When investing money in a bank account, in which situation will you have the most money in your account at the end of three years?

Compounded semiannually
Compounded yearly
Compounded quarterly
Compounded monthly

Given:

Total Yogurt = [tex]8\dfrac{1}{4}[/tex] cups

Yogurt required for each smoothie = [tex]\dfrac{11}{16}[/tex] cup

To find:

The number of smoothies that Paisley can make with the yogurt.

Solution:

We know that,

[tex]\text{Number of smoothies}=\dfrac{\text{Total yogurt}}{\text{Yogurt required for each smoothie}}[/tex]

Substituting the given values, we get

[tex]\text{Number of smoothies}=\dfrac{8\dfrac{1}{4}}{\dfrac{11}{16}}[/tex]

[tex]\text{Number of smoothies}=8\dfrac{1}{4}\times \dfrac{16}{11}[/tex]

[tex]\text{Number of smoothies}=\dfrac{32+1}{4}\times \dfrac{16}{11}[/tex]

[tex]\text{Number of smoothies}=\dfrac{33}{4}\times \dfrac{16}{11}[/tex]

[tex]\text{Number of smoothies}=3\times 4[/tex]

[tex]\text{Number of smoothies}=12[/tex]

Therefore, the number of smoothies is 12.

Answer:

it is the second statement x⇒∞ Y⇒ ∞

Step-by-step explanation:

Answer:

As the x -values go to positive infinity, the functions values go to positive infinity.

Step-by-step explanation:

Answer:

c!

Step-by-step explanation:

Answer:

4. 38 more schools offer basketball than golf.

5. Tennis is offered in the least amount of schools.

Step-by-step explanation:

4. take the number of schools that offer basketball (321) and subtract the number of schools that offer golf (283) to get how many more offer basketball than golf.

5. look at the numbers to the side of the chart and find the lowest number (276). then follow over to the left, and you will find that the least offered sport in schools is tennis.

Answer:

1. (3^3 + 3^2)^2 actually equals (27 + 9)^2

which is the first mistake

2. (27 + 9)^2 does not equal (3^5)2, so (36)^2 does not equal 3^7

3. 3^7 DOES NOT EQUAL 21

Step-by-step explanation:

when you add powered numbers together, it does not multiply it, as your example:

1. (3^3 + 3^2)^2 actually equals (27 + 9)^2

which is the first mistake

2. (27 + 9)^2 does not equal (3^5)2, so (36)^2 does not equal 3^7

3. 3^7 DOES NOT EQUAL 21

Hi there!

Error 1

[tex](3^3+3^2)^2\\= (3^5)^2[/tex]

The student added the exponents of 3³ and 3² and wrote 3⁵. This rule can only be applied to exponents with the same base that are being multiplied. 3³ and 3² were being added, not multiplied, so this rule can't be applied.

Error 2

[tex](3^5)^2\\= 3^7[/tex]

When a power has a power, we multiply them, not add. Here is the correct way of doing it:

[tex](3^5)^2\\= 3^5^*^2\\= 3^1^0[/tex]

Error 3

[tex]3^7\\= 21[/tex]

The student multiplied 3 and 7 to get 21, but 3⁷ actually means 3 multiplied by itself 7 times. The correct answer for this part would be 2187.

I hope this helps!

Answer:

We have 197 g of Co-60 after 18 months.

Step-by-step explanation:

We can use the decay equation.

[tex]M_{f}=M_{i}e^{-\lambda t}[/tex]

Where:

[tex]M_{f}=228e^{-\frac{ln(2)}{7} 1.5}[/tex]    

[tex]M_{f}=197\: g[/tex]    

Therefore, we have 197 g of Co-60 after 18 months.

I hope it helps you!

Answer:

below

Step-by-step explanation:

that is the procedure above

The factorized form of x² + 6x + 5 - 4y - y² is:(x + 1)(x + 5) - (4y + y²)

To factorize the expression x² + 6x + 5 - 4y - y², group the terms and factor them separately.

Rearranging the terms

(x² + 6x + 5) - (4y + y²)

Now let's factor each group separately:

1. Factoring x² + 6x + 5:

The quadratic expression x² + 6x + 5 can be factored into two binomial factors. We look for two numbers that multiply to give 5 and add up to 6 .

These numbers are 1 and 5:

(x + 1)(x + 5)

2. Factoring -4y - y²:

The terms -4y - y² have a common factor of -1.

Factoring out -1 gives

-1(4y + y²)

Combining the factorization of both groups

(x + 1)(x + 5) - 1(4y + y²)

Therefore, the factorized form is (x + 1)(x + 5) - (4y + y²).

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Given:

The tens digit of a two digit number is 5 greater the units digit.

If you subtract double the reversed number from it, the result is a fourth of the original number.

To find:

The original number.

Solution:

Let n be the two digit number and x be the unit digit. Then tens digit is (x+5) and the original number is:

[tex]n=(x+5)\times 10+x\times 1[/tex]

[tex]n=10x+50+x[/tex]

[tex]n=11x+50[/tex]

Reversed number is:

[tex]x\times 10+(x+5)\times 1=10x+x+5[/tex]

[tex]x\times 10+(x+5)\times 1=11x+5[/tex]

If you subtract double the reversed number from it, the result is a fourth of the original number.

[tex]11x+50-2(11x+5)=\dfrac{1}{4}(11x+50)[/tex]

[tex]11x+50-22x-10=\dfrac{1}{4}(11x+50)[/tex]

[tex]40-11x=\dfrac{1}{4}(11x+50)[/tex]

Multiply both sides by 4.

[tex]160-44x=11x+50[/tex]

[tex]160-50=11x+44x[/tex]

[tex]110=55x[/tex]

Divide both sides by 55.

[tex]\dfrac{110}{55}=x[/tex]

[tex]2=x[/tex]

The unit digit is 2. So, the tens digit is [tex]2+5=7[/tex].

Therefore, the original number is 72.

30

Answer:

12÷2/5=12*5/2=30 is a required answer

Answer:

30

Step-by-step explanation:

Answer:

x = 3 y y = 2

Step-by-step explanation:

a) Metodo de reduccion:

Para aplicar este metodo debemos multiplcar por 3 la ecuacion 2 y sumarlas.

[tex]4x-3y=6[/tex]

[tex]5x+y=17[/tex] *3

[tex]4x-3y=6[/tex]

[tex]15x+3y=51[/tex]

-------sumamos las ecuacioens--------

[tex]19x=57[/tex]

[tex]x=3[/tex]

Ahora, remplazamos x en la ecuacion 2.

[tex]5(3)+y=17[/tex]

[tex]y=2[/tex]

b) Igualacion

Debemos despejar x en ambas y luego igualarlas

[tex]x=\frac{6+3y}{4}[/tex]

[tex]x=\frac{17-y}{5}[/tex]

Igualando:

[tex]\frac{6+3y}{4}=\frac{17-y}{5}[/tex]

[tex]5(6+3y)=4(17-y)[/tex]

[tex]19y=8[/tex]

[tex]y=2[/tex]

Ahora, remplazamos y en la ecuacion 2.

[tex]5x+2=17[/tex]

[tex]5x=15[/tex]

[tex]x=3[/tex]

c) Sustitucion

Despejamos x de la primero ecuacion y lo remplazamos en dos.

[tex]x=\frac{6+3y}{4}[/tex]

[tex]5\frac{(6+3y)}{4}+y=17[/tex]

Multiplicamos por 4

[tex]5(6+3y)+4y=68[/tex]

[tex]30+15y+4y=68[/tex]

[tex]30+19y=68[/tex]      

[tex]19y=38[/tex]  

[tex]y=2[/tex]  

Remplazando en 1.

[tex]4x-3(2)=6[/tex]

[tex]4x-6=6[/tex]

[tex]4x=12[/tex]

[tex]x=3[/tex]          

Answer:

x=10  x=-2

Step-by-step explanation:

(x − 3)(x − 5) = 35

FOIL

x^2 -5x-3x+15 = 35

Combine like terms

x^2 -8x+15 = 35

Subtract 35 from each side

x^2 -8x+15-35 = 35-35

x^2 -8x-20 =0

Factor

What 2 numbers multiply to -20 and add to -8

-10*2 = -20

-10 +2 = -8

(x-10)(x+2) =0

Using the zero product property

x-10 =0  x+2 = 0

x=10  x=-2

Answer:

6

Step-by-step explanation:

I think I just answered that question.

"image" 7 means the functional result is 7, and we need to find the value of x to make this happen.

7 = (3x - 4)/2

14 = 3x - 4

18 = 3x

x = 6

#1. Vertical

#2. Adjacent, Complementary

#3. Adjacent, Linear Pair, Supplementary

---A linear pair forms a line, which is equal to 180 degrees

#4. Adjacent

#5. Vertical, Complementary

#6. Vertical, Supplementary

---There is a 90 degree angle within this problem. If one angle is 90 degrees, then they are all 90 degrees, which makes the sum of angle 1 and 2 = 180. So, they are supplementary.

Hope this helps!

The relationship between angle 1 and 2 are as follows:

1. ∠1 ≅ ∠2 (vertical angles)

2. ∠1 and ∠2 are adjacent and complementary angles.

3. ∠1 and ∠2 are linear pairs and supplementary angles

4. ∠1 and ∠2 are adjacent angles

5. ∠1 and ∠2 are vertical angles

6. ∠1 and ∠2 are vertical angles and supplementary angles.

1.

Therefore,

∠1 ≅ 2 (vertical angles)

2.

Therefore,

∠1 and ∠2 are adjacent and complementary angles.

3.

∠1 and ∠2 are linear pairs and supplementary angles.

4.

∠1 and ∠2 are adjacent angles

5.

∠1 and ∠2 are vertical angles

6.

∠1 and ∠2 are vertical angles and supplementary angles

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Answer:

1,3

Step-by-step explanation:

Answer:

(4, 2.5 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Here (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (9, 5) , then

midpoint = ( [tex]\frac{-1+9}{2}[/tex], [tex]\frac{2+5}{2}[/tex] ) = ( [tex]\frac{8}{2}[/tex], [tex]\frac{7}{2}[/tex] ) = (4, 3.5 )

Answer:

[tex]58, 68, 68, 68, 74, 74, 76, 77, 78, 79[/tex]

Step-by-step explanation:

Given

[tex]n=10[/tex]

[tex]Mean = 72[/tex]

[tex]Median = 74[/tex]

[tex]Mode = 68[/tex]

[tex]Range = 21[/tex]

Required

The complete dataset

The question has missing options (available online)

From the mean, we have:

[tex]Mean = \frac{\sum x}{n}[/tex]

This gives:

[tex]72 = \frac{\sum x}{10}[/tex]

Cross  multiply

[tex]\sum x = 72 * 10[/tex]

[tex]\sum x = 720[/tex]

This means that the sum of all elements of the dataset is 720

Next, we test the median

Since n = 10, then:

[tex]Median = \frac{n + 1}{2}[/tex]

[tex]Median = \frac{10 + 1}{2}[/tex]

[tex]Median = \frac{11}{2}[/tex]

[tex]Median = 5.5th[/tex]

This implies that the median is the average of the 5th and 6th item.

So, we have:

[tex]Median = \frac{5th + 6th}{2}[/tex]

Cross multiply

[tex]5th + 6th = 2 * Median[/tex]

[tex]5th + 6th = 2 * 74[/tex]

[tex]5th + 6th = 148[/tex]

This means that the 5th and 6th element add up to 148

Also, we have:

[tex]Mode = 68[/tex]

This means that 68 has to appear at least twice in the dataset

[tex]Range = 21[/tex]

This implies that the difference between the highest and the least is 21.

The dataset that satisfies the above condition is:

[tex]58, 68, 68, 68, 74, 74, 76, 77, 78, 79[/tex]

Answer:

x = -11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4(1) + 12(x + 3) - 6(x - 5) = 4(12) + 4(x)

Step 2: Solve for x

Answer: 2gh

Given set:- x - 7 > - 2

Solving It:-

x - 7 > - 2

x > -2 + 7 [Here '7' is greater than '-2' So Sign Changes To Positive]

x > 5

So Correct Solution Set Will Be

Option C= {x | x R, x > 5}

Answer:

5 hours

Step-by-step explanation:

Company A:

Charge for an hour =$ 25

Charge for 't' hours = 25 *t = 25t

Total cost = Equipment fee + charge for t hours

  AA = 150 + 25t

Company B:

Charge for an hour =$ 35

Charge for 't' hours = 35 *t = 35t

Total cost = Equipment fee + charge for t hours

  BB = 100 + 35t

BB = AA

100 + 35t = 150 + 25t

Subtract 25t from both sides

100 + 35t - 25t = 150

           100 +  10t = 150

Subtract 100 from both sides

10t = 150 - 100

10t = 50

Divide both sides by 10

t = 50/10

t = 5

Answer:

He received 10 dimes and 15 quarters.

Step-by-step explanation:

Dimes = $0.10

Quarters = $0.25

Variable x = dimes

Variable y = quarters

Create a pair of linear equations:

0.10x + 0.25y = 4.75

x + y = 25

Isolate any variable, using an equation of your choice:

x + y = 25

x = 25 - y

Plug in this new value of x into the other equation:

0.10(25 - y) + 0.25y = 4.75

Use the distributive property:

2.5 - 0.10y + 0.25y = 4.75

Combine like terms:

2.5 + 0.15y = 4.75

Isolate variable y:

0.15y = 2.25

y = 15

Plug in the value of y into any equation:

x + y = 25

x + 15 = 25

Isolate variable x:

x = 10

Answer:

∠F = 59°

∠E = 31°

DF = ≅ 3  (2.98)

Step-by-step explanation:

Step-by-step explanation:

What traumatic stressors have you faced in your life? What chronic stressors have you faced or do you currently face? What coping strategies and lifestyle choices do you employ to respond to such stressors?

Answer:

25+144+X=180°

169+X=180°

X= 180-169

Therefore, x= 11°

checking process: (25+144+11= 180°)

Answer:

x = 11 i beileve!

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

You will need expand so you can plug in the givens

Quotient rule: log(b^7)-[log(a^5c^6)]

Product rule: log(b^7)-[log(a^5)+log(c^6)]

Distribute: log(b^7)-log(a^5)-log(c^6)

Power rule: 7log(b)-5log(a)-6log(c)

Plug in: 7(4)-5(3)-6(-1)

Simplify: 28-15+6

Simplify: 13+6

Simplify: 19

Answer:

730.88

Step-by-step explanation:

Area of the entire circle = pi * r^2

r = 16

Area = 3.14 * 16^2

Area = 803.84

1/4 of the circle contains the shaded area. It's area = 1/4 * 803.84

Area of 1/4 circle =

200.96

the area of the triangle

Area = 1/2 AG * G?

AG and G? are equal

Area = 1/2 * 16^2

Area = 128

Area of 1/4 circle - area of the triangle = area of the shaded portion

shaded portion = 200.95 - 128

Shaded Portion = 72.96

So the area of the unshaded part

unshaded = 803.84 - 72.96

Unshaded = 730.88

Answer:

200

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

are you sure this is the right equation ? it would mean that the more toppings the cheaper the ice cream.

but as it is written, the slope is -1.

the slope of a line is always the factor of the variable in the equation.

it is the ratio of y/x indicating how many units y is changing for a given change of x.

in our example here, if x changes 1 unit to the right (+1), then y changes 1 unit down (-1).

so, -1/+1 = -1

The slope of the function f(t) = 3 - t is -1

"It defines a relation between input and output values."

"It is the rate of change of the dependent variable of the function with respect to that of the independent variable."

For given question,

We have been given a function f(t) = 3 - t

We need to find the slope of the function.

[tex]m=\frac{d}{dt}f(t)\\\\ m=\frac{d}{dt}( 3 - t)\\\\m=-1[/tex]

Therefore, the slope of the function f(t) = 3 - t is -1

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Answer:

4/3

Step-by-step explanation:

Since this is a right triangle,

tan C = opp side / adjacent side

tan C = 36/ 27

tan C = 4/3

Answer:

[tex]d=455.38~units[/tex]

Step-by-step explanation:

The coordinates of the dead center of the field, [tex]D\equiv (322,322)[/tex]

Home base in a coordinate system is always the origin, [tex]O\equiv(0,0)[/tex]

The center fielder threw the ball form the dead center to the home base, hence the distance of throw:

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

[tex]d=\sqrt{(322-0)^2+(322-0)^2}[/tex]

[tex]d=455.38~units[/tex]

Answer:Hector threw the ball 65 feet while Tre threw the ball 63 feet far

Step-by-step explanation:

The farthest throw would probably be around 450 feet