Miguel and Grace started collecting rare coins at the same time. Back then, they had the same number of rare coins. Miguel has been collecting 5 coins each week and he now has 38 coins. Grace has been collecting 3 coins each week and she now has 24 coins. How many rare coins did they have altogether when they started collecting?
A) 3
B) 6
C) 7
D) 14

y < -1/2 x + 2

I will try the first-two points. You can then finish.

Let x = 2 and y = 3.

3 < (-1/2)(2) + 2

3 < -1 + 2

3 < 1

False statement. Choice A is not the answer.

Let x = 2 and y = 1

1 < (-1/2)(2) + 2

1 < -1 + 2

1 < 1

False statement. Choice B is not the answer.

Do the same thing with the remaining points. One of the points will make the given inequality a true statement.

The point that is a solution to the linear inequality y < -1/2 x + 2 is (b) (2,1)

The inequality is given as:

y < 1/2x + 2

Next, we test the options

A. (2, 3)

3 < 1/2 * 2 + 2

3 < 3 ---- false

B. (2, 1)

1 < 1/2 * 2 + 2

1 < 3 ---- true

Hence, the point that is a solution to the linear inequality y < -1/2 x + 2 is (b) (2,1)

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Answer:

 94.18                            

Step-by-step explanation:

Given in the question a semi circle and a right angle triangle

Step 1

Find the diameter of the semi circle

To find the diameter we will use pythagorus theorem

here,

hypotenuse will be diameter of semicircle

height = 9

base = 4

Plug values in the formula above

diameter = √(9²+4²)

diameter = √97

Step 2

Find radius

Step 3

Area

π(√97/2)²

= 76.18

Step 4

Total surface area = area of circle + area of right angle triangle

                               = 76.18 + 1/2(9)(4)

                               = 94.18

Answer:

-20

Step-by-step explanation:

-Follow PEMDAS.

-2 negatives equal a positive.

-6 + 54/(-9) - 5 - 3

-6 + (-6) - 5 - 3

-12 - 5 - 3

-20

-20

Use PEMDAS

-6- -54/(-9) -5+-3

-6+54/(-9) -5+-3

-6+-6-5-3

-12-5-3

-17-3

-20

Answer:

2

Step-by-step explanation:

512^(1/9)

Write 512 as power of 2:

(2^9)^(1/9)

Multiply the exponents:

2^(9 × 1/9)

2^1

2

Answer:

2

Step-by-step explanation:

Answer:

x = 56.7°

Step-by-step explanation:

Sin (x) = Oppo. / Hypo.

Sin (x) = 66/79

Sin (x) = 0.8354

     x = 56.7°

Answer:

x ≈ 56.7

Step-by-step explanation:

In the right triangle with hypotenuse 79 use the sine ratio to find x

sinx° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{66}{79}[/tex], hence

x = [tex]sin^{-1}[/tex] ([tex]\frac{66}{79}[/tex] ) ≈ 56.7

well, do a payments table of values, just like before for each mont hmm let's see

1st month.......................3500 + p(1)

2nd month....................3500 + p(2)

3rd month.....................3500 + p(3)

4th month.....................3500 + p(4)

5th month.....................3500 + p(5)

36th month..................3500 + p(36)

[tex]\bf \stackrel{\textit{total value}}{17900}=\stackrel{\textit{down payment}}{3500}+\stackrel{\stackrel{\textit{payments for}}{\textit{36 months}}}{36p} \\\\\\ 14400=36p\implies \cfrac{14400}{36}=p\implies 400=p[/tex]

Answer:

OPTION A

Step-by-step explanation:

The exponential growth functions has the following form:

[tex]y=a(b)^x[/tex]

Where "a" is the principal coefficient and  "b" is the base greater than 1.

To know which of the functions shown has exponential growth, identify which one has a base greater than 1.

[tex]\frac{4}{3}=1.33>1[/tex]

Therefore, the exponential growth function is the function shown in the option A.

The answer is:

The correct answer is:

A) [tex]y=(\frac{4}{3})^{x}[/tex]

To identify which of the given functions is an exponential growth function, we need to remember the form of the exponenial growth or decay functions.

We can define the exponential growth or decay function by the following way:

[tex]P(x)=y=StartValue*(rate)^{x}[/tex]

Where,

P(x) or y, is the function

Start value is the starting amount or value

Rate, is the growth or decay rate

x, is the variable (time)

Now, we can identify if the function is a exponential growth or decay function by the following way:

If [tex]rate>1[/tex] the function is an exponential growth function.

If [tex]rate<1[/tex] the function is an exponential decay function.

Now, we are given the function first function, A)

[tex]y=(\frac{4}{3})^{x}[/tex]

Where,

[tex]rate=\frac{4}{3}=1.33[/tex]

and we have that:

[tex]rate>1\\1.33>1[/tex]

So, the function is an exponential growth function.

Hence, the correct answer is:

A) [tex]y=(\frac{4}{3})^{x}[/tex]

Have a nice day!

Answer:

6

Step-by-step explanation:

Q1 is 3, Q2 is 5, Q3 is 6, which is the upper quartile.

Answer:

x = -2 and y = 2

Step-by-step explanation:

We have the following system of linear equations;

y=x+4

y=-2x-2

To solve the above system, we shall be equating the right hand sides of the two equations since we have y's on the left hand side of both equations;

x + 4 = -2x - 2

add 2x on both sides of the equation;

x + 4 + 2x = -2x - 2 + 2x

3x + 4 = -2

subtract 4 on both sides of the equation;

3x + 4 - 4 = -2 - 4

3x = -6

x = -2

We can use the first equation y=x+4 to determine the value of y;

y = -2 + 4

y = 2

The solution to the system of linear equations is thus;

x = -2 and y = 2

Answer: More bees were observed on both trees from 12:00 p.m. to 6:00 p.m. than from 6:00 p.m. to 9:00 p.m.

Step-by-step explanation:

12:00 p.m. to 6:00 p.m: 135 bees

6:00 p.m to 9:00 p.m: 28 bees

Answer:

√(A/4π) = r

Step-by-step explanation:

A = 4πr²

r² = A/4π

r = √(A/4π)

Answer:

r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]

Step-by-step explanation:

Given

A = 4πr² ( isolate r² by dividing both sides by 4π )

r² = [tex]\frac{A}{4\pi }[/tex]

Take the square root of both sides

r = [tex]\sqrt{\frac{A}{4\pi } }[/tex]

It is important to do the same thing to both sides of an equation because in the end, both sides will be equivalent, or equal, therefor making the problem true. If you didn't do the same thing on both sides of an equation, one side would be incorrect and not equal to the other side. Hope this helps! Please mark brainliest. Thank you v much! :)

It's necessary to do the same thing to both sides of an equation to maintain balance and allow valid operations. This basic principle is crucial for solving and simplifying equations in mathematics.

In mathematics, it is necessary to do the same thing to both sides of an equation to perform valid operations. An equation represents a balance; what is done to one side must also be done to the other to maintain this balance. For instance, if you add, subtract, multiply, or divide a value from/to one side of an equation, you have to do the same to the other side. This principle is essential for solving and simplifying equations. For example, in the equation 5x + 3 = 18, to solve for x, you would subtract 3 from both sides, establishing the new equation 5x = 15, maintaining the balance.

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b and c is the answer .

Number 7 - Second answer

Number 8 - Third answer

Answer:

look at the calculator.

ANSWER

EXPLANATION

We want to graph the inequality:

[tex]3y - 5x \: < \: - 6[/tex]

To this inequality, we must first of all graph the corresponding linear equation:

[tex]3y - 5x = - 6[/tex]

When x=0, we have

[tex]3y - 5(0) = - 6[/tex]

[tex]3y = - 6[/tex]

y=-2

We plot the point (0,-2)

When y=0,

[tex]3(0) - 5x = - 6[/tex]

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

[tex]( \frac{6}{5} ,0)[/tex]

We plot the points and draw a dashed straight line through them.

We test for (0,0).

[tex]3(0)- 5(0)\: < \: - 6[/tex]

[tex]0 < \: - 6[/tex]

This is false hence we shade the lower half plane. See attachment.

Answer:

d

Step-by-step explanation:

Answer:

The value of P( A and B ) is 0.08.

Step-by-step explanation:

When two events are independent then the probability of both occurring is equal to the product of probabilities of both events individually,

That is, If X and Y are independent events,

Then, P(X∩Y) = P(X) × P(Y),

or P(X and Y) = P(X) × P(Y),

Here, P(A) = 0.40 and P(B) = 0.20,

Hence, P(A∩B) = P(A) × P(B)

= 0.40 × 0.20

= 0.08

The value of [tex]\( P(A \text{ and } B) \)[/tex] is 0.08. So option(a) is correct.

To determine[tex]\( P(A \text{ and } B) \)[/tex] for two independent events ( A ) and ( B ) with given probabilities ( P(A) = 0.40 ) and ( P(B) = 0.20 ), follow these steps:

Step 1: Understand the Concept of Independence

For independent events, the probability of both events occurring together (the intersection of A and B, denoted as [tex]\( P(A \cap B) \))[/tex] is the product of their individual probabilities.

Step 2: Apply the Independent Event Formula

Since (A ) and (B ) are self-contained,

[tex]P(A) \times P(B) = P(A \cap B)[/tex]

Step 3: Substitute the Given Probabilities

Insert the given probabilities [tex]\( P(A) = 0.40 \)[/tex] and [tex]\( P(B) = 0.20 \)[/tex] into the formula:

[tex]\[ P(A \cap B) = 0.40 \times 0.20 \][/tex]

Step 4: Perform the Multiplication

Calculate the product of 0.40 and 0.20:

[tex]\[ P(A \cap B) = 0.40 \times 0.20 = 0.08 \][/tex]

Step 5: Interpret the Result

The probability that both events ( A ) and ( B ) occur is 0.08.

Therefore, the correct answer is (a) 0.08.

Complete Question:

A and B are independent events. P(A)=0.40 and P(B)=0.20 . What is P(A and B) ?

A. 0.08

B. 0.60

C. 0

D. 0.80

Answer:

The error was on the diameter. The tire diameter was supposed to be;

4.6+15+4.6=24.2

The student only includes one sidewall width

Step-by-step explanation:

The question is on circumerence of a tire

Here we apply the formulae for circumference of a circle

C=2 [tex]\pi[/tex]×r or [tex]\pi[/tex] × d where r is the radius of the tire and d is the diameter

Finding d= diameter of rim + sidewall to the right +sidewall to the left

d= 15+4.6+4.6=24.2 inches

r=d/2= 12.1

C=2 ×[tex]\pi[/tex]×r

C=2×3.14×12.1 =75.99 Inches

Answer:

Step-by-step explanation:

Givens

Formula

V = (a * b)/2  * h

Solution

V = (10 * 11)/2   * 10

V = 110/2  * 10

V = 55 * 10

V = 550

For this case we have that by definition, the volume of the prism shown is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] It is the area of the base

h: It's the height

[tex]A_ {b} = \frac {b * h} {2}[/tex]

Where:

b: It is the base of the triangle

h: It's the height of the triangle

Substituting the values:

[tex]A_ {b} = \frac {10 * 11} {2}\\A_ {b} = 55 \ cm ^ 2[/tex]

Then, the volume is:

[tex]V = 55 * 10\\V = 550 \ cm ^ 3[/tex]

ANswer:

550

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{8.4\times 8.4}{70.56}\\ h\approx& 8.6 \end{cases}\implies V=\cfrac{1}{3}(70.56)(8.6) \\\\\\ V=202.272\implies \stackrel{\textit{rounded up}}{V=202.3}[/tex]

Answer:

Required system of equation is

4s+3c=26 and 5s+2c=29.

Step-by-step explanation:

Let cost of 1 sundaes = s

Let cost of 1 cone = c

Then statement "Marcus is treating his family to ice cream he buys 4 Sundaes and 3 cones for the total of $26", gives equation:

4s+3c=26...(i)

And statement "Brian also buy ice cream for his family his total is 29 for purchasing 2 cones and 5 Sundaes " gives equation:

5s+2c=29...(ii)

Hence required system of equation is

4s+3c=26 and 5s+2c=29.

Answer:

4s+3c=26

5s+2c=29.

Step-by-step explanation:

Answer:

c=$1.59-s

Step-by-step explanation:

Let

s ----> the sale price per pack

c ---> cost savings

we know that

The  equation that represent this situation is

c=$1.59-s

The volume of a cylinder is given by

[tex]V = A_bh[/tex]

Where [tex]A_b[/tex] is the base area and h is the height.

So, if we call [tex]V_1,\ V_2[/tex] the volumes with the original and the doubled area, we have

[tex]V_1 = A_bh,\quad V_2 = A_b(2h)[/tex]

Since the height was doubled. We deduce that

[tex]\dfrac{V_2}{V_1}=\dfrac{2A_bh}{A_bh}=2[/tex]

So, if the height is doubled, the volume will double as well.

The answer is:

The average speed for the total trip is 753.19 mph.

To calculate the average speed for the total trip, we need to calculate the time of travel for both distances according to their speeds.

So, calculating we have:

- First distance and speed: 3334 miles at 760 mph

Let's use the following formula:

[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]

Then, substituting we have:

[tex]time=\frac{3334miles}{760mph=4.39hours}[/tex]

Therefore, we have that the first distance was covered in 4.39 hours.

- Second distance and speed: 2244.7 miles at 740mph

Let's use the following formula:

[tex]distance=speed*time\\\\time=\frac{distance}{speed}[/tex]

Then, substituting we have:

[tex]time=\frac{2244.7miles}{740mph=3.03hours}[/tex]

Therefore, we have that the second distance was covered in 3.03 hours.

Now, calculating the average speed, we have:

[tex]AverageSpeed=\frac{distance_{1}+distance_{2}}{t_{1}+t_{2}}[/tex]

Substuting we have:

[tex]AverageSpeed=\frac{3344miles+2244.7miles}{4.39hours+3.03hours}[/tex]

[tex]AverageSpeed=\frac{5588.7miles}{7.42hours}=753.19mph[/tex]

Hence, we have that the average speed for the total trip is 753.19 mph.

Have a nice day!

You would need to add 0.25 from t to get the number of hours ( this would be the total number of hours she has raced) and then multiply that by her speed.

The equation would be d = 35(t+0.25)

Answer:

(x + 2)² + (y - 5)² = 7²

Step-by-step explanation:

Incomplete question.  I believe you meant, "write the equation of the circle with center at (-2, 5) and radius 7.

That would be:

(x + 2)² + (y - 5)² = 7²

The equation of the circle with center (-2,5) and radius 7 is (x+2)² + (y-5)² = 49.

The question is asking for the equation of a circle with center at (-2,5) and radius 7. The general equation for a circle is (x-h)² + (y-k)² = r², with (h,k) as the center and r as the radius. In this case, h = -2, k = 5, and r = 7, so substituting these into the equation gives us the solution:

(x-(-2))² + (y-5)² = 7², which simplifies to (x+2)² + (y-5)² = 49.

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Answer:

V =91.125 in ^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3  where s is the side length

V= 4.5 ^ 3

V =91.125 in ^3

Given : Length of side of a cube = 4.5 inches.

We know that,

Volume of cube = (side)³ cu. units

= (4.5)³ inches³

= 91.125 inches³

Hence,

Volume of a cube = 91.125 inches³

Answer: -0.52

Step-by-step explanation:

From the given scatter plot, it can be seen that there is a moderate negative correlation between the variables as variable X increases variable Y decreases.

i.e. the value of correlation coefficient must be negative.

Also, the value of weak correlation coefficient r, lies between the absolute value of 0.40 to 0.59.

From all the given options -0.52  is the value which is contained in interval  0.40 to 0.59 .

Therefore, the best estimate of the correlation coefficient for the variables in the scatter plot = -0.52

Answer:

49b^2 -36 = (7b -6)(7b +6)

so because there you missed some signs in these wrote choices  

hope helped  

Step-by-step explanation:

Answer:

[tex](b+1)^2(b+6)[/tex]

Step-by-step explanation:

The given rational expression is:

[tex]\frac{b}{b^2+2b+1}-\frac{6}{b^2+7b+6}[/tex]

We factor the denominators to get:

[tex]\frac{b}{(b+1)^2}-\frac{6}{(b+1)(b+6)}[/tex]

The least common denominator is the product of the highest powers of the common factors of the denominators.

Therefore the least common denominator is:

[tex](b+1)^2(b+6)[/tex]

Answer:

The probability is  0.977

Step-by-step explanation:

We know that the average [tex]\mu[/tex] is:

[tex]\mu=500[/tex]

The standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=100[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

We seek to find

[tex]P(x>300)[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{300-500}{100}[/tex]

[tex]Z=-2[/tex]

The score of Z = -2 means that 300 is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 1 deviations from the mean has percentage of  2.35% for Z<-2

So

[tex]P(z>-2)=1-P(Z<-2)[/tex]

[tex]P(z>-2)=1-0.0235[/tex]

[tex]P(z>-2)=0.9765[/tex]

Final answer:

The probability of a randomly chosen exam score being above 300, given a normal distribution with a mean of 500 and a standard deviation of 100, is approximately 97.5%.

Explanation:

To find the probability that a randomly chosen exam score is above 300 on a college entrance exam with a mean score of 500 and a standard deviation of 100, we first calculate the z-score. A z-score is a measure of how many standard deviations an element is from the mean. Using the formula z = (X - \\(mu\\))/\\(sigma), where X is the score, \\(mu\\) is the mean, and \\(sigma\\) is the standard deviation, we get:

z = (300 - 500) / 100 = -2.

The z-score of -2 means the score is 2 standard deviations below the mean. The symmetry of the normal curve and the empirical rule tell us that approximately 95% of the scores lie within 2 standard deviations of the mean, or between 300 and 700 in this case. Given that 95% of the scores are between 300 and 700, and the curve is symmetrical, we find that roughly 2.5% of the scores are below 300. Therefore, the probability of a score being above 300 is 100% - 2.5% = 97.5%.