Henry is 4 years younger than Linda. Linda is 20 years old.


After correctly carrying out the Solve step of the five-step problem-solving plan, which solution should you arrive at to find Henry’s age?



28

24

16

12

Answer:

if your asking for the difference between the temperatures then it would be

8, but if your asking for the sum it would be -4

Hope i helped :)

Answer:

The running club has 35 members

Step-by-step explanation:

Let

x ----> the total members of the running club

we know that

The total members of the running club multiplied by 5/7 plus 6 must be equal to 31 people

so

[tex]\frac{5}{7}x+6=31[/tex]

Solve for x

[tex]\frac{5}{7}x=31-6[/tex]

[tex]\frac{5}{7}x=25[/tex]

[tex]x=25(7)/5[/tex]

[tex]x=35\ members[/tex]

therefore

The running club has 35 members

Probability of a male having a blood circulation problem, given he's a smoker, is approximately 0.6667.

Step 1:

Identify the given probabilities:

Let [tex]\( P(A) \)[/tex] be the probability that a randomly chosen male has a blood circulation problem, which is [tex]\( 0.25 \)[/tex].

Let [tex]\( P(B|A) \)[/tex] be the probability that a male is a smoker given that he has a blood circulation problem, and it's twice the probability of being a smoker given not having a blood circulation problem.

Step 2:

Calculate [tex]\( P(B|\neg A) \)[/tex]:

Since males with blood circulation problems are twice as likely to be smokers as those without, \( P(B|\neg A) \) is half of [tex]\( P(B|A) \)[/tex], which is [tex]\( \frac{1}{2} \)[/tex].

Step 3:

Apply Bayes' theorem:

[tex]\[ P(A|B) = \frac{P(B|A) \times P(A)}{P(B)} \][/tex]

Step 4:

Calculate \( P(B) \):

[tex]\[ P(B) = P(B|A) \times P(A) + P(B|\neg A) \times P(\neg A) \][/tex]

Step 5:

Substitute values into Bayes' theorem and solve:

[tex]\[ P(A|B) = \frac{(2 \times P(B|\neg A)) \times P(A)}{(2 \times P(B|\neg A)) \times P(A) + P(B|\neg A) \times (1 - P(A))} \]\[ P(A|B) = \frac{(2 \times \frac{1}{2}) \times 0.25}{(2 \times \frac{1}{2}) \times 0.25 + \frac{1}{2} \times (1 - 0.25)} \]\[ P(A|B) = \frac{0.25}{0.25 + 0.125} \]\[ P(A|B) = \frac{0.25}{0.375} \]\[ P(A|B) \approx 0.6667 \][/tex]

Thus, the probability that a male has a blood circulation problem, given that he is a smoker, is approximately 0.6667.

Answer:1-1/3

Step-by-step explanation:

2/3x2=1-1/3

Answer:

3 loaves of banana bread

Step-by-step explanation:

2/3 x 3= 6/3. 6/3 simplified is 2 cups. I hope this helps!

Answer:

3, 6, 12, 24

Step-by-step explanation:

This is a recursive formula which allows the next term in a sequence to be found from the previous term in the sequence

Given

[tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] with a₁ = 3, then

a₂ = 2 × a₁ = 2 × 3 = 6

a₃ = 2 × a₂ = 2 × 6 = 12

a₄ = 2 × a₃ = 2 × 12 = 24

Thus the first 4 terms are 3, 6, 12, 24

Answer:

B.[tex]3,6,12,24[/tex]

Step-by-step explanation:

We are given that

[tex]a_n=2a_{n-1}[/tex]

[tex]a_1=3[/tex]

We have to find the first four terms of G.P

Substitute n=2

[tex]a_2=2a_1=2(3)=6[/tex]

Substitute n=3

[tex]a_3=2a_2=2(6)=12[/tex]

Substitute n=4

[tex]a_4=2a_3=2(12)=24[/tex]

Hence, the first four terms of G.P are  given by

[tex]3,6,12,24[/tex]

Option B is true.

Answer:

$800

Step-by-step explanation:

40*20=800

$800

Answer:

Vertex of parabola (-1, -10)

Step-by-step explanation:

For a given quadratic y = ax² + bx + c, the vertex (h, k) is found by computing h = –b/2a, and then evaluating y at h to find k. If you've already learned the Quadratic Formula, you may find it easy to memorize the formula for k, since it is related to both the formula for h and the discriminant in the Quadratic Formula: k = (4ac – b2) / 4a.

Answer:

720 shares

Step-by-step explanation:

Find 60% of 1,200, to figure out how many shares Jillian has.

Change 60% to decimal

0.6

Multiply with the total shares

0.6 x 1,200 = 720

720 shares

Jillian owns 720 shares in a catering corporation.

The percentage is defined as a ratio expressed as a fraction of 100.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

We have to determine 60% of 1,200, to figure out how many shares Jillian has.

Convert 60% into a decimal

⇒ 0.6

Multiply with the total shares

⇒ 0.6 × 1200

⇒  720

Hence, Jillian owns 720 shares in a private catering corporation.

Learn more about Arithmetic operations here:

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Answer:

B; 2.25

Step-by-step explanation:

Final answer:

The question asks for the ratio of yellow eggs to colored eggs, which is 10 yellow eggs to 12 colored eggs. Simplifying the ratio, we get 5:6. This concept of ratios is also seen in Mendel's genetic experiments with plants, where traits are passed in specific ratios like 3:1.

Explanation:

In mathematical terms, a student's question regarding the ratio of yellow eggs to the total number of colored eggs can be answered using simple division to derive a fraction or ratio. Given that there are 10 yellow eggs out of 12 colored eggs, the ratio can be expressed as 10:12.

However, ratios should be simplified to their smallest form to be more understandable; therefore, this ratio simplifies to 5:6 since both numbers can be divided by 2.

When looking at historical experiments, such as the ones conducted by Mendel, we find that phenotypic ratios play a significant role in understanding genetics. Mendel observed that traits could manifest in a specific ratio, like a 3:1 ratio for dominant to recessive traits. The ratios observed in the experiments provided can serve as examples to understand how ratios represent the occurrence of certain outcomes over others.

In this case, the ratio of yellow to green seeds in Mendel's experiment can serve as an analogy to understand the ratio of yellow eggs: both ratios quantitatively describe the presence of a certain characteristic compared to another.

Answer:

C. [tex]x=\frac{5}{2}[/tex]

Step-by-step explanation:

The quadratic formula is:

[tex]x_{1,2}=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}[/tex]

Where [tex]a[/tex] is the coefficient of the quadratic team. [tex]b[/tex] is the coefficient of the linear term, and [tex]c[/tex] is the independent term.

So, the given equation is:

[tex]x^2 - 5x + \frac{25}{4}  = 0[/tex]

Where:

[tex]a=1\\b=-5\\c=\frac{25}{4}[/tex]

[tex]x_{1,2}=\frac{-(-5)\±\sqrt{(-5)^{2}-4(1)(\frac{25}{4} )}}{2(1)}\\x_{1,2}=\frac{5\±\sqrt{25-25}}{2}\\x_{1,2}=\frac{5\±\sqrt{0}}{2}\\x_{1,2}=\frac{5}{2}[/tex]

This means that the equation has a unique solution.

Therefore, the right answer is C.

Answer:

[tex]60[/tex]

Step-by-step explanation:

Suzzane can work 10 math problems in 15 minutes. We need to use proportion and raito.

One hour and a half is equal to 90 minutes. But to equal out the math problem, change it to 900.

So:

[tex]\frac{10}{15}[/tex]  [tex]= \frac{x}{900}[/tex]

[tex]= 60[/tex]

3y-14=13

move -14 to the other side

sign changes from -14 to +14

3y-14+14=13+14

3y=13+14

3y=27

divide both sides by 3 to get y by itself

3y/3=27/3

Answer: y=9

Answer: 2400

Step-by-step explanation:

for every pound there is 300 gallons, so

300 x 8 = 2400

Hope this helps!

