Factor the expression using the GCF.

The expression $32z-48$ factored using the GCF is

The size of the squares should be 3 inches in order to create a box with the largest possible volume.

If squares of equal sizes are to be cut out from the four corners so the four sides can be bent upwards, then the length of these squares will be the height of the box. Also twice of this length subtracted from the initial length and width of the material will be the new length and width of the box, respectively.

let x = length of square to be cut = height of the box

length of the box = 30 - 2x

width of the box = 14 - 2x

The volume of the box, which is a rectangular prism, is the product of the length, height and width.

V = l x w x h

V = (30 - 2x)(14 - 2x)(x)

V = 420x - 88x² + 4x³

To obtain the largest volume possible, the first derivative of the volume should be equal to zero.

V'(x) = 0

V = 420x - 88x² + 4x³

420 - 176x + 12x² = 0

Simplify and solve for the value of x.

12x² - 176x + 420 = 0

3x² - 44x + 105 = 0

(3x - 35)(x - 3) = 0

x = 35/3   ;   x = 3

Check each value.

When x = 35/3 = h

l = 30 - 2x = 20/3

w = 14 - 2x = -28/3 ( length should be positive)

When x = 3 = h

l = 30 - 2x = 24

w = 14 - 2x = 8

Hence, the length of square to be cut  is 3 in.

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The Little Monsters of Beast Academy completed 15 problems during the math meet in March.

The issue is a simultaneous equation involving two equations and two unknowns.

These are the equations that are created:

Let the quantity of questions that the students at the Beast Academy have answered in

The Little Monsters of Beast Academy successfully completed $frac1/5$ of the problems in the November = y/5

In Math Meet. they resolved $frac23$ = 2x/3 problems i

Hence:

y/5 + 2x/3 = 12

x + y = 30

When the equation is solved,

x = y = 15

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0.1717 is Probability that none has ever been married from selected 5 young women in age category at random.

In the question we have,

the number of females age 20 to 24 has never been married = 70.3%

the number of young women in this age category (20 to 24) at random = 5

We shall find out the probability that none has been maaried from selected group of 5 females.

Probability of female age 20 to 24 has never been married = 0.703

So, the probability that none has been married from selected group of 5 females ( p)= 0.703×0.703×0.703×0.73×0.73

= 0.1717

Therefore, The probability that none has ever been married is 0.1717.

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Answer:

The range of the data set is 16.

Step-by-step explanation:

The range of a box plot is the difference between the maximum and minimum value. To find the range of the given box plot, we can simply subtract the value located at the lower whisker from the value located at the upper whisker.

18 - 2 = 16

Hope this helps :)

Answer:

9:55 a.m.

Step-by-step explanation:

Sothy starts at 8 a.m. and plans for 10,000 steps. At 8:23 a.m., she walked 2000. We are solving for when she reaches 10,000 steps.

This means that she walks 2,000 steps in 23 minutes

If she walks 2,000 steps in 23 minutes, then we can multiply by 5 to get 10,000 steps in 115 minutes.

Now, we need to add 115 minutes to 8 a.m.

we can round 115 minutes to 120 minutes.

If you add 120 minutes to 8 a.m., you get 10 a.m.

Now subtract the 5 minutes you added earlier to get 9:55 a.m.

Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

What is an Algebraic Expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression. For example, 3x² − 2xy + c is an algebraic expression.

Given,

Total money Preston have = $15

He buys the ticket for = $6.50

And, two snacks = $1.75 each

so the cost of two snacks is = 1.75 * 2 = $3.5

Total cost for ticket and snacks = $3.5 + $6.50 = $10

Now, he spent money on snacks and ticket $10 and he have total money $15 so,

Preston left with = $15 - $10

                           = $5

Therefore, Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

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The number of revolutions taken by a wheel will be 353.68 millimeters.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

Given data as:

The radius of the wheel r = 45 millimeters

Circumference of wheel = Circumference of a circle

Circumference of wheel = 2πr =2π(45) = 282.74 millimeters

The distance traveled by wheel = 100,000 millimeters

Now, the number of revolutions taken by a wheel will be

⇒ distance traveled by wheel / Circumference of wheel

⇒ 100,000 / 282.74

⇒ 353.68

Thus, the number of revolutions taken by a wheel will be 353.68 millimeters.

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Answer: v=-.25

Step-by-step explanation:

Step 1: Subtract 1 from both sides.

64v^3+1−1=0−1

64v^3=−1

Step 2: Divide both sides by 64.

64v^3 64 = −1 64

v^3= −1 64

Step 3: Take cube root.

v=( −1 64 )^(1/3 )

Step 4: There is no step 4 lol

v=−0.25

Answer:

I believe its the FICA and the payroll taxes

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find Mr.Santos's age subtract morgan's age from their combined age

44-15=29

Therefore Mr. Santos age is 29 years

Hope that helps

Answer:

A

Step-by-step explanation:

function because for every x there is only one y

the domain are the value of x

the range are the value of y

The numerical coefficient is -7

From the question,  the expression is given as

-7x

Considering an expression given as

Ax

The numerical coefficient of the above expression is A

When compared to the expression -7x, we have

The numerical coefficient is -7

So, we can conclude that the numerical coefficient of -7x is -7

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Answer:

-7

Step-by-step explanation:

The numerical coefficient is -7

The dimension of the box will be (40 inch × 40 inch × 10 inch).

