Label the vertices and all the elements needed. Find x. Give reasons!

Answer:

110 = 16 + 10h

110 - 16 = 10h

Step-by-step explanation:

Sylvie needs a total of $110, which is the number she is working towards.

She already has $16, which is what we call a constant, or a number that will not change in the equation.

We are told that if she works 10 hours, she will earn enough money to buy the concert ticket. The amount that she is paid per hour is the variable, which would be signified by the letter "h" in this case.

Set the equation:

(amount of hours) * (pay per hour) + (amount she starts out with) = (total she needs).

Or, to put into numerical & variable terms, plug in the corresponding number (or variable) to the corresponding part.

10 * h + 16 = 110

(10h) + 16 = 110

Another way to solve is to do the first step in isolating the variable, h. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation & =

Parenthesis

Exponents & roots

Multiplication

Division

Addition

Subtraction

First, subtract 16 from both sides:

10h + 16 (-16) = 110 (-16)

10h = 110 - 16

10h = 94

Next, divide 10 from both sides:

(10h)/10 = (94)/10

h = 94/10

h = 9.4

Answer:

(x - [-1])² + (y - [-1])² = [13]

Step-by-step explanation:

If P and Q are the end-points of the diameter PQ, midpoint of the segment PQ will be the center of the circle. (Definition of the center of a circle)

Midpoint of a segment having extreme ends [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex]

Coordinates of the center = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Since, extreme ends of the diameter are P(-4, -3) and Q(2, 1)

Center of the circle = [tex](\frac{-4+2}{2},\frac{-3+1}{2} )[/tex]

                                = (-1, -1)

Radius of the circle = Distance between the center and Q,

Since distance between the two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is,

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

Radius of the circle = [tex]\sqrt{(-1-2)^2+(-1-1)^2}[/tex]

                                = [tex]\sqrt{9+4}[/tex]

                                = [tex]\sqrt{13}[/tex]

Equation of the circle will be,

(x - h)² + (y - k)² = r²

Where (h, k) is the center and 'r' is the radius of the circle,

(x - [-1])² + (y - [-1])² = [13]

Answer:

60%

Step-by-step explanation:

Total Cards = 5

Even Numbers = 3

P(even) = 3/5

In %age:

=> 60%

Answer:

60%

Step-by-step explanation:

The numbers that are even from the list are 2, 4, and 6.

3 numbers are even out of 5 total numbers.

3/5 = 0.6

P(even) = 60%

Answer:

an = -6*(1/4)^(n-1)

Step-by-step explanation:

We have that the recursive formula for the given geometric sequence is:

a1 = -6

an = (an-1) * (1/4)

With the above we can assume that:

r = 1/4

following the rule of the explicit formula that is given by:

an = a1 * (r) ^ (n-1)

we substitute and we have:

an = -6 * (1/4) ^ (n-1)

Therefore the explicit formula from the given data would be:

an = -6 * (1/4) ^ (n-1)

Answer:

b. S={(red, red), (red, black), (black, red), (black, black)} where, for example, (red, red) stands for the event "the first card is red and the second card is red."

Step-by-step explanation:

The most appropriate sample space S for the possible outcomes will be S={(red, red), (red, black), (black, red), (black, black)} where, for example, (red, red) stands for the event "the first card is red and the second card is red."

Option B is correct.

The most appropriate sample space S for the possible outcomes will be S={(red, red), (red, black), (black, red), (black, black)} where, for example, (red, red) stands for the event "the first card is red and the second card is red."

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Answer:

Step-by-step explanation:

Given:

  AC + CB = 33

  CB = 2AC

Find:

  AC, CB

Solution:

Using substitution, we have ...

  AC +2AC = 33

  AC = 33/3 = 11

  CB = 2·11 = 22

AC = 11 cm; CB = 22 cm.

Answer:

P-value =0.062

At a signficance level of 0.05, there is not enough evidence to support the claim that the unemployment rate is less than 5%.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the unemployment rate is less than 5%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]

The significance level is 0.05.

The sample has a size n=1500.

The sample proportion is p=0.041.

[tex]p=X/n=61/1500=0.041[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1500}}\\\\\\ \sigma_p=\sqrt{0.000032}=0.0056[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.041-0.05+0.5/1500}{0.0056}=\dfrac{-0.0087}{0.0056}=-1.5401[/tex]

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

[tex]\text{P-value}=P(z<-1.5401)=0.062[/tex]

As the P-value (0.062) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the unemployment rate is less than 5%.

