Henrik buys 40 collectible cards per month. Kharif sells 20 cards from his collection of 180 each month. When will Henrik have more cards than Kharif? Show your work.

Answer: V = 24*(x - 4) with the condition x > 4.

Step-by-step explanation:

The volme of a cube/box is equal to:

V = W*L*H

where W = width, L = lenght and H = heigth.

First:

We know that the cubes cut in the corner have a side length of 2.

Then the remaining part is folded up, and this is now the height.

So the height of the box is equal to 2.

Now, we know that the initial measures of the piece of paper are x by 16

But now, in each extreme, we subtracted 2 units, that are now the new heiht, so now the piece of paper is (x -2 -2) by (16 -2 - 2)

or (x - 4) by 12.

Then the volume of the box is:

V = (x -4)*12*2 = 24*(x -4)

Notice something, if x is equal or smaller than 4, then we have a negative volume or a volume equal to zero. Those are problems in our model, so we should use the condition x > 4.

The student answered 27 out of 30 questions correctly on the history test, achieving a 90% accuracy rate.

To calculate the number of questions the student answered correctly, we can multiply the total number of questions (30) by the percentage of questions answered correctly (90%). The calculation is as follows:

Number of questions answered correctly = Total number of questions × Percentage of questions answered correctly

= 30 × 0.90

= 27

Therefore, the student answered 27 questions correctly on the history test.

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Answer:undefined

Step-by-step explanation:

straight up and down lines are undefined

The point needed for the relation is \(P(x,y) = (3, 4)\) if P and P' are symmetric about the x-axis.

The point needed for the relation is \(P(x,y) = (-3, -4)\) if P and P' are symmetric about the y-axis.

In this exercise we are supposed to determine the coordinates of a point P under an assumption of rigid transformation. Now, we must use the following symmetry transformations:

Reflection about the x-axis

\(S'(x,y) = S(x,y) - 2\cdot (0, s_{y})\) (1)

Reflection about the y-axis

\(S'(x,y) = S(x,y) - 2\cdot (s_{x}, 0)\) (2)

Where:

If we know that \(P'(x,y) = (3, -4)\), the coordinates for each reflection are, respectively:

Reflection about the x-axis

\(P(x,y) = (3,-4) - 2\cdot (0, -4)\)

\(P(x,y) = (3, 4)\)

\(P(x,y) = (3, 4)\) if P and P' are symmetric about the x-axis.

Reflection about the y-axis

\(P(x,y) = (3, -4) - 2\cdot (3, 0)\)

\(P(x,y) = (-3, -4)\)

\(P(x,y) = (-3, -4)\) if P and P' are symmetric about the y-axis.

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Answer:

Below

Step-by-step explanation:

(3x-1)(3x-1)  =  9x^2 -3x -3x+1 = 9x^2 -6x +1

Answer:

rectangle is a parallelogram with 4 right angle

Answer:

C (A rectangle is a parallelogram with four right angles)

Ok, so

We want to simplify:

We could sum or substract the similar terms given. Remember that similar terms, are terms whose variables are the same.

This is:

Simplifying:

Answer:

The answer is C. Pediatrician

Step-by-step explanation:

They are trained to diagnose and treat all kind of minor health problem to serious illness in children.

Consider presenting a particle moving through three dimensions as an illustration. Several x, y, and z-based equations could be used to describe its path.

There are two kinds of parametric equations which are frequently encountered in practical applications.

Circular  Motion:

In parametric equations that model circular motion, sine and cosine have periodic functions for x and y.

Projectile Motion:

The vertical component of projectile motion is quadratic, and the horizontal component is linear.

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Answer : These are points on a coordinate plane

Answer:

Down

Step-by-step explanation:

The negative before the x^2 makes it Down.

In a:  Type 1 error = 0.05, In b: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.  In C: Type 1 error

a) Type 1 error = 0.05

b) When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. ... The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

0.03 < 0.05

c) Type I and type II errors. ... In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding), while a type II error is failing to reject a false null hypothesis (also known as a "false negative" finding). so Type 1 error

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\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &1265\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years\dotfill &7\\ \end{cases} \\\\\\ A = 1265(1 + 0.02)^{7} \implies A = 1265( 1.02 )^{7}\implies A \approx 1453\)

Answer:

A

Step-by-step explanation:

They have the same side, one side is congruent to itself.

alternate interor angle are the same, which is:

Top left of the triangle on the left + botton right of the triangle on the right,

and top left on the triangle on the right + botton right of of the triangle on the left.

Answer:

The second answer is the correct answer and the explanation in the attachment

For S(x)=x*(x+5) ,
(a) To find the critical number(s), we need to take the derivative of the function and set it equal to zero.

S'(x) = 2x+5

2x+5 = 0

x = -5/2

So, the critical number is x = -5/2.

(b) To find the interval(s) where the function is increasing, we need to look at the sign of the derivative.

