Fill in the blank: A student earned a grade of 80% on a math test that had 20 problems. The student answered ______ questions correctly on the math test. (Write the number only.) *

The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

Answer

Step-by-step explanation:

Yes, the random variable X has a binomial distribution. The number of trials n is 30. A binomial distribution follows the same pattern of successes and failure in a series of repeated trials (in this case, the rolling of a die). The number of successes and failures must be fixed. Since we are rolling a die 30 times and the number of times an odd number appears is fixed, then the random variable X has a binomial distribution.

Answer:

c

Step-by-step explanation:

Given that,

A wire of 35 foot secured from the top of the flagpole to stake in the ground.

The steak is 14 feet from the face of a flag pole.

To find,

The length of flagpole.

Solution,

Here, 35 foot is the hypotenuse and 14 feet is one of the leg.

Let the length of flagpole is x feet. Using Pythagoras theorem to find it as follows :

\(x^2=35^2-14^2\\\\x=32.07\ \text{feet}\)

So, the flagpole is 32.07 feet tall.

Answer:

Given that,

The flag pole wire is 35foot

And the length of the foot from the tag flagpole is 14ft

So we want to know the height of the flagpole

So this will form a right angle triangle where the wire is the hypotenuse.

Then, using Pythagoras theorem

c² = a² + b²

35² = 14² + h²

35²-14² = h²

h² =1225-196

h² = 1029

h=√1029

h= 32.09ft

Then, the height of the flag pole is 32.08foot.

Step-by-step explanation:

Answer: 582.7526

Step-by-step explanation:

p =3,14

r =13,4:2=6.7

r^2=44.89

SA= 3,14*44.89+3,14*6,7*21= 582,7526

Answer:

{x|x is a rational non-integer}

Step-by-step explanation:

\( {p}^{2} + 8 - 8p - p \\ = {p}^{2} - p - 8p + 8 \\ = p(p - 1) - 8(p - 1) \\ = (p - 1)(p - 8)\)

\((p - 1)(p - 8)\)

ray4918 here

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Respuesta:

x = 5.656854249

Explicación paso a paso:

[NOTA: Solo quería disculparme de antemano por cualquier mala gramática, ya que estoy usando un traductor para esto.]

x/Sen30°= 8/Sen45° [Multiplica ambos lados por Sen30°]

x = (8/Sen45°) * Sen30° [Resuelve usando una calculadora]

x = 5.656854249

a)

i) The original cube has a side length of 4 cm. The volume of a cube is calculated by cubing the length of one side. So, the volume of the original cube is 4 cm x 4 cm x 4 cm = 64 cm³.

ii) The enlarged cube has a ratio of 3:1 compared to the original cube. This means that each side length of the enlarged cube is three times the length of the original cube. Therefore, the side length of the enlarged cube is 4 cm x 3 = 12 cm. The volume of the enlarged cube is calculated by cubing the length of one side: 12 cm x 12 cm x 12 cm = 1,728 cm³.

b) To find the ratio by which the volume has been increased, we can compare the volumes of the enlarged and original cubes. The ratio of the enlarged cube's volume to the original cube's volume is 1,728 cm³ : 64 cm³, which simplifies to 27 : 1.

This means that the volume of the enlarged cube is 27 times greater than the volume of the original cube. Therefore, the volume has been increased by a ratio of 27:1.

Answer: 15 meters

Step-by-step explanation:

Given the relation:

h(x) = −5(x+1)(x−3)

Where h is the height at time 'x' after diving

At the time of diving, time 'x' = 0, that her height just before making the dive

Therefore,

h(0) = - 5(0 + 1)(0 - 3)

h = - 5(1)(-3)

h = - 5 × - 3

h = 15

Therefore, h = 15 meters

Answer:

15 meters but you should give the other person brainliest!! they did really good!!

Step-by-step explanation:

Answer:

30 cm

Step-by-step explanation:

Make sure all units are the same!

P = Perimeter

A = Area

Formula used for similar figures:

\(\frac{A_{1}}{A_{2}} = (\frac{l_{1}}{l_{2}})^{2}\) —- eq(i)

\(\frac{P_{1}}{P_{2}} = \frac{l_{1}}{l_{2}}\) ———— eq(ii)

Applying eq(ii):

∴\(\frac{25}{P_{2}} = \frac{10}{12}\)

Cross-multiplication is applied:

\((25)(12) = 10P_{2}\)

\(300 = 10P_{2}\)

\(P_{2}\) has to be isolated and made the subject of the equation:

\(P_{2} = \frac{300}{10}\)

∴Perimeter of second figure = 30 cm

To construct a truth table for the given logical expression using De Morgan's Law, we'll break it down step by step and apply the law to simplify the expression.

Let's start with the given expression:

Xyz + X(Y Z)' + X'(Y + Z) + (Xyz)' (X + Y')(X' + Z')(Y' + Z')

Step 1: Apply De Morgan's Law to the term (Xyz)'

(Xyz)' becomes X' + y' + z'

After applying De Morgan's Law, the expression becomes:

Xyz + X(Y Z)' + X'(Y + Z) + (X' + y' + z')(X + Y')(X' + Z')(Y' + Z')

Step 2: Expand the expression by distributing terms:

Xyz + XY'Z' + XYZ' + X'Y + X'Z + X'Y' + X'Z' + y'z' + x'y'z' + x'z'y' + x'z'z' + xy'z' + xyz' + xyz'

Now we have the expanded expression. To construct the truth table, we'll create columns for the variables X, Y, Z, and the corresponding output column based on the expression.

The truth table will have 2^3 = 8 rows to account for all possible combinations of X, Y, and Z.

Here's the complete truth table:

```

| X | Y | Z | Output |

|---|---|---|--------|

| 0 | 0 | 0 |   0    |

| 0 | 0 | 1 |   0    |

| 0 | 1 | 0 |   0    |

| 0 | 1 | 1 |   1    |

| 1 | 0 | 0 |   0    |

| 1 | 0 | 1 |   0    |

| 1 | 1 | 0 |   1    |

| 1 | 1 | 1 |   1    |

```

In the "Output" column, we evaluate the given expression for each combination of X, Y, and Z. For example, when X = 0, Y = 0, and Z = 0, the output is 0. We repeat this process for all possible combinations to fill out the truth table.

Note: The logical operators used in the expression are:

- '+' represents the logical OR operation.

- ' ' represents the logical AND operation.

- ' ' represents the logical NOT operation.

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Performance relative to the whole class refers to an individual's academic achievement in comparison to the rest of their peers in a particular subject or course.

We describe performance relative to the whole class.

To do this, we'll be using the terms "average", "percentile rank", and "standard deviation".
Average:

Calculate the average performance of the whole class by adding all students' scores and then dividing by the number of students.

This will give you a baseline to compare individual performances against the class average.
Percentile Rank:

Determine the percentile rank of a student by calculating the percentage of students in the class who scored lower than them.

For example, if a student is in the 75th percentile, it means they performed better than 75% of the class.
Standard Deviation:

Calculate the standard deviation, which measures the spread of scores within the class.

A low standard deviation indicates that most students have similar performances, while a high standard deviation shows more variability in scores.
By considering these three factors, you can effectively describe a student's performance relative to the whole class. For example, you might say: "John scored above the class average, placing him in the 80th percentile with a moderate standard deviation, indicating that his performance is better than the majority of his classmates."

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Answer: 29.5735 is 1 ounces in ml

There is 0.0338 ounces in 1 ml (Using Units).

What are units?

Units are the tools to measure and compare different things. Comparison becomes easy when all the units for the measurement are the same.  Different units can be classified depending on their use.

There are two type of units

1. Fundamental Units: Fundamental units are all those units that do not depend on any other unit (including themselves). These units cannot be further reduced to the elementary level. In fact, these are elementary units. Only seven fundamental units exist in Metric System or SI system which are

Length (meter, m)

Mass (kilogram, kg)

Time (second, s)

Temperature (kelvin, K)

Amount of substance (mole, mole)

Electric current (ampere, A)

Luminous intensity (candela, cd)

2. Derived units:These units are all those units that are obtained by multiplying and/or dividing one or more fundamental units with or without introducing any other numerical factor. These units can be reduced to their elementary level, which is composed of fundamental units. There exist a large number of derived units in the Metric System.

Examples:

Velocity (m/s)

Acceleration (m/s2)

Momentum (kg-m/s)

Force (N)

Density (kg/m3)

Heat (J)

Energy (J)

Power (W), etc.

Now, To change 1ml to ounces

divide 1ml by 29.574 this will give us value in ounces

Therefore, 1ml/29.574= 0.0338 ounces

hence,

           There is 0.0338 ounces in 1 ml.

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9514 1404 393

Answer:

  5.6 feet

Step-by-step explanation:

Assuming your zip line equation is supposed to be ...

  y = -8/3x +8

we can rewrite it to general form:

  8/3x +y -8 = 0

  8x +3y -24 = 0 . . . . multiply by 3

Now, we can use the formula for the distance from a point to a line:

  d = |ax +by +c|/√(a²+b²) . . . . . distance from (x, y) to ax+by+c=0

Filling in the values we know, we have ...

  d = |8(3) +3(16) -24|/√(8² +3²) = 48/√73 ≈ 5.6

The distance from the tree to the zip line is about 5.6 feet.

The solution of the initial value problem Dy(t)/dt + 8y(t) = 1 + e-6t is option (c) y(t) = (1/8) - (1/8) * e^(-8t).

To solve the given initial value problem, we can use the method of integrating factors.

The given differential equation is:

\(dy(t)/dt + 8y(t) = 1 + e^(-6t)\)

First, we write the equation in the standard form:

\(dy(t)/dt + 8y(t) = 1 + e^(-6t)\)

The integrating factor (IF) is given by the exponential of the integral of the coefficient of y(t), which is 8 in this case:

IF = \(e^(∫8 dt)\)

=\(e^(8t)\)

Now, we multiply both sides of the differential equation by the integrating factor:

\(e^(8t) * dy(t)/dt + 8e^(8t) * y(t) = e^(8t) * (1 + e^(-6t))\)

Next, we can simplify the left side by applying the product rule of differentiation:

\((d/dt)(e^(8t) * y(t)) = e^(8t) * (1 + e^(-6t))\)

Integrating both sides with respect to t gives:

\(∫(d/dt)(e^(8t) * y(t)) dt = ∫e^(8t) * (1 + e^(-6t)) dt\)

Integrating the left side gives:

\(e^(8t) * y(t) = ∫e^(8t) dt\)

\(= (1/8) * e^(8t) + C1\)

For the right side, we can split the integral and solve each term separately:

\(∫e^(8t) * (1 + e^(-6t)) dt = ∫e^(8t) dt + ∫e^(2t) dt\)

\(= (1/8) * e^(8t) + (1/2) * e^(2t) + C2\)

Combining the results, we have:

\(e^(8t) * y(t) = (1/8) * e^(8t) + C1\)

\(y(t) = (1/8) + C1 * e^(-8t)\)

Now, we can apply the initial condition y(0) = 0 to find the value of C1:

0 = (1/8) + C1 * e^(-8 * 0)

0 = (1/8) + C1

Solving for C1, we get C1 = -1/8.

Substituting the value of C1 back into the equation, we have:

\(y(t) = (1/8) - (1/8) * e^(-8t)\)

Therefore, the solution to the initial value problem is:

\(y(t) = (1/8) - (1/8) * e^(-8t)\)

The correct answer is option (c) \(y(t) = (1/8) - (1/8) * e^(-8t).\)

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Answer:

Step-by-step explanation:

The orthocenter of a triangle is the point of intersection of the lines containing its heights.

You find line like that leading line perpendicular to the side of the triangle and crossing the opposite vertex.

Point A is opposite to side BC so line perpendicular to BC that intersects point A is one of the lines needed to find orthocenter.

There are nine 3 number combinations that add up to 19

From the question, we have the following parameters that can be used in our computation:

Summation = 19

Combinations = 3

Using the above as a guide, we have the following:

The combinations of three numbers that add up to 19 are:

(1, 9, 9), (2, 6, 11), (3, 5, 11)

(3, 6, 10), (4, 4, 11), (4, 5, 10)

(5, 5, 9)

These are all the combinations of three positive integers that add up to 19.

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Answer:

After 100 songs

Step-by-step explanation:

2.50x=1.50x+50

.50x=50

÷.50

X=100

Great Songs will be the better deal after 100 songs.

Mathematical operations can also be defined by using built-in functions to subtract, divide, and multiply. The arithmetic operator is the one who conducts the arithmetic operation.

* Multiplication procedure: Values on both sides of the operator are multiplied.

For instance, 7×2 = 14

/ Division: Divides the left operand by the right operand

For instance, 4/2 = 2

MyTunes imposes a fee of $2.50 per song. Great Songs charges $1.50 for each song and includes a $50 one-time membership fee, as stated in the question.

Let the songs that come after Great Songs would be x, the better the deal.

⇒ 2.50x = 1.50x + 50

⇒ 0.50x = 50

Divided by 0.50 into both sides of the equation,

⇒ x = 100

Therefore, Great Songs will be the better deal after 100 songs.

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Answer:

The square root of one hundred and eight √108 = 10.392304845413

The square root of one hundred and forty-four √144 = 12

Step-by-step explanation:

Answer: 12i

Step-by-step explanation:

It will take approximately 4687.9 years for an investment principal of $1500 to reach $1000000 at an interest rate of 14.2% per year

Simple interest is a type of interest calculated only on the principal amount of a loan or deposit, without taking into account the compound interest earned on that principal. It is calculated by multiplying the principal amount, the interest rate and the time period.

The formula of simple interest is given as;

A = P(1 + rt)

where;

In this problem, we have to find the rate first.

The investment doubles after 7 years.

A = p(1 + rt)

2 = 1(1 + r * 7)

2 = (1 + 7r)

2 = 1 + 7r

7r = 2 - 1

7r = 1

r = 1 / 7

r = 0.142

r = 14.2%

The rate is 14.2 %

Now, we can proceed to determine how many years it will take to reach a value of 1000000

Using simple interest formula again;

A = P(1 + rt)

100000 = 1500(1 + 0.142 * t)

1000000 = 1500(1 + 0.142t)

t = 4687.8 years

It will take approximately 4687.8 years

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Answer:

No, they aren't equivalent.

Step-by-step explanation:

First divide 300 by 5 to figure out how many pages he read in each day.

That would be 60 pages each day.

Then, divide 150 by 3.

That would be 50.

Since 60 ≠ 50, the reading rates are not equivalent.

Hope I helped :)

Answer: 34.8

Step-by-step explanation:

Answer:

8, 16, 32

Step-by-step explanation:

using the recursive formula \(U_{n+1}\) = 2\(U_{n}\) and U₁ = 4 , then

U₂ = 2 U₁ = 2 × 4 = 8

U₃ = 2 U₂ = 2 × 8 = 16

U₄ = 2 U₃ = 2 × 16 = 32

Vera used the wrong number in her inequality. Then the correct option is D.

The complete question is given below.

Vera claimed the solution set on the number line represents the inequality Negative 78.9999 greater-than-or-equal-to x.

A number line going from negative 83 to negative 77. A closed circle is at negative 79. Everything to the left of the circle is shaded.

Which error did Vera make?

Vera wrote the inequality with the variable on the left side of the relation symbol.

Vera wrote a relation symbol that does not represent the direction of the ray.

Vera selected an inequality that does not include –79 in its solution set.

Vera used the wrong number in her inequality.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality equation will be

-78.9999 ≥ x

Vera used the wrong number in her inequality.

Then the correct option is D.

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Answer:

it would be cheaper to buy a pack of 45.

Step-by-step explanation:

Shayley would spend $30 on 20 single bottles because 1.50 times 20 = 30