Solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation.

2x-5< -11 or 5x +1> or = to 6.

If a is a positive integer and if the unit's digit of a2 is 9 and (a+1)2 is 4, then the unit's digit of (a+2)2 is 1.

We are given that a is a positive integer, and we need to find the unit's digit of (a+2)². To solve this problem, let's first analyze the information provided:
1. The unit's digit of a² is 9.
2. The unit's digit of (a+1)² is 4.
From the first piece of information, we can conclude that the unit's digit a must be either 3 or 7, as 3² = 9 and 7² = 49 (the unit's digit is 9).
Now, let's check the second piece of information. If the unit's digit of a is 3, then the unit's digit of (a+1) would be 4. Since 4² = 16 (unit's digit is 6), this doesn't match the given condition that the unit's digit of (a+1)² is 4.
So, the unit's digit must be 7. In this case, the unit's digit of (a+1) is 8. Since 8² = 64 (unit's digit is 4), this matches the given condition.
Now that we know the unit's digit of a is 7, let's find the unit's digit of (a+2)². If the unit's digit of a is 7, then the unit's digit of (a+2) is 9. Since 9² = 81 (unit's digit is 1), the unit's digit of (a+2)² is 1.
Therefore, the correct answer is:
A) 1

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it takes approximately 27.1 minutes for the water to cool to 80°F.

To determine the value of the constant a in Newton's law of cooling, we can use the formula:

ΔT/Δt = -a(T - T_r)

where:

ΔT/Δt is the rate of change of temperature,

T is the temperature of the object (whirlpool bath water),

T_r is the ambient temperature (room temperature), and

a is the constant of proportionality.

Given that the temperature cools from 102°F to 86°F in 10 minutes, we can substitute these values into the formula to solve for a:

(86 - 102) / 10 = -a(102 - 69)

-16 / 10 = -33a

-8/5 = -33a

a = (8/5) / 33

a ≈ 0.0242

Therefore, the value of the constant a in Newton's law of cooling is approximately 0.0242.

To find the value of the constant k, we can use the relationship between a and k:

k = a / m

where m is the mass of the object. Since the mass of the whirlpool bath water is not provided, we cannot determine the value of k without additional information.

To find the water temperature after 20 minutes, we can use Newton's law of cooling:ΔT/Δt = -a(T - T_r)

(ΔT/Δt) * Δt = -a(T - T_r) * Δt

(T - T_r) = (T_0 - T_r) * exp(-aΔt)

where T_0 is the initial temperature (102°F), T_r is the room temperature (69°F), and Δt is the time interval (20 minutes).

Plugging in the given values:

(T - 69) = (102 - 69) * exp(-0.0242 * 20)

Simplifying and solving for T:

T ≈ 80.82°F

Therefore, the water temperature after 20 minutes is approximately 80.82°F.

To determine how long it takes the water to cool to 80°F, we can rearrange the equation:

(T - T_r) = (T_0 - T_r) * exp(-aΔt)

80 - 69 = (102 - 69) * exp(-0.0242 * Δt)

11 = 33 * exp(-0.0242 * Δt)

Taking the natural logarithm of both sides:

ln(11/33) = -0.0242 * Δt

Solving for Δt:

Δt ≈ -ln(11/33) / 0.0242

Δt ≈ 27.1 minutes

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Answer:

Area =  l × w

=  18 × 10

=  180 centimeters2

Step-by-step explanation:

Answer:

YXW

Step-by-step explanation:

Answer:

YXW

Step-by-step explanation:

Answer: I think it's A. But correct me if I'm wrong. I don't really do a lot of this math.

Answer:

x= 100

Step-by-step explanation:

x/5 = 20

multiply both the sides by 5 we get

5× x/5 = 20×5

x = 100

We represent with the letter "j" the time spent jogging.

We represnt with the letter "s" the time swiming.

And we need to write a mathematical expression that represents the number of calories burn while exercising.

we know as well that when jogging one burns 15 calories per minute and when swiming one burns 10 calories per minute.

Our equation for number of calolries burnt is;

calories = 15 * j + 10 * s

(where j and s are to be entered in minutes)

so when the person jogs for 20 minutes (and no swiming)

calories = 15 (20) + 10 (0) = 300 + 0 = 300 calories.

The full form of MICR is:-magnetic ink character recognition

U can search the defention in Gogle

Hope it helps

Answer:

2+4=6

20+40=60

200+400=600

2,000+4,000=6,000

Step-by-step explanation:

For the given geometric sequence we have:

a) R = 3/4

b) 243/256

c) Aₙ = 3*(3/4)⁽ⁿ⁻¹⁾

The common reason is given by the quotient between two consecutive terms, so using the first two, we will get:

R = (9/4)/3

R = 3/4

That is the common reason.

b) To find the fifth therm, we need to take the fourth one and multiply it by the common reason, so we will get:

81/64*(3/4) = 243/256

c) The n-th term of the sequence is the first term of the sequence multiplied by the common reason (n - 1) times, it gives:

Aₙ = 3*(3/4)⁽ⁿ⁻¹⁾

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ANSWER

The short piece is 10 meters long and the long piece is 33 meters long

EXPLANATION

Let the length of the shorter piece be x.

Let the length of the longer piece be y.

We have that the total length of the banner is 43 meters. This means that:

x + y = 43 ___(1)

The short piece is 23 meters shorter than the long piece. This means that:

x = y - 23 _____(2)

Now, we have a system of two simultaneous equations:

x + y = 43

x = y - 23

We can solve this by substitution.

Substitute the second equation into the first equation.

That is:

y - 23 + y = 43

Collect like terms:

y + y = 43 + 23

2y = 66

Divide through by 2:

y = 66 / 2

y = 33 m

Recall that:

x = y - 23

Therefore:

x = 33 - 23

x = 10 m

Therefore, the short piece is 10 meters long and the long piece is 33 meters long.

To calculate the 90% confidence interval for the average EPS of all industrials listed on the DJIA, we will use the formula:

Confidence interval = sample mean ± (critical value * standard deviation / √sample size)

Step 1: Find the critical value.
Since we want a 90% confidence interval, the corresponding critical value can be obtained from the z-table. The critical value for a 90% confidence level is 1.645.

Step 2: Calculate the margin of error.
The margin of error is given by (critical value * standard deviation / √sample size).
Substituting the values, we get: 1.645 * 0.395 / √9 = 0.29175.

Step 3: Calculate the confidence interval.
The confidence interval is given by the sample mean ± margin of error.
Substituting the values, we get: 1.85 ± 0.29175.

The 90% confidence interval for the average EPS of all industrials listed on the DJIA is (1.55825, 2.14175).

We can be 90% confident that the true average EPS of all industrials listed on the DJIA falls within the range of 1.55825 to 2.14175.

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Answer & Step-by-step explanation:

8 is 2×2×2.

Doubling a number is the same as multiplying ×2.

So maybe you could take the 9 and double it, 18.

Double it again, 36.

Double it again, 72.

Or anyway that you can "take apart" 8 and 9 in smaller numbers and rearrange, because you can multiply in any order.

For example, if you don't know your 8 or 9 times tables, but you know your 3 and 4 and 6 times tables:

8 is 4×2 and

9 is 3×3.

8×9 is the same as 2×3 and 4×3

6×12

which is 72.

Hope this helps.

Answer:

(5+3 = 8)

Step-by-step explanation:

The value of k is found by dividing the numerator of the original ratio, 5, by the sum of the numerator and denominator of the ratio (5+3 = 8).

Answer:

w = 99 pounds

Step-by-step explanation:

The problem states that Mary's weight is given by the equation:  

w = 92 + g - 1

I believe the "-1" should be "-x."  -1 would mean that Mary lost 1 pound.  But we know that Mary lost 8 pounds, which is designated as x.

The correct equation is:

w = 92 + g - x

============

Using the correct equation, and g=15 and x=8, Mary's new weight is:

w = 92 + 15 - 8

w = 99 pounds

Answer:

the change was 24F

Step-by-step explanation:

Probability that at least one is a boy given that at least 6 of the children are girls is 1 .

Given,

Family has 7 children and at least six are girls .

Here,

The probability that at least one child is a boy given that at least 6 of the children are girls is 1.

This is because if a parent has 7 children, it is certain that at least one of them must be a boy or a girl. Since we are given that at least 6 of the children are girls, it must be the case that at least one of the remaining children is a boy.

Thus the probability is 1 .

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Answer:

60

Step-by-step explanation:

30% of total boxes at the store is equal to 18

so

\((30 \div 100 ) \times x = 18 \\ x = 18 \times( 100 \div 30) = \\ 18 \times (10 \div 3) = \\ 6 \times 10 = 60\)

The 18 boxes of cereal Isaac purchased. This represents 30% of all the boxes in the store then total boxes of cereal at the store exists 60.

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. To exstimate a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

The total no of boxes =  y × 100/x

Given x = 30%

y = 18 boxes

Total boxes at the store = 18 × 100/30 = 60

Therefore, the total boxes of cereal at the store exists 60.

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The value of x and y in the figure is

x = 15 √3

y = 30

The missing sides is solved using trigonometry relations as follows

Using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

using tan, TOA

tan 60 = opposite / Adjacent

tan 60 = x / 15

x = 15 tan 60

x = 15 √3

Using cos

cos 60 = 15 / y

y = 15 / cos 60

y = 30

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Answer:

D

Step-by-step explanation:

The quotient is the result of dividing x by 5

The expression is then

15 - \(\frac{x}{5}\) → D

Answer:

A and C

Step-by-step explanation:

Vertical angles are angles that are created when two lines cross. They are angles opposite from each other. (another way of saying it:) Vertical angles are angles opposite each other where two lines cross.

Hope this helps! :)

Answer:

id-2614656691

ps-0000

gddhh

The equation that represents this direct variation is  (7/4)x flowers planted in x minutes.

Given,

Caroline planted first 7 flowers in 4 minutes.

After 12 minutes, she had planted 21 different flowers.

We have to find the equation that represents this direct variation;

Here,

We can use Unitary method;

Unitary Method;

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

That is,

4 minute ⇒ 7 flowers

1 minute ⇒ 7/4 flowers

Therefore,

x minute ⇒ (7/4)x flowers

Therefore,

The equation that represents this direct variation is  (7/4)x flowers planted in x minutes.

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Answer:

I cant solve number 1 but I can for number 2

Calculate GCF for each

You can learn how to use the prime factorization method to do this

GCF(12, 18, 40, 45) = 1

So I dont get what the problem is because there are no numbers for #2. So either I dont understand the problem or it is a trick question whereas the answer is UNDEFINED/IMPOSSIBLE.

Answer:

D

Step-by-step explanation:

\(8x \sqrt{2} - 4 \sqrt{2} \)

Answer:

Area of the floor not covered = 240ft²

Step-by-step explanation:

Find the diagram attached

The area of the floor not covered = area of the office floor - area of the rug covered

Area of the office floor = 7in×5in = 35in²

Area of the rug = 5in×4in = 20in²

Area of the floor not covered = 35in²-20in² = 15in²

Since 1in = 4ft

1in² = 16ft²

Given the area of the floor not covered to be 15in²

In square feet will be 16×15 = 240ft²

Answer:

22155.84 in

Step-by-step explanation:

r = 84 in

π = 3.14

then area if circle = r² × π

… A = 84² × π = 22155.84 = ( 22.15584 min )