A rectangular piece of paper measures 280 cm by 140 cm . How many circles of radius 7 cm can be cut out from it?

Take pie = 22/7

Answer ASAP

The population of bacteria in the culture after 13 hours to the nearest whole number is 623

The doubling time is the time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest.

P(t) = P(o) 2^(t/d)

P(o) = 230

t = 13hours

d = 9hours

Therefore ;

P(t) = 230 × 2^{13/9}

P(t) = 230 × 2^{ 1.44}

P(t) = 230 × 2.71

P(t) = 623.3

Therefore, the population of bacteria after 13 hours to the nearest whole number is 623

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The sine function for this problem is defined as follows:

y = sin(1/6(x - 2π)) - 5.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The parameter values for this problem are given as follows:

A = 1, D = -5, C = 2π.

Considering the period of 12π, the coefficient B is obtained as follows:

2π/B = 12π

12B = 2

B = 1/6.

Hence the equation is given as follows:

y = sin(1/6(x - 2π)) - 5.

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Simplifying the given expression results to

To simplify the expression using PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right), we'll break it down step by step:

The expression is rewritten as, 1/2 (1/4 ÷ 1/3 - 1/4 - 3/4 + 1/2). hence we start we parenthesis.

Performing division results to

1/2 (3/4 - 1/4 - 3/4 + 1/2)

Performing addition results to

1/2 (3/4 - 1/4 - 5/4)

Performing subtraction results to

1/2 (-3/4)

Now we multiply

-3/8

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A net is a two-dimensional pattern that can be folded into a three-dimensional shape. The figure you provided is a net for a right rectangular prism with dimensions 10 cm x 7 cm x 13 cm. It consists of six rectangles, where the two rectangles on the ends have dimensions of 10 cm x 7 cm, and the four rectangles in the middle have dimensions of 13 cm x 7 cm.

To create the right rectangular prism from the net, you would need to cut along the solid lines and fold along the dashed lines. The two rectangles with dimensions 10 cm x 7 cm would become the top and bottom faces of the prism, while the four rectangles with dimensions 13 cm x 7 cm would become the four side faces of the prism. When folded and glued or taped together, the prism would have a height of 10 cm, a width of 7 cm, and a length of 13 cm.

Answer: B. 6x + 4y ≤ 50 x + y ≥ 10

Step-by-step explanation: To represent this situation with a system of inequalities, we need to consider two constraints: the budget and the number of guests.

The budget constraint is that the total cost of the party favors should not exceed $50. Since each stuffed animal costs $6 and each toy truck costs $4, the total cost can be expressed as 6x + 4y, where x is the number of stuffed animals and y is the number of toy trucks. To satisfy the budget constraint, we need 6x + 4y to be less than or equal to 50. This gives us the first inequality: 6x + 4y ≤ 50.

The number of guests constraint is that Laura wants to provide at least one party favor per person to at least 10 guests. This means that the total number of party favors should be greater than or equal to 10. Since each party favor is either a stuffed animal or a toy truck, the total number of party favors can be expressed as x + y, where x and y are the same as before. To satisfy the number of guests constraint, we need x + y to be greater than or equal to 10. This gives us the second inequality: x + y ≥ 10.

Therefore, the system of inequalities that represents this situation is:

6x + 4y ≤ 50 x + y ≥ 10

Hope this helps, and have a great day! =)

Answer:

Step-by-step explanation:

Yes

The statement that the ratio 1.000 kilograms to 1 gram can be used for converting units is false. The correct Ratio is 1 kilogram to 1000 grams.

The statement "One ratio you could use for converting units is 1.000 kilograms to 1 gram" is false.

When converting units, it is important to use the correct conversion factors that relate the two units being converted. In this case, the ratio given is 1.000 kilograms to 1 gram, which implies that 1 kilogram is equal to 1 gram. However, this is incorrect.

The correct conversion factor between kilograms and grams is that 1 kilogram is equal to 1000 grams. This means that to convert kilograms to grams, you multiply the value in kilograms by 1000. Conversely, to convert grams to kilograms, you divide the value in grams by 1000.

So, the correct ratio for converting kilograms to grams is 1 kilogram to 1000 grams, or 1:1000. Therefore, the statement that the ratio 1.000 kilograms to 1 gram can be used for converting units is false. The correct ratio is 1 kilogram to 1000 grams.

