5^-2 x ³√8

answer as a decimal

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

69.72

Step-by-step explanation:

Thats the answer if its not plz tell me

Answer:

x is 3

Step-by-step explanation:

\( {5}^{(x + 1)} - {5}^{(x + 2)} = - 2500 \\ \)

divide all sides by -1:

\( {5}^{(x + 2)} - 5 {}^{(x + 1)} = 2500\)

from law of indices:

\(( {5}^{x} . {5}^{2} ) - ( {5}^{x} . {5}^{1} ) = 2500\)

factorise out 5^x:

\( {5}^{x} ( {5}^{2} - {5}^{1} ) = 2500 \\ {5}^{x} (20) = 2500 \\ {5}^{x} = 125 \\ {5}^{x} = {5}^{3} \\ x = 3\)

Answer:

A. 103

B. y = n²+3

Step-by-step explanation:

The growth follows a parabolic curve shown in answer B. Using this equation we can put in any number, such as 10 to get answer A.

Answer:

15 meters per second

Step-by-step explanation:

60/4 = 15

Answer:

15 meters per second

From Mark studies of a parallelogram and discovering that the slope of the diagonals are 5/3 and -3/5 the conjecture that can be made is

The diagonals are perpendicular to each other

The two different lines that cross each other at a 90° angle are called perpendicular lines.

If two lines intersect at a 90 degree angle, we say that the two lines are perpendicular.

Perpendicular lines have a feature which relates with the slope of the line as being a negative reciprocal

In the context of the given problem,

diagonal 1 has slope 5/3, the negative reciprocal is -3/5.

Since the two diagonals posses this relationship they are said to be parallel

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Answer:

Step-by-step explanation:

Let's call the number of hotdogs sold "x". According to the problem, the number of sodas sold is three times the number of hotdogs sold, or 3x.

We know that the total number of sodas and hotdogs sold is 136. So we can set up an equation:

x + 3x = 136

Simplifying this equation, we get:

4x = 136

Dividing both sides by 4, we get:

x = 34

This means that 34 hotdogs were sold. To find the number of sodas sold, we can multiply the number of hotdogs sold by 3:

3x = 3(34) = 102

So, 102 sodas were sold.

Answer:

$50400

Step-by-step explanation:

5/100*4000=200+4000=4200*12=50400

Answer:

$4,368

Step-by-step explanation:

At the beginning of the first year, the principal (amount deposited) is $4000 at 4% interest.

The rate of interest in decimal is r = 4%/100 = 0.04

Interest for 1 year = P x r = 4000 x 0.04 = $160

So at the end of the first year, Marty's 4000 deposit will have grown to $4,000 + $160 = $4, 160

He deposits this amount into a new account at 5% interest
Interest rate r = 5%/100 = 0.05
Interest = 4160 x 0.05 = $208.00

Total money at the end of the second year = 4160 + 208 = $4,368

The third number so that the three numbers form a right triangle,

1)40

2)84

Therefore, we can form a right triangle with 9,41,40 and 13,85,84

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

1) By applying Pythagorean theorem,

a²+b²=c²

x²+9²=41²

x²=41²-9²

x²=1681-81

x²=1600

x=√1600

x=40

Therefore, the third number is 40

2) x²+13²=85²

x²=85²-13²

x²=7225-169

x²=7056

x=√7056

x=84

Therefore, the third number is 84

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Answer:

1

Step-by-step explanation:

1. List the prime factors of each number.

2. Circle every common prime factor — that is, every prime factor that's a factor of every number in the set.

3. Multiply all the circled numbers. The result is the GCF.

Answer:

1

Step-by-step explanation:

Answer:

The answer is 2..............

Answer:

Step-by-step explanation

Answer:

$13.47 per hour

Step-by-step explanation:

Total earnings = 9.25 (h) + 8 (t/20)

Where h is the number of hours and t is the number of transformers.

Since he worked for 36 hours and assembled 380 transformers:

Total earnings = 9.25 (36) + 8 (380/20)

Total earnings = 333+152 = $485

Finally, to find how much he earned per hours, we simply have to divide the result by the number of hours worked (36):

485/36 = $13.47 per hour.

The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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The system of equations that shows the situation is option 1.  L+J=29  L=2J-10

The question tells us that the summation of the age of Latifa and Jameel is 29

Let J = Jameel

L = Latifa

L + J = 29

The question says that Latifa's age is 2 time of Jameels age = 2J with 10 years subracted

L = 2J - 10

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Step-by-step explanation:

1.Given .

2.Being vertically opposite angle.

3.Because sum of all interior angle of a triangle is always 180°.

4.From the statement of 3 number.

5.Because angle 4 = angle 3 and angle 6= angle 1 .

6.(suppose ,< is angle sign) solving this equation,

m<1 + m<2+ m<3 = m<3 + m<5 + m<1

Answer:

y = 3/2x - 10

Step-by-step explanation:

Parallelism: The same slope but different intercepts

1 - Using the slope and point given find the new y intercept

y = 3/2x + b

-1 = 3/2(6) + b

-1 = 18/2 + b

-1 = 9 + b

-9  -9

-10 = b

2 - Write the new equation using the same slope but different y-intercepts

y = 3/2x + b

y = 3/2x - 10

Answer:

253

Step-by-step explanation:

23 x 11 = 253

An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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Using a system of equations, it is found that she has 52 nickels and 18 dimes in the desk.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given by:

There are 70 coins, hence:

x + y = 70.

A nickel is worth $0.05, while a dime is worth $0.1, and there is a total of $4.40 in the desk, hence:

0.05x + 0.1y = 4.4.

From the first equation, we have that:

y = 70 - x.

Replacing in the second:

0.05x + 0.1(70 - x) = 4.4.

0.05x = 2.6

x = 2.6/0.05.

x = 52

Then:

y = 70 - x = 70 - 52 = 18.

She has 52 nickels and 18 dimes in the desk.

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A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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The estimated probability P(more than 4) is approximately 0.9678.

P(more than 4) ≈ 0.9678. A.

To determine whether the normal distribution can be used as an approximation to the binomial distribution, we need to check if both np and nq are greater than or equal to 5.

n = 11 and p = 0.6.

np = 11 × 0.6

= 6.6

nq = 11 × (1 - 0.6)

= 4.4

Since np = 6.6 is greater than 5 and nq = 4.4 is not less than 5, the normal distribution can be used as an approximation.

To estimate P(more than 4) using the normal distribution approximation, we need to find the mean and standard deviation of the binomial distribution, which can be approximated by the normal distribution.

Mean (μ) = np

= 11 × 0.6

= 6.6

Standard Deviation (σ) = √(npq)

= √(11 × 0.6 × 0.4)

≈ 1.397

Now we can use the normal distribution to estimate P(more than 4).

Since we are interested in more than 4, we need to find P(X > 4).

We can standardize the value of 4 using the mean and standard deviation calculated above and then look up the corresponding area under the standard normal distribution curve.

Z = (X - μ) / σ

= (4 - 6.6) / 1.397

≈ -1.860

Looking up the corresponding area in the standard normal distribution table or using a calculator, we find that the area to the left of -1.860 is approximately 0.0322.

P(X > 4) = 1 - P(X ≤ 4)

P(X > 4) ≈ 1 - 0.0322

≈ 0.9678

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A statement which could be true for g is that: A. g(-13) = 20.

A domain can be defined as the set of all real numbers for which a particular function is completely defined.

Since the domain of this function is given by -20 ≤ x ≤ 5, it simply means that the value of x must between -20 and 5. Also, with a range of -5 ≤ g(x) ≤ 45, the value of x must between -5 and 45.

By extrapolating the function, we can deduce that:

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Complete Question:

Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.

A. g(-13) = 20

B. g(-4) = -11

C. g(7) = -1

D.g(0) = 2

We need to find the profit made per share first.

Then multiply profit per shares to total shares sold

Profit = Selling price - Cost price

Where:

Selling price = $26.40 per dollar

Cost price = $21.45 per dollar

Profit = $26.40 per dollar - $21.45 per dollar = $4.95 per share.

Gross profit = Profit per share x No of shares.

Gross profit = 4.95 x 120 = $594

Answer:

Step-by-step explanation:

1/2 n + 3 = 6

-3 -3

1/2 = 3

Answer is 1.5=n

Answer:

n = 18

Step-by-step explanation:

(1/2)*n-3 = 6 // - 6

(1/2)*n-6-3 = 0

1/2*n-9 = 0 // + 9

1/2*n = 9 // : 1/2

n = 9/1/2

n = 18

n = 18

PLZ GIVE ME BRAINLIEST

The value of Cot (θ) in terms of sin (θ) is \(cot (\theta) = -{{\frac{\sqrt{1-sin^{2}(\theta)}}{sin(\theta)} }\)when θ is in the second quadrant.

A trigonometric function, sometimes known as a circular function, is a function of an arc or angle that is most easily described in terms of the ratios of pairs of sides of a right-angled triangle. Examples of such functions are sine, cosine, tangent, cotangent, secant, or cosecant.

The trigonometric function cot (θ) can be written as:

cot (θ) = cos (θ) / sin (θ)

Now by using the Pythagorean identity,

sin² (θ) + cos² (θ) = 1

cos² (θ) = 1 - sin² (θ)

cos (θ) = ± √ [  1 - sin² (θ) ]

Therefore, substituting the value of cos (θ) in the expression of cot (θ).

cot (θ) = cos (θ) / sin (θ)

cot (θ) = ± √ [  1 - sin² (θ) ]  / sin (θ)

Now, cos (θ) < 0 because the angle θ is in the second quadrant,

Therefore,

cos (θ) = - √ [  1 - sin² (θ) ]

Hence,

cot (θ) = - √ [  1 - sin² (θ) ]  / sin (θ)

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Answer:

use a calculator

Step-by-step explanation:

also if this is easier change 1/2 and 1/3 to 0.5 and 0.3 where it would be 8.5 x 3.3

Answer:

x≤-3 or 2≤x∠7

Step-by-step explanation:

It would be the first answer on the paper

Answer:

A

Step-by-step explanation:

\(\frac{x^2+x-6}{x-7} \leq 0\\\)

hence numerator and denominator are of opposite sign.

case1 .

let x²+x-6≥ 0

and x-7<0

x²+x≥6

x²+x+1/4≥6+1/4

(x+1/2)²≥25/4

(x+1/2)²≥(5/2)²

|x+1/2|≥5/2

x+1/2≥5/2

x≥5/2-1/2

x≥2

or

x+1/2≤-5/2

x≤-5/2-1/2

x≤-3

also x-7<0

x<7

combining

x≤-3 or 2≤x<7

case 2.

x²+x-6<0

and x-7≥0

x²+x<6

x²+x+1/4<6+1/4

(x+1/2)²<25/4

|x+1/2|<5/2

so -5/2 <x+1/2<5/2

-5/2-1/2<x<5/2-1/2

-3<x<2

also x-7≥0

so x≥7

combining

we get no vlaue satisfying both the values.

Hence rejected.

Answer: 18

Step-by-step explanation:

Multiply number of each item possible

3*2*3=18

Answer:

1700 meters / hour

Step-by-step explanation:

160x20 = 3200

3200/ 2 = 1700