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Answer:

The nth term is: [tex]a_n = \frac{1}{4} + \frac{1}{4}(n-1)[/tex]

a40 = 10

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.

The nth term of a sequence is given by:

[tex]a_n = a_1 + (n-1)d[/tex]

In which [tex]a_1[/tex] is the first term and d is the common difference.

1/4,1/2

This means that:

[tex]d = \frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}[/tex]

1/4

This means that [tex]a_1 = \frac{1}{4}[/tex]

The nth term is:

[tex]a_n = a_1 + (n-1)d[/tex]

[tex]a_n = \frac{1}{4} + \frac{1}{4}(n-1)[/tex]

Then find a40.

[tex]a_{40} = \frac{1}{4} + \frac{1}{4}(40-1) = \frac{1}{4} + \frac{39}{4} = \frac{40}{4} = 10[/tex]

So

a40 = 10

Answer:

The answer is 120

Step-by-step explanation:

I got it by timing 8 and 15 , and I got 120

Answer:

if it will help

y^7

Step-by-step explanation:

y^4+3 = y^7

Answer:

78

Step-by-step explanation:

Arc GHJ is 81*2= 162 (the arc measure of an inscribed angle that does not cross the center of the circle is 2 times the measure of the angle

since arc GH is 84 and we need HJ, subtract 84 from 162=78

Answer:

-6.7+6.8

Step-by-step explanation:

‐4.5+4.4+x=0====> -0.1+x=0===> x= 0.1

so we are looking for the choice with the answer of 0.1

-6.7+6.8=0.1✔

-6.7+(-6.6)= -13.3❌

7.2+(-7.2)=0❌

7.2+(-7.3)=(-0.1)❌

Answer:

if shes losing 2/3 each hour, the her profit would be 41.

Step-by-step explanation:

2/3 x 6 is 4, 45 - 4 is 41.

Answer:

9 cm

Step-by-step explanation:

Answer:

9cm

Step-by-step explanation:

Answer:

(a) and (e)

Step-by-step explanation:

Given

[tex]d = 14cm[/tex]

Required

Select the true statements

First, is a statement about the area.

The area is calculated as:

[tex]Area= \pi*\frac{d^2}{4}[/tex]

So, we have:

[tex]Area= 3.14*\frac{14^2}{4}[/tex]

[tex]Area= 3.14*49[/tex]

(a) is true

Next, is a statement about the circumference.

This is calculated as:

[tex]C = \pi d[/tex]

So, we have:

[tex]C = 3.14 * 14[/tex]

(e) is true

Answer:

1a.2.5x³-2.25x²+3.5x-1.5

1b.No, they aren't equal. (worked out the product for both and they weren't equal, see below)

2a.-2x⁶+7x⁴+3x³-3x²+11x+20

2b.Yes. When multiplying, it doesn't matter which term/expression you put first

3. The equation has two solutions: x=-2, x=3

Step-by-step explanation:

1. (a)

(0.5x-0.25)(5x²-2x+6)

0.5x(5x²-2x+6)-0.25(5x²-2x+6)

2.5x³-x²+3x -1.25x²+0.5x-1.5

2.5x³-2.25x²+3.5x-1.5

(b)

(0.25x-0.5)(5x²-2x+6)

0.25x(5x²-2x+6)-0.5(5x²-2x+6)

1.25x³-0.5x²+1.5x -2.5x²+x-3

1.25x³-3x²+2.5x-3

This is not equal to our answer for 1(a), so we can see they're not the same.

2(a)

(-2x³+x-5)(x³-3x-4)

-2x³(x³-3x-4) +x(x³-3x-4) -5(x³-3x-4)

-2x⁶+6x⁴+8x³ +x⁴-3x²-4x -5x³+15x+20

-2x⁶+7x⁴+3x³-3x²+11x+20

(b)

Yes. When multiplying, it doesn't matter which term/expression you put first: xy=yx. For example, 2(3)=6 and 3(2)=6.

3

2x²-2x-12=0

(divide each term by 2)

x²-x-6=0

(x+2)(x-3)=0

Anything multiplies by zero is zero, so either x+2=0 or x-3=0

If x+2=0, x=-2. If x-3=0, x=3.

The equation has two solutions: x=-2, x=3

9514 1404 393

Answer:

  (x < -7) ∪ (x > 9)

Step-by-step explanation:

The zeros of the function are the values of x that make the factors zero.

  x +7 = 0   ⇒   x = -7

  x -9 = 0   ⇒   x = 9

When this is expanded, we can see that the leading coefficient is positive.

  x² -2x -63 > 0

This means the parabola opens upward. It will be greater than 0 for x-values to the left of the left zero, and to the right of the right zero. (It is less than zero between those values.)

The solution is x < -7 or x > 9.

_____

In general, for polynomial inequalities, look for the locations of the zeros. The sign of the polynomial will have the sign of the leading coefficient for values of x to the right of the right-most zero. (Here, positive for x > 9.) As you progress farther to the left along the number line, the polynomial changes sign at each zero.

Here, the polynomial becomes negative between the values x=9 and x=-7. Then it is positive again for x < -7.

Answer:

<

Explanation:

turn 5/11 into a decimal: 0.45 which is LESS than 0.50 (0.5).

Answer:

<

Step-by-step explanation:

When comparing fractions and decimals/fractions and percentages/decimals and percentages, it's always good to convert them to have the same type on either side. However, you don't really need to with this problem.

Here's a trick: the larger the denominator is in a fraction, the smaller the value of the fraction is. If the fraction on the left were 5/10, then we know that it would be equal to 0.5 (you can convert either one). Now, since the denominator of the fraction is one greater than 10, we know that the fraction's value is just a little bit less than 5/10. This makes the fraction less than 0.5.

