Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Evaluate the numerical expression and match to its value.
8.96
21
13
20.9
27.4
896
5.6 23+ (12.75 + 7.45)
43 × (0.6 +3.6) ÷ 0.3
2 + (2.75 +1.75) ÷ 0.9
20.27

(4) The series diverges by the Comparison Test. Each term is greater than that of a divergent geometric series.

To determine whether the series converges or diverges, we can use the Comparison Test.
First, we can simplify the series by dividing both the numerator and denominator by n:
[Infinity] (4 + 1/n) / (3 - 5/n)

As n approaches infinity, both the numerator and denominator approach 4/3, so we can write:
[Infinity] (4 + 1/n) / (3 - 5/n) = [Infinity] 4/3

Since the harmonic series [Infinity] 1/n diverges, we can conclude that the original series diverges as well.
Therefore, the correct answer is:
4. The series diverges by the Comparison Test. Each term is greater than that of a divergent geometric series.

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As per the given points, the distance is 0.08 meter.

The term distance in math is known as the length of the line joining the two points.

Here we have given that over a period of one year and the two points on opposite sides of a mid-ocean ridge moved a distance of 4 centimeters farther apart.

Here we have to calculate the distance between the two point in  meter.

Let us consider that x be the distance between the two points.

As we know that in each side there is 4 centimeter distance.

Then the total distance between the two points,

=> 4 x 2 = 8 centimeter.

Then the meter equivalent is calculated as,

=> 8/100 = 0.08

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The probability of getting a five or higher on the first roll and getting a total of 7 on the two dice is \(\frac{1}{36}\).

What is probability?

Probability is a measure or quantification of the likelihood or chance of an event occurring. It represents the ratio of the favorable outcomes to the total possible outcomes in a given situation. Probability is expressed as a number between 0 and 1, where 0 indicates impossibility (an event will not occur) and 1 indicates certainty (an event will definitely occur).

The total number of possible outcomes when rolling two dice is 6*6 = 36, as each die has 6 possible outcomes.

Now, let's determine the number of outcomes that satisfy both conditions (five or higher on the first roll and a total of 7). We have one favorable outcome: (6, 1).

Therefore, the probability is given by the number of favorable outcomes divided by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes

= \(\frac{1}{36}\)

So, the correct option is A) 1/36.

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Answer:

4 kilograms

Step-by-step explanation:

The ratios 2/3 and 5/6 are not equivalent.

To determine whether the ratios 2/3 and 5/6 are equivalent, we can simplify both ratios and compare them.

Let's simplify the first ratio, 2/3:

There are no common factors between 2 and 3, so the ratio is already in its simplified form.

Now let's simplify the second ratio, 5/6:

Both 5 and 6 have a common factor of 1, so we can't simplify the ratio further.

Comparing the simplified ratios, we have 2/3 and 5/6. To check if they are equivalent, we can cross-multiply and see if the products are equal:

2 * 6 = 12

3 * 5 = 15

Since 12 is not equal to 15, the ratios 2/3 and 5/6 are not equivalent.

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Answer:

The exact value of cos(45°) is √(2) / 2.

Step-by-step explanation:

Answer:

Answer:√2/2=cos45

√2/2×√2/√2=2/2√2

1/√2

The linear distance traveled in one revolution of a wheel can be calculated using the formula:

Circumference = π * Diameter

Given that the diameter of the wheel is 36 inches, we can substitute the value into the formula:

Circumference = π * 36 inches

Using an approximate value of π as 3.14159, we can calculate the circumference:

Circumference ≈ 3.14159 * 36 inches

Circumference ≈ 113.09724 inches

Therefore, the linear distance traveled in one revolution of a 36-inch diameter wheel is approximately 113.09724 inches.

The Total Area of the Composite Figure is: 5,047.5 ft²

The formula for the area of a rectangle is:

A = Length * Width

The formula for the area of a trapezium is:

A = ¹/₂(sum of parallel sides) * height

Area of the side yard = 33 ft * 5 ft = 165 ft²

Area of Driveway = 25 ft * 20 ft = 500 ft²

Area of Front Yard = (33 * 35) - (8 * 35) = 875 ft²

Area of Vivian's house =  (30 * 50) + (8 * 25) = 1700 ft²

Area of backyard = (¹/₂(58 + 55) * 55) - (22 * 50) - (25 * 8) = 1807.5 ft²

Total Area of Composite Figure = 165 + 500 + 875 + 1700 + 1807.5

Total Area of Composite Figure = 5,047.5 ft²

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After using the formula for the sum of an infinite geometric series, we conclude that the given infinite series does not converge to 1.

To prove that the infinite series ∑(i=1 to ∞) 2^(i-1) equals 1, we can use the formula for the sum of an infinite geometric series.

The sum of an infinite geometric series with a common ratio r (|r| < 1) is given by the formula:

S = a / (1 - r)

where 'a' is the first term of the series.

In this case, our series is ∑(i=1 to ∞) 2^(i-1), and the first term (a) is 2^0 = 1. The common ratio (r) is 2.

Applying the formula, we have:

S = 1 / (1 - 2)

Simplifying, we get:

S = 1 / (-1)

S = -1

However, we know that the sum of a geometric series should be a positive number when the common ratio is between -1 and 1. Therefore, our result of -1 does not make sense in this context.

Hence, we conclude that the given infinite series does not converge to 1.

