Anson estimated he would need 17 hours to complete is science project. He actually needed 19 1/2 hours. What was his percent error?

The graph of the coordinate points of the vertices of ABCD indicates;

Part A The perimeter of ABCD ia approximately 61.2 units

Part B. The area of ABCD is 199.5 square units

The perimeter of a figure is length of the line that goes round the figure.

A. The perimeter of the polygon is the sum of the length of the sides of the polygon, which is found as follows;

AB = √((21-11)²+(11-(-1))²) ≈ 15.6

BC = √((21-26)²+(11-(-1))²) = 13

CD = √((26-2)²+(-1-(-8))²) = 25

AD = √((2-5)²+(-8-(-1))²) ≈ 7.6

The perimeter of the polygon = 15.6 + 13 + 25 + 7.6 = 61.2

B. Plotting the figure indicates that the figure consists of two triangles, ΔABC and ΔACD

The base length of triangle ΔABC = 26 - 5 = 21

The height of triangle ΔABC = 11 - (-1) = 12

The area of triangle ΔABC = 0.5 × 21 × 12 = 126

Base length of triangle ΔADC = 21

Height of triangle ΔADC = -1 - (-8) = 7

Area of triangle ΔADC = 0.5 × 21 × 7 = 73.5

Area of the composite figure is therefore;

A = 126 + 73.5 = 199.5

The area of the figure is therefore; 199.5 square units

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At 2:20 pm they finish the paint of wall.

Given, Al took 6 hours to paint a wall.

Bob took 4 hours and Chuck took 3 hours for same.

Let the work of painting wall is = LCM(6,4,3) = 12 Units

So in 1 hour Al works = 12/6 = 2 units

In 1 hour Bob works = 12/4 = 3 units

In 1 hour Chuck works = 12/3 = 4 units

In 1 hour, Al and Bob together do = 2+3 = 5 units

In 1 hour, all three together do = 2+3+4 = 9 units

Now from noon i.e. 12 to 1.00 pm Al works alone.

So 2 units of work is done.

From 1 pm to 1.30 pm, Al and Bob work together.

In 30 minutes i.e. ½ hour Al and Bob did = (1/2)*5 = 5/2 units

From 1.30 pm they all three work together.

Now the remaining work is = 12-(2+5/2) = 12-9/2 = 15/2 units

So they complete rest in = (15/2)/9 = 5/6 hours = 50 minutes

Hence the time of finishing the work = 1.30 + 50 minutes = 2.20 pm.

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The sample size necessary for a 90% confidence interval about the mean height of a shrub with a margin of error of 0.5 inches and a population standard deviation of 1.3 inches is 18.

Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.

MOE = z x (SD / √n)

where MOE = margin of error = 0.5 inches

z = found by using a z-score table

SD = sample standard deviation = 1.3 inches

n = sample size

At 90% confidence interval, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.

(100 - 90) / 2 = 5

100 - 5 = 95

Find 0.95 in the z-table to get the value of z.

At p = 0.95, z = 1.647

Plug in the values to the formula and solve for the sample size, n.

MOE = z x (SD / √n)

0.5 = 1.647 x (1.3 / √n)

√n = 1.647(1.3) / 0.5

n = 18.34

n = 18

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Answer: 9/2

Step-by-step explanation: Hope this helps.

The solution is Pack #1

The pack which offers Toby the best deal is Pack #1

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the price per card of each pack be = A

Now , the equation is

a)

Pack #1

The number of cards = 12 cards

The cost per pack = $ 29

The equation is

So , the cost of 1 card = cost per pack / number of cards

                                    = $ 2.416

Therefore , the cost of one card in pack 1 is $ 2.416

b)

Pack #2

The number of cards = 24 cards

The cost per pack = $ 89

The equation is

So , the cost of 1 card = cost per pack / number of cards

                                    = $ 3.708

Therefore , the cost of one card in pack 2 is $ 3.708

c)

Pack #3

The number of cards = 24 cards

The cost per pack = $ 213

The equation is

So , the cost of 1 card = cost per pack / number of cards

                                    = $ 8.875

Therefore , the cost of one card in pack 3 is $ 8.875

And ,

cost of one card in pack 3 is $ 8.875 > cost of one card in pack 2 is $ 3.708 > cost of one card in pack 1 is $ 2.416

Therefore , the cost of one card in pack 1 is $ 2.416 and this is the best deal

Hence , The pack which offers Toby the best deal is Pack #1

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The corresponding sides and angles of both the triangles [pre-image and the image] are congruent

Hence,The corresponding sides and angles of both the triangles [pre-image and the image] are congruent

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Answer:

The slope of y = 5x - 4 is 5.

