your aunt and uncle have been visiting at your home. five minutes after they drive away, you realize that they forgot their luggage. you happen to know that they drive slowly, so you get in your car and drive to catch up with them. your average speed is 10 miles an hour faster that their average speed, and you catch up with them in 25 minutes. how fast did you drive?

Bob lifts a 15N rock through a distance of 1.7m, 25.5 J work does Bob do

An item should be converted to energy before being moved. The use of force is one way to transfer energy. The amount of energy used by a force to move an item is referred to as the work done.

The amount of the displacement and the component of the applied force of the object in the displacement direction is the work done by a force. Pushing a block with force "F" causes the body to move more quickly, meaning that work has been completed.

Work done (W) = F × s

Where, F = force

s = displacement

Now putting the values, we get-

or, W = 15 N × 1.7 m

or, W = 25.5 N-m or Joule

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The value of x is 91/9.

What is the value of X triangle?

The two angles' combined angles are subtracted from 180 degrees. A triangle's total angles are always equal to 180 degrees. When you remove the total of the two angles from 180 degrees, note the difference you discovered. This is what X is worth. The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.

(9x+1)+ 88

Remove parentheses: (a)=a

9 x+1+88=180

Add the numbers: 1+88=89

9 x+89=180

Move 89 to the right side

9 x=91

Divide both sides by 9

[tex]\frac{9 x}{9}=\frac{91}{9}$$[/tex]

Simplify

[tex]x=\frac{91}{9}$$[/tex]

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Answer:

  x = 5

Step-by-step explanation:

You want the value of x where one of the base angles in an isosceles triangle is marked (9x+1)° and the vertex angle is marked 88°.

Each base angle of an isosceles triangle is the complement of half the vertex angle. This one is ...

  9x +1 = 90 -(88/2)

  9x = 45 . . . . . . . . . . subtract 1

  x = 5 . . . . . . . . . divide by 5

The area of the circle would be 36π.

What is the area of a circle?

If the circle has a radius then the area of the circle can be computed by using the formula

area = π * radius²

The perimeter of the square = 24

4 * side = 24

Side of a square = 24/4 = 6

Side of a square = radius of the circle

Substituting the radius of 6 into this formula gives:

area = π * 6²

Which simplifies to:

area = π * 36

Hence, the area of the circle would be 36π.

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Answer:

The measure of arc FG is 148°

Step-by-step explanation:

Since the measure of an arc is equal to the measure of the central angle that subtends it, and the measure of central angle CG is 148°, the measure of arc FG is 148°. This is because the arc FG is subtended by the central angle CG.

The probability that the next person who leaves the lecture will have gray hair is 45/163 or 0.2760.

What is Probability?

Probability is the ratio of favorable outcomes to all other potential outcomes of an event. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

To calculate the likelihood that the next person to leave the lecture will have grey hair, one must first make an assumption about the distribution of hair colors among those in attendance. The data of the distribution of hair colors of people in the lecture are assumed below:

Blonde  Red  Brown  Black   Gray  Total

24           32     29        33        45     163

The Probability of the number of people with grey hair to the total number of students in the class is used to calculate the likelihood that the next person to leave the lecture will have grey hair.

P(Gray) =45÷163 =0.2760

So therefore, the probability is 45/163 or 0.2760.

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Answer:

16

Step-by-step explanation:

36 t^2 comes from   6t

 so we have

   (6t -    )^2       the middle term will be represented by

                               2 x m x 6t   =  -48 t

                                    so m = -4

(6t-4)^2      would result in ' * '  = +16

Answer:

b

Step-by-step explanation:

i know

The solution is Option B.

The translation of triangle MNP along T < 2 , -9 > is

M’(−1, −2), N’(2, −5), P’(4, −3)

What is Translation?

