43. At the beginning of the month, Emika had $24 in her school cafeteria account. The table below
shows how her account balance changed over the course of three weeks. (Positive change means
money she added into her account, while negative change means money she spends.)
1.
2
Week
1
2
3
Beginning
Balance
($)
24
8
-18
Final
Balance
($)
8
-18
Change
($)
16
26
-12
Expression to show your work
24-16 = 8
8-26-18
-18--12-6
Complete the table for weeks 2-3.
How much would Emika have to deposit into the account during week 4 so that the final
balance is positive?

The given quadratic equation 4x^2 - 4x + 1 = 0 has one real solution

by its discriminant.

The discriminant of a quadratic equation ax^2 + bx +c = 0 is given by

            D = b^2- 4ac

Now from the equation that we have 4x^2 - 4x +1 = 0

             a = 4

             b = -4   and

             c = 1

Hence the discriminant (D) is given by :

             D = b^2- 4ac

                 = (-4)^2- 4(4)(1)

                 = 0

Now check for discriminant D, (D=0)

Therefore the discriminant of a given equation is 0.

So the roots of given equation are real and equivalent.

Hence the equation given 4x^2 - 4x + 1 =0 has only one real solution.

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53 dollar t is the cost of goods if manufacturing costs equal $50 each ,packaging equals $1.00 each, delivery equals $2.00 each, and advertising equals $1,000

what is cost ?

Definition: A cost function is a mathematical formula used to used to chart how production expenses will change at different output levels. In other words, it estimates the total cost of production given a specific quantity produced.

50$ + 1$ + 2$ = 53$

50 for the production

1$ for packaging

2$ for delivery

Hence 53 dollar t is the cost of goods if manufacturing costs equal $50 each ,packaging equals $1.00 each, delivery equals $2.00 each, and advertising equals $1,000

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12 tons of gravel has been used for the driveway.

Weight of first load = 7 tons

Weight of second load = 8000 pounds

There are 2000 pounds (lb) in one US customary ton (t). Both tons and pounds are measurements of mass/weight in the US customary and imperial systems of measurement. However, the definitions of the ton vary in both systems. For example, there are 2240 pounds in an imperial ton, and 2204.6226 pounds in a metric ton.

The US ton is mostly used in the United States and Canada. The imperial ton was mostly used in the UK, and still is to a degree, but since the UK began the process of metrication, the metric ton is also used in the UK.

Convert pounds to tons:

1 pound = 0.0005 ton

8000 pounds = 4 ton

Then,

Weight of second load = 4 ton

Total weight of the gravel, in tons = Weight of first load + Weight of second load

= 8 tons + 4 tons

= 12 tons

Thus, 12 tons of gravel has been used for the driveway.

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Determining if the method of randomization is either appropriate or not for each given situation includes:

A.           Inappropriate

B.           Appropriate

C.          Appropriate.

Randomization is what?

The technique of randomly assigning study participants to various treatment groups is known as randomization.

Randomization can take the form of selecting names at random to place people in groups or flipping a fair coin to place participants in the experimental or control groups.

In contrast to experiments B and C, the randomization strategy used in experiment A is incorrect.

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Therefore , the solution of the given problem of ratio comes out to be

there are 32 fauvists .

Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.

Here,

Given :

the ratio is 13:4

and there were 104 impressionists

Let x be the fauvisits

=> 13:4 = 104/x

=>  13 /4  = 104/x

=> x = 104 *4 /13

= >x  = 32

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x 2, and the second side is expressed by  2x-25 , The value of x is 5.

What is isosceles triangles ?

An isosceles triangle is a triangle with two sides of equal length. These two sides are called the legs and they are congruent. The third side is called the base and it is not necessarily congruent to the legs. The angle opposite to the base is called the vertex angle.

To solve for x, we can start by isolating x on one side of the equation.

We can do this by subtracting x^2 from both sides ,

x^2 - x^2 = 2x-25 - x^2

we get 0 = 2x - 25 - x^2

Now we can add x^2 to both sides ,

x^2 = 2x - 25

Now we can move the -25 to the other side of the equation ,

x^2 - 2x + 25 = 0

Now we can factor the left side of the equation ,

(x-5)(x-5) = 0

Now we can solve for x by setting each factor equal to zero ,

x-5 = 0 , x = 5

x 2, and the second side is expressed by  2x-25 , The value of x is 5.

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After five decades, the amount is worth to the nearest hundredth is 607.54

Any decimal number is rounded to the nearest hundredth by the term "to the nearest hundredth." A hundredth is 1/100 or 0.01 in decimal form. For instance, 2.17 is the result of rounding 2.167 to the nearest tenth.

Look at the next place value to the right in order to round a number to the closest hundredth (the thousandths this time). The same applies: Simply eliminate all the digits to the right if the number is 4 or fewer. Add 1 to the digit in the hundredths place if the number is five or above, and then eliminate all the digits to the right.

The equation below can be used to describe this amount at intervals of 2t decades. where r is the rate of increase and Q(0) is the initial quantity. A 510-valued quantity increases exponentially at a rate of 7% every 20 years. After five decades, the amount is worth 607.54

Q(t)=Q(0)[tex]e^{xt}[/tex]

Q(2.5)= 510e^(0.07*2.5)

= 607.54

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The probability that a randomly selected student plays basketball, given that they run track is 0.38.

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability.

Assume that events A and B are two independent occurrences with probabilities P(A) and P(B), respectively, such that the probability that event B will occur given that event A is given by: P(B|A) = P(A∩B)/P (A)

Given:

Percentage of the students who play basketball, P(A) = 31%

Percentage of the students who run track, P(B)= 29%

Percentage of the students who participate in both sports, P(A∩B) = 11%

The probability that a randomly selected student plays basketball, given that they run track is:

P(A|B) = P(A∩B)/P(B)

          = 11/29

          = 0.38

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The ticket prices that would allow the theater to make $600 in revenue are $120 and $13.4.

In order for the theater to make $0 in revenue, the ticket price would have to be $4. This can be determined by setting the revenue functions equal to 0 and solving for p.

For p (120p - 4p) = 0

120p - 4p = 0

4p = 120

p = $30

For 120p - 4p2 = 0

120p - 4p2 = 0

4p2 = 120p

p2 = 30p

p = $4

To find the ticket prices that would allow the theater to make $600 in revenue, we can set the revenue functions equal to 600 and solve for p.

For p (120p - 4p) = 600

120p - 4p = 600

4p = 120 + 600

p = $120

For 120p - 4p2 = 600

120p - 4p2 = 600

4p2 = 120 + 600

p2 = 30 + 150

[tex]p = $\sqrt{180} \approx $13.4[/tex]

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Answer:

Step-by-step explanation: Applying BODMAS rule,

[tex](8a-6a^2 +9)+(-10a-8+8a^2)-(-3)\\=8a-6a^2+9-10a-8+8a^2+3\\=2a^2-2a+12[/tex]

The solution of the inequality 5m + 1 ≤ 4 is less than or equal to 0.80.

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 is given below.

5m + 1 ≤ 4

Simplify the equation, then we have

5m + 1 ≤ 4

5m ≤ 4

m ≤ 4 / 5

m ≤ 0.8

The solution of the inequality 5m + 1 ≤ 4 is less than or equal to 0.80.

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The mean of the scores is 8.5. Option B

You should recall that mean simply means average.  Mean in this case is the sum of the product of scores and their frequency divided by the sum of the frequency.

The table below helps to understand the mean very well

Column 1             frequencies              

 x                                  f                       fx

5                                    1                       5

6                                    2                       12

7                                    5                       35

8                                    5                      40

9                                    7                       63

10                                 10                       100

                            ∑f=30                 ∑fx= 255

Mean is calculated by the formula

Therefore the Mean = ∑fx/∑f   = 255/30 Mean = 8.5

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Correct question

A 2-column table with 6 rows. Column 1 is labeled score with entries 5, 6, 7, 8, 9, 10. Column 2 is labeled Frequency with entries 1, 2, 5, 5, 7, 10.

What was the mean score on the quiz?

7.5

8.5

9

10

The probability that exactly one of the 4 players has exactly one ace and one king is 4/221.

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means that an event is impossible and 1 means that an event is certain. Events with a probability of 0.5 or greater are considered likely to happen, while events with a probability of less than 0.5 are considered unlikely to happen.

There are 4 players and each player receives thirteen cards. Each player has 4 aces and 4 kings out of the 52 cards.

The probability that exactly one of the 4 players has exactly one ace and one king ,

There are 4 ways to choose the player who gets the ace and king.

The probability that the chosen player gets an ace is 4/52.

The probability that the chosen player gets a king after getting an ace is 3/51.

so the probability that exactly one of the 4 players has exactly one ace and one king is ,

4*(4/52)*(3/51) = 4/221

Therefore, the probability that exactly one of the 4 players has exactly one ace and one king is 4/221.

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Answer:

2.45%

Step-by-step explanation:

(2.86 - 2.79) / 2.86 = 0.0245

0.0245 x 100 = 2.45%

According to the concept of inverse function, the domain of the function is explained below.

The term inverse function is defined as a function which is a square of a linear function.

Here we have know that we will restrict the domain of the function so that the function is one to one.

And then we will find the inverse and then we will find the domain of the inverse function.

Here we have given that the function is not one-to-one and then delete part of the domain so that the function that remains is one-to-one.

As we all know that a function is the set of inputs accepted by the function.

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The measure of the angles of a triangle are 50°, 60°, 70°. The triangle is acute-angle triangle.

