of the 1248 students enrolled 24% did not like the new mascot design. what is the mean of this binomial distribution
A. 299.5
B. 948.5
C. 17.3
D. 300.3

Answer:

Perimeter of the picture and frame = 38.4inches

Area of the picture and frame = 92.16inches²

Step-by-step explanation:

A square frame is made up of 4 different pieces. The shape of each piece = Rectangle

The perimeter of the rectangle = 24

Perimeter of the rectangle = 24 inches

The perimeter of a rectangle = 2L + 2W

The Width of a Rectangle is always on her than the length hence.

24 = 2L + 2W

24 = 2( L + W)

24/2 = L + W

12 = L + W

Because the width is always longer than the length

W > L

Width of wooden frame = 4 × Length

Therefore;

4 × L = W

Which gives

L + W = 12 inches

4 × L + L = 12 inches

L×(4 + 1)

= 5L = 12 inches

L = 12/5 = 2.4 inches

W = 4 × L = 4 × 12/5

W = 48/5 = 9.6 inches

Side length of wooden frame, L =9.6

The perimeter of the picture frame = 4 × L= 4 × 9.6= 38.4 inches

The area of the picture frame = L²

= L × L

= 9.6 × 9.6 = 92.16inches².

Answer:

3 pairs

Step-by-step explanation:

Top and Bottom

Front and Back

Side and Side.

Cereal Boxes have 6 sides

Answer:

Point of faulty equipment car = 0.2614 (Approx)

Step-by-step explanation:

Given:

Total number of car = 700

Faulty equipment car = 183

Find:

Point of faulty equipment car

Computation:

Point of faulty equipment car = Faulty equipment car / Total number of car

Point of faulty equipment car = 183 / 700

Point of faulty equipment car = 0.261428571

Point of faulty equipment car = 0.2614 (Approx)

Answer:

0

Step-by-step explanation:

Hope this helps

Answer:

Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].

Step-by-step explanation:

The general equation in rectangular form for a 3-dimension plane is represented by:

[tex]a\cdot x + b\cdot y + c\cdot z = d[/tex]

Where:

[tex]x[/tex], [tex]y[/tex], [tex]z[/tex] - Orthogonal inputs.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex], [tex]d[/tex] - Plane constants.

The plane presented in the figure contains the following three points: (2, 0, 0),  (0, 2, 0), (0, 0, 3)

For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:

xy-plane (2, 0, 0) and (0, 2, 0)

[tex]y = m\cdot x + b[/tex]

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - x-Intercept, dimensionless.

If [tex]x_{1} = 2[/tex], [tex]y_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]y_{2} = 2[/tex], then:

Slope

[tex]m = \frac{2-0}{0-2}[/tex]

[tex]m = -1[/tex]

x-Intercept

[tex]b = y_{1} - m\cdot x_{1}[/tex]

[tex]b = 0 -(-1)\cdot (2)[/tex]

[tex]b = 2[/tex]

The equation of the line in the xy-plane is [tex]y = -x+2[/tex] or [tex]x + y = 2[/tex], which is equivalent to [tex]3\cdot x + 3\cdot y = 6[/tex].

yz-plane (0, 2, 0) and (0, 0, 3)

[tex]z = m\cdot y + b[/tex]

[tex]m = \frac{z_{2}-z_{1}}{y_{2}-y_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - y-Intercept, dimensionless.

If [tex]y_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]y_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:

Slope

[tex]m = \frac{3-0}{0-2}[/tex]

[tex]m = -\frac{3}{2}[/tex]

y-Intercept

[tex]b = z_{1} - m\cdot y_{1}[/tex]

[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]

[tex]b = 3[/tex]

The equation of the line in the yz-plane is [tex]z = -\frac{3}{2}\cdot y+3[/tex] or [tex]3\cdot y + 2\cdot z = 6[/tex].

xz-plane (2, 0, 0) and (0, 0, 3)

[tex]z = m\cdot x + b[/tex]

[tex]m = \frac{z_{2}-z_{1}}{x_{2}-x_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - z-Intercept, dimensionless.

If [tex]x_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:

Slope

[tex]m = \frac{3-0}{0-2}[/tex]

[tex]m = -\frac{3}{2}[/tex]

x-Intercept

[tex]b = z_{1} - m\cdot x_{1}[/tex]

[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]

[tex]b = 3[/tex]

The equation of the line in the xz-plane is [tex]z = -\frac{3}{2}\cdot x+3[/tex] or [tex]3\cdot x + 2\cdot z = 6[/tex]

After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:

[tex]a = 3[/tex], [tex]b = 3[/tex], [tex]c = 2[/tex], [tex]d = 6[/tex]

Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].

Answer:

It is A    3x+3y+2z=6

Step-by-step explanation:

Answer:

59 accidents were investigated.

Step-by-step explanation:

The question above is a probability question that involves 2 elements: causes of accidents.

Let

A = Alcohol

E = Excessive speed

In the question, we are given the following information:

18 accidents involved Alcohol and Excessive speed =P(A ∩ E)

26 involved Alcohol = P(A)

12 accidents involved excessive speed but not alcohol = P( E ) Only

21 accidents involved neither alcohol nor excessive speed = neither A U B

We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)

P(A Only) = 26 - 18

= 8

So, only 8 accident involved Alcohol but not excessive speed.

The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)

= 8 + 12 + 18 + 21

= 59

Therefore, 59 accidents were investigated.

Answer:

C. x = 2

Step-by-step explanation:

[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]

Since you have square roots, you need to separate the square roots and square both sides.

[tex] \sqrt{9x + 7} = 7 - \sqrt{2x} [/tex]

Now that one square root is on each side of the equal sign, we square both sides.

[tex] (\sqrt{9x + 7})^2 = (7 - \sqrt{2x})^2 [/tex]

[tex] 9x + 7 = 49 - 14\sqrt{2x} + 2x [/tex]

Now we isolate the square root and square both sides again.

[tex] 7x - 42 = -14\sqrt{2x} [/tex]

Every coefficient is a multiple of 7, so to work with smaller numbers, we divide both sides by 7.

[tex] x - 6 = -2\sqrt{2x} [/tex]

Square both sides.

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

[tex] x^2 - 12x + 36 = 4(2x) [/tex]

[tex] x^2 - 20x + 36 = 0 [/tex]

We need to try to factor the left side.

-2 * (-18) = 36 & -2 + (-18) = -20, so we use -2 and -18.

[tex] (x - 2)(x - 18) = 0 [/tex]

[tex] x = 2 [/tex]   or   [tex] x = 18 [/tex]

Since solving this equation involved the method of squaring both sides, we much check for extraneous solutions by testing our two solutions in the original equation.

Test x = 2:

[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]

[tex] \sqrt{9(2) + 7} + \sqrt{2(2)} = 7 [/tex]

[tex] \sqrt{25} + \sqrt{4} = 7 [/tex]

[tex] 5 + 2 = 7 [/tex]

[tex] 5 = 5 [/tex]

We have a true equation, so x = 2 is a true solution of the original equation.

Now we test x = 18.

[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]

[tex] \sqrt{9(18) + 7} + \sqrt{2(18)} = 7 [/tex]

[tex] \sqrt{162 + 7} + \sqrt{36} = 7 [/tex]

[tex] \sqrt{169} + 6 = 7 [/tex]

[tex] 13 + 6 = 7 [/tex]

[tex] 19 = 7 [/tex]

Since 19 = 7 is a false equation, x = 18 is not a true solution of the original equation and is discarded as an extraneous solution.

Answer: C. x = 2

Answer:

A. a straight line passing

Step-by-step explanation:

Answer:

a straight line passing

Step-by-step explanation:

Looks like the given function is

[tex]f(x)=\dfrac1{9-x}[/tex]

Recall that for |x| < 1, we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

We want the series to be centered around [tex]x=4[/tex], so first we rearrange f(x) :

[tex]\dfrac1{9-x}=\dfrac1{5-(x-4)}=\dfrac15\dfrac1{1-\frac{x-4}5}[/tex]

Then

[tex]\dfrac1{9-x}=\displaystyle\frac15\sum_{n=0}^\infty\left(\frac{x-4}5\right)^n[/tex]

which converges for |(x - 4)/5| < 1, or -1 < x < 9.

Answer:

A sample size of 2080 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

Based on previous evidence, you believe the population proportion is approximately 60%.

This means that [tex]\pi = 0.6[/tex]

How large of a sample size is required?

We need a sample of n.

n is found when [tex]M = 0.025[/tex]. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.025 = 2.327\sqrt{\frac{0.6*0.4}{n}}[/tex]

[tex]0.025\sqrt{n} = 2.327\sqrt{0.6*0.4}[/tex]

[tex]\sqrt{n} = \frac{2.327\sqrt{0.6*0.4}}{0.025}[/tex]

[tex](\sqrt{n})^{2} = (\frac{2.327\sqrt{0.6*0.4}}{0.025})^{2}[/tex]

[tex]n = 2079.3[/tex]

Rounding up

A sample size of 2080 is needed.

Answer:

32.5%

Step-by-step explanation:

0.325 x 100%=32.5%

Answer:

interior angle (2)= 70

interior angle (3)= 60

Step-by-step explanation:

Given:

exterior angle=120°

interior angle (1)=50°

Required:

interior angle (2)=?

interior angle (3)=?

Formula:

exterior angle=interior angle (1) + interior angle (2)

Solution:

exterior angle=interior angle (1)+ interior angle (2)

120°=50°+interior angle (2)

120°+50°=interior angle (2)

70°=interior angle (2)

interior angle (3)= 180°-interior angle (1)- interior angle (2)

interior angle (3)=180°-50°+70°

interior angle (3)=180°-120°

interior angle (3)= 60°

Theorem:

Theorem 1.16

The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

Hope this helps ;) ❤❤❤

Answer:

x≤9  

Step-by-step explanation:

x−15≤−6

Add 15 to each side

x−15+15≤−6+15

x≤9  

Answer:

[tex]\boxed{x\leq 9}[/tex]

Step-by-step explanation:

[tex]x-15 \leq -6[/tex]

[tex]\sf Add \ 15 \ to \ both \ parts.[/tex]

[tex]x-15 +15 \leq -6+15[/tex]

[tex]x\leq 9[/tex]

Answer:

decreases.

Step-by-step explanation:

Type II error is one in which we fail to reject the null hypothesis that is actually false. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The power of Type II error is 1 - [tex]\beta[/tex]. As the power increases the probability of Type II error decreases.

Answer:

  0.0228

Step-by-step explanation:

A suitable probability calculator (or spreadsheet) can tell you this.

It is about 0.0228.

Answer:

x= 45

Step-by-step explanation:

In this diagram, there is an angle that is split into 2 angles.

The angle is a 90 degree angle. We know this because of the little square in the corner that denotes a right angle.

Therefore, the 2 angles inside of the right angle must add to 90 degrees. The 2 angles that make up the right angle are x and 45.

x+45=90

We want to find x. We need to get x by itself. 45 is being added on to x. The inverse of addition is subtraction. Subtract 45 from both sides.

x+45-45=90-45

x= 90-45

x=45

The measure of angle x is 45 degrees.

Answer:

Step-by-step explanation:

Hello!

You have to estimate the mean length of 4000 b.c. human skulls trough a 95% confidence interval.

You know that

n= 6 human skulls

[tex]\frac{}{X}[/tex]= 94.2mm

S= 4.9

Assuming that the variable X: length of a 4000b.c. human skull (mm) has a normal distribution, to construct the interval you have to use the t statistic:

[[tex]\frac{}{X}[/tex] ± [tex]t_{n_1;1-\alpha /2} * \frac{S}{\sqrt{n} }[/tex]]

[tex]t_{n-1;1-\alpha /2}= t_{5; 0.975}= 2.571[/tex]

[94.2 ± 2.571 * [tex]\frac{4.9}{\sqrt{6} }[/tex]]

[89.06; 99.34]mm

With a 95% confidence level you'd expect the interval [89.06; 99.34]mm to contain the value for the average skull length for humans 4000 b.c.

I hope this helps!

Answer:

AB = 20 tan55°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{20}[/tex] ( multiply both sides by 20 )

20 tan55° = AB

Answer:

Answer D

Step-by-step explanation:

The formula is [tex]A = pi r(r+\sqrt{h^2+r^2})[/tex]. We have our r (radius) and h (height), so plugging it all in would give us A = (3.14)(5 + sqrt(12^2)+(5^2). After computing this, you would get answer D, 282.6.

Answer:

Option C.

Step-by-step explanation:

In the given figure we have two parallel lines AB and CD.

A transversal line FB intersect the parallel lines at point B and C.

We know that the if a transversal line intersect two parallel lines, then corresponding angles are congruent.

[tex]\angle ABC=\anle ECF[/tex]

[tex]x=y[/tex]

To prove this by translation, we need a translation along the directed line segment CB maps ine CD onto line AB and angle y onto angle x.

Therefore, the correct option is C.

Answer:

Step-by-step explanation:

The statement

The value of y varies inversely as the square of x is written as

[tex]y = \frac{k}{ {x}^{2} } [/tex]

where k is the constant of proportionality

To find the value of x when y = 1 first find the formula for the variation

y = 16 x = 3

k = yx²

k = 16(3)²

k = 16 × 9

k = 144

The formula for the variation is

[tex]y = \frac{144}{ {x}^{2} } [/tex]

when y = 1

We have

[tex]1 = \frac{144}{ {x}^{2} } [/tex]

Cross multiply

x² = 144

Find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

The beryllium atom; 1.99 times larger.

