Find the surface area of the solid given the net.

Answer:

(a) 36.36%

(b) 0.36%

(c) 0.06%

Step-by-step explanation:

Given that the time intervals measured with a stopwatch have an uncertainty of about 0.2 s.

We want to know what is the percent uncertainty of a hand-timed measurement of:

(a) 5.5 s

Percentage = (0.2/5.5) × 100

≈ 36.36%

(b) 55 s

Percentage = (0.2/55)×100

≈ 0.36%

(c) 5.5 min

5.5 min = 5.5 × 60 s

= 330 s

Percentage = (0.2/330)×100

≈ 0.06%

Answer:

Multiply/divide both sides by the same non-zero constant

Step-by-step explanation:

5x = 20

Divide each side by 5

5x/5 = 20/5

x = 4

To obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"

Given the equations :

To obtain the value ; x = 4 from A

Here, the constant value which can be used is 5 in other to isolate 'x'

5x/5 = 20/5

x = 4

Therefore, to obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"

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Answer:

If the perimeter of the rectangle is 30cm , find its area. W=5 FOR THE WIDTH. 5*10=50 FOR THE AREA.

Step-by-step explanation:

The area of the Rectangle is 50 sq.m

The area of rectangle for a rectangle of length L and width W is given by

                                              A =  L* W

It is measured in square units.

Let the length of the rectangle be L

The width of the rectangle is W

The length of a rectangle is twice its width

L = 2W

Perimeter of the Rectangle is 2( Length + Width)

30 = 2 (L +W)

15 = L + W

15 = 2W +W

15 = 3W

W = 5m

L = 10m

The area of the rectangle is Length * Width

Area = 10 *5

Area = 50 sq.m

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Answer: $12 less.

Step-by-step explanation:

Given: Ms. Cole pays $2 a month  for online banking at her credit union.

In 6 months she will pay = 6 x ($2)

= $12

It means that he balance will be decreased by $12 [as the amount was debited from the balance].

So, the change in the balance of her account if she pays this fee for 6 months = $12 less.

Answer:

32.8 miles

Step-by-step explanation:

Amy is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.95. See the figure below. Amy has 48 miles remaining after 31 minutes of driving. How many miles will be remaining after 47 minutes of driving?

Answer: The general equation of a line is given as y = mx + c, where m is the slope of the line and c is the intercept on the y axis. Given that the slope is -0.95, substituting in the general equation :

y = -0.95x + c

Amy has 48 miles remaining after 31 minutes of driving, to find c, we substitute y = 48 and x = 31. Therefore:

48 = -0.95(31) + c

c = 48 + 0.95(31)

c = 48 + 29.45

c = 77.45

The equation of the line is

y = -0.95x + 77.45

After 47 minutes of driving, the miles remaining can be gotten by substituting x = 47 and finding y.

y = -0.95(47) + 77.45

y = -44.65 + 77.45

y = 32.8 miles

Answer:

Hey there!

Tangent 70=12/y

Tangent 70y=12

y=12/Tangent 70

y=4.37 cm

Let me know if this helps :)

Answer:

  36

Step-by-step explanation:

Each cut creates a triangular face where the corner used to be. That face adds three edges to the figure. The 8 cuts add a total of 8×3 = 24 edges to the 12 edges the prism already had.

The new figure has 12+24 = 36 edges.

Answer:

[tex] d = 7 + 3\sqrt{3} [/tex] and

[tex] d = 7 - 3\sqrt{3} [/tex]

Step-by-step explanation:

To solve the equation, [tex] d^2 - 14d - 22 = 0 [/tex], using the quadratic formula,

Recall: quadratic formula = [tex] \frac{-b ± \sqrt{b^2 - 4ac}}{2a} [/tex]

Where,

a = 1

b = -14

c = 22

Plug in your values into the formula and solve:

[tex] \frac{-(-14) ± \sqrt{(-14)^2 - 4(1)(22)}}{2(1)} [/tex]

[tex] \frac{14 ± \sqrt{196 - 88}}{2} [/tex]

[tex] \frac{14 ± \sqrt{108}}{2} [/tex]

[tex] d = \frac{14 + \sqrt{108}}{2} [/tex]

[tex] d = \frac{14 + 6\sqrt{3}}{2} [/tex]

[tex] d = (\frac{2(7 + 3\sqrt{3})}{2} [/tex]

[tex] d = 7 + 3\sqrt{3} [/tex]

And

[tex] d = \frac{14 - \sqrt{108}}{2} [/tex]

[tex] d = \frac{14 - 6\sqrt{3}}{2} [/tex]

[tex] d = (\frac{2(7 - 3\sqrt{3})}{2} [/tex]

[tex] d = 7 - 3\sqrt{3} [/tex]

Answer:

Rewrite  

( 4 − 3 i ) 2  as  ( 4 − 3 i )( 4 − 3 i ) . ( 4 − 3 i) ( 4 − 3 i ) Expand  ( 4 − 3 i ) ( 4 − 3 i )

using the FOIL Method.

