an
Diego and Lin are drinking milkshakes. Lin starts with 12 ounces and drinks
ounce per second. Diego starts with 20 ounces and drinks.How long will it take lin and Diego to finish their milkshakes?

The correct answer is Translation of negative 6 units x, 1 unit y composition reflection across the x-axis.

Here's the step-by-step breakdown:

Parallelogram A B C D to A' B' C' D':

Reflection across the x-axis: This flips the parallelogram across the x-axis, resulting in A' B' C' D'.

Parallelogram A' B' C' D' to A" B" C" D":

Translation of negative 6 units x, 1 unit y: This shifts the parallelogram 6 units to the left and 1 unit upwards, resulting in A" B" C" D".

Therefore, the overall composition of transformations is Translation of negative 6 units x, 1 unit y composition reflection across the x-axis.

Answer:

Step-by-step explanation:

Ordinary interest rate = principal × rates × ( time / 360)

exact interest rate = principal × rates × ( time / 365)

for states saving and loan of rate 7.25 %

ordinary interest rate = $ 2600 × 0.0725 × ( 90 / 360) = $ 47.125

total amount due after 90 days = $ 2647.125

for Security Bank of 7.5%

exact interest = $2600 × 0.075 × ( 90 / 365) = $ 48.75

amount due after 90 days = $ 2600 + $ 48.75 = $ 2648.75

b) considering the amount to be paid at maturity it is better to borrow state savings and Loan although the difference is not really much.

To determine where Ruth Brown should borrow the money, we compared the maturity value of loans from State Savings and Loan and Security Bank. After computing the interest over 90 days, it is evident that State Savings and Loan offers a better deal with a lower maturity value than Security Bank, making it the preferable option.

To determine the maturity value of each loan offered to Ruth Brown, we will calculate the total amount due, including principal and interest, for both the State Savings and Loan and Security Bank, after 90 days. The interest is calculated using the formulas for ordinary interest (360-day year) and exact interest (365-day year).

State Savings and Loan:

Principal (P) = $2,600

Rate (r) = 7.25%

Time (t) = 90 days

Interest (I) = P * r*(t/360) = $2,600* 0.0725 * (90/360) = $45.125

Maturity value = Principal + Interest = $2,600 + $45.125 = $2,645.125

Security Bank:

Principal (P) = $2,600

Rate (r) = 7.5%

Time (t) = 90 days

Interest (I) = P * r *(t/365) = $2,600* 0.075 * (90/365) = $46.58

Maturity value = Principal + Interest = $2,600 + $46.58 = $2,646.58

Ruth should borrow the money from the institution that offers the lowest maturity value, which in this case would be the State Savings and Loan.

Answer:

1/12

Step-by-step explanation:

Answer:

10 organisms.

Step-by-step explanation:

625 Square feet of lawn.

You would simply divide 6250 by 625 and you would get 10.

Feel free to let me know if you need more help! :)

We have been given that bought a pound of confetti for $12. We are asked to find price per ounce of confetti.

We know that 1 pound equals 16 ounces. To find cost of per ounce confetti, we will divide total cost by 16 as:

[tex]\text{Cost of per ounce confetti}=\frac{\$12}{16}[/tex]

[tex]\text{Cost of per ounce confetti}=\frac{\$3}{4}[/tex]

[tex]\text{Cost of per ounce confetti}=\$0.75[/tex]

Therefore, the cost of per ounce confetti is $0.75

Answer:

-x^2(x-8)

Step-by-step explanation

Answer:

-46

Step-by-step explanation:

We need to find the common difference of this arithmetic sequence:

[tex]\frac{-26-(-10)}{10-6} =\frac{-16}{4} =-4[/tex]

So, the common difference d = -4. We can now write the equation:

[tex]a_n=a_1+d(n-1)[/tex]

[tex]a_{15}=a_6+d(15-6)=-10-4(9)=-10-36=-46[/tex]

So, the 15th term is -46.

Hope this helps!

Step-by-step explanation:

the answer and explanation is in the picture

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Answer: 96 candles in 8 boxes

Step-by-step explanation:

There’s 12 candles in a box

The position of the light source(the focus) is at; (0, 3.516).

The distance from the position of light source to the deepest part of dish is; 3.516 ft.

We know that standard form of a parabola equation is;

x² = 4ay

Now, we are told the dish is 15 ft wide and the depth is 4ft.

This means that the edge of the parabolic cross section will have an x-coordinate of 15/2 = 7.5 ft

While the y-coordinate is the depth of 4ft.

Thus;

Since;

x² = 4ay

Plugging in 7.5 ft for x and 4 ft for y gives;

7.5² = 4a(4)

a = 7.5²/16

a = 3.516 ft

Thus, position of the light source which is the focus is; (0, 3.516)

And distance from the position of light source to the deepest part of dish = 3.516 ft.

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The position of the light source (the focus) in a satellite dish with a parabolic shape, with a 15 ft diameter opening and depth of 4 ft, is calculated using the formula for the focal length of a parabola. Plugging these values into the formula results in the finding that the focus is  14.0625 ft away from the base of the dish.

The parabola can be described by the equation y = x2/4f, where f is the distance of the focus from the vertex. In a practical situation, to determine the position of the light source (the focus) in a satellite dish, which has a parabolic shape, we need to know the dish's width and depth. Here, the dish is 15 ft wide at the opening (which is the diameter of the dish) and the depth is 4 ft.

So, we can use these dimensions to calculate the position of the focus. First, we need to recall that in a parabola, the focus lies at the point (0, p), where p is the focal length. The focal length (p) of a parabolic dish can be calculated using the formula p = D2/16h, where D is the diameter of the dish and h is the depth of the dish. In this case, D = 15 ft and h = 4 ft.

Putting these values in the formula, we get p = (152)/16(4) = 14.0625ft. Therefore, the light source (focus) is placed 14.0625 ft away from the base of the dish.

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Answer:

90

Step-by-step explanation:

If the original price of a bracelet was a

70%a = 63

70/100a = 63

a = 63 × 100/70

a = 90

The price before the decrease is 90 euros.

The amount of decrease is the original amount minus the final amount. For example if you are looking for the percent of decrease from 9 to 6, the original amount is 9 and the final amount is 6.

GIVEN

Based on the given conditions, write z= 63/(1-0.3)

Calculate the sum or difference = 63/0.7

Divide a fraction by multiplying its reciprocal:[tex]=63*10/7 =90[/tex]

Hence, The price before the decrease is 90 euros.

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6 ÷ 3 × 8 + 9

6÷3=2

2×8=16

16+9=25

To solve the problem we will first calculate the radius of the circle and substitute the value in the formula of the area of a circle.

Area of the circle [tex]=\pi r^2[/tex]

The area of the circle is 49π or 153.86 unit².

Radius,

[tex]\rm{ r = \dfrac{Diameter}{2} = \dfrac{d}{2}=\dfrac{14}{2} =7[/tex]

Thus, the radius of the circle is 7.

Area of the circle [tex]=\pi r^2[/tex]

                             [tex]=\pi\times (7)^2\\ = 49\pi[/tex]

Substituting the value of π = 3.14,

Area of the circle [tex]=49\pi\\ = 49 \times 3.14\\ = 153.86[/tex]

Hence, the area of the circle is 49π or 153.86 unit².

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The area of the circle is approximately 4.5m².

The formula to find the area of a circle is A = πr², where π is approximately 3.14 and r is the radius. In this case, we have a radius of 1.2m. Using a calculator with an eight-digit output, we can calculate A = 3.14 x (1.2m)² = 4.5238934m².

However, since the radius only has two significant figures, we need to limit the calculated quantity to two significant figures. So, the area of the circle is approximately 4.5m² (rounded to two significant figures).

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Answer:

-7/5

Step-by-step explanation:

The slope of a perpendicular line is the "negative reciprocal" of the slope of the original line. so just switch the numbers and put the top number into a negative.

The slope of a line is a measure of its steepness. -7/5 is the slope of the line that is perpendicular to the line of slope 5/7.

The slope of a line is a measure of its steepness

Two lines are perpendicular if and only if the product of their

slopes is -1.

The slope of a line is 5 /7, then  slope of the line perpendicular to it.

m1*m2=-1

m1 slope of first line

m2 slope of second line

Here m1=5/7

m2=?/

m1*m2=-1

5/7*m2=-1

m2=-7/5

Therefore slope of second line is -7/5 for line perpendicular to slope of a line 5/7.

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Answer:

47 meters

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  Please have a look at the attached photo.

My answer:

Given

As we know, the formula to find the area of a parallelogram is:

A = the base* the height

=> the base in this question is:

= The area / the height

= 2150 / 25 = 86 meters

As we can see in the photo, x + 39 meters = the base

=> x =  the base  - 39 meters

= 86 meters - 39 meters  

= 47 meters

Answer:

I dont know... Never tried it.

Answer:

47

Step-by-step explanation:

not that difficult

Answer:

x=2            x=-2

Step-by-step explanation:

x² + 2x - 4 = 2x

Subtract 2x from each side

x² + 2x-2x - 4 = 2x-2x

x^2 -4 = 0

Factor

We know this is the difference of squares

(x-2)(x+2) =0

Using the zero product property

x-2 =0      x+2 =0

x=2            x=-2

Step-by-step explanation:

Cylinder volume = 703 [tex]cm^{3}[/tex], height = 18.5 cm

(i) Volume or area of the cylinder = [tex]\pi r^{2} h[/tex]

The formula for the volume of a cyclinder can be applied to find the area of the base.

Option (i) is correct

(ii) Volume or area of the cylinder = [tex]\pi r^{2} h[/tex]

The volume should be divivded by height to get the area

Option (ii) is wrong

(iv) Area of the base  = [tex]\frac{703\pi }{18}[/tex] = 38[tex]\pi cm^{2}[/tex]

Option (iv) is correct

(iii) The radius of the cyclinder is half the height.

[tex]\frac{38}{2}[/tex] = 19 cm not 18.5 cm

Option (iii) is wrong

(v)Area of the base  = [tex]\frac{703\pi }{18}[/tex] = 38[tex]\pi cm^{2}[/tex]

Option (v) is correct

Answer:

1 , 4 , & 5 ... which is also a , d, & e

Step-by-step explanation:

In the given question one word is missing, the correct question is,

If the área of a right triangle is 6.22sq. In. And its base is 3.11 in. Write an equation that relates the área to the height, h, and the base. Solve the equation to determine the height.

The equation that relates the area(A) to the height (h) and the base(b) is [tex]Area = \frac{1}{2} bh[/tex]. Height of right trinagle is 4 inches.

Step-by-step explanation:

The given is,

               Area of right triangle, A = 6.22 square inches

               Its base is 3.11 inches

Step:1

               Formula for area of right angle triangle is,

                             [tex]A = \frac{1}{2} bh[/tex]......................................(1)

               Where, b - Base

                            h - Height

              Equation (1), that relates the área (A) to the height (h) and the base (b).

Step: 2

              From the given values,

                         Base, b = 3.11 inches

                         Area, A = 6.22 square inches

              Equation (1) becomes,

                             6.22 = [tex]\frac{1}{2} (3.11)(h)[/tex]

                      (6.22) (2) = (3.11) (h)

                            12.44 = (3.11) (h)

                                  [tex]h = \frac{12.44}{3.11}[/tex]

                                     = 4

                    Height, h = 4 inches

Result:

        The equation that relates the area(A) to the height (h) and the base(b) is [tex]Area = \frac{1}{2} bh[/tex]. Height of right trinagle is 4 inches.

Answer:

Step-by-step explanation:

Solution:-

- The sample size = n

- The Error of estimation, E = 0.04

- The confidence level, CI = 99%

a)

What size sample should be obtained when she uses previous estimate of p = 0.52​?

- We are given the sample proportion p = 0.52, the required sample size is a function of confidence value and error of estimation (E):

                 [tex]n = p*( 1 - p ) * (\frac{Z-critical}{E})^2[/tex]

Where,

- The critical value of the confidence level = 99% would be:

           significance level ( α ) = 1 - CI = 1 - 0.99 = 0.01

           Z-critical = Z_α/2 = Z_0.005 = 2.575  

- The required sample size (n) can be calculated:

            [tex]n = 0.52*( 1 - 0.52 ) * (\frac{2.575}{0.04})^2\\\\n = 0.2304*(51.5)^2 = 611.0784[/tex]

- Hence, the minimum required sample size (n) should be = 612 adults.  

b)

- If the preliminary estimate of proportion is missing or not given, we are to assume the proportion p = 0.5.

- Similarly, repeat the calculations for sample size (n) when p = 0.5

               [tex]n = 0.5*( 1 - 0.5 ) * (\frac{2.575}{0.04})^2\\\\n = 0.25*(51.5)^2 = 663.0625[/tex]

- Hence, the minimum required sample size (n) should be = 664 adults.  

Answer:

2300

Step-by-step explanation:

Answer:

2,300

Step-by-step explanation:

When we round to the hundreds place, we make sure the numbers behind the hundreds place are zero. Then we round. Here's the general rule for rounding: If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. In this case we round the 2 in the hundreds place up to three because it is followed by a five.

Answer:

8,000 bees

Step-by-step explanation:

Final answer:

Mr. Smith will need approximately 8,000 bees in his bee colony to produce 3.5 pounds of honey each week, based on the rate of 1,000 bees producing 1 ounce of honey per day.

Explanation:

Mr. Smith needs to calculate the number of bees required to produce 3.5 pounds of honey each week.

First, we need to convert pounds to ounces because the rate given is in ounces:

3.5 pounds = 3.5 * 16 ounces/pound = 56 ounces of honey per week.

Now, we use the given rate of honey production:

1,000 bees produce 1 ounce of honey per day.

Therefore, in one week (7 days), 1,000 bees will produce 7 ounces of honey.

To find out how many bees you need to produce 56 ounces, you divide the target ounces by the ounces produced by

1,000 bees per week:

56 ounces / 7 ounces per 1,000 bees = 8,000 bees.

So, Mr. Smith will need approximately 8,000 bees in his colony to produce 3.5 pounds of honey each week.

Answer:

75.

Step-by-step explanation:

The HCF is the highest common factor of two numbers - if these numbers are both divisible by 75 - this is their HCF.

Answer:

17982m-18301

Step-by-step explanation:

The simplified expression is [tex]\( \frac{156}{5}m - 125 \).[/tex]

To combine like terms and simplify the expression [tex]\(2(15m - 25) + \frac{3}{5} \times 2(5m - 52) + \frac{5}{3}\),[/tex] we distribute the coefficients:

[tex]\[ 2 \times 15m - 2 \times 25 + \frac{3}{5} \times 2 \times 5m - \frac{3}{5} \times 2 \times 52 + \frac{5}{3} \][/tex]

[tex]\[ = 30m - 50 + \frac{6}{5}m - \frac{6}{5} \times 52 + \frac{5}{3} \][/tex]

[tex]\[ = 30m - 50 + \frac{6}{5}m - \frac{312}{5} + \frac{5}{3} \][/tex]

Now, let's combine like terms:

[tex]\[ = (30m + \frac{6}{5}m) + (-50 - \frac{312}{5}) + \frac{5}{3} \][/tex]

[tex]\[ = (30 + \frac{6}{5})m + (-50 - \frac{312}{5}) + \frac{5}{3} \][/tex]

[tex]\[ = \frac{156}{5}m - \frac{650}{5} + \frac{25}{15} \][/tex]

[tex]\[ = \frac{156}{5}m - \frac{650}{5} + \frac{75}{15} \][/tex]

