2y + 5x – z = 4y + 6x solve for y

(show work)

Answer:

[tex]\frac{49}{15}[/tex]

Step-by-step explanation:

[tex]\frac{2}{5} \times \frac{7}{-6} \times -7[/tex]

[tex]\frac{2}{5} \times \frac{7}{-6} \times \frac{-7}{1}[/tex]

[tex]\frac{2 \times 7 \times -7}{5 \times -6 \times 1}[/tex]

[tex]\frac{-98}{-30}=\frac{98}{30}=\frac{49}{15}[/tex]

Answer:

-3.26 repeating

Step-by-step explanation:

2×7=14

5×(-6) = -30

14/30×(-7)= -3.26 repeating

Answer: The monthly mortgage payment is $640

Step-by-step explanation:

The cost of the house is $159,000

The down payment made is 20%. This means that the amount paid as down payment is

20/100 × 159000 = 31800

The balance to be paid would be

159000 - 31800 = $127200

We would apply the periodic interest rate formula which is expressed as

P = a/[{(1+r)^n]-1}/{r(1+r)^n}]

Where

P represents the monthly payments.

a represents the amount of the loan

r represents the annual rate.

n represents number of monthly payments. Therefore

a = $127200

r = 0.044/12 = 0.0037

n = 12 × 30 = 360

Therefore,

P = 127200/[{(1+0.0037)^360]-1}/{0.0037(1+0.0037)^360}]

P = 127200/[{(1.0037)^360]-1}/{0.0037(1.0037)^360}]

P = 127200/{3.779 -1}/[0.0037(3.779)]

P = 127200/(2.779/0.0139823)

P = 127200/198.75127840198

P = $640

Answer:

  Exponential; $376.32

Step-by-step explanation:

Generally, an increase of 12% in a month means the prices are 12% more than they were in the previous month. That is, the value has been multiplied by 1.12.

The same would be true for the second month, so the overall multiplier for the two months is ...

  (1.12)(1.12) = 1.12^2 = 1.2544

This makes the food bill for the second month amount to ...

  1.2544 × $300 = $376.32

_____

As with all percentages, you need to be clear about what base is being used. Here, we have assumed the base for a monthly increase is the value at the beginning of the month.

If, instead, it is the value at the beginning of the year, then the increase is linear, not exponential. 12% of the value at the beginning of the year is the same throughout the year.

Answer:

x =2

Step-by-step explanation:

becaue 2-1 is smaller than 3

Answer:

Hello!

I believe your answer is:

x=2

If this is not correct, please let me know and I will try again!

Step-by-step explanation:

Answer:

The first one matches with f(x)√x because a square root cannot be negative

The second one matches with f(x)=√(x-5) because the square root would be negative if it were less than five.

The third one matches with f(x)=8x because there is nothing that makes it a not possible answer

The last one matches with 7/(x-8) because there cannot be a denominator of zero.

Answer:

1) The normal distribution should be used for the sample mean because the population distribution is known to be normal (answer b).

2) C. H0: mu = 519, H_1: mu not equal to 519, reject if z> 1.96 or z< -1.96.

3) Yes. There is enough evidence to support the claim that the true mean is not 519 ml.

Step-by-step explanation:

1) When the population follows a normal distribution, it is correct to assume a normal distribution for the sample mean.

2) As it is a two-tailed decision rule, we are interested in detecting a significant difference below and above the mean. This is why we use the unequal sign in the alternative hypothesis.

The null hypothesis state that there is not significant difference from 519.

The critical value for a significance level of 5% is z=1.96.

[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]

3) The claim is that the true mean is not 519 ml.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]

The significance level is 0.05.

The sample has a size n=16.

The sample mean is M=522.

The standard deviation of the population is known and has a value of σ=6.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{16}}=1.5[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{522-519}{1.5}=\dfrac{3}{1.5}=2[/tex]

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

[tex]\text{P-value}=2\cdot P(z>2)=0.046[/tex]

As the P-value (0.046) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the true mean is not 519 ml.

Answer:

14/50 or 7/25

Step-by-step explanation:

cos x = adj/hyp

adj = 14

hyp = 50

---------

you ca learn more about trig

sin x = opp/hyp

tan x = opp/adj

The value of the trigonometric ratio, cos x in a right angle triangle XYZ is   [tex]\dfrac{14}{50}[/tex].

Trigonometric ratios – The relation between the angles and the sides of a right-angle triangle is called Trigonometric ratios.

