what is cos(75°)cos(15°) =

The function representing the given situation will be f(x) = x², where x is the number of week.

A function is defined as a relation between a set of inputs having one output each.

Given that, Cate started with $0 in her account. After one week, Cate saved $1; after two weeks she saved $4; after three weeks she saved $9; and after four weeks she saved $16.

As we see,

In 1 week the amount is $1

In 2 week the amount is $4

In 3 week the amount is $9

Which is showing that the amount is square of the week.

Hence, we can write the function as f(x) = x², where x is the number of week.

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Hello !

Answer:

\(\Large \boxed{\sf r=\frac{3}{2} }\)

Step-by-step explanation:

Let's remember :

We know that the volume of the sphere is equal to half its surface area.

\(\sf V_{sphere}=\frac{1}{2} A_{sphere}\\\\\sf \frac{4}{3}\pi r^3=\frac{1}{2} 4\pi r^2\\\\\sf \frac{4}{3}\pi r^3=2\pi r^2\)

Let's solve this equation for r.

First, substract \(\sf 2\pi r^2\)  from both sides :

\(\sf \frac{4}{3} \pi r^3-2\pi r^2=0\)

We can now factorize by taking out the highest common factor: 2r²

\(\sf 2r^2(\frac{2}{3} \pi r-\pi )=0\)

We can use the zero-product property.

There are two solutions :

The first solution is absurd : The radius of a sphere cannot be 0.

We conclude that we must keep the second solution.

Have a nice day ;)

Answer:

\(243.2cm^{2}\)

Step-by-step explanation:

Step 1: Understand what this shape is constructed out of

2 Congruent Trapezoid

2 Congruent Rectangles

1 Small Rectangle

1 Large Rectangle

Step 2: Find the surface area of the shapes

Area of 2 Trapezoids =\((\frac{a+b}{2}h)2=(\frac{4+6}{2}2.8)2=(\frac{10}{2}2.8)2=((5)}(2.8))2= (11.6)(2)=23.2cm^{2}\)

Area of 2 Rectangles = \((3)(10)(2)=(60)(2)=120cm^{2}\)

Area of Smaller Rectangle = \((4)(10)=40cm^{2}\)

Area of Larger Rectangle = \((6)(10)=60cm^{2}\)

Step 3: Add the surface areas up

\(23.2cm^{2} +120cm^{2} +40cm^{2} +60^{2} =243.2cm^{2}\)

Therefore the surface area of the Trapezoidal Prism is \(243.2cm^{2}\)

Answer:

for the radius, the cloest i could get was 6.77. therefore the diametre would be double meaning its would be 13.54

so sorry if this is incorrect!

Answer: 6.8 and 13.6

Step-by-step explanation: , so cool am I right, we will be solving this problem on brainly. So first we do 144/3.14 and you get something I think then you do the square root of that and you find the answer of the radius, then you double that and find the diameter.

BRO WHAT IS GETTING TAGGED

Answer and Step-by-step explanation:

We are asked to turn this fraction (\(\frac{9}{10}\)) into an equivalent fraction, but with a denominator of 100.

\(\frac{9 <- Numerator}{10<-Denominator}\)

All we have to do is multiply the numerator and denominator by 10, since 10 times 10 equals 100.

\(\frac{9}{10} * \frac{10}{10} = \frac{90}{100}\)

The answer is:

\(\frac{90}{100}\)

#teamtrees #WAP (Water And Plant)

Answer:

90/100

Step-by-step explanation:

9/10, when multiplied by 10/10, is 90/100.

Hope this helps!

xoxo,

cafeology

The rate of change of y with respect to x when t = 3 is = 3/25 and  the answer is not one of the options given.

An object moves in the xy-plane so that its position at any time tis given by the parametric equations x(t) = t° - 3t + 2 and y (t) = /t² + 16.

