Tiana drew a scale drawing of a picnic area near the river. She used the scale 1 inch : 7 yards. If the picnic area is 7 inches wide in the drawing, how wide is the actual picnic area?

Answer:

31/21

Step-by-step explanation:

First step is to add 17 and 14 = 31

The denominator of the fraction(bottom number stays the same)

so the answer is 31/21

Let me know if it helps

Answer:

EXACT FORM: 31/21

DECIMAL FORM: 1.476190

MIXED NUMBER FORM: 1 10/21

Step-by-step explanation:

The total number of biscuits the baker should place into each, according to the declaration, is 12.

The mathematical expressions consist of at least a couple of integers or issues, no fewer than one math procedure, and a sentence. It's achievable to multiply, divide, add, or remove with this algebraic method. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Arithmetic Operator)

The total number of cookies in both batches is:

36 + 48 = 84

To divide the cookies into seven equal groups, we need to divide the total number of cookies by 7:

84 / 7 = (12 x 7) / 7 = 12

So the baker should put 12 cookies into each of the seven groups.

A numerical expression that shows how to determine the total number of cookies the baker should put into each group with parentheses is:

(36 + 48) / 7 = (84) / 7 = 12

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To calculate your fuel consumption in gallons per hour, divide the speed (in miles per hour) by the fuel efficiency (in miles per gallon). This will give you the gallons per hour (GPH).

For example, if your speed is 50 mph and your fuel efficiency is 30 mpg, your fuel consumption would be 1.67 GPH (50/30). You can then use this result to estimate your fuel costs and overall fuel consumption over a certain period of time.

To understand this concept better, it is important to know that speed (in mph) and fuel efficiency (in mpg) are inversely related. This means that as your speed increases, your fuel efficiency decreases, and as your speed decreases, your fuel efficiency increases.

So, if you want to maximize your fuel efficiency, you need to drive at the lowest possible speed. Additionally, the higher the fuel efficiency, the lower the fuel consumption in GPH.

In short, you can use the readout from your odometer and fuel efficiency meter to calculate your fuel consumption in GPH by dividing the speed (in mph) by the fuel efficiency (in mpg). This result can help you estimate your fuel costs and overall fuel consumption.

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Answer:

20%

Step-by-step explanation:

80 - 64 = 16

16 ÷ 80 = 0.2

0.2 × 100 = 20%

Carter has 13 dimes in his piggy bank

To solve this equation, we need to use the distributive property to simplify the equation:
(x dimes x 10 cents) + (37-x nickels x 5 cents) = $3.10
We can then solve for the number of dimes by isolating the dimes on one side of the equation:
x dimes x 10 cents = $3.10 - (37-x nickels x 5 cents),By dividing both sides of the equation by 10 cents, we can solve for the number of dimes, x:
x dimes = ($3.10 - (37-x nickels x 5 cents)) / 10 cents

Plugging in the value of 37 coins and solving the equation, we get:
x dimes = (3.10 - (37 -x nickels x 5 cents)) / 10 cents
x dimes = (3.10 - 185 + 5x) / 10 centsx dimes = (3.10 - 180) / 10 centsx dimes = 1.30 / 10 centsx dimes = 13 dimes
Therefore, Carter has 13 dimes in his piggy bank.

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Answer:

If the ratio of the number of cats to dogs at the animal shelter is 9 to 5, this means that for every 9 cats at the shelter, there are 5 dogs.

We can express this ratio as:

number of cats : number of dogs = 9 : 5

To find the possible number of cats to dogs, we need to look for pairs of numbers that have a ratio of 9:5. Here are some possible pairs:

   9 cats : 5 dogs

   18 cats : 10 dogs

   27 cats : 15 dogs

   36 cats : 20 dogs

   45 cats : 25 dogs

   54 cats : 30 dogs

   ...

We can see that there are infinitely many possible pairs of numbers that have a ratio of 9:5. To narrow down the possibilities, we need more information such as the total number of animals at the shelter or the number of cats or dogs at the shelter.

Since the two angles are complementary, their sum is 90 degrees. Let x be the measure of the other angle in degrees. Then:

x + 53 = 90

Subtracting 53 from both sides, we get:

x = 37

Therefore, the measure of the other angle is 37 degrees.

