Dadas as sequências identifique quais são PA e a sua razão (r): Lembre-se: para ser uma PA a diferença entre dois termos consecutivos são sempre os mesmos e é chamada de razão (r). A) (1, 1, 1, 1, ...) B) (-1, 0, 1, 2,...) C) (12, 48, 84, 120,...) D) (101, 202, 303, 404,...)

Answer:

a. 20 points

Step-by-step explanation:

Range = Largest given value - Smallest given value.

Identifying the range of test 1

Looking at the dot plot the lowest test grade appears to be 50 while the highest is 90.

So range of test 1 = 90 - 50 = 40

Identifying the range of test 2

Looking at the plot the lowest test grade appears to be 40 while the highest appears to be 100

So range = 100 - 40 = 60

Identifying the differences between the ranges

Test 1 range : 40

Test 2 range : 60

Difference between the two : 60 - 40 = 20 points

Answer:

Answer:answer is 2xsquare × 3xsquare

Step-by-step explanation:

when we multiply both so the answer is 6xsquare y square  More

Answer:

  6x²y³

Step-by-step explanation:

An exponent is used to signify repeated multiplication. Numerical values can be multiplied in the usual way.

__

  (2)(x)(x)(3)(y)(y)(y)

has the factor x repeated 2 times, and the factor y repeated 3 times. The product of 2 and 3 is 6. The expression can be simplified to ...

  = 6x²y³

B. 0.14 mg will be present after 9 hours.

The given function is D(h) = 5e^(-0.4h), which can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given.

To find the milligrams after 9 hours, we need to plug in h = 9 in the function D(h) = 5e^(-0.4h).

D(h) = 5e^(-0.4h)

D(9) = 5e^(-0.4(9))

D(9) = 5e^(-3.6)

D(9) = 5 × 0.024419

D(9) = 0.1220 ≈ 0.12 mg

Hence, the answer is option (c) 1.22 mg.

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Answer:

sensellessness means you have no sense

Step-by-step explanation:

Hope you pass ;)

Answer:

x = 5

Step-by-step explanation:

Step 1: Write equation

5x - 7 = 18

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

5(5) - 7 = 18

25 - 7 = 18

18 = 18

Answer:

Step-by-step explanation:

divide 5 both sides.

x = 5

The given statement if f(x) is a differentiable function on (a, b) and f'(c) = 0 for a number c in (a, b), then f(x) has a local maximum or minimum value at x = c is true

1. Since f(x) is differentiable on (a, b), it is also continuous on (a, b).
2. If f'(c) = 0, it indicates that the tangent line to the curve at x = c is horizontal.
3. To determine if it is a local maximum or minimum, we can use the First Derivative Test:
  a. If f'(x) changes from positive to negative as x increases through c, then f(x) has a local maximum at x = c.
  b. If f'(x) changes from negative to positive as x increases through c, then f(x) has a local minimum at x = c.
  c. If f'(x) does not change sign around c, then there is no local extremum at x = c.
4. Since f'(c) = 0 and f(x) is differentiable, there must be a local maximum or minimum at x = c, unless f'(x) does not change sign around c.

Hence, the given statement is true.

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The measure of the larger acute angle of the triangle can be calculated using trigonometric ratios or by subtracting the measure of the smaller acute angle from 90 degrees. Without further information or given measurements, it is not possible to determine the exact measure of the angle.

Let's consider the general formula for a right triangle where A, B, and C are the angles and a, b, and c are the corresponding sides opposite to each angle:

sin A = a/c, sin B = b/c, and sin C = a/b.

For an acute triangle, we know that the sum of all the angles is equal to 180 degrees, so A + B + C = 180. If the triangle is a right triangle, then one of the angles, say C, is equal to 90 degrees, and A + B = 90 degrees.

In this case, we are only given that the angles of the triangle are acute. Therefore, we can use the formula sin A = a/c, sin B = b/c and sin C = a/b to solve for the angles or use the fact that A + B + C = 180 degrees and A + B = 90 degrees to find the measure of the larger acute angle by subtracting the measure of the smaller acute angle from 90 degrees. However, without specific measurements or additional information, we cannot determine the exact measure of the angle.

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Answer:

\(\boxed{-\frac{7}{12} }\)

Step-by-step explanation:

\(-1\frac{1}{3} +\frac{3}{4}\)

→ Make both denominators the same

\(-1\frac{1}{3} +\frac{3}{4}=-1\frac{4}{12} +\frac{9}{12}\)

→ Convert mixed number into improper fraction

\(-1\frac{1}{3} +\frac{3}{4}=-1\frac{4}{12} +\frac{9}{12}=-\frac{16}{12} +\frac{9}{12}\)

→ Do the -16 + 9 and leave 12 as the denominator

\(-1\frac{1}{3} +\frac{3}{4}=-1\frac{4}{12} +\frac{9}{12}=-\frac{16}{12} +\frac{9}{12}=-\frac{7}{12}\)

The required simplification o f\(-1\frac{1}{3} +\frac{3}{4}\) into fraction form  is -1 / 12

To simplify -1 1 / 3 plus 3 / 4 into fraction form.

The process in mathematics to operate and interpret the function to make the function simple or more understandable called simplifying and the process is called simplification.

Fraction is defined as the number of compositions constituting the Whole. And it is represented as a / b, where a = numerator and b = denominator.

Since the given problem is
\(-1\frac{1}{3} +\frac{3}{4}\)

We need to simplified it into fraction form like a / b.

\(=-1\frac{1}{3}+\frac{3}{4} \\= -2/3 + 3/4\)
=  ( -8 + 9 ) / 12
= -1 / 12

Thus, The required simplification of  \(-1\frac{1}{3} +\frac{3}{4}\)  into fraction form is -1 / 12.

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Answer:

59

Step-by-step explanation:

1) so you start with the mean being 72x5=360

2)100+42+87+66=295

3) 360-295=65

(you get the 5 from the amount of numbers there are) P.S sorry if I'm wrong or this doesn't help

If you started with 100 grams of radon-222 and it has a half-life of 2.183 days, after 4 days, 46.6 grams of radon-222 will remain.

The half-life of a radioactive element is the time it takes for half of the atoms in a sample to decay. This means that after one half-life, the amount of the element remaining will be half of the original amount. After two half-lives, the amount remaining will be a quarter of the original amount, and so on.

To find the amount of radon-222 remaining after 4 days, we can divide the length of time by the half-life to find out how many half-lives have passed. In this case, 4 days / 2.183 days = 1.84 half-lives. This means that the amount of radon-222 remaining will be a quarter of the original amount.

If we started with 100 grams of radon-222 and a quarter remains after 1.84 half-lives, the amount remaining will be 100 grams * 0.25 = 46.6 grams.

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When the base area (30 cm2) and height are multiplied, the right triangular prism's surface area is computed to be 144\(cm^2\).

1. Calculate the area of the triangular base:

A = 1/2(base × height)

A = 1/2(5 × 12)

A = 30 \(cm^2\)

2. Calculate the area of each of the three rectangular faces:

A = length × width

A = 5 × 2 = 10 \(cm^2\)

A = 12 × 2 = 24 \(cm^2\)

A = 13 × 2 = 26\(cm^2\)

3. Calculate the total surface area:

SA = 2×(base area) + 3×(face area)

SA = 2×(30) + 3×(10 + 24 + 26)

SA = 60 + 84

SA = 144\(cm^2\)The area of the triangle can then be multiplied by the prism's height to obtain the total surface area.

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Answer: v=43πr3 where r is the radius. You have the diameter, that is the double of the radius, so r=92=4.5 inches. v=43π4.53=381.69 cubic inches.

Answer:

381.7

Step-by-step explanation:

to get the volume of a sphere the formula is:

V=4 /3πr3

(remember basketball isn't a circle because it is 3-d)

you plug in the radius to that formula and boom you got your answer!

(remember radius is half the diameter, and half of 9 is 4.5)

so your answer would be:

381.7

Answer:

x ≈ 73.3

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos39° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{57}{x}\) ( multiply both sides by x )

x × cos39° = 57 ( divide both sides by cos39° )

x = \(\frac{57}{cos39}\) ≈ 73.3 ( to the nearest tenth )

Answer:

It doesnt

Step-by-step explanation:

Answer:

There are 7 fewer people.

Step-by-step explanation:

This can be calculated just via simple adition and subtraction.

10 people got off the bus, so that is a negative 10 with a positive 7 afterwards as people got on the bus:

-10 + 7 = -3

Now another 4 people got off the bus:

-3 -4 = -7

Therefore there are 7 fewer people on the bus after the second stop when compared to the stop at 2:30.

Hope this helps!

Answer: B) -3x+2=21

Step-by-step explanation:

3(x+2)=21     x = -9

-3x-6=21       x = -9

this answer is correct bc x = the same for both equations.  

The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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Answer:

Both the commutative property of addition and the associative property of addition can be useful in simplifying expressions involving fractions and mixed numbers. The commutative property of addition allows you to reorder terms while the associative property of addition allows you to regroup terms

Step-by-step explanation:

Both the commutative property of addition and the associative property of addition can be useful in simplifying expressions involving fractions and mixed numbers. The commutative property of addition allows you to reorder terms while the associative property of addition allows you to regroup terms

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There are two fractions that are equal, but one of them has a product in the denominator. We need to choose 3 numbers such that the simplified fraction lead to two different numbers. Those numbers are:

Then, there are 4 more numbers: 1, 5, 7, and 8. 1/5 is lower than 3/4, and 7/8 is higher than 3/4. Then, the answer is:

A multiple-choice question with three possible answers is followed by a multiple-choice question with five possible answers. Both questions are answered with random guesses.

To find: the probability that both responses are correct.