To find the rate of change of y with respect to x, we need to find dy/dx, which can be computed using the chain rule of differentiation:

(dy/dt) / (dx/dt) = dy/dx

We first compute dx/dt and dy/dt:

dx/dt = 1 - 3 = -2

dy/dt = 2t / (t² + 16)

When t = 3, we have:

dx/dt = -2

dy/dt = 2(3) / (3² + 16) = 6/25

Therefore, the rate of change of y with respect to x when t = 3 is:

(dy/dt) / (dx/dt) = (6/25) / (-2) = -3/25

So, the answer is not one of the options given.

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Substituting these values back into equation (i), we get D = 4(3) = 12. There are 3 nickels, 12 dimes, and 3 quarters in the collection.

Let's assume the number of nickels is N, the number of dimes is D, and the number of quarters is Q. From the given information, we can deduce three equations:

(i) D = 4N (since there are 4 times more dimes than nickels),

(ii) N + D + Q = 18 (since there are 18 coins in total), and

(iii) 5N + 10D + 25Q = 290 (since the total value of the coins is 290 cents or $2.90).

To solve these equations, we can substitute the value of D from equation (i) into equations (ii) and (iii).

Substituting D = 4N into equation (ii), we get N + 4N + Q = 18, which simplifies to 5N + Q = 18.

Substituting D = 4N into equation (iii), we get 5N + 10(4N) + 25Q = 290, which simplifies to 45N + 25Q = 290.

Now we have a system of two equations with two variables (N and Q). By solving these equations simultaneously, we find N = 3 and Q = 3.

Substituting these values back into equation (i), we get D = 4(3) = 12.

Therefore, there are 3 nickels, 12 dimes, and 3 quarters in the collection.

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The cost of each printer is $568.

To find the cost of each printer, we need to use a system of equations.

Let's call the cost of each printer "p" and the cost of each camera "c".

The first equation we can create is: 6p + 3c = 4773

The second equation we can create is: 4p + 6c = 5002

Now we can use the elimination method to solve for one of the variables.

Let's eliminate the "c" variable by multiplying the first equation by -2: -12p - 6c = -9546

And then add the two equations together: -8p = -4544

Now we can solve for "p" by dividing both sides by -8: p = 568

So the cost of each printer is $568.

To find the cost of each camera, we can plug the value of "p" back into one of the original equations and solve for "c":

6(568) + 3c = 4773

3408 + 3c = 4773

3c = 1365

c = 455

So the cost of each camera is $455.

Therefore, the cost of each printer is $568 and the cost of each camera is $455.

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(a), there are 160 non-French books that are not about mathematics, and in scenario (b), there are 130 non-French books that are not about mathematics.

To find the number of non-French books not about mathematics, we need to subtract the total number of French books and mathematics books from the total number of books, and then subtract the specific category mentioned in each scenario.
(a) If there are 40 French mathematics books, we subtract 40 from the total of 70 French books to get 30 non-French books. We also subtract 100 mathematics books and 40 French mathematics books, which leaves us with 160 non-French books that are not about mathematics.
(b) If there are 60 French non-mathematics books, we subtract 60 from the total of 70 French books to get 10 French mathematics books. We also subtract the 100 mathematics books and the 10 French mathematics books, which leaves us with 190 non-mathematics books. We then subtract the 60 French non-mathematics books mentioned in the scenario, which gives us a total of 130 non-French books that are not about mathematics.
Therefore, in scenario (a), there are 160 non-French books that are not about mathematics, and in scenario (b), there are 130 non-French books that are not about mathematics.

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To find the value of x, we calculate the average of the sample observations. Summing up the observations and dividing by the total number of observations, we get:

x = (125 + 122 + 126 + 100 + 155 + 132 + 121 + 118 + 114 + 125 + 142 + 2 + 130 + 110 + 140 + 129 + 3) / 17 = 114.118 seconds (rounded to three decimal places).b) To find the value of R, we calculate the range of each sample by subtracting the minimum observation from the maximum observation. Then we find the average range across all samples:R = (155 - 100 + 142 - 2 + 140 - 110 + 132 - 114 + 142 - 3) / 5 = 109.2 seconds (rounded to three decimal places).

c) The Upper Control Limit (UCL) and Lower Control Limit (LCL) using 3-sigma can be calculated by adding and subtracting three times the standard deviation from the average:UCL = x + (3 * R / d2) = 114.118 + (3 * 109.2 / 1.693) = 348.351 seconds (rounded to three decimal places).LCL = x - (3 * R / d2) = 114.118 - (3 * 109.2 / 1.693) = -120.115 seconds (rounded to three decimal places).

d) The Upper Control Limit Range (UCLR) and Lower Control Limit Range (LCLR) using 3-sigma can be calculated by multiplying the average range by the appropriate factor:UCLR = R * D4 = 109.2 * 2.115 = 231.108 seconds (rounded to three decimal places).LCLR = R * D3 = 109.2 * 0 = 0 seconds.

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If the rectangle is not a square, then the sides must not be equal.

Thus, the rectangle can be cut horizontally, vertically, and diagonally. Therefore, it must be option D, which is "3 or more".

Answer:

Answer is – 3

Step-by-step explanation:

expand the expression using ( a – b) ( a + b) = a² –b²

( 3 ) ² – ( 6) ² *remember to place your square roots inside the brackets my phone doesn't have one*

then simplify the radical

3–6 = – 3

Answer:

y=-1/4x+3

Step-by-step explanation:

put it into y-y1=m(x-x1) form, which gives you y+3=-1/4x(x+0)

(side note: we change the y- to a y+ becuase the y in the point in negative. another side note, the slope is -1/4x because perpendicular slopes are opposite, in this case 4x (or 4/1x) is the opposite of -1/4 x)

then remove the parenthesis. y+3=-1/4x

then isolate y and balance the equation.

y+3-3=-1/4x-3

this gives you the answer of y=-1/4x-3.

Answer:

y=-2x-3

Step-by-step explanation:

The equation of the line in the slope-intercept form is y=x2−2.  

The slope of the perpendicular line is negative inverse: m=−2.

So, the equation of the perpendicular line is y=−2x+a.

To find a, we use the fact that the line should pass through the given point: −3=(−2)⋅(0)+a.

Thus, a=−3.

Therefore, the equation of the line is y=−2x−3.

Answer: y=−2x−3.

The first cylinder, weighing 2.5 pounds and running at a rate of 6 liters per minute, would last approximately 143.3 minutes.

To calculate the duration, we use the formula: Duration = (Weight of cylinder * Conversion factor) / Flow rate. Here, the conversion factor is 866 (which converts pounds to liters). Plugging in the values, we get (2.5 * 866) / 6 = 143.3 minutes.

Similarly, for the second cylinder weighing 3.5 pounds and running at 7 liters per minute, the estimated duration would be approximately 179.2 minutes. For the third cylinder weighing 7.5 pounds and running at 13 liters per minute, the estimated duration would be approximately 144.2 minutes. Finally, for the fourth cylinder weighing 6.5 pounds and running at 12 liters per minute, the estimated duration would be approximately 169.8 minutes.

By applying the formula and considering the weight of the cylinder and the flow rate, we can calculate an approximate duration for each scenario.

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Answer:

12x+12

Step-by-step explanation:

3(4x+4)

you times both answers to get rid of the 3

=3 • 4x + 3 • 4

= 12x+12

because they are not like terms so you cannot do anything further.

Answer:

5 5/6

Step-by-step explanation: umm math

Answer:

5 5/6

Step-by-step explanation:

hope it helps

its the answer above

Using an equation, the commission percentage (x) that you earn if you work 8 hours with sales of $1,400 and total earnings of $176 for the day is 4%.

The commission percentage can be determined by equating the normal earnings for the day and the sales commission to the total earnings.

An equation represents two or more mathematical expressions using the equal symbol.

