Kim decides to give her old toys to her younger cousins. She gives her cousin Sarah 2/3. Then, she gives her cousin Ryan 2/5 of the remaining toys. She has 6 toys left. How many toys did Kim have to begin

Answer:

\(\frac{9x - 4}{x^2 - 4}\)

Step-by-step explanation:

Did the iReady math diagnostic.

Answer:

10 : 3 , 1 : 3 , 12 : 1

Step-by-step explanation:

before simplifying the ratios both must be in the same units of measure.

(a)

1 litre = 1000 ml

2 litres : 600 ml

= 2000 ml : 600 ml ( divide both parts by 200 )

= 10 : 3

(b)

1 day = 24 hours

8 hr : 1 day

= 8 hr : 24 hr ( divide both parts by 8 )

= 1 : 3

(c)

1 Km = 1000 m

3 Km : 250 m

= 3000 m : 250 m ( divide both parts by 250 )

= 12 : 1

The standard form representation of the equation of a circle as given obviously in the task content is; (x + 12)² + (y + 3)² = 4².

It follows from the task content that the standard form representation of the equation of the circle as given in the task content is to be determined.

The given equation is;

137+6y=-y²-x²-24x

By rearrangement, we have;

x² + 24x + y² + 6y + 137 = 0.

Therefore by the use of completing the square method; we have;

(x + 12)² - 144 + (y + 3)² - 9 + 137 = 0.

Hence, the correct standard form representation of the equation is;

(x + 12)² + (y + 3)² = 16

(x + 12)² + (y + 3)² = 4²

Ultimately, the standard form representation of the equation of a circle as given obviously in the task content is; (x + 12)² + (y + 3)² = 4².

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The correct statement is 5 is prime number .

Given statements,

2 is composite

5 is prime

-2 is composite

-5 is prime

Now,

Composite numbers are numbers which have factors other than 1 and the number itself .

Prime numbers are numbers which have factors other only 1 and the number itself .

So,

According to the statements 5 is a prime number .

Factors of 5 are 1 and 5 .

Thus it is a prime number .

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From the curve given we can see that the graph that shows a function where f(2)= 4 is Graph A.

A quadratic graph is in form of a parabola opened upward or downward.

According to the question, we are to select a graph that has a coordinate (2, 4) on its curve.

To determine thus, we will locate the value of 2 on the x-axis and value of 4 on the y-intercept and trace whether the intersecting point is on the curve.

From the curve given we can see that the graph that shows a function where f(2)= 4 is Graph A.

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Answer:

10.9

Step-by-step explanation:

Formula = Number x 100

Percent = 6 x 100

55 = 10.91

Following shows the steps on how to derive this formula

Step 1: If 55% of a number is 6, then what is 100% of that number? Setup the equation.

6

55% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

55Y = 6 x 100

55Y = 600

Y = 600

100 = 10.91

Temperature is a variable that uses (2) the scale interval and, according to physical theory, represents in the numerical form how hot or cold something is.

The physical concept of temperature indicates in numerical form how hot or cold something is.

A thermometer is used to determine temperature.

One variable that makes use of the scale interval is temperature.

Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points and thermometric substances.

The most popular scales are the Celsius scale, sometimes known as centigrade, with the unit symbol °C, the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being mostly used for scientific purposes.

One of the seven base units in the International System of Units is the kelvin (SI). The lowest point on the thermodynamic temperature scale is absolute zero, or zero Kelvin, or 273.15 °C.

Therefore, the temperature is a variable that uses (2) the scale interval and, according to physical theory, represents in the numerical form how hot or cold something is.

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The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

According to the statement

we have to find that the number of ways are there to select the applicants who will be hired.

So, For this purpose, we know that the

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Here we use the combination.

And from the given information:

20 applicants from a pool of 90 applications will be hired.

And according to this the combination becomes:

\(C_{20} ^{90}\)

then solve it

\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)

\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)

Then after solve it

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)

Now open another factorial

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)

Now solve this then

\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).

So, The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

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The formula to calculate the hardness of water (in ppm) can be written as: Hardness= (2.497 \(*\) Cal + 4.118 \(*\) Mg) \(*\) \(10^6\)

where Cal and Mg are amounts of calcium (Ca2+) and magnesium(Mg2+) in ppm, respectively.

To calculate the hardness of water in parts per million (ppm), you need to first determine the concentrations of calcium and magnesium ions in the water. Then, multiply the concentrations of each ion by the corresponding hardness coefficient.

The hardness coefficient for calcium is 0.04, and the hardness coefficient for magnesium is 0.07. Finally, add the two values together to get the total hardness in ppm.

For example, if the calcium concentration is 5ppm and the magnesium concentration is 3ppm, then the total hardness of the water is            (0.04 x 5ppm) + (0.07 x 3ppm) = 0.32ppm.

The hardness of water in parts per million (ppm) is 0.32ppm

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Answer:

A fraction simply tells us how many parts of a whole we have. You can recognize a fraction by the slash that is written between the two numbers. We have a top number, the numerator, and a bottom number, the denominator. For example, 1/2 is a fraction.

Step-by-step explanation:

Answer:

a quantity that is not a whole number

Answer: a

Step-by-step explanation:  a b

Answer:

X

Rotate

Step-by-step explanation:

correct on edge 2020

Answer:

a. x

c. rotate

Step-by-step explanation:

edge2021 :)

Answer: x =6 or x =-2

Step-by-step explanation:

|x−2|−7=−3

Step 1: Add 7 to both sides.|x−2|−7+7=−3+7|x−2|=4

Step 2: Solve Absolute Value.|x−2|=4 We know either x−2=4orx−2=−4x−2=4(Possibility 1)x−2+2=4+2(Add 2 to both sides)

x=6

and for other

x−2=−4(Possibility 2)x−2+2=−4+2(Add 2 to both sides)x = -2

Anthony's "hiring process" or "recruitment period" was 30 days.

The blank can be filled with "hiring process" or "recruitment period" to indicate the duration between placing the advertisement for a new assistant on November 1 and hiring Marquis on December 1. This period represents the time it took Anthony to evaluate applicants, conduct interviews, and make the decision to hire Marquis.

The hiring process typically involves several steps, such as advertising the job opening, reviewing applications, conducting interviews, and finalizing the selection. The duration of this process can vary depending on various factors, including the number of applicants, the complexity of the position, and the efficiency of the hiring process.

In this case, the hiring process took 30 days, indicating the length of time it took for Anthony to complete the necessary steps and choose Marquis as the new assistant. This duration provides insight into the timeframe Anthony needed to assess candidates and make a hiring decision.

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sin(cos^-1(tan^-1(v))) can be expressed algebraically as v / sqrt(1 + v^2)

We can start by analyzing the innermost function, tan^-1(v). This represents the angle whose tangent is equal to v.

Next, we take the cosine of this angle, which gives us adj/hyp, where adj is the length of the side adjacent to the angle and hyp is the length of the hypotenuse. By definition of the tangent function, we have adj = v and hyp = 1. Thus, cos(tan^-1(v)) = v / sqrt(1 + v^2).

Now we take the sine of the resulting expression, cos(tan^-1(v)). This gives us opp/hyp, where opp is the length of the side opposite to the angle. Using the Pythagorean theorem, we can solve for opp: opp = sqrt(hyp^2 - adj^2) = sqrt(1 - v^2). Therefore, sin(cos^-1(tan^-1(v))) = opp/hyp = sqrt(1 - v^2) / sqrt(1 + v^2).

Simplifying this expression by multiplying the numerator and denominator by sqrt(1 + v^2), we get: sin(cos^-1(tan^-1(v))) = (sqrt(1 - v^2) * sqrt(1 + v^2)) / (sqrt(1 + v^2) * sqrt(1 + v^2)) = sqrt((1 - v^2)(1 + v^2)) / (1 + v^2) = v / sqrt(1 + v^2).

Therefore, sin(cos^-1(tan^-1(v))) can be expressed algebraically as v / sqrt(1 + v^2).

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Answer:

a=-2

Step-by-step explanation:

3a−6=−12

Step 1: Add 6 to both sides.

3a−6+6=−12+6

3a=−6

Step 2: Divide both sides by 3.

3a/ 3 = −6/ 3

a=−2

Answer:

6.61387 stones

Step-by-step explanation:

Answer:

6.6 stones

Step-by-step explanation:

1 kg= 2.2 pounds

1 stone =14 pounds ⇒ 1 pound= 1/14 stone

42 kg= 42*2.2 pounds= 92.4 pounds  

92.4 pounds = 92.4 * 1/14 stone= 6.6 stones

Answer:

70

Step-by-step explanation:

The formula for this question is

60/100 * x = 42

Look carefully at how this is written. You have so many pets (x) in the shop.

60 % of them are dogs. But that 60% we are told is also how many animals are dogs and that is 42.

So you have two facts meaning the same thing.

Multiply the equation by 100

100 * 60/100 *x = 42 * 100

60x = 4200    

Divide by 60

x = 4200/60

x = 70

The total number of animals was 70

So, there are 160,320 ways to line up the ten people with the president next to the secretary and the VP next to the treasurer.

(a) To line up the ten people without any restrictions, we can consider them as distinct individuals. Therefore, the number of ways to line up the ten people is 10!.

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

So, there are 3,628,800 ways to line up the ten people.

(c) If the president must be next to the secretary and the VP must be next to the treasurer, we can consider the pairs (president, secretary) and (VP, treasurer) as single entities. This essentially reduces the problem to arranging eight entities: (president + secretary), (VP + treasurer), and the remaining six members.

Now, we can arrange the eight entities in 8! ways. However, within each pair, the president and secretary can be arranged in 2! ways, and the VP and treasurer can be arranged in 2! ways.

So, the total number of ways to line up the ten people with the given restrictions is:

8! × 2! × 2!

8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320

2! = 2 × 1 = 2

Therefore, the total number of ways is:

40,320 × 2 × 2 = 160,320

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If z is a standard normal variable, the probability that z is less than 1.13 is given by: A. 0.8708.

In Statistics, the standard normal distribution table is designed and developed to provide only the area to the left of a specified z-score.

Additionally, since z-score (z₁) and z-score (z₂) are generally symmetric about z = 0 and are negatives of one another, then, by symmetry, the area to the right of z-score (z₂) is always equal to the area to the left of z-score (z₁).

This ultimately implies that, the total areas under a standard normal distribution curve in two tails can be determined by calculating the area to the left of z-score (z₁) and multiplying the value by two (2).

From the z-score table, the area to the left of z-score (z₁ = 1.13) is the same as the probability that z is less than 1.13 and this is given by:

Area to the left of z-score (z₁ = 1.13) = 0.8708.

Probability, P(z ≤ 1.13) = 0.8708.

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Answer:

648 is your answer

Step-by-step explanation:

hope this helps!!

Answer:

216

Step-by-step explanation:30-12=18 so 18 x 12=216 hope that helped

Answer: She invest 41500 at 7% interest and 900 at 11% interest.

Step-by-step explanation:

Formula for simple interest = \(\dfrac{\text{Principal x rate x Time}}{100}\)

Let \(P_1=\$1500,\ P_2=\$900\ \ \ \ , r_1=r, \ \ r_2=r+4,\ \ \ t_1=t_2=1\)

Simple interest by first investment = \(\dfrac{P_1r_1t_1}{100}=\dfrac{1500(r)(1)}{100}=15r\)

Simple interest by second investment = \(\dfrac{P_2r_2t_2}{100}=\dfrac{900(r+4)(1)}{100}=9(r+4)\)

As per given,

Total interest = $204

\(\Rightarrow 15r+9(r+4)=204\\\\\Rightarrow\ 15r+9r+36=204\\\\\Rightarrow\ 24r=204-36\\\\\Rightarrow\ 24r=168\\\\\Rightarrow\ r=\dfrac{168}{24}\\\\\Rightarrow\ r=7\%\)

Hence, she invest 41500 at 7% interest and 900 at 11% interest.

Answer:

Area = 8 sq cm

Step-by-step explanation:

This shape is a parallelogram. Its like a rectangle that got tipped over. Area is:

base × height.

We don't know the base that is on the bottom of the image as it is shown. But if you turn it sideways, the 4 can be the base and the 2 is the height.

Area = b × h

= 4 × 2

= 8

The area is 8 sq cm.

We need to sum at least the first 10 terms of the series to be sure that the remainder is less than 0.0001 in magnitude

We can use the Alternating Series Estimation Theorem to estimate the remainder Rn of the series:

|Rn| ≤ |an+1|

where an+1 is the first neglected term of the series. For this series, the nth term is \((-1)^(n+1)/(n^4)\), so the (n+1)th term is \((-1)^n+2/((n+1)^4)\).

Thus, we have:

|Rn| ≤ \(|(-1)^(n+2)/((n+1)^4)|\)

We want to find the smallest value of n such that |Rn| < 0.0001. This means we need to solve the inequality:

\(|(-1)^(n+2)/((n+1)^4)|\) < 0.0001

Simplifying, we get:

\(1/((n+1)^4)\) < 0.0001

Taking the fourth root of both sides, we get:

1/(n+1) < 0.1

Solving for n, we get:

n > 9

Therefore, we need to sum at least the first 10 terms of the series to be sure that the remainder is less than 0.0001 in magnitude.

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The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.

To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.

On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.

Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.

Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.

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