Which numbers belong to the solution set of the Inequality? x + 9 < 78

Answer:

A.

Step-by-step explanation:

In the attached file

Answer:

H = 1/30

H = 0.0333

0.033

Step-by-step explanation:

The time spent waiting at a traffic light can be considered a random variable with values from 0 seconds,

it’s green when you approach and can go on through, to 30 seconds with the following distribution shape

The entire area under the distribution curve must be 1.

Let assume the Shape is rectangle

Given

Time taken from 0s to 30s = 30s - 0s = 30s

To find height of the distribution?

Let H = the height of the distribution

Based on the above assumption;.

H * 30 = 1 --- make H the subject of formula

H = 1/30

H = 0.0333

To three decimal places is 0.033

Answer:

57.39% probability that between 50 and 60 of them were in favor of leaving the U.K.

Step-by-step explanation:

I am going to use the normal approximmation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 135, p = 0.38[/tex]

So

[tex]\mu = E(X) = np = 135*0.38 = 51.3[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{135*0.38*0.62} = 5.6397[/tex]

What is the probability that between 50 and 60 of them were in favor of leaving the U.K.?

Using continuity correction, this is [tex]P(50-0.5 \leq X \leq 60 + 0.5) = P(49.5 \leq X \leq 60.5)[/tex]. So this is the pvalue of Z when X = 60.5 subtracted by the pvalue of Z when X = 49.5. So

X = 60.5

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

[tex]Z = \frac{60.5 - 51.3}{5.6397}[/tex]

[tex]Z = 1.63[/tex]

[tex]Z = 1.63[/tex] has a pvalue of 0.9484

X = 49.5

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

[tex]Z = \frac{49.5 - 51.3}{5.6397}[/tex]

[tex]Z = -0.32[/tex]

[tex]Z = -0.32[/tex] has a pvalue of 0.3745

0.9484 - 0.3745 = 0.5739

57.39% probability that between 50 and 60 of them were in favor of leaving the U.K.

Answer:

420 Square Units

Step-by-step explanation:

7*12*5 = 420 units

Answer: I believe this is it

The required reflection of the given points are A' = (5, -1), B' = (1, -3), C' = (-2, -2), D' = (-5, -4)

If we have any point say P(x, y) then their reflection around x -axis is

P'(x, -y)

Therefore around x-axis reflection only y coordinate changes

here we have the points

A = (5, 1), B = (1, 3), C = (-2, 2), D = (-5, 4)

Therefore the reflected points are

A' = (5, -1), B' = (1, -3), C' = (-2, -2), D' = (-5, -4)

The presentation is attached in the image

This is the conclusion to the answer.

Learn ore about reflection of the points here-

https://brainly.com/question/7243416

#SPJ2

Answer:

  0.33%

Step-by-step explanation:

The account value when principal P is compounded continuously at annual rate r for t years is given by ...

  A = Pe^(rt)

For the given values, we can solve for r:

  4193.89 = 4125e^(r·5)

We can divide by 4125, take the natural log, then divide by the coefficient of r to find the value of r:

  ln(4193.89/4125)/5 = r ≈ 0.33%

The interest rate is about 0.33%.

Answer:

D. 39°

Step-by-step explanation:

mAB = (3x + 9°)

mCD = (11x – 71)

From the diagram: |AB|=|CD|

Since arcs AB and CD are subtended by a chord of equal length.

mAB=mCD

3x + 9°=11x – 71°

Collect like terms to solve for x

11x-3x=9°+71°

8x=80°

x=10°

Therefore, the measure of AB:

mAB = (3x + 9°)

=3(10)+9

=30+9

=39°

The correct option is D.

Answer:

Step-by-step explanation:

[tex]V=whl=15*7*6=630ft^3(truck)[/tex]

[tex]V=whl=1.25*2.5*2=6.25ft^2(boxes)[/tex]

To determine how many boxes can go in each truck you have to divide the volumes with ach other so 630/6.25 which equals 100.8

So you could say 2 trucks because each truck can carry 100.8 boxes each

[tex]V=\frac{1}{4} h\sqrt{-a^4+2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4} \\V=\frac{1}{4} *7.1*\sqrt{-4^4+2*(4*5)^2+2*(4*4)^2-5^4+2*(5*4)^2-4^4} \\=55.42m^3\\(chalet)[/tex]

There is allowed 1 person per 15m^3 and there are 5 people. Only 3 people can stay in the chalet equalling 45m^3 leaving 10m^3 left thus, not allowing anymore people to stay in the chalet. So the family cant meet the fire safety standards with 5 people

Answer:

  9) 630 ft^3; 6.25 ft^3; 2 trucks (3, if you consider space utilization)

  10) 71 m^3; 4 persons; no

Step-by-step explanation:

9) The volume of the truck is the product of the dimensions:

  V = LWH = (15 ft)(7 ft)(6 ft) = 630 ft^3 . . . truck V

Likewise, the volume of a storage box is the product of its dimensions:

  V = LWH = (2 ft)(2.5 ft)(1.25 ft) = 6.25 ft^3 . . . box V

If the boxes pack well into the truck (they don't), then the number of boxes that would fit in the truck is the ratio of these volumes:

  number of boxes = (630 ft^3)/(6.25 ft^3) = 100.8

This suggests that half of the 200 boxes will fit in one truck, so 2 trucks are needed.

__

Comment on space utilization

In the real world, not all of the truck's interior space can be utilized. This is because not all of the truck dimensions are integer multiples of the box dimensions. 96 is about the most boxes that can be placed in the truck. (Fitting more than 90 requires boxes be first layered one way, then layered another way to fill as much of the remaining space as possible.) In the real world, 3 trucks are needed to move 200 of these boxes.

___

10) The area of the end triangle of the chalet is ...

  A = (1/2)bh = (1/2)(5 m)(7.1 m) = 17.75 m^2

Then the volume of the chalet is ...

  V = Bh = (17.75 m^2)(4 m) = 71 m^3 . . . volume of the chalet

At 15 m^3 per person, there is enough volume for ...

  (71 m^3)/(15 m^3/person) = 4.73 persons

4 persons can stay in the chalet.

No, the entire family cannot stay in the chalet.

Answer:

The density function of X is : [tex]h_{X} (x) = \left \{ {{\frac{2}{(1+2x)^{2} } \quad x\geq0} \atop {x=0 \qquad x<0 }} \right.[/tex]

Step-by-step explanation:

[tex]h_{X} (x) = \left \{ {{\frac{2}{(1+2x)^{2} } \quad x\geq0} \atop {x=0 \qquad x<0 }} \right.[/tex]

For easiness and clarity of expression, the calculations are handwritten and attached as files. The files are broken into bits for easy understanding. Check the six files below for the calculations.

Answer:

x = 20

Step-by-step explanation:

x° + 2x° + (x+10)° = 90°

3x° + x° + 10° = 90°

4x° + 10° = 90°

4x° = 90°-10°

4x° = 80°

x = 80/4

x = 20

Answer:

20°

Step-by-step explanation:

The sum of all three angles combined is 90°.  You can see this by the square at the corner.  This means that you have to add all of the angles together and set it equal to 90° to solve for x.

x° + 2x° + (x + 10)° = 90°

3x° + (x + 10)° = 90°

4x° + 10° = 90°

4x° = 80°

x = 20°

Answer:

416

Step-by-step explanation: pues creo que esa es tu respuesta :)

Answer:

see below

Step-by-step explanation:

The x intercept is where it crosses the x axis

It crosses at x = -7.5

(-7.5,0)

The y intercept is where it crosses the y axis

It crosses at y = 5.5

(0,5.5)

Answer:

y+6=14/9(x+2)

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

The area of the square garden=[tex]267$ ft^2[/tex]

Area of a Square of Side length s [tex]=s^2[/tex]

Therefore:

[tex]s^2=267$ ft^2\\$Take the square root of both sides\\s=\sqrt{267} \\$Side Lenght, s=16.34 ft (to the nearest hundredth place)[/tex]

Perimeter

Perimeter of a Square of Side length s=4s

Therefore, the perimeter of the garden =4*16.34=65.36 ft

Since 65 ft < 65.36 ft

Therefore, if you had 65 ft of fencing, it will not be enough to go around and cover the garden.

Answer:

110

Step-by-step explanation:

40% is the same as 40/100, which is equal to 0.4. Therefore, you can write the following equation:

0.4x=44

Divide both sides by 0.4 to isolate x:

x=44/0.4=110

Hope this helps!

Answer:

Step-by-step explanation:

The relevant relation is that the product of distances from the point of intersection of secants to the two points of intersection of each with the circle is a constant. The point of tangency counts as both points of intersection.

__

By way of example, the product of distances to the circle for the tangent segment is 10·10 = 100

This is also the product of the distances on the secant that intersects the tangent:

  100 = 5(5+x+9)

  20 = x +14 . . . . . divide by 5

  x = 6 . . . . . . . . . . subtract 14

__

The same is true when the secants intersect inside the circle:

  6·9 = y·3

  y = 18 . . . . . . divide by 3

Answer:

333 miliacres

Step-by-step explanation:

First of all, you should know  that 1 acre is the same as 4046.9 m²

So, 1/3 of those 4046.9 m² is fully covered by strawberries.

By the way, 4046.9m² . 1/3 = 1348.96 m². This is our planted field.

Let's convert the measure to acres, though:

1348.96 m² . 1 acre / 4046.9 m² = 0.333 acres

0.333 acres . 1000 / 1 acre = 333 miliacres

If you want to know in another unit, let's do another conversion

0.333 acre . 43560 square feet / 1 acre = 14520 square feet

Answer:

D

Step-by-step explanation:

Its D because there is one dot that's far away from the rest, so there is one outlier. Hopefully this was helpful, I really am not the best person at giving explanations

Answer:

D. There is one outlier.

Step-by-step explanation:

Most of the points on the scatterplot are contained in one cluster, but there is one point that is not in the same cluster as the others.

Answer:

1 hour and 40 min

Step-by-step explanation:

4 x 1 x 2.5=5/3=1 2/3=1 hr and 40 min

Answer:

16.666%

Step-by-step explanation:

100/6=16.66

Answer:

The null and alternative hypothesis in symbols would be:H0:μ=0.9

H1:μ≠0.9,

The null hypothesis in words would be:_____________.

1. The proportion of all people that prefer Trydint gum is 0.9

Step-by-step explanation:

The Null hypothesis should always be precise such as the given coin is biased. The null hypothesis is assigned a numerical value.

For example the average height of all students in a college is 62 inches. Symbolically it is written as :H0:μ=62

An alternative hypothesis is any other hypothesis which we accept when the null hypothesis is rejected.If the null hpothesis of the height of students is :H0:μ=62 then alternative hypothesis is H1:μ≠ 62

Answer:

H0: p = 0.9

H1: p ≠ 0.9

1. The proportion of all people that prefer Trydint gum is 0.9

Step-by-step explanation:

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 the case above;

The null hypothesis is that the proportion of all people that prefer Trydint gum is 0.9.

H0: p = 0.9

The alternative hypothesis is that the proportion of all people that prefer Trydint gum is not equal to 0.9.

H1: p ≠ 0.9

Answer:

e. two-sample z-test for two proportions

Step-by-step explanation:

He has two machines, which have a proportion of defective motherboards. He want to compare this two proportions.

He takes two samples, one for each machine, and calculate the proportion in order to statistically test if there are significant difference between the proportions.

Then, this is a two-sample z-test for two proportions

Answer:

The team won 33.33% of their games.

Step-by-step explanation:

Proportion and percentage of games won:

The proportion of games won is the number of games won divided by the total number of games.

The percentage of games won is the proportion multiplied by 100.

We have that:

8 wins in 24 games.

So

8/24 = 0.3333

0.3333*100 = 33.33%

The team won 33.33% of their games.

Answer:

Volume of water and air is 3,000 mm³

Step-by-step explanation:

Given:

Length of base = 15 mm

Width of base = 20 mm

Height of figure = 30 mm

Find:

Volume of water and air is inside each of the plastic ice cubes.

Computation:

Height of each rectangular pyramid = Height of figure / 2

Height of each rectangular pyramid = 30 / 2

Height of each rectangular pyramid = 15 mm

Volume of each rectangular pyramid = lbh / 3

Volume of each rectangular pyramid = [15 × 20 × 15] / 3

Volume of each rectangular pyramid = [4,500] / 3

Volume of each rectangular pyramid = 1,500 mm³

Volume of water and air is inside each of the plastic ice cubes = 2 × Volume of each rectangular pyramid

Volume of water and air is inside each of the plastic ice cubes = 2 × 1,500

Volume of water and air is inside each of the plastic ice cubes = 3,000 mm³

Answer:

x = 9

Step-by-step explanation:

First, we want to isolate variable x on the left side of the equation. We can do this by adding 13 to both sides.

x - 13 + 13 = - 4 + 13

x = 9

Answer:

[tex]x=9[/tex]

Step-by-step explanation:

to find the answer, add 13 to both sides of the equation.

[tex]x-13=-4\\ +13 = +13 \\x=9[/tex]

Answer:

  6500 lb

Step-by-step explanation:

The load limit of the bridge is ...

  (5000 kg)(2.2 lb/kg) = 11,000 lb

The total of truck and trailer cannot exceed this value, so the trailer's weight cannot exceed ...

  11,000 lb -4,500 lb = 6,500 lb . . . max trailer weight

Answer:

D : {3,5,7,9}

Step-by-step explanation:

The domain is the input to the function or in this case the x values

D : {3,5,7,9}

_________________________________

Hey!!!

Answer:

Domain:{3,5,7,9}

Explanation:

Let R be a relation from A to B.Then the set of first components or the set of elements of A are called domain.

Hope it helps

Good luck on your assignment

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