How much of salt would you get if you evaporate all water from 20g of a 17% salt solution?

Answer:

The probability that at least one of the 5 donors has Group O blood type is 0.9497.

Step-by-step explanation:

We can model this as a binomial random variable, with n=5 (the sample size) and p=0.45.

The probability that exactly k donors have Group O blood type in the sample can be written as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{5}{k} 0.45^{k} 0.55^{5-k}\\\\\\[/tex]

We have to calculate the probability P(x≥1). In this case it easy to substract from 1 the probabitity that x is exactly 0:

[tex]P(X\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{5}{0} p^{0}(1-p)^{5}=0.55^5=0.0503\\\\\\P(x\geq1)=1-0.0503=0.9497[/tex]

Answer:

The original digit is 62

Step-by-step explanation:

Let the Tens be represented with T

Let the Units be represented with U

Given:

Unknown Two digit number

Required:

Determine the number

Since, it's a two digit number, then the number can be represented as;

[tex]T * 10 + U[/tex]

From the first sentence, we have that;

[tex]T = 4 + U[/tex]

[tex]T = 4+U[/tex]

Interchanging the digit, we have the new digit to be [tex]U * 10 + T[/tex]

So;

[tex](U * 10 + T) + (T * 10+ U) = 88[/tex]

[tex]10U + T + 10T + U= 88[/tex]

Collect Like Terms

[tex]10U + U + T + 10T = 88[/tex]

[tex]11U + 11T = 88[/tex]

Divide through by 11

[tex]U + T = 8[/tex]

Recall that [tex]T = 4+U[/tex]

[tex]U + T = 8[/tex] becomes

[tex]U + 4 + U = 8[/tex]

Collect like terms

[tex]U + U = 8 - 4[/tex]

[tex]2U = 4[/tex]

Divide both sides by 2

[tex]U = 2[/tex]

Substitute 2 for U in [tex]T = 4+U[/tex]

[tex]T = 4 + 2[/tex]

[tex]T = 6[/tex]

Recall that the original digit is [tex]T * 10 + U[/tex]

Substitute 6 for T and 2 for U

[tex]T * 10 + U[/tex]

[tex]6 * 10 + 2[/tex]

[tex]60 + 2[/tex]

[tex]62[/tex]

Hence, the original digit is 62

I'm not sure what exactly you did wrong, but I agree with you that the sample size is too small, so the correct answer will probably be the fourth options. Hope that this gives you some confidence, and 'm sorry not to be able to help you any further...

Answer:

7). y = 140

8). x = 9

Step-by-step explanation:

Question (7).

All-right pencil factory will produce the graphite pencils, table formed will represent a linear graph.

Three points on the graph are (12, 42) and (18, 63), (40, y)

Slope of the line passing through these points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{63-42}{18-12}[/tex] = [tex]\frac{y-42}{40-12}[/tex]

[tex]\frac{21}{6}[/tex] = [tex]\frac{y-42}{40-12}[/tex]

3.5 = [tex]\frac{y-42}{40-12}[/tex]

98 = y - 42

y = 140

Question (8),

If a bicyclist rides at a constant rate, table formed will represent a linear graph.

Slope of a line passing through three points (2, 25), (5, 62.5) and (x, 112.5) given in the table,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{62.5-25}{5-2}=\frac{112.5-62.5}{x-5}[/tex]

[tex]\frac{37.5}{3}=\frac{50}{x-5}[/tex]

37.5x - 187.5 = 150

37.5x = 337.5

x = 9

Answer:

a) The sample mean is M=200.

The sample standard deviation is s=13.19.

b) Right-tailed. The null and alternative hypothesis are:

[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]

c) At a significance level of 0.01, there is  notenough evidence to support the claim that the arrival rate is significantly higher than 195.

Step-by-step explanation:

We start by calculating the sample and standard deviation.

The sample size is n=30.

The sample mean is M=200.

The sample standard deviation is s=13.19.

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{30}(210+215+200+. . .+221)\\\\\\M=\dfrac{6000}{30}\\\\\\M=200\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{29}((210-200)^2+(215-200)^2+(200-200)^2+. . . +(221-200)^2)}\\\\\\s=\sqrt{\dfrac{5048}{29}}\\\\\\s=\sqrt{174.07}=13.19\\\\\\[/tex]

This is a hypothesis test for the population mean.

The claim is that the arrival rate is significantly higher than 195.  As we are interested in only the higher tail for a significant effect, this is a right-tailed test.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]

The significance level is 0.01.

The standard deviation of the population is known and has a value of σ=13.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{13}{\sqrt{30}}=2.373[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{200-195}{2.373}=\dfrac{5}{2.373}=2.107[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>2.107)=0.018[/tex]

As the P-value (0.018) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is  notenough evidence to support the claim that the arrival rate is significantly higher than 195.

