Solve the equation 3x-13y = 2 for y.

Answer:

The discount is 36 dollars

The sale price is 44 dollars

Step-by-step explanation:

First find the discount by multiplying the original price by the discount rate

80*45%

Change to decimal form

80*.45

36

The discount is 36 dollars

The sale price is the original price minus the discount

80-36

44

The sale price is 44 dollars

Answer:

Answer C

Step-by-step explanation:

You are balancing this equation out by subtracting 7x from both sides. This means you are using the subtraction property of equality.

Answer:

      ESCAPES

Step-by-step explanation:

Answer:

-3+(-5)

Checking our answer:

Adding this does indeed give -8

Answer:

15

Step-by-step explanation:

PEMDAS

3x3 = 9

3+3 = 6

9+6 = 15

By the BODMAS rule we get, 3 + 3 × 3 + 3 =​ 15

The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).

3 + 3 × 3 + 3 =​

3 × 3 = 9

3 + 9 + 3 = 15.

Therefore, the correct answer is 15.

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Answer:

(A⋂B) U (A⋂C) = {d, e}

Step-by-step explanation:

U= {a,b,c,d,e,f,g,h}

A = {b,d,e}

B = {a,d,e}

C={a,c,f,g,h}

=> A⋂B = {d,e}

=> A⋂C = ∅

=> (A⋂B) U (A⋂C) = {d, e}

Answer:

[tex]x = 9\ or\ x = 1[/tex]

Step-by-step explanation:

Given

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

Required

Find the value of x

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

We start by taking the square root of 16; Square root of 16 is +4 or -4; So, we have:-

[tex]x = 5 \±4[/tex]

The expression above can be split into two; This is as follows

[tex]x = 5 + 4\ or\ x = 5 - 4[/tex]

[tex]x = 9\ or\ x = 1[/tex]

Hence, the solution to [tex]x = 5 + \sqrt{16}[/tex] is B. 1 and C. 9

Answer:

its b and c

Step-by-step explanation:

the guy who answered first said so

also i just did it

Answer:

49 people

Step-by-step explanation:

Take the amount of candy and divide by the amount in a serving

2 3/4 ÷ 1/18

Change to an improper fraction

(4*2+3)/4 ÷ 1 /18

11/4 ÷ 1/18

Copy dot flip

11/4 * 18/1

198/4

49.5

Round down since people do not want half a serving

49 people

Answer: 2 29/36

Step-by-step explanation:

Answer:

20% jumped the turnstile

80% paid

Step-by-step explanation:

We can calculate the percent of people that jumped it by dividing the number that did by the total:

12/60 = 0.2, which is 20%

If 20% jumped it, then this means 80% paid.

Answer:

jumped= 20%

paid= 80%

Step-by-step explanation:

[tex]\frac{12}{60}[/tex]×100 = 20%

[tex]\frac{48}{60}[/tex]×100 = 80%

Answer:

A) Weighted graph is attached

B) Shortest routes are;

1. A → C → B → D → A

2. A → D → B → C → A

Step-by-step explanation:

A) We are told their home is in City A. So that's where any journey will begin from.

Furthermore we are told that;

City A to City B = 296 ​miles

City A to City C = 206 ​miles

City A to City D = 79 ​miles

City B to City C = 497 ​miles

City B to City D = 241 ​miles

City C to City D = 281 miles.

I have attached an image of the weighted graph showing the distances on the appropriate edges.

B) We want to find the shortest route using Brute force method. The brute force method is by solving a particular problem by checking all the possible cases/routes to get the desired result we are looking for.

In this case, the desired result is the shortest route for the family to complete their vacation. So, i have attached a diagram showing the different routes via brute force method.

From the brute force method, the shortest length route is 1023 miles and this routes are from Cities;

1. A → C → B → D → A

2. A → D → B → C → A

Answer:

2/3x - y = -13/3

Step-by-step explanation:

Step 1: Find slope m

m = (3 - 5)/(-2 - 1)

m = -2/-3

m = 2/3

y = 2/3x + b

Step 2: Find b

5 = 2/3(1) + b

5 = 2/3 + b

b = 13/3

Step 3: Write equation in slope-intercept form

y = 2/3x + 13/3

Step 4: Move 2/3x over

-2/3x + y = 13/3

Step 5: Factor out -1

-1(2/3x - y) = 13/3

Step 6: Divide both sides by -1

2/3x - y = -13/3

Answer:

0.56

Step-by-step explanation:

What is the probability that his mother returns just in time to catch Gabe stealing a cookie?

The probability of this is the same as 1 minus the probability that Gabe is NOT caught.

- Judy could return at anytime in the next 90 seconds

- Gabe spends the first 40 seconds pondering... time wasted=40secs

- It takes 30 seconds (out of the remaining 50secs) to finish eating a cookie without a trace

- The question says that Gabe was going to do it, so he probably did

Now we're looking for the probability that he gets caught. That is, probability that he does not "successfully" complete the 30secs task within the remaining 50secs.

