Simplify. (5b2−3b+2)+(2b−4)
A.5b2+5b+6
B.5b2−5b−6
C.5b2−b−2
D.6b4−2

Answer: 18.75 lb.ft

Step-by-step explanation:

Given

Force required to stretch spring 8 in. is 18 lb

it can be written

[tex]\Rightarrow F=kx\\\Rightarrow 18=k(8)\\\\\Rightarrow k=\dfrac{18}{8}=\dfrac{9}{2}\ lb/in.[/tex]

Work done in stretching from its natural length to 10 in.

[tex]\Rightarrow W=\dfrac{1}{2}kx^2\\\\\Rightarrow W=0.5\times \dfrac{9}{2}\times (10)^2\\\\\Rightarrow W=225\ lb.in.\ or\\\Rightarrow W=18.75\ lb.ft[/tex]

Answer:

Step-by-step explanation:

Since the slide is inclined at an angle of 52.0° to the horizontal, Danny's weight (mass, m) of 46.0 pounds has a component W = mgcos52.0° perpendicular to the incline and W' = mgsin52.0° parallel to the incline where g = acceleration due to gravity = 32 ft/s²

The perpendicular component of Danny's weight is the normal force to the incline. This normal force would determine the magnitude of the friction along the incline.

Since the wax paper makes the incline surface frictionless, so, there is no friction along the surface and thus the only horizontal force acting along the surface is the component of Danny's weight along the surface.

For Stacey to keep Danny from sliding down along the incline, the force she applies along the incline, F must be equal to the component of Danny's weight along the incline.

So, F = W'

F = mgsin52.0°

F = 46lb × 32 ft/s² × sin52°

F = 1472 lb-ft/s² 0.7880

F = 1159.95 lb-f

F ≅ 1160 lb-f

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

May August

95 100

72 80

78 95

50 65

89 85

92 98

75 70

90 96

65 87

The appropriate test is a paired t test :

d = difference between May and August

d = (-5, -8, -17, -15, 4, -6, 5, -6, -22)

The hypothesis :

H0 : μd = 0

H1 : μd ≠ 0

The test statistic :

T = dbar / (Sdbar/√n)

Where, dbar and Sdbar are the mean and standard deviation of 'd' respectively.

Using calculator :

dbar = - 7.777 ; Sdbar = 9.052

Test statistic = - 7.777 / (9.052 /√9)

Test statistic = - 2.577

The Pvalue, df = n - 1 = 9 - 1 = 8

Pvalue(-2.577, 8) = 0.0327

At α = 0.05

Pvalue < α ; WE reject the H0 ; and conclude that there has been a change in score

Answer:

There are 4 questions to answer here and the answers are given below:

1. COMBINATION

2. SET 2  

3. {S2, S3, S4, S5}

4. { }  OR  ∅

Step-by-step explanation:

The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.

The assignment has 5 questions in all. The options for each question are listed below and separated by commas:

1. True, False

2. True, False

3. A, B, C, D

4. A, B, C, D

5. A, B, C, D

Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.

QUESTION 1

If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?

ANSWER TO QUESTION 1

You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only two possible answers (also known as options) while questions 3, 4 and 5 have four possible answers/options to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.

QUESTION 2

Find "Set 1 ∩ Set 2" and explain the notation in the sentence.

ANSWER TO QUESTION 2

First list out relevant information:

- The correct answers to questions 3, 4 and 5 are respectively C, B, A

- The universal set consists of five students: S1, S2, S3, S4, S5 hence

Ц = {S1, S2, S3, S4, S5}

Next, enlist the elements of each defined set

Set 1: {S1, S2, S3, S4, S5}     Set 2: {S2, S3, S4}     Set 3: {S4, S5}

Note: Set 1 is equal to the universal set.

Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.

In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.

If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:

The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.

So the answer to question 2 is

Set 1 ∩ Set 2 = Set 2

QUESTION 3

Find "Set 2 ∪ Set 3" and explain the notation in the sentence.

ANSWER TO QUESTION 3

The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.

So, Set 2 union Set 3 = {S2, S3, S4, S5}

As earlier stated, Student 4 isn't appearing twice in the new set.

QUESTION 4

Find the ' of Set 1 and explain the notation in this sentence.

ANSWER TO QUESTION 4

The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.

Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!

Set 1 ' Ц = { }  or  ∅

where the empty bracket symbol and the slashed zero symbol represent null set.

Kudos!

Answer:

Option d

Step-by-step explanation:

(17+(-2))/2 , (8+1)/2

which is,

15/2, 9/2

Answered by GAUTHMATH

Step-by-step explanation:

The time dilation formula is given by

[tex]F(t) = \dfrac{t}{\sqrt{1-v^2}}[/tex]

where t is the time measured by the moving observer and F(t) is the time measured by the stationary earth-bound observer and v is the velocity of the moving observer expressed as a fraction of the speed of light.

a) If the observer is moving at 80% of the speed of light and observes an event that lasts for 1 second, a stationary observer will see the same event occurring over a time period of

[tex]F(t) = \dfrac{1\:\text{s}}{\sqrt{1-(0.8)^2}}[/tex]

[tex]\:\:\:\:\:\:\:=\dfrac{1\:\text{s}}{\sqrt{1-(0.8)^2}} =\dfrac{1\:\text{s}}{\sqrt{1-(0.64)}}[/tex]

[tex]\:\:\:\:\:\:\:=1.67\:\text{s}[/tex]

This means that any event observed by this moving observer will be seen by a stationary observer to occur 67% longer.

b) Given:

t = 1 second

F(t) = 2 seconds

We need to find the speed of the observer such that an event seen by this observer will occur twice as long as seen by a stationary observer. Move the term containing the radical to the left side so the equation becomes

[tex]\sqrt{1-v^2} = \dfrac{t}{F(t)}[/tex]

Take the square of both sides, we get

[tex]1 - v^2 =\dfrac{t^2}{F^2(t)}[/tex]

Solving for v, we get

[tex]v^2 = 1 - \dfrac{t^2}{F^2(t)}[/tex]

or

[tex]v = \sqrt{1 - \dfrac{t^2}{F^2(t)}}[/tex]

Putting in the values for t and F(t) we get

[tex]v = \sqrt{1 - \dfrac{(1\:\text{s})^2}{(2\:\text{s})^2}}[/tex]

[tex]v = \sqrt{1 - \dfrac{1}{4}} = \sqrt{0.75}[/tex]

[tex]\:\:\:\:=0.866[/tex]

This means that the observer must moves at 86.6% of the speed of light.

Answer:

-17

Step-by-step explanation:

–3(y + 2)2 – 5 + 6y

(–3y -6)2 – 5 + 6y

-6y -12 - 5 + 6y

-17

Answer:

...

Step-by-step explanation:

seeee the above picture

Answer:

y=-1/5x-11/5

Step-by-step explanation:

perpendicular, product of both gradients = -1

hence, slope = -1/5

y=-1/5x+c

sub y=-1, x=-6

-1=-1/5(-6)+c

c = -1-6/5=-11/5

y=-1/5x-11/5

Answer:

The number is 30.

Step-by-step explanation:

Let the number be x

so

x + (130% of x) = 69

x + 13x/10 = 69

or, (10x + 13x)/10 = 69

or, 23x = 690

or, x = 690/23

so, x = 30

Answer: 30

Step-by-step explanation:

its correct on rsm

Let missing side be x

Using basic proportionality theorem

[tex]\\ \sf\longmapsto \dfrac{18}{14}=\dfrac{27}{x}[/tex]

[tex]\\ \sf\longmapsto \dfrac{9}{7}=\dfrac{27}{x}[/tex]

[tex]\\ \sf\longmapsto 9x=7(27)[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{7(27)}{9}[/tex]

[tex]\\ \sf\longmapsto x=21[/tex]

Answer:

allows us to accept the null hypothesis

Explanation:

The z test(in a normal distribution) score for the critical region determines whether we reject the null hypothesis(H0) or accept the null hypothesis(reject or fail to reject the null hypothesis). If we fail to reject the null hypothesis, then we have accepted the alternative hypothesis (H1). The critical region rejection for z test is calculated using alpha and z score, if z score is greater or less than alpha(positive or negative), we reject the null hypothesis.

Answer:

2[(x^2 + 7)(x + 5)]

Step-by-step explanation:

Note that the ratio of the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping, but first we can separate out the common scalar factor 2...

2x3+10x2+14x+70=

2(x3+5x2+7x+35)

2((x3+5x2)+(7x+35))

2(x2(x+5)+7(x+5))

2(x2+7)(x+5)

Answer:

The answer is D. 2[(x2 + 7)(x + 5)]

Step-by-step explanation:

Answer: About 63 in²

Step-by-step explanation:

Area of circle = π · r²

Area of large pizza:

[tex]\pi *r^{2} =3.14*6^{2} =3.14*36=113.04[/tex]

Area of small pizza:

[tex]\pi *r^{2} =3.14*4^{2} =3.14*16=50.24[/tex]

Difference in area:

[tex]113.04-50.24=62.8[/tex]

Answer: A: 22, 33, 45.5, 56, 59

Step-by-step explanation:

The minimum is the lowest number in the data, in this case, it was 22.

Q1 is the median of the lower quartile range, anything below the median of the overall data.

Median, the middle number in the overall data. You first need to put them from lowest to highest (numerical order). After that, I find it a lot easier to cross one from each side until I'm either left with one or two. If I'm left with one, then that is my median for the overall data set. If I'm left with two, then I simply need to add both the numbers together and divide it by 2. Typically if it is a whole number, and the numbers are 1 number value away from each other, it is usually just 0.5 more of the lower value of the two. (For example, the two numbers I come down to is 10 and 11. The median would be 10.5).

Q3 is the exact same principle as Q1 just on the upper quartile range. Just repeat what you did in Q1 but for the numbers above the overall median of the data set.

Maximum is the highest number in the data set, in this case, it was 69.

Hope this helps!

Answer:

F(x) = 45*x - (5/2)*x^2 + C

Step-by-step explanation:

Here we want to find the antiderivative of the function:

f(x) = 45 - 5*x

Remember the general rule that, for a given function:

g(x) = a*x^n

the antiderivative is:

G(x) = (a/(n + 1))*a*x^(n + 1) + C

where C is a constant.

Then for the case of f(x) we have:

F(x) = (45/1)*x^1 - (5/2)*x^2 + C

F(x) = 45*x - (5/2)*x^2 + C

Now if we derivate this, we get:

dF(x)/dx = 1*45*x^0 - 2*(5/2)*x

dF(x)/dx = 45 - 5*x

Answer:

10c^2-c-2

Step-by-step explanation:

FOIL method

or just multiply all of the numbers by each other, if you get 4 numbers you did it right then simplify;

(5c+2)(2c-1) 5c*2c; 2*-1; -1*5c; 2*2c = 10c^2, -2, -5c, 4c, simplify, 10c^2 -c -2. Hope this helps :)

Answer:

10c² - c - 2

Step-by-step explanation:

(5c+2)(2c-1)

10c² - 5c + 4c - 2

10c² - c - 2

x = 4

Every step shown. Once you become used to doing this you will almost be able to do the basic one's in your head without writing much down.

Explanation:

Let the unknown value be  

x

Converting the words into numbers:

First part: "15 times a certain number"  → 15 x

Second part: "plus 5 times the same number" → 15 x + 5 x

The last part: " is 80" ->  15x + 5 x = 80

We are counting  x ' s . 15 of them plus another 5 of them gives a total of 20.

So 15 x + 5 x = 20 x = 80

Divide both sides by 20

20 x ÷ 20 = 80÷ 20

20/20x=80/20

x=4

Let the number be x

ATQ

[tex]\\ \sf\longmapsto 15x+5x=80[/tex]

[tex]\\ \sf\longmapsto (15+5)x=80[/tex]

[tex]\\ \sf\longmapsto 20x=80[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{80}{20}[/tex]

[tex]\\ \sf\longmapsto x=4[/tex]

Answer: C) (1,4)

Step-by-step explanation:

The intersection point is where f(x) = g(x)

x³ + 3x = x² + 3

x³ - x² +3x - 3 = 0

Answer:

A=(78.5)cm²

Step-by-step explanation:

d=10

r=10/2=5

A=πr²

A=3.14*5²

A=3.14*25

A=78.5cm²

Answer: d=10cm

According to the formula i.e. A=πr²

first we need 'r'

as r=d/2

hence,  r= 10cm/2

r=5cm

put r=5 in formula

=3.14(5cm)²

=3.14×25cm²

=78.5cm²

Answer:

62 of the email messages were spam

Step-by-step explanation:

Let the number of spam and other messages be s and o respectively.

Total number of messages= 78

s +o= 78 -----(1)

s= 4o -2 -----(2)

Substitute (2) into (1):

4o -2 +o= 78

Simplify:

5o -2= 78

+2 on both sides:

5o= 78 +2

5o= 80

Divide both sides by 5:

o= 80 ÷5

o= 16

Since s +o= 78, s= 78 -o.

s= 78 -16

s= 62

Rectangular prism and cylinder make up a camera.

A cube is a rectangular prism with all of its sides being the same length, a triangular prism has a triangle as its base, and a rectangular prism has a rectangle as its foundation. Another form of right prism that has a circle as its basis is a cylinder.