I hope it made sense. Brainliest would be cool but no worries.

Answer:

Solution given:

<5+69°=180°[co- interior angle]

<5=180°-69°=111°

<5=111°

Answer:

Well, the number 595 is exceptionally larger. You would be able to tell by simply subtracting 595 and 5 and you would get 590 leaving you with answer. 595 is greater

Step-by-step explanation:

Answer:

the answer is x=7 cause you have to divide 56 by 8 and that will give you 7 cause 8×7=56

Answer:

So far Gerri is 1/3 complete and needs to be 1/2 complete by Friday. In order to find how much needs finished by Friday, we subtract the fractions.

1/2 - 1/3

1/2 + (-1/3)

3/6 + (-2/6)

(3+(-2))/6

1/6

Hope this helps

Answer:

Last one, -36x+9.

Explanation: You need to multiply negative times positive which is negative. But look at the last one -12×-3/4 equals positive 36/4 which equals 9.

Answer:

-7, -13, -19

Step-by-step explanation:

plug in 1,2, and 3 into the part of the equation "n".

Answer:

a1 = -7

a2 = - 13

a3 = - 19

Step-by-step explanation:

n = 1

a1 = 2*(-3)*1`- 1

a1 = -6 - 1

a1 = - 7

n=2

a2 = 2(-3)*2 - 1

a2 = -12 -1

a2 = - 13

n3 = 2(-3)*3 - 1

n3 = -18 - 1

n3 = -19

Each term is - 6 away from the previous one.

Answer:

Step-by-step explanation:

a line graph would show the data over time.I would plot the days along the horizontal axis and each daily profit at points on the vertical axis.I would connect the points with lines.If her profit increasing each day, I would expect the line height to increase over time.

Answer:

There is already another answer:

line graph or bar graph because it shows you what day of the week you sell more lemonade.

Step-by-step explanation:

Answer:

x=4 and y = 3 ...answer : 1

Step-by-step explanation:

hello :

x/8 =5/10 means : x=40/10 so: x=4

y/6 =5/10 means : y=30/10 so: y=3

Answer: 3 hours

Step-by-step explanation:

195/65=3

Answer:

3

Step-by-step explanation:

$195 divided by $65 is 3 hours of work

Answer:

H0 : μ = 120

H1 : μ < 120

We Can conclude that the number of infants that contract typhoid has reduced because the wells were put in place.

Step-by-step explanation:

Average Number of infants who contracted typhoid monthly = 120

Average Number of infants who contracted typhoid monthly after well installation = 90

The null and alternative hypothesis :

H0 : μ = 120

H1 : μ < 120

Obtain the test statistic :

(Xbar - μ) ÷ s/sqrt(n)

(90 - 120) ÷ 40/sqrt(9)

-30 ÷ 13.3333

= - 2.25

The Pvalue at 95% confidence, df = n-1 = 9 - 1 = 8

Tcritical at 95%, df = 8 ; one tailed = 0.02728

Decision region :

Pvalue < α ; Reject H0

0.02728 < 0.05 ; Hence, we conclude that there is significant evidence that the average number of infants that contract typhoid has decreased because the wells were put in place.

Answer:

24 sq cm

Step-by-step explanation:

the big square is 20 and the small one is 4

Answer:

She makes 192.6$$

Step-by-step explanation:

Answer:

29.4

Step-by-step explanation:

then convert to whole number

The image of the labeled spinner isn't attached

Answer:

Kindly check explanation

Step-by-step explanation:

Answering hypothetically ;

First create a sample space using the label of the two spinners ;

Each space will be the sum of the possible number that shows up on each turn of the spinner.

From the sample space, count the number of spaces where, the sun is greater than 4, that is the required outcome ; = x

Then the total number of samples in the sole space = total possible outcomes = y

Hence,

P(obtaining a sum greater than 4) = required outcome / Total possible outcomes

= x / y

Answer:

a) The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.

b) 0.05 = 5% probability that he has four goals and two assists in one game

Step-by-step explanation:

In hockey, a point is counted for each goal or assist of the player.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval. The standard deviation is the square root of the mean.

(a) Find the mean and standard deviation for the total revenue he earns per game.

60% of six are goals, which means that 60% of the time he earned 3K.

40% of six are goals, which means that 40% of the time he earned 1K.

The mean is:

[tex]\mu = 6*0.6*3 + 6*0.4*1 = 13.2[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{\mu} = \sqrt{13.2} = 3.63[/tex]

The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.

(b) What is the probability that he has four goals and two assists in one game

Goals and assists are independent of each other, which means that we find the probability P(A) of scoring four goals, the probability P(B) of getting two assists, and multiply them.

Probability of four goals:

60% of 6 are goals, which means that:

[tex]\mu = 6*0.6 = 3.6[/tex]

The probability of scoring four goals is:

[tex]P(A) = P(X = 4) = \frac{e^{-3.6}*(3.6)^{4}}{(4)!} = 0.19122[/tex]

Probability of two assists:

40% of 2 are assists, which means that:

[tex]\mu = 6*0.4 = 2.4[/tex]

The probability of getting two assists is:

[tex]P(B) = P(X = 2) = \frac{e^{-2.4}*(2.4)^{2}}{(2)!} = 0.26127[/tex]

Probability of four goals and two assists:

[tex]P(A \cap B) = P(A)*P(B) = 0.19122*0.26127 = 0.05[/tex]

0.05 = 5% probability that he has four goals and two assists in one game