The value of x in the given triangle is 1.82 cm using the angle bisector theorem.

A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle with the parts A, B, and C is referred to as triangle ABC. Any three points that are not collinear in Euclidean geometry result in a separate triangle and a distinct plane. A triangle is a type of polygon with three sides; the triangle's apex is the point where the two longest sides meet. Two sides are brought together at an angle.

What is angle bisector theorem?

The ratios of the two segments that a line that bisects the opposing angle splits a triangle's side into are the subject of the angle bisector theorem in mathematics. It contrasts their proportionate lengths with the other two triangle sides' proportional lengths.

In the given triangle,

5/6=x/4-x

20-5x=6x

20=11x

x=20/11= 1.82 cm

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The equivalent equation to f(x) = 7(x - 60) - 28 is f(x) = 7x - 448 and the y-intercept is -448

Given that

f(x) = 7(x - 60) - 28

To produce an equivalent equation that reveals the y-intercept of the function f(x) = 7(x-60) - 28, we need to simplify the expression by evaluating it when x = 0, since this will give us the y-intercept.

When the brackets are expanded, we have the following

f(x) = 7x - 420 - 28

Evaluate the like terms

So, we have

f(x) = 7x - 448

So, substituting x = 0 into f(x) gives:

f(0) = 7(0) - 448

Evaluate the expression

f(0) = -448

Therefore, the y-intercept is -448.

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The characteristic that best describes 5.1 in the polynomial 5.1xy - 4x + y - 1.5 is that it is the coefficient of the term 5.1xy.

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

In a polynomial expression, a coefficient is the numerical factor that is multiplied by a variable or variables raised to a certain power. In the expression 5.1xy - 4x + y - 1.5, the coefficient 5.1 is multiplied by the variables x and y, raised to the first power. Therefore, the term 5.1xy consists of the coefficient 5.1 and the variables x and y.

In contrast, the other terms in the polynomial do not have a coefficient that contains a decimal or a fraction. The term -4x has a coefficient of -4, the term y has a coefficient of 1, and the constant term -1.5 has a coefficient of -1.5.

Thus, the characteristic that best describes 5.1 in the polynomial 5.1xy - 4x + y - 1.5 is that it is the coefficient of the term 5.1xy.

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Answer:

58.3%

Step-by-step explanation:

Since 175 calories out of 300 come from fat, we can just do 175÷300 and multiply by 100 to get the percentage:

[tex] \frac{175}{300} \times 100 = 58.3\% \: (1dp)[/tex]

[tex]\Large\bold{SOLUTION}[/tex]

To find the percentage of calories from fat for one ice cream bar, we need to divide the number of fat calories by the total number of calories, and then multiply by 100 to get the percentage.

First, we know that each ice cream bar contains 300 calories, and 175 of those calories come from fat. So:

[tex]\sf 175\: fat\: calories \div 300\: total\: calories = 0.5833[/tex]

To convert this decimal to a percentage, we multiply by 100:

[tex]\sf 0.5833 \times 100 = 58.33\%[/tex]

Therefore, the percentage of calories from fat for one ice cream bar is 58.33%.

[tex]\rule{200pt}{5pt}[/tex]

The equation of the line in slope-intercept form is y = 6x + 55.

Equations can involve variables, which are placeholders for unknown values that we wish to find. For example, the equation x + 3 = 7 asserts that the value of x plus 3 is equal to 7. We can solve for x by subtracting 3 from both sides of the equation, obtaining x = 4.

Equations can be linear or nonlinear, and they can involve one or more variables. They can be represented in various forms, such as standard form, slope-intercept form, or quadratic form.

To find the equation of the line in point-slope form, we need to first find the slope of the line. We can use any two points from the table to find the slope using the formula:

slope = (change in y)/(change in x)

Let's use the first and last points in the table:

slope = (295 - 175)/(40 - 20) = 120/20 = 6

Now we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is any point on the line. Let's use the first point (20, 175):

y - 175 = 6(x - 20)

To write this equation in slope-intercept form, we need to isolate y:

y - 175 = 6x - 120

y = 6x + 55

So the equation of the line in slope-intercept form is y = 6x + 55.

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Slope of each graph are [tex]\frac{6}{5}[/tex],[tex]\frac{-1}{3}[/tex] and 1 respectively.

