A scientist needs 10mL of a 17% acid solution for an experiment. The lab has available a 20% solution and a 10% solution. How many milliliters of the 20% solution and how many milliliters of the 10% solution should the scientist mix to make the 15% solution?

Answer:

There is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.

Step-by-step explanation:

Here we have our null hypothesis as H₀: σ² = s²

Our alternative hypothesis is then Hₐ: σ² ≠ s²

We therefore have a two tailed test

To test the hypothesis of difference in standard deviation which is the Chi squared test given as follows

[tex]\chi ^{2} = \dfrac{\left (n-1 \right )s^{2}}{\sigma ^{2}}[/tex]

Where:

n = Size of sample

s² = Variance of sample = 950²

σ² = Variance of population = 650²

Degrees of freedom = n - 1 = 71 - 1 = 70

α = Significance level = 0.1

Therefore, we use 1 - 0.1 = 0.9

From the Chi-square table, we have the critical value as

1 - α/2 = 51.739,  

α/2 = 90.531

Plugging the values in the above Chi squared test equation, we have;

[tex]\chi ^{2} = \dfrac{\left (23-1 \right )950^{2}}{650 ^{2}} = 49.994[/tex]

Therefore, since the test value within the critical region, we do not reject the null hypothesis, hence there is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.

Answer:

-3

Step-by-step explanation:

Answer:

[tex](x-4)^2 + y^2= 100[/tex]

Step-by-step explanation:

edgenuity 2020

hope this helps!

ABC and DEC are similar, since the line segments AB and DE are parallel.

This means corresponding sides of these triangles occur in a fixed ratio with one another.

In particular, this tells us

DE/AB = DC/AC

or

7/11 = 15/(15 + x)

Solve for x:

11/7 = (15 + x)/15

11/7 = 1 + x/15

4/7 = x/15

x = 60/7

Answer:

1) D. None of these.

2) False

3) C. No, Jane is too old to be considered a qualifying child and fails the support test of a qualifying relative.

Step-by-step explanation:

1) AGI deductions are subtracted from the gross income to calculate the taxable income. Not all the individual's earnings are subject to taxation, therefore some expenses are deducted to calculate the Adjusted Gross Income, the one that will be taxed.

All of the three options listed ( Standard deduction, Itemized deduction, and personal exemption) are AGI deductions.

2) False

The potential qualifying relative does not have to be family/biologically related with the taxpayer. The IRS condition states that he/she is either family related or have lived in the taxpayer's abode for a whole year to be a qualified relative of the taxpayer. So far any of the two conditions are met, it is fine.

C. For a student to be regarded as a qualifying relative of her parents, she must not be up to 24 years at the end of the year according to IRS. Jane is already 25, she is too old and fails the test as a qualifying relative.

Answer:

12h < 60

Step-by-step explanation:

A rectangle, with height h and base length l, has the following area.

[tex]A = l*h[/tex]

In this question:

[tex]l = 12, A < 60[/tex]

So

[tex]A < 60[/tex]

[tex]l*h < 60[/tex]

[tex]12h < 60[/tex]

So the correct answer is:

12h < 60

Answer:

12h < 60

hope this helps, its right because i took the test and it shows

Answer:

10 units

Explanation:

Create a right triangle, determine the a and b side lengths of the triangle by looking at the graph. (See image)

Then use the Pythagorean theorem to find c.

a² + b² = c²

(8)² + (6)² = c²

64 + 36 = c²

100 = c²

Square root both sides to get c.

[tex]\sqrt{100}[/tex] = c

10 = c

Answer:

[tex]0.4\%[/tex]

Step-by-step explanation:

Given: 60% of the boys play baseball and 24% of the boys play baseball and football in Seaton Park School

To find: percentage of those that play baseball also play football

Solution:

Let B denotes boys who play baseball and F denotes boys who play football.

[tex]P(B)=60\%[/tex]

[tex]P(F\cap B)=24\%[/tex]

Percentage of those that play baseball also play football = [tex]P\left ( F|B \right )=\frac{P(F\cap B)}{P(B)}=\frac{24}{60}=\frac{2}{5}=0.4\%[/tex]

Answer:

11*20!

Step-by-step explanation:

(20!+21!+22!)/44=

20!(1+21+21*22)/44=

20!(22+22*21)/44=

20!*22*22/44= 11*20!

The simplified expression of (20!+21!+22!)/44 is 20! * 11

The expression is given as:

(20!+21!+22!)/44

The factorial of a number n is:

n! = n * (n - 1)!

So, we start by expanding 22!