What is an acute angle?

An acute angle is one that is less than 90 degrees in length. This is a smaller angle than the right angle (which is equal to 90 degrees).

Given that the measure of the angles of a triangle are x, x+10, and x+20.

The sum of the interior angles of a triangle is 180°.

According to the question,

x+x+10+x+20 = 180°

3x + 30 = 180°

3x = 150°

Divide both sides by 3:

x = 50°.

Putting x = 50° in x, x+10, and x+20.

x =50° , x+10 = 60°, and x+20 =70°.

All angles of the triangle is 90°. Thus the triangle is an acute angle triangle.

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The range of the function, considering the context of this problem, is given as follows:

[0.5, 8].

The range of a function is the set that contains all the possible output values for the function.

The output variable in this context is given as follows:

Amount of water into the 8 ounce glass.

The y-intercept of the graph is obtained as follows:

y - 3 = 2.5(0 - 1)

y = -2.5 + 3

y = 0.5.

Hence the lower bound of the range is of 0.5.

The maximum capacity of the glass of water is of 8 ounces, hence the upper bound of the range is of 8.

The range is composed by a closed interval, as the amounts of 0.5 ounces and 8 ounces can be assumed by the function.

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Answer: C

Step-by-step explanation: The slope is -5/4 and the y intercept is -1

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below, keeping in mind that the y-intersect is when the graph intersects the y-axis, so

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-5}{0 +4} \implies \cfrac{ -5 }{ 4 } \implies - \cfrac{5 }{ 4 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\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}\qquad \implies \qquad \begin{array}{llll} y=-\cfrac{5}{4}(~~x-(-1)~~) \\\\ {\Large \begin{array}{llll} y=-\cfrac{5}{4}(x+1) \end{array}} \end{array}[/tex]

Answer:

see explanation

Step-by-step explanation:

(a)

x - 9y = 10 ( add 9y to both sides )

x = 9y + 10 → (1)

3y² = 4x + 7 → (2)

substitute x = 9y + 10 into (2)

3y² = 4(9y + 10) + 7

3y² = 36y + 40 + 7

3y² = 36y + 47 ( subtract 36y + 47 from both sides )

3y² - 36y - 47 = 0 ← as required

(b)

solving using the method of completing the square

add 47 to both sides

3y² - 36y = 47 ← factor out 3 from each term in the left side

3(y² - 12y) = 47

to complete the square on the left

add/subtract ( half the coefficient of the y- term)² to y² - 12y

3(y² + 2(- 6)y + 36 - 36) = 47

3(y - 6)² - 3(36) = 47

3(y - 6)² - 108 = 47 ( add 108 to both sides )

3(y - 6)² = 155 ( divide both sides by 3 )

(y - 6)² = [tex]\frac{155}{3}[/tex] ( take square root of both sides )

y - 6 = ± [tex]\sqrt{\frac{155}{3} }[/tex] ≈ ± 7.2 ( to 1 decimal place )

add 6 to both sides

y = 6 ± 7.2

then

y = 6 - 7.2 = - 1.2

y = 6 + 7.2 = 13.2

substitute these values into ( 1) for corresponding values of x

x = - 1.2 : x = 9(- 1.2) + 10 = - 10.8 + 10 = - 0.8 ⇒ (- 1.2, - 0.8 )

x = 13.2 : x = 9(13.2) + 10 = 118.8 + 10 = 128.8 ⇒ (13.2, 128.8 )

Answer:

  (x, y) ≈ (-0.7, -1.2) or (128.7, 13.2)

Step-by-step explanation:

You want the solution to the simultaneous equations ...

Solving the first equation for x, we can substitute into the second equation to get a quadratic in y.

  x = 9y +10 . . . . . . . add 9y to the first equation

  3y² = 4(9y +10) +7 . . . . . substitute for x

  3y² = 36y +47 . . . . . . . eliminate parentheses

  3y² -36y -47 = 0 . . . . subtract the right-side expression

The equation can be written in vertex form as ...

  3y² -36y = 47

  3(y² -12y +36) = 47 +3(36)

  3(y -6)² = 155

  y -6 = ±√(155/3)

  y = 6 ± (√465)/3 ≈ -1.19, 13.19

  x = 9y +10 ≈ -0.69, 128.69

The approximate solutions are ...

  (x, y) ≈ (-0.7, -1.2), (128.7, 13.2)

__

Additional comment

The attached graph confirms these solution points.

<95141404393>

There are 26 rows and 34 seats per row in the movie theater.

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x represent the number of seats per row and y represent the number of rows.

