jenny planned to solve 2/3 of her homework problems on saturday. however she got home late and had less time than planned. as a result she solved only 7/8 of the problems she planned to solve. how many problems are in jenny's notebook if she solved 28 problems on saturday

Solutions of given exponents are :

1.  \(9^{18}\)   2. \(16x^4\)   3.  \(\frac{6561}{y^2}\)

In, mathematics a exponent or exponential equation or exponential function is inverse of a logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The shows the behavior of something to the power of something. The basic form of the exponential can be written as \(a^x\)

where, a = the base of function

            x = exponential

Important properties of exponential :

According to the question,

1. given, \((9^{3})^6\)

  use the property, \((a^n)^m = a^{nm}\)

   \((9^{3})^6\) = \(9^{3.6} = 9^{18}\)

2. Given, \((2x)^4\)

   use the property, \((ab)^n = a^n.b^n\)

    \((2x)^4\) = \(2^4.x^4 = 16x^4\)

3. Given , \((\frac{3^4}{y}) ^{2}\)

    use the property, \((\frac{a}{b})^n = \frac{a^n}{b^n}\)

     \((\frac{3^4}{y}) ^{2}\) = \(\frac{(3^4)^2}{y^2}\)

    now use ,  \((a^n)^m = a^{nm}\)

     = \(\frac{3^8}{y^2} = \frac{6561}{y^2}\)

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Answer:

18 sets of markers

Answer:

Q = 61.56°

Step-by-step explanation:

cos ∅ = adjacent/hypotenuse

cos Q = 10/21

cos Q = 0.4762

Q = 61.56°

The value of f(3) is 147.3306

The function is given as:

\(f(x)=147+2e^{-0.6x\)

Substitute 3 for x

\(f(3)=147+2e^{-0.6*3\)

Evaluate the product

\(f(3)=147+2e^{-1.8\)

Evaluate the exponent

f(3)=147 + 2* 0.1653

Evaluate the sum

f(3) = 147.3306

Hence, the value of f(3) is 147.3306

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We have an algebraic expression and we have to express it in the form of a complex number.

To do that we have to take into account the definition of the imaginary number i:

We can now work on the expression to find the complex number it represents:

Then, if we define the complex number as a + bi, then a=0 and b = √(3/10).

Answer: a=0 and b = √(3/10)

Thomas packed 1.6 L1.6 L1, point, 6, start text, space, L, and end text of the soup in his kids' lunches and  had firmed 7100 ml of haze.

What's meant by equation?

Given that;

He made 8700 ml haze and he packed1.6 liter haze.

1 liter = 1000 milliliters

liter = 1.6 × 1000

litre = 1600 ml

Chancing the firmed haze-

8700 ml- 1600 ml

7100 ml.

Hence

Frozen haze = 7100 milliliters.

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Answer:

20/1

Step-by-step explanation:

The unit rate in bolts per bookcase is 20bolts per bookcase

There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.

We are Given that 100 bolts in 5 bookcase

We need to find the unit rate in bolts per bookcase

Number of bolts in 5 bookcases= 100

Number of bolts in 1 bookcases= 100/5

                                                     = 20

So, it will be 20 bolts everyday

Thus, the unit rate is 20bolts/sec

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Answer: $5,895

Step-by-step explanation:

First you want to add the earnings in order to find the total value being taxed.

17,500 + 15,250 = 32,750

We can then find the percent as a decimal by dividing it by 100:

\(\frac{18}{100} = .18\)

We can then multiply the total earnings by this decimal to find the total income tax:

\(32,750 * .18 = 5,895\)

Hope this helps

The error interval for the length ,x, of the material is [8.25, 8.35)

We know that error interval is nothing but the limits of accuracy when a number has been rounded.

It is the range of possible values that a number could have been before a number was rounded.

Here, The length L of a some material is 8.3 meters.

The length of the material has been rounded to 8.3 to one decimal place.

The number below 8.3 is 8.2 and the number above is 8.4

Consider a half way between 8.2 and 8.3 for the lower bound and half way between 8.3 and 8.4 for the upper bound.

This means, the length of the material must have been between 8.25 meters and 8.35 meters to round to 8.3 meters to one decimal place.

Therefore, the required error interval would be 8.25 ≤ x < 8.35

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The steps to condensing the expressions
2loga(4)+3loga(X-4)loga(4)

Log(x+3)+log(x-3) is given below.

To condense the   expressions, we can apply the  properties of logarithms. Here are the condensed forms of the given expressions.

