When the car reaches point (A), it has a speed of 25 m/s. If the breaks are applied, its speed is reduced by at= (-1/4t^1/2)m/s^2. Determine the magnitude of acceleration of the car just before it reaches point C

The formula for the volume of a cone, V = (1/3)·π·r²·h, indicates that doubling the radius, quadruples the volume while doubling the height doubles the volume. Therefore;

A cone is a three dimensional figure formed by lines that extend between a point and the circumference of the circular base, where the point is located on the a line perpendicular to and passing through the center of the circular base.

The formula for the volume of a cone is; V = (1/3) × π × r² × h

Where;

V = The volume of the cone

r = The radius of the cone

h = The height of the cone

Therefore;

When the radius is doubled, we get;

V₁ = (1/3) × π × (2·r)² × h = (1/3) × π × 4 × r² × h = 4 × (1/3) × π × r² × h

When the radius of the cone is doubled, the volume of the cone increases 4 times the initial volume

When the height of the cone is doubled, we get;

V₂ = (1/3) × π × r² × 2·h = 2 × (1/3) × π × r² × h = 2·V

When the height of the cone is doubled, the volume of the cone is doubled.

Therefore, doubling the radius of the cone which increases the volume to four times the initial volume has the greater effect on the volume of the cone than doubling the height which doubles the volume of the cone.

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The number of years for the speculation to reach from £785 to £1,105.58 will be 23 years.

Let 'A' is the amount, 'P' is the initial amount, 'r' is the rate of interest, and 'n' is the number of years.

Then the compound interest is written as,

A = P(1 + r)ⁿ

Then the equation is given as,

£1,105.58 = £785 × (1 + 0.015)ⁿ

1.40838 = (1.015)ⁿ

n log 1.015 = log 1.40838

n = 23 years

The number of years for the speculation to reach from £785 to £1,105.58 will be 23 years.

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Answer:240

Step-by-step explanation:

8x30=240

Answer:

240

Step-by-step explanation:

30x2x8 so that is your answer

The measure of the complement of angle is 45 degrees.

Let's call the measure of the angle "x". The complement of the angle is defined as 90 degrees minus the measure of the angle, so the complement of the angle is 90 - x.

If the measure of the angle is less than its complement, then we can write the following inequality:

x < 90 - x

Now we can isolate x by subtracting x from both sides:

0 < 90 - 2x

And then dividing both sides by -2:

0 > -45 + x

Finally, subtracting x from both sides:

-x > -45

So, we have:

x < 45

So, the complement of the angle is 90 - x, which is greater than 90 - 45 = 45 degrees.

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Answer:

60 square inches

Step-by-step explanation:

Measure of length in scale drawing = Measure of actual length

                                             6 inches = 24 feet

                                               ∴ 1 inch = [tex]\frac{24}{6}[/tex] feet

∴Unit multiplier applied:

                  ∴1 inch in scale drawing = 4 feet of actual measurement

         
Measure of width in scale drawing = Measure of actual width

                                             x inches = 40 feet

                                           ∴ x inches = (40 feet) × ([tex]\frac{1 inch}{4 feet}[/tex])

Measure of width in scale drawing   = 10 inches

Area of rectangular floor in the scale drawing = (Length) × (Width)

                                                                                = (6 inches) × (10 inches)

                                                                                = 60 square inches                                          

Answer: To find the critical value for a 80.4% confidence interval for a normal approximation of a binomial distribution, we need to find the z-score that corresponds to the 80.4% confidence level. We can do this using a standard normal table or using a z-score calculator.

Using a z-score calculator, we can find that the z-score corresponding to 80.4% confidence level is approximately 0.931. This means that 80.4% of the data falls within 0.931 standard deviations of the mean.

So, the critical value that corresponds to a confidence level of 80.4% is approximately 0.931.

