What is the mode of this set of data?

Answer:

D

Step-by-step explanation:

2² + 6² = x²

4 + 36 = x²

40 = x²

x = 2√10

Answer:

40 litres

Step-by-step explanation:

V = l x w x h

50 x 40 x 20 = 40000

40000 cm^3

1cm^3 = 1ml

40000 cm^3/ 1cm^3 = 40000ml

40000 x 10^-3 = 40 litres

Answer:

k  ÷  5  <  25

Step-by-step explanation:

Edg.

Answer:

k ÷ 5 < 25

Step-by-step explanation:

Answer:

a) H0:μ=55,000 H1:μ>55,000

b) Yes, since we can can reject the null hypothesis

Step-by-step explanation:

a) The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For this case;

Null hypothesis is that the starting salary will be equal to $55,000/year.

H0:μ=55,000

Alternative hypothesis is that the starting salary will be greater than $55,000/year.

H1:μ>55,000

b) Decision Rule;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

For this case;

P-value = 0.0392

α = 0.05

Since P-value < 0.05, we can reject null hypothesis.

Therefore, we can accept alternative hypothesis which is the starting salary will be greater than $55,000/year, so the student should pursue an actuary career because the starting salary will be greater than $55,000/year.

- Yes, since we can can reject the null hypothesis

Answer:

The 17 disc cases would definitely fit into the box.

Step-by-step explanation:

The given cuboid box has the dimensions 28cm by 15cm by 20cm.

Disc cases are cuboid with dimensions 1.5cm by 14.2cm by 19.3cm.

volume of a cuboid = length × width × height

Volume of the box = 28 × 15 × 20

                               = 8400 cubic centimeters

Volume of each disc case = 1.5 × 14.2 × 19.3

                                           = 411.09 cubic centimeters

When the 17 disc cases are stacked it would have a volume.

The volume of 17 disc cases = 17 × volume of a case

                                               = 17 × 411.09

                                               = 6988.53 cubic centimeters

Thus comparing the volume for 17 disc cases and that of the cuboid box, the disc cases would definitely fit into the box.

i.e           =   [tex]\frac{volume of box}{volume of 17 disc cases}[/tex]  

              = [tex]\frac{8400}{6988.53}[/tex]

             = 1.20

Answer:

Step-by-step explanation:

27.5×14.5×19.5 =7775.625 cm³

1.55 x 14.25 x 19.35=427.393125

427.393125 x 17=7265.683

7775.625>7265.683

19.5x27.5x14.5=7775.625

1.45x14.15x19.25=394.961875

394.961875x17=6714.35

7775.63>6714.35

1.55x17=26.35

27.5>26.35

Answer:

Step-by-step explanation:

Hello!

Given the variables

Y: family spending

X₁: income of a family

X₂: family size

X₃: additions to savings of a family

And the regression output (see attachment)

The population model is Y= α + β₁X₁ + β₂X₂ + β₃X₃

a)

To write the estimated regression equation of the relationship between the variables you have to use the information given in the regression output. Under the column "coefficients", the value that corresponds to "intercept" is the estimation of the y-intercept (a), the value under X₁ corresponds to the estimation for the slop for the variable "income of the family" (b₁), under X₂ is the estimation of the slope for the variable "family size" (b₂) and under X₃ is the estimation for the slope corresponding to the variable "additions to savings" (b₃)

The estimated regression equation is:

^Y= a + b₁X₁ + b₂X₂ + b₃X₃

^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃

b)

Using the SS information you can calculate the coefficient of determination as:

SStotal= SSReg+SSError= 45.9634+2.6218= 48.5852

[tex]R^2= \frac{SS_{Reg}}{SS_{Total}} = \frac{45.9634}{(48.5852)} = 0.946[/tex]

R²= 94.6%

This means that 94.6% of the variability of the average family spending is explained jointly by the family income, the family size and the addition to saving under the estimated model ^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃

c)

The hypotheses are:

H₀: β₁= β₂= β₃= 0

H₁: At least one βi≠0 ∀ i=1, 2, 3

α: 0.05

The statistic for the multiple regression is

[tex]F=\frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg};Df_{Error}}[/tex]

[tex]MS_{Reg}= \frac{SS_{reg}}{Df_{Reg}}= \frac{45.9634}{3} = 15.32[/tex]

[tex]MS_{Error}= \frac{SS_{Error}}{Df_{Error}} = \frac{2.6218}{11} = 0.238[/tex]

[tex]F_{H_0}= \frac{MS_{Reg}}{MS_{Error}}= \frac{15.32}{0.238}= 64.37[/tex]

p-value  < .00001

At a 5% significance level, there is enough evidence to reject the null hypothesis. This means that the family income, family size and the addition to savings modify jointly the average spending of families.

d.

Individual tests:

There are two possible statistics to test the significance of each independent variable: [tex]t= \frac{b_i-\beta_i }{S_{b_i}} ~~t_{n-3}[/tex] ∀ i= 1, 2, 3, or [tex]F=\frac{MS_{X_i}}{MS_{Error}} ~F_{Df_{X_i}; Df_{Error\\}}[/tex]

Since the output doesn't give us the information of the individual ANOVA, you have to use the t-test (Df: n-3= 12-3= 9) for these hypotheses. Using the p-value approach. the decision rule for the three hypothesis will be:

If p-value ≤ α ⇒ Reject null hypothesis.

If p-value > α ⇒ Do not reject the null hypothesis.

1)

H₀: β₁ = 0

H₁: β₁ ≠ 0

α: 0.05

[tex]t_{H_0}= \frac{b_1-\beta_1 }{Sb_1}= \frac{0.7992-0}{0.074}= 10.8[/tex]

p-value < .00001 ⇒ Decision is to reject the null hypothesis.

2)

H₀: β₂ = 0

H₁: β₂ ≠ 0

α: 0.05

[tex]t_{H_0}= \frac{b_2-\beta_2 }{Sb_2}= \frac{0.2280-0}{0.190}= 1.2[/tex]

p-value: 0.260773 ⇒ The decision is to not reject the null hypothesis.

3)

H₀: β₃ = 0

H₁: β₃ ≠ 0

α: 0.05

[tex]t_{H_0}= \frac{b_3-\beta_3 }{Sb_3}= \frac{-0.5796-0}{0.920}= -0.63[/tex]

p-value: 0.544355 ⇒ The decision is to not reject the null hypothesis.

So, at a 5% significance level, it seems that the three independent variables influence jointly the variation on the average spending of the families, but looking at them separately, only the income of the families seems to affect their spending habits significantly while the family size or their addition to savings don't seem to have major effect over their spending habits.

I hope this helps!

Answer:

17.85 feet.

Step-by-step explanation:

Area = 1/4 * 3.14 * r^2  where r is the radius

So r^2 = 19.625 / (1/4 * 3.14)

r^2 = 25

r = 5 feet.

The perimeter = 2r + 1/4 * 2* 3.14*r

= 2*5 + 7.85

= 17.85 feet.

Answer:

D

Step-by-step explanation:

In a 30-60-90 triangle, the longer leg is [tex]\sqrt{3}[/tex] times larger than the smaller leg. The length of the shorter leg is therefore:

[tex]\dfrac{18}{\sqrt{3}}= \\\\\\\dfrac{18\sqrt{3}}{3}= \\\\\\6\sqrt{3}[/tex]

Hope this helps!

Answer:

32 cm^3.

Step-by-step explanation:

Formulas for calculating:

sphere's volume - ;[tex]V_{sphere}=\frac{4\pi r^3}{3}[/tex]

cylinder's volume -  .[tex]V_{cylinder}=\pi r^2 h[/tex]

Note that h=2r (height of the sphere consists of two radius).