Solution: Probability of the first answer to be correct = 1/3

Probability of the second answer is correct = 1/5

The probability of both responses to be correct = Probability of the first response to be correct × Probability of the second response to be correct

Both responses are correct. = (1/3) × (1/5) = 1/15

Therefore, the probability that both responses are correct is 1/15.

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Answer:

Smaller number = 6

Larger number =  36

Step-by-step explanation:

Let the smaller number  be x

Larger number = 4x + 12

Sum of two numbers = 42

x + 4x + 12  = 42               {Add like terms}

    5x  + 12 = 42                {Subtract 12 from both sides}

             5x = 42 - 12

             5x = 30                   {Dive both sides by 5}

         5x/5 = 30/5

x = 6

Smaller number = 6

Larger number = 4*6 + 12 = 24 + 12 = 36

Answer:

0.4 x 10^-1

Step-by-step explanation:

4 x 10^0

=> 4

=> 0.4 x 10^-1

Calculate the sum of the white sugar and the brown sugar quantities. Given that the cake requires 2/3 cup of white sugar and 1/4 cup of brown sugar, we can add this fractions together to find the total sugar needed.

To combine fractions, we first need to find a common denominator. The least common multiple of 3 and 4 is 12. We can convert the fractions to have a common denominator of 12 by multiplying the numerator and denominator of each fraction by appropriate factors.

For the white sugar:

2/3 cup = (2/3) * (4/4) = 8/12 cup

For the brown sugar:

1/4 cup = (1/4) * (3/3) = 3/12 cup

Now, we can add the fractions together:

8/12 cup + 3/12 cup = 11/12 cup

Therefore, the total amount of sugar needed for the cake is 11/12 cup.

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Answer:

On attached graph

Step-by-step explanation:

See attachment

Answer:

\( \frac{11}{12} \)

Step-by-step explanation:

\(( \sin \theta) ^{2} + ( \cos \theta) ^{2} = 1 \\ \\ \therefore \: { \bigg( \frac{ \sqrt{23} }{12} \bigg)}^{2} + ( \cos \theta) ^{2} = 1 \\ \\ \frac{23}{144} + ( \cos \theta) ^{2} = 1 \\ \\ ( \cos \theta) ^{2} = 1 - \frac{23}{144} \\ \\ ( \cos \theta) ^{2} = \frac{144 - 23}{144} \\ \\ ( \cos \theta) ^{2} = \frac{121}{144} \\ \\ ( \cos \theta) = \sqrt{\frac{121}{144} } \\ \\ \cos \theta = \frac{11}{12} \)

Answer:

the slope is -7

Step-by-step explanation:

\(\frac{-2-5}{3-2} =\frac{-7}{1}\)

Answer:

-25=x

Step-by-step explanation:

20=10x-6(2x+5)

20=10x-12x-30

20=-2x-30

+30   +30

____________

50=-2x

÷-2   ÷-2

___________

-25=x

Hope this helps :D

The solution is: solve of the equation 20 = 10x - 6(2x + 5) is: -25=x.

Here, we have,

given that,

the equation is: 20 = 10x - 6(2x + 5)

now, we have to solve this.

so, we have,

20=10x-6(2x+5)

20=10x-12x-30

20+30=-2x-30+30

50 ÷ -2 = -2x ÷ -2

-25=x

Hence, The solution is: solve of the equation 20 = 10x - 6(2x + 5) is: -25=x.

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

There is no mode in these set of numbers.

Seven students were surveyed on the amount of money they make per hour. The results are shown below: $8.00, $8.25, $8.50, $9.00, $9.25, $10.00, $10.50 for this given data there is no mode present in the dataset.

In statistics, the mode is a measure of central tendency that represents the most frequently occurring value in a dataset. It can be used to determine the typical or common value in a given set of data. In this case, we have the hourly wages of seven students, and we need to find the mode of this dataset.

To find the mode, we need to identify the value that occurs most frequently in the dataset. Let's list the data in ascending order:

$8.00, $8.25, $8.50, $9.00, $9.25, $10.00, $10.50.

From the given data, we can observe that no value is repeated. In this case, we say that there is no mode or the dataset has no mode. Since each student earns a different hourly wage, there is no single value that appears more frequently than the others.

Mathematically, we can represent the given dataset as a set of values: {8.00, 8.25, 8.50, 9.00, 9.25, 10.00, 10.50}. The mode, denoted as "Mode(X)", is the value(s) that occur(s) most frequently in the dataset X.

In this case, Mode(X) = None or Mode(X) = ∅ (empty set).

This indicates that there is no mode present in the dataset.

It is important to note that a dataset can have more than one mode or no mode at all. When there are two or more values with the same highest frequency, the dataset is said to be multimodal. In our example, since all values occur only once, there is no mode.

In conclusion, the mode of the given dataset, which represents the most frequently occurring value, is not applicable in this case as there is no value that occurs more frequently than the others.

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