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

The notation for translation is T(h, k) where T is the translation, h is the change in the x-axis, and k is the change in the y-axis

Given data ,

Let the translated triangle be represented as ΔM'N'P'

Now , the translation rule is T < 2 , -9 >

Let the coordinates of the triangle ΔMNP be

The coordinates of M = M ( -3 , 7 )

The coordinates of N = N ( 0 , 4 )

The coordinates of P = P ( 2 , 6 )

Now , applying the translation rule of T < 2 , -9 > for the triangle MNP , we get

The coordinates of M' = M' ( -3 + 2 , 7 - 9 )

The coordinates of M' = M' ( -1 , -2 )

The coordinates of N' = N' ( 0 + 2 , 4 - 9 )

The coordinates of N' = N' ( 2 , -5 )

The coordinates of P' = P' ( 2 + 2 , 6 - 9 )

The coordinates of P' = P' ( 4 , -3 )

Hence , the coordinates of triangle M'N'P' is M’(−1, −2), N’(2, −5), P’(4, −3)

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Answer:

D

Step-by-step explanation:

base area = (6 · 4)/2 = 24/2 = 12 cm²

half base length = 6 : 2 = 3 cm

leg = [tex]\sqrt{3^2+4^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex] cm

perimeter = (5·2) + 6 = 10 + 6 = 16 cm

lateral area = 16 · 20 = 320 cm²

surface area = (2 · 12) + 320 = 24 + 320 = 344 cm²

The scale factor, if The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards, is 1.8.

The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).

Given:

The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards,

Calculate the scale factor as shown below,

Scale factor = Original dimension / new dimension

Scale factor = (4 × 6) / (3 × 4.5)

Scale factor = 1.8

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Answer:

See below

Step-by-step explanation:

If the figures were similar the corresponding sides would be proportional.

[tex]\frac{10}{12}[/tex] = [tex]\frac{8}{10}[/tex]  This statement would be true if the sides were proportional, but it is not true.  Cross multiply.

10(10) ≠ (8)(12)

100≠96

Answer: 0.85

Step-by-step explanation:

The required answer for long division for the decimal division of 6 divided by 7.02 is 0.8547 by rounded to four decimal places.

To perform long division for the decimal division of 6 divided by 7.02, follow these steps:

Step 1: Set up the division problem:

_______

7.02 | 6.00

Step 2: Place the decimal point directly above the division bar in the quotient:

0.

Step 3: Divide the first digit of the dividend (6) by the divisor (7.02). The result is 0.8547 (rounded to four decimal places).

Step 4: Multiply the divisor (7.02) by the quotient digit (0.8547) and write the result below the dividend, aligning the decimal points:

7.02

- 6.03

-----

0.99

Step 5: Subtract the result from the previous step from the dividend, and bring down the next digit (if any):

0.99

- 0.99

-----

0.00

Step 6: Since there are no more digits to bring down and the result is zero, we can conclude the division.

Therefore, the long division for the decimal division of 6 divided by 7.02 is 0.8547(rounded to four decimal places).

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The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

It is a symbol standing in for an unknown numerical value in an equation.

The general form of a one variable linear equation is given by

ax+b = 0

where a and b are two integers, and x is the variable

The one-variable linear equation has only one solution.

Hence, the equation in the form ax+b = 0 is known as a one-variable linear equation.

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Number of years since 2003 x=5 years and number of jobs in thousand y=288.

In this method two equation are added or subtracted depending on the sign of variables. After adding or subtracting we create a new equation with one variable. Therefore, we easily get the solution.

while using addition method of algebra, we either add or subtract two equations to obtain a new equation by eliminating one variable. Hence, this method is called elimination method.

Given equation, 7.4x-y= -254

                         12.4x-y = -231

          using addition method

                -5x= -23

                  after solving x=4.6

            x= 5 (nearest whole number)

                     y = 288.04

                y =288

   hence, number of years 5

 number of jobs in thousand =288

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its A

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Answer:

1,368

Step-by-step explanation:

4.56x36=164.16

164.16/0.12=1368

Answer:

1368

Step-by-step explanation:

1368

The solution of the expression would be 2(-2n + 3).