4 ⋅ 4 + 4 ( -3 i ) − 3 i ⋅ 4 − 3 i ( − 3 i )

Simplify and combine like terms.

7 − 24 i

Step-by-step explanation:

Answer:

7 -24i

Step-by-step explanation:

(4 - 3i) ^2

(4-3i) * (4-3i)

FOIL

first 4*4 = 16

outer 4 * -3i = -12i

inner -3i *4 = -12i

last -3i*-3i = 9i^2 = 9 (-1) = -9

Add together

16 -12i-12i -9

Combine like terms

7 -24i

Answer:

Length of shortest side: 57

Length of medium side:59

Length of long side: 119

Step-by-step explanation:

Answer:

0.8343

Step-by-step explanation:

From the question, we have the following values:

Probability of vehicles that pass within the check point that are from within the state = 75% = 0.75

Probability of vehicles that pass within the check point that are from outsode the state = 100 - 75 = 25% = 0.25

P = 0.25

n = number of random variables = 9

The probability that fewer than 4 of the next 9 vehicles are from out of state is calculated as:

P < 4 = P ≤ 3

n = 9

P(x) = n!/(n - x)! x! × p^x × q^(n - x)

x = 3

p = 0.25

q = 0.75

P(x) = 9! /(9 - 3)! × 3! × 0.25^3 × 0.75^(9 - 3)

P(x) =0.8343

The probability that fewer than 4 (x<4) of the next 9 vehicles are from out of state is 0.83427.

Given information:

75% of the vehicles passing through a checkpoint are from within the state.

So, the probability that the vehicle is from within the state is 0.75.

The probability that the vehicle is from outside the state will be 1-0.75=0.25.

Now, let x be the random variable. So, the value of n=9. and x<4

It is required to calculate the probability that fewer than 4 of the next 9 vehicles are from out of state.

So, [tex]x< 4[/tex], p=0.25 and q=0.75.

So, the required probability can be calculated as,

[tex]P(x\le3) =\sum ^nC_x\times p^x \times q^{(n - x)}\\P(x\le3)=\sum\dfrac{n!}{(n - x)! x!} \times p^x \times q^{(n - x)}\\P(x\le3)= \dfrac{9!}{(9 - 3)! 3!} \times 0.25^3 \times 0.75^{(9 - 3)}+\dfrac{9!}{(9 - 2)! 2!} \times 0.25^2 \times 0.75^{(9 - 2)}+\dfrac{9!}{(9 - 1)! 1!} \times 0.25^1 \times 0.75^{(9 - 1)}+\dfrac{9!}{(9 - 0)! 0!} \times 0.25^0 \times 0.75^{(9 - 0)}\\P(x\le3)=0.83427[/tex]

Therefore, the probability that fewer than 4 of the next 9 vehicles are from out of state is 0.83427.

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Answer:

The probability that the sample mean is more than 110 is 0.0384.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sampling distribution of sample mean is given by:

[tex]\mu_{\bar x}=\mu[/tex]

And the variance of the sampling distribution of sample mean is given by:

[tex]\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}[/tex]

The information provided is:

[tex]n=50\\\\\mu=100\\\\\sigma^{2}=1600[/tex]

Since n = 50 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the normal distribution.

The mean variance of the sampling distribution for the sample mean are:

[tex]\mu_{\bar x}=\mu=100\\\\\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}=\frac{1600}{50}=32[/tex]

That is, [tex]\bar X\sim N(100, 32)[/tex].

Compute the probability that the sample mean is more than 110 as follows:

[tex]P(\bar X>110)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{110-100}{\sqrt{32}})[/tex]

                   [tex]=P(Z>1.77)\\=1-P(Z<1.77)\\=1-0.96164\\=0.03836\\\approx 0.0384[/tex]

*Use a z-table.

Thus, the probability that the sample mean is more than 110 is 0.0384.

