Two systems of equations are given below. For each system, choose the best description of its solution.

x - 5y = 5
-x + 5y = -5

a. The system has no solution.
b. The system has a unique solution:
(x,y) = _______
c. The system has infinitely many solutions. They must satisfy the following equation:
y = ________

Answer:

48 hours

Step-by-step explanation:

12.5/100 = 6/x

1. cross-multiply

12.5 × x = 12.5x

100 × 6 = 600

2. divide

12.5x/12.5 = x

600/12.5 = 48

3. answer

x = 48

Answer:

Step-by-step explanation:

L = 9 mm

W =  9 mm

H = 10 mm

volume = LWH/3 = 9·9·10/3 = 270 mm³

Answer:

[tex]C=\pi d\\\\d=\frac{C}{\pi }[/tex]

Make d the subject:

C = πd

C/π = d

Your answer: d = C/π

Answer: Passes out in slow

Step-by-step explanation:

Step 1 be Einstein

Answer:

a) 0.125 = 12.5% probability that it’s not raining and there is heavy traffic and I am not late.

b) 0.2292 = 22.92% probability that I am late.

c) 0.5454 = 54.54% probability that it rained that day.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Question a:

2/3 probability of not raining.

If not raining, 1/4 probability of heavy traffic.

1 - 0.25 = 0.75 = 3/4 probability of not late.

So

[tex]p = \frac{2}{3} \times \frac{1}{4} \times \frac{3}{4} = \frac{2}{16} = 0.125[/tex]

0.125 = 12.5% probability that it’s not raining and there is heavy traffic and I am not late.

b. What is the probability that I am late?

0.5 of (1/3)*(1/2) = 1/6(rainy and heavy traffic).

0.25 of (1/3)*(1/2) = 1/6(rainy and no traffic).

1/8 = 0.125 of (2/3)*(3/4) = 1/2(not rainy and no traffic).

0.25 of (2/3)*(1/4) = 1/6(not rainy and traffic). So

[tex]P(A) = 0.5\frac{1}{6} + 0.25\frac{1}{6} + 0.125\frac{3}{6} + 0.25\frac{1}{6} = \frac{0.5 + 0.25 + 3*0.125 + 0.25}{6} = 0.2292[/tex]

0.2292 = 22.92% probability that I am late.

c. Given that I arrived late at work, what is the probability that it rained that day?

Event A: Late

Event B: Rained

0.2292 = 22.92% probability that I am late.

This means that [tex]P(A) = 0.2292[/tex]

Probability of late and rain:

0.5 of 1/6(rain and heavy traffic).

0.25 of 1/6(rain and no traffic). So

[tex]P(A \cap B) = 0.5\frac{1}{6} + 0.25\frac{1}{6} = \frac{0.5 + 0.25}{6} = \frac{0.75}{6} = 0.125[/tex]

Probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.125}{0.2292} = 0.5454[/tex]

0.5454 = 54.54% probability that it rained that day.

[tex]\\ \sf\longmapsto \dfrac{5x+3}{7x+3}=\dfrac{3}{4}[/tex]

[tex]\\ \sf\longmapsto 4(5x+3)=3(7x+3)[/tex]

[tex]\\ \sf\longmapsto 20x+12=21x+9[/tex]

[tex]\\ \sf\longmapsto 12-9=21x-20x[/tex]

[tex]\\ \sf\longmapsto x=3[/tex]

[tex]\large\rm \longrightarrow \: {\purple{ \frac{(5x + 3)}{(7x + 3)} \: = \: \frac{3}{4} }} \\ [/tex]

⇛ Now , Cross Multiplying

[tex]\large\rm \longrightarrow \: {\blue{ 4 \: (5x + 3) \: = \: 3 \: (7x + 3)}}[/tex]

[tex]\large\rm \longrightarrow \: {\red{ 20x \: + \: 3 \: = \: 21 \: + \: 3}}[/tex]

[tex]\large\rm \longrightarrow \: {\orange{ 12 \: - \: 9 \: = \: 21x \: - \: 20x }}[/tex]

[tex]\large\rm \longrightarrow \:{\green{ 3 \: = \: x}}[/tex]

⇛ Hence , the value of x is 3

The best option for Kelsie to create a SMART goal is b) "I will get to work before 9 A.M. every day this month."

Option B captures the essence of a smart goal.  A smart goal has the following characteristics: specific, measurable, achievable or attainable, realistic or relevant, and time-bound.

1. Specific: A smart goal like option B is well-defined, clear, and unambiguous.

2. Measurable: A smart goal sets specific criteria that measure Kelsie's progress toward the accomplishment of her goal.  For example, any day that she does not get to work before 9 a.m. she knows that she does not achieve her work arrival goal for that day.

3. Achievable: Kelsie's goal becomes attainable and possible to achieve because there is a set time for her to arrive at her work.

4. Realistic: Kelsie's goal, which she set for this month, is within her reach.  It is realistic, and relevant to her purpose.

5. Time-bound:  Kelsie has set a clearly defined timeline, which creates the needed urgency for her to realize it.  It includes a starting date and a target date, which will encourage her to realize it.

Thus, option B is the correct option that meets the criteria of a SMART goal unlike options A, C, and D, which are ambiguous, unrealistic, and not time-bound.

Learn more about SMART goals from www.brainly.com/question/4939309

Answer:

pentagons

Step-by-step explanation:

In fact, there are pentagons which do not tessellate the plane. The house pentagon has two right angles. Because those two angles sum to 180° they can fit along a line, and the other three angles sum to 360° (= 540° - 180°) and fit around a vertex.

Answer:

The Regular Pentagon.

Explanation

I got a 100 % on the quiz

Answer:

stundeez

Step-by-step explanation:

Nicki Minaj hdhsbskdhsnsk

9514 1404 393

Answer:

  $3277.23

Step-by-step explanation:

The future value of the CD with interest at rate r compounded semiannually for t years will be given by ...

  A = P(1 +r/2)^(2t)

where P is the principal value.

For the given rate and time, this is ...

  A = $2000(1 +0.05/2)^(2·10) = $2000(1.025^20) ≈ $3277.23

The value of the CD at maturity will be $3277.23.

Answer:

This is so hard for me. I can't understand. I am in grade 9 now.

Answer:

[tex]B =102[/tex]

[tex]Y = 32[/tex]

Step-by-step explanation:

Solving (47):

To solve for B, we have:

[tex]B + 50 + 28 = 180[/tex] --- sum of angles in a triangle

This gives

[tex]B + 78 = 180[/tex]

Collect like terms

[tex]B =- 78 + 180[/tex]

[tex]B =102[/tex]

Solving (48):

To solve for Y, we have:

[tex]X + Y+ Z = 180[/tex] --- sum of angles in a triangle

This gives

[tex]Y = 180 - X - Z[/tex]

Where

[tex]W+ X=180[/tex] -- angle on a straight line

Solve for X

[tex]X=180 -W[/tex]

[tex]X=180 -100 = 80[/tex]

So, we have:

[tex]Y = 180 - X - Z[/tex]

[tex]Y = 180 - 80 - 68[/tex]

[tex]Y = 32[/tex]

Answer:

D) a = - 5/2

Step-by-step explanation:

2x -5y - 7 = 0

5y = 2x - 7

y = 2/5 x - 7

the slope of this line is therefore 2/5 (factor of x).

the perpendicular slope is then (exchange y and x and flip the sign) -5/2, which is then a and the factor of x.

The question is incomplete. The complete question is :

A lottery offers one $800 prize, one $700 Prize, two $800 prizes, and four $100 prizes. One thousand tickets are sold at $5 each. Find the expectation if a person buys two tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.

The expected if a person buys two tickets is $__

Answer:

$ -1.52

Step-by-step explanation:

Given :

A lottery offers --

One $800 prize

One $700 prize

Two $800 prize

Four $100 prizes

Let X = net win

    X          P(X)

  795      1/1000

  695      1/1000

  795      2/1000

   95      4/1000

    -5     996/1000

[tex]$E(X) = \sum X \ p(X)$[/tex]

         [tex]$=795 \times \frac{1}{1000} + 695 \times \frac{1}{1000} + 795 \times \frac{2}{1000} + 95 \times \frac{4}{1000} + (-5) \times \frac{996}{1000}$[/tex]

         = 0.795 + 0.695 + 1.59 +  0.38 - 4.98

         = $ -1.52

Answer:

Option 4) The area of the flower bed is smaller than 4 square feet.

Step-by-step explanation:

Let’s solve for the area of the flower bed.

Consider that the flower bed is a rectangle.

The area of a recrangle is given by the formula:

A = length x width

The area of the flower bed is:

4 ft x 4/6 ft = 2 2/3 ft^2

2 2/3 ft ^2 < 4 ft^2

Therefore option 4 is the correct answer.

Answer:

-1/3

Step-by-step explanation:

Perpendicular lines have slopes that multiply to -1

a*b = -1

3 * b = -1

b = -1/3

The slope of line b is -1/3

The equation has 2 valid solutions; no extraneous solutions

The given equation is:

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

First, we determine the solutions

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

Add 5 to both sides

[tex]\sqrt{x - 1} = x - 8 + 5[/tex]

[tex]\sqrt{x - 1} = x - 3[/tex]

Square both sides

[tex]x - 1 = (x - 3)^2[/tex]

Expand

[tex]x - 1 = x^2- 3x - 3x + 9[/tex]

[tex]x - 1 = x^2- 6x + 9[/tex]

Collect like terms

[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]

[tex]x^2 - 7x + 10 = 0[/tex]

Expand again

[tex]x^2 - 2x-5x + 10 = 0[/tex]

Factorize

[tex]x(x - 2) -5(x -2)= 0[/tex]

Factor out x - 2

[tex](x - 5)(x -2)= 0[/tex]

Split

[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]

[tex]x= 5[/tex] or [tex]x = 2[/tex]

The above values are valid values of x.

Hence, the equation has 2 valid solutions; no extraneous solutions

Read more about equations at:

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Answer:

That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.

Step-by-step explanation:

for plato users

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

you just have to expand the trig. functions into their corresponding values and then finish them off.

Answer:

(x – 3)^2+ (y – 2)^2 = r^2

Step-by-step explanation:

The co-ordinates of the center=(3,2)

The formula for the equation of a circle is (x – h)^2+ (y – k)^2 = r^2,

(h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

Therefore, (x – h)^2+ (y – k)^2 = r^2

                 =(x – 3)^2+ (y – 2)^2 = r^2

You can find r^2the equation.

Answer:

Step-by-step explanation:

Answer:

hihihihihihihiihihihihihi

Step-by-step explanation:

Answer:

3/10

Step-by-step explanation:

2/5*3*4

=6/20

=3/10

Answer:

10

Step-by-step explanation:

Applying the segment addition theorem, the value of x = 10

YZ = 60

The segment addition theorem states that if a point, C, lies between two endpoints of a segment, A and B, then: AC + CB = AB.

Given:

XY = 2x+1

YZ = 6x

XZ = 81

Thus:

XY + YZ = XZ (segment addition theorem)

2x + 1 + 6x = 81

Find x

8x = 81 - 1

8x = 80

x = 10

Find YZ:

YZ = 6x

Plug in the value of x

YZ = 6(10)

YZ = 60

Therefore, applying the segment addition theorem, the value of x = 10

YZ = 60

Learn more about the segment addition theorem on:

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Answer:

true

Step-by-step explanation:

the incenter of a triangle is the common intersection of the angle bisectors.hence always remains inside the triangle.

Answer:

The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).

Step-by-step explanation:

Before building the confidence intervals, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

In the morning:

Sample of 57, mean of 5.2, standard deviation of 0.6, so:

[tex]\mu_1 = 5.2[/tex]

[tex]s_1 = \frac{0.6}{\sqrt{57}} = 0.0795[/tex]

In the afternoon/evening:

Sample of 70, mean of 4.5, standard deviation of 0.4, so:

[tex]\mu_2 = 4.5[/tex]

[tex]s_2 = \frac{0.2}{\sqrt{70}} = 0.0239[/tex]

Distribution of the difference:

[tex]\mu = \mu_1 - \mu_2 = 5.2 - 4.5 = 0.7[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0795^2 + 0.0239^2} = 0.083[/tex]

Confidence interval:

The confidence interval is:

[tex]\mu \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower bound of the interval is:

[tex]\mu - zs = 0.7 - 1.96*0.083 = 0.5[/tex]

The upper bound of the interval is:

[tex]\mu + zs = 0.7 + 1.96*0.083 = 0.9[/tex]

The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).

Answer:

b

Step-by-step explanation:

The value of x 85.

The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.

⇒angle= arc/radius

⇒  107°=arc/7

⇒ arc =1o7°*7

⇒arc=107π/180° *7

⇒arc = 85

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