Expression 1 :

- 4n + 6

= -[tex]2^{2}[/tex] . n + 2 x 3

= 2 ( - [tex]\frac{2 * n^{2} }{2}[/tex] + [tex]\frac{2 x 3}{2}[/tex] )

= 2 ( - ([tex]2^{2-1}[/tex] * n ) + 3 )

= 2 ( - (2n) + 3 )

= 2 ( - 2n + 3 )

Expression 2 :

- 4n + 6

Rewrite 4 as 2 . 2

Rewrite 6 as 2 . 3

= - 2 . 2n + 3 . 3

= 2 ( - 2n + 3 )

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The equation of each of the lines are:

1. y = 1/3x - 1

2. y = 3x + 1

3. y = 2/3x - 1

4. y = 3x

5. y = -2/3x - 1

6. y = 1/3x - 1

7. y = -3x + 2

To write the equation of a line, find the following:

1. Slope (m) = rise/run = 1/3

y-intercept (b) = -1.

To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:

y = 1/3x - 1

2. Slope (m) = rise/run = 3/1 = 3

y-intercept (b) = 1.

To write the equation, substitute m = 3 and b = 1 into y = mx + b:

y = 3x + 1

3. Slope (m) = rise/run = 2/3

y-intercept (b) = -1.

To write the equation, substitute m = 2/3 and b = -1 into y = mx + b:

y = 2/3x - 1

4. Slope (m) = rise/run = 3/1 = 3

y-intercept (b) = 0.

To write the equation, substitute m = 3 and b = 0 into y = mx + b:

y = 3x

5. Slope (m) = rise/run = -2/3

y-intercept (b) = -1.

To write the equation, substitute m = -2/3 and b = -1 into y = mx + b:

y = -2/3x - 1

6. Slope (m) = rise/run = 1/3

y-intercept (b) = -1.

To write the equation, substitute m = 1/3 and b = -1 into y = mx + b:

y = 1/3x - 1

7. Slope (m) = rise/run = -3/1 = -3.

y-intercept (b) = 2.

To write the equation, substitute m = -3 and b = 2 into y = mx + b:

y = -3x + 2

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The probability that a randomly chosen person from the united states can donate blood to maria is 0.50

considering blood to be of types A,B,AB and O

further all blood groups are equi probable

Probability of blood type A  = probability of blood type B = probability of blood type AB = probability of blood type O = x

Probability of blood type A  + probability of blood type B + probability of blood type AB + probability of blood type O = 1

⇒ 4x = 1

⇒ x = 1/4

Probability that a random person will have blood of type B or O = x+x

= 1/4 + 1/4

= 1/2

= 0.50

Hence we get the required answer.

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Answer: C: We are 90% confident that the true proportion of times the die would land on the number 3 is between 0.468 and 0.632. Since this is much greater than 1 out of 6, the die appears to be unfair.

Step-by-step explanation:

I took the test, and it was correct. :)

The solution is, C: We are 90% confident that the true proportion of times the die would land on the number 3 is between 0.468 and 0.632. Since this is much greater than 1 out of 6, the die appears to be unfair.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

Jonathan rolled a regular six-sides die 100 times and noticed that it landed on the number 3 exactly 55 times.

so, we get,

Jonathan conclude about the die is,

C: We are 90% confident that the true proportion of times the die would land on the number 3 is between 0.468 and 0.632. Since this is much greater than 1 out of 6, the die appears to be unfair.

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The standard error of the mean is defined as the standard deviation divided by the square root of the number of items

The information provided here is that 14 standard deviations are based on the original population of 200.

No information was provided on the standard deviation of the 49-item sample.

Assuming the sample standard deviation is the same as the original population,

SEM = 14/√49 = 14/7 = 2

the standard error of the mean is 2

What is the mean of mathematics?

The mean (also the arithmetic mean, unlike the geometric mean) of a dataset is the sum of all values ​​divided by the total number of values. This is the most commonly used measure of central tendency and is often called 'mean'.

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Answer:

1155.52cm²

Step-by-step explanation:

A cylinder's volume is π r² h, and its surface area is 2π r h + 2πr²

radius(r) = 8cm

π = 3.14

height(h) = 15

2πrh + 2πr²

=2πr(h + r)

= 2 × 3.14 × 8 ( 15 + 8)

= 50.24(23)

= 1155.52cm²

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Answer:

Step-by-step explanation:

(a)Given:

Principal Amount=$1500

Time = 3 years

Rate of Interest = 8% per annum

Find:

Simple Interest=?

According to the formula of  simple interest

Simple Interest=Principal x Time x Rate of Interest

i.e., SI=PRT

      SI= 1500 X 3 X 8/100

      SI= $360

Therefore, the simple interest for the principal amount of the loan $1500 in 3 years at a rate of 8% per annum will be $360.

(b) According to the formula:

Total Amount= Principal Amount + Simple Interest

i.e., Total Amount = $1500+$360

      Total Amount = $1860

Therefore, the loan amount the borrower will pay the bank is $1860.

The number will be 6.00

What do you mean by an important number?

An important number is a number that has a specific significance or use in a particular situation. For example, in mathematics, some important numbers include pi, the square root of two, and the golden ratio. In finance, important numbers might include the interest rate on a loan, the exchange rate between two currencies, or the daily closing price of a stock. In politics, important numbers may include the population of a state or country, the percentage of the population that is registered to vote, or the number of seats a particular political party holds in a legislature.

Given that:

6.27 should be reduce to 1 significant figure

So as we can see before 6 we have number 2

According to rule for rounding 6 will remain 6

Hence the number will be 6.00.

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The inequality is [tex]115\leq x\leq 495[/tex]

What is inequality?

A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">", "<", "≥". Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

Given [tex]60\leq 0.5x+2.5\leq 250[/tex]

splitting the equation:

[tex]60\leq 0.5x +2.5[/tex] and [tex]0.5x +2.5\leq 250[/tex]

[tex]60-2.5\leq 0.5x\\57.5\leq 0.5x\\115\leq x\\x\geq 115[/tex]

also

[tex]0.5x +2.5\leq 250\\0.5x\leq 247.5\\x\leq 495[/tex]

therefore the equation is

[tex]115\leq x\leq 495[/tex]

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At 95% confidence interval for a sample of size 100 where p = 0.15 , the margin of error is 0.0700  .

In the question ,

it is given that ,

the sample size is = 100 and

the value of p is ⇒ 0.15  .

we have to find the "margin of error"(E) for the 95% confidence interval ,

we know that the z value for the 95% confidence interval is = 1.96

the formula for margin of error is :

E = Z×√p(1-p)/n .

Substituting the values of z , p and n ,

we get ,

E = 1.96×√0.15(1-0.15)/100

= 1.96×√0.15(0.85)/100

= 1.96×√0.1275/100

= 1.96×√0.001275

= 1.96×0.03570

Simplifying further ,

we get ,

= 0.06995899

rounding to the four decimal places ,

≈ 0.0700

Therefore , the required margin of error is 0.0700  .

The given question is incomplete , the complete question is

At 95% confidence,  for a sample of size 100 where p = 0.15 . What is the Margin Of Error ? if required, round your answer to four decimal places.

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Answer:

72+20sqrt3

Step-by-step explanation:

check the attached file

Answer:

Fraction: 4 1/4 = 17/4

Decimal: 17/4 = 4.25

Step-by-step explanation:

Answer:

Bellow

Step-by-step explanation:

QS =√c2 - b2

= √202 - 15.0941916044552

= √172.16537980799

= 13.12118