Billy has x marbles. Write an expression for the number of marbles the following have… a) Charlie has 5 more than Billy b) Danny has 8 fewer than Billy c) Eric has three times as many as Billy

Answer:

The portfolio beta is  [tex]\alpha = 1.354[/tex]

Step-by-step explanation:

From the question we are told that

      The  first investment is [tex]i_1 = \$ 25,000[/tex]

       The  first  beta is  [tex]k = 0.8[/tex]

      The second investment is  [tex]i_2 = \$ 40,000[/tex]

       The  second  beta is  [tex]w = 1.7[/tex]

Generally the portfolio beta is mathematically represented as

           [tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]

substituting values

          [tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]

          [tex]\alpha = 1.354[/tex]

Answer:

-23

Step-by-step explanation:

16x² - 106x - 105

factoring X

14 x -120 = -1680

14 - 120 = -106

16x² + 14x - 120x - 105

(16x² + 14x) -(120x - 105)

factor out 2 and -15 to get the same expression (8x + 7)

2x(8x + 7) - 15(8x + 7)

(8x + 7)(2x - 15)

a = 7

b = -15

a + 2b

7 + (-15 x 2)

7 + (-30)

= -23

Answer:

Step-by-step explanation:

15-10=5 degrees

Answer:

1000

Step-by-step explanation:

I guess, something went wrong with the text up there.

I assume it should say 2cm×2cm×2cm cubes. right ? because a cube has 3 dimensions, not just 2.

otherwise an infinitely large number of "just squares" would fit into the box ...

so, the box is

1m×20cm×4cm = 100cm×20cm×4cm = 8000 cm³

a single cube would be

2cm×2cm×2cm = 8 cm³

therefore,

8000 / 8 = 1000 cubes can be packed into that box, since the dimensions of the box in relation to the dimensions of the cubes do not force to have some empty left over space. the box can be packed tightly.

Answer:

Step-by-step explanation:

Using the value for calculating the confidence interval as given;

CI = xbar + Z*σ/√n

xbar  is the mean = 37.14+42.86/2

xbar= 80/2

xbar = 40

Z is the z-score at the 90% confidence = 1.645

σ is the standard deviation

n is the sample size = 35

Given the confidence interval CI as [37.14, 42.86]

Using  the maximum value of the confidence interval to get the value of the standard deviation, we will have;

42.86 =  xbar + Z*σ/√n

42.86 = 40 + 1.645* σ/√35

42.86-40 = 1.645*σ/√35

2.86 = 1.645*σ/√35

2.86/1.645 = σ/√35

1.739 = σ/√35

1.739 = σ/5.92

σ= 1.739*5.92

σ = 10.295

Hence, the sample standard deviation of a pair of jeans is 10.295

Answer:

Justine graphs the function f(x) = (x – 7)2 – 1. On the same grid, she graphs the function

g(x) = (x + 6)2 – 3. Which transformation will map f(x) on to g(x)?

left 13 units, down 2 units

right 13 units, down 2 units

left 13 units, up 2 units

right 13 units, up 2 units

Answer:

x = 3/2

Step-by-step explanation:

4/3 ( 3x+9) -2x= 15

Distribute 4/3

4x+12 -2x =15

Combine like terms

2x+12 = 15

Subtract 12 from each side

2x+12-12 =15-12

2x = 3

Divide by 2

2x/2 = 3/2

x = 3/2

Answer:

4/3(3x+9)-2x=15

4x+12+9-2x=15

2x+21=15

2x=-6

x=-3

Let me know if this helps!

Answer:

[tex]D = 42.5\ inch[/tex]

Step-by-step explanation:

Given

[tex]L = Length[/tex] and [tex]W = Width[/tex]

[tex]L:W = 8: 5[/tex]

[tex]Perimeter = 117[/tex]

Required

Determine the Diagonal

First, the dimension of the screen has to be calculated;

Recall that; [tex]L:W = 8: 5[/tex]

Convert to division

[tex]\frac{L}{W} = \frac{8}{5}[/tex]

Multiply both sides by W

[tex]W * \frac{L}{W} = \frac{8}{5} * W[/tex]

[tex]L = \frac{8W}{5}[/tex]

The perimeter of a rectangle:

[tex]Perimeter = 2(L+W)[/tex]

Substitute [tex]L = \frac{8W}{5}[/tex]