(20!+21!+22!)/44 = (20!+21!+22 * 21 * 20!)/44

Next, we expand 21!

(20!+21!+22!)/44 = (20!+21 * 20!+22 * 21 * 20!)/44

Factor out 20!

(20!+21!+22!)/44 = 20! * (1 + 21 + 22 * 21)/44

Evaluate the expression in the bracket

(20!+21!+22!)/44 = 20! * 484/44

Divide

(20!+21!+22!)/44 = 20! * 11

Hence, the simplified expression of (20!+21!+22!)/44 is 20! * 11

Read more about simplified expression at:

https://brainly.com/question/723406

#SPJ6

Answer:

Step-by-step explanation:

Twenty-five percent of thirty dollars is $7.50

(30 x 25)/100 = $7.50

Thirty percent of twenty-five dollars is $7.50

(25 x 30)/100 = $7.50

Therefore he is right

I hope this helps

Answer:

Zero(s) of multiplicity one: 11,-9

Zero(s) of multiplicity two: None

Zero(s) of multiplicity three: 5

Step-by-step explanation:

Suppose that we have a polynomial function in the following format:

[tex]f(x) = a*(x - x_{0})^{m_{0}}*(x - x_{1})^{m^{1}}*...*(x - x_{n})^{m^{n}}[/tex]

The zeros are [tex]x_{0}, x_{1}, ..., x_{n}[/tex].

The multiplicites are [tex]m_{0}, m_{1},..., m_{n}[/tex]

In this question:

f(x) = 4(x -11) (x + 9) (x - 5)^3

So

11 is a zero of multiplicity 1

-9 is a zero of multiplicity 1

5 is a zero of multiplicity 3.

So the answer is:

Zero(s) of multiplicity one: 11,-9

Zero(s) of multiplicity two: None

Zero(s) of multiplicity three: 5

Answer:

a) Calculate the current price of the corporate bond? (4 marks)

b) Calculate the current price of the ordinary share if the average return of the shares in the same industry is 9%? (3 marks)

c) Calculate the current price of the preferred share if the average return of the shares in the same industry is 10% (3 marks)

Step-by-step explanation:

total debt = $3,500,000 par value 10$ coupon with a YTM of 12%

YTM = [coupon + (F - P)/n] / [(F + P)/2]

0.12 = [100 + (1,000 - P)/20] / [(1,000 + P)/2]

0.12(500 + 0.5P) = 100 + 50 - 0.05P

60 + 0.06P = 150 - 0.05P

0.11P = 90

P = 90/0.11 = $818.18

total debt = $818.18 x 3,500

stock price:

Div₀ = $8.50

Div₁ = $8.50 x 104% = $8.84

g = 4%

rrr = 9%

using the perpetuity growth model:

stock price = $8.84 / (9% - 4%) = $8.84 / 5% = $176.80

preferred stock:

Div = $12

rrr = 10%

using the perpetuity formula:

preferred stock = $12 / 10% = $120

Answer:

There are 200 4th grades and 360 third graders

Step-by-step explanation:

560/2=280-80=200 280+80=360

Answer:

A. T > 2.539

Step-by-step explanation:

We have a hypothesis test of the mean, with unknown population standard deviation.

The hypothesis are:

[tex]H_0: \mu = 2.1 \\\\H_a: \mu > 2.1[/tex]

From the hypothesis we can see that the test is right-tailed, so the critical value of t should be a positive value.

The degrees of freedom can be calculated as:

[tex]df=n-1=20-1=19[/tex]

The significance level is 0.01, so the critical value tc should be the one that satisfies:

[tex]P(t>t_c)=0.01[/tex]

Looking up in a t-table, for 19 degrees of freedom, this critical value is tc=2.539.

Answer:

  [tex]p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)[/tex]

Step-by-step explanation:

  [tex]p(x)=32x^5y-2xy^5=2xy(16x^4-y^4)=2xy(4x^2-y^2)(4x^2+y^2)\\\\\boxed{p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)}[/tex]

__

The factoring of the difference of squares is applicable:

  a^2 -b^2 = (a -b)(a +b)

Answer:

A. x - 3

Step-by-step explanation:

Set it up like this:

(3x - 2) - (2x + 1)

Combine like terms:

3x - 2 - 2x - 1

3x - 2x = x

-2 - 1 = -3

Put it together:

x - 3

Answer:

pounds

Step-by-step explanation:

pounds : ounces

   10      :      [tex]x[/tex]

    1        :     16

[tex]x=160[/tex]

The numerator would be pounds. [tex]\frac{10 pounds}{160 ounces}[/tex]

Answer:

£77.6 per day

Step-by-step explanation:

388/5 = 77.6

Answer:

£77.60

Step-by-step explanation:

388/5=77.6

but remember that this is money so add the 0.

Answer:

Area of the StarKist label around the can in terms of π = 12π cm²

Step-by-step explanation:

Given;

the volume of a can of StarKist tuna, V = 18 π cm³

height of the can of StarKist tuna, h =  2 cm

To determine the area of the StarKist label that wraps around the entire can and does not overlap, we assume the can to have a shape of a cylinder.

Volume of the can = πr²h

where;

r is radius of the can

h is height of the can

πr² x 2 = 18 π

2r² = 18

r² = 18/2

r² = 9

r = 3

Area around the can = curved surface area of the can (cylinder)

Curved surface area of the can = 2πr × h = 2πrh

Curved surface area of the can = 2πrh = 2π x 3 x 2 = 12π cm²

Area of the StarKist label around the can in terms of π = 12π cm²

Answer:

Step-by-step explanation:

[tex]T: x = \frac{56}{65}u - \frac{33}{65}v, \ \ y = \frac{33}{65}u + \frac{56}{65}v[/tex]

A)

[tex]\frac{d(x,y)}{d(u,v)} =\left|\begin{array}{ccc}x_u&x_v\\y_u&y_v\end{array}\right|[/tex]

[tex]=(\frac{56}{65} )^2+(\frac{33}{65} )^2\\\\=\frac{(56)^2+(33)^2}{(65)^2} \\\\=\frac{4225}{4225} \\\\=1[/tex]

B )

[tex]S:-65 \leq u \leq 65, -65 \leq v \leq 65[/tex]

[tex]T(65,65)=(x=\frac{56}{65} (65)-\frac{33}{65} (65),\ \ y =\frac{33}{65} (65)+\frac{56}{65} (65)\\\\=(23,89)[/tex]

[tex]T(-65,65)=(-56-33,\ \ -33+56)\\\\=(-89,23)[/tex]

[tex]T(-65,-65) = (-56+33,-33-56)\\\\=(-23,-89)[/tex]

[tex]T(65,-65)=(56+33, 33-56)\\\\=(89,-23)[/tex]

C)

[tex]\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}[/tex]

[tex]=\int\limits^{65}_{v=-65} \int\limits^{65}_{u=-65}(x^2+y^2)(\frac{d(x,y)}{d(u,v)} du\ \ dv[/tex]

Now

[tex]x^2+y^2=(\frac{56}{65} u-\frac{33}{65} v)^2+(\frac{33}{65} u+\frac{56}{65} v)^2[/tex]

[tex][(\frac{56}{65} )^2+(\frac{33}{65}) ^2]u^2+[(\frac{33}{65} )^2+(\frac{56}{65}) ^2]v^2[/tex]

[tex]=\frac{(65)^2}{(65)^2} u^2+\frac{(65)^2}{(65)^2} v^2=u^2+v^2[/tex]

[tex]\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}[/tex]

[tex]=\int\limits^{65}_{v=-65} \int\limits^{65}_{u=-65}(u^2+v^2) du\ \ dv[/tex]

[tex]=\int\limits^{65}_{-65}\int\limits^{65}_{-65}u^2du \ \ dv+\int\limits^{65}_{-65}\int\limits^{65}_{-65}v^2du \ \ dv[/tex]

By symmetry of the region

[tex]=4\int\limits^{65}_0 \int\limits^{65}_0u^2 du \ \ dv + u\int\limits^{65}_0 \int\limits^{65}_0v^2 du \ \ dv[/tex]

[tex]= 4(\frac{u^3}{3} )^{65}_{0}(v)_0^{65}+(\frac{v^3}{3} )^{65}_{0}(u)_0^{65}\\\\=4[\frac{(65)^4}{3} +\frac{(65)^4}{3} ][/tex]

[tex]=\frac{8}{3} (65)^4[/tex]

Answer:

  60°

Step-by-step explanation:

The value of y is half the measure of the arc the chord subtends:

  y = 120°/2

  y = 60°

Answer:

250 miles

Step-by-step explanation:

d= sxt

d= 125x2

125x2= 250

or

mph= miles per hour

there are two hours so 125 +125 =250

Answer=250 miles

Answer:444+555=999 then(999)^3=9970029999.97*10^8

Step-by-step explanation:

Answer:

the anwser is c

Step-by-step explanation:

Answer:

The probability that Actuary Rahul examines fewer policies that Actuary Toby = 0.2857

Step-by-step explanation:

