At any given football game that Burbank plays , the probability that Patrick plays during the first half of the game is 5/6 . he plays during the first half, there is only a 3/7 chance that he'll play again during the second half. (He gets tired if he plays all out in the first half.) If he doesn't play during the first half, there is a 5/ 7 chance that he'll play during the second half . Find the probability that Patrick played in the first half, given that he played in the second half.

Answer:

The answer is x = 1

Step-by-step explanation:

Let¿'s solve for x in the equation:

(x + 5)/4 = (2x + 1)/2

x + 5 = 2 * (2x + 1)

x + 5 = 4x + 2

-3x = 2 - 5

-3x = -3

x = 1

Proof of x = 1

1 + 5/4 = 2 + 1/2

6/4 = 3/2

3/2 = 3/2 (Dividing by 2 at the left side)

We proved that x = 1 is correct

c = 2πr = 2π(8) = 16π = 50.3 ft rounded to the nearest tenth

Answer:

If we sketch the line of best fit, we can determine that the slope is positive. 3) ... Based on the trend, predict the number of hybrid cars sold if the price of gas is $4.00 a gallon. A) ... 2 10 5 16 6 15 20 12 28 30 28 35 37 32 45 39 56 52 60 65 ... B). C). D). Explanation: Scatterplot A correctly shows Natalie's data.

Step-by-step explanation:

Answer:

the first one is 5. 5 and second is 5

Step-by-step explanation:

sorry i couldnt do the others

Answer:

Step-by-step explanation:

6) In rectangle, diagonals are equal.

KM = LN

6x + 16 = 49

6x = 49 - 16

6x = 33

x = 33/6

x = 5.5

7) 2x + 4 =  5x - 11

2x - 5x = -11 -4

-3x = -15

x = -15/-3

x = 5

In  rhombus,diagonals make two congruent triangles

So, ∠ACD = ∠ACB

8) In Rectangle, diagonals are equal and bisect each other

x + 10 = 3x - 18

x - 3x =  -18 -10

-2x = -28

x = -28/-2

x = 14

9) a + 36 = 180   { sum of co interior angles is 180}

a = 180 - 36 = 144

a = 144

113 + b = 180    { sum of co interior angles is 180}

b = 180 - 113

b = 67

10)  4th figure

Answer:

Answer: 8

Step-by-step explanation:

Good morning ☕️

Answer:

Step-by-step explanation:

Thé amount of data that is available at the beginning of the cycle

= 8 × 1.5 + 6 = 12 + 6 = 18

:)

Answer:

0.9

Step-by-step explanation:

i) 1 nickel is equal to 5 cents

ii) 36 nickels will equal to = 36 × 5 = 180 cents

iii) 1 dime is equal to 10 cents

iv) 20 dimes will equal to = 20 × 10 = 200 cents

v) the ratio of 36 nickels to 20 dimes will equal to

  =  36 nickels ÷ 20 dimes

 = 180 cents ÷ 200 cents

 = [tex]\frac{9}{10}[/tex]

 = 0.9

To express the comparison of 36 nickels to 20 dimes as a ratio in lowest terms, calculate the value of nickels and dimes in pennies, then simplify the ratio. By converting to pennies and reducing, the ratio of 36 nickels to 20 dimes is 9:10.

The question asks to write the comparison of 36 nickels to 20 dimes as a ratio reduced to lowest terms. To compare the value of nickels and dimes, we must know their value in pennies, the smallest unit of US currency. Since 1 nickel is worth 5 pennies and 1 dime is worth 10 pennies, we can express 36 nickels and 20 dimes in terms of pennies.

36 nickels = 36 x 5 pennies = 180 pennies

20 dimes = 20 x 10 pennies = 200 pennies

Now, we write the comparison as a ratio:

180 pennies : 200 pennies

Next, we reduce this ratio to lowest terms by dividing both numbers by their greatest common divisor, which is 20 in this case:

180 ÷ 20 : 200 ÷ 20

9 : 10

Therefore, the ratio of 36 nickels to 20 dimes reduced to lowest terms is 9:10.

Question 1:

For this case we must solve the following system of equations by the method of elimination:

[tex]8x-6y=-20\\-16x+17y=30[/tex]

We multiply the first equation by 2:

[tex]16x-12y = -40[/tex]

We have the equivalent system:

[tex]16x-12y = -40\\-16x + 17y = 30[/tex]

We add the equations:

[tex]5y = -10[/tex]

We divide between 5 on both sides of the equation:

[tex]y = - \frac {10} {5}\\y = -2[/tex]

We find the value of the variable "x":

[tex]8x-6 (-2) = - 20\\8x + 12 = -20\\8x = -20-12\\8x = -32[/tex]

We divide by 8 on both sides of the equation:

[tex]x = - \frac {32} {8}\\x = -4[/tex]

Thus, the solution of the system is:

[tex](x, y): (- 4, -2)[/tex]

Answer:

[tex](x, y): (- 4, -2)[/tex]

Question 2:

For this case we must solve the following system of equations by the method of elimination:

[tex]-4y-11x = 36\\20 = -10x-10y[/tex]

We multiply the first equation by 10:

[tex]-40y-110x = 360[/tex]

We multiply the second equation by -4:

[tex]40y + 40x = -80[/tex]

We have the equivalent system:

[tex]-40y-110x = 360\\40y + 40x = -80[/tex]

We add the equations:[tex]-70x = 280[/tex]

We divide by -70 on both sides of the equation:

[tex]x = \frac {280} {- 70}\\x = -4[/tex]

We find the value of the variable "y":

[tex]-4y-11 (-4) = 36\\-4y + 44 = 36\\-4y = 36-44\\-4y = -8[/tex]

We divide between -4 on both sides of the equation:

[tex]y = - \frac {8} {- 4}\\y = 2[/tex]

Thus, the solution of the system is:

[tex](x, y): (- 4,2)[/tex]

Answer:

[tex](x, y): (- 4,2)[/tex]

Answer:

Part 1) The sum of the two angles equals 70 degrees

Part 2) The complementary angle is 19 degrees and the supplementary angle is 109 degrees

Step-by-step explanation:

Part 1) we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle JKL

[tex]m\angle JKL+m\angle KLJ+m\angle LJK=180^o[/tex]

we have

[tex]m\angle JKL=110^o[/tex]

substitute

[tex]110^o+m\angle KLJ+m\angle LJK=180^o[/tex]

[tex]m\angle KLJ+m\angle LJK=180^o-110^o[/tex]

[tex]m\angle KLJ+m\angle LJK=70^o[/tex]

therefore

The sum of the two angles equals 70 degrees

Part 2) we know that

If two angles are complementary, then their sum is equal to 90 degrees

If two angles are supplementary, then their sum is equal to 180 degrees

step 1

Find the complementary

Let

c ----> the complementary angle

[tex]m\angle c+71^o=90^o[/tex]

[tex]m\angle c=90^o-71^o=19^o[/tex]

step 2

Find the supplementary

Let

s ----> the supplementary angle

step 1

Find the complementary

Let

c ----> the complementary angle

[tex]m\angle s+71^o=180^o[/tex]

[tex]m\angle s=180^o-71^o[/tex]

[tex]m\angle s=109^o[/tex]

therefore

The complementary angle is 19 degrees and the supplementary angle is 109 degrees

Answer:

D. 5/12

Step-by-step explanation:

I will have a picture attached to the answer. But I will explain it overall.

So let's start off with what information we have: Bella ate 1/4 of the bar and Owen at 1/3 of the same bar.

So how much overall was gone by the two? Well, in this part we will add the two fractions.

1/3 + 1/4 =?

Yet, here's the thing, these two fractions have different denominators. What we have to do is make them the same denominator. In order to do so we have to find the Least Common Multiple of the denominators.

So with that in mind...

Multiples of 3: 3,6,9,12,15,18,21,...

Multiples of 4: 4,8,12,16,20,24...

Do you see a number that 3 and 4 have? Welp, I do! It's 12! So here is what going to happen! We will set up the problem like this!

1/3 times ? equal x/12

+ 1/4 times ? equal x/12

Now you may be wondering what is the question mark for and what is "x"? Here's the thing, since we know the new fraction we have to figure out what times the original denominators equal the new denominator! So with 1/3, what or how do we make the 3 into 12? Well 3 times 4 equals 12! So that is ?. The ? will be 4/4. Because whatever you do to the bottom you do to the top.

1/3 times 4/4 equals 4/12

Now we do the same thing for the 1/4 fraction. Except the question mark will be 3/3 since 4 times 3 equals 12

1/4 times 3/3 equals 3/12

Okay, now we have 4/12 + 3/12= x/12. Let's add the fractions. 4+3=7 and the 12 of the denominator will stay the same. So 1/3+1/4 or 4/12+3/12 now equals 7/12.

The real question is what is LEFTOVER of the granola bar? So we have what was devoured of the bar, so now we can subtract the part that was gone with the whole bar. So...

1 whole bar equals 12/12

- the devoured part equals 7/12

left over or untouched = 5/12

So the answer to the question is D. 5/12

I hope this helps you, I'm sorry this took me a long time, I again do have a picture attached to the answer. If you need any help or have a question please don't be afraid to ask! Have a good day!

Answer: option D.

The total amount of the granola bar is = 1.

Given that they have eaten 1/4 and 1/3 of the bar.

So they have eaten a total of [tex]\frac{1}{4}+\frac{1}{3}=\frac{7}{12}[/tex] of the bar.

So the remaining amount is = [tex]1-\frac{7}{12}=\frac{12}{12}-\frac{7}{12}=\frac{5}{12}[/tex].

So option D is right.

Learn more: https://brainly.com/question/12356025

Answer:

Step-by-step explanation:

[tex]-2\sqrt{-24}=-2\sqrt{24i}=-2\sqrt{2*2*2*3*i}\\\\=-2*2\sqrt{2*3*i}=-4\sqrt{6i}[/tex]

Answer:

The order of the sides of the triangle from shortest to longest:

BC , AC and AB

Step-by-step explanation:

ΔABC, m∠A = 41° and m∠B = 62°

So, m∠C = 180° - ( m∠A + m∠B)

              = 180° - ( 41° + 62°)

              = 180° - 103° = 77°

Arranging the angles from the smallest to the greatest

∠A , ∠B and ∠C

We should know that

The shortest side is opposite to the smallest angle and vice verse.

So, the sides of the triangle in order of shortest to longest is as following:

BC , AC and AB

Answer:

The Law of Cosines (also called the Cosine Rule) says: c2 = a2 + b2 . We know angle C = 37º, and sides a = 8 and b = 11. The Law of .Answer: c = 6.67

explanation:

hope this helped

Answer:

Therefore we can say that 98 boxes will be needed to hold all the paperweights.

Step-by-step explanation:

i) there are 1657 souvenir paperweights that need to be packed in boxes.

ii) each box will hold 17 paperweights

iii) therefore the number of boxes that will be needed are

   = [tex]\dfrac{total\hspace{0.15cm} number\hspace{0.15cm} souvenir\hspace{0.15cm} paperweights}{number\hspace{0.15cm} of\hspace{0.15cm} paperweights\hspace{0.15cm} per\hspace{0.15cm} box}[/tex]  = [tex]\dfrac{1657}{17}[/tex] = 97.471

iv) Therefore we can say that 98 boxes will be needed to hold all the paperweights.

The given equation is not the conditional equation.

Step-by-step explanation:

A conditional equation is true only certain values of the numbers present in it.

    for example  x + 3 = 9  is true only, if x = 6

                         3x - 5 = 10 is true only, if x = 5

The given equation is an Identity equation in which both sides of the equation is equal.    

                     3(x - 4) + 5x = 4x + 4(x - 3)

                     3x - 12 + 5x = 4x + 4x - 12

                                   8x  = 8x.

BB's parents should choose the option with a 4% annual increase on the accumulated amount because it leverages compound interest, likely resulting in significantly higher growth over time compared to the fixed contribution strategy.

The question involves deciding between two financial strategies for Baby Bertha's (BB) savings account: a fixed annual contribution ($1,000 at birth plus $50 per year) versus a dynamic contribution that includes an initial amount plus an annual percentage increase ($1,000 at birth plus an additional 4% of the accumulated amount each year). To determine which option BB's parents should select, we must understand the impact of compound interest and how it can significantly increase the future value of a savings account over time.

With the fixed contribution strategy, the amount added each year is constant, leading to linear growth. In contrast, the 4% annual increase on the accumulated amount option leverages the power of compound interest, likely resulting in exponential growth of the account's value over time. This strategy takes advantage of the principle that earnings are reinvested to generate their own earnings in subsequent years, a core tenet of compound growth.

Given the long-term nature of the saving plan (assuming BB won't withdraw the funds prematurely), the option with a 4% annual increase on the accumulated amount is more advantageous. This decision leverages compound interest, which is known to significantly increase the value of investments over extended periods. Hence, BB's parents should select Grandpa's option for the potential of greater financial growth.

Answer:

2x+4

Step-by-step explanation:

Distribute:

=(2)(x)+(2)(−6)+(2)(8)

=2x+−12+16

Combine Like Terms:

=2x+−12+16

=(2x)+(−12+16)

=2x+4

Final answer:

The simplified expression of 2(x-6)+2(8) is 2x + 4 after distributing the 2 and combining like terms.

Explanation:

To simplify the expression 2(x-6)+2(8), you need to distribute the 2 into the parentheses and then combine like terms. Distributing the 2 into the first set of parentheses gives us 2x - 12.

For the second set, multiplying 2 by 8 gives us 16. So the expression becomes 2x - 12 + 16. Adding together the numerical terms (-12 + 16) gives us 2x + 4. Therefore, the simplified expression is 2x + 4.

Devin buys his clothes in Illinois, so he would pay the sales tax rate of Illinois, which is 6.25%. Therefore, the correct answer is D. 6.25%.

Certainly! Devin buys his clothes in Illinois, where the sales tax rate is 6.25%. This means that for every dollar he spends on clothes, he pays an additional 6.25 cents as tax.

To calculate how much tax Devin pays on a $100 purchase, you can use the formula:

[tex]\[ \text{Tax Amount} = \text{Purchase Amount} \times \text{Tax Rate} \][/tex]

Substitute the values:

[tex]\[ \text{Tax Amount} = \$100 \times 0.0625 \][/tex]

[tex]\[ \text{Tax Amount} = \$6.25 \][/tex]

So, if Devin buys clothes worth $100 in Illinois, he would pay $6.25 as sales tax, which corresponds to the 6.25% tax rate of Illinois.

Answer:

34 is the answer

Step-by-step explanation:

Answer:

the answer is 70/2+(5-6) i think. Sorry if it is wrong

Step-by-step explanation:

the answer about be am number one child so yeah

Answer:

288inches²s

step-by-step explanation:

from metrics

12inches = 1feet

converting

lenght = 3 * 12 = 36 inches

Area of the rectangle = 36 * 8 = 288inches²

420 gallons of 90% antifreeze must be mixed with 60 gallons of 10% antifreeze to get mixture that is 80% antifreeze

Solution:

Let "x" be the gallons of 90% antifreeze

The, final mixture would contain (x + 60) gallons

Then by given question, we can say,

"x" be the gallons of 90% antifreeze must be mixed with 60 gallons of 10% antifreeze to get 80 % of (x + 60) gallons

Thus we frame a equation as:

[tex]x \times 90 \% + 60 \times 10 \% = (x + 60) \times 80 \%[/tex]

Solve the above equation for "x"

[tex]x \times \frac{90}{100} + 60 \times \frac{10}{100} = (x + 60) \times \frac{80}{100}\\\\0.9x + 6 = (x+60) \times 0.8\\\\0.9x + 6 = 0.8x + 48\\\\\text{Combine the like terms }\\\\0.9x - 0.8x = 48 - 6\\\\0.1x = 42\\\\x = \frac{42}{0.1} = 420[/tex]

Thus, 420 gallons of 90% antifreeze is used

Answer:

(1/5)(10/3) = 10/15 = 2/3 mile

The friend lives [tex]$\frac{2}{5}$[/tex] of a mile away.

To solve this problem, we need to calculate the total distance based on the speed at which the bike is ridden and the time it takes to reach the friend's house.

First, we determine the speed at which the bike is ridden, which is given as [tex]$\frac{1}{5}$[/tex] of a mile per minute.

Next, we calculate the time it takes to reach the friend's house, which is [tex]$3\frac{1}{3}$[/tex] minutes. To work with this mixed number easily, we convert it to an improper fraction. [tex]$3\frac{1}{3}$[/tex] minutes is the same as [tex]$\frac{10}{3}$[/tex] minutes because [tex]$3\frac{1}{3} = 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3}$[/tex].

Now, we can find the total distance by multiplying the speed by the time:

[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]

[tex]\[ \text{Distance} = \frac{1}{5} \text{ mile/minute} \times \frac{10}{3} \text{ minutes} \][/tex]

When we multiply these two fractions, we multiply the numerators together and the denominators together:

[tex]\[ \text{Distance} = \frac{1}{5} \times \frac{10}{3} \][/tex]

[tex]\[ \text{Distance} = \frac{1 \times 10}{5 \times 3} \][/tex]

[tex]\[ \text{Distance} = \frac{10}{15} \][/tex]

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

[tex]\[ \text{Distance} = \frac{10 \div 5}{15 \div 5} \][/tex]

[tex]\[ \text{Distance} = \frac{2}{3} \][/tex]

Therefore, the friend lives [tex]$\frac{2}{5}$[/tex] of a mile away.

There are 28 students in first period and 56 students in sceond period and 74 students in third period

Solution:

Let the number of students in first period be "x"

Let the number of students in second period be "y"

Let the number of students in third period be "z"

There are 158 students registered for American History classes.

Therefore,

x + y + z = 158 ---------- eqn 1

There are twice as many students registered in second period as first period

number of students in second period = twice of number of students in first period

y = 2x ------- eqn 2

There are 10 less than three times as many students in third period as in first period

number of students in third period = 3 times number of students in first period - 10

z = 3x - 10 ------ eqn 3

Substitute eqn 2 and eqn 3 in eqn 1

x + 2x + 3x - 10 = 158

6x = 168

Substitute x = 28 in eqn 2

y = 2(28)

Substitute x = 28 in eqn 3

z = 3(28) - 10

z = 84 - 10

Thus there are 28 students in first period and 56 students in sceond period and 74 students in third period

Answer:

Step-by-step explanation:

Slope m = 5/6

The points (-2,1)

So; y1 = 1 and x1 = -2

The equation is y - y1 = m(x - x1)

y - 1 = 5/6(x + 2)

Multiply each term by 6

6y - 6 = 5(x + 2)

6y - 6 = 5x + 10

6y = 5x + 10 + 6

6y = 5x + 16

- 5x + 6y = 16

Multiplying by minus

5x - 6y = -16

Answer:

5x - 6y = -16

Step-by-step explanation:

5/6 = (y - 1)/(x - 2)

cross multiplying,

5x + 10 = 6y - 6

5x - 6y = -16

Answer: -9

Step-by-step explanation: When you're asked to multiply positives and negatives together, the rules are simple.

A positive times a positive is a positive.

A positive times a negative is a negative.

A negative times a positive is a negative.

A negative times a negative times a negative is a positive.

So for the problem you see here, we will use rule 2 which I have highlighted in bold above which states that a positive times a negative is a negative.

So (+3)(-3) = -9

The value is 0

PEDMAS is simply defined as a mathematical acronym that is used to represent the different arithmetic operations.

These letters represents;

From the information given, we have the expression

(3)-3

expand the bracket, we get;

3 - 3

Subtract the values, we have;

0

Learn about PEDMAS at: https://brainly.com/question/345677

#SPJ6

The unit rate is $4.25 per day for lunch.

To find the unit rate of how much it costs to buy lunch for one day, we divide the total cost by the number of days. In this case, the total cost is $21.25 for 5 days of lunch.

Here's the calculation to find the unit rate:

Divide the total cost by the number of days: $21.25 / 5 = $4.25

Hence, the unit rate is $4.25 per day for lunch.

This equation means what would f(x) be if x was -2. F(x) is another way to write y. So this equation can be rewritten as y = 2(-2) - 3.

y = -4 - 3

y = -7

Answer:

2(-2)-3 =-4-3 =-7

Step-by-step explanation:

Answer:370

Step-by-step explanation:

You have to multiply .26 by 500 because it says of. Of means to multiply. You get 130 and subtract that from 500

Answer:

Option A

[tex]m\angle LQR=126^o[/tex]

Step-by-step explanation:

step 1

Find the value of b

we know that

[tex]m\angle MQR=m\angle LQX[/tex] ----> by vertical angles

substitute the given values

[tex](-3b+63)^o=(90-12b)^o[/tex]

solve for b

[tex]12b-3b=90-63\\9b=27\\b=3[/tex]

step 2

Find the measure of angle LQR

we know that

[tex]m\angle LQR+m\angle MQR=180^o[/tex] ---> by supplementary angles (form a linear pair)

[tex]m\angle MQR=(-3b+63)^o[/tex]

substitute the value of b

[tex]m\angle MQR=(-3(3)+63)=54^o[/tex]

substitute in the expression above

[tex]m\angle LQR+54^o=180^o[/tex]

[tex]m\angle LQR=180^o-54^o=126^o[/tex]

Answer:

dude what? provide the image or something at least

Step-by-step explanation:

Given Will ran the diagonal distance across a square field measuring 40 yards each sides .

∴The distance covered by Will was =[tex]\sqrt{40^{2}+40^2 }[/tex] yards

                                                         = [tex]40\sqrt{2}[/tex] yards=56.56 yards

Again James ran diagonal distance across a rectangle field with a length of 25 yards and a width of 35 yards.

So,distance covered by James was =[tex]\sqrt{25^2+35^2}[/tex] yards

                                                             =[tex]5\sqrt{74}[/tex] yards = 43.01 yards

∴Will ran longer distance.

∴Will ran 13.55 yards more than James.

To calculate the longer distance Will ran compared to James, find the diagonal distances each ran. Will ran approximately 13.56 yards longer.

To determine how much longer Will ran compared to James, we need to calculate the diagonal distances for each run.

Will ran 56.57 - 43.01 ≈ 13.56 yards longer than James. Thus, Will ran around 13.56 yards longer than James, as determined by subtracting the diagonal of the rectangular field from that of the square field. This calculation offers a quantitative measure of the difference in running distances, providing insight into their comparative performances.