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In the given figure a right-angle triangle XYZ we know that

ZY is the length of the perpendicular. XY is the base of the triangle and  ZX is the hypotenuse.

By trigonometric ratio, we know that

[tex]Cos \Theta = \dfrac{adjacent}{hypotenuse}[/tex]

Where [tex]\Theta[/tex] is the acute angle between the base and the Hypotenuse

On substituting value,

[tex]Cos \Theta = \dfrac{14}{50}[/tex]

The value of the trigonometric ratio, cos x in a right angle triangle XYZ   [tex]\dfrac{14}{50}[/tex].

Learn more about Trigonometric ratios here:

https://brainly.com/question/25122825

#SPJ2

Answer: The answer is (x-5)^2

Answer:

  GH¢2082.12

Step-by-step explanation:

Let "a" represent the amount invested at 12%. Then (a+580) is the amount invested at 14%. The total amount invested (t) is ...

  t = (a) +(a +580) = 2a+580

Solving for a, we get

  a = (t -580)/2

__

The accumulated amount from the investment at 12% is 1.12a. And the accumulated amount from the investment at 14% is 1.14(a+580). Together, these accumulated amounts total GH¢2358.60.

  1.12(t -580)/2 +1.14((t -580/2 +580) = 2358.60

  0.56t -0.56(580) +0.57t -0.57(580) +1.14(580) = 2358.60 . . . remove parens

  1.13t + 5.8 = 2358.60 . . . . . . . . . simplify

  1.13t = 2352.80 . . . . . . . . . . . . . . subtract 5.8

  t = 2352.80/1.13 = 2082.12 . . . . divide by the coefficient of t

Mr. Azu's total investment was GH¢2082.12.

Answer:

a) -8/9

b) The series is a convergent series

c) 1/17

Step-by-step explanation:

The series a+ar+ar²+ar³⋯ =∑ar^(n−1) is called a geometric series, and r is called the common ratio.

If −1<r<1, the geometric series is convergent and its sum is expressed as ∑ar^(n−1) = a/1-r

a is the first tern of the series.

a) Rewriting the series ∑(-8)^(n−1)/9^n given in the form ∑ar^(n−1) we have;

∑(-8)^(n−1)/9^n

= ∑(-8)^(n−1)/9•(9)^n-1

= ∑1/9 • (-8/9)^(n−1)

From the series gotten, it can be seen in comparison that a = 1/9 and r = -8/9

The common ratio r = -8/9

b) Remember that for the series to be convergent, -1<r<1 i.e r must be less than 1 and since our common ratio which is -8/9 is less than 1, this implies that the series is convergent.

c) Since the sun of the series tends to infinity, we will use the formula for finding the sum to infinity of a geometric series.

S∞ = a/1-r

Given a = 1/9 and r = -8/9

S∞ = (1/9)/1-(-8/9)

S∞ = (1/9)/1+8/9

S∞ = (1/9)/17/9

S∞ = 1/9×9/17

S∞ = 1/17

The sum of the geometric series is 1/17

Answer: The image is (6,-3)

Step-by-step explanation:

The coordinates of R is  ( 4,-2)  and to find the image using the scale factor 1.5 you will multiply the x coordinates by 1.5 and the y coordinate also by 1.5 to have the new image of R.

4 * 1.5 = 6

-2 * 1.5 = -3

The new coordinates care (6, -3)

Answer:

hope this helps you

Answer:

At least 18 of the households have between 2 and 6 televisions.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this question:

Mean = 4

Standard deviation = 1

Percentage of households that have between 2 and 6 televisions.

2 = 4 - 2*1

So 2 is two standard deviations below the mean

6 = 4 + 2*1

So 6 is two standard deviations above the mean

By Chebyshev's Theorem, at least 75% of the measures are within 2 standard deviations of the mean.

Out of 24

0.75*24 = 18

At least 18 of the households have between 2 and 6 televisions.

Answer:

72°

Step-by-step explanation:

This is called an isosceles triangle. This means that the 2 angles related to the equal sides, are also equal. Hence, the answer is 72°

Answer:

A

Step-by-step explanation:

Since it is isosceles triangle (two equal sides) therefore, there are 2 equal angles too which at the base (72°)

The total angle of triange is 180°

So 180-72-72=36°

Answer:

Step-by-step explanation:

This is  the method I am familiar with.

I Hope It helps :)

[tex]METHOD- 1 : Elimination\\6x - 2y=10------(1)\\2x+3y =51------(2)\\Multiply -eq-(1)- by -the-coefficient-of-x-in-equation (2)\\Multiply-eq-(2) -by -the-coefficient-of-x-in-equation (1)\\6x - 2y=10------(1) *2\\2x+3y =51------(2)*6\\\\12x-4y=20 ------(3)\\12x+18y=306 ------(4)\\Subtract -eq- (4)- from- eq -(3)\\-22y =-286\\\frac{-22y}{-22} =\frac{-286}{-22} \\y =13\\[/tex]

[tex]Substitute- 13- for y -in-equation -(1)-or-(2)\\6x - 2y=10------(1)\\6x -2(13)=10\\6x -26=10\\6x =10+26\\6x =36\\\frac{6x}{6} =\frac{36}{6} \\x =6[/tex]

Answer:

Correct answers is

Step-by-step explanation:

1. 3

2. B

3. 6

4. (6,13)

Answer:

The functions g and f are said to commute with each other if g ∘ f = f ∘ g. Commutativity is a special property, attained only by particular functions, and often in special circumstances. For example, |x| + 3 = |x + 3| only when x ≥ 0. ... The composition of one-to-one functions is always one-to-one.

\

Answer:

As per ASA postulate, the two triangles are congruent.

Step-by-step explanation:

We are given two triangles:

[tex]\triangle ABC[/tex] and [tex]\triangle DEC[/tex].

AD bisects BE.

AB || DE.

Let us have a look at two properties.

1. When two lines are parallel and a line intersects both of them, then alternate angles are equal.

i.e. AB || ED and [tex]\angle B[/tex] and [tex]\angle E[/tex] are alternate angles [tex]\Rightarrow[/tex] [tex]\angle B = \angle E[/tex].

2. When two lines are cutting each other, angles formed at the crossing of two, are known as Vertically opposite angles and they are are equal.

[tex]\Rightarrow \angle ACB = \angle DCE[/tex]

Also, it is given that AD bisects BE.

i.e. EC = CB

1. [tex]\angle B = \angle E[/tex]

2. EC = CB

3. [tex]\angle ACB = \angle DCE[/tex]

So, we can in see that in [tex]\triangle ABC[/tex] and [tex]\triangle DEC[/tex], two angles are equal and side between them is also equal to each other.

Hence, proved that [tex]\triangle ABC[/tex] [tex]\cong[/tex] [tex]\triangle DEC[/tex].

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 238

For the alternative hypothesis,

H1: µ < 238

This is a left tailed test

b) Since the population standard deviation is not given, the distribution is a student's t.

Since n = 100

Degrees of freedom, df = n - 1 = 100 - 1 = 99

t = (x - µ)/(s/√n)

Where

x = sample mean = 231

µ = population mean = 238

s = samples standard deviation = 80

t = (231 - 238)/(80/√100) = - 0.88

We would determine the p value using the t test calculator. It becomes

p = 0.19

c) Since alpha, 0.05 < than the p value, 0.19, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed insignificant evidence that the mean weekly unemployment insurance benefit in Virginia was below the national average.

d) Since α = 0.05, the critical value is determined from the t distribution table. Recall that this is a left tailed test. Therefore, we would find the critical value corresponding to 1 - α and reject the null hypothesis if the test statistic is less than the negative of the table value.

1 - α = 1 - 0.05 = 0.95

The negative critical value is - 1.66

Since - 0.88 is greater than - 1.66, then we would fail to reject the null hypothesis.

Answer:

Look at the money bags below!!! (but I'll give you the answer)

Step-by-step explanation:

John F: 7 full bags - 1 half

Juan A: 9 full bags

Jason A: 3 full bags

Nick J: 3 full bags- 1 half

Alfonso S: 8 full bags

Hope this helped and wasn't confusing!!! xx - Asia

Answer:

[tex]x=5/48[/tex]

Step-by-step explanation:

[tex]2/5 + 1/x =10[/tex]

[tex]1/x=10-2/5[/tex]

[tex]1/x=48/5[/tex]

[tex]48x=5[/tex]

[tex]x=5/48[/tex]

Answer:

[tex]x = \frac{5}{48} [/tex]

Step-by-step explanation:

[tex]\frac{2}{5} + \frac{1}{x} = 10 \\ \frac{1}{x} = 10 - \frac{2}{5} \\ \frac{1}{x} = \frac{50 - 2}{5} \\ \frac{1}{ x } = \frac{48}{5} \\

use \: \: \: \: cross \: \: \: multiply

\\ 5 = 48x \\ \frac{5}{48} = \frac{48x}{48} \\ x = \frac{5}{48} \\ [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

169.5 yd²

Step-by-step explanation:

See attachment.

In situations like this, ALWAYS (!) make as sketch.

Divide the areas by adding dotted lines on sensible places, and write in the missing numbers for the correct distances.

The only possible difficult one is the triangle, which is the half of a rectangle. So you are dealing with a series of areas of rectangles. That is really easy if you understand what you are doing.

Total area =

area 1 + area 2 + area 3 + area 4

10*4 + 4*7 + 3*13 + (0.5 * 7*17)

40 + 28 + 42 + 59.5

Total area = 169.5 yd²

Answer:

C.

Step-by-step explanation:

First finding height using Pythagoras theorem

(H)²=(B)²+(P)²

8.2²=5.4²+P²

P² = 67.24 - 29.16

P² = 38.08

P = 6.2

Now

Volume of cone = (1/3)πr²h

= (1/3)(3.14)(5.4)²(6.2)

= (1/3)(567.9)

= 189.2 cm³

Answer:

Ratio of Able's score to Ben=6:1

Ratio of Ben's score to Cal's=1:2

Ratio of able's score to ben;s score to cal's score=6:1:2

Step-by-step explanation:

Let Ben's score =x

Able scored six times Ben's score

Able=6*x

=6x

Cal scored a third of Able's score

Cal=1/3 of 6x

=1/3(6x)

Ratio of Able's score to Ben

6x:x

=6:1

Ratio of Ben's score to Cal's score

x:1/3(6x)

=x:6x/3

=x:2x

=1:2

Ratio of able's score to ben;s score to cal's score=6:1:2

Answer:

0.35 cups/hour

Step-by-step explanation:

To be able to determine the rate at which the water is leaking from the pipe with the information given, you have to divide the number of cups by the number of hours in which they were collected:

12 cups/34 hours= 0.35 cups/hour

According to this, the answer is that the rate at which the water is leaking from the pipe is 0.35 cups/hour.

Answer:

26/3 as an improper fraction in simplest form. :)

Step-by-step explanation:

Answer:

22. positive

Step-by-step explanation:

–68 + 90

22

You are given the equation [tex]f(x)=x+6[/tex] and [tex]g(x)=x^4[/tex]. When you combine G(F(x))  your equation would come out as [tex]g(f(x))=x^4(x+6)[/tex]. Once you distribute the equation you will get [tex]g(f(x))=(x+6)^4[/tex]

Therefore you answer choice would be B. [tex](x+6)^4[/tex]

Answer:

[tex] T_1 = 10*3.5 = 35[/tex]

[tex] T_2 = 20*2.9 = 58[/tex]

[tex] T_3 = 25*3.2 = 80[/tex]

[tex] T_4 = 15*3.4 = 51[/tex]

[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] n_1= 10 , \bar X_1 = 3.5[/tex] for freshmen

[tex] n_2= 20 , \bar X_2 = 2.9[/tex] for sophomores

[tex] n_3= 25 , \bar X_3 = 3.2[/tex] for juniors

[tex] n_4= 15 , \bar X_4 = 3.4[/tex] for seniors

For this case we can use the formula for the sample mean in order to find the total of each group:

[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]T= \sum_{i=1}^n X_i = n *\bar X[/tex]

And replacing we got:

[tex] T_1 = 10*3.5 = 35[/tex]

[tex] T_2 = 20*2.9 = 58[/tex]

[tex] T_3 = 25*3.2 = 80[/tex]

[tex] T_4 = 15*3.4 = 51[/tex]

And the grand mean would be given by:

[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]

Answer:

1/x = 1/2÷4/5

1/x=1/2 x 5/4

1/x=5/8

5x=8

x=1.6

Answer:

-1/2 =x

Step-by-step explanation:

4x - 6 = 10x -3

Subtract 4x from each side

4x-4x - 6 = 10x-4x -3

-6 = 6x-3

Add 3 to each side

-6+3 = 6x

-3 = 6x

Divide each side by 6

-3/6 = 6x/6

-1/2 =x

[tex]answer \\ - \frac{1}{2} \\ solution \\ 4x - 6 = 10x - 3 \\ or \: 4x - 10x = - 3 + 6 \\ or \: - 6x = 3 \\ or \: x = \frac{3}{ - 6} \\ x = - \frac{1}{2} \\ hope \: it \: helps[/tex]