Joseph runs 212 miles on Monday. Each day after that, he runs the same 113 mile route every morning. His goal is to run at least 6 miles by the end of the week. Which inequality represents the least number of days after Monday that Joseph needs to run to reach his goal?

(a) The rate at which the amount of water is changing is -1/2.

(b) It will take 20 more minutes to drain the water completely.

(c) The tank was completely full 3 minutes before Kiran arrive.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

(a) Given that,

When Kiran first sees the tank, it contains 12 gallons of water. Four minutes later, the tank contains 10 gallons of water.

Rate at which the amount of water is changing = (10 - 12) / 4 = -2/4 = -1/2 gallons per minute.

(b) Time taken to drain 1/2 gallon = 1 minute

There are 10 gallons of water remaining in the tank.

Time taken to drain 10 gallons of water = (1 ÷ 1/2) × 10 = 20 minutes

It will take 20 more minutes to drain the water completely.

(c) When Kiran arrived, water tank has 12 gallons of water.

Total amount of water in the tank is 15 gallons.

Tank has lost 3 gallons of water before Kiran arrived.

Time taken to drain 3 gallons = (1 ÷ 1/2) × 3 = 6 minutes

So the tank was completely full 3 minutes before Kiran arrive.

Hence the rate is -1/2 gallons per minute.

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The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.

5/8 - 3/8 = x

5/8 = 5 ÷ 8

= 0.625

3/8 = 3 ÷ 8

= 0.375

0.625 - 0.375 = x

= 0.25

Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.

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Answer: 3x+7+4x-2

Step-by-step explanation: 3x+4=7x

7-2=5

so the answer should be 7x+5

To convert a percentage to a decimal, divide the percentage by 100, The correct answer is B. 0.609.

When the decimal places in the factors are tallied together, they equal the number of decimal places in the product. A decimal number is one with a whole and a fraction part separated by a decimal point.

A base-10 representation of numeric values is used in the decimal numbering system. The system is widely used in daily life to complete routine tasks like grocery shopping, stock trading, keeping track of football scores, or scrolling through cable channels. Decimal numbers include 7, 28, 199, and 532.11.

To convert a percentage to a decimal, divide the percentage by 100.

So, 60.9% as a decimal would be:

60.9 / 100 = 0.609

Therefore, The correct answer is B. 0.609.

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The simplified ratios are shown below:

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

We have ratios

1. 30: 45

= 30/45

= 2 /3

2. 350 : 400

= 350/400

= 7/8

3. 600g : 4 Kg

= 600 / 4000

= 6/ 40

= 3/20

4. 65:91

= 5 / 7

5. 12 cm  : 1 m

= 12 / 100

= 3 /25

6. 3 Km: 50 m

= 3000 / 50

= 60

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The number of tons required when the central HVAC unit will be installed is 1. 73 tons

For the HVAC unit to be installed, the three separate incubation rooms will have to be installed.

This means that the tons required for the central HVAC unit would be the total sum of the three requirement for the other incubation rooms.

The sum would be :

= 1 / 5 + 5 / 6 + 25 / 36

= 0. 2 + 0. 8333 + 0. 69444

= 1. 72774

= 1. 73 tons

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There are quadratic equations as many as lead coefficients are. The functions that represent each parabola are:

Case A: y = (1 / 3) · (x + 4) · (x - 2)

Case B: y = (x + 4) · (x - 2)

Case C: y = 2 · (x + 4) · (x - 2)

Case D: y = - (1 / 3) · (x + 4) · (x - 2)

Case E: y = - 2 · (x + 4) · (x - 2)

In this problem we find five case of quadratic equations whose roots are x = - 4 and x = 2, but whose vertices are different. Quadratic equations can be described as a factor product of the form:

y = a · (x + 4) · (x - 2)

Where a is the lead coefficient.

The following parameters are for each parabola:

Case A: (x, y) = (- 1, - 3)

Case B: (x, y) = (- 1, - 9)

Case C: (x, y) = (- 1, - 18)

Case D: (x, y) = (- 1, 3)

Case E: (x, y) = (- 1, 18)

Now we determine the lead coefficient for each case:

Case A

- 3 = a · (- 1 + 4) · (- 1 - 2)

- 3 = - 9 · a

a = 1 / 3

Case B

- 9 = a · (- 1 + 4) · (- 1 - 2)

- 9 = - 9 · a

a = 1

Case C

- 18 = a · (- 1 + 4) · (- 1 - 2)

- 18 = - 9 · a

a = 2

Case D

3 = a · (- 1 + 4) · (- 1 - 2)

3 = - 9 · a

a = - 1 / 3

Case E

18 = a · (- 1 + 4) · (- 1 - 2)

18 = - 9 · a

a = - 2

All differences between all quadratic equations are due to different lead coefficients.

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The probability of getting 8 or more successes in 9 trials, with given success rate in each trial is 0.8, is 0.9520.

To find the probability , we can use the cumulative distribution function (CDF) of the binomial distribution:

P(X ≥ 8) = 1 - P(X < 8) = 1 - P(X ≤ 7)

Using a binomial calculator or a binomial probability distribution table, we can find:

P(X ≤ 7) = 0.0480 (rounded to four decimal places)

Therefore,

P(X ≥ 8) = 1 - 0.0480 = 0.9520

So the probability of getting 8 or more successes in 9 trials, given the probability of success in each trial is 0.8, is 0.9520 (rounded to four decimal places).

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Answer:6

Step-by-step explanation:

day one-2 bread

day two-4 bread

10-4=6

6 at the end of the day

The number of loaves of bread remaining at the end of second day = 6 loaves of bread

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 equation be represented as A

Now , the value of A is

Let number of loaves of bread remaining at the end of second day be A

The total number of loaves of bread = 10 loaves

The number of loaves of bread sold each day = 2 loaves

Substituting the values in the equation , we get

So , the number of loaves of bread remaining at end of first day = 10 - 2 = 8

Now , the number of loaves of bread remaining at end of second day = 8 -2

The number of loaves of bread remaining at the end of second day = 6

Therefore , the value of A is 6 loaves of bread

Hence , the equation is A = 6 loaves

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The missing angles are

A. = 130 degrees

B. = 55 degrees

C. = 145 degrees

D. = 73 degrees

E. = 43 degrees

F. = 23 degrees

G. = 61 degrees

H. = 90 degrees

I. = 50 degrees

J. = 27 degrees

K. = 25 degrees

Assuming the missing angle in each case is x

A. Angle on a straight line = 180 degree

x + 50 = 180

x = 130 degrees

B. Angle at a point = 360 degrees

209 + 96 + x = 360

x = 360 - 96 - 209

= 55 degrees

C. Angle on a straight line = 180 degree

= 145 degrees

D. Vertical angles are equal, using vertical angle theorem

= 73 degrees

E.  vertical angle theorem

= 43 degrees

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The graph of g(x) = (x - 2)^3 + 7 is a transformation of the parent function f(x) = x^3.

The parent function f(x) = x^3 has a shape that is symmetrical about the origin and increases as x moves away from the origin. The graph of g(x) = (x - 2)^3 + 7 is also symmetrical about the origin, but it has been translated 2 units to the right and 7 units up from the parent function.

So, the graph of g(x) = (x - 2)^3 + 7 is similar in shape to the parent function f(x) = x^3, but it is shifted to the right and up on the coordinate plane.

The price of new Tv is 107,990 including VAT .The percentage increase in price of tv is 8% in rate.

The current price of the plasma TV including VAT at 5% is 99,990 naira.

If the government raises VAT to 8%, the new price of the TV including VAT can be calculated as follows:

New price = current price * (1 + new VAT rate)

New price = 99,990 * (1 + 0.08)

New price = 107,992.2

Rounding the new price to the nearest 10 naira gives: 107,990 naira.

The increase in price of the TV can be calculated as follows:

Price increase = new price - current price

Price increase = 107,990 - 99,990

Price increase = 8,000

The percentage increase in price of the TV can be calculated as follows:

Percentage increase = (price increase / current price) * 100%

Percentage increase = (8,000 / 99,990) * 100%

Percentage increase = 8.0%

Therefore, the new price of the TV including VAT at 8% is 107,990 naira, and there is a 8.0% increase in price.

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____The given question is incomplete, the complete question is given below:

The advertised price of a plasma tv is 99,990 naira including vat at 5%. If the government raises vat to 8%,calculate the new price of the tv ,(to the nearest 10 naira) what is the percentage increase in price of the tv?

Answer:

[tex]49[/tex]

Step-by-step explanation:

[tex]\frac{US}{UD}=\frac{UT}{UC} \implies US=\frac{(56)(14)}{16}=49[/tex]

The volume of the solids A and C will be 1,125 cubic km and 4.608 cubic km, respectively.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

Solid A is dilated using a scale factor of 2/5, resulting in Solid B. Then the volume of solid A is given as,

(Scale factor)³ x (Volume of solid A) = Volume of solid B

(2/5)³ x Volume of solid A = 72

Volume of solid A = 1,125 km³

Solid B is also dilated using a scale factor of 2/5, resulting in Solid C. Then the volume of solid C is given as,

(Scale factor)³ x (Volume of solid B) = Volume of solid C

(2/5)³ x 72 = Volume of solid C

Volume of solid C = 4.608 km³

The volume of the solids A and C will be 1,125 cubic km and 4.608 cubic km, respectively.

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A right isosceles triangle is a triangle with a right angle (90 degrees) and two sides that are equal in length. This means that the triangle is also a special case of an isosceles triangle where the two equal sides are adjacent to the right angle.

To identify a right isosceles triangle among a group of shapes, you should look for the shape that has a right angle and two sides of equal length. One way to check for the right angle is to look for a corner that forms a square angle (i.e., 90 degrees), and one way to check for the equal sides is to compare the length of each side.

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The following question may be like this:

What is a right isosceles triangle?

The value of sin a + cos a is √7/2.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

Based on the right-triangle theorem, which is known as Pythagoras theorem, there are three Pythagorean trigonometric identities in trigonometry as follows

Here we have

sin a × cos a = 3/8  

Multiply with 2 on both sides

=> 2(sin a × cos a) = 2(3/8)

=> 2 sin a cos a = 3/4  

Add sin²a + cos²a on both sides

=> sin²a + cos²a + 2 sin a cos a = 3/4 + sin²a + cos²a    

As we know (a + b)² = a²+ b² + 2ab  

=> (sin a + cos a)² = 3/4 + 1

=> (sin a + cos a)² = 7/4

=> sin a + cos a = √7/2

Therefore,

The value of sin a + cos a is √7/2.

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Answer: 44, -14, 4

Step-by-step explanation:

plug the f(x) into the x and solve itself.

(5)^2 + 3(5) + 4 = 44

(-3)^2 + 3(-3) + 4 = -14

(0)^2 + 3(0) + 4 = 4

The statement that is true about the quadratic functions is:

g(x) > h(x) for x = -1.

Here we have the two quadratic functions:

g(x) = x^2

h(x) = -x^2

Notice that h(x) = -g(x).

Also, g(x) is always positive or zero, while h(x) is always negative, but for x = 0 both have the same value.

g(0) = 0^2 = -0^2 = h(0)

Then the statement that is true is

g(x) > h(x) for x = -1.

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The value of length of z is 5.06 cm.

The value of length of z is calculated by determining the radius of the sector as shown below;

The formula for the perimeter of a sector is given as;

P = 2r  +  (θ/360) × 2πr

where;

20 cm = 2r  + (40/360) x 2πr

20 = 2r  +  0.7r

20 = 2.7r

r = 20/2.7

r = 7.4 cm

A perpendicular bisector of 40⁰ will cut line z into two equal parts, the length of half of z is calculated as;

sin (20) = (z/2) / r

r x sin (20) = (z/2)

2r x sin (20) = z

2 x 7.4 cm x sin(20) = z

5.06 cm = z

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Answer:

small number=3 while Big number is, 13

Step-by-step explanation:

X+y=14

3x+2y=31

3(x+y=14)

3x+3y=42 + 3x+2y=31

X=3,y=11

Answer: If a ball is chosen at random 80 times, with replacement, and there are an equal number of blue, green, pink, and red balls, then the probability of choosing a green ball each time is 1/4. Over many trials, the number of times a green ball is chosen would be roughly proportional to the probability of choosing a green ball, so we would expect the green ball to be chosen about 80 * (1/4) = 20 times.

However, since this is a random process, it is unlikely that the green ball will be chosen exactly 20 times. It is more likely that the actual number of green balls chosen will be slightly different, possibly higher or lower, than 20. So the answer is C: The color green would be chosen roughly 20 times, but probably not exactly 20 times.

Step-by-step explanation:

Both of these are correct. When multiplying 32 and 8, we should follow these steps:

So, the correct answer is 256.

Here is the multiplication shown step-by-step:

 32
   8

 16 --> drop down 6 and carry the 1

1
32
   8

   6

24-   --> drop down the 4 and add 1; carry the 2

 56

2

 32
    8

   6

 5 -

2 - - --> drop down the 2 since no more digits available to multiply

256 --> the answer

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The coordinates of point H are (-1,-3). This is obtained by using the midpoint formula and solving for the coordinates of point H, given the midpoint of GH and the coordinates of point G.

To find the coordinates of point H, we can use the midpoint formula, which states that the midpoint of a line segment is the average of the coordinates of its endpoints.