Step-by-step explanation:

The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.

(1.12 * 10^-10) / (5.6 * 10^-11)

= (1.112 / 5.6) * (10^-10 + 11)

= 0.1985714286 * 10

= 1.985714286 * 10^0

So, the beryllium atom is about 1.99 times larger than the other.

Hope this helps!

Answer:

Step-by-step explanation:

1. Preferred Share dividends.

There are 300,000 preference shares and each of them got $2.85. Total dividends are;

= 300,000 * 2.85

= $855,000‬

2. Total dividends = $3,500,000

Dividends left for Common Shareholders (preference gets paid first)

= 3,500,000 - 855,000

= $2,645,000

Common shares number 2,500,000

Dividend per share of common stock = [tex]\frac{2,645,000}{2,500,000}[/tex]

= $1.06

Answer:

41.1 miles

Step-by-step explanation:

84 - 42.9 = 41.1

Answer:

x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.

Step-by-step explanation:

Step 1: Distribute x

x² + x = 72

Step 2: Move 72 over

x² + x - 72 = 0

Step 3: Factor

(x - 8)(x + 9) = 0

Step 4: Find roots

x - 8 = 0

x = 8

x + 9 = 0

x = -9

Answer:

x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0

Step-by-step explanation:

Let the first consecutive integer be x.

Let the second consecutive integer be x+1.

The product of the two consecutive integers is 72.

x(x + 1) = 72

x² + x = 72

Subtracting 72 from both sides.

x² + x - 72 = 0

Factor left side of the equation.

(x - 8)(x + 9) = 0

Set factors equal to 0.

x - 8 = 0

x = 8

x + 9 = 0

x = -9

8 and -9 are not consecutive integers.

Try 8 and 9 to check.

x = 8

x + 1 = 9

x(x+1) = 72

8(9) = 72

72 = 72

True!

The two consecutive integers are 8 and 9.

Answer:

Step-by-step explanation:

cos^-1(6/13)=62.5136°

sin(2*62.5136°)=0.8189

cos(2*62.5136°)=-0.5740

Answer:

x=8/3 OR 2.7

Step-by-step explanation:

-1.3+4.6x=0.3+4x

4.6x-4x=0.3+1.3

0.6x=1.6

x=1.6/0.6=8/3

x=8/3 OR 2.7

Hope this helps!

Answer:

[tex]\boxed{x = 2\frac{2}{3} }[/tex]

Step-by-step explanation:

[tex]-1.3+4.6x = 0.3 +4x[/tex]

Collecting like terms

[tex]4.6 x -4x = 0.3+1.3[/tex]

[tex]0.6x = 1.6[/tex]

Dividing both sides by 0.6

x = 1.6 / 0.6

x = 2 2/3

Answer:

a = 16

b = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Length of the design 16 inches is represented by the point (0, 16) and length of 12 inches by (1, 12).

That means these points lie on the graph of the function 'f' represented by,

f(x) = a(b)ˣ

For the point (0, 16),

f(0) = a(b)⁰

16 = a(1)

a = 16

For another point (1, 12),

f(1) = a(b)¹

12 = ab

12 = 16(b) [Since a = 16]

b = [tex]\frac{12}{16}[/tex]

b = [tex]\frac{3}{4}[/tex]

Therefore, values of a and b are 16 and [tex]\frac{3}{4}[/tex] respectively.

In general, if we have [tex]x^a=x^b,[/tex] then [tex]a=b.[/tex] Thus, the first answer choice is correct.

Answer:

[tex]\boxed{\red{2x - 1 = 5x - 14}}[/tex]

First answer is correct.

Step-by-step explanation:

we know that,

[tex] {x}^{a} = {x}^{b} [/tex]

[tex]a = b[/tex]

So, according to that,

[tex] {5}^{(2x - 1)} = {5}^{(5x - 14)} [/tex]

Therefore,

[tex]2x - 1 = 5x - 14[/tex]

Answer:

100yd²

Step-by-step explanation:

length=4x

width=x

perimeter=2(l+w)

50=2(4x+x)

50=2(5x)=10x

50=10x

x=5yd

width=5yd

length=20yd

area=length×width

=20×5

=100yd²

Answer:

[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]

Step-by-step explanation:

width = x

length = 4x

so,

perimeter of a rectangle

[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]

So, in this rectangle,

width = 5 yd

length = 4x

= 4*5

= 20yd

Now, let's find the area of this rectangle

[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]