. There is a vertical asymptote at x = -2 and a horizontal line at y = 1. This graph, because it cannot go through the vertical asymptote, is "split" into 2 parts, basically. The left "part" comes in along the horizontal asymptote from negative infinity, almost touching it but not quite, and when it reaches x = -2, it drops along the vertical asymptote, almost touching it but not quite and goes down into negative infinity. The right "part" of the graph comes down from positive infinity along the vertical asymptote, almost touching it but not quite, and when it reaches y = 1, it curves along that line off into positive infinity.

1. The entire expression is the product of 4 factors.

2. In this context, 1/3 is a coefficient.

Factors can be defined as the fundamental building blocks of a number. This ultimately implies that, factors simply refers to numbers which can be multiplied together to get another number.

In Mathematics, a coefficient can be defined as a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.

Based on the given expression 1/3bwh, we can logically deduce that there are four (4) factors and these include the following:

In conclusion, 1/3 is considered as a coefficient of bwh.

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Graphing each of the equation gave the points

The table of values for graphing the linear equation is done as follows

4x + y = 4 rearranging gives y = 4 - 4x

For x = -5, y = 4 - 4 * -5 = 24

For x = 0, y = 4 - 4 * 0 = 4

For x = 5, y = 4 - 4 * 5 = -16

table of values

x    y

-5  24

0    4

5    -16

x + y = -2 rearranging gives y = -2 - x

For x = -5, y = -2 - (-5) = 3

For x = 0, y = -2 - (0 = -2

For x = 5, y = -2 - (5) = -7

table of values

x    y

-5  3

0    -2

5    -7

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Rectangle can be folded once along the length and once along the width. This will give us two lines of symmetry.

Given that,

We have to find why do rectangles only have 2 lines of symmetry.

We know that,

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. For this reason, it is often referred to as an equiangular quadrilateral.

The neighboring sides of a rectangle are at right angles and share their opposite sides.

Therefore, On both the length and width, it may be folded once. This will give us two lines of symmetry.

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Answer:

The answer is 45

Step-by-step explanation:

Follow the steps:

set it up:

18/? = 40%/100%

18 x 100= 1800

1800 divided by 40 equals 45

Hope this helps! :)

Rafe and Ashley used approximately 5353.2 square inches of canvas to make the lamp.

Let's call the length of the base rectangle "L" and the width "W." From the picture, we can see that the base rectangle measures 18 inches by 18 inches. Therefore, the area of one base rectangle is given by:

Area of a rectangle = Length × Width

Area of one base rectangle = L × W = 18 in × 18 in = 324 square inches

Since there are two identical base rectangles, the combined area of both rectangles is:

Total area of base rectangles = 2 × Area of one base rectangle = 2 × 324 square inches = 648 square inches

Let's calculate the perimeter of the base rectangle first:

Perimeter of a rectangle = 2 × (Length + Width)

Perimeter of the base rectangle = 2 × (18 in + 18 in) = 2 × 36 in = 72 inches

Now, the height of the triangular prism is given as 20.1 inches. Therefore, the area of each lateral face rectangle is given by:

Area of a rectangle = Length × Width

Area of one lateral face rectangle = Perimeter of base rectangle × Height = 72 in × 20.1 in = 1447.2 square inches

Since there are three identical lateral face rectangles, the combined area of all three rectangles is:

Total area of lateral face rectangles = 3 × Area of one lateral face rectangle = 3 × 1447.2 square inches = 4341.6 square inches

The height of the triangular face is the same as the height of the prism, given as 20.1 inches. Therefore, the area of each triangular face is given by:

Area of a triangle = (Base × Height) / 2

Area of one triangular face = (18 in × 20.1 in) / 2 = 181.8 square inches

Since there are two identical triangular faces, the combined area of both triangles is:

Total area of triangular faces = 2 × Area of one triangular face = 2 × 181.8 square inches = 363.6 square inches

Now, to find the total surface area of the lamp, we sum up the areas of all the faces:

Total surface area = Total area of base rectangles + Total area of lateral face rectangles + Total area of triangular faces

Total surface area = 648 square inches + 4341.6 square inches + 363.6 square inches

Total surface area = 5353.2 square inches

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Complete Question:

Marius and his dad build a lamp in the shape of a triangular prism, open on the top and bottom. How many square inches of canvas did Marius and his dad use to make the lamp?

Solution

Step 1:

Write the logarithm function

Step 2:

Base = a

Exponent = 4

Hence

Final answer

Answer:

23.64

Step-by-step explanation:

\(\frac{6.6+3.2}{5}\) × (2 - 5)² + 6

= \(\frac{9.8}{5}\) × (- 3)² + 6

= 1.96 × 9 + 6

= 17.64 + 6

= 23.64

The value of the (6.6 + 3.2)/5*(2-5)²+6 is 23.64

An expression is a set of terms combined using the operations +, -, x or ÷, /

Given statement:

The sum of 6.6 and 3.2 all divided by 5 times the quantity of the squared difference of 2 minus 5 plus 6.

Now,

(6.6 + 3.2)/5*(2-5)²+6

=9.8/5*3²+6

=1.96*9+6

=17.64+6

=23.64

Hence, the value is 23.64.

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