Nancy is 5 years younger than her brother Stan. Last year she was twice as young as he was. How old is each of them now?

Answer:

The proportional

Step-by-step explanation:

[tex]\begin{array}{c|c}18&2\\9&3\\3&3\\1\end{array}\\\\18=\boxed2\cdot\boxed3\cdot\boxed3\\\\\begin{array}{c|c}72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\\\\72=2\cdot2\cdot\boxed2\cdot\boxed3\cdot\boxed3\\\\GCF(18,\ 72)=\boxed2\cdot\boxed3\cdot\boxed3=\boxed{\boxed{18}}[/tex]

The greatest common factor of 18 and 72 can be found through prime factorization, by identifying the prime factors of each number, finding the common factors, and multiplying them together. In this case, the greatest common factor is 18.

To find the greatest common factor (GCF) of 18 and 72 through prime factorization, follow these steps:

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It's not a rectangle. Look at the picture.

It is a parallelogram.

The area of the red rectangle:

[tex]A_{\boxed{ \ }}=(4+8)(6+3)=(12)(9)=108[/tex]

The areas of the right triangles:

[tex]A_1=\dfrac{1}{2}(3)(4)=6\\\\A_2=\dfrac{1}{2}(6)(8)=24[/tex]

The area of a parallelogram:

[tex]A=A_{\boxed{ \ }}-(2A_1+2A_2)\\\\A=108-(2\cdot6+2\cdot24)=108-(12+48)=108-60=48[/tex]

Answer:

The number of questions in sixth assignment must be less than or equal to 28.

Step-by-step explanation:

The number of questions in first five assignments are 11,10,13,14 and 14.

It is given that Mrs hawk assigns her students an average of no more than 15 questions on each assignment. Therefore the average of six assignments is less than or equal to 15 questions.

Let the number of questions in sixth assignment be x

[tex]\text{Average}=\frac{\text{Sum of observations}}{\text{Number of observations}}[/tex]

Average of six assignments are

[tex]A=\frac{11+10+13+14+14+x}{6}[/tex]

[tex]A=\frac{62+x}{6}[/tex]

Since the average of questions is no more than 15, therefore

[tex]A\leq 15[/tex]

[tex]\frac{62+x}{6}\leq 15[/tex]

[tex]62+x\leq 90[/tex]

[tex]x\leq 28[/tex]

Therefore the number of questions in sixth assignment must be less than or equal to 28.

Answer:

There are 25 students in Hannah's class.

Step-by-step explanation:

If 20 students in Hannah's class is 80% of the total amount of students, we can use a variable to figure out the total amount of students.

Let's say x is the total amount of students. We can use this equation to solve the problem:

[tex]20 = .8x[/tex]

This is saying 20 equals 80% (.8 when you move the decimal 2 times) of x, or the total amount of students. Let's solve.

20 = .8x

Divide by .8

25 = x

There are 25 students in Hannah's class.

Percentage of a number is the part of the number in every hundred. The total number of students in Hannah's class is 25.

Given information

Total number of students in Hannah's class voted for the pizza is 20.

The total percent of students in Hannah's class voted for the pizza is 80.

Percentage of a number is the part of the number in every hundred. A percentage of a number is the ratio expressed as fraction of hundred.

Suppose the total number of student in Hannah's class is x.

As total number of students in Hannah's class voted for the pizza is 20 and total percent of students in Hannah's class voted for the pizza is 80.

Therefore the the 80 percent of the total student of the class is equal to the number 20. The 80 percent of a number is 20 thus,

[tex]\begin{aligned}\\\dfrac{80}{100} \times x&=20\\\dfrac{4}{5} \times x&=20\\x&=\dfrac{20\times5}{4} \\x&=25\\\end[/tex]

Thus the total number of students in Hannah's class is 25.

Learn more about the percentage here;

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Answer: x = 4

Step-by-step explanation:

[tex]\dfrac{3}{5}(10 + 5x) - \dfrac{1}{3}(6x + 3)=9[/tex]

[tex]\dfrac{3}{5}(10 + 5x)(15) - \dfrac{1}{3}(6x + 3)(15)=9(15)[/tex] multiplied by common denominator

3(10 + 5x)(3) - 1(6x + 3)(5) = 9(15)   reduced all fractions

90 + 45x - 30x - 15 = 135      distributed

15x + 75 = 135      simplified (added like terms)

15x = 60         subtracted 75 from both sides

  x = 4          divided 15 from both sides

Answer:

see explanation

Step-by-step explanation:

given the geometric sequence then the n th term rule is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] . [tex]r^{n-1}[/tex]

where r is the common ratio and [tex]a_{1}[/tex] the first term

here r = [tex]\frac{192}{48}[/tex] = [tex]\frac{48}{12}[/tex] = 4 and [tex]a_{1}[/tex] = 3, hence

[tex]a_{n}[/tex] = 3 . [tex]4^{n-1}[/tex] ← third option

Option 2 .The statement that is NOT TRUE is "A is the complement of B"

Let’s analyze each option:

1. A and B are joint sets: Sets A and B are not joint sets (disjoint sets) because they have common elements. Specifically, both sets contain the elements 2, 3, and 4.

2. A is the complement of B: The complement of a set B relative to A would be the set of elements in A that are not in B The complement of B in A is {1, 5\}, not equal to A Therefore, A is not the complement of B.

3. B ⊆ A: Set B = {2, 3, 4} is indeed a subset of A = {1, 2, 3, 4, 5} , meaning all elements of B are contained in A.

4. Ø ⊆ A: The empty set Ø is a subset of any set, including A

5. A ⊆ B: Set A = {1, 2, 3, 4, 5} is not a subset of B = {2, 3, 4}, since A contains elements (1 and 5) that are not in B.

Complete question

Answer:

1) 11h - 25

2) 8

3) C

Step-by-step explanation:

1) 5h-9+-16+6h

+ and - together makes -

5h - 9 - 16 + 6h

Arrange the like terms together

5h + 6h - 9 - 16

= 11h - (9+16)

= 11h - 25

2) 4x+4=9x-36

Subtract 4x from both sides

4x+4-4x = 9x-36-4x

Cancl out 4x and -4x from the left side

4 = 9x - 4x -36

=> 4 = 5x -36

Add 36 to both sides

4+36 = 5x -36 + 36

Cancel out -36 and +36 from the right side

=> 40 = 5x

Flip both the sides of the equation

5x = 40

Dividing both sides by 5

[tex]\frac{5x}{5} = \frac{40}{5}[/tex]

Cancel out the 5's on the top and bottom of the left side

x = 8

3) 7x+5 = 4x+5+3x

Arrange the like terms together on the right side

7x+5 = 4x+3x+5

=> 7x+5 = 7x+5

Subtract 5 from both sides

7x+5-5 = 7x+5-5

Cancel out +5 and -5 on both the sides

7x = 7x

Divide both sides by 7

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

Cancel out the 7's from the top and bottom of both sides

x = x

which can be true for infinite value of x like 1=1, 2=2, 3=3,.............

Answer:

DAB must equal 52 because same side interior angles are supplementary. Supplementary describes 2 angles whose measures add up to 180

Answer: May or may not be

Step-by-step explanation:

check the picture and trust me

The earnings for selling the same number of each type of sandwich, considering both Turkey and Ham with Pretzel Roll and Bagel options, amount to $48. This is derived from a simplified expression of $29.10x, factored by 11, indicating a total revenue of $4.30 per sandwich.

Earnings for Selling Sandwiches

1: Identify the Given Information

We have two types of sandwiches: Turkey and Ham.

Each type comes in two types of bread: Pretzel Roll and Bagel.

Prices are provided for each combination:

Turkey Pretzel: $2.25

Turkey Bagel: $2.00

Ham Pretzel: $1.55

Ham Bagel: $1.30

2: Represent the Number of Sandwiches with a Variable

Let x represent the number of each type of sandwich sold (both Turkey and Ham, regardless of bread).

3: Calculate Earnings for Each Type of Sandwich

Turkey Sandwich: $11 (given price) * x (number sold) = $11x

Ham Sandwich: $11 (given price) * x (number sold) = $11x

Step 4: Calculate Earnings for Each Bread Type (excluding overlapping information)

Pretzel Roll: (Earnings from Turkey Pretzel + Earnings from Ham Pretzel) = ($2.25 * x) + ($1.55 * x) = $3.80x

Bagel: (Earnings from Turkey Bagel + Earnings from Ham Bagel) = ($2.00 * x) + ($1.30 * x) = $3.30x

5: Combine Earnings for Total Revenue

Total Earnings = Earnings from Turkey Sandwiches + Earnings from Ham Sandwiches + Earnings from Pretzel Rolls + Earnings from Bagels

Total Earnings = $11x + $11x + $3.80x + $3.30x = $29.10x

6: Simplify the Expression

Total Earnings = $29.10x

Since we are selling the same number of each type of sandwich, 11 is a common factor in all four terms.

We can factor out 11 to obtain:

Total Earnings = 11 * ($2.65 + $1 + $0.35 + $0.30) = 11 * $4.30 = $48

Therefore, the earnings for selling the same number of each type of sandwich are $48.

Answer:

The answer would be 998.4

Step-by-step explanation:

251,589 divided by 252 = 998.36

round it to 998.4

Answer:

y = 8

Step-by-step explanation:

If y varies directly as x we can write y = kx where k is some constant.

Y = 8 when x = 2 so  8 = k*2

k = 8/2 = 4

so y = 4x

This is the equation of variation.

When x = 6, y = 4*6 = 24  (answer).

Answer:

y =24

Step-by-step explanation:

The equation for direct variation is

y =kx

If we know x and y we can solve for k

y=kx

8 =k*2

Divide each side by 2

8/2 = k2/2

4 =k

y =4x

We want to find y when x=6

y =4*6

y =24

Answer:

1.61904761905

Step-by-step explanation:

-5 2/3 is equal to -17/3. We then multiply the two fractions: -2/7 *-17/3, the answer is 1.61904761905 as a decimal or 34/21( or 1 13/21).

Hope this helps! <3

In the number game that Valerie and Robbie are playing, based on Valerie's clues, the number she is thinking of can be determined using a mathematical equation: x/4 + 5 - 6 = 6. Solving this equation step-by-step, the number Valerie is thinking of is 28.

In the given scenario, Valerie and Robbie are playing a number game. Valerie tells Robbie that she's thinking of a number which, when divided by 4, then added to 5, and subtracted by 6, equals to 6. This can be translated into a mathematical equation:

x/4 + 5 - 6 = 6

We can simplify this step-by-step. First, we can combine the constants:

x/4 -1 = 6

Next, add 1 to both sides to isolate x/4 on the left:

x/4 = 7

Finally, to find x, multiply both sides by 4:

x = 28

So, the number that Valerie is thinking of is 28.

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Answer:

an = -6+n

or

an = 1 + 7(n-1)

Step-by-step explanation:

a(1)=1 and a(n+1)=a(n)+7

The explicit formula is

an = a1+ d (n-1)

we know a1 =1

Looking at a(n+1)=a(n)+7

We are adding 7 each time so the common difference is +7

an = 1 + 7(n-1)

We can simplify this

an = 1 + 7n -7

an = -6+n

You can use either formula

Answer:

hell have 120,000

Step-by-step explanation:

The distributive property: a(b + c) = ab + ac.

Answer:

d 15+40=5(3+8)

Step-by-step explanation:

Put the values of x to the equation y = 2ˣ:

[tex]x=-1\to y=2^{-1}=\dfrac{1}{2}\to\left(-1,\ \dfrac{1}{2}\right)\\\\x=0\to y=2^0=1\to(0,\ 1)\\\\x=1\to y=2^1=2\to(1,\ 2)\\\\x=2\to y=2^2=4\to(2,\ 4)\\\\x=3\to y=2^3=8\to(3,\ 8)\\\\x=4\to y=2^4=16\to (4,\ 16)[/tex]

Answer:

[tex]\left\{\left(-1,\ \dfrac{1}{2}\right);\ (0,\ 1);\ (1,\ 2);\ (2,\ 4);\ (3,\ 8);\ (4,\ 16)\right\}[/tex]

Answer:

a=3.75 un., b=11.25 un.

[tex]x=7.5\ un.[/tex]

[tex]y=\dfrac{15\sqrt{3}}{4}\ un.[/tex]

[tex]z=\dfrac{15\sqrt{3}}{2}\ un.[/tex]

Step-by-step explanation:

Given triangle is special 30°-60°-90° right triangle. The leg that is opposite to the angle of measure 30° is always equal to half of the hypotenuse. The hypotenuse is of length 15 units, the leg that is opposite to the 30° angle is leg with length of x units, then

[tex]x=\dfrac{15}{2}=7.5\ un.[/tex]

In right triangle with hypotenuse x and legs y and a, angle opposite to the leg a is 30°, then

[tex]a=\dfrac{x}{2}=\dfrac{7.5}{2}=3.75\ un.[/tex]

and

[tex]b=15-a=15-3.75=11.25\ un.[/tex]

By the Pythagorean theorem,

[tex]x^2=y^2+a^2,\\ \\7.5^2=3.75^2+y^2,\\ \\y^2=\left(\dfrac{15}{2}\right)^2-\left(\dfrac{15}{4}\right)^2=\dfrac{225}{4}-\dfrac{225}{16}=\dfrac{675}{16},\\ \\y=\dfrac{15\sqrt{3}}{4}\ un.[/tex]

In right triangle with legs y and b and hypotenuse z, leg y is opposite to 30° angle, then

[tex]z=2y=\dfrac{15\sqrt{3}}{2}\ un.[/tex]

Answer:

[tex]a=3.75[/tex]

Step-by-step explanation:

The hypotenuse of the large triangle is 15.

We can see that the side opposite of 30° angle is [tex]x[/tex]

Trigonometric ratio of SINE relates opposite and hypotenuse.

Thus we can write and cross multiply and solve:

[tex]sin(A)=\frac{Opposite}{Hypotenuse}\\sin(30)=\frac{x}{15}\\x=15*sin(30)=7.5[/tex]

Now if you see the smallest triangle, [tex]a[/tex] is the adjacent side and [tex]x[/tex] becomes the hypotenuse of this triangle.

Trigonometric ratio of COSINE relates adjacent and hypotenuse.

Thus we can write and cross multiply and solve:

[tex]cos(A)=\frac{Adjacent}{Hypotenuse}\\cos(60)=\frac{a}{7.5}\\a=7.5*cos(60)=3.75[/tex]

Thus [tex]a=3.75[/tex]

Answer:

2.3 degrees.      

Step-by-step explanation:

Please find the attachment.

We are told that an airplane must clear a 60-foot pole at the end of a runway 500 yards long.

Let us convert 500 yards to feet.

1 yard= 3 feet.

500 yards= 3*500 feet= 1500 feet.

We can see from our attachment pole and runway are in form of a right triangle. The pole is opposite to angle of elevation of plane and length of runway is adjacent.

Since tangent represents the relation between opposite and adjacent of right triangle, So we will use tangent to find angle of elevation that plane must ascend to clear the pole.  

[tex]tan(\theta)=\frac{60}{1500}[/tex]    

[tex]\theta=\tan^{-1}(\frac{60}{1500} )[/tex]

[tex]\theta=\tan^{-1}(0.04)[/tex]

[tex]\theta=2.290610042639[/tex]

Therefore, the airplane must ascend 2.3 degrees to clear the pole.

Answer:

20

Step-by-step explanation:

Answer:

the father is 40

Step-by-step explanation:

Final answer:

Since ΔACD is an isosceles right triangle, the two legs AC and CD are equal. Given CD = 6 √ 3, AC is also 6 √ 3 units.

Explanation:

In triangle ΔABC, we are given that m∠ACB = 90°, meaning that ΔACB is a right-angled triangle. We are also given that CD is perpendicular to AB and that m∠ACD = 45°. Since CD is perpendicular to AB at D, triangle ΔACD is also a right-angled triangle with a 45° angle, which makes it an isosceles right triangle. In an isosceles right triangle, the lengths of the legs are equal. Therefore, AC will be equal to CD which is given as 6 √ 3.

The length of AC in triangle ΔACB can be found using Pythagoras' theorem, AC = √(AB² + BC²). But here we need only the length of AC in the right-angled ΔACD where AC equals CD.

Hence, AC = 6 √ 3 units.

Answer:

SEgment AC is congruent to segment AB

Step-by-step explanation:

given is a triangle ABC with a segment joining A to D on side BC.

To prove that ABD is congruent to ACD

Let us compare these two triangles.

AD = AD (reflexive) Thus one side is equal.

IF AB = AC, then by isosceles triangles property we have angle B = angle C

Thus we get two sides equal.  But this is a necessary condition not sufficient.

Because to prove congruence we need one more condition either CD = BD or Angle CAD = angle DAB

Thus if either AD is angle bisector, or D is mid point besides AC = AB we get

the two triangles are congruent.

Answer:

-2.4

Step-by-step explanation:

The difference between any two consecutive terms (following - preceding) is -2.4. The negative sign corresponds to the observation that the sequence is decreasing.

The common difference in an arithmetic sequence is the consistent difference between consecutive terms of the sequence. It's calculated by subtracting a term from its subsequent term. For example, in the sequence 3, 5, 7, 9, the common difference is 2.

In the field of mathematics, specifically in sequences, the common difference refers to the difference between consecutive terms in an arithmetic sequence. An arithmetic sequence is a list of numbers in which each term is obtained from the previous one by adding a fixed number.

To find the common difference, you simply subtract the second term from the third, or the first from the second. For instance, if your arithmetic sequence is 3, 5, 7, 9, the common difference would be 5-3 or 7-5, which both yield a common difference of 2.

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PL= sqrt(4^2+12^2)=4sqrt(1+9)=4sqrt(10)

Using similarity gives that AM=4/3.

ML=40/3

[PLMU]=40/3 * 4 = 160/3 (53.33)

Or

PM= sqrt(4^2+16/9)=sqrt(160/9)=4sqrt(10)/3

4sqrt(10)*4sqrt(10)/3=160/3 or approximately 53.33

Answer:

Product A.

Step-by-step explanation:

The unit price of product A is $1.36/8oz = $0.17/oz.

The unit price of product B is $3.20/16oz = $0.20/oz.

Answer:

not 100% about this answer but I think it is the 8oz bottle

Step-by-step explanation:

take $1.36 and divide it by 8 which gives you .17 which is 17 cents per oz now do the same thing for the 16 oz so take $3.20 and divide it by 16 and you get .2 which is 20 cents per oz so the 8oz has the lowest unit price of the two!

Answer:

you will save 18 dollars

Step-by-step explanation:

Answer:

You would save $18

And your final cost would be $102

Step-by-step explanation:

By using the simple addition operation, the total number of cups of coffee sold in the coffee shop, counting espressos, cappuccinos, and lattes, is 8,594 cups.

To find the total number of cups of coffee sold, we should add up the number of espressos, cappuccinos, and lattes. This principle is known as simple summation or addition operation in mathematics. As per the numbers given:

When we add these together, we get the total cups of coffee sold as:

1627 (Espressos) + 2741 (Cappuccinos) + 4226 (Lattes) = 8594 cups of coffee in total

So, the coffee shop has sold a total of 8594 cups of coffee.

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Answer:

20%

Step-by-step explanation:

Percent increase is difference/original

360-300) / 300

60/300 / 60/60 = 1/5 * 20/20 = 20/100

Percent is out of 100