Consider the function:h(x) = -5x3 + 3x2 + 4x + 4Step 2 of 2 . Find the value of h(3).

Answer:

f(-5) = 30

f(0) = 5

f(3) = 14

Step-by-step explanation:

=> f(x) = x²+5

for , f(-5) = (-5)² +5

=> 25 +5

=> 30

for , f(0) = (0)² +5

=> 5

for , f(3) = (3)² + 5

=> 9 + 5

=> 14

Answer:

p<24

Step-by-step explanation:

move all terms not containg p to the right side of the inequality.

ineqyality form:p<24

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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Cost of a bottle of juice is $ 1.62

Equation for determining the cost of juice is 1.56 + 20x = 33.96

Given,

The cost of a bag of chips = $ 1.56

Number of juice bottles bought by Sarah = 20 pack

Total cost before tax = $ 33.96

Cost of one bottle of juice = x

We have to find x:

Then the equation will be:

1.56 + 20x = 33.96

Add -1.56 to both sides:

1.56 + 20x - 1.56 = 33.96 - 1.56

We get,

20x = 32.4

Now find x,

x = 32.4 / 20

Then,

x = 1.62

That is, the equation for finding the cost of a bottle of juice is 1.56 + 20x = 33.96.

The cost of one bottle of juice is $1,62

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We will find the quotient and remainder as follows:

The quotient is 749 and the remainder is 2.

The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.

In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:

Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)

Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)

Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8

Total sugar consumed = 22/8 + 1/4

Total sugar consumed = (22 + 2)/8

Total sugar consumed = 24/8

Total sugar consumed = 3 units of sugar.

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The equation that represents the number of marbles  Marcus has is 28 + m = 47. Option C is the correct option.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Typically, it has a single variable and an equal sign. In essence, equations are questions and attempts to systematically find the answers to these questions have been the driving forces behind the development of mathematics.

Given that  Bobbie has 28 marbles.

Assume that Sam has m marbles.

The total number of marble that both have is (28 + m).

Again they have 47 marbles in all.

According to the question,

28 + m = 47

Subtract 28 from both sides:

m = 47 - 28

m = 19

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Answer:

POSITIVE

Step-by-step explanation:

Because the product of 2 negative numbers is a positive number

Answer:

240 cm³

Step-by-step explanation:

Volume of prism= base area ×height

The base is a rectangle here, and its area has the formula of length ×breadth.

Given

length of base= 10 cm

breadth of base= 6 cm

height of prism= 4 cm

Base area

= 10(6)

= 60 cm²

Volume of prism

= 60(4)

= 240 cm³

Answer:

240 cm³

Step-by-step explanation:

Volume of a rectangular prism: l*w*h

V = l*w*h  <== substitute the numbers (above) for the variables

V = 10*6*4

V = 60*4

V = 240 cm³ (cubed)

Hope this helps!

Answer: The x intercept is (5/4,0) The y intercept is (0,5)

Step-by-step explanation:

Step-by-step explanation:

similar means that they have the same angles, and that there is one and the same scale factor for all corresponding sides and other lines (like heights).

so, either the angle F = 60° (like angle C in ABC), or DE has the same scaling factor with AB as DF has with AC.

some correct answer options are not listed, so we need to adjust to the existing ones.

remember, the sum of all angles in a triangle is always 180°.

so,

angle A + angle B + angle C = 180

40 + angle B + 60 = 180

angle B = 80°

so, angle E = 80° for the triangles to be similar.

AC × c = DF

12 × c = 16

3 × c = 4

c = 4/3

so,

AB × c = DE

9 × 4/3 = DE

36/3 = DE

DE = 12

so, either angle E = 80° or DE = 12.

Given statement solution is :-

1) Gather your electricity bills from the period before the summer break.

2) Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

3) Research or locate the power consumption information for each appliance.

4) Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

5) After the summer break, collect your electricity bill for the corresponding period.

6) Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

To conduct a comparative study of consecutive electric bills and analyze the impact of a reduction plan, you can follow the steps below:

Examine your electricity bills of pre-summer break:

Gather your electricity bills from the period before the summer break.

Look for details such as total energy consumption (in kilowatt-hours or kWh), billing period, and the cost per unit of electricity.

List the various electrical appliances used in your home:

Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

Find out the power consumption and duration for each device in use:

Research or locate the power consumption information for each appliance.

This information is typically provided on the appliance itself or in the user manual.

Note down the power rating of each device in watts (W) or kilowatts (kW).

Estimate the average duration each device is used daily in hours (e.g., 2 hours for a television, 8 hours for a refrigerator).

Calculate the estimated electricity consumption and cost:

Multiply the power rating (in kW) of each device by its average daily usage (in hours) to find the daily energy consumption (in kWh).

Multiply the daily energy consumption by the number of days in the billing period to get the total energy consumption for that period.

Multiply the total energy consumption by the cost per unit of electricity to calculate the estimated cost for each appliance.

Sum up the estimated costs for all appliances to get the total estimated electricity bill.

Make an energy reduction plan and determine implementation:

Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

Unplugging devices when not in use.

Determine the feasibility of implementing these energy reduction measures in your home.

Re-examine your electricity bill of post-summer break:

After the summer break, collect your electricity bill for the corresponding period.

Calculate the actual energy consumption and cost using the same method as in step 4.

Compare the actual post-summer break bill with the estimated pre-summer break bill.

Note any changes in energy consumption and cost, and analyze the effectiveness of your energy reduction plan.

Document your reduction plan and changes in the bill:

Write a report summarizing your findings and observations.

Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

By following these steps, you can conduct a comparative study of consecutive electric bills, analyze the effectiveness of your energy reduction plan, and track changes in energy consumption and costs.

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Answer:

≈ 404.6666667

Step-by-step explanation:

70 - 8 ÷ 6 + 8 x 42

70 - 1.33333333 + 8 x 42

70 - 1.33333333 + 336

68.6666667 + 336

404.6666667

Answer:

meter - yard

kilogram - 2 pounds

liter - quart

Answer:

√3√ab

Step-by-step explanation:

Please look in the attachment! Hope this helps! :D

Answer:

-9

Step-by-step explanation:

Use the order of operations. Do these operations in this order:

Note: when either multiplication and division, or addition and subtraction are there, go left to right.

Equation: -1 - 2 · {(-1) + 5}

Solve:

*Challenge*

Using the same method, see if you can solve this equation:

6 ÷ 2(1+2)

-Chetan K

5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 \(a_5\) =  26- 6( 5)  

\(a_5\) =  26- 30

\(a_5\) = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

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Answer:

2.98

Step-by-step explanation:

First find 3% of 16.05 which is 0.48.

Then add 0.48 to 16.05 which is 16.53.

Then multiply .18 by 16.53 which gets you 2.98

Hope it helps

Answer:

To find the amount of the sales tax, we need to multiply the bill amount by the tax rate of 3% or 0.03:

Sales tax = 0.03 x $16.05 = $0.48

To find the total amount of the bill after the sales tax was added, we need to add the bill amount to the sales tax:

Total bill = $16.05 + $0.48 = $16.53

To find the amount of the tip, we need to calculate 18% of the total bill after the sales tax was added:

Tip = 0.18 x $16.53 = $2.98

Rounding to the nearest cent, Penelope left a tip of $2.98.

Step-by-step explanation:

Answer:

5√3i

Step-by-step explanation:

√-1 = i

So √-108 must equal √108(i)

√108 = √9 * √12 = 3 * √3 * √4 = 6√3i

√-3 = √3i

6√3i - √3i = 5√3i

-Chetan K

The equivalent expression for the given expression is 5√3i. Therefore, option A is the correct answer.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is √(-108)-√(-3).

The expression √(-108)-√(-3) can be simplified as follows

6√3i-√3i

= 5√3i

Therefore, option A is the correct answer.

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Answer:

18

Step-by-step explanation:

.2x15=3

3+15=18

Answer:

18$

Step-by-step explanation:

The probability distribution for the statistic is ; for m = 0 , P(0) =  0.216  , for m = 5 ,P(5) = 0.296 and for m = 10 , P(10) = 0.488  .

