During a radio contest, $50 is added to the prize money each time a caller answers the contest question incorrectly. the first caller has a chance to win $100. which equation represents the amount the 10th caller receives if this caller is the first to answer the question correctly?

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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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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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: 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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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

Probability helps us to know the chances of an event occurring. The number of times Tamika should expect the spinner to land on green or yellow is 60.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Total number of sections on the spinner = 5

Number of sections with green or yellow sections = 2

Number of trials = 150

Now, the number of times Tamika should expect the spinner to land on green or yellow is,

Expected Number of lands on green or yellow = 150 × (2/5) = 60

Hence, the number of times Tamika should expect the spinner to land on green or yellow is 60.

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Using the median concept, it is found that the statement is true.

The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.

In this problem, we have that the 50th percentile is of 33.2 hours, hence the 54th percentile has to be above 33.2 hours = above 31 hours, hence the statement is true.

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Answer: (r+8)/4

Step-by-step explanation:

Not much really to explain...

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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(a) The side length of the square is 8 m, so its area is 64 square m.

(b) The radius of the circle is 4 m, so its area is [tex](\pi)(4^{2})=16\pi[/tex] square m.

(c) Subtracting areas, we get the area of the shaded region is [tex]64-16\pi[/tex] square m.

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:

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

[tex]\displaystyle\\\binom{10}{7}=\dfrac{10!}{7!3!}=\dfrac{8\cdot9\cdot10}{2\cdot3}=4\cdot3\cdot10=120[/tex]

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)

The transformations rule for changing DEF into D"E"F is

(b) T-5,0-RO. 90° (x,y)

To transform a shape is to alter its dimensions and relative placement.

To convert from DEF to D"E"F, use this rule:

(b) T-5,00 RO, 90°(x, y)

From the complete question,

When DEF is spun 90 degrees counterclockwise, it becomes GH.

Then, 5 units were subtracted from the right and translated to the left.

Assume a rotation of 90 degrees counterclockwise, and write it as:

RO, 90°(x,y)

As a symbol, the leftward translation of 5 units looks like this:

T-5,0(x,y)

When both transformations are combined, we have:

T-5,0 R0.90° (x. y)

In conclusion, the transformations rule for changing DEF into D"E"F is

(b) T-5,0-RO. 90° (x,y)

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The question was incomplete. Below you can find the missing content.

ABC is a right-angled triangle.

b=16 cm

∠C=38°

Calculate the length of AB. Give your answer correct to 2 decimal places.

The picture is also attached below.

The length of the side AB is 9.85 cm.

From the triangle, it is given that

b= AC=16 cm

∠C=38°

Given that ΔABC is a right-angled triangle.

where ∠B=90°

So, here we can apply the  SOH CAH TOA identity

As we know the value of sinθ is the ratio of the opposite side and the hypotenuse of the angle θ.

So, sinθ = opposite side/ hypotenuse

In triangle ΔABC

⇒ sin 38°= AB/AC

⇒ sin 38°= AB/16

⇒ AB= 16 sin 38°

⇒ AB= 9.85 cm

Therefore the length of the side AB is 9.85 cm.

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Answer:

The inverse is 5x-6

Step-by-step explanation:

To find the inverse of a function

y = ( x+6) /5

Exchange x and y

x = ( y+6)/5

Solve for y

Multiply each side by 5

5x = (y+6)/5 *5

5x = y+6

Subtract 6  from each side

5x-6 = y+6-6

5x-6 =y

The inverse is 5x-6

Step-by-step explanation:

[tex]f(x) = \frac{x + 6}{5} [/tex]

[tex] \: [/tex]

[tex]y = \frac{x + 6}{5} [/tex]

[tex] \frac{y + 6}{5} = x[/tex]

[tex]y + 6 = 5\times x[/tex]

[tex]y + 6 = 5x[/tex]

[tex]y = 5x - 6[/tex]

[tex] {f}^{ - 1} (x) = 5x - 6[/tex]

The answer is D.

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

Answer:

395.84

Step-by-step explanation:

V=πr2h=π·3^2·14

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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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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Answer:

4

Step-by-step explanation:

1/37 of 111+1/3 of 3= 4

1/37 of 111 +1/3 of 9=6

1/37 of 111 +1/3 of 1=3.3

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:  -17

Step-by-step explanation:

y - 2a

= -7 - 2(5)

= -7 - 10

= -17

The average fat content of the ten hot dog samples is: 21.91

To calculate the average fat of the hot dog samples we must add all the values and divide the result by the number of values as shown below:

Note: This question is incomplete because there is some information missing. Here is the complete information:

Question: What is the average fat of the hot dogs?

Hot Dogs' fat

Sample 1: 25.2

Sample 2: 21.3

Sample 3: 22.9

Sample 4: 17.0

Sample 5: 29.8

Sample 6: 21.0

Sample 7: 25.5

Sample 8: 16.0

Sample 9: 20.9

Sample 10: 19.5

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Answer:

4    ^x27

3

Step-by-step explanation:

2x4^2x2(6x3^2)

9

Simplifies to:

4   ^x27

3

=

4    ^x27

3  

Using the z-distribution, it is found that since the p-value is greater than 0.05, the proportion does not differ from 23%.

At the null hypotheses, it is tested if the proportion is of 23%, that is:

[tex]H_0: p = 0.23[/tex]

At the alternative hypotheses, it is tested if the proportion differs from 23%, hence:

[tex]H_1: p \neq 0.23[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

The parameters are given as follows:

[tex]p = 0.23, n = 200, \overline{p} = \frac{51}{200} = 0.255[/tex]

The value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.255 - 0.23}{\sqrt{\frac{0.23(0.77)}{200}}}[/tex]

z = 0.84.

Using a calculator and considering a two-tailed test, as we are testing if the proportion is different of a value, with z = 0.84, the p-value is of 0.4.

Since the p-value is greater than 0.05, the proportion does not differ from 23%.

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