When surveyed 5 out of 32 students said they ride their bikes to school. Predict how many students in a school of 800 ride their bikes to school.

And please show your work!

The rejection region is not given in the question, so we cannot determine the type of error that can occur when the true survival rate is 50%.

However, we can calculate the probability of making a Type I error (rejecting the null hypothesis when it is actually true) and a Type II error (failing to reject the null hypothesis when it is actually false) for a given rejection region.

Assuming a significance level of 0.05, the rejection region for a one-tailed test of whether the true survival rate is greater than 40% is  with 19 degrees of freedom.

If the true survival rate is actually 50%, the probability of making a Type I error (rejecting the null hypothesis that the true survival rate is 40%) is 0.05, which is the significance level.

The probability of making a Type II error (failing to reject the null hypothesis that the true survival rate is 40% when it is actually 50%) depends on the true survival rate and the sample size. A larger sample size would decrease the probability of making a Type II error.

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A dot plot is a simple graphical representation of data where each data point is represented by a dot on a number line or a coordinate axis. To interpret a dot plot, consider the following steps:

1. Identify the data points: Look at the dots and their positions on the number line or axis to determine the individual data points.
2. Determine the range: Find the minimum and maximum values represented in the plot to establish the range of the data.
3. Assess the distribution: Analyze the concentration of the dots to determine if the data is evenly distributed, skewed, or has clusters.

If you provide the specific dot plot, I'd be happy to help you interpret the data represented by it.

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Answer:

h=9cm

P=(x+5)cm

b=(x-3)cm

by the Pythagoras theorem,

h^2=p^2+b^2

9^2=(x+5)^2+(x-3)^2

81=x^2+10x+25+x^2-6x+9

81=2x^2+4x+34

To calculate the Frobenius inner product (A,B) and the corresponding induced norms ||A||, ||B||, we will follow these steps:


Step 1: Calculate the Frobenius inner product (A,B)

The Frobenius inner product is defined as the sum of the products of the corresponding entries of two matrices. In this case, we have:

(A,B) = (-2*1) + (3*2) + (3*-1) + (-3*2) = -2 + 6 - 3 - 6 = -5

Step 2: Calculate the induced norms ||A|| and ||B||

The induced norm is the square root of the sum of the squares of the elements in the matrix. For matrix A:

||A|| = sqrt((-2)^2 + (3)^2 + (3)^2 + (-3)^2) = sqrt(4 + 9 + 9 + 9) = sqrt(31)

For matrix B:

||B|| = sqrt((1)^2 + (2)^2 + (-1)^2 + (2)^2) = sqrt(1 + 4 + 1 + 4) = sqrt(10)

Now we have all the values:

(A,B) = -5
||A|| = sqrt(31)
||B|| = sqrt(10)

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The number of ways can the selection be made is 84.

Given:

an executive hires 3 office workers from 8 applicants.

a ) .

Number of ways = C ( 8 , 3 )

C ( n , r ) = n! / ( n - r ) ! r!

C ( 8 , 3 ) = 8! / ( 8 - 3 ) ! 3!

= 8! / 5! * 3 !

= 8 * 7 * 6 * 5! / 5! * 3!

= 56 * 6 / 3!

= 56 * 6 / 3 * 2 * 1

= 56 * 3 / 2 * 1

= 28 * 3 / 1

= 28 * 3

= 84 ways

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Answer:

=-1.66

Step-by-step explanation:

Use the distance formula:

Distance = sqrt((x2-x1)^2 + (y2-y1)^2)

Distance = sqrt((6-3)^2 + (13-9)^2)

Distance = sqrt(3^2 + 4^2)

Distance = sqrt(9 + 16)

Distance = sqrt(25)

Distance = 5

The problem says every unit = 1 mile so 5 units = 5 miles.

Answer = 5 miles

Answer:

462 pounds

Step-by-step explanation:

weighs 42 pounds

    and the water 11 times more

 so, 42*11 = 462 pounds

Answer:

1 17/22

Step-by-step explanation:

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

2.77 yd² Will the square mat fit in the kennel.

What in math is a square?

A square is a closed, two-dimensional shape that has four equal sides and four vertices. It has parallel sides on either side. A rectangle with equal length and width can also be used to conceptualize a square.

                      A square is a four-sided polygon with angles measuring 90 degrees and all of its sides being the same length. The square's shape ensures that both parts are symmetrical if it is divided down the middle by a plane.

a square mat = (5/3) (5/3)

                     = 25/9

                     = 2.77 yd²

so, yes because this area is less than area of kennel .

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For the answer of factors of expression (12 + 54), in the form of a(b + c), where a is the GCF of 12 and 54 is equals to 6( 2 + 9).

In math, to factor a number means to express it as a product of (other) whole numbers, called its factors. For example, if 7x5 = 35, 7 and 5 are both factors. The divisors that give the remainder to be 0 are the factors of the number. We have an expression of numbers, 12 + 54. We have to write this expression in form of a( b + c), where a is GCF of 12 and 54. Now, we can write the factors of 12 and 54 are 12 = 2×2×3

54 = 2×3 ×3×3

The greatest common factor, GCF of 12 and 54 is 2×3 = 6. So, 12 + 54 = 6× 2 + 6×9

Taking out the common factor 6 from above expression, 6( 2 + 9) which is required form a( b + c). Hence, required expression is 6( 2 + 9).

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Answer:

141.6 cm cubed

Step-by-step explanation:

The value of x is 5. The value of y is 8.66.

The image attached is that of a right triangle. In order to determine the value of x and y, SOHCAHTOA would be used.  x is he opposite side and y in the adjacent side to the angle 30 degrees.

Sin 30 = opposite / hypotenuse

0.5 = x / 10

x = 5

Cos 30  = adjacent / hypotenuse

0.8660 = y / 10

y = 8.66

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The regression equation is: ŷ= 29.1270 + 0.5906x1 + 0.4980x2. The coefficient of determination (R²) is 0.921. The following is the solution to the problem mentioned: As we know that, SST=SSR+SSE. To compute SSE, we require to calculate Sb (standard error of the estimate). Sb = √SSE/ n - k - 1  Where, n=10.

k=2Sb

= √0.0511/7

= 0.1206

Substitute the given values of SST, SSR, Sb to obtain SSE.

SST = 6,836.875, SSR = 6,303.750, Sb=0.1206SS,

E = SST – SSR

= 6,836.875 – 6,303.750

= 533.125

Now, to get the coefficient of determination (R²), let’s use the following formula: R² = SSR/SSTR²

= 6303.750/6836.875

= 0.92083

≈ 0.921.

To obtain the coefficients b₁ and b₂ for the regression equation, use the following formula: b = r (Sb / Sx) Where,

Sx = √ (Σ(xi – x)²) / (n-1) xi

= Value of the independent variable

= 0.0708/0.5906

= 0.1200 (approx)

Substitute the value of Sx, x₁, and Sb to obtain b₁.

b₁ = r₁ (Sb₁ / Sx₁)

= 0.5906 (0.1206 / 0.1200)

= 0.5906

Let’s compute b₂ in the same way.

b₂ = r₂ (Sb₂ / Sx₂)

= 0.4980 (0.1206 / 0.1200)

= 0.4980

Hence, the regression equation is: ŷ= 29.1270 + 0.5906x₁ + 0.4980x₂. The coefficient of determination (R²) is 0.921.

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Yes, m∠ABC and m∠XYZ are congruent

No, lines FG and DE are not congruent

Yes, OR and OS are congruent

Yes, 2∠ and ∠4 are congruent.

Congruent angles are angles that have the same measure, in degrees and are often represented by the symbol "≅". While congruent line segments are two or more line segments that have the same length.

m∠XYZ = 180° - 140° {supplementary angles}

m∠XYZ = 40°

so;

m∠ABC and m∠XYZ are congruent

line FG = and line DE =

so;

FG and DE are not congruent

OR = 2in and OS = 2in

so;

OR and OS are congruent

∠2 and ∠4 are vertical angles and are equal so;

2∠ and ∠4 are congruent

Therefore, (m∠ABC and m∠XYZ), (2∠ and ∠4), and (OR and OS), are two pairs of angles and line segments respectively which are congruent, while the lines segments FG and DE are not congruent.

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The outcome does the spinner landing on 1 is 1/3.

What is the probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: when flipping a fair coin and spinning a fair three-sided spinner.

We have to find the outcomes does the spinner land on 1.

Total outcomes = 6

Spinner land on 1 = 2

Spinner land on 2 = 2

Spinner land on 3 = 2

The outcome of spinner land on 1 = Spinner land on 1 / total outcome

= 2/6 = 1/3

Hence, the outcome does the spinner landing on 1 is 1/3.

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Answer:

64/27

Step-by-step explanation:

Answer: C: y=1.15x + 10.95

Step-by-step explanation:

look it up

The rationalization of all denominators is 5.74165.

A fraction is represented inside the form of 'x/y', wherein 'x' is the numerator and 'y' is the denominator. The numerator represents the entire variety of parts taken into consideration. whereas, the denominator represents the full quantity of equal components in a fraction. The pinnacle quantity in a fragment is usually taken into consideration as a numerator.

Another phrase for a denominator is the divisor. both of those words check with the range beneath the road in a not unusual fraction. similarly, while you're speakme approximately statistical values, a denominator refers back to the whole number or population from which samples are taken.

In a fallacious fraction, the numerator is extra than or the same as the denominator and the denominator must not be the same as zero. In an incorrect fraction, the numerator is less than the denominator and the numerator is extra than 0. In an unsuitable fraction, the numerator is constantly more than the denominator.

\(5\sqrt{2} /\sqrt{7}- \sqrt{2}\)

\(\frac{5\sqrt{2} }{\sqrt{7}-\sqrt{2} }\)

Multiply by the conjugate

\(\frac{5(\sqrt{7}+\sqrt{2})\sqrt{2} }{(\sqrt{7} -\sqrt{2} )(\sqrt{7} +\sqrt{2} }\)

Expand \((\sqrt{7} -\sqrt{2} )(\sqrt{7} +\sqrt{2} ): 5\)

Factor out the common term 5

\(\frac{(5\sqrt{7}+5 \sqrt{2})\sqrt{2} }{5}\)

Cancel the common factor: 5

\((\sqrt{7} +\sqrt{2}) \sqrt{2}\)

\(= \sqrt{14} +2\)

= Decimal:5.74165

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The series converges for all values of x such that |x| < 1, or in other words, the interval of convergence is (-1, 1).

To find the radius of convergence of the series:

Σ n!xⁿ(7 · 15 · 23 · · (8n − 1))

n=1

we can use the ratio test:

lim |a_{n+1}| / |a_n| = lim [(n+1)!|x|^(n+1) (7·15·23···(8(n+1)-1))] / (n!|x|^n(7·15·23···(8n-1)))

n→∞

Simplifying the expression, we get:

lim (n+1) |x| (8n + 7)(8n + 15) ... (8n + 15 + 2(n+1)) / (8n + 1)(8n + 9) ... (8n + 15 + 2n)

As n goes to infinity, we can see that the ratio test simplifies to:

lim |x|(8n+8)(8n+16) / (8n)(8n+8) = lim |x|(64n² + 128n + 64) / (64n²) = |x|

Since the limit equals |x|, the series converges if |x| < 1, and diverges if |x| > 1. Therefore, the radius of convergence is:

r = 1

So the series converges for all values of x such that |x| < 1, or in other words, the interval of convergence is (-1, 1).

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Answer:

2

Step-by-step explanation:

Answer:

y = 4 - x / 2

Step-by-step explanation:

y = 2x - 4

x = 2y - 4

y = 4 - x

----------

2

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer:

Step-by-step explanation:

The angles remain right angles if you are reflecting over the x axis.

Answer:

my quess is 3 rd one

Step-by-step explanation:

there is a 65% that you fet it right

The value of the double integral is:

∫∫R (4x^2)/(1+x^4) dA = (2/5)(2)^(-1/5) - (2/5)

To evaluate the double integral ∫∫R 4x^2/(1+x^4) da, we need to set up the limits of integration for x and y.

Since the region R is bounded by y = 0, y = x, and x = 1, we can set up the limits of integration as follows:

0 ≤ y ≤ x
0 ≤ x ≤ 1

Now we can set up the double integral as:

∫∫R 4x^2/(1+x^4) da = ∫0^1 ∫0^x 4x^2/(1+x^4) dy dx

Integrating with respect to y first, we get:

∫0^1 ∫0^x 4x^2/(1+x^4) dy dx = ∫0^1 [(4x^2/4) ln|1+x^4|]0^x dx

Simplifying, we get:

∫0^1 [(x^2/1+x^4) ln|1+x^4|] dx

This integral is not easy to evaluate directly, so we can use substitution. Let u = 1+x^4, du/dx = 4x^3. Then the integral becomes:

∫1^2 [(1/u) ln u] du/4

Integrating by parts, we get:

∫1^2 [(1/u) ln u] du/4 = [-ln u/u]1^2/4 - ∫1^2 (-1/u^2)(-ln u) du/4

= [-ln(1+x^4)/(1+x^4)]0^1 - (1/4) ∫1^2 (ln u)/u^2 du

= (-ln2/2) - (1/4) [(-1/u^2) ln u - ∫(-1/u^2) du]1^2

= (-ln2/2) + (1/4) [(1/2) ln2 + (1/2) ln17]

= (-ln2/2) + (1/8) ln(34/17)

Therefore, the value of the double integral is approximately -0.077.

The region R is bounded by y=0, y=x, and x=1. We want to evaluate the double integral of the function 4x^2/(1+x^4) over this region.

First, we set up the integral:

∫∫R (4x^2)/(1+x^4) dA

Since the region R is bounded by y=0 and y=x, we can set the limits for y from 0 to x. Similarly, as the region is also bounded by x=1, we can set the limits for x from 0 to 1:

∫(from 0 to 1) ∫(from 0 to x) (4x^2)/(1+x^4) dy dx

Now we integrate with respect to y:

∫(from 0 to 1) [(4x^2)/(1+x^4)]y |_0^x dx

Which simplifies to:

∫(from 0 to 1) (4x^3)/(1+x^4) dx

Now, we integrate with respect to x:

(2/5)(x^5 + 1)^(-1/5)|_0^1

Evaluating the integral at the limits gives us:

(2/5)(1^5 + 1)^(-1/5) - (2/5)(0^5 + 1)^(-1/5) = (2/5)(2)^(-1/5) - (2/5)

And thus, the value of the double integral is:

∫∫R (4x^2)/(1+x^4) dA = (2/5)(2)^(-1/5) - (2/5)

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Answer:

#1 is 1/4 #2 is 2/5

Step-by-step explanation:

they were able to be divided by a certain number that they were all equal to

Answer:

12/48=1/4 and 6/15=2/5

The formula for the area of this type of quadrilateral is 0.5 multiplied by the sum of the product of the lengths of the diagonals and their respective sides.

To develop a formula for the area of this type of quadrilateral, we can use the fact that a quadrilateral can be divided into two triangles.

Let's label the vertices of the quadrilateral as follows: W, X, Y, and Z. Since WY is one of the diagonals, it divides the quadrilateral into two triangles. Let's call the length of WY as d₁. Similarly, let's call the length of XZ as d₂.

The formula for the area of a triangle is given by the formula: Area = 0.5 * base * height. In this case, both WY and XZ serve as the base for their respective triangles.

So, the formula for the area of the quadrilateral can be derived by finding the sum of the areas of the two triangles formed by the diagonals:

Area of Quadrilateral = Area of Triangle WYZ + Area of Triangle XYZ = (0.5 * WY * d₁) + (0.5 * XZ * d₂)

Simplifying further, we have:

Area of Quadrilateral = 0.5 * (WY * d₁ + XZ * d₂)

In conclusion, the formula for the area of this type of quadrilateral is 0.5 multiplied by the sum of the product of the lengths of the diagonals and their respective sides.

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The formula for the area of this type of quadrilateral is 0.5 multiplied by the sum of the product of the lengths of the diagonals and their respective sides.

To develop a formula for the area of this type of quadrilateral, we can use the fact that a quadrilateral can be divided into two triangles.

Let's label the vertices of the quadrilateral as follows: W, X, Y, and Z. Since WY is one of the diagonals, it divides the quadrilateral into two triangles. Let's call the length of WY as d₁. Similarly, let's call the length of XZ as d₂.

The formula for the area of a triangle is given by the formula: Area = 0.5 * base * height. In this case, both WY and XZ serve as the base for their respective triangles.

So, the formula for the area of the quadrilateral can be derived by finding the sum of the areas of the two triangles formed by the diagonals:

Area of Quadrilateral = Area of Triangle WYZ + Area of Triangle XYZ = (0.5 * WY * d₁) + (0.5 * XZ * d₂)

Simplifying further, we have:

Area of Quadrilateral = 0.5 * (WY * d₁ + XZ * d₂)

In conclusion, the formula for the area of this type of quadrilateral is 0.5 multiplied by the sum of the product of the lengths of the diagonals and their respective sides.

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