help please i’m tired and i just want to finish this and go to bed

Help Please Im Tired And I Just Want To Finish This And Go To Bed

Answers

Answer 1

Answer: 112i + 85.8j

Step-by-step explanation:

Answer 2

Answer:

[tex]\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}[/tex]

Step-by-step explanation:

VectorsThe magnitude of a vector gives the length of the line segment.The direction of a vector gives the angle the line forms with the positive x-axis.

To find the components of a vector given its magnitude and direction, use the following formula:

[tex]\large\boxed{\vec{u}=\left(||\vec{u}|| \cos(\theta),|| \vec{u}|| \sin(\theta)\right)}[/tex]

where:

[tex]||\vec{u}||[/tex] is the magnitudeθ is the angle (in degrees)

Given:

[tex]||\vec{H}||=85.8[/tex][tex]\theta=112^{\circ}[/tex]

Substitute the given values into the formula:

[tex]\vec{H}=\left(85.8 \cos(112^{\circ}),85.8 \sin(112^{\circ})\right)[/tex]

[tex]\vec{H}=\left(-32.1, 79.6\right)[/tex]

Therefore:

[tex]\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}[/tex]


Related Questions

5,609÷7. I need the answer as soon as possible. THANKS!

Answers

Answer:

5609/7 = 801.3 (rounded)

Step-by-step explanation:

Answer:801.2857143

Step-by-step explanation: Remember to enter it in your calculator, if you get a fraction as an answer click shift and then = there you go

Express each of the following in m/second.
(a) 65cm/second
(b) 367km/hour
(c) 1000cm/min
(d) 86km/min

Answers

Answer:

you can see the above explanation

Step-by-step explanation:

thank you for this question

A pyramid has a square base with sides of length 10 units. Each segment that connects the apex to a
midpoint of a side of the base has a length of 13 units. What is the height of the pyramid? What is the volume of the pyramid, units cubed?

Answers

The volume of the pyramid is 400 cubic units.

What is a pyramid?

A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.

The volume of a pyramid with a square base is given as:

Volume = 1/3 x base area x height

We have,

Let's call the height of the pyramid "h".

We can use the Pythagorean theorem to find the slant height of the pyramid, which is the length of one of the edges from the apex to a corner of the base.

To do this, we can consider one of the right triangles formed by the apex, the midpoint of a side, and a corner of the base.

The hypotenuse of this right triangle is the segment connecting the apex to the midpoint of a side, which has a length of 13 units.

One leg of the right triangle is half of one side of the square base, which is 5 units.

The other leg of the right triangle is the height of the pyramid, which we want to find. So, we can write:

h² + 5² = 13²

Simplifying and solving for h, we get:

h²= 13² - 5²

h² = 169 - 25

h² = 144

h = 12

So, the height of the pyramid is 12 units.

To find the volume of the pyramid, we can use the formula:

Volume = (1/3) x Base Area x Height

The base of the pyramid is a square with sides of length 10 units, so its area is:

Base Area = 10² = 100 square units

Plugging in the values we know, we get:

Volume = (1/3) x 100 x 12

Volume = 400 cubic units

Therefore,

The volume of the pyramid is 400 cubic units.

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Please halp
Tysm for it ^-^

Answers

The standard form of the Polynomial is [tex]x^4[/tex] ( x³ -13x² + 145x /4 - 5/4) = 0.

What is Polynomial?

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

given:

The zeroes are 5/2 (multiplicity 2), 3 (multiplicity 1) and 0 (multiplicity 4.)

So, the standard form is

(x- 5/2)² (x-3) [tex]x^4[/tex] = 0

(x² + 25/4 - 10x) (x-3) [tex]x^4[/tex] = 0

(x³ + 25x /4 - 10x² - 3x² -5/4 + 30x) [tex]x^4[/tex] = 0

[tex]x^4[/tex] ( x³ -13x² + 145x /4 - 5/4) = 0

Thus, the Standard form

[tex]x^4[/tex] ( x³ -13x² + 145x /4 - 5/4) = 0

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A dog trainer compared mean numbers of lessons for two

groups of dogs to learn a new trick.

