mindy has m marbles. jason has 6 more than mindy . kaitlyn has four times as many as jason . in total they have 96 marbles .how many marbles does mindy have ?

The exponential growth is: \(f(x) = 15*(1.25)^x\)

And its graph is the first one.

The exponential decay is: \(f(x) = 250*(0.87)^x\)

And its graph is the second one.

The general exponential equation is of the form:

\(y = A*(b)^x\)

Where A is the initial value and b is the base.

Here the two functions are:

\(f(x) = 250*(0.87)^x\)

\(f(x) = 15*(1.25)^x\)

As you can see, the base for the first one is smaller than 1, then it is an exponential decay (and it has a decreasing graph, so the graph of this one is the second graph).

For the second function, we have the base b = 1.25, which is larger than 1, so it is an exponential growth, and its graph is an increasing graph, which is the first one.

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According to Weber's law, two items must differ in weight by "5 percent"of weight in order to detect a difference.

We are given that Weber's law

For weight discrimination, Weber’s law states that the JND is proportional to the weight of the stimulus.

The JND is defined as the smallest difference between two weights that can be detected by an observer.

The proportionality constant is known as Weber’s fraction and varies depending on the type of stimulus and the sensory modality involved.

For weight discrimination, Weber’s fraction is typically around 2-3%.

This means that two items must differ in weight by approximately 2-3% of their weight in order to detect a difference.

The difference of weight in percent is 5%, the correct option is A.

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The half-life of this substance is 828.37 days and it would take 1312.93 days for the sample to decay to one-third of its original amount.

Half-life is defined as the time it will took a substance to reduce to half of its initial amount. The half-life of a substance is determined with respect to the rate of the reaction. It can be calculated using the formula below.

N(t) = N₀(1/2)^(t/T)

where N(t) = amount of substance remaining after time t

N₀ = initial amount of substance

t = time

T = half-life

If a sample of a certain substance decayed to 77.8% of its original amount, then N(t) = 0.778N₀.

Hence,

N(t) = N₀(1/2)^(t/T)

0.778N₀ = N₀(1/2)^(300/T)

0.778 = (1/2)^(300/T)

T = 828.27 days

If the sample is to decay to one-third of its original amount, then N(t) = 1/3N₀.

Hence,

N(t) = N₀(1/2)^(t/T)

1/3N₀ = N₀(1/2)^(t/828.27)

1/3 = (1/2)^(t/828.27)

t = 1312.93 days

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Answer:

B. 2x - 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 3x - 1

g(x) = x + 2

(f - g)(x) is f(x) - g(x)

Step 2: Find

Statement 2; ∠3 and ∠2 are supplementary.

Reason 2; Interior angles on the same side of the transversal

Statement 4; ∠1 and ∠4 are supplementary.

Reason 4; Interior angles on the same side of the transversal

Statement 5; ∠1 ≅ ∠3

Reason 5; Substitution Property

From transverse line theorem, we know that If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary angles.

Secondly, the theorem states that If two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary angles.

Statement 2; ∠3 and ∠2 are supplementary.

Reason 2; Interior angles on the same side of the transversal

Statement 4; ∠1 and ∠4 are supplementary.

Reason 4; Interior angles on the same side of the transversal

Statement 5; ∠1 ≅ ∠3

Reason 5; Substitution Property

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Answer:

cos Q = 28/53

Step-by-step explanation:

cosine = CAH

          = Adjacent / Hypotenuse

adjacent length 25 and hypotenuse is 53

hope this helps!

Answer:  A. (The inverse of a quadratic function is not a function)

Since a parabola (quadratic function) does not pass the horizontal line test, it is not possible for a quadratic equation to will have an inverse that is also a function.

Option B is wrong because the inverse of a linear function is not always a function because when the linear function has slope, the inverse cannot be a function.

Option C is wrong because the inverse of a quadratic function is never a function because a quadratic function does not pass the horizontal line test

Option D is wrong because the inverse of a linear function is a function, provided that the linear function has no slope.

Step-by-step explanation:

The present value of Mark's prize, considering the $10,000 annual payments for 10 years and the subsequent $20,000 annual payments for 30 years, with an 8% discount rate, amounts to $171,391.44.

To calculate the present value of Mark's prize, we need to determine the current worth of the future cash flows he will receive. The $10,000 annual payments for 10 years can be considered an annuity, while the subsequent $20,000 annual payments for 30 years can be viewed as a perpetuity starting from the 11th year.

First, we calculate the present value of the annuity using the formula for the present value of an ordinary annuity:

PV_annuity = \(C * [1 - (1 + r)^(-n)] / r\),

where PV_annuity is the present value of the annuity, C is the annual cash flow, r is the discount rate, and n is the number of years. Plugging in the values, we have:

PV_annuity = $10,000\(* [1 - (1 + 0.08)^(-10)] / 0.08\) = $85,394.45.

Next, we calculate the present value of the perpetuity using the formula for the present value of a perpetuity:

PV_perpetuity = C / r,

where PV_perpetuity is the present value of the perpetuity. Plugging in the values, we have:

PV_perpetuity = $20,000 / 0.08 = $250,000.

Finally, we sum up the present values of the annuity and the perpetuity to obtain the total present value:

Total present value = PV_annuity + PV_perpetuity = $85,394.45 + $250,000 = $335,394.45.

Therefore, with an 8% discount rate, the present value of Mark's prize is $171,391.44.

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Chance is a term used to represent the percentage of time a specific result is expected to occur when the same basic procedure is repeated over and over again, where each repetition is independent.

Chance is a term that is used to describe the probability that a certain outcome will occur given a set of fundamental instructions repeated again with each repetition being independent.

Ultimately, this means the number of times a result of an event occurs when repeated over a number of times is chance.

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To find the critical F-value for a one-tailed test at a significance level of 0.01, with a sample size of four for the numerator and seven for the denominator, we need to refer to the F-distribution table or use statistical software.

The F-distribution is used in hypothesis testing when comparing variances or means of multiple groups. In this case, we have a one-tailed test, which means we are interested in the upper tail of the F-distribution.

Using the given sample sizes, we can calculate the degrees of freedom for the numerator and denominator. The degrees of freedom for the numerator is equal to the sample size minus one, so in this case, it is 4 - 1 = 3. The degrees of freedom for the denominator is calculated similarly, resulting in 7 - 1 = 6.

To find the critical F-value at a significance level of 0.01 with these degrees of freedom, we would consult an F-distribution table or use statistical software. The critical F-value represents the value at which the area under the F-distribution curve is equal to the significance level.

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John's study aims to determine if exercise frequency has an effect on pulse rate. Statistical analysis can be used to verify the alternate hypothesis.

John wants to determine whether the frequency of exercise affects pulse rate. To investigate this, he randomly selects individuals at a local gym who agree to participate in his research. John divides the 55 individuals who agree into three exercise frequency categories: high, moderate, and low.

Following their exercise, he calculates their pulse rates. Is there a difference in pulse rates among those who exercise frequently, moderately, and infrequently?The null hypothesis for this research question would be that there is no relationship between the frequency of exercise and pulse rate. The alternate hypothesis would be that there is a correlation between frequency of exercise and pulse rate. Statistical tools like ANOVA or T-test can be used to test the hypothesis.

In conclusion, John's study aims to determine if exercise frequency has an effect on pulse rate. Statistical analysis can be used to verify the alternate hypothesis.

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The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Answer:

w(w-5)

Step-by-step explanation:

Given Width of rectangle = w

Length of rectangle is 5 less than width of rectangle = w - 5

Area of Rectangle = Length x Width = w * w-5 = w(w-5)

Answer:

the second answer option

Step-by-step explanation:

the area of a rectangle is

length × width

or

l × w

l = w - 5

so, when we use the second in the first equation, we get

(w - 5)×w

or

w(w - 5)

Answer:

₹ 40

Step-by-step explanation:

the cost of 1 kg = 1/ (3¼) × 130

= 1/ (13/4) × 130

= 4/13 × 130 = 40

The emphasis in Grade 7 is on linear expressions. The sum of terms that are either rational numbers or a rational number multiplied by a variable is known as a linear expression (with an exponent of either 0 or 1)

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe the constant changes in specific values in our day-to-day situations.

But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.

For example, Find y, when, y + 15 = 30,

y = 30 - 15

y = 15

Find x, when, 9x = 63.

x = 63 / 9

x = 7

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So, the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3.

A can of soda can be modeled as a right cylinder, which is a three-dimensional geometric shape with two circular bases that are connected by a curved surface. The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where V is the volume, π is a constant (approximately equal to 3.14), r is the radius of the base and h is the height of the cylinder.

Given that the radius of the can is 2.6 cm and the height is 9.2 cm, we can substitute these values into the formula:

V = π (2.6 cm)^2 (9.2 cm)

To get the area of the base we need to square the radius and multiply by π, and then multiply it by the height to get the volume.

V = π * 6.76 * 9.2 = 61.99 cm^3

So the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3. This means that the can can hold 62 cubic centimeters of liquid.

It's worth noting that this is an approximation and the real value of π is not 3.14. Also, this answer is based on the assumption that the can is a perfect cylinder with no other gaps or spaces.

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Explanation:

There are 4 jacks (one of each suit) and 13 clubs. This gives 4+13 = 17 cards that are either jack or club. However, we double-counted the jack of clubs which means there are really 17-1 = 16 cards that are one or the other or both.

This is out of the 52 total mentioned. So we end up with the probability:

16/52 = (4*4)/(4*13) = 4/13

This results in a probability of approximately 0.044, or 4.4%.  the probability of any number of eagles surviving their first year can be calculated using the binomial probability formula.

The probability of a bald eagle surviving its first year of life is 62%. If 45 bald eagles are randomly selected, we can use the binomial probability formula to calculate the probability of a certain number of eagles surviving their first year.

P(x=k) = (n choose k) * p^k * (1-p)^(n-k)

Where n is the total number of trials (45), k is the number of successes (surviving eagles), p is the probability of success (0.62), and (n choose k) is the binomial coefficient.

To find the probability that exactly 20 eagles survive their first year, we plug in the values:

P(x=20) = (45 choose 20) * 0.62^20 * 0.38^25

This results in a probability of approximately 0.044, or 4.4%.

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i) The standard deviation decrease by a factor of 2. ii) The mean of the sample mean weight will remain unchanged. iii) The statement "The distribution of the mean weight of the sampled cans of Ocean brand tuna is Normal" is a correct statement and is a result of the Central Limit Theorem.

i) When the number of cans drawn is doubled, the standard deviation of the sample mean weight will decrease by a factor of 2. According to the Central Limit Theorem, as the sample size increases, the standard deviation of the sample mean decreases.

ii) The mean of the sample mean weight will remain unchanged when the number of cans drawn is doubled. The sample mean is an unbiased estimator of the population mean, and increasing the sample size does not affect the true population mean.

iii) The statement "The distribution of the mean weight of the sampled cans of Ocean brand tuna is Normal" is a correct statement and is a result of the Central Limit Theorem. The Central Limit Theorem states that when independent random variables are added, regardless of their individual distributions, the distribution of their sum tends to be approximately Normal.

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The answer for the first one is 4.47945205479, if you need to round that would be 4.5.

The answer for the second one is 20.4945454545, rounding will be 20.5.

The answer for the last one is 893.84, rounding will be 893.8.

If you need to round just remember 4 or less, will be rounded to 0, and 5 or more would be rounded to 10.

Answer:

A=168ft

Step-by-step explanation:

Area = base * hight

Area = 12 * 14

Area = 168 ft

an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is t minimize the time it takes to travel from $a$ to $b$?

To find the mean and standard deviation of the distribution of excess cleaning solution, we need to calculate the difference between the advertised amount of cleaning solution and the actual amount filled in the bottles.

1 fluid ounce (1 fl oz) is approximately equal to 30 milliliters (30 mL), so we can convert the measurements to milliliters for consistency.

Mean:

The mean of the distribution of excess cleaning solution can be calculated as the difference between the mean amount of filling (33 fl oz) and the advertised amount (32 fl oz), both converted to milliliters:

Mean = (33 - 32) fl oz * 30 mL/fl oz = 30 mL

Therefore, the mean of the distribution of excess cleaning solution is 30 milliliters.

Standard Deviation:

The standard deviation of the distribution can be found using the formula for the propagation of uncertainty. Since the standard deviation of the filling amount is given as 1.5 fl oz, we convert it to milliliters as well:

Standard Deviation = 1.5 fl oz * 30 mL/fl oz = 45 mL

Therefore, the standard deviation of the distribution of excess cleaning solution is 45 milliliters.

In summary, the mean of the distribution of excess cleaning solution is 30 milliliters and the standard deviation is 45 milliliters.

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The diameter of the circle is approximately 45 meters.

The length of an arc is given by the formula:

length = radius * angle

Given that the length of the arc is 70.7 meters and the central angle is 5π/4 radians, we can solve for the radius of the circle:

70.7 = radius * (5π/4)

Simplifying the equation, we have:

radius = (70.7 * 4) / (5π)

To find the diameter, we multiply the radius by 2:

diameter = 2 * radius = 2 * [(70.7 * 4) / (5π)]

Calculating the value, we get approximately 45 meters as the diameter of the circle.

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Answer:

must be multiplied by 1.5

Step-by-step explanation:

Answer:

3/2 or 1.5

Step-by-step explanation:

2/3x = 16

2/3x * y = x

x÷2/3x = 3/2 = 1.5

16 * y = 24

24 / 16 = 3/2 = 1.5

3/2 is equal to decimal 1.5

A number times its reciprocal (numerator and denominator flipped)is 1

EX.

3/2 * 2/3 = 1

7/1 * 1/7 = 1

The answer is 3/2

Hope this helps :)

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

Let's solve ~

Calculate discriminant :

\(\qquad \sf  \dashrightarrow \: 3 {x}^{2} + 6x - 1\)

\(\qquad \sf  \dashrightarrow \: discriminant = {b}^{2} - 4ac\)

\(\qquad \sf  \dashrightarrow \: d = (6) {}^{2} - (4 \times 3 \times 1)\)

\(\qquad \sf  \dashrightarrow \: d = 36 - 12\)

\(\qquad \sf  \dashrightarrow \: d = 24\)

\(\qquad \sf  \dashrightarrow \: \sqrt {d} = 2 \sqrt{6} \)

Now, let's calculate it's roots ( x - intercepts )

\(\qquad \sf  \dashrightarrow \: x = \cfrac{ - b \pm \sqrt{d} }{2a} \)

\(\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{2 \times 3} \)

\(\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{6} \)

So, the intercepts are :

\(\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6 - 2 \sqrt{6} }{6} \)

and

\(\qquad \sf  \dashrightarrow \: x = \cfrac{ - 6 + 2 \sqrt{6} }{6} \)

Answer:

\(\left( \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ 0\right), \ \left(\dfrac{ -3 - 2\sqrt{3}}{ 3}, \ 0\right)\)

Explanation:

Given expression:

f(x) = 3x² + 6x - 1

Use quadratic formula:

\(\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ where \ ax^2 + bx + c = 0\)

Here after finding coefficients:

Applying formula:

\(x = \dfrac{ -6 \pm \sqrt{6^2 - 4(3)(-1)}}{2(3)}\)

\(x = \dfrac{ -6 \pm \sqrt{48}}{6}\)

\(x = \dfrac{ -6 \pm 4\sqrt{3}}{6}\)

\(x = \dfrac{ -6 \pm 4\sqrt{3}}{2 \cdot 3}\)

\(x = \dfrac{ -3 \pm 2\sqrt{3}}{ 3}\)

\(x = \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ \dfrac{ -3 - 2\sqrt{3}}{ 3}\)

Answer:

\(\frac{15}{8}\) or \(1\frac{7}{8}\)

Step-by-step explanation:

\(2\frac{1}{4}-\frac{3}{8}\)

\(2\frac{2}{8}-\frac{3}{8}\) <-- Get same denominator

\(\frac{18}{8}-\frac{3}{8}\) <-- Turn mixed number into improper fraction

\(\frac{15}{8}\) or \(1\frac{7}{8}\)

The number of students in the telescope club by $x$ and the number of students in the math club by $y$.

$y=2x$Now, suppose there are $z$ students who are members of both clubs. Then the total number of students who are in the math club or the telescope club (or both) is given by:$x + y - z$ Substituting $y=2x$ in the above expression, we get:$x + 2x - z=3x - z$ Hence, the expression for the total number of students who are in the math club or the telescope club (or both) is $3x - z$.b)The number of students who are in the math club but not in the telescope club is given by:$y-z$ And the number of students who are in the telescope club but not in the math club is given by:$x-z$ Adding these two expressions, we get the total number of students who are in the math club or the telescope club but not both:$ y-z+x-z $.

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Answer:

B=28

Step-by-step explanation: