Which is a factor of: 2x2+10x+8 ?

Answer:

V =140 units^3

Step-by-step explanation:

The volume of the prism is V = Bh

Where B is the area of the base and h is the height

B is the area of the triangle

B = 1/2 (5 * 7) = 35/2

V = 35/2 * 8

V =140 units^3

let [tex] \gcd(a,b)= G[/tex] , $a\ge b$

$\therefore a=G\cdot m$ and $b=G\cdot n$

$a-b=Gm-Gn=G(m-n)$

Now, $\gcd(a-b,b)$ clearly is, $G$

Complete Question

An IQ test is designed so that the mean is 100 and the standard deviation is 24 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the simple mean is with in 3 IQ points of the true mean. Assume that standard deviation  = 24 and determine the required sample size using technology. Determine if this is a reasonable sample size for a real world calculation.

The required sample size ______ (round up to the nearest integer.

Answer:

The sample size is  [tex]n = 246[/tex]

Step-by-step explanation:

From the question we are told that

    The  mean is  [tex]\mu = 100[/tex]

     The  standard deviation is  [tex]\sigma = 24[/tex]

     The  margin of error is  [tex]E = 3[/tex]

Given that the confidence level  is  95% then the level of significance is mathematically evaluated as

         [tex]\alpha = 100 - 95[/tex]

         [tex]\alpha = 5\%[/tex]

=>        [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table the value is

            [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The sample size is evaluated as

          [tex]n = [ \frac{ Z_{\frac{\alpha }{2} } * \sigma }{E }]^2[/tex]

=>       [tex]n = [ \frac{ 1.96 * 24 }{3 }]^2[/tex]        

=>      [tex]n = 246[/tex]

to check if this n is applicable in real world then we calculate E and  compare it with the given E

Answer:

5(x) +3(y)<26

Step-by-step explanation:

Let x represent the number of cakes she will bake and let you know represent the nymber of quiche she will bake.

She will use less than 26 eggs while baking and 5 eggs for each cake and 3 eggs for each quiche.

The inequality representing the above statement iz given below.

5(x) +3(y)<26

Answer:

x = 8

y = 2√3

Step-by-step explanation:

Since this is a right triangle

x^2 = (4√3)^2 + 4^2 ➡ x^2 = 64 and x = 8

Using Euclidean theorem

y^2 = (x-6)(x - x - 6) = 6x - 36

y^2 = 6×8 - 36

y^2 = 12

y = 2√3

Answer:

1 ) x = 8,

2 ) y = 2√3

Step-by-step explanation:

Take a look at the outermost triangle. I can tell that this is a 30 - 60 - 90 triangle, as if the leg opposite to the 30 degree angle was x, the other respective leg, opposite to the 60 degree angle, would be x√3. Here this " x " would be 4, but don't let that confuse you with the x we have to solve for.

As this outermost triangle is right, x is present as the hypotenuse and we can solve through Pythagorean Theorem,

( 4√3 )² + ( 4 )² = x²,

48 + 16 = x² = 64,

x = √64 = 8

And an inner triangle, present with y being a leg, has a respective leg length of x - 6, or 8 - 6 = 2. Let's solve for y using Pythagorean Theorem once more,

y² + 2² = 4²,

y² = 16 - 4 = 12,

y = √12 = √2 [tex]*[/tex] 2 [tex]*[/tex] 3 = 2√3

Answer:

C y = 3/2x - 1/8

Step-by-step explanation:

We know that the line has a positive slope, because it goes up from the lower left to upper right

We can eliminate B and D

For y = 6x - 11/8

A slope of 6 is very steep

Putting in 6

y = 6*6 -approximately 1 = 35 so the value at 3 would be 35

This is too big

Checking C

y = 3/2(6) - 0 = 9 or 9  This would be about right

Answer:

[tex] s = \sqrt{30} - 2\sqrt{5} m [/tex]

Step-by-step explanation:

Given:

Formula for side length of cube, [tex] s = \sqrt{\frac{SA}{6} [/tex]

Where, S.A = surface area of a cube, and s = side length.

