Learning Task 1: Read and analyze each problem carefully. Write your final answer in your notebook based on the given questions below.
1) There are 2 2/3 pizzas. How many people are sharing when each has 2/3 of pizza?
2) A plastic bottle of mineral holds 600 ml of water when it is 3/5 full. What is the capacity of the bottle
3) Joel spend 4/8 of his monthly salary for their groceries. After spending had Php 980 left. How much his monthly salary?

Grade: V/5
Sub: Math​

Step-by-step explanation:

If they have the same shape, the red graph is a translation of the blue, which is given to be y=x^2.

Since the red graph stays on the y axis at two units above the blue (y=x^2) curve, therefore the red curve is given by y=x^2+2.

The equation of the red graph is f(x) = x² + 2.

Option B is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The graphs of f(x) = x² and f(x) = x² + 2 are both quadratic functions, which means they have a parabolic shape.

The graph of f(x) = x^2 is an upward-opening parabola with its vertex at the origin (0,0).

The parabola is symmetric about the y-axis and the x-axis.

The graph of f(x) = x² + 2 is also an upward-opening parabola, but it has been shifted upward by 2 units compared to the graph of f(x) = x².

This means that the vertex of the parabola has been shifted from (0,0) to (0,2).

Thus,

The equation of the red graph is f(x) = x² + 2.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ7

Answer:

The actual answer is 7 units.

Step-by-step explanation:

Distance between two bodies=

root under[(x2-x1)^2+(y2-y1)^2]

=root under[(-3-4)^2+(5-5)^2]

= root under (49)

=7 units.

Given the exponential equation:

A student solved it.

Let's describe and correct the error the student made in solving the exponential equation.

Let's solve the equation.

Apply the following steps:

Step 1.

Divide both sides by 16

Step 2.

Take the natural logarithm of both sides

Where:

ln(e) = 1

Hence, we have:

The student did not convert to the logarithmic form correctly. The solution should be t = 1.812

ANSWER:

A. The student did not convert to the logarithmic form correctly. The solution should be

t = 1.812

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Answer:

Cele 3 numere naturale sunt:

Primul număr = a = 9

Al doilea număr = b = 6

Al treilea număr = c = 2

Step-by-step explanation:

Fie cele 3 numere naturale reprezentate ca:

Primul număr = a

Al doilea număr = b

Al treilea număr = c

Produsul primelor două este de 54

a × b = 54

ab = 54 ...... Ecuația 1

a = 54 / b

Produsul ultimelor două este 12

b × c = 12

bc = 12 ........ Ecuația 2

c = 12 / b

Suma primului și celui de-al treilea este 11

a + c = 11 ...... Ecuația 3

Înlocuim

54 / b pentru a și 12 / b pentru c

54 / b + 12 / b = 11

54 + 12 / b = 11

Cross Multiply

66 / b = 11

11b = 66

b = 66/11

b = 6

Rezolvarea pentru un

a = 54 / b

a = 54/6

a = 9

c = 12 / b

c = 12/6

c = 2

Prin urmare, cele 3 numere naturale sunt:

Primul număr = a = 9

Al doilea număr = b = 6

Al treilea număr = c = 2

The value of θ in the given triangle is equal to 30 degrees.

Data;

To solve this problem, we have to use trigonometric ratios on this which is SOHCAHTOA.

since sin θ is the ratio between the opposite side to the hypothenuse,

\(sin\theta = \frac{opposite}{hypothenuse}\)

Let's substitute the values into the function and solve.

\(sin\theta = \frac{8}{16} \\\theta = sin^-^1 (0.5)\\\theta = 30^0\)

The value of θ is equal to 30 degrees.

Learn more on trigonometric ratios here;

https://brainly.com/question/24349828

The amount of each paycheck after all $4488.26 is withdrawn for all expenses is $1388.89.

When purchases are made, the balance rises; when payments are made, the balance falls. Your credit card balance is affected by purchases, balance transfers, foreign exchange, fees, and interest, among other things.

The increase in Ivy's account balance is $321.58.

Ivy received three payments and took a total withdrawal of $4488.26 to pay all of her bills and obligations.

Let x be the amount in a single Ivy's paycheck.

Ivy was paid three times = 3x

Ivy withdrew $4,488.26 to cover all her bills and expenses.

Therefore,

3x + 321.48 = 4488.26

3x = 4166.68

x = ( 4166.68 / 3 )

x = $1388.89

The amount on Ivy's paycheck is $1388.89.

Learn more about expenses here:

https://brainly.com/question/935872

#SPJ9

Answer:1/40

Step-by-step explanation: If the Smiths bought 25 raffle tickets, and there were 1000 sold in total, it would mean they have a 25/1000 chance. we can simplify 25/1000 into 1/40. Therefore, the answer is (3)

Answer:

38.9 degrees C

Step-by-step explanation:

Use the equation:

\(C=\frac{5}{9} (F-32)\)

to convert degrees Fahrenheit  to degrees Celsius. So replace the value for the Fahrenheit with 102 and solve for C:

\(C=\frac{5}{9} (F-32)\\C=\frac{5}{9} (102-32)\\C=\frac{5}{9} (70)\\C=\frac{350}{9} \approx38.89\,^oC\)

which to the nearest tenth can be written as: 38.9 degrees C

9514 1404 393

Answer:

  73 ft²

Step-by-step explanation:

The ratio of areas is the square of the ratio of linear dimensions.

  smaller area = larger area × ((10 ft)/(15 ft))² = 165 ft² × (4/9)

  smaller area = 73 1/3 ft² ≈ 73 ft²

Answer:

Area of the smaller triangle = 73 square feet

Step-by-step explanation:

Area of the larger triangle = 165 square feet

Area of a triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

\(\frac{1}{2}(\text{Base})(\text{Height})=165\)

\(\frac{1}{2}(15)(\text{Height})=165\)

Height = 22 ft

Since, both the triangles are similar.

By the property of similar triangles,

Corresponding sides of the similar triangles are proportional.

Let the height of smaller triangle = h ft

Therefore, \(\frac{h}{22}=\frac{10}{15}\)

h = \(\frac{22\times 10}{15}\)

h = 14.67 ft

Area of the smaller triangle = \(\frac{1}{2}(10)(14.67)\)

                                              = 73.33

                                              ≈ 73 square feet

The estimated change in y is apprοximately 20.96 when x changes frοm 0.1 tο 4.

A triangle is a three-sided pοlygοn with three angles. It is οne οf the simplest and mοst basic shapes in geοmetry, and is characterized by its three straight sides and three angles that add up tο 180 degrees.

Tο use linear apprοximatiοn tο estimate the change in y, we need tο first find the equatiοn οf the tangent line tο the curve \(y = 2x^2 + 6x + 4\) at x = 0.1.

The first derivative οf y with respect tο x is:

dy/dx = 4x + 6

At x = 0.1, the slοpe οf the tangent line is:

m = dy/dx at x = 0.1 = 4(0.1) + 6 = 6.4

The equatiοn οf the tangent line is then:

y - y(0.1) = m(x - 0.1)

Substituting \(y(0.1) = 2(0.1)^2 + 6(0.1) + 4 = 4.6\) and m = 6.4, we get:

y - 4.6 = 6.4(x - 0.1)

Simplifying, we get:

y = 6.4x + 3.94

Nοw we can estimate the change in y when x changes frοm 0.1 tο 4 using the tangent line equatiοn:

triangle y = y(4) - y(0.1)

= (6.4)(4) + 3.94 - (6.4)(0.1) - 4.6

= 25.94 - 4.98

= 20.96

Therefore, the estimated change in y is approximately 20.96 when x changes from 0.1 to 4.

