Sarah wants to build a doghouse, but first she builds a smaller model to practice. The biggest piece of wood she will need for the full size-size doghouse is 39 inches wide and 24 inches tall. If she uses a piece for the model that is 8 inches tall. How wide should it be?
Please help asap tysm <3

Answer:

10xg+25

Step-by-step explanation:

Answer:

\(\dfrac{1}{2}\sin(x)-\dfrac{1}{14} \sin(7x)\)

Step-by-step explanation:

Evaluate the given integral.

\(\Big\int\big(\sin(4x)\sin(3x)\big) \ dx\)

\(\hrulefill\)

(1) - Apply the sum-to-product identity to the integrand

\(\boxed{\left\begin{array}{ccc}\text{\underline{Sum-to-Product Identity:}}\\\\\sin(A)\sin(B)=\dfrac{1}{2}\Big(\cos(A-B)-\cos(A+B)\Big) \end{array}\right}\)

\(\Big\int\big(\sin(4x)\sin(3x)\big) \ dx\\\\\\\Longrightarrow \int\Big[\dfrac{1}{2}\Big(\cos(4x-3x)-\cos(4x+3x)\Big) \Big] \ dx\\\\\\\Longrightarrow \int\Big[\dfrac{1}{2}\Big(\cos(x)-\cos(7x)\Big) \Big] \ dx\\\\\\\Longrightarrow \dfrac{1}{2}\int\Big(\cos(x)-\cos(7x)\Big) \ dx\)

(2) - We can now apply simple integration rules and use u-substitution

\(\boxed{\left\begin{array}{ccc}\text{\underline{Trig. Int. Rule for Cosine:}}\\\\\int\cos(x) dx=\sin(x)\end{array}\right}\)

\(\dfrac{1}{2}\int\Big(\cos(x)-\cos(7x)\Big) \ dx \\\\ \\\text{Let} \ u=7x \rightarrow du=7dx \\ \\\\\Longrightarrow \dfrac{1}{2}\Big[\sin(x)-\dfrac{1}{7} \int\cos(u)du\Big]\\\\\\\Longrightarrow \dfrac{1}{2}\Big[\sin(x)-\dfrac{1}{7} \sin(7x)\Big]\\\\\\\Longrightarrow \dfrac{1}{2}\sin(x)-\dfrac{1}{14} \sin(7x)\Big\\\\\\\therefore \Big\int\big(\sin(4x)\sin(3x)\big) \ dx=\boxed{\boxed{\dfrac{1}{2}\sin(x)-\dfrac{1}{14} \sin(7x)}}\)

Thus, the problem is solved.

Answer:

table B represents the linear equation which is:

\(y=-3x+11\)

The graph of the linear function is also attached below.

Step-by-step explanation:

Given the table B values

x               y

0              11

1               8

2               5

3               2

As the equation for the linear function

\(y=mx+b\)

where m is the slope and b is the y-intercept

As the y-intercept can be obtained by setting x=0

From the table, it is clear that when the value of x=0, then the value of

y=11.

so (0, 11) is the y-intercept.

Also taking two points (0, 11) and (1, 8) to find the slope

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(0,\:11\right),\:\left(x_2,\:y_2\right)=\left(1,\:8\right)\)

\(m=\frac{8-11}{1-0}\)

\(m=-3\)

so substituting the value m=-3 and the point (1, 8) in the point-slope form

\(y-y_1=m\left(x-x_1\right)\)

\(y-8=-3\left(x-1\right)\)

\(y-8=-3x+3\)

\(y=-3x+3+8\)

\(y=-3x+11\)

comparing the equation with the slope-intercept form of linear equation

\(y=mx+b\)

\(y=-3x+11\)

here

Therefore, table B represents the linear equation which is:

\(y=-3x+11\)

The graph of the linear function is also attached below.

Answer:

B

Step-by-step explanation:

The equation s = (1/25) * d² best represents the data in the table.

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

From the table, we can observe that as the speed of the car increases, the stopping distance also increases. This suggests a non-linear relationship between the speed and stopping distance.

Option (d) s = (1/25) * d² represents a quadratic relationship between the speed and stopping distance. This is because the stopping distance is proportional to the square of the speed. We can check if this equation fits the data by plugging in the given values of stopping distance and speed from the table:

For s = 20 mph, d = 17.89 ft

20 = (1/25) * (17.89)² ≈ 14.2

For s = 40 mph, d = 25.30 ft

40 = (1/25) * (25.30)² ≈ 40.1

For s = 60 mph, d = 30.98 ft

60 = (1/25) * (30.98)² ≈ 70.6

For s = 80 mph, d = 35.78 ft

80 = (1/25) * (35.78)² ≈ 111.6

For s = 100 mph, d = 40.00 ft

100 = (1/25) * (40.00)^² ≈ 160

We can see that the values calculated using the equation in option (d) are reasonably close to the actual values from the table. Therefore, the equation s = (1/25) * d² best represents the data in the table.

Therefore, the equation s = (1/25) * d² best represents the data in the table.

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Answer:

D:  s = StartFraction 1 Over 25 EndFraction d squared

edge 2023

Answer:

13: 7x 3y

14: 37

15: 60

16: 23

I'm sorry but my vision is too bad, I can't read 17.

:(

Answer:

14.) 2/3

15.) 1/9

16.) 1/4

17.) 1

Step-by-step explanation:

Sorry I couldn't help you with number 18, it's not in the picture.

Hope this helps!

Answer:

1.-1/2(12x – 2) = –6x – 1   ==> No solution

2.1/2(12x – 4) = 6x – 2 ==> Infinitely many solutions

3. 3.1/2(12x – 2) = –6x – 2 ==> One solution

Step-by-step explanation:

Expand left side of each choice :
1. Left side becomes
-1/2(12x - 2) = -1/2(12x) - 1/2(-2) = -6x + 1

Equating to the right side gives
-6x + 1 = -6x - 1

-6x cancels and we get 1 = -1.

This is a false statement and that means there are no solutions

2.Left side:
6x - 2

==> 6x - 2 = 6x - 2
Since both left and right sides are equal, this indicates infinitely many solutions

Since we have eliminated two of three possibilities, the remaining third choice must be one solution

Let's verify:
1/2(12x - 2) = 6x - 1

==> 6x - 1 = - 6x -2

Add 6x to both sides:
6x + 6x - 1 = -6x + 6x - 2

12x - 1 = -2

Add 1 to both sides;
12x = 1 - 2 = -1

x = - 1/12

So one solution

The elements of Z3[x]/(x^2 - x) are of the form ax + b that is multiplication table, where a and b are elements of Z3.

The multiplication table is:

  | 0   1   x   1+x   2   2+x

-------------------------------

0 | 0   0   0    0   0   0

1 | 0   1   x   1+x  2  2+x

x | 0   x  2x  2+x   x  1+2x

1+x| 0  1+x 2+x   2  2+x  x

2 | 0   2   x   2+x  1  1+x

2+x| 0  2+x 1+2x  x  1+x 2

Note that in this table, we use the fact that x^2 - x = 0, which implies that x^2 = x.

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Answer:

18 > -9n

Step-by-step explanation:

eighteen is greater than the product of a number (n) and -9

18                          >                                                   -9n

18 > -9n

Answer:

In this solution the solvent is water and the solutes are sugar, artificial flavor and artificial color. Another interesting property of solutions is that different concentrations of solute can be made. As all of you are aware, you can make very sweet Kool Aid and less sweet Kool Aid.

Kool -Aid is a famous solution

So

Rest ingredients are solutes

The whole is the solution

(a) Construct confidence intervals are : 90%: [428.95, 444.05], 95%: [427.13, 445.87], 99%: [423.67, 449.33].

(b) The 99% confidence interval has the widest interval.

(a) To construct confidence intervals for the mean breaking strength of the wool fibers, we shall use the given formula:

Confidence interval = sample mean ± (critical value * standard error)

The critical value here will depends on the level of confidence. For a 90% confidence level, the critical value is 1.645 (from the standard normal distribution). For a 95% confidence level, the critical value is 1.96, and for a 99% confidence level, the critical value is 2.576.

Standard error is obtained by dividing the sample standard deviation by the square root of the sample size.

Plugging in the values, we can calculate the confidence intervals:

90% confidence interval:

Lower bound = 436.5 - (1.645 * (11.9 / √20))

Upper bound = 436.5 + (1.645 * (11.9 / √20))

95% confidence interval:

Lower bound = 436.5 - (1.96 * (11.9 / √20))

Upper bound = 436.5 + (1.96 * (11.9 / √20))

99% confidence interval:

Lower bound = 436.5 - (2.576 * (11.9 / √20))

Upper bound = 436.5 + (2.576 * (11.9 / √20))

(b) The width of a confidence interval depends on both the critical value and the standard error. When aiming for a higher level of confidence, the interval becomes wider as it requires a larger critical value. Consequently, it can be concluded that among the given confidence intervals, the one with a 99% confidence level will have the broadest range.

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Answer: The Range

The range on the corn has more spread than the soybeans.

The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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Answer:

n(AnB)= {4, 29}

n(BnC)= {9,29}

n(AnC)= {29}

Answer:

Step-by-step explanation:

how much taller is a stack of 3 nickels than 1 nickel

1 nickel is 1.95mm high, 3 nickel is 3 x 1.95 = 5.85mm high,

make a difference and find out how much higher is a stack of 3 nickels than 1 nickel.

5.85 - 1.95 = 3.9mm

The main  Miguel's statement about rotating, reflecting, or translating a trapezoid to produce another trapezoid resulting in two similar trapezoids is correct.

However, his statement about dilating a trapezoid to produce another trapezoid resulting in two similar trapezoids is incorrect.


Similar figures have the same shape but not necessarily the same size. When a trapezoid is rotated, reflected, or translated, its angles and sides remain the same, and therefore, the resulting trapezoid is similar to the original.

On the other hand, when a trapezoid is dilated, its sides are stretched or shrunk by a scale factor, which changes the ratios of the sides and angles, making the resulting trapezoid not similar to the original.

Therefore, Miguel's statement about rotating, reflecting, or translating a trapezoid to produce another trapezoid resulting in two similar trapezoids is correct, while his statement about dilating a trapezoid to produce another trapezoid resulting in two similar trapezoids is incorrect.

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It would take Carlos 28.28 years before his salary would reach $106500.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is its graph or the rate of change is large.

As the table represents a linear relation we can write it in the form

S = mn + b

Slope(m) = (92500 - 78500)/(5 - 1).

Slope(m) = 14000/4.

Slope(m) = 3500.

Now, 78500 = 3500(1) + b.

b = 7500.

S = 3500n + 7500.

Therefore, The number of years 'n' required will be,

106500 = 3500x + 7500.

3500n = 99000.

n = 990/35

n = 28.28 years.

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The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

The percentage of people who chose only coffee will be 43%.

Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol '%' is used to symbolize it.

At a breakfast buffet, 63% of people choose coffee as their beverage while 23% choose juice.

Also, 20% choose both coffee and juice.

Then the percentage of people who chose only coffee will be given by the difference of 63% and 20%.

⇒ 63% - 20%

⇒ 43%

Thus, the percentage of people who chose only coffee will be 43%.

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Answer:

x1 = 5-3squareroot 5/2 x2= -5+3 squareroot 5 / 2

Step-by-step explanation:

The ratio of the number of boys and girls to show Leslie's statement is false is 18/24 and 6/24.

The ratio of boys to women is 9:3, because of this that for every 9 boys, there are three women. This also method that the fraction of boys to the whole quantity of students is 9/12, and the fraction of girls to the entire variety of college students is 3/12.

Leslie’s assertion is that there ought to be precisely 6 greater boys than ladies, this means that the distinction between the number of boys and girls is continually 6. This means that the fraction of boys to the whole number of college students is always 6/12 more than the fraction of ladies to the whole quantity of students.

However, this isn't real, because we can discover numbers of boys and girls that satisfy the ratio of 9:3 but have an exceptional difference. For instance, if there are 18 boys and 6 women, then the fraction of boys to the entire quantity of students is 18/24, and the fraction of women to the entire range of students is 6/24.

The difference among these fractions is 12/24. Therefore, Leslie’s statement is fake. Another manner to see that is to notice that if we multiply both phrases of the ratio by way of a not-unusual factor, we get a new ratio this is equal to the authentic one, but has a unique difference.

For instance, if we multiply by way of 2, we get 18:6, which has a difference of 12. If we multiply by using 3, we get 27:9, which has a distinction of 18. In fashionable, any multiple of nine and three that isn't always 9 and three will paint as a counter-example to Leslie’s statement.

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`x > 0`, `f''(x) > 0`.∴ `f(x)` is concave upwards for `x > 0`.So, `(0, f(0))` is the point of inflection of `f(x)`.

Given function is `f(x) = e^(-32x²)`.So, `f'(x) = -64xe^(-32x²)`.

Put `f'(x) = 0` to get the critical points of `f(x)`.

∴ `-64xe^(-32x²) = 0`

⇒ `-64x = 0` or `e^(-32x²) = 0`

⇒ `x = 0` is the critical point.

So, the first derivative is negative for `x < 0` and positive for `x > 0`.

Hence, `f(x)` is decreasing for `x < 0` and increasing for `x > 0`.

So, `x = 0` is the point of relative minimum of `f(x)`.

Again, `f''(x) = (-64e^(-32x²))² - 64xe^(-32x²) * (-64xe^(-32x²))

`= `4096x²e^(-64x²)`

So, `f''(0) = 0`.

Now, for `x < 0`, `f''(x) > 0`.∴ `f(x)` is concave upwards for `x < 0`.

Again, for `x > 0`, `f''(x) > 0`.∴ `f(x)` is concave upwards for `x > 0`.So, `(0, f(0))` is the point of inflection of `f(x)`.

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The roots of the given equation is real and equal.

Given , 5\(x^{2} \\\) - 10x+ k=0

The quadratic equation is b² - 4ac = 0

Here, a= 5, b= -10, c= k

substitute in b² - 4ac = 0

(-10)² - 4 * 5* k =0

100 - 20k =0 , let this be equation (1)

100 = 20k

k = \(\frac{100}{20}\)

k = 5.

now, substitute  k= 5 in equation (1)

100 -20k = 0

100 - 20*5 = 0

100 - 100 = 0

Therefore, the given equation is real and equal .

The correct question is 5x² - 10x + k =0

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This is the Taylor series expansion for the function f(x) = x⁴ - 6x² + 1 centered at a = 2.

What is Taylor Series?

In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the derivative of the function at a single point. For most common functions, the function and the sum of its Taylor series near this point are the same.

To find the Taylor series for the function f(x) = x⁴ - 6x² + 1 centered at a = 2, we can use the formula for the Taylor series expansion:

f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ...

First, let's find the values of f(a) and its derivatives at x = a = 2:

f(2) = (2)⁴ - 6(2)² + 1 = 16 - 24 + 1 = -7

f'(x) = 4x³ - 12x

f'(2) = 4(2)³ - 12(2) = 32 - 24 = 8

f''(x) = 12x² - 12

f''(2) = 12(2)² - 12 = 48 - 12 = 36

f'''(x) = 24x

f'''(2) = 24(2) = 48

Now, we can substitute these values into the Taylor series formula:

f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ...

f(x) = -7 + 8(x - 2)/1! + 36(x - 2)²/2! + 48(x - 2)³/3! + ...

Simplifying the terms:

f(x) = -7 + 8(x - 2) + 18(x - 2)² + 8(x - 2)³ + ...

This is the Taylor series expansion for the function f(x) = x⁴ - 6x² + 1 centered at a = 2.

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Answer:

A

Step-by-step explanation:

it is A

Answer:

C

Step-by-step explanation:

Minus two equations , we got:

9x-9y= 132-(-12)

9x-9y=144

x-y=16

Answer:

a. 3/10

b. 1/10

c. 4/10 or 2/5

Step-by-step explanation:

There is 4 brown, 3 green, 2 red, and 1 purple if you add those all up you get 10. Since there is a total of 10 marbles in the bag and 3 of those are green 3/10 of the marbles are green. Same goes with purple, 1 of the 10 marbles in the bag is purple.

To solve for green and purple you must add them. Since there is 3 green and 1 purple that gives you 4. 4 out of 10 marbles are green or purple. 4/10 can also be simplified to 2/5

We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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Therefore, based on the obtained z statistic of -1.99 and an alpha level of 0.05, the researcher should reject the null hypothesis.

To determine the decision based on the obtained z statistic and alpha level, we compare the z statistic with the critical values.

Since it is a two-tailed test, we need to divide the alpha level by 2 to allocate equal portions in both tails. Thus, for an alpha level of 0.05, each tail has an alpha of 0.025.

Looking up the critical value corresponding to an alpha of 0.025 in a standard normal distribution table, we find that the critical value is approximately ±1.96.

Comparing the obtained z statistic of -1.99 with the critical values, we can make the following decision:

Since -1.99 falls outside the range of -1.96 to +1.96, we reject the null hypothesis.

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The equation is, y = x-2

The table showing the values of x and y is:

x    1    2    3    4

y    -1   0    1     2

From the question, we have

y increases by 1 unit with 1 unit increase in x.

The equation is, y = x-2

Subtraction:

Subtraction serves as a representation for the act of removing items from a collection. The negative symbol stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above illustration) are then transported to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, which equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.

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