Then  [tex]V_{cylinder}= \pi r^2 h=\pi r^2 2r= 2\pi r^3[/tex]

Since  [tex]V_{sphere}= \frac{4\pi r^3}{3}[/tex]

on calculating we get

[tex]V_{cylinder}= \frac{3V_{sphere}}{2}\\ \Rightarrow V_{sphere}=\frac{2V_{cylinder}}{3} =\frac{2\times48}{3} =32 cm^3[/tex]

Answer:

a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.

b) [tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]

[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]

And within 2 deviations from the mean we have 95% of the values.

Step-by-step explanation:

For this case we know that the distribution of the temperatures have the following parameters:

[tex] \mu = 98.19, \sigma =0.61[/tex]

Part a

From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.

Part b

We can calculate the number of deviations from the mean with the z score with this formula:

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

And using this formula we got:

[tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]

[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]

And within 2 deviations from the mean we have 95% of the values.

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean salary of city 1 librarians

x2 = sample mean salary of city 2 librarians

s1 = sample standard deviation for city 1

s2 = sample standard deviation for city 2

n1 = number of soles for city 1

n1 = number of soles for city 2

For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (15 - 1) + (15 - 1) = 28

z = 2.048

x1 - x2 = 28,900 - 30,300 = - 1400

Margin of error = 2.048√(s1²/n1 + s2²/n2) = 2.036√(2300²/15 + 2100²/15)

= 1647

The upper boundary for the confidence interval is

- 1400 + 1647 = 247

The lower boundary for the confidence interval is

- 1400 - 1647 = - 3047

Answer:

[tex]cos(-\theta) = -0.73[/tex]

Step-by-step explanation:

It is given that:

[tex]sin(\theta -\dfrac{\pi}{2}) = 0.73[/tex]

Formula to be used:

[tex]1.\ sin(-x) = -sinx\\2.\ sin(\dfrac{\pi}{2}-x) = cosx\\3.\ cos(-x) = cosx[/tex]

Using Formula (1) written above:

[tex]\Rightarrow sin (\theta - \dfrac{\pi}{2})=sin(-(\dfrac{\pi}{2}-\theta ))\\\Rightarrow -sin(\dfrac{\pi}{2}-\theta)[/tex]

Now, using Formula (2) written above:

[tex]\Rightarrow -sin(\dfrac{\pi}{2}-\theta) = -cos \theta[/tex]

So, we can say that:

[tex]sin(\theta -\dfrac{\pi}{2}) = -cos\theta = 0.73 ...... (1)[/tex]

We have to find the value of [tex]cos(-\theta)[/tex].

Using Formula (3) written above:

[tex]cos(-\theta) = cos\theta[/tex]

So, ultimately we need to find the value of [tex]cos\theta[/tex]

Using equation (1):

[tex]-cos\theta = 0.73\\\Rightarrow cos\theta = -0.73[/tex]

So, the answer is [tex]cos(-\theta) = -0.73[/tex].

Answer:

The answer is A: ( - ∞, 1 )

Step-by-step explanation:

Answer:

Step-by-step explanation:

Look at the population statistics. Let's say it contains:

- data on the age groups available in the population

- data on the probability that a child in the population has inadequate calcium intake OR data that a child in the population does not have the deficiency. If you're given one of these, the other can be gotten by subtracting the probability value given from 1.

So let's say there are children from ages 5 to 15 in this population and the probability that a child in this population has the deficiency is 0.23 (not all the children in this population of 5-15 year olds may have the deficiency) while the probability that a child in this population does not have the deficiency is [1-0.23] = 0.77

So if you pick a child randomly from the population and he has this deficiency, what is the probability that he or she is between 11 and 13 years old?

From ages 5-15, ages 11, 12 and 13 are 3 ages. The total number of ages is 11 ages.

3÷11 = 0.2727

This is the probability that a child picked or selected at random from the population is 11, 12, or 13 years old.

0.2727 × 0.23 = 0.0627

This is the probability that a child picked at random is BOTH within the age bracket 11 to 13 AND has the deficiency!

Apply this.

Answer:

90/4= 12.9

1*3/4= 0.75

Step-by-step explanation:

Answer:

the elevation of base camp is 35 ft

Step-by-step explanation:

Starting at 65 feet elevation, and the descending 30 feet to reach base camp, that means that base camp is at: 65 ft - 30 ft = 35 ft elevation

Answer:

35 feet

Step-by-step explanation:

65 feet- 30 feet= 35 feet is the elevation of the base

Answer:

B:

Step-by-step explanation:

If we rotate the 3-D figure around y-axis we'll obtain a cone with a radius of 3 units

Answer: 5h/3

Step-by-step explanation:

12 hours passed, and 20 degrees dropped.

Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.

Hope that helped,

-sirswagger21

Answer:

5h 3

Step-by-step explanation:

12 hours passed, and 20 degrees dropped.

Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.

Hope that helped,

-sirswagger21

Answer:

a) (V)  = 904.78 of a sphere = 288pi diameter = 12

(V) = 1728cm^3 of a cube = face diagonal = 16.9cm

b) Difference Volume = 1728-904.78 = 823.22cm^3

Step-by-step explanation:

To find volume of an inscribed sphere within a square cube

We use 4 π/3 * r^3 for the equation

As Radius = 6 = 6cm this is the only thing plugged into the equation to create a division first then a multiplication square of radius and then a multiplication. 4pi /3 * 6^3

r^3 = 216

4pi/3 = 4.18

4.18 * 216 = 904.78

This means the answer is 288 pi cm^3.

Answer:

volume of gemstone = 905 cm^3

volume of empty space = 823 cm^3

Step-by-step explanation:

volume of cube = s^3, where s = length of edge

volume of sphere = (4/3)(pi)r^3, where r = radius of sphere

The cube has a 12-cm edge. The sphere fits tightly inside the cube, so the diameter, d, of the sphere is 12 cm. The radius is half the diameter, so radius = r = diameter/2 = 12 cm/2 = 6 cm.

a)

volume of sphere = (4/3)(pi)r^3

volume of sphere = (4/3)(3.14159)(6 cm)^3

volume of sphere = 905 cm^3

b)

The empty space is the difference between the volume of the cube and the volume of the sphere.

volume of cube = s^3

volume of cube = (12 cm)^3

volume of cube = 1728 cm^3

empty space = volume of cube - volume of sphere

empty space = 1728 cm^3 - 905 cm^3

empty space = 823 cm^3

Step-by-step explanation:

The graph of y = tan x is shown. We need to find what y equals when x = 0 (because in y = tan 0, x is replaced with 0)

So you can either find where x = 0 on the graph, or you can take the tangent of 0 to find your answer.

The value of the trigonometric function [tex]y = \tan x[/tex] at (x = 0) is 0 and this can be determined by using the given graph.

Given :

The graph of [tex]y = \tan x[/tex].

The following steps can be used to determine the value of [tex]y = \tan 0[/tex] :

Step 1 - The graph of the trigonometric function [tex]y = \tan x[/tex] is given.

Step 2 - According to the given graph, at (x = 0) the value of y is also 0.

Step 3 - So, the value of the trigonometric function [tex]y = \tan x[/tex] at (x = 0) is:

[tex]y = \tan 0[/tex]

[tex]y = 0[/tex]

The value of the trigonometric function [tex]y = \tan x[/tex] at (x = 0) is 0.

For more information, refer to the link given below:

https://brainly.com/question/14375099

Answer:

  For each hour that Michelle drove, she traveled an additional 50 miles.

Step-by-step explanation:

The point (0, 350) tells you Michelle's trip is 350 miles long. The point (7, 0) tells you she completed it in 7 hours. The point (6, 50) on the graph tells you she has 50 miles remaining of the original 350 after 6 hours.

True: for each hour Michelle drove, she traveled an additional 50 miles.

Answer:

B. For each hour that Michelle drove, she traveled an additional 50 miles.

Step-by-step explanation:

Answer:

28.26 (Please mark as brainiest if you find it helpful )

Step-by-step explanation:Area the goat will eat is equal to the are of circle having radius 3m.

Area of circle  =  pi * r ^ 2

⇒  3.14 * (3) ^ 2   →  3.14 * 9

⇒ 28.26

Answer:

The slope of two parallel lines will always be the same. If the slope was slightly different, then the lines would intersect at some point, which breaks the definition of parallel lines.

The y-intercepts of two parallel lines have to be different, or else the two lines would be the same line. If the y-intercept and the slope are the same, then the lines will essentially equal each other.

Answer:

Sample Response: Two parallel lines will have the same slope. The slopes of parallel lines have to be equal. The y-intercepts of those two lines have to be different, otherwise they would be the same line. The x-intercepts of the parallel lines would also be different.

Step-by-step explanation:

edge 2020

Answer:

53

Step-by-step explanation:

Plugging in 32 for z, you get:

(32)/2+37=x

16+37=x

x=53

Hope this helps!

The solution of the linear equation z/2 + 37 = x at x at z = 32 will be 53.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given below.

z/2 + 37 = x

Then the solution of the linear equation z/2 + 37 = x at z = 32. Then the equation will be

x = 32/2 + 37

x = 16 + 37

x = 53

Thus, the solution of the linear equation z/2 + 37 = x at z = 32 will be 53.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

Answer: the value of the annuity when you retire is $130919

Step-by-step explanation:

We would apply the future value which is expressed as

FV = C × [{(1 + r)^n - 1}/r]

Where

C represents the yearly payments.

FV represents the amount of money

in your account at the end of 10 years.

r represents the annual rate.

n represents number of years or period.

From the information given,

r = 7% = 7/100 = 0.07

C = 20/100 × 47400 = $9480

n = 10 years

Therefore,

FV = 9480 × [{(1 + 0.07)^10 - 1}/0.07]

FV = 9480 × [{1.967 - 1}/0.07]

FV = 9480 × 13.81

FV = $130919

Answer:

25

Step-by-step explanation:

use a Poisson process to model the arrival.

the mean rate of arrivals  is λ=4.5

The standard deviation is calculated as:

σ==√λ =2.1213

The z-value for a 98% CI is z=2.3262.

If the 98% CI has to be within a error of 0.5 then:

Ul-Ll=2z*σ/√n=2*0.5=1

√n=z*σ=2.3262*2.1213=4.9346

√n=4.9346  and n = 4.9346^2=24.35 rounded to 25

The sample size needed is n=25.

Answer:

B

The mode is 11 and 3

The Median is 10

The mean is 12

Answer:

20:30 goes to 8:12

the rest goes to 6:18

Step-by-step explanation:

i may be wrong

Answer:

7:12 is equivalent to 6:18

20:30 is equivalent to 8:12

5:15 is equivalent to 6:18

Step-by-step explanation:

plz mark brainliest

Answer:

1) Antonio's statement

2) <A = 123

Step-by-step explanation:

1) Antonio's statement is incorrect. This is because the opposite angles of a quadrilateral add up to 180°. Erin was incorrect because the opposite angles of this quadrilateral are unequal.

2) 2x+7+5x-2 = 180° (opposite angles of quadrilateral)

Now

7x+5 = 180

7x = 175

x = 25

<A = 5x-2

= 5(25)-2

= 125-2

= 123

Answer:

  f(x) = -2/3(x +11) +5

Step-by-step explanation:

The point-slope form of the equation of a line will give you the desired linear function:

  y = m(x -h) +k . . . . . for slope m through point (h, k)

You are give point (x, f(x)) = (-11, 5) = (h, k), and you are given slope m = -2/3. Putting these values into the function form gives ...

  f(x) = -2/3(x +11) +5