What is the solution to the system of equations?
5x – 4y = 6
-5x + 4y = -10
O (4,4)
0 (-2,-5)
O infinitely many solutions
O no solution

Answer:16

Step-by-step explanation:

Just divide 80 by 5 or skip count by fives.

The equation of the straight line is [tex]x+y=2[/tex].

Given:

To find: The equation of this line

It is given that a line with intercepts (a,0) and (0,b) has the equation [tex]\frac{x}{a} +\frac{y}{b} =1, a\neq 0, b\neq 0[/tex]

Now, it is given that the referred line has intercepts (a, 0) and (0, a). Then, using the above statement, the equation of this line can be written as,

[tex]\frac{x}{a} +\frac{y}{a}=1[/tex]. It is already given that [tex]a\neq 0[/tex]. So, we need not mention it again.

It is also given that the point (-2, 4) lies on this line. Then, the coordinates of this point must satisfy the equation of the line.

This implies that,

[tex]\frac{-2}{a} +\frac{4}{a} =1[/tex]

[tex]\frac{2}{a} =1[/tex]

[tex]a=2[/tex]

Now, put [tex]a=2[/tex] in the equation of the line, [tex]\frac{x}{a} +\frac{y}{a}=1[/tex] to get,

[tex]\frac{x}{2} +\frac{y}{2} =1[/tex]

[tex]x+y=2[/tex]

So, the equation of the line is [tex]x+y=2[/tex].

Learn more about equations of straight lines here:

https://brainly.com/question/18879008

Answer:

[tex]\boxed{x=1}[/tex] and [tex]\boxed{x=7}[/tex]

Step-by-step explanation:

This quadratic is already factored down to its factors (x - 1) and (x - 7).

Set these equal to zero and solve for x by adding 1 or 7 to both sides of the equation.

[tex]x-1=0\\\\\boxed{x=1}[/tex]

[tex]x-7=0\\\\\boxed{x=7}[/tex]

Answer:

D

Step-by-step explanation:

-0.81 is a high negative correlation, which means the y is decreasing with x increasing, which means y(the number of broken glass) decreases when x(amount of paper used) increased. So we can say that the toilet paper is surely helping.

make me brainly if you find it correct

for x ,

8x + 10x = 180°

[sum of linear pair is equal to 180°]

or, 18x = 180°

or, x = 180/18

therefore, x = 10°……

for z,

10z =8x

[ being corresponding angles are equal ]

or, 10z = 8 × 10°

( replacing x by 10°)

or, 10z = 80°

or, z = 80/10

thus z = 8°…………

Answer:

Step-by-step explanation:

3w + 2c = 32

4w + 3c = 44

Multiply the 1st equation by 4 and 2nd equation by 3, we get:

12w + 8 c = 128

12w + 9 c = 132

Subtracting the top equation from the bottom equation, we get: c = 4

Substituting c = 4 in any one of the above equations and solving, we get: w = 8

Therefore, weight of 2w + 1c = 2(8) + 4 = 20 pounds (Answer)

Answer:

Ashley= 15

Milan= 11

Carlos= 105

Step-by-step explanation:

Let, A, M and C denotes Ashley, Milan and Carlos respectively.

A+M+C= 131 (according to the question)

Here,

C= 7A

A= M+ 4

So, M= A - 4

Now,

A+M+C = 131

or, A+ A-4+ 7A = 131 (putting the values)

or, 9A - 4 = 131 (adding like terms i.e. A + A + 7A)

or, 9A = 131 + 4

or, 9A = 135

or, A = 135 / 9

So, A = 15

C= 7A = 7×15= 105

M= A-4 = 15 - 4 = 11

Answer:

five and forty-four hundredths

Step-by-step explanation:

Answer:

five point four four

Step-by-step explanation:

Answer:

A'=(-9, - 3)

Step-by-step explanation:

A' will be 3*(the coordinates of A), A'=(-9, - 3)

Coordinates of A' are given by (-9,-3).

Coordinates of a point suggest the position of that particular point in the Cartesian Plane.

If the coordinates of a point are (x,y) then x is the distance of the point from Y-axis and y is the distance from the X-axis.

Here in the given graph, we can see that the coordinates of A of quadrilateral ABCD are (-3,-1)

ABCD is dilated by a factor of 3.

So the coordinates of the A' which is the point A after dilating by 3 are given by the product of 3 and corresponding original coordinations.

Hence the coordinates of A' are = (3*(-3),3*(-1)) = (-9,-3)

Learn more about Coordinates here -

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Answer:

f(g(1)) = - 2

Step-by-step explanation:

Find g(1) then use the value obtained to find f(x)

g(1) = 1 ← value of y when x = 1 (1, 1 ) , then

f(1) = - 2 ← value of y when x = 1 (1, - 2 )

Answer:

A.the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]

B. β  = 0.0122

C. β  = 0.0000

Step-by-step explanation:

Given that:

Mean = 100

standard deviation = 2

sample size = 9

The null and the alternative hypothesis can be computed as follows:

[tex]\mathtt{H_o: \mu = 100}[/tex]

[tex]\mathtt{H_1: \mu \neq 100}[/tex]

A. If the acceptance region is defined as [tex]98.5 < \overline x > 101.5[/tex] , find the type I error probability [tex]\alpha[/tex] .

Assuming the critical region lies within [tex]\overline x < 98.5[/tex] or [tex]\overline x > 101.5[/tex], for a type 1 error to take place, then the sample average x will be within the critical region when the true mean heat evolved is [tex]\mu = 100[/tex]

∴

[tex]\mathtt{\alpha = P( type \ 1 \ error ) = P( reject \ H_o)}[/tex]

[tex]\mathtt{\alpha = P( \overline x < 98.5 ) + P( \overline x > 101.5 )}[/tex]

when  [tex]\mu = 100[/tex]

[tex]\mathtt{\alpha = P \begin {pmatrix} \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline 98.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} + \begin {pmatrix}P(\dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{101.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} }[/tex]

[tex]\mathtt{\alpha = P ( Z < \dfrac{-1.5}{\dfrac{2}{3}} ) + P(Z > \dfrac{1.5}{\dfrac{2}{3}}) }[/tex]

[tex]\mathtt{\alpha = P ( Z <-2.25 ) + P(Z > 2.25) }[/tex]

[tex]\mathtt{\alpha = P ( Z <-2.25 ) +( 1- P(Z < 2.25) })[/tex]

From the standard normal distribution tables

[tex]\mathtt{\alpha = 0.0122+( 1- 0.9878) })[/tex]

[tex]\mathtt{\alpha = 0.0122+( 0.0122) })[/tex]

[tex]\mathbf{\alpha = 0.0244 }[/tex]

Thus, the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]

B. Find beta for the case where the true mean heat evolved is 103.

The probability of type II error is represented by β. Type II error implies that we fail to reject null hypothesis [tex]\mathtt{H_o}[/tex]

Thus;

β = P( type II error) - P( fail to reject [tex]\mathtt{H_o}[/tex] )

∴

[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]

Given that [tex]\mu = 103[/tex]

[tex]\mathtt{\beta = P( \dfrac{98.5 -103}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-103}{\dfrac{2}{\sqrt{9}}}) }[/tex]

[tex]\mathtt{\beta = P( \dfrac{-4.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-1.5}{\dfrac{2}{3}}) }[/tex]

[tex]\mathtt{\beta = P(-6.75 \leq Z \leq -2.25) }[/tex]

[tex]\mathtt{\beta = P(z< -2.25) - P(z < -6.75 )}[/tex]

From standard normal distribution table

β  = 0.0122 - 0.0000

β  = 0.0122

C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?

[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]

Given that [tex]\mu = 105[/tex]

[tex]\mathtt{\beta = P( \dfrac{98.5 -105}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-105}{\dfrac{2}{\sqrt{9}}}) }[/tex]

[tex]\mathtt{\beta = P( \dfrac{-6.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-3.5}{\dfrac{2}{3}}) }[/tex]

[tex]\mathtt{\beta = P(-9.75 \leq Z \leq -5.25) }[/tex]

[tex]\mathtt{\beta = P(z< -5.25) - P(z < -9.75 )}[/tex]

From standard normal distribution table

β  = 0.0000 - 0.0000

β  = 0.0000

The reason why the value of beta is smaller here is that since the difference between the value for the true mean and the hypothesized value increases, the probability of type II error decreases.

Answer:

y = 15°

Step-by-step explanation:

Since ∠QOR and ∠UOT are vertical, they are congruent so ∠UOT = 5y. Since POS is a straight line (which has a measure of 180°) and ∠POS = ∠POU + ∠UOT + ∠TOS, we can write:

5y + 5y + 2y = 180

12y = 180

y = 15°

Answer: [tex]A=6000(1.012)^t[/tex]

Step-by-step explanation:

General exponential function:

[tex]A=P(1+r)^t[/tex]

, where P= current  population

r= rate of growth

t= time period

A= population after t years

As per given , we have P=6,000

r= 1.2% = 0.012

Then, the required exponential function:  [tex]A=6000(1+0.012)^t[/tex]

or [tex]A=6000(1.012)^t[/tex]

Answer:

The answer is "(0.9193924 , 0.9206076)".

Step-by-step explanation:

[tex]\text{sample proportion}\ (SP) = 0.92\\\\\text{sample size}\ n = 851\\\\\text{Standard error} \ SE = \sqrt{\frac{(SP \times(1 - SP)}{n})}\\\\[/tex]

                              [tex]= \sqrt{\frac{(0.92 \times (0.08)}{851})}\\\\= \sqrt{\frac{0.0736}{851}}\\\\= \sqrt{8.648\times 10^{-5}}\\\\=0.00031[/tex]

[tex]\text{CI level is}\ 95\% \\\\\therefore\\\\ \alpha = 1 - 0.95 = 0.05\\\\\frac{\alpha}{2} = \frac{0.05}{2} = 0.025\\\\ Z_c = Z_{(\frac{\alpha}{2})} = 1.96[/tex]

Calculating the Margin of Error:

[tex]ME = z_{c} \times SE\\\\[/tex]

       [tex]= 1.96 \times 0.00031\\\\ = 0.0006076[/tex]

[tex]CI = (SP - z*SE, SP + z*SE)[/tex]

      [tex]= (0.92 - 1.96 * 0.00031 , 0.92 + 1.96 * 0.00031)\\\\ = (0.92 - 0.0006076 , 0.92 + 0.0006076)\\\\= (0.9193924 , 0.9206076)[/tex]

Let y = x + 22 and dy = dx, so the integral becomes

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{25}^{31} \frac{\mathrm dy}{(y-1)\sqrt{y}}[/tex]

Now let z = √y, so that z ² = y. Then 2z dz = dy, and the integral becomes

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{\sqrt{25}}^{\sqrt{31}} \frac{2z}{(z^2-1)z} \\\\ = \int_5^{\sqrt{31}} \frac{2}{z^2-1}\,\mathrm dz[/tex]

Expand the integrand into partial fractions:

[tex]\dfrac{2}{z^2-1} = \dfrac1{z-1}-\dfrac1{z+1}[/tex]

Then we have

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_5^{\sqrt{31}}\left(\frac1{z-1}-\frac1{z+1}\right)\,\mathrm dz \\\\ = \left(\ln|z-1|-\ln|z+1|\right)\bigg|_5^{\sqrt{31}} \\\\ =\left[\ln\left|\frac{z-1}{z+1}\right|\right]\bigg|_5^{\sqrt{31}} \\\\ =\ln\left(\frac{\sqrt{31}-1}{\sqrt{31}+1}\right) - \ln\left(\frac{4}{6}\right) \\\\ =\ln\left(32-2\sqrt{31}\right) - \ln\left(\frac23\right) \\\\ =\boxed{\ln\left(48-3\sqrt{31}\right)}[/tex]

Answer:

-10

Step-by-step explanation:

We can substitute c into the equation as -2.

[tex]-(-2) - 12[/tex]

Two negatives make a positive:

[tex]2-12[/tex]

And [tex]2 - 12 = -10[/tex].

Hope this helped!

Answer:

5, 7, 9, 11

or

5, 6, 10, 11.

Step-by-step explanation:

The mean is 8 so the total value of the 4 numbers =  4*8 = 32.

Range is 6 so largest number - smallest = 6

The largest value is 11 so the smallest is 11-6 = 5

The middle 2 numbers add up to 32-(11+5) = 32 - 16

= 16.

- and as there is no mode they must be 7 and 9

or 6 and 10.

Answer:

2x-3

Step-by-step explanation:

f(x) = 3x-1

g(x)= x+2

(f-g) (x) = 3x-1 - (x+2)

Distribute the minus sign

             = 3x-1 -x-2

 Combine like terms

               = 3x-x -1-2

                =2x -3

ans: 257,256.59

if it was sold for $3.99

it would have been 86,047 × $3.99 = 343,303.59 and it was sold for $1 instead so automatically it's $86,047

therefore

343, 303.59

-86, 047 which is equal to a loss of $257, 256.59

Answer:

38%

Step-by-step explanation:

First determine her savings

560-347.49

212.51

Then divide by the total amount

212.51/560

.379482143

Change to percent form

37.948%

Answer:

38%

Step-by-step explanation:

[tex]560.00-347.49=212.51\\212.51\div560.00==38[/tex]

Answer:

KI and HE are parallel

So we apply the law of exterior angles ;

3X=X + 180– 2X

3X +X = 180

4X= 180

X= 180/4

X= 45

I hope I helped you^_^

Answer:

92.9997<[tex]\mu[/tex]<99.5203

Step-by-step explanation:

Using the formula for calculating the confidence interval expressed as:

CI = xbar ± Z * S/√n where;

xbar is the sample mean

Z is the z-score at 90% confidence interval

S is the sample standard deviation

n is the sample size

Given parameters

xbar = 96.52

Z at 90% CI = 1.645

S = 10.70.

n = 25

Required

90% confidence interval for the population mean using the sample data.

Substituting the given parameters into the formula, we will have;

CI = 96.52 ± (1.645 * 10.70/√25)

CI = 96.52 ± (1.645 * 10.70/5)

CI = 96.52 ± (1.645 * 2.14)

CI = 96.52 ± (3.5203)

CI = (96.52-3.5203, 96.52+3.5203)

CI = (92.9997, 99.5203)

Hence a 90% confidence interval for the population mean using this sample data is 92.9997<[tex]\mu[/tex]<99.5203

Answer:

2. 20 oranges

3. 18 yellow tulips

4. 23 students

Answer:

D = 240 - 30t

Step-by-step explanation:

If the equation represents her distance from City A, we need to include 240 in the equation to represent the distance to the city.

Then, we need to subtract 30t from 240 in the equation because 30t represents how far she will have traveled in t hours.

So, D = 240 - 30t is the equation that will represent Layla's distance from the city.

Answer:

3166.7

Step-by-step explanation:

V = πr²h

V = π * (12 km)² * 7 km

V ≈ 3166.7 km³

Hey there!

First, let's review the formula for finding a cylinder's volume.

Formula: [tex]\pi r^2h[/tex]

Our new equation would look like this: [tex]\pi[/tex] x [tex]12^{2}[/tex] x 7.

The original answer would be 3166.72539482, but the question states that it want it rounded to the nearest tenth. So, your answer would be 3166.7.

Hope this helps! Have a great day!

Answer:

Player A has a probability 2/3 of making each of her shots, then she has a probability 1/3 of missing each shot.

Player B has a probability 1/2 of making each of his shots, then he also has a probability 1/2 of missing each shot.

Let's separate each case.

Let's define:

P(x) = probability of winning at the "x" shot.

Player A wins on the first shot.

Because she has a probability 2/3 of making each of her shots, the probability of winning at the first shot is

P(1) = 2/3

Now let's see the next case, player A wins at her second shot.

This means that first, she misses her first shot, with a probability of:

p₁ = 1/3

Player B must miss his shot, the probability is:

p₂ = 1/2

Now player A must make her shot, so the probability is:

p₃ = 2/3

The joint probability is the product of the individual probabilities, so we have:

P(2) = (1/3)*(1/2)*(2/3) = 1/9

Now we can see the pattern, for P(3) we have

A misses: p₁ = 1/3    (first shot of A)

B misses: p₂ = 1/2

A misses: p₃ = 1/3   (Second shot of A)

B misses: p₄ = 1/2

A makes the shot: p₅ = 2/3

P(3) =  (1/3)*(1/2)*(1/3)*(1/2)*(2/3) = 1/54

We already can see the pattern.

P(n) = (1/3)^(n - 1)*(1/2)*(n - 1)*(2/3)

Player A has a probability P of winning, and we can write P as:

P = P(1) + P(2) + P(3) + ...

Then we will have:

P = 2/3 + 1/9 + 1/54 + 1/324 + ... ≈ 0.8