The length of a rectangle is six times its width. The area of the
rectangle is 294 square centimeters. Find the dimensions of the
rectangle.

Answer:

[tex] S.A = 246.6 in^2 [/tex]

Step-by-step explanation:

The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.

Surface area of the square pyramid is given as: [tex] B.A + \frac{1}{2}*P*L [/tex]

Where,

B.A = Base Area of the pyramid = 9*9 = 81 in²

P = perimeter of the base = 4(9) = 36 in

L = slant height of pyramid = 9.2 in

Plug in the values into the given formula to find the surface area

[tex] S.A = 81 + \frac{1}{2}*36*9.2 [/tex]

[tex] = 81 + 18*9.2 [/tex]

[tex] = 81 + 165.6 [/tex]

[tex] S.A = 246.6 in^2 [/tex]

Answer:

x = 3 ± sqrt(11)

Step-by-step explanation:

x^2 - 6x + 9 = 11

Recognizing  that this is a perfect square trinomial

(x-3) ^2 =11

Taking the square root of each side

sqrt((x-3) ^2) = ± sqrt(11)

x-3 =± sqrt(11)

Add 3 to each side

x = 3 ± sqrt(11)

Answer:

[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]

Step-by-step explanation:

Hello,

   [tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]

Do not hesitate if you have any question

Hope this helps

Answer:C

Step-by-step explanation:

Pemdas

3+5(10)

5*10=50

3+50=53

Answer:

x= -5, -1

Step-by-step explanation:

To find the zeroes of a function,

First expand the terms to get the form  [tex]ax^{2} + bx +c[/tex] where 'a, b, and c' are constants

     [tex]f(x)= (x+3)^{2} -4[/tex]

    [tex]f(x)= x^{2}+6x+9-4[/tex]

    [tex]f(x)= x^{2} +6x +5[/tex]

Now, factor the equation

This can be done using the quadratic formula or other methods

  One simple method is to find the two values that would get:

A good way to verify is to expand the terms and make sure the function looks the same

In this case, the equation can broken into

    f(x)= (x+1)*(x+5)

Now, look at each term individually and set each of them to equal 0

   x+1 =0

   x+5=0

Solve for x in each case

  x= -1

  x= -5

Now, ordering them from least to greatest would be: x= -5, -1

Answer:

a dilation by One-fourth and a translation

Step-by-step explanation:

For determining the sequence first we have to find out the scale factor which is shown below:

We can calculate the scale factor to obtain  

[tex]= \frac{1.5}{6} \\\\ = \frac{1}{4}[/tex]

Now as we know that the triangle XYZ and the triangle ABC are similar to each other but in the triangle XYZ is smaller in size and it is a shift to upward and right

Therefore the last option is correct

Answer:

The dentist should fail to reject the Null hypothesis

Step-by-step explanation:

From the question we are told that

       The sample size is  n =  400

       The  sample  mean is  [tex]\= x = 149[/tex]

       The  level of significance is  5%  = 0.05  

       The  Null hypothesis is  [tex]H_o : p = 0.40[/tex]

        The Alternative  hypothesis is  [tex]H_a : p < 0.40[/tex]

         The  p-value is  [tex]p-value = 0.131[/tex]

Looking at the given data we can see that the p-value is greater than the level of significance hence the dentist should fail to reject the Null hypothesis  

Answer:

cars are dum

Step-by-step explanation:

Answer:

-3a

Step-by-step explanation:

3(-a)

Expand brackets.

3 × -1a

-3a

Answer:

see explanation

Step-by-step explanation:

Pythagorean Theorem

7² + 8² = x²

49 + 64 = x²

113 = x²

x = √113 or 10.63

Distance Formula

√(-4 - 4)² + (4 - -3)²

= √8² + 7²

= √113 or 10.63

Answer:

The  probability is  [tex]P(X < 900 ) = 0.0918[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 1100[/tex]

    The  standard deviation is  [tex]\sigma = 150[/tex]

     The random number value is  x =900

The probability that a trainee earn less than 900 a month is mathematically represented as

       [tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]

Generally the z-value for the normal distribution is mathematically represented as

       [tex]z = \frac{x -\mu }{\sigma }[/tex]

So From above we have

      [tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]

      [tex]P(X < 900 ) = P( Z <-1.33)[/tex]

Now from the z-table

    [tex]P(X < 900 ) = 0.0918[/tex]

Answer:

Step-by-step explanation:

Hello!

Miguel has four chips, two have the number "1", one has the number "3" and the other has the number "5"

If the experiment is "choosing two chips and looking at their numbers" there are the following possible outcomes:

S= {(1,1)(1,3)(1,5)(3,1)(5,1)(3,5)(5,3)}

The sample space for the experiment has 7 possible combinations.

a)

Be X: the amount of money Miguel will receive or owe.

If two chips with the same number are chosen he will receive $2

If the chips have different number he will owe $1

Looking at the possible outcomes listed above, out of the 7, in only one he will select the same number (1,1)

So the probability of him receiving $2 will be 1/7

Now out of the 7 possible outcomes, 6 will make Miguel owe $1, so you can calculate its probability as: 6/7

  xi  | $2 | -$1

P(xi) | 1/7 | 6/7

b)

To calculate the expected value or mean you have to use the following formula:

[tex]\frac{}{X}[/tex]= ∑[xi*P(xi)]= (2*1/7)(-1*6/7)= -4/7= $-0.57

c)

The expected value is $-0.57, meaning that Miguel can expect to owe $0.57 at the end of the game.

d)

To make the game fair you have to increase the probability of obtaining two chips with the same number. Any probability close to 50% will make the game easier. For example if you change the experiment so that for earning $2 the probability is 4/7 and for owing $1 the probability is 3/7, the expected earnings will be:

(2*4/7)+(-1*3/7)= $0.71

I hope this helps!

Answer:

I think that is the C

Step-by-step explanation:

Answer:

Option B is the correct answer.

Step-by-step explanation:

here, arc RT =162°

as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.

so, its value must be 81°only.

hope it helps..

Answer:

Barts total cost is (c)213.36

Step-by-step explanation:

First, you subtract 6% from $219

=204.92

add shipping,

+7.50

=213.36

Hope this helps <3

Answer:

C. $213.36

Step-by-step explanation:

The original price is $219 and the discount is 6% which is equal to $13.14

$219 - $13.14 + $7.50 (shipping cost) = $213.36

Answer:

The answer is 15.6/31 or 1/2

Step-by-step explanation:

The data in the question is sufficient to find an answer for it.

1. I look at the temperature and rainfall chart for Brighton, United Kingdom.

2. Check for rainy season and dry season.

3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.

4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.

The number of rainfall days is 15.6 and we know there are 31 days in July.

If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5

Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.

In fraction, 0.5 = 1/2

Add the top and bottom numbers together, divide that by 2 then multiply by the height.

15.3 + 19.5 = 34.8

34.8/2 = 17.4

17.4 x 11.1 = 193.14

Answer is 193.1 m^2

Answer:

The correct option is (D).

Step-by-step explanation:

In this case, we need to test whether the  mean pulse rate (in beats per minute) of students in a large math class is greater than 71.

The hypothesis can be defined as follows:

H₀: The mean pulse rate of students in a large math class is not greater than 71, i.e. μ ≤ 71.

Hₐ: The mean pulse rate of students in a large math class is greater than 71, i.e. μ > 71.

It is provided that the sample mean pulse rate, of a simple random sample of the students is 71.7.

The sample mean is not very different from the population mean.

So, it cannot be said in confidence that the sample is unusual.

Thus, the correct option is (D).

"The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim."

Answer: [tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.

We assume that repetition is not allowed

Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex]  [By permuattaions]

[tex]=\dfrac{4\times3\times2}{2}=12[/tex]

Favourable outcome = First green then red  (only one way)

So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{1}{12}[/tex]

hence, the required probability =[tex]\dfrac{1}{12}[/tex]

Explanation:

For any quadrilateral that is inscribed in a circle, ie has all four points on the circle like this, the opposite angles are always supplementary. They add to 180 degrees.

x+125 = 180

x+125-125 = 180-125 ... subtract 125 from both sides

x = 55

Answer:

lmkjhvjgcfnhjkhbmgnc gfghh

Step-by-step explanation:

Answer:

woman is 37, girl is 7

Step-by-step explanation:

7(x-2) = y-2

4(x+3) = y+3

7x - 14 = y - 2

7x - 12 = y

4x + 9 = y

3x - 21 = 0

x = 7

y = 37

Answer:

a)the proportion of student is 0.1082

b)

H1: p = .08

H2: p not equal to 0.08

H1: p =0 .08

H2: p < .08

H1: p =0 .08

H2: p >0 .08

c)z=1.45

d) the p value is 0.1470

e)null hypothesis cannot be accepted,There is no enough evidence to reject the  null hypothesis.

