Solve the system of equations.


y+4z=0
4x+y-2z=2
-3x-3z=-9

Answer:

(0;-1)

Step-by-step explanation:

for more details see the attachment.

13.13.13.13.13 in exponential form is 13^5

The expression is given as:

13.13.13.13.13

The factors of the above expression are 13.

And each factor is grouped by product

There are five 13s in the expression.

So, we have:

13.13.13.13.13 = 13^5

Hence, 13.13.13.13.13 in exponential form is 13^5

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1.  System B from System A by replacing one equation with itself where the same quantity is added to both sides

2. Yes, both system A and system B are equivalent and therefore has the same solution

System A

x − 4y= 1

5x + 6y= −5

System B

x = 1+4y

5x + 6y= −5

1. System B can be gotten from system A by

from the first equation of A

x − 4y= 1

Make 'x' subject of formula

x = 1 + 4y

This makes it equal to tat of system B

Thus, replacing one equation with itself where the same quantity is added to both sides

2. System A

x = 1 + 4y

5x + 6y= −5

System B

x = 1 + 4y

5x + 6y= −5

From the above equations, we can see that both system A and system B are equivalent and therefore has the same solution.

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Answer:

y = 2x + 3; y = -1/3 x + 3

Step-by-step explanation:

Both lines have y-intercept 3.

The slopes are 2 and -1/3.

The equations are: y = 2x + 3; y = -1/3 x + 3

Answer:

My answer: B

Step-by-step explanation:

The probability mass function of random variable X which represents the number of blue marbles drawn in 2 draws with replacement.

X | P(X)

0 | 0.390625

1 | 0.46875

2 | 0.140625

The probability of drawing exactly one blue marble = 0.46875

Complete Question

A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. an experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome.

To write the Probabilty mass function, we have to establish that in two draws with replacement, the possible number of blue marbles that can be drawn is 0, 1 and 2.

Probability of drawing a blue marble = P(B) = (3/8)

Probability of not drawing a blue marble = P(B') = 1 - (3/8) = (5/8)

- Probability of drawing 0 blue marbles in 2 draws with replacement = P(B') × P(B') = (5/8) × (5/8) = (25/64) = 0.390625

- Probability of drawing one blue marble in 2 draws with replacement

= [P(B) × P(B')] + [P(B') × P(B)]

= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875

- Probability of drawing two blue marble in 2 draws with replacement = P(B) × P(B)

= (3/8) × (3/8) = (9/64) = 0.140625

The probability mass function of random variable X which represents the number of blue marbles draan in 2 draws with replacement.

X | P(X)

0 | 0.390625

1 | 0.46875

2 | 0.140625

b) Probability of drawing one blue marble in 2 draws with replacement

= [P(B) × P(B')] + [P(B') × P(B)]

= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875

So, B is the answer.

Answer:  -17

Step-by-step explanation:

y - 2a

= -7 - 2(5)

= -7 - 10

= -17

Answer:

(x-9) (x-5)

x = 9 x = 5

Step-by-step explanation:

find out which 2 numbers when multiplied give 45 and

when added give -14

they are -9 and -5

(x-9) (x-5)

x = 9 x = 5

Answer:

[tex]x_{1}=9, x_2=5[/tex]

Step-by-step explanation:

Recall a quadratic formula for quadratic equation [tex]ax^2+bx+c=0[/tex]: [tex]x_{1/2}=\frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]

Notice the constant in the given equation [tex]x^2-14x+45[/tex]:

[tex]a=1, b=-14, c=45[/tex]

Substitute the values into the formula:

[tex]x_{1/2}=\frac{-(-14)\pm \sqrt{(-14)^2 -4\cdot 1\cdot 45}}{2\cdot 1}[/tex]

Calculate the values:

[tex]x_{1/2}=\frac{14\pm \sqrt{196 -180}}{2}=\frac{14\pm\sqrt{16}}{2}=\frac{14\pm 4}{2}[/tex]

It follows that there are two solutions:

[tex]x_1=\frac{14+4}{2}=\frac{18}{2}=9[/tex]   and   [tex]x_2=\frac{14-4}{2}=\frac{10}{2}=5[/tex].