Now, let's simplify the fractions:

[tex]\[ = \frac{156}{5}m - \frac{130}{1} + \frac{5}{1} \][/tex]

[tex]\[ = \frac{156}{5}m - 130 + 5 \][/tex]

[tex]\[ = \frac{156}{5}m - 125 \][/tex]

Therefore, the simplified expression is [tex]\( \frac{156}{5}m - 125 \).[/tex]

Answer:

A) middle: 32

Outside: 9

B) 25

C) 47

Step-by-step explanation:

71 = 14 + 25 + intersection

Intersection = 71 - 39 = 32

Outside: 80 - 71 = 9

Only french: 25

Spanish: 14 + 32 = 46

Answer:

40.23

Step-by-step explanation:

Area of a circular pizza is calculated by pi radius^2

or 22/7 × (16/2)^2

Radius is diameter/2 = 16/2

= 22/7 × 8^2

= 22 × 8 × 8 ÷ 7

= 201.143 ....

A circular pizza is cut into 5 slices

so the area of 1 slice of a circular pizza is

201.143 / 5 = 40.23 inches^2

Answer:

0.02

Step-by-step explanation:

Since 60​% of the​ factory's bikes come off assembly line B, Therefore:

The probability that the​ factory's bikes come off assembly line B = 60% = 0.6

Percentage line​ B's products pass inspection  = 93% = 0.93

Percentage line​ B's products that do not pass inspection = 1 - 0.93 = 0.07

The probability that the​ factory's bikes come off assembly line A = 1 - 0.6 = 0.4

Percentage line​ A's products pass inspection  = 95% = 0.95

Percentage line​ A's products that do not pass inspection = 1 - 0.95 = 0.05

Let D represent those that passes inspection and D' represent those that do not pass inspection.

P(A ∩  D') = P(A) × P(D'/A) = 0.4 × 0.05 = 0.02

P()bikes did not pass inspection and came off assembly line A) = P(A ∩  D') =  0.02

Final answer:

The probability that a bicycle failed inspection and came from assembly line A is 2%.

Explanation:

We're tasked with finding the probability that a bike did not pass inspection and came from assembly line A. First, we calculate the probability of a bike failing inspection from each line. Since 95% of line A's products pass, there is a 5% (100%-95%) chance a bike from line A fails inspection. For line B with a 93% pass rate, there's a 7% (100%-93%) chance of failure.

Next, we consider the distribution of production between lines A and B. 60% of bikes are from line B, so 40% are from line A. We then calculate the probability of a bike being from line A and failing inspection using the multiplication rule for independent events, which is P(A) times the probability of failure on line A.

P(Fail and from A) = P(A) * P(Fail | A) = 40% * 5% = 0.40 * 0.05 = 0.02 or 2%.

Therefore, the probability that a bike did not pass inspection and came from assembly line A is 2%.

Answer:

the particle is at point B at t = 3 s

Step-by-step explanation:

Solution:-

- The coordinates of the path that a particle follows through points A to B to C.

- The coordinates of the particle position ( x , y ) are differentiable function of t, where, the rate of change of x-coordinate is given by:

                        [tex]x ' (t) = -9*cos (\frac{\pi *t}{6})*sin (\frac{\pi \sqrt{t + 1} }{2})[/tex]

- The slope of the curve at point B, in mathematical terms that is called the inflection point.

- The independent variable time (t) can be determined for the particle when it is at point B. Where the x'(t) is set to zero, and the critical value defines the point B.

                        [tex]x ' (t) = -9*cos (\frac{\pi *t}{6})*sin (\frac{\pi \sqrt{t + 1} }{2}) = 0\\\\cos (\frac{\pi *t}{6}) = 0 , sin (\frac{\pi \sqrt{t + 1} }{2}) = 0\\\\\frac{\pi *t}{6} = \frac{\pi }{2} , \frac{\pi \sqrt{t + 1} }{2} = \pi \\\\t = 3 , t = 3[/tex]

- Hence, the particle is at point B at t = 3 s.