Answer ASAP will give brainliest

Answers

A true statement on the mean number of lessons for the dogs is The mean number of lessons for group A is greater than the mean for group B by 1 MAD.

How to prove the mean number ?

The difference in the mean number of lessons between the two groups being Group A and Group B is :

= Mean number of lessons Group A - Mean number of lessons Group B

= 5 - 3

= 2

The mean absolute deviation for Group B is 2. The mean number of lessons of group A related to this is :

= 2 / 2

= 1

This shows that the mean number of lessons for group A is greater than the mean for group B by 1 MAD.

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The full question is:

Mean number of lessons Mean Absolute Deviation (MAD)

Group A 5

Group B 3

2

2

Which statement about the data is true?

A. The mean number of lessons for group A is greater than the mean for group B by 1 MAD

B. The mean number of lessons for group A is greater than the mean for group B by 2 MAD

C. The MAD for group A is more than the MAD for group B

D. On average, the dogs in group B required more lessons than the dogs in group A

what do you add to 3 2/7 to make 7

Answers

3/ \s7 \s + 2/ \s7 \s = 3 + 2/ \s7 \s = 5/ \s7

For the purposes of addition, subtracting, and comparing fractions, it is appropriate to convert both fractions to a common (equal, same) denominator. LCM(7, 7) = 7, which is the least common multiple of both denominators, can be used to calculate the common denominator. Adding the denominators together yields the common denominator, which need not be the lowest: 7 x 7 = 49. It cannot further simplify the fraction result by cancelling in the next intermediate step.

In other words, adding three and two sevenths results in five sevenths.

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a jazz concert brought in $157,437 on the sale of 8,856 tickets. if the tickets are sold for $10 and $20 dollars, how many of the $10 dollar ticket were sold?

Answers

1968 of the $10 dollar ticket were sold by jazz & 6873  of the $20 dollar ticket were sold by jazz.

Jazz total amount received = $157,437

Total tickets sold = 8,856

Let the $10 tickets sold = x

The $20  tickets sold = 8,856 - x

Here the solution below :

$10(x) + 8,856 - x($20) = $157,437

$10x + $177120 - $20x = $157,437

-$10x = $157,437 - $177120

-$10x = - $19683

x = 1968.3

1968 of the $10 dollar ticket were sold by jazz & 6873  of the $20 dollar ticket were sold by jazz.

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Ella sees 7 beetles when she weeds her garden. Each beetle has 6 legs.
How many legs are there on all 7 beetles?
Check your work. How many legs are there on 7 beetles? ➡
legs on 7 beetles.

Answers

Step-by-step explanation:

Each beetle has 6 legs with 7 beetles

So 6 legs 7 times would be 6x7

And 6 multiplying by 7 is 42

In 7 beetles there are 42 legs.

A ferris wheel is 50 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn.

Answers

Answer: The height of a person on the ferris wheel can be modeled by the function:

h = 50 * cos(pi * t / 120) + 1

where t is the number of minutes since the wheel started turning, and pi represents the mathematical constant pi. The function takes into account the diameter of the ferris wheel (50 meters), the initial height of the platform (1 meter), and the fact that the wheel completes 1 full revolution in 4 minutes (120 seconds).

Step-by-step explanation:

I need some help on this !
a.13.3 cm to the power of 3


b.15 cm the power of 3

c.66.7 cm to the power of 3

d.75 cm to the power of 3​

Answers

The volume of the pyramid is 66.7 cm cube. Therefore, the answer is c.

How to find the volume of a pyramid?

The above diagram is a square base pyramid. The volume of the square base pyramid can be represented as follows:

volume of the pyramid = 1 / 3 BH

where

B = base areaH = height of the pyramid

Therefore,

base area = l²

where

l = side length

Hence,

base area = 5²

base area = 25 cm²

Therefore, let's find the volume of the pyramid.

Hence,

volume of the pyramid =  1 / 3 × 25 × 8

volume of the pyramid =  200 / 3

volume of the pyramid = 66.6666666667

Therefore,

volume of the pyramid = 66.67 cm³

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For each problem, decide which unit rate from the previous situations you prefer to use. Next, solve the problem, and show your thinking.
If Lin wants to make extra cheesecake filling, how much cream cheese will she need to mix with 35 ounces of sugar?
How many weeks will it take Mai’s family to finish 3 gallons of milk?
How much would all 1,000 raffle tickets cost?

