which integer is √59 closer to

The greatest common factor (GCF) of the monomials [tex]34a^2b[/tex] and [tex]24a^5b^2[/tex] is [tex]2a^2b[/tex]. This is found by determining the GCF of the coefficients and the lowest exponent for each common variable.

To find the GCF of two monomials, we need to find the common factors for the coefficients, and then the lowest exponent for each variable that appears in both terms. The coefficients of the given monomials are 34 and 24. The GCF of these numbers is 2.

Next, look at the variables:

For a, the lowest exponent in both terms is a2

For b, the lowest exponent is just b (since one term is b, and the other is b2)

Therefore, the GCF of [tex]34a^2b[/tex] and [tex]24a^5b^2[/tex] is [tex]2a^2b[/tex].

*(Answer)*= [tex]494.4[/tex]

The solution to the inequality |d + 9| > 3 is d < -12 and d > -6.

The question is asking how to solve the absolute value inequality |d + 9| > 3. For this problem, you need to consider two scenarios because an absolute value represents a distance, which can be either positive or negative. For the first scenario, consider the inequality as (d + 9) > 3 which, when simplified, gives us d > -6. For the second scenario, consider the inequality as -(d + 9) > 3, which simplifies to d < -12. That means any value of 'd' that's greater than -6 or less than -12 will satisfy the inequality.

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Plasma is a form of matter in which many of the electrons wander around freely among the nuclei of the atoms. Plasma has been called the fourth state of matter, the other three being solid, liquid and gas.

Normally, the electrons in a solid, liquid, or gaseous sample of matter stay with the same atomic nucleus. Some electrons can move from atom to atom if an electrical current flows in a solid or liquid, but the motion occurs as short jumps by individual electrons between adjacent nuclei. In a plasma, a significant number of electrons have such high energy levels that no nucleus can hold them.

An atom that has lost some of its electrons, thereby attaining an electric charge, is an ion. When a gas is subjected to heat or an electric field, some of its atoms become ions, and the gas is said to be ionized. An ionized gas, unlike a gas in its normal condition, can conduct electrical current to a limited extent. If the heat or electric field becomes extreme, many of the atoms become ions. The resulting super-ionized gas is a plasma, which can conduct a large and sustained electric current.

The behavior and properties of plasmas have aroused interest and creative work among scientists and engineers. Applications include electric lamps, lasers, medical devices, energy converters, water purifiers and flat-panel video displays. About 99% of the visible universe is formed of plasma.

for A)

if she has $ for the downpayment of $70

for B)

360-70+290

290/ 5=58

amount paid = 290-58(#month)

a=290-58m

ANSWER

A= -58m+290

A) The factors that Alani should consider before deciding on the option to choose are:

B) The amount that Alani would have to pay for the weekly payments is $58.

An equation to model the amount paid for Option A after m months is A = 360 - 70 + mx.

Option A:

Total cost = $360

Initial down payment = $70

Number of weekly payments = 5

Weekly payment = $58 (360 - 70)/5

Option B:

Total cost = $360

Weekly payment = $60 ($360/6)

Equation:

Let the weekly payment = x

Let the number of monthly payments = m

Total amount paid after m months (A) = 360 - 70 + mx

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Alani wants to buy a $360 bicycle.  She is considering two payment options.

Option A consists of making an initial down payment of $70 and then 5 smaller, equal-sized weekly payments until she has paid a total of $360.  

Option B consists of making 6 equal payments over 6 weeks in order to pay a total of $360.

A) What factors should Alani take into consideration before deciding which option to choose?

B) How much would Alani have to pay for each weekly payment with option A?  Write an equation to model the amount paid for Option A after m months

Step 1. Expand

-8n + 12 = 12 - 8n

Step 2. Cancel -8n on both sides

12 = 12

Step 3. Since both sides equal, there are infinitely many solutions

Answer: Infinitely Many Solutions

50,000 or Ten thousands

the value of the digit 5 is 50,000. Think of it as the numbers behind 5 as zeros and you will have the answer.

3458=3,458.00

Hoped this worked out well

:) have a nice day

Answer:

3500 is your answer

Step-by-step explanation:

Note the hundreds place value (underlined): 3458.

Look at the number to the right of the underlined number. It is a 5. You round up if the number is 5 or greater.

3458 rounded to the nearest hundred is 3500.

~Senpai

the is 10 because the √100 is 10. hope this helps mark me as brainliest

4/52 * 3/51 = 12/ 2652  = 1/221

The probability of drawing two aces consecutively from a standard deck is 1/221. This is determined by calculating the individual probabilities of drawing an Ace on each draw, and then multiplying these probabilities together.

The question at hand is about the probability of drawing two aces consecutively from a standard deck of 52 cards. Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0.

Here, the total number of aces in the deck is 4. So, the probability of drawing an Ace on the first draw is 4/52 or 1/13. After drawing one ace, there are only 3 aces left and 51 cards in total. So, the probability of drawing an Ace on the second draw is 3/51.

Since these are independent events, the probability of both events occurring is the product of their individual probabilities. Therefore, the answer is (1/13) * (3/51) = 3/663 = 1/221.

So, option b. 1/221 is the correct answer.

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After one year, by depositing $100 in a savings account with a 2.4% interest rate compounded monthly, you will have $102.43.

You are given $100 for your birthday and decide to put it in a savings account that offers a 2.4% interest rate, compounded monthly. To calculate how much money you will have after one year, we'll use the formula for compound interest, which is [tex]A = P(1 + r/n)^{(nt)[/tex], where:

Plugging these values into the formula, we get:

[tex]A = 100(1 + 0.024/12)^{(12*1)A = 100(1 + 0.002)^{12A = 100(1.002)^{12A = 100(1.0243)A = $102.43[/tex]

Therefore, after one year, you will have $102.43 in your savings account.

Answer:

The bus driver is now driving 100 mph after the stop light.

Step-by-step explanation:

If he slowed down 22 mph from 122 you'd subtract. 122-22=120 mph. Hope it helps!

The bus initially driving at 122 mph slows down by 22 mph at a red light, resulting in a current speed of 100 mph. The calculation is 122 mph minus 22 mph.

Calculating the Speed of the Bus

To determine the current speed of the bus, we need to account for the reduction in speed due to the red light.

The bus is initially driving at 122 mph. When it stops at the red light, its speed is reduced by 22 mph.

So, we use the following calculation:

Speed reduction: 22 mph

Therefore, the final speed is:

122 mph - 22 mph = 100 mph

The bus is now driving at 100 mph.

[tex]2x^2-12xy-32y^2=2(x-8y)(x+By)\qquad|\text{use distributive property}\\\\2x^2-12xy-32y^2=(2x-16y)(x+By)\\\\2x^2-12xy-32y^2=(2x)(x)+(2x)(By)+(-16y)(x)+(-16y)(By)\\\\2x^2-12xy-32y^2=2x^2+2Bxy-16xy-16By^2\\\\2x^2-12xy-32y^2=2x^2+(2B-16)xy+(-16By)[/tex]

[tex]\text{therefore:}\\\\2B-16=-12\ \text{and}\ -16B=-32\\\\2B=4\ \text{and}\ B=2\\\\B=2\ \text{and}\ B=2\qquadCORRECT[/tex]

By finding the Least Common Multiple (LCM) of 4 and 10, we can discover that the math club and Spanish club will coincide every 20 days.

This query relates to the concept of the Least Common Multiple (LCM). As the math club convenes every 10 days and the Spanish club convenes every 4 days, we need to find when these meetings will coincide again. In other words, we are finding the LCM of 4 and 10. This tells us the least common multiple days that the two clubs meet.

Let's breakdown the calculation:

Therefore, the Spanish club and the math club will meet on the same day every 20 days.

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The construction that is shown in the accompanying diagram is the perpendicular bisector of line AB.

What is a perpendicular bisector?

A perpendicular bisector is a line or a line segment that both bisects (cuts in half) another line segment and is perpendicular (forms a right angle) to it. In other words, it is a line that passes through the midpoint of a given line segment and is perpendicular to that segment.

If you have a line segment with endpoints A and B, the perpendicular bisector is the line that passes through the midpoint, in this case (C) of AB and forms a right angle with AB. The perpendicular bisector divides the line segment into two equal parts.

Total number of bedazzled vests made = 8.

We need to find the combinations of the number of buttons, zippers and sparkly stickers that she used to make the vests.

First we need to find all the factors of 8.

Factors of 8 are : 1,2,4,8.

Now we need to find the combinations threes of those factors of 8.

1×2×4 = 8

1×1×8 = 8

2×2×2 = 8.

Therefore, there could be only three combinations of number of buttons, zippers and sparkly stickers that she used to make the vests.

1,2,4

1,2,8 and

2,2,2.

Answer: 25 feet during a climb

Step-by-step explanation:

6 percent because 300/500 equals 0.6.

Well, there are 500 people, but only 300 are coming on the trip. That means that 200 people aren't going on the trip. Therefor, 200/500 is the fraction you would use. Now, just simplify the fraction. 200/100=2, and 500/100=5, so the fraction simplifies down to 2/5. 2/5 equals 40% so 40% of the people were not able to go on the trip.

[tex]|2x+3|\geq23\iff2x+3\geq23\ \vee\ 2x+3\leq-23\qquad|\text{subtract 3 from both sides}\\\\2x\geq20\ \vee\ 2x\leq-26\qquad|\text{divide both sides by 2}\\\\x\geq10\ \vee\ x\leq-13[/tex]

Answer: There are a lot of answers to this product. Some of them include (in the format (w, x), where w is the whole number, and x is the factor you must multiply it by to get 0.24):

(2, 0.12), (3, 0.08), (4, 0.06), (6, 0.04), and so on.

Step-by-step explanation: Well, you could just assign the smallest who number greater than 1 to one of the factors, which is 2. Now you just have to multiply that by another factor to get 0.24. To do this, you could set up an equation like this:

2*x=0.24

Next, you would divide both sides by 2 to cancel out the 2 on the left side of the equation, leaving you with:

x=0.12

There you have it!

Now you can check your work by multiplying 2 and 0.12, and you will get 0.24!

You can do the same thing with other whole numbers, such as 3 and 4, and complete the same process to find the decimal factor that multiplies to 0.24.

Hello!

To find the closet number we first need to understand how our data, and how to find the mean.

The mean is known as the average, which we find when we add all of our data up and divide by the number of factors.

In this case, after reading our graph, our data set is equal to:

3,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,8,9,10,11

When all of these numbers are added we get = 120

120 divided by 20 (the total number of factors) is equal to 6!

Which means that the answer to this question is E. 6

Hope this helps.

Based on the calculations, a number which is closest to the mean of this distribution is equal to: E. 6.

A mean is also known as arithmetic average and it's a ratio of the sum of the total number in a data set to the frequency of the data set.

Mathematically, the mean for this data set would be calculated by using this formula:

Mean = [F(x)]/n

For the total number of data, we have:

F(x) = 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 7 + 8 + 9 + 10 + 11

F(x) = 120.

Substituting the parameters into the formula, we have:

Mean = [F(x)]/n

Mean = [120]/20

Mean = 6.

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The interest rate per annum if a fund paying its clients is the third to the last payment of a depositor became Php 1,040.40 from an initial savings payment of Php 1,000.00 is 1.32%

To get the interest rate, we will use the formula for calculating the compound interest as shown:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P is the amount of investment

n is the time of compounding

t is the time

A is the amount after t years

Given the following parameters

P = 1,000.00

A = Php 1,040.40

n = 1

Substitute the parameters into the formula

[tex]1040.4=1000(1+\frac{r}{1} )^{3}\\\frac{1040.4}{1000}=(1+r)^3\\1.0404 = (1+r)^3\\ln(1.0404) = 3ln(1+r)\\ 0.0396=3ln(1+r)\\ln(1+r)=0.0132\\1+r = e^{0.0132}\\1+r =1.0132\\r=1.0132-1\\r=0.0132\\r=1.32\%[/tex]

Hence the interest rate per annum if a fund paying its clients is the third to the last payment of a depositor became Php 1,040.40 from an initial savings payment of Php 1,000.00 is 1.32%.

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Final answer:

The fund is paying its clients an interest rate of 4.04% per annum.

Explanation:

To determine the interest rate per annum, we can use the formula:

Interest = Final Amount - Initial Amount

In this case, the Final Amount is Php 1,040.40 and the Initial Amount is Php 1,000.00. So, the interest is Php 40.40.

Next, we can use the formula:

Interest Rate = (Interest / Initial Amount) × 100

Substituting the values:

Interest Rate = (40.40 / 1000) × 100 = 4.04%

Therefore, the fund is paying its clients an interest rate of 4.04% per annum.

Answer:

The larger of the two angles is x, which is 75. y is the smaller angle at 15.

Step-by-step explanation:

In order to find these, we can use our solved value for y in the second equation to plug into the first equation. This method is called substitution.

x + y = 90

x + (1/5x) = 90

1.2x = 90

x = 75

Now we can plug that value into either equation to find y

y = 1/5x

y = 1/5(75)

y = 15

Answer:

1.) 75

2.) 15

Step-by-step explanation:

edge 2020 Dec 8

The slope-intercept form: y = mx + b

We have in point-intercept form: y - 5 = 6(x + 1)

Transform:

y - 5 = 6(x + 1)     |use distributive property

y - 5 = (6)(x) + (6)(1)

y - 5 = 6x + 6     |add 5 to both sides

y = 6x + 11

The equation of required line in slope intercept form is y= 6x + 11 First option is correct

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c Where m is the slope of the line and c is the y intercept of the line. Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis. If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by m =  [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

[tex]y - 5 = 6(x + 1)\\y - 5 = 6x + 6\\y = 6x + 6 + 5\\y = 6x +11[/tex]

y= 6x + 11 is the equation written in slope intercept form. First option is correct

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For this case we have the following data:

The original dimensions of the drawing are:

If the copier zoom is at 120%, we can find the new dimensions of the drawing by making a rule of three:

Width:

3 ----------> 100%

x ----------> 120%

Where x represents the new width of the drawing:

[tex]x=\frac{(120*3)}{100}\\x=3.6cm[/tex]

Long:

5 ----------> 100%

y ----------> 120%

Where y represents the new long of the drawing:

[tex]y=\frac{(120*5)}{100}\\y=6cm[/tex]

Thus, the new dimensions are 3.6 cm wide and 6 cm long

Answer:

the longer dimension of the new drawing is 6cm

Answer:

the answer is 6 cm

Step-by-step explanation:

Here’s one way you can solve this problem.

A zoom setting of one hundred twenty percent means that the dimensions of the new copy will be one hundred twenty percent of the dimensions of the original drawing.

First, write the scale that expresses the ratio of the original percent to the copy percent, one hundred to one hundred twenty.

Then, let h represent the height of the copy and write the ratio of copy to original as five centimeters to h centimeters.

Next, write a proportion that equates the two ratios. One hundred to one hundred twenty equals five to h.

Then, cross multiply the terms of the proportion. One hundred twenty times five equals one hundred h.

Next, multiply to get six hundred equals one hundred h.

Finally, divide both sides by one hundred to find h. h equals six.

So, the longer dimension of the new drawing is six centimeters, which is one hundred twenty percent of five centimeters.

hope it helps

16 tables x 22 students = 352 students can be in the lunch room.

Final answer:

The number of students that can be seated at lunch at one time is 352.

Explanation:

To find the number of students that can be seated at lunch at one time, we need to multiply the number of tables by the seating capacity of each table.

Given that there are 16 tables and each table can seat 22 students, we can calculate the total number of students that can be seated at one time by multiplying 16 by 22:

16 tables * 22 students/table = 352 students

Therefore, 352 students can be seated at lunch at one time.