Answer:

0.9 (9/10)

Step-by-step explanation:

(see picture)

Answer:

as it is given in the question that 10 students drink both drinks out of 60

since there are 2 drinks in question, we are sure that these 10 students drink 2 drinks and no one else

so , we have 50 students who drink only one drink and that is your answer

Answer:

5 is the correct answer...

Hope this helps

Answer:

26.95% probability that at least one of them is cleared with an arrest

Step-by-step explanation:

For each burglary, there are only two possible outcomes. Either it is cleared, or it is not. The probability of a burglary being cleared is independent of other burglaries. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

5.1% of burglaries are cleared with arrests.

This means that [tex]p = 0.051[/tex]

A new detective is assigned to six different burglaries.

This means that [tex]n = 6[/tex]

What is the probability that at least one of them is cleared with an arrest?

Either none are cleared, or at least one is. The sum of the probabilities of these events is 100% = 1. So

[tex]P(X = 0) + P(X \geq 1) = 1[/tex]

We want [tex]P(X \geq 1)[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

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

[tex]P(X = 0) = C_{6,0}.(0.051)^{0}.(0.949)^{6} = 0.7305[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7305 = 0.2695[/tex]

26.95% probability that at least one of them is cleared with an arrest

Answer:

see below

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

  = 4/3 pi ( 7)^3

  = 1372/3 pi in^3

Using 3.14 for pi

V =1436.0266666 in^3

Using the pi button

1436.75504 in^3

Answer:

B. y = 3x + 4

Step-by-step explanation:

Step 1: Find slope-intercept form of 1st equation

2y = 6x + 4

2y/2 = 6x/2 + 4/2

y = 3x + 2

A parallel line has the same slope but different y-intercept:

y = -3x + 3 (No, different slope)

y = 3x + 4 (Yes, same slope, different y-int)

y = x + 3 (No, different slope)

y = -2x - 3 (No, different slope)

y = 1/2x + 3 (No, different slope)

Answer:

If we have two quantities x and y, an inverse variation can be written as:

y = k/x

where k is a constant.

Now, we know that for this particular inverse variation the point (3, -4) is included.

Then we can find the value of k by replacing the values of the point in the general equation:

-4 = k/3

k = -4*3 = -12

Then our inverse variation is:

y = -12/x.

Then if we want another point that also does belong in the inverse variation, we can give x a different value and solve the equation for y.

For example, if x = 1

y = -12/1 = -12

then the point (1, -12) also does belong in the inverse variation.

if x = 6

y = -12/6 = -2

the point (6, -2) also does belong to the inverse variation

Answer: Gina have 72 dimes.

Step-by-step explanation:

We know nickel is made up of  5 cents and dimes is made up of  10 cents. so we could write the equation.

0.05x + 0.10y = 8.65   where x is th number of nickels and y is the number of dimes.

We could also write another equation to represent the total coins.Since the coins are only nickels and dimes we could say that   x+y = 101 which means the total number of nickels x and the total number of dimes y has to equal 101.

0.05x + 0.10y = 8.65   solve both system of equation using the elimination

x + y =  101                     method

multiply the down equation by -0.05 to eliminate the x variables.

-0.05(x+y) = 101(-0.05)  

-0.05x - 0.05y = -5.05  

NOw we have a new equation so you could add them up and eliminate the x terms.

0.05x + 0.10y =8.65

-0.05x  - 0.05 = -5.05

   0   +   0 .05y = 3.6

                   y= 72  

Now we know that Gina has 72 dimes and since we know the total subtract it to find how many nickels.

101 - 72 = 29

Let's start this problem by setting up a chart.

The chart is attached below.

Down the left side, you have your different types

of coins, in this case, nickels and dimes.

Across the top of the chart, we will use our total value formula.

number of coins · value of each coin = total value

Since Gina has a total of 101 nickels and dimes,

in the first column of our chart we can represent

her number of nickels as x and her number of dimes as 101 - x.

In the second column, we have the value of a nickel

which is 5 cents and the value of a dime, 10 cents.

To fill our the 3rd column in your chart, multiply

the information in the first two columns together.

So the total value of our nickels is x · 5 or 5x and

the total value of our dimes is 101 - x · 10 or 10(101 - x).

You will always use the information in the last column of your chart,

the total value column, to setup the equation.

If you look back up at the original problem,

the total value of all the coins is $8.65.

That means that the total value of the nickels

plus the total value of our dimes is $8.65.

Solving the equation from here, you'll find that x = 29.

I have showed my work in the image attached.

Going back up into our chart, you'll see that x

represents the number of nickels that Gina has.

So Gina has 29 nickels.

We can find the number of dimes by using the box below the nickels.

Here, we have 101 - x.

Since x is 29, we have 101 - 29 which is 72.

So Gina has 72 dimes.

Answer:

(A) 7

Step-by-step explanation:

[tex] 4y > 10[/tex]

[tex]y > \frac{10}{4} [/tex]

[tex]y > 2.5[/tex]

Since Y is more than 2.5,

the only possible solution is 7, which is (A)

Answer:

1/2

Step-by-step explanation:

The non-even numbers are 1, 3, and 5 on the dice.

3 numbers out of 6.

3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

Total sides of 6-sided die = 6

Numbers not even = 3

Probability of not getting an even = 3/6

=> 1/2

Answer:

2/5

Step-by-step explanation:

Let's find the probability of each condition first.

For P(4), there is only one option: 4. This is 1 out of 5.

For P(even), this includes 4 and 6. However, we already had 4 from our last condition so we can remove this option. This is again 1 out of 5.

Adding them together, we will get 2/5.

The answer is 2/5

Answer:

1. Red red blue blue

2. Red blue red blue

Step-by-step explanation:

A 50 percent chance

Answer:

  13.636

Step-by-step explanation:

The area can be found using Heron's formula:

  A = √(s(s-a)(s-b)(s-c))

where s=(a+b+c)/2.

For the given triangle, ...

  a=9, b=4, c=12, s=(9+4+12)/2 = 12.5

  A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636

The area of the triangle is about 13.636 square units.

Answer:

24 units\

Step-by-step explanation:

The number of barrels of crude oil required to run the car for a year is 61.4

The information given is as follows;

Percentage of crude oil processed into gasoline = 45%

The distance achieved per gallon by car = 31 mi/gal

Distance driven per year = 36,000 miles

Hence, the number of Gasoline usage in one year,

[tex]\text{Gasoline usage in one year} = \dfrac{\text{Distance drievn per year}}{\text{distance achieve per gallon by car}}[/tex]

[tex]\text{Gasoline usage in one year} = \dfrac{36000 \ \text{miles}}{31\ \text{miles/gallon}}[/tex]

[tex]\text{Gasoline usage in one year} = 1,161 \ \text{gallons}[/tex]

Here, Percentage of crude oil processed into gasoline = 45%

Hence, where 45% of the crude oil produces 1000, the volume of crude, x, from which the gasoline is sourced becomes;

[tex]x \times 45\% = 1161[/tex]

[tex]x \times \dfrac{45}{100} = 1161[/tex]

[tex]45x = 1161\times 100[/tex]

[tex]45x = 1,16,100[/tex]

[tex]x = 2580[/tex] gallons of crude

Since 1 barrel of crude oil is approximately 42 gallons of crude oil.

Hence, we have;

[tex]2580 \ \text{gallons of crude }[/tex] = [tex]\dfrac{2580}{42} \text{ barrels of crude}[/tex]

= [tex]61.4[/tex]  [tex]\text{ barrels of crude}[/tex]

Hence the number of barrels of crude oil required to run the car for a year = [tex]61.4[/tex]  [tex]\text{ barrels of crude}[/tex]

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Approximately 61.44 barrels of crude oil are required to run your car for a year.

To determine the number of barrels of crude oil required to run your car for a year, we'll need to calculate the total amount of gasoline consumed and then convert that into the equivalent volume of crude oil.

Volume of a barrel of crude oil: 42 gallons

Approximately 45% of crude oil is processed into gasoline

Car fuel efficiency: 31 miles per gallon

Distance driven in a year: 36,000 miles

First, let's calculate the total amount of gasoline consumed in a year. We'll divide the total distance driven by the car's fuel efficiency:

Gasoline consumed = Distance driven / Fuel efficiency

Gasoline consumed = 36,000 miles / 31 miles per gallon

Gasoline consumed ≈ 1161.29 gallons

Next, we need to calculate the equivalent volume of crude oil required to produce this amount of gasoline. Since only approximately 45% of crude oil is processed into gasoline, we'll multiply the gasoline consumed by the reciprocal of 45% (or 0.45) to account for this conversion:

Equivalent volume of crude oil = Gasoline consumed / Conversion factor

Equivalent volume of crude oil = 1161.29 gallons / 0.45

Equivalent volume of crude oil ≈ 2580.64 gallons

Finally, to determine the number of barrels of crude oil required, we'll divide the equivalent volume of crude oil by the volume of a barrel (42 gallons):

Number of barrels of crude oil = Equivalent volume of crude oil / Volume of a barrel

Number of barrels of crude oil = 2580.64 gallons / 42 gallons

Number of barrels of crude oil ≈ 61.44 barrels

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Answer: 30 percent of people who do not brush theit teeth every night.

Step-by-step explanation:

Given : 7 out of 10 people brush their teeth every night.

That means 3 out of 10 people do not brush their teeth every night. (7-10=3)

Now, the percent of people who do not brush their teeth every night = [tex]\dfrac{\text{Number of people do not brush their teeth}}{\text{Total people}}\times100\%[/tex]

[tex]=\dfrac{3}{10}\times100\%\\\\=30\%[/tex]

Hence, 30 percent of people who do not brush theit teeth every night.

Answer:

30 ways

Step-by-step explanation:

Given the following :

Number of boys in school (n1) = 5

Number of girls in school (n2) = 3

Total number of team members to be selected = 4

Number of boys required in team(r1) = 2

Number of girls required in team(r2) = 2

How many different teams made up of two girls and two boys could be chosen?

= (2 boys from 5) * (2 girls from 3)

Using combination :

5C2 * 3C2

Recall :

nCr = n! ÷ (n-r)! r!

5C2 = 5! ÷ (5-2)! 2!

5C2 = 5! ÷ 3!2!

5C2 = (5*4) / 2 * 1 = 10ways

3C2 = 3! ÷ (3-2)! 2!

3C2 = 3! ÷ 1!2!

3C2 = (3) /  1 = 3ways

3C2 = 3/1 = 3ways

10 * 3 = 30 ways

Answer:

The answer is explained below

Step-by-step explanation:

What use are statistics if there is no engineer to use them? In other words, a statistician corrects, improves, reinforces, and supports an engineer in building / designing / developing a new product and / or improving an existing product.

The statistician provides a special kind of vision through which I see the same problem in a completely different vision. So you can see the strengths, weaknesses of my product and the promise of improvements that can be made.

Each class of statistics is essential for a student to see and understand a problem in a whole new way where it is much easier to understand information.

Answer:

11

Step-by-step explanation:

Without more information, I'm assuming BC and AC are the same length.

5x - 2 = 3x + 20

5x = 3x + 22

2x = 22

x = 11

Answer:

first option

Step-by-step explanation:

It's up by 4 units because because the +4 is outside of the exponent and also, it is a +4 not -4 which indicates that the translation is up.

Answer:

BG is always perpendicular to GF. The measure of angle BGF is always 90 degree

Step-by-step explanation:

Answer:

is always perpendicular to . The measure of  is always 90°.

Step-by-step explanation:

Plato Awnser

Answer:

Slope: -2; y-intercept: 2/3

Step-by-step explanation:

We need to write this equation out in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. First, simplify the equation. We now have 3y + 6x − 2 = 0. We need the y to be first, so we need to move all terms to the other side except 3y. Our equation is now 3y = −6x + 2. We still need the y to be by itself, so now we divide every number by 3. Our final answer is y = −2x + 2/3.

Answer:

- 2 1/4

Step-by-step explanation:

Methods for solving multiplication problems

I will go into details and give methods to solve with and the final answer.

: 1\3 × −6 3\4 = -1/3 ×( (6*4)+3)/4

1/3 × -6 3/4 = -1/3 ×(24+3)/4

1/3 × -6 3/4 =- 1/3 ×(27/4)

1/3 × -6 3/4 = -27/(3*4)

1/3 × -6 3/4 = -27/(12)

1/3 × -6 3/4 =-( 9/4) * 3/3

1/3 × -6 3/4 = -9/4

1/3 × -6 3/4 =- 2 1/4

OR by direct division

1/3 × -6 3/4 =( -6 3/4)/3

1/3 × -6 3/4 = -6/3 (3/4)/3

1/3 × -6 3/4 = -2 1/4

Answer:

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

here is where stephen makes the mistake, he uses the 4 in the rooth and the 3 in the power.

so the expression actually is:

∛(16)/e

Answer:

-$3.80

Step-by-step explanation:

In the raffle, there are a total of 50 ticket and only one price, therefore:

The probability of winning  [tex]=\frac{1}{50}[/tex]

Price to be won = $300

The probability of losing [tex]=\frac{49}{50}[/tex]

Since each ticket costs $10.

The probability distribution of the price is therefore:

[tex]\left|\begin{array}{c|c|c}$Price(x)&-\$10&300\\P(x)&\frac{49}{50} &\frac{1}{50} \end{array}\right|[/tex]

Expected Value

[tex]=(-\$500 \times \frac{49}{50})+(\$300\times\frac{1}{50} )\\\\=-\$3.80[/tex]