Two boxes contained 155 lb of flour. If you take 20 lb from the first and add it to the second, the first box will contain 12/19 of what is now in the second. What amount of flour was originally in each box?

Given the sum of the sequence and the first term, we rearrange the formula for the sum to solve for 'd', the common difference. This will allow us to calculate the term at any given point in the arithmetic sequence.

In an arithmetic sequence, the nth term can be represented by the formula a + (n-1)d where 'a' is the first term, 'n' is the number of terms and 'd' is the common difference between the terms.

The sum, 's', of the first 'n' terms in an arithmetic sequence is given by the formula s = n/2 * (2a + (n - 1)d).

Given the sum, 's', and the first term in the sequence, 'a', we can rearrange the sum formula to find 'd', the common difference, which will then allow us to find any term in the sequence.

We have s16 = -288 and a1 = -21. So, our problem reduces to solve for 'd' in s = n/2 * (2a + (n - 1)d) The solution with most relevance to the student's question will be the calculated 'd' value.

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Place value is the value of a digit in a number.

Before the decimal i.e on the left-hand side, the place values we have are called:

Units, Tens, Hundreds, Thousands, Ten Thousands e.t.c

After the decimal i.e on the right-hand side, the place values we have are called:

Tenth, Hundredth, Thousandth. Ten thousandth e.t.c

We are given the number: 742.891

The digit in the hundredths place is 9

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1.) The center is at (-2,-5).

3.) The con vertices  are at (-2,-4) and (-2,-6).

4.) The distance between the center and each focus is 2√6 units.

Statements 1,3 and 4 about the ellipse are true. Ellipse is the result of carving a cone with an oblique plane that does not intersect the base.

The asymmetrical oval shape is drawn by a spot advancing along a plane so that the sum of its distance from foci is kept the same known as an ellipse.

1.) The center is at (-2,-5).

3.) The cone vertices are at (-2,-4) and (-2,-6).

4.) The distance between the center and each focus is 2√6 units.

Hence statements 1,3 and 4 about the ellipse are true.

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In order to find the answer, put six and three together to obtain nine, then divide nine in half to get 4.5, and then divide 4.5 by seven to get roughly 0.64.

When translated into a mathematical operation, the phrase "half of the sum of six and three then divided by seven" looks like this: Find the value of the sum of 6 + 3 to get 9 first. Then divide by half, or 4.5, to get the answer. Divide this by seven, and you'll arrive at a result that is roughly 0.64 (rounded to two decimal places).

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The correct answer is actually 60 miles more !!

The cost function is an illustration of linear functions

From the question, we have:

[tex]G = 4.50[/tex] --- cost per game

[tex]R = 3.75[/tex] --- cost per shoe rent

Since the cost is a function of number of games, it means that;

The cost of shoe rent is a fixed cost

Let x represents the number of games.

So, the cost function is:

[tex]C(x) = R + G \times x[/tex]

This gives

[tex]C(x) = 3.75 + 4.50 \times x[/tex]

[tex]C(x) = 3.75 + 4.50x[/tex]

Substitute 3 for x; to evaluate the function for 3 games

[tex]C(3) = 3.75 + 4.50 \times 3[/tex]

[tex]C(3) = 3.75 + 13.50[/tex]

[tex]C(3) = 17.25[/tex]

Hence, the cost for three games is $17.25

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Answer:

D is the answer.

"The second sampling method, surveying the both teams, is the most representative. "

Step-by-step explanation:

Answer:

Approximate Total area that will be watered is 5887.5 feet²

Step-by-step explanation:

Radius of the Circular area that sprinkler cover , r = 25 feet

Number of sprinkler = 3

Area covered by 1 sprinkler = Area of circle

                                          = πr²

                                          = 3.14 × (25)²

                                          = 3.14 × 625

                                          = 1962.5 feet²

Area covered by 3 sprinkler = 3 × 1962.5 = 5887.5 feet²

Therefore, Approximate Total area that will be watered is 5887.5 feet²

The approximate total area that will be watered will be 5887.5 feet². Square centimeters and other similar units are used to measure area.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area.

The given data in the problem is;

r is the radius of the Circular area that sprinkler cover = 25 feet

n is the number of sprinklers = 3

The sprinkler executes a circular motion ;

Area covered by sprinkler = Area of the circle

The area covered by sprinklers is found as;

[tex]A_S = \pi r^2 \\\\ A_S = 3.14 \times (25)^2 \\\\\ A_S = 3.14 \times 625 \\\\ A_S= 1962.5 \ feet^2[/tex]

The area covered by the three sprinklers will be;

[tex]\rm A_S = 3 \times 196.25 \\\\ \rm A_S =5887.5 \ feet^2[/tex]

Hence approximate total area that will be watered will be 5887.5 feet².

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Answer:

A. 0.25

Step-by-step explanation:

Final answer:

To measure 9/12 or 3/4 of a cup of syrup using a 1/8 cup, fill and level-off the 1/8 cup measuring cup six times. This uses basic fraction multiplication and measurement skills appropriate for middle school mathematics.

Explanation:

To measure light corn syrup using a 1/8 cup measuring cup, you first need to understand the fraction you're working with, which is 9/12 of a cup. Simplifying this fraction gives you 3/4 of a cup (since 9/12 reduces to 3/4 by dividing both the numerator and denominator by 3). Now, since there are 8 portions of 1/8 in a full cup, you need 6 portions of 1/8 (because 3/4 equals 6/8) to measure out 3/4 of a cup of light corn syrup.

To do this, you'll fill the 1/8 cup measuring cup six times and add each portion to your mixture to reach the desired amount of 9/12 or 3/4 of a cup of syrup. This is a simple example of using measurements and fractions to achieve the correct proportions in a recipe or any culinary preparation.

The numbers are consecutive, meaning they are in arithmetic progression.

Sum of Arithmetic Progression = (n/2)[2a + (n- 1)d]

Where, n = total number of numbers and d = common difference between two successive numbers

Therefore n = 4 and d = 1 ( as the numbers are consecutive )

now (4/2)(2a + (4 - 1)1) = 2

i.e. 2(2a + 3) = 2

i.e. 4a + 6 = 2

i.e. 4a = - 4

i.e. a = - 1

Therefore nos are -1, -1+1 , -1+1+1 , -1+1+1+1

i.e. -1, 0 , 1 , 2

Hope this helps..!!

Thank you :)

Answer:

Jessica patio is made up of two rectangles.

Dimension of one rectangle which is in the shape of cuboid = 7 ft x 4 ft x 5 ft,

Dimension of Second rectangle which is also in the shape of cuboid =10 ft x 8 ft x 6 ft

→Total Area of Patio=Total  Surface Area of Cuboid having Dimension 7 ft x 4 ft x 5 ft,+ Total  Surface Area of Cuboid having Dimension 10 ft x 8 ft x 6 ft

= 2 ×[7×4+4×5+5×7]+2×[10×8+8×6+10×6]

=2×[28+20+35]+2×[80+48+60]

=2×83 +2×188

=166+376

=542 square feet

Upper face of larger cuboid is partially covered , with smaller cuboid.

Area of Lower face of smaller cuboid =7 ×4=28 square feet

Total Area of patio = 542- (Area of lower face of smaller cuboid)

  = 542 - 28

  =514 square feet

Answer:

3 3/4 miles

Step-by-step explanation:

Mr. Connors' pattern is to drive 1 3/12 fewer miles each day. The third day after Tuesday (on Friday), he wll drive 3×(1 1/4) = 3 3/4 fewer miles than on Tuesday.

Final answer:

Mr. Connors will drive 1/12 mile fewer on Friday compared to Tuesday.

Explanation:

To find how many fewer miles Mr. Connors will drive on Friday compared to Tuesday, we need to calculate the difference in the distances driven.

On Tuesday, he drove 77 1/12 miles.

On Friday, he will continue the pattern of subtracting a fraction from the distance driven each day. Therefore, we can subtract the same fraction (1/12) from the distance driven on Friday.

So, the difference in miles driven between Friday and Tuesday will be 77 1/12 - (77 1/12 - 1/12), which simplifies to 1/12 mile.

Therefore, Mr. Connors will drive 1/12 mile fewer on Friday compared to Tuesday.

Answer:

the answer is 14 speed limit signs

Step-by-step explanation:

To find the probability of selecting all blue balls, we divide the number of ways to choose 4 blue balls out of 8 by the number of ways to choose 4 balls out of 8 blue balls and 3 white balls.

To find the probability of selecting all blue balls, we need to consider the number of ways we can choose 4 blue balls out of the 8 blue balls in the urn, divided by the total number of ways we can choose 4 balls out of the 8 blue balls and 3 white balls in the urn.

The probability can be calculated as:

P(All blue balls) = (Number of ways to choose 4 blue balls out of 8) / (Number of ways to choose 4 balls out of 8 blue balls and 3 white balls)

Since the balls are selected without replacement, the number of ways to choose 4 blue balls out of 8 is 8 choose 4. The number of ways to choose 4 balls out of 8 blue balls and 3 white balls is 11 choose 4.

Therefore, the probability of selecting all blue balls is P(All blue balls) = (8 choose 4) / (11 choose 4).

Answer:

The thirtieth term of sequence is 52

Step-by-step explanation:

Given the A.P series

-6, -4, -2, 0, ...

we have to find the thirtieth term of the following sequence.

The A.P is -6, -4, -2, 0, ...

which implies

Common difference, d=-4-(-6)=-4+6=2

First term=a=-6

n=30

[tex]a_n=a+(n-1)d[/tex]

[tex]a_{30}=a+29d[/tex]

[tex]a_{30}=-6+29(2)=-6+58=52[/tex]

hence, the thirtieth term of sequence is 52

The values of x is 0.8 and the right option is O A. 0.8.

Similar shapes are enlargements of two shapes using scale factor.

The ratio of the corresponding lengths of similar shapes is equal.

Formula:

From the diagram,

make x the subject of the equation

Hence, the values of x is 0.8 and the right option is O A. 0.8.

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