How to determine the maximum and minimum values of an expression using differentiation?
Any given expression can have both minimum and maximum outcomes for any number in a real world scenario, which can be determined using differentiation; first order differentiation when equated to zero reveals the value that will solute to produce the maximum or minimum and then the upon differentiating the obtained expression again and then substituting the variable in acceptable positions, if the outcome is a positive number then the obtained number in first differentiation suggests a minimum value of the given expression.

Given, the volume of the box described = 4000 inch³
Let the dimension of the base of the box be = 'a' inch × 'a' inch = a² inch²
Therefore, height of the box = (4000 inch³)/(a² inch²) = (4000/a²) inch
Total surface area of the described box = S = a² + [4a×(4000/a²)]
= [a² + 16000/a] inch
For the limiting values of S, dS/da = 0 ⇒ d[a² + 16000/a]/da = 0
⇒ 2a - [16000/a²] = 0 ⇒ 2a = 16000/a² ⇒ a³ = 8000 ⇒ a = ∛8000 = 20
Therefore, the value of a is 20 inch.
Thus, height of the box = 4000/a² = 4000/400 = 10 inch
For S to have the minimum limited value, d²S/da² > 0 for a = 20 inch, which is satisfied by the available value of S.
∴ The minimal surface area = a² + 16000/a = 400 + (16000/400)
= 440 inch²
We are aware that the least amount of material will be needed to build the box when its overall surface area is the smallest.
Thus, to minimize the amount of material in consideration, the dimension of the box will be (40 inch × 40 inch × 10 inch).

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Answer:

Answer is [tex](\frac{4}{-1})[/tex] option D is correct

Step-by-step explanation:

To find the Area of a Trapezium, we use 1/2(a+b)*h

where a=2.8 and b=4.4, Height=3.5

1/2(2.8+4.4) *3.5

1/2(7.2)*3.5

3.6*3.5

12.6cm2

Answer:

Step-by-step explanation:

Area of a trapezium = 1/2(a + b) x h

1/2 (2.8 + 4.4) x 3.5

1/2 x 7.2 x 3.5

12.6

Considering the definition of an inequality, the maximum number of people who can go to the amusement park is 4.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "x" the maximum number of people who can go to the amusement park, the inequality that expresses the previous relationship is

10.50 + 23.50x ≤ 110

Solving:

23.50x ≤ 110 - 10.50

23.50x ≤ 99.50

x ≤ 99.50÷ 23.50

x ≤ 4.23

Finally, the maximum number of people  is 4.

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Domain of the function is,  (0, ∞).

Range of the function is, (-∞, ∞).

x - intercept of the function is, (1, 0).

Vertical asymptote of the function is,  None.

What is domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

First to find the domain of the function,

Since, all input values shown on the x-axis make up a graph's domain.

We can see that values of x values are from 0 to ∞.

Hence, the domain is (0, ∞).

Now to find the range.

Since, the y-axis on a graph represents the possible output values, or range.

The y - axis having the values from -∞ to ∞.

Hence, the range of the function is, (-∞, ∞).

x - intercept is the point where function crosses the x - axis.

Here function crosses x - axis at (1, 0).

Hence, the x - intercept is (1, 0).

A graph's vertical asymptote is the vertical line at x = a where the graph trends toward positive or negative infinity as the inputs go closer to a.

So, the vertical asymptote is x = 0.

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The solution to the system of inequalities is -6 < x [tex]\leq[/tex] -3

Inequality shows the relationship between two values in an algebraic expression that are not equal. Inequality signs can indicate that one variable of the two sides of the inequality is greater than, greater than or equal to, less than, or less than or equal to another value.

The system of linear equations,

x + 4 > -2 or -4x [tex]\geq[/tex] 12

from first inequality,

x + 4 > -2

making x stand alone,

x > -2 -4

x > -6

from second inequality,

-4x  [tex]\geq[/tex] 12

divide both sides bu -4

x [tex]\leq[/tex] 12/-4

x  [tex]\leq[/tex] -3

The combined inequality is -6 < x [tex]\leq[/tex] -3

In conclusion, -6 < x [tex]\leq[/tex] -3 is the solution for the set of inequalities.

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The probability that Sam gets only one of the two guessess correct is 3/16.

Probability is the likelihood of the occurence of an event.

