the amount in a savings account increased from $200 to $216. what was the percent increase?

Answer:

8/5 or 1 3/5

Step-by-step explanation:

Answer:

[tex] P(27.8 < X <30.5)=P(X>27.8)-P(X>30.5)=0.025-0.0015=0.0235[/tex]

Step-by-step explanation:

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

Let X the random variable who represent the lifespans of tigers in a particular zoo.

From the problem we have the mean and the standard deviation for the random variable X. [tex]\mu=120 , \sigma=110[/tex]

On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

We want to find this probability:

[tex] P(27.8 < X <30.5)[/tex]

And in order to calculate how many deviation we are above/below the mean we can use the z score given by:

[tex]z =\frac{x-\mu}{\sigma}[/tex]

And if we use this formula for the two values given we have:

[tex] z_1 = \frac{27.8-22.4}{2.7}=2[/tex]

[tex] z_1 = \frac{30.5-22.4}{2.7}=3[/tex]

So we have values between 2 and 3 deviations above the mean.

We can use the following probabilities

[tex]P(X<\mu -\sigma)=P(X <19.7)=0.16[/tex]    

[tex]P(X>\mu +\sigma)=P(X >25.1)=0.16[/tex]  

[tex]P(X<\mu -2*\sigma)=P(X<17)=0.025[/tex]    

[tex]P(X>\mu +2*\sigma)=P(X>27.8)=0.025[/tex]

[tex]P(X<\mu -3*\sigma)=P(X<14.3)=0.0015[/tex]

[tex]P(X>\mu +3*\sigma)=P(X>30.5)=0.0015[/tex]

And we can find this probability on this way:

[tex] P(27.8 < X <30.5)=P(X>27.8)-P(X>30.5)=0.025-0.0015=0.0235[/tex]

To estimate the probability of a tiger's lifespan falling between 27.8 and 30.5 years, we can use the empirical rule, which states that approximately 95% of the data falls within two standard deviations of the mean.

To estimate the probability of a tiger living between 27.8 and 30.5 years, we can use the empirical rule. According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, and approximately 95% falls within two standard deviations. Since the mean is 22.4 years and the standard deviation is 2.7 years, we need to find the probability that a tiger's lifespan falls between 27.8 - 22.4 = 5.4 years and 30.5 - 22.4 = 8.1 years.

Since 5.4 years and 8.1 years are less than two and three standard deviations away from the mean, respectively, the probability can be estimated to be approximately 95% using the empirical rule.

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The annual percentage rate is: 1.2%

Step-by-step explanation:

The formula for calculating simple interest is:

[tex]I = Prt[/tex]

Here

P is the principal amount

r is the interest rate

t is the time in years

We are Given:

[tex]P = 1450\\t = 8\ years\\I = 139.20[/tex]

Putting the values in the formula

[tex]139.20 = 1450 * r * 8\\139.20 = 11600r[/tex]

Dividing both sides by 11600

[tex]\frac{11600r}{11600} = \frac{139.20}{11600}\\r = 0.012[/tex]

Converting into percentage

r  = 0.012*100

r = 1.2%

Hence,

The annual percentage rate is: 1.2%

Keywords: Percentage, interest

Learn more about simple interest at:

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Answer:

1 - 3/10 = 7/10 of the distance left

(3/7)(7/10) = 3/10 of the total distance

Zachary's family traveled [tex]\( \frac{51}{70} \)[/tex] of the total distance to his aunt's house.

To find the fraction of the total distance traveled to Zachary's aunt's house, we need to combine the distances traveled and express it as a fraction of the total distance.

Given:

1. Zachary's family traveled [tex]\( \frac{3}{10} \)[/tex] of the total distance to his aunt's house.

2. Then, they traveled [tex]\( \frac{3}{7} \)[/tex] of the remaining distance.

Step 1: Calculate the total distance traveled by combining the two distances.

[tex]\[ \text{Total distance traveled} = \frac{3}{10} + \frac{3}{7} \][/tex]

Step 2: Find a common denominator for [tex]\( \frac{3}{10} \) and \( \frac{3}{7} \).[/tex] The least common multiple (LCM) of 10 and 7 is 70.

Step 3: Rewrite the fractions with the common denominator of 70.

[tex]\[ \frac{3}{10} = \frac{3 \times 7}{10 \times 7} = \frac{21}{70} \][/tex]

[tex]\[ \frac{3}{7} = \frac{3 \times 10}{7 \times 10} = \frac{30}{70} \][/tex]

Step 4: Add the fractions:

[tex]\[ \frac{21}{70} + \frac{30}{70} = \frac{21 + 30}{70} = \frac{51}{70} \][/tex]

Therefore, Zachary's family traveled [tex]\( \frac{51}{70} \)[/tex] of the total distance to his aunt's house.

There are three terms in polynomial

Solution:

Given polynomial is:

[tex]5x^2+3x-4[/tex]

We have to find the number of terms in polynomial

A term can be a signed number, a variable, or a constant multiplied by a variable or variables

When a term is made up of a constant multiplied by a variable or variables, that constant is called a coefficient.

Therefore, terms in polynomial are:

[tex]5x^2+3x-4\\\\Terms: 5x^2 \text{ and 3x and -4 }[/tex]

Thus there are three terms in polynomial

Answer:

15

Step-by-step explanation:

Because if you draw a line straight just like the one below the x, it will connect to the 15.

Answer:

18

Step-by-step explanation:

Because you add 9 more angles to the smaller triangle

Answer:

2/3

Step-by-step explanation:

D

Step-by-step explanation:

answer:

im not sure. what is ur question

step-by-step explanation:

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

By the pythagorean theorem, a triangle is a right triangle if and only if

[tex]\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2[/tex].

In this case,

[tex]\text{longest side}^2 = 17^2 = 289[/tex].

[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}[/tex].

In other words, indeed [tex]\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2[/tex]. Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

Factor out the common factor [tex]2[/tex] to simplify the calculations.

[tex]\text{longest side}^2 = 20^2 = 400[/tex]

[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}[/tex].

[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

[tex]\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121[/tex].

[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}[/tex].

[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

[tex]\text{longest side}^2 = 11^2 = 121[/tex].

[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

You should multiply [tex]\frac{9}{5}[/tex] with [tex]\frac{-5}{9}[/tex] to get a product of -1

Solution:

Let the number to be multiplied be "a"

Given that,

By what number would you multiply 9/5 to get a product of -1

'a" multiplied with 9/5 should give a product -1

Therefore, writing it mathematically we get,

[tex]a \times \frac{9}{5} = -1[/tex]

Solve the above equation for "a"

[tex]a \times \frac{9}{5} = -1\\\\a = -1 \times \frac{5}{9}\\\\a = \frac{-5}{9}[/tex]

Therefore, you should multiply [tex]\frac{9}{5}[/tex] with [tex]\frac{-5}{9}[/tex] to get a product of -1

Final answer:

To multiply 9/5 by a number to get -1, you must multiply it by -5/9. This is found by setting up an equation to solve for the unknown number and then isolating the variable on one side of the equation.

Explanation:

To find by what number you would multiply 9/5 to get a product of -1, we can set up an equation that represents this situation:

Let x be the number we are looking for. Then we have the equation: (9/5) × x = -1

To solve for x, we need to divide both sides of the equation by (9/5): x = -1 ÷ (9/5)

Multiplying by the reciprocal of (9/5), which is (5/9), we get:

x = -1 × (5/9)

x = -5/9

Therefore, you must multiply 9/5 by -5/9 to get a product of -1.

Answer:

8+2x=50

happy to help!!

10 km

Step-by-step explanation:

If 4 cm represents 8 kilometers then 1 cm represents;

8 / 4

= 2

1 cm : 2 km

How, then, about 5 cm – the distance between Sophie's home and school?

5 cm : ? km

A cross multiplication;

1 cm : 2 km

5 cm : x km

(5 * 2) = 1 x

x = 10/1

x = 10

Answer:

8 gumballs.

Step-by-step explanation:

How many cents you have divided by the cost:

32 divided by 8 = 4

The answer times the amount of gumballs:

4 x 2 = 8

8 gumballs.

Answer:

Step-by-step explanation:

The area of the H is 86

Answer: Just draw a line at the end of each

Step-by-step explanation: Like this

H   I I at the end

Answer:

8

Step-by-step explanation:

[tex]\frac{is}{of} = \frac{percent}{100}[/tex]

[tex]\frac{x}{80} = \frac{10}{100}[/tex]

80x10 = 800

800 = 100x

800 divide 100 = 8

answer = 8

Hope this helped!! :)

Answer: you will get 8.75, but the answer should be 9 bags

Step-by-step explanation:

Answer:

a=2

Step-by-step explanation:

Given:                 5a-12=-2

Isolate Variable: 5a=10

Divide:                 a=2

Answer:

5a - 12= -2

5 x 2= 10 so,

5(2) - 12= -2

 ^

10-12= -2

Answer:

Janice required 30 tablespoons of butter, 380 Jet-Puffed Marshmallows and 60 cup of Kellogg's rice krispies cereal to yield 120 servings.

Step-by-step explanation:

Given that 3 tablespoons of butter, 38 Jet-Puffed Marshmallows, and 6 cup of Kellogg's rice krispies cereal) yields 12 servings.

Now, Janice has to make for 30 people and each with 4 servings for the Christmas Party.

So, there are total (30 × 4) = 120 servings required to make.

So, each and every ingredients of the dish will be required to be made 10 times.

Therefore, Janice required 30 tablespoons of butter, 380 Jet-Puffed Marshmallows and 60 cup of Kellogg's rice krispies cereal to yield 120 servings. (Answer)  

Janice will need 30 tablespoons of butter, 380 marshmallows, and 60 cups of rice krispies cereal for the Christmas Party.

To find out how many of each ingredient Janice will need, we need to calculate the total servings required for the Christmas Party. She is expecting 30 people and wants everyone to have 4 servings each. So the total servings required would be 30 * 4 = 120 servings.

Now, we can calculate the ratio of servings to each ingredient. If 12 servings require 3 tablespoons of butter, then 120 servings would require (120/12) * 3 = 30 tablespoons of butter.

Similarly, if 12 servings require 38 marshmallows, then 120 servings would require (120/12) * 38 = 380 marshmallows. And if 12 servings require 6 cups of rice krispies cereal, then 120 servings would require (120/12) * 6 = 60 cups of rice krispies cereal.

So, Janice will need 30 tablespoons of butter, 380 marshmallows, and 60 cups of rice krispies cereal for the Christmas Party.

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Answer:

105/96

Step-by-step explanation:

Answer:

In dividing fractions, you do the inverse. (Also called the reciprocal.)

So take that attachment you attached as a example.

21           3            21               5

----    ÷   ----  =     ------     ÷    ------

32          5           32               3

Another reminder, when you find the reciprocal, you now multiply instead of divide. (Do not question the math world. I questioned it, and I paid the price. TnT)

So 21/32 multiplied by 5/3 would be....

21              5             105

-----    ×   -----    =      -------

32             3              96

You could leave it that way, or simplify it.

Simplest form is-

1 3/32

Non-simplified form is-

105/96

Good night and have a good day~

(Well at least, I'm going to sleep)

Answer:

Boooommm x= -2

Step-by-step explanation:

3x − 14y = –20

ok so 3x-14y=-20

+14 to invert the fraction

-20+14=-6

3x=-6

-6/3=-2

x=-2

Answer:

Since the two angles are across from each other that tells us that they are equal in length, so we want to set them equal to each other

3x+50=6x-10, Now we want to solve it like a normal equation, get x by itself

First add 10 to each side

3x+50+10=6x-10+10

3x+60=6x

Now we want to subtract 3x from each side

3x-3x+60=6x-3x

60=3x

Now divide both sides by 3

60/3=3x/3

20=x

x=20

Hope this helps ;)

Step-by-step explanation:

Answer:

Step-by-step explanation:

function 1 : y = 4x + 5

In y = mx + b form, which is what ur equation is in, the slope can be found in the m position. So the slope of this function is 4.

function 2 : (1,6),(3,10)

slope = (y2 - y1) / (x2 - x1)

(1,6)...x1 = 1 and y1 = 6

(3,10)...x2 = 3 and y2 = 10

now we sub

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

B. Function 1, because the slope is 4 and the slope of function 2 is 2. <==

Answer:

Function 1, because the slope is 4 and the slope of function 2 is 2. Use the slope formula.

Answer:

End time = 9:50

Step-by-step explanation:

Elapsed time = End time - start time

End time = Elapsed time + start time

End time = 2 hour,20 minutes + 7:30

End time = 9:50

Answer:

circumference = 10 pi = 2r pi

then r =5

next area of circle = 5 .5.pi = 25 pi

Step-by-step explanation:

Answer:

92.11 cm³

Step-by-step explanation:

The figure below;

We are required to determine the volume of the figure;

The volume of a hemisphere is given by;

Volume hemisphere = 2/3πr³

Taking π to be 3.14

The Volume  of the two hemisphere;

             = 2/3 × 3.14 × 2³

             = 16.75 cm³

Volume of the cylinder;

Volume = πr²h

             = 3.14 × 2² × 6

             = 75.36 cm³

Thus, volume of the figure;

      = 16.75 cm³ + 75.36 cm³

      = 92.11 cm³

Hence, the volume of the figure is 92.11 cm³

Answer:

-12 or 5

Step-by-step explanation:

p² + (p+7)² = 169

p² + (p²+14p+49) = 169

2p² + 14p + 49 - 169 = 0

2p² + 14p - 120 = 0

2p² + 24p - 10p - 120 = 0

2p(p+12) - 10(p+12) = 0

(p+12)(2p-10) = 0

p+12 = 0 , or 2p-10 = 0

p = -12 or 5

Answer:

p = 3

Step-by-step explanation:

p² + (p +7)²=169

Open the bracket and solve the value in the bracket according to BODMAS

p^2 + p^2 + 7^2 = 13^2

Square Root the both side of the equation.

√{p^2} + √{p^2} + √{7^2} = √{13^2}

p + p +7 = 13

2p + 7 = 13

collect like term of the numbers

2p = 13 - 7

2p = 6

Divide both side by the coefficient of p.

2p/2 = 6/2

p = 3.

Answer:

[tex]y = 2x - 1[/tex]

Step-by-step explanation:

The line shown is a straight line its equation is of the form.

[tex]y = mx + c[/tex]

Where m is the slope and c is the y-intercept.

From the graph, the slope is

[tex]m = \frac{rise}{run} [/tex]

[tex]m = \frac{2}{1} = 2[/tex]

The y-intercept from the graph is where the line intersects the y-axis, so c=-1

We substitute the values to get:

[tex]y = 2x - 1[/tex]

Explanation of how to find the equation of lines based on their slopes and intercepts.

Equation of the line: The equation of the left line is y = -x + 1 and the equation of the right line is y = 1/2x - 1/2.

Using Slope-Intercept Form: The slope-intercept form of the equation y = mx + b helps determine the equations of lines based on their slopes and intercepts.

Point-Slope Formula: By using the point-slope formula, which utilizes a point on the line and the line's slope, we can find the equation of a line.

Answer:

i) let x be the amount of money worth of drinks that Kevin sold.

ii) Kevin sells at most $60 worth of drinks.

iii) therefore the inequality can be written as

   x ≤ $60

Step-by-step explanation:

i) let x be the amount of money worth of drinks that Kevin sold.

ii) Kevin sells at most $60 worth of drinks.

iii) therefore the inequality can be written as

   x ≤ $60

Option c: [tex]-\frac{\pi}{5}[/tex] is the correct answer.

Explanation:

The given degree is –36°

Since, [tex]1^{\circ}=\frac{\pi}{180}[/tex]

The radian of –36° can be determined by multiplying it with [tex]\frac{\pi}{180}[/tex]

Thus, the degree can be converted into radians, by multiplying the degree with [tex]\frac{\pi}{180}[/tex]

Hence, it can be written as

[tex]-36^{\circ} \times \frac{\pi}{180}[/tex]

Multiplying, we get,

[tex]\frac{-36^{\circ} \pi}{180}[/tex]

Dividing, we have,

[tex]-\frac{\pi}{5}[/tex]

Thus, the radian of -36° is [tex]-\frac{\pi}{5}[/tex]

Answer:

the answer is c

Step-by-step explanation: