b. If √2 = 1.414 and √3= 1.732 evaluate i. √3(√12-√3), Ii. 2√2 x 5√6​

Answer:

We have a rectangular prism of measures:

(2 + 1/4)ft by 9ft by 4ft

Let's analyze each one of the statements:

a) The base is a square?

A square has the same length as the width, this prism would have a square base if at least two of the dimensions are equal, but we can see that are all different, so we can conclude that the base can not be a square.

b) The volume of the rectangular prism is 81 cubic feet?

The volume will be equal to the direct product of the 3 dimensions, then the volume is:

V = (2 + 1/4)ft*9ft*4ft = 81 ft^3

This statement is true.

c) The area of the base is 36 square feet.

We know the dimensions, but we do not know which ones describe the base.

In the usual notation, the first two measures will describe the base of the figure, and the third one is the height.

Then the area of the base is:

(2 + 1/4)ft*9ft = 20.25 ft^2

The area of the base is not 36 ft^2

d) if you doubled the height, the volume would be the same:

Of course if we double one of the dimensions the volume will change, but let's calculate this.

The original height is 4ft, if we double this, the new heights Is 2*4ft = 8ft

Then the new volume will be:

V = (2 + 1/4)ft*9ft*8ft = 162 ft^3

The volume changes.

Answer:

Step-by-step explanation:

JOB A: 40*15=600 PER WEEK

600*4=2400 PER MONTH

JOB B; 1375*2=2750 PER MONTH

JOB A PAYS MORE 2750-2400=350.00

WITH 350.00 DOLLARS

The 55th term of the arithmetic sequence is 131.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, the nth term of the sequence is aₙ= -1+3(n−1)

Here, the 55th term in the sequence is

a₅₅= -1+3(55-1)

= -1+132

= 131

Therefore, the 55th term is 131.

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The function g from the indicated transformation of the graph of f is g(x) = 4 - |x  - 2|

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The equation of the function f is given as :

F(x) = 4-|x+1|

Shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit,  add 1 to the function

So the function g(x) is 3 units to the right of the function f(x)

⇒ g(x) = f(x - 3)

So, F(x - 3) = 4 - |x - 3+ 1|

Evaluate both equations,

⇒ F(x - 3) = 4 - |x  - 2|

⇒ g(x) = 4 - |x  - 2|

Hence, the function g from the indicated transformation of the graph of f is g(x) = 4 - |x - 2|

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Answer:

450

Step-by-step explanation:

Area of the base: 1/2(5+7.5)(6)

1/2(75)= 37.5

Volume= Area of the base* height

37.5(12)= 450

The answer to the question is 1/3.

There are three possible outcomes: 5, 6, or 7.

Out of these three outcomes, only two satisfy the condition of being odd or greater than 6: 7.

Therefore, the probability of picking a card that is odd or greater than 6 is 1/3, or approximately 0.333 or 33.3%.

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The perimeter of the square garden is 36 feet, which means that each side of the square is 36/4 = 9 feet long. Therefore, the total cost of the fences is $92.

The length of the outer fence, which is 2 feet away from the garden, is equal to the perimeter of a larger square with sides that are 2 feet longer than the sides of the original garden.

So, the length of the outer fence is 4(9+2) = 44 feet.

The length of the inner fence, which is around the perimeter of the garden, is equal to the perimeter of the original square garden, which is 4(9) = 36 feet.

The total length of both fences is the sum of the lengths of the inner and outer fences:

36 + 44 = 80 feet.

The cost of the fences is the total length of both fences multiplied by the cost per foot:

80 x $1.15 = $92.

Therefore, the total cost of the fences is $92.

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De acuerdo con lo anterior, los valores faltantes son: 7m, 6 pies, 4.5mm, 2.4 yardas.

Para hallar los valores faltantes debemos identificar cuál es el valor de la base que tenemos que cada figura  el área. Una vez tenemos estos valores debemos tener en cuenta que el área es igual a la multiplicación de la base por la altura. En este caso debemos hallar los valores de la altura en los puntos 7 y 8 y hallar la base en los puntos 9 y 10.

De acuerdo con lo anterior, debemos tener el número de la base o la altura dado y multiplicarlo por diferentes números hasta hallar el valor del área que se nos dio. De acuerdo con lo anterior, podemos establecer que los valores faltantes son:

7.

7m

8.

6 pies

9.

4.5mm

10.

2.4 yardas

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Answer:

Look it up

Step-by-step explanation:

Look it up on google

Answer:

7680

Step-by-step explanation:

7.68×10³

7.68×1000

7680

5 holes have been punched into a 12 cm by 12 cm square piece of paper. The area of remaining paper will be 27.714 cm².

Firstly, we will calculate the area of the square of paper in which the holes are punched.

Side of square = 12 cm

Area of square = side²

= (12) ²

= 144 cm²

Now, we will calculate the area of the bigger punch holes

Radius of big punch hole = 3 cm

Area of 1 big punch = π (radius) ²

= 22/7 × (3)²

22 / 7 × 9

= 198 / 7 cm²

Area of 4 punches = 4 × 198/7

= 792/7 cm²

Now, we will calculate the area of smaller punch whose radius is 1cm

Area = 22/7 × 1²

= 22/7 cm²

Now, we will calculate the total area covered by circles

Total area covered by circles = area of small punch + area of 4 big punch

= 22/7 + 792/7

= 814 /7 cm²

Remaining area = area of square - area of circles

= 144 - 814/7

= (1008 - 814) / 7

= 194 / 7

= 27.714 cm²

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Complete question :

Alligators perform a spinning maneuver, referred to as a "death roll," to subdue their prey. In a study of alligator death rolls, one of the variables measured was the degree of the angle between the body and head of the alligator while performing the roll. A sample of 20 rolls yielded the data provided below, in degrees. At the 1% significance level, do the data provide sufficient evidence to conclude that, on average, the angle between the body and head of an alligator during a death roll is greater than 45 ? Note: x =46.255° and s = 12.251° Preliminary data analyses indicate that you can reasonably use a t test to conduct the hypothesis test.

Answer:

H0 : μ = 45

H1 : μ > 45

T statistic = 0.4472

Pvalue = 0.3299

We fail to reject the Null

Step-by-step explanation:

H0 : μ = 45

H1 : μ > 45

Test statistic, T :

(xbar - μ) ÷ (s/√n)

(46.225 - 45) ÷ (12.251/√20)

1.225 ÷ 2.7394068

= 0.4472

Using the Pvalue calculator, the Pvalue can be obtained using the test statistic and degree of freedom

Degree of freedom, df = 20 - 1 = 19

Tscore = 0.4472

α = 0.01

Pvalue = 0.3299

Pvalue > α

0.3299 > 0.01 ; Hence, we fail to reject the Null

We fail to reject the Null; The data does not provide sufficient evidence to conclude that average angle between alligator's body and its head is greater than the 45

Step-by-step explanation:

212 sit-ups = 8 minutes

1 minutes = 212÷8

1 minutes = 26.5

The distance from the pole at which the cable is anchored is about 25 feet from the pole .

Given that a 35-foot cable is run from the top of the pole and anchored to the ground at a distance from the pole. The problem is to determine about how far away from the pole would it be anchored.

Let AB be the pole of length 40 feet, and CD be the 35-foot long cable anchored to the ground at D and attached to the top of the pole at C. Let E be the point on the ground at which the cable is taut and is anchored. The distance ED is to be determined.

we can see that ∆CDE is a right-angled triangle with ∠CED = 90°.

Using Pythagoras Theorem, we have:CD² = CE² + DE²35² = (40 - ED)² + DE² .

Simplifying the above equation

1225 = 1600 - 80ED + ED²

1225 - 1600 + 80ED - ED² = 0ED² - 80ED + 375 = 0

Factorizing the above quadratic equation

ED² - 25ED - 15ED + 375 = 0ED(ED - 25) - 15(ED - 25)

  = 0(ED - 15)(ED - 25) = 0So, ED = 15 ft or ED = 25 ft.

The negative value of ED is extraneous since it represents a point below the ground, which is not possible. Therefore, the distance from the pole at which the cable is anchored is about 25 feet from the pole.

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The value of x such that the 8 has a value of 8 x is 1.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given that,

8 and 8x are equal

Then,

8x = 8

x = 1

Hence "The value of x such that the 8 has a value of 8 x is 1".

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The 70 meters by 50 meters rectangular field having a path with an area of 104 m² around it indicates that the width of the path, found using the quadratic formula is about 0.43 meters.

The quadratic formula is a formula that is used to find the values of x that are the solutions to the the the quadratic equation of the form, a·x² + b·x + c = 0.

The length of the rectangular field = 70 meters

The width of the rectangular field = 50 meters

The width of the path around the field = Uniform width

Area of the path around the field = 104 m²

Let x represent the width of the path, we get;

(70 + 2·x) × (50 + 2·x) - 70 × 50 = 104

4·x² + 240·x = 104

4·x² + 240·x - 104 = 0

The quadratic formula which can be used to find the value of x in the equation a·x² + b·x + c = 0, is presented as follows;

\(x = \dfrac{-b\pm \sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}\)

Comparing the equation 4·x² + 240·x - 104 = 0 to the quadratic equation for the quadratic formula; a·x² + b·x + c = 0, we get;

a = 4, b = 240, c = -104

Therefore;

\(x = \dfrac{-240\pm \sqrt{240^2-4\times 4 \times (-104)} }{2\times 4}\)

x ≈ 0.430 or x ≈ -60.4

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Answer:

−3/2

Step-by-step explanation:

Hope this helps

:D

Sandra's last year salary was $24500

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Sandra saves 10% of her salary for retirement. This year her salary was $1,000 more than in the previous year, and she saved $5,000.

Let her previous salary be x, then according to question,

10% of x + 10% of 1000+x = 5000

x / 10 + (1000+x) / 10 = 5000

x + 1000 + x = 50000

2x = 49000

x = 24500

Hence, Sandra's last year salary was $24500

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The tangent of the smaller acute angle in a right triangle is tanФ = 0.42.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A right triangle with side lengths 5, 12, and 13.

tanФ = 5/12.

tanФ = 0.42.

Ф = tan⁻¹(0.42).

Ф = 22.8°.

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Answer:

20:9

Step-by-step explanation:

Here we will simplify the ratio to 40:18 for you and show you how we did it.

To simplify the ratio 40:18, we find the greatest common divisor of 40 and 18, and then we divide 40 and 18 by the greatest common divisor.

The greatest common divisor that you can use to simplify 40:18 is 2. This means the answer to ratio 40:18 simplified is:

20:9

Answer:

Step-by-step explanation:

If the large Jar is $4.10 for 540g

and  small jar  $2.81 for 360 g

You need to show how much it cost for 1 g,so you can compare how much it cost per gram. You would divide the total cost by the grams to see how much it is for 1 g.

Large jar.   $4.10/540 = $.0076  for 1 gram

Small Jar.   $2.81/360 =$.0078 for 1 gram

Because the large jar is cheaper to buy per gram, the large jar is the best value for the money.

1 ton=2000 pounds

Also, 1 ton=1000 kg.

Answer:

N = 20

Step-by-step explanation:

5/3 = 1 2/3

20/12 = 1 8/20

They are equivalent

A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

A definite integral is a function with the properties of additive, linearity, continuity, monotonicity, and upper & lower sums that gives a value to the area under a curve on a certain interval.

What are definite integrals?

An integral with upper and lower boundaries is said to be definite. The indefinite integral's upper and lower limits are calculated, and the two values are then subtracted to get the definite integral's value.

1. Sum: definite integral is equal to the total of its definite integrals.

2. Linearity: The slope and interval length of a linear function are multiplied to get the definite integral.

3. Continuity: For a continuous function, the area under the curve between any two points is the definite integral.

4. Monotonicity: If a function increases or decreases over a specified timeframe, then it's definite integral will similarly do likewise.

5. Upper and Lower Sums. The areas of rectangles built beneath or over a curve between two points are combined to form a function's upper and lower sums. The difference between the top and lower sums is the function's definite integral.

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Answer:

The answer is 20.

Step-by-step explanation:

You do be struggling.

Answer:

A(Canada) / factor = A(France)

3,851,809/17 = A(France)

226,577 sqmi = A(France)

Hope that helps

NOTE: This answer is a bit off from the actual calculation but it is fine because the original value of Canada's area was given about 5,000 sqmi off.

Answer:

D. 211

Step-by-step explanation:

180-19=161

161+50=211

19+(211(x)-50)=180

211° is the value of x since if u substitute it u will get your answer note that angle on a straight line is 180°