The probability of guessing correctly = 1/4

The probability of guessing incorrectly = 3/4

Therefore, the probability that only one guess is correct will be:

= probability of guessing correctly × probability of guessing incorrectly

= 1/4 × 3/4

= 3/16

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Answer: 1/2

Step-by-step explanation:

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation

We can convert 21/42 by dividing both the numerator and denominator by 21 to get

1/2

Hopes this helps please mark brainliest

The probability of drawing two yellow marbles if the first one is placed back in the bag before the second draw is 0.022

Since the formula we refer to in calculating probability is

P = no of possible outcomes/ total number of outcomes

Since we were provided with 10 marbles out of which 2 are yellow, 3  are pink and  5 are blue

So the total outcomes are = 1,The total number of yellow marble is  2

The probability that  the first ball drawn is yellow :

P₊= 2/10= 1/5

the probability of drawing the second ball to be yellow is:

P₂= 1/9

the total probability of  drawing two yellow marbles if the first one is placed back in the bag before the second draw is :

P= 1/5 *  1/9

= 1/45

= 0.022

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What is the probability of drawing two yellow marbles if the first one is NOT placed back into the bag before the second draw? There are 10 marbles total, 2 yellow, 3 pink, and 5 blue

Answer: C Undefined

Step-by-step explanation:

A vertical line never moves left and right, so the run is 0. Because the quotient of a number divided by 0 is undefined, the slope of a vertical line is always undefined.

The slope is positive

D.Positive

The perimeter of the given figure is 89.12 inches.

Given that, the shape is made up of one half-circle attached to a square with side lengths 16 inches.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

We know that, the perimeter of square is 4a, where a is side of a square.

When, a=16

The perimeter of square =4×16

= 64 inches

We have circumference of circle = 2πr

Circumference of a semi circle= πr

Here, radius(r)=8 inches

= 3.14×8

= 25.12 inches

Total perimeter = 64+25.12

= 89.12 inches

Therefore, the perimeter of the given figure is 89.12 inches.

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x = 2/7

see explanation in image

The statements that are true are:

It should be noted that the two figures can be regrdedas as one that are similar in the case whereby their corresponding angles are congruent ,also their ratios of the lengths with respect to their corresponding sides would also be equal.

In conclusion, when two figures are similar then it can be concluded that their  corresponding angles are congruent .

Hence, the second and third options are correct.

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Answer:

Corresponding angles of congruent figures are the same.

The corresponding sides of congruent figures are the same.

Step-by-step explanation:

The graph of the linear inequality 4x + 0.5y ≤ 40 is given by the image at the end of the answer.

The first step in graphing the linear inequality is identifying the domain of the situation.

Only numbers in the first quadrant are plotted, hence the first two constrains for the domain are given as follows:

The inequality is a linear inequality, hence the next step is identify the intercepts and then trace a line connecting them.

The x-intercept is the value of when y = 0, hence:

4x = 40

x = 40/4

x = 10.

Hence it is represented by point (10,0).

The y-intercept is the value of y when x = 0, hence:

0.5y = 40

2 x 0.5y = 2 x 40

y = 80.

Hence it is represented by point (0,80).

The values less than the inequality are plotted, hence the graph is composed by the points on the first quadrant and below the line 4x + 0.5y = 40, as shown by the image at the end of the answer.

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The relative risk of the disease influences this measure of effect in exposed individuals versus unexposed individuals and the prevalence of exposure in the population.

As stated, the population etiology fraction measures the disease rate in a population attributable to the exposure of interest. A measure that is primarily determined by the exposure caused by a particular disease. Therefore, it may be influenced by the relative risk of the disease in exposed individuals versus unexposed individuals, as well as the prevalence in the population of the exposure.

An epidemiological tool is the Population Attributable Risk, also called the Etiologic Fraction or Attributable Fraction. Efforts to eliminate a given risk factor would be expected to reduce the attributable risk to a specific percentage. The attributable risk of disease is calculated by combining the relative risk for a given exposure with the prevalence of the exposure in the population.

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We can conclude that the table in option (D) represents a linear function.

So, the linear function will be:

Then,

So, option (D) is correct.

Therefore, we can conclude that the table in option (D) represents a linear function.

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The most reasonable estimate of the correlation coefficient is 0.9

The correlation coefficient gives an estimate of how strong is the linear relationship between two variables.

The correlation coefficient, r, is given by the formula;

[tex]r = \dfrac{\sum(x_i-\overline x)\cdot (y_i-\overline y)}{\sqrt{\sum (x_i-\overline x)^2\sum(y_i-\overline y)^2} }[/tex]

Where;

[tex]x_i[/tex] = The ith x-value

[tex]\overline x[/tex] = The mean (average of the x-values)

[tex]y_i[/tex] = The ith y-value

[tex]\overline y[/tex] = The mean (average of the y-values)

The give points on the scatter plot graph are;

(8, 9), (6, 9), (6, 6), (5, 5), (4, 5), (3, 4), (3, 3), (2, 4), (1, 2), (1, 3)

Plotting the above points on MS Excel gives;

The equation of the regression line is; y = 0.9407·x + 1.3313

The square of the correlation coefficient, R² = 0.8322

Therefore, R = √(0.8322) ≈ 0.9122

The option that is the most reasonable estimate of the correlation coefficient is therefore; 0.9

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