Required:

Difference in side length between a cube with S.A of 180 m² and a cube with S.A of 120 m²

Solution:

Difference = (side length of cube with 180 m² S.A) - (side length of cube with 120 m² S.A)

[tex]s = (\sqrt{\frac{180}{6}}) - (\sqrt{\frac{120}{6}})[/tex]

[tex] s = (\sqrt{30}) - (\sqrt{20}) [/tex]

[tex] s = \sqrt{30} - \sqrt{4*5} [/tex]

[tex] s = \sqrt{30} - 2\sqrt{5} m [/tex]

Answer: 2361.53

Step-by-step explanation:

Use long division and round.

(The 3 is repeated)

Answer:

[tex] {x}^{2} + 5x + 10[/tex]

Answer:

[tex]\large \boxed{x^2 +5x+10}[/tex]

Step-by-step explanation:

A polynomial is an expression that has variables, coefficients, and constants.

An example of a polynomial can be x² - 6x + 2.

Nearest 1000: 5000

Nearest 100: 4600

Nearest 10: 4580

Hope that helped!!! k

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Answer:

sorry gave wrong answer

Step-by-step explanation:

Answer:

Hello your question has some missing parts below is the complete question

In a survey of 2065 adults in a certain country conducted during a period of economic​ uncertainty, 63​% thought that wages paid to workers in industry were too low. The margin of error was 4 percentage points with ​95% confidence. For parts​ (a) through​ (d) below, which represent a reasonable interpretation of the survey​ results? For those that are not​ reasonable, explain the flaw.

part a:(We are 95 % confident 63 % of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.)

part b:  We are 91 % to 99 % confident 63 % of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.

part c:  We are 95 % confident the proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low was between 0.59 and 0.67. Is the interpretation reasonable?

part d: In 95 % of samples of adults in the country during the period of economic uncertainty, the proportion who believed wages paid to workers in industry were too low is between 0.59 and 0.67. Is the interpretation reasonable?

Answer : For part A :

The interpretation is flawed. No interval has been provided about the population proportion.  

part B :

The interpretation is flawed. The interpretation indicates that the level of confidence is varying.  

Part C

The interpretation is reasonable.

Part D

The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other intervals, which is not true.

Step-by-step explanation:

Given data: Population = 2065 ,

probability = 63% = 0.6,

margin of error = 4% = 0.04

confidence interval (95%) = ( 0.59,0.67 )  

For part A :

The interpretation is flawed. No interval has been provided about the population proportion.  this is because the confidence interval is not mentioned

part B :

The interpretation is flawed. The interpretation indicates that the level of confidence is varying.  this is because the confidence interval is a fixed value

Part C

The interpretation is reasonable.

this is because the confident level given is fixed

Part D

The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other intervals, which is not true.

Answer:

2 * (x + 2) = 50

Step-by-step explanation:

Let's call the unknown number x. "A number and 2" means that we need to add the numbers, therefore it would be x + 2. "Twice" means 2 times a quantity so "twice a number and 2" would be 2 * (x + 2). "Is" denotes that we need to use the "=" sign and because 50 comes after "is", we know that 50 goes on the right side of the "=" so the final answer is 2 * (x + 2) = 50.

Answer:

1/32v²sin2θ

Step-by-step explanation:

Given the expression r(theta) = 1/16v²sinθcosθ

According to double angle of trigonometry identity;

Sin2θ = sin(θ+θ)

Sin2θ = sinθcosθ + cosθsinθ

Sin2θ = 2sinθcosθ

sinθcosθ = sin2θ/2 ... **

Substituting equation ** into the question

1/16v²sinθcosθ = 1/16v²(sin2θ/2)

1/16v²sinθcosθ = 1/2×1/16v²(sin2θ)

1/16v²sinθcosθ = 1/32v²sin2θ

Hence using the double angle identity, the equivalent expression is 1/32v²sin2θ

Answer:

5/36 ; 1/12 ; 2/9 ; yes

Step-by-step explanation:

Given the following :

Roll of two fair dice : green and red

Probability = (number of required outcomes / number of total possible outcomes)

(a) What is the probability of getting a sum of 6?

Number of required outcomes = 5

P(sum of 6) = 5/36

b.) What is the probability of getting a sum of 10?

Number of required outcomes = 3

P(sum of 10) = 3 / 36 = 1/12

c.) What is the probability of getting a sum of 6 or 10?

P(getting a sum of 6) + P(getting a sum of 10)

(5/36) + (1/12) = (5 + 3) / 36

= 8/36 = 2/9

The events are mutually exclusive because each event cannot occur at the same time.

Answer:

C, 39.3 in²

Step-by-step explanation:

Lets first find the area of the rectangle part of the house.

To find the area of a rectangle its base × height.

So its 6×4=24 in².

Now lets find the area of the top triangle.

Area for a triangle is (base × height)/2.

The height is 3 inches, because its 7-4. While the base is 6 inches.

(6×3)/2=9 in².

To find the area of the half circle the formula, (piR²)/2.

The radius of the circle is 2 because its half of the diamter which is 4.

(pi2²)/2=6.283 in².

Now we just need to add up the area of every part,

24+9+6.283=39.283in²

Answer:

[tex]\{P^2: P\ E\ Z\ and\ 1\leq p\leq 10\}[/tex]

Step-by-step explanation:

Given

Range: = 1 to 100 (Inclusive)

Required

Determine the notation that represents the perfect square in the given range

Represent the range with P

P = 1 to 100

Such that the perfect squares will be P² and integers

In set notation, integers are represented with Z

The set notation becomes

[tex]\{P^2: P\ E\ Z\ and\ 1\leq p\leq 10\}[/tex]

The [tex]\leq[/tex] shows that 1 and 100 are inclusive of the set

Answer:

Distributive property, addition property

Answer:

additive identity

associative property of addition

distributive property

Step-by-step explanation:

Answer:

.25 hour / dollar

Step-by-step explanation:

We want hours per dollar

9 hours/ 36 dollars

1/4 hour / dollar

Work Shown:

T = average Celsius temperature two Sundays ago

8% = 8/100 = 0.08

8% of T = 0.08T

L = average Celsius temperature last sunday

L = 8% higher than T

L = T + (8% of T)

L = T + 0.08T

L = 1.00T + 0.08T

L = (1.00 + 0.08)T

L = 1.08T

The 1.08 refers to the idea that L is 108% of T

Answer:

b and d

Step-by-step explanation:

khan

Answer:

  34.43

Step-by-step explanation:

A differential of length in terms of t will be ...

  dL(t) = √(x'(t)^2 +y'(t)^2)

where ...

  x'(t) = 4cos(4t)

  y'(t) = 7cos(7t)

The length of c(t) will be the integral of this differential on the interval [0, 2π].

Dividing that interval into 10 equal pieces means each one has a width of (2π)/10 = π/5. The midpoint of pieces numbered 1 to 10 will be ...

  (π/5)(n -1/2), so the area of the piece will be ...

  sub-interval area ≈ (π/5)·dL((π/5)(n -1/2))

It is convenient to let a spreadsheet or graphing calculator do the function evaluation and summing of areas.

__

The attachment shows the curve c(t) whose length we are estimating (red), and the differential length function (blue) we are integrating. We use the function p(n) to compute the midpoint of the sub-interval. The sum of sub-interval areas is shown as 34.43.

The length of the curve is estimated to be 34.43.

Answer:

a. The H0 is number of correct guesses is 173

b. Standard Deviation of box is 0.3

c. z-test value is 7.70

d. The difference does not appear due to chances of Variation.

Step-by-step explanation:

The standard deviation is :

[tex]\sqrt{0.1 * 0.9}[/tex] = 0.3

The standard deviation of the box is 0.3 approximately.

Z-score is [tex]\frac{x-u}{standard error}[/tex]

Z-score = [tex]\frac{173-100}{9.4868}[/tex]

the value of z-score is 7.70.

Answer:

[tex]Win = 0.43[/tex]

Step-by-step explanation:

Given

Odds in favor of win = 43 to 57

Required

Express as a probability

We start by getting the sum of both odds

[tex]Sum = 43 + 57[/tex]

[tex]Sum = 100[/tex]

Next, we divide the required odd by the calculated sum to get the probability

Odds in favor of win is calculated as thus

[tex]Win= \frac{43}{100}[/tex]

[tex]Win = 0.43[/tex]

Hence, the probability is 0.43

Answer:

[tex]( - \sqrt{3} \: an d \: 1)[/tex]

Answer:

Step-by-step explanation:

Given a plane passing through the point(1, 5,-1) and perpendicular to the vector (1, 5, 1), the equation of the plane can be expressed generally as;

a(x-x₀)+b(y-y₀)+c(z-z₀) = 0 where (x₀, y₀, z₀) is the point on the plane and (a, b,c) is the normal vector perpendicular to the plane i.e (1,5,1)

Given the point P (1, 5, -1) and the normal vector n(1, 5, 1)

x₀ = 1, y₀ =5, z₀ = -1, a = 1, b = 5 and c = 1

Substituting this point in the formula we will have;

a(x-x₀)+b(y-y₀)+c(z-z₀) = 0

1(x-1)+5(y-5)+1(z-(-1)) = 0

(x-1)+5(y-5)+(z+1) = 0

x-1+5y-25+z+1 = 0

x+5y+z-1-25+1 = 0

x+5y+z-25 = 0

x+5y+z = 25

The final expression gives the equation of the plane.

Answer:

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

Step-by-step explanation:

Let be [tex]f(m, b) = m\cdot b - m^{2}[/tex], if [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex], the value of the expression:

[tex]f(3.48,96.52) = (3.48)\cdot (96.52)-3.48^{2}[/tex]

[tex]f(3.48,96.52) = 323.779[/tex]

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

Answer:

16.50

Step-by-step explanation:

Constant of proportionality = no of gallons of water per 1 minute.

In the first row, we have 16.50 gallons of water per 1 minute.

In the 2nd row, we have 24.75 gallons of water in 1.5 minutes. In 1 minute, we will have 24.75 ÷ 1.5 = 16.50 gallons

In the 3rd row, we have 33 gallons in 2 minutes. In 1 minute, we will have 33 ÷ 2 = 16.50 gallons.

We can see that there seems to be the same constant of proportionality for the 2nd and 3rd row, which is 16.50.

Thus, a relationship between gallons of water (w) and time (t), considering the constant, 16.50, can be written as: [tex] w = 16.50t [/tex]

This means the constant of proportionality, 16.50, is same for all rows.

Answer:

−4<x<−2

Step-by-step explanation:

8 > 4 − x > 6

8 > −x + 4 > 6

8 + −4 > −x + 4 + −4 > 6 + −4

4 > −x > 2

Since x is negative we need to divide everything by -1 which gives us...

−4 < x < −2

Answer:

As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means  chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.

Step-by-step explanation:

We formulate our null and alternative hypotheses as

H0 u≤ 6 ug     Ha : u > 6 ug

The significance level ∝ = 0.05

The test statistic used is

t = X` - u / s/ √n

which if H0 is true, has the students' t test with n-1 = 11 degrees of freedom.

The critical region t > t (0.05,11) = 1.796

We compute the t value from the data

Xi               Xi²

8.92         79.5664

6.99          48.8601

5.54          30.6916

5.73           32.8329

6.38           40.7044

5.51            30.3601

6.45           41.6025

7.50           56.25

8.48           71.9104

5.56          30.9136

6.90          47.61

6.46          41.7316          

80.42         553.0336      

Now x` = ∑x/ n = 80.42/12 = 6.70

S²= 1/n-1 ( ∑(xi- x`)²= 1/11 ( 553.034 - (80.42)²/12)

= 1/11 (553.034-538.948) = 1.2805

s= 1.1316

Putting the values in the test statistics

t = X` - u / s/ √n = 6.70- 6 / 1.1316 / √12

= 2.1698

The critical region t > t (0.05,11) = 1.796

As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means  chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.

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▹ Answer

x = 5

▹ Step-by-Step Explanation

The x-axis and y-axis are labeled on the graph. The x-axis is the horizontal axis. Between 4 and 6, there is a missing number. That number should be 5, leaving us with an x-value of 5 for Point A.

Hope this helps!

CloutAnswers ❁

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Answer:

The x value is 5

Step-by-step explanation:

The x value is the value going across

Starting where the two axis meet, we go 5 units to the right

That is the x value