Answers

Answer:

The distance from Jerusalem to Galilee is approximately 150 km depending on the route you take. You can get a bus from Jerusalem's central bus station to Tiberias, on the edge of the Sea of Galilee. The journey takes about 2-3 hours.Sep 4, 2019

5
Copy the diagram and write in the size of all the other angles.
Work out the unknown angles a, b and c
(It’s question 5)

Answers

In the diagram, one line is transversal of two parallel lines, so the value of a is 113°, value of b is 67° and value of c is 67°.

The parallel lines are what?

On a plane, lines that are parallel to one another never cross or come together. They are always parallel and equally spaced apart from one another. Parallel lines are lines that do not intersect. Lines are referred to as parallel if they never intersect and do not have a common intersection.

One line crosses two parallel lines in the diagram.

Angle an is the 113°'s vertically opposite angle.

Therefore, the angle's value is 113°.

Here, a and b have the same side interior angles since a line is transversal to two parallel lines.

So, a + b = 180°

⇒ 113° + b = 180°

⇒ b = 180° - 113°

⇒ b = 67°

And c is vertically opposite angle of b

So, the value of angle c = 67°

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What is the value of the angle marked with x?

Answers

Answer:

146

Step-by-step explanation:

becuase it's parallel, so x = 146

Brown's Car Repair charges $45 to tow the car plus $55 an hour to fix a car. Which expression shows how to find out how much a repair will cost ?

Answers

The expression shows how to find out how much a repair will cost  is 45 + 55x

How to determine the linear expression

From the question, we have the following parameters that can be used in our computation:

Brown's Car Repair charges $45 to tow the car $55 an hour to fix a car.

Using the above as a guide, we have the following:

Total charges = Tow + Rate per hour * x

Substitute the known values in the above equation, so, we have the following representation

Total charges = 45 + 55x

Hence, the expression is 45 + 55x

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Ernest took a total of 12 quizzes over the course of 4 weeks. How many weeks of school will Ernest have to attend this quarter before he will have taken a total of 30 quizzes? Solve using unit rates. __weeks

Answers

The number of weeks for taking 30 Quizzes will be 10.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Ernest took a total of 12 quizzes over the course of 4 weeks. The number of weeks required to take 30quizzes will be calculated as;-

12 quiz = 4 weeks

1 quiz = 4 / 12 weeks

30 quiz = ( 4 x 30 ) / 12 week

30 quiz = 10 week

Therefore, there will be 10 weeks total for taking the 30 quizzes.

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given the following fitnesses and starting frequency of the b1 allele, what is the frequency of the b1 allele after selection? specify your answer to two decimal places. assume random mating.

Answers

The frequency of the b1 allele after selection genotype frequency = 0.36

Genes can change into a variety of forms, with each form having a slightly different basic DNA sequence. These gene variations differ in the manner in which the trait is manifested, but they nonetheless code for the same feature (hair color) (i.e. brown vs blonde hair). Alleles are various variations of a single gene.

A genotype is a numerical representation of the type of mutation found at a particular locus (i.e., region) in the genome. It can be represented symbolically. As an example, the letters BB, Bb, and bb could be used to indicate a certain gene variant.

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Complete question:

A1A1 relative

fitness = 1

genotype frequency = 0.36

A1A2

relative fitness = 1

genotype frequency = 0.48

A2A2

relative fitness = 0.6

genotype frequency = 0.16

2
Write the fraction when:
30 is the numerator and 57 is the denominator.

29 is the numerator and 54 is the denominator.

Answers

Answer:

30/57   29/54

Step-by-step explanation:

The numerator is the number on top of the fraction

the denominator is the number on the bottom

[tex]\frac{30}{57}[/tex]  30 is the numerator

    57 is the denominator

Answer:

[tex]\frac{30}{57}[/tex]

[tex]\frac{29}{54}[/tex]

Step-by-step explanation:

The numerator of a fraction is the number that is above the line and the denominator of a fraction is the number that is below the line. We can use this to help find fractions with only the numerator and denominator.

