what is the sum or difference of cos 61° + cos 45°?

The largest number of boxes that can fit in the crate will be 27.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The dimension of the crate is 24cm by 18cm by 15cm.

And, it is to be packed with boxes that are 8cm by 6cm by 5cm.

Now,

By the given data;

Volume of the crate = 24 x 18 x 15

                               = 6480 cm³

And, The volume of the box = 8 x 6 x 5

                                            = 240 cm³

Thus, The largest number of boxes that can fit in the crate = 6480 / 240

                                                                                           = 27

Therefore, The largest number of boxes that can fit in the crate will be 27.

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Answer:

Jasmine spent 1.45$ more on water than popcorn.

Step-by-step explanation:

Jasmine buys 4 bottles of water and spends 1.30$ for each one individually. To find out how much all of these 4 costs, we multiply 4 by 1.30$ which is 5.20$

To find out how much more money Jasmine spent on the water than popcorn, we subtract 5.20$ - 3.75$ = 1.45$

The true statement about the function is that (b) the y-intercept of the function is 3

The mathematical statement of the representation of the function is given as

The function f(x) is the absolute value of 3 more than the value of x.

Mathematically, this can be represented as

f(x) = |x + 3|

To determine the y-intercept, we set the x value of the function to 0

This means that we calculate f(x) when x = 0

i.e. f(0)

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

f(0) = |0 + 3|

Evaluate the sum

This gives

f(0) = |3|

Remove the absolute bracket

f(0) = 3

Hence, the y-intercept is 3

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Possible question

If the function f(x) is the absolute value of 3 more than the value of x. Select all the true statements.

A. The x-intercept of the function is 3.

B. The y-intercept of the function is 3.

Answer:

D 11%

$30

Step-by-step explanation:

1. A cyclist estimates that he will bike 80 miles this week. He actually bikes 90 miles. What is the percent error of the cyclists estimate rounded to the nearest percent?

A 8%

B 9%

C 10%

D 11%

Actual distance: 90 miles

Estimated distance: 80 miles

percent error = (estimate - real)/real × 100%

percent error = (80 - 90)/90 × 100%

percent error = -11%

His error is 11%. The negative sign just means his estimate is 11% less than the real distance.

Answer: 11%

2. Jack borrows $3,000 at a rate of 4% per year. How much total will he pay if it takes 3 months to repay the loan?

$10

$20

$30

$40

interest = Prt

where P = principal (the amount borrowed or deposited)

r = annual rate of interest

t = time

We have P = $3,000

r = 4% = 0.04

t = 3 months = (3 months)/(12 months) = 0.25 year

interest = $3,000 × 0.04 × 0.25

interest = $30

He pays a total interest of $30.

Answer:

=57×2of4+2

=57×8+2

=456+2

=458.

hope it will help you

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Answer:

x=48

Step-by-step explanation:

the 2 given angles if added together we know it’ll be 180 degrees

3x-12+x=180

4x-12=180

   +12. +12

4x=192

x=48

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The exact value of tan195° is 0.2679.

The given trigonometric ratio is tan195°.

Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.

Now, the value of  trigonometric ratio is

tan195°=0.2679

Hence, the exact value of tan195° is 0.2679.

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Answer:

-1

Step-by-step explanation:

you would do -11 + (-5) which will be -16. Then do -16 - (-15) which will get you -1.

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line G

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 8 } \implies {\Large \begin{array}{llll} - \cfrac{3 }{ 8 } \end{array}}[/tex]

Answer:

  $1377.06

Step-by-step explanation:

You want the monthly payment on a 30 year loan of $162359 at 9.6% interest.

The payment value can be computed by any spreadsheet and most graphing calculators using built-in financial functions. Numerous apps and web sites are available for the same purpose.

The monthly payment is $1377.06 according to the attached calculator output.

The formula used for the purpose is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12·t))

where P is the loan value, r is the annual interest rate, and t is the number of years. For P=162359, r=0.096, and t=30, you have ...

  A = 162359(0.096/12)/(1 -(1 +0.096/12)^-360) ≈ 1377.06

__

Additional comment

The formula assumes the payment is made at the end of the month. Spreadsheet and calculator functions often need to be told that's when the payment is made.

Answer:

20/7 km/hr

Step-by-step explanation:

To solve this problem, we use the formula of:

speed x time = distance

Both the raft and boat have their own speeds, times and distances, so we would write two equations based on the formula.

One for the raft: [tex](s_{r} )(t_{r} )=d_{r}[/tex]

And one for the boat: [tex](s_{b} )(t_{b} )=d_{b}[/tex]

Both vehicles travelled as total of 20 km, so both [tex]d_{r} =d_{b} =20[/tex]. We are also given that the boat goes 12 km/hr, so [tex]s_{b} = 12[/tex]. Lastly, the boat had been going for five hours and 20 minutes less than the raft. This is the same as 5 1/3 hrs. This can also be written as 16/3 hrs, so [tex]t_{r} = t_{b} +\frac{16}{3}[/tex]. We can now plug these in:

raft: [tex](s_{r} )(t_{b}+\frac{16}{3} )=20[/tex]

boat: [tex](12 )(t_{b} )=20[/tex]

We only have one variable in the boat equation, so we can solve for time:

[tex]t_{b} =\frac{20}{12} \\\\t_{b} = \frac{5}{3}[/tex]

Now, we can plug [tex]t_{b}[/tex] into the raft equation and solve for speed:

[tex](s_{r} )(t_{b}+\frac{16}{3} )=20\\\\(s_{r} )(\frac{5}{3} +\frac{16}{3} )=20\\\\(s_{r} )(\frac{21}{3} )=20\\\\(s_{r} )(7)=20\\\\s_{r}=\frac{20}{7}[/tex]

Therefore, the speed of the raft would be 20/7 km/hr

The speed of the raft if the speed of the patrol boat was 12 km/hr will be 20/7 km/hr.

Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.

For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.

It is known that,

Speed = total distance / total time taken

The time is taken by petrol boat to reach the raft craft

Time = total distance/speed

Time = 20/12 = 5/3 hour.

The time taken the raft boat to reach 20 km = (5 hour + 20 minutes) + 5/3 hour

⇒ 5 + 1/3 + 5/3

⇒ 16/3 + 5/3 = 21/3 = 7

The speed of the raft will be as,

Speed of raft = 20/7 km/hr

Hence "The speed of the raft, if the speed of the patrol boat was 12 km/hr, will be 20/7 km/hr".

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The horizontal distance which the cable is placed on is 57.74 feet

Trigonometric functions are the periodic functions which denote the relationship between angle and sides of a right-angled triangle. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Data;

Using tangent ratio;

tanθ = opposite / adjacent

tan 60 = 100 / x

x = 100 / tan 60

x = 57.74 ft

The distance which the cable is anchored to the ground is 57.74ft.

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Answer:

x = 36°

Step-by-step explanation:

Hello!

If angles are supplementary, that means that the sum of those angles is 180°.

Set up an equation and solve for x.

The measure of x is 36°.

The distance between point A and point B is 5 units.

According to the question,

We have the following information:

Point A = (-2,2)

Point B = (1,2)

Now, we know that the following formula is used to find the distance between two points:

Distance between two points = [tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} )}[/tex]

In this case, we have the values of x1 = -2, y1 = -2, x2 = 1 and y2 = 2.

Distance between two points = [tex]\sqrt{(2+2)^{2} +(1+2)^{2} )}[/tex]

(The sign has been changed from negative to positive because the multiplication of two negative integers is positive.)

Distance = [tex]\sqrt{(4)^{2} +(3)^{2} )}[/tex]

Distance = [tex]\sqrt{16+9}[/tex]

Distance = [tex]\sqrt{25}[/tex]

Distance = 5 units

Hence, the distance between point A and point B is 5 units.

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Proved that Triangle ABD ≅ Triangle CBD

Consider the triangle ABD and the triangle CBD

The length of the side AB = The length of the side BC

The length of the side AD = The length of the side cd

The third side is common

According to the SSS rule congruent . If the three side of the triangle is equal to the three sides of the another triangle then the both triangles are congruent

Then three sides of the triangle ABD is equal to the three sides of the triangle CBD, Therefore the triangle ABD and triangle CBD are congruent

Hence, proved that Triangle ABD ≅ Triangle CBD

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Answer:

"i agree because.."

Step-by-step explanation:

50 x 20 = 1000

5 x 2 = 10

there are 2 zeros in both factors so placing the 2 zeros at the end of 10 (making 1000) would work since they are the same answer

The trigonometric measures in the context of this problem are given as follows:

We are given the measure of the sine for the angle and we need to find the three measures, sine, cosine and tangent for half the angle.

To find the measure for half the angle, the cosine is needed to apply the identities, and the cosine is calculated by the following identity:

sin²(x) + cos²(x) = 1

[tex]\left(\frac{2}{3}\right)^2 + \cos^2{x} = 1[/tex]

[tex]\cos^2{x} = 1 - \frac{4}{9}[/tex]

[tex]\cos{x} = \pm \sqrt{\frac{5}{9}}[/tex]

The angle is in the first quadrant, in which the cosine is positive, hence:

[tex]\cos{x} = \sqrt{\frac{5}{9}}[/tex]

[tex]\cos{x} = \frac{\sqrt{3}}{3}[/tex]

Then, applying an identity, the sine for half the angle is given as follows:

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \cos{x}}{2}}[/tex]

Considering the calculated value for the cosine:

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \frac{\sqrt{3}}{3}}{2}}[/tex]

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3-\sqrt{3}}{6}}[/tex]

The identity for the cosine is:

[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 + \cos{x}}{2}}[/tex]

Hence:

[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3+\sqrt{3}}{6}}[/tex]

The tangent is obtained by the division of the sine and the cosine. The entire division can be placed into a single square root, and the common denominators of six are simplified, hence:

[tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]

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The amount that should be deposited in the account to earn a balance of $5, 000 after 19 years and 6 months is $2, 099.43

First, find the periodic rate:

= 4.5% / 2 semi annual periods per year

= 2.25%

Find the number of periods:

= 19 years and 6 months = 19.5 years

= 19.5 years x 2 semi annual periods per year

= 39 periods

The amount to deposit in the account can be found by the future value formula:

Future value = Deposit x ( 1 + rate) ^ number of periods

5, 000 = Deposit x ( 1 + 2.25%)³⁹

Deposit = 5,000 / ( 1 + 2.25%)³⁹

= $2, 099.43

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To find the height, envision it as a third side to a right triangle. We have the first side, with a length of 7cm, and the hypotenuse, with a length of 15cm. When we have two sides of a right triangle with given lengths, we can employ the Pythagorean Theorem.

The Pythagorean Theorem states that the square of the hypotenuse, c, is equal to the sum of the squares of the other two sides, or:

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

Well, we have a and c, so we can solve for b.

[tex]7^2 + b^2 = 15^2\\49+b^2 = 225\\49 - 49 + b^2 = 225 - 49\\b^2 = 176\\\sqrt{b^2}=\sqrt{176}\\b = 13.27[/tex]

b ≈ 13.27

The total cups of water the pitcher can hold is 72

A fraction is the ratio of two integers.

It is divided into two parts by a division line and the part above the line is called the numerator and the part below the line is called the denominator.

Fraction are of three types: proper, improper and mixed fractions.

Let the total number of cups to fill the pitcher be x.

The pitcher is 3-fourths full of water, that is 3/4 of x = [tex]\frac{3x}{4}[/tex]

when 6 cups were taken away from the Pitcher it became 2/3 of x = [tex]\frac{2x}{3}[/tex]

So that,

[tex]\frac{3x}{4}[/tex] -  [tex]\frac{2x}{3}[/tex] = 6

multiply  [tex]\frac{2x}{3}[/tex] by 4/4 and  [tex]\frac{3x}{4}[/tex] by 3/3

it becomes

[tex]\frac{9x}{12}[/tex] - [tex]\frac{8x}{12}[/tex] = 6

simplifying the numerator

x/12 = 6

cross multiplying

x = 12 x 6

x = 72

In conclusion, the total number of cups to fill the pitcher is 72

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The equation of the inverse function is f⁻¹(x) = x/7 - 3/7

The function f(x) is given as

f(x) = 7x + 3

As a general rule, we start by writing f(x) as a variable (say f(x) = y).

So, the equation of the function becomes

y = 7x + 3

The next step is to switch/swap the positions of x and y in the above equation y = x + 5

The equation becomes

x = 7y + 3

The next step is to make y the subject of the formula in the above equation

The equation becomes

y = x/7 - 3/7

Express as an inverse function

f⁻¹(x) = x/7 - 3/7

Hence, the inverse is f⁻¹(x) = x/7 - 3/7

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a) The sample proportion would be of: 0.93.

b) The margin of error would be of: 0.037.

c) The critical value would be of: z = 1.96.

d) The standard error would be of: 0.0189.

e) The critical value for the 90% confidence interval would be of: z = 1.645.

f) The 90% confidence interval would be narrower.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

From the equation, the confidence interval can be described as follows:

The sample proportion plus/minus the margin of error.

For this problem, the interval is given as follows:

(.893, .967).

From the description, the sample proportion is the mean of the two bounds, hence:

Sample proportion = (0.893 + 0.967)/2 = 0.93.

The margin of error is the absolute value of the difference of each bound and the sample proportion, hence:

Margin of error = |0.967 - 0.93| = |0.893 - 0.93| = 0.037.

The critical values are found using the z-table, as follows:

The greater the critical value, the wider the interval, hence a 90% confidence interval would be narrower than the 95% confidence interval;

The standard error is the division of the margin of error by the critical value, hence:

Standard error = 0.037/1.96 = 0.0189 = 1.89%.

The complete problem is given by the image shown at the end of the answer.

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Answer: bro You need To add more about the question

Step-by-step explanation:

Answer:

100 seconds

Step-by-step explanation:

200/2 = 100s

y=35x+350  is the equation to show the total cost of the party (y) based on the number of guests (x) he invites.

Two or more expressions with an Equal sign is called as Equation.

Given,

James is having a birthday party.

It costs $350 to rent the hall plus $35 per person for food

We need to write an equation to show the total cost of the party (y) based on the number of guests (x) he invites.

y=35x+350

Where x represents the number of guests.

350 is a constant value because it is the cost of the hall.

As 35 is the cost per person, 35x

Hence y=35x+350  is the equation to show the total cost of the party (y) based on the number of guests (x) he invites.

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The composition of the fuctions g(x) and f(x) evaluated in x = 4 is equal to:

g( f(4)) = 45

Here we have two functions f(x) and g(x), such that:

g(x) = 3.25*x + 6

And f(x) is defined by the table:

x            f(x)

-2            -1

0             3

 4            12

7              9

19             6

And we want to find the composition of g(x) and f(x) evaluated in x = 4.

g( f(4))

By using the table of f(x), we can see that f(4) = 12

Then:

g( f(4)) = g(12)

Evaluating g(x) in x = 12 we get:

g(12) = 3.25*12 + 6 = 45

Then we conclude that g( f(4)) = 45

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Answer:

Green x = 10

Purple x = 19

Step-by-step explanation:

Are we solve for x?

Green:

It is not staighted, but this looks like a straight angle.  That would total 180

3x + 5 + 6x -5 +90 = 180  A right angle is 90  Combine like terms

9x + 90 = 180  Subtract each side by 90

9x = 90  Divide both sides by 9

x = 10

Purple:

5x - 19 + 2x + 5 = 119  Combine like terms

7x -14 = 119  Add 14 to both sides

7x = 133  Divide both sides by 7

x = 19

Answer:

See below

Step-by-step explanation:

13 - 5x = 48  Subtract 13 from both sides

-5x = 35

-5x = 35 is the not the same as 5x = 35

-5x = 35  Divide both sides by -5

x = -7

5x  = 35  Divide both sides by 5

x = 7

7 and -7 are not the same solution.  They are two different numbers.

Answer:

2/3

Step-by-step explanation:

we use y2-y1/x2-x1 to find slope

5-3/4-1

2/3

The slope is 2/3

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