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The price of the widgets for which it should be sold to make the maximum profit is $25.4   .

We know that the quadratic equation ax² + bx + c ,

if a < 0 , then the maximum value of the quadratic equation will be at x = -b/2a .

In the question ,

it is given that ,

a company is selling a widget ,

the selling price of each widget is = x ,

the profit made by the company = y ,

the equation of profit is given as y = −3x² + 152x − 1150 ,

where a = -3 , b = 152 and c = -1150,

we can see that in the given quadratic equation ,

a < 0 , so , the maximum will be at

x = -b/2a

x = -152/2(-3)

x = 152/6

x = 25.333

x ≈ 25.4

Therefore , the price of the widget is $25.4  .

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Answer:

Jeremy did not make a good inference. The ratio is not in proportion to 2/15. The correct inference would be about 26 students who did not read any books in July. The sample might be biased since it was limited to those at the pool.

Step-by-step explanation:

Answer:

he did not make a good inference

Step-by-step explanation:

did it on edge

The total prize is $854. and in order to split the amount of money equally we divide the total price in 5 equal parts(You should identigy the word "split" to let you know you need to divide):

So, every member will get $170.8

Answer:

104,000

Step-by-step explanation:

Length x width x height:

32.5 x 160 x 20

Answer:

There will be 97 trees in each orchard.

Step-by-step explanation:

Given that,

Nissa is going to plant 485 trees this year.

Nissa plants 5 orchards of trees.

We need to find the number of trees in each orchard. Let it is n. So, we can find it as follows :

\(n=\dfrac{485}{5}\\\\n=97\)

So, there will be 97 trees in each orchard.

The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

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Answer:

9.3 ft

Step-by-step explanation:

Step-by-step explanation:

a. To find dy/dx when y = 2xlog e (2x), we can use the chain rule. First, we rewrite the function as y = 2x(ln(2x) + 1) where ln is the natural logarithm. Then, we can take the derivative of y with respect to x:

dy/dx = 2(ln(2x) + 1) + 2x(1/2x) = 2ln(2x) + 2 + 2/x

b. To find f′(0) when f(x) = e^x^2/e^x+1, we can take the derivative of the function with respect to x:

f′(x) = (2xe^x^2(e^x+1) - e^x^2(e^x+1)) / (e^x+1)^2

Setting x = 0, we get:

f′(0) = 2e^0(e^0 + 1) - e^0(e^0 + 1) / (e^0 + 1)^2 = 1 / (e^0 + 1)^2 = 1 / 2^2 = 1/4

Answer:

Intrest(I) = 780

Step-by-step explanation:

Here, Intrest = ?

Principal = Rs 2000

Rate = 13percent

Time = 3 years

Now,Intrest = PTR/100

= (2000×3×13)/100

= RS 780

Answer:

Using point-slope form we get:

y - 6 = 1/3(x + 6)

y - 6 = 1/3x + 2

y = 1/3x + 8

Answer:

Volume of prism: 5,400 cubic feet

Volume of pyramid: 1,800 cubic feet

Volume of composite figure:

3,600 cubic feet

Step-by-step explanation:

Volume of prism:

\(30 \times 12 \times 15 = 5400\)

Volume of pyramid:

Area of base: 30 × 12 = 360 square feet

Height: 15 feet

\( \frac{1}{3} (30 \times 12 \times 15) \)

\( \frac{1}{3} \times 5400 = 1800\)

Volume of composite figure:

\(5400 - 1800 = 3600\)

3,600 cubic feet

Answer:

d

Step-by-step explanation:

Answer: 8

Step-by-step explanation: it’s 1/3 out of 24.

Answer:

8

Step-by-step explanation:

1/3 of 24

= 1/3 x 24

= 24/3

= 8

The correct answer is D. $2.75 / $3.24

To determine how much you should expect to pay for gas in Philadelphia versus Cleveland, we need to compare the transportation expenses in both cities. Based on the given data, the transportation expenses are as follows:

Philadelphia: $117

Cleveland: $106

To calculate the expected gas prices, we need to consider the transportation expenses relative to the national average. The formula to find the expected gas price is:

Expected Gas Price = National Average * (Transportation Expense / National Average)

National Average for gas = $2.59

For Philadelphia:

Expected Gas Price in Philadelphia = $2.59 * ($117 / 92) ≈ $3.30

For Cleveland:

Expected Gas Price in Cleveland = $2.59 * ($106 / 78) ≈ $3.51

Comparing the expected gas prices, we find that:

A. $3.03 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

B. $1.95 / $2.59: This option does not match the expected gas prices in Philadelphia and Cleveland.

C. $2.34 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

D. $2.75 / $3.24: This option matches the expected gas prices in Philadelphia and Cleveland.

Therefore, the correct answer is:

D. $2.75 / $3.24

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Answer:

-5/4 or -1.25 or -1 1/4

Step-by-step explanation:

The cart that uses less battery cells per seat is the 4 seater carts.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Since 2 seater street cart uses 100 battery cells, this will be:

= 100 / 2

= 50

4 seater cart uses 120 battery cells. This will be:

= 120 / 4

= 30

The cart that uses less battery cells per seat is the 4 seater carts.

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Complete question

Tesla junoir is a new compny that makes electric go carts. They have 2 models; 2 seater street cart uses 100 battery cells and 4 seater cart uses 120 battery cells. Which cart uses less battery cells per seat?