Tο learn more about triangle from the given link: brainly.com/question/2773823

#SPJ1

The inequality in standard form that will represent the maximum number of cans of apple juice and cans of pineapple juice Stewart can use would be = 240ounce = 10a + 18p.

The total quantity of fruit punch that would be used for the birthday = 240 ounce.

The quantity of juice each can holds for apple juice,a, = 10 ounces.

The quantity of juice each can hold for pineapple juice,p,= 18 ounces.

Therefore the best expression in standard form would be = 240ounce = 10a + 18p.

Learn more about volume here:

https://brainly.com/question/27710307

#SPJ1

The implicit derivative is given as follows:

dx/dt(x = 4)  = 1/12.

The function in this problem is given as follows:

y = 3x² + 1.

The implicit derivative, relative to the variable t, is given as follows:

dy/dt = 6x dx/dt.

(the derivative of the constant 1 is of zero).

The parameters for this problem are given as follows:

x = 4, dy/dt = 2.

Hence the derivative is obtained as follows:

2 = 6(4) dx/dt

dx/dt = 2/24

dx/dt = 1/12.

More can be learned about implicit differentiation at https://brainly.com/question/25081524

#SPJ1

Answer:

c) 6× (9+8) = (6 × 9) + (6× 8)

Step-by-step explanation:

Distributive property of multiplication

The distributive property of multiplication

a(b+c) = a b + a c

(a+b)c = ac + bc

6× (9+8)  = (6× 9) + (6×8)

Answer:

There are 3 feet in a yard, so divide 34 by 3, which is 11 with a remainder of 1, the remainder 1 is the remaining foot, so 34 feet is 11 yards and 1 foot.

Step-by-step explanation:

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-11)=4(x-(-3)}\)

Simplify.

\(\rm{y+11=4(x+3)}\)

Simplified to slope intercept:

\(\rm{y+11=4x+12}\)

\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation

After making all the necessary adjustments, the reconciled bank balance for ABC Company's ledger at the end of July is Br. 4,164.42.

To reconcile the bank statement balance with the company's ledger balance for ABC Company, we need to go through the provided information step by step and make the necessary adjustments. Let's calculate the adjusted bank balance:

Starting with the bank statement balance: Br. 4,964.47

Add the deposit made after banking hours: + Br. 410.90

New bank balance: Br. 5,375.37

Now let's make adjustments for the outstanding checks and other transactions:

Deduct the erroneously charged check: - Br. 973

New bank balance: Br. 4,402.37

Deduct the outstanding checks:

Check No. 801: Br. 100.00

Check No. 888: Br. 10.25

Check No. 890: Br. 294.50

Check No. 891: Br. 205.00

Total deduction: Br. 609.75

New bank balance: Br. 3,792.62

Correct the incorrectly charged check: + Br. 90

New bank balance: Br. 3,882.62

Add the proceeds from the collection of the interest-bearing note: + Br. 500.00

New bank balance: Br. 4,382.62

Add the interest earned on the average account balance: + Br. 24.75

New bank balance: Br. 4,407.37

Deduct the incorrectly recorded check: - Br. 90

New bank balance: Br. 4,317.37

Deduct the fee charged for handling the collection of the note: - Br. 5.00

New bank balance: Br. 4,312.37

Deduct the check returned due to insufficient funds: - Br. 50.25

New bank balance: Br. 4,262.12

Deduct the service charge for the month of July: - Br. 12.70

New bank balance: Br. 4,249.42

Deduct the erroneously recorded check: - Br. 85.00

New bank balance: Br. 4,164.42

Now, we compare the adjusted bank balance (Br. 4,164.42) with the ledger balance provided (Br. 4,173.83).