A rectangular prism includes a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it contains three dimensions- the base width, the height, and the length. The top and base of the rectangular prism exist rectangular. The pairs of opposite faces of a rectangular prism exist as identical or congruent.

A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it includes been regarded as a prism with a circle as its base.

Hence, Rectangular prism and cylinder make up a camera.

To learn more about rectangular prisms and cylinders refer to:

https://brainly.com/question/15594686

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Answer:

20kg of rice in each bag

Step-by-step explanation:

we have 60kg of rice and 3 bags. we know that we need to have an eqal amount of rice in each bag so we can divide the 60kgs of rice by 3.

60÷3=20

Checking our Answer:

we can check our work by doing the opposite of division which is multiplication. to check our work we'd have to multiply the dividend (in our case 3) and our quotient (in our case 20) to see if we get the larger dividend (in our case 60) as our answer.

3×20=60

Answer:

D. isosceles triangle

Step-by-step explanation:

Ed22

A triangle with at least 1-fold reflectional symmetry is isosceles triangle, option D is correct.

A triangle is a three-sided polygon that consists of three edges and three vertices.

An isosceles triangle will always have at least 1-fold reflectional symmetry.

This is because an isosceles triangle has two congruent sides and two congruent angles.

If we draw a perpendicular bisector of the base (the side that is not congruent), it will bisect the base and the angle opposite to the base.

This means that the triangle is symmetric with respect to this line of reflection, which is the line of symmetry.

Therefore, the correct answer is isosceles triangle.

To learn more on Triangles click:

https://brainly.com/question/2773823

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Answer:

The 90% confidence interval is (0.0131, 0.0845).

Step-by-step explanation:

Before finding the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Old process:

125 out of 580, so:

[tex]p_O = \frac{125}{580} = 0.2155[/tex]

[tex]s_O = \sqrt{\frac{0.2155*0.7845}{580}} = 0.0171[/tex]

New process:

130 out of 780. So

[tex]p_N = \frac{130}{780} = 0.1667[/tex]

[tex]s_N = \sqrt{\frac{0.1667*0.8333}{780}} = 0.0133[/tex]

Distribution of the difference:

[tex]p = p_O - p_N = 0.2155 - 0.1667 = 0.0488[/tex]

[tex]s = \sqrt{s_O^2+s_N^2} = \sqrt{0.0171^2 + 0.0133^2} = 0.0217[/tex]

Confidence interval:

[tex]p \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower bound of the interval is:

[tex]p - zs = 0.0488 - 1.645*0.0217 = 0.0131[/tex]

The upper bound of the interval is:

[tex]p + zs = 0.0488 + 1.645*0.0217 = 0.0845[/tex]

The 90% confidence interval is (0.0131, 0.0845).

Answer:

D. 212 degrees Fahrenheit and 100 degrees Celsius.

Step-by-step explanation:

The boiling point of water in Celsius is 100.

The way to calculate Celsius to Fahrenheit:

F = (C × 9/5) + 32

So we plug in 100 for C.

F = (100 × 9/5) + 32

F = 180 + 32

F = 212

Therefore, the numbered pair is 212 degrees F and 100 degrees  C.

Answer:

The inequality shown in the graphic is [tex]y > 4x + 1[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line is given by:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept(value of y when x = 0).

Inequality:

Values greater than the dashed line, dashed so the line is not part of the inequality, thus, the inequality is:

[tex]y > mx + b[/tex]

Dashed line:

The dashed line goes through (0,1) and (1,5).

Point (0,1) means that when [tex]x = 0, y = 1[/tex], so [tex]b = 1[/tex], and:

[tex]y > mx + 1[/tex]

Finding the slope:

When we have two points, the slope is given by the change in y divided by the change in x. In this question, we have point (0,1) and (1,5), so:

Change in y: 5 - 1 = 4

Change in x: 1 - 0 = 1

Slope: [tex]m = \frac{4}{1} = 4[/tex]

What inequality is shown in the graph?

[tex]y > 4x + 1[/tex]

Answer:

[tex]L_x=5.3 inches[/tex]

Step-by-step explanation:

Average length [tex]\=x =5.3 inches[/tex]

Standard deviation [tex]\sigma=0.2 inches[/tex]

Sample size [tex]n=50[/tex]

Generally The point estimate for the mean length of all bolts in inventory is

[tex]L_x= \=x[/tex]

[tex]L_x=5.3 inches[/tex]

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