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Answer:

[tex]\huge\boxed{\sf b = 4/3}[/tex]

Step-by-step explanation:

[tex]9^2 \times b^2 = 12^2[/tex]

So,

81 × b² = 144

b² = 144 / 81

b² = (12 × 12) / (9 × 9)

b² = 12² / 9²

√b² = √(12²/9²)

b = 12 / 9

[tex]\rule[225]{225}{2}[/tex]

The largest interval in which x0 must lie is:√2 − 10−4 √2 ≤ x0 ≤ √2 + 10−4 √2

To find the largest interval in which x0 must lie to approximate √2 with relative error at most 10−4, let's first recall the formula for the relative error. What is relative error? Relative error is the ratio of the absolute error to the true value. It is expressed as a fraction or a percentage. If the exact value is known, relative error can be calculated using the following formula: Relative error = (approximate value − exact value) / exact value.

Let x0 be the approximation to √2. We want to find the largest interval for x0 that ensures that the relative error is at most 10−4. We can use the formula for relative error to write:10−4 ≥ | (√2 − x0) / √2 |. Multiplying both sides by √2 gives: 10−4√2 ≥ | √2 − x0 |. Taking the square of both sides, we get:10−8 × 2 ≥ ( √2 − x0 )².

Simplifying:10−8 × 2 ≥ 2 − 2√2x0 + x0²10−8 ≥ x0² − 2√2x0. Solving the quadratic inequality: x0² − 2√2x0 − 10−8 ≤ 0. The solutions of this inequality are:x0 ≤ √2 + 10−4 √2x0 ≥ √2 − 10−4 √2.

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Step-by-step explanation:

the answer geheieoeokejrhdhhshejekdkhfhsjsjjs

The numbers that correspond to the members who will raise and lower the flag are 97836, 74547, 79986, and 58820.

To select 4 members from a group of 25, we can use the random number table provided to assign numbers to each student and choose the corresponding numbers to identify the members who will raise and lower the flag. Let's go through the process step by step:

Step 1: Assign a two-digit number from 01 to 25 to each student.

We have 25 students, so we can assign each student a number from 01 to 25. Let's match the given numbers with the students:

97836 - Student 1

74547 - Student 2

79986 - Student 3

58820 - Student 4

36071 - Student 5

17996 - Student 6

59066 - Student 7

36220 - Student 8

46340 - Student 9

66069 - Student 10

51761 - Student 11

41740 - Student 12

39326 - Student 13

52760 - Student 14

Note: The remaining students from 15 to 25 are not provided in the given random number table, so we cannot assign numbers to them based on the given information.

Step 2: Choose the corresponding numbers to identify the members who will raise and lower the flag.

Since we need 4 members, we can select any four numbers from the given list that correspond to the assigned numbers of the students. Let's say we choose the first four numbers:

97836 - Student 1 (Will raise and lower the flag)

74547 - Student 2 (Will raise and lower the flag)

79986 - Student 3 (Will raise and lower the flag)

58820 - Student 4 (Will raise and lower the flag)

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The expression that is equivalent to the composite function (f ° g) (5) is; Option A: f (5) times g (5)

A composite function is defined as an operation where two functions say f and g, generate a new function say h in such a way that h(x) = g(f(x)). It means here that function g is said to be applied to the function of x. So, this basically,l tells us that a function is applied to the result of another function.

We want to find (f ° g) (5)

This simply means f(5) × g(5)

The composite function definition demands that must be the expression of the the question and as such option A is the only correct option.

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Answer:

f(5) x g(5)

Step-by-step explanation:

(fg)(5) = (f x g)(5) = f(5) x g(5)

The answer is angle 3, i think

The length of fabric Mary need to buy if she wants to sew 2 shirts is:

[tex]4\frac{3}{4}[/tex]  yards

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

We have that:

3 1/6 yards of the fabric  can make only 1 1/3 shirts.

To find the length of fabric that will sew 2 shirts. We will use the ratio of the number of yards to number of shirts.

Let L be the length of fabric for 2 shirts. Thus, we can say:

[tex]\frac{3\frac{1}{6} }{1\frac{1}{3} } = \frac{L}{2}[/tex]

[tex]L = 2 * \frac{3\frac{1}{6} }{1\frac{1}{3} }[/tex]

[tex]L = 2 * 2\frac{3}{8}[/tex]

[tex]L = 4\frac{3}{4}[/tex]  yards

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Complete Question

Mary is making some shirts for her school's drama department. The fabric store has 3 1/6 yards of the fabric she wants in stock. But this quantity of fabric can make only 1 1/3 shirts. What length of fabric does Mary need to buy if she wants to sew 2 shirts?

According to the information we can infer that the option A, a 2-pack of paper towels for $2.24, has a lower unit price than Quick 'N Clean paper towels.

To compare the unit prices, we need to calculate the price per roll for each option.

For the Quick 'N Clean paper towels, we have a 4-pack for $4.28, so the unit price per roll is 4.28 / 4 = $1.07 per roll.

Among the given options, option A has the lowest unit price per roll ($1.12), which is lower than the unit price of the Quick 'N Clean paper towels ($1.07). Therefore, option A has a lower unit price than the Quick 'N Clean paper towels.

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[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-1}{0 +4} \implies \cfrac{ -1 }{ 4 } \implies - \cfrac{1}{4}[/tex]

Answer:

B(-8, 4)

Step-by-step explanation:

To find the coordinates of B, use the midpoint formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\$M=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where:\\\phantom{ww}$\bullet$ $M$ is the midpoint.\\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]

Let point A be (x₁, y₁). Therefore, (x₁, y₁) = (6, -4).

Let point B be (x₂, y₂).

The midpoint M is (-1, 0).

Substitute these values into the midpoint formula:

[tex](-1, 0)=\left(\dfrac{x_2+6}{2},\dfrac{y_2-4}{2}\right)[/tex]

Solve the x and y coordinates separately:

[tex]\begin{aligned}\dfrac{x_2+6}{2}&=-1\\\\x_2+6&=-2\\\\x_2&=-8\end{aligned}[/tex]                              [tex]\begin{aligned}\dfrac{y_2-4}{2}&=0\\\\y_2-4&=0\\\\y_2&=4\end{aligned}[/tex]

Therefore, the coordinates of point B are (-8, 4).

The equivalent expressions are listed as;

-10x+3/2

Algebraic expressions are defined as expressions that are made up of terms, coefficients, constants and factors.

These algebraic expressions are made up of arithmetic operations. They include;

From the information given, we have that;

-2(5x - 3/4)

expand the bracket, we get;

-10x + 6/4

Divide the values, we have;

-10x + 3/2

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The population increases by 1200 people each year starting from the base population of 28,000 in 2003.

To write an equation for the population, P, years after 2003, we can use the information given about the population growth.

We know that in 2003, the population was 28,000. Since the population has been growing linearly by 1200 people each year, we can express the growth rate as 1200 people per year.

Let's denote the number of years after 2003 as 'x'. Since the growth rate is constant, we can use the slope-intercept form of a linear equation to represent the population:

P = mx + b

Where:

P represents the population

m represents the slope (growth rate)

x represents the number of years after 2003

b represents the y-intercept (population in the base year)

In this case, the slope, m, is 1200 people per year, and the y-intercept, b, is 28,000 people in 2003.

Plugging in the values, the equation for the population, P, years after 2003 becomes:

P = 1200x + 28000

This equation represents the linear growth of the town's population, where the population increases by 1200 people each year starting from the base population of 28,000 in 2003.

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Answer:

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

Step-by-step explanation:

We are given:

4x+3(2-x)=8-2x

To solve this, we first distribute the 3 among the numbers in parenthesis:

[tex]4x+3(2-x)=8-2x\\4x+6-3x=8-2x[/tex]

next, we rearrange terms that are the same next to each other

[tex]4x-3x+6=8-2x[/tex]

combine like terms

[tex]x+6=8-2x[/tex]

add 2x to both sides

[tex]3x+6=8[/tex]

subtract 6 from both sides

[tex]3x=2[/tex]

divide both sides by 3

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

Hope this helps! :)

Answer:

6 by 36 is the answer.....

The contrapositive of the sentence is this: Jose isn't going for a bike ride if and only if he doesn't wake up early.