The number of seats in a row is 8 greater than the number of rows, hence:

x = y + 8    (1)

The total number of seats in the theater is 884, hence:

xy = 884

but x = y + 8. Substituting:

(y + 8)(y) = 884

y² + 8y - 884 = 0

y = 26

x = y + 8 = 26 + 8 = 34

There are 26 rows

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The circumference of a circle is the distance encircling its edge. The length measured through the centre of a circle is its diameter. The radius of a circle is the distance from the centre to any point on the edge. The diameter and radius are identical in size, or 2r=d2 r=d.

Circumference =2×227×21=132 cm. Q.

Another way to think about the circle's circumference curve is to look at its 360-degree arc. As a result, a circle's diameter is equal to its 360-degree arc's length.

(a) Circumference of the circle = 2πr

= 2 × 22/7 × 14 cm

= 2 × 22 × 2 cm

= 88 cm

(b) Circumference of the circle = 2πr

= 2 × 22/7 × 28 mm

= 2 × 22 × 4 mm

= 176 mm

© Circumference of the circle = 2πr

= 2 × 22/7 × 21 cm

= 2 × 22 × 3 cm

= 132 cm

Therefore, 176 mm and 132 cm is the circumference of a circle.

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The sample size (n) needed can be calculated using

[tex]0.025 =2.33\sqrt{\frac{0.79*0.21}{n} }[/tex].

Given:

We have the following confidence interval of proportions in a sample of n people who were polled, with a success probability of [tex]\pi[/tex] and a confidence level of [tex]1- \alpha[/tex].

π ± [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]

Here z is the z score which has a pvalue of

[tex]1 -\alpha /2[/tex]

The margin of error is given as:

[tex]M = z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]

79 percent of adults age 18 years and older in the United States use the Internet as found by a survey.

So, [tex]\pi =0.79[/tex]

98% confidence level

Now [tex]\pi =0.02[/tex], z is the value of Z that has a pvalue of  [tex]1-\frac{0.02}{2} =0.99[/tex].

So, Z =2.33.

The sample size (n) needed can be estimated using:

We have to find n for which M = 0.025

The required equation is:

[tex]M =z\sqrt{ \frac{\pi (1-\pi )}{n} }[/tex]

[tex]0.025 = 2.33\sqrt{\frac{0.79*0.21}{n} }[/tex]

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An answer is- More information is needed before t can be found.  So, option(D) is the correct answer.

Here initial rotation speed is given, the final rotation speed is given, and the asking for time( in a sec) is.

If we use,

A) θ=θ0+ω0t+(1/2)αt2

For this equation, we don't have any details about the value of angular displacement and angular acceleration, so it is not useful.

B) We use,

ω=ω0+αt

For this equation, we don't have any details about angular acceleration, so it is not useful.

C) We know that,

ω2=ω02+2α(θ−θ0)

In this equation, time is not included, hence it is not useful.

D) So, more information is needed.

Thus, option (D) is the correct answer.

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The complete question is:

Suppose you are asked to find the amount of time t, in seconds, it takes for the turntable to reach its final rotational speed. Which of the following equations could you use to directly solve for the numerical value of t?

A) θ=θ0+ω0t+(1/2)αt2

B) ω=ω0+αt

C) ω2=ω02+2α(θ−θ0)

D) More information is needed before t can be found.

The height of a student who weighs 146 pounds is about 67.5 inches. Option ( a )

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things. types of Graphs in Statistics. The four basic graphs used in statistics include bar, line, histogram and pie charts.

if we see the graph properly in the given image, we can clearly see the line of best fit in which the height of a student who weighs 146 pounds is about 67.5 inches.

Option ( a ) .

About 67.5 inches

Therefore, the height of a student who weighs 146 pounds is about 67.5 inches. Option ( a )

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Given the facts, the percentage of the left brick is 7/12.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.

Total Bricks = 12

Use Brick = 5

Left Brick = 12-5

                = 7

fraction of left brick = 7/12

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Answer: -2/5 is the answer.

Step-by-step explanation:

Answer:

1.96

Step-by-step explanation:

Answer:

A quadrilateral is a parallelogram if and only if opposite angles are equal.

So, to make the quadrilateral a parallelogram, we can set the following equalities:

(4x + 13) deg = (5x - 12) deg

(4y + 7) deg = (3x - 8) deg

Solving the first equation,

4x + 13 = 5x - 12

x = -5

Solving the second equation,

4y + 7 = 3(-5) - 8

4y + 7 = -17

4y = -24

y = -6

So, the values of x and y that make the quadrilateral a parallelogram are x = -5 and y = -6

Answer: (y + 7) = 2(x + 6)

Step-by-step explanation:

       A point-slope form equation is given as (y - y1) = m(x - x1) where (x1, y1) is a given coordinate point, m is the slope, and x and y are variables. We will substitute the given information into this base equation.

(y - y1) = m(x - x1)

(y - - 7) = 2(x - - 6)

(y + 7) = 2(x + 6)

Answer:

----------------------------

Parallel lines divide transversals proportionally.

Set proportions and solve for x: