With the aid of a power reducing formula, 14sin² acos² a = ?

Using the normal distribution, it is found that the probabilities are given as follows:

a) 0.8871 = 88.71%.

b) 0.0778 = 7.78%.

c) 0.8485 = 84.85%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters in this problem are given as follows:

[tex]\mu = 1140, \sigma = 310, n = 16, s = \frac{310}{\sqrt{16}} = 77.5[/tex]

Item a:

The probability is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000, hence:

X = 1250:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1250 - 1140}{77.5}[/tex]

Z = 1.42

Z = 1.42 has a p-value of 0.9222.

X = 1000:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1000 - 1140}{77.5}[/tex]

Z = -1.81

Z = -1.81 has a p-value of 0.0351.

0.9222 - 0.0351 = 0.8871 = 88.71% probability.

Item b:

The probability is one subtracted by the p-value of Z when X = 1250, hence:

1 - 0.9222 = 0.0778 = 7.78%.

Item c:

The probability is the p-value of Z when X = 1220, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1220 - 1140}{77.5}[/tex]

Z = 1.03

Z = 1.03 has a p-value of 0.8485.

0.8485 = 84.85% probability.

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Answer: 101.6

Step-by-step explanation:

y∝(1/x)

this implies that

y=k/x    eq(*)

when y=12.7 and x=8

12.7=k/8

(12.7)(8)=k

101.6 =k

[tex]\large\displaystyle\text{$\begin{gathered}\sf 7x-2(x+1)=6x+4 \end{gathered}$}[/tex]

Use the distributive property to multiply −2 by x+1.

Combine 7x and −2x to get 5x.

Subtract 6x on both sides.

Combine 5x and −6x to get −x.

Add 2 to both sides.

Add 14 and 2 to get 16.

Multiply both sides by −1.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{7x - 2(x + 1) = 6x + 14}[/tex]

[tex]\huge\textbf{DISTRIBUTE 2 WITHIN the}\\\\\huge\textbf{PARENTHESES:}[/tex]

[tex]\mathsf{7x - 2(x) + 2(1) = 6x + 14}[/tex]

[tex]\mathsf{7x - 2x - 2 = 6x + 14}[/tex]

[tex]\huge\textbf{COMBINE the LIKE TERMS (if you}\\\\\huge\textbf{have any):}[/tex]

[tex]\mathsf{(7x - 2x) - 2 = 6x + 14}[/tex]

[tex]\mathsf{5x - 2 = 6x + 14}[/tex]

[tex]\huge\textbf{ADD 2 to BOTH SIDES:}[/tex]

[tex]\mathsf{5x - 2 + 2 = 6x + 14 + 2}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathsf{5x = 6x + 16}[/tex]

[tex]\huge\textbf{SUBTRACT 6x to BOTH SIDES}[/tex]

[tex]\mathsf{5x - 6x = 6x + 16 - 6x}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathsf{-x = 16}[/tex]

[tex]\mathsf{-1x = 16}[/tex]

[tex]\huge\textbf{DIVIDE -1 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{-1x}{-1} = \dfrac{16}{-1}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathsf{x = \dfrac{16}{-1}}[/tex]

[tex]\mathsf{x = -16}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -16}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The width of the model is 3.6 inches.

The figures with the same shape are said similar when the sides of both the figures are in proportion.

Sara has a model of length = 18inches.

The original ship has a length is 160 ft

The width of the original ship is 32 ft

The model is a scaled-down version of the original figure and so the length and width of the model will be in the same proportion as the original dimensions.

Let x represents the width of the model then,

160/18 = 32/x

x = 32 * 18 / 160

x= 3.6 inches.

Therefore, the width of the model is 3.6 inches.

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Step-by-step explanation:

1 subract 6

2 add 8

3 add 11

4 subract 5

5 add 10

The total contribution to the GDP is $5.49.

GDP, the gross domestic product is the sum of all final goods and services produced in an economy within a given period.

When calculating GDP, only the value added of final goods and services are included. Intermediate goods are not added.

Therefore,

Total contribution to GDP = 7.99 - (10 X 0.25) = $5.49.

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Answer:

[tex]\dfrac{5}{12}[/tex]

Explanation:

[tex]\dfrac{1}{4} + \dfrac{1}{6}[/tex]

The least common multiple of 4 and 6 is 12

So, make the denominator's same

[tex]\dfrac{3(1)}{12} + \dfrac{2(1)}{12}[/tex]

multiply numbers

[tex]\dfrac{3}{12} + \dfrac{2}{12}[/tex]

Join both fractions

[tex]\dfrac{3+ 2}{12}[/tex]

simplify following

[tex]\dfrac{5}{12}[/tex]

Answer:

Step-by-step explanation:

for reflection around x-axis.