Step-by-step explanation:

The possible number of equal sized group is given by set N = 5 groups

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the total number of pencils be represented as n = 5 dozen = 60 pencils

The number of equal groups should be at least 3 and less than 11

So , the groups are represented by sets A , B , C , D , E

where the value of set A is

Set A = { 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 }

The set A contains 6 pencils of 10 groups

Set B = { 10 , 10 , 10 , 10 , 10 , 10 }

The set B contains 10 pencils of 6 groups

Set C = { 12 , 12 , 12 , 12 , 12 }

The set C contains 12 pencils of 5 groups

Set D = { 15 , 15 , 15 , 15 }

The set D contains 15 pencils of 4 groups

Set E = { 20 , 20 , 20 }

The set E contains 20 pencils of 3 groups

Therefore , the total number of sets N = 5 sets

Hence , the sets are solved

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The subtraction problem represented by the fraction model is given above.

Given is a figure as shown in the image.

We can write the fractional problem as -

" A rectangle is divided into eight equal rectangles. Smith colored six of these rectangles. How much percentage fraction of the image is colored."

Therefore, the subtraction problem represented by the fraction model is given above.

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We can infer from the foregoing description that the typical annual cost of living for a retiree is (A) around $50,000.

One who has retired is known as a retiree.

Many seniors underestimate their retirement income by not accounting for inflation.

Wages, a gauge of the income that retirees must replace, will be the basis for benefits.

One who has retired is known as a retiree.

According to the U.S. Bureau of Labor Statistics most recent Consumer Expenditure Survey, the typical retiree household—one that is headed by a person 65 or older—spends $50,220 annually.

Comparatively, the average yearly household expenditure is $63,036.

So, from the above description, we can state that the average cost of living for a retiree per year is (A) around $50,000.

Therefore, we can infer from the foregoing description that the typical annual cost of living for a retiree is (A) around $50,000.

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Complete question:

What is the average cost of living for a retiree per year?

A. around $50,000

B. around $60,000

C. around $70,000

D. around $80,000

From the calculations, the best loan option is

A. 3-year loan with a 7% annual simple interest rate

To determine which loan option would allow the customer to pay the least amount of interest, we need to compare the amount of interest charged by each loan option.

For the 3-year loan with a 7% annual simple interest rate,

the interest charged would be $15,000 x 7% x 3 = $2,550.

For the 4-year loan with a 5% annual simple interest rate,

the interest charged would be $15,000 x 5% x 4 = $3,000.

For the 5-year loan with a 4.5% annual simple interest rate,

the interest charged would be $15,000 x 4.5% x 5 = $3,375.

For the 6-year loan with a 3.7% annual simple interest rate,

the interest charged would be $15,000 x 3.7% x 6 = $3,870.

From the calculations, it is clear that the 3-year loan with a 7% annual simple interest rate would result in the least amount of interest charged, with $2,550.

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The probability of hitting the bullseye if the dart is thrown 40 times is approx. 3 times.

The quantity of occurrences of an event is referred to as its frequency. The concept of relative frequency is experimental rather than theoretical. It is experimental, therefore if we repeat the trials, we can get different relative frequencies. To determine the frequency, we must first:

Number of occurrences for the entire population

Frequency count for a particular demographic segment

If we know the two frequencies mentioned above, we can use the following formula to get the relative frequency probability. A subgroup's formula is as follows:

Subgroup Count / Overall Count: Relative Frequency

Given that, a player hits the bullseye with a dart 8% of the time.

The probability of hitting the dart is = 8/100.

Now, the probability of hitting the bullseye if the dart is thrown 40 times is:

p = 40 (8/100) = 3.2 times = 3 times.

Hence, the probability of hitting the bullseye if the dart is thrown 40 times is approx. 3 times.

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The solution is Option B.

The equation of line is y = x + 8 , where the slope is m = 1

Yolanda had eight books and bought one new book each week

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P (

Let the second point be Q (

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we getWhat is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 8 )

Let the second point be Q ( 1 , 9 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 9 - 8 ) / ( 1 - 0 )

Slope m = 1

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 8 = 1 ( x - 0 )

On simplifying the equation , we get

y - 8 = x

Adding 8 on both sides of the equation , we get

y = x + 8

Hence , the equation of line is y = x + 8

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Answer: B

Step-by-step explanation:

Given:-

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

The volume of the cylinder is 90π in³

[tex] \: [/tex]

hope it helps!:)

Answer:

67,914

Step-by-step explanation:

Let x = total employees.