2loga (4) + 3loga(X - 4) - loga 4 )  

By using the product and quotient rules of logarithms, we can simplify this expression as follows

2 loga( 4) + 3 loga( X-4) - log a(4)

= loga(4 ²) + loga((X-4)³) -  loga (4) = loga (16 ) + loga((X-4)³) - loga (4)

Combining the logarithms  using the power rule and quotient rule we have

= loga(16(X-4)³/4)

log(x+3) + log (x-3)

By using the product rule of logarithms, we can combine these logarithms

log (x +3) +log (x - 3) = log ((x +3 )(x -3 ))

Simplifying further, we get

= log (x² - 9 )

So this means that the condensed forms of the given expressions are

2loga( 4) + 3loga(X -4) - loga (4) = loga(16 (X-4) ³/4)

log (x+ 3) + log(x- 3) = log(x² - 9)

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Answer:

A. False

B. False

C. False

D. False

E. False

Explanation:

A. The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade B is 2:1, but this statement only holds true for the first set of values provided.

B. The statement is not true since the table does not provide information about the proportion of blue to red paint in shade A or B.

C. The statement is not true since the table does not provide information about the proportion of blue to red paint in shade A or B.

D. The statement is not true since the table does not provide information about the proportion of blue to red paint in shade A or B.

E. The statement is not true since there's no information about how the shade A is made.

Step-by-step explanation:

So the vector  form of the equation is: y = -1(x - 2)² + 3.

To convert from standard form to vertex form, we complete the square by following these steps:

Factor out the coefficient of the x-squared term:

y = -x² + 4x - 1

= -1(x² - 4x) - 1

To complete the square inside the parentheses, add and subtract the square of half of the coefficient of the x-term (-4/2)^2 = 4:

y = -1(x² - 4x + 4 - 4) - 1

Simplify the expression inside the parentheses by factoring a perfect square:

y = -1((x - 2)² - 4) - 1

Distribute the -1 and simplify:

y = -1(x - 2)² + 3

Therefore, the vertex of the parabola is at (2, 3), and the negative coefficient of the x-squared term means that the parabola opens downwards.

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Answer:

40%

Step-by-step explanation:

I divided 10 by 25.

25 is the total amount of brownies.

10 is the amount of caramel brownies.

Answer:

40%

Step-by-step explanation:

Based on both a) the classical method and b) the p-value method, we reject the claim made by the magazine and agree that the average distance traveled by cars is less than 20,000 kilometers per year.

To determine whether the average distance traveled by cars is less than 20,000 kilometers per year, we can perform a hypothesis test using the given sample mean and standard deviation.

a) The classical method:

In the classical method, we set up the null and alternative hypotheses based on the claim and the sample data. The null hypothesis (H0) assumes that the average distance is 20,000 kilometers or more, while the alternative hypothesis (H1) assumes that the average distance is less than 20,000 kilometers.

H0: μ ≥ 20,000 (claim made by the magazine)

H1: μ < 20,000 (alternative hypothesis)

Next, we determine the test statistic using the sample mean, sample standard deviation, and the sample size. Since the population standard deviation is not known, we use the t-distribution for the test statistic.

The test statistic (t-value) is calculated as:

t = (x - μ) / (s / \(\sqrt{n}\))

where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Substituting the given values:

x = 19,000 kilometers

μ = 20,000 kilometers

s = 3,900 kilometers

n = 100

t = (19,000 - 20,000) / (3,900 / \(\sqrt{100}\))

t = -100 / (3,900 / 10)

t ≈ -2.5641

Next, we compare the t-value with the critical value from the t-distribution table. Since the alternative hypothesis assumes a less than relationship, we look for the critical value corresponding to the left tail area of 0.05 with degrees of freedom (df) equal to the sample size minus 1 (df = 100 - 1 = 99).

Looking up the critical value for a significance level of 0.05 and df = 99, we find the critical t-value to be approximately -1.6602.

Since the calculated t-value (-2.5641) is smaller in magnitude than the critical t-value (-1.6602), we reject the null hypothesis. This means we have evidence to support the claim that the average distance traveled by cars is less than 20,000 kilometers per year based on the given sample data.

b) The P-value method:

The P-value method involves calculating the p-value, which represents the probability of obtaining a test statistic as extreme as the observed value (or more extreme), assuming the null hypothesis is true.

Using the t-value (-2.5641) calculated earlier and the t-distribution table (or a calculator), we can find the p-value associated with this test statistic. For a one-tailed test, the p-value is the probability of observing a t-value smaller than -2.5641.

Looking up the p-value in the t-distribution table (or using a calculator), we find that the p-value is approximately 0.0076.

Since the p-value (0.0076) is less than the significance level of 0.05, we reject the null hypothesis. This provides further evidence to support the claim that the average distance traveled by cars is less than 20,000 kilometers per year based on the given sample data.

In conclusion, based on both the classical method and the p-value method, we reject the claim made by the magazine and agree that the average distance traveled by cars is less than 20,000 kilometers per year.

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Answer:

4:50 hrs to school activities

Step-by-step explanation:

the entire school day 6:10 hrs (with breaks)

so if we remove the breaks (which are 1:20hrs in total) we'll have 4:50hrs.

the equation would be: (the time the full day is)-(the total of breaks)= the school activity time.

so: 6:10hrs-1:20hrs= 4:50hrs

there's your answer. 4:50 hrs

*just remember i am working in the hrs format meaning 60 mins= 1hrs*

Answer:y=-7/9x+1/9 and y= -7/9x + 1/9

Step-by-step explanation:

Answer:

23) 30°

24) 12°

Step-by-step explanation:

23) Lines will be parallel if the co interior angles are supplementary.

               ∠3 + ∠5 = 180°

 3x+ 25 + 4x - 55 = 180

3x + 4x + 25 -55 = 180

Combine like terms,

            7x -  30    = 180

Add 30 to both sides,

                7x = 180 + 30

               7x = 210

Divide both sides by 7,

                x = 210 ÷ 7

                x = 30

24)    If the lines are parallel, then the alternate interior angles are congruent.

                  ∠7 = ∠2

           11x - 36 = 8x

Add 36 to both sides,

                 11x   = 8x + 36

Subtract 8x from both sides,

          11x - 8x  = 36

                  3x = 36

                    x = 36 ÷ 3

x = 12°

The correct solution are,

(C) a=1, b=2, c=3.

The code segment does not work in the case where a > b, c > b, but a < c.

In this case, the value of 'low' is set to 'b' instead of 'a', which causes the code segment to print the incorrect value.

The values of a, b, and c that fall into this case are a=1, b=2, and c=3.

Let's trace through the code segment using a=1, b=2, and c=3:

Since a=1 and b=2, the first conditional statement (a > b && b > c) evaluates to false, so we skip the first 'if' block.

Since a=1 and c=3, the second conditional statement (a > b && c > b) evaluates to true, so we set 'low' to 'b'.

However, since we have an 'else' block following the second conditional statement, it will always be executed. So, 'low' is set to 'a' instead.

Finally, the code segment prints the sum of a + b + c - low, which is 1+2+3-1 = 5, which is incorrect.

The correct answer should be 1 + 3 = 4.

Therefore, the answer is (C) a=1, b=2, c=3.

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Answer: A teapot.

Step-by-step explanation:

Answer: See equation

Step-by-step explanation:

Absolute value basically means the positive value of anything

Essentially, the absolute value of a negative number is the same number but positive, and the absolute value of a positive number is itself.

|-6|+|-10|=16

|number| is usually used to signify absolute value

In the given research design, there are three independent variables. The notation "2x2x4" represents the number of levels or conditions for each independent variable.

The first independent variable has two levels (2x), the second independent variable has two levels (2x), and the third independent variable has four levels (4). Each independent variable is manipulated or varied independently of the others in order to examine their effects on the dependent variable(s). Therefore, there are three independent variables in this 2x2x4 research design.

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Solution:

Explanation:

The position, velocity, and acceleration of mass A can be found by taking the first and second derivatives of the given equation with respect to time, t. The first derivative will give us the velocity, and the second derivative will give us the acceleration.

(a) When t = 1 s:
Position, x = 10 sin 2(1) + 15cos2(1) + 100 = 10 sin 2 + 15cos2 + 100 = 114.96 mm
Velocity, v = dx/dt = 20 cos 2t - 30 sin 2t = 20 cos 2(1) - 30 sin 2(1) = -17.32 mm/s
Acceleration, a = dv/dt = -40 sin 2t - 60 cos 2t = -40 sin 2(1) - 60 cos 2(1) = -41.23 mm/s^2

(b) The maximum velocity and acceleration can be found by finding the critical points of the first and second derivatives, respectively. This is done by setting the derivatives equal to zero and solving for t.

For maximum velocity:
0 = 20 cos 2t - 30 sin 2t
30 sin 2t = 20 cos 2t
tan 2t = 2/3
2t = tan^-1(2/3)
t = 0.2915 s

For maximum acceleration:
0 = -40 sin 2t - 60 cos 2t
60 cos 2t = -40 sin 2t
tan 2t = -3/2
2t = tan^-1(-3/2)
t = 0.6405 s

Therefore, the maximum velocity occurs at t = 0.2915 s and the maximum acceleration occurs at t = 0.6405 s.

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(a) The position, velocity and acceleration of mass A is 110 mm,  -10 mm/s,  -50 mm/s2 respectively.

(b) The maximum velocity and the maximum acceleration of A is 20.81 mm/s, -61.87 mm/s2 respectively.

The position, velocity and acceleration of mass A when t = 1 s can be determined by substituting t = 1 s into the given equation, x = 10 sin 2t + 15cos2t + 100.

Position: x = 10 sin 2(1) + 15cos2(1) + 100 = 110 mm

Velocity: x' = 20 cos 2(1) - 30 sin 2(1) = -10 mm/s

Acceleration: x'' = -40 sin 2(1) - 30 cos 2(1) = -50 mm/s2

The maximum velocity of A can be determined by finding the points of inflection in the equation. This occurs when x'' = 0. Solving for t:

-40 sin 2t - 30 cos 2t = 0

sin 2t = 0.75

2t = sin-1(0.75) ≈ 0.927 radians

t = 0.464 s

Maximum Velocity: x' = 20 cos 2(0.464) - 30 sin 2(0.464) = 20.81 mm/s

The maximum acceleration of A can be determined by finding the points of extrema in the equation. This occurs when x' = 0. Solving for t:

20 cos 2t - 30 sin 2t = 0

cos 2t = 1.5

2t = cos-1(1.5) ≈ 0.524 radians

t = 0.262 s

Maximum Acceleration: x'' = -40 sin 2(0.262) - 30 cos 2(0.262) = -61.87 mm/s2.

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The Poisson distribution with a parameter λ = 1 accurately models the production stoppages, where on average, the company experiences one stoppage per month with a relatively small amount of variability.

The  scenario describes a company's production stoppages, which can be modeled using a Poisson distribution with a parameter (mean) of λ = 1. In a Poisson distribution, the mean, variance, and standard deviation are all equal.

The mean (μ) represents the average number of stoppages per month, which in this case is 1. This means that, on average, the company experiences one production stoppage per month.

The variance (σ^2) also has a value of 1 in a Poisson distribution. It measures the spread or variability of the data around the mean. In this case, the variance of 1 indicates that there is some fluctuation in the number of stoppages, but it is relatively small.

The standard deviation (σ) is equal to the square root of the variance, which is also 1 in this scenario. It represents the average amount of deviation from the mean. A standard deviation of 1 suggests that most of the observations will be within one unit of the mean.

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The best graph to present the data is Multiple bar diagram

The term graph in math refers easiest ways to represent data is using graphs. And it is also used to compare different values, understand how different parts impact the whole, or analyze trends.

By using the graph you can easily understand the data.

Basically, the types of graph that are suitable for specific data depends on the nature and the given conditions of the data.

Here we have some mostly used types of diagrams used to represent data are line diagrams, bar diagrams, semi-logarithmic charts, multiple bar diagrams, subdivided bar diagrams, pie diagrams, stem and leaf plots, box plots, and ogives.

Here the best graph to display the data is a Multiple bar diagram (MBD).

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If it's 9 years, then you have to replace t = 9 in the expression that models the price. With that we have the price 9 years from today:

Rounded to the nearest dollar, the price 9 years from today is $1539

And the current price is the first number of the expression: $1200

As per the given equation of the parabola, the directrix of the parabola is equal to y = -2.5.

What is directrix?

A directrix in mathematics is a curve which is associated with the process generating a geometric object, such as:

Directrix - conic section

Directrix - generatrix

Directrix - rational normal scroll

The equation of a quadratic function, with vertex (h,k), is:

y = (a)(x - h)² + k

In which, a is the leading coefficient.

The directrix is: y = k + 4a.

In this problem, the equation of parabola is given as:

y = (1/8)(x-2)² - 3

The coefficients in the given equation are a = 1/8 = 0.125,

h = 2, k = -3,

Hence the directrix is given by:

y = -3 + 4 x 0.125

y = -3 + 0.5

y = -2.5.

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Answer:

18 inches cubed

Step-by-step explanation:

to get the volume for something you must multiply it. length × width × hight

so in this case it would be 3×2×3=18 inches cubed