Notice that the equation, y = 5x - 4, of the line is written in the form y = mx + b. Thus, it is in slope-intercept form. When the equation of a line is in slope-intercept form, we know that the slope of the line is equal to m, the coefficient of x.

In y = 5x - 4, the coefficient of x is 5. Thus, the slope of the line, y = 5x - 4, is 5.

The statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."

What is a regular hexagon?

It is a regular hexagon when the lengths of all the sides and the measures of all the angles are equal. In a regular hexagon, each inside angle is 120 degrees. The characteristics of a regular hexagon. The lengths of each side are equal.

Here, we let

P = it has exactly four sides.

Q = it is not an hexagon.

The negation is like this;

If it is a hexagon, then it does not have exactly four sides.

Thus, we concluded that “it is a hexagon” is your hypothesis (p) and “it has exactly 6 congruent sides” is your conclusion (q).

Hence, the statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."

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Answer:

1. 384 cm square

2. m

3. -3 and 4

4.   1

Answer:

1) B

2) B

3) C

4) A

Step-by-step explanation:

     [tex]\sf \boxed{\text{Area of cube = $6a^2$}}[/tex]

Here, a is the side of the cube.

     Area of cube = 6 * 8 * 8

                            = 384 square cm  

Option B

2) y = mx + c.

Here, m is the slope or gradient and c is the y-intercept.

Option B

3) y = -3x + 4

Compare with y =mx + c,

         where m is the gradient and c is the y-intercept.

m = -3 and  = 4

Option C

4)

[tex]\sf Slope = \dfrac{y_2-y_1}{x_2-x_1}\\\\[/tex]

         [tex]\sf =\dfrac{-3-[-2]}{2-3}\\\\=\dfrac{-3+2}{-1}\\\\=\dfrac{-1}{-1}\\\\=1[/tex]

Option A

The value of j based on the equation d = j + 3.16 if d = 158 is 154.84 meters.

d = j + 3.16

substitute the value of d into the equation

d = j + 3.16

158 = j + 3.16

substract 3.16 from both sides

158 - 3.16 = j

j = 154.84

So therefore, based on the given equation d = j + 3.16, j = 154.84

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The value of j in the equation = 154.84

Distance

Distance is the length of space covered by the car when it moves from one location to another

Given;

Equation d=j+3.16 represent the situation

distance travelled by the car= 3.16meters

d=158

Step 1: Substituting the value of d into the equation d=j+3.16

158= j +3.16

Step 2: Subtract 3.16 from both sides

158-3.16 = j + 3.16 -3.16

Step 3: Add the equation

j= 154.84

Therefore, the value of j in the equation = 154.84

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The equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are (b) 2.3p – 10.1 = 6.49p – 4 and (c) 230p – 1010 = 650p – 400 – p

The equation is given as

2.3p – 10.1 = 6.5p – 4 – 0.01p

Evaluate the like terms on the right-hand side

So, we have the following representation

2.3p – 10.1 = 6.49p – 4

The above equation is indicated in option (b)

Multiply through the equation by 100

So, we have:

100(2.3p – 10.1 = 6.5p – 4 – 0.01p)

Evaluate

230p – 1010 = 650p – 400 – p

The above equation is indicated in option (c)

Hence, the equations with the same solution are (b) and (c)

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Using the elimination method, the solution to the system of linear equations is: x = 4.5 and y = -5.

Solving a system of linear equations by elimination involves eliminating one of the variables, then solve to find the other variable.

Given the equations:

6x + 5y = 2 --> eqn. 1

4x + 2y = 8 --> eqn. 2

Multiply eqn. 1 by 2 and eqn. 2 by 5:

12x + 10y = 4 --> eqn. 3

20x + 10y = 40 --> eqn. 4

Subtract

-8x = -36

x = 4.5

Substitute x = 4.5 into eqn. 2

4(4.5) + 2y = 8

18 + 2y = 8

2y = 8 - 18

2y = -10

y = -5

The solution is: x = 4.5 and y = -5.

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The density of this sand is 1600 kg/m³.

What is the meaning of density?

The amount of something per unit of length, area, or volume: as. : the substance's mass per unit volume. In grams per cubic centimeter, density.

Given that the dimension of a cuboid is length 45 cm, width 30 cm and height 42 cm.

The volume of the cuboid is (45 × 30 × 42) cm³

                                              = 56,700 cm³

                                              = (56,700/100³) m³

                                              = 0.0567 m³

The mass of the sand is 90.72 kg.

The density of the sand is

= mass /volume

=90.72 kg / 0.0567 m³

= 1600 kg/m³

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The table of solutions for the given equation (y = -2x²) include the following:

x                    y_

-2                  -8

-1                   -2

0                   -0

1                    -2

2                   -8

Also, a graph of the solution of this equation (y = -2x²) has been plotted in the image attached below.

In order to determine the valid and true solutions to the given quadratic equation, we would have to substitute the values of contained in the table into the quadratic equations as follows;

At x = -2, the value of point y is as follows:

y = -2x²

y = -2(-2)²

y = -2 × 4

y = -8

At x = -1, the value of point y is as follows:

y = -2x²

y = -2(-1)²

y = -2 × 1

y = -2

At x = 0, the value of point y is as follows:

y = -2x²

y = -2(0)²

y = -2 × 0

y = 0

At x = 1, the value of point y is as follows:

y = -2x²

y = -2(1)²

y = -2 × 1

y = -2

At x = 2, the value of point y is as follows:

y = -2x²

y = -2(2)²

y = -2 × 4

y = -8

In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.

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A stratified sample in this case can be selected as follows:

The rooms are divided by whether they overlook the ocean or the street, and 25 of each are selected.

The five most common classifications for sampling are listed as follows:

In this problem, the groups are given as follows:

50 rooms will be sampled, hence the number that is sampled from each group is given as follows:

50/2 = 25 rooms from each group.

The problem asks to describe a stratified sample for this situation.

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Jimmy will take 24 hours to do the given job alone.

What is the teamwork equation for problem solving?
Problems with teamwork are resolved using this technique. If the first person completes a task in 'A' units of time and a second person completes a task in 'B' units of time, they can complete a task in 'T' units of time together (total).
The teamwork equation can be applied, that is: (1/A) + (1/B) = (1/T)

Given, time taken by Britney to do the job individually = B = 12 hours
Also, time taken by Britney and Jimmy to do the job together = A = 8 hours
Let the time taken by Jimmy to do the job individually = A hours
Thus, using the equation established in the literature above and substituting the given values, we have:
(1/A) + (1/B) = (1/T) ⇒ (1/A) + (1/12) = 1/8 ⇒ 1/A = (1/8) - (1/12)
⇒ 1/A = (3/24) - (2/24) ⇒ 1/A = 1/24 ⇒ A = 24
Thus, Jimmy will take 24 hours to do the given job alone.

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The equation of the line that is parallel to the given line and passes through the point (-3,1) is y - 1 = 3/2(x + 3)

The line is passing through (-2, -4) and (2, 2)

The slope of the line is change in y coordinate with respect to the change in x coordinate of the line
Slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

Slope of the line = (2--4) / (2--2)

= 6/2

= 3/2

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

The point is given that (-3, 1)

The slope of the line = 3/2

because both are parallel lines

Substitute the both values in the equation

y - 1 = 3/2( x - (-3))

y - 1 = 3/2(x + 3)

Hence, the equation of the line that is parallel to the given line and passes through the point (-3,1) is y - 1 = 3/2(x + 3)

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Answer:

y – 1 = 3/2(x + 3)

Step-by-step explanation:

New current if the voltage is increased to 4 volts. = 0.1 A or 100 mA

What is a current simple definition?

amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit.

=> I  ∝  V

=> I  = V/R    

R is a constant

and R  is resistance

When 3 volts are applied to a circuit, 75 milliamperes of current flow through the circuit.

=> 75 x 10⁻³  = 3 /R

=> R = 3 x 10³/75

=> R =  10³/25

=> R = 40

I  = V/R    

V = 4

R = 40

=> I  = 4/40

=> I  = 1/10

=> I = 0.1 A

or 100 mA

new current if the voltage is increased to 4 volts. = 0.1 A or 100 mA

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The inequality that can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget is 26.03d + 0.13m ≤ 350.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, the rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven

Let the number of days be d.

Let the number of miles be m.

The appropriate inequality to illustrate this is 26.03d + 0.13m ≤ 350.

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Based on this if we find the 10% of the population we have:

15000000 × 0.1 = 1500000 And we see that our sample 1600 & lt;

1500000 and we satisfy the 10% condition.