When x < -5/2, S'(x) < 0, which means the function is decreasing.

When x > -5/2, S'(x) > 0, which means the function is increasing.

So, the interval where the function is increasing is (-5/2, ∞) in interval notation.

For P(x)=-(x-4)*(x-23),
(a) To find the critical number(s), we need to take the derivative of the function and set it equal to zero.

P'(x) = -2x+27

-2x+27 = 0

x = 27/2

So, the critical number is x = 27/2.

(b) To find the interval(s) where the function is increasing, we need to look at the sign of the derivative.

When x < 27/2, P'(x) < 0, which means the function is decreasing.

When x > 27/2, P'(x) > 0, which means the function is increasing.

So, the interval where the function is increasing is (27/2, ∞) in interval notation.

Note: The condition is given in the doll maker's profit function (0

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Answer:x+y=36

xy=256

x=256/y

256/y + y = 36

256/y + y²/y = 36y/y

y² - 36y +256 = 0

use the quadratic formula to get 18+2√17 and 18-2√17.

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be False.

In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.

Here,

False.

The order of operations we use to solve two-step equations is the same order we use to solve every other mathematical statement,

which is commonly recalled by the acronym PEMDAS. (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).

The fundamental distinction is that we are carrying out the operations against the equation's representation. For instance, consider the following equation:

=> 2x + 5 = 11

To get the following result, we would first subtract 5 from both sides, then divide by 2.

=> x = 3

In order to "undo" the operations that were carried out on the variable in the original equation, we are utilising the same series of operations as usual, but in reverse order.

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Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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Answer:

To find the equation of the line that contains the points (3,0) and (4,6), you can use the slope-intercept form of a line, which is given by the equation:

y = mx + b

Where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

To find the slope of the line, you can use the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the points (3,0) and (4,6), you get:

m = (6 - 0) / (4 - 3) = 6/1 = 6

So the slope of the line is 6.

To find the y-intercept, you can plug the slope and one of the points into the slope-intercept form of the equation and solve for b:

0 = 6*3 + b

b = -18

So the y-intercept is -18.

Therefore, the equation of the line that contains the points (3,0) and (4,6) is:

y = 6x - 18

This equation is in slope-intercept form and can be used to plot the line on a graph or to find the y-value for a given x-value.

The probability of having at least two girls is 50% and the probability of having all children of the same gender is 25%.

The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes.

P(A) = n(A) / n(S) , where:

n(A) = number of events favorable to event A

n(S) = number of outcomes

In this case, we are looking at the probability of having at least two girls and the probability of having all children of the same gender.

(a) To find the probability of having at least two girls, we need to consider the possible outcomes of having 3 children.

There are 2³ = 8 possible outcomes: BBB, BBG, BGB, GBB, GGB, GBG, BGG, and GGG.

Out of these 8 outcomes, 4 of them have at least two girls (GGB, GBG, BGG, and GGG).

Therefore, the probability of having at least two girls is 4/8 or 50%

(b) To find the probability of having all children of the same gender, we need to consider the possible outcomes of having 3 children again.

Out of these 8 outcomes, 2 of them have all children of the same gender (BBB and GGG).

Therefore, the probability of having all children of the same gender is 2/8 or 25%

So, the probability of having at least two girls is 50% and the probability of having all children of the same gender is 25%.

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The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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The statistical technique used to estimate future values by successive observations of a variable at regular intervals of time that suggest patterns is called trend analysis.

Trend analysis is a statistical technique that helps identify patterns and tendencies in a variable over time. It involves analyzing historical data collected at regular intervals to identify a consistent upward or downward movement in the variable.

By examining the sequential observations of the variable, trend analysis aims to identify the underlying trend or direction in which the variable is moving. This technique is particularly useful when there is a time-dependent relationship in the data, and past observations can provide insights into future values.

Trend analysis typically involves plotting the data points on a time series chart and visually inspecting the pattern. It helps in identifying trends such as upward or downward trends, seasonality, or cyclic patterns. Additionally, mathematical models and statistical methods can be applied to quantify and forecast the future values based on the observed trend.

This statistical technique is widely used in various fields, including finance, economics, marketing, and environmental sciences. It assists in making informed decisions and predictions by understanding the historical behavior of a variable and extrapolating it into the future.

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Answer:

15 days

Step-by-step explanation:

35 divided by 7 equal 5

5 times 3 equal 15

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}}{\stackrel{slope}{\cfrac{2}{3}}~\hfill \stackrel{reciprocal}{\cfrac{3}{2}}~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{2}}}\)

so, we're really looking for the equation of a line whose slope is -3/2 and that it passes through (2 , -6)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{- \cfrac{3}{2}}(x-\stackrel{x_1}{2}) \implies y +6= -\cfrac{3}{2} (x -2) \\\\\\ y+6=-\cfrac{3}{2}x+3\implies y=-\cfrac{3}{2}x-3\)