(09.06 mc) write an expression for the area bounded by r = 3 − cos4θ.

To find a set of two numbers with a greatest common factor (GCF) of 20, we can start by selecting a common multiple of 20, such as 20 itself. Let's choose the number 20 as one of the numbers in the set.

Now, we need to find another number that has a GCF of 20 with 20. Since 20 is divisible by 20 without any remainder, any multiple of 20 will have a GCF of 20 with it. Let's choose another multiple of 20, such as 40, as the second number in the set.

Therefore, a set of two numbers with a GCF of 20 is {20, 40}.

To verify that the GCF of these numbers is indeed 20, we can use the Euclidean algorithm. The GCF of two numbers can be found by repeatedly dividing the larger number by the smaller number and taking the remainder as the new divisor until we reach a remainder of 0. The divisor at that point will be the GCF.

Using the Euclidean algorithm:

GCF(20, 40):

40 ÷ 20 = 2 with no remainder

Since the remainder is 0, the GCF is 20.

Hence, the set {20, 40} has a GCF of 20, and this is one possible solution. Note that there can be multiple sets of numbers with a GCF of 20, but this is just one example.

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Answer:

y=6x+8 or y=6x-22

Step-by-step explanation:

use the equation y=mx+b

m is the slope and b is the y-intercept

to find the slope use the equation m = y2-y1 over x2-x1

-22 - 8 / -2 - 3 = -30 / -5 = 6

6 is your slope and for the y-intercept you can choose whichever y-intercept to put into the equation.

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The average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night

According to the given data,

Sample size n = 101

Sample mean x = 6.5

Standard deviation s = 2.14

Level of confidence C = 96%

Using a 96% confidence level, the value of t* for 100 degrees of freedom is 2.081, as given in the question.

Now, the formula for the confidence interval is:x ± (t* × s/√n)Here, x = 6.5, s = 2.14, n = 101, and t* = 2.081

Substituting the values in the above formula, we get:

Lower limit = x - (t* × s/√n) = 6.5 - (2.081 × 2.14/√101) = 6.28

Upper limit = x + (t* × s/√n) = 6.5 + (2.081 × 2.14/√101) = 6.72

Therefore, the 96% confidence interval for the average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night.

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Answer: 48

Step-by-step explanation:

The share of sand in the mixture is 3/7

To make 112 kgs. of concrete, he will need

3/7 x 112 = 48 units of sand

Answer:

solution,

Ratio of cement:sand:aggregate

=1:3:3

Total of ratios=1+3+3

=7

Total concrete=112 kg

Amount of sand required:

\( \frac{ratio \: of \: sand}{total \: ratio} \times amount \: of \: concrete \\ = \frac{3}{7} \times 112 \\ = 48 \: kg\)

Hope this helps...

Good luck on your assignment...

Answer:

Step-by-step explanation:

Answer:

D) -22

Step-by-step explanation:

We can find the answer by substituting all possibilities into the equation:

(8) + 11 = 19 (NOT = LESS THAN -5)

(-14) + 11 = -3 (NOT = LESS THAN -5)

(-16) + 11 = -4 (NOT = LESS THAN -5)

(-22) + 11 = -11 (This is the only subsititution that makes the expression correct)

Answer:

D. -22

Step-by-step explanation:

8 makes the inequality wrong

-14 is not enough to make it less so that's wrong

-16 makes it equal    -5>-16+11 ---> -5>-5 so not true

-22 is the only one that makes it true.

-5 > -22 +11 ---->  -5 > -11 so its true

Answer:

keeping in mind that 21 months is more than a year, since there are 12 months in a year,  then 21 months is really 21/12 years.

Step-by-step explanation:

(picture)

so, clearly, you can see who's greater.

Algorithm Il always works correctly, but Algorithm I only works correctly when the maximum value is greater than or equal to - 1

=====================================================

Explanation:

Let's say we have the data set {-4,-3,-2}. The value -2 is the largest.

If we follow algorithm 1, then the max will erroneously be -1 after all is said and done. This is because the max is set to -1 at the start even if -1 isn't in the data set. Then we see if each data value is larger than -1.

Each statement being false means we do not update the max to its proper value -2. It stays at -1.

This is why we shouldn't set the max to some random value at the start.

It's better to use the some value in the data set to initialize the max. Algorithm 2 is the better algorithm. Algorithm 1 only works if the max is -1 or larger.