Answer:

The margin of error  = 2.13

Step-by-step explanation:

Explanation:-

Given random sample size 'n' =19

mean of the sample(x⁻) = 55 applicants

Given standard deviation of the Population(S.D)  = 4

Given confidence intervals are

((52.87.57.14)

we know that The Margin of error is determined by

[tex]M.E = Z_{\alpha } \frac{S.D}{\sqrt{n} }[/tex]

The confidence intervals are determined by

(x⁻ - M.E , x⁻+ M.E)

Step(ii):-

Given confidence intervals are

((52.87.57.14)

Now equating

(x⁻ - M.E , x⁻+ M.E) = ((52.87  , 57.14)

Given mean of the sample x⁻ = 55

( 55 - M.E , 55 + M.E) =((52.87.57.14)

   Equating

                55 - M.E = 52.87

                M.E = 55 - 52.87

                M.E = 2.13

Final answer:-

The margin of error  = 2.13

Answer: 4 to 10 then it’s 6 to 20 then it’s 8 to 25   Then it’s 10 to 30 then it’s 12 to 35  I hope this is the answer

Step-by-step explanation:

Step-by-step explanation:

Ava is walking at a constant rate of 5 feet each 2s so :

We should keep adding 2s in the time and 5 feet in the distance

Let's complete the chart:

Answer:

-7

Step-by-step explanation:

4 + (−3 − 8)

PEMDAS

Parentheses first

4 + (-11)

Add and subtract next

-7

Answer:

first I'm using BODMAS

4+(-11)

= -7

hope it helps

Answer:

b 150

Step-by-step explanation:

Answer:

7,273 Pesos

Step-by-step explanation:

1 Peso = $0.055

The formula below converts pesos to dollars:

1 Peso x 0.055 = $1

The formula below converts dollars to pesos:

$1/0.055= 1 Pesos

We use the second formula because we are coverting

from dollars to pesos.

$400/0.055=7,273 Pesos

Answer:

22

Step-by-step explanation:

If one Mexican peso is .055 U.S dollars that means it has a greater value than the dollar so we can make the following ratio 1:.055. But if the .055 is a 400 1:400 we just multiply to get 22.

Answer:

[tex]X \sim Unif (a=40, b=60)[/tex]

And for this case we want to find the probability density function and we know that is given by:

[tex] f(x) =\frac{1}{b-a}=\frac{1}{60-40}= \frac{1}{20}, 40\leq X\leq 60[/tex]

Step-by-step explanation:

Let X the random variable who represent the length of time it takes students to complete a statistics examination. And the distribution for x is given by:

[tex]X \sim Unif (a=40, b=60)[/tex]

And for this case we want to find the probability density function and we know that is given by:

[tex] f(x) =\frac{1}{b-a}=\frac{1}{60-40}= \frac{1}{20}, 40\leq X\leq 60[/tex]

Answer:

940.8 N

1254.4 N

Step-by-step explanation:

I would think the questions would be to calculate the forces at the top of the cube and at the sides. Thus:

On the top:

F = pressure * area

P = density * gravity * height

the height would be:

1m - 0.4m = 0.6m

replacing:

P = 1000 * 9.8 * 0.6 = 5880

A = (0.4) ^ 2 = 0.16

F = 5880 * 0.16

F = 940.8 N

On the sides:

dF = d * g * h * dA

dA = 0.4 * dh replacing

dF = 1000 * 9.8 * h * 0.4 * dh

dF = 3920 * h * dh

We integrate both sides and we have:

F = 3920 * (h ^ 2/2), h = 0.6 up to h = 1

F = (3920/2) * (1 ^ 2 - 0.6 ^ 2)

F = 1254.4 N

Answer:

b. 11 apples; 1 orange

Step-by-step explanation:

We test each option, and see if the total is $3.50(what you spend). If the result is different, it is not a possible solution.

a. 1 apple; 11 oranges

1 apple for $0.20

11 oranges for $0.30 each

0.20 + 11*0.30 = $3.50

Possible solution

b. 11 apples; 1 orange

11 apples for $0.20 each

1 orange for $0.30

11*0.2 + 0.3 = 2.5

Not $3.5, so this is not a possible solution.

This is the answer

c. 7 apples; 7 oranges

7*0.2 + 7*0.3 = $3.5

Possible

d. 4 apples; 9 oranges

4*0.2 + 9*0.3 = $3.5

Possible

Answer:

95 ft²

Step-by-step explanation:

Given:

regular pyramid with,

Square base of side length (s) = 5 ft

Slant height (l) = 7 ft

Required:

Surface area

Solution:

Surface area of a regular pyramid = ½*P*l + B

Where,

P = perimeter of the square base = 4(s) = 4(5) = 20 ft

l = slant height = 7 ft

B = area of base = s² = 5² = 25 ft²

Surface area = ½*20*7 + 25

= 10*7 + 25

= 70 + 25

Surface area of regular pyramid = 95 ft²

Answer:

B. [tex]4^2[/tex]

Step-by-step explanation:

[tex]4^7 \times 4^{-5}[/tex]

Apply rule (if bases are same) : [tex]a^b \times a^c = a^{b + c}[/tex]

[tex]4^{7 + -5}[/tex]

Add exponents.

[tex]=4^2[/tex]

Answer:

Step by step explanation

[tex] {4}^{7} \times {4}^{ - 5} [/tex]

Use product law of indices

i.e

[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]

( powers are added in multiplication of same base)

[tex] = {4}^{7 + ( - 5)} [/tex]

[tex] = {4}^{7 - 5} [/tex]

[tex] = {4}^{2} [/tex]

Hope this helps...

Best regards!

Answer: C - 600cm^2

Step-by-step explanation:

Area of one triangle:

(12)(5) ÷ 2 = 30

Area of two triangles:

30 x 2 = 60

Area of top rectangle:

Step 1: Figure out side length of triangle by using pythagorean:

√a^2 + b^2 =  c

√(5)^2 + (12)^2 =  c

√25 + 144 = c

√ 169 = c

13 = c

Step 2: Find area of top rectangle:

(18) x (13)

234

Find area of bottom rectangle:

(18) x (12)

216

Find area of back rectangle:

(18) x (5)

90

Add all the underlined numbers:

Area of two triangles + Area of top rectangle + Area of bottom rectangle + Area of back rectangle

60 + 234 + 216 + 90 = 600cm^2

1 - complementary =  90- 30 = 60

    suplementary = 180- 30 = 150

2 - area = hb/2 = 360 = hb/2 =  h = 72

3 - similar

4- see number 3

5 - asa, ssa, sas

6 - polygon that had all equal angle measures and sides (equiangular and equilateral)

7 - length x width = area so

   240 / 24 = 10

8 - line

9 - triangle

10 - 180, as see in question 1

vote me brainliest ):>

Answer:

First one is (x+2.4)

Second one is 4(x+2.4)=14.8

Step-by-step explanation:

Answer:

What expression would represent how far Bijan runs everyday?

✔ (x + 2.4)

What is the equation that represents his total distance after 4 days?

✔ 4(x + 2.4) = 14.8

Step-by-step explanation: I TOOK THE TEST

Answer:

3

Step-by-step explanation:

Given  

y

=

2

x

2

−

4

x

+

3

The y-intercept is the value of  

y

when  

x

=

0

XXX

y

=

2

(

0

)

2

−

4

(

0

)

+

3

=

3

For a quadratic in the general form:

XXX

y

=

a

x

2

+

b

x

+

c

the determinant  

Δ

=

b

2

−

4

a

c

indicates the number of zeros.

Δ

⎧

⎪

⎨

⎪

⎩

<

0

==⇒  

no solutions

=

0

==⇒  

one solution

>

0

==⇒  

two solutions

In this case

XXX

Δ

=

(

−

4

)

2

−

4

(

2

)

(

3

)

<

0

so there are no solutions (i.e. no values for which the expression is equal to zero).

This can also be seen from a graph of this equation:

graph{2x^2-4x+3 [-6.66, 13.34, -0.64, 9.36]}

Answer link

Vinícius Ferraz

Nov 13, 2015

(

0

,

3

)

Explanation:

x

=

0

⇒

y

=

0

−

0

+

3

y

=

0

⇒

x

=

−

b

±

√

b

2

−

4

a

c

2

a

a

=

2

,

b

=

−

4

,

c

=

3

But  

Δ

< 0, then there is no real root  

(

x

0

,

0

)

.

Answer:

it has 2

Step-by-step explanation:

I hope this helps!

Answer:

The common difference is 1/2

Step-by-step explanation:

Data obtained from the question include:

3rd term (a3) = 0

Common difference (d) =.?

From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:

a7 – 2a4 = 1

Recall:

a7 = a + 6d

a4 = a + 3d

a3 = a + 2d

Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.

But, a3 = 0

a3 = a + 2d

0 = a + 2d

Rearrange

a = – 2d

Now:

a7 – 2a4 = 1

Substituting the value of a7 and a4, we have

a + 6d – 2(a + 3d) = 1

Sustitute the value of 'a' i.e –2d into the above equation, we have:

–2d + 6d – 2(–2d + 3d) = 1

4d –2(d) = 1

4d –2d = 1

2d = 1

Divide both side by 2

d = 1/2

Therefore, the common difference is 1/2

***Check:

d = 1/2

a = –2d = –2 x 1/2 = –1

a3 = 0

a3 = a + 2d

0 = –1 + 2(1/2)

0 = –1 + 1

0 = 0

a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2

a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2

= (–2 + 3)/2 = 1/2

a7 – 2a4 = 1

2 – 2(1/2 = 1

2 – 1 = 1

1 = 1

Answer:

Domain is all real numbers or (negative infinity, positive infinity)

Step-by-step explanation:

Domain is all values of x (inputs) that will work with the function. Since a parabola has no limits for x, and all numbers work for x, then the domain can be any number. That leaves us with All Real Numbers as our answer.

Answer: 144

Step-by-step explanation:

ABD plus DBC makes up ABC so when you add the two it will give you a whole (76+68).

Answer:

Let the number be x

The statement is written as

[tex] \frac{3}{7}x = \frac{29}{14} [/tex]

Multiply through by 14

That's

[tex] 14 \times \frac{3}{7} x = \frac{29}{14} \times 14[/tex]

We get

2 × 3x = 29

6x = 29

Divide both sides by 6

That's

[tex] \frac{6x}{6} = \frac{29}{6} [/tex]

[tex]x \: = \frac{29}{6} \: \: or \\ 4 \frac{5}{6} [/tex]

Hope this helps you

Answer:

B. -1.

Step-by-step explanation:

[tex]i^1[/tex] = i

[tex]i^2 = -1[/tex]

[tex]i^3 = -i[/tex]

[tex]i^4 = 1[/tex]

...And it keeps going in a pattern, from i to -1 to -i to 1. And so, we have four values.

34 / 4 = 8 with a remainder of 2. That means that the value of [tex]i^{34}[/tex] is the same thing as [tex]i^2\\[/tex], so it is B. -1.

Hope this helps!

Answer:

L'(3, 2)

M'(0, 2)

N'(0, -2)

O'(3, -2)

Step-by-step explanation:

Vertices of a rectangle LMNO are L(-4, 6), M(-1, 6), N(-1, 2) and O(-4, 2).

If a point (x, y) is reflected across y-axis, rule to be followed,

(x, y) → (-x, y)

After reflection across y-axis new ordered pairs will be,

L(-4, 6)   → L"(4, 6)

M(-1, 6)   → M"(1, 6)

N(-1, 2)   → N"(1, 2)

O(-4, 2)  → O"(4, 2)

Then these points were translated 4 units down and 1 unit left,

Rule to be followed for the translation will be,

(x'', y'') → [(x' - 1), (y' - 4)]

By this rule vertices of the rectangle after translation will be,

L''(4, 6) → L'(3, 2)

M''(1, 6) → M'(0, 2)

N''(1, 2) → N'(0, -2)

O''(4, 2) → O'(3, -2)

Answer:

L'(3, 2)

M'(0, 2)

N'(0, -2)

O'(3, -2)

Step-by-step explanation:

Answer:

$26,096

Step-by-step explanation:

property taxes = 31 January + 28 February + 31 March + 30 April + 31 May + 4 June = 155 days

property taxes = (155 days/365 days) x $5,309 = $2,254

agent's commission = 7% x $547,000 = $38,290

seller's net = $547,000 - $480,000 (mortgage) - $38,290 (agent's commission) - $360 (home warranty) - $2,254 (property taxes) = $26,096

Answer:

26,096

Step-by-step explanation:

Proration using 365-day method:

Buyer days are June - December 210 days (June 30 + July 31 + August 31 + September 30 + October 31 + November 30 + December 31 - June 4 days)

Seller days are January - June 155 days (January 31 + February 28 + March 31 + April 30 + May 31 + June 30 - June 26 days)

Formula with closing day to buyer: 210/365 x $5,309 = $3,054.49 --> $5,309 - $3,054.49 = $2,254.51 property taxes

Commission:

$547,000 sale price x .07 commission fee = $38,290 commission

Seller Net:

$547,000 sale price - $480,000 mortgage = $67,000 - $38,290 commission = $28,710 - $360.00 home warranty = $28,350 - $2,254.51 = $26,096

Answer:

2049.

Step-by-step explanation:

2045 - 1983 = 62 years.

So the competition will take place in 1983 + 60 = 2043.

After 2045  the competition takes place in 2049.

8x + 3 > 2x - 15

8x - 2x > -15 - 3

6x > -18

x > -3

Answer:

x > -3

Step-by-step explanation:

8x + 3 > 2x - 15​

Add -3 and -2x on both sides.

8x - 2x > -15 - 3

6x > -18

Divide 6 into both sides.

x > -18/6

x > -3

Answer:

x > -2

Step-by-step explanation:

2(3x–1)>4x–6

Divide each side by 2

2/2(3x–1)>4x/2–6/2

3x-1 > 2x-3

Subtract 2x from each side

3x-2x-1 > 2x-3-2x

x-1 > -3

Add 1 to each side

x-1+1 > -3+1

x > -2