[tex]Perimeter = 2(\frac{8W}{5}+W)[/tex]

Take LCM

[tex]Perimeter = 2(\frac{8W + 5W}{5})[/tex]

[tex]Perimeter = 2(\frac{13W}{5})[/tex]

Substitute 117 for Perimeter

[tex]117 = 2(\frac{13W}{5})[/tex]

[tex]117 = \frac{26W}{5}[/tex]

Multiply both sides by [tex]\frac{5}{26}[/tex]

[tex]\frac{5}{26} * 117 = \frac{26W}{5} * \frac{5}{26}[/tex]

[tex]\frac{5 * 117}{26} = W[/tex]

[tex]\frac{585}{26} = W[/tex]

[tex]22.5 = W[/tex]

[tex]W = 22.5[/tex]

Recall that

[tex]L = \frac{8W}{5}[/tex]

[tex]L = \frac{8 * 22.5}{5}[/tex]

[tex]L = \frac{180}{5}[/tex]

[tex]L = 36[/tex]

The diagonal of a rectangle is calculated using Pythagoras theorem as thus;

[tex]D = \sqrt{L^2 + W^2}[/tex]

Substitute values for L and W

[tex]D = \sqrt{36^2 + 22.5^2}[/tex]

[tex]D = \sqrt{1296 + 506.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = 42.4529150943[/tex]

[tex]D = 42.5\ inch[/tex] (Approximated)

Answer:

Step-by-step explanation:

x² + 5x - 24

To factorize first write 5x as a difference so that when subtracted will give you 5 and when multiplied will give you - 24

That's

x² + 8x - 3x - 24

Factorize x out

That's

x( x + 8) - 3(x + 8)

Factor x + 8 out

We have the final answer as

Hope this helps you

Answer:(x-3)(x+8)

Step-by-step explanation:

Answer:

Number 1: A

Number 2:D

Step-by-step explanation:

Answer:

Hello,

Just using the theorem of Thalès,

Step-by-step explanation:

Let say h the hight of the building

[tex]\dfrac{h}{3} =\dfrac{42.75}{1.23}\\\\h=104.268296...\approx{104(m)}[/tex]

Answer:

To find the volume of this cube, you would have to multiply 1.08 by 5.25 by 3.3 feet. If you did this, you would get: 18.711 feet^3. This is the volume of the rectangular prism.

Hope this helped!

5

Answer:

1050

Step-by-step explanation:

Natural Numbers are positive whole numbers. They aren't negative, decimals, fractions. We can just divide 5 into 100 to find how many natural numbers go up to 100 and just add them but that is just to much.

There is a easier method.

E.g: Natural Numbers that are divisible by a Nth Number. is the same as adding the Nth Numbers to a multiple of that Nth Term. For example, let say we need to find numbers divisible by 2. We know that 4 is divisible by 2 because 4/2=2. We can add the Nth numbers which is 2 to 4. 4+2=6. And 6 is divisible by 2 because 6/2=3. We can call this a arithmetic series. A series which has a pattern of adding a common difference

Back to the problem, we can use the sum of arithmetic series formula,

[tex]y = x( \frac{z {}^{1} + {z}^{n} }{2} )[/tex]

Where x is the number of terms in our sequence. Z1 is the fist term of our series. ZN is our last term. And y is the sum of all of the terms

The first term is 5, the numbers of terms being added is 20 because 100/5=20. The last term is 100.

[tex]y = 20( \frac{5 + 100}{2} )[/tex]

[tex]y = 20( \frac{105}{2} )[/tex]

[tex]y = 1050[/tex]

Answer:

Step-by-step explanation:

[tex]3-(-4) \\-\times - = +\\3+4 \\=7[/tex]

Answer:

7

Step-by-step explanation:

because you when multiply -1 by -4 u get positive 4 then 3 + 4 equals 7

Answer:

P(multiple of 5) = 0.1667

Step-by-step explanation:

    The multiples of 5 on the spinner are 5 and 10. This means out of 12 numbers, only 2 multiples of 5. Therefore, there is a 2/12 chance to get a multiple of 5.

[tex]\frac{2}{12}=\frac{1}{6}=0.1667[/tex]

Therefore, P(multiple of 5) = 0.1667.

Answer:

2.8 < x < 5.4

Step-by-step explanation:

Given the triangle with two known sides, 4.1 and 1.3, the range of possible values of the third side, x, can be ascertained by considering the triangle inequality theorem.

According to the theorem, when you add any two of the angles in a triangle, it should give you a value greater than the third side.

If a, b, and c are 3 sides of a triangle, the theorem implies that:

a + b > c.

Therefore, a - b < c < a + b

We can use this logic to find the possibly values of x in the given triangle above.

Thus,

4.1 - 1.3 < x < 4.1 + 1.3

2.8 < x < 5.4

Range of possible sizes of x is 2.8 < x < 5.4

Answer:

35.991

Step-by-step explanation:

Answer: 56.9 years to 63.1 years.

Step-by-step explanation:

Confidence interval for population mean (when population standard deviation is unknown):

[tex]\overline{x}\pm t_{\alpha/2}{\dfrac{s}{\sqrt{n}}}[/tex]

, where [tex]\overline{x}[/tex]= sample mean, n= sample size, s= sample standard deviation, [tex]t_{\alpha/2}[/tex]= Two tailed t-value for [tex]\alpha[/tex].

Given: n= 24

degree of freedom = n- 1= 23

[tex]\overline{x}[/tex]= 60 years

s= 7.4 years

[tex]\alpha=0.05[/tex]

Two tailed t-critical value for significance level of [tex]\alpha=0.05[/tex] and degree of freedom 23:

[tex]t_{\alpha/2}=2.0687[/tex]

A 95% confidence interval on the true mean age:

[tex]60\pm (2.0686){\dfrac{7.4}{\sqrt{24}}}\\\\\approx60\pm3.1\\\\=(60-3.1,\ 60+3.1)\\\\=(56.9,\ 63.1)[/tex]

Hence, a 95% confidence interval on the true mean age. : 56.9 years to 63.1 years.

Answer:

a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication

Step-by-step explanation:

a) This expression can be solved by using the Compatibility of Equality with Addition, that is:

1) [tex]3+x = 27[/tex] Given

2) [tex]x+3 = 27[/tex] Commutative property

3) [tex](x + 3)+(-3) = 27 +(-3)[/tex] Compatibility of Equality with Addition

4) [tex]x + [3+(-3)] = 27+(-3)[/tex] Associative property

5) [tex]x + 0 = 27-3[/tex] Existence of Additive Inverse/Definition of subtraction

6) [tex]x=24[/tex] Modulative property/Subtraction/Result.

b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:

1) [tex]\frac{x}{6} = 5[/tex] Given

2) [tex](6)^{-1}\cdot x = 5[/tex] Definition of division

3) [tex]6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6[/tex] Compatibility of Equality with Multiplication

4) [tex][6\cdot (6)^{-1}]\cdot x = 30[/tex] Associative property

5) [tex]1\cdot x = 30[/tex] Existence of multiplicative inverse

6) [tex]x = 30[/tex] Modulative property/Result

Answer:

3 + x = 27

✔ subtraction property of equality with 3

x over 6  = 5

✔ multiplication property of equality with 6

36×7

=252

Explaination :

First Multiply 6 and 7 we get 42 !

Write 2 and 4 will be added to the product of 3×7

We get 21 and add 4 here

So we get 252

Answer:

[tex]36 \times 7 = 252[/tex]

Step-by-step explanation:

Firstly multiply 6 with 7 you have to write 2 and take 4 carry and then multiply 7 with 3 u get 21 now add the number u carry in 21 u get ur answer. 252.

Hope it helps u mate

Answer:

No, -12 is not a solution.

Step-by-step explanation:

8u-1=6u

8(-12)-1=6(-12)

-96-1=-72

-97=-72

Untrue, to it’s not a solution

Answer:

Bank A spending= $20

Bank B spending= $22.5

Bank A is cheaper with $2.5

Step-by-step explanation:

Bank A charges $20 monthly fee for a checking account and debit card, with unlimited transactions.

Sheade 35 transactions.

Total charges from bank A

= $20 monthly

Bank B charged a $5 monthly fee for a checking account and debit card, plus

$ 0.50 for each transaction.

She made 35 transactions.

Total charges on bank B= $5 + (0.5)35

Total charges on bank B= $5+17.5

Total charges on bank B= $22.5

Answer:

8[2]×88888

Step-by-step explanation:

[8×8]=8[2]×88888

Answer:

405

Step-by-step explanation:

We can use a ratio to solve

3 infected           x infected

------------------ = ----------------

50 sampled     6750 population

Using cross products

3*6750 = 50x

Divide each side by 50

3*6750/50 = x

405

Answer:

Around 405 elk should be infected with the parasite.

Step-by-step explanation:

6,750/50=135

135 * 3 = 405

hope this helps :)

Answer:

Option A. 4√5

Step-by-step explanation:

To obtain the value of x, we must first obtain the value of y as shown in the attached photo.

The value of y can be obtained by using the pythagoras theory as illustrated below:

In this case y is the longest side i.e the Hypothenus.

y² = 4² + [4√3]²

y² = 4² + [4² × (√3)²]

y² = 4² + [4² × 3]

y² = 16 + [16 × 3]

y² = 16 + 48

y² = 64

Take the square root of both side

y = √64

y = 8

Finally, we shall determine the value of x by using the pythagoras theory as illustrated below.

Note: x is the longest side i.e the Hypothenus in this case.

x² = 4² + 8²

x² = 16 + 64

x² = 80

Take the square root of both side

x = √80

x = √(16 × 5)

x = √16 × √5

x = 4√5

Therefore, the value of x is 4√5.

Answer: a. $40,800 b. 36

Step-by-step explanation:

Given : a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207].

[tex]\sigma= \$14,900[/tex]

a. Since Point estimate of of the mean = Average of upper limit and lower limit of the interval.

Therefore , the point estimate of the mean salary for all college graduates in this town = [tex]\dfrac{34393+47207}{2}=\dfrac{81600}{2}[/tex]

= 40,800

hence, the point estimate of the mean salary for all college graduates in this town = $40,800

b.  Since  lower limit = Point estimate - margin of error, where Margin of error is the half of the difference between upper limit and lower limit.

Margin of error[tex]=\dfrac{47207-34393}{2}=6407[/tex]

Also, margin of error = [tex]z\times\dfrac{\sigma}{\sqrt{n}}[/tex], where z= critical z-value for confidence level and n is the sample size.

z-value for 99% confidence level  = 2.576

So,

[tex]6407=2.576\times\dfrac{14900}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=2.576\times\dfrac{14900}{6407}=5.99\\\\\Rightarrow\ n=(5.99)^2=35.8801\approx 36[/tex]

The sample size used for the analysis =36

Answer:

hope this answer helps.

Answer:

Explained below.

Step-by-step explanation:

Let X = systolic blood pressure measurements.

It is provided that, [tex]X\sim N(\mu=80,\sigma^{2}=3^{2})[/tex].

(a)

Compute the percentage of measurements that are between 71 and 89 as follows:

[tex]P(71<X<89)=P(\frac{71-80}{3}<\frac{X-\mu}{\sigma}<\frac{89-80}{3})[/tex]

                        [tex]=P(-3<Z<3)\\=P(Z<3)-P(Z<-3)\\=0.99865-0.00135\\=0.9973[/tex]

The percentage is, 0.9973 × 100 = 99.73%.

Thus, the percentage of measurements that are between 71 and 89 is 99.73%.

(b)

Compute the probability that a person's blood systolic pressure measures more than 89 as follows:

[tex]P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})[/tex]

                [tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]

Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.

(c)

Compute the probability that a person's blood systolic pressure being at most 75 as follows:

Apply continuity correction:

[tex]P(X\leq 75)=P(X<75-0.5)[/tex]

                [tex]=P(X<74.5)\\\\=P(\frac{X-\mu}{\sigma}<\frac{74.5-80}{3})\\\\=P(Z<-1.83)\\\\=0.03362\\\\\approx 0.034[/tex]

Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.

(d)

Let x be the blood pressure required.

Then,

P (X < x) = 0.15

⇒ P (Z < z) = 0.15

⇒ z = -1.04

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9[/tex]

Thus, the 15% of patients are expected to have a blood pressure below 76.9.

(e)

A z-score more than 2 or less than -2 are considered as unusual.

Compute the z score for [tex]\bar x[/tex] as follows:

[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]

  [tex]=\frac{84-80}{3/\sqrt{3}}\\\\=2.31[/tex]

The z-score for the mean blood pressure measurement of 3 patients is more than 2.

Thus, it would be unusual.

Answer:

7.745

Step-by-step explanation:

Square root of 60 equals X.