Answer:

To have one significant figure means to have one number with a significant value. Since all of the answers are greater than one, the final answer with the correct sig figs involves using the two leftmost numbers. If the second leftmost number is greater than 5, round the leftmost number up one unit. If the number is less than 5, leave the leftmost number alone. Finally, change all of the values besides the leftmost to zero. There should be no decimal place because having it would mean the zeros to the left of the decimal place are significant.

 29 x 31
--------------  =  3329.6      ------>     3,000
   0.27

 4.8 x 37
---------------  =  845.7       -------->    800
   0.21

 9.7 x 26
---------------   =  11463.6      ------->   10,000
  0.022

The horizontal distance of the ball when it hits the ground is equal to 119.671 feet.

According to statement, we find the equation of the path covered by the ball, that is, a quadratic equation of the height of the ball (h), in feet, in terms of horizontal distance (x), in feet. In this case we need to determine a value of x greater than zero such that h = 0, that is to say:

- 0.01 · x² + 1.18 · x + 2 = 0

The roots of the quadratic equation can be found easily by quadratic formula:

x = - 1.18 / [2 · (- 0.01)] ± [1 / [2 · (- 0.01)]] · √(1.18² - 4 · (- 0.01) · 2)

x = 59 ± 60.671

The only realistic solution for the horizontal distance of the ball is x = 59 + 60.671 = 119.671 feet.

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Answer:

\(\huge\boxed{(3^4)^4=3^8\cdot3^8}\\\boxed{4^3\cdot5^3=20^3}\\\boxed{(4^3)^3=4^3\cdot4^3\cdo4^3}\)

Step-by-step explanation:

\(a^n\cdot a^n=a^{n+m}\\\\(a^n)^m=a^{n\cdot m}\\\\(a\cdot b)^n=a^n\cdot b^n\\=====================\)

\((4^3)^3=4^{3\cdot3}=4^9\\4^3\cdot4^3=4^{3+3}=4^6\\\\4^9\neq4^6\to(4^3)^3\neq4^3\cdot4^3\\==================\)

\((3^4)^4=3^{4\cdot4}=3^{16}\\3^8\cdot3^8=3^{8+8}=3^{16}\\\\(3^4)^4=3^8\cdot3^8\\================\)

\(6^4\cdot3^4=(6\cdot3)^4=18^4\\\\18^4\neq18^8\to6^4\cdot3^4\neq18^8\\=================\)

\(4^3\cdot5^3=(4\cdot5)^3=20^3\\\\4^3\cdot5^3=20^3\\=================\)

\((4^3)^3=4^{3\cdot3}=4^9\\4^3\cdot4^3\cdot4^3=4^{3+3+3}=4^9\\\\(4^3)^3=4^3\cdot4^3\cdot4^3\)

the in this equation x=50 pictures and y -$12.

What is an Equations?

Equations are mathematical expressions with two algebraic expressions on either side of the equals (=) symbol. The equivalence of the expressions written on the left and right sides is demonstrated by this. You can solve equations to find the value of a variable that represents an unknown quantity. If a sentence does not contain a "equal to" symbol, it is not an equation. That will be considered a phrase.

According to the information above, Lightning Quick Foto charges a $5 base cost plus an extra $0.20 each shot. Thus, the following equation can be used to describe the entire cost, y:

Equation 1: y = 0.2x + 5

With regard to the second choice, Snappy Shots charges a base fee of $7 plus an extra $0.10 each picture. Hence, this equation can be used to describe the overall cost, y:

Equation 2 reads "y = 0.10x + 7"

Equation 1 and equation 2 are equal, giving us the results as follows:

0.10x + 7 = 0.2x + 5

0.2x - 0.1x = 7 - 5

0.1x = 5

x = 50 pictures.

Given that x = 50, the value of y is as follows:

y = 0.10(50) + 7

y = 5 + 7

y = $12.

Hence, the in this equation x=50 pictures and y -$12.

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Substitute 0 for x in the equation to determine the y-intercept.

So y-intercept of function f(x) is more than y-intercept of g(x).

Substitute 1 for x in the equation to obtain the value of function at x = 1.

The function f(x) and g(x) have different vlue at x = 1.

Substitute 3 for x in the function to obtain f(3).

So g(x) > f(x)

The quadratic function is defined for all values of x and exponential function is also defined for all values of x. So domain of both function f(x) and g(x) is all real numbers.

So correct option is option C.

Answer: 10 x -5 - 2 x 4 = -58

Step-by-step explanation: the z from the 10 z becomes -5 and the x becomes 2 and the y becomes 4 simply just answer it

Answer:

Area rhombus = 110

Step-by-step explanation:

The diagonals of a rhombus intersect at right angles.

They bisect each other.

So the diagonals form 4 right angle triangles whose legs are 1/2 of each of them.

Leg of 1 triangle = 1/2 * 10 = 5

Other leg of 1 triangle = 1/2 * 22 = 11

Area of 1 triangle = (1/2 ) * 5 * 11 = 1/2 * 55 = 27.5

Area of all 4 triangles = 4 * 27.5

Area of all 4 triangles = 110

Area of rhombus = 110

Answer:

225 km

Step-by-step explanation:

D=S*T

D=45*5=225

Have a nice Day , Hope this helped you I would appreciate it if you could mark my answer brainliest

Answer:

19.4%

Step-by-step explanation:

Given data

Initial height=36in

Final height= 43in

% increase= Final-initial/initial*100

Substitute

% increase= 43-36/36*100

%increase= 7/36*100

%increase= 0.194*100

%increase= 19.4%

Hence the increase is 19.4%

Answer:

5

Step-by-step explanation:

2+2-3+4=5

(2+2)=4

(4-3)=1

(1+4)=5

The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.

To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:

∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C

where C is the constant of integration.

Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.

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\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{-9}-\underset{x_1}{(-2)}}} \implies \cfrac{-15}{-9 +2} \implies \cfrac{ -15 }{ -7 } \implies \cfrac{ 15 }{ 7 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ \cfrac{ 15 }{ 7 }}(x-\stackrel{x_1}{(-2)}) \implies y -10 = \cfrac{ 15 }{ 7 } ( x +2) \\\\\\ y-10=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }\implies y=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }+10\implies {\Large \begin{array}{llll} y=\cfrac{ 15 }{ 7 }x+\cfrac{100}{7} \end{array}}\)

The magnification n can be found by using the formula n = -s'/s, where s' is the image distance and s is the object distance. The value of s' obtained from this new equation can be found by rearranging the formula to s' = -ns.

To find the magnification n, we can use the formula n = -s'/s, where s' is the image distance and s is the object distance. In this case, the object is placed 45.0 centimeters from the mirror, so s = 45.0 cm. The magnification can be found by calculating the ratio of the image distance to the object distance. By rearranging the formula, we get n = -s'/s.

To find the value of s' obtained from this new equation, we can rearrange the formula n = -s'/s to solve for s'. This gives us s' = -ns. By substituting the value of n calculated earlier, we can find the value of s'. The negative sign indicates that the image is inverted.

Using the given values, we can now calculate the magnification and the value of s'. Plugging in s = 45.0 cm, we find that s' = -ns = -(2/3)(45.0 cm) = -30.0 cm. This means that the image is located 30.0 centimeters from the mirror and is inverted compared to the object.

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The total cost of the meal, including tax and tip, is approximately $18.87.

To calculate the total cost of the meal, including tax and tip, we'll follow these steps:

Step 1: Calculate the tax amount.

Tax amount = 9% of the bill amount before tax

Tax amount = 0.09 × $15

Step 2: Calculate the bill amount after tax.

Bill amount after tax = Bill amount before tax + Tax amount

Step 3: Calculate the tip amount.

Tip amount = 14% of the bill amount after tax

Tip amount = 0.14 × (Bill amount before tax + Tax amount)

Step 4: Calculate the total cost of the meal.

Total cost = Bill amount before tax + Tax amount + Tip amount

Let's compute the values:

Step 1:

Tax amount = 0.09 × $15 = $1.35

Step 2:

Bill amount after tax = $15 + $1.35

= $16.35

Step 3:

Tip amount = 0.14 × ($15 + $1.35)

= $2.519

Step 4:

Total cost = $15 + $1.35 + $2.519

≈ $18.87

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0.18x + 4 - 0.40x = 2

-0.22x = -2

x = 9.09

Therefore, the pharmacist should mix 9.09 liters of 18% alcohol solution and 0.91 liters of 40% alcohol solution to make 10 liters of 20% alcohol solution.