Answer:

Ian need to keep the website for site B less than 10 months

Step-by-step explanation:

Let

x -----> the number of months

y ----> the cost for website hosting

we know that

Site A

[tex]y=4.95x+49.95[/tex] -----> equation A

Site B

[tex]y=9.95x[/tex] -----> equation B

Equate equation A and equation B and solve for x

[tex]9.95x=4.95x+49.95[/tex]

[tex]9.95x-4.95x=49.95[/tex]

[tex]5x=49.95[/tex]

[tex]x=9.99\ months[/tex]

Round the number of months

[tex]x=10\ months[/tex]

For x=10 months ----> the cost for website hosting is the same in both sites

For x>10 months ---> the cost for website hosting is less expensive in site A

For x<10 months ---> the cost for website hosting is less expensive in site B

therefore

Ian need to keep the website for site B less than 10 months

When comparing the two hosting sites, Site B becomes cheaper than Site A after around 10 months, if the website is kept active during this period. This calculation is made by setting up an equation for the costs and solving for the number of months.

When Ian wants to promote his band on the Internet by creating a website, he needs to make a decision about the cost effectiveness between the two hosting sites. Let's break down the costs for each site:

To find out when Site B would be cheaper than Site A, we need to set up an equation where the left-hand side is the cost for Site A and the right-hand side is the cost for Site B. The equation would therefore be, $49.95 + $4.95n (with n being the number of months) = $9.95n.

To solve for n, subtract $4.95n from both sides leaving $49.95 = $5n. Dividing $49.95 by $5 gives us n = 9.99, which means after around 10 months, Site B becomes cheaper than Site A provided Ian keeps the site active.

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Answer:

A. $301

B. $721

Step-by-step explanation:

Let $x be the amount of money they raised.

Rowena tried to put the $1 bills into two equal piles and found one left over at the end, then

[tex]x=2q_1+1[/tex]

Polly tried to put the $1 bills into three equal piles and found one left over at the end, then

[tex]x=3q_2+1[/tex]

Frustrated, they tried 4, 5, and 6 equal piles and each time had $1 left over, then

[tex]x=4q_3+1\\ \\x=5q_4+1\\ \\x=6q_5+1[/tex]

Finally Rowena put all the bills evenly into 7 equal piles, and none were left over, then

[tex]x=7q_6[/tex]

This means [tex]x-1[/tex] is divisible by 2, 3, 4, 5 and 6 without remainder, so

[tex]x-1=2\cdot 3\cdot 2\cdot 5n=60n[/tex]

Hence,

[tex]x=60n+1, \ n\in N[/tex]

The smallest amount of money they could have raised is $301, because

[tex]x=60\cdot 5+1=301[/tex] is divisible by 7.

Now, the number [tex]x=60n+1[/tex] should be divisible by 7 and must be greater than 500.

So,

[tex]60n+1>500\\ \\60n>499\\ \\n>8[/tex]

When n = 9,

[tex]x=60\cdot 9+1=541[/tex] is not divisible by 7.

When n = 10,

[tex]x=60\cdot 10+1=601[/tex] is not divisible by 7.

When n = 11,

[tex]x=60\cdot 11+1=661[/tex] is not divisible by 7.

When n = 12,

[tex]x=60\cdot 12+1=721[/tex] is divisible by 7.

B. The least amount of money they could have raised is $721

Answer:

A:301 and b: 721

Answer:

Yes

Step-by-step explanation:

A function correlates elements from a set one and only one element from a different set. Think of a train timetable: you can't have the same train in two points at a given time.

An easy way to solve the problem is to take a ruler (or the edge of a sheet of paper, as long as it's straight) and scan the graph parallel to the Y axis. As long as you don't touch the graph more than once, it's a function (zero points is ok!)