The hourly rate of earnings = $15

The number of hours worked for the day = 8 hours

The commission percentage = x

The Sales for the day = $1,400

The total earnings for the day = $176

Total earnings = hourly rate x 8 hours + 1,400x

176 = 15 x 8 + 1,400x

176 = 120 + 1,400x

56 = 1,400x

x = 0.04

x = 4%

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a.8.25 kg is equivalent to 8250 grams.

b. 0.0002948 Ms is equivalent to 0.2948 seconds.

c. 6,400,000,000 nL is equivalent to 0.0064 L.

d. 9,113 mg is equivalent to 9.113 grams.

e. 0.0048 ks is equivalent to 4.8 seconds.

f. 3.0 cL is equivalent to 0.03 L.

The following is the conversion of given terms to grams, liters or seconds: a. 8.25 kg

To convert kg to grams, multiply by 1000

Thus, 8.25 kg is equivalent to 8250 grams.

b. 0.0002948Ms

To convert Ms to seconds, multiply by 1000. Thus, 0.0002948 Ms is equivalent to 0.2948 seconds.

c. 6,400,000,000 nL

To convert nL to liters, divide by 1,000,000,000. Thus, 6,400,000,000 nL is equivalent to 0.0064 L.

d. 9,113 mg

To convert mg to grams, divide by 1000. Thus, 9,113 mg is equivalent to 9.113 grams.

e. 0.0048 ks

To convert ks to seconds, multiply by 1000. Thus, 0.0048 ks is equivalent to 4.8 seconds.

f. 3.0 cL

To convert cL to liters, divide by 100. Thus, 3.0 cL is equivalent to 0.03 L.

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1. The table of values for the repayment of the loan by Annabelle is as follows:

Week        Loan Balance

0                    $70

1                     $60

2                    $50

3                     $40

4                     $30

5                     $20

6                      $10

7                       $0

2. An equation for L, in terms of t, representing the amount Annabelle owes her friend after t weeks is L = 70 - 10t.

3. After 3 weeks, for example, Annebelle will be owing her friend $40.

A table of values is an ordered pair of numbers resulting from the substitution of an unknown variable with numbers in an equation.

In a table of values, the equation determines the numerical or value relationship between each pair of numbers.

Week        Loan Balance

0                    $70

1                     $60 ($70 - $10(1)

2                   $50 ($70 - $10(2)

3                   $40 ($70 - $10(3)

4                   $30 ($70 - $10(4)

5                   $20 ($70 - $10(5)

6                   $10 ($70 - $10(6)

7                    $0 ($70 - $10(7)

Thus, based on the table of values, Annabelle's debt balance can be represented in the equation L = 70 - 10t.

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Answer:

24

Step-by-step explanation:

The numerators are being multiplied by -2

Answer:

Surface area of cube = 24 ft²

Step-by-step explanation:

Given:

Volume of cube = 8 ft³

Find:

Surface area of cube

Computation:

Volume of cube = Side³

Side³ = 8 ft³

Side³ = (2 ft)³

Side = 2 ft

Surface area of cube = 6a²

Surface area of cube = 6(2)²

Surface area of cube = 6(4)

Surface area of cube = 24 ft²

Answer:

c(x) = 5.50 + 21.60x

Step-by-step explanation:

To start, we are told that the service fee of 5.50 is added to the set price per ticket. So we can automatically eliminate B and D

Now, to find how much it costs per ticket, we have to divide 108.00 by 5 since we are told that it costs $108 to buy 5 tickets

108.00/5 = 21.60

This means that it costs $21.60 per baseball ticket

So the third answer choice is correct

If right triangle BAC, m∠A = 90, m∠B = 45, and AC = 8, the length of BC is 4√2 units. So, correct option is A.

In a right triangle, the side opposite to the 90-degree angle is called the hypotenuse, and the other two sides are called the legs. In triangle BAC, AC is the hypotenuse and AB and BC are the legs. We are given that AC = 8 and ∠B = 45 degrees. We can use trigonometric ratios to find the length of BC.

The trigonometric ratio for the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. The trigonometric ratio for the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. Since we know that ∠B = 45 degrees, we can use the fact that sin(45) = cos(45) = 1/√2.

