A carpenter has two different-sized circular saws. The smaller saw has the radius shown. The larger saw has a diameter that is 1.5 inches greater than the diameter of the smaller one.



How much greater is the circumference of the larger saw than the smaller saw? Use 3.14 for π
.

Mathematical statement  μ = 18000 where μ is the mean, Null hypothesis H₀ : μ = 18000, Alternate hypothesis Hₐ : μ ≠ 18000.

A mathematical statement is a meaningful string of words that can be either true or false.

For instance , 3+4=7 is always true. Consequently, it is a true statement.

Similar to this ,  3+4=8 is never true  Therefore,  it is a false statement.

Here the amusement park makes the claim that the mean daily attendence at the park is 18000 people

∴ μ = 18000 is the statement .

A null hypothesis is known as statistical hypothesis that proposes that no statistical significance exists in a set of given observations. Hypothesis testing is used to assess the credibility of a hypothesis by using sample data. Sometimes referred to simply as the "null," it is represented as H₀.

∴  Here the null hypothesis is μ = 18000

The alternative hypothesis is an assertion used in statistical inference experiment. It is contradictory to the null hypothesis and indicated by Ha or H₁ . We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing.

For instance :  A school principal claims that students in her school score an average of seven out of 10 in exams. The alternate hypothesis is μ ≠ 7.0.

Similarly here in this question alternate hypotesis will be μ ≠ 18000.

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The rate of change of the amount of laundry with respect to the number of loads is a constant value of -1.6 fluid ounces per load.

Any equation that has terms that are either constants or the product of a constant and a variable of the first degree (exponent 1) is said to be linear. In other words, the equation's greatest degree for any variable is 1. One way to express a linear equation is as follows:

ax + b = 0

If an is not equal to zero, a and b are constants, and x is the variable. This is how a linear equation is typically expressed.

The given function is f(x) = 50 - 1.6x.

Now, the rate of change is the slope of the equation.

Comparing the equation with that of the linear equation y = mx + c we see that the slope is -1.6.

Hence, the rate of change of the amount of laundry with respect to the number of loads is a constant value of -1.6 fluid ounces per load.

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Labor Variances Ellen Chenoweth, the manager of the city of St. Paul road maintenance shop, uses standards to judge performance, the actual labor rate per hour for April was $19.35.

1. Actual Labor Rate per Hour:

The labor price variance formula is:

Labor Price Variance = (Actual Labor Rate - Standard Labor Rate) x Actual Hours

We are given that the labor price variance for April was unfavorable and equal to $1,157. We also know that the standard labor rate was $20 per hour. Using the formula above and plugging in the known values, we can solve for the actual labor rate:

-1,157 = (Actual Labor Rate - 20) x 1,780

-1,157 = 1,780Actual Labor Rate - 35,600

1,780Actual Labor Rate = 34,443

Actual Labor Rate = 19.35

Therefore, the actual labor rate per hour for April was $19.35.

2. Standard Hours Allowed for the Output Achieved:

The flexible-budget variance formula is:

Flexible-Budget Variance = (Actual Hours - Standard Hours) x Standard Labor Rate

We are given that the flexible-budget variance for April was favorable and equal to $1,643. We also know that the standard labor rate was $20 per hour.

Using the formula above and plugging in the known values, we can solve for the standard hours allowed:

1,643 = (1,780 - Standard Hours) x 20

1,643 = 35,600 - 20Standard Hours

20Standard Hours = 33,957

Standard Hours = 1,697.85

Therefore, the standard hours allowed for the output achieved in April was 1,697.85.

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Answer: i. y = 60÷5

Step-by-step explanation: If he has 60 sheets of paper and 5 notebooks, it would only make sense to divide the number of sheets by the number of notebooks to get the sum. Which is 12 btw! <33

Answer: 6,450 words per minute

Step-by-step explanation:

Each hour is 60minutes long, making your total number of minutes 150.

The last step would be to multiply 150 by the wpm (43) and making the total number typed 6,450

Answer:

range = 22

Step-by-step explanation:

the range is the difference between the largest and smallest values in the data set.

largest value = 25 , smallest value = 3

range = 25 - 3 = 22

Using the given angle of depression the equation (D) cos(24) = x/45 will be used to find the answer.