Remember that each second has an equal probability of being the second that Judy comes back in. The latter of the 90 seconds does not carry a higher probability!

So the probability of catching Gabe (despite the 30secs it takes to complete his task) is 50/90 which is equal to 0.56

Answer:

Step-by-step explanation:

The independent variables are the input values which are not dependent on the other value.

The dependent variables are the output values whose values depends on the value of some other number.

The independent variable in this case is the data on the set of distances she measured out.

The dependent variable in this case is the the time (measured by the stopwatch) it takes for the ball to roll.

The control variable in this case study is the size of ball, slope of hill, weight of ball etc.

Answer:

125 times

Step-by-step explanation:

30x5=150

25x5=125

Answer:

See Explanation

Step-by-step explanation:

[tex]f(x) = 4 - 6x + 3 {x}^{2}...(1) \\ plug \: x = a \: in \: (1) \\ f(a) = \boxed{ 4 - 6a + 3 {a}^{2} } \\ \\ next \: plug \: x = (a + h) \: in \: (1) \\ f(a + h) = 4 - 6(a + h) + 3 {(a + h)}^{2} \\ = 4 - 6a - 6h + 3( {a}^{2} + {h}^{2} + 2ah) \\ = 4 - 6a - 6h + 3 {a}^{2} + 3{h}^{2} + 6ah \\ f(a + h) = \boxed{3 {a}^{2} + 3{h}^{2} + 6ah - 6a - 6h + 4} \\ \\ now \\ \\ \frac{f(a + h) - f(a)}{h} \\ \\ = \frac{(3 {a}^{2} + 3{h}^{2} + 6ah - 6a - 6h + 4) -(4 - 6a + 3 {a}^{2} ) }{h} \\ \\ = \frac{3 {a}^{2} + 3{h}^{2} + 6ah - 6a - 6h + 4 -4 + 6a - 3 {a}^{2} }{h} \\ \\ = \frac{ 3{h}^{2} + 6ah - 6h }{h} \\ \\ = \frac{3h( {h} + 2a - 2) }{h} \\ \\ \frac{f(a + h) - f(a)}{h} = \boxed{ 3( 2a + h - 2)}[/tex]

The 4 angles need to add to 360.

2 of them are 70

The other two need to equal 360-140 = 220

They are both the same so one angle needs to equal 220/2 = 110

Now find x:

X + 60 = 110

Subtract 60 from both sides:

X = 50. The answer is D

Answer:

с.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/g

Step-by-step explanation:

The given options

a.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to g 70

b. if yt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/1

с.i fyt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/g  

d. if yt grows at a rate of g percent per year, then the number of years it takes yt to triple is approximately equal to 70/g  

е.ifyt grows at a rate of g percent per year, then the number of years it takes yt to double is exactly equal to 70/g

The rule of 70 refers to the time period in which the investment you make is doubled. It analyzed that in how many years it took for doubling the amount by considering the specific rate of return  

Now we go through the options and as we can see that the option c meets the requirement as the g represents the growth rate and it fits to the above explanation

Answer:

[tex]t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =2*P(t_{(9)}>2.32)=0.0455[/tex]    

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

Step-by-step explanation:

Information given

data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0

We can calculate the sample mean and deviation with the following formulas:

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

[tex]\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

[tex]\bar X=201.77[/tex] represent the sample mean    

[tex]s=2.41[/tex] represent the sample standard deviation    

[tex]n=10[/tex] sample size    

[tex]\mu_o =200[/tex] represent the value that we want to test    

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.    

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

Hypothesis to test

We want to determine if the true mean is equal to 200, the system of hypothesis are :    

Null hypothesis:[tex]\mu = 200[/tex]    

Alternative hypothesis:[tex]\mu = 200[/tex]    

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)    

The statistic is given by:

[tex]t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =2*P(t_{(9)}>2.32)=0.0455[/tex]    

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

Answer:

27% of the possible Z values are greater than 0.613

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 0, \sigma = 1[/tex]

27% of the possible Z values are greater than

The 100 - 27 = 73rd percentile, which is X when Z has a pvalue of 0.73. So X when the z-score is 0.613.

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

[tex]0.613 = \frac{X - 0}{1}[/tex]

[tex]X = 0.613[/tex]

27% of the possible Z values are greater than 0.613

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

How large of a sample of state employees should be taken if we want to estimate with 98% confidence the mean salary to be within $2,000? The population standard deviation is assumed to be $10,500. z-value for 98% confidence level is 2.326.

Answer:

Sample size = n = 150

Step-by-step explanation:

Recall that the margin of error is given by

[tex]$ MoE = z \cdot (\frac{\sigma}{\sqrt{n} } ) $\\\\[/tex]

Re-arranging for the sample size (n)

[tex]$ n = (\frac{z \cdot \sigma }{MoE})^{2} $[/tex]

Where z is the value of z-score corresponding to the 98% confidence level.

Since we want mean salary to be within $2,000, therefore, the margin of error is 2,000.

The z-score for a 98% confidence level is 2.326

So the required sample size is

[tex]n = (\frac{2.326 \cdot 10,500 }{2,000})^{2}\\\\n = (12.212)^{2}\\\\n = 149.13\\\\n = 150[/tex]

Therefore, we need to take a sample size of at least 150 state employees to estimate with 98% confidence the mean salary to be within $2,000.

Answer:

if the order of the digit matters, we have:

options: 1, 2, 3, 4.

We want to select two digits.

First selection: we have 4 options

Second selection: we have 3 options (because we already selected one in the first selection)

The total number of elements in the sample space, or the total number of combinations, is equal to the product of the number of options in each selection, this is:

P = 4*3 = 12

Answer:

[tex]sin(A+B)=-\dfrac{345}{377}[/tex]

Step-by-step explanation:

Given that:

[tex]sin(A)=-\dfrac{20}{29}\\cos(B)=\dfrac{12}{13}[/tex]

A is in 3rd quadrant and B is in 1st quadrant.

To find: sin(A+B)

Solution:

We know the Formula:

1. [tex]sin(A+B) = sinAcosB+cosAsinB[/tex]

2. [tex]sin^{2} \theta+cos^{2} \theta=1[/tex]

Now, let us find the values of cosA and sinB.

[tex]sin^{2} A+cos^{2} A=1\\\Rightarrow (\frac{-20}{29})^2+cos^{2} A=1\\\Rightarrow cos^{2} A=1- \dfrac{400}{941}\\\Rightarrow cos^{2} A=\dfrac{941-400}{941}\\\Rightarrow cos^{2} A=\dfrac{441}{941}\\\Rightarrow cos A=\pm \dfrac{21}{29}[/tex]

A is in 3rd quadrant, so cosA will be negative,

[tex]\therefore cos A=-\dfrac{21}{29}[/tex]

[tex]sin^{2} B+cos^{2} B=1\\\Rightarrow sin^{2} A+(\frac{12}{13})^2=1\\\Rightarrow sin^{2} B=1- \dfrac{144}{169}\\\Rightarrow sin^{2} B=\dfrac{169-144}{169}\\\Rightarrow sin^{2} B=\dfrac{25}{169}\\\Rightarrow sinB=\pm \dfrac{5}{13}[/tex]

B is in 1st quadrant, sin B will be positive.

[tex]sinB =\dfrac{5}{13}[/tex]

Now, using the formula:

[tex]sin(A+B) = sinAcosB+cosAsinB\\\Rightarrow -\dfrac{20}{29} \times \dfrac{12}{13}-\dfrac{21}{29}\times \dfrac{5}{13}\\\Rightarrow -\dfrac{20\times 12+21\times 5}{29\times 13} \\\Rightarrow -\dfrac{240+105}{29\times 13} \\\Rightarrow -\dfrac{345}{377}[/tex]

[tex]sin(A+B)=-\dfrac{345}{377}[/tex]

Answer:

3ab

Step-by-step explanation:

area = length * width

width = area/length

width = (12ab^2)/(4b)

width = 3ab

Answer:

1/5

Step-by-step explanation:

Gradient is another word for slope. To find the gradient, we have to use a formula.

Answer:

1.25 lbs

Step-by-step explanation:

Since we are given 25% of a number is equal to 1 pound, we simply add 25% to 1 to get our number:

1(1 + 0.25)

1(1.25)

1.25 lbs

Answer:

4a lb

Step-by-step explanation:

If 25% is 1 a lb, then just multiply by 4 to get 4 a lb

Answer: 5/26

Step-by-step explanation: 6/13 x 5/12

Answer:

Option (C)

Step-by-step explanation:

Parent function g(x) = x² [Vertex at the origin (0, 0)]

When this function is shifted 3 units down,

Rule to be followed,

g(x) → g(x) - 3

So, g'(x) = x² - 3

Followed by 2 units shift to the left,

Rule to be followed,

g'(x) → g'(x + 2)

F(x) = (x + 2)² - 3

Therefore, Option (C) will be the answer.

Answer:

"30 years or less when, in reality, the average age is more than 30 years"

Step-by-step explanation:

Type I error is produced when conclusion rejects a true null hypothesis.

The null hypothesis is

"The average gamer is more than 30 years old"

(deduced from the wording, not explicitly stated).

Then if the conclusion is "the average gamer is less than or equal to 30 years old" when in reality the average age is more than 30 years, then there is a type I error, since the null hypothesis is rejected.

Answer is D:

"30 years or less when, in reality, the average age is more than 30 years"

Answer:

A

Step-by-step explanation:

Two congruent chords in a circle have the same distance from the center.

If two chords in a circle are congruent, then they are the same distance from the center of the circle .

The properties of Equal Chords of a Circle are:

According to the question

If two chords in a circle are congruent, then they are

Now,

By properties of Equal Chords of a Circle

The equal chords will be equal distance from the center of the circle .

Hence, If two chords in a circle are congruent, then they are the same distance from the center of the circle .

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