What is the solution to the following system of equations?

|3x - 2y = 12
[6x - 4y= 24

It has infinitely many solutions.
It has no solution.
It has one solution (2, -3).
It has one solution (4,0)​

Answer: The answer is two

Step-by-step explanation: If you look for opposites of a number its either negative or positive. So when the answer is negative, the opposite is positive and if the answer is positive, the opposite is negative.

Answer:

[tex]\boxed{2}[/tex]

Step-by-step explanation:

The opposite of a number is the number that is the same distance from 0 on the number line.

-2 opposite is 2.

Answer:

m∠N = 51°

m∠M = 31°

m∠O = 98°

Step-by-step explanation:

It is given that ΔMNO is an isosceles triangle with base NM.

m∠N = (4x + 7)° and m∠M = (2x + 29)°

By the property of an isosceles triangle,

Two legs of an isosceles triangle are equal in measure.

ON ≅ OM

And angles opposite to these equal sides measure the same.

m∠N = m∠M

(4x + 7) = (2x + 29)

4x - 2x = 29 - 7

2x = 22

x = 11

m∠N = (4x + 7)° = 51°

m∠M = (2x + 9)° = 31°

m∠O = 180° - (m∠N + m∠M)

         = 180° - (51° + 31°)

         = 180° - 82°

         = 98°

Answer:

clearly the value of the test statistics shows that there are no enough evidence to support the claim that the proportion of the grads are the same.

Step-by-step explanation:

lets prove the statement by counter example, where if we have found the statement to be false for one then we conclude that it is false for all.

first lets explain what proportion is all about; proportion can be explained as the numerical relationship that compares things together.

in particular lets take grade A proportional to grade B which implies that 18:20

clearly if we observe here grade A is not same proportion with grade B. hence we conclude that there are no enough evidence to support the professor's claim.

Answer:

54.5 years.

Step-by-step explanation:

From the above question, we are asked to find the time

The formula for Time(t) =

t = log(A/P) / n[log(1 + r/n)]

A = Amount accumulated after a particular interest and period of time = $80,000

P = Principal (Money invested) = $4,000

r = rate = 5.5% = 0.055

n = compounding frequency = compounding continuously

n = number of days in a year × number of hours in a day

= 365 days × 24 hours = 8760

t = log(A/P) / n[log(1 + r/n)]

t = log(80,000/4,000) /8760[log(1 + 0.055/8760)]

t = log(80000 ÷ 4000) ÷ (8760 × [log(1 + 0.0000062785)]

t = 54.468367222 years

Approximately to the nearest tenth of a year, therefore, the length of time it will it take for his money to reach $80,000 is 54.5 years

Answer:

54.5

Step-by-step explanation:

Answer:

Option d: The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

The data are continuous if they can take on any value within a range. In this case study, there are different elephants including small/young ones and big ones/old ones.

Thus, their heights will vary and can take on any value within a particular range.

Answer:

x=8

Step-by-step explanation:

[tex]\sqrt{x+8}-\sqrt{x-4}=2\\\sqrt{x+8}=2+\sqrt{x-4}\\\left(\sqrt{x+8}\right)^2=\left(2+\sqrt{x-4}\right)^2\\x+8=x+4\sqrt{x-4}\\8=4\sqrt{x-4}\\8^2=\left(4\sqrt{x-4}\right)^2\\64=16x-64\\x=8[/tex]

Answer:

Option (D)

Step-by-step explanation:

Zero of any function is defined by the x-value of the function when y = 0.

Let the equation of the line given in the graph is,

y = mx + b

where m = slope of the line

b = y-intercept of the line

Slope of a line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by the formula,

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

If the passes through (0, -3) and (-2, 0)

m = [tex]\frac{-3-0}{0+2}[/tex]

m = [tex]-\frac{3}{2}[/tex]

Fro the graph,

y-intercept 'b' = -3

Therefore, equation of the line is,

[tex]y=-\frac{3}{2}x-3[/tex]

For y = 0,

[tex]0=-\frac{3}{2}x-3[/tex]

[tex]\frac{3}{2}x=-3[/tex]

x = -2

Therefore, option (D) will be the answer.

Answer:

d- -2

Step-by-step explanation:

Answer:

y=9x

Step-by-step explanation:

rise over run the rise is the y=9 and run is x=1.

9/1=9x

Answer:

72°

Step-by-step explanation:

Given two vectors a and b, The vector i+3j will form a right angled triangle with the x-axis (i.e the horizontal axis).

The opposite side of the triangle on the Cartesian plane will be 3units along the y axis while the adjacent will be 1 unit along the x axis.

The angle between thus two vectors is expressed as tan (theta) = opp/adj

tantheta = 3/1

theta = tan^-1(3)

Theta = 71.57° ≈ 72° to nearest degree

Answer: 9.0876544e+58

Step-by-step explanation:

Answer:

90876543579645968765443223456789009876543212345678909876544

Step-by-step explanation:

90876543579645968765443223456789009876543212345678909876543

+

1

=

90876543579645968765443223456789009876543212345678909876544

Answer:

0

Step-by-step explanation:

Solution:-

We are given two functions as follows:

                      [tex]f ( x ) = x^2 - 15\\\\g ( x ) = 2x[/tex]

We need to determine the composite function defined as ( g - f ) ( x ). To determine this function we need to make sure that both function exist for all real positive value of x.

The function f ( x ) is a quadratic function which has real values for all values of x. Similarly, function g ( x ) is a linear line that starts from the origin. Hence, both functions are defined over the domain ( -∞, ∞ )

We will perform arithmetic operation of subtracting function f ( x ) from g ( x ) as follows:

                       [tex][ g - f ] ( x ) = g ( x ) - f ( x )\\\\\\( g - f ) ( x ) = x^2 - 15 - 2x\\\\[/tex]

Now evaluate the above determined function at x = -3 as follows:

                       [tex]( g - f ) ( -3 ) = ( -3 )^2 - 2 ( -3 ) - 15\\\\( g - f ) ( -3 ) = 9 + 6 - 15\\\\( g - f ) ( -3 ) = 0[/tex]

Answer:

30

Step-by-step explanation:

We can call the number of boys 4x and girls 6x so we can write:

4x + 6x = 50

10x = 50

x = 5, therefore the number of girls is 6x = 6 * 5 = 30.

Answer:

30

Step-by-step explanation:

In the ratio 4:6, we can think of this like 4 boys and 6 girls out of 10 team members.

We can find how many girls play by multiplying 6 by 5, since 50 divided by 10 is 5.

6(5) = 30, so 30 girls play in the soccer league.

The true statement about the given transformation is; B: It is a dilation because the transformation is not isometric.

An isometric transformation is a shape-preserving transformation in the plane or in space. They include reflection, rotation and translation.

Now, from the given attachment showing the two figures, we can see that there is a dilation which means that it can't be isometric as the definition of Isometric transformation does not include Dilation.

Read more about Transformation at; https://brainly.com/question/4289712

#SPJ5

Answer:

b

Step-by-step explanation:

just took the test

Answer:

D. x^2 - 6x + 7.

Step-by-step explanation:

The roots are 3 plus or minus sqrt(2). That means the equation is...

(x - [3 + sqrt(2)]) * (x - [3 - sqrt(2)])

= [x - 3 - sqrt(2)] * [x - 3 + sqrt(2)]

= x^2 - 3x - xsqrt(2) - 3x + 9 + 3sqrt(2) + xsqrt(2) - 3sqrt(2) - (sqrt(2))^2

= x^2 - 3x - 3x + 9 - 2 - xsqrt(2) + xsqrt(2) + 3sqrt(2) - 3sqrt(2)

= x^2 - 6x + 7.

Hope this helps!

Answer:

A. 1.812

B. 1.753

C. 2.602

D. 3.747

E. 2.069

F. 2.453

Step-by-step explanation:

A. 95% confidence level, the level of significance = 5% or 0.05

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 10 degrees of freedom = 1.182

B. 95% confidence interval = 0.05 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 15 degrees of freedom = 1.753

C. 99% confidence interval = 0.01 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 15 degrees of freedom = 2.602

D. 99% confidence interval = 0.01 level of significance; DF (n - 1) = 5- 1 = 4

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 4 degrees of freedom = 3.747

E. 98% confidence interval = 0.02 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.02 significance level with 23 degrees of freedom = 2.069

F. 99% confidence interval = 0.01 level of significance; df (n - 1) = 32 - 1 = 31

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 31 degrees of freedom = 2.453

Answer:

Step-by-step explanation:

Assuming the colon between 40 and 8 is a mistype...

PEMDAS(Parenthesis, Exponents, Multiplication + Division, Addition + Subtraction)

[tex]40-8+3^2+(15-7)*2\\\\Parenthesis\\\\40-8+3^2+8*2\\\\Exponents\\\\40-8+9+8*2\\\\Multiplication\\\\40-8+9+16\\\\Subtraction\\\\32+9+16\\\\Addition\\\\41+16\\\\Addition\\\\57[/tex]

Hope it helps <3

━━━━━━━☆☆━━━━━━━

▹ Answer

57

▹ Step-by-Step Explanation

You need to follow PEMDAS:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

40 - 8 + 3² + (15 - 7)* 2

40 - 8 + 9 + (15 - 7) * 2

40 - 8 + 9 + 8 * 2

40 - 8 + 9 + 16

= 57

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

Step-by-step explanation:

3(−2a - 4)+3a

=-6a - 12 +3a

A: -6a - 12 +3a

[tex]hope \: this \: helps[/tex]

Answer:

the answer is A

Step-by-step explanation:

you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a

Answer:

[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]

which agrees with the first answer in the list of possible options.

Step-by-step explanation:

We can use the fact that the addition of all four internal angles of a quadrilateral must render [tex]360^o[/tex]. Then we can create the following equation and solve for the unknown "h":

[tex]2h+2h+h+h = 360^o\\6h=360^o\\h=60^o[/tex]

Therefore the angles of this quadrilateral are:

[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]

Answer:60,60,120,120

Step-by-step explanation:All qualdrilaterals equal to 360, so if you add all of the different numbers you should get 360

Answer:

probability that all of the sprinklers will operate correctly in a fire: 0.0282

Step-by-step explanation:

In order to solve this question we will use Binomial  probability distribution because:

A binomial distribution is a probability of a success or failures outcomes in an  repeated multiple or n times.

Number of outcomes of this distributions are two.

The formula is:

b(x; n, P) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

b = binomial probability  also represented as P(X=x)

x =no of successes

P = probability of a success on a single trial

n = no of trials

[tex]C_{n,x}[/tex] is calculated as:

[tex]C_{n,x}[/tex] = n! / x!(n – x)!

        = 10!  / 10!(10-10)!

        = 1

According to given question:

probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.

number of trials i.e. n = 10 as number of sprinklers are 10

To find: probability that all of the sprinklers will operate correctly in a fire

X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them

So putting these into the formula:

P(X=x) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

           = C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰

           =  1 * 0.0282 * (0.3) ⁰

           = 1 * 0.0282 * 1

  P(X=x)        = 0.0282

Answer:

a=6

b=5.5

Step-by-step explanation:

not very sure but..

since 8X2=16,

a=3X2

b=11/2

Answer:

The null hypothesis is ;

H0 ≥ 12

While the alternative hypothesis H1 is ;

H1 < 12

Step-by-step explanation:

Here, we want to correctly identify the null hypothesis H0 and the alternative hypothesis H1

The null hypothesis is as follows ;

H0 ≥ 12

While the alternative hypothesis H1 is ;

H1 < 12

Answer:

[tex]\dfrac{15}{16}[/tex]

Step-by-step explanation:

When a six sided die is rolled, the possible outcomes can be:

{1, 2, 3, 4, 5, 6}

Even numbers are {2, 4, 6}

Odd Numbers are {1, 3, 5}

Probability of even numbers:

[tex]\dfrac{\text{Favorable cases}}{\text{Total cases }} = \dfrac{3}{6} = \dfrac{1}{2}[/tex]

This is binomial distribution.

where probability of even numbers,  [tex]p =\frac{1}{2}[/tex]

Probability of not getting even numbers (Getting odd numbers) [tex]q =\frac{1}{2}[/tex]

Probability of getting r successes out of n trials:

[tex]P(r) = _nC_r\times p^r q^{n-r}[/tex]

Probability of getting even numbers at most 5 times out of 7 is given as:

P(0) + P(1) +P(2) + P(3) +P(4) + P(5)

[tex]\Rightarrow _7C_0\times \frac{1}{2}^0 \frac{1}{2}^{7}+_7C_1\times \frac{1}{2}^1 \frac{1}{2}^{6}+_7C_2\times \frac{1}{2}^2 \frac{1}{2}^{5}+_7C_3\times \frac{1}{2}^3 \frac{1}{2}^{4}+_7C_4\times \frac{1}{2}^4 \frac{1}{2}^{3}+_7C_5\times \frac{1}{2}^5 \frac{1}{2}^{2}[/tex]

[tex]\Rightarrow (\dfrac{1}{2})^7 (_7C_0+_7C_1+_7C_2+_7C_3+_7C_4+_7C_5)\\[/tex]

[tex]\Rightarrow (\dfrac{1}{2})^7 (1+7+\dfrac{7 \times 6}{2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6}{2})\\\Rightarrow \dfrac{120}{128} \\\Rightarrow \dfrac{15}{16}[/tex]

Answer:

Problem 1: We conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2: We conclude that the volume of Google stock has changed.

Step-by-step explanation:

Problem 1:

We are given that in a recent survey conducted by Pew Research, it was found that 156 of 295 adult Americans without a high school diploma were worried about having enough saved for retirement.

Let p = proportion of adult Americans without a high school diploma who are worried about having enough saved for retirement

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%    {means that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement}

Alternate Hypothesis, [tex]H_A[/tex] : p > 50%     {means that a majority of adult Americans without a high school diploma are worried about having enough saved for retirement}

This is a right-tailed test.

The test statistics that would be used here is One-sample z-test for proportions;

                       T.S.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of adult Americans who were worried about having enough saved for retirement = [tex]\frac{156}{295}[/tex] = 0.53

           n = sample of adult Americans = 295

So, the test statistics =  [tex]\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{295} } }[/tex]

                                    =  1.03

The value of z-test statistics is 1.03.

Also, the P-value of the test statistics is given by;

              P-value = P(Z > 1.03) = 1 - P(Z [tex]\leq[/tex] 1.03)

                           = 1 - 0.8485 = 0.1515

Now, at a 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.03 < 1.645, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that less than or equal to 50% of adult Americans without a high school diploma are worried about having enough saved for retirement.

Problem 2:

We are given that a random sample of 35 trading days in 2014 resulted in a  sample mean of 3.28 million shares with a standard deviation of 1.68 million shares.

Let [tex]\mu[/tex] = mean daily volume in Google stock

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 5.44 million shares    {means that the volume of Google stock has not changed}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 5.44 million shares     {means that the volume of Google stock has changed}

This is a two-tailed test.

The test statistics that would be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                       T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean volume in Google stock = 3.28 million shares

            s = sample standard deviation = 1.68 million shares

           n = sample of trading days = 35

So, the test statistics =  [tex]\frac{3.28-5.44}{\frac{1.68}{\sqrt{35} } }[/tex]  ~ [tex]t_3_4[/tex]

                                    =  -7.606

The value of t-test statistics is -7.606.

Also, the P-value of the test statistics is given by;

              P-value = P([tex]t_3_4[/tex] < -7.606) = Less than 0.05%

Now, at a 0.05 level of significance, the t table gives a critical value of -2.032 and 2.032 at 34 degrees of freedom for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of t, so we sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the volume of Google stock has changed.

Hey there! I'm happy to help!

The words at most means that there is a maximum point that is included as a probability. This means that we will use the less than or equal sign (≤) in our inequality.

Let's write this all out as an inequality now. We will use i to represent how much the baby ate.

1,800≤2i+250  

This inequality shows that Alexandria's 1,800 calories is at most 250 more than twice those of her baby sister. Therefore, the correct option is A. 1,800≤250+2i .

Have a wonderful day!

Answer:

The correct option is A. 1,800≤250+2i.

Answer:

[tex]\dfrac{21}{10}\text{ km}[/tex].

Step-by-step explanation:

It is given that,

Area of rectangular plot [tex]=\dfrac{7}{10}\text{ km}^2[/tex]

Width of rectangular plot [tex]=\dfrac{1}{3}\text{ km}[/tex]

We need to find the length of the parking lot.

We know that,

[tex]\text{Area of rectangle}=length\times width[/tex]

[tex]\dfrac{7}{10}=length\times \dfrac{1}{3}[/tex]

[tex]\dfrac{7\times 3}{10}=length[/tex]

[tex]length=\dfrac{21}{10}[/tex]

Therefore, length of the parking lot is [tex]\dfrac{21}{10}\text{ km}[/tex].

Answer:

5:1

Step-by-step explanation:

20/4= 5

1*5 = 5

5:1 ratio

Hope this helps!

Answer:

[tex]\boxed{Area\ of\ sector = 141.4\ cm^2}[/tex]

Step-by-step explanation:

Radius = r = 9 cm

Angle = θ = 200° = 3.5 radians

Now,

[tex]Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]

Area = 1/2 (9)²(3.5)

Area = 1/2 (81)(3.5)

Area = 282.7 / 2

Area of sector = 141.4 cm²

Answer:

45 pi cm^2 or 141.3 cm^2

Step-by-step explanation:

First find the area of the circle

A = pi r^2

A = pi (9)^2

A = 81 pi

A circle has 360 degrees

The shaded part has 200

The fraction that is shaded is

200/360 =5/9

Multiply by the total area

5/9 * 81 pi

45 pi

Using 3.14 for pi

141.3

45 pi cm^2 or 141.3 cm^2

hii

Step-by-step explanation:

length-10x

width-x

perimeter-2(l+b)

66=2(10x+x)

66-2=10x+x

64=11x

x=11/64

lenght-11

width-64

The graph shows f(x) to have a y intercept at -1, which is where the diagonal line crosses the y axis. We want the y intercept to move to 3. So we must add 4 to the old y intercept to get the new y intercept.

We do this with every single point on f(x) to get g(x) = f(x)+4. This shifts the graph up 4 units.

Answer:

Step-by-step explanation:

Let x represent the number of pounds of chocolate in the mix. Then the total price of 10 pounds of mix is ...

  10x +5(10 -x) = 80

  5x +50 = 80

  5x = 30

  x = 6 . . . . . . . . pounds of chocolate

  10 -x = 4 . . . . . pounds of jelly candy

6 pounds of chocolate and 4 pounds of jelly should be used to make the mixture.