13. Simplify completely:
√(64 +16)

The figure verifies triangle inequality theorem: B. by showing that the sides with lengths of 7 and 4 will only meet when they lie on the third side.

In Euclidean geometry, the triangle inequality theorem states that the sum of any two (2) sides of a triangle must be greater than or equal (≥) to the third side of the triangle.

Mathematically, the triangle inequality theorem is given by this expression (a + b ≥ c).

In this context, we can logically deduce that the figure would verify triangle inequality theorem by showing that the sides with lengths of 7 and 4 would only meet when they lie on the third side of the triangle.

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The initial temperature of the soda is 22 degrees Celsius, and its temperature after 20 minutes is approximately 10 degrees Celsius.

To find the initial temperature of the soda, we need to evaluate the temperature function T(x) at x = 0.

T(x) = -5 + 27e^(-0.03x)

T(0) = -5 + 27e^(-0.03(0))

T(0) = -5 + 27e^0

Since any number raised to the power of 0 is 1, we have:

T(0) = -5 + 27(1)

T(0) = -5 + 27

T(0) = 22

Therefore, the initial temperature of the soda is 22 degrees Celsius.

To find the temperature of the soda after 20 minutes, we evaluate the temperature function at x = 20.

T(x) = -5 + 27e^(-0.03x)

T(20) = -5 + 27e^(-0.03(20))

T(20) = -5 + 27e^(-0.6)

Using a calculator, we can compute e^(-0.6) ≈ 0.5488.

T(20) = -5 + 27(0.5488)

T(20) = -5 + 14.8152

T(20) ≈ 9.8152

Therefore, the temperature of the soda after 20 minutes is approximately 10 degrees Celsius (rounded to the nearest degree).

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The volume of the cylindrical shaped pool with water is V = 75.4 feet³

Given data ,

Let the diameter of the pool be d = 8 feet

So , radius r = 4 feet

And , the height of the cylindrical pool is h = 3 feet

Now , the water is half full

So , Volume of Cylindrical pool is V = ( 1/2 ) πr²h

V = ( 1/2 ) ( 3.14 ) ( 4 )² ( 3 )

On simplifying , we get

V = 75.4 feet³

Hence , the amount of water in pool is V = 75.4 feet³

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The volume of the figure, by splitting it into two cuboids comes to be 3300 ft³.

The volume of a cuboid is the product of its three dimensions i.e. length, breadth, and height.

Let us split the given figure into two cuboids

So, the volume of the figure will be the sum of the volume of both the cuboids.

So, the volume of the cuboid with dimensions 20 ft x 25 ft x 5ft

= 20 x 25 x 5

=2500 ft³.

The volume of the cuboid with dimensions  4 ft x 25ft x 8ft

=4 x 25x 8

=800 ft³.

So, the volume of the figure = 2500 + 800 =3300 ft³.

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The system of linear equations can be resolved as x = 123/112, y = -22/49, and z = 17/112.

To solve this system of linear equations using the elimination method, we will eliminate one variable at a time by adding or subtracting equations.

Step 1: Add the first and second equations to eliminate x

-3x - 4y + z = -21

3x - 3y + 5z = 19

-7y + 6z = -2

Step 2: Multiply the third equation by 3 and add it to the result of step 1 to eliminate y

-7y + 6z = -2

-12x + 15y + 6z = -18

-12x + 21z = -20

Step 3: Solve for z by multiplying the result of step 2 by 2/3 and substituting it back into step 1 to solve for y

-12x + 21z = -20

(2/3)(-12x + 21z) = (2/3)(-20)

-8x + 14z = -40/3

-7y + 6z = -2

-7y + 6((2/3)x - (20/9)) = -2

-7y + 4x - 40/3 = -2

-7y + 4x = 34/3

y = (4/7)x - (34/21)

Step 4: Substitute the values of y and z back into any of the original equations to solve for x

3x - 3y + 5z = 19

3x - 3((4/7)x - (34/21)) + 5((2/3)x - (20/9)) = 19

3x - (12/7)x + 6 + (10/3)x - (100/9) = 19

(41/21)x = 53/3

x = 41/21 x (3/53) = 123/112

Step 5: Substitute the value of x into the equations we used to solve for y and z to solve for the remaining variables

y = (4/7)x - (34/21) = (4/7) x (123/112) - (34/21) = -22/49

z = (2/3)x - (20/9) = (2/3) x (123/112) - (20/9) = 17/112

Therefore, the solution to the system of linear equations is x = 123/112, y = -22/49, and z = 17/112.

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Answer:

The answer is A) 675 ÷ 1600.

Step-by-step explanation:

The answer is A) 675 ÷ 1600. 675 divided by 1600 means that the 675 will be split into 1600 parts. It's like you have 50 apples and you want to split it into two, can also be said or written as 50 DIVIDED BY 2.

In addition, If the statement says that 675 divides 1600 it means that the 1600 will be split into 675 part.

The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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Answer:

481

Step-by-step explanation:

The range of the give graph is 0 ≤ y ≤ 4

The range of a function is the set of all the values of y for which the function is defined.

Given that, Ezra threw a ball from a point modelled by (0, 3) on the coordinate plane. This ball reached a maximum height at the point (1, 4) and then hit the ground at the point (3, 0).

We see, that the graph reach maximum height at (1, 4)

so, the range will be between 0 and 4.

Hence, The range will be 0 ≤ y ≤ 4

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Answer:

12-4r

Step-by-step explanation:

4r<12 because r<3 so you flip it.

This is False in light of the stated statement. due to the employment of a regression line to calculate the mean of y for x that are outside the x-range of the data.

Y = mX + b, where X is the predictive (independent) factor, m is really the approx slope, and b is the expected intercept, is the methodology for simple linear regression.

Regress, from whence the word "regression" is derived, means "to go back" in Latin (to something). Regression is the method that enables "going back" from muddled, challenging data to a clearer and more significant model in this manner.

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The solution of fractions 3/14 + 15/21 is,

⇒ 3/14 + 15/21 = 39/42

We have to given that,

To add the fractions 3/14 and 15/21.

Now, We can add the fractions as,

⇒ 3/14 + 15/21

Since, LCM of 1 and 21 are 42.

Hence, Make the denominator same,

⇒ 9/42 + 30/42

⇒ (9 + 30) / 42

⇒ 39/42

Therefore, The solution of fractions 3/14 + 15/21 is,

3/14 + 15/21 = 39/42

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The maximum volume of the cylinder is approximately 1257 cubic centimeters.

The volume V of a right circular cylinder with radius r and height h is given by:

V = πr²h

Substituting the given expressions for the radius and height of the cylinder, we get:

V = πx²(800/πx - x)

Simplifying the expression, we get:

V = 800x - πx³

To find the maximum value of V, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

dV/dx = 800 - 3πx² = 0

3πx² = 800

x² = 800/3π

x ≈ 6.43

Substituting this value of x back into the expression for V, we get:

V ≈ 1257

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The graph of the function f ( x ) = sin ( πx/4 ) is plotted

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is given as

f ( x ) = sin ( πx/4 )

The periodicity of the function is 8 where the domain and range is

The domain of function = ( -∝ , ∝ )

The range of the function is = [ -1 , 1 ]

The graph of the function is plotted below

Hence , the equation of graph is plotted

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The equation that best describes the relation is y = -x+1 ( optionD)

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Taking x(0,1) and y ( 1,0)

therefore the slope of the line

= 0-1/1-0

= -1/1 = -1

the equation a line is given as

y-y1 = m(x-x1)

= y-1 = -1( x - 0)

= y-1 = -x

y = -x +1

therefore the equation that describe relation is y = 1-x or y = -x+1

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Answer:

The total number of ways to choose 2 students from a class of 16 is given by the combination formula:

C(16,2) = 16! / (2! * (16-2)!) = (1615) / (21) = 120

This means there are 120 possible pairs of students that could be drawn.

The probability of you and your best friend being chosen is the number of ways that you and your friend can be selected divided by the total number of possible pairs. There is only 1 way to select you and your best friend out of the class of 16, so the probability is:

P(you and your best friend are chosen) = 1/120

Therefore, the probability that you and your best friend will be chosen is 1/120. Option (B) is the correct answer.

Answer:

The probability of choosing one specific student out of 16 is 1/16. After one student is chosen, there are 15 students left, so the probability of choosing the second specific student out of the remaining 15 is 1/15. The probability of both events happening is the product of the probabilities: (1/16) x (1/15) = 1/240. However, there are two ways that the students can be chosen (your friend first, then you or you first, then your friend), so we need to multiply the probability by 2: 2 x (1/240) = 1/120. Therefore, the probability of you and your best friend being chosen is 1/120. Answer: 1/120.

Answer:

-2

Step-by-step explanation:

Answer:False

Step-by-step explanation:

Answer:

f(x)=100x

Step-by-step explanation:

Answer:

\(x + y - x = 6 - y - 4 \\ y = 2 - y \\ 2y = y \\ y = 1 \\ x + y = 6 \\ x + 1 = 6 \\ x = 5\)

The quadratic equation that fits each set of points (0.-8), (2, 0), and (-3, -5) is -3x² + 10x - 8 = 0

Quadratic equation:

Quadratic equation refers algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Given,

Here we have the set of points (0.-8), (2, 0), and (-3, -5).

Now, we have to find the quadratic equation for this points.

We know that the standard form of the quadratic equation is,

y = ax² +  bx + c

Here we have to use each point value in order to find the value of a, b and c to find the quadratic equation of the points,

First we have to take the point (0, -8) and apply it on the formula, then we get,

-8 = a(0)² +  b(0) + c

-8 = c

Now, use the point (2,0), then we get,

0 = a(2)² +  b(2) + c

0 = 4a + 2b + c --------------------(1)

Finally, take the point (-3, -5), then we get the equations,

-5 = a(-3)² +  b(-3) + c

-5 = 9a - 3b + c --------------------(2)

Now, apply the value of c as -8, then we get,

4a + 2b = 8 ----------------(3)

9a -3b = 3 -----------------(4)

Divide equation (4) by 3 and equation (3) by 2 on both sides then we get,

2a + b = 4

3a - b = 1

When we subtract these equation then we get the value of

a = -3

Then the value of b is

2(-3) + b = 4

b = 4 + 6

b = 10

Therefore, the quadratic equation is -3x² + 10x -8 = 0

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Problem:

Noah picked 3 kg of cherries. Mai picked half as many cherries as Noah. How many total kg of cherries did Mai and Noah pick?

Solution:

Cherries picked by Noah: 3kg

Cherries picked by Mai: 3/2 kg. Because she picked half as many cherries as Noah.

Therefore, the total number of cherries would be the sum of Noah's cherries and Mai's cherries, that is:

9/2 kg

Answer:

36

Step-by-step explanation:

2850/78 = 36.538

Answer:

36.538

Step-by-step explanation:

since he has 2,850 worth of string and he needs 78 pieces, you would divide 2,850 by 78 which gives you 36.53846154 but you would make it 36.538. if you needed to round by the tenths, its 36.5, hundredths is 36.54, and thousandths is 36.538.

The value of the side length x is equal to 14 using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

sin45 = 7√2/x {opposite/hypotenuse}

√2/2 = 7√2/x {sin45 = √2/2}

x = 7√2 × 2/√2 {cross multiplication}

x = 7 × 2

x = 14

Therefore, the value of the side length x is equal to 14 using the trigonometric ratio of sine.

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Answer: p=50 h=2

Step-by-step explanation:

so its 50 x 2=100 is the answer then u add 3

Answer

Length of the field = 70 feet.

Width of the field = 32 feet.

Explanation

The perimeter of a figure is the sum of all the exterior sides of that figure.

So, for the rectangular fencing to be done, Perimeter = 204 feet

For a rectangle,

Perimeter = 2 (L + W)

L = Length

W = Width

For this question, the length is supposes to be 6 feet longer than twice the width.

L = 6 + 2W

W = ?

Perimeter = 204 feet

Perimeter = 2 (L + W)

204 = 2 (6 + 2W + W)

204 = 2 (6 + 3W)

204 = 12 + 6W

We can rewrite this as

12 + 6W = 204

6W = 204 - 12

6W = 192

Divide both sides by 6

(6W/6) = (192/6)

W = 32 feet

L = 6 + 2W

L = 6 + 2(32)

L = 6 + 64

L = 70 feet

Hope this Helps!!!

Answer:

39

Step-by-step explanation:

The median is the middle number

16, 23, 24, 39, 45, 78, 95

There are 7 numbers so the middle number is the 4th number

6, 23, 24,    39    , 45, 78, 95

The median is 39

Answer:

39

Step-by-step explanation:

The median is the number in the middle of a data set.

First, arrange the numbers from least to greatest.

16, 23, 24, 39, 45, 78, 95

Then, cross one number off both sides of the data set until the middle is reached.

16, 23, 24, 39, 45, 78, 95

23, 24, 39, 45, 78

24, 39, 45,

39

The median is 39

Experimental designs offer researchers the most advantageous position to establish causal relationships between interventions and outcomes.

By randomly assigning participants to either an intervention group or a control group, researchers can confidently attribute any differences between the two groups to the intervention, rather than other extraneous variables. This level of control is not typically possible in other designs, such as observational studies or non-experimental designs, which are more prone to confounding variables and other biases. Experimental designs also allow for the manipulation of variables, which is not possible in other designs. For example, researchers can manipulate the dosage, timing, or mode of delivery of an intervention to investigate the optimal conditions for producing desired outcomes. This level of control enables researchers to identify the most effective interventions and to refine them for better outcomes. Moreover, experimental designs allow for the replication of studies, which increases the confidence in the results obtained. The results obtained from one study can be replicated using different samples and contexts, which increases the generalizability and external validity of the findings. In summary, experimental designs offer researchers the most powerful tools to investigate the causal relationship between interventions and outcomes, with high levels of control, manipulation, and replication. These designs are particularly useful for evaluating new interventions or interventions with unknown effects, and for informing evidence-based practice and policy.

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The situation Veronica receives $21 for babysitting, and then spends the same amount, $21, on a new shirt quantities combine to make 0.The correct answer is option C.

When we add +21 (the money she receives) and subtract -21 (the money she spends), the result is 0. This means that the net change in Veronica's money is zero, indicating that the quantities combine to make 0.

In situations A, B, and D, the quantities do not combine to make 0. In situation A, the player earns 4 points for getting an answer right and then earns an additional 4 points for making it around the board.

The total points earned in this situation would be 8, which is not equal to 0.

In situation B, the car is initially filled with 10 gallons of gas, but then half of that, which is 5 gallons, is used on a day's drive. The remaining fuel in the car would be 5 gallons, which is also not equal to 0.

In situation D, the bird flies 25 feet up in the air and then 25 feet across to its nest. The total distance traveled by the bird would be 50 feet, which is not equal to 0.

Therefore, only in situation C, where Veronica receives and spends the same amount of money, do the quantities combine to make 0.

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The probable question may be:

In which of these situations do the quantities combine to make 0?

A. A player a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board.

B. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive.

C. Veronica receives $21 for babysitting. She then spends $21 on a new shirt.

D. A bird flies 25 feet up in the air. It then flies 25 feet across to its nest.