the model below represents the equation 2x + 3 = 11. What is the first step in finding the value of x?

Answer:

the answer is B

Step-by-step explanation:

Applying the multiplication principle in probability, there are eight different combinations possible when choosing between bus or train, full fare or concession, morning or afternoon for your travel.

Your question is asking how many different combinations of travel mode, fare type, and time of day are possible under given conditions. For this situation, we can apply simple probability rules with concept of multiplication principle, which states that if there are n ways to do something, and m ways to do another, then there are n * m ways to do both.

In this case, you have two choices for each category: mode of transportation (bus or train), fare type (full fare or concession), and time of day (morning or afternoon). The combination is simply 2 (mode of transport) * 2 (fare type) * 2 (time of day) = 8. So, there are eight possible outcomes.

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The content of care package would be a board game and several snack packs.

Given is the weight of board game = 4 pounds.

The weight of one snack pack = [tex] \frac{1}{2} \;pounds = 0.5 \;pounds [/tex]

The total weight would be less than 25 pounds.

Solving for part A :

Let 'x' represents the number of snack packs.

So the weight of all snack packs would be 0.5x pounds.

Now weight of care pack = weight of board game + weight of all snack packs.

weight of care pack = 4 + 0.5x

But total weight must be less than 25 pounds.

So the inequality would be: 4 + 0.5x < 25

Solving for part B :

Solving the inequality 4 + 0.5x < 25

⇒ 4 + 0.5x - 4 < 25 - 4

⇒ 0.5x < 21

⇒ x < 42

Solving for part C :

Since x < 42 and x is an integer number, so x = 41.

She can include maximum of 41 snack packs in the care package.

if you played the game 1000​ times, [tex]\$ 263.20[/tex] are expected to​ lose.

[tex]Probability=\dfrac{Favourable\; outcomes}{Total\; number\; of\; outcomes}[/tex]

Probability of winning[tex]=\dfrac{1}{38}[/tex]

if out of total [tex]38[/tex], [tex]1[/tex] game has been won, so rest have been lost,so

Probability of losing [tex]=\dfrac{37}{38}[/tex]

Hence Expected of the game to the player  [tex]=175 \times \dfrac{1}{38}-5 \times \dfrac{37}{38}[/tex]

                                                                        [tex]=\dfrac{175}{38}- \dfrac{185}{38}\\\\=\$ -0.2632[/tex]

A)The expected value is [tex]\$ -0..2632[/tex] (is losing)

B)if you played the game [tex]1000[/tex] times,

so it will be [tex]1000 \times \$ -0.2632=\$263.20[/tex]

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It takes approximately 60/7 seconds for the population to grow by one person.

To find out how many seconds it takes for the population to grow by one person, we need to determine the difference between the rate of births and the rate of deaths. The rate of population growth per second can be calculated by subtracting the rate of deaths per second from the rate of births per second. In this case, a person is born every 5 seconds and a person dies every 12 seconds. So, the rate of population growth per second is 1/5 - 1/12 = 12/60 - 5/60 = 7/60.

Therefore, it takes approximately 60/7 seconds for the population to grow by one person.

Answer:

4 batches

Step-by-step explanation:

Let

x -----> the number of cups of apples

y -----> the number of cups of mangoes

z -----> the number of cups of Blueberries

w -----> the number of cups of Blackberries

we know that

x/y=3/1 -----> equation A

x/z=3/2 ----> equation B

x/w=3/1 ----> equation C

x+w=16 ----> equation D

Solve the system of equations C and D

x=3w ----> equation C

x+w=16 ----> equation D

Substitute equation C in equation d and solve for w

3w+w=16

4w=16

w=4 cups of Blackberries

Remember that

For 1 batch of the recipe are used 1 cup of Blackberries

so

For 4 cups of Blackberries

The number of batches are

(1)*4=4 batches

Answer:

the answer is b

Step-by-step explanation:

it is

Answer: (8,-6)

Step-by-step explanation:

the coordinates are  (3,-2)

(x+5, y-4)

(3+5,-2-4)

(8,-6)

Catie needs to babysit for more than 10.33 hours to start making a profit in her new babysitting business. She must babysit for at least 11 hours to cover her initial $36 advertising cost and start earning a profit.

The question involves creating and solving an inequality to determine how many hours Catie needs to babysit to make a profit in her new babysitting business. Catie spent $36 on advertising and charges an initial fee of $5 plus $3 per hour of babysitting. We represent the total earnings as a function of the number of hours (h) she works, with the equation being 5 + 3h (the $5 initial fee plus $3 for each hour). To find out when Catie starts to make a profit, we set her earnings greater than her initial investment of $36.

The inequality is: 5 + 3h > 36.

To solve this inequality:

Interpreting the solution, Catie needs to babysit for more than 10.33 hours to start making a profit. Since she cannot babysit for a fraction of an hour, she must babysit for at least 11 hours to ensure a profit.

Answer: ITS NOT 1/6, ITS 1/12

Step-by-step explanation:

I took the test :)

If triangle ABC is a right triangle with ∠C = 90°, then angles A and B must be complementary.

If triangle ABC is a right triangle with ∠C = 90°, then angles A and B must be complementary. This means that the sum of angles A and B will be equal to 90°. Therefore, the correct answer is option b.

