In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 47 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 41 and 53? Do not enter the percent symbol.

Answer:

Step-by-step explanation:

Note that the equation should be

f(t) = t^2 + 6t - 20

A. Completing the square

coefficient of the t term: 6

divide it in half: 3

square it: 3²

add 3² to complete the square and subtract 3² to keep the equation balanced:

f(t) = (t² + 6t + 3²) - 3² - 20

f(t) = (t+3)² - 29. This is the equation in vertex form.

:::::

B. Vertex (-3, -29)

The leading coefficient of the equation is +1. Since the leading coefficient is positive, the parabola opens upwards. Therefore, the vertex is a minimum.

:::::

The axis of symmetry is the vertical line passing through the vertex: x = -3

9514 1404 393

Answer:

  C(-1, -4)

Step-by-step explanation:

We want ...

  AC/CB = 1/5

  5(C-A) = B-C . . . . multiply by 5CB

  6C = B +5A . . . . . add 5A-C

  C = (B +5A)/6 . . . divide by 6

  C = ((4, 6) +5(-2,-6))/6 = (4-10,6-30)/6 = (-6, -24)/6

  C = (-1, -4)

Answer:

232.045

Step-by-step explanation:

217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105

5105 / 22 = 232.045454545

Answer:

See explanation

Step-by-step explanation:

Given

[tex]A = (-1,1)[/tex]

[tex]B = (3,3)[/tex]

[tex]C =(4,-2)[/tex]

Solving (a): [tex]P(0,0) \to Q(1,3)[/tex]

This means that:

[tex](x,y) \to (x+1,y+2)[/tex]

So, we have:

[tex]A = (-1,1)[/tex]

[tex]A' = (-1 + 1,1+2)[/tex]

[tex]A' = (0,3)[/tex]

[tex]B = (3,3)[/tex]

[tex]B'= (3 + 1,3+2)[/tex]

[tex]B'= (4,5)[/tex]

[tex]C =(4,-2)[/tex]

[tex]C' = (4+1,-2+1)[/tex]

[tex]C' = (5,-1)[/tex]

Solving (b): [tex]P(0,-1) \to Q(4,-2)[/tex]

This means that:

[tex](x,y) \to (x+4,y-1)[/tex]

So, we have:

[tex]A = (-1,1)[/tex]

[tex]A' = (-1+4,1-1)[/tex]

[tex]A' = (3,0)[/tex]

[tex]B = (3,3)[/tex]

[tex]B'= (3+4,3-1)[/tex]

[tex]B'= (7,2)[/tex]

[tex]C =(4,-2)[/tex]

[tex]C' = (4+4,-2-1)[/tex]

[tex]C' = (8,-3)[/tex]

Solving (c): [tex]P(-1,-2) \to Q(-2,-2)[/tex]

This means that:

[tex](x,y) \to (x-1,y)[/tex]

So, we have:

[tex]A = (-1,1)[/tex]

[tex]A' = (-1-1,1)[/tex]

[tex]A' = (-2,1)[/tex]

[tex]B = (3,3)[/tex]

[tex]B'= (3-1,3)[/tex]

[tex]B'= (2,3)[/tex]

[tex]C =(4,-2)[/tex]

[tex]C'= (4-1,-2)[/tex]

[tex]C'= (3,-2)[/tex]

Answer:

4.5%

Step-by-step explanation:

The tax rate=(2152.6/47800)*100=4.5%

Answer:

The width is 36 feet

Step-by-step explanation:

If the width of the fence is x then its length is x+3.

The perimeter is 150 feet, so we have the equation:

2(x + x + 3) = 150

4x + 6 = 150

x = 144/4 = 36 feet

9514 1404 393

Answer:

  |x| = 1/2

Step-by-step explanation:

Perhaps the simplest equation is ...

  |x| = 1/2

__

You could get more elaborate:

  |2x| = 1

  3 -|6x| = 0

Answer:

1.8

Step-by-step explanation:

First, find 40% of 15:

15(0.4)

= 6

Next, find 30% of this:

6(0.3)

= 1.8

So, the answer is 1.8

Answer:

(-3, -6)

Step-by-step explanation:

always start from the origin! Hope this helps!

Answer/Step-by-step explanation:

Hola amigo. Mucho gusto. En Brainly.com puede responder a sus preguntas y obtener explicaciones exhaustivas. Esto le permite aprender de forma más inteligente.

Y... yo hablo pequeno español.

Answer:

d

Step-by-step explanation:

h

The number of sides of a regular polygon with an interior angle [tex]\[{178^ \circ }\][/tex] is 180.

A polygon is regular when all angles are equal and all sides are equal.

A regular polygon has if each interior angle.

Interior angle of given polygon =178

An exterior angle of polygon =180 −178 =2

The sum of exterior angles of any polygon is 360

Number of sides of a regular polygon

[tex]=\frac{360}{2}[/tex]

[tex]=180[/tex]

Therefore, The number of sides of a regular polygon is 180.

To learn more about the side of regular polygon visit:

https://brainly.com/question/1592456

​

5(2x+1)+4=6(3x+2)-7

10x+5+4=18x+12-7

10x-18x=12-7-5-4

-8x=-4 (-1)

8x=4

x=4/8 (/4)

x=1/2

Answer:

x = 1/2

Step-by-step explanation:

5(2x + 1) + 4 = 6 (3x + 2) - 7

~Simplify both sides

10x + 9 = 18x + 5

~Subtract 9 from both sides

10x = 18x - 4

~Subtract 18x to both sides

-8x = -4

~Divide -8 to both sides

x = 1/2

Best of Luck!

Answer B.ED

Step-by-step explanation:

Geometric figures are basically figures that have a boundary. The geometric figures and their real life examples are:

To determine the real life object of each geometric figure, we simply identify objects that have similar features as the geometric figure.

For instance, a rectangular prism has 6 rectangular faces; building blocks, some gift box and cabinets also have 6 rectangular faces.

So, these three real life objects can be used as examples of a rectangular prism.

When the above explanation is applied to the other geometric figures, we come up with the following list:

Read more about geometric figures at:

https://brainly.com/question/8430622

In the photo are a couple possible answers you could use.

Answer:

x = 1

Step-by-step explanation:

-2x + 8x + 3 - 7 = 2

Combine like terms

-2x + 8x = 6x

3 - 7 = -4

We now have

6x - 4 = 2

Add 4 to both sides

6x - 4 + 4 = 2 + 4

6x = 6

Divide both sides by 6

6x/6 = 6/6

x = 1

Answer:

1/5

Step-by-step explanation:

the two points are(7,5) and (2,4)

let,(x1,y1)=(7,5) and (x2,y2)=(2,4)

slope (m)=y2-y1/x2-x1

=4-5/2-7

=-1/-5

=1/5(minus ,minus are cut)

Answer:-10

-3+-4+-3

-3-4=-7

-7+-3=-7-3

=-10

Answer:

Here the answer is given as follows,

Answer:

x = -1/4

Step-by-step explanation:

[tex]81^{x}[/tex] = 1/3

[tex]3^{4}^{x}[/tex] = [tex]3^{-1}[/tex]

4x = -1

x = -1/4

Answer:

x = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Using the rules of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

Given

[tex]81^{x}[/tex] = [tex]\frac{1}{3}[/tex] [ note that 81 = [tex]3^{4}[/tex] ] , then

[tex](3^4)^{x}[/tex] = [tex]3^{-1}[/tex] , that is

[tex]3^{4x}[/tex] = [tex]3^{-1}[/tex]

Since the bases on both sides are equal, both 3, then equate exponents

4x = - 1 ( divide both sides by 4 )

x = - [tex]\frac{1}{4}[/tex]

Answer:

-2 from both sides

Step-by-step explanation:

32=5x+2

-2        -2

________

30=5x

__=__

5      5

6=x

The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides.

We are given the algebraic equation;

32 = 5X + 2

The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides to get;

32 - 2 = 5X + 2 - 2

30 = 5X

Divide both sides by 5 using division property of equality to get;

X = 6

Read more about Algebraic Equations at; https://brainly.com/question/16863577

#SPJ6

Answer:

henc X = 30°

Step-by-step explanation:

here is the proof

when X=30° then

sin2x = sin2×30

=sin 60°

= √3/2

or else,

putting value of X = 30° then

sin2x= 2sinxcosx

= 2×sin30°×cos30°

=2×1/2×√3/2

= 2√3/4

= √3/2

hence proved sin2x= √3/2.

Answer:

± 3

Step-by-step explanation:

let n be the number then the number squared is n² , so

6n² = 54 ( divide both sides by 6 )

n² = 9 ( take the square root of both sides )

n = ± [tex]\sqrt{9}[/tex] = ± 3

That is the number is 3 or - 3

Answer:

Step-by-step explanation:

You have not provided the answers to choose from.

The expression can be simplified to δ⁴/a, but I cannot tell if that is one of the choices.

Answer:

C. 98

Step-by-step explanation:

The proposed regression equation is weight = b + width * m

R2 = 0.423

A.) What is the regression equation for this example?

The estimate for the y-intercepts is b= 2.3013 and the estimate for the slope is m= 0.7963

In general, we can symbolize the estimated regression equation as ^Y= b + m*Xi. For this example you have to replace it with the calculated values of the regression coefficients to obtain the estimated regression equation:

^Y= 2.3013 + 0.7963Xi

B.) What is the explanatory, or predictor, variable in this study?

The explanatory or predictor variable is the variable that is suspected to have an effect over the response variable. In this example the predictor variable is:

X: Width of a horseshoe crab (cm)

C.) If the researcher wanted to test whether there is a statistically significant relationship between these two variables, what would the test statistic be? Calculate it from the table above.

To test if the regression is significant, the parameter of study will be the slope of the regression equation, symbolically: β. If the slope is equal to zero "β=0" then there is no linear regression between the response and explanatory variable. If the slope is different from zero "β≠0" then the regression is significant and the explanatory variable affects the response variable.

The hypotheses are:

H₀: β=0

H₁: β≠0

α: 0.05

The value of the statistic under the null hypothesis is t= 8.48

D.) What can we say about the p-value?

This test is two-tailed and so is the p-value, remember that the p-value is the probabulity of obtaining a value as extreme as the value of the statistic under the null hypothesis. The distribution for this test is a t with n-2= 100-2= 98 degrees of freedom. You can calculate the p-value as:

P(t₉₈≤-8.48) + P(t₉₈≥8.48)= P(t₉₈ ≤ -8.48) + (1 - P(t₉₈ < 8.48) ≅ 0.00001

E.) Ultimately, the reason that we find test statistics is so that we can compare them to a null distribution. For regression, that is a t-distribution based on the degrees of freedom. With 98 degrees of freedom (100-2), we can safely say that the critical t (or the confidence multiplier) is what?

As mentioned before, this test is two tailed, meaning that the rejection region is divided in two:

Critical values ± = ± = ± 1.984

This means that you'll reject the null hypothesis when the statistic is t ≤ -1.984 or if the statistic is t ≥ 1.984-

F.) Find the confidence interval for the slope.

Using a 95% confidence level, the interval for the slope is:

[m ± Sm]

[0.7963 ± 1.984 * 0.0939]

[0.61; 0.98]

G.) Is there a statistically significant relationship? Answer with the test statistic and the confidence interval.

Yes, there is a significant relationship between the width and weight of the horseshoe crabs.

Using the critical value approach:

The calculated statistic is 8.48 and the critical value is ± 1.984, since the statistic is greater than the positive critical value, the decision is to reject the null hypothesis.

If you pay attention to the confidence interval, which was made at a confidence level complementary to the significance level of the hypothesis test, this interval [0.61; 0.98] doesn't include the "zero". Since the interval doesn't include the value of the parameter stated in the null hypothesis, you can conclude that this hypothesis is not true and therefore reject it.

Answer: See explanation

Step-by-step explanation:

From the information given in the question, we are informed that a newsletter publisher believes that less than 61% of their readers own a laptop.

The null hypothesis will be: H0: p ≥ 0.61

The alternative hypothesis will be: Ha: p < 0.61.

Subtracting 10 from the original equation will shift the graph down 10 units

The answer is D.