The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item.

When we know the angles and the distance of an object from the ground, it is primarily utilized to find the distance between the two objects.

The angle from the horizontal downward to an item is referred to as the "angle of depression."

The line of sight of an observer would be below the horizontal.

So, in the given situation:
We will find the base which is the distance of the boat from the land.

Which means:
hypotenuse/Base

Which is represented by Cosx.

The angle is 24°.

Then, the equation for a solution would be:

cos(24) = x/45

Therefore, using the given angle of depression the equation (D) cos(24) = x/45 will be used to find the answer.

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You would need to purchase 720 different tickets to guarantee a win.

You must pick the first three finishers in the correct order to win a trifecta race with 10 entries.

Since there are ten participants in the race, there are ten ways to select the winner of the first place prize. In the wake of choosing the primary spot finisher, there are just 9 passages remaining, so the quantity of ways of choosing the second-place finisher is 9.

Finally, since there are only eight entries left after selecting the first two, there are 8 ways to select the third-place finisher.

Therefore, the total number of possible winning trifecta combinations is:

10 x 9 x 8 = 720

This indicates that in order to guarantee a win, you would need to purchase 720 distinct tickets. However, it is essential to keep in mind that betting on a race in this manner may not always be the most profitable or efficient option, and that purchasing each and every possible combination can be very costly. It's vital to painstakingly think about the chances, payouts, and your financial plan prior to putting down any wagers.

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Answer:

D. A = s × s

Step-by-step explanation:

D. A = s × s is an area formula. Area is side times side. This is an area formula for a square. The units of area are square units. Since Jennifer has square inches in her answer, she was working on an area problem.

A. and C. are perimeter formulas. Perimeter is the distance around the outside of a shape. The units of perimeter are straight up plain, one-dimensional units like inches (or feet, meters, miles, km)

B. is a volume formula. The units of volume is cubic units or units to the third power.

The answer is D.

Answer:

the other two sides of the rectangle is 147

Step-by-step explanation:

because since u told us that there is a side with a length of 6 cm and u also gave us the preimeter which can help us do this so what I did is 6 x 2 why because if one side is 6cm then the other side will also be 6cm and then 6 x 2 = 12 and this is what I did 306 - 12 = which equalls 294 and then divide that by 2 = 147 please mark as brainliest bye have a great day :D

Answer:

B

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 7 and h = 4 , then

A = [tex]\frac{1}{2}[/tex] × 7 × 4 = [tex]\frac{1}{2}[/tex] × 28 = 14 cm²

A line plot that represents the data is shown in the image attached below.

A fraction of an hour which Rita spend most days writing is 3/4.

The difference between the greatest amount of time spend writing and the least is 3/4.

In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.

Additionally, we can logically deduce that the mode of the data set is equal to 3/4 (the fraction of an hour Rita spend most days writing) because it has the highest frequency of 5.

Difference = greatest amount of time - least amount of time

Difference = 1 - 1/4

Difference = 3/4.

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You rented the car for 10 days.

Let's begin by setting up the equation to solve for the number of days:

Total rental cost = (daily rental cost + CDW fee) x number of days + gasoline cost

We know that the daily rental cost is 37.45, and the CDW fee is 19.40, so we can substitute those values into the equation:

646.50 = (37.45 + 19.40) x number of days + 78

Simplifying the equation:

646.50 = 56.85 x number of days + 78

Subtracting 78 from both sides:

568.50 = 56.85 x number of days

Dividing both sides by 56.85:

number of days = 10

Therefore, You rented the car for 10 days.

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The answer on shape of house is , (1) A rectangle for the main structure of the house. (2) A triangle for the roof. (3) A rectangle for the front porch. (4) Two trapezoids for the roof of the front porch. (5) A rectangular door.

A trapezoid is a four-sided geometric shape with two parallel sides, called the bases, that are of different lengths, and two non-parallel sides that connect the bases. The non-parallel sides are also called legs, and they may or may not be equal in length.

Trapezoids are often encountered in geometry and in real-life situations, such as in construction and architecture. They can be classified as either right trapezoids or oblique trapezoids depending on whether one of the angles formed by the bases and a leg is a right angle or not.

Based on the image provided, the shapes that make up the front of the house are:

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The amount she charges for each necklace is $7.50 (option B).

Profit is the total difference between total revenue and total cost. Total cost is the sum of fixed cost and variable cost.

Profit = total revenue - total cost

Profit = (price x quantity sold) - (fixed cost + total variable cost)

Profit = (price x quantity sold) - (fixed cost +(variable cost per unit x quantity sold)

P = 7.5n - (2.25n + 15)

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Answer:

We can use trigonometry to find AB.

First, we can use the fact that the sum of the angles in a triangle is 180° to find angle A:

A + B + C = 180°

A + 90° + 30° = 180°

A = 60°

Now, we can use the sine function to find AB:

sin A = opposite/hypotenuse

sin 60° = AB/96

AB = 96 * sin 60°

AB = 96 * √3/2

AB = 48√3

Therefore, AB is approximately 83.14 cm (rounded to two decimal places).

Answer:

C.

Step-by-step explanation:

C. is an impossible equation.

Answer:

The student's claim is incorrect. While it is true that √x^2 = x for all non-negative values of x, this property does not apply to expressions with multiple terms, such as 4√x^2.

Step-by-step explanation:

consider the case where x = -1. Then, √x^2 = √(-1)^2 = 1, but 4√x^2 = 4√1 = 4. On the other hand, √x = √(-1) is undefined, so the equation 4√x^2 = √x is not true for this value of x.

Therefore, the student's claim is not true for all values of x, and it is important to be careful when applying algebraic properties to expressions with multiple terms.

The equivalent expression of log4 ( 1/4x²) is log4(1/4) + log4(x²) ( option D)

The logarithm is the inverse function to exponentiation. For example log2 (8) = 3 and 2³ = 8

The following are math logarithm rules:

loga (MN) = loga M + loga N.

loga (M/N) = loga M - loga N.

IogaMn = n Ioga M.

For example Log5 (5²) = Log5 (5) + Log5 (5)

= 1+1 = 2

this means Log5 ( 5²) = log5 ( 25) = 2

Therefore if loga (MN) = loga M + loga N.,

we can say that,

log4( 1/4x²) can also be written as ;

log4 (1/4) + log4 (x²) .

therefore the equivalent expressions for

log4 ( 1/4x²) is log4 (1/4) + log4 (x²) .

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Answer: #1

Step-by-step explanation:

In situation number one, the equation for the garden's area would be [tex]x^2[/tex] which is nonlinear. The other questions map to linear equations in the form [tex]y = mx + b[/tex]

Answer:

Linear relationship always produces a straight line and are without exponential.

2.the height, y, of a 6-foot tree that grows 0.2 feet per month for x months

3.the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days

4. the total miles, y, traveled by a car going 62 miles per hour in x hours

Step-by-step explanation:

Hope this helps! =D

A circle-based model is highly suitable for the design and construction of roundabouts, which present themselves as practical solutions to tackle traffic-related issues.

Roundabout intersections involve vehicles circulating around a central island in a counterclockwise direction. The circular form guarantees fluidity in traffic movements and significantly reduces the requirement for traffic lights and stops signs while enhancing security.

This model entails using a circle, ascertaining that the diameter corresponds with the width of the roadway, with its center accommodating the location of the island at equidistant distances from all contact points on the circle's periphery, thus ensuring optimal functionality.

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The dimensions of the strongest beam are 27 inches x 13.5 inches.

In general, dimension refers to a measurable extent of a physical quantity, such as length, width, height, depth, or time. These dimensions provide a framework for describing and measuring objects and events in the physical world. In geometry, dimension are refers to the number of coordinates needed to specify a point in a space. In physics, the concept of dimension is used to describe the properties of space and time.

We know that the strength of the beam is directly proportional to its width multiplied with the square of its height. Let's call the width of the beam "w" and the height "h". Then we can write the strength of the beam as:

S = kwh², where "k" is the constant of proportionality.

We want to find the dimensions of the strongest beam, which means we want to find the values of "w" and "h" that will maximize the strength "S". To do this, we need to find the maximum value of the function S = kwh² subject to the constraint that the diameter of the log is 18 inches.

The diameter of the log is equal to the width of the beam plus twice the height of the beam:

d = w + 2h

Since the diameter of the log is 18 inches, we can write:

w + 2h = 18

or

w = 18 - 2h

Substituting this expression for "w" into the equation for the strength of the beam, we get:

S = k × w(18-2h) × h²

Expanding and simplifying this expression, we get:

S = 36kh³ - 2kh⁴

To find the maximum value of S, we take the derivative of S with respect to h and set it equal to zero:

dS/dh = 108kh² - 8kh³ = 0

Simplifying this expression, we get:

h²(108 - 8h) = 0

This equation has two solutions: h = 0 and h = 13.5.

Since a beam with height equal to zero would have zero strength, we reject the solution h = 0. Therefore, the maximum strength is achieved when h = 13.5 inches.

To find the corresponding width, we can use the equation we derived earlier:

w = 18 - 2h = 18 - 27 = -9

Since the width of the beam cannot be negative, we reject this solution as well.

Therefore, the required dimensions of the strongest beam are:

Width = 2h = 2(13.5) = 27 inches

Height = h = 13.5 inches

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The two lines are parallel because they have thesame slope and different y intercept

If two non-vertical lines that are in the same plane has the same slope. However the lines will have different y intercept.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Therefore putting the equations 15x−6y=−5 and 5x−2y=5 into that form.

15x-6y = -5

-6y = -15x-5

y = 5x/2 +5/6

for the second equation,

5x-2y =5

-2y = -5x-5

y = 5x/2 +5/2

therefore , the two lines are parallel because they have the same slope( 5/2) and different y intercept.

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Answer: So, what are you asking?

Step-by-step explanation:

Since this is about the angle theorem and the angle theorem is a theorem that helps us know the relationship between angles. Being a corresponding angle, x = 105°. Hence option A is correct.

A corresponding angle is an angle that occupies the same relative position as another angle elsewhere in the diagram. The corresponding angle in planar geometry occurs when a transverse line crosses his two straight lines. Two angles correspond or relate to each other by being on the same side of the horizontal line. One is the exterior angle (outside the parallel lines) and the other is the interior angle (inside the parallel lines).

You can see that the transversal line intersects two parallel lines DE and XY. From the transversal theorem of angles in mathematics, we know that when a transversal line intersects two parallel lines, the corresponding angles formed are congruent and therefore equal to each other.

In this question we see that one of the angles is 105°. Therefore x° is congruent to it, x = 105°.

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The complete question is as follows:

The incorrect statement regarding the dilation is given as follows:

2. The transformation can be represented by (7x/3, 7y/3).

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, we have that:

Hence the scale factor is given as follows:

k = 3/7.

And the rule is then given as follows:

(3x/7, 3y/7).

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The requried,  3025 bacteria are present after 12 hours.

To find the number of bacteria present after 12 hours, we simply need to substitute t=12 in the given equation:

[tex]n(12) = 500e^{(0.15*12)}[/tex]

[tex]n(12) = 500e^{1.8}[/tex]

n(12) ≈ 3024.82

Rounding this to the nearest whole number, we get:

n(12) ≈ 47,416 ≈ 3025

Therefore, there are approximately 3025 bacteria present after 12 hours.

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Answer:

Step-by-step explanation:

1,2,3,4,6,8,12,16,24,48

hope i helped

Answer:

Therefore, Frank's monthly credit card payment will be $454.31.

Step-by-step explanation:

Monthly payment = (PV * r) / (1 - (1 + r)^-n)

PV = $2,500 + $1,000 + $3,000 + $1,500

= $8,000

r = 0.18 / 12

= 0.015

Monthly payment = ($8,000 * 0.015) / (1 - (1 + 0.015)^-24)

= $454.31