[tex]\text{Solve for x:}\\\\-3x+9-2x=-12-5x\\\\\text{Combine like terms}\\\\-5x+9=-12-5x\\\\\text{Add 5x to both sides}\\\\9=-12\\\\\text{Since that's not valid, there would be no solutions}\\\\\boxed{\text{No solutions}}[/tex]

Answer:

Answer is below

Step-by-step explanation:

The width of the CI is directly proportional to critical value. When t* is greater than z value, the t value would then cause the margin of error to be larger and this will in turn cause the width of the confidence interval to be larger.

Greater t*df than z* gives us a bigger margin of error. This would in turn give bigger width of confidence interval. t distribution has greater width confidence interval compared to z distribution.

The width of confidence interval is a function of the margin of error. If the critical value of t(t*) is slightly larger than the critical value of z(z*), then the width of the confidence interval will be larger.

The margin of error is the product of the critical value and the standard error. Therefore, given the same standard error value, the value of the margin of error will increases based on the value of the critical value.

Since, t* is slightly larger than z*, then the confidence interval, t will be wider.

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Answer:

i [tex]\to[/tex] a

    [tex]n = 96040000[/tex]

i [tex]\to[/tex] b

    [tex]n_1 =24010000[/tex]

i [tex]\to[/tex] c

    [tex]n_2 =41602500[/tex]

ii[tex]\to[/tex]a

     [tex]E = 58.16[/tex]

ii[tex]\to[/tex]b

    [tex]291.84 < \mu < 408.16[/tex]\

ii[tex]\to[/tex]c

    There is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval

Step-by-step explanation:

From the question we are told that

     The sample size is [tex]n = 8[/tex]

      The sample mean is  [tex]\= x = \$ 350[/tex]    

      The sample standard deviation is  [tex]\$ 100[/tex]

Considering question i

    i [tex]\to[/tex] a

         At   [tex]E = 0.02[/tex]  

given that the confidence level is 95%  =  0.95

         the level of significance would be  [tex]\alpha =1-0.95 = 0.05[/tex]

The critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

        [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

So  the sample size is mathematically evaluated as

            [tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]

=>        [tex]n =[ \frac{ 1.96 * 100}{ 0.02} ]^2[/tex]

=>         [tex]n = 96040000[/tex]

 i [tex]\to[/tex] b

  At  [tex]E_1 = 0.04[/tex]    and  confidence level  = 95%  =>  [tex]\alpha_1 = 0.05[/tex]   =>  [tex]Z_{\frac{\alpha_1 }{2} } = 1.96[/tex]

             [tex]n_1 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_1} ]^2[/tex]

=>           [tex]n_1 =[ \frac{ 1.96 * 100}{ 0.04} ]^2[/tex]

=>           [tex]n_1 =24010000[/tex]

 i [tex]\to[/tex] c

       At   [tex]E_2 = 0.04[/tex]     confidence level  = 99%  =>    [tex]\alpha_2 = 0.01[/tex]

The critical value of  [tex]\frac{\alpha_2 }{2}[/tex] from the normal distribution table is  

        [tex]Z_{\frac{ \alpha_2 }{2} } = 2.58[/tex]

=>    [tex]n_2 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_2} ]^2[/tex]

=>    [tex]n_2 =[ \frac{ 2.58 * 100}{ 0.04} ]^2[/tex]

=>    [tex]n_2 =41602500[/tex]

Considering ii

Given that the level of significance is  [tex]\alpha = 0.10[/tex]

Then the critical value  of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

           [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

Generally the margin of error is mathematically represented as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]E = 1.645 * \frac{100 }{\sqrt{8} }[/tex]

         [tex]E = 58.16[/tex]

Generally the 90% confidence interval is mathematically evaluated as

         [tex]\= x - E < \mu < \= x + E[/tex]

=>      [tex]350 - 58.16 < \mu < 350 + 58.16[/tex]

=>     [tex]291.84 < \mu < 408.16[/tex]

So the interpretation is that there is 90% confidence that the mean  fee charged to H&R Block customers last year is in the interval .So there is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval.

Answer:

[tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex] converges.

Step-by-step explanation:

The convergence analysis of this sequence is done by Ratio Test. That is to say:

[tex]r = \frac{a_{n+1}}{a_{n}}[/tex], where sequence converges if and only if [tex]|r| < 1[/tex].

Let be [tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex], the ratio for the expression is:

[tex]r =-\frac{3}{n+1}[/tex]

[tex]|r| = \frac{3}{n+1}[/tex]

Inasmuch [tex]n[/tex] becomes bigger, then [tex]r \longrightarrow 0[/tex]. Hence, [tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex] converges.

Answer:

C Stratified sampling

Step-by-step explanation:

Stratified sampling : Stratified sampling is a type of sampling technique in which the total population is divided into smaller groups or strata to complete the sampling process. The strata is formed based on some common characteristics in the data of the population.

One of the advantage of stratified random sampling is that it covers important population characteristics in the sample.

Answer:

The  confidence interval is  [tex]0.304 < p < 0.324[/tex]

Step-by-step explanation:

From the question we are told

      The sample proportion [tex]\r p = 0.314[/tex]

      The margin of error  is [tex]E = 0.01[/tex]

The confidence interval for  p is mathematically represented as

       [tex]\r p - E < p < \r p + E[/tex]

=>    [tex]0.314 - 0.01 < p < 0.314 + 0.01[/tex]

=>   [tex]0.304 < p < 0.324[/tex]

Complete Question

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25? The standard deviation in a pre-selected sample is  7.5

Answer:

The minimum sample size is  [tex]n =97[/tex]

Step-by-step explanation:

From the question  we are told that

 The margin of error is  [tex]E = 1.25[/tex]

   The  standard deviation is  [tex]s = 7.5[/tex]

Given that the confidence level is  90% then the level of significance is mathematically represented as

             [tex]\alpha = 100 - 90[/tex]  

             [tex]\alpha =10\%[/tex]  

             [tex]\alpha =0.10[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table  

    The value is  [tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]

   The  minimum sample size is mathematically evaluated as

         [tex]n = \frac{Z_{\frac{\alpha }{2} * s^2 }}{E^2 }[/tex]

=>        [tex]n = \frac{1.645^2 * 7.5^2 }{1.25^2 }[/tex]

=>        [tex]n =97[/tex]

Answer:

17,720 ft

Step-by-step explanation:

5.4 km * (1 mile)/(1.609 km) * (5280 ft)/(1 mile) = 17,720 ft

Answer:

The sample proportion of 'successful' people is [tex]\frac{3}{4}[/tex].

Step-by-step explanation:

The sample consist of 64 people and 48 of them are 'successful'. Hence, the proportion of 'successful' people is:

[tex]p = \frac{n}{N}[/tex]

Where:

[tex]N[/tex] - People that forms the sample, dimensionless.

[tex]n[/tex] - People classified as 'successful', dimensionless.

Given that [tex]n = 48[/tex] and [tex]N = 64[/tex], the sample proportion of 'successful' people is:

[tex]p = \frac{48}{64}[/tex]

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

The sample proportion of 'successful' people is [tex]\frac{3}{4}[/tex].

Answer:

Hey!

Your answer is 9.164!!

Step-by-step explanation:

Adding 0.01 means just adding 1 to THE DIGIT IN THE HUNDRETH PLACE...2 SPACES RIGHT OF DECIMAL POINT!

5+1=6

SUB IN:

9.164

Answer:

63 people.

Step-by-step explanation:

If you have a contagious disease and met with 9 different people each day for 7 days, that'll be 63 people that have gotten infected. 9 x 7 = 63. Hope this helps you!

Answer:

vol = 17,148 cu. in.

Step-by-step explanation:

vol = 4 / 3 * pi * r³

vol = 4 / 3 *3.14 * 16³

vol = 17,148 cu. in.

Answer:

The answer is

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

where r is the radius of the sphere

π = 3.14

From the question

r = 16 inches

Volume of the sphere is

[tex]V = \frac{4}{3} (3.14) {16}^{3} [/tex]

V = 17148.586

We have the final answer as

V = 17149 cubic inches to the nearest cubic inch

Hope this helps you

Answer:

D

Step-by-step explanation:A set is said to be closed under an operation when the application of the operation between any two elements of the set leads to an element that belongs to the same set. If a set is closed under an operation, it is said to have the closure property of that operation. When we combine two rational expressions by adding, subtracting, multiplying, or dividing, we get a rational expression. This pattern indicates that rational expressions are closed for all four operations.

Answer:

Area of ΔEDF = 2.7 in²

Step-by-step explanation:

It's given in the question,

ΔBAC ~ ΔEDF

In these similar triangles,

Scale factor of the sides = [tex]\frac{\text{Measure of one side of triangle BAC}}{\text{Measure of one side of triangle EDF}}[/tex]

                                        [tex]=\frac{\text{BC}}{\text{EF}}[/tex]

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

Area scale factor = (Scale factor of the sides)²

[tex]\frac{\text{Area of triangle BAC}}{\text{Area of triangle EDF}}=(\frac{3}{2})^2[/tex]

[tex]\frac{6}{\text{Area of triangle EDF}}=(\frac{9}{4})[/tex]

Area of ΔEDF = [tex]\frac{6\times 4}{9}[/tex]

                       = 2.67

                       ≈ 2.7 in²

Therefore, area of the ΔEDF is 2.7 in²                            

Answer:

a) 20, 21, 28 : acute

b) 3, 6, 4 : obtuse

c) 8, 12, 15 : obtuse

Step-by-step explanation:

You can see if a triangle is acute, obtuse, or right using the Pythagorean theorem as follows:

If [tex]a^2+b^2=c^2[/tex] , then the triangle is right.

If [tex]a^2+b^2>c^2[/tex] , then the triangle is acute.

If [tex]a^2+b^2<c^2[/tex] , then the triangle is obtuse.

Solve each to find if the given lengths form an acute, obtuse, or right triangle ( The biggest number is the hypotenuse length, since the hypotenuse is always the longest side in a triangle. This is represented by c):

a) 20, 21, 28

Insert numbers, using 28 as c:

[tex]20^2+21^2[/tex]_[tex]28^2[/tex]

Simplify exponents ([tex]x^2=x*x[/tex]):

[tex]400+441[/tex]_[tex]784[/tex]

Simplify addition:

[tex]841[/tex]_[tex]784[/tex]

Identify relationship:

[tex]841>784[/tex]

The sum of the squares of a and b is greater than the square of c. This triangle is acute.

b) 3, 6, 4

Insert numbers, using 6 as c:

[tex]3^2+4^2[/tex]_[tex]6^2[/tex]

Simplify exponents:

[tex]9+16[/tex]_[tex]36[/tex]

Simplify addition:

[tex]25[/tex]_[tex]36[/tex]

Identify relationship:

[tex]25<36[/tex]

The sum of the squares of a and b is less than the square of c. This triangle is obtuse.

c) 8, 12, 15

Insert numbers, using 15 as c:

[tex]8^2+12^2[/tex]_[tex]15^2[/tex]

Simplify exponents:

[tex]64+144[/tex]_[tex]225[/tex]

Simplify addition:

[tex]208[/tex]_[tex]225[/tex]

Identify relationship:

[tex]208<225[/tex]

The sum of the squares of a and b is less than the square of c. This triangle is obtuse.

:Done.

The correct values are,

a) 20, 21, 28  = Acute

b) 3, 6, 4  = Obtuse

c) 8, 12, 15 = Obtuse

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The sides are,

a) 20, 21, 28

b) 3, 6, 4

c) 8, 12, 15

Now,

We know that;

If three sides of a triangle are a, b and c.

Then, We get;

If a² + b² = c², then the triangle is right triangle.

If a² + b² > c², then the triangle is acute triangle.

If a² + b² < c², then the triangle is obtuse triangle.

Here, For option a;

⇒ 20, 21, 28

Clearly, a² + b² = 20² + 21²

                       = 400 + 441

                       = 841

And, c² = 28² = 784

Thus, a² + b² > c²

Hence, It shows the acute angle.

For option b;

⇒ 3, 6, 4

Clearly, a² + b² = 3² + 4²

                       = 9 + 16

                       = 25

And, c² = 6² = 36

Thus, a² + b² < c²

Hence, It shows the obtuse angle.

For option c;

⇒ 8, 12, 15

Clearly, a² + b² = 8² + 12²

                       = 64 + 144

                       = 208

And, c² = 15² = 225

Thus, a² + b² < c²

Hence, It shows the obtuse angle.

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Answer:

The third option.

Step-by-step explanation:

Mathematical induction is a 2 step mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number.

Step 1 (Base step) - It proves that a statement is true for the initial value.

Step 2 (Inductive step) - It proves that if the statement is true for the nth iteration (or number n), then it is also true for (n + 1)th iteration (or number n + 1)

Hope this helps.

Please mark Brainliest.

Answer:

A method of improving statments

Step-by-step explanation:

"Mathematical Induction is a mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number."