When 30 is the numerator and 57 is the denominator.

[tex]\frac{30}{57}[/tex]

When 29 is the numerator and 54 is the denominator.

[tex]\frac{29}{54}[/tex]

the triangular region shows the number of possible walnuts, x, and number of possible chocolate chips, y, a baker can use in a recipe.which combination of walnuts and chocolate chips can the baker use?

Answers

28 walnuts and 20 chocolate chips are the combinations that the baker can use.

X stands for the total number of possible walnuts and y stands for the number of potential chocolate chips.

From the graph we can see:

a) 25 chocolate chips and 33 walnuts

Specifically, points (33,25) on the graph are outside the shaded region or the feasible region.

Therefore, it cannot be a solution.

b) With 10 chocolate chips and 45 walnuts.

i.e., the coordinate point (45,10) also lies outside the shaded area, making it impossible for this to be a solution to the problem.

c) The given problem will have an answer at point (28,20), which is located inside the shaded area.

d)  with 12 chocolate chips and 55 walnuts.

Point (55, 12) is not a viable solution because it lies outside the shaded area.

Hence, 28 walnuts and 20 chocolate chips in combination are the ones baker can use.

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The full question is:

The triangular region shows the number of possible walnuts, x, and the number of possible chocolate chips, y, a baker can use in a recipe.

Which combination of walnuts and chocolate chips can the baker use?

A. 33 walnuts and 25 chocolate chips

B. 45 walnuts and 10 chocolate chips

C. 28 walnuts and 20 chocolate chips

D. 55 walnuts and 12 chocolate chips

4. Given: AGEO = AOMG
Prove: GEOM is a parallelogram
Statements
1. AGEO AOMG
2. 4EGO
4GOM, 4MGO 4GOE
3. GM || EO
GE || MO
4. GEOM is a parallelogram
"
2.
1. Given
3.
M
4.
G
Justifications
O
E

Answers

The table of the statements and justifications used to prove that the quadrilateral GEOM is a parallelogram can be completed as follows;

            Statements           [tex]{}[/tex]                           Justifications

1.        [tex]{}[/tex]ΔGEO ≅ ΔOMG                                  1. Given

2. ∡EGO ≅ ∡GOM, ∡MGO ≅ ∡GOE [tex]{}[/tex]          2. CPCTC

3. [tex]\overline{GM}[/tex]║ [tex]\overline{EO}[/tex], [tex]\overline{GE}[/tex] ║ [tex]\overline{MO}[/tex]      [tex]{}[/tex]             3. Converse of alt. int. ∠s Theorem

4. GEOM is a parallelogram[tex]{}[/tex]                         4. Definition of a parallelogram

What is a parallelogram?

A parallelogram is a quadrilateral that have opposite parallel sides.

The details of the justifications in the table used to prove that quadrilateral GEOM is a parallelogram are presented as follows;

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent, which indicates that if teo triangles are congruent, then the corresponding sides and angles in both triangles are also congruent.

Converse of the alt. int ∠s theorem

The converse of the alternate interior angles theorem states that if the alternate interior angles formed by two lines and their common transversal are congruent, then the lines are parallel.

The angles ∡EGO, and ∡GOM are alternate interior angles, similarly, the angles ∡MGO and ∡GOE are alternate interior angle.

Whereby ∡EGO ≅ ∡GOM and ∡MGO ≅ ∡GOE, according to the convderse of the alternate interior angles theorem, the lines [tex]\overline{GE}[/tex] is parallel to [tex]\overline{MO}[/tex], and [tex]\overline{GM}[/tex] is parallel to [tex]\overline{EO}[/tex],  [tex]\overline{GE}[/tex] ║ [tex]\overline{MO}[/tex], and [tex]\overline{GM}[/tex] ║ [tex]\overline{EO}[/tex]

Definition of a parallelogram

The definition of a parallelogram, indicates that, where  [tex]\overline{GE}[/tex] ║ [tex]\overline{MO}[/tex], and [tex]\overline{GM}[/tex] ║ [tex]\overline{EO}[/tex], then the quadrilateral GEOM is a parallelogram.

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Please answer I will give brainliest
whats the excluded value

Answers

The excluded value of the function is x = -1

How to determine the excluded value

From the question, we have the following parameters that can be used in our computation:

The function

The definition of the function is given as

y = 2/(x + 1) + 1

Set the denominator to 0 to determine the excluded value

So, we have

x + 1 = 0

Evaluate the like terms

x = -1

Hence, the value that is excluded is x = -1

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a. Rotate triangle ABC 90^ counterclockwise about the origin. Label the 8 B 4 2

Answers

Coordinates of the image of Quadrilateral ABCD are

A' = (1 , -1)

B' = (2 , -4)

C' = (7 , -1)

D' = (6 , -4)

What is reflection ?

In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

Given,

Graph of a quadrilateral ABCD

A(1 , 1)

B(2,4)

C(7 , 1)

D(6 , 4)

After reflection over x - axis,

y = f(x) → y = -f(x)

(1, 1)  → (1 , -1)

(2 , 4) → (2 , -4)

(7 , 1) → (7 , -1)

(6 , 4) → (6 , -4)

Hence, After reflection the coordinates are:

A' = (1 , -1)

B' = (2 , -4)

C' = (7 , -1)

D' = (6 , -4)

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Please help me find the ratio for cos b. Faction only!

Answers

Answer:

20/29

Step-by-step explanation:

Recall that cosine of an angle is the side adjacent to it over the hypotenuse (SOH-CAH-TOA).
For this question the ratio is: 20/29

using all digits 3247 make the smallest number

Answers

Answer:  2347

To form the smallest number, use the smallest digits first. The smaller digits are on the left. The larger digits are on the right.

Consider this smaller example of 23 vs 32.

Find the number that makes the ratio equivalent to 2:6.
6:

Answers

18 is the number that makes the ratio equivalent to 2:6

How to find the number that makes the ratio equivalent to 2:6?

Equivalent ratios are ratios that have the same value, but may have different numerator and denominator values. They are related to each other by multiplication or division of both the numerator and denominator by the same non-zero value.

For example, the ratios 2/4 and 1/2 are equivalent ratios because both represent the same fraction (1/2) and therefore have the same value.

In this case we have:

2:6 = 6: x

2/6 = 6/x

2 * x = 6 * 6

2x = 36

x = 36/2

x = 18

Thus, the number that makes the ratio equivalent to 2:6 is 18

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Which number line represents the solution set for the inequality 2x 2 47
-10-8-6-4-20
-10 -8 -6
-4
-2

+
2 4
2 4
-10 -8 -6 -4 -2 02
6 8 10
6 8 10
4 6 8
-10 -8 -6 -4 -2 0 2 4 6 8
10
10

Answers

The number line that shows the solution set of the inequality is B

How to solve the inequality

In math, an inequality is a statement that describes a relationship between two values or expressions that are not equal. An inequality is written using mathematical symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

-1/2x ≥ 4

we are to get the value of x

-x ≥ 4 ÷ 1/2

- x ≥ 4 x 2

-x ≥ 8

x ≤ -8

The provided inequality is represented by an arrow with a solid point at x = -8 and an arrow pointing in the direction of negative values.

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Four integers have a mean of 9, a median of 8.5, a mode of 5 and a range of 9.

Find the four integers.

Answers

The four integers are 5, 5, 12 and 14.

What is Mean, Mode and Median?

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set.

When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.

Given:

Mean= 9

Median = 8.5

Mode = 5

Range = 9.

let the numbers arranged in ascending order are a,b,c,d

Median: b+ c /2 = 8.5

b+ c = 17 (number in the middle)

Mode: a = 5, b= 5 {because mode is the most repeating data}

Range: d- a = 9 (last one minus first one)

d= 9 + 5

d= 14

Now, b+c = 17

c= 17-5

c= 12

So, the data is 5 ,5, 12, 14.

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given that tan x = 1/5 then tan y =?

Answers

Answer:

  D.  1/2

Step-by-step explanation:

Given the side adjacent to an angle is 25 and the tangent of the angle is 1/5, you want to know the tangent of an angle with the same opposite side, but an adjacent side of 10.

Tangent

The tangent of an angle is the ratio of the opposite side to the adjacent side.

  Tan = Opposite/Adjacent

Then the Opposite side is ...

  Opposite = Adjacent · Tan(x) = 25·1/5 = 5

Angle y

For angle y, the opposite side is the same, but the adjacent side is only 10:

  Tan(y) = Opposite/Adjacent = 5/10

  tan(y) = 1/2

Sin Cos Tan
Geometry

Answers

Answer:

[tex]\sf Sin \ A = \dfrac{30}{50}\\\\\\Cos \ A = \dfrac{40}{50}\\\\\\Tan \ A = \dfrac{30}{40}[/tex]

Step-by-step explanation:

Trigonometric ratios:

1)

              [tex]\sf Sin \ A = \dfrac{opposite \ side \ of \ \angle \ A}{hypotenuse}[/tex]

                        [tex]\sf =\dfrac{BC}{AC}\\\\=\dfrac{30}{50}[/tex]

                       

             [tex]\sf \sf Cos \ A = \dfrac{adjacent \ side \ of \ \angle \ A}{hypotenuse}[/tex]

                       [tex]\sf = \dfrac{AB}{AC}\\\\= \dfrac{40}{50}[/tex]

             

             [tex]\sf \sf Tan \ A = \dfrac{opposite \ side \ of \ \angle \ A}{adjacent \ side \ of \ \angle \ A }[/tex]

                        [tex]\sf = \dfrac{BC}{AB}\\\\= \dfrac{30}{40}[/tex]

Sin= opp/hyp
Cos= adjacent/hyp
Tan= opp/adj
1•Sin= 30/50= 0.6
1•cos= 40/50= 0.8
1•tan= 30/40= 0.75
For question 2 goes the same:
2. Sin= 36/27= 1.33
2.cos= 45/27= 1.66
2.tan= 36/45= 0.8
For question 3:
3. Sin= 8/15= 0.533
3. Cos= 17/15= 1.1333
3.tan = 8/17= 0.47

Please tell me the answer I only have an 80 in math i need a 90 please help me!!!

Answers

The results of the divisions are:

1. 955/8 = 115 remainder 3

2. 249/7 = 35 remainder 4

3. 1,557/9 = 173 remainder 0

4. 2,448/8 = 306 remainder 0

5. 499/2 = 249 remiander 1

6. 396/6 =  66 remainder 0

7. The quotient will be in the tens since the value of 425 is between the product of 9 and 10 and 9 and 100.

What are the results of the following divisions?

The results of the given divisions are found as follows by means of long division:

1. 955/8 = 115 remainder 3

115 * 8 + 3 = 955

2. 249/7 = 35 remainder 4

35 * 7 + 4 = 249

3. 1,557/9 = 173 remainder 0

173 * 9 = 1557

4. 2,448/8 = 306 remainder 0

306 * 8 = 2448

5. 499/2 = 249 remiander 1

249 * 2 + 1 = 499

6. 396/6 =  66 remainder 0

66 * 6 = 396

7. 425/9 = 47 remainder 2

47 * 9 + 2 = 425

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Renata and her family go through an average of more then 15 cans of sparkling water each day. They buy cases of 24 cans at $3. 5 a case. Write an inequality for the number of cases they go through in 30 days. ​

Answers

The number of cases they go through in (x > 18.75 ) 30 days is greater than 18.75.

In this problem, Renata and her family go through an average of more than 15 cans of sparkling water each day. This means that in 30 days, they will go through a total of more than 15 * 30 = 450 cans of sparkling water.

They buy the sparkling water in cases of 24 cans each, and each case costs $3.5. To calculate the number of cases they need to buy, we divide the total number of cans they need by the number of cans in each case.

450 cans ÷ 24 cans per case = 18.75 cases

Since they need to buy more than 18.75 cases, we use the inequality symbol ">" to express this as:

x > 18.75

where x represents the number of cases of sparkling water they go through in 30 days.

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