It is said that Actuary Rahul examines a low risk policy

Probability of a low risk policy having a claim = 10% = 0.1

Actuary Toby examines high risk policy

Probability of a high risk policy having a claim = 20% = 0.2

Let the number of policies examined by actuary Rahul before he finds a claim and stop be n

Probability that actuary Rahul examines exactly n policies =  [tex]0.9^{n-1} (0.1)[/tex]

Probability that Toby examines more than n policies = [tex]0.8^n[/tex]

Since the claim statuses of policies are mutually independent, the probability that both events happen simultaneously = [tex]0.9^{n-1} (0.1) (0.8)^n[/tex]

probability that both events happen simultaneously = [tex]\frac{0.1}{0.9} (0.72^{n})[/tex]

The probability that Actuary Rahul examines fewer policies that Actuary Toby = [tex]\sum\limits^ \infty_1 {\frac{0.1}{0.9} 0.72^{n} }[/tex] = [tex]\frac{1}{9}\sum\limits^ \infty_1 { 0.72^{n} } = \frac{1}{9} (\frac{0.72}{1-0.72} ) = \frac{1}{9} (\frac{0.72}{0.28} )[/tex]

The probability that Actuary Rahul examines fewer policies that Actuary Toby = 0.2857

Answer:

Rate = 51.74%

Step-by-step explanation:

Principal amount= $48000

Amount paid is done 2 times in a year for ten years

= $4000*2*10

Amount paid= $80000

A= p(1+r/n)^nt

80000= 48000(1+r/20)^(20*10)

(80000/48000)= (1+r/20)^(200)

(200)√(1.6667)= 1+ r/20

1.025870255-1= r/20

0.025870255*20= r

0.5174= r

Rate in decimal= 0.5174

In percentage= 51.74%

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A tangent to a circle forms a right angle with the radius

As it is a right angled triangle, we can use Pythagoras' theorem

a^2 + b^2 = c^2

Rearrange this for a side length:

a^2 = c^2 - b^2

Sub the values in:

a^2 = 6.5^2 - 6^2

a^2 = 6.25

Square root this for the answer

a = 2.5

Thus, your answer is option D

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Answer:

2.5 ft

Step-by-step explanation:

As radius is perpendicular to tangent ,

LT [tex]\perp[/tex]KT

By pythagoras theorem:

LT² = LK² - KT²

LT² = (6.5)² - 6²

LT² = 42.25 - 36

LT² = 6.25

LT = 2.5 ft

LT = radius = 2.5 ft

Answer:

0

Step-by-step explanation:

The 0, or the last digit is the insignificant digit because it serves no purpose.

Answer:

The last zero in the number is insignificant.

Step-by-step explanation:

The 0 at the extreme right indicates that the number is accurate to the fifth decimal place, that is, one in ten thousandths.

Answer:

the cheapest for the 3 shirts you can get is 43.83 (Baja Coast)

Step-by-step explanation:

For the three shirts at Pogo it costs $44.97. However, at the Baja Coast it costs $43.83. So the least amount you pay is $43.87.

Answer:

Step-by-step explanation:

f(x) = -2(64) + 3 is not a function of x; it's a constant with the single value -125.

Ensure that you have copied down this problem correctly.

Answer: -2 multiply 64 add 3 equals -125

Step-by-step explanation:

-2 multiply 64 add 3

then multiply 2 and 64 which is 128

then add/subtract: -128 add 3 which is -125

Then final answer -2 multiply 64 add 3 equals -125

Answer:

Parallelogram (A)

Question:

Sides KM and FH in the triangles below will be placed together to form a quadrilateral.

Triangle M L K. Side M L has a length of 15 and side L K has a length of 35. Angle L is 110 degrees. Triangle F G H. Side F G has a length of 35 and side G H has a length of 15. Angle G is 110 degrees.

Which best describes the quadrilateral that will be formed?

parallelogram

rectangle

rhombus

trapezoid

Step-by-step explanation:

Given:

∆MLK:

Side ML = 15

Side LK = 35

Angle L = 110°

∆ FGH:

Side FG = 35

Side GH = 15

Angle G = 110°

Side MK and FH placed together to form a quadrilateral.

A quadrilateral is a polygon which has 4 sides.

See attachment for diagram

From the diagram and information given:

LK is parallel to FG

ML is parallel to GH

MK = FH

∠L = ∠G (opposite angles are congruent)

Since two pairs of opposite sides are parallel and opposite angles are congruent, it is a paralellogram.

A parallelogram is a quadrilateral which has pairs of opposite sides are parallel and equal.

Answer: Option  A

(A) parallelogram

Step-by-step explanation: