–2x + 2y = -4
3х + Зу = -18

Answer:

-707/704

Step-by-step explanation:

4x + 2 - 2116 - 2116x = 7

-2112x = 2121

x = 2121/-2112 = -707/704

Answer:

 x= 2121/-2112 = -707/704 = -1.00426136

Step-by-step explanation:

4x + 2 – 23(92 + 92x) = 7

               4x - 23(92+92x) = 5

    2. Discriminate by multiplying -23 with 92 and -23 with 92x

               4x - 2116 -2116x = 5

    3. Add 2116 both sides to eliminate -2116

              4x -2116x = 2121

    4. combine 4x-2116x together

             -2112x = 2121

    5. Divide both sides with -2112

              x= 2121/-2112 = -707/704 = -1.00426136

Answer:

8 to 25

Step-by-step explanation:

The total number of lunches sold i

220+120+160 =500

We want the ratio of salads to total lunches

salads: lunches

160:    500

Divide each side by 20

160/20 : 500/20

8:25

Answer:Close to 60 country songs but probably not exactly 60 country songs.

Step-by-step explanation:

Mekala player Jumble has 4 techno songs, 2 country songs, and 3 jazz songs on it.

Represent this songs in ratio format

Ratio of techno songs,to country songs,to jazz songs= 4: 2 : 3

Total number of songs is unknowns ,let it be represented by x

total number of songs is therefore 4 x, 2 x, and 3 x.

Total number of songs that Mekala plans to Listen = 2 70

Then , 4 x + 2 x + 3 x= 270

9 x = 270

Dividing both sides by 9, we get

x = 30

So, Number of techno songs = 4 × 30= 120

Number of country songs = 2 × 30= 60

Number of jazz songs = 3 × 30= 90

Answer:

Close to 60 country songs but probably not exactly 60 country songs

Step-by-step explanation:

Answer:

x,y( 27/13 ,43/13)

Step-by-step explanation:

x=5-4y

•1-2x+5y=16

1-2(5-4y)+5y=16

y=27/13

x=5-4y

x=5-4×27/13

x=-43/13

Answer:

$36

Step-by-step explanation:

You are going to want to use the simple interest formula for this. The one below is modified for solving the interest earned.

[tex]I = Prt[/tex]

I = interest amount

P = principal amount

r = interest rate (decimal form)

t = time (years)

First, change 4% into a decimal:

4% -> [tex]\frac{4}{100}[/tex] -> 0.04

Now, plug the values into the equation:

[tex]I=300(0.04)(3)[/tex]

[tex]I=36[/tex]

The interest earned is $36

Given:

Given that the figure DEFG with vertices D(1,2), E(2,6), F(6,7) and G(5,3)

We need to determine the perimeter of DEFG.

The length of the sides can be determined using the formula,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Length of DE:

Substituting the coordinates D(1,2), E(2,6) in the formula, we get;

[tex]DE=\sqrt{(2-1)^2+(6-2)^2}[/tex]

[tex]DE=\sqrt{(1)^2+(4)^2}[/tex]

[tex]DE=\sqrt{17}[/tex]

Length of EF:

Substituting the coordinates E(2,6), F(6,7) in the formula, we get;

[tex]EF=\sqrt{(6-2)^2+(7-6)^2}[/tex]

[tex]EF=\sqrt{(4)^2+(1)^2}[/tex]

[tex]EF=\sqrt{17}[/tex]

Length of FG:

Substituting the coordinates F(6,7), G(5,3) in the formula, we get;

[tex]FG=\sqrt{(5-6)^2+(3-7)^2}[/tex]

[tex]FG=\sqrt{(-1)^2+(-4)^2}[/tex]

[tex]FG=\sqrt{17}[/tex]

Length of DG:

Substituting the coordinates D(1,2), G(5,3) in the formula, we get;

[tex]DG=\sqrt{(5-1)^2+(3-2)^2}[/tex]

[tex]DG=\sqrt{(4)^2+(1)^2}[/tex]

[tex]DG=\sqrt{17}[/tex]

Perimeter of DEFG:

The perimeter of DEFG can be determined by adding the side lengths DE, EF, FG and DG.

Thus, we have;

[tex]Perimeter=DE+EF+FG+DG[/tex]

Substituting the values, we have;

[tex]Perimeter=\sqrt{17}+\sqrt{17}+\sqrt{17}+\sqrt{17}[/tex]

[tex]Perimeter=4\sqrt{17}[/tex]

Thus, the perimeter of DEFG is 4√17

Hence, Option b is the correct answer.

Answer:

-5

Step-by-step explanation:

Answer:

The answer is -5

Step-by-step explanation:

Answer:

116

Step-by-step explanation: You would have to split the figure into a square and a triangle as you can see in the picture. You then find the area of each figure.

Area of Square : 8 * 8 = 64

Area of Triangle : 8 * 13 /2 = 52

Then, you add the areas of both figures together to get 116.

Answer:

19

Step-by-step explanation:

if x=3

Answer:

x = 2

Answer: The third option.

Step-by-step explanation:

This is an equation because it has an equals sign that can be solved for, making it an equation.

Answer:

x + 3 = 12

Step-by-step explanation:

This is an equation because it contains an equal sign, if it does not contain an equal sign then it is an expression.

Answer:

Length in feet is equal to [tex]\frac{2P}{6.5}[/tex], where P is the perimeter

Step-by-step explanation:

Let the width (W) of the yard be "X"

[tex]W = w[/tex]

Then the length(L) of the yard will be

[tex]2\frac{1}{4} * w[/tex]

[tex]L = \frac{9}{4} *w[/tex]

The perimeter of the yard will be equal to the sum of twice the length and width of the yard

Thus,

[tex]P = 2 W + 2L\\[/tex]

Substituting the given values in above equation, we get -

[tex]P = 2 w + 2 (\frac{9}{4})w\\P = 2w + 4.5 w\\P = 6.5w[/tex]

Thus, width in terms of perimeter is equal to

[tex]w = \frac{P}{6.5}[/tex]

Length in feet is equal to [tex]\frac{2P}{6.5}[/tex]

Answer:

The median. 80 because the mean is 80.454545

Step-by-step explanation:

When dividing two fractions, it is important to know to multiply the first fraction by the reciprocal of the second fraction.

Reciprocal means basically a flipped fraction. 2/3 as a reciprocal is 3/2, etc.

1/3 / 1/2= 1/3 x 2/1=2/3

Answer:

6 periods

Step-by-step explanation:

The investment is compounded semi-annually which means it is compounded twice in a year. Period of investment is 3 years. So, number of periods compounded is 3 multiplied by 2 that is 6 periods.

Rate would be 8% divided by 2 that is 4%.

Initial investment can be calculated usinf spreadsheet function as =PV(rate,nper, pmt, FV)

Where,

rate is 0.04

nper is 6

pmt is 0

FV is 7,000

So, initial investment is $5,532.20.

It is negative as it is a cash outflow.

Answer:

3.4

Step-by-step explanation:

3.4+3.4= 6.8

10.2-6.8=3.4

Answer:

(4/3) x 3.14 x (13^3) = 9198.1066666... (repeating decimal)

Step-by-step explanation:

The result of multiplication is: 4/3 x 3.14 x 13³ =9198.11.

Here, we have,

given that,

4/3 x 3.14 x 13³

now, we have to multiply the terms.

so, we get,

4/3 x 3.14 x 13³

=4/3 x 3.14 x 13 x 13 x 13

=4/3 x 3.14 x 2197

=4/3 x 6898.58

=27594.32 /3

=9198.11

Hence, The result of multiplication is: 4/3 x 3.14 x 13³ =9198.11.

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Answer:

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

300:51*100 =

(300*100):51 =

30000:51 = 588.24

Now we have: 300 is what percent of 51 = 588.24

Question: 300 is what percent of 51?

Percentage solution with steps:

Step 1: We make the assumption that 51 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$x​.

Step 3: From step 1, it follows that $100\%=51$100%=51​.

Step 4: In the same vein, $x\%=300$x%=300​.

Step 5: This gives us a pair of simple equations:

$100\%=51(1)$100%=51(1)​.

$x\%=300(2)$x%=300(2)​.

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

$\frac{100\%}{x\%}=\frac{51}{300}$

100%

x%​=

51

300​​

Step 7: Taking the inverse (or reciprocal) of both sides yields

$\frac{x\%}{100\%}=\frac{300}{51}$

x%

100%​=

300

51​​

$\Rightarrow x=588.24\%$⇒x=588.24%​

Therefore, 17% of 300 is 51

Answer:

Answer 17%

Step-by-step explanation:

Solution for 300 is what percent of 51:

300:51*100 =

(300*100):51 =

30000:51 = 588.24

588.24 as a percentage is 17%

Answer:

Step-by-step explanation:

hello :

let: A = 3√16+√-9

16=4²   and  -9 = 9i² =(3i)²   .... ( i² = -1)

√16 =√4² = 4     and  √-9 = √9i²= √(3i)² ± 3i

A= 12  ± 3i

Complete Question:

a) Is it plausible that X is normally distributed?

b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 100 min and 125 min?

Answer:

a) It is plausible that X is normally distributed

b) probability that the sample mean courtship time is between 100 min and 125 min is 0.5269

Step-by-step explanation:

a)X denotes the courtship time for the scorpion flies which indicates that is a real - valued random variable, and since normal distribution is a continuous probability distribution for a real valued random variable, it is plausible that X is normally distributed.

b) Probability that the sample mean courtship time is between 100 min and 125 min

[tex]\mu = 120\\n = 50[/tex]

[tex]P(x_{1} < \bar{X} < x_{2} ) = P(z_{2} < \frac{x_{2}- \mu }{SD} ) - P(z_{1} < \frac{x_{2}- \mu }{SD})[/tex]

[tex]SD = \sqrt{\frac{\sigma^{2} }{n} } \\SD = \sqrt{\frac{110^{2} }{50} } \\SD = 15.56[/tex]

[tex]P(100 < \bar{X} <125 ) = P(z_{2} < \frac{125- 120 }{15.56} ) - P(z_{1} < \frac{100- 120 }{15.56})\\P(100 < \bar{X} <125 ) = P(z_{2} < 0.32 ) - P(z_{1} < -1.29)[/tex]

From the probability distribution table:

[tex]P(z_{2} < 0.32 ) = 0.6255\\ P(z_{1} < -1.29) = 0.0986[/tex]

[tex]P(100 < \bar{X} <125 ) = 0.6255 - 0.0986\\P(100 < \bar{X} <125 ) =0.5269[/tex]

Answer:

Population size:8

Lower quartile (xL): 0.925

Upper quartile (xU): 5.85

Interquartile range (xU-xL): 4.925

Step-by-step explanation:

Answer:

4.65

Step-by-step explanation:

7.8, 0.6, 1.9, 5, 5.7, 0.7, 1.6, 5.9

Sort the data

0.6, 0.7, 1.6, 1.9, 5, 5.7, 5.9, 7.8

Q1: (0.7+1.6)/2

= 1.15

Q3: (5.7+5.9)/2

= 5.8

IQR = 5.8 - 1.15

= 4.65

Answer:

(x+5y)(x+6y)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find attached the solution

Answer:

The probability that Tony removes one yellow, one green ,one blue,and then one more blue tennis ball is 0.0039.

Step-by-step explanation:

We are given that a bucket contains five green tennis balls, two yellow tennis balls, six red tennis balls, and eight blue tennis balls.

As we know that, Probability of an event  =  [tex]\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}[/tex]

Number of green tennis balls = 5

Number of yellow tennis balls = 2

Number of red tennis balls = 6

Number of blue tennis balls = 8

Total number of tennis balls = 5 + 2 + 6 + 8 = 21

{Now it should be notes that Tony removes for tennis balls, without replacement from the bucket means that every time the total number of remaining balls available for selecting will be one less}.

Now, Probability that Tony removes one yellow =  [tex]\frac{2}{21}[/tex]

Probability that Tony removes one green =  [tex]\frac{5}{20}[/tex]

Probability that Tony removes one blue =  [tex]\frac{8}{19}[/tex]

Probability that Tony removes one blue again =  [tex]\frac{7}{18}[/tex]

SO, final probability is =  [tex]\frac{2}{21} \times \frac{5}{20} \times \frac{8}{19} \times \frac{7}{18}[/tex]  

                                      =  [tex]\frac{2}{513}[/tex]

                                      =  0.0039

Answer:

a.   0.71

b.   0.9863

Step-by-step explanation:

a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.

-To estimate the probability that a randomly selected house  has a value less than $500,000:

[tex]P(X<500,000)=P(X=0)+P(X=500)\\\\=0.34+0.37\\\\=0.71[/tex]

Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b. -since 40 is larger than or equal to 30, we assume normal distribution.

-The probability can therefore be calculated as:

[tex]P(\bar X)=P(z<\frac{\bar X-\mu}{\sigma/\sqrt{n}})\\\\=P(z<\frac{500-403}{278/\sqrt{40}})\\\\=P(z<2.2068)\\\\=0.986336\\\\\approx 0.9863[/tex]

Hence, the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

To estimate the probability that a house is valued less than $500,000, we count the bars below that value on the histogram. To estimate the probability that the mean value of 40 houses is less than $500,000, we use the Central Limit Theorem to calculate the z-score.

(a) To estimate the probability that the selected house is valued at less than $500,000, we need to find the area under the histogram below the value of $500,000. Looking at the histogram, we see that there are 3 bars below $500,000. Each bar represents a count of houses, so we add up the counts of those 3 bars. The estimated probability is given by:

Estimated Probability = (Count of houses valued less than $500,000) / (Total count of houses)

(b) To estimate the probability that the mean value of the 40 houses is less than $500,000, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. We can then calculate the z-score for $500,000 using the formula:

z = (x - mean) / (standard deviation / sqrt(sample size))

Once we have the z-score, we can find the estimated probability using a standard normal distribution table or calculator.

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Answer:

The correct option is;

D. This method uses the binomial probability distribution with the P-value method ans uses the value of p assumed  in the null hypothesis

Step-by-step explanation:

Here we have the binomial probability distribution is used to test claims about a proportion then the requirement is np > 5 and nq >5

In a left-tailed test, the P value is the probability of getting x or fewer successes among n trials while in a right tailed test, the P-value is the probability of getting x or more successes among n trials

However, the P-value where a binomial distribution is used to test a claim about a proportion is derived from the z score of the parameters of the statistic and not from the p assumed in the null hypothesis.

The incorrect statement is option B. A left-tailed test in binomial probability distribution does not correspond to the probability of getting x or fewer successes among n trials.

The statement among the given options that is NOT true of using the binomial probability distribution for testing claims about a proportion is option B. A left-tailed test does not entail the probability of getting x or fewer successes in the n trials. Instead, it approximates the probability of observing a value as extreme as the test statistic or even more extreme, which leans to the left or lower end of the distribution. Thus, the P-value in a left-tailed test corresponds to the total probability of the shaded region of the curve that falls to the left of observed value or test statistic. The remainder of the options (A, C, and D) are accurate statements.

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Answer:

B. No, the equation is not a good fit because the sum of the residuals is far from zero. Should be your answer

Step-by-step explanation:

Have a nice day :)

No, the equation is not a good fit because the sum of the residuals is far from zero.

Two or more expressions with an Equal sign is called as Equation. An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

An equation was created for the line of best fit from the actual enrollment data. which was used to predict the dance studio enrollment values shown in the table.

We need to check whether the equation that produced the predicted values represents a good line of best fit.

No, the equation is not a good fit because the sum of the residuals is far from zero.

A line of best fit is meant to compensate for positive and negative deviation in a matter that balances them. A large residual values' sum shows that they are not balanced.

Hence, No, the equation is not a good fit because the sum of the residuals is far from zero.

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Answer:

B. The value of the ones digit is the same as the value of the tenths digit.

Step-by-step explanation:

346.68

From the above digit, the value of one is 6 and the value of tenth is 6.

3 = hundred

4 = ten

6 = unit

6 = tenth

8 = hundredth

The unit is the same for ones.

From the above we can see that unit and tenth have the same value.

So, therefore, the answer is:

B. The value of the ones digit is the same as the value of the tenths digit.

Answer:

[tex](9 - 4) \\ ( {3}^{2} - {2}^{2}) \\ (3 - 2)(3 + 2) \\ 1 \times 5 = 5 [/tex]

hope this helps you.