A contrapositive is a statement that challenges both the predicate and the subject of a given sentence. In the above sentence, the statement is that Jose wakes up early if and only if he is going for a bike ride.

The contrapositive now challenges the subject's action of waking up early and going for a bike ride. The hypothesis and conclusion are disputed.

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Answer:

Let s = smaller number

l = larger number

s + l = 31

2s = l + 11

2(31 - l) = l + 11

62 - 2l = l + 11

3l = 51, so l = 17 and s = 14.

The larger number is 17, and the smaller number is 14.

Solution for the given system of equations is : a = -2, b = -13 by substitution method.

To solve the system of equations:

a - 4b = 50    ...(1)

b + 5 = 4a    ...(2)

We can use the method of substitution or elimination. Let's solve it using the substitution method.

From equation (2), we can express b in terms of a:

b = 4a - 5

Now we substitute this value of b in equation (1):

a - 4(4a - 5) = 50

a - 16a + 20 = 50

-15a = 50 - 20

-15a = 30

a = 30 / -15

a = -2

Substitute this value of a back into equation (2) to solve for b:

b + 5 = 4(-2)

b + 5 = -8

b = -8 - 5

b = -13

Therefore, the solution to the system of equations is a = -2 and b = -13.

To verify the solution, substitute these values back into the original equations:

For equation (1): -2 - 4(-13) = 50

-2 + 52 = 50 (True)

For equation (2): -13 + 5 = 4(-2)

-8 = -8 (True)

Thus, the solution is confirmed to be correct. The values a = -2 and b = -13 satisfy both equations in the system.

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Answer:

How many numbers can divide 21

3

7

Answer:

Since segments AC and BD are diameters of Circle E, angle ACD is a central angle that intercepts arc ACD, and angle BCD is also a central angle that intercepts arc ACD. Therefore, arc ACD is divided into two equal arcs, arc CDB and arc CAB, by the diameter CD.

Since arc ACD is 326 degrees, each of arc CDB and arc CAB is 326/2 = 163 degrees.

Therefore, arc CDB equals 163 degrees.

The solution to the multiplication of the decimals is; 39.15

One of the ways to multiply decimals is as follows;

To multiply decimals, first multiply as if there is no decimal.

Second step is to count the number of digits after the decimal in each factor.

Last step is to put the same number of digits behind the decimal in the product.

Now, we want to multiply the decimals given as;

8.7 × 0.45

Converting them to fractions gives us;

(87/10) × (45/10)

= 3915/100

= 39.15

Thus, that is the solution to the multiplication of the decimals.

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The surface area of the larger pot is  2,205 cm².

When we have two similar figures related by a scale factor K, then:

If A is the area of the smaller figure, the area of the larger one is:

A' = A*K²

If V is the volume of the smaller figure, then the volume of the other one is:

V' = V*K³

Now, in this case, the surface area of the smaller pot is 45cm² and the scale factor is 7, then the surface area of the other one is:

A' = 45cm²*7² =  2,205 cm².

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The percentage change is 83.82%.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentages is %. In order to convert a number to percentage, multiply the number by 100.

Percentage change = [tex](\frac{new value}{intial value} -1)[/tex] x 100

[tex](\frac{125}{68}- 1)[/tex] x 100 = 83.82%

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The value of z such that 0.516 of the area lies between -z and z is approximately 0.05.

To find the value of z such that 0.516 of the area lies between -z and z, we can use the standard normal distribution table or a statistical calculator.

First, we need to find the area under the standard normal curve that lies between -z and z.

Since the standard normal distribution is symmetric, we can find the area to the right of z and then double it to account for both tails.

From the given information, we know that the total area between -z and z is 0.516.

Since the standard normal distribution is standardized with a mean of 0 and a standard deviation of 1, we can use the standard normal distribution table to find the corresponding z-value.

Using the standard normal distribution table, we can look up the area of 0.516.

Looking at the table, we find that the closest area is 0.5149, corresponding to a z-value of approximately 0.05.

Since the standard normal distribution is symmetric, the area to the left of -0.05 is also 0.5149.

Therefore, the z-value that corresponds to an area of 0.516 lies between -0.05 and 0.05.

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