\(x=\textit{Liters of solution at 18\%}\\\\ ~~~~~~ 18\%~of~x\implies \cfrac{18}{100}(x)\implies 0.18 (x) \\\\\\ y=\textit{Liters of solution at 40\%}\\\\ ~~~~~~ 40\%~of~y\implies \cfrac{40}{100}(y)\implies 0.4 (y) \\\\\\ \textit{10 Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~10\implies \cfrac{20}{100}(10)\implies 2 \\\\[-0.35em] ~\dotfill\)

\(\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{alcohol only}}&\stackrel{\textit{Liters of}}{\textit{alcohol only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.18&0.18x\\ \textit{2nd Sol'n}&y&0.4&0.4y\\ \cline{2-4}&\\ mixture&10&0.2&2 \end{array}~\hfill \begin{cases} x + y = 10\\\\ 0.18x+0.4y=2 \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 1st equation}}{x+y=10\implies y=10-x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation from above}}{0.18x+0.4(10-x)=2}\implies 0.18x+4-0.40x=2 \\\\\\ -0.22x+4=2\implies -0.22x=-2\implies x=\cfrac{-2}{-0.22}\implies \boxed{x\approx 9.09} \\\\\\ \stackrel{\textit{since we know that}}{y=10-x}\implies y\approx 10-9.09\implies \boxed{y\approx 0.91}\)

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

2l

Step-by-step explanation:

hence.f10 divido 8-2

Therefore, the surface area of the prism is 453.5 square meters.

Surface area is the total area that the surface of a three-dimensional object occupies. It is the sum of the areas of all the faces, surfaces, or sides of the object. Surface area is measured in square units, such as square inches, square feet, or square meters, depending on the units used to measure the object's dimensions. Surface area is an important concept in geometry and is used in many real-world applications, such as calculating the amount of paint needed to cover a surface or the amount of material required to build a structure.

Here,

To find the surface area of the prism, we need to find the area of all six faces and then add them together. The prism has two congruent rectangular faces (front and back) and four trapezoidal faces (top, bottom, left, and right).

The area of the rectangular faces is:

20 m × 4 m = 80 m² (each face)

The area of the trapezoidal faces can be found using the formula for the area of a trapezoid:

Area = (a + b) × h / 2

where a and b are the lengths of the parallel sides, h is the height, and the slanting height is used to calculate the height.

For the top and bottom faces, the parallel sides are 5 m and 20 m, and the height is 4.47 m. So, the area of each face is:

(5 m + 20 m) × 4.47 m / 2 = 56.75 m² (each face)

For the left and right faces, the parallel sides are 4 m and 5 m, and the height is 20 m. So, the area of each face is:

(4 m + 5 m) × 20 m / 2 = 90 m² (each face)

Now, we can add up the areas of all six faces to get the total surface area:

Total surface area = 2 × 80 m² + 2 × 56.75 m² + 2 × 90 m²

Total surface area = 160 m² + 113.5 m² + 180 m²

Total surface area = 453.5 m²

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Answer:

The z-score for this data point is -1.5

Step-by-step explanation:

Mean = M = 150

Standard Deviation = S = 20

Value = x = 120

We find the z value,

\(z = (x-M)/S\\z = (120 - 150)/20\\z = (-30)/20\\z=-3/2\\z=-1.5\)

Hence the z value is z = -1.5

The probability that neither of your two groupmates have studied any statistics is 4/45.

Let, E be the event that none of the two groupmates have studied any statistics. The event of interest is that "one of your groupmates has not studied any statistics" Out of the total n students, you select any 2 students out of n−1, but the person who has not studied statistics must be in the team of three. If there are k people who have not studied statistics, then the probability of this person being selected is k/n.

The probability that none of your two groupmates has studied any statistics, given that one of your groupmates has not studied any statistics can be obtained as follows:

P(E | F) = (1/(n-1)) (k/(n-1)) / [1 - k/(n-1)]P(E | F)

= (k / (n-1) ) x (1 / (n-k-1)) (k+1)/(n-k-1)P(E | F)

= k(k+1)/(n-1)(n-2)

Therefore, the probability that neither of your two groupmates has studied any statistics is k(k+1)/(n-1)(n-2). Hence, the required probability is 4/45 (rounded to four decimal places).

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