roblem: Report Error A partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the order of the numbers in the sum. For example, the number 4 can be written as a sum of one or more positive integers (where we don't care about the order of the numbers in the sum) in exactly five ways: \[4,\; 3 + 1,\; 2 + 2,\; 2 + 1 + 1,\; 1 + 1 + 1 + 1.\] So 4 has five partitions. What is the number of partitions of the number 7?

Answer:

  B.)  32

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, so ...

  BE = DE

  y+10 = 4y - 8 . . . substitute the given expressions

  18 = 3y . . . . . . . . add 8-y

  6 = y . . . . . . . . . . divide by 3

Then BE = y+10 = 16 and ...

  BD = 2×BE = 2×16

  BD = 32

Answer:

B.) 32

Step-by-step explanation:

Given parallelogram ABCD, diagonals AC and BD intersect at point E, AE = 2x, BE=y+10, CE=x+2 and DE=4y - 8, the length of BD is 32.

BD = 2×BE = 2×16

Answer:

a = sqrt( 3x+1)

Step-by-step explanation:

f(x) = sqrt(x-1)

g(x) = 3x+2

(f°g)(x) means replace g(x) in f(x) every place you see an x

(f°g)(x) = sqrt( g(x) -1)

          = sqrt( 3x+2 -1)

     Simplifying

          =sqrt( 3x+1)

The change in the X values is in multiples of 2.

The change in the h(x) values need to be: -0.3 x 2 = -0.6

Now find the h(x) values that have a difference of -0.6

A negative value is a decrease.

2 to 4 is an increase.

4 to 6 is an increase.

6 to 8 is an increase.

8 to 10 is an increase.

10 to 12 = 20-19.8 = 0.2

12 to 14 = 19.8 - 19.2 = 0.6

The two columns are 12 and 14

Answer:

0.68

Step-by-step explanation:

Given

Mean = μ = 6 cm

SD = σ = 1.5 cm

We have to find the z-scores for 4.5 and 7.5

z-score for 4.5 = z_1 = (x-μ)/σ = (4.5-6)/1.5 = -1.5/1.5 = -1

z-score for 4.5 = z_2 = (x-μ)/σ = (7.5-6)/1.5 = 1.5/1.5 = 1

We have to find area to the left of z-scores

Using the rule of thumb for SD from mean, 68% of data lies between one standard deviation from mean. So the probability of choosing a band with length between 4.5 and 7.5 cm is 0.68 ..

Answer:

  3 mph

Step-by-step explanation:

Let c represent the current of the river in miles per hour. Then the ratio of speed downstream to speed upstream is ...

  (21 +c)/(21 -c) = 2.4/1.8

  1.8(21 +c) = 2.4(21 -c) . . . . . . multiply by 1.8(21-c)

  37.8 + 1.8c = 50.4 -2.4c . . . . eliminate parentheses

  4.2c = 12.6 . . . . . . . . . . . . . . . add 2.4c-37.8

  c = 3 . . . . . . . . . . . . . . . . . . . .divide by 4.2

The current of the river is 3 miles per hour.

Answer:

a

Step-by-step explanation:

Given

x² + 20x + 100 = 36 ( subtract 36 from both sides )

x² + 20x + 64 = 0 ← in standard form

Consider the factors of the constant term ( + 64) which sum to give the coefficient of the x- term ( + 20)

The factors are + 16 and + 4, since

16 × 4 = + 64 and 16 + 4 = + 20, hence

(x + 16)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 16 = 0 ⇒ x = - 16

x + 4 = 0 ⇒ x = - 4

Answer:

see explanation

Step-by-step explanation:

To determine the magnitude of the scale factor, calculate the ratio of corresponding sides of image to original, that is

scale factor = [tex]\frac{A'B'}{AB}[/tex] = [tex]\frac{2}{5}[/tex]

ΔA''B''C'' is a reflection of ΔA'B'C' in the y- axis ( corresponding vertices are equidistant from the y- axis )

Answer:

Exterior

Step-by-step explanation:

In any triangle an exterior angle is equal to the sum of the two opposite interior angles.

Answer:

  D.  X-7

Step-by-step explanation:

The table tells you that when x=7, g(x) = 0. In order for g(7) to be zero, at least one factor must be zero when x=7. The only factor on the list that is zero when x=7 is (x-7).

To see if (x - a) is a factor of g(x), a polynomial function, you check if g(a) = 0 from the values in the table. Unfortunately, without the table of values, we cannot definitively determine which of the options must be a factor of the function g(x).

In order to determine which of the options given must be a factor of the function g(x), we need to understand a property about polynomial functions and their factors. If (x - a) is a factor of a polynomial, then the function g(a) = 0. This means that (a,0) is a point on the graph of the function.

Unfortunately, without the values of x and g(x) from the table above we cannot definitively conclude which of the options A, B, C, or D must be a factor of the polynomial g(x). However, if for example, g(1) = 0 in the table, then (x - 1) or option A would be a factor of g(x). The same logic applies to the other options.

Remember to always check any similar question using the table of values provided to determine if a given expression is a factor of a function!

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Answer:

Y

Step-by-step explanation:

The answer is no, the result of the joint test for the null hypothesis that both [tex]\( \beta_1 = 0 \) and \( \beta_2 = 0 \)[/tex] is not necessarily implied by the results of two separate tests for each coefficient.

To understand why, let's consider the two scenarios:

1. Separate Tests: When we conduct two separate tests for [tex]\( \beta_1 = 0 \) and \( \beta_2 = 0 \)[/tex], we are looking at the significance of each predictor independently. We might find that neither [tex]\( \beta_1 \) nor \( \beta_2 \)[/tex] is significantly different from zero on its own. However, this does not account for the potential multicollinearity between [tex]\( X_1 \) and \( X_2 \)[/tex]. Multicollinearity can result in high variance of the coefficient estimates, leading to insignificant t-tests even if the predictors have a joint effect on the response variable.

2. Joint Test (F-test): The joint test, typically conducted using an F-test, assesses whether both [tex]\( \beta_1 \) and \( \beta_2 \)[/tex] are simultaneously equal to zero. This test takes into account the correlation between [tex]\( X_1 \) and \( X_2 \)[/tex] and evaluates the combined effect of both variables on the response variable. It is possible that while neither variable alone is significant, together they might have a significant effect.

The F-test for the joint hypothesis is based on the reduction in the sum of squared residuals when including [tex]\( X_1 \) and \( X_2 \)[/tex] in the model compared to a model with only the intercept (reduced model). The test statistic is calculated as:

[tex]\[ F = \frac{(\text{SSR}_{\text{reduced}} - \text{SSR}_{\text{full}}) / k}{\text{SSR}_{\text{full}} / (n - p - 1)} \][/tex]

where:

- [tex]\( \text{SSR}_{\text{reduced}} \)[/tex] is the sum of squared residuals from the reduced model.

- [tex]\( \text{SSR}_{\text{full}} \)[/tex] is the sum of squared residuals from the full model.

- [tex]\( k \)[/tex]is the number of restrictions (in this case, 2, since we are testing two coefficients).

- [tex]\( n \)[/tex] is the number of observations.

-  [tex]\( p \)[/tex] is the number of predictors in the full model (not including the intercept).

The degrees of freedom for the numerator are k and for the denominator are [tex]\( n - p - 1 \)[/tex].

In summary, the results from separate t-tests for [tex]\( \beta_1 \) and \( \beta_2 \)[/tex] do not necessarily inform us about the joint significance of these coefficients. It is entirely possible for the separate tests to show non-significance while the joint F-test shows significance, indicating that the predictors have a joint effect on the dependent variable even if their individual effects are not significant. Conversely, it is also possible for the separate tests to show significance for one or both coefficients, while the joint test does not show significance, suggesting that the combined effect of the predictors is not significant.

Answer:

[tex]0.060[/tex]

Step-by-step explanation:

In a two tailed test the probability of occurrence is the total area under the critical range of values on both the sides of the curve (negative side and positive side)

Thus, the probability values for a two tailed test as compared to a one tailed test is given by the under given relation -

[tex]p-value = P(Z< -\frac{\alpha }{2} )+P(Z >\frac{\alpha}{2})[/tex]\

Here [tex]P\frac{\alpha}{2} = 0.030[/tex]

Substituting the given value in above equation, we get -

probability values for a two tailed test

=[tex]0.030 + 0.030\\= 0.060[/tex]

Answer: She will have $700 left over.

Step-by-step explanation: Since we know that a rectangle has two sides with the measurement, we can add the sides. 37+37+25+25=124. The fencing in 124 feet in total. Multiply the 124 feet by the price per foot. 124 x 75 =9,300. Subtract the price from your total amount of money. 10,000 - 9,300 = $700. She will have $700 left over.

Answer:

there would be $700 left over

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The answer is C

Answer:

Your answer would be C

Step-by-step explanation:

I got it right on edge <3

Answer:

c

Step-by-step explanation:

C is your answer. Since this is a parallelogram, is means that there are two sets of sides with the same length. Because the measurement of angle K is 82 the angle directly opposite would have the same measurement. That's why angle M is also 82. When you add all the angles of a quadrilateral it adds up to 360 degrees. multiply 82 by 2 to get 164 and subtract that from 360 to get 196. you then have to divide that by 2 and you will get 98 which is the measurement for both angles L and N

Answer:

The correct answer is option C.

m<L = 98°, m<M = 82° and m<N = 98°

Step-by-step explanation:

From the figure we can see a parallelogram KLMN

Properties of parallelogram

1)Opposite sides are equal and parallel.

2) Opposite angles are equal.

3) Adjacent angles are supplementary.

To find the correct option

It is given that, m<K = 82°

By using properties of parallelogram we get

m<L = 98°, m<M = 82° and m<N = 98°

Therefore the correct answer is option C

Answer:

Option A is the correct choice.

Step-by-step explanation:

We have been given a histogram and we are asked to choose the correct statement about our given histogram.

Upon looking at our given histogram, we can see that our given data set is skewed to right. This means that means that the mean of the given data will be greater than median as our given data set has a long tail towards right or our data set is positively skewed.

Therefore, option A is the correct choice.

Answer:

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic. For repetitive calculations, it is convenient to define a function in a graphing calculator or spreadsheet.

Answer: About 8.5 cubic yards

Step-by-step explanation:

Given : The length of the garden = 16 ft.

The width of the garden = 34 ft.

The depth of the thick layer of topsoil on the garden = 5 inch

=[tex]\dfrac{5}{12}\text{ ft.}[/tex]               [Since 1 foot = 12 inches]

The volume of a rectangular prism :-

[tex]V=l*w*h[/tex], where l is length , w is width and h is height.

The number of cubic feet of topsoil required will be

[tex]V=16\times34\times\dfrac{5}{12}=\dfrac{680}{3}\text{cubic feet}[/tex]

Since 1 yard = 3 feet

[tex]1\text{ foot}=\dfrac{1}{3}\text{ yard}[/tex]

[tex]V=\dfrac{680}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}=8.3950617284\approx8.50\text{cubic yards}[/tex]

Answer:

= 1/2[sin2Acos7A + cos2Asin7A + sin2Acos7A - cos2Asin7A]

we cut out

cos2Asin7A - cos2Asin7A

then we have

=1/2[sin2Acos7A + sin2Acos7A ]

= 1/2*2[ sin2Acos7A ]

cut out 2 we get

#sin2Acos7A

Answer:

  A.  $14,500

Step-by-step explanation:

The van depreciates ($16000 -1000 = $15000 in 5 years, so $3000 per year. It will be assumed to depreciate half that amount in half a year, so will be worth $1500 less than $16000 at the end of the first calendar year. The book value will be $14,500.

Final answer:

The book value of the minivan at the end of Year 1 is $14,500 after accounting for 6 months of straight-line depreciation of $1,500 from the original cost of $16,000.

Therefore, the correct answer is A. $14,500.

Explanation:

The student's question is related to calculating the book value of a minivan at the end of year 1 using the straight-line depreciation method. To find the book value, we need to first calculate the annual depreciation expense and then subtract it from the original cost of the minivan.

First, we calculate the annual depreciation expense:

Purchase price of minivan: $16,000

Residual value: $1,000

Useful life: 5 years

So, the annual depreciation expense is
(

$16,000

-

$1,000

) /

5 years

= $3,000 per year.

Since the minivan was bought on July 3, we need to account for a partial year of depreciation for year 1. Assuming the end of the year is December 31, that's 6 months (July through December) of depreciation in the first year. Therefore, it would be
$3,000 / 2 = $1,500 for 6 months.

To find the book value at the end of Year 1, we subtract the depreciation for the first 6 months from the purchase price:
$16,000 - $1,500 = $14,500.

Answer:

Step-by-step explanation:

It is convenient to let a spreadsheet or graphing calculator do the repetitive evaluation of a function like this. That simplifies the work and reduces errors.

The function is shown in the attachment written in Horner form, which is convenient for evaluation by hand or using a calculator.

Answer:

Step-by-step explanation:

The vertex order ABC is clockwise in the original figure and also in the first image: A'B'C'. The altitude from AC to B is up in the original and left in the first image, indicating a rotation 90° CCW.

  The first transformation is a rotation 90° CCW.

The vertex order of A''B''C'' is CCW, indicating a reflection. The direction of the altitude from A''C'' to B'' is still to the left, so the reflection must be over a horizontal line. We find the x-axis bisects the segments A'A'', B'B'', and C'C'', confirming that it is the line of reflection.

  The second transformation is reflection across the x-axis.

_____

Algebraically, the transformations are ...

  1st: (x, y) ⇒ (-y, x)

  2nd: (x, y) ⇒ (x, -y)

Both together: (x, y) ⇒ (-y, -x).

Answer:

So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach.  You have to let me know if you want this done another way.

Here are some rules I'm going to use:

[tex](f+g)'=f'+g'[/tex]       (Sum rule)

[tex](cf)'=c(f)'[/tex]          (Constant multiple rule)

[tex](x^n)'=nx^{n-1}[/tex] (Power rule)

[tex](c)'=0[/tex]               (Constant rule)

[tex](x)'=1[/tex]                (Slope of y=x is 1)

[tex]y=4x^3+13x^2-12x-56[/tex]

[tex]y'=(4x^3+13x^2-12x-56)'[/tex]

[tex]y'=(4x^3)'+(13x^2)'-(12x)'-(56)'[/tex]

[tex]y'=4(x^3)'+13(x^2)'-12(x)'-0[/tex]

[tex]y'=4(3x^2)+13(2x^1)-12(1)[/tex]

[tex]y'=12x^2+26x-12[/tex]

Now we set y' equal to 0 and solve for the critical numbers.

[tex]12x^2+26x-12=0[/tex]

Divide both sides by 2:

[tex]6x^2+13x-6=0[/tex]

Compaer [tex]6x^2+13x-6=0[/tex] to [tex]ax^2+bx+c=0[/tex] to determine the values for [tex]a=6,b=13,c=-6[/tex].

[tex]a=6[/tex]

[tex]b=13[/tex]

[tex]c=-6[/tex]

We are going to use the quadratic formula to solve for our critical numbers, x.

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}[/tex]

[tex]x=\frac{-13 \pm \sqrt{169+144}}{12}[/tex]

[tex]x=\frac{-13 \pm \sqrt{313}}{12}[/tex]

Let's separate the choices:

[tex]x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}[/tex]

Let's approximate both of these:

[tex]x=0.3909838 \text{ or } -2.5576505[/tex].

This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.

The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

[tex]f(x)=4x^3+13x^2-12x-56[/tex]

[tex]f'(x)=12x^2+26x-12[/tex]

[tex]f''(x)=24x+26[/tex]

So if f''(a) is positive then we have a minimum at x=a.

If f''(a) is negative then we have a maximum at x=a.

Rounding to nearest tenths here:  x=-2.6 and x=.4

Let's see what f'' gives us at both of these x's.

[tex]24(-2.6)+25[/tex]

[tex]-37.5[/tex]  

So we have a maximum at x=-2.6.

[tex]24(.4)+25[/tex]

[tex]9.6+25[/tex]

[tex]34.6[/tex]

So we have a minimum at x=.4.

Now let's find the corresponding y-value for our relative minimum point since that would complete your question.

We are going to use the equation that relates x and y.

I'm going to use 0.3909838 instead of .4 just so we can be closer to the correct y value.

[tex]y=4(0.3909838)^3+13(0.3909838)^2-12(0.3909838)-56[/tex]

I'm shoving this into a calculator:

[tex]y=-58.4654411[/tex]

So the approximate relative minimum is (0.4,-58.5).

If you graph [tex]y=4x^3+13x^2-12x-56[/tex] you should see the graph taking a dip at this point.

Answer:

Step-by-step explanation:

speed x time = distance

s (1.5) = 105

1.5s=105

s = 70mph

d(t) = 70t

Answer:

The equation that relates y and x is [tex]y=x+612 mi[/tex], and the equation that relates x and d is [tex]4d=x[/tex].

Step-by-step explanation:

Step 1: First we know that the total distance is equal to y. The distance traveled in 4 hours equals x, and the distance from point x to y equals 612 miles. Adding x to the remaining 612 miles gives the total distance y.

[tex]y=x+612 mi[/tex]

Step 2: To know the relationship between x and d, we must first raise the speed during the journey to x.

[tex]v=\frac{x}{4h}[/tex]

Then, we set the speed d e equal v:

[tex]v=\frac{d}{h}[/tex]

[tex]\frac{x}{4h} = \frac{d}{h}[/tex]

Clearing x we get:

[tex]x=4h * \frac{d}{h}[/tex]

[tex]x=4d[/tex]

Have a nice day!

Answer:

-7 is real and complex

Step-by-step explanation:

Every number is complex.

Complex numbers are in the form of a+bi where a and b are real numbers.

Pure imaginary are complex numbers with a being 0.

Real numbers are complex number with b being 0.

-7 is a real number and a complex number.

(It doesn't have an imaginary part)

-7 is a real and complex number.

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Answer:

95%

Step-by-step explanation:

For a given sample data, the width of the confidence interval would vary directly with the confidence level i.e. more the confidence level,  wider will be the confidence interval.

This is because the critical value associated with the confidence level(e.g z value) becomes larger as the confidence level is increased which results in an increased interval.

The confidence interval for a population proportion is given by the formula:

[tex]p \pm z\sqrt{\frac{pq}{n} }[/tex]

So, for a fixed value of p,q and n, the larger the value of z the wider will be the confidence interval.

Hence 95% confidence interval will be wider than 80% confidence interval.

The 95% confidence interval is wider than the 80% confidence interval because it includes a larger area under the curve of a normal distribution, offering a higher level of confidence the true population parameter falls within this range.

In statistical analysis, especially for polls like the one mentioned about favorite pies, the confidence interval plays a significant role in interpreting the reliability of the results. The 95% confidence interval is wider than the 80% confidence interval. This is because a higher confidence level, in this case 95%, means we are more sure that the actual population parameter lies within the interval, but in order to gain this certainty, the interval necessarily needs to be wider.

This can also be understood in the context of a normal distribution. For a 95% confidence interval, we are including a larger area under the curve of the distribution, thus the interval has to be wider than the one for the 80% confidence interval, which covers a smaller area.

It's important to note, however, that a wider confidence interval doesn't necessarily imply better predictability. It simply means there's a higher level of confidence that the true population parameter falls within the specified range.

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Answer:

The correct option is 1.

Step-by-step explanation:

Given information: AD = 25, CD = 5, DB = 1 and CD⊥AB.

According to the Pythagoras theorem,

[tex]hypotenuse^2=base^2+perpendicular^2[/tex]

In triangle BCD,

[tex]CB^2=DB^2+CD^2[/tex]

[tex]CB^2=1^2+5^2[/tex]

[tex]CB^2=26[/tex]

Taking square root both sides.

[tex]CB=\sqrt{26}[/tex]

In a right angled triangle,

[tex]\sin\theta=\frac{opposite}{hypotenuse}[/tex]

[tex]\sin B=\frac{CD}{CB}[/tex]

[tex]\sin B=\frac{5}{\sqrt{26}}[/tex]

[tex]\sin B=0.980580675691[/tex]

[tex]\sin B\approx 0.9806[/tex]

Therefore the correct option is 1.

Answer:

0.9806 is the correct answer.

Step-by-step explanation:

Answer:

S = -9,372 ⇒ 1st answer

Step-by-step explanation:

* Lets revise the geometric series

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)

* General term (nth term) of a Geometric series:

 U1 = a  ,  U2  = ar  ,  U3  = ar2  ,  U4 = ar3  ,  U5 = ar4

 Un = ar^(n-1), where a is the first term, r is the constant ratio between

 each two consecutive terms

- The sum of first n terms of a geometric series is calculate from

  [tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex]

* Lets solve the problem

∵ The series is geometric

∵ a1 = -12

∴ a = -12

∵ a5 = -7500

∵ a5 = ar^4

∴ -7500 = -12(r^4) ⇒ divide both sides by -12

∴ 625 = r^4 take root four to both sides

∴ r = ± 5

∵ r = 5 ⇒ given

∵ [tex]Sn=\frac{a(1-r^{n})}{1-r}[/tex]

∵ n = 5

∴ [tex]S_{5}=\frac{-12[1-(5)^{5}]}{1-5}=\frac{-12[1-3125]}{-4}=3[-3124]=-9372[/tex]

* S = -9,372

Answer:

11 years old

Step-by-step explanation:

Let Jimmy's age be represented as x. His big brother's age is x+5 and his sister's age is 2x. Adding these gives us 4x+5=29. Solving for x gives us 6. His brother's age is 6+5=11.

11 years old is Jimmy's brother.

Let Jimmy's age be represented as x. His big brother's age is x+5 and his sister's age is 2x. Adding these gives us 4x+5=29. Solving for x gives us 6. His brother's age is 6+5=11.

J=Jimmy's age; S=sister's age=2J; B=brother's age=J+5

.

J+S+B=29

J+(2J)+(J+5)=29

4J+5=20

4J=24

J=6

Jimmy is 6 years old.

B=J+5=6+5=11

ANSWER: Jimmy's brother is 11 years old.

.

CHECK:

S=2J=2(6)=12

Jimmy's sister is 12 years old.

.

J+S+B=29

6+12+11=29

29=29.

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