In the question ,

it is given that ,

the box has 10 sealed envelopes , that contains number from 1,2,...,10 .

the first six envelopes has no money .

next two envelopes has $5

and the last two contains $10 bill .

if x₁, x₂, and x₃ denote the amounts in the selected envelopes,

the statistic of interest is m = maximum of X₁ , X₂ and X₃ .

we need to find probability distribution for the statistic m,

So , P(m = 0) = P( all three envelope contains no money) = (6/10)³ = 0.216

and P(m = 5) = P( all from 8 envelope which contains at most $5) - P(all three envelope with 0 money)

= (8/10)³ - 0.216

= 0.296

and P(m = 10) = 1 - (8/10)³ = 0.488

Therefore , the required probability is P(0) = 0.216 ,   P(5) =  0.296 and P(10) = 0.488  .

The given question is incomplete , the complete question is

A box contains ten sealed envelopes numbered 1, . . . , 10. the first six contain no money, the next two each contains $5, and there is a $10 bill in each of the last two. a sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. if x₁, x₂, and x₃ denote the amounts in the selected envelopes, the statistic of interest is M = the maximum of X₁ ; X₂ , and X₃ .  Obtain the probability distribution of this statistic ?

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Step-by-step explanation:

Step-by-step explanation:

Lets break this word problem down:

"The difference" means we're going to be finding x - y ("difference" means we're finding how much one value "differs" from the other)

"a number and it's opposite" so we're doing x - y, where y = -x. So already, we can re-write this as x - (-x) or x + x

"is 28" so x + x = 28 ("is" always means "equals")

"Find the number" so we're finding x.

x - (-x) = 28  (I went back a step so I could write everything out more plainly)

simplify

x + x = 28

add

2x = 28

divide both sides by 2 to get x on its own

x = 14

Answer:

14

Answer:

Graph the line y = -2.

Step-by-step explanation:

A line with zero slope is a horizontal line.  Find (0, -2) on the y-axis and draw a horizontal line through it.  This will fully address this question.

The probability of the event for the given odds in favor (4 to 7) is found as 4/11.

To continue solving, we must represent the ratio as a fraction.

Thus, we have the depiction shown below.

Odds ratio equals 4/7

We use the following equation to translate the aforementioned odd's expression into a probability expression.

This is displayed as

P = (Odds + 1)/(Odds).

Replace the unknown values in the equation above.

The following equation is what we have.

P = (4/7)/(4/7 + 1)

Analyze the amount

This results

P = (4/7)/(11/7)

Put the quotient in product form.

P = (4/7) * (7/11)

Evaluate

P = 4/11

Thus, the probability of event for the given odds in favor (4 to 7) is found as 4/11.

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Yes, the proof of congruence of two triangles ∆ABC ≅ ∆GHF is possible.

The convergence method which proves this congruence is SSS(side-side-side) congruence.

We have given the sketch of two triangles as seen above. We have to prove ∆ABC ≅ ∆GHF

Now , AB = √(-7+7)² + 5² = 5 in triangle ABC and FG = 5 in triangle FGH,

so, AB ≅ FG

Because AC = 3 in triangle ABC and FH = 3 in triangle FGH,

so, AC ≅ FH

To find the lengths of BC and GH , we can use distance formula.

Length of BC :

BC = √[(x₂ - x₁)² + (y₂ - y₁)²]

(x₁, y₁) = B(-7, 0) and (x₂, y₂) = C(-4, 5).

BC = √[(-4 + 7)² + (5 - 0)²]

= √[32 + 52]

= √[9 + 25]

= √34

Length of GH :

GH = √[(x₂ - x₁)² + (y₂ - y₁)²]

(x₁, y₁) = G(1, 2) and (x₂, y₂) = H(6, 5).

GH = √[(6 - 1)² + (5 - 2)²]

= √[52 + 32]

= √[25 + 9]

= √34

Conclusion :because BC = √34 and GH = √34,

=>BC ≅ GH

All the three sides of one triangle is congruent to the corresponding sides of other triangle.

By SSS congruence postulate,

ΔABC ≅ ΔFGH

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Answer:

C : 20

good luck, hope this helped!

The surface area of the triangular prism is 313.47 cm².

Given is a triangular prism, we need to find the surface area,

A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.

Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.

so, the surface area of a triangular prism =

perimeter × length + 2 × base area

So,

SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9

= 167.67 + 145.8

= 313.47

Hence the surface area of the triangular prism is 313.47 cm².

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