PLZ HELP :) 10 PTS

Justify whether matrix A is invertible.


A.

Yes, because its determinant is not equal to zero.

B.

Yes, because its determinant is greater than zero.

C.

No, because its determinant is zero.

D.

No, because its determinant is less than zero.

E.

No, because its determinant is not equal to zero.

After solving an equation as per given relation of Lan, Lisa and Jim height ,now Lan's height is 174centimeters.

As given ,

Let h be Lan's height today in centimeters.

As per the relation between  Lan, Lisa and Jim height we have,

Lan=h cm

Lisa=h + 4

Jim=h -8

After 4 months, every month their heights increase by 2 cm

Lan=h + 8

Lisa=h + 4 +8

Jim=h -8 +8

Required equation for given condition:

Lan + Jim=170 +Lisa

⇒h +8 + h -8 + 8=170 + h + 4+8

⇒2h+8=h+182

⇒h=174cm

Therefore, after solving an equation as per given relation of Lan, Lisa and Jim height ,now Lan's height is 174centimeters.

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The volume of the cylinder are:

V₁ = 4.8 unit³

V₂ = 5.6 unit³

V = 10.4 unit³

To read the volume in a cylindrical tube, you need to locate the meniscus. The meniscus is the curve at the surface of the liquid in the tube. The bottom of the meniscus indicates the volume measurement.

In this case, the meniscus is at 4.8 and 5.6 for V₁ and V₂ respectively. Thus, the volume readings are:

V₁ = 4.8 unit³

V₂ = 5.6 unit³

V = V₁ + V₂

V = 4.8 + 5.6 = 10.4 unit³

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Answer:

C

Step-by-step explanation:

It's not rational. It can't be represented as a fraction.

It can't be a decimal the ends. If I told you want the hundredth digit was, you could not establish the 101st digit.

If you try to find the square of 7 using the calculator that comes with winds, you get an answer that goes out to 2 followed by the decimal followed by 31 digits. You cannot find a pattern nor can you find an ending.

sqrt(7) is irrational.

Answer:

87 ft/sec

Step-by-step explanation:

mile/hr *  hr/ seconds * feet/mile    =  feet per second

  ( see how  'mile' and 'hr' cancel out and you are left with feet/sec ?)

  Now, put in the numbers :

     59    *  1/3600  *  5280 = 86.533 = 87 ft/sec

Answer:

What is the variable behind the 5?

Step-by-step explanation:

\(\frac{13*5^{3}*z^{10}}{x^{5}}\)

OR

\(\frac{1625 z^{10}}{x^{5}}\)

Answer:

(13x * 10^53) + 10.

Step-by-step explanation:

To simplify the expression "13x 10^53--10" and write it using only positive exponents, we can follow these steps:

Step 1: Remove the double negative signs by converting them to positive signs:

13x 10^53 + 10

Step 2: Rewrite the expression by moving the term with a positive exponent to the denominator:

13x / (10^-53) + 10

Step 3: To simplify the denominator, we can rewrite 10^-53 as (1/10^53):

13x / (1/10^53) + 10

Step 4: Simplify the division of a fraction by multiplying by its reciprocal:

13x * (10^53/1) + 10

Step 5: Multiply 13x by 10^53:

(13x * 10^53) + 10

The simplified expression, written using only positive exponents, is (13x * 10^53) + 1

You would need approximately 381.51 cubic inches of air to fill up the basketball. The correct option is 381.51.

To calculate the volume of a sphere (which a basketball is approximately shaped like), you use the formula V = (4/3)πr³, where r is the radius (half the diameter) of the sphere.

So, the radius of the basketball would be 4.5 inches (half of 9 inches), and plugging that into the formula we get:

V = (4/3)π(4.5)³
V = (4/3)π(91.125)
V = 381.51 cubic inches

Therefore, the correct option is 381.51.

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Answer:

x=83

y=69

k=71

a=117

q=51

x=9

p=-42

Step-by-step explanation:

Answer:

B 6,17

Step-by-step explanation: If you plug in the value of x from each of the choices only b gives the correct value of y. If you put 6 in the place of x in y= 3x-1    then y= 18-1 which is 17, and it does say 17 in 6,17.

Answer: B. (6, 17)

Step-by-step explanation:

The length of AD is 5 units. so, option A is the correct answer.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

The length of DC is given as 13 units.

The length of AC is given as 12  units. We can see that angle D is a right angle, so the triangle will be a right-angle triangle.

by Pythagoras theorem;

\(DC ^2 = AD^2 + AC^2\\\\13^2 = AD^2 + 12^2\\\\AD^2 = 169 - 144\\\\AD^2 = 25\\\\AD = 5\)

Hence, the length of AD is 5 units. so, option A is the correct answer.

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With 60 random samples, the auditor should communicate the finding of the material misstatement to the appropriate level of management.

What is random sampling?

In statistics, sampling is a way of picking a subset of the population from which to draw statistical conclusions. The characteristics of the entire population may be approximated from the sample. Market research sampling may be divided into two types: probability sampling and non-probability sampling.

Now,

Based on the information provided, the auditor should evaluate whether the overstatement of $4,000 in the sample is indicative of a material misstatement in the population of purchase orders.

To do this, the auditor can calculate the projected misstatement and compare it to the tolerable misstatement for purchases.

The projected misstatement can be calculated as follows:

Projected misstatement = (Total population / Sample size) x Sample misstatement

Projected misstatement = (1,200 / 60) x $4,000

Projected misstatement = $80,000

Since the projected misstatement of $80,000 exceeds the tolerable misstatement of $50,000, the auditor should conclude that there is a material misstatement in the population of purchase orders.

As the materiality threshold of the company is $65,000, the auditor should communicate the finding of the material misstatement to the appropriate level of management and consider adjusting the financial statements accordingly. The auditor may also need to perform additional audit procedures to further evaluate the extent of the misstatement and identify the cause of the overstatements.

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Answer:

38 yards²

Step-by-step explanation:

Area of trapeziods= ½(a+b)×height

a and b are the parallel lengths of the trapezoid.

Area of trapeziod= ½ (5.6+13.4)×4= 38 yards²

Therefore, the correct option is B

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Answer:900g

Step-by-step explanation:

150*6=900

Answer:

900 grams of flour

Since you already know that 150 grams of flour is used for one large egg

Just do 150×6 and that will give you the answer of 900.

I hope that helps :)

Answer: 11 weekends

Step-by-step explanation: I did 470.80 divided by 37.50 and got 12 with a decimal, so then I multiplied 37.50 by 11 and got 412.5, then added the 58.30 .

Answer:

Step-by-step explanation:

So first you have to subtract the total that the computer costs by how much zach already has. Then you get 411.7. Then you have to divide 411.7 by 37.50 to get how many weeks it takes to get the computer. Which is 10.96 or 11. 11 weeks is the answer! You can check this by multiplying 37.50 by 11 and add 58 because he already has that money, you will get 470! which is close so there you go!

a formula for the surface area of the box in terms of only x , the length of one side of the square base is A =  x² + 170368 cm³/x

The volume of the box with square base is V = x²h where x = length of side of square base and h = height of box.

Now, the area of the of box open at the top with dimensions of length, l , width, w and height, h are

A = 2lh + lw + 2wh

Now for a box of square base, l = w = x.

So, A = 2xh + x² + 2xh

A = x² + 4xh

Since V = x²h and V = 42592 cm³,

h = V/x² = 42592/x²

substituting h into A, we have

A =   x² + 4xh

A =  x² + 4x(42592 cm³/x²)

A =  x² + 4 × 42592 cm³/x

A =  x² + 170368 cm³/x

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The correct factorization would be equal to \((a^2 - 3)(a^2 - 3)\).

To express the expression \(a^4 - 3a^2 + 9\) as a product of two monic quadratics with integer coefficients, we can start by factoring it using the difference of squares formula. Let's break it down step by step:

\(a^4 - 3a^2 + 9\)

We can rewrite the expression as:

\((a^2)^2 - 3(a^2) + 3^2\)

Now, the difference of squares formula:

\((a^2 - 3)^2\)

So, the expression can be factored as the square of the binomial \((a^2 - 3)\).

Therefore, the correct factorization is \((a^2 - 3)(a^2 - 3)\).

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Answer:

0.2248307402

Step-by-step explanation:

Let 'success', p = 0.16,

and 'failure', q = 1 - 0.16 = 0.84

and the number of trials, n = 7

r = 2

\(P(X = r) = \binom{n}{r} {p}^{r} {q}^{n - r} \\ P(X = 2) = \binom{7}{2} {(0.16)}^{2} {0.84}^{5 - 2} \\ = 0.2248307402\)

The probability that you will wait for at most 5 seconds is 6.7%

The given parameters are:

Green = 40

Yellow = 5

Red = 30

When you spend a maximum of 5 seconds, it means that you get to the traffic light at the yellow cycle.

The probability is then calculated as:

P(Yellow) = 5/(40 + 5 + 30)

Evaluate

P(Yellow) = 6.7%

Hence, the probability that you will wait for at most 5 seconds is 6.7%

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Answer:

The value of H(F(-2)) is 379

Step-by-step explanation:

Soln,

Given,

F(x)= 2x^2+4x+10

G(x)= 3x-11

H(x)= 3x^2+x^2-21

Now,

F(-2) = 2(-2)^2 + 4×(-2) + 10

= 2×4 + (-8) + 10

= 8-8+10

= 18 - 8

= 10

Again,

H(F(-2)) = 3x^2 + x^2 - 21

Putting the value of F(-2) , we get

H(10) = 3×10^2 + 10^2 - 21

= 3×100 + 100 - 21

= 300 + 100 - 21

= 400 - 21

= 379

Therefore, H(F(-2)) = 379.

Step-by-step explanation:

To find probability ratio wise

Sports Cars: Total Cars

3 + 3 + 2 = 8 total cars

2 sports cars

Ratio is 2:8

Reduces to 1:4

The function g(x) to represent the price after the $200 rebate is g(x) = x - $200.

The function g(x) represents the final price after applying the $200 rebate. To calculate the final price, we subtract the rebate amount from the original price.

The original price is denoted by x. Since the manufacturer offers a $200 rebate for each purchase of a computer, we subtract $200 from the original price to obtain the final price.

Therefore, the function g(x) = x - $200 represents the price after the $200 rebate is applied.

This function can be used to calculate the final price for any given original price x. For example, if the original price is $1000, we can substitute x = $1000 into the function to find g($1000) = $1000 - $200 = $800, indicating that the final price after the rebate would be $800.

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110.25 kW. The minimum power rating of the motor can be calculated using the formula for power, P = Fv, where P is the power, F is the force, and v is the velocity.

First, we need to convert the mass from tons to kilograms:
1.5 ton = 1.5 x 1000 kg = 1500 kg
Next, we need to calculate the force required to lift the mass at a constant speed. Since the elevator is moving at a constant speed, the force required is equal to the weight of the mass:
F = mg
F = (1500 kg)(9.8 m/s^2)
F = 14700 N

Now, we can plug in the values for force and velocity into the formula for power:
P = Fv
P = (14700 N)(7.5 m/s)
P = 110250 W
Finally, we need to convert the power from watts to kilowatts:
P = 110250 W / 1000
P = 110.25 kW
Therefore, the minimum power rating of the motor should be 110.25 kW.

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Answer:

your closest number should be A

Answer:

A.√99

Step-by-step explanation:

10^2 = 100

Or vise versa √100 = 10

The closest number to 100 is 99

So √99 is closest to 10

Answer:

1. 3/8

Step-by-step explanation:

Total tossed times = 3

Total Possibilities = 8

Possibilities = (Head, Head, Head), (Tails,Tail,Tails), (Head,Head,Tails), (Head,Tail,Head), (Tails,Head,Head), (Head,Tail,Tail), (Tail,Tail,Head), (Tail,Head,Tail)

Number of options with a head and two tails = 3

So, Probability = Number of correct options ÷ Number of total possibilities

= 3 ÷ 8 or 3/8

Answer:

h = 66

h = 68

h = 71

Step-by-step explanation:

We have two inequalities:

h < 75  (h is strictly smaller than 75)

h > 64  (h is strictly greater than 64)

That represents the height restrictions in inches.

Now, we want to find 3 possible solutions to both inequalities.

To do it, we can write the two inequalities as one:

64 < h and h < 75

Writing these as one inequality, we get:

64 < h < 75

So the solutions can be any value of h larger than 64 and smaller than 75.

Then the solutions can be:

h = 66

h = 68

h = 71

These 3 values are solutions for both inequalities.

The domain for the given graph would be [-5,10] and range for the graph would be [0.4,5.6]. in both the case whether increasing or decreasing graph.

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). The entire range of independent variable values is the domain of a function.

The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs. In the function machine metaphor, the range is the set of objects that actually come out of the machine when you feed it all the inputs.

Graphs can also be used to determine the domain and range of functions. The domain of a graph consists of all the input values shown on the x-axis because the domain refers to the set of possible input values. The range represents the set of possible output values shown on the y-axis.

Here, The domain would be [-5,10] as the graph is depicting.

The range would be[0.4,5.6].

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The object must be thrown upward with an initial velocity of approximately 28.427 to reach its peak height after 3 sec.

What is Velocity ?

Velocity is a physical quantity that describes the rate at which an object changes its position. It is a vector quantity, meaning that it has both magnitude (speed) and direction.

A. The equation representing the velocity v(t) of the object at time t seconds given the initial velocity vo and the fact that acceleration due to gravity is -9.8  is:

v(t) = (-g÷k) + (vo + g÷k) * \(e^{(-kt) }\)

where g = 9.8 is the acceleration due to gravity and vo is the initial velocity of the object.

B. At terminal velocity, the velocity of the object is -49 m/sec. We can use this information to find the value of k as follows:

-49 = (-9.8÷k) + (vo + 9.8÷k) * 1

Since the object is at terminal velocity, its velocity will not change any further and will remain constant, so the velocity at time infinity is equal to -49. Therefore, we can simplify the equation to:

-49 = -9.8÷k + vo

Solving for k, we get:

k = -9.8 ÷ (-49 - vo)

C. To find the velocity at which the object must be thrown upward to reach its peak height after 3 sec, we need to first find the peak height. The peak height can be found using the equation:

y(t) = (vo÷k) - (g÷k*k)  * \(e^{(-kt) }\) + (g/k*k)

Setting t = 3, we get:

y(3) = (vo÷k) - (g÷k*k) * \(e^{(-3k) }\) + (g÷k*k)

We want to find the initial velocity vo that will result in a peak height of 0, so we can set y(3) = 0 and solve for vo. Using the value of k we derived in part B, we get:

0 = (vo÷k) - (g÷k*k) * \(e^{(-3k) }\) + (g÷k*k)

0 = (vo÷k) - (9.8÷k*k) * \(e^{(-3k) }\) + (9.8÷k*k)

(9.8/k*k) * * \(e^{(-3k) }\) = vo÷k

vo = (9.8÷k) * \(e^{(3k) }\)

Substituting the value of k we derived in part B, we get:

vo = (9.8 ÷ (-49 - vo)) * \(e^ { (3 * (-9.8 / (-49 - vo)) }\) )

Solving this equation using numerical methods, we get:

vo ≈ 28.427 (rounded to three decimal places)

Therefore, the object must be thrown upward with an initial velocity of approximately 28.427 to reach its peak height after 3 sec.

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Answer:

x represents the trip distance.

x = 300 miles

Rate of bus = 50 mph

Rate of train = 75 mph

Step-by-step explanation:

Let the trip distance be x miles.

\( \because \: speed = \frac{distance}{time} \\ time \: taken \: by \: bus \: to \: complete \: \\ the \: trip \: = 6 \: hours \\ \therefore \: speed \: of \: bus = \frac{x}{6} \: mph \\ \\ time \: taken \: by \: train \: to \: complete \: \\ the \: same \: trip \: = 4 \: hours \\ \therefore \: speed \: of \: train = \frac{x}{4} \: mph \\ \\ \because \: \: speed \: of \: train \\ =speed \: of \: bus \: + 25 \: mph \\ \therefore \: \frac{x}{4} = \frac{x}{6} + 25 \\ \\ \therefore \: \frac{x}{4} - \frac{x}{6} = 25 \\ \\ \therefore \: \frac{6x - 4x}{4 \times 6} = 25 \\ \\ \therefore \: \frac{2x}{24} = 25 \\ \\\therefore \: \frac{x}{12} = 25 \\ \\ \implies \: x = 25 \times 12 \\ \implies \: x =300 \: miles \\ \\ rate \: of \: bus = \frac{x}{6} = \frac{300}{6} = 50 \: mph\\ \\ rate \: of \: train = \frac{x}{4} = \frac{300}{4} = 75 \: mph\)