find two numbers adding to 40 such that the sum of their square is as small as possible

Answer:

27

Step-by-step explanation:

Givens

b1 = 13

b2 = ?

h = 6

Area = 120

Formula

Area = (b1 + b2) * h/2         Multiply by 2

2Area = (b1 + b2)*h           Divide by h

2Area/h = b1 + b2              Subtract b1 from both sides

2Area/h - b1 = b2

Solution

2*120 / 6 - 13 = b2

40 - 13 = b2

b2 = 27

It is always handy to solve an equation in the form that finds the unknown on one side. It makes the solution much easier.

Answer:

3/5

Step-by-step explanation:

Hi! i see your having trouble the answer is 3/5

answer: 3/5 as a decimal its 0.6

Answer: ig the equations would be 1.5x+1y>25 and 35x+35y>1000 (the < symbols also have _ at the bottom, i couldn’t figure out how to include it)

Step-by-step explanation: this is middle school, not high school

The required inequalities for the given gym are 1.5x + y ≥ 25 and 35(x + y) ≤ 1000.

"Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values."

Let, there are 'x' yoga classes and 'y' circuit training classes per week.

Total hours of yoga class per week in the schedule is

= 1.5 × x hours

= 1.5x hours

Again, total hours of circuit training class per week in the schedule is

= 1 × y hours

= y hours

Therefore, the required inequality:

1.5x + y ≥ 25

Similarly, total payment of yoga class per week is

= $35 × x

= $35x

total payment of circuit training class per week is

= $35 × y

= $35y

Therefore, the required inequality is:

35x + 35y ≤ 1000

⇒ 35(x + y) ≤ 1000

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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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The list that gives the sample space for pulling 2 marbles from the bag with replacement is given as follows:

List 4.

A sample space is a set that contains all possible outcomes in the context of an experiment.

The fact that the experiment is with replacement means that for each of the two marbles, there are two possible outcomes.

Then, applying the Fundamental Counting Theorem, the total number of outcomes is given as follows:

4 x 4 = 16.

This means that the correct list is either the list 3 or the list 4.

As there is replacement, it is possible to take two purple marbles, even though there is only one purple marble, as the same can be taken with replacement, and thus the correct list is given by list 4.

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Answer: List 4

Step-by-step explanation: This answer is here to confirm the other answer. It got me 100% on my test.

Also I know the right answer because I got it right

So good luck on y'all's math tests :)

Here is some proof that the answer is List 4

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

Step-by-step explanation:

9x + y = -12

8x -y = 5

17X = -7

x -7/17

8(-7/17) -y = 5

-3.3 - Y = 5

-y = 8.3

Y = -8.3

Answer: B (The cost of a notebook is $0.75, and the cost of a folder is $0.25.)

Step-by-step explanation:

No need for explanation. i know i’m right!!

The chief advantage of using a confidence interval to test the hypothesis about the proportion of households with high-speed internet service is that it provides a set of plausible values for the proportion, allowing for a more informative interpretation of the data.

The chief advantage of using a confidence interval to test this hypothesis is that it provides a range of plausible values for the proportion of households with high-speed internet service. Instead of simply determining whether the proportion is equal to 0.7 or not (as done in a significance test), a confidence interval gives a range of values within which the true proportion is likely to fall. This allows for a more nuanced interpretation of the data, taking into account the uncertainty inherent in statistical estimates.

In contrast, a significance test typically provides a binary result, indicating whether the data provide enough evidence to reject the null hypothesis (in this case, the proportion being equal to 0.7) or not. While significance tests can be useful in determining statistical significance, they do not provide an estimate of the magnitude or range of possible values for the parameter being tested.

Furthermore, the conditions for using a confidence interval are generally less restrictive than those for a significance test. Confidence intervals rely on assumptions about the sampling distribution of the data, but they are more flexible in terms of sample size and distributional assumptions compared to significance tests.

Finally, it's worth noting that both confidence intervals and significance tests can be one- or two-sided, depending on the specific research question and hypothesis being tested. The choice between the two depends on the nature of the hypothesis and the desired interpretation of the results.

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Answer:

The Akkadian and Assyrian empires were two of the world’s first empires. Their conquests reshaped Mesopotamia. The many empires that would follow, worldwide,

Step-by-step explanation:

Answer:

A. 24

Step-by-step explanation:

3 . (9) + 8 ÷ 2 - (7)

27 + 4 - 7

31 - 7

24

The answer is 24.

Simplifying an expression basically means writing the equation in the simplest form.

Given : 3.3/2+ 8 divided by 2- (4 + 3)

3 . (9) + 8 ÷ 2 - (7)

=>27 + 4 - 7

=>31 - 7

=>24.

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The simplified trigonometric expression in this problem is defined as follows:

sin(3x)/sin²(x) = 3csc(x) - 4sin(x).

The trigonometric expression in this problem is defined as follows:

sin(3x)/sin²(x).

The equivalent expression for the sine of 3x is given as follows:

sin(3x) = 3sin(x) - 4 sin³(x).

Then the expression can be written as follows:

(3sin(x) - 4 sin³(x))/sin²(x)

The subtraction is in the numerator, hence the expression can be simplified as follows:

3sin(x)/sin²(x) - 4sin³(x)/sin²(x)

3/sin(x) - 4sin(x)

One divided by the sine is equivalent to the cossecant, hence:

3/sin(x) - 4sin(x) = 3csc(x) - 4sin(x).

Meaning that the first option among those given on the image at the end of the answer is correct.

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

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The total length of the curve is:

L = L₁ + L₂ + L₃ = 2.841 + 2 + 4 = 8.841.

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

To find the length of the curve, we need to break it into its three segments and find the length of each segment separately.

Segment 1: y = x² from (0,0) to (2,4)

The length of this segment can be found using the arc length formula for a curve y = f(x) from x = a to x = b:

L = ∫[a,b] √[1 + (dy/dx)²] dx

In this case, f(x) = x², so dy/dx = 2x. Thus, the length of this segment is:

L1 = ∫[0,2] √[1 + (2x)²] dx ≈ 2.841

Segment 2: Straight line from (2,4) to (0,4)

The length of this segment is simply the distance between the two points:

L₂ = √[(0-2)² + (4-4)²] = 2

Segment 3: y-axis from (0,4) to (0,0)

The length of this segment is simply the distance between the two points:

L3 = √[(0-0)² + (4-0)²] = 4

Therefore, the total length of the curve is:

L = L₁ + L₂ + L₃ = 2.841 + 2 + 4 = 8.841

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Answer:

2 Tablespoons make 4 cups. Popcorn pops to 40 times its original size. One ounce. 2 Tablespoons of kernels makes about 4 cups of popcorn. Four cups of popcorn have 125 calories :))

Authors note:

I really hoped this helped! :)))

Answer:

19 cubes

Step-by-step explanation:

7/4 + 1 + 1 = 4.75

4.75 divided by 1/4 (0.25) is 19

The number of 1/4-cubes that will fill the given prism in the image is: 224 cubes.

Volume of prism = length × width × height

Volume of cube = a³, where a is the side length of the cube.

Number of cubes that will fill the prism = volume of prism / volume of 1 cube

Volume of prism = 1 × 7/4 × 2 = 3.5 cm³

Volume of 1 cube = (1/4)³ = 0.015625 cm³

Number of cubes that will fill the prism = 3.5/0.015625 = 224 cubes.

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After using linear equation - Randy paid $7.25 for each sub sandwich.

What are linear equations with one variable?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 4x+4=8 only has one variable.

we are given that,

cost of one hamburger = $5.75

let us assume the cost of one sub sandwich to be $x

thus the cost of three sub sandwiches will be $3x.

we know his total came out to be $27.50

therefore,

we are given that

cost of one hamburger + 3 sub sandwiches = $27.50

= 5.75 + 3x = 27.50

= 3x = 27.50 - 5.75

= 3x = 21.75

= x = 21.75/3

= x = $7.25

thus we know that one sub sandwich costs randy $7.25.

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For  triangle EFD, the value of x is 24 units.

We know that the side-splitting theorem states that, 'if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.'

For  triangle EFD we can obaserve that GH is parallel to side ED.

By applying the side-splitter theorem to triangle EFD,

⇒ FG/GE = FH/HD

Here, FG = 18 units, GE = 6 units, HD = 8 units

substituting values,

⇒ 18/6 = x/8

⇒ 3 = x/8

⇒ x = 3 × 8

⇒ x = 24 units

Therefore, the value of x is 24 units.

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Divide the number of micrometers by 10,000 to get the equivalent number of centimeters.

To convert micrometers to centimeters, you need to use the conversion factor between the two units. There are 10,000 micrometers in a centimeter.

Here are the steps to convert micrometers to centimeters:

1. Start with the number of micrometers you want to convert.
2. Divide the number of micrometers by 10,000 to get the equivalent number of centimeters.
3. The result is the number of centimeters equivalent to the given number of micrometers.

For example, if you want to convert 50,000 micrometers to centimeters, you would divide 50,000 by 10,000 to get 5 centimeters.

So, the conversion formula is:

centimeters = micrometers ÷ 10,000

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Siddharth and Alek's new restaurant, located near the UW campus, is experiencing great success.

Despite being takeout-only, the restaurant is able to accept orders through multiple food delivery apps, including UberEats, DoorDash, Fantuan, and more. The restaurant utilizes a total of k apps, each having its own queue of customers.