Let x be the length of BC. Then, we have:

sin(45) = x/8

x/8 = 1/√2

x = 8/√2

We can simplify this expression by rationalizing the denominator:

x = 8/√2 * √2/√2

x = 8√2/2

x = 4√2

So, correct option is A.

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It is not always true that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction.

The statement that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction is not always correct. This is because the value of a fraction is determined by both its numerator and denominator, and if the denominators of two fractions with the same numerator are different, then the fractions are not directly comparable.

Consider the fractions 3/4 and 3/5. Both have a numerator of 3, but the denominator of the first fraction is greater than the denominator of the second fraction. However, 3/5 is actually the greater fraction because it represents a larger portion of the whole.Consider the fractions 5/7 and 5/9. Both have a numerator of 5, but the denominator of the second fraction is smaller than the denominator of the first fraction. Therefore, 5/7 is the greater fraction because it represents a larger portion of the whole.

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Answer:

0

3

Step-by-step explanation:

Answer:

The expansion of a metre stick (also known as meter stick) in the Sun will affect the meters stick accuracy by reducing the values of the actual length of the dimensions measured with the meter stick

The linear expansion, ΔL, of the meter stick is given according to the following formula;

ΔL = ∝·L₀·ΔT

Where;

ΔL = The expansion (change in length) of the meter stick

∝ =  The coefficient of linear expansion for the meter stick

L₀ = The initial length of the meter stick = 1 meter

ΔT = The temperature change of the meter stick

Due to the small value of ∝ for a meter stick, the change in length of the meter stick is small but the difference will affect the accuracy of the measurements made by the meter stick and the length of an item with actual length of 1 meter can be given by the expanded meter stick as 99 cm  

Step-by-step explanation:

Answer: The answer is C. 6x3 + 3x - 6

Step-by-step explanation: I learned it at school

Answer: C

Step-by-step explanation: I took the FLVS test

A(1,3),B(5,3),and D(1,-2) are three vertices of rectangle ABCD the coordinates of vertex C are select from the drop down menu (5,2),(-5,1),(5,-2),(2, -5)

(5,-2)

we know that,

the midpoint of the diagonals of a rectangle bisect each other,

so,

\( \huge \rightarrow \frac{x + 1}{2},\frac{y+ 3}{2} = \frac{5 + 1}{2},\frac{3 - 2}{2} \\ \)

\( \huge \rightarrow \: x = 5 \: \\ \huge \rightarrow \: y = - 2\)

Answer:

(5,-2)

Step-by-step explanation:

Cause me smart

Answer:

Maria (I THINK)

Step-by-step explanation:

Tanya is running 70 yards in all, while maria would be running more based on the pythagorean theorem

The pythagorean theorem is that on a right triangle, the square root of the two legs equal the hypotenuse

40^2+ 70^2 =c^2

6500=c^2

square root both sides

and roughly c= 80.6 yards so maria runs more

(Im not sure it is a right angle though?)

The line of reflection would be x+y =4, Hence the correct option is C.

The equation of a line's standard form is given as follows:

\(y = mx+c\)

Where m is the slope and c is the y-intercept of the line.

The slope can be determined by

\(m =\dfrac{(y_2 - y_1)}{(x_2 - x_1)}\)

Now, Along its diagonals should be reflected in order to reflect it back to itself.

The diagonals will pass through the points \(A(3, 1)\) and \(C( 1,3)\)

Hence, The slope of the line is,

\(m =\dfrac{(y_2 - y_1)}{(x_2 - x_1)}\)

\(m =\dfrac{(3 - 1)}{(1 - 3}\)

\(m =\dfrac{(2)}{(- 2)}\)

\(m = - 1\)

Hence, The equation of the line AC,

\((y - y_1) = m(x-x_1)\)

It passes through the point (1,3)

\((y - 3) = -1( x-1 )\)

\(y - 3 = -x +1\)

\(y +x =4\)

Therefore, Option C is true.

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