Slope of a line in mathematics is defined as the ratio of the change in the y coordinate w.r.t the change in the x coordinate.

Both the change in the y-coordinate and the net change in the x-coordinate are denoted by y₂-y₁ and x₂-x₁, respectively.

Thus, the formula for the change in y-coordinate with regard to the change in x-coordinate is

m=y₂-y₁/ x₂-x₁

Taking two points as per observation

Point1: (x₁ y₁)=(0,-3)

Point2:(x₂, y₂)=(5/2,0)

Slope of line=y₂-y₁/ x₂-x₁

=[tex]\frac{0+3}{5/2-0}[/tex]

=[tex]\frac{6}{5}[/tex]

Taking two points as per observation

Point1: (x₁ y₁)=(0,3)

Point2:(x₂, y₂)=(2,2)

Slope of line=y2-y1/x2-x1

=[tex]\frac{2-3}{2-0}[/tex]

=-⅓

Taking two points as per observation

Point1: (x₁ y₁)=(-2,0)

Point2:(x₂, y₂)=(0,2)

Slope of line=y2-y1/x2-x1

=[tex]\frac{2-0}{0+2}[/tex]

=1

Hence, Slope of each graph are 6/5,-⅓ and 1 respectively.

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Answer: 3.9b−2.6

Step-by-step explanation: Hope this helps

Answer:

1.3b

Step-by-step explanation:

The equation is -2.6+3.9b. A negative number acts like subtraction, so we would subtract 2.6 from 3.9 to get 1.3. The b is still there, and we don't know what it is, so we simplify the equation to 1.3b.

Sorry, this explanation isn't the best. Hope it helped! :)

The quadratic function to represent the total area of the park and its path is given by: f(x) = 2x² + 18x + 36.

In this problem, we are given that the length of a rectangular park is twice its width, and it is surrounded by a 3-foot wide path.

We are required to write a quadratic function to represent the total area of the park and its path.

The rectangular park can be represented as follows:

Length = 2x (twice the width)

Width = x

Therefore, the total length of the park including the 3-foot wide path can be represented as (2x + 2*3),

and the total width of the park including the 3-foot wide path can be represented as (x + 2*3).

The area of the park is given by the product of its length and width.

Thus, the area of the park can be represented as follows: Area of the park = (2x + 6)(x + 6)

To represent this as a quadratic function,

we can simplify the above expression using the distributive property.

Area of the park = 2x² + 6x + 12x + 36 = 2x² + 18x + 36.

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Answer:

3

Step-by-step explanation:

Number of people in the choir = 80

Number of women = half of 80 = 40

Number of men in the choir is ¼ of the women = 40/4 = 10

Number of men plus women = 10 +40 = 50

Number of children = 80 - 50 = 30

Ratio of children to men = n:1 = 30:10

Divide both sides by 10

30:10 = 3:1

n = 3

Answer: Simplifying this equation, we get the ANSWER 5

Step-by-step explanation: Since g(x) = 3, we can plug this into the given equation 4x-7.

now we rewrite the given equation, which is now 4(3)-7

Now we find 4(3), simplifying/multiplying that, we get 12.

We minus 12 by 7 which is 5

The percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

Percent error is a measure of the difference between an actual value and an estimated or measured value, expressed as a percentage of the actual value. It is used to evaluate the accuracy of measurements or calculations.

To calculate the percent error for Jason's measurement, we first need to find the absolute error, which is the difference between his measurement and the actual value:

Actual value minus measured value equals absolute error.

Absolute error = |14 - 13|

Absolute error = 1 inch

Next, we can use the formula for percent error:

(Absolute error / Actual Value) x 100% equals the percent of error.

Percent error = (1 / 14) x 100%

Percent error = 0.0714 x 100%

Percent error = 7.14%

Therefore, the percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

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Ben's net earnings after 5 years are $171,563.23, and Arthur's net earnings after 5 years are $163,534.49.

To calculate their net earnings, we first need to calculate their total earnings from their investments, and then subtract their initial investments.

For Ben:

Using the compound interest formula: A = P(1 + r/n)^(nt)

A = future value of the investment

P = initial principal (investment)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = number of years

A = 500,000(1 + 0.06/12)^(12 * 5)

A ≈ $671,563.23

Net earnings for Ben: $671,563.23 - $500,000 = $171,563.23

For Arthur:

A = 600,000(1 + 0.05/4)^(4 * 5)

A ≈ $763,534.49

Net earnings for Arthur: $763,534.49 - $600,000 = $163,534.49

Ben's net earnings after 5 years are $171,563.23, and Arthur's net earnings after 5 years are $163,534.49.

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Ben invested $500,000 at an annual interest rate of 6%, compounded monthly, for 5 years. Arthur invested $600,000 at an annual interest rate of 5%, compounded quarterly, for 5 years. What are their net earnings after 5 years?

Answer:

The value of t is 9.

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

In this case, we are given two points: (t, 5) and (10, -4), and the slope is given as -9. So we can set up the equation:

-9 = (-4 - 5) / (10 - t)

Simplifying, we get:

-9 = -9 / (10 - t)

Multiplying both sides by (10 - t), we get:

-9(10 - t) = -9

Expanding the left side, we get:

-90 + 9t = -9

Adding 90 to both sides, we get:

9t = 81

Dividing both sides by 9, we get:

t = 9

Therefore, the value of t is 9.

a) r = 30 cm

b) The angle AOC is 0.523598775 radian

c) The area of the shaded region is 541.9 cm²

d) The perimeter of the shaded region is 106.8 cm.

The area of a circle is a measure of the size of the surface of the circle. It is calculated by multiplying the radius of the circle (the length from the center of the circle to its edge) by itself, and then multiplying the result by the constant pi (3.14). The formula for calculating the area of a circle is A = πr2, where “A” represents the area, “π” is pi, and “r” is the radius of the circle.

The radius of the circle, r, can be determined by the Pythagorean theorem. Since AC = 36 cm and AP = 6 cm, the hypotenuse of the right triangle formed by AC and AP is the radius of the circle, r. By applying the Pythagorean theorem, we get:

r² = 362 + 62

r² = 1296

r = √1296

r = 36 cm

b) The angle AOC is 0.523598775 radians

The angle AOC can be determined using the formula for arc length. The arc length of ABC is 36 cm and the radius of the circle is 30 cm. Therefore, the angle AOC is:

AOC = 36/30

AOC = 1.2 radians

c) The area of the shaded region is 541.9 cm²

The area of the shaded region can be determined using the formula for the area of a sector. The angle AOC is 1.2 radians and the radius of the circle is 30 cm. Therefore, the area of the shaded region is:

Area = (1.2)(30)(30)/2

Area = 541.9 cm²

d) The perimeter of the shaded region is 106.8 cm

The perimeter of the shaded region can be determined using the formula for the circumference of a circle. The radius of the circle is 30 cm. Therefore, the perimeter of the shaded region is:

Perimeter = 2π(30)

Perimeter = 106.8 cm

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In summary, the force required to give the wheel an acceleration of 4.46 rad/s2 when using a 9.00-cm-diameter sprocket is 8,550.54 N, and the force required when using a 5.58-cm-diameter sprocket is 13,764.83 N.

To answer (a) and (b), we need to determine the rotational inertia of the wheel, then calculate the torque and force required to accelerate the wheel with a given angular acceleration.
The rotational inertia of a wheel with all its mass concentrated on the outside radius can be calculated using the formula I = mr^2, where m is the mass of the wheel and r is its radius. In this case, the radius of the wheel is 63.8/2 cm (31.9 cm) and its mass is 1.71 kg, so the rotational inertia is I = [tex]1.71 * (31.9 cm)^2 = 17,214.939 cm^4.[/tex]
To calculate the torque and force required to accelerate the wheel, we use the equation T = I * alpha, where T is the torque, I is the rotational inertia, and alpha is the angular acceleration. Plugging in the values given in the question, we get[tex]T = 17,214.939 cm^4 * 4.46[/tex] rad/[tex]s2 = 76,954.848 Nm.[/tex]
To calculate the force required to accelerate the wheel, we use the equation F = T / r, where F is the force, T is the torque, and r is the radius of the sprocket. For the 9.00-cm-diameter sprocket, the force required is F = 76,954.848 Nm / 9 cm = 8,550.54 N. For the 5.58-cm-diameter sprocket, the force required is F = [tex]76,954.848 Nm / 5.58[/tex] cm = [tex]13,764.83 N.[/tex]

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Answer: 7x - 7y + 21

Step-by-step explanation:

7( x - y + 3) = 7x - 7y + 21

The interval is known as a prediction interval when it is created using the estimated regression equation to forecast the mean for all units that satisfy a specific set of supplied criteria.

A prediction Interval is a statistical interval that provides a range of values within which a future observation is likely to fall. It takes into account both the variability of the data and the uncertainty in the estimates of the regression coefficients.

In contrast, a confidence interval is a statistical interval that provides a range of values within which a population parameter is likely to fall. It is used to estimate the true value of a population parameter based on a sample of data.

Therefore, a prediction interval is specific to the individual unit being predicted, while a confidence interval is specific to the population parameter being estimated.

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Therefore, a monthly payment of $168.62 must be made to pay off the $3,500 balance on the credit card in two years.

Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life.

Here,

To calculate the monthly payment required to pay off the $3,500 balance on a credit card that charges 16.5% interest, compounded monthly, in two years, we can use the formula for the present value of an annuity:

[tex]PMT = PV * r / (1 - (1 + r)^{-n})[/tex]

where PMT is the monthly payment, PV is the present value of the loan, r is the monthly interest rate, and n is the total number of payments.

First, we need to convert the annual interest rate of 16.5% to a monthly interest rate:

r = 0.165 / 12

= 0.01375

Next, we need to calculate the total number of payments over two years:

n = 2 * 12

= 24

Now we can plug in the values into the formula:

[tex]PMT = 3500 * 0.01375 / (1 - (1 + 0.01375)^{-24}) = $168.62[/tex]

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Step-by-step explanation:

hope this is correct

Random sample of size is selected from a population:

The sample statistic that is calculated for the sample values serves as the foundation for the sampling distribution. To estimate the population percentage, the sample proportion, a sample statistic, is computed from the sample values.

In statistics, a simple random sample is a subset of individuals selected at random from a larger population with an equal probability of selection.

Given that we have,

n = 100

p = 0.40

a) The expected value of the sample proportion is defined as:

E(p) = p = 0.40

b) The standard error of the sample proportion is defined as:

[tex]S.E = \sqrt{\frac{p(1-p)}{n} }[/tex]

= [tex]\sqrt{\frac{0.40(1-0.40)}{100} }[/tex]

S.E = 0.0024.

c) The sample proportion's sampling distribution follows a normal distribution, with an expected value of 0.40.

E(p) = 0.40

d) According to the central limit theorem, as the sample size approaches infinity, the sample statistic (sample percentage) tends to the population parameter (population proportion).

so,

p ∼ N ([tex]p, \frac{p(-p)}{n}[/tex]) as n → ∞.

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Complete question:

A random sample of size 100 is selected from a population with p = 0.40 .

a. what is the expected value of p (to decimals)? .

b. what is the standard error of p (to decimals)?

c. show the sampling distribution of p

d. what does the sampling distribution of show?

Answer:

Step-by-step explanation:

To find out how much more fabric is required for the chair than the footstool, we need to subtract the amount of fabric required for the footstool from the amount of fabric required for the chair.

The amount of fabric required for the chair is 5/7 of a yard.

The amount of fabric required for the footstool is 2/3 of a yard.

So to find the difference, we need to subtract:

5/7 - 2/3

To do this, we need to find a common denominator, which is 21 in this case. We get:

(15/21) - (14/21) = 1/21

Therefore, Aron needs 1/21 more yard of fabric to cover the chair than the footstool.

The probability of winning the New York State Numbers Lottery is 1 in 1000.

When you pay for a ticket, you pick a number between 000 and 999. If your number is drawn, you win $500, meaning you made a profit of $490. If you don't win, you will lose the $1 that you paid for the ticket.

To calculate the probability of winning the New York State Numbers Lottery, you must first consider the total number of possible outcomes. Since you can pick a number between 000 and 999, there are 1000 possible outcomes. This means that your chance of winning is 1 in 1000, or 0.1%.

It is important to remember that the New York State Numbers Lottery is a game of chance, meaning that there is no guarantee of winning.

However, if your number is drawn, you can win up to $500, which is a profit of $490. The odds of winning are 1 in 1000, and if you lose, you will only lose the amount you paid for the ticket.

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