Adjusted bank balance: Br. 4,164.42

Ledger balance: Br. 4,173.83

The difference between the adjusted bank balance and the ledger balance is Br. 9.41. This difference is likely due to some unrecorded transactions or errors in recording. To reconcile the balances fully, further investigation is required to identify the specific cause of the discrepancy and make the necessary adjustments in the company's ledger.

for such more question on bank balance

https://brainly.com/question/15525383

#SPJ8

Answer:

  2.5%

Step-by-step explanation:

You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.

The z-score of 335 is ...

  Z = (X -µ)/σ

  Z = (335 -555)/110 = -220/110 = -2

The empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.

  P(X < 335) = 5%/2 = 2.5%

The percentage of people taking the test who score below 335 is 2.5%.

<95141404393>

Explanation:

She scored 92 points in 4 games. The unit rate is 92/4 = 23 points per game.

Over the course of 17 games, Maria would have a total of 17*23 = 391 points assuming her scoring rate is kept the same.

Answer:

met up with who?

Step-by-step explanation:

Answer:

315

Step-by-step explanation:

The difference between the depths in February and July is 31 feet.

The method of measuring depth depends on what we are trying to measure the depth of. Here are some general methods for measuring different types of depth:

Depth of water: The depth of water can be measured using a sounding device such as a sonar or a simple depth gauge. A sonar uses sound waves to determine the distance from the water's surface to the bottom. A depth gauge is a simple device that measures the distance from the surface of the water to the bottom using a weight and a line.

Depth of a hole: The depth of a hole can be measured using a tape measure or a ruler. Simply insert the measuring device into the hole and measure the distance from the top of the hole to the bottom.

Depth of a trench: The depth of a trench can be measured using a measuring tape or a surveyor's level. Place the measuring device at the edge of the trench and measure the distance from the top of the trench to the bottom.

Depth of a pool: The depth of a pool can be measured using a pool depth marker or by using a measuring tape. A depth marker is usually located on the side of the pool and indicates the depth at various points. Alternatively, you can use a measuring tape to measure the distance from the surface of the water to the bottom of the pool.

Depth of a well: The depth of a well can be measured using a well sounder or a tape measure. A well sounder is a device that sends a signal down the well and measures the time it takes for the signal to bounce back. The time it takes is then used to calculate the depth of the well. Alternatively, a tape measure can be used to measure the distance from the surface of the water to the bottom.

Given, In February, it measured 6 ft deep, or |−6| and in July, it was 25 ft deep, or |−25|.

The difference between the depths in February and July is:

|−6| − |−25| = 6 − (−25) = 6 + 25 = 31

Therefore, the correct choice is B) 31 feet.

Learn more about depth here:

brainly.com/question/20070144

#SPJ1

The tax revenue generated from property taxes is often used to fund expressions public services such as schools, parks, and infrastructure projects in the local community.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the expression 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +. The calculation of property tax is typically based on the assessed value of the property and the tax rate set by the local government. The assessed value is determined by a government-appointed assessor who evaluates the value of the property based on factors such as its location, size, age, and condition. The tax rate is then applied to the assessed value to determine the amount of tax owed by the property owner. The tax revenue generated from property taxes is often used to fund public services such as schools, parks, and infrastructure projects in the local community.

To know more about expressions visit :-

https://brainly.com/question/14083225

#SPJ1

The probability of randomly drawing 2 red marbles is P = 0.476

On the box we have 7 marbles, 5 red ones and 2 green ones. If we assume all the marbles have the same probability of being randomly drawn, then the probability of drawing a red marble is equal to the quotient between the number of red marbles and the total number of marbles.

So the probability for the first red marble is:

p = 5/7

For the second one, we will have one red marble less and one marble of the total less, so the probability is:

q = 4/6

The joint probability is the product of these two:

P = (5/7)*(4/6) = 0.476

Learn more about probability:

https://brainly.com/question/25870256

#SPJ!

Answer:

y = 6

Step-by-step explanation:

y = -4(1) + 10 = -4 + 10 = 6

Answer:

Already answered it

Step-by-step explanation: