A restaurant has 1,996 forks, 1,745 knives and 2,116 spoons. The owner wants to have 2,000 of each utensil. She can buy more utensils or donate extra utensils. How many additional forks and knives are need? How many extra spoons are there?

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.

Suppose the length of each side of the cube is x, so the volume must be:  

x^3.  

If the volume is 15 cm^3, so the length must be cuberoot(15) which is not integer,. So, the volume of the cube with integer side never equal with 15 cm^3

Final answer:

The volume of a cube with integer edge lengths must be a perfect cube of an integer, and since 15,000,000 (15m^3) is not a perfect cube, the cube's volume cannot be 15m^3.

Explanation:

The volume of a cube is calculated by cubing the edge length, which means multiplying the length of an edge by itself three times (x3). If the length of each edge of a cube is x centimeters and x is an integer, the volume in cubic centimeters will also be an integer because the cube of any integer is an integer. Since the question specifies a volume of 15m3, which is 15,000,000 cm3 (because 1m3 equals 1,000,000 cm3), and 15,000,000 is not a perfect cube of any integer, the edge length x cannot be an integer, thus the volume of the cube cannot be 15m3.

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

Y6z2/x4

The 6, 2, and 4 are exponents

[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]

[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]

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.

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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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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proportional relationship between the amount of raisins, r (cups), and the amount of peanuts, p (cups), in this recipe is [tex]r = \frac{2}{3} p[/tex]

What is proportional relationship?

We can state that two variables are in a proportional relationship if one of them is always equal to a constant multiplied by the other (quantity).

A mathematical comparison of two numbers is called a proportion. Let's examine proportionality in greater detail.

Different sorts of proportions can be categorized based on the type of relationship that two or more amounts share. Two different proportions exist.

1.Direct Proportion relationship

2. Indirect Proportion relationship

For every 6 cups of peanuts, a trail mix recipe calls for 4 cups of raisins.

The quantity of raisins, measured in cups, and the quantity of peanuts, measured in cups, are inversely proportionate in this recipe.

Ratio of raisins to peanuts is either 4:6 or 2:3.

It would apply to all mixtures equally.

If there are p cups of peanuts and r cups of raisins, then r:p is the mixed ratio.

Therefore,

[tex]\frac{r}{p} = \frac{2}{3}[/tex]

[tex]r= \frac{2}{3}p[/tex]

Therefore, the proportional relationship between the amount of  raisins, r (cups), and the amount of peanuts, p (cups), in this recipe. is

[tex]r = \frac{2}{3} p[/tex]

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Final answer:

In this question, the student is asking about the proportional relationship between the amount of raisins and peanuts in a trail mix recipe.

Explanation:

In this question, the subject is Mathematics and the grade level is Middle School.

The question is related to proportional relationships in a trail mix recipe. The recipe calls for 4 cups of raisins for every 6 cups of peanuts. This means that for every 6 cups of peanuts, you need to add 4 cups of raisins. The relationship between the amount of raisins and the amount of peanuts is proportional, with a ratio of 4:6 or simplified as 2:3.

To determine the amount of raisins needed for a given amount of peanuts, you can set up a proportion. For example, if you have 12 cups of peanuts, you can use the ratio 2:3 to find out how many cups of raisins you need. Cross-multiplying, you get 2x = 3x 12, where x represents the number of cups of raisins. Solving for x, you find that x = 8. Therefore, you would need 8 cups of raisins for 12 cups of peanuts.

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.

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].

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

Answer:

9 birds landed on the fence. 18 - 9 = 9

Why hello there!

The correct answer is 9 your equation is down below

9+x=18 we use the oppisie of adding so subracting and turn the eqation to this

9-18=x so x=9

If my answer helped please mark me as brainliest thank you and have the best day ever!

The answer:

25 feet per 1 second

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

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

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

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.

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:

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.

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.

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.

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