Label the following statements as being true or false. (a) The rank of a matrix is equal to the number of its nonzero columns. (b) The product of two matrices always has rank equal to the lesser of the ranks of the two matrices.

The equation that could be used to determine the total number of people is given as y is equal to 3^x.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent y = a^x

where a is a constant and a>1

Let y be the total number of people that will be tagged.

And let x be a number of the round.

We are assuming the first is when Kyla posted a photo challenge on social media and tagged 3 friends.

So from the problem the equation becomes:

\(\rm y = 3^x\)

At first round x = 1, y =3

At second round x = 2, y = 9

At third round x = 3, y = 27

Thus, the equation that could be used to determine the total number of people is given as y is equal to 3^x.

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The best description of the standard deviation is "Approximately the mean distance between the individual salaries of employees and the mean of all employees' salaries."

Standard deviation, denoted by σ, is defined as the measure which indicates the average distance of the observations from the mean of the data set. It tells how spread out numbers are. It is equal to the square root of the variance. Variance is the average of the squared differences from the mean.

For the given problem, the standard deviation can be describe as the average(mean) distance of the individual salaries of employees from the mean of all employees' salaries.

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Answer:

Step-by-step explanation:

2n + 1.6 = 17.6 what is the value of n?​

2n + 1.6 = 17.6

2n = 17.6 - 1.6

2n = 16

n = 16 : 2

n = 8

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

check

2n + 1.6 = 17.6

2*8+1.6=17.6

16+1.6=17.6

17.6=17.6

the answer is good

Therefore, the correct answer is (B) No, she needs 1/2 cup more.

To determine if Patricia has enough rice cereal for her recipe, we need to calculate the total amount of rice cereal she has after all her actions and compare it to the 3 cups required for the cereal clusters.

Initially, Patricia had 5 cups of rice cereal. She used 3 cups to make granola bars, leaving her with 2 cups. She then borrowed 0.5 cup from her friend, which brings her total to 2.5 cups.

Finally, she needs 3 cups of rice cereal for the cereal clusters recipe. Since she only has 2.5 cups, she does not have enough rice cereal and needs to get more. Therefore, the correct answer is B) No, she needs 1/2 cup more.

She then borrows 0.5 cup, so she now has 2 + 0.5 = 2.5 cups.

needs 3 - 2.5 = 0.5 cups more.

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The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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Answer:

The two numbers are 18, and 81.

step-by-step explanation:

If you divide both sides of the ratio by 2 to get 4.5/1, you can then graph that as y=4.5x, finally you just find two numbers that have a difference of 63, which in this case is 18, and 81.

Answer:

55

Step-by-step explanation:

I believe it's 55 because the triangle has to equal 180

so I subtracted 70 from 180 and x can't be 70 because they don't have the same lengths

subtracting  70 from 180 gave me 110 then I divided by 2 since both the top angle and x would have the same angle in degrees xD

The function  f is increasing on the intervals ( − ∞ , 0 ) (−∞,0) and ( 6 , + ∞ ) (6,+∞).

The function  f is decreasing on the intervals ( 0 , 3 )  and ( 3 , 6 ).

To find the intervals where the function  f is increasing and decreasing, we need to determine the sign of its derivative. Let's begin by finding the derivative of f(x):

f(x)=x²/x-3

Now differentiate with respect to x.

f'(x)=(x-3)(2x)-x²(1)/(x-3)²

f'(x)=2x(x-3)-x²/(x-3)²

Now, to find the intervals of increase and decrease, we need to analyze the sign of f'(x).

Let's determine the critical points by setting f'(x)=0.

2x(x-3)-x²/(x-3)²=0

2x²-6x-x²=0

x(x-6)=0

x=0 and x=6

For x<0: Choose  x=−1.

Substituting this value intof ′ (x), we get:

f'(-1)=3/8

since , f'(-1)>0, the function is increasing in the interval.

For 0<x<3: Choose x=1.

Substituting this value into f ′ (x), we get:

f'(1)=-3/4

Since f ′ (1)<0, the function is decreasing on this interval.

For 3<x<6: Choose x=4.

Substituting this value into f ′ (x), we get:

f'(4)=-4

Since  f ′ (4)<0, the function is decreasing on this interval.

For x>6: Choose x=7.

Substituting this value into f ′ (x), we get:

f'(7)=7/8

Since  f ′ (7)>0, the function is increasing on this interval.

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Answer:

I think it's A

Step-by-step explanation:

Sorry if I'm wrong

Answer: 75-30

Step-by-step explanation:

15(5-2)=

(15 * 5) - (15 * 2)=       ==> multiply 15 by 5 and 2

75-30

Answer: See attached.

Step-by-step explanation:

        We see from the given values that for every table there is 3* the number of guests and vise versa (for every 3 guests there is one table). Using this information we can complete the other values by multiplying or dividing.

3 tables * 3 = 6 guests

15 guests / 3 = 5 tables

9 tables * 3 = 27 guests

30 guests / 3 = 10 tables

Answer:

Subtract each column, starting on the right and working left. If the top number is smaller than the bottom number, borrow from the top number at the left. Place the decimal point in the answer directly below the decimal points in the terms. Check the answer by adding.

Step-by-step explanation:

Answer:

 3.416 x 10^(" + * + 1)

Step-by-step explanation:

The exponents of (5.6 x 10") (6.1 x 10* ) seem incorrect.  Whatever they are, do the following:

1) multiply 5.6 times 6.1.  Result = 34.16

Add the two exponents:  (" + *)

The result is 34.16 x 10^(" + *)

Then move the decimal point one to the left and add 1 to the 10 exponent:

3.416 x 10^(" + * + 1)

Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

Tommy's average rate of change is given as follows:

-3.4 feet per second.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The parameters for this problem are given as follows:

Hence the average rate of change is given as follows:

-17/5 = -3.4 feet per second.

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Answer:

√10 + (-√10) = 0, and 0 is not irrational

Step-by-step explanation:

Answer:

P(grey region) = 0.27512

P(black circle) = 0.36243

P(not in black circle) = 0.63757

Step-by-step explanation:

The circles are congruent and each circle has a diameter of 6 inch

Therefore radius of each circle = 6/2 = 3in

Area of each circle = πr² = π ·3² = 9π = 28.27 square inches

The area of the trapezoid is given by the formula
A = (a+b)/2 x h
where a and b are the top and bottom sides and h is the vertical height

A = (11+15)/2 x 6 = 26/2 x 6 = 13 x 6 = 78 square inches

Area of the grey region - Area of trapezoid - Area of both circles

= 78 - 2(28.27) = 21.46 square inches

P(grey region) = Area of grey region/Area of trapezoid
= 21.46/78

= 0.27512

P(black circle) = Area of black circle/Area of trapezoid
= 28.27 / 78

= 0.36243

P(not in black circle) = 1 - P(black circle)

= 1 - 0.36243

= 0.63757

Answer:

D. -1/7

Step-by-step explanation:

Substitute and solve

Answer:

\(-\frac{1}{7}\)

Step-by-step explanation:

When given the following expression,

\(\frac{a+c}{a^2-c^2}\)

With the information that the values (a = -2) and (c = 5), one is asked to evaluate the expression. One's first instinct is probably to substitute the values into the expression and solve, however, a faster approach is to simplify the expression. The denominator is the difference of squares, thus one can rewrite it as the product of two linear expressions. Then one can simplify it by canceling out like terms in the denominator and the numerator. Finally, one can then substitute the values of the (a) and (c) into the simplified expression and solve.

\(\frac{a+c}{a^2-c^2}\)

\(=\frac{a+c}{(a+c)(a-c)}\)

Cross out like terms in the numerator and denominator,

\(=\frac{a+c}{(a+c)(a-c)}\)

\(=\frac{1}{a-c}\)

Now substitute the values of (a) and (c) into the expression and simplify to evaluate,

\(=\frac{1}{a-c}\)

\(=\frac{1}{(-2)-(5)}\\\\=\frac{1}{-2-5}\\\\=-\frac{1}{7}\)

Completing the equalities using the given options, we have:

\(a) sin^(-1)(1) = 90°\\b) cos^(-1)(1/2) = 60°\\c) tan^(-1)(√3) = 60°\)

a) \(sin^(-1)(1) = 90°\)

The inverse sine function, \(sin^(-1)(x)\)gives the angle whose sine is equal to x. In this case, we are looking for the angle whose sine is equal to 1. The angle that satisfies this condition is 90 degrees, so\(sin^(-1)(1) = 90°\).

b) \(cos^(-1)(1/2) = 60°\)

The inverse cosine function, cos^(-1)(x), gives the angle whose cosine is equal to x. Here, we are looking for the angle whose cosine is equal to 1/2. The angle that satisfies this condition is 60 degrees, so \(cos^(-1)(1/2)\)= 60°.

c) \(tan^(-1)(√3) = 60°\)

The inverse tangent function, tan^(-1)(x), gives the angle whose tangent is equal to x. In this case, we are looking for the angle whose tangent is equal to √3. The angle that satisfies this condition is 60 degrees, so tan^(-1)(√3) = 60°.

Completing the equalities using the given options, we have:

\(a) sin^(-1)(1) = 90° b) cos^(-1)(1/2) = 60°c) tan^(-1)(√3) = 60°\)

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a) The completed equalities are:

sin-¹(x) = 30°, sin-¹(x) = 45°, sin-¹(x) = 60°

b) The completed equalities are:

cos-¹(x) = 30°, cos-¹(x) = 45°, cos-¹(x) = 60°

c) The completed equalities are:

tan-¹(x) = 30°, tan-¹(x) = 45°, tan-¹(x) = 60°. C.

a) sin-¹(x) = 30°, 45°, 60°

The inverse sine function, sin-¹(x), gives the angle whose sine is equal to x.

Let's find the angles for each option given:

sin-¹(x) = 30°:

If sin-¹(x) = 30°, it means that sin(30°) = x.

The sine of 30° is 0.5, so x = 0.5.

sin-¹(x) = 45°:

If sin-¹(x) = 45°, it means that sin(45°) = x.
The sine of 45° is √2/2, so x = √2/2.

sin-¹(x) = 60°:

If sin-¹(x) = 60°, it means that sin(60°) = x.

The sine of 60° is √3/2, so x = √3/2.

The completed equalities are:

b) cos-¹(x) = 30°, 45°, 60°

The inverse cosine function, cos-¹(x), gives the angle whose cosine is equal to x.

Let's find the angles for each option given:

cos-¹(x) = 30°:

If cos-¹(x) = 30°, it means that cos(30°) = x.

The cosine of 30° is √3/2, so x = √3/2.

cos-¹(x) = 45°:

If cos-¹(x) = 45°, it means that cos(45°) = x.
The cosine of 45° is √2/2, so x = √2/2.

cos-¹(x) = 60°:

If cos-¹(x) = 60°, it means that cos(60°) = x.

The cosine of 60° is 0.5, so x = 0.5.

Therefore, the completed equalities are:

c) tan-¹(x) = 30°, 45°, 60°

The inverse tangent function, tan-¹(x), gives the angle whose tangent is equal to x.

Let's find the angles for each option given:

tan-¹(x) = 30°:

If tan-¹(x) = 30°, it means that tan(30°) = x.

The tangent of 30° is 1/√3, so x = 1/√3.

tan-¹(x) = 45°:

If tan-¹(x) = 45°, it means that tan(45°) = x.

The tangent of 45° is 1, so x = 1.

tan-¹(x) = 60°:

If tan-¹(x) = 60°, it means that tan(60°) = x.

The tangent of 60° is √3, so x = √3.

The completed equalities are:

tan-¹(x) = 30°, tan-¹(x) = 45°, tan-¹(x) = 60°. c)

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Answer:

4.023 kilometres=4,03 km

Step-by-step explanation:

1 mile=1.609 km

2.5 miles x 1.609=4.023 kilometres

The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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Answer:

Step-by-step explanation:

2/9 x + 6/7 + 2.35x = -4/5 x.

the like terms are 2/9 x ,  2.35x, and  -4/5 x.

they all have the variable x

Answer:

\(\frac{(x-3)^2}{(3-x)(3+x)}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\(\frac{(x-3)^2}{(3-x)(3+x)}\)

Thanks.

Answer:

that means that the new ones contains c-14*32/100

Hope This Helps!!!

The total time taken by the elevator for the entire trip is 45 s + 15 s + 15 s + 15 s + 45 s = 135 seconds i.e., it takes the elevator 135 seconds to complete the entire trip.

The remote control car travels forward for 4 seconds at a speed of 2.0 m/s, then stops for 3 seconds, and finally travels backward for 3 seconds at a speed of 1.5 m/s.

The elevator travels from the lobby to the 36th floor in 45 seconds, stops for 15 seconds, descends to the 28th floor, stops for 15 seconds again, and returns to the lobby.

The total time taken by the elevator to complete this trip is calculated by adding up the times for each segment.

For the remote control car, it travels forward at 2.0 m/s for 4 seconds, covering a distance of 2.0 m/s * 4 s = 8 meters.

It then stops for 3 seconds, and finally travels backward at 1.5 m/s for 3 seconds, covering a distance of 1.5 m/s * 3 s = 4.5 meters.

Therefore, the total distance covered by the car is 8 m + 4.5 m = 12.5 meters.

For the elevator, it takes 45 seconds to go from the lobby to the 36th floor, and it stops for 15 seconds to let people off.

Similarly, it takes 15 seconds to go from the 36th floor to the 28th floor, and another 15 seconds to let people off.

Finally, it takes 45 seconds to return from the 28th floor to the lobby.

Therefore, the total time taken by the elevator for the entire trip is 45 s + 15 s + 15 s + 15 s + 45 s = 135 seconds.

In conclusion, it takes the elevator 135 seconds to complete the entire trip, including stops at different floors, based on the given information.

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