18.7% of x = 12,700

0.187x = 12,700

x = [tex]\frac{12700}{0.187}[/tex] = 67914.438 → 67,914

A congruent triangles worksheet is a type of educational resource that provides practice problems and exercises for students to work on to help them understand and apply the concept of congruent triangles.

The worksheet typically includes a variety of problems, such as identifying pairs of congruent triangles, determining congruent sides and angles, and applying congruence postulates or theorems to solve problems. The problems may involve using the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), or hypotenuse-leg (HL) congruence criteria.

Congruent triangles are triangles that have the same size and shape. In other words, they are identical in every way except for their position and orientation in space. Understanding congruent triangles is important in geometry, as it can help students to solve problems involving triangles, as well as more complex geometric figures.

Worksheets are a useful tool for students to practice and reinforce their understanding of congruent triangles, and can be used in the classroom or as homework assignments.

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The total surplus at the equilibrium point is: $200,000

This is the maximum total surplus that can be achieved in the market for the digital camera.

To compute the maximum total surplus, we need to find the equilibrium quantity and price in the market for the digital camera, and then calculate the consumer and producer surplus at that point.

First, we need to set the demand and supply functions equal to each other to find the equilibrium quantity:

50 - 2P = 2P - 10

4P = 60

P = 15

Substituting this equilibrium price into either the demand or supply function, we can find the equilibrium quantity:

Q = 50 - 2(15) = 20

So the equilibrium price is $15, and the equilibrium quantity is 20,000 digital cameras.

Next, we can calculate the consumer and producer surplus at the equilibrium point. Consumer surplus is the difference between the maximum price a consumer is willing to pay for a good and the market price, summed over all consumers in the market. Producer surplus is the difference between the market price and the minimum price a producer is willing to accept for a good, summed over all producers in the market.

The demand function gives us the maximum price consumers are willing to pay for each quantity of digital cameras:

P = 25 - 0.5Q

So at the equilibrium quantity of 20,000 digital cameras, the maximum price consumers are willing to pay is:

P = 25 - 0.5(20) = 15

This is exactly the same as the market price, so there is no consumer surplus at the equilibrium point.

The supply function gives us the minimum price producers are willing to accept for each quantity of digital cameras:

P = 0.5Q - 5

So at the equilibrium quantity of 20,000 digital cameras, the minimum price producers are willing to accept is:

P = 0.5(20) - 5 = 5

The market price is $15, so the producer surplus is:

(15 - 5) * 20 = $200,000

Therefore, the total surplus at the equilibrium point is:

$200,000

This is the maximum total surplus that can be achieved in the market for the digital camera.

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Answer:

Y will be 65°

Step-by-step explanation:

Since angle S is 65°, angle Y will also be 65°

What are similar shape ?

Similar shapes are shapes that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Since quadrilateral QRST is similar to quadrilateral WXYZ, then angle Q = angle W , angle R = angle X and angle S = angle Y and angle T = angle Z.

Since angle S is 65° from the diagram shown, angle will be measured as 65°.

Answer:

The decimal 6.25 would be 6 25/100 as a mixed number. In lowest terms, it would be 6 1/4.

Answer:

Height = 16

Step-by-step explanation:

Area = (Base * Height) / 2

Height = (2 * Area) / Base

Height = (2 * 10) / (5/4)

Height = (2 * 10) / (5/4) * (4/4)

Height = (2 * 10 * 4) / 5

Height = (80 / 5)

Height = 16

The weight of the other children are 37.5 kg and 31.25 kg

The weight of the three children are 6:5:4

6x, 5x and 4x

The weight of the smallest child is 4x

4x= 25

x= 6.25

The weight of the other two children can be calculated as follows

6(6.25)

= 37.5

5(6.25)

= 31.25

Hence the weight of the other two children are 37.5 kg and 31.25 kg

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The line plot which can be used to represent the teachers record of how many miles each student ran during gym class is attached.

A Line plot can be defined as a graphical representation of data as points or check marks above a number line, showing the frequency of each value along a line. It is used to analyze data

Given Data:

3/4, 1/4, 1/2, 3/4, 1/2, 1/2, 1/4, 3/4, 1/4, 1/2, 1/4, 3/4

From the given Data, the frequency of

1/4 = 5

1/2 = 4

3/4 = 3

Therefore, the line plot is attached as a diagram.

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on solving the provided question we can say that length of the major arc angle  is [tex](29/6)\pi or 4.83\pi[/tex].

In Euclidean geometry, an angle is a shape that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to form an angle in the plane where they are positioned. When two planes collide, an angle is also created. These are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays or lines that share a termination. The origin of the English term "angle" is the Latin word "angulus," which meaning "horn." The vertex is the point where the two rays, also known as the sides of the angle, converge.

circle with center K has an arc with a radius = 3 yards

angle subtended at the center = 70 degrees.

Angle  = 360 - 70  = 290

Length of arc = (∅/360) x 2πr

Angle   = 290,

r = 3,

Length of arc

[tex]= (290/360) X 2 X\pi X 3\\= (29/36) X 6\pi \\= (29 X \pi X 6)/36\\= 29\pi /6[/tex]

= (29/6)π or 4.83π

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Stuart has enough money to buy 4 kg of onions.

we must first  find the cost of 4 kg of onions.

We know that 2.5 kg of onions and 2 kg of carrots cost £2.36.

The cost of 15 2.5 kg of onions is 15 × 2.5 = 37.5 kg of onions.

The cost of 1 kg of onions is 2.36 ÷ 37.5 = 0.06293 = £0.063.

3 kg of carrots cost £1.74. and we need to find how much 1kg of carrots cost.

Therefore, the cost of 1 kg of carrots is 1.74 ÷ 3 = 0.58 = £0.58.

Now we can use the above information to find the cost of 4 kg of onions:

The cost of 1 kg of onions is £0.063.

Hence, the cost of 4 kg of onions is 4 × 0.063 = £0.252.

We then can say since Stuart has £2, and we have found that the cost of 4 kg of onions is £0.252. Stuart has enough money to buy 4 kg of onions.

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Answer:

d. 6

Step-by-step explanation:

Given, a-5> -1

Both sides add 5, and we get

a > 4

So a is 6.

The estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is 0.45 which is denoted as option C.

This is referred to as a number that indicates how likely the event is to occur.

Probability for drawing at least 5 beads before she picks a grey bead from her collection

= 1-Probability for drawing at least one grey bead in the first 5 draws.

No of grey beads drawn in first 5 trials = (5, 80/80+160+240)

                                                                 = (5, 1/6)

Probability for drawing at least one grey bead in the first 5 draws.

=1 - Prob of no grey

Required probability = P(X=0 in first 5 draws) = (1/6)⁵ = 0.4018 and th nearest value is therefore 0.45.

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answer :

9(2p+1)

steps

(10p+10)+(8p−1)

18p+9

9(2p+1)

chatgpt

The angles in the quadrilateral are as follows;

x = 77°

y = 103 degrees

z = 52 degrees

The diagram above is a quadrilateral. The angles x, y and z can be found as follows:

x + 103 = 180(sum of angles on a straight line)

x = 180 - 103

x = 77 degrees

Therefore,

y = 103 degree(vertically opposite angles)

Vertically opposite angles are congruent.

The sum of angles in a triangle is 180 degrees.

Therefore,

103 + 25 + z = 180

z = 180 - 128

z = 52 degrees.

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Total No. of cards in a deck = 52

Total no. of suits = 4

Total number of cards in one suit = [tex]\frac{52}{4} \\[/tex] = 13

Ways of selecting combinations of 4 from 13 hearts (combination) = [tex]\frac{13!}{9! 4!}[/tex]

= 715

Ways of selecting combinations of 3 from 13 spades (combination) = [tex]\frac{13!}{10! 3!}[/tex]

= 286

Combining the two independent choices, there are  715×286=204490

ways to select a seven-card hand with 4 hearts and 3 spades.

Ways of selecting 7 cards from 52 cards = [tex]\frac{52!}{7! 45!}[/tex] = 133784560

Probability of getting 4 hearts and 3 spades on drwaing 7 cards from the deck = [tex]\frac{204490}{133784560}[/tex] = 0.0015285 (approx.)

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