Step-by-step explanation:

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

Dian has $250 originally.

Step-by-step explanation:

Let the total money Dian has originally = $S

Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,

Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]

Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]

                                   = [tex]\frac{\text{5S-2S}}{5}[/tex]

                                   = [tex]\frac{3S}{5}[/tex]

Since Dian has $150 left then the equation will be,

[tex]\frac{3S}{5}=150[/tex]

S = [tex]\frac{150\times 5}{3}[/tex]

S = $250

Therefore, Dian has $250 originally.

Answer:

Option b.

Step-by-step explanation:

Note: The given expression is not in correct form. Consider the given expression is [tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex].

Let as consider the given expression is  

[tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex]

We know that,

[tex]i^0=1,i^2=-1,i^3=-i,i^4=1[/tex]

Using these values, we get

[tex]i^0\times i^1\times i^2\times i^3\times i^4=1\times i\times (-1)\times (-i)\times 1[/tex]

[tex]=i^2[/tex]

[tex]=-1[/tex]

The value of given expression is -1.

Therefore, the correct option is b.

Answer:

Probability of obtaining no more than two defective tubes = 0.816

Step-by-step explanation:

The Probability of obtaining no more than two defective tubes in a randomly selected sample of 15 tubes is obtained using the binomial distribution formula: nCr × p^r × q^(n -r).

Where n is number of samples;

r is maximum number of defective tubes, r ≤ 2;

p is probability of defective tubes = 10% or 0.1

q is probability of non-defective tubes, q = 1 - p

Further explanations and calculations are given in the attachment below:

Answer:

A. 0.89.

Step-by-step explanation:

The value of correlation coefficient ranges from -1 to 1. Any value outside this range cannot possibly be correlation coefficient of a scatter plot representing relationship between two variables.

The scatter plot given shows a positive correlation between average daily temperatures and number of visitors, as the trend shows the two variables are moving in the same direction. As daily temperature increases, visitors also increases.

From the options given, the only plausible correlation that can represent this positive relationship is A. 0.89.

Answer:

[tex]\Large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]

Step-by-step explanation:

Hello,

Based on the indication, we can write this polynomial as below, k being a real number that we will have to identify (degree = 3 and we have three zeroes -3, -1, and 2).

   [tex]\Large \boxed{k(x+3)(x+1)(x-2)}[/tex]

We know that the point (1,10) is on the graph of this function, so we can say.

[tex]k(1+3)(1+1)(1-2)=10}\\\\4*2*(-1)*k=10\\\\-8k=10\\\\k=\dfrac{10}{-8}=-\dfrac{5}{4}[/tex]

Then the solution is:

[tex]\large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

A

Step-by-step explanation:

[tex]g(x) = \frac{3}{{x}^{2} + 2x} \\ {x}^{2} + 2x - \frac{3}{g(x)} = 0 \\ x = \frac{1}{2} \Big( - 2 + \sqrt{12 + \frac{12}{g(x)} }\Big) \\ x = - 1 + \sqrt{1 \pm \frac{3}{g(x)} } [/tex]

Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.

Answer:

(H1, T1)

Step-by-step explanation:

Since we know that the only number option is 1, we can cancel out the first 3 options. and obviously, there are only heads, and tails. So, using only the # 1 and heads and tails, we can conclude that the answer is (H1, T1).

Answer:

D. (H1, T1)

Step-by-step explanation:

Since all outcomes require card #1 is chosen, so any answer with 2 or 3 can be rejected, therefore the answer is

D. (H1, T1)

Answer:

84%

Step-by-step explanation:

We find the z-score here

z= x-mean/SD = 32-40/8 = -1

So the probability we want to find is;

P(z>-1)

This can be obtained using the standard score table

P(z>-1) = 0.84 = 84%

Answer:

1.7

Step-by-step explanation:

1. Find the volume of Glass 2 (volume of a cone = 1/3πr² ·h)

1/3 · 3.14 · 2.5² · 6 = 39.25 cm³

2. Subtract the volume of Glass 2 from the amount of water poured

60 - 39.25 = 20.75 cm³

3. Set up the equation for Glass A using x for the height being solved for (volume of a cylinder = πr² · h)

3.14 · 2² · x = 20.75

12.56x = 20.75

4. Solve for x by dividing both sides by 12.56 (round to the nearest tenth)

x = 1.7

The answer should be 1.7