Answer:

yes

Step-by-step explanation:

Answer:

no .8 9 10 are false statement

Step-by-step explanation:

8.angle 3 and angle 5 are not vertical angles because the two lines do not intersect

9 angle 3 and angle 4 are not complementary angle because their non common arms are two opposite rays.

10.angle 1 and angle 2 are not supplementary angles because their non common arms are not two opposite rays.

The answers for #8-10 involve finding the derivative of a function, solving a system of equations, and finding the slope of a line.

For question #8, you need to find the derivative of the given function. This involves using the power rule and the chain rule. For question #9, you are given a system of equations and you need to solve for the values of x and y. This can be done using substitution or elimination. Finally, for question #10, you are asked to find the slope of a line given two points. You can use the formula (y2 - y1) / (x2 - x1) to find the slope.

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Answer:

42.4285714286

Step-by-step explanation:

If you divide 7.5 by 5/6, the answer comes out to 9. If you multiply 4 5/7 by 9, the answer is 42.4285714286.

Answer:

x=-3/4

Step-by-step explanation:

Use the distributive property a(a+b)= ab+bc:

-4x-2=1

Add a 2 to both sides:

-4x=3

Divide both sides by -4:

x=3/-4

This can be rewritten as -3/4

Hey!

--------------------------------

Lets try -10:

2(3(-10) - 1) = 4(-10) - 6

2(-30 - 1) = (-40) - 6

2(-31) = (-40) - 6

-62 ≠ -46

Incorrect.

--------------------------------

Lets try -5:

2(3(-5) - 1) = 4(-5) - 6

2(-15 - 1) = (-20) - 6

2(-16) = (-20) - 6

-32 ≠ -26

Incorrect.

--------------------------------

Lets try -3:

2(3(-3) - 1) = 4(-3) - 6

2(-9 - 1) = (-12) - 6

2(-10) = (-12) - 6

-20 ≠ -18

Incorrect.

--------------------------------

Lets try -1:

2(3(-1) - 1) = 4(-1) - 6

2(-3 - 1) = (-4) - 6

2(-4) = (-4) - 6

-8 ≠ -10

Incorrect.

--------------------------------

So all the options are incorrect.

--------------------------------

Lets solve for x:

2(3x - 1) = 4x - 6

(2 * 3x) + (2 * -1) = 4x + (-6)

6x + (-2) = 4x + (-6)

6x - 2 = 4x - 6

6x - 2 - 4x = 4x - 6 - 4x

2x - 2 = -6

2x + 2 - 2 = -6 + 2

2x = -4

2x/2 = -4/2

x = -2

--------------------------------

Hope This Helped! Good Luck!

Answer:

-1 is the answer

Step-by-step explanation:

Answer:

Equation: [tex]3(x-6)^2=12[/tex]

Solutions: [tex]x=4\text{ or }x=8[/tex]

Step-by-step explanation:

Unknown variable [tex]= x[/tex]

Difference of x and 6 [tex]= x - 6[/tex]

Square of the difference of x and 6 [tex]=(x-6)^2[/tex]

Three times the square of the difference of x and 6 [tex]=3(x-6)^2[/tex]

Three times the square of the difference of x and 6 is 12, then

[tex]3(x-6)^2=12[/tex]

Divide this equation by 3:

[tex](x-6)^2 =4[/tex]

Now

[tex]x-6=2\text{ or }x-6=-2\\ \\x=2+6\text{ or }x=-2+6\\ \\x=8\text{ or }x=4[/tex]

Answer:

The answer is x=4 or x=8

Step-by-step explanation:

The price after Allie uses the coupon to buy two tubes of toothpaste is $1.93.

To find the price after Allie uses the coupon, you first need to calculate the total cost of two tubes of toothpaste without the coupon and then subtract the coupon value. The total cost of two tubes of toothpaste, which is $1.39 times 2. The result is $2.78.

So now, we need Allie's coupon by subtracting the discount, which is $0.85, from the total cost ($2.78 - $0.85).

Therefore, The final cost, or the price after using the coupon, is $1.93.

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The price of two tubes of toothpaste after Allie uses the coupon is $1.93.

To calculate the price of two tubes of toothpaste after Allie uses the coupon, we can use the following steps:

Calculate the price of two tubes of toothpaste without the coupon.

Subtract the value of the coupon from the price of two tubes of toothpaste without the coupon.

Step 1: Calculate the price of two tubes of toothpaste without the coupon.

The price of one tube of toothpaste is $1.39, so the price of two tubes of toothpaste is:

$1.39/tube * 2 tubes = $2.78

Step 2: Subtract the value of the coupon from the price of two tubes of toothpaste without the coupon.

The value of the coupon is $0.85, so the price of two tubes of toothpaste after Allie uses the coupon is

$2.78 - $0.85 = $1.93

Therefore, the price of two tubes of toothpaste after Allie uses the coupon is $1.93.

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Answer:

84.9*64=5433.6

3900/2.6=1500

1080/15.9=67.9245283019

2.86*8.77*200=5016.44

1500/64=23.4375

6007/5.5=1092.1818....

Step-by-step explanation:

Answer:

y=6

Step-by-step explanation:

8y-5y-2=16

8y-5y=16+2

3y=18

y=18/3

y=6

Hey!

------------------------------

Solution:

8y - (5y + 2) = 16

3y - 2 = 16

3y + (-2) + 2 = 16 + 2

3y = 18

3y/3 = 18/3

y = 6

------------------------------

Answer:

y = 6

------------------------------

Hope This Helped! Good Luck!

Simplifying

64 + -12w = 6w

Solving

64 + -12w = 6w

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-6w' to each side of the equation.

64 + -12w + -6w = 6w + -6w

Combine like terms: -12w + -6w = -18w

64 + -18w = 6w + -6w

Combine like terms: 6w + -6w = 0

64 + -18w = 0

Add '-64' to each side of the equation.

64 + -64 + -18w = 0 + -64

Combine like terms: 64 + -64 = 0

0 + -18w = 0 + -64

-18w = 0 + -64

Combine like terms: 0 + -64 = -64

-18w = -64

Divide each side by '-18'.

w = 3.555555556

Simplifying

w = 3.555555556

Answer: 8 x 80

Step-by-step explanation: if you multiply 8 x 80 then you can just act as if the 80 is 8 and once you do the multiplication add the 0 at the end when your done.

Answer:

The vertical distance is 25.825 ft

Step-by-step explanation:

we know that

To find out the vertical distance between Cece and the base of the mountain, subtract the height of the base of the mountain from the height of Cece

Let

x -----> the height of Cece

y ----> the height of the base of the mountain

we have

[tex]x=15\frac{5}{8}\ ft[/tex] ----> is positive because is above sea level

convert to an improper fraction

[tex]x=15\frac{5}{8}\ ft=\frac{15*8+5}{8}=\frac{125}{8}=15.625\ ft[/tex]

[tex]y=-10.2\ ft[/tex] -----> is negative because is below sea level

so

[tex]x-y=15.625-(-10.2)=15.625+10.2=25.825\ ft[/tex]

Remember that -1*(-1)=+1

Answer:

8a + 5 - 10a - 11 simplified equals -2a - 6

Step-by-step explanation:

1st group like terms: 8a - 10a + 5 - 11

2nd add similar elements: 8a - 10a = -2a,

-2a + 5 - 11

3rd add/subtract the numbers: 5 - 11 = -6

-2a - 6

I am joyous to assist :)

Good evening ,

______

Answer:

x=2ln2.

___________________

Step-by-step explanation:

Look at the photo below for the details.

:)

Answer:   b) 225.2 mg

Step-by-step explanation:

Convert 1 kg to 2.2 lbs.

[tex]\dfrac{3.3\ mg}{1\ kg}\times \dfrac{1\ kg}{2.2\ lbs}\times 150.1\ lbs\quad =\dfrac{3.3(150.1)\ mg}{2.2}\quad =\dfrac{495.33\ mg}{2.2}\\\\\\=\large\boxed{225.15\ mg}[/tex]