Answer:

(3x-2)

Step-by-step explanation:

3x² + 4x - 4

look for two factors whose product is (3)(-4)=-12 and sum is +4

The factors will be +6 and -2

substitute these factors inplace of 4x to get:

3x² - 2x + 6x - 4

then factorize:

x(3x-2)+2(3x-2)

finally we get factors: (3x-2)(x+2)

Using the binomial distribution, the probabilities are given as follows:

a) 0.0747 = 7.47%.

b) 0.8725 = 87.25%.

c) 0.1256 = 12.56%.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are:

n = 20, p = 0.6.

Item a:

The probability is P(X = 15), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 15) = C_{20,15}.(0.6)^{15}.(0.4)^{5} = 0.0747[/tex]

Item b:

The probability is:

[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + \cdots + P(X = 20)[/tex]

Finding each value with the equation we used in item a, we have that:

[tex]P(X \geq 10) = 0.8725[/tex]

Item c:

At least 20 - 5 = 15 on the road, hence the probability is:

[tex]P(X \geq 15) = P(X = 15) + P(X = 16) + \cdots + P(X = 20)[/tex]

Then, using the same procedure as item b, we have that:

[tex]P(X \geq 15) = 0.1256[/tex]

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Answer:

StepWhat is the measure of z? Z X y 4 9 z = [ ? ]VI-by-step explanation:

The average rate of change of the function, over the given interval is 2.

This question is incomplete, the complete question is:

What is the average rate of change of f(x) = 2x+10, if this function interval are x = -3 to x = 0.

The average rate of change of f(x) over the interval [a,b] is expressed as;

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Given that;

We substitute our values into the expression above.

[tex]\frac{f(b)-f(a)}{b-a}\\\\\frac{f(0)-f(-3)}{0-(-3)}\\\\\frac{[2(0)+10]-[2(-3)+10]}{0-(-3)}\\\\\frac{[10]-[-6+10]}{3}\\\\\frac{[10]-[4]}{3}=\frac{6}{3}=2[/tex]

Therefore, the average rate of change of the function, over the given interval is 2.

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Answer:

Area = length * width

= 4/5 * 2/3

= 8/15

Answer:

[tex]area = \frac{8}{15} {in}^{2} [/tex]

Step-by-step explanation:

The solution is in the attached file

Answer:

21 y power 5

Step-by-step explanation:

Answer: y=kx/w^2

Step-by-step explanation:

y is directly proportional to x

y∝x        

y=kx

y inversely proportional to the square of w.

y ∝ (1/(w)^2)

y=k/w^2

y=kx/w^2

Answer:

  (c)  36°

Step-by-step explanation:

We assume the pentagon is regular, so each central angle is congruent to the others. Each central angle is bisected by an apothem.

Angle 1 is one of 5 congruent central angles, so its measure is ...

  ∠1 = 360°/5 = 72°

Angle 2 is the result of one of the isosceles triangles having its central angle being bisected by an altitude. Its measure is half that of angle 1:

  ∠2 = 72°/2 = 36°

The measure of angle 2 is 36°.

Angle 3 is the other acute angle in the right triangle in which angle 2 is one of the acute angles. Its measure is ...

  ∠3 = 90° -∠2 = 90° -36° = 54°

[tex]\large\boxed{\textsf{A.}\ m=-\frac{1}{5}}[/tex]

We can use the slope formula, where our points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]:

[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

This is also known as "rise over run" because it represents the change in vertical ([tex]y[/tex]) position divided by the change in horizontal ([tex]x[/tex]) position.

Substitute the values from the points given:

[tex]\dfrac{(-5)-(-4)}{3-(-2)}[/tex]

Subtract:

[tex]\boxed{\dfrac{-1}{5}}[/tex]

Answer:

Try using the permutations formulae - nPr

n = 10

r = 4

you should get the answer. I don't have calculator on me and I'm lazy searching an online calculator. cheers

Answer:

There's no underlined digit

Answer:

See below

Step-by-step explanation:

3 is in the 10 000 place    = 30 000

   ( just put zeroes in place of all of the following numbers)

Answer: 8, 24

Step-by-step explanation:

Since the sum of two numbers is 32 and one number is 3 times as large as the other, the first number can be defined as x and the second number is 3x.

Divide 32 by (3+1) = 4 and you get 8, which is x.

The second number is 3(8) = 24.

Answer:

D) 12pm

Step-by-step explanation:

8 pm = 20:00

20:00 + 16:00*4 = 20:00 + 64:00 = 84:00

subtract the 24 hours in 84:00

84:00 - 3 X 24:00 = 12:00

12:00 = 12pm

The angle ∠4 of the given transversal shown in the diagram is gotten as; 26°.

The alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

Now, we are told that ∠1 = 26° as seen in the attached diagram. However, it is clear that ∠2 is an alternate angle to ∠1. Thus, we can say that ∠2 = 26°.

Now, Corresponding angles are the pairs of angles that are found in the same relative position on different intersections.

From the diagram we see that ∠4 is a corresponding angle to ∠2. Thus;

∠4 = 26°.

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Lenny's net proceeds algebraically are found as;[tex]\rm |xy + 20 - \frac{98}{100} |[/tex]

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Let the bought share will be $ x, and $y is the price per share

Paid fees to the broker = $ 20

The total amount spent = $(xy+20)

The price at which each share sells = $ A

Broker commission = 2 %

The total amount obtained after selling the shares;

⇒ ax - 2% of ax

⇒ 98 % of ax

Hence, Lenny's net proceeds algebraically are found as;[tex]\rm |xy + 20 - \frac{98}{100} |[/tex]

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Answer:

Step-by-step explanation:

what were Laura net proceeds

Answer: Option 4

Step-by-step explanation:

[tex]\sin \frac{7\pi}{6}=\sin \left(-\frac{\pi}{6} \right)=\sin \frac{11\pi}{6}[/tex]

Using equivalent angles, the equivalent expression to [tex]\sin{\left(\frac{7\pi}{6}\right)}[/tex] is:

[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, we have that [tex]\frac{7\pi}{6}[/tex] is on the third quadrant, as [tex]\pi < \frac{7\pi}{6} < \frac{3\pi}{2}[/tex]. Hence the equivalent angle on the first quadrant is:

[tex]\frac{7\pi}{6} - \pi = \frac{7\pi}{6} - \frac{6\pi}{6} = \frac{\pi}{6}[/tex]

The sine is negative on the third and fourth quadrants, hence the equivalent angle on the fourth quadrant is:

[tex]2\pi - \frac{\pi}{6} = \frac{11\pi}{6}[/tex]

Thus, the equivalent expression is:

[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]

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The probability of matching three out of five numbers is 153/33649

The numbers are given as:

1 to 23

There are five matching numbers

The  probability of getting a match is:

p = 5-k/n where k = 0, 1, 2

While the complement probability is

q = (n - 2)/n

Using the above formulas, the probability of getting from 5 is:

P = 5/23 * 4/22 * 3/21 * 18/20 * 17/19

Evaluate the product

P = 153/33649

Hence, the probability of matching three out of five numbers is 153/33649

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Answer:

Step-by-step explanation:

The area of a sector in terms of radians as opposed to degrees is

[tex]A=\frac{\theta}{2\pi }*\pi r^2[/tex]

Filling in the formula accordingly gives us

[tex]A=\frac{1.75rad}{2\pi rad}*\pi (2)^2[/tex]

The radians cancel out, the pi's cancel out, the 2 in the denominator cancels out (divides into 2-squared once), leaving us with

A = 1.75(2) so

A = 3.5 units squared

The frequency table and histogram are shown in the attached picture.

It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.

We have:

The ages of the participants were recorded as follows:

36, 48, 54, 92, 57, 63, 66, 76, 66, 80, 82, 65, 39, 77, 45

The classes can be made:

30-42, 43-55, 56-68, 69-81, and 82-94

The histogram is shown in the picture.

Thus, the frequency table and histogram are shown in the attached picture.

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The slope of the parallel line is 3/4

The equation is given as:

3x - 4y = 8

Rewrite as:

4y = 3x - 8

Divide through by 4

y = 3x/4 -  2

A linear equation is represented as:

y = mx + b

Where m represents the slope

By comparison:

m = 3/4

Parallel lines have equal slope

Hence, the slope of the parallel line is 3/4

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