(x,y)→(x,-y)

so P' is (-7,4)

Answer:

Step-by-step explanation:

The required length of GH is 7.7.

Given, HJ = 10
         m∠J = 40°

These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.

Let assume that there is right angle triangle GHJ.
Where HJ is base and GH is perpendicular.
Now,
cos40 = GH/HJ
GH = cos40 HJ
GH = 10 cos40
GH = 7.7

Thus, the required length of GH is 7.7.

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Answer:

[tex]y^2 + 55[/tex]

Step-by-step explanation:

Solution

Step 1: Plug in value of b as 5.

Step 2: Simplify

Therefore, the answer is y^2 + 55.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{2b^2 + b + y^2}[/tex]

[tex]\huge\textbf{Conversion:}[/tex]

[tex]\mathbf{2(5)^2 + 5 + y^2}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{2(5)^2 + 5 + y^2}[/tex]

[tex]\mathbf{= 2(5\times5) + 5 + y^2}[/tex]

[tex]\mathbf{= 2(25) + 5 + y^2}[/tex]

[tex]\mathbf{= 50 + 5 + y^2}[/tex]

[tex]\mathbf{= 55 + y^2}[/tex]

[tex]\mathbf{= y^2 + 55}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\textsf y\frak{^2 + 55}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

-5

Step-by-step explanation:

x+8=3

x=3-8

we can easily say +3-8=-5

Answer:

[tex]\{-\frac{1}{2} \} \cup \{\frac{2}{5}\}[/tex]

Step-by-step explanation:

[tex]10x^2 + x - 2 = 0; \\ a = 10, b = 1, c = -2; \\ D = b^2 - 4ac = 1^2 - 4 * 10 * (-2) = 1 + 80 = 81 = 9^2, > 0; \\ x_{1, 2} = \frac{-b \pm \sqrt{D}}{2a} = \frac{-1 \pm \sqrt{9^2}}{2 * 10} = \frac{-1 \pm 9}{20} = \left \ [ {{\frac{-1 - 9}{20} = -\frac{10}{20} = -\frac{1}{2} } \atop {\frac{-1 + 9}{20} = \frac{8}{20} = \frac{2}{5}}} \right.[/tex]

The measure of m<WUV is 53 degrees

Given the following parameters

m<TUW = 22 +7x,

m<WUV = 41+ 6x

m<TUV. = 89

The related expression is given as:

m<TUV + m<WUV = m<TUV.

Substitute

22+7x+41+6x = 89

63 + 13x = 89

13x = 89 - 63

13x = 26

x = 2

Determine the measure of m<WUV

m<WUV = 41 + 6(2)

m<WUV = 41 + 12

m<WUV =53 degrees

Hence the measure of m<WUV is 53 degrees

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Answer:

Last graph that slopes upwards from left to right and that has an y-intercept of -1

Step-by-step explanation:

let us pick some points!(you can chose any two)

when x =3 , y = 14 : helps us get points (3,14)

when x =1 , y = 4 : helps us get points (1,4)

so we find the gradient using the two points:

[tex]gradient \ =\frac{14-4}{3-1} =\frac{10}{2} \\[/tex]

we now use gradient 10/2 and point (1,4) to find the equation  of the line:

[tex]\frac{10}{2} =\frac{y-4}{x-1} \\2(y-4)=10(x-1)\\2y-8=10x-10\\2y=10x-10+8\\2y=10x-2\\y=5x-1[/tex]

from the equation of the line found we are able to find the y- intercept of the line is -1 and that the line has a positive gradient thus should slope upwards from left to right.

From the pictures you posted, we pick the last graph as it seem to slope upwards from left to right and has the line cutting y axis at around -1

a. [tex]x^4 + 4x^2 + 4[/tex]

b. x = ∛-1 and -3

a.  Given

(x² + 2)²

First, we open up the bracket

[tex](x^2 + 2) (x^2 + 2)[/tex]

Multiply through

[tex]x^4 + 2x^2 + 2x^2 + 4[/tex]

Collect like terms

[tex]x^4 + 4x^2 + 4[/tex]

b. Let's factorize

[tex]x^4 + 4x + 3[/tex]

Find the factors of 3 that are products of 4, they are 3 and 1

Use it to replace 4x as 3x and x

[tex]x^4 + 3x + x + 3[/tex]

Let's make the expression two

[tex](x^4 + 3x) (x+ 3)[/tex]

Find the common factor

[tex]x^3(x + 3)+ 1(x+ 3)[/tex]

So,

[tex]x^3 + 1 = 0[/tex] and [tex]x + 3 = 0[/tex]

[tex]x = 3\sqrt{-1}[/tex] and x = -3

Thus, x = ∛-1 and -3

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The amount of interest you would be paying in Year 2 is: $2,492.62.

First step is to calculate the Equal Monthly Payment

Equal Monthly Payment=P×r×(1+r)^t/(1+r)^t-1

Where:

P=Principal=$36,500

r=Rate=7.7%

t=Time=7 years

Equal Monthly Payment=36,500×0.077×(1+0.077)^7÷(1+0.077)^7-1

Equal Monthly Payment=36,500×0.077×(1.077)^7÷(1.077)^7-1

Equal Monthly Payment=36,500×0.077×1.6807763÷1.6807763-1

Equal Monthly Payment=4,723.82/0.6807763

Equal Monthly Payment=$6,938.875

Second step is to calculate Year 1 Closing balance

Year 1 Closing balance  = Beginning  balance + Interest - EMI Payment

Year 1 Closing balance=  $36,500 +($36,500×7.7%) - $6,938.875

Year 1 Closing balance=  $36,500 + $2,810.5 -$6,938.875

Year 1 Closing balance =   $32,371.625

Third step is to calculate year 2 interest

Year 2 Interest= $32,371.625×7.7%

Year 2 Interest=$2,492.62

Therefore the amount of interest you would be paying in Year 2 is: $2,492.62.

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Answer:

Here you go with your answer

Mark me as brainlist may your parents live long life

Answer:

C 12/48

Step-by-step explanation:

Original fraction:

x/y

The ratio of the numerator to the denominator is 1:4, so

x/y = 1/4

Cross multiply:

y = 4x

If three is added to the numerator and subtracted from the denominator, the new fraction reduces to one-third.

(x + 3)/(y - 3) = 1/3

Cross multiply:

3(x + 3) = 1(y - 3)

3x + 9 = y - 3

Above, we have y = 4x, so substitute 4x for y in the equation just above and solve for x.

3x + 9 = 4x - 3

12 = x

x = 12

y = 4(12) = 48

The original fraction is x/y = 12/48

Answer:

11 , 17 , 24

Step-by-step explanation:

• Since the Lowest number is 11 and the range is 13 then

The greatest number is 11 + 13 = 24

• Therefore the three numbers are  11 , 17 and 24

because the median of the set 11 , 17 , 24 is 17

Answer:

  6

Step-by-step explanation:

The average of a set of numbers is their sum divided by their number. This fact lets us write an equation to find the missing number.

Let x represent the missing number. The average of the 4 numbers is ...

  (x +18 +11 +25)/4 = 15

Multiplying by 4 gives ...

  x +54 = 60

Subtracting 54, we find the missing number:

  x = 6

The other number is 6.

The correct option is C which is The z-statistic is 3.32, so the null hypothesis should be rejected. One can reject the null hypothesis.

When there are two possibilities then we calculate the null hypothesis if the hypothesis is true hypothesis is accepted if it is

To conduct a hypothesis test for the above situation. We define the null hypothesis and the alternative hypothesis.

The null hypothesis is the claim that the average commute time to downtown is 20 minutes while the alternative hypothesis is a contradiction of the null hypothesis which is that the average commute time to downtown is not 20 minutes.

i.e. H0: μ = 20 and H1:  μ ≠ 20.

The z-statistics is given by (sample mean - hypothesized mean) divided by (standard deviation divided by the square root of the sample size).

i.e.

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

x = 26,  [tex]\mu[/tex] = 20, [tex]\sigma[/tex] = 7 and n = 15 putting the values in the question we will get the z-score value.

[tex]z = \dfrac{26-20}{\dfrac{7}{\sqrt15}}[/tex]

z = 6 / 1.807

z = 3.32

Therefore, the z-statistic is 3.32, so the null hypothesis should be rejected. Because the calculated value of z (3.32) is greater than the table value of z (1.96).

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The functions that the left endpoint lead to an under approximation and right endpoints lead to and over approximation is the positive and increasing function.

It should be noted that function simply means the illustration that shows the relationship between the variables.

In this case, the functions that the left endpoint lead to an under approximation and right endpoints lead to and over approximation is the positive and increasing function.

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Using translation concepts, the changes are described as follows:

a) The function is vertically stretched by a factor of 3, and shifted down 2 units.

b) The function is shifted 1 unit right and 4 units down.

c) The function is horizontally compressed by a factor of 2 and shifted up  5 units.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Item a:

The changes are as follows:

Item b:

The changes are as follows:

Item c:

The changes are as follows:

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Answer:

20%

Step-by-step explanation:

Total Litres in mixture=(0.60+0.4)=1 Litre

alcohol in first portion:=0.10(0.60)=0.06 Litres

alcohol in second portion:=0.35(0.40)=0.14 Litres

Total alcohol in mixture = 0.06 +0.14 = 0.20

% of alcohol in mixture:

                                          [tex]\frac{0.2}{1} (100) = 20%[/tex]%

Answer: 20%. Based on the given conditions, formulate:: 35% * 0.4 + 0.6 * 10% / 0.4 + 0.6Calculate the product

The problem proves that the distributor's claim is true and he has a right to complain.

But when the confidence interval is changed from 95% to 90% the distributor's claim proves to be false.

The Confidence Interval for 95%  is 0.9687;0.98532

For a sample size of n>30 the central limit theorem allows us to assume that the sampling distribution of x~ is approximately normal.

The critical region is Z ≥ 1.28 therefore the 1.877 lies in the rejection region that the distributor's claim is not true.

The Confidence Interval for 90%  is 0.97156;0.982431

Here

μ = 0.977

s= σ= 0.03

95 % confidence interval is given by

x~± z∝/2 (s/√n)

Putting the values

0.977 ± 1.96 (0.03/√50)

=0.977 ± 0.008315

0.9687;0.98532

Part B:

x~+ 0.95= 0.977+0.95= 1.927

The critical region is Z ≥ 1.96 therefore the 1.927 lies in the acceptance region that the distributor's claim is true.

Part C:

For a sample size of n>30 the central limit theorem allows us to assume that the sampling distribution of x~ is approximately normal.

Part D:

μ = 0.977

s= σ= 0.03

90 % confidence interval is given by

x~± z∝/2 (s/√n)

Putting the values

0.977 ± 1.28 (0.03/√50)

=0.977 ± 0.005431

0.97156;0.982431

Part D:

x~+ 0.90= 0.977+0.90= 1.877

The critical region is Z ≥ 1.28 therefore the 1.877 lies in the rejection region that the distributor's claim is not true.

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The rational expression written using the least common denominator  [tex]\frac{x+1}{4x^{2} }+\frac{x+1}{x^{2} }\\[/tex] is [tex]\frac{x+1}{4x^{2} }+\frac{4(x+1)}{4x^{2} }[/tex].

The ratio of two polynomials is displayed in rational expressions. It indicates that the denominator and numerator are polynomials. It is an algebraic expression that has a ratio and an unknown variable, just like a fraction. Although we can simplify this kind of equation with the aid of a calculator.

Because one is divided by the other, just like a ratio, it is a "rational expression."

The polynomial that we divide by cannot be zero, as a reminder.

The least common denominator for [tex]4x^{2}[/tex] and [tex]x^{2}[/tex] is calculated to be [tex]4x^{2}[/tex].

Thus, the required rational expression is [tex]\frac{x+1}{4x^{2} }+\frac{4(x+1)}{4x^{2} }[/tex].

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Answer:

Rs 328

Step-by-step explanation:

Find the principal amount invested.

Simple Interest Formula

I = Prt

where:

Given:

Substitute the given values into the formula and solve for P:

⇒ 320 = P(0.05)(2)

⇒ 320 = P(0.1)

⇒ P = 3200

Compound Interest Formula

[tex]\large \text{$ \sf I=P\left(1+\frac{r}{n}\right)^{nt} -P$}[/tex]

where:

Given:

Substitute the given values into the formula and solve for I:

[tex]\implies \sf I=3200\left(1+\frac{0.05}{1}\right)^{2} -3200[/tex]

[tex]\implies \sf I=3200\left(1.05\right)^{2} -3200[/tex]

[tex]\implies \sf I=3200\left(1.1025\right) -3200[/tex]

[tex]\implies \sf I=3528-3200[/tex]

[tex]\implies \sf I=328[/tex]

Therefore, the compound interest on the same sum for the same time at the same rate is Rs 328.

Answer:

Step-by-step explanation:

Givens

t1 = 2

r = 3

n = 10

Formula

tn = a*r^(n -1)         Substitute the givens into the this formula

Solution

t10 = 2 * 3^(10 - 1)

t10 = 2 * 3^9

t10 = 2 * 19683

t10 = 39366

Answer: 39366