If the midpoint of GH is (1,-4) and the coordinates of point G are (3,-5), we can write: (1,-4) = [(3 + x)/2, (-5 + y)/2]

where x and y are the coordinates of point H. We can solve for x and y as follows:

2(1,-4) = (3 + x, -5 + y)

(2, -8) = (3 + x, -5 + y)

2 = 3 + x --> x = -1

-8 = -5 + y --> y = -3

Therefore, the coordinates of point H are (-1, -3).

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=4t + 8

=4×3 + 8

= 12 +8

= 20

[tex]...[/tex]

The total value of the investment of $1000.00 at 5% simple interest for 5 years equals $1,250.

Total principal 'P' amount invested by Ivy is equal to $1,000.

Time period of investment 't' = 5 years

Rate of simple interest 'r' = 5%

Simple interest = ( Principal × rate of interest × time ) / 100

⇒ Simple interest = ( 1000 × 5 × 5 ) / 100

⇒ Simple interest = $250

Total value of the invested principal amount is equal to

= Principal amount + simple interest

= $1,000 + $250

= $1,250

Therefore, the total investment value of the principal amount at simple interest rate for 5 years is equal to $1,250.

The above question is incomplete, the complete question is:

Ivy invested $1000. 00 at 5% simple interest per annum for 5 years. How much was her investment worth after her investment ?

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The amount of wrapping paper used by Gavin to wrap a triangular prism box is 647.75 m².

What is a prism?

A prism is a polyhedron in geometry made up of an n-sided polygon basis, a second base that is a rigidly translated copy of the first base, and n additional faces that must all be parallelograms and connect the corresponding sides of the two bases.

The formula for area of rectangle is -

Area = length × breadth

The area of rectangle ABFG is -

Area = AB × BF

The value for line segment AB = 15 m

The value for line segment BF is -

BF = BC + CE + EF

BF = 14 + 7 + 15.65

BF = 36.65 m

So, the area of rectangle ABFG is -

Area = 15 × 36.65

Area = 549.75 m²

Now, the triangular prism has triangle part left.

The formula for area of triangle is -

Area = 1/2 × base × height

So, the area of triangle IJH is -

Area = 1/2 × IJ × JH

The value for line segment IJ = 14 m

The value for line segment JH = 7 m

So, the area of triangle IJH is -

Area = 1/2 × 14 × 7

Area = 49 m²

Since, there are two triangles (Δ IJH = Δ CDE ) so the area of total shape is -

Total area = Area of ABFG + 2(Area of Δ IJH)

Total area = 549.75 + 2(49)

Total area = 647.75 m²

Therefore, the area of triangular prism box is 647.75 m².

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his selling rate is: 750 balloons / 15 days = 50 balloons per day . To calculate Jack's selling rate in balloons per day, we need to divide the total number of balloons he sold by the number of days he worked.

This means that Jack sold an average of 50 balloons per day over the last 15 days. This information is useful for several reasons. For example, the party supply store might use this information to evaluate Jack's performance and determine whether he is meeting their expectations. It might also be useful for forecasting future sales, since if Jack continues to sell balloons at a rate of 50 per day, we can estimate how many balloons he will sell in a future period of time by multiplying the number of days by 50. In this case,

Jack sold 750 balloons in 15 days, so his selling rate is: 750 balloons / 15 days = 50 balloons per day

It's important to note that the selling rate of 50 balloons per day is an average, and it's possible that Jack's sales varied from day to day. For example, he might have sold more balloons on some days and fewer on others. However, by calculating the average selling rate, we get a general sense of how many balloons Jack sold per day over the course of the last 15 days.

In conclusion, Jack's selling rate in balloons per day over the last 15 days was 50 balloons. This information provides insight into Jack's performance and can be used to make informed decisions about future sales.

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Answer:

a = 6 ft.

------------------------------

Given is an isosceles right triangle.

As per property of a such triangle, its hypotenuse is √2 times its leg.

That is:

Answer:

a = 6 ft

Step-by-step explanation:

We have to find,

→ The value of a in the diagram.

Formula we use,

=> Using Pythagoras theorem.

→ (Hyp)² = (Opp)² + (Base)²

Forming the equation,

→ (6√2)² = (a)² + (a)²

Now the value of a will be,

→ (6√2)² = (a)² + (a)²

→ (a)² + (a)² = (6√2)²

→ 2a² = 36 × 2

→ 2a² = 72

→ a² = 72 ÷ 2

→ a² = 36

→ a = √(36)

→ [ a = 6 ft ]

Hence, the value of a is 6 ft.