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The true statement about angles A and B is that a. Angles A and B are complementary.

Since triangle ABC is a right triangle with m∠C = 90°, we know that m∠A + m∠B = 90°.

This means that the sum of the measures of angles A and B is 90 degrees.

So, angles A and B are complementary angles.

In other words, if two angles are complementary, then the sum of their measures is equal to 90 degrees.

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Question

if aabc is a triangle with mlc = 90, which of the following must be true about angles a and b?

Angles A and B are complementary.

Angle B is greater than angle A.

Angles A and B are supplementary

Angle A is greater than angle B.

We have to prove that [tex]\sqrt{2}+\sqrt{5}[/tex] is irrational. We can prove this statement by contradiction.

Let us assume that [tex]\sqrt{2}+\sqrt{5}[/tex] is a rational number. Therefore, we can express:

[tex]a=\sqrt{2}+\sqrt{5}[/tex]

Let us represent this equation as:

[tex]a-\sqrt{2}=\sqrt{5}[/tex]

Upon squaring both the sides:

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

Since a has been assumed to be rational, therefore, [tex]\frac{a^{2}-3}{2a}[/tex] must as well be rational.

But we know that [tex]\sqrt{2}[/tex] is irrational, therefore, from equation [tex]\sqrt{2}=\frac{a^{2}-3}{2a}[/tex] the expression [tex]\frac{a^{2}-3}{2a}[/tex] must be irrational, which contradicts with our claim.

Therefore, by contradiction,  [tex]\sqrt{2}+\sqrt{5}[/tex] is irrational.

Step-by-step explanation:

Let us assume [tex]\bf \sqrt{2}+\sqrt{5} [/tex] as rational.

[tex]\therefore \: \:\bf \sqrt{2}+\sqrt{5} = \dfrac{a}{b}[/tex]

[tex]\implies\:\:\bf \sqrt{5} = \dfrac{a}{b} - \sqrt{2} [/tex]

[tex]\implies\:\:\bf(\sqrt{5})^{2} = \bigg( \dfrac{a}{b} -\sqrt{2}\bigg)^{2} [/tex]

[tex]\implies\:\:\bf 5 = \dfrac{a^{2} }{b^{2}} - 2 \bigg(\dfrac{a}{b}\bigg) (\sqrt{2}) + (\sqrt{2})^{2}[/tex]

[tex]\implies\:\:\bf 5 = \dfrac{a^{2} }{b^{2}} - 2 \sqrt{2} \bigg( \dfrac{a}{b} \bigg) + 2[/tex]

[tex]\implies\:\:\bf 5-2 = \dfrac{a^{2}}{b^{2}}- 2 \sqrt{2} \bigg( \dfrac{a}{b} \bigg)[/tex]

[tex]\implies\:\:\bf 3 = \dfrac{a^{2}}{b^{2}}- 2 \sqrt{2} \bigg( \dfrac{a}{b} \bigg)[/tex]

[tex]\implies\:\:\bf 2 \sqrt{2} \bigg( \dfrac{a}{b} \bigg)= \dfrac{a^{2}}{b^{2}} -3[/tex]

[tex]\implies\:\:\bf 2 \sqrt{2} \bigg( \dfrac{a}{b} \bigg)=\dfrac{a^{2}-3b^{2}}{b^{2}}[/tex]

[tex]\implies\:\:\bf 2 \sqrt{2} = \bigg( \dfrac{a^{2}-3b^{2}}{b^{2}} \bigg) \bigg( \dfrac{b}{a}\bigg) [/tex]

[tex]\implies\:\:\bf \sqrt{2} =\dfrac{a^{2}-3b^{2} }{2ab}[/tex]

[tex]\textsf Hence, our assumption is wrong [/tex]

[tex] \therefore \:\:\sf {{\bf{\sqrt{2}+\sqrt{5}}} is irrational }[/tex]

[tex]\mathfrak\purple{{\purple{\bf{H}}}ence\: {\purple{\bf{P}}}roved}[/tex]

Answer:

C. commutative property

Step-by-step explanation:

For the first part, part a, we are given that:

0.01b^2+ ∗ +100c^2

In quadratic equations we know that the middle term (the one that is missing) will be twice the square root of the first and the last terms.

Now, we know that the square root of the first term is: [tex] \sqrt{0.01b^2} =0.1b [/tex] Let us represent this by [tex] x [/tex]. Therefore, [tex] x=0.1b [/tex]

and the square root of the last term is: [tex] \sqrt{100c^2} =10c [/tex]

Let this be [tex] y [/tex]. Therefore, [tex] y=10c [/tex]

Therefore, the middle term, * is: [tex] 2xy=2\times0.1b\times 10c=2bc [/tex]

Likewise in the part b, we will have the middle term to be:

[tex] 2\times \sqrt{25a^2} \times \sqrt{\frac{1}{4}b^2} =2\times 5a\times \frac{1}{2}b=5ab [/tex]

because the first and the last terms are 25a^2 and 1/4 b^2 and we know that the middle term will be twice the square root of the first and the last terms.

Answer:

140

Step-by-step explanation:

that's the answer on ttm