The restaurant's decision to accept orders through various food delivery apps allows them to reach a wider customer base and cater to the preferences of different users.

By partnering with multiple platforms like UberEats, DoorDash, and Fantuan, the restaurant can tap into their respective user bases and leverage their delivery infrastructure. Each of these apps likely operates independently, maintaining their own queues of customers and managing orders received through their platform.

By utilizing k total apps, the restaurant can efficiently handle a large volume of orders and effectively serve its customers while benefiting from the popularity and reach of multiple delivery platforms.

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Answer:

3 +40+2=6u-30

45-6u-30

The initial size of the bacteria culture was approximately 202.02.

To solve this problem, we can use the formula for exponential growth:

N(t) = N0 * e^(kt)

where N(t) is the size of the culture at time t, N0 is the initial size of the culture, k is the growth rate, and e is the natural logarithmic base.

We can use the given information to set up two equations:

300 = N0 * e^(k10)

1400 = N0 * e^(k40)

Dividing the second equation by the first equation gives:

1400/300 = e^(k40) / e^(k10)

Simplifying:

4.67 = e^(k*30)

Taking the natural logarithm of both sides:

ln(4.67) = k*30

Solving for k:

k = ln(4.67) / 30

Substituting back into the first equation:

300 = N0 * e^(ln(4.67)/3)

300 = N0 * 1.484

Solving for N0:

N0 = 300 / 1.484

N0 ≈ 202.02

Therefore, the initial size of the bacteria culture was approximately 202.02.

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The forecast for the first week in April is Option B, 217.33.

By using a three-week moving average to forecast the rate of new driver's license applications for the first week of April, means that we will average the rate of new driver's license applications over the last three weeks to forecast the rate for the next week.

Let's calculate the moving average for the first week of April.

Given weeks 2, 3, and 4 of March are 199, 215, and 212, respectively.

To find the three-week moving average, we add these three rates and divide by three:

(199 + 215 + 212) / 3 = 208.67

Therefore, the forecast for the rate of new driver's license applications for the first week of April using the three-week moving average is 208.67, rounded to two decimal places, the closest option to 208.67 is option B, which is 217.33.

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the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis is  8π

y = x^2 and x = 2

=> y = 4

Volume = [int 0 to 4] π x^2 dy

= [int 0 to 4] π y dy

= 8π

In mathematics, "volume" is a mathematical quantity that describes the three-dimensional space occupied by an object or closed surface. Volume units are cubic units such as m3, cm3, and in3. Volume is sometimes called capacity.

Volume is a measure of the volume contained in an object. For example, if 100ml of water fills the rim of the cup, the capacity is said to be 100ml. Volume can also be defined as the amount of space occupied by a three-dimensional object.

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Answer:

The table displays a higher rate because the slope in the table is bigger than the slope in the graph.

What does a graph's slope mean?

The graph's slope serves as a gauge for a line's steepness. It is the ratio of any two places on the line's vertical change (rise) to horizontal change (run). Slope is defined mathematically as: Slope (m) = (change in y)/(change in x).

The slope from the table is:

y2 - y1/x2 - x1

m = 42 - 30/7 - 5

= 6

The slope from the graph is:

8 - 0/1.5 - 0

m = 5.33

Answer:

Put p(x)=0.

Step-by-step explanation:

2x-1=0 will give x=1/2. This means, If x=1/2 is given to the polynomial p(x), it will give a zero. P(1/2)=0.

Answer:

Required equations:

Solve by substitution x = 8 - y

Find x:

Answer: 5 adults and 3 students

Equations:

Solve by elimination, subtract the equations:

Find x:

Answer: Gloves cost $8.5, hats cost $6.5

Answer:

Gretchen has mostly more than Manuel.

Step-by-step explanation:

Plz mark as Brainliest!

Answer: Yes it does.

Step-by-step explanation:

To solve questions 1 and 2, convert your weight of 130 pounds to 58.5 kilograms by multiplying by 0.45. Convert your height of 5'2" to 1.57 meters by converting feet to inches and then to meters using the provided conversion factor.

For question 1, convert your weight from pounds to kilograms by multiplying it by the conversion factor 0.45 kg/lb. In this case, 130 pounds would be equal to 58.5 kilograms (130 * 0.45).

For question 2, convert your height from feet and inches to meters. First, convert your height in feet to inches by multiplying it by 12 (since 1 foot = 12 inches). Then, add the inches to the total. Next, convert the total inches to meters by multiplying it by the conversion factor 0.0254 m/inch.

In this case, 5 feet and 2 inches would be equal to 1.57 meters ((5 * 12 + 2) * 0.0254).

By converting your weight to kilograms and your height to meters, you can now express your weight and height in metric units.

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