For this case we have the following data given:

n = 1600 represent the sample size select.

dp = 0.43, which,  represent the estimated proportion of high school students that have a part time job

N= 15000000 represent the total population size

And we want to check if the 10% condition is satisfied. So we can use the following definitions for the 10% condition: “We need to have Bernoulli trials must be independent.

If that assumption is not satisfied, it is  still okay to proceed if we have that the sample is smaller than 10% of the population.”"One of the conditions to be checked before using the normal model for sample proportions is, “The sample size, n, must be no larger than 10% of the population.

”So based on this if we find the 10% of the population we have:

15000000 × 0.1 = 1500000

And we see that our sample 1600 & lt;

1500000 and we satisfy the 10% condition.

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Both the pairs of the points are linear.

Here i made the plot for the points and both the pairs of the points shows that the it follows a straight path which means it will be linear i nature.

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The ΔABC placed on top of ΔADE, and having angles ∠ABC and ∠BAC congruent to ∠ADE and ∠DAE in ΔADE is similar to ΔADE. The side CB is 3 indicating that the side ED, which has a length of x = 5

Similar triangles are triangles that have similar (the same shape), such that one triangles has side lengths that are a constant multiple of the other.

Please find attached a possible drawing that is based on the parameters of the question

From the question and the drawing created with MS Word, we have;

Length of AB = 9

Side CB = 3

Segment BD = 6

∠ABC = ∠ADE = 90°

∠ABC ≅ ∠ADE by definition of congruency

From the drawing, ∠BAC ≅ ∠BAC by reflexive property of equality

Triangle ΔBAC is similar to triangle ΔDAE by AA similarity postulate

Segment AD = Segment AB + Segment BD by segment addition postulate

AD = 9 + 6 = 15

The pair of corresponding sides of similar triangles are proportional, therefore;

[tex]\dfrac{\overline{AB}}{\overline{AD}} = \dfrac{\overline{BC}}{\overline{DE}}[/tex]

Which gives;

[tex]\dfrac{9}{15} = \dfrac{3}{x}[/tex]

9 × x = 15 × 3 = 45

x = 45 ÷ 9 = 5

The  length of side ED, x = 5

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Answer: 12

Step-by-step explanation: Because 9 x 2 is 18, and 7 x 2 is 14, we want to multiply 6 by 2. This gives us the answer 12.

9 x 2 = 18

7 x 2 = 14

6 x 2 = 12

Answer:

51.3

Step-by-step explanation:

Since it's telling us that (x=7) then that means 8.2x is going to be multiplied

8.2(7) or 8.2 x 7.

Then you end up getting an answer of 57.4

But you are not finished yet and need to subtract 6.1

so 57.4 - 6.1 = 51.3

And your result will be (51.3)

I hope this helps you understand this problem!

Answer:

(f+g)(x) = x - 7

Step-by-step explanation:

(f+g)(x) tells you to add the functions together. It means

f(x) + g(x)

= -3x - 5 + 4x - 2

combine like terms.

= 4x-3x - 5 - 2

= x - 5 - 2

simplify.

= x - 7

(f+g)(x) means

f(x) + g(x)

= x - 7

(y + 7) = -2/3(x - 1) is the point-slope form of the equation of a line passing through (1, -7) and having a slope of -2/3.

The query revealed information include

a slope of -2/3

point (1, -7)

Those functions with exponents of 1 are known as linear functions.

The form represents the equation of a line in point-slope form.

(y - y₁) = m (x - x₁)

Variables in the y direction are described by  (y and y₁).

variables in the x direction are described by (x and x₁).

m = slope

substituting into the slope and point (1, -7) equation gives

()y + 7) = -2/3 (x - 1)

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Answer:

x = 12

Step-by-step explanation: You start off with this

3x + 2

Then since AC is 38 you make it

3x+2=38

Then you do -2 getting rid of the 2 and doing 38 - 2 which is 36

you now have:

3x = 36

then you do 3x divided by 3 on both sides

you do 36 divided by 3 then you get

x = 12

He can fill a total of 25 bags.

The values are,

50 blueberry scones total.

75 cranberry scones total.

For each bag to have an equal quantity of blueberry scones & cranberry scones, he must determine the maximum amount of bags he can fill.

H.C.F. of 50 & 75 is thus 25.

As a result, he can fill 25 bags.

There would be scones with blueberries in each bag of

50 ÷ 25 = 2

There would be cranberry scones for each bag, for a total of

75 ÷ 25 = 3

As a result, he may fill a total of 25 bags.

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Answer:

X-2=1

X-3=2

X+1=2

X+5=6